Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [294,6,Mod(1,294)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(294, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("294.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 294 = 2 \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 294.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: | \(47.1528430250\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 294.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.00000 | 0.707107 | ||||||||
\(3\) | 9.00000 | 0.577350 | ||||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | −61.0711 | −1.09247 | −0.546236 | − | 0.837631i | \(-0.683940\pi\) | ||||
−0.546236 | + | 0.837631i | \(0.683940\pi\) | |||||||
\(6\) | 36.0000 | 0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 64.0000 | 0.353553 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | −244.284 | −0.772495 | ||||||||
\(11\) | −36.5442 | −0.0910618 | −0.0455309 | − | 0.998963i | \(-0.514498\pi\) | ||||
−0.0455309 | + | 0.998963i | \(0.514498\pi\) | |||||||
\(12\) | 144.000 | 0.288675 | ||||||||
\(13\) | 34.5656 | 0.0567264 | 0.0283632 | − | 0.999598i | \(-0.490970\pi\) | ||||
0.0283632 | + | 0.999598i | \(0.490970\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −549.640 | −0.630739 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | −2061.04 | −1.72967 | −0.864836 | − | 0.502054i | \(-0.832578\pi\) | ||||
−0.864836 | + | 0.502054i | \(0.832578\pi\) | |||||||
\(18\) | 324.000 | 0.235702 | ||||||||
\(19\) | 452.238 | 0.287398 | 0.143699 | − | 0.989621i | \(-0.454100\pi\) | ||||
0.143699 | + | 0.989621i | \(0.454100\pi\) | |||||||
\(20\) | −977.137 | −0.546236 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −146.177 | −0.0643904 | ||||||||
\(23\) | 1684.25 | 0.663875 | 0.331938 | − | 0.943301i | \(-0.392298\pi\) | ||||
0.331938 | + | 0.943301i | \(0.392298\pi\) | |||||||
\(24\) | 576.000 | 0.204124 | ||||||||
\(25\) | 604.675 | 0.193496 | ||||||||
\(26\) | 138.262 | 0.0401116 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4765.22 | −1.05217 | −0.526087 | − | 0.850431i | \(-0.676341\pi\) | ||||
−0.526087 | + | 0.850431i | \(0.676341\pi\) | |||||||
\(30\) | −2198.56 | −0.446000 | ||||||||
\(31\) | −5260.87 | −0.983225 | −0.491613 | − | 0.870814i | \(-0.663592\pi\) | ||||
−0.491613 | + | 0.870814i | \(0.663592\pi\) | |||||||
\(32\) | 1024.00 | 0.176777 | ||||||||
\(33\) | −328.897 | −0.0525746 | ||||||||
\(34\) | −8244.16 | −1.22306 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1296.00 | 0.166667 | ||||||||
\(37\) | −12822.0 | −1.53975 | −0.769875 | − | 0.638195i | \(-0.779681\pi\) | ||||
−0.769875 | + | 0.638195i | \(0.779681\pi\) | |||||||
\(38\) | 1808.95 | 0.203221 | ||||||||
\(39\) | 311.090 | 0.0327510 | ||||||||
\(40\) | −3908.55 | −0.386247 | ||||||||
\(41\) | −7126.74 | −0.662111 | −0.331056 | − | 0.943611i | \(-0.607405\pi\) | ||||
−0.331056 | + | 0.943611i | \(0.607405\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11141.7 | 0.918925 | 0.459462 | − | 0.888197i | \(-0.348042\pi\) | ||||
0.459462 | + | 0.888197i | \(0.348042\pi\) | |||||||
\(44\) | −584.706 | −0.0455309 | ||||||||
\(45\) | −4946.76 | −0.364157 | ||||||||
\(46\) | 6736.99 | 0.469431 | ||||||||
\(47\) | −23443.2 | −1.54800 | −0.774002 | − | 0.633183i | \(-0.781748\pi\) | ||||
−0.774002 | + | 0.633183i | \(0.781748\pi\) | |||||||
\(48\) | 2304.00 | 0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 2418.70 | 0.136822 | ||||||||
\(51\) | −18549.4 | −0.998627 | ||||||||
\(52\) | 553.049 | 0.0283632 | ||||||||
\(53\) | −7030.30 | −0.343783 | −0.171891 | − | 0.985116i | \(-0.554988\pi\) | ||||
−0.171891 | + | 0.985116i | \(0.554988\pi\) | |||||||
\(54\) | 2916.00 | 0.136083 | ||||||||
\(55\) | 2231.79 | 0.0994825 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4070.14 | 0.165929 | ||||||||
\(58\) | −19060.9 | −0.744000 | ||||||||
\(59\) | −44222.8 | −1.65393 | −0.826964 | − | 0.562255i | \(-0.809934\pi\) | ||||
−0.826964 | + | 0.562255i | \(0.809934\pi\) | |||||||
\(60\) | −8794.23 | −0.315370 | ||||||||
\(61\) | 19380.5 | 0.666868 | 0.333434 | − | 0.942773i | \(-0.391793\pi\) | ||||
0.333434 | + | 0.942773i | \(0.391793\pi\) | |||||||
\(62\) | −21043.5 | −0.695245 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | −2110.96 | −0.0619721 | ||||||||
\(66\) | −1315.59 | −0.0371758 | ||||||||
\(67\) | 20944.1 | 0.569999 | 0.285000 | − | 0.958528i | \(-0.408007\pi\) | ||||
0.285000 | + | 0.958528i | \(0.408007\pi\) | |||||||
\(68\) | −32976.6 | −0.864836 | ||||||||
\(69\) | 15158.2 | 0.383289 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 79843.4 | 1.87972 | 0.939860 | − | 0.341560i | \(-0.110955\pi\) | ||||
0.939860 | + | 0.341560i | \(0.110955\pi\) | |||||||
\(72\) | 5184.00 | 0.117851 | ||||||||
\(73\) | −37065.8 | −0.814079 | −0.407039 | − | 0.913411i | \(-0.633439\pi\) | ||||
−0.407039 | + | 0.913411i | \(0.633439\pi\) | |||||||
\(74\) | −51287.8 | −1.08877 | ||||||||
\(75\) | 5442.08 | 0.111715 | ||||||||
\(76\) | 7235.81 | 0.143699 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1244.36 | 0.0231585 | ||||||||
\(79\) | 42072.0 | 0.758448 | 0.379224 | − | 0.925305i | \(-0.376191\pi\) | ||||
0.379224 | + | 0.925305i | \(0.376191\pi\) | |||||||
\(80\) | −15634.2 | −0.273118 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | −28506.9 | −0.468184 | ||||||||
\(83\) | −6311.34 | −0.100560 | −0.0502801 | − | 0.998735i | \(-0.516011\pi\) | ||||
−0.0502801 | + | 0.998735i | \(0.516011\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 125870. | 1.88962 | ||||||||
\(86\) | 44566.8 | 0.649778 | ||||||||
\(87\) | −42887.0 | −0.607473 | ||||||||
\(88\) | −2338.83 | −0.0321952 | ||||||||
\(89\) | −51495.8 | −0.689123 | −0.344562 | − | 0.938764i | \(-0.611972\pi\) | ||||
−0.344562 | + | 0.938764i | \(0.611972\pi\) | |||||||
\(90\) | −19787.0 | −0.257498 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 26948.0 | 0.331938 | ||||||||
\(93\) | −47347.8 | −0.567665 | ||||||||
\(94\) | −93772.8 | −1.09460 | ||||||||
\(95\) | −27618.7 | −0.313974 | ||||||||
\(96\) | 9216.00 | 0.102062 | ||||||||
\(97\) | −127357. | −1.37434 | −0.687171 | − | 0.726496i | \(-0.741148\pi\) | ||||
−0.687171 | + | 0.726496i | \(0.741148\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2960.08 | −0.0303539 | ||||||||
\(100\) | 9674.81 | 0.0967481 | ||||||||
\(101\) | 65757.9 | 0.641423 | 0.320712 | − | 0.947177i | \(-0.396078\pi\) | ||||
0.320712 | + | 0.947177i | \(0.396078\pi\) | |||||||
\(102\) | −74197.4 | −0.706136 | ||||||||
\(103\) | 170010. | 1.57900 | 0.789499 | − | 0.613751i | \(-0.210340\pi\) | ||||
0.789499 | + | 0.613751i | \(0.210340\pi\) | |||||||
\(104\) | 2212.20 | 0.0200558 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −28121.2 | −0.243091 | ||||||||
\(107\) | −107933. | −0.911369 | −0.455685 | − | 0.890141i | \(-0.650605\pi\) | ||||
−0.455685 | + | 0.890141i | \(0.650605\pi\) | |||||||
\(108\) | 11664.0 | 0.0962250 | ||||||||
\(109\) | −222698. | −1.79536 | −0.897679 | − | 0.440651i | \(-0.854748\pi\) | ||||
−0.897679 | + | 0.440651i | \(0.854748\pi\) | |||||||
\(110\) | 8927.16 | 0.0703448 | ||||||||
