Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [735,4,Mod(1,735)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(735, 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("735.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 735 = 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 735.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: | \(43.3664038542\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 105) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 735.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.23607 | −1.49768 | −0.748838 | − | 0.662753i | \(-0.769388\pi\) | ||||
−0.748838 | + | 0.662753i | \(0.769388\pi\) | |||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 9.94427 | 1.24303 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 12.7082 | 0.864684 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −8.23607 | −0.363986 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −21.1803 | −0.669781 | ||||||||
\(11\) | −41.5279 | −1.13828 | −0.569142 | − | 0.822239i | \(-0.692725\pi\) | ||||
−0.569142 | + | 0.822239i | \(0.692725\pi\) | |||||||
\(12\) | −29.8328 | −0.717666 | ||||||||
\(13\) | −88.9706 | −1.89815 | −0.949077 | − | 0.315044i | \(-0.897981\pi\) | ||||
−0.949077 | + | 0.315044i | \(0.897981\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −15.0000 | −0.258199 | ||||||||
\(16\) | −44.6656 | −0.697900 | ||||||||
\(17\) | 120.387 | 1.71754 | 0.858769 | − | 0.512364i | \(-0.171230\pi\) | ||||
0.858769 | + | 0.512364i | \(0.171230\pi\) | |||||||
\(18\) | −38.1246 | −0.499225 | ||||||||
\(19\) | 112.138 | 1.35401 | 0.677004 | − | 0.735979i | \(-0.263278\pi\) | ||||
0.677004 | + | 0.735979i | \(0.263278\pi\) | |||||||
\(20\) | 49.7214 | 0.555902 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 175.915 | 1.70478 | ||||||||
\(23\) | −115.279 | −1.04510 | −0.522549 | − | 0.852609i | \(-0.675019\pi\) | ||||
−0.522549 | + | 0.852609i | \(0.675019\pi\) | |||||||
\(24\) | 24.7082 | 0.210148 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 376.885 | 2.84282 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −144.833 | −0.927406 | −0.463703 | − | 0.885991i | \(-0.653480\pi\) | ||||
−0.463703 | + | 0.885991i | \(0.653480\pi\) | |||||||
\(30\) | 63.5410 | 0.386698 | ||||||||
\(31\) | 258.079 | 1.49524 | 0.747618 | − | 0.664128i | \(-0.231197\pi\) | ||||
0.747618 | + | 0.664128i | \(0.231197\pi\) | |||||||
\(32\) | 255.095 | 1.40922 | ||||||||
\(33\) | 124.584 | 0.657188 | ||||||||
\(34\) | −509.967 | −2.57231 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 89.4984 | 0.414345 | ||||||||
\(37\) | 48.3344 | 0.214760 | 0.107380 | − | 0.994218i | \(-0.465754\pi\) | ||||
0.107380 | + | 0.994218i | \(0.465754\pi\) | |||||||
\(38\) | −475.023 | −2.02787 | ||||||||
\(39\) | 266.912 | 1.09590 | ||||||||
\(40\) | −41.1803 | −0.162780 | ||||||||
\(41\) | −200.885 | −0.765196 | −0.382598 | − | 0.923915i | \(-0.624971\pi\) | ||||
−0.382598 | + | 0.923915i | \(0.624971\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −218.217 | −0.773901 | −0.386950 | − | 0.922101i | \(-0.626472\pi\) | ||||
−0.386950 | + | 0.922101i | \(0.626472\pi\) | |||||||
\(44\) | −412.964 | −1.41493 | ||||||||
\(45\) | 45.0000 | 0.149071 | ||||||||
\(46\) | 488.328 | 1.56522 | ||||||||
\(47\) | −575.659 | −1.78657 | −0.893283 | − | 0.449496i | \(-0.851604\pi\) | ||||
−0.893283 | + | 0.449496i | \(0.851604\pi\) | |||||||
\(48\) | 133.997 | 0.402933 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −105.902 | −0.299535 | ||||||||
\(51\) | −361.161 | −0.991621 | ||||||||
\(52\) | −884.748 | −2.35947 | ||||||||
\(53\) | −184.302 | −0.477657 | −0.238828 | − | 0.971062i | \(-0.576763\pi\) | ||||
−0.238828 | + | 0.971062i | \(0.576763\pi\) | |||||||
\(54\) | 114.374 | 0.288228 | ||||||||
\(55\) | −207.639 | −0.509056 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −336.413 | −0.781737 | ||||||||
\(58\) | 613.522 | 1.38895 | ||||||||
\(59\) | 151.502 | 0.334302 | 0.167151 | − | 0.985931i | \(-0.446543\pi\) | ||||
0.167151 | + | 0.985931i | \(0.446543\pi\) | |||||||
\(60\) | −149.164 | −0.320950 | ||||||||
\(61\) | 529.830 | 1.11209 | 0.556047 | − | 0.831151i | \(-0.312317\pi\) | ||||
0.556047 | + | 0.831151i | \(0.312317\pi\) | |||||||
\(62\) | −1093.24 | −2.23938 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −723.276 | −1.41265 | ||||||||
\(65\) | −444.853 | −0.848880 | ||||||||
\(66\) | −527.745 | −0.984256 | ||||||||
\(67\) | 1.28485 | 0.00234283 | 0.00117142 | − | 0.999999i | \(-0.499627\pi\) | ||||
0.00117142 | + | 0.999999i | \(0.499627\pi\) | |||||||
\(68\) | 1197.16 | 2.13496 | ||||||||
\(69\) | 345.836 | 0.603388 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −61.4226 | −0.102669 | −0.0513347 | − | 0.998682i | \(-0.516348\pi\) | ||||
−0.0513347 | + | 0.998682i | \(0.516348\pi\) | |||||||
\(72\) | −74.1246 | −0.121329 | ||||||||
\(73\) | −484.800 | −0.777282 | −0.388641 | − | 0.921389i | \(-0.627055\pi\) | ||||
−0.388641 | + | 0.921389i | \(0.627055\pi\) | |||||||
\(74\) | −204.748 | −0.321641 | ||||||||
\(75\) | −75.0000 | −0.115470 | ||||||||
\(76\) | 1115.13 | 1.68308 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1130.66 | −1.64130 | ||||||||
\(79\) | 878.257 | 1.25078 | 0.625390 | − | 0.780312i | \(-0.284940\pi\) | ||||
0.625390 | + | 0.780312i | \(0.284940\pi\) | |||||||
\(80\) | −223.328 | −0.312111 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 850.964 | 1.14602 | ||||||||
\(83\) | −491.830 | −0.650426 | −0.325213 | − | 0.945641i | \(-0.605436\pi\) | ||||
−0.325213 | + | 0.945641i | \(0.605436\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 601.935 | 0.768106 | ||||||||
\(86\) | 924.381 | 1.15905 | ||||||||
\(87\) | 434.498 | 0.535438 | ||||||||
\(88\) | 342.026 | 0.414320 | ||||||||
\(89\) | 415.560 | 0.494936 | 0.247468 | − | 0.968896i | \(-0.420401\pi\) | ||||
0.247468 | + | 0.968896i | \(0.420401\pi\) | |||||||
\(90\) | −190.623 | −0.223260 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1146.36 | −1.29909 | ||||||||
\(93\) | −774.237 | −0.863275 | ||||||||
\(94\) | 2438.53 | 2.67570 | ||||||||
\(95\) | 560.689 | 0.605531 | ||||||||
\(96\) | −765.286 | −0.813611 | ||||||||
\(97\) | 1031.70 | 1.07993 | 0.539964 | − | 0.841688i | \(-0.318438\pi\) | ||||
0.539964 | + | 0.841688i | \(0.318438\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −373.751 | −0.379428 | ||||||||
\(100\) | 248.607 | 0.248607 | ||||||||
\(101\) | −1447.19 | −1.42576 | −0.712878 | − | 0.701288i | \(-0.752609\pi\) | ||||
−0.712878 | + | 0.701288i | \(0.752609\pi\) | |||||||
\(102\) | 1529.90 | 1.48513 | ||||||||
\(103\) | 163.567 | 0.156473 | 0.0782364 | − | 0.996935i | \(-0.475071\pi\) | ||||
0.0782364 | + | 0.996935i | \(0.475071\pi\) | |||||||
\(104\) | 732.768 | 0.690902 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 780.715 | 0.715375 | ||||||||
\(107\) | −129.653 | −0.117141 | −0.0585703 | − | 0.998283i | \(-0.518654\pi\) | ||||
−0.0585703 | + | 0.998283i | \(0.518654\pi\) | |||||||
\(108\) | −268.495 | −0.239222 | ||||||||
