Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,7,Mod(31,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.31");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.l (of order \(4\), degree \(2\), 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: | \(88.3407681100\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 48) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 31.6 | ||
Character | \(\chi\) | \(=\) | 384.31 |
Dual form | 384.7.l.a.223.6 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −11.0227 | − | 11.0227i | −0.408248 | − | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 55.7840 | + | 55.7840i | 0.446272 | + | 0.446272i | 0.894113 | − | 0.447841i | \(-0.147807\pi\) |
−0.447841 | + | 0.894113i | \(0.647807\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −496.753 | −1.44826 | −0.724130 | − | 0.689664i | \(-0.757758\pi\) | ||||
−0.724130 | + | 0.689664i | \(0.757758\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 243.000i | 0.333333i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 694.522 | − | 694.522i | 0.521805 | − | 0.521805i | −0.396311 | − | 0.918116i | \(-0.629710\pi\) |
0.918116 | + | 0.396311i | \(0.129710\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −214.555 | + | 214.555i | −0.0976581 | + | 0.0976581i | −0.754248 | − | 0.656590i | \(-0.771998\pi\) |
0.656590 | + | 0.754248i | \(0.271998\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 1229.78i | − | 0.364379i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4131.33 | −0.840897 | −0.420449 | − | 0.907316i | \(-0.638127\pi\) | ||||
−0.420449 | + | 0.907316i | \(0.638127\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7221.52 | − | 7221.52i | −1.05285 | − | 1.05285i | −0.998523 | − | 0.0543305i | \(-0.982698\pi\) |
−0.0543305 | − | 0.998523i | \(-0.517302\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5475.56 | + | 5475.56i | 0.591249 | + | 0.591249i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 20205.1 | 1.66065 | 0.830323 | − | 0.557283i | \(-0.188156\pi\) | ||||
0.830323 | + | 0.557283i | \(0.188156\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 9401.30i | − | 0.601683i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2678.52 | − | 2678.52i | 0.136083 | − | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −25794.6 | + | 25794.6i | −1.05763 | + | 1.05763i | −0.0593977 | + | 0.998234i | \(0.518918\pi\) |
−0.998234 | + | 0.0593977i | \(0.981082\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 35543.8i | − | 1.19311i | −0.802574 | − | 0.596553i | \(-0.796537\pi\) | ||
0.802574 | − | 0.596553i | \(-0.203463\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −15311.0 | −0.426052 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −27710.9 | − | 27710.9i | −0.646317 | − | 0.646317i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 12024.7 | + | 12024.7i | 0.237394 | + | 0.237394i | 0.815770 | − | 0.578376i | \(-0.196313\pi\) |
−0.578376 | + | 0.815770i | \(0.696313\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4729.95 | 0.0797375 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 5598.69i | − | 0.0812335i | −0.999175 | − | 0.0406167i | \(-0.987068\pi\) | ||
0.999175 | − | 0.0406167i | \(-0.0129323\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −12263.5 | + | 12263.5i | −0.154244 | + | 0.154244i | −0.780010 | − | 0.625766i | \(-0.784786\pi\) |
0.625766 | + | 0.780010i | \(0.284786\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −13555.5 | + | 13555.5i | −0.148757 | + | 0.148757i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 126271.i | 1.21621i | 0.793857 | + | 0.608105i | \(0.208070\pi\) | ||||
−0.793857 | + | 0.608105i | \(0.791930\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 129115. | 1.09746 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 45538.4 | + | 45538.4i | 0.343295 | + | 0.343295i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 69107.7 | + | 69107.7i | 0.464193 | + | 0.464193i | 0.900027 | − | 0.435834i | \(-0.143546\pi\) |
−0.435834 | + | 0.900027i | \(0.643546\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 77486.4 | 0.465734 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 159201.i | 0.859651i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −101232. | + | 101232.i | −0.492903 | + | 0.492903i | −0.909220 | − | 0.416316i | \(-0.863321\pi\) |
0.416316 | + | 0.909220i | \(0.363321\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −123707. | + | 123707.i | −0.545011 | + | 0.545011i | −0.924994 | − | 0.379982i | \(-0.875930\pi\) |
0.379982 | + | 0.924994i | \(0.375930\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 120711.i | − | 0.482753i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −23937.4 | −0.0871641 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −394365. | − | 394365.i | −1.31121 | − | 1.31121i | −0.920521 | − | 0.390694i | \(-0.872235\pi\) |
−0.390694 | − | 0.920521i | \(-0.627765\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −222715. | − | 222715.i | −0.677956 | − | 0.677956i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 264238. | 0.738280 | 0.369140 | − | 0.929374i | \(-0.379652\pi\) | ||||
0.369140 | + | 0.929374i | \(0.379652\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 230983.i | − | 0.593761i | −0.954915 | − | 0.296880i | \(-0.904054\pi\) | ||
0.954915 | − | 0.296880i | \(-0.0959462\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −103628. | + | 103628.i | −0.245636 | + | 0.245636i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −345006. | + | 345006.i | −0.755709 | + | 0.755709i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 278466.i | − | 0.564795i | −0.959297 | − | 0.282398i | \(-0.908870\pi\) | ||
0.959297 | − | 0.282398i | \(-0.0911298\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −59049.0 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 605066. | + | 605066.i | 1.05820 | + | 1.05820i | 0.998198 | + | 0.0600039i | \(0.0191113\pi\) |
0.0600039 | + | 0.998198i | \(0.480889\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −230462. | − | 230462.i | −0.375269 | − | 0.375269i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 568652. | 0.863553 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 526452.i | 0.746773i | 0.927676 | + | 0.373386i | \(0.121803\pi\) | ||||
−0.927676 | + | 0.373386i | \(0.878197\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 106581. | − | 106581.i | 0.141434 | − | 0.141434i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −391789. | + | 391789.i | −0.487083 | + | 0.487083i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 805690.i | − | 0.939718i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 840241. | 0.920637 | 0.460319 | − | 0.887754i | \(-0.347735\pi\) | ||||
0.460319 | + | 0.887754i | \(0.347735\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 168769. | + | 168769.i | 0.173935 | + | 0.173935i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 222739. | + | 222739.i | 0.216188 | + | 0.216188i | 0.806890 | − | 0.590702i | \(-0.201149\pi\) |
−0.590702 | + | 0.806890i | \(0.701149\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 660421. | 0.604379 | 0.302189 | − | 0.953248i | \(-0.402283\pi\) | ||||
0.302189 | + | 0.953248i | \(0.402283\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 610897.i | 0.527716i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −79564.2 | + | 79564.2i | −0.0649481 | + | 0.0649481i | −0.738835 | − | 0.673887i | \(-0.764624\pi\) |
0.673887 | + | 0.738835i | \(0.264624\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.17937e6 | + | 1.17937e6i | −0.910694 | + | 0.910694i | −0.996327 | − | 0.0856332i | \(-0.972709\pi\) |