\(111\) | −115398. | −0.888975 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 181055. | 1.33387 | 0.666936 | − | 0.745115i | \(-0.267605\pi\) | ||||
0.666936 | + | 0.745115i | \(0.267605\pi\) | |||||||
\(114\) | 16280.6 | 0.117330 | ||||||||
\(115\) | −102859. | −0.725265 | ||||||||
\(116\) | −76243.5 | −0.526087 | ||||||||
\(117\) | 2799.81 | 0.0189088 | ||||||||
\(118\) | −176891. | −1.16950 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −35176.9 | −0.223000 | ||||||||
\(121\) | −159716. | −0.991708 | ||||||||
\(122\) | 77521.9 | 0.471547 | ||||||||
\(123\) | −64140.6 | −0.382270 | ||||||||
\(124\) | −84173.9 | −0.491613 | ||||||||
\(125\) | 153919. | 0.881083 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 91474.7 | 0.503259 | 0.251630 | − | 0.967824i | \(-0.419034\pi\) | ||||
0.251630 | + | 0.967824i | \(0.419034\pi\) | |||||||
\(128\) | 16384.0 | 0.0883883 | ||||||||
\(129\) | 100275. | 0.530541 | ||||||||
\(130\) | −8443.83 | −0.0438209 | ||||||||
\(131\) | −19343.9 | −0.0984840 | −0.0492420 | − | 0.998787i | \(-0.515681\pi\) | ||||
−0.0492420 | + | 0.998787i | \(0.515681\pi\) | |||||||
\(132\) | −5262.36 | −0.0262873 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 83776.3 | 0.403050 | ||||||||
\(135\) | −44520.8 | −0.210246 | ||||||||
\(136\) | −131906. | −0.611532 | ||||||||
\(137\) | −3077.04 | −0.0140065 | −0.00700327 | − | 0.999975i | \(-0.502229\pi\) | ||||
−0.00700327 | + | 0.999975i | \(0.502229\pi\) | |||||||
\(138\) | 60632.9 | 0.271026 | ||||||||
\(139\) | 370001. | 1.62430 | 0.812149 | − | 0.583450i | \(-0.198298\pi\) | ||||
0.812149 | + | 0.583450i | \(0.198298\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −210989. | −0.893741 | ||||||||
\(142\) | 319374. | 1.32916 | ||||||||
\(143\) | −1263.17 | −0.00516561 | ||||||||
\(144\) | 20736.0 | 0.0833333 | ||||||||
\(145\) | 291017. | 1.14947 | ||||||||
\(146\) | −148263. | −0.575641 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −205151. | −0.769875 | ||||||||
\(149\) | −454120. | −1.67573 | −0.837866 | − | 0.545875i | \(-0.816197\pi\) | ||||
−0.837866 | + | 0.545875i | \(0.816197\pi\) | |||||||
\(150\) | 21768.3 | 0.0789945 | ||||||||
\(151\) | 177592. | 0.633841 | 0.316921 | − | 0.948452i | \(-0.397351\pi\) | ||||
0.316921 | + | 0.948452i | \(0.397351\pi\) | |||||||
\(152\) | 28943.2 | 0.101610 | ||||||||
\(153\) | −166944. | −0.576558 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 321287. | 1.07415 | ||||||||
\(156\) | 4977.44 | 0.0163755 | ||||||||
\(157\) | −248981. | −0.806153 | −0.403076 | − | 0.915166i | \(-0.632059\pi\) | ||||
−0.403076 | + | 0.915166i | \(0.632059\pi\) | |||||||
\(158\) | 168288. | 0.536303 | ||||||||
\(159\) | −63272.7 | −0.198483 | ||||||||
\(160\) | −62536.8 | −0.193124 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 26244.0 | 0.0785674 | ||||||||
\(163\) | 202248. | 0.596231 | 0.298116 | − | 0.954530i | \(-0.403642\pi\) | ||||
0.298116 | + | 0.954530i | \(0.403642\pi\) | |||||||
\(164\) | −114028. | −0.331056 | ||||||||
\(165\) | 20086.1 | 0.0574363 | ||||||||
\(166\) | −25245.3 | −0.0711068 | ||||||||
\(167\) | 475790. | 1.32015 | 0.660076 | − | 0.751199i | \(-0.270524\pi\) | ||||
0.660076 | + | 0.751199i | \(0.270524\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −370098. | −0.996782 | ||||||||
\(170\) | 503479. | 1.33616 | ||||||||
\(171\) | 36631.3 | 0.0957992 | ||||||||
\(172\) | 178267. | 0.459462 | ||||||||
\(173\) | −284703. | −0.723231 | −0.361616 | − | 0.932327i | \(-0.617775\pi\) | ||||
−0.361616 | + | 0.932327i | \(0.617775\pi\) | |||||||
\(174\) | −171548. | −0.429548 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −9355.30 | −0.0227654 | ||||||||
\(177\) | −398005. | −0.954895 | ||||||||
\(178\) | −205983. | −0.487284 | ||||||||
\(179\) | 347958. | 0.811699 | 0.405849 | − | 0.913940i | \(-0.366976\pi\) | ||||
0.405849 | + | 0.913940i | \(0.366976\pi\) | |||||||
\(180\) | −79148.1 | −0.182079 | ||||||||
\(181\) | 379706. | 0.861492 | 0.430746 | − | 0.902473i | \(-0.358250\pi\) | ||||
0.430746 | + | 0.902473i | \(0.358250\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 174424. | 0.385016 | ||||||||
\(184\) | 107792. | 0.234715 | ||||||||
\(185\) | 783051. | 1.68213 | ||||||||
\(186\) | −189391. | −0.401400 | ||||||||
\(187\) | 75318.9 | 0.157507 | ||||||||
\(188\) | −375091. | −0.774002 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −110475. | −0.222013 | ||||||||
\(191\) | 194492. | 0.385762 | 0.192881 | − | 0.981222i | \(-0.438217\pi\) | ||||
0.192881 | + | 0.981222i | \(0.438217\pi\) | |||||||
\(192\) | 36864.0 | 0.0721688 | ||||||||
\(193\) | 877401. | 1.69553 | 0.847763 | − | 0.530375i | \(-0.177949\pi\) | ||||
0.847763 | + | 0.530375i | \(0.177949\pi\) | |||||||
\(194\) | −509430. | −0.971806 | ||||||||
\(195\) | −18998.6 | −0.0357796 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −752368. | −1.38123 | −0.690613 | − | 0.723225i | \(-0.742659\pi\) | ||||
−0.690613 | + | 0.723225i | \(0.742659\pi\) | |||||||
\(198\) | −11840.3 | −0.0214635 | ||||||||
\(199\) | −155453. | −0.278270 | −0.139135 | − | 0.990273i | \(-0.544432\pi\) | ||||
−0.139135 | + | 0.990273i | \(0.544432\pi\) | |||||||
\(200\) | 38699.2 | 0.0684112 | ||||||||
\(201\) | 188497. | 0.329089 | ||||||||
\(202\) | 263032. | 0.453555 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −296790. | −0.499313 | ||||||||
\(205\) | 435237. | 0.723339 | ||||||||
\(206\) | 680041. | 1.11652 | ||||||||
\(207\) | 136424. | 0.221292 | ||||||||
\(208\) | 8848.79 | 0.0141816 | ||||||||
\(209\) | −16526.7 | −0.0261709 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3898.23 | 0.00602783 | 0.00301391 | − | 0.999995i | \(-0.499041\pi\) | ||||
0.00301391 | + | 0.999995i | \(0.499041\pi\) | |||||||
\(212\) | −112485. | −0.171891 | ||||||||
\(213\) | 718591. | 1.08526 | ||||||||
\(214\) | −431731. | −0.644435 | ||||||||
\(215\) | −680435. | −1.00390 | ||||||||
\(216\) | 46656.0 | 0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −890794. | −1.26951 | ||||||||
\(219\) | −333592. | −0.470009 | ||||||||
\(220\) | 35708.6 | 0.0497413 | ||||||||
\(221\) | −71241.0 | −0.0981182 | ||||||||
\(222\) | −461590. | −0.628600 | ||||||||
\(223\) | 782574. | 1.05381 | 0.526906 | − | 0.849924i | \(-0.323352\pi\) | ||||
0.526906 | + | 0.849924i | \(0.323352\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 48978.7 | 0.0644987 | ||||||||
\(226\) | 724220. | 0.943190 | ||||||||
\(227\) | 796543. | 1.02599 | 0.512997 | − | 0.858391i | \(-0.328535\pi\) | ||||
0.512997 | + | 0.858391i | \(0.328535\pi\) | |||||||
\(228\) | 65122.3 | 0.0829645 | ||||||||
\(229\) | 387045. | 0.487722 | 0.243861 | − | 0.969810i | \(-0.421586\pi\) | ||||
0.243861 | + | 0.969810i | \(0.421586\pi\) | |||||||
\(230\) | −411435. | −0.512840 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −304974. | −0.372000 | ||||||||
\(233\) | −383759. | −0.463093 | −0.231547 | − | 0.972824i | \(-0.574379\pi\) | ||||
−0.231547 | + | 0.972824i | \(0.574379\pi\) | |||||||
\(234\) | 11199.2 | 0.0133705 | ||||||||
\(235\) | 1.43170e6 | 1.69115 | ||||||||
\(236\) | −707565. | −0.826964 | ||||||||
\(237\) | 378648. | 0.437890 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −465409. | −0.527036 | −0.263518 | − | 0.964654i | \(-0.584883\pi\) | ||||