\(109\) | 566.681 | 0.497965 | 0.248983 | − | 0.968508i | \(-0.419904\pi\) | ||||
0.248983 | + | 0.968508i | \(0.419904\pi\) | |||||||
\(110\) | 879.574 | 0.762401 | ||||||||
\(111\) | −145.003 | −0.123992 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 809.890 | 0.674230 | 0.337115 | − | 0.941463i | \(-0.390549\pi\) | ||||
0.337115 | + | 0.941463i | \(0.390549\pi\) | |||||||
\(114\) | 1425.07 | 1.17079 | ||||||||
\(115\) | −576.393 | −0.467382 | ||||||||
\(116\) | −1440.26 | −1.15280 | ||||||||
\(117\) | −800.735 | −0.632718 | ||||||||
\(118\) | −641.771 | −0.500676 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 123.541 | 0.0939808 | ||||||||
\(121\) | 393.563 | 0.295690 | ||||||||
\(122\) | −2244.39 | −1.66556 | ||||||||
\(123\) | 602.656 | 0.441786 | ||||||||
\(124\) | 2566.41 | 1.85863 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2584.25 | −1.80563 | −0.902816 | − | 0.430028i | \(-0.858504\pi\) | ||||
−0.902816 | + | 0.430028i | \(0.858504\pi\) | |||||||
\(128\) | 1023.08 | 0.706473 | ||||||||
\(129\) | 654.650 | 0.446812 | ||||||||
\(130\) | 1884.43 | 1.27135 | ||||||||
\(131\) | 1421.10 | 0.947804 | 0.473902 | − | 0.880578i | \(-0.342845\pi\) | ||||
0.473902 | + | 0.880578i | \(0.342845\pi\) | |||||||
\(132\) | 1238.89 | 0.816908 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −5.44272 | −0.00350880 | ||||||||
\(135\) | −135.000 | −0.0860663 | ||||||||
\(136\) | −991.515 | −0.625160 | ||||||||
\(137\) | 104.878 | 0.0654037 | 0.0327019 | − | 0.999465i | \(-0.489589\pi\) | ||||
0.0327019 | + | 0.999465i | \(0.489589\pi\) | |||||||
\(138\) | −1464.98 | −0.903679 | ||||||||
\(139\) | 913.160 | 0.557217 | 0.278609 | − | 0.960405i | \(-0.410127\pi\) | ||||
0.278609 | + | 0.960405i | \(0.410127\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1726.98 | 1.03147 | ||||||||
\(142\) | 260.190 | 0.153765 | ||||||||
\(143\) | 3694.76 | 2.16064 | ||||||||
\(144\) | −401.991 | −0.232633 | ||||||||
\(145\) | −724.164 | −0.414749 | ||||||||
\(146\) | 2053.65 | 1.16412 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 480.650 | 0.266954 | ||||||||
\(149\) | 1781.45 | 0.979476 | 0.489738 | − | 0.871870i | \(-0.337092\pi\) | ||||
0.489738 | + | 0.871870i | \(0.337092\pi\) | |||||||
\(150\) | 317.705 | 0.172937 | ||||||||
\(151\) | 1407.53 | 0.758564 | 0.379282 | − | 0.925281i | \(-0.376171\pi\) | ||||
0.379282 | + | 0.925281i | \(0.376171\pi\) | |||||||
\(152\) | −923.574 | −0.492841 | ||||||||
\(153\) | 1083.48 | 0.572512 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1290.39 | 0.668690 | ||||||||
\(156\) | 2654.24 | 1.36224 | ||||||||
\(157\) | 1598.94 | 0.812798 | 0.406399 | − | 0.913696i | \(-0.366784\pi\) | ||||
0.406399 | + | 0.913696i | \(0.366784\pi\) | |||||||
\(158\) | −3720.36 | −1.87326 | ||||||||
\(159\) | 552.906 | 0.275775 | ||||||||
\(160\) | 1275.48 | 0.630220 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −343.122 | −0.166408 | ||||||||
\(163\) | −204.892 | −0.0984562 | −0.0492281 | − | 0.998788i | \(-0.515676\pi\) | ||||
−0.0492281 | + | 0.998788i | \(0.515676\pi\) | |||||||
\(164\) | −1997.66 | −0.951165 | ||||||||
\(165\) | 622.918 | 0.293904 | ||||||||
\(166\) | 2083.42 | 0.974127 | ||||||||
\(167\) | 1165.94 | 0.540259 | 0.270129 | − | 0.962824i | \(-0.412933\pi\) | ||||
0.270129 | + | 0.962824i | \(0.412933\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5718.76 | 2.60299 | ||||||||
\(170\) | −2549.84 | −1.15037 | ||||||||
\(171\) | 1009.24 | 0.451336 | ||||||||
\(172\) | −2170.01 | −0.961985 | ||||||||
\(173\) | 2538.00 | 1.11538 | 0.557690 | − | 0.830049i | \(-0.311688\pi\) | ||||
0.557690 | + | 0.830049i | \(0.311688\pi\) | |||||||
\(174\) | −1840.56 | −0.801913 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1854.87 | 0.794409 | ||||||||
\(177\) | −454.505 | −0.193009 | ||||||||
\(178\) | −1760.34 | −0.741254 | ||||||||
\(179\) | 392.255 | 0.163791 | 0.0818954 | − | 0.996641i | \(-0.473903\pi\) | ||||
0.0818954 | + | 0.996641i | \(0.473903\pi\) | |||||||
\(180\) | 447.492 | 0.185301 | ||||||||
\(181\) | 2978.08 | 1.22298 | 0.611489 | − | 0.791253i | \(-0.290571\pi\) | ||||
0.611489 | + | 0.791253i | \(0.290571\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1589.49 | −0.642068 | ||||||||
\(184\) | 949.443 | 0.380401 | ||||||||
\(185\) | 241.672 | 0.0960436 | ||||||||
\(186\) | 3279.72 | 1.29291 | ||||||||
\(187\) | −4999.41 | −1.95504 | ||||||||
\(188\) | −5724.51 | −2.22076 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2375.12 | −0.906890 | ||||||||
\(191\) | −1097.37 | −0.415722 | −0.207861 | − | 0.978158i | \(-0.566650\pi\) | ||||
−0.207861 | + | 0.978158i | \(0.566650\pi\) | |||||||
\(192\) | 2169.83 | 0.815592 | ||||||||
\(193\) | 3500.31 | 1.30548 | 0.652740 | − | 0.757582i | \(-0.273619\pi\) | ||||
0.652740 | + | 0.757582i | \(0.273619\pi\) | |||||||
\(194\) | −4370.34 | −1.61738 | ||||||||
\(195\) | 1334.56 | 0.490101 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1573.96 | 0.569237 | 0.284618 | − | 0.958641i | \(-0.408133\pi\) | ||||
0.284618 | + | 0.958641i | \(0.408133\pi\) | |||||||
\(198\) | 1583.23 | 0.568260 | ||||||||
\(199\) | 3396.62 | 1.20995 | 0.604976 | − | 0.796244i | \(-0.293183\pi\) | ||||
0.604976 | + | 0.796244i | \(0.293183\pi\) | |||||||
\(200\) | −205.902 | −0.0727972 | ||||||||
\(201\) | −3.85456 | −0.00135263 | ||||||||
\(202\) | 6130.42 | 2.13532 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −3591.48 | −1.23262 | ||||||||
\(205\) | −1004.43 | −0.342206 | ||||||||
\(206\) | −692.879 | −0.234346 | ||||||||
\(207\) | −1037.51 | −0.348366 | ||||||||
\(208\) | 3973.93 | 1.32472 | ||||||||
\(209\) | −4656.84 | −1.54125 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3337.81 | 1.08903 | 0.544513 | − | 0.838753i | \(-0.316715\pi\) | ||||
0.544513 | + | 0.838753i | \(0.316715\pi\) | |||||||
\(212\) | −1832.75 | −0.593744 | ||||||||
\(213\) | 184.268 | 0.0592762 | ||||||||
\(214\) | 549.220 | 0.175439 | ||||||||
\(215\) | −1091.08 | −0.346099 | ||||||||
\(216\) | 222.374 | 0.0700492 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −2400.50 | −0.745791 | ||||||||
\(219\) | 1454.40 | 0.448764 | ||||||||
\(220\) | −2064.82 | −0.632774 | ||||||||
\(221\) | −10710.9 | −3.26015 | ||||||||
\(222\) | 614.243 | 0.185700 | ||||||||
\(223\) | −127.328 | −0.0382356 | −0.0191178 | − | 0.999817i | \(-0.506086\pi\) | ||||
−0.0191178 | + | 0.999817i | \(0.506086\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 225.000 | 0.0666667 | ||||||||
\(226\) | −3430.75 | −1.00978 | ||||||||
\(227\) | −3844.12 | −1.12398 | −0.561990 | − | 0.827144i | \(-0.689964\pi\) | ||||
−0.561990 | + | 0.827144i | \(0.689964\pi\) | |||||||
\(228\) | −3345.39 | −0.971726 | ||||||||
\(229\) | −2536.95 | −0.732080 | −0.366040 | − | 0.930599i | \(-0.619287\pi\) | ||||
−0.366040 | + | 0.930599i | \(0.619287\pi\) | |||||||
\(230\) | 2441.64 | 0.699987 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1192.85 | 0.337563 | ||||||||
\(233\) | 3987.44 | 1.12114 | 0.560570 | − | 0.828107i | \(-0.310582\pi\) | ||||
0.560570 | + | 0.828107i | \(0.310582\pi\) | |||||||
