Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [128,5,Mod(31,128)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(128, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("128.31");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 128 = 2^{7} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 128.f (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(13.2313552747\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Relative dimension: | \(7\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 4 x^{13} + 15 x^{12} - 34 x^{11} + 62 x^{10} - 312 x^{9} + 1432 x^{8} - 4960 x^{7} + 11456 x^{6} - 19968 x^{5} + 31744 x^{4} - 139264 x^{3} + 491520 x^{2} + \cdots + 2097152 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{42} \) |
Twist minimal: | no (minimal twist has level 16) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 31.6 | ||
Root | \(2.24452 - 1.72109i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 128.31 |
Dual form | 128.5.f.a.95.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 5.54016 | + | 5.54016i | 0.615573 | + | 0.615573i | 0.944393 | − | 0.328820i | \(-0.106651\pi\) |
−0.328820 | + | 0.944393i | \(0.606651\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −21.7374 | − | 21.7374i | −0.869495 | − | 0.869495i | 0.122921 | − | 0.992416i | \(-0.460774\pi\) |
−0.992416 | + | 0.122921i | \(0.960774\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 6.62054 | 0.135113 | 0.0675565 | − | 0.997715i | \(-0.478480\pi\) | ||||
0.0675565 | + | 0.997715i | \(0.478480\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 19.6133i | − | 0.242140i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −90.9986 | + | 90.9986i | −0.752054 | + | 0.752054i | −0.974862 | − | 0.222808i | \(-0.928478\pi\) |
0.222808 | + | 0.974862i | \(0.428478\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −221.402 | + | 221.402i | −1.31007 | + | 1.31007i | −0.388707 | + | 0.921362i | \(0.627078\pi\) |
−0.921362 | + | 0.388707i | \(0.872922\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 240.857i | − | 1.07048i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −132.575 | −0.458738 | −0.229369 | − | 0.973339i | \(-0.573666\pi\) | ||||
−0.229369 | + | 0.973339i | \(0.573666\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −402.520 | − | 402.520i | −1.11501 | − | 1.11501i | −0.992462 | − | 0.122552i | \(-0.960892\pi\) |
−0.122552 | − | 0.992462i | \(-0.539108\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 36.6788 | + | 36.6788i | 0.0831720 | + | 0.0831720i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −27.5037 | −0.0519918 | −0.0259959 | − | 0.999662i | \(-0.508276\pi\) | ||||
−0.0259959 | + | 0.999662i | \(0.508276\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 320.028i | 0.512044i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 557.414 | − | 557.414i | 0.764628 | − | 0.764628i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −174.909 | + | 174.909i | −0.207978 | + | 0.207978i | −0.803407 | − | 0.595430i | \(-0.796982\pi\) |
0.595430 | + | 0.803407i | \(0.296982\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 1083.96i | − | 1.12795i | −0.825791 | − | 0.563976i | \(-0.809271\pi\) | ||
0.825791 | − | 0.563976i | \(-0.190729\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1008.29 | −0.925888 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −143.913 | − | 143.913i | −0.117480 | − | 0.117480i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −553.474 | − | 553.474i | −0.404291 | − | 0.404291i | 0.475451 | − | 0.879742i | \(-0.342285\pi\) |
−0.879742 | + | 0.475451i | \(0.842285\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2453.20 | −1.61289 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1803.47i | 1.07285i | 0.843947 | + | 0.536427i | \(0.180226\pi\) | ||||
−0.843947 | + | 0.536427i | \(0.819774\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 17.8633 | − | 17.8633i | 0.00966108 | − | 0.00966108i | −0.702260 | − | 0.711921i | \(-0.747825\pi\) |
0.711921 | + | 0.702260i | \(0.247825\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −426.342 | + | 426.342i | −0.210539 | + | 0.210539i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2268.26i | 1.02683i | 0.858141 | + | 0.513414i | \(0.171620\pi\) | ||||
−0.858141 | + | 0.513414i | \(0.828380\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2357.17 | −0.981744 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −734.489 | − | 734.489i | −0.282387 | − | 0.282387i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 822.415 | + | 822.415i | 0.292779 | + | 0.292779i | 0.838177 | − | 0.545398i | \(-0.183622\pi\) |
−0.545398 | + | 0.838177i | \(0.683622\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3956.14 | 1.30782 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 4460.05i | − | 1.37275i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −972.483 | + | 972.483i | −0.279369 | + | 0.279369i | −0.832857 | − | 0.553488i | \(-0.813296\pi\) |
0.553488 | + | 0.832857i | \(0.313296\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2056.32 | − | 2056.32i | 0.552626 | − | 0.552626i | −0.374572 | − | 0.927198i | \(-0.622210\pi\) |
0.927198 | + | 0.374572i | \(0.122210\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 129.851i | − | 0.0327163i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 9625.38 | 2.27820 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4611.22 | + | 4611.22i | 1.02723 | + | 1.02723i | 0.999619 | + | 0.0276077i | \(0.00878893\pi\) |
0.0276077 | + | 0.999619i | \(0.491211\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −152.375 | − | 152.375i | −0.0320048 | − | 0.0320048i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3105.84 | 0.616115 | 0.308058 | − | 0.951368i | \(-0.400321\pi\) | ||||
0.308058 | + | 0.951368i | \(0.400321\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 723.400i | − | 0.135748i | −0.997694 | − | 0.0678739i | \(-0.978378\pi\) | ||
0.997694 | − | 0.0678739i | \(-0.0216216\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1773.00 | + | 1773.00i | −0.315200 | + | 0.315200i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −602.460 | + | 602.460i | −0.101612 | + | 0.101612i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 3418.44i | − | 0.547739i | −0.961767 | − | 0.273869i | \(-0.911696\pi\) | ||
0.961767 | − | 0.273869i | \(-0.0883036\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4587.64 | 0.699228 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −161.591 | − | 161.591i | −0.0234563 | − | 0.0234563i | 0.695281 | − | 0.718738i | \(-0.255280\pi\) |
−0.718738 | + | 0.695281i | \(0.755280\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2881.84 | + | 2881.84i | 0.398871 | + | 0.398871i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1938.05 | −0.256051 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1464.04i | 0.184830i | 0.995721 | + | 0.0924150i | \(0.0294586\pi\) | ||||
−0.995721 | + | 0.0924150i | \(0.970541\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1465.80 | + | 1465.80i | −0.177007 | + | 0.177007i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6005.32 | − | 6005.32i | 0.694337 | − | 0.694337i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 17499.5i | 1.93900i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8264.99 | −0.878413 | −0.439207 | − | 0.898386i | \(-0.644740\pi\) | ||||
−0.439207 | + | 0.898386i | \(0.644740\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1784.78 | + | 1784.78i | 0.182102 | + | 0.182102i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5035.04 | − | 5035.04i | −0.493583 | − | 0.493583i | 0.415850 | − | 0.909433i | \(-0.363484\pi\) |
