Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [448,6,Mod(1,448)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(448, 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("448.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 448 = 2^{6} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 448.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: | \(71.8519512762\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{193}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 48 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 56) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(7.44622\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 448.1 |
$q$-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 | ||||||||
\(3\) | −20.8924 | −1.34025 | −0.670125 | − | 0.742248i | \(-0.733760\pi\) | ||||
−0.670125 | + | 0.742248i | \(0.733760\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −90.4622 | −1.61824 | −0.809119 | − | 0.587645i | \(-0.800055\pi\) | ||||
−0.809119 | + | 0.587645i | \(0.800055\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 49.0000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 193.494 | 0.796272 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −552.494 | −1.37672 | −0.688361 | − | 0.725369i | \(-0.741669\pi\) | ||||
−0.688361 | + | 0.725369i | \(0.741669\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 593.172 | 0.973469 | 0.486734 | − | 0.873550i | \(-0.338188\pi\) | ||||
0.486734 | + | 0.873550i | \(0.338188\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1889.98 | 2.16884 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1422.19 | −1.19354 | −0.596769 | − | 0.802413i | \(-0.703549\pi\) | ||||
−0.596769 | + | 0.802413i | \(0.703549\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 318.997 | 0.202723 | 0.101361 | − | 0.994850i | \(-0.467680\pi\) | ||||
0.101361 | + | 0.994850i | \(0.467680\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1023.73 | −0.506567 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −659.954 | −0.260132 | −0.130066 | − | 0.991505i | \(-0.541519\pi\) | ||||
−0.130066 | + | 0.991505i | \(0.541519\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5058.41 | 1.61869 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1034.30 | 0.273046 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8185.27 | 1.80733 | 0.903667 | − | 0.428237i | \(-0.140865\pi\) | ||||
0.903667 | + | 0.428237i | \(0.140865\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9598.03 | 1.79382 | 0.896908 | − | 0.442217i | \(-0.145808\pi\) | ||||
0.896908 | + | 0.442217i | \(0.145808\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 11543.0 | 1.84515 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4432.65 | −0.611636 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5180.56 | −0.622118 | −0.311059 | − | 0.950391i | \(-0.600684\pi\) | ||||
−0.311059 | + | 0.950391i | \(0.600684\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −12392.8 | −1.30469 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2192.46 | −0.203691 | −0.101846 | − | 0.994800i | \(-0.532475\pi\) | ||||
−0.101846 | + | 0.994800i | \(0.532475\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7458.29 | 0.615131 | 0.307566 | − | 0.951527i | \(-0.400486\pi\) | ||||
0.307566 | + | 0.951527i | \(0.400486\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −17503.9 | −1.28856 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 19561.8 | 1.29171 | 0.645853 | − | 0.763462i | \(-0.276502\pi\) | ||||
0.645853 | + | 0.763462i | \(0.276502\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2401.00 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 29713.1 | 1.59964 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −36569.6 | −1.78826 | −0.894129 | − | 0.447809i | \(-0.852205\pi\) | ||||
−0.894129 | + | 0.447809i | \(0.852205\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 49979.9 | 2.22786 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6664.63 | −0.271700 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 16361.7 | 0.611927 | 0.305963 | − | 0.952043i | \(-0.401021\pi\) | ||||
0.305963 | + | 0.952043i | \(0.401021\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10893.1 | 0.374825 | 0.187412 | − | 0.982281i | \(-0.439990\pi\) | ||||
0.187412 | + | 0.982281i | \(0.439990\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 9481.22 | 0.300963 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −53659.6 | −1.57530 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8035.91 | 0.218700 | 0.109350 | − | 0.994003i | \(-0.465123\pi\) | ||||
0.109350 | + | 0.994003i | \(0.465123\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 13788.0 | 0.348642 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −55983.3 | −1.31799 | −0.658996 | − | 0.752146i | \(-0.729019\pi\) | ||||
−0.658996 | + | 0.752146i | \(0.729019\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −77752.5 | −1.70768 | −0.853841 | − | 0.520533i | \(-0.825733\pi\) | ||||
−0.853841 | + | 0.520533i | \(0.825733\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −105683. | −2.16945 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −27072.2 | −0.520352 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3208.43 | 0.0578396 | 0.0289198 | − | 0.999582i | \(-0.490793\pi\) | ||||
0.0289198 | + | 0.999582i | \(0.490793\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −68628.1 | −1.16222 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 76626.9 | 1.22092 | 0.610458 | − | 0.792049i | \(-0.290985\pi\) | ||||
0.610458 | + | 0.792049i | \(0.290985\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 128655. | 1.93143 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −171010. | −2.42228 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −84288.6 | −1.12796 | −0.563980 | − | 0.825788i | \(-0.690731\pi\) | ||||
−0.563980 | + | 0.825788i | \(0.690731\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 29065.4 | 0.367937 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −200526. | −2.40416 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −28857.2 | −0.328054 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 101273. | 1.09286 | 0.546428 | − | 0.837506i | \(-0.315987\pi\) | ||||
0.546428 | + | 0.837506i | \(0.315987\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −106904. | −1.09625 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −77456.5 | −0.755535 | −0.377767 | − | 0.925901i | \(-0.623308\pi\) | ||||
−0.377767 | + | 0.925901i | \(0.623308\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 56716.9 | 0.526768 | 0.263384 | − | 0.964691i | \(-0.415161\pi\) | ||||
