Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [84,9,Mod(61,84)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(84, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("84.61");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 84 = 2^{2} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 84.m (of order \(6\), degree \(2\), minimal) |
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: | no |
Analytic conductor: | \(34.2198032451\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} + 148097 x^{10} + 46071824 x^{9} + 21578502553 x^{8} + 3561445462121 x^{7} + 576413321817541 x^{6} + \cdots + 45\!\cdots\!96 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{20}\cdot 3^{10}\cdot 7^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 73.5 | ||
Root | \(221.993 - 384.503i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 84.73 |
Dual form | 84.9.m.b.61.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/84\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(43\) | \(73\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 40.5000 | + | 23.3827i | 0.500000 | + | 0.288675i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 632.551 | − | 365.204i | 1.01208 | − | 0.584326i | 0.100282 | − | 0.994959i | \(-0.468026\pi\) |
0.911801 | + | 0.410633i | \(0.134692\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 984.437 | − | 2189.91i | 0.410011 | − | 0.912080i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1093.50 | + | 1894.00i | 0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6353.95 | − | 11005.4i | 0.433983 | − | 0.751681i | −0.563229 | − | 0.826301i | \(-0.690441\pi\) |
0.997212 | + | 0.0746198i | \(0.0237743\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 21176.4i | − | 0.741444i | −0.928744 | − | 0.370722i | \(-0.879110\pi\) | ||
0.928744 | − | 0.370722i | \(-0.120890\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 34157.8 | 0.674721 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −82551.9 | − | 47661.3i | −0.988397 | − | 0.570651i | −0.0836020 | − | 0.996499i | \(-0.526642\pi\) |
−0.904795 | + | 0.425848i | \(0.859976\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −133336. | + | 76981.8i | −1.02314 | + | 0.590709i | −0.915011 | − | 0.403428i | \(-0.867818\pi\) |
−0.108126 | + | 0.994137i | \(0.534485\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 91075.6 | − | 65672.4i | 0.468301 | − | 0.337680i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −47111.5 | − | 81599.5i | −0.168351 | − | 0.291593i | 0.769489 | − | 0.638660i | \(-0.220511\pi\) |
−0.937840 | + | 0.347067i | \(0.887178\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 71435.0 | − | 123729.i | 0.182874 | − | 0.316746i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 102276.i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 541664. | 0.765840 | 0.382920 | − | 0.923782i | \(-0.374919\pi\) | ||||
0.382920 | + | 0.923782i | \(0.374919\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −185730. | − | 107231.i | −0.201110 | − | 0.116111i | 0.396063 | − | 0.918223i | \(-0.370376\pi\) |
−0.597173 | + | 0.802112i | \(0.703710\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 514670. | − | 297145.i | 0.433983 | − | 0.250560i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −177055. | − | 1.74475e6i | −0.117987 | − | 1.16268i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −370376. | − | 641510.i | −0.197622 | − | 0.342292i | 0.750135 | − | 0.661285i | \(-0.229989\pi\) |
−0.947757 | + | 0.318993i | \(0.896655\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 495160. | − | 857643.i | 0.214036 | − | 0.370722i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 782599.i | 0.276952i | 0.990366 | + | 0.138476i | \(0.0442203\pi\) | ||||
−0.990366 | + | 0.138476i | \(0.955780\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −221324. | −0.0647373 | −0.0323687 | − | 0.999476i | \(-0.510305\pi\) | ||||
−0.0323687 | + | 0.999476i | \(0.510305\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.38339e6 | + | 798700.i | 0.337361 | + | 0.194775i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.13230e6 | − | 4.11784e6i | 1.46163 | − | 0.843874i | 0.462546 | − | 0.886595i | \(-0.346936\pi\) |
0.999087 | + | 0.0427209i | \(0.0136026\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.82657e6 | − | 4.31165e6i | −0.663782 | − | 0.747926i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.22890e6 | − | 3.86057e6i | −0.329466 | − | 0.570651i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 659083. | − | 1.14157e6i | 0.0835289 | − | 0.144676i | −0.821235 | − | 0.570591i | \(-0.806714\pi\) |
0.904763 | + | 0.425915i | \(0.140048\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 9.28194e6i | − | 1.01435i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.20016e6 | −0.682092 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.52865e6 | − | 4.34667e6i | −0.621311 | − | 0.358714i | 0.156068 | − | 0.987746i | \(-0.450118\pi\) |
−0.777379 | + | 0.629032i | \(0.783451\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.31192e7 | − | 7.57439e6i | 0.947521 | − | 0.547052i | 0.0552112 | − | 0.998475i | \(-0.482417\pi\) |
0.892310 | + | 0.451423i | \(0.149083\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.22416e6 | − | 530140.i | 0.331630 | − | 0.0336534i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −7.73369e6 | − | 1.33951e7i | −0.433245 | − | 0.750402i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.99100e7 | − | 3.44851e7i | 0.988033 | − | 1.71132i | 0.360436 | − | 0.932784i | \(-0.382628\pi\) |
0.627596 | − | 0.778539i | \(-0.284039\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 4.40638e6i | − | 0.194395i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.34713e6 | −0.367828 | −0.183914 | − | 0.982942i | \(-0.558877\pi\) | ||||
−0.183914 | + | 0.982942i | \(0.558877\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.94520e7 | + | 1.70041e7i | 1.03711 | + | 0.598774i | 0.919012 | − | 0.394229i | \(-0.128988\pi\) |
0.118094 | + | 0.993002i | \(0.462321\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.78623e6 | − | 3.34068e6i | 0.182874 | − | 0.105582i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.78456e7 | − | 2.47486e7i | −0.507656 | − | 0.704025i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.26450e7 | + | 3.92223e7i | 0.581385 | + | 1.00699i | 0.995316 | + | 0.0966799i | \(0.0308223\pi\) |
−0.413931 | + | 0.910308i | \(0.635844\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.39148e6 | + | 4.14217e6i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.58893e7i | 1.38836i | 0.719801 | + | 0.694180i | \(0.244233\pi\) | ||||
−0.719801 | + | 0.694180i | \(0.755767\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.96244e7 | −1.33378 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.19374e7 | + | 1.26656e7i | 0.382920 | + | 0.221079i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.09902e7 | + | 6.34517e6i | −0.175164 | + | 0.101131i | −0.585018 | − | 0.811020i | \(-0.698913\pi\) |
0.409855 | + | 0.912151i | \(0.365579\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.63742e7 | − | 2.08468e7i | −0.676256 | − | 0.304000i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.01470e6 | − | 8.68571e6i | −0.0670368 | − | 0.116111i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.62280e7 | + | 9.73898e7i | −0.690333 | + | 1.19569i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.15780e6i | 0.0695566i | 0.999395 | + | 0.0347783i | \(0.0110725\pi\) | ||||
−0.999395 | + | 0.0347783i | \(0.988927\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.77922e7 | 0.289322 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.15329e8 | + | 6.65855e7i | 1.10829 | + | 0.639874i | 0.938387 | − | 0.345587i | \(-0.112320\pi\) |
0.169907 | + | 0.985460i | \(0.445653\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.81925e7 | − | 2.78240e7i | 0.428184 | − | 0.247212i | −0.270389 | − | 0.962751i | \(-0.587152\pi\) |
0.698573 | + | 0.715539i | \(0.253819\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.36262e7 | − | 7.48023e7i | 0.276643 | − | 0.615400i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.23667e6 | + | 1.25343e7i | 0.0552082 | + | 0.0956234i | 0.892309 | − | 0.451426i | \(-0.149084\pi\) |
