Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [22,5,Mod(21,22)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(22, 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("22.21");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 22 = 2 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 22.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: | \(2.27413918784\) |
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: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 21.4 | ||
Root | \(12.2580 - 1.41421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 22.21 |
Dual form | 22.5.b.a.21.2 |
$q$-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 \(\left(\mathbb{Z}/22\mathbb{Z}\right)^\times\).
\(n\) | \(13\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.82843i | 0.707107i | ||||||||
\(3\) | 12.2580 | 1.36200 | 0.680999 | − | 0.732285i | \(-0.261546\pi\) | ||||
0.680999 | + | 0.732285i | \(0.261546\pi\) | |||||||
\(4\) | −8.00000 | −0.500000 | ||||||||
\(5\) | 4.25798 | 0.170319 | 0.0851595 | − | 0.996367i | \(-0.472860\pi\) | ||||
0.0851595 | + | 0.996367i | \(0.472860\pi\) | |||||||
\(6\) | 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 | ||||||||
\(10\) | 12.0434i | 0.120434i | ||||||||
\(11\) | −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 | ||||||||
\(15\) | 52.1942 | 0.231974 | ||||||||
\(16\) | 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 | \(0.00555200\pi\) | ||||
−0.999848 | + | 0.0174412i | \(0.994448\pi\) | |||||||
\(20\) | −34.0638 | −0.0851595 | ||||||||
\(21\) | 416.050i | 0.943423i | ||||||||
\(22\) | 222.191 | − | 260.306i | 0.459073 | − | 0.537821i | ||||
\(23\) | 184.641 | 0.349037 | 0.174519 | − | 0.984654i | \(-0.444163\pi\) | ||||
0.174519 | + | 0.984654i | \(0.444163\pi\) | |||||||
\(24\) | − | 277.366i | − | 0.481539i | ||||||
\(25\) | −606.870 | −0.970991 | ||||||||
\(26\) | 924.383 | 1.36743 | ||||||||
\(27\) | −143.933 | −0.197440 | ||||||||
\(28\) | − | 271.529i | − | 0.346338i | ||||||
\(29\) | 1039.58i | 1.23613i | 0.786128 | + | 0.618063i | \(0.212082\pi\) | ||||
−0.786128 | + | 0.618063i | \(0.787918\pi\) | |||||||
\(30\) | 147.627i | 0.164030i | ||||||||
\(31\) | 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 | ||||||||
\(35\) | 144.520i | 0.117976i | ||||||||
\(36\) | −554.064 | −0.427518 | ||||||||
\(37\) | −1400.64 | −1.02311 | −0.511554 | − | 0.859251i | \(-0.670930\pi\) | ||||
−0.511554 | + | 0.859251i | \(0.670930\pi\) | |||||||
\(38\) | −35.6172 | −0.0246656 | ||||||||
\(39\) | − | 4006.14i | − | 2.63388i | ||||||
\(40\) | − | 96.3470i | − | 0.0602169i | ||||||
\(41\) | 2563.10i | 1.52475i | 0.647138 | + | 0.762373i | \(0.275966\pi\) | ||||
−0.647138 | + | 0.762373i | \(0.724034\pi\) | |||||||
\(42\) | −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 | ||||
\(45\) | 294.899 | 0.145629 | ||||||||
\(46\) | 522.243i | 0.246807i | ||||||||
\(47\) | 3021.08 | 1.36763 | 0.683813 | − | 0.729658i | \(-0.260321\pi\) | ||||
0.683813 | + | 0.729658i | \(0.260321\pi\) | |||||||
\(48\) | 784.510 | 0.340499 | ||||||||
\(49\) | 1249.00 | 0.520200 | ||||||||
\(50\) | − | 1716.49i | − | 0.686595i | ||||||
\(51\) | 3435.73i | 1.32093i | ||||||||
\(52\) | 2614.55i | 0.966919i | ||||||||
\(53\) | −260.724 | −0.0928173 | −0.0464087 | − | 0.998923i | \(-0.514778\pi\) | ||||
−0.0464087 | + | 0.998923i | \(0.514778\pi\) | |||||||
\(54\) | − | 407.105i | − | 0.139611i | ||||||
\(55\) | −391.870 | − | 334.492i | −0.129544 | − | 0.110576i | ||||
\(56\) | 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 | \(0.486599\pi\) | |||||||
\(60\) | −417.553 | −0.115987 | ||||||||
\(61\) | − | 3593.92i | − | 0.965849i | −0.875662 | − | 0.482924i | \(-0.839575\pi\) | ||
0.875662 | − | 0.482924i | \(-0.160425\pi\) | |||||||
\(62\) | 4221.46i | 1.09820i | ||||||||
\(63\) | 2350.69i | 0.592263i | ||||||||
\(64\) | −512.000 | −0.125000 | ||||||||
\(65\) | − | 1391.59i | − | 0.329370i | ||||||
\(66\) | 2723.62 | − | 3190.82i | 0.625256 | − | 0.732511i | ||||
\(67\) | −2359.87 | −0.525701 | −0.262850 | − | 0.964837i | \(-0.584663\pi\) | ||||
−0.262850 | + | 0.964837i | \(0.584663\pi\) | |||||||
\(68\) | − | 2242.28i | − | 0.484922i | ||||||
\(69\) | 2263.32 | 0.475388 | ||||||||
\(70\) | −408.766 | −0.0834216 | ||||||||
\(71\) | −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 | ||||||
\(75\) | −7438.99 | −1.32249 | ||||||||
\(76\) | − | 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 | \(-0.716924\pi\) | ||
0.629949 | − | 0.776637i | \(-0.283076\pi\) | |||||||
\(80\) | 272.510 | 0.0425798 | ||||||||
\(81\) | −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 | ||||||
\(85\) | 1193.45i | 0.165183i | ||||||||
\(86\) | 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 | \(0.705122\pi\) | |||||||
\(90\) | 834.100i | 0.102975i | ||||||||
\(91\) | 11092.6 | 1.33952 | ||||||||
\(92\) | −1477.13 | −0.174519 | ||||||||
\(93\) | 18295.2 | 2.11530 | ||||||||
\(94\) | 8544.92i | 0.967057i | ||||||||
\(95\) | 53.6188i | 0.00594115i | ||||||||
\(96\) | 2218.93i | 0.240769i | ||||||||
\(97\) | 6401.66 | 0.680376 | 0.340188 | − | 0.940357i | \(-0.389509\pi\) | ||||
0.340188 | + | 0.940357i | \(0.389509\pi\) | |||||||
\(98\) | 3532.71i | 0.367837i | ||||||||
\(99\) | −6373.94 | − | 5440.67i | −0.650336 | − | 0.555113i | ||||
\(100\) | 4854.96 | 0.485496 | ||||||||
\(101\) | 15.9343i | 0.00156203i | 1.00000 | 0.000781015i | \(0.000248605\pi\) | |||||
−1.00000 | 0.000781015i | \(0.999751\pi\) | ||||||||
\(102\) | −9717.70 | −0.934035 | ||||||||
\(103\) | 12891.5 | 1.21514 | 0.607572 | − | 0.794265i | \(-0.292144\pi\) | ||||
0.607572 | + | 0.794265i | \(0.292144\pi\) | |||||||
\(104\) | −7395.06 | −0.683715 | ||||||||
\(105\) | 1771.53i | 0.160683i | ||||||||
\(106\) | − | 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 | \(-0.883980\pi\) | ||
0.934307 | − | 0.356470i | \(-0.116020\pi\) | |||||||
\(110\) | 946.086 | − | 1108.37i | 0.0781889 | − | 0.0916012i | ||||