0.263384 | + | 0.964691i | \(0.415161\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 92608.9 | 0.819746 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −38699.2 | −0.326770 | −0.163385 | − | 0.986562i | \(-0.552241\pi\) | ||||
−0.163385 | + | 0.986562i | \(0.552241\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 16595.3 | 0.133788 | 0.0668941 | − | 0.997760i | \(-0.478691\pi\) | ||||
0.0668941 | + | 0.997760i | \(0.478691\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 108235. | 0.833794 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −76723.9 | −0.565242 | −0.282621 | − | 0.959232i | \(-0.591204\pi\) | ||||
−0.282621 | + | 0.959232i | \(0.591204\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 59700.9 | 0.420955 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 114775. | 0.775146 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −69687.4 | −0.451115 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 144199. | 0.895361 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 45805.9 | 0.272997 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −174901. | −1.00119 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −68539.3 | −0.377077 | −0.188539 | − | 0.982066i | \(-0.560375\pi\) | ||||
−0.188539 | + | 0.982066i | \(0.560375\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −155822. | −0.824430 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 95936.2 | 0.488432 | 0.244216 | − | 0.969721i | \(-0.421469\pi\) | ||||
0.244216 | + | 0.969721i | \(0.421469\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 15630.9 | 0.0766221 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −93564.8 | −0.441853 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 291295. | 1.32597 | 0.662983 | − | 0.748635i | \(-0.269290\pi\) | ||||
0.662983 | + | 0.748635i | \(0.269290\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −281554. | −1.23602 | −0.618009 | − | 0.786171i | \(-0.712061\pi\) | ||||
−0.618009 | + | 0.786171i | \(0.712061\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −408693. | −1.73121 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −327724. | −1.34019 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −740458. | −2.92469 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −50162.8 | −0.191464 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 128283. | 0.473372 | 0.236686 | − | 0.971586i | \(-0.423939\pi\) | ||||
0.236686 | + | 0.971586i | \(0.423939\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19017.7 | −0.0678760 | −0.0339380 | − | 0.999424i | \(-0.510805\pi\) | ||||
−0.0339380 | + | 0.999424i | \(0.510805\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −275186. | −0.950381 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −868259. | −2.90282 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 272988. | 0.883883 | 0.441941 | − | 0.897044i | \(-0.354290\pi\) | ||||
0.441941 | + | 0.897044i | \(0.354290\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 764028. | 2.39672 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −32337.7 | −0.0983207 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 315849. | 0.931131 | 0.465565 | − | 0.885013i | \(-0.345851\pi\) | ||||
0.465565 | + | 0.885013i | \(0.345851\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.04420e6 | −2.98589 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 588655. | 1.63331 | 0.816657 | − | 0.577123i | \(-0.195825\pi\) | ||||
0.816657 | + | 0.577123i | \(0.195825\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −19440.5 | −0.0523590 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 61724.1 | 0.161423 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −718256. | −1.82458 | −0.912292 | − | 0.409540i | \(-0.865689\pi\) | ||||
−0.912292 | + | 0.409540i | \(0.865689\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 247862. | 0.611808 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −341837. | −0.820136 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 53637.2 | 0.125122 | 0.0625610 | − | 0.998041i | \(-0.480073\pi\) | ||||
0.0625610 | + | 0.998041i | \(0.480073\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 392213. | 0.889867 | 0.444934 | − | 0.895564i | \(-0.353227\pi\) | ||||
0.444934 | + | 0.895564i | \(0.353227\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −227584. | −0.502359 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 468645. | 1.00673 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 785753. | 1.64317 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 50680.5 | 0.103202 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −395509. | −0.784463 | −0.392232 | − | 0.919866i | \(-0.628297\pi\) | ||||
−0.392232 | + | 0.919866i | \(0.628297\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −562892. | −1.08776 | −0.543878 | − | 0.839164i | \(-0.683045\pi\) | ||||
−0.543878 | + | 0.839164i | \(0.683045\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.12108e6 | 2.11130 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −402202. | −0.738378 | −0.369189 | − | 0.929354i | \(-0.620365\pi\) | ||||
−0.369189 | + | 0.929354i | \(0.620365\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 455975. | 0.816222 | 0.408111 | − | 0.912932i | \(-0.366188\pi\) | ||||
0.408111 | + | 0.912932i | \(0.366188\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −167890. | −0.293112 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 401078. | 0.683108 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 198335. | 0.329621 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −127697. | −0.207136 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −176244. | −0.279093 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.18264e6 | −1.82871 | −0.914356 | − | 0.404911i | \(-0.867302\pi\) | ||||
−0.914356 | + | 0.404911i | \(0.867302\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.16963e6 | 1.76644 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −674693. | −0.995429 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 470303. | 0.677999 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.62444e6 | 2.28872 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −843604. | −1.16187 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −931112. | −1.25383 | −0.626917 | − | 0.779086i | \(-0.715683\pi\) | ||||
−0.626917 | + | 0.779086i | \(0.715683\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 978774. | 1.28892 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 192653. | 0.248149 | 0.124074 | − | 0.992273i | \(-0.460404\pi\) | ||||
0.124074 | + | 0.992273i | \(0.460404\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 783934. | 0.987850 | 0.493925 | − | 0.869505i | \(-0.335562\pi\) | ||||