−0.837101 | + | 0.547049i | \(0.815751\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.01793e7 | + | 1.56195e8i | −0.638853 | + | 1.10653i | 0.346832 | + | 0.937927i | \(0.387257\pi\) |
−0.985685 | + | 0.168598i | \(0.946076\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 3.46415e7i | − | 0.228195i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.21791e7 | −0.136028 | −0.0680142 | − | 0.997684i | \(-0.521666\pi\) | ||||
−0.0680142 | + | 0.997684i | \(0.521666\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.96009e7 | − | 3.44106e7i | −0.340770 | − | 0.196744i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.01080e7 | − | 2.31564e7i | 0.214036 | − | 0.123574i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.85641e8 | + | 1.33861e8i | −0.925733 | + | 0.667524i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.64341e7 | + | 4.57852e7i | 0.123317 | + | 0.213591i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.82993e7 | + | 3.16953e7i | −0.0799490 | + | 0.138476i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.80962e8i | 0.741221i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.77711e8 | 0.683123 | 0.341561 | − | 0.939859i | \(-0.389044\pi\) | ||||
0.341561 | + | 0.939859i | \(0.389044\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.96362e6 | − | 5.17515e6i | −0.0323687 | − | 0.0186881i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.83164e8 | + | 2.78955e8i | −1.64062 | + | 0.947215i | −0.660012 | + | 0.751255i | \(0.729449\pi\) |
−0.980612 | + | 0.195960i | \(0.937218\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.73216e7 | + | 3.67778e8i | 0.119276 | + | 1.17538i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.73515e7 | + | 6.46947e7i | 0.112454 | + | 0.194775i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.96914e8 | + | 3.41064e8i | −0.558977 | + | 0.968176i | 0.438606 | + | 0.898680i | \(0.355472\pi\) |
−0.997582 | + | 0.0694962i | \(0.977861\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 4.85677e8i | − | 1.30103i | −0.759492 | − | 0.650516i | \(-0.774553\pi\) | ||
0.759492 | − | 0.650516i | \(-0.225447\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.85144e8 | 0.974422 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.33054e8 | − | 1.34554e8i | −0.557329 | − | 0.321774i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.42630e8 | − | 1.97818e8i | 0.775093 | − | 0.447500i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.41582e7 | − | 2.64097e8i | −0.115983 | − | 0.565580i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.60563e8 | + | 2.78103e8i | 0.325762 | + | 0.564236i | 0.981666 | − | 0.190608i | \(-0.0610459\pi\) |
−0.655905 | + | 0.754844i | \(0.727713\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.12702e8 | − | 7.14822e8i | 0.793833 | − | 1.37496i | −0.129744 | − | 0.991547i | \(-0.541416\pi\) |
0.923577 | − | 0.383412i | \(-0.125251\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 2.08471e8i | − | 0.380434i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.56645e8 | −0.271387 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.15549e8 | + | 5.28592e8i | 1.50689 | + | 0.870006i | 0.999968 | + | 0.00801653i | \(0.00255177\pi\) |
0.506926 | + | 0.861989i | \(0.330782\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.33857e7 | − | 3.08223e7i | 0.0835289 | − | 0.0482254i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.25074e8 | + | 2.28402e7i | −0.334982 | + | 0.0339935i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.67831e8 | − | 9.83512e8i | −0.804394 | − | 1.39325i | −0.916699 | − | 0.399577i | \(-0.869157\pi\) |
0.112306 | − | 0.993674i | \(-0.464176\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.17037e8 | − | 3.75919e8i | 0.292818 | − | 0.507175i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 1.00076e9i | − | 1.28666i | −0.765591 | − | 0.643328i | \(-0.777553\pi\) | ||
0.765591 | − | 0.643328i | \(-0.222447\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.67292e8 | 0.450261 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.91606e8 | − | 1.68359e8i | −0.341046 | − | 0.196903i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.46649e8 | + | 3.15608e8i | −0.610273 | + | 0.352341i | −0.773072 | − | 0.634318i | \(-0.781281\pi\) |
0.162799 | + | 0.986659i | \(0.447948\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.00632e8 | − | 2.78239e8i | −0.213918 | − | 0.296665i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.03274e8 | − | 3.52080e8i | −0.207104 | − | 0.358714i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.77342e8 | + | 9.99986e8i | −0.562369 | + | 0.974052i | 0.434920 | + | 0.900469i | \(0.356777\pi\) |
−0.997289 | + | 0.0735826i | \(0.976557\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 1.42212e9i | − | 1.32502i | −0.749052 | − | 0.662511i | \(-0.769491\pi\) | ||
0.749052 | − | 0.662511i | \(-0.230509\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.08438e8 | 0.631681 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.68564e8 | − | 2.70525e8i | −0.400020 | − | 0.230952i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.04906e9 | + | 6.05676e8i | −0.857895 | + | 0.495306i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.23974e8 | + | 1.00684e8i | 0.175530 | + | 0.0789067i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.05844e8 | + | 5.29737e8i | 0.229809 | + | 0.398040i | 0.957751 | − | 0.287598i | \(-0.0928566\pi\) |
−0.727943 | + | 0.685638i | \(0.759523\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.49542e8 | − | 1.64465e9i | 0.684360 | − | 1.18535i | −0.289277 | − | 0.957245i | \(-0.593415\pi\) |
0.973637 | − | 0.228101i | \(-0.0732518\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 7.23338e8i | − | 0.500268i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.00843e9 | 0.669544 | 0.334772 | − | 0.942299i | \(-0.391341\pi\) | ||||
0.334772 | + | 0.942299i | \(0.391341\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.76255e8 | + | 1.59496e8i | 0.176156 | + | 0.101704i | 0.585485 | − | 0.810683i | \(-0.300904\pi\) |
−0.409329 | + | 0.912387i | \(0.634237\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.61271e9 | − | 9.31097e8i | 0.988033 | − | 0.570441i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.33234e8 | − | 1.18619e9i | 0.314003 | − | 0.698507i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.85808e8 | + | 4.95034e8i | 0.161830 | + | 0.280298i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.03033e8 | − | 1.78458e8i | 0.0561170 | − | 0.0971975i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.95655e9i | 1.02543i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.39969e9 | −0.706160 | −0.353080 | − | 0.935593i | \(-0.614866\pi\) | ||||
−0.353080 | + | 0.935593i | \(0.614866\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.78559e8 | − | 2.18561e8i | −0.183914 | − | 0.106183i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.39999e8 | + | 8.08283e7i | −0.0655195 | + | 0.0378277i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.17665e8 | + | 3.01168e8i | −0.188360 | + | 0.135822i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 7.95204e8 | + | 1.37733e9i | 0.345702 | + | 0.598774i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.00929e9 | + | 1.74815e9i | −0.423106 | + | 0.732840i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.09118e9i | 1.24999i | 0.780630 | + | 0.624993i | \(0.214898\pi\) | ||||
−0.780630 | + | 0.624993i | \(0.785102\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.12457e8 | 0.121916 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.27805e9 | − | 1.89258e9i | −1.23456 | − | 0.712774i | −0.266583 | − | 0.963812i | \(-0.585895\pi\) |
−0.967977 | + | 0.251038i | \(0.919228\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.74391e9 | + | 1.58420e9i | −0.997763 | + | 0.576059i | −0.907586 | − | 0.419867i | \(-0.862077\pi\) |
