Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [98,5,Mod(97,98)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(98, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("98.97");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 98 = 2 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 98.b (of order \(2\), degree \(1\), 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: | \(10.1302563822\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.0.2048.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 4x^{2} + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 97.1 | ||
Root | \(0.765367i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 98.97 |
Dual form | 98.5.b.a.97.2 |
$q$-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 \(\left(\mathbb{Z}/98\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.82843 | −0.707107 | ||||||||
\(3\) | − 15.9958i | − 1.77731i | −0.458577 | − | 0.888654i | \(-0.651641\pi\) | ||||
0.458577 | − | 0.888654i | \(-0.348359\pi\) | |||||||
\(4\) | 8.00000 | 0.500000 | ||||||||
\(5\) | 27.8477i | 1.11391i | 0.830543 | + | 0.556954i | \(0.188030\pi\) | ||||
−0.830543 | + | 0.556954i | \(0.811970\pi\) | |||||||
\(6\) | 45.2429i | 1.25675i | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −22.6274 | −0.353553 | ||||||||
\(9\) | −174.865 | −2.15883 | ||||||||
\(10\) | − 78.7652i | − 0.787652i | ||||||||
\(11\) | −139.664 | −1.15425 | −0.577124 | − | 0.816657i | \(-0.695825\pi\) | ||||
−0.577124 | + | 0.816657i | \(0.695825\pi\) | |||||||
\(12\) | − 127.966i | − 0.888654i | ||||||||
\(13\) | 101.931i | 0.603140i | 0.953444 | + | 0.301570i | \(0.0975106\pi\) | ||||
−0.953444 | + | 0.301570i | \(0.902489\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 445.446 | 1.97976 | ||||||||
\(16\) | 64.0000 | 0.250000 | ||||||||
\(17\) | 542.887i | 1.87850i | 0.343232 | + | 0.939251i | \(0.388478\pi\) | ||||
−0.343232 | + | 0.939251i | \(0.611522\pi\) | |||||||
\(18\) | 494.593 | 1.52652 | ||||||||
\(19\) | − 139.953i | − 0.387682i | −0.981033 | − | 0.193841i | \(-0.937905\pi\) | ||||
0.981033 | − | 0.193841i | \(-0.0620947\pi\) | |||||||
\(20\) | 222.782i | 0.556954i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 395.029 | 0.816177 | ||||||||
\(23\) | 229.647 | 0.434115 | 0.217057 | − | 0.976159i | \(-0.430354\pi\) | ||||
0.217057 | + | 0.976159i | \(0.430354\pi\) | |||||||
\(24\) | 361.943i | 0.628374i | ||||||||
\(25\) | −150.495 | −0.240791 | ||||||||
\(26\) | − 288.303i | − 0.426484i | ||||||||
\(27\) | 1501.44i | 2.05959i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −383.113 | −0.455544 | −0.227772 | − | 0.973714i | \(-0.573144\pi\) | ||||
−0.227772 | + | 0.973714i | \(0.573144\pi\) | |||||||
\(30\) | −1259.91 | −1.39990 | ||||||||
\(31\) | 397.492i | 0.413623i | 0.978381 | + | 0.206812i | \(0.0663087\pi\) | ||||
−0.978381 | + | 0.206812i | \(0.933691\pi\) | |||||||
\(32\) | −181.019 | −0.176777 | ||||||||
\(33\) | 2234.03i | 2.05146i | ||||||||
\(34\) | − 1535.52i | − 1.32830i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1398.92 | −1.07941 | ||||||||
\(37\) | −898.912 | −0.656619 | −0.328310 | − | 0.944570i | \(-0.606479\pi\) | ||||
−0.328310 | + | 0.944570i | \(0.606479\pi\) | |||||||
\(38\) | 395.848i | 0.274133i | ||||||||
\(39\) | 1630.46 | 1.07197 | ||||||||
\(40\) | − 630.122i | − 0.393826i | ||||||||
\(41\) | 657.862i | 0.391352i | 0.980669 | + | 0.195676i | \(0.0626900\pi\) | ||||
−0.980669 | + | 0.195676i | \(0.937310\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1155.70 | 0.625041 | 0.312521 | − | 0.949911i | \(-0.398827\pi\) | ||||
0.312521 | + | 0.949911i | \(0.398827\pi\) | |||||||
\(44\) | −1117.31 | −0.577124 | ||||||||
\(45\) | − 4869.59i | − 2.40474i | ||||||||
\(46\) | −649.539 | −0.306966 | ||||||||
\(47\) | − 1294.51i | − 0.586015i | −0.956110 | − | 0.293007i | \(-0.905344\pi\) | ||||
0.956110 | − | 0.293007i | \(-0.0946561\pi\) | |||||||
\(48\) | − 1023.73i | − 0.444327i | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 425.663 | 0.170265 | ||||||||
\(51\) | 8683.90 | 3.33868 | ||||||||
\(52\) | 815.445i | 0.301570i | ||||||||
\(53\) | −5168.43 | −1.83996 | −0.919978 | − | 0.391971i | \(-0.871793\pi\) | ||||
−0.919978 | + | 0.391971i | \(0.871793\pi\) | |||||||
\(54\) | − 4246.73i | − 1.45635i | ||||||||
\(55\) | − 3889.32i | − 1.28573i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2238.66 | −0.689031 | ||||||||
\(58\) | 1083.61 | 0.322118 | ||||||||
\(59\) | 4155.24i | 1.19369i | 0.802356 | + | 0.596846i | \(0.203580\pi\) | ||||
−0.802356 | + | 0.596846i | \(0.796420\pi\) | |||||||
\(60\) | 3563.57 | 0.989879 | ||||||||
\(61\) | 1840.09i | 0.494514i | 0.968950 | + | 0.247257i | \(0.0795292\pi\) | ||||
−0.968950 | + | 0.247257i | \(0.920471\pi\) | |||||||
\(62\) | − 1124.28i | − 0.292476i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 512.000 | 0.125000 | ||||||||
\(65\) | −2838.53 | −0.671842 | ||||||||
\(66\) | − 6318.80i | − 1.45060i | ||||||||
\(67\) | −6315.57 | −1.40690 | −0.703450 | − | 0.710745i | \(-0.748358\pi\) | ||||
−0.703450 | + | 0.710745i | \(0.748358\pi\) | |||||||
\(68\) | 4343.09i | 0.939251i | ||||||||
\(69\) | − 3673.38i | − 0.771556i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1263.28 | 0.250601 | 0.125301 | − | 0.992119i | \(-0.460010\pi\) | ||||
0.125301 | + | 0.992119i | \(0.460010\pi\) | |||||||
\(72\) | 3956.74 | 0.763261 | ||||||||
\(73\) | − 3995.44i | − 0.749753i | −0.927075 | − | 0.374877i | \(-0.877685\pi\) | ||||
0.927075 | − | 0.374877i | \(-0.122315\pi\) | |||||||
\(74\) | 2542.51 | 0.464300 | ||||||||
\(75\) | 2407.28i | 0.427960i | ||||||||
\(76\) | − 1119.63i | − 0.193841i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −4611.63 | −0.757994 | ||||||||
\(79\) | −10614.3 | −1.70073 | −0.850366 | − | 0.526192i | \(-0.823619\pi\) | ||||
−0.850366 | + | 0.526192i | \(0.823619\pi\) | |||||||
\(80\) | 1782.25i | 0.278477i | ||||||||
\(81\) | 9852.71 | 1.50171 | ||||||||
\(82\) | − 1860.71i | − 0.276727i | ||||||||
\(83\) | 5750.31i | 0.834709i | 0.908744 | + | 0.417355i | \(0.137043\pi\) | ||||
−0.908744 | + | 0.417355i | \(0.862957\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −15118.2 | −2.09248 | ||||||||
\(86\) | −3268.82 | −0.441971 | ||||||||
\(87\) | 6128.19i | 0.809643i | ||||||||
\(88\) | 3160.24 | 0.408088 | ||||||||
\(89\) | 4187.05i | 0.528601i | 0.964440 | + | 0.264301i | \(0.0851411\pi\) | ||||
−0.964440 | + | 0.264301i | \(0.914859\pi\) | |||||||
\(90\) | 13773.3i | 1.70040i | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1837.17 | 0.217057 | ||||||||
\(93\) | 6358.19 | 0.735136 | ||||||||
\(94\) | 3661.42i | 0.414375i | ||||||||
\(95\) | 3897.38 | 0.431843 | ||||||||
\(96\) | 2895.55i | 0.314187i | ||||||||
\(97\) | − 3814.28i | − 0.405386i | −0.979242 | − | 0.202693i | \(-0.935031\pi\) | ||||
0.979242 | − | 0.202693i | \(-0.0649694\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 24422.3 | 2.49182 | ||||||||
\(100\) | −1203.96 | −0.120396 | ||||||||
\(101\) | 4925.41i | 0.482836i | 0.970421 | + | 0.241418i | \(0.0776126\pi\) | ||||
−0.970421 | + | 0.241418i | \(0.922387\pi\) | |||||||
\(102\) | −24561.8 | −2.36080 | ||||||||
\(103\) | − 18892.6i | − 1.78081i | −0.455166 | − | 0.890407i | \(-0.650420\pi\) | ||||
0.455166 | − | 0.890407i | \(-0.349580\pi\) | |||||||
