Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [160,6,Mod(1,160)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(160, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("160.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 160 = 2^{5} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 160.a (trivial) |
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: | yes |
Analytic conductor: | \(25.6614111701\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.39180.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 36x - 24 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(6.80681\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 160.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | 29.2272 | 1.87493 | 0.937464 | − | 0.348081i | \(-0.113167\pi\) | ||||
0.937464 | + | 0.348081i | \(0.113167\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −25.0000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 44.5253 | 0.343449 | 0.171724 | − | 0.985145i | \(-0.445066\pi\) | ||||
0.171724 | + | 0.985145i | \(0.445066\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 611.232 | 2.51536 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −349.258 | −0.870290 | −0.435145 | − | 0.900360i | \(-0.643303\pi\) | ||||
−0.435145 | + | 0.900360i | \(0.643303\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 255.040 | 0.418552 | 0.209276 | − | 0.977857i | \(-0.432889\pi\) | ||||
0.209276 | + | 0.977857i | \(0.432889\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −730.681 | −0.838494 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1505.12 | 1.26313 | 0.631566 | − | 0.775322i | \(-0.282412\pi\) | ||||
0.631566 | + | 0.775322i | \(0.282412\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2431.11 | 1.54498 | 0.772488 | − | 0.635030i | \(-0.219012\pi\) | ||||
0.772488 | + | 0.635030i | \(0.219012\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1301.35 | 0.643942 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1435.50 | 0.565825 | 0.282913 | − | 0.959146i | \(-0.408699\pi\) | ||||
0.282913 | + | 0.959146i | \(0.408699\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 10762.4 | 2.84119 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2872.04 | 0.634156 | 0.317078 | − | 0.948400i | \(-0.397298\pi\) | ||||
0.317078 | + | 0.948400i | \(0.397298\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8940.96 | −1.67101 | −0.835507 | − | 0.549480i | \(-0.814826\pi\) | ||||
−0.835507 | + | 0.549480i | \(0.814826\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −10207.8 | −1.63173 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1113.13 | −0.153595 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −14536.6 | −1.74566 | −0.872830 | − | 0.488024i | \(-0.837718\pi\) | ||||
−0.872830 | + | 0.488024i | \(0.837718\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 7454.11 | 0.784756 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7504.01 | 0.697162 | 0.348581 | − | 0.937279i | \(-0.386664\pi\) | ||||
0.348581 | + | 0.937279i | \(0.386664\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 13490.7 | 1.11266 | 0.556331 | − | 0.830961i | \(-0.312209\pi\) | ||||
0.556331 | + | 0.830961i | \(0.312209\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −15280.8 | −1.12490 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8449.69 | 0.557951 | 0.278975 | − | 0.960298i | \(-0.410005\pi\) | ||||
0.278975 | + | 0.960298i | \(0.410005\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −14824.5 | −0.882043 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 43990.5 | 2.36828 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −28317.3 | −1.38472 | −0.692360 | − | 0.721553i | \(-0.743429\pi\) | ||||
−0.692360 | + | 0.721553i | \(0.743429\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8731.44 | 0.389206 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 71054.8 | 2.89672 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3530.13 | −0.132026 | −0.0660131 | − | 0.997819i | \(-0.521028\pi\) | ||||
−0.0660131 | + | 0.997819i | \(0.521028\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 45644.9 | 1.57061 | 0.785304 | − | 0.619110i | \(-0.212506\pi\) | ||||
0.785304 | + | 0.619110i | \(0.212506\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 27215.3 | 0.863896 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6376.00 | −0.187182 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −69849.6 | −1.90098 | −0.950489 | − | 0.310759i | \(-0.899417\pi\) | ||||
−0.950489 | + | 0.310759i | \(0.899417\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 41955.6 | 1.06088 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 60090.2 | 1.41468 | 0.707339 | − | 0.706874i | \(-0.249895\pi\) | ||||
0.707339 | + | 0.706874i | \(0.249895\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −49204.6 | −1.08068 | −0.540342 | − | 0.841445i | \(-0.681705\pi\) | ||||
−0.540342 | + | 0.841445i | \(0.681705\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 18267.0 | 0.374986 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −15550.8 | −0.298900 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −981.509 | −0.0176940 | −0.00884702 | − | 0.999961i | \(-0.502816\pi\) | ||||
−0.00884702 | + | 0.999961i | \(0.502816\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 166026. | 2.81167 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −38372.3 | −0.611396 | −0.305698 | − | 0.952129i | \(-0.598890\pi\) | ||||
−0.305698 | + | 0.952129i | \(0.598890\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −37628.0 | −0.564890 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 83941.9 | 1.18900 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 39418.6 | 0.527504 | 0.263752 | − | 0.964591i | \(-0.415040\pi\) | ||||
0.263752 | + | 0.964591i | \(0.415040\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 11355.7 | 0.143751 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −261320. | −3.13303 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −60777.9 | −0.690934 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 51340.9 | 0.554031 | 0.277016 | − | 0.960865i | \(-0.410655\pi\) | ||||
0.277016 | + | 0.960865i | \(0.410655\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −213477. | −2.18909 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −51557.0 | −0.502903 | −0.251451 | − | 0.967870i | \(-0.580908\pi\) | ||||
−0.251451 | + | 0.967870i | \(0.580908\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6370.92 | 0.0591710 | 0.0295855 | − | 0.999562i | \(-0.490581\pi\) | ||||