\(111\) | −17169.0 | −1.39347 | ||||||||
\(112\) | 2172.23i | 0.173169i | ||||||||
\(113\) | −1009.87 | −0.0790874 | −0.0395437 | − | 0.999218i | \(-0.512590\pi\) | ||||
−0.0395437 | + | 0.999218i | \(0.512590\pi\) | |||||||
\(114\) | −436.594 | −0.0335945 | ||||||||
\(115\) | 786.196 | 0.0594477 | ||||||||
\(116\) | − | 8316.66i | − | 0.618063i | ||||||
\(117\) | − | 22634.8i | − | 1.65350i | ||||||
\(118\) | 828.796i | 0.0595228i | ||||||||
\(119\) | −9513.19 | −0.671788 | ||||||||
\(120\) | − | 1181.02i | − | 0.0820152i | ||||||
\(121\) | 2298.74 | + | 14459.4i | 0.157007 | + | 0.987597i | ||||
\(122\) | 10165.1 | 0.682958 | ||||||||
\(123\) | 31418.4i | 2.07670i | ||||||||
\(124\) | −11940.1 | −0.776542 | ||||||||
\(125\) | −5245.27 | −0.335697 | ||||||||
\(126\) | −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 | ||||||
\(130\) | 3936.00 | 0.232899 | ||||||||
\(131\) | − | 24418.3i | − | 1.42290i | −0.702738 | − | 0.711448i | \(-0.748040\pi\) | ||
0.702738 | − | 0.711448i | \(-0.251960\pi\) | |||||||
\(132\) | 9025.00 | + | 7703.55i | 0.517964 | + | 0.442123i | ||||
\(133\) | −427.406 | −0.0241622 | ||||||||
\(134\) | − | 6674.72i | − | 0.371726i | ||||||
\(135\) | −612.865 | −0.0336277 | ||||||||
\(136\) | 6342.13 | 0.342892 | ||||||||
\(137\) | −2895.91 | −0.154292 | −0.0771462 | − | 0.997020i | \(-0.524581\pi\) | ||||
−0.0771462 | + | 0.997020i | \(0.524581\pi\) | |||||||
\(138\) | 6401.64i | 0.336150i | ||||||||
\(139\) | − | 14602.9i | − | 0.755807i | −0.925845 | − | 0.377903i | \(-0.876645\pi\) | ||
0.925845 | − | 0.377903i | \(-0.123355\pi\) | |||||||
\(140\) | − | 1156.16i | − | 0.0589880i | ||||||
\(141\) | 37032.4 | 1.86270 | ||||||||
\(142\) | − | 7054.21i | − | 0.349842i | ||||||
\(143\) | −25673.7 | + | 30077.7i | −1.25550 | + | 1.47087i | ||||
\(144\) | 4432.51 | 0.213759 | ||||||||
\(145\) | 4426.52i | 0.210536i | ||||||||
\(146\) | −12675.1 | −0.594627 | ||||||||
\(147\) | 15310.2 | 0.708511 | ||||||||
\(148\) | 11205.1 | 0.511554 | ||||||||
\(149\) | 9469.08i | 0.426516i | 0.976996 | + | 0.213258i | \(0.0684075\pi\) | ||||
−0.976996 | + | 0.213258i | \(0.931593\pi\) | |||||||
\(150\) | − | 21040.7i | − | 0.935140i | ||||||
\(151\) | 15335.9i | 0.672597i | 0.941755 | + | 0.336298i | \(0.109175\pi\) | ||||
−0.941755 | + | 0.336298i | \(0.890825\pi\) | |||||||
\(152\) | 284.937 | 0.0123328 | ||||||||
\(153\) | 19412.0i | 0.829253i | ||||||||
\(154\) | 8835.06 | + | 7541.43i | 0.372536 | + | 0.317989i | ||||
\(155\) | 6355.09 | 0.264520 | ||||||||
\(156\) | 32049.1i | 1.31694i | ||||||||
\(157\) | −4810.17 | −0.195147 | −0.0975733 | − | 0.995228i | \(-0.531108\pi\) | ||||
−0.0975733 | + | 0.995228i | \(0.531108\pi\) | |||||||
\(158\) | 27418.7 | 1.09833 | ||||||||
\(159\) | −3195.95 | −0.126417 | ||||||||
\(160\) | 770.776i | 0.0301084i | ||||||||
\(161\) | 6266.92i | 0.241770i | ||||||||
\(162\) | − | 20857.5i | − | 0.794752i | ||||||
\(163\) | −9875.98 | −0.371711 | −0.185855 | − | 0.982577i | \(-0.559506\pi\) | ||||
−0.185855 | + | 0.982577i | \(0.559506\pi\) | |||||||
\(164\) | − | 20504.8i | − | 0.762373i | ||||||
\(165\) | −4803.53 | − | 4100.19i | −0.176438 | − | 0.150604i | ||||
\(166\) | −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 | ||||||||
\(170\) | −3375.58 | −0.116802 | ||||||||
\(171\) | 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 | ||||||||
\(175\) | − | 20597.8i | − | 0.672582i | ||||||
\(176\) | −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 | \(0.181523\pi\) | |||||||
\(180\) | −2359.19 | −0.0728145 | ||||||||
\(181\) | 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 | ||||||
\(185\) | −5963.87 | −0.174255 | ||||||||
\(186\) | 51746.6i | 1.49574i | ||||||||
\(187\) | 22018.2 | − | 25795.2i | 0.629650 | − | 0.737658i | ||||
\(188\) | −24168.7 | −0.683813 | ||||||||
\(189\) | − | 4885.26i | − | 0.136762i | ||||||
\(190\) | −151.657 | −0.00420102 | ||||||||
\(191\) | 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 | ||||||||
\(195\) | − | 17058.0i | − | 0.448600i | ||||||
\(196\) | −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 | \(0.423280\pi\) | |||||||
\(200\) | 13731.9i | 0.343297i | ||||||||
\(201\) | −28927.2 | −0.716003 | ||||||||
\(202\) | −45.0689 | −0.00110452 | ||||||||
\(203\) | −35284.6 | −0.856235 | ||||||||
\(204\) | − | 27485.8i | − | 0.660463i | ||||||
\(205\) | 10913.6i | 0.259693i | ||||||||
\(206\) | 36462.6i | 0.859237i | ||||||||
\(207\) | 12787.8 | 0.298440 | ||||||||
\(208\) | − | 20916.4i | − | 0.483460i | ||||||
\(209\) | 989.228 | − | 1158.92i | 0.0226466 | − | 0.0265314i | ||||
\(210\) | −5010.64 | −0.113620 | ||||||||
\(211\) | − | 30974.3i | − | 0.695723i | −0.937546 | − | 0.347862i | \(-0.886908\pi\) | ||
0.937546 | − | 0.347862i | \(-0.113092\pi\) | |||||||
\(212\) | 2085.79 | 0.0464087 | ||||||||
\(213\) | −30571.9 | −0.673849 | ||||||||
\(214\) | 30563.6 | 0.667386 | ||||||||
\(215\) | − | 3708.52i | − | 0.0802277i | ||||||
\(216\) | 3256.84i | 0.0698054i | ||||||||
\(217\) | 50657.6i | 1.07578i | ||||||||
\(218\) | 23958.0 | 0.504124 | ||||||||
\(219\) | 54931.8i | 1.14534i | ||||||||
\(220\) | 3134.96 | + | 2675.93i | 0.0647718 | + | 0.0552879i | ||||
\(221\) | 91602.4 | 1.87552 | ||||||||
\(222\) | − | 48561.1i | − | 0.985333i | ||||||
\(223\) | −19890.6 | −0.399980 | −0.199990 | − | 0.979798i | \(-0.564091\pi\) | ||||
−0.199990 | + | 0.979798i | \(0.564091\pi\) | |||||||
\(224\) | −6144.00 | −0.122449 | ||||||||
\(225\) | −42030.6 | −0.830233 | ||||||||
\(226\) | − | 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 | \(0.679574\pi\) | |||||||
\(230\) | 2223.70i | 0.0420359i | ||||||||
\(231\) | 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 | ||||||||
\(235\) | 12863.7 | 0.232933 | ||||||||
\(236\) | −2344.19 | −0.0420890 | ||||||||
\(237\) | − | 118829.i | − | 2.11555i | ||||||
\(238\) | − | 26907.4i | − | 0.475026i | ||||||
\(239\) | 8629.71i | 0.151078i | 0.997143 | + | 0.0755388i | \(0.0240677\pi\) | ||||
