Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [240,6,Mod(49,240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(240, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("240.49");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 240 = 2^{4} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 240.f (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(38.4921167551\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 30) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 49.2 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 240.49 |
Dual form | 240.6.f.a.49.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/240\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(97\) | \(161\) | \(181\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 9.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −55.0000 | − | 10.0000i | −0.983870 | − | 0.178885i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 4.00000i | − | 0.0308542i | −0.999881 | − | 0.0154271i | \(-0.995089\pi\) | ||
0.999881 | − | 0.0154271i | \(-0.00491080\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −81.0000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 500.000 | 1.24591 | 0.622957 | − | 0.782256i | \(-0.285931\pi\) | ||||
0.622957 | + | 0.782256i | \(0.285931\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 288.000i | − | 0.472644i | −0.971675 | − | 0.236322i | \(-0.924058\pi\) | ||
0.971675 | − | 0.236322i | \(-0.0759420\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 90.0000 | − | 495.000i | 0.103280 | − | 0.568038i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 1516.00i | − | 1.27226i | −0.771581 | − | 0.636132i | \(-0.780534\pi\) | ||
0.771581 | − | 0.636132i | \(-0.219466\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1344.00 | −0.854113 | −0.427056 | − | 0.904225i | \(-0.640449\pi\) | ||||
−0.427056 | + | 0.904225i | \(0.640449\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 36.0000 | 0.0178137 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4100.00i | 1.61609i | 0.589124 | + | 0.808043i | \(0.299473\pi\) | ||||
−0.589124 | + | 0.808043i | \(0.700527\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2925.00 | + | 1100.00i | 0.936000 | + | 0.352000i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 729.000i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2646.00 | 0.584245 | 0.292122 | − | 0.956381i | \(-0.405639\pi\) | ||||
0.292122 | + | 0.956381i | \(0.405639\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5612.00 | 1.04885 | 0.524425 | − | 0.851457i | \(-0.324280\pi\) | ||||
0.524425 | + | 0.851457i | \(0.324280\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4500.00i | 0.719329i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −40.0000 | + | 220.000i | −0.00551937 | + | 0.0303566i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7288.00i | 0.875193i | 0.899171 | + | 0.437597i | \(0.144170\pi\) | ||||
−0.899171 | + | 0.437597i | \(0.855830\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2592.00 | 0.272881 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −18986.0 | −1.76390 | −0.881950 | − | 0.471343i | \(-0.843769\pi\) | ||||
−0.881950 | + | 0.471343i | \(0.843769\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2404.00i | 0.198273i | 0.995074 | + | 0.0991364i | \(0.0316080\pi\) | ||||
−0.995074 | + | 0.0991364i | \(0.968392\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4455.00 | + | 810.000i | 0.327957 | + | 0.0596285i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8900.00i | 0.587686i | 0.955854 | + | 0.293843i | \(0.0949343\pi\) | ||||
−0.955854 | + | 0.293843i | \(0.905066\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 16791.0 | 0.999048 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 13644.0 | 0.734541 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 39804.0i | 1.94642i | 0.229913 | + | 0.973211i | \(0.426156\pi\) | ||||
−0.229913 | + | 0.973211i | \(0.573844\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −27500.0 | − | 5000.00i | −1.22582 | − | 0.222876i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 12096.0i | − | 0.493122i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −28300.0 | −1.05842 | −0.529208 | − | 0.848492i | \(-0.677511\pi\) | ||||
−0.529208 | + | 0.848492i | \(0.677511\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 18290.0 | 0.629345 | 0.314673 | − | 0.949200i | \(-0.398105\pi\) | ||||
0.314673 | + | 0.949200i | \(0.398105\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 324.000i | 0.0102847i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2880.00 | + | 15840.0i | −0.0845491 | + | 0.465020i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 65956.0i | 1.79501i | 0.441002 | + | 0.897506i | \(0.354623\pi\) | ||||
−0.441002 | + | 0.897506i | \(0.645377\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −36900.0 | −0.933047 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 28800.0 | 0.678026 | 0.339013 | − | 0.940782i | \(-0.389907\pi\) | ||||
0.339013 | + | 0.940782i | \(0.389907\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 30808.0i | − | 0.676638i | −0.941031 | − | 0.338319i | \(-0.890142\pi\) | ||
0.941031 | − | 0.338319i | \(-0.109858\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −9900.00 | + | 26325.0i | −0.203227 | + | 0.540400i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 2000.00i | − | 0.0384418i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 60228.0 | 1.08575 | 0.542876 | − | 0.839813i | \(-0.317335\pi\) | ||||
0.542876 | + | 0.839813i | \(0.317335\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2468.00i | 0.0393233i | 0.999807 | + | 0.0196616i | \(0.00625890\pi\) | ||||
−0.999807 | + | 0.0196616i | \(0.993741\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −15160.0 | + | 83380.0i | −0.227589 | + | 1.25174i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 23814.0i | 0.337314i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −22678.0 | −0.303480 | −0.151740 | − | 0.988420i | \(-0.548488\pi\) | ||||
−0.151740 | + | 0.988420i | \(0.548488\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1152.00 | −0.0145831 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 50508.0i | 0.605554i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 73920.0 | + | 13440.0i | 0.840336 | + | 0.152788i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 36968.0i | 0.398930i | 0.979905 | + | 0.199465i | \(0.0639204\pi\) | ||||
−0.979905 | + | 0.199465i | \(0.936080\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −40500.0 | −0.415305 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 167918. | 1.63792 | 0.818962 | − | 0.573848i | \(-0.194550\pi\) | ||||
0.818962 | + | 0.573848i | \(0.194550\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 154364.i | 1.43368i | 0.697236 | + | 0.716841i | \(0.254413\pi\) | ||||
−0.697236 | + | 0.716841i | \(0.745587\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1980.00 | − | 360.000i | −0.0175264 | − | 0.00318661i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 136788.i | 1.15502i | 0.816385 | + | 0.577509i | \(0.195975\pi\) | ||||
