Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [304,9,Mod(113,304)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(304, base_ring=CyclotomicField(2))
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("304.113");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 304 = 2^{4} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 304.e (of order \(2\), degree \(1\), not 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: | \(123.843097459\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 46118 x^{10} + 738386961 x^{8} + 5214446299656 x^{6} + \cdots + 92\!\cdots\!64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{25}\cdot 3^{3} \) |
Twist minimal: | no (minimal twist has level 38) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 113.9 | ||
Root | \(61.5968i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 304.113 |
Dual form | 304.9.e.e.113.4 |
$q$-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 \(\left(\mathbb{Z}/304\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(191\) | \(229\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 74.3247i | 0.917589i | 0.888542 | + | 0.458795i | \(0.151719\pi\) | ||||
−0.888542 | + | 0.458795i | \(0.848281\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −154.845 | −0.247752 | −0.123876 | − | 0.992298i | \(-0.539532\pi\) | ||||
−0.123876 | + | 0.992298i | \(0.539532\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1585.07 | −0.660172 | −0.330086 | − | 0.943951i | \(-0.607078\pi\) | ||||
−0.330086 | + | 0.943951i | \(0.607078\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1036.83 | 0.158030 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 25549.2 | 1.74505 | 0.872524 | − | 0.488572i | \(-0.162482\pi\) | ||||
0.872524 | + | 0.488572i | \(0.162482\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 10369.3i | 0.363060i | 0.983385 | + | 0.181530i | \(0.0581049\pi\) | ||||
−0.983385 | + | 0.181530i | \(0.941895\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 11508.8i | − | 0.227334i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −132967. | −1.59202 | −0.796008 | − | 0.605286i | \(-0.793059\pi\) | ||||
−0.796008 | + | 0.605286i | \(0.793059\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −13145.5 | − | 129656.i | −0.100870 | − | 0.994900i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 117810.i | − | 0.605767i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 334889. | 1.19671 | 0.598355 | − | 0.801231i | \(-0.295821\pi\) | ||||
0.598355 | + | 0.801231i | \(0.295821\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −366648. | −0.938619 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 564707.i | 1.06260i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 605325.i | − | 0.855848i | −0.903815 | − | 0.427924i | \(-0.859245\pi\) | ||
0.903815 | − | 0.427924i | \(-0.140755\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 141494.i | − | 0.153211i | −0.997061 | − | 0.0766055i | \(-0.975592\pi\) | ||
0.997061 | − | 0.0766055i | \(-0.0244082\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.89894e6i | 1.60124i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 245440. | 0.163559 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.45048e6i | 1.30751i | 0.756706 | + | 0.653755i | \(0.226807\pi\) | ||||
−0.756706 | + | 0.653755i | \(0.773193\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −770699. | −0.333140 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.38955e6i | 0.845629i | 0.906216 | + | 0.422815i | \(0.138958\pi\) | ||||
−0.906216 | + | 0.422815i | \(0.861042\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.53889e6 | −0.450126 | −0.225063 | − | 0.974344i | \(-0.572259\pi\) | ||||
−0.225063 | + | 0.974344i | \(0.572259\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −160548. | −0.0391521 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.01339e6 | −1.02740 | −0.513701 | − | 0.857970i | \(-0.671726\pi\) | ||||
−0.513701 | + | 0.857970i | \(0.671726\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.25235e6 | −0.564173 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 9.88272e6i | − | 1.46082i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 1.18301e7i | − | 1.49929i | −0.661840 | − | 0.749645i | \(-0.730224\pi\) | ||
0.661840 | − | 0.749645i | \(-0.269776\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.95616e6 | −0.432338 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 9.63667e6 | − | 977036.i | 0.912909 | − | 0.0925574i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 7.32369e6i | − | 0.604396i | −0.953245 | − | 0.302198i | \(-0.902280\pi\) | ||
0.953245 | − | 0.302198i | \(-0.0977204\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.12872e7 | −0.815203 | −0.407602 | − | 0.913160i | \(-0.633635\pi\) | ||||
−0.407602 | + | 0.913160i | \(0.633635\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.64346e6 | −0.104327 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 1.60564e6i | − | 0.0899486i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 1.87052e7i | − | 0.928245i | −0.885771 | − | 0.464122i | \(-0.846370\pi\) | ||
0.885771 | − | 0.464122i | \(-0.153630\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.48905e7i | 1.09809i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.17638e7i | 0.856450i | 0.903672 | + | 0.428225i | \(0.140861\pi\) | ||||
−0.903672 | + | 0.428225i | \(0.859139\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.89170e6 | −0.313107 | −0.156554 | − | 0.987669i | \(-0.550038\pi\) | ||||
−0.156554 | + | 0.987669i | \(0.550038\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 2.72510e7i | − | 0.861267i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.04974e7 | −1.15203 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.26495e7i | 1.35172i | 0.737031 | + | 0.675859i | \(0.236227\pi\) | ||||
−0.737031 | + | 0.675859i | \(0.763773\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.51690e7 | −0.816997 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.76587e7 | −0.793511 | −0.396756 | − | 0.917924i | \(-0.629864\pi\) | ||||
−0.396756 | + | 0.917924i | \(0.629864\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.05892e7 | 0.394424 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.49906e7 | 0.785317 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 1.06654e8i | − | 1.69988i | −0.526883 | − | 0.849938i | \(-0.676640\pi\) | ||
0.526883 | − | 0.849938i | \(-0.323360\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 1.64362e7i | − | 0.239682i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.05165e7 | 0.140585 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.03551e6 | + | 2.00766e7i | 0.0249907 | + | 0.246488i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.45621e7i | 0.277446i | 0.990331 | + | 0.138723i | \(0.0442998\pi\) | ||||
−0.990331 | + | 0.138723i | \(0.955700\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.64903e7 | 0.275769 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.35309e7 | 0.418323 | 0.209162 | − | 0.977881i | \(-0.432927\pi\) | ||||
