Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3549,2,Mod(1,3549)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3549, 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("3549.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3549 = 3 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3549.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: | \(28.3389076774\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - x^{8} - 11x^{7} + 8x^{6} + 37x^{5} - 18x^{4} - 41x^{3} + 12x^{2} + 6x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(0.494186\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3549.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.494186 | 0.349442 | 0.174721 | − | 0.984618i | \(-0.444098\pi\) | ||||
0.174721 | + | 0.984618i | \(0.444098\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.75578 | −0.877890 | ||||||||
\(5\) | 1.64627 | 0.736236 | 0.368118 | − | 0.929779i | \(-0.380002\pi\) | ||||
0.368118 | + | 0.929779i | \(0.380002\pi\) | |||||||
\(6\) | −0.494186 | −0.201751 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.85605 | −0.656214 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.813565 | 0.257272 | ||||||||
\(11\) | 1.00650 | 0.303472 | 0.151736 | − | 0.988421i | \(-0.451514\pi\) | ||||
0.151736 | + | 0.988421i | \(0.451514\pi\) | |||||||
\(12\) | 1.75578 | 0.506850 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −0.494186 | −0.132077 | ||||||||
\(15\) | −1.64627 | −0.425066 | ||||||||
\(16\) | 2.59432 | 0.648581 | ||||||||
\(17\) | −4.38900 | −1.06449 | −0.532244 | − | 0.846591i | \(-0.678651\pi\) | ||||
−0.532244 | + | 0.846591i | \(0.678651\pi\) | |||||||
\(18\) | 0.494186 | 0.116481 | ||||||||
\(19\) | 1.17541 | 0.269657 | 0.134829 | − | 0.990869i | \(-0.456952\pi\) | ||||
0.134829 | + | 0.990869i | \(0.456952\pi\) | |||||||
\(20\) | −2.89049 | −0.646334 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 0.497400 | 0.106046 | ||||||||
\(23\) | 2.62816 | 0.548010 | 0.274005 | − | 0.961728i | \(-0.411652\pi\) | ||||
0.274005 | + | 0.961728i | \(0.411652\pi\) | |||||||
\(24\) | 1.85605 | 0.378866 | ||||||||
\(25\) | −2.28979 | −0.457957 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.75578 | 0.331811 | ||||||||
\(29\) | 5.13954 | 0.954388 | 0.477194 | − | 0.878798i | \(-0.341654\pi\) | ||||
0.477194 | + | 0.878798i | \(0.341654\pi\) | |||||||
\(30\) | −0.813565 | −0.148536 | ||||||||
\(31\) | −0.705141 | −0.126647 | −0.0633235 | − | 0.997993i | \(-0.520170\pi\) | ||||
−0.0633235 | + | 0.997993i | \(0.520170\pi\) | |||||||
\(32\) | 4.99419 | 0.882856 | ||||||||
\(33\) | −1.00650 | −0.175210 | ||||||||
\(34\) | −2.16898 | −0.371977 | ||||||||
\(35\) | −1.64627 | −0.278271 | ||||||||
\(36\) | −1.75578 | −0.292630 | ||||||||
\(37\) | 2.72506 | 0.447997 | 0.223999 | − | 0.974589i | \(-0.428089\pi\) | ||||
0.223999 | + | 0.974589i | \(0.428089\pi\) | |||||||
\(38\) | 0.580871 | 0.0942297 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.05557 | −0.483128 | ||||||||
\(41\) | −3.05611 | −0.477284 | −0.238642 | − | 0.971108i | \(-0.576702\pi\) | ||||
−0.238642 | + | 0.971108i | \(0.576702\pi\) | |||||||
\(42\) | 0.494186 | 0.0762546 | ||||||||
\(43\) | −10.5077 | −1.60242 | −0.801208 | − | 0.598386i | \(-0.795809\pi\) | ||||
−0.801208 | + | 0.598386i | \(0.795809\pi\) | |||||||
\(44\) | −1.76720 | −0.266415 | ||||||||
\(45\) | 1.64627 | 0.245412 | ||||||||
\(46\) | 1.29880 | 0.191498 | ||||||||
\(47\) | −2.16111 | −0.315231 | −0.157615 | − | 0.987501i | \(-0.550381\pi\) | ||||
−0.157615 | + | 0.987501i | \(0.550381\pi\) | |||||||
\(48\) | −2.59432 | −0.374458 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.13158 | −0.160030 | ||||||||
\(51\) | 4.38900 | 0.614582 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.96782 | −0.270301 | −0.135150 | − | 0.990825i | \(-0.543152\pi\) | ||||
−0.135150 | + | 0.990825i | \(0.543152\pi\) | |||||||
\(54\) | −0.494186 | −0.0672502 | ||||||||
\(55\) | 1.65698 | 0.223427 | ||||||||
\(56\) | 1.85605 | 0.248026 | ||||||||
\(57\) | −1.17541 | −0.155687 | ||||||||
\(58\) | 2.53989 | 0.333504 | ||||||||
\(59\) | −4.90995 | −0.639221 | −0.319611 | − | 0.947549i | \(-0.603552\pi\) | ||||
−0.319611 | + | 0.947549i | \(0.603552\pi\) | |||||||
\(60\) | 2.89049 | 0.373161 | ||||||||
\(61\) | 0.563211 | 0.0721117 | 0.0360559 | − | 0.999350i | \(-0.488521\pi\) | ||||
0.0360559 | + | 0.999350i | \(0.488521\pi\) | |||||||
\(62\) | −0.348471 | −0.0442558 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | −2.72059 | −0.340073 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.497400 | −0.0612258 | ||||||||
\(67\) | 13.1061 | 1.60116 | 0.800580 | − | 0.599225i | \(-0.204525\pi\) | ||||
0.800580 | + | 0.599225i | \(0.204525\pi\) | |||||||
\(68\) | 7.70611 | 0.934503 | ||||||||
\(69\) | −2.62816 | −0.316394 | ||||||||
\(70\) | −0.813565 | −0.0972397 | ||||||||
\(71\) | 15.3807 | 1.82536 | 0.912678 | − | 0.408678i | \(-0.134010\pi\) | ||||
0.912678 | + | 0.408678i | \(0.134010\pi\) | |||||||
\(72\) | −1.85605 | −0.218738 | ||||||||
\(73\) | 13.5942 | 1.59108 | 0.795541 | − | 0.605900i | \(-0.207187\pi\) | ||||
0.795541 | + | 0.605900i | \(0.207187\pi\) | |||||||
\(74\) | 1.34669 | 0.156549 | ||||||||
\(75\) | 2.28979 | 0.264402 | ||||||||
\(76\) | −2.06376 | −0.236729 | ||||||||
\(77\) | −1.00650 | −0.114702 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.63275 | 0.858751 | 0.429376 | − | 0.903126i | \(-0.358734\pi\) | ||||
0.429376 | + | 0.903126i | \(0.358734\pi\) | |||||||
\(80\) | 4.27096 | 0.477508 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −1.51029 | −0.166783 | ||||||||
\(83\) | 0.0542580 | 0.00595559 | 0.00297779 | − | 0.999996i | \(-0.499052\pi\) | ||||
0.00297779 | + | 0.999996i | \(0.499052\pi\) | |||||||
\(84\) | −1.75578 | −0.191571 | ||||||||
\(85\) | −7.22548 | −0.783714 | ||||||||
\(86\) | −5.19278 | −0.559952 | ||||||||
\(87\) | −5.13954 | −0.551016 | ||||||||
\(88\) | −1.86813 | −0.199143 | ||||||||
\(89\) | −0.601205 | −0.0637276 | −0.0318638 | − | 0.999492i | \(-0.510144\pi\) | ||||
−0.0318638 | + | 0.999492i | \(0.510144\pi\) | |||||||
\(90\) | 0.813565 | 0.0857573 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −4.61447 | −0.481092 | ||||||||
\(93\) | 0.705141 | 0.0731197 | ||||||||
\(94\) | −1.06799 | −0.110155 | ||||||||
\(95\) | 1.93504 | 0.198531 | ||||||||
\(96\) | −4.99419 | −0.509717 | ||||||||
\(97\) | 1.74080 | 0.176751 | 0.0883757 | − | 0.996087i | \(-0.471832\pi\) | ||||
0.0883757 | + | 0.996087i | \(0.471832\pi\) | |||||||
\(98\) | 0.494186 | 0.0499203 | ||||||||
\(99\) | 1.00650 | 0.101157 | ||||||||
\(100\) | 4.02036 | 0.402036 | ||||||||
\(101\) | 12.8587 | 1.27949 | 0.639746 | − | 0.768586i | \(-0.279039\pi\) | ||||
0.639746 | + | 0.768586i | \(0.279039\pi\) | |||||||
\(102\) | 2.16898 | 0.214761 | ||||||||
\(103\) | 14.6917 | 1.44761 | 0.723806 | − | 0.690004i | \(-0.242391\pi\) | ||||
0.723806 | + | 0.690004i | \(0.242391\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.64627 | 0.160660 | ||||||||
\(106\) | −0.972469 | −0.0944546 | ||||||||
\(107\) | 3.37556 | 0.326328 | 0.163164 | − | 0.986599i | \(-0.447830\pi\) | ||||
