Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,6,Mod(1,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.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: | \(132.316651346\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.18257.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 26x + 8 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 165) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.305203\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.694797 | −0.122824 | −0.0614120 | − | 0.998113i | \(-0.519560\pi\) | ||||
−0.0614120 | + | 0.998113i | \(0.519560\pi\) | |||||||
\(3\) | 9.00000 | 0.577350 | ||||||||
\(4\) | −31.5173 | −0.984914 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −6.25317 | −0.0709124 | ||||||||
\(7\) | −83.1683 | −0.641523 | −0.320762 | − | 0.947160i | \(-0.603939\pi\) | ||||
−0.320762 | + | 0.947160i | \(0.603939\pi\) | |||||||
\(8\) | 44.1316 | 0.243795 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 121.000 | 0.301511 | ||||||||
\(12\) | −283.655 | −0.568641 | ||||||||
\(13\) | 674.655 | 1.10719 | 0.553597 | − | 0.832785i | \(-0.313255\pi\) | ||||
0.553597 | + | 0.832785i | \(0.313255\pi\) | |||||||
\(14\) | 57.7851 | 0.0787944 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 977.890 | 0.954970 | ||||||||
\(17\) | −1927.66 | −1.61774 | −0.808868 | − | 0.587991i | \(-0.799919\pi\) | ||||
−0.808868 | + | 0.587991i | \(0.799919\pi\) | |||||||
\(18\) | −56.2785 | −0.0409413 | ||||||||
\(19\) | −149.751 | −0.0951666 | −0.0475833 | − | 0.998867i | \(-0.515152\pi\) | ||||
−0.0475833 | + | 0.998867i | \(0.515152\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −748.514 | −0.370384 | ||||||||
\(22\) | −84.0704 | −0.0370328 | ||||||||
\(23\) | 1355.59 | 0.534330 | 0.267165 | − | 0.963651i | \(-0.413913\pi\) | ||||
0.267165 | + | 0.963651i | \(0.413913\pi\) | |||||||
\(24\) | 397.184 | 0.140755 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −468.748 | −0.135990 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | 2621.24 | 0.631846 | ||||||||
\(29\) | −7320.99 | −1.61650 | −0.808248 | − | 0.588842i | \(-0.799584\pi\) | ||||
−0.808248 | + | 0.588842i | \(0.799584\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4215.76 | −0.787901 | −0.393951 | − | 0.919132i | \(-0.628892\pi\) | ||||
−0.393951 | + | 0.919132i | \(0.628892\pi\) | |||||||
\(32\) | −2091.65 | −0.361088 | ||||||||
\(33\) | 1089.00 | 0.174078 | ||||||||
\(34\) | 1339.33 | 0.198697 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2552.90 | −0.328305 | ||||||||
\(37\) | 13420.1 | 1.61158 | 0.805792 | − | 0.592199i | \(-0.201740\pi\) | ||||
0.805792 | + | 0.592199i | \(0.201740\pi\) | |||||||
\(38\) | 104.046 | 0.0116887 | ||||||||
\(39\) | 6071.90 | 0.639238 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2865.39 | 0.266210 | 0.133105 | − | 0.991102i | \(-0.457505\pi\) | ||||
0.133105 | + | 0.991102i | \(0.457505\pi\) | |||||||
\(42\) | 520.065 | 0.0454920 | ||||||||
\(43\) | 22078.1 | 1.82092 | 0.910458 | − | 0.413601i | \(-0.135729\pi\) | ||||
0.910458 | + | 0.413601i | \(0.135729\pi\) | |||||||
\(44\) | −3813.59 | −0.296963 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −941.861 | −0.0656285 | ||||||||
\(47\) | 14556.4 | 0.961192 | 0.480596 | − | 0.876942i | \(-0.340420\pi\) | ||||
0.480596 | + | 0.876942i | \(0.340420\pi\) | |||||||
\(48\) | 8801.01 | 0.551352 | ||||||||
\(49\) | −9890.04 | −0.588448 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −17348.9 | −0.934000 | ||||||||
\(52\) | −21263.3 | −1.09049 | ||||||||
\(53\) | −13349.7 | −0.652805 | −0.326402 | − | 0.945231i | \(-0.605836\pi\) | ||||
−0.326402 | + | 0.945231i | \(0.605836\pi\) | |||||||
\(54\) | −506.507 | −0.0236375 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3670.35 | −0.156400 | ||||||||
\(57\) | −1347.76 | −0.0549445 | ||||||||
\(58\) | 5086.60 | 0.198544 | ||||||||
\(59\) | 45803.3 | 1.71304 | 0.856518 | − | 0.516117i | \(-0.172623\pi\) | ||||
0.856518 | + | 0.516117i | \(0.172623\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 18996.5 | 0.653655 | 0.326827 | − | 0.945084i | \(-0.394020\pi\) | ||||
0.326827 | + | 0.945084i | \(0.394020\pi\) | |||||||
\(62\) | 2929.10 | 0.0967731 | ||||||||
\(63\) | −6736.63 | −0.213841 | ||||||||
\(64\) | −29839.2 | −0.910620 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −756.634 | −0.0213809 | ||||||||
\(67\) | −6651.05 | −0.181010 | −0.0905052 | − | 0.995896i | \(-0.528848\pi\) | ||||
−0.0905052 | + | 0.995896i | \(0.528848\pi\) | |||||||
\(68\) | 60754.5 | 1.59333 | ||||||||
\(69\) | 12200.3 | 0.308495 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −61028.7 | −1.43677 | −0.718386 | − | 0.695644i | \(-0.755119\pi\) | ||||
−0.718386 | + | 0.695644i | \(0.755119\pi\) | |||||||
\(72\) | 3574.66 | 0.0812650 | ||||||||
\(73\) | 17353.4 | 0.381134 | 0.190567 | − | 0.981674i | \(-0.438967\pi\) | ||||
0.190567 | + | 0.981674i | \(0.438967\pi\) | |||||||
\(74\) | −9324.27 | −0.197941 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4719.73 | 0.0937309 | ||||||||
\(77\) | −10063.4 | −0.193427 | ||||||||
\(78\) | −4218.74 | −0.0785138 | ||||||||
\(79\) | 61676.5 | 1.11187 | 0.555933 | − | 0.831227i | \(-0.312361\pi\) | ||||
0.555933 | + | 0.831227i | \(0.312361\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | −1990.87 | −0.0326969 | ||||||||
\(83\) | 65230.8 | 1.03934 | 0.519670 | − | 0.854367i | \(-0.326055\pi\) | ||||
0.519670 | + | 0.854367i | \(0.326055\pi\) | |||||||
\(84\) | 23591.1 | 0.364796 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −15339.8 | −0.223652 | ||||||||
\(87\) | −65888.9 | −0.933284 | ||||||||
\(88\) | 5339.92 | 0.0735069 | ||||||||
\(89\) | −109563. | −1.46618 | −0.733091 | − | 0.680131i | \(-0.761923\pi\) | ||||
−0.733091 | + | 0.680131i | \(0.761923\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −56109.9 | −0.710291 | ||||||||
\(92\) | −42724.5 | −0.526269 | ||||||||
\(93\) | −37941.8 | −0.454895 | ||||||||
\(94\) | −10113.8 | −0.118057 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −18824.8 | −0.208474 | ||||||||
\(97\) | −83736.1 | −0.903615 | −0.451808 | − | 0.892115i | \(-0.649221\pi\) | ||||
−0.451808 | + | 0.892115i | \(0.649221\pi\) | |||||||
\(98\) | 6871.57 | 0.0722754 | ||||||||
\(99\) | 9801.00 | 0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −129877. | −1.26686 | −0.633428 | − | 0.773801i | \(-0.718353\pi\) | ||||
−0.633428 | + | 0.773801i | \(0.718353\pi\) | |||||||
\(102\) | 12054.0 | 0.114718 | ||||||||
\(103\) | −201851. | −1.87472 | −0.937362 | − | 0.348358i | \(-0.886739\pi\) | ||||
−0.937362 | + | 0.348358i | \(0.886739\pi\) | |||||||
\(104\) | 29773.6 | 0.269928 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 9275.36 | 0.0801800 | ||||||||
\(107\) | 132285. | 1.11699 | 0.558496 | − | 0.829507i | \(-0.311378\pi\) | ||||
0.558496 | + | 0.829507i | \(0.311378\pi\) | |||||||
\(108\) | −22976.1 | −0.189547 | ||||||||
\(109\) | −144044. | −1.16126 | −0.580629 | − | 0.814168i | \(-0.697193\pi\) | ||||