0.209162 | + | 0.977881i | \(0.432927\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.50911e7i | 0.222931i | 0.993768 | + | 0.111465i | \(0.0355544\pi\) | ||||
−0.993768 | + | 0.111465i | \(0.964446\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.82423e7i | 0.150080i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 2.68160e7i | − | 0.204578i | −0.994755 | − | 0.102289i | \(-0.967383\pi\) | ||
0.994755 | − | 0.102289i | \(-0.0326167\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 1.10533e8i | − | 0.783041i | −0.920169 | − | 0.391521i | \(-0.871949\pi\) | ||
0.920169 | − | 0.391521i | \(-0.128051\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.82132e8 | −1.19976 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1.51426e8i | − | 0.928723i | −0.885646 | − | 0.464361i | \(-0.846284\pi\) | ||
0.885646 | − | 0.464361i | \(-0.153716\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.18557e7 | −0.296487 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.07513e7i | 0.0573743i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.10762e8 | 1.05100 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.38405e8 | 2.04519 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.77602e8 | −0.775941 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.17260e8 | 0.480296 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 4.59385e8i | − | 1.76588i | −0.469482 | − | 0.882942i | \(-0.655559\pi\) | ||
0.469482 | − | 0.882942i | \(-0.344441\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 1.14378e8i | − | 0.413031i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.08184e8 | 1.04646 | 0.523232 | − | 0.852190i | \(-0.324726\pi\) | ||||
0.523232 | + | 0.852190i | \(0.324726\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.08366e7 | + | 2.05515e8i | 0.0665916 | + | 0.656805i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 8.74419e7i | − | 0.263260i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.53360e8 | −1.28695 | −0.643473 | − | 0.765468i | \(-0.722507\pi\) | ||||
−0.643473 | + | 0.765468i | \(0.722507\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.86640e8 | 1.03573 | 0.517866 | − | 0.855462i | \(-0.326726\pi\) | ||||
0.517866 | + | 0.855462i | \(0.326726\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 3.72619e8i | − | 0.942732i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.64929e8i | 0.633556i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.37314e7i | 0.212038i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 2.41730e8i | − | 0.517679i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.42202e8 | 1.10006 | 0.550029 | − | 0.835145i | \(-0.314617\pi\) | ||||
0.550029 | + | 0.835145i | \(0.314617\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.75171e7i | 0.0336942i | 0.999858 | + | 0.0168471i | \(0.00536285\pi\) | ||||
−0.999858 | + | 0.0168471i | \(0.994637\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.37864e8 | −0.251586 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.19095e7i | 0.0379583i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.98783e8 | −1.15012 | −0.575061 | − | 0.818111i | \(-0.695022\pi\) | ||||
−0.575061 | + | 0.818111i | \(0.695022\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.79271e8 | 1.37573 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.30823e8 | −0.790035 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.03342e8 | −0.429716 | −0.214858 | − | 0.976645i | \(-0.568929\pi\) | ||||
−0.214858 | + | 0.976645i | \(0.568929\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 2.94041e8i | − | 0.396709i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 1.38262e9i | − | 1.77761i | −0.458286 | − | 0.888805i | \(-0.651536\pi\) | ||
0.458286 | − | 0.888805i | \(-0.348464\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.08207e8 | 0.868188 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.36297e7 | − | 1.34432e8i | −0.0159405 | − | 0.157224i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 6.31095e8i | − | 0.704547i | −0.935897 | − | 0.352274i | \(-0.885409\pi\) | ||
0.935897 | − | 0.352274i | \(-0.114591\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.81164e8 | 0.619650 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.44331e8 | 0.554588 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 1.63061e9i | − | 1.58832i | −0.607711 | − | 0.794158i | \(-0.707912\pi\) | ||
0.607711 | − | 0.794158i | \(-0.292088\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.11994e8i | 0.756551i | 0.925693 | + | 0.378276i | \(0.123483\pi\) | ||||
−0.925693 | + | 0.378276i | \(0.876517\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 8.38916e8i | − | 0.748022i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 3.79444e8i | − | 0.323938i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.39720e9 | −2.77814 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 8.95101e8i | − | 0.701496i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.14327e9 | 0.859041 | 0.429521 | − | 0.903057i | \(-0.358683\pi\) | ||||
0.429521 | + | 0.903057i | \(0.358683\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 1.21153e9i | − | 0.873185i | −0.899659 | − | 0.436592i | \(-0.856185\pi\) | ||
0.899659 | − | 0.436592i | \(-0.143815\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.19339e8 | 0.0825359 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.99652e8 | 0.331744 | 0.165872 | − | 0.986147i | \(-0.446956\pi\) | ||||
0.165872 | + | 0.986147i | \(0.446956\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.04764e9 | −1.30570 | −0.652848 | − | 0.757489i | \(-0.726426\pi\) | ||||
−0.652848 | + | 0.757489i | \(0.726426\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.39026e9 | 0.851747 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.59484e8i | 0.565007i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 3.70009e8i | − | 0.209506i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.47224e8 | 0.189116 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.35857e8 | − | 3.31262e9i | −0.176023 | − | 1.73615i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.24079e8i | 0.314854i | 0.987531 | + | 0.157427i | \(0.0503199\pi\) | ||||
−0.987531 | + | 0.157427i | \(0.949680\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.61759e9 | −0.785870 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.38289e8 | 0.111520 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.24277e8i | 0.101146i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 6.60873e8i | − | 0.287304i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 1.37878e9i | − | 0.577997i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.29270e9i | 0.927102i | 0.886070 | + | 0.463551i | \(0.153425\pi\) | ||||
−0.886070 | + | 0.463551i | \(0.846575\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.80153e8 | −0.148330 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 3.90434e9i | − | 1.47043i | −0.677835 | − | 0.735214i | \(-0.737082\pi\) | ||
