Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1089,6,Mod(1,1089)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1089, 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("1089.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1089 = 3^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 1089.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: | \(174.657979776\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - x^{9} - 252 x^{8} + 45 x^{7} + 21644 x^{6} + 14121 x^{5} - 727612 x^{4} - 1049829 x^{3} + \cdots - 5072980 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2}\cdot 11^{4} \) |
Twist minimal: | no (minimal twist has level 33) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-3.80353\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1089.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.80353 | 0.849151 | 0.424576 | − | 0.905392i | \(-0.360423\pi\) | ||||
0.424576 | + | 0.905392i | \(0.360423\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −8.92614 | −0.278942 | ||||||||
\(5\) | −59.7896 | −1.06955 | −0.534775 | − | 0.844995i | \(-0.679603\pi\) | ||||
−0.534775 | + | 0.844995i | \(0.679603\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 72.0300 | 0.555608 | 0.277804 | − | 0.960638i | \(-0.410393\pi\) | ||||
0.277804 | + | 0.960638i | \(0.410393\pi\) | |||||||
\(8\) | −196.590 | −1.08602 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −287.201 | −0.908209 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −540.791 | −0.887506 | −0.443753 | − | 0.896149i | \(-0.646353\pi\) | ||||
−0.443753 | + | 0.896149i | \(0.646353\pi\) | |||||||
\(14\) | 345.998 | 0.471795 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −658.687 | −0.643249 | ||||||||
\(17\) | 1510.71 | 1.26782 | 0.633912 | − | 0.773405i | \(-0.281448\pi\) | ||||
0.633912 | + | 0.773405i | \(0.281448\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −315.677 | −0.200613 | −0.100306 | − | 0.994957i | \(-0.531982\pi\) | ||||
−0.100306 | + | 0.994957i | \(0.531982\pi\) | |||||||
\(20\) | 533.691 | 0.298342 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2610.94 | 1.02914 | 0.514572 | − | 0.857447i | \(-0.327951\pi\) | ||||
0.514572 | + | 0.857447i | \(0.327951\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 449.799 | 0.143936 | ||||||||
\(26\) | −2597.71 | −0.753627 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −642.950 | −0.154982 | ||||||||
\(29\) | 6630.81 | 1.46410 | 0.732052 | − | 0.681249i | \(-0.238563\pi\) | ||||
0.732052 | + | 0.681249i | \(0.238563\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7435.70 | 1.38969 | 0.694845 | − | 0.719160i | \(-0.255473\pi\) | ||||
0.694845 | + | 0.719160i | \(0.255473\pi\) | |||||||
\(32\) | 3126.85 | 0.539799 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 7256.73 | 1.07657 | ||||||||
\(35\) | −4306.65 | −0.594250 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6440.18 | 0.773381 | 0.386691 | − | 0.922209i | \(-0.373618\pi\) | ||||
0.386691 | + | 0.922209i | \(0.373618\pi\) | |||||||
\(38\) | −1516.36 | −0.170351 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 11754.0 | 1.16155 | ||||||||
\(41\) | −1194.66 | −0.110990 | −0.0554950 | − | 0.998459i | \(-0.517674\pi\) | ||||
−0.0554950 | + | 0.998459i | \(0.517674\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −21637.2 | −1.78456 | −0.892278 | − | 0.451487i | \(-0.850894\pi\) | ||||
−0.892278 | + | 0.451487i | \(0.850894\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 12541.7 | 0.873900 | ||||||||
\(47\) | −1352.89 | −0.0893339 | −0.0446670 | − | 0.999002i | \(-0.514223\pi\) | ||||
−0.0446670 | + | 0.999002i | \(0.514223\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −11618.7 | −0.691300 | ||||||||
\(50\) | 2160.62 | 0.122223 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4827.18 | 0.247563 | ||||||||
\(53\) | −12845.1 | −0.628126 | −0.314063 | − | 0.949402i | \(-0.601690\pi\) | ||||
−0.314063 | + | 0.949402i | \(0.601690\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −14160.4 | −0.603399 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 31851.3 | 1.24325 | ||||||||
\(59\) | 5548.05 | 0.207496 | 0.103748 | − | 0.994604i | \(-0.466916\pi\) | ||||
0.103748 | + | 0.994604i | \(0.466916\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 16044.8 | 0.552090 | 0.276045 | − | 0.961145i | \(-0.410976\pi\) | ||||
0.276045 | + | 0.961145i | \(0.410976\pi\) | |||||||
\(62\) | 35717.6 | 1.18006 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 36097.9 | 1.10162 | ||||||||
\(65\) | 32333.7 | 0.949232 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −71743.7 | −1.95253 | −0.976263 | − | 0.216587i | \(-0.930508\pi\) | ||||
−0.976263 | + | 0.216587i | \(0.930508\pi\) | |||||||
\(68\) | −13484.8 | −0.353649 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −20687.1 | −0.504608 | ||||||||
\(71\) | −34182.3 | −0.804740 | −0.402370 | − | 0.915477i | \(-0.631813\pi\) | ||||
−0.402370 | + | 0.915477i | \(0.631813\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −15613.4 | −0.342918 | −0.171459 | − | 0.985191i | \(-0.554848\pi\) | ||||
−0.171459 | + | 0.985191i | \(0.554848\pi\) | |||||||
\(74\) | 30935.6 | 0.656718 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2817.78 | 0.0559593 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 44250.7 | 0.797724 | 0.398862 | − | 0.917011i | \(-0.369405\pi\) | ||||
0.398862 | + | 0.917011i | \(0.369405\pi\) | |||||||
\(80\) | 39382.7 | 0.687987 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −5738.57 | −0.0942474 | ||||||||
\(83\) | 19538.0 | 0.311304 | 0.155652 | − | 0.987812i | \(-0.450252\pi\) | ||||
0.155652 | + | 0.987812i | \(0.450252\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −90324.8 | −1.35600 | ||||||||
\(86\) | −103935. | −1.51536 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −111152. | −1.48745 | −0.743725 | − | 0.668486i | \(-0.766943\pi\) | ||||
−0.743725 | + | 0.668486i | \(0.766943\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −38953.2 | −0.493105 | ||||||||
\(92\) | −23305.6 | −0.287072 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −6498.62 | −0.0758580 | ||||||||
\(95\) | 18874.2 | 0.214565 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 85165.0 | 0.919034 | 0.459517 | − | 0.888169i | \(-0.348022\pi\) | ||||
0.459517 | + | 0.888169i | \(0.348022\pi\) | |||||||
\(98\) | −55810.6 | −0.587018 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4014.97 | −0.0401497 | ||||||||
\(101\) | 96798.9 | 0.944207 | 0.472103 | − | 0.881543i | \(-0.343495\pi\) | ||||
0.472103 | + | 0.881543i | \(0.343495\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −197258. | −1.83207 | −0.916034 | − | 0.401102i | \(-0.868627\pi\) | ||||
