Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9,66,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, 66, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9.1");
S:= CuspForms(chi, 66);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9 = 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 66 \) |
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: | \(240.815120825\) |
Analytic rank: | \(0\) |
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: | \( x^{5} - x^{4} + \cdots - 10\!\cdots\!36 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{40}\cdot 3^{20}\cdot 5^{4}\cdot 7^{2}\cdot 11\cdot 13^{2} \) |
Twist minimal: | no (minimal twist has level 1) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.76800e8\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −7.69444e9 | −1.26678 | −0.633391 | − | 0.773832i | \(-0.718338\pi\) | ||||
−0.633391 | + | 0.773832i | \(0.718338\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.23108e19 | 0.604737 | ||||||||
\(5\) | −6.36641e22 | −1.22284 | −0.611420 | − | 0.791306i | \(-0.709401\pi\) | ||||
−0.611420 | + | 0.791306i | \(0.709401\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.82854e27 | 0.625774 | 0.312887 | − | 0.949790i | \(-0.398704\pi\) | ||||
0.312887 | + | 0.949790i | \(0.398704\pi\) | |||||||
\(8\) | 1.12205e29 | 0.500712 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 4.89860e32 | 1.54907 | ||||||||
\(11\) | 6.60418e31 | 0.00943098 | 0.00471549 | − | 0.999989i | \(-0.498499\pi\) | ||||
0.00471549 | + | 0.999989i | \(0.498499\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.71546e36 | −1.70092 | −0.850462 | − | 0.526036i | \(-0.823678\pi\) | ||||
−0.850462 | + | 0.526036i | \(0.823678\pi\) | |||||||
\(14\) | −1.40696e37 | −0.792720 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.68648e39 | −1.23903 | ||||||||
\(17\) | −2.66707e39 | −0.273177 | −0.136589 | − | 0.990628i | \(-0.543614\pi\) | ||||
−0.136589 | + | 0.990628i | \(0.543614\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.18513e41 | −1.42978 | −0.714888 | − | 0.699239i | \(-0.753522\pi\) | ||||
−0.714888 | + | 0.699239i | \(0.753522\pi\) | |||||||
\(20\) | −1.42040e42 | −0.739496 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.08155e41 | −0.0119470 | ||||||||
\(23\) | 9.69847e43 | 0.537711 | 0.268855 | − | 0.963181i | \(-0.413355\pi\) | ||||
0.268855 | + | 0.963181i | \(0.413355\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.34262e45 | 0.495338 | ||||||||
\(26\) | 2.08940e46 | 2.15470 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.07962e46 | 0.378429 | ||||||||
\(29\) | −8.81829e46 | −0.261487 | −0.130743 | − | 0.991416i | \(-0.541736\pi\) | ||||
−0.130743 | + | 0.991416i | \(0.541736\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.18148e48 | −0.401026 | −0.200513 | − | 0.979691i | \(-0.564261\pi\) | ||||
−0.200513 | + | 0.979691i | \(0.564261\pi\) | |||||||
\(32\) | 8.83687e48 | 1.06887 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.05216e49 | 0.346056 | ||||||||
\(35\) | −1.16412e50 | −0.765222 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.45413e50 | 0.481068 | 0.240534 | − | 0.970641i | \(-0.422677\pi\) | ||||
0.240534 | + | 0.970641i | \(0.422677\pi\) | |||||||
\(38\) | 3.98967e51 | 1.81121 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −7.14345e51 | −0.612291 | ||||||||
\(41\) | 1.11431e52 | 0.428086 | 0.214043 | − | 0.976824i | \(-0.431337\pi\) | ||||
0.214043 | + | 0.976824i | \(0.431337\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.95096e53 | −1.59413 | −0.797066 | − | 0.603892i | \(-0.793616\pi\) | ||||
−0.797066 | + | 0.603892i | \(0.793616\pi\) | |||||||
\(44\) | 1.47345e51 | 0.00570326 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7.46243e53 | −0.681162 | ||||||||
\(47\) | 1.87891e54 | 0.852561 | 0.426280 | − | 0.904591i | \(-0.359824\pi\) | ||||
0.426280 | + | 0.904591i | \(0.359824\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.19477e54 | −0.608407 | ||||||||
\(50\) | −1.03307e55 | −0.627486 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −6.05843e55 | −1.02861 | ||||||||
\(53\) | −1.20429e56 | −1.10095 | −0.550474 | − | 0.834852i | \(-0.685553\pi\) | ||||
−0.550474 | + | 0.834852i | \(0.685553\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.20450e54 | −0.0115326 | ||||||||
\(56\) | 2.05171e56 | 0.313333 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 6.78518e56 | 0.331247 | ||||||||
\(59\) | −1.90217e57 | −0.532794 | −0.266397 | − | 0.963863i | \(-0.585833\pi\) | ||||
−0.266397 | + | 0.963863i | \(0.585833\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.82531e57 | −0.362616 | −0.181308 | − | 0.983426i | \(-0.558033\pi\) | ||||
−0.181308 | + | 0.983426i | \(0.558033\pi\) | |||||||
\(62\) | 9.09084e57 | 0.508012 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −5.77461e57 | −0.114993 | ||||||||
\(65\) | 1.72878e59 | 2.07996 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.48352e59 | 1.11593 | 0.557963 | − | 0.829866i | \(-0.311583\pi\) | ||||
0.557963 | + | 0.829866i | \(0.311583\pi\) | |||||||
\(68\) | −5.95046e58 | −0.165200 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 8.95727e59 | 0.969369 | ||||||||
\(71\) | 8.10901e59 | 0.553441 | 0.276721 | − | 0.960950i | \(-0.410752\pi\) | ||||
0.276721 | + | 0.960950i | \(0.410752\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.44135e60 | −0.675518 | −0.337759 | − | 0.941233i | \(-0.609669\pi\) | ||||
−0.337759 | + | 0.941233i | \(0.609669\pi\) | |||||||
\(74\) | −3.42720e60 | −0.609409 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.15685e61 | −0.864638 | ||||||||
\(77\) | 1.20760e59 | 0.00590166 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.39042e61 | −1.14483 | −0.572416 | − | 0.819963i | \(-0.693994\pi\) | ||||
−0.572416 | + | 0.819963i | \(0.693994\pi\) | |||||||
\(80\) | 1.07368e62 | 1.51514 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −8.57399e61 | −0.542291 | ||||||||
\(83\) | −2.95526e62 | −1.26054 | −0.630271 | − | 0.776375i | \(-0.717056\pi\) | ||||
−0.630271 | + | 0.776375i | \(0.717056\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.69797e62 | 0.334052 | ||||||||
\(86\) | 1.50116e63 | 2.01942 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 7.41024e60 | 0.00472221 | ||||||||
\(89\) | −1.30157e63 | −0.574503 | −0.287252 | − | 0.957855i | \(-0.592742\pi\) | ||||
−0.287252 | + | 0.957855i | \(0.592742\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.96533e63 | −1.06439 | ||||||||
\(92\) | 2.16381e63 | 0.325173 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.44571e64 | −1.08001 | ||||||||
\(95\) | 3.30107e64 | 1.74839 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.88312e64 | −0.506752 | −0.253376 | − | 0.967368i | \(-0.581541\pi\) | ||||
−0.253376 | + | 0.967368i | \(0.581541\pi\) | |||||||
\(98\) | 3.99708e64 | 0.770719 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.99549e64 | 0.299549 | ||||||||
\(101\) | −1.93492e65 | −1.40029 | −0.700147 | − | 0.713999i | \(-0.746882\pi\) | ||||
