Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [80,6,Mod(49,80)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(80, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("80.49");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 80 = 2^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 80.c (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: | \(12.8307055850\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{-11}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 5) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 49.2 | ||
Root | \(0.500000 - 1.65831i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 80.49 |
Dual form | 80.6.c.a.49.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/80\mathbb{Z}\right)^\times\).
\(n\) | \(17\) | \(21\) | \(31\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 19.8997i | 1.27657i | 0.769800 | + | 0.638285i | \(0.220356\pi\) | ||||
−0.769800 | + | 0.638285i | \(0.779644\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −45.0000 | + | 33.1662i | −0.804984 | + | 0.593296i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 59.6992i | 0.460494i | 0.973132 | + | 0.230247i | \(0.0739534\pi\) | ||||
−0.973132 | + | 0.230247i | \(0.926047\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −153.000 | −0.629630 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −252.000 | −0.627941 | −0.313970 | − | 0.949433i | \(-0.601659\pi\) | ||||
−0.313970 | + | 0.949433i | \(0.601659\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 119.398i | − | 0.195948i | −0.995189 | − | 0.0979739i | \(-0.968764\pi\) | ||
0.995189 | − | 0.0979739i | \(-0.0312362\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −660.000 | − | 895.489i | −0.757383 | − | 1.02762i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 689.858i | − | 0.578945i | −0.957186 | − | 0.289473i | \(-0.906520\pi\) | ||
0.957186 | − | 0.289473i | \(-0.0934799\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 220.000 | 0.139810 | 0.0699051 | − | 0.997554i | \(-0.477730\pi\) | ||||
0.0699051 | + | 0.997554i | \(0.477730\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1188.00 | −0.587852 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 2434.40i | − | 0.959561i | −0.877388 | − | 0.479781i | \(-0.840716\pi\) | ||
0.877388 | − | 0.479781i | \(-0.159284\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 925.000 | − | 2984.96i | 0.296000 | − | 0.955188i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1790.98i | 0.472804i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6930.00 | −1.53016 | −0.765082 | − | 0.643932i | \(-0.777302\pi\) | ||||
−0.765082 | + | 0.643932i | \(0.777302\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6752.00 | −1.26191 | −0.630955 | − | 0.775820i | \(-0.717337\pi\) | ||||
−0.630955 | + | 0.775820i | \(0.717337\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 5014.74i | − | 0.801610i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1980.00 | − | 2686.47i | −0.273209 | − | 0.370690i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 13969.6i | 1.67757i | 0.544464 | + | 0.838785i | \(0.316733\pi\) | ||||
−0.544464 | + | 0.838785i | \(0.683267\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2376.00 | 0.250141 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −198.000 | −0.0183952 | −0.00919762 | − | 0.999958i | \(-0.502928\pi\) | ||||
−0.00919762 | + | 0.999958i | \(0.502928\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 417.895i | 0.0344664i | 0.999851 | + | 0.0172332i | \(0.00548577\pi\) | ||||
−0.999851 | + | 0.0172332i | \(0.994514\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6885.00 | − | 5074.44i | 0.506842 | − | 0.373557i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10540.2i | 0.695994i | 0.937496 | + | 0.347997i | \(0.113138\pi\) | ||||
−0.937496 | + | 0.347997i | \(0.886862\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 13243.0 | 0.787945 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 13728.0 | 0.739064 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 5823.99i | − | 0.284794i | −0.989810 | − | 0.142397i | \(-0.954519\pi\) | ||
0.989810 | − | 0.142397i | \(-0.0454810\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 11340.0 | − | 8357.89i | 0.505483 | − | 0.372555i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4377.94i | 0.178477i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 24660.0 | 0.922281 | 0.461140 | − | 0.887327i | \(-0.347440\pi\) | ||||
0.461140 | + | 0.887327i | \(0.347440\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5698.00 | −0.196064 | −0.0980320 | − | 0.995183i | \(-0.531255\pi\) | ||||
−0.0980320 | + | 0.995183i | \(0.531255\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 9133.98i | − | 0.289941i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3960.00 | + | 5372.93i | 0.116255 | + | 0.157735i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 43640.1i | 1.18768i | 0.804583 | + | 0.593840i | \(0.202389\pi\) | ||||
−0.804583 | + | 0.593840i | \(0.797611\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 48444.0 | 1.22495 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −53352.0 | −1.25604 | −0.628022 | − | 0.778196i | \(-0.716135\pi\) | ||||
−0.628022 | + | 0.778196i | \(0.716135\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 70922.7i | 1.55768i | 0.627223 | + | 0.778840i | \(0.284192\pi\) | ||||
−0.627223 | + | 0.778840i | \(0.715808\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 59400.0 | + | 18407.3i | 1.21936 | + | 0.377865i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 15044.2i | − | 0.289163i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −51920.0 | −0.935981 | −0.467990 | − | 0.883734i | \(-0.655022\pi\) | ||||
−0.467990 | + | 0.883734i | \(0.655022\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −72819.0 | −1.23320 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 61841.8i | 0.985342i | 0.870216 | + | 0.492671i | \(0.163979\pi\) | ||||
−0.870216 | + | 0.492671i | \(0.836021\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 22880.0 | + | 31043.6i | 0.343486 | + | 0.466042i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 137905.i | − | 1.95336i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9990.00 | −0.133687 | −0.0668437 | − | 0.997763i | \(-0.521293\pi\) | ||||
−0.0668437 | + | 0.997763i | \(0.521293\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7128.00 | 0.0902328 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 134363.i | − | 1.61092i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −9900.00 | + | 7296.57i | −0.112545 | + | 0.0829488i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 101250.i | − | 1.09261i | −0.837586 | − | 0.546305i | \(-0.816034\pi\) | ||
0.837586 | − | 0.546305i | \(-0.183966\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 38556.0 | 0.395370 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −109098. | −1.06418 | −0.532088 | − | 0.846689i | \(-0.678592\pi\) | ||||
−0.532088 | + | 0.846689i | \(0.678592\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 70624.2i | − | 0.655935i | −0.944689 | − | 0.327967i | \(-0.893636\pi\) | ||
