Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9,68,Mod(1,9)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 68, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9.1");
S:= CuspForms(chi, 68);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9 = 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 68 \) |
Character orbit: | \([\chi]\) | \(=\) | 9.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: | \(255.861316737\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} + \cdots - 17\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | multiple of \( 2^{40}\cdot 3^{20}\cdot 5^{3}\cdot 7^{2}\cdot 11\cdot 17 \) |
Twist minimal: | no (minimal twist has level 3) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(1.48809e8\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.03939e10 | 0.855602 | 0.427801 | − | 0.903873i | \(-0.359288\pi\) | ||||
0.427801 | + | 0.903873i | \(0.359288\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −3.95417e19 | −0.267945 | ||||||||
\(5\) | −1.67944e23 | −0.645164 | −0.322582 | − | 0.946542i | \(-0.604551\pi\) | ||||
−0.322582 | + | 0.946542i | \(0.604551\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.85597e28 | −1.88516 | −0.942582 | − | 0.333974i | \(-0.891610\pi\) | ||||
−0.942582 | + | 0.333974i | \(0.891610\pi\) | |||||||
\(8\) | −1.94485e30 | −1.08486 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.74559e33 | −0.552003 | ||||||||
\(11\) | 2.10881e34 | 0.273768 | 0.136884 | − | 0.990587i | \(-0.456291\pi\) | ||||
0.136884 | + | 0.990587i | \(0.456291\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.64496e37 | 1.27443 | 0.637217 | − | 0.770684i | \(-0.280085\pi\) | ||||
0.637217 | + | 0.770684i | \(0.280085\pi\) | |||||||
\(14\) | −4.00784e38 | −1.61295 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.43792e40 | −0.660260 | ||||||||
\(17\) | 1.55302e41 | 0.935703 | 0.467851 | − | 0.883807i | \(-0.345028\pi\) | ||||
0.467851 | + | 0.883807i | \(0.345028\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.02214e42 | 0.583730 | 0.291865 | − | 0.956460i | \(-0.405724\pi\) | ||||
0.291865 | + | 0.956460i | \(0.405724\pi\) | |||||||
\(20\) | 6.64081e42 | 0.172869 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.19187e44 | 0.234237 | ||||||||
\(23\) | −5.77103e45 | −1.39114 | −0.695570 | − | 0.718458i | \(-0.744848\pi\) | ||||
−0.695570 | + | 0.718458i | \(0.744848\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.95574e46 | −0.583764 | ||||||||
\(26\) | 2.74914e47 | 1.09041 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.52472e48 | 0.505121 | ||||||||
\(29\) | 8.56944e48 | 0.876233 | 0.438117 | − | 0.898918i | \(-0.355646\pi\) | ||||
0.438117 | + | 0.898918i | \(0.355646\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.43118e49 | −0.266195 | −0.133097 | − | 0.991103i | \(-0.542492\pi\) | ||||
−0.133097 | + | 0.991103i | \(0.542492\pi\) | |||||||
\(32\) | 1.37554e50 | 0.519937 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.61419e51 | 0.800589 | ||||||||
\(35\) | 6.47588e51 | 1.21624 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.12588e52 | 1.49627 | 0.748137 | − | 0.663545i | \(-0.230949\pi\) | ||||
0.748137 | + | 0.663545i | \(0.230949\pi\) | |||||||
\(38\) | 4.18056e52 | 0.499440 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.26627e53 | 0.699910 | ||||||||
\(41\) | 1.27508e54 | 1.19475 | 0.597376 | − | 0.801962i | \(-0.296210\pi\) | ||||
0.597376 | + | 0.801962i | \(0.296210\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.40780e54 | 1.21763 | 0.608815 | − | 0.793312i | \(-0.291645\pi\) | ||||
0.608815 | + | 0.793312i | \(0.291645\pi\) | |||||||
\(44\) | −8.33861e53 | −0.0733549 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.99833e55 | −1.19026 | ||||||||
\(47\) | −1.57548e56 | −1.52102 | −0.760508 | − | 0.649328i | \(-0.775050\pi\) | ||||
−0.760508 | + | 0.649328i | \(0.775050\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.06847e57 | 2.55384 | ||||||||
\(50\) | −4.11154e56 | −0.499470 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.04586e57 | −0.341479 | ||||||||
\(53\) | −4.51622e57 | −0.778992 | −0.389496 | − | 0.921028i | \(-0.627351\pi\) | ||||
−0.389496 | + | 0.921028i | \(0.627351\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.54163e57 | −0.176625 | ||||||||
\(56\) | 7.49929e58 | 2.04513 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 8.90696e58 | 0.749707 | ||||||||
\(59\) | 1.96190e59 | 0.931396 | 0.465698 | − | 0.884944i | \(-0.345803\pi\) | ||||
0.465698 | + | 0.884944i | \(0.345803\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.54683e59 | −0.395776 | −0.197888 | − | 0.980225i | \(-0.563408\pi\) | ||||
−0.197888 | + | 0.980225i | \(0.563408\pi\) | |||||||
\(62\) | −2.52693e59 | −0.227757 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 3.55172e60 | 1.10512 | ||||||||
\(65\) | −4.44206e60 | −0.822218 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.16510e61 | −1.45202 | −0.726008 | − | 0.687686i | \(-0.758626\pi\) | ||||
−0.726008 | + | 0.687686i | \(0.758626\pi\) | |||||||
\(68\) | −6.14091e60 | −0.250717 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 6.73093e61 | 1.04062 | ||||||||
\(71\) | 6.59771e61 | 0.634218 | 0.317109 | − | 0.948389i | \(-0.397288\pi\) | ||||
0.317109 | + | 0.948389i | \(0.397288\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.31948e62 | −0.500133 | −0.250067 | − | 0.968229i | \(-0.580453\pi\) | ||||
−0.250067 | + | 0.968229i | \(0.580453\pi\) | |||||||
\(74\) | 5.32777e62 | 1.28021 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.59043e62 | −0.156408 | ||||||||
\(77\) | −8.13151e62 | −0.516098 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.95091e63 | −1.06216 | −0.531079 | − | 0.847322i | \(-0.678213\pi\) | ||||
−0.531079 | + | 0.847322i | \(0.678213\pi\) | |||||||
\(80\) | 2.41490e63 | 0.425976 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.32530e64 | 1.02223 | ||||||||
\(83\) | −3.05217e63 | −0.156853 | −0.0784264 | − | 0.996920i | \(-0.524990\pi\) | ||||
−0.0784264 | + | 0.996920i | \(0.524990\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.60821e64 | −0.603681 | ||||||||
\(86\) | 6.66017e64 | 1.04181 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4.10133e64 | −0.296999 | ||||||||
\(89\) | 1.74764e65 | 0.866734 | 0.433367 | − | 0.901217i | \(-0.357325\pi\) | ||||
0.433367 | + | 0.901217i | \(0.357325\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.01989e66 | −2.40252 | ||||||||
\(92\) | 2.28197e65 | 0.372749 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.63753e66 | −1.30138 | ||||||||
\(95\) | −6.75496e65 | −0.376601 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.23298e66 | 0.619488 | 0.309744 | − | 0.950820i | \(-0.399757\pi\) | ||||
0.309744 | + | 0.950820i | \(0.399757\pi\) | |||||||
\(98\) | 1.11055e67 | 2.18507 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.56417e66 | 0.156417 | ||||||||
\(101\) | 1.97014e67 | 1.41166 | 0.705831 | − | 0.708380i | \(-0.250574\pi\) | ||||
