Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [675,4,Mod(1,675)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(675, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("675.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 675 = 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 675.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: | \(39.8262892539\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.1772.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 12x + 8 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 135) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-3.32803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 675.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.12612 | 0.751697 | 0.375848 | − | 0.926681i | \(-0.377351\pi\) | ||||
0.375848 | + | 0.926681i | \(0.377351\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −3.47962 | −0.434952 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −30.7000 | −1.65765 | −0.828823 | − | 0.559511i | \(-0.810989\pi\) | ||||
−0.828823 | + | 0.559511i | \(0.810989\pi\) | |||||||
\(8\) | −24.4070 | −1.07865 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −50.1548 | −1.37475 | −0.687375 | − | 0.726303i | \(-0.741237\pi\) | ||||
−0.687375 | + | 0.726303i | \(0.741237\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 15.9592 | 0.340484 | 0.170242 | − | 0.985402i | \(-0.445545\pi\) | ||||
0.170242 | + | 0.985402i | \(0.445545\pi\) | |||||||
\(14\) | −65.2720 | −1.24605 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −24.0553 | −0.375865 | ||||||||
\(17\) | 105.668 | 1.50755 | 0.753774 | − | 0.657134i | \(-0.228231\pi\) | ||||
0.753774 | + | 0.657134i | \(0.228231\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −21.3040 | −0.257235 | −0.128618 | − | 0.991694i | \(-0.541054\pi\) | ||||
−0.128618 | + | 0.991694i | \(0.541054\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −106.635 | −1.03339 | ||||||||
\(23\) | 136.137 | 1.23420 | 0.617098 | − | 0.786886i | \(-0.288308\pi\) | ||||
0.617098 | + | 0.786886i | \(0.288308\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 33.9312 | 0.255941 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 106.824 | 0.720997 | ||||||||
\(29\) | 224.323 | 1.43641 | 0.718203 | − | 0.695834i | \(-0.244965\pi\) | ||||
0.718203 | + | 0.695834i | \(0.244965\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −225.982 | −1.30928 | −0.654638 | − | 0.755943i | \(-0.727179\pi\) | ||||
−0.654638 | + | 0.755943i | \(0.727179\pi\) | |||||||
\(32\) | 144.112 | 0.796112 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 224.663 | 1.13322 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 416.386 | 1.85009 | 0.925046 | − | 0.379854i | \(-0.124026\pi\) | ||||
0.925046 | + | 0.379854i | \(0.124026\pi\) | |||||||
\(38\) | −45.2948 | −0.193363 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −76.1411 | −0.290030 | −0.145015 | − | 0.989429i | \(-0.546323\pi\) | ||||
−0.145015 | + | 0.989429i | \(0.546323\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −31.7372 | −0.112555 | −0.0562777 | − | 0.998415i | \(-0.517923\pi\) | ||||
−0.0562777 | + | 0.998415i | \(0.517923\pi\) | |||||||
\(44\) | 174.519 | 0.597950 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 289.443 | 0.927741 | ||||||||
\(47\) | 60.8026 | 0.188701 | 0.0943507 | − | 0.995539i | \(-0.469922\pi\) | ||||
0.0943507 | + | 0.995539i | \(0.469922\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 599.493 | 1.74779 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −55.5320 | −0.148094 | ||||||||
\(53\) | −466.532 | −1.20911 | −0.604557 | − | 0.796562i | \(-0.706650\pi\) | ||||
−0.604557 | + | 0.796562i | \(0.706650\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 749.297 | 1.78802 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 476.938 | 1.07974 | ||||||||
\(59\) | −95.4239 | −0.210562 | −0.105281 | − | 0.994443i | \(-0.533574\pi\) | ||||
−0.105281 | + | 0.994443i | \(0.533574\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −357.174 | −0.749696 | −0.374848 | − | 0.927086i | \(-0.622305\pi\) | ||||
−0.374848 | + | 0.927086i | \(0.622305\pi\) | |||||||
\(62\) | −480.464 | −0.984178 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 498.842 | 0.974300 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −87.8344 | −0.160159 | −0.0800797 | − | 0.996788i | \(-0.525517\pi\) | ||||
−0.0800797 | + | 0.996788i | \(0.525517\pi\) | |||||||
\(68\) | −367.685 | −0.655711 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −412.693 | −0.689826 | −0.344913 | − | 0.938635i | \(-0.612092\pi\) | ||||
−0.344913 | + | 0.938635i | \(0.612092\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 331.133 | 0.530906 | 0.265453 | − | 0.964124i | \(-0.414478\pi\) | ||||
0.265453 | + | 0.964124i | \(0.414478\pi\) | |||||||
\(74\) | 885.286 | 1.39071 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 74.1296 | 0.111885 | ||||||||
\(77\) | 1539.75 | 2.27885 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −248.123 | −0.353368 | −0.176684 | − | 0.984268i | \(-0.556537\pi\) | ||||
−0.176684 | + | 0.984268i | \(0.556537\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −161.885 | −0.218015 | ||||||||
\(83\) | −552.505 | −0.730667 | −0.365333 | − | 0.930877i | \(-0.619045\pi\) | ||||
−0.365333 | + | 0.930877i | \(0.619045\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −67.4771 | −0.0846075 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1224.13 | 1.48287 | ||||||||
\(89\) | 291.478 | 0.347153 | 0.173577 | − | 0.984820i | \(-0.444468\pi\) | ||||
0.173577 | + | 0.984820i | \(0.444468\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −489.949 | −0.564402 | ||||||||
\(92\) | −473.704 | −0.536816 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 129.274 | 0.141846 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −198.606 | −0.207891 | −0.103946 | − | 0.994583i | \(-0.533147\pi\) | ||||
−0.103946 | + | 0.994583i | \(0.533147\pi\) | |||||||
\(98\) | 1274.59 | 1.31381 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −816.235 | −0.804143 | −0.402071 | − | 0.915608i | \(-0.631710\pi\) | ||||
−0.402071 | + | 0.915608i | \(0.631710\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1402.37 | 1.34155 | 0.670776 | − | 0.741660i | \(-0.265961\pi\) | ||||
