Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9800,2,Mod(1,9800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9800.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9800 = 2^{3} \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9800.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: | \(78.2533939809\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.239575536.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 12x^{4} + 8x^{3} + 35x^{2} - 15x - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 280) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.751428\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9800.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.751428 | −0.433837 | −0.216918 | − | 0.976190i | \(-0.569601\pi\) | ||||
−0.216918 | + | 0.976190i | \(0.569601\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.43536 | −0.811785 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.27702 | −1.59108 | −0.795540 | − | 0.605901i | \(-0.792813\pi\) | ||||
−0.795540 | + | 0.605901i | \(0.792813\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.43536 | 0.675446 | 0.337723 | − | 0.941245i | \(-0.390343\pi\) | ||||
0.337723 | + | 0.941245i | \(0.390343\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.12660 | 1.48592 | 0.742959 | − | 0.669337i | \(-0.233422\pi\) | ||||
0.742959 | + | 0.669337i | \(0.233422\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.441311 | 0.101244 | 0.0506218 | − | 0.998718i | \(-0.483880\pi\) | ||||
0.0506218 | + | 0.998718i | \(0.483880\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.18678 | 0.664490 | 0.332245 | − | 0.943193i | \(-0.392194\pi\) | ||||
0.332245 | + | 0.943193i | \(0.392194\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.08428 | 0.786020 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.25215 | −0.232518 | −0.116259 | − | 0.993219i | \(-0.537090\pi\) | ||||
−0.116259 | + | 0.993219i | \(0.537090\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.645348 | 0.115908 | 0.0579539 | − | 0.998319i | \(-0.481542\pi\) | ||||
0.0579539 | + | 0.998319i | \(0.481542\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.96530 | 0.690269 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.7511 | −1.76747 | −0.883737 | − | 0.467984i | \(-0.844980\pi\) | ||||
−0.883737 | + | 0.467984i | \(0.844980\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.82999 | −0.293034 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.90154 | −1.39019 | −0.695093 | − | 0.718920i | \(-0.744637\pi\) | ||||
−0.695093 | + | 0.718920i | \(0.744637\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.4159 | 1.58841 | 0.794204 | − | 0.607651i | \(-0.207888\pi\) | ||||
0.794204 | + | 0.607651i | \(0.207888\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.52994 | −1.09835 | −0.549177 | − | 0.835706i | \(-0.685059\pi\) | ||||
−0.549177 | + | 0.835706i | \(0.685059\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.60370 | −0.644646 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.34077 | −0.458891 | −0.229445 | − | 0.973322i | \(-0.573691\pi\) | ||||
−0.229445 | + | 0.973322i | \(0.573691\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.331613 | −0.0439232 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.15535 | 1.06174 | 0.530868 | − | 0.847455i | \(-0.321866\pi\) | ||||
0.530868 | + | 0.847455i | \(0.321866\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.47036 | 0.444335 | 0.222167 | − | 0.975009i | \(-0.428687\pi\) | ||||
0.222167 | + | 0.975009i | \(0.428687\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.78644 | −0.584756 | −0.292378 | − | 0.956303i | \(-0.594447\pi\) | ||||
−0.292378 | + | 0.956303i | \(0.594447\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.39464 | −0.288281 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.7064 | 1.62665 | 0.813326 | − | 0.581808i | \(-0.197654\pi\) | ||||
0.813326 | + | 0.581808i | \(0.197654\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.32590 | −0.623350 | −0.311675 | − | 0.950189i | \(-0.600890\pi\) | ||||
−0.311675 | + | 0.950189i | \(0.600890\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.40439 | 0.608042 | 0.304021 | − | 0.952665i | \(-0.401671\pi\) | ||||
0.304021 | + | 0.952665i | \(0.401671\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.23703 | 0.470781 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.9379 | 1.31036 | 0.655178 | − | 0.755475i | \(-0.272594\pi\) | ||||
0.655178 | + | 0.755475i | \(0.272594\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.940897 | 0.100875 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.60237 | −0.911849 | −0.455925 | − | 0.890018i | \(-0.650691\pi\) | ||||
−0.455925 | + | 0.890018i | \(0.650691\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.484932 | −0.0502851 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.6714 | −1.38812 | −0.694061 | − | 0.719917i | \(-0.744180\pi\) | ||||
−0.694061 | + | 0.719917i | \(0.744180\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 12.8514 | 1.29162 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.6814 | 1.16234 | 0.581172 | − | 0.813781i | \(-0.302594\pi\) | ||||
0.581172 | + | 0.813781i | \(0.302594\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.450595 | 0.0443984 | 0.0221992 | − | 0.999754i | \(-0.492933\pi\) | ||||