0.705831 | + | 0.708380i | \(0.250574\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.45814e67 | −0.541691 | −0.270845 | − | 0.962623i | \(-0.587303\pi\) | ||||
−0.270845 | + | 0.962623i | \(0.587303\pi\) | |||||||
\(104\) | −5.14407e67 | −1.38258 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.69409e67 | −0.666507 | ||||||||
\(107\) | 1.53387e67 | 0.159013 | 0.0795066 | − | 0.996834i | \(-0.474666\pi\) | ||||
0.0795066 | + | 0.996834i | \(0.474666\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.61115e68 | −0.898149 | −0.449074 | − | 0.893494i | \(-0.648246\pi\) | ||||
−0.449074 | + | 0.893494i | \(0.648246\pi\) | |||||||
\(110\) | −3.68112e67 | −0.151121 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 5.54457e68 | 1.24470 | ||||||||
\(113\) | −3.93638e68 | −0.656098 | −0.328049 | − | 0.944661i | \(-0.606391\pi\) | ||||
−0.328049 | + | 0.944661i | \(0.606391\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.69211e68 | 0.897513 | ||||||||
\(116\) | −3.38851e68 | −0.234783 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.03917e69 | 0.796904 | ||||||||
\(119\) | −5.98839e69 | −1.76395 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.48878e69 | −0.925051 | ||||||||
\(122\) | −2.64713e69 | −0.338627 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 9.61329e68 | 0.0713256 | ||||||||
\(125\) | 1.80238e70 | 1.02179 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.98306e70 | −0.660557 | −0.330278 | − | 0.943884i | \(-0.607143\pi\) | ||||
−0.330278 | + | 0.943884i | \(0.607143\pi\) | |||||||
\(128\) | 1.66166e70 | 0.425605 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −4.61702e70 | −0.703492 | ||||||||
\(131\) | −3.11780e69 | −0.0367502 | −0.0183751 | − | 0.999831i | \(-0.505849\pi\) | ||||
−0.0183751 | + | 0.999831i | \(0.505849\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.55093e71 | −1.10043 | ||||||||
\(134\) | −2.25037e71 | −1.24235 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.02039e71 | −1.01510 | ||||||||
\(137\) | 3.78607e71 | 0.995518 | 0.497759 | − | 0.867315i | \(-0.334156\pi\) | ||||
0.497759 | + | 0.867315i | \(0.334156\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.76617e71 | −1.41845 | −0.709225 | − | 0.704982i | \(-0.750955\pi\) | ||||
−0.709225 | + | 0.704982i | \(0.750955\pi\) | |||||||
\(140\) | −2.56067e71 | −0.325886 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 6.85756e71 | 0.542638 | ||||||||
\(143\) | 5.57773e71 | 0.348900 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.43919e72 | −0.565314 | ||||||||
\(146\) | −1.37144e72 | −0.427915 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.02686e72 | −0.400919 | ||||||||
\(149\) | −1.21287e73 | −1.91458 | −0.957289 | − | 0.289131i | \(-0.906634\pi\) | ||||
−0.957289 | + | 0.289131i | \(0.906634\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.99913e72 | 0.403867 | 0.201933 | − | 0.979399i | \(-0.435278\pi\) | ||||
0.201933 | + | 0.979399i | \(0.435278\pi\) | |||||||
\(152\) | −7.82248e72 | −0.633263 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −8.45178e72 | −0.441574 | ||||||||
\(155\) | 4.08302e72 | 0.171739 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.62592e73 | 0.718858 | 0.359429 | − | 0.933172i | \(-0.382971\pi\) | ||||
0.359429 | + | 0.933172i | \(0.382971\pi\) | |||||||
\(158\) | −4.10652e73 | −0.908785 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.31015e73 | −0.335444 | ||||||||
\(161\) | 2.22529e74 | 2.62253 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.03139e74 | −0.803784 | −0.401892 | − | 0.915687i | \(-0.631647\pi\) | ||||
−0.401892 | + | 0.915687i | \(0.631647\pi\) | |||||||
\(164\) | −5.04188e73 | −0.320128 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.17238e73 | −0.134204 | ||||||||
\(167\) | −5.86661e73 | −0.202948 | −0.101474 | − | 0.994838i | \(-0.532356\pi\) | ||||
−0.101474 | + | 0.994838i | \(0.532356\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.68854e74 | 0.624182 | ||||||||
\(170\) | −2.71093e74 | −0.516511 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.53376e74 | −0.326258 | ||||||||
\(173\) | 1.50339e75 | 1.59415 | 0.797074 | − | 0.603882i | \(-0.206380\pi\) | ||||
0.797074 | + | 0.603882i | \(0.206380\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.52532e75 | 1.10049 | ||||||||
\(176\) | −3.03230e74 | −0.180758 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.81647e75 | 0.741579 | ||||||||
\(179\) | 4.91440e75 | 1.66301 | 0.831503 | − | 0.555520i | \(-0.187481\pi\) | ||||
0.831503 | + | 0.555520i | \(0.187481\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.79651e74 | −0.135187 | −0.0675934 | − | 0.997713i | \(-0.521532\pi\) | ||||
−0.0675934 | + | 0.997713i | \(0.521532\pi\) | |||||||
\(182\) | −1.06006e76 | −2.05560 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.12238e76 | 1.50919 | ||||||||
\(185\) | −8.60862e75 | −0.965341 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.27503e75 | 0.256166 | ||||||||
\(188\) | 6.22971e75 | 0.407549 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −7.02100e75 | −0.322221 | ||||||||
\(191\) | −1.62221e76 | −0.624436 | −0.312218 | − | 0.950010i | \(-0.601072\pi\) | ||||
−0.312218 | + | 0.950010i | \(0.601072\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.49053e76 | −1.21935 | −0.609674 | − | 0.792652i | \(-0.708700\pi\) | ||||
−0.609674 | + | 0.792652i | \(0.708700\pi\) | |||||||
\(194\) | 2.32093e76 | 0.530035 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.22492e76 | −0.684291 | ||||||||
\(197\) | 9.61352e76 | 1.31300 | 0.656498 | − | 0.754327i | \(-0.272037\pi\) | ||||
0.656498 | + | 0.754327i | \(0.272037\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.55638e77 | −1.51544 | −0.757720 | − | 0.652580i | \(-0.773687\pi\) | ||||
−0.757720 | + | 0.652580i | \(0.773687\pi\) | |||||||
\(200\) | 7.69333e76 | 0.633300 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.04773e77 | 1.20782 | ||||||||
\(203\) | −3.30435e77 | −1.65184 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.14142e77 | −0.770810 | ||||||||
\(206\) | −1.51557e77 | −0.463472 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.80324e77 | −0.841458 | ||||||||
\(209\) | 8.48194e76 | 0.159807 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.91131e77 | 0.809509 | 0.404754 | − | 0.914425i | \(-0.367357\pi\) | ||||
0.404754 | + | 0.914425i | \(0.367357\pi\) | |||||||
\(212\) | 1.78579e77 | 0.208727 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.59429e77 | 0.136052 | ||||||||
\(215\) | −1.07615e78 | −0.785571 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.37454e77 | 0.501821 | ||||||||
\(218\) | −1.67461e78 | −0.768458 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.40042e77 | 0.0473259 | ||||||||
\(221\) | 4.10768e78 | 1.19249 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.78857e78 | 1.24268 | 0.621339 | − | 0.783542i | \(-0.286589\pi\) | ||||
0.621339 | + | 0.783542i | \(0.286589\pi\) | |||||||
\(224\) | −5.30406e78 | −0.980166 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.09141e78 | −0.561359 | ||||||||