0.670776 | + | 0.741660i | \(0.265961\pi\) | |||||||
\(104\) | −389.518 | −0.367263 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −991.902 | −0.908887 | ||||||||
\(107\) | −978.996 | −0.884515 | −0.442258 | − | 0.896888i | \(-0.645822\pi\) | ||||
−0.442258 | + | 0.896888i | \(0.645822\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2122.96 | 1.86553 | 0.932766 | − | 0.360484i | \(-0.117388\pi\) | ||||
0.932766 | + | 0.360484i | \(0.117388\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 738.500 | 0.623051 | ||||||||
\(113\) | 1794.80 | 1.49416 | 0.747082 | − | 0.664732i | \(-0.231454\pi\) | ||||
0.747082 | + | 0.664732i | \(0.231454\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −780.559 | −0.624768 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −202.883 | −0.158278 | ||||||||
\(119\) | −3244.02 | −2.49898 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1184.50 | 0.889935 | ||||||||
\(122\) | −759.395 | −0.563544 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 786.330 | 0.569472 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 748.894 | 0.523257 | 0.261628 | − | 0.965169i | \(-0.415741\pi\) | ||||
0.261628 | + | 0.965169i | \(0.415741\pi\) | |||||||
\(128\) | −92.2971 | −0.0637343 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2396.11 | 1.59808 | 0.799042 | − | 0.601275i | \(-0.205340\pi\) | ||||
0.799042 | + | 0.601275i | \(0.205340\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 654.033 | 0.426405 | ||||||||
\(134\) | −186.746 | −0.120391 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2579.05 | −1.62611 | ||||||||
\(137\) | 1004.48 | 0.626409 | 0.313205 | − | 0.949686i | \(-0.398597\pi\) | ||||
0.313205 | + | 0.949686i | \(0.398597\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2403.02 | 1.46634 | 0.733172 | − | 0.680043i | \(-0.238039\pi\) | ||||
0.733172 | + | 0.680043i | \(0.238039\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −877.435 | −0.518540 | ||||||||
\(143\) | −800.432 | −0.468080 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 704.028 | 0.399081 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1448.86 | −0.804701 | ||||||||
\(149\) | −509.648 | −0.280215 | −0.140107 | − | 0.990136i | \(-0.544745\pi\) | ||||
−0.140107 | + | 0.990136i | \(0.544745\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1443.30 | 0.777840 | 0.388920 | − | 0.921272i | \(-0.372848\pi\) | ||||
0.388920 | + | 0.921272i | \(0.372848\pi\) | |||||||
\(152\) | 519.967 | 0.277466 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3273.70 | 1.71300 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2155.64 | 1.09579 | 0.547895 | − | 0.836547i | \(-0.315429\pi\) | ||||
0.547895 | + | 0.836547i | \(0.315429\pi\) | |||||||
\(158\) | −527.539 | −0.265625 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4179.41 | −2.04586 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 529.909 | 0.254636 | 0.127318 | − | 0.991862i | \(-0.459363\pi\) | ||||
0.127318 | + | 0.991862i | \(0.459363\pi\) | |||||||
\(164\) | 264.942 | 0.126149 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1174.69 | −0.549240 | ||||||||
\(167\) | −2979.28 | −1.38050 | −0.690250 | − | 0.723571i | \(-0.742499\pi\) | ||||
−0.690250 | + | 0.723571i | \(0.742499\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1942.30 | −0.884071 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 110.433 | 0.0489562 | ||||||||
\(173\) | 1779.88 | 0.782205 | 0.391103 | − | 0.920347i | \(-0.372094\pi\) | ||||
0.391103 | + | 0.920347i | \(0.372094\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1206.49 | 0.516720 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 619.718 | 0.260954 | ||||||||
\(179\) | 2836.26 | 1.18431 | 0.592157 | − | 0.805823i | \(-0.298276\pi\) | ||||
0.592157 | + | 0.805823i | \(0.298276\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 811.890 | 0.333410 | 0.166705 | − | 0.986007i | \(-0.446687\pi\) | ||||
0.166705 | + | 0.986007i | \(0.446687\pi\) | |||||||
\(182\) | −1041.69 | −0.424259 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3322.70 | −1.33126 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5299.77 | −2.07250 | ||||||||
\(188\) | −211.570 | −0.0820761 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1148.46 | −0.435077 | −0.217539 | − | 0.976052i | \(-0.569803\pi\) | ||||
−0.217539 | + | 0.976052i | \(0.569803\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2150.93 | 0.802215 | 0.401107 | − | 0.916031i | \(-0.368625\pi\) | ||||
0.401107 | + | 0.916031i | \(0.368625\pi\) | |||||||
\(194\) | −422.261 | −0.156271 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2086.00 | −0.760206 | ||||||||
\(197\) | −5057.51 | −1.82910 | −0.914551 | − | 0.404471i | \(-0.867456\pi\) | ||||
−0.914551 | + | 0.404471i | \(0.867456\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3554.12 | −1.26605 | −0.633027 | − | 0.774130i | \(-0.718188\pi\) | ||||
−0.633027 | + | 0.774130i | \(0.718188\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1735.41 | −0.604471 | ||||||||
\(203\) | −6886.73 | −2.38105 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2981.61 | 1.00844 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −383.905 | −0.127976 | ||||||||
\(209\) | 1068.50 | 0.353634 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −107.909 | −0.0352075 | −0.0176038 | − | 0.999845i | \(-0.505604\pi\) | ||||
−0.0176038 | + | 0.999845i | \(0.505604\pi\) | |||||||
\(212\) | 1623.35 | 0.525907 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2081.46 | −0.664887 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6937.65 | 2.17032 | ||||||||
\(218\) | 4513.67 | 1.40231 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1686.38 | 0.513296 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1942.03 | 0.583174 | 0.291587 | − | 0.956544i | \(-0.405817\pi\) | ||||
0.291587 | + | 0.956544i | \(0.405817\pi\) | |||||||
\(224\) | −4424.24 | −1.31967 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3815.96 | 1.12316 | ||||||||
\(227\) | 3443.99 | 1.00698 | 0.503492 | − | 0.864000i | \(-0.332048\pi\) | ||||