0.0221992 | + | 0.999754i | \(0.492933\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.462608 | 0.0447220 | 0.0223610 | − | 0.999750i | \(-0.492882\pi\) | ||||
0.0223610 | + | 0.999750i | \(0.492882\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.40606 | 0.230459 | 0.115229 | − | 0.993339i | \(-0.463240\pi\) | ||||
0.115229 | + | 0.993339i | \(0.463240\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.07869 | 0.766795 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.2753 | 1.24884 | 0.624420 | − | 0.781089i | \(-0.285335\pi\) | ||||
0.624420 | + | 0.781089i | \(0.285335\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.93096 | −0.548318 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 16.8469 | 1.53154 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.68886 | 0.603114 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.17855 | −0.459522 | −0.229761 | − | 0.973247i | \(-0.573795\pi\) | ||||
−0.229761 | + | 0.973247i | \(0.573795\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.82679 | −0.689110 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.15344 | −0.799740 | −0.399870 | − | 0.916572i | \(-0.630945\pi\) | ||||
−0.399870 | + | 0.916572i | \(0.630945\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.89528 | −0.674539 | −0.337270 | − | 0.941408i | \(-0.609503\pi\) | ||||
−0.337270 | + | 0.941408i | \(0.609503\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.92998 | 0.333337 | 0.166668 | − | 0.986013i | \(-0.446699\pi\) | ||||
0.166668 | + | 0.986013i | \(0.446699\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.65820 | 0.476507 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −12.8514 | −1.07469 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.04202 | −0.576904 | −0.288452 | − | 0.957494i | \(-0.593141\pi\) | ||||
−0.288452 | + | 0.957494i | \(0.593141\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.715364 | −0.0582155 | −0.0291077 | − | 0.999576i | \(-0.509267\pi\) | ||||
−0.0291077 | + | 0.999576i | \(0.509267\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −14.9205 | −1.20625 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.7454 | −1.25662 | −0.628310 | − | 0.777963i | \(-0.716253\pi\) | ||||
−0.628310 | + | 0.777963i | \(0.716253\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.51035 | 0.199084 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.9431 | 1.01379 | 0.506893 | − | 0.862009i | \(-0.330794\pi\) | ||||
0.506893 | + | 0.862009i | \(0.330794\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.70185 | −0.363840 | −0.181920 | − | 0.983313i | \(-0.558231\pi\) | ||||
−0.181920 | + | 0.983313i | \(0.558231\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.06904 | −0.543772 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.07475 | −0.0821881 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.18518 | −0.622308 | −0.311154 | − | 0.950360i | \(-0.600715\pi\) | ||||
−0.311154 | + | 0.950360i | \(0.600715\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.12816 | −0.460620 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 20.1942 | 1.50938 | 0.754691 | − | 0.656080i | \(-0.227787\pi\) | ||||
0.754691 | + | 0.656080i | \(0.227787\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.542841 | 0.0403490 | 0.0201745 | − | 0.999796i | \(-0.493578\pi\) | ||||
0.0201745 | + | 0.999796i | \(0.493578\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.60773 | −0.192769 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −32.3302 | −2.36422 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.9911 | −0.940000 | −0.470000 | − | 0.882666i | \(-0.655746\pi\) | ||||
−0.470000 | + | 0.882666i | \(0.655746\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.83540 | −0.348060 | −0.174030 | − | 0.984740i | \(-0.555679\pi\) | ||||
−0.174030 | + | 0.984740i | \(0.555679\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.5967 | 1.18246 | 0.591232 | − | 0.806502i | \(-0.298642\pi\) | ||||
0.591232 | + | 0.806502i | \(0.298642\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.6444 | 1.10900 | 0.554502 | − | 0.832183i | \(-0.312909\pi\) | ||||
0.554502 | + | 0.832183i | \(0.312909\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.59666 | 0.253689 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −7.76096 | −0.539424 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.32880 | −0.161087 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.5521 | −1.62139 | −0.810697 | − | 0.585465i | \(-0.800912\pi\) | ||||
−0.810697 | + | 0.585465i | \(0.800912\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −10.2994 | −0.705702 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.00203 | 0.270432 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 14.9205 | 1.00366 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −21.4669 | −1.43753 | −0.718765 | − | 0.695253i | \(-0.755292\pi\) | ||||
−0.718765 | + | 0.695253i | \(0.755292\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −16.6047 | −1.10209 | −0.551046 | − | 0.834475i | \(-0.685771\pi\) | ||||
−0.551046 | + | 0.834475i | \(0.685771\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.7459 | −0.842276 | −0.421138 | − | 0.906997i | \(-0.638369\pi\) | ||||
−0.421138 | + | 0.906997i | \(0.638369\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −15.4073 | −1.00937 | −0.504684 | − | 0.863304i | \(-0.668391\pi\) | ||||