0.944689 | − | 0.327967i | \(-0.106364\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 53460.0 | − | 39401.5i | 0.473212 | − | 0.348770i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 97117.4i | − | 0.820045i | −0.912075 | − | 0.410022i | \(-0.865521\pi\) | ||
0.912075 | − | 0.410022i | \(-0.134479\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −21010.0 | −0.169379 | −0.0846895 | − | 0.996407i | \(-0.526990\pi\) | ||||
−0.0846895 | + | 0.996407i | \(0.526990\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −277992. | −2.14153 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 105018.i | 0.773688i | 0.922145 | + | 0.386844i | \(0.126435\pi\) | ||||
−0.922145 | + | 0.386844i | \(0.873565\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 80740.0 | + | 109548.i | 0.569304 | + | 0.772432i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 18268.0i | 0.123375i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 41184.0 | 0.266601 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −97547.0 | −0.605690 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 3940.15i | − | 0.0234828i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 57375.0 | + | 165002.i | 0.328434 | + | 0.944527i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 87220.6i | 0.479855i | 0.970791 | + | 0.239927i | \(0.0771236\pi\) | ||||
−0.970791 | + | 0.239927i | \(0.922876\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8316.00 | −0.0439987 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −192852. | −0.981852 | −0.490926 | − | 0.871201i | \(-0.663341\pi\) | ||||
−0.490926 | + | 0.871201i | \(0.663341\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 13133.8i | 0.0643817i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −59400.0 | − | 80594.0i | −0.280512 | − | 0.380599i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 143570.i | − | 0.653525i | −0.945106 | − | 0.326763i | \(-0.894042\pi\) | ||
0.945106 | − | 0.326763i | \(-0.105958\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 318340. | 1.39751 | 0.698754 | − | 0.715362i | \(-0.253738\pi\) | ||||
0.698754 | + | 0.715362i | \(0.253738\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −209748. | −0.888485 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 30088.4i | 0.123044i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 311850. | − | 229842.i | 1.23176 | − | 0.907841i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 263532.i | 1.00587i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 84150.0 | 0.310519 | 0.155260 | − | 0.987874i | \(-0.450379\pi\) | ||||
0.155260 | + | 0.987874i | \(0.450379\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 155848. | 0.556236 | 0.278118 | − | 0.960547i | \(-0.410289\pi\) | ||||
0.278118 | + | 0.960547i | \(0.410289\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 105548.i | 0.364521i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 303840. | − | 223939.i | 1.01582 | − | 0.748686i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 356643.i | 1.15474i | 0.816482 | + | 0.577371i | \(0.195921\pi\) | ||||
−0.816482 | + | 0.577371i | \(0.804079\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 115896. | 0.363560 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 145332. | 0.441872 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 144890.i | 0.427139i | 0.976928 | + | 0.213570i | \(0.0685090\pi\) | ||||
−0.976928 | + | 0.213570i | \(0.931491\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 166320. | + | 225663.i | 0.475592 | + | 0.645284i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18102.1i | 0.0502272i | 0.999685 | + | 0.0251136i | \(0.00799474\pi\) | ||||
−0.999685 | + | 0.0251136i | \(0.992005\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 357037. | 0.961604 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −33660.0 | −0.0880286 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 492572.i | − | 1.25128i | −0.780112 | − | 0.625640i | \(-0.784838\pi\) | ||
0.780112 | − | 0.625640i | \(-0.215162\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 178200. | + | 55221.8i | 0.439858 | + | 0.136306i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 490728.i | 1.17736i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −444420. | −1.03672 | −0.518359 | − | 0.855163i | \(-0.673457\pi\) | ||||
−0.518359 | + | 0.855163i | \(0.673457\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 156902. | 0.355985 | 0.177993 | − | 0.984032i | \(-0.443040\pi\) | ||||
0.177993 | + | 0.984032i | \(0.443040\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 113389.i | − | 0.250289i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −463320. | − | 628633.i | −0.995295 | − | 1.35042i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 173844.i | 0.363543i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −106920. | −0.217723 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −332352. | −0.659196 | −0.329598 | − | 0.944121i | \(-0.606913\pi\) | ||||
−0.329598 | + | 0.944121i | \(0.606913\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 786120.i | 1.51913i | 0.650430 | + | 0.759566i | \(0.274589\pi\) | ||||
−0.650430 | + | 0.759566i | \(0.725411\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −106920. | + | 78803.0i | −0.201360 | + | 0.148408i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 59606.4i | 0.109428i | 0.998502 | + | 0.0547138i | \(0.0174247\pi\) | ||||
−0.998502 | + | 0.0547138i | \(0.982575\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 395800. | 0.708505 | 0.354253 | − | 0.935150i | \(-0.384735\pi\) | ||||
0.354253 | + | 0.935150i | \(0.384735\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −868428. | −1.51616 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 413716.i | − | 0.704631i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8910.00 | − | 6566.92i | 0.0148079 | − | 0.0109138i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 372464.i | 0.604168i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −55440.0 | −0.0877925 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 251548. | 0.388969 | 0.194484 | − | 0.980906i | \(-0.437697\pi\) | ||||
0.194484 | + | 0.980906i | \(0.437697\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 1.06169e6i | − | 1.60343i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −13860.0 | − | 18805.3i | −0.0204488 | − | 0.0277449i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 403089.i | − | 0.581101i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.41134e6 | −1.98849 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −82368.0 | −0.113443 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 288765.i | 0.388851i | 0.980917 | + | 0.194425i | \(0.0622842\pi\) | ||||
−0.980917 | + | 0.194425i | \(0.937716\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −141525. | + | 456699.i | −0.186370 | + | 0.601415i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 1.16414e6i | − | 1.49948i | −0.661731 | − | 0.749741i | \(-0.730178\pi\) | ||
0.661731 | − | 0.749741i | \(-0.269822\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 547670. | 0.690129 | 0.345064 | − | 0.938579i | \(-0.387857\pi\) | ||||
0.345064 | + | 0.938579i | \(0.387857\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 299376. | 0.369137 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 48104.3i | 0.0580489i | 0.999579 | + | 0.0290245i | \(0.00924007\pi\) | ||||
