Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [50,18,Mod(1,50)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(50, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 18, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("50.1");
S:= CuspForms(chi, 18);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 50 = 2 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 18 \) |
Character orbit: | \([\chi]\) | \(=\) | 50.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: | \(91.6110436723\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{36061}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - x - 9015 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{5}\cdot 5 \) |
Twist minimal: | no (minimal twist has level 10) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-94.4487\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 50.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 256.000 | 0.707107 | ||||||||
\(3\) | 18345.8 | 1.61438 | 0.807190 | − | 0.590292i | \(-0.200987\pi\) | ||||
0.807190 | + | 0.590292i | \(0.200987\pi\) | |||||||
\(4\) | 65536.0 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 4.69652e6 | 1.14154 | ||||||||
\(7\) | −1.60786e7 | −1.05418 | −0.527090 | − | 0.849809i | \(-0.676717\pi\) | ||||
−0.527090 | + | 0.849809i | \(0.676717\pi\) | |||||||
\(8\) | 1.67772e7 | 0.353553 | ||||||||
\(9\) | 2.07428e8 | 1.60622 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 7.88217e8 | 1.10868 | 0.554342 | − | 0.832289i | \(-0.312970\pi\) | ||||
0.554342 | + | 0.832289i | \(0.312970\pi\) | |||||||
\(12\) | 1.20231e9 | 0.807190 | ||||||||
\(13\) | 2.87409e9 | 0.977195 | 0.488597 | − | 0.872509i | \(-0.337509\pi\) | ||||
0.488597 | + | 0.872509i | \(0.337509\pi\) | |||||||
\(14\) | −4.11612e9 | −0.745418 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.29497e9 | 0.250000 | ||||||||
\(17\) | −2.01570e10 | −0.700826 | −0.350413 | − | 0.936595i | \(-0.613959\pi\) | ||||
−0.350413 | + | 0.936595i | \(0.613959\pi\) | |||||||
\(18\) | 5.31015e10 | 1.13577 | ||||||||
\(19\) | −2.28657e10 | −0.308872 | −0.154436 | − | 0.988003i | \(-0.549356\pi\) | ||||
−0.154436 | + | 0.988003i | \(0.549356\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.94975e11 | −1.70185 | ||||||||
\(22\) | 2.01784e11 | 0.783959 | ||||||||
\(23\) | 6.65718e11 | 1.77257 | 0.886285 | − | 0.463140i | \(-0.153277\pi\) | ||||
0.886285 | + | 0.463140i | \(0.153277\pi\) | |||||||
\(24\) | 3.07791e11 | 0.570769 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 7.35766e11 | 0.690981 | ||||||||
\(27\) | 1.43625e12 | 0.978672 | ||||||||
\(28\) | −1.05373e12 | −0.527090 | ||||||||
\(29\) | −2.42182e12 | −0.899000 | −0.449500 | − | 0.893280i | \(-0.648398\pi\) | ||||
−0.449500 | + | 0.893280i | \(0.648398\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.75874e12 | 1.84445 | 0.922226 | − | 0.386651i | \(-0.126368\pi\) | ||||
0.922226 | + | 0.386651i | \(0.126368\pi\) | |||||||
\(32\) | 1.09951e12 | 0.176777 | ||||||||
\(33\) | 1.44605e13 | 1.78984 | ||||||||
\(34\) | −5.16020e12 | −0.495559 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.35940e13 | 0.803111 | ||||||||
\(37\) | −2.75298e13 | −1.28851 | −0.644255 | − | 0.764810i | \(-0.722833\pi\) | ||||
−0.644255 | + | 0.764810i | \(0.722833\pi\) | |||||||
\(38\) | −5.85361e12 | −0.218405 | ||||||||
\(39\) | 5.27274e13 | 1.57756 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.91759e13 | 0.766225 | 0.383112 | − | 0.923702i | \(-0.374852\pi\) | ||||
0.383112 | + | 0.923702i | \(0.374852\pi\) | |||||||
\(42\) | −7.55135e13 | −1.20339 | ||||||||
\(43\) | 1.29981e14 | 1.69589 | 0.847947 | − | 0.530082i | \(-0.177839\pi\) | ||||
0.847947 | + | 0.530082i | \(0.177839\pi\) | |||||||
\(44\) | 5.16566e13 | 0.554342 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.70424e14 | 1.25340 | ||||||||
\(47\) | 3.00620e14 | 1.84156 | 0.920781 | − | 0.390079i | \(-0.127552\pi\) | ||||
0.920781 | + | 0.390079i | \(0.127552\pi\) | |||||||
\(48\) | 7.87946e13 | 0.403595 | ||||||||
\(49\) | 2.58908e13 | 0.111296 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.69796e14 | −1.13140 | ||||||||
\(52\) | 1.88356e14 | 0.488597 | ||||||||
\(53\) | −1.01926e14 | −0.224874 | −0.112437 | − | 0.993659i | \(-0.535866\pi\) | ||||
−0.112437 | + | 0.993659i | \(0.535866\pi\) | |||||||
\(54\) | 3.67679e14 | 0.692026 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.69754e14 | −0.372709 | ||||||||
\(57\) | −4.19488e14 | −0.498636 | ||||||||
\(58\) | −6.19987e14 | −0.635689 | ||||||||
\(59\) | −9.67154e14 | −0.857538 | −0.428769 | − | 0.903414i | \(-0.641053\pi\) | ||||
−0.428769 | + | 0.903414i | \(0.641053\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.14011e15 | −0.761455 | −0.380727 | − | 0.924687i | \(-0.624326\pi\) | ||||
−0.380727 | + | 0.924687i | \(0.624326\pi\) | |||||||
\(62\) | 2.24224e15 | 1.30422 | ||||||||
\(63\) | −3.33515e15 | −1.69325 | ||||||||
\(64\) | 2.81475e14 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.70188e15 | 1.26561 | ||||||||
\(67\) | 4.04577e15 | 1.21721 | 0.608605 | − | 0.793473i | \(-0.291729\pi\) | ||||
0.608605 | + | 0.793473i | \(0.291729\pi\) | |||||||
\(68\) | −1.32101e15 | −0.350413 | ||||||||
\(69\) | 1.22131e16 | 2.86160 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.35604e15 | −1.35191 | −0.675955 | − | 0.736943i | \(-0.736269\pi\) | ||||
−0.675955 | + | 0.736943i | \(0.736269\pi\) | |||||||
\(72\) | 3.48006e15 | 0.567885 | ||||||||
\(73\) | −6.99946e14 | −0.101583 | −0.0507914 | − | 0.998709i | \(-0.516174\pi\) | ||||
−0.0507914 | + | 0.998709i | \(0.516174\pi\) | |||||||
\(74\) | −7.04762e15 | −0.911115 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.49852e15 | −0.154436 | ||||||||
\(77\) | −1.26734e16 | −1.16875 | ||||||||
\(78\) | 1.34982e16 | 1.11551 | ||||||||
\(79\) | 1.08787e16 | 0.806761 | 0.403381 | − | 0.915032i | \(-0.367835\pi\) | ||||
0.403381 | + | 0.915032i | \(0.367835\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.38165e14 | −0.0262733 | ||||||||
\(82\) | 1.00290e16 | 0.541803 | ||||||||
\(83\) | 1.23277e16 | 0.600783 | 0.300391 | − | 0.953816i | \(-0.402883\pi\) | ||||
0.300391 | + | 0.953816i | \(0.402883\pi\) | |||||||
\(84\) | −1.93315e16 | −0.850924 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 3.32752e16 | 1.19918 | ||||||||
\(87\) | −4.44303e16 | −1.45133 | ||||||||
\(88\) | 1.32241e16 | 0.391979 | ||||||||
\(89\) | −2.21332e16 | −0.595976 | −0.297988 | − | 0.954570i | \(-0.596316\pi\) | ||||
−0.297988 | + | 0.954570i | \(0.596316\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.62113e16 | −1.03014 | ||||||||
\(92\) | 4.36285e16 | 0.886285 | ||||||||
\(93\) | 1.60686e17 | 2.97765 | ||||||||
\(94\) | 7.69588e16 | 1.30218 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.01714e16 | 0.285385 | ||||||||
\(97\) | −9.41354e16 | −1.21953 | −0.609766 | − | 0.792581i | \(-0.708737\pi\) | ||||
−0.609766 | + | 0.792581i | \(0.708737\pi\) | |||||||
\(98\) | 6.62805e15 | 0.0786981 | ||||||||
\(99\) | 1.63498e17 | 1.78079 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.77746e16 | 0.347111 | 0.173556 | − | 0.984824i | \(-0.444474\pi\) | ||||
0.173556 | + | 0.984824i | \(0.444474\pi\) | |||||||
\(102\) | −9.46679e16 | −0.800021 | ||||||||
\(103\) | −1.63051e17 | −1.26826 | −0.634130 | − | 0.773226i | \(-0.718642\pi\) | ||||