\(104\) | − 2306.43i | − 0.213242i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 14618.5 | 1.30104 | ||||||||
\(107\) | −8479.39 | −0.740623 | −0.370311 | − | 0.928908i | \(-0.620749\pi\) | ||||
−0.370311 | + | 0.928908i | \(0.620749\pi\) | |||||||
\(108\) | 12011.6i | 1.02980i | ||||||||
\(109\) | 11678.0 | 0.982911 | 0.491455 | − | 0.870903i | \(-0.336465\pi\) | ||||
0.491455 | + | 0.870903i | \(0.336465\pi\) | |||||||
\(110\) | 11000.7i | 0.909146i | ||||||||
\(111\) | 14378.8i | 1.16702i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 19683.8 | 1.54153 | 0.770763 | − | 0.637121i | \(-0.219875\pi\) | ||||
0.770763 | + | 0.637121i | \(0.219875\pi\) | |||||||
\(114\) | 6331.90 | 0.487219 | ||||||||
\(115\) | 6395.13i | 0.483564i | ||||||||
\(116\) | −3064.90 | −0.227772 | ||||||||
\(117\) | − 17824.1i | − 1.30207i | ||||||||
\(118\) | − 11752.8i | − 0.844067i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −10079.3 | −0.699950 | ||||||||
\(121\) | 4865.03 | 0.332288 | ||||||||
\(122\) | − 5204.55i | − 0.349674i | ||||||||
\(123\) | 10523.0 | 0.695553 | ||||||||
\(124\) | 3179.94i | 0.206812i | ||||||||
\(125\) | 13213.9i | 0.845689i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −27965.5 | −1.73386 | −0.866931 | − | 0.498428i | \(-0.833911\pi\) | ||||
−0.866931 | + | 0.498428i | \(0.833911\pi\) | |||||||
\(128\) | −1448.15 | −0.0883883 | ||||||||
\(129\) | − 18486.3i | − 1.11089i | ||||||||
\(130\) | 8028.58 | 0.475064 | ||||||||
\(131\) | 1169.73i | 0.0681622i | 0.999419 | + | 0.0340811i | \(0.0108505\pi\) | ||||
−0.999419 | + | 0.0340811i | \(0.989150\pi\) | |||||||
\(132\) | 17872.3i | 1.02573i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 17863.1 | 0.994828 | ||||||||
\(135\) | −41811.8 | −2.29420 | ||||||||
\(136\) | − 12284.1i | − 0.664150i | ||||||||
\(137\) | −20884.6 | −1.11272 | −0.556359 | − | 0.830942i | \(-0.687802\pi\) | ||||
−0.556359 | + | 0.830942i | \(0.687802\pi\) | |||||||
\(138\) | 10389.9i | 0.545573i | ||||||||
\(139\) | − 3499.87i | − 0.181143i | −0.995890 | − | 0.0905716i | \(-0.971131\pi\) | ||||
0.995890 | − | 0.0905716i | \(-0.0288694\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −20706.6 | −1.04153 | ||||||||
\(142\) | −3573.10 | −0.177202 | ||||||||
\(143\) | − 14236.0i | − 0.696173i | ||||||||
\(144\) | −11191.4 | −0.539707 | ||||||||
\(145\) | − 10668.8i | − 0.507434i | ||||||||
\(146\) | 11300.8i | 0.530156i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −7191.29 | −0.328310 | ||||||||
\(149\) | 29533.8 | 1.33029 | 0.665146 | − | 0.746713i | \(-0.268369\pi\) | ||||
0.665146 | + | 0.746713i | \(0.268369\pi\) | |||||||
\(150\) | − 6808.81i | − 0.302614i | ||||||||
\(151\) | 25780.8 | 1.13069 | 0.565344 | − | 0.824856i | \(-0.308744\pi\) | ||||
0.565344 | + | 0.824856i | \(0.308744\pi\) | |||||||
\(152\) | 3166.78i | 0.137066i | ||||||||
\(153\) | − 94931.9i | − 4.05536i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −11069.2 | −0.460738 | ||||||||
\(156\) | 13043.7 | 0.535983 | ||||||||
\(157\) | 25629.4i | 1.03977i | 0.854235 | + | 0.519887i | \(0.174026\pi\) | ||||
−0.854235 | + | 0.519887i | \(0.825974\pi\) | |||||||
\(158\) | 30021.7 | 1.20260 | ||||||||
\(159\) | 82673.2i | 3.27017i | ||||||||
\(160\) | − 5040.97i | − 0.196913i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −27867.7 | −1.06187 | ||||||||
\(163\) | −6182.78 | −0.232707 | −0.116353 | − | 0.993208i | \(-0.537120\pi\) | ||||
−0.116353 | + | 0.993208i | \(0.537120\pi\) | |||||||
\(164\) | 5262.90i | 0.195676i | ||||||||
\(165\) | −62212.7 | −2.28513 | ||||||||
\(166\) | − 16264.3i | − 0.590229i | ||||||||
\(167\) | 39270.9i | 1.40811i | 0.710144 | + | 0.704056i | \(0.248630\pi\) | ||||
−0.710144 | + | 0.704056i | \(0.751370\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 18171.2 | 0.636223 | ||||||||
\(170\) | 42760.6 | 1.47961 | ||||||||
\(171\) | 24472.9i | 0.836939i | ||||||||
\(172\) | 9245.61 | 0.312521 | ||||||||
\(173\) | − 32905.9i | − 1.09946i | −0.835341 | − | 0.549732i | \(-0.814730\pi\) | ||||
0.835341 | − | 0.549732i | \(-0.185270\pi\) | |||||||
\(174\) | − 17333.1i | − 0.572504i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −8938.50 | −0.288562 | ||||||||
\(177\) | 66466.3 | 2.12156 | ||||||||
\(178\) | − 11842.8i | − 0.373777i | ||||||||
\(179\) | −4767.88 | −0.148806 | −0.0744029 | − | 0.997228i | \(-0.523705\pi\) | ||||
−0.0744029 | + | 0.997228i | \(0.523705\pi\) | |||||||
\(180\) | − 38956.7i | − 1.20237i | ||||||||
\(181\) | − 35195.4i | − 1.07431i | −0.843484 | − | 0.537154i | \(-0.819499\pi\) | ||||
0.843484 | − | 0.537154i | \(-0.180501\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 29433.6 | 0.878904 | ||||||||
\(184\) | −5196.31 | −0.153483 | ||||||||
\(185\) | − 25032.6i | − 0.731413i | ||||||||
\(186\) | −17983.7 | −0.519820 | ||||||||
\(187\) | − 75821.7i | − 2.16826i | ||||||||
\(188\) | − 10356.1i | − 0.293007i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −11023.5 | −0.305359 | ||||||||
\(191\) | 23315.1 | 0.639101 | 0.319551 | − | 0.947569i | \(-0.396468\pi\) | ||||
0.319551 | + | 0.947569i | \(0.396468\pi\) | |||||||
\(192\) | − 8189.84i | − 0.222164i | ||||||||
\(193\) | 59183.8 | 1.58887 | 0.794434 | − | 0.607350i | \(-0.207768\pi\) | ||||
0.794434 | + | 0.607350i | \(0.207768\pi\) | |||||||
\(194\) | 10788.4i | 0.286651i | ||||||||
\(195\) | 45404.5i | 1.19407i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −60902.2 | −1.56928 | −0.784640 | − | 0.619952i | \(-0.787152\pi\) | ||||
−0.784640 | + | 0.619952i | \(0.787152\pi\) | |||||||
\(198\) | −69076.8 | −1.76198 | ||||||||
\(199\) | − 40116.7i | − 1.01302i | −0.862233 | − | 0.506512i | \(-0.830935\pi\) | ||||
0.862233 | − | 0.506512i | \(-0.169065\pi\) | |||||||
\(200\) | 3405.30 | 0.0851326 | ||||||||
\(201\) | 101023.i | 2.50050i | ||||||||
\(202\) | − 13931.2i | − 0.341417i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 69471.2 | 1.66934 | ||||||||
\(205\) | −18319.9 | −0.435930 | ||||||||
\(206\) | 53436.5i | 1.25923i | ||||||||
\(207\) | −40157.2 | −0.937179 | ||||||||
\(208\) | 6523.56i | 0.150785i | ||||||||
\(209\) | 19546.4i | 0.447482i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 21929.0 | 0.492554 | 0.246277 | − | 0.969200i | \(-0.420793\pi\) | ||||
0.246277 | + | 0.969200i | \(0.420793\pi\) | |||||||
\(212\) | −41347.5 | −0.919978 | ||||||||
\(213\) | − 20207.2i | − 0.445396i | ||||||||
\(214\) | 23983.3 | 0.523699 | ||||||||
\(215\) | 32183.6i | 0.696238i | ||||||||
\(216\) | − 33973.8i | − 0.728176i | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −33030.3 | −0.695023 | ||||||||
\(219\) | −63910.1 | −1.33254 | ||||||||
\(220\) | − 31114.6i | − 0.642863i | ||||||||
\(221\) | −55336.8 | −1.13300 | ||||||||
\(222\) | − 40669.4i | − 0.825204i | ||||||||
\(223\) | 64358.0i | 1.29418i | 0.762416 | + | 0.647088i | \(0.224013\pi\) | ||||
−0.762416 | + | 0.647088i | \(0.775987\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 26316.2 | 0.519827 | ||||||||
\(226\) | −55674.1 | −1.09002 | ||||||||
\(227\) | − 43774.8i | − 0.849517i | −0.905307 | − | 0.424759i | \(-0.860359\pi\) | ||||
0.905307 | − | 0.424759i | \(-0.139641\pi\) | |||||||
\(228\) | −17909.3 | −0.344516 | ||||||||
\(229\) | − 28506.4i | − 0.543590i | −0.962355 | − | 0.271795i | \(-0.912383\pi\) | ||||