−0.816385 | + | 0.577509i | \(0.804025\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 53810.0 | 0.433807 | 0.216904 | − | 0.976193i | \(-0.430404\pi\) | ||||
0.216904 | + | 0.976193i | \(0.430404\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −65592.0 | −0.505293 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 82692.0i | 0.609211i | 0.952479 | + | 0.304605i | \(0.0985245\pi\) | ||||
−0.952479 | + | 0.304605i | \(0.901475\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 41000.0 | − | 225500.i | 0.289094 | − | 1.59002i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 23328.0i | 0.157548i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6064.00 | −0.0392547 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 88949.0 | 0.552303 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 170874.i | − | 1.01839i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −149875. | − | 89750.0i | −0.857935 | − | 0.513759i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 211780.i | − | 1.16513i | −0.812783 | − | 0.582567i | \(-0.802048\pi\) | ||
0.812783 | − | 0.582567i | \(-0.197952\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −21636.0 | −0.114473 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −169500. | −0.862962 | −0.431481 | − | 0.902122i | \(-0.642009\pi\) | ||||
−0.431481 | + | 0.902122i | \(0.642009\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5376.00i | 0.0263530i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −7290.00 | + | 40095.0i | −0.0344265 | + | 0.189346i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 252036.i | − | 1.14726i | −0.819115 | − | 0.573629i | \(-0.805535\pi\) | ||
0.819115 | − | 0.573629i | \(-0.194465\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 192016. | 0.842947 | 0.421474 | − | 0.906841i | \(-0.361513\pi\) | ||||
0.421474 | + | 0.906841i | \(0.361513\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −80100.0 | −0.339301 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 144000.i | − | 0.588874i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −145530. | − | 26460.0i | −0.574821 | − | 0.104513i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 151119.i | 0.576801i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −235694. | −0.869727 | −0.434863 | − | 0.900496i | \(-0.643203\pi\) | ||||
−0.434863 | + | 0.900496i | \(0.643203\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 371492. | 1.32589 | 0.662944 | − | 0.748669i | \(-0.269307\pi\) | ||||
0.662944 | + | 0.748669i | \(0.269307\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 122796.i | 0.424088i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −308660. | − | 56120.0i | −1.03193 | − | 0.187624i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 264952.i | − | 0.857863i | −0.903337 | − | 0.428932i | \(-0.858890\pi\) | ||
0.903337 | − | 0.428932i | \(-0.141110\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −358236. | −1.12377 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 16400.0 | 0.0498631 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 403124.i | 1.18842i | 0.804310 | + | 0.594210i | \(0.202535\pi\) | ||||
−0.804310 | + | 0.594210i | \(0.797465\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 45000.0 | − | 247500.i | 0.128678 | − | 0.707726i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 261900.i | − | 0.726682i | −0.931656 | − | 0.363341i | \(-0.881636\pi\) | ||
0.931656 | − | 0.363341i | \(-0.118364\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 288349. | 0.776608 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 108864. | 0.284704 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 326228.i | 0.828716i | 0.910114 | + | 0.414358i | \(0.135994\pi\) | ||||
−0.910114 | + | 0.414358i | \(0.864006\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4400.00 | − | 11700.0i | 0.0108607 | − | 0.0288796i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 254700.i | − | 0.611077i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −109516. | −0.255473 | −0.127736 | − | 0.991808i | \(-0.540771\pi\) | ||||
−0.127736 | + | 0.991808i | \(0.540771\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −53146.0 | −0.120580 | −0.0602898 | − | 0.998181i | \(-0.519202\pi\) | ||||
−0.0602898 | + | 0.998181i | \(0.519202\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 164610.i | 0.363353i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 72880.0 | − | 400840.i | 0.156559 | − | 0.861076i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 758000.i | − | 1.58513i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2916.00 | −0.00593790 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −232056. | −0.460267 | −0.230133 | − | 0.973159i | \(-0.573916\pi\) | ||||
−0.230133 | + | 0.973159i | \(0.573916\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 1.03067e6i | − | 1.99172i | −0.0909274 | − | 0.995858i | \(-0.528983\pi\) | ||
0.0909274 | − | 0.995858i | \(-0.471017\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −142560. | − | 25920.0i | −0.268480 | − | 0.0488145i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 522796.i | 0.959769i | 0.877332 | + | 0.479884i | \(0.159321\pi\) | ||||
−0.877332 | + | 0.479884i | \(0.840679\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −215292. | −0.385385 | −0.192693 | − | 0.981259i | \(-0.561722\pi\) | ||||
−0.192693 | + | 0.981259i | \(0.561722\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −593604. | −1.03635 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 10584.0i | − | 0.0180264i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.04423e6 | + | 189860.i | 1.73545 | + | 0.315536i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 332100.i | − | 0.538695i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −672000. | −1.06415 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.03008e6 | 1.59281 | 0.796407 | − | 0.604762i | \(-0.206732\pi\) | ||||
0.796407 | + | 0.604762i | \(0.206732\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 259200.i | 0.391459i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 24040.0 | − | 132220.i | 0.0354681 | − | 0.195075i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 22448.0i | − | 0.0323615i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 277272. | 0.390657 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −436608. | −0.601327 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 456020.i | − | 0.614075i | −0.951697 | − | 0.307038i | \(-0.900662\pi\) | ||
0.951697 | − | 0.307038i | \(-0.0993378\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −236925. | − | 89100.0i | −0.312000 | − | 0.117333i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 434252.i | − | 0.559342i | −0.960096 | − | 0.279671i | \(-0.909775\pi\) | ||
0.960096 | − | 0.279671i | \(-0.0902253\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 722710. | 0.910700 | 0.455350 | − | 0.890313i | \(-0.349514\pi\) | ||||
0.455350 | + | 0.890313i | \(0.349514\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 18000.0 | 0.0221944 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 565348.i | − | 0.682223i | −0.940023 | − | 0.341111i | \(-0.889197\pi\) | ||