0.677835 | − | 0.735214i | \(-0.262918\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.02177e8 | −0.109880 | −0.0549401 | − | 0.998490i | \(-0.517497\pi\) | ||||
−0.0549401 | + | 0.998490i | \(0.517497\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 3.00996e9i | − | 1.05709i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4.59616e9 | −1.55945 | −0.779726 | − | 0.626121i | \(-0.784641\pi\) | ||||
−0.779726 | + | 0.626121i | \(0.784641\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.76297e8 | 0.254540 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.91316e9 | −1.24032 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.85947e9 | 0.569897 | 0.284949 | − | 0.958543i | \(-0.408023\pi\) | ||||
0.284949 | + | 0.958543i | \(0.408023\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.35931e8i | 0.129226i | 0.997910 | + | 0.0646130i | \(0.0205813\pi\) | ||||
−0.997910 | + | 0.0646130i | \(0.979419\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.09111e9i | 0.312928i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.03609e8 | 0.139775 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.34445e9 | − | 1.36310e8i | 0.361208 | − | 0.0366219i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 2.79897e9i | − | 0.728117i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.73172e9 | −0.436297 | −0.218148 | − | 0.975916i | \(-0.570002\pi\) | ||||
−0.218148 | + | 0.975916i | \(0.570002\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.55615e9 | 2.08832 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.53029e9i | 0.361920i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 7.49270e9i | − | 1.71754i | −0.512364 | − | 0.858768i | \(-0.671230\pi\) | ||
0.512364 | − | 0.858768i | \(-0.328770\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 3.88419e9i | − | 0.863181i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 6.27621e8i | − | 0.135249i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.66900e9 | 0.975890 | 0.487945 | − | 0.872874i | \(-0.337747\pi\) | ||||
0.487945 | + | 0.872874i | \(0.337747\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.83183e9i | 0.371452i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.92703e9 | 1.55979 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 2.06571e9i | − | 0.394512i | −0.980352 | − | 0.197256i | \(-0.936797\pi\) | ||
0.980352 | − | 0.197256i | \(-0.0632030\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.24856e9 | −0.231490 | −0.115745 | − | 0.993279i | \(-0.536926\pi\) | ||||
−0.115745 | + | 0.993279i | \(0.536926\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.22161e9 | 0.219929 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −9.36758e9 | −1.63793 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.05391e8 | −0.0179013 | −0.00895067 | − | 0.999960i | \(-0.502849\pi\) | ||||
−0.00895067 | + | 0.999960i | \(0.502849\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 1.46705e8i | − | 0.0242119i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.25009e9i | 1.48361i | 0.670614 | + | 0.741807i | \(0.266031\pi\) | ||||
−0.670614 | + | 0.741807i | \(0.733969\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.95944e9 | −1.24090 | −0.620450 | − | 0.784246i | \(-0.713050\pi\) | ||||
−0.620450 | + | 0.784246i | \(0.713050\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.49219e9 | + | 1.51289e8i | −0.226175 | + | 0.0229312i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 3.78760e9i | − | 0.558261i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.07044e10 | 1.53451 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.82557e9 | −0.254582 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.46284e9i | 0.198484i | 0.995063 | + | 0.0992420i | \(0.0316418\pi\) | ||||
−0.995063 | + | 0.0992420i | \(0.968358\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.13403e9i | 0.149740i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.44278e10i | 1.85428i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.47258e9i | 0.434477i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.43926e9 | 0.297161 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.23542e9i | 0.383849i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.74776e9 | 0.201968 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 1.59981e9i | − | 0.180101i | −0.995937 | − | 0.0900504i | \(-0.971297\pi\) | ||
0.995937 | − | 0.0900504i | \(-0.0287028\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.86489e9 | −0.204559 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.36371e10 | 1.45775 | 0.728873 | − | 0.684649i | \(-0.240045\pi\) | ||||
0.728873 | + | 0.684649i | \(0.240045\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.84472e9 | −0.713146 | −0.356573 | − | 0.934268i | \(-0.616055\pi\) | ||||
−0.356573 | + | 0.934268i | \(0.616055\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.54481e8 | 0.0258471 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.91136e9i | 0.486368i | 0.969980 | + | 0.243184i | \(0.0781919\pi\) | ||||
−0.969980 | + | 0.243184i | \(0.921808\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 1.54656e10i | − | 1.49349i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.99310e9 | 0.187719 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.74791e9 | + | 1.72400e10i | 0.160587 | + | 1.58390i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 3.80190e9i | − | 0.340775i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.21531e9 | 0.718510 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.94658e9 | 0.678261 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 1.69481e10i | − | 1.41192i | −0.708252 | − | 0.705960i | \(-0.750516\pi\) | ||
0.708252 | − | 0.705960i | \(-0.249484\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.54074e9i | 0.206626i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.89640e9i | 0.229974i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 2.45355e10i | − | 1.90229i | −0.308750 | − | 0.951143i | \(-0.599911\pi\) | ||
0.308750 | − | 0.951143i | \(-0.400089\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.12547e10 | 0.852186 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 3.61505e9i | − | 0.267360i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.42928e10 | 1.03262 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 3.85416e9i | − | 0.272053i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.97537e10 | −1.36248 | −0.681239 | − | 0.732061i | \(-0.738559\pi\) | ||||
−0.681239 | + | 0.732061i | \(0.738559\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.25657e9 | −0.489136 | −0.244568 | − | 0.969632i | \(-0.578646\pi\) | ||||
−0.244568 | + | 0.969632i | \(0.578646\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.85564e9 | −0.385786 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.86135e10 | −1.19875 | −0.599375 | − | 0.800468i | \(-0.704584\pi\) | ||||
