Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [175,5,Mod(43,175)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(175, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("175.43");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 175 = 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 175.g (of order \(4\), degree \(2\), 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: | \(18.0897435397\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 57.15 | ||
Character | \(\chi\) | \(=\) | 175.57 |
Dual form | 175.5.g.d.43.15 |
$q$-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 \(\left(\mathbb{Z}/175\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.62285 | + | 4.62285i | 1.15571 | + | 1.15571i | 0.985388 | + | 0.170324i | \(0.0544814\pi\) |
0.170324 | + | 0.985388i | \(0.445519\pi\) | |||||||
\(3\) | −6.85998 | + | 6.85998i | −0.762220 | + | 0.762220i | −0.976723 | − | 0.214503i | \(-0.931187\pi\) |
0.214503 | + | 0.976723i | \(0.431187\pi\) | |||||||
\(4\) | 26.7415i | 1.67134i | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −63.4253 | −1.76181 | ||||||||
\(7\) | −13.0958 | − | 13.0958i | −0.267261 | − | 0.267261i | ||||
\(8\) | −49.6561 | + | 49.6561i | −0.775877 | + | 0.775877i | ||||
\(9\) | − | 13.1187i | − | 0.161959i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −172.486 | −1.42550 | −0.712752 | − | 0.701416i | \(-0.752551\pi\) | ||||
−0.712752 | + | 0.701416i | \(0.752551\pi\) | |||||||
\(12\) | −183.446 | − | 183.446i | −1.27393 | − | 1.27393i | ||||
\(13\) | −26.0429 | + | 26.0429i | −0.154100 | + | 0.154100i | −0.779946 | − | 0.625846i | \(-0.784754\pi\) |
0.625846 | + | 0.779946i | \(0.284754\pi\) | |||||||
\(14\) | − | 121.080i | − | 0.617754i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −31.2422 | −0.122040 | ||||||||
\(17\) | −294.876 | − | 294.876i | −1.02033 | − | 1.02033i | −0.999789 | − | 0.0205430i | \(-0.993460\pi\) |
−0.0205430 | − | 0.999789i | \(-0.506540\pi\) | |||||||
\(18\) | 60.6456 | − | 60.6456i | 0.187178 | − | 0.187178i | ||||
\(19\) | 223.155i | 0.618157i | 0.951037 | + | 0.309079i | \(0.100021\pi\) | ||||
−0.951037 | + | 0.309079i | \(0.899979\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 179.674 | 0.407424 | ||||||||
\(22\) | −797.376 | − | 797.376i | −1.64747 | − | 1.64747i | ||||
\(23\) | 337.468 | − | 337.468i | 0.637936 | − | 0.637936i | −0.312110 | − | 0.950046i | \(-0.601036\pi\) |
0.950046 | + | 0.312110i | \(0.101036\pi\) | |||||||
\(24\) | − | 681.280i | − | 1.18278i | ||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −240.785 | −0.356191 | ||||||||
\(27\) | −465.665 | − | 465.665i | −0.638772 | − | 0.638772i | ||||
\(28\) | 350.201 | − | 350.201i | 0.446685 | − | 0.446685i | ||||
\(29\) | 1228.04i | 1.46021i | 0.683336 | + | 0.730104i | \(0.260528\pi\) | ||||
−0.683336 | + | 0.730104i | \(0.739472\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1202.61 | 1.25142 | 0.625710 | − | 0.780056i | \(-0.284809\pi\) | ||||
0.625710 | + | 0.780056i | \(0.284809\pi\) | |||||||
\(32\) | 650.070 | + | 650.070i | 0.634834 | + | 0.634834i | ||||
\(33\) | 1183.25 | − | 1183.25i | 1.08655 | − | 1.08655i | ||||
\(34\) | − | 2726.33i | − | 2.35842i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 350.812 | 0.270688 | ||||||||
\(37\) | 481.756 | + | 481.756i | 0.351904 | + | 0.351904i | 0.860817 | − | 0.508914i | \(-0.169953\pi\) |
−0.508914 | + | 0.860817i | \(0.669953\pi\) | |||||||
\(38\) | −1031.61 | + | 1031.61i | −0.714412 | + | 0.714412i | ||||
\(39\) | − | 357.308i | − | 0.234916i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2145.36 | −1.27624 | −0.638120 | − | 0.769937i | \(-0.720287\pi\) | ||||
−0.638120 | + | 0.769937i | \(0.720287\pi\) | |||||||
\(42\) | 830.605 | + | 830.605i | 0.470865 | + | 0.470865i | ||||
\(43\) | −1748.18 | + | 1748.18i | −0.945471 | + | 0.945471i | −0.998588 | − | 0.0531168i | \(-0.983084\pi\) |
0.0531168 | + | 0.998588i | \(0.483084\pi\) | |||||||
\(44\) | − | 4612.53i | − | 2.38250i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3120.13 | 1.47454 | ||||||||
\(47\) | −2202.77 | − | 2202.77i | −0.997179 | − | 0.997179i | 0.00281662 | − | 0.999996i | \(-0.499103\pi\) |
−0.999996 | + | 0.00281662i | \(0.999103\pi\) | |||||||
\(48\) | 214.321 | − | 214.321i | 0.0930211 | − | 0.0930211i | ||||
\(49\) | 343.000i | 0.142857i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4045.69 | 1.55544 | ||||||||
\(52\) | −696.426 | − | 696.426i | −0.257554 | − | 0.257554i | ||||
\(53\) | −3012.92 | + | 3012.92i | −1.07259 | + | 1.07259i | −0.0754442 | + | 0.997150i | \(0.524037\pi\) |
−0.997150 | + | 0.0754442i | \(0.975963\pi\) | |||||||
\(54\) | − | 4305.39i | − | 1.47647i | ||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1300.57 | 0.414724 | ||||||||
\(57\) | −1530.84 | − | 1530.84i | −0.471172 | − | 0.471172i | ||||
\(58\) | −5677.02 | + | 5677.02i | −1.68758 | + | 1.68758i | ||||
\(59\) | 1080.84i | 0.310496i | 0.987876 | + | 0.155248i | \(0.0496177\pi\) | ||||
−0.987876 | + | 0.155248i | \(0.950382\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1793.51 | −0.481997 | −0.240998 | − | 0.970526i | \(-0.577475\pi\) | ||||
−0.240998 | + | 0.970526i | \(0.577475\pi\) | |||||||
\(62\) | 5559.50 | + | 5559.50i | 1.44628 | + | 1.44628i | ||||
\(63\) | −171.799 | + | 171.799i | −0.0432853 | + | 0.0432853i | ||||
\(64\) | 6510.23i | 1.58941i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 10940.0 | 2.51147 | ||||||||
\(67\) | 1517.25 | + | 1517.25i | 0.337993 | + | 0.337993i | 0.855611 | − | 0.517619i | \(-0.173181\pi\) |
−0.517619 | + | 0.855611i | \(0.673181\pi\) | |||||||
\(68\) | 7885.41 | − | 7885.41i | 1.70532 | − | 1.70532i | ||||
\(69\) | 4630.05i | 0.972495i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7861.02 | −1.55942 | −0.779708 | − | 0.626143i | \(-0.784633\pi\) | ||||
−0.779708 | + | 0.626143i | \(0.784633\pi\) | |||||||
\(72\) | 651.422 | + | 651.422i | 0.125660 | + | 0.125660i | ||||
\(73\) | −654.271 | + | 654.271i | −0.122776 | + | 0.122776i | −0.765825 | − | 0.643049i | \(-0.777669\pi\) |
0.643049 | + | 0.765825i | \(0.277669\pi\) | |||||||
\(74\) | 4454.17i | 0.813398i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5967.48 | −1.03315 | ||||||||
\(77\) | 2258.84 | + | 2258.84i | 0.380982 | + | 0.380982i | ||||
\(78\) | 1651.78 | − | 1651.78i | 0.271496 | − | 0.271496i | ||||
\(79\) | − | 1243.55i | − | 0.199255i | −0.995025 | − | 0.0996275i | \(-0.968235\pi\) | ||
0.995025 | − | 0.0996275i | \(-0.0317651\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7451.51 | 1.13573 | ||||||||
\(82\) | −9917.66 | − | 9917.66i | −1.47497 | − | 1.47497i | ||||
\(83\) | 6982.20 | − | 6982.20i | 1.01353 | − | 1.01353i | 0.0136219 | − | 0.999907i | \(-0.495664\pi\) |
0.999907 | − | 0.0136219i | \(-0.00433611\pi\) | |||||||
\(84\) | 4804.74i | 0.680944i | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −16163.1 | −2.18539 | ||||||||
\(87\) | −8424.30 | − | 8424.30i | −1.11300 | − | 1.11300i | ||||
\(88\) | 8564.98 | − | 8564.98i | 1.10602 | − | 1.10602i | ||||
\(89\) | 9246.50i | 1.16734i | 0.811991 | + | 0.583670i | \(0.198384\pi\) | ||||
−0.811991 | + | 0.583670i | \(0.801616\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 682.106 | 0.0823700 | ||||||||
\(92\) | 9024.38 | + | 9024.38i | 1.06621 | + | 1.06621i | ||||
\(93\) | −8249.91 | + | 8249.91i | −0.953857 | + | 0.953857i | ||||
\(94\) | − | 20366.1i | − | 2.30490i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −8918.94 | −0.967767 | ||||||||
\(97\) | −8539.81 | − | 8539.81i | −0.907621 | − | 0.907621i | 0.0884588 | − | 0.996080i | \(-0.471806\pi\) |
−0.996080 | + | 0.0884588i | \(0.971806\pi\) | |||||||
\(98\) | −1585.64 | + | 1585.64i | −0.165102 | + | 0.165102i | ||||
\(99\) | 2262.79i | 0.230873i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6421.19 | 0.629467 | 0.314734 | − | 0.949180i | \(-0.398085\pi\) | ||||
0.314734 | + | 0.949180i | \(0.398085\pi\) | |||||||
\(102\) | 18702.6 | + | 18702.6i | 1.79764 | + | 1.79764i | ||||
\(103\) | −6962.39 | + | 6962.39i | −0.656272 | + | 0.656272i | −0.954496 | − | 0.298224i | \(-0.903606\pi\) |
0.298224 | + | 0.954496i | \(0.403606\pi\) | |||||||
\(104\) | − | 2586.38i | − | 0.239125i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −27856.5 | −2.47922 | ||||||||
\(107\) | 775.586 | + | 775.586i | 0.0677427 | + | 0.0677427i | 0.740166 | − | 0.672424i | \(-0.234747\pi\) |
−0.672424 | + | 0.740166i | \(0.734747\pi\) | |||||||