−0.0901773 | + | 0.995926i | \(0.528743\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.44059e8 | − | 1.41960e9i | −0.0505932 | − | 0.498560i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.76314e9 | + | 4.78590e9i | 0.937518 | + | 1.62383i | 0.770081 | + | 0.637946i | \(0.220216\pi\) |
0.167437 | + | 0.985883i | \(0.446451\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.00770e9 | − | 5.20949e9i | 0.986195 | − | 1.70814i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.11800e9i | 0.671326i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.93530e9 | −1.20611 | −0.603054 | − | 0.797701i | \(-0.706049\pi\) | ||||
−0.603054 | + | 0.797701i | \(0.706049\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.76301e9 | + | 3.32727e9i | 1.70837 | + | 0.986326i | 0.936586 | + | 0.350437i | \(0.113967\pi\) |
0.771780 | + | 0.635889i | \(0.219367\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.93710e8 | + | 1.11839e8i | −0.0555556 | + | 0.0320750i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.99513e9 | − | 1.32986e9i | −1.10883 | − | 0.369098i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.63019e9 | + | 2.82358e9i | 0.437977 | + | 0.758599i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.54067e9 | + | 2.66852e9i | −0.400785 | + | 0.694180i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.25680e9i | 1.07248i | 0.844066 | + | 0.536239i | \(0.180155\pi\) | ||||
−0.844066 | + | 0.536239i | \(0.819845\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.19738e9 | −0.292246 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.81979e9 | − | 1.62801e9i | −0.666892 | − | 0.385031i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.63398e9 | + | 1.52073e9i | −0.603782 | + | 0.348593i | −0.770528 | − | 0.637406i | \(-0.780007\pi\) |
0.166746 | + | 0.986000i | \(0.446674\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.76946e9 | + | 1.79562e8i | −0.393225 | + | 0.0399039i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.92309e8 | + | 1.02591e9i | 0.127640 | + | 0.221079i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.20815e9 | − | 7.28873e9i | 0.879566 | − | 1.52345i | 0.0277486 | − | 0.999615i | \(-0.491166\pi\) |
0.851818 | − | 0.523838i | \(-0.175500\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 9.62798e8i | − | 0.195232i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.93468e8 | −0.116776 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.40038e9 | + | 3.69526e9i | 1.22235 | + | 0.705726i | 0.965419 | − | 0.260703i | \(-0.0839542\pi\) |
0.256934 | + | 0.966429i | \(0.417288\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.72934e9 | + | 2.15314e9i | −0.691441 | + | 0.399204i | −0.804152 | − | 0.594424i | \(-0.797380\pi\) |
0.112711 | + | 0.993628i | \(0.464047\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.39070e9 | − | 1.92865e9i | −0.250371 | − | 0.347218i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −9.07789e8 | − | 1.57234e9i | −0.158728 | − | 0.274925i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.54312e7 | + | 4.40481e7i | −0.00431964 | + | 0.00748183i | −0.868177 | − | 0.496254i | \(-0.834708\pi\) |
0.863858 | + | 0.503736i | \(0.168042\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 4.69028e8i | − | 0.0774074i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.03421e10 | 1.65877 | 0.829383 | − | 0.558680i | \(-0.188692\pi\) | ||||
0.829383 | + | 0.558680i | \(0.188692\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.55984e9 | − | 1.47792e9i | −0.399086 | − | 0.230412i | 0.287003 | − | 0.957930i | \(-0.407341\pi\) |
−0.686090 | + | 0.727517i | \(0.740674\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.55447e9 | + | 2.62953e9i | −0.690333 | + | 0.398564i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.71382e9 | + | 7.70419e8i | 0.252602 | + | 0.113553i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.05533e9 | + | 1.82788e9i | 0.151285 | + | 0.262034i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.43986e8 | + | 2.49391e8i | −0.0200793 | + | 0.0347783i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 4.22563e9i | − | 0.573351i | −0.958028 | − | 0.286676i | \(-0.907450\pi\) | ||
0.958028 | − | 0.286676i | \(-0.0925502\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.34968e9 | −0.838424 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.12558e9 | + | 6.49856e8i | 0.144661 | + | 0.0835201i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.72798e9 | + | 9.97651e8i | −0.216199 | + | 0.124823i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.17880e8 | + | 4.84679e8i | −0.0265430 | + | 0.0590456i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.11390e9 | + | 5.39343e9i | 0.369431 | + | 0.639874i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.53239e9 | − | 9.58238e9i | 0.639313 | − | 1.10732i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.96070e9i | 0.333304i | 0.986016 | + | 0.166652i | \(0.0532956\pi\) | ||||
−0.986016 | + | 0.166652i | \(0.946704\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.60240e9 | 0.285456 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.74956e9 | − | 4.47421e9i | −0.828391 | − | 0.478272i | 0.0249101 | − | 0.999690i | \(-0.492070\pi\) |
−0.853302 | + | 0.521418i | \(0.825403\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.04664e9 | + | 2.91368e9i | −0.525806 | + | 0.303574i | −0.739307 | − | 0.673369i | \(-0.764847\pi\) |
0.213501 | + | 0.976943i | \(0.431513\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.11094e9 | − | 2.24322e9i | 0.315972 | − | 0.227840i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.50614e9 | + | 4.34076e9i | 0.248181 | + | 0.429861i | 0.963021 | − | 0.269426i | \(-0.0868340\pi\) |
−0.714840 | + | 0.699288i | \(0.753501\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.44171e9 | − | 5.96121e9i | 0.332362 | − | 0.575667i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.76851e8i | 0.0637489i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.46762e10 | 1.34835 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.62013e9 | − | 1.51273e9i | −0.234850 | − | 0.135590i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −7.30452e9 | + | 4.21727e9i | −0.638853 | + | 0.368842i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.99637e9 | − | 1.96728e10i | −0.170395 | − | 1.67912i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.78357e9 | + | 8.28539e9i | 0.398511 | + | 0.690242i | 0.993542 | − | 0.113461i | \(-0.0361937\pi\) |
−0.595031 | + | 0.803703i | \(0.702860\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.10012e8 | − | 1.40298e9i | 0.0658741 | − | 0.114097i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 2.90848e10i | − | 2.30933i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.32884e9 | 0.180560 | 0.0902798 | − | 0.995916i | \(-0.471224\pi\) | ||||
0.0902798 | + | 0.995916i | \(0.471224\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8.98252e8 | − | 5.18606e8i | −0.0680142 | − | 0.0392680i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.36023e9 | + | 1.36268e9i | −0.174557 | + | 0.100781i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.32091e10 | + | 4.13528e9i | −0.954327 | + | 0.298764i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.60922e9 | − | 2.78726e9i | −0.113590 | − | 0.196744i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.04233e10 | − | 1.80536e10i | 0.718928 | − | 1.24522i | −0.242497 | − | 0.970152i | \(-0.577966\pi\) |
0.961425 | − | 0.275068i | \(-0.0887002\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 2.91490e10i | − | 1.96482i | −0.186745 | − | 0.982409i | \(-0.559794\pi\) | ||
0.186745 | − | 0.982409i | \(-0.440206\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.16583e9 | 0.142691 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.78829e8 | + | 5.65127e8i | 0.0630388 | + | 0.0363955i | 0.531188 | − | 0.847254i | \(-0.321746\pi\) |
−0.468149 | + | 0.883649i | \(0.655079\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.91254e9 | + | 3.41361e9i | −0.372272 | + | 0.214932i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.06485e10 | + | 1.08059e9i | −0.655564 | + | 0.0665258i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.49405e9 | + | 9.51597e9i | 0.330761 | + | 0.572896i | 0.982661 | − | 0.185409i | \(-0.0593611\pi\) |
