Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,9,Mod(197,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.197");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.c (of order \(2\), degree \(1\), 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: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 4002260 x^{14} + 6534459751956 x^{12} + \cdots + 19\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 2^{32}\cdot 3^{37}\cdot 7^{12} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 197.16 | ||
Root | \(1013.87i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.197 |
Dual form | 252.9.c.a.197.1 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1013.87i | 1.62218i | 0.584918 | + | 0.811092i | \(0.301127\pi\) | ||||
−0.584918 | + | 0.811092i | \(0.698873\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −907.493 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 9545.60i | − 0.651978i | −0.945374 | − | 0.325989i | \(-0.894303\pi\) | ||||
0.945374 | − | 0.325989i | \(-0.105697\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1998.60 | 0.0699765 | 0.0349883 | − | 0.999388i | \(-0.488861\pi\) | ||||
0.0349883 | + | 0.999388i | \(0.488861\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 46137.9i | 0.552411i | 0.961099 | + | 0.276205i | \(0.0890770\pi\) | ||||
−0.961099 | + | 0.276205i | \(0.910923\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −34120.9 | −0.261822 | −0.130911 | − | 0.991394i | \(-0.541790\pi\) | ||||
−0.130911 | + | 0.991394i | \(0.541790\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 97009.8i | − 0.346660i | −0.984864 | − | 0.173330i | \(-0.944547\pi\) | ||||
0.984864 | − | 0.173330i | \(-0.0554528\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −637298. | −1.63148 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 833372.i | − 1.17828i | −0.808033 | − | 0.589138i | \(-0.799467\pi\) | ||||
0.808033 | − | 0.589138i | \(-0.200533\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.03301e6 | −1.11856 | −0.559280 | − | 0.828979i | \(-0.688922\pi\) | ||||
−0.559280 | + | 0.828979i | \(0.688922\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 920075.i | − 0.613128i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.96878e6 | −1.05048 | −0.525242 | − | 0.850953i | \(-0.676025\pi\) | ||||
−0.525242 | + | 0.850953i | \(0.676025\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 1.24983e6i | − 0.442298i | −0.975240 | − | 0.221149i | \(-0.929019\pi\) | ||||
0.975240 | − | 0.221149i | \(-0.0709808\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.48518e6 | 0.434414 | 0.217207 | − | 0.976126i | \(-0.430305\pi\) | ||||
0.217207 | + | 0.976126i | \(0.430305\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.69893e6i | 0.348165i | 0.984731 | + | 0.174082i | \(0.0556959\pi\) | ||||
−0.984731 | + | 0.174082i | \(0.944304\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 823543. | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 6.91772e6i | − 0.876718i | −0.898800 | − | 0.438359i | \(-0.855560\pi\) | ||||
0.898800 | − | 0.438359i | \(-0.144440\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.67796e6 | 1.05763 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.43342e7i | 1.18295i | 0.806324 | + | 0.591474i | \(0.201454\pi\) | ||||
−0.806324 | + | 0.591474i | \(0.798546\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.12764e6 | 0.153666 | 0.0768332 | − | 0.997044i | \(-0.475519\pi\) | ||||
0.0768332 | + | 0.997044i | \(0.475519\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.02631e6i | 0.113515i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 696928. | 0.0345851 | 0.0172925 | − | 0.999850i | \(-0.494495\pi\) | ||||
0.0172925 | + | 0.999850i | \(0.494495\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 1.02684e6i | − 0.0404080i | −0.999796 | − | 0.0202040i | \(-0.993568\pi\) | ||||
0.999796 | − | 0.0202040i | \(-0.00643158\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.22586e7 | 1.13594 | 0.567969 | − | 0.823050i | \(-0.307729\pi\) | ||||
0.567969 | + | 0.823050i | \(0.307729\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.66257e6i | 0.246424i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.61512e7 | 1.18488 | 0.592440 | − | 0.805614i | \(-0.298165\pi\) | ||||
0.592440 | + | 0.805614i | \(0.298165\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.08432e6i | 0.107132i | 0.998564 | + | 0.0535662i | \(0.0170588\pi\) | ||||
−0.998564 | + | 0.0535662i | \(0.982941\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.67776e7 | −0.896112 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 5.60351e7i | − 0.893100i | −0.894759 | − | 0.446550i | \(-0.852653\pi\) | ||||
0.894759 | − | 0.446550i | \(-0.147347\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.81371e6 | −0.0264486 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 3.45940e7i | − 0.424723i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.04787e7 | −0.457235 | −0.228617 | − | 0.973516i | \(-0.573420\pi\) | ||||
−0.228617 | + | 0.973516i | \(0.573420\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 1.32286e8i | − 1.27125i | −0.772000 | − | 0.635623i | \(-0.780743\pi\) | ||||