0.503492 | + | 0.864000i | \(0.332048\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2069.39 | 0.597159 | 0.298579 | − | 0.954385i | \(-0.403487\pi\) | ||||
0.298579 | + | 0.954385i | \(0.403487\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5475.07 | −1.54938 | ||||||||
\(233\) | −2769.24 | −0.778622 | −0.389311 | − | 0.921106i | \(-0.627287\pi\) | ||||
−0.389311 | + | 0.921106i | \(0.627287\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 332.038 | 0.0915842 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −6897.17 | −1.87848 | ||||||||
\(239\) | 2943.84 | 0.796742 | 0.398371 | − | 0.917224i | \(-0.369576\pi\) | ||||
0.398371 | + | 0.917224i | \(0.369576\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4474.54 | 1.19598 | 0.597988 | − | 0.801505i | \(-0.295967\pi\) | ||||
0.597988 | + | 0.801505i | \(0.295967\pi\) | |||||||
\(242\) | 2518.40 | 0.668961 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1242.83 | 0.326082 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −339.995 | −0.0875845 | ||||||||
\(248\) | 5515.55 | 1.41225 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2121.41 | 0.533474 | 0.266737 | − | 0.963769i | \(-0.414055\pi\) | ||||
0.266737 | + | 0.963769i | \(0.414055\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6827.92 | −1.69671 | ||||||||
\(254\) | 1592.24 | 0.393330 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4186.97 | −1.02221 | ||||||||
\(257\) | 4548.24 | 1.10393 | 0.551967 | − | 0.833866i | \(-0.313877\pi\) | ||||
0.551967 | + | 0.833866i | \(0.313877\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −12783.1 | −3.06680 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 5094.42 | 1.20127 | ||||||||
\(263\) | −3499.84 | −0.820567 | −0.410284 | − | 0.911958i | \(-0.634570\pi\) | ||||
−0.410284 | + | 0.911958i | \(0.634570\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1390.55 | 0.320527 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 305.630 | 0.0696616 | ||||||||
\(269\) | −2594.25 | −0.588008 | −0.294004 | − | 0.955804i | \(-0.594988\pi\) | ||||
−0.294004 | + | 0.955804i | \(0.594988\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8518.20 | 1.90939 | 0.954693 | − | 0.297593i | \(-0.0961838\pi\) | ||||
0.954693 | + | 0.297593i | \(0.0961838\pi\) | |||||||
\(272\) | −2541.89 | −0.566634 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2135.63 | 0.470870 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1890.50 | 0.410068 | 0.205034 | − | 0.978755i | \(-0.434269\pi\) | ||||
0.205034 | + | 0.978755i | \(0.434269\pi\) | |||||||
\(278\) | 5109.12 | 1.10225 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3138.68 | −0.666328 | −0.333164 | − | 0.942869i | \(-0.608116\pi\) | ||||
−0.333164 | + | 0.942869i | \(0.608116\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4069.09 | −0.854708 | −0.427354 | − | 0.904084i | \(-0.640554\pi\) | ||||
−0.427354 | + | 0.904084i | \(0.640554\pi\) | |||||||
\(284\) | 1436.01 | 0.300041 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1701.81 | −0.351854 | ||||||||
\(287\) | 2337.54 | 0.480768 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6252.77 | 1.27270 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1152.22 | −0.230919 | ||||||||
\(293\) | 3637.95 | 0.725362 | 0.362681 | − | 0.931913i | \(-0.381861\pi\) | ||||
0.362681 | + | 0.931913i | \(0.381861\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −10162.7 | −1.99560 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1083.57 | −0.210637 | ||||||||
\(299\) | 2172.64 | 0.420224 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 974.334 | 0.186577 | ||||||||
\(302\) | 3068.62 | 0.584700 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 512.474 | 0.0966856 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6829.07 | 1.26956 | 0.634781 | − | 0.772692i | \(-0.281090\pi\) | ||||
0.634781 | + | 0.772692i | \(0.281090\pi\) | |||||||
\(308\) | −5357.75 | −0.991189 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6601.03 | −1.20357 | −0.601785 | − | 0.798659i | \(-0.705543\pi\) | ||||
−0.601785 | + | 0.798659i | \(0.705543\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2766.59 | −0.499607 | −0.249803 | − | 0.968297i | \(-0.580366\pi\) | ||||
−0.249803 | + | 0.968297i | \(0.580366\pi\) | |||||||
\(314\) | 4583.15 | 0.823701 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 863.373 | 0.153698 | ||||||||
\(317\) | 4564.41 | 0.808716 | 0.404358 | − | 0.914601i | \(-0.367495\pi\) | ||||
0.404358 | + | 0.914601i | \(0.367495\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −11250.9 | −1.97470 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −8885.92 | −1.53787 | ||||||||
\(323\) | −2251.15 | −0.387794 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1126.65 | 0.191409 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1858.38 | 0.312841 | ||||||||
\(329\) | −1866.64 | −0.312800 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4665.62 | −0.774760 | −0.387380 | − | 0.921920i | \(-0.626620\pi\) | ||||
−0.387380 | + | 0.921920i | \(0.626620\pi\) | |||||||
\(332\) | 1922.51 | 0.317805 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −6334.30 | −1.03772 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3807.06 | 0.615382 | 0.307691 | − | 0.951486i | \(-0.400444\pi\) | ||||
0.307691 | + | 0.951486i | \(0.400444\pi\) | |||||||
\(338\) | −4129.57 | −0.664553 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11334.1 | 1.79993 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7874.33 | −1.23957 | ||||||||
\(344\) | 774.612 | 0.121408 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3784.23 | 0.587981 | ||||||||
\(347\) | 2311.26 | 0.357565 | 0.178783 | − | 0.983889i | \(-0.442784\pi\) | ||||
0.178783 | + | 0.983889i | \(0.442784\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10873.2 | −1.66771 | −0.833854 | − | 0.551984i | \(-0.813871\pi\) | ||||
−0.833854 | + | 0.551984i | \(0.813871\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −7227.89 | −1.09445 | ||||||||
\(353\) | −2893.74 | −0.436312 | −0.218156 | − | 0.975914i | \(-0.570004\pi\) | ||||
−0.218156 | + | 0.975914i | \(0.570004\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1014.23 | −0.150995 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6030.23 | 0.890245 | ||||||||
