Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [324,6,Mod(109,324)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(324, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("324.109");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 324 = 2^{2} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 324.e (of order \(3\), 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: | \(51.9643576194\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{5} \) |
Twist minimal: | no (minimal twist has level 108) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 217.2 | ||
Root | \(-1.22474 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 324.217 |
Dual form | 324.6.e.e.109.2 |
$q$-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 \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).
\(n\) | \(163\) | \(245\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 44.0908 | + | 76.3675i | 0.788720 | + | 1.36610i | 0.926751 | + | 0.375676i | \(0.122589\pi\) |
−0.138031 | + | 0.990428i | \(0.544077\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −14.5000 | + | 25.1147i | −0.111847 | + | 0.193724i | −0.916515 | − | 0.400001i | \(-0.869010\pi\) |
0.804668 | + | 0.593725i | \(0.202343\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 44.0908 | − | 76.3675i | 0.109867 | − | 0.190295i | −0.805849 | − | 0.592121i | \(-0.798291\pi\) |
0.915716 | + | 0.401826i | \(0.131624\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −164.500 | − | 284.922i | −0.269965 | − | 0.467593i | 0.698887 | − | 0.715232i | \(-0.253679\pi\) |
−0.968853 | + | 0.247638i | \(0.920345\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2204.54 | 1.85010 | 0.925051 | − | 0.379842i | \(-0.124022\pi\) | ||||
0.925051 | + | 0.379842i | \(0.124022\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1799.00 | 1.14327 | 0.571633 | − | 0.820510i | \(-0.306310\pi\) | ||||
0.571633 | + | 0.820510i | \(0.306310\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1807.72 | + | 3131.07i | 0.712545 | + | 1.23416i | 0.963899 | + | 0.266269i | \(0.0857910\pi\) |
−0.251354 | + | 0.967895i | \(0.580876\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2325.50 | + | 4027.88i | −0.744160 | + | 1.28892i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 705.453 | − | 1221.88i | 0.155766 | − | 0.269795i | −0.777572 | − | 0.628794i | \(-0.783549\pi\) |
0.933338 | + | 0.359000i | \(0.116882\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2614.00 | − | 4527.58i | −0.488541 | − | 0.846178i | 0.511372 | − | 0.859360i | \(-0.329138\pi\) |
−0.999913 | + | 0.0131811i | \(0.995804\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2557.27 | −0.352863 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8783.00 | 1.05472 | 0.527362 | − | 0.849641i | \(-0.323181\pi\) | ||||
0.527362 | + | 0.849641i | \(0.323181\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7759.98 | − | 13440.7i | −0.720943 | − | 1.24871i | −0.960622 | − | 0.277858i | \(-0.910375\pi\) |
0.239679 | − | 0.970852i | \(-0.422958\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9988.00 | + | 17299.7i | −0.823773 | + | 1.42682i | 0.0790810 | + | 0.996868i | \(0.474801\pi\) |
−0.902854 | + | 0.429948i | \(0.858532\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5423.17 | + | 9393.21i | −0.358104 | + | 0.620254i | −0.987644 | − | 0.156714i | \(-0.949910\pi\) |
0.629540 | + | 0.776968i | \(0.283243\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7983.00 | + | 13827.0i | 0.474981 | + | 0.822691i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −29452.7 | −1.44024 | −0.720120 | − | 0.693849i | \(-0.755913\pi\) | ||||
−0.720120 | + | 0.693849i | \(0.755913\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7776.00 | 0.346617 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2865.90 | + | 4963.89i | 0.107184 | + | 0.185649i | 0.914629 | − | 0.404295i | \(-0.132483\pi\) |
−0.807444 | + | 0.589944i | \(0.799150\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 534.500 | − | 925.781i | 0.0183918 | − | 0.0318555i | −0.856683 | − | 0.515843i | \(-0.827479\pi\) |
0.875075 | + | 0.483988i | \(0.160812\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 14505.9 | − | 25124.9i | 0.425854 | − | 0.737601i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 31038.5 | + | 53760.3i | 0.844722 | + | 1.46310i | 0.885863 | + | 0.463948i | \(0.153567\pi\) |
−0.0411407 | + | 0.999153i | \(0.513099\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 46383.5 | 1.09199 | 0.545994 | − | 0.837789i | \(-0.316152\pi\) | ||||
0.545994 | + | 0.837789i | \(0.316152\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −48079.0 | −1.05596 | −0.527981 | − | 0.849256i | \(-0.677051\pi\) | ||||
−0.527981 | + | 0.849256i | \(0.677051\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1278.63 | + | 2214.66i | 0.0245765 | + | 0.0425677i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −24989.5 | + | 43283.1i | −0.450495 | + | 0.780280i | −0.998417 | − | 0.0562495i | \(-0.982086\pi\) |
0.547922 | + | 0.836530i | \(0.315419\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −28835.4 | + | 49944.4i | −0.459442 | + | 0.795777i | −0.998931 | − | 0.0462155i | \(-0.985284\pi\) |
0.539490 | + | 0.841992i | \(0.318617\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 97200.0 | + | 168355.i | 1.45921 | + | 2.52743i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 87917.1 | 1.17652 | 0.588259 | − | 0.808673i | \(-0.299814\pi\) | ||||
0.588259 | + | 0.808673i | \(0.299814\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9541.00 | 0.120779 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 79319.4 | + | 137385.i | 0.901717 | + | 1.56182i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6458.50 | + | 11186.5i | −0.0696951 | + | 0.120715i | −0.898767 | − | 0.438426i | \(-0.855536\pi\) |
0.829072 | + | 0.559142i | \(0.188869\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 56436.2 | − | 97750.4i | 0.550497 | − | 0.953488i | −0.447742 | − | 0.894163i | \(-0.647772\pi\) |