−0.916034 | + | 0.401102i | \(0.868627\pi\) | |||||||
\(104\) | 106314. | 0.963845 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −61701.7 | −0.533374 | ||||||||
\(107\) | 209592. | 1.76976 | 0.884881 | − | 0.465816i | \(-0.154239\pi\) | ||||
0.884881 | + | 0.465816i | \(0.154239\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −22068.0 | −0.177909 | −0.0889544 | − | 0.996036i | \(-0.528353\pi\) | ||||
−0.0889544 | + | 0.996036i | \(0.528353\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −47445.3 | −0.357394 | ||||||||
\(113\) | −9246.95 | −0.0681243 | −0.0340622 | − | 0.999420i | \(-0.510844\pi\) | ||||
−0.0340622 | + | 0.999420i | \(0.510844\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −156107. | −1.10072 | ||||||||
\(116\) | −59187.6 | −0.408400 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 26650.2 | 0.176196 | ||||||||
\(119\) | 108816. | 0.704413 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 77071.7 | 0.468808 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −66372.2 | −0.387643 | ||||||||
\(125\) | 159949. | 0.915603 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −97644.1 | −0.537201 | −0.268600 | − | 0.963252i | \(-0.586561\pi\) | ||||
−0.268600 | + | 0.963252i | \(0.586561\pi\) | |||||||
\(128\) | 73338.0 | 0.395643 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 155316. | 0.806041 | ||||||||
\(131\) | 57856.1 | 0.294558 | 0.147279 | − | 0.989095i | \(-0.452948\pi\) | ||||
0.147279 | + | 0.989095i | \(0.452948\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −22738.2 | −0.111462 | ||||||||
\(134\) | −344623. | −1.65799 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −296990. | −1.37688 | ||||||||
\(137\) | 325451. | 1.48144 | 0.740720 | − | 0.671814i | \(-0.234485\pi\) | ||||
0.740720 | + | 0.671814i | \(0.234485\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −212039. | −0.930848 | −0.465424 | − | 0.885088i | \(-0.654098\pi\) | ||||
−0.465424 | + | 0.885088i | \(0.654098\pi\) | |||||||
\(140\) | 38441.8 | 0.165761 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −164196. | −0.683346 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −396454. | −1.56593 | ||||||||
\(146\) | −74999.4 | −0.291189 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −57486.0 | −0.215729 | ||||||||
\(149\) | −314649. | −1.16108 | −0.580539 | − | 0.814232i | \(-0.697158\pi\) | ||||
−0.580539 | + | 0.814232i | \(0.697158\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 225926. | 0.806352 | 0.403176 | − | 0.915122i | \(-0.367906\pi\) | ||||
0.403176 | + | 0.915122i | \(0.367906\pi\) | |||||||
\(152\) | 62058.8 | 0.217869 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −444578. | −1.48634 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 351696. | 1.13872 | 0.569362 | − | 0.822087i | \(-0.307190\pi\) | ||||
0.569362 | + | 0.822087i | \(0.307190\pi\) | |||||||
\(158\) | 212560. | 0.677389 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −186953. | −0.577342 | ||||||||
\(161\) | 188066. | 0.571801 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −461915. | −1.36174 | −0.680868 | − | 0.732406i | \(-0.738397\pi\) | ||||
−0.680868 | + | 0.732406i | \(0.738397\pi\) | |||||||
\(164\) | 10663.7 | 0.0309598 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 93851.1 | 0.264344 | ||||||||
\(167\) | −215682. | −0.598444 | −0.299222 | − | 0.954184i | \(-0.596727\pi\) | ||||
−0.299222 | + | 0.954184i | \(0.596727\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −78837.7 | −0.212333 | ||||||||
\(170\) | −433877. | −1.15145 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 193137. | 0.497787 | ||||||||
\(173\) | 234410. | 0.595471 | 0.297736 | − | 0.954648i | \(-0.403769\pi\) | ||||
0.297736 | + | 0.954648i | \(0.403769\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 32399.0 | 0.0799718 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −533921. | −1.26307 | ||||||||
\(179\) | 102032. | 0.238015 | 0.119008 | − | 0.992893i | \(-0.462029\pi\) | ||||
0.119008 | + | 0.992893i | \(0.462029\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −524833. | −1.19076 | −0.595381 | − | 0.803443i | \(-0.702999\pi\) | ||||
−0.595381 | + | 0.803443i | \(0.702999\pi\) | |||||||
\(182\) | −187113. | −0.418721 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −513283. | −1.11767 | ||||||||
\(185\) | −385056. | −0.827169 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 12076.1 | 0.0249190 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 90662.7 | 0.182198 | ||||||||
\(191\) | −878656. | −1.74275 | −0.871375 | − | 0.490617i | \(-0.836771\pi\) | ||||
−0.871375 | + | 0.490617i | \(0.836771\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −470133. | −0.908506 | −0.454253 | − | 0.890873i | \(-0.650094\pi\) | ||||
−0.454253 | + | 0.890873i | \(0.650094\pi\) | |||||||
\(194\) | 409092. | 0.780399 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 103710. | 0.192833 | ||||||||
\(197\) | −439293. | −0.806471 | −0.403235 | − | 0.915096i | \(-0.632114\pi\) | ||||
−0.403235 | + | 0.915096i | \(0.632114\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −802118. | −1.43584 | −0.717920 | − | 0.696126i | \(-0.754905\pi\) | ||||
−0.717920 | + | 0.696126i | \(0.754905\pi\) | |||||||
\(200\) | −88425.9 | −0.156316 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 464976. | 0.801774 | ||||||||
\(203\) | 477617. | 0.813467 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 71428.2 | 0.118709 | ||||||||
\(206\) | −947533. | −1.55570 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 356212. | 0.570888 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 149733. | 0.231533 | 0.115766 | − | 0.993276i | \(-0.463068\pi\) | ||||
0.115766 | + | 0.993276i | \(0.463068\pi\) | |||||||
\(212\) | 114657. | 0.175211 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.00678e6 | 1.50280 | ||||||||
\(215\) | 1.29368e6 | 1.90867 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 535594. | 0.772122 | ||||||||
\(218\) | −106004. | −0.151072 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −816979. | −1.12520 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −349490. | −0.470623 | −0.235311 | − | 0.971920i | \(-0.575611\pi\) | ||||
−0.235311 | + | 0.971920i | \(0.575611\pi\) | |||||||
\(224\) | 225227. | 0.299917 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −44417.9 | −0.0578479 | ||||||||
\(227\) | −1.25342e6 | −1.61448 | −0.807238 | − | 0.590226i | \(-0.799039\pi\) | ||||
−0.807238 | + | 0.590226i | \(0.799039\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 217491. | 0.274065 | 0.137032 | − | 0.990567i | \(-0.456244\pi\) | ||||
