Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2025,4,Mod(1,2025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2025, 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("2025.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2025 = 3^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2025.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: | \(119.478867762\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 38x^{4} + 42x^{3} + 393x^{2} - 72x - 432 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2\cdot 3^{3} \) |
Twist minimal: | no (minimal twist has level 405) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-3.53444\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.53444 | 1.60317 | 0.801583 | − | 0.597883i | \(-0.203991\pi\) | ||||
0.801583 | + | 0.597883i | \(0.203991\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 12.5612 | 1.57014 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.63618 | 0.142340 | 0.0711702 | − | 0.997464i | \(-0.477327\pi\) | ||||
0.0711702 | + | 0.997464i | \(0.477327\pi\) | |||||||
\(8\) | 20.6823 | 0.914036 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −20.9310 | −0.573722 | −0.286861 | − | 0.957972i | \(-0.592612\pi\) | ||||
−0.286861 | + | 0.957972i | \(0.592612\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −60.9451 | −1.30024 | −0.650120 | − | 0.759832i | \(-0.725281\pi\) | ||||
−0.650120 | + | 0.759832i | \(0.725281\pi\) | |||||||
\(14\) | 11.9536 | 0.228195 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −6.70667 | −0.104792 | ||||||||
\(17\) | 86.8178 | 1.23861 | 0.619306 | − | 0.785150i | \(-0.287414\pi\) | ||||
0.619306 | + | 0.785150i | \(0.287414\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 41.8063 | 0.504791 | 0.252395 | − | 0.967624i | \(-0.418782\pi\) | ||||
0.252395 | + | 0.967624i | \(0.418782\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −94.9105 | −0.919772 | ||||||||
\(23\) | −97.3186 | −0.882275 | −0.441138 | − | 0.897439i | \(-0.645425\pi\) | ||||
−0.441138 | + | 0.897439i | \(0.645425\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −276.352 | −2.08450 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 33.1135 | 0.223495 | ||||||||
\(29\) | −157.070 | −1.00576 | −0.502882 | − | 0.864355i | \(-0.667727\pi\) | ||||
−0.502882 | + | 0.864355i | \(0.667727\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 95.3961 | 0.552698 | 0.276349 | − | 0.961057i | \(-0.410875\pi\) | ||||
0.276349 | + | 0.961057i | \(0.410875\pi\) | |||||||
\(32\) | −195.869 | −1.08203 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 393.670 | 1.98570 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 160.833 | 0.714617 | 0.357309 | − | 0.933986i | \(-0.383694\pi\) | ||||
0.357309 | + | 0.933986i | \(0.383694\pi\) | |||||||
\(38\) | 189.568 | 0.809263 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 233.189 | 0.888245 | 0.444123 | − | 0.895966i | \(-0.353515\pi\) | ||||
0.444123 | + | 0.895966i | \(0.353515\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −487.694 | −1.72960 | −0.864798 | − | 0.502121i | \(-0.832553\pi\) | ||||
−0.864798 | + | 0.502121i | \(0.832553\pi\) | |||||||
\(44\) | −262.918 | −0.900826 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −441.285 | −1.41443 | ||||||||
\(47\) | −24.3079 | −0.0754399 | −0.0377200 | − | 0.999288i | \(-0.512009\pi\) | ||||
−0.0377200 | + | 0.999288i | \(0.512009\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −336.051 | −0.979739 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −765.540 | −2.04156 | ||||||||
\(53\) | −709.828 | −1.83967 | −0.919834 | − | 0.392308i | \(-0.871677\pi\) | ||||
−0.919834 | + | 0.392308i | \(0.871677\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 54.5222 | 0.130104 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −712.225 | −1.61241 | ||||||||
\(59\) | −191.998 | −0.423661 | −0.211831 | − | 0.977306i | \(-0.567943\pi\) | ||||
−0.211831 | + | 0.977306i | \(0.567943\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −744.633 | −1.56296 | −0.781480 | − | 0.623931i | \(-0.785535\pi\) | ||||
−0.781480 | + | 0.623931i | \(0.785535\pi\) | |||||||
\(62\) | 432.568 | 0.886067 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −834.504 | −1.62989 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 823.567 | 1.50171 | 0.750856 | − | 0.660466i | \(-0.229641\pi\) | ||||
0.750856 | + | 0.660466i | \(0.229641\pi\) | |||||||
\(68\) | 1090.53 | 1.94480 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1068.85 | −1.78661 | −0.893304 | − | 0.449452i | \(-0.851619\pi\) | ||||
−0.893304 | + | 0.449452i | \(0.851619\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 132.416 | 0.212302 | 0.106151 | − | 0.994350i | \(-0.466147\pi\) | ||||
0.106151 | + | 0.994350i | \(0.466147\pi\) | |||||||
\(74\) | 729.289 | 1.14565 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 525.135 | 0.792594 | ||||||||
\(77\) | −55.1780 | −0.0816638 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −704.577 | −1.00343 | −0.501716 | − | 0.865033i | \(-0.667298\pi\) | ||||
−0.501716 | + | 0.865033i | \(0.667298\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1057.38 | 1.42401 | ||||||||
\(83\) | 1419.76 | 1.87758 | 0.938790 | − | 0.344489i | \(-0.111948\pi\) | ||||
0.938790 | + | 0.344489i | \(0.111948\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2211.42 | −2.77283 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −432.901 | −0.524402 | ||||||||
\(89\) | 401.847 | 0.478604 | 0.239302 | − | 0.970945i | \(-0.423081\pi\) | ||||
0.239302 | + | 0.970945i | \(0.423081\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −160.662 | −0.185077 | ||||||||
\(92\) | −1222.43 | −1.38530 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −110.223 | −0.120943 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −530.880 | −0.555698 | −0.277849 | − | 0.960625i | \(-0.589622\pi\) | ||||
−0.277849 | + | 0.960625i | \(0.589622\pi\) | |||||||
\(98\) | −1523.80 | −1.57069 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −998.463 | −0.983671 | −0.491835 | − | 0.870688i | \(-0.663674\pi\) | ||||