\(108\) | 12452.6 | − | 12452.6i | 1.06761 | − | 1.06761i | ||||
\(109\) | 19331.6i | 1.62710i | 0.581495 | + | 0.813550i | \(0.302468\pi\) | ||||
−0.581495 | + | 0.813550i | \(0.697532\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6609.67 | −0.536456 | ||||||||
\(112\) | 409.141 | + | 409.141i | 0.0326165 | + | 0.0326165i | ||||
\(113\) | 7047.82 | − | 7047.82i | 0.551947 | − | 0.551947i | −0.375055 | − | 0.927003i | \(-0.622376\pi\) |
0.927003 | + | 0.375055i | \(0.122376\pi\) | |||||||
\(114\) | − | 14153.7i | − | 1.08908i | ||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −32839.5 | −2.44051 | ||||||||
\(117\) | 341.648 | + | 341.648i | 0.0249579 | + | 0.0249579i | ||||
\(118\) | −4996.54 | + | 4996.54i | −0.358844 | + | 0.358844i | ||||
\(119\) | 7723.27i | 0.545390i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 15110.4 | 1.03206 | ||||||||
\(122\) | −8291.12 | − | 8291.12i | −0.557049 | − | 0.557049i | ||||
\(123\) | 14717.1 | − | 14717.1i | 0.972775 | − | 0.972775i | ||||
\(124\) | 32159.7i | 2.09155i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1588.41 | −0.100051 | ||||||||
\(127\) | 8849.78 | + | 8849.78i | 0.548688 | + | 0.548688i | 0.926061 | − | 0.377373i | \(-0.123173\pi\) |
−0.377373 | + | 0.926061i | \(0.623173\pi\) | |||||||
\(128\) | −19694.7 | + | 19694.7i | −1.20207 | + | 1.20207i | ||||
\(129\) | − | 23984.9i | − | 1.44131i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 29995.2 | 1.74787 | 0.873936 | − | 0.486040i | \(-0.161559\pi\) | ||||
0.873936 | + | 0.486040i | \(0.161559\pi\) | |||||||
\(132\) | 31641.8 | + | 31641.8i | 1.81599 | + | 1.81599i | ||||
\(133\) | 2922.39 | − | 2922.39i | 0.165209 | − | 0.165209i | ||||
\(134\) | 14028.0i | 0.781244i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 29284.8 | 1.58330 | ||||||||
\(137\) | 20217.5 | + | 20217.5i | 1.07718 | + | 1.07718i | 0.996761 | + | 0.0804160i | \(0.0256249\pi\) |
0.0804160 | + | 0.996761i | \(0.474375\pi\) | |||||||
\(138\) | −21404.0 | + | 21404.0i | −1.12392 | + | 1.12392i | ||||
\(139\) | 23970.9i | 1.24067i | 0.784338 | + | 0.620333i | \(0.213003\pi\) | ||||
−0.784338 | + | 0.620333i | \(0.786997\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 30221.9 | 1.52014 | ||||||||
\(142\) | −36340.3 | − | 36340.3i | −1.80224 | − | 1.80224i | ||||
\(143\) | 4492.04 | − | 4492.04i | 0.219670 | − | 0.219670i | ||||
\(144\) | 409.855i | 0.0197654i | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −6049.19 | −0.283787 | ||||||||
\(147\) | −2352.97 | − | 2352.97i | −0.108889 | − | 0.108889i | ||||
\(148\) | −12882.9 | + | 12882.9i | −0.588151 | + | 0.588151i | ||||
\(149\) | 4953.16i | 0.223105i | 0.993759 | + | 0.111553i | \(0.0355824\pi\) | ||||
−0.993759 | + | 0.111553i | \(0.964418\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18226.3 | 0.799366 | 0.399683 | − | 0.916653i | \(-0.369120\pi\) | ||||
0.399683 | + | 0.916653i | \(0.369120\pi\) | |||||||
\(152\) | −11081.0 | − | 11081.0i | −0.479614 | − | 0.479614i | ||||
\(153\) | −3868.38 | + | 3868.38i | −0.165252 | + | 0.165252i | ||||
\(154\) | 20884.6i | 0.880611i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 9554.93 | 0.392625 | ||||||||
\(157\) | −17966.9 | − | 17966.9i | −0.728911 | − | 0.728911i | 0.241492 | − | 0.970403i | \(-0.422363\pi\) |
−0.970403 | + | 0.241492i | \(0.922363\pi\) | |||||||
\(158\) | 5748.74 | − | 5748.74i | 0.230281 | − | 0.230281i | ||||
\(159\) | − | 41337.1i | − | 1.63511i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8838.82 | −0.340991 | ||||||||
\(162\) | 34447.2 | + | 34447.2i | 1.31257 | + | 1.31257i | ||||
\(163\) | 14457.8 | − | 14457.8i | 0.544160 | − | 0.544160i | −0.380586 | − | 0.924746i | \(-0.624278\pi\) |
0.924746 | + | 0.380586i | \(0.124278\pi\) | |||||||
\(164\) | − | 57370.0i | − | 2.13303i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 64555.3 | 2.34270 | ||||||||
\(167\) | 17249.0 | + | 17249.0i | 0.618488 | + | 0.618488i | 0.945144 | − | 0.326655i | \(-0.105922\pi\) |
−0.326655 | + | 0.945144i | \(0.605922\pi\) | |||||||
\(168\) | −8921.91 | + | 8921.91i | −0.316111 | + | 0.316111i | ||||
\(169\) | 27204.5i | 0.952506i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2927.49 | 0.100116 | ||||||||
\(172\) | −46748.8 | − | 46748.8i | −1.58021 | − | 1.58021i | ||||
\(173\) | −12009.4 | + | 12009.4i | −0.401262 | + | 0.401262i | −0.878678 | − | 0.477416i | \(-0.841574\pi\) |
0.477416 | + | 0.878678i | \(0.341574\pi\) | |||||||
\(174\) | − | 77888.5i | − | 2.57262i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5388.83 | 0.173968 | ||||||||
\(177\) | −7414.52 | − | 7414.52i | −0.236666 | − | 0.236666i | ||||
\(178\) | −42745.2 | + | 42745.2i | −1.34911 | + | 1.34911i | ||||
\(179\) | − | 41320.5i | − | 1.28961i | −0.764346 | − | 0.644807i | \(-0.776938\pi\) | ||
0.764346 | − | 0.644807i | \(-0.223062\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −37181.6 | −1.13494 | −0.567468 | − | 0.823396i | \(-0.692077\pi\) | ||||
−0.567468 | + | 0.823396i | \(0.692077\pi\) | |||||||
\(182\) | 3153.27 | + | 3153.27i | 0.0951960 | + | 0.0951960i | ||||
\(183\) | 12303.4 | − | 12303.4i | 0.367387 | − | 0.367387i | ||||
\(184\) | 33514.7i | 0.989919i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −76276.2 | −2.20477 | ||||||||
\(187\) | 50862.0 | + | 50862.0i | 1.45449 | + | 1.45449i | ||||
\(188\) | 58905.3 | − | 58905.3i | 1.66663 | − | 1.66663i | ||||
\(189\) | 12196.5i | 0.341438i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1197.41 | 0.0328227 | 0.0164114 | − | 0.999865i | \(-0.494776\pi\) | ||||
0.0164114 | + | 0.999865i | \(0.494776\pi\) | |||||||
\(192\) | −44660.0 | − | 44660.0i | −1.21148 | − | 1.21148i | ||||
\(193\) | −9123.80 | + | 9123.80i | −0.244941 | + | 0.244941i | −0.818891 | − | 0.573950i | \(-0.805410\pi\) |
0.573950 | + | 0.818891i | \(0.305410\pi\) | |||||||
\(194\) | − | 78956.5i | − | 2.09790i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −9172.32 | −0.238763 | ||||||||
\(197\) | −23440.8 | − | 23440.8i | −0.604004 | − | 0.604004i | 0.337369 | − | 0.941373i | \(-0.390463\pi\) |
−0.941373 | + | 0.337369i | \(0.890463\pi\) | |||||||
\(198\) | −10460.5 | + | 10460.5i | −0.266823 | + | 0.266823i | ||||
\(199\) | − | 11182.0i | − | 0.282367i | −0.989983 | − | 0.141183i | \(-0.954909\pi\) | ||
0.989983 | − | 0.141183i | \(-0.0450907\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −20816.6 | −0.515250 | ||||||||
\(202\) | 29684.2 | + | 29684.2i | 0.727483 | + | 0.727483i | ||||
\(203\) | 16082.1 | − | 16082.1i | 0.390257 | − | 0.390257i | ||||
\(204\) | 108188.i | 2.59966i | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −64372.1 | −1.51692 | ||||||||
\(207\) | −4427.13 | − | 4427.13i | −0.103319 | − | 0.103319i | ||||
\(208\) | 813.637 | − | 813.637i | 0.0188063 | − | 0.0188063i | ||||
\(209\) | − | 38491.0i | − | 0.881185i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15642.1 | −0.351341 | −0.175670 | − | 0.984449i | \(-0.556209\pi\) | ||||
−0.175670 | + | 0.984449i | \(0.556209\pi\) | |||||||
\(212\) | −80569.8 | − | 80569.8i | −1.79267 | − | 1.79267i | ||||
\(213\) | 53926.4 | − | 53926.4i | 1.18862 | − | 1.18862i | ||||
\(214\) | 7170.84i | 0.156582i | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 46246.2 | 0.991217 | ||||||||
\(217\) | −15749.2 | − | 15749.2i | −0.334456 | − | 0.334456i | ||||
\(218\) | −89366.9 | + | 89366.9i | −1.88046 | + | 1.88046i | ||||
\(219\) | − | 8976.58i | − | 0.187164i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 15358.9 | 0.314467 | ||||||||
\(222\) | −30555.5 | − | 30555.5i | −0.619989 | − | 0.619989i | ||||
\(223\) | 55429.7 | − | 55429.7i | 1.11464 | − | 1.11464i | 0.122120 | − | 0.992515i | \(-0.461031\pi\) |
0.992515 | − | 0.122120i | \(-0.0389693\pi\) | |||||||
\(224\) | − | 17026.4i | − | 0.339333i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 65162.0 | 1.27578 | ||||||||
\(227\) | −46119.3 | − | 46119.3i | −0.895017 | − | 0.895017i | 0.0999730 | − | 0.994990i | \(-0.468124\pi\) |
−0.994990 | + | 0.0999730i | \(0.968124\pi\) | |||||||
\(228\) | 40936.8 | − | 40936.8i | 0.787489 | − | 0.787489i | ||||
\(229\) | 35036.6i | 0.668114i | 0.942553 | + | 0.334057i | \(0.108418\pi\) | ||||
−0.942553 | + | 0.334057i | \(0.891582\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −30991.2 | −0.580784 | ||||||||
\(232\) | −60979.5 | − | 60979.5i | −1.13294 | − | 1.13294i | ||||