−0.997143 | + | 0.0755388i | \(0.975932\pi\) | |||||||
\(240\) | 3340.43 | 0.0579935 | ||||||||
\(241\) | − | 101396.i | − | 1.74577i | −0.487924 | − | 0.872886i | \(-0.662246\pi\) | ||
0.487924 | − | 0.872886i | \(-0.337754\pi\) | |||||||
\(242\) | −40897.4 | + | 6501.83i | −0.698337 | + | 0.111021i | ||||
\(243\) | −78734.5 | −1.33338 | ||||||||
\(244\) | 28751.4i | 0.482924i | ||||||||
\(245\) | 5318.21 | 0.0886000 | ||||||||
\(246\) | −88864.6 | −1.46845 | ||||||||
\(247\) | 4115.49 | 0.0674570 | ||||||||
\(248\) | − | 33771.7i | − | 0.549098i | ||||||
\(249\) | 76465.1i | 1.23329i | ||||||||
\(250\) | − | 14835.9i | − | 0.237374i | ||||||
\(251\) | −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 | ||||||||
\(255\) | 14629.2i | 0.224979i | ||||||||
\(256\) | 4096.00 | 0.0625000 | ||||||||
\(257\) | 56962.9 | 0.862434 | 0.431217 | − | 0.902248i | \(-0.358084\pi\) | ||||
0.431217 | + | 0.902248i | \(0.358084\pi\) | |||||||
\(258\) | 30196.9 | 0.453651 | ||||||||
\(259\) | − | 47539.1i | − | 0.708683i | ||||||
\(260\) | 11132.7i | 0.164685i | ||||||||
\(261\) | 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 | ||||
\(265\) | −1110.16 | −0.0158086 | ||||||||
\(266\) | − | 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 | \(0.445111\pi\) | |||||||
\(270\) | − | 1733.44i | − | 0.0237784i | ||||||
\(271\) | 65976.9i | 0.898367i | 0.893440 | + | 0.449183i | \(0.148285\pi\) | ||||
−0.893440 | + | 0.449183i | \(0.851715\pi\) | |||||||
\(272\) | 17938.2i | 0.242461i | ||||||||
\(273\) | 135973. | 1.82443 | ||||||||
\(274\) | − | 8190.88i | − | 0.109101i | ||||||
\(275\) | 55851.4 | + | 47673.6i | 0.738530 | + | 0.630394i | ||||
\(276\) | −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 | ||||||||
\(280\) | 3270.13 | 0.0417108 | ||||||||
\(281\) | − | 130542.i | − | 1.65325i | −0.562753 | − | 0.826625i | \(-0.690258\pi\) | ||
0.562753 | − | 0.826625i | \(-0.309742\pi\) | |||||||
\(282\) | 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 | ||||||||
\(285\) | 657.258i | 0.00809182i | ||||||||
\(286\) | −85072.7 | − | 72616.3i | −1.04006 | − | 0.887773i | ||||
\(287\) | −86994.4 | −1.05615 | ||||||||
\(288\) | 12537.0i | 0.151151i | ||||||||
\(289\) | 4961.32 | 0.0594020 | ||||||||
\(290\) | −12520.1 | −0.148871 | ||||||||
\(291\) | 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 | ||||||||
\(295\) | 1247.69 | 0.0143371 | ||||||||
\(296\) | 31692.8i | 0.361723i | ||||||||
\(297\) | 13246.5 | + | 11306.9i | 0.150171 | + | 0.128183i | ||||
\(298\) | −26782.6 | −0.301592 | ||||||||
\(299\) | − | 60344.1i | − | 0.674982i | ||||||
\(300\) | 59511.9 | 0.661244 | ||||||||
\(301\) | 29561.3 | 0.326281 | ||||||||
\(302\) | −43376.4 | −0.475598 | ||||||||
\(303\) | 195.322i | 0.00212748i | ||||||||
\(304\) | 805.924i | 0.00872061i | ||||||||
\(305\) | − | 15302.8i | − | 0.164502i | ||||||
\(306\) | −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 | ||||||||
\(310\) | 17974.9i | 0.187044i | ||||||||
\(311\) | −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 | \(-0.826930\pi\) | ||||
−0.855793 | + | 0.517318i | \(0.826930\pi\) | |||||||
\(314\) | − | 13605.2i | − | 0.137989i | ||||||
\(315\) | 10009.2i | 0.100874i | ||||||||
\(316\) | 77551.9i | 0.776637i | ||||||||
\(317\) | −43569.8 | −0.433577 | −0.216789 | − | 0.976219i | \(-0.569558\pi\) | ||||
−0.216789 | + | 0.976219i | \(0.569558\pi\) | |||||||
\(318\) | − | 9039.50i | − | 0.0893903i | ||||||
\(319\) | 81666.0 | − | 95674.7i | 0.802527 | − | 0.940191i | ||||
\(320\) | −2180.08 | −0.0212899 | ||||||||
\(321\) | − | 132458.i | − | 1.28549i | ||||||
\(322\) | −17725.5 | −0.170957 | ||||||||
\(323\) | −3529.51 | −0.0338305 | ||||||||
\(324\) | 58993.8 | 0.561974 | ||||||||
\(325\) | 198336.i | 1.87774i | ||||||||
\(326\) | − | 27933.5i | − | 0.262839i | ||||||
\(327\) | − | 103830.i | − | 0.971021i | ||||||
\(328\) | 57996.3 | 0.539079 | ||||||||
\(329\) | 102539.i | 0.947321i | ||||||||
\(330\) | 11597.1 | − | 13586.4i | 0.106493 | − | 0.124761i | ||||
\(331\) | −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 | ||||||||
\(335\) | −10048.3 | −0.0895368 | ||||||||
\(336\) | 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 | ||||||||
\(340\) | − | 9547.57i | − | 0.0825915i | ||||||
\(341\) | −137359. | − | 117247.i | −1.18127 | − | 1.00830i | ||||
\(342\) | −2466.77 | −0.0210900 | ||||||||
\(343\) | 123885.i | 1.05301i | ||||||||
\(344\) | −19707.6 | −0.166539 | ||||||||
\(345\) | 9637.17 | 0.0809676 | ||||||||
\(346\) | 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 | \(0.0219516\pi\) | ||||
−0.997623 | + | 0.0689083i | \(0.978048\pi\) | |||||||
\(350\) | 58259.5 | 0.475588 | ||||||||
\(351\) | 47040.1i | 0.381816i | ||||||||
\(352\) | 14220.3 | − | 16659.6i | 0.114768 | − | 0.134455i | ||||
\(353\) | 116711. | 0.936618 | 0.468309 | − | 0.883565i | \(-0.344863\pi\) | ||||
0.468309 | + | 0.883565i | \(0.344863\pi\) | |||||||
\(354\) | 10159.4i | 0.0810700i | ||||||||
\(355\) | −10619.6 | −0.0842655 | ||||||||
\(356\) | 76133.8 | 0.600727 | ||||||||
\(357\) | −116612. | −0.914973 | ||||||||
\(358\) | 152569.i | 1.19042i | ||||||||
\(359\) | 35393.9i | 0.274625i | 0.990528 | + | 0.137312i | \(0.0438464\pi\) | ||||
−0.990528 | + | 0.137312i | \(0.956154\pi\) | |||||||
\(360\) | − | 6672.80i | − | 0.0514876i | ||||||
\(361\) | 130162. | 0.998783 | ||||||||
\(362\) | 66127.5i | 0.504621i | ||||||||
\(363\) | 28177.9 | + | 177243.i | 0.213843 | + | 1.34511i | ||||
\(364\) | −88740.8 | −0.669762 | ||||||||
\(365\) | 19081.3i | 0.143226i | ||||||||
\(366\) | 124604. | 0.930187 | ||||||||
\(367\) | −91892.5 | −0.682257 | −0.341128 | − | 0.940017i | \(-0.610809\pi\) | ||||
−0.341128 | + | 0.940017i | \(0.610809\pi\) | |||||||
\(368\) | 11817.0 | 0.0872594 | ||||||||
\(369\) | 177515.i | 1.30371i | ||||||||
\(370\) | − | 16868.4i | − | 0.123217i | ||||||
\(371\) | − | 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 | ||||
