Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,4,Mod(1,1344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1344.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.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: | \(79.2985670477\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 21) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1344.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.00000 | 0.357771 | 0.178885 | − | 0.983870i | \(-0.442751\pi\) | ||||
0.178885 | + | 0.983870i | \(0.442751\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 62.0000 | 1.69943 | 0.849714 | − | 0.527244i | \(-0.176775\pi\) | ||||
0.849714 | + | 0.527244i | \(0.176775\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 62.0000 | 1.32275 | 0.661373 | − | 0.750057i | \(-0.269974\pi\) | ||||
0.661373 | + | 0.750057i | \(0.269974\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −12.0000 | −0.206559 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 84.0000 | 1.19841 | 0.599206 | − | 0.800595i | \(-0.295483\pi\) | ||||
0.599206 | + | 0.800595i | \(0.295483\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 100.000 | 1.20745 | 0.603726 | − | 0.797192i | \(-0.293682\pi\) | ||||
0.603726 | + | 0.797192i | \(0.293682\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −21.0000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 42.0000 | 0.380765 | 0.190383 | − | 0.981710i | \(-0.439027\pi\) | ||||
0.190383 | + | 0.981710i | \(0.439027\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −109.000 | −0.872000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 10.0000 | 0.0640329 | 0.0320164 | − | 0.999487i | \(-0.489807\pi\) | ||||
0.0320164 | + | 0.999487i | \(0.489807\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 48.0000 | 0.278099 | 0.139049 | − | 0.990285i | \(-0.455595\pi\) | ||||
0.139049 | + | 0.990285i | \(0.455595\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −186.000 | −0.981165 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 28.0000 | 0.135225 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 246.000 | 1.09303 | 0.546516 | − | 0.837449i | \(-0.315954\pi\) | ||||
0.546516 | + | 0.837449i | \(0.315954\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −186.000 | −0.763688 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −248.000 | −0.944661 | −0.472330 | − | 0.881422i | \(-0.656587\pi\) | ||||
−0.472330 | + | 0.881422i | \(0.656587\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 68.0000 | 0.241161 | 0.120580 | − | 0.992704i | \(-0.461524\pi\) | ||||
0.120580 | + | 0.992704i | \(0.461524\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 36.0000 | 0.119257 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −324.000 | −1.00554 | −0.502769 | − | 0.864421i | \(-0.667685\pi\) | ||||
−0.502769 | + | 0.864421i | \(0.667685\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −252.000 | −0.691903 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −258.000 | −0.668661 | −0.334330 | − | 0.942456i | \(-0.608510\pi\) | ||||
−0.334330 | + | 0.942456i | \(0.608510\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 248.000 | 0.608006 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −300.000 | −0.697122 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 120.000 | 0.264791 | 0.132396 | − | 0.991197i | \(-0.457733\pi\) | ||||
0.132396 | + | 0.991197i | \(0.457733\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −622.000 | −1.30556 | −0.652778 | − | 0.757549i | \(-0.726397\pi\) | ||||
−0.652778 | + | 0.757549i | \(0.726397\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 63.0000 | 0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 248.000 | 0.473240 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 904.000 | 1.64838 | 0.824188 | − | 0.566316i | \(-0.191632\pi\) | ||||
0.824188 | + | 0.566316i | \(0.191632\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −126.000 | −0.219835 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 678.000 | 1.13329 | 0.566646 | − | 0.823961i | \(-0.308241\pi\) | ||||
0.566646 | + | 0.823961i | \(0.308241\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −642.000 | −1.02932 | −0.514660 | − | 0.857394i | \(-0.672082\pi\) | ||||
−0.514660 | + | 0.857394i | \(0.672082\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 327.000 | 0.503449 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 434.000 | 0.642323 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −740.000 | −1.05388 | −0.526940 | − | 0.849903i | \(-0.676661\pi\) | ||||
−0.526940 | + | 0.849903i | \(0.676661\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 468.000 | 0.618912 | 0.309456 | − | 0.950914i | \(-0.399853\pi\) | ||||
0.309456 | + | 0.950914i | \(0.399853\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 336.000 | 0.428757 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −30.0000 | −0.0369694 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 200.000 | 0.238202 | 0.119101 | − | 0.992882i | \(-0.461999\pi\) | ||||
0.119101 | + | 0.992882i | \(0.461999\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 434.000 | 0.499951 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −144.000 | −0.160560 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 400.000 | 0.431991 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1266.00 | −1.32518 | −0.662592 | − | 0.748981i | \(-0.730544\pi\) | ||||
−0.662592 | + | 0.748981i | \(0.730544\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 558.000 | 0.566476 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −232.000 | −0.228563 | −0.114281 | − | 0.993448i | \(-0.536457\pi\) | ||||
−0.114281 | + | 0.993448i | \(0.536457\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1792.00 | 1.71428 | 0.857141 | − | 0.515082i | \(-0.172239\pi\) | ||||
0.857141 | + | 0.515082i | \(0.172239\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −84.0000 | −0.0780720 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1906.00 | −1.72206 | −0.861028 | − | 0.508558i | \(-0.830179\pi\) | ||||
−0.861028 | + | 0.508558i | \(0.830179\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 90.0000 | 0.0790866 | 0.0395433 | − | 0.999218i | \(-0.487410\pi\) | ||||
0.0395433 | + | 0.999218i | \(0.487410\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −738.000 | −0.631062 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 458.000 | 0.381283 | 0.190642 | − | 0.981660i | \(-0.438943\pi\) | ||||