0.998239 | − | 0.0593254i | \(-0.0188949\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 38751.5 | + | 67119.6i | 0.359911 | + | 0.623385i | 0.987946 | − | 0.154801i | \(-0.0494736\pi\) |
−0.628034 | + | 0.778186i | \(0.716140\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −111726. | −0.943399 | −0.471699 | − | 0.881759i | \(-0.656359\pi\) | ||||
−0.471699 | + | 0.881759i | \(0.656359\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −17710.0 | −0.142775 | −0.0713875 | − | 0.997449i | \(-0.522743\pi\) | ||||
−0.0713875 | + | 0.997449i | \(0.522743\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −125791. | − | 217877.i | −0.926731 | − | 1.60515i | −0.788753 | − | 0.614710i | \(-0.789273\pi\) |
−0.137978 | − | 0.990435i | \(-0.544060\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −159408. | + | 276103.i | −1.12400 | + | 1.94682i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −31965.8 | + | 55366.5i | −0.206928 | + | 0.358409i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 76637.5 | + | 132740.i | 0.475859 | + | 0.824211i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −134565. | −0.770296 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 269444. | 1.48238 | 0.741189 | − | 0.671296i | \(-0.234262\pi\) | ||||
0.741189 | + | 0.671296i | \(0.234262\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −77070.7 | − | 133490.i | −0.392384 | − | 0.679629i | 0.600379 | − | 0.799715i | \(-0.295016\pi\) |
−0.992763 | + | 0.120086i | \(0.961683\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −26085.5 | + | 45181.4i | −0.127870 | + | 0.221478i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −135932. | + | 235441.i | −0.618757 | + | 1.07172i | 0.370956 | + | 0.928651i | \(0.379030\pi\) |
−0.989713 | + | 0.143068i | \(0.954303\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −91352.5 | − | 158227.i | −0.401036 | − | 0.694615i | 0.592815 | − | 0.805339i | \(-0.298016\pi\) |
−0.993851 | + | 0.110724i | \(0.964683\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −29011.8 | −0.118641 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 124416. | 0.491424 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 173630. | + | 300735.i | 0.640705 | + | 1.10973i | 0.985276 | + | 0.170973i | \(0.0546912\pi\) |
−0.344571 | + | 0.938760i | \(0.611975\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −217176. | + | 376159.i | −0.775119 | + | 1.34255i | 0.159608 | + | 0.987180i | \(0.448977\pi\) |
−0.934727 | + | 0.355365i | \(0.884356\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 230507. | − | 399249.i | 0.770645 | − | 1.33480i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11489.0 | + | 19899.5i | 0.0371992 | + | 0.0644308i | 0.884026 | − | 0.467439i | \(-0.154823\pi\) |
−0.846826 | + | 0.531869i | \(0.821490\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −104848. | −0.318783 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 109961. | 0.324168 | 0.162084 | − | 0.986777i | \(-0.448179\pi\) | ||||
0.162084 | + | 0.986777i | \(0.448179\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −153568. | − | 265988.i | −0.426099 | − | 0.738025i | 0.570423 | − | 0.821351i | \(-0.306779\pi\) |
−0.996522 | + | 0.0833258i | \(0.973446\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 131526. | − | 227810.i | 0.354238 | − | 0.613558i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2116.36 | + | 3665.64i | −0.00537618 | + | 0.00931182i | −0.868701 | − | 0.495337i | \(-0.835045\pi\) |
0.863325 | + | 0.504649i | \(0.168378\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −67439.5 | − | 116809.i | −0.166464 | − | 0.288323i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 831906. | 1.94062 | 0.970312 | − | 0.241856i | \(-0.0777563\pi\) | ||||
0.970312 | + | 0.241856i | \(0.0777563\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −327187. | −0.742334 | −0.371167 | − | 0.928566i | \(-0.621042\pi\) | ||||
−0.371167 | + | 0.928566i | \(0.621042\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 387250. | + | 670736.i | 0.831882 | + | 1.44086i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 97200.0 | − | 168355.i | 0.203265 | − | 0.352065i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −234431. | + | 406046.i | −0.464977 | + | 0.805364i | −0.999200 | − | 0.0399796i | \(-0.987271\pi\) |
0.534224 | + | 0.845343i | \(0.320604\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −76115.5 | − | 131836.i | −0.147089 | − | 0.254765i | 0.783061 | − | 0.621944i | \(-0.213657\pi\) |
−0.930150 | + | 0.367179i | \(0.880324\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 653514. | 1.19975 | 0.599873 | − | 0.800095i | \(-0.295218\pi\) | ||||
0.599873 | + | 0.800095i | \(0.295218\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −645895. | −1.15619 | −0.578095 | − | 0.815969i | \(-0.696204\pi\) | ||||
−0.578095 | + | 0.815969i | \(0.696204\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 20458.1 | + | 35434.5i | 0.0348438 | + | 0.0603513i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 684288. | − | 1.18522e6i | 1.13725 | − | 1.96977i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 79319.4 | − | 137385.i | 0.125607 | − | 0.217558i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −84818.5 | − | 146910.i | −0.131155 | − | 0.227167i | 0.792967 | − | 0.609264i | \(-0.208535\pi\) |
−0.924122 | + | 0.382097i | \(0.875202\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.76152e6 | −2.59891 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 151612. | 0.218567 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −362647. | − | 628123.i | −0.499463 | − | 0.865095i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 345638. | − | 598663.i | 0.465435 | − | 0.806158i | −0.533786 | − | 0.845620i | \(-0.679231\pi\) |
0.999221 | + | 0.0394622i | \(0.0125645\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 494963. | − | 857302.i | 0.637542 | − | 1.10425i | −0.348429 | − | 0.937335i | \(-0.613285\pi\) |
