Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [74,5,Mod(31,74)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(74, base_ring=CyclotomicField(4))
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("74.31");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 74 = 2 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 74.d (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: | \(7.64937726820\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Relative dimension: | \(7\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} + 727 x^{12} + 198453 x^{10} + 24875201 x^{8} + 1392846203 x^{6} + 29089700589 x^{4} + 220261242916 x^{2} + 446074380544 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 31.3 | ||
Root | \(-4.34447i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 74.31 |
Dual form | 74.5.d.a.43.5 |
$q$-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 \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).
\(n\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00000 | − | 2.00000i | −0.500000 | − | 0.500000i | ||||
\(3\) | − | 5.34447i | − | 0.593830i | −0.954904 | − | 0.296915i | \(-0.904042\pi\) | ||
0.954904 | − | 0.296915i | \(-0.0959577\pi\) | |||||||
\(4\) | 8.00000i | 0.500000i | ||||||||
\(5\) | 10.1818 | − | 10.1818i | 0.407273 | − | 0.407273i | −0.473513 | − | 0.880787i | \(-0.657014\pi\) |
0.880787 | + | 0.473513i | \(0.157014\pi\) | |||||||
\(6\) | −10.6889 | + | 10.6889i | −0.296915 | + | 0.296915i | ||||
\(7\) | −94.0964 | −1.92033 | −0.960167 | − | 0.279427i | \(-0.909855\pi\) | ||||
−0.960167 | + | 0.279427i | \(0.909855\pi\) | |||||||
\(8\) | 16.0000 | − | 16.0000i | 0.250000 | − | 0.250000i | ||||
\(9\) | 52.4367 | 0.647366 | ||||||||
\(10\) | −40.7273 | −0.407273 | ||||||||
\(11\) | − | 104.701i | − | 0.865297i | −0.901563 | − | 0.432649i | \(-0.857579\pi\) | ||
0.901563 | − | 0.432649i | \(-0.142421\pi\) | |||||||
\(12\) | 42.7557 | 0.296915 | ||||||||
\(13\) | −156.979 | + | 156.979i | −0.928871 | + | 0.928871i | −0.997633 | − | 0.0687618i | \(-0.978095\pi\) |
0.0687618 | + | 0.997633i | \(0.478095\pi\) | |||||||
\(14\) | 188.193 | + | 188.193i | 0.960167 | + | 0.960167i | ||||
\(15\) | −54.4165 | − | 54.4165i | −0.241851 | − | 0.241851i | ||||
\(16\) | −64.0000 | −0.250000 | ||||||||
\(17\) | −288.653 | + | 288.653i | −0.998801 | + | 0.998801i | −0.999999 | − | 0.00119826i | \(-0.999619\pi\) |
0.00119826 | + | 0.999999i | \(0.499619\pi\) | |||||||
\(18\) | −104.873 | − | 104.873i | −0.323683 | − | 0.323683i | ||||
\(19\) | −257.997 | + | 257.997i | −0.714672 | + | 0.714672i | −0.967509 | − | 0.252837i | \(-0.918636\pi\) |
0.252837 | + | 0.967509i | \(0.418636\pi\) | |||||||
\(20\) | 81.4547 | + | 81.4547i | 0.203637 | + | 0.203637i | ||||
\(21\) | 502.895i | 1.14035i | ||||||||
\(22\) | −209.402 | + | 209.402i | −0.432649 | + | 0.432649i | ||||
\(23\) | 226.710 | − | 226.710i | 0.428563 | − | 0.428563i | −0.459575 | − | 0.888139i | \(-0.651998\pi\) |
0.888139 | + | 0.459575i | \(0.151998\pi\) | |||||||
\(24\) | −85.5115 | − | 85.5115i | −0.148457 | − | 0.148457i | ||||