0.962355 | − | 0.271795i | \(-0.0876173\pi\) | |||||||
\(230\) | − 18088.2i | − 0.341931i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8668.85 | 0.161059 | ||||||||
\(233\) | −2194.89 | −0.0404298 | −0.0202149 | − | 0.999796i | \(-0.506435\pi\) | ||||
−0.0202149 | + | 0.999796i | \(0.506435\pi\) | |||||||
\(234\) | 50414.1i | 0.920705i | ||||||||
\(235\) | 36049.0 | 0.652767 | ||||||||
\(236\) | 33241.9i | 0.596846i | ||||||||
\(237\) | 169783.i | 3.02273i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 80942.6 | 1.41704 | 0.708519 | − | 0.705692i | \(-0.249364\pi\) | ||||
0.708519 | + | 0.705692i | \(0.249364\pi\) | |||||||
\(240\) | 28508.5 | 0.494940 | ||||||||
\(241\) | 43016.6i | 0.740631i | 0.928906 | + | 0.370316i | \(0.120751\pi\) | ||||
−0.928906 | + | 0.370316i | \(0.879249\pi\) | |||||||
\(242\) | −13760.4 | −0.234963 | ||||||||
\(243\) | − 35984.7i | − 0.609405i | ||||||||
\(244\) | 14720.7i | 0.247257i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −29763.6 | −0.491830 | ||||||||
\(247\) | 14265.5 | 0.233827 | ||||||||
\(248\) | − 8994.21i | − 0.146238i | ||||||||
\(249\) | 91980.7 | 1.48354 | ||||||||
\(250\) | − 37374.5i | − 0.597992i | ||||||||
\(251\) | − 31568.5i | − 0.501080i | −0.968106 | − | 0.250540i | \(-0.919392\pi\) | ||||
0.968106 | − | 0.250540i | \(-0.0806082\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −32073.4 | −0.501076 | ||||||||
\(254\) | 79098.3 | 1.22603 | ||||||||
\(255\) | 241827.i | 3.71898i | ||||||||
\(256\) | 4096.00 | 0.0625000 | ||||||||
\(257\) | 68105.9i | 1.03114i | 0.856847 | + | 0.515571i | \(0.172420\pi\) | ||||
−0.856847 | + | 0.515571i | \(0.827580\pi\) | |||||||
\(258\) | 52287.3i | 0.785519i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −22708.3 | −0.335921 | ||||||||
\(261\) | 66993.0 | 0.983441 | ||||||||
\(262\) | − 3308.50i | − 0.0481980i | ||||||||
\(263\) | −8347.56 | −0.120684 | −0.0603418 | − | 0.998178i | \(-0.519219\pi\) | ||||
−0.0603418 | + | 0.998178i | \(0.519219\pi\) | |||||||
\(264\) | − 50550.4i | − 0.725299i | ||||||||
\(265\) | − 143929.i | − 2.04954i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 66975.1 | 0.939488 | ||||||||
\(268\) | −50524.6 | −0.703450 | ||||||||
\(269\) | − 91921.0i | − 1.27031i | −0.772384 | − | 0.635156i | \(-0.780936\pi\) | ||||
0.772384 | − | 0.635156i | \(-0.219064\pi\) | |||||||
\(270\) | 118262. | 1.62224 | ||||||||
\(271\) | 5134.36i | 0.0699114i | 0.999389 | + | 0.0349557i | \(0.0111290\pi\) | ||||
−0.999389 | + | 0.0349557i | \(0.988871\pi\) | |||||||
\(272\) | 34744.8i | 0.469625i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 59070.5 | 0.786810 | ||||||||
\(275\) | 21018.7 | 0.277933 | ||||||||
\(276\) | − 29387.0i | − 0.385778i | ||||||||
\(277\) | −66254.2 | −0.863483 | −0.431741 | − | 0.901997i | \(-0.642101\pi\) | ||||
−0.431741 | + | 0.901997i | \(0.642101\pi\) | |||||||
\(278\) | 9899.12i | 0.128088i | ||||||||
\(279\) | − 69507.4i | − 0.892941i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 38156.4 | 0.483230 | 0.241615 | − | 0.970372i | \(-0.422323\pi\) | ||||
0.241615 | + | 0.970372i | \(0.422323\pi\) | |||||||
\(282\) | 58567.2 | 0.736473 | ||||||||
\(283\) | 110233.i | 1.37638i | 0.725528 | + | 0.688192i | \(0.241595\pi\) | ||||
−0.725528 | + | 0.688192i | \(0.758405\pi\) | |||||||
\(284\) | 10106.3 | 0.125301 | ||||||||
\(285\) | − 62341.6i | − 0.767518i | ||||||||
\(286\) | 40265.6i | 0.492268i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 31653.9 | 0.381630 | ||||||||
\(289\) | −211205. | −2.52877 | ||||||||
\(290\) | 30175.9i | 0.358810i | ||||||||
\(291\) | −61012.4 | −0.720497 | ||||||||
\(292\) | − 31963.5i | − 0.374877i | ||||||||
\(293\) | − 79011.7i | − 0.920357i | −0.887826 | − | 0.460179i | \(-0.847785\pi\) | ||||
0.887826 | − | 0.460179i | \(-0.152215\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −115714. | −1.32966 | ||||||||
\(296\) | 20340.0 | 0.232150 | ||||||||
\(297\) | − 209698.i | − 2.37728i | ||||||||
\(298\) | −83534.2 | −0.940659 | ||||||||
\(299\) | 23408.0i | 0.261832i | ||||||||
\(300\) | 19258.2i | 0.213980i | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −72919.1 | −0.799517 | ||||||||
\(303\) | 78785.9 | 0.858150 | ||||||||
\(304\) | − 8957.01i | − 0.0969206i | ||||||||
\(305\) | −51242.2 | −0.550843 | ||||||||
\(306\) | 268508.i | 2.86757i | ||||||||
\(307\) | 2801.57i | 0.0297252i | 0.999890 | + | 0.0148626i | \(0.00473109\pi\) | ||||
−0.999890 | + | 0.0148626i | \(0.995269\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −302203. | −3.16506 | ||||||||
\(310\) | 31308.5 | 0.325791 | ||||||||
\(311\) | − 20659.3i | − 0.213597i | −0.994281 | − | 0.106799i | \(-0.965940\pi\) | ||||
0.994281 | − | 0.106799i | \(-0.0340600\pi\) | |||||||
\(312\) | −36893.1 | −0.378997 | ||||||||
\(313\) | 37376.1i | 0.381509i | 0.981638 | + | 0.190755i | \(0.0610935\pi\) | ||||
−0.981638 | + | 0.190755i | \(0.938907\pi\) | |||||||
\(314\) | − 72490.8i | − 0.735231i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −84914.1 | −0.850366 | ||||||||
\(317\) | −106666. | −1.06147 | −0.530735 | − | 0.847538i | \(-0.678084\pi\) | ||||
−0.530735 | + | 0.847538i | \(0.678084\pi\) | |||||||
\(318\) | − 233835.i | − 2.31236i | ||||||||
\(319\) | 53507.1 | 0.525811 | ||||||||
\(320\) | 14258.0i | 0.139239i | ||||||||
\(321\) | 135634.i | 1.31632i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 75978.8 | 0.728262 | ||||||||
\(324\) | 78821.6 | 0.750854 | ||||||||
\(325\) | − 15340.0i | − 0.145231i | ||||||||
\(326\) | 17487.5 | 0.164548 | ||||||||
\(327\) | − 186798.i | − 1.74694i | ||||||||
\(328\) | − 14885.7i | − 0.138364i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 175964. | 1.61583 | ||||||||
\(331\) | 108363. | 0.989063 | 0.494532 | − | 0.869160i | \(-0.335340\pi\) | ||||
0.494532 | + | 0.869160i | \(0.335340\pi\) | |||||||
\(332\) | 46002.5i | 0.417355i | ||||||||
\(333\) | 157188. | 1.41753 | ||||||||
\(334\) | − 111075.i | − 0.995686i | ||||||||
\(335\) | − 175874.i | − 1.56716i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 186946. | 1.64610 | 0.823050 | − | 0.567968i | \(-0.192270\pi\) | ||||
0.823050 | + | 0.567968i | \(0.192270\pi\) | |||||||
\(338\) | −51395.8 | −0.449877 | ||||||||
\(339\) | − 314857.i | − 2.73977i | ||||||||
\(340\) | −120945. | −1.04624 | ||||||||
\(341\) | − 55515.3i | − 0.477424i | ||||||||
\(342\) | − 69219.9i | − 0.591805i | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −26150.5 | −0.220985 | ||||||||
\(345\) | 102295. | 0.859443 | ||||||||
\(346\) | 93071.9i | 0.777439i | ||||||||
\(347\) | −63227.3 | −0.525105 | −0.262552 | − | 0.964918i | \(-0.584564\pi\) | ||||
−0.262552 | + | 0.964918i | \(0.584564\pi\) | |||||||
\(348\) | 49025.5i | 0.404821i | ||||||||
\(349\) | − 93605.0i | − 0.768508i | −0.923227 | − | 0.384254i | \(-0.874459\pi\) | ||||
0.923227 | − | 0.384254i | \(-0.125541\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −153043. | −1.24222 | ||||||||
\(352\) | 25281.9 | 0.204044 | ||||||||
\(353\) | 143251.i | 1.14960i | 0.818294 | + | 0.574800i | \(0.194920\pi\) | ||||
−0.818294 | + | 0.574800i | \(0.805080\pi\) | |||||||
\(354\) | −187995. | −1.50017 | ||||||||
\(355\) | 35179.5i | 0.279147i | ||||||||
\(356\) | 33496.4i | 0.264301i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 13485.6 | 0.105222 | ||||||||