0.493925 | + | 0.869505i | \(0.335562\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 565605. | 0.697402 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.39976e6 | −1.68914 | −0.844568 | − | 0.535448i | \(-0.820143\pi\) | ||||
−0.844568 | + | 0.535448i | \(0.820143\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.76960e6 | −2.09029 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −67032.0 | −0.0775196 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 643631. | 0.728857 | 0.364429 | − | 0.931231i | \(-0.381264\pi\) | ||||
0.364429 | + | 0.931231i | \(0.381264\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −58756.4 | −0.0651647 | −0.0325824 | − | 0.999469i | \(-0.510373\pi\) | ||||
−0.0325824 | + | 0.999469i | \(0.510373\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.18247e6 | 1.28462 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −217200. | −0.231177 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 189220. | 0.197344 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.60092e6 | −1.63633 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −641680. | −0.642886 | −0.321443 | − | 0.946929i | \(-0.604168\pi\) | ||||
−0.321443 | + | 0.946929i | \(0.604168\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 364621. | 0.358129 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.68791e6 | −2.58860 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 810671. | 0.765617 | 0.382809 | − | 0.923828i | \(-0.374957\pi\) | ||||
0.382809 | + | 0.923828i | \(0.374957\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −253848. | −0.235138 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.58380e6 | 1.43913 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.04061e6 | 1.81916 | 0.909581 | − | 0.415526i | \(-0.136403\pi\) | ||||
0.909581 | + | 0.415526i | \(0.136403\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.30817e6 | 2.89383 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.76100e6 | 1.51175 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.28300e6 | 1.08105 | 0.540524 | − | 0.841328i | \(-0.318226\pi\) | ||||
0.540524 | + | 0.841328i | \(0.318226\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 22511.3 | 0.0186199 | 0.00930994 | − | 0.999957i | \(-0.497037\pi\) | ||||
0.00930994 | + | 0.999957i | \(0.497037\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −607247. | −0.493127 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.79474e6 | −2.22849 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −368210. | −0.288334 | −0.144167 | − | 0.989553i | \(-0.546050\pi\) | ||||
−0.144167 | + | 0.989553i | \(0.546050\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.85716e6 | 1.42837 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.03709e6 | 1.53902 | 0.769511 | − | 0.638634i | \(-0.220500\pi\) | ||||
0.769511 | + | 0.638634i | \(0.220500\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −656410. | −0.487202 | −0.243601 | − | 0.969876i | \(-0.578329\pi\) | ||||
−0.243601 | + | 0.969876i | \(0.578329\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 602897. | 0.439675 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −107431. | −0.0769880 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 602773. | 0.424531 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.11583e6 | −1.46470 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 962295. | 0.654846 | 0.327423 | − | 0.944878i | \(-0.393820\pi\) | ||||
0.327423 | + | 0.944878i | \(0.393820\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.48012e6 | −0.990243 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −571443. | −0.375908 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −391466. | −0.253230 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 365456. | 0.232498 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.61826e6 | 1.01261 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −985418. | −0.606556 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −296468. | −0.179528 | −0.0897638 | − | 0.995963i | \(-0.528611\pi\) | ||||
−0.0897638 | + | 0.995963i | \(0.528611\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.18495e6 | −0.706001 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.12063e6 | −0.656996 | −0.328498 | − | 0.944505i | \(-0.606542\pi\) | ||||
−0.328498 | + | 0.944505i | \(0.606542\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.74908e6 | 1.00913 | 0.504567 | − | 0.863373i | \(-0.331652\pi\) | ||||
0.504567 | + | 0.863373i | \(0.331652\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −857692. | −0.487029 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.17498e6 | −1.77457 | −0.887284 | − | 0.461223i | \(-0.847411\pi\) | ||||
−0.887284 | + | 0.461223i | \(0.847411\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.52232e6 | −2.48819 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 808520. | 0.437954 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −453675. | −0.241957 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.00051e6 | 1.57575 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −346715. | −0.179310 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 958526. | 0.488219 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 878405. | 0.440681 | 0.220341 | − | 0.975423i | \(-0.429283\pi\) | ||||
0.220341 | + | 0.975423i | \(0.429283\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.00241e6 | −0.495375 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −726946. | −0.353908 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.05261e6 | 0.984536 | 0.492268 | − | 0.870444i | \(-0.336168\pi\) | ||||
0.492268 | + | 0.870444i | \(0.336168\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.60295e6 | 0.757566 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.30286e6 | −2.46958 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 117649. | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.24730e6 | −0.564186 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 476182. | 0.212300 | 0.106150 | − | 0.994350i | \(-0.466148\pi\) | ||||
0.106150 | + | 0.994350i | \(0.466148\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −351681. | −0.154556 | −0.0772780 | − | 0.997010i | \(-0.524623\pi\) | ||||
−0.0772780 | + | 0.997010i | \(0.524623\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 613515. | 0.265802 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.73722e6 | −0.742023 | −0.371011 | − | 0.928628i | \(-0.620989\pi\) | ||||
−0.371011 | + | 0.928628i | \(0.620989\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.06438e6 | 2.13282 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.45594e6 | 0.604607 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.69731e6 | 0.695063 | 0.347531 | − | 0.937668i | \(-0.387020\pi\) | ||||