0.0856332 | + | 0.996327i | \(0.472709\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 265090.i | − | 0.193832i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.00498e6 | 1.38955 | 0.694777 | − | 0.719226i | \(-0.255503\pi\) | ||||
0.694777 | + | 0.719226i | \(0.255503\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.12712e6 | + | 1.12712e6i | 0.741099 | + | 0.741099i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −52136.8 | − | 52136.8i | −0.0325527 | − | 0.0325527i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.05225e6 | 1.21784 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 806839.i | 0.455439i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −61712.7 | + | 61712.7i | −0.0331634 | + | 0.0331634i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.39607e6 | − | 1.39607e6i | 0.714786 | − | 0.714786i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.68727e6i | 1.80009i | 0.435800 | + | 0.900043i | \(0.356465\pi\) | ||||
−0.435800 | + | 0.900043i | \(0.643535\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 270353. | 0.125940 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.70561e6 | + | 1.70561e6i | 0.758691 | + | 0.758691i | 0.976084 | − | 0.217393i | \(-0.0697554\pi\) |
−0.217393 | + | 0.976084i | \(0.569755\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.58731e6 | + | 3.58731e6i | 1.52481 | + | 1.52481i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 298837. | 0.121460 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.48475e6i | 0.966318i | 0.875533 | + | 0.483159i | \(0.160511\pi\) | ||||
−0.875533 | + | 0.483159i | \(0.839489\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.44106e6 | − | 3.44106e6i | 1.28129 | − | 1.28129i | 0.341359 | − | 0.939933i | \(-0.389113\pi\) |
0.939933 | − | 0.341359i | \(-0.110887\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.39184e6 | − | 1.39184e6i | 0.496516 | − | 0.496516i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 298026.i | 0.101917i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.87785e6 | −0.943983 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.42319e6 | − | 1.42319e6i | −0.448034 | − | 0.448034i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.43736e6 | + | 2.43736e6i | 0.736819 | + | 0.736819i | 0.971961 | − | 0.235142i | \(-0.0755555\pi\) |
−0.235142 | + | 0.971961i | \(0.575556\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.62460e6 | 1.92411 | 0.962053 | − | 0.272863i | \(-0.0879706\pi\) | ||||
0.962053 | + | 0.272863i | \(0.0879706\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 1.00391e6i | − | 0.280299i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.98278e6 | − | 1.98278e6i | 0.532449 | − | 0.532449i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.45318e6 | + | 3.45318e6i | −0.892320 | + | 0.892320i | −0.994741 | − | 0.102421i | \(-0.967341\pi\) |
0.102421 | + | 0.994741i | \(0.467341\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 1.52351e6i | − | 0.379012i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.00369e7 | −2.40505 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.39390e6 | − | 1.39390e6i | −0.321860 | − | 0.321860i | 0.527620 | − | 0.849480i | \(-0.323084\pi\) |
−0.849480 | + | 0.527620i | \(0.823084\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −854110. | − | 854110.i | −0.190135 | − | 0.190135i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.08424e6 | −1.30634 | −0.653171 | − | 0.757211i | \(-0.726562\pi\) | ||||
−0.653171 | + | 0.757211i | \(0.726562\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.73474e6i | 0.980926i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.75483e6 | − | 1.75483e6i | 0.350951 | − | 0.350951i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.58288e6 | + | 1.58288e6i | −0.305710 | + | 0.305710i | −0.843243 | − | 0.537533i | \(-0.819356\pi\) |
0.537533 | + | 0.843243i | \(0.319356\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.67012e6i | 0.871393i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.23170e6 | 0.402454 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.83249e6 | + | 5.83249e6i | 1.01694 | + | 1.01694i | 0.999854 | + | 0.0170847i | \(0.00543851\pi\) |
0.0170847 | + | 0.999854i | \(0.494561\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.51655e6 | − | 1.51655e6i | −0.255754 | − | 0.255754i | 0.567571 | − | 0.823325i | \(-0.307883\pi\) |
−0.823325 | + | 0.567571i | \(0.807883\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.72718e6 | 0.445000 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.34157e6i | 0.211885i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.86930e6 | + | 2.86930e6i | −0.438784 | + | 0.438784i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.33056e6 | + | 1.33056e6i | −0.197083 | + | 0.197083i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 8.72584e6i | − | 1.25230i | −0.779704 | − | 0.626148i | \(-0.784631\pi\) | ||
0.779704 | − | 0.626148i | \(-0.215369\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.56415e6 | 0.495774 | 0.247887 | − | 0.968789i | \(-0.420264\pi\) | ||||
0.247887 | + | 0.968789i | \(0.420264\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 263855. | + | 263855.i | 0.0355846 | + | 0.0355846i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.20680e6 | + | 5.20680e6i | 0.681039 | + | 0.681039i | 0.960234 | − | 0.279195i | \(-0.0900677\pi\) |
−0.279195 | + | 0.960234i | \(0.590068\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.78464e6 | −0.860929 | −0.430464 | − | 0.902608i | \(-0.641650\pi\) | ||||
−0.430464 | + | 0.902608i | \(0.641650\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.69393e6i | 1.07060i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.28135e7 | − | 1.28135e7i | 1.53173 | − | 1.53173i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 312317. | − | 312317.i | 0.0362522 | − | 0.0362522i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.90983e6i | 0.553549i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.00310e7 | −1.09877 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.46771e6 | + | 6.46771e6i | 0.688499 | + | 0.688499i | 0.961900 | − | 0.273401i | \(-0.0881487\pi\) |
−0.273401 | + | 0.961900i | \(0.588149\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.91262e6 | − | 2.91262e6i | −0.301401 | − | 0.301401i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.36821e6 | −0.137670 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.76565e7i | 1.72793i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.54606e6 | + | 2.54606e6i | −0.242402 | + | 0.242402i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 886396. | − | 886396.i | 0.0821204 | − | 0.0821204i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 9.39293e6i | − | 0.847006i | −0.905895 | − | 0.423503i | \(-0.860800\pi\) | ||
0.905895 | − | 0.423503i | \(-0.139200\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.28452e6 | 0.200561 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.85693e6 | + | 1.85693e6i | 0.158751 | + | 0.158751i | 0.782013 | − | 0.623262i | \(-0.214193\pi\) |
−0.623262 | + | 0.782013i | \(0.714193\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.24949e6 | + | 2.24949e6i | 0.187317 | + | 0.187317i | 0.794535 | − | 0.607218i | \(-0.207715\pi\) |
−0.607218 | + | 0.794535i | \(0.707715\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7.60580e6 | 0.617034 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 1.06680e7i | − | 0.843363i | −0.906744 | − | 0.421681i | \(-0.861440\pi\) | ||
