Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,9,Mod(73,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.73");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.z (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: | \(102.659409735\) |
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: | \( x^{12} - 3 x^{11} + 148097 x^{10} + 46071824 x^{9} + 21578502553 x^{8} + 3561445462121 x^{7} + \cdots + 45\!\cdots\!96 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{20}\cdot 3^{10}\cdot 7^{4} \) |
Twist minimal: | no (minimal twist has level 84) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 145.2 | ||
Root | \(221.993 + 384.503i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.145 |
Dual form | 252.9.z.d.73.2 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −632.551 | − | 365.204i | −1.01208 | − | 0.584326i | −0.100282 | − | 0.994959i | \(-0.531974\pi\) |
−0.911801 | + | 0.410633i | \(0.865308\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 984.437 | + | 2189.91i | 0.410011 | + | 0.912080i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −6353.95 | − | 11005.4i | −0.433983 | − | 0.751681i | 0.563229 | − | 0.826301i | \(-0.309559\pi\) |
−0.997212 | + | 0.0746198i | \(0.976226\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 21176.4i | 0.741444i | 0.928744 | + | 0.370722i | \(0.120890\pi\) | ||||
−0.928744 | + | 0.370722i | \(0.879110\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 82551.9 | − | 47661.3i | 0.988397 | − | 0.570651i | 0.0836020 | − | 0.996499i | \(-0.473358\pi\) |
0.904795 | + | 0.425848i | \(0.140024\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −133336. | − | 76981.8i | −1.02314 | − | 0.590709i | −0.108126 | − | 0.994137i | \(-0.534485\pi\) |
−0.915011 | + | 0.403428i | \(0.867818\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 47111.5 | − | 81599.5i | 0.168351 | − | 0.291593i | −0.769489 | − | 0.638660i | \(-0.779489\pi\) |
0.937840 | + | 0.347067i | \(0.112822\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 71435.0 | + | 123729.i | 0.182874 | + | 0.316746i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −541664. | −0.765840 | −0.382920 | − | 0.923782i | \(-0.625081\pi\) | ||||
−0.382920 | + | 0.923782i | \(0.625081\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −185730. | + | 107231.i | −0.201110 | + | 0.116111i | −0.597173 | − | 0.802112i | \(-0.703710\pi\) |
0.396063 | + | 0.918223i | \(0.370376\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 177055. | − | 1.74475e6i | 0.117987 | − | 1.16268i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −370376. | + | 641510.i | −0.197622 | + | 0.342292i | −0.947757 | − | 0.318993i | \(-0.896655\pi\) |
0.750135 | + | 0.661285i | \(0.229989\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 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 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.13230e6 | − | 4.11784e6i | −1.46163 | − | 0.843874i | −0.462546 | − | 0.886595i | \(-0.653064\pi\) |
−0.999087 | + | 0.0427209i | \(0.986397\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.82657e6 | + | 4.31165e6i | −0.663782 | + | 0.747926i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −659083. | − | 1.14157e6i | −0.0835289 | − | 0.144676i | 0.821235 | − | 0.570591i | \(-0.193286\pi\) |
−0.904763 | + | 0.425915i | \(0.859952\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.28194e6i | 1.01435i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.52865e6 | − | 4.34667e6i | 0.621311 | − | 0.358714i | −0.156068 | − | 0.987746i | \(-0.549882\pi\) |
0.777379 | + | 0.629032i | \(0.216549\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.31192e7 | + | 7.57439e6i | 0.947521 | + | 0.547052i | 0.892310 | − | 0.451423i | \(-0.149083\pi\) |
0.0552112 | + | 0.998475i | \(0.482417\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7.73369e6 | − | 1.33951e7i | 0.433245 | − | 0.750402i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.99100e7 | + | 3.44851e7i | 0.988033 | + | 1.71132i | 0.627596 | + | 0.778539i | \(0.284039\pi\) |
0.360436 | + | 0.932784i | \(0.382628\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.34713e6 | 0.367828 | 0.183914 | − | 0.982942i | \(-0.441123\pi\) | ||||
0.183914 | + | 0.982942i | \(0.441123\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.94520e7 | − | 1.70041e7i | 1.03711 | − | 0.598774i | 0.118094 | − | 0.993002i | \(-0.462321\pi\) |
0.919012 | + | 0.394229i | \(0.128988\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.78456e7 | − | 2.47486e7i | 0.507656 | − | 0.704025i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.26450e7 | − | 3.92223e7i | 0.581385 | − | 1.00699i | −0.413931 | − | 0.910308i | \(-0.635844\pi\) |
0.995316 | − | 0.0966799i | \(-0.0308223\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 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 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.09902e7 | + | 6.34517e6i | 0.175164 | + | 0.101131i | 0.585018 | − | 0.811020i | \(-0.301087\pi\) |
−0.409855 | + | 0.912151i | \(0.634421\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.63742e7 | + | 2.08468e7i | −0.676256 | + | 0.304000i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.62280e7 | + | 9.73898e7i | 0.690333 | + | 1.19569i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 6.15780e6i | − | 0.0695566i | −0.999395 | − | 0.0347783i | \(-0.988927\pi\) | ||