0.347531 | + | 0.937668i | \(0.387020\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.37434e6 | −0.958903 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.01267e6 | −1.20001 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.03366e6 | 2.76344 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.11920e6 | 0.433752 | 0.216876 | − | 0.976199i | \(-0.430413\pi\) | ||||
0.216876 | + | 0.976199i | \(0.430413\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −424228. | −0.162194 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.79191e6 | −0.675898 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 837822. | 0.311803 | 0.155901 | − | 0.987773i | \(-0.450172\pi\) | ||||
0.155901 | + | 0.987773i | \(0.450172\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.65411e6 | 1.34185 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.85527e6 | 1.75938 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.94713e6 | −0.696300 | −0.348150 | − | 0.937439i | \(-0.613190\pi\) | ||||
−0.348150 | + | 0.937439i | \(0.613190\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.43195e6 | 0.505378 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 202063. | 0.0703866 | 0.0351933 | − | 0.999381i | \(-0.488795\pi\) | ||||
0.0351933 | + | 0.999381i | \(0.488795\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.44901e6 | 0.842053 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.44314e6 | 0.489812 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.23741e6 | −1.08473 | −0.542367 | − | 0.840141i | \(-0.682472\pi\) | ||||
−0.542367 | + | 0.840141i | \(0.682472\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 938581. | 0.310477 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.00434e6 | −0.654622 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −290242. | −0.0935982 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −823921. | −0.262367 | −0.131183 | − | 0.991358i | \(-0.541878\pi\) | ||||
−0.131183 | + | 0.991358i | \(0.541878\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −326567. | −0.102693 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.39337e6 | 0.743273 | 0.371637 | − | 0.928378i | \(-0.378797\pi\) | ||||
0.371637 | + | 0.928378i | \(0.378797\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.69328e6 | 1.74622 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 6.20825e6 | 1.88075 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.86223e6 | 0.856483 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −581801. | −0.171975 | −0.0859876 | − | 0.996296i | \(-0.527405\pi\) | ||||
−0.0859876 | + | 0.996296i | \(0.527405\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.08587e6 | −1.77713 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 801725. | 0.231287 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.93184e6 | −1.97573 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.88236e6 | 1.65658 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.11898e6 | 0.867915 | 0.433957 | − | 0.900933i | \(-0.357117\pi\) | ||||
0.433957 | + | 0.900933i | \(0.357117\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.14481e6 | 0.314796 | 0.157398 | − | 0.987535i | \(-0.449689\pi\) | ||||
0.157398 | + | 0.987535i | \(0.449689\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.78509e6 | 1.02855 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.19403e6 | −1.93197 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 533764. | 0.141671 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.84695e6 | 1.79620 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.31012e6 | 1.11762 | 0.558812 | − | 0.829294i | \(-0.311257\pi\) | ||||
0.558812 | + | 0.829294i | \(0.311257\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.79301e6 | −0.715901 | −0.357950 | − | 0.933741i | \(-0.616524\pi\) | ||||
−0.357950 | + | 0.933741i | \(0.616524\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.54700e7 | 3.91982 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −210523. | −0.0527347 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −252467. | −0.0625236 | −0.0312618 | − | 0.999511i | \(-0.509953\pi\) | ||||
−0.0312618 | + | 0.999511i | \(0.509953\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 464580. | 0.113753 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.43282e6 | −0.831077 | −0.415539 | − | 0.909576i | \(-0.636407\pi\) | ||||
−0.415539 | + | 0.909576i | \(0.636407\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.62494e6 | 1.82531 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.68014e6 | −0.634437 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.68031e6 | −0.393345 | −0.196673 | − | 0.980469i | \(-0.563014\pi\) | ||||
−0.196673 | + | 0.980469i | \(0.563014\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.21132e6 | 0.280426 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 397327. | 0.0909709 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.62932e6 | −0.595409 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.94585e6 | −0.659812 | −0.329906 | − | 0.944014i | \(-0.607017\pi\) | ||||
−0.329906 | + | 0.944014i | \(0.607017\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.47097e6 | −0.325890 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.91583e6 | 0.419860 | 0.209930 | − | 0.977716i | \(-0.432676\pi\) | ||||
0.209930 | + | 0.977716i | \(0.432676\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.75401e6 | 0.813847 | 0.406924 | − | 0.913462i | \(-0.366602\pi\) | ||||
0.406924 | + | 0.913462i | \(0.366602\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.81401e7 | 3.89051 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.10594e6 | −0.446842 | −0.223421 | − | 0.974722i | \(-0.571722\pi\) | ||||
−0.223421 | + | 0.974722i | \(0.571722\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 393759. | 0.0826607 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.70339e6 | −1.18462 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.12066e6 | −0.846864 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.61362e6 | 0.328146 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.07600e6 | −1.42394 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 274926. | 0.0547491 | 0.0273745 | − | 0.999625i | \(-0.491285\pi\) | ||||
0.0273745 | + | 0.999625i | \(0.491285\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.07296e6 | −0.605612 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 675614. | 0.131774 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −9.16135e6 | −1.76850 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.67128e6 | −1.46570 | −0.732851 | − | 0.680389i | \(-0.761811\pi\) | ||||