\(375\) | −64296.4 | −0.457219 | ||||||||
\(376\) | − | 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 | \(0.227419\pi\) | |||||||
\(380\) | − | 428.951i | − | 0.00297057i | ||||||
\(381\) | 96336.5i | 0.663653i | ||||||||
\(382\) | 131837.i | 0.903462i | ||||||||
\(383\) | −199025. | −1.35678 | −0.678390 | − | 0.734702i | \(-0.737322\pi\) | ||||
−0.678390 | + | 0.734702i | \(0.737322\pi\) | |||||||
\(384\) | − | 17751.4i | − | 0.120385i | ||||||
\(385\) | 11353.0 | − | 13300.5i | 0.0765932 | − | 0.0897318i | ||||
\(386\) | −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 | \(0.654734\pi\) | |||||||
\(390\) | 48247.4 | 0.317208 | ||||||||
\(391\) | 51752.1i | 0.338512i | ||||||||
\(392\) | − | 28261.6i | − | 0.183918i | ||||||
\(393\) | − | 299319.i | − | 1.93798i | ||||||
\(394\) | −112501. | −0.724710 | ||||||||
\(395\) | − | 41276.7i | − | 0.264552i | ||||||
\(396\) | 50991.5 | + | 43525.3i | 0.325168 | + | 0.277557i | ||||
\(397\) | 109000. | 0.691585 | 0.345793 | − | 0.938311i | \(-0.387610\pi\) | ||||
0.345793 | + | 0.938311i | \(0.387610\pi\) | |||||||
\(398\) | 53472.1i | 0.337568i | ||||||||
\(399\) | −5239.13 | −0.0329089 | ||||||||
\(400\) | −38839.7 | −0.242748 | ||||||||
\(401\) | −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 | ||||||
\(405\) | −31399.3 | −0.191430 | ||||||||
\(406\) | − | 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 | \(0.129818\pi\) | ||||
−0.917982 | + | 0.396622i | \(0.870182\pi\) | |||||||
\(410\) | −30868.3 | −0.183631 | ||||||||
\(411\) | −35498.0 | −0.210146 | ||||||||
\(412\) | −103132. | −0.607572 | ||||||||
\(413\) | 9945.55i | 0.0583081i | ||||||||
\(414\) | 36169.5i | 0.211029i | ||||||||
\(415\) | 26561.2i | 0.154224i | ||||||||
\(416\) | 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 | \(0.450036\pi\) | |||||||
\(420\) | − | 14172.2i | − | 0.0803414i | ||||||
\(421\) | 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 | ||||||||
\(425\) | − | 170096.i | − | 0.941710i | ||||||
\(426\) | − | 86470.3i | − | 0.476483i | ||||||
\(427\) | 121982. | 0.669020 | ||||||||
\(428\) | 86447.0i | 0.471913i | ||||||||
\(429\) | −314708. | + | 368692.i | −1.70999 | + | 2.00332i | ||||
\(430\) | 10489.3 | 0.0567295 | ||||||||
\(431\) | 157298.i | 0.846776i | 0.905949 | + | 0.423388i | \(0.139159\pi\) | ||||
−0.905949 | + | 0.423388i | \(0.860841\pi\) | |||||||
\(432\) | −9211.74 | −0.0493599 | ||||||||
\(433\) | −134223. | −0.715900 | −0.357950 | − | 0.933741i | \(-0.616524\pi\) | ||||
−0.357950 | + | 0.933741i | \(0.616524\pi\) | |||||||
\(434\) | −143281. | −0.760694 | ||||||||
\(435\) | 54260.1i | 0.286749i | ||||||||
\(436\) | 67763.4i | 0.356470i | ||||||||
\(437\) | 2325.10i | 0.0121753i | ||||||||
\(438\) | −155371. | −0.809880 | ||||||||
\(439\) | − | 304612.i | − | 1.58059i | −0.612729 | − | 0.790293i | \(-0.709928\pi\) | ||
0.612729 | − | 0.790293i | \(-0.290072\pi\) | |||||||
\(440\) | −7568.69 | + | 8867.00i | −0.0390945 | + | 0.0458006i | ||||
\(441\) | 86503.2 | 0.444790 | ||||||||
\(442\) | 259091.i | 1.32619i | ||||||||
\(443\) | −116115. | −0.591671 | −0.295835 | − | 0.955239i | \(-0.595598\pi\) | ||||
−0.295835 | + | 0.955239i | \(0.595598\pi\) | |||||||
\(444\) | 137352. | 0.696735 | ||||||||
\(445\) | −40522.0 | −0.204631 | ||||||||
\(446\) | − | 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 | \(0.373501\pi\) | |||||||
\(450\) | − | 118880.i | − | 0.587064i | ||||||
\(451\) | 201348. | − | 235887.i | 0.989906 | − | 1.15971i | ||||
\(452\) | 8078.94 | 0.0395437 | ||||||||
\(453\) | 187987.i | 0.916075i | ||||||||
\(454\) | −216456. | −1.05017 | ||||||||
\(455\) | 47232.0 | 0.228146 | ||||||||
\(456\) | 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 | ||||||
\(460\) | −6289.57 | −0.0297239 | ||||||||
\(461\) | 324927.i | 1.52892i | 0.644674 | + | 0.764458i | \(0.276993\pi\) | ||||
−0.644674 | + | 0.764458i | \(0.723007\pi\) | |||||||
\(462\) | 108300. | + | 92442.6i | 0.507393 | + | 0.433100i | ||||
\(463\) | −135116. | −0.630295 | −0.315147 | − | 0.949043i | \(-0.602054\pi\) | ||||
−0.315147 | + | 0.949043i | \(0.602054\pi\) | |||||||
\(464\) | 66533.3i | 0.309032i | ||||||||
\(465\) | 77900.5 | 0.360275 | ||||||||
\(466\) | −9484.83 | −0.0436775 | ||||||||
\(467\) | 217618. | 0.997840 | 0.498920 | − | 0.866648i | \(-0.333730\pi\) | ||||
0.498920 | + | 0.866648i | \(0.333730\pi\) | |||||||
\(468\) | 181078.i | 0.826751i | ||||||||
\(469\) | − | 80096.6i | − | 0.364140i | ||||||
\(470\) | 36384.1i | 0.164708i | ||||||||
\(471\) | −58962.9 | −0.265789 | ||||||||
\(472\) | − | 6630.37i | − | 0.0297614i | ||||||
\(473\) | −68419.6 | + | 80156.1i | −0.305814 | + | 0.358273i | ||||
\(474\) | 336098. | 1.49592 | ||||||||
\(475\) | − | 7642.05i | − | 0.0338706i | ||||||
\(476\) | 76105.5 | 0.335894 | ||||||||
\(477\) | −18057.2 | −0.0793622 | ||||||||
\(478\) | −24408.5 | −0.106828 | ||||||||
\(479\) | − | 2332.66i | − | 0.0101667i | −0.999987 | − | 0.00508335i | \(-0.998382\pi\) | ||
0.999987 | − | 0.00508335i | \(-0.00161809\pi\) | |||||||
\(480\) | 9448.15i | 0.0410076i | ||||||||
\(481\) | 457754.i | 1.97853i | ||||||||
\(482\) | 286792. | 1.23445 | ||||||||
\(483\) | 76819.7i | 0.329290i | ||||||||
\(484\) | −18389.9 | − | 115675.i | −0.0785036 | − | 0.493799i | ||||
\(485\) | 27258.1 | 0.115881 | ||||||||
\(486\) | − | 222695.i | − | 0.942839i | ||||||
\(487\) | 307695. | 1.29737 | 0.648683 | − | 0.761059i | \(-0.275320\pi\) | ||||
0.648683 | + | 0.761059i | \(0.275320\pi\) | |||||||
\(488\) | −81321.2 | −0.341479 | ||||||||
\(489\) | −121060. | −0.506269 | ||||||||
\(490\) | 15042.2i | 0.0626496i | ||||||||
\(491\) | 165203.i | 0.685258i | 0.939471 | + | 0.342629i | \(0.111317\pi\) | ||||
−0.939471 | + | 0.342629i | \(0.888683\pi\) | |||||||
\(492\) | − | 251347.i | − | 1.03835i | ||||||
\(493\) | −291379. | −1.19885 | ||||||||
\(494\) | 11640.4i | 0.0476993i | ||||||||