0.940023 | − | 0.341111i | \(-0.110803\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 89000.0 | − | 489500.i | 0.105128 | − | 0.578207i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 542052.i | 0.626859i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 324904. | 0.367926 | 0.183963 | − | 0.982933i | \(-0.441107\pi\) | ||||
0.183963 | + | 0.982933i | \(0.441107\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 915262. | 1.01509 | 0.507543 | − | 0.861626i | \(-0.330554\pi\) | ||||
0.507543 | + | 0.861626i | \(0.330554\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 59049.0i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −923505. | − | 167910.i | −0.982933 | − | 0.178715i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 387072.i | 0.403691i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −22212.0 | −0.0227033 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.36708e6 | −1.36965 | −0.684823 | − | 0.728709i | \(-0.740121\pi\) | ||||
−0.684823 | + | 0.728709i | \(0.740121\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.05000e6i | 2.01350i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −750420. | − | 136440.i | −0.722693 | − | 0.131399i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 892932.i | − | 0.843307i | −0.906757 | − | 0.421653i | \(-0.861450\pi\) | ||
0.906757 | − | 0.421653i | \(-0.138550\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 29152.0 | 0.0270034 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −214326. | −0.194748 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.86650e6i | 1.66394i | 0.554818 | + | 0.831972i | \(0.312788\pi\) | ||||
−0.554818 | + | 0.831972i | \(0.687212\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 398040. | − | 2.18922e6i | 0.348187 | − | 1.91503i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 204102.i | − | 0.175214i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.37227e6 | 1.15627 | 0.578133 | − | 0.815943i | \(-0.303782\pi\) | ||||
0.578133 | + | 0.815943i | \(0.303782\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −458644. | −0.379361 | −0.189680 | − | 0.981846i | \(-0.560745\pi\) | ||||
−0.189680 | + | 0.981846i | \(0.560745\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 10368.0i | − | 0.00841954i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.46250e6 | + | 550000.i | 1.16618 | + | 0.438562i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 985408.i | 0.771643i | 0.922573 | + | 0.385822i | \(0.126082\pi\) | ||||
−0.922573 | + | 0.385822i | \(0.873918\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −454572. | −0.349617 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 165798. | 0.125260 | 0.0626302 | − | 0.998037i | \(-0.480051\pi\) | ||||
0.0626302 | + | 0.998037i | \(0.480051\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.66471e6i | 1.23558i | 0.786342 | + | 0.617792i | \(0.211972\pi\) | ||||
−0.786342 | + | 0.617792i | \(0.788028\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −120960. | + | 665280.i | −0.0882124 | + | 0.485168i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 75944.0i | 0.0544238i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −878399. | −0.618653 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −332712. | −0.230322 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.55104e6i | 1.73600i | 0.496567 | + | 0.867998i | \(0.334594\pi\) | ||||
−0.496567 | + | 0.867998i | \(0.665406\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.55650e6 | + | 283000.i | 1.04134 | + | 0.189335i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 364500.i | − | 0.239776i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.18080e6 | 0.763833 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9616.00 | 0.00611756 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.51126e6i | 0.945656i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.00595e6 | − | 182900.i | −0.619194 | − | 0.112581i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 736020.i | 0.445701i | 0.974853 | + | 0.222851i | \(0.0715362\pi\) | ||||
−0.974853 | + | 0.222851i | \(0.928464\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.38928e6 | −0.827737 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.71660e6 | −1.00639 | −0.503197 | − | 0.864172i | \(-0.667843\pi\) | ||||
−0.503197 | + | 0.864172i | \(0.667843\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.83851e6i | 1.63768i | 0.574020 | + | 0.818842i | \(0.305383\pi\) | ||||
−0.574020 | + | 0.818842i | \(0.694617\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3240.00 | − | 17820.0i | 0.00183979 | − | 0.0101189i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.27605e6i | 0.713215i | 0.934254 | + | 0.356607i | \(0.116067\pi\) | ||||
−0.934254 | + | 0.356607i | \(0.883933\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.32300e6 | 0.727919 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.23109e6 | −0.666850 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.03750e6i | 1.08666i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 316800. | − | 842400.i | 0.166371 | − | 0.442395i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 484290.i | 0.250459i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 35600.0 | 0.0181326 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −443992. | −0.222744 | −0.111372 | − | 0.993779i | \(-0.535524\pi\) | ||||
−0.111372 | + | 0.993779i | \(0.535524\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 590328.i | − | 0.291731i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 659560. | − | 3.62758e6i | 0.321101 | − | 1.76606i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 2.71326e6i | − | 1.30142i | −0.759328 | − | 0.650708i | \(-0.774472\pi\) | ||
0.759328 | − | 0.650708i | \(-0.225528\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −744228. | −0.351728 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.80600e6 | 1.30678 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 134392.i | − | 0.0616791i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.02950e6 | + | 369000.i | 0.917997 | + | 0.166909i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 1.31051e6i | − | 0.584273i | −0.956377 | − | 0.292137i | \(-0.905634\pi\) | ||
0.956377 | − | 0.292137i | \(-0.0943662\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 298910. | 0.131364 | 0.0656821 | − | 0.997841i | \(-0.479078\pi\) | ||||
0.0656821 | + | 0.997841i | \(0.479078\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −209952. | −0.0909604 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 737996.i | 0.315223i | 0.987501 | + | 0.157611i | \(0.0503793\pi\) | ||||
−0.987501 | + | 0.157611i | \(0.949621\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.58400e6 | − | 288000.i | −0.667090 | − | 0.121289i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 54576.0i | − | 0.0226637i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.34074e6 | −0.958557 | −0.479278 | − | 0.877663i | \(-0.659102\pi\) | ||||
−0.479278 | + | 0.877663i | \(0.659102\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −669763. | −0.270491 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 800541.i | 0.318872i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −308080. | + | 1.69444e6i | −0.121041 | + | 0.665724i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 127292.i | 0.0493328i | 0.999696 | + | 0.0246664i | \(0.00785236\pi\) | ||||
