Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [550,5,Mod(351,550)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(550, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("550.351");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 550 = 2 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 550.d (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: | \(56.8534796961\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{553})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} - 2x^{3} - 271x^{2} + 272x + 19602 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 22) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 351.3 | ||
Root | \(12.2580 + 1.41421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 550.351 |
Dual form | 550.5.d.a.351.1 |
$q$-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 \(\left(\mathbb{Z}/550\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(177\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.82843i | 0.707107i | ||||||||
\(3\) | −12.2580 | −1.36200 | −0.680999 | − | 0.732285i | \(-0.738454\pi\) | ||||
−0.680999 | + | 0.732285i | \(0.738454\pi\) | |||||||
\(4\) | −8.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | − | 34.6708i | − | 0.963078i | ||||||
\(7\) | 33.9411i | 0.692676i | 0.938110 | + | 0.346338i | \(0.112575\pi\) | ||||
−0.938110 | + | 0.346338i | \(0.887425\pi\) | |||||||
\(8\) | − | 22.6274i | − | 0.353553i | ||||||
\(9\) | 69.2580 | 0.855037 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −92.0319 | + | 78.5565i | −0.760594 | + | 0.649228i | ||||
\(12\) | 98.0638 | 0.680999 | ||||||||
\(13\) | − | 326.819i | − | 1.93384i | −0.255083 | − | 0.966919i | \(-0.582103\pi\) | ||
0.255083 | − | 0.966919i | \(-0.417897\pi\) | |||||||
\(14\) | −96.0000 | −0.489796 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 64.0000 | 0.250000 | ||||||||
\(17\) | 280.285i | 0.969844i | 0.874557 | + | 0.484922i | \(0.161152\pi\) | ||||
−0.874557 | + | 0.484922i | \(0.838848\pi\) | |||||||
\(18\) | 195.891i | 0.604602i | ||||||||
\(19\) | − | 12.5926i | − | 0.0348825i | −0.999848 | − | 0.0174412i | \(-0.994448\pi\) | ||
0.999848 | − | 0.0174412i | \(-0.00555200\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 416.050i | − | 0.943423i | ||||||
\(22\) | −222.191 | − | 260.306i | −0.459073 | − | 0.537821i | ||||
\(23\) | −184.641 | −0.349037 | −0.174519 | − | 0.984654i | \(-0.555837\pi\) | ||||
−0.174519 | + | 0.984654i | \(0.555837\pi\) | |||||||
\(24\) | 277.366i | 0.481539i | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 924.383 | 1.36743 | ||||||||
\(27\) | 143.933 | 0.197440 | ||||||||
\(28\) | − | 271.529i | − | 0.346338i | ||||||
\(29\) | − | 1039.58i | − | 1.23613i | −0.786128 | − | 0.618063i | \(-0.787918\pi\) | ||
0.786128 | − | 0.618063i | \(-0.212082\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1492.51 | 1.55308 | 0.776542 | − | 0.630066i | \(-0.216972\pi\) | ||||
0.776542 | + | 0.630066i | \(0.216972\pi\) | |||||||
\(32\) | 181.019i | 0.176777i | ||||||||
\(33\) | 1128.12 | − | 962.944i | 1.03593 | − | 0.884246i | ||||
\(34\) | −792.766 | −0.685783 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −554.064 | −0.427518 | ||||||||
\(37\) | 1400.64 | 1.02311 | 0.511554 | − | 0.859251i | \(-0.329070\pi\) | ||||
0.511554 | + | 0.859251i | \(0.329070\pi\) | |||||||
\(38\) | 35.6172 | 0.0246656 | ||||||||
\(39\) | 4006.14i | 2.63388i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 2563.10i | − | 1.52475i | −0.647138 | − | 0.762373i | \(-0.724034\pi\) | ||
0.647138 | − | 0.762373i | \(-0.275966\pi\) | |||||||
\(42\) | 1176.77 | 0.667101 | ||||||||
\(43\) | − | 870.960i | − | 0.471044i | −0.971869 | − | 0.235522i | \(-0.924320\pi\) | ||
0.971869 | − | 0.235522i | \(-0.0756799\pi\) | |||||||
\(44\) | 736.255 | − | 628.452i | 0.380297 | − | 0.324614i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − | 522.243i | − | 0.246807i | ||||||
\(47\) | −3021.08 | −1.36763 | −0.683813 | − | 0.729658i | \(-0.739679\pi\) | ||||
−0.683813 | + | 0.729658i | \(0.739679\pi\) | |||||||
\(48\) | −784.510 | −0.340499 | ||||||||
\(49\) | 1249.00 | 0.520200 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 3435.73i | − | 1.32093i | ||||||
\(52\) | 2614.55i | 0.966919i | ||||||||
\(53\) | 260.724 | 0.0928173 | 0.0464087 | − | 0.998923i | \(-0.485222\pi\) | ||||
0.0464087 | + | 0.998923i | \(0.485222\pi\) | |||||||
\(54\) | 407.105i | 0.139611i | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 768.000 | 0.244898 | ||||||||
\(57\) | 154.359i | 0.0475098i | ||||||||
\(58\) | 2940.38 | 0.874073 | ||||||||
\(59\) | 293.024 | 0.0841780 | 0.0420890 | − | 0.999114i | \(-0.486599\pi\) | ||||
0.0420890 | + | 0.999114i | \(0.486599\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3593.92i | 0.965849i | 0.875662 | + | 0.482924i | \(0.160425\pi\) | ||||
−0.875662 | + | 0.482924i | \(0.839575\pi\) | |||||||
\(62\) | 4221.46i | 1.09820i | ||||||||
\(63\) | 2350.69i | 0.592263i | ||||||||
\(64\) | −512.000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2723.62 | + | 3190.82i | 0.625256 | + | 0.732511i | ||||
\(67\) | 2359.87 | 0.525701 | 0.262850 | − | 0.964837i | \(-0.415337\pi\) | ||||
0.262850 | + | 0.964837i | \(0.415337\pi\) | |||||||
\(68\) | − | 2242.28i | − | 0.484922i | ||||||
\(69\) | 2263.32 | 0.475388 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2494.04 | −0.494751 | −0.247375 | − | 0.968920i | \(-0.579568\pi\) | ||||
−0.247375 | + | 0.968920i | \(0.579568\pi\) | |||||||
\(72\) | − | 1567.13i | − | 0.302301i | ||||||
\(73\) | 4481.31i | 0.840929i | 0.907309 | + | 0.420465i | \(0.138133\pi\) | ||||
−0.907309 | + | 0.420465i | \(0.861867\pi\) | |||||||
\(74\) | 3961.59i | 0.723447i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 100.741i | 0.0174412i | ||||||||
\(77\) | −2666.30 | − | 3123.67i | −0.449704 | − | 0.526845i | ||||
\(78\) | −11331.1 | −1.86244 | ||||||||
\(79\) | 9693.98i | 1.55327i | 0.629949 | + | 0.776637i | \(0.283076\pi\) | ||||
−0.629949 | + | 0.776637i | \(0.716924\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7374.23 | −1.12395 | ||||||||
\(82\) | 7249.53 | 1.07816 | ||||||||
\(83\) | 6237.99i | 0.905500i | 0.891638 | + | 0.452750i | \(0.149557\pi\) | ||||
−0.891638 | + | 0.452750i | \(0.850443\pi\) | |||||||
\(84\) | 3328.40i | 0.471711i | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2463.45 | 0.333078 | ||||||||
\(87\) | 12743.2i | 1.68360i | ||||||||
\(88\) | 1777.53 | + | 2082.44i | 0.229537 | + | 0.268911i | ||||
\(89\) | −9516.72 | −1.20145 | −0.600727 | − | 0.799454i | \(-0.705122\pi\) | ||||
−0.600727 | + | 0.799454i | \(0.705122\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 11092.6 | 1.33952 | ||||||||
\(92\) | 1477.13 | 0.174519 | ||||||||
\(93\) | −18295.2 | −2.11530 | ||||||||
\(94\) | − | 8544.92i | − | 0.967057i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | − | 2218.93i | − | 0.240769i | ||||||
\(97\) | −6401.66 | −0.680376 | −0.340188 | − | 0.940357i | \(-0.610491\pi\) | ||||
−0.340188 | + | 0.940357i | \(0.610491\pi\) | |||||||
\(98\) | 3532.71i | 0.367837i | ||||||||
\(99\) | −6373.94 | + | 5440.67i | −0.650336 | + | 0.555113i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 15.9343i | − | 0.00156203i | −1.00000 | 0.000781015i | \(-0.999751\pi\) | |||
1.00000 | 0.000781015i | \(-0.000248605\pi\) | ||||||||
\(102\) | 9717.70 | 0.934035 | ||||||||
\(103\) | −12891.5 | −1.21514 | −0.607572 | − | 0.794265i | \(-0.707856\pi\) | ||||
−0.607572 | + | 0.794265i | \(0.707856\pi\) | |||||||
\(104\) | −7395.06 | −0.683715 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 737.438i | 0.0656318i | ||||||||