−0.263518 | + | 0.964654i | \(0.584883\pi\) | |||||||
\(240\) | −140708. | −0.157685 | ||||||||
\(241\) | −348744. | −0.386781 | −0.193390 | − | 0.981122i | \(-0.561948\pi\) | ||||
−0.193390 | + | 0.981122i | \(0.561948\pi\) | |||||||
\(242\) | −638862. | −0.701243 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | 310088. | 0.333434 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −256563. | −0.270306 | ||||||||
\(247\) | 15631.9 | 0.0163030 | ||||||||
\(248\) | −336695. | −0.347623 | ||||||||
\(249\) | −56802.0 | −0.0580584 | ||||||||
\(250\) | 615676. | 0.623020 | ||||||||
\(251\) | −186543. | −0.186894 | −0.0934468 | − | 0.995624i | \(-0.529789\pi\) | ||||
−0.0934468 | + | 0.995624i | \(0.529789\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −61549.4 | −0.0604537 | ||||||||
\(254\) | 365899. | 0.355858 | ||||||||
\(255\) | 1.13283e6 | 1.09097 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | 1.55355e6 | 1.46721 | 0.733605 | − | 0.679577i | \(-0.237836\pi\) | ||||
0.733605 | + | 0.679577i | \(0.237836\pi\) | |||||||
\(258\) | 401101. | 0.375149 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −33775.3 | −0.0309860 | ||||||||
\(261\) | −385983. | −0.350725 | ||||||||
\(262\) | −77375.6 | −0.0696387 | ||||||||
\(263\) | −1.25960e6 | −1.12290 | −0.561451 | − | 0.827510i | \(-0.689757\pi\) | ||||
−0.561451 | + | 0.827510i | \(0.689757\pi\) | |||||||
\(264\) | −21049.4 | −0.0185879 | ||||||||
\(265\) | 429348. | 0.375573 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −463462. | −0.397866 | ||||||||
\(268\) | 335105. | 0.285000 | ||||||||
\(269\) | −170461. | −0.143630 | −0.0718149 | − | 0.997418i | \(-0.522879\pi\) | ||||
−0.0718149 | + | 0.997418i | \(0.522879\pi\) | |||||||
\(270\) | −178083. | −0.148667 | ||||||||
\(271\) | 2.22743e6 | 1.84239 | 0.921194 | − | 0.389104i | \(-0.127215\pi\) | ||||
0.921194 | + | 0.389104i | \(0.127215\pi\) | |||||||
\(272\) | −527626. | −0.432418 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −12308.1 | −0.00990412 | ||||||||
\(275\) | −22097.3 | −0.0176201 | ||||||||
\(276\) | 242532. | 0.191644 | ||||||||
\(277\) | 1.98339e6 | 1.55314 | 0.776568 | − | 0.630034i | \(-0.216959\pi\) | ||||
0.776568 | + | 0.630034i | \(0.216959\pi\) | |||||||
\(278\) | 1.48000e6 | 1.14855 | ||||||||
\(279\) | −426130. | −0.327742 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.16687e6 | −0.881573 | −0.440786 | − | 0.897612i | \(-0.645300\pi\) | ||||
−0.440786 | + | 0.897612i | \(0.645300\pi\) | |||||||
\(282\) | −843955. | −0.631970 | ||||||||
\(283\) | −1.90090e6 | −1.41089 | −0.705445 | − | 0.708765i | \(-0.749253\pi\) | ||||
−0.705445 | + | 0.708765i | \(0.749253\pi\) | |||||||
\(284\) | 1.27749e6 | 0.939860 | ||||||||
\(285\) | −248568. | −0.181273 | ||||||||
\(286\) | −5052.68 | −0.00365264 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 82944.0 | 0.0589256 | ||||||||
\(289\) | 2.82802e6 | 1.99177 | ||||||||
\(290\) | 1.16407e6 | 0.812799 | ||||||||
\(291\) | −1.14622e6 | −0.793477 | ||||||||
\(292\) | −593053. | −0.407039 | ||||||||
\(293\) | 1.65009e6 | 1.12289 | 0.561445 | − | 0.827514i | \(-0.310245\pi\) | ||||
0.561445 | + | 0.827514i | \(0.310245\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.70073e6 | 1.80687 | ||||||||
\(296\) | −820605. | −0.544384 | ||||||||
\(297\) | −26640.7 | −0.0175249 | ||||||||
\(298\) | −1.81648e6 | −1.18492 | ||||||||
\(299\) | 58217.0 | 0.0376593 | ||||||||
\(300\) | 87073.2 | 0.0558575 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 710367. | 0.448194 | ||||||||
\(303\) | 591821. | 0.370326 | ||||||||
\(304\) | 115773. | 0.0718494 | ||||||||
\(305\) | −1.18359e6 | −0.728535 | ||||||||
\(306\) | −667777. | −0.407688 | ||||||||
\(307\) | 597936. | 0.362084 | 0.181042 | − | 0.983475i | \(-0.442053\pi\) | ||||
0.181042 | + | 0.983475i | \(0.442053\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.53009e6 | 0.911635 | ||||||||
\(310\) | 1.28515e6 | 0.759536 | ||||||||
\(311\) | 230480. | 0.135124 | 0.0675620 | − | 0.997715i | \(-0.478478\pi\) | ||||
0.0675620 | + | 0.997715i | \(0.478478\pi\) | |||||||
\(312\) | 19909.8 | 0.0115792 | ||||||||
\(313\) | 442577. | 0.255346 | 0.127673 | − | 0.991816i | \(-0.459249\pi\) | ||||
0.127673 | + | 0.991816i | \(0.459249\pi\) | |||||||
\(314\) | −995925. | −0.570036 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 673152. | 0.379224 | ||||||||
\(317\) | −1.26248e6 | −0.705627 | −0.352813 | − | 0.935694i | \(-0.614775\pi\) | ||||
−0.352813 | + | 0.935694i | \(0.614775\pi\) | |||||||
\(318\) | −253091. | −0.140349 | ||||||||
\(319\) | 174141. | 0.0958129 | ||||||||
\(320\) | −250147. | −0.136559 | ||||||||
\(321\) | −971396. | −0.526179 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −932080. | −0.497104 | ||||||||
\(324\) | 104976. | 0.0555556 | ||||||||
\(325\) | 20901.0 | 0.0109763 | ||||||||
\(326\) | 808991. | 0.421599 | ||||||||
\(327\) | −2.00429e6 | −1.03655 | ||||||||
\(328\) | −456111. | −0.234092 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 80344.5 | 0.0406136 | ||||||||
\(331\) | −468936. | −0.235257 | −0.117629 | − | 0.993058i | \(-0.537529\pi\) | ||||
−0.117629 | + | 0.993058i | \(0.537529\pi\) | |||||||
\(332\) | −100981. | −0.0502801 | ||||||||
\(333\) | −1.03858e6 | −0.513250 | ||||||||
\(334\) | 1.90316e6 | 0.933489 | ||||||||
\(335\) | −1.27908e6 | −0.622708 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.46798e6 | −1.18377 | −0.591884 | − | 0.806023i | \(-0.701616\pi\) | ||||
−0.591884 | + | 0.806023i | \(0.701616\pi\) | |||||||
\(338\) | −1.48039e6 | −0.704831 | ||||||||
\(339\) | 1.62949e6 | 0.770112 | ||||||||
\(340\) | 2.01392e6 | 0.944810 | ||||||||
\(341\) | 192254. | 0.0895343 | ||||||||
\(342\) | 146525. | 0.0677402 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 713068. | 0.324889 | ||||||||
\(345\) | −925729. | −0.418732 | ||||||||
\(346\) | −1.13881e6 | −0.511402 | ||||||||
\(347\) | −4.28250e6 | −1.90930 | −0.954648 | − | 0.297736i | \(-0.903769\pi\) | ||||
−0.954648 | + | 0.297736i | \(0.903769\pi\) | |||||||
\(348\) | −686191. | −0.303737 | ||||||||
\(349\) | −1.84999e6 | −0.813028 | −0.406514 | − | 0.913645i | \(-0.633256\pi\) | ||||
−0.406514 | + | 0.913645i | \(0.633256\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 25198.3 | 0.0109170 | ||||||||
\(352\) | −37421.2 | −0.0160976 | ||||||||
\(353\) | −2.27380e6 | −0.971213 | −0.485607 | − | 0.874177i | \(-0.661401\pi\) | ||||
−0.485607 | + | 0.874177i | \(0.661401\pi\) | |||||||
\(354\) | −1.59202e6 | −0.675213 | ||||||||
\(355\) | −4.87612e6 | −2.05354 | ||||||||
\(356\) | −823933. | −0.344562 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.39183e6 | 0.573958 | ||||||||
\(359\) | −4.39992e6 | −1.80181 | −0.900905 | − | 0.434017i | \(-0.857096\pi\) | ||||
−0.900905 | + | 0.434017i | \(0.857096\pi\) | |||||||
\(360\) | −316592. | −0.128749 | ||||||||
\(361\) | −2.27158e6 | −0.917403 | ||||||||
\(362\) | 1.51882e6 | 0.609167 | ||||||||
\(363\) | −1.43744e6 | −0.572563 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.26365e6 | 0.889359 | ||||||||
\(366\) | 697697. | 0.272248 | ||||||||
