Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [240,10,Mod(1,240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(240, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("240.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 240 = 2^{4} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 240.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: | \(123.608600679\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{4729}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1182 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 15) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-33.8839\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 240.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −81.0000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −625.000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7861.50 | 1.23755 | 0.618777 | − | 0.785567i | \(-0.287629\pi\) | ||||
0.618777 | + | 0.785567i | \(0.287629\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6561.00 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 49373.3 | 1.01678 | 0.508388 | − | 0.861128i | \(-0.330242\pi\) | ||||
0.508388 | + | 0.861128i | \(0.330242\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 24250.7 | 0.235494 | 0.117747 | − | 0.993044i | \(-0.462433\pi\) | ||||
0.117747 | + | 0.993044i | \(0.462433\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 50625.0 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 268222. | 0.778888 | 0.389444 | − | 0.921050i | \(-0.372667\pi\) | ||||
0.389444 | + | 0.921050i | \(0.372667\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 168364. | 0.296387 | 0.148193 | − | 0.988958i | \(-0.452654\pi\) | ||||
0.148193 | + | 0.988958i | \(0.452654\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −636781. | −0.714502 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.12200e6 | 1.58114 | 0.790569 | − | 0.612373i | \(-0.209785\pi\) | ||||
0.790569 | + | 0.612373i | \(0.209785\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 390625. | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −531441. | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 389624. | 0.102295 | 0.0511475 | − | 0.998691i | \(-0.483712\pi\) | ||||
0.0511475 | + | 0.998691i | \(0.483712\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −90532.2 | −0.0176066 | −0.00880330 | − | 0.999961i | \(-0.502802\pi\) | ||||
−0.00880330 | + | 0.999961i | \(0.502802\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.99924e6 | −0.587036 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.91344e6 | −0.553451 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.31991e6 | −0.291218 | −0.145609 | − | 0.989342i | \(-0.546514\pi\) | ||||
−0.145609 | + | 0.989342i | \(0.546514\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.96431e6 | −0.135963 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.32694e7 | 1.28605 | 0.643024 | − | 0.765846i | \(-0.277679\pi\) | ||||
0.643024 | + | 0.765846i | \(0.277679\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.91140e7 | −0.852597 | −0.426298 | − | 0.904583i | \(-0.640183\pi\) | ||||
−0.426298 | + | 0.904583i | \(0.640183\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.10062e6 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.28153e7 | −1.87770 | −0.938848 | − | 0.344332i | \(-0.888105\pi\) | ||||
−0.938848 | + | 0.344332i | \(0.888105\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.14495e7 | 0.531539 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.17260e7 | −0.449691 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −180207. | −0.00313711 | −0.00156856 | − | 0.999999i | \(-0.500499\pi\) | ||||
−0.00156856 | + | 0.999999i | \(0.500499\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.08583e7 | −0.454716 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.36375e7 | −0.171119 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.84564e7 | −0.413175 | −0.206588 | − | 0.978428i | \(-0.566236\pi\) | ||||
−0.206588 | + | 0.978428i | \(0.566236\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −553620. | −0.00511950 | −0.00255975 | − | 0.999997i | \(-0.500815\pi\) | ||||
−0.00255975 | + | 0.999997i | \(0.500815\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.15793e7 | 0.412518 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.51567e7 | −0.105316 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.39163e8 | 1.44996 | 0.724982 | − | 0.688768i | \(-0.241848\pi\) | ||||
0.724982 | + | 0.688768i | \(0.241848\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.71882e8 | −0.912871 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.28653e8 | −0.600838 | −0.300419 | − | 0.953807i | \(-0.597127\pi\) | ||||
−0.300419 | + | 0.953807i | \(0.597127\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.39376e8 | −0.986569 | −0.493284 | − | 0.869868i | \(-0.664204\pi\) | ||||
−0.493284 | + | 0.869868i | \(0.664204\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.16406e7 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.88148e8 | 1.25831 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.28027e8 | 1.52523 | 0.762613 | − | 0.646855i | \(-0.223916\pi\) | ||||
0.762613 | + | 0.646855i | \(0.223916\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.30467e7 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.12210e8 | −0.490812 | −0.245406 | − | 0.969420i | \(-0.578921\pi\) | ||||
−0.245406 | + | 0.969420i | \(0.578921\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.67639e8 | −0.348329 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.15595e7 | −0.0590601 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.07724e8 | −0.350939 | −0.175469 | − | 0.984485i | \(-0.556144\pi\) | ||||
−0.175469 | + | 0.984485i | \(0.556144\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.90647e8 | 0.291436 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.33311e6 | 0.0101652 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.05228e8 | −0.132548 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.70780e9 | 1.95868 | 0.979341 | − | 0.202214i | \(-0.0648136\pi\) | ||||
0.979341 | + | 0.202214i | \(0.0648136\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.23938e8 | 0.338925 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.81384e8 | −0.173441 | −0.0867206 | − | 0.996233i | \(-0.527639\pi\) | ||||
−0.0867206 | + | 0.996233i | \(0.527639\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.70453e9 | 1.49223 | 0.746116 | − | 0.665816i | \(-0.231917\pi\) | ||||
0.746116 | + | 0.665816i | \(0.231917\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.97988e8 | 0.319535 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.73298e9 | −1.27811 | −0.639053 | − | 0.769163i | \(-0.720674\pi\) | ||||