\(25\) | 417.660i | 0.668257i | ||||||||
\(26\) | 627.917 | 0.928871 | ||||||||
\(27\) | − | 713.148i | − | 0.978255i | ||||||
\(28\) | − | 752.771i | − | 0.960167i | ||||||
\(29\) | −59.2294 | − | 59.2294i | −0.0704274 | − | 0.0704274i | 0.671016 | − | 0.741443i | \(-0.265858\pi\) |
−0.741443 | + | 0.671016i | \(0.765858\pi\) | |||||||
\(30\) | 217.666i | 0.241851i | ||||||||
\(31\) | −608.888 | − | 608.888i | −0.633598 | − | 0.633598i | 0.315371 | − | 0.948969i | \(-0.397871\pi\) |
−0.948969 | + | 0.315371i | \(0.897871\pi\) | |||||||
\(32\) | 128.000 | + | 128.000i | 0.125000 | + | 0.125000i | ||||
\(33\) | −559.571 | −0.513839 | ||||||||
\(34\) | 1154.61 | 0.998801 | ||||||||
\(35\) | −958.074 | + | 958.074i | −0.782101 | + | 0.782101i | ||||
\(36\) | 419.493i | 0.323683i | ||||||||
\(37\) | −913.654 | − | 1019.51i | −0.667388 | − | 0.744711i | ||||
\(38\) | 1031.99 | 0.714672 | ||||||||
\(39\) | 838.970 | + | 838.970i | 0.551591 | + | 0.551591i | ||||
\(40\) | − | 325.819i | − | 0.203637i | ||||||
\(41\) | − | 1818.47i | − | 1.08178i | −0.841093 | − | 0.540891i | \(-0.818087\pi\) | ||
0.841093 | − | 0.540891i | \(-0.181913\pi\) | |||||||
\(42\) | 1005.79 | − | 1005.79i | 0.570175 | − | 0.570175i | ||||
\(43\) | 1889.70 | − | 1889.70i | 1.02201 | − | 1.02201i | 0.0222575 | − | 0.999752i | \(-0.492915\pi\) |
0.999752 | − | 0.0222575i | \(-0.00708538\pi\) | |||||||
\(44\) | 837.608 | 0.432649 | ||||||||
\(45\) | 533.902 | − | 533.902i | 0.263655 | − | 0.263655i | ||||
\(46\) | −906.840 | −0.428563 | ||||||||
\(47\) | −2515.46 | −1.13873 | −0.569367 | − | 0.822084i | \(-0.692812\pi\) | ||||
−0.569367 | + | 0.822084i | \(0.692812\pi\) | |||||||
\(48\) | 342.046i | 0.148457i | ||||||||
\(49\) | 6453.12 | 2.68768 | ||||||||
\(50\) | 835.321 | − | 835.321i | 0.334128 | − | 0.334128i | ||||
\(51\) | 1542.70 | + | 1542.70i | 0.593118 | + | 0.593118i | ||||
\(52\) | −1255.83 | − | 1255.83i | −0.464436 | − | 0.464436i | ||||
\(53\) | −185.050 | −0.0658777 | −0.0329388 | − | 0.999457i | \(-0.510487\pi\) | ||||
−0.0329388 | + | 0.999457i | \(0.510487\pi\) | |||||||
\(54\) | −1426.30 | + | 1426.30i | −0.489127 | + | 0.489127i | ||||
\(55\) | −1066.05 | − | 1066.05i | −0.352413 | − | 0.352413i | ||||
\(56\) | −1505.54 | + | 1505.54i | −0.480083 | + | 0.480083i | ||||
\(57\) | 1378.85 | + | 1378.85i | 0.424393 | + | 0.424393i | ||||
\(58\) | 236.918i | 0.0704274i | ||||||||
\(59\) | −1987.36 | + | 1987.36i | −0.570916 | + | 0.570916i | −0.932384 | − | 0.361468i | \(-0.882276\pi\) |
0.361468 | + | 0.932384i | \(0.382276\pi\) | |||||||
\(60\) | 435.332 | − | 435.332i | 0.120925 | − | 0.120925i | ||||
\(61\) | −4805.67 | − | 4805.67i | −1.29150 | − | 1.29150i | −0.933859 | − | 0.357642i | \(-0.883581\pi\) |
−0.357642 | − | 0.933859i | \(-0.616419\pi\) | |||||||
\(62\) | 2435.55i | 0.633598i | ||||||||
\(63\) | −4934.10 | −1.24316 | ||||||||
\(64\) | − | 512.000i | − | 0.125000i | ||||||
\(65\) | 3196.67i | 0.756609i | ||||||||
\(66\) | 1119.14 | + | 1119.14i | 0.256920 | + | 0.256920i | ||||
\(67\) | − | 2627.87i | − | 0.585402i | −0.956204 | − | 0.292701i | \(-0.905446\pi\) | ||