\(367\) | −1.89743e6 | −0.735362 | −0.367681 | − | 0.929952i | \(-0.619848\pi\) | ||||
−0.367681 | + | 0.929952i | \(0.619848\pi\) | |||||||
\(368\) | 431168. | 0.165969 | ||||||||
\(369\) | −577266. | −0.220704 | ||||||||
\(370\) | 3.13220e6 | 1.18945 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −757565. | −0.283833 | ||||||||
\(373\) | 4.56260e6 | 1.69801 | 0.849005 | − | 0.528385i | \(-0.177202\pi\) | ||||
0.849005 | + | 0.528385i | \(0.177202\pi\) | |||||||
\(374\) | 301276. | 0.111374 | ||||||||
\(375\) | 1.38527e6 | 0.508694 | ||||||||
\(376\) | −1.50037e6 | −0.547302 | ||||||||
\(377\) | −164713. | −0.0596861 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.99400e6 | 1.78587 | 0.892936 | − | 0.450184i | \(-0.148642\pi\) | ||||
0.892936 | + | 0.450184i | \(0.148642\pi\) | |||||||
\(380\) | −441898. | −0.156987 | ||||||||
\(381\) | 823273. | 0.290557 | ||||||||
\(382\) | 777970. | 0.272775 | ||||||||
\(383\) | −3.67907e6 | −1.28157 | −0.640783 | − | 0.767722i | \(-0.721390\pi\) | ||||
−0.640783 | + | 0.767722i | \(0.721390\pi\) | |||||||
\(384\) | 147456. | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.50960e6 | 1.19892 | ||||||||
\(387\) | 902477. | 0.306308 | ||||||||
\(388\) | −2.03772e6 | −0.687171 | ||||||||
\(389\) | 257234. | 0.0861894 | 0.0430947 | − | 0.999071i | \(-0.486278\pi\) | ||||
0.0430947 | + | 0.999071i | \(0.486278\pi\) | |||||||
\(390\) | −75994.5 | −0.0253000 | ||||||||
\(391\) | −3.47130e6 | −1.14829 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −174095. | −0.0568598 | ||||||||
\(394\) | −3.00947e6 | −0.976674 | ||||||||
\(395\) | −2.56938e6 | −0.828583 | ||||||||
\(396\) | −47361.2 | −0.0151770 | ||||||||
\(397\) | 433280. | 0.137972 | 0.0689862 | − | 0.997618i | \(-0.478024\pi\) | ||||
0.0689862 | + | 0.997618i | \(0.478024\pi\) | |||||||
\(398\) | −621811. | −0.196766 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 154797. | 0.0483740 | ||||||||
\(401\) | −1.13824e6 | −0.353488 | −0.176744 | − | 0.984257i | \(-0.556556\pi\) | ||||
−0.176744 | + | 0.984257i | \(0.556556\pi\) | |||||||
\(402\) | 753987. | 0.232701 | ||||||||
\(403\) | −181845. | −0.0557749 | ||||||||
\(404\) | 1.05213e6 | 0.320712 | ||||||||
\(405\) | −400687. | −0.121386 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 468568. | 0.140212 | ||||||||
\(408\) | −1.18716e6 | −0.353068 | ||||||||
\(409\) | −5.02438e6 | −1.48516 | −0.742581 | − | 0.669756i | \(-0.766399\pi\) | ||||
−0.742581 | + | 0.669756i | \(0.766399\pi\) | |||||||
\(410\) | 1.74095e6 | 0.511478 | ||||||||
\(411\) | −27693.3 | −0.00808668 | ||||||||
\(412\) | 2.72016e6 | 0.789499 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 545696. | 0.156477 | ||||||||
\(415\) | 385440. | 0.109859 | ||||||||
\(416\) | 35395.2 | 0.0100279 | ||||||||
\(417\) | 3.33001e6 | 0.937789 | ||||||||
\(418\) | −66106.6 | −0.0185056 | ||||||||
\(419\) | −2.57295e6 | −0.715974 | −0.357987 | − | 0.933727i | \(-0.616537\pi\) | ||||
−0.357987 | + | 0.933727i | \(0.616537\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 336425. | 0.0925089 | 0.0462545 | − | 0.998930i | \(-0.485271\pi\) | ||||
0.0462545 | + | 0.998930i | \(0.485271\pi\) | |||||||
\(422\) | 15592.9 | 0.00426232 | ||||||||
\(423\) | −1.89890e6 | −0.516002 | ||||||||
\(424\) | −449939. | −0.121546 | ||||||||
\(425\) | −1.24626e6 | −0.334685 | ||||||||
\(426\) | 2.87436e6 | 0.767392 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −1.72693e6 | −0.455685 | ||||||||
\(429\) | −11368.5 | −0.00298237 | ||||||||
\(430\) | −2.72174e6 | −0.709864 | ||||||||
\(431\) | 236410. | 0.0613018 | 0.0306509 | − | 0.999530i | \(-0.490242\pi\) | ||||
0.0306509 | + | 0.999530i | \(0.490242\pi\) | |||||||
\(432\) | 186624. | 0.0481125 | ||||||||
\(433\) | −2.33004e6 | −0.597232 | −0.298616 | − | 0.954373i | \(-0.596525\pi\) | ||||
−0.298616 | + | 0.954373i | \(0.596525\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.61915e6 | 0.663648 | ||||||||
\(436\) | −3.56317e6 | −0.897679 | ||||||||
\(437\) | 761681. | 0.190796 | ||||||||
\(438\) | −1.33437e6 | −0.332346 | ||||||||
\(439\) | 3.19962e6 | 0.792387 | 0.396193 | − | 0.918167i | \(-0.370331\pi\) | ||||
0.396193 | + | 0.918167i | \(0.370331\pi\) | |||||||
\(440\) | 142835. | 0.0351724 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −284964. | −0.0693800 | ||||||||
\(443\) | 1.13240e6 | 0.274152 | 0.137076 | − | 0.990561i | \(-0.456230\pi\) | ||||
0.137076 | + | 0.990561i | \(0.456230\pi\) | |||||||
\(444\) | −1.84636e6 | −0.444487 | ||||||||
\(445\) | 3.14490e6 | 0.752848 | ||||||||
\(446\) | 3.13029e6 | 0.745157 | ||||||||
\(447\) | −4.08708e6 | −0.967485 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.23687e6 | −1.92817 | −0.964087 | − | 0.265585i | \(-0.914435\pi\) | ||||
−0.964087 | + | 0.265585i | \(0.914435\pi\) | |||||||
\(450\) | 195915. | 0.0456075 | ||||||||
\(451\) | 260441. | 0.0602931 | ||||||||
\(452\) | 2.89688e6 | 0.666936 | ||||||||
\(453\) | 1.59833e6 | 0.365949 | ||||||||
\(454\) | 3.18617e6 | 0.725487 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 260489. | 0.0586648 | ||||||||
\(457\) | −365132. | −0.0817824 | −0.0408912 | − | 0.999164i | \(-0.513020\pi\) | ||||
−0.0408912 | + | 0.999164i | \(0.513020\pi\) | |||||||
\(458\) | 1.54818e6 | 0.344872 | ||||||||
\(459\) | −1.50250e6 | −0.332876 | ||||||||
\(460\) | −1.64574e6 | −0.362633 | ||||||||
\(461\) | 332567. | 0.0728832 | 0.0364416 | − | 0.999336i | \(-0.488398\pi\) | ||||
0.0364416 | + | 0.999336i | \(0.488398\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.69992e6 | 0.368533 | 0.184266 | − | 0.982876i | \(-0.441009\pi\) | ||||
0.184266 | + | 0.982876i | \(0.441009\pi\) | |||||||
\(464\) | −1.21990e6 | −0.263044 | ||||||||
\(465\) | 2.89158e6 | 0.620159 | ||||||||
\(466\) | −1.53504e6 | −0.327456 | ||||||||
\(467\) | −990465. | −0.210159 | −0.105079 | − | 0.994464i | \(-0.533510\pi\) | ||||
−0.105079 | + | 0.994464i | \(0.533510\pi\) | |||||||
\(468\) | 44797.0 | 0.00945441 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 5.72681e6 | 1.19583 | ||||||||
\(471\) | −2.24083e6 | −0.465432 | ||||||||
\(472\) | −2.83026e6 | −0.584752 | ||||||||
\(473\) | −407164. | −0.0836789 | ||||||||
\(474\) | 1.51459e6 | 0.309635 | ||||||||
\(475\) | 273457. | 0.0556103 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −569454. | −0.114594 | ||||||||
\(478\) | −1.86164e6 | −0.372671 | ||||||||
\(479\) | −6.08065e6 | −1.21091 | −0.605454 | − | 0.795880i | \(-0.707009\pi\) | ||||
−0.605454 | + | 0.795880i | \(0.707009\pi\) | |||||||
\(480\) | −562831. | −0.111500 | ||||||||
\(481\) | −443198. | −0.0873445 | ||||||||
\(482\) | −1.39498e6 | −0.273495 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.55545e6 | −0.495854 | ||||||||
\(485\) | 7.77785e6 | 1.50143 | ||||||||
\(486\) | 236196. | 0.0453609 | ||||||||
\(487\) | −6.71098e6 | −1.28222 | −0.641112 | − | 0.767448i | \(-0.721526\pi\) | ||||
−0.641112 | + | 0.767448i | \(0.721526\pi\) | |||||||
\(488\) | 1.24035e6 | 0.235773 | ||||||||
\(489\) | 1.82023e6 | 0.344234 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −914042. | −0.171105 | −0.0855525 | − | 0.996334i | \(-0.527266\pi\) | ||||
−0.0855525 | + | 0.996334i | \(0.527266\pi\) | |||||||
