Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2898,2,Mod(1,2898)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2898, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("2898.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2898 = 2 \cdot 3^{2} \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2898.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: | \(23.1406465058\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.568.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 6x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.363328\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2898.1 |
$q$-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 | ||||||||
\(5\) | −3.14134 | −1.40485 | −0.702424 | − | 0.711759i | \(-0.747899\pi\) | ||||
−0.702424 | + | 0.711759i | \(0.747899\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.14134 | 0.993378 | ||||||||
\(11\) | 0.726656 | 0.219095 | 0.109548 | − | 0.993982i | \(-0.465060\pi\) | ||||
0.109548 | + | 0.993982i | \(0.465060\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.36333 | 0.655469 | 0.327735 | − | 0.944770i | \(-0.393715\pi\) | ||||
0.327735 | + | 0.944770i | \(0.393715\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.77801 | −0.673766 | −0.336883 | − | 0.941547i | \(-0.609373\pi\) | ||||
−0.336883 | + | 0.941547i | \(0.609373\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.50466 | −0.345194 | −0.172597 | − | 0.984993i | \(-0.555216\pi\) | ||||
−0.172597 | + | 0.984993i | \(0.555216\pi\) | |||||||
\(20\) | −3.14134 | −0.702424 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.726656 | −0.154924 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.86799 | 0.973599 | ||||||||
\(26\) | −2.36333 | −0.463487 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | −7.86799 | −1.46105 | −0.730525 | − | 0.682886i | \(-0.760724\pi\) | ||||
−0.730525 | + | 0.682886i | \(0.760724\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.778008 | −0.139734 | −0.0698672 | − | 0.997556i | \(-0.522258\pi\) | ||||
−0.0698672 | + | 0.997556i | \(0.522258\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.77801 | 0.476424 | ||||||||
\(35\) | 3.14134 | 0.530983 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.86799 | 0.964692 | 0.482346 | − | 0.875981i | \(-0.339785\pi\) | ||||
0.482346 | + | 0.875981i | \(0.339785\pi\) | |||||||
\(38\) | 1.50466 | 0.244089 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.14134 | 0.496689 | ||||||||
\(41\) | −1.58532 | −0.247585 | −0.123793 | − | 0.992308i | \(-0.539506\pi\) | ||||
−0.123793 | + | 0.992308i | \(0.539506\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.15066 | −1.24296 | −0.621482 | − | 0.783428i | \(-0.713469\pi\) | ||||
−0.621482 | + | 0.783428i | \(0.713469\pi\) | |||||||
\(44\) | 0.726656 | 0.109548 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | 2.64600 | 0.385959 | 0.192979 | − | 0.981203i | \(-0.438185\pi\) | ||||
0.192979 | + | 0.981203i | \(0.438185\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −4.86799 | −0.688438 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.36333 | 0.327735 | ||||||||
\(53\) | −7.73599 | −1.06262 | −0.531310 | − | 0.847178i | \(-0.678300\pi\) | ||||
−0.531310 | + | 0.847178i | \(0.678300\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.28267 | −0.307795 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 7.86799 | 1.03312 | ||||||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.55602 | 0.967449 | 0.483724 | − | 0.875220i | \(-0.339284\pi\) | ||||
0.483724 | + | 0.875220i | \(0.339284\pi\) | |||||||
\(62\) | 0.778008 | 0.0988071 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −7.42401 | −0.920835 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.45331 | −0.177550 | −0.0887752 | − | 0.996052i | \(-0.528295\pi\) | ||||
−0.0887752 | + | 0.996052i | \(0.528295\pi\) | |||||||
\(68\) | −2.77801 | −0.336883 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.14134 | −0.375461 | ||||||||
\(71\) | −9.29200 | −1.10276 | −0.551379 | − | 0.834255i | \(-0.685898\pi\) | ||||
−0.551379 | + | 0.834255i | \(0.685898\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.00933 | −0.118133 | −0.0590665 | − | 0.998254i | \(-0.518812\pi\) | ||||
−0.0590665 | + | 0.998254i | \(0.518812\pi\) | |||||||
\(74\) | −5.86799 | −0.682140 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.50466 | −0.172597 | ||||||||
\(77\) | −0.726656 | −0.0828102 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.72666 | 0.306773 | 0.153386 | − | 0.988166i | \(-0.450982\pi\) | ||||
0.153386 | + | 0.988166i | \(0.450982\pi\) | |||||||
\(80\) | −3.14134 | −0.351212 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.58532 | 0.175069 | ||||||||
\(83\) | 7.78734 | 0.854771 | 0.427386 | − | 0.904069i | \(-0.359435\pi\) | ||||
0.427386 | + | 0.904069i | \(0.359435\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.72666 | 0.946539 | ||||||||
\(86\) | 8.15066 | 0.878909 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.726656 | −0.0774618 | ||||||||
\(89\) | 17.5233 | 1.85747 | 0.928734 | − | 0.370746i | \(-0.120898\pi\) | ||||
0.928734 | + | 0.370746i | \(0.120898\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.36333 | −0.247744 | ||||||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.64600 | −0.272914 | ||||||||
\(95\) | 4.72666 | 0.484945 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.63667 | 0.166179 | 0.0830894 | − | 0.996542i | \(-0.473521\pi\) | ||||
0.0830894 | + | 0.996542i | \(0.473521\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.86799 | 0.486799 | ||||||||
\(101\) | 7.24065 | 0.720472 | 0.360236 | − | 0.932861i | \(-0.382696\pi\) | ||||
0.360236 | + | 0.932861i | \(0.382696\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 19.4240 | 1.91390 | 0.956952 | − | 0.290246i | \(-0.0937370\pi\) | ||||
0.956952 | + | 0.290246i | \(0.0937370\pi\) | |||||||
\(104\) | −2.36333 | −0.231743 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.73599 | 0.751385 | ||||||||
\(107\) | 8.72666 | 0.843638 | 0.421819 | − | 0.906680i | \(-0.361392\pi\) | ||||
0.421819 | + | 0.906680i | \(0.361392\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.41468 | −0.231284 | −0.115642 | − | 0.993291i | \(-0.536893\pi\) | ||||
−0.115642 | + | 0.993291i | \(0.536893\pi\) | |||||||
\(110\) | 2.28267 | 0.217644 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | 3.14134 | 0.295512 | 0.147756 | − | 0.989024i | \(-0.452795\pi\) | ||||
0.147756 | + | 0.989024i | \(0.452795\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.14134 | −0.292931 | ||||||||