0.137032 | + | 0.990567i | \(0.456244\pi\) | |||||||
\(230\) | −749863. | −0.934679 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.30355e6 | −1.59004 | ||||||||
\(233\) | −1.44863e6 | −1.74811 | −0.874055 | − | 0.485827i | \(-0.838519\pi\) | ||||
−0.874055 | + | 0.485827i | \(0.838519\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 80888.5 | 0.0955470 | ||||||||
\(236\) | −49522.7 | −0.0578795 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 522703. | 0.598153 | ||||||||
\(239\) | −952015. | −1.07808 | −0.539038 | − | 0.842282i | \(-0.681212\pi\) | ||||
−0.539038 | + | 0.842282i | \(0.681212\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.69481e6 | −1.87965 | −0.939826 | − | 0.341653i | \(-0.889013\pi\) | ||||
−0.939826 | + | 0.341653i | \(0.889013\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −143218. | −0.154001 | ||||||||
\(245\) | 694676. | 0.739379 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 170715. | 0.178045 | ||||||||
\(248\) | −1.46178e6 | −1.50922 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 768320. | 0.777486 | ||||||||
\(251\) | 1.08988e6 | 1.09193 | 0.545963 | − | 0.837809i | \(-0.316164\pi\) | ||||
0.545963 | + | 0.837809i | \(0.316164\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −469036. | −0.456165 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −802852. | −0.765660 | ||||||||
\(257\) | −1.56490e6 | −1.47793 | −0.738967 | − | 0.673742i | \(-0.764686\pi\) | ||||
−0.738967 | + | 0.673742i | \(0.764686\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 463886. | 0.429697 | ||||||||
\(260\) | −288615. | −0.264781 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 277913. | 0.250124 | ||||||||
\(263\) | −892520. | −0.795662 | −0.397831 | − | 0.917459i | \(-0.630237\pi\) | ||||
−0.397831 | + | 0.917459i | \(0.630237\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 768002. | 0.671812 | ||||||||
\(266\) | −109224. | −0.0946482 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 640395. | 0.544642 | ||||||||
\(269\) | −229826. | −0.193650 | −0.0968250 | − | 0.995301i | \(-0.530869\pi\) | ||||
−0.0968250 | + | 0.995301i | \(0.530869\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.48098e6 | 1.22497 | 0.612487 | − | 0.790480i | \(-0.290169\pi\) | ||||
0.612487 | + | 0.790480i | \(0.290169\pi\) | |||||||
\(272\) | −995086. | −0.815527 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.56331e6 | 1.25797 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.48183e6 | 1.16038 | 0.580188 | − | 0.814482i | \(-0.302979\pi\) | ||||
0.580188 | + | 0.814482i | \(0.302979\pi\) | |||||||
\(278\) | −1.01854e6 | −0.790431 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 846643. | 0.645365 | ||||||||
\(281\) | −8168.06 | −0.00617097 | −0.00308548 | − | 0.999995i | \(-0.500982\pi\) | ||||
−0.00308548 | + | 0.999995i | \(0.500982\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.45081e6 | 1.07683 | 0.538413 | − | 0.842681i | \(-0.319024\pi\) | ||||
0.538413 | + | 0.842681i | \(0.319024\pi\) | |||||||
\(284\) | 305116. | 0.224476 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −86051.3 | −0.0616670 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 862388. | 0.607376 | ||||||||
\(290\) | −1.90438e6 | −1.32971 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 139368. | 0.0956543 | ||||||||
\(293\) | 2.19477e6 | 1.49355 | 0.746776 | − | 0.665075i | \(-0.231601\pi\) | ||||
0.746776 | + | 0.665075i | \(0.231601\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −331716. | −0.221928 | ||||||||
\(296\) | −1.26607e6 | −0.839904 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.51143e6 | −0.985931 | ||||||||
\(299\) | −1.41197e6 | −0.913372 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.55853e6 | −0.991513 | ||||||||
\(302\) | 1.08524e6 | 0.684715 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 207932. | 0.129044 | ||||||||
\(305\) | −959313. | −0.590488 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −537035. | −0.325205 | −0.162602 | − | 0.986692i | \(-0.551989\pi\) | ||||
−0.162602 | + | 0.986692i | \(0.551989\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2.13554e6 | −1.26213 | ||||||||
\(311\) | 1.21907e6 | 0.714704 | 0.357352 | − | 0.933970i | \(-0.383680\pi\) | ||||
0.357352 | + | 0.933970i | \(0.383680\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 547802. | 0.316055 | 0.158028 | − | 0.987435i | \(-0.449486\pi\) | ||||
0.158028 | + | 0.987435i | \(0.449486\pi\) | |||||||
\(314\) | 1.68938e6 | 0.966949 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −394989. | −0.222519 | ||||||||
\(317\) | 2.94125e6 | 1.64393 | 0.821967 | − | 0.569536i | \(-0.192877\pi\) | ||||
0.821967 | + | 0.569536i | \(0.192877\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −2.15828e6 | −1.17824 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 903378. | 0.485546 | ||||||||
\(323\) | −476896. | −0.254342 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −243247. | −0.127744 | ||||||||
\(326\) | −2.21882e6 | −1.15632 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 234858. | 0.120537 | ||||||||
\(329\) | −97448.4 | −0.0496346 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.11045e6 | −0.557092 | −0.278546 | − | 0.960423i | \(-0.589853\pi\) | ||||
−0.278546 | + | 0.960423i | \(0.589853\pi\) | |||||||
\(332\) | −174399. | −0.0868356 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.03604e6 | −0.508169 | ||||||||
\(335\) | 4.28953e6 | 2.08832 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.44316e6 | 0.692213 | 0.346107 | − | 0.938195i | \(-0.387504\pi\) | ||||
0.346107 | + | 0.938195i | \(0.387504\pi\) | |||||||
\(338\) | −378699. | −0.180303 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 806252. | 0.378245 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.04750e6 | −0.939700 | ||||||||
\(344\) | 4.25365e6 | 1.93805 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.12599e6 | 0.505645 | ||||||||
\(347\) | 1.63468e6 | 0.728800 | 0.364400 | − | 0.931243i | \(-0.381274\pi\) | ||||
0.364400 | + | 0.931243i | \(0.381274\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.72087e6 | −1.63524 | −0.817620 | − | 0.575758i | \(-0.804707\pi\) | ||||
−0.817620 | + | 0.575758i | \(0.804707\pi\) | |||||||
\(350\) | 155630. | 0.0679081 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 991536. | 0.423518 | 0.211759 | − | 0.977322i | \(-0.432081\pi\) | ||||
0.211759 | + | 0.977322i | \(0.432081\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.04375e6 | 0.860709 | ||||||||