0.999395 | − | 0.0347783i | \(-0.0110725\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.15329e8 | + | 6.65855e7i | −1.10829 | + | 0.639874i | −0.938387 | − | 0.345587i | \(-0.887680\pi\) |
−0.169907 | + | 0.985460i | \(0.554347\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.81925e7 | + | 2.78240e7i | 0.428184 | + | 0.247212i | 0.698573 | − | 0.715539i | \(-0.253819\pi\) |
−0.270389 | + | 0.962751i | \(0.587152\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.23667e6 | + | 1.25343e7i | −0.0552082 | + | 0.0956234i | −0.892309 | − | 0.451426i | \(-0.850916\pi\) |
0.837101 | + | 0.547049i | \(0.184249\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.01793e7 | − | 1.56195e8i | −0.638853 | − | 1.10653i | −0.985685 | − | 0.168598i | \(-0.946076\pi\) |
0.346832 | − | 0.937927i | \(-0.387257\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.21791e7 | 0.136028 | 0.0680142 | − | 0.997684i | \(-0.478334\pi\) | ||||
0.0680142 | + | 0.997684i | \(0.478334\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.96009e7 | + | 3.44106e7i | −0.340770 | + | 0.196744i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 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 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 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 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.83164e8 | + | 2.78955e8i | 1.64062 | + | 0.947215i | 0.980612 | + | 0.195960i | \(0.0627823\pi\) |
0.660012 | + | 0.751255i | \(0.270551\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.73216e7 | − | 3.67778e8i | 0.119276 | − | 1.17538i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.96914e8 | + | 3.41064e8i | 0.558977 | + | 0.968176i | 0.997582 | + | 0.0694962i | \(0.0221392\pi\) |
−0.438606 | + | 0.898680i | \(0.644528\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.85677e8i | 1.30103i | 0.759492 | + | 0.650516i | \(0.225447\pi\) | ||||
−0.759492 | + | 0.650516i | \(0.774553\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 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 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.60563e8 | + | 2.78103e8i | −0.325762 | + | 0.564236i | −0.981666 | − | 0.190608i | \(-0.938954\pi\) |
0.655905 | + | 0.754844i | \(0.272287\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.12702e8 | + | 7.14822e8i | 0.793833 | + | 1.37496i | 0.923577 | + | 0.383412i | \(0.125251\pi\) |
−0.129744 | + | 0.991547i | \(0.541416\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.56645e8 | 0.271387 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.15549e8 | − | 5.28592e8i | 1.50689 | − | 0.870006i | 0.506926 | − | 0.861989i | \(-0.330782\pi\) |
0.999968 | − | 0.00801653i | \(-0.00255177\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.25074e8 | + | 2.28402e7i | 0.334982 | + | 0.0339935i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.67831e8 | + | 9.83512e8i | −0.804394 | + | 1.39325i | 0.112306 | + | 0.993674i | \(0.464176\pi\) |
−0.916699 | + | 0.399577i | \(0.869157\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 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 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.46649e8 | + | 3.15608e8i | 0.610273 | + | 0.352341i | 0.773072 | − | 0.634318i | \(-0.218719\pi\) |
−0.162799 | + | 0.986659i | \(0.552052\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.00632e8 | + | 2.78239e8i | −0.213918 | + | 0.296665i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.77342e8 | + | 9.99986e8i | 0.562369 | + | 0.974052i | 0.997289 | + | 0.0735826i | \(0.0234433\pi\) |
−0.434920 | + | 0.900469i | \(0.643223\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.42212e9i | 1.32502i | 0.749052 | + | 0.662511i | \(0.230509\pi\) | ||||
−0.749052 | + | 0.662511i | \(0.769491\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 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 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.05844e8 | + | 5.29737e8i | −0.229809 | + | 0.398040i | −0.957751 | − | 0.287598i | \(-0.907143\pi\) |
0.727943 | + | 0.685638i | \(0.240477\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.49542e8 | + | 1.64465e9i | 0.684360 | + | 1.18535i | 0.973637 | + | 0.228101i | \(0.0732518\pi\) |
−0.289277 | + | 0.957245i | \(0.593415\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.00843e9 | −0.669544 | −0.334772 | − | 0.942299i | \(-0.608659\pi\) | ||||
−0.334772 | + | 0.942299i | \(0.608659\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.76255e8 | − | 1.59496e8i | 0.176156 | − | 0.101704i | −0.409329 | − | 0.912387i | \(-0.634237\pi\) |
0.585485 | + | 0.810683i | \(0.300904\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 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 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 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 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 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 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.00929e9 | + | 1.74815e9i | 0.423106 | + | 0.732840i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 3.09118e9i | − | 1.24999i | −0.780630 | − | 0.624993i | \(-0.785102\pi\) | ||