−0.504684 | + | 0.863304i | \(0.668391\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.06101 | −0.263791 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.60666 | −0.103926 | −0.0519631 | − | 0.998649i | \(-0.516548\pi\) | ||||
−0.0519631 | + | 0.998649i | \(0.516548\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −21.8152 | −1.40524 | −0.702620 | − | 0.711565i | \(-0.747987\pi\) | ||||
−0.702620 | + | 0.711565i | \(0.747987\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.4367 | −0.990262 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.07475 | 0.0683847 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8.97047 | −0.568481 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.23904 | 0.520044 | 0.260022 | − | 0.965603i | \(-0.416270\pi\) | ||||
0.260022 | + | 0.965603i | \(0.416270\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −16.8167 | −1.05726 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.31792 | −0.456479 | −0.228240 | − | 0.973605i | \(-0.573297\pi\) | ||||
−0.228240 | + | 0.973605i | \(0.573297\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.04942 | 0.188754 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −15.8872 | −0.979650 | −0.489825 | − | 0.871821i | \(-0.662939\pi\) | ||||
−0.489825 | + | 0.871821i | \(0.662939\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.46406 | 0.395594 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −11.0777 | −0.675422 | −0.337711 | − | 0.941250i | \(-0.609653\pi\) | ||||
−0.337711 | + | 0.941250i | \(0.609653\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.82105 | 0.171366 | 0.0856832 | − | 0.996322i | \(-0.472693\pi\) | ||||
0.0856832 | + | 0.996322i | \(0.472693\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.44948 | −0.0870908 | −0.0435454 | − | 0.999051i | \(-0.513865\pi\) | ||||
−0.0435454 | + | 0.999051i | \(0.513865\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.57165 | −0.0940923 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −20.2681 | −1.20909 | −0.604546 | − | 0.796570i | \(-0.706645\pi\) | ||||
−0.604546 | + | 0.796570i | \(0.706645\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.63007 | −0.0968975 | −0.0484487 | − | 0.998826i | \(-0.515428\pi\) | ||||
−0.0484487 | + | 0.998826i | \(0.515428\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 20.5352 | 1.20795 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.2731 | 0.602218 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 20.5114 | 1.19829 | 0.599144 | − | 0.800641i | \(-0.295507\pi\) | ||||
0.599144 | + | 0.800641i | \(0.295507\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −21.5528 | −1.25062 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.76096 | 0.448828 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −8.77773 | −0.504268 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.58019 | 0.0901860 | 0.0450930 | − | 0.998983i | \(-0.485642\pi\) | ||||
0.0450930 | + | 0.998983i | \(0.485642\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.338589 | −0.0192617 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −20.8410 | −1.18179 | −0.590894 | − | 0.806749i | \(-0.701225\pi\) | ||||
−0.590894 | + | 0.806749i | \(0.701225\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −22.9695 | −1.29831 | −0.649155 | − | 0.760656i | \(-0.724877\pi\) | ||||
−0.649155 | + | 0.760656i | \(0.724877\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 19.6447 | 1.10336 | 0.551678 | − | 0.834057i | \(-0.313988\pi\) | ||||
0.551678 | + | 0.834057i | \(0.313988\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.60759 | 0.369954 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.347616 | −0.0194021 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.70374 | 0.150440 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.80798 | −0.0999815 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.95702 | −0.382393 | −0.191196 | − | 0.981552i | \(-0.561237\pi\) | ||||
−0.191196 | + | 0.981552i | \(0.561237\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 26.1828 | 1.43481 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 31.0168 | 1.68959 | 0.844796 | − | 0.535089i | \(-0.179722\pi\) | ||||
0.844796 | + | 0.535089i | \(0.179722\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.97547 | −0.541793 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.40551 | −0.184419 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.81047 | −0.311922 | −0.155961 | − | 0.987763i | \(-0.549847\pi\) | ||||
−0.155961 | + | 0.987763i | \(0.549847\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 28.0316 | 1.50050 | 0.750249 | − | 0.661155i | \(-0.229934\pi\) | ||||
0.750249 | + | 0.661155i | \(0.229934\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.94667 | 0.530914 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 32.9076 | 1.75150 | 0.875748 | − | 0.482768i | \(-0.160369\pi\) | ||||
0.875748 | + | 0.482768i | \(0.160369\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −28.3368 | −1.49556 | −0.747778 | − | 0.663948i | \(-0.768879\pi\) | ||||
−0.747778 | + | 0.663948i | \(0.768879\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.8052 | −0.989750 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −12.6592 | −0.664437 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −23.7654 | −1.24054 | −0.620271 | − | 0.784388i | \(-0.712977\pi\) | ||||