−0.634130 | + | 0.773226i | \(0.718642\pi\) | |||||||
\(104\) | 4.82192e16 | 0.345491 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.60930e16 | −0.159010 | ||||||||
\(107\) | 2.33848e17 | 1.31574 | 0.657871 | − | 0.753131i | \(-0.271457\pi\) | ||||
0.657871 | + | 0.753131i | \(0.271457\pi\) | |||||||
\(108\) | 9.41259e16 | 0.489336 | ||||||||
\(109\) | −4.47257e16 | −0.214997 | −0.107498 | − | 0.994205i | \(-0.534284\pi\) | ||||
−0.107498 | + | 0.994205i | \(0.534284\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.05055e17 | −2.08015 | ||||||||
\(112\) | −6.90571e16 | −0.263545 | ||||||||
\(113\) | 2.41764e17 | 0.855510 | 0.427755 | − | 0.903895i | \(-0.359305\pi\) | ||||
0.427755 | + | 0.903895i | \(0.359305\pi\) | |||||||
\(114\) | −1.07389e17 | −0.352589 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.58717e17 | −0.449500 | ||||||||
\(117\) | 5.96165e17 | 1.56959 | ||||||||
\(118\) | −2.47591e17 | −0.606371 | ||||||||
\(119\) | 3.24097e17 | 0.738797 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.15840e17 | 0.229182 | ||||||||
\(122\) | −2.91869e17 | −0.538430 | ||||||||
\(123\) | 7.18713e17 | 1.23698 | ||||||||
\(124\) | 5.74013e17 | 0.922226 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −8.53798e17 | −1.19731 | ||||||||
\(127\) | −1.14453e17 | −0.150070 | −0.0750352 | − | 0.997181i | \(-0.523907\pi\) | ||||
−0.0750352 | + | 0.997181i | \(0.523907\pi\) | |||||||
\(128\) | 7.20576e16 | 0.0883883 | ||||||||
\(129\) | 2.38461e18 | 2.73782 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.93656e16 | 0.0497300 | 0.0248650 | − | 0.999691i | \(-0.492084\pi\) | ||||
0.0248650 | + | 0.999691i | \(0.492084\pi\) | |||||||
\(132\) | 9.47681e17 | 0.894919 | ||||||||
\(133\) | 3.67648e17 | 0.325606 | ||||||||
\(134\) | 1.03572e18 | 0.860698 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.38179e17 | −0.247780 | ||||||||
\(137\) | 4.16706e17 | 0.286883 | 0.143442 | − | 0.989659i | \(-0.454183\pi\) | ||||
0.143442 | + | 0.989659i | \(0.454183\pi\) | |||||||
\(138\) | 3.12656e18 | 2.02346 | ||||||||
\(139\) | 5.01647e17 | 0.305332 | 0.152666 | − | 0.988278i | \(-0.451214\pi\) | ||||
0.152666 | + | 0.988278i | \(0.451214\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.51512e18 | 2.97298 | ||||||||
\(142\) | −1.88315e18 | −0.955945 | ||||||||
\(143\) | 2.26540e18 | 1.08340 | ||||||||
\(144\) | 8.90895e17 | 0.401555 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.79186e17 | −0.0718298 | ||||||||
\(147\) | 4.74987e17 | 0.179674 | ||||||||
\(148\) | −1.80419e18 | −0.644255 | ||||||||
\(149\) | −1.16146e18 | −0.391670 | −0.195835 | − | 0.980637i | \(-0.562742\pi\) | ||||
−0.195835 | + | 0.980637i | \(0.562742\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.58219e18 | −1.68074 | −0.840371 | − | 0.542012i | \(-0.817663\pi\) | ||||
−0.840371 | + | 0.542012i | \(0.817663\pi\) | |||||||
\(152\) | −3.83622e17 | −0.109203 | ||||||||
\(153\) | −4.18113e18 | −1.12568 | ||||||||
\(154\) | −3.24440e18 | −0.826434 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 3.45554e18 | 0.788782 | ||||||||
\(157\) | 2.25949e18 | 0.488499 | 0.244249 | − | 0.969712i | \(-0.421458\pi\) | ||||
0.244249 | + | 0.969712i | \(0.421458\pi\) | |||||||
\(158\) | 2.78494e18 | 0.570466 | ||||||||
\(159\) | −1.86991e18 | −0.363033 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.07038e19 | −1.86861 | ||||||||
\(162\) | −1.12170e17 | −0.0185780 | ||||||||
\(163\) | 2.17080e18 | 0.341212 | 0.170606 | − | 0.985339i | \(-0.445427\pi\) | ||||
0.170606 | + | 0.985339i | \(0.445427\pi\) | |||||||
\(164\) | 2.56743e18 | 0.383112 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.15589e18 | 0.424818 | ||||||||
\(167\) | −2.02306e18 | −0.258772 | −0.129386 | − | 0.991594i | \(-0.541301\pi\) | ||||
−0.129386 | + | 0.991594i | \(0.541301\pi\) | |||||||
\(168\) | −4.94885e18 | −0.601694 | ||||||||
\(169\) | −3.90047e17 | −0.0450900 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.74297e18 | −0.496116 | ||||||||
\(172\) | 8.51844e18 | 0.847947 | ||||||||
\(173\) | −1.22669e19 | −1.16237 | −0.581183 | − | 0.813773i | \(-0.697410\pi\) | ||||
−0.581183 | + | 0.813773i | \(0.697410\pi\) | |||||||
\(174\) | −1.13741e19 | −1.02624 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.38537e18 | 0.277171 | ||||||||
\(177\) | −1.77432e19 | −1.38439 | ||||||||
\(178\) | −5.66610e18 | −0.421419 | ||||||||
\(179\) | −1.77359e19 | −1.25778 | −0.628888 | − | 0.777496i | \(-0.716490\pi\) | ||||
−0.628888 | + | 0.777496i | \(0.716490\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.40303e19 | −0.905315 | −0.452657 | − | 0.891684i | \(-0.649524\pi\) | ||||
−0.452657 | + | 0.891684i | \(0.649524\pi\) | |||||||
\(182\) | −1.18301e19 | −0.728419 | ||||||||
\(183\) | −2.09163e19 | −1.22928 | ||||||||
\(184\) | 1.11689e19 | 0.626698 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 4.11356e19 | 2.10551 | ||||||||
\(187\) | −1.58881e19 | −0.776996 | ||||||||
\(188\) | 1.97015e19 | 0.920781 | ||||||||
\(189\) | −2.30928e19 | −1.03170 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.22487e19 | 0.500387 | 0.250194 | − | 0.968196i | \(-0.419506\pi\) | ||||
0.250194 | + | 0.968196i | \(0.419506\pi\) | |||||||
\(192\) | 5.16388e18 | 0.201797 | ||||||||
\(193\) | −3.98799e19 | −1.49114 | −0.745568 | − | 0.666430i | \(-0.767821\pi\) | ||||
−0.745568 | + | 0.666430i | \(0.767821\pi\) | |||||||
\(194\) | −2.40987e19 | −0.862340 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.69678e18 | 0.0556479 | ||||||||
\(197\) | 1.32923e19 | 0.417481 | 0.208740 | − | 0.977971i | \(-0.433064\pi\) | ||||
0.208740 | + | 0.977971i | \(0.433064\pi\) | |||||||
\(198\) | 4.18555e19 | 1.25921 | ||||||||
\(199\) | 6.95301e18 | 0.200411 | 0.100206 | − | 0.994967i | \(-0.468050\pi\) | ||||
0.100206 | + | 0.994967i | \(0.468050\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.42229e19 | 1.96504 | ||||||||
\(202\) | 9.67031e18 | 0.245445 | ||||||||
\(203\) | 3.89395e19 | 0.947708 | ||||||||
\(204\) | −2.42350e19 | −0.565700 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −4.17412e19 | −0.896795 | ||||||||
\(207\) | 1.38088e20 | 2.84714 | ||||||||
\(208\) | 1.23441e19 | 0.244299 | ||||||||
\(209\) | −1.80231e19 | −0.342441 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.70414e19 | −0.298611 | −0.149305 | − | 0.988791i | \(-0.547704\pi\) | ||||
−0.149305 | + | 0.988791i | \(0.547704\pi\) | |||||||
\(212\) | −6.67982e18 | −0.112437 | ||||||||
\(213\) | −1.34952e20 | −2.18250 | ||||||||
\(214\) | 5.98650e19 | 0.930370 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.40962e19 | 0.346013 | ||||||||
\(217\) | −1.40828e20 | −1.94439 | ||||||||
\(218\) | −1.14498e19 | −0.152026 | ||||||||
\(219\) | −1.28411e19 | −0.163993 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.79330e19 | −0.684844 | ||||||||
\(222\) | −1.29294e20 | −1.47088 | ||||||||
\(223\) | −2.89177e19 | −0.316645 | −0.158322 | − | 0.987387i | \(-0.550609\pi\) | ||||
−0.158322 | + | 0.987387i | \(0.550609\pi\) | |||||||
\(224\) | −1.76786e19 | −0.186354 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.18916e19 | 0.604937 | ||||||||
\(227\) | 1.32244e20 | 1.24496 | 0.622481 | − | 0.782635i | \(-0.286125\pi\) | ||||
0.622481 | + | 0.782635i | \(0.286125\pi\) | |||||||