−0.700147 | + | 0.713999i | \(0.746882\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.56312e63 | 0.0251131 | 0.0125565 | − | 0.999921i | \(-0.496003\pi\) | ||||
0.0125565 | + | 0.999921i | \(0.496003\pi\) | |||||||
\(104\) | −3.04689e65 | −0.851674 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 9.26636e65 | 1.39466 | ||||||||
\(107\) | 2.60336e65 | 0.288776 | 0.144388 | − | 0.989521i | \(-0.453879\pi\) | ||||
0.144388 | + | 0.989521i | \(0.453879\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.08454e65 | −0.430478 | −0.215239 | − | 0.976561i | \(-0.569053\pi\) | ||||
−0.215239 | + | 0.976561i | \(0.569053\pi\) | |||||||
\(110\) | 3.23512e64 | 0.0146093 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.08379e66 | −0.775353 | ||||||||
\(113\) | −9.27922e66 | −1.74768 | −0.873840 | − | 0.486214i | \(-0.838378\pi\) | ||||
−0.873840 | + | 0.486214i | \(0.838378\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.17445e66 | −0.657534 | ||||||||
\(116\) | −1.96744e66 | −0.158131 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.46361e67 | 0.674933 | ||||||||
\(119\) | −4.87684e66 | −0.170947 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.90327e67 | −0.999911 | ||||||||
\(122\) | 2.94336e67 | 0.459356 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.63599e67 | −0.242515 | ||||||||
\(125\) | 8.70854e67 | 0.617120 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.13148e68 | −1.32474 | −0.662368 | − | 0.749179i | \(-0.730448\pi\) | ||||
−0.662368 | + | 0.749179i | \(0.730448\pi\) | |||||||
\(128\) | −2.81591e68 | −0.923197 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.33020e69 | −2.63485 | ||||||||
\(131\) | 1.75019e68 | 0.270252 | 0.135126 | − | 0.990828i | \(-0.456856\pi\) | ||||
0.135126 | + | 0.990828i | \(0.456856\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −9.48121e68 | −0.894717 | ||||||||
\(134\) | −1.91092e69 | −1.41364 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.99259e68 | −0.136783 | ||||||||
\(137\) | −1.86067e69 | −0.670271 | −0.335135 | − | 0.942170i | \(-0.608782\pi\) | ||||
−0.335135 | + | 0.942170i | \(0.608782\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.01831e68 | −0.0453948 | −0.0226974 | − | 0.999742i | \(-0.507225\pi\) | ||||
−0.0226974 | + | 0.999742i | \(0.507225\pi\) | |||||||
\(140\) | −2.59726e69 | −0.462758 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −6.23943e69 | −0.701089 | ||||||||
\(143\) | −1.79334e68 | −0.0160414 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.61409e69 | 0.319756 | ||||||||
\(146\) | 1.87848e70 | 0.855734 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 9.93754e69 | 0.290920 | ||||||||
\(149\) | −6.22808e70 | −1.46488 | −0.732438 | − | 0.680834i | \(-0.761617\pi\) | ||||
−0.732438 | + | 0.680834i | \(0.761617\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.46222e70 | −1.29043 | −0.645214 | − | 0.764002i | \(-0.723232\pi\) | ||||
−0.645214 | + | 0.764002i | \(0.723232\pi\) | |||||||
\(152\) | −5.81799e70 | −0.715907 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −9.29180e68 | −0.00747612 | ||||||||
\(155\) | 7.52180e70 | 0.490390 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.56741e71 | 1.53326 | 0.766628 | − | 0.642091i | \(-0.221933\pi\) | ||||
0.766628 | + | 0.642091i | \(0.221933\pi\) | |||||||
\(158\) | 4.14762e71 | 1.45025 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −5.62592e71 | −1.30706 | ||||||||
\(161\) | 1.77340e71 | 0.336485 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.70096e71 | 0.597158 | 0.298579 | − | 0.954385i | \(-0.403487\pi\) | ||||
0.298579 | + | 0.954385i | \(0.403487\pi\) | |||||||
\(164\) | 2.48612e71 | 0.258879 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.27390e72 | 1.59683 | ||||||||
\(167\) | 2.51276e72 | 1.45166 | 0.725832 | − | 0.687872i | \(-0.241455\pi\) | ||||
0.725832 | + | 0.687872i | \(0.241455\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.82505e72 | 1.89314 | ||||||||
\(170\) | −1.30649e72 | −0.423172 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4.35277e72 | −0.964030 | ||||||||
\(173\) | −6.07054e72 | −1.11360 | −0.556800 | − | 0.830647i | \(-0.687971\pi\) | ||||
−0.556800 | + | 0.830647i | \(0.687971\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.45503e72 | 0.309970 | ||||||||
\(176\) | −1.11378e71 | −0.0116853 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.00148e73 | 0.727770 | ||||||||
\(179\) | −1.50731e73 | −0.913019 | −0.456509 | − | 0.889719i | \(-0.650901\pi\) | ||||
−0.456509 | + | 0.889719i | \(0.650901\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.08872e73 | −1.30384 | −0.651921 | − | 0.758287i | \(-0.726037\pi\) | ||||
−0.651921 | + | 0.758287i | \(0.726037\pi\) | |||||||
\(182\) | 3.82054e73 | 1.34836 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.08822e73 | 0.269238 | ||||||||
\(185\) | −2.83568e73 | −0.588270 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.76138e71 | −0.00257633 | ||||||||
\(188\) | 4.19201e73 | 0.515575 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.53999e74 | −2.21483 | ||||||||
\(191\) | −1.07944e74 | −0.793619 | −0.396810 | − | 0.917901i | \(-0.629883\pi\) | ||||
−0.396810 | + | 0.917901i | \(0.629883\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.82335e73 | 0.0955561 | 0.0477780 | − | 0.998858i | \(-0.484786\pi\) | ||||
0.0477780 | + | 0.998858i | \(0.484786\pi\) | |||||||
\(194\) | 1.44895e74 | 0.641945 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.15900e74 | −0.367926 | ||||||||
\(197\) | −2.66005e74 | −0.715710 | −0.357855 | − | 0.933777i | \(-0.616492\pi\) | ||||
−0.357855 | + | 0.933777i | \(0.616492\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.37150e74 | −1.62210 | −0.811051 | − | 0.584975i | \(-0.801104\pi\) | ||||
−0.811051 | + | 0.584975i | \(0.801104\pi\) | |||||||
\(200\) | 1.50649e74 | 0.248022 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.48881e75 | 1.77387 | ||||||||
\(203\) | −1.61246e74 | −0.163632 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.09416e74 | −0.523481 | ||||||||
\(206\) | −5.04995e73 | −0.0318128 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.57958e75 | 2.10750 | ||||||||
\(209\) | −3.42436e73 | −0.0134842 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.64754e75 | 1.34290 | 0.671450 | − | 0.741050i | \(-0.265672\pi\) | ||||
0.671450 | + | 0.741050i | \(0.265672\pi\) | |||||||
\(212\) | −2.68688e75 | −0.665784 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.00314e75 | −0.365817 | ||||||||
\(215\) | 1.24206e76 | 1.94937 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.16038e75 | −0.250951 | ||||||||
\(218\) | 5.45116e75 | 0.545321 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −9.38059e73 | −0.00697418 | ||||||||
\(221\) | 7.24234e75 | 0.464654 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.05561e76 | −0.984087 | −0.492044 | − | 0.870571i | \(-0.663750\pi\) | ||||
−0.492044 | + | 0.870571i | \(0.663750\pi\) | |||||||
\(224\) | 1.61586e76 | 0.668870 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7.13983e76 | 2.21393 | ||||||||