0.190642 | + | 0.981660i | \(0.438943\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 168.000 | 0.136227 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 558.000 | 0.440916 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 588.000 | 0.452957 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2513.00 | 1.88805 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 744.000 | 0.545400 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −936.000 | −0.669747 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −804.000 | −0.561760 | −0.280880 | − | 0.959743i | \(-0.590626\pi\) | ||||
−0.280880 | + | 0.959743i | \(0.590626\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −204.000 | −0.139234 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 812.000 | 0.541563 | 0.270782 | − | 0.962641i | \(-0.412718\pi\) | ||||
0.270782 | + | 0.962641i | \(0.412718\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 700.000 | 0.456374 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −108.000 | −0.0688530 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 414.000 | 0.258178 | 0.129089 | − | 0.991633i | \(-0.458795\pi\) | ||||
0.129089 | + | 0.991633i | \(0.458795\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1620.00 | −0.988537 | −0.494268 | − | 0.869309i | \(-0.664564\pi\) | ||||
−0.494268 | + | 0.869309i | \(0.664564\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 972.000 | 0.580547 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3844.00 | 2.24791 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 40.0000 | 0.0229091 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −147.000 | −0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2370.00 | −1.30307 | −0.651537 | − | 0.758617i | \(-0.725875\pi\) | ||||
−0.651537 | + | 0.758617i | \(0.725875\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 568.000 | 0.306114 | 0.153057 | − | 0.988217i | \(-0.451088\pi\) | ||||
0.153057 | + | 0.988217i | \(0.451088\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 756.000 | 0.399470 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 192.000 | 0.0994956 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 266.000 | 0.135217 | 0.0676086 | − | 0.997712i | \(-0.478463\pi\) | ||||
0.0676086 | + | 0.997712i | \(0.478463\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 774.000 | 0.386052 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 294.000 | 0.143916 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −272.000 | −0.130704 | −0.0653518 | − | 0.997862i | \(-0.520817\pi\) | ||||
−0.0653518 | + | 0.997862i | \(0.520817\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −744.000 | −0.351032 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1876.00 | 0.869277 | 0.434638 | − | 0.900605i | \(-0.356876\pi\) | ||||
0.434638 | + | 0.900605i | \(0.356876\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1647.00 | 0.749659 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 900.000 | 0.402484 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 152.000 | 0.0667997 | 0.0333998 | − | 0.999442i | \(-0.489367\pi\) | ||||
0.0333998 | + | 0.999442i | \(0.489367\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −763.000 | −0.329585 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −360.000 | −0.152877 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 610.000 | 0.254713 | 0.127356 | − | 0.991857i | \(-0.459351\pi\) | ||||
0.127356 | + | 0.991857i | \(0.459351\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1042.00 | −0.427907 | −0.213954 | − | 0.976844i | \(-0.568634\pi\) | ||||
−0.213954 | + | 0.976844i | \(0.568634\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1866.00 | 0.753763 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 984.000 | 0.391055 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5208.00 | 2.03661 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −189.000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2038.00 | 0.772065 | 0.386033 | − | 0.922485i | \(-0.373845\pi\) | ||||
0.386033 | + | 0.922485i | \(0.373845\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2602.00 | −0.970446 | −0.485223 | − | 0.874390i | \(-0.661262\pi\) | ||||
−0.485223 | + | 0.874390i | \(0.661262\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −744.000 | −0.273225 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2354.00 | −0.851348 | −0.425674 | − | 0.904877i | \(-0.639963\pi\) | ||||
−0.425674 | + | 0.904877i | \(0.639963\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1680.00 | −0.598452 | −0.299226 | − | 0.954182i | \(-0.596729\pi\) | ||||
−0.299226 | + | 0.954182i | \(0.596729\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2712.00 | −0.951690 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 70.0000 | 0.0242022 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −992.000 | −0.337972 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 378.000 | 0.126922 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6200.00 | 2.05198 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −668.000 | −0.217948 | −0.108974 | − | 0.994045i | \(-0.534757\pi\) | ||||
−0.108974 | + | 0.994045i | \(0.534757\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2034.00 | −0.654307 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 272.000 | 0.0862802 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 336.000 | 0.105111 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1926.00 | 0.594279 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5208.00 | 1.58519 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1832.00 | 0.550134 | 0.275067 | − | 0.961425i | \(-0.411300\pi\) | ||||
0.275067 | + | 0.961425i | \(0.411300\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −981.000 | −0.290667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4944.00 | 1.44557 | 0.722786 | − | 0.691072i | \(-0.242861\pi\) | ||||
0.722786 | + | 0.691072i | \(0.242861\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5470.00 | 1.57846 | 0.789231 | − | 0.614096i | \(-0.210479\pi\) | ||||
0.789231 | + | 0.614096i | \(0.210479\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1302.00 | −0.370846 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2802.00 | −0.787833 | −0.393917 | − | 0.919146i | \(-0.628880\pi\) | ||||
−0.393917 | + | 0.919146i | \(0.628880\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1296.00 | −0.359752 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2220.00 | 0.608458 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1170.00 | 0.316657 | 0.158328 | − | 0.987386i | \(-0.449390\pi\) | ||||
0.158328 | + | 0.987386i | \(0.449390\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2338.00 | −0.624912 | −0.312456 | − | 0.949932i | \(-0.601152\pi\) | ||||