−0.651900 | + | 0.758305i | \(0.726028\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.36060e9 | − | 5.82073e9i | 0.197874 | − | 0.342727i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.47240e9i | 0.142394i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.48399e10 | 1.39952 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.47539e9 | − | 1.42917e9i | −0.136452 | − | 0.0787805i | 0.430220 | − | 0.902724i | \(-0.358436\pi\) |
−0.566672 | + | 0.823944i | \(0.691769\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.48224e9 | + | 8.55772e8i | −0.0799490 | + | 0.0461586i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.85109e9 | − | 2.56713e9i | −0.0977086 | − | 0.135504i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.91785e9 | + | 1.54462e10i | 0.460707 | + | 0.797968i | 0.998996 | − | 0.0447919i | \(-0.0142625\pi\) |
−0.538289 | + | 0.842760i | \(0.680929\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4.23138e9 | + | 7.32897e9i | −0.213972 | + | 0.370610i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 1.14705e10i | − | 0.567827i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.25934e10 | 1.57969 | 0.789847 | − | 0.613303i | \(-0.210160\pi\) | ||||
0.789847 | + | 0.613303i | \(0.210160\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.19729e9 | + | 4.15536e9i | 0.341561 | + | 0.197201i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.90349e10 | + | 1.09898e10i | −0.884619 | + | 0.510735i | −0.872179 | − | 0.489187i | \(-0.837293\pi\) |
−0.0124407 | + | 0.999923i | \(0.503960\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.03266e10 | − | 9.13749e9i | −0.925170 | − | 0.415895i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.42018e8 | − | 4.19187e8i | −0.0107896 | − | 0.0186881i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.09555e10 | + | 1.89755e10i | −0.478448 | + | 0.828695i | −0.999695 | − | 0.0247103i | \(-0.992134\pi\) |
0.521247 | + | 0.853406i | \(0.325467\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.98159e9i | 0.384279i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.60908e10 | −1.09375 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.86482e10 | + | 1.65401e10i | 1.17682 | + | 0.679437i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.10594e10 | + | 2.37057e10i | −1.65292 | + | 0.954312i | −0.677052 | + | 0.735936i | \(0.736743\pi\) |
−0.975865 | + | 0.218376i | \(0.929924\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −7.08810e9 | + | 1.57677e10i | −0.279665 | + | 0.622123i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.47336e8 | + | 1.12122e9i | 0.0250353 | + | 0.0433623i | 0.878272 | − | 0.478162i | \(-0.158697\pi\) |
−0.853236 | + | 0.521524i | \(0.825364\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.27076e9 | + | 3.93308e9i | −0.0860898 | + | 0.149112i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.49352e9i | 0.129850i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9.41340e9 | −0.343059 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.05517e10 | + | 6.09204e9i | 0.377077 | + | 0.217705i | 0.676546 | − | 0.736401i | \(-0.263476\pi\) |
−0.299469 | + | 0.954106i | \(0.596809\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.59500e10 | + | 9.20874e9i | −0.558977 | + | 0.322725i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.69303e10 | + | 1.22080e10i | −0.581921 | + | 0.419609i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.40630e10 | + | 4.16783e10i | 0.811255 | + | 1.40514i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.13564e10 | − | 1.96699e10i | 0.375576 | − | 0.650516i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.83249e9i | 0.0918992i | 0.998944 | + | 0.0459496i | \(0.0146314\pi\) | ||||
−0.998944 | + | 0.0459496i | \(0.985369\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.47344e10 | 0.469033 | 0.234517 | − | 0.972112i | \(-0.424649\pi\) | ||||
0.234517 | + | 0.972112i | \(0.424649\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.55983e10 | + | 9.00571e9i | 0.487211 | + | 0.281291i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.17942e10 | + | 6.80938e9i | −0.361503 | + | 0.208714i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.67214e9 | − | 3.61864e10i | −0.110461 | − | 1.08851i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.29245e9 | − | 1.08988e10i | −0.185776 | − | 0.321774i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.99404e10 | − | 3.45377e10i | 0.577862 | − | 1.00089i | −0.417862 | − | 0.908510i | \(-0.637220\pi\) |
0.995724 | − | 0.0923761i | \(-0.0294462\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.77901e10i | 1.07505i | 0.843249 | + | 0.537523i | \(0.180640\pi\) | ||||
−0.843249 | + | 0.537523i | \(0.819360\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.85020e10 | 0.516729 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.25634e10 | + | 7.25345e9i | 0.344493 | + | 0.198893i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.02545e9 | − | 4.05614e9i | 0.189154 | − | 0.109208i | −0.402432 | − | 0.915450i | \(-0.631835\pi\) |
0.591587 | + | 0.806242i | \(0.298502\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.98190e9 | − | 1.19623e10i | 0.105277 | − | 0.316272i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.85877e10 | + | 4.95154e10i | 0.742274 | + | 1.28566i | 0.951457 | + | 0.307780i | \(0.0995861\pi\) |
−0.209183 | + | 0.977876i | \(0.567081\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.63456e9 | + | 8.02729e9i | −0.118187 | + | 0.204705i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.50176e10i | 0.376157i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.27811e10 | −1.54470 | −0.772349 | − | 0.635199i | \(-0.780918\pi\) | ||||
−0.772349 | + | 0.635199i | \(0.780918\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.61279e9 | + | 4.97259e9i | 0.208179 | + | 0.120192i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.34289e10 | − | 1.93002e10i | 0.793833 | − | 0.458320i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.69474e10 | + | 3.74937e9i | −0.862062 | + | 0.0874809i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.34859e9 | − | 1.44602e10i | −0.191403 | − | 0.331519i | 0.754313 | − | 0.656515i | \(-0.227970\pi\) |
−0.945715 | + | 0.324996i | \(0.894637\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.87461e9 | − | 8.44306e9i | 0.109822 | − | 0.190217i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.39906e10i | 0.309766i | 0.987933 | + | 0.154883i | \(0.0495001\pi\) | ||||
−0.987933 | + | 0.154883i | \(0.950500\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.56476e10 | −0.558114 | −0.279057 | − | 0.960274i | \(-0.590022\pi\) | ||||
−0.279057 | + | 0.960274i | \(0.590022\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6.34411e9 | − | 3.66277e9i | −0.135693 | − | 0.0783426i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.36726e10 | + | 1.94409e10i | −0.707960 | + | 0.408741i | −0.810305 | − | 0.586008i | \(-0.800699\pi\) |
0.102345 | + | 0.994749i | \(0.467365\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.59189e10 | − | 7.75493e10i | −1.15576 | − | 1.60283i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.47198e10 | + | 4.28160e10i | 0.502298 | + | 0.870006i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.40628e9 | + | 2.43575e9i | −0.0280949 | + | 0.0486618i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.19968e10i | 0.432100i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.88283e9 | 0.0556859 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.40797e9 | + | 3.69965e9i | 0.121725 | + | 0.0702778i | 0.559626 | − | 0.828745i | \(-0.310945\pi\) |
−0.437901 | + | 0.899023i | \(0.644278\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.35849e10 | + | 7.84322e9i | −0.253790 | + | 0.146526i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −9.64954e9 | − | 4.33780e9i | −0.177304 | − | 0.0797041i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.24885e9 | + | 3.89512e9i | 0.0406437 | + | 0.0703970i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.11183e10 | + | 1.92575e10i | −0.197662 | + | 0.342361i | −0.947770 | − | 0.318954i | \(-0.896668\pi\) |
