Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [150,6,Mod(1,150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(150, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("150.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 150 = 2 \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 150.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: | \(24.0575729719\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{1249}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 312 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2\cdot 5 \) |
Twist minimal: | no (minimal twist has level 30) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(18.1706\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 150.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.00000 | −0.707107 | ||||||||
\(3\) | −9.00000 | −0.577350 | ||||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 36.0000 | 0.408248 | ||||||||
\(7\) | −233.706 | −1.80271 | −0.901353 | − | 0.433086i | \(-0.857425\pi\) | ||||
−0.901353 | + | 0.433086i | \(0.857425\pi\) | |||||||
\(8\) | −64.0000 | −0.353553 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −89.7060 | −0.223532 | −0.111766 | − | 0.993735i | \(-0.535651\pi\) | ||||
−0.111766 | + | 0.993735i | \(0.535651\pi\) | |||||||
\(12\) | −144.000 | −0.288675 | ||||||||
\(13\) | 209.118 | 0.343189 | 0.171594 | − | 0.985168i | \(-0.445108\pi\) | ||||
0.171594 | + | 0.985168i | \(0.445108\pi\) | |||||||
\(14\) | 934.824 | 1.27471 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | −226.882 | −0.190405 | −0.0952024 | − | 0.995458i | \(-0.530350\pi\) | ||||
−0.0952024 | + | 0.995458i | \(0.530350\pi\) | |||||||
\(18\) | −324.000 | −0.235702 | ||||||||
\(19\) | −2180.47 | −1.38569 | −0.692846 | − | 0.721086i | \(-0.743643\pi\) | ||||
−0.692846 | + | 0.721086i | \(0.743643\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2103.35 | 1.04079 | ||||||||
\(22\) | 358.824 | 0.158061 | ||||||||
\(23\) | −4296.47 | −1.69353 | −0.846764 | − | 0.531969i | \(-0.821452\pi\) | ||||
−0.846764 | + | 0.531969i | \(0.821452\pi\) | |||||||
\(24\) | 576.000 | 0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −836.472 | −0.242671 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | −3739.30 | −0.901353 | ||||||||
\(29\) | 3556.06 | 0.785189 | 0.392595 | − | 0.919712i | \(-0.371578\pi\) | ||||
0.392595 | + | 0.919712i | \(0.371578\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6902.24 | 1.28999 | 0.644994 | − | 0.764188i | \(-0.276860\pi\) | ||||
0.644994 | + | 0.764188i | \(0.276860\pi\) | |||||||
\(32\) | −1024.00 | −0.176777 | ||||||||
\(33\) | 807.354 | 0.129056 | ||||||||
\(34\) | 907.528 | 0.134637 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1296.00 | 0.166667 | ||||||||
\(37\) | 5435.59 | 0.652743 | 0.326371 | − | 0.945242i | \(-0.394174\pi\) | ||||
0.326371 | + | 0.945242i | \(0.394174\pi\) | |||||||
\(38\) | 8721.89 | 0.979832 | ||||||||
\(39\) | −1882.06 | −0.198140 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6484.00 | 0.602398 | 0.301199 | − | 0.953561i | \(-0.402613\pi\) | ||||
0.301199 | + | 0.953561i | \(0.402613\pi\) | |||||||
\(42\) | −8413.41 | −0.735951 | ||||||||
\(43\) | 21979.5 | 1.81279 | 0.906395 | − | 0.422432i | \(-0.138823\pi\) | ||||
0.906395 | + | 0.422432i | \(0.138823\pi\) | |||||||
\(44\) | −1435.30 | −0.111766 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 17185.9 | 1.19751 | ||||||||
\(47\) | 7718.24 | 0.509652 | 0.254826 | − | 0.966987i | \(-0.417982\pi\) | ||||
0.254826 | + | 0.966987i | \(0.417982\pi\) | |||||||
\(48\) | −2304.00 | −0.144338 | ||||||||
\(49\) | 37811.5 | 2.24975 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2041.94 | 0.109930 | ||||||||
\(52\) | 3345.89 | 0.171594 | ||||||||
\(53\) | −12765.4 | −0.624228 | −0.312114 | − | 0.950045i | \(-0.601037\pi\) | ||||
−0.312114 | + | 0.950045i | \(0.601037\pi\) | |||||||
\(54\) | 2916.00 | 0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 14957.2 | 0.637353 | ||||||||
\(57\) | 19624.2 | 0.800029 | ||||||||
\(58\) | −14224.2 | −0.555212 | ||||||||
\(59\) | −44555.6 | −1.66637 | −0.833187 | − | 0.552992i | \(-0.813486\pi\) | ||||
−0.833187 | + | 0.552992i | \(0.813486\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11598.2 | 0.399086 | 0.199543 | − | 0.979889i | \(-0.436054\pi\) | ||||
0.199543 | + | 0.979889i | \(0.436054\pi\) | |||||||
\(62\) | −27608.9 | −0.912159 | ||||||||
\(63\) | −18930.2 | −0.600902 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3229.41 | −0.0912565 | ||||||||
\(67\) | 3961.29 | 0.107808 | 0.0539038 | − | 0.998546i | \(-0.482834\pi\) | ||||
0.0539038 | + | 0.998546i | \(0.482834\pi\) | |||||||
\(68\) | −3630.11 | −0.0952024 | ||||||||
\(69\) | 38668.2 | 0.977759 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 46413.6 | 1.09270 | 0.546348 | − | 0.837559i | \(-0.316018\pi\) | ||||
0.546348 | + | 0.837559i | \(0.316018\pi\) | |||||||
\(72\) | −5184.00 | −0.117851 | ||||||||
\(73\) | 61591.2 | 1.35273 | 0.676365 | − | 0.736566i | \(-0.263554\pi\) | ||||
0.676365 | + | 0.736566i | \(0.263554\pi\) | |||||||
\(74\) | −21742.3 | −0.461559 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −34887.5 | −0.692846 | ||||||||
\(77\) | 20964.8 | 0.402962 | ||||||||
\(78\) | 7528.24 | 0.140106 | ||||||||
\(79\) | −27877.8 | −0.502563 | −0.251281 | − | 0.967914i | \(-0.580852\pi\) | ||||
−0.251281 | + | 0.967914i | \(0.580852\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | −25936.0 | −0.425959 | ||||||||
\(83\) | 50941.0 | 0.811656 | 0.405828 | − | 0.913949i | \(-0.366983\pi\) | ||||
0.405828 | + | 0.913949i | \(0.366983\pi\) | |||||||
\(84\) | 33653.7 | 0.520396 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −87918.1 | −1.28184 | ||||||||
\(87\) | −32004.6 | −0.453329 | ||||||||
\(88\) | 5741.18 | 0.0790305 | ||||||||
\(89\) | 5131.19 | 0.0686663 | 0.0343331 | − | 0.999410i | \(-0.489069\pi\) | ||||
0.0343331 | + | 0.999410i | \(0.489069\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −48872.1 | −0.618668 | ||||||||
\(92\) | −68743.5 | −0.846764 | ||||||||
\(93\) | −62120.1 | −0.744775 | ||||||||
\(94\) | −30872.9 | −0.360378 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 9216.00 | 0.102062 | ||||||||
\(97\) | 88435.3 | 0.954325 | 0.477162 | − | 0.878815i | \(-0.341665\pi\) | ||||
0.477162 | + | 0.878815i | \(0.341665\pi\) | |||||||
\(98\) | −151246. | −1.59081 | ||||||||
\(99\) | −7266.18 | −0.0745107 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −116471. | −1.13609 | −0.568047 | − | 0.822996i | \(-0.692301\pi\) | ||||
−0.568047 | + | 0.822996i | \(0.692301\pi\) | |||||||
\(102\) | −8167.76 | −0.0777324 | ||||||||
\(103\) | −22369.1 | −0.207756 | −0.103878 | − | 0.994590i | \(-0.533125\pi\) | ||||
−0.103878 | + | 0.994590i | \(0.533125\pi\) | |||||||
\(104\) | −13383.5 | −0.121335 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 51061.5 | 0.441396 | ||||||||
\(107\) | 130626. | 1.10299 | 0.551495 | − | 0.834178i | \(-0.314058\pi\) | ||||
0.551495 | + | 0.834178i | \(0.314058\pi\) | |||||||
\(108\) | −11664.0 | −0.0962250 | ||||||||
\(109\) | −51443.5 | −0.414729 | −0.207365 | − | 0.978264i | \(-0.566489\pi\) | ||||