−0.999579 | + | 0.0290245i | \(0.990760\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −349580. | − | 474311.i | −0.412930 | − | 0.560264i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 1.03319e6i | − | 1.19484i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.00584e6 | 1.13903 | 0.569514 | − | 0.821982i | \(-0.307132\pi\) | ||||
0.569514 | + | 0.821982i | \(0.307132\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 895202. | 0.992838 | 0.496419 | − | 0.868083i | \(-0.334648\pi\) | ||||
0.496419 | + | 0.868083i | \(0.334648\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 1.01387e6i | − | 1.10146i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −595935. | + | 439221.i | −0.634284 | + | 0.467485i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 26267.7i | − | 0.0273955i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.23064e6 | −1.25786 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −558252. | −0.559301 | −0.279651 | − | 0.960102i | \(-0.590219\pi\) | ||||
−0.279651 | + | 0.960102i | \(0.590219\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 613469.i | 0.602548i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −617760. | + | 455306.i | −0.594935 | + | 0.438483i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 787924.i | − | 0.744135i | −0.928206 | − | 0.372067i | \(-0.878649\pi\) | ||
0.928206 | − | 0.372067i | \(-0.121351\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −833976. | −0.772510 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.06029e6 | 0.963437 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.63173e6i | 1.45465i | 0.686291 | + | 0.727327i | \(0.259238\pi\) | ||||
−0.686291 | + | 0.727327i | \(0.740762\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 193160. | + | 262080.i | 0.168967 | + | 0.229255i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 198798.i | − | 0.170661i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.73637e6 | −1.46306 | −0.731529 | − | 0.681810i | \(-0.761193\pi\) | ||||
−0.731529 | + | 0.681810i | \(0.761193\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.72005e6 | 1.42271 | 0.711357 | − | 0.702831i | \(-0.248081\pi\) | ||||
0.711357 | + | 0.702831i | \(0.248081\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 141845.i | 0.115188i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −233100. | + | 752211.i | −0.185871 | + | 0.599802i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.27243e6i | 0.996402i | 0.867062 | + | 0.498201i | \(0.166006\pi\) | ||||
−0.867062 | + | 0.498201i | \(0.833994\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.03306e6 | 0.794536 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.46500e6 | 1.10681 | 0.553404 | − | 0.832913i | \(-0.313329\pi\) | ||||
0.553404 | + | 0.832913i | \(0.313329\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.65051e6i | 1.22504i | 0.790455 | + | 0.612521i | \(0.209844\pi\) | ||||
−0.790455 | + | 0.612521i | \(0.790156\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −145200. | − | 197008.i | −0.105890 | − | 0.143672i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 11820.5i | − | 0.00847089i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 943953. | 0.664823 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.01485e6 | 1.39479 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.38772e6i | 1.62485i | 0.583064 | + | 0.812426i | \(0.301854\pi\) | ||||
−0.583064 | + | 0.812426i | \(0.698146\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.10970e6 | + | 817880.i | −0.742422 | + | 0.547185i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 451326.i | − | 0.296893i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −290664. | −0.188024 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −24948.0 | −0.0158716 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 2.17102e6i | − | 1.35849i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 256410. | − | 188981.i | 0.157828 | − | 0.116324i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 928264.i | − | 0.562115i | −0.959691 | − | 0.281058i | \(-0.909315\pi\) | ||
0.959691 | − | 0.281058i | \(-0.0906852\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.40540e6 | 0.837346 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −568152. | −0.333092 | −0.166546 | − | 0.986034i | \(-0.553261\pi\) | ||||
−0.166546 | + | 0.986034i | \(0.553261\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 1.72244e6i | − | 0.993766i | −0.867818 | − | 0.496883i | \(-0.834478\pi\) | ||
0.867818 | − | 0.496883i | \(-0.165522\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 302940. | + | 411029.i | 0.172021 | + | 0.233398i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 131643.i | 0.0735785i | 0.999323 | + | 0.0367893i | \(0.0117130\pi\) | ||||
−0.999323 | + | 0.0367893i | \(0.988287\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.74636e6 | 0.960853 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.93261e6 | 1.04684 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 151769.i | − | 0.0809424i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −356400. | − | 110444.i | −0.187167 | − | 0.0580006i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 418094.i | − | 0.216224i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −629244. | −0.320501 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.58055e6 | 0.792935 | 0.396468 | − | 0.918049i | \(-0.370236\pi\) | ||||
0.396468 | + | 0.918049i | \(0.370236\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 2.13735e6i | − | 1.05625i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.44738e6 | − | 1.96381e6i | −0.704645 | − | 0.956063i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.22885e6i | 0.589419i | 0.955587 | + | 0.294709i | \(0.0952228\pi\) | ||||
−0.955587 | + | 0.294709i | \(0.904777\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.08982e6 | −0.987667 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.70150e6 | 0.792405 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.79396e6i | 0.823338i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.17998e6 | + | 1.60671e6i | −0.986063 | + | 0.726756i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.84224e6i | 1.71301i | 0.516137 | + | 0.856506i | \(0.327370\pi\) | ||||
−0.516137 | + | 0.856506i | \(0.672630\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.59445e6 | −0.700725 | −0.350362 | − | 0.936614i | \(-0.613942\pi\) | ||||
−0.350362 | + | 0.936614i | \(0.613942\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 213840. | 0.0926448 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 295365.i | − | 0.126160i | −0.998008 | − | 0.0630802i | \(-0.979908\pi\) | ||
0.998008 | − | 0.0630802i | \(-0.0200924\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.40084e6 | − | 1.76949e6i | 1.01110 | − | 0.745206i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 819551.i | 0.340334i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.10484e6 | −0.452442 | −0.226221 | − | 0.974076i | \(-0.572637\pi\) | ||||
−0.226221 | + | 0.974076i | \(0.572637\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.42770e6 | −0.980453 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 1.94116e6i | − | 0.773206i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.35224e6 | − | 3.19152e6i | −0.924165 | − | 1.25391i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.83760e6i | 0.712174i | 0.934453 | + | 0.356087i | \(0.115889\pi\) | ||||