\(107\) | − | 10805.9i | − | 0.943827i | −0.881645 | − | 0.471913i | \(-0.843564\pi\) | ||
0.881645 | − | 0.471913i | \(-0.156436\pi\) | |||||||
\(108\) | −1151.47 | −0.0987198 | ||||||||
\(109\) | 8470.43i | 0.712939i | 0.934307 | + | 0.356470i | \(0.116020\pi\) | ||||
−0.934307 | + | 0.356470i | \(0.883980\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −17169.0 | −1.39347 | ||||||||
\(112\) | 2172.23i | 0.173169i | ||||||||
\(113\) | 1009.87 | 0.0790874 | 0.0395437 | − | 0.999218i | \(-0.487410\pi\) | ||||
0.0395437 | + | 0.999218i | \(0.487410\pi\) | |||||||
\(114\) | −436.594 | −0.0335945 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 8316.66i | 0.618063i | ||||||||
\(117\) | − | 22634.8i | − | 1.65350i | ||||||
\(118\) | 828.796i | 0.0595228i | ||||||||
\(119\) | −9513.19 | −0.671788 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2298.74 | − | 14459.4i | 0.157007 | − | 0.987597i | ||||
\(122\) | −10165.1 | −0.682958 | ||||||||
\(123\) | 31418.4i | 2.07670i | ||||||||
\(124\) | −11940.1 | −0.776542 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −6648.77 | −0.418794 | ||||||||
\(127\) | 7859.09i | 0.487264i | 0.969868 | + | 0.243632i | \(0.0783390\pi\) | ||||
−0.969868 | + | 0.243632i | \(0.921661\pi\) | |||||||
\(128\) | − | 1448.15i | − | 0.0883883i | ||||||
\(129\) | 10676.2i | 0.641560i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 24418.3i | 1.42290i | 0.702738 | + | 0.711448i | \(0.251960\pi\) | ||||
−0.702738 | + | 0.711448i | \(0.748040\pi\) | |||||||
\(132\) | −9025.00 | + | 7703.55i | −0.517964 | + | 0.442123i | ||||
\(133\) | 427.406 | 0.0241622 | ||||||||
\(134\) | 6674.72i | 0.371726i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6342.13 | 0.342892 | ||||||||
\(137\) | 2895.91 | 0.154292 | 0.0771462 | − | 0.997020i | \(-0.475419\pi\) | ||||
0.0771462 | + | 0.997020i | \(0.475419\pi\) | |||||||
\(138\) | 6401.64i | 0.336150i | ||||||||
\(139\) | 14602.9i | 0.755807i | 0.925845 | + | 0.377903i | \(0.123355\pi\) | ||||
−0.925845 | + | 0.377903i | \(0.876645\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 37032.4 | 1.86270 | ||||||||
\(142\) | − | 7054.21i | − | 0.349842i | ||||||
\(143\) | 25673.7 | + | 30077.7i | 1.25550 | + | 1.47087i | ||||
\(144\) | 4432.51 | 0.213759 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −12675.1 | −0.594627 | ||||||||
\(147\) | −15310.2 | −0.708511 | ||||||||
\(148\) | −11205.1 | −0.511554 | ||||||||
\(149\) | − | 9469.08i | − | 0.426516i | −0.976996 | − | 0.213258i | \(-0.931593\pi\) | ||
0.976996 | − | 0.213258i | \(-0.0684075\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 15335.9i | − | 0.672597i | −0.941755 | − | 0.336298i | \(-0.890825\pi\) | ||
0.941755 | − | 0.336298i | \(-0.109175\pi\) | |||||||
\(152\) | −284.937 | −0.0123328 | ||||||||
\(153\) | 19412.0i | 0.829253i | ||||||||
\(154\) | 8835.06 | − | 7541.43i | 0.372536 | − | 0.317989i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | − | 32049.1i | − | 1.31694i | ||||||
\(157\) | 4810.17 | 0.195147 | 0.0975733 | − | 0.995228i | \(-0.468892\pi\) | ||||
0.0975733 | + | 0.995228i | \(0.468892\pi\) | |||||||
\(158\) | −27418.7 | −1.09833 | ||||||||
\(159\) | −3195.95 | −0.126417 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 6266.92i | − | 0.241770i | ||||||
\(162\) | − | 20857.5i | − | 0.794752i | ||||||
\(163\) | 9875.98 | 0.371711 | 0.185855 | − | 0.982577i | \(-0.440494\pi\) | ||||
0.185855 | + | 0.982577i | \(0.440494\pi\) | |||||||
\(164\) | 20504.8i | 0.762373i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −17643.7 | −0.640285 | ||||||||
\(167\) | − | 13437.3i | − | 0.481812i | −0.970548 | − | 0.240906i | \(-0.922555\pi\) | ||
0.970548 | − | 0.240906i | \(-0.0774445\pi\) | |||||||
\(168\) | −9414.13 | −0.333550 | ||||||||
\(169\) | −78249.5 | −2.73973 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 872.136i | − | 0.0298258i | ||||||
\(172\) | 6967.68i | 0.235522i | ||||||||
\(173\) | − | 37664.1i | − | 1.25845i | −0.777223 | − | 0.629225i | \(-0.783373\pi\) | ||
0.777223 | − | 0.629225i | \(-0.216627\pi\) | |||||||
\(174\) | −36043.1 | −1.19049 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −5890.04 | + | 5027.62i | −0.190149 | + | 0.162307i | ||||
\(177\) | −3591.88 | −0.114650 | ||||||||
\(178\) | − | 26917.3i | − | 0.849556i | ||||||
\(179\) | 53941.3 | 1.68351 | 0.841755 | − | 0.539860i | \(-0.181523\pi\) | ||||
0.841755 | + | 0.539860i | \(0.181523\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 23379.6 | 0.713642 | 0.356821 | − | 0.934173i | \(-0.383861\pi\) | ||||
0.356821 | + | 0.934173i | \(0.383861\pi\) | |||||||
\(182\) | 31374.6i | 0.947186i | ||||||||
\(183\) | − | 44054.2i | − | 1.31548i | ||||||
\(184\) | 4177.94i | 0.123403i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | − | 51746.6i | − | 1.49574i | ||||||
\(187\) | −22018.2 | − | 25795.2i | −0.629650 | − | 0.737658i | ||||
\(188\) | 24168.7 | 0.683813 | ||||||||
\(189\) | 4885.26i | 0.136762i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 46611.4 | 1.27769 | 0.638844 | − | 0.769336i | \(-0.279413\pi\) | ||||
0.638844 | + | 0.769336i | \(0.279413\pi\) | |||||||
\(192\) | 6276.08 | 0.170250 | ||||||||
\(193\) | 57585.6i | 1.54596i | 0.634428 | + | 0.772982i | \(0.281236\pi\) | ||||
−0.634428 | + | 0.772982i | \(0.718764\pi\) | |||||||
\(194\) | − | 18106.6i | − | 0.481099i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −9992.00 | −0.260100 | ||||||||
\(197\) | 39775.2i | 1.02490i | 0.858718 | + | 0.512448i | \(0.171261\pi\) | ||||
−0.858718 | + | 0.512448i | \(0.828739\pi\) | |||||||
\(198\) | −15388.5 | − | 18028.2i | −0.392524 | − | 0.459857i | ||||
\(199\) | 18905.2 | 0.477393 | 0.238697 | − | 0.971094i | \(-0.423280\pi\) | ||||
0.238697 | + | 0.971094i | \(0.423280\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −28927.2 | −0.716003 | ||||||||
\(202\) | 45.0689 | 0.00110452 | ||||||||
\(203\) | 35284.6 | 0.856235 | ||||||||
\(204\) | 27485.8i | 0.660463i | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 36462.6i | − | 0.859237i | ||||||
\(207\) | −12787.8 | −0.298440 | ||||||||
\(208\) | − | 20916.4i | − | 0.483460i | ||||||
\(209\) | 989.228 | + | 1158.92i | 0.0226466 | + | 0.0265314i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 30974.3i | 0.695723i | 0.937546 | + | 0.347862i | \(0.113092\pi\) | ||||
−0.937546 | + | 0.347862i | \(0.886908\pi\) | |||||||
\(212\) | −2085.79 | −0.0464087 | ||||||||
\(213\) | 30571.9 | 0.673849 | ||||||||
\(214\) | 30563.6 | 0.667386 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 3256.84i | − | 0.0698054i | ||||||
\(217\) | 50657.6i | 1.07578i | ||||||||
\(218\) | −23958.0 | −0.504124 | ||||||||
\(219\) | − | 54931.8i | − | 1.14534i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 91602.4 | 1.87552 | ||||||||
\(222\) | − | 48561.1i | − | 0.985333i | ||||||
\(223\) | 19890.6 | 0.399980 | 0.199990 | − | 0.979798i | \(-0.435909\pi\) | ||||
0.199990 | + | 0.979798i | \(0.435909\pi\) | |||||||
\(224\) | −6144.00 | −0.122449 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2856.34i | 0.0559233i | ||||||||
\(227\) | 76528.9i | 1.48516i | 0.669757 | + | 0.742581i | \(0.266398\pi\) | ||||
−0.669757 | + | 0.742581i | \(0.733602\pi\) | |||||||
\(228\) | − | 1234.87i | − | 0.0237549i | ||||||
\(229\) | −56079.9 | −1.06939 | −0.534695 | − | 0.845045i | \(-0.679574\pi\) | ||||
−0.534695 | + | 0.845045i | \(0.679574\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 32683.4 | + | 38289.8i | 0.612496 | + | 0.717562i | ||||
\(232\) | −23523.1 | −0.437037 | ||||||||