0.772000 | − | 0.635623i | \(-0.219257\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.57094e7 | 0.672668 | 0.336334 | − | 0.941743i | \(-0.390813\pi\) | ||||
0.336334 | + | 0.941743i | \(0.390813\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 9.42571e7i | − 0.719083i | −0.933129 | − | 0.359541i | \(-0.882933\pi\) | ||||
0.933129 | − | 0.359541i | \(-0.117067\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.33918e8 | −0.948711 | −0.474355 | − | 0.880333i | \(-0.657319\pi\) | ||||
−0.474355 | + | 0.880333i | \(0.657319\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 2.65742e8i | − 1.62984i | −0.579570 | − | 0.814922i | \(-0.696779\pi\) | ||||
0.579570 | − | 0.814922i | \(-0.303221\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.83549e7 | 0.562347 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 4.18698e7i | − 0.208792i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.23240e8 | 0.574925 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 2.50093e8i | − 1.02438i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.05365e7 | −0.348024 | −0.174012 | − | 0.984744i | \(-0.555673\pi\) | ||||
−0.174012 | + | 0.984744i | \(0.555673\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.17212e8i | 1.07712i | 0.842587 | + | 0.538561i | \(0.181032\pi\) | ||||
−0.842587 | + | 0.538561i | \(0.818968\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.09645e7 | 0.0989594 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 3.82637e8i | − 1.08619i | −0.839672 | − | 0.543094i | \(-0.817253\pi\) | ||||
0.839672 | − | 0.543094i | \(-0.182747\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.25504e8 | 1.67560 | 0.837801 | − | 0.545976i | \(-0.183841\pi\) | ||||
0.837801 | + | 0.545976i | \(0.183841\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 1.90778e7i | − 0.0456231i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.44927e8 | 1.91138 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.20466e8i | 0.650185i | 0.945682 | + | 0.325092i | \(0.105395\pi\) | ||||
−0.945682 | + | 0.325092i | \(0.894605\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.82464e8 | 1.69742 | 0.848710 | − | 0.528859i | \(-0.177380\pi\) | ||||
0.848710 | + | 0.528859i | \(0.177380\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 1.04734e9i | − 1.81451i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.34353e8 | −0.714898 | −0.357449 | − | 0.933933i | \(-0.616353\pi\) | ||||
−0.357449 | + | 0.933933i | \(0.616353\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.80357e7i | 0.131025i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.00912e8 | 1.13458 | 0.567289 | − | 0.823519i | \(-0.307992\pi\) | ||||
0.567289 | + | 0.823519i | \(0.307992\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.38508e8i | 0.435214i | 0.976036 | + | 0.217607i | \(0.0698251\pi\) | ||||
−0.976036 | + | 0.217607i | \(0.930175\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.11736e8 | −0.995103 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 1.12498e9i | − 1.25592i | −0.778245 | − | 0.627960i | \(-0.783890\pi\) | ||||
0.778245 | − | 0.627960i | \(-0.216110\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.78343e8 | 0.616643 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 8.77566e8i | − 0.854806i | −0.904061 | − | 0.427403i | \(-0.859429\pi\) | ||||
0.904061 | − | 0.427403i | \(-0.140571\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.66077e8 | 0.900114 | 0.450057 | − | 0.893000i | \(-0.351404\pi\) | ||||
0.450057 | + | 0.893000i | \(0.351404\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 1.99607e9i | − 1.70408i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.40414e8 | 0.360159 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 1.74119e9i | − 1.30832i | −0.756357 | − | 0.654159i | \(-0.773023\pi\) | ||||
0.756357 | − | 0.654159i | \(-0.226977\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.34770e9 | −0.971323 | −0.485661 | − | 0.874147i | \(-0.661421\pi\) | ||||
−0.485661 | + | 0.874147i | \(0.661421\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 1.96552e9i | − 1.30500i | −0.757787 | − | 0.652502i | \(-0.773719\pi\) | ||||
0.757787 | − | 0.652502i | \(-0.226281\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.20469e8 | −0.331881 | −0.165940 | − | 0.986136i | \(-0.553066\pi\) | ||||
−0.165940 | + | 0.986136i | \(0.553066\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.56279e8i | 0.445346i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.26716e9 | 0.717490 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.25705e8i | 0.170702i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.68752e9 | −1.86039 | −0.930195 | − | 0.367065i | \(-0.880363\pi\) | ||||
−0.930195 | + | 0.367065i | \(0.880363\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.50577e9i | 0.704700i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.37453e8 | 0.422776 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.22112e7i | 0.0386558i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.02281e9 | 1.22234 | 0.611170 | − | 0.791499i | \(-0.290699\pi\) | ||||