−0.639053 | + | 0.769163i | \(0.720674\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.17238e9 | −0.795515 | −0.397757 | − | 0.917491i | \(-0.630211\pi\) | ||||
−0.397757 | + | 0.917491i | \(0.630211\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.68913e8 | 0.168135 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.22180e9 | −0.704935 | −0.352467 | − | 0.935824i | \(-0.614657\pi\) | ||||
−0.352467 | + | 0.935824i | \(0.614657\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.32625e9 | −0.707107 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.59109e8 | 0.0784980 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.10863e9 | 0.963916 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.97750e7 | 0.0338324 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.88482e9 | −0.742501 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.44141e8 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.50324e8 | 0.324157 | 0.162078 | − | 0.986778i | \(-0.448180\pi\) | ||||
0.162078 | + | 0.986778i | \(0.448180\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.54823e9 | 0.492247 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.03050e9 | 1.19574 | 0.597872 | − | 0.801592i | \(-0.296013\pi\) | ||||
0.597872 | + | 0.801592i | \(0.296013\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.32360e9 | 0.366795 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.32151e8 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.51871e9 | 1.33843 | 0.669214 | − | 0.743070i | \(-0.266631\pi\) | ||||
0.669214 | + | 0.743070i | \(0.266631\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.97776e9 | 0.903798 | 0.451899 | − | 0.892069i | \(-0.350747\pi\) | ||||
0.451899 | + | 0.892069i | \(0.350747\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.08804e9 | 1.08409 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.19734e9 | 0.239445 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.43515e8 | −0.0457478 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.73741e9 | −0.306884 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.26538e9 | −0.376533 | −0.188266 | − | 0.982118i | \(-0.560287\pi\) | ||||
−0.188266 | + | 0.982118i | \(0.560287\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.49158e9 | 1.32921 | 0.664603 | − | 0.747197i | \(-0.268601\pi\) | ||||
0.664603 | + | 0.747197i | \(0.268601\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.75981e9 | 0.259629 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.65826e7 | 0.00787391 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.28379e9 | 0.956774 | 0.478387 | − | 0.878149i | \(-0.341222\pi\) | ||||
0.478387 | + | 0.878149i | \(0.341222\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.45968e7 | 0.00181121 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.66821e10 | 1.95674 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.38419e10 | −1.53586 | −0.767929 | − | 0.640535i | \(-0.778712\pi\) | ||||
−0.767929 | + | 0.640535i | \(0.778712\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.49952e9 | 0.262530 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.92038e9 | 0.688503 | 0.344252 | − | 0.938877i | \(-0.388133\pi\) | ||||
0.344252 | + | 0.938877i | \(0.388133\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.00164e10 | −0.944543 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.10464e9 | 0.0987957 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.26987e9 | 0.277539 | 0.138769 | − | 0.990325i | \(-0.455685\pi\) | ||||
0.138769 | + | 0.990325i | \(0.455685\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.07090e9 | 0.247511 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.11497e9 | 0.238547 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.12431e10 | 0.818556 | 0.409278 | − | 0.912410i | \(-0.365781\pi\) | ||||
0.409278 | + | 0.912410i | \(0.365781\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.75039e9 | 0.259731 | 0.129865 | − | 0.991532i | \(-0.458546\pi\) | ||||
0.129865 | + | 0.991532i | \(0.458546\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.48432e7 | 0.00295574 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.07494e9 | 0.130237 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.32430e10 | 0.791954 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.17792e9 | −0.238167 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.72426e10 | −0.937460 | −0.468730 | − | 0.883342i | \(-0.655288\pi\) | ||||
−0.468730 | + | 0.883342i | \(0.655288\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.01060e9 | −0.311824 | −0.155912 | − | 0.987771i | \(-0.549832\pi\) | ||||
−0.155912 | + | 0.987771i | \(0.549832\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.22769e9 | 0.0608043 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.19077e10 | −0.563289 | −0.281645 | − | 0.959519i | \(-0.590880\pi\) | ||||
−0.281645 | + | 0.959519i | \(0.590880\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.10946e9 | 0.276162 | 0.138081 | − | 0.990421i | \(-0.455907\pi\) | ||||
0.138081 | + | 0.990421i | \(0.455907\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.93722e10 | −0.837137 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.06303e9 | 0.126596 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.45434e10 | −0.575139 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.39224e10 | 0.527046 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.31271e9 | 0.301359 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.67892e10 | 1.27776 | 0.638881 | − | 0.769306i | \(-0.279398\pi\) | ||||
0.638881 | + | 0.769306i | \(0.279398\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.04209e10 | 0.346894 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.19463e10 | 0.381293 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.11719e8 | −0.0217891 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.93894e10 | 0.569596 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.50459e9 | 0.183423 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.01307e9 | 0.135747 | 0.0678737 | − | 0.997694i | \(-0.478379\pi\) | ||||
0.0678737 | + | 0.997694i | \(0.478379\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.56289e9 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.73858e10 | 0.684555 | 0.342278 | − | 0.939599i | \(-0.388802\pi\) | ||||
0.342278 | + | 0.939599i | \(0.388802\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.36868e10 | 1.29005 | 0.645027 | − | 0.764159i | \(-0.276846\pi\) | ||||
0.645027 | + | 0.764159i | \(0.276846\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.14400e10 | −0.726488 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.25874e10 | 1.61347 | 0.806733 | − | 0.590916i | \(-0.201234\pi\) | ||||