\(233\) | 3353.39i | 0.0617693i | 0.999523 | + | 0.0308847i | \(0.00983246\pi\) | ||||
−0.999523 | + | 0.0308847i | \(0.990168\pi\) | |||||||
\(234\) | 64020.9 | 1.16920 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2344.19 | −0.0420890 | ||||||||
\(237\) | − | 118829.i | − | 2.11555i | ||||||
\(238\) | − | 26907.4i | − | 0.475026i | ||||||
\(239\) | − | 8629.71i | − | 0.151078i | −0.997143 | − | 0.0755388i | \(-0.975932\pi\) | ||
0.997143 | − | 0.0755388i | \(-0.0240677\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 101396.i | 1.74577i | 0.487924 | + | 0.872886i | \(0.337754\pi\) | ||||
−0.487924 | + | 0.872886i | \(0.662246\pi\) | |||||||
\(242\) | 40897.4 | + | 6501.83i | 0.698337 | + | 0.111021i | ||||
\(243\) | 78734.5 | 1.33338 | ||||||||
\(244\) | − | 28751.4i | − | 0.482924i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −88864.6 | −1.46845 | ||||||||
\(247\) | −4115.49 | −0.0674570 | ||||||||
\(248\) | − | 33771.7i | − | 0.549098i | ||||||
\(249\) | − | 76465.1i | − | 1.23329i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −81244.8 | −1.28958 | −0.644790 | − | 0.764360i | \(-0.723055\pi\) | ||||
−0.644790 | + | 0.764360i | \(0.723055\pi\) | |||||||
\(252\) | − | 18805.5i | − | 0.296132i | ||||||
\(253\) | 16992.8 | − | 14504.7i | 0.265476 | − | 0.226605i | ||||
\(254\) | −22228.9 | −0.344548 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4096.00 | 0.0625000 | ||||||||
\(257\) | −56962.9 | −0.862434 | −0.431217 | − | 0.902248i | \(-0.641916\pi\) | ||||
−0.431217 | + | 0.902248i | \(0.641916\pi\) | |||||||
\(258\) | −30196.9 | −0.453651 | ||||||||
\(259\) | 47539.1i | 0.708683i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 71999.4i | − | 1.05693i | ||||||
\(262\) | −69065.5 | −1.00614 | ||||||||
\(263\) | − | 6000.71i | − | 0.0867543i | −0.999059 | − | 0.0433772i | \(-0.986188\pi\) | ||
0.999059 | − | 0.0433772i | \(-0.0138117\pi\) | |||||||
\(264\) | −21788.9 | − | 25526.6i | −0.312628 | − | 0.366256i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1208.89i | 0.0170853i | ||||||||
\(267\) | 116656. | 1.63638 | ||||||||
\(268\) | −18879.0 | −0.262850 | ||||||||
\(269\) | 24832.0 | 0.343169 | 0.171584 | − | 0.985169i | \(-0.445111\pi\) | ||||
0.171584 | + | 0.985169i | \(0.445111\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 65976.9i | − | 0.898367i | −0.893440 | − | 0.449183i | \(-0.851715\pi\) | ||
0.893440 | − | 0.449183i | \(-0.148285\pi\) | |||||||
\(272\) | 17938.2i | 0.242461i | ||||||||
\(273\) | −135973. | −1.82443 | ||||||||
\(274\) | 8190.88i | 0.109101i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −18106.6 | −0.237694 | ||||||||
\(277\) | 31675.1i | 0.412818i | 0.978466 | + | 0.206409i | \(0.0661778\pi\) | ||||
−0.978466 | + | 0.206409i | \(0.933822\pi\) | |||||||
\(278\) | −41303.4 | −0.534436 | ||||||||
\(279\) | 103368. | 1.32794 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 130542.i | 1.65325i | 0.562753 | + | 0.826625i | \(0.309742\pi\) | ||||
−0.562753 | + | 0.826625i | \(0.690258\pi\) | |||||||
\(282\) | 104743.i | 1.31713i | ||||||||
\(283\) | 77156.4i | 0.963384i | 0.876341 | + | 0.481692i | \(0.159978\pi\) | ||||
−0.876341 | + | 0.481692i | \(0.840022\pi\) | |||||||
\(284\) | 19952.3 | 0.247375 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −85072.7 | + | 72616.3i | −1.04006 | + | 0.887773i | ||||
\(287\) | 86994.4 | 1.05615 | ||||||||
\(288\) | 12537.0i | 0.151151i | ||||||||
\(289\) | 4961.32 | 0.0594020 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 78471.4 | 0.926671 | ||||||||
\(292\) | − | 35850.5i | − | 0.420465i | ||||||
\(293\) | − | 73563.5i | − | 0.856894i | −0.903567 | − | 0.428447i | \(-0.859061\pi\) | ||
0.903567 | − | 0.428447i | \(-0.140939\pi\) | |||||||
\(294\) | − | 43303.8i | − | 0.500993i | ||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 31692.8i | − | 0.361723i | ||||||
\(297\) | −13246.5 | + | 11306.9i | −0.150171 | + | 0.128183i | ||||
\(298\) | 26782.6 | 0.301592 | ||||||||
\(299\) | 60344.1i | 0.674982i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 29561.3 | 0.326281 | ||||||||
\(302\) | 43376.4 | 0.475598 | ||||||||
\(303\) | 195.322i | 0.00212748i | ||||||||
\(304\) | − | 805.924i | − | 0.00872061i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −54905.3 | −0.586370 | ||||||||
\(307\) | 14140.6i | 0.150034i | 0.997182 | + | 0.0750171i | \(0.0239011\pi\) | ||||
−0.997182 | + | 0.0750171i | \(0.976099\pi\) | |||||||
\(308\) | 21330.4 | + | 24989.3i | 0.224852 | + | 0.263423i | ||||
\(309\) | 158023. | 1.65502 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −115950. | −1.19881 | −0.599406 | − | 0.800445i | \(-0.704596\pi\) | ||||
−0.599406 | + | 0.800445i | \(0.704596\pi\) | |||||||
\(312\) | 90648.5 | 0.931218 | ||||||||
\(313\) | 167682. | 1.71159 | 0.855793 | − | 0.517318i | \(-0.173070\pi\) | ||||
0.855793 | + | 0.517318i | \(0.173070\pi\) | |||||||
\(314\) | 13605.2i | 0.137989i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 77551.9i | − | 0.776637i | ||||||
\(317\) | 43569.8 | 0.433577 | 0.216789 | − | 0.976219i | \(-0.430442\pi\) | ||||
0.216789 | + | 0.976219i | \(0.430442\pi\) | |||||||
\(318\) | − | 9039.50i | − | 0.0893903i | ||||||
\(319\) | 81666.0 | + | 95674.7i | 0.802527 | + | 0.940191i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 132458.i | 1.28549i | ||||||||
\(322\) | 17725.5 | 0.170957 | ||||||||
\(323\) | 3529.51 | 0.0338305 | ||||||||
\(324\) | 58993.8 | 0.561974 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 27933.5i | 0.262839i | ||||||||
\(327\) | − | 103830.i | − | 0.971021i | ||||||
\(328\) | −57996.3 | −0.539079 | ||||||||
\(329\) | − | 102539.i | − | 0.947321i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13167.8 | −0.120187 | −0.0600934 | − | 0.998193i | \(-0.519140\pi\) | ||||
−0.0600934 | + | 0.998193i | \(0.519140\pi\) | |||||||
\(332\) | − | 49903.9i | − | 0.452750i | ||||||
\(333\) | 97005.2 | 0.874795 | ||||||||
\(334\) | 38006.3 | 0.340692 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | − | 26627.2i | − | 0.235856i | ||||||
\(337\) | − | 41741.2i | − | 0.367540i | −0.982969 | − | 0.183770i | \(-0.941170\pi\) | ||
0.982969 | − | 0.183770i | \(-0.0588302\pi\) | |||||||
\(338\) | − | 221323.i | − | 1.93728i | ||||||
\(339\) | −12378.9 | −0.107717 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −137359. | + | 117247.i | −1.18127 | + | 1.00830i | ||||
\(342\) | 2466.77 | 0.0210900 | ||||||||
\(343\) | 123885.i | 1.05301i | ||||||||
\(344\) | −19707.6 | −0.166539 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 106530. | 0.889858 | ||||||||
\(347\) | − | 8110.63i | − | 0.0673590i | −0.999433 | − | 0.0336795i | \(-0.989277\pi\) | ||
0.999433 | − | 0.0336795i | \(-0.0107225\pi\) | |||||||
\(348\) | − | 101945.i | − | 0.841800i | ||||||
\(349\) | − | 16786.2i | − | 0.137817i | −0.997623 | − | 0.0689083i | \(-0.978048\pi\) | ||
0.997623 | − | 0.0689083i | \(-0.0219516\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 47040.1i | − | 0.381816i | ||||||
\(352\) | −14220.3 | − | 16659.6i | −0.114768 | − | 0.134455i | ||||
\(353\) | −116711. | −0.936618 | −0.468309 | − | 0.883565i | \(-0.655137\pi\) | ||||
−0.468309 | + | 0.883565i | \(0.655137\pi\) | |||||||
\(354\) | − | 10159.4i | − | 0.0810700i | ||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 76133.8 | 0.600727 | ||||||||
\(357\) | 116612. | 0.914973 | ||||||||
\(358\) | 152569.i | 1.19042i | ||||||||
\(359\) | − | 35393.9i | − | 0.274625i | −0.990528 | − | 0.137312i | \(-0.956154\pi\) | ||
0.990528 | − | 0.137312i | \(-0.0438464\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 130162. | 0.998783 | ||||||||