0.163164 | + | 0.986599i | \(0.447830\pi\) | |||||||
\(108\) | 1.75578 | 0.168950 | ||||||||
\(109\) | −9.90520 | −0.948746 | −0.474373 | − | 0.880324i | \(-0.657325\pi\) | ||||
−0.474373 | + | 0.880324i | \(0.657325\pi\) | |||||||
\(110\) | 0.818857 | 0.0780749 | ||||||||
\(111\) | −2.72506 | −0.258651 | ||||||||
\(112\) | −2.59432 | −0.245141 | ||||||||
\(113\) | −13.5673 | −1.27631 | −0.638154 | − | 0.769909i | \(-0.720302\pi\) | ||||
−0.638154 | + | 0.769909i | \(0.720302\pi\) | |||||||
\(114\) | −0.580871 | −0.0544035 | ||||||||
\(115\) | 4.32667 | 0.403464 | ||||||||
\(116\) | −9.02390 | −0.837848 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.42643 | −0.223371 | ||||||||
\(119\) | 4.38900 | 0.402339 | ||||||||
\(120\) | 3.05557 | 0.278934 | ||||||||
\(121\) | −9.98695 | −0.907905 | ||||||||
\(122\) | 0.278331 | 0.0251989 | ||||||||
\(123\) | 3.05611 | 0.275560 | ||||||||
\(124\) | 1.23807 | 0.111182 | ||||||||
\(125\) | −12.0010 | −1.07340 | ||||||||
\(126\) | −0.494186 | −0.0440256 | ||||||||
\(127\) | 7.65651 | 0.679405 | 0.339703 | − | 0.940533i | \(-0.389674\pi\) | ||||
0.339703 | + | 0.940533i | \(0.389674\pi\) | |||||||
\(128\) | −11.3329 | −1.00169 | ||||||||
\(129\) | 10.5077 | 0.925155 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.25502 | 0.109652 | 0.0548258 | − | 0.998496i | \(-0.482540\pi\) | ||||
0.0548258 | + | 0.998496i | \(0.482540\pi\) | |||||||
\(132\) | 1.76720 | 0.153815 | ||||||||
\(133\) | −1.17541 | −0.101921 | ||||||||
\(134\) | 6.47684 | 0.559514 | ||||||||
\(135\) | −1.64627 | −0.141689 | ||||||||
\(136\) | 8.14622 | 0.698532 | ||||||||
\(137\) | 2.55836 | 0.218576 | 0.109288 | − | 0.994010i | \(-0.465143\pi\) | ||||
0.109288 | + | 0.994010i | \(0.465143\pi\) | |||||||
\(138\) | −1.29880 | −0.110561 | ||||||||
\(139\) | 5.63993 | 0.478373 | 0.239186 | − | 0.970974i | \(-0.423119\pi\) | ||||
0.239186 | + | 0.970974i | \(0.423119\pi\) | |||||||
\(140\) | 2.89049 | 0.244291 | ||||||||
\(141\) | 2.16111 | 0.181999 | ||||||||
\(142\) | 7.60094 | 0.637857 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 2.59432 | 0.216194 | ||||||||
\(145\) | 8.46108 | 0.702655 | ||||||||
\(146\) | 6.71807 | 0.555992 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | −4.78461 | −0.393292 | ||||||||
\(149\) | 5.49922 | 0.450514 | 0.225257 | − | 0.974299i | \(-0.427678\pi\) | ||||
0.225257 | + | 0.974299i | \(0.427678\pi\) | |||||||
\(150\) | 1.13158 | 0.0923932 | ||||||||
\(151\) | 8.31087 | 0.676329 | 0.338165 | − | 0.941087i | \(-0.390194\pi\) | ||||
0.338165 | + | 0.941087i | \(0.390194\pi\) | |||||||
\(152\) | −2.18162 | −0.176953 | ||||||||
\(153\) | −4.38900 | −0.354829 | ||||||||
\(154\) | −0.497400 | −0.0400817 | ||||||||
\(155\) | −1.16085 | −0.0932420 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.8123 | 1.02253 | 0.511265 | − | 0.859423i | \(-0.329177\pi\) | ||||
0.511265 | + | 0.859423i | \(0.329177\pi\) | |||||||
\(158\) | 3.77200 | 0.300084 | ||||||||
\(159\) | 1.96782 | 0.156058 | ||||||||
\(160\) | 8.22180 | 0.649990 | ||||||||
\(161\) | −2.62816 | −0.207128 | ||||||||
\(162\) | 0.494186 | 0.0388269 | ||||||||
\(163\) | 10.7587 | 0.842684 | 0.421342 | − | 0.906902i | \(-0.361559\pi\) | ||||
0.421342 | + | 0.906902i | \(0.361559\pi\) | |||||||
\(164\) | 5.36585 | 0.419003 | ||||||||
\(165\) | −1.65698 | −0.128996 | ||||||||
\(166\) | 0.0268135 | 0.00208113 | ||||||||
\(167\) | −25.0059 | −1.93502 | −0.967509 | − | 0.252838i | \(-0.918636\pi\) | ||||
−0.967509 | + | 0.252838i | \(0.918636\pi\) | |||||||
\(168\) | −1.85605 | −0.143198 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −3.57073 | −0.273863 | ||||||||
\(171\) | 1.17541 | 0.0898857 | ||||||||
\(172\) | 18.4493 | 1.40675 | ||||||||
\(173\) | 16.7347 | 1.27232 | 0.636159 | − | 0.771558i | \(-0.280522\pi\) | ||||
0.636159 | + | 0.771558i | \(0.280522\pi\) | |||||||
\(174\) | −2.53989 | −0.192549 | ||||||||
\(175\) | 2.28979 | 0.173092 | ||||||||
\(176\) | 2.61120 | 0.196826 | ||||||||
\(177\) | 4.90995 | 0.369055 | ||||||||
\(178\) | −0.297107 | −0.0222691 | ||||||||
\(179\) | 12.2780 | 0.917699 | 0.458849 | − | 0.888514i | \(-0.348262\pi\) | ||||
0.458849 | + | 0.888514i | \(0.348262\pi\) | |||||||
\(180\) | −2.89049 | −0.215445 | ||||||||
\(181\) | 22.8077 | 1.69528 | 0.847640 | − | 0.530572i | \(-0.178023\pi\) | ||||
0.847640 | + | 0.530572i | \(0.178023\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.563211 | −0.0416337 | ||||||||
\(184\) | −4.87801 | −0.359612 | ||||||||
\(185\) | 4.48619 | 0.329831 | ||||||||
\(186\) | 0.348471 | 0.0255511 | ||||||||
\(187\) | −4.41754 | −0.323043 | ||||||||
\(188\) | 3.79444 | 0.276738 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 0.956271 | 0.0693752 | ||||||||
\(191\) | 27.4058 | 1.98302 | 0.991508 | − | 0.130047i | \(-0.0415128\pi\) | ||||
0.991508 | + | 0.130047i | \(0.0415128\pi\) | |||||||
\(192\) | 2.72059 | 0.196342 | ||||||||
\(193\) | −6.41304 | −0.461621 | −0.230810 | − | 0.972999i | \(-0.574138\pi\) | ||||
−0.230810 | + | 0.972999i | \(0.574138\pi\) | |||||||
\(194\) | 0.860279 | 0.0617644 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.75578 | −0.125413 | ||||||||
\(197\) | −17.2081 | −1.22603 | −0.613014 | − | 0.790072i | \(-0.710043\pi\) | ||||
−0.613014 | + | 0.790072i | \(0.710043\pi\) | |||||||
\(198\) | 0.497400 | 0.0353487 | ||||||||
\(199\) | −3.01028 | −0.213393 | −0.106696 | − | 0.994292i | \(-0.534027\pi\) | ||||
−0.106696 | + | 0.994292i | \(0.534027\pi\) | |||||||
\(200\) | 4.24997 | 0.300518 | ||||||||
\(201\) | −13.1061 | −0.924431 | ||||||||
\(202\) | 6.35461 | 0.447109 | ||||||||
\(203\) | −5.13954 | −0.360725 | ||||||||
\(204\) | −7.70611 | −0.539536 | ||||||||
\(205\) | −5.03119 | −0.351393 | ||||||||
\(206\) | 7.26041 | 0.505857 | ||||||||
\(207\) | 2.62816 | 0.182670 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.18305 | 0.0818335 | ||||||||
\(210\) | 0.813565 | 0.0561413 | ||||||||
\(211\) | 26.6548 | 1.83499 | 0.917497 | − | 0.397743i | \(-0.130207\pi\) | ||||
0.917497 | + | 0.397743i | \(0.130207\pi\) | |||||||
\(212\) | 3.45506 | 0.237294 | ||||||||
\(213\) | −15.3807 | −1.05387 | ||||||||
\(214\) | 1.66815 | 0.114033 | ||||||||
\(215\) | −17.2986 | −1.17976 | ||||||||
\(216\) | 1.85605 | 0.126289 | ||||||||
\(217\) | 0.705141 | 0.0478681 | ||||||||
\(218\) | −4.89501 | −0.331532 | ||||||||
\(219\) | −13.5942 | −0.918612 | ||||||||
\(220\) | −2.90929 | −0.196144 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −1.34669 | −0.0903837 | ||||||||
\(223\) | 13.8795 | 0.929443 | 0.464722 | − | 0.885457i | \(-0.346154\pi\) | ||||
0.464722 | + | 0.885457i | \(0.346154\pi\) | |||||||
\(224\) | −4.99419 | −0.333688 | ||||||||
\(225\) | −2.28979 | −0.152652 | ||||||||
\(226\) | −6.70479 | −0.445996 | ||||||||
\(227\) | 13.7180 | 0.910496 | 0.455248 | − | 0.890365i | \(-0.349551\pi\) | ||||
0.455248 | + | 0.890365i | \(0.349551\pi\) | |||||||
\(228\) | 2.06376 | 0.136676 | ||||||||
\(229\) | 9.93225 | 0.656342 | 0.328171 | − | 0.944618i | \(-0.393568\pi\) | ||||
0.328171 | + | 0.944618i | \(0.393568\pi\) | |||||||
\(230\) | 2.13818 | 0.140988 | ||||||||