\(234\) | 3391.97 | 0.947607 | ||||||||
\(235\) | −2878.30 | −0.798976 | ||||||||
\(236\) | 1506.57 | 0.415549 | ||||||||
\(237\) | −2634.77 | −0.722138 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3367.18 | −0.911317 | −0.455659 | − | 0.890155i | \(-0.650596\pi\) | ||||
−0.455659 | + | 0.890155i | \(0.650596\pi\) | |||||||
\(240\) | 669.984 | 0.180197 | ||||||||
\(241\) | 939.551 | 0.251128 | 0.125564 | − | 0.992086i | \(-0.459926\pi\) | ||||
0.125564 | + | 0.992086i | \(0.459926\pi\) | |||||||
\(242\) | −1667.16 | −0.442848 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 5268.77 | 1.38237 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2552.89 | −0.661653 | ||||||||
\(247\) | −9976.96 | −2.57012 | ||||||||
\(248\) | −2125.56 | −0.544246 | ||||||||
\(249\) | 1475.49 | 0.375523 | ||||||||
\(250\) | −529.508 | −0.133956 | ||||||||
\(251\) | 1403.96 | 0.353056 | 0.176528 | − | 0.984296i | \(-0.443513\pi\) | ||||
0.176528 | + | 0.984296i | \(0.443513\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4787.28 | 1.18962 | ||||||||
\(254\) | 10947.1 | 2.70425 | ||||||||
\(255\) | −1805.80 | −0.443466 | ||||||||
\(256\) | 1452.36 | 0.354579 | ||||||||
\(257\) | 1964.86 | 0.476905 | 0.238453 | − | 0.971154i | \(-0.423360\pi\) | ||||
0.238453 | + | 0.971154i | \(0.423360\pi\) | |||||||
\(258\) | −2773.14 | −0.669179 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −4423.74 | −1.05519 | ||||||||
\(261\) | −1303.50 | −0.309135 | ||||||||
\(262\) | −6019.89 | −1.41950 | ||||||||
\(263\) | −393.821 | −0.0923347 | −0.0461673 | − | 0.998934i | \(-0.514701\pi\) | ||||
−0.0461673 | + | 0.998934i | \(0.514701\pi\) | |||||||
\(264\) | −1026.08 | −0.239208 | ||||||||
\(265\) | −921.509 | −0.213615 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1246.68 | −0.285751 | ||||||||
\(268\) | 12.7769 | 0.00291222 | ||||||||
\(269\) | 1877.03 | 0.425444 | 0.212722 | − | 0.977113i | \(-0.431767\pi\) | ||||
0.212722 | + | 0.977113i | \(0.431767\pi\) | |||||||
\(270\) | 571.869 | 0.128899 | ||||||||
\(271\) | 689.909 | 0.154646 | 0.0773228 | − | 0.997006i | \(-0.475363\pi\) | ||||
0.0773228 | + | 0.997006i | \(0.475363\pi\) | |||||||
\(272\) | −5377.16 | −1.19867 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −444.269 | −0.0979536 | ||||||||
\(275\) | −1038.20 | −0.227657 | ||||||||
\(276\) | 3439.09 | 0.750031 | ||||||||
\(277\) | 6289.13 | 1.36418 | 0.682088 | − | 0.731270i | \(-0.261072\pi\) | ||||
0.682088 | + | 0.731270i | \(0.261072\pi\) | |||||||
\(278\) | −3868.21 | −0.834531 | ||||||||
\(279\) | 2322.71 | 0.498412 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1954.87 | −0.415010 | −0.207505 | − | 0.978234i | \(-0.566534\pi\) | ||||
−0.207505 | + | 0.978234i | \(0.566534\pi\) | |||||||
\(282\) | −7315.60 | −1.54481 | ||||||||
\(283\) | −5033.96 | −1.05738 | −0.528688 | − | 0.848816i | \(-0.677316\pi\) | ||||
−0.528688 | + | 0.848816i | \(0.677316\pi\) | |||||||
\(284\) | −610.803 | −0.127621 | ||||||||
\(285\) | −1682.07 | −0.349604 | ||||||||
\(286\) | −15651.2 | −3.23594 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 2295.86 | 0.469738 | ||||||||
\(289\) | 9580.03 | 1.94993 | ||||||||
\(290\) | 3067.61 | 0.621159 | ||||||||
\(291\) | −3095.09 | −0.623497 | ||||||||
\(292\) | −4820.99 | −0.966188 | ||||||||
\(293\) | −6369.12 | −1.26993 | −0.634963 | − | 0.772543i | \(-0.718985\pi\) | ||||
−0.634963 | + | 0.772543i | \(0.718985\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 757.508 | 0.149504 | ||||||||
\(296\) | −398.085 | −0.0781697 | ||||||||
\(297\) | 1121.25 | 0.219063 | ||||||||
\(298\) | −7546.34 | −1.46694 | ||||||||
\(299\) | 10256.4 | 1.98376 | ||||||||
\(300\) | −745.820 | −0.143533 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −5962.39 | −1.13608 | ||||||||
\(303\) | 4341.58 | 0.823160 | ||||||||
\(304\) | −5008.70 | −0.944963 | ||||||||
\(305\) | 2649.15 | 0.497344 | ||||||||
\(306\) | −4589.71 | −0.857438 | ||||||||
\(307\) | 6619.83 | 1.23066 | 0.615332 | − | 0.788268i | \(-0.289022\pi\) | ||||
0.615332 | + | 0.788268i | \(0.289022\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −490.700 | −0.0903396 | ||||||||
\(310\) | −5466.20 | −1.00148 | ||||||||
\(311\) | 9909.22 | 1.80675 | 0.903377 | − | 0.428848i | \(-0.141080\pi\) | ||||
0.903377 | + | 0.428848i | \(0.141080\pi\) | |||||||
\(312\) | −2198.30 | −0.398892 | ||||||||
\(313\) | 422.336 | 0.0762678 | 0.0381339 | − | 0.999273i | \(-0.487859\pi\) | ||||
0.0381339 | + | 0.999273i | \(0.487859\pi\) | |||||||
\(314\) | −6773.22 | −1.21731 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8733.63 | 1.55476 | ||||||||
\(317\) | −4902.78 | −0.868668 | −0.434334 | − | 0.900752i | \(-0.643016\pi\) | ||||
−0.434334 | + | 0.900752i | \(0.643016\pi\) | |||||||
\(318\) | −2342.15 | −0.413022 | ||||||||
\(319\) | 6014.60 | 1.05565 | ||||||||
\(320\) | −3616.38 | −0.631755 | ||||||||
\(321\) | 388.960 | 0.0676312 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13499.9 | 2.32556 | ||||||||
\(324\) | 805.486 | 0.138115 | ||||||||
\(325\) | −2224.26 | −0.379631 | ||||||||
\(326\) | 867.935 | 0.147455 | ||||||||
\(327\) | −1700.04 | −0.287500 | ||||||||
\(328\) | 1654.51 | 0.278521 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −2638.72 | −0.440172 | ||||||||
\(331\) | −5281.74 | −0.877071 | −0.438535 | − | 0.898714i | \(-0.644503\pi\) | ||||
−0.438535 | + | 0.898714i | \(0.644503\pi\) | |||||||
\(332\) | −4890.89 | −0.808501 | ||||||||
\(333\) | 435.009 | 0.0715867 | ||||||||
\(334\) | −4939.01 | −0.809133 | ||||||||
\(335\) | 6.42426 | 0.00104775 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4459.60 | 0.720860 | 0.360430 | − | 0.932786i | \(-0.382630\pi\) | ||||
0.360430 | + | 0.932786i | \(0.382630\pi\) | |||||||
\(338\) | −24225.1 | −3.89843 | ||||||||
\(339\) | −2429.67 | −0.389267 | ||||||||
\(340\) | 5985.80 | 0.954782 | ||||||||
\(341\) | −10717.5 | −1.70200 | ||||||||
\(342\) | −4275.21 | −0.675956 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 1797.25 | 0.281689 | ||||||||
\(345\) | 1729.18 | 0.269843 | ||||||||
\(346\) | −10751.2 | −1.67048 | ||||||||
\(347\) | 5261.97 | 0.814056 | 0.407028 | − | 0.913416i | \(-0.366565\pi\) | ||||
0.407028 | + | 0.913416i | \(0.366565\pi\) | |||||||
\(348\) | 4320.77 | 0.665568 | ||||||||
\(349\) | −960.325 | −0.147292 | −0.0736461 | − | 0.997284i | \(-0.523464\pi\) | ||||
−0.0736461 | + | 0.997284i | \(0.523464\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2402.21 | 0.365300 | ||||||||
\(352\) | −10593.6 | −1.60409 | ||||||||
\(353\) | 8925.80 | 1.34581 | 0.672907 | − | 0.739727i | \(-0.265045\pi\) | ||||
0.672907 | + | 0.739727i | \(0.265045\pi\) | |||||||
\(354\) | 1925.31 | 0.289066 | ||||||||
\(355\) | −307.113 | −0.0459151 | ||||||||
\(356\) | 4132.45 | 0.615222 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1661.62 | −0.245306 | ||||||||
\(359\) | −3056.27 | −0.449314 | −0.224657 | − | 0.974438i | \(-0.572126\pi\) | ||||
−0.224657 | + | 0.974438i | \(0.572126\pi\) | |||||||
\(360\) | −370.623 | −0.0542599 | ||||||||