−0.599375 | + | 0.800468i | \(0.704584\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 3.37002e9i | − | 0.212187i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.56648e10i | 0.964390i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.90002e10 | −1.14388 | −0.571940 | − | 0.820296i | \(-0.693809\pi\) | ||||
−0.571940 | + | 0.820296i | \(0.693809\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.66380e10 | + | 3.40879e9i | −0.979650 | + | 0.200711i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.25843e10i | 1.87664i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.37683e9 | 0.0775729 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.69812e10 | 0.936061 | 0.468030 | − | 0.883712i | \(-0.344964\pi\) | ||||
0.468030 | + | 0.883712i | \(0.344964\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.47756e9i | 0.133635i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.87516e10i | 0.989789i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.35760e10i | 1.73458i | 0.497805 | + | 0.867289i | \(0.334140\pi\) | ||||
−0.497805 | + | 0.867289i | \(0.665860\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 8.71530e9i | 0.440714i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.27683e9 | 0.310724 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 3.39145e9i | − | 0.164372i | −0.996617 | − | 0.0821860i | \(-0.973810\pi\) | ||
0.996617 | − | 0.0821860i | \(-0.0261902\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.41437e10 | 1.62036 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.19332e10i | 1.94878i | 0.224864 | + | 0.974390i | \(0.427806\pi\) | ||||
−0.224864 | + | 0.974390i | \(0.572194\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.27081e9 | 0.285417 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.59558e9 | −0.0711334 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.91799e10 | −0.837620 | −0.418810 | − | 0.908074i | \(-0.637553\pi\) | ||||
−0.418810 | + | 0.908074i | \(0.637553\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.45291e10 | −1.90518 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.29057e10i | 0.960224i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 8.15250e9i | − | 0.334890i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.73055e10 | −1.50180 | −0.750899 | − | 0.660417i | \(-0.770379\pi\) | ||||
−0.750899 | + | 0.660417i | \(0.770379\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.52748e10 | + | 1.54867e9i | −0.602677 | + | 0.0611038i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 1.19174e10i | − | 0.460895i | −0.973085 | − | 0.230448i | \(-0.925981\pi\) | ||
0.973085 | − | 0.230448i | \(-0.0740191\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.46720e9 | 0.0556247 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 5.44574e9 | 0.202412 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.26080e10i | 2.28167i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 1.57301e10i | − | 0.562133i | −0.959688 | − | 0.281066i | \(-0.909312\pi\) | ||
0.959688 | − | 0.281066i | \(-0.0906881\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 3.36958e10i | − | 1.18089i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.16086e10i | 0.399005i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.83125e9 | 0.196594 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.87369e10i | 0.950377i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.53760e10 | −1.14776 | −0.573882 | − | 0.818938i | \(-0.694563\pi\) | ||||
−0.573882 | + | 0.818938i | \(0.694563\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.22556e10i | 0.708454i | 0.935159 | + | 0.354227i | \(0.115256\pi\) | ||||
−0.935159 | + | 0.354227i | \(0.884744\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.19805e9 | −0.162360 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.87520e10 | 1.49430 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.78910e10 | 0.538174 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.96908e10 | −0.581345 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 6.16218e10i | − | 1.78577i | −0.450285 | − | 0.892885i | \(-0.648678\pi\) | ||
0.450285 | − | 0.892885i | \(-0.351322\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 4.72412e9i | − | 0.134391i | −0.997740 | − | 0.0671954i | \(-0.978595\pi\) | ||
0.997740 | − | 0.0671954i | \(-0.0214051\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.96656e9 | −0.194563 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.40228e9 | − | 4.34204e10i | −0.120712 | − | 1.19061i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.36060e10i | 1.17405i | 0.809568 | + | 0.587027i | \(0.199702\pi\) | ||||
−0.809568 | + | 0.587027i | \(0.800298\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.37214e9 | −0.0891562 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.41307e10 | 1.14585 | 0.572923 | − | 0.819610i | \(-0.305810\pi\) | ||||
0.572923 | + | 0.819610i | \(0.305810\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.65148e10i | 0.421147i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.02990e10i | 1.00940i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.32868e10i | 0.572961i | 0.958086 | + | 0.286481i | \(0.0924854\pi\) | ||||
−0.958086 | + | 0.286481i | \(0.907515\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.10511e10i | 1.47566i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.30196e9 | −0.0309174 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.54505e9i | 0.0593815i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.60367e10 | −1.05545 | −0.527727 | − | 0.849414i | \(-0.676956\pi\) | ||||
−0.527727 | + | 0.849414i | \(0.676956\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 7.50873e10i | − | 1.69167i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.61112e10 | 0.799537 | 0.399769 | − | 0.916616i | \(-0.369091\pi\) | ||||
0.399769 | + | 0.916616i | \(0.369091\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.50543e9 | −0.0762812 | −0.0381406 | − | 0.999272i | \(-0.512143\pi\) | ||||
−0.0381406 | + | 0.999272i | \(0.512143\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.62842e9 | −0.0348301 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4.73893e9 | −0.0996352 | −0.0498176 | − | 0.998758i | \(-0.515864\pi\) | ||||
−0.0498176 | + | 0.998758i | \(0.515864\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.96490e10i | 0.612801i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 5.19369e10i | − | 1.05534i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.93175e10 | −0.785492 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.81977e9 | + | 4.75382e10i | 0.0946787 | + | 0.933832i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 1.22659e10i | − | 0.236933i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.54648e9 | 0.143352 | 0.0716758 | − | 0.997428i | \(-0.477165\pi\) | ||||