\(231\) | 1.00650 | 0.0662231 | ||||||||
\(232\) | −9.53927 | −0.626283 | ||||||||
\(233\) | 19.4424 | 1.27371 | 0.636857 | − | 0.770982i | \(-0.280234\pi\) | ||||
0.636857 | + | 0.770982i | \(0.280234\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.55778 | −0.232084 | ||||||||
\(236\) | 8.62080 | 0.561166 | ||||||||
\(237\) | −7.63275 | −0.495800 | ||||||||
\(238\) | 2.16898 | 0.140594 | ||||||||
\(239\) | 16.3885 | 1.06009 | 0.530043 | − | 0.847971i | \(-0.322176\pi\) | ||||
0.530043 | + | 0.847971i | \(0.322176\pi\) | |||||||
\(240\) | −4.27096 | −0.275690 | ||||||||
\(241\) | −16.0048 | −1.03096 | −0.515479 | − | 0.856902i | \(-0.672386\pi\) | ||||
−0.515479 | + | 0.856902i | \(0.672386\pi\) | |||||||
\(242\) | −4.93541 | −0.317260 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −0.988874 | −0.0633062 | ||||||||
\(245\) | 1.64627 | 0.105177 | ||||||||
\(246\) | 1.51029 | 0.0962923 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 1.30878 | 0.0831076 | ||||||||
\(249\) | −0.0542580 | −0.00343846 | ||||||||
\(250\) | −5.93072 | −0.375091 | ||||||||
\(251\) | −13.7389 | −0.867193 | −0.433597 | − | 0.901107i | \(-0.642756\pi\) | ||||
−0.433597 | + | 0.901107i | \(0.642756\pi\) | |||||||
\(252\) | 1.75578 | 0.110604 | ||||||||
\(253\) | 2.64526 | 0.166306 | ||||||||
\(254\) | 3.78374 | 0.237413 | ||||||||
\(255\) | 7.22548 | 0.452477 | ||||||||
\(256\) | −0.159364 | −0.00996028 | ||||||||
\(257\) | 25.1001 | 1.56570 | 0.782851 | − | 0.622210i | \(-0.213765\pi\) | ||||
0.782851 | + | 0.622210i | \(0.213765\pi\) | |||||||
\(258\) | 5.19278 | 0.323289 | ||||||||
\(259\) | −2.72506 | −0.169327 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.13954 | 0.318129 | ||||||||
\(262\) | 0.620214 | 0.0383169 | ||||||||
\(263\) | 6.86224 | 0.423144 | 0.211572 | − | 0.977362i | \(-0.432142\pi\) | ||||
0.211572 | + | 0.977362i | \(0.432142\pi\) | |||||||
\(264\) | 1.86813 | 0.114975 | ||||||||
\(265\) | −3.23957 | −0.199005 | ||||||||
\(266\) | −0.580871 | −0.0356155 | ||||||||
\(267\) | 0.601205 | 0.0367931 | ||||||||
\(268\) | −23.0114 | −1.40564 | ||||||||
\(269\) | 18.2175 | 1.11074 | 0.555369 | − | 0.831604i | \(-0.312577\pi\) | ||||
0.555369 | + | 0.831604i | \(0.312577\pi\) | |||||||
\(270\) | −0.813565 | −0.0495120 | ||||||||
\(271\) | 15.0414 | 0.913697 | 0.456849 | − | 0.889544i | \(-0.348978\pi\) | ||||
0.456849 | + | 0.889544i | \(0.348978\pi\) | |||||||
\(272\) | −11.3865 | −0.690406 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.26431 | 0.0763797 | ||||||||
\(275\) | −2.30468 | −0.138977 | ||||||||
\(276\) | 4.61447 | 0.277759 | ||||||||
\(277\) | 1.39436 | 0.0837787 | 0.0418894 | − | 0.999122i | \(-0.486662\pi\) | ||||
0.0418894 | + | 0.999122i | \(0.486662\pi\) | |||||||
\(278\) | 2.78718 | 0.167164 | ||||||||
\(279\) | −0.705141 | −0.0422157 | ||||||||
\(280\) | 3.05557 | 0.182605 | ||||||||
\(281\) | 11.2011 | 0.668200 | 0.334100 | − | 0.942538i | \(-0.391568\pi\) | ||||
0.334100 | + | 0.942538i | \(0.391568\pi\) | |||||||
\(282\) | 1.06799 | 0.0635981 | ||||||||
\(283\) | −14.8446 | −0.882422 | −0.441211 | − | 0.897403i | \(-0.645451\pi\) | ||||
−0.441211 | + | 0.897403i | \(0.645451\pi\) | |||||||
\(284\) | −27.0052 | −1.60246 | ||||||||
\(285\) | −1.93504 | −0.114622 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.05611 | 0.180396 | ||||||||
\(288\) | 4.99419 | 0.294285 | ||||||||
\(289\) | 2.26328 | 0.133134 | ||||||||
\(290\) | 4.18135 | 0.245537 | ||||||||
\(291\) | −1.74080 | −0.102047 | ||||||||
\(292\) | −23.8684 | −1.39680 | ||||||||
\(293\) | −17.8257 | −1.04139 | −0.520695 | − | 0.853743i | \(-0.674327\pi\) | ||||
−0.520695 | + | 0.853743i | \(0.674327\pi\) | |||||||
\(294\) | −0.494186 | −0.0288215 | ||||||||
\(295\) | −8.08312 | −0.470618 | ||||||||
\(296\) | −5.05786 | −0.293982 | ||||||||
\(297\) | −1.00650 | −0.0584033 | ||||||||
\(298\) | 2.71764 | 0.157429 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −4.02036 | −0.232116 | ||||||||
\(301\) | 10.5077 | 0.605656 | ||||||||
\(302\) | 4.10712 | 0.236338 | ||||||||
\(303\) | −12.8587 | −0.738716 | ||||||||
\(304\) | 3.04939 | 0.174894 | ||||||||
\(305\) | 0.927198 | 0.0530912 | ||||||||
\(306\) | −2.16898 | −0.123992 | ||||||||
\(307\) | −30.6385 | −1.74863 | −0.874317 | − | 0.485356i | \(-0.838690\pi\) | ||||
−0.874317 | + | 0.485356i | \(0.838690\pi\) | |||||||
\(308\) | 1.76720 | 0.100696 | ||||||||
\(309\) | −14.6917 | −0.835779 | ||||||||
\(310\) | −0.573678 | −0.0325827 | ||||||||
\(311\) | 9.27236 | 0.525788 | 0.262894 | − | 0.964825i | \(-0.415323\pi\) | ||||
0.262894 | + | 0.964825i | \(0.415323\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −25.7441 | −1.45514 | −0.727572 | − | 0.686031i | \(-0.759351\pi\) | ||||
−0.727572 | + | 0.686031i | \(0.759351\pi\) | |||||||
\(314\) | 6.33164 | 0.357315 | ||||||||
\(315\) | −1.64627 | −0.0927570 | ||||||||
\(316\) | −13.4014 | −0.753889 | ||||||||
\(317\) | 5.98521 | 0.336163 | 0.168082 | − | 0.985773i | \(-0.446243\pi\) | ||||
0.168082 | + | 0.985773i | \(0.446243\pi\) | |||||||
\(318\) | 0.972469 | 0.0545334 | ||||||||
\(319\) | 5.17297 | 0.289631 | ||||||||
\(320\) | −4.47883 | −0.250374 | ||||||||
\(321\) | −3.37556 | −0.188405 | ||||||||
\(322\) | −1.29880 | −0.0723794 | ||||||||
\(323\) | −5.15886 | −0.287047 | ||||||||
\(324\) | −1.75578 | −0.0975433 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 5.31679 | 0.294470 | ||||||||
\(327\) | 9.90520 | 0.547759 | ||||||||
\(328\) | 5.67230 | 0.313200 | ||||||||
\(329\) | 2.16111 | 0.119146 | ||||||||
\(330\) | −0.818857 | −0.0450766 | ||||||||
\(331\) | −24.7010 | −1.35769 | −0.678846 | − | 0.734281i | \(-0.737520\pi\) | ||||
−0.678846 | + | 0.734281i | \(0.737520\pi\) | |||||||
\(332\) | −0.0952651 | −0.00522835 | ||||||||
\(333\) | 2.72506 | 0.149332 | ||||||||
\(334\) | −12.3576 | −0.676177 | ||||||||
\(335\) | 21.5762 | 1.17883 | ||||||||
\(336\) | 2.59432 | 0.141532 | ||||||||
\(337\) | −6.44446 | −0.351052 | −0.175526 | − | 0.984475i | \(-0.556163\pi\) | ||||
−0.175526 | + | 0.984475i | \(0.556163\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 13.5673 | 0.736877 | ||||||||
\(340\) | 12.6864 | 0.688014 | ||||||||
\(341\) | −0.709727 | −0.0384339 | ||||||||
\(342\) | 0.580871 | 0.0314099 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 19.5029 | 1.05153 | ||||||||
\(345\) | −4.32667 | −0.232940 | ||||||||
\(346\) | 8.27008 | 0.444602 | ||||||||
\(347\) | 15.7956 | 0.847955 | 0.423977 | − | 0.905673i | \(-0.360634\pi\) | ||||
0.423977 | + | 0.905673i | \(0.360634\pi\) | |||||||
\(348\) | 9.02390 | 0.483732 | ||||||||
\(349\) | 21.2652 | 1.13830 | 0.569150 | − | 0.822234i | \(-0.307273\pi\) | ||||
0.569150 | + | 0.822234i | \(0.307273\pi\) | |||||||
\(350\) | 1.13158 | 0.0604855 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.02667 | 0.267922 | ||||||||
\(353\) | 10.0764 | 0.536311 | 0.268156 | − | 0.963376i | \(-0.413586\pi\) | ||||
0.268156 | + | 0.963376i | \(0.413586\pi\) | |||||||
\(354\) | 2.42643 | 0.128963 | ||||||||
\(355\) | 25.3209 | 1.34389 | ||||||||
\(356\) | 1.05558 | 0.0559458 | ||||||||
\(357\) | −4.38900 | −0.232290 | ||||||||