\(361\) | 5715.88 | 0.833340 | ||||||||
\(362\) | −12615.4 | −1.83162 | ||||||||
\(363\) | −1180.69 | −0.170717 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2424.00 | −0.347611 | ||||||||
\(366\) | 6733.18 | 0.961610 | ||||||||
\(367\) | 1813.52 | 0.257943 | 0.128971 | − | 0.991648i | \(-0.458832\pi\) | ||||
0.128971 | + | 0.991648i | \(0.458832\pi\) | |||||||
\(368\) | 5148.99 | 0.729375 | ||||||||
\(369\) | −1807.97 | −0.255065 | ||||||||
\(370\) | −1023.74 | −0.143842 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −7699.22 | −1.07308 | ||||||||
\(373\) | −4517.48 | −0.627094 | −0.313547 | − | 0.949573i | \(-0.601517\pi\) | ||||
−0.313547 | + | 0.949573i | \(0.601517\pi\) | |||||||
\(374\) | 21177.9 | 2.92802 | ||||||||
\(375\) | −375.000 | −0.0516398 | ||||||||
\(376\) | 4741.17 | 0.650285 | ||||||||
\(377\) | 12885.9 | 1.76036 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4931.24 | −0.668340 | −0.334170 | − | 0.942513i | \(-0.608456\pi\) | ||||
−0.334170 | + | 0.942513i | \(0.608456\pi\) | |||||||
\(380\) | 5575.64 | 0.752696 | ||||||||
\(381\) | 7752.75 | 1.04248 | ||||||||
\(382\) | 4648.53 | 0.622617 | ||||||||
\(383\) | 1482.37 | 0.197770 | 0.0988849 | − | 0.995099i | \(-0.468472\pi\) | ||||
0.0988849 | + | 0.995099i | \(0.468472\pi\) | |||||||
\(384\) | −3069.25 | −0.407883 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −14827.5 | −1.95519 | ||||||||
\(387\) | −1963.95 | −0.257967 | ||||||||
\(388\) | 10259.5 | 1.34239 | ||||||||
\(389\) | −5448.98 | −0.710217 | −0.355109 | − | 0.934825i | \(-0.615556\pi\) | ||||
−0.355109 | + | 0.934825i | \(0.615556\pi\) | |||||||
\(390\) | −5653.28 | −0.734013 | ||||||||
\(391\) | −13878.0 | −1.79500 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4263.31 | −0.547215 | ||||||||
\(394\) | −6667.38 | −0.852532 | ||||||||
\(395\) | 4391.28 | 0.559366 | ||||||||
\(396\) | −3716.68 | −0.471642 | ||||||||
\(397\) | 13675.9 | 1.72891 | 0.864453 | − | 0.502713i | \(-0.167665\pi\) | ||||
0.864453 | + | 0.502713i | \(0.167665\pi\) | |||||||
\(398\) | −14388.3 | −1.81212 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1116.64 | −0.139580 | ||||||||
\(401\) | 14109.9 | 1.75714 | 0.878570 | − | 0.477613i | \(-0.158498\pi\) | ||||
0.878570 | + | 0.477613i | \(0.158498\pi\) | |||||||
\(402\) | 16.3282 | 0.00202581 | ||||||||
\(403\) | −22961.4 | −2.83819 | ||||||||
\(404\) | −14391.3 | −1.77226 | ||||||||
\(405\) | 405.000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2007.22 | −0.244458 | ||||||||
\(408\) | 2974.55 | 0.360936 | ||||||||
\(409\) | 13995.6 | 1.69203 | 0.846015 | − | 0.533159i | \(-0.178995\pi\) | ||||
0.846015 | + | 0.533159i | \(0.178995\pi\) | |||||||
\(410\) | 4254.82 | 0.512514 | ||||||||
\(411\) | −314.633 | −0.0377609 | ||||||||
\(412\) | 1626.55 | 0.194501 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 4394.95 | 0.521740 | ||||||||
\(415\) | −2459.15 | −0.290879 | ||||||||
\(416\) | −22696.0 | −2.67491 | ||||||||
\(417\) | −2739.48 | −0.321709 | ||||||||
\(418\) | 19726.7 | 2.30829 | ||||||||
\(419\) | 9840.61 | 1.14736 | 0.573682 | − | 0.819078i | \(-0.305515\pi\) | ||||
0.573682 | + | 0.819078i | \(0.305515\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12660.5 | −1.46564 | −0.732822 | − | 0.680420i | \(-0.761797\pi\) | ||||
−0.732822 | + | 0.680420i | \(0.761797\pi\) | |||||||
\(422\) | −14139.2 | −1.63101 | ||||||||
\(423\) | −5180.93 | −0.595522 | ||||||||
\(424\) | 1517.92 | 0.173860 | ||||||||
\(425\) | 3009.67 | 0.343507 | ||||||||
\(426\) | −780.571 | −0.0887765 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −1289.31 | −0.145610 | ||||||||
\(429\) | −11084.3 | −1.24744 | ||||||||
\(430\) | 4621.90 | 0.518344 | ||||||||
\(431\) | −4578.91 | −0.511736 | −0.255868 | − | 0.966712i | \(-0.582361\pi\) | ||||
−0.255868 | + | 0.966712i | \(0.582361\pi\) | |||||||
\(432\) | 1205.97 | 0.134311 | ||||||||
\(433\) | 3279.88 | 0.364020 | 0.182010 | − | 0.983297i | \(-0.441740\pi\) | ||||
0.182010 | + | 0.983297i | \(0.441740\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2172.49 | 0.239455 | ||||||||
\(436\) | 5635.23 | 0.618988 | ||||||||
\(437\) | −12927.1 | −1.41507 | ||||||||
\(438\) | −6160.94 | −0.672103 | ||||||||
\(439\) | 427.807 | 0.0465105 | 0.0232552 | − | 0.999730i | \(-0.492597\pi\) | ||||
0.0232552 | + | 0.999730i | \(0.492597\pi\) | |||||||
\(440\) | 1710.13 | 0.185289 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 45372.1 | 4.88265 | ||||||||
\(443\) | 15441.2 | 1.65605 | 0.828027 | − | 0.560688i | \(-0.189463\pi\) | ||||
0.828027 | + | 0.560688i | \(0.189463\pi\) | |||||||
\(444\) | −1441.95 | −0.154126 | ||||||||
\(445\) | 2077.80 | 0.221342 | ||||||||
\(446\) | 539.371 | 0.0572645 | ||||||||
\(447\) | −5344.35 | −0.565501 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9382.02 | 0.986113 | 0.493057 | − | 0.869997i | \(-0.335880\pi\) | ||||
0.493057 | + | 0.869997i | \(0.335880\pi\) | |||||||
\(450\) | −953.115 | −0.0998451 | ||||||||
\(451\) | 8342.34 | 0.871010 | ||||||||
\(452\) | 8053.77 | 0.838091 | ||||||||
\(453\) | −4222.59 | −0.437957 | ||||||||
\(454\) | 16284.0 | 1.68336 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2770.72 | 0.284542 | ||||||||
\(457\) | 13570.4 | 1.38905 | 0.694524 | − | 0.719469i | \(-0.255615\pi\) | ||||
0.694524 | + | 0.719469i | \(0.255615\pi\) | |||||||
\(458\) | 10746.7 | 1.09642 | ||||||||
\(459\) | −3250.45 | −0.330540 | ||||||||
\(460\) | −5731.81 | −0.580972 | ||||||||
\(461\) | −1251.88 | −0.126477 | −0.0632386 | − | 0.997998i | \(-0.520143\pi\) | ||||
−0.0632386 | + | 0.997998i | \(0.520143\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7934.36 | 0.796417 | 0.398209 | − | 0.917295i | \(-0.369632\pi\) | ||||
0.398209 | + | 0.917295i | \(0.369632\pi\) | |||||||
\(464\) | 6469.05 | 0.647237 | ||||||||
\(465\) | −3871.18 | −0.386069 | ||||||||
\(466\) | −16891.1 | −1.67911 | ||||||||
\(467\) | −7583.76 | −0.751466 | −0.375733 | − | 0.926728i | \(-0.622609\pi\) | ||||
−0.375733 | + | 0.926728i | \(0.622609\pi\) | |||||||
\(468\) | −7962.73 | −0.786490 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 12192.7 | 1.19661 | ||||||||
\(471\) | −4796.82 | −0.469269 | ||||||||
\(472\) | −1247.78 | −0.121681 | ||||||||
\(473\) | 9062.07 | 0.880919 | ||||||||
\(474\) | 11161.1 | 1.08153 | ||||||||
\(475\) | 2803.44 | 0.270802 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1658.72 | −0.159219 | ||||||||
\(478\) | 14263.6 | 1.36486 | ||||||||
\(479\) | 5829.34 | 0.556053 | 0.278027 | − | 0.960573i | \(-0.410320\pi\) | ||||
0.278027 | + | 0.960573i | \(0.410320\pi\) | |||||||
\(480\) | −3826.43 | −0.363858 | ||||||||
\(481\) | −4300.34 | −0.407648 | ||||||||
\(482\) | −3980.00 | −0.376108 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3913.70 | 0.367553 | ||||||||
\(485\) | 5158.49 | 0.482959 | ||||||||
\(486\) | 1029.36 | 0.0960760 | ||||||||
\(487\) | −19902.1 | −1.85185 | −0.925925 | − | 0.377708i | \(-0.876712\pi\) | ||||
−0.925925 | + | 0.377708i | \(0.876712\pi\) | |||||||
\(488\) | −4363.71 | −0.404787 | ||||||||
