Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1856,4,Mod(1,1856)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1856, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1856.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1856 = 2^{6} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1856.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: | \(109.507544971\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} - 217 x^{10} + 520 x^{9} + 16022 x^{8} - 37368 x^{7} - 509640 x^{6} + 989168 x^{5} + \cdots + 14751072 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{17} \) |
Twist minimal: | no (minimal twist has level 928) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-10.7228\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1856.1 |
$q$-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 | ||||||||
\(3\) | −9.72277 | −1.87115 | −0.935574 | − | 0.353130i | \(-0.885117\pi\) | ||||
−0.935574 | + | 0.353130i | \(0.885117\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 6.27199 | 0.560984 | 0.280492 | − | 0.959856i | \(-0.409502\pi\) | ||||
0.280492 | + | 0.959856i | \(0.409502\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −31.0130 | −1.67455 | −0.837273 | − | 0.546785i | \(-0.815851\pi\) | ||||
−0.837273 | + | 0.546785i | \(0.815851\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 67.5323 | 2.50120 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 8.24716 | 0.226056 | 0.113028 | − | 0.993592i | \(-0.463945\pi\) | ||||
0.113028 | + | 0.993592i | \(0.463945\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −32.0907 | −0.684644 | −0.342322 | − | 0.939583i | \(-0.611213\pi\) | ||||
−0.342322 | + | 0.939583i | \(0.611213\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −60.9811 | −1.04968 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 51.1369 | 0.729560 | 0.364780 | − | 0.931094i | \(-0.381144\pi\) | ||||
0.364780 | + | 0.931094i | \(0.381144\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 158.789 | 1.91730 | 0.958648 | − | 0.284593i | \(-0.0918586\pi\) | ||||
0.958648 | + | 0.284593i | \(0.0918586\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 301.533 | 3.13332 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −129.494 | −1.17398 | −0.586988 | − | 0.809596i | \(-0.699686\pi\) | ||||
−0.586988 | + | 0.809596i | \(0.699686\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −85.6622 | −0.685297 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −394.086 | −2.80896 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −29.0000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 14.6426 | 0.0848353 | 0.0424177 | − | 0.999100i | \(-0.486494\pi\) | ||||
0.0424177 | + | 0.999100i | \(0.486494\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −80.1853 | −0.422984 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −194.513 | −0.939393 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 257.398 | 1.14367 | 0.571837 | − | 0.820367i | \(-0.306231\pi\) | ||||
0.571837 | + | 0.820367i | \(0.306231\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 312.011 | 1.28107 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −26.0208 | −0.0991163 | −0.0495582 | − | 0.998771i | \(-0.515781\pi\) | ||||
−0.0495582 | + | 0.998771i | \(0.515781\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.40346 | 0.0120703 | 0.00603516 | − | 0.999982i | \(-0.498079\pi\) | ||||
0.00603516 | + | 0.999982i | \(0.498079\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 423.562 | 1.40313 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −482.228 | −1.49660 | −0.748300 | − | 0.663361i | \(-0.769129\pi\) | ||||
−0.748300 | + | 0.663361i | \(0.769129\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 618.808 | 1.80410 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −497.192 | −1.36511 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −169.104 | −0.438269 | −0.219135 | − | 0.975695i | \(-0.570323\pi\) | ||||
−0.219135 | + | 0.975695i | \(0.570323\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 51.7261 | 0.126814 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1543.87 | −3.58755 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −569.745 | −1.25719 | −0.628597 | − | 0.777731i | \(-0.716370\pi\) | ||||
−0.628597 | + | 0.777731i | \(0.716370\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 500.616 | 1.05078 | 0.525388 | − | 0.850863i | \(-0.323920\pi\) | ||||
0.525388 | + | 0.850863i | \(0.323920\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2094.38 | −4.18837 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −201.273 | −0.384074 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 335.555 | 0.611859 | 0.305930 | − | 0.952054i | \(-0.401033\pi\) | ||||
0.305930 | + | 0.952054i | \(0.401033\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1259.04 | 2.19668 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −958.137 | −1.60155 | −0.800774 | − | 0.598966i | \(-0.795578\pi\) | ||||
−0.800774 | + | 0.598966i | \(0.795578\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −946.043 | −1.51679 | −0.758397 | − | 0.651793i | \(-0.774017\pi\) | ||||
−0.758397 | + | 0.651793i | \(0.774017\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 832.874 | 1.28229 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −255.769 | −0.378541 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 179.326 | 0.255389 | 0.127694 | − | 0.991814i | \(-0.459242\pi\) | ||||
0.127694 | + | 0.991814i | \(0.459242\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2008.24 | 2.75479 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −285.090 | −0.377020 | −0.188510 | − | 0.982071i | \(-0.560366\pi\) | ||||
−0.188510 | + | 0.982071i | \(0.560366\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 320.730 | 0.409271 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 281.960 | 0.347464 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 832.078 | 0.991013 | 0.495506 | − | 0.868604i | \(-0.334983\pi\) | ||||
0.495506 | + | 0.868604i | \(0.334983\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 995.231 | 1.14647 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −142.367 | −0.158740 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 995.921 | 1.07557 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −908.370 | −0.950835 | −0.475417 | − | 0.879760i | \(-0.657703\pi\) | ||||
−0.475417 | + | 0.879760i | \(0.657703\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 556.950 | 0.565410 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −996.317 | −0.981557 | −0.490778 | − | 0.871284i | \(-0.663288\pi\) | ||||