\(358\) | 6.06761 | 0.320683 | ||||||||
\(359\) | −22.7145 | −1.19883 | −0.599413 | − | 0.800440i | \(-0.704599\pi\) | ||||
−0.599413 | + | 0.800440i | \(0.704599\pi\) | |||||||
\(360\) | −3.05557 | −0.161043 | ||||||||
\(361\) | −17.6184 | −0.927285 | ||||||||
\(362\) | 11.2712 | 0.592403 | ||||||||
\(363\) | 9.98695 | 0.524179 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 22.3798 | 1.17141 | ||||||||
\(366\) | −0.278331 | −0.0145486 | ||||||||
\(367\) | −19.7830 | −1.03267 | −0.516333 | − | 0.856388i | \(-0.672703\pi\) | ||||
−0.516333 | + | 0.856388i | \(0.672703\pi\) | |||||||
\(368\) | 6.81830 | 0.355429 | ||||||||
\(369\) | −3.05611 | −0.159095 | ||||||||
\(370\) | 2.21701 | 0.115257 | ||||||||
\(371\) | 1.96782 | 0.102164 | ||||||||
\(372\) | −1.23807 | −0.0641910 | ||||||||
\(373\) | −4.21238 | −0.218109 | −0.109054 | − | 0.994036i | \(-0.534782\pi\) | ||||
−0.109054 | + | 0.994036i | \(0.534782\pi\) | |||||||
\(374\) | −2.18309 | −0.112885 | ||||||||
\(375\) | 12.0010 | 0.619728 | ||||||||
\(376\) | 4.01115 | 0.206859 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0.494186 | 0.0254182 | ||||||||
\(379\) | 1.62828 | 0.0836393 | 0.0418197 | − | 0.999125i | \(-0.486685\pi\) | ||||
0.0418197 | + | 0.999125i | \(0.486685\pi\) | |||||||
\(380\) | −3.39751 | −0.174289 | ||||||||
\(381\) | −7.65651 | −0.392255 | ||||||||
\(382\) | 13.5436 | 0.692950 | ||||||||
\(383\) | 3.21481 | 0.164269 | 0.0821346 | − | 0.996621i | \(-0.473826\pi\) | ||||
0.0821346 | + | 0.996621i | \(0.473826\pi\) | |||||||
\(384\) | 11.3329 | 0.578327 | ||||||||
\(385\) | −1.65698 | −0.0844475 | ||||||||
\(386\) | −3.16924 | −0.161310 | ||||||||
\(387\) | −10.5077 | −0.534139 | ||||||||
\(388\) | −3.05646 | −0.155168 | ||||||||
\(389\) | −4.30323 | −0.218183 | −0.109091 | − | 0.994032i | \(-0.534794\pi\) | ||||
−0.109091 | + | 0.994032i | \(0.534794\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.5350 | −0.583350 | ||||||||
\(392\) | −1.85605 | −0.0937449 | ||||||||
\(393\) | −1.25502 | −0.0633074 | ||||||||
\(394\) | −8.50402 | −0.428426 | ||||||||
\(395\) | 12.5656 | 0.632243 | ||||||||
\(396\) | −1.76720 | −0.0888051 | ||||||||
\(397\) | −31.5480 | −1.58335 | −0.791673 | − | 0.610945i | \(-0.790790\pi\) | ||||
−0.791673 | + | 0.610945i | \(0.790790\pi\) | |||||||
\(398\) | −1.48764 | −0.0745685 | ||||||||
\(399\) | 1.17541 | 0.0588440 | ||||||||
\(400\) | −5.94045 | −0.297022 | ||||||||
\(401\) | 21.7130 | 1.08429 | 0.542147 | − | 0.840284i | \(-0.317612\pi\) | ||||
0.542147 | + | 0.840284i | \(0.317612\pi\) | |||||||
\(402\) | −6.47684 | −0.323035 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −22.5771 | −1.12325 | ||||||||
\(405\) | 1.64627 | 0.0818040 | ||||||||
\(406\) | −2.53989 | −0.126053 | ||||||||
\(407\) | 2.74278 | 0.135955 | ||||||||
\(408\) | −8.14622 | −0.403298 | ||||||||
\(409\) | −9.98412 | −0.493683 | −0.246842 | − | 0.969056i | \(-0.579393\pi\) | ||||
−0.246842 | + | 0.969056i | \(0.579393\pi\) | |||||||
\(410\) | −2.48634 | −0.122792 | ||||||||
\(411\) | −2.55836 | −0.126195 | ||||||||
\(412\) | −25.7953 | −1.27084 | ||||||||
\(413\) | 4.90995 | 0.241603 | ||||||||
\(414\) | 1.29880 | 0.0638326 | ||||||||
\(415\) | 0.0893234 | 0.00438472 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.63993 | −0.276189 | ||||||||
\(418\) | 0.584649 | 0.0285961 | ||||||||
\(419\) | −25.9114 | −1.26586 | −0.632928 | − | 0.774211i | \(-0.718147\pi\) | ||||
−0.632928 | + | 0.774211i | \(0.718147\pi\) | |||||||
\(420\) | −2.89049 | −0.141042 | ||||||||
\(421\) | 22.8898 | 1.11558 | 0.557791 | − | 0.829981i | \(-0.311649\pi\) | ||||
0.557791 | + | 0.829981i | \(0.311649\pi\) | |||||||
\(422\) | 13.1724 | 0.641225 | ||||||||
\(423\) | −2.16111 | −0.105077 | ||||||||
\(424\) | 3.65238 | 0.177375 | ||||||||
\(425\) | 10.0499 | 0.487490 | ||||||||
\(426\) | −7.60094 | −0.368267 | ||||||||
\(427\) | −0.563211 | −0.0272557 | ||||||||
\(428\) | −5.92674 | −0.286480 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −8.54874 | −0.412257 | ||||||||
\(431\) | −18.1818 | −0.875787 | −0.437893 | − | 0.899027i | \(-0.644275\pi\) | ||||
−0.437893 | + | 0.899027i | \(0.644275\pi\) | |||||||
\(432\) | −2.59432 | −0.124819 | ||||||||
\(433\) | −22.5154 | −1.08202 | −0.541010 | − | 0.841016i | \(-0.681958\pi\) | ||||
−0.541010 | + | 0.841016i | \(0.681958\pi\) | |||||||
\(434\) | 0.348471 | 0.0167271 | ||||||||
\(435\) | −8.46108 | −0.405678 | ||||||||
\(436\) | 17.3913 | 0.832894 | ||||||||
\(437\) | 3.08916 | 0.147775 | ||||||||
\(438\) | −6.71807 | −0.321002 | ||||||||
\(439\) | 7.31288 | 0.349025 | 0.174512 | − | 0.984655i | \(-0.444165\pi\) | ||||
0.174512 | + | 0.984655i | \(0.444165\pi\) | |||||||
\(440\) | −3.07545 | −0.146616 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.00281 | −0.332714 | −0.166357 | − | 0.986066i | \(-0.553200\pi\) | ||||
−0.166357 | + | 0.986066i | \(0.553200\pi\) | |||||||
\(444\) | 4.78461 | 0.227067 | ||||||||
\(445\) | −0.989747 | −0.0469185 | ||||||||
\(446\) | 6.85908 | 0.324787 | ||||||||
\(447\) | −5.49922 | −0.260104 | ||||||||
\(448\) | 2.72059 | 0.128536 | ||||||||
\(449\) | 1.74630 | 0.0824132 | 0.0412066 | − | 0.999151i | \(-0.486880\pi\) | ||||
0.0412066 | + | 0.999151i | \(0.486880\pi\) | |||||||
\(450\) | −1.13158 | −0.0533432 | ||||||||
\(451\) | −3.07598 | −0.144842 | ||||||||
\(452\) | 23.8213 | 1.12046 | ||||||||
\(453\) | −8.31087 | −0.390479 | ||||||||
\(454\) | 6.77925 | 0.318166 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.18162 | 0.102164 | ||||||||
\(457\) | −18.2001 | −0.851367 | −0.425683 | − | 0.904872i | \(-0.639966\pi\) | ||||
−0.425683 | + | 0.904872i | \(0.639966\pi\) | |||||||
\(458\) | 4.90838 | 0.229354 | ||||||||
\(459\) | 4.38900 | 0.204861 | ||||||||
\(460\) | −7.59668 | −0.354197 | ||||||||
\(461\) | −36.4349 | −1.69694 | −0.848471 | − | 0.529242i | \(-0.822477\pi\) | ||||
−0.848471 | + | 0.529242i | \(0.822477\pi\) | |||||||
\(462\) | 0.497400 | 0.0231412 | ||||||||
\(463\) | 33.5410 | 1.55878 | 0.779391 | − | 0.626538i | \(-0.215529\pi\) | ||||
0.779391 | + | 0.626538i | \(0.215529\pi\) | |||||||
\(464\) | 13.3336 | 0.618998 | ||||||||
\(465\) | 1.16085 | 0.0538333 | ||||||||
\(466\) | 9.60817 | 0.445090 | ||||||||
\(467\) | 3.86589 | 0.178892 | 0.0894461 | − | 0.995992i | \(-0.471490\pi\) | ||||
0.0894461 | + | 0.995992i | \(0.471490\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13.1061 | −0.605182 | ||||||||
\(470\) | −1.75821 | −0.0811001 | ||||||||
\(471\) | −12.8123 | −0.590358 | ||||||||
\(472\) | 9.11314 | 0.419466 | ||||||||
\(473\) | −10.5761 | −0.486289 | ||||||||
\(474\) | −3.77200 | −0.173254 | ||||||||
\(475\) | −2.69143 | −0.123491 | ||||||||
\(476\) | −7.70611 | −0.353209 | ||||||||
\(477\) | −1.96782 | −0.0901003 | ||||||||
\(478\) | 8.09899 | 0.370439 | ||||||||
\(479\) | 37.2104 | 1.70019 | 0.850094 | − | 0.526631i | \(-0.176545\pi\) | ||||
0.850094 | + | 0.526631i | \(0.176545\pi\) | |||||||
\(480\) | −8.22180 | −0.375272 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −7.90934 | −0.360261 | ||||||||
\(483\) | 2.62816 | 0.119586 | ||||||||