0.956204 | − | 0.292701i | \(-0.0945540\pi\) | |||||||
\(68\) | −2309.23 | − | 2309.23i | −0.499401 | − | 0.499401i | ||||
\(69\) | −1211.64 | − | 1211.64i | −0.254494 | − | 0.254494i | ||||
\(70\) | 3832.29 | 0.782101 | ||||||||
\(71\) | 5726.26 | 1.13594 | 0.567968 | − | 0.823050i | \(-0.307730\pi\) | ||||
0.567968 | + | 0.823050i | \(0.307730\pi\) | |||||||
\(72\) | 838.987 | − | 838.987i | 0.161842 | − | 0.161842i | ||||
\(73\) | 7873.75i | 1.47753i | 0.673964 | + | 0.738764i | \(0.264590\pi\) | ||||
−0.673964 | + | 0.738764i | \(0.735410\pi\) | |||||||
\(74\) | −211.711 | + | 3866.32i | −0.0386615 | + | 0.706049i | ||||
\(75\) | 2232.17 | 0.396831 | ||||||||
\(76\) | −2063.97 | − | 2063.97i | −0.357336 | − | 0.357336i | ||||
\(77\) | 9851.98i | 1.66166i | ||||||||
\(78\) | − | 3355.88i | − | 0.551591i | ||||||
\(79\) | 3214.81 | − | 3214.81i | 0.515112 | − | 0.515112i | −0.400977 | − | 0.916088i | \(-0.631329\pi\) |
0.916088 | + | 0.400977i | \(0.131329\pi\) | |||||||
\(80\) | −651.637 | + | 651.637i | −0.101818 | + | 0.101818i | ||||
\(81\) | 435.978 | 0.0664499 | ||||||||
\(82\) | −3636.95 | + | 3636.95i | −0.540891 | + | 0.540891i | ||||
\(83\) | −9870.10 | −1.43273 | −0.716367 | − | 0.697724i | \(-0.754196\pi\) | ||||
−0.716367 | + | 0.697724i | \(0.754196\pi\) | |||||||
\(84\) | −4023.16 | −0.570175 | ||||||||
\(85\) | 5878.04i | 0.813570i | ||||||||
\(86\) | −7558.78 | −1.02201 | ||||||||
\(87\) | −316.550 | + | 316.550i | −0.0418218 | + | 0.0418218i | ||||
\(88\) | −1675.22 | − | 1675.22i | −0.216324 | − | 0.216324i | ||||
\(89\) | 3659.89 | + | 3659.89i | 0.462049 | + | 0.462049i | 0.899327 | − | 0.437278i | \(-0.144057\pi\) |
−0.437278 | + | 0.899327i | \(0.644057\pi\) | |||||||
\(90\) | −2135.61 | −0.263655 | ||||||||
\(91\) | 14771.2 | − | 14771.2i | 1.78374 | − | 1.78374i | ||||
\(92\) | 1813.68 | + | 1813.68i | 0.214282 | + | 0.214282i | ||||
\(93\) | −3254.18 | + | 3254.18i | −0.376249 | + | 0.376249i | ||||
\(94\) | 5030.93 | + | 5030.93i | 0.569367 | + | 0.569367i | ||||
\(95\) | 5253.76i | 0.582134i | ||||||||
\(96\) | 684.092 | − | 684.092i | 0.0742287 | − | 0.0742287i | ||||
\(97\) | 945.694 | − | 945.694i | 0.100510 | − | 0.100510i | −0.655064 | − | 0.755573i | \(-0.727358\pi\) |
0.755573 | + | 0.655064i | \(0.227358\pi\) | |||||||
\(98\) | −12906.2 | − | 12906.2i | −1.34384 | − | 1.34384i | ||||
\(99\) | − | 5490.17i | − | 0.560164i | ||||||
\(100\) | −3341.28 | −0.334128 | ||||||||
\(101\) | − | 18425.6i | − | 1.80625i | −0.429378 | − | 0.903125i | \(-0.641267\pi\) | ||
0.429378 | − | 0.903125i | \(-0.358733\pi\) | |||||||
\(102\) | − | 6170.79i | − | 0.593118i | ||||||
\(103\) | −663.465 | − | 663.465i | −0.0625379 | − | 0.0625379i | 0.675146 | − | 0.737684i | \(-0.264081\pi\) |
−0.737684 | + | 0.675146i | \(0.764081\pi\) | |||||||
\(104\) | 5023.34i | 0.464436i | ||||||||
\(105\) | 5120.39 | + | 5120.39i | 0.464435 | + | 0.464435i | ||||
\(106\) | 370.101 | + | 370.101i | 0.0329388 | + | 0.0329388i | ||||
\(107\) | −1562.94 | −0.136513 | −0.0682565 | − | 0.997668i | \(-0.521744\pi\) | ||||