\(362\) | 66127.5i | 0.504621i | ||||||||
\(363\) | −28177.9 | + | 177243.i | −0.213843 | + | 1.34511i | ||||
\(364\) | −88740.8 | −0.669762 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 124604. | 0.930187 | ||||||||
\(367\) | 91892.5 | 0.682257 | 0.341128 | − | 0.940017i | \(-0.389191\pi\) | ||||
0.341128 | + | 0.940017i | \(0.389191\pi\) | |||||||
\(368\) | −11817.0 | −0.0872594 | ||||||||
\(369\) | − | 177515.i | − | 1.30371i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8849.26i | 0.0642923i | ||||||||
\(372\) | 146362. | 1.05765 | ||||||||
\(373\) | − | 35452.4i | − | 0.254817i | −0.991850 | − | 0.127408i | \(-0.959334\pi\) | ||
0.991850 | − | 0.127408i | \(-0.0406659\pi\) | |||||||
\(374\) | 72959.7 | − | 62276.9i | 0.521603 | − | 0.445230i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 68359.3i | 0.483529i | ||||||||
\(377\) | −339755. | −2.39047 | ||||||||
\(378\) | −13817.6 | −0.0967051 | ||||||||
\(379\) | 217027. | 1.51090 | 0.755449 | − | 0.655207i | \(-0.227419\pi\) | ||||
0.755449 | + | 0.655207i | \(0.227419\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 96336.5i | − | 0.663653i | ||||||
\(382\) | 131837.i | 0.903462i | ||||||||
\(383\) | 199025. | 1.35678 | 0.678390 | − | 0.734702i | \(-0.262678\pi\) | ||||
0.678390 | + | 0.734702i | \(0.262678\pi\) | |||||||
\(384\) | 17751.4i | 0.120385i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −162877. | −1.09316 | ||||||||
\(387\) | − | 60320.9i | − | 0.402760i | ||||||
\(388\) | 51213.3 | 0.340188 | ||||||||
\(389\) | −141391. | −0.934380 | −0.467190 | − | 0.884157i | \(-0.654734\pi\) | ||||
−0.467190 | + | 0.884157i | \(0.654734\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 51752.1i | − | 0.338512i | ||||||
\(392\) | − | 28261.6i | − | 0.183918i | ||||||
\(393\) | − | 299319.i | − | 1.93798i | ||||||
\(394\) | −112501. | −0.724710 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 50991.5 | − | 43525.3i | 0.325168 | − | 0.277557i | ||||
\(397\) | −109000. | −0.691585 | −0.345793 | − | 0.938311i | \(-0.612390\pi\) | ||||
−0.345793 | + | 0.938311i | \(0.612390\pi\) | |||||||
\(398\) | 53472.1i | 0.337568i | ||||||||
\(399\) | −5239.13 | −0.0329089 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −262604. | −1.63310 | −0.816549 | − | 0.577277i | \(-0.804115\pi\) | ||||
−0.816549 | + | 0.577277i | \(0.804115\pi\) | |||||||
\(402\) | − | 81818.5i | − | 0.506290i | ||||||
\(403\) | − | 487781.i | − | 3.00341i | ||||||
\(404\) | 127.474i | 0.000781015i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 99799.9i | 0.605450i | ||||||||
\(407\) | −128903. | + | 110029.i | −0.778170 | + | 0.664230i | ||||
\(408\) | −77741.6 | −0.467018 | ||||||||
\(409\) | − | 132695.i | − | 0.793244i | −0.917982 | − | 0.396622i | \(-0.870182\pi\) | ||
0.917982 | − | 0.396622i | \(-0.129818\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −35498.0 | −0.210146 | ||||||||
\(412\) | 103132. | 0.607572 | ||||||||
\(413\) | 9945.55i | 0.0583081i | ||||||||
\(414\) | − | 36169.5i | − | 0.211029i | ||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 59160.5 | 0.341858 | ||||||||
\(417\) | − | 179003.i | − | 1.02941i | ||||||
\(418\) | −3277.91 | + | 2797.96i | −0.0187605 | + | 0.0160136i | ||||
\(419\) | 54888.5 | 0.312646 | 0.156323 | − | 0.987706i | \(-0.450036\pi\) | ||||
0.156323 | + | 0.987706i | \(0.450036\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20412.0 | 0.115165 | 0.0575826 | − | 0.998341i | \(-0.481661\pi\) | ||||
0.0575826 | + | 0.998341i | \(0.481661\pi\) | |||||||
\(422\) | −87608.5 | −0.491951 | ||||||||
\(423\) | −209234. | −1.16937 | ||||||||
\(424\) | − | 5899.51i | − | 0.0328159i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 86470.3i | 0.476483i | ||||||||
\(427\) | −121982. | −0.669020 | ||||||||
\(428\) | 86447.0i | 0.471913i | ||||||||
\(429\) | −314708. | − | 368692.i | −1.70999 | − | 2.00332i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 157298.i | − | 0.846776i | −0.905949 | − | 0.423388i | \(-0.860841\pi\) | ||
0.905949 | − | 0.423388i | \(-0.139159\pi\) | |||||||
\(432\) | 9211.74 | 0.0493599 | ||||||||
\(433\) | 134223. | 0.715900 | 0.357950 | − | 0.933741i | \(-0.383476\pi\) | ||||
0.357950 | + | 0.933741i | \(0.383476\pi\) | |||||||
\(434\) | −143281. | −0.760694 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − | 67763.4i | − | 0.356470i | ||||||
\(437\) | 2325.10i | 0.0121753i | ||||||||
\(438\) | 155371. | 0.809880 | ||||||||
\(439\) | 304612.i | 1.58059i | 0.612729 | + | 0.790293i | \(0.290072\pi\) | ||||
−0.612729 | + | 0.790293i | \(0.709928\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 86503.2 | 0.444790 | ||||||||
\(442\) | 259091.i | 1.32619i | ||||||||
\(443\) | 116115. | 0.591671 | 0.295835 | − | 0.955239i | \(-0.404402\pi\) | ||||
0.295835 | + | 0.955239i | \(0.404402\pi\) | |||||||
\(444\) | 137352. | 0.696735 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 56259.1i | 0.282828i | ||||||||
\(447\) | 116072.i | 0.580913i | ||||||||
\(448\) | − | 17377.9i | − | 0.0865845i | ||||||
\(449\) | 156051. | 0.774059 | 0.387030 | − | 0.922067i | \(-0.373501\pi\) | ||||
0.387030 | + | 0.922067i | \(0.373501\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 201348. | + | 235887.i | 0.989906 | + | 1.15971i | ||||
\(452\) | −8078.94 | −0.0395437 | ||||||||
\(453\) | 187987.i | 0.916075i | ||||||||
\(454\) | −216456. | −1.05017 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3492.75 | 0.0167973 | ||||||||
\(457\) | − | 154609.i | − | 0.740290i | −0.928974 | − | 0.370145i | \(-0.879308\pi\) | ||
0.928974 | − | 0.370145i | \(-0.120692\pi\) | |||||||
\(458\) | − | 158618.i | − | 0.756173i | ||||||
\(459\) | 40342.4i | 0.191486i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 324927.i | − | 1.52892i | −0.644674 | − | 0.764458i | \(-0.723007\pi\) | ||
0.644674 | − | 0.764458i | \(-0.276993\pi\) | |||||||
\(462\) | −108300. | + | 92442.6i | −0.507393 | + | 0.433100i | ||||
\(463\) | 135116. | 0.630295 | 0.315147 | − | 0.949043i | \(-0.397946\pi\) | ||||
0.315147 | + | 0.949043i | \(0.397946\pi\) | |||||||
\(464\) | − | 66533.3i | − | 0.309032i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −9484.83 | −0.0436775 | ||||||||
\(467\) | −217618. | −0.997840 | −0.498920 | − | 0.866648i | \(-0.666270\pi\) | ||||
−0.498920 | + | 0.866648i | \(0.666270\pi\) | |||||||
\(468\) | 181078.i | 0.826751i | ||||||||
\(469\) | 80096.6i | 0.364140i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −58962.9 | −0.265789 | ||||||||
\(472\) | − | 6630.37i | − | 0.0297614i | ||||||
\(473\) | 68419.6 | + | 80156.1i | 0.305814 | + | 0.358273i | ||||
\(474\) | 336098. | 1.49592 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 76105.5 | 0.335894 | ||||||||
\(477\) | 18057.2 | 0.0793622 | ||||||||
\(478\) | 24408.5 | 0.106828 | ||||||||
\(479\) | 2332.66i | 0.0101667i | 0.999987 | + | 0.00508335i | \(0.00161809\pi\) | ||||
−0.999987 | + | 0.00508335i | \(0.998382\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 457754.i | − | 1.97853i | ||||||
\(482\) | −286792. | −1.23445 | ||||||||
\(483\) | 76819.7i | 0.329290i | ||||||||
\(484\) | −18389.9 | + | 115675.i | −0.0785036 | + | 0.493799i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 222695.i | 0.942839i | ||||||||
\(487\) | −307695. | −1.29737 | −0.648683 | − | 0.761059i | \(-0.724680\pi\) | ||||
−0.648683 | + | 0.761059i | \(0.724680\pi\) | |||||||
\(488\) | 81321.2 | 0.341479 | ||||||||
\(489\) | −121060. | −0.506269 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 165203.i | − | 0.685258i | −0.939471 | − | 0.342629i | \(-0.888683\pi\) | ||