−0.909433 | + | 0.415850i | \(0.863484\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1427.24 | −0.134531 | −0.0672653 | − | 0.997735i | \(-0.521427\pi\) | ||||
−0.0672653 | + | 0.997735i | \(0.521427\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 1594.60i | − | 0.144635i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9978.53 | − | 9978.53i | 0.871564 | − | 0.871564i | −0.121079 | − | 0.992643i | \(-0.538635\pi\) |
0.992643 | + | 0.121079i | \(0.0386355\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.47842 | + | 9.47842i | −0.000797780 | + | 0.000797780i | −0.707506 | − | 0.706708i | \(-0.750180\pi\) |
0.706708 | + | 0.707506i | \(0.250180\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 6132.67i | − | 0.497741i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13634.7 | −1.06780 | −0.533900 | − | 0.845548i | \(-0.679274\pi\) | ||||
−0.533900 | + | 0.845548i | \(0.679274\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 597.858 | + | 597.858i | 0.0452067 | + | 0.0452067i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4342.42 | + | 4342.42i | 0.317220 | + | 0.317220i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −877.721 | −0.0619816 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 1920.47i | − | 0.131171i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −9991.49 | + | 9991.49i | −0.660419 | + | 0.660419i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6629.30 | + | 6629.30i | −0.424275 | + | 0.424275i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 8047.14i | − | 0.498923i | −0.968385 | − | 0.249462i | \(-0.919746\pi\) | ||
0.968385 | − | 0.249462i | \(-0.0802537\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 197.931 | 0.0118942 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15904.8 | − | 15904.8i | −0.926799 | − | 0.926799i | 0.0706991 | − | 0.997498i | \(-0.477477\pi\) |
−0.997498 | + | 0.0706991i | \(0.977477\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2664.90 | − | 2664.90i | −0.150653 | − | 0.150653i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −24233.4 | −1.32968 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 31169.3i | 1.66068i | 0.557257 | + | 0.830340i | \(0.311854\pi\) | ||||
−0.557257 | + | 0.830340i | \(0.688146\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 21432.1 | − | 21432.1i | 1.10926 | − | 1.10926i | 0.116017 | − | 0.993247i | \(-0.462987\pi\) |
0.993247 | − | 0.116017i | \(-0.0370126\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −12566.5 | + | 12566.5i | −0.632088 | + | 0.632088i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 40294.4i | − | 1.97048i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7604.14 | 0.361671 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −13059.1 | − | 13059.1i | −0.604335 | − | 0.604335i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −11772.7 | − | 11772.7i | −0.530276 | − | 0.530276i | 0.390378 | − | 0.920654i | \(-0.372344\pi\) |
−0.920654 | + | 0.390378i | \(0.872344\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19454.9 | 0.853246 | 0.426623 | − | 0.904429i | \(-0.359703\pi\) | ||||
0.426623 | + | 0.904429i | \(0.359703\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2600.25i | 0.111079i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −23562.5 | + | 23562.5i | −0.980749 | + | 0.980749i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18097.5 | + | 18097.5i | −0.734208 | + | 0.734208i | −0.971450 | − | 0.237242i | \(-0.923756\pi\) |
0.237242 | + | 0.971450i | \(0.423756\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9112.62i | 0.360453i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −182.089 | −0.00702478 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17673.1 | + | 17673.1i | 0.665178 | + | 0.665178i | 0.956596 | − | 0.291418i | \(-0.0941270\pi\) |
−0.291418 | + | 0.956596i | \(0.594127\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 21917.6 | + | 21917.6i | 0.805056 | + | 0.805056i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11374.1 | 0.407834 | 0.203917 | − | 0.978988i | \(-0.434633\pi\) | ||||
0.203917 | + | 0.978988i | \(0.434633\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 69476.3i | − | 2.43256i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7894.76 | + | 7894.76i | −0.269989 | + | 0.269989i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11289.3 | − | 11289.3i | 0.377204 | − | 0.377204i | −0.492888 | − | 0.870092i | \(-0.664059\pi\) |
0.870092 | + | 0.492888i | \(0.164059\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2118.76i | 0.0691838i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −10775.4 | −0.343944 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −25338.8 | − | 25338.8i | −0.790825 | − | 0.790825i | 0.190803 | − | 0.981628i | \(-0.438891\pi\) |
−0.981628 | + | 0.190803i | \(0.938891\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −22579.8 | − | 22579.8i | −0.689228 | − | 0.689228i | 0.272833 | − | 0.962061i | \(-0.412039\pi\) |
−0.962061 | + | 0.272833i | \(0.912039\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 22784.7 | 0.680363 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 24062.2i | 0.703058i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12064.2 | − | 12064.2i | 0.344996 | − | 0.344996i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3690.38 | − | 3690.38i | 0.103311 | − | 0.103311i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 62994.4i | 1.72677i | 0.504543 | + | 0.863386i | \(0.331661\pi\) | ||||
−0.504543 | + | 0.863386i | \(0.668339\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −25039.7 | −0.672225 | −0.336112 | − | 0.941822i | \(-0.609112\pi\) | ||||
−0.336112 | + | 0.941822i | \(0.609112\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 53326.1 | + | 53326.1i | 1.40240 | + | 1.40240i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6468.96 | + | 6468.96i | 0.166687 | + | 0.166687i | 0.785521 | − | 0.618834i | \(-0.212395\pi\) |
−0.618834 | + | 0.785521i | \(0.712395\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −55793.6 | −1.40889 | −0.704446 | − | 0.709757i | \(-0.748805\pi\) | ||||
−0.704446 | + | 0.709757i | \(0.748805\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 51093.8i | 1.26467i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1157.99 | + | 1157.99i | −0.0281005 | + | 0.0281005i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 39202.6 | − | 39202.6i | 0.932841 | − | 0.932841i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 539.439i | 0.0125893i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 73257.5 | 1.67710 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11403.6 | − | 11403.6i | −0.256139 | − | 0.256139i | 0.567343 | − | 0.823482i | \(-0.307971\pi\) |
−0.823482 | + | 0.567343i | \(0.807971\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 17206.8 | + | 17206.8i | 0.379264 | + | 0.379264i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −776.604 | −0.0168005 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 7176.41i | − | 0.152401i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4007.75 | − | 4007.75i | 0.0835627 | − | 0.0835627i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 29352.4 | − | 29352.4i | 0.600979 | − | 0.600979i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 15194.4i | − | 0.305545i | −0.988261 | − | 0.152772i | \(-0.951180\pi\) | ||
0.988261 | − | 0.152772i | \(-0.0488201\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6276.81 | 0.123986 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 47509.0 | + | 47509.0i | 0.921986 | + | 0.921986i | 0.997170 | − | 0.0751841i | \(-0.0239544\pi\) |