−0.312456 | + | 0.949932i | \(0.601152\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 196.000 | 0.0511101 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6200.00 | 1.59715 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1404.00 | −0.357329 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2792.00 | 0.702109 | 0.351055 | − | 0.936355i | \(-0.385823\pi\) | ||||
0.351055 | + | 0.936355i | \(0.385823\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2604.00 | 0.647083 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1008.00 | −0.247543 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7024.00 | 1.70484 | 0.852422 | − | 0.522854i | \(-0.175133\pi\) | ||||
0.852422 | + | 0.522854i | \(0.175133\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1722.00 | 0.413127 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 90.0000 | 0.0213443 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2438.00 | −0.571610 | −0.285805 | − | 0.958288i | \(-0.592261\pi\) | ||||
−0.285805 | + | 0.958288i | \(0.592261\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1032.00 | −0.239227 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −600.000 | −0.137526 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6780.00 | 1.53674 | 0.768372 | − | 0.640004i | \(-0.221067\pi\) | ||||
0.768372 | + | 0.640004i | \(0.221067\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1928.00 | 0.432168 | 0.216084 | − | 0.976375i | \(-0.430671\pi\) | ||||
0.216084 | + | 0.976375i | \(0.430671\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1302.00 | −0.288647 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6758.00 | −1.48190 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5554.00 | −1.20472 | −0.602360 | − | 0.798224i | \(-0.705773\pi\) | ||||
−0.602360 | + | 0.798224i | \(0.705773\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 432.000 | 0.0926995 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1942.00 | 0.412278 | 0.206139 | − | 0.978523i | \(-0.433910\pi\) | ||||
0.206139 | + | 0.978523i | \(0.433910\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4828.00 | 1.01412 | 0.507058 | − | 0.861912i | \(-0.330733\pi\) | ||||
0.507058 | + | 0.861912i | \(0.330733\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1200.00 | −0.249410 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1736.00 | −0.357048 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2143.00 | 0.436190 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3798.00 | 0.765095 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6152.00 | 1.22663 | 0.613317 | − | 0.789837i | \(-0.289835\pi\) | ||||
0.613317 | + | 0.789837i | \(0.289835\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 480.000 | 0.0947345 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1674.00 | −0.327055 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2604.00 | 0.503656 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 476.000 | 0.0911501 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 696.000 | 0.131961 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2488.00 | −0.467090 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5884.00 | 1.09387 | 0.546934 | − | 0.837176i | \(-0.315795\pi\) | ||||
0.546934 | + | 0.837176i | \(0.315795\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5376.00 | −0.989741 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9132.00 | −1.66504 | −0.832521 | − | 0.553993i | \(-0.813103\pi\) | ||||
−0.832521 | + | 0.553993i | \(0.813103\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9382.00 | −1.69426 | −0.847128 | − | 0.531389i | \(-0.821670\pi\) | ||||
−0.847128 | + | 0.531389i | \(0.821670\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 252.000 | 0.0450749 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3114.00 | −0.551734 | −0.275867 | − | 0.961196i | \(-0.588965\pi\) | ||||
−0.275867 | + | 0.961196i | \(0.588965\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 620.000 | 0.108819 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5718.00 | 0.994229 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8400.00 | 1.44702 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6758.00 | −1.15344 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −270.000 | −0.0456607 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2268.00 | −0.380057 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1532.00 | 0.254400 | 0.127200 | − | 0.991877i | \(-0.459401\pi\) | ||||
0.127200 | + | 0.991877i | \(0.459401\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2214.00 | 0.364344 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3616.00 | 0.589741 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4166.00 | −0.673402 | −0.336701 | − | 0.941612i | \(-0.609311\pi\) | ||||
−0.336701 | + | 0.941612i | \(0.609311\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1374.00 | −0.220134 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2976.00 | 0.472608 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −504.000 | −0.0786506 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −11366.0 | −1.75838 | −0.879191 | − | 0.476469i | \(-0.841917\pi\) | ||||
−0.879191 | + | 0.476469i | \(0.841917\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9310.00 | −1.42795 | −0.713973 | − | 0.700174i | \(-0.753106\pi\) | ||||
−0.713973 | + | 0.700174i | \(0.753106\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1674.00 | −0.254563 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8572.00 | −1.29247 | −0.646234 | − | 0.763139i | \(-0.723657\pi\) | ||||
−0.646234 | + | 0.763139i | \(0.723657\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2712.00 | 0.405459 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1764.00 | −0.261515 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4790.00 | 0.704196 | 0.352098 | − | 0.935963i | \(-0.385468\pi\) | ||||
0.352098 | + | 0.935963i | \(0.385468\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3141.00 | 0.457938 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −7539.00 | −1.09007 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2568.00 | −0.368261 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5424.00 | −0.771473 | −0.385736 | − | 0.922609i | \(-0.626053\pi\) | ||||
−0.385736 | + | 0.922609i | \(0.626053\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2232.00 | −0.314887 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1806.00 | −0.252730 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1838.00 | −0.255142 | −0.127571 | − | 0.991829i | \(-0.540718\pi\) | ||||