0.906744 | − | 0.421681i | \(-0.138560\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.04387e6 | + | 7.04387e6i | −0.542760 | + | 0.542760i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.06945e6 | + | 3.06945e6i | −0.230577 | + | 0.230577i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.18359e6i | 0.233198i | 0.993179 | + | 0.116599i | \(0.0371992\pi\) | ||||
−0.993179 | + | 0.116599i | \(0.962801\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.52000e7 | 1.80032 | 0.900158 | − | 0.435564i | \(-0.143451\pi\) | ||||
0.900158 | + | 0.435564i | \(0.143451\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 650880. | + | 650880.i | 0.0453609 | + | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 7.20252e6 | + | 7.20252e6i | 0.489763 | + | 0.489763i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.09882e6 | 0.205639 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 1.33389e7i | − | 0.864018i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −903606. | + | 903606.i | −0.0571423 | + | 0.0571423i | −0.735100 | − | 0.677958i | \(-0.762865\pi\) |
0.677958 | + | 0.735100i | \(0.262865\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.40329e7 | − | 1.40329e7i | 0.866533 | − | 0.866533i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.08063e6i | 0.306406i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −909145. | −0.0535591 | −0.0267796 | − | 0.999641i | \(-0.508525\pi\) | ||||
−0.0267796 | + | 0.999641i | \(0.508525\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.97332e6 | − | 5.97332e6i | −0.343809 | − | 0.343809i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.26809e6 | − | 6.26809e6i | −0.352544 | − | 0.352544i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.10225e7 | 0.605915 | 0.302957 | − | 0.953004i | \(-0.402026\pi\) | ||||
0.302957 | + | 0.953004i | \(0.402026\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.71021e6i | 0.414313i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.80292e6 | − | 5.80292e6i | 0.304869 | − | 0.304869i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.78576e7 | + | 1.78576e7i | −0.917416 | + | 0.917416i | −0.996841 | − | 0.0794249i | \(-0.974692\pi\) |
0.0794249 | + | 0.996841i | \(0.474692\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 2.40422e6i | − | 0.120800i | −0.998174 | − | 0.0604000i | \(-0.980762\pi\) | ||
0.998174 | − | 0.0604000i | \(-0.0192376\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.34962e6 | −0.115481 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.52941e6 | − | 6.52941e6i | −0.313961 | − | 0.313961i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.70939e6 | − | 6.70939e6i | −0.315678 | − | 0.315678i | 0.531427 | − | 0.847104i | \(-0.321656\pi\) |
−0.847104 | + | 0.531427i | \(0.821656\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.63715e6 | 0.397702 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 1.26165e7i | − | 0.568616i | −0.958733 | − | 0.284308i | \(-0.908236\pi\) | ||
0.958733 | − | 0.284308i | \(-0.0917638\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.79614e7 | + | 1.79614e7i | −0.792464 | + | 0.792464i | −0.981894 | − | 0.189430i | \(-0.939336\pi\) |
0.189430 | + | 0.981894i | \(0.439336\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −8.88089e6 | + | 8.88089e6i | −0.383638 | + | 0.383638i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.78117e6i | 0.117647i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.06970e6 | −0.292892 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.26173e6 | − | 9.26173e6i | −0.375849 | − | 0.375849i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.10111e7 | − | 1.10111e7i | −0.437752 | − | 0.437752i | 0.453503 | − | 0.891255i | \(-0.350174\pi\) |
−0.891255 | + | 0.453503i | \(0.850174\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.12942e7 | −0.439938 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 3.72058e6i | − | 0.142017i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.33510e6 | + | 4.33510e6i | −0.162175 | + | 0.162175i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.09192e6 | − | 6.09192e6i | 0.223385 | − | 0.223385i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 4.91037e6i | − | 0.176517i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.38018e7 | −0.486446 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.55938e7 | − | 3.55938e7i | −1.23015 | − | 1.23015i | −0.963904 | − | 0.266250i | \(-0.914215\pi\) |
−0.266250 | − | 0.963904i | \(-0.585785\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.27962e6 | − | 7.27962e6i | −0.246737 | − | 0.246737i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.92583e7 | −0.640230 | −0.320115 | − | 0.947379i | \(-0.603722\pi\) | ||||
−0.320115 | + | 0.947379i | \(0.603722\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 4.68811e7i | − | 1.52885i | −0.644714 | − | 0.764424i | \(-0.723023\pi\) | ||
0.644714 | − | 0.764424i | \(-0.276977\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.73374e6 | − | 6.73374e6i | 0.215439 | − | 0.215439i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.62609e7 | − | 3.62609e7i | 1.13831 | − | 1.13831i | 0.149556 | − | 0.988753i | \(-0.452216\pi\) |
0.988753 | − | 0.149556i | \(-0.0477844\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.58298e7i | 1.10376i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.75403e6 | 0.0530299 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.98345e7 | + | 2.98345e7i | 0.885342 | + | 0.885342i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.01709e6 | + | 2.01709e6i | 0.0587592 | + | 0.0587592i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.59998e7 | 0.743578 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 6.27253e7i | − | 1.76139i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.94385e7 | + | 4.94385e7i | −1.36327 | + | 1.36327i | −0.493550 | + | 0.869717i | \(0.664301\pi\) |
−0.869717 | + | 0.493550i | \(0.835699\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.92201e6 | + | 2.92201e6i | −0.0791314 | + | 0.0791314i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 4.39985e7i | − | 1.17032i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.97311e7 | 1.82195 | 0.910976 | − | 0.412460i | \(-0.135330\pi\) | ||||
0.910976 | + | 0.412460i | \(0.135330\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.21003e7 | − | 2.21003e7i | −0.567283 | − | 0.567283i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.46860e7 | − | 2.46860e7i | −0.622568 | − | 0.622568i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5.69554e6 | −0.141141 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 2.48478e7i | − | 0.605105i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.21474e7 | + | 2.21474e7i | −0.530070 | + | 0.530070i | −0.920593 | − | 0.390523i | \(-0.872294\pi\) |
0.390523 | + | 0.920593i | \(0.372294\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.60324e7 | + | 3.60324e7i | −0.847651 | + | 0.847651i | −0.989840 | − | 0.142188i | \(-0.954586\pi\) |
0.142188 | + | 0.989840i | \(0.454586\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.14938e6i | 0.0265792i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.11146e7 | 0.480020 | 0.240010 | − | 0.970770i | \(-0.422849\pi\) | ||||
0.240010 | + | 0.970770i | \(0.422849\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.47403e7 | + | 1.47403e7i | 0.329473 | + | 0.329473i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.26213e7 | − | 2.26213e7i | −0.497180 | − | 0.497180i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.86766e7 | −1.05205 | −0.526025 | − | 0.850469i | \(-0.676318\pi\) | ||||