0.0295855 | + | 0.999562i | \(0.490581\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −32533.8 | −0.287979 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5654.13 | −0.0477426 | −0.0238713 | − | 0.999715i | \(-0.507599\pi\) | ||||
−0.0238713 | + | 0.999715i | \(0.507599\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −217953. | −1.75710 | −0.878550 | − | 0.477650i | \(-0.841489\pi\) | ||||
−0.878550 | + | 0.477650i | \(0.841489\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −424866. | −3.27299 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −129389. | −0.953240 | −0.476620 | − | 0.879109i | \(-0.658138\pi\) | ||||
−0.476620 | + | 0.879109i | \(0.658138\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −35887.4 | −0.253045 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 155889. | 1.05281 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 67015.9 | 0.433821 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −39070.1 | −0.242595 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 219322. | 1.30713 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −15625.0 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 106258. | 0.584594 | 0.292297 | − | 0.956328i | \(-0.405580\pi\) | ||||
0.292297 | + | 0.956328i | \(0.405580\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 394296. | 2.08616 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 132808. | 0.676155 | 0.338077 | − | 0.941118i | \(-0.390223\pi\) | ||||
0.338077 | + | 0.941118i | \(0.390223\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 108246. | 0.530619 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −269060. | −1.27062 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −301171. | −1.37092 | −0.685460 | − | 0.728110i | \(-0.740399\pi\) | ||||
−0.685460 | + | 0.728110i | \(0.740399\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −139021. | −0.610298 | −0.305149 | − | 0.952305i | \(-0.598706\pi\) | ||||
−0.305149 | + | 0.952305i | \(0.598706\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 246961. | 1.04612 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −89074.6 | −0.364262 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −71801.1 | −0.283603 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −433279. | −1.65377 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −195083. | −0.719869 | −0.359934 | − | 0.932978i | \(-0.617201\pi\) | ||||
−0.359934 | + | 0.932978i | \(0.617201\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −161597. | −0.576755 | −0.288378 | − | 0.957517i | \(-0.593116\pi\) | ||||
−0.288378 | + | 0.957517i | \(0.593116\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 919977. | 3.17723 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 223524. | 0.747300 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 108055. | 0.349860 | 0.174930 | − | 0.984581i | \(-0.444030\pi\) | ||||
0.174930 | + | 0.984581i | \(0.444030\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −827636. | −2.59625 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 63915.9 | 0.194332 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −35513.9 | −0.104696 | −0.0523479 | − | 0.998629i | \(-0.516670\pi\) | ||||
−0.0523479 | + | 0.998629i | \(0.516670\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 255196. | 0.729733 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 377413. | 1.04719 | 0.523595 | − | 0.851967i | \(-0.324591\pi\) | ||||
0.523595 | + | 0.851967i | \(0.324591\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −306248. | −0.824814 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.48598e6 | 3.88617 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −142405. | −0.361752 | −0.180876 | − | 0.983506i | \(-0.557893\pi\) | ||||
−0.180876 | + | 0.983506i | \(0.557893\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 27828.3 | 0.0686897 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −103176. | −0.247540 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −457275. | −1.06671 | −0.533353 | − | 0.845893i | \(-0.679068\pi\) | ||||
−0.533353 | + | 0.845893i | \(0.679068\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −871860. | −1.97811 | −0.989055 | − | 0.147549i | \(-0.952862\pi\) | ||||
−0.989055 | + | 0.147549i | \(0.952862\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.33408e6 | 2.94478 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 363416. | 0.780683 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −525675. | −1.09929 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 479199. | 0.975802 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 330154. | 0.654837 | 0.327418 | − | 0.944879i | \(-0.393821\pi\) | ||||
0.327418 | + | 0.944879i | \(0.393821\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −152914. | −0.295498 | −0.147749 | − | 0.989025i | \(-0.547203\pi\) | ||||
−0.147749 | + | 0.989025i | \(0.547203\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −186353. | −0.350953 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −714867. | −1.31238 | −0.656190 | − | 0.754596i | \(-0.727833\pi\) | ||||
−0.656190 | + | 0.754596i | \(0.727833\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 292872. | 0.524258 | 0.262129 | − | 0.965033i | \(-0.415575\pi\) | ||||
0.262129 | + | 0.965033i | \(0.415575\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.04151e6 | −3.56420 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 127879. | 0.217800 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −187600. | −0.311780 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 877421. | 1.42325 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −849085. | −1.34458 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 365716. | 0.565507 | 0.282754 | − | 0.959193i | \(-0.408752\pi\) | ||||
0.282754 | + | 0.959193i | \(0.408752\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.75627e6 | 2.65242 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −337267. | −0.497597 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −398099. | −0.573907 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.43812e6 | −2.02621 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 383866. | 0.528687 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 748539. | 1.00798 | 0.503990 | − | 0.863709i | \(-0.331865\pi\) | ||||
0.503990 | + | 0.863709i | \(0.331865\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 382020. | 0.503072 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 424142. | 0.546319 | 0.273159 | − | 0.961969i | \(-0.411931\pi\) | ||||
0.273159 | + | 0.961969i | \(0.411931\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.02868e6 | 1.29625 | 0.648126 | − | 0.761533i | \(-0.275553\pi\) | ||||