\(484\) | 17.5349 | 0.797040 | ||||||||
\(485\) | 2.86583 | 0.130131 | ||||||||
\(486\) | −0.494186 | −0.0224167 | ||||||||
\(487\) | 19.0179 | 0.861783 | 0.430892 | − | 0.902404i | \(-0.358199\pi\) | ||||
0.430892 | + | 0.902404i | \(0.358199\pi\) | |||||||
\(488\) | −1.04535 | −0.0473208 | ||||||||
\(489\) | −10.7587 | −0.486524 | ||||||||
\(490\) | 0.813565 | 0.0367531 | ||||||||
\(491\) | 14.7990 | 0.667868 | 0.333934 | − | 0.942596i | \(-0.391624\pi\) | ||||
0.333934 | + | 0.942596i | \(0.391624\pi\) | |||||||
\(492\) | −5.36585 | −0.241911 | ||||||||
\(493\) | −22.5574 | −1.01593 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.65698 | 0.0744757 | ||||||||
\(496\) | −1.82936 | −0.0821408 | ||||||||
\(497\) | −15.3807 | −0.689920 | ||||||||
\(498\) | −0.0268135 | −0.00120154 | ||||||||
\(499\) | −27.5937 | −1.23526 | −0.617632 | − | 0.786467i | \(-0.711908\pi\) | ||||
−0.617632 | + | 0.786467i | \(0.711908\pi\) | |||||||
\(500\) | 21.0711 | 0.942327 | ||||||||
\(501\) | 25.0059 | 1.11718 | ||||||||
\(502\) | −6.78959 | −0.303034 | ||||||||
\(503\) | 42.9458 | 1.91486 | 0.957428 | − | 0.288671i | \(-0.0932135\pi\) | ||||
0.957428 | + | 0.288671i | \(0.0932135\pi\) | |||||||
\(504\) | 1.85605 | 0.0826752 | ||||||||
\(505\) | 21.1690 | 0.942008 | ||||||||
\(506\) | 1.30725 | 0.0581143 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −13.4431 | −0.596443 | ||||||||
\(509\) | −25.7321 | −1.14056 | −0.570278 | − | 0.821452i | \(-0.693165\pi\) | ||||
−0.570278 | + | 0.821452i | \(0.693165\pi\) | |||||||
\(510\) | 3.57073 | 0.158115 | ||||||||
\(511\) | −13.5942 | −0.601373 | ||||||||
\(512\) | 22.5870 | 0.998212 | ||||||||
\(513\) | −1.17541 | −0.0518955 | ||||||||
\(514\) | 12.4041 | 0.547122 | ||||||||
\(515\) | 24.1865 | 1.06578 | ||||||||
\(516\) | −18.4493 | −0.812185 | ||||||||
\(517\) | −2.17517 | −0.0956639 | ||||||||
\(518\) | −1.34669 | −0.0591700 | ||||||||
\(519\) | −16.7347 | −0.734573 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 33.4269 | 1.46446 | 0.732229 | − | 0.681059i | \(-0.238480\pi\) | ||||
0.732229 | + | 0.681059i | \(0.238480\pi\) | |||||||
\(522\) | 2.53989 | 0.111168 | ||||||||
\(523\) | −23.8931 | −1.04477 | −0.522386 | − | 0.852709i | \(-0.674958\pi\) | ||||
−0.522386 | + | 0.852709i | \(0.674958\pi\) | |||||||
\(524\) | −2.20354 | −0.0962621 | ||||||||
\(525\) | −2.28979 | −0.0999345 | ||||||||
\(526\) | 3.39123 | 0.147864 | ||||||||
\(527\) | 3.09486 | 0.134814 | ||||||||
\(528\) | −2.61120 | −0.113638 | ||||||||
\(529\) | −16.0928 | −0.699685 | ||||||||
\(530\) | −1.60095 | −0.0695408 | ||||||||
\(531\) | −4.90995 | −0.213074 | ||||||||
\(532\) | 2.06376 | 0.0894753 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0.297107 | 0.0128571 | ||||||||
\(535\) | 5.55709 | 0.240254 | ||||||||
\(536\) | −24.3256 | −1.05070 | ||||||||
\(537\) | −12.2780 | −0.529834 | ||||||||
\(538\) | 9.00282 | 0.388139 | ||||||||
\(539\) | 1.00650 | 0.0433532 | ||||||||
\(540\) | 2.89049 | 0.124387 | ||||||||
\(541\) | 5.29873 | 0.227810 | 0.113905 | − | 0.993492i | \(-0.463664\pi\) | ||||
0.113905 | + | 0.993492i | \(0.463664\pi\) | |||||||
\(542\) | 7.43323 | 0.319285 | ||||||||
\(543\) | −22.8077 | −0.978770 | ||||||||
\(544\) | −21.9195 | −0.939789 | ||||||||
\(545\) | −16.3067 | −0.698500 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 37.2193 | 1.59138 | 0.795691 | − | 0.605703i | \(-0.207108\pi\) | ||||
0.795691 | + | 0.605703i | \(0.207108\pi\) | |||||||
\(548\) | −4.49192 | −0.191886 | ||||||||
\(549\) | 0.563211 | 0.0240372 | ||||||||
\(550\) | −1.13894 | −0.0485646 | ||||||||
\(551\) | 6.04106 | 0.257358 | ||||||||
\(552\) | 4.87801 | 0.207622 | ||||||||
\(553\) | −7.63275 | −0.324577 | ||||||||
\(554\) | 0.689072 | 0.0292758 | ||||||||
\(555\) | −4.48619 | −0.190428 | ||||||||
\(556\) | −9.90248 | −0.419959 | ||||||||
\(557\) | 5.40182 | 0.228883 | 0.114441 | − | 0.993430i | \(-0.463492\pi\) | ||||
0.114441 | + | 0.993430i | \(0.463492\pi\) | |||||||
\(558\) | −0.348471 | −0.0147519 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −4.27096 | −0.180481 | ||||||||
\(561\) | 4.41754 | 0.186509 | ||||||||
\(562\) | 5.53541 | 0.233497 | ||||||||
\(563\) | −10.9360 | −0.460898 | −0.230449 | − | 0.973084i | \(-0.574019\pi\) | ||||
−0.230449 | + | 0.973084i | \(0.574019\pi\) | |||||||
\(564\) | −3.79444 | −0.159775 | ||||||||
\(565\) | −22.3355 | −0.939663 | ||||||||
\(566\) | −7.33602 | −0.308356 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | −28.5475 | −1.19783 | ||||||||
\(569\) | −30.5762 | −1.28182 | −0.640911 | − | 0.767615i | \(-0.721443\pi\) | ||||
−0.640911 | + | 0.767615i | \(0.721443\pi\) | |||||||
\(570\) | −0.956271 | −0.0400538 | ||||||||
\(571\) | 6.37732 | 0.266882 | 0.133441 | − | 0.991057i | \(-0.457397\pi\) | ||||
0.133441 | + | 0.991057i | \(0.457397\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −27.4058 | −1.14489 | ||||||||
\(574\) | 1.51029 | 0.0630381 | ||||||||
\(575\) | −6.01793 | −0.250965 | ||||||||
\(576\) | −2.72059 | −0.113358 | ||||||||
\(577\) | 0.900721 | 0.0374975 | 0.0187487 | − | 0.999824i | \(-0.494032\pi\) | ||||
0.0187487 | + | 0.999824i | \(0.494032\pi\) | |||||||
\(578\) | 1.11848 | 0.0465227 | ||||||||
\(579\) | 6.41304 | 0.266517 | ||||||||
\(580\) | −14.8558 | −0.616854 | ||||||||
\(581\) | −0.0542580 | −0.00225100 | ||||||||
\(582\) | −0.860279 | −0.0356597 | ||||||||
\(583\) | −1.98062 | −0.0820288 | ||||||||
\(584\) | −25.2316 | −1.04409 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −8.80923 | −0.363906 | ||||||||
\(587\) | −43.8262 | −1.80890 | −0.904451 | − | 0.426577i | \(-0.859719\pi\) | ||||
−0.904451 | + | 0.426577i | \(0.859719\pi\) | |||||||
\(588\) | 1.75578 | 0.0724071 | ||||||||
\(589\) | −0.828828 | −0.0341513 | ||||||||
\(590\) | −3.99457 | −0.164454 | ||||||||
\(591\) | 17.2081 | 0.707848 | ||||||||
\(592\) | 7.06969 | 0.290562 | ||||||||
\(593\) | −30.8733 | −1.26781 | −0.633907 | − | 0.773409i | \(-0.718550\pi\) | ||||
−0.633907 | + | 0.773409i | \(0.718550\pi\) | |||||||
\(594\) | −0.497400 | −0.0204086 | ||||||||
\(595\) | 7.22548 | 0.296216 | ||||||||
\(596\) | −9.65543 | −0.395502 | ||||||||
\(597\) | 3.01028 | 0.123202 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 33.0466 | 1.35025 | 0.675123 | − | 0.737705i | \(-0.264091\pi\) | ||||
0.675123 | + | 0.737705i | \(0.264091\pi\) | |||||||
\(600\) | −4.24997 | −0.173504 | ||||||||
\(601\) | −23.2566 | −0.948658 | −0.474329 | − | 0.880348i | \(-0.657309\pi\) | ||||
−0.474329 | + | 0.880348i | \(0.657309\pi\) | |||||||
\(602\) | 5.19278 | 0.211642 | ||||||||
\(603\) | 13.1061 | 0.533720 | ||||||||
\(604\) | −14.5921 | −0.593743 | ||||||||
\(605\) | −16.4412 | −0.668432 | ||||||||
\(606\) | −6.35461 | −0.258139 | ||||||||
\(607\) | 36.9583 | 1.50009 | 0.750045 | − | 0.661386i | \(-0.230032\pi\) | ||||
0.750045 | + | 0.661386i | \(0.230032\pi\) | |||||||
\(608\) | 5.87021 | 0.238068 | ||||||||
\(609\) | 5.13954 | 0.208265 | ||||||||
\(610\) | 0.458209 | 0.0185523 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 7.70611 | 0.311501 | ||||||||
\(613\) | −6.74925 | −0.272600 | −0.136300 | − | 0.990668i | \(-0.543521\pi\) | ||||
