Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,6,Mod(1,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.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: | \(132.316651346\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - x^{6} - 209x^{5} + 137x^{4} + 12724x^{3} - 1040x^{2} - 218208x - 8784 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3\cdot 5 \) |
Twist minimal: | no (minimal twist has level 165) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-10.8333\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 10.8333 | 1.91508 | 0.957538 | − | 0.288306i | \(-0.0930919\pi\) | ||||
0.957538 | + | 0.288306i | \(0.0930919\pi\) | |||||||
\(3\) | −9.00000 | −0.577350 | ||||||||
\(4\) | 85.3606 | 2.66752 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −97.4998 | −1.10567 | ||||||||
\(7\) | 188.476 | 1.45382 | 0.726911 | − | 0.686732i | \(-0.240955\pi\) | ||||
0.726911 | + | 0.686732i | \(0.240955\pi\) | |||||||
\(8\) | 578.072 | 3.19343 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 121.000 | 0.301511 | ||||||||
\(12\) | −768.246 | −1.54009 | ||||||||
\(13\) | −1062.44 | −1.74359 | −0.871795 | − | 0.489870i | \(-0.837044\pi\) | ||||
−0.871795 | + | 0.489870i | \(0.837044\pi\) | |||||||
\(14\) | 2041.82 | 2.78418 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3530.89 | 3.44814 | ||||||||
\(17\) | 2033.15 | 1.70627 | 0.853135 | − | 0.521690i | \(-0.174698\pi\) | ||||
0.853135 | + | 0.521690i | \(0.174698\pi\) | |||||||
\(18\) | 877.498 | 0.638359 | ||||||||
\(19\) | 285.586 | 0.181490 | 0.0907451 | − | 0.995874i | \(-0.471075\pi\) | ||||
0.0907451 | + | 0.995874i | \(0.471075\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1696.29 | −0.839365 | ||||||||
\(22\) | 1310.83 | 0.577417 | ||||||||
\(23\) | 589.341 | 0.232299 | 0.116149 | − | 0.993232i | \(-0.462945\pi\) | ||||
0.116149 | + | 0.993232i | \(0.462945\pi\) | |||||||
\(24\) | −5202.65 | −1.84373 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −11509.7 | −3.33911 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | 16088.4 | 3.87810 | ||||||||
\(29\) | 5682.63 | 1.25474 | 0.627371 | − | 0.778721i | \(-0.284131\pi\) | ||||
0.627371 | + | 0.778721i | \(0.284131\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1897.21 | 0.354577 | 0.177289 | − | 0.984159i | \(-0.443267\pi\) | ||||
0.177289 | + | 0.984159i | \(0.443267\pi\) | |||||||
\(32\) | 19753.0 | 3.41002 | ||||||||
\(33\) | −1089.00 | −0.174078 | ||||||||
\(34\) | 22025.8 | 3.26764 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 6914.21 | 0.889173 | ||||||||
\(37\) | −6513.03 | −0.782130 | −0.391065 | − | 0.920363i | \(-0.627893\pi\) | ||||
−0.391065 | + | 0.920363i | \(0.627893\pi\) | |||||||
\(38\) | 3093.84 | 0.347568 | ||||||||
\(39\) | 9561.93 | 1.00666 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −17560.3 | −1.63144 | −0.815721 | − | 0.578445i | \(-0.803660\pi\) | ||||
−0.815721 | + | 0.578445i | \(0.803660\pi\) | |||||||
\(42\) | −18376.4 | −1.60745 | ||||||||
\(43\) | −8948.19 | −0.738013 | −0.369007 | − | 0.929427i | \(-0.620302\pi\) | ||||
−0.369007 | + | 0.929427i | \(0.620302\pi\) | |||||||
\(44\) | 10328.6 | 0.804287 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6384.51 | 0.444870 | ||||||||
\(47\) | 12072.6 | 0.797176 | 0.398588 | − | 0.917130i | \(-0.369500\pi\) | ||||
0.398588 | + | 0.917130i | \(0.369500\pi\) | |||||||
\(48\) | −31778.1 | −1.99078 | ||||||||
\(49\) | 18716.2 | 1.11360 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −18298.4 | −0.985116 | ||||||||
\(52\) | −90690.2 | −4.65106 | ||||||||
\(53\) | 7805.32 | 0.381681 | 0.190841 | − | 0.981621i | \(-0.438879\pi\) | ||||
0.190841 | + | 0.981621i | \(0.438879\pi\) | |||||||
\(54\) | −7897.48 | −0.368557 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 108953. | 4.64267 | ||||||||
\(57\) | −2570.28 | −0.104783 | ||||||||
\(58\) | 61561.7 | 2.40293 | ||||||||
\(59\) | 32104.2 | 1.20069 | 0.600347 | − | 0.799740i | \(-0.295029\pi\) | ||||
0.600347 | + | 0.799740i | \(0.295029\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 360.190 | 0.0123939 | 0.00619693 | − | 0.999981i | \(-0.498027\pi\) | ||||
0.00619693 | + | 0.999981i | \(0.498027\pi\) | |||||||
\(62\) | 20553.1 | 0.679043 | ||||||||
\(63\) | 15266.6 | 0.484607 | ||||||||
\(64\) | 101001. | 3.08232 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −11797.5 | −0.333372 | ||||||||
\(67\) | −40493.0 | −1.10203 | −0.551015 | − | 0.834496i | \(-0.685759\pi\) | ||||
−0.551015 | + | 0.834496i | \(0.685759\pi\) | |||||||
\(68\) | 173551. | 4.55151 | ||||||||
\(69\) | −5304.07 | −0.134118 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 72765.1 | 1.71308 | 0.856539 | − | 0.516082i | \(-0.172610\pi\) | ||||
0.856539 | + | 0.516082i | \(0.172610\pi\) | |||||||
\(72\) | 46823.8 | 1.06448 | ||||||||
\(73\) | −22289.1 | −0.489536 | −0.244768 | − | 0.969582i | \(-0.578712\pi\) | ||||
−0.244768 | + | 0.969582i | \(0.578712\pi\) | |||||||
\(74\) | −70557.7 | −1.49784 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 24377.8 | 0.484129 | ||||||||
\(77\) | 22805.6 | 0.438344 | ||||||||
\(78\) | 103587. | 1.92784 | ||||||||
\(79\) | 51779.4 | 0.933446 | 0.466723 | − | 0.884403i | \(-0.345434\pi\) | ||||
0.466723 | + | 0.884403i | \(0.345434\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | −190236. | −3.12434 | ||||||||
\(83\) | −77834.1 | −1.24015 | −0.620076 | − | 0.784542i | \(-0.712898\pi\) | ||||
−0.620076 | + | 0.784542i | \(0.712898\pi\) | |||||||
\(84\) | −144796. | −2.23902 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −96938.5 | −1.41335 | ||||||||
\(87\) | −51143.6 | −0.724425 | ||||||||
\(88\) | 69946.7 | 0.962855 | ||||||||
\(89\) | 48019.3 | 0.642601 | 0.321300 | − | 0.946977i | \(-0.395880\pi\) | ||||
0.321300 | + | 0.946977i | \(0.395880\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −200244. | −2.53487 | ||||||||
\(92\) | 50306.5 | 0.619661 | ||||||||
\(93\) | −17074.9 | −0.204715 | ||||||||
\(94\) | 130786. | 1.52665 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −177777. | −1.96878 | ||||||||
\(97\) | 115985. | 1.25161 | 0.625807 | − | 0.779978i | \(-0.284770\pi\) | ||||
0.625807 | + | 0.779978i | \(0.284770\pi\) | |||||||
\(98\) | 202759. | 2.13263 | ||||||||
\(99\) | 9801.00 | 0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 125600. | 1.22514 | 0.612569 | − | 0.790417i | \(-0.290136\pi\) | ||||
0.612569 | + | 0.790417i | \(0.290136\pi\) | |||||||
\(102\) | −198232. | −1.88657 | ||||||||
\(103\) | −197051. | −1.83015 | −0.915073 | − | 0.403288i | \(-0.867867\pi\) | ||||
−0.915073 | + | 0.403288i | \(0.867867\pi\) | |||||||
\(104\) | −614165. | −5.56803 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 84557.4 | 0.730949 | ||||||||
\(107\) | −148145. | −1.25091 | −0.625456 | − | 0.780259i | \(-0.715087\pi\) | ||||
−0.625456 | + | 0.780259i | \(0.715087\pi\) | |||||||
\(108\) | −62227.9 | −0.513364 | ||||||||
\(109\) | −100008. | −0.806246 | −0.403123 | − | 0.915146i | \(-0.632075\pi\) | ||||