−0.127571 | + | 0.991829i | \(0.540718\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2808.00 | 0.386679 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 620.000 | 0.0846993 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4260.00 | −0.577365 | −0.288683 | − | 0.957425i | \(-0.593217\pi\) | ||||
−0.288683 | + | 0.957425i | \(0.593217\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2412.00 | 0.324332 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9048.00 | −1.20713 | −0.603566 | − | 0.797313i | \(-0.706254\pi\) | ||||
−0.603566 | + | 0.797313i | \(0.706254\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1736.00 | 0.229805 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 612.000 | 0.0803868 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11490.0 | 1.49760 | 0.748800 | − | 0.662796i | \(-0.230631\pi\) | ||||
0.748800 | + | 0.662796i | \(0.230631\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3528.00 | 0.456314 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2436.00 | −0.312672 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2960.00 | −0.377048 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1866.00 | 0.235899 | 0.117949 | − | 0.993020i | \(-0.462368\pi\) | ||||
0.117949 | + | 0.993020i | \(0.462368\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2100.00 | −0.263487 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13662.0 | 1.70137 | 0.850683 | − | 0.525679i | \(-0.176189\pi\) | ||||
0.850683 | + | 0.525679i | \(0.176189\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2976.00 | 0.367854 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 324.000 | 0.0397523 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 15252.0 | 1.85753 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13210.0 | −1.59705 | −0.798524 | − | 0.601963i | \(-0.794385\pi\) | ||||
−0.798524 | + | 0.601963i | \(0.794385\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1242.00 | −0.149059 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 840.000 | 0.100082 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1872.00 | 0.221429 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4860.00 | 0.570732 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6960.00 | 0.811499 | 0.405750 | − | 0.913984i | \(-0.367010\pi\) | ||||
0.405750 | + | 0.913984i | \(0.367010\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8162.00 | −0.944873 | −0.472437 | − | 0.881365i | \(-0.656625\pi\) | ||||
−0.472437 | + | 0.881365i | \(0.656625\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2916.00 | −0.335179 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −9156.00 | −1.04501 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4354.00 | −0.493454 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −11532.0 | −1.29783 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16602.0 | −1.85543 | −0.927715 | − | 0.373290i | \(-0.878230\pi\) | ||||
−0.927715 | + | 0.373290i | \(0.878230\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7738.00 | 0.858810 | 0.429405 | − | 0.903112i | \(-0.358723\pi\) | ||||
0.429405 | + | 0.903112i | \(0.358723\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −120.000 | −0.0132266 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4200.00 | 0.459756 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 840.000 | 0.0913235 | 0.0456617 | − | 0.998957i | \(-0.485460\pi\) | ||||
0.0456617 | + | 0.998957i | \(0.485460\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6618.00 | 0.709776 | 0.354888 | − | 0.934909i | \(-0.384519\pi\) | ||||
0.354888 | + | 0.934909i | \(0.384519\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 800.000 | 0.0852217 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7110.00 | 0.752330 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3090.00 | 0.324780 | 0.162390 | − | 0.986727i | \(-0.448080\pi\) | ||||
0.162390 | + | 0.986727i | \(0.448080\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −15376.0 | −1.60538 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1704.00 | −0.176735 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1736.00 | 0.178868 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5914.00 | 0.605351 | 0.302675 | − | 0.953094i | \(-0.402120\pi\) | ||||
0.302675 | + | 0.953094i | \(0.402120\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2268.00 | −0.230634 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15968.0 | 1.61324 | 0.806620 | − | 0.591070i | \(-0.201294\pi\) | ||||
0.806620 | + | 0.591070i | \(0.201294\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1172.00 | 0.117640 | 0.0588202 | − | 0.998269i | \(-0.481266\pi\) | ||||
0.0588202 | + | 0.998269i | \(0.481266\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −576.000 | −0.0574438 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5304.00 | 0.525567 | 0.262784 | − | 0.964855i | \(-0.415359\pi\) | ||||
0.262784 | + | 0.964855i | \(0.415359\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6328.00 | 0.623027 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −798.000 | −0.0780677 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4216.00 | 0.409835 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10900.0 | −1.05290 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2322.00 | −0.222887 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5740.00 | −0.547531 | −0.273765 | − | 0.961796i | \(-0.588269\pi\) | ||||
−0.273765 | + | 0.961796i | \(0.588269\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15252.0 | 1.44580 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −882.000 | −0.0830898 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5064.00 | −0.474112 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8944.00 | −0.832220 | −0.416110 | − | 0.909314i | \(-0.636607\pi\) | ||||
−0.416110 | + | 0.909314i | \(0.636607\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 816.000 | 0.0754617 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5558.00 | −0.510853 | −0.255427 | − | 0.966828i | \(-0.582216\pi\) | ||||
−0.255427 | + | 0.966828i | \(0.582216\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 840.000 | 0.0767377 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2232.00 | 0.202669 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4746.00 | 0.428344 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19820.0 | −1.77809 | −0.889043 | − | 0.457823i | \(-0.848629\pi\) | ||||
−0.889043 | + | 0.457823i | \(0.848629\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5628.00 | −0.501877 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1848.00 | −0.163814 | −0.0819068 | − | 0.996640i | \(-0.526101\pi\) | ||||