\(359\) | 102340. | 0.794065 | 0.397032 | − | 0.917805i | \(-0.370040\pi\) | ||||
0.397032 | + | 0.917805i | \(0.370040\pi\) | |||||||
\(360\) | 110186.i | 0.850202i | ||||||||
\(361\) | 110734. | 0.849702 | ||||||||
\(362\) | 99547.7i | 0.759651i | ||||||||
\(363\) | − 77820.0i | − 0.590579i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 111264. | 0.835156 | ||||||||
\(366\) | −83250.8 | −0.621479 | ||||||||
\(367\) | 15366.4i | 0.114088i | 0.998372 | + | 0.0570442i | \(0.0181676\pi\) | ||||
−0.998372 | + | 0.0570442i | \(0.981832\pi\) | |||||||
\(368\) | 14697.4 | 0.108529 | ||||||||
\(369\) | − 115037.i | − 0.844861i | ||||||||
\(370\) | 70803.0i | 0.517187i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 50865.5 | 0.367568 | ||||||||
\(373\) | 97490.8 | 0.700722 | 0.350361 | − | 0.936615i | \(-0.386059\pi\) | ||||
0.350361 | + | 0.936615i | \(0.386059\pi\) | |||||||
\(374\) | 214456.i | 1.53319i | ||||||||
\(375\) | 211366. | 1.50305 | ||||||||
\(376\) | 29291.3i | 0.207188i | ||||||||
\(377\) | − 39050.9i | − 0.274757i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −66090.7 | −0.460110 | −0.230055 | − | 0.973178i | \(-0.573891\pi\) | ||||
−0.230055 | + | 0.973178i | \(0.573891\pi\) | |||||||
\(380\) | 31179.0 | 0.215921 | ||||||||
\(381\) | 447329.i | 3.08161i | ||||||||
\(382\) | −65944.9 | −0.451913 | ||||||||
\(383\) | − 208901.i | − 1.42411i | −0.702126 | − | 0.712053i | \(-0.747766\pi\) | ||||
0.702126 | − | 0.712053i | \(-0.252234\pi\) | |||||||
\(384\) | 23164.4i | 0.157093i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −167397. | −1.12350 | ||||||||
\(387\) | −202092. | −1.34936 | ||||||||
\(388\) | − 30514.2i | − 0.202693i | ||||||||
\(389\) | −143999. | −0.951614 | −0.475807 | − | 0.879550i | \(-0.657844\pi\) | ||||
−0.475807 | + | 0.879550i | \(0.657844\pi\) | |||||||
\(390\) | − 128423.i | − 0.844336i | ||||||||
\(391\) | 124672.i | 0.815485i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 18710.8 | 0.121145 | ||||||||
\(394\) | 172257. | 1.10965 | ||||||||
\(395\) | − 295583.i | − 1.89446i | ||||||||
\(396\) | 195379. | 1.24591 | ||||||||
\(397\) | 284577.i | 1.80559i | 0.430070 | + | 0.902796i | \(0.358489\pi\) | ||||
−0.430070 | + | 0.902796i | \(0.641511\pi\) | |||||||
\(398\) | 113467.i | 0.716316i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −9631.65 | −0.0601978 | ||||||||
\(401\) | −107846. | −0.670680 | −0.335340 | − | 0.942097i | \(-0.608851\pi\) | ||||
−0.335340 | + | 0.942097i | \(0.608851\pi\) | |||||||
\(402\) | − 285735.i | − 1.76812i | ||||||||
\(403\) | −40516.6 | −0.249472 | ||||||||
\(404\) | 39403.3i | 0.241418i | ||||||||
\(405\) | 274375.i | 1.67276i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 125546. | 0.757901 | ||||||||
\(408\) | −196494. | −1.18040 | ||||||||
\(409\) | 84932.2i | 0.507722i | 0.967241 | + | 0.253861i | \(0.0817005\pi\) | ||||
−0.967241 | + | 0.253861i | \(0.918299\pi\) | |||||||
\(410\) | 51816.6 | 0.308249 | ||||||||
\(411\) | 334065.i | 1.97764i | ||||||||
\(412\) | − 151141.i | − 0.890407i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 113582. | 0.662686 | ||||||||
\(415\) | −160133. | −0.929789 | ||||||||
\(416\) | − 18451.4i | − 0.106621i | ||||||||
\(417\) | −55983.1 | −0.321947 | ||||||||
\(418\) | − 55285.7i | − 0.316417i | ||||||||
\(419\) | 331905.i | 1.89054i | 0.326292 | + | 0.945269i | \(0.394201\pi\) | ||||
−0.326292 | + | 0.945269i | \(0.605799\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 101490. | 0.572609 | 0.286304 | − | 0.958139i | \(-0.407573\pi\) | ||||
0.286304 | + | 0.958139i | \(0.407573\pi\) | |||||||
\(422\) | −62024.5 | −0.348288 | ||||||||
\(423\) | 226364.i | 1.26510i | ||||||||
\(424\) | 116948. | 0.650522 | ||||||||
\(425\) | − 81701.5i | − 0.452327i | ||||||||
\(426\) | 57154.5i | 0.314943i | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −67835.1 | −0.370311 | ||||||||
\(429\) | −227716. | −1.23731 | ||||||||
\(430\) | − 91029.0i | − 0.492315i | ||||||||
\(431\) | 229798. | 1.23706 | 0.618530 | − | 0.785761i | \(-0.287728\pi\) | ||||
0.618530 | + | 0.785761i | \(0.287728\pi\) | |||||||
\(432\) | 96092.4i | 0.514899i | ||||||||
\(433\) | 114264.i | 0.609442i | 0.952442 | + | 0.304721i | \(0.0985632\pi\) | ||||
−0.952442 | + | 0.304721i | \(0.901437\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −170656. | −0.901868 | ||||||||
\(436\) | 93423.7 | 0.491455 | ||||||||
\(437\) | − 32139.8i | − 0.168299i | ||||||||
\(438\) | 180765. | 0.942250 | ||||||||
\(439\) | 352339.i | 1.82823i | 0.405453 | + | 0.914116i | \(0.367114\pi\) | ||||
−0.405453 | + | 0.914116i | \(0.632886\pi\) | |||||||
\(440\) | 88005.3i | 0.454573i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 156516. | 0.801151 | ||||||||
\(443\) | −196316. | −1.00034 | −0.500172 | − | 0.865926i | \(-0.666730\pi\) | ||||
−0.500172 | + | 0.865926i | \(0.666730\pi\) | |||||||
\(444\) | 115030.i | 0.583508i | ||||||||
\(445\) | −116600. | −0.588813 | ||||||||
\(446\) | − 182032.i | − 0.915120i | ||||||||
\(447\) | − 472416.i | − 2.36434i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 77520.3 | 0.384523 | 0.192262 | − | 0.981344i | \(-0.438418\pi\) | ||||
0.192262 | + | 0.981344i | \(0.438418\pi\) | |||||||
\(450\) | −74433.5 | −0.367573 | ||||||||
\(451\) | − 91879.6i | − 0.451717i | ||||||||
\(452\) | 157470. | 0.770763 | ||||||||
\(453\) | − 412384.i | − 2.00958i | ||||||||
\(454\) | 123814.i | 0.600699i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 50655.2 | 0.243609 | ||||||||
\(457\) | 189872. | 0.909137 | 0.454568 | − | 0.890712i | \(-0.349794\pi\) | ||||
0.454568 | + | 0.890712i | \(0.349794\pi\) | |||||||
\(458\) | 80628.3i | 0.384376i | ||||||||
\(459\) | −815114. | −3.86895 | ||||||||
\(460\) | 51161.1i | 0.241782i | ||||||||
\(461\) | 52599.9i | 0.247505i | 0.992313 | + | 0.123752i | \(0.0394928\pi\) | ||||
−0.992313 | + | 0.123752i | \(0.960507\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −244268. | −1.13947 | −0.569736 | − | 0.821828i | \(-0.692955\pi\) | ||||
−0.569736 | + | 0.821828i | \(0.692955\pi\) | |||||||
\(464\) | −24519.2 | −0.113886 | ||||||||
\(465\) | 177061.i | 0.818874i | ||||||||
\(466\) | 6208.09 | 0.0285882 | ||||||||
\(467\) | − 297615.i | − 1.36465i | −0.731050 | − | 0.682324i | \(-0.760969\pi\) | ||||
0.731050 | − | 0.682324i | \(-0.239031\pi\) | |||||||
\(468\) | − 142593.i | − 0.651037i | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −101962. | −0.461576 | ||||||||
\(471\) | 409962. | 1.84800 | ||||||||
\(472\) | − 94022.3i | − 0.422034i | ||||||||
\(473\) | −161410. | −0.721452 | ||||||||
\(474\) | − 480220.i | − 2.13739i | ||||||||
\(475\) | 21062.2i | 0.0933505i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 903778. | 3.97215 | ||||||||
\(478\) | −228940. | −1.00200 | ||||||||
\(479\) | − 46870.8i | − 0.204283i | −0.994770 | − | 0.102141i | \(-0.967431\pi\) | ||||
0.994770 | − | 0.102141i | \(-0.0325694\pi\) | |||||||
\(480\) | −80634.3 | −0.349975 | ||||||||
\(481\) | − 91626.6i | − 0.396033i | ||||||||
\(482\) | − 121669.i | − 0.523706i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 38920.3 | 0.166144 | ||||||||
\(485\) | 106219. | 0.451563 | ||||||||
\(486\) | 101780.i | 0.430914i | ||||||||
\(487\) | 107184. | 0.451930 | 0.225965 | − | 0.974135i | \(-0.427446\pi\) | ||||
