Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [98,10,Mod(1,98)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(98, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("98.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 98 = 2 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 98.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: | \(50.4735119441\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 1115x + 2100 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{3}\cdot 3\cdot 7 \) |
Twist minimal: | no (minimal twist has level 14) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(32.9264\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 98.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 16.0000 | 0.707107 | ||||||||
\(3\) | −270.819 | −1.93034 | −0.965171 | − | 0.261621i | \(-0.915743\pi\) | ||||
−0.965171 | + | 0.261621i | \(0.915743\pi\) | |||||||
\(4\) | 256.000 | 0.500000 | ||||||||
\(5\) | −1369.57 | −0.979985 | −0.489992 | − | 0.871727i | \(-0.663000\pi\) | ||||
−0.489992 | + | 0.871727i | \(0.663000\pi\) | |||||||
\(6\) | −4333.11 | −1.36496 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 4096.00 | 0.353553 | ||||||||
\(9\) | 53660.1 | 2.72622 | ||||||||
\(10\) | −21913.1 | −0.692954 | ||||||||
\(11\) | −10924.3 | −0.224972 | −0.112486 | − | 0.993653i | \(-0.535881\pi\) | ||||
−0.112486 | + | 0.993653i | \(0.535881\pi\) | |||||||
\(12\) | −69329.8 | −0.965171 | ||||||||
\(13\) | 7968.27 | 0.0773783 | 0.0386891 | − | 0.999251i | \(-0.487682\pi\) | ||||
0.0386891 | + | 0.999251i | \(0.487682\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 370906. | 1.89170 | ||||||||
\(16\) | 65536.0 | 0.250000 | ||||||||
\(17\) | 324012. | 0.940894 | 0.470447 | − | 0.882428i | \(-0.344093\pi\) | ||||
0.470447 | + | 0.882428i | \(0.344093\pi\) | |||||||
\(18\) | 858562. | 1.92773 | ||||||||
\(19\) | 231878. | 0.408195 | 0.204098 | − | 0.978951i | \(-0.434574\pi\) | ||||
0.204098 | + | 0.978951i | \(0.434574\pi\) | |||||||
\(20\) | −350610. | −0.489992 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −174789. | −0.159079 | ||||||||
\(23\) | 2.10662e6 | 1.56968 | 0.784841 | − | 0.619698i | \(-0.212745\pi\) | ||||
0.784841 | + | 0.619698i | \(0.212745\pi\) | |||||||
\(24\) | −1.10928e6 | −0.682479 | ||||||||
\(25\) | −77402.7 | −0.0396302 | ||||||||
\(26\) | 127492. | 0.0547147 | ||||||||
\(27\) | −9.20167e6 | −3.33219 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.46332e6 | −1.43438 | −0.717192 | − | 0.696876i | \(-0.754573\pi\) | ||||
−0.717192 | + | 0.696876i | \(0.754573\pi\) | |||||||
\(30\) | 5.93450e6 | 1.33764 | ||||||||
\(31\) | 1.97867e6 | 0.384810 | 0.192405 | − | 0.981316i | \(-0.438371\pi\) | ||||
0.192405 | + | 0.981316i | \(0.438371\pi\) | |||||||
\(32\) | 1.04858e6 | 0.176777 | ||||||||
\(33\) | 2.95852e6 | 0.434272 | ||||||||
\(34\) | 5.18419e6 | 0.665312 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.37370e7 | 1.36311 | ||||||||
\(37\) | 4.76533e6 | 0.418008 | 0.209004 | − | 0.977915i | \(-0.432978\pi\) | ||||
0.209004 | + | 0.977915i | \(0.432978\pi\) | |||||||
\(38\) | 3.71005e6 | 0.288638 | ||||||||
\(39\) | −2.15796e6 | −0.149366 | ||||||||
\(40\) | −5.60976e6 | −0.346477 | ||||||||
\(41\) | −5.57398e6 | −0.308062 | −0.154031 | − | 0.988066i | \(-0.549226\pi\) | ||||
−0.154031 | + | 0.988066i | \(0.549226\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.11341e7 | −1.38876 | −0.694382 | − | 0.719607i | \(-0.744322\pi\) | ||||
−0.694382 | + | 0.719607i | \(0.744322\pi\) | |||||||
\(44\) | −2.79663e6 | −0.112486 | ||||||||
\(45\) | −7.34913e7 | −2.67165 | ||||||||
\(46\) | 3.37060e7 | 1.10993 | ||||||||
\(47\) | −4.31190e6 | −0.128893 | −0.0644464 | − | 0.997921i | \(-0.520528\pi\) | ||||
−0.0644464 | + | 0.997921i | \(0.520528\pi\) | |||||||
\(48\) | −1.77484e7 | −0.482585 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −1.23844e6 | −0.0280228 | ||||||||
\(51\) | −8.77486e7 | −1.81625 | ||||||||
\(52\) | 2.03988e6 | 0.0386891 | ||||||||
\(53\) | −9.02903e7 | −1.57181 | −0.785905 | − | 0.618348i | \(-0.787802\pi\) | ||||
−0.785905 | + | 0.618348i | \(0.787802\pi\) | |||||||
\(54\) | −1.47227e8 | −2.35621 | ||||||||
\(55\) | 1.49616e7 | 0.220469 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.27970e7 | −0.787957 | ||||||||
\(58\) | −8.74131e7 | −1.01426 | ||||||||
\(59\) | 7.29111e7 | 0.783357 | 0.391678 | − | 0.920102i | \(-0.371895\pi\) | ||||
0.391678 | + | 0.920102i | \(0.371895\pi\) | |||||||
\(60\) | 9.49520e7 | 0.945852 | ||||||||
\(61\) | 7.43497e6 | 0.0687535 | 0.0343768 | − | 0.999409i | \(-0.489055\pi\) | ||||
0.0343768 | + | 0.999409i | \(0.489055\pi\) | |||||||
\(62\) | 3.16588e7 | 0.272102 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.67772e7 | 0.125000 | ||||||||
\(65\) | −1.09131e7 | −0.0758295 | ||||||||
\(66\) | 4.73363e7 | 0.307077 | ||||||||
\(67\) | 1.05787e8 | 0.641352 | 0.320676 | − | 0.947189i | \(-0.396090\pi\) | ||||
0.320676 | + | 0.947189i | \(0.396090\pi\) | |||||||
\(68\) | 8.29470e7 | 0.470447 | ||||||||
\(69\) | −5.70514e8 | −3.03002 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.10248e8 | 0.514884 | 0.257442 | − | 0.966294i | \(-0.417120\pi\) | ||||
0.257442 | + | 0.966294i | \(0.417120\pi\) | |||||||
\(72\) | 2.19792e8 | 0.963863 | ||||||||
\(73\) | −2.04449e8 | −0.842621 | −0.421311 | − | 0.906916i | \(-0.638430\pi\) | ||||
−0.421311 | + | 0.906916i | \(0.638430\pi\) | |||||||
\(74\) | 7.62452e7 | 0.295576 | ||||||||
\(75\) | 2.09622e7 | 0.0764998 | ||||||||
\(76\) | 5.93607e7 | 0.204098 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −3.45274e7 | −0.105618 | ||||||||
\(79\) | 8.87846e7 | 0.256458 | 0.128229 | − | 0.991745i | \(-0.459071\pi\) | ||||
0.128229 | + | 0.991745i | \(0.459071\pi\) | |||||||
\(80\) | −8.97561e7 | −0.244996 | ||||||||
\(81\) | 1.43580e9 | 3.70604 | ||||||||
\(82\) | −8.91836e7 | −0.217833 | ||||||||
\(83\) | −2.41708e8 | −0.559035 | −0.279517 | − | 0.960141i | \(-0.590174\pi\) | ||||
−0.279517 | + | 0.960141i | \(0.590174\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.43757e8 | −0.922061 | ||||||||
\(86\) | −4.98146e8 | −0.982004 | ||||||||
\(87\) | 1.47957e9 | 2.76885 | ||||||||
\(88\) | −4.47461e7 | −0.0795395 | ||||||||
\(89\) | −5.48690e8 | −0.926984 | −0.463492 | − | 0.886101i | \(-0.653404\pi\) | ||||
−0.463492 | + | 0.886101i | \(0.653404\pi\) | |||||||
\(90\) | −1.17586e9 | −1.88914 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 5.39295e8 | 0.784841 | ||||||||
\(93\) | −5.35863e8 | −0.742814 | ||||||||
\(94\) | −6.89905e7 | −0.0911410 | ||||||||
\(95\) | −3.17573e8 | −0.400025 | ||||||||
\(96\) | −2.83975e8 | −0.341239 | ||||||||
\(97\) | 1.16746e9 | 1.33897 | 0.669483 | − | 0.742828i | \(-0.266516\pi\) | ||||
0.669483 | + | 0.742828i | \(0.266516\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.86201e8 | −0.613322 | ||||||||
\(100\) | −1.98151e7 | −0.0198151 | ||||||||
\(101\) | −1.38986e9 | −1.32900 | −0.664498 | − | 0.747290i | \(-0.731354\pi\) | ||||
−0.664498 | + | 0.747290i | \(0.731354\pi\) | |||||||
\(102\) | −1.40398e9 | −1.28428 | ||||||||
\(103\) | −9.38808e8 | −0.821881 | −0.410941 | − | 0.911662i | \(-0.634800\pi\) | ||||
−0.410941 | + | 0.911662i | \(0.634800\pi\) | |||||||
\(104\) | 3.26380e7 | 0.0273573 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.44465e9 | −1.11144 | ||||||||
\(107\) | 2.59288e8 | 0.191230 | 0.0956149 | − | 0.995418i | \(-0.469518\pi\) | ||||