−0.526025 | + | 0.850469i | \(0.676318\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.72549e7i | 1.21700i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.89354e6 | − | 8.89354e6i | 0.185932 | − | 0.185932i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.28851e7 | − | 1.28851e7i | 0.264979 | − | 0.264979i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.99759e6i | 0.161793i | 0.996722 | + | 0.0808967i | \(0.0257784\pi\) | ||||
−0.996722 | + | 0.0808967i | \(0.974222\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.36048e6 | 0.0270778 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.43295e7 | − | 3.43295e7i | −0.672272 | − | 0.672272i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.69021e7 | + | 2.69021e7i | 0.518394 | + | 0.518394i | 0.917085 | − | 0.398692i | \(-0.130536\pi\) |
−0.398692 | + | 0.917085i | \(0.630536\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.07768e7 | −0.583620 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 1.10687e7i | − | 0.206573i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.06914e7 | + | 3.06914e7i | −0.563765 | + | 0.563765i | −0.930375 | − | 0.366610i | \(-0.880519\pi\) |
0.366610 | + | 0.930375i | \(0.380519\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.06437e7 | − | 4.06437e7i | 0.734882 | − | 0.734882i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.04427e7i | 0.719853i | 0.932981 | + | 0.359926i | \(0.117198\pi\) | ||||
−0.932981 | + | 0.359926i | \(0.882802\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.84916e7 | −0.674503 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.98003e6 | − | 2.98003e6i | −0.0514147 | − | 0.0514147i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.80046e7 | + | 1.80046e7i | 0.305869 | + | 0.305869i | 0.843305 | − | 0.537436i | \(-0.180607\pi\) |
−0.537436 | + | 0.843305i | \(0.680607\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.34738e7 | −1.39643 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 3.76008e7i | − | 0.619468i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.55339e7 | − | 1.55339e7i | 0.252052 | − | 0.252052i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.46768e7 | − | 2.46768e7i | 0.394383 | − | 0.394383i | −0.481863 | − | 0.876246i | \(-0.660040\pi\) |
0.876246 | + | 0.481863i | \(0.160040\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 7.90838e7i | − | 1.24500i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.93037e7 | −1.07479 | −0.537394 | − | 0.843331i | \(-0.680591\pi\) | ||||
−0.537394 | + | 0.843331i | \(0.680591\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.62609e6 | + | 7.62609e6i | 0.116516 | + | 0.116516i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.29399e6 | − | 3.29399e6i | −0.0495858 | − | 0.0495858i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.67029e7 | 0.247747 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.56422e7i | 1.10559i | 0.833317 | + | 0.552795i | \(0.186439\pi\) | ||||
−0.833317 | + | 0.552795i | \(0.813561\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.73886e7 | − | 2.73886e7i | 0.394498 | − | 0.394498i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.02873e7 | − | 5.02873e7i | 0.713852 | − | 0.713852i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.75060e7i | 0.944491i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.58596e7 | −1.04617 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.91448e7 | − | 2.91448e7i | −0.396204 | − | 0.396204i | 0.480688 | − | 0.876892i | \(-0.340387\pi\) |
−0.876892 | + | 0.480688i | \(0.840387\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.16659e6 | + | 2.16659e6i | 0.0290355 | + | 0.0290355i | 0.721476 | − | 0.692440i | \(-0.243464\pi\) |
−0.692440 | + | 0.721476i | \(0.743464\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.06837e7 | −0.405403 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.88398e7i | 0.505954i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.14519e7 | − | 6.14519e7i | 0.789318 | − | 0.789318i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.28505e6 | − | 3.28505e6i | 0.0416074 | − | 0.0416074i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 1.18801e8i | − | 1.48385i | −0.670485 | − | 0.741923i | \(-0.733914\pi\) | ||
0.670485 | − | 0.741923i | \(-0.266086\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.58626e7 | −0.318572 | −0.159286 | − | 0.987232i | \(-0.550919\pi\) | ||||
−0.159286 | + | 0.987232i | \(0.550919\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.17217e7 | + | 3.17217e7i | 0.385379 | + | 0.385379i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.45911e8 | − | 1.45911e8i | −1.74842 | − | 1.74842i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.54103e8 | −1.82145 | −0.910725 | − | 0.413013i | \(-0.864477\pi\) | ||||
−0.910725 | + | 0.413013i | \(0.864477\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.13748e7i | 0.365818i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.89562e7 | − | 8.89562e7i | 1.02321 | − | 1.02321i | 0.0234864 | − | 0.999724i | \(-0.492523\pi\) |
0.999724 | − | 0.0234864i | \(-0.00747663\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.93676e7 | + | 2.93676e7i | −0.333264 | + | 0.333264i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 5.37326e7i | − | 0.601610i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.15494e8 | 1.27591 | 0.637956 | − | 0.770073i | \(-0.279780\pi\) | ||||
0.637956 | + | 0.770073i | \(0.279780\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.88842e6 | − | 3.88842e6i | −0.0423880 | − | 0.0423880i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7.30210e7 | − | 7.30210e7i | −0.785513 | − | 0.785513i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.18910e7 | 0.126236 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 1.19475e8i | − | 1.25178i | −0.779913 | − | 0.625888i | \(-0.784737\pi\) | ||
0.779913 | − | 0.625888i | \(-0.215263\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.10658e7 | + | 1.10658e7i | −0.114432 | + | 0.114432i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.11301e7 | + | 4.11301e7i | −0.419814 | + | 0.419814i | −0.885140 | − | 0.465326i | \(-0.845937\pi\) |
0.465326 | + | 0.885140i | \(0.345937\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.63639e7i | 0.769388i | 0.923044 | + | 0.384694i | \(0.125693\pi\) | ||||
−0.923044 | + | 0.384694i | \(0.874307\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.37111e7 | −0.434743 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.02857e7 | − | 5.02857e7i | −0.493734 | − | 0.493734i | 0.415746 | − | 0.909481i | \(-0.363520\pi\) |
−0.909481 | + | 0.415746i | \(0.863520\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.95902e8 | + | 1.95902e8i | 1.89898 | + | 1.89898i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.61269e7 | 0.728577 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.70345e7i | 0.160971i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.78917e7 | + | 6.78917e7i | −0.633484 | + | 0.633484i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.67932e7 | + | 1.67932e7i | −0.154731 | + | 0.154731i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.03911e7i | 0.640489i | 0.947335 | + | 0.320244i | \(0.103765\pi\) | ||||
−0.947335 | + | 0.320244i | \(0.896235\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.15993e6 | −0.0463669 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.10634e8 | + | 1.10634e8i | 0.981856 | + | 0.981856i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.68720e7 | + | 4.68720e7i | 0.410854 | + | 0.410854i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.50586e7 | −0.563272 | −0.281636 | − | 0.959521i | \(-0.590877\pi\) | ||||
−0.281636 | + | 0.959521i | \(0.590877\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.07290e7i | 0.262798i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.38935e7 | + | 7.38935e7i | −0.624254 | + | 0.624254i | −0.946616 | − | 0.322362i | \(-0.895523\pi\) |