−0.0751841 | + | 0.997170i | \(0.523954\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15628.9 | − | 15628.9i | −0.298028 | − | 0.298028i | 0.542213 | − | 0.840241i | \(-0.317587\pi\) |
−0.840241 | + | 0.542213i | \(0.817587\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6675.44 | −0.125100 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 63151.2i | − | 1.16324i | −0.813460 | − | 0.581621i | \(-0.802419\pi\) | ||
0.813460 | − | 0.581621i | \(-0.197581\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 49306.1 | − | 49306.1i | 0.892823 | − | 0.892823i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 18938.7 | − | 18938.7i | 0.337173 | − | 0.337173i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 33331.4i | 0.583522i | 0.956491 | + | 0.291761i | \(0.0942412\pi\) | ||||
−0.956491 | + | 0.291761i | \(0.905759\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5625.72 | 0.0968599 | 0.0484299 | − | 0.998827i | \(-0.484578\pi\) | ||||
0.0484299 | + | 0.998827i | \(0.484578\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −19734.3 | − | 19734.3i | −0.334202 | − | 0.334202i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 51238.7 | + | 51238.7i | 0.853622 | + | 0.853622i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 178237. | 2.92149 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 1790.47i | − | 0.0288782i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −62195.0 | + | 62195.0i | −0.987206 | + | 0.987206i | −0.999919 | − | 0.0127130i | \(-0.995953\pi\) |
0.0127130 | + | 0.999919i | \(0.495953\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2502.80 | − | 2502.80i | 0.0391007 | − | 0.0391007i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 31931.7i | 0.491068i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 22791.9 | 0.345075 | 0.172538 | − | 0.985003i | \(-0.444803\pi\) | ||||
0.172538 | + | 0.985003i | \(0.444803\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3664.30 | − | 3664.30i | −0.0546250 | − | 0.0546250i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3430.55 | + | 3430.55i | 0.0503597 | + | 0.0503597i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −126611. | −1.83047 | −0.915233 | − | 0.402926i | \(-0.867993\pi\) | ||||
−0.915233 | + | 0.402926i | \(0.867993\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 35754.3i | − | 0.509139i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8111.00 | + | 8111.00i | −0.113776 | + | 0.113776i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −65428.7 | + | 65428.7i | −0.904198 | + | 0.904198i | −0.995796 | − | 0.0915982i | \(-0.970802\pi\) |
0.0915982 | + | 0.995796i | \(0.470802\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 93429.2i | − | 1.27217i | −0.771621 | − | 0.636083i | \(-0.780554\pi\) | ||
0.771621 | − | 0.636083i | \(-0.219446\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −16241.5 | −0.217922 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −29122.0 | − | 29122.0i | −0.385085 | − | 0.385085i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −105271. | − | 105271.i | −1.37198 | − | 1.37198i | −0.857504 | − | 0.514477i | \(-0.827986\pi\) |
−0.514477 | − | 0.857504i | \(-0.672014\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −21260.1 | −0.273122 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 42955.1i | 0.544004i | 0.962297 | + | 0.272002i | \(0.0876857\pi\) | ||||
−0.962297 | + | 0.272002i | \(0.912314\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −36538.7 | + | 36538.7i | −0.456226 | + | 0.456226i | −0.897414 | − | 0.441189i | \(-0.854557\pi\) |
0.441189 | + | 0.897414i | \(0.354557\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −96949.8 | + | 96949.8i | −1.19360 | + | 1.19360i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11939.9i | 0.144957i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −65944.8 | −0.789559 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −45789.3 | − | 45789.3i | −0.540727 | − | 0.540727i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 45359.7 | + | 45359.7i | 0.528367 | + | 0.528367i | 0.920085 | − | 0.391719i | \(-0.128119\pi\) |
−0.391719 | + | 0.920085i | \(0.628119\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 42278.5 | 0.485820 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 101448.i | 1.15008i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6089.36 | − | 6089.36i | 0.0681129 | − | 0.0681129i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 118.265 | − | 118.265i | 0.00130534 | − | 0.00130534i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 55789.9i | − | 0.607673i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −89398.0 | −0.961011 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10035.4 | − | 10035.4i | −0.106478 | − | 0.106478i | 0.651861 | − | 0.758339i | \(-0.273989\pi\) |
−0.758339 | + | 0.651861i | \(0.773989\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7907.11 | − | 7907.11i | −0.0828134 | − | 0.0828134i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −102401. | −1.05873 | −0.529365 | − | 0.848394i | \(-0.677570\pi\) | ||||
−0.529365 | + | 0.848394i | \(0.677570\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 60933.1i | − | 0.621963i | −0.950416 | − | 0.310981i | \(-0.899342\pi\) | ||
0.950416 | − | 0.310981i | \(-0.100658\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2822.62 | + | 2822.62i | −0.0284466 | + | 0.0284466i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10217.2 | − | 10217.2i | 0.101675 | − | 0.101675i | −0.654439 | − | 0.756115i | \(-0.727095\pi\) |
0.756115 | + | 0.654439i | \(0.227095\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 31833.0i | − | 0.312821i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 110565. | 1.07302 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 53364.3 | + | 53364.3i | 0.511500 | + | 0.511500i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −70854.6 | − | 70854.6i | −0.670813 | − | 0.670813i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −105.024 | −0.000982183 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 15017.1i | 0.138738i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 123603. | − | 123603.i | 1.12817 | − | 1.12817i | 0.137692 | − | 0.990475i | \(-0.456032\pi\) |
0.990475 | − | 0.137692i | \(-0.0439684\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −10855.5 | + | 10855.5i | −0.0978949 | + | 0.0978949i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 200472.i | − | 1.78634i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −102441. | −0.902018 | −0.451009 | − | 0.892519i | \(-0.648936\pi\) | ||||
−0.451009 | + | 0.892519i | \(0.648936\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −75538.6 | − | 75538.6i | −0.657309 | − | 0.657309i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 98639.0 | + | 98639.0i | 0.848281 | + | 0.848281i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −31501.6 | −0.267760 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 6624.45i | 0.0556560i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 63342.4 | − | 63342.4i | 0.526061 | − | 0.526061i | −0.393335 | − | 0.919395i | \(-0.628679\pi\) |
0.919395 | + | 0.393335i | \(0.128679\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 114645. | − | 114645.i | 0.941247 | − | 0.941247i | −0.0571205 | − | 0.998367i | \(-0.518192\pi\) |
0.998367 | + | 0.0571205i | \(0.0181919\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 246824.i | 2.00343i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −94430.7 | −0.757816 | −0.378908 | − | 0.925434i | \(-0.623700\pi\) | ||||
−0.378908 | + | 0.925434i | \(0.623700\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −67512.8 | − | 67512.8i | −0.535709 | − | 0.535709i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4862.71 | − | 4862.71i | −0.0381542 | − | 0.0381542i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 59001.0 | 0.457794 | 0.228897 | − | 0.973451i | \(-0.426488\pi\) | ||||