−0.732851 | + | 0.680389i | \(0.761811\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.59886e6 | −1.24795 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.42352e6 | −0.453673 | −0.226837 | − | 0.973933i | \(-0.572838\pi\) | ||||
−0.226837 | + | 0.973933i | \(0.572838\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.16410e7 | −2.15712 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 9.67081e6 | 1.77399 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.74318e6 | −0.498154 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.22317e6 | −1.47839 | −0.739193 | − | 0.673494i | \(-0.764793\pi\) | ||||
−0.739193 | + | 0.673494i | \(0.764793\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.22984e7 | −2.18905 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.98186e6 | −0.525493 | −0.262746 | − | 0.964865i | \(-0.584628\pi\) | ||||
−0.262746 | + | 0.964865i | \(0.584628\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.00689e6 | 1.22263 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 406160. | 0.0701741 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.26867e6 | 1.07246 | 0.536230 | − | 0.844072i | \(-0.319848\pi\) | ||||
0.536230 | + | 0.844072i | \(0.319848\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.80987e6 | −0.645443 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 329938. | 0.0553527 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.13073e6 | −0.852435 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.08078e7 | −1.77832 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.50061e7 | 2.44540 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.12134e6 | −0.665188 | −0.332594 | − | 0.943070i | \(-0.607924\pi\) | ||||
−0.332594 | + | 0.943070i | \(0.607924\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.70469e6 | −0.752102 | −0.376051 | − | 0.926599i | \(-0.622718\pi\) | ||||
−0.376051 | + | 0.926599i | \(0.622718\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5.17845e6 | −0.819976 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.36502e7 | −2.14099 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.00080e6 | −0.932331 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.16590e6 | 0.487261 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.30051e6 | −0.198287 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.50081e6 | 0.528791 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.12061e6 | −0.167695 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.32654e6 | −0.196674 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.47840e6 | −0.657855 | −0.328927 | − | 0.944355i | \(-0.606687\pi\) | ||||
−0.328927 | + | 0.944355i | \(0.606687\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8.19428e6 | −1.19265 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.50124e6 | −0.216501 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.49187e6 | −0.927687 | −0.463843 | − | 0.885917i | \(-0.653530\pi\) | ||||
−0.463843 | + | 0.885917i | \(0.653530\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.10776e6 | 0.298463 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.61108e6 | 0.366388 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 157213. | 0.0218613 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −9.79115e6 | −1.34928 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.50858e6 | 0.342602 | 0.171301 | − | 0.985219i | \(-0.445203\pi\) | ||||
0.171301 | + | 0.985219i | \(0.445203\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.42404e6 | 0.598811 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.64163e7 | −2.20226 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3.52702e6 | −0.468961 | −0.234480 | − | 0.972121i | \(-0.575339\pi\) | ||||
−0.234480 | + | 0.972121i | \(0.575339\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.94061e6 | 0.914696 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.36278e6 | −0.439279 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9.75283e6 | 1.26284 | 0.631422 | − | 0.775439i | \(-0.282471\pi\) | ||||
0.631422 | + | 0.775439i | \(0.282471\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.70085e6 | 0.218312 | 0.109156 | − | 0.994025i | \(-0.465185\pi\) | ||||
0.109156 | + | 0.994025i | \(0.465185\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.26314e6 | 1.05138 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.33832e6 | −0.421074 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.17066e7 | −1.46383 | −0.731914 | − | 0.681397i | \(-0.761373\pi\) | ||||
−0.731914 | + | 0.681397i | \(0.761373\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.17602e7 | 1.45787 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.75472e6 | 0.461463 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.02045e7 | 2.46193 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.03828e7 | −1.25437 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.75683e6 | −0.450015 | −0.225007 | − | 0.974357i | \(-0.572241\pi\) | ||||
−0.225007 | + | 0.974357i | \(0.572241\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.06175e6 | 0.363648 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.40299e6 | 0.989612 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.64338e6 | 1.00936 | 0.504681 | − | 0.863306i | \(-0.331610\pi\) | ||||
0.504681 | + | 0.863306i | \(0.331610\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.30408e6 | 0.730011 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −9.52643e6 | −1.09394 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.31930e6 | −1.06125 | −0.530623 | − | 0.847608i | \(-0.678042\pi\) | ||||
−0.530623 | + | 0.847608i | \(0.678042\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 910438. | 0.102817 | 0.0514084 | − | 0.998678i | \(-0.483629\pi\) | ||||
0.0514084 | + | 0.998678i | \(0.483629\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.55490e6 | 0.174144 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.30445e7 | −1.44891 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.70173e6 | −0.628109 | −0.314054 | − | 0.949405i | \(-0.601687\pi\) | ||||
−0.314054 | + | 0.949405i | \(0.601687\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −8.37951e6 | −0.915536 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.16035e7 | 1.25743 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.61327e7 | −1.73403 | −0.867016 | − | 0.498280i | \(-0.833965\pi\) | ||||
−0.867016 | + | 0.498280i | \(0.833965\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4.14370e6 | −0.441774 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.53575e6 | −0.585415 | −0.292708 | − | 0.956202i | \(-0.594556\pi\) | ||||
−0.292708 | + | 0.956202i | \(0.594556\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.88448e7 | −1.97681 | −0.988407 | − | 0.151828i | \(-0.951484\pi\) | ||||