−0.934453 | + | 0.356087i | \(0.884111\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 30294.0 | 0.0115822 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 347688. | 0.131146 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.93350e6i | 1.09173i | 0.837874 | + | 0.545864i | \(0.183798\pi\) | ||||
−0.837874 | + | 0.545864i | \(0.816202\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.28350e6 | + | 1.14175e6i | −1.20575 | + | 0.419268i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 827432.i | 0.299832i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.09342e6 | −1.82143 | −0.910713 | − | 0.413040i | \(-0.864467\pi\) | ||||
−0.910713 | + | 0.413040i | \(0.864467\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.73567e6 | −0.612568 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 3.17485e6i | − | 1.10593i | −0.833205 | − | 0.552964i | \(-0.813497\pi\) | ||
0.833205 | − | 0.552964i | \(-0.186503\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 498960. | + | 676989.i | 0.171559 | + | 0.232772i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 63937.9i | − | 0.0217011i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.79991e6 | 0.603083 | 0.301541 | − | 0.953453i | \(-0.402499\pi\) | ||||
0.301541 | + | 0.953453i | \(0.402499\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.67939e6 | −0.555533 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 3.83771e6i | − | 1.25340i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.33640e6 | − | 1.72199e6i | 0.753450 | − | 0.555314i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 4.90405e6i | − | 1.56163i | −0.624760 | − | 0.780817i | \(-0.714803\pi\) | ||
0.624760 | − | 0.780817i | \(-0.285197\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −261360. | −0.0821877 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −642798. | −0.199624 | −0.0998122 | − | 0.995006i | \(-0.531824\pi\) | ||||
−0.0998122 | + | 0.995006i | \(0.531824\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 806179.i | 0.247268i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.27686e6 | − | 2.41513e6i | 0.992704 | − | 0.731650i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 3.52035e6i | − | 1.05341i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.05711e6 | −0.608064 | −0.304032 | − | 0.952662i | \(-0.598333\pi\) | ||||
−0.304032 | + | 0.952662i | \(0.598333\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.85701e6 | 0.834271 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.47218e6i | 0.424704i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.05106e6 | − | 2.78288e6i | −0.584599 | − | 0.793185i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.33489e6i | 1.78402i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.93742e6 | 0.817393 | 0.408697 | − | 0.912670i | \(-0.365983\pi\) | ||||
0.408697 | + | 0.912670i | \(0.365983\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.71770e6 | 0.747303 | 0.373651 | − | 0.927569i | \(-0.378106\pi\) | ||||
0.373651 | + | 0.927569i | \(0.378106\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 1.61266e6i | − | 0.438219i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.05920e6 | − | 638119.i | −0.553001 | − | 0.171368i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 340166.i | − | 0.0902862i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −598752. | −0.157074 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.99435e6 | −1.29505 | −0.647524 | − | 0.762045i | \(-0.724196\pi\) | ||||
−0.647524 | + | 0.762045i | \(0.724196\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 2.08183e6i | − | 0.533612i | −0.963750 | − | 0.266806i | \(-0.914032\pi\) | ||
0.963750 | − | 0.266806i | \(-0.0859684\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.57380e6 | + | 6.20574e6i | 1.15892 | + | 1.57243i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 535569.i | − | 0.134156i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.70404e6 | 1.16496 | 0.582478 | − | 0.812846i | \(-0.302083\pi\) | ||||
0.582478 | + | 0.812846i | \(0.302083\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.02618e6 | −0.496114 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.70103e6i | 1.38021i | 0.723711 | + | 0.690103i | \(0.242435\pi\) | ||||
−0.723711 | + | 0.690103i | \(0.757565\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 449550. | − | 331331.i | 0.107616 | − | 0.0793162i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.67456e6i | 0.396399i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.20325e6 | 1.45212 | 0.726062 | − | 0.687630i | \(-0.241349\pi\) | ||||
0.726062 | + | 0.687630i | \(0.241349\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 49896.0 | 0.0115511 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.10134e6i | 0.710074i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −320760. | + | 236409.i | −0.0726360 | + | 0.0535347i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 2.15371e6i | − | 0.482388i | −0.970477 | − | 0.241194i | \(-0.922461\pi\) | ||
0.970477 | − | 0.241194i | \(-0.0775391\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.23552e6 | 0.273727 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.85130e6 | −0.844024 | −0.422012 | − | 0.906590i | \(-0.638676\pi\) | ||||
−0.422012 | + | 0.906590i | \(0.638676\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.08213e6i | 0.451394i | 0.974198 | + | 0.225697i | \(0.0724659\pi\) | ||||
−0.974198 | + | 0.225697i | \(0.927534\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.45632e6 | + | 6.04634e6i | 0.955749 | + | 1.29676i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 1.30822e6i | − | 0.277579i | −0.990322 | − | 0.138790i | \(-0.955679\pi\) | ||
0.990322 | − | 0.138790i | \(-0.0443212\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.60528e6 | −0.546919 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.09711e6 | −1.47411 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 105309.i | − | 0.0216429i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 203500. | − | 656692.i | 0.0413838 | − | 0.133545i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 891071.i | 0.179315i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.76368e6 | 1.34693 | 0.673464 | − | 0.739220i | \(-0.264806\pi\) | ||||
0.673464 | + | 0.739220i | \(0.264806\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.66795e6 | 0.328716 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.89207e6i | 0.564080i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.35808e6 | + | 4.55625e6i | 0.648241 | + | 0.879534i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 6.67193e6i | − | 1.27476i | −0.770549 | − | 0.637381i | \(-0.780018\pi\) | ||
0.770549 | − | 0.637381i | \(-0.219982\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.88328e6 | −0.545273 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.87575e6 | 1.28711 | 0.643556 | − | 0.765399i | \(-0.277458\pi\) | ||||