−0.490778 | + | 0.871284i | \(0.663288\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1295.46 | −1.23928 | −0.619639 | − | 0.784887i | \(-0.712721\pi\) | ||||
−0.619639 | + | 0.784887i | \(0.712721\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1891.21 | 1.75774 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1276.23 | 1.15307 | 0.576533 | − | 0.817074i | \(-0.304405\pi\) | ||||
0.576533 | + | 0.817074i | \(0.304405\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1481.99 | −1.30228 | −0.651141 | − | 0.758957i | \(-0.725709\pi\) | ||||
−0.651141 | + | 0.758957i | \(0.725709\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2502.62 | −2.13998 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 565.572 | 0.470837 | 0.235418 | − | 0.971894i | \(-0.424354\pi\) | ||||
0.235418 | + | 0.971894i | \(0.424354\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −812.187 | −0.658581 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2167.16 | −1.71243 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1585.91 | −1.22168 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1262.98 | −0.948899 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 252.995 | 0.185461 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1321.27 | −0.945424 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2132.64 | 1.49009 | 0.745045 | − | 0.667014i | \(-0.232428\pi\) | ||||
0.745045 | + | 0.667014i | \(0.232428\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −33.0911 | −0.0225853 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2518.91 | 1.67999 | 0.839993 | − | 0.542598i | \(-0.182559\pi\) | ||||
0.839993 | + | 0.542598i | \(0.182559\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4924.52 | −3.21060 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2471.71 | −1.57578 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −57.5792 | −0.0359075 | −0.0179537 | − | 0.999839i | \(-0.505715\pi\) | ||||
−0.0179537 | + | 0.999839i | \(0.505715\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1250.64 | −0.763148 | −0.381574 | − | 0.924338i | \(-0.624618\pi\) | ||||
−0.381574 | + | 0.924338i | \(0.624618\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4688.59 | 2.80036 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −264.658 | −0.154768 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −181.888 | −0.104172 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6016.52 | −3.37575 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1811.93 | 0.996235 | 0.498118 | − | 0.867109i | \(-0.334025\pi\) | ||||
0.498118 | + | 0.867109i | \(0.334025\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −680.525 | −0.366757 | −0.183379 | − | 0.983042i | \(-0.558703\pi\) | ||||
−0.183379 | + | 0.983042i | \(0.558703\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3453.39 | 1.82477 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 91.8385 | 0.0475912 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1422.01 | 0.722858 | 0.361429 | − | 0.932400i | \(-0.382289\pi\) | ||||
0.361429 | + | 0.932400i | \(0.382289\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1644.16 | 0.820066 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4016.01 | 1.96588 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3154.01 | −1.51559 | −0.757794 | − | 0.652493i | \(-0.773723\pi\) | ||||
−0.757794 | + | 0.652493i | \(0.773723\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −502.921 | −0.237287 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1539.64 | 0.713417 | 0.356708 | − | 0.934216i | \(-0.383899\pi\) | ||||
0.356708 | + | 0.934216i | \(0.383899\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1167.18 | −0.531263 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 10723.4 | 4.79554 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2816.06 | −1.23758 | −0.618789 | − | 0.785557i | \(-0.712376\pi\) | ||||
−0.618789 | + | 0.785557i | \(0.712376\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2656.64 | 1.14756 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5539.50 | 2.35240 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3564.28 | −1.48830 | −0.744152 | − | 0.668010i | \(-0.767146\pi\) | ||||
−0.744152 | + | 0.668010i | \(0.767146\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 261.021 | 0.107191 | 0.0535953 | − | 0.998563i | \(-0.482932\pi\) | ||||
0.0535953 | + | 0.998563i | \(0.482932\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4867.38 | −1.96616 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1614.40 | 0.641583 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 421.734 | 0.164921 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 12221.8 | 4.70373 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2242.54 | 0.849551 | 0.424776 | − | 0.905299i | \(-0.360353\pi\) | ||||
0.424776 | + | 0.905299i | \(0.360353\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 120.858 | 0.0450752 | 0.0225376 | − | 0.999746i | \(-0.492825\pi\) | ||||
0.0225376 | + | 0.999746i | \(0.492825\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1956.93 | 0.718660 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 864.591 | 0.312688 | 0.156344 | − | 0.987703i | \(-0.450029\pi\) | ||||
0.156344 | + | 0.987703i | \(0.450029\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4885.39 | 1.74028 | 0.870140 | − | 0.492804i | \(-0.164028\pi\) | ||||
0.870140 | + | 0.492804i | \(0.164028\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3262.52 | −1.14488 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 899.378 | 0.310955 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −163.202 | −0.0556027 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −8745.06 | −2.93634 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1309.56 | 0.433416 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5261.82 | 1.71677 | 0.858386 | − | 0.513005i | \(-0.171468\pi\) | ||||
0.858386 | + | 0.513005i | \(0.171468\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9315.75 | 2.99673 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 21.3465 | 0.00677125 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −454.112 | −0.142061 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9198.16 | 2.83815 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1641.02 | −0.499489 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2726.49 | −0.818740 | −0.409370 | − | 0.912368i | \(-0.634252\pi\) | ||||
−0.409370 | + | 0.912368i | \(0.634252\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −5784.96 | −1.71406 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6079.66 | 1.77763 | 0.888813 | − | 0.458270i | \(-0.151531\pi\) | ||||