0.611170 | + | 0.791499i | \(0.290699\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 4.46138e9i | − 1.68022i | −0.542418 | − | 0.840108i | \(-0.682491\pi\) | ||||
0.542418 | − | 0.840108i | \(-0.317509\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.98782e9 | 1.81372 | 0.906858 | − | 0.421437i | \(-0.138474\pi\) | ||||
0.906858 | + | 0.421437i | \(0.138474\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.24117e9i | 0.760416i | 0.924901 | + | 0.380208i | \(0.124148\pi\) | ||||
−0.924901 | + | 0.380208i | \(0.875852\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.72249e9 | −0.564787 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 1.50773e9i | − 0.462095i | −0.972943 | − | 0.231047i | \(-0.925785\pi\) | ||||
0.972943 | − | 0.231047i | \(-0.0742152\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.10570e9 | −0.920644 | −0.460322 | − | 0.887752i | \(-0.652266\pi\) | ||||
−0.460322 | + | 0.887752i | \(0.652266\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 8.34962e8i | 0.231741i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.81940e7 | −0.0183214 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.08641e9i | 0.777605i | 0.921321 | + | 0.388802i | \(0.127111\pi\) | ||||
−0.921321 | + | 0.388802i | \(0.872889\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.26017e8 | −0.226015 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.74391e9i | 1.31666i | 0.752727 | + | 0.658332i | \(0.228738\pi\) | ||||
−0.752727 | + | 0.658332i | \(0.771262\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.78665e9 | 0.397045 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 2.29821e9i | − 0.480361i | −0.970728 | − | 0.240180i | \(-0.922793\pi\) | ||||
0.970728 | − | 0.240180i | \(-0.0772066\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.01364e9 | 1.42220 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.76923e9i | 1.10182i | 0.834566 | + | 0.550908i | \(0.185718\pi\) | ||||
−0.834566 | + | 0.550908i | \(0.814282\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.15973e9 | 0.400426 | 0.200213 | − | 0.979752i | \(-0.435837\pi\) | ||||
0.200213 | + | 0.979752i | \(0.435837\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6.08339e9i | 1.06369i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.42498e9 | 0.411898 | 0.205949 | − | 0.978563i | \(-0.433972\pi\) | ||||
0.205949 | + | 0.978563i | \(0.433972\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 8.33664e9i | − 1.33711i | −0.743665 | − | 0.668553i | \(-0.766914\pi\) | ||||
0.743665 | − | 0.668553i | \(-0.233086\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.43925e9 | −1.15980 | −0.579900 | − | 0.814688i | \(-0.696908\pi\) | ||||
−0.579900 | + | 0.814688i | \(0.696908\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.13421e9i | 0.167173i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.84705e9 | 0.694842 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.71851e9i | 0.775913i | 0.921678 | + | 0.387956i | \(0.126819\pi\) | ||||
−0.921678 | + | 0.387956i | \(0.873181\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.45330e10 | −1.91896 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 1.93884e8i | − 0.0242581i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.34779e9 | −0.164193 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.15714e9i | 0.249275i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.59969e10 | −1.80087 | −0.900437 | − | 0.434986i | \(-0.856753\pi\) | ||||
−0.900437 | + | 0.434986i | \(0.856753\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.54565e9i | 0.913489i | 0.889598 | + | 0.456745i | \(0.150985\pi\) | ||||
−0.889598 | + | 0.456745i | \(0.849015\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.44401e9 | −0.567207 | −0.283604 | − | 0.958942i | \(-0.591530\pi\) | ||||
−0.283604 | + | 0.958942i | \(0.591530\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 2.70932e8i | − 0.0268302i | −0.999910 | − | 0.0134151i | \(-0.995730\pi\) | ||||
0.999910 | − | 0.0134151i | \(-0.00427028\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.95504e9 | −0.768209 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 1.57427e9i | − 0.144633i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.27370e9 | −0.114166 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 1.54177e9i | − 0.131594i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.60297e9 | −0.716698 | −0.358349 | − | 0.933588i | \(-0.616660\pi\) | ||||
−0.358349 | + | 0.933588i | \(0.616660\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.06591e8i | 0.0561034i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.62536e10 | −1.26017 | −0.630086 | − | 0.776526i | \(-0.716980\pi\) | ||||
−0.630086 | + | 0.776526i | \(0.716980\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.86074e9i | 0.729276i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.47359e8 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.12989e10i | 1.46906i | 0.678577 | + | 0.734529i | \(0.262597\pi\) | ||||
−0.678577 | + | 0.734529i | \(0.737403\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.42208e9 | 0.230669 | 0.115334 | − | 0.993327i | \(-0.463206\pi\) | ||||