\(228\) | −2.74916e19 | −0.249318 | ||||||||
\(229\) | −1.21349e19 | −0.106031 | −0.0530157 | − | 0.998594i | \(-0.516883\pi\) | ||||
−0.0530157 | + | 0.998594i | \(0.516883\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.32504e20 | −1.88681 | ||||||||
\(232\) | −4.06315e19 | −0.317844 | ||||||||
\(233\) | −1.12741e20 | −0.850271 | −0.425135 | − | 0.905130i | \(-0.639773\pi\) | ||||
−0.425135 | + | 0.905130i | \(0.639773\pi\) | |||||||
\(234\) | 1.52618e20 | 1.10987 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −6.33834e19 | −0.428769 | ||||||||
\(237\) | 1.99578e20 | 1.30242 | ||||||||
\(238\) | 8.29687e19 | 0.522409 | ||||||||
\(239\) | −1.64296e20 | −0.998261 | −0.499131 | − | 0.866527i | \(-0.666347\pi\) | ||||
−0.499131 | + | 0.866527i | \(0.666347\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.25647e20 | 0.711223 | 0.355612 | − | 0.934634i | \(-0.384273\pi\) | ||||
0.355612 | + | 0.934634i | \(0.384273\pi\) | |||||||
\(242\) | 2.96549e19 | 0.162056 | ||||||||
\(243\) | −1.93516e20 | −1.02109 | ||||||||
\(244\) | −7.47184e19 | −0.380727 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.83990e20 | 0.874675 | ||||||||
\(247\) | −6.57178e19 | −0.301828 | ||||||||
\(248\) | 1.46947e20 | 0.652112 | ||||||||
\(249\) | 2.26161e20 | 0.969892 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.37960e20 | −0.552746 | −0.276373 | − | 0.961050i | \(-0.589133\pi\) | ||||
−0.276373 | + | 0.961050i | \(0.589133\pi\) | |||||||
\(252\) | −2.18572e20 | −0.846624 | ||||||||
\(253\) | 5.24730e20 | 1.96522 | ||||||||
\(254\) | −2.92999e19 | −0.106116 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.84467e19 | 0.0625000 | ||||||||
\(257\) | 1.08129e19 | 0.0354414 | 0.0177207 | − | 0.999843i | \(-0.494359\pi\) | ||||
0.0177207 | + | 0.999843i | \(0.494359\pi\) | |||||||
\(258\) | 6.10459e20 | 1.93593 | ||||||||
\(259\) | 4.42640e20 | 1.35832 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.02353e20 | −1.44399 | ||||||||
\(262\) | 1.26376e19 | 0.0351644 | ||||||||
\(263\) | 7.17651e20 | 1.93326 | 0.966628 | − | 0.256185i | \(-0.0824658\pi\) | ||||
0.966628 | + | 0.256185i | \(0.0824658\pi\) | |||||||
\(264\) | 2.42606e20 | 0.632803 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 9.41178e19 | 0.230238 | ||||||||
\(267\) | −4.06051e20 | −0.962132 | ||||||||
\(268\) | 2.65144e20 | 0.608605 | ||||||||
\(269\) | −5.80280e20 | −1.29046 | −0.645228 | − | 0.763990i | \(-0.723238\pi\) | ||||
−0.645228 | + | 0.763990i | \(0.723238\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.64836e20 | 0.344201 | 0.172101 | − | 0.985079i | \(-0.444945\pi\) | ||||
0.172101 | + | 0.985079i | \(0.444945\pi\) | |||||||
\(272\) | −8.65737e19 | −0.175207 | ||||||||
\(273\) | −8.47782e20 | −1.66304 | ||||||||
\(274\) | 1.06677e20 | 0.202857 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 8.00399e20 | 1.43080 | ||||||||
\(277\) | −1.52391e20 | −0.264168 | −0.132084 | − | 0.991239i | \(-0.542167\pi\) | ||||
−0.132084 | + | 0.991239i | \(0.542167\pi\) | |||||||
\(278\) | 1.28422e20 | 0.215902 | ||||||||
\(279\) | 1.81681e21 | 2.96260 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.60032e20 | 0.245586 | 0.122793 | − | 0.992432i | \(-0.460815\pi\) | ||||
0.122793 | + | 0.992432i | \(0.460815\pi\) | |||||||
\(282\) | 1.41187e21 | 2.10222 | ||||||||
\(283\) | −2.34430e20 | −0.338711 | −0.169356 | − | 0.985555i | \(-0.554169\pi\) | ||||
−0.169356 | + | 0.985555i | \(0.554169\pi\) | |||||||
\(284\) | −4.82085e20 | −0.675955 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.79943e20 | 0.766080 | ||||||||
\(287\) | −6.29894e20 | −0.807739 | ||||||||
\(288\) | 2.28069e20 | 0.283943 | ||||||||
\(289\) | −4.20935e20 | −0.508842 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.72699e21 | −1.96879 | ||||||||
\(292\) | −4.58716e19 | −0.0507914 | ||||||||
\(293\) | −1.57885e21 | −1.69811 | −0.849056 | − | 0.528303i | \(-0.822828\pi\) | ||||
−0.849056 | + | 0.528303i | \(0.822828\pi\) | |||||||
\(294\) | 1.21597e20 | 0.127049 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −4.61873e20 | −0.455557 | ||||||||
\(297\) | 1.13208e21 | 1.08504 | ||||||||
\(298\) | −2.97333e20 | −0.276952 | ||||||||
\(299\) | 1.91333e21 | 1.73215 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.08991e21 | −1.78778 | ||||||||
\(302\) | −1.42904e21 | −1.18846 | ||||||||
\(303\) | 6.93005e20 | 0.560369 | ||||||||
\(304\) | −9.82072e19 | −0.0772179 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.07037e21 | −0.795978 | ||||||||
\(307\) | 2.38391e21 | 1.72430 | 0.862152 | − | 0.506650i | \(-0.169116\pi\) | ||||
0.862152 | + | 0.506650i | \(0.169116\pi\) | |||||||
\(308\) | −8.30566e20 | −0.584377 | ||||||||
\(309\) | −2.99131e21 | −2.04745 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.58302e21 | 1.02570 | 0.512852 | − | 0.858477i | \(-0.328589\pi\) | ||||
0.512852 | + | 0.858477i | \(0.328589\pi\) | |||||||
\(312\) | 8.84618e20 | 0.557753 | ||||||||
\(313\) | 2.98369e20 | 0.183074 | 0.0915370 | − | 0.995802i | \(-0.470822\pi\) | ||||
0.0915370 | + | 0.995802i | \(0.470822\pi\) | |||||||
\(314\) | 5.78430e20 | 0.345421 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.12944e20 | 0.403381 | ||||||||
\(317\) | 1.01873e21 | 0.561117 | 0.280559 | − | 0.959837i | \(-0.409480\pi\) | ||||
0.280559 | + | 0.959837i | \(0.409480\pi\) | |||||||
\(318\) | −4.78697e20 | −0.256703 | ||||||||
\(319\) | −1.90892e21 | −0.996707 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.29012e21 | 2.12411 | ||||||||
\(322\) | −2.74017e21 | −1.32131 | ||||||||
\(323\) | 4.60903e20 | 0.216465 | ||||||||
\(324\) | −2.87156e19 | −0.0131366 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 5.55724e20 | 0.241273 | ||||||||
\(327\) | −8.20527e20 | −0.347086 | ||||||||
\(328\) | 6.57263e20 | 0.270901 | ||||||||
\(329\) | −4.83355e21 | −1.94134 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.27305e20 | −0.239299 | −0.119649 | − | 0.992816i | \(-0.538177\pi\) | ||||
−0.119649 | + | 0.992816i | \(0.538177\pi\) | |||||||
\(332\) | 8.07907e20 | 0.300391 | ||||||||
\(333\) | −5.71044e21 | −2.06963 | ||||||||
\(334\) | −5.17903e20 | −0.182980 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.26691e21 | −0.425462 | ||||||||
\(337\) | −3.61857e21 | −1.18490 | −0.592451 | − | 0.805606i | \(-0.701840\pi\) | ||||
−0.592451 | + | 0.805606i | \(0.701840\pi\) | |||||||
\(338\) | −9.98521e19 | −0.0318834 | ||||||||
\(339\) | 4.43535e21 | 1.38112 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.90379e21 | 2.04492 | ||||||||
\(342\) | −1.21420e21 | −0.350807 | ||||||||
\(343\) | 3.32408e21 | 0.936854 | ||||||||
\(344\) | 2.18072e21 | 0.599589 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.14033e21 | −0.821917 | ||||||||
\(347\) | −7.74896e21 | −1.97899 | −0.989493 | − | 0.144579i | \(-0.953817\pi\) | ||||
−0.989493 | + | 0.144579i | \(0.953817\pi\) | |||||||
\(348\) | −2.91178e21 | −0.725663 | ||||||||
\(349\) | −7.13117e21 | −1.73438 | −0.867191 | − | 0.497976i | \(-0.834077\pi\) | ||||
−0.867191 | + | 0.497976i | \(0.834077\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.12790e21 | 0.956354 | ||||||||
\(352\) | 8.66654e20 | 0.195990 | ||||||||
\(353\) | 7.70298e21 | 1.70049 | 0.850244 | − | 0.526388i | \(-0.176454\pi\) | ||||
0.850244 | + | 0.526388i | \(0.176454\pi\) | |||||||