−0.207365 | + | 0.978264i | \(0.566489\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −48920.3 | −0.376861 | ||||||||
\(112\) | −59828.7 | −0.450676 | ||||||||
\(113\) | −138259. | −1.01858 | −0.509291 | − | 0.860594i | \(-0.670092\pi\) | ||||
−0.509291 | + | 0.860594i | \(0.670092\pi\) | |||||||
\(114\) | −78497.0 | −0.565706 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 56897.0 | 0.392595 | ||||||||
\(117\) | 16938.6 | 0.114396 | ||||||||
\(118\) | 178222. | 1.17830 | ||||||||
\(119\) | 53023.7 | 0.343244 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −153004. | −0.950033 | ||||||||
\(122\) | −46392.9 | −0.282197 | ||||||||
\(123\) | −58356.0 | −0.347794 | ||||||||
\(124\) | 110436. | 0.644994 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 75720.7 | 0.424902 | ||||||||
\(127\) | 199662. | 1.09847 | 0.549233 | − | 0.835669i | \(-0.314920\pi\) | ||||
0.549233 | + | 0.835669i | \(0.314920\pi\) | |||||||
\(128\) | −16384.0 | −0.0883883 | ||||||||
\(129\) | −197816. | −1.04661 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −314223. | −1.59978 | −0.799889 | − | 0.600148i | \(-0.795109\pi\) | ||||
−0.799889 | + | 0.600148i | \(0.795109\pi\) | |||||||
\(132\) | 12917.7 | 0.0645281 | ||||||||
\(133\) | 509589. | 2.49799 | ||||||||
\(134\) | −15845.1 | −0.0762315 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 14520.5 | 0.0673183 | ||||||||
\(137\) | −256841. | −1.16913 | −0.584564 | − | 0.811348i | \(-0.698734\pi\) | ||||
−0.584564 | + | 0.811348i | \(0.698734\pi\) | |||||||
\(138\) | −154673. | −0.691380 | ||||||||
\(139\) | −10777.2 | −0.0473118 | −0.0236559 | − | 0.999720i | \(-0.507531\pi\) | ||||
−0.0236559 | + | 0.999720i | \(0.507531\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −69464.1 | −0.294247 | ||||||||
\(142\) | −185654. | −0.772652 | ||||||||
\(143\) | −18759.1 | −0.0767136 | ||||||||
\(144\) | 20736.0 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −246365. | −0.956525 | ||||||||
\(147\) | −340303. | −1.29889 | ||||||||
\(148\) | 86969.4 | 0.326371 | ||||||||
\(149\) | 4103.27 | 0.0151413 | 0.00757067 | − | 0.999971i | \(-0.497590\pi\) | ||||
0.00757067 | + | 0.999971i | \(0.497590\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 107449. | 0.383495 | 0.191748 | − | 0.981444i | \(-0.438585\pi\) | ||||
0.191748 | + | 0.981444i | \(0.438585\pi\) | |||||||
\(152\) | 139550. | 0.489916 | ||||||||
\(153\) | −18377.4 | −0.0634683 | ||||||||
\(154\) | −83859.3 | −0.284937 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −30113.0 | −0.0990700 | ||||||||
\(157\) | 345824. | 1.11971 | 0.559855 | − | 0.828591i | \(-0.310857\pi\) | ||||
0.559855 | + | 0.828591i | \(0.310857\pi\) | |||||||
\(158\) | 111511. | 0.355366 | ||||||||
\(159\) | 114888. | 0.360398 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.00411e6 | 3.05293 | ||||||||
\(162\) | −26244.0 | −0.0785674 | ||||||||
\(163\) | −58776.3 | −0.173274 | −0.0866370 | − | 0.996240i | \(-0.527612\pi\) | ||||
−0.0866370 | + | 0.996240i | \(0.527612\pi\) | |||||||
\(164\) | 103744. | 0.301199 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −203764. | −0.573928 | ||||||||
\(167\) | −154654. | −0.429111 | −0.214556 | − | 0.976712i | \(-0.568830\pi\) | ||||
−0.214556 | + | 0.976712i | \(0.568830\pi\) | |||||||
\(168\) | −134615. | −0.367976 | ||||||||
\(169\) | −327563. | −0.882222 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −176618. | −0.461897 | ||||||||
\(172\) | 351673. | 0.906395 | ||||||||
\(173\) | −171600. | −0.435916 | −0.217958 | − | 0.975958i | \(-0.569940\pi\) | ||||
−0.217958 | + | 0.975958i | \(0.569940\pi\) | |||||||
\(174\) | 128018. | 0.320552 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −22964.7 | −0.0558830 | ||||||||
\(177\) | 401000. | 0.962081 | ||||||||
\(178\) | −20524.8 | −0.0485544 | ||||||||
\(179\) | 595571. | 1.38932 | 0.694658 | − | 0.719340i | \(-0.255556\pi\) | ||||
0.694658 | + | 0.719340i | \(0.255556\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 144518. | 0.327889 | 0.163944 | − | 0.986470i | \(-0.447578\pi\) | ||||
0.163944 | + | 0.986470i | \(0.447578\pi\) | |||||||
\(182\) | 195488. | 0.437464 | ||||||||
\(183\) | −104384. | −0.230413 | ||||||||
\(184\) | 274974. | 0.598753 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 248480. | 0.526635 | ||||||||
\(187\) | 20352.7 | 0.0425616 | ||||||||
\(188\) | 123492. | 0.254826 | ||||||||
\(189\) | 170372. | 0.346931 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 815918. | 1.61831 | 0.809157 | − | 0.587592i | \(-0.199924\pi\) | ||||
0.809157 | + | 0.587592i | \(0.199924\pi\) | |||||||
\(192\) | −36864.0 | −0.0721688 | ||||||||
\(193\) | 665030. | 1.28513 | 0.642566 | − | 0.766230i | \(-0.277870\pi\) | ||||
0.642566 | + | 0.766230i | \(0.277870\pi\) | |||||||
\(194\) | −353741. | −0.674810 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 604984. | 1.12487 | ||||||||
\(197\) | −332972. | −0.611283 | −0.305642 | − | 0.952147i | \(-0.598871\pi\) | ||||
−0.305642 | + | 0.952147i | \(0.598871\pi\) | |||||||
\(198\) | 29064.7 | 0.0526870 | ||||||||
\(199\) | −19565.3 | −0.0350231 | −0.0175115 | − | 0.999847i | \(-0.505574\pi\) | ||||
−0.0175115 | + | 0.999847i | \(0.505574\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −35651.6 | −0.0622427 | ||||||||
\(202\) | 465884. | 0.803339 | ||||||||
\(203\) | −831073. | −1.41546 | ||||||||
\(204\) | 32671.0 | 0.0549651 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 89476.2 | 0.146906 | ||||||||
\(207\) | −348014. | −0.564509 | ||||||||
\(208\) | 53534.2 | 0.0857971 | ||||||||
\(209\) | 195601. | 0.309746 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −669474. | −1.03521 | −0.517604 | − | 0.855620i | \(-0.673176\pi\) | ||||
−0.517604 | + | 0.855620i | \(0.673176\pi\) | |||||||
\(212\) | −204246. | −0.312114 | ||||||||
\(213\) | −417722. | −0.630868 | ||||||||
\(214\) | −522506. | −0.779932 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 46656.0 | 0.0680414 | ||||||||
\(217\) | −1.61309e6 | −2.32547 | ||||||||
\(218\) | 205774. | 0.293258 | ||||||||
\(219\) | −554321. | −0.781000 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −47445.1 | −0.0653448 | ||||||||
\(222\) | 195681. | 0.266481 | ||||||||
\(223\) | −841915. | −1.13372 | −0.566860 | − | 0.823814i | \(-0.691842\pi\) | ||||
−0.566860 | + | 0.823814i | \(0.691842\pi\) | |||||||
\(224\) | 239315. | 0.318676 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 553034. | 0.720246 | ||||||||
\(227\) | 106296. | 0.136916 | 0.0684580 | − | 0.997654i | \(-0.478192\pi\) | ||||
0.0684580 | + | 0.997654i | \(0.478192\pi\) | |||||||
\(228\) | 313988. | 0.400015 | ||||||||
\(229\) | 1.52931e6 | 1.92711 | 0.963553 | − | 0.267518i | \(-0.0862033\pi\) | ||||
0.963553 | + | 0.267518i | \(0.0862033\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −188683. | −0.232650 | ||||||||
\(232\) | −227588. | −0.277606 | ||||||||
\(233\) | 362144. | 0.437011 | 0.218505 | − | 0.975836i | \(-0.429882\pi\) | ||||
0.218505 | + | 0.975836i | \(0.429882\pi\) | |||||||
\(234\) | −67754.2 | −0.0808903 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −712890. | −0.833187 | ||||||||