0.0956149 | + | 0.995418i | \(0.469518\pi\) | |||||||
\(108\) | −2.35563e9 | −1.66609 | ||||||||
\(109\) | −8.25786e7 | −0.0560336 | −0.0280168 | − | 0.999607i | \(-0.508919\pi\) | ||||
−0.0280168 | + | 0.999607i | \(0.508919\pi\) | |||||||
\(110\) | 2.39386e8 | 0.155895 | ||||||||
\(111\) | −1.29054e9 | −0.806899 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.17279e9 | 0.676654 | 0.338327 | − | 0.941029i | \(-0.390139\pi\) | ||||
0.338327 | + | 0.941029i | \(0.390139\pi\) | |||||||
\(114\) | −1.00475e9 | −0.557169 | ||||||||
\(115\) | −2.88517e9 | −1.53826 | ||||||||
\(116\) | −1.39861e9 | −0.717192 | ||||||||
\(117\) | 4.27578e8 | 0.210950 | ||||||||
\(118\) | 1.16658e9 | 0.553917 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.51923e9 | 0.668819 | ||||||||
\(121\) | −2.23861e9 | −0.949388 | ||||||||
\(122\) | 1.18960e8 | 0.0486161 | ||||||||
\(123\) | 1.50954e9 | 0.594664 | ||||||||
\(124\) | 5.06540e8 | 0.192405 | ||||||||
\(125\) | 2.78095e9 | 1.01882 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.85883e9 | −0.975150 | −0.487575 | − | 0.873081i | \(-0.662118\pi\) | ||||
−0.487575 | + | 0.873081i | \(0.662118\pi\) | |||||||
\(128\) | 2.68435e8 | 0.0883883 | ||||||||
\(129\) | 8.43172e9 | 2.68079 | ||||||||
\(130\) | −1.74610e8 | −0.0536196 | ||||||||
\(131\) | 5.17100e9 | 1.53410 | 0.767050 | − | 0.641587i | \(-0.221724\pi\) | ||||
0.767050 | + | 0.641587i | \(0.221724\pi\) | |||||||
\(132\) | 7.57382e8 | 0.217136 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.69260e9 | 0.453505 | ||||||||
\(135\) | 1.26023e10 | 3.26549 | ||||||||
\(136\) | 1.32715e9 | 0.332656 | ||||||||
\(137\) | −1.69648e9 | −0.411440 | −0.205720 | − | 0.978611i | \(-0.565954\pi\) | ||||
−0.205720 | + | 0.978611i | \(0.565954\pi\) | |||||||
\(138\) | −9.12823e9 | −2.14255 | ||||||||
\(139\) | −5.00914e9 | −1.13814 | −0.569071 | − | 0.822288i | \(-0.692697\pi\) | ||||
−0.569071 | + | 0.822288i | \(0.692697\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.16775e9 | 0.248807 | ||||||||
\(142\) | 1.76397e9 | 0.364078 | ||||||||
\(143\) | −8.70480e7 | −0.0174079 | ||||||||
\(144\) | 3.51667e9 | 0.681554 | ||||||||
\(145\) | 7.48240e9 | 1.40567 | ||||||||
\(146\) | −3.27119e9 | −0.595823 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.21992e9 | 0.209004 | ||||||||
\(149\) | 1.67994e9 | 0.279226 | 0.139613 | − | 0.990206i | \(-0.455414\pi\) | ||||
0.139613 | + | 0.990206i | \(0.455414\pi\) | |||||||
\(150\) | 3.35395e8 | 0.0540935 | ||||||||
\(151\) | −6.81460e9 | −1.06671 | −0.533353 | − | 0.845893i | \(-0.679068\pi\) | ||||
−0.533353 | + | 0.845893i | \(0.679068\pi\) | |||||||
\(152\) | 9.49772e8 | 0.144319 | ||||||||
\(153\) | 1.73865e10 | 2.56508 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.70993e9 | −0.377108 | ||||||||
\(156\) | −5.52438e8 | −0.0746832 | ||||||||
\(157\) | −9.56661e8 | −0.125664 | −0.0628318 | − | 0.998024i | \(-0.520013\pi\) | ||||
−0.0628318 | + | 0.998024i | \(0.520013\pi\) | |||||||
\(158\) | 1.42055e9 | 0.181343 | ||||||||
\(159\) | 2.44524e10 | 3.03413 | ||||||||
\(160\) | −1.43610e9 | −0.173238 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 2.29728e10 | 2.62057 | ||||||||
\(163\) | −6.21953e9 | −0.690102 | −0.345051 | − | 0.938584i | \(-0.612138\pi\) | ||||
−0.345051 | + | 0.938584i | \(0.612138\pi\) | |||||||
\(164\) | −1.42694e9 | −0.154031 | ||||||||
\(165\) | −4.05190e9 | −0.425580 | ||||||||
\(166\) | −3.86732e9 | −0.395297 | ||||||||
\(167\) | 3.33475e9 | 0.331771 | 0.165886 | − | 0.986145i | \(-0.446952\pi\) | ||||
0.165886 | + | 0.986145i | \(0.446952\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.05410e10 | −0.994013 | ||||||||
\(170\) | −7.10011e9 | −0.651996 | ||||||||
\(171\) | 1.24426e10 | 1.11283 | ||||||||
\(172\) | −7.97033e9 | −0.694382 | ||||||||
\(173\) | −1.13002e10 | −0.959131 | −0.479566 | − | 0.877506i | \(-0.659206\pi\) | ||||
−0.479566 | + | 0.877506i | \(0.659206\pi\) | |||||||
\(174\) | 2.36732e10 | 1.95787 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −7.15937e8 | −0.0562429 | ||||||||
\(177\) | −1.97457e10 | −1.51215 | ||||||||
\(178\) | −8.77904e9 | −0.655477 | ||||||||
\(179\) | 1.85514e9 | 0.135063 | 0.0675316 | − | 0.997717i | \(-0.478488\pi\) | ||||
0.0675316 | + | 0.997717i | \(0.478488\pi\) | |||||||
\(180\) | −1.88138e10 | −1.33583 | ||||||||
\(181\) | −1.64314e9 | −0.113794 | −0.0568972 | − | 0.998380i | \(-0.518121\pi\) | ||||
−0.0568972 | + | 0.998380i | \(0.518121\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.01353e9 | −0.132718 | ||||||||
\(184\) | 8.62873e9 | 0.554966 | ||||||||
\(185\) | −6.52645e9 | −0.409642 | ||||||||
\(186\) | −8.57380e9 | −0.525249 | ||||||||
\(187\) | −3.53961e9 | −0.211674 | ||||||||
\(188\) | −1.10385e9 | −0.0644464 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −5.08117e9 | −0.282861 | ||||||||
\(191\) | 1.13687e10 | 0.618103 | 0.309052 | − | 0.951045i | \(-0.399988\pi\) | ||||
0.309052 | + | 0.951045i | \(0.399988\pi\) | |||||||
\(192\) | −4.54360e9 | −0.241293 | ||||||||
\(193\) | −3.81022e10 | −1.97671 | −0.988354 | − | 0.152175i | \(-0.951372\pi\) | ||||
−0.988354 | + | 0.152175i | \(0.951372\pi\) | |||||||
\(194\) | 1.86794e10 | 0.946792 | ||||||||
\(195\) | 2.95548e9 | 0.146377 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.71349e10 | −0.810558 | −0.405279 | − | 0.914193i | \(-0.632826\pi\) | ||||
−0.405279 | + | 0.914193i | \(0.632826\pi\) | |||||||
\(198\) | −9.37922e9 | −0.433684 | ||||||||
\(199\) | 2.30179e10 | 1.04046 | 0.520232 | − | 0.854025i | \(-0.325845\pi\) | ||||
0.520232 | + | 0.854025i | \(0.325845\pi\) | |||||||
\(200\) | −3.17042e8 | −0.0140114 | ||||||||
\(201\) | −2.86492e10 | −1.23803 | ||||||||
\(202\) | −2.22377e10 | −0.939741 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −2.24637e10 | −0.908123 | ||||||||
\(205\) | 7.63395e9 | 0.301896 | ||||||||
\(206\) | −1.50209e10 | −0.581158 | ||||||||
\(207\) | 1.13042e11 | 4.27929 | ||||||||
\(208\) | 5.22209e8 | 0.0193446 | ||||||||
\(209\) | −2.53311e9 | −0.0918324 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.95907e10 | 1.72238 | 0.861190 | − | 0.508283i | \(-0.169720\pi\) | ||||
0.861190 | + | 0.508283i | \(0.169720\pi\) | |||||||
\(212\) | −2.31143e10 | −0.785905 | ||||||||
\(213\) | −2.98574e10 | −0.993901 | ||||||||
\(214\) | 4.14861e9 | 0.135220 | ||||||||
\(215\) | 4.26403e10 | 1.36097 | ||||||||
\(216\) | −3.76900e10 | −1.17811 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1.32126e9 | −0.0396217 | ||||||||
\(219\) | 5.53688e10 | 1.62655 | ||||||||
\(220\) | 3.83018e9 | 0.110234 | ||||||||
\(221\) | 2.58181e9 | 0.0728047 | ||||||||
\(222\) | −2.06487e10 | −0.570563 | ||||||||
\(223\) | −5.54434e10 | −1.50134 | −0.750669 | − | 0.660679i | \(-0.770269\pi\) | ||||
−0.750669 | + | 0.660679i | \(0.770269\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.15344e9 | −0.108041 | ||||||||
\(226\) | 1.87646e10 | 0.478466 | ||||||||
\(227\) | 3.53834e9 | 0.0884471 | 0.0442236 | − | 0.999022i | \(-0.485919\pi\) | ||||
0.0442236 | + | 0.999022i | \(0.485919\pi\) | |||||||
\(228\) | −1.60760e10 | −0.393978 | ||||||||
\(229\) | 3.04328e10 | 0.731278 | 0.365639 | − | 0.930757i | \(-0.380850\pi\) | ||||
0.365639 | + | 0.930757i | \(0.380850\pi\) | |||||||
\(230\) | −4.61627e10 | −1.08772 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.23777e10 | −0.507131 | ||||||||
\(233\) | 6.16096e9 | 0.136945 | 0.0684725 | − | 0.997653i | \(-0.478187\pi\) | ||||