0.322362 | + | 0.946616i | \(0.395523\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.06566e8 | − | 1.06566e8i | 0.889360 | − | 0.889360i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.88292e7i | 0.155245i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.31261e8 | −1.06922 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.88982e7 | − | 1.88982e7i | −0.152097 | − | 0.152097i | 0.626957 | − | 0.779054i | \(-0.284300\pi\) |
−0.779054 | + | 0.626957i | \(0.784300\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.70647e7 | + | 6.70647e7i | 0.533312 | + | 0.533312i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.97908e8 | 1.55511 | 0.777554 | − | 0.628817i | \(-0.216460\pi\) | ||||
0.777554 | + | 0.628817i | \(0.216460\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.48505e7i | 0.192958i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.21897e7 | − | 5.21897e7i | 0.400461 | − | 0.400461i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.61874e7 | + | 3.61874e7i | −0.274412 | + | 0.274412i | −0.830874 | − | 0.556461i | \(-0.812159\pi\) |
0.556461 | + | 0.830874i | \(0.312159\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.14741e8i | 0.859919i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.86859e7 | −0.286550 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.68409e7 | + | 3.68409e7i | 0.269717 | + | 0.269717i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.76977e7 | + | 8.76977e7i | 0.634624 | + | 0.634624i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.48952e7 | 0.249611 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 1.38334e8i | − | 0.978175i | −0.872235 | − | 0.489087i | \(-0.837330\pi\) | ||
0.872235 | − | 0.489087i | \(-0.162670\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.07473e7 | + | 8.07473e7i | −0.564446 | + | 0.564446i | −0.930567 | − | 0.366121i | \(-0.880686\pi\) |
0.366121 | + | 0.930567i | \(0.380686\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.14774e7 | − | 5.14774e7i | 0.355745 | − | 0.355745i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.46843e8i | 1.00328i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.60209e8 | 1.75774 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.45994e7 | − | 2.45994e7i | −0.164301 | − | 0.164301i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.20123e6 | + | 1.20123e6i | 0.00793311 | + | 0.00793311i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.87681e6 | −0.0579690 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 1.28580e8i | − | 0.830327i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 8.96729e7 | − | 8.96729e7i | 0.572658 | − | 0.572658i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.12188e7 | − | 4.12188e7i | 0.260318 | − | 0.260318i | −0.564865 | − | 0.825183i | \(-0.691072\pi\) |
0.825183 | + | 0.564865i | \(0.191072\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.34330e7i | 0.208822i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.31580e8 | −0.812834 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.64952e7 | + | 3.64952e7i | 0.222984 | + | 0.222984i | 0.809754 | − | 0.586770i | \(-0.199601\pi\) |
−0.586770 | + | 0.809754i | \(0.699601\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.00609e7 | − | 3.00609e7i | −0.181670 | − | 0.181670i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.72552e8 | 2.22706 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.38329e8i | 0.817970i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.47878e7 | − | 1.47878e7i | 0.0865016 | − | 0.0865016i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.55783e8 | + | 1.55783e8i | −0.901477 | + | 0.901477i | −0.995564 | − | 0.0940866i | \(-0.970007\pi\) |
0.0940866 | + | 0.995564i | \(0.470007\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 5.26238e6i | − | 0.0301264i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.32549e7 | 0.358266 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.52051e7 | + | 5.52051e7i | 0.309353 | + | 0.309353i | 0.844658 | − | 0.535306i | \(-0.179804\pi\) |
−0.535306 | + | 0.844658i | \(0.679804\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.11846e8 | + | 1.11846e8i | 0.620118 | + | 0.620118i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.93328e7 | 0.160918 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.17482e8i | 1.72338i | 0.507433 | + | 0.861691i | \(0.330595\pi\) | ||||
−0.507433 | + | 0.861691i | \(0.669405\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.83480e7 | + | 5.83480e7i | −0.313413 | + | 0.313413i | −0.846230 | − | 0.532817i | \(-0.821133\pi\) |
0.532817 | + | 0.846230i | \(0.321133\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9.61823e7 | + | 9.61823e7i | −0.511248 | + | 0.511248i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 1.89954e8i | − | 0.999182i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.26597e8 | 0.659015 | 0.329507 | − | 0.944153i | \(-0.393117\pi\) | ||||
0.329507 | + | 0.944153i | \(0.393117\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.92865e7 | − | 3.92865e7i | −0.202399 | − | 0.202399i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.00568e8 | − | 3.00568e8i | −1.53255 | − | 1.53255i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.59937e7 | 0.484437 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 5.81680e6i | − | 0.0290547i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.49945e8 | − | 1.49945e8i | 0.741342 | − | 0.741342i | −0.231494 | − | 0.972836i | \(-0.574361\pi\) |
0.972836 | + | 0.231494i | \(0.0743614\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.56680e8 | + | 2.56680e8i | −1.25617 | + | 1.25617i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 1.14786e8i | − | 0.556066i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.26564e8 | 1.08649 | 0.543245 | − | 0.839574i | \(-0.317195\pi\) | ||||
0.543245 | + | 0.839574i | \(0.317195\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.14483e8 | + | 1.14483e8i | 0.543486 | + | 0.543486i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7.47850e7 | + | 7.47850e7i | 0.351473 | + | 0.351473i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.65861e7 | 0.0771727 | 0.0385864 | − | 0.999255i | \(-0.487715\pi\) | ||||
0.0385864 | + | 0.999255i | \(0.487715\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.72359e8i | 1.71529i | 0.514238 | + | 0.857647i | \(0.328075\pi\) | ||||
−0.514238 | + | 0.857647i | \(0.671925\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.58307e7 | − | 9.58307e7i | 0.437072 | − | 0.437072i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.50087e7 | + | 4.50087e7i | −0.203250 | + | 0.203250i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 2.68278e8i | − | 1.19955i | −0.800168 | − | 0.599776i | \(-0.795256\pi\) | ||
0.800168 | − | 0.599776i | \(-0.204744\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.82480e8 | −1.25065 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.70920e7 | − | 2.70920e7i | −0.118773 | − | 0.118773i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.58322e7 | + | 1.58322e7i | 0.0687322 | + | 0.0687322i | 0.740637 | − | 0.671905i | \(-0.234524\pi\) |
−0.671905 | + | 0.740637i | \(0.734524\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6.88516e6 | −0.0295998 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 1.28338e7i | − | 0.0546387i | −0.999627 | − | 0.0273193i | \(-0.991303\pi\) | ||
0.999627 | − | 0.0273193i | \(-0.00869710\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.76902e8 | − | 1.76902e8i | 0.745864 | − | 0.745864i | −0.227835 | − | 0.973700i | \(-0.573165\pi\) |