−0.403123 | + | 0.915146i | \(0.632075\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 58617.3 | 0.451563 | ||||||||
\(112\) | 665489. | 5.01298 | ||||||||
\(113\) | 22869.8 | 0.168487 | 0.0842435 | − | 0.996445i | \(-0.473153\pi\) | ||||
0.0842435 | + | 0.996445i | \(0.473153\pi\) | |||||||
\(114\) | −27844.6 | −0.200668 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 485073. | 3.34705 | ||||||||
\(117\) | −86057.3 | −0.581197 | ||||||||
\(118\) | 347795. | 2.29942 | ||||||||
\(119\) | 383201. | 2.48061 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | 3902.05 | 0.0237352 | ||||||||
\(123\) | 158042. | 0.941914 | ||||||||
\(124\) | 161947. | 0.945842 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 165387. | 0.928060 | ||||||||
\(127\) | −10903.4 | −0.0599861 | −0.0299931 | − | 0.999550i | \(-0.509549\pi\) | ||||
−0.0299931 | + | 0.999550i | \(0.509549\pi\) | |||||||
\(128\) | 462085. | 2.49285 | ||||||||
\(129\) | 80533.7 | 0.426092 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 75423.0 | 0.383995 | 0.191997 | − | 0.981395i | \(-0.438503\pi\) | ||||
0.191997 | + | 0.981395i | \(0.438503\pi\) | |||||||
\(132\) | −92957.7 | −0.464355 | ||||||||
\(133\) | 53826.2 | 0.263854 | ||||||||
\(134\) | −438674. | −2.11047 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.17531e6 | 5.44885 | ||||||||
\(137\) | 371462. | 1.69088 | 0.845440 | − | 0.534071i | \(-0.179338\pi\) | ||||
0.845440 | + | 0.534071i | \(0.179338\pi\) | |||||||
\(138\) | −57460.6 | −0.256846 | ||||||||
\(139\) | −7305.52 | −0.0320711 | −0.0160356 | − | 0.999871i | \(-0.505104\pi\) | ||||
−0.0160356 | + | 0.999871i | \(0.505104\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −108653. | −0.460250 | ||||||||
\(142\) | 788287. | 3.28068 | ||||||||
\(143\) | −128555. | −0.525712 | ||||||||
\(144\) | 286002. | 1.14938 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −241464. | −0.937499 | ||||||||
\(147\) | −168446. | −0.642936 | ||||||||
\(148\) | −555956. | −2.08635 | ||||||||
\(149\) | −116850. | −0.431185 | −0.215593 | − | 0.976483i | \(-0.569168\pi\) | ||||
−0.215593 | + | 0.976483i | \(0.569168\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 165567. | 0.590925 | 0.295462 | − | 0.955354i | \(-0.404526\pi\) | ||||
0.295462 | + | 0.955354i | \(0.404526\pi\) | |||||||
\(152\) | 165089. | 0.579576 | ||||||||
\(153\) | 164685. | 0.568757 | ||||||||
\(154\) | 247060. | 0.839462 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 816212. | 2.68529 | ||||||||
\(157\) | −305132. | −0.987958 | −0.493979 | − | 0.869474i | \(-0.664458\pi\) | ||||
−0.493979 | + | 0.869474i | \(0.664458\pi\) | |||||||
\(158\) | 560942. | 1.78762 | ||||||||
\(159\) | −70247.9 | −0.220364 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 111077. | 0.337721 | ||||||||
\(162\) | 71077.3 | 0.212786 | ||||||||
\(163\) | 446634. | 1.31669 | 0.658344 | − | 0.752718i | \(-0.271257\pi\) | ||||
0.658344 | + | 0.752718i | \(0.271257\pi\) | |||||||
\(164\) | −1.49896e6 | −4.35190 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −843201. | −2.37499 | ||||||||
\(167\) | −134567. | −0.373377 | −0.186688 | − | 0.982419i | \(-0.559775\pi\) | ||||
−0.186688 | + | 0.982419i | \(0.559775\pi\) | |||||||
\(168\) | −980575. | −2.68045 | ||||||||
\(169\) | 757478. | 2.04011 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 23132.5 | 0.0604967 | ||||||||
\(172\) | −763823. | −1.96866 | ||||||||
\(173\) | −559521. | −1.42135 | −0.710676 | − | 0.703520i | \(-0.751611\pi\) | ||||
−0.710676 | + | 0.703520i | \(0.751611\pi\) | |||||||
\(174\) | −554055. | −1.38733 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 427238. | 1.03965 | ||||||||
\(177\) | −288938. | −0.693221 | ||||||||
\(178\) | 520208. | 1.23063 | ||||||||
\(179\) | 123724. | 0.288617 | 0.144309 | − | 0.989533i | \(-0.453904\pi\) | ||||
0.144309 | + | 0.989533i | \(0.453904\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 665605. | 1.51015 | 0.755075 | − | 0.655638i | \(-0.227600\pi\) | ||||
0.755075 | + | 0.655638i | \(0.227600\pi\) | |||||||
\(182\) | −2.16930e6 | −4.85447 | ||||||||
\(183\) | −3241.71 | −0.00715560 | ||||||||
\(184\) | 340681. | 0.741829 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −184977. | −0.392046 | ||||||||
\(187\) | 246012. | 0.514460 | ||||||||
\(188\) | 1.03052e6 | 2.12648 | ||||||||
\(189\) | −137399. | −0.279788 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 310886. | 0.616621 | 0.308311 | − | 0.951286i | \(-0.400236\pi\) | ||||
0.308311 | + | 0.951286i | \(0.400236\pi\) | |||||||
\(192\) | −909013. | −1.77958 | ||||||||
\(193\) | −76821.1 | −0.148452 | −0.0742262 | − | 0.997241i | \(-0.523649\pi\) | ||||
−0.0742262 | + | 0.997241i | \(0.523649\pi\) | |||||||
\(194\) | 1.25650e6 | 2.39694 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.59763e6 | 2.97054 | ||||||||
\(197\) | 670364. | 1.23068 | 0.615340 | − | 0.788262i | \(-0.289019\pi\) | ||||
0.615340 | + | 0.788262i | \(0.289019\pi\) | |||||||
\(198\) | 106177. | 0.192472 | ||||||||
\(199\) | −793545. | −1.42049 | −0.710247 | − | 0.703953i | \(-0.751417\pi\) | ||||
−0.710247 | + | 0.703953i | \(0.751417\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 364437. | 0.636257 | ||||||||
\(202\) | 1.36066e6 | 2.34623 | ||||||||
\(203\) | 1.07104e6 | 1.82417 | ||||||||
\(204\) | −1.56196e6 | −2.62781 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2.13472e6 | −3.50487 | ||||||||
\(207\) | 47736.6 | 0.0774329 | ||||||||
\(208\) | −3.75135e6 | −6.01214 | ||||||||
\(209\) | 34555.9 | 0.0547214 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −106650. | −0.164913 | −0.0824563 | − | 0.996595i | \(-0.526276\pi\) | ||||
−0.0824563 | + | 0.996595i | \(0.526276\pi\) | |||||||
\(212\) | 666267. | 1.01814 | ||||||||
\(213\) | −654886. | −0.989046 | ||||||||
\(214\) | −1.60490e6 | −2.39559 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −421415. | −0.614575 | ||||||||
\(217\) | 357579. | 0.515492 | ||||||||
\(218\) | −1.08342e6 | −1.54402 | ||||||||
\(219\) | 200602. | 0.282634 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.16010e6 | −2.97504 | ||||||||
\(222\) | 635019. | 0.864778 | ||||||||
\(223\) | 832483. | 1.12102 | 0.560510 | − | 0.828148i | \(-0.310605\pi\) | ||||
0.560510 | + | 0.828148i | \(0.310605\pi\) | |||||||
\(224\) | 3.72296e6 | 4.95757 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 247756. | 0.322666 | ||||||||
\(227\) | −1.12488e6 | −1.44891 | −0.724455 | − | 0.689322i | \(-0.757909\pi\) | ||||
−0.724455 | + | 0.689322i | \(0.757909\pi\) | |||||||
\(228\) | −219400. | −0.279512 | ||||||||
\(229\) | −1.28251e6 | −1.61611 | −0.808057 | − | 0.589104i | \(-0.799481\pi\) | ||||
−0.808057 | + | 0.589104i | \(0.799481\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −205250. | −0.253078 | ||||||||
\(232\) | 3.28497e6 | 4.00692 | ||||||||
\(233\) | −482579. | −0.582343 | −0.291171 | − | 0.956671i | \(-0.594045\pi\) | ||||
−0.291171 | + | 0.956671i | \(0.594045\pi\) | |||||||
\(234\) | −932286. | −1.11304 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.74044e6 | 3.20287 | ||||||||