\(359\) | 9875.47 | 1.45183 | 0.725915 | − | 0.687784i | \(-0.241416\pi\) | ||||
0.725915 | + | 0.687784i | \(0.241416\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6405.14 | −0.933830 | ||||||||
\(362\) | 1726.17 | 0.250624 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1704.83 | 0.245488 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10722.2 | −1.52505 | −0.762523 | − | 0.646961i | \(-0.776040\pi\) | ||||
−0.762523 | + | 0.646961i | \(0.776040\pi\) | |||||||
\(368\) | −3274.82 | −0.463891 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 14322.5 | 2.00428 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4175.90 | −0.579678 | −0.289839 | − | 0.957075i | \(-0.593602\pi\) | ||||
−0.289839 | + | 0.957075i | \(0.593602\pi\) | |||||||
\(374\) | −11267.9 | −1.55789 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1484.01 | −0.203543 | ||||||||
\(377\) | 3580.03 | 0.489074 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1715.14 | 0.232457 | 0.116228 | − | 0.993223i | \(-0.462920\pi\) | ||||
0.116228 | + | 0.993223i | \(0.462920\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2441.77 | −0.327046 | ||||||||
\(383\) | 5139.06 | 0.685624 | 0.342812 | − | 0.939404i | \(-0.388621\pi\) | ||||
0.342812 | + | 0.939404i | \(0.388621\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4573.14 | 0.603022 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 691.074 | 0.0904226 | ||||||||
\(389\) | −8996.53 | −1.17260 | −0.586301 | − | 0.810093i | \(-0.699416\pi\) | ||||
−0.586301 | + | 0.810093i | \(0.699416\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14385.3 | 1.86061 | ||||||||
\(392\) | −14631.8 | −1.88525 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −10752.9 | −1.37493 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 105.823 | 0.0133781 | 0.00668905 | − | 0.999978i | \(-0.497871\pi\) | ||||
0.00668905 | + | 0.999978i | \(0.497871\pi\) | |||||||
\(398\) | −7556.48 | −0.951688 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14481.8 | −1.80346 | −0.901730 | − | 0.432300i | \(-0.857702\pi\) | ||||
−0.901730 | + | 0.432300i | \(0.857702\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3606.50 | −0.445788 | ||||||||
\(404\) | 2840.18 | 0.349763 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −14642.0 | −1.78983 | ||||||||
\(407\) | −20883.8 | −2.54341 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −861.065 | −0.104100 | −0.0520500 | − | 0.998644i | \(-0.516576\pi\) | ||||
−0.0520500 | + | 0.998644i | \(0.516576\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4879.72 | −0.583511 | ||||||||
\(413\) | 2929.52 | 0.349037 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2299.91 | 0.271064 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2271.75 | 0.265825 | ||||||||
\(419\) | 13017.7 | 1.51780 | 0.758900 | − | 0.651207i | \(-0.225737\pi\) | ||||
0.758900 | + | 0.651207i | \(0.225737\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14546.6 | 1.68398 | 0.841991 | − | 0.539492i | \(-0.181384\pi\) | ||||
0.841991 | + | 0.539492i | \(0.181384\pi\) | |||||||
\(422\) | −229.428 | −0.0264654 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 11386.7 | 1.30421 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10965.3 | 1.24273 | ||||||||
\(428\) | 3406.53 | 0.384722 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3539.94 | 0.395622 | 0.197811 | − | 0.980240i | \(-0.436617\pi\) | ||||
0.197811 | + | 0.980240i | \(0.436617\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −669.471 | −0.0743019 | −0.0371509 | − | 0.999310i | \(-0.511828\pi\) | ||||
−0.0371509 | + | 0.999310i | \(0.511828\pi\) | |||||||
\(434\) | 14750.3 | 1.63142 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7387.09 | −0.811416 | ||||||||
\(437\) | −2900.26 | −0.317478 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12568.5 | 1.36643 | 0.683216 | − | 0.730216i | \(-0.260581\pi\) | ||||
0.683216 | + | 0.730216i | \(0.260581\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3585.45 | 0.385843 | ||||||||
\(443\) | 11060.3 | 1.18621 | 0.593106 | − | 0.805124i | \(-0.297901\pi\) | ||||
0.593106 | + | 0.805124i | \(0.297901\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 4128.98 | 0.438370 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −15314.5 | −1.61504 | ||||||||
\(449\) | −18553.9 | −1.95014 | −0.975072 | − | 0.221891i | \(-0.928777\pi\) | ||||
−0.975072 | + | 0.221891i | \(0.928777\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3818.84 | 0.398719 | ||||||||
\(452\) | −6245.21 | −0.649889 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 7322.33 | 0.756947 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6802.26 | 0.696272 | 0.348136 | − | 0.937444i | \(-0.386815\pi\) | ||||
0.348136 | + | 0.937444i | \(0.386815\pi\) | |||||||
\(458\) | 4399.78 | 0.448882 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14894.4 | −1.50477 | −0.752386 | − | 0.658722i | \(-0.771097\pi\) | ||||
−0.752386 | + | 0.658722i | \(0.771097\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14288.7 | 1.43423 | 0.717117 | − | 0.696952i | \(-0.245461\pi\) | ||||
0.717117 | + | 0.696952i | \(0.245461\pi\) | |||||||
\(464\) | −5396.17 | −0.539895 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5887.74 | −0.585288 | ||||||||
\(467\) | 13115.1 | 1.29956 | 0.649780 | − | 0.760122i | \(-0.274861\pi\) | ||||
0.649780 | + | 0.760122i | \(0.274861\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2696.52 | 0.265488 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2329.01 | 0.227122 | ||||||||
\(473\) | 1591.77 | 0.154735 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 11287.9 | 1.08694 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 6258.96 | 0.598908 | ||||||||
\(479\) | −7919.79 | −0.755458 | −0.377729 | − | 0.925916i | \(-0.623295\pi\) | ||||
−0.377729 | + | 0.925916i | \(0.623295\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6645.20 | 0.629927 | ||||||||
\(482\) | 9513.40 | 0.899011 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4121.62 | −0.387079 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17003.1 | 1.58210 | 0.791051 | − | 0.611751i | \(-0.209534\pi\) | ||||
0.791051 | + | 0.611751i | \(0.209534\pi\) | |||||||