0.225965 | + | 0.974135i | \(0.427446\pi\) | |||||||
\(488\) | − 41636.4i | − 0.174837i | ||||||||
\(489\) | 98898.4i | 0.413592i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −116367. | −0.482687 | −0.241344 | − | 0.970440i | \(-0.577588\pi\) | ||||
−0.241344 | + | 0.970440i | \(0.577588\pi\) | |||||||
\(492\) | 84184.1 | 0.347776 | ||||||||
\(493\) | − 207987.i | − 0.855740i | ||||||||
\(494\) | −40349.0 | −0.165340 | ||||||||
\(495\) | 680106.i | 2.77566i | ||||||||
\(496\) | 25439.5i | 0.103406i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −260161. | −1.04902 | ||||||||
\(499\) | 442908. | 1.77874 | 0.889369 | − | 0.457190i | \(-0.151144\pi\) | ||||
0.889369 | + | 0.457190i | \(0.151144\pi\) | |||||||
\(500\) | 105711.i | 0.422844i | ||||||||
\(501\) | 628168. | 2.50265 | ||||||||
\(502\) | 89289.3i | 0.354317i | ||||||||
\(503\) | 68955.1i | 0.272540i | 0.990672 | + | 0.136270i | \(0.0435115\pi\) | ||||
−0.990672 | + | 0.136270i | \(0.956489\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −137161. | −0.537835 | ||||||||
\(506\) | 90717.2 | 0.354314 | ||||||||
\(507\) | − 290662.i | − 1.13076i | ||||||||
\(508\) | −223724. | −0.866931 | ||||||||
\(509\) | 92773.5i | 0.358087i | 0.983841 | + | 0.179044i | \(0.0573003\pi\) | ||||
−0.983841 | + | 0.179044i | \(0.942700\pi\) | |||||||
\(510\) | − 683989.i | − 2.62972i | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −11585.2 | −0.0441942 | ||||||||
\(513\) | 210132. | 0.798468 | ||||||||
\(514\) | − 192632.i | − 0.729127i | ||||||||
\(515\) | 526117. | 1.98366 | ||||||||
\(516\) | − 147891.i | − 0.555446i | ||||||||
\(517\) | 180796.i | 0.676406i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −526355. | −1.95409 | ||||||||
\(520\) | 64228.7 | 0.237532 | ||||||||
\(521\) | 142912.i | 0.526495i | 0.964728 | + | 0.263248i | \(0.0847936\pi\) | ||||
−0.964728 | + | 0.263248i | \(0.915206\pi\) | |||||||
\(522\) | −189485. | −0.695398 | ||||||||
\(523\) | − 22203.5i | − 0.0811742i | −0.999176 | − | 0.0405871i | \(-0.987077\pi\) | ||||
0.999176 | − | 0.0405871i | \(-0.0129228\pi\) | |||||||
\(524\) | 9357.85i | 0.0340811i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 23610.5 | 0.0853361 | ||||||||
\(527\) | −215793. | −0.776992 | ||||||||
\(528\) | 142978.i | 0.512864i | ||||||||
\(529\) | −227103. | −0.811544 | ||||||||
\(530\) | 407093.i | 1.44924i | ||||||||
\(531\) | − 726606.i | − 2.57697i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −67056.3 | −0.236040 | ||||||||
\(534\) | −189434. | −0.664318 | ||||||||
\(535\) | − 236132.i | − 0.824986i | ||||||||
\(536\) | 142905. | 0.497414 | ||||||||
\(537\) | 76266.0i | 0.264474i | ||||||||
\(538\) | 259992.i | 0.898246i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −334494. | −1.14710 | ||||||||
\(541\) | 211209. | 0.721636 | 0.360818 | − | 0.932636i | \(-0.382498\pi\) | ||||
0.360818 | + | 0.932636i | \(0.382498\pi\) | |||||||
\(542\) | − 14522.2i | − 0.0494348i | ||||||||
\(543\) | −562978. | −1.90938 | ||||||||
\(544\) | − 98273.0i | − 0.332075i | ||||||||
\(545\) | 325204.i | 1.09487i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 254227. | 0.849664 | 0.424832 | − | 0.905272i | \(-0.360333\pi\) | ||||
0.424832 | + | 0.905272i | \(0.360333\pi\) | |||||||
\(548\) | −167077. | −0.556359 | ||||||||
\(549\) | − 321767.i | − 1.06757i | ||||||||
\(550\) | −59449.8 | −0.196528 | ||||||||
\(551\) | 53617.9i | 0.176606i | ||||||||
\(552\) | 83119.1i | 0.272786i | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 187395. | 0.610575 | ||||||||
\(555\) | −400416. | −1.29995 | ||||||||
\(556\) | − 27998.9i | − 0.0905716i | ||||||||
\(557\) | 46139.2 | 0.148717 | 0.0743584 | − | 0.997232i | \(-0.476309\pi\) | ||||
0.0743584 | + | 0.997232i | \(0.476309\pi\) | |||||||
\(558\) | 196597.i | 0.631405i | ||||||||
\(559\) | 117801.i | 0.376987i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.21283e6 | −3.85366 | ||||||||
\(562\) | −107922. | −0.341695 | ||||||||
\(563\) | − 349629.i | − 1.10304i | −0.834162 | − | 0.551519i | \(-0.814048\pi\) | ||||
0.834162 | − | 0.551519i | \(-0.185952\pi\) | |||||||
\(564\) | −165653. | −0.520765 | ||||||||
\(565\) | 548147.i | 1.71712i | ||||||||
\(566\) | − 311787.i | − 0.973251i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −28584.8 | −0.0886010 | ||||||||
\(569\) | −176196. | −0.544217 | −0.272109 | − | 0.962267i | \(-0.587721\pi\) | ||||
−0.272109 | + | 0.962267i | \(0.587721\pi\) | |||||||
\(570\) | 176329.i | 0.542717i | ||||||||
\(571\) | −176527. | −0.541426 | −0.270713 | − | 0.962660i | \(-0.587259\pi\) | ||||
−0.270713 | + | 0.962660i | \(0.587259\pi\) | |||||||
\(572\) | − 113888.i | − 0.348086i | ||||||||
\(573\) | − 372943.i | − 1.13588i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −34560.6 | −0.104531 | ||||||||
\(576\) | −89530.9 | −0.269853 | ||||||||
\(577\) | 226863.i | 0.681416i | 0.940169 | + | 0.340708i | \(0.110667\pi\) | ||||
−0.940169 | + | 0.340708i | \(0.889333\pi\) | |||||||
\(578\) | 597378. | 1.78811 | ||||||||
\(579\) | − 946690.i | − 2.82391i | ||||||||
\(580\) | − 85350.5i | − 0.253717i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 172569. | 0.509468 | ||||||||
\(583\) | 721844. | 2.12376 | ||||||||
\(584\) | 90406.4i | 0.265078i | ||||||||
\(585\) | 496360. | 1.45039 | ||||||||
\(586\) | 223479.i | 0.650791i | ||||||||
\(587\) | − 349659.i | − 1.01477i | −0.861719 | − | 0.507386i | \(-0.830612\pi\) | ||||
0.861719 | − | 0.507386i | \(-0.169388\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 55630.3 | 0.160354 | ||||||||
\(590\) | 327288. | 0.940213 | ||||||||
\(591\) | 974178.i | 2.78910i | ||||||||
\(592\) | −57530.3 | −0.164155 | ||||||||
\(593\) | − 137755.i | − 0.391739i | −0.980630 | − | 0.195870i | \(-0.937247\pi\) | ||||
0.980630 | − | 0.195870i | \(-0.0627529\pi\) | |||||||
\(594\) | 593115.i | 1.68099i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 236271. | 0.665146 | ||||||||
\(597\) | −641699. | −1.80046 | ||||||||
\(598\) | − 66207.9i | − 0.185143i | ||||||||
\(599\) | 80877.2 | 0.225410 | 0.112705 | − | 0.993629i | \(-0.464049\pi\) | ||||
0.112705 | + | 0.993629i | \(0.464049\pi\) | |||||||
\(600\) | − 54470.5i | − 0.151307i | ||||||||
\(601\) | 228798.i | 0.633438i | 0.948519 | + | 0.316719i | \(0.102581\pi\) | ||||
−0.948519 | + | 0.316719i | \(0.897419\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.10437e6 | 3.03725 | ||||||||
\(604\) | 206246. | 0.565344 | ||||||||
\(605\) | 135480.i | 0.370139i | ||||||||
\(606\) | −222840. | −0.606803 | ||||||||
\(607\) | − 265951.i | − 0.721812i | −0.932602 | − | 0.360906i | \(-0.882468\pi\) | ||||
0.932602 | − | 0.360906i | \(-0.117532\pi\) | |||||||
\(608\) | 25334.3i | 0.0685332i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 144935. | 0.389505 | ||||||||
\(611\) | 131950. | 0.353449 | ||||||||
\(612\) | − 759455.i | − 2.02768i | ||||||||
\(613\) | −306522. | −0.815718 | −0.407859 | − | 0.913045i | \(-0.633725\pi\) | ||||
−0.407859 | + | 0.913045i | \(0.633725\pi\) | |||||||
\(614\) | − 7924.04i | − 0.0210189i | ||||||||
\(615\) | 293042.i | 0.774782i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 491906. | 1.29215 | 0.646074 | − | 0.763275i | \(-0.276410\pi\) | ||||
0.646074 | + | 0.763275i | \(0.276410\pi\) | |||||||