0.985971 | − | 0.166919i | \(-0.0533819\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −176125. | − | 305057.i | −0.221938 | − | 0.384408i | 0.733458 | − | 0.679735i | \(-0.237905\pi\) |
−0.955397 | + | 0.295326i | \(0.904572\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −381297. | −0.460123 | −0.230062 | − | 0.973176i | \(-0.573893\pi\) | ||||
−0.230062 | + | 0.973176i | \(0.573893\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −956448. | −1.12977 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −392849. | − | 680435.i | −0.444868 | − | 0.770534i | 0.553175 | − | 0.833065i | \(-0.313416\pi\) |
−0.998043 | + | 0.0625312i | \(0.980083\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 601312. | − | 1.04150e6i | 0.666894 | − | 1.15509i | −0.311874 | − | 0.950124i | \(-0.600957\pi\) |
0.978768 | − | 0.204971i | \(-0.0657100\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −703954. | + | 1.21928e6i | −0.749254 | + | 1.29775i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −295936. | − | 512575.i | −0.308642 | − | 0.534583i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 416570. | 0.417353 | 0.208677 | − | 0.977985i | \(-0.433084\pi\) | ||||
0.208677 | + | 0.977985i | \(0.433084\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 318816. | 0.313140 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −22486.3 | − | 38947.4i | −0.0212366 | − | 0.0367829i | 0.855212 | − | 0.518279i | \(-0.173427\pi\) |
−0.876448 | + | 0.481496i | \(0.840094\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −127353. | + | 220583.i | −0.117967 | + | 0.204325i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −257579. | + | 446139.i | −0.229626 | + | 0.397723i | −0.957697 | − | 0.287778i | \(-0.907084\pi\) |
0.728072 | + | 0.685501i | \(0.240417\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.29859e6 | − | 2.24923e6i | −1.13595 | − | 1.96752i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −197439. | −0.166361 | −0.0831805 | − | 0.996534i | \(-0.526508\pi\) | ||||
−0.0831805 | + | 0.996534i | \(0.526508\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.01499e6 | −0.839530 | −0.419765 | − | 0.907633i | \(-0.637888\pi\) | ||||
−0.419765 | + | 0.907633i | \(0.637888\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 205066. | + | 355185.i | 0.163517 | + | 0.283220i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 189659. | − | 328499.i | 0.148516 | − | 0.257238i | −0.782163 | − | 0.623074i | \(-0.785884\pi\) |
0.930679 | + | 0.365836i | \(0.119217\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 477944. | − | 827824.i | 0.361087 | − | 0.625421i | −0.627053 | − | 0.778976i | \(-0.715739\pi\) |
0.988140 | + | 0.153556i | \(0.0490725\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −331456. | − | 574099.i | −0.246014 | − | 0.426109i | 0.716402 | − | 0.697688i | \(-0.245788\pi\) |
−0.962416 | + | 0.271579i | \(0.912454\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 450079. | 0.322540 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.44014e6 | 2.42288 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 223761. | + | 387565.i | 0.152270 | + | 0.263740i | 0.932062 | − | 0.362300i | \(-0.118008\pi\) |
−0.779791 | + | 0.626039i | \(0.784675\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −252720. | + | 437724.i | −0.169077 | + | 0.292850i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 594741. | − | 1.03012e6i | 0.384725 | − | 0.666362i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −289652. | − | 501692.i | −0.184272 | − | 0.319169i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 94266.2 | 0.0580238 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.17362e6 | −0.710690 | −0.355345 | − | 0.934735i | \(-0.615637\pi\) | ||||
−0.355345 | + | 0.934735i | \(0.615637\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.20610e6 | + | 2.08903e6i | 0.707105 | + | 1.22474i | 0.965926 | + | 0.258817i | \(0.0833325\pi\) |
−0.258822 | + | 0.965925i | \(0.583334\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −864834. | + | 1.49794e6i | −0.498967 | + | 0.864236i | −0.999999 | − | 0.00119261i | \(-0.999620\pi\) |
0.501032 | + | 0.865428i | \(0.332954\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 587378. | − | 1.01737e6i | 0.328299 | − | 0.568630i | −0.653876 | − | 0.756602i | \(-0.726858\pi\) |
0.982174 | + | 0.187972i | \(0.0601913\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −62208.0 | − | 107747.i | −0.0342271 | − | 0.0592830i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.96597e6 | 2.11516 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.53018e6 | 0.803589 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −157272. | − | 272403.i | −0.0801053 | − | 0.138747i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −225500. | + | 390578.i | −0.113130 | + | 0.195947i | −0.917031 | − | 0.398817i | \(-0.869421\pi\) |
0.803901 | + | 0.594763i | \(0.202754\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.73703e6 | + | 4.74067e6i | −1.33250 | + | 2.30796i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.08969e6 | − | 1.88739e6i | −0.522669 | − | 0.905289i | −0.999652 | − | 0.0263769i | \(-0.991603\pi\) |
0.476983 | − | 0.878913i | \(-0.341730\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −461014. | −0.214698 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −950417. | −0.436193 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −190737. | − | 330366.i | −0.0850376 | − | 0.147289i | 0.820370 | − | 0.571834i | \(-0.193768\pi\) |
−0.905407 | + | 0.424544i | \(0.860434\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.14798e6 | − | 1.98836e6i | 0.504511 | − | 0.873839i | −0.495475 | − | 0.868622i | \(-0.665006\pi\) |
0.999986 | − | 0.00521712i | \(-0.00166067\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.62051e6 | − | 2.80681e6i | 0.692175 | − | 1.19888i | −0.278949 | − | 0.960306i | \(-0.589986\pi\) |