\(227\) | 4.22273e78 | 0.499720 | 0.249860 | − | 0.968282i | \(-0.419615\pi\) | ||||
0.249860 | + | 0.968282i | \(0.419615\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.58937e78 | 0.404822 | 0.202411 | − | 0.979301i | \(-0.435122\pi\) | ||||
0.202411 | + | 0.979301i | \(0.435122\pi\) | |||||||
\(230\) | 1.00738e79 | 0.767914 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.66663e79 | −0.950587 | ||||||||
\(233\) | 1.72317e79 | 0.850950 | 0.425475 | − | 0.904970i | \(-0.360107\pi\) | ||||
0.425475 | + | 0.904970i | \(0.360107\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.64592e79 | 0.981304 | ||||||||
\(236\) | −7.75769e78 | −0.249563 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −6.22425e79 | −1.50924 | ||||||||
\(239\) | −4.25827e79 | −0.897229 | −0.448614 | − | 0.893725i | \(-0.648082\pi\) | ||||
−0.448614 | + | 0.893725i | \(0.648082\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.62697e79 | −1.05620 | −0.528098 | − | 0.849184i | \(-0.677095\pi\) | ||||
−0.528098 | + | 0.849184i | \(0.677095\pi\) | |||||||
\(242\) | −5.70495e79 | −0.791475 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.00706e79 | 0.106046 | ||||||||
\(245\) | −1.79444e80 | −1.64765 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.06384e80 | 0.743925 | ||||||||
\(248\) | 4.72828e79 | 0.288783 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.87336e80 | 0.874243 | ||||||||
\(251\) | −1.15208e80 | −0.470340 | −0.235170 | − | 0.971954i | \(-0.575565\pi\) | ||||
−0.235170 | + | 0.971954i | \(0.575565\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.21700e80 | −0.380850 | ||||||||
\(254\) | −2.06116e80 | −0.565174 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3.51431e80 | −0.740970 | ||||||||
\(257\) | −7.44854e80 | −1.37820 | −0.689099 | − | 0.724667i | \(-0.741993\pi\) | ||||
−0.689099 | + | 0.724667i | \(0.741993\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.97652e81 | −2.82072 | ||||||||
\(260\) | 1.75647e80 | 0.220310 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.24059e79 | −0.0314435 | ||||||||
\(263\) | −8.44350e79 | −0.0721115 | −0.0360558 | − | 0.999350i | \(-0.511479\pi\) | ||||
−0.0360558 | + | 0.999350i | \(0.511479\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.58472e80 | 0.502577 | ||||||||
\(266\) | −1.61201e81 | −0.941527 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 8.56117e80 | 0.389061 | ||||||||
\(269\) | 1.30791e81 | 0.524658 | 0.262329 | − | 0.964978i | \(-0.415509\pi\) | ||||
0.262329 | + | 0.964978i | \(0.415509\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.76858e81 | −0.866533 | −0.433267 | − | 0.901266i | \(-0.642639\pi\) | ||||
−0.433267 | + | 0.901266i | \(0.642639\pi\) | |||||||
\(272\) | −2.23312e81 | −0.617807 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.93518e81 | 0.851767 | ||||||||
\(275\) | −8.34191e80 | −0.159816 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.18239e81 | 0.628569 | 0.314284 | − | 0.949329i | \(-0.398235\pi\) | ||||
0.314284 | + | 0.949329i | \(0.398235\pi\) | |||||||
\(278\) | −9.11143e81 | −1.21363 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.25946e82 | −1.31945 | ||||||||
\(281\) | −1.50887e82 | −1.40278 | −0.701392 | − | 0.712776i | \(-0.747438\pi\) | ||||
−0.701392 | + | 0.712776i | \(0.747438\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.73170e81 | −0.420182 | −0.210091 | − | 0.977682i | \(-0.567376\pi\) | ||||
−0.210091 | + | 0.977682i | \(0.567376\pi\) | |||||||
\(284\) | −2.60885e81 | −0.169936 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.79741e81 | 0.298519 | ||||||||
\(287\) | −4.91666e82 | −2.25230 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.42853e81 | −0.124460 | ||||||||
\(290\) | −1.49587e82 | −0.483684 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5.21744e81 | 0.134008 | ||||||||
\(293\) | 6.47811e82 | 1.48383 | 0.741913 | − | 0.670496i | \(-0.233919\pi\) | ||||
0.741913 | + | 0.670496i | \(0.233919\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.29490e82 | −0.600903 | ||||||||
\(296\) | −9.96909e82 | −1.62324 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.26064e83 | −1.63812 | ||||||||
\(299\) | −1.52642e83 | −1.77292 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.47083e83 | −2.29543 | ||||||||
\(302\) | 4.15664e82 | 0.345549 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −5.78352e82 | −0.385413 | ||||||||
\(305\) | 4.27725e82 | 0.255340 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.02311e83 | 0.970249 | 0.485124 | − | 0.874445i | \(-0.338774\pi\) | ||||
0.485124 | + | 0.874445i | \(0.338774\pi\) | |||||||
\(308\) | 3.21534e82 | 0.138286 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 4.24383e82 | 0.146940 | ||||||||
\(311\) | −3.12987e83 | −0.972868 | −0.486434 | − | 0.873717i | \(-0.661703\pi\) | ||||
−0.486434 | + | 0.873717i | \(0.661703\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.95394e82 | 0.199456 | 0.0997279 | − | 0.995015i | \(-0.468203\pi\) | ||||
0.0997279 | + | 0.995015i | \(0.468203\pi\) | |||||||
\(314\) | 2.72934e83 | 0.615056 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.56226e83 | 0.284600 | ||||||||
\(317\) | −7.58586e83 | −1.24314 | −0.621569 | − | 0.783359i | \(-0.713505\pi\) | ||||
−0.621569 | + | 0.783359i | \(0.713505\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.80713e83 | 0.239885 | ||||||||
\(320\) | −5.96490e83 | −0.712982 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.31294e84 | 2.24384 | ||||||||
\(323\) | 6.24647e83 | 0.546198 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.04628e84 | −0.743969 | ||||||||
\(326\) | −1.07201e84 | −0.687719 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.47984e84 | −1.29613 | ||||||||
\(329\) | 6.07499e84 | 2.86737 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.80638e84 | 1.46647 | 0.733236 | − | 0.679974i | \(-0.238009\pi\) | ||||
0.733236 | + | 0.679974i | \(0.238009\pi\) | |||||||
\(332\) | 1.20688e83 | 0.0420280 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −6.09767e83 | −0.173643 | ||||||||
\(335\) | 3.63615e84 | 0.936787 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.36745e84 | 0.288608 | 0.144304 | − | 0.989533i | \(-0.453906\pi\) | ||||
0.144304 | + | 0.989533i | \(0.453906\pi\) | |||||||
\(338\) | 2.79443e84 | 0.534052 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.03133e84 | 0.161754 | ||||||||
\(341\) | −5.12689e83 | −0.0728757 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.50674e85 | −2.92925 | ||||||||
\(344\) | −1.24622e85 | −1.32095 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.56261e85 | 1.36396 | ||||||||
\(347\) | 1.91444e85 | 1.51707 | 0.758533 | − | 0.651634i | \(-0.225916\pi\) | ||||
0.758533 | + | 0.651634i | \(0.225916\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.32098e85 | 1.51712 | 0.758560 | − | 0.651603i | \(-0.225903\pi\) | ||||
0.758560 | + | 0.651603i | \(0.225903\pi\) | |||||||