\(618\) | 854758. | 2.23803 | ||||||||
\(619\) | 115230.i | 0.300735i | 0.988630 | + | 0.150368i | \(0.0480457\pi\) | ||||
−0.988630 | + | 0.150368i | \(0.951954\pi\) | |||||||
\(620\) | −88553.9 | −0.230369 | ||||||||
\(621\) | 344802.i | 0.894100i | ||||||||
\(622\) | 58433.5i | 0.151036i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 104349. | 0.267991 | ||||||||
\(625\) | −462035. | −1.18281 | ||||||||
\(626\) | − 105716.i | − 0.269768i | ||||||||
\(627\) | 312661. | 0.795313 | ||||||||
\(628\) | 205035.i | 0.519887i | ||||||||
\(629\) | − 488007.i | − 1.23346i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 72815.9 | 0.182880 | 0.0914402 | − | 0.995811i | \(-0.470853\pi\) | ||||
0.0914402 | + | 0.995811i | \(0.470853\pi\) | |||||||
\(632\) | 240173. | 0.601299 | ||||||||
\(633\) | − 350771.i | − 0.875420i | ||||||||
\(634\) | 301697. | 0.750572 | ||||||||
\(635\) | − 778774.i | − 1.93136i | ||||||||
\(636\) | 661385.i | 1.63508i | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −151341. | −0.371805 | ||||||||
\(639\) | −220904. | −0.541005 | ||||||||
\(640\) | − 40327.8i | − 0.0984565i | ||||||||
\(641\) | −757794. | −1.84431 | −0.922157 | − | 0.386815i | \(-0.873575\pi\) | ||||
−0.922157 | + | 0.386815i | \(0.873575\pi\) | |||||||
\(642\) | − 383632.i | − 0.930776i | ||||||||
\(643\) | 353082.i | 0.853992i | 0.904254 | + | 0.426996i | \(0.140428\pi\) | ||||
−0.904254 | + | 0.426996i | \(0.859572\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 514802. | 1.23743 | ||||||||
\(646\) | −214901. | −0.514959 | ||||||||
\(647\) | 214561.i | 0.512557i | 0.966603 | + | 0.256279i | \(0.0824965\pi\) | ||||
−0.966603 | + | 0.256279i | \(0.917504\pi\) | |||||||
\(648\) | −222941. | −0.530934 | ||||||||
\(649\) | − 580337.i | − 1.37782i | ||||||||
\(650\) | 43388.1i | 0.102694i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −49462.3 | −0.116353 | ||||||||
\(653\) | −497591. | −1.16693 | −0.583467 | − | 0.812137i | \(-0.698304\pi\) | ||||
−0.583467 | + | 0.812137i | \(0.698304\pi\) | |||||||
\(654\) | 528345.i | 1.23527i | ||||||||
\(655\) | −32574.3 | −0.0759264 | ||||||||
\(656\) | 42103.2i | 0.0978379i | ||||||||
\(657\) | 698662.i | 1.61859i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −197464. | −0.454692 | −0.227346 | − | 0.973814i | \(-0.573005\pi\) | ||||
−0.227346 | + | 0.973814i | \(0.573005\pi\) | |||||||
\(660\) | −497702. | −1.14257 | ||||||||
\(661\) | 668423.i | 1.52985i | 0.644121 | + | 0.764924i | \(0.277223\pi\) | ||||
−0.644121 | + | 0.764924i | \(0.722777\pi\) | |||||||
\(662\) | −306496. | −0.699373 | ||||||||
\(663\) | 885155.i | 2.01369i | ||||||||
\(664\) | − 130115.i | − 0.295114i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −444595. | −1.00234 | ||||||||
\(667\) | −87980.6 | −0.197759 | ||||||||
\(668\) | 314167.i | 0.704056i | ||||||||
\(669\) | 1.02946e6 | 2.30015 | ||||||||
\(670\) | 497447.i | 1.10815i | ||||||||
\(671\) | − 256994.i | − 0.570792i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −404534. | −0.893151 | −0.446575 | − | 0.894746i | \(-0.647357\pi\) | ||||
−0.446575 | + | 0.894746i | \(0.647357\pi\) | |||||||
\(674\) | −528763. | −1.16397 | ||||||||
\(675\) | − 225959.i | − 0.495932i | ||||||||
\(676\) | 145369. | 0.318111 | ||||||||
\(677\) | 211169.i | 0.460737i | 0.973103 | + | 0.230369i | \(0.0739932\pi\) | ||||
−0.973103 | + | 0.230369i | \(0.926007\pi\) | |||||||
\(678\) | 890550.i | 1.93731i | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 342085. | 0.739803 | ||||||||
\(681\) | −700212. | −1.50985 | ||||||||
\(682\) | 157021.i | 0.337590i | ||||||||
\(683\) | −170109. | −0.364657 | −0.182329 | − | 0.983238i | \(-0.558363\pi\) | ||||
−0.182329 | + | 0.983238i | \(0.558363\pi\) | |||||||
\(684\) | 195784.i | 0.418470i | ||||||||
\(685\) | − 581588.i | − 1.23946i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −455983. | −0.966128 | ||||||||
\(688\) | 73964.9 | 0.156260 | ||||||||
\(689\) | − 526822.i | − 1.10975i | ||||||||
\(690\) | −289334. | −0.607718 | ||||||||
\(691\) | 168630.i | 0.353167i | 0.984286 | + | 0.176583i | \(0.0565045\pi\) | ||||
−0.984286 | + | 0.176583i | \(0.943496\pi\) | |||||||
\(692\) | − 263247.i | − 0.549732i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 178834. | 0.371305 | ||||||||
\(695\) | 97463.3 | 0.201777 | ||||||||
\(696\) | − 138665.i | − 0.286252i | ||||||||
\(697\) | −357145. | −0.735154 | ||||||||
\(698\) | 264755.i | 0.543417i | ||||||||
\(699\) | 35109.0i | 0.0718562i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −487646. | −0.992359 | −0.496179 | − | 0.868220i | \(-0.665264\pi\) | ||||
−0.496179 | + | 0.868220i | \(0.665264\pi\) | |||||||
\(702\) | 432871. | 0.878384 | ||||||||
\(703\) | 125806.i | 0.254560i | ||||||||
\(704\) | −71508.0 | −0.144281 | ||||||||
\(705\) | − 576633.i | − 1.16017i | ||||||||
\(706\) | − 405174.i | − 0.812890i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 531730. | 1.06078 | ||||||||
\(709\) | −386929. | −0.769731 | −0.384865 | − | 0.922973i | \(-0.625752\pi\) | ||||
−0.384865 | + | 0.922973i | \(0.625752\pi\) | |||||||
\(710\) | − 99502.6i | − 0.197387i | ||||||||
\(711\) | 1.85606e6 | 3.67159 | ||||||||
\(712\) | − 94742.1i | − 0.186889i | ||||||||
\(713\) | 91282.7i | 0.179560i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 396441. | 0.775472 | ||||||||
\(716\) | −38143.1 | −0.0744029 | ||||||||
\(717\) | − 1.29474e6i | − 2.51851i | ||||||||
\(718\) | −289461. | −0.561489 | ||||||||
\(719\) | 188374.i | 0.364388i | 0.983263 | + | 0.182194i | \(0.0583199\pi\) | ||||
−0.983263 | + | 0.182194i | \(0.941680\pi\) | |||||||
\(720\) | − 311654.i | − 0.601184i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −313203. | −0.600830 | ||||||||
\(723\) | 688084. | 1.31633 | ||||||||
\(724\) | − 281563.i | − 0.537154i | ||||||||
\(725\) | 57656.4 | 0.109691 | ||||||||
\(726\) | 220108.i | 0.417602i | ||||||||
\(727\) | 901538.i | 1.70575i | 0.522115 | + | 0.852875i | \(0.325143\pi\) | ||||
−0.522115 | + | 0.852875i | \(0.674857\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 222465. | 0.418607 | ||||||||
\(730\) | −314701. | −0.590545 | ||||||||
\(731\) | 627415.i | 1.17414i | ||||||||
\(732\) | 235469. | 0.439452 | ||||||||
\(733\) | 402482.i | 0.749098i | 0.927207 | + | 0.374549i | \(0.122202\pi\) | ||||
−0.927207 | + | 0.374549i | \(0.877798\pi\) | |||||||
\(734\) | − 43462.9i | − 0.0806726i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −41570.5 | −0.0767414 | ||||||||
\(737\) | 882058. | 1.62391 | ||||||||
\(738\) | 325374.i | 0.597407i | ||||||||
\(739\) | −37301.1 | −0.0683020 | −0.0341510 | − | 0.999417i | \(-0.510873\pi\) | ||||
−0.0341510 | + | 0.999417i | \(0.510873\pi\) | |||||||
\(740\) | − 200261.i | − 0.365707i | ||||||||
\(741\) | − 228188.i | − 0.415582i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −831221. | −1.50570 | −0.752851 | − | 0.658191i | \(-0.771322\pi\) | ||||
−0.752851 | + | 0.658191i | \(0.771322\pi\) | |||||||
\(744\) | −143869. | −0.259910 | ||||||||
\(745\) | 822449.i | 1.48182i | ||||||||
\(746\) | −275746. | −0.495486 | ||||||||
\(747\) | − 1.00553e6i | − 1.80199i | ||||||||
\(748\) | − 606574.i | − 1.08413i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −597835. | −1.06282 | ||||||||
\(751\) | −251098. | −0.445209 | −0.222605 | − | 0.974909i | \(-0.571456\pi\) | ||||