−0.491835 | + | 0.870688i | \(0.663674\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 837.473 | 0.801152 | 0.400576 | − | 0.916264i | \(-0.368810\pi\) | ||||
0.400576 | + | 0.916264i | \(0.368810\pi\) | |||||||
\(104\) | −1260.48 | −1.18847 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3218.67 | −2.94929 | ||||||||
\(107\) | −1109.39 | −1.00233 | −0.501163 | − | 0.865353i | \(-0.667094\pi\) | ||||
−0.501163 | + | 0.865353i | \(0.667094\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1071.73 | −0.941769 | −0.470885 | − | 0.882195i | \(-0.656065\pi\) | ||||
−0.470885 | + | 0.882195i | \(0.656065\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −17.6800 | −0.0149161 | ||||||||
\(113\) | 1089.50 | 0.907003 | 0.453501 | − | 0.891256i | \(-0.350175\pi\) | ||||
0.453501 | + | 0.891256i | \(0.350175\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1972.98 | −1.57920 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −870.604 | −0.679200 | ||||||||
\(119\) | 228.867 | 0.176305 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −892.892 | −0.670843 | ||||||||
\(122\) | −3376.50 | −2.50568 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1198.28 | 0.867816 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 371.442 | 0.259529 | 0.129764 | − | 0.991545i | \(-0.458578\pi\) | ||||
0.129764 | + | 0.991545i | \(0.458578\pi\) | |||||||
\(128\) | −2217.05 | −1.53095 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 265.266 | 0.176919 | 0.0884597 | − | 0.996080i | \(-0.471806\pi\) | ||||
0.0884597 | + | 0.996080i | \(0.471806\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 110.209 | 0.0718521 | ||||||||
\(134\) | 3734.42 | 2.40749 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1795.59 | 1.13214 | ||||||||
\(137\) | 270.721 | 0.168827 | 0.0844134 | − | 0.996431i | \(-0.473098\pi\) | ||||
0.0844134 | + | 0.996431i | \(0.473098\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1212.09 | −0.739627 | −0.369814 | − | 0.929106i | \(-0.620578\pi\) | ||||
−0.369814 | + | 0.929106i | \(0.620578\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4846.64 | −2.86423 | ||||||||
\(143\) | 1275.64 | 0.745976 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 600.431 | 0.340356 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2020.25 | 1.12205 | ||||||||
\(149\) | 2413.33 | 1.32690 | 0.663450 | − | 0.748221i | \(-0.269092\pi\) | ||||
0.663450 | + | 0.748221i | \(0.269092\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1169.19 | −0.630114 | −0.315057 | − | 0.949073i | \(-0.602024\pi\) | ||||
−0.315057 | + | 0.949073i | \(0.602024\pi\) | |||||||
\(152\) | 864.649 | 0.461397 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −250.201 | −0.130921 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2928.23 | 1.48852 | 0.744262 | − | 0.667888i | \(-0.232801\pi\) | ||||
0.744262 | + | 0.667888i | \(0.232801\pi\) | |||||||
\(158\) | −3194.86 | −1.60867 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −256.549 | −0.125583 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 936.208 | 0.449874 | 0.224937 | − | 0.974373i | \(-0.427782\pi\) | ||||
0.224937 | + | 0.974373i | \(0.427782\pi\) | |||||||
\(164\) | 2929.13 | 1.39467 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6437.83 | 3.01008 | ||||||||
\(167\) | −3133.05 | −1.45175 | −0.725876 | − | 0.687826i | \(-0.758565\pi\) | ||||
−0.725876 | + | 0.687826i | \(0.758565\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1517.30 | 0.690624 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −6125.99 | −2.71571 | ||||||||
\(173\) | −239.265 | −0.105150 | −0.0525751 | − | 0.998617i | \(-0.516743\pi\) | ||||
−0.0525751 | + | 0.998617i | \(0.516743\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 140.377 | 0.0601212 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1822.15 | 0.767282 | ||||||||
\(179\) | 332.030 | 0.138643 | 0.0693215 | − | 0.997594i | \(-0.477917\pi\) | ||||
0.0693215 | + | 0.997594i | \(0.477917\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3405.54 | 1.39852 | 0.699259 | − | 0.714869i | \(-0.253514\pi\) | ||||
0.699259 | + | 0.714869i | \(0.253514\pi\) | |||||||
\(182\) | −728.513 | −0.296709 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2012.77 | −0.806431 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1817.18 | −0.710619 | ||||||||
\(188\) | −305.336 | −0.118452 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5261.72 | −1.99332 | −0.996661 | − | 0.0816469i | \(-0.973982\pi\) | ||||
−0.996661 | + | 0.0816469i | \(0.973982\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −408.973 | −0.152531 | −0.0762656 | − | 0.997088i | \(-0.524300\pi\) | ||||
−0.0762656 | + | 0.997088i | \(0.524300\pi\) | |||||||
\(194\) | −2407.24 | −0.890877 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4221.18 | −1.53833 | ||||||||
\(197\) | 946.927 | 0.342466 | 0.171233 | − | 0.985231i | \(-0.445225\pi\) | ||||
0.171233 | + | 0.985231i | \(0.445225\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4917.06 | 1.75156 | 0.875782 | − | 0.482707i | \(-0.160346\pi\) | ||||
0.875782 | + | 0.482707i | \(0.160346\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −4527.47 | −1.57699 | ||||||||
\(203\) | −414.065 | −0.143161 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 3797.47 | 1.28438 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 408.738 | 0.136254 | ||||||||
\(209\) | −875.048 | −0.289609 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2449.40 | 0.799163 | 0.399582 | − | 0.916698i | \(-0.369155\pi\) | ||||
0.399582 | + | 0.916698i | \(0.369155\pi\) | |||||||
\(212\) | −8916.26 | −2.88854 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −5030.47 | −1.60690 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 251.481 | 0.0786713 | ||||||||
\(218\) | −4859.68 | −1.50981 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5291.11 | −1.61049 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1006.44 | 0.302227 | 0.151113 | − | 0.988516i | \(-0.451714\pi\) | ||||
0.151113 | + | 0.988516i | \(0.451714\pi\) | |||||||
\(224\) | −516.347 | −0.154017 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4940.26 | 1.45408 | ||||||||
\(227\) | 2024.04 | 0.591807 | 0.295903 | − | 0.955218i | \(-0.404379\pi\) | ||||