\(495\) | −27140.1 | − | 23166.2i | −0.110765 | − | 0.0945464i | ||||
\(496\) | 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 | \(0.316684\pi\) | |||||||
\(500\) | 41962.2 | 0.167849 | ||||||||
\(501\) | − | 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 | ||||||||
\(505\) | 67.8477i | 0.000266043i | ||||||||
\(506\) | 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 | \(0.647270\pi\) | |||||||
\(510\) | −41377.7 | −0.159084 | ||||||||
\(511\) | −152101. | −0.582491 | ||||||||
\(512\) | 11585.2i | 0.0441942i | ||||||||
\(513\) | − | 1812.49i | − | 0.00688718i | ||||||
\(514\) | 161116.i | 0.609833i | ||||||||
\(515\) | 54891.6 | 0.206962 | ||||||||
\(516\) | 85409.6i | 0.320780i | ||||||||
\(517\) | −278036. | − | 237326.i | −1.04021 | − | 0.887900i | ||||
\(518\) | 134461. | 0.501114 | ||||||||
\(519\) | − | 461686.i | − | 1.71400i | ||||||
\(520\) | −31488.0 | −0.116450 | ||||||||
\(521\) | −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 | ||||||||
\(525\) | − | 252488.i | − | 0.916056i | ||||||
\(526\) | 16972.6 | 0.0613446 | ||||||||
\(527\) | 418329.i | 1.50625i | ||||||||
\(528\) | −72200.0 | − | 61628.4i | −0.258982 | − | 0.221062i | ||||
\(529\) | −245749. | −0.878173 | ||||||||
\(530\) | − | 3139.99i | − | 0.0111783i | ||||||
\(531\) | 20294.2 | 0.0719753 | ||||||||
\(532\) | 3419.25 | 0.0120811 | ||||||||
\(533\) | 837668. | 2.94861 | ||||||||
\(534\) | − | 329952.i | − | 1.15709i | ||||||
\(535\) | − | 46011.1i | − | 0.160752i | ||||||
\(536\) | 53397.8i | 0.185863i | ||||||||
\(537\) | 661211. | 2.29293 | ||||||||
\(538\) | 70235.6i | 0.242657i | ||||||||
\(539\) | −114948. | − | 98117.1i | −0.395661 | − | 0.337728i | ||||
\(540\) | 4902.92 | 0.0168139 | ||||||||
\(541\) | − | 211511.i | − | 0.722669i | −0.932436 | − | 0.361334i | \(-0.882321\pi\) | ||
0.932436 | − | 0.361334i | \(-0.117679\pi\) | |||||||
\(542\) | −186611. | −0.635241 | ||||||||
\(543\) | 286587. | 0.971978 | ||||||||
\(544\) | −50737.0 | −0.171446 | ||||||||
\(545\) | − | 36066.9i | − | 0.121427i | ||||||
\(546\) | 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 | ||||||
\(550\) | −134841. | + | 157972.i | −0.445756 | + | 0.522220i | ||||
\(551\) | −13091.0 | −0.0431191 | ||||||||
\(552\) | − | 51213.1i | − | 0.168075i | ||||||
\(553\) | 329025. | 1.07592 | ||||||||
\(554\) | −89590.8 | −0.291907 | ||||||||
\(555\) | −73105.0 | −0.237335 | ||||||||
\(556\) | 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 | ||||||||
\(560\) | 9249.31i | 0.0294940i | ||||||||
\(561\) | 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 | ||||||||
\(565\) | −4299.99 | −0.0134701 | ||||||||
\(566\) | −218231. | −0.681215 | ||||||||
\(567\) | − | 250290.i | − | 0.778532i | ||||||
\(568\) | 56433.7i | 0.174921i | ||||||||
\(569\) | − | 393771.i | − | 1.21624i | −0.793845 | − | 0.608120i | \(-0.791924\pi\) | ||
0.793845 | − | 0.608120i | \(-0.208076\pi\) | |||||||
\(570\) | −1859.01 | −0.00572178 | ||||||||
\(571\) | − | 152076.i | − | 0.466431i | −0.972425 | − | 0.233215i | \(-0.925075\pi\) | ||
0.972425 | − | 0.233215i | \(-0.0749247\pi\) | |||||||
\(572\) | 205390. | − | 240622.i | 0.627751 | − | 0.735433i | ||||
\(573\) | 571361. | 1.74021 | ||||||||
\(574\) | − | 246057.i | − | 0.746814i | ||||||
\(575\) | −112053. | −0.338912 | ||||||||
\(576\) | −35460.1 | −0.106880 | ||||||||
\(577\) | −260379. | −0.782086 | −0.391043 | − | 0.920372i | \(-0.627886\pi\) | ||||
−0.391043 | + | 0.920372i | \(0.627886\pi\) | |||||||
\(578\) | 14032.7i | 0.0420036i | ||||||||
\(579\) | 705883.i | 2.10560i | ||||||||
\(580\) | − | 35412.1i | − | 0.105268i | ||||||
\(581\) | −211724. | −0.627218 | ||||||||
\(582\) | 221951.i | 0.655255i | ||||||||
\(583\) | 23994.9 | + | 20481.6i | 0.0705963 | + | 0.0602596i | ||||
\(584\) | 101401. | 0.297313 | ||||||||
\(585\) | − | 96378.4i | − | 0.281623i | ||||||
\(586\) | 208069. | 0.605916 | ||||||||
\(587\) | −197623. | −0.573538 | −0.286769 | − | 0.958000i | \(-0.592581\pi\) | ||||
−0.286769 | + | 0.958000i | \(0.592581\pi\) | |||||||
\(588\) | −122482. | −0.354255 | ||||||||
\(589\) | 18794.6i | 0.0541754i | ||||||||
\(590\) | 3528.99i | 0.0101379i | ||||||||
\(591\) | 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 | ||||
\(595\) | −40506.9 | −0.114418 | ||||||||
\(596\) | − | 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 | \(0.407940\pi\) | |||||||
\(600\) | 168325.i | 0.467570i | ||||||||
\(601\) | 140115.i | 0.387913i | 0.981010 | + | 0.193957i | \(0.0621321\pi\) | ||||
−0.981010 | + | 0.193957i | \(0.937868\pi\) | |||||||
\(602\) | 83612.1i | 0.230715i | ||||||||
\(603\) | −163440. | −0.449493 | ||||||||
\(604\) | − | 122687.i | − | 0.336298i | ||||||
\(605\) | 9787.99 | + | 61567.8i | 0.0267413 | + | 0.168207i | ||||
\(606\) | −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 | ||||||||
\(610\) | 43283.0 | 0.116321 | ||||||||
\(611\) | − | 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 | ||||||||
\(615\) | 133779.i | 0.353701i | ||||||||
\(616\) | −70680.5 | − | 60331.4i | −0.186268 | − | 0.158994i | ||||
\(617\) | −284417. | −0.747112 | −0.373556 | − | 0.927608i | \(-0.621862\pi\) | ||||
−0.373556 | + | 0.927608i | \(0.621862\pi\) | |||||||
\(618\) | 446957.i | 1.17028i | ||||||||
\(619\) | −231315. | −0.603702 | −0.301851 | − | 0.953355i | \(-0.597605\pi\) | ||||
−0.301851 | + | 0.953355i | \(0.597605\pi\) | |||||||
\(620\) | −50840.7 | −0.132260 | ||||||||
\(621\) | −26576.0 | −0.0689138 | ||||||||
\(622\) | − | 327957.i | − | 0.847688i | ||||||
\(623\) | − | 323008.i | − | 0.832219i | ||||||
\(624\) | − | 256393.i | − | 0.658471i | ||||||
\(625\) | 356959. | 0.913816 | ||||||||
\(626\) | − | 474278.i | − | 1.21027i | ||||||
\(627\) | 12125.9 | − | 14206.0i | 0.0308447 | − | 0.0361357i | ||||
\(628\) | 38481.3 | 0.0975733 | ||||||||
\(629\) | − | 392577.i | − | 0.992256i | ||||||
\(630\) | −28310.3 | −0.0713285 | ||||||||
\(631\) | 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 | ||||||