0.888813 | + | 0.458270i | \(0.151531\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −538.146 | −0.155291 | −0.0776456 | − | 0.996981i | \(-0.524740\pi\) | ||||
−0.0776456 | + | 0.996981i | \(0.524740\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2486.79 | 0.708306 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2834.78 | 0.797051 | 0.398525 | − | 0.917157i | \(-0.369522\pi\) | ||||
0.398525 | + | 0.917157i | \(0.369522\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3024.53 | −0.839568 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1743.54 | −0.477870 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 354.937 | 0.0960627 | 0.0480313 | − | 0.998846i | \(-0.484705\pi\) | ||||
0.0480313 | + | 0.998846i | \(0.484705\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4887.24 | 1.30628 | 0.653142 | − | 0.757235i | \(-0.273450\pi\) | ||||
0.653142 | + | 0.757235i | \(0.273450\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −8885.33 | −2.34565 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3881.15 | 1.01207 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5095.65 | −1.31267 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2771.86 | 0.705461 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −250.836 | −0.0630783 | −0.0315391 | − | 0.999503i | \(-0.510041\pi\) | ||||
−0.0315391 | + | 0.999503i | \(0.510041\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1067.96 | −0.265384 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3118.38 | −0.765807 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 721.700 | 0.175169 | 0.0875845 | − | 0.996157i | \(-0.472085\pi\) | ||||
0.0875845 | + | 0.996157i | \(0.472085\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7982.68 | −1.91513 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1958.44 | −0.464461 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3765.00 | 0.882737 | 0.441368 | − | 0.897326i | \(-0.354493\pi\) | ||||
0.441368 | + | 0.897326i | \(0.354493\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1060.62 | −0.245862 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8090.11 | −1.85433 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −552.384 | −0.125202 | −0.0626012 | − | 0.998039i | \(-0.519940\pi\) | ||||
−0.0626012 | + | 0.998039i | \(0.519940\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5370.32 | 1.20378 | 0.601888 | − | 0.798580i | \(-0.294415\pi\) | ||||
0.601888 | + | 0.798580i | \(0.294415\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −9676.40 | −2.14521 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −706.470 | −0.154915 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3413.04 | 0.740324 | 0.370162 | − | 0.928967i | \(-0.379302\pi\) | ||||
0.370162 | + | 0.928967i | \(0.379302\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 988.851 | 0.212190 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6727.56 | −1.42823 | −0.714115 | − | 0.700028i | \(-0.753171\pi\) | ||||
−0.714115 | + | 0.700028i | \(0.753171\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8718.25 | 1.83126 | 0.915630 | − | 0.402023i | \(-0.131693\pi\) | ||||
0.915630 | + | 0.402023i | \(0.131693\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −9683.11 | −2.01256 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 806.984 | 0.165975 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2298.02 | −0.467742 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8831.87 | 1.77915 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1279.00 | −0.255018 | −0.127509 | − | 0.991837i | \(-0.540698\pi\) | ||||
−0.127509 | + | 0.991837i | \(0.540698\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3573.43 | −0.705265 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3250.09 | −0.634982 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4155.57 | 0.803755 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −105.552 | −0.0202123 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 9686.96 | 1.83664 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3139.86 | 0.589468 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8483.52 | −1.57713 | −0.788567 | − | 0.614949i | \(-0.789177\pi\) | ||||
−0.788567 | + | 0.614949i | \(0.789177\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 12595.5 | 2.31887 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7130.60 | 1.30013 | 0.650063 | − | 0.759880i | \(-0.274743\pi\) | ||||
0.650063 | + | 0.759880i | \(0.274743\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3430.86 | 0.619565 | 0.309782 | − | 0.950808i | \(-0.399744\pi\) | ||||
0.309782 | + | 0.950808i | \(0.399744\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −13135.9 | −2.34961 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7352.21 | −1.30265 | −0.651327 | − | 0.758797i | \(-0.725787\pi\) | ||||
−0.651327 | + | 0.758797i | \(0.725787\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −239.168 | −0.0419775 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12408.5 | −2.15756 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8119.96 | 1.39878 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2748.96 | 0.469185 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 14409.0 | 2.43676 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 14955.3 | 2.50612 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5975.85 | 0.992333 | 0.496166 | − | 0.868227i | \(-0.334741\pi\) | ||||
0.496166 | + | 0.868227i | \(0.334741\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 17382.7 | 2.86055 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2104.60 | 0.343243 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6455.18 | 1.04343 | 0.521715 | − | 0.853120i | \(-0.325292\pi\) | ||||
0.521715 | + | 0.853120i | \(0.325292\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5498.93 | −0.881005 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 120.760 | 0.0191775 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8553.62 | −1.34651 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 7896.71 | 1.23230 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12624.0 | 1.95300 | 0.976502 | − | 0.215509i | \(-0.0691410\pi\) | ||||
0.976502 | + | 0.215509i | \(0.0691410\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 35.6888 | 0.00547386 | 0.00273693 | − | 0.999996i | \(-0.499129\pi\) | ||||
0.00273693 | + | 0.999996i | \(0.499129\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 12646.5 | 1.92314 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −639.322 | −0.0963957 | −0.0481978 | − | 0.998838i | \(-0.515348\pi\) | ||||