0.780630 | − | 0.624993i | \(-0.214898\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.27805e9 | − | 1.89258e9i | 1.23456 | − | 0.712774i | 0.266583 | − | 0.963812i | \(-0.414105\pi\) |
0.967977 | + | 0.251038i | \(0.0807719\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.74391e9 | − | 1.58420e9i | −0.997763 | − | 0.576059i | −0.0901773 | − | 0.995926i | \(-0.528743\pi\) |
−0.907586 | + | 0.419867i | \(0.862077\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.76314e9 | + | 4.78590e9i | −0.937518 | + | 1.62383i | −0.167437 | + | 0.985883i | \(0.553549\pi\) |
−0.770081 | + | 0.637946i | \(0.779784\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.00770e9 | + | 5.20949e9i | 0.986195 | + | 1.70814i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.93530e9 | 1.20611 | 0.603054 | − | 0.797701i | \(-0.293951\pi\) | ||||
0.603054 | + | 0.797701i | \(0.293951\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.76301e9 | − | 3.32727e9i | 1.70837 | − | 0.986326i | 0.771780 | − | 0.635889i | \(-0.219367\pi\) |
0.936586 | − | 0.350437i | \(-0.113967\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 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 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 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 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.63398e9 | + | 1.52073e9i | 0.603782 | + | 0.348593i | 0.770528 | − | 0.637406i | \(-0.219993\pi\) |
−0.166746 | + | 0.986000i | \(0.553326\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.76946e9 | − | 1.79562e8i | −0.393225 | − | 0.0399039i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.20815e9 | − | 7.28873e9i | −0.879566 | − | 1.52345i | −0.851818 | − | 0.523838i | \(-0.824500\pi\) |
−0.0277486 | − | 0.999615i | \(-0.508834\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.62798e8i | 0.195232i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.40038e9 | + | 3.69526e9i | −1.22235 | + | 0.705726i | −0.965419 | − | 0.260703i | \(-0.916046\pi\) |
−0.256934 | + | 0.966429i | \(0.582712\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.72934e9 | − | 2.15314e9i | −0.691441 | − | 0.399204i | 0.112711 | − | 0.993628i | \(-0.464047\pi\) |
−0.804152 | + | 0.594424i | \(0.797380\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 9.07789e8 | − | 1.57234e9i | 0.158728 | − | 0.274925i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.54312e7 | − | 4.40481e7i | −0.00431964 | − | 0.00748183i | 0.863858 | − | 0.503736i | \(-0.168042\pi\) |
−0.868177 | + | 0.496254i | \(0.834708\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.03421e10 | −1.65877 | −0.829383 | − | 0.558680i | \(-0.811308\pi\) | ||||
−0.829383 | + | 0.558680i | \(0.811308\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.55984e9 | + | 1.47792e9i | −0.399086 | + | 0.230412i | −0.686090 | − | 0.727517i | \(-0.740674\pi\) |
0.287003 | + | 0.957930i | \(0.407341\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 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 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 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 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 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 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.53239e9 | − | 9.58238e9i | −0.639313 | − | 1.10732i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 2.96070e9i | − | 0.333304i | −0.986016 | − | 0.166652i | \(-0.946704\pi\) | ||
0.986016 | − | 0.166652i | \(-0.0532956\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.74956e9 | − | 4.47421e9i | 0.828391 | − | 0.478272i | −0.0249101 | − | 0.999690i | \(-0.507930\pi\) |
0.853302 | + | 0.521418i | \(0.174597\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.04664e9 | − | 2.91368e9i | −0.525806 | − | 0.303574i | 0.213501 | − | 0.976943i | \(-0.431513\pi\) |
−0.739307 | + | 0.673369i | \(0.764847\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.50614e9 | + | 4.34076e9i | −0.248181 | + | 0.429861i | −0.963021 | − | 0.269426i | \(-0.913166\pi\) |
0.714840 | + | 0.699288i | \(0.246499\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.44171e9 | + | 5.96121e9i | 0.332362 | + | 0.575667i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.46762e10 | −1.34835 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.62013e9 | + | 1.51273e9i | −0.234850 | + | 0.135590i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.99637e9 | − | 1.96728e10i | 0.170395 | − | 1.67912i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.78357e9 | − | 8.28539e9i | 0.398511 | − | 0.690242i | −0.595031 | − | 0.803703i | \(-0.702860\pi\) |
0.993542 | + | 0.113461i | \(0.0361937\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 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 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 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 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.04233e10 | − | 1.80536e10i | −0.718928 | − | 1.24522i | −0.961425 | − | 0.275068i | \(-0.911300\pi\) |
0.242497 | − | 0.970152i | \(-0.422034\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.91490e10i | 1.96482i | 0.186745 | + | 0.982409i | \(0.440206\pi\) | ||||
−0.186745 | + | 0.982409i | \(0.559794\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9.78829e8 | + | 5.65127e8i | −0.0630388 | + | 0.0363955i | −0.531188 | − | 0.847254i | \(-0.678254\pi\) |