\(227\) | 6.07971e75 | 0.163321 | 0.0816606 | − | 0.996660i | \(-0.473978\pi\) | ||||
0.0816606 | + | 0.996660i | \(0.473978\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.28178e76 | −0.258918 | −0.129459 | − | 0.991585i | \(-0.541324\pi\) | ||||
−0.129459 | + | 0.991585i | \(0.541324\pi\) | |||||||
\(230\) | 4.75089e76 | 0.832953 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −9.89458e75 | −0.130930 | ||||||||
\(233\) | −1.53244e77 | −1.76326 | −0.881628 | − | 0.471945i | \(-0.843552\pi\) | ||||
−0.881628 | + | 0.471945i | \(0.843552\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.19619e77 | −1.04255 | ||||||||
\(236\) | −4.24390e76 | −0.322200 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.75246e76 | 0.216553 | ||||||||
\(239\) | 9.89282e76 | 0.498182 | 0.249091 | − | 0.968480i | \(-0.419868\pi\) | ||||
0.249091 | + | 0.968480i | \(0.419868\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.95874e77 | −0.752354 | −0.376177 | − | 0.926548i | \(-0.622762\pi\) | ||||
−0.376177 | + | 0.926548i | \(0.622762\pi\) | |||||||
\(242\) | 3.77279e77 | 1.26667 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −8.53459e76 | −0.219287 | ||||||||
\(245\) | 3.30721e77 | 0.743984 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.40800e78 | 2.43194 | ||||||||
\(248\) | −1.32568e77 | −0.200799 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −6.70073e77 | −0.781757 | ||||||||
\(251\) | −1.01010e77 | −0.103506 | −0.0517531 | − | 0.998660i | \(-0.516481\pi\) | ||||
−0.0517531 | + | 0.998660i | \(0.516481\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.40505e75 | 0.00507114 | ||||||||
\(254\) | 2.40950e78 | 1.67815 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2.37973e78 | 1.28448 | ||||||||
\(257\) | 4.05414e78 | 1.92785 | 0.963923 | − | 0.266183i | \(-0.0857624\pi\) | ||||
0.963923 | + | 0.266183i | \(0.0857624\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.14454e77 | 0.301040 | ||||||||
\(260\) | 3.85705e78 | 1.25783 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.34667e78 | −0.342350 | ||||||||
\(263\) | −3.09616e78 | −0.695444 | −0.347722 | − | 0.937598i | \(-0.613045\pi\) | ||||
−0.347722 | + | 0.937598i | \(0.613045\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.66703e78 | 1.34628 | ||||||||
\(266\) | 7.29526e78 | 1.13341 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5.54093e78 | 0.674842 | ||||||||
\(269\) | 1.10328e79 | 1.19052 | 0.595258 | − | 0.803534i | \(-0.297050\pi\) | ||||
0.595258 | + | 0.803534i | \(0.297050\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.37650e79 | 1.16755 | 0.583775 | − | 0.811915i | \(-0.301575\pi\) | ||||
0.583775 | + | 0.811915i | \(0.301575\pi\) | |||||||
\(272\) | 4.49797e78 | 0.338475 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.43168e79 | 0.849087 | ||||||||
\(275\) | 8.86689e76 | 0.00467153 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.54069e79 | 0.641392 | 0.320696 | − | 0.947182i | \(-0.396083\pi\) | ||||
0.320696 | + | 0.947182i | \(0.396083\pi\) | |||||||
\(278\) | 1.55297e78 | 0.0575053 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.30621e79 | −0.383156 | ||||||||
\(281\) | 5.34712e79 | 1.39690 | 0.698449 | − | 0.715659i | \(-0.253874\pi\) | ||||
0.698449 | + | 0.715659i | \(0.253874\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.25172e79 | −1.91939 | −0.959695 | − | 0.281043i | \(-0.909320\pi\) | ||||
−0.959695 | + | 0.281043i | \(0.909320\pi\) | |||||||
\(284\) | 1.80919e79 | 0.334686 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.37988e78 | 0.0203209 | ||||||||
\(287\) | 2.03756e79 | 0.267885 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.82058e79 | −0.925374 | ||||||||
\(290\) | −4.31973e79 | −0.405062 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −5.44686e79 | −0.408511 | ||||||||
\(293\) | 1.15528e80 | 0.775337 | 0.387669 | − | 0.921799i | \(-0.373280\pi\) | ||||
0.387669 | + | 0.921799i | \(0.373280\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.21100e80 | 0.651522 | ||||||||
\(296\) | 4.99777e79 | 0.240877 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4.79216e80 | 1.85568 | ||||||||
\(299\) | −2.63358e80 | −0.914605 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.56741e80 | −0.997567 | ||||||||
\(302\) | 6.51120e80 | 1.63469 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 8.74463e80 | 1.77154 | ||||||||
\(305\) | 2.43535e80 | 0.443422 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.91973e80 | 0.282647 | 0.141323 | − | 0.989963i | \(-0.454864\pi\) | ||||
0.141323 | + | 0.989963i | \(0.454864\pi\) | |||||||
\(308\) | 2.69426e78 | 0.00356895 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −5.78760e80 | −0.621218 | ||||||||
\(311\) | −1.25133e81 | −1.20965 | −0.604825 | − | 0.796358i | \(-0.706757\pi\) | ||||
−0.604825 | + | 0.796358i | \(0.706757\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.06493e80 | 0.633009 | 0.316504 | − | 0.948591i | \(-0.397491\pi\) | ||||
0.316504 | + | 0.948591i | \(0.397491\pi\) | |||||||
\(314\) | −2.74492e81 | −1.94230 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.20265e81 | −0.692322 | ||||||||
\(317\) | 2.97272e80 | 0.154429 | 0.0772144 | − | 0.997015i | \(-0.475397\pi\) | ||||
0.0772144 | + | 0.997015i | \(0.475397\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.82376e78 | −0.00246608 | ||||||||
\(320\) | 3.67635e80 | 0.140619 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.36453e81 | −0.426254 | ||||||||
\(323\) | 1.38291e81 | 0.390583 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.64583e81 | −0.842533 | ||||||||
\(326\) | −3.61712e81 | −0.756469 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.25031e81 | 0.214348 | ||||||||
\(329\) | 3.43566e81 | 0.533511 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.10080e82 | −1.40378 | −0.701892 | − | 0.712283i | \(-0.747661\pi\) | ||||
−0.701892 | + | 0.712283i | \(0.747661\pi\) | |||||||
\(332\) | −6.59343e81 | −0.762296 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.93343e82 | −1.83894 | ||||||||
\(335\) | −1.58111e82 | −1.36460 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.66720e81 | 0.474211 | 0.237105 | − | 0.971484i | \(-0.423801\pi\) | ||||
0.237105 | + | 0.971484i | \(0.423801\pi\) | |||||||
\(338\) | −3.71260e82 | −2.39820 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3.78831e81 | 0.202014 | ||||||||
\(341\) | −7.80272e79 | −0.00378206 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.51115e82 | −1.00650 | ||||||||
\(344\) | −2.18908e82 | −0.798202 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.67094e82 | 1.41069 | ||||||||
\(347\) | 2.67024e82 | 0.734248 | 0.367124 | − | 0.930172i | \(-0.380342\pi\) | ||||
0.367124 | + | 0.930172i | \(0.380342\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.03770e81 | 0.206173 | 0.103086 | − | 0.994672i | \(-0.467128\pi\) | ||||
0.103086 | + | 0.994672i | \(0.467128\pi\) | |||||||