−0.222605 | + | 0.974909i | \(0.571456\pi\) | |||||||
\(752\) | − 82848.4i | − 0.146504i | ||||||||
\(753\) | −504964. | −0.890574 | ||||||||
\(754\) | 110453.i | 0.194282i | ||||||||
\(755\) | 717936.i | 1.25948i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −422399. | −0.737108 | −0.368554 | − | 0.929606i | \(-0.620147\pi\) | ||||
−0.368554 | + | 0.929606i | \(0.620147\pi\) | |||||||
\(758\) | 186933. | 0.325347 | ||||||||
\(759\) | 513039.i | 0.890567i | ||||||||
\(760\) | −88187.6 | −0.152679 | ||||||||
\(761\) | 247203.i | 0.426859i | 0.976958 | + | 0.213430i | \(0.0684634\pi\) | ||||
−0.976958 | + | 0.213430i | \(0.931537\pi\) | |||||||
\(762\) | − 1.26524e6i | − 2.17903i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 186520. | 0.319551 | ||||||||
\(765\) | 2.64364e6 | 4.51730 | ||||||||
\(766\) | 590860.i | 1.00699i | ||||||||
\(767\) | −423546. | −0.719962 | ||||||||
\(768\) | − 65518.7i | − 0.111082i | ||||||||
\(769\) | − 903767.i | − 1.52828i | −0.645049 | − | 0.764141i | \(-0.723163\pi\) | ||||
0.645049 | − | 0.764141i | \(-0.276837\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.08941e6 | 1.83266 | ||||||||
\(772\) | 473470. | 0.794434 | ||||||||
\(773\) | − 244667.i | − 0.409464i | −0.978818 | − | 0.204732i | \(-0.934368\pi\) | ||||
0.978818 | − | 0.204732i | \(-0.0656323\pi\) | |||||||
\(774\) | 571602. | 0.954139 | ||||||||
\(775\) | − 59820.4i | − 0.0995968i | ||||||||
\(776\) | 86307.3i | 0.143326i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 407291. | 0.672893 | ||||||||
\(779\) | 92070.0 | 0.151720 | ||||||||
\(780\) | 363236.i | 0.597035i | ||||||||
\(781\) | −176435. | −0.289256 | ||||||||
\(782\) | − 352626.i | − 0.576635i | ||||||||
\(783\) | − 575222.i | − 0.938236i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −713719. | −1.15821 | ||||||||
\(786\) | −52922.0 | −0.0856627 | ||||||||
\(787\) | − 950431.i | − 1.53452i | −0.641339 | − | 0.767258i | \(-0.721621\pi\) | ||||
0.641339 | − | 0.767258i | \(-0.278379\pi\) | |||||||
\(788\) | −487218. | −0.784640 | ||||||||
\(789\) | 133526.i | 0.214492i | ||||||||
\(790\) | 836035.i | 1.33958i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −552615. | −0.880992 | ||||||||
\(793\) | −187561. | −0.298261 | ||||||||
\(794\) | − 804907.i | − 1.27675i | ||||||||
\(795\) | −2.30226e6 | −3.64267 | ||||||||
\(796\) | − 320934.i | − 0.506512i | ||||||||
\(797\) | − 560412.i | − 0.882248i | −0.897446 | − | 0.441124i | \(-0.854580\pi\) | ||||
0.897446 | − | 0.441124i | \(-0.145420\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 702771. | 1.10083 | ||||||||
\(800\) | 27242.4 | 0.0425663 | ||||||||
\(801\) | − 732168.i | − 1.14116i | ||||||||
\(802\) | 305035. | 0.474242 | ||||||||
\(803\) | 558019.i | 0.865401i | ||||||||
\(804\) | 808180.i | 1.25025i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 114598. | 0.176404 | ||||||||
\(807\) | −1.47035e6 | −2.25774 | ||||||||
\(808\) | − 111449.i | − 0.170708i | ||||||||
\(809\) | −51864.2 | −0.0792447 | −0.0396224 | − | 0.999215i | \(-0.512615\pi\) | ||||
−0.0396224 | + | 0.999215i | \(0.512615\pi\) | |||||||
\(810\) | − 776050.i | − 1.18282i | ||||||||
\(811\) | − 978879.i | − 1.48829i | −0.668019 | − | 0.744145i | \(-0.732857\pi\) | ||||
0.668019 | − | 0.744145i | \(-0.267143\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 82128.1 | 0.124254 | ||||||||
\(814\) | −355097. | −0.535917 | ||||||||
\(815\) | − 172176.i | − 0.259214i | ||||||||
\(816\) | 555770. | 0.834669 | ||||||||
\(817\) | − 161744.i | − 0.242317i | ||||||||
\(818\) | − 240224.i | − 0.359013i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −146560. | −0.217965 | ||||||||
\(821\) | 148798. | 0.220755 | 0.110377 | − | 0.993890i | \(-0.464794\pi\) | ||||
0.110377 | + | 0.993890i | \(0.464794\pi\) | |||||||
\(822\) | − 944879.i | − 1.39840i | ||||||||
\(823\) | 1.33907e6 | 1.97698 | 0.988490 | − | 0.151287i | \(-0.0483416\pi\) | ||||
0.988490 | + | 0.151287i | \(0.0483416\pi\) | |||||||
\(824\) | 427492.i | 0.629613i | ||||||||
\(825\) | − 336210.i | − 0.493972i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −127284. | −0.186108 | −0.0930538 | − | 0.995661i | \(-0.529663\pi\) | ||||
−0.0930538 | + | 0.995661i | \(0.529663\pi\) | |||||||
\(828\) | −321257. | −0.468589 | ||||||||
\(829\) | − 445598.i | − 0.648386i | −0.945991 | − | 0.324193i | \(-0.894907\pi\) | ||||
0.945991 | − | 0.324193i | \(-0.105093\pi\) | |||||||
\(830\) | 452924. | 0.657460 | ||||||||
\(831\) | 1.05979e6i | 1.53468i | ||||||||
\(832\) | 52188.5i | 0.0753924i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 158344. | 0.227651 | ||||||||
\(835\) | −1.09360e6 | −1.56851 | ||||||||
\(836\) | 156372.i | 0.223741i | ||||||||
\(837\) | −596812. | −0.851896 | ||||||||
\(838\) | − 938768.i | − 1.33681i | ||||||||
\(839\) | − 552232.i | − 0.784509i | −0.919857 | − | 0.392254i | \(-0.871695\pi\) | ||||
0.919857 | − | 0.392254i | \(-0.128305\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −560506. | −0.792479 | ||||||||
\(842\) | −287056. | −0.404896 | ||||||||
\(843\) | − 610341.i | − 0.858850i | ||||||||
\(844\) | 175432. | 0.246277 | ||||||||
\(845\) | 506025.i | 0.708694i | ||||||||
\(846\) | − 640254.i | − 0.894564i | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −330780. | −0.459989 | ||||||||
\(849\) | 1.76327e6 | 2.44626 | ||||||||
\(850\) | 231087.i | 0.319843i | ||||||||
\(851\) | −206432. | −0.285048 | ||||||||
\(852\) | − 161657.i | − 0.222698i | ||||||||
\(853\) | 753308.i | 1.03532i | 0.855586 | + | 0.517660i | \(0.173197\pi\) | ||||
−0.855586 | + | 0.517660i | \(0.826803\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −681515. | −0.932274 | ||||||||
\(856\) | 191867. | 0.261850 | ||||||||
\(857\) | 1.30117e6i | 1.77163i | 0.464037 | + | 0.885816i | \(0.346400\pi\) | ||||
−0.464037 | + | 0.885816i | \(0.653600\pi\) | |||||||
\(858\) | 644079. | 0.874913 | ||||||||
\(859\) | 982372.i | 1.33134i | 0.746245 | + | 0.665671i | \(0.231855\pi\) | ||||
−0.746245 | + | 0.665671i | \(0.768145\pi\) | |||||||
\(860\) | 257469.i | 0.348119i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −649966. | −0.874734 | ||||||||
\(863\) | −721435. | −0.968670 | −0.484335 | − | 0.874883i | \(-0.660938\pi\) | ||||
−0.484335 | + | 0.874883i | \(0.660938\pi\) | |||||||
\(864\) | − 271790.i | − 0.364088i | ||||||||
\(865\) | 916353. | 1.22470 | ||||||||
\(866\) | − 323186.i | − 0.430940i | ||||||||
\(867\) | 3.37839e6i | 4.49440i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.48243e6 | 1.96307 | ||||||||
\(870\) | 482688. | 0.637717 | ||||||||
\(871\) | − 643750.i | − 0.848557i | ||||||||
\(872\) | −264242. | −0.347511 | ||||||||
\(873\) | 666984.i | 0.875159i | ||||||||
\(874\) | 90905.2i | 0.119005i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −511281. | −0.666272 | ||||||||
\(877\) | −717008. | −0.932234 | −0.466117 | − | 0.884723i | \(-0.654347\pi\) | ||||
−0.466117 | + | 0.884723i | \(0.654347\pi\) | |||||||
\(878\) | − 996564.i | − 1.29276i | ||||||||
\(879\) | −1.26385e6 | −1.63576 | ||||||||
\(880\) | − 248917.i | − 0.321432i | ||||||||
\(881\) | 79128.9i | 0.101949i | 0.998700 | + | 0.0509745i | \(0.0162327\pi\) | ||||
−0.998700 | + | 0.0509745i | \(0.983767\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −286591. | −0.367571 | −0.183786 | − | 0.982966i | \(-0.558835\pi\) | ||||