0.0684725 | + | 0.997653i | \(0.478187\pi\) | |||||||
\(234\) | 6.84126e9 | 0.149164 | ||||||||
\(235\) | 5.90545e9 | 0.126313 | ||||||||
\(236\) | 1.86652e10 | 0.391678 | ||||||||
\(237\) | −2.40446e10 | −0.495051 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.33526e10 | −1.25595 | −0.627977 | − | 0.778232i | \(-0.716117\pi\) | ||||
−0.627977 | + | 0.778232i | \(0.716117\pi\) | |||||||
\(240\) | 2.43077e10 | 0.472926 | ||||||||
\(241\) | −7.51528e10 | −1.43506 | −0.717528 | − | 0.696530i | \(-0.754726\pi\) | ||||
−0.717528 | + | 0.696530i | \(0.754726\pi\) | |||||||
\(242\) | −3.58177e10 | −0.671319 | ||||||||
\(243\) | −2.07725e11 | −3.82174 | ||||||||
\(244\) | 1.90335e9 | 0.0343768 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.41527e10 | 0.420491 | ||||||||
\(247\) | 1.84767e9 | 0.0315855 | ||||||||
\(248\) | 8.10464e9 | 0.136051 | ||||||||
\(249\) | 6.54591e10 | 1.07913 | ||||||||
\(250\) | 4.44952e10 | 0.720416 | ||||||||
\(251\) | −1.01701e11 | −1.61731 | −0.808653 | − | 0.588286i | \(-0.799803\pi\) | ||||
−0.808653 | + | 0.588286i | \(0.799803\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.30135e10 | −0.353134 | ||||||||
\(254\) | −4.57413e10 | −0.689535 | ||||||||
\(255\) | 1.20178e11 | 1.77989 | ||||||||
\(256\) | 4.29497e9 | 0.0625000 | ||||||||
\(257\) | −5.51693e10 | −0.788857 | −0.394429 | − | 0.918927i | \(-0.629057\pi\) | ||||
−0.394429 | + | 0.918927i | \(0.629057\pi\) | |||||||
\(258\) | 1.34908e11 | 1.89560 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −2.79375e9 | −0.0379147 | ||||||||
\(261\) | −2.93162e11 | −3.91044 | ||||||||
\(262\) | 8.27360e10 | 1.08477 | ||||||||
\(263\) | −2.24461e10 | −0.289294 | −0.144647 | − | 0.989483i | \(-0.546205\pi\) | ||||
−0.144647 | + | 0.989483i | \(0.546205\pi\) | |||||||
\(264\) | 1.21181e10 | 0.153538 | ||||||||
\(265\) | 1.23659e11 | 1.54035 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.48596e11 | 1.78940 | ||||||||
\(268\) | 2.70815e10 | 0.320676 | ||||||||
\(269\) | −2.35215e9 | −0.0273892 | −0.0136946 | − | 0.999906i | \(-0.504359\pi\) | ||||
−0.0136946 | + | 0.999906i | \(0.504359\pi\) | |||||||
\(270\) | 2.01637e11 | 2.30905 | ||||||||
\(271\) | 1.49406e11 | 1.68269 | 0.841346 | − | 0.540496i | \(-0.181764\pi\) | ||||
0.841346 | + | 0.540496i | \(0.181764\pi\) | |||||||
\(272\) | 2.12344e10 | 0.235223 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.71437e10 | −0.290932 | ||||||||
\(275\) | 8.45573e8 | 0.00891567 | ||||||||
\(276\) | −1.46052e11 | −1.51501 | ||||||||
\(277\) | −1.44399e11 | −1.47368 | −0.736842 | − | 0.676065i | \(-0.763684\pi\) | ||||
−0.736842 | + | 0.676065i | \(0.763684\pi\) | |||||||
\(278\) | −8.01463e10 | −0.804788 | ||||||||
\(279\) | 1.06176e11 | 1.04908 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.04301e10 | −0.673876 | −0.336938 | − | 0.941527i | \(-0.609391\pi\) | ||||
−0.336938 | + | 0.941527i | \(0.609391\pi\) | |||||||
\(282\) | 1.86840e10 | 0.175933 | ||||||||
\(283\) | −2.04558e11 | −1.89574 | −0.947868 | − | 0.318665i | \(-0.896766\pi\) | ||||
−0.947868 | + | 0.318665i | \(0.896766\pi\) | |||||||
\(284\) | 2.82235e10 | 0.257442 | ||||||||
\(285\) | 8.60049e10 | 0.772185 | ||||||||
\(286\) | −1.39277e9 | −0.0123093 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 5.62667e10 | 0.481932 | ||||||||
\(289\) | −1.36043e10 | −0.114719 | ||||||||
\(290\) | 1.19718e11 | 0.993962 | ||||||||
\(291\) | −3.16171e11 | −2.58466 | ||||||||
\(292\) | −5.23390e10 | −0.421311 | ||||||||
\(293\) | −1.08283e11 | −0.858335 | −0.429168 | − | 0.903225i | \(-0.641193\pi\) | ||||
−0.429168 | + | 0.903225i | \(0.641193\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.98569e10 | −0.767677 | ||||||||
\(296\) | 1.95188e10 | 0.147788 | ||||||||
\(297\) | 1.00522e11 | 0.749648 | ||||||||
\(298\) | 2.68790e10 | 0.197443 | ||||||||
\(299\) | 1.67861e10 | 0.121459 | ||||||||
\(300\) | 5.36631e9 | 0.0382499 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −1.09034e11 | −0.754274 | ||||||||
\(303\) | 3.76400e11 | 2.56541 | ||||||||
\(304\) | 1.51964e10 | 0.102049 | ||||||||
\(305\) | −1.01827e10 | −0.0673774 | ||||||||
\(306\) | 2.78184e11 | 1.81379 | ||||||||
\(307\) | 1.17650e11 | 0.755912 | 0.377956 | − | 0.925824i | \(-0.376627\pi\) | ||||
0.377956 | + | 0.925824i | \(0.376627\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.54247e11 | 1.58651 | ||||||||
\(310\) | −4.33589e10 | −0.266655 | ||||||||
\(311\) | 1.77275e10 | 0.107455 | 0.0537273 | − | 0.998556i | \(-0.482890\pi\) | ||||
0.0537273 | + | 0.998556i | \(0.482890\pi\) | |||||||
\(312\) | −8.83901e9 | −0.0528090 | ||||||||
\(313\) | −1.06637e11 | −0.627996 | −0.313998 | − | 0.949424i | \(-0.601669\pi\) | ||||
−0.313998 | + | 0.949424i | \(0.601669\pi\) | |||||||
\(314\) | −1.53066e10 | −0.0888576 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.27288e10 | 0.128229 | ||||||||
\(317\) | −3.31101e10 | −0.184159 | −0.0920797 | − | 0.995752i | \(-0.529351\pi\) | ||||
−0.0920797 | + | 0.995752i | \(0.529351\pi\) | |||||||
\(318\) | 3.91238e11 | 2.14545 | ||||||||
\(319\) | 5.96831e10 | 0.322696 | ||||||||
\(320\) | −2.29776e10 | −0.122498 | ||||||||
\(321\) | −7.02203e10 | −0.369139 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.51311e10 | 0.384068 | ||||||||
\(324\) | 3.67564e11 | 1.85302 | ||||||||
\(325\) | −6.16766e8 | −0.00306652 | ||||||||
\(326\) | −9.95125e10 | −0.487976 | ||||||||
\(327\) | 2.23639e10 | 0.108164 | ||||||||
\(328\) | −2.28310e10 | −0.108916 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −6.48304e10 | −0.300931 | ||||||||
\(331\) | −2.20016e11 | −1.00746 | −0.503730 | − | 0.863861i | \(-0.668039\pi\) | ||||
−0.503730 | + | 0.863861i | \(0.668039\pi\) | |||||||
\(332\) | −6.18771e10 | −0.279517 | ||||||||
\(333\) | 2.55708e11 | 1.13958 | ||||||||
\(334\) | 5.33560e10 | 0.234598 | ||||||||
\(335\) | −1.44883e11 | −0.628515 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.58927e11 | 0.671217 | 0.335609 | − | 0.942001i | \(-0.391058\pi\) | ||||
0.335609 | + | 0.942001i | \(0.391058\pi\) | |||||||
\(338\) | −1.68656e11 | −0.702873 | ||||||||
\(339\) | −3.17614e11 | −1.30617 | ||||||||
\(340\) | −1.13602e11 | −0.461031 | ||||||||
\(341\) | −2.16157e10 | −0.0865713 | ||||||||
\(342\) | 1.99082e11 | 0.786889 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −1.27525e11 | −0.491002 | ||||||||
\(345\) | 7.81359e11 | 2.96937 | ||||||||
\(346\) | −1.80803e11 | −0.678208 | ||||||||
\(347\) | 9.05893e10 | 0.335424 | 0.167712 | − | 0.985836i | \(-0.446362\pi\) | ||||
0.167712 | + | 0.985836i | \(0.446362\pi\) | |||||||
\(348\) | 3.78771e11 | 1.38443 | ||||||||
\(349\) | 1.82702e11 | 0.659219 | 0.329609 | − | 0.944117i | \(-0.393083\pi\) | ||||
0.329609 | + | 0.944117i | \(0.393083\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7.33214e10 | −0.257839 | ||||||||
\(352\) | −1.14550e10 | −0.0397698 | ||||||||
\(353\) | −2.89147e11 | −0.991136 | −0.495568 | − | 0.868569i | \(-0.665040\pi\) | ||||
−0.495568 | + | 0.868569i | \(0.665040\pi\) | |||||||
\(354\) | −3.15932e11 | −1.06925 | ||||||||
\(355\) | −1.50993e11 | −0.504578 | ||||||||
\(356\) | −1.40465e11 | −0.463492 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.96822e10 | 0.0955041 | ||||||||
\(359\) | −3.29047e11 | −1.04552 | −0.522761 | − | 0.852479i | \(-0.675098\pi\) | ||||
−0.522761 | + | 0.852479i | \(0.675098\pi\) | |||||||