\(237\) | −466015. | −0.538926 | ||||||||
\(238\) | 4.15133e6 | 4.75056 | ||||||||
\(239\) | 218277. | 0.247180 | 0.123590 | − | 0.992333i | \(-0.460559\pi\) | ||||
0.123590 | + | 0.992333i | \(0.460559\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 673119. | 0.746533 | 0.373267 | − | 0.927724i | \(-0.378238\pi\) | ||||
0.373267 | + | 0.927724i | \(0.378238\pi\) | |||||||
\(242\) | 158610. | 0.174098 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | 30746.0 | 0.0330609 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.71212e6 | 1.80384 | ||||||||
\(247\) | −303417. | −0.316445 | ||||||||
\(248\) | 1.09672e6 | 1.13232 | ||||||||
\(249\) | 700507. | 0.716002 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −924557. | −0.926295 | −0.463148 | − | 0.886281i | \(-0.653280\pi\) | ||||
−0.463148 | + | 0.886281i | \(0.653280\pi\) | |||||||
\(252\) | 1.30316e6 | 1.29270 | ||||||||
\(253\) | 71310.2 | 0.0700407 | ||||||||
\(254\) | −118119. | −0.114878 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.77386e6 | 1.69169 | ||||||||
\(257\) | 471931. | 0.445704 | 0.222852 | − | 0.974852i | \(-0.428463\pi\) | ||||
0.222852 | + | 0.974852i | \(0.428463\pi\) | |||||||
\(258\) | 872447. | 0.815999 | ||||||||
\(259\) | −1.22755e6 | −1.13708 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 460293. | 0.418247 | ||||||||
\(262\) | 817081. | 0.735380 | ||||||||
\(263\) | −869418. | −0.775067 | −0.387534 | − | 0.921856i | \(-0.626673\pi\) | ||||
−0.387534 | + | 0.921856i | \(0.626673\pi\) | |||||||
\(264\) | −629521. | −0.555904 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 583116. | 0.505302 | ||||||||
\(267\) | −432174. | −0.371006 | ||||||||
\(268\) | −3.45651e6 | −2.93968 | ||||||||
\(269\) | −460155. | −0.387725 | −0.193862 | − | 0.981029i | \(-0.562102\pi\) | ||||
−0.193862 | + | 0.981029i | \(0.562102\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −488213. | −0.403818 | −0.201909 | − | 0.979404i | \(-0.564715\pi\) | ||||
−0.201909 | + | 0.979404i | \(0.564715\pi\) | |||||||
\(272\) | 7.17885e6 | 5.88346 | ||||||||
\(273\) | 1.80219e6 | 1.46351 | ||||||||
\(274\) | 4.02416e6 | 3.23816 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −452758. | −0.357762 | ||||||||
\(277\) | 1.94033e6 | 1.51942 | 0.759708 | − | 0.650264i | \(-0.225342\pi\) | ||||
0.759708 | + | 0.650264i | \(0.225342\pi\) | |||||||
\(278\) | −79142.9 | −0.0614186 | ||||||||
\(279\) | 153674. | 0.118192 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.76289e6 | −1.33186 | −0.665930 | − | 0.746015i | \(-0.731965\pi\) | ||||
−0.665930 | + | 0.746015i | \(0.731965\pi\) | |||||||
\(282\) | −1.17707e6 | −0.881414 | ||||||||
\(283\) | 461211. | 0.342321 | 0.171160 | − | 0.985243i | \(-0.445248\pi\) | ||||
0.171160 | + | 0.985243i | \(0.445248\pi\) | |||||||
\(284\) | 6.21127e6 | 4.56967 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.39267e6 | −1.00678 | ||||||||
\(287\) | −3.30969e6 | −2.37183 | ||||||||
\(288\) | 1.59999e6 | 1.13667 | ||||||||
\(289\) | 2.71386e6 | 1.91136 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.04386e6 | −0.722620 | ||||||||
\(292\) | −1.90261e6 | −1.30585 | ||||||||
\(293\) | −1.72981e6 | −1.17715 | −0.588573 | − | 0.808444i | \(-0.700310\pi\) | ||||
−0.588573 | + | 0.808444i | \(0.700310\pi\) | |||||||
\(294\) | −1.82483e6 | −1.23127 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3.76500e6 | −2.49768 | ||||||||
\(297\) | −88209.0 | −0.0580259 | ||||||||
\(298\) | −1.26588e6 | −0.825753 | ||||||||
\(299\) | −626137. | −0.405034 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.68652e6 | −1.07294 | ||||||||
\(302\) | 1.79364e6 | 1.13167 | ||||||||
\(303\) | −1.13040e6 | −0.707334 | ||||||||
\(304\) | 1.00837e6 | 0.625804 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.78409e6 | 1.08921 | ||||||||
\(307\) | −502403. | −0.304233 | −0.152117 | − | 0.988363i | \(-0.548609\pi\) | ||||
−0.152117 | + | 0.988363i | \(0.548609\pi\) | |||||||
\(308\) | 1.94670e6 | 1.16929 | ||||||||
\(309\) | 1.77346e6 | 1.05664 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.84484e6 | −1.08158 | −0.540789 | − | 0.841158i | \(-0.681874\pi\) | ||||
−0.540789 | + | 0.841158i | \(0.681874\pi\) | |||||||
\(312\) | 5.52748e6 | 3.21470 | ||||||||
\(313\) | −2.25237e6 | −1.29951 | −0.649753 | − | 0.760146i | \(-0.725128\pi\) | ||||
−0.649753 | + | 0.760146i | \(0.725128\pi\) | |||||||
\(314\) | −3.30559e6 | −1.89202 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.41992e6 | 2.48999 | ||||||||
\(317\) | −1.22564e6 | −0.685039 | −0.342520 | − | 0.939511i | \(-0.611280\pi\) | ||||
−0.342520 | + | 0.939511i | \(0.611280\pi\) | |||||||
\(318\) | −761017. | −0.422014 | ||||||||
\(319\) | 687598. | 0.378319 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.33330e6 | 0.722214 | ||||||||
\(322\) | 1.20333e6 | 0.646762 | ||||||||
\(323\) | 580640. | 0.309671 | ||||||||
\(324\) | 560051. | 0.296391 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 4.83852e6 | 2.52156 | ||||||||
\(327\) | 900070. | 0.465487 | ||||||||
\(328\) | −1.01511e7 | −5.20989 | ||||||||
\(329\) | 2.27539e6 | 1.15895 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −841537. | −0.422185 | −0.211093 | − | 0.977466i | \(-0.567702\pi\) | ||||
−0.211093 | + | 0.977466i | \(0.567702\pi\) | |||||||
\(332\) | −6.64397e6 | −3.30813 | ||||||||
\(333\) | −527556. | −0.260710 | ||||||||
\(334\) | −1.45781e6 | −0.715045 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −5.98940e6 | −2.89425 | ||||||||
\(337\) | −1.88515e6 | −0.904214 | −0.452107 | − | 0.891964i | \(-0.649327\pi\) | ||||
−0.452107 | + | 0.891964i | \(0.649327\pi\) | |||||||
\(338\) | 8.20599e6 | 3.90696 | ||||||||
\(339\) | −205828. | −0.0972760 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 229562. | 0.106909 | ||||||||
\(342\) | 250601. | 0.115856 | ||||||||
\(343\) | 359847. | 0.165152 | ||||||||
\(344\) | −5.17270e6 | −2.35679 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6.06147e6 | −2.72200 | ||||||||
\(347\) | 1.60117e6 | 0.713860 | 0.356930 | − | 0.934131i | \(-0.383823\pi\) | ||||
0.356930 | + | 0.934131i | \(0.383823\pi\) | |||||||
\(348\) | −4.36565e6 | −1.93242 | ||||||||
\(349\) | −4.20595e6 | −1.84842 | −0.924209 | − | 0.381887i | \(-0.875274\pi\) | ||||
−0.924209 | + | 0.381887i | \(0.875274\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 774516. | 0.335554 | ||||||||
\(352\) | 2.39011e6 | 1.02816 | ||||||||
\(353\) | 3.54610e6 | 1.51466 | 0.757328 | − | 0.653035i | \(-0.226505\pi\) | ||||
0.757328 | + | 0.653035i | \(0.226505\pi\) | |||||||
\(354\) | −3.13015e6 | −1.32757 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 4.09896e6 | 1.71415 | ||||||||
\(357\) | −3.44881e6 | −1.43218 | ||||||||
\(358\) | 1.34034e6 | 0.552724 | ||||||||
\(359\) | −3.28782e6 | −1.34639 | −0.673197 | − | 0.739463i | \(-0.735080\pi\) | ||||
−0.673197 | + | 0.739463i | \(0.735080\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.39454e6 | −0.967061 | ||||||||