0.468149 | + | 0.883649i | \(0.344921\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.91254e9 | − | 3.41361e9i | −0.372272 | − | 0.214932i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.49405e9 | + | 9.51597e9i | −0.330761 | + | 0.572896i | −0.982661 | − | 0.185409i | \(-0.940639\pi\) |
0.651900 | + | 0.758305i | \(0.273972\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.36060e9 | + | 5.82073e9i | 0.197874 | + | 0.342727i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.48399e10 | −1.39952 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.47539e9 | + | 1.42917e9i | −0.136452 | + | 0.0787805i | −0.566672 | − | 0.823944i | \(-0.691769\pi\) |
0.430220 | + | 0.902724i | \(0.358436\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.85109e9 | − | 2.56713e9i | 0.0977086 | − | 0.135504i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.91785e9 | − | 1.54462e10i | 0.460707 | − | 0.797968i | −0.538289 | − | 0.842760i | \(-0.680929\pi\) |
0.998996 | + | 0.0447919i | \(0.0142625\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 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 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.90349e10 | + | 1.09898e10i | 0.884619 | + | 0.510735i | 0.872179 | − | 0.489187i | \(-0.162707\pi\) |
0.0124407 | + | 0.999923i | \(0.496040\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.03266e10 | + | 9.13749e9i | −0.925170 | + | 0.415895i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.09555e10 | + | 1.89755e10i | 0.478448 | + | 0.828695i | 0.999695 | − | 0.0247103i | \(-0.00786634\pi\) |
−0.521247 | + | 0.853406i | \(0.674533\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 8.98159e9i | − | 0.384279i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.86482e10 | + | 1.65401e10i | −1.17682 | + | 0.679437i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.10594e10 | − | 2.37057e10i | −1.65292 | − | 0.954312i | −0.975865 | − | 0.218376i | \(-0.929924\pi\) |
−0.677052 | − | 0.735936i | \(-0.736743\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.47336e8 | + | 1.12122e9i | −0.0250353 | + | 0.0433623i | −0.878272 | − | 0.478162i | \(-0.841303\pi\) |
0.853236 | + | 0.521524i | \(0.174636\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.27076e9 | − | 3.93308e9i | −0.0860898 | − | 0.149112i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.41340e9 | 0.343059 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.05517e10 | − | 6.09204e9i | 0.377077 | − | 0.217705i | −0.299469 | − | 0.954106i | \(-0.596809\pi\) |
0.676546 | + | 0.736401i | \(0.263476\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 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 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 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 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 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 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.99404e10 | − | 3.45377e10i | −0.577862 | − | 1.00089i | −0.995724 | − | 0.0923761i | \(-0.970554\pi\) |
0.417862 | − | 0.908510i | \(-0.362780\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 3.77901e10i | − | 1.07505i | −0.843249 | − | 0.537523i | \(-0.819360\pi\) | ||
0.843249 | − | 0.537523i | \(-0.180640\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.25634e10 | + | 7.25345e9i | −0.344493 | + | 0.198893i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.02545e9 | + | 4.05614e9i | 0.189154 | + | 0.109208i | 0.591587 | − | 0.806242i | \(-0.298502\pi\) |
−0.402432 | + | 0.915450i | \(0.631835\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.85877e10 | + | 4.95154e10i | −0.742274 | + | 1.28566i | 0.209183 | + | 0.977876i | \(0.432919\pi\) |
−0.951457 | + | 0.307780i | \(0.900414\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.63456e9 | − | 8.02729e9i | −0.118187 | − | 0.204705i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.27811e10 | 1.54470 | 0.772349 | − | 0.635199i | \(-0.219082\pi\) | ||||
0.772349 | + | 0.635199i | \(0.219082\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.61279e9 | − | 4.97259e9i | 0.208179 | − | 0.120192i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.69474e10 | + | 3.74937e9i | 0.862062 | + | 0.0874809i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.34859e9 | + | 1.44602e10i | −0.191403 | + | 0.331519i | −0.945715 | − | 0.324996i | \(-0.894637\pi\) |
0.754313 | + | 0.656515i | \(0.227970\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 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 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.36726e10 | + | 1.94409e10i | 0.707960 | + | 0.408741i | 0.810305 | − | 0.586008i | \(-0.199301\pi\) |
−0.102345 | + | 0.994749i | \(0.532635\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.59189e10 | + | 7.75493e10i | −1.15576 | + | 1.60283i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.40628e9 | + | 2.43575e9i | 0.0280949 | + | 0.0486618i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 2.19968e10i | − | 0.432100i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.40797e9 | + | 3.69965e9i | −0.121725 | + | 0.0702778i | −0.559626 | − | 0.828745i | \(-0.689055\pi\) |