\(116\) | −7.86799 | −0.730525 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.77801 | 0.254660 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.4720 | −0.951997 | ||||||||
\(122\) | −7.55602 | −0.684090 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.778008 | −0.0698672 | ||||||||
\(125\) | 0.414680 | 0.0370901 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.85866 | 0.253665 | 0.126833 | − | 0.991924i | \(-0.459519\pi\) | ||||
0.126833 | + | 0.991924i | \(0.459519\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 7.42401 | 0.651129 | ||||||||
\(131\) | 0.264015 | 0.0230671 | 0.0115335 | − | 0.999933i | \(-0.496329\pi\) | ||||
0.0115335 | + | 0.999933i | \(0.496329\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.50466 | 0.130471 | ||||||||
\(134\) | 1.45331 | 0.125547 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.77801 | 0.238212 | ||||||||
\(137\) | 2.15066 | 0.183744 | 0.0918718 | − | 0.995771i | \(-0.470715\pi\) | ||||
0.0918718 | + | 0.995771i | \(0.470715\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.0480 | 1.02189 | 0.510947 | − | 0.859612i | \(-0.329295\pi\) | ||||
0.510947 | + | 0.859612i | \(0.329295\pi\) | |||||||
\(140\) | 3.14134 | 0.265491 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 9.29200 | 0.779767 | ||||||||
\(143\) | 1.71733 | 0.143610 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 24.7160 | 2.05255 | ||||||||
\(146\) | 1.00933 | 0.0835326 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5.86799 | 0.482346 | ||||||||
\(149\) | 20.8480 | 1.70794 | 0.853968 | − | 0.520325i | \(-0.174189\pi\) | ||||
0.853968 | + | 0.520325i | \(0.174189\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.42401 | 0.278642 | 0.139321 | − | 0.990247i | \(-0.455508\pi\) | ||||
0.139321 | + | 0.990247i | \(0.455508\pi\) | |||||||
\(152\) | 1.50466 | 0.122044 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.726656 | 0.0585556 | ||||||||
\(155\) | 2.44398 | 0.196306 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.5653 | 1.16244 | 0.581221 | − | 0.813746i | \(-0.302575\pi\) | ||||
0.581221 | + | 0.813746i | \(0.302575\pi\) | |||||||
\(158\) | −2.72666 | −0.216921 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.14134 | 0.248344 | ||||||||
\(161\) | −1.00000 | −0.0788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.5747 | −1.06325 | −0.531625 | − | 0.846980i | \(-0.678419\pi\) | ||||
−0.531625 | + | 0.846980i | \(0.678419\pi\) | |||||||
\(164\) | −1.58532 | −0.123793 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −7.78734 | −0.604415 | ||||||||
\(167\) | −3.22199 | −0.249325 | −0.124663 | − | 0.992199i | \(-0.539785\pi\) | ||||
−0.124663 | + | 0.992199i | \(0.539785\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.41468 | −0.570360 | ||||||||
\(170\) | −8.72666 | −0.669304 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −8.15066 | −0.621482 | ||||||||
\(173\) | 5.32469 | 0.404829 | 0.202415 | − | 0.979300i | \(-0.435121\pi\) | ||||
0.202415 | + | 0.979300i | \(0.435121\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.86799 | −0.367986 | ||||||||
\(176\) | 0.726656 | 0.0547738 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −17.5233 | −1.31343 | ||||||||
\(179\) | −1.86799 | −0.139620 | −0.0698102 | − | 0.997560i | \(-0.522239\pi\) | ||||
−0.0698102 | + | 0.997560i | \(0.522239\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.5560 | −0.858952 | −0.429476 | − | 0.903078i | \(-0.641302\pi\) | ||||
−0.429476 | + | 0.903078i | \(0.641302\pi\) | |||||||
\(182\) | 2.36333 | 0.175182 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | −18.4333 | −1.35525 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.01866 | −0.147619 | ||||||||
\(188\) | 2.64600 | 0.192979 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.72666 | −0.342908 | ||||||||
\(191\) | 21.8387 | 1.58019 | 0.790096 | − | 0.612983i | \(-0.210031\pi\) | ||||
0.790096 | + | 0.612983i | \(0.210031\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 22.1693 | 1.59578 | 0.797891 | − | 0.602801i | \(-0.205949\pi\) | ||||
0.797891 | + | 0.602801i | \(0.205949\pi\) | |||||||
\(194\) | −1.63667 | −0.117506 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −11.7067 | −0.834066 | −0.417033 | − | 0.908891i | \(-0.636930\pi\) | ||||
−0.417033 | + | 0.908891i | \(0.636930\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.70668 | 0.688088 | 0.344044 | − | 0.938953i | \(-0.388203\pi\) | ||||
0.344044 | + | 0.938953i | \(0.388203\pi\) | |||||||
\(200\) | −4.86799 | −0.344219 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −7.24065 | −0.509450 | ||||||||
\(203\) | 7.86799 | 0.552225 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.98002 | 0.347820 | ||||||||
\(206\) | −19.4240 | −1.35333 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.36333 | 0.163867 | ||||||||
\(209\) | −1.09337 | −0.0756303 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.83869 | 0.677323 | 0.338662 | − | 0.940908i | \(-0.390026\pi\) | ||||
0.338662 | + | 0.940908i | \(0.390026\pi\) | |||||||
\(212\) | −7.73599 | −0.531310 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −8.72666 | −0.596542 | ||||||||
\(215\) | 25.6040 | 1.74618 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.778008 | 0.0528146 | ||||||||
\(218\) | 2.41468 | 0.163543 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.28267 | −0.153898 | ||||||||
\(221\) | −6.56534 | −0.441633 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.79667 | −0.455138 | −0.227569 | − | 0.973762i | \(-0.573078\pi\) | ||||
−0.227569 | + | 0.973762i | \(0.573078\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.14134 | −0.208959 | ||||||||
\(227\) | 7.63667 | 0.506864 | 0.253432 | − | 0.967353i | \(-0.418441\pi\) | ||||
0.253432 | + | 0.967353i | \(0.418441\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.57467 | −0.368385 | −0.184192 | − | 0.982890i | \(-0.558967\pi\) | ||||
−0.184192 | + | 0.982890i | \(0.558967\pi\) | |||||||
\(230\) | 3.14134 | 0.207134 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.86799 | 0.516559 | ||||||||
\(233\) | 10.0000 | 0.655122 | 0.327561 | − | 0.944830i | \(-0.393773\pi\) | ||||
0.327561 | + | 0.944830i | \(0.393773\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.31198 | −0.542214 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.77801 | −0.180072 | ||||||||
\(239\) | −9.29200 | −0.601050 | −0.300525 | − | 0.953774i | \(-0.597162\pi\) | ||||