0.295903 | + | 0.955218i | \(0.404379\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6787.92 | −1.95877 | −0.979385 | − | 0.202004i | \(-0.935255\pi\) | ||||
−0.979385 | + | 0.202004i | \(0.935255\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3248.57 | −0.919305 | ||||||||
\(233\) | 4129.88 | 1.16119 | 0.580595 | − | 0.814193i | \(-0.302820\pi\) | ||||
0.580595 | + | 0.814193i | \(0.302820\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2411.72 | −0.665209 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1037.79 | 0.282646 | ||||||||
\(239\) | −2978.73 | −0.806185 | −0.403093 | − | 0.915159i | \(-0.632065\pi\) | ||||
−0.403093 | + | 0.915159i | \(0.632065\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1843.94 | −0.492858 | −0.246429 | − | 0.969161i | \(-0.579257\pi\) | ||||
−0.246429 | + | 0.969161i | \(0.579257\pi\) | |||||||
\(242\) | −4048.77 | −1.07547 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −9353.45 | −2.45407 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2547.89 | −0.656349 | ||||||||
\(248\) | 1973.01 | 0.505186 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2360.72 | 0.593656 | 0.296828 | − | 0.954931i | \(-0.404071\pi\) | ||||
0.296828 | + | 0.954931i | \(0.404071\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2036.98 | 0.506181 | ||||||||
\(254\) | 1684.28 | 0.416068 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3377.07 | −0.824481 | ||||||||
\(257\) | 2472.64 | 0.600151 | 0.300076 | − | 0.953915i | \(-0.402988\pi\) | ||||
0.300076 | + | 0.953915i | \(0.402988\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 423.986 | 0.101719 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1202.83 | 0.283631 | ||||||||
\(263\) | −2167.17 | −0.508112 | −0.254056 | − | 0.967189i | \(-0.581765\pi\) | ||||
−0.254056 | + | 0.967189i | \(0.581765\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 499.736 | 0.115191 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 10344.9 | 2.35790 | ||||||||
\(269\) | 4346.79 | 0.985236 | 0.492618 | − | 0.870246i | \(-0.336040\pi\) | ||||
0.492618 | + | 0.870246i | \(0.336040\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3923.45 | −0.879456 | −0.439728 | − | 0.898131i | \(-0.644925\pi\) | ||||
−0.439728 | + | 0.898131i | \(0.644925\pi\) | |||||||
\(272\) | −582.258 | −0.129796 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1227.57 | 0.270657 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6035.89 | −1.30925 | −0.654624 | − | 0.755955i | \(-0.727173\pi\) | ||||
−0.654624 | + | 0.755955i | \(0.727173\pi\) | |||||||
\(278\) | −5496.15 | −1.18575 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2296.92 | 0.487626 | 0.243813 | − | 0.969822i | \(-0.421602\pi\) | ||||
0.243813 | + | 0.969822i | \(0.421602\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5496.61 | 1.15456 | 0.577279 | − | 0.816547i | \(-0.304115\pi\) | ||||
0.577279 | + | 0.816547i | \(0.304115\pi\) | |||||||
\(284\) | −13426.0 | −2.80523 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5784.32 | 1.19592 | ||||||||
\(287\) | 614.729 | 0.126433 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2624.32 | 0.534159 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1663.29 | 0.333345 | ||||||||
\(293\) | 4094.98 | 0.816490 | 0.408245 | − | 0.912872i | \(-0.366141\pi\) | ||||
0.408245 | + | 0.912872i | \(0.366141\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 3326.40 | 0.653186 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 10943.1 | 2.12724 | ||||||||
\(299\) | 5931.09 | 1.14717 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1285.65 | −0.246191 | ||||||||
\(302\) | −5301.62 | −1.01018 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −280.381 | −0.0528978 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7535.90 | −1.40097 | −0.700483 | − | 0.713669i | \(-0.747032\pi\) | ||||
−0.700483 | + | 0.713669i | \(0.747032\pi\) | |||||||
\(308\) | −693.099 | −0.128224 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6330.89 | −1.15432 | −0.577158 | − | 0.816633i | \(-0.695838\pi\) | ||||
−0.577158 | + | 0.816633i | \(0.695838\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8981.97 | −1.62202 | −0.811008 | − | 0.585036i | \(-0.801080\pi\) | ||||
−0.811008 | + | 0.585036i | \(0.801080\pi\) | |||||||
\(314\) | 13277.9 | 2.38635 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8850.29 | −1.57553 | ||||||||
\(317\) | 3236.48 | 0.573435 | 0.286718 | − | 0.958015i | \(-0.407436\pi\) | ||||
0.286718 | + | 0.958015i | \(0.407436\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3287.64 | 0.577029 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1163.31 | −0.201331 | ||||||||
\(323\) | 3629.53 | 0.625240 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 4245.18 | 0.721223 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4822.89 | 0.811888 | ||||||||
\(329\) | −64.0801 | −0.0107381 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6615.59 | 1.09857 | 0.549283 | − | 0.835636i | \(-0.314901\pi\) | ||||
0.549283 | + | 0.835636i | \(0.314901\pi\) | |||||||
\(332\) | 17833.9 | 2.94807 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −14206.6 | −2.32740 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2028.29 | −0.327858 | −0.163929 | − | 0.986472i | \(-0.552417\pi\) | ||||
−0.163929 | + | 0.986472i | \(0.552417\pi\) | |||||||
\(338\) | 6880.11 | 1.10718 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1996.74 | −0.317095 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1790.10 | −0.281797 | ||||||||
\(344\) | −10086.6 | −1.58091 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1084.93 | −0.168573 | ||||||||
\(347\) | 3223.38 | 0.498675 | 0.249337 | − | 0.968417i | \(-0.419787\pi\) | ||||
0.249337 | + | 0.968417i | \(0.419787\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9628.52 | −1.47680 | −0.738399 | − | 0.674364i | \(-0.764418\pi\) | ||||
−0.738399 | + | 0.674364i | \(0.764418\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4099.74 | 0.620787 | ||||||||
\(353\) | −2352.31 | −0.354677 | −0.177339 | − | 0.984150i | \(-0.556749\pi\) | ||||