0.115334 | + | 0.993327i | \(0.463206\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 1.70364e10i | − 1.09719i | −0.836090 | − | 0.548593i | \(-0.815164\pi\) | ||||
0.836090 | − | 0.548593i | \(-0.184836\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.04107e9 | 0.0655493 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.00228e10i | 1.20545i | 0.797950 | + | 0.602723i | \(0.205918\pi\) | ||||
−0.797950 | + | 0.602723i | \(0.794082\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.58193e10 | −0.931449 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.27059e10i | 1.84270i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.18172e10 | 1.20264 | 0.601320 | − | 0.799008i | \(-0.294642\pi\) | ||||
0.601320 | + | 0.799008i | \(0.294642\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.27778e9i | 0.331368i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.07371e9 | −0.158792 | −0.0793958 | − | 0.996843i | \(-0.525299\pi\) | ||||
−0.0793958 | + | 0.996843i | \(0.525299\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 1.66558e9i | − 0.0824517i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.44231e10 | 1.66837 | 0.834187 | − | 0.551481i | \(-0.185937\pi\) | ||||
0.834187 | + | 0.551481i | \(0.185937\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 4.13176e9i | − 0.192017i | −0.995381 | − | 0.0960086i | \(-0.969392\pi\) | ||||
0.995381 | − | 0.0960086i | \(-0.0306076\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.78268e9 | −0.399746 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 5.47550e9i | − 0.239125i | −0.992827 | − | 0.119563i | \(-0.961851\pi\) | ||||
0.992827 | − | 0.119563i | \(-0.0381493\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.47583e9 | 0.191499 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.67911e10i | 1.92210i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.24142e9 | 0.331772 | 0.165886 | − | 0.986145i | \(-0.446952\pi\) | ||||
0.165886 | + | 0.986145i | \(0.446952\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 2.16226e10i | − 0.836240i | −0.908392 | − | 0.418120i | \(-0.862689\pi\) | ||||
0.908392 | − | 0.418120i | \(-0.137311\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.06458e9 | −0.0782730 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.87931e10i | 0.684892i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.39407e9 | −0.192763 | −0.0963815 | − | 0.995344i | \(-0.530727\pi\) | ||||
−0.0963815 | + | 0.995344i | \(0.530727\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 1.30082e10i | − 0.447112i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.15482e9 | −0.173789 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.42840e9i | 0.0787887i | 0.999224 | + | 0.0393944i | \(0.0125429\pi\) | ||||
−0.999224 | + | 0.0393944i | \(0.987457\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.69140e10 | 1.49339 | 0.746696 | − | 0.665165i | \(-0.231639\pi\) | ||||
0.746696 | + | 0.665165i | \(0.231639\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 2.94036e10i | − 0.901249i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.93082e9 | −0.0580804 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 1.98912e9i | − 0.0576436i | −0.999585 | − | 0.0288218i | \(-0.990824\pi\) | ||||
0.999585 | − | 0.0288218i | \(-0.00917553\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.78975e10 | −1.64706 | −0.823528 | − | 0.567276i | \(-0.807997\pi\) | ||||
−0.823528 | + | 0.567276i | \(0.807997\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.31006e9i | 0.0907633i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.87960e10 | −1.85227 | −0.926137 | − | 0.377188i | \(-0.876891\pi\) | ||||
−0.926137 | + | 0.377188i | \(0.876891\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.88688e9i | 0.0489924i | 0.999700 | + | 0.0244962i | \(0.00779816\pi\) | ||||
−0.999700 | + | 0.0244962i | \(0.992202\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.68120e10 | 1.44877 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 2.03669e10i | − 0.501117i | −0.968101 | − | 0.250559i | \(-0.919386\pi\) | ||||
0.968101 | − | 0.250559i | \(-0.0806143\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.19304e10 | −0.288369 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 1.83886e9i | − 0.0429046i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.31506e10 | −1.44781 | −0.723907 | − | 0.689898i | \(-0.757655\pi\) | ||||
−0.723907 | + | 0.689898i | \(0.757655\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 5.65698e10i | − 1.25251i | −0.779619 | − | 0.626255i | \(-0.784587\pi\) | ||||
0.779619 | − | 0.626255i | \(-0.215413\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.67294e10 | 1.01687 | 0.508436 | − | 0.861100i | \(-0.330224\pi\) | ||||
0.508436 | + | 0.861100i | \(0.330224\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 8.15355e10i | − 1.71427i | −0.515091 | − | 0.857135i | \(-0.672242\pi\) | ||||
0.515091 | − | 0.857135i | \(-0.327758\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.32457e8 | −0.0130719 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 1.41769e10i | − 0.283228i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.17452e10 | 0.427158 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.57462e9i | 0.105894i | 0.998597 | + | 0.0529472i | \(0.0168615\pi\) | ||||