\(354\) | −4.54226e21 | −0.978913 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.45052e21 | −0.297988 | ||||||||
\(357\) | 5.94581e21 | 1.19270 | ||||||||
\(358\) | −4.54040e21 | −0.889382 | ||||||||
\(359\) | −4.55697e21 | −0.871712 | −0.435856 | − | 0.900016i | \(-0.643554\pi\) | ||||
−0.435856 | + | 0.900016i | \(0.643554\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.95755e21 | −0.904598 | ||||||||
\(362\) | −3.59176e21 | −0.640154 | ||||||||
\(363\) | 2.12517e21 | 0.369987 | ||||||||
\(364\) | −3.02850e21 | −0.515070 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −5.35456e21 | −0.869230 | ||||||||
\(367\) | 6.69643e19 | 0.0106214 | 0.00531070 | − | 0.999986i | \(-0.498310\pi\) | ||||
0.00531070 | + | 0.999986i | \(0.498310\pi\) | |||||||
\(368\) | 2.85924e21 | 0.443142 | ||||||||
\(369\) | 8.12617e21 | 1.23073 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.63883e21 | 0.237058 | ||||||||
\(372\) | 1.05307e22 | 1.48882 | ||||||||
\(373\) | −5.61068e21 | −0.775336 | −0.387668 | − | 0.921799i | \(-0.626719\pi\) | ||||
−0.387668 | + | 0.921799i | \(0.626719\pi\) | |||||||
\(374\) | −4.06736e21 | −0.549419 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.04357e21 | 0.651091 | ||||||||
\(377\) | −6.96053e21 | −0.878498 | ||||||||
\(378\) | −5.91177e21 | −0.729520 | ||||||||
\(379\) | 6.43379e21 | 0.776307 | 0.388153 | − | 0.921595i | \(-0.373113\pi\) | ||||
0.388153 | + | 0.921595i | \(0.373113\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.09973e21 | −0.242271 | ||||||||
\(382\) | 3.13567e21 | 0.353827 | ||||||||
\(383\) | −1.11213e22 | −1.22735 | −0.613674 | − | 0.789560i | \(-0.710309\pi\) | ||||
−0.613674 | + | 0.789560i | \(0.710309\pi\) | |||||||
\(384\) | 1.32195e21 | 0.142692 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.02093e22 | −1.05439 | ||||||||
\(387\) | 2.69617e22 | 2.72398 | ||||||||
\(388\) | −6.16926e21 | −0.609766 | ||||||||
\(389\) | 6.91791e21 | 0.668965 | 0.334483 | − | 0.942402i | \(-0.391438\pi\) | ||||
0.334483 | + | 0.942402i | \(0.391438\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.34189e22 | −1.24226 | ||||||||
\(392\) | 4.34376e20 | 0.0393490 | ||||||||
\(393\) | 9.05651e20 | 0.0802831 | ||||||||
\(394\) | 3.40282e21 | 0.295204 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.07150e22 | 0.890397 | ||||||||
\(397\) | −2.17800e22 | −1.77149 | −0.885746 | − | 0.464171i | \(-0.846352\pi\) | ||||
−0.885746 | + | 0.464171i | \(0.846352\pi\) | |||||||
\(398\) | 1.77997e21 | 0.141712 | ||||||||
\(399\) | 6.74479e21 | 0.525652 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.05717e21 | 0.303037 | 0.151519 | − | 0.988454i | \(-0.451584\pi\) | ||||
0.151519 | + | 0.988454i | \(0.451584\pi\) | |||||||
\(402\) | 1.90011e22 | 1.38949 | ||||||||
\(403\) | 2.51734e22 | 1.80239 | ||||||||
\(404\) | 2.47560e21 | 0.173556 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 9.96852e21 | 0.670130 | ||||||||
\(407\) | −2.16994e22 | −1.42855 | ||||||||
\(408\) | −6.20415e21 | −0.400010 | ||||||||
\(409\) | −6.48833e21 | −0.409717 | −0.204859 | − | 0.978792i | \(-0.565673\pi\) | ||||
−0.204859 | + | 0.978792i | \(0.565673\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.64480e21 | 0.463138 | ||||||||
\(412\) | −1.06857e22 | −0.634130 | ||||||||
\(413\) | 1.55505e22 | 0.904000 | ||||||||
\(414\) | 3.53506e22 | 2.01323 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.16009e21 | 0.172745 | ||||||||
\(417\) | 9.20310e21 | 0.492922 | ||||||||
\(418\) | −4.61391e21 | −0.242143 | ||||||||
\(419\) | 2.17453e22 | 1.11827 | 0.559135 | − | 0.829077i | \(-0.311133\pi\) | ||||
0.559135 | + | 0.829077i | \(0.311133\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.45920e22 | 0.720638 | 0.360319 | − | 0.932829i | \(-0.382668\pi\) | ||||
0.360319 | + | 0.932829i | \(0.382668\pi\) | |||||||
\(422\) | −4.36261e21 | −0.211150 | ||||||||
\(423\) | 6.23570e22 | 2.95796 | ||||||||
\(424\) | −1.71003e21 | −0.0795051 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −3.45478e22 | −1.54326 | ||||||||
\(427\) | 1.83314e22 | 0.802710 | ||||||||
\(428\) | 1.53254e22 | 0.657871 | ||||||||
\(429\) | 4.15606e22 | 1.74902 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.61293e22 | −1.05699 | −0.528495 | − | 0.848937i | \(-0.677243\pi\) | ||||
−0.528495 | + | 0.848937i | \(0.677243\pi\) | |||||||
\(432\) | 6.16864e21 | 0.244668 | ||||||||
\(433\) | 1.27697e22 | 0.496632 | 0.248316 | − | 0.968679i | \(-0.420123\pi\) | ||||
0.248316 | + | 0.968679i | \(0.420123\pi\) | |||||||
\(434\) | −3.60521e22 | −1.37489 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.93114e21 | −0.107498 | ||||||||
\(437\) | −1.52221e22 | −0.547497 | ||||||||
\(438\) | −3.28731e21 | −0.115961 | ||||||||
\(439\) | −2.83409e22 | −0.980540 | −0.490270 | − | 0.871571i | \(-0.663102\pi\) | ||||
−0.490270 | + | 0.871571i | \(0.663102\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.37047e21 | 0.178766 | ||||||||
\(442\) | −1.48308e22 | −0.484258 | ||||||||
\(443\) | 1.45222e22 | 0.465158 | 0.232579 | − | 0.972578i | \(-0.425284\pi\) | ||||
0.232579 | + | 0.972578i | \(0.425284\pi\) | |||||||
\(444\) | −3.30993e22 | −1.04007 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −7.40293e21 | −0.223902 | ||||||||
\(447\) | −2.13078e22 | −0.632303 | ||||||||
\(448\) | −4.52572e21 | −0.131773 | ||||||||
\(449\) | 1.38898e22 | 0.396828 | 0.198414 | − | 0.980118i | \(-0.436421\pi\) | ||||
0.198414 | + | 0.980118i | \(0.436421\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.08791e22 | 0.849502 | ||||||||
\(452\) | 1.58443e22 | 0.427755 | ||||||||
\(453\) | −1.02410e23 | −2.71335 | ||||||||
\(454\) | 3.38544e22 | 0.880321 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −7.03785e21 | −0.176294 | ||||||||
\(457\) | 3.72555e22 | 0.916016 | 0.458008 | − | 0.888948i | \(-0.348563\pi\) | ||||
0.458008 | + | 0.888948i | \(0.348563\pi\) | |||||||
\(458\) | −3.10653e21 | −0.0749755 | ||||||||
\(459\) | −2.89505e22 | −0.685879 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.60242e22 | 0.365864 | 0.182932 | − | 0.983126i | \(-0.441441\pi\) | ||||
0.182932 | + | 0.983126i | \(0.441441\pi\) | |||||||
\(462\) | −5.95210e22 | −1.33418 | ||||||||
\(463\) | −6.01797e22 | −1.32438 | −0.662189 | − | 0.749337i | \(-0.730372\pi\) | ||||
−0.662189 | + | 0.749337i | \(0.730372\pi\) | |||||||
\(464\) | −1.04017e22 | −0.224750 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.88617e22 | −0.601232 | ||||||||
\(467\) | 4.21105e22 | 0.861384 | 0.430692 | − | 0.902499i | \(-0.358270\pi\) | ||||
0.430692 | + | 0.902499i | \(0.358270\pi\) | |||||||
\(468\) | 3.90703e22 | 0.784796 | ||||||||
\(469\) | −6.50504e22 | −1.28316 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.14521e22 | 0.788622 | ||||||||
\(472\) | −1.62262e22 | −0.303186 | ||||||||
\(473\) | 1.02453e23 | 1.88021 | ||||||||
\(474\) | 5.10919e22 | 0.920949 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2.12400e22 | 0.369399 | ||||||||
\(477\) | −2.11423e22 | −0.361198 | ||||||||
\(478\) | −4.20597e22 | −0.705877 | ||||||||
\(479\) | −4.13412e22 | −0.681603 | −0.340801 | − | 0.940135i | \(-0.610698\pi\) | ||||
−0.340801 | + | 0.940135i | \(0.610698\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.91229e22 | −1.25913 | ||||||||