0.939471 | − | 0.342629i | \(-0.111317\pi\) | |||||||
\(492\) | − | 251347.i | − | 1.03835i | ||||||
\(493\) | 291379. | 1.19885 | ||||||||
\(494\) | − | 11640.4i | − | 0.0476993i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 95520.8 | 0.388271 | ||||||||
\(497\) | − | 84650.5i | − | 0.342702i | ||||||
\(498\) | 216276. | 0.872067 | ||||||||
\(499\) | 271209. | 1.08919 | 0.544594 | − | 0.838700i | \(-0.316684\pi\) | ||||
0.544594 | + | 0.838700i | \(0.316684\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 164713.i | 0.656226i | ||||||||
\(502\) | − | 229795.i | − | 0.911870i | ||||||
\(503\) | − | 242593.i | − | 0.958831i | −0.877588 | − | 0.479415i | \(-0.840849\pi\) | ||
0.877588 | − | 0.479415i | \(-0.159151\pi\) | |||||||
\(504\) | 53190.1 | 0.209397 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 41025.6 | + | 48063.0i | 0.160234 | + | 0.187720i | ||||
\(507\) | 959180. | 3.73151 | ||||||||
\(508\) | − | 62872.7i | − | 0.243632i | ||||||
\(509\) | −231272. | −0.892663 | −0.446331 | − | 0.894868i | \(-0.647270\pi\) | ||||
−0.446331 | + | 0.894868i | \(0.647270\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −152101. | −0.582491 | ||||||||
\(512\) | 11585.2i | 0.0441942i | ||||||||
\(513\) | − | 1812.49i | − | 0.00688718i | ||||||
\(514\) | − | 161116.i | − | 0.609833i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | − | 85409.6i | − | 0.320780i | ||||||
\(517\) | 278036. | − | 237326.i | 1.04021 | − | 0.887900i | ||||
\(518\) | −134461. | −0.501114 | ||||||||
\(519\) | 461686.i | 1.71400i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −19525.5 | −0.0719327 | −0.0359664 | − | 0.999353i | \(-0.511451\pi\) | ||||
−0.0359664 | + | 0.999353i | \(0.511451\pi\) | |||||||
\(522\) | 203645. | 0.747365 | ||||||||
\(523\) | 493543.i | 1.80435i | 0.431366 | + | 0.902177i | \(0.358032\pi\) | ||||
−0.431366 | + | 0.902177i | \(0.641968\pi\) | |||||||
\(524\) | − | 195347.i | − | 0.711448i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 16972.6 | 0.0613446 | ||||||||
\(527\) | 418329.i | 1.50625i | ||||||||
\(528\) | 72200.0 | − | 61628.4i | 0.258982 | − | 0.221062i | ||||
\(529\) | −245749. | −0.878173 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 20294.2 | 0.0719753 | ||||||||
\(532\) | −3419.25 | −0.0120811 | ||||||||
\(533\) | −837668. | −2.94861 | ||||||||
\(534\) | 329952.i | 1.15709i | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 53397.8i | − | 0.185863i | ||||||
\(537\) | −661211. | −2.29293 | ||||||||
\(538\) | 70235.6i | 0.242657i | ||||||||
\(539\) | −114948. | + | 98117.1i | −0.395661 | + | 0.337728i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 211511.i | 0.722669i | 0.932436 | + | 0.361334i | \(0.117679\pi\) | ||||
−0.932436 | + | 0.361334i | \(0.882321\pi\) | |||||||
\(542\) | 186611. | 0.635241 | ||||||||
\(543\) | −286587. | −0.971978 | ||||||||
\(544\) | −50737.0 | −0.171446 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | − | 384589.i | − | 1.29007i | ||||||
\(547\) | 271731.i | 0.908163i | 0.890960 | + | 0.454082i | \(0.150033\pi\) | ||||
−0.890960 | + | 0.454082i | \(0.849967\pi\) | |||||||
\(548\) | −23167.3 | −0.0771462 | ||||||||
\(549\) | 248908.i | 0.825836i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −13091.0 | −0.0431191 | ||||||||
\(552\) | − | 51213.1i | − | 0.168075i | ||||||
\(553\) | −329025. | −1.07592 | ||||||||
\(554\) | −89590.8 | −0.291907 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 116824.i | − | 0.377903i | ||||||
\(557\) | 420797.i | 1.35632i | 0.734914 | + | 0.678160i | \(0.237223\pi\) | ||||
−0.734914 | + | 0.678160i | \(0.762777\pi\) | |||||||
\(558\) | 292370.i | 0.938998i | ||||||||
\(559\) | −284646. | −0.910922 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 269899. | + | 316196.i | 0.857581 | + | 1.00469i | ||||
\(562\) | −369229. | −1.16902 | ||||||||
\(563\) | 199781.i | 0.630285i | 0.949044 | + | 0.315142i | \(0.102052\pi\) | ||||
−0.949044 | + | 0.315142i | \(0.897948\pi\) | |||||||
\(564\) | −296259. | −0.931351 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −218231. | −0.681215 | ||||||||
\(567\) | − | 250290.i | − | 0.778532i | ||||||
\(568\) | 56433.7i | 0.174921i | ||||||||
\(569\) | 393771.i | 1.21624i | 0.793845 | + | 0.608120i | \(0.208076\pi\) | ||||
−0.793845 | + | 0.608120i | \(0.791924\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 152076.i | 0.466431i | 0.972425 | + | 0.233215i | \(0.0749247\pi\) | ||||
−0.972425 | + | 0.233215i | \(0.925075\pi\) | |||||||
\(572\) | −205390. | − | 240622.i | −0.627751 | − | 0.735433i | ||||
\(573\) | −571361. | −1.74021 | ||||||||
\(574\) | 246057.i | 0.746814i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −35460.1 | −0.106880 | ||||||||
\(577\) | 260379. | 0.782086 | 0.391043 | − | 0.920372i | \(-0.372114\pi\) | ||||
0.391043 | + | 0.920372i | \(0.372114\pi\) | |||||||
\(578\) | 14032.7i | 0.0420036i | ||||||||
\(579\) | − | 705883.i | − | 2.10560i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −211724. | −0.627218 | ||||||||
\(582\) | 221951.i | 0.655255i | ||||||||
\(583\) | −23994.9 | + | 20481.6i | −0.0705963 | + | 0.0602596i | ||||
\(584\) | 101401. | 0.297313 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 208069. | 0.605916 | ||||||||
\(587\) | 197623. | 0.573538 | 0.286769 | − | 0.958000i | \(-0.407419\pi\) | ||||
0.286769 | + | 0.958000i | \(0.407419\pi\) | |||||||
\(588\) | 122482. | 0.354255 | ||||||||
\(589\) | − | 18794.6i | − | 0.0541754i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 487563.i | − | 1.39590i | ||||||
\(592\) | 89640.7 | 0.255777 | ||||||||
\(593\) | 103667.i | 0.294803i | 0.989077 | + | 0.147401i | \(0.0470909\pi\) | ||||
−0.989077 | + | 0.147401i | \(0.952909\pi\) | |||||||
\(594\) | −31980.8 | − | 37466.7i | −0.0906392 | − | 0.106187i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 75752.6i | 0.213258i | ||||||||
\(597\) | −231740. | −0.650208 | ||||||||
\(598\) | −170679. | −0.477284 | ||||||||
\(599\) | 204660. | 0.570399 | 0.285199 | − | 0.958468i | \(-0.407940\pi\) | ||||
0.285199 | + | 0.958468i | \(0.407940\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 140115.i | − | 0.387913i | −0.981010 | − | 0.193957i | \(-0.937868\pi\) | ||
0.981010 | − | 0.193957i | \(-0.0621321\pi\) | |||||||
\(602\) | 83612.1i | 0.230715i | ||||||||
\(603\) | 163440. | 0.449493 | ||||||||
\(604\) | 122687.i | 0.336298i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −552.453 | −0.00150436 | ||||||||
\(607\) | − | 69648.7i | − | 0.189032i | −0.995523 | − | 0.0945160i | \(-0.969870\pi\) | ||
0.995523 | − | 0.0945160i | \(-0.0301304\pi\) | |||||||
\(608\) | 2279.50 | 0.00616640 | ||||||||
\(609\) | −432518. | −1.16619 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 987347.i | 2.64477i | ||||||||
\(612\) | − | 155296.i | − | 0.414626i | ||||||
\(613\) | 619709.i | 1.64917i | 0.565735 | + | 0.824587i | \(0.308593\pi\) | ||||
−0.565735 | + | 0.824587i | \(0.691407\pi\) | |||||||
\(614\) | −39995.6 | −0.106090 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −70680.5 | + | 60331.4i | −0.186268 | + | 0.158994i | ||||
\(617\) | 284417. | 0.747112 | 0.373556 | − | 0.927608i | \(-0.378138\pi\) | ||||
0.373556 | + | 0.927608i | \(0.378138\pi\) | |||||||
\(618\) | 446957.i | 1.17028i | ||||||||
\(619\) | −231315. | −0.603702 | −0.301851 | − | 0.953355i | \(-0.597605\pi\) | ||||
−0.301851 | + | 0.953355i | \(0.597605\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −26576.0 | −0.0689138 | ||||||||
\(622\) | − | 327957.i | − | 0.847688i | ||||||