−0.620271 | + | 0.784388i | \(0.712977\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 21.6784 | 1.12853 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9.08860 | −0.470590 | −0.235295 | − | 0.971924i | \(-0.575606\pi\) | ||||
−0.235295 | + | 0.971924i | \(0.575606\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.04942 | −0.157053 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.08377 | −0.415235 | −0.207618 | − | 0.978210i | \(-0.566571\pi\) | ||||
−0.207618 | + | 0.978210i | \(0.566571\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.89131 | 0.199358 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.52866 | 0.282501 | 0.141251 | − | 0.989974i | \(-0.454888\pi\) | ||||
0.141251 | + | 0.989974i | \(0.454888\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −25.3664 | −1.28945 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −22.3057 | −1.13094 | −0.565472 | − | 0.824768i | \(-0.691306\pi\) | ||||
−0.565472 | + | 0.824768i | \(0.691306\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 19.5241 | 0.987379 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.87815 | 0.346957 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −32.2201 | −1.61708 | −0.808539 | − | 0.588443i | \(-0.799741\pi\) | ||||
−0.808539 | + | 0.588443i | \(0.799741\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.94427 | 0.296843 | 0.148421 | − | 0.988924i | \(-0.452581\pi\) | ||||
0.148421 | + | 0.988924i | \(0.452581\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.57165 | 0.0782895 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 56.7338 | 2.81219 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −30.5234 | −1.50929 | −0.754643 | − | 0.656136i | \(-0.772190\pi\) | ||||
−0.754643 | + | 0.656136i | \(0.772190\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.93273 | 0.292640 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.95310 | −0.144614 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.06306 | −0.198493 | −0.0992466 | − | 0.995063i | \(-0.531643\pi\) | ||||
−0.0992466 | + | 0.995063i | \(0.531643\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.34322 | −0.114201 | −0.0571007 | − | 0.998368i | \(-0.518186\pi\) | ||||
−0.0571007 | + | 0.998368i | \(0.518186\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 18.3381 | 0.891628 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 9.65691 | 0.466240 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.43702 | −0.310060 | −0.155030 | − | 0.987910i | \(-0.549547\pi\) | ||||
−0.155030 | + | 0.987910i | \(0.549547\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −22.4161 | −1.07725 | −0.538624 | − | 0.842547i | \(-0.681055\pi\) | ||||
−0.538624 | + | 0.842547i | \(0.681055\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.40636 | 0.0672755 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17.4077 | −0.830824 | −0.415412 | − | 0.909633i | \(-0.636363\pi\) | ||||
−0.415412 | + | 0.909633i | \(0.636363\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −35.6871 | −1.69555 | −0.847773 | − | 0.530359i | \(-0.822057\pi\) | ||||
−0.847773 | + | 0.530359i | \(0.822057\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.29157 | 0.250282 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.24155 | −0.247364 | −0.123682 | − | 0.992322i | \(-0.539470\pi\) | ||||
−0.123682 | + | 0.992322i | \(0.539470\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 46.9736 | 2.21190 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.537544 | 0.0252560 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.9695 | −0.700241 | −0.350121 | − | 0.936705i | \(-0.613859\pi\) | ||||
−0.350121 | + | 0.936705i | \(0.613859\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 25.0227 | 1.16796 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.92904 | 0.462441 | 0.231221 | − | 0.972901i | \(-0.425728\pi\) | ||||
0.231221 | + | 0.972901i | \(0.425728\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.07448 | −0.142883 | −0.0714415 | − | 0.997445i | \(-0.522760\pi\) | ||||
−0.0714415 | + | 0.997445i | \(0.522760\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 19.9442 | 0.922909 | 0.461455 | − | 0.887164i | \(-0.347328\pi\) | ||||
0.461455 | + | 0.887164i | \(0.347328\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11.8315 | 0.545168 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −54.9648 | −2.52729 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.13598 | 0.372521 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 40.3391 | 1.84314 | 0.921571 | − | 0.388209i | \(-0.126906\pi\) | ||||
0.921571 | + | 0.388209i | \(0.126906\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −26.1828 | −1.19383 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.92314 | −0.268403 | −0.134202 | − | 0.990954i | \(-0.542847\pi\) | ||||
−0.134202 | + | 0.990954i | \(0.542847\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9.72584 | −0.439818 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −26.3855 | −1.19076 | −0.595380 | − | 0.803444i | \(-0.702999\pi\) | ||||
−0.595380 | + | 0.803444i | \(0.702999\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.67139 | −0.345502 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.02895 | −0.269893 | −0.134946 | − | 0.990853i | \(-0.543086\pi\) | ||||