\(362\) | 7.21071e6 | 2.89205 | ||||||||
\(363\) | −131769. | −0.0524864 | ||||||||
\(364\) | −1.70929e7 | −6.76181 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −35118.4 | −0.0137035 | ||||||||
\(367\) | −2.05002e6 | −0.794499 | −0.397250 | − | 0.917711i | \(-0.630035\pi\) | ||||
−0.397250 | + | 0.917711i | \(0.630035\pi\) | |||||||
\(368\) | 2.08090e6 | 0.800998 | ||||||||
\(369\) | −1.42238e6 | −0.543814 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.47112e6 | 0.554897 | ||||||||
\(372\) | −1.45752e6 | −0.546082 | ||||||||
\(373\) | −390699. | −0.145402 | −0.0727010 | − | 0.997354i | \(-0.523162\pi\) | ||||
−0.0727010 | + | 0.997354i | \(0.523162\pi\) | |||||||
\(374\) | 2.66512e6 | 0.985230 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.97881e6 | 2.54573 | ||||||||
\(377\) | −6.03743e6 | −2.18775 | ||||||||
\(378\) | −1.48849e6 | −0.535816 | ||||||||
\(379\) | −1.42019e6 | −0.507864 | −0.253932 | − | 0.967222i | \(-0.581724\pi\) | ||||
−0.253932 | + | 0.967222i | \(0.581724\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 98130.2 | 0.0346330 | ||||||||
\(382\) | 3.36793e6 | 1.18088 | ||||||||
\(383\) | −2.23045e6 | −0.776953 | −0.388476 | − | 0.921459i | \(-0.626998\pi\) | ||||
−0.388476 | + | 0.921459i | \(0.626998\pi\) | |||||||
\(384\) | −4.15876e6 | −1.43925 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −832226. | −0.284298 | ||||||||
\(387\) | −724803. | −0.246004 | ||||||||
\(388\) | 9.90051e6 | 3.33871 | ||||||||
\(389\) | −1.57882e6 | −0.529005 | −0.264502 | − | 0.964385i | \(-0.585208\pi\) | ||||
−0.264502 | + | 0.964385i | \(0.585208\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.19822e6 | 0.396364 | ||||||||
\(392\) | 1.08193e7 | 3.55620 | ||||||||
\(393\) | −678807. | −0.221700 | ||||||||
\(394\) | 7.26226e6 | 2.35685 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 836619. | 0.268096 | ||||||||
\(397\) | 1.46256e6 | 0.465734 | 0.232867 | − | 0.972509i | \(-0.425189\pi\) | ||||
0.232867 | + | 0.972509i | \(0.425189\pi\) | |||||||
\(398\) | −8.59672e6 | −2.72035 | ||||||||
\(399\) | −484436. | −0.152336 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.26635e6 | 0.703828 | 0.351914 | − | 0.936032i | \(-0.385531\pi\) | ||||
0.351914 | + | 0.936032i | \(0.385531\pi\) | |||||||
\(402\) | 3.94806e6 | 1.21848 | ||||||||
\(403\) | −2.01566e6 | −0.618238 | ||||||||
\(404\) | 1.07213e7 | 3.26808 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.16029e7 | 3.49343 | ||||||||
\(407\) | −788077. | −0.235821 | ||||||||
\(408\) | −1.05778e7 | −3.14590 | ||||||||
\(409\) | −5.88429e6 | −1.73935 | −0.869673 | − | 0.493628i | \(-0.835670\pi\) | ||||
−0.869673 | + | 0.493628i | \(0.835670\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.34316e6 | −0.976230 | ||||||||
\(412\) | −1.68204e7 | −4.88195 | ||||||||
\(413\) | 6.05088e6 | 1.74559 | ||||||||
\(414\) | 517145. | 0.148290 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.09863e7 | −5.94569 | ||||||||
\(417\) | 65749.6 | 0.0185163 | ||||||||
\(418\) | 374355. | 0.104796 | ||||||||
\(419\) | −3.04647e6 | −0.847737 | −0.423869 | − | 0.905724i | \(-0.639328\pi\) | ||||
−0.423869 | + | 0.905724i | \(0.639328\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.55503e6 | 0.702571 | 0.351286 | − | 0.936268i | \(-0.385745\pi\) | ||||
0.351286 | + | 0.936268i | \(0.385745\pi\) | |||||||
\(422\) | −1.15537e6 | −0.315820 | ||||||||
\(423\) | 977877. | 0.265725 | ||||||||
\(424\) | 4.51204e6 | 1.21887 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −7.09458e6 | −1.89410 | ||||||||
\(427\) | 67887.2 | 0.0180185 | ||||||||
\(428\) | −1.26457e7 | −3.33683 | ||||||||
\(429\) | 1.15699e6 | 0.303520 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.99185e6 | −0.775794 | −0.387897 | − | 0.921703i | \(-0.626798\pi\) | ||||
−0.387897 | + | 0.921703i | \(0.626798\pi\) | |||||||
\(432\) | −2.57402e6 | −0.663595 | ||||||||
\(433\) | −1.22139e6 | −0.313064 | −0.156532 | − | 0.987673i | \(-0.550031\pi\) | ||||
−0.156532 | + | 0.987673i | \(0.550031\pi\) | |||||||
\(434\) | 3.87376e6 | 0.987207 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8.53673e6 | −2.15068 | ||||||||
\(437\) | 168308. | 0.0421599 | ||||||||
\(438\) | 2.17318e6 | 0.541265 | ||||||||
\(439\) | −2.06150e6 | −0.510530 | −0.255265 | − | 0.966871i | \(-0.582163\pi\) | ||||
−0.255265 | + | 0.966871i | \(0.582163\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.51602e6 | 0.371199 | ||||||||
\(442\) | −2.34010e7 | −5.69742 | ||||||||
\(443\) | 1.37260e6 | 0.332303 | 0.166151 | − | 0.986100i | \(-0.446866\pi\) | ||||
0.166151 | + | 0.986100i | \(0.446866\pi\) | |||||||
\(444\) | 5.00361e6 | 1.20455 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 9.01855e6 | 2.14684 | ||||||||
\(447\) | 1.05165e6 | 0.248945 | ||||||||
\(448\) | 1.90364e7 | 4.48114 | ||||||||
\(449\) | 1.54405e6 | 0.361448 | 0.180724 | − | 0.983534i | \(-0.442156\pi\) | ||||
0.180724 | + | 0.983534i | \(0.442156\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.12479e6 | −0.491898 | ||||||||
\(452\) | 1.95218e6 | 0.449442 | ||||||||
\(453\) | −1.49011e6 | −0.341171 | ||||||||
\(454\) | −1.21862e7 | −2.77477 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.48580e6 | −0.334618 | ||||||||
\(457\) | −5.05440e6 | −1.13208 | −0.566042 | − | 0.824376i | \(-0.691526\pi\) | ||||
−0.566042 | + | 0.824376i | \(0.691526\pi\) | |||||||
\(458\) | −1.38938e7 | −3.09498 | ||||||||
\(459\) | −1.48217e6 | −0.328372 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.79144e6 | −0.392601 | −0.196300 | − | 0.980544i | \(-0.562893\pi\) | ||||
−0.196300 | + | 0.980544i | \(0.562893\pi\) | |||||||
\(462\) | −2.22354e6 | −0.484664 | ||||||||
\(463\) | 641130. | 0.138993 | 0.0694966 | − | 0.997582i | \(-0.477861\pi\) | ||||
0.0694966 | + | 0.997582i | \(0.477861\pi\) | |||||||
\(464\) | 2.00648e7 | 4.32652 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5.22793e6 | −1.11523 | ||||||||
\(467\) | −6.65471e6 | −1.41201 | −0.706004 | − | 0.708208i | \(-0.749504\pi\) | ||||
−0.706004 | + | 0.708208i | \(0.749504\pi\) | |||||||
\(468\) | −7.34591e6 | −1.55035 | ||||||||
\(469\) | −7.63197e6 | −1.60215 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.74619e6 | 0.570398 | ||||||||
\(472\) | 1.85586e7 | 3.83433 | ||||||||
\(473\) | −1.08273e6 | −0.222519 | ||||||||
\(474\) | −5.04848e6 | −1.03208 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 3.27103e7 | 6.61708 | ||||||||
\(477\) | 632231. | 0.127227 | ||||||||
\(478\) | 2.36466e6 | 0.473368 | ||||||||
\(479\) | −260876. | −0.0519511 | −0.0259755 | − | 0.999663i | \(-0.508269\pi\) | ||||
−0.0259755 | + | 0.999663i | \(0.508269\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.91968e6 | 1.36371 | ||||||||
\(482\) | 7.29210e6 | 1.42967 | ||||||||
\(483\) | −999690. | −0.194983 | ||||||||
\(484\) | 1.24976e6 | 0.242502 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −639696. | −0.122852 | ||||||||
\(487\) | 1.01034e6 | 0.193038 | 0.0965191 | − | 0.995331i | \(-0.469229\pi\) | ||||