−0.988407 | + | 0.151828i | \(0.951484\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −682588. | −0.0710280 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.13014e6 | −0.426329 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14378.1 | 0.00147232 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.68217e6 | 0.374055 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.36776e6 | 0.742521 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.63269e6 | −0.263224 | −0.131612 | − | 0.991301i | \(-0.542015\pi\) | ||||
−0.131612 | + | 0.991301i | \(0.542015\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.47082e7 | 2.45093 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.20021e6 | 0.610200 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.42420e6 | 0.139067 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.08324e7 | −1.04948 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.42939e7 | 1.37406 | 0.687028 | − | 0.726631i | \(-0.258915\pi\) | ||||
0.687028 | + | 0.726631i | \(0.258915\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.63874e7 | −1.56308 | −0.781542 | − | 0.623853i | \(-0.785566\pi\) | ||||
−0.781542 | + | 0.623853i | \(0.785566\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.40960e7 | 1.33412 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.19303e7 | −1.12045 | −0.560224 | − | 0.828341i | \(-0.689285\pi\) | ||||
−0.560224 | + | 0.828341i | \(0.689285\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.03977e6 | −0.842453 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9.82579e6 | −0.908688 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.47862e6 | −0.319245 | −0.159622 | − | 0.987178i | \(-0.551028\pi\) | ||||
−0.159622 | + | 0.987178i | \(0.551028\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.67860e6 | −0.790399 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.50447e7 | −1.35978 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.09397e7 | 1.87826 | 0.939131 | − | 0.343560i | \(-0.111633\pi\) | ||||
0.939131 | + | 0.343560i | \(0.111633\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.02566e7 | 0.913059 | 0.456530 | − | 0.889708i | \(-0.349092\pi\) | ||||
0.456530 | + | 0.889708i | \(0.349092\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.76249e7 | 1.55720 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.41400e6 | −0.123993 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.40190e6 | −0.470145 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.94532e7 | 1.68045 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.01840e6 | −0.516029 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 716398. | 0.0609701 | 0.0304851 | − | 0.999535i | \(-0.490295\pi\) | ||||
0.0304851 | + | 0.999535i | \(0.490295\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.23190e6 | 0.441977 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −945625. | −0.0792953 | −0.0396476 | − | 0.999214i | \(-0.512624\pi\) | ||||
−0.0396476 | + | 0.999214i | \(0.512624\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.96236e6 | 0.413061 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.02500e6 | −0.332582 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.56992e6 | 0.292824 | 0.146412 | − | 0.989224i | \(-0.453227\pi\) | ||||
0.146412 | + | 0.989224i | \(0.453227\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.63512e7 | −2.14573 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.63783e7 | −1.32397 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.16920e7 | −1.74081 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.67811e6 | 0.771073 | 0.385536 | − | 0.922693i | \(-0.374016\pi\) | ||||
0.385536 | + | 0.922693i | \(0.374016\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5.23832e6 | −0.414342 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.54700e7 | 2.00017 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.11810e6 | 0.243113 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.92445e7 | 2.26387 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.52404e7 | −1.94000 | −0.970000 | − | 0.243105i | \(-0.921834\pi\) | ||||
−0.970000 | + | 0.243105i | \(0.921834\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.65259e6 | −0.126118 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.69713e7 | 2.80151 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.79537e6 | −0.285565 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.74744e7 | 1.30553 | 0.652765 | − | 0.757560i | \(-0.273609\pi\) | ||||
0.652765 | + | 0.757560i | \(0.273609\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 620813. | 0.0460561 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.33426e6 | −0.466629 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.96466e7 | 2.16875 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.34470e7 | −0.976852 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.73361e6 | 0.702185 | 0.351093 | − | 0.936341i | \(-0.385810\pi\) | ||||
0.351093 | + | 0.936341i | \(0.385810\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.77913e6 | 0.199100 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.22756e6 | 0.0873371 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.14045e7 | 2.92552 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.60454e7 | 1.12594 | 0.562971 | − | 0.826477i | \(-0.309658\pi\) | ||||
0.562971 | + | 0.826477i | \(0.309658\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −8.02815e6 | −0.559496 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.06071e7 | −0.734182 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.04534e7 | −0.718615 | −0.359307 | − | 0.933219i | \(-0.616987\pi\) | ||||
−0.359307 | + | 0.933219i | \(0.616987\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.53783e6 | 0.309835 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.43979e6 | −0.301088 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.47638e6 | −0.503594 | −0.251797 | − | 0.967780i | \(-0.581022\pi\) | ||||
−0.251797 | + | 0.967780i | \(0.581022\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.95327e6 | −0.264491 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.33998e7 | 0.890483 | 0.445241 | − | 0.895411i | \(-0.353118\pi\) | ||||
0.445241 | + | 0.895411i | \(0.353118\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.16047e7 | −0.766028 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.48269e7 | 0.972182 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.89626e6 | −0.123507 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.13903e6 | −0.591290 | −0.295645 | − | 0.955298i | \(-0.595535\pi\) | ||||