−0.0481978 | + | 0.998838i | \(0.515348\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6009.42 | −0.898443 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 15419.4 | 2.28595 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7152.10 | −1.05146 | −0.525729 | − | 0.850652i | \(-0.676207\pi\) | ||||
−0.525729 | + | 0.850652i | \(0.676207\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18354.9 | 2.67603 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 12279.7 | 1.77553 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5933.57 | −0.850897 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6894.06 | 0.980564 | 0.490282 | − | 0.871564i | \(-0.336894\pi\) | ||||
0.490282 | + | 0.871564i | \(0.336894\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1757.25 | −0.247909 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5244.43 | 0.733902 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8479.89 | 1.17714 | 0.588569 | − | 0.808447i | \(-0.299692\pi\) | ||||
0.588569 | + | 0.808447i | \(0.299692\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 12846.4 | 1.76903 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 930.631 | 0.127135 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4935.89 | −0.668970 | −0.334485 | − | 0.942401i | \(-0.608562\pi\) | ||||
−0.334485 | + | 0.942401i | \(0.608562\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −20735.2 | −2.78818 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1790.95 | −0.238938 | −0.119469 | − | 0.992838i | \(-0.538119\pi\) | ||||
−0.119469 | + | 0.992838i | \(0.538119\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1604.18 | −0.212355 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 229.844 | 0.0301902 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6332.31 | 0.825350 | 0.412675 | − | 0.910878i | \(-0.364595\pi\) | ||||
0.412675 | + | 0.910878i | \(0.364595\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6621.94 | −0.856486 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −24490.8 | −3.14350 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1124.73 | 0.143269 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14324.5 | −1.81089 | −0.905446 | − | 0.424462i | \(-0.860463\pi\) | ||||
−0.905446 | + | 0.424462i | \(0.860463\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 47880.0 | 6.00751 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6430.30 | 0.800783 | 0.400392 | − | 0.916344i | \(-0.368874\pi\) | ||||
0.400392 | + | 0.916344i | \(0.368874\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −469.893 | −0.0580820 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 12595.7 | 1.54539 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2122.80 | 0.258534 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 44.4605 | 0.00537513 | 0.00268757 | − | 0.999996i | \(-0.499145\pi\) | ||||
0.00268757 | + | 0.999996i | \(0.499145\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 559.830 | 0.0671882 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 17669.5 | 2.10523 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1788.08 | −0.211502 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12159.7 | 1.42796 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −23.4862 | −0.00273837 | −0.00136918 | − | 0.999999i | \(-0.500436\pi\) | ||||
−0.00136918 | + | 0.999999i | \(0.500436\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3365.39 | −0.389594 | −0.194797 | − | 0.980844i | \(-0.562405\pi\) | ||||
−0.194797 | + | 0.980844i | \(0.562405\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −32566.0 | −3.74329 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4380.50 | −0.499965 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −15525.6 | −1.75957 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2573.21 | 0.289593 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9557.80 | 1.06817 | 0.534087 | − | 0.845429i | \(-0.320655\pi\) | ||||
0.534087 | + | 0.845429i | \(0.320655\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11660.3 | 1.29413 | 0.647065 | − | 0.762435i | \(-0.275996\pi\) | ||||
0.647065 | + | 0.762435i | \(0.275996\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1768.45 | 0.194921 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −20562.3 | −2.25086 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16716.4 | −1.81738 | −0.908689 | − | 0.417474i | \(-0.862916\pi\) | ||||
−0.908689 | + | 0.417474i | \(0.862916\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 41789.5 | 4.51242 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −367.759 | −0.0394419 | −0.0197209 | − | 0.999806i | \(-0.506278\pi\) | ||||
−0.0197209 | + | 0.999806i | \(0.506278\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5218.79 | 0.555942 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −17617.0 | −1.86410 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4823.82 | −0.507015 | −0.253508 | − | 0.967333i | \(-0.581584\pi\) | ||||
−0.253508 | + | 0.967333i | \(0.581584\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −214.598 | −0.0224058 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6616.59 | 0.686257 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6242.08 | 0.643150 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2785.87 | −0.285159 | −0.142579 | − | 0.989783i | \(-0.545540\pi\) | ||||
−0.142579 | + | 0.989783i | \(0.545540\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −20152.4 | −2.04931 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9052.88 | 0.914608 | 0.457304 | − | 0.889310i | \(-0.348815\pi\) | ||||
0.457304 | + | 0.889310i | \(0.348815\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3825.06 | −0.383943 | −0.191972 | − | 0.981400i | \(-0.561488\pi\) | ||||
−0.191972 | + | 0.981400i | \(0.561488\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −892.924 | −0.0890503 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3943.34 | 0.390741 | 0.195371 | − | 0.980729i | \(-0.437409\pi\) | ||||
0.195371 | + | 0.980729i | \(0.437409\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10406.6 | −1.02459 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −13825.9 | −1.35258 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 28.0689 | 0.00272856 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −13602.2 | −1.31392 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −11420.0 | −1.09620 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7621.40 | −0.726995 | −0.363497 | − | 0.931595i | \(-0.618417\pi\) | ||||