−0.999696 | + | 0.0246664i | \(0.992148\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.53787e6 | 0.587966 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 159216. | 0.0600554 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.03870e6i | 1.50303i | 0.659713 | + | 0.751517i | \(0.270678\pi\) | ||||
−0.659713 | + | 0.751517i | \(0.729322\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 807750. | − | 1.34888e6i | 0.296619 | − | 0.495329i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 762048.i | − | 0.276140i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.01214e6 | 0.361944 | 0.180972 | − | 0.983488i | \(-0.442076\pi\) | ||||
0.180972 | + | 0.983488i | \(0.442076\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.90602e6 | 0.672690 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.37610e6i | 0.827690i | 0.910347 | + | 0.413845i | \(0.135814\pi\) | ||||
−0.910347 | + | 0.413845i | \(0.864186\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −20000.0 | + | 110000.i | −0.00687667 | + | 0.0378217i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 194724.i | − | 0.0660910i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.42497e6 | −0.477456 | −0.238728 | − | 0.971087i | \(-0.576730\pi\) | ||||
−0.238728 | + | 0.971087i | \(0.576730\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.21560e6 | 2.05609 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 1.52550e6i | − | 0.498231i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.31254e6 | − | 602280.i | −1.06824 | − | 0.194225i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 1.69345e6i | − | 0.539257i | −0.962964 | − | 0.269628i | \(-0.913099\pi\) | ||
0.962964 | − | 0.269628i | \(-0.0869009\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −48384.0 | −0.0152149 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.84501e6 | −0.883532 | −0.441766 | − | 0.897130i | \(-0.645648\pi\) | ||||
−0.441766 | + | 0.897130i | \(0.645648\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 1.61626e6i | − | 0.495733i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −360855. | − | 65610.0i | −0.109319 | − | 0.0198762i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.64400e6i | 1.09042i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.89069e6 | 0.558873 | 0.279436 | − | 0.960164i | \(-0.409852\pi\) | ||||
0.279436 | + | 0.960164i | \(0.409852\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.26832e6 | 0.662370 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 113200.i | 0.0326566i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 24680.0 | − | 135740.i | 0.00703437 | − | 0.0386890i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.72814e6i | 0.486676i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.60930e6 | 1.28263 | 0.641313 | − | 0.767280i | \(-0.278390\pi\) | ||||
0.641313 | + | 0.767280i | \(0.278390\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.04151e6 | −1.66127 | −0.830635 | − | 0.556817i | \(-0.812022\pi\) | ||||
−0.830635 | + | 0.556817i | \(0.812022\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 720900.i | − | 0.195895i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.66760e6 | − | 4.43430e6i | 0.447837 | − | 1.19084i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 73160.0i | − | 0.0194180i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.29600e6 | 0.339987 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3800.00 | 0.000985350 | 0.000492675 | − | 1.00000i | \(-0.499843\pi\) | ||||
0.000492675 | 1.00000i | \(0.499843\pi\) | ||||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 250736.i | 0.0642683i | 0.999484 | + | 0.0321342i | \(0.0102304\pi\) | ||||
−0.999484 | + | 0.0321342i | \(0.989770\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 238140. | − | 1.30977e6i | 0.0603405 | − | 0.331873i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 5.51040e6i | − | 1.38032i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.58873e6 | −0.888750 | −0.444375 | − | 0.895841i | \(-0.646574\pi\) | ||||
−0.444375 | + | 0.895841i | \(0.646574\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.36007e6 | −0.333016 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.41479e6i | 0.342517i | 0.985226 | + | 0.171258i | \(0.0547833\pi\) | ||||
−0.985226 | + | 0.171258i | \(0.945217\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.24729e6 | + | 226780.i | 0.298585 | + | 0.0542881i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 2.12125e6i | − | 0.502137i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 829806. | 0.194250 | 0.0971249 | − | 0.995272i | \(-0.469035\pi\) | ||||
0.0971249 | + | 0.995272i | \(0.469035\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.49300e6 | −2.19767 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.34343e6i | 0.765502i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 63360.0 | + | 11520.0i | 0.0143478 | + | 0.00260870i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 4.68198e6i | − | 1.04867i | −0.851512 | − | 0.524335i | \(-0.824314\pi\) | ||
0.851512 | − | 0.524335i | \(-0.175686\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.10516e6 | −0.244847 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −141930. | −0.0311044 | −0.0155522 | − | 0.999879i | \(-0.504951\pi\) | ||||
−0.0155522 | + | 0.999879i | \(0.504951\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 727476.i | − | 0.157713i | −0.996886 | − | 0.0788563i | \(-0.974873\pi\) | ||
0.996886 | − | 0.0788563i | \(-0.0251268\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 505080. | − | 2.77794e6i | 0.108325 | − | 0.595786i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 4.47640e6i | − | 0.949809i | −0.880037 | − | 0.474905i | \(-0.842483\pi\) | ||
0.880037 | − | 0.474905i | \(-0.157517\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 263824. | 0.0553837 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.38457e6 | 0.495288 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.20200e6i | 0.247031i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.93120e6 | − | 1.47840e6i | −0.799450 | − | 0.300648i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 3.22412e6i | − | 0.648807i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.32718e6 | −0.264297 | −0.132149 | − | 0.991230i | \(-0.542188\pi\) | ||||
−0.132149 | + | 0.991230i | \(0.542188\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.09894e6 | 0.413655 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 147600.i | 0.0287885i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 369680. | − | 2.03324e6i | 0.0713628 | − | 0.392495i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 4.11647e6i | − | 0.786507i | −0.919430 | − | 0.393253i | \(-0.871350\pi\) | ||
0.919430 | − | 0.393253i | \(-0.128650\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3.62812e6 | −0.686134 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.12316e6 | 1.14623 | 0.573115 | − | 0.819475i | \(-0.305735\pi\) | ||||