−0.134946 | + | 0.990853i | \(0.543086\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.53310 | 0.157847 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 37.5173 | 1.67281 | 0.836407 | − | 0.548109i | \(-0.184652\pi\) | ||||
0.836407 | + | 0.548109i | \(0.184652\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.31187 | 0.235908 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 15.9162 | 0.705472 | 0.352736 | − | 0.935723i | \(-0.385251\pi\) | ||||
0.352736 | + | 0.935723i | \(0.385251\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.80244 | 0.0795795 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 39.7356 | 1.74757 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.15057 | 0.269980 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −19.3893 | −0.849460 | −0.424730 | − | 0.905320i | \(-0.639631\pi\) | ||||
−0.424730 | + | 0.905320i | \(0.639631\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.92314 | −0.259001 | −0.129500 | − | 0.991579i | \(-0.541337\pi\) | ||||
−0.129500 | + | 0.991579i | \(0.541337\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.95379 | 0.172230 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12.8444 | −0.558452 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −19.8612 | −0.861902 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −21.6784 | −0.938996 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −15.1744 | −0.654826 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.4343 | −1.00752 | −0.503759 | − | 0.863844i | \(-0.668050\pi\) | ||||
−0.503759 | + | 0.863844i | \(0.668050\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.407905 | −0.0175049 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 40.9760 | 1.75201 | 0.876003 | − | 0.482306i | \(-0.160201\pi\) | ||||
0.876003 | + | 0.482306i | \(0.160201\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8.45157 | −0.360704 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.552586 | −0.0235409 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.69824 | 0.326185 | 0.163092 | − | 0.986611i | \(-0.447853\pi\) | ||||
0.163092 | + | 0.986611i | \(0.447853\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 25.3664 | 1.07288 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 24.2938 | 1.02568 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −24.1993 | −1.01988 | −0.509939 | − | 0.860211i | \(-0.670332\pi\) | ||||
−0.509939 | + | 0.860211i | \(0.670332\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 16.3014 | 0.683392 | 0.341696 | − | 0.939811i | \(-0.388999\pi\) | ||||
0.341696 | + | 0.939811i | \(0.388999\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 31.0604 | 1.29984 | 0.649918 | − | 0.760005i | \(-0.274803\pi\) | ||||
0.649918 | + | 0.760005i | \(0.274803\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.76184 | 0.407807 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.33948 | −0.263916 | −0.131958 | − | 0.991255i | \(-0.542126\pi\) | ||||
−0.131958 | + | 0.991255i | \(0.542126\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.63345 | 0.151001 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 17.6293 | 0.730132 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −14.8548 | −0.613122 | −0.306561 | − | 0.951851i | \(-0.599178\pi\) | ||||
−0.306561 | + | 0.951851i | \(0.599178\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.284799 | 0.0117349 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.4712 | −0.512996 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −12.2841 | −0.504446 | −0.252223 | − | 0.967669i | \(-0.581162\pi\) | ||||
−0.252223 | + | 0.967669i | \(0.581162\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −11.7556 | −0.481127 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −22.8175 | −0.932296 | −0.466148 | − | 0.884707i | \(-0.654359\pi\) | ||||
−0.466148 | + | 0.884707i | \(0.654359\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25.8612 | −1.05490 | −0.527450 | − | 0.849586i | \(-0.676852\pi\) | ||||
−0.527450 | + | 0.849586i | \(0.676852\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 11.6567 | 0.474697 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.23081 | 0.0905459 | 0.0452730 | − | 0.998975i | \(-0.485584\pi\) | ||||
0.0452730 | + | 0.998975i | \(0.485584\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −18.3381 | −0.741880 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.9320 | 0.805047 | 0.402524 | − | 0.915410i | \(-0.368133\pi\) | ||||
0.402524 | + | 0.915410i | \(0.368133\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.1435 | −0.488880 | −0.244440 | − | 0.969664i | \(-0.578604\pi\) | ||||
−0.244440 | + | 0.969664i | \(0.578604\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.930105 | −0.0373841 | −0.0186920 | − | 0.999825i | \(-0.505950\pi\) | ||||
−0.0186920 | + | 0.999825i | \(0.505950\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 13.0157 | 0.522302 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.74993 | 0.0698854 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −65.8678 | −2.62632 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 35.8314 | 1.42643 | 0.713214 | − | 0.700947i | \(-0.247239\pi\) | ||||