−0.177339 | + | 0.984150i | \(0.556749\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 5047.67 | 0.751477 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1505.57 | 0.222268 | ||||||||
\(359\) | −6464.01 | −0.950299 | −0.475150 | − | 0.879905i | \(-0.657606\pi\) | ||||
−0.475150 | + | 0.879905i | \(0.657606\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5111.23 | −0.745187 | ||||||||
\(362\) | 15442.2 | 2.24206 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2018.10 | −0.290597 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9156.74 | 1.30239 | 0.651196 | − | 0.758910i | \(-0.274268\pi\) | ||||
0.651196 | + | 0.758910i | \(0.274268\pi\) | |||||||
\(368\) | 652.683 | 0.0924551 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1871.24 | −0.261859 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7929.65 | −1.10075 | −0.550377 | − | 0.834916i | \(-0.685516\pi\) | ||||
−0.550377 | + | 0.834916i | \(0.685516\pi\) | |||||||
\(374\) | −8239.91 | −1.13924 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −502.743 | −0.0689548 | ||||||||
\(377\) | 9572.64 | 1.30774 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9302.25 | 1.26075 | 0.630375 | − | 0.776290i | \(-0.282901\pi\) | ||||
0.630375 | + | 0.776290i | \(0.282901\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −23859.0 | −3.19563 | ||||||||
\(383\) | 10435.9 | 1.39229 | 0.696146 | − | 0.717900i | \(-0.254896\pi\) | ||||
0.696146 | + | 0.717900i | \(0.254896\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1854.47 | −0.244533 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −6668.47 | −0.872526 | ||||||||
\(389\) | 3360.81 | 0.438046 | 0.219023 | − | 0.975720i | \(-0.429713\pi\) | ||||
0.219023 | + | 0.975720i | \(0.429713\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8448.98 | −1.09280 | ||||||||
\(392\) | −6950.29 | −0.895517 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 4293.78 | 0.549030 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1324.66 | 0.167463 | 0.0837314 | − | 0.996488i | \(-0.473316\pi\) | ||||
0.0837314 | + | 0.996488i | \(0.473316\pi\) | |||||||
\(398\) | 22296.1 | 2.80805 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14010.8 | 1.74480 | 0.872402 | − | 0.488789i | \(-0.162561\pi\) | ||||
0.872402 | + | 0.488789i | \(0.162561\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5813.92 | −0.718640 | ||||||||
\(404\) | −12541.8 | −1.54450 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1877.55 | −0.229511 | ||||||||
\(407\) | −3366.41 | −0.409991 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3616.01 | 0.437165 | 0.218582 | − | 0.975818i | \(-0.429857\pi\) | ||||
0.218582 | + | 0.975818i | \(0.429857\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 10519.6 | 1.25792 | ||||||||
\(413\) | −506.142 | −0.0603041 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 11937.3 | 1.40690 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3967.85 | −0.464292 | ||||||||
\(419\) | 816.065 | 0.0951489 | 0.0475745 | − | 0.998868i | \(-0.484851\pi\) | ||||
0.0475745 | + | 0.998868i | \(0.484851\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14965.7 | 1.73250 | 0.866252 | − | 0.499607i | \(-0.166522\pi\) | ||||
0.866252 | + | 0.499607i | \(0.166522\pi\) | |||||||
\(422\) | 11106.6 | 1.28119 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −14680.9 | −1.68152 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1962.99 | −0.222472 | ||||||||
\(428\) | −13935.2 | −1.57380 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9752.30 | −1.08991 | −0.544955 | − | 0.838465i | \(-0.683453\pi\) | ||||
−0.544955 | + | 0.838465i | \(0.683453\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4546.03 | −0.504545 | −0.252273 | − | 0.967656i | \(-0.581178\pi\) | ||||
−0.252273 | + | 0.967656i | \(0.581178\pi\) | |||||||
\(434\) | 1140.33 | 0.126123 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −13462.1 | −1.47871 | ||||||||
\(437\) | −4068.53 | −0.445364 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8618.63 | −0.937004 | −0.468502 | − | 0.883462i | \(-0.655206\pi\) | ||||
−0.468502 | + | 0.883462i | \(0.655206\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −23992.2 | −2.58189 | ||||||||
\(443\) | 12269.8 | 1.31593 | 0.657966 | − | 0.753048i | \(-0.271417\pi\) | ||||
0.657966 | + | 0.753048i | \(0.271417\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 4563.66 | 0.484520 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2199.90 | −0.231999 | ||||||||
\(449\) | 7617.88 | 0.800690 | 0.400345 | − | 0.916364i | \(-0.368890\pi\) | ||||
0.400345 | + | 0.916364i | \(0.368890\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4880.89 | −0.509606 | ||||||||
\(452\) | 13685.3 | 1.42412 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 9177.88 | 0.948765 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6062.05 | −0.620505 | −0.310253 | − | 0.950654i | \(-0.600414\pi\) | ||||
−0.310253 | + | 0.950654i | \(0.600414\pi\) | |||||||
\(458\) | −30779.4 | −3.14023 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13819.5 | 1.39618 | 0.698090 | − | 0.716010i | \(-0.254034\pi\) | ||||
0.698090 | + | 0.716010i | \(0.254034\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16845.0 | −1.69083 | −0.845415 | − | 0.534110i | \(-0.820647\pi\) | ||||
−0.845415 | + | 0.534110i | \(0.820647\pi\) | |||||||
\(464\) | 1053.42 | 0.105396 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 18726.7 | 1.86158 | ||||||||
\(467\) | 8573.64 | 0.849552 | 0.424776 | − | 0.905299i | \(-0.360353\pi\) | ||||
0.424776 | + | 0.905299i | \(0.360353\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2171.07 | 0.213754 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3970.96 | −0.387242 | ||||||||
\(473\) | 10207.9 | 0.992306 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2874.84 | 0.276823 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −13506.9 | −1.29245 | ||||||||
\(479\) | −297.354 | −0.0283642 | −0.0141821 | − | 0.999899i | \(-0.504514\pi\) | ||||
−0.0141821 | + | 0.999899i | \(0.504514\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9802.00 | −0.929174 | ||||||||