−0.295645 | + | 0.955298i | \(0.595535\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.34063e7 | 0.861629 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.72039e6 | 0.109840 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.16376e7 | 0.738117 | 0.369059 | − | 0.929406i | \(-0.379680\pi\) | ||||
0.369059 | + | 0.929406i | \(0.379680\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −7.61782e6 | −0.479983 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8.07072e6 | −0.505186 | −0.252593 | − | 0.967573i | \(-0.581283\pi\) | ||||
−0.252593 | + | 0.967573i | \(0.581283\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 813167. | 0.0505672 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.48939e7 | 1.53794 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.70532e6 | 0.595692 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.30085e7 | −0.793255 | −0.396628 | − | 0.917980i | \(-0.629820\pi\) | ||||
−0.396628 | + | 0.917980i | \(0.629820\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.69369e7 | −1.02612 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.37637e7 | −1.43043 | −0.715214 | − | 0.698906i | \(-0.753671\pi\) | ||||
−0.715214 | + | 0.698906i | \(0.753671\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.85508e7 | 2.90364 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5.30350e6 | 0.315145 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −699389. | −0.0412929 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.09305e7 | 1.81451 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.46600e6 | 0.493485 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.46951e7 | −1.43033 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.84940e7 | −1.63989 | −0.819947 | − | 0.572439i | \(-0.805997\pi\) | ||||
−0.819947 | + | 0.572439i | \(0.805997\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.26334e7 | −2.43813 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.75947e6 | −0.213641 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.46150e6 | 0.364880 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −6.91157e7 | −3.87845 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.43450e7 | −0.799938 | −0.399969 | − | 0.916529i | \(-0.630979\pi\) | ||||
−0.399969 | + | 0.916529i | \(0.630979\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.78206e7 | −1.54170 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.63094e7 | −0.898164 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.29578e7 | 2.35100 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.92534e6 | 0.159106 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.68050e7 | −1.44888 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.59284e6 | −0.193004 | −0.0965020 | − | 0.995333i | \(-0.530765\pi\) | ||||
−0.0965020 | + | 0.995333i | \(0.530765\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.52968e7 | 1.88445 | 0.942223 | − | 0.334988i | \(-0.108732\pi\) | ||||
0.942223 | + | 0.334988i | \(0.108732\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −470316. | −0.0249553 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.85724e7 | −1.50679 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.37917e6 | 0.124701 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.62399e6 | 0.292978 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.04558e7 | −0.541378 | −0.270689 | − | 0.962667i | \(-0.587252\pi\) | ||||
−0.270689 | + | 0.962667i | \(0.587252\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.99190e6 | −0.256901 | −0.128451 | − | 0.991716i | \(-0.541000\pi\) | ||||
−0.128451 | + | 0.991716i | \(0.541000\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5.83890e7 | 2.98673 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.06198e7 | −1.04839 | −0.524193 | − | 0.851599i | \(-0.675633\pi\) | ||||
−0.524193 | + | 0.851599i | \(0.675633\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 506843. | 0.0256146 | 0.0128073 | − | 0.999918i | \(-0.495923\pi\) | ||||
0.0128073 | + | 0.999918i | \(0.495923\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.69281e6 | 0.386440 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.41468e6 | −0.170505 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.32511e7 | −2.64309 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 9.92721e6 | 0.489794 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.41851e6 | 0.216706 | 0.108353 | − | 0.994112i | \(-0.465442\pi\) | ||||
0.108353 | + | 0.994112i | \(0.465442\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.64876e7 | 2.26645 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −4.25598e7 | −2.06267 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.75863e6 | 0.0847292 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.06574e6 | 0.338415 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.37140e7 | 0.652973 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.41893e6 | 0.161833 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.11737e7 | 0.525806 | 0.262903 | − | 0.964822i | \(-0.415320\pi\) | ||||
0.262903 | + | 0.964822i | \(0.415320\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.58370e6 | −0.261220 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.12308e7 | 0.987448 | 0.493724 | − | 0.869619i | \(-0.335635\pi\) | ||||
0.493724 | + | 0.869619i | \(0.335635\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.64229e7 | 1.68419 | 0.842096 | − | 0.539328i | \(-0.181322\pi\) | ||||
0.842096 | + | 0.539328i | \(0.181322\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.24449e6 | 0.103183 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.53298e7 | 1.15772 | 0.578861 | − | 0.815426i | \(-0.303497\pi\) | ||||
0.578861 | + | 0.815426i | \(0.303497\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.49750e7 | 2.95261 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.25934e7 | −0.568978 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.77264e6 | −0.0796290 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.76667e6 | 0.212897 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.95957e7 | 0.870211 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −8.57014e6 | −0.378415 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 577138. | 0.0253385 | 0.0126692 | − | 0.999920i | \(-0.495967\pi\) | ||||
0.0126692 | + | 0.999920i | \(0.495967\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.01047e7 | −0.877658 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.15071e7 | −0.933561 | −0.466781 | − | 0.884373i | \(-0.654586\pi\) | ||||
−0.466781 | + | 0.884373i | \(0.654586\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.71948e6 | −0.160539 | −0.0802695 | − | 0.996773i | \(-0.525578\pi\) | ||||