0.228897 | + | 0.973451i | \(0.426488\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 193724.i | 1.48651i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10639.7 | − | 10639.7i | 0.0807453 | − | 0.0807453i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −15724.8 | + | 15724.8i | −0.118032 | + | 0.118032i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 120112.i | 0.891775i | 0.895089 | + | 0.445888i | \(0.147112\pi\) | ||||
−0.895089 | + | 0.445888i | \(0.852888\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 35372.0 | 0.259781 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5444.83 | + | 5444.83i | 0.0395582 | + | 0.0395582i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 113849. | + | 113849.i | 0.818300 | + | 0.818300i | 0.985862 | − | 0.167562i | \(-0.0535894\pi\) |
−0.167562 | + | 0.985862i | \(0.553589\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −73454.7 | −0.522345 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 77450.4i | − | 0.544930i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −75841.4 | + | 75841.4i | −0.527993 | + | 0.527993i | −0.919973 | − | 0.391981i | \(-0.871790\pi\) |
0.391981 | + | 0.919973i | \(0.371790\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 44582.4 | − | 44582.4i | 0.307124 | − | 0.307124i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 80282.4i | − | 0.547297i | −0.961830 | − | 0.273648i | \(-0.911770\pi\) | ||
0.961830 | − | 0.273648i | \(-0.0882304\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 26191.8 | 0.176703 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −350.360 | − | 350.360i | −0.00233933 | − | 0.00233933i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −89476.2 | − | 89476.2i | −0.591301 | − | 0.591301i | 0.346682 | − | 0.937983i | \(-0.387308\pi\) |
−0.937983 | + | 0.346682i | \(0.887308\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3646.31 | 0.0238507 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 176230.i | − | 1.14102i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −74307.8 | + | 74307.8i | −0.476256 | + | 0.476256i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −128824. | + | 128824.i | −0.817363 | + | 0.817363i | −0.985725 | − | 0.168362i | \(-0.946152\pi\) |
0.168362 | + | 0.985725i | \(0.446152\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 29527.9i | − | 0.185476i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 71110.1 | 0.442224 | 0.221112 | − | 0.975248i | \(-0.429031\pi\) | ||||
0.221112 | + | 0.975248i | \(0.429031\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 239991. | + | 239991.i | 1.47769 | + | 1.47769i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −99723.2 | − | 99723.2i | −0.607976 | − | 0.607976i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 100731. | 0.608097 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 87416.4i | − | 0.522572i | −0.965261 | − | 0.261286i | \(-0.915853\pi\) | ||
0.965261 | − | 0.261286i | \(-0.0841466\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −172683. | + | 172683.i | −1.02227 | + | 1.02227i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6438.36 | + | 6438.36i | −0.0377464 | + | 0.0377464i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7025.11i | 0.0407903i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 237474. | 1.36567 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 156666. | + | 156666.i | 0.892373 | + | 0.892373i | 0.994746 | − | 0.102373i | \(-0.0326436\pi\) |
−0.102373 | + | 0.994746i | \(0.532644\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20636.7 | − | 20636.7i | −0.116433 | − | 0.116433i | 0.646490 | − | 0.762923i | \(-0.276236\pi\) |
−0.762923 | + | 0.646490i | \(0.776236\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 44488.2 | 0.248636 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 42427.8i | − | 0.234894i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13614.0 | − | 13614.0i | 0.0746670 | − | 0.0746670i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 223238. | − | 223238.i | 1.21298 | − | 1.21298i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 294349.i | 1.58456i | 0.610160 | + | 0.792279i | \(0.291105\pi\) | ||||
−0.610160 | + | 0.792279i | \(0.708895\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 240460. | 1.28253 | 0.641264 | − | 0.767321i | \(-0.278411\pi\) | ||||
0.641264 | + | 0.767321i | \(0.278411\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 42128.1 | + | 42128.1i | 0.222635 | + | 0.222635i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 11070.8 | + | 11070.8i | 0.0579716 | + | 0.0579716i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 294699. | 1.52915 | 0.764574 | − | 0.644536i | \(-0.222949\pi\) | ||||
0.764574 | + | 0.644536i | \(0.222949\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 46231.9i | 0.237719i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 118964. | − | 118964.i | 0.606187 | − | 0.606187i | −0.335760 | − | 0.941948i | \(-0.608993\pi\) |
0.941948 | + | 0.335760i | \(0.108993\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 31824.4 | − | 31824.4i | 0.160709 | − | 0.160709i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 130445.i | − | 0.652847i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −82129.5 | −0.407386 | −0.203693 | − | 0.979035i | \(-0.565294\pi\) | ||||
−0.203693 | + | 0.979035i | \(0.565294\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −164113. | − | 164113.i | −0.806844 | − | 0.806844i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 107783. | + | 107783.i | 0.525235 | + | 0.525235i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 63725.2 | 0.307814 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 172358.i | − | 0.825277i | −0.910895 | − | 0.412638i | \(-0.864607\pi\) | ||
0.910895 | − | 0.412638i | \(-0.135393\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −73899.3 | + | 73899.3i | −0.350764 | + | 0.350764i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −96898.8 | + | 96898.8i | −0.455950 | + | 0.455950i | −0.897323 | − | 0.441374i | \(-0.854491\pi\) |
0.441374 | + | 0.897323i | \(0.354491\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 142244.i | 0.663549i | 0.943359 | + | 0.331775i | \(0.107647\pi\) | ||||
−0.943359 | + | 0.331775i | \(0.892353\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −261080. | −1.20745 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −139194. | − | 139194.i | −0.638246 | − | 0.638246i | 0.311877 | − | 0.950123i | \(-0.399042\pi\) |
−0.950123 | + | 0.311877i | \(0.899042\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 30528.8 | + | 30528.8i | 0.138792 | + | 0.138792i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −200526. | −0.903917 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3251.08i | 0.0145313i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 128818. | − | 128818.i | 0.570936 | − | 0.570936i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 16130.3 | − | 16130.3i | 0.0708934 | − | 0.0708934i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 216764.i | − | 0.944749i | −0.881398 | − | 0.472374i | \(-0.843397\pi\) | ||
0.881398 | − | 0.472374i | \(-0.156603\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 245080. | 1.05930 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1008.80 | − | 1008.80i | −0.00432426 | − | 0.00432426i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 179659. | + | 179659.i | 0.763776 | + | 0.763776i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −146986. | −0.619752 | −0.309876 | − | 0.950777i | \(-0.600287\pi\) | ||||
