Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [432,7,Mod(161,432)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(432, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("432.161");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 432 = 2^{4} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 432.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: | \(99.3833641238\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 75x^{4} - 90x^{3} + 1861x^{2} + 7864x + 10098 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{23}\cdot 3^{6} \) |
Twist minimal: | no (minimal twist has level 216) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 161.3 | ||
Root | \(7.70376 - 1.41421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 432.161 |
Dual form | 432.7.e.k.161.4 |
$q$-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 \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).
\(n\) | \(271\) | \(325\) | \(353\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(5\) | − 62.7833i | − 0.502266i | −0.967953 | − | 0.251133i | \(-0.919197\pi\) | ||||
0.967953 | − | 0.251133i | \(-0.0808032\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 496.882 | 1.44863 | 0.724317 | − | 0.689467i | \(-0.242155\pi\) | ||||
0.724317 | + | 0.689467i | \(0.242155\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 1437.06i | − 1.07969i | −0.841765 | − | 0.539844i | \(-0.818483\pi\) | ||||
0.841765 | − | 0.539844i | \(-0.181517\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3905.03 | 1.77744 | 0.888719 | − | 0.458452i | \(-0.151596\pi\) | ||||
0.888719 | + | 0.458452i | \(0.151596\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 8385.53i | 1.70681i | 0.521252 | + | 0.853403i | \(0.325465\pi\) | ||||
−0.521252 | + | 0.853403i | \(0.674535\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3625.19 | 0.528531 | 0.264265 | − | 0.964450i | \(-0.414871\pi\) | ||||
0.264265 | + | 0.964450i | \(0.414871\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 24070.3i | 1.97833i | 0.146820 | + | 0.989163i | \(0.453096\pi\) | ||||
−0.146820 | + | 0.989163i | \(0.546904\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 11683.3 | 0.747729 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 38898.5i | − 1.59492i | −0.603372 | − | 0.797460i | \(-0.706177\pi\) | ||||
0.603372 | − | 0.797460i | \(-0.293823\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10728.8 | 0.360136 | 0.180068 | − | 0.983654i | \(-0.442368\pi\) | ||||
0.180068 | + | 0.983654i | \(0.442368\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 31195.9i | − 0.727600i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −45162.5 | −0.891606 | −0.445803 | − | 0.895131i | \(-0.647082\pi\) | ||||
−0.445803 | + | 0.895131i | \(0.647082\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 35120.1i | 0.509571i | 0.966998 | + | 0.254785i | \(0.0820048\pi\) | ||||
−0.966998 | + | 0.254785i | \(0.917995\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 21584.6 | 0.271481 | 0.135740 | − | 0.990744i | \(-0.456659\pi\) | ||||
0.135740 | + | 0.990744i | \(0.456659\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 103509.i | 0.996974i | 0.866897 | + | 0.498487i | \(0.166111\pi\) | ||||
−0.866897 | + | 0.498487i | \(0.833889\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 129242. | 1.09854 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 70152.9i | − 0.471214i | −0.971848 | − | 0.235607i | \(-0.924292\pi\) | ||||
0.971848 | − | 0.235607i | \(-0.0757078\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −90223.6 | −0.542291 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 185774.i | 0.904541i | 0.891881 | + | 0.452271i | \(0.149386\pi\) | ||||
−0.891881 | + | 0.452271i | \(0.850614\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −301079. | −1.32645 | −0.663226 | − | 0.748419i | \(-0.730813\pi\) | ||||
−0.663226 | + | 0.748419i | \(0.730813\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 245171.i | − 0.892748i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 130275. | 0.433148 | 0.216574 | − | 0.976266i | \(-0.430512\pi\) | ||||
0.216574 | + | 0.976266i | \(0.430512\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 464741.i | 1.29848i | 0.760583 | + | 0.649241i | \(0.224913\pi\) | ||||
−0.760583 | + | 0.649241i | \(0.775087\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 274352. | 0.705245 | 0.352623 | − | 0.935766i | \(-0.385290\pi\) | ||||
0.352623 | + | 0.935766i | \(0.385290\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 714051.i | − 1.56407i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −705830. | −1.43159 | −0.715795 | − | 0.698311i | \(-0.753935\pi\) | ||||
−0.715795 | + | 0.698311i | \(0.753935\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 233654.i | 0.408639i | 0.978904 | + | 0.204319i | \(0.0654981\pi\) | ||||
−0.978904 | + | 0.204319i | \(0.934502\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 526471. | 0.857271 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 1.16112e6i | − 1.64706i | −0.567275 | − | 0.823529i | \(-0.692002\pi\) | ||||