−0.0802695 | + | 0.996773i | \(0.525578\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.09233e7 | 1.32717 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.81760e7 | −0.775694 | −0.387847 | − | 0.921724i | \(-0.626781\pi\) | ||||
−0.387847 | + | 0.921724i | \(0.626781\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.35842e6 | −0.142522 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.79166e7 | 1.60006 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.24015e6 | 0.261858 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.85214e6 | −0.202477 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.17868e6 | 0.339392 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 7.85625e7 | 3.24202 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.20090e7 | 2.13435 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −7.63527e6 | −0.311605 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.54804e7 | −1.44002 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.35430e7 | −0.546635 | −0.273317 | − | 0.961924i | \(-0.588121\pi\) | ||||
−0.273317 | + | 0.961924i | \(0.588121\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.49874e7 | −0.601612 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 412746. | 0.0164773 | 0.00823866 | − | 0.999966i | \(-0.497378\pi\) | ||||
0.00823866 | + | 0.999966i | \(0.497378\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.23359e7 | −1.68086 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.05878e7 | 0.812937 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.70087e6 | 0.184610 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.79059e7 | −1.08995 | −0.544976 | − | 0.838452i | \(-0.683461\pi\) | ||||
−0.544976 | + | 0.838452i | \(0.683461\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.19394e6 | 0.240612 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.32077e7 | −1.28302 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.62054e7 | −1.00702 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.09744e7 | 0.419451 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.94840e7 | −0.740695 | −0.370348 | − | 0.928893i | \(-0.620761\pi\) | ||||
−0.370348 | + | 0.928893i | \(0.620761\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 765912. | 0.0289604 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.34128e7 | 0.880539 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.10809e7 | −2.65904 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.89631e7 | −0.705602 | −0.352801 | − | 0.935698i | \(-0.614771\pi\) | ||||
−0.352801 | + | 0.935698i | \(0.614771\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.65425e7 | −1.35249 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.30498e7 | 0.848579 | 0.424290 | − | 0.905526i | \(-0.360524\pi\) | ||||
0.424290 | + | 0.905526i | \(0.360524\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.44692e6 | 0.0529866 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.58467e6 | −0.167005 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3.49310e7 | −1.26572 | −0.632858 | − | 0.774268i | \(-0.718118\pi\) | ||||
−0.632858 | + | 0.774268i | \(0.718118\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.61206e7 | −1.66238 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.63331e7 | 2.37837 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.74501e7 | 0.979066 | 0.489533 | − | 0.871985i | \(-0.337167\pi\) | ||||
0.489533 | + | 0.871985i | \(0.337167\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.57786e7 | 1.26945 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.44822e7 | 3.33480 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.42735e7 | 0.501168 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.34930e7 | 2.21778 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.48807e6 | −0.260198 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.09204e7 | 1.76025 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9.37608e6 | 0.322445 | 0.161222 | − | 0.986918i | \(-0.448456\pi\) | ||||
0.161222 | + | 0.986918i | \(0.448456\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 9.47839e6 | 0.324284 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.23359e6 | 0.246210 | 0.123105 | − | 0.992394i | \(-0.460715\pi\) | ||||
0.123105 | + | 0.992394i | \(0.460715\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.37962e7 | −0.467171 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6.26879e7 | −2.11190 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.88022e7 | −0.965360 | −0.482680 | − | 0.875797i | \(-0.660337\pi\) | ||||
−0.482680 | + | 0.875797i | \(0.660337\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.65690e7 | 1.55289 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.21109e6 | 0.106532 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.21848e7 | −1.72250 | −0.861252 | − | 0.508178i | \(-0.830319\pi\) | ||||
−0.861252 | + | 0.508178i | \(0.830319\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.63841e7 | 1.19487 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.00260e7 | −0.654335 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.92212e6 | −0.160015 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.89578e7 | 1.26012 | 0.630058 | − | 0.776548i | \(-0.283031\pi\) | ||||
0.630058 | + | 0.776548i | \(0.283031\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.83520e7 | −0.590624 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.12485e7 | −1.32084 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.01716e7 | 0.961305 | 0.480652 | − | 0.876911i | \(-0.340400\pi\) | ||||
0.480652 | + | 0.876911i | \(0.340400\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.35824e6 | −0.169867 |
(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 | 448.6.a.r.1.1 | 2 | ||
4.3 | odd | 2 | 448.6.a.x.1.2 | 2 | |||
8.3 | odd | 2 | 56.6.a.d.1.1 | ✓ | 2 | ||
8.5 | even | 2 | 112.6.a.j.1.2 | 2 | |||
24.5 | odd | 2 | 1008.6.a.bi.1.1 | 2 | |||
24.11 | even | 2 | 504.6.a.m.1.1 | 2 | |||
56.3 | even | 6 | 392.6.i.h.177.1 | 4 | |||
56.11 | odd | 6 | 392.6.i.k.177.2 | 4 | |||
56.13 | odd | 2 | 784.6.a.q.1.1 | 2 | |||
56.19 | even | 6 | 392.6.i.h.361.1 | 4 | |||
56.27 | even | 2 | 392.6.a.e.1.2 | 2 | |||
56.51 | odd | 6 | 392.6.i.k.361.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.6.a.d.1.1 | ✓ | 2 | 8.3 | odd | 2 | ||
112.6.a.j.1.2 | 2 | 8.5 | even | 2 | |||
392.6.a.e.1.2 | 2 | 56.27 | even | 2 | |||
392.6.i.h.177.1 | 4 | 56.3 | even | 6 | |||
392.6.i.h.361.1 | 4 | 56.19 | even | 6 | |||
392.6.i.k.177.2 | 4 | 56.11 | odd | 6 | |||
392.6.i.k.361.2 | 4 | 56.51 | odd | 6 | |||
448.6.a.r.1.1 | 2 | 1.1 | even | 1 | trivial | ||
448.6.a.x.1.2 | 2 | 4.3 | odd | 2 | |||
504.6.a.m.1.1 | 2 | 24.11 | even | 2 | |||
784.6.a.q.1.1 | 2 | 56.13 | odd | 2 | |||
1008.6.a.bi.1.1 | 2 | 24.5 | odd | 2 |