−0.580629 | + | 0.814168i | \(0.697193\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 120781. | 0.930448 | ||||||||
\(112\) | −81329.4 | −0.612636 | ||||||||
\(113\) | 1095.62 | 0.00807165 | 0.00403582 | − | 0.999992i | \(-0.498715\pi\) | ||||
0.00403582 | + | 0.999992i | \(0.498715\pi\) | |||||||
\(114\) | 936.416 | 0.00674849 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 230737. | 1.59211 | ||||||||
\(117\) | 54647.1 | 0.369065 | ||||||||
\(118\) | −31824.0 | −0.210402 | ||||||||
\(119\) | 160320. | 1.03782 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | −13198.7 | −0.0802844 | ||||||||
\(123\) | 25788.5 | 0.153696 | ||||||||
\(124\) | 132869. | 0.776015 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 4680.59 | 0.0262648 | ||||||||
\(127\) | −315758. | −1.73718 | −0.868591 | − | 0.495529i | \(-0.834974\pi\) | ||||
−0.868591 | + | 0.495529i | \(0.834974\pi\) | |||||||
\(128\) | 87664.9 | 0.472934 | ||||||||
\(129\) | 198703. | 1.05131 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −187001. | −0.952064 | −0.476032 | − | 0.879428i | \(-0.657925\pi\) | ||||
−0.476032 | + | 0.879428i | \(0.657925\pi\) | |||||||
\(132\) | −34322.3 | −0.171452 | ||||||||
\(133\) | 12454.5 | 0.0610516 | ||||||||
\(134\) | 4621.13 | 0.0222324 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −85070.6 | −0.394396 | ||||||||
\(137\) | −232301. | −1.05743 | −0.528713 | − | 0.848801i | \(-0.677325\pi\) | ||||
−0.528713 | + | 0.848801i | \(0.677325\pi\) | |||||||
\(138\) | −8476.75 | −0.0378906 | ||||||||
\(139\) | −311665. | −1.36820 | −0.684102 | − | 0.729386i | \(-0.739806\pi\) | ||||
−0.684102 | + | 0.729386i | \(0.739806\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 131008. | 0.554944 | ||||||||
\(142\) | 42402.5 | 0.176470 | ||||||||
\(143\) | 81633.3 | 0.333831 | ||||||||
\(144\) | 79209.1 | 0.318323 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −12057.1 | −0.0468124 | ||||||||
\(147\) | −89010.4 | −0.339740 | ||||||||
\(148\) | −422966. | −1.58727 | ||||||||
\(149\) | 30354.5 | 0.112010 | 0.0560050 | − | 0.998430i | \(-0.482164\pi\) | ||||
0.0560050 | + | 0.998430i | \(0.482164\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 131015. | 0.467604 | 0.233802 | − | 0.972284i | \(-0.424883\pi\) | ||||
0.233802 | + | 0.972284i | \(0.424883\pi\) | |||||||
\(152\) | −6608.73 | −0.0232011 | ||||||||
\(153\) | −156140. | −0.539245 | ||||||||
\(154\) | 6991.99 | 0.0237574 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −191370. | −0.629595 | ||||||||
\(157\) | −326922. | −1.05851 | −0.529255 | − | 0.848463i | \(-0.677528\pi\) | ||||
−0.529255 | + | 0.848463i | \(0.677528\pi\) | |||||||
\(158\) | −42852.7 | −0.136564 | ||||||||
\(159\) | −120148. | −0.376897 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −112742. | −0.342785 | ||||||||
\(162\) | −4558.56 | −0.0136471 | ||||||||
\(163\) | 501854. | 1.47948 | 0.739739 | − | 0.672894i | \(-0.234949\pi\) | ||||
0.739739 | + | 0.672894i | \(0.234949\pi\) | |||||||
\(164\) | −90309.3 | −0.262194 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −45322.2 | −0.127656 | ||||||||
\(167\) | 590462. | 1.63833 | 0.819164 | − | 0.573559i | \(-0.194438\pi\) | ||||
0.819164 | + | 0.573559i | \(0.194438\pi\) | |||||||
\(168\) | −33033.1 | −0.0902977 | ||||||||
\(169\) | 83866.7 | 0.225877 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −12129.8 | −0.0317222 | ||||||||
\(172\) | −695840. | −1.79345 | ||||||||
\(173\) | −570934. | −1.45034 | −0.725172 | − | 0.688568i | \(-0.758240\pi\) | ||||
−0.725172 | + | 0.688568i | \(0.758240\pi\) | |||||||
\(174\) | 45779.4 | 0.114630 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 118325. | 0.287934 | ||||||||
\(177\) | 412230. | 0.989022 | ||||||||
\(178\) | 76123.9 | 0.180082 | ||||||||
\(179\) | −464402. | −1.08333 | −0.541666 | − | 0.840594i | \(-0.682206\pi\) | ||||
−0.541666 | + | 0.840594i | \(0.682206\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −409792. | −0.929751 | −0.464876 | − | 0.885376i | \(-0.653901\pi\) | ||||
−0.464876 | + | 0.885376i | \(0.653901\pi\) | |||||||
\(182\) | 38985.0 | 0.0872407 | ||||||||
\(183\) | 170968. | 0.377388 | ||||||||
\(184\) | 59824.4 | 0.130267 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 26361.9 | 0.0558720 | ||||||||
\(187\) | −233247. | −0.487766 | ||||||||
\(188\) | −458778. | −0.946691 | ||||||||
\(189\) | −60629.7 | −0.123461 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −591029. | −1.17226 | −0.586132 | − | 0.810216i | \(-0.699350\pi\) | ||||
−0.586132 | + | 0.810216i | \(0.699350\pi\) | |||||||
\(192\) | −268553. | −0.525747 | ||||||||
\(193\) | 310907. | 0.600811 | 0.300405 | − | 0.953812i | \(-0.402878\pi\) | ||||
0.300405 | + | 0.953812i | \(0.402878\pi\) | |||||||
\(194\) | 58179.6 | 0.110986 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 311707. | 0.579571 | ||||||||
\(197\) | −161613. | −0.296695 | −0.148348 | − | 0.988935i | \(-0.547395\pi\) | ||||
−0.148348 | + | 0.988935i | \(0.547395\pi\) | |||||||
\(198\) | −6809.70 | −0.0123443 | ||||||||
\(199\) | 435622. | 0.779790 | 0.389895 | − | 0.920859i | \(-0.372511\pi\) | ||||
0.389895 | + | 0.920859i | \(0.372511\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −59859.5 | −0.104506 | ||||||||
\(202\) | 90237.8 | 0.155600 | ||||||||
\(203\) | 608874. | 1.03702 | ||||||||
\(204\) | 546790. | 0.919910 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 140245. | 0.230261 | ||||||||
\(207\) | 109803. | 0.178110 | ||||||||
\(208\) | 659738. | 1.05734 | ||||||||
\(209\) | −18119.8 | −0.0286938 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −539434. | −0.834127 | −0.417063 | − | 0.908877i | \(-0.636941\pi\) | ||||
−0.417063 | + | 0.908877i | \(0.636941\pi\) | |||||||
\(212\) | 420747. | 0.642957 | ||||||||
\(213\) | −549258. | −0.829521 | ||||||||
\(214\) | −91911.1 | −0.137193 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 32171.9 | 0.0469184 | ||||||||
\(217\) | 350618. | 0.505457 | ||||||||
\(218\) | 100081. | 0.142630 | ||||||||
\(219\) | 156181. | 0.220048 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.30050e6 | −1.79115 | ||||||||
\(222\) | −83918.5 | −0.114281 | ||||||||
\(223\) | −452834. | −0.609786 | −0.304893 | − | 0.952387i | \(-0.598621\pi\) | ||||
−0.304893 | + | 0.952387i | \(0.598621\pi\) | |||||||
\(224\) | 173959. | 0.231646 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −761.230 | −0.000991391 0 | ||||||||
\(227\) | 40608.6 | 0.0523062 | 0.0261531 | − | 0.999658i | \(-0.491674\pi\) | ||||
0.0261531 | + | 0.999658i | \(0.491674\pi\) | |||||||
\(228\) | 42477.5 | 0.0541156 | ||||||||
\(229\) | 988410. | 1.24551 | 0.622757 | − | 0.782415i | \(-0.286013\pi\) | ||||
0.622757 | + | 0.782415i | \(0.286013\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −90570.2 | −0.111675 | ||||||||
\(232\) | −323087. | −0.394093 | ||||||||
\(233\) | 47673.4 | 0.0575289 | 0.0287645 | − | 0.999586i | \(-0.490843\pi\) | ||||
0.0287645 | + | 0.999586i | \(0.490843\pi\) | |||||||
\(234\) | −37968.6 | −0.0453299 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.44359e6 | −1.68719 | ||||||||