0.0716758 | + | 0.997428i | \(0.477165\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.54099e10 | −0.474704 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 3.94533e10i | − | 0.724927i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 3.80332e9i | − | 0.0687378i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 8.92286e10i | − | 1.58631i | −0.609020 | − | 0.793155i | \(-0.708437\pi\) | ||
0.609020 | − | 0.793155i | \(-0.291563\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 2.25458e10i | − | 0.394303i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.26865e10 | 0.562397 | 0.281198 | − | 0.959650i | \(-0.409268\pi\) | ||||
0.281198 | + | 0.959650i | \(0.409268\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.04881e10i | 1.36252i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.10188e9 | −0.0683223 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 3.44973e10i | − | 0.565404i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.51579e10 | 1.53477 | 0.767384 | − | 0.641188i | \(-0.221558\pi\) | ||||
0.767384 | + | 0.641188i | \(0.221558\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.02763e11 | 1.63112 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.90098e10 | −0.296966 | −0.148483 | − | 0.988915i | \(-0.547439\pi\) | ||||
−0.148483 | + | 0.988915i | \(0.547439\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.74053e9 | −0.103640 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.26373e10i | 0.796640i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.06082e11i | 1.58041i | 0.612845 | + | 0.790203i | \(0.290025\pi\) | ||||
−0.612845 | + | 0.790203i | \(0.709975\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.40940e10 | 0.206705 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.32178e10 | − | 7.42335e9i | 1.05718 | − | 0.107184i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 3.88522e9i | − | 0.0552315i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.28088e11 | −1.79286 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.69060e10 | 0.646485 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 5.55106e10i | − | 0.753399i | −0.926335 | − | 0.376700i | \(-0.877059\pi\) | ||
0.926335 | − | 0.376700i | \(-0.122941\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.05842e11i | 1.41465i | 0.706888 | + | 0.707326i | \(0.250098\pi\) | ||||
−0.706888 | + | 0.707326i | \(0.749902\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.31948e10i | 0.568584i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.88139e10i | 0.243914i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.38395e10 | 0.432116 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 7.59345e9i | − | 0.0955126i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.47780e10 | −0.307014 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.15232e9i | 0.0506846i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.21194e11 | 1.45742 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −8.30950e10 | −0.984509 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.69196e10 | 0.781204 | 0.390602 | − | 0.920560i | \(-0.372267\pi\) | ||||
0.390602 | + | 0.920560i | \(0.372267\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6.03512e10 | −0.694204 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.71154e10i | 0.194000i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.76775e9i | 0.109105i | 0.998511 | + | 0.0545526i | \(0.0173732\pi\) | ||||
−0.998511 | + | 0.0545526i | \(0.982627\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.17029e10 | −0.128826 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.84842e10 | + | 7.95730e9i | −0.851483 | + | 0.0863295i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 8.34533e10i | − | 0.892366i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.82021e10 | 0.297242 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.59399e10 | 0.165602 | 0.0828010 | − | 0.996566i | \(-0.473613\pi\) | ||||
0.0828010 | + | 0.996566i | \(0.473613\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 1.59573e10i | − | 0.163423i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 2.52496e11i | − | 2.54919i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 1.84760e10i | − | 0.183897i | −0.995764 | − | 0.0919483i | \(-0.970691\pi\) | ||
0.995764 | − | 0.0919483i | \(-0.0293094\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.34475e10i | 0.230093i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 5.57455e10 | 0.539358 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 5.39118e10i | − | 0.514322i | −0.966369 | − | 0.257161i | \(-0.917213\pi\) | ||
0.966369 | − | 0.257161i | \(-0.0827870\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.13331e9 | −0.0482896 | −0.0241448 | − | 0.999708i | \(-0.507686\pi\) | ||||
−0.0241448 | + | 0.999708i | \(0.507686\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.49730e10i | 0.788247i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.22786e11 | −1.12326 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.51019e9 | −0.0406903 | −0.0203452 | − | 0.999793i | \(-0.506477\pi\) | ||||
−0.0203452 | + | 0.999793i | \(0.506477\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9.00469e10 | 0.801225 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.96918e10 | 0.523854 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 3.02251e11i | − | 2.61633i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 1.66478e9i | − | 0.0142146i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.32145e10 | 0.448206 | 0.224103 | − | 0.974565i | \(-0.428055\pi\) | ||||
0.224103 | + | 0.974565i | \(0.428055\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.83455e10 | + | 1.86000e9i | −0.152430 | + | 0.0154544i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.71365e10i | 0.304404i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.81590e10 | −0.227719 | −0.113859 | − | 0.993497i | \(-0.536321\pi\) | ||||
−0.113859 | + | 0.993497i | \(0.536321\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.26354e10 | −0.260388 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 1.52191e11i | − | 1.19809i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.53599e10i | 0.119311i | 0.998219 | + | 0.0596554i | \(0.0190002\pi\) | ||||
−0.998219 | + | 0.0596554i | \(0.981000\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 1.08743e11i | − | 0.833494i | −0.909023 | − | 0.416747i | \(-0.863170\pi\) | ||
0.909023 | − | 0.416747i | \(-0.136830\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 1.93941e10i | − | 0.146690i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6.78846e10 | −0.506699 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 1.12346e11i | − | 0.827565i | −0.910376 | − | 0.413783i | \(-0.864207\pi\) | ||
0.910376 | − | 0.413783i | \(-0.135793\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7.13134e10 | −0.518444 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 5.19856e10i | − | 0.373008i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.12496e10 | −0.150490 | −0.0752451 | − | 0.997165i | \(-0.523974\pi\) | ||||