\(489\) | 614.675 | 0.0568437 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16821.6 | −1.54613 | −0.773065 | − | 0.634327i | \(-0.781277\pi\) | ||||
−0.773065 | + | 0.634327i | \(0.781277\pi\) | |||||||
\(492\) | 5992.98 | 0.549155 | ||||||||
\(493\) | −17436.0 | −1.59285 | ||||||||
\(494\) | 42263.1 | 3.84920 | ||||||||
\(495\) | −1868.75 | −0.169685 | ||||||||
\(496\) | −11527.3 | −1.04353 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −6250.27 | −0.562412 | ||||||||
\(499\) | 6031.83 | 0.541126 | 0.270563 | − | 0.962702i | \(-0.412790\pi\) | ||||
0.270563 | + | 0.962702i | \(0.412790\pi\) | |||||||
\(500\) | 1243.03 | 0.111180 | ||||||||
\(501\) | −3497.82 | −0.311919 | ||||||||
\(502\) | −5947.27 | −0.528764 | ||||||||
\(503\) | 17176.4 | 1.52258 | 0.761290 | − | 0.648412i | \(-0.224566\pi\) | ||||
0.761290 | + | 0.648412i | \(0.224566\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7235.97 | −0.637617 | ||||||||
\(506\) | −20279.2 | −1.78166 | ||||||||
\(507\) | −17156.3 | −1.50284 | ||||||||
\(508\) | −25698.5 | −2.24446 | ||||||||
\(509\) | −4706.59 | −0.409854 | −0.204927 | − | 0.978777i | \(-0.565696\pi\) | ||||
−0.204927 | + | 0.978777i | \(0.565696\pi\) | |||||||
\(510\) | 7649.51 | 0.664169 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −14336.9 | −1.23752 | ||||||||
\(513\) | −3027.72 | −0.260579 | ||||||||
\(514\) | −8323.28 | −0.714250 | ||||||||
\(515\) | 817.833 | 0.0699768 | ||||||||
\(516\) | 6510.02 | 0.555402 | ||||||||
\(517\) | 23905.9 | 2.03362 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7614.01 | −0.643965 | ||||||||
\(520\) | 3663.84 | 0.308981 | ||||||||
\(521\) | 8557.18 | 0.719572 | 0.359786 | − | 0.933035i | \(-0.382850\pi\) | ||||
0.359786 | + | 0.933035i | \(0.382850\pi\) | |||||||
\(522\) | 5521.69 | 0.462985 | ||||||||
\(523\) | −18248.5 | −1.52572 | −0.762858 | − | 0.646566i | \(-0.776204\pi\) | ||||
−0.762858 | + | 0.646566i | \(0.776204\pi\) | |||||||
\(524\) | 14131.8 | 1.17815 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1668.25 | 0.138287 | ||||||||
\(527\) | 31069.3 | 2.56813 | ||||||||
\(528\) | −5564.60 | −0.458652 | ||||||||
\(529\) | 1122.16 | 0.0922302 | ||||||||
\(530\) | 3903.58 | 0.319925 | ||||||||
\(531\) | 1363.51 | 0.111434 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 17872.9 | 1.45246 | ||||||||
\(534\) | 5281.03 | 0.427963 | ||||||||
\(535\) | −648.266 | −0.0523869 | ||||||||
\(536\) | −10.5821 | −0.000852758 0 | ||||||||
\(537\) | −1176.77 | −0.0945646 | ||||||||
\(538\) | −7951.22 | −0.637177 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1342.48 | −0.106983 | ||||||||
\(541\) | −5734.17 | −0.455696 | −0.227848 | − | 0.973697i | \(-0.573169\pi\) | ||||
−0.227848 | + | 0.973697i | \(0.573169\pi\) | |||||||
\(542\) | −2922.50 | −0.231609 | ||||||||
\(543\) | −8934.24 | −0.706087 | ||||||||
\(544\) | 30710.1 | 2.42038 | ||||||||
\(545\) | 2833.41 | 0.222697 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8002.52 | −0.625527 | −0.312763 | − | 0.949831i | \(-0.601255\pi\) | ||||
−0.312763 | + | 0.949831i | \(0.601255\pi\) | |||||||
\(548\) | 1042.93 | 0.0812991 | ||||||||
\(549\) | 4768.47 | 0.370698 | ||||||||
\(550\) | 4397.87 | 0.340956 | ||||||||
\(551\) | −16241.2 | −1.25572 | ||||||||
\(552\) | −2848.33 | −0.219625 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −26641.2 | −2.04310 | ||||||||
\(555\) | −725.016 | −0.0554508 | ||||||||
\(556\) | 9080.71 | 0.692640 | ||||||||
\(557\) | 1276.82 | 0.0971289 | 0.0485644 | − | 0.998820i | \(-0.484535\pi\) | ||||
0.0485644 | + | 0.998820i | \(0.484535\pi\) | |||||||
\(558\) | −9839.16 | −0.746460 | ||||||||
\(559\) | 19414.9 | 1.46898 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 14998.2 | 1.12875 | ||||||||
\(562\) | 8280.96 | 0.621550 | ||||||||
\(563\) | −11027.7 | −0.825507 | −0.412753 | − | 0.910843i | \(-0.635433\pi\) | ||||
−0.412753 | + | 0.910843i | \(0.635433\pi\) | |||||||
\(564\) | 17173.5 | 1.28216 | ||||||||
\(565\) | 4049.45 | 0.301525 | ||||||||
\(566\) | 21324.2 | 1.58361 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 505.881 | 0.0373702 | ||||||||
\(569\) | −4519.03 | −0.332948 | −0.166474 | − | 0.986046i | \(-0.553238\pi\) | ||||
−0.166474 | + | 0.986046i | \(0.553238\pi\) | |||||||
\(570\) | 7125.35 | 0.523593 | ||||||||
\(571\) | 3598.81 | 0.263758 | 0.131879 | − | 0.991266i | \(-0.457899\pi\) | ||||
0.131879 | + | 0.991266i | \(0.457899\pi\) | |||||||
\(572\) | 36741.7 | 2.68575 | ||||||||
\(573\) | 3292.11 | 0.240017 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2881.97 | −0.209020 | ||||||||
\(576\) | −6509.48 | −0.470883 | ||||||||
\(577\) | 3439.23 | 0.248140 | 0.124070 | − | 0.992273i | \(-0.460405\pi\) | ||||
0.124070 | + | 0.992273i | \(0.460405\pi\) | |||||||
\(578\) | −40581.6 | −2.92037 | ||||||||
\(579\) | −10500.9 | −0.753720 | ||||||||
\(580\) | −7201.28 | −0.515547 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 13111.0 | 0.933797 | ||||||||
\(583\) | 7653.66 | 0.543709 | ||||||||
\(584\) | 3992.85 | 0.282920 | ||||||||
\(585\) | −4003.68 | −0.282960 | ||||||||
\(586\) | 26980.0 | 1.90194 | ||||||||
\(587\) | −21285.2 | −1.49665 | −0.748327 | − | 0.663330i | \(-0.769143\pi\) | ||||
−0.748327 | + | 0.663330i | \(0.769143\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 28940.4 | 2.02456 | ||||||||
\(590\) | −3208.85 | −0.223909 | ||||||||
\(591\) | −4721.87 | −0.328649 | ||||||||
\(592\) | −2158.89 | −0.149881 | ||||||||
\(593\) | 14200.8 | 0.983404 | 0.491702 | − | 0.870764i | \(-0.336375\pi\) | ||||
0.491702 | + | 0.870764i | \(0.336375\pi\) | |||||||
\(594\) | −4749.70 | −0.328085 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 17715.2 | 1.21752 | ||||||||
\(597\) | −10189.9 | −0.698566 | ||||||||
\(598\) | −43446.8 | −2.97103 | ||||||||
\(599\) | −8885.05 | −0.606065 | −0.303033 | − | 0.952980i | \(-0.597999\pi\) | ||||
−0.303033 | + | 0.952980i | \(0.597999\pi\) | |||||||
\(600\) | 617.705 | 0.0420295 | ||||||||
\(601\) | 2052.89 | 0.139333 | 0.0696664 | − | 0.997570i | \(-0.477807\pi\) | ||||
0.0696664 | + | 0.997570i | \(0.477807\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 11.5637 | 0.000780943 0 | ||||||||
\(604\) | 13996.9 | 0.942920 | ||||||||
\(605\) | 1967.82 | 0.132237 | ||||||||
\(606\) | −18391.2 | −1.23283 | ||||||||
\(607\) | −10280.0 | −0.687404 | −0.343702 | − | 0.939079i | \(-0.611681\pi\) | ||||
−0.343702 | + | 0.939079i | \(0.611681\pi\) | |||||||
\(608\) | 28605.8 | 1.90809 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −11222.0 | −0.744860 | ||||||||
\(611\) | 51216.8 | 3.39118 | ||||||||
\(612\) | 10774.4 | 0.711652 | ||||||||
\(613\) | 23409.5 | 1.54242 | 0.771208 | − | 0.636584i | \(-0.219653\pi\) | ||||
0.771208 | + | 0.636584i | \(0.219653\pi\) | |||||||
\(614\) | −28042.0 | −1.84314 | ||||||||
\(615\) | 3013.28 | 0.197573 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6632.75 | −0.432779 | −0.216389 | − | 0.976307i | \(-0.569428\pi\) | ||||
−0.216389 | + | 0.976307i | \(0.569428\pi\) | |||||||
\(618\) | 2078.64 | 0.135299 | ||||||||