\(237\) | 250900. | 0.290155 | ||||||||
\(238\) | −212095. | −0.242710 | ||||||||
\(239\) | 38495.6 | 0.0435929 | 0.0217965 | − | 0.999762i | \(-0.493061\pi\) | ||||
0.0217965 | + | 0.999762i | \(0.493061\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 567433. | 0.629320 | 0.314660 | − | 0.949204i | \(-0.398109\pi\) | ||||
0.314660 | + | 0.949204i | \(0.398109\pi\) | |||||||
\(242\) | 612015. | 0.671775 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | 185572. | 0.199543 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 233424. | 0.245928 | ||||||||
\(247\) | −455976. | −0.475553 | ||||||||
\(248\) | −441743. | −0.456080 | ||||||||
\(249\) | −458469. | −0.468610 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 19067.0 | 0.0191028 | 0.00955141 | − | 0.999954i | \(-0.496960\pi\) | ||||
0.00955141 | + | 0.999954i | \(0.496960\pi\) | |||||||
\(252\) | −302883. | −0.300451 | ||||||||
\(253\) | 385419. | 0.378558 | ||||||||
\(254\) | −798649. | −0.776733 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | 854054. | 0.806589 | 0.403295 | − | 0.915070i | \(-0.367865\pi\) | ||||
0.403295 | + | 0.915070i | \(0.367865\pi\) | |||||||
\(258\) | 791263. | 0.740068 | ||||||||
\(259\) | −1.27033e6 | −1.17670 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 288041. | 0.261730 | ||||||||
\(262\) | 1.25689e6 | 1.13121 | ||||||||
\(263\) | 755220. | 0.673262 | 0.336631 | − | 0.941637i | \(-0.390712\pi\) | ||||
0.336631 | + | 0.941637i | \(0.390712\pi\) | |||||||
\(264\) | −51670.6 | −0.0456283 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2.03836e6 | −1.76635 | ||||||||
\(267\) | −46180.7 | −0.0396445 | ||||||||
\(268\) | 63380.6 | 0.0539038 | ||||||||
\(269\) | −256615. | −0.216222 | −0.108111 | − | 0.994139i | \(-0.534480\pi\) | ||||
−0.108111 | + | 0.994139i | \(0.534480\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 598518. | 0.495056 | 0.247528 | − | 0.968881i | \(-0.420382\pi\) | ||||
0.247528 | + | 0.968881i | \(0.420382\pi\) | |||||||
\(272\) | −58081.8 | −0.0476012 | ||||||||
\(273\) | 439849. | 0.357188 | ||||||||
\(274\) | 1.02736e6 | 0.826698 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 618692. | 0.488879 | ||||||||
\(277\) | 425045. | 0.332840 | 0.166420 | − | 0.986055i | \(-0.446779\pi\) | ||||
0.166420 | + | 0.986055i | \(0.446779\pi\) | |||||||
\(278\) | 43108.9 | 0.0334545 | ||||||||
\(279\) | 559081. | 0.429996 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −949963. | −0.717696 | −0.358848 | − | 0.933396i | \(-0.616830\pi\) | ||||
−0.358848 | + | 0.933396i | \(0.616830\pi\) | |||||||
\(282\) | 277856. | 0.208064 | ||||||||
\(283\) | −2.12422e6 | −1.57664 | −0.788321 | − | 0.615264i | \(-0.789050\pi\) | ||||
−0.788321 | + | 0.615264i | \(0.789050\pi\) | |||||||
\(284\) | 742617. | 0.546348 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 75036.5 | 0.0542447 | ||||||||
\(287\) | −1.51535e6 | −1.08595 | ||||||||
\(288\) | −82944.0 | −0.0589256 | ||||||||
\(289\) | −1.36838e6 | −0.963746 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −795918. | −0.550980 | ||||||||
\(292\) | 985459. | 0.676365 | ||||||||
\(293\) | 1.17556e6 | 0.799977 | 0.399988 | − | 0.916520i | \(-0.369014\pi\) | ||||
0.399988 | + | 0.916520i | \(0.369014\pi\) | |||||||
\(294\) | 1.36121e6 | 0.918455 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −347878. | −0.230779 | ||||||||
\(297\) | 65395.7 | 0.0430187 | ||||||||
\(298\) | −16413.1 | −0.0107065 | ||||||||
\(299\) | −898469. | −0.581199 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.13675e6 | −3.26792 | ||||||||
\(302\) | −429796. | −0.271172 | ||||||||
\(303\) | 1.04824e6 | 0.655924 | ||||||||
\(304\) | −558201. | −0.346423 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 73509.8 | 0.0448788 | ||||||||
\(307\) | −588520. | −0.356382 | −0.178191 | − | 0.983996i | \(-0.557024\pi\) | ||||
−0.178191 | + | 0.983996i | \(0.557024\pi\) | |||||||
\(308\) | 335437. | 0.201481 | ||||||||
\(309\) | 201321. | 0.119948 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.61863e6 | 0.948958 | 0.474479 | − | 0.880267i | \(-0.342637\pi\) | ||||
0.474479 | + | 0.880267i | \(0.342637\pi\) | |||||||
\(312\) | 120452. | 0.0700531 | ||||||||
\(313\) | 1.58901e6 | 0.916783 | 0.458392 | − | 0.888750i | \(-0.348426\pi\) | ||||
0.458392 | + | 0.888750i | \(0.348426\pi\) | |||||||
\(314\) | −1.38329e6 | −0.791754 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −446045. | −0.251281 | ||||||||
\(317\) | 2.35137e6 | 1.31423 | 0.657117 | − | 0.753789i | \(-0.271776\pi\) | ||||
0.657117 | + | 0.753789i | \(0.271776\pi\) | |||||||
\(318\) | −459553. | −0.254840 | ||||||||
\(319\) | −319000. | −0.175515 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.17564e6 | −0.636811 | ||||||||
\(322\) | −4.01644e6 | −2.15875 | ||||||||
\(323\) | 494710. | 0.263842 | ||||||||
\(324\) | 104976. | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 235105. | 0.122523 | ||||||||
\(327\) | 462992. | 0.239444 | ||||||||
\(328\) | −414976. | −0.212980 | ||||||||
\(329\) | −1.80380e6 | −0.918752 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 480922. | 0.241271 | 0.120635 | − | 0.992697i | \(-0.461507\pi\) | ||||
0.120635 | + | 0.992697i | \(0.461507\pi\) | |||||||
\(332\) | 815056. | 0.405828 | ||||||||
\(333\) | 440283. | 0.217581 | ||||||||
\(334\) | 618616. | 0.303427 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 538459. | 0.260198 | ||||||||
\(337\) | 981449. | 0.470753 | 0.235376 | − | 0.971904i | \(-0.424368\pi\) | ||||
0.235376 | + | 0.971904i | \(0.424368\pi\) | |||||||
\(338\) | 1.31025e6 | 0.623825 | ||||||||
\(339\) | 1.24433e6 | 0.588079 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −619172. | −0.288353 | ||||||||
\(342\) | 706473. | 0.326611 | ||||||||
\(343\) | −4.90887e6 | −2.25292 | ||||||||
\(344\) | −1.40669e6 | −0.640918 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 686400. | 0.308239 | ||||||||
\(347\) | −1.91647e6 | −0.854432 | −0.427216 | − | 0.904150i | \(-0.640506\pi\) | ||||
−0.427216 | + | 0.904150i | \(0.640506\pi\) | |||||||
\(348\) | −512073. | −0.226665 | ||||||||
\(349\) | 1.22795e6 | 0.539658 | 0.269829 | − | 0.962908i | \(-0.413033\pi\) | ||||
0.269829 | + | 0.962908i | \(0.413033\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −152447. | −0.0660467 | ||||||||
\(352\) | 91858.9 | 0.0395152 | ||||||||
\(353\) | 547823. | 0.233993 | 0.116997 | − | 0.993132i | \(-0.462673\pi\) | ||||
0.116997 | + | 0.993132i | \(0.462673\pi\) | |||||||
\(354\) | −1.60400e6 | −0.680294 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 82099.1 | 0.0343331 | ||||||||
\(357\) | −477213. | −0.198172 | ||||||||
\(358\) | −2.38228e6 | −0.982395 | ||||||||
\(359\) | 1.02314e6 | 0.418984 | 0.209492 | − | 0.977810i | \(-0.432819\pi\) | ||||
0.209492 | + | 0.977810i | \(0.432819\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.27836e6 | 0.920140 | ||||||||
\(362\) | −578073. | −0.231852 | ||||||||
\(363\) | 1.37703e6 | 0.548502 | ||||||||
\(364\) | −781954. | −0.309334 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 417536. | 0.162926 | ||||||||