−0.0752451 | + | 0.997165i | \(0.523974\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.75008e10 | 0.192240 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.05896e11 | −1.42072 | −0.710359 | − | 0.703840i | \(-0.751467\pi\) | ||||
−0.710359 | + | 0.703840i | \(0.751467\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.59468e9 | −0.0108620 | −0.00543100 | − | 0.999985i | \(-0.501729\pi\) | ||||
−0.00543100 | + | 0.999985i | \(0.501729\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.89114e11i | 1.27162i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.69054e11i | 1.12221i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.25065e11 | 0.819625 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.46210e11 | − | 2.49625e10i | 1.59307 | − | 0.161517i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 3.25833e11i | − | 2.08158i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.84477e11 | −1.79444 | −0.897222 | − | 0.441580i | \(-0.854418\pi\) | ||||
−0.897222 | + | 0.441580i | \(0.854418\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.63845e10 | −0.288907 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7.11334e10i | 0.437501i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 3.37247e10i | − | 0.204829i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.25655e10i | 0.135345i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 5.30174e10i | − | 0.314041i | −0.987595 | − | 0.157021i | \(-0.949811\pi\) | ||
0.987595 | − | 0.157021i | \(-0.0501889\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.79754e10 | −0.339156 | −0.169578 | − | 0.985517i | \(-0.554241\pi\) | ||||
−0.169578 | + | 0.985517i | \(0.554241\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.77108e10i | 0.102329i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.75434e11 | 1.57181 | 0.785904 | − | 0.618348i | \(-0.212198\pi\) | ||||
0.785904 | + | 0.618348i | \(0.212198\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 1.87115e11i | − | 1.05470i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.66694e10 | −0.0928101 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.69428e11 | −1.48180 | −0.740900 | − | 0.671615i | \(-0.765601\pi\) | ||||
−0.740900 | + | 0.671615i | \(0.765601\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.77206e10 | −0.259263 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −9.21921e9 | −0.0494803 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 8.80932e10i | − | 0.467090i | −0.972346 | − | 0.233545i | \(-0.924967\pi\) | ||
0.972346 | − | 0.233545i | \(-0.0750326\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.53825e10i | 0.132962i | 0.997788 | + | 0.0664811i | \(0.0211772\pi\) | ||||
−0.997788 | + | 0.0664811i | \(0.978823\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.02477e11 | 0.530364 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.22643e9 | − | 3.18229e10i | −0.0164982 | − | 0.162724i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 2.02716e11i | − | 1.02420i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.70404e11 | −0.850699 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.88379e11 | −1.42257 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.21341e11i | 0.591490i | 0.955267 | + | 0.295745i | \(0.0955679\pi\) | ||||
−0.955267 | + | 0.295745i | \(0.904432\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 2.07049e11i | − | 0.997373i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.38640e11i | 1.61207i | 0.591870 | + | 0.806034i | \(0.298390\pi\) | ||||
−0.591870 | + | 0.806034i | \(0.701610\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 3.89328e10i | − | 0.183162i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.90189e11 | 1.34925 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 1.36488e11i | − | 0.627208i | −0.949554 | − | 0.313604i | \(-0.898464\pi\) | ||
0.949554 | − | 0.313604i | \(-0.101536\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.02004e10 | 0.318843 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 2.24592e10i | − | 0.100825i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.22671e11 | 0.544332 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.85706e11 | −1.69178 | −0.845890 | − | 0.533358i | \(-0.820930\pi\) | ||||
−0.845890 | + | 0.533358i | \(0.820930\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.19891e10 | −0.182055 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5.98692e10 | −0.256604 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 3.17730e11i | − | 1.34626i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 3.41609e11i | − | 1.43094i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.23246e11 | 1.75275 | 0.876377 | − | 0.481626i | \(-0.159954\pi\) | ||||
0.876377 | + | 0.481626i | \(0.159954\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.17721e11 | − | 3.22128e10i | 1.30084 | − | 0.131889i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.76981e10i | 0.233563i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.89996e10 | −0.276165 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.73862e10 | 0.187529 | 0.0937643 | − | 0.995594i | \(-0.470110\pi\) | ||||
0.0937643 | + | 0.995594i | \(0.470110\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.45888e10i | 0.213612i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 4.73846e10i | − | 0.183349i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 4.10229e10i | − | 0.156965i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.38204e11i | 0.522932i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.26152e11 | 0.472039 | 0.236020 | − | 0.971748i | \(-0.424157\pi\) | ||||
0.236020 | + | 0.971748i | \(0.424157\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 3.97711e10i | − | 0.147173i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.24005e10 | −0.118576 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.21941e11i | 0.803315i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.49520e10 | −0.304114 | −0.152057 | − | 0.988372i | \(-0.548590\pi\) | ||||
−0.152057 | + | 0.988372i | \(0.548590\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3.11841e11 | −1.10414 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.04622e11 | 0.716608 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.23738e11 | 1.81426 | 0.907128 | − | 0.420855i | \(-0.138270\pi\) | ||||
0.907128 | + | 0.420855i | \(0.138270\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.74306e10i | 0.128256i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 4.77903e11i | − | 1.61983i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.44499e11 | −1.15508 | −0.577538 | − | 0.816364i | \(-0.695986\pi\) | ||||
−0.577538 | + | 0.816364i | \(0.695986\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.01312e10 | + | 9.99260e10i | 0.0336039 | + | 0.331441i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 4.53922e10i | − | 0.148945i | −0.997223 | − | 0.0744726i | \(-0.976273\pi\) | ||