0.567275 | − | 0.823529i | \(-0.307998\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.94034e6 | 2.57486 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 227602.i | − 0.265463i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 129972. | 0.142408 | 0.0712038 | − | 0.997462i | \(-0.477316\pi\) | ||||
0.0712038 | + | 0.997462i | \(0.477316\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 44362.7i | − 0.0430580i | −0.999768 | − | 0.0215290i | \(-0.993147\pi\) | ||||
0.999768 | − | 0.0215290i | \(-0.00685342\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.21733e6 | 1.11403 | 0.557013 | − | 0.830504i | \(-0.311947\pi\) | ||||
0.557013 | + | 0.830504i | \(0.311947\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 194040.i | 0.158394i | 0.996859 | + | 0.0791972i | \(0.0252357\pi\) | ||||
−0.996859 | + | 0.0791972i | \(0.974764\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.22984e6 | 1.72184 | 0.860921 | − | 0.508738i | \(-0.169888\pi\) | ||||
0.860921 | + | 0.508738i | \(0.169888\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.17695e6i | 0.815684i | 0.913052 | + | 0.407842i | \(0.133719\pi\) | ||||
−0.913052 | + | 0.407842i | \(0.866281\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.51121e6 | 0.993647 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.16662e6i | 2.47254i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −293593. | −0.165725 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 1.71450e6i | − 0.877825i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.57158e6 | −1.25542 | −0.627710 | − | 0.778448i | \(-0.716007\pi\) | ||||
−0.627710 | + | 0.778448i | \(0.716007\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.08627e6i | 0.928020i | 0.885830 | + | 0.464010i | \(0.153590\pi\) | ||||
−0.885830 | + | 0.464010i | \(0.846410\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.80129e6 | 0.765648 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 2.52222e6i | − 0.980892i | −0.871471 | − | 0.490446i | \(-0.836834\pi\) | ||||
0.871471 | − | 0.490446i | \(-0.163166\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −558638. | −0.208011 | −0.104006 | − | 0.994577i | \(-0.533166\pi\) | ||||
−0.104006 | + | 0.994577i | \(0.533166\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 5.61178e6i | − 1.91908i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.44218e6 | −0.801074 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 951789.i | 0.287728i | 0.989597 | + | 0.143864i | \(0.0459528\pi\) | ||||
−0.989597 | + | 0.143864i | \(0.954047\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.52962e6 | 1.02517 | 0.512586 | − | 0.858636i | \(-0.328687\pi\) | ||||
0.512586 | + | 0.858636i | \(0.328687\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 673590.i | − 0.180884i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 678623. | 0.175360 | 0.0876798 | − | 0.996149i | \(-0.472055\pi\) | ||||
0.0876798 | + | 0.996149i | \(0.472055\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.19601e7i | 2.86587i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.74597e6 | 0.634064 | 0.317032 | − | 0.948415i | \(-0.397314\pi\) | ||||
0.317032 | + | 0.948415i | \(0.397314\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 6.51214e6i | − 1.39822i | −0.715016 | − | 0.699108i | \(-0.753580\pi\) | ||||
0.715016 | − | 0.699108i | \(-0.246420\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.04225e7 | 2.15929 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 3.02492e6i | − 0.584220i | −0.956385 | − | 0.292110i | \(-0.905643\pi\) | ||||
0.956385 | − | 0.292110i | \(-0.0943573\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.80520e6 | 1.08319 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.43892e6i | 0.599602i | 0.954002 | + | 0.299801i | \(0.0969202\pi\) | ||||
−0.954002 | + | 0.299801i | \(0.903080\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.76769e6 | 0.804030 | 0.402015 | − | 0.915633i | \(-0.368310\pi\) | ||||
0.402015 | + | 0.915633i | \(0.368310\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.83545e6i | 0.447824i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.20506e7 | 1.84282 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 1.43616e6i | − 0.206112i | −0.994676 | − | 0.103056i | \(-0.967138\pi\) | ||||
0.994676 | − | 0.103056i | \(-0.0328621\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.88018e6 | 0.957036 | 0.478518 | − | 0.878078i | \(-0.341174\pi\) | ||||
0.478518 | + | 0.878078i | \(0.341174\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 4.46415e6i | − 0.583902i | −0.956433 | − | 0.291951i | \(-0.905696\pi\) | ||||
0.956433 | − | 0.291951i | \(-0.0943045\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.21686e7 | 1.54412 | 0.772058 | − | 0.635552i | \(-0.219227\pi\) | ||||
0.772058 | + | 0.635552i | \(0.219227\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 1.93280e7i | − 2.31046i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.20496e6 | 0.255940 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 5.20964e6i | − 0.570648i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.68577e7 | −1.79453 | −0.897265 | − | 0.441491i | \(-0.854450\pi\) | ||||