0.750108 | + | 0.661316i | \(0.230002\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 5.31097e10i | − | 0.928834i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.62576e10 | 0.623839 | 0.311920 | − | 0.950109i | \(-0.399028\pi\) | ||||
0.311920 | + | 0.950109i | \(0.399028\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.47154e10 | − | 2.58164e10i | −0.756953 | − | 0.437027i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.75800e10 | − | 1.01498e10i | 0.292818 | − | 0.169058i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.20166e9 | + | 2.04693e10i | −0.150814 | + | 0.335489i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.67859e10 | + | 6.37151e10i | 0.593307 | + | 1.02764i | 0.993783 | + | 0.111331i | \(0.0355114\pi\) |
−0.400476 | + | 0.916307i | \(0.631155\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.34004e10 | − | 4.05306e10i | 0.371425 | − | 0.643328i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 5.49729e10i | − | 0.858770i | −0.903122 | − | 0.429385i | \(-0.858730\pi\) | ||
0.903122 | − | 0.429385i | \(-0.141270\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.72691e10 | 1.49558 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.48753e10 | + | 8.58827e9i | 0.225131 | + | 0.129979i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.64437e10 | + | 3.25878e10i | −0.840900 | + | 0.485494i | −0.857570 | − | 0.514367i | \(-0.828027\pi\) |
0.0166697 | + | 0.999861i | \(0.494694\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.62311e10 | − | 4.77576e10i | 0.971355 | − | 0.700421i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7.87338e9 | − | 1.36371e10i | −0.113682 | − | 0.196903i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.03228e10 | − | 3.52002e10i | 0.288905 | − | 0.500398i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 1.04658e11i | − | 1.46491i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.95190e10 | −0.406849 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.65862e9 | + | 3.84435e9i | 0.0903718 | + | 0.0521762i | 0.544505 | − | 0.838758i | \(-0.316718\pi\) |
−0.454133 | + | 0.890934i | \(0.650051\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.07896e11 | − | 6.22937e10i | 1.44211 | − | 0.832602i | 0.444119 | − | 0.895968i | \(-0.353517\pi\) |
0.997990 | + | 0.0633652i | \(0.0201833\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.61960e9 | − | 1.59600e10i | −0.0213192 | − | 0.210085i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.02215e10 | + | 1.77042e10i | 0.132518 | + | 0.229528i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.47165e10 | − | 6.01307e10i | 0.443316 | − | 0.767846i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 1.90123e10i | − | 0.239143i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.65726e10 | 0.205344 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.15513e9 | + | 5.28572e9i | 0.111750 | + | 0.0645191i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.67647e10 | + | 2.69996e10i | −0.562369 | + | 0.324684i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7.17651e10 | + | 1.47168e10i | −0.850272 | + | 0.174365i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.97811e10 | − | 8.62233e10i | −0.581132 | − | 1.00655i | −0.995346 | − | 0.0963708i | \(-0.969277\pi\) |
0.414213 | − | 0.910180i | \(-0.364057\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.32531e10 | − | 5.75960e10i | 0.382501 | − | 0.662511i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.31735e11i | 1.49319i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.34938e10 | −0.262424 | −0.131212 | − | 0.991354i | \(-0.541887\pi\) | ||||
−0.131212 | + | 0.991354i | \(0.541887\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.86918e10 | + | 1.65652e10i | 0.315840 | + | 0.182351i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.22235e10 | + | 4.16982e10i | −0.783559 | + | 0.452388i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.08186e11 | − | 1.09785e10i | 1.15683 | − | 0.117393i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.26512e10 | − | 2.19126e10i | −0.133340 | − | 0.230952i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.24108e10 | − | 2.14962e10i | 0.128938 | − | 0.223327i | −0.794328 | − | 0.607490i | \(-0.792177\pi\) |
0.923265 | + | 0.384163i | \(0.125510\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.68684e9i | 0.0479991i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.66493e10 | −0.571930 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.47632e11 | − | 8.52355e10i | −1.46942 | − | 0.848373i | −0.470013 | − | 0.882660i | \(-0.655751\pi\) |
−0.999412 | + | 0.0342868i | \(0.989084\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.40294e10 | + | 8.09988e9i | −0.137672 | + | 0.0794849i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 6.71670e9 | + | 9.31483e9i | 0.0649866 | + | 0.0901245i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.03247e10 | − | 3.52033e10i | −0.193898 | − | 0.335842i | 0.752640 | − | 0.658432i | \(-0.228780\pi\) |
−0.946539 | + | 0.322590i | \(0.895447\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.24414e9 | − | 7.35107e9i | 0.0399250 | − | 0.0691522i | −0.845372 | − | 0.534177i | \(-0.820621\pi\) |
0.885297 | + | 0.465025i | \(0.153955\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.86058e10i | 0.265360i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.34616e10 | −0.123148 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.94782e10 | − | 3.43397e10i | −0.536604 | − | 0.309809i | 0.207097 | − | 0.978320i | \(-0.433598\pi\) |
−0.743702 | + | 0.668512i | \(0.766932\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.69129e10 | − | 4.44057e10i | 0.684360 | − | 0.395116i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.44291e11 | + | 6.48638e10i | 1.26630 | + | 0.569243i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.37556e9 | − | 1.45069e10i | −0.0725003 | − | 0.125574i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.69136e10 | − | 2.92952e10i | 0.144415 | − | 0.250134i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 1.43383e11i | − | 1.20766i | −0.797114 | − | 0.603829i | \(-0.793641\pi\) | ||
0.797114 | − | 0.603829i | \(-0.206359\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.30193e10 | 0.274351 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.08413e10 | + | 2.35797e10i | 0.334772 | + | 0.193281i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.30721e11 | + | 7.54720e10i | −1.05713 | + | 0.610333i | −0.924636 | − | 0.380851i | \(-0.875631\pi\) |
−0.132491 | + | 0.991184i | \(0.542298\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.85408e10 | + | 1.52471e11i | −0.546867 | + | 1.21652i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7.45888e9 | + | 1.29192e10i | 0.0587187 | + | 0.101704i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.29322e10 | + | 1.43643e11i | −0.644193 | + | 1.11577i | 0.340294 | + | 0.940319i | \(0.389473\pi\) |
−0.984487 | + | 0.175456i | \(0.943860\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.04035e10i | 0.539630i | 0.962912 | + | 0.269815i | \(0.0869625\pi\) | ||||
−0.962912 | + | 0.269815i | \(0.913037\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.70862e10 | 0.658688 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.34418e10 | + | 1.93076e10i | 0.249614 | + | 0.144115i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.15559e10 | + | 2.97658e10i | −0.379773 | + | 0.219262i | −0.677719 | − | 0.735321i | \(-0.737032\pi\) |
0.297947 | + | 0.954583i | \(0.403698\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.93323e10 | − | 3.55724e10i | 0.358643 | − | 0.258609i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.72009e10 | − | 1.51036e11i | −0.625685 | − | 1.08372i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.14654e11 | − | 1.98587e11i | 0.811986 | − | 1.40640i | −0.0994852 | − | 0.995039i | \(-0.531720\pi\) |
0.911472 | − | 0.411363i | \(-0.134947\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.67318e10i | 0.186865i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.93904e11 | 1.33797 | 0.668986 | − | 0.743275i | \(-0.266728\pi\) | ||||