\(619\) | −10734.0 | −0.696990 | −0.348495 | − | 0.937311i | \(-0.613307\pi\) | ||||
−0.348495 | + | 0.937311i | \(0.613307\pi\) | |||||||
\(620\) | 12832.0 | 0.831205 | ||||||||
\(621\) | 3112.52 | 0.201129 | ||||||||
\(622\) | −41976.1 | −2.70593 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −11921.8 | −0.764829 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | −1789.04 | −0.114225 | ||||||||
\(627\) | 13970.5 | 0.889839 | ||||||||
\(628\) | 15900.3 | 1.01034 | ||||||||
\(629\) | 5818.83 | 0.368858 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17071.0 | −1.07700 | −0.538499 | − | 0.842626i | \(-0.681008\pi\) | ||||
−0.538499 | + | 0.842626i | \(0.681008\pi\) | |||||||
\(632\) | −7233.38 | −0.455267 | ||||||||
\(633\) | −10013.4 | −0.628749 | ||||||||
\(634\) | 20768.5 | 1.30098 | ||||||||
\(635\) | −12921.3 | −0.807503 | ||||||||
\(636\) | 5498.24 | 0.342798 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −25478.2 | −1.58102 | ||||||||
\(639\) | −552.804 | −0.0342231 | ||||||||
\(640\) | 5115.41 | 0.315945 | ||||||||
\(641\) | −19389.7 | −1.19477 | −0.597386 | − | 0.801954i | \(-0.703794\pi\) | ||||
−0.597386 | + | 0.801954i | \(0.703794\pi\) | |||||||
\(642\) | −1647.66 | −0.101290 | ||||||||
\(643\) | 25409.3 | 1.55839 | 0.779196 | − | 0.626780i | \(-0.215628\pi\) | ||||
0.779196 | + | 0.626780i | \(0.215628\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3273.25 | 0.199820 | ||||||||
\(646\) | −57186.6 | −3.48294 | ||||||||
\(647\) | 6039.08 | 0.366956 | 0.183478 | − | 0.983024i | \(-0.441264\pi\) | ||||
0.183478 | + | 0.983024i | \(0.441264\pi\) | |||||||
\(648\) | −667.122 | −0.0404429 | ||||||||
\(649\) | −6291.54 | −0.380531 | ||||||||
\(650\) | 9422.14 | 0.568564 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2037.50 | −0.122384 | ||||||||
\(653\) | −30666.2 | −1.83776 | −0.918882 | − | 0.394532i | \(-0.870907\pi\) | ||||
−0.918882 | + | 0.394532i | \(0.870907\pi\) | |||||||
\(654\) | 7201.50 | 0.430582 | ||||||||
\(655\) | 7105.51 | 0.423871 | ||||||||
\(656\) | 8972.67 | 0.534031 | ||||||||
\(657\) | −4363.20 | −0.259094 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2765.96 | −0.163500 | −0.0817500 | − | 0.996653i | \(-0.526051\pi\) | ||||
−0.0817500 | + | 0.996653i | \(0.526051\pi\) | |||||||
\(660\) | 6194.47 | 0.365332 | ||||||||
\(661\) | −27261.8 | −1.60418 | −0.802089 | − | 0.597204i | \(-0.796278\pi\) | ||||
−0.802089 | + | 0.597204i | \(0.796278\pi\) | |||||||
\(662\) | 22373.8 | 1.31357 | ||||||||
\(663\) | 32132.7 | 1.88225 | ||||||||
\(664\) | 4050.74 | 0.236746 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1842.73 | −0.107214 | ||||||||
\(667\) | 16696.1 | 0.969230 | ||||||||
\(668\) | 11594.4 | 0.671560 | ||||||||
\(669\) | 381.985 | 0.0220753 | ||||||||
\(670\) | −27.2136 | −0.00156918 | ||||||||
\(671\) | −22002.7 | −1.26588 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1048.17 | −0.0600356 | −0.0300178 | − | 0.999549i | \(-0.509556\pi\) | ||||
−0.0300178 | + | 0.999549i | \(0.509556\pi\) | |||||||
\(674\) | −18891.2 | −1.07961 | ||||||||
\(675\) | −675.000 | −0.0384900 | ||||||||
\(676\) | 56869.0 | 3.23560 | ||||||||
\(677\) | 34554.7 | 1.96166 | 0.980831 | − | 0.194860i | \(-0.0624252\pi\) | ||||
0.980831 | + | 0.194860i | \(0.0624252\pi\) | |||||||
\(678\) | 10292.2 | 0.582996 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −4957.58 | −0.279580 | ||||||||
\(681\) | 11532.4 | 0.648930 | ||||||||
\(682\) | 45399.9 | 2.54905 | ||||||||
\(683\) | 14711.6 | 0.824192 | 0.412096 | − | 0.911140i | \(-0.364797\pi\) | ||||
0.412096 | + | 0.911140i | \(0.364797\pi\) | |||||||
\(684\) | 10036.2 | 0.561026 | ||||||||
\(685\) | 524.389 | 0.0292494 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7610.85 | 0.422667 | ||||||||
\(688\) | 9746.79 | 0.540106 | ||||||||
\(689\) | 16397.4 | 0.906666 | ||||||||
\(690\) | −7324.92 | −0.404138 | ||||||||
\(691\) | 24522.6 | 1.35005 | 0.675024 | − | 0.737796i | \(-0.264133\pi\) | ||||
0.675024 | + | 0.737796i | \(0.264133\pi\) | |||||||
\(692\) | 25238.6 | 1.38646 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −22290.1 | −1.21919 | ||||||||
\(695\) | 4565.80 | 0.249195 | ||||||||
\(696\) | −3578.56 | −0.194892 | ||||||||
\(697\) | −24184.0 | −1.31425 | ||||||||
\(698\) | 4068.00 | 0.220596 | ||||||||
\(699\) | −11962.3 | −0.647291 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19912.2 | 1.07286 | 0.536429 | − | 0.843946i | \(-0.319773\pi\) | ||||
0.536429 | + | 0.843946i | \(0.319773\pi\) | |||||||
\(702\) | −10175.9 | −0.547101 | ||||||||
\(703\) | 5420.11 | 0.290787 | ||||||||
\(704\) | 30036.1 | 1.60799 | ||||||||
\(705\) | 8634.89 | 0.461289 | ||||||||
\(706\) | −37810.3 | −2.01559 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −4519.72 | −0.239917 | ||||||||
\(709\) | 6208.79 | 0.328880 | 0.164440 | − | 0.986387i | \(-0.447418\pi\) | ||||
0.164440 | + | 0.986387i | \(0.447418\pi\) | |||||||
\(710\) | 1300.95 | 0.0687660 | ||||||||
\(711\) | 7904.31 | 0.416927 | ||||||||
\(712\) | −3422.58 | −0.180150 | ||||||||
\(713\) | −29751.0 | −1.56267 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 18473.8 | 0.966267 | ||||||||
\(716\) | 3900.69 | 0.203597 | ||||||||
\(717\) | 10101.5 | 0.526149 | ||||||||
\(718\) | 12946.6 | 0.672927 | ||||||||
\(719\) | −13063.6 | −0.677593 | −0.338797 | − | 0.940860i | \(-0.610020\pi\) | ||||
−0.338797 | + | 0.940860i | \(0.610020\pi\) | |||||||
\(720\) | −2009.95 | −0.104037 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −24212.9 | −1.24807 | ||||||||
\(723\) | −2818.65 | −0.144989 | ||||||||
\(724\) | 29614.8 | 1.52020 | ||||||||
\(725\) | −3620.82 | −0.185481 | ||||||||
\(726\) | 5001.49 | 0.255678 | ||||||||
\(727\) | 12897.0 | 0.657940 | 0.328970 | − | 0.944340i | \(-0.393298\pi\) | ||||
0.328970 | + | 0.944340i | \(0.393298\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 10268.2 | 0.520609 | ||||||||
\(731\) | −26270.5 | −1.32920 | ||||||||
\(732\) | −15806.3 | −0.798112 | ||||||||
\(733\) | −11699.6 | −0.589540 | −0.294770 | − | 0.955568i | \(-0.595243\pi\) | ||||
−0.294770 | + | 0.955568i | \(0.595243\pi\) | |||||||
\(734\) | −7682.19 | −0.386315 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −29407.0 | −1.47277 | ||||||||
\(737\) | −53.3571 | −0.00266681 | ||||||||
\(738\) | 7658.68 | 0.382005 | ||||||||
\(739\) | 14974.0 | 0.745368 | 0.372684 | − | 0.927958i | \(-0.378438\pi\) | ||||
0.372684 | + | 0.927958i | \(0.378438\pi\) | |||||||
\(740\) | 2403.25 | 0.119385 | ||||||||
\(741\) | 29930.9 | 1.48386 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18500.7 | 0.913492 | 0.456746 | − | 0.889597i | \(-0.349015\pi\) | ||||
0.456746 | + | 0.889597i | \(0.349015\pi\) | |||||||
\(744\) | 6376.67 | 0.314220 | ||||||||
\(745\) | 8907.24 | 0.438035 | ||||||||
\(746\) | 19136.3 | 0.939184 | ||||||||
\(747\) | −4426.47 | −0.216809 | ||||||||
\(748\) | −49715.5 | −2.43019 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 1588.53 | 0.0773397 | ||||||||
\(751\) | −26348.4 | −1.28025 | −0.640125 | − | 0.768271i | \(-0.721117\pi\) | ||||