\(233\) | 49452.5 | − | 49452.5i | 0.910912 | − | 0.910912i | −0.0854321 | − | 0.996344i | \(-0.527227\pi\) |
0.996344 | + | 0.0854321i | \(0.0272271\pi\) | |||||||
\(234\) | 3158.78i | 0.0576882i | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −28903.1 | −0.518945 | ||||||||
\(237\) | 8530.73 | + | 8530.73i | 0.151876 | + | 0.151876i | ||||
\(238\) | −35703.5 | + | 35703.5i | −0.630314 | + | 0.630314i | ||||
\(239\) | − | 82663.3i | − | 1.44716i | −0.690240 | − | 0.723581i | \(-0.742495\pi\) | ||
0.690240 | − | 0.723581i | \(-0.257505\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 49073.7 | 0.844918 | 0.422459 | − | 0.906382i | \(-0.361167\pi\) | ||||
0.422459 | + | 0.906382i | \(0.361167\pi\) | |||||||
\(242\) | 69853.1 | + | 69853.1i | 1.19277 | + | 1.19277i | ||||
\(243\) | −13398.4 | + | 13398.4i | −0.226903 | + | 0.226903i | ||||
\(244\) | − | 47961.0i | − | 0.805581i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 136070. | 2.24850 | ||||||||
\(247\) | −5811.60 | − | 5811.60i | −0.0952581 | − | 0.0952581i | ||||
\(248\) | −59717.2 | + | 59717.2i | −0.970948 | + | 0.970948i | ||||
\(249\) | 95795.5i | 1.54506i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 26692.3 | 0.423680 | 0.211840 | − | 0.977304i | \(-0.432054\pi\) | ||||
0.211840 | + | 0.977304i | \(0.432054\pi\) | |||||||
\(252\) | −4594.17 | − | 4594.17i | −0.0723445 | − | 0.0723445i | ||||
\(253\) | −58208.5 | + | 58208.5i | −0.909379 | + | 0.909379i | ||||
\(254\) | 81822.4i | 1.26825i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −77927.3 | −1.18908 | ||||||||
\(257\) | 29469.9 | + | 29469.9i | 0.446183 | + | 0.446183i | 0.894083 | − | 0.447901i | \(-0.147828\pi\) |
−0.447901 | + | 0.894083i | \(0.647828\pi\) | |||||||
\(258\) | 110879. | − | 110879.i | 1.66574 | − | 1.66574i | ||||
\(259\) | − | 12618.0i | − | 0.188100i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 16110.2 | 0.236494 | ||||||||
\(262\) | 138663. | + | 138663.i | 2.02004 | + | 2.02004i | ||||
\(263\) | 19630.8 | − | 19630.8i | 0.283809 | − | 0.283809i | −0.550817 | − | 0.834626i | \(-0.685684\pi\) |
0.834626 | + | 0.550817i | \(0.185684\pi\) | |||||||
\(264\) | 117511.i | 1.68605i | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 27019.5 | 0.381869 | ||||||||
\(267\) | −63430.8 | − | 63430.8i | −0.889770 | − | 0.889770i | ||||
\(268\) | −40573.4 | + | 40573.4i | −0.564901 | + | 0.564901i | ||||
\(269\) | 31695.7i | 0.438021i | 0.975722 | + | 0.219011i | \(0.0702830\pi\) | ||||
−0.975722 | + | 0.219011i | \(0.929717\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −77598.0 | −1.05660 | −0.528301 | − | 0.849057i | \(-0.677171\pi\) | ||||
−0.528301 | + | 0.849057i | \(0.677171\pi\) | |||||||
\(272\) | 9212.56 | + | 9212.56i | 0.124521 | + | 0.124521i | ||||
\(273\) | −4679.23 | + | 4679.23i | −0.0627841 | + | 0.0627841i | ||||
\(274\) | 186925.i | 2.48981i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −123814. | −1.62537 | ||||||||
\(277\) | 33166.3 | + | 33166.3i | 0.432252 | + | 0.432252i | 0.889394 | − | 0.457142i | \(-0.151127\pi\) |
−0.457142 | + | 0.889394i | \(0.651127\pi\) | |||||||
\(278\) | −110814. | + | 110814.i | −1.43385 | + | 1.43385i | ||||
\(279\) | − | 15776.7i | − | 0.202678i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −124135. | −1.57211 | −0.786053 | − | 0.618160i | \(-0.787879\pi\) | ||||
−0.786053 | + | 0.618160i | \(0.787879\pi\) | |||||||
\(282\) | 139711. | + | 139711.i | 1.75684 | + | 1.75684i | ||||
\(283\) | −21549.5 | + | 21549.5i | −0.269069 | + | 0.269069i | −0.828725 | − | 0.559656i | \(-0.810933\pi\) |
0.559656 | + | 0.828725i | \(0.310933\pi\) | |||||||
\(284\) | − | 210215.i | − | 2.60632i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 41532.0 | 0.507751 | ||||||||
\(287\) | 28095.2 | + | 28095.2i | 0.341089 | + | 0.341089i | ||||
\(288\) | 8528.05 | − | 8528.05i | 0.102817 | − | 0.102817i | ||||
\(289\) | 90382.7i | 1.08215i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 117166. | 1.38361 | ||||||||
\(292\) | −17496.2 | − | 17496.2i | −0.205200 | − | 0.205200i | ||||
\(293\) | −18857.8 | + | 18857.8i | −0.219663 | + | 0.219663i | −0.808356 | − | 0.588694i | \(-0.799642\pi\) |
0.588694 | + | 0.808356i | \(0.299642\pi\) | |||||||
\(294\) | − | 21754.9i | − | 0.251688i | ||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −47844.3 | −0.546068 | ||||||||
\(297\) | 80320.6 | + | 80320.6i | 0.910572 | + | 0.910572i | ||||
\(298\) | −22897.7 | + | 22897.7i | −0.257846 | + | 0.257846i | ||||
\(299\) | 17577.3i | 0.196612i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 45787.5 | 0.505376 | ||||||||
\(302\) | 84257.6 | + | 84257.6i | 0.923837 | + | 0.923837i | ||||
\(303\) | −44049.3 | + | 44049.3i | −0.479792 | + | 0.479792i | ||||
\(304\) | − | 6971.84i | − | 0.0754397i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −35765.9 | −0.381967 | ||||||||
\(307\) | 23749.9 | + | 23749.9i | 0.251991 | + | 0.251991i | 0.821786 | − | 0.569796i | \(-0.192978\pi\) |
−0.569796 | + | 0.821786i | \(0.692978\pi\) | |||||||
\(308\) | −60404.7 | + | 60404.7i | −0.636751 | + | 0.636751i | ||||
\(309\) | − | 95523.7i | − | 1.00045i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 20548.8 | 0.212454 | 0.106227 | − | 0.994342i | \(-0.466123\pi\) | ||||
0.106227 | + | 0.994342i | \(0.466123\pi\) | |||||||
\(312\) | 17742.5 | + | 17742.5i | 0.182266 | + | 0.182266i | ||||
\(313\) | 5019.39 | − | 5019.39i | 0.0512345 | − | 0.0512345i | −0.681025 | − | 0.732260i | \(-0.738466\pi\) |
0.732260 | + | 0.681025i | \(0.238466\pi\) | |||||||
\(314\) | − | 166117.i | − | 1.68482i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 33254.3 | 0.333023 | ||||||||
\(317\) | 66659.0 | + | 66659.0i | 0.663346 | + | 0.663346i | 0.956167 | − | 0.292821i | \(-0.0945941\pi\) |
−0.292821 | + | 0.956167i | \(0.594594\pi\) | |||||||
\(318\) | 191095. | − | 191095.i | 1.88971 | − | 1.88971i | ||||
\(319\) | − | 211819.i | − | 2.08153i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10641.0 | −0.103270 | ||||||||
\(322\) | −40860.5 | − | 40860.5i | −0.394087 | − | 0.394087i | ||||
\(323\) | 65802.9 | − | 65802.9i | 0.630725 | − | 0.630725i | ||||
\(324\) | 199264.i | 1.89819i | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 133672. | 1.25778 | ||||||||
\(327\) | −132614. | − | 132614.i | −1.24021 | − | 1.24021i | ||||
\(328\) | 106530. | − | 106530.i | 0.990204 | − | 0.990204i | ||||
\(329\) | 57694.1i | 0.533015i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 97809.4 | 0.892739 | 0.446369 | − | 0.894849i | \(-0.352717\pi\) | ||||
0.446369 | + | 0.894849i | \(0.352717\pi\) | |||||||
\(332\) | 186714. | + | 186714.i | 1.69395 | + | 1.69395i | ||||
\(333\) | 6319.99 | − | 6319.99i | 0.0569939 | − | 0.0569939i | ||||
\(334\) | 159479.i | 1.42959i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −5613.40 | −0.0497219 | ||||||||
\(337\) | −81259.9 | − | 81259.9i | −0.715511 | − | 0.715511i | 0.252172 | − | 0.967683i | \(-0.418855\pi\) |
−0.967683 | + | 0.252172i | \(0.918855\pi\) | |||||||
\(338\) | −125762. | + | 125762.i | −1.10082 | + | 1.10082i | ||||
\(339\) | 96695.8i | 0.841411i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −207434. | −1.78390 | ||||||||
\(342\) | 13533.3 | + | 13533.3i | 0.115705 | + | 0.115705i | ||||
\(343\) | 4491.86 | − | 4491.86i | 0.0381802 | − | 0.0381802i | ||||
\(344\) | − | 173615.i | − | 1.46714i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −111035. | −0.927487 | ||||||||
\(347\) | −71853.6 | − | 71853.6i | −0.596746 | − | 0.596746i | 0.342699 | − | 0.939445i | \(-0.388659\pi\) |
−0.939445 | + | 0.342699i | \(0.888659\pi\) | |||||||
\(348\) | 225278. | − | 225278.i | 1.86020 | − | 1.86020i | ||||
\(349\) | 134969.i | 1.10811i | 0.832481 | + | 0.554054i | \(0.186920\pi\) | ||||
−0.832481 | + | 0.554054i | \(0.813080\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 24254.5 | 0.196870 | ||||||||
\(352\) | −112128. | − | 112128.i | −0.904958 | − | 0.904958i | ||||
\(353\) | −126341. | + | 126341.i | −1.01390 | + | 1.01390i | −0.0139944 | + | 0.999902i | \(0.504455\pi\) |
−0.999902 | + | 0.0139944i | \(0.995545\pi\) | |||||||
\(354\) | − | 68552.4i | − | 0.547036i | ||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −247265. | −1.95102 | ||||||||
\(357\) | −52981.5 | − | 52981.5i | −0.415708 | − | 0.415708i | ||||
\(358\) | 191018. | − | 191018.i | 1.49042 | − | 1.49042i | ||||
\(359\) | 172842.i | 1.34110i | 0.741864 | + | 0.670550i | \(0.233942\pi\) | ||||