−0.300525 | + | 0.953774i | \(0.597162\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.09931 | −0.392891 | −0.196446 | − | 0.980515i | \(-0.562940\pi\) | ||||
−0.196446 | + | 0.980515i | \(0.562940\pi\) | |||||||
\(242\) | 10.4720 | 0.673164 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 7.55602 | 0.483724 | ||||||||
\(245\) | −3.14134 | −0.200693 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.55602 | −0.226264 | ||||||||
\(248\) | 0.778008 | 0.0494035 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.414680 | −0.0262266 | ||||||||
\(251\) | −26.8446 | −1.69442 | −0.847209 | − | 0.531260i | \(-0.821719\pi\) | ||||
−0.847209 | + | 0.531260i | \(0.821719\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.726656 | 0.0456845 | ||||||||
\(254\) | −2.85866 | −0.179369 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 3.55602 | 0.221818 | 0.110909 | − | 0.993831i | \(-0.464624\pi\) | ||||
0.110909 | + | 0.993831i | \(0.464624\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.86799 | −0.364619 | ||||||||
\(260\) | −7.42401 | −0.460417 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −0.264015 | −0.0163109 | ||||||||
\(263\) | 16.1507 | 0.995893 | 0.497946 | − | 0.867208i | \(-0.334088\pi\) | ||||
0.497946 | + | 0.867208i | \(0.334088\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 24.3013 | 1.49282 | ||||||||
\(266\) | −1.50466 | −0.0922569 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.45331 | −0.0887752 | ||||||||
\(269\) | 3.66598 | 0.223519 | 0.111759 | − | 0.993735i | \(-0.464351\pi\) | ||||
0.111759 | + | 0.993735i | \(0.464351\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.40196 | 0.571128 | 0.285564 | − | 0.958360i | \(-0.407819\pi\) | ||||
0.285564 | + | 0.958360i | \(0.407819\pi\) | |||||||
\(272\) | −2.77801 | −0.168441 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.15066 | −0.129926 | ||||||||
\(275\) | 3.53736 | 0.213311 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.9414 | −0.837657 | −0.418828 | − | 0.908065i | \(-0.637559\pi\) | ||||
−0.418828 | + | 0.908065i | \(0.637559\pi\) | |||||||
\(278\) | −12.0480 | −0.722589 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3.14134 | −0.187731 | ||||||||
\(281\) | 2.41468 | 0.144048 | 0.0720239 | − | 0.997403i | \(-0.477054\pi\) | ||||
0.0720239 | + | 0.997403i | \(0.477054\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 24.1473 | 1.43541 | 0.717703 | − | 0.696349i | \(-0.245193\pi\) | ||||
0.717703 | + | 0.696349i | \(0.245193\pi\) | |||||||
\(284\) | −9.29200 | −0.551379 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.71733 | −0.101548 | ||||||||
\(287\) | 1.58532 | 0.0935785 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.28267 | −0.546040 | ||||||||
\(290\) | −24.7160 | −1.45137 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.00933 | −0.0590665 | ||||||||
\(293\) | 14.4626 | 0.844917 | 0.422458 | − | 0.906382i | \(-0.361167\pi\) | ||||
0.422458 | + | 0.906382i | \(0.361167\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −5.86799 | −0.341070 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −20.8480 | −1.20769 | ||||||||
\(299\) | 2.36333 | 0.136675 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.15066 | 0.469797 | ||||||||
\(302\) | −3.42401 | −0.197030 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.50466 | −0.0862984 | ||||||||
\(305\) | −23.7360 | −1.35912 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −30.0666 | −1.71599 | −0.857996 | − | 0.513656i | \(-0.828291\pi\) | ||||
−0.857996 | + | 0.513656i | \(0.828291\pi\) | |||||||
\(308\) | −0.726656 | −0.0414051 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2.44398 | −0.138809 | ||||||||
\(311\) | −1.24065 | −0.0703508 | −0.0351754 | − | 0.999381i | \(-0.511199\pi\) | ||||
−0.0351754 | + | 0.999381i | \(0.511199\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.7780 | 0.835302 | 0.417651 | − | 0.908607i | \(-0.362853\pi\) | ||||
0.417651 | + | 0.908607i | \(0.362853\pi\) | |||||||
\(314\) | −14.5653 | −0.821970 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.72666 | 0.153386 | ||||||||
\(317\) | 7.76529 | 0.436142 | 0.218071 | − | 0.975933i | \(-0.430024\pi\) | ||||
0.218071 | + | 0.975933i | \(0.430024\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.71733 | −0.320109 | ||||||||
\(320\) | −3.14134 | −0.175606 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.00000 | 0.0557278 | ||||||||
\(323\) | 4.17997 | 0.232580 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 11.5047 | 0.638164 | ||||||||
\(326\) | 13.5747 | 0.751832 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.58532 | 0.0875347 | ||||||||
\(329\) | −2.64600 | −0.145879 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −23.7360 | −1.30465 | −0.652324 | − | 0.757940i | \(-0.726206\pi\) | ||||
−0.652324 | + | 0.757940i | \(0.726206\pi\) | |||||||
\(332\) | 7.78734 | 0.427386 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3.22199 | 0.176300 | ||||||||
\(335\) | 4.56534 | 0.249431 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.64939 | 0.253268 | 0.126634 | − | 0.991949i | \(-0.459583\pi\) | ||||
0.126634 | + | 0.991949i | \(0.459583\pi\) | |||||||
\(338\) | 7.41468 | 0.403305 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 8.72666 | 0.473269 | ||||||||
\(341\) | −0.565344 | −0.0306151 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 8.15066 | 0.439454 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5.32469 | −0.286257 | ||||||||
\(347\) | 11.7653 | 0.631594 | 0.315797 | − | 0.948827i | \(-0.397728\pi\) | ||||
0.315797 | + | 0.948827i | \(0.397728\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 22.8153 | 1.22128 | 0.610638 | − | 0.791910i | \(-0.290913\pi\) | ||||
0.610638 | + | 0.791910i | \(0.290913\pi\) | |||||||
\(350\) | 4.86799 | 0.260205 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.726656 | −0.0387309 | ||||||||
\(353\) | 19.8094 | 1.05435 | 0.527174 | − | 0.849758i | \(-0.323252\pi\) | ||||
0.527174 | + | 0.849758i | \(0.323252\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 29.1893 | 1.54921 | ||||||||
\(356\) | 17.5233 | 0.928734 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.86799 | 0.0987265 | ||||||||
\(359\) | 11.1413 | 0.588017 | 0.294009 | − | 0.955803i | \(-0.405011\pi\) | ||||
0.294009 | + | 0.955803i | \(0.405011\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.7360 | −0.880841 | ||||||||
\(362\) | 11.5560 | 0.607371 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.36333 | −0.123872 | ||||||||