\(367\) | 3.05305e6 | 1.18323 | 0.591614 | − | 0.806221i | \(-0.298491\pi\) | ||||
0.591614 | + | 0.806221i | \(0.298491\pi\) | |||||||
\(368\) | −1.09990e6 | −0.423382 | ||||||||
\(369\) | 525204. | 0.200799 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.98334e6 | 1.12530 | ||||||||
\(372\) | −993922. | −0.372387 | ||||||||
\(373\) | −3.69411e6 | −1.37479 | −0.687397 | − | 0.726282i | \(-0.741247\pi\) | ||||
−0.687397 | + | 0.726282i | \(0.741247\pi\) | |||||||
\(374\) | −81410.7 | −0.0300956 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −493967. | −0.180189 | ||||||||
\(377\) | 743636. | 0.269468 | ||||||||
\(378\) | −681487. | −0.245317 | ||||||||
\(379\) | 4.48524e6 | 1.60394 | 0.801969 | − | 0.597365i | \(-0.203786\pi\) | ||||
0.801969 | + | 0.597365i | \(0.203786\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.79696e6 | −0.634200 | ||||||||
\(382\) | −3.26367e6 | −1.14432 | ||||||||
\(383\) | −4.53062e6 | −1.57819 | −0.789097 | − | 0.614269i | \(-0.789451\pi\) | ||||
−0.789097 | + | 0.614269i | \(0.789451\pi\) | |||||||
\(384\) | 147456. | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.66012e6 | −0.908726 | ||||||||
\(387\) | 1.78034e6 | 0.604263 | ||||||||
\(388\) | 1.41496e6 | 0.477162 | ||||||||
\(389\) | 2.73557e6 | 0.916588 | 0.458294 | − | 0.888801i | \(-0.348461\pi\) | ||||
0.458294 | + | 0.888801i | \(0.348461\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 974792. | 0.322456 | ||||||||
\(392\) | −2.41993e6 | −0.795405 | ||||||||
\(393\) | 2.82801e6 | 0.923633 | ||||||||
\(394\) | 1.33189e6 | 0.432242 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −116259. | −0.0372553 | ||||||||
\(397\) | −1.54948e6 | −0.493413 | −0.246707 | − | 0.969090i | \(-0.579348\pi\) | ||||
−0.246707 | + | 0.969090i | \(0.579348\pi\) | |||||||
\(398\) | 78261.3 | 0.0247651 | ||||||||
\(399\) | −4.58630e6 | −1.44222 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.46136e6 | 1.38550 | 0.692749 | − | 0.721179i | \(-0.256399\pi\) | ||||
0.692749 | + | 0.721179i | \(0.256399\pi\) | |||||||
\(402\) | 142606. | 0.0440123 | ||||||||
\(403\) | 1.44338e6 | 0.442709 | ||||||||
\(404\) | −1.86353e6 | −0.568047 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.32429e6 | 1.00088 | ||||||||
\(407\) | −487605. | −0.145909 | ||||||||
\(408\) | −130684. | −0.0388662 | ||||||||
\(409\) | −2.36815e6 | −0.700003 | −0.350002 | − | 0.936749i | \(-0.613819\pi\) | ||||
−0.350002 | + | 0.936749i | \(0.613819\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.31156e6 | 0.674996 | ||||||||
\(412\) | −357905. | −0.103878 | ||||||||
\(413\) | 1.04129e7 | 3.00398 | ||||||||
\(414\) | 1.39206e6 | 0.399168 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −214137. | −0.0606677 | ||||||||
\(417\) | 96995.0 | 0.0273155 | ||||||||
\(418\) | −782405. | −0.219024 | ||||||||
\(419\) | 5.76363e6 | 1.60384 | 0.801920 | − | 0.597432i | \(-0.203812\pi\) | ||||
0.801920 | + | 0.597432i | \(0.203812\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.26572e6 | 0.897995 | 0.448998 | − | 0.893533i | \(-0.351781\pi\) | ||||
0.448998 | + | 0.893533i | \(0.351781\pi\) | |||||||
\(422\) | 2.67789e6 | 0.732002 | ||||||||
\(423\) | 625177. | 0.169884 | ||||||||
\(424\) | 816983. | 0.220698 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1.67089e6 | 0.446091 | ||||||||
\(427\) | −2.71057e6 | −0.719435 | ||||||||
\(428\) | 2.09002e6 | 0.551495 | ||||||||
\(429\) | 168832. | 0.0442906 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.62110e6 | −1.45756 | −0.728782 | − | 0.684745i | \(-0.759913\pi\) | ||||
−0.728782 | + | 0.684745i | \(0.759913\pi\) | |||||||
\(432\) | −186624. | −0.0481125 | ||||||||
\(433\) | 3.18656e6 | 0.816774 | 0.408387 | − | 0.912809i | \(-0.366091\pi\) | ||||
0.408387 | + | 0.912809i | \(0.366091\pi\) | |||||||
\(434\) | 6.45237e6 | 1.64435 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −823097. | −0.207365 | ||||||||
\(437\) | 9.36833e6 | 2.34671 | ||||||||
\(438\) | 2.21728e6 | 0.552250 | ||||||||
\(439\) | −7.41102e6 | −1.83534 | −0.917671 | − | 0.397342i | \(-0.869933\pi\) | ||||
−0.917671 | + | 0.397342i | \(0.869933\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.06273e6 | 0.749915 | ||||||||
\(442\) | 189780. | 0.0462057 | ||||||||
\(443\) | −2.62862e6 | −0.636382 | −0.318191 | − | 0.948027i | \(-0.603075\pi\) | ||||
−0.318191 | + | 0.948027i | \(0.603075\pi\) | |||||||
\(444\) | −782724. | −0.188431 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 3.36766e6 | 0.801662 | ||||||||
\(447\) | −36929.4 | −0.00874185 | ||||||||
\(448\) | −957260. | −0.225338 | ||||||||
\(449\) | 71764.4 | 0.0167994 | 0.00839969 | − | 0.999965i | \(-0.497326\pi\) | ||||
0.00839969 | + | 0.999965i | \(0.497326\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −581653. | −0.134655 | ||||||||
\(452\) | −2.21214e6 | −0.509291 | ||||||||
\(453\) | −967040. | −0.221411 | ||||||||
\(454\) | −425186. | −0.0968142 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.25595e6 | −0.282853 | ||||||||
\(457\) | 3.51471e6 | 0.787225 | 0.393613 | − | 0.919276i | \(-0.371225\pi\) | ||||
0.393613 | + | 0.919276i | \(0.371225\pi\) | |||||||
\(458\) | −6.11722e6 | −1.36267 | ||||||||
\(459\) | 165397. | 0.0366434 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.35569e6 | 0.735410 | 0.367705 | − | 0.929943i | \(-0.380144\pi\) | ||||
0.367705 | + | 0.929943i | \(0.380144\pi\) | |||||||
\(462\) | 754734. | 0.164509 | ||||||||
\(463\) | 3.47269e6 | 0.752860 | 0.376430 | − | 0.926445i | \(-0.377152\pi\) | ||||
0.376430 | + | 0.926445i | \(0.377152\pi\) | |||||||
\(464\) | 910352. | 0.196297 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.44858e6 | −0.309013 | ||||||||
\(467\) | 2.35495e6 | 0.499678 | 0.249839 | − | 0.968287i | \(-0.419622\pi\) | ||||
0.249839 | + | 0.968287i | \(0.419622\pi\) | |||||||
\(468\) | 271017. | 0.0571981 | ||||||||
\(469\) | −925776. | −0.194345 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.11241e6 | −0.646465 | ||||||||
\(472\) | 2.85156e6 | 0.589152 | ||||||||
\(473\) | −1.97170e6 | −0.405216 | ||||||||
\(474\) | −1.00360e6 | −0.205170 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 848379. | 0.171622 | ||||||||
\(477\) | −1.03399e6 | −0.208076 | ||||||||
\(478\) | −153982. | −0.0308249 | ||||||||
\(479\) | −187771. | −0.0373929 | −0.0186964 | − | 0.999825i | \(-0.505952\pi\) | ||||
−0.0186964 | + | 0.999825i | \(0.505952\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.13668e6 | 0.224014 | ||||||||
\(482\) | −2.26973e6 | −0.444997 | ||||||||
\(483\) | −9.03700e6 | −1.76261 | ||||||||
\(484\) | −2.44806e6 | −0.475017 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 236196. | 0.0453609 | ||||||||
\(487\) | −2.01505e6 | −0.385002 | −0.192501 | − | 0.981297i | \(-0.561660\pi\) | ||||
−0.192501 | + | 0.981297i | \(0.561660\pi\) | |||||||
\(488\) | −742287. | −0.141098 | ||||||||
\(489\) | 528987. | 0.100040 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.80814e6 | 1.08726 | 0.543630 | − | 0.839325i | \(-0.317049\pi\) | ||||
0.543630 | + | 0.839325i | \(0.317049\pi\) | |||||||
\(492\) | −933696. | −0.173897 | ||||||||
\(493\) | −806807. | −0.149504 | ||||||||