\(360\) | −3.01020e11 | −0.944571 | ||||||||
\(361\) | −2.68920e11 | −0.833376 | ||||||||
\(362\) | −2.62902e10 | −0.0804647 | ||||||||
\(363\) | 6.06258e11 | 1.83264 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.80007e11 | 0.825756 | ||||||||
\(366\) | −3.22165e10 | −0.0938456 | ||||||||
\(367\) | 4.16454e11 | 1.19831 | 0.599156 | − | 0.800632i | \(-0.295503\pi\) | ||||
0.599156 | + | 0.800632i | \(0.295503\pi\) | |||||||
\(368\) | 1.38060e11 | 0.392420 | ||||||||
\(369\) | −2.99100e11 | −0.839843 | ||||||||
\(370\) | −1.04423e11 | −0.289660 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −1.37181e11 | −0.371407 | ||||||||
\(373\) | 1.07630e11 | 0.287900 | 0.143950 | − | 0.989585i | \(-0.454020\pi\) | ||||
0.143950 | + | 0.989585i | \(0.454020\pi\) | |||||||
\(374\) | −5.66338e10 | −0.149676 | ||||||||
\(375\) | −7.53135e11 | −1.96667 | ||||||||
\(376\) | −1.76616e10 | −0.0455705 | ||||||||
\(377\) | −4.35332e10 | −0.110990 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.34243e11 | 1.33003 | 0.665016 | − | 0.746829i | \(-0.268425\pi\) | ||||
0.665016 | + | 0.746829i | \(0.268425\pi\) | |||||||
\(380\) | −8.12987e10 | −0.200013 | ||||||||
\(381\) | 7.74226e11 | 1.88237 | ||||||||
\(382\) | 1.81899e11 | 0.437065 | ||||||||
\(383\) | 3.07903e11 | 0.731173 | 0.365586 | − | 0.930777i | \(-0.380868\pi\) | ||||
0.365586 | + | 0.930777i | \(0.380868\pi\) | |||||||
\(384\) | −7.26975e10 | −0.170620 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6.09635e11 | −1.39774 | ||||||||
\(387\) | −1.67066e12 | −3.78607 | ||||||||
\(388\) | 2.98870e11 | 0.669483 | ||||||||
\(389\) | 5.87210e11 | 1.30023 | 0.650115 | − | 0.759836i | \(-0.274721\pi\) | ||||
0.650115 | + | 0.759836i | \(0.274721\pi\) | |||||||
\(390\) | 4.72877e10 | 0.103504 | ||||||||
\(391\) | 6.82570e11 | 1.47690 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.40041e12 | −2.96134 | ||||||||
\(394\) | −2.74159e11 | −0.573151 | ||||||||
\(395\) | −1.21597e11 | −0.251324 | ||||||||
\(396\) | −1.50068e11 | −0.306661 | ||||||||
\(397\) | −5.93603e11 | −1.19933 | −0.599665 | − | 0.800251i | \(-0.704699\pi\) | ||||
−0.599665 | + | 0.800251i | \(0.704699\pi\) | |||||||
\(398\) | 3.68287e11 | 0.735720 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −5.07267e9 | −0.00990755 | ||||||||
\(401\) | 4.50186e11 | 0.869446 | 0.434723 | − | 0.900564i | \(-0.356846\pi\) | ||||
0.434723 | + | 0.900564i | \(0.356846\pi\) | |||||||
\(402\) | −4.58388e11 | −0.875419 | ||||||||
\(403\) | 1.57666e10 | 0.0297759 | ||||||||
\(404\) | −3.55803e11 | −0.664498 | ||||||||
\(405\) | −1.96643e12 | −3.63187 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.20580e10 | −0.0940400 | ||||||||
\(408\) | −3.59418e11 | −0.642140 | ||||||||
\(409\) | −4.34640e11 | −0.768023 | −0.384012 | − | 0.923328i | \(-0.625458\pi\) | ||||
−0.384012 | + | 0.923328i | \(0.625458\pi\) | |||||||
\(410\) | 1.22143e11 | 0.213473 | ||||||||
\(411\) | 4.59440e11 | 0.794219 | ||||||||
\(412\) | −2.40335e11 | −0.410941 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1.80867e12 | 3.02592 | ||||||||
\(415\) | 3.31036e11 | 0.547846 | ||||||||
\(416\) | 8.35534e9 | 0.0136787 | ||||||||
\(417\) | 1.35657e12 | 2.19700 | ||||||||
\(418\) | −4.05298e10 | −0.0649353 | ||||||||
\(419\) | 4.94533e11 | 0.783848 | 0.391924 | − | 0.919998i | \(-0.371810\pi\) | ||||
0.391924 | + | 0.919998i | \(0.371810\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.78076e11 | 1.05198 | 0.525992 | − | 0.850490i | \(-0.323694\pi\) | ||||
0.525992 | + | 0.850490i | \(0.323694\pi\) | |||||||
\(422\) | 7.93451e11 | 1.21791 | ||||||||
\(423\) | −2.31377e11 | −0.351390 | ||||||||
\(424\) | −3.69829e11 | −0.555718 | ||||||||
\(425\) | −2.50794e10 | −0.0372878 | ||||||||
\(426\) | −4.77718e11 | −0.702794 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 6.63778e10 | 0.0956149 | ||||||||
\(429\) | 2.35743e10 | 0.0336032 | ||||||||
\(430\) | 6.82245e11 | 0.962349 | ||||||||
\(431\) | 1.14262e12 | 1.59497 | 0.797485 | − | 0.603339i | \(-0.206163\pi\) | ||||
0.797485 | + | 0.603339i | \(0.206163\pi\) | |||||||
\(432\) | −6.03040e11 | −0.833047 | ||||||||
\(433\) | −9.94314e11 | −1.35934 | −0.679670 | − | 0.733518i | \(-0.737877\pi\) | ||||
−0.679670 | + | 0.733518i | \(0.737877\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.02638e12 | −2.71343 | ||||||||
\(436\) | −2.11401e10 | −0.0280168 | ||||||||
\(437\) | 4.88479e11 | 0.640737 | ||||||||
\(438\) | 8.85901e11 | 1.15014 | ||||||||
\(439\) | −2.16942e11 | −0.278775 | −0.139387 | − | 0.990238i | \(-0.544513\pi\) | ||||
−0.139387 | + | 0.990238i | \(0.544513\pi\) | |||||||
\(440\) | 6.12829e10 | 0.0779475 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.13090e10 | 0.0514807 | ||||||||
\(443\) | 1.06952e12 | 1.31939 | 0.659693 | − | 0.751535i | \(-0.270686\pi\) | ||||
0.659693 | + | 0.751535i | \(0.270686\pi\) | |||||||
\(444\) | −3.30379e11 | −0.403449 | ||||||||
\(445\) | 7.51470e11 | 0.908430 | ||||||||
\(446\) | −8.87095e11 | −1.06161 | ||||||||
\(447\) | −4.54960e11 | −0.539001 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.65225e12 | 1.91853 | 0.959264 | − | 0.282510i | \(-0.0911669\pi\) | ||||
0.959264 | + | 0.282510i | \(0.0911669\pi\) | |||||||
\(450\) | −6.64551e10 | −0.0763962 | ||||||||
\(451\) | 6.08920e10 | 0.0693052 | ||||||||
\(452\) | 3.00234e11 | 0.338327 | ||||||||
\(453\) | 1.84553e12 | 2.05910 | ||||||||
\(454\) | 5.66135e10 | 0.0625416 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.57217e11 | −0.278585 | ||||||||
\(457\) | −7.46509e10 | −0.0800594 | −0.0400297 | − | 0.999198i | \(-0.512745\pi\) | ||||
−0.0400297 | + | 0.999198i | \(0.512745\pi\) | |||||||
\(458\) | 4.86925e11 | 0.517092 | ||||||||
\(459\) | −2.98145e12 | −3.13524 | ||||||||
\(460\) | −7.38603e11 | −0.769132 | ||||||||
\(461\) | −5.63966e11 | −0.581565 | −0.290783 | − | 0.956789i | \(-0.593916\pi\) | ||||
−0.290783 | + | 0.956789i | \(0.593916\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.11377e11 | 0.921687 | 0.460844 | − | 0.887481i | \(-0.347547\pi\) | ||||
0.460844 | + | 0.887481i | \(0.347547\pi\) | |||||||
\(464\) | −3.58044e11 | −0.358596 | ||||||||
\(465\) | 7.33902e11 | 0.727947 | ||||||||
\(466\) | 9.85753e10 | 0.0968348 | ||||||||
\(467\) | 1.91784e11 | 0.186589 | 0.0932946 | − | 0.995639i | \(-0.470260\pi\) | ||||
0.0932946 | + | 0.995639i | \(0.470260\pi\) | |||||||
\(468\) | 1.09460e11 | 0.105475 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 9.44873e10 | 0.0893168 | ||||||||
\(471\) | 2.59082e11 | 0.242574 | ||||||||
\(472\) | 2.98644e11 | 0.276958 | ||||||||
\(473\) | 3.40119e11 | 0.312433 | ||||||||
\(474\) | −3.84713e11 | −0.350054 | ||||||||
\(475\) | −1.79480e10 | −0.0161769 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.84499e12 | −4.28509 | ||||||||
\(478\) | −1.01364e12 | −0.888093 | ||||||||
\(479\) | −1.49058e12 | −1.29373 | −0.646866 | − | 0.762604i | \(-0.723921\pi\) | ||||
−0.646866 | + | 0.762604i | \(0.723921\pi\) | |||||||
\(480\) | 3.88923e11 | 0.334409 | ||||||||
\(481\) | 3.79714e10 | 0.0323447 | ||||||||
\(482\) | −1.20245e12 | −1.01474 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.73083e11 | −0.474694 | ||||||||
\(485\) | −1.59892e12 | −1.31217 | ||||||||
\(486\) | −3.32361e12 | −2.70238 | ||||||||
\(487\) | −1.26948e12 | −1.02269 | −0.511345 | − | 0.859376i | \(-0.670853\pi\) | ||||
−0.511345 | + | 0.859376i | \(0.670853\pi\) | |||||||
\(488\) | 3.04536e10 | 0.0243080 | ||||||||