\(482\) | −8361.24 | −0.790133 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −11215.8 | −1.05332 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6827.58 | 0.635292 | 0.317646 | − | 0.948209i | \(-0.397108\pi\) | ||||
0.317646 | + | 0.948209i | \(0.397108\pi\) | |||||||
\(488\) | −15400.7 | −1.42860 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5170.75 | 0.475260 | 0.237630 | − | 0.971356i | \(-0.423629\pi\) | ||||
0.237630 | + | 0.971356i | \(0.423629\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −13636.5 | −1.24575 | ||||||||
\(494\) | −11553.2 | −1.05224 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −639.790 | −0.0579181 | ||||||||
\(497\) | −2817.68 | −0.254307 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10754.0 | −0.964757 | −0.482379 | − | 0.875963i | \(-0.660227\pi\) | ||||
−0.482379 | + | 0.875963i | \(0.660227\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 10704.6 | 0.951730 | ||||||||
\(503\) | −2141.00 | −0.189786 | −0.0948930 | − | 0.995487i | \(-0.530251\pi\) | ||||
−0.0948930 | + | 0.995487i | \(0.530251\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 9236.55 | 0.811492 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4665.74 | 0.407498 | ||||||||
\(509\) | 6060.50 | 0.527754 | 0.263877 | − | 0.964556i | \(-0.414999\pi\) | ||||
0.263877 | + | 0.964556i | \(0.414999\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 349.071 | 0.0302192 | ||||||||
\(512\) | 2423.30 | 0.209172 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 11212.0 | 0.962143 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 508.790 | 0.0432815 | ||||||||
\(518\) | 1922.54 | 0.163072 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8685.61 | 0.730371 | 0.365186 | − | 0.930935i | \(-0.381006\pi\) | ||||
0.365186 | + | 0.930935i | \(0.381006\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20944.4 | 1.75112 | 0.875561 | − | 0.483108i | \(-0.160492\pi\) | ||||
0.875561 | + | 0.483108i | \(0.160492\pi\) | |||||||
\(524\) | 3332.05 | 0.277789 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9826.91 | −0.814589 | ||||||||
\(527\) | 8282.07 | 0.684578 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2696.09 | −0.221590 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1384.35 | 0.112818 | ||||||||
\(533\) | −14211.7 | −1.15493 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 17033.2 | 1.37262 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 19710.3 | 1.57950 | ||||||||
\(539\) | 7033.88 | 0.562098 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17178.0 | −1.36513 | −0.682567 | − | 0.730823i | \(-0.739137\pi\) | ||||
−0.682567 | + | 0.730823i | \(0.739137\pi\) | |||||||
\(542\) | −17790.7 | −1.40992 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −17004.9 | −1.34022 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22293.5 | 1.74260 | 0.871300 | − | 0.490751i | \(-0.163278\pi\) | ||||
0.871300 | + | 0.490751i | \(0.163278\pi\) | |||||||
\(548\) | 3400.57 | 0.265082 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6566.52 | −0.507701 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1857.39 | −0.142829 | ||||||||
\(554\) | −27369.4 | −2.09894 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −15225.3 | −1.16132 | ||||||||
\(557\) | −10050.0 | −0.764512 | −0.382256 | − | 0.924056i | \(-0.624853\pi\) | ||||
−0.382256 | + | 0.924056i | \(0.624853\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 29722.5 | 2.24889 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 10415.2 | 0.781745 | ||||||||
\(563\) | 2469.40 | 0.184854 | 0.0924269 | − | 0.995719i | \(-0.470538\pi\) | ||||
0.0924269 | + | 0.995719i | \(0.470538\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 24924.1 | 1.85095 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −22106.3 | −1.63303 | ||||||||
\(569\) | 1734.73 | 0.127810 | 0.0639048 | − | 0.997956i | \(-0.479645\pi\) | ||||
0.0639048 | + | 0.997956i | \(0.479645\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5164.53 | 0.378509 | 0.189255 | − | 0.981928i | \(-0.439393\pi\) | ||||
0.189255 | + | 0.981928i | \(0.439393\pi\) | |||||||
\(572\) | 16023.5 | 1.17129 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2787.45 | 0.202693 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3796.17 | 0.273894 | 0.136947 | − | 0.990578i | \(-0.456271\pi\) | ||||
0.136947 | + | 0.990578i | \(0.456271\pi\) | |||||||
\(578\) | 11899.8 | 0.856346 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3742.75 | 0.267256 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14857.4 | 1.05546 | ||||||||
\(584\) | 2738.66 | 0.194052 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 18568.5 | 1.30897 | ||||||||
\(587\) | 13603.2 | 0.956501 | 0.478250 | − | 0.878224i | \(-0.341271\pi\) | ||||
0.478250 | + | 0.878224i | \(0.341271\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3988.16 | 0.278997 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1078.66 | −0.0748859 | ||||||||
\(593\) | −82.8252 | −0.00573562 | −0.00286781 | − | 0.999996i | \(-0.500913\pi\) | ||||
−0.00286781 | + | 0.999996i | \(0.500913\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 30314.3 | 2.08342 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 26894.2 | 1.83910 | ||||||||
\(599\) | −1131.04 | −0.0771504 | −0.0385752 | − | 0.999256i | \(-0.512282\pi\) | ||||
−0.0385752 | + | 0.999256i | \(0.512282\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2722.67 | −0.184792 | −0.0923960 | − | 0.995722i | \(-0.529453\pi\) | ||||
−0.0923960 | + | 0.995722i | \(0.529453\pi\) | |||||||
\(602\) | −5829.70 | −0.394686 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −14686.4 | −0.989370 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11017.7 | −0.736732 | −0.368366 | − | 0.929681i | \(-0.620083\pi\) | ||||
−0.368366 | + | 0.929681i | \(0.620083\pi\) | |||||||
\(608\) | −8188.56 | −0.546201 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1481.45 | 0.0980900 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12198.6 | 0.803750 | 0.401875 | − | 0.915695i | \(-0.368359\pi\) | ||||
0.401875 | + | 0.915695i | \(0.368359\pi\) | |||||||
\(614\) | −34171.1 | −2.24598 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1141.21 | −0.0746437 | ||||||||