0.573115 | + | 0.819475i | \(0.305735\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 4.01134e6i | − | 0.743313i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.22750e6 | + | 405000.i | 0.408606 | + | 0.0742920i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 115200.i | − | 0.0209200i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.90490e6 | −1.42117 | −0.710584 | − | 0.703613i | \(-0.751569\pi\) | ||||
−0.710584 | + | 0.703613i | \(0.751569\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.35710e6 | 0.419550 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 3.97628e6i | − | 0.700741i | −0.936611 | − | 0.350370i | \(-0.886056\pi\) | ||
0.936611 | − | 0.350370i | \(-0.113944\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.23549e6 | − | 1.67918e6i | −1.61150 | − | 0.293001i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.59514e6i | 0.448375i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −781914. | −0.133772 | −0.0668859 | − | 0.997761i | \(-0.521306\pi\) | ||||
−0.0668859 | + | 0.997761i | \(0.521306\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −123232. | −0.0208772 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 979776.i | 0.164374i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.54364e6 | − | 8.49002e6i | 0.256465 | − | 1.41056i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.45000e6i | 0.732207i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.93605e6 | −0.478460 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.82694e6 | 0.940472 | 0.470236 | − | 0.882541i | \(-0.344169\pi\) | ||||
0.470236 | + | 0.882541i | \(0.344169\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.78938e6i | 1.56495i | 0.622681 | + | 0.782476i | \(0.286043\pi\) | ||||
−0.622681 | + | 0.782476i | \(0.713957\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 105300. | + | 39600.0i | 0.0166736 | + | 0.00627042i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 8.50779e6i | − | 1.33441i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.03737e7 | −1.61173 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.29230e6 | 0.352805 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.46797e6i | 0.833696i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.36788e6 | − | 7.52334e6i | 0.206616 | − | 1.13639i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 985644.i | − | 0.147497i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 8.39550e6 | 1.24473 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.76059e6 | 0.699307 | 0.349653 | − | 0.936879i | \(-0.386299\pi\) | ||||
0.349653 | + | 0.936879i | \(0.386299\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 478314.i | − | 0.0696167i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.95955e6 | − | 538100.i | −0.426810 | − | 0.0776018i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 1.16595e6i | − | 0.166614i | −0.996524 | − | 0.0833069i | \(-0.973452\pi\) | ||
0.996524 | − | 0.0833069i | \(-0.0265482\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.48149e6 | −0.209782 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.55622e6 | −0.499011 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 240912.i | − | 0.0335001i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.60756e6 | + | 655920.i | 0.497143 | + | 0.0903896i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.61293e6i | 0.220282i | 0.993916 | + | 0.110141i | \(0.0351302\pi\) | ||||
−0.993916 | + | 0.110141i | \(0.964870\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 692352. | 0.0937125 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.82200e6 | 0.915176 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 3.40603e6i | − | 0.452874i | −0.974026 | − | 0.226437i | \(-0.927292\pi\) | ||
0.974026 | − | 0.226437i | \(-0.0727077\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 826920. | − | 4.54806e6i | 0.108979 | − | 0.599384i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 26244.0i | − | 0.00342825i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.44009e7 | 1.86470 | 0.932350 | − | 0.361557i | \(-0.117755\pi\) | ||||
0.932350 | + | 0.361557i | \(0.117755\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.74772e6 | −0.609389 | −0.304695 | − | 0.952450i | \(-0.598554\pi\) | ||||
−0.304695 | + | 0.952450i | \(0.598554\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 2.08850e6i | − | 0.265735i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.51000e6 | + | 1.19925e7i | −0.568862 | + | 1.51266i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.09094e7i | 1.36415i | 0.731283 | + | 0.682074i | \(0.238922\pi\) | ||||
−0.731283 | + | 0.682074i | \(0.761078\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9.27605e6 | 1.14992 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9872.00 | 0.00121329 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.99020e7i | 2.42508i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 233280. | − | 1.28304e6i | 0.0281830 | − | 0.155007i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8.53223e6i | 1.02204i | 0.859569 | + | 0.511019i | \(0.170732\pi\) | ||||
−0.859569 | + | 0.511019i | \(0.829268\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.54253e6 | −0.895836 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.70516e6 | −0.554123 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 4.63182e6i | − | 0.540897i | −0.962734 | − | 0.270449i | \(-0.912828\pi\) | ||
0.962734 | − | 0.270449i | \(-0.0871721\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 333520. | + | 60640.0i | 0.0386215 | + | 0.00702210i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 1.93763e6i | − | 0.222502i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.27598e6 | 0.714684 | 0.357342 | − | 0.933974i | \(-0.383683\pi\) | ||||
0.357342 | + | 0.933974i | \(0.383683\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.71988e6 | 0.871815 | 0.435907 | − | 0.899992i | \(-0.356428\pi\) | ||||
0.435907 | + | 0.899992i | \(0.356428\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 5.34244e6i | − | 0.598337i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.89220e6 | − | 889490.i | −0.543395 | − | 0.0987990i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 6.06160e6i | − | 0.667753i | −0.942617 | − | 0.333876i | \(-0.891643\pi\) | ||
0.942617 | − | 0.333876i | \(-0.108357\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 95256.0 | 0.0104076 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.56320e6 | 0.277766 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 3.66489e6i | − | 0.393921i | −0.980411 | − | 0.196961i | \(-0.936893\pi\) | ||
0.980411 | − | 0.196961i | \(-0.0631071\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.70874e6 | + | 9.39807e6i | −0.182175 | + | 1.00196i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.32522e6i | 0.986157i | 0.869985 | + | 0.493079i | \(0.164129\pi\) | ||||
−0.869985 | + | 0.493079i | \(0.835871\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.40162e6 | −0.776426 | −0.388213 | − | 0.921570i | \(-0.626907\pi\) | ||||