\(237\) | 555089. | 0.641936 | ||||||||
\(238\) | −111390. | −0.127469 | ||||||||
\(239\) | −165174. | −0.187045 | −0.0935224 | − | 0.995617i | \(-0.529813\pi\) | ||||
−0.0935224 | + | 0.995617i | \(0.529813\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.13302e6 | −1.25659 | −0.628294 | − | 0.777976i | \(-0.716247\pi\) | ||||
−0.628294 | + | 0.777976i | \(0.716247\pi\) | |||||||
\(242\) | −10172.5 | −0.0111658 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | −598717. | −0.643794 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −17917.8 | −0.0188776 | ||||||||
\(247\) | −101030. | −0.105368 | ||||||||
\(248\) | −186048. | −0.192086 | ||||||||
\(249\) | 587078. | 0.600063 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.08030e6 | −1.08233 | −0.541165 | − | 0.840917i | \(-0.682016\pi\) | ||||
−0.541165 | + | 0.840917i | \(0.682016\pi\) | |||||||
\(252\) | 212320. | 0.210615 | ||||||||
\(253\) | 164027. | 0.161106 | ||||||||
\(254\) | 219388. | 0.213368 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 893945. | 0.852533 | ||||||||
\(257\) | −301460. | −0.284707 | −0.142353 | − | 0.989816i | \(-0.545467\pi\) | ||||
−0.142353 | + | 0.989816i | \(0.545467\pi\) | |||||||
\(258\) | −138058. | −0.129126 | ||||||||
\(259\) | −1.11613e6 | −1.03387 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −593000. | −0.538832 | ||||||||
\(262\) | 129928. | 0.116936 | ||||||||
\(263\) | 347755. | 0.310016 | 0.155008 | − | 0.987913i | \(-0.450460\pi\) | ||||
0.155008 | + | 0.987913i | \(0.450460\pi\) | |||||||
\(264\) | 48059.3 | 0.0424392 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −8653.34 | −0.00749860 | ||||||||
\(267\) | −986065. | −0.846501 | ||||||||
\(268\) | 209623. | 0.178280 | ||||||||
\(269\) | 980953. | 0.826547 | 0.413274 | − | 0.910607i | \(-0.364385\pi\) | ||||
0.413274 | + | 0.910607i | \(0.364385\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9630.73 | 0.00796592 | 0.00398296 | − | 0.999992i | \(-0.498732\pi\) | ||||
0.00398296 | + | 0.999992i | \(0.498732\pi\) | |||||||
\(272\) | −1.88504e6 | −1.54489 | ||||||||
\(273\) | −504989. | −0.410086 | ||||||||
\(274\) | 161402. | 0.129877 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −384521. | −0.303842 | ||||||||
\(277\) | −324368. | −0.254003 | −0.127001 | − | 0.991903i | \(-0.540535\pi\) | ||||
−0.127001 | + | 0.991903i | \(0.540535\pi\) | |||||||
\(278\) | 216544. | 0.168048 | ||||||||
\(279\) | −341477. | −0.262634 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 866856. | 0.654909 | 0.327455 | − | 0.944867i | \(-0.393809\pi\) | ||||
0.327455 | + | 0.944867i | \(0.393809\pi\) | |||||||
\(282\) | −91023.8 | −0.0681604 | ||||||||
\(283\) | 575157. | 0.426895 | 0.213447 | − | 0.976955i | \(-0.431531\pi\) | ||||
0.213447 | + | 0.976955i | \(0.431531\pi\) | |||||||
\(284\) | 1.92346e6 | 1.41510 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −56718.6 | −0.0410025 | ||||||||
\(287\) | −238310. | −0.170780 | ||||||||
\(288\) | −169423. | −0.120363 | ||||||||
\(289\) | 2.29601e6 | 1.61707 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −753625. | −0.521702 | ||||||||
\(292\) | −546932. | −0.375384 | ||||||||
\(293\) | −1.96073e6 | −1.33429 | −0.667144 | − | 0.744929i | \(-0.732483\pi\) | ||||
−0.667144 | + | 0.744929i | \(0.732483\pi\) | |||||||
\(294\) | 61844.1 | 0.0417282 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 592252. | 0.392896 | ||||||||
\(297\) | 88209.0 | 0.0580259 | ||||||||
\(298\) | −21090.2 | −0.0137575 | ||||||||
\(299\) | 914557. | 0.591606 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.83620e6 | −1.16816 | ||||||||
\(302\) | −91028.8 | −0.0574330 | ||||||||
\(303\) | −1.16889e6 | −0.731420 | ||||||||
\(304\) | −146440. | −0.0908813 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 108486. | 0.0662322 | ||||||||
\(307\) | −1.60549e6 | −0.972215 | −0.486108 | − | 0.873899i | \(-0.661584\pi\) | ||||
−0.486108 | + | 0.873899i | \(0.661584\pi\) | |||||||
\(308\) | 317170. | 0.190509 | ||||||||
\(309\) | −1.81666e6 | −1.08237 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6622.52 | 0.00388260 | 0.00194130 | − | 0.999998i | \(-0.499382\pi\) | ||||
0.00194130 | + | 0.999998i | \(0.499382\pi\) | |||||||
\(312\) | 267963. | 0.155843 | ||||||||
\(313\) | 1.08764e6 | 0.627516 | 0.313758 | − | 0.949503i | \(-0.398412\pi\) | ||||
0.313758 | + | 0.949503i | \(0.398412\pi\) | |||||||
\(314\) | 227144. | 0.130010 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.94387e6 | −1.09509 | ||||||||
\(317\) | 456183. | 0.254971 | 0.127486 | − | 0.991840i | \(-0.459309\pi\) | ||||
0.127486 | + | 0.991840i | \(0.459309\pi\) | |||||||
\(318\) | 83478.2 | 0.0462920 | ||||||||
\(319\) | −885839. | −0.487392 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.19056e6 | 0.644896 | ||||||||
\(322\) | 78332.9 | 0.0421022 | ||||||||
\(323\) | 288668. | 0.153954 | ||||||||
\(324\) | −206785. | −0.109435 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −348687. | −0.181715 | ||||||||
\(327\) | −1.29640e6 | −0.670452 | ||||||||
\(328\) | 126454. | 0.0649006 | ||||||||
\(329\) | −1.21063e6 | −0.616627 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.73077e6 | 0.868297 | 0.434149 | − | 0.900841i | \(-0.357049\pi\) | ||||
0.434149 | + | 0.900841i | \(0.357049\pi\) | |||||||
\(332\) | −2.05590e6 | −1.02366 | ||||||||
\(333\) | 1.08703e6 | 0.537194 | ||||||||
\(334\) | −410251. | −0.201226 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −731965. | −0.353706 | ||||||||
\(337\) | −3.01707e6 | −1.44714 | −0.723571 | − | 0.690250i | \(-0.757501\pi\) | ||||
−0.723571 | + | 0.690250i | \(0.757501\pi\) | |||||||
\(338\) | −58270.3 | −0.0277431 | ||||||||
\(339\) | 9860.54 | 0.00466017 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −510107. | −0.237561 | ||||||||
\(342\) | 8427.75 | 0.00389624 | ||||||||
\(343\) | 2.22035e6 | 1.01903 | ||||||||
\(344\) | 974341. | 0.443930 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 396683. | 0.178137 | ||||||||
\(347\) | −1.26947e6 | −0.565978 | −0.282989 | − | 0.959123i | \(-0.591326\pi\) | ||||
−0.282989 | + | 0.959123i | \(0.591326\pi\) | |||||||
\(348\) | 2.07664e6 | 0.919205 | ||||||||
\(349\) | 3.26420e6 | 1.43454 | 0.717270 | − | 0.696795i | \(-0.245391\pi\) | ||||
0.717270 | + | 0.696795i | \(0.245391\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 491824. | 0.213079 | ||||||||
\(352\) | −253089. | −0.108872 | ||||||||
\(353\) | −1.70741e6 | −0.729290 | −0.364645 | − | 0.931147i | \(-0.618810\pi\) | ||||
−0.364645 | + | 0.931147i | \(0.618810\pi\) | |||||||
\(354\) | −286416. | −0.121476 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3.45312e6 | 1.44406 | ||||||||
\(357\) | 1.44288e6 | 0.599183 | ||||||||
\(358\) | 322665. | 0.133059 | ||||||||
\(359\) | 257688. | 0.105526 | 0.0527628 | − | 0.998607i | \(-0.483197\pi\) | ||||
0.0527628 | + | 0.998607i | \(0.483197\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.45367e6 | −0.990943 | ||||||||
\(362\) | 284722. | 0.114196 | ||||||||