0.643556 | + | 0.765399i | \(0.277458\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.78072e6i | 0.885881i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.73502e6 | + | 1.27876e6i | −0.318267 | + | 0.234572i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 3.18507e6i | − | 0.578400i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.94010e6 | −1.24771 | −0.623856 | − | 0.781539i | \(-0.714435\pi\) | ||||
−0.623856 | + | 0.781539i | \(0.714435\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −360228. | −0.0641185 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 921007.i | − | 0.162309i | −0.996702 | − | 0.0811546i | \(-0.974139\pi\) | ||
0.996702 | − | 0.0811546i | \(-0.0258607\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.90941e6 | − | 3.61837e6i | 0.856645 | − | 0.631371i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.10495e6i | 1.22755i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.97979e6 | 0.851955 | 0.425977 | − | 0.904734i | \(-0.359930\pi\) | ||||
0.425977 | + | 0.904734i | \(0.359930\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.23403e6 | −0.717302 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 394015.i | 0.0661027i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.34234e6 | + | 3.17809e6i | 0.389163 | + | 0.528017i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 2.65614e6i | − | 0.437043i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.80206e6 | 1.59735 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −147798. | −0.0238547 | −0.0119274 | − | 0.999929i | \(-0.503797\pi\) | ||||
−0.0119274 | + | 0.999929i | \(0.503797\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 1.23884e7i | − | 1.98043i | −0.139543 | − | 0.990216i | \(-0.544563\pi\) | ||
0.139543 | − | 0.990216i | \(-0.455437\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.09890e6 | + | 3.54614e6i | −0.174004 | + | 0.561509i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.65792e6i | 0.730576i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 510027. | 0.0792417 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.77298e6 | −0.580695 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 23640.9i | 0.00360451i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.22102e6 | + | 4.37028e6i | 0.486529 | + | 0.660123i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 8.84385e6i | − | 1.32344i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.33724e6 | −0.494783 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.99810e6 | −1.46867 | −0.734335 | − | 0.678787i | \(-0.762506\pi\) | ||||
−0.734335 | + | 0.678787i | \(0.762506\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.12231e6i | 0.454440i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 945450. | − | 696823.i | 0.136348 | − | 0.100492i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 1.18580e7i | − | 1.69451i | −0.531189 | − | 0.847253i | \(-0.678255\pi\) | ||
0.531189 | − | 0.847253i | \(-0.321745\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 871794. | 0.123448 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.52460e6 | −0.213933 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 3.09958e6i | − | 0.431013i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.25096e7 | − | 9.21995e6i | 1.72390 | − | 1.27056i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 904550.i | 0.123536i | 0.998091 | + | 0.0617681i | \(0.0196739\pi\) | ||||
−0.998091 | + | 0.0617681i | \(0.980326\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 49896.0 | 0.00675361 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.45946e6 | −0.464088 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8.68719e6i | 1.15507i | 0.816366 | + | 0.577535i | \(0.195985\pi\) | ||||
−0.816366 | + | 0.577535i | \(0.804015\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.48304e6 | − | 4.72579e6i | −0.459026 | − | 0.622807i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 4.34724e6i | − | 0.567879i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.27007e6 | −0.293940 | −0.146970 | − | 0.989141i | \(-0.546952\pi\) | ||||
−0.146970 | + | 0.989141i | \(0.546952\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.43807e7 | −1.84582 | −0.922908 | − | 0.385021i | \(-0.874194\pi\) | ||||
−0.922908 | + | 0.385021i | \(0.874194\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 6.61372e6i | − | 0.841510i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7.26660e6 | − | 2.25182e6i | −0.916562 | − | 0.284030i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.63943e6i | 0.705173i | 0.935779 | + | 0.352586i | \(0.114698\pi\) | ||||
−0.935779 | + | 0.352586i | \(0.885302\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.56436e7 | −1.93928 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.69191e6 | −0.453744 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.46765e6i | 0.178834i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −605880. | − | 822059.i | −0.0731976 | − | 0.0993146i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 1.28473e6i | − | 0.153893i | −0.997035 | − | 0.0769464i | \(-0.975483\pi\) | ||
0.997035 | − | 0.0769464i | \(-0.0245170\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.48544e6 | −0.176428 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.18615e6 | −0.139692 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.00943e6i | 0.818552i | 0.912411 | + | 0.409276i | \(0.134219\pi\) | ||||
−0.912411 | + | 0.409276i | \(0.865781\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.85328e6 | + | 1.36592e6i | −0.214609 | + | 0.158173i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7.87632e6i | 0.904456i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.80020e6 | 1.00213 | 0.501067 | − | 0.865409i | \(-0.332941\pi\) | ||||
0.501067 | + | 0.865409i | \(0.332941\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.07670e7 | −1.21593 | −0.607965 | − | 0.793964i | \(-0.708014\pi\) | ||||
−0.607965 | + | 0.793964i | \(0.708014\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 6.67694e6i | − | 0.747798i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.38962e6 | − | 3.23527e6i | 0.487571 | − | 0.359353i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.51219e7i | 1.66584i | 0.553391 | + | 0.832921i | \(0.313333\pi\) | ||||
−0.553391 | + | 0.832921i | \(0.686667\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 8.23284e6 | 0.899511 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.25849e6 | 0.136379 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 8.31622e6i | − | 0.893871i | −0.894566 | − | 0.446936i | \(-0.852515\pi\) | ||
0.894566 | − | 0.446936i | \(-0.147485\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 130680. | + | 177307.i | 0.0139323 | + | 0.0189033i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.21083e7i | 1.28047i | 0.768178 | + | 0.640237i | \(0.221164\pi\) | ||||
−0.768178 | + | 0.640237i | \(0.778836\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.73238e6 | −1.02092 | −0.510461 | − | 0.859901i | \(-0.670525\pi\) | ||||
−0.510461 | + | 0.859901i | \(0.670525\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.35996e6 | 0.453684 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 596395.i | − | 0.0615622i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.05437e6 | − | 5.52218e6i | −0.824768 | − | 0.565471i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 1.10324e6i | − | 0.112073i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9.63706e6 | 0.971220 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.60145e6 | 0.859999 | 0.430000 | − | 0.902829i | \(-0.358514\pi\) | ||||