−0.363497 | + | 0.931595i | \(0.618417\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8260.09 | −0.783009 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −39046.8 | −3.67845 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5697.28 | −0.533403 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2939.21 | −0.273488 | −0.136744 | − | 0.990606i | \(-0.543664\pi\) | ||||
−0.136744 | + | 0.990606i | \(0.543664\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 30665.7 | 2.83589 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −21365.5 | −1.96377 | −0.981886 | − | 0.189473i | \(-0.939322\pi\) | ||||
−0.981886 | + | 0.189473i | \(0.939322\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1482.97 | −0.135476 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3493.18 | 0.317186 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 29714.7 | 2.68187 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5450.33 | 0.488958 | 0.244479 | − | 0.969655i | \(-0.421383\pi\) | ||||
0.244479 | + | 0.969655i | \(0.421383\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −14969.5 | −1.33491 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −19531.8 | −1.73137 | −0.865686 | − | 0.500587i | \(-0.833118\pi\) | ||||
−0.865686 | + | 0.500587i | \(0.833118\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6248.89 | −0.550637 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 11348.3 | 0.994072 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7726.61 | −0.672841 | −0.336420 | − | 0.941712i | \(-0.609216\pi\) | ||||
−0.336420 | + | 0.941712i | \(0.609216\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 29339.7 | 2.53994 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −62576.5 | −5.38561 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8125.12 | −0.695215 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3977.01 | −0.338315 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 27379.9 | 2.31569 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7915.18 | −0.665586 | −0.332793 | − | 0.943000i | \(-0.607991\pi\) | ||||
−0.332793 | + | 0.943000i | \(0.607991\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8078.88 | 0.675459 | 0.337729 | − | 0.941243i | \(-0.390341\pi\) | ||||
0.337729 | + | 0.941243i | \(0.390341\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −25829.9 | −2.14726 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 748.779 | 0.0618925 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4601.80 | 0.378220 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −38476.2 | −3.14449 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 835.028 | 0.0678594 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8004.51 | 0.646851 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 34654.6 | 2.78484 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5103.41 | 0.407828 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12220.5 | 0.971163 | 0.485582 | − | 0.874191i | \(-0.338608\pi\) | ||||
0.485582 | + | 0.874191i | \(0.338608\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2537.84 | −0.200570 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9295.01 | −0.730559 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6172.25 | 0.482462 | 0.241231 | − | 0.970468i | \(-0.422449\pi\) | ||||
0.241231 | + | 0.970468i | \(0.422449\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 33807.8 | 2.62820 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4604.87 | −0.356033 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5561.43 | −0.427660 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −15696.4 | −1.20050 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3103.59 | 0.236092 | 0.118046 | − | 0.993008i | \(-0.462337\pi\) | ||||
0.118046 | + | 0.993008i | \(0.462337\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −109.220 | −0.00826386 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4100.43 | −0.308592 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 21390.9 | 1.60128 | 0.800639 | − | 0.599147i | \(-0.204494\pi\) | ||||
0.800639 | + | 0.599147i | \(0.204494\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3547.26 | 0.264132 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −62281.6 | −4.61302 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −23212.7 | −1.71024 | −0.855120 | − | 0.518431i | \(-0.826516\pi\) | ||||
−0.855120 | + | 0.518431i | \(0.826516\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11439.8 | −0.838424 | −0.419212 | − | 0.907888i | \(-0.637694\pi\) | ||||
−0.419212 | + | 0.907888i | \(0.637694\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −21803.7 | −1.58964 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 11092.8 | 0.804523 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8568.11 | −0.618189 | −0.309095 | − | 0.951031i | \(-0.600026\pi\) | ||||
−0.309095 | + | 0.951031i | \(0.600026\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1175.07 | −0.0843425 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8841.50 | 0.631338 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1394.63 | −0.0990732 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −13592.4 | −0.960645 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2184.34 | −0.153590 | −0.0767950 | − | 0.997047i | \(-0.524469\pi\) | ||||
−0.0767950 | + | 0.997047i | \(0.524469\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2325.09 | 0.162655 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8406.22 | −0.585086 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8518.37 | −0.589895 | −0.294947 | − | 0.955513i | \(-0.595302\pi\) | ||||
−0.294947 | + | 0.955513i | \(0.595302\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9946.81 | −0.685343 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −47499.5 | −3.25632 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 17697.5 | 1.20718 | 0.603591 | − | 0.797294i | \(-0.293736\pi\) | ||||
0.603591 | + | 0.797294i | \(0.293736\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25751.4 | 1.74779 | 0.873894 | − | 0.486116i | \(-0.161587\pi\) | ||||
0.873894 | + | 0.486116i | \(0.161587\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 22660.8 | 1.53038 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7921.42 | −0.532317 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12644.9 | −0.845538 | −0.422769 | − | 0.906238i | \(-0.638942\pi\) | ||||
−0.422769 | + | 0.906238i | \(0.638942\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −8744.44 | −0.581844 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 15475.1 | 1.02464 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −18792.6 | −1.23821 | −0.619107 | − | 0.785307i | \(-0.712505\pi\) | ||||