\(365\) | 3.17064 | 0.165959 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.59465 | 0.344238 | 0.172119 | − | 0.985076i | \(-0.444939\pi\) | ||||
0.172119 | + | 0.985076i | \(0.444939\pi\) | |||||||
\(368\) | 1.00000 | 0.0521286 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 18.4333 | 0.958304 | ||||||||
\(371\) | 7.73599 | 0.401632 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 28.3013 | 1.46539 | 0.732694 | − | 0.680559i | \(-0.238263\pi\) | ||||
0.732694 | + | 0.680559i | \(0.238263\pi\) | |||||||
\(374\) | 2.01866 | 0.104382 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.64600 | −0.136457 | ||||||||
\(377\) | −18.5946 | −0.957673 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.1600 | 0.778717 | 0.389358 | − | 0.921086i | \(-0.372697\pi\) | ||||
0.389358 | + | 0.921086i | \(0.372697\pi\) | |||||||
\(380\) | 4.72666 | 0.242472 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −21.8387 | −1.11736 | ||||||||
\(383\) | 5.71733 | 0.292142 | 0.146071 | − | 0.989274i | \(-0.453337\pi\) | ||||
0.146071 | + | 0.989274i | \(0.453337\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.28267 | 0.116336 | ||||||||
\(386\) | −22.1693 | −1.12839 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.63667 | 0.0830894 | ||||||||
\(389\) | −0.887968 | −0.0450218 | −0.0225109 | − | 0.999747i | \(-0.507166\pi\) | ||||
−0.0225109 | + | 0.999747i | \(0.507166\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.77801 | −0.140490 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 11.7067 | 0.589774 | ||||||||
\(395\) | −8.56534 | −0.430969 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.76868 | 0.389899 | 0.194949 | − | 0.980813i | \(-0.437546\pi\) | ||||
0.194949 | + | 0.980813i | \(0.437546\pi\) | |||||||
\(398\) | −9.70668 | −0.486552 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.86799 | 0.243400 | ||||||||
\(401\) | 22.5653 | 1.12686 | 0.563430 | − | 0.826164i | \(-0.309482\pi\) | ||||
0.563430 | + | 0.826164i | \(0.309482\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.83869 | −0.0915916 | ||||||||
\(404\) | 7.24065 | 0.360236 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7.86799 | −0.390482 | ||||||||
\(407\) | 4.26401 | 0.211359 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.1120 | 0.648348 | 0.324174 | − | 0.945997i | \(-0.394914\pi\) | ||||
0.324174 | + | 0.945997i | \(0.394914\pi\) | |||||||
\(410\) | −4.98002 | −0.245946 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 19.4240 | 0.956952 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −24.4626 | −1.20082 | ||||||||
\(416\) | −2.36333 | −0.115872 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.09337 | 0.0534787 | ||||||||
\(419\) | 7.68463 | 0.375419 | 0.187709 | − | 0.982225i | \(-0.439894\pi\) | ||||
0.187709 | + | 0.982225i | \(0.439894\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −24.9987 | −1.21836 | −0.609181 | − | 0.793032i | \(-0.708502\pi\) | ||||
−0.609181 | + | 0.793032i | \(0.708502\pi\) | |||||||
\(422\) | −9.83869 | −0.478940 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 7.73599 | 0.375693 | ||||||||
\(425\) | −13.5233 | −0.655977 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.55602 | −0.365661 | ||||||||
\(428\) | 8.72666 | 0.421819 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −25.6040 | −1.23473 | ||||||||
\(431\) | 0.678694 | 0.0326916 | 0.0163458 | − | 0.999866i | \(-0.494797\pi\) | ||||
0.0163458 | + | 0.999866i | \(0.494797\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.5620 | −0.892031 | −0.446015 | − | 0.895025i | \(-0.647157\pi\) | ||||
−0.446015 | + | 0.895025i | \(0.647157\pi\) | |||||||
\(434\) | −0.778008 | −0.0373456 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.41468 | −0.115642 | ||||||||
\(437\) | −1.50466 | −0.0719779 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 23.7287 | 1.13251 | 0.566255 | − | 0.824230i | \(-0.308392\pi\) | ||||
0.566255 | + | 0.824230i | \(0.308392\pi\) | |||||||
\(440\) | 2.28267 | 0.108822 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 6.56534 | 0.312282 | ||||||||
\(443\) | 9.15999 | 0.435204 | 0.217602 | − | 0.976038i | \(-0.430176\pi\) | ||||
0.217602 | + | 0.976038i | \(0.430176\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −55.0466 | −2.60946 | ||||||||
\(446\) | 6.79667 | 0.321831 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | −3.92273 | −0.185125 | −0.0925626 | − | 0.995707i | \(-0.529506\pi\) | ||||
−0.0925626 | + | 0.995707i | \(0.529506\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.15198 | −0.0542448 | ||||||||
\(452\) | 3.14134 | 0.147756 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −7.63667 | −0.358407 | ||||||||
\(455\) | 7.42401 | 0.348043 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −33.6774 | −1.57536 | −0.787681 | − | 0.616084i | \(-0.788718\pi\) | ||||
−0.787681 | + | 0.616084i | \(0.788718\pi\) | |||||||
\(458\) | 5.57467 | 0.260487 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −3.14134 | −0.146466 | ||||||||
\(461\) | −34.5140 | −1.60748 | −0.803738 | − | 0.594983i | \(-0.797159\pi\) | ||||
−0.803738 | + | 0.594983i | \(0.797159\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.6974 | 1.24073 | 0.620366 | − | 0.784313i | \(-0.286984\pi\) | ||||
0.620366 | + | 0.784313i | \(0.286984\pi\) | |||||||
\(464\) | −7.86799 | −0.365262 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −10.0000 | −0.463241 | ||||||||
\(467\) | 17.9193 | 0.829208 | 0.414604 | − | 0.910002i | \(-0.363920\pi\) | ||||
0.414604 | + | 0.910002i | \(0.363920\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.45331 | 0.0671078 | ||||||||
\(470\) | 8.31198 | 0.383403 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.92273 | −0.272328 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.32469 | −0.336080 | ||||||||
\(476\) | 2.77801 | 0.127330 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 9.29200 | 0.425006 | ||||||||
\(479\) | −15.3693 | −0.702240 | −0.351120 | − | 0.936331i | \(-0.614199\pi\) | ||||
−0.351120 | + | 0.936331i | \(0.614199\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.8680 | 0.632326 | ||||||||
\(482\) | 6.09931 | 0.277816 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.4720 | −0.475999 | ||||||||
\(485\) | −5.14134 | −0.233456 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13.3026 | −0.602801 | −0.301400 | − | 0.953498i | \(-0.597454\pi\) | ||||
−0.301400 | + | 0.953498i | \(0.597454\pi\) | |||||||
\(488\) | −7.55602 | −0.342045 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 3.14134 | 0.141911 | ||||||||