0.973700 | + | 0.227835i | \(0.0731648\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.41196e7 | − | 5.41196e7i | 0.225985 | − | 0.225985i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 2.61516e8i | − | 1.08152i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8.86098e6 | 0.0362946 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.10569e8 | + | 1.10569e8i | 0.448570 | + | 0.448570i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.96781e7 | − | 4.96781e7i | −0.199624 | − | 0.199624i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.96825e8 | 1.18144 | 0.590721 | − | 0.806876i | \(-0.298843\pi\) | ||||
0.590721 | + | 0.806876i | \(0.298843\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 1.42583e8i | − | 0.562157i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.05690e8 | + | 2.05690e8i | −0.803328 | + | 0.803328i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.77021e7 | + | 2.77021e7i | −0.107175 | + | 0.107175i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.42099e7i | 0.246093i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.80696e8 | 1.82514 | 0.912571 | − | 0.408918i | \(-0.134094\pi\) | ||||
0.912571 | + | 0.408918i | \(0.134094\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.10391e8 | + | 1.10391e8i | 0.415242 | + | 0.415242i | 0.883560 | − | 0.468318i | \(-0.155140\pi\) |
−0.468318 | + | 0.883560i | \(0.655140\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.50814e7 | + | 1.50814e7i | 0.0562034 | + | 0.0562034i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.38174e6 | 0.00510170 | 0.00255085 | − | 0.999997i | \(-0.499188\pi\) | ||||
0.00255085 | + | 0.999997i | \(0.499188\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.40616e8i | 0.514399i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.94622e8 | − | 1.94622e8i | 0.705423 | − | 0.705423i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9.70802e7 | + | 9.70802e7i | −0.348651 | + | 0.348651i | −0.859607 | − | 0.510956i | \(-0.829292\pi\) |
0.510956 | + | 0.859607i | \(0.329292\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.90291e8i | 0.677165i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5.61289e7 | 0.197920 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.68632e8 | − | 1.68632e8i | −0.589229 | − | 0.589229i | 0.348194 | − | 0.937423i | \(-0.386795\pi\) |
−0.937423 | + | 0.348194i | \(0.886795\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.28246e7 | + | 3.28246e7i | 0.113657 | + | 0.113657i | 0.761648 | − | 0.647991i | \(-0.224391\pi\) |
−0.647991 | + | 0.761648i | \(0.724391\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.95410e7 | −0.0670510 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.00229e8i | 1.36095i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.21182e8 | + | 5.21182e8i | −1.75635 | + | 1.75635i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.03535e8 | + | 1.03535e8i | −0.345789 | + | 0.345789i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.71835e8i | 0.568779i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.71251e8 | −0.889870 | −0.444935 | − | 0.895563i | \(-0.646773\pi\) | ||||
−0.444935 | + | 0.895563i | \(0.646773\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.51815e7 | − | 2.51815e7i | −0.0818787 | − | 0.0818787i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.72402e8 | + | 2.72402e8i | 0.877897 | + | 0.877897i | 0.993317 | − | 0.115420i | \(-0.0368214\pi\) |
−0.115420 | + | 0.993317i | \(0.536821\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.17392e8 | −1.33332 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 4.09367e7i | − | 0.129620i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.80546e8 | − | 1.80546e8i | 0.566664 | − | 0.566664i | −0.364528 | − | 0.931192i | \(-0.618770\pi\) |
0.931192 | + | 0.364528i | \(0.118770\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.38609e8 | + | 1.38609e8i | −0.431241 | + | 0.431241i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 4.95908e7i | − | 0.152944i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.96548e7 | −0.0906645 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.41248e8 | + | 2.41248e8i | 0.731189 | + | 0.731189i | 0.970855 | − | 0.239666i | \(-0.0770380\pi\) |
−0.239666 | + | 0.970855i | \(0.577038\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −8.38365e7 | − | 8.38365e7i | −0.251903 | − | 0.251903i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.83912e8 | 1.14361 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.31300e7i | 0.0683090i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.17590e8 | + | 1.17590e8i | −0.344301 | + | 0.344301i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.64461e7 | − | 7.64461e7i | 0.221922 | − | 0.221922i | −0.587385 | − | 0.809308i | \(-0.699843\pi\) |
0.809308 | + | 0.587385i | \(0.199843\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1.73674e8i | − | 0.499883i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.55285e8 | 0.443162 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.10646e8 | − | 1.10646e8i | −0.313097 | − | 0.313097i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.09088e7 | − | 9.09088e7i | −0.255074 | − | 0.255074i | 0.567973 | − | 0.823047i | \(-0.307728\pi\) |
−0.823047 | + | 0.567973i | \(0.807728\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.76673e7 | 0.188265 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 7.18165e8i | − | 1.98133i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.66251e7 | + | 1.66251e7i | −0.0454826 | + | 0.0454826i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.50918e7 | − | 3.50918e7i | 0.0952025 | − | 0.0952025i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.32498e8i | 1.16358i | 0.813338 | + | 0.581791i | \(0.197648\pi\) | ||||
−0.813338 | + | 0.581791i | \(0.802352\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.28066e8 | −0.875297 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.77772e8 | − | 2.77772e8i | −0.734976 | − | 0.734976i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.42503e8 | + | 2.42503e8i | 0.636359 | + | 0.636359i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.23063e8 | 1.10104 | 0.550518 | − | 0.834823i | \(-0.314430\pi\) | ||||
0.550518 | + | 0.834823i | \(0.314430\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 1.43489e7i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.06645e7 | − | 5.06645e7i | 0.129703 | − | 0.129703i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.01686e8 | − | 2.01686e8i | 0.512111 | − | 0.512111i | −0.403062 | − | 0.915173i | \(-0.632054\pi\) |
0.915173 | + | 0.403062i | \(0.132054\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − | 1.58783e8i | − | 0.399890i | ||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.47790e8 | −1.36840 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.56114e8 | − | 2.56114e8i | −0.634601 | − | 0.634601i | 0.314617 | − | 0.949219i | \(-0.398124\pi\) |
−0.949219 | + | 0.314617i | \(0.898124\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.41574e7 | − | 3.41574e7i | −0.0839519 | − | 0.0839519i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.27129e8 | −1.04134 | −0.520670 | − | 0.853758i | \(-0.674318\pi\) | ||||
−0.520670 | + | 0.853758i | \(0.674318\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.71931e8i | 0.657643i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.47031e8 | + | 1.47031e8i | −0.352734 | + | 0.352734i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.95238e7 | − | 3.95238e7i | 0.0940617 | − | 0.0940617i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.54989e8i | 1.31028i | 0.755507 | + | 0.655140i | \(0.227391\pi\) | ||||