0.648126 | + | 0.761533i | \(0.275553\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −454507. | −0.560416 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 614128. | 0.741087 | 0.370544 | − | 0.928815i | \(-0.379171\pi\) | ||||
0.370544 | + | 0.928815i | \(0.379171\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −211242. | −0.249523 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −28686.8 | −0.0331750 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.36204e6 | 1.54239 | 0.771197 | − | 0.636597i | \(-0.219658\pi\) | ||||
0.771197 | + | 0.636597i | \(0.219658\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 354377. | 0.393027 | 0.196514 | − | 0.980501i | \(-0.437038\pi\) | ||||
0.196514 | + | 0.980501i | \(0.437038\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2.23722e6 | 2.43049 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 370612. | 0.394462 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 620031. | 0.646653 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.12152e6 | −1.14632 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −826955. | −0.828509 | −0.414255 | − | 0.910161i | \(-0.635958\pi\) | ||||
−0.414255 | + | 0.910161i | \(0.635958\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −501358. | −0.492432 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.09976e6 | −1.05913 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.47307e6 | 1.39121 | 0.695603 | − | 0.718426i | \(-0.255137\pi\) | ||||
0.695603 | + | 0.718426i | \(0.255137\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −647248. | −0.599545 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.75548e6 | 1.59513 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 669755. | 0.597072 | 0.298536 | − | 0.954398i | \(-0.403502\pi\) | ||||
0.298536 | + | 0.954398i | \(0.403502\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 707932. | 0.619265 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.15210e6 | 0.989032 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −161730. | −0.136273 | −0.0681367 | − | 0.997676i | \(-0.521705\pi\) | ||||
−0.0681367 | + | 0.997676i | \(0.521705\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −709813. | −0.587112 | −0.293556 | − | 0.955942i | \(-0.594839\pi\) | ||||
−0.293556 | + | 0.955942i | \(0.594839\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 331897. | 0.269523 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −218286. | −0.174058 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.25136e6 | 0.979904 | 0.489952 | − | 0.871749i | \(-0.337014\pi\) | ||||
0.489952 | + | 0.871749i | \(0.337014\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.46500e6 | −4.20320 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.14718e6 | −0.866692 | −0.433346 | − | 0.901228i | \(-0.642667\pi\) | ||||
−0.433346 | + | 0.901228i | \(0.642667\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.01151e6 | −0.750766 | −0.375383 | − | 0.926870i | \(-0.622489\pi\) | ||||
−0.375383 | + | 0.926870i | \(0.622489\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.77637e6 | −1.29545 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 334118. | 0.239439 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 845528. | 0.595502 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.50055e6 | 1.03877 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −161999. | −0.110241 | −0.0551204 | − | 0.998480i | \(-0.517554\pi\) | ||||
−0.0551204 | + | 0.998480i | \(0.517554\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 88253.2 | 0.0590439 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.75885e6 | −2.47266 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 366109. | 0.236828 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 600677. | 0.382142 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.50687e6 | −0.942907 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.14112e6 | −0.702398 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.20761e6 | −0.731276 | −0.365638 | − | 0.930757i | \(-0.619149\pi\) | ||||
−0.365638 | + | 0.930757i | \(0.619149\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 186204. | 0.110941 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.90780e6 | 1.70476 | 0.852382 | − | 0.522920i | \(-0.175157\pi\) | ||||
0.852382 | + | 0.522920i | \(0.175157\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.27324e6 | −0.734597 | −0.367298 | − | 0.930103i | \(-0.619717\pi\) | ||||
−0.367298 | + | 0.930103i | \(0.619717\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −680382. | −0.386346 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.34305e6 | 0.750659 | 0.375330 | − | 0.926891i | \(-0.377530\pi\) | ||||
0.375330 | + | 0.926891i | \(0.377530\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.00308e6 | −0.551899 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −165255. | −0.0895140 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.65912e6 | 1.95151 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 159400. | 0.0837105 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6.37016e6 | −3.29444 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 376225. | 0.191627 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.59250e6 | −0.798929 | −0.399464 | − | 0.916749i | \(-0.630804\pi\) | ||||
−0.399464 | + | 0.916749i | \(0.630804\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −8.88526e6 | −4.39096 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.74624e6 | 0.850143 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.34715e6 | 0.646163 | 0.323082 | − | 0.946371i | \(-0.395281\pi\) | ||||
0.323082 | + | 0.946371i | \(0.395281\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.78169e6 | −1.78726 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.12270e6 | 1.45427 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.40840e6 | −0.646385 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.04889e6 | −0.474441 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.61456e6 | −0.719832 | −0.359916 | − | 0.932985i | \(-0.617195\pi\) | ||||
−0.359916 | + | 0.932985i | \(0.617195\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.78417e6 | −0.784103 | −0.392052 | − | 0.919943i | \(-0.628235\pi\) | ||||
−0.392052 | + | 0.919943i | \(0.628235\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.74484e6 | 1.18919 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.02848e6 | 0.439299 | 0.219650 | − | 0.975579i | \(-0.429509\pi\) | ||||
0.219650 | + | 0.975579i | \(0.429509\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.50226e6 | −0.632664 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.95869e6 | 0.813383 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −719588. | −0.294678 | −0.147339 | − | 0.989086i | \(-0.547071\pi\) | ||||