−0.388213 | + | 0.921570i | \(0.626907\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.98890e6 | 0.311016 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 90712.0i | 0.00936364i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.34562e6 | + | 6.43500e6i | 0.752192 | + | 0.658944i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 6.04800e6i | − | 0.614388i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.10486e7 | 1.11348 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −160052. | −0.0160025 | −0.00800125 | − | 0.999968i | \(-0.502547\pi\) | ||||
−0.00800125 | + | 0.999968i | \(0.502547\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 9.27072e6i | 0.919611i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.11780e6 | + | 1.16479e7i | −0.208425 | + | 1.14634i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 4.83581e6i | − | 0.472194i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.33280e6 | −0.226009 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.69565e7 | −1.63002 | −0.815008 | − | 0.579450i | \(-0.803268\pi\) | ||||
−0.815008 | + | 0.579450i | \(0.803268\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 1.10128e7i | − | 1.05044i | −0.850967 | − | 0.525219i | \(-0.823984\pi\) | ||
0.850967 | − | 0.525219i | \(-0.176016\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.18998e6 | + | 216360.i | 0.112626 | + | 0.0204775i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.33848e6i | 0.313537i | 0.987635 | + | 0.156768i | \(0.0501076\pi\) | ||||
−0.987635 | + | 0.156768i | \(0.949892\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.41500e7 | −1.31870 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 202032. | 0.0186839 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 4.76181e6i | − | 0.437008i | −0.975836 | − | 0.218504i | \(-0.929882\pi\) | ||
0.975836 | − | 0.218504i | \(-0.0701177\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.32250e6 | + | 1.69500e6i | 0.849042 | + | 0.154371i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.49545e6i | 0.225546i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 798188. | 0.0715965 | 0.0357982 | − | 0.999359i | \(-0.488603\pi\) | ||||
0.0357982 | + | 0.999359i | \(0.488603\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.54048e7 | −1.37136 | −0.685682 | − | 0.727901i | \(-0.740496\pi\) | ||||
−0.685682 | + | 0.727901i | \(0.740496\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 3.92947e6i | − | 0.347177i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 53760.0 | − | 295680.i | 0.00471417 | − | 0.0259279i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.08486e7i | 0.944189i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.10418e6 | 0.354537 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.14500e6 | 0.784111 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 976704.i | − | 0.0831238i | −0.999136 | − | 0.0415619i | \(-0.986767\pi\) | ||
0.999136 | − | 0.0415619i | \(-0.0132334\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 801900. | − | 2.13232e6i | 0.0677424 | − | 0.180133i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 1.93885e7i | − | 1.62582i | −0.582388 | − | 0.812911i | \(-0.697881\pi\) | ||
0.582388 | − | 0.812911i | \(-0.302119\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 147872. | 0.0123087 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.90827e6 | 0.322936 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.25573e6i | 0.431103i | 0.976492 | + | 0.215552i | \(0.0691550\pi\) | ||||
−0.976492 | + | 0.215552i | \(0.930845\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.52036e6 | + | 1.38620e7i | −0.205228 | + | 1.12875i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.50439e6i | 0.525793i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.14636e7 | 0.919965 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.45034e6 | 0.434238 | 0.217119 | − | 0.976145i | \(-0.430334\pi\) | ||||
0.217119 | + | 0.976145i | \(0.430334\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 162000.i | 0.0128139i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.05609e7 | − | 1.92016e6i | −0.829350 | − | 0.150791i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.87828e7i | 2.24414i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.08813e6 | 0.393881 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.43961e6 | −0.341232 | −0.170616 | − | 0.985338i | \(-0.554576\pi\) | ||||
−0.170616 | + | 0.985338i | \(0.554576\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 9.79507e6i | − | 0.747514i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.40550e6 | + | 801000.i | 0.333828 | + | 0.0606960i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 671672.i | − | 0.0505369i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.55918e6 | −0.340621 | −0.170310 | − | 0.985390i | \(-0.554477\pi\) | ||||
−0.170310 | + | 0.985390i | \(0.554477\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.87847e6 | −0.361917 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.30092e7i | 1.69503i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.44000e6 | + | 7.92000e6i | −0.105341 | + | 0.579375i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.92414e6i | 0.212422i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.06630e7 | −1.49063 | −0.745317 | − | 0.666710i | \(-0.767702\pi\) | ||||
−0.745317 | + | 0.666710i | \(0.767702\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 617456. | 0.0442352 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 8.23736e6i | 0.586060i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.73955e6 | + | 2.91060e6i | 0.546853 | + | 0.205654i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.48161e6i | 0.384656i | 0.981331 | + | 0.192328i | \(0.0616037\pi\) | ||||
−0.981331 | + | 0.192328i | \(0.938396\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −531441. | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.64446e6 | 0.252255 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 8.55579e6i | − | 0.588166i | −0.955780 | − | 0.294083i | \(-0.904986\pi\) | ||
0.955780 | − | 0.294083i | \(-0.0950143\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.51119e6 | − | 8.31154e6i | 0.103181 | − | 0.567497i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.29780e7i | 2.23643i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.29119e6 | −0.356404 | −0.178202 | − | 0.983994i | \(-0.557028\pi\) | ||||
−0.178202 | + | 0.983994i | \(0.557028\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.48365e6 | −0.233071 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.36432e6i | 0.157121i | 0.996909 | + | 0.0785606i | \(0.0250324\pi\) | ||||
−0.996909 | + | 0.0785606i | \(0.974968\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.29632e7 | + | 2.35694e6i | 0.855698 | + | 0.155581i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 199908.i | − | 0.0131078i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 547152. | 0.0356372 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.79694e6 | 0.569157 | 0.284578 | − | 0.958653i | \(-0.408146\pi\) | ||||
0.284578 | + | 0.958653i | \(0.408146\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 1.23037e7i | − | 0.790766i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.04321e7 | − | 3.71492e6i | −1.30450 | − | 0.237182i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 2.95808e7i | − | 1.87616i | −0.346421 | − | 0.938079i | \(-0.612603\pi\) | ||