\(623\) | − | 323008.i | − | 0.832219i | ||||||
\(624\) | 256393.i | 0.658471i | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 474278.i | 1.21027i | ||||||||
\(627\) | −12125.9 | − | 14206.0i | −0.0308447 | − | 0.0361357i | ||||
\(628\) | −38481.3 | −0.0975733 | ||||||||
\(629\) | 392577.i | 0.992256i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 311488. | 0.782316 | 0.391158 | − | 0.920324i | \(-0.372075\pi\) | ||||
0.391158 | + | 0.920324i | \(0.372075\pi\) | |||||||
\(632\) | 219350. | 0.549165 | ||||||||
\(633\) | − | 379682.i | − | 0.947573i | ||||||
\(634\) | 123234.i | 0.306586i | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 25567.6 | 0.0632085 | ||||||||
\(637\) | − | 408197.i | − | 1.00598i | ||||||
\(638\) | −270609. | + | 230986.i | −0.664815 | + | 0.567473i | ||||
\(639\) | −172732. | −0.423030 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −297618. | −0.724341 | −0.362170 | − | 0.932112i | \(-0.617964\pi\) | ||||
−0.362170 | + | 0.932112i | \(0.617964\pi\) | |||||||
\(642\) | −374648. | −0.908978 | ||||||||
\(643\) | 121820. | 0.294645 | 0.147322 | − | 0.989089i | \(-0.452935\pi\) | ||||
0.147322 | + | 0.989089i | \(0.452935\pi\) | |||||||
\(644\) | 50135.3i | 0.120885i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9982.95i | 0.0239218i | ||||||||
\(647\) | 377550. | 0.901917 | 0.450958 | − | 0.892545i | \(-0.351082\pi\) | ||||
0.450958 | + | 0.892545i | \(0.351082\pi\) | |||||||
\(648\) | 166860.i | 0.397376i | ||||||||
\(649\) | −26967.5 | + | 23018.9i | −0.0640253 | + | 0.0546507i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 620959.i | − | 1.46521i | ||||||
\(652\) | −79007.8 | −0.185855 | ||||||||
\(653\) | 558170. | 1.30900 | 0.654501 | − | 0.756061i | \(-0.272879\pi\) | ||||
0.654501 | + | 0.756061i | \(0.272879\pi\) | |||||||
\(654\) | 293677. | 0.686616 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 164038.i | − | 0.381186i | ||||||
\(657\) | 310367.i | 0.719025i | ||||||||
\(658\) | 290024. | 0.669857 | ||||||||
\(659\) | 357653.i | 0.823551i | 0.911285 | + | 0.411776i | \(0.135091\pi\) | ||||
−0.911285 | + | 0.411776i | \(0.864909\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 290959. | 0.665931 | 0.332965 | − | 0.942939i | \(-0.391951\pi\) | ||||
0.332965 | + | 0.942939i | \(0.391951\pi\) | |||||||
\(662\) | − | 37244.1i | − | 0.0849849i | ||||||
\(663\) | −1.12286e6 | −2.55446 | ||||||||
\(664\) | 141150. | 0.320143 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 274372.i | 0.618574i | ||||||||
\(667\) | 191949.i | 0.431454i | ||||||||
\(668\) | 107498.i | 0.240906i | ||||||||
\(669\) | −243818. | −0.544771 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −282326. | − | 330756.i | −0.627056 | − | 0.734619i | ||||
\(672\) | 75313.0 | 0.166775 | ||||||||
\(673\) | 465570.i | 1.02791i | 0.857817 | + | 0.513955i | \(0.171820\pi\) | ||||
−0.857817 | + | 0.513955i | \(0.828180\pi\) | |||||||
\(674\) | 118062. | 0.259890 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 625996. | 1.36987 | ||||||||
\(677\) | 361627.i | 0.789012i | 0.918893 | + | 0.394506i | \(0.129084\pi\) | ||||
−0.918893 | + | 0.394506i | \(0.870916\pi\) | |||||||
\(678\) | − | 35012.9i | − | 0.0761673i | ||||||
\(679\) | − | 217280.i | − | 0.471280i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 938089.i | − | 2.02279i | ||||||
\(682\) | −331624. | − | 388509.i | −0.712979 | − | 0.835281i | ||||
\(683\) | −673707. | −1.44421 | −0.722103 | − | 0.691785i | \(-0.756825\pi\) | ||||
−0.722103 | + | 0.691785i | \(0.756825\pi\) | |||||||
\(684\) | 6977.08i | 0.0149129i | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −350400. | −0.744588 | ||||||||
\(687\) | 687426. | 1.45651 | ||||||||
\(688\) | − | 55741.4i | − | 0.117761i | ||||||
\(689\) | − | 85209.4i | − | 0.179494i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 66171.2 | 0.138584 | 0.0692920 | − | 0.997596i | \(-0.477926\pi\) | ||||
0.0692920 | + | 0.997596i | \(0.477926\pi\) | |||||||
\(692\) | 301313.i | 0.629225i | ||||||||
\(693\) | −184662. | − | 216339.i | −0.384514 | − | 0.450472i | ||||
\(694\) | 22940.3 | 0.0476300 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 288345. | 0.595243 | ||||||||
\(697\) | 718397. | 1.47877 | ||||||||
\(698\) | 47478.5 | 0.0974510 | ||||||||
\(699\) | − | 41105.8i | − | 0.0841297i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 439863.i | 0.895121i | 0.894254 | + | 0.447560i | \(0.147707\pi\) | ||||
−0.894254 | + | 0.447560i | \(0.852293\pi\) | |||||||
\(702\) | 133050. | 0.269985 | ||||||||
\(703\) | − | 17637.6i | − | 0.0356885i | ||||||
\(704\) | 47120.3 | − | 40220.9i | 0.0950743 | − | 0.0811534i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 330109.i | − | 0.662289i | ||||||
\(707\) | 540.827 | 0.00108198 | ||||||||
\(708\) | 28735.0 | 0.0573251 | ||||||||
\(709\) | 511529. | 1.01760 | 0.508801 | − | 0.860884i | \(-0.330089\pi\) | ||||
0.508801 | + | 0.860884i | \(0.330089\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 671386.i | 1.32811i | ||||||||
\(712\) | 215339.i | 0.424778i | ||||||||
\(713\) | −275579. | −0.542084 | ||||||||
\(714\) | 329830.i | 0.646984i | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −431531. | −0.841755 | ||||||||
\(717\) | 105783.i | 0.205767i | ||||||||
\(718\) | 100109. | 0.194189 | ||||||||
\(719\) | 683729. | 1.32259 | 0.661297 | − | 0.750124i | \(-0.270006\pi\) | ||||
0.661297 | + | 0.750124i | \(0.270006\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 437551.i | − | 0.841701i | ||||||
\(722\) | 368155.i | 0.706246i | ||||||||
\(723\) | − | 1.24291e6i | − | 2.37774i | ||||||
\(724\) | −187037. | −0.356821 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −501319. | − | 79699.2i | −0.951133 | − | 0.151210i | ||||
\(727\) | −258952. | −0.489949 | −0.244974 | − | 0.969530i | \(-0.578780\pi\) | ||||
−0.244974 | + | 0.969530i | \(0.578780\pi\) | |||||||
\(728\) | − | 250997.i | − | 0.473593i | ||||||
\(729\) | −367813. | −0.692105 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 244117. | 0.456839 | ||||||||
\(732\) | 352434.i | 0.657742i | ||||||||
\(733\) | − | 474044.i | − | 0.882288i | −0.897436 | − | 0.441144i | \(-0.854573\pi\) | ||
0.897436 | − | 0.441144i | \(-0.145427\pi\) | |||||||
\(734\) | 259911.i | 0.482428i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 33423.6i | − | 0.0617017i | ||||||
\(737\) | −217183. | + | 185383.i | −0.399845 | + | 0.341299i | ||||
\(738\) | 502088. | 0.921864 | ||||||||
\(739\) | 758640.i | 1.38914i | 0.719424 | + | 0.694571i | \(0.244406\pi\) | ||||
−0.719424 | + | 0.694571i | \(0.755594\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 50447.5 | 0.0918763 | ||||||||
\(742\) | −25029.5 | −0.0454615 | ||||||||
\(743\) | 579823.i | 1.05031i | 0.851006 | + | 0.525156i | \(0.175993\pi\) | ||||
−0.851006 | + | 0.525156i | \(0.824007\pi\) | |||||||
\(744\) | 413973.i | 0.747870i | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 100275. | 0.180183 | ||||||||
\(747\) | 432030.i | 0.774236i | ||||||||
\(748\) | 176146. | + | 206361.i | 0.314825 | + | 0.368829i | ||||
\(749\) | 366763. | 0.653766 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −844322. | −1.49702 | −0.748511 | − | 0.663122i | \(-0.769231\pi\) | ||||
−0.748511 | + | 0.663122i | \(0.769231\pi\) | |||||||
\(752\) | −193349. | −0.341906 | ||||||||
\(753\) | 995897. | 1.75640 | ||||||||
\(754\) | − | 960972.i | − | 1.69032i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | − | 39082.1i | − | 0.0683808i | ||||||
\(757\) | −801567. | −1.39877 | −0.699387 | − | 0.714743i | \(-0.746544\pi\) | ||||