0.713214 | + | 0.700947i | \(0.247239\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 17.6977 | 0.703421 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −33.3800 | −1.32049 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.19676 | −0.244757 | −0.122379 | − | 0.992483i | \(-0.539052\pi\) | ||||
−0.122379 | + | 0.992483i | \(0.539052\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20.2885 | −0.800102 | −0.400051 | − | 0.916493i | \(-0.631008\pi\) | ||||
−0.400051 | + | 0.916493i | \(0.631008\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −23.8180 | −0.936381 | −0.468191 | − | 0.883627i | \(-0.655094\pi\) | ||||
−0.468191 | + | 0.883627i | \(0.655094\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −43.0359 | −1.68931 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.93646 | 0.388844 | 0.194422 | − | 0.980918i | \(-0.437717\pi\) | ||||
0.194422 | + | 0.980918i | \(0.437717\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 12.9705 | 0.506026 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 45.4504 | 1.77050 | 0.885249 | − | 0.465118i | \(-0.153988\pi\) | ||||
0.885249 | + | 0.465118i | \(0.153988\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.54038 | −0.215496 | −0.107748 | − | 0.994178i | \(-0.534364\pi\) | ||||
−0.107748 | + | 0.994178i | \(0.534364\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −11.2116 | −0.435424 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.99032 | −0.154506 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 16.1308 | 0.623654 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −18.3132 | −0.706972 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.34880 | 0.360370 | 0.180185 | − | 0.983633i | \(-0.442330\pi\) | ||||
0.180185 | + | 0.983633i | \(0.442330\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −32.8344 | −1.26193 | −0.630965 | − | 0.775811i | \(-0.717341\pi\) | ||||
−0.630965 | + | 0.775811i | \(0.717341\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.4772 | 0.478128 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −13.0893 | −0.500847 | −0.250424 | − | 0.968136i | \(-0.580570\pi\) | ||||
−0.250424 | + | 0.968136i | \(0.580570\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9.57766 | 0.365410 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8.13598 | −0.309956 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.9796 | 0.874186 | 0.437093 | − | 0.899416i | \(-0.356008\pi\) | ||||
0.437093 | + | 0.899416i | \(0.356008\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −54.5362 | −2.06570 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 11.5775 | 0.437901 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.12916 | 0.118187 | 0.0590934 | − | 0.998252i | \(-0.481179\pi\) | ||||
0.0590934 | + | 0.998252i | \(0.481179\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.74459 | −0.178946 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 37.8712 | 1.42228 | 0.711141 | − | 0.703049i | \(-0.248179\pi\) | ||||
0.711141 | + | 0.703049i | \(0.248179\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −13.1616 | −0.493599 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.05658 | 0.0770196 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.20729 | 0.0450870 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 25.8182 | 0.962855 | 0.481427 | − | 0.876486i | \(-0.340118\pi\) | ||||
0.481427 | + | 0.876486i | \(0.340118\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 16.3925 | 0.609645 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −24.1385 | −0.895248 | −0.447624 | − | 0.894222i | \(-0.647730\pi\) | ||||
−0.447624 | + | 0.894222i | \(0.647730\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.11156 | −0.0411690 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 63.8140 | 2.36025 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10.9064 | −0.402837 | −0.201418 | − | 0.979505i | \(-0.564555\pi\) | ||||
−0.201418 | + | 0.979505i | \(0.564555\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 25.2581 | 0.930394 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −43.6153 | −1.60442 | −0.802208 | − | 0.597045i | \(-0.796341\pi\) | ||||
−0.802208 | + | 0.597045i | \(0.796341\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.807597 | −0.0296678 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 36.1676 | 1.32686 | 0.663431 | − | 0.748238i | \(-0.269100\pi\) | ||||
0.663431 | + | 0.748238i | \(0.269100\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −29.0731 | −1.06373 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 41.9165 | 1.52955 | 0.764777 | − | 0.644295i | \(-0.222849\pi\) | ||||
0.764777 | + | 0.644295i | \(0.222849\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6.19105 | −0.225614 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −27.3777 | −0.995060 | −0.497530 | − | 0.867447i | \(-0.665759\pi\) | ||||
−0.497530 | + | 0.867447i | \(0.665759\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 12.6365 | 0.458677 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14.2133 | 0.515232 | 0.257616 | − | 0.966247i | \(-0.417063\pi\) | ||||
0.257616 | + | 0.966247i | \(0.417063\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 19.8612 | 0.717146 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −38.1788 | −1.37676 | −0.688381 | − | 0.725349i | \(-0.741678\pi\) | ||||