0.0965191 | + | 0.995331i | \(0.469229\pi\) | |||||||
\(488\) | 208216. | 0.0395789 | ||||||||
\(489\) | −4.01970e6 | −0.760190 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 259876. | 0.0486477 | 0.0243239 | − | 0.999704i | \(-0.492257\pi\) | ||||
0.0243239 | + | 0.999704i | \(0.492257\pi\) | |||||||
\(492\) | 1.34906e7 | 2.51257 | ||||||||
\(493\) | 1.15537e7 | 2.14093 | ||||||||
\(494\) | −3.28701e6 | −0.606016 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.69885e6 | 1.22263 | ||||||||
\(497\) | 1.37145e7 | 2.49051 | ||||||||
\(498\) | 7.58881e6 | 1.37120 | ||||||||
\(499\) | −454122. | −0.0816434 | −0.0408217 | − | 0.999166i | \(-0.512998\pi\) | ||||
−0.0408217 | + | 0.999166i | \(0.512998\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.21110e6 | 0.215569 | ||||||||
\(502\) | −1.00160e7 | −1.77393 | ||||||||
\(503\) | −4.20300e6 | −0.740695 | −0.370347 | − | 0.928893i | \(-0.620761\pi\) | ||||
−0.370347 | + | 0.928893i | \(0.620761\pi\) | |||||||
\(504\) | 8.82518e6 | 1.54756 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 772526. | 0.134133 | ||||||||
\(507\) | −6.81730e6 | −1.17786 | ||||||||
\(508\) | −930717. | −0.160014 | ||||||||
\(509\) | 4.32091e6 | 0.739231 | 0.369616 | − | 0.929185i | \(-0.379489\pi\) | ||||
0.369616 | + | 0.929185i | \(0.379489\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.20096e6 | −0.711698 | ||||||||
\(512\) | 4.43009e6 | 0.746858 | ||||||||
\(513\) | −208192. | −0.0349278 | ||||||||
\(514\) | 5.11258e6 | 0.853557 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 6.87441e6 | 1.13661 | ||||||||
\(517\) | 1.46078e6 | 0.240358 | ||||||||
\(518\) | −1.32984e7 | −2.17759 | ||||||||
\(519\) | 5.03569e6 | 0.820618 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.81457e6 | 1.58408 | 0.792040 | − | 0.610469i | \(-0.209019\pi\) | ||||
0.792040 | + | 0.610469i | \(0.209019\pi\) | |||||||
\(522\) | 4.98649e6 | 0.800975 | ||||||||
\(523\) | −9.06730e6 | −1.44952 | −0.724759 | − | 0.689002i | \(-0.758049\pi\) | ||||
−0.724759 | + | 0.689002i | \(0.758049\pi\) | |||||||
\(524\) | 6.43815e6 | 1.02431 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9.41868e6 | −1.48431 | ||||||||
\(527\) | 3.85732e6 | 0.605005 | ||||||||
\(528\) | −3.84514e6 | −0.600244 | ||||||||
\(529\) | −6.08902e6 | −0.946037 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.60044e6 | 0.400231 | ||||||||
\(532\) | 4.59464e6 | 0.703837 | ||||||||
\(533\) | 1.86567e7 | 2.84457 | ||||||||
\(534\) | −4.68188e6 | −0.710504 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −2.34079e7 | −3.51925 | ||||||||
\(537\) | −1.11352e6 | −0.166633 | ||||||||
\(538\) | −4.98500e6 | −0.742523 | ||||||||
\(539\) | 2.26467e6 | 0.335763 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.82663e6 | −0.415217 | −0.207609 | − | 0.978212i | \(-0.566568\pi\) | ||||
−0.207609 | + | 0.978212i | \(0.566568\pi\) | |||||||
\(542\) | −5.28896e6 | −0.773343 | ||||||||
\(543\) | −5.99045e6 | −0.871886 | ||||||||
\(544\) | 4.01608e7 | 5.81842 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.95237e7 | 2.80273 | ||||||||
\(547\) | 4.57486e6 | 0.653746 | 0.326873 | − | 0.945068i | \(-0.394005\pi\) | ||||
0.326873 | + | 0.945068i | \(0.394005\pi\) | |||||||
\(548\) | 3.17082e7 | 4.51045 | ||||||||
\(549\) | 29175.4 | 0.00413129 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.62288e6 | 0.227723 | ||||||||
\(552\) | −3.06613e6 | −0.428295 | ||||||||
\(553\) | 9.75918e6 | 1.35706 | ||||||||
\(554\) | 2.10202e7 | 2.90980 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −623603. | −0.0855503 | ||||||||
\(557\) | 1.10502e6 | 0.150915 | 0.0754573 | − | 0.997149i | \(-0.475958\pi\) | ||||
0.0754573 | + | 0.997149i | \(0.475958\pi\) | |||||||
\(558\) | 1.66480e6 | 0.226348 | ||||||||
\(559\) | 9.50688e6 | 1.28679 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.21410e6 | −0.297024 | ||||||||
\(562\) | −1.90979e7 | −2.55061 | ||||||||
\(563\) | −650286. | −0.0864637 | −0.0432318 | − | 0.999065i | \(-0.513765\pi\) | ||||
−0.0432318 | + | 0.999065i | \(0.513765\pi\) | |||||||
\(564\) | −9.27468e6 | −1.22773 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 4.99644e6 | 0.655571 | ||||||||
\(567\) | 1.23659e6 | 0.161536 | ||||||||
\(568\) | 4.20635e7 | 5.47059 | ||||||||
\(569\) | 1.07156e7 | 1.38751 | 0.693754 | − | 0.720212i | \(-0.255956\pi\) | ||||
0.693754 | + | 0.720212i | \(0.255956\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.51877e7 | 1.94941 | 0.974703 | − | 0.223506i | \(-0.0717503\pi\) | ||||
0.974703 | + | 0.223506i | \(0.0717503\pi\) | |||||||
\(572\) | −1.09735e7 | −1.40235 | ||||||||
\(573\) | −2.79798e6 | −0.356006 | ||||||||
\(574\) | −3.58549e7 | −4.54223 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 8.18112e6 | 1.02744 | ||||||||
\(577\) | 3.85869e6 | 0.482503 | 0.241251 | − | 0.970463i | \(-0.422442\pi\) | ||||
0.241251 | + | 0.970463i | \(0.422442\pi\) | |||||||
\(578\) | 2.94000e7 | 3.66040 | ||||||||
\(579\) | 691390. | 0.0857090 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.46699e7 | −1.80296 | ||||||||
\(582\) | −1.13085e7 | −1.38387 | ||||||||
\(583\) | 944444. | 0.115081 | ||||||||
\(584\) | −1.28847e7 | −1.56330 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.87396e7 | −2.25432 | ||||||||
\(587\) | −1.52399e7 | −1.82552 | −0.912758 | − | 0.408501i | \(-0.866052\pi\) | ||||
−0.912758 | + | 0.408501i | \(0.866052\pi\) | |||||||
\(588\) | −1.43787e7 | −1.71504 | ||||||||
\(589\) | 541817. | 0.0643523 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.03328e6 | −0.710533 | ||||||||
\(592\) | −2.29968e7 | −2.69689 | ||||||||
\(593\) | 7.49470e6 | 0.875221 | 0.437610 | − | 0.899165i | \(-0.355825\pi\) | ||||
0.437610 | + | 0.899165i | \(0.355825\pi\) | |||||||
\(594\) | −955595. | −0.111124 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −9.97441e6 | −1.15020 | ||||||||
\(597\) | 7.14191e6 | 0.820122 | ||||||||
\(598\) | −6.78313e6 | −0.775671 | ||||||||
\(599\) | −2.30188e6 | −0.262129 | −0.131064 | − | 0.991374i | \(-0.541839\pi\) | ||||
−0.131064 | + | 0.991374i | \(0.541839\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.48232e6 | 0.957918 | 0.478959 | − | 0.877837i | \(-0.341014\pi\) | ||||
0.478959 | + | 0.877837i | \(0.341014\pi\) | |||||||
\(602\) | −1.82706e7 | −2.05476 | ||||||||
\(603\) | −3.27994e6 | −0.367343 | ||||||||
\(604\) | 1.41329e7 | 1.57630 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.22459e7 | −1.35460 | ||||||||
\(607\) | 8.51451e6 | 0.937968 | 0.468984 | − | 0.883207i | \(-0.344620\pi\) | ||||
0.468984 | + | 0.883207i | \(0.344620\pi\) | |||||||
\(608\) | 5.64118e6 | 0.618886 | ||||||||
\(609\) | −9.63936e6 | −1.05319 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.28263e7 | −1.38995 | ||||||||
\(612\) | 1.40576e7 | 1.51717 | ||||||||
\(613\) | 5.62250e6 | 0.604336 | 0.302168 | − | 0.953255i | \(-0.402290\pi\) | ||||
0.302168 | + | 0.953255i | \(0.402290\pi\) | |||||||
\(614\) | −5.44269e6 | −0.582630 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.31833e7 | 1.39982 | ||||||||