\(617\) | −894.243 | −0.0583482 | −0.0291741 | − | 0.999574i | \(-0.509288\pi\) | ||||
−0.0291741 | + | 0.999574i | \(0.509288\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −27671.1 | −1.79676 | −0.898381 | − | 0.439218i | \(-0.855256\pi\) | ||||
−0.898381 | + | 0.439218i | \(0.855256\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −28707.1 | −1.85056 | ||||||||
\(623\) | 1059.34 | 0.0681247 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −40728.2 | −2.60036 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 36782.0 | 2.33720 | ||||||||
\(629\) | 13963.2 | 0.885133 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4377.81 | −0.276193 | −0.138097 | − | 0.990419i | \(-0.544098\pi\) | ||||
−0.138097 | + | 0.990419i | \(0.544098\pi\) | |||||||
\(632\) | −14572.2 | −0.917172 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 14675.6 | 0.919312 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 20480.6 | 1.27390 | ||||||||
\(638\) | 14907.6 | 0.925074 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −24915.6 | −1.53527 | −0.767633 | − | 0.640890i | \(-0.778565\pi\) | ||||
−0.767633 | + | 0.640890i | \(0.778565\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10773.0 | −0.660727 | −0.330363 | − | 0.943854i | \(-0.607171\pi\) | ||||
−0.330363 | + | 0.943854i | \(0.607171\pi\) | |||||||
\(644\) | −3222.56 | −0.197184 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 16457.9 | 1.00236 | ||||||||
\(647\) | −19872.6 | −1.20753 | −0.603766 | − | 0.797162i | \(-0.706334\pi\) | ||||
−0.603766 | + | 0.797162i | \(0.706334\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4018.71 | 0.243064 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 11759.9 | 0.706367 | ||||||||
\(653\) | 4132.19 | 0.247634 | 0.123817 | − | 0.992305i | \(-0.460486\pi\) | ||||
0.123817 | + | 0.992305i | \(0.460486\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1563.92 | −0.0930807 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −290.567 | −0.0172150 | ||||||||
\(659\) | 23260.1 | 1.37494 | 0.687470 | − | 0.726213i | \(-0.258721\pi\) | ||||
0.687470 | + | 0.726213i | \(0.258721\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11316.5 | 0.665900 | 0.332950 | − | 0.942945i | \(-0.391956\pi\) | ||||
0.332950 | + | 0.942945i | \(0.391956\pi\) | |||||||
\(662\) | 29998.0 | 1.76119 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 29363.9 | 1.71618 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 15285.8 | 0.887361 | ||||||||
\(668\) | −39354.7 | −2.27946 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 15585.9 | 0.896704 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −26072.2 | −1.49332 | −0.746662 | − | 0.665203i | \(-0.768345\pi\) | ||||
−0.746662 | + | 0.665203i | \(0.768345\pi\) | |||||||
\(674\) | −9197.16 | −0.525611 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 19059.0 | 1.08438 | ||||||||
\(677\) | 15251.9 | 0.865848 | 0.432924 | − | 0.901430i | \(-0.357482\pi\) | ||||
0.432924 | + | 0.901430i | \(0.357482\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1399.50 | −0.0790983 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −9054.09 | −0.508356 | ||||||||
\(683\) | 33196.1 | 1.85976 | 0.929878 | − | 0.367867i | \(-0.119912\pi\) | ||||
0.929878 | + | 0.367867i | \(0.119912\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −8117.10 | −0.451767 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3270.80 | 0.181247 | ||||||||
\(689\) | 43260.5 | 2.39201 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −31327.4 | −1.72467 | −0.862337 | − | 0.506334i | \(-0.831000\pi\) | ||||
−0.862337 | + | 0.506334i | \(0.831000\pi\) | |||||||
\(692\) | −3005.45 | −0.165101 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 14616.2 | 0.799459 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 20245.0 | 1.10019 | ||||||||
\(698\) | −43659.9 | −2.36755 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21416.8 | 1.15392 | 0.576962 | − | 0.816771i | \(-0.304238\pi\) | ||||
0.576962 | + | 0.816771i | \(0.304238\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6723.85 | 0.360732 | ||||||||
\(704\) | 17467.0 | 0.935104 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −10666.4 | −0.568607 | ||||||||
\(707\) | −2632.13 | −0.140016 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6678.58 | 0.353765 | 0.176883 | − | 0.984232i | \(-0.443399\pi\) | ||||
0.176883 | + | 0.984232i | \(0.443399\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 8311.12 | 0.437461 | ||||||||
\(713\) | −9283.81 | −0.487632 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4170.68 | 0.217689 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −29310.7 | −1.52349 | ||||||||
\(719\) | 25245.9 | 1.30947 | 0.654737 | − | 0.755857i | \(-0.272779\pi\) | ||||
0.654737 | + | 0.755857i | \(0.272779\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2207.73 | 0.114036 | ||||||||
\(722\) | −23176.6 | −1.19466 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 42777.5 | 2.19587 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −35186.7 | −1.79505 | −0.897527 | − | 0.440960i | \(-0.854638\pi\) | ||||
−0.897527 | + | 0.440960i | \(0.854638\pi\) | |||||||
\(728\) | −3322.86 | −0.169167 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −42340.5 | −2.14230 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17068.6 | 0.860087 | 0.430043 | − | 0.902808i | \(-0.358498\pi\) | ||||
0.430043 | + | 0.902808i | \(0.358498\pi\) | |||||||
\(734\) | 41520.7 | 2.08795 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 19061.7 | 0.954652 | ||||||||
\(737\) | −17238.1 | −0.861565 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −38144.8 | −1.89875 | −0.949376 | − | 0.314141i | \(-0.898283\pi\) | ||||
−0.949376 | + | 0.314141i | \(0.898283\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −8485.01 | −0.419804 | ||||||||
\(743\) | 5147.73 | 0.254175 | 0.127087 | − | 0.991892i | \(-0.459437\pi\) | ||||
0.127087 | + | 0.991892i | \(0.459437\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −35956.5 | −1.76469 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −22825.9 | −1.11577 | ||||||||