−0.309876 | + | 0.950777i | \(0.600287\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 195824.i | 0.818931i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −207292. | + | 207292.i | −0.859843 | + | 0.859843i | −0.991319 | − | 0.131476i | \(-0.958028\pi\) |
0.131476 | + | 0.991319i | \(0.458028\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 23188.7 | − | 23188.7i | 0.0954074 | − | 0.0954074i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 77593.1i | − | 0.316674i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 20562.3 | 0.0832452 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5591.76 | + | 5591.76i | 0.0224568 | + | 0.0224568i | 0.718246 | − | 0.695789i | \(-0.244945\pi\) |
−0.695789 | + | 0.718246i | \(0.744945\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 63014.2 | + | 63014.2i | 0.251051 | + | 0.251051i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −154345. | −0.610037 | −0.305018 | − | 0.952346i | \(-0.598663\pi\) | ||||
−0.305018 | + | 0.952346i | \(0.598663\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 218897.i | 0.858337i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 384909. | − | 384909.i | 1.49742 | − | 1.49742i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7996.84 | − | 7996.84i | 0.0308662 | − | 0.0308662i | −0.691505 | − | 0.722371i | \(-0.743052\pi\) |
0.722371 | + | 0.691505i | \(0.243052\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 4789.30i | − | 0.0183413i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −448740. | −1.70514 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 31024.4 | + | 31024.4i | 0.116974 | + | 0.116974i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −206409. | − | 206409.i | −0.772231 | − | 0.772231i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 125089. | 0.464393 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 215831.i | 0.795130i | 0.917574 | + | 0.397565i | \(0.130145\pi\) | ||||
−0.917574 | + | 0.397565i | \(0.869855\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −73690.2 | + | 73690.2i | −0.269405 | + | 0.269405i | −0.828861 | − | 0.559455i | \(-0.811010\pi\) |
0.559455 | + | 0.828861i | \(0.311010\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −11738.2 | + | 11738.2i | −0.0425877 | + | 0.0425877i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 143707.i | 0.517435i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −279085. | −0.997297 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 19073.6 | + | 19073.6i | 0.0676464 | + | 0.0676464i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −399290. | − | 399290.i | −1.40551 | − | 1.40551i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −433814. | −1.51564 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 280762.i | − | 0.973622i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 214499. | − | 214499.i | 0.738325 | − | 0.738325i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −260589. | + | 260589.i | −0.890352 | + | 0.890352i | −0.994556 | − | 0.104204i | \(-0.966771\pi\) |
0.104204 | + | 0.994556i | \(0.466771\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 250191.i | − | 0.848540i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 412.072 | 0.00138733 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −87290.1 | − | 87290.1i | −0.291736 | − | 0.291736i | 0.546030 | − | 0.837766i | \(-0.316139\pi\) |
−0.837766 | + | 0.546030i | \(0.816139\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −40331.3 | − | 40331.3i | −0.133813 | − | 0.133813i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 140809. | 0.463796 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 22631.9i | − | 0.0740066i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −133308. | + | 133308.i | −0.432783 | + | 0.432783i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 342322. | − | 342322.i | 1.10338 | − | 1.10338i | 0.109377 | − | 0.994000i | \(-0.465114\pi\) |
0.994000 | − | 0.109377i | \(-0.0348855\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7909.94i | 0.0253134i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 133675. | 0.424741 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −77521.3 | − | 77521.3i | −0.244571 | − | 0.244571i | 0.574167 | − | 0.818738i | \(-0.305326\pi\) |
−0.818738 | + | 0.574167i | \(0.805326\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 296383. | + | 296383.i | 0.928447 | + | 0.928447i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 30372.6 | 0.0944749 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 304409.i | 0.940229i | 0.882605 | + | 0.470115i | \(0.155787\pi\) | ||||
−0.882605 | + | 0.470115i | \(0.844213\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −254051. | + | 254051.i | −0.779201 | + | 0.779201i | −0.979695 | − | 0.200494i | \(-0.935745\pi\) |
0.200494 | + | 0.979695i | \(0.435745\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −348999. | + | 348999.i | −1.06295 | + | 1.06295i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 8801.94i | − | 0.0266221i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −486229. | −1.46046 | −0.730229 | − | 0.683202i | \(-0.760587\pi\) | ||||
−0.730229 | + | 0.683202i | \(0.760587\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −138724. | − | 138724.i | −0.413803 | − | 0.413803i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1069.82 | − | 1069.82i | −0.00316926 | − | 0.00316926i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −149677. | −0.440371 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 188786.i | − | 0.551642i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −26612.4 | + | 26612.4i | −0.0772339 | + | 0.0772339i | −0.744668 | − | 0.667435i | \(-0.767392\pi\) |
0.667435 | + | 0.744668i | \(0.267392\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −436317. | + | 436317.i | −1.25768 | + | 1.25768i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 71678.1i | 0.205216i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 301795. | 0.858228 | 0.429114 | − | 0.903250i | \(-0.358826\pi\) | ||||
0.429114 | + | 0.903250i | \(0.358826\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 19079.4 | + | 19079.4i | 0.0538927 | + | 0.0538927i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −309105. | − | 309105.i | −0.867276 | − | 0.867276i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 208748. | 0.581795 | 0.290897 | − | 0.956754i | \(-0.406046\pi\) | ||||
0.290897 | + | 0.956754i | \(0.406046\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 355946.i | 0.985451i | 0.870185 | + | 0.492725i | \(0.163999\pi\) | ||||
−0.870185 | + | 0.492725i | \(0.836001\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 90441.4 | − | 90441.4i | 0.248733 | − | 0.248733i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −41746.1 | + | 41746.1i | −0.114053 | + | 0.114053i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 680696.i | − | 1.84746i | −0.383040 | − | 0.923732i | \(-0.625123\pi\) | ||
0.383040 | − | 0.923732i | \(-0.374877\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −12830.9 | −0.0345958 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −502197. | − | 502197.i | −1.34522 | − | 1.34522i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 504818. | + | 504818.i | 1.34343 | + | 1.34343i | 0.892625 | + | 0.450800i | \(0.148861\pi\) |
0.450800 | + | 0.892625i | \(0.351139\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 434378. | 1.14846 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 601668.i | − | 1.58047i | −0.612803 | − | 0.790236i | \(-0.709958\pi\) | ||