\(350\) | −1.88900e82 | −0.392664 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.83603e80 | 0.0100805 | ||||||||
\(353\) | 5.79038e82 | 0.912072 | 0.456036 | − | 0.889961i | \(-0.349269\pi\) | ||||
0.456036 | + | 0.889961i | \(0.349269\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.16253e82 | −0.676770 | ||||||||
\(356\) | −2.90391e82 | −0.347423 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.15979e83 | 1.15660 | ||||||||
\(359\) | 8.10181e82 | 0.737926 | 0.368963 | − | 0.929444i | \(-0.379713\pi\) | ||||
0.368963 | + | 0.929444i | \(0.379713\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.37338e83 | 1.04426 | ||||||||
\(362\) | 2.37660e83 | 1.65168 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.10781e83 | −0.643679 | ||||||||
\(365\) | 1.55426e83 | 0.826051 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.23295e82 | −0.0993645 | −0.0496823 | − | 0.998765i | \(-0.515821\pi\) | ||||
−0.0496823 | + | 0.998765i | \(0.515821\pi\) | |||||||
\(368\) | −1.63563e83 | −0.666240 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.18190e83 | 0.745210 | ||||||||
\(371\) | −2.20210e83 | −0.688945 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.67990e83 | −0.966717 | −0.483358 | − | 0.875423i | \(-0.660583\pi\) | ||||
−0.483358 | + | 0.875423i | \(0.660583\pi\) | |||||||
\(374\) | 1.35529e81 | 0.00326365 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.10823e83 | 0.426888 | ||||||||
\(377\) | 2.39458e83 | 0.444769 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.08921e83 | −0.326744 | −0.163372 | − | 0.986565i | \(-0.552237\pi\) | ||||
−0.163372 | + | 0.986565i | \(0.552237\pi\) | |||||||
\(380\) | 7.36497e83 | 1.05731 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 8.30565e83 | 1.00534 | ||||||||
\(383\) | 6.21778e83 | 0.691314 | 0.345657 | − | 0.938361i | \(-0.387656\pi\) | ||||
0.345657 | + | 0.938361i | \(0.387656\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.68808e81 | −0.00721679 | ||||||||
\(386\) | −1.40297e83 | −0.121049 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4.20139e83 | −0.306452 | ||||||||
\(389\) | −1.44566e84 | −0.969850 | −0.484925 | − | 0.874556i | \(-0.661153\pi\) | ||||
−0.484925 | + | 0.874556i | \(0.661153\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.58665e83 | −0.146890 | ||||||||
\(392\) | −5.82880e83 | −0.304637 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.04676e84 | 0.906648 | ||||||||
\(395\) | 3.43176e84 | 1.39995 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.56097e84 | −0.886569 | −0.443285 | − | 0.896381i | \(-0.646187\pi\) | ||||
−0.443285 | + | 0.896381i | \(0.646187\pi\) | |||||||
\(398\) | 6.44140e84 | 2.05485 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.26430e84 | −0.613739 | ||||||||
\(401\) | 8.35388e82 | 0.0208783 | 0.0104392 | − | 0.999946i | \(-0.496677\pi\) | ||||
0.0104392 | + | 0.999946i | \(0.496677\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.20827e84 | 0.682114 | ||||||||
\(404\) | −4.31698e84 | −0.846809 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.24070e84 | 0.207286 | ||||||||
\(407\) | 2.94159e82 | 0.00453695 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.47461e84 | 0.851541 | 0.425771 | − | 0.904831i | \(-0.360003\pi\) | ||||
0.425771 | + | 0.904831i | \(0.360003\pi\) | |||||||
\(410\) | 5.45856e84 | 0.663136 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.46429e83 | 0.0151868 | ||||||||
\(413\) | −3.47819e84 | −0.333409 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.88144e85 | 1.54144 | ||||||||
\(416\) | −2.39962e85 | −1.81807 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.63485e83 | 0.0170815 | ||||||||
\(419\) | 1.03548e85 | 0.621133 | 0.310567 | − | 0.950552i | \(-0.399481\pi\) | ||||
0.310567 | + | 0.950552i | \(0.399481\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.49789e85 | −1.28353 | −0.641765 | − | 0.766902i | \(-0.721797\pi\) | ||||
−0.641765 | + | 0.766902i | \(0.721797\pi\) | |||||||
\(422\) | −3.57602e85 | −1.70116 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.35128e85 | −0.551258 | ||||||||
\(425\) | −3.58086e84 | −0.135315 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.99473e84 | −0.226916 | ||||||||
\(428\) | 5.80832e84 | 0.174634 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −9.55699e85 | −2.46943 | ||||||||
\(431\) | −5.31382e85 | −1.27320 | −0.636599 | − | 0.771195i | \(-0.719659\pi\) | ||||
−0.636599 | + | 0.771195i | \(0.719659\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.06333e85 | 0.837578 | 0.418789 | − | 0.908083i | \(-0.362455\pi\) | ||||
0.418789 | + | 0.908083i | \(0.362455\pi\) | |||||||
\(434\) | 1.66229e85 | 0.317901 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.58062e85 | −0.260326 | ||||||||
\(437\) | −5.02879e85 | −0.768806 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.80579e85 | −0.896977 | −0.448489 | − | 0.893789i | \(-0.648038\pi\) | ||||
−0.448489 | + | 0.893789i | \(0.648038\pi\) | |||||||
\(440\) | −4.71766e83 | −0.00577451 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −5.57257e85 | −0.588616 | ||||||||
\(443\) | −4.98621e85 | −0.489384 | −0.244692 | − | 0.969601i | \(-0.578687\pi\) | ||||
−0.244692 | + | 0.969601i | \(0.578687\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.28633e85 | 0.702526 | ||||||||
\(446\) | 1.58168e86 | 1.24662 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.05591e85 | −0.0719600 | ||||||||
\(449\) | −2.19217e86 | −1.38953 | −0.694765 | − | 0.719237i | \(-0.744492\pi\) | ||||
−0.694765 | + | 0.719237i | \(0.744492\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.35911e83 | 0.00403727 | ||||||||
\(452\) | −2.07027e86 | −1.05689 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −4.67800e85 | −0.206892 | ||||||||
\(455\) | 3.16113e86 | 1.30158 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.33189e86 | 1.90373 | 0.951864 | − | 0.306520i | \(-0.0991648\pi\) | ||||
0.951864 | + | 0.306520i | \(0.0991648\pi\) | |||||||
\(458\) | 9.86260e85 | 0.327992 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.37757e86 | −0.397635 | ||||||||
\(461\) | 6.25225e86 | 1.68173 | 0.840865 | − | 0.541245i | \(-0.182047\pi\) | ||||
0.840865 | + | 0.541245i | \(0.182047\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.64512e85 | 0.225385 | 0.112693 | − | 0.993630i | \(-0.464052\pi\) | ||||
0.112693 | + | 0.993630i | \(0.464052\pi\) | |||||||
\(464\) | 1.48719e86 | 0.323990 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.17912e87 | 2.23366 | ||||||||
\(467\) | −5.11330e86 | −0.903447 | −0.451723 | − | 0.892158i | \(-0.649191\pi\) | ||||
−0.451723 | + | 0.892158i | \(0.649191\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.54120e86 | 0.698318 | ||||||||
\(470\) | 9.20402e86 | 1.32068 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.13433e86 | −0.266776 | ||||||||
\(473\) | −1.28845e85 | −0.0150342 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.96165e86 | −0.708223 | ||||||||
\(476\) | −1.08806e86 | −0.103378 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −7.61197e86 | −0.631088 | ||||||||