−0.136300 | + | 0.990668i | \(0.543521\pi\) | |||||||
\(614\) | −15.1411 | −0.611047 | ||||||||
\(615\) | 5.03119 | 0.202877 | ||||||||
\(616\) | 1.86813 | 0.0752690 | ||||||||
\(617\) | 34.7076 | 1.39727 | 0.698637 | − | 0.715476i | \(-0.253790\pi\) | ||||
0.698637 | + | 0.715476i | \(0.253790\pi\) | |||||||
\(618\) | −7.26041 | −0.292057 | ||||||||
\(619\) | 7.42759 | 0.298540 | 0.149270 | − | 0.988796i | \(-0.452308\pi\) | ||||
0.149270 | + | 0.988796i | \(0.452308\pi\) | |||||||
\(620\) | 2.03820 | 0.0818562 | ||||||||
\(621\) | −2.62816 | −0.105465 | ||||||||
\(622\) | 4.58227 | 0.183732 | ||||||||
\(623\) | 0.601205 | 0.0240868 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.30795 | −0.332318 | ||||||||
\(626\) | −12.7224 | −0.508489 | ||||||||
\(627\) | −1.18305 | −0.0472466 | ||||||||
\(628\) | −22.4955 | −0.897668 | ||||||||
\(629\) | −11.9603 | −0.476887 | ||||||||
\(630\) | −0.813565 | −0.0324132 | ||||||||
\(631\) | −30.4787 | −1.21334 | −0.606669 | − | 0.794954i | \(-0.707495\pi\) | ||||
−0.606669 | + | 0.794954i | \(0.707495\pi\) | |||||||
\(632\) | −14.1668 | −0.563525 | ||||||||
\(633\) | −26.6548 | −1.05943 | ||||||||
\(634\) | 2.95781 | 0.117470 | ||||||||
\(635\) | 12.6047 | 0.500202 | ||||||||
\(636\) | −3.45506 | −0.137002 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 2.55641 | 0.101209 | ||||||||
\(639\) | 15.3807 | 0.608452 | ||||||||
\(640\) | −18.6570 | −0.737481 | ||||||||
\(641\) | 27.6795 | 1.09328 | 0.546638 | − | 0.837369i | \(-0.315907\pi\) | ||||
0.546638 | + | 0.837369i | \(0.315907\pi\) | |||||||
\(642\) | −1.66815 | −0.0658368 | ||||||||
\(643\) | −29.0749 | −1.14660 | −0.573302 | − | 0.819344i | \(-0.694338\pi\) | ||||
−0.573302 | + | 0.819344i | \(0.694338\pi\) | |||||||
\(644\) | 4.61447 | 0.181836 | ||||||||
\(645\) | 17.2986 | 0.681132 | ||||||||
\(646\) | −2.54944 | −0.100306 | ||||||||
\(647\) | 8.93804 | 0.351391 | 0.175695 | − | 0.984445i | \(-0.443783\pi\) | ||||
0.175695 | + | 0.984445i | \(0.443783\pi\) | |||||||
\(648\) | −1.85605 | −0.0729127 | ||||||||
\(649\) | −4.94189 | −0.193986 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.705141 | −0.0276366 | ||||||||
\(652\) | −18.8899 | −0.739784 | ||||||||
\(653\) | −27.1525 | −1.06256 | −0.531280 | − | 0.847196i | \(-0.678289\pi\) | ||||
−0.531280 | + | 0.847196i | \(0.678289\pi\) | |||||||
\(654\) | 4.89501 | 0.191410 | ||||||||
\(655\) | 2.06611 | 0.0807295 | ||||||||
\(656\) | −7.92853 | −0.309557 | ||||||||
\(657\) | 13.5942 | 0.530361 | ||||||||
\(658\) | 1.06799 | 0.0416347 | ||||||||
\(659\) | −5.63077 | −0.219344 | −0.109672 | − | 0.993968i | \(-0.534980\pi\) | ||||
−0.109672 | + | 0.993968i | \(0.534980\pi\) | |||||||
\(660\) | 2.90929 | 0.113244 | ||||||||
\(661\) | −12.6352 | −0.491453 | −0.245727 | − | 0.969339i | \(-0.579027\pi\) | ||||
−0.245727 | + | 0.969339i | \(0.579027\pi\) | |||||||
\(662\) | −12.2069 | −0.474435 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −0.100706 | −0.00390814 | ||||||||
\(665\) | −1.93504 | −0.0750377 | ||||||||
\(666\) | 1.34669 | 0.0521831 | ||||||||
\(667\) | 13.5075 | 0.523014 | ||||||||
\(668\) | 43.9049 | 1.69873 | ||||||||
\(669\) | −13.8795 | −0.536614 | ||||||||
\(670\) | 10.6626 | 0.411934 | ||||||||
\(671\) | 0.566874 | 0.0218839 | ||||||||
\(672\) | 4.99419 | 0.192655 | ||||||||
\(673\) | −45.5652 | −1.75641 | −0.878204 | − | 0.478286i | \(-0.841258\pi\) | ||||
−0.878204 | + | 0.478286i | \(0.841258\pi\) | |||||||
\(674\) | −3.18476 | −0.122673 | ||||||||
\(675\) | 2.28979 | 0.0881339 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −26.6074 | −1.02261 | −0.511303 | − | 0.859400i | \(-0.670837\pi\) | ||||
−0.511303 | + | 0.859400i | \(0.670837\pi\) | |||||||
\(678\) | 6.70479 | 0.257496 | ||||||||
\(679\) | −1.74080 | −0.0668057 | ||||||||
\(680\) | 13.4109 | 0.514284 | ||||||||
\(681\) | −13.7180 | −0.525675 | ||||||||
\(682\) | −0.350737 | −0.0134304 | ||||||||
\(683\) | 21.5696 | 0.825338 | 0.412669 | − | 0.910881i | \(-0.364597\pi\) | ||||
0.412669 | + | 0.910881i | \(0.364597\pi\) | |||||||
\(684\) | −2.06376 | −0.0789098 | ||||||||
\(685\) | 4.21177 | 0.160923 | ||||||||
\(686\) | −0.494186 | −0.0188681 | ||||||||
\(687\) | −9.93225 | −0.378939 | ||||||||
\(688\) | −27.2605 | −1.03930 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −2.13818 | −0.0813992 | ||||||||
\(691\) | −36.2297 | −1.37824 | −0.689121 | − | 0.724646i | \(-0.742003\pi\) | ||||
−0.689121 | + | 0.724646i | \(0.742003\pi\) | |||||||
\(692\) | −29.3825 | −1.11696 | ||||||||
\(693\) | −1.00650 | −0.0382339 | ||||||||
\(694\) | 7.80599 | 0.296311 | ||||||||
\(695\) | 9.28487 | 0.352195 | ||||||||
\(696\) | 9.53927 | 0.361585 | ||||||||
\(697\) | 13.4132 | 0.508063 | ||||||||
\(698\) | 10.5090 | 0.397770 | ||||||||
\(699\) | −19.4424 | −0.735379 | ||||||||
\(700\) | −4.02036 | −0.151955 | ||||||||
\(701\) | 4.73093 | 0.178685 | 0.0893424 | − | 0.996001i | \(-0.471523\pi\) | ||||
0.0893424 | + | 0.996001i | \(0.471523\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.20306 | 0.120806 | ||||||||
\(704\) | −2.73828 | −0.103203 | ||||||||
\(705\) | 3.55778 | 0.133994 | ||||||||
\(706\) | 4.97961 | 0.187410 | ||||||||
\(707\) | −12.8587 | −0.483603 | ||||||||
\(708\) | −8.62080 | −0.323989 | ||||||||
\(709\) | 23.5959 | 0.886163 | 0.443082 | − | 0.896481i | \(-0.353885\pi\) | ||||
0.443082 | + | 0.896481i | \(0.353885\pi\) | |||||||
\(710\) | 12.5132 | 0.469613 | ||||||||
\(711\) | 7.63275 | 0.286250 | ||||||||
\(712\) | 1.11587 | 0.0418190 | ||||||||
\(713\) | −1.85322 | −0.0694038 | ||||||||
\(714\) | −2.16898 | −0.0811721 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −21.5574 | −0.805639 | ||||||||
\(717\) | −16.3885 | −0.612041 | ||||||||
\(718\) | −11.2252 | −0.418921 | ||||||||
\(719\) | 16.1744 | 0.603203 | 0.301601 | − | 0.953434i | \(-0.402479\pi\) | ||||
0.301601 | + | 0.953434i | \(0.402479\pi\) | |||||||
\(720\) | 4.27096 | 0.159169 | ||||||||
\(721\) | −14.6917 | −0.547146 | ||||||||
\(722\) | −8.70678 | −0.324033 | ||||||||
\(723\) | 16.0048 | 0.595224 | ||||||||
\(724\) | −40.0452 | −1.48827 | ||||||||
\(725\) | −11.7684 | −0.437069 | ||||||||
\(726\) | 4.93541 | 0.183170 | ||||||||
\(727\) | −12.1774 | −0.451633 | −0.225817 | − | 0.974170i | \(-0.572505\pi\) | ||||
−0.225817 | + | 0.974170i | \(0.572505\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 11.0598 | 0.409341 | ||||||||
\(731\) | 46.1184 | 1.70575 | ||||||||
\(732\) | 0.988874 | 0.0365498 | ||||||||
\(733\) | −35.6552 | −1.31695 | −0.658477 | − | 0.752601i | \(-0.728799\pi\) | ||||
−0.658477 | + | 0.752601i | \(0.728799\pi\) | |||||||
\(734\) | −9.77650 | −0.360857 | ||||||||
\(735\) | −1.64627 | −0.0607237 | ||||||||
\(736\) | 13.1255 | 0.483814 | ||||||||
\(737\) | 13.1913 | 0.485908 | ||||||||
\(738\) | −1.51029 | −0.0555944 | ||||||||
\(739\) | −18.0473 | −0.663880 | −0.331940 | − | 0.943300i | \(-0.607703\pi\) | ||||
−0.331940 | + | 0.943300i | \(0.607703\pi\) | |||||||
\(740\) | −7.87677 | −0.289556 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.972469 | 0.0357005 | ||||||||