\(749\) | −2924.56 | −0.142672 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 23597.8 | 1.14660 | 0.573300 | − | 0.819346i | \(-0.305663\pi\) | ||||
0.573300 | + | 0.819346i | \(0.305663\pi\) | |||||||
\(752\) | 163.025 | 0.00790547 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 43406.6 | 2.09652 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1343.38 | −0.0644995 | −0.0322497 | − | 0.999480i | \(-0.510267\pi\) | ||||
−0.0322497 | + | 0.999480i | \(0.510267\pi\) | |||||||
\(758\) | 42180.5 | 2.02119 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8016.38 | −0.381858 | −0.190929 | − | 0.981604i | \(-0.561150\pi\) | ||||
−0.190929 | + | 0.981604i | \(0.561150\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2825.27 | −0.134052 | ||||||||
\(764\) | −66093.3 | −3.12980 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 47320.8 | 2.23208 | ||||||||
\(767\) | 11701.3 | 0.550861 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −23044.0 | −1.08061 | −0.540305 | − | 0.841469i | \(-0.681691\pi\) | ||||
−0.540305 | + | 0.841469i | \(0.681691\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −5137.18 | −0.239496 | ||||||||
\(773\) | 31884.9 | 1.48359 | 0.741797 | − | 0.670624i | \(-0.233974\pi\) | ||||
0.741797 | + | 0.670624i | \(0.233974\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −10979.8 | −0.507928 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 15239.4 | 0.702261 | ||||||||
\(779\) | 9748.78 | 0.448378 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 22372.1 | 1.02502 | ||||||||
\(782\) | −38311.4 | −1.75194 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2253.78 | 0.102668 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17033.0 | −0.771488 | −0.385744 | − | 0.922606i | \(-0.626055\pi\) | ||||
−0.385744 | + | 0.922606i | \(0.626055\pi\) | |||||||
\(788\) | 11894.5 | 0.537720 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2872.11 | 0.129103 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 45381.7 | 2.03222 | ||||||||
\(794\) | 6006.59 | 0.268471 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 61764.0 | 2.75021 | ||||||||
\(797\) | −41750.0 | −1.85553 | −0.927767 | − | 0.373159i | \(-0.878275\pi\) | ||||
−0.927767 | + | 0.373159i | \(0.878275\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2110.36 | −0.0934408 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 63531.2 | 2.79721 | ||||||||
\(803\) | −2771.59 | −0.121802 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −26362.9 | −1.15210 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −20650.5 | −0.899111 | ||||||||
\(809\) | 163.059 | 0.00708636 | 0.00354318 | − | 0.999994i | \(-0.498872\pi\) | ||||
0.00354318 | + | 0.999994i | \(0.498872\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9958.10 | 0.431167 | 0.215583 | − | 0.976485i | \(-0.430835\pi\) | ||||
0.215583 | + | 0.976485i | \(0.430835\pi\) | |||||||
\(812\) | −5201.14 | −0.224783 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −15264.8 | −0.657285 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −20388.7 | −0.873083 | ||||||||
\(818\) | 16396.6 | 0.700848 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −32273.2 | −1.37191 | −0.685957 | − | 0.727642i | \(-0.740616\pi\) | ||||
−0.685957 | + | 0.727642i | \(0.740616\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −32710.6 | −1.38544 | −0.692722 | − | 0.721205i | \(-0.743589\pi\) | ||||
−0.692722 | + | 0.721205i | \(0.743589\pi\) | |||||||
\(824\) | 17320.8 | 0.732282 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2295.07 | −0.0966776 | ||||||||
\(827\) | 9763.68 | 0.410540 | 0.205270 | − | 0.978705i | \(-0.434193\pi\) | ||||
0.205270 | + | 0.978705i | \(0.434193\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 34886.9 | 1.46160 | 0.730802 | − | 0.682589i | \(-0.239146\pi\) | ||||
0.730802 | + | 0.682589i | \(0.239146\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 50858.9 | 2.11925 | ||||||||
\(833\) | −29175.2 | −1.21352 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −10991.6 | −0.454728 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3700.40 | 0.152540 | ||||||||
\(839\) | −25642.1 | −1.05514 | −0.527570 | − | 0.849512i | \(-0.676897\pi\) | ||||
−0.527570 | + | 0.849512i | \(0.676897\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 282.003 | 0.0115627 | ||||||||
\(842\) | 67861.1 | 2.77749 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 30767.2 | 1.25480 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2353.83 | −0.0954881 | ||||||||
\(848\) | 4760.58 | 0.192782 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −15652.1 | −0.630489 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4502.72 | 0.180739 | 0.0903694 | − | 0.995908i | \(-0.471195\pi\) | ||||
0.0903694 | + | 0.995908i | \(0.471195\pi\) | |||||||
\(854\) | −8901.05 | −0.356660 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −22944.8 | −0.916163 | ||||||||
\(857\) | −27439.1 | −1.09370 | −0.546851 | − | 0.837230i | \(-0.684174\pi\) | ||||
−0.546851 | + | 0.837230i | \(0.684174\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 26746.7 | 1.06238 | 0.531190 | − | 0.847253i | \(-0.321745\pi\) | ||||
0.531190 | + | 0.847253i | \(0.321745\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −44221.2 | −1.74731 | ||||||||
\(863\) | 4198.80 | 0.165618 | 0.0828092 | − | 0.996565i | \(-0.473611\pi\) | ||||
0.0828092 | + | 0.996565i | \(0.473611\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −20613.7 | −0.808870 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 3158.90 | 0.123525 | ||||||||
\(869\) | 14747.5 | 0.575690 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −50192.3 | −1.95259 | ||||||||
\(872\) | −22165.8 | −0.860811 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −18448.5 | −0.713993 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 19404.6 | 0.747147 | 0.373574 | − | 0.927601i | \(-0.378132\pi\) | ||||
0.373574 | + | 0.927601i | \(0.378132\pi\) | |||||||
\(878\) | −39080.7 | −1.50217 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −8562.17 | −0.327431 | −0.163716 | − | 0.986508i | \(-0.552348\pi\) | ||||