−0.998597 | + | 0.0529472i | \(0.983138\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.93479e9 | −0.0735092 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 4.10399e10i | − 0.741719i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.40461e9 | 0.0960834 | 0.0480417 | − | 0.998845i | \(-0.484702\pi\) | ||||
0.0480417 | + | 0.998845i | \(0.484702\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.58242e10i | 0.616383i | 0.951324 | + | 0.308191i | \(0.0997237\pi\) | ||||
−0.951324 | + | 0.308191i | \(0.900276\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.84500e10 | 0.650892 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.31846e8i | 0.0152728i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.29005e9 | −0.149836 | −0.0749179 | − | 0.997190i | \(-0.523869\pi\) | ||||
−0.0749179 | + | 0.997190i | \(0.523869\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 3.48297e10i | − 0.544099i | −0.962283 | − | 0.272050i | \(-0.912299\pi\) | ||||
0.962283 | − | 0.272050i | \(-0.0877015\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.34120e11 | 2.06219 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 7.35332e10i | − 1.09550i | −0.836642 | − | 0.547750i | \(-0.815484\pi\) | ||||
0.836642 | − | 0.547750i | \(-0.184516\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.92745e10 | −0.429344 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.67591e10i | 1.09119i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.62173e10 | 0.226996 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 8.62629e10i | − 1.17077i | −0.810754 | − | 0.585387i | \(-0.800943\pi\) | ||||
0.810754 | − | 0.585387i | \(-0.199057\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.40847e10 | −0.188252 | −0.0941260 | − | 0.995560i | \(-0.530006\pi\) | ||||
−0.0941260 | + | 0.995560i | \(0.530006\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 4.76611e10i | − 0.617905i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.89001e10 | 0.879827 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 2.49791e9i | − 0.0309505i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.55640e10 | 1.16648 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 7.86122e9i | − 0.0931397i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.32399e10 | 1.08846 | 0.544230 | − | 0.838936i | \(-0.316822\pi\) | ||||
0.544230 | + | 0.838936i | \(0.316822\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 1.35775e11i | − 1.53898i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.51789e10 | 0.281247 | 0.140623 | − | 0.990063i | \(-0.455089\pi\) | ||||
0.140623 | + | 0.990063i | \(0.455089\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.84354e10i | 0.308498i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.18819e10 | −0.447843 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.43202e10i | 0.668231i | 0.942532 | + | 0.334115i | \(0.108438\pi\) | ||||
−0.942532 | + | 0.334115i | \(0.891562\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.96827e9 | 0.0303988 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 1.65235e10i | − 0.164463i | −0.996613 | − | 0.0822314i | \(-0.973795\pi\) | ||||
0.996613 | − | 0.0822314i | \(-0.0262047\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.69427e11 | 2.64391 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.28229e10i | 0.313132i | 0.987667 | + | 0.156566i | \(0.0500424\pi\) | ||||
−0.987667 | + | 0.156566i | \(0.949958\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.16352e11 | −1.09454 | −0.547269 | − | 0.836957i | \(-0.684332\pi\) | ||||
−0.547269 | + | 0.836957i | \(0.684332\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.18242e10i | 0.565571i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.44383e10 | 0.130260 | 0.0651302 | − | 0.997877i | \(-0.479254\pi\) | ||||
0.0651302 | + | 0.997877i | \(0.479254\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 4.61399e9i | − 0.0404922i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.60339e10 | −0.571600 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.46230e11i | 1.23164i | 0.787886 | + | 0.615821i | \(0.211175\pi\) | ||||
−0.787886 | + | 0.615821i | \(0.788825\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.52474e10 | 0.292864 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 1.76245e11i | − 1.42527i | −0.701534 | − | 0.712636i | \(-0.747501\pi\) | ||||
0.701534 | − | 0.712636i | \(-0.252499\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.24503e10 | 0.338699 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 1.77720e11i | − 1.38047i | −0.723583 | − | 0.690237i | \(-0.757506\pi\) | ||||
0.723583 | − | 0.690237i | \(-0.242494\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.20993e10 | −0.246035 | −0.123018 | − | 0.992404i | \(-0.539257\pi\) | ||||
−0.123018 | + | 0.992404i | \(0.539257\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.24949e11i | 0.932635i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.41329e11 | −1.04107 | −0.520533 | − | 0.853842i | \(-0.674267\pi\) | ||||