\(479\) | 1.99037e86 | 0.154180 | 0.0770901 | − | 0.997024i | \(-0.475437\pi\) | ||||
0.0770901 | + | 0.997024i | \(0.475437\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.20950e87 | −0.818261 | ||||||||
\(482\) | 1.50714e87 | 0.953068 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.09396e87 | −0.604683 | ||||||||
\(485\) | 1.19887e87 | 0.619677 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.95350e86 | 0.269204 | 0.134602 | − | 0.990900i | \(-0.457024\pi\) | ||||
0.134602 | + | 0.990900i | \(0.457024\pi\) | |||||||
\(488\) | −4.29220e86 | −0.181566 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.54471e87 | −0.942466 | ||||||||
\(491\) | 5.25079e87 | 1.82002 | 0.910010 | − | 0.414587i | \(-0.136074\pi\) | ||||
0.910010 | + | 0.414587i | \(0.136074\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.35190e86 | 0.0714323 | ||||||||
\(494\) | −1.08338e88 | −3.08074 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.99255e87 | 0.496883 | ||||||||
\(497\) | 1.48276e87 | 0.346329 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.37774e87 | 1.51236 | 0.756181 | − | 0.654363i | \(-0.227063\pi\) | ||||
0.756181 | + | 0.654363i | \(0.227063\pi\) | |||||||
\(500\) | 1.94295e87 | 0.373195 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 7.77212e86 | 0.131120 | ||||||||
\(503\) | −1.28406e87 | −0.203061 | −0.101530 | − | 0.994832i | \(-0.532374\pi\) | ||||
−0.101530 | + | 0.994832i | \(0.532374\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.23185e88 | 1.71234 | ||||||||
\(506\) | −4.92832e85 | −0.00642403 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −6.98660e87 | −0.801116 | ||||||||
\(509\) | −2.60784e87 | −0.280513 | −0.140257 | − | 0.990115i | \(-0.544793\pi\) | ||||
−0.140257 | + | 0.990115i | \(0.544793\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.46410e87 | −0.422722 | ||||||||
\(512\) | −7.92179e87 | −0.703963 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3.11943e88 | −2.44216 | ||||||||
\(515\) | −4.17835e86 | −0.0307093 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.24087e86 | 0.00804049 | ||||||||
\(518\) | −6.26677e87 | −0.381352 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.93978e88 | 1.04146 | ||||||||
\(521\) | 1.32543e88 | 0.668548 | 0.334274 | − | 0.942476i | \(-0.391509\pi\) | ||||
0.334274 | + | 0.942476i | \(0.391509\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.46812e87 | 0.243519 | 0.121760 | − | 0.992560i | \(-0.461146\pi\) | ||||
0.121760 | + | 0.992560i | \(0.461146\pi\) | |||||||
\(524\) | 3.90483e87 | 0.163431 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.38232e88 | 0.880975 | ||||||||
\(527\) | 3.15110e87 | 0.109551 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.31259e88 | −0.710867 | ||||||||
\(530\) | −5.89935e88 | −1.70545 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.11534e88 | −0.541068 | ||||||||
\(533\) | −3.02587e88 | −0.728142 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.65741e88 | −0.353128 | ||||||||
\(536\) | 2.78663e88 | 0.558758 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −8.48909e88 | −1.50813 | ||||||||
\(539\) | −3.43072e86 | −0.00573787 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.12366e88 | 0.908029 | 0.454015 | − | 0.890994i | \(-0.349991\pi\) | ||||
0.454015 | + | 0.890994i | \(0.349991\pi\) | |||||||
\(542\) | −1.05914e89 | −1.47903 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.35686e88 | −0.291991 | ||||||||
\(545\) | 4.51031e88 | 0.526406 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.21753e88 | −0.333376 | −0.166688 | − | 0.986010i | \(-0.553307\pi\) | ||||
−0.166688 | + | 0.986010i | \(0.553307\pi\) | |||||||
\(548\) | −4.15131e88 | −0.405337 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −6.82257e86 | −0.00591781 | ||||||||
\(551\) | 4.57240e88 | 0.373867 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.85658e88 | −0.716406 | ||||||||
\(554\) | −1.18548e89 | −0.812503 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.50301e87 | −0.0274519 | ||||||||
\(557\) | 2.75914e88 | 0.158664 | 0.0793322 | − | 0.996848i | \(-0.474721\pi\) | ||||
0.0793322 | + | 0.996848i | \(0.474721\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.29777e89 | 2.71150 | ||||||||
\(560\) | 1.96327e89 | 0.948133 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4.11431e89 | −1.76957 | ||||||||
\(563\) | 1.72931e89 | 0.702020 | 0.351010 | − | 0.936372i | \(-0.385838\pi\) | ||||
0.351010 | + | 0.936372i | \(0.385838\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.90753e89 | 2.13713 | ||||||||
\(566\) | 7.11868e89 | 2.43145 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9.09873e88 | 0.277115 | ||||||||
\(569\) | 3.33657e89 | 0.959735 | 0.479867 | − | 0.877341i | \(-0.340685\pi\) | ||||
0.479867 | + | 0.877341i | \(0.340685\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.14714e88 | −0.157761 | −0.0788805 | − | 0.996884i | \(-0.525135\pi\) | ||||
−0.0788805 | + | 0.996884i | \(0.525135\pi\) | |||||||
\(572\) | −4.00110e87 | −0.00970081 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.56779e89 | −0.339352 | ||||||||
\(575\) | 1.30213e89 | 0.266349 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.35935e89 | 1.16198 | 0.580991 | − | 0.813910i | \(-0.302665\pi\) | ||||
0.580991 | + | 0.813910i | \(0.302665\pi\) | |||||||
\(578\) | 6.78694e89 | 1.17225 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.25255e89 | 0.193368 | ||||||||
\(581\) | −5.40380e89 | −0.788815 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.95338e87 | −0.0103830 | ||||||||
\(584\) | −2.73932e89 | −0.338240 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −8.88925e89 | −0.982183 | ||||||||
\(587\) | −1.85837e90 | −1.94265 | −0.971323 | − | 0.237762i | \(-0.923586\pi\) | ||||
−0.971323 | + | 0.237762i | \(0.923586\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.12614e89 | 0.573377 | ||||||||
\(590\) | −9.31796e89 | −0.825336 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −7.51180e89 | −0.596058 | ||||||||
\(593\) | 2.24950e90 | 1.68970 | 0.844850 | − | 0.535004i | \(-0.179690\pi\) | ||||
0.844850 | + | 0.535004i | \(0.179690\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.10480e89 | 0.209041 | ||||||||
\(596\) | −1.38954e90 | −0.885864 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.02639e90 | 1.15861 | ||||||||
\(599\) | −9.74495e89 | −0.527725 | −0.263863 | − | 0.964560i | \(-0.584997\pi\) | ||||
−0.263863 | + | 0.964560i | \(0.584997\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.26000e90 | −1.09822 | −0.549108 | − | 0.835751i | \(-0.685033\pi\) | ||||
−0.549108 | + | 0.835751i | \(0.685033\pi\) | |||||||
\(602\) | 2.74492e90 | 1.26370 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.88799e90 | −0.780369 | ||||||||
\(605\) | 3.12163e90 | 1.22273 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.77122e90 | −1.32693 | −0.663467 | − | 0.748206i | \(-0.730916\pi\) | ||||
−0.663467 | + | 0.748206i | \(0.730916\pi\) | |||||||