−0.755507 | + | 0.655140i | \(0.772609\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.99204e7 | 0.0466565 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.69547e8 | + | 3.69547e8i | 0.858674 | + | 0.858674i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.31247e8 | + | 1.31247e8i | 0.302553 | + | 0.302553i | 0.842012 | − | 0.539459i | \(-0.181371\pi\) |
−0.539459 | + | 0.842012i | \(0.681371\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.09360e8 | −0.707521 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 4.29874e8i | − | 0.975411i | −0.873008 | − | 0.487705i | \(-0.837834\pi\) | ||
0.873008 | − | 0.487705i | \(-0.162166\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.85858e8 | − | 5.85858e8i | 1.31892 | − | 1.31892i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.60022e7 | − | 5.60022e7i | 0.125090 | − | 0.125090i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 4.34396e7i | − | 0.0962720i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.99225e8 | 0.438091 | 0.219045 | − | 0.975715i | \(-0.429706\pi\) | ||||
0.219045 | + | 0.975715i | \(0.429706\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.00212e7 | + | 1.00212e7i | 0.0218654 | + | 0.0218654i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.29385e8 | − | 1.29385e8i | −0.280121 | − | 0.280121i | 0.553036 | − | 0.833157i | \(-0.313469\pi\) |
−0.833157 | + | 0.553036i | \(0.813469\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.34158e8 | −0.717871 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.31684e8i | 0.280718i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.04311e7 | + | 4.04311e7i | −0.0855270 | + | 0.0855270i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.83519e8 | − | 1.83519e8i | 0.385238 | − | 0.385238i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.38182e8i | 0.287851i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.85265e8 | −0.796435 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.68473e7 | − | 2.68473e7i | −0.0550778 | − | 0.0550778i | 0.679031 | − | 0.734109i | \(-0.262400\pi\) |
−0.734109 | + | 0.679031i | \(0.762400\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.21497e8 | − | 1.21497e8i | −0.247364 | − | 0.247364i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.95981e8 | −2.01243 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 5.30840e7i | − | 0.106450i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 8.49873e7 | − | 8.49873e7i | 0.169143 | − | 0.169143i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.83661e8 | − | 5.83661e8i | 1.15288 | − | 1.15288i | 0.166913 | − | 0.985972i | \(-0.446620\pi\) |
0.985972 | − | 0.166913i | \(-0.0533798\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 5.21665e8i | − | 1.02271i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.27928e8 | −0.248924 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.60423e8 | − | 1.60423e8i | −0.309827 | − | 0.309827i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.59900e8 | − | 5.59900e8i | −1.07330 | − | 1.07330i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.93678e8 | 0.749067 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 2.19319e8i | − | 0.414219i | −0.978318 | − | 0.207110i | \(-0.933594\pi\) | ||
0.978318 | − | 0.207110i | \(-0.0664057\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.12226e6 | − | 5.12226e6i | 0.00960282 | − | 0.00960282i | −0.702289 | − | 0.711892i | \(-0.747839\pi\) |
0.711892 | + | 0.702289i | \(0.247839\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.65010e7 | + | 2.65010e7i | −0.0493164 | + | 0.0493164i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 1.55514e8i | − | 0.287274i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.77122e8 | 0.324793 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.58991e7 | + | 2.58991e7i | 0.0471447 | + | 0.0471447i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.18920e8 | + | 6.18920e8i | 1.11842 | + | 1.11842i | 0.991973 | + | 0.126447i | \(0.0403574\pi\) |
0.126447 | + | 0.991973i | \(0.459643\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.08281e8 | −0.732420 | −0.366210 | − | 0.930532i | \(-0.619345\pi\) | ||||
−0.366210 | + | 0.930532i | \(0.619345\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.43943e8i | 0.256348i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.35915e8 | − | 2.35915e8i | 0.417099 | − | 0.417099i | −0.467103 | − | 0.884203i | \(-0.654702\pi\) |
0.884203 | + | 0.467103i | \(0.154702\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.79611e8 | − | 1.79611e8i | 0.315260 | − | 0.315260i | −0.531683 | − | 0.846943i | \(-0.678440\pi\) |
0.846943 | + | 0.531683i | \(0.178440\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.47911e8i | 0.257750i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.33415e8 | −0.922847 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.39403e8 | − | 3.39403e8i | −0.582983 | − | 0.582983i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −9.52047e7 | − | 9.52047e7i | −0.162361 | − | 0.162361i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.16608e7 | −0.0197444 | −0.00987221 | − | 0.999951i | \(-0.503142\pi\) | ||||
−0.00987221 | + | 0.999951i | \(0.503142\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 7.35898e8i | − | 1.23717i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.39068e8 | + | 1.39068e8i | −0.232136 | + | 0.232136i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.64123e8 | + | 2.64123e8i | −0.437760 | + | 0.437760i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 4.00800e8i | − | 0.659594i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.95965e8 | 0.647044 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.42961e8 | + | 2.42961e8i | 0.394228 | + | 0.394228i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −9.74736e7 | − | 9.74736e7i | −0.157051 | − | 0.157051i | 0.624208 | − | 0.781258i | \(-0.285422\pi\) |
−0.781258 | + | 0.624208i | \(0.785422\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.95783e8 | 0.313239 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.03691e8i | 1.43575i | 0.696174 | + | 0.717873i | \(0.254884\pi\) | ||||
−0.696174 | + | 0.717873i | \(0.745116\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.52064e8 | − | 1.52064e8i | 0.239909 | − | 0.239909i | −0.576903 | − | 0.816812i | \(-0.695739\pi\) |
0.816812 | + | 0.576903i | \(0.195739\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.06560e7 | − | 3.06560e7i | 0.0480293 | − | 0.0480293i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.80994e8i | 0.592770i | 0.955069 | + | 0.296385i | \(0.0957811\pi\) | ||||
−0.955069 | + | 0.296385i | \(0.904219\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.76598e8 | −0.272859 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 7.79272e7 | + | 7.79272e7i | 0.119573 | + | 0.119573i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.93401e8 | − | 1.93401e8i | −0.294713 | − | 0.294713i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.69226e8 | 0.256101 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.04179e8i | 0.306879i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6.93500e8 | + | 6.93500e8i | −1.03520 | + | 1.03520i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.62865e8 | − | 5.62865e8i | 0.834460 | − | 0.834460i | −0.153663 | − | 0.988123i | \(-0.549107\pi\) |
0.988123 | + | 0.153663i | \(0.0491071\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.42744e8i | 0.357423i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.19313e9 | 1.74486 | 0.872428 | − | 0.488743i | \(-0.162544\pi\) | ||||