−0.699387 | + | 0.714743i | \(0.746544\pi\) | |||||||
\(758\) | 613845.i | 1.06837i | ||||||||
\(759\) | −208298. | + | 177799.i | −0.361577 | + | 0.308635i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6823.03i | 0.0117817i | 0.999983 | + | 0.00589085i | \(0.00187513\pi\) | ||||
−0.999983 | + | 0.00589085i | \(0.998125\pi\) | |||||||
\(762\) | 272481. | 0.469273 | ||||||||
\(763\) | −287496. | −0.493836 | ||||||||
\(764\) | −372891. | −0.638844 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 562927.i | 0.959389i | ||||||||
\(767\) | − | 95765.6i | − | 0.162787i | ||||||
\(768\) | −50208.7 | −0.0851248 | ||||||||
\(769\) | 375862.i | 0.635588i | 0.948160 | + | 0.317794i | \(0.102942\pi\) | ||||
−0.948160 | + | 0.317794i | \(0.897058\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 698250. | 1.17463 | ||||||||
\(772\) | − | 460685.i | − | 0.772982i | ||||||
\(773\) | 857421. | 1.43494 | 0.717472 | − | 0.696587i | \(-0.245299\pi\) | ||||
0.717472 | + | 0.696587i | \(0.245299\pi\) | |||||||
\(774\) | 170613. | 0.284794 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 144853.i | 0.240549i | ||||||||
\(777\) | − | 582734.i | − | 0.965224i | ||||||
\(778\) | − | 399915.i | − | 0.660707i | ||||||
\(779\) | −32276.0 | −0.0531868 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 229531. | − | 195923.i | 0.376305 | − | 0.321206i | ||||
\(782\) | 146377. | 0.239364 | ||||||||
\(783\) | − | 149631.i | − | 0.244060i | ||||||
\(784\) | 79936.0 | 0.130050 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 846603. | 1.37036 | ||||||||
\(787\) | 1.02294e6i | 1.65158i | 0.563976 | + | 0.825791i | \(0.309271\pi\) | ||||
−0.563976 | + | 0.825791i | \(0.690729\pi\) | |||||||
\(788\) | − | 318201.i | − | 0.512448i | ||||||
\(789\) | 73556.6i | 0.118159i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 34276.0i | 0.0547820i | ||||||||
\(792\) | 123108. | + | 144226.i | 0.196262 | + | 0.229929i | ||||
\(793\) | 1.17456e6 | 1.86780 | ||||||||
\(794\) | − | 308299.i | − | 0.489024i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −151242. | −0.238697 | ||||||||
\(797\) | −865636. | −1.36276 | −0.681379 | − | 0.731931i | \(-0.738619\pi\) | ||||
−0.681379 | + | 0.731931i | \(0.738619\pi\) | |||||||
\(798\) | − | 14818.5i | − | 0.0232701i | ||||||
\(799\) | − | 846765.i | − | 1.32638i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −659109. | −1.02729 | ||||||||
\(802\) | − | 742755.i | − | 1.15477i | ||||||
\(803\) | −352036. | − | 412424.i | −0.545954 | − | 0.639606i | ||||
\(804\) | 231418. | 0.358001 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.37965e6 | 2.12373 | ||||||||
\(807\) | −304390. | −0.467395 | ||||||||
\(808\) | −360.551 | −0.000552261 | ||||||||
\(809\) | − | 886947.i | − | 1.35519i | −0.735435 | − | 0.677596i | \(-0.763022\pi\) | ||
0.735435 | − | 0.677596i | \(-0.236978\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 608105.i | 0.924563i | 0.886733 | + | 0.462282i | \(0.152969\pi\) | ||||
−0.886733 | + | 0.462282i | \(0.847031\pi\) | |||||||
\(812\) | −282277. | −0.428118 | ||||||||
\(813\) | 808744.i | 1.22357i | ||||||||
\(814\) | −311209. | − | 364593.i | −0.469682 | − | 0.550250i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | − | 219887.i | − | 0.330231i | ||||||
\(817\) | −10967.6 | −0.0164312 | ||||||||
\(818\) | 375317. | 0.560908 | ||||||||
\(819\) | 768251. | 1.14534 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 102607.i | − | 0.152227i | −0.997099 | − | 0.0761133i | \(-0.975749\pi\) | ||
0.997099 | − | 0.0761133i | \(-0.0242511\pi\) | |||||||
\(822\) | − | 100404.i | − | 0.148596i | ||||||
\(823\) | −338801. | −0.500202 | −0.250101 | − | 0.968220i | \(-0.580464\pi\) | ||||
−0.250101 | + | 0.968220i | \(0.580464\pi\) | |||||||
\(824\) | 291701.i | 0.429618i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −28130.3 | −0.0412300 | ||||||||
\(827\) | 303788.i | 0.444181i | 0.975026 | + | 0.222090i | \(0.0712880\pi\) | ||||
−0.975026 | + | 0.222090i | \(0.928712\pi\) | |||||||
\(828\) | 102303. | 0.149220 | ||||||||
\(829\) | 923889. | 1.34435 | 0.672173 | − | 0.740394i | \(-0.265361\pi\) | ||||
0.672173 | + | 0.740394i | \(0.265361\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 388273.i | − | 0.562258i | ||||||
\(832\) | 167331.i | 0.241730i | ||||||||
\(833\) | 350076.i | 0.504513i | ||||||||
\(834\) | 506296. | 0.727901 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −7913.83 | − | 9271.34i | −0.0113233 | − | 0.0132657i | ||||
\(837\) | 214823. | 0.306640 | ||||||||
\(838\) | 155248.i | 0.221074i | ||||||||
\(839\) | −44067.7 | −0.0626032 | −0.0313016 | − | 0.999510i | \(-0.509965\pi\) | ||||
−0.0313016 | + | 0.999510i | \(0.509965\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −373450. | −0.528009 | ||||||||
\(842\) | 57733.8i | 0.0814340i | ||||||||
\(843\) | − | 1.60018e6i | − | 2.25172i | ||||||
\(844\) | − | 247794.i | − | 0.347862i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | − | 591804.i | − | 0.826869i | ||||||
\(847\) | 490769. | + | 78021.9i | 0.684085 | + | 0.108755i | ||||
\(848\) | 16686.3 | 0.0232043 | ||||||||
\(849\) | − | 945782.i | − | 1.31213i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −258614. | −0.357103 | ||||||||
\(852\) | −244575. | −0.336925 | ||||||||
\(853\) | − | 1.02952e6i | − | 1.41494i | −0.706746 | − | 0.707468i | \(-0.749837\pi\) | ||
0.706746 | − | 0.707468i | \(-0.250163\pi\) | |||||||
\(854\) | − | 345017.i | − | 0.473069i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −244509. | −0.333693 | ||||||||
\(857\) | − | 571557.i | − | 0.778212i | −0.921193 | − | 0.389106i | \(-0.872784\pi\) | ||
0.921193 | − | 0.389106i | \(-0.127216\pi\) | |||||||
\(858\) | 1.04282e6 | − | 890129.i | 1.41656 | − | 1.20914i | ||||
\(859\) | −479749. | −0.650172 | −0.325086 | − | 0.945685i | \(-0.605393\pi\) | ||||
−0.325086 | + | 0.945685i | \(0.605393\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.06637e6 | −1.43848 | ||||||||
\(862\) | 444906. | 0.598761 | ||||||||
\(863\) | 220319. | 0.295822 | 0.147911 | − | 0.989001i | \(-0.452745\pi\) | ||||
0.147911 | + | 0.989001i | \(0.452745\pi\) | |||||||
\(864\) | 26054.7i | 0.0349027i | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 379641.i | 0.506218i | ||||||||
\(867\) | −60815.7 | −0.0809054 | ||||||||
\(868\) | − | 405261.i | − | 0.537892i | ||||||
\(869\) | −761526. | − | 892156.i | −1.00843 | − | 1.18141i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 771250.i | − | 1.01662i | ||||||
\(872\) | 191664. | 0.252062 | ||||||||
\(873\) | −443366. | −0.581747 | ||||||||
\(874\) | −6576.38 | −0.00860922 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 439454.i | 0.572672i | ||||||||
\(877\) | − | 1.23303e6i | − | 1.60315i | −0.597893 | − | 0.801576i | \(-0.703995\pi\) | ||
0.597893 | − | 0.801576i | \(-0.296005\pi\) | |||||||
\(878\) | −861573. | −1.11764 | ||||||||
\(879\) | 901740.i | 1.16709i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 227150. | 0.292659 | 0.146329 | − | 0.989236i | \(-0.453254\pi\) | ||||
0.146329 | + | 0.989236i | \(0.453254\pi\) | |||||||
\(882\) | 244668.i | 0.314514i | ||||||||
\(883\) | 136322. | 0.174842 | 0.0874210 | − | 0.996171i | \(-0.472137\pi\) | ||||
0.0874210 | + | 0.996171i | \(0.472137\pi\) | |||||||
\(884\) | −732819. | −0.937761 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 328422.i | 0.418374i | ||||||||
\(887\) | − | 852106.i | − | 1.08304i | −0.840686 | − | 0.541522i | \(-0.817848\pi\) | ||
0.840686 | − | 0.541522i | \(-0.182152\pi\) | |||||||
\(888\) | 388489.i | 0.492666i | ||||||||