\(608\) | −4.58204e90 | −1.52824 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.87387e90 | −0.561719 | ||||||||
\(611\) | −5.10211e90 | −1.45014 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.13613e90 | −0.545962 | −0.272981 | − | 0.962019i | \(-0.588010\pi\) | ||||
−0.272981 | + | 0.962019i | \(0.588010\pi\) | |||||||
\(614\) | −1.47713e90 | −0.358052 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.35499e88 | 0.00295504 | ||||||||
\(617\) | −1.72839e89 | −0.0357581 | −0.0178790 | − | 0.999840i | \(-0.505691\pi\) | ||||
−0.0178790 | + | 0.999840i | \(0.505691\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.38513e90 | 0.444186 | 0.222093 | − | 0.975025i | \(-0.428711\pi\) | ||||
0.222093 | + | 0.975025i | \(0.428711\pi\) | |||||||
\(620\) | 1.67818e90 | 0.296557 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 9.62829e90 | 1.53236 | ||||||||
\(623\) | −2.37997e90 | −0.359509 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.18339e90 | −1.24998 | ||||||||
\(626\) | −6.20551e90 | −0.801884 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 7.95920e90 | 0.927216 | ||||||||
\(629\) | −1.18795e90 | −0.131417 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.66487e90 | 0.565244 | 0.282622 | − | 0.959231i | \(-0.408796\pi\) | ||||
0.282622 | + | 0.959231i | \(0.408796\pi\) | |||||||
\(632\) | −6.04833e90 | −0.573232 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −2.28734e90 | −0.195628 | ||||||||
\(635\) | 1.99363e91 | 1.61994 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.41062e91 | 1.03485 | ||||||||
\(638\) | 4.48106e88 | 0.00312398 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.79272e91 | 1.12892 | ||||||||
\(641\) | −1.34848e91 | −0.807161 | −0.403580 | − | 0.914944i | \(-0.632234\pi\) | ||||
−0.403580 | + | 0.914944i | \(0.632234\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.26536e91 | −1.76634 | −0.883171 | − | 0.469050i | \(-0.844596\pi\) | ||||
−0.883171 | + | 0.469050i | \(0.844596\pi\) | |||||||
\(644\) | 3.95661e90 | 0.203485 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.06407e91 | −0.494783 | ||||||||
\(647\) | 4.26660e90 | 0.188666 | 0.0943328 | − | 0.995541i | \(-0.469928\pi\) | ||||
0.0943328 | + | 0.995541i | \(0.469928\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.25623e89 | −0.00502477 | ||||||||
\(650\) | 2.80526e91 | 1.06731 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.04882e91 | 0.361123 | ||||||||
\(653\) | −3.32079e91 | −1.08784 | −0.543918 | − | 0.839139i | \(-0.683060\pi\) | ||||
−0.543918 | + | 0.839139i | \(0.683060\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.11425e91 | −0.330475 | ||||||||
\(656\) | −1.87926e91 | −0.530411 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2.64354e91 | −0.675842 | ||||||||
\(659\) | 4.45167e90 | 0.108330 | 0.0541648 | − | 0.998532i | \(-0.482750\pi\) | ||||
0.0541648 | + | 0.998532i | \(0.482750\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.71335e91 | −0.598354 | −0.299177 | − | 0.954198i | \(-0.596712\pi\) | ||||
−0.299177 | + | 0.954198i | \(0.596712\pi\) | |||||||
\(662\) | 8.47007e91 | 1.77829 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.31595e91 | −0.631169 | ||||||||
\(665\) | 6.03613e91 | 1.09410 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.55240e90 | −0.140604 | ||||||||
\(668\) | 5.60618e91 | 0.877874 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.21657e92 | 1.72865 | ||||||||
\(671\) | −2.52631e89 | −0.00341983 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.15118e90 | 0.0387243 | 0.0193622 | − | 0.999813i | \(-0.493836\pi\) | ||||
0.0193622 | + | 0.999813i | \(0.493836\pi\) | |||||||
\(674\) | −5.13003e91 | −0.600722 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.07651e92 | 1.14485 | ||||||||
\(677\) | −8.74365e91 | −0.886260 | −0.443130 | − | 0.896457i | \(-0.646132\pi\) | ||||
−0.443130 | + | 0.896457i | \(0.646132\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.44335e91 | −0.317112 | ||||||||
\(680\) | 1.90521e91 | 0.167264 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 6.00376e89 | 0.00479105 | ||||||||
\(683\) | −1.38127e92 | −1.05101 | −0.525505 | − | 0.850791i | \(-0.676123\pi\) | ||||
−0.525505 | + | 0.850791i | \(0.676123\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.18458e92 | 0.819634 | ||||||||
\(686\) | 1.93219e92 | 1.27502 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3.29026e92 | 1.97518 | ||||||||
\(689\) | 3.27022e92 | 1.87263 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.00192e92 | −0.522153 | −0.261076 | − | 0.965318i | \(-0.584077\pi\) | ||||
−0.261076 | + | 0.965318i | \(0.584077\pi\) | |||||||
\(692\) | −1.35439e92 | −0.673434 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2.05460e92 | −0.930132 | ||||||||
\(695\) | 1.28494e91 | 0.0555106 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.97195e91 | −0.116943 | ||||||||
\(698\) | −6.95400e91 | −0.261176 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 5.47737e91 | 0.187450 | ||||||||
\(701\) | −3.27880e92 | −1.07122 | −0.535610 | − | 0.844465i | \(-0.679918\pi\) | ||||
−0.535610 | + | 0.844465i | \(0.679918\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.30953e92 | −0.687820 | ||||||||
\(704\) | −3.81366e89 | −0.00108450 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4.45537e92 | −1.15540 | ||||||||
\(707\) | −3.53808e92 | −0.876268 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.04617e91 | 0.0236374 | 0.0118187 | − | 0.999930i | \(-0.496238\pi\) | ||||
0.0118187 | + | 0.999930i | \(0.496238\pi\) | |||||||
\(710\) | 3.97228e92 | 0.857320 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.46043e92 | −0.287661 | ||||||||
\(713\) | −1.14586e92 | −0.215636 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.14172e91 | 0.0196161 | ||||||||
\(716\) | −3.36294e92 | −0.552136 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −6.23389e92 | −0.934791 | ||||||||
\(719\) | −7.52266e92 | −1.07816 | −0.539079 | − | 0.842255i | \(-0.681228\pi\) | ||||
−0.539079 | + | 0.842255i | \(0.681228\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.20009e91 | 0.0157151 | ||||||||
\(722\) | −1.05674e93 | −1.32285 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −6.89120e92 | −0.788481 | ||||||||
\(725\) | −1.18396e92 | −0.129524 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.53972e92 | 0.854231 | 0.427116 | − | 0.904197i | \(-0.359530\pi\) | ||||
0.427116 | + | 0.904197i | \(0.359530\pi\) | |||||||
\(728\) | −5.57136e92 | −0.532956 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.19592e93 | −1.04643 | ||||||||
\(731\) | 5.20336e92 | 0.435481 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.08934e92 | −0.389746 | −0.194873 | − | 0.980828i | \(-0.562430\pi\) | ||||
−0.194873 | + | 0.980828i | \(0.562430\pi\) | |||||||
\(734\) | 1.71813e92 | 0.125873 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 8.57042e92 | 0.574742 | ||||||||
\(737\) | 1.64016e91 | 0.0105243 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.59512e92 | 0.0937234 | 0.0468617 | − | 0.998901i | \(-0.485078\pi\) | ||||