0.430000 | + | 0.902829i | \(0.358514\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.00574e6i | 0.496546i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.89278e6 | − | 3.92493e6i | −0.284696 | − | 0.386276i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 1.58119e6i | − | 0.154396i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.16286e6 | 0.790842 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.42440e6 | −0.617572 | −0.308786 | − | 0.951132i | \(-0.599923\pi\) | ||||
−0.308786 | + | 0.951132i | \(0.599923\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 3.64721e6i | − | 0.347883i | −0.984756 | − | 0.173941i | \(-0.944350\pi\) | ||
0.984756 | − | 0.173941i | \(-0.0556503\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 374220. | − | 275811.i | 0.0354183 | − | 0.0261043i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 3.78036e6i | − | 0.355036i | −0.984118 | − | 0.177518i | \(-0.943193\pi\) | ||
0.984118 | − | 0.177518i | \(-0.0568068\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.21432e6 | −0.579138 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.02138e6 | 0.741816 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 1.66957e7i | − | 1.53223i | −0.642706 | − | 0.766113i | \(-0.722188\pi\) | ||
0.642706 | − | 0.766113i | \(-0.277812\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.67834e6 | − | 6.39618e6i | 0.790375 | − | 0.582529i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 1.08512e7i | − | 0.980761i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.22166e6 | 0.109581 | 0.0547907 | − | 0.998498i | \(-0.482551\pi\) | ||||
0.0547907 | + | 0.998498i | \(0.482551\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.62789e7 | 1.44918 | 0.724589 | − | 0.689182i | \(-0.242030\pi\) | ||||
0.724589 | + | 0.689182i | \(0.242030\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 1.63910e6i | − | 0.144818i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −435600. | − | 591023.i | −0.0381974 | − | 0.0518263i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.68704e7i | 1.46829i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5.74636e6 | −0.496395 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.43590e6 | 0.123117 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.43928e7i | 1.22492i | 0.790503 | + | 0.612459i | \(0.209819\pi\) | ||||
−0.790503 | + | 0.612459i | \(0.790181\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.34600e6 | + | 1.65665e6i | 0.451616 | + | 0.139950i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.62429e6i | 0.220059i | 0.993928 | + | 0.110030i | \(0.0350946\pi\) | ||||
−0.993928 | + | 0.110030i | \(0.964905\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.04454e6 | 0.503140 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.31661e7 | 1.91419 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 1.03039e7i | − | 0.845184i | −0.906320 | − | 0.422592i | \(-0.861120\pi\) | ||
0.906320 | − | 0.422592i | \(-0.138880\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.76168e6 | + | 6.46065e6i | 0.387734 | + | 0.526078i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.08985e7i | 0.880998i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −695376. | −0.0558048 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.50285e6 | −0.358751 | −0.179375 | − | 0.983781i | \(-0.557408\pi\) | ||||
−0.179375 | + | 0.983781i | \(0.557408\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.30176e6i | 0.182066i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.43253e7 | + | 1.05581e7i | −1.12497 | + | 0.829136i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 136592.i | 0.0106498i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −957264. | −0.0741035 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.88090e6 | −0.375150 | −0.187575 | − | 0.982250i | \(-0.560063\pi\) | ||||
−0.187575 | + | 0.982250i | \(0.560063\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.07332e6i | 0.234541i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 9.43866e6 | − | 6.95655e6i | 0.715217 | − | 0.527134i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 6.51307e6i | − | 0.490046i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.96961e6 | −0.744839 | −0.372420 | − | 0.928064i | \(-0.621472\pi\) | ||||
−0.372420 | + | 0.928064i | \(0.621472\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.94376e6 | 0.589321 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.64371e7i | 1.21088i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −997920. | − | 1.35398e6i | −0.0730013 | − | 0.0990482i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.00160e7i | 1.45405i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.19167e7 | 0.859675 | 0.429838 | − | 0.902906i | \(-0.358571\pi\) | ||||
0.429838 | + | 0.902906i | \(0.358571\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.21621e6 | 0.302054 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.78143e7i | 1.26743i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.41025e6 | + | 2.06858e7i | −0.452929 | + | 1.46160i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.38269e6i | 0.0970264i | 0.998823 | + | 0.0485132i | \(0.0154483\pi\) | ||||
−0.998823 | + | 0.0485132i | \(0.984552\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.48079e6 | 0.172890 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 288288. | 0.0199541 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 6.09661e6i | − | 0.419110i | −0.977797 | − | 0.209555i | \(-0.932798\pi\) | ||
0.977797 | − | 0.209555i | \(-0.0672016\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −8.74038e6 | − | 1.18590e7i | −0.596777 | − | 0.809707i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 1.09973e7i | − | 0.745793i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.16946e6 | −0.415562 | −0.207781 | − | 0.978175i | \(-0.566624\pi\) | ||||
−0.207781 | + | 0.978175i | \(0.566624\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 522720. | 0.0349723 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.57574e7i | 1.04716i | 0.851978 | + | 0.523578i | \(0.175403\pi\) | ||||
−0.851978 | + | 0.523578i | \(0.824597\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.78675e6 | + | 2.79094e6i | −0.249963 | + | 0.184230i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 9.46179e6i | − | 0.620400i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.79784e6 | 0.377626 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.51816e7 | 0.982243 | 0.491122 | − | 0.871091i | \(-0.336587\pi\) | ||||
0.491122 | + | 0.871091i | \(0.336587\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 1.11091e7i | − | 0.713987i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7.01316e6 | + | 5.16889e6i | −0.447761 | + | 0.330012i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 652274.i | − | 0.0413705i | −0.999786 | − | 0.0206852i | \(-0.993415\pi\) | ||
0.999786 | − | 0.0206852i | \(-0.00658478\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.22079e7 | −0.769194 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.51420e6 | 0.282566 | 0.141283 | − | 0.989969i | \(-0.454877\pi\) | ||||