\(889\) | −266746. | −0.337516 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 678664. | − | 579294.i | 0.854869 | − | 0.729699i | ||||
\(892\) | −159125. | −0.199990 | ||||||||
\(893\) | 38043.2i | 0.0477061i | ||||||||
\(894\) | −328300. | −0.410768 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 49152.0 | 0.0612245 | ||||||||
\(897\) | − | 739696.i | − | 0.919324i | ||||||
\(898\) | 441379.i | 0.547342i | ||||||||
\(899\) | − | 1.55159e6i | − | 1.91981i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 73077.0i | 0.0900183i | ||||||||
\(902\) | −667188. | + | 569498.i | −0.820040 | + | 0.699970i | ||||
\(903\) | −362362. | −0.444393 | ||||||||
\(904\) | − | 22850.7i | − | 0.0279616i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −531707. | −0.647763 | ||||||||
\(907\) | 945937. | 1.14987 | 0.574934 | − | 0.818200i | \(-0.305028\pi\) | ||||
0.574934 | + | 0.818200i | \(0.305028\pi\) | |||||||
\(908\) | − | 612231.i | − | 0.742581i | ||||||
\(909\) | − | 1103.57i | − | 0.00133559i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −13013.5 | −0.0156803 | −0.00784017 | − | 0.999969i | \(-0.502496\pi\) | ||||
−0.00784017 | + | 0.999969i | \(0.502496\pi\) | |||||||
\(912\) | 9879.00i | 0.0118775i | ||||||||
\(913\) | −490035. | − | 574094.i | −0.587875 | − | 0.688718i | ||||
\(914\) | 437300. | 0.523464 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 448639. | 0.534695 | ||||||||
\(917\) | −828786. | −0.985607 | ||||||||
\(918\) | −114106. | −0.135401 | ||||||||
\(919\) | 809716.i | 0.958742i | 0.877612 | + | 0.479371i | \(0.159135\pi\) | ||||
−0.877612 | + | 0.479371i | \(0.840865\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 173335.i | − | 0.204346i | ||||||
\(922\) | 919032. | 1.08111 | ||||||||
\(923\) | 815099.i | 0.956768i | ||||||||
\(924\) | −261467. | − | 306319.i | −0.306248 | − | 0.358781i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 382165.i | 0.445686i | ||||||||
\(927\) | −892837. | −1.03899 | ||||||||
\(928\) | 188185. | 0.218518 | ||||||||
\(929\) | 731171. | 0.847203 | 0.423601 | − | 0.905849i | \(-0.360766\pi\) | ||||
0.423601 | + | 0.905849i | \(0.360766\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 15728.1i | − | 0.0181458i | ||||||
\(932\) | − | 26827.2i | − | 0.0308847i | ||||||
\(933\) | 1.42131e6 | 1.63278 | ||||||||
\(934\) | − | 615517.i | − | 0.705580i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −512167. | −0.584602 | ||||||||
\(937\) | − | 637069.i | − | 0.725617i | −0.931864 | − | 0.362809i | \(-0.881818\pi\) | ||
0.931864 | − | 0.362809i | \(-0.118182\pi\) | |||||||
\(938\) | −226547. | −0.257486 | ||||||||
\(939\) | −2.05545e6 | −2.33118 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 77429.7i | 0.0874437i | 0.999044 | + | 0.0437218i | \(0.0139215\pi\) | ||||
−0.999044 | + | 0.0437218i | \(0.986078\pi\) | |||||||
\(942\) | − | 166772.i | − | 0.187941i | ||||||
\(943\) | 473252.i | 0.532193i | ||||||||
\(944\) | 18753.5 | 0.0210445 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −226716. | + | 193520.i | −0.253337 | + | 0.216243i | ||||
\(947\) | −362138. | −0.403807 | −0.201904 | − | 0.979405i | \(-0.564713\pi\) | ||||
−0.201904 | + | 0.979405i | \(0.564713\pi\) | |||||||
\(948\) | 950629.i | 1.05778i | ||||||||
\(949\) | 1.46458e6 | 1.62622 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −534077. | −0.590531 | ||||||||
\(952\) | 215259.i | 0.237513i | ||||||||
\(953\) | 1.11862e6i | 1.23168i | 0.787873 | + | 0.615838i | \(0.211182\pi\) | ||||
−0.787873 | + | 0.615838i | \(0.788818\pi\) | |||||||
\(954\) | 51073.5i | 0.0561176i | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 69037.7i | 0.0755388i | ||||||||
\(957\) | −1.00106e6 | − | 1.17278e6i | −1.09304 | − | 1.28054i | ||||
\(958\) | −6597.75 | −0.00718894 | ||||||||
\(959\) | 98290.6i | 0.106875i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.30407e6 | 1.41207 | ||||||||
\(962\) | 1.29472e6 | 1.39903 | ||||||||
\(963\) | − | 748393.i | − | 0.807006i | ||||||
\(964\) | − | 811170.i | − | 0.872886i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −217279. | −0.232843 | ||||||||
\(967\) | 104836.i | 0.112113i | 0.998428 | + | 0.0560565i | \(0.0178527\pi\) | ||||
−0.998428 | + | 0.0560565i | \(0.982147\pi\) | |||||||
\(968\) | −327179. | − | 52014.6i | −0.349168 | − | 0.0555104i | ||||
\(969\) | −43264.6 | −0.0460771 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.63144e6 | −1.73034 | −0.865170 | − | 0.501478i | \(-0.832790\pi\) | ||||
−0.865170 | + | 0.501478i | \(0.832790\pi\) | |||||||
\(972\) | −629876. | −0.666688 | ||||||||
\(973\) | −495640. | −0.523529 | ||||||||
\(974\) | − | 870293.i | − | 0.917376i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 230011.i | 0.241462i | ||||||||
\(977\) | −4386.95 | −0.00459593 | −0.00229796 | − | 0.999997i | \(-0.500731\pi\) | ||||
−0.00229796 | + | 0.999997i | \(0.500731\pi\) | |||||||
\(978\) | − | 342408.i | − | 0.357986i | ||||||
\(979\) | 875842. | − | 747600.i | 0.913819 | − | 0.780017i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 586645.i | 0.609589i | ||||||||
\(982\) | 467264. | 0.484551 | ||||||||
\(983\) | −147531. | −0.152678 | −0.0763388 | − | 0.997082i | \(-0.524323\pi\) | ||||
−0.0763388 | + | 0.997082i | \(0.524323\pi\) | |||||||
\(984\) | 710917. | 0.734224 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 824145.i | 0.847715i | ||||||||
\(987\) | 1.25692e6i | 1.29025i | ||||||||
\(988\) | 32923.9 | 0.0337285 | ||||||||
\(989\) | 160815.i | 0.164412i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 373627. | 0.380444 | 0.190222 | − | 0.981741i | \(-0.439079\pi\) | ||||
0.190222 | + | 0.981741i | \(0.439079\pi\) | |||||||
\(992\) | 270174.i | 0.274549i | ||||||||
\(993\) | 161410. | 0.163694 | ||||||||
\(994\) | 239428. | 0.242327 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 611721.i | 0.616644i | ||||||||
\(997\) | 71451.7i | 0.0718824i | 0.999354 | + | 0.0359412i | \(0.0114429\pi\) | ||||
−0.999354 | + | 0.0359412i | \(0.988557\pi\) | |||||||
\(998\) | 767094.i | 0.770172i | ||||||||
\(999\) | 201598. | 0.202002 |
(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 | 550.5.d.a.351.3 | 4 | ||
5.2 | odd | 4 | 550.5.c.a.549.4 | 8 | |||
5.3 | odd | 4 | 550.5.c.a.549.5 | 8 | |||
5.4 | even | 2 | 22.5.b.a.21.2 | ✓ | 4 | ||
11.10 | odd | 2 | inner | 550.5.d.a.351.1 | 4 | ||
15.14 | odd | 2 | 198.5.d.a.109.3 | 4 | |||
20.19 | odd | 2 | 176.5.h.e.65.2 | 4 | |||
40.19 | odd | 2 | 704.5.h.j.65.4 | 4 | |||
40.29 | even | 2 | 704.5.h.i.65.1 | 4 | |||
55.32 | even | 4 | 550.5.c.a.549.8 | 8 | |||
55.43 | even | 4 | 550.5.c.a.549.1 | 8 | |||
55.54 | odd | 2 | 22.5.b.a.21.4 | yes | 4 | ||
165.164 | even | 2 | 198.5.d.a.109.1 | 4 | |||
220.219 | even | 2 | 176.5.h.e.65.1 | 4 | |||
440.109 | odd | 2 | 704.5.h.i.65.2 | 4 | |||
440.219 | even | 2 | 704.5.h.j.65.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
22.5.b.a.21.2 | ✓ | 4 | 5.4 | even | 2 | ||
22.5.b.a.21.4 | yes | 4 | 55.54 | odd | 2 | ||
176.5.h.e.65.1 | 4 | 220.219 | even | 2 | |||
176.5.h.e.65.2 | 4 | 20.19 | odd | 2 | |||
198.5.d.a.109.1 | 4 | 165.164 | even | 2 | |||
198.5.d.a.109.3 | 4 | 15.14 | odd | 2 | |||
550.5.c.a.549.1 | 8 | 55.43 | even | 4 | |||
550.5.c.a.549.4 | 8 | 5.2 | odd | 4 | |||
550.5.c.a.549.5 | 8 | 5.3 | odd | 4 | |||
550.5.c.a.549.8 | 8 | 55.32 | even | 4 | |||
550.5.d.a.351.1 | 4 | 11.10 | odd | 2 | inner | ||
550.5.d.a.351.3 | 4 | 1.1 | even | 1 | trivial | ||
704.5.h.i.65.1 | 4 | 40.29 | even | 2 | |||
704.5.h.i.65.2 | 4 | 440.109 | odd | 2 | |||
704.5.h.j.65.3 | 4 | 440.219 | even | 2 | |||
704.5.h.j.65.4 | 4 | 40.19 | odd | 2 |