0.0468617 | + | 0.998901i | \(0.485078\pi\) | |||||||
\(740\) | −6.32665e92 | −0.355748 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.69439e93 | 0.872743 | ||||||||
\(743\) | 1.89948e93 | 0.936481 | 0.468240 | − | 0.883601i | \(-0.344888\pi\) | ||||
0.468240 | + | 0.883601i | \(0.344888\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.96506e93 | 1.79131 | ||||||||
\(746\) | 2.83148e93 | 1.22462 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −3.92980e90 | −0.00155800 | ||||||||
\(749\) | 4.76035e92 | 0.180709 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.38707e93 | 0.482839 | 0.241419 | − | 0.970421i | \(-0.422387\pi\) | ||||
0.241419 | + | 0.970421i | \(0.422387\pi\) | |||||||
\(752\) | −3.16874e93 | −1.05635 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.84249e93 | −0.563426 | ||||||||
\(755\) | 5.38740e93 | 1.57799 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.02487e93 | −0.544228 | −0.272114 | − | 0.962265i | \(-0.587723\pi\) | ||||
−0.272114 | + | 0.962265i | \(0.587723\pi\) | |||||||
\(758\) | 1.60753e93 | 0.413913 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.70397e93 | 0.875439 | ||||||||
\(761\) | 2.55933e93 | 0.579595 | 0.289797 | − | 0.957088i | \(-0.406412\pi\) | ||||
0.289797 | + | 0.957088i | \(0.406412\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.29544e93 | −0.269382 | ||||||||
\(764\) | −2.40831e93 | −0.479931 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.78423e93 | −0.875744 | ||||||||
\(767\) | 5.16527e93 | 0.906242 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.46450e93 | 0.397304 | 0.198652 | − | 0.980070i | \(-0.436344\pi\) | ||||
0.198652 | + | 0.980070i | \(0.436344\pi\) | |||||||
\(770\) | 5.91554e91 | 0.00914210 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 4.06806e92 | 0.0577863 | ||||||||
\(773\) | 1.11858e94 | 1.52347 | 0.761735 | − | 0.647889i | \(-0.224348\pi\) | ||||
0.761735 | + | 0.647889i | \(0.224348\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.58628e93 | −0.198643 | ||||||||
\(776\) | −2.11295e93 | −0.253737 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.11235e94 | 1.22859 | ||||||||
\(779\) | −5.77785e93 | −0.612067 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.35534e91 | 0.00521949 | ||||||||
\(782\) | 1.99028e93 | 0.186078 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 8.76088e93 | 0.753834 | ||||||||
\(785\) | −2.27116e94 | −1.87493 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.14732e93 | −0.391203 | −0.195602 | − | 0.980683i | \(-0.562666\pi\) | ||||
−0.195602 | + | 0.980683i | \(0.562666\pi\) | |||||||
\(788\) | −5.93479e93 | −0.432816 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2.64055e94 | −1.77343 | ||||||||
\(791\) | −1.69674e94 | −1.09365 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.03875e94 | 0.616783 | ||||||||
\(794\) | 1.97052e94 | 1.12309 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.86775e94 | −0.980945 | ||||||||
\(797\) | −1.71138e93 | −0.0862880 | −0.0431440 | − | 0.999069i | \(-0.513737\pi\) | ||||
−0.0431440 | + | 0.999069i | \(0.513737\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.01119e93 | −0.232900 | ||||||||
\(800\) | 1.18645e94 | 0.529452 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −6.42784e92 | −0.0264483 | ||||||||
\(803\) | −1.61231e92 | −0.00637080 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.12902e94 | −0.411468 | ||||||||
\(806\) | −2.46858e94 | −0.864090 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −2.17109e94 | −0.701145 | ||||||||
\(809\) | 4.00552e94 | 1.24260 | 0.621300 | − | 0.783572i | \(-0.286605\pi\) | ||||
0.621300 | + | 0.783572i | \(0.286605\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.51220e94 | 0.432944 | 0.216472 | − | 0.976289i | \(-0.430545\pi\) | ||||
0.216472 | + | 0.976289i | \(0.430545\pi\) | |||||||
\(812\) | −3.59753e93 | −0.0989541 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2.26339e92 | −0.00574732 | ||||||||
\(815\) | −2.99282e94 | −0.730229 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.01160e95 | 2.27925 | ||||||||
\(818\) | −4.98184e94 | −1.07872 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.58277e94 | −0.316568 | ||||||||
\(821\) | 6.13335e94 | 1.17909 | 0.589543 | − | 0.807737i | \(-0.299308\pi\) | ||||
0.589543 | + | 0.807737i | \(0.299308\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.29274e93 | 0.111775 | 0.0558876 | − | 0.998437i | \(-0.482201\pi\) | ||||
0.0558876 | + | 0.998437i | \(0.482201\pi\) | |||||||
\(824\) | 7.36416e92 | 0.0125744 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.67627e94 | 0.422356 | ||||||||
\(827\) | −1.31042e94 | −0.198830 | −0.0994150 | − | 0.995046i | \(-0.531697\pi\) | ||||
−0.0994150 | + | 0.995046i | \(0.531697\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.97591e94 | 0.417443 | 0.208722 | − | 0.977975i | \(-0.433070\pi\) | ||||
0.208722 | + | 0.977975i | \(0.433070\pi\) | |||||||
\(830\) | −1.44766e95 | −1.95267 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.56807e94 | 0.195595 | ||||||||
\(833\) | 1.38548e94 | 0.166203 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.59973e95 | −1.77515 | ||||||||
\(836\) | −7.64003e92 | −0.00815438 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −7.96741e94 | −0.786840 | ||||||||
\(839\) | −1.23639e95 | −1.17460 | −0.587302 | − | 0.809368i | \(-0.699810\pi\) | ||||
−0.587302 | + | 0.809368i | \(0.699810\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.05952e95 | −0.931625 | ||||||||
\(842\) | 1.92199e95 | 1.62595 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.03691e95 | 0.812101 | ||||||||
\(845\) | −3.07183e95 | −2.31501 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.96582e94 | −0.625719 | ||||||||
\(848\) | 2.03102e95 | 1.36411 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.75527e94 | 0.171415 | ||||||||
\(851\) | 4.31983e94 | 0.258676 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.72798e94 | 0.262320 | 0.131160 | − | 0.991361i | \(-0.458130\pi\) | ||||
0.131160 | + | 0.991361i | \(0.458130\pi\) | |||||||
\(854\) | 5.38205e94 | 0.287453 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.92111e94 | 0.144594 | ||||||||
\(857\) | 3.75717e95 | 1.79054 | 0.895271 | − | 0.445521i | \(-0.146982\pi\) | ||||
0.895271 | + | 0.445521i | \(0.146982\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.87427e95 | −1.26984 | −0.634921 | − | 0.772577i | \(-0.718967\pi\) | ||||
−0.634921 | + | 0.772577i | \(0.718967\pi\) | |||||||
\(860\) | 2.77115e95 | 1.17886 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 4.08869e95 | 1.61286 | ||||||||
\(863\) | 8.10537e94 | 0.307909 | 0.153954 | − | 0.988078i | \(-0.450799\pi\) | ||||
0.153954 | + | 0.988078i | \(0.450799\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.86476e95 | 1.36175 | ||||||||
\(866\) | −3.12650e95 | −1.06103 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4.82000e94 | −0.151760 | ||||||||
\(869\) | −3.55993e93 | −0.0107969 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.74390e95 | −1.89811 | ||||||||