\(363\) | 131769. | 0.0524864 | ||||||||
\(364\) | 1.76843e6 | 0.699575 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −118788. | −0.0463522 | ||||||||
\(367\) | 683489. | 0.264891 | 0.132445 | − | 0.991190i | \(-0.457717\pi\) | ||||
0.132445 | + | 0.991190i | \(0.457717\pi\) | |||||||
\(368\) | 1.32562e6 | 0.510269 | ||||||||
\(369\) | 232097. | 0.0887367 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.11027e6 | 0.418790 | ||||||||
\(372\) | 1.19582e6 | 0.448033 | ||||||||
\(373\) | −3.58176e6 | −1.33298 | −0.666492 | − | 0.745512i | \(-0.732205\pi\) | ||||
−0.666492 | + | 0.745512i | \(0.732205\pi\) | |||||||
\(374\) | 162059. | 0.0599093 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 642398. | 0.234334 | ||||||||
\(377\) | −4.93914e6 | −1.78977 | ||||||||
\(378\) | 42125.3 | 0.0151640 | ||||||||
\(379\) | −4.87955e6 | −1.74494 | −0.872472 | − | 0.488665i | \(-0.837484\pi\) | ||||
−0.872472 | + | 0.488665i | \(0.837484\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.84182e6 | −1.00296 | ||||||||
\(382\) | 410645. | 0.143982 | ||||||||
\(383\) | −4.97559e6 | −1.73319 | −0.866597 | − | 0.499008i | \(-0.833698\pi\) | ||||
−0.866597 | + | 0.499008i | \(0.833698\pi\) | |||||||
\(384\) | 788984. | 0.273049 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −216017. | −0.0737939 | ||||||||
\(387\) | 1.78832e6 | 0.606972 | ||||||||
\(388\) | 2.63913e6 | 0.889983 | ||||||||
\(389\) | −4.09866e6 | −1.37331 | −0.686654 | − | 0.726984i | \(-0.740921\pi\) | ||||
−0.686654 | + | 0.726984i | \(0.740921\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.61312e6 | −0.864404 | ||||||||
\(392\) | −436463. | −0.143461 | ||||||||
\(393\) | −1.68301e6 | −0.549674 | ||||||||
\(394\) | 112288. | 0.0364413 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −308901. | −0.0989876 | ||||||||
\(397\) | −1.61215e6 | −0.513369 | −0.256684 | − | 0.966495i | \(-0.582630\pi\) | ||||
−0.256684 | + | 0.966495i | \(0.582630\pi\) | |||||||
\(398\) | −302669. | −0.0957768 | ||||||||
\(399\) | 112090. | 0.0352482 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −648362. | −0.201352 | −0.100676 | − | 0.994919i | \(-0.532101\pi\) | ||||
−0.100676 | + | 0.994919i | \(0.532101\pi\) | |||||||
\(402\) | 41590.2 | 0.0128359 | ||||||||
\(403\) | −2.84419e6 | −0.872359 | ||||||||
\(404\) | 4.09335e6 | 1.24775 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −423044. | −0.127371 | ||||||||
\(407\) | 1.62384e6 | 0.485911 | ||||||||
\(408\) | −765635. | −0.227704 | ||||||||
\(409\) | 1.88327e6 | 0.556677 | 0.278338 | − | 0.960483i | \(-0.410216\pi\) | ||||
0.278338 | + | 0.960483i | \(0.410216\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.09071e6 | −0.610505 | ||||||||
\(412\) | 6.36178e6 | 1.84644 | ||||||||
\(413\) | −3.80938e6 | −1.09895 | ||||||||
\(414\) | −76290.7 | −0.0218762 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.41114e6 | −0.399794 | ||||||||
\(417\) | −2.80499e6 | −0.789933 | ||||||||
\(418\) | 12589.6 | 0.00352429 | ||||||||
\(419\) | −5.10510e6 | −1.42059 | −0.710296 | − | 0.703903i | \(-0.751439\pi\) | ||||
−0.710296 | + | 0.703903i | \(0.751439\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.48811e6 | 1.50910 | 0.754550 | − | 0.656243i | \(-0.227855\pi\) | ||||
0.754550 | + | 0.656243i | \(0.227855\pi\) | |||||||
\(422\) | 374797. | 0.102451 | ||||||||
\(423\) | 1.17907e6 | 0.320397 | ||||||||
\(424\) | −589145. | −0.159150 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 381623. | 0.101885 | ||||||||
\(427\) | −1.57990e6 | −0.419335 | ||||||||
\(428\) | −4.16925e6 | −1.10014 | ||||||||
\(429\) | 734700. | 0.192738 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.59589e6 | −0.932424 | −0.466212 | − | 0.884673i | \(-0.654382\pi\) | ||||
−0.466212 | + | 0.884673i | \(0.654382\pi\) | |||||||
\(432\) | 712882. | 0.183784 | ||||||||
\(433\) | 5.03603e6 | 1.29083 | 0.645414 | − | 0.763833i | \(-0.276685\pi\) | ||||
0.645414 | + | 0.763833i | \(0.276685\pi\) | |||||||
\(434\) | −243608. | −0.0620822 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.53987e6 | 1.14374 | ||||||||
\(437\) | −203001. | −0.0508503 | ||||||||
\(438\) | −108514. | −0.0270271 | ||||||||
\(439\) | −3.25961e6 | −0.807244 | −0.403622 | − | 0.914926i | \(-0.632249\pi\) | ||||
−0.403622 | + | 0.914926i | \(0.632249\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −801093. | −0.196149 | ||||||||
\(442\) | 903586. | 0.219996 | ||||||||
\(443\) | 1.35658e6 | 0.328424 | 0.164212 | − | 0.986425i | \(-0.447492\pi\) | ||||
0.164212 | + | 0.986425i | \(0.447492\pi\) | |||||||
\(444\) | −3.80669e6 | −0.916412 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 314628. | 0.0748962 | ||||||||
\(447\) | 273190. | 0.0646690 | ||||||||
\(448\) | 2.48167e6 | 0.584184 | ||||||||
\(449\) | −6.80906e6 | −1.59394 | −0.796969 | − | 0.604020i | \(-0.793565\pi\) | ||||
−0.796969 | + | 0.604020i | \(0.793565\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 346712. | 0.0802653 | ||||||||
\(452\) | −34530.8 | −0.00794988 | ||||||||
\(453\) | 1.17913e6 | 0.269972 | ||||||||
\(454\) | −28214.7 | −0.00642445 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −59478.6 | −0.0133952 | ||||||||
\(457\) | 3.03977e6 | 0.680848 | 0.340424 | − | 0.940272i | \(-0.389429\pi\) | ||||
0.340424 | + | 0.940272i | \(0.389429\pi\) | |||||||
\(458\) | −686744. | −0.152979 | ||||||||
\(459\) | −1.40526e6 | −0.311333 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.27858e6 | 0.718511 | 0.359256 | − | 0.933239i | \(-0.383031\pi\) | ||||
0.359256 | + | 0.933239i | \(0.383031\pi\) | |||||||
\(462\) | 62927.9 | 0.0137163 | ||||||||
\(463\) | −5.51970e6 | −1.19664 | −0.598319 | − | 0.801258i | \(-0.704164\pi\) | ||||
−0.598319 | + | 0.801258i | \(0.704164\pi\) | |||||||
\(464\) | −7.15912e6 | −1.54371 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −33123.3 | −0.00706593 | ||||||||
\(467\) | 4.07534e6 | 0.864711 | 0.432356 | − | 0.901703i | \(-0.357683\pi\) | ||||
0.432356 | + | 0.901703i | \(0.357683\pi\) | |||||||
\(468\) | −1.72233e6 | −0.363497 | ||||||||
\(469\) | 553157. | 0.116122 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.94230e6 | −0.611131 | ||||||||
\(472\) | 2.02137e6 | 0.417630 | ||||||||
\(473\) | 2.67145e6 | 0.549027 | ||||||||
\(474\) | −385674. | −0.0788450 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −5.05284e6 | −1.02216 | ||||||||
\(477\) | −1.08133e6 | −0.217602 | ||||||||
\(478\) | 114762. | 0.0229736 | ||||||||
\(479\) | 4.77799e6 | 0.951495 | 0.475748 | − | 0.879582i | \(-0.342178\pi\) | ||||
0.475748 | + | 0.879582i | \(0.342178\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.05397e6 | 1.78433 | ||||||||
\(482\) | 787216. | 0.154339 | ||||||||
\(483\) | −1.01468e6 | −0.197907 | ||||||||
\(484\) | −461444. | −0.0895377 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −41027.1 | −0.00787916 | ||||||||
\(487\) | −1.76923e6 | −0.338035 | −0.169017 | − | 0.985613i | \(-0.554059\pi\) | ||||
−0.169017 | + | 0.985613i | \(0.554059\pi\) | |||||||