\(491\) | 34.9694 | 1.57815 | 0.789073 | − | 0.614300i | \(-0.210561\pi\) | ||||
0.789073 | + | 0.614300i | \(0.210561\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 21.8573 | 0.984405 | ||||||||
\(494\) | 3.55602 | 0.159993 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.778008 | −0.0349336 | ||||||||
\(497\) | 9.29200 | 0.416803 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −37.5161 | −1.67945 | −0.839725 | − | 0.543012i | \(-0.817284\pi\) | ||||
−0.839725 | + | 0.543012i | \(0.817284\pi\) | |||||||
\(500\) | 0.414680 | 0.0185450 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 26.8446 | 1.19813 | ||||||||
\(503\) | 15.7360 | 0.701633 | 0.350816 | − | 0.936444i | \(-0.385904\pi\) | ||||
0.350816 | + | 0.936444i | \(0.385904\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −22.7453 | −1.01215 | ||||||||
\(506\) | −0.726656 | −0.0323038 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.85866 | 0.126833 | ||||||||
\(509\) | 6.61670 | 0.293280 | 0.146640 | − | 0.989190i | \(-0.453154\pi\) | ||||
0.146640 | + | 0.989190i | \(0.453154\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.00933 | 0.0446501 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3.55602 | −0.156849 | ||||||||
\(515\) | −61.0173 | −2.68875 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.92273 | 0.0845617 | ||||||||
\(518\) | 5.86799 | 0.257825 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 7.42401 | 0.325564 | ||||||||
\(521\) | −6.57260 | −0.287951 | −0.143975 | − | 0.989581i | \(-0.545989\pi\) | ||||
−0.143975 | + | 0.989581i | \(0.545989\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17.6074 | −0.769916 | −0.384958 | − | 0.922934i | \(-0.625784\pi\) | ||||
−0.384958 | + | 0.922934i | \(0.625784\pi\) | |||||||
\(524\) | 0.264015 | 0.0115335 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −16.1507 | −0.704202 | ||||||||
\(527\) | 2.16131 | 0.0941482 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −24.3013 | −1.05558 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.50466 | 0.0652355 | ||||||||
\(533\) | −3.74663 | −0.162285 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −27.4134 | −1.18518 | ||||||||
\(536\) | 1.45331 | 0.0627736 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −3.66598 | −0.158051 | ||||||||
\(539\) | 0.726656 | 0.0312993 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.9813 | −0.515118 | −0.257559 | − | 0.966263i | \(-0.582918\pi\) | ||||
−0.257559 | + | 0.966263i | \(0.582918\pi\) | |||||||
\(542\) | −9.40196 | −0.403849 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.77801 | 0.119106 | ||||||||
\(545\) | 7.58532 | 0.324919 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.28267 | 0.268628 | 0.134314 | − | 0.990939i | \(-0.457117\pi\) | ||||
0.134314 | + | 0.990939i | \(0.457117\pi\) | |||||||
\(548\) | 2.15066 | 0.0918718 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −3.53736 | −0.150833 | ||||||||
\(551\) | 11.8387 | 0.504345 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.72666 | −0.115949 | ||||||||
\(554\) | 13.9414 | 0.592313 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 12.0480 | 0.510947 | ||||||||
\(557\) | 26.6027 | 1.12719 | 0.563595 | − | 0.826051i | \(-0.309418\pi\) | ||||
0.563595 | + | 0.826051i | \(0.309418\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −19.2627 | −0.814725 | ||||||||
\(560\) | 3.14134 | 0.132746 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.41468 | −0.101857 | ||||||||
\(563\) | 23.6367 | 0.996167 | 0.498083 | − | 0.867129i | \(-0.334037\pi\) | ||||
0.498083 | + | 0.867129i | \(0.334037\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.86799 | −0.415150 | ||||||||
\(566\) | −24.1473 | −1.01499 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9.29200 | 0.389884 | ||||||||
\(569\) | −44.2066 | −1.85324 | −0.926619 | − | 0.376001i | \(-0.877299\pi\) | ||||
−0.926619 | + | 0.376001i | \(0.877299\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −31.4720 | −1.31706 | −0.658530 | − | 0.752554i | \(-0.728822\pi\) | ||||
−0.658530 | + | 0.752554i | \(0.728822\pi\) | |||||||
\(572\) | 1.71733 | 0.0718051 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.58532 | −0.0661700 | ||||||||
\(575\) | 4.86799 | 0.203009 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −20.1800 | −0.840103 | −0.420052 | − | 0.907500i | \(-0.637988\pi\) | ||||
−0.420052 | + | 0.907500i | \(0.637988\pi\) | |||||||
\(578\) | 9.28267 | 0.386108 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 24.7160 | 1.02628 | ||||||||
\(581\) | −7.78734 | −0.323073 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.62140 | −0.232815 | ||||||||
\(584\) | 1.00933 | 0.0417663 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −14.4626 | −0.597446 | ||||||||
\(587\) | −16.9907 | −0.701280 | −0.350640 | − | 0.936510i | \(-0.614036\pi\) | ||||
−0.350640 | + | 0.936510i | \(0.614036\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.17064 | 0.0482354 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 5.86799 | 0.241173 | ||||||||
\(593\) | 30.8773 | 1.26798 | 0.633990 | − | 0.773341i | \(-0.281416\pi\) | ||||
0.633990 | + | 0.773341i | \(0.281416\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.72666 | −0.357758 | ||||||||
\(596\) | 20.8480 | 0.853968 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2.36333 | −0.0966437 | ||||||||
\(599\) | 7.67738 | 0.313689 | 0.156845 | − | 0.987623i | \(-0.449868\pi\) | ||||
0.156845 | + | 0.987623i | \(0.449868\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.8039 | 0.522283 | 0.261141 | − | 0.965301i | \(-0.415901\pi\) | ||||
0.261141 | + | 0.965301i | \(0.415901\pi\) | |||||||
\(602\) | −8.15066 | −0.332196 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3.42401 | 0.139321 | ||||||||
\(605\) | 32.8960 | 1.33741 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.50466 | 0.385782 | 0.192891 | − | 0.981220i | \(-0.438214\pi\) | ||||
0.192891 | + | 0.981220i | \(0.438214\pi\) | |||||||
\(608\) | 1.50466 | 0.0610222 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 23.7360 | 0.961042 | ||||||||
\(611\) | 6.25337 | 0.252984 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.1133 | −0.408474 | −0.204237 | − | 0.978921i | \(-0.565471\pi\) | ||||
−0.204237 | + | 0.978921i | \(0.565471\pi\) | |||||||
\(614\) | 30.0666 | 1.21339 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.726656 | 0.0292778 | ||||||||
\(617\) | 28.5840 | 1.15075 | 0.575374 | − | 0.817890i | \(-0.304856\pi\) | ||||