0.971124 | − | 0.238576i | \(-0.0766808\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.04509e6 | + | 3.54220e6i | 0.861274 | + | 1.49177i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.15044e6 | −1.69965 | −0.849823 | − | 0.527068i | \(-0.823291\pi\) | ||||
−0.849823 | + | 0.527068i | \(0.823291\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 760302. | 0.307056 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.11984e6 | − | 3.67167e6i | −0.832859 | − | 1.44255i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.69956e6 | + | 2.94372e6i | −0.658674 | + | 1.14086i | 0.322285 | + | 0.946643i | \(0.395549\pi\) |
−0.980959 | + | 0.194214i | \(0.937784\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 427064. | − | 739696.i | 0.161086 | − | 0.279009i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.57247e6 | + | 2.72360e6i | 0.585207 | + | 1.01361i | 0.994850 | + | 0.101363i | \(0.0323203\pi\) |
−0.409642 | + | 0.912246i | \(0.634346\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −464188. | −0.168206 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.76635e6 | −0.989257 | −0.494628 | − | 0.869105i | \(-0.664696\pi\) | ||||
−0.494628 | + | 0.869105i | \(0.664696\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.12449e6 | + | 1.94768e6i | 0.391705 | + | 0.678454i | 0.992675 | − | 0.120819i | \(-0.0385519\pi\) |
−0.600969 | + | 0.799272i | \(0.705219\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −112752. | + | 195292.i | −0.0387679 | + | 0.0671480i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 277993. | − | 481497.i | 0.0931449 | − | 0.161332i | −0.815688 | − | 0.578492i | \(-0.803641\pi\) |
0.908833 | + | 0.417160i | \(0.136975\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.98520e6 | + | 6.90257e6i | 1.31828 | + | 2.28333i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.40723e6 | −1.42126 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 836174. | 0.266269 | 0.133134 | − | 0.991098i | \(-0.457496\pi\) | ||||
0.133134 | + | 0.991098i | \(0.457496\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.00642e6 | − | 1.74317e6i | −0.312548 | − | 0.541349i | 0.666365 | − | 0.745626i | \(-0.267849\pi\) |
−0.978913 | + | 0.204276i | \(0.934516\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −860006. | + | 1.48957e6i | −0.263778 | + | 0.456877i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 387250. | − | 670736.i | 0.115879 | − | 0.200708i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 686356. | + | 1.18880e6i | 0.202881 | + | 0.351400i | 0.949455 | − | 0.313902i | \(-0.101636\pi\) |
−0.746575 | + | 0.665302i | \(0.768303\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −166222. | −0.0479528 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.08550e6 | −1.44949 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.77152e6 | − | 3.06837e6i | −0.492961 | − | 0.853833i | 0.507007 | − | 0.861942i | \(-0.330752\pi\) |
−0.999967 | + | 0.00810943i | \(0.997419\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.74442e6 | − | 3.02142e6i | 0.479673 | − | 0.830819i | −0.520055 | − | 0.854133i | \(-0.674088\pi\) |
0.999728 | + | 0.0233141i | \(0.00742179\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.12666e6 | + | 8.87963e6i | −1.37677 | + | 2.38464i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 15500.5 | + | 26847.7i | 0.00411411 | + | 0.00712585i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.43754e6 | 1.40997 | 0.704985 | − | 0.709223i | \(-0.250954\pi\) | ||||
0.704985 | + | 0.709223i | \(0.250954\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.96023e6 | 1.27140 | 0.635699 | − | 0.771937i | \(-0.280712\pi\) | ||||
0.635699 | + | 0.771937i | \(0.280712\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.25209e6 | + | 5.63279e6i | 0.814628 | + | 1.41098i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.87535e6 | + | 4.98026e6i | −0.712082 | + | 1.23336i | 0.251992 | + | 0.967729i | \(0.418914\pi\) |
−0.964074 | + | 0.265633i | \(0.914419\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.81555e6 | − | 4.87668e6i | 0.681639 | − | 1.18063i | −0.292842 | − | 0.956161i | \(-0.594601\pi\) |
0.974481 | − | 0.224472i | \(-0.0720656\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.87634e6 | + | 6.71401e6i | 0.927943 | + | 1.60724i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.45310e6 | 0.808340 | 0.404170 | − | 0.914684i | \(-0.367560\pi\) | ||||
0.404170 | + | 0.914684i | \(0.367560\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.36858e6 | −0.316831 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 420670. | + | 728623.i | 0.0952606 | + | 0.164996i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −983995. | + | 1.70433e6i | −0.220395 | + | 0.381736i | −0.954928 | − | 0.296837i | \(-0.904068\pi\) |
0.734533 | + | 0.678573i | \(0.237401\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.31664e6 | − | 5.74459e6i | 0.726853 | − | 1.25895i | −0.231354 | − | 0.972870i | \(-0.574316\pi\) |
0.958207 | − | 0.286076i | \(-0.0923511\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 812842. | + | 1.40788e6i | 0.176219 | + | 0.305221i | 0.940583 | − | 0.339565i | \(-0.110280\pi\) |
−0.764363 | + | 0.644786i | \(0.776947\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.48346e6 | 0.526944 | 0.263472 | − | 0.964667i | \(-0.415132\pi\) | ||||
0.263472 | + | 0.964667i | \(0.415132\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.80023e6 | −0.377917 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 880758. | + | 1.52552e6i | 0.181011 | + | 0.313519i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.18357e6 | + | 7.24616e6i | −0.850773 | + | 1.47358i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 798132. | − | 1.38241e6i | 0.158941 | − | 0.275294i | −0.775546 | − | 0.631291i | \(-0.782525\pi\) |