\(635\) | 33463.8i | 0.0829904i | ||||||||
\(636\) | 25567.6 | 0.0632085 | ||||||||
\(637\) | − | 408197.i | − | 1.00598i | ||||||
\(638\) | 270609. | + | 230986.i | 0.664815 | + | 0.567473i | ||||
\(639\) | −172732. | −0.423030 | ||||||||
\(640\) | − | 6166.21i | − | 0.0150542i | ||||||
\(641\) | −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 | \(-0.547065\pi\) | ||||
−0.147322 | + | 0.989089i | \(0.547065\pi\) | |||||||
\(644\) | − | 50135.3i | − | 0.120885i | ||||||
\(645\) | − | 45459.0i | − | 0.109270i | ||||||
\(646\) | − | 9982.95i | − | 0.0239218i | ||||||
\(647\) | −377550. | −0.901917 | −0.450958 | − | 0.892545i | \(-0.648918\pi\) | ||||
−0.450958 | + | 0.892545i | \(0.648918\pi\) | |||||||
\(648\) | 166860.i | 0.397376i | ||||||||
\(649\) | −26967.5 | − | 23018.9i | −0.0640253 | − | 0.0546507i | ||||
\(650\) | −560980. | −1.32776 | ||||||||
\(651\) | 620959.i | 1.46521i | ||||||||
\(652\) | 79007.8 | 0.185855 | ||||||||
\(653\) | −558170. | −1.30900 | −0.654501 | − | 0.756061i | \(-0.727121\pi\) | ||||
−0.654501 | + | 0.756061i | \(0.727121\pi\) | |||||||
\(654\) | 293677. | 0.686616 | ||||||||
\(655\) | − | 103973.i | − | 0.242346i | ||||||
\(656\) | 164038.i | 0.381186i | ||||||||
\(657\) | 310367.i | 0.719025i | ||||||||
\(658\) | −290024. | −0.669857 | ||||||||
\(659\) | − | 357653.i | − | 0.823551i | −0.911285 | − | 0.411776i | \(-0.864909\pi\) | ||
0.911285 | − | 0.411776i | \(-0.135091\pi\) | |||||||
\(660\) | 38428.2 | + | 32801.5i | 0.0882191 | + | 0.0753020i | ||||
\(661\) | 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 | ||||||||
\(665\) | −1819.88 | −0.00411529 | ||||||||
\(666\) | − | 274372.i | − | 0.618574i | ||||||
\(667\) | 191949.i | 0.431454i | ||||||||
\(668\) | 107498.i | 0.240906i | ||||||||
\(669\) | −243818. | −0.544771 | ||||||||
\(670\) | − | 28420.8i | − | 0.0633121i | ||||||
\(671\) | −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 | ||||||||
\(675\) | 87348.8 | 0.191712 | ||||||||
\(676\) | 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 | ||||||||
\(680\) | 27004.6 | 0.0584010 | ||||||||
\(681\) | 938089.i | 2.02279i | ||||||||
\(682\) | 331624. | − | 388509.i | 0.712979 | − | 0.835281i | ||||
\(683\) | 673707. | 1.44421 | 0.722103 | − | 0.691785i | \(-0.243175\pi\) | ||||
0.722103 | + | 0.691785i | \(0.243175\pi\) | |||||||
\(684\) | − | 6977.08i | − | 0.0149129i | ||||||
\(685\) | −12330.7 | −0.0262789 | ||||||||
\(686\) | −350400. | −0.744588 | ||||||||
\(687\) | −687426. | −1.45651 | ||||||||
\(688\) | − | 55741.4i | − | 0.117761i | ||||||
\(689\) | 85209.4i | 0.179494i | ||||||||
\(690\) | 27258.0i | 0.0572528i | ||||||||
\(691\) | 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 | ||||||||
\(695\) | − | 62179.0i | − | 0.128728i | ||||||
\(696\) | 288345. | 0.595243 | ||||||||
\(697\) | −718397. | −1.47877 | ||||||||
\(698\) | −47478.5 | −0.0974510 | ||||||||
\(699\) | 41105.8i | 0.0841297i | ||||||||
\(700\) | 164783.i | 0.336291i | ||||||||
\(701\) | − | 439863.i | − | 0.895121i | −0.894254 | − | 0.447560i | \(-0.852293\pi\) | ||
0.894254 | − | 0.447560i | \(-0.147707\pi\) | |||||||
\(702\) | −133050. | −0.269985 | ||||||||
\(703\) | − | 17637.6i | − | 0.0356885i | ||||||
\(704\) | 47120.3 | + | 40220.9i | 0.0950743 | + | 0.0811534i | ||||
\(705\) | 157683. | 0.317254 | ||||||||
\(706\) | 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 | \(0.330089\pi\) | |||||||
\(710\) | − | 30036.6i | − | 0.0595847i | ||||||
\(711\) | − | 671386.i | − | 1.32811i | ||||||
\(712\) | 215339.i | 0.424778i | ||||||||
\(713\) | 275579. | 0.542084 | ||||||||
\(714\) | − | 329830.i | − | 0.646984i | ||||||
\(715\) | −109318. | + | 128070.i | −0.213836 | + | 0.250517i | ||||
\(716\) | −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 | \(0.270006\pi\) | |||||||
\(720\) | 18873.5 | 0.0364073 | ||||||||
\(721\) | 437551.i | 0.841701i | ||||||||
\(722\) | 368155.i | 0.706246i | ||||||||
\(723\) | − | 1.24291e6i | − | 2.37774i | ||||||
\(724\) | −187037. | −0.356821 | ||||||||
\(725\) | − | 630891.i | − | 1.20027i | ||||||
\(726\) | −501319. | + | 79699.2i | −0.951133 | + | 0.151210i | ||||
\(727\) | 258952. | 0.489949 | 0.244974 | − | 0.969530i | \(-0.421220\pi\) | ||||
0.244974 | + | 0.969530i | \(0.421220\pi\) | |||||||
\(728\) | − | 250997.i | − | 0.473593i | ||||||
\(729\) | −367813. | −0.692105 | ||||||||
\(730\) | −53970.1 | −0.101276 | ||||||||
\(731\) | 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 | ||||||
\(735\) | 65190.5 | 0.120673 | ||||||||
\(736\) | 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 | \(-0.755594\pi\) | ||
0.719424 | − | 0.694571i | \(-0.244406\pi\) | |||||||
\(740\) | 47711.0 | 0.0871274 | ||||||||
\(741\) | 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 | ||||||
\(745\) | 40319.1i | 0.0726438i | ||||||||
\(746\) | 100275. | 0.180183 | ||||||||
\(747\) | 432030.i | 0.774236i | ||||||||
\(748\) | −176146. | + | 206361.i | −0.314825 | + | 0.368829i | ||||
\(749\) | 366763. | 0.653766 | ||||||||
\(750\) | − | 181858.i | − | 0.323303i | ||||||
\(751\) | −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 | ||||||||
\(755\) | 65299.8i | 0.114556i | ||||||||
\(756\) | 39082.1i | 0.0683808i | ||||||||
\(757\) | 801567. | 1.39877 | 0.699387 | − | 0.714743i | \(-0.253456\pi\) | ||||
0.699387 | + | 0.714743i | \(0.253456\pi\) | |||||||
\(758\) | 613845.i | 1.06837i | ||||||||
\(759\) | −208298. | − | 177799.i | −0.361577 | − | 0.308635i | ||||
\(760\) | 1213.26 | 0.00210051 | ||||||||
\(761\) | − | 6823.03i | − | 0.0117817i | −0.999983 | − | 0.00589085i | \(-0.998125\pi\) | ||
0.999983 | − | 0.00589085i | \(-0.00187513\pi\) | |||||||
\(762\) | −272481. | −0.469273 | ||||||||
\(763\) | 287496. | 0.493836 | ||||||||
\(764\) | −372891. | −0.638844 | ||||||||
\(765\) | 82655.7i | 0.141237i | ||||||||
\(766\) | − | 562927.i | − | 0.959389i | ||||||
\(767\) | − | 95765.6i | − | 0.162787i | ||||||