0.806733 | + | 0.590916i | \(0.201234\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.92596e10 | 0.839731 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.27702e10 | −0.880590 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.73313e10 | −0.343589 | −0.171795 | − | 0.985133i | \(-0.554957\pi\) | ||||
−0.171795 | + | 0.985133i | \(0.554957\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.06448e10 | 0.776119 | 0.388059 | − | 0.921634i | \(-0.373146\pi\) | ||||
0.388059 | + | 0.921634i | \(0.373146\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3.48678e9 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.34059e10 | −0.237711 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.08296e9 | 0.0697973 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.71890e10 | 0.283371 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.00920e11 | −1.60490 | −0.802448 | − | 0.596723i | \(-0.796469\pi\) | ||||
−0.802448 | + | 0.596723i | \(0.796469\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.04770e11 | 1.60766 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.35788e10 | 0.201108 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.03660e10 | 0.720176 | 0.360088 | − | 0.932918i | \(-0.382747\pi\) | ||||
0.360088 | + | 0.932918i | \(0.382747\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.60995e10 | −0.360398 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.55632e9 | 0.0340984 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.58677e10 | 0.720046 | 0.360023 | − | 0.932943i | \(-0.382769\pi\) | ||||
0.360023 | + | 0.932943i | \(0.382769\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.12629e8 | 0.00140296 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.68256e10 | 0.202614 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.05175e11 | −1.22469 | −0.612345 | − | 0.790590i | \(-0.709774\pi\) | ||||
−0.612345 | + | 0.790590i | \(0.709774\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.44180e10 | 0.612887 | 0.306444 | − | 0.951889i | \(-0.400861\pi\) | ||||
0.306444 | + | 0.951889i | \(0.400861\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.54424e10 | −0.168261 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.92864e10 | 0.203355 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.64528e11 | 1.67912 | 0.839560 | − | 0.543268i | \(-0.182813\pi\) | ||||
0.839560 | + | 0.543268i | \(0.182813\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.93982e8 | −0.00586887 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.74255e10 | −0.645128 | −0.322564 | − | 0.946548i | \(-0.604545\pi\) | ||||
−0.322564 | + | 0.946548i | \(0.604545\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.41917e11 | −1.31521 | −0.657603 | − | 0.753364i | \(-0.728430\pi\) | ||||
−0.657603 | + | 0.753364i | \(0.728430\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 8.52345e9 | 0.0765268 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.82932e11 | 1.59155 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.66446e10 | −0.393333 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.38332e11 | −1.13085 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.79097e10 | 0.221233 | 0.110617 | − | 0.993863i | \(-0.464717\pi\) | ||||
0.110617 | + | 0.993863i | \(0.464717\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.40352e10 | 0.184778 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.62390e10 | −0.195679 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.14600e10 | 0.372349 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.50265e11 | −1.05513 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.46921e10 | 0.100136 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.46012e8 | 0.00228951 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.59767e11 | −1.02651 | −0.513257 | − | 0.858235i | \(-0.671561\pi\) | ||||
−0.513257 | + | 0.858235i | \(0.671561\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.38067e11 | −0.861540 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.84292e10 | 0.475396 | 0.237698 | − | 0.971339i | \(-0.423607\pi\) | ||||
0.237698 | + | 0.971339i | \(0.423607\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.26229e11 | −0.743378 | −0.371689 | − | 0.928357i | \(-0.621221\pi\) | ||||
−0.371689 | + | 0.928357i | \(0.621221\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.22370e10 | −0.184484 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.59499e10 | −0.533676 | −0.266838 | − | 0.963741i | \(-0.585979\pi\) | ||||
−0.266838 | + | 0.963741i | \(0.585979\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.92370e10 | 0.104011 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.40372e11 | 0.737915 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.51591e10 | 0.230852 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.47294e9 | 0.0470988 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 9.49626e10 | 0.459291 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.93822e11 | −2.32375 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.73728e10 | −0.354293 | −0.177146 | − | 0.984185i | \(-0.556687\pi\) | ||||
−0.177146 | + | 0.984185i | \(0.556687\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.17819e10 | −0.0970727 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.49477e11 | −0.648443 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.73809e11 | 0.734071 | 0.367035 | − | 0.930207i | \(-0.380373\pi\) | ||||
0.367035 | + | 0.930207i | \(0.380373\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9.89662e10 | 0.406994 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.46987e9 | −0.0179020 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.48614e11 | −0.579746 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.07426e11 | 0.408248 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.11335e11 | −1.52305 | −0.761523 | − | 0.648138i | \(-0.775548\pi\) | ||||
−0.761523 | + | 0.648138i | \(0.775548\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.97923e11 | 1.07495 | 0.537477 | − | 0.843278i | \(-0.319377\pi\) | ||||
0.537477 | + | 0.843278i | \(0.319377\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.28878e10 | −0.0453208 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.69499e9 | 0.0195212 | 0.00976061 | − | 0.999952i | \(-0.496893\pi\) | ||||
0.00976061 | + | 0.999952i | \(0.496893\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.04082e10 | 0.268703 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.70799e11 | −0.556517 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6.19565e11 | −1.96862 | −0.984310 | − | 0.176446i | \(-0.943540\pi\) | ||||