\(494\) | 1.82390e6 | 0.336267 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.76697e6 | 0.322497 | ||||||||
\(497\) | −1.08471e7 | −1.96981 | ||||||||
\(498\) | 1.83388e6 | 0.331357 | ||||||||
\(499\) | 580611. | 0.104384 | 0.0521920 | − | 0.998637i | \(-0.483379\pi\) | ||||
0.0521920 | + | 0.998637i | \(0.483379\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.39188e6 | 0.247747 | ||||||||
\(502\) | −76267.9 | −0.0135077 | ||||||||
\(503\) | −557751. | −0.0982926 | −0.0491463 | − | 0.998792i | \(-0.515650\pi\) | ||||
−0.0491463 | + | 0.998792i | \(0.515650\pi\) | |||||||
\(504\) | 1.21153e6 | 0.212451 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.54168e6 | −0.267681 | ||||||||
\(507\) | 2.94806e6 | 0.509351 | ||||||||
\(508\) | 3.19460e6 | 0.549233 | ||||||||
\(509\) | −2.63318e6 | −0.450491 | −0.225246 | − | 0.974302i | \(-0.572318\pi\) | ||||
−0.225246 | + | 0.974302i | \(0.572318\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.43942e7 | −2.43858 | ||||||||
\(512\) | −262144. | −0.0441942 | ||||||||
\(513\) | 1.58956e6 | 0.266676 | ||||||||
\(514\) | −3.41621e6 | −0.570345 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −3.16505e6 | −0.523307 | ||||||||
\(517\) | −692372. | −0.113923 | ||||||||
\(518\) | 5.08132e6 | 0.832055 | ||||||||
\(519\) | 1.54440e6 | 0.251676 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.78129e6 | −1.09451 | −0.547253 | − | 0.836967i | \(-0.684326\pi\) | ||||
−0.547253 | + | 0.836967i | \(0.684326\pi\) | |||||||
\(522\) | −1.15216e6 | −0.185071 | ||||||||
\(523\) | 1.55863e6 | 0.249166 | 0.124583 | − | 0.992209i | \(-0.460241\pi\) | ||||
0.124583 | + | 0.992209i | \(0.460241\pi\) | |||||||
\(524\) | −5.02757e6 | −0.799889 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.02088e6 | −0.476068 | ||||||||
\(527\) | −1.56599e6 | −0.245620 | ||||||||
\(528\) | 206683. | 0.0322641 | ||||||||
\(529\) | 1.20233e7 | 1.86804 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.60900e6 | −0.555458 | ||||||||
\(532\) | 8.15343e6 | 1.24900 | ||||||||
\(533\) | 1.35592e6 | 0.206736 | ||||||||
\(534\) | 184723. | 0.0280329 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −253522. | −0.0381157 | ||||||||
\(537\) | −5.36014e6 | −0.802122 | ||||||||
\(538\) | 1.02646e6 | 0.152892 | ||||||||
\(539\) | −3.39192e6 | −0.502890 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.29465e6 | 1.07155 | 0.535774 | − | 0.844362i | \(-0.320020\pi\) | ||||
0.535774 | + | 0.844362i | \(0.320020\pi\) | |||||||
\(542\) | −2.39407e6 | −0.350057 | ||||||||
\(543\) | −1.30066e6 | −0.189307 | ||||||||
\(544\) | 232327. | 0.0336591 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −1.75940e6 | −0.252570 | ||||||||
\(547\) | −5.15944e6 | −0.737283 | −0.368642 | − | 0.929572i | \(-0.620177\pi\) | ||||
−0.368642 | + | 0.929572i | \(0.620177\pi\) | |||||||
\(548\) | −4.10945e6 | −0.584564 | ||||||||
\(549\) | 939456. | 0.133029 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.75389e6 | −1.08803 | ||||||||
\(552\) | −2.47477e6 | −0.345690 | ||||||||
\(553\) | 6.51520e6 | 0.905973 | ||||||||
\(554\) | −1.70018e6 | −0.235353 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −172436. | −0.0236559 | ||||||||
\(557\) | −2.18378e6 | −0.298244 | −0.149122 | − | 0.988819i | \(-0.547645\pi\) | ||||
−0.149122 | + | 0.988819i | \(0.547645\pi\) | |||||||
\(558\) | −2.23632e6 | −0.304053 | ||||||||
\(559\) | 4.59631e6 | 0.622129 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −183174. | −0.0245729 | ||||||||
\(562\) | 3.79985e6 | 0.507488 | ||||||||
\(563\) | −1.13003e7 | −1.50252 | −0.751259 | − | 0.660007i | \(-0.770553\pi\) | ||||
−0.751259 | + | 0.660007i | \(0.770553\pi\) | |||||||
\(564\) | −1.11143e6 | −0.147124 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 8.49688e6 | 1.11485 | ||||||||
\(567\) | −1.53334e6 | −0.200301 | ||||||||
\(568\) | −2.97047e6 | −0.386326 | ||||||||
\(569\) | −1.01686e7 | −1.31669 | −0.658343 | − | 0.752718i | \(-0.728742\pi\) | ||||
−0.658343 | + | 0.752718i | \(0.728742\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −284871. | −0.0365644 | −0.0182822 | − | 0.999833i | \(-0.505820\pi\) | ||||
−0.0182822 | + | 0.999833i | \(0.505820\pi\) | |||||||
\(572\) | −300146. | −0.0383568 | ||||||||
\(573\) | −7.34326e6 | −0.934334 | ||||||||
\(574\) | 6.06140e6 | 0.767879 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 331776. | 0.0416667 | ||||||||
\(577\) | 9.14119e6 | 1.14304 | 0.571522 | − | 0.820587i | \(-0.306353\pi\) | ||||
0.571522 | + | 0.820587i | \(0.306353\pi\) | |||||||
\(578\) | 5.47353e6 | 0.681471 | ||||||||
\(579\) | −5.98527e6 | −0.741971 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.19052e7 | −1.46318 | ||||||||
\(582\) | 3.18367e6 | 0.389602 | ||||||||
\(583\) | 1.14513e6 | 0.139535 | ||||||||
\(584\) | −3.94184e6 | −0.478263 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.70226e6 | −0.565669 | ||||||||
\(587\) | −1.85347e6 | −0.222019 | −0.111010 | − | 0.993819i | \(-0.535408\pi\) | ||||
−0.111010 | + | 0.993819i | \(0.535408\pi\) | |||||||
\(588\) | −5.44485e6 | −0.649446 | ||||||||
\(589\) | −1.50501e7 | −1.78752 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.99675e6 | 0.352924 | ||||||||
\(592\) | 1.39151e6 | 0.163186 | ||||||||
\(593\) | −1.30967e7 | −1.52941 | −0.764705 | − | 0.644380i | \(-0.777116\pi\) | ||||
−0.764705 | + | 0.644380i | \(0.777116\pi\) | |||||||
\(594\) | −261583. | −0.0304188 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 65652.3 | 0.00757067 | ||||||||
\(597\) | 176088. | 0.0202206 | ||||||||
\(598\) | 3.59388e6 | 0.410970 | ||||||||
\(599\) | −7.13874e6 | −0.812933 | −0.406466 | − | 0.913666i | \(-0.633239\pi\) | ||||
−0.406466 | + | 0.913666i | \(0.633239\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.27856e6 | −0.821976 | −0.410988 | − | 0.911641i | \(-0.634816\pi\) | ||||
−0.410988 | + | 0.911641i | \(0.634816\pi\) | |||||||
\(602\) | 2.05470e7 | 2.31077 | ||||||||
\(603\) | 320864. | 0.0359359 | ||||||||
\(604\) | 1.71918e6 | 0.191748 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −4.19295e6 | −0.463808 | ||||||||
\(607\) | −466696. | −0.0514117 | −0.0257058 | − | 0.999670i | \(-0.508183\pi\) | ||||
−0.0257058 | + | 0.999670i | \(0.508183\pi\) | |||||||
\(608\) | 2.23280e6 | 0.244958 | ||||||||
\(609\) | 7.47965e6 | 0.817219 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.61402e6 | 0.174907 | ||||||||
\(612\) | −294039. | −0.0317341 | ||||||||
\(613\) | 9.21342e6 | 0.990307 | 0.495153 | − | 0.868806i | \(-0.335112\pi\) | ||||
0.495153 | + | 0.868806i | \(0.335112\pi\) | |||||||
\(614\) | 2.35408e6 | 0.252000 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.34175e6 | −0.142469 | ||||||||
\(617\) | −8.53638e6 | −0.902736 | −0.451368 | − | 0.892338i | \(-0.649064\pi\) | ||||
−0.451368 | + | 0.892338i | \(0.649064\pi\) | |||||||
\(618\) | −805286. | −0.0848162 | ||||||||
\(619\) | 7.72476e6 | 0.810323 | 0.405162 | − | 0.914245i | \(-0.367215\pi\) | ||||
0.405162 | + | 0.914245i | \(0.367215\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.13213e6 | 0.325920 | ||||||||
\(622\) | −6.47452e6 | −0.671014 | ||||||||
\(623\) | −1.19919e6 | −0.123785 | ||||||||