\(617\) | −754007. | −0.0797375 | −0.0398687 | − | 0.999205i | \(-0.512694\pi\) | ||||
−0.0398687 | + | 0.999205i | \(0.512694\pi\) | |||||||
\(618\) | 1.92124e7 | 2.02354 | ||||||||
\(619\) | 1.08312e7 | 1.13619 | 0.568095 | − | 0.822963i | \(-0.307681\pi\) | ||||
0.568095 | + | 0.822963i | \(0.307681\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −429629. | −0.0447059 | ||||||||
\(622\) | −1.99857e7 | −2.07130 | ||||||||
\(623\) | 9.05050e6 | 0.934227 | ||||||||
\(624\) | 3.37622e7 | 3.47111 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −2.44006e7 | −2.48865 | ||||||||
\(627\) | −311003. | −0.0315934 | ||||||||
\(628\) | −2.60462e7 | −2.63540 | ||||||||
\(629\) | −1.32420e7 | −1.33453 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.23176e7 | −1.23156 | −0.615778 | − | 0.787920i | \(-0.711158\pi\) | ||||
−0.615778 | + | 0.787920i | \(0.711158\pi\) | |||||||
\(632\) | 2.99322e7 | 2.98089 | ||||||||
\(633\) | 959848. | 0.0952123 | ||||||||
\(634\) | −1.32778e7 | −1.31190 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −5.99640e6 | −0.587825 | ||||||||
\(637\) | −1.98848e7 | −1.94166 | ||||||||
\(638\) | 7.44896e6 | 0.724509 | ||||||||
\(639\) | 5.89397e6 | 0.571026 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.56214e7 | −1.50167 | −0.750835 | − | 0.660490i | \(-0.770348\pi\) | ||||
−0.750835 | + | 0.660490i | \(0.770348\pi\) | |||||||
\(642\) | 1.44441e7 | 1.38310 | ||||||||
\(643\) | 9.36087e6 | 0.892871 | 0.446435 | − | 0.894816i | \(-0.352693\pi\) | ||||
0.446435 | + | 0.894816i | \(0.352693\pi\) | |||||||
\(644\) | 9.48157e6 | 0.900877 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.29026e6 | 0.593044 | ||||||||
\(647\) | −3.69425e6 | −0.346949 | −0.173474 | − | 0.984838i | \(-0.555499\pi\) | ||||
−0.173474 | + | 0.984838i | \(0.555499\pi\) | |||||||
\(648\) | 3.79273e6 | 0.354825 | ||||||||
\(649\) | 3.88461e6 | 0.362023 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.21821e6 | −0.297620 | ||||||||
\(652\) | 3.81249e7 | 3.51229 | ||||||||
\(653\) | 1.75496e7 | 1.61059 | 0.805294 | − | 0.592875i | \(-0.202007\pi\) | ||||
0.805294 | + | 0.592875i | \(0.202007\pi\) | |||||||
\(654\) | 9.75074e6 | 0.891443 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −6.20035e7 | −5.62544 | ||||||||
\(657\) | −1.80541e6 | −0.163179 | ||||||||
\(658\) | 2.46500e7 | 2.21948 | ||||||||
\(659\) | −1.36928e7 | −1.22822 | −0.614112 | − | 0.789219i | \(-0.710486\pi\) | ||||
−0.614112 | + | 0.789219i | \(0.710486\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.06556e6 | −0.807032 | −0.403516 | − | 0.914973i | \(-0.632212\pi\) | ||||
−0.403516 | + | 0.914973i | \(0.632212\pi\) | |||||||
\(662\) | −9.11663e6 | −0.808518 | ||||||||
\(663\) | 1.94409e7 | 1.71764 | ||||||||
\(664\) | −4.49937e7 | −3.96034 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −5.71517e6 | −0.499280 | ||||||||
\(667\) | 3.34900e6 | 0.291475 | ||||||||
\(668\) | −1.14867e7 | −0.995990 | ||||||||
\(669\) | −7.49235e6 | −0.647221 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 43583.0 | 0.00373689 | ||||||||
\(672\) | −3.35067e7 | −2.86225 | ||||||||
\(673\) | −4.40527e6 | −0.374917 | −0.187458 | − | 0.982273i | \(-0.560025\pi\) | ||||
−0.187458 | + | 0.982273i | \(0.560025\pi\) | |||||||
\(674\) | −2.04224e7 | −1.73164 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.46588e7 | 5.44203 | ||||||||
\(677\) | −1.84727e7 | −1.54903 | −0.774514 | − | 0.632557i | \(-0.782005\pi\) | ||||
−0.774514 | + | 0.632557i | \(0.782005\pi\) | |||||||
\(678\) | −2.22980e6 | −0.186291 | ||||||||
\(679\) | 2.18603e7 | 1.81963 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.01239e7 | 0.836529 | ||||||||
\(682\) | 2.48692e6 | 0.204739 | ||||||||
\(683\) | −8.03048e6 | −0.658703 | −0.329352 | − | 0.944207i | \(-0.606830\pi\) | ||||
−0.329352 | + | 0.944207i | \(0.606830\pi\) | |||||||
\(684\) | 1.97460e6 | 0.161376 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 3.89834e6 | 0.316278 | ||||||||
\(687\) | 1.15426e7 | 0.933064 | ||||||||
\(688\) | −3.15951e7 | −2.54477 | ||||||||
\(689\) | −8.29265e6 | −0.665496 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.59119e7 | 1.26773 | 0.633864 | − | 0.773444i | \(-0.281468\pi\) | ||||
0.633864 | + | 0.773444i | \(0.281468\pi\) | |||||||
\(692\) | −4.77611e7 | −3.79148 | ||||||||
\(693\) | 1.84725e6 | 0.146115 | ||||||||
\(694\) | 1.73459e7 | 1.36710 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −2.95647e7 | −2.31340 | ||||||||
\(697\) | −3.57027e7 | −2.78368 | ||||||||
\(698\) | −4.55643e7 | −3.53986 | ||||||||
\(699\) | 4.34321e6 | 0.336216 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.66506e6 | −0.435421 | −0.217710 | − | 0.976013i | \(-0.569859\pi\) | ||||
−0.217710 | + | 0.976013i | \(0.569859\pi\) | |||||||
\(702\) | 8.39057e6 | 0.642612 | ||||||||
\(703\) | −1.86003e6 | −0.141949 | ||||||||
\(704\) | 1.22212e7 | 0.929354 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.84160e7 | 2.90068 | ||||||||
\(707\) | 2.36725e7 | 1.78113 | ||||||||
\(708\) | −2.46639e7 | −1.84918 | ||||||||
\(709\) | 1.42504e7 | 1.06466 | 0.532332 | − | 0.846535i | \(-0.321316\pi\) | ||||
0.532332 | + | 0.846535i | \(0.321316\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.19413e6 | 0.311149 | ||||||||
\(712\) | 2.77586e7 | 2.05210 | ||||||||
\(713\) | 1.11810e6 | 0.0823678 | ||||||||
\(714\) | −3.73620e7 | −2.74274 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.05612e7 | 0.769892 | ||||||||
\(717\) | −1.96449e6 | −0.142709 | ||||||||
\(718\) | −3.56180e7 | −2.57845 | ||||||||
\(719\) | 9.73583e6 | 0.702345 | 0.351173 | − | 0.936311i | \(-0.385783\pi\) | ||||
0.351173 | + | 0.936311i | \(0.385783\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.71394e7 | −2.66071 | ||||||||
\(722\) | −2.59408e7 | −1.85200 | ||||||||
\(723\) | −6.05807e6 | −0.431011 | ||||||||
\(724\) | 5.68165e7 | 4.02836 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.42749e6 | −0.100515 | ||||||||
\(727\) | 1.67013e7 | 1.17196 | 0.585982 | − | 0.810324i | \(-0.300709\pi\) | ||||
0.585982 | + | 0.810324i | \(0.300709\pi\) | |||||||
\(728\) | −1.15755e8 | −8.09492 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.81930e7 | −1.25925 | ||||||||
\(732\) | −276714. | −0.0190877 | ||||||||
\(733\) | −6.25234e6 | −0.429816 | −0.214908 | − | 0.976634i | \(-0.568945\pi\) | ||||
−0.214908 | + | 0.976634i | \(0.568945\pi\) | |||||||
\(734\) | −2.22085e7 | −1.52153 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.16412e7 | 0.792144 | ||||||||
\(737\) | −4.89966e6 | −0.332274 | ||||||||
\(738\) | −1.54091e7 | −1.04145 | ||||||||
\(739\) | −5.71072e6 | −0.384662 | −0.192331 | − | 0.981330i | \(-0.561605\pi\) | ||||
−0.192331 | + | 0.981330i | \(0.561605\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.73075e6 | 0.182699 | ||||||||
\(742\) | 1.59371e7 | 1.06267 | ||||||||
\(743\) | −1.76929e7 | −1.17578 | −0.587892 | − | 0.808940i | \(-0.700042\pi\) | ||||
−0.587892 | + | 0.808940i | \(0.700042\pi\) | |||||||