\(489\) | 1.68437e12 | 1.33213 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.11119e11 | −0.552173 | −0.276087 | − | 0.961133i | \(-0.589038\pi\) | ||||
−0.276087 | + | 0.961133i | \(0.589038\pi\) | |||||||
\(492\) | 3.86442e11 | 0.297332 | ||||||||
\(493\) | −1.77018e12 | −1.34960 | ||||||||
\(494\) | 2.95626e10 | 0.0223343 | ||||||||
\(495\) | 8.02844e11 | 0.601046 | ||||||||
\(496\) | 1.29674e11 | 0.0962025 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 1.04735e12 | 0.763059 | ||||||||
\(499\) | 1.60263e12 | 1.15712 | 0.578562 | − | 0.815639i | \(-0.303614\pi\) | ||||
0.578562 | + | 0.815639i | \(0.303614\pi\) | |||||||
\(500\) | 7.11923e11 | 0.509411 | ||||||||
\(501\) | −9.03114e11 | −0.640432 | ||||||||
\(502\) | −1.62721e12 | −1.14361 | ||||||||
\(503\) | 6.48944e11 | 0.452013 | 0.226007 | − | 0.974126i | \(-0.427433\pi\) | ||||
0.226007 | + | 0.974126i | \(0.427433\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.90350e12 | 1.30239 | ||||||||
\(506\) | −3.68215e11 | −0.249703 | ||||||||
\(507\) | 2.85471e12 | 1.91878 | ||||||||
\(508\) | −7.31860e11 | −0.487575 | ||||||||
\(509\) | 3.81925e10 | 0.0252202 | 0.0126101 | − | 0.999920i | \(-0.495986\pi\) | ||||
0.0126101 | + | 0.999920i | \(0.495986\pi\) | |||||||
\(510\) | 1.92285e12 | 1.25857 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 6.87195e10 | 0.0441942 | ||||||||
\(513\) | −2.13366e12 | −1.36018 | ||||||||
\(514\) | −8.82709e11 | −0.557806 | ||||||||
\(515\) | 1.28576e12 | 0.805431 | ||||||||
\(516\) | 2.15852e12 | 1.34039 | ||||||||
\(517\) | 4.71047e10 | 0.0289972 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.06031e12 | 1.85145 | ||||||||
\(520\) | −4.47001e10 | −0.0268098 | ||||||||
\(521\) | 1.16818e12 | 0.694606 | 0.347303 | − | 0.937753i | \(-0.387098\pi\) | ||||
0.347303 | + | 0.937753i | \(0.387098\pi\) | |||||||
\(522\) | −4.69060e12 | −2.76510 | ||||||||
\(523\) | −1.51866e12 | −0.887572 | −0.443786 | − | 0.896133i | \(-0.646365\pi\) | ||||
−0.443786 | + | 0.896133i | \(0.646365\pi\) | |||||||
\(524\) | 1.32378e12 | 0.767050 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.59137e11 | −0.204562 | ||||||||
\(527\) | 6.41113e11 | 0.362065 | ||||||||
\(528\) | 1.93890e11 | 0.108568 | ||||||||
\(529\) | 2.63671e12 | 1.46390 | ||||||||
\(530\) | 1.97854e12 | 1.08919 | ||||||||
\(531\) | 3.91242e12 | 2.13560 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.44149e10 | −0.0238373 | ||||||||
\(534\) | 2.37754e12 | 1.26529 | ||||||||
\(535\) | −3.55113e11 | −0.187402 | ||||||||
\(536\) | 4.33304e11 | 0.226752 | ||||||||
\(537\) | −5.02407e11 | −0.260718 | ||||||||
\(538\) | −3.76344e10 | −0.0193671 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 3.22620e12 | 1.63275 | ||||||||
\(541\) | 1.19442e12 | 0.599473 | 0.299736 | − | 0.954022i | \(-0.403101\pi\) | ||||
0.299736 | + | 0.954022i | \(0.403101\pi\) | |||||||
\(542\) | 2.39049e12 | 1.18984 | ||||||||
\(543\) | 4.44994e11 | 0.219662 | ||||||||
\(544\) | 3.39751e11 | 0.166328 | ||||||||
\(545\) | 1.13097e11 | 0.0549120 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.52503e11 | −0.168353 | −0.0841764 | − | 0.996451i | \(-0.526826\pi\) | ||||
−0.0841764 | + | 0.996451i | \(0.526826\pi\) | |||||||
\(548\) | −4.34299e11 | −0.205720 | ||||||||
\(549\) | 3.98962e11 | 0.187437 | ||||||||
\(550\) | 1.35292e10 | 0.00630433 | ||||||||
\(551\) | −1.26682e12 | −0.585509 | ||||||||
\(552\) | −2.33683e12 | −1.07127 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −2.31038e12 | −1.04205 | ||||||||
\(555\) | 1.76749e12 | 0.790748 | ||||||||
\(556\) | −1.28234e12 | −0.569071 | ||||||||
\(557\) | −1.81198e12 | −0.797638 | −0.398819 | − | 0.917030i | \(-0.630580\pi\) | ||||
−0.398819 | + | 0.917030i | \(0.630580\pi\) | |||||||
\(558\) | 1.69881e12 | 0.741808 | ||||||||
\(559\) | −2.48085e11 | −0.107460 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.58595e11 | 0.408604 | ||||||||
\(562\) | −1.12688e12 | −0.476502 | ||||||||
\(563\) | 2.83080e12 | 1.18747 | 0.593733 | − | 0.804662i | \(-0.297654\pi\) | ||||
0.593733 | + | 0.804662i | \(0.297654\pi\) | |||||||
\(564\) | 2.98943e11 | 0.124404 | ||||||||
\(565\) | −1.60621e12 | −0.663110 | ||||||||
\(566\) | −3.27293e12 | −1.34049 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.51577e11 | 0.182039 | ||||||||
\(569\) | 3.53471e12 | 1.41367 | 0.706837 | − | 0.707377i | \(-0.250122\pi\) | ||||
0.706837 | + | 0.707377i | \(0.250122\pi\) | |||||||
\(570\) | 1.37608e12 | 0.546017 | ||||||||
\(571\) | 1.06393e12 | 0.418842 | 0.209421 | − | 0.977826i | \(-0.432842\pi\) | ||||
0.209421 | + | 0.977826i | \(0.432842\pi\) | |||||||
\(572\) | −2.22843e10 | −0.00870396 | ||||||||
\(573\) | −3.07887e12 | −1.19315 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.63058e11 | −0.0622068 | ||||||||
\(576\) | 9.00268e11 | 0.340777 | ||||||||
\(577\) | −3.55526e12 | −1.33530 | −0.667652 | − | 0.744474i | \(-0.732700\pi\) | ||||
−0.667652 | + | 0.744474i | \(0.732700\pi\) | |||||||
\(578\) | −2.17669e11 | −0.0811188 | ||||||||
\(579\) | 1.03188e13 | 3.81572 | ||||||||
\(580\) | 1.91549e12 | 0.702837 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −5.05873e12 | −1.82763 | ||||||||
\(583\) | 9.86362e11 | 0.353613 | ||||||||
\(584\) | −8.37424e11 | −0.297912 | ||||||||
\(585\) | −5.85599e11 | −0.206728 | ||||||||
\(586\) | −1.73253e12 | −0.606935 | ||||||||
\(587\) | 5.01945e12 | 1.74496 | 0.872478 | − | 0.488653i | \(-0.162512\pi\) | ||||
0.872478 | + | 0.488653i | \(0.162512\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.58810e11 | 0.157078 | ||||||||
\(590\) | −1.59771e12 | −0.542830 | ||||||||
\(591\) | 4.64047e12 | 1.56465 | ||||||||
\(592\) | 3.12300e11 | 0.104502 | ||||||||
\(593\) | 3.61438e12 | 1.20029 | 0.600146 | − | 0.799890i | \(-0.295109\pi\) | ||||
0.600146 | + | 0.799890i | \(0.295109\pi\) | |||||||
\(594\) | 1.60835e12 | 0.530081 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4.30065e11 | 0.139613 | ||||||||
\(597\) | −6.23370e12 | −2.00845 | ||||||||
\(598\) | 2.68578e11 | 0.0858846 | ||||||||
\(599\) | −8.96553e11 | −0.284548 | −0.142274 | − | 0.989827i | \(-0.545441\pi\) | ||||
−0.142274 | + | 0.989827i | \(0.545441\pi\) | |||||||
\(600\) | 8.58610e10 | 0.0270468 | ||||||||
\(601\) | −2.12154e11 | −0.0663310 | −0.0331655 | − | 0.999450i | \(-0.510559\pi\) | ||||
−0.0331655 | + | 0.999450i | \(0.510559\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.67656e12 | 1.74847 | ||||||||
\(604\) | −1.74454e12 | −0.533353 | ||||||||
\(605\) | 3.06593e12 | 0.930385 | ||||||||
\(606\) | 6.02240e12 | 1.81402 | ||||||||
\(607\) | −1.97565e12 | −0.590692 | −0.295346 | − | 0.955390i | \(-0.595435\pi\) | ||||
−0.295346 | + | 0.955390i | \(0.595435\pi\) | |||||||
\(608\) | 2.43142e11 | 0.0721594 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.62923e11 | −0.0476430 | ||||||||
\(611\) | −3.43584e10 | −0.00997350 | ||||||||
\(612\) | 4.45095e12 | 1.28254 | ||||||||
\(613\) | −3.85941e12 | −1.10395 | −0.551974 | − | 0.833861i | \(-0.686125\pi\) | ||||
−0.551974 | + | 0.833861i | \(0.686125\pi\) | |||||||
\(614\) | 1.88241e12 | 0.534510 | ||||||||
\(615\) | −2.06742e12 | −0.582762 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.19932e12 | −0.888738 | −0.444369 | − | 0.895844i | \(-0.646572\pi\) | ||||
−0.444369 | + | 0.895844i | \(0.646572\pi\) | |||||||
\(618\) | 4.06796e12 | 1.12183 | ||||||||