−0.897265 | + | 0.441491i | \(0.854450\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 1.35515e6i | − 0.136356i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.33095e6 | 0.521706 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.27458e7i | 3.03374i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.09013e6 | 0.0983019 | 0.0491510 | − | 0.998791i | \(-0.484348\pi\) | ||||
0.0491510 | + | 0.998791i | \(0.484348\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.12524e6i | 0.523656i | 0.965115 | + | 0.261828i | \(0.0843253\pi\) | ||||
−0.965115 | + | 0.261828i | \(0.915675\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.73155e6 | −0.810356 | −0.405178 | − | 0.914238i | \(-0.632790\pi\) | ||||
−0.405178 | + | 0.914238i | \(0.632790\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.98923e6i | 0.473482i | 0.971573 | + | 0.236741i | \(0.0760793\pi\) | ||||
−0.971573 | + | 0.236741i | \(0.923921\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.49862e6 | 0.500746 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.14769e6i | 0.523567i | 0.965127 | + | 0.261783i | \(0.0843106\pi\) | ||||
−0.965127 | + | 0.261783i | \(0.915689\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.98986e6 | −0.213599 | −0.106800 | − | 0.994281i | \(-0.534060\pi\) | ||||
−0.106800 | + | 0.994281i | \(0.534060\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 8.11427e6i | − 0.551761i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.41565e7 | 0.939431 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 2.85894e7i | − 1.80794i | −0.427598 | − | 0.903969i | \(-0.640640\pi\) | ||||
0.427598 | − | 0.903969i | \(-0.359360\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.45906e7 | 2.13597 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 9.45391e6i | − 0.556945i | −0.960444 | − | 0.278472i | \(-0.910172\pi\) | ||||
0.960444 | − | 0.278472i | \(-0.0898281\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.24404e7 | −1.29161 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.26436e7i | 0.695030i | 0.937674 | + | 0.347515i | \(0.112974\pi\) | ||||
−0.937674 | + | 0.347515i | \(0.887026\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.40443e6 | −0.236675 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.91952e7i | 0.986133i | 0.869992 | + | 0.493067i | \(0.164124\pi\) | ||||
−0.869992 | + | 0.493067i | \(0.835876\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.10242e6 | 0.155881 | 0.0779404 | − | 0.996958i | \(-0.475166\pi\) | ||||
0.0779404 | + | 0.996958i | \(0.475166\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 1.67896e7i | − 0.807313i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.97207e7 | −0.927861 | −0.463930 | − | 0.885872i | \(-0.653561\pi\) | ||||
−0.463930 | + | 0.885872i | \(0.653561\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 3.26616e7i | − 1.47203i | −0.676963 | − | 0.736017i | \(-0.736704\pi\) | ||||
0.676963 | − | 0.736017i | \(-0.263296\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.16099e7 | 0.512233 | 0.256117 | − | 0.966646i | \(-0.417557\pi\) | ||||
0.256117 | + | 0.966646i | \(0.417557\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.74506e7i | 0.738182i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.61796e7 | −1.91318 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 3.03466e7i | − 1.20645i | −0.797573 | − | 0.603223i | \(-0.793883\pi\) | ||||
0.797573 | − | 0.603223i | \(-0.206117\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.16635e7 | 0.454321 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9.39953e7i | 3.51635i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.07250e7 | 0.393276 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.89027e7i | 0.666232i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.99035e6 | −0.172471 | −0.0862355 | − | 0.996275i | \(-0.527484\pi\) | ||||
−0.0862355 | + | 0.996275i | \(0.527484\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 1.75448e7i | − 0.583266i | −0.956530 | − | 0.291633i | \(-0.905801\pi\) | ||||
0.956530 | − | 0.291633i | \(-0.0941985\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.42107e7 | 0.463429 | 0.231714 | − | 0.972784i | \(-0.425567\pi\) | ||||
0.231714 | + | 0.972784i | \(0.425567\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 3.79914e7i | − 1.19264i | −0.802749 | − | 0.596318i | \(-0.796630\pi\) | ||||
0.802749 | − | 0.596318i | \(-0.203370\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.58996e7 | −1.72202 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.03992e7i | 0.902099i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.56235e7 | 1.32904 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.14316e7i | 1.44425i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.85294e6 | −0.106245 | −0.0531224 | − | 0.998588i | \(-0.516917\pi\) | ||||
−0.0531224 | + | 0.998588i | \(0.516917\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 8.17909e6i | − 0.217556i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.67260e7 | −1.22087 | −0.610434 | − | 0.792067i | \(-0.709005\pi\) | ||||
−0.610434 | + | 0.792067i | \(0.709005\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 1.54180e7i | − 0.388835i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.76057e6 | 0.142752 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 8.68841e6i | − 0.207947i | −0.994580 | − | 0.103973i | \(-0.966844\pi\) | ||||