0.437901 | + | 0.899023i | \(0.355722\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.35849e10 | − | 7.84322e9i | −0.253790 | − | 0.146526i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.24885e9 | + | 3.89512e9i | −0.0406437 | + | 0.0703970i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.11183e10 | − | 1.92575e10i | −0.197662 | − | 0.342361i | 0.750108 | − | 0.661316i | \(-0.230002\pi\) |
−0.947770 | + | 0.318954i | \(0.896668\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.62576e10 | −0.623839 | −0.311920 | − | 0.950109i | \(-0.600972\pi\) | ||||
−0.311920 | + | 0.950109i | \(0.600972\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.47154e10 | + | 2.58164e10i | −0.756953 | + | 0.437027i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.20166e9 | + | 2.04693e10i | 0.150814 | + | 0.335489i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.67859e10 | − | 6.37151e10i | 0.593307 | − | 1.02764i | −0.400476 | − | 0.916307i | \(-0.631155\pi\) |
0.993783 | − | 0.111331i | \(-0.0355114\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 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 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.64437e10 | + | 3.25878e10i | 0.840900 | + | 0.485494i | 0.857570 | − | 0.514367i | \(-0.171973\pi\) |
−0.0166697 | + | 0.999861i | \(0.505306\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.62311e10 | + | 4.77576e10i | 0.971355 | + | 0.700421i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.03228e10 | − | 3.52002e10i | −0.288905 | − | 0.500398i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.04658e11i | 1.46491i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.65862e9 | + | 3.84435e9i | −0.0903718 | + | 0.0521762i | −0.544505 | − | 0.838758i | \(-0.683282\pi\) |
0.454133 | + | 0.890934i | \(0.349949\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.07896e11 | + | 6.22937e10i | 1.44211 | + | 0.832602i | 0.997990 | − | 0.0633652i | \(-0.0201833\pi\) |
0.444119 | + | 0.895968i | \(0.353517\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 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 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.65726e10 | −0.205344 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.15513e9 | − | 5.28572e9i | 0.111750 | − | 0.0645191i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7.17651e10 | + | 1.47168e10i | 0.850272 | + | 0.174365i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.97811e10 | + | 8.62233e10i | −0.581132 | + | 1.00655i | 0.414213 | + | 0.910180i | \(0.364057\pi\) |
−0.995346 | + | 0.0963708i | \(0.969277\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 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 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 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 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.24108e10 | − | 2.14962e10i | −0.128938 | − | 0.223327i | 0.794328 | − | 0.607490i | \(-0.207823\pi\) |
−0.923265 | + | 0.384163i | \(0.874490\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 4.68684e9i | − | 0.0479991i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.47632e11 | − | 8.52355e10i | 1.46942 | − | 0.848373i | 0.470013 | − | 0.882660i | \(-0.344249\pi\) |
0.999412 | + | 0.0342868i | \(0.0109160\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.40294e10 | − | 8.09988e9i | −0.137672 | − | 0.0794849i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.03247e10 | − | 3.52033e10i | 0.193898 | − | 0.335842i | −0.752640 | − | 0.658432i | \(-0.771220\pi\) |
0.946539 | + | 0.322590i | \(0.104553\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.24414e9 | + | 7.35107e9i | 0.0399250 | + | 0.0691522i | 0.885297 | − | 0.465025i | \(-0.153955\pi\) |
−0.845372 | + | 0.534177i | \(0.820621\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.34616e10 | 0.123148 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.94782e10 | + | 3.43397e10i | −0.536604 | + | 0.309809i | −0.743702 | − | 0.668512i | \(-0.766932\pi\) |
0.207097 | + | 0.978320i | \(0.433598\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 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 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 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 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.30721e11 | + | 7.54720e10i | 1.05713 | + | 0.610333i | 0.924636 | − | 0.380851i | \(-0.124369\pi\) |
0.132491 | + | 0.991184i | \(0.457702\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.85408e10 | − | 1.52471e11i | −0.546867 | − | 1.21652i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.29322e10 | + | 1.43643e11i | 0.644193 | + | 1.11577i | 0.984487 | + | 0.175456i | \(0.0561399\pi\) |
−0.340294 | + | 0.940319i | \(0.610527\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 7.04035e10i | − | 0.539630i | −0.962912 | − | 0.269815i | \(-0.913037\pi\) | ||
0.962912 | − | 0.269815i | \(-0.0869625\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.34418e10 | + | 1.93076e10i | −0.249614 | + | 0.144115i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.15559e10 | − | 2.97658e10i | −0.379773 | − | 0.219262i | 0.297947 | − | 0.954583i | \(-0.403698\pi\) |
−0.677719 | + | 0.735321i | \(0.737032\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.72009e10 | − | 1.51036e11i | 0.625685 | − | 1.08372i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.14654e11 | + | 1.98587e11i | 0.811986 | + | 1.40640i | 0.911472 | + | 0.411363i | \(0.134947\pi\) |