\(872\) | −7.94923e94 | −0.215546 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 3.86937e95 | 0.973909 | ||||||||
\(875\) | 1.59239e95 | 0.386178 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.33882e95 | 0.751806 | 0.375903 | − | 0.926659i | \(-0.377333\pi\) | ||||
0.375903 | + | 0.926659i | \(0.377333\pi\) | |||||||
\(878\) | 5.23667e95 | 1.13627 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 7.09080e93 | 0.0142892 | ||||||||
\(881\) | 6.50620e95 | 1.26360 | 0.631801 | − | 0.775130i | \(-0.282316\pi\) | ||||
0.631801 | + | 0.775130i | \(0.282316\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.79206e95 | 1.04498 | 0.522492 | − | 0.852644i | \(-0.325002\pi\) | ||||
0.522492 | + | 0.852644i | \(0.325002\pi\) | |||||||
\(884\) | 1.61583e95 | 0.280993 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.83661e95 | 0.619943 | ||||||||
\(887\) | −4.38872e95 | −0.683628 | −0.341814 | − | 0.939768i | \(-0.611041\pi\) | ||||
−0.341814 | + | 0.939768i | \(0.611041\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.72603e95 | −0.828985 | ||||||||
\(890\) | −6.37587e95 | −0.889947 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −4.58625e95 | −0.595114 | ||||||||
\(893\) | −9.74240e95 | −1.21897 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.59617e95 | 1.11648 | ||||||||
\(896\) | −5.14899e95 | −0.577713 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.68675e96 | 1.76023 | ||||||||
\(899\) | 1.04187e95 | 0.104863 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.21194e95 | 0.300754 | ||||||||
\(902\) | −5.66242e93 | −0.00511434 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.04118e96 | −0.875085 | ||||||||
\(905\) | 1.96641e96 | 1.59439 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.30624e96 | −1.74048 | −0.870239 | − | 0.492630i | \(-0.836036\pi\) | ||||
−0.870239 | + | 0.492630i | \(0.836036\pi\) | |||||||
\(908\) | 1.35644e95 | 0.0987664 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.43231e96 | −1.64882 | ||||||||
\(911\) | 9.24387e95 | 0.604654 | 0.302327 | − | 0.953204i | \(-0.402237\pi\) | ||||
0.302327 | + | 0.953204i | \(0.402237\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.95171e94 | −0.0118882 | ||||||||
\(914\) | −4.10259e96 | −2.41161 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.85977e95 | −0.156577 | ||||||||
\(917\) | 3.20029e95 | 0.169117 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.74967e96 | −0.861394 | −0.430697 | − | 0.902497i | \(-0.641732\pi\) | ||||
−0.430697 | + | 0.902497i | \(0.641732\pi\) | |||||||
\(920\) | −6.92805e95 | −0.329236 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −4.81075e96 | −2.13038 | ||||||||
\(923\) | −2.20197e96 | −0.941362 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.98019e95 | 0.238292 | ||||||||
\(926\) | −7.42138e95 | −0.285514 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −7.79262e95 | −0.279495 | ||||||||
\(929\) | −9.02077e95 | −0.312416 | −0.156208 | − | 0.987724i | \(-0.549927\pi\) | ||||
−0.156208 | + | 0.987724i | \(0.549927\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.69356e96 | 0.869885 | ||||||||
\(932\) | −3.41900e96 | −1.06631 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 3.93440e96 | 1.14447 | ||||||||
\(935\) | 1.12137e94 | 0.00315044 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.66813e96 | 1.48561 | 0.742803 | − | 0.669511i | \(-0.233496\pi\) | ||||
0.742803 | + | 0.669511i | \(0.233496\pi\) | |||||||
\(938\) | −3.49420e96 | −0.884617 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2.66880e96 | −0.630466 | ||||||||
\(941\) | 3.88472e96 | 0.886538 | 0.443269 | − | 0.896389i | \(-0.353819\pi\) | ||||
0.443269 | + | 0.896389i | \(0.353819\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.08071e96 | 0.230186 | ||||||||
\(944\) | 3.20797e96 | 0.660147 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 9.91391e94 | 0.0190451 | ||||||||
\(947\) | −1.45061e96 | −0.269262 | −0.134631 | − | 0.990896i | \(-0.542985\pi\) | ||||
−0.134631 | + | 0.990896i | \(0.542985\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.62940e96 | 1.14901 | ||||||||
\(950\) | 5.35660e96 | 0.897164 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −5.47207e95 | −0.0855955 | ||||||||
\(953\) | 1.02285e97 | 1.54629 | 0.773144 | − | 0.634230i | \(-0.218683\pi\) | ||||
0.773144 | + | 0.634230i | \(0.218683\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.87213e96 | 0.970470 | ||||||||
\(956\) | 2.20717e96 | 0.301269 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.53147e96 | −0.195313 | ||||||||
\(959\) | −3.40230e96 | −0.419438 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.28391e96 | −0.839178 | ||||||||
\(962\) | 9.30644e96 | 1.03656 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −4.37011e96 | −0.454976 | ||||||||
\(965\) | −1.16082e96 | −0.116850 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.31294e97 | 1.23562 | 0.617808 | − | 0.786329i | \(-0.288021\pi\) | ||||
0.617808 | + | 0.786329i | \(0.288021\pi\) | |||||||
\(968\) | −5.50173e96 | −0.500668 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −9.22462e96 | −0.784996 | ||||||||
\(971\) | 8.40882e96 | 0.692006 | 0.346003 | − | 0.938233i | \(-0.387539\pi\) | ||||
0.346003 | + | 0.938233i | \(0.387539\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.69055e95 | −0.0284069 | ||||||||
\(974\) | −4.58088e96 | −0.341022 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.45131e96 | 0.449292 | ||||||||
\(977\) | 8.22971e95 | 0.0554385 | 0.0277192 | − | 0.999616i | \(-0.491176\pi\) | ||||
0.0277192 | + | 0.999616i | \(0.491176\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.59581e94 | −0.00541813 | ||||||||
\(980\) | 7.37866e96 | 0.449915 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −4.04018e97 | −2.30557 | ||||||||
\(983\) | 1.65515e97 | 0.913792 | 0.456896 | − | 0.889520i | \(-0.348961\pi\) | ||||
0.456896 | + | 0.889520i | \(0.348961\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.69350e97 | 0.875199 | ||||||||
\(986\) | −1.80966e96 | −0.0904891 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.14138e97 | 1.47068 | ||||||||
\(989\) | −1.89214e97 | −0.857182 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.01523e97 | −0.854930 | −0.427465 | − | 0.904032i | \(-0.640593\pi\) | ||||
−0.427465 | + | 0.904032i | \(0.640593\pi\) | |||||||
\(992\) | −1.04406e97 | −0.428644 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.14090e97 | −0.438724 | ||||||||
\(995\) | 5.32964e97 | 1.98357 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.09099e97 | 0.380389 | 0.190194 | − | 0.981746i | \(-0.439088\pi\) | ||||
0.190194 | + | 0.981746i | \(0.439088\pi\) | |||||||
\(998\) | −5.67675e97 | −1.91583 | ||||||||
\(999\) | 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 | 9.66.a.b.1.2 | 5 | ||
3.2 | odd | 2 | 1.66.a.a.1.4 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.66.a.a.1.4 | ✓ | 5 | 3.2 | odd | 2 | ||
9.66.a.b.1.2 | 5 | 1.1 | even | 1 | trivial |