\(492\) | −1.02625e6 | −0.191135 | ||||||||
\(493\) | 9.82130e6 | 1.81992 | ||||||||
\(494\) | 62527.5 | 0.0115280 | ||||||||
\(495\) | 180775. | 0.0331608 | ||||||||
\(496\) | −1.34678e6 | −0.245806 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −227208. | −0.0410535 | ||||||||
\(499\) | −7.75492e6 | −1.39420 | −0.697101 | − | 0.716972i | \(-0.745527\pi\) | ||||
−0.697101 | + | 0.716972i | \(0.745527\pi\) | |||||||
\(500\) | 2.46270e6 | 0.440542 | ||||||||
\(501\) | 4.28211e6 | 0.762190 | ||||||||
\(502\) | −746172. | −0.132154 | ||||||||
\(503\) | −3.79381e6 | −0.668584 | −0.334292 | − | 0.942470i | \(-0.608497\pi\) | ||||
−0.334292 | + | 0.942470i | \(0.608497\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.01591e6 | −0.700737 | ||||||||
\(506\) | −246198. | −0.0427472 | ||||||||
\(507\) | −3.33088e6 | −0.575492 | ||||||||
\(508\) | 1.46360e6 | 0.251630 | ||||||||
\(509\) | −8.53160e6 | −1.45961 | −0.729804 | − | 0.683657i | \(-0.760389\pi\) | ||||
−0.729804 | + | 0.683657i | \(0.760389\pi\) | |||||||
\(510\) | 4.53131e6 | 0.771434 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 262144. | 0.0441942 | ||||||||
\(513\) | 329681. | 0.0553097 | ||||||||
\(514\) | 6.21419e6 | 1.03747 | ||||||||
\(515\) | −1.03827e7 | −1.72501 | ||||||||
\(516\) | 1.60440e6 | 0.265271 | ||||||||
\(517\) | 856712. | 0.140964 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.56233e6 | −0.417558 | ||||||||
\(520\) | −135101. | −0.0219104 | ||||||||
\(521\) | 3.19066e6 | 0.514976 | 0.257488 | − | 0.966282i | \(-0.417105\pi\) | ||||
0.257488 | + | 0.966282i | \(0.417105\pi\) | |||||||
\(522\) | −1.54393e6 | −0.248000 | ||||||||
\(523\) | 9.60678e6 | 1.53576 | 0.767880 | − | 0.640593i | \(-0.221311\pi\) | ||||
0.767880 | + | 0.640593i | \(0.221311\pi\) | |||||||
\(524\) | −309502. | −0.0492420 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.03838e6 | −0.794012 | ||||||||
\(527\) | 1.08429e7 | 1.70066 | ||||||||
\(528\) | −84197.7 | −0.0131436 | ||||||||
\(529\) | −3.59965e6 | −0.559270 | ||||||||
\(530\) | 1.71739e6 | 0.265570 | ||||||||
\(531\) | −3.58205e6 | −0.551309 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −246340. | −0.0375592 | ||||||||
\(534\) | −1.85385e6 | −0.281333 | ||||||||
\(535\) | 6.59158e6 | 0.995646 | ||||||||
\(536\) | 1.34042e6 | 0.201525 | ||||||||
\(537\) | 3.13163e6 | 0.468634 | ||||||||
\(538\) | −681844. | −0.101562 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −712333. | −0.105123 | ||||||||
\(541\) | 1.02366e7 | 1.50371 | 0.751855 | − | 0.659328i | \(-0.229159\pi\) | ||||
0.751855 | + | 0.659328i | \(0.229159\pi\) | |||||||
\(542\) | 8.90972e6 | 1.30276 | ||||||||
\(543\) | 3.41736e6 | 0.497383 | ||||||||
\(544\) | −2.11050e6 | −0.305766 | ||||||||
\(545\) | 1.36004e7 | 1.96138 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.27757e6 | −1.32576 | −0.662882 | − | 0.748724i | \(-0.730667\pi\) | ||||
−0.662882 | + | 0.748724i | \(0.730667\pi\) | |||||||
\(548\) | −49232.6 | −0.00700327 | ||||||||
\(549\) | 1.56982e6 | 0.222289 | ||||||||
\(550\) | −88389.4 | −0.0124593 | ||||||||
\(551\) | −2.15501e6 | −0.302392 | ||||||||
\(552\) | 970127. | 0.135513 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 7.93357e6 | 1.09823 | ||||||||
\(555\) | 7.04745e6 | 0.971180 | ||||||||
\(556\) | 5.92001e6 | 0.812149 | ||||||||
\(557\) | 620098. | 0.0846881 | 0.0423441 | − | 0.999103i | \(-0.486517\pi\) | ||||
0.0423441 | + | 0.999103i | \(0.486517\pi\) | |||||||
\(558\) | −1.70452e6 | −0.231748 | ||||||||
\(559\) | 385119. | 0.0521273 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 677870. | 0.0909368 | ||||||||
\(562\) | −4.66750e6 | −0.623366 | ||||||||
\(563\) | −7.36664e6 | −0.979487 | −0.489744 | − | 0.871867i | \(-0.662910\pi\) | ||||
−0.489744 | + | 0.871867i | \(0.662910\pi\) | |||||||
\(564\) | −3.37582e6 | −0.446871 | ||||||||
\(565\) | −1.10572e7 | −1.45722 | ||||||||
\(566\) | −7.60360e6 | −0.997650 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5.10998e6 | 0.664581 | ||||||||
\(569\) | 3.68222e6 | 0.476792 | 0.238396 | − | 0.971168i | \(-0.423378\pi\) | ||||
0.238396 | + | 0.971168i | \(0.423378\pi\) | |||||||
\(570\) | −994272. | −0.128179 | ||||||||
\(571\) | 1.03320e7 | 1.32615 | 0.663077 | − | 0.748551i | \(-0.269250\pi\) | ||||
0.663077 | + | 0.748551i | \(0.269250\pi\) | |||||||
\(572\) | −20210.7 | −0.00258281 | ||||||||
\(573\) | 1.75043e6 | 0.222720 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.01842e6 | 0.128457 | ||||||||
\(576\) | 331776. | 0.0416667 | ||||||||
\(577\) | 1.25123e7 | 1.56458 | 0.782292 | − | 0.622911i | \(-0.214050\pi\) | ||||
0.782292 | + | 0.622911i | \(0.214050\pi\) | |||||||
\(578\) | 1.13121e7 | 1.40839 | ||||||||
\(579\) | 7.89661e6 | 0.978913 | ||||||||
\(580\) | 4.65627e6 | 0.574736 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −4.58487e6 | −0.561073 | ||||||||
\(583\) | 256916. | 0.0313055 | ||||||||
\(584\) | −2.37221e6 | −0.287820 | ||||||||
\(585\) | −170988. | −0.0206574 | ||||||||
\(586\) | 6.60034e6 | 0.794004 | ||||||||
\(587\) | 1.60865e7 | 1.92694 | 0.963468 | − | 0.267823i | \(-0.0863042\pi\) | ||||
0.963468 | + | 0.267823i | \(0.0863042\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.37916e6 | −0.282577 | ||||||||
\(590\) | 1.08029e7 | 1.27765 | ||||||||
\(591\) | −6.77131e6 | −0.797451 | ||||||||
\(592\) | −3.28242e6 | −0.384937 | ||||||||
\(593\) | 9.46330e6 | 1.10511 | 0.552556 | − | 0.833476i | \(-0.313653\pi\) | ||||
0.552556 | + | 0.833476i | \(0.313653\pi\) | |||||||
\(594\) | −106563. | −0.0123919 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −7.26592e6 | −0.837866 | ||||||||
\(597\) | −1.39908e6 | −0.160659 | ||||||||
\(598\) | 232868. | 0.0266291 | ||||||||
\(599\) | 5.01498e6 | 0.571087 | 0.285544 | − | 0.958366i | \(-0.407826\pi\) | ||||
0.285544 | + | 0.958366i | \(0.407826\pi\) | |||||||
\(600\) | 348293. | 0.0394972 | ||||||||
\(601\) | −1.26473e7 | −1.42828 | −0.714139 | − | 0.700004i | \(-0.753182\pi\) | ||||
−0.714139 | + | 0.700004i | \(0.753182\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.69647e6 | 0.190000 | ||||||||
\(604\) | 2.84147e6 | 0.316921 | ||||||||
\(605\) | 9.75400e6 | 1.08341 | ||||||||
\(606\) | 2.36729e6 | 0.261860 | ||||||||
\(607\) | 2.87702e6 | 0.316936 | 0.158468 | − | 0.987364i | \(-0.449345\pi\) | ||||
0.158468 | + | 0.987364i | \(0.449345\pi\) | |||||||
\(608\) | 463092. | 0.0508052 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.73434e6 | −0.515152 | ||||||||
\(611\) | −810328. | −0.0878128 | ||||||||
\(612\) | −2.67111e6 | −0.288279 | ||||||||
\(613\) | −3.72582e6 | −0.400471 | −0.200236 | − | 0.979748i | \(-0.564171\pi\) | ||||
−0.200236 | + | 0.979748i | \(0.564171\pi\) | |||||||
\(614\) | 2.39174e6 | 0.256032 | ||||||||
\(615\) | 3.91714e6 | 0.417620 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.15861e7 | −1.22525 | −0.612625 | − | 0.790374i | \(-0.709886\pi\) | ||||
−0.612625 | + | 0.790374i | \(0.709886\pi\) | |||||||
\(618\) | 6.12037e6 | 0.644624 | ||||||||
\(619\) | −1.85608e6 | −0.194702 | −0.0973508 | − | 0.995250i | \(-0.531037\pi\) | ||||
−0.0973508 | + | 0.995250i | \(0.531037\pi\) | |||||||
\(620\) | 5.14059e6 | 0.537073 | ||||||||