0.612803 | − | 0.790236i | \(-0.290042\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −34687.6 | + | 34687.6i | −0.0905300 | + | 0.0905300i | −0.750922 | − | 0.660391i | \(-0.770390\pi\) |
0.660391 | + | 0.750922i | \(0.270390\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −15330.9 | + | 15330.9i | −0.0397544 | + | 0.0397544i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9692.72i | 0.0249729i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 488225. | 1.24985 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 405858. | + | 405858.i | 1.03238 | + | 1.03238i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 73377.0 | + | 73377.0i | 0.185464 | + | 0.185464i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −557209. | −1.39946 | −0.699728 | − | 0.714409i | \(-0.746696\pi\) | ||||
−0.699728 | + | 0.714409i | \(0.746696\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 126355.i | − | 0.315345i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −174924. | + | 174924.i | −0.433812 | + | 0.433812i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 521881. | − | 521881.i | 1.28615 | − | 1.28615i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 60915.8i | − | 0.149186i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 354670. | 0.863193 | 0.431597 | − | 0.902067i | \(-0.357950\pi\) | ||||
0.431597 | + | 0.902067i | \(0.357950\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −89105.3 | − | 89105.3i | −0.215517 | − | 0.215517i | 0.591089 | − | 0.806606i | \(-0.298698\pi\) |
−0.806606 | + | 0.591089i | \(0.798698\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4302.51 | − | 4302.51i | −0.0103420 | − | 0.0103420i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 669197. | 1.59862 | 0.799311 | − | 0.600918i | \(-0.205198\pi\) | ||||
0.799311 | + | 0.600918i | \(0.205198\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 176989.i | − | 0.420201i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 39758.5 | − | 39758.5i | 0.0938140 | − | 0.0938140i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6136.50 | + | 6136.50i | −0.0143911 | + | 0.0143911i | −0.714266 | − | 0.699875i | \(-0.753239\pi\) |
0.699875 | + | 0.714266i | \(0.253239\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 691457.i | 1.61169i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −14188.3 | −0.0328700 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 484888. | + | 484888.i | 1.11653 | + | 1.11653i | 0.992247 | + | 0.124283i | \(0.0396632\pi\) |
0.124283 | + | 0.992247i | \(0.460337\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 71185.1 | + | 71185.1i | 0.162924 | + | 0.162924i | 0.783861 | − | 0.620937i | \(-0.213248\pi\) |
−0.620937 | + | 0.783861i | \(0.713248\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 325234. | 0.739892 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 115856.i | 0.261984i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4810.65 | − | 4810.65i | 0.0108131 | − | 0.0108131i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 84179.5 | − | 84179.5i | 0.188085 | − | 0.188085i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 374244.i | 0.831209i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 116807. | 0.257893 | 0.128947 | − | 0.991652i | \(-0.458840\pi\) | ||||
0.128947 | + | 0.991652i | \(0.458840\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 178388. | + | 178388.i | 0.391523 | + | 0.391523i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −562443. | − | 562443.i | −1.22716 | − | 1.22716i | −0.965033 | − | 0.262127i | \(-0.915576\pi\) |
−0.262127 | − | 0.965033i | \(-0.584424\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −54718.7 | −0.118685 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 526415.i | 1.13510i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 392290. | − | 392290.i | 0.840941 | − | 0.840941i | −0.148040 | − | 0.988981i | \(-0.547297\pi\) |
0.988981 | + | 0.148040i | \(0.0472965\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 677539. | − | 677539.i | 1.44395 | − | 1.44395i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 173173.i | − | 0.366916i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −364168. | −0.767120 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 424716. | + | 424716.i | 0.889493 | + | 0.889493i | 0.994474 | − | 0.104981i | \(-0.0334781\pi\) |
−0.104981 | + | 0.994474i | \(0.533478\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 11816.2 | + | 11816.2i | 0.0246044 | + | 0.0246044i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −931755. | −1.92900 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 239095.i | − | 0.492159i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 349868. | − | 349868.i | 0.716060 | − | 0.716060i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 92393.5 | − | 92393.5i | 0.188021 | − | 0.188021i | −0.606819 | − | 0.794840i | \(-0.707555\pi\) |
0.794840 | + | 0.606819i | \(0.207555\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 445569.i | 0.901580i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 546327. | 1.09920 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −33334.7 | − | 33334.7i | −0.0666896 | − | 0.0666896i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −29997.3 | − | 29997.3i | −0.0596746 | − | 0.0596746i | 0.676640 | − | 0.736314i | \(-0.263435\pi\) |
−0.736314 | + | 0.676640i | \(0.763435\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −67046.9 | −0.132629 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 29812.9i | 0.0586443i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −875896. | + | 875896.i | −1.71333 | + | 1.71333i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −184661. | + | 184661.i | −0.359200 | + | 0.359200i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 284133.i | 0.549622i | 0.961498 | + | 0.274811i | \(0.0886152\pi\) | ||||
−0.961498 | + | 0.274811i | \(0.911385\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9449.07 | −0.0181769 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 31167.4 | + | 31167.4i | 0.0596243 | + | 0.0596243i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −55975.8 | − | 55975.8i | −0.106494 | − | 0.106494i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −39096.3 | −0.0739719 | −0.0369860 | − | 0.999316i | \(-0.511776\pi\) | ||||
−0.0369860 | + | 0.999316i | \(0.511776\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 590261.i | − | 1.11068i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2368.24 | + | 2368.24i | −0.00443191 | + | 0.00443191i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −82927.3 | + | 82927.3i | −0.154344 | + | 0.154344i | −0.780055 | − | 0.625711i | \(-0.784809\pi\) |
0.625711 | + | 0.780055i | \(0.284809\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 567741.i | 1.05093i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −839229. | −1.54506 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −97643.8 | − | 97643.8i | −0.178795 | − | 0.178795i | 0.612035 | − | 0.790830i | \(-0.290351\pi\) |
−0.790830 | + | 0.612035i | \(0.790351\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 987462. | + | 987462.i | 1.79839 | + | 1.79839i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 552181. | 1.00024 | 0.500120 | − | 0.865956i | \(-0.333289\pi\) | ||||
0.500120 | + | 0.865956i | \(0.333289\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 511813.i | 0.922145i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3169.33 | + | 3169.33i | −0.00567971 | + | 0.00567971i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 66063.3 | − | 66063.3i | 0.117760 | − | 0.117760i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 318447.i | − | 0.564621i | −0.959323 | − | 0.282310i | \(-0.908899\pi\) | ||