−0.0819068 | + | 0.996640i | \(0.526101\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −928.000 | −0.0817732 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4941.00 | −0.432816 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −340.000 | −0.0296075 | −0.0148038 | − | 0.999890i | \(-0.504712\pi\) | ||||
−0.0148038 | + | 0.999890i | \(0.504712\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4494.00 | −0.389047 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2700.00 | −0.232374 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7168.00 | 0.613320 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −20088.0 | −1.70884 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −456.000 | −0.0385668 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10212.0 | 0.858725 | 0.429363 | − | 0.903132i | \(-0.358738\pi\) | ||||
0.429363 | + | 0.903132i | \(0.358738\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9332.00 | −0.780229 | −0.390115 | − | 0.920766i | \(-0.627565\pi\) | ||||
−0.390115 | + | 0.920766i | \(0.627565\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2289.00 | 0.190286 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4032.00 | 0.333276 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10403.0 | −0.855018 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1080.00 | 0.0882637 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −15376.0 | −1.24955 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7624.00 | −0.616101 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1830.00 | −0.147058 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3038.00 | 0.242775 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8998.00 | 0.715073 | 0.357536 | − | 0.933899i | \(-0.383617\pi\) | ||||
0.357536 | + | 0.933899i | \(0.383617\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3126.00 | 0.247052 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 360.000 | 0.0282949 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3416.00 | −0.267016 | −0.133508 | − | 0.991048i | \(-0.542624\pi\) | ||||
−0.133508 | + | 0.991048i | \(0.542624\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5598.00 | −0.435185 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1000.00 | 0.0773166 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5180.00 | −0.398329 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2952.00 | −0.225776 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 526.000 | 0.0400132 | 0.0200066 | − | 0.999800i | \(-0.493631\pi\) | ||||
0.0200066 | + | 0.999800i | \(0.493631\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4216.00 | 0.318994 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −15624.0 | −1.17584 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6712.00 | −0.502446 | −0.251223 | − | 0.967929i | \(-0.580833\pi\) | ||||
−0.251223 | + | 0.967929i | \(0.580833\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1832.00 | 0.136412 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 567.000 | 0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4190.00 | 0.308706 | 0.154353 | − | 0.988016i | \(-0.450671\pi\) | ||||
0.154353 | + | 0.988016i | \(0.450671\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3032.00 | 0.222216 | 0.111108 | − | 0.993808i | \(-0.464560\pi\) | ||||
0.111108 | + | 0.993808i | \(0.464560\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6114.00 | −0.445752 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4578.00 | −0.332027 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5434.00 | 0.392063 | 0.196032 | − | 0.980598i | \(-0.437195\pi\) | ||||
0.196032 | + | 0.980598i | \(0.437195\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7806.00 | 0.560287 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3276.00 | 0.233927 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −15996.0 | −1.13634 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2232.00 | 0.157747 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 464.000 | 0.0326258 | 0.0163129 | − | 0.999867i | \(-0.494807\pi\) | ||||
0.0163129 | + | 0.999867i | \(0.494807\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4800.00 | 0.335790 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7062.00 | 0.491526 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11748.0 | 0.813546 | 0.406773 | − | 0.913529i | \(-0.366654\pi\) | ||||
0.406773 | + | 0.913529i | \(0.366654\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2352.00 | 0.162055 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5040.00 | 0.345517 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7650.00 | −0.521821 | −0.260910 | − | 0.965363i | \(-0.584023\pi\) | ||||
−0.260910 | + | 0.965363i | \(0.584023\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22878.0 | −1.55277 | −0.776384 | − | 0.630261i | \(-0.782948\pi\) | ||||
−0.776384 | + | 0.630261i | \(0.782948\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8136.00 | 0.549459 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10052.0 | 0.675491 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −704.000 | −0.0470749 | −0.0235375 | − | 0.999723i | \(-0.507493\pi\) | ||||
−0.0235375 | + | 0.999723i | \(0.507493\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −210.000 | −0.0139731 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −20088.0 | −1.33007 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −24958.0 | −1.64444 | −0.822222 | − | 0.569167i | \(-0.807266\pi\) | ||||
−0.822222 | + | 0.569167i | \(0.807266\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2976.00 | 0.195128 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8826.00 | −0.575886 | −0.287943 | − | 0.957648i | \(-0.592971\pi\) | ||||
−0.287943 | + | 0.957648i | \(0.592971\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21220.0 | 1.37787 | 0.688937 | − | 0.724821i | \(-0.258078\pi\) | ||||
0.688937 | + | 0.724821i | \(0.258078\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1134.00 | −0.0732783 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1400.00 | 0.0900318 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9881.00 | 0.632384 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −18600.0 | −1.18471 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 20664.0 | 1.30990 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3268.00 | 0.206176 | 0.103088 | − | 0.994672i | \(-0.467128\pi\) | ||||
0.103088 | + | 0.994672i | \(0.467128\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2004.00 | 0.125832 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3216.00 | −0.200981 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3038.00 | 0.188964 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6102.00 | 0.377764 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13062.0 | 0.804864 | 0.402432 | − | 0.915450i | \(-0.368165\pi\) | ||||