0.141283 | + | 0.989969i | \(0.454877\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 1.25428e6i | − | 0.0779980i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.50064e6 | − | 4.74967e6i | −0.216269 | − | 0.293434i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 2.94437e6i | − | 0.180719i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.20799e7 | −0.736625 | −0.368312 | − | 0.929702i | \(-0.620064\pi\) | ||||
−0.368312 | + | 0.929702i | \(0.620064\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.56795e7 | 0.949939 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 1.04245e7i | − | 0.627492i | −0.949507 | − | 0.313746i | \(-0.898416\pi\) | ||
0.949507 | − | 0.313746i | \(-0.101584\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.24560e6 | + | 2.01545e7i | −0.373525 | + | 1.20536i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 1.65959e7i | − | 0.986163i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −43560.0 | −0.00257184 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.34447e7 | 0.788721 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 1.24115e7i | − | 0.723467i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.18285e7 | − | 1.60489e7i | −0.685104 | − | 0.929549i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 3.45366e7i | − | 1.98766i | −0.110913 | − | 0.993830i | \(-0.535378\pi\) | ||
0.110913 | − | 0.993830i | \(-0.464622\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.24711e7 | −1.85697 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.26947e6 | −0.356279 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 680333.i | 0.0384183i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.21532e6 | + | 3.84384e6i | −0.292660 | + | 0.215698i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 2.09287e7i | − | 1.16707i | −0.812089 | − | 0.583533i | \(-0.801670\pi\) | ||
0.812089 | − | 0.583533i | \(-0.198330\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.27126e6 | 0.402942 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.52847e6 | 0.0841735 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 1.78725e7i | − | 0.978131i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.53994e6 | + | 4.82012e6i | −0.355700 | + | 0.262161i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 3.45533e7i | − | 1.86770i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.48797e7 | 1.33651 | 0.668257 | − | 0.743930i | \(-0.267041\pi\) | ||||
0.668257 | + | 0.743930i | \(0.267041\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.95415e6 | 0.211106 | 0.105553 | − | 0.994414i | \(-0.466339\pi\) | ||||
0.105553 | + | 0.994414i | \(0.466339\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.42285e7i | 1.81619i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.80546e6 | − | 6.52005e6i | −0.253420 | − | 0.343841i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 91936.8i | 0.00481875i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.09058e6 | −0.0568132 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.43550e6 | −0.177882 | −0.0889410 | − | 0.996037i | \(-0.528348\pi\) | ||||
−0.0889410 | + | 0.996037i | \(0.528348\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.94833e6i | 0.203195i | 0.994826 | + | 0.101598i | \(0.0323954\pi\) | ||||
−0.994826 | + | 0.101598i | \(0.967605\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.49688e7 | − | 4.63863e6i | −0.765688 | − | 0.237277i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.38176e7i | 1.71941i | 0.510791 | + | 0.859705i | \(0.329353\pi\) | ||||
−0.510791 | + | 0.859705i | \(0.670647\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.52015e7 | 0.768244 | 0.384122 | − | 0.923282i | \(-0.374504\pi\) | ||||
0.384122 | + | 0.923282i | \(0.374504\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.53210e7 | −1.27198 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 9.13579e6i | − | 0.456177i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −600380. | − | 814596.i | −0.0297996 | − | 0.0404321i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 1.20927e7i | − | 0.596635i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.89012e7 | −1.41746 | −0.708729 | − | 0.705481i | \(-0.750731\pi\) | ||||
−0.708729 | + | 0.705481i | \(0.750731\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.75138e7 | 1.34140 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.91532e7i | 1.41292i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.60667e7 | + | 1.18416e7i | −0.774077 | + | 0.570516i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 5.82348e6i | − | 0.278917i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.28446e7 | −1.56385 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.40077e7 | 1.60973 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 2.02107e7i | − | 0.951062i | −0.879699 | − | 0.475531i | \(-0.842256\pi\) | ||
0.879699 | − | 0.475531i | \(-0.157744\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.51470e6 | − | 1.11638e6i | 0.0708617 | − | 0.0522270i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.70522e7i | 0.793101i | 0.918013 | + | 0.396550i | \(0.129793\pi\) | ||||
−0.918013 | + | 0.396550i | \(0.870207\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.95505e7 | −0.904015 | −0.452008 | − | 0.892014i | \(-0.649292\pi\) | ||||
−0.452008 | + | 0.892014i | \(0.649292\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 235224. | 0.0108137 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 2.70896e7i | − | 1.23816i | −0.785330 | − | 0.619078i | \(-0.787507\pi\) | ||
0.785330 | − | 0.619078i | \(-0.212493\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.63368e7 | + | 2.21657e7i | 0.742379 | + | 1.00726i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.87844e7i | 0.848692i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.30838e7 | 0.587741 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.21057e6 | 0.232723 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.54912e7i | 0.687940i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9.85050e6 | + | 3.42524e6i | −0.434949 | + | 0.151242i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.98285e6i | 0.0870545i | 0.999052 | + | 0.0435272i | \(0.0138595\pi\) | ||||
−0.999052 | + | 0.0435272i | \(0.986140\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4.75150e7 | −2.07424 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.22840e7 | −1.83542 | −0.917712 | − | 0.397247i | \(-0.869966\pi\) | ||||
−0.917712 | + | 0.397247i | \(0.869966\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 134502.i | − | 0.00580535i | −0.999996 | − | 0.00290267i | \(-0.999076\pi\) | ||
0.999996 | − | 0.00290267i | \(-0.000923951\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.62756e7 | − | 2.20828e7i | −0.698520 | − | 0.947753i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 3.87668e6i | − | 0.165444i | −0.996573 | − | 0.0827219i | \(-0.973639\pi\) | ||