\(482\) | 3.21655e22 | 0.502911 | ||||||||
\(483\) | −1.96370e23 | −3.01664 | ||||||||
\(484\) | 7.59166e21 | 0.114591 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −4.95400e22 | −0.722018 | ||||||||
\(487\) | −9.82373e22 | −1.40696 | −0.703478 | − | 0.710717i | \(-0.748370\pi\) | ||||
−0.703478 | + | 0.710717i | \(0.748370\pi\) | |||||||
\(488\) | −1.91279e22 | −0.269215 | ||||||||
\(489\) | 3.98250e22 | 0.550846 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.86911e21 | −0.0383314 | −0.0191657 | − | 0.999816i | \(-0.506101\pi\) | ||||
−0.0191657 | + | 0.999816i | \(0.506101\pi\) | |||||||
\(492\) | 4.71016e22 | 0.618489 | ||||||||
\(493\) | 4.88167e22 | 0.630043 | ||||||||
\(494\) | −1.68238e22 | −0.213424 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.76185e22 | 0.461113 | ||||||||
\(497\) | 1.18275e23 | 1.42516 | ||||||||
\(498\) | 5.78972e22 | 0.685817 | ||||||||
\(499\) | −8.68275e22 | −1.01112 | −0.505560 | − | 0.862791i | \(-0.668714\pi\) | ||||
−0.505560 | + | 0.862791i | \(0.668714\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.71146e22 | −0.417757 | ||||||||
\(502\) | −3.53177e22 | −0.390851 | ||||||||
\(503\) | −2.63166e22 | −0.286353 | −0.143177 | − | 0.989697i | \(-0.545732\pi\) | ||||
−0.143177 | + | 0.989697i | \(0.545732\pi\) | |||||||
\(504\) | −5.59545e22 | −0.598653 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.34331e23 | 1.38962 | ||||||||
\(507\) | −7.15572e21 | −0.0727924 | ||||||||
\(508\) | −7.50078e21 | −0.0750352 | ||||||||
\(509\) | 2.52122e22 | 0.248033 | 0.124017 | − | 0.992280i | \(-0.460422\pi\) | ||||
0.124017 | + | 0.992280i | \(0.460422\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.12541e22 | 0.107087 | ||||||||
\(512\) | 4.72237e21 | 0.0441942 | ||||||||
\(513\) | −3.28407e22 | −0.302284 | ||||||||
\(514\) | 2.76810e21 | 0.0250608 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.56278e23 | 1.36891 | ||||||||
\(517\) | 2.36954e23 | 2.04171 | ||||||||
\(518\) | 1.13316e23 | 0.960479 | ||||||||
\(519\) | −2.25046e23 | −1.87650 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.93522e22 | 0.721082 | 0.360541 | − | 0.932743i | \(-0.382592\pi\) | ||||
0.360541 | + | 0.932743i | \(0.382592\pi\) | |||||||
\(522\) | −1.28602e23 | −1.02106 | ||||||||
\(523\) | −9.62048e22 | −0.751506 | −0.375753 | − | 0.926720i | \(-0.622616\pi\) | ||||
−0.375753 | + | 0.926720i | \(0.622616\pi\) | |||||||
\(524\) | 3.23523e21 | 0.0248650 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.83719e23 | 1.36702 | ||||||||
\(527\) | −1.76550e23 | −1.29264 | ||||||||
\(528\) | 6.21072e22 | 0.447460 | ||||||||
\(529\) | 3.02130e23 | 2.14200 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.00615e23 | −1.37740 | ||||||||
\(532\) | 2.40942e22 | 0.162803 | ||||||||
\(533\) | 1.12595e23 | 0.748751 | ||||||||
\(534\) | −1.03949e23 | −0.680330 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 6.78768e22 | 0.430349 | ||||||||
\(537\) | −3.25380e23 | −2.03053 | ||||||||
\(538\) | −1.48552e23 | −0.912490 | ||||||||
\(539\) | 2.04076e22 | 0.123392 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.09224e23 | −0.639944 | −0.319972 | − | 0.947427i | \(-0.603673\pi\) | ||||
−0.319972 | + | 0.947427i | \(0.603673\pi\) | |||||||
\(542\) | 4.21979e22 | 0.243387 | ||||||||
\(543\) | −2.57397e23 | −1.46152 | ||||||||
\(544\) | −2.21629e22 | −0.123890 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −2.17032e23 | −1.17594 | ||||||||
\(547\) | 2.52518e23 | 1.34710 | 0.673551 | − | 0.739140i | \(-0.264768\pi\) | ||||
0.673551 | + | 0.739140i | \(0.264768\pi\) | |||||||
\(548\) | 2.73092e22 | 0.143442 | ||||||||
\(549\) | −2.36491e23 | −1.22307 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.53766e22 | 0.277675 | ||||||||
\(552\) | 2.04902e23 | 1.01173 | ||||||||
\(553\) | −1.74914e23 | −0.850472 | ||||||||
\(554\) | −3.90120e22 | −0.186795 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.28759e22 | 0.152666 | ||||||||
\(557\) | −1.44437e23 | −0.660554 | −0.330277 | − | 0.943884i | \(-0.607142\pi\) | ||||
−0.330277 | + | 0.943884i | \(0.607142\pi\) | |||||||
\(558\) | 4.65102e23 | 2.09487 | ||||||||
\(559\) | 3.73577e23 | 1.65722 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.91480e23 | −1.25437 | ||||||||
\(562\) | 4.09682e22 | 0.173655 | ||||||||
\(563\) | −7.42080e22 | −0.309834 | −0.154917 | − | 0.987927i | \(-0.549511\pi\) | ||||
−0.154917 | + | 0.987927i | \(0.549511\pi\) | |||||||
\(564\) | 3.61439e23 | 1.48649 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −6.00142e22 | −0.239505 | ||||||||
\(567\) | 7.04507e21 | 0.0276968 | ||||||||
\(568\) | −1.23414e23 | −0.477972 | ||||||||
\(569\) | 1.99386e23 | 0.760747 | 0.380373 | − | 0.924833i | \(-0.375795\pi\) | ||||
0.380373 | + | 0.924833i | \(0.375795\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.76243e22 | 0.213402 | 0.106701 | − | 0.994291i | \(-0.465971\pi\) | ||||
0.106701 | + | 0.994291i | \(0.465971\pi\) | |||||||
\(572\) | 1.48466e23 | 0.541701 | ||||||||
\(573\) | 2.24712e23 | 0.807815 | ||||||||
\(574\) | −1.61253e23 | −0.571158 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 5.83857e22 | 0.200778 | ||||||||
\(577\) | 2.51358e23 | 0.851722 | 0.425861 | − | 0.904789i | \(-0.359971\pi\) | ||||
0.425861 | + | 0.904789i | \(0.359971\pi\) | |||||||
\(578\) | −1.07759e23 | −0.359806 | ||||||||
\(579\) | −7.31628e23 | −2.40726 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.98212e23 | −0.633333 | ||||||||
\(582\) | −4.42109e23 | −1.39214 | ||||||||
\(583\) | −8.03398e22 | −0.249315 | ||||||||
\(584\) | −1.17431e22 | −0.0359149 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.04186e23 | −1.20075 | ||||||||
\(587\) | −2.04262e23 | −0.598087 | −0.299043 | − | 0.954240i | \(-0.596668\pi\) | ||||
−0.299043 | + | 0.954240i | \(0.596668\pi\) | |||||||
\(588\) | 3.11288e22 | 0.0898369 | ||||||||
\(589\) | −2.00274e23 | −0.569699 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.43857e23 | 0.673973 | ||||||||
\(592\) | −1.18239e23 | −0.322128 | ||||||||
\(593\) | 2.40118e23 | 0.644851 | 0.322425 | − | 0.946595i | \(-0.395502\pi\) | ||||
0.322425 | + | 0.946595i | \(0.395502\pi\) | |||||||
\(594\) | 2.89811e23 | 0.767239 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −7.61172e22 | −0.195835 | ||||||||
\(597\) | 1.27558e23 | 0.323539 | ||||||||
\(598\) | 4.89812e23 | 1.22481 | ||||||||
\(599\) | 6.64163e23 | 1.63737 | 0.818684 | − | 0.574244i | \(-0.194704\pi\) | ||||
0.818684 | + | 0.574244i | \(0.194704\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.64984e23 | −1.35395 | −0.676975 | − | 0.736006i | \(-0.736710\pi\) | ||||
−0.676975 | + | 0.736006i | \(0.736710\pi\) | |||||||
\(602\) | −5.35018e23 | −1.26415 | ||||||||
\(603\) | 8.39206e23 | 1.95511 | ||||||||
\(604\) | −3.65835e23 | −0.840371 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1.77409e23 | 0.396241 | ||||||||
\(607\) | 2.77451e23 | 0.611057 | 0.305529 | − | 0.952183i | \(-0.401167\pi\) | ||||
0.305529 | + | 0.952183i | \(0.401167\pi\) | |||||||
\(608\) | −2.51411e22 | −0.0546013 | ||||||||
\(609\) | 7.14376e23 | 1.52996 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.64009e23 | 1.79957 | ||||||||
\(612\) | −2.74014e23 | −0.562841 | ||||||||
\(613\) | 3.66032e23 | 0.741491 | 0.370745 | − | 0.928735i | \(-0.379102\pi\) | ||||