0.994580 | − | 0.103973i | \(-0.0331557\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.56685e7 | 0.839089 | 0.419545 | − | 0.907735i | \(-0.362190\pi\) | ||||
0.419545 | + | 0.907735i | \(0.362190\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 6.34071e7i | − 1.44150i | −0.693196 | − | 0.720749i | \(-0.743798\pi\) | ||||
0.693196 | − | 0.720749i | \(-0.256202\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.91780e7 | 0.652184 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 4.47602e7i | − 0.967405i | −0.875233 | − | 0.483702i | \(-0.839292\pi\) | ||||
0.875233 | − | 0.483702i | \(-0.160708\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.39039e7 | −0.720655 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 1.72247e7i | − 0.354221i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.51940e7 | −0.307378 | −0.153689 | − | 0.988119i | \(-0.549115\pi\) | ||||
−0.153689 | + | 0.988119i | \(0.549115\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 3.48577e7i | − 0.682616i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9.43540e7 | −1.81817 | −0.909084 | − | 0.416614i | \(-0.863217\pi\) | ||||
−0.909084 | + | 0.416614i | \(0.863217\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 1.51900e8i | − 2.83487i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.08369e6 | −0.148488 | −0.0742441 | − | 0.997240i | \(-0.523654\pi\) | ||||
−0.0742441 | + | 0.997240i | \(0.523654\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.63217e7i | 1.71446i | 0.514932 | + | 0.857231i | \(0.327817\pi\) | ||||
−0.514932 | + | 0.857231i | \(0.672183\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.48305e7 | −0.785581 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.43211e7i | 0.413176i | 0.978428 | + | 0.206588i | \(0.0662360\pi\) | ||||
−0.978428 | + | 0.206588i | \(0.933764\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.01842e8 | −3.37662 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.43143e7i | 0.719039i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.70196e7 | 0.751463 | 0.375732 | − | 0.926729i | \(-0.377391\pi\) | ||||
0.375732 | + | 0.926729i | \(0.377391\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.79234e6i | 0.105338i | 0.998612 | + | 0.0526692i | \(0.0167729\pi\) | ||||
−0.998612 | + | 0.0526692i | \(0.983227\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.18964e7 | 0.640120 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.49015e7i | 0.962656i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.43151e7 | −1.23235 | −0.616177 | − | 0.787608i | \(-0.711319\pi\) | ||||
−0.616177 | + | 0.787608i | \(0.711319\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.23076e7i | 1.31035i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.46696e7 | 0.205245 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 1.72937e7i | − 0.235097i | −0.993067 | − | 0.117548i | \(-0.962496\pi\) | ||||
0.993067 | − | 0.117548i | \(-0.0375035\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.25301e8 | −1.67922 | −0.839612 | − | 0.543187i | \(-0.817217\pi\) | ||||
−0.839612 | + | 0.543187i | \(0.817217\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 9.79704e7i | 1.27623i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.49601e8 | −1.92154 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 6.28715e7i | − 0.785275i | −0.919693 | − | 0.392638i | \(-0.871563\pi\) | ||||
0.919693 | − | 0.392638i | \(-0.128437\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.66021e7 | −0.697219 | −0.348609 | − | 0.937268i | \(-0.613346\pi\) | ||||
−0.348609 | + | 0.937268i | \(0.613346\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.72595e7i | 1.04561i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.82688e7 | −0.452326 | −0.226163 | − | 0.974089i | \(-0.572618\pi\) | ||||
−0.226163 | + | 0.974089i | \(0.572618\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 8.79866e7i | − 1.01206i | −0.862517 | − | 0.506029i | \(-0.831113\pi\) | ||||
0.862517 | − | 0.506029i | \(-0.168887\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.28992e7 | −0.827262 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.97838e7i | 0.991879i | 0.868357 | + | 0.495940i | \(0.165176\pi\) | ||||
−0.868357 | + | 0.495940i | \(0.834824\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.04699e7 | 0.550177 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 1.21821e8i | − 1.29327i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.76314e8 | 1.84731 | 0.923653 | − | 0.383229i | \(-0.125188\pi\) | ||||
0.923653 | + | 0.383229i | \(0.125188\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 5.28602e7i | − 0.539543i | −0.962924 | − | 0.269771i | \(-0.913052\pi\) | ||||
0.962924 | − | 0.269771i | \(-0.0869481\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.74136e6 | 0.0679211 | 0.0339605 | − | 0.999423i | \(-0.489188\pi\) | ||||
0.0339605 | + | 0.999423i | \(0.489188\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.62620e7i | 0.159670i | 0.996808 | + | 0.0798351i | \(0.0254394\pi\) | ||||