−0.984310 | + | 0.176446i | \(0.943540\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.94341e11 | −0.912155 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6.46178e9 | −0.0195331 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.49610e11 | 0.441207 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.06833e9 | 0.0117063 | 0.00585314 | − | 0.999983i | \(-0.498137\pi\) | ||||
0.00585314 | + | 0.999983i | \(0.498137\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.52670e11 | 0.428683 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.41670e9 | −0.00388235 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.75397e11 | −1.80663 | −0.903315 | − | 0.428978i | \(-0.858874\pi\) | ||||
−0.903315 | + | 0.428978i | \(0.858874\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.97754e10 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.44867e9 | 0.0240899 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.67146e11 | 0.914033 | 0.457017 | − | 0.889458i | \(-0.348918\pi\) | ||||
0.457017 | + | 0.889458i | \(0.348918\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.69763e10 | −0.187152 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.22057e11 | −0.527314 | −0.263657 | − | 0.964616i | \(-0.584929\pi\) | ||||
−0.263657 | + | 0.964616i | \(0.584929\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.42593e11 | −0.562735 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.25407e11 | −0.284199 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.23043e11 | −1.60100 | −0.800499 | − | 0.599334i | \(-0.795432\pi\) | ||||
−0.800499 | + | 0.599334i | \(0.795432\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.69168e11 | 1.23153 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.26470e11 | −0.690363 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.30017e11 | −0.682102 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.06161e11 | 1.22470 | 0.612352 | − | 0.790585i | \(-0.290224\pi\) | ||||
0.612352 | + | 0.790585i | \(0.290224\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.07211e11 | −0.211769 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.72510e11 | 1.29882 | 0.649411 | − | 0.760438i | \(-0.275016\pi\) | ||||
0.649411 | + | 0.760438i | \(0.275016\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.19547e9 | −0.00414625 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.69042e10 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.63915e11 | −0.296103 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.02482e10 | −0.0534497 | −0.0267248 | − | 0.999643i | \(-0.508508\pi\) | ||||
−0.0267248 | + | 0.999643i | \(0.508508\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.47015e11 | −0.772742 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.02325e11 | −0.511326 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.32632e11 | 0.219498 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.22198e11 | −0.521808 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.61938e11 | 0.256676 | 0.128338 | − | 0.991731i | \(-0.459036\pi\) | ||||
0.128338 | + | 0.991731i | \(0.459036\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.06547e11 | −1.25130 | −0.625648 | − | 0.780105i | \(-0.715165\pi\) | ||||
−0.625648 | + | 0.780105i | \(0.715165\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.12131e11 | −0.625899 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.04774e11 | 0.155778 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.35228e9 | −0.00633565 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −9.69844e10 | −0.138243 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.54653e11 | −1.19300 | −0.596502 | − | 0.802611i | \(-0.703443\pi\) | ||||
−0.596502 | + | 0.802611i | \(0.703443\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.21884e11 | 1.12361 | 0.561804 | − | 0.827270i | \(-0.310107\pi\) | ||||
0.561804 | + | 0.827270i | \(0.310107\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.97247e10 | 0.0264125 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.57269e11 | 0.468629 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.97807e11 | −1.28220 | −0.641100 | − | 0.767457i | \(-0.721522\pi\) | ||||
−0.641100 | + | 0.767457i | \(0.721522\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.40730e11 | 0.177180 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.22586e11 | 0.274588 | 0.137294 | − | 0.990530i | \(-0.456160\pi\) | ||||
0.137294 | + | 0.990530i | \(0.456160\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.29827e11 | 0.156945 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.83496e11 | 0.217391 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.28886e12 | 1.49657 | 0.748287 | − | 0.663375i | \(-0.230877\pi\) | ||||
0.748287 | + | 0.663375i | \(0.230877\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.14889e12 | 1.30762 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6.87818e11 | −0.767417 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.19154e11 | −0.130334 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.77644e11 | 0.941230 | 0.470615 | − | 0.882339i | \(-0.344032\pi\) | ||||
0.470615 | + | 0.882339i | \(0.344032\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.42544e11 | −0.149897 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.31142e11 | −0.341476 | −0.170738 | − | 0.985316i | \(-0.554615\pi\) | ||||
−0.170738 | + | 0.985316i | \(0.554615\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.05840e12 | 1.07037 | 0.535186 | − | 0.844735i | \(-0.320242\pi\) | ||||
0.535186 | + | 0.844735i | \(0.320242\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.58319e9 | −0.00454600 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.49420e12 | 1.45373 | 0.726864 | − | 0.686782i | \(-0.240977\pi\) | ||||
0.726864 | + | 0.686782i | \(0.240977\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.88018e12 | 1.79441 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.89987e11 | −0.552394 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −9.43722e11 | −0.866900 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.57674e10 | 0.0592774 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.18234e9 | −0.00104570 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.04497e12 | −0.906970 | −0.453485 | − | 0.891264i | \(-0.649819\pi\) | ||||
−0.453485 | + | 0.891264i | \(0.649819\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.05102e10 | −0.0685801 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.35125e12 | −1.12973 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.06737e12 | −0.875950 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.30343e12 | 1.85564 | 0.927820 | − | 0.373027i | \(-0.121680\pi\) | ||||