\(743\) | −52.9988 | −1.94434 | −0.972168 | − | 0.234285i | \(-0.924725\pi\) | ||||
−0.972168 | + | 0.234285i | \(0.924725\pi\) | |||||||
\(744\) | −1.30878 | −0.0479822 | ||||||||
\(745\) | 9.05322 | 0.331684 | ||||||||
\(746\) | −2.08170 | −0.0762165 | ||||||||
\(747\) | 0.0542580 | 0.00198520 | ||||||||
\(748\) | 7.75623 | 0.283596 | ||||||||
\(749\) | −3.37556 | −0.123340 | ||||||||
\(750\) | 5.93072 | 0.216559 | ||||||||
\(751\) | 38.3089 | 1.39791 | 0.698956 | − | 0.715165i | \(-0.253648\pi\) | ||||
0.698956 | + | 0.715165i | \(0.253648\pi\) | |||||||
\(752\) | −5.60663 | −0.204453 | ||||||||
\(753\) | 13.7389 | 0.500674 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 13.6820 | 0.497938 | ||||||||
\(756\) | −1.75578 | −0.0638571 | ||||||||
\(757\) | 26.3033 | 0.956010 | 0.478005 | − | 0.878357i | \(-0.341360\pi\) | ||||
0.478005 | + | 0.878357i | \(0.341360\pi\) | |||||||
\(758\) | 0.804675 | 0.0292271 | ||||||||
\(759\) | −2.64526 | −0.0960167 | ||||||||
\(760\) | −3.59155 | −0.130279 | ||||||||
\(761\) | 41.3290 | 1.49818 | 0.749088 | − | 0.662470i | \(-0.230492\pi\) | ||||
0.749088 | + | 0.662470i | \(0.230492\pi\) | |||||||
\(762\) | −3.78374 | −0.137071 | ||||||||
\(763\) | 9.90520 | 0.358592 | ||||||||
\(764\) | −48.1186 | −1.74087 | ||||||||
\(765\) | −7.22548 | −0.261238 | ||||||||
\(766\) | 1.58872 | 0.0574026 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0.159364 | 0.00575057 | ||||||||
\(769\) | −19.8950 | −0.717431 | −0.358715 | − | 0.933447i | \(-0.616785\pi\) | ||||
−0.358715 | + | 0.933447i | \(0.616785\pi\) | |||||||
\(770\) | −0.818857 | −0.0295095 | ||||||||
\(771\) | −25.1001 | −0.903958 | ||||||||
\(772\) | 11.2599 | 0.405252 | ||||||||
\(773\) | −37.3499 | −1.34338 | −0.671692 | − | 0.740831i | \(-0.734432\pi\) | ||||
−0.671692 | + | 0.740831i | \(0.734432\pi\) | |||||||
\(774\) | −5.19278 | −0.186651 | ||||||||
\(775\) | 1.61462 | 0.0579989 | ||||||||
\(776\) | −3.23102 | −0.115987 | ||||||||
\(777\) | 2.72506 | 0.0977610 | ||||||||
\(778\) | −2.12660 | −0.0762422 | ||||||||
\(779\) | −3.59217 | −0.128703 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15.4808 | 0.553945 | ||||||||
\(782\) | −5.70043 | −0.203847 | ||||||||
\(783\) | −5.13954 | −0.183672 | ||||||||
\(784\) | 2.59432 | 0.0926544 | ||||||||
\(785\) | 21.0925 | 0.752822 | ||||||||
\(786\) | −0.620214 | −0.0221223 | ||||||||
\(787\) | 15.9051 | 0.566955 | 0.283478 | − | 0.958979i | \(-0.408512\pi\) | ||||
0.283478 | + | 0.958979i | \(0.408512\pi\) | |||||||
\(788\) | 30.2137 | 1.07632 | ||||||||
\(789\) | −6.86224 | −0.244302 | ||||||||
\(790\) | 6.20974 | 0.220933 | ||||||||
\(791\) | 13.5673 | 0.482399 | ||||||||
\(792\) | −1.86813 | −0.0663810 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −15.5906 | −0.553288 | ||||||||
\(795\) | 3.23957 | 0.114896 | ||||||||
\(796\) | 5.28538 | 0.187335 | ||||||||
\(797\) | 13.5259 | 0.479111 | 0.239555 | − | 0.970883i | \(-0.422998\pi\) | ||||
0.239555 | + | 0.970883i | \(0.422998\pi\) | |||||||
\(798\) | 0.580871 | 0.0205626 | ||||||||
\(799\) | 9.48512 | 0.335560 | ||||||||
\(800\) | −11.4356 | −0.404310 | ||||||||
\(801\) | −0.601205 | −0.0212425 | ||||||||
\(802\) | 10.7302 | 0.378898 | ||||||||
\(803\) | 13.6826 | 0.482849 | ||||||||
\(804\) | 23.0114 | 0.811548 | ||||||||
\(805\) | −4.32667 | −0.152495 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −18.2175 | −0.641285 | ||||||||
\(808\) | −23.8665 | −0.839622 | ||||||||
\(809\) | 7.60313 | 0.267312 | 0.133656 | − | 0.991028i | \(-0.457328\pi\) | ||||
0.133656 | + | 0.991028i | \(0.457328\pi\) | |||||||
\(810\) | 0.813565 | 0.0285858 | ||||||||
\(811\) | −23.9460 | −0.840859 | −0.420429 | − | 0.907325i | \(-0.638121\pi\) | ||||
−0.420429 | + | 0.907325i | \(0.638121\pi\) | |||||||
\(812\) | 9.02390 | 0.316677 | ||||||||
\(813\) | −15.0414 | −0.527523 | ||||||||
\(814\) | 1.35545 | 0.0475084 | ||||||||
\(815\) | 17.7117 | 0.620414 | ||||||||
\(816\) | 11.3865 | 0.398606 | ||||||||
\(817\) | −12.3509 | −0.432103 | ||||||||
\(818\) | −4.93402 | −0.172514 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 8.83366 | 0.308485 | ||||||||
\(821\) | 13.5062 | 0.471370 | 0.235685 | − | 0.971829i | \(-0.424267\pi\) | ||||
0.235685 | + | 0.971829i | \(0.424267\pi\) | |||||||
\(822\) | −1.26431 | −0.0440978 | ||||||||
\(823\) | 26.6348 | 0.928430 | 0.464215 | − | 0.885723i | \(-0.346336\pi\) | ||||
0.464215 | + | 0.885723i | \(0.346336\pi\) | |||||||
\(824\) | −27.2685 | −0.949944 | ||||||||
\(825\) | 2.30468 | 0.0802386 | ||||||||
\(826\) | 2.42643 | 0.0844263 | ||||||||
\(827\) | 32.3365 | 1.12445 | 0.562225 | − | 0.826984i | \(-0.309945\pi\) | ||||
0.562225 | + | 0.826984i | \(0.309945\pi\) | |||||||
\(828\) | −4.61447 | −0.160364 | ||||||||
\(829\) | −38.3742 | −1.33279 | −0.666395 | − | 0.745598i | \(-0.732164\pi\) | ||||
−0.666395 | + | 0.745598i | \(0.732164\pi\) | |||||||
\(830\) | 0.0441424 | 0.00153221 | ||||||||
\(831\) | −1.39436 | −0.0483697 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.38900 | −0.152070 | ||||||||
\(834\) | −2.78718 | −0.0965120 | ||||||||
\(835\) | −41.1666 | −1.42463 | ||||||||
\(836\) | −2.07718 | −0.0718408 | ||||||||
\(837\) | 0.705141 | 0.0243732 | ||||||||
\(838\) | −12.8051 | −0.442344 | ||||||||
\(839\) | −15.9684 | −0.551290 | −0.275645 | − | 0.961260i | \(-0.588891\pi\) | ||||
−0.275645 | + | 0.961260i | \(0.588891\pi\) | |||||||
\(840\) | −3.05557 | −0.105427 | ||||||||
\(841\) | −2.58514 | −0.0891427 | ||||||||
\(842\) | 11.3118 | 0.389832 | ||||||||
\(843\) | −11.2011 | −0.385785 | ||||||||
\(844\) | −46.8000 | −1.61092 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.06799 | −0.0367184 | ||||||||
\(847\) | 9.98695 | 0.343156 | ||||||||
\(848\) | −5.10516 | −0.175312 | ||||||||
\(849\) | 14.8446 | 0.509467 | ||||||||
\(850\) | 4.96650 | 0.170350 | ||||||||
\(851\) | 7.16190 | 0.245507 | ||||||||
\(852\) | 27.0052 | 0.925182 | ||||||||
\(853\) | 17.3245 | 0.593181 | 0.296590 | − | 0.955005i | \(-0.404150\pi\) | ||||
0.296590 | + | 0.955005i | \(0.404150\pi\) | |||||||
\(854\) | −0.278331 | −0.00952429 | ||||||||
\(855\) | 1.93504 | 0.0661771 | ||||||||
\(856\) | −6.26522 | −0.214141 | ||||||||
\(857\) | −42.8681 | −1.46435 | −0.732174 | − | 0.681118i | \(-0.761494\pi\) | ||||
−0.732174 | + | 0.681118i | \(0.761494\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.98645 | −0.204255 | −0.102128 | − | 0.994771i | \(-0.532565\pi\) | ||||
−0.102128 | + | 0.994771i | \(0.532565\pi\) | |||||||
\(860\) | 30.3726 | 1.03570 | ||||||||
\(861\) | −3.05611 | −0.104152 | ||||||||
\(862\) | −8.98520 | −0.306037 | ||||||||
\(863\) | 9.24121 | 0.314575 | 0.157287 | − | 0.987553i | \(-0.449725\pi\) | ||||
0.157287 | + | 0.987553i | \(0.449725\pi\) | |||||||
\(864\) | −4.99419 | −0.169906 | ||||||||
\(865\) | 27.5499 | 0.936726 | ||||||||
\(866\) | −11.1268 | −0.378104 | ||||||||
\(867\) | −2.26328 | −0.0768650 | ||||||||
\(868\) | −1.23807 | −0.0420229 | ||||||||
\(869\) | 7.68239 | 0.260607 | ||||||||
\(870\) | −4.18135 | −0.141761 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 18.3846 | 0.622581 | ||||||||
\(873\) | 1.74080 | 0.0589171 | ||||||||