0.402432 | + | 0.915450i | \(0.368165\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −28012.0 | −1.71802 | −0.859009 | − | 0.511961i | \(-0.828919\pi\) | ||||
−0.859009 | + | 0.511961i | \(0.828919\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −816.000 | −0.0498139 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3844.00 | −0.233575 | −0.116788 | − | 0.993157i | \(-0.537260\pi\) | ||||
−0.116788 | + | 0.993157i | \(0.537260\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7440.00 | 0.449993 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1008.00 | −0.0606861 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 28482.0 | 1.70687 | 0.853436 | − | 0.521198i | \(-0.174515\pi\) | ||||
0.853436 | + | 0.521198i | \(0.174515\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3248.00 | 0.193756 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5778.00 | −0.343107 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9330.00 | −0.551510 | −0.275755 | − | 0.961228i | \(-0.588928\pi\) | ||||
−0.275755 | + | 0.961228i | \(0.588928\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8782.00 | −0.516763 | −0.258381 | − | 0.966043i | \(-0.583189\pi\) | ||||
−0.258381 | + | 0.966043i | \(0.583189\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −15624.0 | −0.915212 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2800.00 | 0.163277 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 420.000 | 0.0243815 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5496.00 | −0.317620 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −38564.0 | −2.21870 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10562.0 | −0.604956 | −0.302478 | − | 0.953156i | \(-0.597814\pi\) | ||||
−0.302478 | + | 0.953156i | \(0.597814\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2943.00 | 0.167816 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 26016.0 | 1.47692 | 0.738461 | − | 0.674296i | \(-0.235553\pi\) | ||||
0.738461 | + | 0.674296i | \(0.235553\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8862.00 | −0.500872 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14832.0 | −0.834601 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8898.00 | 0.498496 | 0.249248 | − | 0.968440i | \(-0.419817\pi\) | ||||
0.249248 | + | 0.968440i | \(0.419817\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1656.00 | 0.0923686 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −16410.0 | −0.911325 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −15996.0 | −0.884469 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 30572.0 | 1.68309 | 0.841544 | − | 0.540189i | \(-0.181647\pi\) | ||||
0.841544 | + | 0.540189i | \(0.181647\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3906.00 | 0.214108 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6480.00 | −0.353670 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −20832.0 | −1.13209 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8406.00 | 0.454856 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30618.0 | 1.64968 | 0.824840 | − | 0.565366i | \(-0.191265\pi\) | ||||
0.824840 | + | 0.565366i | \(0.191265\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 24600.0 | 1.31978 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3888.00 | 0.207703 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1624.00 | −0.0863887 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8130.00 | 0.430647 | 0.215323 | − | 0.976543i | \(-0.430919\pi\) | ||||
0.215323 | + | 0.976543i | \(0.430919\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6660.00 | −0.351293 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2016.00 | 0.105890 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 15376.0 | 0.804237 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3510.00 | −0.182822 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 27840.0 | 1.44403 | 0.722014 | − | 0.691878i | \(-0.243216\pi\) | ||||
0.722014 | + | 0.691878i | \(0.243216\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12544.0 | 0.647938 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7014.00 | 0.360793 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1090.00 | −0.0558367 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14624.0 | −0.746044 | −0.373022 | − | 0.927822i | \(-0.621678\pi\) | ||||
−0.373022 | + | 0.927822i | \(0.621678\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5712.00 | 0.289010 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20862.0 | 1.05124 | 0.525618 | − | 0.850721i | \(-0.323834\pi\) | ||||
0.525618 | + | 0.850721i | \(0.323834\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −588.000 | −0.0295084 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 56048.0 | 2.80130 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13920.0 | −0.692903 | −0.346452 | − | 0.938068i | \(-0.612614\pi\) | ||||
−0.346452 | + | 0.938068i | \(0.612614\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −18600.0 | −0.922116 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −25578.0 | −1.26294 | −0.631471 | − | 0.775400i | \(-0.717548\pi\) | ||||
−0.631471 | + | 0.775400i | \(0.717548\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9480.00 | −0.466202 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4212.00 | 0.206304 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −13342.0 | −0.650876 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −33472.0 | −1.62638 | −0.813189 | − | 0.581999i | \(-0.802271\pi\) | ||||
−0.813189 | + | 0.581999i | \(0.802271\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −8376.00 | −0.405363 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2272.00 | 0.109519 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −25934.0 | −1.24516 | −0.622581 | − | 0.782556i | \(-0.713916\pi\) | ||||
−0.622581 | + | 0.782556i | \(0.713916\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −7812.00 | −0.373594 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 26952.0 | 1.28385 | 0.641925 | − | 0.766768i | \(-0.278136\pi\) | ||||
0.641925 | + | 0.766768i | \(0.278136\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 630.000 | 0.0298919 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3024.00 | 0.142919 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7440.00 | 0.350251 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 23450.0 | 1.09965 | 0.549824 | − | 0.835281i | \(-0.314695\pi\) | ||||