0.997223 | − | 0.0744726i | \(-0.0237273\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.39571e10 | −0.272541 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.90458e10 | −0.125398 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.25054e10i | 0.135057i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 8.96270e10i | − | 0.281760i | −0.990027 | − | 0.140880i | \(-0.955007\pi\) | ||
0.990027 | − | 0.140880i | \(-0.0449931\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 1.28709e11i | − | 0.400341i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 2.71243e9i | − | 0.00834779i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.94573e11 | −1.81060 | −0.905298 | − | 0.424778i | \(-0.860352\pi\) | ||||
−0.905298 | + | 0.424778i | \(0.860352\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.35934e11i | 1.91622i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.29954e11 | −1.28199 | −0.640993 | − | 0.767547i | \(-0.721477\pi\) | ||||
−0.640993 | + | 0.767547i | \(0.721477\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.75202e11i | 0.516942i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.13476e10 | 0.0623308 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.59419e10 | 0.219432 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.94606e11 | 1.12839 | 0.564194 | − | 0.825642i | \(-0.309187\pi\) | ||||
0.564194 | + | 0.825642i | \(0.309187\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.56893e11 | 1.57599 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.34209e10i | 0.0936053i | 0.998904 | + | 0.0468026i | \(0.0149032\pi\) | ||||
−0.998904 | + | 0.0468026i | \(0.985097\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.18783e10i | 0.143807i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.88692e11 | 0.792046 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.09820e11 | − | 3.14118e10i | 0.841316 | − | 0.0852988i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.56049e11i | 1.49455i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.41831e11 | 0.909420 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.08203e11 | 0.284944 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.01627e11i | 1.30762i | 0.756658 | + | 0.653811i | \(0.226831\pi\) | ||||
−0.756658 | + | 0.653811i | \(0.773169\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.47022e11i | 0.895467i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.40021e11i | 0.613116i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 1.17041e11i | − | 0.295967i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.36150e11 | −0.340840 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.80292e11i | 0.942505i | 0.881998 | + | 0.471253i | \(0.156198\pi\) | ||||
−0.881998 | + | 0.471253i | \(0.843802\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.66614e11 | 1.63564 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 1.10582e11i | − | 0.268631i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.27176e11 | −0.546387 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.21951e10 | 0.195732 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.53533e11 | 0.362000 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.33585e11 | −0.545319 | −0.272660 | − | 0.962111i | \(-0.587903\pi\) | ||||
−0.272660 | + | 0.962111i | \(0.587903\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.37656e10i | 0.0549371i | 0.999623 | + | 0.0274685i | \(0.00874461\pi\) | ||||
−0.999623 | + | 0.0274685i | \(0.991255\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 9.27991e10i | − | 0.212413i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.69709e10 | 0.106463 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.02295e10 | + | 1.99527e11i | 0.0454043 | + | 0.447831i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 1.70416e10i | − | 0.0378769i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.15004e11 | −1.13354 | −0.566771 | − | 0.823875i | \(-0.691808\pi\) | ||||
−0.566771 | + | 0.823875i | \(0.691808\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.28392e11 | −0.497831 | −0.248916 | − | 0.968525i | \(-0.580074\pi\) | ||||
−0.248916 | + | 0.968525i | \(0.580074\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 6.96243e11i | − | 1.50295i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.97217e10i | 0.149055i | 0.997219 | + | 0.0745274i | \(0.0237448\pi\) | ||||
−0.997219 | + | 0.0745274i | \(0.976255\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 4.08026e11i | − | 0.863913i | −0.901894 | − | 0.431956i | \(-0.857823\pi\) | ||
0.901894 | − | 0.431956i | \(-0.142177\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 7.83318e9i | − | 0.0164261i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.32454e11 | 0.898173 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.14091e11i | 0.440406i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.99024e10 | 0.162801 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 9.01495e11i | − | 1.81935i | −0.415325 | − | 0.909673i | \(-0.636332\pi\) | ||
0.415325 | − | 0.909673i | \(-0.363668\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.33828e11 | 0.267524 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −6.87511e11 | −1.36135 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.09662e11 | −0.215095 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.94903e11 | −1.35018 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 5.91583e11i | − | 1.13864i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.20639e11i | 1.56471i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5.99808e10 | −0.113296 | −0.0566482 | − | 0.998394i | \(-0.518041\pi\) | ||||
−0.0566482 | + | 0.998394i | \(0.518041\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.11049e9 | + | 2.08161e10i | 0.00394928 | + | 0.0389524i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 2.70130e10i | − | 0.0500783i | −0.999686 | − | 0.0250391i | \(-0.992029\pi\) | ||
0.999686 | − | 0.0250391i | \(-0.00797104\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.98513e10 | 0.146659 | 0.0733296 | − | 0.997308i | \(-0.476637\pi\) | ||||
0.0733296 | + | 0.997308i | \(0.476637\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.81513e11 | 0.512254 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 1.02525e12i | − | 1.84836i | −0.381954 | − | 0.924181i | \(-0.624749\pi\) | ||
0.381954 | − | 0.924181i | \(-0.375251\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.77217e10i | 0.174553i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 7.95602e11i | 1.40805i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.34516e12i | 2.35881i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.93960e11 | 0.337008 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.54669e10i | 0.0438448i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.85865e11 | −0.317078 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 9.55040e11i | − | 1.61445i | −0.590247 | − | 0.807223i | \(-0.700970\pi\) | ||