\(350\) | 1.58540e85 | 0.941582 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.90077e84 | 0.142342 | ||||||||
\(353\) | 2.89966e85 | 1.29388 | 0.646941 | − | 0.762540i | \(-0.276048\pi\) | ||||
0.646941 | + | 0.762540i | \(0.276048\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.10805e85 | −0.409174 | ||||||||
\(356\) | −6.91046e84 | −0.232237 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5.10795e85 | 1.42287 | ||||||||
\(359\) | −5.20267e85 | −1.31996 | −0.659982 | − | 0.751281i | \(-0.729436\pi\) | ||||
−0.659982 | + | 0.751281i | \(0.729436\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.13002e85 | −0.659259 | ||||||||
\(362\) | −6.02481e84 | −0.115666 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.03282e85 | 0.643743 | ||||||||
\(365\) | 2.21598e85 | 0.322668 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.99070e85 | 0.605129 | 0.302565 | − | 0.953129i | \(-0.402157\pi\) | ||||
0.302565 | + | 0.953129i | \(0.402157\pi\) | |||||||
\(368\) | 8.29827e85 | 0.918514 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −8.94768e85 | −0.825948 | ||||||||
\(371\) | 1.74144e86 | 1.46853 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.82399e85 | −0.480609 | −0.240305 | − | 0.970698i | \(-0.577247\pi\) | ||||
−0.240305 | + | 0.970698i | \(0.577247\pi\) | |||||||
\(374\) | 3.40401e85 | 0.219176 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.06407e86 | 1.65008 | ||||||||
\(377\) | 2.26659e86 | 1.11670 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.31157e86 | −0.541225 | −0.270613 | − | 0.962688i | \(-0.587226\pi\) | ||||
−0.270613 | + | 0.962688i | \(0.587226\pi\) | |||||||
\(380\) | 2.67103e85 | 0.100909 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.68610e86 | −0.534269 | ||||||||
\(383\) | −4.70284e86 | −1.36522 | −0.682608 | − | 0.730785i | \(-0.739154\pi\) | ||||
−0.682608 | + | 0.730785i | \(0.739154\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.36564e86 | 0.332968 | ||||||||
\(386\) | −4.66739e86 | −1.04328 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −8.82961e85 | −0.165989 | ||||||||
\(389\) | −1.41077e86 | −0.243301 | −0.121650 | − | 0.992573i | \(-0.538819\pi\) | ||||
−0.121650 | + | 0.992573i | \(0.538819\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.96252e86 | −1.30169 | ||||||||
\(392\) | −2.07802e87 | −2.77055 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 9.99215e86 | 1.12340 | ||||||||
\(395\) | 6.63532e86 | 0.685266 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.34451e87 | −1.17241 | −0.586207 | − | 0.810161i | \(-0.699380\pi\) | ||||
−0.586207 | + | 0.810161i | \(0.699380\pi\) | |||||||
\(398\) | −1.61768e87 | −1.29661 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 5.68803e86 | 0.385436 | ||||||||
\(401\) | 1.23685e87 | 0.770870 | 0.385435 | − | 0.922735i | \(-0.374051\pi\) | ||||
0.385435 | + | 0.922735i | \(0.374051\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.43037e86 | −0.339248 | ||||||||
\(404\) | −7.79027e86 | −0.378248 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.43449e87 | −1.41332 | ||||||||
\(407\) | 1.08095e87 | 0.409632 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.43261e87 | −0.460678 | −0.230339 | − | 0.973110i | \(-0.573984\pi\) | ||||
−0.230339 | + | 0.973110i | \(0.573984\pi\) | |||||||
\(410\) | −2.22576e87 | −0.659506 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 5.76573e86 | 0.145143 | ||||||||
\(413\) | −7.56502e87 | −1.75583 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.12594e86 | 0.101196 | ||||||||
\(416\) | 3.63827e87 | 0.662625 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 8.81601e86 | 0.136731 | ||||||||
\(419\) | 3.24220e87 | 0.464162 | 0.232081 | − | 0.972696i | \(-0.425447\pi\) | ||||
0.232081 | + | 0.972696i | \(0.425447\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.60594e87 | −0.684224 | −0.342112 | − | 0.939659i | \(-0.611142\pi\) | ||||
−0.342112 | + | 0.939659i | \(0.611142\pi\) | |||||||
\(422\) | 6.14413e87 | 0.692617 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 8.78338e87 | 0.845095 | ||||||||
\(425\) | −6.14334e87 | −0.546230 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.82048e87 | 0.746103 | ||||||||
\(428\) | −6.06521e86 | −0.0426069 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.11854e88 | −0.672136 | ||||||||
\(431\) | 1.10616e88 | 0.614934 | 0.307467 | − | 0.951559i | \(-0.400519\pi\) | ||||
0.307467 | + | 0.951559i | \(0.400519\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.08620e88 | 1.46919 | 0.734596 | − | 0.678504i | \(-0.237372\pi\) | ||||
0.734596 | + | 0.678504i | \(0.237372\pi\) | |||||||
\(434\) | 9.74376e87 | 0.429359 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.37077e87 | 0.240655 | ||||||||
\(437\) | −2.32119e88 | −0.812050 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.34418e88 | 0.403548 | 0.201774 | − | 0.979432i | \(-0.435329\pi\) | ||||
0.201774 | + | 0.979432i | \(0.435329\pi\) | |||||||
\(440\) | 6.88795e87 | 0.191613 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.26946e88 | 1.02030 | ||||||||
\(443\) | −2.87068e88 | −0.636005 | −0.318002 | − | 0.948090i | \(-0.603012\pi\) | ||||
−0.318002 | + | 0.948090i | \(0.603012\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.93505e88 | −0.559185 | ||||||||
\(446\) | 6.01655e88 | 1.06324 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.36953e89 | −2.08333 | ||||||||
\(449\) | 1.13335e89 | 1.59997 | 0.799987 | − | 0.600018i | \(-0.204840\pi\) | ||||
0.799987 | + | 0.600018i | \(0.204840\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.68890e88 | 0.327085 | ||||||||
\(452\) | 1.55651e88 | 0.175798 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4.38904e88 | 0.427561 | ||||||||
\(455\) | 1.71285e89 | 1.55002 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.05288e89 | −1.60388 | −0.801939 | − | 0.597406i | \(-0.796198\pi\) | ||||
−0.801939 | + | 0.597406i | \(0.796198\pi\) | |||||||
\(458\) | 4.77012e88 | 0.346367 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −3.83243e88 | −0.240484 | ||||||||
\(461\) | −1.13552e89 | −0.662544 | −0.331272 | − | 0.943535i | \(-0.607478\pi\) | ||||
−0.331272 | + | 0.943535i | \(0.607478\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.34175e89 | 1.18189 | 0.590944 | − | 0.806712i | \(-0.298755\pi\) | ||||
0.590944 | + | 0.806712i | \(0.298755\pi\) | |||||||
\(464\) | −1.23222e89 | −0.578542 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.79103e89 | 0.728074 | ||||||||
\(467\) | −1.26348e89 | −0.478027 | −0.239013 | − | 0.971016i | \(-0.576824\pi\) | ||||
−0.239013 | + | 0.971016i | \(0.576824\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.34854e89 | 2.73729 | ||||||||
\(470\) | 2.75013e89 | 0.839606 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3.81561e89 | −1.01043 | ||||||||
\(473\) | 1.35128e89 | 0.333349 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.59105e89 | −0.340760 | ||||||||
\(476\) | 2.36792e89 | 0.472643 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −4.42598e89 | −0.767671 | ||||||||