0.927820 | + | 0.373027i | \(0.121680\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.12119e12 | 0.886728 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.37950e11 | 0.417711 | 0.208855 | − | 0.977947i | \(-0.433026\pi\) | ||||
0.208855 | + | 0.977947i | \(0.433026\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.04506e11 | 0.0796764 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.02461e11 | −0.151572 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.01141e12 | −0.743570 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.01572e12 | 0.733364 | 0.366682 | − | 0.930346i | \(-0.380494\pi\) | ||||
0.366682 | + | 0.930346i | \(0.380494\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.60551e11 | −0.397508 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.07349e12 | 0.747723 | 0.373861 | − | 0.927485i | \(-0.378034\pi\) | ||||
0.373861 | + | 0.927485i | \(0.378034\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.13365e11 | 0.0775653 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.11329e11 | 0.545332 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.48831e12 | −0.982799 | −0.491400 | − | 0.870934i | \(-0.663515\pi\) | ||||
−0.491400 | + | 0.870934i | \(0.663515\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.88185e12 | −1.22093 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −8.94758e10 | −0.0570397 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.06533e12 | −0.667346 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.10140e12 | −1.90919 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.64860e11 | −0.160237 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.98544e11 | −0.593742 | −0.296871 | − | 0.954918i | \(-0.595943\pi\) | ||||
−0.296871 | + | 0.954918i | \(0.595943\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.59973e12 | 0.934954 | 0.467477 | − | 0.884005i | \(-0.345163\pi\) | ||||
0.467477 | + | 0.884005i | \(0.345163\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.48743e11 | −0.142900 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.42828e10 | −0.0137136 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.70173e12 | 1.50000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.52312e11 | −0.137725 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.64300e11 | 0.302857 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.08311e12 | 0.571586 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −9.10693e11 | −0.472593 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.05903e12 | 0.540456 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.11810e11 | 0.256875 | 0.128437 | − | 0.991718i | \(-0.459004\pi\) | ||||
0.128437 | + | 0.991718i | \(0.459004\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.03782e11 | −0.149956 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.32736e11 | 0.355765 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.40910e12 | −0.672977 | −0.336489 | − | 0.941688i | \(-0.609239\pi\) | ||||
−0.336489 | + | 0.941688i | \(0.609239\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.63230e9 | −0.00170650 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.55988e10 | 0.0303189 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.15108e12 | 1.88755 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.68070e11 | −0.0751922 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.36835e12 | 1.04255 | 0.521276 | − | 0.853388i | \(-0.325456\pi\) | ||||
0.521276 | + | 0.853388i | \(0.325456\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.63529e11 | −0.200781 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.07269e12 | −0.457235 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.36245e12 | 0.991005 | 0.495502 | − | 0.868607i | \(-0.334984\pi\) | ||||
0.495502 | + | 0.868607i | \(0.334984\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.63628e11 | 0.315256 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.38412e11 | 0.137506 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.25679e11 | 0.0902582 | 0.0451291 | − | 0.998981i | \(-0.485630\pi\) | ||||
0.0451291 | + | 0.998981i | \(0.485630\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.15389e11 | 0.360366 | 0.180183 | − | 0.983633i | \(-0.442331\pi\) | ||||
0.180183 | + | 0.983633i | \(0.442331\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.39665e12 | 0.541243 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.28906e11 | 0.316228 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.22404e12 | 0.835318 | 0.417659 | − | 0.908604i | \(-0.362851\pi\) | ||||
0.417659 | + | 0.908604i | \(0.362851\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.86859e11 | 0.180032 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.66829e12 | −0.607407 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.89741e9 | −0.00318974 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −9.94432e10 | −0.0351054 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5.60186e12 | −1.94742 | −0.973712 | − | 0.227783i | \(-0.926852\pi\) | ||||
−0.973712 | + | 0.227783i | \(0.926852\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.52424e10 | −0.00521837 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.64527e11 | 0.325215 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.78326e12 | 0.924289 | 0.462145 | − | 0.886805i | \(-0.347080\pi\) | ||||
0.462145 | + | 0.886805i | \(0.347080\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.31789e12 | −0.431076 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.94867e11 | −0.159442 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.36720e12 | 0.433922 | 0.216961 | − | 0.976180i | \(-0.430386\pi\) | ||||
0.216961 | + | 0.976180i | \(0.430386\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.74171e12 | 1.48252 | 0.741259 | − | 0.671219i | \(-0.234229\pi\) | ||||
0.741259 | + | 0.671219i | \(0.234229\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.56915e12 | 0.483321 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.98594e10 | −0.0151303 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.74836e12 | 1.71868 | 0.859339 | − | 0.511406i | \(-0.170875\pi\) | ||||
0.859339 | + | 0.511406i | \(0.170875\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.48105e11 | −0.0730900 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.52332e12 | −0.442186 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.99054e12 | 0.855416 | 0.427708 | − | 0.903917i | \(-0.359321\pi\) | ||||
0.427708 | + | 0.903917i | \(0.359321\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.17801e12 | 0.332056 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.27174e12 | 1.74223 | 0.871114 | − | 0.491081i | \(-0.163398\pi\) | ||||
0.871114 | + | 0.491081i | \(0.163398\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.67240e12 | 0.731632 | 0.365816 | − | 0.930687i | \(-0.380790\pi\) | ||||