−0.147339 | + | 0.989086i | \(0.547071\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.43422e6 | 1.38695 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.14191e6 | −0.454848 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.23012e6 | 0.483297 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −412535. | −0.159881 | −0.0799403 | − | 0.996800i | \(-0.525473\pi\) | ||||
−0.0799403 | + | 0.996800i | \(0.525473\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.58669e6 | 1.75361 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.26083e6 | −0.475580 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.01227e6 | −1.49320 | −0.746600 | − | 0.665273i | \(-0.768315\pi\) | ||||
−0.746600 | + | 0.665273i | \(0.768315\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −456676. | −0.167699 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 732485. | 0.265427 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 725543. | 0.259457 | 0.129728 | − | 0.991550i | \(-0.458589\pi\) | ||||
0.129728 | + | 0.991550i | \(0.458589\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.10564e6 | 1.09607 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.16948e6 | 1.45240 | 0.726199 | − | 0.687485i | \(-0.241285\pi\) | ||||
0.726199 | + | 0.687485i | \(0.241285\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 388770. | 0.133672 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.24594e6 | 2.79874 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 710805. | 0.238164 | 0.119082 | − | 0.992884i | \(-0.462005\pi\) | ||||
0.119082 | + | 0.992884i | \(0.462005\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.16059e6 | 0.714712 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.88161e6 | 1.26774 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 24537.7 | 0.00791301 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.60119e6 | 0.828315 | 0.414157 | − | 0.910205i | \(-0.364076\pi\) | ||||
0.414157 | + | 0.910205i | \(0.364076\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.16374e6 | 0.994874 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.82517e6 | 0.566817 | 0.283409 | − | 0.958999i | \(-0.408535\pi\) | ||||
0.283409 | + | 0.958999i | \(0.408535\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.28030e6 | −0.699407 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.15066e6 | −1.25742 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.07703e6 | 1.51923 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −527537. | −0.155935 | −0.0779677 | − | 0.996956i | \(-0.524843\pi\) | ||||
−0.0779677 | + | 0.996956i | \(0.524843\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.80241e6 | −2.57038 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −157180. | −0.0453442 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 959307. | 0.273425 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.06319e6 | −1.14427 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.11729e6 | 0.589175 | 0.294587 | − | 0.955625i | \(-0.404818\pi\) | ||||
0.294587 | + | 0.955625i | \(0.404818\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.67556e6 | 0.460738 | 0.230369 | − | 0.973103i | \(-0.426007\pi\) | ||||
0.230369 | + | 0.973103i | \(0.426007\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.16472e6 | 1.40345 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 940700. | 0.252626 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.03235e6 | 0.539423 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.60341e6 | −0.682965 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.44216e6 | 0.373957 | 0.186978 | − | 0.982364i | \(-0.440131\pi\) | ||||
0.186978 | + | 0.982364i | \(0.440131\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.49118e6 | 1.40749 | 0.703746 | − | 0.710452i | \(-0.251509\pi\) | ||||
0.703746 | + | 0.710452i | \(0.251509\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.09855e6 | −0.531735 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.48986e6 | 0.874186 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.57088e6 | −0.884329 | −0.442165 | − | 0.896934i | \(-0.645789\pi\) | ||||
−0.442165 | + | 0.896934i | \(0.645789\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −9.06121e6 | −2.21865 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.15711e6 | −0.522231 | −0.261116 | − | 0.965308i | \(-0.584090\pi\) | ||||
−0.261116 | + | 0.965308i | \(0.584090\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −985464. | −0.235907 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5.70174e6 | −1.34970 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.15945e6 | −0.973689 | −0.486845 | − | 0.873489i | \(-0.661852\pi\) | ||||
−0.486845 | + | 0.873489i | \(0.661852\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.62083e6 | −0.606733 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.72304e6 | −1.08138 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −283893. | −0.0642875 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.32204e6 | 1.41601 | 0.708006 | − | 0.706207i | \(-0.249595\pi\) | ||||
0.708006 | + | 0.706207i | \(0.249595\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.61987e7 | 3.58880 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.12007e6 | −1.77954 | −0.889769 | − | 0.456411i | \(-0.849135\pi\) | ||||
−0.889769 | + | 0.456411i | \(0.849135\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.51746e6 | −1.19615 | −0.598076 | − | 0.801439i | \(-0.704068\pi\) | ||||
−0.598076 | + | 0.801439i | \(0.704068\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6.53299e6 | 1.40113 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.98287e6 | 1.69382 | 0.846909 | − | 0.531737i | \(-0.178461\pi\) | ||||
0.846909 | + | 0.531737i | \(0.178461\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.11007e6 | −0.652888 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.15814e6 | 0.655963 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.71172e6 | −0.968338 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.51945e6 | 0.308995 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.73084e7 | −3.48307 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.21796e6 | 1.43739 | 0.718697 | − | 0.695323i | \(-0.244739\pi\) | ||||
0.718697 | + | 0.695323i | \(0.244739\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.70742e6 | −0.730650 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.86809e6 | 0.364358 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.28352e6 | −0.247770 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.74447e6 | 0.333305 | 0.166652 | − | 0.986016i | \(-0.446704\pi\) | ||||