−0.183786 | + | 0.982966i | \(0.558835\pi\) | |||||||
\(884\) | −442694. | −0.566499 | ||||||||
\(885\) | 1.85093e6i | 2.36322i | ||||||||
\(886\) | 555267. | 0.707350 | ||||||||
\(887\) | − 837465.i | − 1.06444i | −0.846607 | − | 0.532218i | \(-0.821359\pi\) | ||||
0.846607 | − | 0.532218i | \(-0.178641\pi\) | |||||||
\(888\) | − 325355.i | − 0.412602i | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 329794. | 0.416354 | ||||||||
\(891\) | −1.37607e6 | −1.73334 | ||||||||
\(892\) | 514864.i | 0.647088i | ||||||||
\(893\) | −181171. | −0.227188 | ||||||||
\(894\) | 1.33620e6i | 1.67184i | ||||||||
\(895\) | − 132775.i | − 0.165756i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 374430. | 0.465356 | ||||||||
\(898\) | −219261. | −0.271899 | ||||||||
\(899\) | − 152284.i | − 0.188424i | ||||||||
\(900\) | 210530. | 0.259913 | ||||||||
\(901\) | − 2.80588e6i | − 3.45636i | ||||||||
\(902\) | 259875.i | 0.319412i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −445393. | −0.545012 | ||||||||
\(905\) | 980112. | 1.19668 | ||||||||
\(906\) | 1.16640e6i | 1.42099i | ||||||||
\(907\) | −846569. | −1.02908 | −0.514538 | − | 0.857467i | \(-0.672037\pi\) | ||||
−0.514538 | + | 0.857467i | \(0.672037\pi\) | |||||||
\(908\) | − 350198.i | − 0.424759i | ||||||||
\(909\) | − 861283.i | − 1.04236i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 167017. | 0.201244 | 0.100622 | − | 0.994925i | \(-0.467917\pi\) | ||||
0.100622 | + | 0.994925i | \(0.467917\pi\) | |||||||
\(912\) | −143274. | −0.172258 | ||||||||
\(913\) | − 803112.i | − 0.963461i | ||||||||
\(914\) | −537040. | −0.642857 | ||||||||
\(915\) | 819658.i | 0.979018i | ||||||||
\(916\) | − 228051.i | − 0.271795i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 2.30549e6 | 2.73576 | ||||||||
\(919\) | 1.12203e6 | 1.32854 | 0.664268 | − | 0.747494i | \(-0.268743\pi\) | ||||
0.664268 | + | 0.747494i | \(0.268743\pi\) | |||||||
\(920\) | − 144705.i | − 0.170966i | ||||||||
\(921\) | 44813.3 | 0.0528309 | ||||||||
\(922\) | − 148775.i | − 0.175012i | ||||||||
\(923\) | 128767.i | 0.151148i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 135281. | 0.158108 | ||||||||
\(926\) | 690893. | 0.805729 | ||||||||
\(927\) | 3.30366e6i | 3.84447i | ||||||||
\(928\) | 69350.8 | 0.0805296 | ||||||||
\(929\) | 1.42663e6i | 1.65302i | 0.562921 | + | 0.826511i | \(0.309677\pi\) | ||||
−0.562921 | + | 0.826511i | \(0.690323\pi\) | |||||||
\(930\) | − 500804.i | − 0.579032i | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −17559.1 | −0.0202149 | ||||||||
\(933\) | −330462. | −0.379628 | ||||||||
\(934\) | 841781.i | 0.964952i | ||||||||
\(935\) | 2.11146e6 | 2.41524 | ||||||||
\(936\) | 403313.i | 0.460353i | ||||||||
\(937\) | − 265587.i | − 0.302502i | −0.988495 | − | 0.151251i | \(-0.951670\pi\) | ||||
0.988495 | − | 0.151251i | \(-0.0483301\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 597860. | 0.678060 | ||||||||
\(940\) | 288392. | 0.326383 | ||||||||
\(941\) | − 598591.i | − 0.676007i | −0.941145 | − | 0.338003i | \(-0.890249\pi\) | ||||
0.941145 | − | 0.338003i | \(-0.109751\pi\) | |||||||
\(942\) | −1.15955e6 | −1.30673 | ||||||||
\(943\) | 151076.i | 0.169892i | ||||||||
\(944\) | 265935.i | 0.298423i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 456536. | 0.510144 | ||||||||
\(947\) | 1.15085e6 | 1.28328 | 0.641639 | − | 0.767007i | \(-0.278255\pi\) | ||||
0.641639 | + | 0.767007i | \(0.278255\pi\) | |||||||
\(948\) | 1.35827e6i | 1.51136i | ||||||||
\(949\) | 407257. | 0.452206 | ||||||||
\(950\) | − 59572.9i | − 0.0660088i | ||||||||
\(951\) | 1.70621e6i | 1.88656i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 464604. | 0.511561 | 0.255781 | − | 0.966735i | \(-0.417668\pi\) | ||||
0.255781 | + | 0.966735i | \(0.417668\pi\) | |||||||
\(954\) | −2.55627e6 | −2.80873 | ||||||||
\(955\) | 649271.i | 0.711900i | ||||||||
\(956\) | 647541. | 0.708519 | ||||||||
\(957\) | − 855887.i | − 0.934529i | ||||||||
\(958\) | 132571.i | 0.144450i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 228068. | 0.247470 | ||||||||
\(961\) | 765521. | 0.828916 | ||||||||
\(962\) | 259159.i | 0.280038i | ||||||||
\(963\) | 1.48275e6 | 1.59888 | ||||||||
\(964\) | 344133.i | 0.370316i | ||||||||
\(965\) | 1.64813e6i | 1.76985i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 101298. | 0.108330 | 0.0541648 | − | 0.998532i | \(-0.482750\pi\) | ||||
0.0541648 | + | 0.998532i | \(0.482750\pi\) | |||||||
\(968\) | −110083. | −0.117482 | ||||||||
\(969\) | − 1.21534e6i | − 1.29435i | ||||||||
\(970\) | −300432. | −0.319303 | ||||||||
\(971\) | 326280.i | 0.346060i | 0.984917 | + | 0.173030i | \(0.0553558\pi\) | ||||
−0.984917 | + | 0.173030i | \(0.944644\pi\) | |||||||
\(972\) | − 287878.i | − 0.304702i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −303162. | −0.319563 | ||||||||
\(975\) | −245375. | −0.258120 | ||||||||
\(976\) | 117765.i | 0.123628i | ||||||||
\(977\) | 741928. | 0.777272 | 0.388636 | − | 0.921391i | \(-0.372946\pi\) | ||||
0.388636 | + | 0.921391i | \(0.372946\pi\) | |||||||
\(978\) | − 279727.i | − 0.292453i | ||||||||
\(979\) | − 584780.i | − 0.610137i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.04207e6 | −2.12193 | ||||||||
\(982\) | 329135. | 0.341311 | ||||||||
\(983\) | 584497.i | 0.604888i | 0.953167 | + | 0.302444i | \(0.0978026\pi\) | ||||
−0.953167 | + | 0.302444i | \(0.902197\pi\) | |||||||
\(984\) | −238109. | −0.245915 | ||||||||
\(985\) | − 1.69599e6i | − 1.74803i | ||||||||
\(986\) | 588276.i | 0.605100i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 114124. | 0.116913 | ||||||||
\(989\) | 265403. | 0.271340 | ||||||||
\(990\) | − 1.92363e6i | − 1.96269i | ||||||||
\(991\) | 582343. | 0.592969 | 0.296484 | − | 0.955038i | \(-0.404186\pi\) | ||||
0.296484 | + | 0.955038i | \(0.404186\pi\) | |||||||
\(992\) | − 71953.7i | − 0.0731189i | ||||||||
\(993\) | − 1.73335e6i | − 1.75787i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.11716e6 | 1.12842 | ||||||||
\(996\) | 735846. | 0.741768 | ||||||||
\(997\) | − 1.36934e6i | − 1.37759i | −0.724954 | − | 0.688797i | \(-0.758139\pi\) | ||||
0.724954 | − | 0.688797i | \(-0.241861\pi\) | |||||||
\(998\) | −1.25273e6 | −1.25776 | ||||||||
\(999\) | − 1.34967e6i | − 1.35237i |
(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 | 98.5.b.a.97.1 | ✓ | 4 | |
3.2 | odd | 2 | 882.5.c.c.685.3 | 4 | |||
4.3 | odd | 2 | 784.5.c.a.97.4 | 4 | |||
7.2 | even | 3 | 98.5.d.c.31.4 | 8 | |||
7.3 | odd | 6 | 98.5.d.c.19.4 | 8 | |||
7.4 | even | 3 | 98.5.d.c.19.3 | 8 | |||
7.5 | odd | 6 | 98.5.d.c.31.3 | 8 | |||
7.6 | odd | 2 | inner | 98.5.b.a.97.2 | yes | 4 | |
21.20 | even | 2 | 882.5.c.c.685.4 | 4 | |||
28.27 | even | 2 | 784.5.c.a.97.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
98.5.b.a.97.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
98.5.b.a.97.2 | yes | 4 | 7.6 | odd | 2 | inner | |
98.5.d.c.19.3 | 8 | 7.4 | even | 3 | |||
98.5.d.c.19.4 | 8 | 7.3 | odd | 6 | |||
98.5.d.c.31.3 | 8 | 7.5 | odd | 6 | |||
98.5.d.c.31.4 | 8 | 7.2 | even | 3 | |||
784.5.c.a.97.1 | 4 | 28.27 | even | 2 | |||
784.5.c.a.97.4 | 4 | 4.3 | odd | 2 | |||
882.5.c.c.685.3 | 4 | 3.2 | odd | 2 | |||
882.5.c.c.685.4 | 4 | 21.20 | even | 2 |