\(356\) | 992159. | 0.414912 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 490114. | 0.202111 | ||||||||
\(359\) | −838000. | −0.343169 | −0.171584 | − | 0.985169i | \(-0.554889\pi\) | ||||
−0.171584 | + | 0.985169i | \(0.554889\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.37645e6 | −0.959754 | ||||||||
\(362\) | −2.52105e6 | −1.01114 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 347702. | 0.137548 | ||||||||
\(365\) | 933520. | 0.366768 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.08625e6 | 1.97121 | 0.985604 | − | 0.169071i | \(-0.0540766\pi\) | ||||
0.985604 | + | 0.169071i | \(0.0540766\pi\) | |||||||
\(368\) | −1.71979e6 | −0.661997 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.84963e6 | −0.702392 | ||||||||
\(371\) | −925231. | −0.348992 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.08135e6 | −1.51891 | −0.759455 | − | 0.650559i | \(-0.774534\pi\) | ||||
−0.759455 | + | 0.650559i | \(0.774534\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 265963. | 0.0970180 | ||||||||
\(377\) | −3.58589e6 | −1.29940 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 34844.5 | 0.0124605 | 0.00623026 | − | 0.999981i | \(-0.498017\pi\) | ||||
0.00623026 | + | 0.999981i | \(0.498017\pi\) | |||||||
\(380\) | −168474. | −0.0598513 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −4.22064e6 | −1.47986 | ||||||||
\(383\) | −2.54395e6 | −0.886157 | −0.443079 | − | 0.896483i | \(-0.646114\pi\) | ||||
−0.443079 | + | 0.896483i | \(0.646114\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.25830e6 | −0.771459 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −760195. | −0.256357 | ||||||||
\(389\) | 2.36422e6 | 0.792163 | 0.396081 | − | 0.918215i | \(-0.370370\pi\) | ||||
0.396081 | + | 0.918215i | \(0.370370\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.94437e6 | 1.30477 | ||||||||
\(392\) | 2.28411e6 | 0.750762 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.11015e6 | −0.684816 | ||||||||
\(395\) | −2.64574e6 | −0.853206 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.56436e6 | 1.13502 | 0.567512 | − | 0.823365i | \(-0.307906\pi\) | ||||
0.567512 | + | 0.823365i | \(0.307906\pi\) | |||||||
\(398\) | −3.85300e6 | −1.21924 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −296277. | −0.0925865 | ||||||||
\(401\) | 6.21116e6 | 1.92891 | 0.964454 | − | 0.264251i | \(-0.0851249\pi\) | ||||
0.964454 | + | 0.264251i | \(0.0851249\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.02116e6 | −1.23336 | ||||||||
\(404\) | −864041. | −0.263379 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.29425e6 | 0.690757 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 799568. | 0.236345 | 0.118173 | − | 0.992993i | \(-0.462296\pi\) | ||||
0.118173 | + | 0.992993i | \(0.462296\pi\) | |||||||
\(410\) | 343107. | 0.100802 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.76075e6 | 0.511040 | ||||||||
\(413\) | 399626. | 0.115287 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.16817e6 | −0.332954 | ||||||||
\(416\) | −1.69097e6 | −0.479075 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.19844e6 | 0.333490 | 0.166745 | − | 0.986000i | \(-0.446674\pi\) | ||||
0.166745 | + | 0.986000i | \(0.446674\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.83223e6 | 0.503819 | 0.251910 | − | 0.967751i | \(-0.418941\pi\) | ||||
0.251910 | + | 0.967751i | \(0.418941\pi\) | |||||||
\(422\) | 719247. | 0.196606 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.52521e6 | 0.682155 | ||||||||
\(425\) | 679516. | 0.182485 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.15571e6 | 0.306746 | ||||||||
\(428\) | −1.87085e6 | −0.493661 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 6.21423e6 | 1.62075 | ||||||||
\(431\) | −1.52861e6 | −0.396373 | −0.198187 | − | 0.980164i | \(-0.563505\pi\) | ||||
−0.198187 | + | 0.980164i | \(0.563505\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.29350e6 | −1.35682 | −0.678412 | − | 0.734682i | \(-0.737331\pi\) | ||||
−0.678412 | + | 0.734682i | \(0.737331\pi\) | |||||||
\(434\) | 2.57274e6 | 0.655649 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 196983. | 0.0496263 | ||||||||
\(437\) | −824212. | −0.206460 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.22914e6 | −0.799698 | −0.399849 | − | 0.916581i | \(-0.630937\pi\) | ||||
−0.399849 | + | 0.916581i | \(0.630937\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.92438e6 | −0.955466 | ||||||||
\(443\) | −156436. | −0.0378727 | −0.0189363 | − | 0.999821i | \(-0.506028\pi\) | ||||
−0.0189363 | + | 0.999821i | \(0.506028\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.64574e6 | 1.59090 | ||||||||
\(446\) | −1.67879e6 | −0.399630 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.60013e6 | 0.612069 | ||||||||
\(449\) | −4.08810e6 | −0.956986 | −0.478493 | − | 0.878091i | \(-0.658817\pi\) | ||||
−0.478493 | + | 0.878091i | \(0.658817\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 82539.6 | 0.0190027 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −6.02083e6 | −1.37093 | ||||||||
\(455\) | 2.32900e6 | 0.527401 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.01684e6 | −0.675712 | −0.337856 | − | 0.941198i | \(-0.609702\pi\) | ||||
−0.337856 | + | 0.941198i | \(0.609702\pi\) | |||||||
\(458\) | 1.04472e6 | 0.232722 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.39343e6 | 0.307037 | ||||||||
\(461\) | 798809. | 0.175061 | 0.0875307 | − | 0.996162i | \(-0.472102\pi\) | ||||
0.0875307 | + | 0.996162i | \(0.472102\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 587910. | 0.127455 | 0.0637277 | − | 0.997967i | \(-0.479701\pi\) | ||||
0.0637277 | + | 0.997967i | \(0.479701\pi\) | |||||||
\(464\) | −4.36763e6 | −0.941783 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.95855e6 | −1.48441 | ||||||||
\(467\) | −2.05580e6 | −0.436203 | −0.218101 | − | 0.975926i | \(-0.569986\pi\) | ||||
−0.218101 | + | 0.975926i | \(0.569986\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.16770e6 | −1.08484 | ||||||||
\(470\) | 388550. | 0.0811339 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.09069e6 | −0.225344 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −141991. | −0.0288753 | ||||||||
\(476\) | −971312. | −0.196490 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −4.57303e6 | −0.915449 | ||||||||
\(479\) | 2.52635e6 | 0.503101 | 0.251551 | − | 0.967844i | \(-0.419059\pi\) | ||||
0.251551 | + | 0.967844i | \(0.419059\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.48279e6 | −0.686381 | ||||||||
\(482\) | −8.14105e6 | −1.59611 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5.09198e6 | −0.982952 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 29503.9 | 0.00563711 | 0.00281856 | − | 0.999996i | \(-0.499103\pi\) | ||||