−0.619107 | + | 0.785307i | \(0.712505\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1586.78 | 0.104041 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8630.30 | −0.563116 | −0.281558 | − | 0.959544i | \(-0.590851\pi\) | ||||
−0.281558 | + | 0.959544i | \(0.590851\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 26553.4 | 1.72419 | 0.862094 | − | 0.506748i | \(-0.169153\pi\) | ||||
0.862094 | + | 0.506748i | \(0.169153\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 51032.0 | 3.29765 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −25805.3 | −1.65950 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2420.78 | 0.154930 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −12732.5 | −0.810985 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 13162.5 | 0.834379 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18310.6 | −1.15521 | −0.577603 | − | 0.816318i | \(-0.696012\pi\) | ||||
−0.577603 | + | 0.816318i | \(0.696012\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −51159.5 | −3.21233 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 13375.9 | 0.835916 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −19858.0 | −1.23517 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −64705.2 | −4.00579 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7753.98 | −0.477790 | −0.238895 | − | 0.971045i | \(-0.576785\pi\) | ||||
−0.238895 | + | 0.971045i | \(0.576785\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24720.7 | −1.51616 | −0.758078 | − | 0.652163i | \(-0.773862\pi\) | ||||
−0.758078 | + | 0.652163i | \(0.773862\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −207.547 | −0.0126700 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −10318.0 | −0.626957 | −0.313478 | − | 0.949595i | \(-0.601494\pi\) | ||||
−0.313478 | + | 0.949595i | \(0.601494\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4698.78 | −0.284196 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4415.23 | 0.265817 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 15277.3 | 0.915542 | 0.457771 | − | 0.889070i | \(-0.348648\pi\) | ||||
0.457771 | + | 0.889070i | \(0.348648\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 15798.6 | 0.942444 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −63888.5 | −3.79380 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9600.60 | 0.567506 | 0.283753 | − | 0.958897i | \(-0.408420\pi\) | ||||
0.283753 | + | 0.958897i | \(0.408420\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6812.43 | −0.400866 | −0.200433 | − | 0.979707i | \(-0.564235\pi\) | ||||
−0.200433 | + | 0.979707i | \(0.564235\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 15955.3 | 0.934617 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −30886.5 | −1.80109 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3755.34 | 0.218002 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 26509.0 | 1.53198 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4128.66 | 0.237534 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9459.01 | 0.541780 | 0.270890 | − | 0.962610i | \(-0.412682\pi\) | ||||
0.270890 | + | 0.962610i | \(0.412682\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 33758.3 | 1.92497 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 25231.8 | 1.43241 | 0.716203 | − | 0.697892i | \(-0.245879\pi\) | ||||
0.716203 | + | 0.697892i | \(0.245879\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 28171.3 | 1.59222 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −59111.1 | −3.32620 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −16443.6 | −0.921226 | −0.460613 | − | 0.887601i | \(-0.652370\pi\) | ||||
−0.460613 | + | 0.887601i | \(0.652370\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −361.136 | −0.0201435 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5232.27 | 0.290573 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5426.68 | 0.300058 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8693.86 | 0.478625 | 0.239313 | − | 0.970943i | \(-0.423078\pi\) | ||||
0.239313 | + | 0.970943i | \(0.423078\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −17272.7 | −0.946805 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7843.98 | −0.428114 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1330.62 | −0.0723113 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −27562.0 | −1.49140 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2006.88 | 0.108130 | 0.0540648 | − | 0.998537i | \(-0.482782\pi\) | ||||
0.0540648 | + | 0.998537i | \(0.482782\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 40871.9 | 2.19276 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 29406.8 | 1.57096 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 30898.8 | 1.64366 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10597.0 | 0.561322 | 0.280661 | − | 0.959807i | \(-0.409446\pi\) | ||||
0.280661 | + | 0.959807i | \(0.409446\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12110.3 | 0.638778 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1896.14 | −0.0995947 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1659.93 | −0.0868221 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3450.97 | −0.179748 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2248.05 | 0.116604 | 0.0583020 | − | 0.998299i | \(-0.481431\pi\) | ||||
0.0583020 | + | 0.998299i | \(0.481431\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 40176.2 | 2.07523 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −47517.5 | −2.44425 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2484.20 | 0.127257 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26960.8 | 1.37541 | 0.687704 | − | 0.725991i | \(-0.258619\pi\) | ||||
0.687704 | + | 0.725991i | \(0.258619\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 32167.5 | 1.63428 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 174.043 | 0.00880601 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10345.6 | −0.521317 | −0.260658 | − | 0.965431i | \(-0.583940\pi\) | ||||
−0.260658 | + | 0.965431i | \(0.583940\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −37735.6 | −1.89374 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2767.38 | 0.138314 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11942.7 | 0.594479 | 0.297239 | − | 0.954803i | \(-0.403934\pi\) | ||||
0.297239 | + | 0.954803i | \(0.403934\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 49543.8 | 2.45619 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1334.16 | −0.0658754 | −0.0329377 | − | 0.999457i | \(-0.510486\pi\) | ||||