−0.0682565 | + | 0.997668i | \(0.521744\pi\) | |||||||
\(108\) | 5705.18 | 0.489127 | ||||||||
\(109\) | −10571.0 | + | 10571.0i | −0.889738 | + | 0.889738i | −0.994498 | − | 0.104759i | \(-0.966593\pi\) |
0.104759 | + | 0.994498i | \(0.466593\pi\) | |||||||
\(110\) | 4264.19i | 0.352413i | ||||||||
\(111\) | −5448.73 | + | 4882.99i | −0.442231 | + | 0.396314i | ||||
\(112\) | 6022.17 | 0.480083 | ||||||||
\(113\) | 4684.76 | + | 4684.76i | 0.366886 | + | 0.366886i | 0.866340 | − | 0.499455i | \(-0.166466\pi\) |
−0.499455 | + | 0.866340i | \(0.666466\pi\) | |||||||
\(114\) | − | 5515.42i | − | 0.424393i | ||||||
\(115\) | − | 4616.65i | − | 0.349085i | ||||||
\(116\) | 473.835 | − | 473.835i | 0.0352137 | − | 0.0352137i | ||||
\(117\) | −8231.47 | + | 8231.47i | −0.601320 | + | 0.601320i | ||||
\(118\) | 7949.43 | 0.570916 | ||||||||
\(119\) | 27161.2 | − | 27161.2i | 1.91803 | − | 1.91803i | ||||
\(120\) | −1741.33 | −0.120925 | ||||||||
\(121\) | 3678.71 | 0.251261 | ||||||||
\(122\) | 19222.7i | 1.29150i | ||||||||
\(123\) | −9718.77 | −0.642394 | ||||||||
\(124\) | 4871.10 | − | 4871.10i | 0.316799 | − | 0.316799i | ||||
\(125\) | 10616.2 | + | 10616.2i | 0.679437 | + | 0.679437i | ||||
\(126\) | 9868.20 | + | 9868.20i | 0.621580 | + | 0.621580i | ||||
\(127\) | 860.617 | 0.0533584 | 0.0266792 | − | 0.999644i | \(-0.491507\pi\) | ||||
0.0266792 | + | 0.999644i | \(0.491507\pi\) | |||||||
\(128\) | −1024.00 | + | 1024.00i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | −10099.4 | − | 10099.4i | −0.606900 | − | 0.606900i | ||||
\(130\) | 6393.35 | − | 6393.35i | 0.378305 | − | 0.378305i | ||||
\(131\) | 9264.84 | + | 9264.84i | 0.539878 | + | 0.539878i | 0.923493 | − | 0.383615i | \(-0.125321\pi\) |
−0.383615 | + | 0.923493i | \(0.625321\pi\) | |||||||
\(132\) | − | 4476.57i | − | 0.256920i | ||||||
\(133\) | 24276.5 | − | 24276.5i | 1.37241 | − | 1.37241i | ||||
\(134\) | −5255.74 | + | 5255.74i | −0.292701 | + | 0.292701i | ||||
\(135\) | −7261.15 | − | 7261.15i | −0.398417 | − | 0.398417i | ||||
\(136\) | 9236.91i | 0.499401i | ||||||||
\(137\) | −12740.7 | −0.678817 | −0.339409 | − | 0.940639i | \(-0.610227\pi\) | ||||
−0.339409 | + | 0.940639i | \(0.610227\pi\) | |||||||
\(138\) | 4846.58i | 0.254494i | ||||||||
\(139\) | 2561.90i | 0.132597i | 0.997800 | + | 0.0662984i | \(0.0211189\pi\) | ||||
−0.997800 | + | 0.0662984i | \(0.978881\pi\) | |||||||
\(140\) | −7664.59 | − | 7664.59i | −0.391050 | − | 0.391050i | ||||
\(141\) | 13443.8i | 0.676214i | ||||||||
\(142\) | −11452.5 | − | 11452.5i | −0.567968 | − | 0.567968i | ||||
\(143\) | 16435.9 | + | 16435.9i | 0.803750 | + | 0.803750i | ||||
\(144\) | −3355.95 | −0.161842 | ||||||||
\(145\) | −1206.13 | −0.0573664 | ||||||||
\(146\) | 15747.5 | − | 15747.5i | 0.738764 | − | 0.738764i | ||||
\(147\) | − | 34488.5i | − | 1.59602i | ||||||
\(148\) | 8156.07 | − | 7309.23i | 0.372355 | − | 0.333694i | ||||
\(149\) | −16513.4 | −0.743814 | −0.371907 | − | 0.928270i | \(-0.621296\pi\) | ||||
−0.371907 | + | 0.928270i | \(0.621296\pi\) | |||||||