0.872428 | + | 0.488743i | \(0.162544\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.93429e8 | − | 3.93429e8i | −0.571458 | − | 0.571458i | 0.361078 | − | 0.932536i | \(-0.382409\pi\) |
−0.932536 | + | 0.361078i | \(0.882409\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.24493e8 | + | 1.24493e8i | 0.179604 | + | 0.179604i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −6.77947e8 | −0.971460 | −0.485730 | − | 0.874109i | \(-0.661446\pi\) | ||||
−0.485730 | + | 0.874109i | \(0.661446\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 1.83166e9i | − | 2.60699i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.10108e7 | + | 4.10108e7i | −0.0579783 | + | 0.0579783i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9.11866e8 | − | 9.11866e8i | 1.28049 | − | 1.28049i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.50719e8i | 0.907662i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.55689e7 | 0.132416 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.16838e8 | + | 9.16838e8i | 1.26187 | + | 1.26187i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.85507e8 | − | 2.85507e8i | −0.390339 | − | 0.390339i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.34299e8 | −0.182393 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 1.69199e8i | − | 0.228271i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.68493e8 | + | 4.68493e8i | −0.627887 | + | 0.627887i | −0.947536 | − | 0.319649i | \(-0.896435\pi\) |
0.319649 | + | 0.947536i | \(0.396435\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5.41256e7 | + | 5.41256e7i | −0.0720628 | + | 0.0720628i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 3.97237e8i | − | 0.525406i | −0.964877 | − | 0.262703i | \(-0.915386\pi\) | ||
0.964877 | − | 0.262703i | \(-0.0846139\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.40464e8 | 1.10435 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.52133e8 | + | 1.52133e8i | 0.198591 | + | 0.198591i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8.47265e8 | − | 8.47265e8i | −1.09878 | − | 1.09878i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.37068e8 | −0.691963 | −0.345982 | − | 0.938241i | \(-0.612454\pi\) | ||||
−0.345982 | + | 0.938241i | \(0.612454\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.84680e8i | 1.00442i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.66936e7 | + | 5.66936e7i | −0.0720989 | + | 0.0720989i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.13048e8 | − | 1.13048e8i | 0.142836 | − | 0.142836i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.60482e8i | 0.201460i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.33360e9 | −1.66333 | −0.831667 | − | 0.555275i | \(-0.812613\pi\) | ||||
−0.831667 | + | 0.555275i | \(0.812613\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.32403e8 | − | 9.32403e8i | −1.15546 | − | 1.15546i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.12278e8 | + | 2.12278e8i | 0.261373 | + | 0.261373i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.20122e8 | −0.391634 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 6.89471e8i | − | 0.838102i | −0.907963 | − | 0.419051i | \(-0.862363\pi\) | ||
0.907963 | − | 0.419051i | \(-0.137637\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5.16756e8 | + | 5.16756e8i | −0.624150 | + | 0.624150i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.75999e8 | + | 5.75999e8i | −0.691278 | + | 0.691278i | −0.962513 | − | 0.271235i | \(-0.912568\pi\) |
0.271235 | + | 0.962513i | \(0.412568\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 1.13122e8i | − | 0.134900i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.48448e8 | −0.175905 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3.25772e8 | − | 3.25772e8i | −0.383587 | − | 0.383587i | 0.488806 | − | 0.872393i | \(-0.337433\pi\) |
−0.872393 | + | 0.488806i | \(0.837433\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.95585e7 | + | 4.95585e7i | 0.0579855 | + | 0.0579855i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7.99385e8 | −0.929426 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 7.99405e7i | − | 0.0923609i | −0.998933 | − | 0.0461804i | \(-0.985295\pi\) | ||
0.998933 | − | 0.0461804i | \(-0.0147049\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.86762e8 | − | 4.86762e8i | 0.558864 | − | 0.558864i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.94942e8 | − | 3.94942e8i | 0.450606 | − | 0.450606i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 1.23430e9i | − | 1.39948i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.75859e8 | −0.423501 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.93341e7 | − | 1.93341e7i | −0.0216494 | − | 0.0216494i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.98822e8 | + | 1.98822e8i | 0.221250 | + | 0.221250i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.19083e9 | 1.31696 | 0.658479 | − | 0.752599i | \(-0.271200\pi\) | ||||
0.658479 | + | 0.752599i | \(0.271200\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 6.57713e8i | − | 0.722878i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.36800e8 | + | 7.36800e8i | −0.804808 | + | 0.804808i | −0.983843 | − | 0.179035i | \(-0.942702\pi\) |
0.179035 | + | 0.983843i | \(0.442702\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.70936e9 | + | 1.70936e9i | −1.85564 | + | 1.85564i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 4.44676e7i | − | 0.0479767i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 7.27724e8 | 0.780338 | 0.390169 | − | 0.920743i | \(-0.372417\pi\) | ||||
0.390169 | + | 0.920743i | \(0.372417\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.65632e8 | + | 3.65632e8i | 0.389670 | + | 0.389670i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.86588e8 | − | 2.86588e8i | −0.303565 | − | 0.303565i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.20246e8 | −0.442428 | −0.221214 | − | 0.975225i | \(-0.571002\pi\) | ||||
−0.221214 | + | 0.975225i | \(0.571002\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.80912e8i | 0.607857i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.91402e8 | + | 6.91402e8i | −0.719083 | + | 0.719083i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.47785e8 | + | 2.47785e8i | −0.256145 | + | 0.256145i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.01934e8i | 0.207486i | 0.994604 | + | 0.103743i | \(0.0330820\pi\) | ||||
−0.994604 | + | 0.103743i | \(0.966918\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.08989e9 | 1.11310 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.78474e8 | − | 3.78474e8i | −0.384208 | − | 0.384208i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.25907e9 | − | 1.25907e9i | −1.27047 | − | 1.27047i | −0.945842 | − | 0.324626i | \(-0.894761\pi\) |
−0.324626 | − | 0.945842i | \(-0.605239\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6.44169e7 | 0.0646105 |
(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 | 384.7.l.a.31.6 | 48 | ||
4.3 | odd | 2 | 384.7.l.b.31.19 | 48 | |||
8.3 | odd | 2 | 48.7.l.a.43.3 | yes | 48 | ||
8.5 | even | 2 | 192.7.l.a.79.19 | 48 | |||
16.3 | odd | 4 | inner | 384.7.l.a.223.6 | 48 | ||
16.5 | even | 4 | 48.7.l.a.19.3 | ✓ | 48 | ||
16.11 | odd | 4 | 192.7.l.a.175.19 | 48 | |||
16.13 | even | 4 | 384.7.l.b.223.19 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.7.l.a.19.3 | ✓ | 48 | 16.5 | even | 4 | ||
48.7.l.a.43.3 | yes | 48 | 8.3 | odd | 2 | ||
192.7.l.a.79.19 | 48 | 8.5 | even | 2 | |||
192.7.l.a.175.19 | 48 | 16.11 | odd | 4 | |||
384.7.l.a.31.6 | 48 | 1.1 | even | 1 | trivial | ||
384.7.l.a.223.6 | 48 | 16.3 | odd | 4 | inner | ||
384.7.l.b.31.19 | 48 | 4.3 | odd | 2 | |||
384.7.l.b.223.19 | 48 | 16.13 | even | 4 |