\(488\) | 8717.56 | 0.808659 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6391.74 | −0.587485 | −0.293743 | − | 0.955885i | \(-0.594901\pi\) | ||||
−0.293743 | + | 0.955885i | \(0.594901\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 23703.8 | 2.16545 | ||||||||
\(494\) | −722.870 | −0.0658370 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5436.07 | 0.492111 | ||||||||
\(497\) | 12669.7 | 1.14349 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2674.12 | −0.239900 | −0.119950 | − | 0.992780i | \(-0.538273\pi\) | ||||
−0.119950 | + | 0.992780i | \(0.538273\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 4510.36 | 0.401011 | ||||||||
\(503\) | 1263.13 | 0.111969 | 0.0559843 | − | 0.998432i | \(-0.482170\pi\) | ||||
0.0559843 | + | 0.998432i | \(0.482170\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −14517.0 | −1.27541 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2605.86 | −0.227592 | ||||||||
\(509\) | −1380.84 | −0.120245 | −0.0601226 | − | 0.998191i | \(-0.519149\pi\) | ||||
−0.0601226 | + | 0.998191i | \(0.519149\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10165.8 | −0.880055 | ||||||||
\(512\) | −8163.62 | −0.704657 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 9670.09 | 0.829824 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3049.54 | −0.259417 | ||||||||
\(518\) | −27178.3 | −2.30530 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2689.80 | −0.226185 | −0.113092 | − | 0.993584i | \(-0.536076\pi\) | ||||
−0.113092 | + | 0.993584i | \(0.536076\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7144.18 | −0.597310 | −0.298655 | − | 0.954361i | \(-0.596538\pi\) | ||||
−0.298655 | + | 0.954361i | \(0.596538\pi\) | |||||||
\(524\) | −8337.54 | −0.695090 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7441.07 | −0.616818 | ||||||||
\(527\) | −23879.1 | −1.97379 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6366.25 | 0.523239 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2275.78 | −0.185466 | ||||||||
\(533\) | −1215.15 | −0.0987508 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2143.78 | 0.172756 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −5515.68 | −0.442004 | ||||||||
\(539\) | −30067.4 | −2.40278 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3310.57 | −0.263091 | −0.131546 | − | 0.991310i | \(-0.541994\pi\) | ||||
−0.131546 | + | 0.991310i | \(0.541994\pi\) | |||||||
\(542\) | 18110.7 | 1.43528 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 15228.0 | 1.20018 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2286.52 | −0.178729 | −0.0893643 | − | 0.995999i | \(-0.528484\pi\) | ||||
−0.0893643 | + | 0.995999i | \(0.528484\pi\) | |||||||
\(548\) | −3495.19 | −0.272458 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4778.98 | −0.369494 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7617.39 | 0.585758 | ||||||||
\(554\) | 4019.42 | 0.308247 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8361.60 | −0.637789 | ||||||||
\(557\) | −13846.6 | −1.05332 | −0.526658 | − | 0.850077i | \(-0.676555\pi\) | ||||
−0.526658 | + | 0.850077i | \(0.676555\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −506.502 | −0.0383233 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6673.21 | −0.500876 | ||||||||
\(563\) | 16164.4 | 1.21003 | 0.605017 | − | 0.796213i | \(-0.293166\pi\) | ||||
0.605017 | + | 0.796213i | \(0.293166\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −8651.37 | −0.642481 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 10072.6 | 0.744080 | ||||||||
\(569\) | 496.334 | 0.0365684 | 0.0182842 | − | 0.999833i | \(-0.494180\pi\) | ||||
0.0182842 | + | 0.999833i | \(0.494180\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5971.18 | 0.437629 | 0.218815 | − | 0.975766i | \(-0.429781\pi\) | ||||
0.218815 | + | 0.975766i | \(0.429781\pi\) | |||||||
\(572\) | 2785.20 | 0.203592 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 4969.88 | 0.361392 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9571.82 | −0.690607 | −0.345304 | − | 0.938491i | \(-0.612224\pi\) | ||||
−0.345304 | + | 0.938491i | \(0.612224\pi\) | |||||||
\(578\) | 13294.1 | 0.956684 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 16961.9 | 1.21119 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 23398.8 | 1.66223 | ||||||||
\(584\) | −8081.97 | −0.572662 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7734.71 | 0.545253 | ||||||||
\(587\) | −5322.18 | −0.374225 | −0.187112 | − | 0.982339i | \(-0.559913\pi\) | ||||
−0.187112 | + | 0.982339i | \(0.559913\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4814.31 | 0.336791 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −10016.3 | −0.695385 | ||||||||
\(593\) | 11066.5 | 0.766354 | 0.383177 | − | 0.923675i | \(-0.374830\pi\) | ||||
0.383177 | + | 0.923675i | \(0.374830\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1773.38 | 0.121880 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 4619.29 | 0.315881 | ||||||||
\(599\) | 18385.0 | 1.25407 | 0.627037 | − | 0.778989i | \(-0.284267\pi\) | ||||
0.627037 | + | 0.778989i | \(0.284267\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −617.830 | −0.0419331 | −0.0209666 | − | 0.999780i | \(-0.506674\pi\) | ||||
−0.0209666 | + | 0.999780i | \(0.506674\pi\) | |||||||
\(602\) | 2071.55 | 0.140249 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −5022.12 | −0.338323 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13839.8 | −0.925436 | −0.462718 | − | 0.886506i | \(-0.653126\pi\) | ||||
−0.462718 | + | 0.886506i | \(0.653126\pi\) | |||||||
\(608\) | −3070.15 | −0.204788 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 970.362 | 0.0642498 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 25655.4 | 1.69039 | 0.845196 | − | 0.534457i | \(-0.179484\pi\) | ||||
0.845196 | + | 0.534457i | \(0.179484\pi\) | |||||||
\(614\) | 14519.4 | 0.954326 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −37580.8 | −2.45808 | ||||||||
\(617\) | −4218.26 | −0.275236 | −0.137618 | − | 0.990485i | \(-0.543945\pi\) | ||||
−0.137618 | + | 0.990485i | \(0.543945\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12182.6 | 0.791047 | 0.395524 | − | 0.918456i | \(-0.370563\pi\) | ||||