−0.996808 | + | 0.0798351i | \(0.974561\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.47312e7 | 0.627473 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 3.10185e7i | − 0.293114i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.23541e7 | 0.395198 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 6.65819e6i | − 0.0605829i | −0.999541 | − | 0.0302914i | \(-0.990356\pi\) | ||||
0.999541 | − | 0.0302914i | \(-0.00964354\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.76361e8 | −1.58478 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 8.16004e6i | − 0.0715265i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.41405e7 | 0.728481 | 0.364241 | − | 0.931305i | \(-0.381329\pi\) | ||||
0.364241 | + | 0.931305i | \(0.381329\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 2.06143e7i | − 0.174150i | −0.996202 | − | 0.0870751i | \(-0.972248\pi\) | ||||
0.996202 | − | 0.0870751i | \(-0.0277520\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.26185e8 | 2.72222 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.30921e8i | 1.88103i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.76628e7 | −0.544563 | −0.272282 | − | 0.962218i | \(-0.587778\pi\) | ||||
−0.272282 | + | 0.962218i | \(0.587778\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 8.12807e7i | − 0.638680i | −0.947640 | − | 0.319340i | \(-0.896539\pi\) | ||||
0.947640 | − | 0.319340i | \(-0.103461\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.78523e6 | −0.0216266 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 1.46456e8i | − 1.11059i | −0.831655 | − | 0.555293i | \(-0.812606\pi\) | ||||
0.831655 | − | 0.555293i | \(-0.187394\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.36321e8 | 1.02164 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 7.64278e7i | − 0.559538i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.48749e8 | 1.07642 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.00866e8i | 0.713232i | 0.934251 | + | 0.356616i | \(0.116069\pi\) | ||||
−0.934251 | + | 0.356616i | \(0.883931\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.23966e8 | −0.866555 | −0.433277 | − | 0.901261i | \(-0.642643\pi\) | ||||
−0.433277 | + | 0.901261i | \(0.642643\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.99669e7i | 0.614682i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.31343e8 | −2.91378 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.37145e8i | 0.905731i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.21825e7 | 0.0795562 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 1.85730e8i | − 1.18608i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.57932e8 | 0.997419 | 0.498709 | − | 0.866769i | \(-0.333807\pi\) | ||||
0.498709 | + | 0.866769i | \(0.333807\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 1.39996e8i | − 0.864823i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.50060e7 | −0.0916862 | −0.0458431 | − | 0.998949i | \(-0.514597\pi\) | ||||
−0.0458431 | + | 0.998949i | \(0.514597\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 1.41015e8i | − 0.842964i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.50714e8 | −2.07385 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 9.89257e7i | − 0.572458i | −0.958161 | − | 0.286229i | \(-0.907598\pi\) | ||||
0.958161 | − | 0.286229i | \(-0.0924018\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.42886e7 | 0.482540 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8.24717e7i | 0.462146i | 0.972936 | + | 0.231073i | \(0.0742237\pi\) | ||||
−0.972936 | + | 0.231073i | \(0.925776\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.38927e7 | 0.409691 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.93991e8i | 1.05304i | 0.850162 | + | 0.526521i | \(0.176504\pi\) | ||||
−0.850162 | + | 0.526521i | \(0.823496\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.87396e8 | −1.00659 | −0.503293 | − | 0.864116i | \(-0.667878\pi\) | ||||
−0.503293 | + | 0.864116i | \(0.667878\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.81220e8i | 1.47925i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.29755e8 | 0.675457 | 0.337729 | − | 0.941244i | \(-0.390341\pi\) | ||||
0.337729 | + | 0.941244i | \(0.390341\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.16099e8i | 0.591968i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.00814e8 | −0.508764 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 3.63761e8i | − 1.79846i | −0.437473 | − | 0.899231i | \(-0.644127\pi\) | ||||
0.437473 | − | 0.899231i | \(-0.355873\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.88940e7 | 0.190343 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 6.88503e7i | − 0.330173i | −0.986279 | − | 0.165086i | \(-0.947210\pi\) | ||||
0.986279 | − | 0.165086i | \(-0.0527903\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.61594e8 | 1.24187 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.17543e8i | 0.546911i | 0.961885 | + | 0.273455i | \(0.0881666\pi\) | ||||
−0.961885 | + | 0.273455i | \(0.911833\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.38103e7 | −0.0636179 | −0.0318090 | − | 0.999494i | \(-0.510127\pi\) | ||||
−0.0318090 | + | 0.999494i | \(0.510127\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.84327e7i | 0.0832383i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.93369e8 | 1.31174 | 0.655871 | − | 0.754873i | \(-0.272302\pi\) | ||||