0.668986 | + | 0.743275i | \(0.266728\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.77090e10 | + | 1.02243e10i | 0.120623 | + | 0.0696418i | 0.559098 | − | 0.829102i | \(-0.311148\pi\) |
−0.438474 | + | 0.898744i | \(0.644481\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.34566e9 | − | 4.81837e9i | 0.0561170 | − | 0.0323992i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.07621e9 | + | 3.03138e10i | 0.0204203 | + | 0.201228i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.39923e10 | + | 1.62799e11i | 0.615988 | + | 1.06692i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4.57495e10 | + | 7.92404e10i | −0.296016 | + | 0.512716i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.06105e10i | 0.451094i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.43159e11 | −0.903030 | −0.451515 | − | 0.892263i | \(-0.649116\pi\) | ||||
−0.451515 | + | 0.892263i | \(0.649116\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.66876e10 | − | 3.27286e10i | −0.353080 | − | 0.203851i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.12411e11 | − | 6.49006e10i | 0.691377 | − | 0.399166i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9.13050e10 | + | 8.10328e10i | −0.554545 | + | 0.492157i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.02211e10 | − | 1.77034e10i | −0.0613047 | − | 0.106183i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.32450e11 | + | 2.29411e11i | −0.784551 | + | 1.35888i | 0.144716 | + | 0.989473i | \(0.453773\pi\) |
−0.929267 | + | 0.369409i | \(0.879560\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 1.18901e9i | − | 0.00695572i | −0.999994 | − | 0.00347786i | \(-0.998893\pi\) | ||
0.999994 | − | 0.00347786i | \(-0.00110704\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −7.55994e9 | −0.0436797 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8.24205e10 | − | 4.75855e10i | −0.470347 | − | 0.271555i | 0.246038 | − | 0.969260i | \(-0.420871\pi\) |
−0.716385 | + | 0.697705i | \(0.754204\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.56733e10 | + | 5.52370e10i | −0.539277 | + | 0.311352i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.39575e10 | + | 2.43118e9i | −0.133388 | + | 0.0135361i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.66756e11 | + | 2.88829e11i | 0.917124 | + | 1.58850i | 0.803762 | + | 0.594951i | \(0.202829\pi\) |
0.113362 | + | 0.993554i | \(0.463838\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.03751e11 | + | 3.52906e11i | −1.10696 | + | 1.91732i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.43760e10i | 0.399183i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.17025e11 | 0.620493 | 0.310246 | − | 0.950656i | \(-0.399588\pi\) | ||||
0.310246 | + | 0.950656i | \(0.399588\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.68769e10 | + | 1.55174e10i | 0.140791 | + | 0.0812855i | 0.568741 | − | 0.822517i | \(-0.307431\pi\) |
−0.427950 | + | 0.903802i | \(0.640764\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −8.17528e10 | + | 4.72000e10i | −0.423106 | + | 0.244280i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.57922e11 | + | 2.19008e11i | 0.807523 | + | 1.11989i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.55186e10 | − | 4.41995e10i | −0.128930 | − | 0.223313i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7.22801e10 | + | 1.25193e11i | −0.360840 | + | 0.624993i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 1.92509e11i | − | 0.949645i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.12193e11 | −1.03436 | −0.517179 | − | 0.855877i | \(-0.673018\pi\) | ||||
−0.517179 | + | 0.855877i | \(0.673018\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.26545e10 | + | 7.30608e9i | 0.0609579 | + | 0.0351940i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9.30441e10 | − | 5.37191e10i | 0.442929 | − | 0.255725i | −0.261910 | − | 0.965092i | \(-0.584352\pi\) |
0.704839 | + | 0.709367i | \(0.251019\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.34850e10 | + | 6.06196e9i | 0.0634412 | + | 0.0285190i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.85074e10 | − | 1.53299e11i | −0.411520 | − | 0.712774i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.88995e10 | − | 1.02017e11i | 0.270663 | − | 0.468802i | −0.698369 | − | 0.715738i | \(-0.746091\pi\) |
0.969032 | + | 0.246936i | \(0.0794238\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.87654e11i | 1.30650i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.48171e11 | −0.665175 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.41742e10 | − | 1.39570e10i | −0.107269 | − | 0.0619320i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.96618e11 | − | 1.71253e11i | 1.30103 | − | 0.751148i | 0.320446 | − | 0.947267i | \(-0.396167\pi\) |
0.980580 | + | 0.196119i | \(0.0628339\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.73596e10 | − | 6.08622e10i | 0.118625 | − | 0.263885i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.77371e11 | − | 3.07215e11i | −0.760227 | − | 1.31675i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.72997e10 | − | 6.46050e10i | 0.158043 | − | 0.273738i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.58439e11i | 1.08255i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.15900e11 | −0.479967 | −0.239984 | − | 0.970777i | \(-0.577142\pi\) | ||||
−0.239984 | + | 0.970777i | \(0.577142\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.87691e10 | + | 5.70244e10i | 0.404390 | + | 0.233474i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.43624e11 | − | 1.40656e11i | 0.986195 | − | 0.569380i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.59351e11 | − | 1.87011e11i | 1.03803 | − | 0.748498i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.71407e10 | − | 1.33612e11i | −0.305280 | − | 0.528761i | 0.672044 | − | 0.740512i | \(-0.265417\pi\) |
−0.977324 | + | 0.211751i | \(0.932083\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.95246e10 | + | 8.57791e10i | −0.193795 | + | 0.335663i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.02073e10i | 0.0781897i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.96558e11 | −0.752084 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.59380e11 | − | 9.20178e10i | −0.603054 | − | 0.348173i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.82639e11 | − | 1.05447e11i | 0.683404 | − | 0.394564i | −0.117732 | − | 0.993045i | \(-0.537562\pi\) |
0.801136 | + | 0.598482i | \(0.204229\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.34893e10 | − | 1.32928e11i | −0.0499172 | − | 0.491898i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.55601e11 | + | 2.69509e11i | 0.569456 | + | 0.986326i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.86938e10 | − | 6.70195e10i | 0.140052 | − | 0.242577i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.28475e10i | 0.0817900i | 0.999163 | + | 0.0408950i | \(0.0130209\pi\) | ||||
−0.999163 | + | 0.0408950i | \(0.986979\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.04604e10 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.82707e10 | + | 1.05486e10i | 0.0639861 | + | 0.0369424i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.90685e11 | − | 2.25562e11i | 1.35335 | − | 0.781358i | 0.364634 | − | 0.931151i | \(-0.381194\pi\) |
0.988717 | + | 0.149793i | \(0.0478609\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.30707e11 | − | 1.47276e11i | −0.447868 | − | 0.504642i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.53014e11 | − | 4.38233e11i | −0.857579 | − | 1.48537i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.06607e10 | − | 1.39708e11i | 0.270448 | − | 0.468430i | −0.698528 | − | 0.715582i | \(-0.746161\pi\) |
0.968977 | + | 0.247152i | \(0.0794948\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.52473e11i | 0.505733i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.11855e11 | −0.695159 | −0.347579 | − | 0.937651i | \(-0.612996\pi\) | ||||