0.166652 | + | 0.986016i | \(0.446704\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.03797e6 | −0.196297 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.10988e6 | 1.70533 | 0.852666 | − | 0.522457i | \(-0.174985\pi\) | ||||
0.852666 | + | 0.522457i | \(0.174985\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.32277e6 | 0.801022 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.33694e6 | 0.978992 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.67553e6 | 0.485869 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.94465e6 | −1.06875 | −0.534374 | − | 0.845248i | \(-0.679452\pi\) | ||||
−0.534374 | + | 0.845248i | \(0.679452\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.10307e7 | 1.96341 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.53195e6 | −0.446207 | −0.223103 | − | 0.974795i | \(-0.571619\pi\) | ||||
−0.223103 | + | 0.974795i | \(0.571619\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.28892e6 | 0.224905 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −8.95078e6 | −1.54647 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.91009e6 | 0.840030 | 0.420015 | − | 0.907517i | \(-0.362025\pi\) | ||||
0.420015 | + | 0.907517i | \(0.362025\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.19085e6 | −0.371160 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.61647e7 | 4.38957 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −159273. | −0.0264621 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.95112e6 | −0.485579 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.16211e6 | −0.678259 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.90160e6 | −0.952522 | −0.476261 | − | 0.879304i | \(-0.658008\pi\) | ||||
−0.476261 | + | 0.879304i | \(0.658008\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.73830e6 | 1.07720 | 0.538600 | − | 0.842562i | \(-0.318953\pi\) | ||||
0.538600 | + | 0.842562i | \(0.318953\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 813345. | 0.128788 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.34572e7 | −2.11071 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.37569e6 | −0.679842 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.15773e6 | −0.332093 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.91382e6 | 0.291799 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 141353. | 0.0213511 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.33649e7 | −2.00000 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.17757e6 | 0.767634 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.56711e6 | −0.964675 | −0.482337 | − | 0.875986i | \(-0.660212\pi\) | ||||
−0.482337 | + | 0.875986i | \(0.660212\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.54821e7 | −3.70881 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.44882e6 | 0.785799 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.27471e7 | −1.82156 | −0.910778 | − | 0.412896i | \(-0.864517\pi\) | ||||
−0.910778 | + | 0.412896i | \(0.864517\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.78997e7 | 3.95064 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.98226e6 | 0.979755 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −43702.0 | −0.00607699 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.06217e7 | 1.46373 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.22479e7 | 1.67273 | 0.836364 | − | 0.548175i | \(-0.184677\pi\) | ||||
0.836364 | + | 0.548175i | \(0.184677\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.44066e6 | 0.465707 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.53640e7 | −2.06109 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.23945e6 | −0.297763 | −0.148882 | − | 0.988855i | \(-0.547567\pi\) | ||||
−0.148882 | + | 0.988855i | \(0.547567\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.23473e6 | 0.426302 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7.39237e6 | 0.965664 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.95223e6 | −0.511755 | −0.255877 | − | 0.966709i | \(-0.582364\pi\) | ||||
−0.255877 | + | 0.966709i | \(0.582364\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.99947e6 | −0.898411 | −0.449206 | − | 0.893428i | \(-0.648293\pi\) | ||||
−0.449206 | + | 0.893428i | \(0.648293\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.64949e6 | 1.22777 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 897185. | 0.113165 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.20338e6 | 0.400561 | 0.200280 | − | 0.979739i | \(-0.435815\pi\) | ||||
0.200280 | + | 0.979739i | \(0.435815\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.46927e6 | −0.554039 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.70854e6 | −0.209983 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.89002e6 | 1.20511 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.89721e6 | −0.470831 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.35926e7 | 1.62820 | 0.814102 | − | 0.580722i | \(-0.197230\pi\) | ||||
0.814102 | + | 0.580722i | \(0.197230\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.17365e7 | −2.58168 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.08936e7 | −2.46062 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 713635. | 0.0833373 | 0.0416687 | − | 0.999131i | \(-0.486733\pi\) | ||||
0.0416687 | + | 0.999131i | \(0.486733\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.67540e6 | −0.194011 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8.55984e6 | 0.982946 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.09641e6 | 0.580359 | 0.290180 | − | 0.956972i | \(-0.406285\pi\) | ||||
0.290180 | + | 0.956972i | \(0.406285\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 136310. | 0.0153937 | 0.00769683 | − | 0.999970i | \(-0.497550\pi\) | ||||
0.00769683 | + | 0.999970i | \(0.497550\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.26943e7 | −4.78164 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 976753. | 0.108492 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.23096e6 | 0.686409 | 0.343204 | − | 0.939261i | \(-0.388488\pi\) | ||||
0.343204 | + | 0.939261i | \(0.388488\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.73754e6 | 0.408359 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.15501e6 | 0.233532 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.37774e7 | −1.48087 | −0.740435 | − | 0.672128i | \(-0.765380\pi\) | ||||
−0.740435 | + | 0.672128i | \(0.765380\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.48304e6 | −0.584566 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8.85147e6 | −0.936058 | −0.468029 | − | 0.883713i | \(-0.655036\pi\) | ||||