−0.640125 | + | 0.768271i | \(0.721117\pi\) | |||||||
\(752\) | 25712.2 | 1.24684 | ||||||||
\(753\) | −4211.88 | −0.203837 | ||||||||
\(754\) | −54585.4 | −2.63645 | ||||||||
\(755\) | 7037.65 | 0.339240 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −28061.7 | −1.34732 | −0.673659 | − | 0.739042i | \(-0.735278\pi\) | ||||
−0.673659 | + | 0.739042i | \(0.735278\pi\) | |||||||
\(758\) | 20889.1 | 1.00096 | ||||||||
\(759\) | −14361.8 | −0.686826 | ||||||||
\(760\) | −4617.87 | −0.220405 | ||||||||
\(761\) | 3579.22 | 0.170495 | 0.0852476 | − | 0.996360i | \(-0.472832\pi\) | ||||
0.0852476 | + | 0.996360i | \(0.472832\pi\) | |||||||
\(762\) | −32841.2 | −1.56130 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −10912.5 | −0.516757 | ||||||||
\(765\) | 5417.41 | 0.256035 | ||||||||
\(766\) | −6279.44 | −0.296195 | ||||||||
\(767\) | −13479.2 | −0.634557 | ||||||||
\(768\) | −4357.07 | −0.204716 | ||||||||
\(769\) | −4339.61 | −0.203499 | −0.101749 | − | 0.994810i | \(-0.532444\pi\) | ||||
−0.101749 | + | 0.994810i | \(0.532444\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5894.58 | −0.275341 | ||||||||
\(772\) | 34808.0 | 1.62276 | ||||||||
\(773\) | −10005.1 | −0.465537 | −0.232769 | − | 0.972532i | \(-0.574778\pi\) | ||||
−0.232769 | + | 0.972532i | \(0.574778\pi\) | |||||||
\(774\) | 8319.43 | 0.386351 | ||||||||
\(775\) | 6451.97 | 0.299047 | ||||||||
\(776\) | −8497.14 | −0.393079 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 23082.3 | 1.06368 | ||||||||
\(779\) | −22526.8 | −1.03608 | ||||||||
\(780\) | 13271.2 | 0.609212 | ||||||||
\(781\) | 2550.75 | 0.116867 | ||||||||
\(782\) | 58788.4 | 2.68832 | ||||||||
\(783\) | 3910.49 | 0.178479 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7994.70 | 0.363494 | ||||||||
\(786\) | 18059.7 | 0.819550 | ||||||||
\(787\) | −17826.8 | −0.807443 | −0.403721 | − | 0.914882i | \(-0.632284\pi\) | ||||
−0.403721 | + | 0.914882i | \(0.632284\pi\) | |||||||
\(788\) | 15651.8 | 0.707581 | ||||||||
\(789\) | 1181.46 | 0.0533094 | ||||||||
\(790\) | −18601.8 | −0.837749 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 3078.24 | 0.138107 | ||||||||
\(793\) | −47139.3 | −2.11093 | ||||||||
\(794\) | −57932.2 | −2.58934 | ||||||||
\(795\) | 2764.53 | 0.123330 | ||||||||
\(796\) | 33777.0 | 1.50401 | ||||||||
\(797\) | −36723.0 | −1.63211 | −0.816057 | − | 0.577971i | \(-0.803845\pi\) | ||||
−0.816057 | + | 0.577971i | \(0.803845\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −69301.9 | −3.06849 | ||||||||
\(800\) | 6377.38 | 0.281843 | ||||||||
\(801\) | 3740.04 | 0.164979 | ||||||||
\(802\) | −59770.4 | −2.63163 | ||||||||
\(803\) | 20132.7 | 0.884767 | ||||||||
\(804\) | −38.3307 | −0.00168137 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 97266.2 | 4.25069 | ||||||||
\(807\) | −5631.08 | −0.245630 | ||||||||
\(808\) | 11919.2 | 0.518955 | ||||||||
\(809\) | 5657.55 | 0.245870 | 0.122935 | − | 0.992415i | \(-0.460769\pi\) | ||||
0.122935 | + | 0.992415i | \(0.460769\pi\) | |||||||
\(810\) | −1715.61 | −0.0744201 | ||||||||
\(811\) | −7532.41 | −0.326139 | −0.163070 | − | 0.986615i | \(-0.552139\pi\) | ||||
−0.163070 | + | 0.986615i | \(0.552139\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2069.73 | −0.0892847 | ||||||||
\(814\) | 8502.73 | 0.366119 | ||||||||
\(815\) | −1024.46 | −0.0440309 | ||||||||
\(816\) | 16131.5 | 0.692053 | ||||||||
\(817\) | −24470.3 | −1.04787 | ||||||||
\(818\) | −59286.5 | −2.53411 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −9988.30 | −0.425374 | ||||||||
\(821\) | −6489.25 | −0.275854 | −0.137927 | − | 0.990442i | \(-0.544044\pi\) | ||||
−0.137927 | + | 0.990442i | \(0.544044\pi\) | |||||||
\(822\) | 1332.81 | 0.0565535 | ||||||||
\(823\) | 7901.57 | 0.334668 | 0.167334 | − | 0.985900i | \(-0.446484\pi\) | ||||
0.167334 | + | 0.985900i | \(0.446484\pi\) | |||||||
\(824\) | −1347.15 | −0.0569539 | ||||||||
\(825\) | 3114.59 | 0.131438 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −37815.8 | −1.59007 | −0.795033 | − | 0.606566i | \(-0.792547\pi\) | ||||
−0.795033 | + | 0.606566i | \(0.792547\pi\) | |||||||
\(828\) | −10317.3 | −0.433031 | ||||||||
\(829\) | −26073.5 | −1.09236 | −0.546182 | − | 0.837667i | \(-0.683919\pi\) | ||||
−0.546182 | + | 0.837667i | \(0.683919\pi\) | |||||||
\(830\) | 10417.1 | 0.435643 | ||||||||
\(831\) | −18867.4 | −0.787608 | ||||||||
\(832\) | 64350.2 | 2.68142 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 11604.6 | 0.481817 | ||||||||
\(835\) | 5829.71 | 0.241611 | ||||||||
\(836\) | −46308.9 | −1.91582 | ||||||||
\(837\) | −6968.13 | −0.287758 | ||||||||
\(838\) | −41685.5 | −1.71838 | ||||||||
\(839\) | 15590.3 | 0.641523 | 0.320762 | − | 0.947160i | \(-0.396061\pi\) | ||||
0.320762 | + | 0.947160i | \(0.396061\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3412.46 | −0.139918 | ||||||||
\(842\) | 53630.8 | 2.19506 | ||||||||
\(843\) | 5864.61 | 0.239606 | ||||||||
\(844\) | 33192.1 | 1.35370 | ||||||||
\(845\) | 28593.8 | 1.16409 | ||||||||
\(846\) | 21946.8 | 0.891899 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 8231.96 | 0.333357 | ||||||||
\(849\) | 15101.9 | 0.610477 | ||||||||
\(850\) | −12749.2 | −0.514463 | ||||||||
\(851\) | −5571.92 | −0.224445 | ||||||||
\(852\) | 1832.41 | 0.0736823 | ||||||||
\(853\) | 17476.1 | 0.701488 | 0.350744 | − | 0.936471i | \(-0.385929\pi\) | ||||
0.350744 | + | 0.936471i | \(0.385929\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5046.20 | 0.201844 | ||||||||
\(856\) | 1067.83 | 0.0426376 | ||||||||
\(857\) | 5694.54 | 0.226980 | 0.113490 | − | 0.993539i | \(-0.463797\pi\) | ||||
0.113490 | + | 0.993539i | \(0.463797\pi\) | |||||||
\(858\) | 46953.7 | 1.86827 | ||||||||
\(859\) | −27313.6 | −1.08490 | −0.542448 | − | 0.840089i | \(-0.682503\pi\) | ||||
−0.542448 | + | 0.840089i | \(0.682503\pi\) | |||||||
\(860\) | −10850.0 | −0.430213 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 19396.6 | 0.766415 | ||||||||
\(863\) | −9046.07 | −0.356815 | −0.178408 | − | 0.983957i | \(-0.557095\pi\) | ||||
−0.178408 | + | 0.983957i | \(0.557095\pi\) | |||||||
\(864\) | −6887.57 | −0.271204 | ||||||||
\(865\) | 12690.0 | 0.498813 | ||||||||
\(866\) | −13893.8 | −0.545185 | ||||||||
\(867\) | −28740.1 | −1.12580 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −36472.1 | −1.42374 | ||||||||
\(870\) | −9202.82 | −0.358626 | ||||||||
\(871\) | −114.314 | −0.00444705 | ||||||||
\(872\) | −4667.22 | −0.181252 | ||||||||
\(873\) | 9285.28 | 0.359976 | ||||||||
\(874\) | 54760.0 | 2.11932 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 14463.0 | 0.557829 | ||||||||
\(877\) | −2104.29 | −0.0810224 | −0.0405112 | − | 0.999179i | \(-0.512899\pi\) | ||||
−0.0405112 | + | 0.999179i | \(0.512899\pi\) | |||||||
\(878\) | −1812.22 | −0.0696576 | ||||||||
\(879\) | 19107.4 | 0.733192 | ||||||||
\(880\) | 9274.34 | 0.355270 | ||||||||
\(881\) | 22589.6 | 0.863861 | 0.431931 | − | 0.901907i | \(-0.357833\pi\) | ||||