0.934487 | + | 0.355997i | \(0.115859\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.44480e6 | − | 2.50247e6i | −0.284738 | − | 0.493181i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.13904e6 | −0.219880 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.95245e6 | 1.51942 | 0.759712 | − | 0.650260i | \(-0.225340\pi\) | ||||
0.759712 | + | 0.650260i | \(0.225340\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.02798e6 | + | 1.78051e6i | 0.192433 | + | 0.333304i | 0.946056 | − | 0.324003i | \(-0.105029\pi\) |
−0.753623 | + | 0.657307i | \(0.771695\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.55520e6 | − | 2.69369e6i | 0.288183 | − | 0.499148i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −672561. | + | 1.16491e6i | −0.122135 | + | 0.211544i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.46770e6 | − | 4.27417e6i | −0.443650 | − | 0.768424i | 0.554307 | − | 0.832312i | \(-0.312983\pi\) |
−0.997957 | + | 0.0638881i | \(0.979650\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −836755. | −0.147461 | −0.0737307 | − | 0.997278i | \(-0.523491\pi\) | ||||
−0.0737307 | + | 0.997278i | \(0.523491\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.95328e6 | 1.73675 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.95078e6 | + | 5.11090e6i | 0.504826 | + | 0.874385i | 0.999984 | + | 0.00558204i | \(0.00177683\pi\) |
−0.495158 | + | 0.868803i | \(0.664890\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 697146. | − | 1.20749e6i | 0.118106 | − | 0.204565i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.41717e6 | + | 5.91871e6i | −0.567739 | + | 0.983352i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 478224. | + | 828308.i | 0.0786874 | + | 0.136291i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 163577. | 0.0264014 | 0.0132007 | − | 0.999913i | \(-0.495798\pi\) | ||||
0.0132007 | + | 0.999913i | \(0.495798\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.95232e6 | −0.471965 | −0.235983 | − | 0.971757i | \(-0.575831\pi\) | ||||
−0.235983 | + | 0.971757i | \(0.575831\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5.76267e6 | − | 9.98124e6i | −0.903852 | − | 1.56552i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.31756e6 | + | 5.74618e6i | −0.515441 | + | 0.892770i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.55303e6 | + | 4.42199e6i | −0.389259 | + | 0.674216i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.92610e6 | − | 8.53225e6i | −0.744078 | − | 1.28878i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.40791e6 | 0.208738 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.58390e6 | −1.40783 | −0.703913 | − | 0.710286i | \(-0.748566\pi\) | ||||
−0.703913 | + | 0.710286i | \(0.748566\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −780848. | − | 1.35247e6i | −0.112610 | − | 0.195046i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.08907e6 | + | 1.05466e7i | −0.870127 | + | 1.50710i | −0.00826306 | + | 0.999966i | \(0.502630\pi\) |
−0.861864 | + | 0.507139i | \(0.830703\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.26911e6 | − | 2.19816e6i | 0.178082 | − | 0.308447i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −724695. | − | 1.25521e6i | −0.100773 | − | 0.174543i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5.32679e6 | −0.727491 | −0.363745 | − | 0.931498i | \(-0.618502\pi\) | ||||
−0.363745 | + | 0.931498i | \(0.618502\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.57210e6 | 0.889559 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.11949e6 | − | 7.13517e6i | −0.547738 | − | 0.948710i | −0.998429 | − | 0.0560299i | \(-0.982156\pi\) |
0.450691 | − | 0.892680i | \(-0.351178\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.10925e7 | − | 1.92127e7i | 1.46186 | − | 2.53202i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.71205e6 | − | 6.42946e6i | 0.480655 | − | 0.832518i | −0.519099 | − | 0.854714i | \(-0.673732\pi\) |
0.999754 | + | 0.0221959i | \(0.00706575\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 144276. | + | 249894.i | 0.0185185 | + | 0.0320749i | 0.875136 | − | 0.483877i | \(-0.160772\pi\) |
−0.856618 | + | 0.515952i | \(0.827438\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.68154e7 | −2.12099 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 933299. | 0.116703 | 0.0583514 | − | 0.998296i | \(-0.481416\pi\) | ||||
0.0583514 | + | 0.998296i | \(0.481416\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −836226. | − | 1.44839e6i | −0.102774 | − | 0.178010i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.29859e6 | + | 2.24923e6i | −0.158235 | + | 0.274070i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.07712e6 | − | 7.06178e6i | 0.488381 | − | 0.845900i | −0.511530 | − | 0.859265i | \(-0.670921\pi\) |
0.999911 | + | 0.0133653i | \(0.00425444\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.70259e6 | − | 8.14512e6i | −0.558533 | − | 0.967407i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.18214e6 | −0.254828 | −0.127414 | − | 0.991850i | \(-0.540668\pi\) | ||||
−0.127414 | + | 0.991850i | \(0.540668\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.63760e6 | −0.652833 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.42995e6 | + | 2.47675e6i | 0.162838 | + | 0.282043i | 0.935885 | − | 0.352305i | \(-0.114602\pi\) |
−0.773048 | + | 0.634348i | \(0.781269\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.63064e6 | − | 1.32167e7i | 0.861737 | − | 1.49257i | −0.00851319 | − | 0.999964i | \(-0.502710\pi\) |
0.870251 | − | 0.492609i | \(-0.163957\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6.75802e6 | + | 1.17052e7i | −0.750639 | + | 1.30014i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.18678e6 | − | 2.05556e6i | −0.130737 | − | 0.226443i | 0.793224 | − | 0.608930i | \(-0.208401\pi\) |
−0.923961 | + | 0.382487i | \(0.875068\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.56845e6 | 0.386702 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.21002e6 | −0.452515 | −0.226258 | − | 0.974068i | \(-0.572649\pi\) | ||||