−0.468029 | + | 0.883713i | \(0.655036\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.22847e7 | 1.28866 | 0.644329 | − | 0.764748i | \(-0.277137\pi\) | ||||
0.644329 | + | 0.764748i | \(0.277137\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.54494e7 | 1.60762 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.75512e6 | 0.181170 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.48164e7 | −2.52099 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.18794e7 | −2.20500 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.75131e7 | −1.75101 | −0.875506 | − | 0.483207i | \(-0.839472\pi\) | ||||
−0.875506 | + | 0.483207i | \(0.839472\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.06889e7 | 1.06029 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.65646e6 | −0.261438 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.78084e6 | −0.369181 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.67291e7 | 3.55842 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.24879e7 | −1.20045 | −0.600223 | − | 0.799832i | \(-0.704922\pi\) | ||||
−0.600223 | + | 0.799832i | \(0.704922\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.50652e6 | 0.525231 | 0.262615 | − | 0.964901i | \(-0.415415\pi\) | ||||
0.262615 | + | 0.964901i | \(0.415415\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −9.85739e6 | −0.932959 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.74623e6 | 0.257915 | 0.128957 | − | 0.991650i | \(-0.458837\pi\) | ||||
0.128957 | + | 0.991650i | \(0.458837\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.23292e6 | 0.114901 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.16353e7 | −1.07604 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.24705e7 | −1.14446 | −0.572232 | − | 0.820092i | \(-0.693922\pi\) | ||||
−0.572232 | + | 0.820092i | \(0.693922\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.32020e6 | −0.302386 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.00755e7 | −2.71831 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.75360e7 | −1.57296 | −0.786478 | − | 0.617618i | \(-0.788098\pi\) | ||||
−0.786478 | + | 0.617618i | \(0.788098\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.04528e6 | 0.805227 | 0.402613 | − | 0.915370i | \(-0.368102\pi\) | ||||
0.402613 | + | 0.915370i | \(0.368102\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.12193e7 | 0.991250 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.70615e6 | −0.237300 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.12281e6 | 0.358821 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.18777e7 | 1.88989 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.59418e7 | −1.36689 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.09208e6 | −0.773794 | −0.386897 | − | 0.922123i | \(-0.626453\pi\) | ||||
−0.386897 | + | 0.922123i | \(0.626453\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 6.72651e6 | 0.568238 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.55584e7 | 1.30465 | 0.652325 | − | 0.757940i | \(-0.273794\pi\) | ||||
0.652325 | + | 0.757940i | \(0.273794\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.28597e6 | 0.190281 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.23965e7 | 1.02431 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.22623e6 | 0.428684 | 0.214342 | − | 0.976759i | \(-0.431239\pi\) | ||||
0.214342 | + | 0.976759i | \(0.431239\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.52928e6 | 0.613094 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.00653e7 | 2.43038 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −7.22203e6 | −0.579577 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.01073e7 | 1.60199 | 0.800994 | − | 0.598672i | \(-0.204305\pi\) | ||||
0.800994 | + | 0.598672i | \(0.204305\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −9.50515e6 | −0.751840 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.47551e6 | 0.272934 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.12944e7 | 0.880608 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.79493e7 | 1.38949 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.57869e7 | 1.21339 | 0.606695 | − | 0.794934i | \(-0.292495\pi\) | ||||
0.606695 | + | 0.794934i | \(0.292495\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.53402e7 | −2.69700 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.17403e6 | −0.467838 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.29559e6 | −0.172721 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.13552e6 | −0.383680 | −0.191840 | − | 0.981426i | \(-0.561445\pi\) | ||||
−0.191840 | + | 0.981426i | \(0.561445\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −599930. | −0.0445068 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.28347e7 | −0.945502 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.22687e6 | 0.162903 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.98087e7 | 2.89188 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.90785e6 | 0.209773 | 0.104886 | − | 0.994484i | \(-0.466552\pi\) | ||||
0.104886 | + | 0.994484i | \(0.466552\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 283667. | 0.0203222 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.03575e7 | 0.736898 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.79503e6 | 0.126831 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.85123e6 | −0.550937 | −0.275468 | − | 0.961310i | \(-0.588833\pi\) | ||||
−0.275468 | + | 0.961310i | \(0.588833\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.50435e7 | 1.74533 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.03051e7 | 1.40544 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.41173e7 | −0.970491 | −0.485245 | − | 0.874378i | \(-0.661270\pi\) | ||||
−0.485245 | + | 0.874378i | \(0.661270\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.08320e7 | 0.739588 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.43955e7 | 1.65440 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.20049e6 | −0.282937 | −0.141468 | − | 0.989943i | \(-0.545182\pi\) | ||||
−0.141468 | + | 0.989943i | \(0.545182\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.81218e7 | 1.21243 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.18490e6 | 0.0787425 | 0.0393712 | − | 0.999225i | \(-0.487465\pi\) | ||||
0.0393712 | + | 0.999225i | \(0.487465\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.87707e6 | 0.321935 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.34544e7 | −1.53788 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −251752. | −0.0163971 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.94605e6 | −0.255307 | −0.127653 | − | 0.991819i | \(-0.540745\pi\) | ||||