0.431931 | + | 0.901907i | \(0.357833\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2419.71 | −0.0922193 | −0.0461096 | − | 0.998936i | \(-0.514682\pi\) | ||||
−0.0461096 | + | 0.998936i | \(0.514682\pi\) | |||||||
\(884\) | −106512. | −4.05248 | ||||||||
\(885\) | −2272.52 | −0.0863164 | ||||||||
\(886\) | −65409.8 | −2.48023 | ||||||||
\(887\) | −13177.0 | −0.498806 | −0.249403 | − | 0.968400i | \(-0.580234\pi\) | ||||
−0.249403 | + | 0.968400i | \(0.580234\pi\) | |||||||
\(888\) | 1194.26 | 0.0451313 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −8801.71 | −0.331499 | ||||||||
\(891\) | −3363.76 | −0.126476 | ||||||||
\(892\) | −1266.19 | −0.0475281 | ||||||||
\(893\) | −64553.2 | −2.41902 | ||||||||
\(894\) | 22639.0 | 0.846937 | ||||||||
\(895\) | 1961.28 | 0.0732495 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −30769.2 | −1.14532 | ||||||||
\(898\) | −39742.9 | −1.47688 | ||||||||
\(899\) | −37378.3 | −1.38669 | ||||||||
\(900\) | 2237.46 | 0.0828689 | ||||||||
\(901\) | −22187.5 | −0.820393 | ||||||||
\(902\) | −35338.7 | −1.30449 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6670.31 | −0.245411 | ||||||||
\(905\) | 14890.4 | 0.546932 | ||||||||
\(906\) | 17887.2 | 0.655918 | ||||||||
\(907\) | 9189.14 | 0.336406 | 0.168203 | − | 0.985752i | \(-0.446204\pi\) | ||||
0.168203 | + | 0.985752i | \(0.446204\pi\) | |||||||
\(908\) | −38227.0 | −1.39714 | ||||||||
\(909\) | −13024.8 | −0.475252 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −17045.8 | −0.619928 | −0.309964 | − | 0.950748i | \(-0.600317\pi\) | ||||
−0.309964 | + | 0.950748i | \(0.600317\pi\) | |||||||
\(912\) | 15026.1 | 0.545575 | ||||||||
\(913\) | 20424.6 | 0.740369 | ||||||||
\(914\) | −57485.0 | −2.08034 | ||||||||
\(915\) | −7947.45 | −0.287141 | ||||||||
\(916\) | −25228.1 | −0.910001 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 13769.1 | 0.495042 | ||||||||
\(919\) | −30825.0 | −1.10645 | −0.553223 | − | 0.833033i | \(-0.686602\pi\) | ||||
−0.553223 | + | 0.833033i | \(0.686602\pi\) | |||||||
\(920\) | 4747.21 | 0.170121 | ||||||||
\(921\) | −19859.5 | −0.710524 | ||||||||
\(922\) | 5303.06 | 0.189422 | ||||||||
\(923\) | 5464.81 | 0.194882 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1208.36 | 0.0429520 | ||||||||
\(926\) | −33610.5 | −1.19277 | ||||||||
\(927\) | 1472.10 | 0.0521576 | ||||||||
\(928\) | −36946.2 | −1.30691 | ||||||||
\(929\) | 5785.88 | 0.204336 | 0.102168 | − | 0.994767i | \(-0.467422\pi\) | ||||
0.102168 | + | 0.994767i | \(0.467422\pi\) | |||||||
\(930\) | 16398.6 | 0.578206 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 39652.2 | 1.39362 | ||||||||
\(933\) | −29727.7 | −1.04313 | ||||||||
\(934\) | 32125.3 | 1.12545 | ||||||||
\(935\) | −24997.1 | −0.874323 | ||||||||
\(936\) | 6594.91 | 0.230301 | ||||||||
\(937\) | 13680.9 | 0.476986 | 0.238493 | − | 0.971144i | \(-0.423347\pi\) | ||||
0.238493 | + | 0.971144i | \(0.423347\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1267.01 | −0.0440333 | ||||||||
\(940\) | −28622.6 | −0.993155 | ||||||||
\(941\) | 45448.8 | 1.57448 | 0.787242 | − | 0.616644i | \(-0.211508\pi\) | ||||
0.787242 | + | 0.616644i | \(0.211508\pi\) | |||||||
\(942\) | 20319.6 | 0.702813 | ||||||||
\(943\) | 23157.8 | 0.799705 | ||||||||
\(944\) | −6766.91 | −0.233310 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −38387.6 | −1.31933 | ||||||||
\(947\) | −7788.45 | −0.267255 | −0.133628 | − | 0.991032i | \(-0.542663\pi\) | ||||
−0.133628 | + | 0.991032i | \(0.542663\pi\) | |||||||
\(948\) | −26200.9 | −0.897642 | ||||||||
\(949\) | 43133.0 | 1.47540 | ||||||||
\(950\) | −11875.6 | −0.405573 | ||||||||
\(951\) | 14708.4 | 0.501526 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6149.43 | 0.209024 | 0.104512 | − | 0.994524i | \(-0.466672\pi\) | ||||
0.104512 | + | 0.994524i | \(0.466672\pi\) | |||||||
\(954\) | 7026.44 | 0.238458 | ||||||||
\(955\) | −5486.85 | −0.185917 | ||||||||
\(956\) | −33484.2 | −1.13280 | ||||||||
\(957\) | −18043.8 | −0.609481 | ||||||||
\(958\) | −24693.5 | −0.832788 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 10849.1 | 0.364744 | ||||||||
\(961\) | 36813.7 | 1.23573 | ||||||||
\(962\) | 18216.5 | 0.610524 | ||||||||
\(963\) | −1166.88 | −0.0390469 | ||||||||
\(964\) | 9343.15 | 0.312160 | ||||||||
\(965\) | 17501.5 | 0.583829 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23902.9 | 0.794896 | 0.397448 | − | 0.917625i | \(-0.369896\pi\) | ||||
0.397448 | + | 0.917625i | \(0.369896\pi\) | |||||||
\(968\) | −3241.42 | −0.107627 | ||||||||
\(969\) | −40499.8 | −1.34266 | ||||||||
\(970\) | −21851.7 | −0.723316 | ||||||||
\(971\) | 8015.06 | 0.264898 | 0.132449 | − | 0.991190i | \(-0.457716\pi\) | ||||
0.132449 | + | 0.991190i | \(0.457716\pi\) | |||||||
\(972\) | −2416.46 | −0.0797407 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 84306.7 | 2.77347 | ||||||||
\(975\) | 6672.79 | 0.219180 | ||||||||
\(976\) | −23665.2 | −0.776131 | ||||||||
\(977\) | −34861.1 | −1.14156 | −0.570780 | − | 0.821103i | \(-0.693359\pi\) | ||||
−0.570780 | + | 0.821103i | \(0.693359\pi\) | |||||||
\(978\) | −2603.80 | −0.0851334 | ||||||||
\(979\) | −17257.3 | −0.563378 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5100.13 | 0.165988 | ||||||||
\(982\) | 71257.6 | 2.31560 | ||||||||
\(983\) | −6620.83 | −0.214824 | −0.107412 | − | 0.994215i | \(-0.534256\pi\) | ||||
−0.107412 | + | 0.994215i | \(0.534256\pi\) | |||||||
\(984\) | −4963.52 | −0.160804 | ||||||||
\(985\) | 7869.78 | 0.254570 | ||||||||
\(986\) | 73860.0 | 2.38558 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −99213.6 | −3.19474 | ||||||||
\(989\) | 25155.7 | 0.808802 | ||||||||
\(990\) | 7916.17 | 0.254134 | ||||||||
\(991\) | 10360.1 | 0.332089 | 0.166045 | − | 0.986118i | \(-0.446900\pi\) | ||||
0.166045 | + | 0.986118i | \(0.446900\pi\) | |||||||
\(992\) | 65834.7 | 2.10711 | ||||||||
\(993\) | 15845.2 | 0.506377 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 16983.1 | 0.541107 | ||||||||
\(996\) | 14672.7 | 0.466788 | ||||||||
\(997\) | 40309.3 | 1.28045 | 0.640225 | − | 0.768188i | \(-0.278841\pi\) | ||||
0.640225 | + | 0.768188i | \(0.278841\pi\) | |||||||
\(998\) | −25551.3 | −0.810432 | ||||||||
\(999\) | −1305.03 | −0.0413306 |
(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 | 735.4.a.m.1.1 | 2 | ||
3.2 | odd | 2 | 2205.4.a.be.1.2 | 2 | |||
7.6 | odd | 2 | 105.4.a.d.1.1 | ✓ | 2 | ||
21.20 | even | 2 | 315.4.a.l.1.2 | 2 | |||
28.27 | even | 2 | 1680.4.a.bd.1.1 | 2 | |||
35.13 | even | 4 | 525.4.d.k.274.4 | 4 | |||
35.27 | even | 4 | 525.4.d.k.274.1 | 4 | |||
35.34 | odd | 2 | 525.4.a.o.1.2 | 2 | |||
105.104 | even | 2 | 1575.4.a.n.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.a.d.1.1 | ✓ | 2 | 7.6 | odd | 2 | ||
315.4.a.l.1.2 | 2 | 21.20 | even | 2 | |||
525.4.a.o.1.2 | 2 | 35.34 | odd | 2 | |||
525.4.d.k.274.1 | 4 | 35.27 | even | 4 | |||
525.4.d.k.274.4 | 4 | 35.13 | even | 4 | |||
735.4.a.m.1.1 | 2 | 1.1 | even | 1 | trivial | ||
1575.4.a.n.1.1 | 2 | 105.104 | even | 2 | |||
1680.4.a.bd.1.1 | 2 | 28.27 | even | 2 | |||
2205.4.a.be.1.2 | 2 | 3.2 | odd | 2 |