0.959323 | − | 0.282310i | \(-0.0911008\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −689140. | −1.21539 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −422898. | − | 422898.i | −0.741894 | − | 0.741894i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 478701. | + | 478701.i | 0.835357 | + | 0.835357i | 0.988244 | − | 0.152886i | \(-0.0488569\pi\) |
−0.152886 | + | 0.988244i | \(0.548857\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 27731.8 | 0.0481386 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 398315.i | − | 0.687793i | −0.939008 | − | 0.343896i | \(-0.888253\pi\) | ||
0.939008 | − | 0.343896i | \(-0.111747\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −62.7523 | + | 62.7523i | −0.000107790 | + | 0.000107790i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 56522.5 | − | 56522.5i | 0.0965826 | − | 0.0965826i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 430619.i | − | 0.731985i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 658868. | 1.11416 | 0.557078 | − | 0.830460i | \(-0.311922\pi\) | ||||
0.557078 | + | 0.830460i | \(0.311922\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 126271. | + | 126271.i | 0.212419 | + | 0.212419i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −833367. | − | 833367.i | −1.39469 | − | 1.39469i | −0.814439 | − | 0.580250i | \(-0.802955\pi\) |
−0.580250 | − | 0.814439i | \(-0.697045\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 346898. | 0.577561 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 40601.6i | − | 0.0672513i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 725932. | − | 725932.i | 1.19625 | − | 1.19625i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −282627. | + | 282627.i | −0.463352 | + | 0.463352i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 194994.i | 0.318051i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 786784. | 1.27678 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −265518. | − | 265518.i | −0.428691 | − | 0.428691i | 0.459491 | − | 0.888182i | \(-0.348032\pi\) |
−0.888182 | + | 0.459491i | \(0.848032\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −701447. | − | 701447.i | −1.12679 | − | 1.12679i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −90269.3 | −0.144274 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 910545.i | 1.44795i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 198084. | − | 198084.i | 0.313412 | − | 0.313412i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −51155.1 | + | 51155.1i | −0.0805327 | + | 0.0805327i | −0.746226 | − | 0.665693i | \(-0.768136\pi\) |
0.665693 | + | 0.746226i | \(0.268136\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 300716.i | − | 0.471046i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 28714.7 | 0.0447547 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 65828.4 | + | 65828.4i | 0.102090 | + | 0.102090i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3958.14 | + | 3958.14i | 0.00610801 | + | 0.00610801i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −724970. | −1.11320 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 608654.i | − | 0.929979i | −0.885316 | − | 0.464990i | \(-0.846058\pi\) | ||
0.885316 | − | 0.464990i | \(-0.153942\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −693367. | + | 693367.i | −1.05420 | + | 1.05420i | −0.0557512 | + | 0.998445i | \(0.517755\pi\) |
−0.998445 | + | 0.0557512i | \(0.982245\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 517612. | − | 517612.i | 0.783111 | − | 0.783111i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 768335.i | − | 1.15674i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −14380.7 | −0.0215445 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 28749.2 | + | 28749.2i | 0.0428605 | + | 0.0428605i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 843960. | + | 843960.i | 1.25209 | + | 1.25209i | 0.954781 | + | 0.297308i | \(0.0960890\pi\) |
0.297308 | + | 0.954781i | \(0.403911\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 562057. | 0.829815 | 0.414907 | − | 0.909864i | \(-0.363814\pi\) | ||||
0.414907 | + | 0.909864i | \(0.363814\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 322681.i | − | 0.474096i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 49278.3 | − | 49278.3i | 0.0720518 | − | 0.0720518i | −0.670163 | − | 0.742214i | \(-0.733776\pi\) |
0.742214 | + | 0.670163i | \(0.233776\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −519755. | + | 519755.i | −0.756291 | + | 0.756291i | −0.975645 | − | 0.219354i | \(-0.929605\pi\) |
0.219354 | + | 0.975645i | \(0.429605\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 1.16643e6i | − | 1.68911i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 312503. | 0.450364 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −247243. | − | 247243.i | −0.354610 | − | 0.354610i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −604215. | − | 604215.i | −0.862464 | − | 0.862464i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 311968. | 0.443186 | 0.221593 | − | 0.975139i | \(-0.428874\pi\) | ||||
0.221593 | + | 0.975139i | \(0.428874\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 646094.i | 0.913491i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −237978. | + | 237978.i | −0.334874 | + | 0.334874i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.51023e6 | + | 1.51023e6i | −2.11510 | + | 2.11510i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 12714.6i | − | 0.0177229i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −404860. | −0.561681 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 15222.6 | + | 15222.6i | 0.0210198 | + | 0.0210198i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −306461. | − | 306461.i | −0.421190 | − | 0.421190i | 0.464424 | − | 0.885613i | \(-0.346262\pi\) |
−0.885613 | + | 0.464424i | \(0.846262\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 343223. | 0.469509 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 16157.2i | − | 0.0219991i | −0.999940 | − | 0.0109995i | \(-0.996499\pi\) | ||
0.999940 | − | 0.0109995i | \(-0.00350133\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 74800.4 | − | 74800.4i | 0.101372 | − | 0.101372i | −0.654602 | − | 0.755974i | \(-0.727164\pi\) |
0.755974 | + | 0.654602i | \(0.227164\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −66149.0 | + | 66149.0i | −0.0892313 | + | 0.0892313i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 902987.i | − | 1.21244i | −0.795297 | − | 0.606220i | \(-0.792685\pi\) | ||
0.795297 | − | 0.606220i | \(-0.207315\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −490801. | −0.655954 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −365344. | − | 365344.i | −0.486031 | − | 0.486031i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 311073. | + | 311073.i | 0.411929 | + | 0.411929i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.04186e6 | −2.69147 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 162104.i | 0.212699i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −43889.6 | + | 43889.6i | −0.0573251 | + | 0.0573251i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −526163. | + | 526163.i | −0.684102 | + | 0.684102i | −0.960922 | − | 0.276820i | \(-0.910719\pi\) |
0.276820 | + | 0.960922i | \(0.410719\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 502600.i | 0.650496i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.39036e6 | −1.79133 | −0.895664 | − | 0.444732i | \(-0.853299\pi\) | ||||
−0.895664 | + | 0.444732i | \(0.853299\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −717884. | − | 717884.i | −0.920731 | − | 0.920731i | 0.0763499 | − | 0.997081i | \(-0.475673\pi\) |