\(479\) | −2.55611e89 | −0.413371 | −0.206686 | − | 0.978407i | \(-0.566268\pi\) | ||||
−0.206686 | + | 0.978407i | \(0.566268\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.35578e90 | 1.90690 | ||||||||
\(482\) | −6.88798e89 | −0.903683 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.17036e89 | 0.247863 | ||||||||
\(485\) | −3.75017e89 | −0.399671 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.83594e90 | −1.70466 | −0.852329 | − | 0.523005i | \(-0.824811\pi\) | ||||
−0.852329 | + | 0.523005i | \(0.824811\pi\) | |||||||
\(488\) | 4.95320e89 | 0.429360 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.86511e90 | −1.40973 | ||||||||
\(491\) | −1.54963e90 | −1.09395 | −0.546976 | − | 0.837148i | \(-0.684221\pi\) | ||||
−0.546976 | + | 0.837148i | \(0.684221\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.33085e90 | 0.819894 | ||||||||
\(494\) | 1.10574e90 | 0.636504 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.49583e89 | 0.175758 | ||||||||
\(497\) | −2.54406e90 | −1.19561 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.16417e90 | −1.29985 | −0.649923 | − | 0.760000i | \(-0.725199\pi\) | ||||
−0.649923 | + | 0.760000i | \(0.725199\pi\) | |||||||
\(500\) | −7.12691e89 | −0.273783 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.19745e90 | −0.402424 | ||||||||
\(503\) | 2.63171e90 | 0.827391 | 0.413696 | − | 0.910415i | \(-0.364238\pi\) | ||||
0.413696 | + | 0.910415i | \(0.364238\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.30873e90 | −0.910753 | ||||||||
\(506\) | −1.26493e90 | −0.325856 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 7.84135e89 | 0.176993 | ||||||||
\(509\) | −5.29884e90 | −1.11979 | −0.559893 | − | 0.828565i | \(-0.689158\pi\) | ||||
−0.559893 | + | 0.828565i | \(0.689158\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.08786e90 | 0.942834 | ||||||||
\(512\) | −6.10489e90 | −1.05958 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −7.74190e90 | −1.17919 | ||||||||
\(515\) | 2.44886e90 | 0.349479 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.32239e90 | −0.416406 | ||||||||
\(518\) | −2.05437e91 | −2.41341 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 8.63916e90 | 0.891989 | ||||||||
\(521\) | 1.77125e91 | 1.71481 | 0.857403 | − | 0.514646i | \(-0.172077\pi\) | ||||
0.857403 | + | 0.514646i | \(0.172077\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.54877e90 | 0.813094 | 0.406547 | − | 0.913630i | \(-0.366733\pi\) | ||||
0.406547 | + | 0.913630i | \(0.366733\pi\) | |||||||
\(524\) | 1.23283e89 | 0.00984704 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.77605e89 | −0.0616988 | ||||||||
\(527\) | −3.77566e90 | −0.249079 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.60954e91 | 0.935271 | ||||||||
\(530\) | 7.88345e90 | 0.430006 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 6.13263e90 | 0.294854 | ||||||||
\(533\) | 3.37253e91 | 1.52263 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.57605e90 | −0.102590 | ||||||||
\(536\) | 4.21079e91 | 1.57523 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.35942e91 | 0.448899 | ||||||||
\(539\) | 2.25321e91 | 0.699161 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.95124e91 | −1.08299 | −0.541495 | − | 0.840704i | \(-0.682142\pi\) | ||||
−0.541495 | + | 0.840704i | \(0.682142\pi\) | |||||||
\(542\) | −2.87762e91 | −0.741407 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.13625e91 | 0.486506 | ||||||||
\(545\) | 2.70583e91 | 0.579453 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.26253e91 | −1.37566 | −0.687832 | − | 0.725870i | \(-0.741437\pi\) | ||||
−0.687832 | + | 0.725870i | \(0.741437\pi\) | |||||||
\(548\) | −1.49708e91 | −0.266744 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −8.67046e90 | −0.136739 | ||||||||
\(551\) | 3.44675e91 | 0.511484 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.52346e92 | 2.00234 | ||||||||
\(554\) | 4.34712e91 | 0.537804 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.46630e91 | 0.380067 | ||||||||
\(557\) | 1.39421e91 | 0.143940 | 0.0719698 | − | 0.997407i | \(-0.477071\pi\) | ||||
0.0719698 | + | 0.997407i | \(0.477071\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.69484e92 | 1.55179 | ||||||||
\(560\) | −9.31178e91 | −0.803034 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.56830e92 | −1.20022 | ||||||||
\(563\) | 1.57237e91 | 0.113377 | 0.0566884 | − | 0.998392i | \(-0.481946\pi\) | ||||
0.0566884 | + | 0.998392i | \(0.481946\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.61092e91 | 0.423291 | ||||||||
\(566\) | −5.95745e91 | −0.359509 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.28316e92 | −0.688036 | ||||||||
\(569\) | −1.12945e92 | −0.570962 | −0.285481 | − | 0.958384i | \(-0.592153\pi\) | ||||
−0.285481 | + | 0.958384i | \(0.592153\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.66161e92 | −0.746824 | −0.373412 | − | 0.927666i | \(-0.621812\pi\) | ||||
−0.373412 | + | 0.927666i | \(0.621812\pi\) | |||||||
\(572\) | −2.20553e91 | −0.0934860 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −5.11031e92 | −1.92707 | ||||||||
\(575\) | 2.28287e92 | 0.812098 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.72309e92 | 1.17900 | 0.589500 | − | 0.807769i | \(-0.299325\pi\) | ||||
0.589500 | + | 0.807769i | \(0.299325\pi\) | |||||||
\(578\) | −3.56356e91 | −0.106488 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 5.69080e91 | 0.151473 | ||||||||
\(581\) | 1.17691e92 | 0.295693 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.52385e91 | −0.213263 | ||||||||
\(584\) | 2.56619e92 | 0.542573 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.73325e92 | 1.26956 | ||||||||
\(587\) | −4.35735e92 | −0.775973 | −0.387986 | − | 0.921665i | \(-0.626829\pi\) | ||||
−0.387986 | + | 0.921665i | \(0.626829\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.77854e91 | −0.155386 | ||||||||
\(590\) | −3.42467e92 | −0.514134 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −7.37061e92 | −0.987930 | ||||||||
\(593\) | 1.52013e92 | 0.192553 | 0.0962763 | − | 0.995355i | \(-0.469307\pi\) | ||||
0.0962763 | + | 0.995355i | \(0.469307\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.00572e93 | 1.13804 | ||||||||
\(596\) | 4.79589e92 | 0.513002 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.58654e93 | −1.51691 | ||||||||
\(599\) | −1.85461e93 | −1.67669 | −0.838345 | − | 0.545139i | \(-0.816477\pi\) | ||||
−0.838345 | + | 0.545139i | \(0.816477\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.29011e91 | −0.0104311 | −0.00521556 | − | 0.999986i | \(-0.501660\pi\) | ||||
−0.00521556 | + | 0.999986i | \(0.501660\pi\) | |||||||
\(602\) | −2.56814e93 | −1.96398 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.58133e92 | −0.108214 | ||||||||
\(605\) | 9.21808e92 | 0.596809 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.54230e93 | 0.894020 | 0.447010 | − | 0.894529i | \(-0.352489\pi\) | ||||
0.447010 | + | 0.894529i | \(0.352489\pi\) | |||||||