−0.226258 | + | 0.974068i | \(0.572649\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.59790e6 | + | 2.76764e6i | 0.168980 | + | 0.292682i | 0.938062 | − | 0.346469i | \(-0.112619\pi\) |
−0.769081 | + | 0.639151i | \(0.779286\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.51032e6 | − | 1.12762e7i | 0.682930 | − | 1.18287i | −0.291153 | − | 0.956677i | \(-0.594039\pi\) |
0.974083 | − | 0.226192i | \(-0.0726278\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.27480e6 | + | 2.20801e6i | −0.131589 | + | 0.227920i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.33410e6 | + | 2.31073e6i | 0.136612 | + | 0.236619i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.93625e7 | 1.95135 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.44185e7 | −1.44161 | −0.720803 | − | 0.693140i | \(-0.756227\pi\) | ||||
−0.720803 | + | 0.693140i | \(0.756227\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.18800e7 | + | 2.05768e7i | 1.16918 | + | 2.02508i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.62641e6 | − | 4.54907e6i | 0.256456 | − | 0.444195i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.70411e6 | − | 2.95161e6i | 0.163815 | − | 0.283735i | −0.772419 | − | 0.635113i | \(-0.780953\pi\) |
0.936234 | + | 0.351378i | \(0.114287\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.15083e6 | − | 1.23856e7i | −0.682070 | − | 1.18138i | −0.974348 | − | 0.225046i | \(-0.927747\pi\) |
0.292278 | − | 0.956333i | \(-0.405587\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.59891e7 | 1.50163 | 0.750815 | − | 0.660512i | \(-0.229661\pi\) | ||||
0.750815 | + | 0.660512i | \(0.229661\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 505440. | 0.0471040 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9.15158e6 | − | 1.58510e7i | −0.839872 | − | 1.45470i | −0.890001 | − | 0.455958i | \(-0.849297\pi\) |
0.0501295 | − | 0.998743i | \(-0.484037\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.79622e6 | − | 1.17714e7i | 0.618963 | − | 1.07207i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.41362e6 | + | 4.18051e6i | −0.216499 | + | 0.374987i | −0.953735 | − | 0.300648i | \(-0.902797\pi\) |
0.737236 | + | 0.675635i | \(0.236130\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.25635e6 | + | 1.25684e7i | 0.645973 | + | 1.11886i | 0.984076 | + | 0.177749i | \(0.0568815\pi\) |
−0.338103 | + | 0.941109i | \(0.609785\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.60052e6 | −0.403416 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.10106e6 | 0.443962 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −47133.1 | − | 81636.9i | −0.00404129 | − | 0.00699971i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.61637e6 | − | 4.53168e6i | 0.222670 | − | 0.385675i | −0.732948 | − | 0.680285i | \(-0.761856\pi\) |
0.955618 | + | 0.294609i | \(0.0951896\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.65945e6 | − | 2.87424e6i | 0.139153 | − | 0.241019i | −0.788023 | − | 0.615645i | \(-0.788895\pi\) |
0.927176 | + | 0.374626i | \(0.122229\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −187296. | − | 324407.i | −0.0155903 | − | 0.0270032i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −350257. | −0.0287300 | −0.0143650 | − | 0.999897i | \(-0.504573\pi\) | ||||
−0.0143650 | + | 0.999897i | \(0.504573\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.39734e7 | −1.95211 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.84496e6 | + | 8.39172e6i | 0.388814 | + | 0.673446i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.81372e6 | − | 8.33761e6i | 0.383518 | − | 0.664273i | −0.608044 | − | 0.793903i | \(-0.708046\pi\) |
0.991562 | + | 0.129630i | \(0.0413790\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.05561e6 | − | 1.39527e7i | 0.632611 | − | 1.09571i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.71072e7 | − | 2.96305e7i | −1.33382 | − | 2.31024i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.75325e7 | −1.34756 | −0.673782 | − | 0.738930i | \(-0.735332\pi\) | ||||
−0.673782 | + | 0.738930i | \(0.735332\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.58006e7 | 1.20583 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.63665e6 | + | 2.83476e6i | 0.123142 | + | 0.213289i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.66079e6 | + | 4.60863e6i | −0.198790 | + | 0.344315i | −0.948136 | − | 0.317863i | \(-0.897035\pi\) |
0.749346 | + | 0.662179i | \(0.230368\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.45078e6 | − | 1.63692e7i | 0.696216 | − | 1.20588i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.27915e6 | − | 2.21556e6i | −0.0935744 | − | 0.162076i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.74700e7 | 1.26029 | 0.630146 | − | 0.776477i | \(-0.282995\pi\) | ||||
0.630146 | + | 0.776477i | \(0.282995\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.24759e6 | −0.161019 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.28106e6 | + | 5.68297e6i | 0.231830 | + | 0.401541i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.93487e6 | − | 5.08334e6i | 0.205945 | − | 0.356708i | −0.744488 | − | 0.667636i | \(-0.767306\pi\) |
0.950434 | + | 0.310928i | \(0.100640\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.20190e7 | + | 3.81379e7i | −1.52406 | + | 2.63976i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.80147e6 | + | 4.85229e6i | 0.192587 | + | 0.333570i | 0.946107 | − | 0.323855i | \(-0.104979\pi\) |
−0.753520 | + | 0.657425i | \(0.771646\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.47405e6 | 0.371227 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.56792e6 | −0.375044 | −0.187522 | − | 0.982260i | \(-0.560046\pi\) | ||||
−0.187522 | + | 0.982260i | \(0.560046\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.89242e6 | + | 3.27777e6i | 0.125761 | + | 0.217824i | 0.922030 | − | 0.387118i | \(-0.126529\pi\) |