0.00281856 | + | 0.999996i | \(0.499103\pi\) | |||||||
\(488\) | −3.15425e6 | −0.599578 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 3.33690e6 | 0.627845 | ||||||||
\(491\) | 3.21878e6 | 0.602542 | 0.301271 | − | 0.953539i | \(-0.402589\pi\) | ||||
0.301271 | + | 0.953539i | \(0.402589\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.00172e7 | 1.85622 | ||||||||
\(494\) | 820035. | 0.151187 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.89780e6 | −0.893917 | ||||||||
\(497\) | −2.46215e6 | −0.447120 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.68764e6 | 1.56189 | 0.780945 | − | 0.624599i | \(-0.214738\pi\) | ||||
0.780945 | + | 0.624599i | \(0.214738\pi\) | |||||||
\(500\) | −1.42773e6 | −0.255400 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5.23525e6 | 0.927211 | ||||||||
\(503\) | −440914. | −0.0777023 | −0.0388512 | − | 0.999245i | \(-0.512370\pi\) | ||||
−0.0388512 | + | 0.999245i | \(0.512370\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.78757e6 | −1.00988 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 871585. | 0.149848 | ||||||||
\(509\) | −2.70392e6 | −0.462594 | −0.231297 | − | 0.972883i | \(-0.574297\pi\) | ||||
−0.231297 | + | 0.972883i | \(0.574297\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.12463e6 | −0.190528 | ||||||||
\(512\) | −6.20334e6 | −1.04580 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −7.51705e6 | −1.25499 | ||||||||
\(515\) | 1.17940e7 | 1.95949 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 2.22829e6 | 0.364878 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −6.35648e6 | −1.03088 | ||||||||
\(521\) | −6.40024e6 | −1.03300 | −0.516502 | − | 0.856286i | \(-0.672766\pi\) | ||||
−0.516502 | + | 0.856286i | \(0.672766\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.79308e6 | −1.24582 | −0.622909 | − | 0.782294i | \(-0.714049\pi\) | ||||
−0.622909 | + | 0.782294i | \(0.714049\pi\) | |||||||
\(524\) | −516432. | −0.0821646 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.28724e6 | −0.675637 | ||||||||
\(527\) | 1.12332e7 | 1.76188 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 380641. | 0.0591393 | ||||||||
\(530\) | 3.68912e6 | 0.570470 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 202965. | 0.0310915 | ||||||||
\(533\) | 646061. | 0.0985044 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.25314e7 | −1.89285 | ||||||||
\(536\) | 1.41041e7 | 2.12047 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1.10397e6 | −0.164438 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.77128e6 | 1.43535 | 0.717676 | − | 0.696378i | \(-0.245206\pi\) | ||||
0.717676 | + | 0.696378i | \(0.245206\pi\) | |||||||
\(542\) | 7.11395e6 | 1.04019 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.72377e6 | 0.684370 | ||||||||
\(545\) | 1.31944e6 | 0.190282 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.46761e6 | −0.352621 | −0.176311 | − | 0.984335i | \(-0.556416\pi\) | ||||
−0.176311 | + | 0.984335i | \(0.556416\pi\) | |||||||
\(548\) | −2.90502e6 | −0.413236 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.09319e6 | −0.293718 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.18738e6 | 0.443222 | ||||||||
\(554\) | 7.11801e6 | 0.985335 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.89269e6 | 0.259653 | ||||||||
\(557\) | 4.18102e6 | 0.571010 | 0.285505 | − | 0.958377i | \(-0.407839\pi\) | ||||
0.285505 | + | 0.958377i | \(0.407839\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.17012e7 | 1.58380 | ||||||||
\(560\) | 2.83673e6 | 0.382251 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −39235.5 | −0.00524008 | ||||||||
\(563\) | −1.01719e6 | −0.135249 | −0.0676244 | − | 0.997711i | \(-0.521542\pi\) | ||||
−0.0676244 | + | 0.997711i | \(0.521542\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 552871. | 0.0728623 | ||||||||
\(566\) | 6.96902e6 | 0.914388 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.71989e6 | 0.873960 | ||||||||
\(569\) | −1.02955e7 | −1.33311 | −0.666555 | − | 0.745456i | \(-0.732232\pi\) | ||||
−0.666555 | + | 0.745456i | \(0.732232\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.45391e6 | 0.443323 | 0.221662 | − | 0.975124i | \(-0.428852\pi\) | ||||
0.221662 | + | 0.975124i | \(0.428852\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −413350. | −0.0523646 | ||||||||
\(575\) | 1.17440e6 | 0.148131 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −797397. | −0.0997092 | −0.0498546 | − | 0.998756i | \(-0.515876\pi\) | ||||
−0.0498546 | + | 0.998756i | \(0.515876\pi\) | |||||||
\(578\) | 4.14250e6 | 0.515755 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 3.53880e6 | 0.436804 | ||||||||
\(581\) | 1.40732e6 | 0.172963 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 3.06944e6 | 0.372414 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.05426e7 | 1.26825 | ||||||||
\(587\) | −192576. | −0.0230678 | −0.0115339 | − | 0.999933i | \(-0.503671\pi\) | ||||
−0.0115339 | + | 0.999933i | \(0.503671\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.34728e6 | −0.278790 | ||||||||
\(590\) | −1.59341e6 | −0.188450 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.24206e6 | −0.497477 | ||||||||
\(593\) | −6.70390e6 | −0.782872 | −0.391436 | − | 0.920205i | \(-0.628022\pi\) | ||||
−0.391436 | + | 0.920205i | \(0.628022\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.50610e6 | −0.753404 | ||||||||
\(596\) | 2.80861e6 | 0.323873 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −6.78244e6 | −0.775591 | ||||||||
\(599\) | −1.47361e6 | −0.167809 | −0.0839044 | − | 0.996474i | \(-0.526739\pi\) | ||||
−0.0839044 | + | 0.996474i | \(0.526739\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.38731e6 | −0.269602 | −0.134801 | − | 0.990873i | \(-0.543040\pi\) | ||||
−0.134801 | + | 0.990873i | \(0.543040\pi\) | |||||||
\(602\) | −7.48643e6 | −0.841944 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2.01665e6 | −0.224925 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.25721e6 | 0.579141 | 0.289570 | − | 0.957157i | \(-0.406488\pi\) | ||||
0.289570 | + | 0.957157i | \(0.406488\pi\) | |||||||
\(608\) | −987075. | −0.108291 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.60809e6 | −0.501413 | ||||||||
\(611\) | 731629. | 0.0792844 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.22410e7 | 1.31572 | 0.657862 | − | 0.753138i | \(-0.271461\pi\) | ||||
0.657862 | + | 0.753138i | \(0.271461\pi\) | |||||||
\(614\) | −2.57966e6 | −0.276148 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.32157e6 | −0.351261 | −0.175631 | − | 0.984456i | \(-0.556196\pi\) | ||||