0.365816 | + | 0.930687i | \(0.380790\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.12772e12 | −0.304290 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.63302e12 | −0.434305 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.52588e11 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.73329e11 | −0.173990 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8.90474e11 | −0.226826 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.73608e12 | −0.687064 | −0.343532 | − | 0.939141i | \(-0.611623\pi\) | ||||
−0.343532 | + | 0.939141i | \(0.611623\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.97993e12 | −0.737716 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.93953e11 | −0.144967 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.20167e11 | 0.125174 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.44093e11 | −0.200279 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.58542e12 | −0.604882 | −0.302441 | − | 0.953168i | \(-0.597802\pi\) | ||||
−0.302441 | + | 0.953168i | \(0.597802\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.53865e12 | 1.04707 | 0.523537 | − | 0.852003i | \(-0.324612\pi\) | ||||
0.523537 | + | 0.852003i | \(0.324612\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −9.67647e11 | −0.220140 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.68597e12 | −0.602604 | −0.301302 | − | 0.953529i | \(-0.597421\pi\) | ||||
−0.301302 | + | 0.953529i | \(0.597421\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.89872e12 | −0.420106 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.76492e10 | 0.0125799 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.39120e12 | −1.37554 | −0.687770 | − | 0.725929i | \(-0.741410\pi\) | ||||
−0.687770 | + | 0.725929i | \(0.741410\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.51906e12 | −0.534753 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.57054e12 | −0.328856 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.23105e12 | 0.873904 | 0.436952 | − | 0.899485i | \(-0.356058\pi\) | ||||
0.436952 | + | 0.899485i | \(0.356058\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.77872e12 | −0.769907 | −0.384953 | − | 0.922936i | \(-0.625782\pi\) | ||||
−0.384953 | + | 0.922936i | \(0.625782\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.26872e11 | −0.105900 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8.27248e11 | −0.164036 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.26782e11 | 0.161743 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4.06058e11 | −0.0783738 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.73340e10 | −0.00520538 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.75736e12 | 0.518114 | 0.259057 | − | 0.965862i | \(-0.416588\pi\) | ||||
0.259057 | + | 0.965862i | \(0.416588\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.07594e11 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.40567e12 | −0.440136 | −0.220068 | − | 0.975485i | \(-0.570628\pi\) | ||||
−0.220068 | + | 0.975485i | \(0.570628\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.34259e13 | 2.42397 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.21825e12 | −0.395228 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.88192e11 | 0.138592 | 0.0692961 | − | 0.997596i | \(-0.477925\pi\) | ||||
0.0692961 | + | 0.997596i | \(0.477925\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.44919e12 | −0.598563 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.34863e12 | −0.744813 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.37015e9 | −0.000738771 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.54288e12 | −0.591161 | −0.295580 | − | 0.955318i | \(-0.595513\pi\) | ||||
−0.295580 | + | 0.955318i | \(0.595513\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.54664e12 | 0.419438 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.48610e12 | −0.404191 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.24137e12 | 1.00169 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.87958e12 | −0.931535 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.66998e12 | −0.574027 | −0.287014 | − | 0.957926i | \(-0.592663\pi\) | ||||
−0.287014 | + | 0.957926i | \(0.592663\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.58955e11 | −0.0863133 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.18003e12 | −0.484819 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.42595e12 | −0.214643 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.68373e12 | 0.993369 | 0.496685 | − | 0.867931i | \(-0.334551\pi\) | ||||
0.496685 | + | 0.867931i | \(0.334551\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.46438e12 | 0.508409 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.92109e11 | −0.0278385 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.48337e11 | −0.107083 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.40383e12 | 0.198371 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.23056e13 | 1.71721 | 0.858604 | − | 0.512640i | \(-0.171332\pi\) | ||||
0.858604 | + | 0.512640i | \(0.171332\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.34001e13 | 1.84672 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.29223e12 | −0.448092 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.52197e11 | 0.0204590 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.07672e13 | 1.42954 | 0.714770 | − | 0.699360i | \(-0.246531\pi\) | ||||
0.714770 | + | 0.699360i | \(0.246531\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.82430e11 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.12681e12 | −0.664078 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.06410e13 | −1.36149 | −0.680744 | − | 0.732521i | \(-0.738343\pi\) | ||||
−0.680744 | + | 0.732521i | \(0.738343\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.08588e12 | 0.137243 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.18083e13 | 1.47429 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.24704e12 | 0.523825 | 0.261912 | − | 0.965092i | \(-0.415647\pi\) | ||||
0.261912 | + | 0.965092i | \(0.415647\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.30720e11 | −0.0402975 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.10732e13 | −1.33298 | −0.666488 | − | 0.745516i | \(-0.732203\pi\) | ||||
−0.666488 | + | 0.745516i | \(0.732203\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.41586e12 | 0.168391 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.39231e12 | −0.163604 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.36238e13 | −1.58172 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.45365e13 | −1.66755 | −0.833777 | − | 0.552102i | \(-0.813826\pi\) | ||||