0.370745 | + | 0.928735i | \(0.379102\pi\) | |||||||
\(614\) | 6.10281e23 | 1.21927 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.12625e23 | −0.413217 | ||||||||
\(617\) | 5.54311e23 | 1.06250 | 0.531251 | − | 0.847215i | \(-0.321722\pi\) | ||||
0.531251 | + | 0.847215i | \(0.321722\pi\) | |||||||
\(618\) | −7.65775e23 | −1.44777 | ||||||||
\(619\) | 7.96802e23 | 1.48587 | 0.742934 | − | 0.669365i | \(-0.233434\pi\) | ||||
0.742934 | + | 0.669365i | \(0.233434\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 9.56135e23 | 1.73476 | ||||||||
\(622\) | 4.05252e23 | 0.725282 | ||||||||
\(623\) | 3.55871e23 | 0.628266 | ||||||||
\(624\) | 2.26462e23 | 0.394391 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 7.63825e22 | 0.129453 | ||||||||
\(627\) | −3.30648e23 | −0.552830 | ||||||||
\(628\) | 1.48078e23 | 0.244249 | ||||||||
\(629\) | 5.54918e23 | 0.903022 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.62634e23 | 0.732804 | 0.366402 | − | 0.930457i | \(-0.380590\pi\) | ||||
0.366402 | + | 0.930457i | \(0.380590\pi\) | |||||||
\(632\) | 1.82514e23 | 0.285233 | ||||||||
\(633\) | −3.12639e23 | −0.482071 | ||||||||
\(634\) | 2.60794e23 | 0.396770 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.22547e23 | −0.181516 | ||||||||
\(637\) | 7.44124e22 | 0.108758 | ||||||||
\(638\) | −4.88684e23 | −0.704779 | ||||||||
\(639\) | −1.52585e24 | −2.17147 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.38553e23 | 0.330592 | 0.165296 | − | 0.986244i | \(-0.447142\pi\) | ||||
0.165296 | + | 0.986244i | \(0.447142\pi\) | |||||||
\(642\) | 1.09827e24 | 1.50197 | ||||||||
\(643\) | 1.39064e24 | 1.87681 | 0.938405 | − | 0.345536i | \(-0.112303\pi\) | ||||
0.938405 | + | 0.345536i | \(0.112303\pi\) | |||||||
\(644\) | −7.01485e23 | −0.934304 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.17991e23 | 0.153064 | ||||||||
\(647\) | 1.93162e23 | 0.247306 | 0.123653 | − | 0.992325i | \(-0.460539\pi\) | ||||
0.123653 | + | 0.992325i | \(0.460539\pi\) | |||||||
\(648\) | −7.35118e21 | −0.00928901 | ||||||||
\(649\) | −7.62328e23 | −0.950740 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.58361e24 | −3.13898 | ||||||||
\(652\) | 1.42265e23 | 0.170606 | ||||||||
\(653\) | −1.41423e24 | −1.67401 | −0.837007 | − | 0.547192i | \(-0.815697\pi\) | ||||
−0.837007 | + | 0.547192i | \(0.815697\pi\) | |||||||
\(654\) | −2.10055e23 | −0.245427 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.68259e23 | 0.191556 | ||||||||
\(657\) | −1.45188e23 | −0.163164 | ||||||||
\(658\) | −1.23739e24 | −1.37273 | ||||||||
\(659\) | −3.77712e23 | −0.413651 | −0.206826 | − | 0.978378i | \(-0.566313\pi\) | ||||
−0.206826 | + | 0.978378i | \(0.566313\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.30952e23 | 0.673416 | 0.336708 | − | 0.941609i | \(-0.390686\pi\) | ||||
0.336708 | + | 0.941609i | \(0.390686\pi\) | |||||||
\(662\) | −1.60590e23 | −0.169210 | ||||||||
\(663\) | −1.06283e24 | −1.10560 | ||||||||
\(664\) | 2.06824e23 | 0.212409 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.46187e24 | −1.46345 | ||||||||
\(667\) | −1.61225e24 | −1.59354 | ||||||||
\(668\) | −1.32583e23 | −0.129386 | ||||||||
\(669\) | −5.30518e23 | −0.511185 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.98656e23 | −0.844213 | ||||||||
\(672\) | −3.24328e23 | −0.300847 | ||||||||
\(673\) | −1.46706e24 | −1.34375 | −0.671876 | − | 0.740663i | \(-0.734511\pi\) | ||||
−0.671876 | + | 0.740663i | \(0.734511\pi\) | |||||||
\(674\) | −9.26353e23 | −0.837852 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.55621e22 | −0.0225450 | ||||||||
\(677\) | −8.89634e22 | −0.0774832 | −0.0387416 | − | 0.999249i | \(-0.512335\pi\) | ||||
−0.0387416 | + | 0.999249i | \(0.512335\pi\) | |||||||
\(678\) | 1.13545e24 | 0.976598 | ||||||||
\(679\) | 1.51357e24 | 1.28561 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.42612e24 | 2.00984 | ||||||||
\(682\) | 1.76737e24 | 1.44597 | ||||||||
\(683\) | 8.93594e23 | 0.722045 | 0.361022 | − | 0.932557i | \(-0.382428\pi\) | ||||
0.361022 | + | 0.932557i | \(0.382428\pi\) | |||||||
\(684\) | −3.10835e23 | −0.248058 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 8.50966e23 | 0.662456 | ||||||||
\(687\) | −2.22624e23 | −0.171175 | ||||||||
\(688\) | 5.58265e23 | 0.423973 | ||||||||
\(689\) | −2.92944e23 | −0.219746 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.89975e23 | −0.578162 | −0.289081 | − | 0.957305i | \(-0.593350\pi\) | ||||
−0.289081 | + | 0.957305i | \(0.593350\pi\) | |||||||
\(692\) | −8.03924e23 | −0.581183 | ||||||||
\(693\) | −2.62882e24 | −1.87728 | ||||||||
\(694\) | −1.98373e24 | −1.39935 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −7.45416e23 | −0.513121 | ||||||||
\(697\) | −7.89669e23 | −0.536991 | ||||||||
\(698\) | −1.82558e24 | −1.22639 | ||||||||
\(699\) | −2.06833e24 | −1.37266 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.61705e23 | 0.234288 | 0.117144 | − | 0.993115i | \(-0.462626\pi\) | ||||
0.117144 | + | 0.993115i | \(0.462626\pi\) | |||||||
\(702\) | 1.05674e24 | 0.676244 | ||||||||
\(703\) | 6.29486e23 | 0.397984 | ||||||||
\(704\) | 2.21863e23 | 0.138586 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.97196e24 | 1.20243 | ||||||||
\(707\) | −6.07363e23 | −0.365918 | ||||||||
\(708\) | −1.16282e24 | −0.692196 | ||||||||
\(709\) | 4.46298e23 | 0.262501 | 0.131251 | − | 0.991349i | \(-0.458101\pi\) | ||||
0.131251 | + | 0.991349i | \(0.458101\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.25654e24 | 1.29584 | ||||||||
\(712\) | −3.71333e23 | −0.210709 | ||||||||
\(713\) | 5.83085e24 | 3.26942 | ||||||||
\(714\) | 1.52213e24 | 0.843366 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.16234e24 | −0.628888 | ||||||||
\(717\) | −3.01414e24 | −1.61157 | ||||||||
\(718\) | −1.16658e24 | −0.616393 | ||||||||
\(719\) | 1.55258e24 | 0.810698 | 0.405349 | − | 0.914162i | \(-0.367150\pi\) | ||||
0.405349 | + | 0.914162i | \(0.367150\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.62164e24 | 1.33697 | ||||||||
\(722\) | −1.26913e24 | −0.639648 | ||||||||
\(723\) | 2.30509e24 | 1.14818 | ||||||||
\(724\) | −9.19491e23 | −0.452657 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 5.44043e23 | 0.261621 | ||||||||
\(727\) | −1.38114e23 | −0.0656439 | −0.0328219 | − | 0.999461i | \(-0.510449\pi\) | ||||
−0.0328219 | + | 0.999461i | \(0.510449\pi\) | |||||||
\(728\) | −7.75296e23 | −0.364209 | ||||||||
\(729\) | −3.49361e24 | −1.62215 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.62003e24 | −1.18853 | ||||||||
\(732\) | −1.37077e24 | −0.614639 | ||||||||
\(733\) | −1.51067e24 | −0.669555 | −0.334778 | − | 0.942297i | \(-0.608661\pi\) | ||||
−0.334778 | + | 0.942297i | \(0.608661\pi\) | |||||||
\(734\) | 1.71428e22 | 0.00751046 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.31964e23 | 0.313349 | ||||||||
\(737\) | 3.18895e24 | 1.34950 | ||||||||
\(738\) | 2.08030e24 | 0.870255 | ||||||||
\(739\) | −3.13836e24 | −1.29785 | −0.648926 | − | 0.760851i | \(-0.724782\pi\) | ||||
−0.648926 | + | 0.760851i | \(0.724782\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.20565e24 | −0.487265 | ||||||||
\(742\) | 4.19540e23 | 0.167625 | ||||||||
\(743\) | 4.99845e23 | 0.197438 | 0.0987190 | − | 0.995115i | \(-0.468526\pi\) | ||||
0.0987190 | + | 0.995115i | \(0.468526\pi\) | |||||||