−0.0329377 | + | 0.999457i | \(0.510486\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11364.4 | 0.558872 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −19252.8 | −0.943002 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −39579.8 | −1.93086 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17347.0 | 0.842876 | 0.421438 | − | 0.906857i | \(-0.361526\pi\) | ||||
0.421438 | + | 0.906857i | \(0.361526\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2438.82 | 0.118029 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4268.25 | −0.205745 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5359.59 | −0.257328 | −0.128664 | − | 0.991688i | \(-0.541069\pi\) | ||||
−0.128664 | + | 0.991688i | \(0.541069\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 10383.5 | 0.496573 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10355.3 | 0.493272 | 0.246636 | − | 0.969108i | \(-0.420675\pi\) | ||||
0.246636 | + | 0.969108i | \(0.420675\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 45960.9 | 2.18073 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 21659.6 | 1.02367 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 18283.5 | 0.860730 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9339.42 | −0.437956 | −0.218978 | − | 0.975730i | \(-0.570272\pi\) | ||||
−0.218978 | + | 0.975730i | \(0.570272\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7016.93 | −0.327767 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −21743.9 | −1.01174 | −0.505869 | − | 0.862610i | \(-0.668828\pi\) | ||||
−0.505869 | + | 0.862610i | \(0.668828\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1254.32 | −0.0581374 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 77613.8 | 3.58350 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4131.81 | −0.190035 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7901.91 | −0.362039 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 11428.5 | 0.521611 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8918.83 | 0.405512 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 26378.6 | 1.19478 | 0.597391 | − | 0.801950i | \(-0.296204\pi\) | ||||
0.597391 | + | 0.801950i | \(0.296204\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −36606.2 | −1.65173 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −17540.1 | −0.788438 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16065.1 | −0.719407 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 10312.2 | 0.460044 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 36134.8 | 1.60597 | 0.802986 | − | 0.595999i | \(-0.203244\pi\) | ||||
0.802986 | + | 0.595999i | \(0.203244\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −24659.6 | −1.09186 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 56192.2 | 2.47872 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7802.17 | −0.342880 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 25188.4 | 1.10282 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5370.70 | 0.234272 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 368.546 | 0.0160166 | 0.00800828 | − | 0.999968i | \(-0.497451\pi\) | ||||
0.00800828 | + | 0.999968i | \(0.497451\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24252.1 | 1.05007 | 0.525034 | − | 0.851081i | \(-0.324052\pi\) | ||||
0.525034 | + | 0.851081i | \(0.324052\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −52214.4 | −2.25244 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −19781.9 | −0.850221 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 540.432 | 0.0231424 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 67210.2 | 2.86754 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8693.57 | −0.369559 | −0.184779 | − | 0.982780i | \(-0.559157\pi\) | ||||
−0.184779 | + | 0.982780i | \(0.559157\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4674.45 | −0.197984 | −0.0989922 | − | 0.995088i | \(-0.531562\pi\) | ||||
−0.0989922 | + | 0.995088i | \(0.531562\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6868.84 | 0.289870 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 18877.2 | 0.793740 | 0.396870 | − | 0.917875i | \(-0.370096\pi\) | ||||
0.396870 | + | 0.917875i | \(0.370096\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −30674.6 | −1.28513 | −0.642565 | − | 0.766231i | \(-0.722130\pi\) | ||||
−0.642565 | + | 0.766231i | \(0.722130\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −33184.2 | −1.38526 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 31643.9 | 1.31620 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9656.58 | 0.400215 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5770.46 | −0.238299 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6238.05 | 0.256688 | 0.128344 | − | 0.991730i | \(-0.459034\pi\) | ||||
0.128344 | + | 0.991730i | \(0.459034\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 841.000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 65410.5 | 2.67243 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7320.57 | −0.298030 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 39169.0 | 1.58897 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −84765.6 | −3.42656 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −33331.6 | −1.34265 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16138.1 | 0.647780 | 0.323890 | − | 0.946095i | \(-0.395009\pi\) | ||||
0.323890 | + | 0.946095i | \(0.395009\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 67256.9 | 2.69022 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 47596.5 | 1.89716 | 0.948579 | − | 0.316541i | \(-0.102522\pi\) | ||||
0.948579 | + | 0.316541i | \(0.102522\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 572.644 | 0.0227455 | 0.0113727 | − | 0.999935i | \(-0.496380\pi\) | ||||
0.0113727 | + | 0.999935i | \(0.496380\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7846.13 | −0.310564 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −23203.3 | −0.915237 | −0.457619 | − | 0.889149i | \(-0.651297\pi\) | ||||
−0.457619 | + | 0.889149i | \(0.651297\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −17662.3 | −0.694261 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 22343.1 | 0.875215 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1478.93 | 0.0577321 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10768.2 | −0.418906 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −61344.3 | −2.37822 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 40976.6 | 1.58316 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 41334.1 | 1.59151 | 0.795755 | − | 0.605619i | \(-0.207074\pi\) | ||||