−0.520533 | + | 0.853842i | \(0.674267\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.39549e9i | 0.0243633i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.44012e10 | 0.385271 | 0.192636 | − | 0.981270i | \(-0.438296\pi\) | ||||
0.192636 | + | 0.981270i | \(0.438296\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 2.79721e11i | − 1.93012i | −0.262029 | − | 0.965060i | \(-0.584392\pi\) | ||||
0.262029 | − | 0.965060i | \(-0.415608\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.53977e11 | −1.04880 | −0.524401 | − | 0.851471i | \(-0.675711\pi\) | ||||
−0.524401 | + | 0.851471i | \(0.675711\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.08514e10i | 0.337560i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.61634e9 | 0.0302536 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 9.08352e10i | − 0.580298i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.78193e11 | −1.12402 | −0.562008 | − | 0.827132i | \(-0.689971\pi\) | ||||
−0.562008 | + | 0.827132i | \(0.689971\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 9.17918e10i | − 0.564558i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.64593e9 | 0.00999665 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 4.15099e9i | − 0.0245878i | −0.999924 | − | 0.0122939i | \(-0.996087\pi\) | ||||
0.999924 | − | 0.0122939i | \(-0.00391337\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.08912e10 | −0.122213 | −0.0611067 | − | 0.998131i | \(-0.519463\pi\) | ||||
−0.0611067 | + | 0.998131i | \(0.519463\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.96707e11i | 1.12254i | 0.827632 | + | 0.561272i | \(0.189688\pi\) | ||||
−0.827632 | + | 0.561272i | \(0.810312\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.36829e11 | 0.771255 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.19791e11i | 0.658826i | 0.944186 | + | 0.329413i | \(0.106851\pi\) | ||||
−0.944186 | + | 0.329413i | \(0.893149\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.21611e11 | −1.74729 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 1.57428e11i | − 0.834718i | −0.908742 | − | 0.417359i | \(-0.862956\pi\) | ||||
0.908742 | − | 0.417359i | \(-0.137044\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.18188e11 | −0.619108 | −0.309554 | − | 0.950882i | \(-0.600180\pi\) | ||||
−0.309554 | + | 0.950882i | \(0.600180\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.13938e10i | 0.160530i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.08453e10 | −0.408462 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 2.03096e10i | − 0.100187i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.81868e11 | −1.37400 | −0.686999 | − | 0.726658i | \(-0.741072\pi\) | ||||
−0.686999 | + | 0.726658i | \(0.741072\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.16668e11i | 0.555388i | 0.960670 | + | 0.277694i | \(0.0895701\pi\) | ||||
−0.960670 | + | 0.277694i | \(0.910430\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.67341e10 | 0.172818 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.48480e11i | 0.682316i | 0.940006 | + | 0.341158i | \(0.110819\pi\) | ||||
−0.940006 | + | 0.341158i | \(0.889181\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.87943e11 | 1.76200 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 1.38258e10i | − 0.0613497i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.22512e11 | 0.537363 | 0.268681 | − | 0.963229i | \(-0.413412\pi\) | ||||
0.268681 | + | 0.963229i | \(0.413412\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.34177e11i | 2.71813i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.76645e10 | 0.244330 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 2.62323e11i | − 1.08634i | −0.839623 | − | 0.543169i | \(-0.817224\pi\) | ||||
0.839623 | − | 0.543169i | \(-0.182776\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.71764e10 | 0.275040 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.20049e11i | 0.480486i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.26919e11 | 0.502276 | 0.251138 | − | 0.967951i | \(-0.419195\pi\) | ||||
0.251138 | + | 0.967951i | \(0.419195\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.00212e11i | 0.387761i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.93424e10 | 0.0740091 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.80440e10i | 0.329446i | 0.986340 | + | 0.164723i | \(0.0526730\pi\) | ||||
−0.986340 | + | 0.164723i | \(0.947327\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.87057e10 | −0.254245 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.31106e11i | 1.92234i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.70730e11 | 0.611185 | 0.305593 | − | 0.952162i | \(-0.401145\pi\) | ||||
0.305593 | + | 0.952162i | \(0.401145\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.85229e10i | 0.239975i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.96253e11 | 1.37264 | 0.686321 | − | 0.727299i | \(-0.259225\pi\) | ||||
0.686321 | + | 0.727299i | \(0.259225\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 6.65260e9i | − 0.0225487i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.07867e11 | −1.70283 | −0.851417 | − | 0.524489i | \(-0.824256\pi\) | ||||