−0.741864 | + | 0.670550i | \(0.766058\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 80523.0 | 0.617882 | ||||||||
\(362\) | −171885. | − | 171885.i | −1.31166 | − | 1.31166i | ||||
\(363\) | −103657. | + | 103657.i | −0.786657 | + | 0.786657i | ||||
\(364\) | 18240.5i | 0.137668i | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 113754. | 0.849188 | ||||||||
\(367\) | 130065. | + | 130065.i | 0.965671 | + | 0.965671i | 0.999430 | − | 0.0337588i | \(-0.0107478\pi\) |
−0.0337588 | + | 0.999430i | \(0.510748\pi\) | |||||||
\(368\) | −10543.2 | + | 10543.2i | −0.0778535 | + | 0.0778535i | ||||
\(369\) | 28144.2i | 0.206698i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 78913.1 | 0.573326 | ||||||||
\(372\) | −220615. | − | 220615.i | −1.59422 | − | 1.59422i | ||||
\(373\) | 47428.3 | − | 47428.3i | 0.340894 | − | 0.340894i | −0.515809 | − | 0.856704i | \(-0.672509\pi\) |
0.856704 | + | 0.515809i | \(0.172509\pi\) | |||||||
\(374\) | 470254.i | 3.36194i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 218762. | 1.54738 | ||||||||
\(377\) | −31981.6 | − | 31981.6i | −0.225018 | − | 0.225018i | ||||
\(378\) | −56382.6 | + | 56382.6i | −0.394604 | + | 0.394604i | ||||
\(379\) | − | 165306.i | − | 1.15083i | −0.817861 | − | 0.575415i | \(-0.804840\pi\) | ||
0.817861 | − | 0.575415i | \(-0.195160\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −121419. | −0.836442 | ||||||||
\(382\) | 5535.42 | + | 5535.42i | 0.0379336 | + | 0.0379336i | ||||
\(383\) | −169294. | + | 169294.i | −1.15410 | + | 1.15410i | −0.168380 | + | 0.985722i | \(0.553854\pi\) |
−0.985722 | + | 0.168380i | \(0.946146\pi\) | |||||||
\(384\) | − | 270210.i | − | 1.83248i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −84355.9 | −0.566162 | ||||||||
\(387\) | 22933.7 | + | 22933.7i | 0.153127 | + | 0.153127i | ||||
\(388\) | 228367. | − | 228367.i | 1.51694 | − | 1.51694i | ||||
\(389\) | 81630.3i | 0.539452i | 0.962937 | + | 0.269726i | \(0.0869331\pi\) | ||||
−0.962937 | + | 0.269726i | \(0.913067\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −199022. | −1.30181 | ||||||||
\(392\) | −17032.0 | − | 17032.0i | −0.110840 | − | 0.110840i | ||||
\(393\) | −205767. | + | 205767.i | −1.33226 | + | 1.33226i | ||||
\(394\) | − | 216726.i | − | 1.39611i | ||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −60510.2 | −0.385867 | ||||||||
\(397\) | 151107. | + | 151107.i | 0.958744 | + | 0.958744i | 0.999182 | − | 0.0404377i | \(-0.0128752\pi\) |
−0.0404377 | + | 0.999182i | \(0.512875\pi\) | |||||||
\(398\) | 51692.7 | − | 51692.7i | 0.326335 | − | 0.326335i | ||||
\(399\) | 40095.1i | 0.251852i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −166443. | −1.03509 | −0.517543 | − | 0.855657i | \(-0.673153\pi\) | ||||
−0.517543 | + | 0.855657i | \(0.673153\pi\) | |||||||
\(402\) | −96232.0 | − | 96232.0i | −0.595480 | − | 0.595480i | ||||
\(403\) | −31319.6 | + | 31319.6i | −0.192844 | + | 0.192844i | ||||
\(404\) | 171712.i | 1.05205i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 148690. | 0.902050 | ||||||||
\(407\) | −83096.1 | − | 83096.1i | −0.501640 | − | 0.501640i | ||||
\(408\) | −200893. | + | 200893.i | −1.20683 | + | 1.20683i | ||||
\(409\) | − | 194400.i | − | 1.16212i | −0.813861 | − | 0.581059i | \(-0.802639\pi\) | ||
0.813861 | − | 0.581059i | \(-0.197361\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −277384. | −1.64209 | ||||||||
\(412\) | −186184. | − | 186184.i | −1.09685 | − | 1.09685i | ||||
\(413\) | 14154.4 | − | 14154.4i | 0.0829836 | − | 0.0829836i | ||||
\(414\) | − | 40931.9i | − | 0.238815i | ||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −33859.5 | −0.195656 | ||||||||
\(417\) | −164440. | − | 164440.i | −0.945661 | − | 0.945661i | ||||
\(418\) | 177938. | − | 177938.i | 1.01840 | − | 1.01840i | ||||
\(419\) | − | 261923.i | − | 1.49192i | −0.665991 | − | 0.745959i | \(-0.731991\pi\) | ||
0.665991 | − | 0.745959i | \(-0.268009\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 217041. | 1.22455 | 0.612275 | − | 0.790645i | \(-0.290254\pi\) | ||||
0.612275 | + | 0.790645i | \(0.290254\pi\) | |||||||
\(422\) | −72310.8 | − | 72310.8i | −0.406049 | − | 0.406049i | ||||
\(423\) | −28897.4 | + | 28897.4i | −0.161502 | + | 0.161502i | ||||
\(424\) | − | 299220.i | − | 1.66440i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 498588. | 2.74740 | ||||||||
\(427\) | 23487.4 | + | 23487.4i | 0.128819 | + | 0.128819i | ||||
\(428\) | −20740.3 | + | 20740.3i | −0.113221 | + | 0.113221i | ||||
\(429\) | 61630.6i | 0.334874i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −98525.8 | −0.530390 | −0.265195 | − | 0.964195i | \(-0.585436\pi\) | ||||
−0.265195 | + | 0.964195i | \(0.585436\pi\) | |||||||
\(432\) | 14548.4 | + | 14548.4i | 0.0779555 | + | 0.0779555i | ||||
\(433\) | −124989. | + | 124989.i | −0.666647 | + | 0.666647i | −0.956938 | − | 0.290291i | \(-0.906248\pi\) |
0.290291 | + | 0.956938i | \(0.406248\pi\) | |||||||
\(434\) | − | 145612.i | − | 0.773070i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −516954. | −2.71944 | ||||||||
\(437\) | 75307.5 | + | 75307.5i | 0.394344 | + | 0.394344i | ||||
\(438\) | 41497.4 | − | 41497.4i | 0.216308 | − | 0.216308i | ||||
\(439\) | − | 111878.i | − | 0.580520i | −0.956948 | − | 0.290260i | \(-0.906258\pi\) | ||
0.956948 | − | 0.290260i | \(-0.0937419\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4499.70 | 0.0231370 | ||||||||
\(442\) | 71001.7 | + | 71001.7i | 0.363433 | + | 0.363433i | ||||
\(443\) | −143058. | + | 143058.i | −0.728963 | + | 0.728963i | −0.970413 | − | 0.241450i | \(-0.922377\pi\) |
0.241450 | + | 0.970413i | \(0.422377\pi\) | |||||||
\(444\) | − | 176752.i | − | 0.896601i | ||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 512486. | 2.57640 | ||||||||
\(447\) | −33978.6 | − | 33978.6i | −0.170055 | − | 0.170055i | ||||
\(448\) | 85256.6 | − | 85256.6i | 0.424788 | − | 0.424788i | ||||
\(449\) | − | 95250.7i | − | 0.472471i | −0.971696 | − | 0.236236i | \(-0.924086\pi\) | ||
0.971696 | − | 0.236236i | \(-0.0759137\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 370044. | 1.81928 | ||||||||
\(452\) | 188469. | + | 188469.i | 0.922492 | + | 0.922492i | ||||
\(453\) | −125032. | + | 125032.i | −0.609293 | + | 0.609293i | ||||
\(454\) | − | 426405.i | − | 2.06876i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 152031. | 0.731142 | ||||||||
\(457\) | 155248. | + | 155248.i | 0.743350 | + | 0.743350i | 0.973221 | − | 0.229871i | \(-0.0738305\pi\) |
−0.229871 | + | 0.973221i | \(0.573831\pi\) | |||||||
\(458\) | −161969. | + | 161969.i | −0.772148 | + | 0.772148i | ||||
\(459\) | 274627.i | 1.30352i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18536.5 | 0.0872217 | 0.0436109 | − | 0.999049i | \(-0.486114\pi\) | ||||
0.0436109 | + | 0.999049i | \(0.486114\pi\) | |||||||
\(462\) | −143268. | − | 143268.i | −0.671219 | − | 0.671219i | ||||
\(463\) | −189728. | + | 189728.i | −0.885055 | + | 0.885055i | −0.994043 | − | 0.108988i | \(-0.965239\pi\) |
0.108988 | + | 0.994043i | \(0.465239\pi\) | |||||||
\(464\) | − | 38366.5i | − | 0.178203i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 457223. | 2.10550 | ||||||||
\(467\) | 136538. | + | 136538.i | 0.626064 | + | 0.626064i | 0.947075 | − | 0.321011i | \(-0.104023\pi\) |
−0.321011 | + | 0.947075i | \(0.604023\pi\) | |||||||
\(468\) | −9136.18 | + | 9136.18i | −0.0417131 | + | 0.0417131i | ||||
\(469\) | − | 39739.2i | − | 0.180665i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 246506. | 1.11118 | ||||||||
\(472\) | −53670.2 | − | 53670.2i | −0.240907 | − | 0.240907i | ||||
\(473\) | 301536. | − | 301536.i | 1.34777 | − | 1.34777i | ||||
\(474\) | 78872.5i | 0.351050i | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −206532. | −0.911533 | ||||||||
\(477\) | 39525.5 | + | 39525.5i | 0.173716 | + | 0.173716i | ||||
\(478\) | 382140. | − | 382140.i | 1.67250 | − | 1.67250i | ||||
\(479\) | 296151.i | 1.29075i | 0.763867 | + | 0.645374i | \(0.223299\pi\) | ||||
−0.763867 | + | 0.645374i | \(0.776701\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −25092.7 | −0.108457 | ||||||||
\(482\) | 226860. | + | 226860.i | 0.976482 | + | 0.976482i | ||||
\(483\) | 60634.2 | − | 60634.2i | 0.259910 | − | 0.259910i | ||||
\(484\) | 404074.i | 1.72493i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −123878. | −0.524469 | ||||||||
\(487\) | −269739. | − | 269739.i | −1.13733 | − | 1.13733i | −0.988927 | − | 0.148401i | \(-0.952587\pi\) |