\(874\) | 1.52662 | 0.0516388 | ||||||||
\(875\) | 12.0010 | 0.405707 | ||||||||
\(876\) | 23.8684 | 0.806440 | ||||||||
\(877\) | −36.2804 | −1.22510 | −0.612551 | − | 0.790431i | \(-0.709856\pi\) | ||||
−0.612551 | + | 0.790431i | \(0.709856\pi\) | |||||||
\(878\) | 3.61392 | 0.121964 | ||||||||
\(879\) | 17.8257 | 0.601247 | ||||||||
\(880\) | 4.29874 | 0.144911 | ||||||||
\(881\) | 35.8216 | 1.20686 | 0.603431 | − | 0.797416i | \(-0.293800\pi\) | ||||
0.603431 | + | 0.797416i | \(0.293800\pi\) | |||||||
\(882\) | 0.494186 | 0.0166401 | ||||||||
\(883\) | 2.07802 | 0.0699311 | 0.0349655 | − | 0.999389i | \(-0.488868\pi\) | ||||
0.0349655 | + | 0.999389i | \(0.488868\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8.08312 | 0.271711 | ||||||||
\(886\) | −3.46069 | −0.116264 | ||||||||
\(887\) | 5.39229 | 0.181055 | 0.0905277 | − | 0.995894i | \(-0.471145\pi\) | ||||
0.0905277 | + | 0.995894i | \(0.471145\pi\) | |||||||
\(888\) | 5.05786 | 0.169731 | ||||||||
\(889\) | −7.65651 | −0.256791 | ||||||||
\(890\) | −0.489119 | −0.0163953 | ||||||||
\(891\) | 1.00650 | 0.0337191 | ||||||||
\(892\) | −24.3694 | −0.815949 | ||||||||
\(893\) | −2.54019 | −0.0850043 | ||||||||
\(894\) | −2.71764 | −0.0908915 | ||||||||
\(895\) | 20.2129 | 0.675642 | ||||||||
\(896\) | 11.3329 | 0.378604 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0.862999 | 0.0287987 | ||||||||
\(899\) | −3.62410 | −0.120870 | ||||||||
\(900\) | 4.02036 | 0.134012 | ||||||||
\(901\) | 8.63675 | 0.287732 | ||||||||
\(902\) | −1.52011 | −0.0506141 | ||||||||
\(903\) | −10.5077 | −0.349676 | ||||||||
\(904\) | 25.1817 | 0.837532 | ||||||||
\(905\) | 37.5476 | 1.24813 | ||||||||
\(906\) | −4.10712 | −0.136450 | ||||||||
\(907\) | −22.5753 | −0.749601 | −0.374801 | − | 0.927105i | \(-0.622289\pi\) | ||||
−0.374801 | + | 0.927105i | \(0.622289\pi\) | |||||||
\(908\) | −24.0858 | −0.799315 | ||||||||
\(909\) | 12.8587 | 0.426498 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 55.3163 | 1.83271 | 0.916355 | − | 0.400367i | \(-0.131117\pi\) | ||||
0.916355 | + | 0.400367i | \(0.131117\pi\) | |||||||
\(912\) | −3.04939 | −0.100975 | ||||||||
\(913\) | 0.0546109 | 0.00180736 | ||||||||
\(914\) | −8.99426 | −0.297504 | ||||||||
\(915\) | −0.927198 | −0.0306522 | ||||||||
\(916\) | −17.4388 | −0.576196 | ||||||||
\(917\) | −1.25502 | −0.0414444 | ||||||||
\(918\) | 2.16898 | 0.0715870 | ||||||||
\(919\) | −13.0981 | −0.432067 | −0.216034 | − | 0.976386i | \(-0.569312\pi\) | ||||
−0.216034 | + | 0.976386i | \(0.569312\pi\) | |||||||
\(920\) | −8.03054 | −0.264759 | ||||||||
\(921\) | 30.6385 | 1.00957 | ||||||||
\(922\) | −18.0056 | −0.592984 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −1.76720 | −0.0581366 | ||||||||
\(925\) | −6.23980 | −0.205164 | ||||||||
\(926\) | 16.5755 | 0.544704 | ||||||||
\(927\) | 14.6917 | 0.482537 | ||||||||
\(928\) | 25.6678 | 0.842588 | ||||||||
\(929\) | −35.5476 | −1.16628 | −0.583139 | − | 0.812372i | \(-0.698176\pi\) | ||||
−0.583139 | + | 0.812372i | \(0.698176\pi\) | |||||||
\(930\) | 0.573678 | 0.0188116 | ||||||||
\(931\) | 1.17541 | 0.0385225 | ||||||||
\(932\) | −34.1366 | −1.11818 | ||||||||
\(933\) | −9.27236 | −0.303564 | ||||||||
\(934\) | 1.91047 | 0.0625125 | ||||||||
\(935\) | −7.27248 | −0.237835 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.01075 | −0.0656884 | −0.0328442 | − | 0.999460i | \(-0.510457\pi\) | ||||
−0.0328442 | + | 0.999460i | \(0.510457\pi\) | |||||||
\(938\) | −6.47684 | −0.211476 | ||||||||
\(939\) | 25.7441 | 0.840128 | ||||||||
\(940\) | 6.24669 | 0.203744 | ||||||||
\(941\) | 47.7893 | 1.55789 | 0.778943 | − | 0.627095i | \(-0.215756\pi\) | ||||
0.778943 | + | 0.627095i | \(0.215756\pi\) | |||||||
\(942\) | −6.33164 | −0.206296 | ||||||||
\(943\) | −8.03194 | −0.261556 | ||||||||
\(944\) | −12.7380 | −0.414587 | ||||||||
\(945\) | 1.64627 | 0.0535533 | ||||||||
\(946\) | −5.22656 | −0.169930 | ||||||||
\(947\) | 40.3924 | 1.31258 | 0.656288 | − | 0.754510i | \(-0.272126\pi\) | ||||
0.656288 | + | 0.754510i | \(0.272126\pi\) | |||||||
\(948\) | 13.4014 | 0.435258 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −1.33007 | −0.0431531 | ||||||||
\(951\) | −5.98521 | −0.194084 | ||||||||
\(952\) | −8.14622 | −0.264020 | ||||||||
\(953\) | 27.0429 | 0.876007 | 0.438003 | − | 0.898973i | \(-0.355686\pi\) | ||||
0.438003 | + | 0.898973i | \(0.355686\pi\) | |||||||
\(954\) | −0.972469 | −0.0314849 | ||||||||
\(955\) | 45.1175 | 1.45997 | ||||||||
\(956\) | −28.7747 | −0.930639 | ||||||||
\(957\) | −5.17297 | −0.167218 | ||||||||
\(958\) | 18.3889 | 0.594118 | ||||||||
\(959\) | −2.55836 | −0.0826139 | ||||||||
\(960\) | 4.47883 | 0.144554 | ||||||||
\(961\) | −30.5028 | −0.983961 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.37556 | 0.108776 | ||||||||
\(964\) | 28.1009 | 0.905069 | ||||||||
\(965\) | −10.5576 | −0.339862 | ||||||||
\(966\) | 1.29880 | 0.0417882 | ||||||||
\(967\) | 33.5839 | 1.07998 | 0.539992 | − | 0.841670i | \(-0.318427\pi\) | ||||
0.539992 | + | 0.841670i | \(0.318427\pi\) | |||||||
\(968\) | 18.5363 | 0.595780 | ||||||||
\(969\) | 5.15886 | 0.165727 | ||||||||
\(970\) | 1.41625 | 0.0454732 | ||||||||
\(971\) | 37.0838 | 1.19008 | 0.595038 | − | 0.803698i | \(-0.297137\pi\) | ||||
0.595038 | + | 0.803698i | \(0.297137\pi\) | |||||||
\(972\) | 1.75578 | 0.0563167 | ||||||||
\(973\) | −5.63993 | −0.180808 | ||||||||
\(974\) | 9.39838 | 0.301144 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.46115 | 0.0467703 | ||||||||
\(977\) | −44.9088 | −1.43676 | −0.718379 | − | 0.695652i | \(-0.755116\pi\) | ||||
−0.718379 | + | 0.695652i | \(0.755116\pi\) | |||||||
\(978\) | −5.31679 | −0.170012 | ||||||||
\(979\) | −0.605115 | −0.0193396 | ||||||||
\(980\) | −2.89049 | −0.0923334 | ||||||||
\(981\) | −9.90520 | −0.316249 | ||||||||
\(982\) | 7.31344 | 0.233381 | ||||||||
\(983\) | 6.22613 | 0.198583 | 0.0992914 | − | 0.995058i | \(-0.468342\pi\) | ||||
0.0992914 | + | 0.995058i | \(0.468342\pi\) | |||||||
\(984\) | −5.67230 | −0.180826 | ||||||||
\(985\) | −28.3293 | −0.902646 | ||||||||
\(986\) | −11.1476 | −0.355011 | ||||||||
\(987\) | −2.16111 | −0.0687890 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −27.6161 | −0.878139 | ||||||||
\(990\) | 0.818857 | 0.0260250 | ||||||||
\(991\) | 23.7212 | 0.753529 | 0.376765 | − | 0.926309i | \(-0.377037\pi\) | ||||
0.376765 | + | 0.926309i | \(0.377037\pi\) | |||||||
\(992\) | −3.52160 | −0.111811 | ||||||||
\(993\) | 24.7010 | 0.783864 | ||||||||
\(994\) | −7.60094 | −0.241087 | ||||||||
\(995\) | −4.95573 | −0.157107 | ||||||||
\(996\) | 0.0952651 | 0.00301859 | ||||||||
\(997\) | −55.6549 | −1.76261 | −0.881303 | − | 0.472551i | \(-0.843333\pi\) | ||||
−0.881303 | + | 0.472551i | \(0.843333\pi\) | |||||||
\(998\) | −13.6364 | −0.431654 | ||||||||
\(999\) | −2.72506 | −0.0862171 |
(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 | 3549.2.a.bf.1.6 | yes | 9 | |
13.12 | even | 2 | 3549.2.a.be.1.4 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3549.2.a.be.1.4 | ✓ | 9 | 13.12 | even | 2 | ||
3549.2.a.bf.1.6 | yes | 9 | 1.1 | even | 1 | trivial |