0.590247 | − | 0.807223i | \(-0.299030\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.08725e11 | −0.182127 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.13499e12 | 1.88403 | 0.942014 | − | 0.335573i | \(-0.108930\pi\) | ||||
0.942014 | + | 0.335573i | \(0.108930\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.78656e10 | −0.0458379 | −0.0229190 | − | 0.999737i | \(-0.507296\pi\) | ||||
−0.0229190 | + | 0.999737i | \(0.507296\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −8.42868e10 | −0.137400 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.71858e11i | 1.08538i | 0.839932 | + | 0.542691i | \(0.182595\pi\) | ||||
−0.839932 | + | 0.542691i | \(0.817405\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.28159e11i | 1.16579i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −8.98542e11 | −1.42570 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.59035e10 | + | 6.50018e11i | 0.103634 | + | 1.02216i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.52491e11i | 0.393508i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.58098e11 | −0.398672 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −8.56496e10 | −0.131125 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.57301e12i | 2.38689i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.81297e11i | 0.272672i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 1.25733e11i | − | 0.187437i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.08911e11i | 0.899757i | 0.893090 | + | 0.449878i | \(0.148533\pi\) | ||||
−0.893090 | + | 0.449878i | \(0.851467\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.51343e10 | 0.0661075 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.07571e10i | 0.102730i | 0.998680 | + | 0.0513649i | \(0.0163572\pi\) | ||||
−0.998680 | + | 0.0513649i | \(0.983643\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.62151e11 | −1.38471 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.29902e11i | 0.185324i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.88493e11 | −0.690846 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.81891e11 | 0.395202 | 0.197601 | − | 0.980283i | \(-0.436685\pi\) | ||||
0.197601 | + | 0.980283i | \(0.436685\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.18906e11 | 0.165259 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.25677e11 | −0.310943 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 8.98465e11i | − | 1.22725i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.60153e10i | 0.0352297i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.08860e12 | −1.46152 | −0.730762 | − | 0.682632i | \(-0.760835\pi\) | ||||
−0.730762 | + | 0.682632i | \(0.760835\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.27537e10 | + | 4.21687e11i | 0.0569082 | + | 0.561296i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.01358e12i | 1.33761i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.26038e11 | 0.688289 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −8.13586e11 | −1.05547 | −0.527734 | − | 0.849410i | \(-0.676958\pi\) | ||||
−0.527734 | + | 0.849410i | \(0.676958\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 5.08732e11i | − | 0.654375i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.38430e12i | 1.76552i | 0.469827 | + | 0.882759i | \(0.344316\pi\) | ||||
−0.469827 | + | 0.882759i | \(0.655684\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.00232e11i | 1.01197i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.38602e11i | 0.173797i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −5.32762e11 | −0.662420 | −0.331210 | − | 0.943557i | \(-0.607457\pi\) | ||||
−0.331210 | + | 0.943557i | \(0.607457\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 9.22011e10i | − | 0.113677i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.65036e11 | −0.446286 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 5.73373e11i | − | 0.695129i | −0.937656 | − | 0.347564i | \(-0.887009\pi\) | ||
0.937656 | − | 0.347564i | \(-0.112991\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.77029e11 | −0.212829 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.14948e12 | 1.37042 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.18608e11 | 0.849606 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.32871e11 | 0.976526 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 2.78038e10i | − | 0.0323295i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.87600e11i | 0.216333i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.36489e12 | 1.56096 | 0.780479 | − | 0.625182i | \(-0.214975\pi\) | ||||
0.780479 | + | 0.625182i | \(0.214975\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.28136e12 | + | 1.29913e11i | −1.45337 | + | 0.147353i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1.57922e12i | − | 1.77650i | −0.459361 | − | 0.888250i | \(-0.651922\pi\) | ||
0.459361 | − | 0.888250i | \(-0.348078\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.12853e11 | −0.683762 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.82575e11 | 0.312691 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 5.51758e11i | 0.605578i | 0.953058 | + | 0.302789i | \(0.0979178\pi\) | ||||
−0.953058 | + | 0.302789i | \(0.902082\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 2.72493e12i | − | 2.96636i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 1.14604e11i | − | 0.123744i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 8.60977e11i | 0.922099i | 0.887374 | + | 0.461050i | \(0.152527\pi\) | ||||
−0.887374 | + | 0.461050i | \(0.847473\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.73684e10 | −0.0821900 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 5.90628e11i | 0.622365i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.15358e11 | −0.538671 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.27354e11i | 0.132044i | 0.997818 | + | 0.0660220i | \(0.0210308\pi\) | ||||
−0.997818 | + | 0.0660220i | \(0.978969\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.25967e12 | 1.29556 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.17067e11 | 0.323488 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.40891e12 | −1.42595 | −0.712975 | − | 0.701190i | \(-0.752653\pi\) | ||||
−0.712975 | + | 0.701190i | \(0.752653\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.38381e12 | −1.38935 |
(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 | 304.9.e.e.113.9 | 12 | ||
4.3 | odd | 2 | 38.9.b.a.37.9 | yes | 12 | ||
12.11 | even | 2 | 342.9.d.a.37.4 | 12 | |||
19.18 | odd | 2 | inner | 304.9.e.e.113.4 | 12 | ||
76.75 | even | 2 | 38.9.b.a.37.4 | ✓ | 12 | ||
228.227 | odd | 2 | 342.9.d.a.37.10 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
38.9.b.a.37.4 | ✓ | 12 | 76.75 | even | 2 | ||
38.9.b.a.37.9 | yes | 12 | 4.3 | odd | 2 | ||
304.9.e.e.113.4 | 12 | 19.18 | odd | 2 | inner | ||
304.9.e.e.113.9 | 12 | 1.1 | even | 1 | trivial | ||
342.9.d.a.37.4 | 12 | 12.11 | even | 2 | |||
342.9.d.a.37.10 | 12 | 228.227 | odd | 2 |