−0.997081 | + | 0.0763499i | \(0.975673\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 234229. | + | 234229.i | 0.299058 | + | 0.299058i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 398604. | 0.506633 | 0.253317 | − | 0.967383i | \(-0.418479\pi\) | ||||
0.253317 | + | 0.967383i | \(0.418479\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 53276.4i | − | 0.0674111i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −417468. | + | 417468.i | −0.525858 | + | 0.525858i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 913022. | − | 913022.i | 1.14493 | − | 1.14493i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.10160e6i | 1.37524i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 67472.0 | 0.0838569 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 189595. | + | 189595.i | 0.234589 | + | 0.234589i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −109032. | − | 109032.i | −0.134309 | − | 0.134309i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1310.41 | 0.00160706 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 981651.i | 1.19856i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 954485. | − | 954485.i | 1.16026 | − | 1.16026i | 0.175840 | − | 0.984419i | \(-0.443736\pi\) |
0.984419 | − | 0.175840i | \(-0.0562640\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −98754.0 | + | 98754.0i | −0.119516 | + | 0.119516i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 876782.i | 1.05646i | 0.849100 | + | 0.528232i | \(0.177145\pi\) | ||||
−0.849100 | + | 0.528232i | \(0.822855\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 29409.0 | 0.0352808 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −495279. | − | 495279.i | −0.591572 | − | 0.591572i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −105298. | − | 105298.i | −0.125223 | − | 0.125223i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 146433. | 0.173384 | 0.0866920 | − | 0.996235i | \(-0.472370\pi\) | ||||
0.0866920 | + | 0.996235i | \(0.472370\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 111196.i | − | 0.131090i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −687637. | + | 687637.i | −0.807153 | + | 0.807153i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 177127. | − | 177127.i | 0.207015 | − | 0.207015i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 27992.8i | 0.0325752i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −357969. | −0.414776 | −0.207388 | − | 0.978259i | \(-0.566496\pi\) | ||||
−0.207388 | + | 0.978259i | \(0.566496\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 948808. | + | 948808.i | 1.09466 | + | 1.09466i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −567320. | − | 567320.i | −0.651726 | − | 0.651726i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −524487. | −0.599945 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1.49027e6i | − | 1.69740i | −0.528871 | − | 0.848702i | \(-0.677384\pi\) | ||
0.528871 | − | 0.848702i | \(-0.322616\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 337579. | − | 337579.i | 0.382863 | − | 0.382863i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 977475. | − | 977475.i | 1.10389 | − | 1.10389i | 0.109954 | − | 0.993937i | \(-0.464929\pi\) |
0.993937 | − | 0.109954i | \(-0.0350705\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 49602.0i | − | 0.0557796i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −160438. | −0.179657 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 573883. | + | 573883.i | 0.639917 | + | 0.639917i | 0.950535 | − | 0.310618i | \(-0.100536\pi\) |
−0.310618 | + | 0.950535i | \(0.600536\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 160162. | + | 160162.i | 0.177839 | + | 0.177839i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 113210. | 0.125177 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 356334.i | 0.392348i | 0.980569 | + | 0.196174i | \(0.0628517\pi\) | ||||
−0.980569 | + | 0.196174i | \(0.937148\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.36933e6 | − | 1.36933e6i | 1.50142 | − | 1.50142i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 176360. | − | 176360.i | 0.192564 | − | 0.192564i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 206358.i | 0.224380i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −251453. | −0.272276 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −195712. | − | 195712.i | −0.211040 | − | 0.211040i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 544298. | + | 544298.i | 0.584496 | + | 0.584496i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.37297e6 | 1.46828 | 0.734138 | − | 0.679001i | \(-0.237587\pi\) | ||||
0.734138 | + | 0.679001i | \(0.237587\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 591293.i | 0.629731i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −424934. | + | 424934.i | −0.450696 | + | 0.450696i | −0.895585 | − | 0.444890i | \(-0.853243\pi\) |
0.444890 | + | 0.895585i | \(0.353243\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 141892. | − | 141892.i | 0.149876 | − | 0.149876i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 785091.i | − | 0.825868i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 985948. | 1.03292 | 0.516458 | − | 0.856313i | \(-0.327250\pi\) | ||||
0.516458 | + | 0.856313i | \(0.327250\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −133225. | − | 133225.i | −0.139002 | − | 0.139002i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 185.903 | + | 185.903i | 0.000193174 | + | 0.000193174i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −92886.2 | −0.0961268 | −0.0480634 | − | 0.998844i | \(-0.515305\pi\) | ||||
−0.0480634 | + | 0.998844i | \(0.515305\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 281236.i | − | 0.289867i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −83197.3 | + | 83197.3i | −0.0854034 | + | 0.0854034i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −491.308 | + | 491.308i | −0.000502297 | + | 0.000502297i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.28759e6i | 1.31109i | 0.755157 | + | 0.655543i | \(0.227560\pi\) | ||||
−0.755157 | + | 0.655543i | \(0.772440\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.36956e6 | 1.38894 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.21281e6 | + | 1.21281e6i | 1.22503 | + | 1.22503i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 388032. | + | 388032.i | 0.390370 | + | 0.390370i | 0.874819 | − | 0.484449i | \(-0.160980\pi\) |
−0.484449 | + | 0.874819i | \(0.660980\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −617028. | −0.618264 |
(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 | 128.5.f.a.31.6 | 14 | ||
4.3 | odd | 2 | 128.5.f.b.31.2 | 14 | |||
8.3 | odd | 2 | 16.5.f.a.11.1 | yes | 14 | ||
8.5 | even | 2 | 64.5.f.a.15.2 | 14 | |||
16.3 | odd | 4 | inner | 128.5.f.a.95.6 | 14 | ||
16.5 | even | 4 | 16.5.f.a.3.1 | ✓ | 14 | ||
16.11 | odd | 4 | 64.5.f.a.47.2 | 14 | |||
16.13 | even | 4 | 128.5.f.b.95.2 | 14 | |||
24.5 | odd | 2 | 576.5.m.a.271.2 | 14 | |||
24.11 | even | 2 | 144.5.m.a.91.7 | 14 | |||
48.5 | odd | 4 | 144.5.m.a.19.7 | 14 | |||
48.11 | even | 4 | 576.5.m.a.559.2 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
16.5.f.a.3.1 | ✓ | 14 | 16.5 | even | 4 | ||
16.5.f.a.11.1 | yes | 14 | 8.3 | odd | 2 | ||
64.5.f.a.15.2 | 14 | 8.5 | even | 2 | |||
64.5.f.a.47.2 | 14 | 16.11 | odd | 4 | |||
128.5.f.a.31.6 | 14 | 1.1 | even | 1 | trivial | ||
128.5.f.a.95.6 | 14 | 16.3 | odd | 4 | inner | ||
128.5.f.b.31.2 | 14 | 4.3 | odd | 2 | |||
128.5.f.b.95.2 | 14 | 16.13 | even | 4 | |||
144.5.m.a.19.7 | 14 | 48.5 | odd | 4 | |||
144.5.m.a.91.7 | 14 | 24.11 | even | 2 | |||
576.5.m.a.271.2 | 14 | 24.5 | odd | 2 | |||
576.5.m.a.559.2 | 14 | 48.11 | even | 4 |