−0.148401 | − | 0.988927i | \(-0.547413\pi\) | |||||||
\(488\) | 89058.7 | − | 89058.7i | 0.373970 | − | 0.373970i | ||||
\(489\) | 198360.i | 0.829539i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 27623.0 | 0.114580 | 0.0572899 | − | 0.998358i | \(-0.481754\pi\) | ||||
0.0572899 | + | 0.998358i | \(0.481754\pi\) | |||||||
\(492\) | 393557. | + | 393557.i | 1.62584 | + | 1.62584i | ||||
\(493\) | 362118. | − | 362118.i | 1.48990 | − | 1.48990i | ||||
\(494\) | − | 53732.3i | − | 0.220182i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −37572.3 | −0.152723 | ||||||||
\(497\) | 102946. | + | 102946.i | 0.416772 | + | 0.416772i | ||||
\(498\) | −442848. | + | 442848.i | −1.78565 | + | 1.78565i | ||||
\(499\) | − | 194010.i | − | 0.779153i | −0.920994 | − | 0.389577i | \(-0.872621\pi\) | ||
0.920994 | − | 0.389577i | \(-0.127379\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −236656. | −0.942848 | ||||||||
\(502\) | 123394. | + | 123394.i | 0.489653 | + | 0.489653i | ||||
\(503\) | 217646. | − | 217646.i | 0.860230 | − | 0.860230i | −0.131135 | − | 0.991365i | \(-0.541862\pi\) |
0.991365 | + | 0.131135i | \(0.0418620\pi\) | |||||||
\(504\) | − | 17061.8i | − | 0.0671682i | ||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −538178. | −2.10196 | ||||||||
\(507\) | −186623. | − | 186623.i | −0.726019 | − | 0.726019i | ||||
\(508\) | −236656. | + | 236656.i | −0.917044 | + | 0.917044i | ||||
\(509\) | − | 269020.i | − | 1.03836i | −0.854664 | − | 0.519182i | \(-0.826237\pi\) | ||
0.854664 | − | 0.519182i | \(-0.173763\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 17136.4 | 0.0656263 | ||||||||
\(512\) | −45131.4 | − | 45131.4i | −0.172163 | − | 0.172163i | ||||
\(513\) | 103915. | − | 103915.i | 0.394861 | − | 0.394861i | ||||
\(514\) | 272470.i | 1.03132i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 641392. | 2.40893 | ||||||||
\(517\) | 379947. | + | 379947.i | 1.42148 | + | 1.42148i | ||||
\(518\) | 58330.9 | − | 58330.9i | 0.217390 | − | 0.217390i | ||||
\(519\) | − | 164768.i | − | 0.611700i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 287409. | 1.05883 | 0.529413 | − | 0.848364i | \(-0.322412\pi\) | ||||
0.529413 | + | 0.848364i | \(0.322412\pi\) | |||||||
\(522\) | 74474.9 | + | 74474.9i | 0.273319 | + | 0.273319i | ||||
\(523\) | −291190. | + | 291190.i | −1.06457 | + | 1.06457i | −0.0667989 | + | 0.997766i | \(0.521279\pi\) |
−0.997766 | + | 0.0667989i | \(0.978721\pi\) | |||||||
\(524\) | 802117.i | 2.92129i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 181500. | 0.656003 | ||||||||
\(527\) | −354622. | − | 354622.i | −1.27686 | − | 1.27686i | ||||
\(528\) | −36967.3 | + | 36967.3i | −0.132602 | + | 0.132602i | ||||
\(529\) | 52071.8i | 0.186076i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 14179.1 | 0.0502876 | ||||||||
\(532\) | 78148.9 | + | 78148.9i | 0.276121 | + | 0.276121i | ||||
\(533\) | 55871.4 | − | 55871.4i | 0.196669 | − | 0.196669i | ||||
\(534\) | − | 586462.i | − | 2.05664i | ||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −150681. | −0.524481 | ||||||||
\(537\) | 283458. | + | 283458.i | 0.982969 | + | 0.982969i | ||||
\(538\) | −146524. | + | 146524.i | −0.506227 | + | 0.506227i | ||||
\(539\) | − | 59162.7i | − | 0.203643i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2540.09 | 0.00867871 | 0.00433936 | − | 0.999991i | \(-0.498619\pi\) | ||||
0.00433936 | + | 0.999991i | \(0.498619\pi\) | |||||||
\(542\) | −358724. | − | 358724.i | −1.22113 | − | 1.22113i | ||||
\(543\) | 255065. | − | 255065.i | 0.865071 | − | 0.865071i | ||||
\(544\) | − | 383380.i | − | 1.29548i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −43262.8 | −0.145121 | ||||||||
\(547\) | 78242.0 | + | 78242.0i | 0.261496 | + | 0.261496i | 0.825662 | − | 0.564166i | \(-0.190802\pi\) |
−0.564166 | + | 0.825662i | \(0.690802\pi\) | |||||||
\(548\) | −540647. | + | 540647.i | −1.80033 | + | 1.80033i | ||||
\(549\) | 23528.4i | 0.0780636i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −274042. | −0.902638 | ||||||||
\(552\) | −229910. | − | 229910.i | −0.754536 | − | 0.754536i | ||||
\(553\) | −16285.3 | + | 16285.3i | −0.0532531 | + | 0.0532531i | ||||
\(554\) | 306645.i | 0.999118i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −641017. | −2.07358 | ||||||||
\(557\) | −334567. | − | 334567.i | −1.07838 | − | 1.07838i | −0.996655 | − | 0.0817273i | \(-0.973956\pi\) |
−0.0817273 | − | 0.996655i | \(-0.526044\pi\) | |||||||
\(558\) | 72933.3 | − | 72933.3i | 0.234238 | − | 0.234238i | ||||
\(559\) | − | 91055.3i | − | 0.291395i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −697824. | −2.21728 | ||||||||
\(562\) | −573857. | − | 573857.i | −1.81690 | − | 1.81690i | ||||
\(563\) | −350328. | + | 350328.i | −1.10524 | + | 1.10524i | −0.111476 | + | 0.993767i | \(0.535558\pi\) |
−0.993767 | + | 0.111476i | \(0.964442\pi\) | |||||||
\(564\) | 808178.i | 2.54067i | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −199240. | −0.621932 | ||||||||
\(567\) | −97583.5 | − | 97583.5i | −0.303536 | − | 0.303536i | ||||
\(568\) | 390348. | − | 390348.i | 1.20992 | − | 1.20992i | ||||
\(569\) | 52610.6i | 0.162498i | 0.996694 | + | 0.0812492i | \(0.0258910\pi\) | ||||
−0.996694 | + | 0.0812492i | \(0.974109\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −318898. | −0.978093 | −0.489047 | − | 0.872258i | \(-0.662655\pi\) | ||||
−0.489047 | + | 0.872258i | \(0.662655\pi\) | |||||||
\(572\) | 120124. | + | 120124.i | 0.367144 | + | 0.367144i | ||||
\(573\) | −8214.18 | + | 8214.18i | −0.0250181 | + | 0.0250181i | ||||
\(574\) | 259760.i | 0.788402i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 85405.5 | 0.257419 | ||||||||
\(577\) | 228263. | + | 228263.i | 0.685621 | + | 0.685621i | 0.961261 | − | 0.275640i | \(-0.0888896\pi\) |
−0.275640 | + | 0.961261i | \(0.588890\pi\) | |||||||
\(578\) | −417825. | + | 417825.i | −1.25066 | + | 1.25066i | ||||
\(579\) | − | 125178.i | − | 0.373398i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −182875. | −0.541754 | ||||||||
\(582\) | 541640. | + | 541640.i | 1.59906 | + | 1.59906i | ||||
\(583\) | 519686. | − | 519686.i | 1.52899 | − | 1.52899i | ||||
\(584\) | − | 64977.1i | − | 0.190518i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −174354. | −0.507733 | ||||||||
\(587\) | −244137. | − | 244137.i | −0.708529 | − | 0.708529i | 0.257697 | − | 0.966226i | \(-0.417036\pi\) |
−0.966226 | + | 0.257697i | \(0.917036\pi\) | |||||||
\(588\) | 62921.9 | − | 62921.9i | 0.181990 | − | 0.181990i | ||||
\(589\) | 268369.i | 0.773574i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 321607. | 0.920768 | ||||||||
\(592\) | −15051.1 | − | 15051.1i | −0.0429462 | − | 0.0429462i | ||||
\(593\) | 98281.5 | − | 98281.5i | 0.279488 | − | 0.279488i | −0.553417 | − | 0.832904i | \(-0.686676\pi\) |
0.832904 | + | 0.553417i | \(0.186676\pi\) | |||||||
\(594\) | 742620.i | 2.10472i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −132455. | −0.372885 | ||||||||
\(597\) | 76708.4 | + | 76708.4i | 0.215226 | + | 0.215226i | ||||
\(598\) | −81257.2 | + | 81257.2i | −0.227227 | + | 0.227227i | ||||
\(599\) | − | 279180.i | − | 0.778092i | −0.921218 | − | 0.389046i | \(-0.872805\pi\) | ||
0.921218 | − | 0.389046i | \(-0.127195\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −640601. | −1.77353 | −0.886766 | − | 0.462219i | \(-0.847053\pi\) | ||||
−0.886766 | + | 0.462219i | \(0.847053\pi\) | |||||||
\(602\) | 211669. | + | 211669.i | 0.584069 | + | 0.584069i | ||||
\(603\) | 19904.3 | − | 19904.3i | 0.0547409 | − | 0.0547409i | ||||
\(604\) | 487399.i | 1.33601i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −407266. | −1.10900 | ||||||||
\(607\) | −115131. | − | 115131.i | −0.312475 | − | 0.312475i | 0.533393 | − | 0.845868i | \(-0.320917\pi\) |
−0.845868 | + | 0.533393i | \(0.820917\pi\) | |||||||
\(608\) | −145066. | + | 145066.i | −0.392427 | + | 0.392427i | ||||
\(609\) | 220646.i | 0.594924i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 114733. | 0.307331 | ||||||||
\(612\) | −103446. | − | 103446.i | −0.276192 | − | 0.276192i | ||||
\(613\) | 260483. | − | 260483.i | 0.693200 | − | 0.693200i | −0.269734 | − | 0.962935i | \(-0.586936\pi\) |
0.962935 | + | 0.269734i | \(0.0869359\pi\) | |||||||
\(614\) | 219584.i | 0.582457i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −224331. | −0.591190 | ||||||||