0.549824 | + | 0.835281i | \(0.314695\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −21072.0 | −0.984293 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −39568.0 | −1.84109 | −0.920545 | − | 0.390637i | \(-0.872255\pi\) | ||||
−0.920545 | + | 0.390637i | \(0.872255\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5232.00 | −0.242502 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5166.00 | −0.238519 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −24800.0 | −1.14063 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 42036.0 | 1.92595 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −270.000 | −0.0123231 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1064.00 | 0.0483768 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12356.0 | −0.559649 | −0.279825 | − | 0.960051i | \(-0.590276\pi\) | ||||
−0.279825 | + | 0.960051i | \(0.590276\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 7314.00 | 0.330019 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3206.00 | 0.144112 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −38564.0 | −1.72692 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3096.00 | 0.138118 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 21736.0 | 0.966033 | 0.483017 | − | 0.875611i | \(-0.339541\pi\) | ||||
0.483017 | + | 0.875611i | \(0.339541\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −27216.0 | −1.20505 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1800.00 | 0.0794006 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −39804.0 | −1.74926 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1176.00 | 0.0514889 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −20340.0 | −0.887239 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −38310.0 | −1.66490 | −0.832452 | − | 0.554097i | \(-0.813064\pi\) | ||||
−0.832452 | + | 0.554097i | \(0.813064\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2132.00 | 0.0923115 | 0.0461558 | − | 0.998934i | \(-0.485303\pi\) | ||||
0.0461558 | + | 0.998934i | \(0.485303\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5784.00 | −0.249513 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1088.00 | −0.0467619 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6800.00 | 0.291190 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3906.00 | 0.166650 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5002.00 | −0.212632 | −0.106316 | − | 0.994332i | \(-0.533906\pi\) | ||||
−0.106316 | + | 0.994332i | \(0.533906\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3612.00 | 0.152985 | 0.0764923 | − | 0.997070i | \(-0.475628\pi\) | ||||
0.0764923 | + | 0.997070i | \(0.475628\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 20274.0 | 0.855576 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −27666.0 | −1.16329 | −0.581645 | − | 0.813443i | \(-0.697591\pi\) | ||||
−0.581645 | + | 0.813443i | \(0.697591\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12890.0 | −0.540034 | −0.270017 | − | 0.962856i | \(-0.587029\pi\) | ||||
−0.270017 | + | 0.962856i | \(0.587029\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 16662.0 | 0.695546 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4116.00 | 0.171202 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7504.00 | 0.311002 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1296.00 | −0.0535201 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9340.00 | 0.384330 | 0.192165 | − | 0.981363i | \(-0.438449\pi\) | ||||
0.192165 | + | 0.981363i | \(0.438449\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24289.0 | −0.995900 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −5826.00 | −0.238029 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6588.00 | 0.268206 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 17591.0 | 0.713617 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −14484.0 | −0.585500 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10332.0 | 0.416188 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 33082.0 | 1.32791 | 0.663954 | − | 0.747773i | \(-0.268877\pi\) | ||||
0.663954 | + | 0.747773i | \(0.268877\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3600.00 | 0.143997 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7544.00 | 0.300698 | 0.150349 | − | 0.988633i | \(-0.451960\pi\) | ||||
0.150349 | + | 0.988633i | \(0.451960\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8180.00 | 0.324910 | 0.162455 | − | 0.986716i | \(-0.448059\pi\) | ||||
0.162455 | + | 0.986716i | \(0.448059\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5208.00 | 0.206142 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −10518.0 | −0.414875 | −0.207437 | − | 0.978248i | \(-0.566512\pi\) | ||||
−0.207437 | + | 0.978248i | \(0.566512\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 608.000 | 0.0238990 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −6429.00 | −0.251834 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −45880.0 | −1.79099 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 56048.0 | 2.18038 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −11394.0 | −0.441728 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6552.00 | −0.253141 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14134.0 | −0.544209 | −0.272104 | − | 0.962268i | \(-0.587720\pi\) | ||||
−0.272104 | + | 0.962268i | \(0.587720\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −18456.0 | −0.708197 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6492.00 | 0.248265 | 0.124132 | − | 0.992266i | \(-0.460385\pi\) | ||||
0.124132 | + | 0.992266i | \(0.460385\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 38228.0 | 1.45694 | 0.728468 | − | 0.685080i | \(-0.240233\pi\) | ||||
0.728468 | + | 0.685080i | \(0.240233\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1440.00 | −0.0546950 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 43076.0 | 1.63061 | 0.815305 | − | 0.579032i | \(-0.196569\pi\) | ||||
0.815305 | + | 0.579032i | \(0.196569\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5628.00 | −0.212325 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5022.00 | 0.188825 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −32400.0 | −1.21414 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2440.00 | 0.0911287 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7812.00 | −0.290786 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 480.000 | 0.0178074 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −21672.0 | −0.801331 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1428.00 | −0.0526255 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4168.00 | −0.153093 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −32236.0 | −1.18013 | −0.590065 | − | 0.807355i | \(-0.700898\pi\) | ||||