−0.0994852 | + | 0.995039i | \(0.531720\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.93904e11 | −1.33797 | −0.668986 | − | 0.743275i | \(-0.733272\pi\) | ||||
−0.668986 | + | 0.743275i | \(0.733272\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.77090e10 | − | 1.02243e10i | 0.120623 | − | 0.0696418i | −0.438474 | − | 0.898744i | \(-0.644481\pi\) |
0.559098 | + | 0.829102i | \(0.311148\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 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 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 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 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 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 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.32450e11 | + | 2.29411e11i | 0.784551 | + | 1.35888i | 0.929267 | + | 0.369409i | \(0.120440\pi\) |
−0.144716 | + | 0.989473i | \(0.546227\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.18901e9i | 0.00695572i | 0.999994 | + | 0.00347786i | \(0.00110704\pi\) | ||||
−0.999994 | + | 0.00347786i | \(0.998893\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.24205e10 | − | 4.75855e10i | 0.470347 | − | 0.271555i | −0.246038 | − | 0.969260i | \(-0.579129\pi\) |
0.716385 | + | 0.697705i | \(0.245796\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.56733e10 | − | 5.52370e10i | −0.539277 | − | 0.311352i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.66756e11 | + | 2.88829e11i | −0.917124 | + | 1.58850i | −0.113362 | + | 0.993554i | \(0.536162\pi\) |
−0.803762 | + | 0.594951i | \(0.797171\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.03751e11 | − | 3.52906e11i | −1.10696 | − | 1.91732i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.17025e11 | −0.620493 | −0.310246 | − | 0.950656i | \(-0.600412\pi\) | ||||
−0.310246 | + | 0.950656i | \(0.600412\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.68769e10 | − | 1.55174e10i | 0.140791 | − | 0.0812855i | −0.427950 | − | 0.903802i | \(-0.640764\pi\) |
0.568741 | + | 0.822517i | \(0.307431\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 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 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 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 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9.30441e10 | − | 5.37191e10i | −0.442929 | − | 0.255725i | 0.261910 | − | 0.965092i | \(-0.415648\pi\) |
−0.704839 | + | 0.709367i | \(0.748981\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.34850e10 | − | 6.06196e9i | 0.0634412 | − | 0.0285190i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.88995e10 | − | 1.02017e11i | −0.270663 | − | 0.468802i | 0.698369 | − | 0.715738i | \(-0.253909\pi\) |
−0.969032 | + | 0.246936i | \(0.920576\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 2.87654e11i | − | 1.30650i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.41742e10 | − | 1.39570e10i | 0.107269 | − | 0.0619320i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.96618e11 | + | 1.71253e11i | 1.30103 | + | 0.751148i | 0.980580 | − | 0.196119i | \(-0.0628339\pi\) |
0.320446 | + | 0.947267i | \(0.396167\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 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 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.15900e11 | 0.479967 | 0.239984 | − | 0.970777i | \(-0.422858\pi\) | ||||
0.239984 | + | 0.970777i | \(0.422858\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.87691e10 | − | 5.70244e10i | 0.404390 | − | 0.233474i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.59351e11 | − | 1.87011e11i | −1.03803 | − | 0.748498i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.71407e10 | + | 1.33612e11i | −0.305280 | + | 0.528761i | −0.977324 | − | 0.211751i | \(-0.932083\pi\) |
0.672044 | + | 0.740512i | \(0.265417\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.02073e10i | 0.0781897i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.96558e11 | −0.752084 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.82639e11 | − | 1.05447e11i | −0.683404 | − | 0.394564i | 0.117732 | − | 0.993045i | \(-0.462438\pi\) |
−0.801136 | + | 0.598482i | \(0.795771\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.34893e10 | + | 1.32928e11i | −0.0499172 | + | 0.491898i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.86938e10 | − | 6.70195e10i | −0.140052 | − | 0.242577i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 2.28475e10i | − | 0.0817900i | −0.999163 | − | 0.0408950i | \(-0.986979\pi\) | ||
0.999163 | − | 0.0408950i | \(-0.0130209\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.82707e10 | + | 1.05486e10i | −0.0639861 | + | 0.0369424i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.90685e11 | + | 2.25562e11i | 1.35335 | + | 0.781358i | 0.988717 | − | 0.149793i | \(-0.0478609\pi\) |
0.364634 | + | 0.931151i | \(0.381194\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.53014e11 | − | 4.38233e11i | 0.857579 | − | 1.48537i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.06607e10 | + | 1.39708e11i | 0.270448 | + | 0.468430i | 0.968977 | − | 0.247152i | \(-0.0794948\pi\) |