\(617\) | 265228. | + | 265228.i | 0.696706 | + | 0.696706i | 0.963699 | − | 0.266992i | \(-0.0860299\pi\) |
−0.266992 | + | 0.963699i | \(0.586030\pi\) | |||||||
\(618\) | 441592. | − | 441592.i | 1.15623 | − | 1.15623i | ||||
\(619\) | − | 653363.i | − | 1.70519i | −0.522571 | − | 0.852595i | \(-0.675027\pi\) | ||
0.522571 | − | 0.852595i | \(-0.324973\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −314294. | −0.814990 | ||||||||
\(622\) | 94993.9 | + | 94993.9i | 0.245536 | + | 0.245536i | ||||
\(623\) | 121090. | − | 121090.i | 0.311985 | − | 0.311985i | ||||
\(624\) | 11163.1i | 0.0286691i | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 46407.8 | 0.118425 | ||||||||
\(627\) | 264048. | + | 264048.i | 0.671657 | + | 0.671657i | ||||
\(628\) | 480462. | − | 480462.i | 1.21826 | − | 1.21826i | ||||
\(629\) | − | 284116.i | − | 0.718117i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 98543.0 | 0.247495 | 0.123748 | − | 0.992314i | \(-0.460509\pi\) | ||||
0.123748 | + | 0.992314i | \(0.460509\pi\) | |||||||
\(632\) | 61749.9 | + | 61749.9i | 0.154597 | + | 0.154597i | ||||
\(633\) | 107304. | − | 107304.i | 0.267799 | − | 0.267799i | ||||
\(634\) | 616308.i | 1.53327i | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1.10541e6 | 2.73282 | ||||||||
\(637\) | −8932.72 | − | 8932.72i | −0.0220143 | − | 0.0220143i | ||||
\(638\) | 979206. | − | 979206.i | 2.40565 | − | 2.40565i | ||||
\(639\) | 103126.i | 0.252561i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 390699. | 0.950882 | 0.475441 | − | 0.879748i | \(-0.342289\pi\) | ||||
0.475441 | + | 0.879748i | \(0.342289\pi\) | |||||||
\(642\) | −49191.8 | − | 49191.8i | −0.119350 | − | 0.119350i | ||||
\(643\) | −526218. | + | 526218.i | −1.27275 | + | 1.27275i | −0.328115 | + | 0.944638i | \(0.606413\pi\) |
−0.944638 | + | 0.328115i | \(0.893587\pi\) | |||||||
\(644\) | − | 236363.i | − | 0.569912i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 608394. | 1.45787 | ||||||||
\(647\) | −386057. | − | 386057.i | −0.922238 | − | 0.922238i | 0.0749495 | − | 0.997187i | \(-0.476120\pi\) |
−0.997187 | + | 0.0749495i | \(0.976120\pi\) | |||||||
\(648\) | −370013. | + | 370013.i | −0.881185 | + | 0.881185i | ||||
\(649\) | − | 186429.i | − | 0.442613i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 216078. | 0.509858 | ||||||||
\(652\) | 386622. | + | 386622.i | 0.909476 | + | 0.909476i | ||||
\(653\) | 122162. | − | 122162.i | 0.286491 | − | 0.286491i | −0.549200 | − | 0.835691i | \(-0.685067\pi\) |
0.835691 | + | 0.549200i | \(0.185067\pi\) | |||||||
\(654\) | − | 1.22611e6i | − | 2.86665i | ||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 67025.6 | 0.155752 | ||||||||
\(657\) | 8583.17 | + | 8583.17i | 0.0198846 | + | 0.0198846i | ||||
\(658\) | −266711. | + | 266711.i | −0.616012 | + | 0.616012i | ||||
\(659\) | − | 570740.i | − | 1.31422i | −0.753795 | − | 0.657110i | \(-0.771779\pi\) | ||
0.753795 | − | 0.657110i | \(-0.228221\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 130218. | 0.298035 | 0.149017 | − | 0.988835i | \(-0.452389\pi\) | ||||
0.149017 | + | 0.988835i | \(0.452389\pi\) | |||||||
\(662\) | 452158. | + | 452158.i | 1.03175 | + | 1.03175i | ||||
\(663\) | −105362. | + | 105362.i | −0.239693 | + | 0.239693i | ||||
\(664\) | 693418.i | 1.57275i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 58432.8 | 0.131737 | ||||||||
\(667\) | 414422. | + | 414422.i | 0.931519 | + | 0.931519i | ||||
\(668\) | −461264. | + | 461264.i | −1.03370 | + | 1.03370i | ||||
\(669\) | 760493.i | 1.69919i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 309355. | 0.687088 | ||||||||
\(672\) | 116801. | + | 116801.i | 0.258647 | + | 0.258647i | ||||
\(673\) | 299201. | − | 299201.i | 0.660591 | − | 0.660591i | −0.294928 | − | 0.955519i | \(-0.595296\pi\) |
0.955519 | + | 0.294928i | \(0.0952958\pi\) | |||||||
\(674\) | − | 751304.i | − | 1.65385i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −727489. | −1.59196 | ||||||||
\(677\) | −308222. | − | 308222.i | −0.672492 | − | 0.672492i | 0.285798 | − | 0.958290i | \(-0.407741\pi\) |
−0.958290 | + | 0.285798i | \(0.907741\pi\) | |||||||
\(678\) | −447010. | + | 447010.i | −0.972429 | + | 0.972429i | ||||
\(679\) | 223671.i | 0.485144i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 632755. | 1.36440 | ||||||||
\(682\) | −958936. | − | 958936.i | −2.06168 | − | 2.06168i | ||||
\(683\) | 122960. | − | 122960.i | 0.263585 | − | 0.263585i | −0.562924 | − | 0.826509i | \(-0.690323\pi\) |
0.826509 | + | 0.562924i | \(0.190323\pi\) | |||||||
\(684\) | 78285.4i | 0.167328i | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 41530.4 | 0.0882506 | ||||||||
\(687\) | −240350. | − | 240350.i | −0.509250 | − | 0.509250i | ||||
\(688\) | 54616.8 | − | 54616.8i | 0.115385 | − | 0.115385i | ||||
\(689\) | − | 156930.i | − | 0.330574i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 511145. | 1.07050 | 0.535251 | − | 0.844693i | \(-0.320217\pi\) | ||||
0.535251 | + | 0.844693i | \(0.320217\pi\) | |||||||
\(692\) | −321148. | − | 321148.i | −0.670646 | − | 0.670646i | ||||
\(693\) | 29633.0 | − | 29633.0i | 0.0617034 | − | 0.0617034i | ||||
\(694\) | − | 664336.i | − | 1.37933i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 836636. | 1.72710 | ||||||||
\(697\) | 632614. | + | 632614.i | 1.30219 | + | 1.30219i | ||||
\(698\) | −623939. | + | 623939.i | −1.28065 | + | 1.28065i | ||||
\(699\) | 678486.i | 1.38863i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −624118. | −1.27008 | −0.635039 | − | 0.772480i | \(-0.719016\pi\) | ||||
−0.635039 | + | 0.772480i | \(0.719016\pi\) | |||||||
\(702\) | 112125. | + | 112125.i | 0.227525 | + | 0.227525i | ||||
\(703\) | −107506. | + | 107506.i | −0.217532 | + | 0.217532i | ||||
\(704\) | − | 1.12292e6i | − | 2.26571i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.16811e6 | −2.34354 | ||||||||
\(707\) | −84090.7 | − | 84090.7i | −0.168232 | − | 0.168232i | ||||
\(708\) | 198275. | − | 198275.i | 0.395550 | − | 0.395550i | ||||
\(709\) | 148682.i | 0.295779i | 0.989004 | + | 0.147889i | \(0.0472480\pi\) | ||||
−0.989004 | + | 0.147889i | \(0.952752\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −16313.7 | −0.0322711 | ||||||||
\(712\) | −459146. | − | 459146.i | −0.905713 | − | 0.905713i | ||||
\(713\) | 405844. | − | 405844.i | 0.798325 | − | 0.798325i | ||||
\(714\) | − | 489851.i | − | 0.960876i | ||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.10497e6 | 2.15538 | ||||||||
\(717\) | 567069. | + | 567069.i | 1.10306 | + | 1.10306i | ||||
\(718\) | −799024. | + | 799024.i | −1.54993 | + | 1.54993i | ||||
\(719\) | − | 259924.i | − | 0.502792i | −0.967884 | − | 0.251396i | \(-0.919110\pi\) | ||
0.967884 | − | 0.251396i | \(-0.0808897\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 182356. | 0.350792 | ||||||||
\(722\) | 372246. | + | 372246.i | 0.714094 | + | 0.714094i | ||||
\(723\) | −336645. | + | 336645.i | −0.644014 | + | 0.644014i | ||||
\(724\) | − | 994291.i | − | 1.89686i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −958382. | −1.81830 | ||||||||
\(727\) | −188187. | − | 188187.i | −0.356058 | − | 0.356058i | 0.506300 | − | 0.862358i | \(-0.331013\pi\) |
−0.862358 | + | 0.506300i | \(0.831013\pi\) | |||||||
\(728\) | −33870.7 | + | 33870.7i | −0.0639090 | + | 0.0639090i | ||||
\(729\) | 419747.i | 0.789828i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.03099e6 | 1.92939 | ||||||||
\(732\) | 329012. | + | 329012.i | 0.614030 | + | 0.614030i | ||||
\(733\) | −279698. | + | 279698.i | −0.520573 | + | 0.520573i | −0.917745 | − | 0.397171i | \(-0.869992\pi\) |
0.397171 | + | 0.917745i | \(0.369992\pi\) | |||||||
\(734\) | 1.20254e6i | 2.23208i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 438756. | 0.809967 | ||||||||
\(737\) | −261704. | − | 261704.i | −0.481810 | − | 0.481810i | ||||
\(738\) | −130107. | + | 130107.i | −0.238884 | + | 0.238884i | ||||
\(739\) | 390065.i | 0.714246i | 0.934057 | + | 0.357123i | \(0.116242\pi\) | ||||
−0.934057 | + | 0.357123i | \(0.883758\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 79734.9 | 0.145215 | ||||||||
\(742\) | 364803. | + | 364803.i | 0.662599 | + | 0.662599i | ||||
\(743\) | 76893.6 | − | 76893.6i | 0.139288 | − | 0.139288i | −0.634025 | − | 0.773313i | \(-0.718598\pi\) |
0.773313 | + | 0.634025i | \(0.218598\pi\) | |||||||
\(744\) | − | 819317.i | − | 1.48015i | ||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 438508. | 0.787951 | ||||||||