\(744\) | 2.69586e24 | 1.05276 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.43633e24 | −0.548246 | ||||||||
\(747\) | 2.55710e24 | 0.964991 | ||||||||
\(748\) | −1.04124e24 | −0.388498 | ||||||||
\(749\) | −3.75994e24 | −1.38703 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.01494e24 | 1.44790 | 0.723952 | − | 0.689851i | \(-0.242324\pi\) | ||||
0.723952 | + | 0.689851i | \(0.242324\pi\) | |||||||
\(752\) | 1.29115e24 | 0.460391 | ||||||||
\(753\) | −2.53098e24 | −0.892342 | ||||||||
\(754\) | −1.78190e24 | −0.621192 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.51341e24 | −0.515848 | ||||||||
\(757\) | 3.79032e24 | 1.27750 | 0.638750 | − | 0.769414i | \(-0.279452\pi\) | ||||
0.638750 | + | 0.769414i | \(0.279452\pi\) | |||||||
\(758\) | 1.64705e24 | 0.548932 | ||||||||
\(759\) | 9.62659e24 | 3.17261 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.23826e24 | −0.399065 | −0.199532 | − | 0.979891i | \(-0.563942\pi\) | ||||
−0.199532 | + | 0.979891i | \(0.563942\pi\) | |||||||
\(762\) | −5.37530e23 | −0.171311 | ||||||||
\(763\) | 7.19126e23 | 0.226645 | ||||||||
\(764\) | 8.02731e23 | 0.250194 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.84706e24 | −0.867866 | ||||||||
\(767\) | −2.77968e24 | −0.837982 | ||||||||
\(768\) | 3.38420e23 | 0.100899 | ||||||||
\(769\) | 3.58282e24 | 1.05646 | 0.528228 | − | 0.849102i | \(-0.322857\pi\) | ||||
0.528228 | + | 0.849102i | \(0.322857\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.98371e23 | 0.0572158 | ||||||||
\(772\) | −2.61357e24 | −0.745568 | ||||||||
\(773\) | −1.21994e24 | −0.344203 | −0.172101 | − | 0.985079i | \(-0.555056\pi\) | ||||
−0.172101 | + | 0.985079i | \(0.555056\pi\) | |||||||
\(774\) | 6.90219e24 | 1.92615 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −1.57933e24 | −0.431170 | ||||||||
\(777\) | 8.12058e24 | 2.19285 | ||||||||
\(778\) | 1.77099e24 | 0.473030 | ||||||||
\(779\) | −8.95783e23 | −0.236665 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.79815e24 | −1.49884 | ||||||||
\(782\) | −3.43523e24 | −0.878413 | ||||||||
\(783\) | −3.47834e24 | −0.879826 | ||||||||
\(784\) | 1.11200e23 | 0.0278240 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 2.31847e23 | 0.0567688 | ||||||||
\(787\) | 1.07097e24 | 0.259414 | 0.129707 | − | 0.991552i | \(-0.458596\pi\) | ||||
0.129707 | + | 0.991552i | \(0.458596\pi\) | |||||||
\(788\) | 8.71123e23 | 0.208740 | ||||||||
\(789\) | 1.31659e25 | 3.12101 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.88723e24 | −0.901862 | ||||||||
\(792\) | 2.74304e24 | 0.629606 | ||||||||
\(793\) | −3.27678e24 | −0.744090 | ||||||||
\(794\) | −5.57569e24 | −1.25263 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4.55672e23 | 0.100206 | ||||||||
\(797\) | −5.86608e22 | −0.0127630 | −0.00638149 | − | 0.999980i | \(-0.502031\pi\) | ||||
−0.00638149 | + | 0.999980i | \(0.502031\pi\) | |||||||
\(798\) | 1.72667e24 | 0.371692 | ||||||||
\(799\) | −6.05961e24 | −1.29062 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.59104e24 | −0.957270 | ||||||||
\(802\) | 1.03864e24 | 0.214280 | ||||||||
\(803\) | −5.51709e23 | −0.112623 | ||||||||
\(804\) | 4.86427e24 | 0.982520 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 6.44439e24 | 1.27448 | ||||||||
\(807\) | −1.06457e25 | −2.08329 | ||||||||
\(808\) | 6.33753e23 | 0.122722 | ||||||||
\(809\) | 2.47056e24 | 0.473406 | 0.236703 | − | 0.971582i | \(-0.423933\pi\) | ||||
0.236703 | + | 0.971582i | \(0.423933\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.80457e24 | 1.83972 | 0.919859 | − | 0.392249i | \(-0.128303\pi\) | ||||
0.919859 | + | 0.392249i | \(0.128303\pi\) | |||||||
\(812\) | 2.55194e24 | 0.473854 | ||||||||
\(813\) | 3.02404e24 | 0.555671 | ||||||||
\(814\) | −5.55506e24 | −1.01014 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1.58826e24 | −0.282850 | ||||||||
\(817\) | −2.97210e24 | −0.523813 | ||||||||
\(818\) | −1.66101e24 | −0.289714 | ||||||||
\(819\) | −9.58550e24 | −1.65463 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.65428e23 | 0.0617853 | 0.0308927 | − | 0.999523i | \(-0.490165\pi\) | ||||
0.0308927 | + | 0.999523i | \(0.490165\pi\) | |||||||
\(822\) | 1.95707e24 | 0.327488 | ||||||||
\(823\) | 9.20886e24 | 1.52513 | 0.762565 | − | 0.646911i | \(-0.223940\pi\) | ||||
0.762565 | + | 0.646911i | \(0.223940\pi\) | |||||||
\(824\) | −2.73555e24 | −0.448398 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.98092e24 | 0.639224 | ||||||||
\(827\) | −2.05375e24 | −0.326400 | −0.163200 | − | 0.986593i | \(-0.552182\pi\) | ||||
−0.163200 | + | 0.986593i | \(0.552182\pi\) | |||||||
\(828\) | 9.04975e24 | 1.42357 | ||||||||
\(829\) | 2.35707e24 | 0.366994 | 0.183497 | − | 0.983020i | \(-0.441258\pi\) | ||||
0.183497 | + | 0.983020i | \(0.441258\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.79573e24 | −0.426468 | ||||||||
\(832\) | 8.08983e23 | 0.122149 | ||||||||
\(833\) | −5.21882e23 | −0.0779991 | ||||||||
\(834\) | 2.35599e24 | 0.348548 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1.18116e24 | −0.171221 | ||||||||
\(837\) | 1.25797e25 | 1.80511 | ||||||||
\(838\) | 5.56680e24 | 0.790736 | ||||||||
\(839\) | 4.69193e24 | 0.659743 | 0.329872 | − | 0.944026i | \(-0.392994\pi\) | ||||
0.329872 | + | 0.944026i | \(0.392994\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.39192e24 | −0.191800 | ||||||||
\(842\) | 3.73555e24 | 0.509568 | ||||||||
\(843\) | 2.93591e24 | 0.396469 | ||||||||
\(844\) | −1.11683e24 | −0.149305 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.59634e25 | 2.09159 | ||||||||
\(847\) | −1.86254e24 | −0.241600 | ||||||||
\(848\) | −4.37769e23 | −0.0562186 | ||||||||
\(849\) | −4.30081e24 | −0.546808 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.83271e25 | −2.28398 | ||||||||
\(852\) | −8.84423e24 | −1.09125 | ||||||||
\(853\) | 8.89565e24 | 1.08670 | 0.543352 | − | 0.839505i | \(-0.317155\pi\) | ||||
0.543352 | + | 0.839505i | \(0.317155\pi\) | |||||||
\(854\) | 4.69284e24 | 0.567602 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.92331e24 | 0.465185 | ||||||||
\(857\) | −1.23863e25 | −1.45413 | −0.727066 | − | 0.686567i | \(-0.759117\pi\) | ||||
−0.727066 | + | 0.686567i | \(0.759117\pi\) | |||||||
\(858\) | 1.06395e25 | 1.23674 | ||||||||
\(859\) | 3.17743e24 | 0.365708 | 0.182854 | − | 0.983140i | \(-0.441466\pi\) | ||||
0.182854 | + | 0.983140i | \(0.441466\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.15559e25 | −1.30400 | ||||||||
\(862\) | −6.68909e24 | −0.747404 | ||||||||
\(863\) | −1.42021e25 | −1.57130 | −0.785652 | − | 0.618669i | \(-0.787672\pi\) | ||||
−0.785652 | + | 0.618669i | \(0.787672\pi\) | |||||||
\(864\) | 1.57917e24 | 0.173006 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 3.26905e24 | 0.351172 | ||||||||
\(867\) | −7.72238e24 | −0.821465 | ||||||||
\(868\) | −9.22933e24 | −0.972193 | ||||||||
\(869\) | 8.57475e24 | 0.894444 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.16279e25 | 1.18945 | ||||||||
\(872\) | −7.50372e23 | −0.0760128 | ||||||||
\(873\) | −1.95263e25 | −1.95884 | ||||||||
\(874\) | −3.89685e24 | −0.387139 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −8.41551e23 | −0.0819966 | ||||||||
\(877\) | 8.28800e24 | 0.799748 | 0.399874 | − | 0.916570i | \(-0.369054\pi\) | ||||