−0.127653 | + | 0.991819i | \(0.540745\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.41696e7 | −1.55340 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.03993e6 | 0.257933 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.22109e6 | −0.0774479 | −0.0387239 | − | 0.999250i | \(-0.512329\pi\) | ||||
−0.0387239 | + | 0.999250i | \(0.512329\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.46533e7 | −0.923276 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.91652e7 | 1.19964 | 0.599822 | − | 0.800134i | \(-0.295238\pi\) | ||||
0.599822 | + | 0.800134i | \(0.295238\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.70442e6 | −0.603473 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.29994e7 | −1.42090 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −900323. | −0.0552599 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.50951e6 | 0.579886 | 0.289943 | − | 0.957044i | \(-0.406364\pi\) | ||||
0.289943 | + | 0.957044i | \(0.406364\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.30539e7 | 2.60841 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 526263. | 0.0316777 | 0.0158389 | − | 0.999875i | \(-0.494958\pi\) | ||||
0.0158389 | + | 0.999875i | \(0.494958\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.58810e6 | −0.334203 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.89173e7 | −1.12410 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.82431e7 | 1.07710 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.09870e7 | −1.23118 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.09101e7 | 1.80176 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.70137e6 | −0.156462 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.05915e7 | 1.18509 | 0.592544 | − | 0.805538i | \(-0.298123\pi\) | ||||
0.592544 | + | 0.805538i | \(0.298123\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.95751e7 | 1.11947 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.76109e6 | −0.327389 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.16413e7 | 0.657382 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.06909e7 | 1.16108 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.08952e7 | −1.16520 | −0.582599 | − | 0.812760i | \(-0.697964\pi\) | ||||
−0.582599 | + | 0.812760i | \(0.697964\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.27178e7 | 0.704766 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.40939e7 | 1.32686 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.71851e7 | 0.940509 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.59790e6 | −0.0869079 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4.72694e6 | −0.255503 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.38823e7 | −1.82013 | −0.910063 | − | 0.414470i | \(-0.863967\pi\) | ||||
−0.910063 | + | 0.414470i | \(0.863967\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.25428e6 | 0.440684 | 0.220342 | − | 0.975423i | \(-0.429283\pi\) | ||||
0.220342 | + | 0.975423i | \(0.429283\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.07459e7 | −1.10079 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 887847. | 0.0468214 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.27974e7 | 1.71903 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.94098e6 | 0.361586 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.99898e6 | 0.103503 | 0.0517513 | − | 0.998660i | \(-0.483520\pi\) | ||||
0.0517513 | + | 0.998660i | \(0.483520\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.28086e7 | 0.659176 | 0.329588 | − | 0.944125i | \(-0.393090\pi\) | ||||
0.329588 | + | 0.944125i | \(0.393090\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −6.37990e6 | −0.326347 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.83308e7 | −1.44044 | −0.720221 | − | 0.693745i | \(-0.755960\pi\) | ||||
−0.720221 | + | 0.693745i | \(0.755960\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.91663e6 | 0.400087 | 0.200043 | − | 0.979787i | \(-0.435892\pi\) | ||||
0.200043 | + | 0.979787i | \(0.435892\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.65739e7 | 1.83725 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.23126e7 | −1.11414 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.43532e6 | −0.468317 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −9.62263e7 | −4.74767 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.18676e7 | −1.07250 | −0.536249 | − | 0.844060i | \(-0.680159\pi\) | ||||
−0.536249 | + | 0.844060i | \(0.680159\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.22625e7 | −0.597847 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.35289e7 | −1.62499 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7.65619e6 | 0.368868 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.73961e6 | −0.0833188 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.95637e7 | −1.40763 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.08673e7 | −0.987739 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.73771e6 | −0.317059 | −0.158529 | − | 0.987354i | \(-0.550675\pi\) | ||||
−0.158529 | + | 0.987354i | \(0.550675\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.71494e7 | −1.73795 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.01368e7 | 0.936565 | 0.468283 | − | 0.883579i | \(-0.344873\pi\) | ||||
0.468283 | + | 0.883579i | \(0.344873\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.31020e7 | −1.06823 | −0.534117 | − | 0.845410i | \(-0.679356\pi\) | ||||
−0.534117 | + | 0.845410i | \(0.679356\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9.76535e6 | 0.448932 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.79582e7 | −1.27785 | −0.638927 | − | 0.769267i | \(-0.720622\pi\) | ||||
−0.638927 | + | 0.769267i | \(0.720622\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.56013e6 | 0.161780 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.47125e7 | 1.11652 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 342800. | 0.0153989 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.78144e7 | −0.795658 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.13812e7 | 1.39359 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −695708. | −0.0307190 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.75058e7 | 1.64664 | 0.823322 | − | 0.567574i | \(-0.192118\pi\) | ||||
0.823322 | + | 0.567574i | \(0.192118\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4.73477e6 | −0.206693 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.94116e6 | −0.0842601 | −0.0421300 | − | 0.999112i | \(-0.513414\pi\) | ||||
−0.0421300 | + | 0.999112i | \(0.513414\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.90752e7 | 1.68655 | 0.843276 | − | 0.537481i | \(-0.180624\pi\) | ||||