\(621\) | 1.22782e6 | 0.127763 | ||||||||
\(622\) | 921921. | 0.0955471 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 79639.1 | 0.00818776 | ||||||||
\(625\) | −1.12896e7 | −1.15606 | ||||||||
\(626\) | 1.77031e6 | 0.180557 | ||||||||
\(627\) | −148740. | −0.0151098 | ||||||||
\(628\) | −3.98370e6 | −0.403076 | ||||||||
\(629\) | 2.64266e7 | 2.66326 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.92135e6 | 0.891984 | 0.445992 | − | 0.895037i | \(-0.352851\pi\) | ||||
0.445992 | + | 0.895037i | \(0.352851\pi\) | |||||||
\(632\) | 2.69261e6 | 0.268152 | ||||||||
\(633\) | 35084.0 | 0.00348017 | ||||||||
\(634\) | −5.04990e6 | −0.498953 | ||||||||
\(635\) | −5.58646e6 | −0.549797 | ||||||||
\(636\) | −1.01236e6 | −0.0992415 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 696563. | 0.0677499 | ||||||||
\(639\) | 6.46731e6 | 0.626573 | ||||||||
\(640\) | −1.00059e6 | −0.0965618 | ||||||||
\(641\) | 1.31866e7 | 1.26762 | 0.633810 | − | 0.773489i | \(-0.281490\pi\) | ||||
0.633810 | + | 0.773489i | \(0.281490\pi\) | |||||||
\(642\) | −3.88558e6 | −0.372065 | ||||||||
\(643\) | −9.67813e6 | −0.923132 | −0.461566 | − | 0.887106i | \(-0.652712\pi\) | ||||
−0.461566 | + | 0.887106i | \(0.652712\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.12391e6 | −0.579602 | ||||||||
\(646\) | −3.72832e6 | −0.351505 | ||||||||
\(647\) | −1.72491e6 | −0.161996 | −0.0809982 | − | 0.996714i | \(-0.525811\pi\) | ||||
−0.0809982 | + | 0.996714i | \(0.525811\pi\) | |||||||
\(648\) | 419904. | 0.0392837 | ||||||||
\(649\) | 1.61609e6 | 0.150610 | ||||||||
\(650\) | 83603.8 | 0.00776145 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.23596e6 | 0.298116 | ||||||||
\(653\) | 597510. | 0.0548356 | 0.0274178 | − | 0.999624i | \(-0.491272\pi\) | ||||
0.0274178 | + | 0.999624i | \(0.491272\pi\) | |||||||
\(654\) | −8.01714e6 | −0.732951 | ||||||||
\(655\) | 1.18135e6 | 0.107591 | ||||||||
\(656\) | −1.82444e6 | −0.165528 | ||||||||
\(657\) | −3.00233e6 | −0.271360 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.47605e7 | 1.32400 | 0.662001 | − | 0.749503i | \(-0.269707\pi\) | ||||
0.662001 | + | 0.749503i | \(0.269707\pi\) | |||||||
\(660\) | 321378. | 0.0287181 | ||||||||
\(661\) | 1.69041e7 | 1.50484 | 0.752418 | − | 0.658686i | \(-0.228888\pi\) | ||||
0.752418 | + | 0.658686i | \(0.228888\pi\) | |||||||
\(662\) | −1.87574e6 | −0.166352 | ||||||||
\(663\) | −641169. | −0.0566486 | ||||||||
\(664\) | −403925. | −0.0355534 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4.15431e6 | −0.362922 | ||||||||
\(667\) | −8.02581e6 | −0.698512 | ||||||||
\(668\) | 7.61264e6 | 0.660076 | ||||||||
\(669\) | 7.04316e6 | 0.608418 | ||||||||
\(670\) | −5.11631e6 | −0.440321 | ||||||||
\(671\) | −708243. | −0.0607262 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.58960e7 | −1.35285 | −0.676425 | − | 0.736512i | \(-0.736472\pi\) | ||||
−0.676425 | + | 0.736512i | \(0.736472\pi\) | |||||||
\(674\) | −9.87191e6 | −0.837050 | ||||||||
\(675\) | 440808. | 0.0372383 | ||||||||
\(676\) | −5.92157e6 | −0.498391 | ||||||||
\(677\) | −1.95361e6 | −0.163820 | −0.0819099 | − | 0.996640i | \(-0.526102\pi\) | ||||
−0.0819099 | + | 0.996640i | \(0.526102\pi\) | |||||||
\(678\) | 6.51798e6 | 0.544551 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 8.05567e6 | 0.668081 | ||||||||
\(681\) | 7.16889e6 | 0.592357 | ||||||||
\(682\) | 769016. | 0.0633103 | ||||||||
\(683\) | −9.23970e6 | −0.757890 | −0.378945 | − | 0.925419i | \(-0.623713\pi\) | ||||
−0.378945 | + | 0.925419i | \(0.623713\pi\) | |||||||
\(684\) | 586100. | 0.0478996 | ||||||||
\(685\) | 187918. | 0.0153018 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.48340e6 | 0.281587 | ||||||||
\(688\) | 2.85227e6 | 0.229731 | ||||||||
\(689\) | −243006. | −0.0195016 | ||||||||
\(690\) | −3.70292e6 | −0.296088 | ||||||||
\(691\) | −1.45698e7 | −1.16080 | −0.580401 | − | 0.814331i | \(-0.697104\pi\) | ||||
−0.580401 | + | 0.814331i | \(0.697104\pi\) | |||||||
\(692\) | −4.55525e6 | −0.361616 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.71300e7 | −1.35008 | ||||||||
\(695\) | −2.25964e7 | −1.77450 | ||||||||
\(696\) | −2.74476e6 | −0.214774 | ||||||||
\(697\) | 1.46885e7 | 1.14524 | ||||||||
\(698\) | −7.39995e6 | −0.574898 | ||||||||
\(699\) | −3.45383e6 | −0.267367 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.70190e6 | −0.284531 | −0.142266 | − | 0.989829i | \(-0.545439\pi\) | ||||
−0.142266 | + | 0.989829i | \(0.545439\pi\) | |||||||
\(702\) | 100793. | 0.00771949 | ||||||||
\(703\) | −5.79858e6 | −0.442520 | ||||||||
\(704\) | −149685. | −0.0113827 | ||||||||
\(705\) | 1.28853e7 | 0.976387 | ||||||||
\(706\) | −9.09518e6 | −0.686751 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −6.36809e6 | −0.477448 | ||||||||
\(709\) | −2.52937e7 | −1.88971 | −0.944857 | − | 0.327484i | \(-0.893799\pi\) | ||||
−0.944857 | + | 0.327484i | \(0.893799\pi\) | |||||||
\(710\) | −1.95045e7 | −1.45207 | ||||||||
\(711\) | 3.40783e6 | 0.252816 | ||||||||
\(712\) | −3.29573e6 | −0.243642 | ||||||||
\(713\) | −8.86061e6 | −0.652739 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 77143.1 | 0.00564329 | ||||||||
\(716\) | 5.56734e6 | 0.405849 | ||||||||
\(717\) | −4.18868e6 | −0.304284 | ||||||||
\(718\) | −1.75997e7 | −1.27407 | ||||||||
\(719\) | 1.45185e7 | 1.04737 | 0.523683 | − | 0.851913i | \(-0.324557\pi\) | ||||
0.523683 | + | 0.851913i | \(0.324557\pi\) | |||||||
\(720\) | −1.26637e6 | −0.0910394 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −9.08632e6 | −0.648702 | ||||||||
\(723\) | −3.13870e6 | −0.223308 | ||||||||
\(724\) | 6.07530e6 | 0.430746 | ||||||||
\(725\) | −2.88141e6 | −0.203592 | ||||||||
\(726\) | −5.74976e6 | −0.404863 | ||||||||
\(727\) | −1.42855e7 | −1.00244 | −0.501222 | − | 0.865319i | \(-0.667116\pi\) | ||||
−0.501222 | + | 0.865319i | \(0.667116\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 9.05460e6 | 0.628872 | ||||||||
\(731\) | −2.29635e7 | −1.58944 | ||||||||
\(732\) | 2.79079e6 | 0.192508 | ||||||||
\(733\) | −8.21556e6 | −0.564777 | −0.282389 | − | 0.959300i | \(-0.591127\pi\) | ||||
−0.282389 | + | 0.959300i | \(0.591127\pi\) | |||||||
\(734\) | −7.58973e6 | −0.519979 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.72467e6 | 0.117358 | ||||||||
\(737\) | −765384. | −0.0519052 | ||||||||
\(738\) | −2.30906e6 | −0.156061 | ||||||||
\(739\) | −3.43896e6 | −0.231641 | −0.115821 | − | 0.993270i | \(-0.536950\pi\) | ||||
−0.115821 | + | 0.993270i | \(0.536950\pi\) | |||||||
\(740\) | 1.25288e7 | 0.841067 | ||||||||
\(741\) | 140687. | 0.00941256 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.53588e6 | 0.102067 | 0.0510334 | − | 0.998697i | \(-0.483748\pi\) | ||||
0.0510334 | + | 0.998697i | \(0.483748\pi\) | |||||||
\(744\) | −3.03026e6 | −0.200700 | ||||||||
\(745\) | 2.77336e7 | 1.83069 | ||||||||
\(746\) | 1.82504e7 | 1.20067 | ||||||||
\(747\) | −511218. | −0.0335201 | ||||||||
\(748\) | 1.20510e6 | 0.0787535 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 5.54108e6 | 0.359701 | ||||||||
\(751\) | −2.01146e7 | −1.30140 | −0.650700 | − | 0.759335i | \(-0.725524\pi\) | ||||
−0.650700 | + | 0.759335i | \(0.725524\pi\) | |||||||