−0.796269 | + | 0.604942i | \(0.793196\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.53109e7 | + | 2.65193e7i | −1.01067 | + | 1.75054i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.62003e6 | − | 2.80597e6i | 0.105516 | − | 0.182759i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.38329e6 | + | 5.86002e6i | 0.218897 | + | 0.379140i | 0.954471 | − | 0.298304i | \(-0.0964209\pi\) |
−0.735574 | + | 0.677444i | \(0.763088\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.83018e7 | −2.44541 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.46970e7 | 1.56640 | 0.783202 | − | 0.621768i | \(-0.213585\pi\) | ||||
0.783202 | + | 0.621768i | \(0.213585\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.50435e7 | − | 2.60561e7i | −0.941644 | − | 1.63097i | −0.762336 | − | 0.647182i | \(-0.775947\pi\) |
−0.179308 | − | 0.983793i | \(-0.557386\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 256795. | − | 444782.i | 0.0159689 | − | 0.0276590i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 942882. | − | 1.63312e6i | 0.0578721 | − | 0.100237i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.62559e6 | − | 2.81561e6i | −0.0991278 | − | 0.171694i | 0.812196 | − | 0.583385i | \(-0.198272\pi\) |
−0.911324 | + | 0.411690i | \(0.864939\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.30628e6 | 0.199017 | 0.0995087 | − | 0.995037i | \(-0.468273\pi\) | ||||
0.0995087 | + | 0.995037i | \(0.468273\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.43154e7 | 1.45421 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.39602e7 | − | 2.41798e7i | −0.824230 | − | 1.42761i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.04509e6 | − | 3.54220e6i | 0.119973 | − | 0.207800i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.01312e6 | + | 1.75477e6i | −0.0586795 | + | 0.101636i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.50778e6 | − | 1.47359e7i | −0.489643 | − | 0.848087i | 0.510286 | − | 0.860005i | \(-0.329540\pi\) |
−0.999929 | + | 0.0119182i | \(0.996206\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.29588e6 | 0.414607 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −351701. | −0.0198605 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6.56336e6 | − | 1.13681e7i | −0.365999 | − | 0.633930i | 0.622937 | − | 0.782272i | \(-0.285939\pi\) |
−0.988936 | + | 0.148343i | \(0.952606\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.19556e7 | + | 2.07077e7i | −0.662528 | + | 1.14753i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.11984e6 | + | 3.67167e6i | −0.116015 | + | 0.200944i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.62283e6 | − | 8.00698e6i | −0.251431 | − | 0.435491i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.90313e7 | −1.55954 | −0.779768 | − | 0.626068i | \(-0.784663\pi\) | ||||
−0.779768 | + | 0.626068i | \(0.784663\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.70345e7 | −1.44333 | −0.721666 | − | 0.692241i | \(-0.756623\pi\) | ||||
−0.721666 | + | 0.692241i | \(0.756623\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.84827e6 | + | 8.39745e6i | 0.255678 | + | 0.442847i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.79684e7 | + | 3.11222e7i | −0.941791 | + | 1.63123i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.07418e7 | − | 1.86053e7i | 0.556185 | − | 0.963341i | −0.441625 | − | 0.897200i | \(-0.645598\pi\) |
0.997810 | − | 0.0661410i | \(-0.0210687\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.23141e7 | + | 2.13286e7i | 0.633727 | + | 1.09765i | 0.986783 | + | 0.162045i | \(0.0518091\pi\) |
−0.353056 | + | 0.935602i | \(0.614858\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −5.10933e6 | −0.259777 | −0.129888 | − | 0.991529i | \(-0.541462\pi\) | ||||
−0.129888 | + | 0.991529i | \(0.541462\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.04805e7 | 1.54041 | 0.770205 | − | 0.637797i | \(-0.220154\pi\) | ||||
0.770205 | + | 0.637797i | \(0.220154\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.75988e7 | + | 3.04821e7i | 0.878763 | + | 1.52206i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.35419e7 | − | 2.34553e7i | 0.672146 | − | 1.16419i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.84034e6 | − | 1.18478e7i | 0.335485 | − | 0.581076i | −0.648093 | − | 0.761561i | \(-0.724433\pi\) |
0.983578 | + | 0.180485i | \(0.0577666\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.26025e6 | + | 1.60392e7i | 0.451474 | + | 0.781976i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.31964e7 | 1.11758 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.44498e6 | −0.212893 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.58772e7 | + | 2.75002e7i | 0.751538 | + | 1.30170i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.72040e7 | + | 2.97981e7i | −0.809572 | + | 1.40222i | 0.103588 | + | 0.994620i | \(0.466968\pi\) |
−0.913160 | + | 0.407600i | \(0.866366\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.36778e7 | + | 2.36906e7i | −0.636155 | + | 1.10185i | 0.350114 | + | 0.936707i | \(0.386143\pi\) |
−0.986269 | + | 0.165146i | \(0.947190\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.68909e6 | + | 4.65764e6i | 0.124343 | + | 0.215369i | 0.921476 | − | 0.388435i | \(-0.126984\pi\) |
−0.797133 | + | 0.603804i | \(0.793651\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.64604e7 | 1.20940 | 0.604699 | − | 0.796454i | \(-0.293293\pi\) | ||||
0.604699 | + | 0.796454i | \(0.293293\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −373248. | −0.0169612 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.20361e6 | + | 3.81677e6i | 0.0989888 | + | 0.171454i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.02117e7 | − | 1.76871e7i | 0.456091 | − | 0.789972i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.95119e6 | − | 3.37957e6i | 0.0861550 | − | 0.149225i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.85541e6 | + | 1.53380e7i | 0.388785 | + | 0.673396i | 0.992286 | − | 0.123966i | \(-0.0395615\pi\) |
−0.603501 | + | 0.797362i | \(0.706228\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.04035e7 | 1.31973 | 0.659864 | − | 0.751385i | \(-0.270614\pi\) | ||||