0.395524 | + | 0.918456i | \(0.370563\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −14034.6 | −0.904719 | ||||||||
\(623\) | −8948.40 | −0.575458 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −5882.10 | −0.375553 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −7500.80 | −0.476616 | ||||||||
\(629\) | 43998.8 | 2.78910 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16673.2 | 1.05190 | 0.525951 | − | 0.850515i | \(-0.323709\pi\) | ||||
0.525951 | + | 0.850515i | \(0.323709\pi\) | |||||||
\(632\) | 6055.95 | 0.381159 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 9704.48 | 0.607909 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9567.44 | 0.595096 | ||||||||
\(638\) | −23920.7 | −1.48437 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 26270.8 | 1.61878 | 0.809388 | − | 0.587275i | \(-0.199799\pi\) | ||||
0.809388 | + | 0.587275i | \(0.199799\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11556.3 | −0.708767 | −0.354384 | − | 0.935100i | \(-0.615309\pi\) | ||||
−0.354384 | + | 0.935100i | \(0.615309\pi\) | |||||||
\(644\) | 14542.7 | 0.889851 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4786.22 | −0.291504 | ||||||||
\(647\) | 25395.2 | 1.54310 | 0.771552 | − | 0.636166i | \(-0.219481\pi\) | ||||
0.771552 | + | 0.636166i | \(0.219481\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4785.96 | 0.289469 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1843.88 | −0.110754 | ||||||||
\(653\) | 6182.84 | 0.370526 | 0.185263 | − | 0.982689i | \(-0.440686\pi\) | ||||
0.185263 | + | 0.982689i | \(0.440686\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1831.60 | 0.109012 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −3968.70 | −0.235131 | ||||||||
\(659\) | −8885.32 | −0.525224 | −0.262612 | − | 0.964901i | \(-0.584584\pi\) | ||||
−0.262612 | + | 0.964901i | \(0.584584\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7171.60 | −0.422001 | −0.211001 | − | 0.977486i | \(-0.567672\pi\) | ||||
−0.211001 | + | 0.977486i | \(0.567672\pi\) | |||||||
\(662\) | −9919.66 | −0.582385 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 13485.0 | 0.788133 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 30538.7 | 1.77281 | ||||||||
\(668\) | 10366.7 | 0.600451 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 17914.0 | 1.03064 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4250.52 | 0.243455 | 0.121728 | − | 0.992564i | \(-0.461157\pi\) | ||||
0.121728 | + | 0.992564i | \(0.461157\pi\) | |||||||
\(674\) | 8094.27 | 0.462581 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6758.47 | 0.384528 | ||||||||
\(677\) | −2233.65 | −0.126804 | −0.0634019 | − | 0.997988i | \(-0.520195\pi\) | ||||
−0.0634019 | + | 0.997988i | \(0.520195\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6097.23 | 0.344610 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 24097.6 | 1.35300 | ||||||||
\(683\) | 6071.62 | 0.340153 | 0.170076 | − | 0.985431i | \(-0.445599\pi\) | ||||
0.170076 | + | 0.985431i | \(0.445599\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −16741.8 | −0.931784 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 763.450 | 0.0423056 | ||||||||
\(689\) | −7445.49 | −0.411684 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −765.784 | −0.0421589 | −0.0210794 | − | 0.999778i | \(-0.506710\pi\) | ||||
−0.0210794 | + | 0.999778i | \(0.506710\pi\) | |||||||
\(692\) | −6193.29 | −0.340222 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4914.02 | 0.268780 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8045.70 | −0.437235 | ||||||||
\(698\) | −23117.8 | −1.25361 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 23564.3 | 1.26963 | 0.634814 | − | 0.772665i | \(-0.281077\pi\) | ||||
0.634814 | + | 0.772665i | \(0.281077\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8870.67 | −0.475909 | ||||||||
\(704\) | −25019.3 | −1.33942 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6152.43 | −0.327974 | ||||||||
\(707\) | 25058.4 | 1.33298 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 24172.3 | 1.28041 | 0.640204 | − | 0.768205i | \(-0.278850\pi\) | ||||
0.640204 | + | 0.768205i | \(0.278850\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −7114.13 | −0.374457 | ||||||||
\(713\) | −30764.5 | −1.61590 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −9869.11 | −0.515120 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 20996.4 | 1.09134 | ||||||||
\(719\) | 12829.0 | 0.665424 | 0.332712 | − | 0.943028i | \(-0.392036\pi\) | ||||
0.332712 | + | 0.943028i | \(0.392036\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −43052.9 | −2.22382 | ||||||||
\(722\) | −13618.1 | −0.701957 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2825.06 | −0.145018 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24724.7 | 1.26133 | 0.630666 | − | 0.776054i | \(-0.282782\pi\) | ||||
0.630666 | + | 0.776054i | \(0.282782\pi\) | |||||||
\(728\) | 11958.2 | 0.608792 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3353.62 | −0.169683 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20172.2 | 1.01648 | 0.508239 | − | 0.861216i | \(-0.330297\pi\) | ||||
0.508239 | + | 0.861216i | \(0.330297\pi\) | |||||||
\(734\) | −22796.6 | −1.14637 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 19618.9 | 0.982559 | ||||||||
\(737\) | 4405.32 | 0.220179 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16452.8 | −0.818979 | −0.409489 | − | 0.912315i | \(-0.634293\pi\) | ||||
−0.409489 | + | 0.912315i | \(0.634293\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 30451.4 | 1.50661 | ||||||||
\(743\) | −20864.6 | −1.03021 | −0.515107 | − | 0.857126i | \(-0.672248\pi\) | ||||
−0.515107 | + | 0.857126i | \(0.672248\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −8878.47 | −0.435742 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 18441.2 | 0.901438 | ||||||||
\(749\) | 30055.2 | 1.46621 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15525.7 | 0.754381 | 0.377191 | − | 0.926136i | \(-0.376890\pi\) | ||||
0.377191 | + | 0.926136i | \(0.376890\pi\) | |||||||
\(752\) | −1462.63 | −0.0709262 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 7611.56 | 0.367635 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −30105.7 | −1.44546 | −0.722729 | − | 0.691132i | \(-0.757112\pi\) | ||||