\(624\) | −481808. | −0.0495350 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −6.35605e6 | −0.648264 | ||||||||
\(627\) | −1.76041e6 | −0.178832 | ||||||||
\(628\) | 5.53318e6 | 0.559855 | ||||||||
\(629\) | −1.23324e6 | −0.124285 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.50119e7 | 1.50094 | 0.750470 | − | 0.660904i | \(-0.229827\pi\) | ||||
0.750470 | + | 0.660904i | \(0.229827\pi\) | |||||||
\(632\) | 1.78418e6 | 0.177683 | ||||||||
\(633\) | 6.02526e6 | 0.597677 | ||||||||
\(634\) | −9.40547e6 | −0.929303 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1.83821e6 | 0.180199 | ||||||||
\(637\) | 7.90706e6 | 0.772087 | ||||||||
\(638\) | 1.27600e6 | 0.124108 | ||||||||
\(639\) | 3.75950e6 | 0.364232 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.60718e6 | −0.827401 | −0.413700 | − | 0.910413i | \(-0.635764\pi\) | ||||
−0.413700 | + | 0.910413i | \(0.635764\pi\) | |||||||
\(642\) | 4.70255e6 | 0.450294 | ||||||||
\(643\) | 1.97196e7 | 1.88092 | 0.940460 | − | 0.339904i | \(-0.110395\pi\) | ||||
0.940460 | + | 0.339904i | \(0.110395\pi\) | |||||||
\(644\) | 1.60658e7 | 1.52647 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.97884e6 | −0.186565 | ||||||||
\(647\) | 541311. | 0.0508378 | 0.0254189 | − | 0.999677i | \(-0.491908\pi\) | ||||
0.0254189 | + | 0.999677i | \(0.491908\pi\) | |||||||
\(648\) | −419904. | −0.0392837 | ||||||||
\(649\) | 3.99690e6 | 0.372488 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.45178e7 | 1.34261 | ||||||||
\(652\) | −940421. | −0.0866370 | ||||||||
\(653\) | 9.28231e6 | 0.851870 | 0.425935 | − | 0.904754i | \(-0.359945\pi\) | ||||
0.425935 | + | 0.904754i | \(0.359945\pi\) | |||||||
\(654\) | −1.85197e6 | −0.169312 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.65990e6 | 0.150599 | ||||||||
\(657\) | 4.98889e6 | 0.450910 | ||||||||
\(658\) | 7.21519e6 | 0.649655 | ||||||||
\(659\) | 1.79964e7 | 1.61425 | 0.807127 | − | 0.590378i | \(-0.201021\pi\) | ||||
0.807127 | + | 0.590378i | \(0.201021\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.78607e6 | 0.693130 | 0.346565 | − | 0.938026i | \(-0.387348\pi\) | ||||
0.346565 | + | 0.938026i | \(0.387348\pi\) | |||||||
\(662\) | −1.92369e6 | −0.170604 | ||||||||
\(663\) | 427006. | 0.0377268 | ||||||||
\(664\) | −3.26022e6 | −0.286964 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.76113e6 | −0.153853 | ||||||||
\(667\) | −1.52785e7 | −1.32974 | ||||||||
\(668\) | −2.47446e6 | −0.214556 | ||||||||
\(669\) | 7.57724e6 | 0.654554 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.04043e6 | −0.0892086 | ||||||||
\(672\) | −2.15383e6 | −0.183988 | ||||||||
\(673\) | −1.35540e7 | −1.15353 | −0.576766 | − | 0.816910i | \(-0.695685\pi\) | ||||
−0.576766 | + | 0.816910i | \(0.695685\pi\) | |||||||
\(674\) | −3.92579e6 | −0.332872 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.24100e6 | −0.441111 | ||||||||
\(677\) | −1.46008e7 | −1.22435 | −0.612173 | − | 0.790724i | \(-0.709704\pi\) | ||||
−0.612173 | + | 0.790724i | \(0.709704\pi\) | |||||||
\(678\) | −4.97731e6 | −0.415834 | ||||||||
\(679\) | −2.06679e7 | −1.72037 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −956668. | −0.0790485 | ||||||||
\(682\) | 2.47669e6 | 0.203897 | ||||||||
\(683\) | 9.71085e6 | 0.796536 | 0.398268 | − | 0.917269i | \(-0.369611\pi\) | ||||
0.398268 | + | 0.917269i | \(0.369611\pi\) | |||||||
\(684\) | −2.82589e6 | −0.230949 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.96355e7 | 1.59306 | ||||||||
\(687\) | −1.37638e7 | −1.11262 | ||||||||
\(688\) | 5.62676e6 | 0.453197 | ||||||||
\(689\) | −2.66947e6 | −0.214228 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.30382e7 | 1.03878 | 0.519389 | − | 0.854538i | \(-0.326159\pi\) | ||||
0.519389 | + | 0.854538i | \(0.326159\pi\) | |||||||
\(692\) | −2.74560e6 | −0.217958 | ||||||||
\(693\) | 1.69815e6 | 0.134321 | ||||||||
\(694\) | 7.66587e6 | 0.604175 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 2.04829e6 | 0.160276 | ||||||||
\(697\) | −1.47110e6 | −0.114699 | ||||||||
\(698\) | −4.91182e6 | −0.381596 | ||||||||
\(699\) | −3.25930e6 | −0.252308 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.65952e6 | 0.358134 | 0.179067 | − | 0.983837i | \(-0.442692\pi\) | ||||
0.179067 | + | 0.983837i | \(0.442692\pi\) | |||||||
\(702\) | 609788. | 0.0467021 | ||||||||
\(703\) | −1.18521e7 | −0.904500 | ||||||||
\(704\) | −367436. | −0.0279415 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.19129e6 | −0.165458 | ||||||||
\(707\) | 2.72199e7 | 2.04804 | ||||||||
\(708\) | 6.41601e6 | 0.481041 | ||||||||
\(709\) | 1.94059e7 | 1.44983 | 0.724916 | − | 0.688837i | \(-0.241878\pi\) | ||||
0.724916 | + | 0.688837i | \(0.241878\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.25810e6 | −0.167521 | ||||||||
\(712\) | −328396. | −0.0242772 | ||||||||
\(713\) | −2.96553e7 | −2.18463 | ||||||||
\(714\) | 1.90885e6 | 0.140129 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 9.52914e6 | 0.694658 | ||||||||
\(717\) | −346460. | −0.0251684 | ||||||||
\(718\) | −4.09254e6 | −0.296266 | ||||||||
\(719\) | 1.20100e7 | 0.866405 | 0.433202 | − | 0.901297i | \(-0.357384\pi\) | ||||
0.433202 | + | 0.901297i | \(0.357384\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.22778e6 | 0.374524 | ||||||||
\(722\) | −9.11343e6 | −0.650637 | ||||||||
\(723\) | −5.10689e6 | −0.363338 | ||||||||
\(724\) | 2.31229e6 | 0.163944 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −5.50814e6 | −0.387850 | ||||||||
\(727\) | 1.14993e7 | 0.806927 | 0.403463 | − | 0.914996i | \(-0.367806\pi\) | ||||
0.403463 | + | 0.914996i | \(0.367806\pi\) | |||||||
\(728\) | 3.12781e6 | 0.218732 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.98676e6 | −0.345164 | ||||||||
\(732\) | −1.67014e6 | −0.115206 | ||||||||
\(733\) | −2.04473e7 | −1.40565 | −0.702823 | − | 0.711364i | \(-0.748078\pi\) | ||||
−0.702823 | + | 0.711364i | \(0.748078\pi\) | |||||||
\(734\) | −1.22122e7 | −0.836668 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.39959e6 | 0.299376 | ||||||||
\(737\) | −355351. | −0.0240984 | ||||||||
\(738\) | −2.10082e6 | −0.141986 | ||||||||
\(739\) | 220621. | 0.0148606 | 0.00743030 | − | 0.999972i | \(-0.497635\pi\) | ||||
0.00743030 | + | 0.999972i | \(0.497635\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.10378e6 | 0.274561 | ||||||||
\(742\) | −1.19334e7 | −0.795707 | ||||||||
\(743\) | 2.51435e7 | 1.67091 | 0.835456 | − | 0.549558i | \(-0.185204\pi\) | ||||
0.835456 | + | 0.549558i | \(0.185204\pi\) | |||||||
\(744\) | 3.97569e6 | 0.263318 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1.47764e7 | 0.972126 | ||||||||
\(747\) | 4.12622e6 | 0.270552 | ||||||||
\(748\) | 325643. | 0.0212808 | ||||||||
\(749\) | −3.05282e7 | −1.98837 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −667547. | −0.0431899 | −0.0215950 | − | 0.999767i | \(-0.506874\pi\) | ||||
−0.0215950 | + | 0.999767i | \(0.506874\pi\) | |||||||
\(752\) | 1.97587e6 | 0.127413 | ||||||||
\(753\) | −171603. | −0.0110290 | ||||||||
\(754\) | −2.97454e6 | −0.190543 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.72595e6 | 0.173465 | ||||||||