\(488\) | 838345. | 0.159358 | ||||||||
\(489\) | 4.51669e6 | 0.854177 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.04139e6 | −0.194943 | −0.0974716 | − | 0.995238i | \(-0.531076\pi\) | ||||
−0.0974716 | + | 0.995238i | \(0.531076\pi\) | |||||||
\(492\) | −812784. | −0.151378 | ||||||||
\(493\) | 1.41124e7 | 2.61506 | ||||||||
\(494\) | 70195.3 | 0.0129417 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.12255e6 | −0.752422 | ||||||||
\(497\) | 5.07565e6 | 0.921723 | ||||||||
\(498\) | −407900. | −0.0737021 | ||||||||
\(499\) | 2.03068e6 | 0.365082 | 0.182541 | − | 0.983198i | \(-0.441568\pi\) | ||||
0.182541 | + | 0.983198i | \(0.441568\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.31416e6 | 0.945890 | ||||||||
\(502\) | 750588. | 0.132936 | ||||||||
\(503\) | 5.06008e6 | 0.891739 | 0.445869 | − | 0.895098i | \(-0.352895\pi\) | ||||
0.445869 | + | 0.895098i | \(0.352895\pi\) | |||||||
\(504\) | −297298. | −0.0521334 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −113965. | −0.0197877 | ||||||||
\(507\) | 754800. | 0.130410 | ||||||||
\(508\) | 9.95183e6 | 1.71098 | ||||||||
\(509\) | 5.64302e6 | 0.965421 | 0.482711 | − | 0.875780i | \(-0.339652\pi\) | ||||
0.482711 | + | 0.875780i | \(0.339652\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.44325e6 | −0.244506 | ||||||||
\(512\) | −3.42639e6 | −0.577645 | ||||||||
\(513\) | −109168. | −0.0183148 | ||||||||
\(514\) | 209454. | 0.0349688 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −6.26256e6 | −1.03545 | ||||||||
\(517\) | 1.76133e6 | 0.289810 | ||||||||
\(518\) | 775484. | 0.126984 | ||||||||
\(519\) | −5.13841e6 | −0.837356 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.37673e6 | 0.867809 | 0.433905 | − | 0.900959i | \(-0.357136\pi\) | ||||
0.433905 | + | 0.900959i | \(0.357136\pi\) | |||||||
\(522\) | 412014. | 0.0661814 | ||||||||
\(523\) | −8.42403e6 | −1.34668 | −0.673342 | − | 0.739331i | \(-0.735142\pi\) | ||||
−0.673342 | + | 0.739331i | \(0.735142\pi\) | |||||||
\(524\) | 5.89376e6 | 0.937701 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −241619. | −0.0380773 | ||||||||
\(527\) | 8.12654e6 | 1.27462 | ||||||||
\(528\) | 1.06492e6 | 0.166239 | ||||||||
\(529\) | −4.59871e6 | −0.714492 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.71007e6 | 0.571012 | ||||||||
\(532\) | −392532. | −0.0601306 | ||||||||
\(533\) | 1.93315e6 | 0.294746 | ||||||||
\(534\) | 685115. | 0.103970 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −293522. | −0.0441294 | ||||||||
\(537\) | −4.17962e6 | −0.625462 | ||||||||
\(538\) | −681563. | −0.101520 | ||||||||
\(539\) | −1.19669e6 | −0.177424 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.85130e6 | 1.30021 | 0.650106 | − | 0.759844i | \(-0.274725\pi\) | ||||
0.650106 | + | 0.759844i | \(0.274725\pi\) | |||||||
\(542\) | −6691.40 | −0.000978405 0 | ||||||||
\(543\) | −3.68813e6 | −0.536792 | ||||||||
\(544\) | 4.03198e6 | 0.584145 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 350865. | 0.0503684 | ||||||||
\(547\) | −3.13327e6 | −0.447744 | −0.223872 | − | 0.974619i | \(-0.571870\pi\) | ||||
−0.223872 | + | 0.974619i | \(0.571870\pi\) | |||||||
\(548\) | 7.32150e6 | 1.04147 | ||||||||
\(549\) | 1.53871e6 | 0.217885 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.09632e6 | 0.153836 | ||||||||
\(552\) | 538420. | 0.0752096 | ||||||||
\(553\) | −5.12953e6 | −0.713288 | ||||||||
\(554\) | 225370. | 0.0311976 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9.82283e6 | 1.34756 | ||||||||
\(557\) | 5.46691e6 | 0.746627 | 0.373313 | − | 0.927705i | \(-0.378222\pi\) | ||||
0.373313 | + | 0.927705i | \(0.378222\pi\) | |||||||
\(558\) | 237257. | 0.0322577 | ||||||||
\(559\) | 1.48951e7 | 2.01611 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.09922e6 | −0.281612 | ||||||||
\(562\) | −602289. | −0.0804385 | ||||||||
\(563\) | −5.19043e6 | −0.690132 | −0.345066 | − | 0.938578i | \(-0.612143\pi\) | ||||
−0.345066 | + | 0.938578i | \(0.612143\pi\) | |||||||
\(564\) | −4.12901e6 | −0.546573 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −399618. | −0.0524329 | ||||||||
\(567\) | −545667. | −0.0712804 | ||||||||
\(568\) | −2.69329e6 | −0.350278 | ||||||||
\(569\) | 1.24058e7 | 1.60636 | 0.803180 | − | 0.595737i | \(-0.203140\pi\) | ||||
0.803180 | + | 0.595737i | \(0.203140\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.79234e6 | 1.12853 | 0.564266 | − | 0.825593i | \(-0.309159\pi\) | ||||
0.564266 | + | 0.825593i | \(0.309159\pi\) | |||||||
\(572\) | −2.57286e6 | −0.328795 | ||||||||
\(573\) | −5.31926e6 | −0.676807 | ||||||||
\(574\) | 165577. | 0.0209759 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.41698e6 | −0.303540 | ||||||||
\(577\) | 1.14336e7 | 1.42969 | 0.714845 | − | 0.699283i | \(-0.246497\pi\) | ||||
0.714845 | + | 0.699283i | \(0.246497\pi\) | |||||||
\(578\) | −1.59526e6 | −0.198615 | ||||||||
\(579\) | 2.79817e6 | 0.346878 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.42514e6 | −0.666761 | ||||||||
\(582\) | 523616. | 0.0640775 | ||||||||
\(583\) | −1.61532e6 | −0.196828 | ||||||||
\(584\) | 765834. | 0.0929185 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.36231e6 | 0.163882 | ||||||||
\(587\) | 2.32244e6 | 0.278195 | 0.139097 | − | 0.990279i | \(-0.455580\pi\) | ||||
0.139097 | + | 0.990279i | \(0.455580\pi\) | |||||||
\(588\) | 2.80536e6 | 0.334615 | ||||||||
\(589\) | 631313. | 0.0749819 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.45452e6 | −0.171297 | ||||||||
\(592\) | 1.31234e7 | 1.53901 | ||||||||
\(593\) | −7.98435e6 | −0.932401 | −0.466201 | − | 0.884679i | \(-0.654377\pi\) | ||||
−0.466201 | + | 0.884679i | \(0.654377\pi\) | |||||||
\(594\) | −61287.3 | −0.00712697 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −956690. | −0.110320 | ||||||||
\(597\) | 3.92060e6 | 0.450212 | ||||||||
\(598\) | −635431. | −0.0726634 | ||||||||
\(599\) | −139225. | −0.0158544 | −0.00792721 | − | 0.999969i | \(-0.502523\pi\) | ||||
−0.00792721 | + | 0.999969i | \(0.502523\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.55602e7 | 1.75723 | 0.878616 | − | 0.477529i | \(-0.158467\pi\) | ||||
0.878616 | + | 0.477529i | \(0.158467\pi\) | |||||||
\(602\) | 1.27578e6 | 0.143478 | ||||||||
\(603\) | −538735. | −0.0603368 | ||||||||
\(604\) | −4.12923e6 | −0.460550 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 812141. | 0.0898358 | ||||||||
\(607\) | 6.00544e6 | 0.661566 | 0.330783 | − | 0.943707i | \(-0.392687\pi\) | ||||
0.330783 | + | 0.943707i | \(0.392687\pi\) | |||||||
\(608\) | 313225. | 0.0343635 | ||||||||
\(609\) | 5.47986e6 | 0.598724 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.82057e6 | 1.06423 | ||||||||
\(612\) | 4.92111e6 | 0.531110 | ||||||||
\(613\) | 2.32775e6 | 0.250199 | 0.125099 | − | 0.992144i | \(-0.460075\pi\) | ||||
0.125099 | + | 0.992144i | \(0.460075\pi\) | |||||||
\(614\) | 1.11549e6 | 0.119411 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −444112. | −0.0471564 | ||||||||
\(617\) | −1.30284e7 | −1.37777 | −0.688886 | − | 0.724870i | \(-0.741900\pi\) | ||||