−0.347579 | + | 0.937651i | \(0.612996\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.03129e11 | + | 1.17276e11i | 0.659395 | + | 0.380702i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.24794e11 | + | 7.20499e10i | −0.400785 | + | 0.231393i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.45729e10 | − | 3.50841e9i | 0.109852 | − | 0.0111477i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.80633e11 | − | 4.86071e11i | −0.882224 | − | 1.52806i | −0.848862 | − | 0.528614i | \(-0.822712\pi\) |
−0.0333617 | − | 0.999443i | \(-0.510621\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −9.95354e10 | + | 1.72400e11i | −0.309598 | + | 0.536239i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 6.02882e11i | − | 1.85543i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.12454e11 | −0.646967 | −0.323483 | − | 0.946234i | \(-0.604854\pi\) | ||||
−0.323483 | + | 0.946234i | \(0.604854\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.84938e10 | − | 2.79979e10i | −0.146123 | − | 0.0843642i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.11683e11 | − | 1.79950e11i | 0.929338 | − | 0.536554i | 0.0427362 | − | 0.999086i | \(-0.486393\pi\) |
0.886602 | + | 0.462533i | \(0.153059\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.53277e11 | + | 3.51248e11i | 0.747304 | + | 1.03637i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −7.61343e10 | − | 1.31868e11i | −0.222297 | − | 0.385031i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9.20467e10 | + | 1.59429e11i | −0.265966 | + | 0.460667i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.74232e11i | 0.498222i | 0.968475 | + | 0.249111i | \(0.0801385\pi\) | ||||
−0.968475 | + | 0.249111i | \(0.919862\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.42235e11 | −0.402521 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.44377e11 | + | 1.41091e11i | 0.684450 | + | 0.395168i | 0.801530 | − | 0.597955i | \(-0.204020\pi\) |
−0.117079 | + | 0.993123i | \(0.537353\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.65352e10 | + | 1.53201e10i | −0.0735555 | + | 0.0424673i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −7.58617e10 | − | 3.41024e10i | −0.208132 | − | 0.0935623i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.02458e10 | − | 1.04349e11i | −0.163598 | − | 0.283360i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.93912e10 | + | 1.02869e11i | −0.159631 | + | 0.276490i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.53991e10i | 0.147386i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.72175e11 | 2.03347 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.01252e11 | + | 2.89398e11i | 1.30664 | + | 0.754391i | 0.981535 | − | 0.191285i | \(-0.0612654\pi\) |
0.325110 | + | 0.945676i | \(0.394599\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.40860e11 | − | 1.96796e11i | 0.879566 | − | 0.507818i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.18339e10 | + | 4.85701e10i | −0.0557732 | + | 0.124069i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.60398e11 | − | 2.77818e11i | −0.405608 | − | 0.702534i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.25128e10 | − | 3.89933e10i | 0.0563587 | − | 0.0976162i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 1.44708e11i | − | 0.358640i | −0.983791 | − | 0.179320i | \(-0.942610\pi\) | ||
0.983791 | − | 0.179320i | \(-0.0573898\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.85047e11 | −1.92623 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.40355e10 | − | 1.38769e10i | −0.0583879 | − | 0.0337103i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.74273e11 | − | 2.16087e11i | 0.900174 | − | 0.519716i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.34029e11 | + | 9.66453e10i | −0.319166 | + | 0.230143i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.72810e11 | + | 2.99316e11i | 0.407451 | + | 0.705726i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.04878e11 | + | 1.81654e11i | −0.244844 | + | 0.424083i | −0.962088 | − | 0.272740i | \(-0.912070\pi\) |
0.717244 | + | 0.696823i | \(0.245404\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 5.06101e10i | − | 0.116991i | −0.998288 | − | 0.0584957i | \(-0.981370\pi\) | ||
0.998288 | − | 0.0584957i | \(-0.0186304\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.01384e11 | −0.460961 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.18365e11 | − | 4.14748e11i | −1.62823 | − | 0.940056i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.95105e10 | − | 1.70379e10i | 0.0662352 | − | 0.0382409i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.12264e10 | − | 1.10629e11i | −0.0249521 | − | 0.245885i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.52706e10 | − | 6.10905e10i | −0.0776319 | − | 0.134462i | 0.824596 | − | 0.565722i | \(-0.191403\pi\) |
−0.902228 | + | 0.431260i | \(0.858069\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.72986e11 | + | 2.99621e11i | −0.377061 | + | 0.653089i | −0.990633 | − | 0.136550i | \(-0.956399\pi\) |
0.613572 | + | 0.789639i | \(0.289732\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 8.49062e10i | − | 0.183284i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7.36661e11 | 1.57487 | 0.787436 | − | 0.616396i | \(-0.211408\pi\) | ||||
0.787436 | + | 0.616396i | \(0.211408\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.55082e10 | − | 3.20477e10i | −0.117527 | − | 0.0678545i | 0.440084 | − | 0.897957i | \(-0.354949\pi\) |
−0.557611 | + | 0.830102i | \(0.688282\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.05992e9 | + | 1.18930e9i | −0.00431964 | + | 0.00249394i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.10392e11 | + | 5.38314e11i | 0.229275 | + | 1.11804i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.65480e11 | − | 6.33029e11i | −0.751826 | − | 1.30220i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.09671e10 | − | 1.89957e10i | 0.0223456 | − | 0.0387037i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 3.78990e11i | − | 0.764857i | −0.923985 | − | 0.382428i | \(-0.875088\pi\) | ||
0.923985 | − | 0.382428i | \(-0.124912\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.06847e11 | −0.413489 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.18857e11 | + | 2.41827e11i | 0.829383 | + | 0.478845i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.32331e11 | − | 1.34136e11i | 0.455701 | − | 0.263099i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.26288e11 | − | 1.28155e10i | 0.245374 | − | 0.0249002i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6.91156e10 | − | 1.19712e11i | −0.133029 | − | 0.230412i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.48980e10 | + | 6.04450e10i | −0.0665398 | + | 0.115250i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.34365e11i | 0.631575i | 0.948830 | + | 0.315787i | \(0.102269\pi\) | ||||
−0.948830 | + | 0.315787i | \(0.897731\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.45941e11 | −0.460222 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.45660e11 | − | 1.41832e11i | −0.455419 | − | 0.262937i | 0.254697 | − | 0.967021i | \(-0.418024\pi\) |
−0.710116 | + | 0.704084i | \(0.751358\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.58194e11 | − | 2.64539e11i | 0.841544 | − | 0.485866i | −0.0162447 | − | 0.999868i | \(-0.505171\pi\) |
0.857789 | + | 0.514002i | \(0.171838\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.13951e10 | + | 7.12756e10i | 0.0935211 | + | 0.129697i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 8.74072e10 | + | 1.51394e11i | 0.157581 | + | 0.272938i | 0.933996 | − | 0.357284i | \(-0.116297\pi\) |
−0.776415 | + | 0.630222i | \(0.782964\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.30522e11 | + | 3.99276e11i | −0.411764 | + | 0.713197i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9.87057e10i | 0.174689i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.75541e11 | 1.00925 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.30269e11 | − | 4.21621e11i | −1.26885 | − | 0.732571i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.16629e10 | + | 6.73355e9i | −0.0200793 | + | 0.0115928i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.96290e11 | + | 1.78146e11i | 0.676053 | + | 0.303909i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.49143e11 | + | 4.31528e11i | 0.421162 | + | 0.729475i | 0.996053 | − | 0.0887553i | \(-0.0282889\pi\) |