0.575374 | + | 0.817890i | \(0.304856\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −37.9673 | −1.52603 | −0.763017 | − | 0.646378i | \(-0.776283\pi\) | ||||
−0.763017 | + | 0.646378i | \(0.776283\pi\) | |||||||
\(620\) | 2.44398 | 0.0981528 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.24065 | 0.0497455 | ||||||||
\(623\) | −17.5233 | −0.702057 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −25.6426 | −1.02570 | ||||||||
\(626\) | −14.7780 | −0.590648 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 14.5653 | 0.581221 | ||||||||
\(629\) | −16.3013 | −0.649977 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.6867 | 0.982762 | 0.491381 | − | 0.870945i | \(-0.336492\pi\) | ||||
0.491381 | + | 0.870945i | \(0.336492\pi\) | |||||||
\(632\) | −2.72666 | −0.108461 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −7.76529 | −0.308399 | ||||||||
\(635\) | −8.98002 | −0.356361 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.36333 | 0.0936385 | ||||||||
\(638\) | 5.71733 | 0.226351 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 3.14134 | 0.124172 | ||||||||
\(641\) | −29.5853 | −1.16855 | −0.584275 | − | 0.811556i | \(-0.698621\pi\) | ||||
−0.584275 | + | 0.811556i | \(0.698621\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −15.6260 | −0.616230 | −0.308115 | − | 0.951349i | \(-0.599698\pi\) | ||||
−0.308115 | + | 0.951349i | \(0.599698\pi\) | |||||||
\(644\) | −1.00000 | −0.0394055 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.17997 | −0.164459 | ||||||||
\(647\) | 42.2686 | 1.66175 | 0.830876 | − | 0.556458i | \(-0.187840\pi\) | ||||
0.830876 | + | 0.556458i | \(0.187840\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −11.5047 | −0.451250 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −13.5747 | −0.531625 | ||||||||
\(653\) | −1.32131 | −0.0517067 | −0.0258533 | − | 0.999666i | \(-0.508230\pi\) | ||||
−0.0258533 | + | 0.999666i | \(0.508230\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.829359 | −0.0324057 | ||||||||
\(656\) | −1.58532 | −0.0618964 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2.64600 | 0.103152 | ||||||||
\(659\) | 17.1307 | 0.667317 | 0.333658 | − | 0.942694i | \(-0.391717\pi\) | ||||
0.333658 | + | 0.942694i | \(0.391717\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −34.7267 | −1.35071 | −0.675355 | − | 0.737493i | \(-0.736010\pi\) | ||||
−0.675355 | + | 0.737493i | \(0.736010\pi\) | |||||||
\(662\) | 23.7360 | 0.922525 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −7.78734 | −0.302207 | ||||||||
\(665\) | −4.72666 | −0.183292 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.86799 | −0.304650 | ||||||||
\(668\) | −3.22199 | −0.124663 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −4.56534 | −0.176375 | ||||||||
\(671\) | 5.49063 | 0.211963 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −26.1107 | −1.00649 | −0.503247 | − | 0.864143i | \(-0.667861\pi\) | ||||
−0.503247 | + | 0.864143i | \(0.667861\pi\) | |||||||
\(674\) | −4.64939 | −0.179088 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7.41468 | −0.285180 | ||||||||
\(677\) | −25.9346 | −0.996748 | −0.498374 | − | 0.866962i | \(-0.666069\pi\) | ||||
−0.498374 | + | 0.866962i | \(0.666069\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.63667 | −0.0628097 | ||||||||
\(680\) | −8.72666 | −0.334652 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.565344 | 0.0216482 | ||||||||
\(683\) | 6.72666 | 0.257388 | 0.128694 | − | 0.991684i | \(-0.458921\pi\) | ||||
0.128694 | + | 0.991684i | \(0.458921\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.75596 | −0.258132 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −8.15066 | −0.310741 | ||||||||
\(689\) | −18.2827 | −0.696514 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.7253 | −0.446053 | −0.223026 | − | 0.974812i | \(-0.571594\pi\) | ||||
−0.223026 | + | 0.974812i | \(0.571594\pi\) | |||||||
\(692\) | 5.32469 | 0.202415 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −11.7653 | −0.446604 | ||||||||
\(695\) | −37.8467 | −1.43561 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.40403 | 0.166815 | ||||||||
\(698\) | −22.8153 | −0.863573 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −4.86799 | −0.183993 | ||||||||
\(701\) | 34.0373 | 1.28557 | 0.642786 | − | 0.766046i | \(-0.277779\pi\) | ||||
0.642786 | + | 0.766046i | \(0.277779\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.82936 | −0.333006 | ||||||||
\(704\) | 0.726656 | 0.0273869 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −19.8094 | −0.745536 | ||||||||
\(707\) | −7.24065 | −0.272313 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −46.5254 | −1.74730 | −0.873649 | − | 0.486557i | \(-0.838253\pi\) | ||||
−0.873649 | + | 0.486557i | \(0.838253\pi\) | |||||||
\(710\) | −29.1893 | −1.09545 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −17.5233 | −0.656714 | ||||||||
\(713\) | −0.778008 | −0.0291366 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.39470 | −0.201750 | ||||||||
\(716\) | −1.86799 | −0.0698102 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −11.1413 | −0.415791 | ||||||||
\(719\) | −10.0220 | −0.373759 | −0.186880 | − | 0.982383i | \(-0.559837\pi\) | ||||
−0.186880 | + | 0.982383i | \(0.559837\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −19.4240 | −0.723388 | ||||||||
\(722\) | 16.7360 | 0.622849 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −11.5560 | −0.429476 | ||||||||
\(725\) | −38.3013 | −1.42248 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 34.6867 | 1.28646 | 0.643229 | − | 0.765674i | \(-0.277594\pi\) | ||||
0.643229 | + | 0.765674i | \(0.277594\pi\) | |||||||
\(728\) | 2.36333 | 0.0875908 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −3.17064 | −0.117351 | ||||||||
\(731\) | 22.6426 | 0.837467 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.3760 | 0.494056 | 0.247028 | − | 0.969008i | \(-0.420546\pi\) | ||||
0.247028 | + | 0.969008i | \(0.420546\pi\) | |||||||
\(734\) | −6.59465 | −0.243413 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | −1.05606 | −0.0389004 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16.6867 | 0.613830 | 0.306915 | − | 0.951737i | \(-0.400703\pi\) | ||||
0.306915 | + | 0.951737i | \(0.400703\pi\) | |||||||
\(740\) | −18.4333 | −0.677623 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −7.73599 | −0.283997 | ||||||||
\(743\) | 18.1613 | 0.666274 | 0.333137 | − | 0.942878i | \(-0.391893\pi\) | ||||
0.333137 | + | 0.942878i | \(0.391893\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −65.4906 | −2.39939 | ||||||||