\(757\) | 1.62490e7 | 1.03059 | 0.515297 | − | 0.857012i | \(-0.327682\pi\) | ||||
0.515297 | + | 0.857012i | \(0.327682\pi\) | |||||||
\(758\) | −1.79410e7 | −1.13416 | ||||||||
\(759\) | −3.46877e6 | −0.218560 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.43662e7 | −0.899253 | −0.449626 | − | 0.893217i | \(-0.648443\pi\) | ||||
−0.449626 | + | 0.893217i | \(0.648443\pi\) | |||||||
\(762\) | 7.18784e6 | 0.448447 | ||||||||
\(763\) | 1.20227e7 | 0.747634 | ||||||||
\(764\) | 1.30547e7 | 0.809157 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.81225e7 | 1.11595 | ||||||||
\(767\) | −9.31737e6 | −0.571880 | ||||||||
\(768\) | −589824. | −0.0360844 | ||||||||
\(769\) | 1.92705e7 | 1.17511 | 0.587553 | − | 0.809185i | \(-0.300091\pi\) | ||||
0.587553 | + | 0.809185i | \(0.300091\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.68648e6 | −0.465684 | ||||||||
\(772\) | 1.06405e7 | 0.642566 | ||||||||
\(773\) | 2.40693e7 | 1.44882 | 0.724410 | − | 0.689370i | \(-0.242112\pi\) | ||||
0.724410 | + | 0.689370i | \(0.242112\pi\) | |||||||
\(774\) | −7.12137e6 | −0.427279 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −5.65986e6 | −0.337405 | ||||||||
\(777\) | 1.14330e7 | 0.679370 | ||||||||
\(778\) | −1.09423e7 | −0.648125 | ||||||||
\(779\) | −1.41382e7 | −0.834737 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.16357e6 | −0.244252 | ||||||||
\(782\) | −3.89917e6 | −0.228011 | ||||||||
\(783\) | −2.59237e6 | −0.151110 | ||||||||
\(784\) | 9.67974e6 | 0.562436 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1.13120e7 | −0.653107 | ||||||||
\(787\) | 3.76223e6 | 0.216525 | 0.108263 | − | 0.994122i | \(-0.465471\pi\) | ||||
0.108263 | + | 0.994122i | \(0.465471\pi\) | |||||||
\(788\) | −5.32756e6 | −0.305642 | ||||||||
\(789\) | −6.79698e6 | −0.388708 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.23119e7 | 1.83620 | ||||||||
\(792\) | 465036. | 0.0263435 | ||||||||
\(793\) | 2.42540e6 | 0.136962 | ||||||||
\(794\) | 6.19794e6 | 0.348896 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −313045. | −0.0175115 | ||||||||
\(797\) | 9.10423e6 | 0.507689 | 0.253844 | − | 0.967245i | \(-0.418305\pi\) | ||||
0.253844 | + | 0.967245i | \(0.418305\pi\) | |||||||
\(798\) | 1.83452e7 | 1.01980 | ||||||||
\(799\) | −1.75113e6 | −0.0970401 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 415627. | 0.0228888 | ||||||||
\(802\) | −1.78454e7 | −0.979695 | ||||||||
\(803\) | −5.52510e6 | −0.302379 | ||||||||
\(804\) | −570425. | −0.0311214 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −5.77352e6 | −0.313043 | ||||||||
\(807\) | 2.30953e6 | 0.124836 | ||||||||
\(808\) | 7.45414e6 | 0.401670 | ||||||||
\(809\) | 1.20232e7 | 0.645877 | 0.322938 | − | 0.946420i | \(-0.395329\pi\) | ||||
0.322938 | + | 0.946420i | \(0.395329\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.50728e6 | −0.294026 | −0.147013 | − | 0.989135i | \(-0.546966\pi\) | ||||
−0.147013 | + | 0.989135i | \(0.546966\pi\) | |||||||
\(812\) | −1.32972e7 | −0.707732 | ||||||||
\(813\) | −5.38666e6 | −0.285821 | ||||||||
\(814\) | 1.95042e6 | 0.103173 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 522736. | 0.0274826 | ||||||||
\(817\) | −4.79258e7 | −2.51197 | ||||||||
\(818\) | 9.47258e6 | 0.494977 | ||||||||
\(819\) | −3.95864e6 | −0.206223 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.33971e7 | 0.693672 | 0.346836 | − | 0.937926i | \(-0.387256\pi\) | ||||
0.346836 | + | 0.937926i | \(0.387256\pi\) | |||||||
\(822\) | −9.24626e6 | −0.477295 | ||||||||
\(823\) | −1.41005e7 | −0.725664 | −0.362832 | − | 0.931855i | \(-0.618190\pi\) | ||||
−0.362832 | + | 0.931855i | \(0.618190\pi\) | |||||||
\(824\) | 1.43162e6 | 0.0734530 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.16516e7 | −2.12413 | ||||||||
\(827\) | 1.28958e7 | 0.655669 | 0.327834 | − | 0.944735i | \(-0.393681\pi\) | ||||
0.327834 | + | 0.944735i | \(0.393681\pi\) | |||||||
\(828\) | −5.56823e6 | −0.282255 | ||||||||
\(829\) | −372726. | −0.0188366 | −0.00941831 | − | 0.999956i | \(-0.502998\pi\) | ||||
−0.00941831 | + | 0.999956i | \(0.502998\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.82541e6 | −0.192165 | ||||||||
\(832\) | 856547. | 0.0428986 | ||||||||
\(833\) | −8.57875e6 | −0.428362 | ||||||||
\(834\) | −387980. | −0.0193150 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 3.12962e6 | 0.154873 | ||||||||
\(837\) | −5.03173e6 | −0.248258 | ||||||||
\(838\) | −2.30545e7 | −1.13409 | ||||||||
\(839\) | 1.57724e7 | 0.773560 | 0.386780 | − | 0.922172i | \(-0.373587\pi\) | ||||
0.386780 | + | 0.922172i | \(0.373587\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.86558e6 | −0.383478 | ||||||||
\(842\) | −1.30629e7 | −0.634978 | ||||||||
\(843\) | 8.54966e6 | 0.414362 | ||||||||
\(844\) | −1.07116e7 | −0.517604 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −2.50071e6 | −0.120126 | ||||||||
\(847\) | 3.57579e7 | 1.71263 | ||||||||
\(848\) | −3.26793e6 | −0.156057 | ||||||||
\(849\) | 1.91180e7 | 0.910275 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.33538e7 | −1.10544 | ||||||||
\(852\) | −6.68355e6 | −0.315434 | ||||||||
\(853\) | 3.39555e6 | 0.159786 | 0.0798928 | − | 0.996803i | \(-0.474542\pi\) | ||||
0.0798928 | + | 0.996803i | \(0.474542\pi\) | |||||||
\(854\) | 1.08423e7 | 0.508718 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8.36009e6 | −0.389966 | ||||||||
\(857\) | −4.62981e6 | −0.215333 | −0.107667 | − | 0.994187i | \(-0.534338\pi\) | ||||
−0.107667 | + | 0.994187i | \(0.534338\pi\) | |||||||
\(858\) | −675329. | −0.0313182 | ||||||||
\(859\) | −1.57703e7 | −0.729218 | −0.364609 | − | 0.931161i | \(-0.618797\pi\) | ||||
−0.364609 | + | 0.931161i | \(0.618797\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.36381e7 | 0.626971 | ||||||||
\(862\) | 2.24844e7 | 1.03065 | ||||||||
\(863\) | 3.26217e7 | 1.49101 | 0.745503 | − | 0.666502i | \(-0.232209\pi\) | ||||
0.745503 | + | 0.666502i | \(0.232209\pi\) | |||||||
\(864\) | 746496. | 0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1.27462e7 | −0.577546 | ||||||||
\(867\) | 1.23154e7 | 0.556419 | ||||||||
\(868\) | −2.58095e7 | −1.16273 | ||||||||
\(869\) | 2.50080e6 | 0.112339 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 828376. | 0.0369983 | ||||||||
\(872\) | 3.29239e6 | 0.146629 | ||||||||
\(873\) | 7.16326e6 | 0.318108 | ||||||||
\(874\) | −3.74733e7 | −1.65937 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −8.86913e6 | −0.390500 | ||||||||
\(877\) | −3.88139e6 | −0.170407 | −0.0852037 | − | 0.996364i | \(-0.527154\pi\) | ||||
−0.0852037 | + | 0.996364i | \(0.527154\pi\) | |||||||
\(878\) | 2.96441e7 | 1.29778 | ||||||||
\(879\) | −1.05801e7 | −0.461867 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.11909e7 | −0.919834 | −0.459917 | − | 0.887962i | \(-0.652121\pi\) | ||||
−0.459917 | + | 0.887962i | \(0.652121\pi\) | |||||||
\(882\) | −1.22509e7 | −0.530270 | ||||||||
\(883\) | −257162. | −0.0110995 | −0.00554976 | − | 0.999985i | \(-0.501767\pi\) | ||||
−0.00554976 | + | 0.999985i | \(0.501767\pi\) | |||||||
\(884\) | −759122. | −0.0326724 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.05145e7 | 0.449990 | ||||||||