\(752\) | −6.00146e6 | −0.387001 | ||||||||
\(753\) | −1.67889e6 | −0.107903 | ||||||||
\(754\) | −658850. | −0.0422044 | ||||||||
\(755\) | −1.08457e7 | −0.692454 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 202045. | 0.0128147 | 0.00640733 | − | 0.999979i | \(-0.497960\pi\) | ||||
0.00640733 | + | 0.999979i | \(0.497960\pi\) | |||||||
\(758\) | 1.99760e7 | 1.26280 | ||||||||
\(759\) | −553945. | −0.0349029 | ||||||||
\(760\) | −1.76759e6 | −0.111007 | ||||||||
\(761\) | −1.08202e6 | −0.0677290 | −0.0338645 | − | 0.999426i | \(-0.510781\pi\) | ||||
−0.0338645 | + | 0.999426i | \(0.510781\pi\) | |||||||
\(762\) | 3.29309e6 | 0.205455 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 3.11188e6 | 0.192881 | ||||||||
\(765\) | 1.01955e7 | 0.629873 | ||||||||
\(766\) | −1.47163e7 | −0.906205 | ||||||||
\(767\) | −1.52859e6 | −0.0938214 | ||||||||
\(768\) | 589824. | 0.0360844 | ||||||||
\(769\) | 1.19305e7 | 0.727517 | 0.363759 | − | 0.931493i | \(-0.381493\pi\) | ||||
0.363759 | + | 0.931493i | \(0.381493\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.39819e7 | 0.847094 | ||||||||
\(772\) | 1.40384e7 | 0.847763 | ||||||||
\(773\) | −6.58657e6 | −0.396470 | −0.198235 | − | 0.980155i | \(-0.563521\pi\) | ||||
−0.198235 | + | 0.980155i | \(0.563521\pi\) | |||||||
\(774\) | 3.60991e6 | 0.216593 | ||||||||
\(775\) | −3.18112e6 | −0.190250 | ||||||||
\(776\) | −8.15087e6 | −0.485903 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.02894e6 | 0.0609451 | ||||||||
\(779\) | −3.22298e6 | −0.190289 | ||||||||
\(780\) | −303978. | −0.0178898 | ||||||||
\(781\) | −2.91781e6 | −0.171171 | ||||||||
\(782\) | −1.38852e7 | −0.811961 | ||||||||
\(783\) | −3.47384e6 | −0.202491 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.52055e7 | 0.880700 | ||||||||
\(786\) | −696380. | −0.0402059 | ||||||||
\(787\) | −1.92720e7 | −1.10915 | −0.554575 | − | 0.832134i | \(-0.687119\pi\) | ||||
−0.554575 | + | 0.832134i | \(0.687119\pi\) | |||||||
\(788\) | −1.20379e7 | −0.690613 | ||||||||
\(789\) | −1.13364e7 | −0.648308 | ||||||||
\(790\) | −1.02775e7 | −0.585897 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −189445. | −0.0107317 | ||||||||
\(793\) | 669897. | 0.0378290 | ||||||||
\(794\) | 1.73312e6 | 0.0975613 | ||||||||
\(795\) | 3.86413e6 | 0.216837 | ||||||||
\(796\) | −2.48724e6 | −0.139135 | ||||||||
\(797\) | 1.54906e7 | 0.863816 | 0.431908 | − | 0.901918i | \(-0.357841\pi\) | ||||
0.431908 | + | 0.901918i | \(0.357841\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.83174e7 | 2.67754 | ||||||||
\(800\) | 619188. | 0.0342056 | ||||||||
\(801\) | −4.17116e6 | −0.229708 | ||||||||
\(802\) | −4.55298e6 | −0.249954 | ||||||||
\(803\) | 1.35454e6 | 0.0741315 | ||||||||
\(804\) | 3.01595e6 | 0.164545 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −727380. | −0.0394388 | ||||||||
\(807\) | −1.53415e6 | −0.0829247 | ||||||||
\(808\) | 4.20851e6 | 0.226777 | ||||||||
\(809\) | −1.77071e6 | −0.0951210 | −0.0475605 | − | 0.998868i | \(-0.515145\pi\) | ||||
−0.0475605 | + | 0.998868i | \(0.515145\pi\) | |||||||
\(810\) | −1.60275e6 | −0.0858327 | ||||||||
\(811\) | 6.80547e6 | 0.363334 | 0.181667 | − | 0.983360i | \(-0.441851\pi\) | ||||
0.181667 | + | 0.983360i | \(0.441851\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.00469e7 | 1.06370 | ||||||||
\(814\) | 1.87427e6 | 0.0991451 | ||||||||
\(815\) | −1.23515e7 | −0.651366 | ||||||||
\(816\) | −4.74863e6 | −0.249657 | ||||||||
\(817\) | 5.03869e6 | 0.264097 | ||||||||
\(818\) | −2.00975e7 | −1.05017 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.96380e6 | 0.361669 | ||||||||
\(821\) | 2.27127e7 | 1.17601 | 0.588006 | − | 0.808857i | \(-0.299913\pi\) | ||||
0.588006 | + | 0.808857i | \(0.299913\pi\) | |||||||
\(822\) | −110773. | −0.00571815 | ||||||||
\(823\) | −3.03576e7 | −1.56231 | −0.781156 | − | 0.624336i | \(-0.785370\pi\) | ||||
−0.781156 | + | 0.624336i | \(0.785370\pi\) | |||||||
\(824\) | 1.08807e7 | 0.558260 | ||||||||
\(825\) | −198876. | −0.0101730 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −5.80776e6 | −0.295287 | −0.147644 | − | 0.989041i | \(-0.547169\pi\) | ||||
−0.147644 | + | 0.989041i | \(0.547169\pi\) | |||||||
\(828\) | 2.18279e6 | 0.110646 | ||||||||
\(829\) | −9.04916e6 | −0.457322 | −0.228661 | − | 0.973506i | \(-0.573435\pi\) | ||||
−0.228661 | + | 0.973506i | \(0.573435\pi\) | |||||||
\(830\) | 1.54176e6 | 0.0776822 | ||||||||
\(831\) | 1.78505e7 | 0.896703 | ||||||||
\(832\) | 141581. | 0.00709080 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 1.33200e7 | 0.663117 | ||||||||
\(835\) | −2.90570e7 | −1.44223 | ||||||||
\(836\) | −264426. | −0.0130855 | ||||||||
\(837\) | −3.83517e6 | −0.189222 | ||||||||
\(838\) | −1.02918e7 | −0.506270 | ||||||||
\(839\) | −8.17101e6 | −0.400747 | −0.200374 | − | 0.979720i | \(-0.564216\pi\) | ||||
−0.200374 | + | 0.979720i | \(0.564216\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.19614e6 | 0.107071 | ||||||||
\(842\) | 1.34570e6 | 0.0654137 | ||||||||
\(843\) | −1.05019e7 | −0.508976 | ||||||||
\(844\) | 62371.6 | 0.00301391 | ||||||||
\(845\) | 2.26023e7 | 1.08896 | ||||||||
\(846\) | −7.59560e6 | −0.364868 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −1.79976e6 | −0.0859457 | ||||||||
\(849\) | −1.71081e7 | −0.814578 | ||||||||
\(850\) | −4.98504e6 | −0.236658 | ||||||||
\(851\) | −2.15954e7 | −1.02220 | ||||||||
\(852\) | 1.14974e7 | 0.542628 | ||||||||
\(853\) | 2.88437e7 | 1.35731 | 0.678654 | − | 0.734458i | \(-0.262564\pi\) | ||||
0.678654 | + | 0.734458i | \(0.262564\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.23711e6 | −0.104658 | ||||||||
\(856\) | −6.90770e6 | −0.322218 | ||||||||
\(857\) | −2.69462e7 | −1.25327 | −0.626637 | − | 0.779311i | \(-0.715569\pi\) | ||||
−0.626637 | + | 0.779311i | \(0.715569\pi\) | |||||||
\(858\) | −45474.1 | −0.00210885 | ||||||||
\(859\) | −7.49124e6 | −0.346394 | −0.173197 | − | 0.984887i | \(-0.555410\pi\) | ||||
−0.173197 | + | 0.984887i | \(0.555410\pi\) | |||||||
\(860\) | −1.08870e7 | −0.501950 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 945641. | 0.0433469 | ||||||||
\(863\) | −1.41552e6 | −0.0646977 | −0.0323489 | − | 0.999477i | \(-0.510299\pi\) | ||||
−0.0323489 | + | 0.999477i | \(0.510299\pi\) | |||||||
\(864\) | 746496. | 0.0340207 | ||||||||
\(865\) | 1.73871e7 | 0.790110 | ||||||||
\(866\) | −9.32015e6 | −0.422307 | ||||||||
\(867\) | 2.54522e7 | 1.14995 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.53749e6 | −0.0690656 | ||||||||
\(870\) | 1.04766e7 | 0.469270 | ||||||||
\(871\) | 723944. | 0.0323340 | ||||||||
\(872\) | −1.42527e7 | −0.634755 | ||||||||
\(873\) | −1.03159e7 | −0.458114 | ||||||||
\(874\) | 3.04672e6 | 0.134913 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −5.33748e6 | −0.235004 | ||||||||
\(877\) | 2.55232e7 | 1.12056 | 0.560281 | − | 0.828303i | \(-0.310693\pi\) | ||||
0.560281 | + | 0.828303i | \(0.310693\pi\) | |||||||
\(878\) | 1.27985e7 | 0.560302 | ||||||||
\(879\) | 1.48508e7 | 0.648301 | ||||||||
\(880\) | 571338. | 0.0248706 | ||||||||
\(881\) | −2.07516e6 | −0.0900764 | −0.0450382 | − | 0.998985i | \(-0.514341\pi\) | ||||