0.996573 | − | 0.0827219i | \(-0.0263613\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.20700e6 | −0.220970 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.83504e7 | 0.774374 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.31885e6i | 0.0973070i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.99989e7 | − | 1.47397e7i | 0.834543 | − | 0.615081i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 5.78414e6i | − | 0.240026i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.67914e7 | 1.93093 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.01773e6 | −0.164880 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 496459.i | − | 0.0202611i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −7.06059e6 | + | 5.20385e6i | −0.286563 | + | 0.211205i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.87363e7i | 1.15988i | 0.814660 | + | 0.579939i | \(0.196924\pi\) | ||||
−0.814660 | + | 0.579939i | \(0.803076\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.66920e7 | 0.670037 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.87675e6 | −0.0749223 | −0.0374611 | − | 0.999298i | \(-0.511927\pi\) | ||||
−0.0374611 | + | 0.999298i | \(0.511927\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 1.55841e7i | − | 0.618736i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.76068e6 | + | 5.10249e6i | 0.148496 | + | 0.201479i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 1.15131e7i | − | 0.452137i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.76852e6 | 0.264366 | 0.132183 | − | 0.991225i | \(-0.457801\pi\) | ||||
0.132183 | + | 0.991225i | \(0.457801\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.84722e7 | 0.717579 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.37015e6i | 0.246119i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.16988e7 | + | 1.29219e7i | 1.60239 | + | 0.496560i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.08055e7i | 0.412996i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.15356e7 | 0.438530 | 0.219265 | − | 0.975665i | \(-0.429634\pi\) | ||||
0.219265 | + | 0.975665i | \(0.429634\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.91346e6 | 0.110163 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 1.13061e7i | − | 0.425214i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.76576e6 | − | 7.82299e6i | −0.215689 | − | 0.292647i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.92632e7i | 1.46096i | 0.682936 | + | 0.730478i | \(0.260703\pi\) | ||||
−0.682936 | + | 0.730478i | \(0.739297\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.42762e7 | 1.26861 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.94919e7 | 1.08575 | 0.542874 | − | 0.839814i | \(-0.317336\pi\) | ||||
0.542874 | + | 0.839814i | \(0.317336\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 482012.i | 0.0176514i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.81140e6 | − | 3.54614e6i | 0.175264 | − | 0.129174i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 2.09628e7i | − | 0.759581i | −0.925072 | − | 0.379791i | \(-0.875996\pi\) | ||
0.925072 | − | 0.379791i | \(-0.124004\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.46806e6 | 0.305224 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.61967e6 | −0.0939281 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1.64122e7i | − | 0.585375i | −0.956208 | − | 0.292687i | \(-0.905451\pi\) | ||
0.956208 | − | 0.292687i | \(-0.0945495\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.49558e7 | − | 1.10229e7i | 0.530643 | − | 0.391099i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.47521e7i | 1.22660i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8.57102e6 | 0.300944 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.69604e7 | 0.592416 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.48590e7i | 0.516325i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.60726e7 | − | 3.53754e7i | −0.901295 | − | 1.22288i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.71911e7i | 1.62291i | 0.584416 | + | 0.811454i | \(0.301324\pi\) | ||||
−0.584416 | + | 0.811454i | \(0.698676\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.02016e6 | 0.103329 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.84771e7 | −1.30965 | −0.654823 | − | 0.755783i | \(-0.727257\pi\) | ||||
−0.654823 | + | 0.755783i | \(0.727257\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.90047e7i | 0.643544i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.19780e6 | − | 7.09227e6i | 0.0740417 | − | 0.238932i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.70184e7i | 0.905572i | 0.891619 | + | 0.452786i | \(0.149570\pi\) | ||||
−0.891619 | + | 0.452786i | \(0.850430\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.51748e6 | 0.0839478 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.21453e6 | 0.106646 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 2.88475e7i | − | 0.952192i | −0.879393 | − | 0.476096i | \(-0.842051\pi\) | ||
0.879393 | − | 0.476096i | \(-0.157949\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.97692e6 | − | 2.68229e6i | −0.0649230 | − | 0.0880876i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 1.25218e7i | − | 0.409142i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.01732e6 | 0.0330726 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.21596e7 | 1.68714 | 0.843569 | − | 0.537021i | \(-0.180450\pi\) | ||||
0.843569 | + | 0.537021i | \(0.180450\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.14525e7i | 1.01224i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.78110e7 | + | 1.31272e7i | −0.570336 | + | 0.420353i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 9.78148e6i | − | 0.311650i | −0.987785 | − | 0.155825i | \(-0.950196\pi\) | ||
0.987785 | − | 0.155825i | \(-0.0498036\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.50193e7 | −0.793161 |
(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 | 80.6.c.a.49.2 | 2 | ||
3.2 | odd | 2 | 720.6.f.f.289.1 | 2 | |||
4.3 | odd | 2 | 5.6.b.a.4.2 | yes | 2 | ||
5.2 | odd | 4 | 400.6.a.t.1.2 | 2 | |||
5.3 | odd | 4 | 400.6.a.t.1.1 | 2 | |||
5.4 | even | 2 | inner | 80.6.c.a.49.1 | 2 | ||
8.3 | odd | 2 | 320.6.c.f.129.2 | 2 | |||
8.5 | even | 2 | 320.6.c.g.129.1 | 2 | |||
12.11 | even | 2 | 45.6.b.b.19.1 | 2 | |||
15.14 | odd | 2 | 720.6.f.f.289.2 | 2 | |||
20.3 | even | 4 | 25.6.a.c.1.2 | 2 | |||
20.7 | even | 4 | 25.6.a.c.1.1 | 2 | |||
20.19 | odd | 2 | 5.6.b.a.4.1 | ✓ | 2 | ||
28.27 | even | 2 | 245.6.b.a.99.2 | 2 | |||
40.19 | odd | 2 | 320.6.c.f.129.1 | 2 | |||
40.29 | even | 2 | 320.6.c.g.129.2 | 2 | |||
60.23 | odd | 4 | 225.6.a.n.1.1 | 2 | |||
60.47 | odd | 4 | 225.6.a.n.1.2 | 2 | |||
60.59 | even | 2 | 45.6.b.b.19.2 | 2 | |||
140.139 | even | 2 | 245.6.b.a.99.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.6.b.a.4.1 | ✓ | 2 | 20.19 | odd | 2 | ||
5.6.b.a.4.2 | yes | 2 | 4.3 | odd | 2 | ||
25.6.a.c.1.1 | 2 | 20.7 | even | 4 | |||
25.6.a.c.1.2 | 2 | 20.3 | even | 4 | |||
45.6.b.b.19.1 | 2 | 12.11 | even | 2 | |||
45.6.b.b.19.2 | 2 | 60.59 | even | 2 | |||
80.6.c.a.49.1 | 2 | 5.4 | even | 2 | inner | ||
80.6.c.a.49.2 | 2 | 1.1 | even | 1 | trivial | ||
225.6.a.n.1.1 | 2 | 60.23 | odd | 4 | |||
225.6.a.n.1.2 | 2 | 60.47 | odd | 4 | |||
245.6.b.a.99.1 | 2 | 140.139 | even | 2 | |||
245.6.b.a.99.2 | 2 | 28.27 | even | 2 | |||
320.6.c.f.129.1 | 2 | 40.19 | odd | 2 | |||
320.6.c.f.129.2 | 2 | 8.3 | odd | 2 | |||
320.6.c.g.129.1 | 2 | 8.5 | even | 2 | |||
320.6.c.g.129.2 | 2 | 40.29 | even | 2 | |||
400.6.a.t.1.1 | 2 | 5.3 | odd | 4 | |||
400.6.a.t.1.2 | 2 | 5.2 | odd | 4 | |||
720.6.f.f.289.1 | 2 | 3.2 | odd | 2 | |||
720.6.f.f.289.2 | 2 | 15.14 | odd | 2 |