\(744\) | −9.87051e6 | −0.653743 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −4.23257e6 | −0.278456 | ||||||||
\(747\) | −6.30457e6 | −0.413384 | ||||||||
\(748\) | 2.09997e7 | 1.37233 | ||||||||
\(749\) | −2.79217e7 | −1.81860 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.42479e6 | 0.545078 | 0.272539 | − | 0.962145i | \(-0.412137\pi\) | ||||
0.272539 | + | 0.962145i | \(0.412137\pi\) | |||||||
\(752\) | 4.26269e7 | 2.74878 | ||||||||
\(753\) | 8.32102e6 | 0.534797 | ||||||||
\(754\) | −6.54053e7 | −4.18972 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.17285e7 | −0.746340 | ||||||||
\(757\) | 1.85996e7 | 1.17968 | 0.589840 | − | 0.807520i | \(-0.299191\pi\) | ||||
0.589840 | + | 0.807520i | \(0.299191\pi\) | |||||||
\(758\) | −1.53853e7 | −0.972599 | ||||||||
\(759\) | −641792. | −0.0404380 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.84836e7 | 1.78292 | 0.891462 | − | 0.453096i | \(-0.149681\pi\) | ||||
0.891462 | + | 0.453096i | \(0.149681\pi\) | |||||||
\(762\) | 1.06308e6 | 0.0663249 | ||||||||
\(763\) | −1.88491e7 | −1.17214 | ||||||||
\(764\) | 2.65375e7 | 1.64485 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.41631e7 | −1.48792 | ||||||||
\(767\) | −3.41087e7 | −2.09352 | ||||||||
\(768\) | −1.59648e7 | −0.976696 | ||||||||
\(769\) | −7.45086e6 | −0.454350 | −0.227175 | − | 0.973854i | \(-0.572949\pi\) | ||||
−0.227175 | + | 0.973854i | \(0.572949\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.24738e6 | −0.257327 | ||||||||
\(772\) | −6.55749e6 | −0.395999 | ||||||||
\(773\) | 5.32037e6 | 0.320253 | 0.160126 | − | 0.987097i | \(-0.448810\pi\) | ||||
0.160126 | + | 0.987097i | \(0.448810\pi\) | |||||||
\(774\) | −7.85202e6 | −0.471117 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 6.70474e7 | 3.99694 | ||||||||
\(777\) | 1.10480e7 | 0.656492 | ||||||||
\(778\) | −1.71039e7 | −1.01308 | ||||||||
\(779\) | −5.01497e6 | −0.296091 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.80458e6 | 0.516513 | ||||||||
\(782\) | 1.29807e7 | 0.759068 | ||||||||
\(783\) | −4.14264e6 | −0.241475 | ||||||||
\(784\) | 6.60851e7 | 3.83984 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −7.35373e6 | −0.424572 | ||||||||
\(787\) | 1.42655e7 | 0.821013 | 0.410507 | − | 0.911858i | \(-0.365352\pi\) | ||||
0.410507 | + | 0.911858i | \(0.365352\pi\) | |||||||
\(788\) | 5.72227e7 | 3.28286 | ||||||||
\(789\) | 7.82477e6 | 0.447485 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.31041e6 | 0.244950 | ||||||||
\(792\) | 5.66568e6 | 0.320952 | ||||||||
\(793\) | −382679. | −0.0216098 | ||||||||
\(794\) | 1.58444e7 | 0.891916 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6.77375e7 | −3.78919 | ||||||||
\(797\) | 3.82425e6 | 0.213256 | 0.106628 | − | 0.994299i | \(-0.465995\pi\) | ||||
0.106628 | + | 0.994299i | \(0.465995\pi\) | |||||||
\(798\) | −5.24804e6 | −0.291736 | ||||||||
\(799\) | 2.45453e7 | 1.36020 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.88957e6 | 0.214200 | ||||||||
\(802\) | 2.45521e7 | 1.34788 | ||||||||
\(803\) | −2.69698e6 | −0.147601 | ||||||||
\(804\) | 3.11086e7 | 1.69723 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2.18363e7 | −1.18397 | ||||||||
\(807\) | 4.14140e6 | 0.223853 | ||||||||
\(808\) | 7.26056e7 | 3.91239 | ||||||||
\(809\) | 2.01604e7 | 1.08300 | 0.541499 | − | 0.840701i | \(-0.317857\pi\) | ||||
0.541499 | + | 0.840701i | \(0.317857\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8.80372e6 | −0.470017 | −0.235009 | − | 0.971993i | \(-0.575512\pi\) | ||||
−0.235009 | + | 0.971993i | \(0.575512\pi\) | |||||||
\(812\) | 9.14246e7 | 4.86601 | ||||||||
\(813\) | 4.39391e6 | 0.233144 | ||||||||
\(814\) | −8.53748e6 | −0.451615 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −6.46097e7 | −3.39682 | ||||||||
\(817\) | −2.55548e6 | −0.133942 | ||||||||
\(818\) | −6.37464e7 | −3.33098 | ||||||||
\(819\) | −1.62198e7 | −0.844957 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.33018e7 | 0.688734 | 0.344367 | − | 0.938835i | \(-0.388094\pi\) | ||||
0.344367 | + | 0.938835i | \(0.388094\pi\) | |||||||
\(822\) | −3.62174e7 | −1.86955 | ||||||||
\(823\) | −2.17096e7 | −1.11726 | −0.558628 | − | 0.829419i | \(-0.688672\pi\) | ||||
−0.558628 | + | 0.829419i | \(0.688672\pi\) | |||||||
\(824\) | −1.13910e8 | −5.84444 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.55510e7 | 3.34295 | ||||||||
\(827\) | 1.18446e7 | 0.602220 | 0.301110 | − | 0.953589i | \(-0.402643\pi\) | ||||
0.301110 | + | 0.953589i | \(0.402643\pi\) | |||||||
\(828\) | 4.07482e6 | 0.206554 | ||||||||
\(829\) | −6.82282e6 | −0.344808 | −0.172404 | − | 0.985026i | \(-0.555153\pi\) | ||||
−0.172404 | + | 0.985026i | \(0.555153\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.74630e7 | −0.877235 | ||||||||
\(832\) | −1.07308e8 | −5.37430 | ||||||||
\(833\) | 3.80530e7 | 1.90010 | ||||||||
\(834\) | 712286. | 0.0354601 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 2.94972e6 | 0.145970 | ||||||||
\(837\) | −1.38307e6 | −0.0682384 | ||||||||
\(838\) | −3.30033e7 | −1.62348 | ||||||||
\(839\) | 1.51092e6 | 0.0741030 | 0.0370515 | − | 0.999313i | \(-0.488203\pi\) | ||||
0.0370515 | + | 0.999313i | \(0.488203\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.17811e7 | 0.574375 | ||||||||
\(842\) | 2.76794e7 | 1.34548 | ||||||||
\(843\) | 1.58660e7 | 0.768949 | ||||||||
\(844\) | −9.10369e6 | −0.439908 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.05936e7 | 0.508885 | ||||||||
\(847\) | 2.75948e6 | 0.132166 | ||||||||
\(848\) | 2.75598e7 | 1.31609 | ||||||||
\(849\) | −4.15090e6 | −0.197639 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.83839e6 | −0.181688 | ||||||||
\(852\) | −5.59015e7 | −2.63830 | ||||||||
\(853\) | 4.40414e6 | 0.207247 | 0.103624 | − | 0.994617i | \(-0.466956\pi\) | ||||
0.103624 | + | 0.994617i | \(0.466956\pi\) | |||||||
\(854\) | 735443. | 0.0345068 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8.56383e7 | −3.99470 | ||||||||
\(857\) | −2.26455e6 | −0.105324 | −0.0526622 | − | 0.998612i | \(-0.516771\pi\) | ||||
−0.0526622 | + | 0.998612i | \(0.516771\pi\) | |||||||
\(858\) | 1.25341e7 | 0.581264 | ||||||||
\(859\) | 1.55123e7 | 0.717288 | 0.358644 | − | 0.933474i | \(-0.383239\pi\) | ||||
0.358644 | + | 0.933474i | \(0.383239\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.97872e7 | 1.36937 | ||||||||
\(862\) | −3.24116e7 | −1.48570 | ||||||||
\(863\) | 2.26673e7 | 1.03603 | 0.518016 | − | 0.855371i | \(-0.326671\pi\) | ||||
0.518016 | + | 0.855371i | \(0.326671\pi\) | |||||||
\(864\) | −1.43999e7 | −0.656260 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1.32316e7 | −0.599541 | ||||||||
\(867\) | −2.44247e7 | −1.10352 | ||||||||
\(868\) | 3.05231e7 | 1.37509 | ||||||||
\(869\) | 6.26531e6 | 0.281445 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.30213e7 | 1.92149 | ||||||||
\(872\) | −5.78117e7 | −2.57469 | ||||||||
\(873\) | 9.39475e6 | 0.417205 | ||||||||
\(874\) | 1.82333e6 | 0.0807395 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.71235e7 | 0.753931 | ||||||||