−0.698528 | + | 0.715582i | \(0.746161\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.11855e11 | 0.695159 | 0.347579 | − | 0.937651i | \(-0.387004\pi\) | ||||
0.347579 | + | 0.937651i | \(0.387004\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.03129e11 | − | 1.17276e11i | 0.659395 | − | 0.380702i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.45729e10 | − | 3.50841e9i | −0.109852 | − | 0.0111477i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.80633e11 | + | 4.86071e11i | −0.882224 | + | 1.52806i | −0.0333617 | + | 0.999443i | \(0.510621\pi\) |
−0.848862 | + | 0.528614i | \(0.822712\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 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 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.11683e11 | − | 1.79950e11i | −0.929338 | − | 0.536554i | −0.0427362 | − | 0.999086i | \(-0.513607\pi\) |
−0.886602 | + | 0.462533i | \(0.846941\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.53277e11 | − | 3.51248e11i | 0.747304 | − | 1.03637i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.20467e10 | + | 1.59429e11i | 0.265966 | + | 0.460667i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 1.74232e11i | − | 0.498222i | −0.968475 | − | 0.249111i | \(-0.919862\pi\) | ||
0.968475 | − | 0.249111i | \(-0.0801385\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.44377e11 | + | 1.41091e11i | −0.684450 | + | 0.395168i | −0.801530 | − | 0.597955i | \(-0.795980\pi\) |
0.117079 | + | 0.993123i | \(0.462647\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.65352e10 | − | 1.53201e10i | −0.0735555 | − | 0.0424673i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 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 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.72175e11 | −2.03347 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.01252e11 | − | 2.89398e11i | 1.30664 | − | 0.754391i | 0.325110 | − | 0.945676i | \(-0.394599\pi\) |
0.981535 | + | 0.191285i | \(0.0612654\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 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 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 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 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 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 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.04878e11 | + | 1.81654e11i | 0.244844 | + | 0.424083i | 0.962088 | − | 0.272740i | \(-0.0879298\pi\) |
−0.717244 | + | 0.696823i | \(0.754596\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.06101e10i | 0.116991i | 0.998288 | + | 0.0584957i | \(0.0186304\pi\) | ||||
−0.998288 | + | 0.0584957i | \(0.981370\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 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 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.52706e10 | − | 6.10905e10i | 0.0776319 | − | 0.134462i | −0.824596 | − | 0.565722i | \(-0.808597\pi\) |
0.902228 | + | 0.431260i | \(0.141931\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.72986e11 | − | 2.99621e11i | −0.377061 | − | 0.653089i | 0.613572 | − | 0.789639i | \(-0.289732\pi\) |
−0.990633 | + | 0.136550i | \(0.956399\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −7.36661e11 | −1.57487 | −0.787436 | − | 0.616396i | \(-0.788592\pi\) | ||||
−0.787436 | + | 0.616396i | \(0.788592\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.55082e10 | + | 3.20477e10i | −0.117527 | + | 0.0678545i | −0.557611 | − | 0.830102i | \(-0.688282\pi\) |
0.440084 | + | 0.897957i | \(0.354949\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 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 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 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 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 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 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.48980e10 | + | 6.04450e10i | 0.0665398 | + | 0.115250i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 3.34365e11i | − | 0.631575i | −0.948830 | − | 0.315787i | \(-0.897731\pi\) | ||
0.948830 | − | 0.315787i | \(-0.102269\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.45660e11 | − | 1.41832e11i | 0.455419 | − | 0.262937i | −0.254697 | − | 0.967021i | \(-0.581976\pi\) |
0.710116 | + | 0.704084i | \(0.248642\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.58194e11 | + | 2.64539e11i | 0.841544 | + | 0.485866i | 0.857789 | − | 0.514002i | \(-0.171838\pi\) |
−0.0162447 | + | 0.999868i | \(0.505171\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −8.74072e10 | + | 1.51394e11i | −0.157581 | + | 0.272938i | −0.933996 | − | 0.357284i | \(-0.883703\pi\) |
0.776415 | + | 0.630222i | \(0.217036\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.30522e11 | − | 3.99276e11i | −0.411764 | − | 0.713197i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.75541e11 | −1.00925 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.30269e11 | + | 4.21621e11i | −1.26885 | + | 0.732571i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.96290e11 | + | 1.78146e11i | −0.676053 | + | 0.303909i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.49143e11 | − | 4.31528e11i | 0.421162 | − | 0.729475i | −0.574891 | − | 0.818230i | \(-0.694956\pi\) |