\(608\) | 5.53264e92 | 0.303503 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.44571e92 | 0.218470 | ||||||||
\(611\) | −4.16708e93 | −1.93844 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.38764e93 | −0.578565 | −0.289283 | − | 0.957244i | \(-0.593417\pi\) | ||||
−0.289283 | + | 0.957244i | \(0.593417\pi\) | |||||||
\(614\) | 2.10279e93 | 0.830147 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.58146e93 | 0.559892 | ||||||||
\(617\) | 3.43145e93 | 1.15060 | 0.575300 | − | 0.817942i | \(-0.304885\pi\) | ||||
0.575300 | + | 0.817942i | \(0.304885\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.77920e93 | −0.836148 | −0.418074 | − | 0.908413i | \(-0.637295\pi\) | ||||
−0.418074 | + | 0.908413i | \(0.637295\pi\) | |||||||
\(620\) | −1.61450e92 | −0.0460167 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −3.25315e93 | −0.832388 | ||||||||
\(623\) | −6.73883e93 | −1.63394 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.46475e92 | −0.0754555 | ||||||||
\(626\) | 8.26721e92 | 0.170655 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.03833e93 | −0.192615 | ||||||||
\(629\) | 7.96060e93 | 1.40007 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.80746e93 | −0.918338 | −0.459169 | − | 0.888349i | \(-0.651853\pi\) | ||||
−0.459169 | + | 0.888349i | \(0.651853\pi\) | |||||||
\(632\) | 7.68394e93 | 1.15229 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −7.88463e93 | −1.06363 | ||||||||
\(635\) | 3.33043e93 | 0.426167 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.82607e94 | 3.25471 | ||||||||
\(638\) | 1.87831e93 | 0.205246 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2.79065e93 | −0.274585 | ||||||||
\(641\) | 1.55793e94 | 1.45480 | 0.727402 | − | 0.686212i | \(-0.240728\pi\) | ||||
0.727402 | + | 0.686212i | \(0.240728\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.20388e93 | 0.774289 | 0.387145 | − | 0.922019i | \(-0.373461\pi\) | ||||
0.387145 | + | 0.922019i | \(0.373461\pi\) | |||||||
\(644\) | −8.79919e93 | −0.702694 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.49249e93 | 0.467328 | ||||||||
\(647\) | 3.77051e93 | 0.257695 | 0.128848 | − | 0.991664i | \(-0.458872\pi\) | ||||
0.128848 | + | 0.991664i | \(0.458872\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.13728e93 | 0.254987 | ||||||||
\(650\) | −1.08749e94 | −0.636541 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4.07831e93 | 0.215370 | ||||||||
\(653\) | 1.24838e94 | 0.626261 | 0.313130 | − | 0.949710i | \(-0.398622\pi\) | ||||
0.313130 | + | 0.949710i | \(0.398622\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.23616e92 | 0.0237099 | ||||||||
\(656\) | −1.83346e94 | −0.788846 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 6.31426e94 | 2.45332 | ||||||||
\(659\) | −7.87386e93 | −0.290754 | −0.145377 | − | 0.989376i | \(-0.546440\pi\) | ||||
−0.145377 | + | 0.989376i | \(0.546440\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.77483e94 | −1.59297 | −0.796487 | − | 0.604656i | \(-0.793311\pi\) | ||||
−0.796487 | + | 0.604656i | \(0.793311\pi\) | |||||||
\(662\) | 3.95629e94 | 1.25472 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5.93602e93 | 0.170163 | ||||||||
\(665\) | 2.60469e94 | 0.709955 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.94545e94 | −1.21896 | ||||||||
\(668\) | 2.31976e93 | 0.0543790 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 3.77936e94 | 0.801517 | ||||||||
\(671\) | −5.37078e93 | −0.108351 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.75749e94 | −0.686109 | −0.343054 | − | 0.939316i | \(-0.611462\pi\) | ||||
−0.343054 | + | 0.939316i | \(0.611462\pi\) | |||||||
\(674\) | 1.42130e94 | 0.246934 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.06309e94 | −0.167247 | ||||||||
\(677\) | 7.42048e93 | 0.111099 | 0.0555497 | − | 0.998456i | \(-0.482309\pi\) | ||||
0.0555497 | + | 0.998456i | \(0.482309\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.61032e94 | −1.16784 | ||||||||
\(680\) | 5.07258e94 | 0.654908 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −5.32882e93 | −0.0623526 | ||||||||
\(683\) | −1.53091e95 | −1.70552 | −0.852759 | − | 0.522304i | \(-0.825073\pi\) | ||||
−0.852759 | + | 0.522304i | \(0.825073\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.35848e94 | −0.642272 | ||||||||
\(686\) | −2.60547e95 | −2.50627 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −9.21390e94 | −0.803953 | ||||||||
\(689\) | −1.19452e95 | −0.992774 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.70611e95 | −1.28675 | −0.643373 | − | 0.765553i | \(-0.722466\pi\) | ||||
−0.643373 | + | 0.765553i | \(0.722466\pi\) | |||||||
\(692\) | −5.94468e94 | −0.427144 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.98984e95 | 1.29800 | ||||||||
\(695\) | 1.47223e95 | 0.915132 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.98022e95 | 1.11793 | ||||||||
\(698\) | 2.41239e95 | 1.29805 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −6.03138e94 | −0.294871 | ||||||||
\(701\) | 6.03623e94 | 0.281327 | 0.140664 | − | 0.990057i | \(-0.455076\pi\) | ||||
0.140664 | + | 0.990057i | \(0.455076\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.06170e95 | 0.873419 | ||||||||
\(704\) | 7.48990e94 | 0.302546 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.01387e95 | 1.10705 | ||||||||
\(707\) | −7.59679e95 | −2.66121 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.74967e94 | 0.0557579 | 0.0278789 | − | 0.999611i | \(-0.491125\pi\) | ||||
0.0278789 | + | 0.999611i | \(0.491125\pi\) | |||||||
\(710\) | −1.15169e95 | −0.350090 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.39890e95 | −0.940282 | ||||||||
\(713\) | 1.40304e95 | 0.370314 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.36748e94 | −0.225097 | ||||||||
\(716\) | −1.94324e95 | −0.445595 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −5.40758e95 | −1.12936 | ||||||||
\(719\) | 5.94055e95 | 1.18416 | 0.592078 | − | 0.805881i | \(-0.298308\pi\) | ||||
0.592078 | + | 0.805881i | \(0.298308\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.62253e95 | 1.02118 | ||||||||
\(722\) | −3.25330e95 | −0.564064 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2.29204e94 | 0.0362227 | ||||||||
\(725\) | −3.38985e95 | −0.511513 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.88760e95 | −0.259721 | −0.129861 | − | 0.991532i | \(-0.541453\pi\) | ||||
−0.129861 | + | 0.991532i | \(0.541453\pi\) | |||||||
\(728\) | 1.98354e96 | 2.60639 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.30326e95 | 0.276075 | ||||||||
\(731\) | 9.95144e95 | 1.13934 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.47346e95 | −0.989750 | −0.494875 | − | 0.868964i | \(-0.664786\pi\) | ||||
−0.494875 | + | 0.868964i | \(0.664786\pi\) | |||||||
\(734\) | 5.18726e95 | 0.517750 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.93831e95 | −0.723305 | ||||||||
\(737\) | −4.56578e95 | −0.397516 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.24915e95 | 0.337841 | 0.168921 | − | 0.985630i | \(-0.445972\pi\) | ||||