\(619\) | −5.73209e12 | −1.56930 | −0.784649 | − | 0.619940i | \(-0.787157\pi\) | ||||
−0.784649 | + | 0.619940i | \(0.787157\pi\) | |||||||
\(620\) | −6.93742e11 | −0.188554 | ||||||||
\(621\) | −1.93844e13 | −5.23048 | ||||||||
\(622\) | 2.83639e11 | 0.0759819 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −1.41424e11 | −0.0373416 | ||||||||
\(625\) | −3.65753e12 | −0.958799 | ||||||||
\(626\) | −1.70619e12 | −0.444060 | ||||||||
\(627\) | 6.86016e11 | 0.177268 | ||||||||
\(628\) | −2.44905e11 | −0.0628318 | ||||||||
\(629\) | 1.54402e12 | 0.393301 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.65474e12 | 1.67109 | 0.835543 | − | 0.549425i | \(-0.185153\pi\) | ||||
0.835543 | + | 0.549425i | \(0.185153\pi\) | |||||||
\(632\) | 3.63662e11 | 0.0906714 | ||||||||
\(633\) | −1.34301e13 | −3.32478 | ||||||||
\(634\) | −5.29762e11 | −0.130220 | ||||||||
\(635\) | 3.91537e12 | 0.955632 | ||||||||
\(636\) | 6.25981e12 | 1.51706 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 9.54930e11 | 0.228180 | ||||||||
\(639\) | 5.91594e12 | 1.40368 | ||||||||
\(640\) | −3.67641e11 | −0.0866192 | ||||||||
\(641\) | −4.60320e12 | −1.07696 | −0.538479 | − | 0.842639i | \(-0.681001\pi\) | ||||
−0.538479 | + | 0.842639i | \(0.681001\pi\) | |||||||
\(642\) | −1.12352e12 | −0.261021 | ||||||||
\(643\) | −6.55681e12 | −1.51267 | −0.756333 | − | 0.654186i | \(-0.773011\pi\) | ||||
−0.756333 | + | 0.654186i | \(0.773011\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.15478e13 | −2.62713 | ||||||||
\(646\) | 1.20210e12 | 0.271577 | ||||||||
\(647\) | −1.79575e12 | −0.402880 | −0.201440 | − | 0.979501i | \(-0.564562\pi\) | ||||
−0.201440 | + | 0.979501i | \(0.564562\pi\) | |||||||
\(648\) | 5.88103e12 | 1.31028 | ||||||||
\(649\) | −7.96505e11 | −0.176233 | ||||||||
\(650\) | −9.86825e9 | −0.00216835 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.59220e12 | −0.345051 | ||||||||
\(653\) | −6.30641e12 | −1.35729 | −0.678645 | − | 0.734466i | \(-0.737433\pi\) | ||||
−0.678645 | + | 0.734466i | \(0.737433\pi\) | |||||||
\(654\) | 3.57822e11 | 0.0764834 | ||||||||
\(655\) | −7.08205e12 | −1.50339 | ||||||||
\(656\) | −3.65296e11 | −0.0770154 | ||||||||
\(657\) | −1.09708e13 | −2.29717 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.63478e12 | −1.37038 | −0.685191 | − | 0.728363i | \(-0.740281\pi\) | ||||
−0.685191 | + | 0.728363i | \(0.740281\pi\) | |||||||
\(660\) | −1.03729e12 | −0.212790 | ||||||||
\(661\) | 2.38444e11 | 0.0485825 | 0.0242913 | − | 0.999705i | \(-0.492267\pi\) | ||||
0.0242913 | + | 0.999705i | \(0.492267\pi\) | |||||||
\(662\) | −3.52025e12 | −0.712382 | ||||||||
\(663\) | −6.99205e11 | −0.140538 | ||||||||
\(664\) | −9.90034e11 | −0.197649 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.09133e12 | 0.805806 | ||||||||
\(667\) | −1.15091e13 | −2.25153 | ||||||||
\(668\) | 8.53695e11 | 0.165886 | ||||||||
\(669\) | 1.50152e13 | 2.89809 | ||||||||
\(670\) | −2.31813e12 | −0.444427 | ||||||||
\(671\) | −8.12221e10 | −0.0154676 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.84956e12 | 1.47495 | 0.737475 | − | 0.675374i | \(-0.236018\pi\) | ||||
0.737475 | + | 0.675374i | \(0.236018\pi\) | |||||||
\(674\) | 2.54283e12 | 0.474622 | ||||||||
\(675\) | 7.12234e11 | 0.132055 | ||||||||
\(676\) | −2.69850e12 | −0.497006 | ||||||||
\(677\) | 7.27382e11 | 0.133080 | 0.0665401 | − | 0.997784i | \(-0.478804\pi\) | ||||
0.0665401 | + | 0.997784i | \(0.478804\pi\) | |||||||
\(678\) | −5.08182e12 | −0.923603 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −1.81763e12 | −0.325998 | ||||||||
\(681\) | −9.58252e11 | −0.170733 | ||||||||
\(682\) | −3.45851e11 | −0.0612152 | ||||||||
\(683\) | −2.03252e11 | −0.0357390 | −0.0178695 | − | 0.999840i | \(-0.505688\pi\) | ||||
−0.0178695 | + | 0.999840i | \(0.505688\pi\) | |||||||
\(684\) | 3.18531e12 | 0.556415 | ||||||||
\(685\) | 2.32345e12 | 0.403205 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −8.24180e12 | −1.41162 | ||||||||
\(688\) | −2.04040e12 | −0.347191 | ||||||||
\(689\) | −7.19458e11 | −0.121624 | ||||||||
\(690\) | 1.25017e13 | 2.09966 | ||||||||
\(691\) | −4.66699e12 | −0.778728 | −0.389364 | − | 0.921084i | \(-0.627305\pi\) | ||||
−0.389364 | + | 0.921084i | \(0.627305\pi\) | |||||||
\(692\) | −2.89285e12 | −0.479566 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.44943e12 | 0.237181 | ||||||||
\(695\) | 6.86037e12 | 1.11536 | ||||||||
\(696\) | 6.06033e12 | 0.978937 | ||||||||
\(697\) | −1.80603e12 | −0.289853 | ||||||||
\(698\) | 2.92324e12 | 0.466138 | ||||||||
\(699\) | −1.66851e12 | −0.264351 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.00377e12 | −0.157001 | −0.0785003 | − | 0.996914i | \(-0.525013\pi\) | ||||
−0.0785003 | + | 0.996914i | \(0.525013\pi\) | |||||||
\(702\) | −1.17314e12 | −0.182320 | ||||||||
\(703\) | 1.10497e12 | 0.170629 | ||||||||
\(704\) | −1.83280e11 | −0.0281215 | ||||||||
\(705\) | −1.59931e12 | −0.243827 | ||||||||
\(706\) | −4.62636e12 | −0.700839 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −5.05491e12 | −0.756073 | ||||||||
\(709\) | 3.02087e12 | 0.448977 | 0.224488 | − | 0.974477i | \(-0.427929\pi\) | ||||
0.224488 | + | 0.974477i | \(0.427929\pi\) | |||||||
\(710\) | −2.41588e12 | −0.356791 | ||||||||
\(711\) | 4.76419e12 | 0.699159 | ||||||||
\(712\) | −2.24744e12 | −0.327738 | ||||||||
\(713\) | 4.16832e12 | 0.604029 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.19218e11 | 0.0170595 | ||||||||
\(716\) | 4.74915e11 | 0.0675316 | ||||||||
\(717\) | 1.71571e13 | 2.42442 | ||||||||
\(718\) | −5.26476e12 | −0.739296 | ||||||||
\(719\) | 1.09553e13 | 1.52877 | 0.764386 | − | 0.644758i | \(-0.223042\pi\) | ||||
0.764386 | + | 0.644758i | \(0.223042\pi\) | |||||||
\(720\) | −4.81633e12 | −0.667913 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −4.30273e12 | −0.589286 | ||||||||
\(723\) | 2.03528e13 | 2.77015 | ||||||||
\(724\) | −4.20643e11 | −0.0568972 | ||||||||
\(725\) | 4.22876e11 | 0.0568449 | ||||||||
\(726\) | 9.70013e12 | 1.29587 | ||||||||
\(727\) | −1.28144e13 | −1.70135 | −0.850674 | − | 0.525694i | \(-0.823806\pi\) | ||||
−0.850674 | + | 0.525694i | \(0.823806\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.79953e13 | 3.67122 | ||||||||
\(730\) | 4.48012e12 | 0.583898 | ||||||||
\(731\) | −1.00878e13 | −1.30668 | ||||||||
\(732\) | −5.15465e11 | −0.0663589 | ||||||||
\(733\) | −7.12017e12 | −0.911009 | −0.455505 | − | 0.890233i | \(-0.650541\pi\) | ||||
−0.455505 | + | 0.890233i | \(0.650541\pi\) | |||||||
\(734\) | 6.66326e12 | 0.847334 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.20895e12 | 0.277483 | ||||||||
\(737\) | −1.15566e12 | −0.144286 | ||||||||
\(738\) | −4.78560e12 | −0.593859 | ||||||||
\(739\) | −5.53361e12 | −0.682509 | −0.341254 | − | 0.939971i | \(-0.610852\pi\) | ||||
−0.341254 | + | 0.939971i | \(0.610852\pi\) | |||||||
\(740\) | −1.67077e12 | −0.204821 | ||||||||
\(741\) | −5.00384e11 | −0.0609707 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.58825e12 | 0.311571 | 0.155785 | − | 0.987791i | \(-0.450209\pi\) | ||||
0.155785 | + | 0.987791i | \(0.450209\pi\) | |||||||
\(744\) | −2.19489e12 | −0.262625 | ||||||||
\(745\) | −2.30080e12 | −0.273637 | ||||||||
\(746\) | 1.72207e12 | 0.203576 | ||||||||
\(747\) | −1.29701e13 | −1.52405 | ||||||||
\(748\) | −9.06141e11 | −0.105837 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −1.20502e13 | −1.39065 | ||||||||