−0.175631 | + | 0.984456i | \(0.556196\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.16769e7 | 1.22490 | 0.612449 | − | 0.790510i | \(-0.290185\pi\) | ||||
0.612449 | + | 0.790510i | \(0.290185\pi\) | |||||||
\(620\) | 3.96837e6 | 0.414603 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 5.85581e6 | 0.606892 | ||||||||
\(623\) | −8.00628e6 | −0.826439 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.09689e7 | −1.12322 | ||||||||
\(626\) | 2.63138e6 | 0.268379 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.13929e6 | −0.317638 | ||||||||
\(629\) | 9.72924e6 | 0.980511 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.25895e6 | 0.825756 | 0.412878 | − | 0.910786i | \(-0.364524\pi\) | ||||
0.412878 | + | 0.910786i | \(0.364524\pi\) | |||||||
\(632\) | −8.69924e6 | −0.866341 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.41284e7 | 1.39595 | ||||||||
\(635\) | 5.83810e6 | 0.574563 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.28328e6 | 0.613533 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −4.38485e6 | −0.423160 | ||||||||
\(641\) | −1.50046e7 | −1.44238 | −0.721189 | − | 0.692738i | \(-0.756404\pi\) | ||||
−0.721189 | + | 0.692738i | \(0.756404\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.75733e7 | −1.67620 | −0.838100 | − | 0.545516i | \(-0.816334\pi\) | ||||
−0.838100 | + | 0.545516i | \(0.816334\pi\) | |||||||
\(644\) | −1.67870e6 | −0.159499 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.29078e6 | −0.215975 | ||||||||
\(647\) | −924911. | −0.0868639 | −0.0434319 | − | 0.999056i | \(-0.513829\pi\) | ||||
−0.0434319 | + | 0.999056i | \(0.513829\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −1.16844e6 | −0.108474 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4.12312e6 | 0.379845 | ||||||||
\(653\) | 8.03324e6 | 0.737238 | 0.368619 | − | 0.929581i | \(-0.379831\pi\) | ||||
0.368619 | + | 0.929581i | \(0.379831\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.45919e6 | −0.315044 | ||||||||
\(656\) | 786906. | 0.0713943 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −468096. | −0.0421473 | ||||||||
\(659\) | −8.78898e6 | −0.788360 | −0.394180 | − | 0.919033i | \(-0.628971\pi\) | ||||
−0.394180 | + | 0.919033i | \(0.628971\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.05882e7 | −0.942579 | −0.471290 | − | 0.881979i | \(-0.656211\pi\) | ||||
−0.471290 | + | 0.881979i | \(0.656211\pi\) | |||||||
\(662\) | −5.33405e6 | −0.473056 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.84096e6 | −0.338080 | ||||||||
\(665\) | 1.35951e6 | 0.119214 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.73126e7 | 1.50677 | ||||||||
\(668\) | 1.92521e6 | 0.166931 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2.06049e7 | 1.77330 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.09744e7 | −1.78505 | −0.892526 | − | 0.450996i | \(-0.851069\pi\) | ||||
−0.892526 | + | 0.450996i | \(0.851069\pi\) | |||||||
\(674\) | 6.93226e6 | 0.587794 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 703717. | 0.0592285 | ||||||||
\(677\) | −6.29560e6 | −0.527916 | −0.263958 | − | 0.964534i | \(-0.585028\pi\) | ||||
−0.263958 | + | 0.964534i | \(0.585028\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.13443e6 | 0.510623 | ||||||||
\(680\) | 1.77569e7 | 1.47264 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.09791e6 | 0.418158 | 0.209079 | − | 0.977899i | \(-0.432953\pi\) | ||||
0.209079 | + | 0.977899i | \(0.432953\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.94586e7 | −1.58447 | ||||||||
\(686\) | −9.83523e6 | −0.797947 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.42522e7 | 1.14791 | ||||||||
\(689\) | 6.94651e6 | 0.557466 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.27923e7 | −1.01918 | −0.509592 | − | 0.860416i | \(-0.670204\pi\) | ||||
−0.509592 | + | 0.860416i | \(0.670204\pi\) | |||||||
\(692\) | −2.09238e6 | −0.166102 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7.85221e6 | 0.618862 | ||||||||
\(695\) | 1.26777e7 | 0.995588 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.80478e6 | −0.140716 | ||||||||
\(698\) | −1.78733e7 | −1.38857 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −289198. | −0.0223075 | ||||||||
\(701\) | −961596. | −0.0739091 | −0.0369545 | − | 0.999317i | \(-0.511766\pi\) | ||||
−0.0369545 | + | 0.999317i | \(0.511766\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.03302e6 | −0.155150 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.76287e6 | 0.359631 | ||||||||
\(707\) | 6.97243e6 | 0.524609 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.78426e6 | −0.133304 | −0.0666521 | − | 0.997776i | \(-0.521232\pi\) | ||||
−0.0666521 | + | 0.997776i | \(0.521232\pi\) | |||||||
\(710\) | 9.81720e6 | 0.730872 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2.18513e7 | 1.61539 | ||||||||
\(713\) | 1.94141e7 | 1.43019 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −910754. | −0.0663924 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −4.02535e6 | −0.291402 | ||||||||
\(719\) | −5.82070e6 | −0.419907 | −0.209953 | − | 0.977711i | \(-0.567331\pi\) | ||||
−0.209953 | + | 0.977711i | \(0.567331\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.42085e7 | −1.01791 | ||||||||
\(722\) | −1.14153e7 | −0.814977 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 4.68474e6 | 0.332154 | ||||||||
\(725\) | 2.98253e6 | 0.210737 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.27069e6 | 0.510199 | 0.255100 | − | 0.966915i | \(-0.417892\pi\) | ||||
0.255100 | + | 0.966915i | \(0.417892\pi\) | |||||||
\(728\) | 7.65780e6 | 0.535520 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 4.48418e6 | 0.311441 | ||||||||
\(731\) | −3.26875e7 | −2.26250 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.17267e7 | 0.806147 | 0.403074 | − | 0.915168i | \(-0.367942\pi\) | ||||
0.403074 | + | 0.915168i | \(0.367942\pi\) | |||||||
\(734\) | 2.44319e7 | 1.67385 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 8.16401e6 | 0.555532 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.37182e6 | 0.631267 | 0.315633 | − | 0.948881i | \(-0.397783\pi\) | ||||
0.315633 | + | 0.948881i | \(0.397783\pi\) | |||||||
\(740\) | 3.43706e6 | 0.230732 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4.44437e6 | −0.296347 | ||||||||
\(743\) | −8.19123e6 | −0.544348 | −0.272174 | − | 0.962248i | \(-0.587743\pi\) | ||||
−0.272174 | + | 0.962248i | \(0.587743\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.88128e7 | 1.24183 | ||||||||