\(877\) | −587041. | −0.0257733 | −0.0128866 | − | 0.999917i | \(-0.504102\pi\) | ||||
−0.0128866 | + | 0.999917i | \(0.504102\pi\) | |||||||
\(878\) | −2.23328e7 | −0.977705 | ||||||||
\(879\) | 1.55683e7 | 0.679625 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.61087e7 | −1.13330 | −0.566651 | − | 0.823958i | \(-0.691761\pi\) | ||||
−0.566651 | + | 0.823958i | \(0.691761\pi\) | |||||||
\(882\) | 1.64235e7 | 0.710875 | ||||||||
\(883\) | 2.97921e6 | 0.128588 | 0.0642939 | − | 0.997931i | \(-0.479520\pi\) | ||||
0.0642939 | + | 0.997931i | \(0.479520\pi\) | |||||||
\(884\) | −1.84387e8 | −7.93597 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.48698e7 | 0.636385 | ||||||||
\(887\) | −489724. | −0.0208998 | −0.0104499 | − | 0.999945i | \(-0.503326\pi\) | ||||
−0.0104499 | + | 0.999945i | \(0.503326\pi\) | |||||||
\(888\) | 3.38850e7 | 1.44203 | ||||||||
\(889\) | −2.05502e6 | −0.0872092 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 793881. | 0.0335013 | ||||||||
\(892\) | 7.10613e7 | 2.99034 | ||||||||
\(893\) | 3.44775e6 | 0.144680 | ||||||||
\(894\) | 1.13929e7 | 0.476749 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 8.70920e7 | 3.62417 | ||||||||
\(897\) | 5.63523e6 | 0.233846 | ||||||||
\(898\) | 1.67272e7 | 0.692200 | ||||||||
\(899\) | 1.07811e7 | 0.444903 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.58694e7 | 0.651252 | ||||||||
\(902\) | −2.30185e7 | −0.942023 | ||||||||
\(903\) | 1.51787e7 | 0.619462 | ||||||||
\(904\) | 1.32204e7 | 0.538051 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −1.61428e7 | −0.653368 | ||||||||
\(907\) | 8.30654e6 | 0.335275 | 0.167638 | − | 0.985849i | \(-0.446386\pi\) | ||||
0.167638 | + | 0.985849i | \(0.446386\pi\) | |||||||
\(908\) | −9.60204e7 | −3.86500 | ||||||||
\(909\) | 1.01736e7 | 0.408379 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.30461e7 | 1.31924 | 0.659620 | − | 0.751599i | \(-0.270717\pi\) | ||||
0.659620 | + | 0.751599i | \(0.270717\pi\) | |||||||
\(912\) | −9.07537e6 | −0.361308 | ||||||||
\(913\) | −9.41793e6 | −0.373920 | ||||||||
\(914\) | −5.47559e7 | −2.16803 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.09476e8 | −4.31102 | ||||||||
\(917\) | 1.42154e7 | 0.558260 | ||||||||
\(918\) | −1.60568e7 | −0.628857 | ||||||||
\(919\) | 1.92221e7 | 0.750779 | 0.375389 | − | 0.926867i | \(-0.377509\pi\) | ||||
0.375389 | + | 0.926867i | \(0.377509\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.52163e6 | 0.175649 | ||||||||
\(922\) | −1.94073e7 | −0.751860 | ||||||||
\(923\) | −7.73083e7 | −2.98691 | ||||||||
\(924\) | −1.75203e7 | −0.675090 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 6.94556e6 | 0.266183 | ||||||||
\(927\) | −1.59611e7 | −0.610049 | ||||||||
\(928\) | 1.12249e8 | 4.27870 | ||||||||
\(929\) | −1.05025e7 | −0.399258 | −0.199629 | − | 0.979872i | \(-0.563974\pi\) | ||||
−0.199629 | + | 0.979872i | \(0.563974\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.34510e6 | 0.202107 | ||||||||
\(932\) | −4.11932e7 | −1.55341 | ||||||||
\(933\) | 1.66036e7 | 0.624449 | ||||||||
\(934\) | −7.20925e7 | −2.70410 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −4.97473e7 | −1.85601 | ||||||||
\(937\) | 1.83991e7 | 0.684616 | 0.342308 | − | 0.939588i | \(-0.388791\pi\) | ||||
0.342308 | + | 0.939588i | \(0.388791\pi\) | |||||||
\(938\) | −8.26795e7 | −3.06825 | ||||||||
\(939\) | 2.02713e7 | 0.750270 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.48290e7 | −1.28223 | −0.641117 | − | 0.767443i | \(-0.721529\pi\) | ||||
−0.641117 | + | 0.767443i | \(0.721529\pi\) | |||||||
\(942\) | 2.97503e7 | 1.09236 | ||||||||
\(943\) | −1.03490e7 | −0.378982 | ||||||||
\(944\) | 1.13357e8 | 4.14016 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.17296e7 | −0.426142 | ||||||||
\(947\) | 1.51753e7 | 0.549871 | 0.274936 | − | 0.961463i | \(-0.411343\pi\) | ||||
0.274936 | + | 0.961463i | \(0.411343\pi\) | |||||||
\(948\) | −3.97793e7 | −1.43759 | ||||||||
\(949\) | 2.36807e7 | 0.853550 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.10308e7 | 0.395508 | ||||||||
\(952\) | 2.21518e8 | 7.92166 | ||||||||
\(953\) | 4.86395e7 | 1.73483 | 0.867415 | − | 0.497586i | \(-0.165780\pi\) | ||||
0.867415 | + | 0.497586i | \(0.165780\pi\) | |||||||
\(954\) | 6.84915e6 | 0.243650 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.86322e7 | 0.659356 | ||||||||
\(957\) | −6.18838e6 | −0.218422 | ||||||||
\(958\) | −2.82615e6 | −0.0994903 | ||||||||
\(959\) | 7.00117e7 | 2.45824 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.50297e7 | −0.874275 | ||||||||
\(962\) | 7.49631e7 | 2.61162 | ||||||||
\(963\) | −1.19997e7 | −0.416971 | ||||||||
\(964\) | 5.74578e7 | 1.99139 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.08299e7 | −0.373408 | ||||||||
\(967\) | −5.63261e7 | −1.93706 | −0.968531 | − | 0.248893i | \(-0.919933\pi\) | ||||
−0.968531 | + | 0.248893i | \(0.919933\pi\) | |||||||
\(968\) | 8.46355e6 | 0.290312 | ||||||||
\(969\) | −5.22576e6 | −0.178789 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.29679e7 | 0.781759 | 0.390880 | − | 0.920442i | \(-0.372171\pi\) | ||||
0.390880 | + | 0.920442i | \(0.372171\pi\) | |||||||
\(972\) | −5.04046e6 | −0.171121 | ||||||||
\(973\) | −1.37692e6 | −0.0466257 | ||||||||
\(974\) | 1.09453e7 | 0.369683 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.27179e6 | 0.0427358 | ||||||||
\(977\) | −3.90870e7 | −1.31008 | −0.655038 | − | 0.755596i | \(-0.727347\pi\) | ||||
−0.655038 | + | 0.755596i | \(0.727347\pi\) | |||||||
\(978\) | −4.35467e7 | −1.45582 | ||||||||
\(979\) | 5.81034e6 | 0.193751 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.10063e6 | −0.268749 | ||||||||
\(982\) | 2.81532e6 | 0.0931641 | ||||||||
\(983\) | 3.76365e7 | 1.24230 | 0.621148 | − | 0.783693i | \(-0.286667\pi\) | ||||
0.621148 | + | 0.783693i | \(0.286667\pi\) | |||||||
\(984\) | 9.13600e7 | 3.00793 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1.25164e8 | 4.10004 | ||||||||
\(987\) | −2.04785e7 | −0.669122 | ||||||||
\(988\) | −2.58999e7 | −0.844122 | ||||||||
\(989\) | −5.27353e6 | −0.171439 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.08100e7 | 0.673112 | 0.336556 | − | 0.941663i | \(-0.390738\pi\) | ||||
0.336556 | + | 0.941663i | \(0.390738\pi\) | |||||||
\(992\) | 3.74755e7 | 1.20912 | ||||||||
\(993\) | 7.57383e6 | 0.243749 | ||||||||
\(994\) | 1.48573e8 | 4.76952 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 5.97957e7 | 1.90995 | ||||||||
\(997\) | −4.32288e6 | −0.137732 | −0.0688661 | − | 0.997626i | \(-0.521938\pi\) | ||||
−0.0688661 | + | 0.997626i | \(0.521938\pi\) | |||||||
\(998\) | −4.91965e6 | −0.156353 | ||||||||
\(999\) | 4.74800e6 | 0.150521 |
(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 | 825.6.a.n.1.7 | 7 | ||
5.4 | even | 2 | 165.6.a.h.1.1 | ✓ | 7 | ||
15.14 | odd | 2 | 495.6.a.n.1.7 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.6.a.h.1.1 | ✓ | 7 | 5.4 | even | 2 | ||
495.6.a.n.1.7 | 7 | 15.14 | odd | 2 | |||
825.6.a.n.1.7 | 7 | 1.1 | even | 1 | trivial |