−0.574891 | + | 0.818230i | \(0.694956\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9.88065e10 | − | 1.71138e11i | 0.165512 | − | 0.286676i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.65089e11i | 0.440035i | 0.975496 | + | 0.220018i | \(0.0706115\pi\) | ||||
−0.975496 | + | 0.220018i | \(0.929389\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.64089e11 | 0.434418 | 0.217209 | − | 0.976125i | \(-0.430305\pi\) | ||||
0.217209 | + | 0.976125i | \(0.430305\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.57162e11 | − | 1.48473e11i | −0.419212 | − | 0.242032i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.00397e12 | + | 5.79640e11i | −1.62190 | + | 0.936406i | −0.635491 | + | 0.772108i | \(0.719202\pi\) |
−0.986411 | + | 0.164297i | \(0.947464\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.74945e11 | − | 3.89170e11i | 0.280088 | − | 0.623063i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.03907e10 | + | 5.26383e10i | 0.0482204 | + | 0.0835201i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.33997e11 | + | 1.09811e12i | −0.996968 | + | 1.72680i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.43390e11i | 1.31443i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −9.33110e10 | −0.144133 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.00603e11 | − | 5.80832e10i | −0.154018 | − | 0.0889225i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.08817e11 | + | 6.28256e10i | −0.165119 | + | 0.0953317i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.01572e10 | + | 1.45349e10i | −0.0303165 | + | 0.0218605i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.19365e11 | − | 8.99566e11i | −0.774244 | − | 1.34103i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.24197e9 | + | 3.88320e9i | −0.00331284 | + | 0.00573801i | −0.867677 | − | 0.497128i | \(-0.834388\pi\) |
0.864364 | + | 0.502866i | \(0.167721\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.91245e11i | 0.426582i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.14100e11 | −1.18196 | −0.590982 | − | 0.806685i | \(-0.701260\pi\) | ||||
−0.590982 | + | 0.806685i | \(0.701260\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.25135e11 | + | 4.18657e11i | 1.04360 | + | 0.602525i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.48124e11 | − | 2.58724e11i | 0.639313 | − | 0.369107i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.35240e11 | + | 1.33270e12i | 0.191262 | + | 1.88475i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.26562e11 | + | 9.12032e11i | 0.738222 | + | 1.27864i | 0.953295 | + | 0.302041i | \(0.0976679\pi\) |
−0.215073 | + | 0.976598i | \(0.568999\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.92290e10 | + | 1.19908e11i | −0.0962166 | + | 0.166652i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.97938e11i | 0.272724i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.05831e11 | −0.144560 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.05397e11 | + | 6.08510e10i | 0.142728 | + | 0.0824041i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −8.96093e11 | + | 5.17360e11i | −1.20307 | + | 0.694592i | −0.961236 | − | 0.275726i | \(-0.911082\pi\) |
−0.241832 | + | 0.970318i | \(0.577748\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.42139e11 | + | 2.80323e11i | 1.12095 | + | 0.373130i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.09238e11 | − | 3.62411e11i | −0.276130 | − | 0.478272i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.42390e11 | + | 7.66242e11i | −0.578840 | + | 1.00258i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 8.31714e11i | − | 1.07899i | −0.841990 | − | 0.539493i | \(-0.818616\pi\) | ||
0.841990 | − | 0.539493i | \(-0.181384\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.72519e11 | −0.350537 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.14487e12 | − | 6.60992e11i | −1.46015 | − | 0.843020i | −0.461135 | − | 0.887330i | \(-0.652558\pi\) |
−0.999018 | + | 0.0443103i | \(0.985891\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.38597e10 | − | 3.68694e10i | 0.0807570 | − | 0.0466251i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.78446e11 | − | 1.81084e10i | 0.223758 | − | 0.0227067i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.20176e11 | + | 3.81357e11i | 0.273760 | + | 0.474167i | 0.969822 | − | 0.243815i | \(-0.0783991\pi\) |
−0.696061 | + | 0.717982i | \(0.745066\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.60086e11 | − | 6.23687e11i | 0.443957 | − | 0.768956i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.34401e11i | 0.286574i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 7.16416e11 | 0.868547 | 0.434274 | − | 0.900781i | \(-0.357005\pi\) | ||||
0.434274 | + | 0.900781i | \(0.357005\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.86924e11 | + | 2.23391e11i | 0.465171 | + | 0.268566i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.78778e11 | − | 1.60953e11i | 0.332362 | − | 0.191889i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.53050e11 | + | 7.66979e11i | 0.653868 | + | 0.906795i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.03449e11 | − | 6.98793e11i | −0.473036 | − | 0.819323i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.58266e10 | + | 2.74125e10i | −0.0184027 | + | 0.0318745i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 1.38710e12i | − | 1.59956i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.18405e12 | 1.35414 | 0.677070 | − | 0.735919i | \(-0.263249\pi\) | ||||
0.677070 | + | 0.735919i | \(0.263249\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.94387e11 | + | 3.43169e11i | 0.674177 | + | 0.389236i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.17425e12 | + | 6.77952e11i | −1.32094 | + | 0.762645i | −0.983879 | − | 0.178838i | \(-0.942766\pi\) |
−0.337061 | + | 0.941483i | \(0.609433\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.06359e12 | − | 4.78118e11i | −1.18665 | − | 0.533438i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −7.07436e10 | − | 1.22531e11i | −0.0782832 | − | 0.135590i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.61277e11 | − | 4.52545e11i | 0.286763 | − | 0.496688i | −0.686272 | − | 0.727345i | \(-0.740754\pi\) |
0.973035 | + | 0.230657i | \(0.0740874\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.61268e11i | 0.175556i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.94444e11 | −0.425902 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.35501e12 | + | 7.82318e11i | 1.45121 | + | 0.837855i | 0.998550 | − | 0.0538289i | \(-0.0171426\pi\) |
0.452658 | + | 0.891684i | \(0.350476\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.37882e11 | − | 3.68281e11i | 0.677634 | − | 0.391232i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.79150e11 | − | 8.43430e11i | 0.399524 | − | 0.888751i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.04269e10 | + | 1.80599e10i | 0.0108986 | + | 0.0188769i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.30845e11 | + | 2.26630e11i | −0.135663 | + | 0.234975i | −0.925851 | − | 0.377890i | \(-0.876650\pi\) |
0.790187 | + | 0.612865i | \(0.209983\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.47411e11i | 0.460161i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.32994e11 | 0.237713 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.55089e12 | − | 8.95405e11i | −1.56964 | − | 0.906231i | −0.996211 | − | 0.0869745i | \(-0.972280\pi\) |
−0.573427 | − | 0.819256i | \(-0.694387\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6.56110e10 | − | 3.78805e10i | 0.0658741 | − | 0.0380324i |
(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 | 84.9.m.b.73.5 | yes | 12 | |
3.2 | odd | 2 | 252.9.z.d.73.2 | 12 | |||
7.5 | odd | 6 | inner | 84.9.m.b.61.5 | ✓ | 12 | |
21.5 | even | 6 | 252.9.z.d.145.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.9.m.b.61.5 | ✓ | 12 | 7.5 | odd | 6 | inner | |
84.9.m.b.73.5 | yes | 12 | 1.1 | even | 1 | trivial | |
252.9.z.d.73.2 | 12 | 3.2 | odd | 2 | |||
252.9.z.d.145.2 | 12 | 21.5 | even | 6 |