\(747\) | −91597.2 | − | 91597.2i | −0.164150 | − | 0.164150i | ||||
\(748\) | −1.36012e6 | + | 1.36012e6i | −2.43094 | + | 2.43094i | ||||
\(749\) | − | 20313.8i | − | 0.0362100i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 691655. | 1.22634 | 0.613168 | − | 0.789952i | \(-0.289895\pi\) | ||||
0.613168 | + | 0.789952i | \(0.289895\pi\) | |||||||
\(752\) | 68819.3 | + | 68819.3i | 0.121695 | + | 0.121695i | ||||
\(753\) | −183109. | + | 183109.i | −0.322938 | + | 0.322938i | ||||
\(754\) | − | 295692.i | − | 0.520113i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −326152. | −0.570659 | ||||||||
\(757\) | −176521. | − | 176521.i | −0.308039 | − | 0.308039i | 0.536110 | − | 0.844148i | \(-0.319893\pi\) |
−0.844148 | + | 0.536110i | \(0.819893\pi\) | |||||||
\(758\) | 764187. | − | 764187.i | 1.33003 | − | 1.33003i | ||||
\(759\) | − | 798618.i | − | 1.38629i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −873004. | −1.50746 | −0.753732 | − | 0.657182i | \(-0.771748\pi\) | ||||
−0.753732 | + | 0.657182i | \(0.771748\pi\) | |||||||
\(762\) | −561300. | − | 561300.i | −0.966686 | − | 0.966686i | ||||
\(763\) | 253162. | − | 253162.i | 0.434861 | − | 0.434861i | ||||
\(764\) | 32020.4i | 0.0548580i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.56524e6 | −2.66762 | ||||||||
\(767\) | −28148.1 | − | 28148.1i | −0.0478475 | − | 0.0478475i | ||||
\(768\) | 534580. | − | 534580.i | 0.906338 | − | 0.906338i | ||||
\(769\) | 184914.i | 0.312692i | 0.987702 | + | 0.156346i | \(0.0499715\pi\) | ||||
−0.987702 | + | 0.156346i | \(0.950028\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −404326. | −0.680179 | ||||||||
\(772\) | −243984. | − | 243984.i | −0.409380 | − | 0.409380i | ||||
\(773\) | −528554. | + | 528554.i | −0.884566 | + | 0.884566i | −0.993995 | − | 0.109429i | \(-0.965098\pi\) |
0.109429 | + | 0.993995i | \(0.465098\pi\) | |||||||
\(774\) | 212038.i | 0.353943i | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 848107. | 1.40840 | ||||||||
\(777\) | 86559.0 | + | 86559.0i | 0.143374 | + | 0.143374i | ||||
\(778\) | −377365. | + | 377365.i | −0.623451 | + | 0.623451i | ||||
\(779\) | − | 478747.i | − | 0.788916i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.35592e6 | 2.22295 | ||||||||
\(782\) | −920050. | − | 920050.i | −1.50452 | − | 1.50452i | ||||
\(783\) | 571853. | − | 571853.i | 0.932740 | − | 0.932740i | ||||
\(784\) | − | 10716.1i | − | 0.0174342i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1.90246e6 | −3.07943 | ||||||||
\(787\) | 460572. | + | 460572.i | 0.743614 | + | 0.743614i | 0.973272 | − | 0.229657i | \(-0.0737606\pi\) |
−0.229657 | + | 0.973272i | \(0.573761\pi\) | |||||||
\(788\) | 626841. | − | 626841.i | 1.00950 | − | 1.00950i | ||||
\(789\) | 269333.i | 0.432650i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −184594. | −0.295028 | ||||||||
\(792\) | −112361. | − | 112361.i | −0.179129 | − | 0.179129i | ||||
\(793\) | 46708.2 | − | 46708.2i | 0.0742757 | − | 0.0742757i | ||||
\(794\) | 1.39709e6i | 2.21606i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 299023. | 0.471931 | ||||||||
\(797\) | −35127.1 | − | 35127.1i | −0.0553001 | − | 0.0553001i | 0.678916 | − | 0.734216i | \(-0.262450\pi\) |
−0.734216 | + | 0.678916i | \(0.762450\pi\) | |||||||
\(798\) | −185353. | + | 185353.i | −0.291068 | + | 0.291068i | ||||
\(799\) | 1.29909e6i | 2.03491i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 121302. | 0.189061 | ||||||||
\(802\) | −769441. | − | 769441.i | −1.19626 | − | 1.19626i | ||||
\(803\) | 112853. | − | 112853.i | 0.175017 | − | 0.175017i | ||||
\(804\) | − | 556666.i | − | 0.861158i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −289571. | −0.445744 | ||||||||
\(807\) | −217432. | − | 217432.i | −0.333869 | − | 0.333869i | ||||
\(808\) | −318852. | + | 318852.i | −0.488389 | + | 0.488389i | ||||
\(809\) | 293002.i | 0.447687i | 0.974625 | + | 0.223843i | \(0.0718604\pi\) | ||||
−0.974625 | + | 0.223843i | \(0.928140\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 928790. | 1.41213 | 0.706067 | − | 0.708145i | \(-0.250468\pi\) | ||||
0.706067 | + | 0.708145i | \(0.250468\pi\) | |||||||
\(812\) | 430059. | + | 430059.i | 0.652253 | + | 0.652253i | ||||
\(813\) | 532321. | − | 532321.i | 0.805364 | − | 0.805364i | ||||
\(814\) | − | 768282.i | − | 1.15950i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −126396. | −0.189825 | ||||||||
\(817\) | −390114. | − | 390114.i | −0.584450 | − | 0.584450i | ||||
\(818\) | 898683. | − | 898683.i | 1.34307 | − | 1.34307i | ||||
\(819\) | − | 8948.32i | − | 0.0133405i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.04744e6 | 1.55397 | 0.776985 | − | 0.629519i | \(-0.216748\pi\) | ||||
0.776985 | + | 0.629519i | \(0.216748\pi\) | |||||||
\(822\) | −1.28230e6 | − | 1.28230e6i | −1.89779 | − | 1.89779i | ||||
\(823\) | −553267. | + | 553267.i | −0.816836 | + | 0.816836i | −0.985648 | − | 0.168812i | \(-0.946007\pi\) |
0.168812 | + | 0.985648i | \(0.446007\pi\) | |||||||
\(824\) | − | 691451.i | − | 1.01837i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 130867. | 0.191810 | ||||||||
\(827\) | −240884. | − | 240884.i | −0.352206 | − | 0.352206i | 0.508724 | − | 0.860930i | \(-0.330117\pi\) |
−0.860930 | + | 0.508724i | \(0.830117\pi\) | |||||||
\(828\) | 118388. | − | 118388.i | 0.172682 | − | 0.172682i | ||||
\(829\) | 1.27420e6i | 1.85409i | 0.374956 | + | 0.927043i | \(0.377658\pi\) | ||||
−0.374956 | + | 0.927043i | \(0.622342\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −455040. | −0.658943 | ||||||||
\(832\) | −169545. | − | 169545.i | −0.244928 | − | 0.244928i | ||||
\(833\) | 101142. | − | 101142.i | 0.145762 | − | 0.145762i | ||||
\(834\) | − | 1.52036e6i | − | 2.18582i | ||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.02931e6 | 1.47276 | ||||||||
\(837\) | −560015. | − | 560015.i | −0.799371 | − | 0.799371i | ||||
\(838\) | 1.21083e6 | − | 1.21083e6i | 1.72423 | − | 1.72423i | ||||
\(839\) | 26951.6i | 0.0382878i | 0.999817 | + | 0.0191439i | \(0.00609407\pi\) | ||||
−0.999817 | + | 0.0191439i | \(0.993906\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −800790. | −1.13221 | ||||||||
\(842\) | 1.00335e6 | + | 1.00335e6i | 1.41523 | + | 1.41523i | ||||
\(843\) | 851564. | − | 851564.i | 1.19829 | − | 1.19829i | ||||
\(844\) | − | 418291.i | − | 0.587211i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −267177. | −0.373300 | ||||||||
\(847\) | −197883. | − | 197883.i | −0.275830 | − | 0.275830i | ||||
\(848\) | 94130.1 | − | 94130.1i | 0.130899 | − | 0.130899i | ||||
\(849\) | − | 295658.i | − | 0.410179i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 325154. | 0.448984 | ||||||||
\(852\) | 1.44207e6 | + | 1.44207e6i | 1.98659 | + | 1.98659i | ||||
\(853\) | −546317. | + | 546317.i | −0.750838 | + | 0.750838i | −0.974636 | − | 0.223798i | \(-0.928155\pi\) |
0.223798 | + | 0.974636i | \(0.428155\pi\) | |||||||
\(854\) | 217158.i | 0.297755i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −77025.2 | −0.105120 | ||||||||
\(857\) | −223047. | − | 223047.i | −0.303692 | − | 0.303692i | 0.538764 | − | 0.842457i | \(-0.318891\pi\) |
−0.842457 | + | 0.538764i | \(0.818891\pi\) | |||||||
\(858\) | −284909. | + | 284909.i | −0.387018 | + | 0.387018i | ||||
\(859\) | − | 737032.i | − | 0.998849i | −0.866357 | − | 0.499425i | \(-0.833545\pi\) | ||
0.866357 | − | 0.499425i | \(-0.166455\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −385465. | −0.519970 | ||||||||
\(862\) | −455470. | − | 455470.i | −0.612978 | − | 0.612978i | ||||
\(863\) | −352024. | + | 352024.i | −0.472662 | + | 0.472662i | −0.902775 | − | 0.430113i | \(-0.858474\pi\) |
0.430113 | + | 0.902775i | \(0.358474\pi\) | |||||||
\(864\) | − | 605429.i | − | 0.811028i | ||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1.15561e6 | −1.54090 | ||||||||
\(867\) | −620023. | − | 620023.i | −0.824840 | − | 0.824840i | ||||
\(868\) | 421156. | − | 421156.i | 0.558990 | − | 0.558990i | ||||
\(869\) | 214495.i | 0.284039i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −79027.2 | −0.104169 | ||||||||
\(872\) | −959931. | − | 959931.i | −1.26243 | − | 1.26243i | ||||
\(873\) | −112031. | + | 112031.i | −0.146997 | + | 0.146997i | ||||
\(874\) | 696271.i | 0.911497i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 240047. | 0.312815 | ||||||||
\(877\) | 409187. | + | 409187.i | 0.532014 | + | 0.532014i | 0.921171 | − | 0.389157i | \(-0.127234\pi\) |