\(751\) | −5.64331e12 | −0.647373 | −0.323686 | − | 0.946164i | \(-0.604922\pi\) | ||||
−0.323686 | + | 0.946164i | \(0.604922\pi\) | |||||||
\(752\) | −2.82585e11 | −0.0322232 | ||||||||
\(753\) | 2.75425e13 | 3.12195 | ||||||||
\(754\) | −6.96531e11 | −0.0784819 | ||||||||
\(755\) | 9.33308e12 | 1.04535 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.51570e13 | −1.67757 | −0.838786 | − | 0.544462i | \(-0.816734\pi\) | ||||
−0.838786 | + | 0.544462i | \(0.816734\pi\) | |||||||
\(758\) | 8.54789e12 | 0.940475 | ||||||||
\(759\) | 6.23249e12 | 0.681669 | ||||||||
\(760\) | −1.30078e12 | −0.141430 | ||||||||
\(761\) | 8.05711e12 | 0.870860 | 0.435430 | − | 0.900222i | \(-0.356596\pi\) | ||||
0.435430 | + | 0.900222i | \(0.356596\pi\) | |||||||
\(762\) | 1.23876e13 | 1.33104 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 2.91039e12 | 0.309052 | ||||||||
\(765\) | −2.38120e13 | −2.51374 | ||||||||
\(766\) | 4.92646e12 | 0.517017 | ||||||||
\(767\) | 5.80975e11 | 0.0606148 | ||||||||
\(768\) | −1.16316e12 | −0.120646 | ||||||||
\(769\) | 2.31836e12 | 0.239063 | 0.119531 | − | 0.992830i | \(-0.461861\pi\) | ||||
0.119531 | + | 0.992830i | \(0.461861\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.49409e13 | 1.52276 | ||||||||
\(772\) | −9.75417e12 | −0.988354 | ||||||||
\(773\) | 1.70922e13 | 1.72183 | 0.860916 | − | 0.508747i | \(-0.169891\pi\) | ||||
0.860916 | + | 0.508747i | \(0.169891\pi\) | |||||||
\(774\) | −2.67306e13 | −2.67716 | ||||||||
\(775\) | −1.53155e11 | −0.0152501 | ||||||||
\(776\) | 4.78192e12 | 0.473396 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 9.39536e12 | 0.919402 | ||||||||
\(779\) | −1.29248e12 | −0.125749 | ||||||||
\(780\) | 7.56603e11 | 0.0731884 | ||||||||
\(781\) | −1.20439e12 | −0.115834 | ||||||||
\(782\) | 1.09211e13 | 1.04433 | ||||||||
\(783\) | 5.02716e13 | 4.77964 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.31021e12 | 0.123148 | ||||||||
\(786\) | −2.24065e13 | −2.09398 | ||||||||
\(787\) | 4.18824e12 | 0.389176 | 0.194588 | − | 0.980885i | \(-0.437663\pi\) | ||||
0.194588 | + | 0.980885i | \(0.437663\pi\) | |||||||
\(788\) | −4.38654e12 | −0.405279 | ||||||||
\(789\) | 6.07883e12 | 0.558436 | ||||||||
\(790\) | −1.94555e12 | −0.177713 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −2.40108e12 | −0.216842 | ||||||||
\(793\) | 5.92438e10 | 0.00532003 | ||||||||
\(794\) | −9.49764e12 | −0.848054 | ||||||||
\(795\) | −3.34892e13 | −2.97340 | ||||||||
\(796\) | 5.89259e12 | 0.520232 | ||||||||
\(797\) | −1.78707e13 | −1.56884 | −0.784421 | − | 0.620229i | \(-0.787040\pi\) | ||||
−0.784421 | + | 0.620229i | \(0.787040\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.39711e12 | −0.121274 | ||||||||
\(800\) | −8.11626e10 | −0.00700570 | ||||||||
\(801\) | −2.94428e13 | −2.52716 | ||||||||
\(802\) | 7.20298e12 | 0.614791 | ||||||||
\(803\) | 2.23347e12 | 0.189566 | ||||||||
\(804\) | −7.33420e12 | −0.619014 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.52265e11 | 0.0210547 | ||||||||
\(807\) | 6.37007e11 | 0.0528705 | ||||||||
\(808\) | −5.69285e12 | −0.469871 | ||||||||
\(809\) | −3.19043e12 | −0.261867 | −0.130934 | − | 0.991391i | \(-0.541797\pi\) | ||||
−0.130934 | + | 0.991391i | \(0.541797\pi\) | |||||||
\(810\) | −3.14628e13 | −2.56812 | ||||||||
\(811\) | 1.37637e12 | 0.111722 | 0.0558612 | − | 0.998439i | \(-0.482210\pi\) | ||||
0.0558612 | + | 0.998439i | \(0.482210\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.04619e13 | −3.24817 | ||||||||
\(814\) | −8.32928e11 | −0.0664963 | ||||||||
\(815\) | 8.51808e12 | 0.676290 | ||||||||
\(816\) | −5.75069e12 | −0.454061 | ||||||||
\(817\) | −7.21931e12 | −0.566887 | ||||||||
\(818\) | −6.95423e12 | −0.543075 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.95429e12 | 0.150948 | ||||||||
\(821\) | 2.10169e13 | 1.61445 | 0.807223 | − | 0.590247i | \(-0.200970\pi\) | ||||
0.807223 | + | 0.590247i | \(0.200970\pi\) | |||||||
\(822\) | 7.35104e12 | 0.561598 | ||||||||
\(823\) | −1.36094e13 | −1.03405 | −0.517024 | − | 0.855971i | \(-0.672960\pi\) | ||||
−0.517024 | + | 0.855971i | \(0.672960\pi\) | |||||||
\(824\) | −3.84536e12 | −0.290579 | ||||||||
\(825\) | −2.28998e11 | −0.0172103 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.02944e13 | 0.765288 | 0.382644 | − | 0.923896i | \(-0.375014\pi\) | ||||
0.382644 | + | 0.923896i | \(0.375014\pi\) | |||||||
\(828\) | 2.89387e13 | 2.13965 | ||||||||
\(829\) | −2.59127e13 | −1.90554 | −0.952769 | − | 0.303695i | \(-0.901780\pi\) | ||||
−0.952769 | + | 0.303695i | \(0.901780\pi\) | |||||||
\(830\) | 5.29657e12 | 0.387385 | ||||||||
\(831\) | 3.91059e13 | 2.84471 | ||||||||
\(832\) | 1.33685e11 | 0.00967228 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 2.17052e13 | 1.55352 | ||||||||
\(835\) | −4.56717e12 | −0.325131 | ||||||||
\(836\) | −6.48477e11 | −0.0459162 | ||||||||
\(837\) | −1.82071e13 | −1.28226 | ||||||||
\(838\) | 7.91252e12 | 0.554264 | ||||||||
\(839\) | 5.20978e12 | 0.362986 | 0.181493 | − | 0.983392i | \(-0.441907\pi\) | ||||
0.181493 | + | 0.983392i | \(0.441907\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.53407e13 | 1.05746 | ||||||||
\(842\) | 1.08492e13 | 0.743864 | ||||||||
\(843\) | 1.90738e13 | 1.30081 | ||||||||
\(844\) | 1.26952e13 | 0.861190 | ||||||||
\(845\) | 1.44366e13 | 0.974117 | ||||||||
\(846\) | −3.70204e12 | −0.248470 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −5.91727e12 | −0.392952 | ||||||||
\(849\) | 5.53983e13 | 3.65942 | ||||||||
\(850\) | −4.01270e11 | −0.0263665 | ||||||||
\(851\) | 1.00387e13 | 0.656140 | ||||||||
\(852\) | −7.64348e12 | −0.496951 | ||||||||
\(853\) | 2.58714e12 | 0.167321 | 0.0836604 | − | 0.996494i | \(-0.473339\pi\) | ||||
0.0836604 | + | 0.996494i | \(0.473339\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.70410e13 | −1.09056 | ||||||||
\(856\) | 1.06204e12 | 0.0676100 | ||||||||
\(857\) | 1.91338e13 | 1.21168 | 0.605838 | − | 0.795588i | \(-0.292838\pi\) | ||||
0.605838 | + | 0.795588i | \(0.292838\pi\) | |||||||
\(858\) | 3.77189e11 | 0.0237611 | ||||||||
\(859\) | −2.66475e13 | −1.66989 | −0.834945 | − | 0.550334i | \(-0.814501\pi\) | ||||
−0.834945 | + | 0.550334i | \(0.814501\pi\) | |||||||
\(860\) | 1.09159e13 | 0.680483 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.82819e13 | 1.12781 | ||||||||
\(863\) | −2.48333e13 | −1.52401 | −0.762003 | − | 0.647574i | \(-0.775784\pi\) | ||||
−0.762003 | + | 0.647574i | \(0.775784\pi\) | |||||||
\(864\) | −9.64865e12 | −0.589053 | ||||||||
\(865\) | 1.54764e13 | 0.939934 | ||||||||
\(866\) | −1.59090e13 | −0.961198 | ||||||||
\(867\) | 3.68431e12 | 0.221447 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9.69912e11 | −0.0576957 | ||||||||
\(870\) | −3.24220e13 | −1.91869 | ||||||||
\(871\) | 8.42941e11 | 0.0496267 | ||||||||
\(872\) | −3.38242e11 | −0.0198109 | ||||||||
\(873\) | 6.26461e13 | 3.65031 | ||||||||
\(874\) | 7.81567e12 | 0.453069 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.41744e13 | 0.813273 | ||||||||
\(877\) | 1.18382e13 | 0.675753 | 0.337876 | − | 0.941190i | \(-0.390291\pi\) | ||||
0.337876 | + | 0.941190i | \(0.390291\pi\) | |||||||
\(878\) | −3.47107e12 | −0.197124 | ||||||||
\(879\) | 2.93252e13 | 1.65688 | ||||||||
\(880\) | 9.80526e11 | 0.0551172 | ||||||||
\(881\) | −2.57086e13 | −1.43776 | −0.718882 | − | 0.695133i | \(-0.755346\pi\) | ||||
−0.718882 | + | 0.695133i | \(0.755346\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.32530e13 | −0.733656 | −0.366828 | − | 0.930289i | \(-0.619556\pi\) | ||||