\(887\) | 1.02364e7 | 0.436856 | 0.218428 | − | 0.975853i | \(-0.429907\pi\) | ||||
0.218428 | + | 0.975853i | \(0.429907\pi\) | |||||||
\(888\) | 3.13090e6 | 0.133241 | ||||||||
\(889\) | −4.66623e7 | −1.98021 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −588561. | −0.0248369 | ||||||||
\(892\) | −1.34706e7 | −0.566860 | ||||||||
\(893\) | −1.68294e7 | −0.706220 | ||||||||
\(894\) | 147718. | 0.00618142 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 3.82904e6 | 0.159338 | ||||||||
\(897\) | 8.08622e6 | 0.335556 | ||||||||
\(898\) | −287058. | −0.0118790 | ||||||||
\(899\) | 2.45448e7 | 1.01288 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.89623e6 | 0.118856 | ||||||||
\(902\) | 2.32661e6 | 0.0952155 | ||||||||
\(903\) | 4.62307e7 | 1.88674 | ||||||||
\(904\) | 8.84855e6 | 0.360123 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 3.86816e6 | 0.156561 | ||||||||
\(907\) | −1.30652e7 | −0.527350 | −0.263675 | − | 0.964612i | \(-0.584935\pi\) | ||||
−0.263675 | + | 0.964612i | \(0.584935\pi\) | |||||||
\(908\) | 1.70074e6 | 0.0684580 | ||||||||
\(909\) | −9.43414e6 | −0.378698 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.81608e6 | −0.391870 | −0.195935 | − | 0.980617i | \(-0.562774\pi\) | ||||
−0.195935 | + | 0.980617i | \(0.562774\pi\) | |||||||
\(912\) | 5.02381e6 | 0.200007 | ||||||||
\(913\) | −4.56971e6 | −0.181431 | ||||||||
\(914\) | −1.40588e7 | −0.556652 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.44689e7 | 0.963553 | ||||||||
\(917\) | 7.34358e7 | 2.88393 | ||||||||
\(918\) | −661588. | −0.0259108 | ||||||||
\(919\) | 2.71414e6 | 0.106009 | 0.0530045 | − | 0.998594i | \(-0.483120\pi\) | ||||
0.0530045 | + | 0.998594i | \(0.483120\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.29668e6 | 0.205757 | ||||||||
\(922\) | −1.34228e7 | −0.520013 | ||||||||
\(923\) | 9.70591e6 | 0.375000 | ||||||||
\(924\) | −3.01893e6 | −0.116325 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −1.38908e7 | −0.532352 | ||||||||
\(927\) | −1.81189e6 | −0.0692522 | ||||||||
\(928\) | −3.64141e6 | −0.138803 | ||||||||
\(929\) | −4.31963e6 | −0.164213 | −0.0821064 | − | 0.996624i | \(-0.526165\pi\) | ||||
−0.0821064 | + | 0.996624i | \(0.526165\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.24469e7 | −3.11745 | ||||||||
\(932\) | 5.79431e6 | 0.218505 | ||||||||
\(933\) | −1.45677e7 | −0.547881 | ||||||||
\(934\) | −9.41981e6 | −0.353326 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.08407e6 | −0.0404452 | ||||||||
\(937\) | −2.17380e7 | −0.808854 | −0.404427 | − | 0.914570i | \(-0.632529\pi\) | ||||
−0.404427 | + | 0.914570i | \(0.632529\pi\) | |||||||
\(938\) | 3.70311e6 | 0.137423 | ||||||||
\(939\) | −1.43011e7 | −0.529305 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.17794e7 | −0.801811 | −0.400905 | − | 0.916119i | \(-0.631304\pi\) | ||||
−0.400905 | + | 0.916119i | \(0.631304\pi\) | |||||||
\(942\) | 1.24496e7 | 0.457120 | ||||||||
\(943\) | −2.78583e7 | −1.02018 | ||||||||
\(944\) | −1.14062e7 | −0.416593 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7.88678e6 | 0.286531 | ||||||||
\(947\) | −4.93262e7 | −1.78732 | −0.893660 | − | 0.448745i | \(-0.851871\pi\) | ||||
−0.893660 | + | 0.448745i | \(0.851871\pi\) | |||||||
\(948\) | 4.01440e6 | 0.145077 | ||||||||
\(949\) | 1.28798e7 | 0.464242 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.11623e7 | −0.758773 | ||||||||
\(952\) | −3.39352e6 | −0.121355 | ||||||||
\(953\) | −3.37247e7 | −1.20286 | −0.601432 | − | 0.798924i | \(-0.705403\pi\) | ||||
−0.601432 | + | 0.798924i | \(0.705403\pi\) | |||||||
\(954\) | 4.13598e6 | 0.147132 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 615929. | 0.0217965 | ||||||||
\(957\) | 2.87100e6 | 0.101334 | ||||||||
\(958\) | 751082. | 0.0264407 | ||||||||
\(959\) | 6.00252e7 | 2.10759 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.90117e7 | 0.664068 | ||||||||
\(962\) | −4.54671e6 | −0.158402 | ||||||||
\(963\) | 1.05807e7 | 0.367663 | ||||||||
\(964\) | 9.07892e6 | 0.314660 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 3.61480e7 | 1.24635 | ||||||||
\(967\) | 2.77310e7 | 0.953673 | 0.476836 | − | 0.878992i | \(-0.341783\pi\) | ||||
0.476836 | + | 0.878992i | \(0.341783\pi\) | |||||||
\(968\) | 9.79225e6 | 0.335888 | ||||||||
\(969\) | −4.45239e6 | −0.152329 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6.67841e6 | −0.227314 | −0.113657 | − | 0.993520i | \(-0.536256\pi\) | ||||
−0.113657 | + | 0.993520i | \(0.536256\pi\) | |||||||
\(972\) | −944784. | −0.0320750 | ||||||||
\(973\) | 2.51870e6 | 0.0852893 | ||||||||
\(974\) | 8.06018e6 | 0.272237 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.96915e6 | 0.0997716 | ||||||||
\(977\) | −4.34946e7 | −1.45780 | −0.728902 | − | 0.684618i | \(-0.759969\pi\) | ||||
−0.728902 | + | 0.684618i | \(0.759969\pi\) | |||||||
\(978\) | −2.11595e6 | −0.0707388 | ||||||||
\(979\) | −460299. | −0.0153491 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.16693e6 | −0.138243 | ||||||||
\(982\) | −2.32326e7 | −0.768809 | ||||||||
\(983\) | 1.24213e7 | 0.410000 | 0.205000 | − | 0.978762i | \(-0.434281\pi\) | ||||
0.205000 | + | 0.978762i | \(0.434281\pi\) | |||||||
\(984\) | 3.73478e6 | 0.122964 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 3.22723e6 | 0.105715 | ||||||||
\(987\) | 1.62342e7 | 0.530441 | ||||||||
\(988\) | −7.29561e6 | −0.237777 | ||||||||
\(989\) | −9.44344e7 | −3.07001 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.93479e7 | 1.91965 | 0.959824 | − | 0.280604i | \(-0.0905348\pi\) | ||||
0.959824 | + | 0.280604i | \(0.0905348\pi\) | |||||||
\(992\) | −7.06789e6 | −0.228040 | ||||||||
\(993\) | −4.32830e6 | −0.139298 | ||||||||
\(994\) | 4.33885e7 | 1.39286 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −7.33550e6 | −0.234305 | ||||||||
\(997\) | −2.44456e7 | −0.778867 | −0.389434 | − | 0.921055i | \(-0.627329\pi\) | ||||
−0.389434 | + | 0.921055i | \(0.627329\pi\) | |||||||
\(998\) | −2.32244e6 | −0.0738107 | ||||||||
\(999\) | −3.96254e6 | −0.125620 |
(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 | 150.6.a.n.1.1 | 2 | ||
3.2 | odd | 2 | 450.6.a.bc.1.1 | 2 | |||
5.2 | odd | 4 | 30.6.c.b.19.2 | ✓ | 4 | ||
5.3 | odd | 4 | 30.6.c.b.19.4 | yes | 4 | ||
5.4 | even | 2 | 150.6.a.o.1.2 | 2 | |||
15.2 | even | 4 | 90.6.c.c.19.3 | 4 | |||
15.8 | even | 4 | 90.6.c.c.19.1 | 4 | |||
15.14 | odd | 2 | 450.6.a.bb.1.2 | 2 | |||
20.3 | even | 4 | 240.6.f.b.49.4 | 4 | |||
20.7 | even | 4 | 240.6.f.b.49.2 | 4 | |||
60.23 | odd | 4 | 720.6.f.i.289.1 | 4 | |||
60.47 | odd | 4 | 720.6.f.i.289.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
30.6.c.b.19.2 | ✓ | 4 | 5.2 | odd | 4 | ||
30.6.c.b.19.4 | yes | 4 | 5.3 | odd | 4 | ||
90.6.c.c.19.1 | 4 | 15.8 | even | 4 | |||
90.6.c.c.19.3 | 4 | 15.2 | even | 4 | |||
150.6.a.n.1.1 | 2 | 1.1 | even | 1 | trivial | ||
150.6.a.o.1.2 | 2 | 5.4 | even | 2 | |||
240.6.f.b.49.2 | 4 | 20.7 | even | 4 | |||
240.6.f.b.49.4 | 4 | 20.3 | even | 4 | |||
450.6.a.bb.1.2 | 2 | 15.14 | odd | 2 | |||
450.6.a.bc.1.1 | 2 | 3.2 | odd | 2 | |||
720.6.f.i.289.1 | 4 | 60.23 | odd | 4 | |||
720.6.f.i.289.2 | 4 | 60.47 | odd | 4 |