−0.722729 | + | 0.691132i | \(0.757112\pi\) | |||||||
\(758\) | 3646.60 | 0.174737 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −21739.9 | −1.03557 | −0.517786 | − | 0.855510i | \(-0.673244\pi\) | ||||
−0.517786 | + | 0.855510i | \(0.673244\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −65175.0 | −3.09239 | ||||||||
\(764\) | 3996.21 | 0.189238 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 10926.3 | 0.515381 | ||||||||
\(767\) | −1522.89 | −0.0716929 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1942.22 | 0.0910772 | 0.0455386 | − | 0.998963i | \(-0.485500\pi\) | ||||
0.0455386 | + | 0.998963i | \(0.485500\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −7484.42 | −0.348925 | ||||||||
\(773\) | −7921.02 | −0.368563 | −0.184282 | − | 0.982873i | \(-0.558996\pi\) | ||||
−0.184282 | + | 0.982873i | \(0.558996\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 4847.40 | 0.224241 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −19127.7 | −0.881441 | ||||||||
\(779\) | 1622.11 | 0.0746060 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 20698.5 | 0.948338 | ||||||||
\(782\) | 30585.0 | 1.39861 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −14421.0 | −0.656933 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1361.40 | 0.0616630 | 0.0308315 | − | 0.999525i | \(-0.490184\pi\) | ||||
0.0308315 | + | 0.999525i | \(0.490184\pi\) | |||||||
\(788\) | 17598.2 | 0.795571 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −55100.4 | −2.47679 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5700.22 | −0.255260 | ||||||||
\(794\) | 224.992 | 0.0100563 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 12367.0 | 0.550672 | ||||||||
\(797\) | 27917.5 | 1.24076 | 0.620381 | − | 0.784300i | \(-0.286978\pi\) | ||||
0.620381 | + | 0.784300i | \(0.286978\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6424.90 | 0.284476 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −30790.1 | −1.35565 | ||||||||
\(803\) | −16607.9 | −0.729863 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −7667.84 | −0.335097 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 19921.9 | 0.867388 | ||||||||
\(809\) | −5275.87 | −0.229283 | −0.114641 | − | 0.993407i | \(-0.536572\pi\) | ||||
−0.114641 | + | 0.993407i | \(0.536572\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −23769.1 | −1.02916 | −0.514579 | − | 0.857443i | \(-0.672052\pi\) | ||||
−0.514579 | + | 0.857443i | \(0.672052\pi\) | |||||||
\(812\) | 23963.2 | 1.03564 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −44401.4 | −1.91188 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 676.129 | 0.0289532 | ||||||||
\(818\) | −1830.73 | −0.0782516 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 34209.3 | 1.45422 | 0.727108 | − | 0.686523i | \(-0.240864\pi\) | ||||
0.727108 | + | 0.686523i | \(0.240864\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1240.13 | −0.0525252 | −0.0262626 | − | 0.999655i | \(-0.508361\pi\) | ||||
−0.0262626 | + | 0.999655i | \(0.508361\pi\) | |||||||
\(824\) | −34227.8 | −1.44706 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6228.50 | 0.262370 | ||||||||
\(827\) | −26971.0 | −1.13407 | −0.567034 | − | 0.823694i | \(-0.691909\pi\) | ||||
−0.567034 | + | 0.823694i | \(0.691909\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −26743.1 | −1.12042 | −0.560208 | − | 0.828352i | \(-0.689279\pi\) | ||||
−0.560208 | + | 0.828352i | \(0.689279\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 7961.13 | 0.331734 | ||||||||
\(833\) | 63347.3 | 2.63488 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −3717.96 | −0.153814 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 27677.3 | 1.14093 | ||||||||
\(839\) | 5273.14 | 0.216983 | 0.108492 | − | 0.994097i | \(-0.465398\pi\) | ||||
0.108492 | + | 0.994097i | \(0.465398\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25931.9 | 1.06326 | ||||||||
\(842\) | 30927.7 | 1.26584 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 375.483 | 0.0153136 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −36364.3 | −1.47520 | ||||||||
\(848\) | 11222.6 | 0.454464 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 56685.5 | 2.28338 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5043.46 | −0.202444 | −0.101222 | − | 0.994864i | \(-0.532275\pi\) | ||||
−0.101222 | + | 0.994864i | \(0.532275\pi\) | |||||||
\(854\) | 23313.5 | 0.934157 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 23894.4 | 0.954081 | ||||||||
\(857\) | −14478.5 | −0.577103 | −0.288552 | − | 0.957464i | \(-0.593174\pi\) | ||||
−0.288552 | + | 0.957464i | \(0.593174\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7873.88 | −0.312751 | −0.156376 | − | 0.987698i | \(-0.549981\pi\) | ||||
−0.156376 | + | 0.987698i | \(0.549981\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 7526.35 | 0.297388 | ||||||||
\(863\) | 24166.0 | 0.953209 | 0.476604 | − | 0.879118i | \(-0.341867\pi\) | ||||
0.476604 | + | 0.879118i | \(0.341867\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1423.38 | −0.0558525 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −24140.4 | −0.943983 | ||||||||
\(869\) | 12444.6 | 0.485792 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1401.77 | −0.0545317 | ||||||||
\(872\) | −51815.2 | −2.01225 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −6166.29 | −0.238647 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6411.82 | −0.246878 | −0.123439 | − | 0.992352i | \(-0.539392\pi\) | ||||
−0.123439 | + | 0.992352i | \(0.539392\pi\) | |||||||
\(878\) | 26722.2 | 1.02714 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −22908.5 | −0.876059 | −0.438029 | − | 0.898961i | \(-0.644323\pi\) | ||||
−0.438029 | + | 0.898961i | \(0.644323\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −39198.4 | −1.49392 | −0.746960 | − | 0.664869i | \(-0.768487\pi\) | ||||
−0.746960 | + | 0.664869i | \(0.768487\pi\) | |||||||
\(884\) | −5867.97 | −0.223259 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 23515.6 | 0.891672 | ||||||||
\(887\) | 5422.19 | 0.205253 | 0.102626 | − | 0.994720i | \(-0.467275\pi\) | ||||