\(746\) | −1.96049e7 | −1.28979 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.50969e7 | 0.983294 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.22457e7 | −1.43928 | −0.719640 | − | 0.694347i | \(-0.755693\pi\) | ||||
−0.719640 | + | 0.694347i | \(0.755693\pi\) | |||||||
\(752\) | 891129. | 0.0574640 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.72249e7 | −1.10339 | ||||||||
\(755\) | −1.35081e7 | −0.862433 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.46824e6 | −0.219973 | −0.109987 | − | 0.993933i | \(-0.535081\pi\) | ||||
−0.109987 | + | 0.993933i | \(0.535081\pi\) | |||||||
\(758\) | 167376. | 0.0105809 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.71047e6 | −0.233021 | ||||||||
\(761\) | 1.24057e7 | 0.776531 | 0.388265 | − | 0.921548i | \(-0.373074\pi\) | ||||
0.388265 | + | 0.921548i | \(0.373074\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.58956e6 | −0.0988476 | ||||||||
\(764\) | 7.84301e6 | 0.486126 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.22199e7 | −0.752482 | ||||||||
\(767\) | −3.00034e6 | −0.184154 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.84783e7 | −1.12680 | −0.563398 | − | 0.826185i | \(-0.690506\pi\) | ||||
−0.563398 | + | 0.826185i | \(0.690506\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 4.19648e6 | 0.253420 | ||||||||
\(773\) | −1.97874e6 | −0.119108 | −0.0595540 | − | 0.998225i | \(-0.518968\pi\) | ||||
−0.0595540 | + | 0.998225i | \(0.518968\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.34457e6 | 0.200026 | ||||||||
\(776\) | −1.67426e7 | −0.998085 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.13566e7 | 0.672666 | ||||||||
\(779\) | 377126. | 0.0222660 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 1.89469e7 | 1.10795 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 7.65307e6 | 0.444678 | ||||||||
\(785\) | −2.10278e7 | −1.21792 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.55012e7 | −1.46765 | −0.733827 | − | 0.679337i | \(-0.762268\pi\) | ||||
−0.733827 | + | 0.679337i | \(0.762268\pi\) | |||||||
\(788\) | 3.92119e6 | 0.224959 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.27089e7 | −0.724501 | ||||||||
\(791\) | −666058. | −0.0378504 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.67690e6 | −0.489983 | ||||||||
\(794\) | 1.71215e7 | 0.963807 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7.15983e6 | 0.400516 | ||||||||
\(797\) | −1.36157e7 | −0.759269 | −0.379634 | − | 0.925137i | \(-0.623950\pi\) | ||||
−0.379634 | + | 0.925137i | \(0.623950\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.04382e6 | −0.113260 | ||||||||
\(800\) | 1.40645e6 | 0.0776964 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2.98354e7 | 1.63793 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.12444e7 | −0.611569 | ||||||||
\(806\) | −1.93158e7 | −1.04731 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.90297e7 | −1.02542 | ||||||||
\(809\) | −3.79535e6 | −0.203883 | −0.101941 | − | 0.994790i | \(-0.532505\pi\) | ||||
−0.101941 | + | 0.994790i | \(0.532505\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.11854e6 | −0.486825 | −0.243413 | − | 0.969923i | \(-0.578267\pi\) | ||||
−0.243413 | + | 0.969923i | \(0.578267\pi\) | |||||||
\(812\) | −4.26328e6 | −0.226910 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.76177e7 | 1.45644 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.83036e6 | 0.358005 | ||||||||
\(818\) | 3.84075e6 | 0.200693 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −637578. | −0.0331130 | ||||||||
\(821\) | −2.19307e7 | −1.13552 | −0.567760 | − | 0.823194i | \(-0.692190\pi\) | ||||
−0.567760 | + | 0.823194i | \(0.692190\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.45045e7 | 1.77572 | 0.887862 | − | 0.460109i | \(-0.152190\pi\) | ||||
0.887862 | + | 0.460109i | \(0.152190\pi\) | |||||||
\(824\) | 3.87789e7 | 1.98965 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.91962e6 | 0.0978958 | ||||||||
\(827\) | −2.15914e6 | −0.109778 | −0.0548892 | − | 0.998492i | \(-0.517481\pi\) | ||||
−0.0548892 | + | 0.998492i | \(0.517481\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.84351e6 | 0.446929 | 0.223464 | − | 0.974712i | \(-0.428263\pi\) | ||||
0.223464 | + | 0.974712i | \(0.428263\pi\) | |||||||
\(830\) | −5.61132e6 | −0.282729 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.95214e7 | −0.977695 | ||||||||
\(833\) | −1.75525e7 | −0.876446 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.28956e7 | 0.640065 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 5.75675e6 | 0.283183 | ||||||||
\(839\) | −1.99568e7 | −0.978780 | −0.489390 | − | 0.872065i | \(-0.662780\pi\) | ||||
−0.489390 | + | 0.872065i | \(0.662780\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.34565e7 | 1.14360 | ||||||||
\(842\) | 8.80116e6 | 0.427819 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.33654e6 | −0.0645842 | ||||||||
\(845\) | 4.71368e6 | 0.227100 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 8.46089e6 | 0.404042 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3.26407e6 | 0.154957 | ||||||||
\(851\) | 1.68149e7 | 0.795922 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.98067e6 | 0.469664 | 0.234832 | − | 0.972036i | \(-0.424546\pi\) | ||||
0.234832 | + | 0.972036i | \(0.424546\pi\) | |||||||
\(854\) | 5.55147e6 | 0.260474 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.12036e7 | −1.92199 | ||||||||
\(857\) | 1.15246e7 | 0.536012 | 0.268006 | − | 0.963417i | \(-0.413635\pi\) | ||||
0.268006 | + | 0.963417i | \(0.413635\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.88299e7 | 0.870693 | 0.435346 | − | 0.900263i | \(-0.356626\pi\) | ||||
0.435346 | + | 0.900263i | \(0.356626\pi\) | |||||||
\(860\) | −1.15476e7 | −0.532408 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −7.34273e6 | −0.336581 | ||||||||
\(863\) | −1.03363e6 | −0.0472432 | −0.0236216 | − | 0.999721i | \(-0.507520\pi\) | ||||
−0.0236216 | + | 0.999721i | \(0.507520\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.40153e7 | −0.636886 | ||||||||
\(866\) | −2.54275e7 | −1.15215 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4.78079e6 | −0.215377 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.87984e7 | 1.73288 | ||||||||
\(872\) | 4.33835e6 | 0.193212 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −3.95912e6 | −0.175316 | ||||||||
\(875\) | 1.15211e7 | 0.508716 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.19038e6 | −0.183973 | −0.0919865 | − | 0.995760i | \(-0.529322\pi\) | ||||
−0.0919865 | + | 0.995760i | \(0.529322\pi\) | |||||||
\(878\) | −1.55113e7 | −0.679065 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.02320e7 | −1.74635 | −0.873177 | − | 0.487403i | \(-0.837944\pi\) | ||||