0.655871 | + | 0.754873i | \(0.272302\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.04205e8i | 1.77206i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.86835e8 | 1.24523 | 0.622617 | − | 0.782526i | \(-0.286069\pi\) | ||||
0.622617 | + | 0.782526i | \(0.286069\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.64357e7i | 0.325417i | 0.986674 | + | 0.162709i | \(0.0520230\pi\) | ||||
−0.986674 | + | 0.162709i | \(0.947977\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.68179e7 | −0.155234 | −0.0776170 | − | 0.996983i | \(-0.524731\pi\) | ||||
−0.0776170 | + | 0.996983i | \(0.524731\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 5.76942e8i | − 2.38598i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.49088e7 | 0.306826 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 3.78712e8i | − 1.52180i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.91018e8 | 0.760301 | 0.380150 | − | 0.924925i | \(-0.375872\pi\) | ||||
0.380150 | + | 0.924925i | \(0.375872\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.61452e8i | 0.630555i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.04696e8 | 1.95259 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 5.16010e8i | − 1.95922i | −0.200899 | − | 0.979612i | \(-0.564386\pi\) | ||||
0.200899 | − | 0.979612i | \(-0.435614\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.35849e8 | −1.26332 | −0.631658 | − | 0.775248i | \(-0.717625\pi\) | ||||
−0.631658 | + | 0.775248i | \(0.717625\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.13350e8i | 1.15695i | 0.815698 | + | 0.578477i | \(0.196353\pi\) | ||||
−0.815698 | + | 0.578477i | \(0.803647\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.66969e8 | 0.976622 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 3.59248e8i | − 1.29019i | −0.764102 | − | 0.645096i | \(-0.776817\pi\) | ||||
0.764102 | − | 0.645096i | \(-0.223183\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.30983e8 | 0.466113 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.36947e8i | 1.87618i | 0.346389 | + | 0.938091i | \(0.387408\pi\) | ||||
−0.346389 | + | 0.938091i | \(0.612592\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.98758e8 | 1.03446 | 0.517231 | − | 0.855846i | \(-0.326963\pi\) | ||||
0.517231 | + | 0.855846i | \(0.326963\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 1.13091e8i | − 0.384559i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.36298e8 | 3.15527 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.32670e8i | 1.43215i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.23451e8 | −1.06112 | −0.530558 | − | 0.847649i | \(-0.678018\pi\) | ||||
−0.530558 | + | 0.847649i | \(0.678018\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.09203e8i | 1.31878i | 0.751800 | + | 0.659391i | \(0.229186\pi\) | ||||
−0.751800 | + | 0.659391i | \(0.770814\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.45805e7 | 0.206297 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.86785e8i | 0.586244i | 0.956075 | + | 0.293122i | \(0.0946943\pi\) | ||||
−0.956075 | + | 0.293122i | \(0.905306\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.58353e8 | −0.492669 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 2.73949e8i | − 0.837553i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.75447e8 | 1.13793 | 0.568964 | − | 0.822362i | \(-0.307344\pi\) | ||||
0.568964 | + | 0.822362i | \(0.307344\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.50732e7i | 0.104477i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.94501e8 | −0.869738 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.11037e8i | 1.48354i | 0.670657 | + | 0.741768i | \(0.266012\pi\) | ||||
−0.670657 | + | 0.741768i | \(0.733988\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.63723e8 | −0.471242 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 2.20430e7i | − 0.0623753i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.42507e8 | 1.24160 | 0.620800 | − | 0.783969i | \(-0.286808\pi\) | ||||
0.620800 | + | 0.783969i | \(0.286808\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.58246e8i | 0.712467i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.52326e8 | −0.963889 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 7.20610e8i | − 1.93871i | −0.245659 | − | 0.969356i | \(-0.579004\pi\) | ||||
0.245659 | − | 0.969356i | \(-0.420996\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.04867e8 | 1.61382 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 4.54461e8i | − 1.19257i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.46407e8 | 0.641282 | 0.320641 | − | 0.947201i | \(-0.396102\pi\) | ||||
0.320641 | + | 0.947201i | \(0.396102\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.80998e8i | 0.463364i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.34987e8 | −0.342751 | −0.171375 | − | 0.985206i | \(-0.554821\pi\) | ||||
−0.171375 | + | 0.985206i | \(0.554821\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 1.87213e8i | − 0.467665i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.93121e8 | −1.46964 | −0.734819 | − | 0.678264i | \(-0.762733\pi\) | ||||