0.659864 | + | 0.751385i | \(0.270614\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.93557e7 | 1.26704 | 0.633521 | − | 0.773726i | \(-0.281609\pi\) | ||||
0.633521 | + | 0.773726i | \(0.281609\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.32281e6 | − | 2.29118e6i | −0.0564533 | − | 0.0977800i | 0.836418 | − | 0.548093i | \(-0.184646\pi\) |
−0.892871 | + | 0.450313i | \(0.851313\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.90694e6 | + | 6.76702e6i | −0.165799 | + | 0.287172i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9.75628e6 | + | 1.68984e7i | −0.409407 | + | 0.709115i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.66794e7 | + | 6.35306e7i | 1.53061 | + | 2.65109i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7.37622e6 | −0.304393 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.49296e7 | −2.66459 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.44259e7 | − | 2.49865e7i | −0.585494 | − | 1.01411i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.03696e7 | + | 1.79607e7i | −0.418548 | + | 0.724946i | −0.995794 | − | 0.0916246i | \(-0.970794\pi\) |
0.577246 | + | 0.816570i | \(0.304127\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.27546e7 | − | 3.94121e7i | 0.908390 | − | 1.57338i | 0.0920903 | − | 0.995751i | \(-0.470645\pi\) |
0.816300 | − | 0.577628i | \(-0.196021\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.54275e6 | + | 4.40418e6i | 0.100955 | + | 0.174859i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.47010e6 | 0.175547 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.89012e7 | 0.738247 | 0.369123 | − | 0.929380i | \(-0.379658\pi\) | ||||
0.369123 | + | 0.929380i | \(0.379658\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −7.63009e6 | − | 1.32157e7i | −0.294799 | − | 0.510606i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.04249e7 | + | 3.53769e7i | −0.784883 | + | 1.35946i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.54195e7 | + | 2.67074e7i | −0.586181 | + | 1.01530i | 0.408546 | + | 0.912738i | \(0.366036\pi\) |
−0.994727 | + | 0.102558i | \(0.967297\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.43614e7 | + | 2.48747e7i | 0.543029 | + | 0.940554i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.71425e7 | 0.641277 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5.36296e6 | −0.199552 | −0.0997758 | − | 0.995010i | \(-0.531813\pi\) | ||||
−0.0997758 | + | 0.995010i | \(0.531813\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.88393e7 | + | 3.26305e7i | 0.693569 | + | 1.20130i | 0.970661 | + | 0.240453i | \(0.0772961\pi\) |
−0.277092 | + | 0.960843i | \(0.589371\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.80558e7 | − | 4.85941e7i | 1.02741 | − | 1.77953i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9.81104e6 | − | 1.69932e7i | 0.355501 | − | 0.615745i | −0.631703 | − | 0.775211i | \(-0.717644\pi\) |
0.987203 | + | 0.159466i | \(0.0509771\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.90900e6 | + | 1.36988e7i | 0.285073 | + | 0.493761i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.36730e7 | −0.487676 | −0.243838 | − | 0.969816i | \(-0.578407\pi\) | ||||
−0.243838 | + | 0.969816i | \(0.578407\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.13450e7 | −1.46695 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.94203e6 | − | 6.82779e6i | −0.138412 | − | 0.239736i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 648584. | − | 1.12338e6i | 0.0226547 | − | 0.0392390i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.71199e6 | − | 1.16255e7i | 0.232024 | − | 0.401877i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.81912e7 | − | 3.15081e7i | −0.625597 | − | 1.08357i | −0.988425 | − | 0.151710i | \(-0.951522\pi\) |
0.362828 | − | 0.931856i | \(-0.381811\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9.46886e6 | −0.322292 | −0.161146 | − | 0.986931i | \(-0.551519\pi\) | ||||
−0.161146 | + | 0.986931i | \(0.551519\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.29844e6 | 0.179418 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.79944e7 | + | 3.11673e7i | 0.603117 | + | 1.04463i | 0.992346 | + | 0.123489i | \(0.0394082\pi\) |
−0.389229 | + | 0.921141i | \(0.627258\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.87634e6 | − | 6.71401e6i | 0.129260 | − | 0.223885i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.30278e7 | + | 2.25648e7i | −0.430019 | + | 0.744815i | −0.996874 | − | 0.0790021i | \(-0.974827\pi\) |
0.566855 | + | 0.823818i | \(0.308160\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.88140e7 | + | 4.99073e7i | 0.946264 | + | 1.63898i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.22222e7 | −2.34790 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.92232e7 | 0.621788 | 0.310894 | − | 0.950445i | \(-0.399372\pi\) | ||||
0.310894 | + | 0.950445i | \(0.399372\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.84780e7 | − | 4.93254e7i | −0.911911 | − | 1.57948i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.46644e7 | + | 2.53994e7i | −0.467224 | + | 0.809256i | −0.999299 | − | 0.0374417i | \(-0.988079\pi\) |
0.532075 | + | 0.846697i | \(0.321412\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 324.6.e.e.217.2 | 4 | ||
3.2 | odd | 2 | inner | 324.6.e.e.217.1 | 4 | ||
9.2 | odd | 6 | 108.6.a.d.1.2 | yes | 2 | ||
9.4 | even | 3 | inner | 324.6.e.e.109.2 | 4 | ||
9.5 | odd | 6 | inner | 324.6.e.e.109.1 | 4 | ||
9.7 | even | 3 | 108.6.a.d.1.1 | ✓ | 2 | ||
36.7 | odd | 6 | 432.6.a.p.1.1 | 2 | |||
36.11 | even | 6 | 432.6.a.p.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.6.a.d.1.1 | ✓ | 2 | 9.7 | even | 3 | ||
108.6.a.d.1.2 | yes | 2 | 9.2 | odd | 6 | ||
324.6.e.e.109.1 | 4 | 9.5 | odd | 6 | inner | ||
324.6.e.e.109.2 | 4 | 9.4 | even | 3 | inner | ||
324.6.e.e.217.1 | 4 | 3.2 | odd | 2 | inner | ||
324.6.e.e.217.2 | 4 | 1.1 | even | 1 | trivial | ||
432.6.a.p.1.1 | 2 | 36.7 | odd | 6 | |||
432.6.a.p.1.2 | 2 | 36.11 | even | 6 |