−0.851417 | + | 0.524489i | \(0.824256\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.71694e11i | 0.891508i | 0.895155 | + | 0.445754i | \(0.147064\pi\) | ||||
−0.895155 | + | 0.445754i | \(0.852936\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.24909e11 | −1.05472 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.55376e10i | 0.271788i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.61830e11 | −0.823115 | −0.411557 | − | 0.911384i | \(-0.635015\pi\) | ||||
−0.411557 | + | 0.911384i | \(0.635015\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.94699e11i | 2.75353i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.81228e11 | −1.46544 | −0.732720 | − | 0.680531i | \(-0.761749\pi\) | ||||
−0.732720 | + | 0.680531i | \(0.761749\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.99450e10i | 0.0892863i | 0.999003 | + | 0.0446432i | \(0.0142151\pi\) | ||||
−0.999003 | + | 0.0446432i | \(0.985785\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.21530e11 | 0.358579 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.86483e10i | 0.0827786i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.60756e11 | −1.03159 | −0.515796 | − | 0.856712i | \(-0.672504\pi\) | ||||
−0.515796 | + | 0.856712i | \(0.672504\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 6.41322e11i | − 1.79621i | −0.439776 | − | 0.898107i | \(-0.644942\pi\) | ||||
0.439776 | − | 0.898107i | \(-0.355058\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.58338e11 | 1.82491 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.26453e10i | 0.115803i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.80177e9 | −0.0263451 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 4.40376e11i | − 1.15970i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.13315e11 | −1.59876 | −0.799382 | − | 0.600823i | \(-0.794840\pi\) | ||||
−0.799382 | + | 0.600823i | \(0.794840\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.41159e11i | 0.616023i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.25230e9 | 0.0107530 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 3.02614e11i | − 0.749990i | −0.927027 | − | 0.374995i | \(-0.877644\pi\) | ||||
0.927027 | − | 0.374995i | \(-0.122356\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.83852e10 | −0.192330 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 3.07928e11i | − 0.740606i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.92563e10 | −0.212547 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.95071e11i | 0.922320i | 0.887317 | + | 0.461160i | \(0.152567\pi\) | ||||
−0.887317 | + | 0.461160i | \(0.847433\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.52971e11 | 1.27826 | 0.639129 | − | 0.769099i | \(-0.279295\pi\) | ||||
0.639129 | + | 0.769099i | \(0.279295\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.12017e11i | 1.84049i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.06755e10 | −0.113739 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.37182e11i | 0.522047i | 0.965332 | + | 0.261024i | \(0.0840601\pi\) | ||||
−0.965332 | + | 0.261024i | \(0.915940\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.39357e11 | −1.39362 | −0.696809 | − | 0.717256i | \(-0.745398\pi\) | ||||
−0.696809 | + | 0.717256i | \(0.745398\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 2.61243e11i | − 0.558500i | −0.960218 | − | 0.279250i | \(-0.909914\pi\) | ||||
0.960218 | − | 0.279250i | \(-0.0900859\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.75999e11 | −1.21956 | −0.609781 | − | 0.792570i | \(-0.708742\pi\) | ||||
−0.609781 | + | 0.792570i | \(0.708742\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.79965e10i | 0.0789158i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.43201e11 | −0.705997 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 6.46156e11i | − 1.30404i | −0.758203 | − | 0.652018i | \(-0.773923\pi\) | ||||
0.758203 | − | 0.652018i | \(-0.226077\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.94263e11 | −0.388334 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 8.22991e11i | − 1.61424i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.11840e11 | −0.217301 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.90991e11i | 0.364161i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.56405e11 | −1.23987 | −0.619934 | − | 0.784654i | \(-0.712841\pi\) | ||||
−0.619934 | + | 0.784654i | \(0.712841\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 1.41157e11i | − 0.261686i | −0.991403 | − | 0.130843i | \(-0.958232\pi\) | ||||
0.991403 | − | 0.130843i | \(-0.0417684\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.85464e11 | 0.524299 | 0.262149 | − | 0.965027i | \(-0.415569\pi\) | ||||
0.262149 | + | 0.965027i | \(0.415569\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.38850e11i | 0.791176i | 0.918428 | + | 0.395588i | \(0.129459\pi\) | ||||
−0.918428 | + | 0.395588i | \(0.870541\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.14058e12 | 2.03733 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 4.40541e11i | − 0.772516i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.39288e9 | 0.00242014 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.26958e11i | 0.387180i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.30388e11 | 0.220414 | 0.110207 | − | 0.993909i | \(-0.464849\pi\) | ||||