−0.734819 | + | 0.678264i | \(0.762733\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.95231e6i | 0.0120737i | 0.999982 | + | 0.00603686i | \(0.00192160\pi\) | ||||
−0.999982 | + | 0.00603686i | \(0.998078\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.97564e7 | 0.144516 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.64149e7i | 0.229456i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.35754e7 | −0.197314 | −0.0986572 | − | 0.995121i | \(-0.531455\pi\) | ||||
−0.0986572 | + | 0.995121i | \(0.531455\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 2.21601e8i | − 0.514910i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.99345e7 | 0.207319 | 0.103659 | − | 0.994613i | \(-0.466945\pi\) | ||||
0.103659 | + | 0.994613i | \(0.466945\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 3.68572e8i | − 0.836312i | −0.908375 | − | 0.418156i | \(-0.862677\pi\) | ||||
0.908375 | − | 0.418156i | \(-0.137323\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.10796e9 | 2.49432 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.25453e8i | 1.60777i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.28138e8 | −1.16136 | −0.580682 | − | 0.814130i | \(-0.697214\pi\) | ||||
−0.580682 | + | 0.814130i | \(0.697214\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 3.87278e8i | − 0.838465i | −0.907879 | − | 0.419232i | \(-0.862299\pi\) | ||||
0.907879 | − | 0.419232i | \(-0.137701\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.25348e8 | 0.269284 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.27317e8i | 0.269324i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.67862e8 | 1.40195 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 4.26062e7i | − 0.0880772i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.36033e8 | 1.30483 | 0.652417 | − | 0.757860i | \(-0.273755\pi\) | ||||
0.652417 | + | 0.757860i | \(0.273755\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.84804e8i | 1.18163i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.17572e9 | −2.35769 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.61669e8i | 0.911918i | 0.890001 | + | 0.455959i | \(0.150704\pi\) | ||||
−0.890001 | + | 0.455959i | \(0.849296\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.67976e8 | −1.70164 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 3.94262e8i | − 0.761444i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.50894e8 | 1.43943 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.25161e8i | 0.425252i | 0.977134 | + | 0.212626i | \(0.0682016\pi\) | ||||
−0.977134 | + | 0.212626i | \(0.931798\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.06936e8 | −0.575420 | −0.287710 | − | 0.957718i | \(-0.592894\pi\) | ||||
−0.287710 | + | 0.957718i | \(0.592894\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 1.72401e8i | − 0.318469i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.82484e7 | 0.143486 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 2.73840e8i | − 0.494843i | −0.968908 | − | 0.247422i | \(-0.920417\pi\) | ||||
0.968908 | − | 0.247422i | \(-0.0795832\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.03168e9 | −1.85073 | −0.925366 | − | 0.379074i | \(-0.876243\pi\) | ||||
−0.925366 | + | 0.379074i | \(0.876243\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 5.97417e8i | − 1.05624i | −0.849171 | − | 0.528118i | \(-0.822898\pi\) | ||||
0.849171 | − | 0.528118i | \(-0.177102\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.40482e8 | 0.422103 | 0.211051 | − | 0.977475i | \(-0.432311\pi\) | ||||
0.211051 | + | 0.977475i | \(0.432311\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.08377e9i | 1.87500i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.08854e8 | −0.702277 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 6.75223e8i | − 1.14330i | −0.820497 | − | 0.571651i | \(-0.806303\pi\) | ||||
0.820497 | − | 0.571651i | \(-0.193697\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.18270e8 | −1.54377 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 6.54357e8i | − 1.08454i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.45881e8 | −0.240076 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 1.08708e9i | − 1.76389i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.33689e8 | 0.376522 | 0.188261 | − | 0.982119i | \(-0.439715\pi\) | ||||
0.188261 | + | 0.982119i | \(0.439715\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 4.09818e8i | − 0.651102i | −0.945525 | − | 0.325551i | \(-0.894450\pi\) | ||||
0.945525 | − | 0.325551i | \(-0.105550\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.80708e8 | 0.758406 | 0.379203 | − | 0.925314i | \(-0.376198\pi\) | ||||
0.379203 | + | 0.925314i | \(0.376198\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.08940e8i | 0.169495i | 0.996402 | + | 0.0847475i | \(0.0270083\pi\) | ||||
−0.996402 | + | 0.0847475i | \(0.972992\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.89915e8 | −0.293434 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.01432e9i | 1.54567i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.08728e8 | 0.769894 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 8.51905e8i | − 1.27165i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.29815e7 | 0.0192454 | 0.00962271 | − | 0.999954i | \(-0.496937\pi\) | ||||