−0.688381 | + | 0.725349i | \(0.741678\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.49889 | 0.198038 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −29.9828 | −1.07841 | −0.539203 | − | 0.842176i | \(-0.681274\pi\) | ||||
−0.539203 | + | 0.842176i | \(0.681274\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.92835 | −0.140748 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −72.3290 | −2.58813 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.11411 | −0.182763 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −29.0783 | −1.03653 | −0.518265 | − | 0.855220i | \(-0.673422\pi\) | ||||
−0.518265 | + | 0.855220i | \(0.673422\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 11.9381 | 0.425008 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.45157 | 0.300124 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −42.5726 | −1.50800 | −0.753999 | − | 0.656875i | \(-0.771878\pi\) | ||||
−0.753999 | + | 0.656875i | \(0.771878\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −46.1329 | −1.63207 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 20.9498 | 0.740226 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 28.1049 | 0.991799 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.32412 | 0.293023 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 21.3774 | 0.751589 | 0.375794 | − | 0.926703i | \(-0.377370\pi\) | ||||
0.375794 | + | 0.926703i | \(0.377370\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −23.3902 | −0.821342 | −0.410671 | − | 0.911784i | \(-0.634706\pi\) | ||||
−0.410671 | + | 0.911784i | \(0.634706\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.11981 | −0.0743451 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.59665 | 0.160816 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.59645 | −0.0906166 | −0.0453083 | − | 0.998973i | \(-0.514427\pi\) | ||||
−0.0453083 | + | 0.998973i | \(0.514427\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.3513 | 0.395681 | 0.197840 | − | 0.980234i | \(-0.436607\pi\) | ||||
0.197840 | + | 0.980234i | \(0.436607\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −28.8025 | −1.00156 | −0.500781 | − | 0.865574i | \(-0.666954\pi\) | ||||
−0.500781 | + | 0.865574i | \(0.666954\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.33167 | 0.115714 | 0.0578569 | − | 0.998325i | \(-0.481573\pi\) | ||||
0.0578569 | + | 0.998325i | \(0.481573\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.08918 | 0.0377832 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.63578 | 0.0911058 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 30.6414 | 1.05786 | 0.528929 | − | 0.848666i | \(-0.322594\pi\) | ||||
0.528929 | + | 0.848666i | \(0.322594\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.4321 | −0.945936 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 15.2300 | 0.524549 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.22488 | 0.0420377 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −34.2615 | −1.17447 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −11.0513 | −0.378390 | −0.189195 | − | 0.981940i | \(-0.560588\pi\) | ||||
−0.189195 | + | 0.981940i | \(0.560588\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 11.4894 | 0.392469 | 0.196235 | − | 0.980557i | \(-0.437129\pi\) | ||||
0.196235 | + | 0.980557i | \(0.437129\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 50.6348 | 1.72764 | 0.863819 | − | 0.503802i | \(-0.168066\pi\) | ||||
0.863819 | + | 0.503802i | \(0.168066\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −51.3958 | −1.74953 | −0.874766 | − | 0.484545i | \(-0.838985\pi\) | ||||
−0.874766 | + | 0.484545i | \(0.838985\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −15.4307 | −0.524055 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −28.5191 | −0.967443 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11.6567 | −0.394971 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 33.2948 | 1.12686 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.16086 | 0.208038 | 0.104019 | − | 0.994575i | \(-0.466830\pi\) | ||||
0.104019 | + | 0.994575i | \(0.466830\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −15.4128 | −0.519862 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.10894 | 0.172124 | 0.0860622 | − | 0.996290i | \(-0.472572\pi\) | ||||
0.0860622 | + | 0.996290i | \(0.472572\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.26283 | −0.244414 | −0.122207 | − | 0.992505i | \(-0.538997\pi\) | ||||
−0.122207 | + | 0.992505i | \(0.538997\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −31.2210 | −1.04830 | −0.524150 | − | 0.851626i | \(-0.675617\pi\) | ||||
−0.524150 | + | 0.851626i | \(0.675617\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −22.3589 | −0.749051 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.32304 | −0.111201 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.83180 | −0.194718 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.808069 | −0.0269506 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −20.4676 | −0.681874 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −28.2350 | −0.937526 | −0.468763 | − | 0.883324i | \(-0.655300\pi\) | ||||
−0.468763 | + | 0.883324i | \(0.655300\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −28.4484 | −0.943574 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 48.7700 | 1.61582 | 0.807911 | − | 0.589304i | \(-0.200598\pi\) | ||||