\(768\) | 50208.7 | 0.0851248 | ||||||||
\(769\) | − | 375862.i | − | 0.635588i | −0.948160 | − | 0.317794i | \(-0.897058\pi\) | ||
0.948160 | − | 0.317794i | \(-0.102942\pi\) | |||||||
\(770\) | 37619.5 | + | 32111.2i | 0.0634500 | + | 0.0541596i | ||||
\(771\) | 698250. | 1.17463 | ||||||||
\(772\) | − | 460685.i | − | 0.772982i | ||||||
\(773\) | −857421. | −1.43494 | −0.717472 | − | 0.696587i | \(-0.754701\pi\) | ||||
−0.717472 | + | 0.696587i | \(0.754701\pi\) | |||||||
\(774\) | 170613. | 0.284794 | ||||||||
\(775\) | −905761. | −1.50803 | ||||||||
\(776\) | − | 144853.i | − | 0.240549i | ||||||
\(777\) | − | 582734.i | − | 0.965224i | ||||||
\(778\) | − | 399915.i | − | 0.660707i | ||||||
\(779\) | −32276.0 | −0.0531868 | ||||||||
\(780\) | 136464.i | 0.224300i | ||||||||
\(781\) | 229531. | + | 195923.i | 0.376305 | + | 0.321206i | ||||
\(782\) | −146377. | −0.239364 | ||||||||
\(783\) | − | 149631.i | − | 0.244060i | ||||||
\(784\) | 79936.0 | 0.130050 | ||||||||
\(785\) | −20481.6 | −0.0332372 | ||||||||
\(786\) | 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 | ||||||
\(790\) | 116748. | 0.187067 | ||||||||
\(791\) | − | 34276.0i | − | 0.0547820i | ||||||
\(792\) | −123108. | + | 144226.i | −0.196262 | + | 0.229929i | ||||
\(793\) | −1.17456e6 | −1.86780 | ||||||||
\(794\) | 308299.i | 0.489024i | ||||||||
\(795\) | −13608.3 | −0.0215312 | ||||||||
\(796\) | −151242. | −0.238697 | ||||||||
\(797\) | 865636. | 1.36276 | 0.681379 | − | 0.731931i | \(-0.261381\pi\) | ||||
0.681379 | + | 0.731931i | \(0.261381\pi\) | |||||||
\(798\) | − | 14818.5i | − | 0.0232701i | ||||||
\(799\) | 846765.i | 1.32638i | ||||||||
\(800\) | − | 109855.i | − | 0.171649i | ||||||
\(801\) | −659109. | −1.02729 | ||||||||
\(802\) | − | 742755.i | − | 1.15477i | ||||||
\(803\) | 352036. | − | 412424.i | 0.545954 | − | 0.639606i | ||||
\(804\) | 231418. | 0.358001 | ||||||||
\(805\) | 26684.4i | 0.0411780i | ||||||||
\(806\) | 1.37965e6 | 2.12373 | ||||||||
\(807\) | 304390. | 0.467395 | ||||||||
\(808\) | 360.551 | 0.000552261 | ||||||||
\(809\) | 886947.i | 1.35519i | 0.735435 | + | 0.677596i | \(0.236978\pi\) | ||||
−0.735435 | + | 0.677596i | \(0.763022\pi\) | |||||||
\(810\) | − | 88810.6i | − | 0.135361i | ||||||
\(811\) | − | 608105.i | − | 0.924563i | −0.886733 | − | 0.462282i | \(-0.847031\pi\) | ||
0.886733 | − | 0.462282i | \(-0.152969\pi\) | |||||||
\(812\) | 282277. | 0.428118 | ||||||||
\(813\) | 808744.i | 1.22357i | ||||||||
\(814\) | −311209. | + | 364593.i | −0.469682 | + | 0.550250i | ||||
\(815\) | −42051.7 | −0.0633094 | ||||||||
\(816\) | 219887.i | 0.330231i | ||||||||
\(817\) | 10967.6 | 0.0164312 | ||||||||
\(818\) | −375317. | −0.560908 | ||||||||
\(819\) | 768251. | 1.14534 | ||||||||
\(820\) | − | 87308.8i | − | 0.129847i | ||||||
\(821\) | 102607.i | 0.152227i | 0.997099 | + | 0.0761133i | \(0.0242511\pi\) | ||||
−0.997099 | + | 0.0761133i | \(0.975749\pi\) | |||||||
\(822\) | − | 100404.i | − | 0.148596i | ||||||
\(823\) | 338801. | 0.500202 | 0.250101 | − | 0.968220i | \(-0.419536\pi\) | ||||
0.250101 | + | 0.968220i | \(0.419536\pi\) | |||||||
\(824\) | − | 291701.i | − | 0.429618i | ||||||
\(825\) | 684625. | + | 584382.i | 1.00588 | + | 0.858595i | ||||
\(826\) | −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 | \(0.265361\pi\) | |||||||
\(830\) | −75126.4 | −0.109053 | ||||||||
\(831\) | 388273.i | 0.562258i | ||||||||
\(832\) | 167331.i | 0.241730i | ||||||||
\(833\) | 350076.i | 0.504513i | ||||||||
\(834\) | 506296. | 0.727901 | ||||||||
\(835\) | − | 57215.5i | − | 0.0820617i | ||||||
\(836\) | −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 | \(0.509965\pi\) | |||||||
\(840\) | 40085.1 | 0.0568100 | ||||||||
\(841\) | −373450. | −0.528009 | ||||||||
\(842\) | 57733.8i | 0.0814340i | ||||||||
\(843\) | − | 1.60018e6i | − | 2.25172i | ||||||
\(844\) | 247794.i | 0.347862i | ||||||||
\(845\) | −333184. | −0.466628 | ||||||||
\(846\) | 591804.i | 0.826869i | ||||||||
\(847\) | −490769. | + | 78021.9i | −0.684085 | + | 0.108755i | ||||
\(848\) | −16686.3 | −0.0232043 | ||||||||
\(849\) | 945782.i | 1.31213i | ||||||||
\(850\) | 481105. | 0.665890 | ||||||||
\(851\) | −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 | ||||||||
\(855\) | 3713.53i | 0.00507990i | ||||||||
\(856\) | −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 | \(0.605393\pi\) | |||||||
\(860\) | 29668.2i | 0.0401138i | ||||||||
\(861\) | −1.06637e6 | −1.43848 | ||||||||
\(862\) | −444906. | −0.598761 | ||||||||
\(863\) | −220319. | −0.295822 | −0.147911 | − | 0.989001i | \(-0.547255\pi\) | ||||
−0.147911 | + | 0.989001i | \(0.547255\pi\) | |||||||
\(864\) | − | 26054.7i | − | 0.0349027i | ||||||
\(865\) | − | 160373.i | − | 0.214338i | ||||||
\(866\) | − | 379641.i | − | 0.506218i | ||||||
\(867\) | 60815.7 | 0.0809054 | ||||||||
\(868\) | − | 405261.i | − | 0.537892i | ||||||
\(869\) | −761526. | + | 892156.i | −1.00843 | + | 1.18141i | ||||
\(870\) | −153471. | −0.202762 | ||||||||
\(871\) | 771250.i | 1.01662i | ||||||||
\(872\) | −191664. | −0.252062 | ||||||||
\(873\) | 443366. | 0.581747 | ||||||||
\(874\) | −6576.38 | −0.00860922 | ||||||||
\(875\) | − | 178030.i | − | 0.232530i | ||||||
\(876\) | − | 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 | ||||||
\(880\) | −25079.7 | − | 21407.5i | −0.0323859 | − | 0.0276440i | ||||
\(881\) | 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 | \(-0.527863\pi\) | ||||
−0.0874210 | + | 0.996171i | \(0.527863\pi\) | |||||||
\(884\) | −732819. | −0.937761 | ||||||||
\(885\) | 15294.1 | 0.0195271 | ||||||||
\(886\) | − | 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 | ||||||||
\(890\) | − | 114613.i | − | 0.144696i | ||||||
\(891\) | 678664. | + | 579294.i | 0.854869 | + | 0.729699i | ||||
\(892\) | 159125. | 0.199990 | ||||||||
\(893\) | 38043.2i | 0.0477061i | ||||||||
\(894\) | −328300. | −0.410768 | ||||||||
\(895\) | 229681. | 0.286734 | ||||||||