−0.688886 | + | 0.724870i | \(0.741900\pi\) | |||||||
\(618\) | 1.26221e6 | 0.132941 | ||||||||
\(619\) | −2.53159e6 | −0.265562 | −0.132781 | − | 0.991145i | \(-0.542391\pi\) | ||||
−0.132781 | + | 0.991145i | \(0.542391\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 988226. | 0.102832 | ||||||||
\(622\) | −4601.30 | −0.000476876 0 | ||||||||
\(623\) | 9.11214e6 | 0.940590 | ||||||||
\(624\) | 5.93765e6 | 0.610454 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −755689. | −0.0770739 | ||||||||
\(627\) | −163078. | −0.0165664 | ||||||||
\(628\) | 1.03037e7 | 1.04254 | ||||||||
\(629\) | −2.58694e7 | −2.60712 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.17733e6 | −0.217696 | −0.108848 | − | 0.994058i | \(-0.534716\pi\) | ||||
−0.108848 | + | 0.994058i | \(0.534716\pi\) | |||||||
\(632\) | 2.72188e6 | 0.271067 | ||||||||
\(633\) | −4.85491e6 | −0.481583 | ||||||||
\(634\) | −316955. | −0.0313166 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 3.78673e6 | 0.371211 | ||||||||
\(637\) | −6.67237e6 | −0.651525 | ||||||||
\(638\) | 615478. | 0.0598634 | ||||||||
\(639\) | −4.94332e6 | −0.478924 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.58180e6 | −0.248187 | −0.124093 | − | 0.992271i | \(-0.539602\pi\) | ||||
−0.124093 | + | 0.992271i | \(0.539602\pi\) | |||||||
\(642\) | −827200. | −0.0792087 | ||||||||
\(643\) | 1.67813e7 | 1.60066 | 0.800329 | − | 0.599561i | \(-0.204658\pi\) | ||||
0.800329 | + | 0.599561i | \(0.204658\pi\) | |||||||
\(644\) | 3.55333e6 | 0.337614 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −200566. | −0.0189093 | ||||||||
\(647\) | 1.01691e7 | 0.955037 | 0.477518 | − | 0.878622i | \(-0.341536\pi\) | ||||
0.477518 | + | 0.878622i | \(0.341536\pi\) | |||||||
\(648\) | 289547. | 0.0270883 | ||||||||
\(649\) | 5.54220e6 | 0.516500 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.15556e6 | 0.291826 | ||||||||
\(652\) | −1.58171e7 | −1.45716 | ||||||||
\(653\) | 8.99282e6 | 0.825302 | 0.412651 | − | 0.910889i | \(-0.364603\pi\) | ||||
0.412651 | + | 0.910889i | \(0.364603\pi\) | |||||||
\(654\) | 900731. | 0.0823476 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 2.80204e6 | 0.254223 | ||||||||
\(657\) | 1.40563e6 | 0.127045 | ||||||||
\(658\) | 841144. | 0.0757365 | ||||||||
\(659\) | −1.03480e7 | −0.928203 | −0.464102 | − | 0.885782i | \(-0.653623\pi\) | ||||
−0.464102 | + | 0.885782i | \(0.653623\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.48595e7 | 1.32282 | 0.661409 | − | 0.750025i | \(-0.269959\pi\) | ||||
0.661409 | + | 0.750025i | \(0.269959\pi\) | |||||||
\(662\) | −1.20253e6 | −0.106648 | ||||||||
\(663\) | −1.17045e7 | −1.03412 | ||||||||
\(664\) | 2.87874e6 | 0.253386 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −755266. | −0.0659803 | ||||||||
\(667\) | −9.92427e6 | −0.863742 | ||||||||
\(668\) | −1.86098e7 | −1.61361 | ||||||||
\(669\) | −4.07551e6 | −0.352060 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.29857e6 | 0.197084 | ||||||||
\(672\) | 1.56563e6 | 0.133741 | ||||||||
\(673\) | −217545. | −0.0185145 | −0.00925725 | − | 0.999957i | \(-0.502947\pi\) | ||||
−0.00925725 | + | 0.999957i | \(0.502947\pi\) | |||||||
\(674\) | 2.09625e6 | 0.177744 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.64325e6 | −0.222470 | ||||||||
\(677\) | 2.64314e6 | 0.221640 | 0.110820 | − | 0.993840i | \(-0.464652\pi\) | ||||
0.110820 | + | 0.993840i | \(0.464652\pi\) | |||||||
\(678\) | −6851.07 | −0.000572380 0 | ||||||||
\(679\) | 6.96419e6 | 0.579690 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 365477. | 0.0301990 | ||||||||
\(682\) | 354421. | 0.0291782 | ||||||||
\(683\) | −4.66785e6 | −0.382882 | −0.191441 | − | 0.981504i | \(-0.561316\pi\) | ||||
−0.191441 | + | 0.981504i | \(0.561316\pi\) | |||||||
\(684\) | 382298. | 0.0312436 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.54269e6 | −0.125161 | ||||||||
\(687\) | 8.89569e6 | 0.719098 | ||||||||
\(688\) | 2.15899e7 | 1.73892 | ||||||||
\(689\) | −9.00647e6 | −0.722781 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.11273e6 | 0.247997 | 0.123998 | − | 0.992282i | \(-0.460428\pi\) | ||||
0.123998 | + | 0.992282i | \(0.460428\pi\) | |||||||
\(692\) | 1.79943e7 | 1.42846 | ||||||||
\(693\) | −815132. | −0.0644755 | ||||||||
\(694\) | 882026. | 0.0695156 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −2.90778e6 | −0.227530 | ||||||||
\(697\) | −5.52349e6 | −0.430657 | ||||||||
\(698\) | −2.26795e6 | −0.176196 | ||||||||
\(699\) | 429061. | 0.0332143 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.16786e7 | 0.897629 | 0.448815 | − | 0.893625i | \(-0.351846\pi\) | ||||
0.448815 | + | 0.893625i | \(0.351846\pi\) | |||||||
\(702\) | −341718. | −0.0261713 | ||||||||
\(703\) | −2.00967e6 | −0.153369 | ||||||||
\(704\) | −3.61054e6 | −0.274562 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.18630e6 | 0.0895743 | ||||||||
\(707\) | 1.08016e7 | 0.812718 | ||||||||
\(708\) | −1.29923e7 | −0.974102 | ||||||||
\(709\) | −1.96571e7 | −1.46860 | −0.734302 | − | 0.678823i | \(-0.762490\pi\) | ||||
−0.734302 | + | 0.678823i | \(0.762490\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.99580e6 | 0.370622 | ||||||||
\(712\) | −4.83518e6 | −0.357448 | ||||||||
\(713\) | −5.71485e6 | −0.420999 | ||||||||
\(714\) | −1.00251e6 | −0.0735940 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.46367e7 | 1.06699 | ||||||||
\(717\) | −1.48656e6 | −0.107990 | ||||||||
\(718\) | −179041. | −0.0129611 | ||||||||
\(719\) | −1.89013e7 | −1.36354 | −0.681772 | − | 0.731565i | \(-0.738790\pi\) | ||||
−0.681772 | + | 0.731565i | \(0.738790\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.67876e7 | 1.20268 | ||||||||
\(722\) | 1.70480e6 | 0.121712 | ||||||||
\(723\) | −1.01971e7 | −0.725492 | ||||||||
\(724\) | 1.29155e7 | 0.915725 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −91552.7 | −0.00644658 | ||||||||
\(727\) | −6.78994e6 | −0.476463 | −0.238232 | − | 0.971208i | \(-0.576568\pi\) | ||||
−0.238232 | + | 0.971208i | \(0.576568\pi\) | |||||||
\(728\) | −2.47622e6 | −0.173165 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.25590e7 | −2.94576 | ||||||||
\(732\) | −5.38845e6 | −0.371695 | ||||||||
\(733\) | 3.60300e6 | 0.247688 | 0.123844 | − | 0.992302i | \(-0.460478\pi\) | ||||
0.123844 | + | 0.992302i | \(0.460478\pi\) | |||||||
\(734\) | −474886. | −0.0325349 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.83542e6 | −0.192940 | ||||||||
\(737\) | −804778. | −0.0545767 | ||||||||
\(738\) | −161260. | −0.0108990 | ||||||||
\(739\) | −7.58466e6 | −0.510887 | −0.255443 | − | 0.966824i | \(-0.582221\pi\) | ||||
−0.255443 | + | 0.966824i | \(0.582221\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −909270. | −0.0608341 | ||||||||
\(742\) | −771416. | −0.0514374 | ||||||||
\(743\) | −1.17473e7 | −0.780669 | −0.390335 | − | 0.920673i | \(-0.627641\pi\) | ||||
−0.390335 | + | 0.920673i | \(0.627641\pi\) | |||||||
\(744\) | −1.67443e6 | −0.110901 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 2.48860e6 | 0.163722 | ||||||||