0.346421 | − | 0.938079i | \(-0.387397\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.84500e7 | −1.16250 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.26296e7 | −0.790549 | −0.395274 | − | 0.918563i | \(-0.629351\pi\) | ||||
−0.395274 | + | 0.918563i | \(0.629351\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 215240.i | − | 0.0133848i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.22796e6 | − | 6.75378e6i | 0.0758631 | − | 0.417247i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.15040e6i | 0.500254i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.32186e7 | 1.41586 | 0.707929 | − | 0.706283i | \(-0.249630\pi\) | ||||
0.707929 | + | 0.706283i | \(0.249630\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.03639e6 | 0.486883 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 1.73201e7i | − | 1.04256i | −0.853386 | − | 0.521280i | \(-0.825455\pi\) | ||
0.853386 | − | 0.521280i | \(-0.174545\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.64151e7 | + | 6.17320e6i | 0.981724 | + | 0.369195i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 262368.i | 0.0155904i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.55172e7 | 1.50657 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.44000e7 | 0.844763 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 1.92893e6i | − | 0.112438i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.64952e6 | + | 1.45724e7i | −0.153459 | + | 0.844026i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 556676.i | 0.0320380i | 0.999872 | + | 0.0160190i | \(0.00509923\pi\) | ||||
−0.999872 | + | 0.0160190i | \(0.994901\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.67985e7 | −0.960678 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 330768. | 0.0187967 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 5.26752e6i | − | 0.297456i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.97030e7 | + | 3.58236e6i | 1.10564 | + | 0.201026i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 3.00562e6i | − | 0.167606i | −0.996482 | − | 0.0838028i | \(-0.973293\pi\) | ||
0.996482 | − | 0.0838028i | \(-0.0267066\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.34924e7 | 0.747691 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.83692e6 | 0.101160 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 1.54040e7i | − | 0.843033i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −902000. | − | 164000.i | −0.0490588 | − | 0.00891978i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.23504e7i | 0.667570i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.23153e6 | −0.119876 | −0.0599378 | − | 0.998202i | \(-0.519090\pi\) | ||||
−0.0599378 | + | 0.998202i | \(0.519090\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.24862e7 | −1.20051 | −0.600253 | − | 0.799810i | \(-0.704933\pi\) | ||||
−0.600253 | + | 0.799810i | \(0.704933\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 4.12780e6i | − | 0.219024i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.03124e6 | − | 2.21718e7i | 0.212591 | − | 1.16925i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 3.23098e6i | − | 0.169347i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 93312.0 | 0.00486102 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.65921e7 | −0.859098 | −0.429549 | − | 0.903044i | \(-0.641327\pi\) | ||||
−0.429549 | + | 0.903044i | \(0.641327\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 1.47544e7i | − | 0.759316i | −0.925127 | − | 0.379658i | \(-0.876042\pi\) | ||
0.925127 | − | 0.379658i | \(-0.123958\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.95000e6 | + | 1.31625e7i | −0.253204 | + | 0.673292i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 3.39475e6i | − | 0.172601i | −0.996269 | − | 0.0863006i | \(-0.972495\pi\) | ||
0.996269 | − | 0.0863006i | \(-0.0275045\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 509442. | 0.0257459 | 0.0128730 | − | 0.999917i | \(-0.495902\pi\) | ||||
0.0128730 | + | 0.999917i | \(0.495902\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.86867e6 | −0.445509 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 2.54552e7i | − | 1.27105i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.61900e6 | + | 1.44045e7i | −0.129993 | + | 0.714960i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 4.09115e6i | − | 0.201851i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.00609e7 | 1.96479 | 0.982394 | − | 0.186819i | \(-0.0598178\pi\) | ||||
0.982394 | + | 0.186819i | \(0.0598178\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.35098e7 | −0.658658 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.49218e6i | 0.0723191i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.58592e7 | − | 2.88349e6i | −0.764081 | − | 0.138924i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 355796.i | − | 0.0170409i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.49824e7 | −0.713364 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.98808e7 | −1.41439 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.67506e6i | 0.455283i | 0.973745 | + | 0.227641i | \(0.0731014\pi\) | ||||
−0.973745 | + | 0.227641i | \(0.926899\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.98752e6 | − | 1.08864e6i | −0.280112 | − | 0.0509295i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 3.27535e7i | − | 1.52337i | −0.647946 | − | 0.761686i | \(-0.724372\pi\) | ||
0.647946 | − | 0.761686i | \(-0.275628\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.17420e7 | −1.00535 | −0.502675 | − | 0.864476i | \(-0.667651\pi\) | ||||
−0.502675 | + | 0.864476i | \(0.667651\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −683496. | −0.0314216 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 2.08744e7i | − | 0.954087i | −0.878880 | − | 0.477043i | \(-0.841708\pi\) | ||
0.878880 | − | 0.477043i | \(-0.158292\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.26228e6 | − | 1.79425e7i | 0.148245 | − | 0.815349i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 7.90559e6i | − | 0.357180i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.01140e7 | 1.35275 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.89953e7 | 0.848401 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 2.99441e6i | − | 0.132977i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −359000. | + | 599500.i | −0.0158516 | + | 0.0264709i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 3.96804e7i | − | 1.74212i | −0.491181 | − | 0.871058i | \(-0.663434\pi\) | ||
0.491181 | − | 0.871058i | \(-0.336566\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.29594e7 | −1.00228 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.60742e7 | 1.13180 | 0.565902 | − | 0.824472i | \(-0.308528\pi\) | ||||
0.565902 | + | 0.824472i | \(0.308528\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 4.10486e7i | − | 1.77172i | −0.463949 | − | 0.885862i | \(-0.653568\pi\) | ||