0.843276 | + | 0.537481i | \(0.180624\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.57940e6 | 0.110703 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.87662e7 | 0.800878 | 0.400439 | − | 0.916323i | \(-0.368858\pi\) | ||||
0.400439 | + | 0.916323i | \(0.368858\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.73119e6 | 0.200778 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.79859e7 | −2.44697 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.05422e7 | 0.862020 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.14319e7 | 0.477045 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.07004e7 | 0.444035 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.56788e7 | −1.05968 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.26209e7 | −1.74908 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.75561e7 | 0.716489 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.17965e7 | 0.884637 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.79416e7 | 1.12780 | 0.563901 | − | 0.825842i | \(-0.309300\pi\) | ||||
0.563901 | + | 0.825842i | \(0.309300\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.15133e7 | −1.26498 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.32374e7 | −0.528452 | −0.264226 | − | 0.964461i | \(-0.585116\pi\) | ||||
−0.264226 | + | 0.964461i | \(0.585116\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.34018e7 | 0.532092 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.33519e7 | −1.31695 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.91332e6 | 0.232224 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.80433e7 | 1.09532 | 0.547660 | − | 0.836701i | \(-0.315519\pi\) | ||||
0.547660 | + | 0.836701i | \(0.315519\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.52951e7 | −1.37109 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.53254e7 | 0.592117 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.08540e6 | −0.349132 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.89411e6 | 0.148836 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.96341e7 | 0.746400 | 0.373200 | − | 0.927751i | \(-0.378261\pi\) | ||||
0.373200 | + | 0.927751i | \(0.378261\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.60401e7 | −1.36273 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8.49871e7 | 3.19631 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.31419e7 | 0.491618 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.71944e7 | 1.01188 | 0.505942 | − | 0.862567i | \(-0.331145\pi\) | ||||
0.505942 | + | 0.862567i | \(0.331145\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.72133e7 | −1.37732 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.74326e7 | 1.00993 | 0.504966 | − | 0.863139i | \(-0.331505\pi\) | ||||
0.504966 | + | 0.863139i | \(0.331505\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.07720e7 | 0.394472 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.19800e7 | −0.436392 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.42413e7 | −0.516029 | −0.258014 | − | 0.966141i | \(-0.583068\pi\) | ||||
−0.258014 | + | 0.966141i | \(0.583068\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.25491e7 | −0.452323 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.92535e7 | 1.40743 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.25786e7 | 1.16198 | 0.580992 | − | 0.813910i | \(-0.302665\pi\) | ||||
0.580992 | + | 0.813910i | \(0.302665\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.25385e6 | −0.292852 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.93173e7 | −1.03477 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.34097e7 | −0.470841 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.13117e7 | 1.79229 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.45598e6 | −0.120090 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.82286e6 | 0.132151 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.03932e6 | 0.138913 | 0.0694564 | − | 0.997585i | \(-0.477874\pi\) | ||||
0.0694564 | + | 0.997585i | \(0.477874\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.06946e8 | 3.65894 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.98023e7 | −1.01438 | −0.507191 | − | 0.861834i | \(-0.669316\pi\) | ||||
−0.507191 | + | 0.861834i | \(0.669316\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.18993e6 | −0.209606 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.65882e6 | 0.156951 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.70486e7 | −0.906586 | −0.453293 | − | 0.891362i | \(-0.649751\pi\) | ||||
−0.453293 | + | 0.891362i | \(0.649751\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.37672e7 | −0.459082 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.33220e8 | −4.41974 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.15761e7 | −1.04226 | −0.521128 | − | 0.853479i | \(-0.674489\pi\) | ||||
−0.521128 | + | 0.853479i | \(0.674489\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.78717e7 | 0.586914 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.09960e7 | 0.359288 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.93658e7 | 0.629572 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.49963e6 | 0.210235 | 0.105117 | − | 0.994460i | \(-0.466478\pi\) | ||||
0.105117 | + | 0.994460i | \(0.466478\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.65443e7 | −1.49794 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7.32180e6 | −0.234455 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.34950e7 | −0.429966 | −0.214983 | − | 0.976618i | \(-0.568970\pi\) | ||||
−0.214983 | + | 0.976618i | \(0.568970\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.56449e8 | −4.95975 |
(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 | 160.6.a.g.1.3 | yes | 3 | |
4.3 | odd | 2 | 160.6.a.f.1.1 | ✓ | 3 | ||
5.2 | odd | 4 | 800.6.c.j.449.1 | 6 | |||
5.3 | odd | 4 | 800.6.c.j.449.6 | 6 | |||
5.4 | even | 2 | 800.6.a.n.1.1 | 3 | |||
8.3 | odd | 2 | 320.6.a.y.1.3 | 3 | |||
8.5 | even | 2 | 320.6.a.x.1.1 | 3 | |||
20.3 | even | 4 | 800.6.c.k.449.1 | 6 | |||
20.7 | even | 4 | 800.6.c.k.449.6 | 6 | |||
20.19 | odd | 2 | 800.6.a.o.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
160.6.a.f.1.1 | ✓ | 3 | 4.3 | odd | 2 | ||
160.6.a.g.1.3 | yes | 3 | 1.1 | even | 1 | trivial | |
320.6.a.x.1.1 | 3 | 8.5 | even | 2 | |||
320.6.a.y.1.3 | 3 | 8.3 | odd | 2 | |||
800.6.a.n.1.1 | 3 | 5.4 | even | 2 | |||
800.6.a.o.1.3 | 3 | 20.19 | odd | 2 | |||
800.6.c.j.449.1 | 6 | 5.2 | odd | 4 | |||
800.6.c.j.449.6 | 6 | 5.3 | odd | 4 | |||
800.6.c.k.449.1 | 6 | 20.3 | even | 4 | |||
800.6.c.k.449.6 | 6 | 20.7 | even | 4 |