\(747\) | 5.28370e6 | 0.346447 | ||||||||
\(748\) | 7.35129e6 | 0.480407 | ||||||||
\(749\) | −1.10019e7 | −0.716577 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.05057e6 | 0.262070 | 0.131035 | − | 0.991378i | \(-0.458170\pi\) | ||||
0.131035 | + | 0.991378i | \(0.458170\pi\) | |||||||
\(752\) | 1.42346e7 | 0.917910 | ||||||||
\(753\) | −9.72269e6 | −0.624883 | ||||||||
\(754\) | 3.43170e6 | 0.219827 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.91088e6 | 0.121599 | ||||||||
\(757\) | −2.12290e7 | −1.34645 | −0.673225 | − | 0.739438i | \(-0.735091\pi\) | ||||
−0.673225 | + | 0.739438i | \(0.735091\pi\) | |||||||
\(758\) | 3.39029e6 | 0.214321 | ||||||||
\(759\) | 1.47624e6 | 0.0930149 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.06438e7 | −0.666247 | −0.333123 | − | 0.942883i | \(-0.608103\pi\) | ||||
−0.333123 | + | 0.942883i | \(0.608103\pi\) | |||||||
\(762\) | 1.97449e6 | 0.123188 | ||||||||
\(763\) | 1.19799e7 | 0.744974 | ||||||||
\(764\) | 1.86276e7 | 1.15458 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.45702e6 | 0.212878 | ||||||||
\(767\) | 3.09014e7 | 1.89666 | ||||||||
\(768\) | 8.04551e6 | 0.492210 | ||||||||
\(769\) | 3.17109e6 | 0.193372 | 0.0966859 | − | 0.995315i | \(-0.469176\pi\) | ||||
0.0966859 | + | 0.995315i | \(0.469176\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.71314e6 | −0.164375 | ||||||||
\(772\) | −9.79894e6 | −0.591747 | ||||||||
\(773\) | −1.80501e7 | −1.08650 | −0.543252 | − | 0.839570i | \(-0.682807\pi\) | ||||
−0.543252 | + | 0.839570i | \(0.682807\pi\) | |||||||
\(774\) | −1.24252e6 | −0.0745507 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −3.69541e6 | −0.220297 | ||||||||
\(777\) | −1.00452e7 | −0.596904 | ||||||||
\(778\) | 2.84774e6 | 0.168675 | ||||||||
\(779\) | −429094. | −0.0253343 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.38447e6 | −0.433203 | ||||||||
\(782\) | 1.81559e6 | 0.106169 | ||||||||
\(783\) | −5.33700e6 | −0.311095 | ||||||||
\(784\) | −9.67137e6 | −0.561950 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.16935e6 | 0.0675132 | ||||||||
\(787\) | 2.58223e7 | 1.48614 | 0.743068 | − | 0.669216i | \(-0.233370\pi\) | ||||
0.743068 | + | 0.669216i | \(0.233370\pi\) | |||||||
\(788\) | 5.09360e6 | 0.292219 | ||||||||
\(789\) | 3.12979e6 | 0.178988 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −91120.5 | −0.00517815 | ||||||||
\(792\) | 432534. | 0.0245023 | ||||||||
\(793\) | 1.28161e7 | 0.723722 | ||||||||
\(794\) | 1.12012e6 | 0.0630540 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.37296e7 | −0.768026 | ||||||||
\(797\) | −1.50658e7 | −0.840129 | −0.420065 | − | 0.907494i | \(-0.637993\pi\) | ||||
−0.420065 | + | 0.907494i | \(0.637993\pi\) | |||||||
\(798\) | −77880.1 | −0.00432932 | ||||||||
\(799\) | −2.80598e7 | −1.55495 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.87458e6 | −0.488727 | ||||||||
\(802\) | 450480. | 0.0247309 | ||||||||
\(803\) | 2.09976e6 | 0.114916 | ||||||||
\(804\) | 1.88661e6 | 0.102930 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.97613e6 | 0.107147 | ||||||||
\(807\) | 8.82858e6 | 0.477207 | ||||||||
\(808\) | −5.73166e6 | −0.308853 | ||||||||
\(809\) | −2.08560e7 | −1.12037 | −0.560183 | − | 0.828369i | \(-0.689269\pi\) | ||||
−0.560183 | + | 0.828369i | \(0.689269\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.46233e6 | 0.451791 | 0.225896 | − | 0.974152i | \(-0.427469\pi\) | ||||
0.225896 | + | 0.974152i | \(0.427469\pi\) | |||||||
\(812\) | −1.91900e7 | −1.02138 | ||||||||
\(813\) | 86676.5 | 0.00459912 | ||||||||
\(814\) | −1.12824e6 | −0.0596814 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1.69653e7 | −0.891943 | ||||||||
\(817\) | −3.30620e6 | −0.173290 | ||||||||
\(818\) | −1.30849e6 | −0.0683732 | ||||||||
\(819\) | −4.54490e6 | −0.236764 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.67359e6 | 0.449098 | 0.224549 | − | 0.974463i | \(-0.427909\pi\) | ||||
0.224549 | + | 0.974463i | \(0.427909\pi\) | |||||||
\(822\) | 1.45262e6 | 0.0749846 | ||||||||
\(823\) | 1.24194e7 | 0.639148 | 0.319574 | − | 0.947561i | \(-0.396460\pi\) | ||||
0.319574 | + | 0.947561i | \(0.396460\pi\) | |||||||
\(824\) | −8.90799e6 | −0.457048 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.64675e6 | 0.134978 | ||||||||
\(827\) | 2.38473e7 | 1.21248 | 0.606242 | − | 0.795280i | \(-0.292676\pi\) | ||||
0.606242 | + | 0.795280i | \(0.292676\pi\) | |||||||
\(828\) | −3.46069e6 | −0.175423 | ||||||||
\(829\) | −3.26873e7 | −1.65193 | −0.825967 | − | 0.563719i | \(-0.809370\pi\) | ||||
−0.825967 | + | 0.563719i | \(0.809370\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.91931e6 | −0.146649 | ||||||||
\(832\) | −2.01312e7 | −1.00823 | ||||||||
\(833\) | 1.90646e7 | 0.951953 | ||||||||
\(834\) | 1.94890e6 | 0.0970227 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 571087. | 0.0282609 | ||||||||
\(837\) | −3.07329e6 | −0.151632 | ||||||||
\(838\) | 3.54701e6 | 0.174483 | ||||||||
\(839\) | 8.09423e6 | 0.396982 | 0.198491 | − | 0.980103i | \(-0.436396\pi\) | ||||
0.198491 | + | 0.980103i | \(0.436396\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.30857e7 | 1.61306 | ||||||||
\(842\) | −3.81313e6 | −0.185354 | ||||||||
\(843\) | 7.80171e6 | 0.378112 | ||||||||
\(844\) | 1.70015e7 | 0.821544 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −819214. | −0.0393524 | ||||||||
\(847\) | −1.21767e6 | −0.0583203 | ||||||||
\(848\) | −1.30546e7 | −0.623409 | ||||||||
\(849\) | 5.17642e6 | 0.246468 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.81922e7 | 0.861117 | ||||||||
\(852\) | 1.73111e7 | 0.817007 | ||||||||
\(853\) | −3.67970e6 | −0.173157 | −0.0865785 | − | 0.996245i | \(-0.527593\pi\) | ||||
−0.0865785 | + | 0.996245i | \(0.527593\pi\) | |||||||
\(854\) | 1.09771e6 | 0.0515043 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.83794e6 | 0.272317 | ||||||||
\(857\) | −2.17589e7 | −1.01201 | −0.506004 | − | 0.862531i | \(-0.668878\pi\) | ||||
−0.506004 | + | 0.862531i | \(0.668878\pi\) | |||||||
\(858\) | −510467. | −0.0236728 | ||||||||
\(859\) | −3.76305e7 | −1.74003 | −0.870015 | − | 0.493025i | \(-0.835891\pi\) | ||||
−0.870015 | + | 0.493025i | \(0.835891\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.14479e6 | −0.0985998 | ||||||||
\(862\) | 2.49841e6 | 0.114524 | ||||||||
\(863\) | 2.50264e7 | 1.14386 | 0.571928 | − | 0.820304i | \(-0.306196\pi\) | ||||
0.571928 | + | 0.820304i | \(0.306196\pi\) | |||||||
\(864\) | −1.52481e6 | −0.0694914 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −3.49902e6 | −0.158545 | ||||||||
\(867\) | 2.06641e7 | 0.933615 | ||||||||
\(868\) | −1.10505e7 | −0.497832 | ||||||||
\(869\) | 7.46286e6 | 0.335240 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.48717e6 | −0.200414 | ||||||||
\(872\) | −6.35689e6 | −0.283109 | ||||||||
\(873\) | −6.78263e6 | −0.301205 | ||||||||
\(874\) | 141044. | 0.00624564 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4.92239e6 | −0.216728 | ||||||||