\(746\) | −28.3013 | −1.03619 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.01866 | −0.0738094 | ||||||||
\(749\) | −8.72666 | −0.318865 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.58400 | 0.0942916 | 0.0471458 | − | 0.998888i | \(-0.484987\pi\) | ||||
0.0471458 | + | 0.998888i | \(0.484987\pi\) | |||||||
\(752\) | 2.64600 | 0.0964897 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 18.5946 | 0.677177 | ||||||||
\(755\) | −10.7560 | −0.391450 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21.2666 | 0.772946 | 0.386473 | − | 0.922301i | \(-0.373693\pi\) | ||||
0.386473 | + | 0.922301i | \(0.373693\pi\) | |||||||
\(758\) | −15.1600 | −0.550636 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.72666 | −0.171454 | ||||||||
\(761\) | −29.7801 | −1.07953 | −0.539764 | − | 0.841817i | \(-0.681486\pi\) | ||||
−0.539764 | + | 0.841817i | \(0.681486\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.41468 | 0.0874173 | ||||||||
\(764\) | 21.8387 | 0.790096 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −5.71733 | −0.206575 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.0807 | 0.579883 | 0.289942 | − | 0.957044i | \(-0.406364\pi\) | ||||
0.289942 | + | 0.957044i | \(0.406364\pi\) | |||||||
\(770\) | −2.28267 | −0.0822618 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 22.1693 | 0.797891 | ||||||||
\(773\) | −10.1507 | −0.365094 | −0.182547 | − | 0.983197i | \(-0.558434\pi\) | ||||
−0.182547 | + | 0.983197i | \(0.558434\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.78734 | −0.136045 | ||||||||
\(776\) | −1.63667 | −0.0587531 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0.887968 | 0.0318352 | ||||||||
\(779\) | 2.38538 | 0.0854649 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.75209 | −0.241609 | ||||||||
\(782\) | 2.77801 | 0.0993414 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −45.7546 | −1.63305 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 30.7967 | 1.09778 | 0.548891 | − | 0.835894i | \(-0.315050\pi\) | ||||
0.548891 | + | 0.835894i | \(0.315050\pi\) | |||||||
\(788\) | −11.7067 | −0.417033 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 8.56534 | 0.304741 | ||||||||
\(791\) | −3.14134 | −0.111693 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 17.8573 | 0.634133 | ||||||||
\(794\) | −7.76868 | −0.275700 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 9.70668 | 0.344044 | ||||||||
\(797\) | −46.7160 | −1.65477 | −0.827383 | − | 0.561638i | \(-0.810171\pi\) | ||||
−0.827383 | + | 0.561638i | \(0.810171\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.35061 | −0.260046 | ||||||||
\(800\) | −4.86799 | −0.172110 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −22.5653 | −0.796810 | ||||||||
\(803\) | −0.733435 | −0.0258824 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.14134 | 0.110718 | ||||||||
\(806\) | 1.83869 | 0.0647650 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −7.24065 | −0.254725 | ||||||||
\(809\) | −38.9253 | −1.36854 | −0.684270 | − | 0.729229i | \(-0.739879\pi\) | ||||
−0.684270 | + | 0.729229i | \(0.739879\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.0759 | 0.599618 | 0.299809 | − | 0.953999i | \(-0.403077\pi\) | ||||
0.299809 | + | 0.953999i | \(0.403077\pi\) | |||||||
\(812\) | 7.86799 | 0.276112 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −4.26401 | −0.149454 | ||||||||
\(815\) | 42.6426 | 1.49371 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.2640 | 0.429064 | ||||||||
\(818\) | −13.1120 | −0.458451 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.98002 | 0.173910 | ||||||||
\(821\) | 13.3693 | 0.466591 | 0.233295 | − | 0.972406i | \(-0.425049\pi\) | ||||
0.233295 | + | 0.972406i | \(0.425049\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.93593 | −0.172056 | −0.0860279 | − | 0.996293i | \(-0.527417\pi\) | ||||
−0.0860279 | + | 0.996293i | \(0.527417\pi\) | |||||||
\(824\) | −19.4240 | −0.676667 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −17.6519 | −0.613818 | −0.306909 | − | 0.951739i | \(-0.599295\pi\) | ||||
−0.306909 | + | 0.951739i | \(0.599295\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −28.7967 | −1.00015 | −0.500075 | − | 0.865982i | \(-0.666694\pi\) | ||||
−0.500075 | + | 0.865982i | \(0.666694\pi\) | |||||||
\(830\) | 24.4626 | 0.849111 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.36333 | 0.0819337 | ||||||||
\(833\) | −2.77801 | −0.0962523 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.1214 | 0.350264 | ||||||||
\(836\) | −1.09337 | −0.0378151 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −7.68463 | −0.265461 | ||||||||
\(839\) | −33.6960 | −1.16332 | −0.581658 | − | 0.813433i | \(-0.697596\pi\) | ||||
−0.581658 | + | 0.813433i | \(0.697596\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 32.9053 | 1.13467 | ||||||||
\(842\) | 24.9987 | 0.861511 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 9.83869 | 0.338662 | ||||||||
\(845\) | 23.2920 | 0.801269 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.4720 | 0.359821 | ||||||||
\(848\) | −7.73599 | −0.265655 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 13.5233 | 0.463846 | ||||||||
\(851\) | 5.86799 | 0.201152 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.28861 | −0.112600 | −0.0563000 | − | 0.998414i | \(-0.517930\pi\) | ||||
−0.0563000 | + | 0.998414i | \(0.517930\pi\) | |||||||
\(854\) | 7.55602 | 0.258562 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8.72666 | −0.298271 | ||||||||
\(857\) | −31.2440 | −1.06728 | −0.533638 | − | 0.845713i | \(-0.679176\pi\) | ||||
−0.533638 | + | 0.845713i | \(0.679176\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18.9546 | 0.646722 | 0.323361 | − | 0.946276i | \(-0.395187\pi\) | ||||
0.323361 | + | 0.946276i | \(0.395187\pi\) | |||||||
\(860\) | 25.6040 | 0.873088 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −0.678694 | −0.0231164 | ||||||||
\(863\) | −5.91595 | −0.201381 | −0.100691 | − | 0.994918i | \(-0.532105\pi\) | ||||
−0.100691 | + | 0.994918i | \(0.532105\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −16.7267 | −0.568723 | ||||||||
\(866\) | 18.5620 | 0.630761 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0.778008 | 0.0264073 | ||||||||
\(869\) | 1.98134 | 0.0672124 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.43466 | −0.116379 | ||||||||
\(872\) | 2.41468 | 0.0817714 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.50466 | 0.0508960 | ||||||||
\(875\) | −0.414680 | −0.0140187 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.82003 | 0.264064 | 0.132032 | − | 0.991245i | \(-0.457850\pi\) | ||||