0.807911 | + | 0.589304i | \(0.200598\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −62.9965 | −2.08488 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −43.8963 | −1.44800 | −0.724002 | − | 0.689797i | \(-0.757700\pi\) | ||||
−0.724002 | + | 0.689797i | \(0.757700\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.18740 | −0.0391260 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 33.3800 | 1.09872 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.09736 | −0.0360420 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 33.9542 | 1.11400 | 0.557000 | − | 0.830513i | \(-0.311952\pi\) | ||||
0.557000 | + | 0.830513i | \(0.311952\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 15.6605 | 0.512703 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −16.4081 | −0.536028 | −0.268014 | − | 0.963415i | \(-0.586367\pi\) | ||||
−0.268014 | + | 0.963415i | \(0.586367\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 17.2599 | 0.563255 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −28.7404 | −0.936912 | −0.468456 | − | 0.883487i | \(-0.655190\pi\) | ||||
−0.468456 | + | 0.883487i | \(0.655190\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −28.3673 | −0.923766 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −6.44139 | −0.209317 | −0.104659 | − | 0.994508i | \(-0.533375\pi\) | ||||
−0.104659 | + | 0.994508i | \(0.533375\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.9705 | −0.421039 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −14.7616 | −0.478677 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 17.4655 | 0.565762 | 0.282881 | − | 0.959155i | \(-0.408710\pi\) | ||||
0.282881 | + | 0.959155i | \(0.408710\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.96513 | −0.160500 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.5835 | −0.986565 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.12662 | −0.0363047 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −43.5117 | −1.39924 | −0.699620 | − | 0.714515i | \(-0.746648\pi\) | ||||
−0.699620 | + | 0.714515i | \(0.746648\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.03166 | −0.0652664 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 43.8608 | 1.40756 | 0.703780 | − | 0.710418i | \(-0.251494\pi\) | ||||
0.703780 | + | 0.710418i | \(0.251494\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.91400 | 0.0612343 | 0.0306171 | − | 0.999531i | \(-0.490253\pi\) | ||||
0.0306171 | + | 0.999531i | \(0.490253\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 45.3948 | 1.45083 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.85961 | −0.187083 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.03107 | −0.128571 | −0.0642855 | − | 0.997932i | \(-0.520477\pi\) | ||||
−0.0642855 | + | 0.997932i | \(0.520477\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 33.1932 | 1.05548 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 36.8258 | 1.16981 | 0.584905 | − | 0.811102i | \(-0.301132\pi\) | ||||
0.584905 | + | 0.811102i | \(0.301132\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 5.22770 | 0.165896 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −39.7812 | −1.25988 | −0.629942 | − | 0.776642i | \(-0.716921\pi\) | ||||
−0.629942 | + | 0.776642i | \(0.716921\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −43.9106 | −1.38927 |
(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 | 9800.2.a.cw.1.3 | 6 | ||
5.2 | odd | 4 | 1960.2.g.e.1569.8 | 12 | |||
5.3 | odd | 4 | 1960.2.g.e.1569.5 | 12 | |||
5.4 | even | 2 | 9800.2.a.cy.1.4 | 6 | |||
7.3 | odd | 6 | 1400.2.q.n.401.3 | 12 | |||
7.5 | odd | 6 | 1400.2.q.n.1201.3 | 12 | |||
7.6 | odd | 2 | 9800.2.a.cx.1.4 | 6 | |||
35.3 | even | 12 | 280.2.bg.a.9.8 | yes | 24 | ||
35.12 | even | 12 | 280.2.bg.a.249.8 | yes | 24 | ||
35.13 | even | 4 | 1960.2.g.f.1569.8 | 12 | |||
35.17 | even | 12 | 280.2.bg.a.9.5 | ✓ | 24 | ||
35.19 | odd | 6 | 1400.2.q.o.1201.4 | 12 | |||
35.24 | odd | 6 | 1400.2.q.o.401.4 | 12 | |||
35.27 | even | 4 | 1960.2.g.f.1569.5 | 12 | |||
35.33 | even | 12 | 280.2.bg.a.249.5 | yes | 24 | ||
35.34 | odd | 2 | 9800.2.a.cv.1.3 | 6 | |||
140.3 | odd | 12 | 560.2.bw.f.289.5 | 24 | |||
140.47 | odd | 12 | 560.2.bw.f.529.5 | 24 | |||
140.87 | odd | 12 | 560.2.bw.f.289.8 | 24 | |||
140.103 | odd | 12 | 560.2.bw.f.529.8 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.bg.a.9.5 | ✓ | 24 | 35.17 | even | 12 | ||
280.2.bg.a.9.8 | yes | 24 | 35.3 | even | 12 | ||
280.2.bg.a.249.5 | yes | 24 | 35.33 | even | 12 | ||
280.2.bg.a.249.8 | yes | 24 | 35.12 | even | 12 | ||
560.2.bw.f.289.5 | 24 | 140.3 | odd | 12 | |||
560.2.bw.f.289.8 | 24 | 140.87 | odd | 12 | |||
560.2.bw.f.529.5 | 24 | 140.47 | odd | 12 | |||
560.2.bw.f.529.8 | 24 | 140.103 | odd | 12 | |||
1400.2.q.n.401.3 | 12 | 7.3 | odd | 6 | |||
1400.2.q.n.1201.3 | 12 | 7.5 | odd | 6 | |||
1400.2.q.o.401.4 | 12 | 35.24 | odd | 6 | |||
1400.2.q.o.1201.4 | 12 | 35.19 | odd | 6 | |||
1960.2.g.e.1569.5 | 12 | 5.3 | odd | 4 | |||
1960.2.g.e.1569.8 | 12 | 5.2 | odd | 4 | |||
1960.2.g.f.1569.5 | 12 | 35.27 | even | 4 | |||
1960.2.g.f.1569.8 | 12 | 35.13 | even | 4 | |||
9800.2.a.cv.1.3 | 6 | 35.34 | odd | 2 | |||
9800.2.a.cw.1.3 | 6 | 1.1 | even | 1 | trivial | ||
9800.2.a.cx.1.4 | 6 | 7.6 | odd | 2 | |||
9800.2.a.cy.1.4 | 6 | 5.4 | even | 2 |