−0.0450382 | + | 0.998985i | \(0.514341\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.80641e7 | 0.779677 | 0.389839 | − | 0.920883i | \(-0.372531\pi\) | ||||
0.389839 | + | 0.920883i | \(0.372531\pi\) | |||||||
\(884\) | −1.13986e6 | −0.0490591 | ||||||||
\(885\) | 2.43066e7 | 1.04320 | ||||||||
\(886\) | 4.52961e6 | 0.193855 | ||||||||
\(887\) | −9.28389e6 | −0.396206 | −0.198103 | − | 0.980181i | \(-0.563478\pi\) | ||||
−0.198103 | + | 0.980181i | \(0.563478\pi\) | |||||||
\(888\) | −7.38545e6 | −0.314300 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 1.25796e7 | 0.532344 | ||||||||
\(891\) | −239766. | −0.0101180 | ||||||||
\(892\) | 1.25212e7 | 0.526906 | ||||||||
\(893\) | −1.06019e7 | −0.444893 | ||||||||
\(894\) | −1.63483e7 | −0.684115 | ||||||||
\(895\) | −2.12502e7 | −0.886758 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 523953. | 0.0217426 | ||||||||
\(898\) | −3.29475e7 | −1.36343 | ||||||||
\(899\) | 2.50692e7 | 1.03452 | ||||||||
\(900\) | 783659. | 0.0322494 | ||||||||
\(901\) | 1.44897e7 | 0.594631 | ||||||||
\(902\) | 1.04176e6 | 0.0426336 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.15875e7 | 0.471595 | ||||||||
\(905\) | −2.31891e7 | −0.941156 | ||||||||
\(906\) | 6.39331e6 | 0.258765 | ||||||||
\(907\) | −4.20818e7 | −1.69854 | −0.849270 | − | 0.527958i | \(-0.822958\pi\) | ||||
−0.849270 | + | 0.527958i | \(0.822958\pi\) | |||||||
\(908\) | 1.27447e7 | 0.512997 | ||||||||
\(909\) | 5.32639e6 | 0.213808 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.33510e7 | 0.932199 | 0.466100 | − | 0.884732i | \(-0.345659\pi\) | ||||
0.466100 | + | 0.884732i | \(0.345659\pi\) | |||||||
\(912\) | 1.04196e6 | 0.0414823 | ||||||||
\(913\) | 230642. | 0.00915719 | ||||||||
\(914\) | −1.46053e6 | −0.0578289 | ||||||||
\(915\) | −1.06523e7 | −0.420620 | ||||||||
\(916\) | 6.19272e6 | 0.243861 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −6.00999e6 | −0.235379 | ||||||||
\(919\) | 1.54594e7 | 0.603817 | 0.301908 | − | 0.953337i | \(-0.402376\pi\) | ||||
0.301908 | + | 0.953337i | \(0.402376\pi\) | |||||||
\(920\) | −6.58296e6 | −0.256420 | ||||||||
\(921\) | 5.38142e6 | 0.209049 | ||||||||
\(922\) | 1.33027e6 | 0.0515362 | ||||||||
\(923\) | 2.75983e6 | 0.106630 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.75312e6 | −0.297935 | ||||||||
\(926\) | 6.79968e6 | 0.260592 | ||||||||
\(927\) | 1.37708e7 | 0.526333 | ||||||||
\(928\) | −4.87958e6 | −0.186000 | ||||||||
\(929\) | 1.49993e7 | 0.570204 | 0.285102 | − | 0.958497i | \(-0.407972\pi\) | ||||
0.285102 | + | 0.958497i | \(0.407972\pi\) | |||||||
\(930\) | 1.15663e7 | 0.438519 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −6.14014e6 | −0.231547 | ||||||||
\(933\) | 2.07432e6 | 0.0780139 | ||||||||
\(934\) | −3.96186e6 | −0.148605 | ||||||||
\(935\) | −4.59981e6 | −0.172072 | ||||||||
\(936\) | 179188. | 0.00668527 | ||||||||
\(937\) | 1.52742e7 | 0.568343 | 0.284172 | − | 0.958773i | \(-0.408281\pi\) | ||||
0.284172 | + | 0.958773i | \(0.408281\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.98320e6 | 0.147424 | ||||||||
\(940\) | 2.29072e7 | 0.845576 | ||||||||
\(941\) | −5.13600e6 | −0.189082 | −0.0945412 | − | 0.995521i | \(-0.530138\pi\) | ||||
−0.0945412 | + | 0.995521i | \(0.530138\pi\) | |||||||
\(942\) | −8.96332e6 | −0.329110 | ||||||||
\(943\) | −1.20032e7 | −0.439559 | ||||||||
\(944\) | −1.13210e7 | −0.413482 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.62865e6 | −0.0591699 | ||||||||
\(947\) | −4.50054e7 | −1.63076 | −0.815379 | − | 0.578928i | \(-0.803471\pi\) | ||||
−0.815379 | + | 0.578928i | \(0.803471\pi\) | |||||||
\(948\) | 6.05837e6 | 0.218945 | ||||||||
\(949\) | −1.28120e6 | −0.0461798 | ||||||||
\(950\) | 1.09383e6 | 0.0393224 | ||||||||
\(951\) | −1.13623e7 | −0.407394 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.49596e7 | −1.60358 | −0.801789 | − | 0.597607i | \(-0.796118\pi\) | ||||
−0.801789 | + | 0.597607i | \(0.796118\pi\) | |||||||
\(954\) | −2.27782e6 | −0.0810303 | ||||||||
\(955\) | −1.18779e7 | −0.421434 | ||||||||
\(956\) | −7.44655e6 | −0.263518 | ||||||||
\(957\) | 1.56727e6 | 0.0553176 | ||||||||
\(958\) | −2.43226e7 | −0.856242 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −2.25132e6 | −0.0788424 | ||||||||
\(961\) | −952428. | −0.0332678 | ||||||||
\(962\) | −1.77279e6 | −0.0617619 | ||||||||
\(963\) | −8.74256e6 | −0.303790 | ||||||||
\(964\) | −5.57991e6 | −0.193390 | ||||||||
\(965\) | −5.35838e7 | −1.85232 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.04364e7 | 0.358907 | 0.179454 | − | 0.983766i | \(-0.442567\pi\) | ||||
0.179454 | + | 0.983766i | \(0.442567\pi\) | |||||||
\(968\) | −1.02218e7 | −0.350622 | ||||||||
\(969\) | −8.38872e6 | −0.287003 | ||||||||
\(970\) | 3.11114e7 | 1.06167 | ||||||||
\(971\) | −1.72207e7 | −0.586142 | −0.293071 | − | 0.956091i | \(-0.594677\pi\) | ||||
−0.293071 | + | 0.956091i | \(0.594677\pi\) | |||||||
\(972\) | 944784. | 0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −2.68439e7 | −0.906669 | ||||||||
\(975\) | 188109. | 0.00633720 | ||||||||
\(976\) | 4.96140e6 | 0.166717 | ||||||||
\(977\) | 3.24376e7 | 1.08721 | 0.543603 | − | 0.839343i | \(-0.317060\pi\) | ||||
0.543603 | + | 0.839343i | \(0.317060\pi\) | |||||||
\(978\) | 7.28092e6 | 0.243410 | ||||||||
\(979\) | 1.88187e6 | 0.0627528 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.80386e7 | −0.598452 | ||||||||
\(982\) | −3.65617e6 | −0.120989 | ||||||||
\(983\) | 3.19804e7 | 1.05560 | 0.527801 | − | 0.849368i | \(-0.323017\pi\) | ||||
0.527801 | + | 0.849368i | \(0.323017\pi\) | |||||||
\(984\) | −4.10500e6 | −0.135153 | ||||||||
\(985\) | 4.59479e7 | 1.50895 | ||||||||
\(986\) | 3.92852e7 | 1.28688 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 250110. | 0.00815152 | ||||||||
\(989\) | 1.87654e7 | 0.610051 | ||||||||
\(990\) | 723100. | 0.0234483 | ||||||||
\(991\) | 5.49614e7 | 1.77776 | 0.888880 | − | 0.458139i | \(-0.151484\pi\) | ||||
0.888880 | + | 0.458139i | \(0.151484\pi\) | |||||||
\(992\) | −5.38713e6 | −0.173811 | ||||||||
\(993\) | −4.22042e6 | −0.135826 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9.49367e6 | 0.304002 | ||||||||
\(996\) | −908832. | −0.0290292 | ||||||||
\(997\) | 7.51010e6 | 0.239281 | 0.119640 | − | 0.992817i | \(-0.461826\pi\) | ||||
0.119640 | + | 0.992817i | \(0.461826\pi\) | |||||||
\(998\) | −3.10197e7 | −0.985850 | ||||||||
\(999\) | −9.34721e6 | −0.296325 |
(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 | 294.6.a.u.1.1 | yes | 2 | |
3.2 | odd | 2 | 882.6.a.bj.1.2 | 2 | |||
7.2 | even | 3 | 294.6.e.u.67.2 | 4 | |||
7.3 | odd | 6 | 294.6.e.v.79.1 | 4 | |||
7.4 | even | 3 | 294.6.e.u.79.2 | 4 | |||
7.5 | odd | 6 | 294.6.e.v.67.1 | 4 | |||
7.6 | odd | 2 | 294.6.a.t.1.2 | ✓ | 2 | ||
21.20 | even | 2 | 882.6.a.z.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
294.6.a.t.1.2 | ✓ | 2 | 7.6 | odd | 2 | ||
294.6.a.u.1.1 | yes | 2 | 1.1 | even | 1 | trivial | |
294.6.e.u.67.2 | 4 | 7.2 | even | 3 | |||
294.6.e.u.79.2 | 4 | 7.4 | even | 3 | |||
294.6.e.v.67.1 | 4 | 7.5 | odd | 6 | |||
294.6.e.v.79.1 | 4 | 7.3 | odd | 6 | |||
882.6.a.z.1.1 | 2 | 21.20 | even | 2 | |||
882.6.a.bj.1.2 | 2 | 3.2 | odd | 2 |