0.110207 | + | 0.993909i | \(0.464849\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 2.22271e11i | − 0.368960i | −0.982836 | − | 0.184480i | \(-0.940940\pi\) | ||||
0.982836 | − | 0.184480i | \(-0.0590600\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.44193e11 | 1.22417 | 0.612086 | − | 0.790791i | \(-0.290330\pi\) | ||||
0.612086 | + | 0.790791i | \(0.290330\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 6.60994e11i | − 1.06783i | −0.845538 | − | 0.533916i | \(-0.820720\pi\) | ||||
0.845538 | − | 0.533916i | \(-0.179280\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.21612e10 | 0.131541 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 5.79691e10i | − 0.0911571i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.89734e11 | 1.38665 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.60885e11i | 1.31797i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.19169e11 | 0.484308 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 9.79473e11i | 1.46015i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.10739e12 | −1.63634 | −0.818168 | − | 0.574980i | \(-0.805010\pi\) | ||||
−0.818168 | + | 0.574980i | \(0.805010\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 9.17243e10i | − 0.133171i | −0.997781 | − | 0.0665857i | \(-0.978789\pi\) | ||||
0.997781 | − | 0.0665857i | \(-0.0212106\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.85330e10 | 0.0698479 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 2.87868e11i | − 0.407114i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.14021e11 | −1.14123 | −0.570615 | − | 0.821218i | \(-0.693295\pi\) | ||||
−0.570615 | + | 0.821218i | \(0.693295\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 2.05223e9i | − 0.00282761i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.25470e12 | 1.71385 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 8.69774e11i | − 1.16773i | −0.811849 | − | 0.583867i | \(-0.801539\pi\) | ||||
0.811849 | − | 0.583867i | \(-0.198461\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.81000e10 | −0.0374031 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.46521e11i | 0.584245i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.17180e11 | 1.18986 | 0.594930 | − | 0.803777i | \(-0.297180\pi\) | ||||
0.594930 | + | 0.803777i | \(0.297180\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.00191e11i | 0.382859i | 0.981506 | + | 0.191430i | \(0.0613123\pi\) | ||||
−0.981506 | + | 0.191430i | \(0.938688\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.21246e11 | −0.153327 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 7.39412e11i | − 0.919362i | −0.888084 | − | 0.459681i | \(-0.847964\pi\) | ||||
0.888084 | − | 0.459681i | \(-0.152036\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.44721e10 | 0.0794890 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 1.49547e11i | − 0.181303i | −0.995883 | − | 0.0906516i | \(-0.971105\pi\) | ||||
0.995883 | − | 0.0906516i | \(-0.0288950\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.76534e12 | 2.12233 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.47240e11i | 0.410540i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.14227e11 | 0.251177 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 1.36639e12i | − 1.57566i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.07075e12 | 1.22456 | 0.612282 | − | 0.790639i | \(-0.290252\pi\) | ||||
0.612282 | + | 0.790639i | \(0.290252\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 1.54708e12i | − 1.74035i | −0.492743 | − | 0.870175i | \(-0.664006\pi\) | ||||
0.492743 | − | 0.870175i | \(-0.335994\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.67640e11 | −0.633318 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.50352e12i | 1.65017i | 0.565006 | + | 0.825087i | \(0.308874\pi\) | ||||
−0.565006 | + | 0.825087i | \(0.691126\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.34889e11 | −0.582281 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 5.92520e11i | − 0.634584i | −0.948328 | − | 0.317292i | \(-0.897227\pi\) | ||||
0.948328 | − | 0.317292i | \(-0.102773\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.99277e12 | 2.11696 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 1.44077e11i | − 0.150594i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.60363e11 | −0.788363 | −0.394182 | − | 0.919033i | \(-0.628972\pi\) | ||||
−0.394182 | + | 0.919033i | \(0.628972\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 5.27685e11i | − 0.538372i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.93177e10 | −0.0600349 | −0.0300175 | − | 0.999549i | \(-0.509556\pi\) | ||||
−0.0300175 | + | 0.999549i | \(0.509556\pi\) | |||||||
\(998\) | 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.c.a.197.16 | yes | 16 | |
3.2 | odd | 2 | inner | 252.9.c.a.197.1 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.9.c.a.197.1 | ✓ | 16 | 3.2 | odd | 2 | inner | |
252.9.c.a.197.16 | yes | 16 | 1.1 | even | 1 | trivial |