−0.389157 | + | 0.921171i | \(0.627234\pi\) | |||||||
\(878\) | 517197. | − | 517197.i | 0.670914 | − | 0.670914i | ||||
\(879\) | − | 258728.i | − | 0.334862i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −640306. | −0.824966 | −0.412483 | − | 0.910965i | \(-0.635338\pi\) | ||||
−0.412483 | + | 0.910965i | \(0.635338\pi\) | |||||||
\(882\) | 20801.4 | + | 20801.4i | 0.0267397 | + | 0.0267397i | ||||
\(883\) | −399939. | + | 399939.i | −0.512947 | + | 0.512947i | −0.915428 | − | 0.402481i | \(-0.868148\pi\) |
0.402481 | + | 0.915428i | \(0.368148\pi\) | |||||||
\(884\) | 410718.i | 0.525581i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.32267e6 | −1.68494 | ||||||||
\(887\) | 509945. | + | 509945.i | 0.648150 | + | 0.648150i | 0.952546 | − | 0.304395i | \(-0.0984544\pi\) |
−0.304395 | + | 0.952546i | \(0.598454\pi\) | |||||||
\(888\) | 328211. | − | 328211.i | 0.416224 | − | 0.416224i | ||||
\(889\) | − | 231790.i | − | 0.293286i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.28528e6 | −1.61898 | ||||||||
\(892\) | 1.48227e6 | + | 1.48227e6i | 1.86294 | + | 1.86294i | ||||
\(893\) | 491558. | − | 491558.i | 0.616413 | − | 0.616413i | ||||
\(894\) | − | 314156.i | − | 0.393070i | ||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 515835. | 0.642532 | ||||||||
\(897\) | −120580. | − | 120580.i | −0.149862 | − | 0.149862i | ||||
\(898\) | 440329. | − | 440329.i | 0.546041 | − | 0.546041i | ||||
\(899\) | 1.47685e6i | 1.82733i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.77687e6 | 2.18880 | ||||||||
\(902\) | 1.71066e6 | + | 1.71066e6i | 2.10257 | + | 2.10257i | ||||
\(903\) | −314102. | + | 314102.i | −0.385208 | + | 0.385208i | ||||
\(904\) | 699934.i | 0.856486i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −1.15601e6 | −1.40833 | ||||||||
\(907\) | 207779. | + | 207779.i | 0.252573 | + | 0.252573i | 0.822025 | − | 0.569452i | \(-0.192845\pi\) |
−0.569452 | + | 0.822025i | \(0.692845\pi\) | |||||||
\(908\) | 1.23330e6 | − | 1.23330e6i | 1.49588 | − | 1.49588i | ||||
\(909\) | − | 84237.5i | − | 0.101948i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −398980. | −0.480745 | −0.240372 | − | 0.970681i | \(-0.577270\pi\) | ||||
−0.240372 | + | 0.970681i | \(0.577270\pi\) | |||||||
\(912\) | 47826.7 | + | 47826.7i | 0.0575017 | + | 0.0575017i | ||||
\(913\) | −1.20433e6 | + | 1.20433e6i | −1.44479 | + | 1.44479i | ||||
\(914\) | 1.43537e6i | 1.71820i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −936929. | −1.11665 | ||||||||
\(917\) | −392812. | − | 392812.i | −0.467139 | − | 0.467139i | ||||
\(918\) | −1.26956e6 | + | 1.26956e6i | −1.50649 | + | 1.50649i | ||||
\(919\) | 547724.i | 0.648531i | 0.945966 | + | 0.324265i | \(0.105117\pi\) | ||||
−0.945966 | + | 0.324265i | \(0.894883\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −325847. | −0.384144 | ||||||||
\(922\) | 85691.2 | + | 85691.2i | 0.100803 | + | 0.100803i | ||||
\(923\) | 204724. | − | 204724.i | 0.240306 | − | 0.240306i | ||||
\(924\) | − | 828750.i | − | 0.970688i | ||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −1.75417e6 | −2.04574 | ||||||||
\(927\) | 91337.3 | + | 91337.3i | 0.106289 | + | 0.106289i | ||||
\(928\) | −798309. | + | 798309.i | −0.926990 | + | 0.926990i | ||||
\(929\) | − | 163754.i | − | 0.189740i | −0.995490 | − | 0.0948701i | \(-0.969756\pi\) | ||
0.995490 | − | 0.0948701i | \(-0.0302436\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −76542.1 | −0.0883081 | ||||||||
\(932\) | 1.32243e6 | + | 1.32243e6i | 1.52244 | + | 1.52244i | ||||
\(933\) | −140964. | + | 140964.i | −0.161937 | + | 0.161937i | ||||
\(934\) | 1.26239e6i | 1.44710i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −33929.9 | −0.0387285 | ||||||||
\(937\) | −208041. | − | 208041.i | −0.236958 | − | 0.236958i | 0.578632 | − | 0.815589i | \(-0.303587\pi\) |
−0.815589 | + | 0.578632i | \(0.803587\pi\) | |||||||
\(938\) | 183708. | − | 183708.i | 0.208796 | − | 0.208796i | ||||
\(939\) | 68865.9i | 0.0781039i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −224861. | −0.253942 | −0.126971 | − | 0.991906i | \(-0.540525\pi\) | ||||
−0.126971 | + | 0.991906i | \(0.540525\pi\) | |||||||
\(942\) | 1.13956e6 | + | 1.13956e6i | 1.28421 | + | 1.28421i | ||||
\(943\) | −723989. | + | 723989.i | −0.814158 | + | 0.814158i | ||||
\(944\) | − | 33767.7i | − | 0.0378928i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.78791e6 | 3.11528 | ||||||||
\(947\) | 215253. | + | 215253.i | 0.240021 | + | 0.240021i | 0.816859 | − | 0.576838i | \(-0.195714\pi\) |
−0.576838 | + | 0.816859i | \(0.695714\pi\) | |||||||
\(948\) | −228124. | + | 228124.i | −0.253837 | + | 0.253837i | ||||
\(949\) | − | 34078.3i | − | 0.0378395i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −914558. | −1.01123 | ||||||||
\(952\) | −383508. | − | 383508.i | −0.423156 | − | 0.423156i | ||||
\(953\) | −579508. | + | 579508.i | −0.638078 | + | 0.638078i | −0.950081 | − | 0.312003i | \(-0.899000\pi\) |
0.312003 | + | 0.950081i | \(0.399000\pi\) | |||||||
\(954\) | 365440.i | 0.401532i | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 2.21054e6 | 2.41870 | ||||||||
\(957\) | 1.45307e6 | + | 1.45307e6i | 1.58659 | + | 1.58659i | ||||
\(958\) | −1.36906e6 | + | 1.36906e6i | −1.49173 | + | 1.49173i | ||||
\(959\) | − | 529530.i | − | 0.575776i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 522760. | 0.566051 | ||||||||
\(962\) | −116000. | − | 116000.i | −0.125345 | − | 0.125345i | ||||
\(963\) | 10174.7 | − | 10174.7i | 0.0109715 | − | 0.0109715i | ||||
\(964\) | 1.31230e6i | 1.41215i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 560605. | 0.600763 | ||||||||
\(967\) | −630473. | − | 630473.i | −0.674239 | − | 0.674239i | 0.284452 | − | 0.958690i | \(-0.408188\pi\) |
−0.958690 | + | 0.284452i | \(0.908188\pi\) | |||||||
\(968\) | −750324. | + | 750324.i | −0.800752 | + | 0.800752i | ||||
\(969\) | 902814.i | 0.961503i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 964569. | 1.02304 | 0.511522 | − | 0.859270i | \(-0.329082\pi\) | ||||
0.511522 | + | 0.859270i | \(0.329082\pi\) | |||||||
\(972\) | −358293. | − | 358293.i | −0.379232 | − | 0.379232i | ||||
\(973\) | 313918. | − | 313918.i | 0.331582 | − | 0.331582i | ||||
\(974\) | − | 2.49393e6i | − | 2.62885i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 56033.1 | 0.0588227 | ||||||||
\(977\) | 284782. | + | 284782.i | 0.298348 | + | 0.298348i | 0.840367 | − | 0.542018i | \(-0.182340\pi\) |
−0.542018 | + | 0.840367i | \(0.682340\pi\) | |||||||
\(978\) | −916989. | + | 916989.i | −0.958708 | + | 0.958708i | ||||
\(979\) | − | 1.59489e6i | − | 1.66405i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 253604. | 0.263523 | ||||||||
\(982\) | 127697. | + | 127697.i | 0.132421 | + | 0.132421i | ||||
\(983\) | 973234. | − | 973234.i | 1.00719 | − | 1.00719i | 0.00721380 | − | 0.999974i | \(-0.497704\pi\) |
0.999974 | − | 0.00721380i | \(-0.00229625\pi\) | |||||||
\(984\) | 1.46159e6i | 1.50951i | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 3.34803e6 | 3.44378 | ||||||||
\(987\) | −395780. | − | 395780.i | −0.406275 | − | 0.406275i | ||||
\(988\) | 155411. | − | 155411.i | 0.159209 | − | 0.159209i | ||||
\(989\) | 1.17991e6i | 1.20630i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.59169e6 | −1.62073 | −0.810364 | − | 0.585926i | \(-0.800731\pi\) | ||||
−0.810364 | + | 0.585926i | \(0.800731\pi\) | |||||||
\(992\) | 781784. | + | 781784.i | 0.794444 | + | 0.794444i | ||||
\(993\) | −670970. | + | 670970.i | −0.680464 | + | 0.680464i | ||||
\(994\) | 951811.i | 0.963336i | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −2.56171e6 | −2.58233 | ||||||||
\(997\) | 247611. | + | 247611.i | 0.249104 | + | 0.249104i | 0.820603 | − | 0.571499i | \(-0.193638\pi\) |
−0.571499 | + | 0.820603i | \(0.693638\pi\) | |||||||
\(998\) | 896879. | − | 896879.i | 0.900477 | − | 0.900477i | ||||
\(999\) | − | 448673.i | − | 0.449572i |
(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 | 175.5.g.d.57.15 | yes | 32 | |
5.2 | odd | 4 | inner | 175.5.g.d.43.2 | ✓ | 32 | |
5.3 | odd | 4 | inner | 175.5.g.d.43.15 | yes | 32 | |
5.4 | even | 2 | inner | 175.5.g.d.57.2 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
175.5.g.d.43.2 | ✓ | 32 | 5.2 | odd | 4 | inner | |
175.5.g.d.43.15 | yes | 32 | 5.3 | odd | 4 | inner | |
175.5.g.d.57.2 | yes | 32 | 5.4 | even | 2 | inner | |
175.5.g.d.57.15 | yes | 32 | 1.1 | even | 1 | trivial |