0.795755 | + | 0.605619i | \(0.207074\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 12435.5 | 0.477176 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −30870.9 | −1.18055 | −0.590276 | − | 0.807202i | \(-0.700981\pi\) | ||||
−0.590276 | + | 0.807202i | \(0.700981\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11615.6 | −0.442691 | −0.221346 | − | 0.975195i | \(-0.571045\pi\) | ||||
−0.221346 | + | 0.975195i | \(0.571045\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 34743.7 | 1.31966 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 9853.82 | 0.373009 | 0.186505 | − | 0.982454i | \(-0.440284\pi\) | ||||
0.186505 | + | 0.982454i | \(0.440284\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −66139.7 | −2.49522 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 16562.3 | 0.622735 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −76572.4 | −2.86942 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −22355.1 | −0.834914 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −40403.7 | −1.50395 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −424.637 | −0.0157535 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8647.47 | −0.319744 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1026.26 | 0.0378202 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1637.12 | 0.0601322 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10244.0 | −0.375024 | −0.187512 | − | 0.982262i | \(-0.560042\pi\) | ||||
−0.187512 | + | 0.982262i | \(0.560042\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −67283.6 | −2.45507 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −20813.9 | −0.756966 | −0.378483 | − | 0.925608i | \(-0.623554\pi\) | ||||
−0.378483 | + | 0.925608i | \(0.623554\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2351.18 | −0.0852276 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −30528.1 | −1.10298 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −78119.0 | −2.81321 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9794.71 | 0.351575 | 0.175788 | − | 0.984428i | \(-0.443753\pi\) | ||||
0.175788 | + | 0.984428i | \(0.443753\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 82483.3 | 2.95105 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 30747.3 | 1.09649 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −22049.3 | −0.783757 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −87485.5 | −3.09968 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −29395.4 | −1.03814 | −0.519070 | − | 0.854732i | \(-0.673722\pi\) | ||||
−0.519070 | + | 0.854732i | \(0.673722\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 98259.7 | 3.45900 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −69329.2 | −2.43273 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2645.11 | 0.0925181 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 50174.1 | 1.74932 | 0.874661 | − | 0.484735i | \(-0.161084\pi\) | ||||
0.874661 | + | 0.484735i | \(0.161084\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −33357.5 | −1.15930 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 37984.8 | 1.31591 | 0.657955 | − | 0.753058i | \(-0.271422\pi\) | ||||
0.657955 | + | 0.753058i | \(0.271422\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3369.55 | 0.116360 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 76655.0 | 2.63872 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 15217.3 | 0.522171 | 0.261085 | − | 0.965316i | \(-0.415920\pi\) | ||||
0.261085 | + | 0.965316i | \(0.415920\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 30359.2 | 1.03846 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 71483.9 | 2.43746 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 17012.1 | 0.578253 | 0.289126 | − | 0.957291i | \(-0.406635\pi\) | ||||
0.289126 | + | 0.957291i | \(0.406635\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 14065.2 | 0.476584 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2325.37 | 0.0785461 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1785.71 | 0.0601287 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29576.6 | −0.992803 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 86186.9 | 2.88404 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 758.018 | 0.0252865 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 37192.8 | 1.23686 | 0.618428 | − | 0.785841i | \(-0.287770\pi\) | ||||
0.618428 | + | 0.785841i | \(0.287770\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −78948.5 | −2.61733 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 55741.1 | 1.84224 | 0.921121 | − | 0.389276i | \(-0.127275\pi\) | ||||
0.921121 | + | 0.389276i | \(0.127275\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 38786.0 | 1.27793 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −26727.5 | −0.877914 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 7356.33 | 0.240890 | 0.120445 | − | 0.992720i | \(-0.461568\pi\) | ||||
0.120445 | + | 0.992720i | \(0.461568\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6862.29 | 0.224024 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −100082. | −3.25726 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1951.93 | −0.0633337 | −0.0316668 | − | 0.999498i | \(-0.510082\pi\) | ||||
−0.0316668 | + | 0.999498i | \(0.510082\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5422.70 | 0.175413 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −145407. | −4.68933 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −440.729 | −0.0141703 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 31606.2 | 1.01312 | 0.506561 | − | 0.862204i | \(-0.330917\pi\) | ||||
0.506561 | + | 0.862204i | \(0.330917\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −58101.8 | −1.85680 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 30641.1 | 0.976269 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6443.52 | 0.204682 | 0.102341 | − | 0.994749i | \(-0.467367\pi\) | ||||
0.102341 | + | 0.994749i | \(0.467367\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −101437. | −3.21254 |
(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 | 1856.4.a.bl.1.1 | 12 | ||
4.3 | odd | 2 | 1856.4.a.bj.1.12 | 12 | |||
8.3 | odd | 2 | 928.4.a.j.1.1 | yes | 12 | ||
8.5 | even | 2 | 928.4.a.h.1.12 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
928.4.a.h.1.12 | ✓ | 12 | 8.5 | even | 2 | ||
928.4.a.j.1.1 | yes | 12 | 8.3 | odd | 2 | ||
1856.4.a.bj.1.12 | 12 | 4.3 | odd | 2 | |||
1856.4.a.bl.1.1 | 12 | 1.1 | even | 1 | trivial |