0.00962271 | + | 0.999954i | \(0.496937\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.01837e8i | 0.587655i | 0.955859 | + | 0.293827i | \(0.0949290\pi\) | ||||
−0.955859 | + | 0.293827i | \(0.905071\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.93666e8 | −0.571803 | −0.285901 | − | 0.958259i | \(-0.592293\pi\) | ||||
−0.285901 | + | 0.958259i | \(0.592293\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 8.78240e8i | − 1.25847i | −0.777216 | − | 0.629234i | \(-0.783369\pi\) | ||||
0.777216 | − | 0.629234i | \(-0.216631\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.27777e9 | −1.81864 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.75239e8i | 0.526931i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.15907e8 | 0.301160 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 4.17335e8i | − 0.574388i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.88269e8 | 0.804270 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 2.99331e8i | − 0.403837i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.02203e8 | −0.673066 | −0.336533 | − | 0.941672i | \(-0.609254\pi\) | ||||
−0.336533 | + | 0.941672i | \(0.609254\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.26644e9i | 1.67506i | 0.546393 | + | 0.837529i | \(0.316001\pi\) | ||||
−0.546393 | + | 0.837529i | \(0.683999\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.35776e8 | 0.441202 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.03663e9i | 1.34436i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.07637e9 | 1.38681 | 0.693405 | − | 0.720548i | \(-0.256110\pi\) | ||||
0.693405 | + | 0.720548i | \(0.256110\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.81483e9i | 2.30797i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.27646e8 | −0.666680 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8.92619e8i | 1.11332i | 0.830741 | + | 0.556658i | \(0.187917\pi\) | ||||
−0.830741 | + | 0.556658i | \(0.812083\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.68529e8 | 0.580614 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 7.56573e8i | − 0.925585i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.04330e8 | 0.126821 | 0.0634105 | − | 0.997988i | \(-0.479802\pi\) | ||||
0.0634105 | + | 0.997988i | \(0.479802\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.03692e9i | 1.24445i | 0.782839 | + | 0.622224i | \(0.213771\pi\) | ||||
−0.782839 | + | 0.622224i | \(0.786229\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.45352e8 | −1.00810 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.27799e9i | 1.50479i | 0.658710 | + | 0.752397i | \(0.271102\pi\) | ||||
−0.658710 | + | 0.752397i | \(0.728898\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.07135e9 | 1.25353 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.38519e8i | 0.622189i | 0.950379 | + | 0.311095i | \(0.100696\pi\) | ||||
−0.950379 | + | 0.311095i | \(0.899304\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9.01670e7 | −0.103523 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 1.25325e9i | − 1.42095i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.72396e8 | −0.870302 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 4.31961e8i | − 0.480687i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.17113e8 | 0.240108 | 0.120054 | − | 0.992767i | \(-0.461693\pi\) | ||||
0.120054 | + | 0.992767i | \(0.461693\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 1.72634e8i | − 0.188568i | −0.995545 | − | 0.0942841i | \(-0.969944\pi\) | ||||
0.995545 | − | 0.0942841i | \(-0.0300562\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.77577e8 | −0.301332 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 7.23627e8i | − 0.775946i | −0.921671 | − | 0.387973i | \(-0.873175\pi\) | ||||
0.921671 | − | 0.387973i | \(-0.126825\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.66861e9 | −1.77831 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 7.66788e7i | − 0.0807263i | −0.999185 | − | 0.0403631i | \(-0.987149\pi\) | ||||
0.999185 | − | 0.0403631i | \(-0.0128515\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.80274e8 | −0.293274 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.19548e8i | 0.537077i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.77700e8 | −0.490834 | −0.245417 | − | 0.969418i | \(-0.578925\pi\) | ||||
−0.245417 | + | 0.969418i | \(0.578925\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 7.63983e8i | − 0.775558i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.42542e9 | −1.43833 | −0.719165 | − | 0.694839i | \(-0.755475\pi\) | ||||
−0.719165 | + | 0.694839i | \(0.755475\pi\) | |||||||
\(998\) | 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 | 432.7.e.k.161.3 | 6 | ||
3.2 | odd | 2 | inner | 432.7.e.k.161.4 | 6 | ||
4.3 | odd | 2 | 216.7.e.b.161.3 | ✓ | 6 | ||
12.11 | even | 2 | 216.7.e.b.161.4 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
216.7.e.b.161.3 | ✓ | 6 | 4.3 | odd | 2 | ||
216.7.e.b.161.4 | yes | 6 | 12.11 | even | 2 | ||
432.7.e.k.161.3 | 6 | 1.1 | even | 1 | trivial | ||
432.7.e.k.161.4 | 6 | 3.2 | odd | 2 | inner |