−0.873177 | + | 0.487403i | \(0.837944\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.47547e6 | −0.0636839 | −0.0318419 | − | 0.999493i | \(-0.510137\pi\) | ||||
−0.0318419 | + | 0.999493i | \(0.510137\pi\) | |||||||
\(884\) | 7.29247e6 | 0.313866 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −751442. | −0.0321597 | ||||||||
\(887\) | −1.07269e6 | −0.0457791 | −0.0228895 | − | 0.999738i | \(-0.507287\pi\) | ||||
−0.0228895 | + | 0.999738i | \(0.507287\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.03330e6 | −0.298473 | ||||||||
\(890\) | 3.19230e7 | 1.35092 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.11960e6 | 0.131277 | ||||||||
\(893\) | 427075. | 0.0179215 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.10047e6 | −0.254569 | ||||||||
\(896\) | 5.28253e6 | 0.219823 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.96373e7 | −0.812626 | ||||||||
\(899\) | 4.93047e7 | 2.03465 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.94052e7 | −0.796353 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.81786e6 | 0.0739841 | ||||||||
\(905\) | 3.13796e7 | 1.27358 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.17276e7 | −0.473361 | −0.236681 | − | 0.971588i | \(-0.576059\pi\) | ||||
−0.236681 | + | 0.971588i | \(0.576059\pi\) | |||||||
\(908\) | 1.11882e7 | 0.450345 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.11874e7 | 0.447843 | ||||||||
\(911\) | −2.62021e7 | −1.04602 | −0.523010 | − | 0.852326i | \(-0.675191\pi\) | ||||
−0.523010 | + | 0.852326i | \(0.675191\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −1.44915e7 | −0.573781 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.94136e6 | −0.0764482 | ||||||||
\(917\) | 4.16738e6 | 0.163659 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.91878e7 | 1.14002 | 0.570010 | − | 0.821637i | \(-0.306939\pi\) | ||||
0.570010 | + | 0.821637i | \(0.306939\pi\) | |||||||
\(920\) | 3.06890e7 | 1.19540 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 3.83710e6 | 0.148654 | ||||||||
\(923\) | 1.84855e7 | 0.714212 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.89679e6 | 0.111317 | ||||||||
\(926\) | 2.82404e6 | 0.108229 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.07336e7 | 0.790322 | ||||||||
\(929\) | −1.02623e7 | −0.390126 | −0.195063 | − | 0.980791i | \(-0.562491\pi\) | ||||
−0.195063 | + | 0.980791i | \(0.562491\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.66775e6 | 0.138684 | ||||||||
\(932\) | 1.29307e7 | 0.487621 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −9.87508e6 | −0.370402 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.02516e7 | 0.753548 | 0.376774 | − | 0.926305i | \(-0.377033\pi\) | ||||
0.376774 | + | 0.926305i | \(0.377033\pi\) | |||||||
\(938\) | −2.48232e7 | −0.921193 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −722023. | −0.0266521 | ||||||||
\(941\) | −1.48963e7 | −0.548408 | −0.274204 | − | 0.961672i | \(-0.588414\pi\) | ||||
−0.274204 | + | 0.961672i | \(0.588414\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.11918e6 | −0.114225 | ||||||||
\(944\) | −3.65443e6 | −0.133472 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.90445e7 | 1.77711 | 0.888557 | − | 0.458767i | \(-0.151709\pi\) | ||||
0.888557 | + | 0.458767i | \(0.151709\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.44359e6 | 0.304342 | ||||||||
\(950\) | −682058. | −0.0245195 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −2.13922e7 | −0.765003 | ||||||||
\(953\) | −4.09514e7 | −1.46062 | −0.730309 | − | 0.683117i | \(-0.760624\pi\) | ||||
−0.730309 | + | 0.683117i | \(0.760624\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.25345e7 | 1.86396 | ||||||||
\(956\) | 8.49782e6 | 0.300720 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1.21354e7 | 0.427209 | ||||||||
\(959\) | 2.34422e7 | 0.823100 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.66605e7 | 0.931237 | ||||||||
\(962\) | −1.67297e7 | −0.582841 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.51281e7 | 0.524314 | ||||||||
\(965\) | 2.81091e7 | 0.971691 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.37084e7 | 0.471433 | 0.235717 | − | 0.971822i | \(-0.424256\pi\) | ||||
0.235717 | + | 0.971822i | \(0.424256\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.44595e7 | −0.834675 | ||||||||
\(971\) | 9.26748e6 | 0.315438 | 0.157719 | − | 0.987484i | \(-0.449586\pi\) | ||||
0.157719 | + | 0.987484i | \(0.449586\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.52732e7 | −0.517187 | ||||||||
\(974\) | 141723. | 0.00478676 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.05685e7 | −0.355132 | ||||||||
\(977\) | 3.31740e7 | 1.11189 | 0.555945 | − | 0.831219i | \(-0.312357\pi\) | ||||
0.555945 | + | 0.831219i | \(0.312357\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −6.20078e6 | −0.206244 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.54615e7 | 0.511649 | ||||||||
\(983\) | 3.23287e7 | 1.06710 | 0.533549 | − | 0.845769i | \(-0.320858\pi\) | ||||
0.533549 | + | 0.845769i | \(0.320858\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.62652e7 | 0.862560 | ||||||||
\(986\) | 4.81180e7 | 1.57622 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.52383e6 | −0.0496643 | ||||||||
\(989\) | −5.64933e7 | −1.83657 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.51169e7 | 0.812424 | 0.406212 | − | 0.913779i | \(-0.366850\pi\) | ||||
0.406212 | + | 0.913779i | \(0.366850\pi\) | |||||||
\(992\) | 2.32503e7 | 0.750153 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.18270e7 | −0.379673 | ||||||||
\(995\) | 4.79584e7 | 1.53570 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.52150e6 | −0.271505 | −0.135753 | − | 0.990743i | \(-0.543345\pi\) | ||||
−0.135753 | + | 0.990743i | \(0.543345\pi\) | |||||||
\(998\) | 4.17313e7 | 1.32628 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1089.6.a.bl.1.7 | 10 | ||
3.2 | odd | 2 | 363.6.a.q.1.4 | 10 | |||
11.7 | odd | 10 | 99.6.f.c.82.2 | 20 | |||
11.8 | odd | 10 | 99.6.f.c.64.2 | 20 | |||
11.10 | odd | 2 | 1089.6.a.bh.1.4 | 10 | |||
33.8 | even | 10 | 33.6.e.a.31.4 | yes | 20 | ||
33.29 | even | 10 | 33.6.e.a.16.4 | ✓ | 20 | ||
33.32 | even | 2 | 363.6.a.u.1.7 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.6.e.a.16.4 | ✓ | 20 | 33.29 | even | 10 | ||
33.6.e.a.31.4 | yes | 20 | 33.8 | even | 10 | ||
99.6.f.c.64.2 | 20 | 11.8 | odd | 10 | |||
99.6.f.c.82.2 | 20 | 11.7 | odd | 10 | |||
363.6.a.q.1.4 | 10 | 3.2 | odd | 2 | |||
363.6.a.u.1.7 | 10 | 33.32 | even | 2 | |||
1089.6.a.bh.1.4 | 10 | 11.10 | odd | 2 | |||
1089.6.a.bl.1.7 | 10 | 1.1 | even | 1 | trivial |