−0.163716 | + | 0.986508i | \(0.552348\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −44660.0 | −1.70207 | −0.851036 | − | 0.525107i | \(-0.824025\pi\) | ||||
−0.851036 | + | 0.525107i | \(0.824025\pi\) | |||||||
\(884\) | −66462.5 | −2.52871 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 55636.9 | 2.10966 | ||||||||
\(887\) | −8179.87 | −0.309643 | −0.154821 | − | 0.987942i | \(-0.549480\pi\) | ||||
−0.154821 | + | 0.987942i | \(0.549480\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 979.189 | 0.0369415 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 12642.1 | 0.474539 | ||||||||
\(893\) | −1016.22 | −0.0380814 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −5844.56 | −0.217916 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 34542.8 | 1.28364 | ||||||||
\(899\) | −14983.9 | −0.555884 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −61625.7 | −2.27863 | ||||||||
\(902\) | −22132.1 | −0.816983 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 22533.3 | 0.829033 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 33509.0 | 1.22673 | 0.613366 | − | 0.789798i | \(-0.289815\pi\) | ||||
0.613366 | + | 0.789798i | \(0.289815\pi\) | |||||||
\(908\) | 25424.3 | 0.929222 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 44665.2 | 1.62440 | 0.812198 | − | 0.583382i | \(-0.198271\pi\) | ||||
0.812198 | + | 0.583382i | \(0.198271\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −29717.1 | −1.07721 | ||||||||
\(914\) | −27488.0 | −0.994773 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −85264.1 | −3.07555 | ||||||||
\(917\) | 699.290 | 0.0251828 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13156.3 | 0.472237 | 0.236118 | − | 0.971724i | \(-0.424125\pi\) | ||||
0.236118 | + | 0.971724i | \(0.424125\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 62663.7 | 2.23831 | ||||||||
\(923\) | 65141.2 | 2.32302 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −76382.7 | −2.71068 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 30765.2 | 1.08827 | ||||||||
\(929\) | 37667.8 | 1.33029 | 0.665146 | − | 0.746714i | \(-0.268369\pi\) | ||||
0.665146 | + | 0.746714i | \(0.268369\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −14049.0 | −0.494563 | ||||||||
\(932\) | 51876.0 | 1.82323 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 38876.7 | 1.36197 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 37999.6 | 1.32486 | 0.662429 | − | 0.749125i | \(-0.269526\pi\) | ||||
0.662429 | + | 0.749125i | \(0.269526\pi\) | |||||||
\(938\) | 9844.60 | 0.342684 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10238.6 | 0.354697 | 0.177348 | − | 0.984148i | \(-0.443248\pi\) | ||||
0.177348 | + | 0.984148i | \(0.443248\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −22693.7 | −0.783677 | ||||||||
\(944\) | 1287.67 | 0.0443962 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 46287.2 | 1.59083 | ||||||||
\(947\) | 10377.2 | 0.356088 | 0.178044 | − | 0.984023i | \(-0.443023\pi\) | ||||
0.178044 | + | 0.984023i | \(0.443023\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8070.07 | −0.276044 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 4733.50 | 0.161149 | ||||||||
\(953\) | −54309.6 | −1.84602 | −0.923012 | − | 0.384772i | \(-0.874280\pi\) | ||||
−0.923012 | + | 0.384772i | \(0.874280\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −37416.3 | −1.26583 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1348.33 | −0.0454725 | ||||||||
\(959\) | 713.670 | 0.0240309 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20690.6 | −0.694525 | ||||||||
\(962\) | −44446.6 | −1.48962 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −23162.0 | −0.773858 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12701.3 | 0.422386 | 0.211193 | − | 0.977444i | \(-0.432265\pi\) | ||||
0.211193 | + | 0.977444i | \(0.432265\pi\) | |||||||
\(968\) | −18467.0 | −0.613175 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3767.34 | −0.124511 | −0.0622553 | − | 0.998060i | \(-0.519829\pi\) | ||||
−0.0622553 | + | 0.998060i | \(0.519829\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3195.29 | −0.105279 | ||||||||
\(974\) | 30959.2 | 1.01848 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4994.01 | 0.163785 | ||||||||
\(977\) | 13359.9 | 0.437482 | 0.218741 | − | 0.975783i | \(-0.429805\pi\) | ||||
0.218741 | + | 0.975783i | \(0.429805\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8411.07 | −0.274585 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 23446.5 | 0.761921 | ||||||||
\(983\) | −31707.1 | −1.02879 | −0.514394 | − | 0.857554i | \(-0.671983\pi\) | ||||
−0.514394 | + | 0.857554i | \(0.671983\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −61833.8 | −1.99715 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −32004.4 | −1.03056 | ||||||||
\(989\) | 47461.7 | 1.52598 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19393.7 | −0.621657 | −0.310829 | − | 0.950466i | \(-0.600606\pi\) | ||||
−0.310829 | + | 0.950466i | \(0.600606\pi\) | |||||||
\(992\) | −18685.2 | −0.598039 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −12776.6 | −0.407696 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −41543.1 | −1.31964 | −0.659821 | − | 0.751423i | \(-0.729368\pi\) | ||||
−0.659821 | + | 0.751423i | \(0.729368\pi\) | |||||||
\(998\) | −48763.3 | −1.54667 | ||||||||
\(999\) | 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 | 2025.4.a.z.1.5 | 6 | ||
3.2 | odd | 2 | 2025.4.a.y.1.2 | 6 | |||
5.4 | even | 2 | 405.4.a.k.1.2 | ✓ | 6 | ||
15.14 | odd | 2 | 405.4.a.l.1.5 | yes | 6 | ||
45.4 | even | 6 | 405.4.e.x.136.5 | 12 | |||
45.14 | odd | 6 | 405.4.e.w.136.2 | 12 | |||
45.29 | odd | 6 | 405.4.e.w.271.2 | 12 | |||
45.34 | even | 6 | 405.4.e.x.271.5 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
405.4.a.k.1.2 | ✓ | 6 | 5.4 | even | 2 | ||
405.4.a.l.1.5 | yes | 6 | 15.14 | odd | 2 | ||
405.4.e.w.136.2 | 12 | 45.14 | odd | 6 | |||
405.4.e.w.271.2 | 12 | 45.29 | odd | 6 | |||
405.4.e.x.136.5 | 12 | 45.4 | even | 6 | |||
405.4.e.x.271.5 | 12 | 45.34 | even | 6 | |||
2025.4.a.y.1.2 | 6 | 3.2 | odd | 2 | |||
2025.4.a.z.1.5 | 6 | 1.1 | even | 1 | trivial |