0.399874 | + | 0.916570i | \(0.369054\pi\) | |||||||
\(878\) | −7.25527e24 | −0.693347 | ||||||||
\(879\) | −2.89653e25 | −2.74140 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.02937e24 | 0.652561 | 0.326281 | − | 0.945273i | \(-0.394205\pi\) | ||||
0.326281 | + | 0.945273i | \(0.394205\pi\) | |||||||
\(882\) | 1.37484e24 | 0.126407 | ||||||||
\(883\) | 3.64222e23 | 0.0331665 | 0.0165833 | − | 0.999862i | \(-0.494721\pi\) | ||||
0.0165833 | + | 0.999862i | \(0.494721\pi\) | |||||||
\(884\) | −3.79670e24 | −0.342422 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.71768e24 | 0.328916 | ||||||||
\(887\) | −1.85309e25 | −1.62385 | −0.811923 | − | 0.583765i | \(-0.801579\pi\) | ||||
−0.811923 | + | 0.583765i | \(0.801579\pi\) | |||||||
\(888\) | −8.47342e24 | −0.735442 | ||||||||
\(889\) | 1.84024e24 | 0.158201 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.45369e23 | −0.0291288 | ||||||||
\(892\) | −1.89515e24 | −0.158322 | ||||||||
\(893\) | −6.87388e24 | −0.568807 | ||||||||
\(894\) | −5.45481e24 | −0.447106 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.15859e24 | −0.0931772 | ||||||||
\(897\) | 3.51015e25 | 2.79634 | ||||||||
\(898\) | 3.55579e24 | 0.280600 | ||||||||
\(899\) | −2.12121e25 | −1.65816 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.05452e24 | 0.157598 | ||||||||
\(902\) | 7.90506e24 | 0.600689 | ||||||||
\(903\) | −3.83411e25 | −2.88615 | ||||||||
\(904\) | 4.05613e24 | 0.302469 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −2.62169e25 | −1.91863 | ||||||||
\(907\) | 1.87024e25 | 1.35592 | 0.677962 | − | 0.735097i | \(-0.262863\pi\) | ||||
0.677962 | + | 0.735097i | \(0.262863\pi\) | |||||||
\(908\) | 8.66674e24 | 0.622481 | ||||||||
\(909\) | 7.83551e24 | 0.557538 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.41129e25 | −0.985620 | −0.492810 | − | 0.870137i | \(-0.664030\pi\) | ||||
−0.492810 | + | 0.870137i | \(0.664030\pi\) | |||||||
\(912\) | −1.80169e24 | −0.124659 | ||||||||
\(913\) | 9.71689e24 | 0.666079 | ||||||||
\(914\) | 9.53741e24 | 0.647721 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −7.95273e23 | −0.0530157 | ||||||||
\(917\) | −7.93730e23 | −0.0524244 | ||||||||
\(918\) | −7.41132e24 | −0.484990 | ||||||||
\(919\) | −2.33638e25 | −1.51482 | −0.757411 | − | 0.652938i | \(-0.773536\pi\) | ||||
−0.757411 | + | 0.652938i | \(0.773536\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.37347e25 | 2.78368 | ||||||||
\(922\) | 4.10221e24 | 0.258705 | ||||||||
\(923\) | −2.11419e25 | −1.32108 | ||||||||
\(924\) | −1.52374e25 | −0.943406 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −1.54060e25 | −0.936476 | ||||||||
\(927\) | −3.38214e25 | −2.03711 | ||||||||
\(928\) | −2.66282e24 | −0.158922 | ||||||||
\(929\) | 2.98004e25 | 1.76234 | 0.881169 | − | 0.472802i | \(-0.156757\pi\) | ||||
0.881169 | + | 0.472802i | \(0.156757\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.92010e23 | −0.0343761 | ||||||||
\(932\) | −7.38860e24 | −0.425135 | ||||||||
\(933\) | 2.90417e25 | 1.65588 | ||||||||
\(934\) | 1.07803e25 | 0.609090 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.00020e25 | 0.554935 | ||||||||
\(937\) | 2.48730e25 | 1.36755 | 0.683774 | − | 0.729694i | \(-0.260337\pi\) | ||||
0.683774 | + | 0.729694i | \(0.260337\pi\) | |||||||
\(938\) | −1.66529e25 | −0.907331 | ||||||||
\(939\) | 5.47381e24 | 0.295551 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.05795e25 | −1.62150 | −0.810752 | − | 0.585390i | \(-0.800941\pi\) | ||||
−0.810752 | + | 0.585390i | \(0.800941\pi\) | |||||||
\(942\) | 1.06117e25 | 0.557640 | ||||||||
\(943\) | 2.60801e25 | 1.35819 | ||||||||
\(944\) | −4.15389e24 | −0.214385 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.62281e25 | 1.32951 | ||||||||
\(947\) | 3.09044e25 | 1.55255 | 0.776276 | − | 0.630393i | \(-0.217106\pi\) | ||||
0.776276 | + | 0.630393i | \(0.217106\pi\) | |||||||
\(948\) | 1.30795e25 | 0.651210 | ||||||||
\(949\) | −2.01170e24 | −0.0992661 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.86893e25 | 0.905856 | ||||||||
\(952\) | 5.43744e24 | 0.261204 | ||||||||
\(953\) | −2.50647e24 | −0.119337 | −0.0596683 | − | 0.998218i | \(-0.519004\pi\) | ||||
−0.0596683 | + | 0.998218i | \(0.519004\pi\) | |||||||
\(954\) | −5.41242e24 | −0.255406 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1.07673e25 | −0.499131 | ||||||||
\(957\) | −3.50207e25 | −1.60906 | ||||||||
\(958\) | −1.05834e25 | −0.481966 | ||||||||
\(959\) | −6.70005e24 | −0.302426 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.41655e25 | 2.40200 | ||||||||
\(962\) | −2.02555e25 | −0.890337 | ||||||||
\(963\) | 4.85065e25 | 2.11337 | ||||||||
\(964\) | 8.23438e24 | 0.355612 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −5.02707e25 | −2.13309 | ||||||||
\(967\) | 1.13278e25 | 0.476455 | 0.238228 | − | 0.971209i | \(-0.423434\pi\) | ||||
0.238228 | + | 0.971209i | \(0.423434\pi\) | |||||||
\(968\) | 1.94347e24 | 0.0810282 | ||||||||
\(969\) | 8.45564e24 | 0.349457 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.00712e25 | 1.62731 | 0.813653 | − | 0.581351i | \(-0.197476\pi\) | ||||
0.813653 | + | 0.581351i | \(0.197476\pi\) | |||||||
\(972\) | −1.26822e25 | −0.510544 | ||||||||
\(973\) | −8.06578e24 | −0.321875 | ||||||||
\(974\) | −2.51488e25 | −0.994868 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.89675e24 | −0.190364 | ||||||||
\(977\) | −8.86356e24 | −0.341589 | −0.170795 | − | 0.985307i | \(-0.554633\pi\) | ||||
−0.170795 | + | 0.985307i | \(0.554633\pi\) | |||||||
\(978\) | 1.01952e25 | 0.389507 | ||||||||
\(979\) | −1.74458e25 | −0.660750 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.27734e24 | −0.345332 | ||||||||
\(982\) | −7.34492e23 | −0.0271044 | ||||||||
\(983\) | 1.56885e25 | 0.573954 | 0.286977 | − | 0.957938i | \(-0.407350\pi\) | ||||
0.286977 | + | 0.957938i | \(0.407350\pi\) | |||||||
\(984\) | 1.20580e25 | 0.437338 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1.24971e25 | 0.445507 | ||||||||
\(987\) | −8.86754e25 | −3.13406 | ||||||||
\(988\) | −4.30688e24 | −0.150914 | ||||||||
\(989\) | 8.65307e25 | 3.00609 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.85830e25 | −0.976073 | −0.488037 | − | 0.872823i | \(-0.662287\pi\) | ||||
−0.488037 | + | 0.872823i | \(0.662287\pi\) | |||||||
\(992\) | 9.63034e24 | 0.326056 | ||||||||
\(993\) | −1.15084e25 | −0.386319 | ||||||||
\(994\) | 3.02783e25 | 1.00774 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.48217e25 | 0.484946 | ||||||||
\(997\) | 6.58977e24 | 0.213777 | 0.106889 | − | 0.994271i | \(-0.465911\pi\) | ||||
0.106889 | + | 0.994271i | \(0.465911\pi\) | |||||||
\(998\) | −2.22278e25 | −0.714970 | ||||||||
\(999\) | −3.95396e25 | −1.26103 |
(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 | 50.18.a.g.1.2 | 2 | ||
5.2 | odd | 4 | 50.18.b.e.49.3 | 4 | |||
5.3 | odd | 4 | 50.18.b.e.49.2 | 4 | |||
5.4 | even | 2 | 10.18.a.b.1.1 | ✓ | 2 | ||
15.14 | odd | 2 | 90.18.a.n.1.2 | 2 | |||
20.19 | odd | 2 | 80.18.a.e.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.18.a.b.1.1 | ✓ | 2 | 5.4 | even | 2 | ||
50.18.a.g.1.2 | 2 | 1.1 | even | 1 | trivial | ||
50.18.b.e.49.2 | 4 | 5.3 | odd | 4 | |||
50.18.b.e.49.3 | 4 | 5.2 | odd | 4 | |||
80.18.a.e.1.2 | 2 | 20.19 | odd | 2 | |||
90.18.a.n.1.2 | 2 | 15.14 | odd | 2 |