0.102626 | + | 0.994720i | \(0.467275\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −22991.1 | −0.867375 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −6757.51 | −0.253653 | ||||||||
\(893\) | −1295.34 | −0.0485406 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2833.53 | 0.105649 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −39447.9 | −1.46592 | ||||||||
\(899\) | −50693.0 | −1.88065 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −49297.6 | −1.82280 | ||||||||
\(902\) | 8119.32 | 0.299716 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −43805.7 | −1.61168 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 30727.0 | 1.12489 | 0.562444 | − | 0.826836i | \(-0.309861\pi\) | ||||
0.562444 | + | 0.826836i | \(0.309861\pi\) | |||||||
\(908\) | −11983.8 | −0.437990 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4101.34 | −0.149159 | −0.0745793 | − | 0.997215i | \(-0.523761\pi\) | ||||
−0.0745793 | + | 0.997215i | \(0.523761\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 27710.8 | 1.00448 | ||||||||
\(914\) | 14462.4 | 0.523385 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −7200.69 | −0.259735 | ||||||||
\(917\) | −73560.7 | −2.64906 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −50926.3 | −1.82797 | −0.913984 | − | 0.405750i | \(-0.867010\pi\) | ||||
−0.913984 | + | 0.405750i | \(0.867010\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −31667.2 | −1.13113 | ||||||||
\(923\) | −6586.26 | −0.234875 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 30379.4 | 1.07811 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 32327.6 | 1.14354 | ||||||||
\(929\) | −22040.8 | −0.778402 | −0.389201 | − | 0.921153i | \(-0.627249\pi\) | ||||
−0.389201 | + | 0.921153i | \(0.627249\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −12771.6 | −0.449593 | ||||||||
\(932\) | 9635.89 | 0.338663 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 27884.3 | 0.976875 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −28111.2 | −0.980097 | −0.490049 | − | 0.871695i | \(-0.663021\pi\) | ||||
−0.490049 | + | 0.871695i | \(0.663021\pi\) | |||||||
\(938\) | 5733.12 | 0.199566 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −52811.3 | −1.82954 | −0.914770 | − | 0.403974i | \(-0.867629\pi\) | ||||
−0.914770 | + | 0.403974i | \(0.867629\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10365.6 | −0.357954 | ||||||||
\(944\) | 2295.45 | 0.0791427 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3384.30 | 0.116314 | ||||||||
\(947\) | −1826.23 | −0.0626657 | −0.0313329 | − | 0.999509i | \(-0.509975\pi\) | ||||
−0.0313329 | + | 0.999509i | \(0.509975\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5284.63 | 0.180765 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 79176.9 | 2.69552 | ||||||||
\(953\) | −41164.2 | −1.39920 | −0.699601 | − | 0.714534i | \(-0.746639\pi\) | ||||
−0.699601 | + | 0.714534i | \(0.746639\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −10243.4 | −0.346545 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −16838.4 | −0.567875 | ||||||||
\(959\) | −30837.4 | −1.03837 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 21276.8 | 0.714202 | ||||||||
\(962\) | 14128.5 | 0.473514 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −15569.7 | −0.520192 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7088.78 | 0.235739 | 0.117870 | − | 0.993029i | \(-0.462394\pi\) | ||||
0.117870 | + | 0.993029i | \(0.462394\pi\) | |||||||
\(968\) | −28910.2 | −0.959927 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2355.90 | −0.0778625 | −0.0389312 | − | 0.999242i | \(-0.512395\pi\) | ||||
−0.0389312 | + | 0.999242i | \(0.512395\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −73773.0 | −2.43068 | ||||||||
\(974\) | 36150.6 | 1.18926 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8591.95 | 0.281784 | ||||||||
\(977\) | −16795.1 | −0.549972 | −0.274986 | − | 0.961448i | \(-0.588673\pi\) | ||||
−0.274986 | + | 0.961448i | \(0.588673\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14619.0 | −0.477249 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −13589.6 | −0.441611 | ||||||||
\(983\) | −14733.8 | −0.478063 | −0.239032 | − | 0.971012i | \(-0.576830\pi\) | ||||
−0.239032 | + | 0.971012i | \(0.576830\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 50397.2 | 1.62776 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1183.05 | 0.0380950 | ||||||||
\(989\) | −4320.61 | −0.138915 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 36809.2 | 1.17990 | 0.589950 | − | 0.807440i | \(-0.299147\pi\) | ||||
0.589950 | + | 0.807440i | \(0.299147\pi\) | |||||||
\(992\) | −32566.6 | −1.04233 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 26937.3 | 0.859556 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21210.0 | 0.673749 | 0.336875 | − | 0.941550i | \(-0.390630\pi\) | ||||
0.336875 | + | 0.941550i | \(0.390630\pi\) | |||||||
\(998\) | −5685.49 | −0.180332 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 675.4.a.s.1.2 | 3 | ||
3.2 | odd | 2 | 675.4.a.p.1.2 | 3 | |||
5.2 | odd | 4 | 675.4.b.m.649.4 | 6 | |||
5.3 | odd | 4 | 675.4.b.m.649.3 | 6 | |||
5.4 | even | 2 | 135.4.a.e.1.2 | ✓ | 3 | ||
15.2 | even | 4 | 675.4.b.n.649.3 | 6 | |||
15.8 | even | 4 | 675.4.b.n.649.4 | 6 | |||
15.14 | odd | 2 | 135.4.a.h.1.2 | yes | 3 | ||
20.19 | odd | 2 | 2160.4.a.bi.1.1 | 3 | |||
45.4 | even | 6 | 405.4.e.v.136.2 | 6 | |||
45.14 | odd | 6 | 405.4.e.q.136.2 | 6 | |||
45.29 | odd | 6 | 405.4.e.q.271.2 | 6 | |||
45.34 | even | 6 | 405.4.e.v.271.2 | 6 | |||
60.59 | even | 2 | 2160.4.a.bq.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
135.4.a.e.1.2 | ✓ | 3 | 5.4 | even | 2 | ||
135.4.a.h.1.2 | yes | 3 | 15.14 | odd | 2 | ||
405.4.e.q.136.2 | 6 | 45.14 | odd | 6 | |||
405.4.e.q.271.2 | 6 | 45.29 | odd | 6 | |||
405.4.e.v.136.2 | 6 | 45.4 | even | 6 | |||
405.4.e.v.271.2 | 6 | 45.34 | even | 6 | |||
675.4.a.p.1.2 | 3 | 3.2 | odd | 2 | |||
675.4.a.s.1.2 | 3 | 1.1 | even | 1 | trivial | ||
675.4.b.m.649.3 | 6 | 5.3 | odd | 4 | |||
675.4.b.m.649.4 | 6 | 5.2 | odd | 4 | |||
675.4.b.n.649.3 | 6 | 15.2 | even | 4 | |||
675.4.b.n.649.4 | 6 | 15.8 | even | 4 | |||
2160.4.a.bi.1.1 | 3 | 20.19 | odd | 2 | |||
2160.4.a.bq.1.1 | 3 | 60.59 | even | 2 |