0.996053 | + | 0.0887553i | \(0.0282889\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 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 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.00397e12 | + | 5.79640e11i | 1.62190 | + | 0.936406i | 0.986411 | + | 0.164297i | \(0.0525357\pi\) |
0.635491 | + | 0.772108i | \(0.280798\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.74945e11 | + | 3.89170e11i | 0.280088 | + | 0.623063i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.33997e11 | + | 1.09811e12i | 0.996968 | + | 1.72680i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 8.43390e11i | − | 1.31443i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 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 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.19365e11 | − | 8.99566e11i | 0.774244 | − | 1.34103i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.24197e9 | − | 3.88320e9i | −0.00331284 | − | 0.00573801i | 0.864364 | − | 0.502866i | \(-0.167721\pi\) |
−0.867677 | + | 0.497128i | \(0.834388\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.14100e11 | 1.18196 | 0.590982 | − | 0.806685i | \(-0.298740\pi\) | ||||
0.590982 | + | 0.806685i | \(0.298740\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.25135e11 | − | 4.18657e11i | 1.04360 | − | 0.602525i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.35240e11 | + | 1.33270e12i | −0.191262 | + | 1.88475i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.26562e11 | − | 9.12032e11i | 0.738222 | − | 1.27864i | −0.215073 | − | 0.976598i | \(-0.568999\pi\) |
0.953295 | − | 0.302041i | \(-0.0976679\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.97938e11i | 0.272724i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.05831e11 | −0.144560 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8.96093e11 | + | 5.17360e11i | 1.20307 | + | 0.694592i | 0.961236 | − | 0.275726i | \(-0.0889182\pi\) |
0.241832 | + | 0.970318i | \(0.422252\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.42139e11 | − | 2.80323e11i | 1.12095 | − | 0.373130i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.42390e11 | + | 7.66242e11i | 0.578840 | + | 1.00258i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.31714e11i | 1.07899i | 0.841990 | + | 0.539493i | \(0.181384\pi\) | ||||
−0.841990 | + | 0.539493i | \(0.818616\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.14487e12 | − | 6.60992e11i | 1.46015 | − | 0.843020i | 0.461135 | − | 0.887330i | \(-0.347442\pi\) |
0.999018 | + | 0.0443103i | \(0.0141090\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.38597e10 | + | 3.68694e10i | 0.0807570 | + | 0.0466251i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.20176e11 | + | 3.81357e11i | −0.273760 | + | 0.474167i | −0.969822 | − | 0.243815i | \(-0.921601\pi\) |
0.696061 | + | 0.717982i | \(0.254934\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.60086e11 | + | 6.23687e11i | 0.443957 | + | 0.768956i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −7.16416e11 | −0.868547 | −0.434274 | − | 0.900781i | \(-0.642995\pi\) | ||||
−0.434274 | + | 0.900781i | \(0.642995\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.86924e11 | − | 2.23391e11i | 0.465171 | − | 0.268566i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 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 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 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 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.17425e12 | + | 6.77952e11i | 1.32094 | + | 0.762645i | 0.983879 | − | 0.178838i | \(-0.0572338\pi\) |
0.337061 | + | 0.941483i | \(0.390567\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.06359e12 | + | 4.78118e11i | −1.18665 | + | 0.533438i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.61277e11 | − | 4.52545e11i | −0.286763 | − | 0.496688i | 0.686272 | − | 0.727345i | \(-0.259246\pi\) |
−0.973035 | + | 0.230657i | \(0.925913\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 1.61268e11i | − | 0.175556i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.35501e12 | + | 7.82318e11i | −1.45121 | + | 0.837855i | −0.998550 | − | 0.0538289i | \(-0.982857\pi\) |
−0.452658 | + | 0.891684i | \(0.649524\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.37882e11 | + | 3.68281e11i | 0.677634 | + | 0.391232i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.04269e10 | + | 1.80599e10i | −0.0108986 | + | 0.0188769i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.30845e11 | − | 2.26630e11i | −0.135663 | − | 0.234975i | 0.790187 | − | 0.612865i | \(-0.209983\pi\) |
−0.925851 | + | 0.377890i | \(0.876650\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.32994e11 | −0.237713 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.55089e12 | + | 8.95405e11i | −1.56964 | + | 0.906231i | −0.573427 | + | 0.819256i | \(0.694387\pi\) |
−0.996211 | + | 0.0869745i | \(0.972280\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 252.9.z.d.145.2 | 12 | ||
3.2 | odd | 2 | 84.9.m.b.61.5 | ✓ | 12 | ||
7.3 | odd | 6 | inner | 252.9.z.d.73.2 | 12 | ||
21.17 | even | 6 | 84.9.m.b.73.5 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.9.m.b.61.5 | ✓ | 12 | 3.2 | odd | 2 | ||
84.9.m.b.73.5 | yes | 12 | 21.17 | even | 6 | ||
252.9.z.d.73.2 | 12 | 7.3 | odd | 6 | inner | ||
252.9.z.d.145.2 | 12 | 1.1 | even | 1 | trivial |