−0.366828 | + | 0.930289i | \(0.619556\pi\) | |||||||
\(884\) | 6.60944e11 | 0.0364024 | ||||||||
\(885\) | 2.70432e13 | 1.48188 | ||||||||
\(886\) | 1.71123e13 | 0.932947 | ||||||||
\(887\) | 3.14489e11 | 0.0170588 | 0.00852941 | − | 0.999964i | \(-0.497285\pi\) | ||||
0.00852941 | + | 0.999964i | \(0.497285\pi\) | |||||||
\(888\) | −5.28606e12 | −0.285282 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 1.20235e13 | 0.642357 | ||||||||
\(891\) | −1.56851e13 | −0.833755 | ||||||||
\(892\) | −1.41935e13 | −0.750669 | ||||||||
\(893\) | −9.99835e11 | −0.0526135 | ||||||||
\(894\) | −7.27937e12 | −0.381131 | ||||||||
\(895\) | −2.54074e12 | −0.132360 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.54601e12 | −0.234458 | ||||||||
\(898\) | 2.64361e13 | 1.35660 | ||||||||
\(899\) | −1.08101e13 | −0.551965 | ||||||||
\(900\) | −1.06328e12 | −0.0540203 | ||||||||
\(901\) | −2.92551e13 | −1.47891 | ||||||||
\(902\) | 9.74272e11 | 0.0490062 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4.80374e12 | 0.239233 | ||||||||
\(905\) | 2.25039e12 | 0.111517 | ||||||||
\(906\) | 2.95284e13 | 1.45601 | ||||||||
\(907\) | 3.68141e12 | 0.180627 | 0.0903133 | − | 0.995913i | \(-0.471213\pi\) | ||||
0.0903133 | + | 0.995913i | \(0.471213\pi\) | |||||||
\(908\) | 9.05816e11 | 0.0442236 | ||||||||
\(909\) | −7.45798e13 | −3.62313 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.58776e13 | −1.24478 | −0.622388 | − | 0.782709i | \(-0.713837\pi\) | ||||
−0.622388 | + | 0.782709i | \(0.713837\pi\) | |||||||
\(912\) | −4.11547e12 | −0.196989 | ||||||||
\(913\) | 2.64049e12 | 0.125767 | ||||||||
\(914\) | −1.19441e12 | −0.0566105 | ||||||||
\(915\) | 2.75768e12 | 0.130061 | ||||||||
\(916\) | 7.79080e12 | 0.365639 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −4.77032e13 | −2.21695 | ||||||||
\(919\) | −1.22244e13 | −0.565340 | −0.282670 | − | 0.959217i | \(-0.591220\pi\) | ||||
−0.282670 | + | 0.959217i | \(0.591220\pi\) | |||||||
\(920\) | −1.18176e13 | −0.543858 | ||||||||
\(921\) | −3.18620e13 | −1.45917 | ||||||||
\(922\) | −9.02345e12 | −0.411229 | ||||||||
\(923\) | 8.78488e11 | 0.0398408 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.68849e11 | −0.0165657 | ||||||||
\(926\) | 1.45820e13 | 0.651731 | ||||||||
\(927\) | −5.03765e13 | −2.24063 | ||||||||
\(928\) | −5.72870e12 | −0.253566 | ||||||||
\(929\) | −2.78231e13 | −1.22556 | −0.612780 | − | 0.790254i | \(-0.709949\pi\) | ||||
−0.612780 | + | 0.790254i | \(0.709949\pi\) | |||||||
\(930\) | 1.17424e13 | 0.514736 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 1.57720e12 | 0.0684725 | ||||||||
\(933\) | −4.80094e12 | −0.207424 | ||||||||
\(934\) | 3.06855e12 | 0.131939 | ||||||||
\(935\) | 4.84775e12 | 0.207438 | ||||||||
\(936\) | 1.75136e12 | 0.0745821 | ||||||||
\(937\) | 3.45042e13 | 1.46232 | 0.731162 | − | 0.682204i | \(-0.238978\pi\) | ||||
0.731162 | + | 0.682204i | \(0.238978\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.88793e13 | 1.21225 | ||||||||
\(940\) | 1.51180e12 | 0.0631565 | ||||||||
\(941\) | 4.18564e13 | 1.74024 | 0.870119 | − | 0.492842i | \(-0.164042\pi\) | ||||
0.870119 | + | 0.492842i | \(0.164042\pi\) | |||||||
\(942\) | 4.14532e12 | 0.171526 | ||||||||
\(943\) | −1.17423e13 | −0.483559 | ||||||||
\(944\) | 4.77830e12 | 0.195839 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.44191e12 | 0.220923 | ||||||||
\(947\) | −1.65956e13 | −0.670529 | −0.335265 | − | 0.942124i | \(-0.608826\pi\) | ||||
−0.335265 | + | 0.942124i | \(0.608826\pi\) | |||||||
\(948\) | −6.15541e12 | −0.247525 | ||||||||
\(949\) | −1.62911e12 | −0.0652006 | ||||||||
\(950\) | −2.87168e11 | −0.0114388 | ||||||||
\(951\) | 8.96686e12 | 0.355491 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.49663e13 | 0.587756 | 0.293878 | − | 0.955843i | \(-0.405054\pi\) | ||||
0.293878 | + | 0.955843i | \(0.405054\pi\) | |||||||
\(954\) | −7.75199e13 | −3.03002 | ||||||||
\(955\) | −1.55702e13 | −0.605732 | ||||||||
\(956\) | −1.62183e13 | −0.627977 | ||||||||
\(957\) | −1.61633e13 | −0.622913 | ||||||||
\(958\) | −2.38492e13 | −0.914806 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 6.22277e12 | 0.236463 | ||||||||
\(961\) | −2.25245e13 | −0.851921 | ||||||||
\(962\) | 6.07542e11 | 0.0228712 | ||||||||
\(963\) | 1.39134e13 | 0.521334 | ||||||||
\(964\) | −1.92391e13 | −0.717528 | ||||||||
\(965\) | 5.21837e13 | 1.93714 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.21214e13 | 0.813568 | 0.406784 | − | 0.913524i | \(-0.366650\pi\) | ||||
0.406784 | + | 0.913524i | \(0.366650\pi\) | |||||||
\(968\) | −9.16933e12 | −0.335659 | ||||||||
\(969\) | −2.03470e13 | −0.741383 | ||||||||
\(970\) | −2.55827e13 | −0.927841 | ||||||||
\(971\) | 1.17366e13 | 0.423696 | 0.211848 | − | 0.977303i | \(-0.432052\pi\) | ||||
0.211848 | + | 0.977303i | \(0.432052\pi\) | |||||||
\(972\) | −5.31777e13 | −1.91087 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −2.03116e13 | −0.723151 | ||||||||
\(975\) | 1.67032e11 | 0.00591942 | ||||||||
\(976\) | 4.87258e11 | 0.0171884 | ||||||||
\(977\) | 5.58753e13 | 1.96198 | 0.980989 | − | 0.194065i | \(-0.0621674\pi\) | ||||
0.980989 | + | 0.194065i | \(0.0621674\pi\) | |||||||
\(978\) | 2.69499e13 | 0.941960 | ||||||||
\(979\) | 5.99408e12 | 0.208545 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.43118e12 | −0.152760 | ||||||||
\(982\) | −1.13779e13 | −0.390445 | ||||||||
\(983\) | 3.86757e13 | 1.32113 | 0.660567 | − | 0.750767i | \(-0.270316\pi\) | ||||
0.660567 | + | 0.750767i | \(0.270316\pi\) | |||||||
\(984\) | 6.18308e12 | 0.210246 | ||||||||
\(985\) | 2.34675e13 | 0.794334 | ||||||||
\(986\) | −2.83229e13 | −0.954313 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.73002e11 | 0.0157927 | ||||||||
\(989\) | −6.55878e13 | −2.17992 | ||||||||
\(990\) | 1.28455e13 | 0.425004 | ||||||||
\(991\) | −2.49912e13 | −0.823106 | −0.411553 | − | 0.911386i | \(-0.635014\pi\) | ||||
−0.411553 | + | 0.911386i | \(0.635014\pi\) | |||||||
\(992\) | 2.07479e12 | 0.0680254 | ||||||||
\(993\) | 5.95845e13 | 1.94474 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.15247e13 | −1.01964 | ||||||||
\(996\) | 1.67575e13 | 0.539564 | ||||||||
\(997\) | −1.35204e13 | −0.433373 | −0.216687 | − | 0.976241i | \(-0.569525\pi\) | ||||
−0.216687 | + | 0.976241i | \(0.569525\pi\) | |||||||
\(998\) | 2.56420e13 | 0.818210 | ||||||||
\(999\) | −4.38489e13 | −1.39288 |
(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 | 98.10.a.i.1.1 | 3 | ||
7.2 | even | 3 | 98.10.c.k.67.3 | 6 | |||
7.3 | odd | 6 | 14.10.c.a.9.1 | ✓ | 6 | ||
7.4 | even | 3 | 98.10.c.k.79.3 | 6 | |||
7.5 | odd | 6 | 14.10.c.a.11.1 | yes | 6 | ||
7.6 | odd | 2 | 98.10.a.j.1.3 | 3 | |||
21.5 | even | 6 | 126.10.g.f.109.3 | 6 | |||
21.17 | even | 6 | 126.10.g.f.37.3 | 6 | |||
28.3 | even | 6 | 112.10.i.b.65.3 | 6 | |||
28.19 | even | 6 | 112.10.i.b.81.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
14.10.c.a.9.1 | ✓ | 6 | 7.3 | odd | 6 | ||
14.10.c.a.11.1 | yes | 6 | 7.5 | odd | 6 | ||
98.10.a.i.1.1 | 3 | 1.1 | even | 1 | trivial | ||
98.10.a.j.1.3 | 3 | 7.6 | odd | 2 | |||
98.10.c.k.67.3 | 6 | 7.2 | even | 3 | |||
98.10.c.k.79.3 | 6 | 7.4 | even | 3 | |||
112.10.i.b.65.3 | 6 | 28.3 | even | 6 | |||
112.10.i.b.81.3 | 6 | 28.19 | even | 6 | |||
126.10.g.f.37.3 | 6 | 21.17 | even | 6 | |||
126.10.g.f.109.3 | 6 | 21.5 | even | 6 |