0.463949 | − | 0.885862i | \(-0.346432\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.54700e6 | + | 1.40085e7i | −0.109313 | + | 0.601220i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.37553e7i | 0.587031i | 0.955954 | + | 0.293515i | \(0.0948252\pi\) | ||||
−0.955954 | + | 0.293515i | \(0.905175\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −847120. | −0.0359493 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.28050e6 | 0.138435 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 1.19616e7i | − | 0.501950i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.02338e6 | + | 1.09516e6i | 0.251352 | + | 0.0457004i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.06272e7i | 0.440999i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.48494e7 | 0.612785 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.03429e7 | 2.47636 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 86544.0i | 0.00353197i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.92303e6 | + | 531460.i | 0.118635 | + | 0.0215699i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 5.86936e6i | − | 0.236904i | −0.992960 | − | 0.118452i | \(-0.962207\pi\) | ||
0.992960 | − | 0.118452i | \(-0.0377932\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.36014e7 | −0.545975 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.63982e7 | −1.85227 | −0.926137 | − | 0.377188i | \(-0.876891\pi\) | ||||
−0.926137 | + | 0.377188i | \(0.876891\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.23400e6i | 0.0489935i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.64610e6 | − | 9.05355e6i | 0.0649985 | − | 0.357492i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 678000.i | 0.0266260i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.27859e7 | 0.889975 | 0.444988 | − | 0.895537i | \(-0.353208\pi\) | ||||
0.444988 | + | 0.895537i | \(0.353208\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.62418e6 | −0.257326 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 8.29440e6i | − | 0.320465i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.01680e6 | + | 2.13174e7i | −0.308068 | + | 0.819181i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 1.25035e7i | − | 0.477894i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.70352e7 | −1.02775 | −0.513877 | − | 0.857864i | \(-0.671791\pi\) | ||||
−0.513877 | + | 0.857864i | \(0.671791\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.25671e7 | −0.853300 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 1.54494e7i | − | 0.581042i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.58000e6 | + | 4.16900e7i | −0.283557 | + | 1.55956i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.86149e7i | 1.06474i | 0.846512 | + | 0.532370i | \(0.178699\pi\) | ||||
−0.846512 | + | 0.532370i | \(0.821301\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.55466e7 | −0.945517 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.67892e7 | −1.35440 | −0.677200 | − | 0.735799i | \(-0.736807\pi\) | ||||
−0.677200 | + | 0.735799i | \(0.736807\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 7.78426e7i | − | 2.85061i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 160380. | + | 29160.0i | 0.00584212 | + | 0.00106220i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.96828e6i | 0.288728i | 0.989525 | + | 0.144364i | \(0.0461137\pi\) | ||||
−0.989525 | + | 0.144364i | \(0.953886\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.87270e6 | −0.319809 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.14845e7 | −0.411775 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 4.82202e7i | − | 1.71987i | −0.510400 | − | 0.859937i | \(-0.670503\pi\) | ||
0.510400 | − | 0.859937i | \(-0.329497\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.27631e7 | + | 2.32056e6i | 0.452842 | + | 0.0823350i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.19070e7i | 0.420264i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.00814e6 | −0.0353978 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.86539e6 | 0.100087 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 1.10798e7i | − | 0.385006i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.03067e7 | + | 5.66870e7i | −0.356289 | + | 1.95959i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.83510e7i | 1.66280i | 0.555678 | + | 0.831398i | \(0.312459\pi\) | ||||
−0.555678 | + | 0.831398i | \(0.687541\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.83375e7 | −0.627381 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.05515e7 | 1.38025 | 0.690127 | − | 0.723688i | \(-0.257555\pi\) | ||||
0.690127 | + | 0.723688i | \(0.257555\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 768064.i | − | 0.0260085i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 7.58160e6 | + | 2.85120e6i | 0.255417 | + | 0.0960542i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.34929e7i | 1.45775i | 0.684648 | + | 0.728874i | \(0.259956\pi\) | ||||
−0.684648 | + | 0.728874i | \(0.740044\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.13390e7 | −0.378110 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.35861e6 | −0.144602 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.34896e6i | 0.110542i | 0.998471 | + | 0.0552709i | \(0.0176022\pi\) | ||||
−0.998471 | + | 0.0552709i | \(0.982398\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.22796e6 | − | 2.87538e7i | 0.171689 | − | 0.944288i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 320400.i | 0.0104689i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.85640e6 | −0.320426 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.55726e7 | 1.79753 | 0.898766 | − | 0.438429i | \(-0.144465\pi\) | ||||
0.898766 | + | 0.438429i | \(0.144465\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 3.99593e6i | − | 0.128601i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.18411e7 | + | 2.15292e6i | 0.379169 | + | 0.0689398i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.27342e7i | 0.405726i | 0.979207 | + | 0.202863i | \(0.0650247\pi\) | ||||
−0.979207 | + | 0.202863i | \(0.934975\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.31295e6 | 0.168431 |
(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 | 240.6.f.a.49.2 | 2 | ||
3.2 | odd | 2 | 720.6.f.g.289.2 | 2 | |||
4.3 | odd | 2 | 30.6.c.a.19.1 | ✓ | 2 | ||
5.4 | even | 2 | inner | 240.6.f.a.49.1 | 2 | ||
12.11 | even | 2 | 90.6.c.b.19.2 | 2 | |||
15.14 | odd | 2 | 720.6.f.g.289.1 | 2 | |||
20.3 | even | 4 | 150.6.a.f.1.1 | 1 | |||
20.7 | even | 4 | 150.6.a.j.1.1 | 1 | |||
20.19 | odd | 2 | 30.6.c.a.19.2 | yes | 2 | ||
60.23 | odd | 4 | 450.6.a.s.1.1 | 1 | |||
60.47 | odd | 4 | 450.6.a.f.1.1 | 1 | |||
60.59 | even | 2 | 90.6.c.b.19.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
30.6.c.a.19.1 | ✓ | 2 | 4.3 | odd | 2 | ||
30.6.c.a.19.2 | yes | 2 | 20.19 | odd | 2 | ||
90.6.c.b.19.1 | 2 | 60.59 | even | 2 | |||
90.6.c.b.19.2 | 2 | 12.11 | even | 2 | |||
150.6.a.f.1.1 | 1 | 20.3 | even | 4 | |||
150.6.a.j.1.1 | 1 | 20.7 | even | 4 | |||
240.6.f.a.49.1 | 2 | 5.4 | even | 2 | inner | ||
240.6.f.a.49.2 | 2 | 1.1 | even | 1 | trivial | ||
450.6.a.f.1.1 | 1 | 60.47 | odd | 4 | |||
450.6.a.s.1.1 | 1 | 60.23 | odd | 4 | |||
720.6.f.g.289.1 | 2 | 15.14 | odd | 2 | |||
720.6.f.g.289.2 | 2 | 3.2 | odd | 2 |