−0.833777 | + | 0.552102i | \(0.813826\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8.17454e12 | 0.926587 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.30724e12 | −0.594439 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.75556e12 | −0.637025 | −0.318512 | − | 0.947919i | \(-0.603183\pi\) | ||||
−0.318512 | + | 0.947919i | \(0.603183\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −8.48638e12 | −0.928184 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.44303e13 | −1.55971 | −0.779854 | − | 0.625961i | \(-0.784707\pi\) | ||||
−0.779854 | + | 0.625961i | \(0.784707\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.21664e12 | −0.984492 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.09988e12 | −0.116110 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9.32595e11 | −0.0973003 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.65690e12 | 0.273973 | 0.136986 | − | 0.990573i | \(-0.456258\pi\) | ||||
0.136986 | + | 0.990573i | \(0.456258\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.07965e12 | −0.415794 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.35569e12 | −0.438783 | −0.219391 | − | 0.975637i | \(-0.570407\pi\) | ||||
−0.219391 | + | 0.975637i | \(0.570407\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.53641e10 | −0.00352132 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.11406e12 | 0.208076 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.91774e12 | 0.381168 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.35203e12 | −0.610918 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.07062e11 | −0.0196867 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.55237e12 | −0.427882 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.02013e13 | 1.87713 | 0.938564 | − | 0.345106i | \(-0.112157\pi\) | ||||
0.938564 | + | 0.345106i | \(0.112157\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.52529e12 | −0.415719 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.60521e12 | −0.872394 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.34257e10 | −0.00120561 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −9.12298e9 | −0.000809999 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.07284e12 | −0.181971 | −0.0909857 | − | 0.995852i | \(-0.529002\pi\) | ||||
−0.0909857 | + | 0.995852i | \(0.529002\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.68485e13 | −1.46251 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.36288e12 | −0.116980 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.18188e13 | −1.00312 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.04263e13 | −0.875082 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.51916e12 | 0.707075 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.41673e13 | 1.16284 | 0.581418 | − | 0.813605i | \(-0.302498\pi\) | ||||
0.581418 | + | 0.813605i | \(0.302498\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.04580e12 | −0.166062 | −0.0830310 | − | 0.996547i | \(-0.526460\pi\) | ||||
−0.0830310 | + | 0.996547i | \(0.526460\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.40786e12 | −0.353851 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.65117e12 | 0.686856 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.21812e12 | −0.252699 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.25084e12 | 0.0971455 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.27265e13 | −0.977607 | −0.488804 | − | 0.872394i | \(-0.662567\pi\) | ||||
−0.488804 | + | 0.872394i | \(0.662567\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.94698e12 | −0.527833 | −0.263917 | − | 0.964546i | \(-0.585014\pi\) | ||||
−0.263917 | + | 0.964546i | \(0.585014\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.56220e12 | −0.117407 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −5.09129e11 | −0.0378489 | −0.0189244 | − | 0.999821i | \(-0.506024\pi\) | ||||
−0.0189244 | + | 0.999821i | \(0.506024\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.87663e13 | −1.38001 | −0.690006 | − | 0.723804i | \(-0.742392\pi\) | ||||
−0.690006 | + | 0.723804i | \(0.742392\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.33268e13 | −0.969440 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.75324e12 | 0.414009 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.32524e12 | −0.307908 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.81125e10 | 0.00338839 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −6.68721e12 | −0.465925 | −0.232962 | − | 0.972486i | \(-0.574842\pi\) | ||||
−0.232962 | + | 0.972486i | \(0.574842\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.43553e13 | −0.989536 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.46147e12 | 0.372465 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6.26025e12 | 0.422412 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.27151e11 | 0.0418694 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.14952e13 | 0.759335 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.04484e12 | −0.460456 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.37029e12 | 0.606014 | 0.303007 | − | 0.952988i | \(-0.402009\pi\) | ||||
0.303007 | + | 0.952988i | \(0.402009\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6.90399e11 | −0.0441828 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 8.81996e12 | 0.558538 | 0.279269 | − | 0.960213i | \(-0.409908\pi\) | ||||
0.279269 | + | 0.960213i | \(0.409908\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.98932e13 | −1.24663 | −0.623313 | − | 0.781973i | \(-0.714214\pi\) | ||||
−0.623313 | + | 0.781973i | \(0.714214\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.48175e13 | −0.918884 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.20953e13 | 0.742278 | 0.371139 | − | 0.928577i | \(-0.378967\pi\) | ||||
0.371139 | + | 0.928577i | \(0.378967\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.04367e12 | −0.124119 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.77821e12 | 0.227091 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.60704e13 | 1.55081 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.79987e12 | 0.341458 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.12049e13 | 0.652894 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.91931e12 | −0.110690 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.52693e13 | −1.44243 | −0.721216 | − | 0.692710i | \(-0.756416\pi\) | ||||
−0.721216 | + | 0.692710i | \(0.756416\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.26068e12 | −0.127729 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.23113e12 | 0.236628 | 0.118314 | − | 0.992976i | \(-0.462251\pi\) | ||||