0.168921 | + | 0.985630i | \(0.445972\pi\) | |||||||
\(740\) | 3.40400e95 | 0.258659 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.81003e96 | 1.25648 | ||||||||
\(743\) | −1.87178e96 | −1.24202 | −0.621010 | − | 0.783803i | \(-0.713277\pi\) | ||||
−0.621010 | + | 0.783803i | \(0.713277\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.03694e96 | 1.23522 | ||||||||
\(746\) | −7.09275e95 | −0.411210 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.29500e95 | −0.0686384 | ||||||||
\(749\) | −5.91457e95 | −0.299766 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.84305e96 | −0.854278 | −0.427139 | − | 0.904186i | \(-0.640478\pi\) | ||||
−0.427139 | + | 0.904186i | \(0.640478\pi\) | |||||||
\(752\) | 2.26541e96 | 1.00427 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.35586e96 | 0.955452 | ||||||||
\(755\) | −6.71631e95 | −0.260560 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.99008e96 | −1.06162 | −0.530812 | − | 0.847489i | \(-0.678113\pi\) | ||||
−0.530812 | + | 0.847489i | \(0.678113\pi\) | |||||||
\(758\) | −1.36323e96 | −0.463073 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.31374e96 | 0.408558 | ||||||||
\(761\) | 3.97451e96 | 1.18276 | 0.591381 | − | 0.806392i | \(-0.298583\pi\) | ||||
0.591381 | + | 0.806392i | \(0.298583\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.21254e96 | 1.69316 | ||||||||
\(764\) | 6.41448e95 | 0.167315 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.88806e96 | −1.16808 | ||||||||
\(767\) | 5.18915e96 | 1.18700 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.62342e96 | −0.549964 | −0.274982 | − | 0.961449i | \(-0.588672\pi\) | ||||
−0.274982 | + | 0.961449i | \(0.588672\pi\) | |||||||
\(770\) | 1.41943e96 | 0.284888 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.77563e96 | 0.326719 | ||||||||
\(773\) | −1.63182e96 | −0.287515 | −0.143757 | − | 0.989613i | \(-0.545918\pi\) | ||||
−0.143757 | + | 0.989613i | \(0.545918\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.61709e95 | 0.155395 | ||||||||
\(776\) | −4.34283e96 | −0.672055 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.46633e96 | −0.208169 | ||||||||
\(779\) | 5.12855e96 | 0.697412 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.39133e96 | 0.173629 | ||||||||
\(782\) | −9.31551e96 | −1.11373 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.53638e97 | −1.68620 | ||||||||
\(785\) | −4.41008e96 | −0.463781 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.52024e97 | 1.46811 | 0.734053 | − | 0.679092i | \(-0.237626\pi\) | ||||
0.734053 | + | 0.679092i | \(0.237626\pi\) | |||||||
\(788\) | −3.80135e96 | −0.351811 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 6.89666e96 | 0.586315 | ||||||||
\(791\) | 1.51786e97 | 1.23685 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.73626e96 | −0.504391 | ||||||||
\(794\) | −1.39746e97 | −1.00312 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6.15421e96 | 0.406055 | ||||||||
\(797\) | −2.51897e97 | −1.59356 | −0.796782 | − | 0.604266i | \(-0.793466\pi\) | ||||
−0.796782 | + | 0.604266i | \(0.793466\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.44675e97 | −1.42322 | ||||||||
\(800\) | −5.44130e96 | −0.303520 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.28557e97 | 0.659558 | ||||||||
\(803\) | −2.78253e96 | −0.136921 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.73725e97 | −1.69196 | ||||||||
\(806\) | −6.68363e96 | −0.290261 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −3.83163e97 | −1.53145 | ||||||||
\(809\) | −4.33159e97 | −1.66101 | −0.830505 | − | 0.557011i | \(-0.811948\pi\) | ||||
−0.830505 | + | 0.557011i | \(0.811948\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.13849e97 | 1.46098 | 0.730488 | − | 0.682926i | \(-0.239293\pi\) | ||||
0.730488 | + | 0.682926i | \(0.239293\pi\) | |||||||
\(812\) | 1.30660e97 | 0.442604 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.12353e97 | 0.350482 | ||||||||
\(815\) | 1.73216e97 | 0.518572 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.57731e97 | 0.710767 | ||||||||
\(818\) | −1.48904e97 | −0.394157 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 8.46754e96 | 0.206535 | ||||||||
\(821\) | −1.13510e97 | −0.265791 | −0.132895 | − | 0.991130i | \(-0.542427\pi\) | ||||
−0.132895 | + | 0.991130i | \(0.542427\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.60119e96 | −0.185637 | −0.0928184 | − | 0.995683i | \(-0.529588\pi\) | ||||
−0.0928184 | + | 0.995683i | \(0.529588\pi\) | |||||||
\(824\) | 2.83586e97 | 0.587657 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.86298e97 | −1.50230 | ||||||||
\(827\) | 3.87968e97 | 0.711805 | 0.355902 | − | 0.934523i | \(-0.384174\pi\) | ||||
0.355902 | + | 0.934523i | \(0.384174\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.96648e97 | −0.501955 | −0.250977 | − | 0.967993i | \(-0.580752\pi\) | ||||
−0.250977 | + | 0.967993i | \(0.580752\pi\) | |||||||
\(830\) | 5.32782e96 | 0.0865832 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 9.39416e97 | 1.40840 | ||||||||
\(833\) | 1.65936e98 | 2.38964 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.85263e96 | 0.130935 | ||||||||
\(836\) | −3.35391e96 | −0.0428194 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3.36989e97 | 0.397138 | ||||||||
\(839\) | 1.34167e98 | 1.51922 | 0.759608 | − | 0.650381i | \(-0.225391\pi\) | ||||
0.759608 | + | 0.650381i | \(0.225391\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.22104e97 | −0.232215 | ||||||||
\(842\) | −5.82673e97 | −0.585423 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2.33744e97 | −0.216904 | ||||||||
\(845\) | −4.51524e97 | −0.402700 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.11646e98 | 1.74387 | ||||||||
\(848\) | 6.49395e97 | 0.514337 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −6.38530e97 | −0.467355 | ||||||||
\(851\) | −2.95816e98 | −2.08153 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.26854e98 | 1.47555 | 0.737774 | − | 0.675048i | \(-0.235877\pi\) | ||||
0.737774 | + | 0.675048i | \(0.235877\pi\) | |||||||
\(854\) | 1.02073e98 | 0.638367 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.98316e97 | −0.172507 | ||||||||
\(857\) | −2.17739e97 | −0.121082 | −0.0605409 | − | 0.998166i | \(-0.519283\pi\) | ||||
−0.0605409 | + | 0.998166i | \(0.519283\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.55887e98 | 1.31606 | 0.658032 | − | 0.752990i | \(-0.271389\pi\) | ||||
0.658032 | + | 0.752990i | \(0.271389\pi\) | |||||||
\(860\) | 4.25530e97 | 0.210490 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.14972e98 | 0.526139 | ||||||||
\(863\) | 1.48428e98 | 0.653364 | 0.326682 | − | 0.945134i | \(-0.394069\pi\) | ||||
0.326682 | + | 0.945134i | \(0.394069\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.52486e98 | −1.02849 | ||||||||
\(866\) | 3.20775e98 | 1.25704 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −3.70686e97 | −0.134461 | ||||||||
\(869\) | −8.33172e97 | −0.290785 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.72660e98 | −1.85050 | ||||||||