−0.590065 | + | 0.807355i | \(0.700898\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2088.00 | −0.0761877 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 46518.0 | 1.69178 | 0.845889 | − | 0.533359i | \(-0.179070\pi\) | ||||
0.845889 | + | 0.533359i | \(0.179070\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 29016.0 | 1.05180 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 7464.00 | 0.269675 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5684.00 | 0.204692 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17840.0 | −0.640356 | −0.320178 | − | 0.947357i | \(-0.603743\pi\) | ||||
−0.320178 | + | 0.947357i | \(0.603743\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −17652.0 | −0.631545 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 42036.0 | 1.49906 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −26814.0 | −0.953123 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 16128.0 | 0.571427 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 7000.00 | 0.247215 | 0.123607 | − | 0.992331i | \(-0.460554\pi\) | ||||
0.123607 | + | 0.992331i | \(0.460554\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4900.00 | 0.172493 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 27396.0 | 0.961313 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 20832.0 | 0.728641 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 36114.0 | 1.25912 | 0.629559 | − | 0.776953i | \(-0.283236\pi\) | ||||
0.629559 | + | 0.776953i | \(0.283236\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 28146.0 | 0.978179 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4748.00 | 0.164485 | 0.0822425 | − | 0.996612i | \(-0.473792\pi\) | ||||
0.0822425 | + | 0.996612i | \(0.473792\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10416.0 | −0.359694 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −756.000 | −0.0260240 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 42694.0 | 1.46501 | 0.732507 | − | 0.680759i | \(-0.238350\pi\) | ||||
0.732507 | + | 0.680759i | \(0.238350\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −39804.0 | −1.36153 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9342.00 | 0.318544 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −16742.0 | −0.569073 | −0.284537 | − | 0.958665i | \(-0.591840\pi\) | ||||
−0.284537 | + | 0.958665i | \(0.591840\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8152.00 | 0.276223 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1860.00 | −0.0628268 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2898.00 | 0.0975822 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27487.0 | −0.922661 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −17154.0 | −0.574019 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −10408.0 | −0.347197 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9956.00 | 0.331089 | 0.165545 | − | 0.986202i | \(-0.447062\pi\) | ||||
0.165545 | + | 0.986202i | \(0.447062\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −25200.0 | −0.835439 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −26388.0 | −0.872123 | −0.436061 | − | 0.899917i | \(-0.643627\pi\) | ||||
−0.436061 | + | 0.899917i | \(0.643627\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −11340.0 | −0.373632 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 20274.0 | 0.665936 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −786.000 | −0.0257383 | −0.0128692 | − | 0.999917i | \(-0.504096\pi\) | ||||
−0.0128692 | + | 0.999917i | \(0.504096\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12400.0 | 0.404807 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 810.000 | 0.0263622 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −51888.0 | −1.68359 | −0.841796 | − | 0.539796i | \(-0.818501\pi\) | ||||
−0.841796 | + | 0.539796i | \(0.818501\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9416.00 | −0.304588 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6804.00 | 0.219426 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2856.00 | 0.0918256 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 51928.0 | 1.66453 | 0.832264 | − | 0.554379i | \(-0.187044\pi\) | ||||
0.832264 | + | 0.554379i | \(0.187044\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4596.00 | −0.146878 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6720.00 | −0.214109 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 386.000 | 0.0122615 | 0.00613076 | − | 0.999981i | \(-0.498049\pi\) | ||||
0.00613076 | + | 0.999981i | \(0.498049\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6642.00 | −0.210354 |
(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 | 1344.4.a.i.1.1 | 1 | ||
4.3 | odd | 2 | 1344.4.a.w.1.1 | 1 | |||
8.3 | odd | 2 | 21.4.a.b.1.1 | ✓ | 1 | ||
8.5 | even | 2 | 336.4.a.h.1.1 | 1 | |||
24.5 | odd | 2 | 1008.4.a.m.1.1 | 1 | |||
24.11 | even | 2 | 63.4.a.a.1.1 | 1 | |||
40.3 | even | 4 | 525.4.d.b.274.1 | 2 | |||
40.19 | odd | 2 | 525.4.a.b.1.1 | 1 | |||
40.27 | even | 4 | 525.4.d.b.274.2 | 2 | |||
56.3 | even | 6 | 147.4.e.b.79.1 | 2 | |||
56.11 | odd | 6 | 147.4.e.c.79.1 | 2 | |||
56.13 | odd | 2 | 2352.4.a.l.1.1 | 1 | |||
56.19 | even | 6 | 147.4.e.b.67.1 | 2 | |||
56.27 | even | 2 | 147.4.a.g.1.1 | 1 | |||
56.51 | odd | 6 | 147.4.e.c.67.1 | 2 | |||
120.59 | even | 2 | 1575.4.a.k.1.1 | 1 | |||
168.11 | even | 6 | 441.4.e.m.226.1 | 2 | |||
168.59 | odd | 6 | 441.4.e.n.226.1 | 2 | |||
168.83 | odd | 2 | 441.4.a.b.1.1 | 1 | |||
168.107 | even | 6 | 441.4.e.m.361.1 | 2 | |||
168.131 | odd | 6 | 441.4.e.n.361.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.4.a.b.1.1 | ✓ | 1 | 8.3 | odd | 2 | ||
63.4.a.a.1.1 | 1 | 24.11 | even | 2 | |||
147.4.a.g.1.1 | 1 | 56.27 | even | 2 | |||
147.4.e.b.67.1 | 2 | 56.19 | even | 6 | |||
147.4.e.b.79.1 | 2 | 56.3 | even | 6 | |||
147.4.e.c.67.1 | 2 | 56.51 | odd | 6 | |||
147.4.e.c.79.1 | 2 | 56.11 | odd | 6 | |||
336.4.a.h.1.1 | 1 | 8.5 | even | 2 | |||
441.4.a.b.1.1 | 1 | 168.83 | odd | 2 | |||
441.4.e.m.226.1 | 2 | 168.11 | even | 6 | |||
441.4.e.m.361.1 | 2 | 168.107 | even | 6 | |||
441.4.e.n.226.1 | 2 | 168.59 | odd | 6 | |||
441.4.e.n.361.1 | 2 | 168.131 | odd | 6 | |||
525.4.a.b.1.1 | 1 | 40.19 | odd | 2 | |||
525.4.d.b.274.1 | 2 | 40.3 | even | 4 | |||
525.4.d.b.274.2 | 2 | 40.27 | even | 4 | |||
1008.4.a.m.1.1 | 1 | 24.5 | odd | 2 | |||
1344.4.a.i.1.1 | 1 | 1.1 | even | 1 | trivial | ||
1344.4.a.w.1.1 | 1 | 4.3 | odd | 2 | |||
1575.4.a.k.1.1 | 1 | 120.59 | even | 2 | |||
2352.4.a.l.1.1 | 1 | 56.13 | odd | 2 |