0.118314 | + | 0.992976i | \(0.462251\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.41348e12 | −0.299677 | −0.149839 | − | 0.988710i | \(-0.547875\pi\) | ||||
−0.149839 | + | 0.988710i | \(0.547875\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.94685e12 | −0.106681 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.28957e12 | 0.341165 | 0.170583 | − | 0.985343i | \(-0.445435\pi\) | ||||
0.170583 | + | 0.985343i | \(0.445435\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.47097e12 | 0.401161 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.12536e12 | 0.112975 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.05759e13 | −0.556525 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.02695e12 | −0.366069 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.16826e12 | −0.214976 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.52735e10 | −0.00180107 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.83356e10 | −0.00244346 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.21714e13 | 0.609182 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.34400e12 | −0.116155 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.27094e13 | 0.623580 | 0.311790 | − | 0.950151i | \(-0.399072\pi\) | ||||
0.311790 | + | 0.950151i | \(0.399072\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.19006e12 | −0.0578138 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.10912e12 | −0.438171 | −0.219086 | − | 0.975706i | \(-0.570307\pi\) | ||||
−0.219086 | + | 0.975706i | \(0.570307\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.04775e13 | −0.499046 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.80270e10 | −0.00132185 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.16858e13 | 1.47980 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.78526e12 | 0.313795 | 0.156898 | − | 0.987615i | \(-0.449851\pi\) | ||||
0.156898 | + | 0.987615i | \(0.449851\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.29411e13 | 0.592658 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.11993e12 | −0.141494 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.29684e12 | −0.0582436 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.11834e13 | 0.497410 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.16131e12 | 0.139250 | 0.0696252 | − | 0.997573i | \(-0.477820\pi\) | ||||
0.0696252 | + | 0.997573i | \(0.477820\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.61134e12 | 0.157541 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −6.35276e12 | −0.274470 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8.27689e12 | −0.354173 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.75670e13 | 1.59213 | 0.796065 | − | 0.605211i | \(-0.206911\pi\) | ||||
0.796065 | + | 0.605211i | \(0.206911\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.02246e13 | 0.429190 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.13713e13 | −1.30431 | −0.652153 | − | 0.758087i | \(-0.726134\pi\) | ||||
−0.652153 | + | 0.758087i | \(0.726134\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.93776e13 | 2.03342 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.61120e12 | 0.106512 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.78574e13 | 0.721513 | 0.360757 | − | 0.932660i | \(-0.382519\pi\) | ||||
0.360757 | + | 0.932660i | \(0.382519\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.80504e12 | −0.232331 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.77194e12 | 0.308118 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 8.76602e12 | 0.344258 | 0.172129 | − | 0.985074i | \(-0.444935\pi\) | ||||
0.172129 | + | 0.985074i | \(0.444935\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.07766e13 | 0.419245 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.55820e12 | −0.0600509 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.33853e13 | 1.65638 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.64314e13 | −0.999690 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.13701e13 | −0.426035 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.75663e12 | 0.139452 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.92145e13 | −1.07443 | −0.537217 | − | 0.843444i | \(-0.680524\pi\) | ||||
−0.537217 | + | 0.843444i | \(0.680524\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.65789e12 | −0.133283 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.10119e13 | −0.397536 | −0.198768 | − | 0.980047i | \(-0.563694\pi\) | ||||
−0.198768 | + | 0.980047i | \(0.563694\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.12711e13 | 1.11850 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −7.67308e11 | −0.0271925 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 8.77989e12 | 0.308293 | 0.154146 | − | 0.988048i | \(-0.450737\pi\) | ||||
0.154146 | + | 0.988048i | \(0.450737\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.02560e13 | −0.356826 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.69197e12 | −0.265172 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5.68473e13 | 1.94186 | 0.970932 | − | 0.239355i | \(-0.0769359\pi\) | ||||
0.970932 | + | 0.239355i | \(0.0769359\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.44234e12 | 0.251911 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.99996e13 | 1.34162 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.05599e13 | −1.34807 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.32479e13 | −1.42440 | −0.712202 | − | 0.701974i | \(-0.752302\pi\) | ||||
−0.712202 | + | 0.701974i | \(0.752302\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6.26720e12 | 0.204551 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.81841e12 | −0.123503 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.30139e13 | 1.69927 | 0.849633 | − | 0.527374i | \(-0.176823\pi\) | ||||
0.849633 | + | 0.527374i | \(0.176823\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.76434e12 | 0.0560450 |
(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 | 240.10.a.m.1.2 | 2 | ||
4.3 | odd | 2 | 15.10.a.c.1.2 | ✓ | 2 | ||
12.11 | even | 2 | 45.10.a.e.1.1 | 2 | |||
20.3 | even | 4 | 75.10.b.e.49.1 | 4 | |||
20.7 | even | 4 | 75.10.b.e.49.4 | 4 | |||
20.19 | odd | 2 | 75.10.a.g.1.1 | 2 | |||
60.23 | odd | 4 | 225.10.b.g.199.4 | 4 | |||
60.47 | odd | 4 | 225.10.b.g.199.1 | 4 | |||
60.59 | even | 2 | 225.10.a.j.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.10.a.c.1.2 | ✓ | 2 | 4.3 | odd | 2 | ||
45.10.a.e.1.1 | 2 | 12.11 | even | 2 | |||
75.10.a.g.1.1 | 2 | 20.19 | odd | 2 | |||
75.10.b.e.49.1 | 4 | 20.3 | even | 4 | |||
75.10.b.e.49.4 | 4 | 20.7 | even | 4 | |||
225.10.a.j.1.2 | 2 | 60.59 | even | 2 | |||
225.10.b.g.199.1 | 4 | 60.47 | odd | 4 | |||
225.10.b.g.199.4 | 4 | 60.23 | odd | 4 | |||
240.10.a.m.1.2 | 2 | 1.1 | even | 1 | trivial |