\(872\) | 3.13345e98 | 0.974363 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.41261e98 | −0.694792 | ||||||||
\(875\) | −6.94991e98 | −1.92624 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.00787e98 | −1.02903 | −0.514514 | − | 0.857482i | \(-0.672028\pi\) | ||||
−0.514514 | + | 0.857482i | \(0.672028\pi\) | |||||||
\(878\) | 1.39712e98 | 0.345277 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 5.09257e97 | 0.116619 | ||||||||
\(881\) | −2.58772e98 | −0.570459 | −0.285230 | − | 0.958459i | \(-0.592070\pi\) | ||||
−0.285230 | + | 0.958459i | \(0.592070\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.62436e97 | 0.135351 | 0.0676754 | − | 0.997707i | \(-0.478442\pi\) | ||||
0.0676754 | + | 0.997707i | \(0.478442\pi\) | |||||||
\(884\) | −1.62425e98 | −0.319523 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.98375e98 | −0.544167 | ||||||||
\(887\) | 5.91704e98 | 1.03911 | 0.519557 | − | 0.854436i | \(-0.326097\pi\) | ||||
0.519557 | + | 0.854436i | \(0.326097\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.64660e98 | 1.24526 | ||||||||
\(890\) | −3.05065e98 | −0.478440 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2.28890e98 | −0.332969 | ||||||||
\(893\) | −6.33680e98 | −0.887863 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.25345e98 | −1.07291 | ||||||||
\(896\) | −6.40729e98 | −0.802336 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.17799e99 | 1.36894 | ||||||||
\(899\) | −2.08338e98 | −0.233249 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.01377e98 | −0.728905 | ||||||||
\(902\) | 2.79480e98 | 0.279854 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7.65568e98 | 0.711773 | ||||||||
\(905\) | 9.73490e97 | 0.0872176 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.08456e98 | 0.173449 | 0.0867244 | − | 0.996232i | \(-0.472360\pi\) | ||||
0.0867244 | + | 0.996232i | \(0.472360\pi\) | |||||||
\(908\) | −1.66974e98 | −0.133898 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.78031e99 | 1.32620 | ||||||||
\(911\) | −5.32981e98 | −0.382689 | −0.191345 | − | 0.981523i | \(-0.561285\pi\) | ||||
−0.191345 | + | 0.981523i | \(0.561285\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.43645e97 | −0.0429413 | ||||||||
\(914\) | −2.13373e99 | −1.37228 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.81472e98 | −0.108470 | ||||||||
\(917\) | 1.20221e98 | 0.0692801 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.92351e99 | −1.03044 | −0.515221 | − | 0.857057i | \(-0.672290\pi\) | ||||
−0.515221 | + | 0.857057i | \(0.672290\pi\) | |||||||
\(920\) | −1.88497e99 | −0.973673 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1.18025e99 | −0.566874 | ||||||||
\(923\) | 1.74507e99 | 0.808269 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.02767e99 | −0.873471 | ||||||||
\(926\) | 2.43398e99 | 1.01123 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.17877e99 | 0.455586 | ||||||||
\(929\) | 1.75066e98 | 0.0652644 | 0.0326322 | − | 0.999467i | \(-0.489611\pi\) | ||||
0.0326322 | + | 0.999467i | \(0.489611\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.29755e99 | 1.49076 | ||||||||
\(932\) | −6.81370e98 | −0.228008 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.31324e99 | −0.409001 | ||||||||
\(935\) | −5.50022e98 | −0.165269 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.21598e98 | −0.0619856 | −0.0309928 | − | 0.999520i | \(-0.509867\pi\) | ||||
−0.0309928 | + | 0.999520i | \(0.509867\pi\) | |||||||
\(938\) | 8.67735e99 | 2.34203 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.04624e99 | −0.262936 | ||||||||
\(941\) | 4.01175e99 | 0.972929 | 0.486464 | − | 0.873700i | \(-0.338286\pi\) | ||||
0.486464 | + | 0.873700i | \(0.338286\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.35851e99 | −1.66207 | ||||||||
\(944\) | −2.82105e99 | −0.614964 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.40451e99 | 0.285214 | ||||||||
\(947\) | −3.46437e99 | −0.679048 | −0.339524 | − | 0.940597i | \(-0.610266\pi\) | ||||
−0.339524 | + | 0.940597i | \(0.610266\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.48997e99 | −0.637387 | ||||||||
\(950\) | −1.65372e99 | −0.291555 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.16465e100 | 1.91364 | ||||||||
\(953\) | 3.05518e99 | 0.484645 | 0.242323 | − | 0.970196i | \(-0.422091\pi\) | ||||
0.242323 | + | 0.970196i | \(0.422091\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.72440e99 | 0.402864 | ||||||||
\(956\) | 1.68379e99 | 0.240408 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −2.65679e99 | −0.353681 | ||||||||
\(959\) | −1.45989e100 | −1.87671 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.75023e99 | −0.929140 | ||||||||
\(962\) | 1.40918e100 | 1.63155 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2.62042e99 | 0.283003 | ||||||||
\(965\) | 7.54159e99 | 0.786679 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.53190e100 | 1.49088 | 0.745441 | − | 0.666572i | \(-0.232239\pi\) | ||||
0.745441 | + | 0.666572i | \(0.232239\pi\) | |||||||
\(968\) | 1.06749e100 | 1.00355 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −3.89787e99 | −0.341959 | ||||||||
\(971\) | −6.24686e99 | −0.529441 | −0.264720 | − | 0.964325i | \(-0.585280\pi\) | ||||
−0.264720 | + | 0.964325i | \(0.585280\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.38021e100 | 2.67401 | ||||||||
\(974\) | −1.90825e100 | −1.45851 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.66213e99 | 0.261315 | ||||||||
\(977\) | 4.20953e99 | 0.290246 | 0.145123 | − | 0.989414i | \(-0.453642\pi\) | ||||
0.145123 | + | 0.989414i | \(0.453642\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.68544e99 | 0.237284 | ||||||||
\(980\) | 7.09551e99 | 0.441479 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.61066e100 | −0.935988 | ||||||||
\(983\) | 2.77525e100 | 1.55869 | 0.779344 | − | 0.626596i | \(-0.215553\pi\) | ||||
0.779344 | + | 0.626596i | \(0.215553\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.61453e100 | −0.847098 | ||||||||
\(986\) | 1.38327e100 | 0.701503 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4.20662e99 | −0.199331 | ||||||||
\(989\) | −3.69796e100 | −1.69390 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.60539e99 | −0.368386 | −0.184193 | − | 0.982890i | \(-0.558967\pi\) | ||||
−0.184193 | + | 0.982890i | \(0.558967\pi\) | |||||||
\(992\) | −3.34419e99 | −0.138404 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2.64426e100 | −1.02296 | ||||||||
\(995\) | 2.61386e100 | 0.977707 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.15408e100 | −0.753310 | −0.376655 | − | 0.926354i | \(-0.622926\pi\) | ||||
−0.376655 | + | 0.926354i | \(0.622926\pi\) | |||||||
\(998\) | −3.28880e100 | −1.11215 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 9.68.a.b.1.4 | 5 | ||
3.2 | odd | 2 | 3.68.a.a.1.2 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.68.a.a.1.2 | ✓ | 5 | 3.2 | odd | 2 | ||
9.68.a.b.1.4 | 5 | 1.1 | even | 1 | trivial |