\(877\) | −1.12677e7 | −0.494692 | −0.247346 | − | 0.968927i | \(-0.579558\pi\) | ||||
−0.247346 | + | 0.968927i | \(0.579558\pi\) | |||||||
\(878\) | 2.26477e6 | 0.0991488 | ||||||||
\(879\) | −1.76466e7 | −0.770351 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.36223e7 | −1.89352 | −0.946758 | − | 0.321947i | \(-0.895663\pi\) | ||||
−0.946758 | + | 0.321947i | \(0.895663\pi\) | |||||||
\(882\) | 556597. | 0.0240918 | ||||||||
\(883\) | 3.14744e7 | 1.35849 | 0.679244 | − | 0.733912i | \(-0.262308\pi\) | ||||
0.679244 | + | 0.733912i | \(0.262308\pi\) | |||||||
\(884\) | 4.09883e7 | 1.76413 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −942545. | −0.0403383 | ||||||||
\(887\) | −2.33777e7 | −0.997684 | −0.498842 | − | 0.866693i | \(-0.666241\pi\) | ||||
−0.498842 | + | 0.866693i | \(0.666241\pi\) | |||||||
\(888\) | 5.33027e6 | 0.226839 | ||||||||
\(889\) | 2.62611e7 | 1.11444 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 793881. | 0.0335013 | ||||||||
\(892\) | 1.42721e7 | 0.600587 | ||||||||
\(893\) | −2.17983e6 | −0.0914733 | ||||||||
\(894\) | −189812. | −0.00794290 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −7.29093e6 | −0.303398 | ||||||||
\(897\) | 8.23101e6 | 0.341564 | ||||||||
\(898\) | 4.73091e6 | 0.195774 | ||||||||
\(899\) | 3.08635e7 | 1.27364 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.57337e7 | 1.05607 | ||||||||
\(902\) | −240895. | −0.00985850 | ||||||||
\(903\) | −1.65258e7 | −0.674438 | ||||||||
\(904\) | 48351.3 | 0.00196783 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −819259. | −0.0331590 | ||||||||
\(907\) | −2.58345e7 | −1.04275 | −0.521377 | − | 0.853326i | \(-0.674582\pi\) | ||||
−0.521377 | + | 0.853326i | \(0.674582\pi\) | |||||||
\(908\) | −1.27987e6 | −0.0515171 | ||||||||
\(909\) | −1.05200e7 | −0.422285 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.24995e7 | 0.498996 | 0.249498 | − | 0.968375i | \(-0.419734\pi\) | ||||
0.249498 | + | 0.968375i | \(0.419734\pi\) | |||||||
\(912\) | −1.31796e6 | −0.0524703 | ||||||||
\(913\) | 7.89293e6 | 0.313373 | ||||||||
\(914\) | −2.11202e6 | −0.0836244 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.11520e7 | −1.22672 | ||||||||
\(917\) | 1.55526e7 | 0.610771 | ||||||||
\(918\) | 976372. | 0.0382392 | ||||||||
\(919\) | 1.24766e7 | 0.487313 | 0.243657 | − | 0.969862i | \(-0.421653\pi\) | ||||
0.243657 | + | 0.969862i | \(0.421653\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.44494e7 | −0.561309 | ||||||||
\(922\) | −2.27795e6 | −0.0882503 | ||||||||
\(923\) | −4.11733e7 | −1.59079 | ||||||||
\(924\) | 2.85453e6 | 0.109990 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 3.83507e6 | 0.146976 | ||||||||
\(927\) | −1.63499e7 | −0.624908 | ||||||||
\(928\) | 1.53129e7 | 0.583697 | ||||||||
\(929\) | −1.63852e6 | −0.0622891 | −0.0311445 | − | 0.999515i | \(-0.509915\pi\) | ||||
−0.0311445 | + | 0.999515i | \(0.509915\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.48104e6 | 0.0560006 | ||||||||
\(932\) | −1.50253e6 | −0.0566611 | ||||||||
\(933\) | 59602.7 | 0.00224162 | ||||||||
\(934\) | −2.83153e6 | −0.106207 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.41166e6 | 0.0899760 | ||||||||
\(937\) | −1.03137e7 | −0.383766 | −0.191883 | − | 0.981418i | \(-0.561459\pi\) | ||||
−0.191883 | + | 0.981418i | \(0.561459\pi\) | |||||||
\(938\) | −384331. | −0.0142626 | ||||||||
\(939\) | 9.78876e6 | 0.362296 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.30200e7 | −0.479332 | −0.239666 | − | 0.970855i | \(-0.577038\pi\) | ||||
−0.239666 | + | 0.970855i | \(0.577038\pi\) | |||||||
\(942\) | 2.04430e6 | 0.0750615 | ||||||||
\(943\) | 3.88430e6 | 0.142244 | ||||||||
\(944\) | 4.47906e7 | 1.63590 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.85611e6 | −0.0674336 | ||||||||
\(947\) | −4.07950e7 | −1.47820 | −0.739098 | − | 0.673598i | \(-0.764748\pi\) | ||||
−0.739098 | + | 0.673598i | \(0.764748\pi\) | |||||||
\(948\) | −1.74949e7 | −0.632252 | ||||||||
\(949\) | 1.17076e7 | 0.421989 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.10565e6 | 0.147208 | ||||||||
\(952\) | 7.07517e6 | 0.253014 | ||||||||
\(953\) | −4.68439e7 | −1.67078 | −0.835392 | − | 0.549654i | \(-0.814760\pi\) | ||||
−0.835392 | + | 0.549654i | \(0.814760\pi\) | |||||||
\(954\) | 751304. | 0.0267267 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 5.20582e6 | 0.184223 | ||||||||
\(957\) | −7.97255e6 | −0.281396 | ||||||||
\(958\) | −3.31973e6 | −0.116866 | ||||||||
\(959\) | 1.93201e7 | 0.678364 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.08565e7 | −0.379212 | ||||||||
\(962\) | −6.29067e6 | −0.219159 | ||||||||
\(963\) | 1.07151e7 | 0.372331 | ||||||||
\(964\) | 3.57095e7 | 1.23763 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 704996. | 0.0243077 | ||||||||
\(967\) | −1.63484e7 | −0.562223 | −0.281111 | − | 0.959675i | \(-0.590703\pi\) | ||||
−0.281111 | + | 0.959675i | \(0.590703\pi\) | |||||||
\(968\) | 646131. | 0.0221632 | ||||||||
\(969\) | 2.59801e6 | 0.0888856 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.62139e6 | −0.0551875 | −0.0275937 | − | 0.999619i | \(-0.508784\pi\) | ||||
−0.0275937 | + | 0.999619i | \(0.508784\pi\) | |||||||
\(972\) | −1.86106e6 | −0.0631823 | ||||||||
\(973\) | 2.59206e7 | 0.877735 | ||||||||
\(974\) | 1.22925e6 | 0.0415187 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.85765e7 | 0.624221 | ||||||||
\(977\) | 2.33840e7 | 0.783759 | 0.391880 | − | 0.920017i | \(-0.371825\pi\) | ||||
0.391880 | + | 0.920017i | \(0.371825\pi\) | |||||||
\(978\) | −3.13818e6 | −0.104913 | ||||||||
\(979\) | −1.32571e7 | −0.442070 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.16676e7 | −0.387086 | ||||||||
\(982\) | 723552. | 0.0239437 | ||||||||
\(983\) | −1.96781e7 | −0.649529 | −0.324764 | − | 0.945795i | \(-0.605285\pi\) | ||||
−0.324764 | + | 0.945795i | \(0.605285\pi\) | |||||||
\(984\) | 1.13809e6 | 0.0374704 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −9.80522e6 | −0.321192 | ||||||||
\(987\) | −1.08957e7 | −0.356010 | ||||||||
\(988\) | 3.18419e6 | 0.103778 | ||||||||
\(989\) | 2.99289e7 | 0.972970 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.56015e7 | 0.504642 | 0.252321 | − | 0.967644i | \(-0.418806\pi\) | ||||
0.252321 | + | 0.967644i | \(0.418806\pi\) | |||||||
\(992\) | 8.81788e6 | 0.284502 | ||||||||
\(993\) | 1.55769e7 | 0.501312 | ||||||||
\(994\) | −3.52654e6 | −0.113210 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.85031e7 | −0.591011 | ||||||||
\(997\) | 5.71913e6 | 0.182218 | 0.0911091 | − | 0.995841i | \(-0.470959\pi\) | ||||
0.0911091 | + | 0.995841i | \(0.470959\pi\) | |||||||
\(998\) | −1.41091e6 | −0.0448408 | ||||||||
\(999\) | 9.78328e6 | 0.310149 |
(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 | 825.6.a.g.1.2 | 3 | ||
5.4 | even | 2 | 165.6.a.c.1.2 | ✓ | 3 | ||
15.14 | odd | 2 | 495.6.a.b.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.6.a.c.1.2 | ✓ | 3 | 5.4 | even | 2 | ||
495.6.a.b.1.2 | 3 | 15.14 | odd | 2 | |||
825.6.a.g.1.2 | 3 | 1.1 | even | 1 | trivial |