\(896\) | 49152.0 | 0.0612245 | ||||||||
\(897\) | − | 739696.i | − | 0.919324i | ||||||
\(898\) | 441379.i | 0.547342i | ||||||||
\(899\) | 1.55159e6i | 1.91981i | ||||||||
\(900\) | 336245. | 0.415117 | ||||||||
\(901\) | − | 73077.0i | − | 0.0900183i | ||||||
\(902\) | 667188. | + | 569498.i | 0.820040 | + | 0.699970i | ||||
\(903\) | 362362. | 0.444393 | ||||||||
\(904\) | 22850.7i | 0.0279616i | ||||||||
\(905\) | 99549.8 | 0.121547 | ||||||||
\(906\) | −531707. | −0.647763 | ||||||||
\(907\) | −945937. | −1.14987 | −0.574934 | − | 0.818200i | \(-0.694972\pi\) | ||||
−0.574934 | + | 0.818200i | \(0.694972\pi\) | |||||||
\(908\) | − | 612231.i | − | 0.742581i | ||||||
\(909\) | 1103.57i | 0.00133559i | ||||||||
\(910\) | 133592.i | 0.161324i | ||||||||
\(911\) | −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 | ||||||||
\(915\) | − | 187582.i | − | 0.224052i | ||||||
\(916\) | 448639. | 0.534695 | ||||||||
\(917\) | 828786. | 0.985607 | ||||||||
\(918\) | 114106. | 0.135401 | ||||||||
\(919\) | − | 809716.i | − | 0.958742i | −0.877612 | − | 0.479371i | \(-0.840865\pi\) | ||
0.877612 | − | 0.479371i | \(-0.159135\pi\) | |||||||
\(920\) | − | 17789.6i | − | 0.0210179i | ||||||
\(921\) | 173335.i | 0.204346i | ||||||||
\(922\) | −919032. | −1.08111 | ||||||||
\(923\) | 815099.i | 0.956768i | ||||||||
\(924\) | −261467. | + | 306319.i | −0.306248 | + | 0.358781i | ||||
\(925\) | 850003. | 0.993429 | ||||||||
\(926\) | − | 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 | \(0.360766\pi\) | |||||||
\(930\) | 220336.i | 0.254753i | ||||||||
\(931\) | 15728.1i | 0.0181458i | ||||||||
\(932\) | − | 26827.2i | − | 0.0308847i | ||||||
\(933\) | −1.42131e6 | −1.63278 | ||||||||
\(934\) | 615517.i | 0.705580i | ||||||||
\(935\) | 93753.0 | − | 109835.i | 0.107241 | − | 0.125637i | ||||
\(936\) | −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 | ||||||||
\(940\) | −102910. | −0.116466 | ||||||||
\(941\) | − | 77429.7i | − | 0.0874437i | −0.999044 | − | 0.0437218i | \(-0.986078\pi\) | ||
0.999044 | − | 0.0437218i | \(-0.0139215\pi\) | |||||||
\(942\) | − | 166772.i | − | 0.187941i | ||||||
\(943\) | 473252.i | 0.532193i | ||||||||
\(944\) | 18753.5 | 0.0210445 | ||||||||
\(945\) | − | 20801.3i | − | 0.0232931i | ||||||
\(946\) | −226716. | − | 193520.i | −0.253337 | − | 0.216243i | ||||
\(947\) | 362138. | 0.403807 | 0.201904 | − | 0.979405i | \(-0.435287\pi\) | ||||
0.201904 | + | 0.979405i | \(0.435287\pi\) | |||||||
\(948\) | 950629.i | 1.05778i | ||||||||
\(949\) | 1.46458e6 | 1.62622 | ||||||||
\(950\) | 21615.0 | 0.0239501 | ||||||||
\(951\) | −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 | ||||||
\(955\) | 198470. | 0.217615 | ||||||||
\(956\) | − | 69037.7i | − | 0.0755388i | ||||||
\(957\) | 1.00106e6 | − | 1.17278e6i | 1.09304 | − | 1.28054i | ||||
\(958\) | 6597.75 | 0.00718894 | ||||||||
\(959\) | − | 98290.6i | − | 0.106875i | ||||||
\(960\) | −26723.4 | −0.0289968 | ||||||||
\(961\) | 1.30407e6 | 1.41207 | ||||||||
\(962\) | −1.29472e6 | −1.39903 | ||||||||
\(963\) | − | 748393.i | − | 0.807006i | ||||||
\(964\) | 811170.i | 0.872886i | ||||||||
\(965\) | 245198.i | 0.263307i | ||||||||
\(966\) | −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 | ||||||||
\(970\) | 77097.6i | 0.0819403i | ||||||||
\(971\) | −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 | ||||||||
\(975\) | 2.43120e6i | 2.55748i | ||||||||
\(976\) | − | 230011.i | − | 0.241462i | ||||||
\(977\) | 4386.95 | 0.00459593 | 0.00229796 | − | 0.999997i | \(-0.499269\pi\) | ||||
0.00229796 | + | 0.999997i | \(0.499269\pi\) | |||||||
\(978\) | − | 342408.i | − | 0.357986i | ||||||
\(979\) | 875842. | + | 747600.i | 0.913819 | + | 0.780017i | ||||
\(980\) | −42545.7 | −0.0443000 | ||||||||
\(981\) | − | 586645.i | − | 0.609589i | ||||||
\(982\) | −467264. | −0.484551 | ||||||||
\(983\) | 147531. | 0.152678 | 0.0763388 | − | 0.997082i | \(-0.475677\pi\) | ||||
0.0763388 | + | 0.997082i | \(0.475677\pi\) | |||||||
\(984\) | 710917. | 0.734224 | ||||||||
\(985\) | 169362.i | 0.174559i | ||||||||
\(986\) | − | 824145.i | − | 0.847715i | ||||||
\(987\) | 1.25692e6i | 1.29025i | ||||||||
\(988\) | −32923.9 | −0.0337285 | ||||||||
\(989\) | − | 160815.i | − | 0.164412i | ||||||
\(990\) | 65524.0 | − | 76763.8i | 0.0668544 | − | 0.0783224i | ||||
\(991\) | 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 | ||||||||
\(995\) | 80498.1 | 0.0813092 | ||||||||
\(996\) | − | 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 | 22.5.b.a.21.4 | yes | 4 | |
3.2 | odd | 2 | 198.5.d.a.109.1 | 4 | |||
4.3 | odd | 2 | 176.5.h.e.65.1 | 4 | |||
5.2 | odd | 4 | 550.5.c.a.549.1 | 8 | |||
5.3 | odd | 4 | 550.5.c.a.549.8 | 8 | |||
5.4 | even | 2 | 550.5.d.a.351.1 | 4 | |||
8.3 | odd | 2 | 704.5.h.j.65.3 | 4 | |||
8.5 | even | 2 | 704.5.h.i.65.2 | 4 | |||
11.10 | odd | 2 | inner | 22.5.b.a.21.2 | ✓ | 4 | |
33.32 | even | 2 | 198.5.d.a.109.3 | 4 | |||
44.43 | even | 2 | 176.5.h.e.65.2 | 4 | |||
55.32 | even | 4 | 550.5.c.a.549.5 | 8 | |||
55.43 | even | 4 | 550.5.c.a.549.4 | 8 | |||
55.54 | odd | 2 | 550.5.d.a.351.3 | 4 | |||
88.21 | odd | 2 | 704.5.h.i.65.1 | 4 | |||
88.43 | even | 2 | 704.5.h.j.65.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
22.5.b.a.21.2 | ✓ | 4 | 11.10 | odd | 2 | inner | |
22.5.b.a.21.4 | yes | 4 | 1.1 | even | 1 | trivial | |
176.5.h.e.65.1 | 4 | 4.3 | odd | 2 | |||
176.5.h.e.65.2 | 4 | 44.43 | even | 2 | |||
198.5.d.a.109.1 | 4 | 3.2 | odd | 2 | |||
198.5.d.a.109.3 | 4 | 33.32 | even | 2 | |||
550.5.c.a.549.1 | 8 | 5.2 | odd | 4 | |||
550.5.c.a.549.4 | 8 | 55.43 | even | 4 | |||
550.5.c.a.549.5 | 8 | 55.32 | even | 4 | |||
550.5.c.a.549.8 | 8 | 5.3 | odd | 4 | |||
550.5.d.a.351.1 | 4 | 5.4 | even | 2 | |||
550.5.d.a.351.3 | 4 | 55.54 | odd | 2 | |||
704.5.h.i.65.1 | 4 | 88.21 | odd | 2 | |||
704.5.h.i.65.2 | 4 | 8.5 | even | 2 | |||
704.5.h.j.65.3 | 4 | 8.3 | odd | 2 | |||
704.5.h.j.65.4 | 4 | 88.43 | even | 2 |