0.132032 | + | 0.991245i | \(0.457850\pi\) | |||||||
\(878\) | −23.7287 | −0.800806 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.28267 | −0.0769489 | ||||||||
\(881\) | 4.43673 | 0.149477 | 0.0747386 | − | 0.997203i | \(-0.476188\pi\) | ||||
0.0747386 | + | 0.997203i | \(0.476188\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20.7453 | 0.698135 | 0.349068 | − | 0.937098i | \(-0.386498\pi\) | ||||
0.349068 | + | 0.937098i | \(0.386498\pi\) | |||||||
\(884\) | −6.56534 | −0.220816 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −9.15999 | −0.307736 | ||||||||
\(887\) | −28.1473 | −0.945093 | −0.472547 | − | 0.881306i | \(-0.656665\pi\) | ||||
−0.472547 | + | 0.881306i | \(0.656665\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.85866 | −0.0958765 | ||||||||
\(890\) | 55.0466 | 1.84517 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −6.79667 | −0.227569 | ||||||||
\(893\) | −3.98134 | −0.133231 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.86799 | 0.196145 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3.92273 | 0.130903 | ||||||||
\(899\) | 6.12136 | 0.204159 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 21.4906 | 0.715957 | ||||||||
\(902\) | 1.15198 | 0.0383568 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3.14134 | −0.104479 | ||||||||
\(905\) | 36.3013 | 1.20670 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 26.2347 | 0.871109 | 0.435555 | − | 0.900162i | \(-0.356552\pi\) | ||||
0.435555 | + | 0.900162i | \(0.356552\pi\) | |||||||
\(908\) | 7.63667 | 0.253432 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −7.42401 | −0.246103 | ||||||||
\(911\) | −15.4054 | −0.510402 | −0.255201 | − | 0.966888i | \(-0.582142\pi\) | ||||
−0.255201 | + | 0.966888i | \(0.582142\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.65872 | 0.187276 | ||||||||
\(914\) | 33.6774 | 1.11395 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5.57467 | −0.184192 | ||||||||
\(917\) | −0.264015 | −0.00871854 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −29.0466 | −0.958160 | −0.479080 | − | 0.877771i | \(-0.659030\pi\) | ||||
−0.479080 | + | 0.877771i | \(0.659030\pi\) | |||||||
\(920\) | 3.14134 | 0.103567 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 34.5140 | 1.13666 | ||||||||
\(923\) | −21.9600 | −0.722824 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 28.5653 | 0.939223 | ||||||||
\(926\) | −26.6974 | −0.877329 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 7.86799 | 0.258280 | ||||||||
\(929\) | −23.2440 | −0.762612 | −0.381306 | − | 0.924449i | \(-0.624526\pi\) | ||||
−0.381306 | + | 0.924449i | \(0.624526\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.50466 | −0.0493134 | ||||||||
\(932\) | 10.0000 | 0.327561 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −17.9193 | −0.586339 | ||||||||
\(935\) | 6.34128 | 0.207382 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.10609 | −0.0688030 | −0.0344015 | − | 0.999408i | \(-0.510953\pi\) | ||||
−0.0344015 | + | 0.999408i | \(0.510953\pi\) | |||||||
\(938\) | −1.45331 | −0.0474523 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −8.31198 | −0.271107 | ||||||||
\(941\) | −4.80005 | −0.156477 | −0.0782387 | − | 0.996935i | \(-0.524930\pi\) | ||||
−0.0782387 | + | 0.996935i | \(0.524930\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.58532 | −0.0516251 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.92273 | 0.192565 | ||||||||
\(947\) | −14.5174 | −0.471752 | −0.235876 | − | 0.971783i | \(-0.575796\pi\) | ||||
−0.235876 | + | 0.971783i | \(0.575796\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.38538 | −0.0774326 | ||||||||
\(950\) | 7.32469 | 0.237644 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −2.77801 | −0.0900358 | ||||||||
\(953\) | 3.76142 | 0.121844 | 0.0609222 | − | 0.998143i | \(-0.480596\pi\) | ||||
0.0609222 | + | 0.998143i | \(0.480596\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −68.6027 | −2.21993 | ||||||||
\(956\) | −9.29200 | −0.300525 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 15.3693 | 0.496558 | ||||||||
\(959\) | −2.15066 | −0.0694486 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.3947 | −0.980474 | ||||||||
\(962\) | −13.8680 | −0.447122 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −6.09931 | −0.196446 | ||||||||
\(965\) | −69.6413 | −2.24183 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 46.2241 | 1.48647 | 0.743233 | − | 0.669033i | \(-0.233291\pi\) | ||||
0.743233 | + | 0.669033i | \(0.233291\pi\) | |||||||
\(968\) | 10.4720 | 0.336582 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 5.14134 | 0.165078 | ||||||||
\(971\) | −23.1566 | −0.743131 | −0.371565 | − | 0.928407i | \(-0.621179\pi\) | ||||
−0.371565 | + | 0.928407i | \(0.621179\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.0480 | −0.386240 | ||||||||
\(974\) | 13.3026 | 0.426244 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.55602 | 0.241862 | ||||||||
\(977\) | −34.2466 | −1.09565 | −0.547823 | − | 0.836594i | \(-0.684543\pi\) | ||||
−0.547823 | + | 0.836594i | \(0.684543\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.7334 | 0.406962 | ||||||||
\(980\) | −3.14134 | −0.100346 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −34.9694 | −1.11592 | ||||||||
\(983\) | 35.4347 | 1.13019 | 0.565095 | − | 0.825026i | \(-0.308840\pi\) | ||||
0.565095 | + | 0.825026i | \(0.308840\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 36.7746 | 1.17174 | ||||||||
\(986\) | −21.8573 | −0.696080 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.55602 | −0.113132 | ||||||||
\(989\) | −8.15066 | −0.259176 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 53.6306 | 1.70363 | 0.851817 | − | 0.523840i | \(-0.175501\pi\) | ||||
0.851817 | + | 0.523840i | \(0.175501\pi\) | |||||||
\(992\) | 0.778008 | 0.0247018 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −9.29200 | −0.294724 | ||||||||
\(995\) | −30.4919 | −0.966660 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −40.3713 | −1.27857 | −0.639287 | − | 0.768969i | \(-0.720770\pi\) | ||||
−0.639287 | + | 0.768969i | \(0.720770\pi\) | |||||||
\(998\) | 37.5161 | 1.18755 | ||||||||
\(999\) | 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 | 2898.2.a.bf.1.1 | ✓ | 3 | |
3.2 | odd | 2 | 2898.2.a.bg.1.3 | yes | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2898.2.a.bf.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
2898.2.a.bg.1.3 | yes | 3 | 3.2 | odd | 2 |