\(150\) | −4464.34 | − | 4464.34i | −0.198415 | − | 0.198415i | ||||
\(151\) | 3594.24i | 0.157635i | 0.996889 | + | 0.0788176i | \(0.0251145\pi\) | ||||
−0.996889 | + | 0.0788176i | \(0.974886\pi\) | |||||||
\(152\) | 8255.89i | 0.357336i | ||||||||
\(153\) | −15136.0 | + | 15136.0i | −0.646590 | + | 0.646590i | ||||
\(154\) | 19704.0 | − | 19704.0i | 0.830830 | − | 0.830830i | ||||
\(155\) | −12399.2 | −0.516095 | ||||||||
\(156\) | −6711.76 | + | 6711.76i | −0.275796 | + | 0.275796i | ||||
\(157\) | 1308.30 | 0.0530772 | 0.0265386 | − | 0.999648i | \(-0.491552\pi\) | ||||
0.0265386 | + | 0.999648i | \(0.491552\pi\) | |||||||
\(158\) | −12859.3 | −0.515112 | ||||||||
\(159\) | 988.995i | 0.0391201i | ||||||||
\(160\) | 2606.55 | 0.101818 | ||||||||
\(161\) | −21332.6 | + | 21332.6i | −0.822985 | + | 0.822985i | ||||
\(162\) | −871.955 | − | 871.955i | −0.0332249 | − | 0.0332249i | ||||
\(163\) | −19856.3 | − | 19856.3i | −0.747347 | − | 0.747347i | 0.226633 | − | 0.973980i | \(-0.427228\pi\) |
−0.973980 | + | 0.226633i | \(0.927228\pi\) | |||||||
\(164\) | 14547.8 | 0.540891 | ||||||||
\(165\) | −5697.46 | + | 5697.46i | −0.209273 | + | 0.209273i | ||||
\(166\) | 19740.2 | + | 19740.2i | 0.716367 | + | 0.716367i | ||||
\(167\) | −16420.6 | + | 16420.6i | −0.588786 | + | 0.588786i | −0.937303 | − | 0.348517i | \(-0.886685\pi\) |
0.348517 | + | 0.937303i | \(0.386685\pi\) | |||||||
\(168\) | 8046.32 | + | 8046.32i | 0.285088 | + | 0.285088i | ||||
\(169\) | − | 20724.0i | − | 0.725604i | ||||||
\(170\) | 11756.1 | − | 11756.1i | 0.406785 | − | 0.406785i | ||||
\(171\) | −13528.5 | + | 13528.5i | −0.462655 | + | 0.462655i | ||||
\(172\) | 15117.6 | + | 15117.6i | 0.511005 | + | 0.511005i | ||||
\(173\) | − | 1380.88i | − | 0.0461384i | −0.999734 | − | 0.0230692i | \(-0.992656\pi\) | ||
0.999734 | − | 0.0230692i | \(-0.00734381\pi\) | |||||||
\(174\) | 1266.20 | 0.0418218 | ||||||||
\(175\) | − | 39300.3i | − | 1.28328i | ||||||
\(176\) | 6700.86i | 0.216324i | ||||||||
\(177\) | 10621.4 | + | 10621.4i | 0.339027 | + | 0.339027i | ||||
\(178\) | − | 14639.6i | − | 0.462049i | ||||||
\(179\) | −11082.5 | − | 11082.5i | −0.345886 | − | 0.345886i | 0.512688 | − | 0.858575i | \(-0.328650\pi\) |
−0.858575 | + | 0.512688i | \(0.828650\pi\) | |||||||
\(180\) | 4271.21 | + | 4271.21i | 0.131828 | + | 0.131828i | ||||
\(181\) | 17811.1 | 0.543667 | 0.271833 | − | 0.962344i | \(-0.412370\pi\) | ||||
0.271833 | + | 0.962344i | \(0.412370\pi\) | |||||||
\(182\) | −59084.7 | −1.78374 | ||||||||
\(183\) | −25683.8 | + | 25683.8i | −0.766931 | + | 0.766931i | ||||
\(184\) | − | 7254.72i | − | 0.214282i | ||||||
\(185\) | −19683.1 | − | 1077.80i | −0.575110 | − | 0.0314916i | ||||
\(186\) | 13016.7 | 0.376249 | ||||||||
\(187\) | 30222.3 | + | 30222.3i | 0.864260 | + | 0.864260i | ||||
\(188\) | − | 20123.7i | − | 0.569367i | ||||||
\(189\) | 67104.6i | 1.87858i | ||||||||
\(190\) | 10507.5 | − | 10507.5i | 0.291067 | − | 0.291067i | ||||
\(191\) | −14170.9 | + | 14170.9i | −0.388446 | + | 0.388446i | −0.874133 | − | 0.485687i | \(-0.838569\pi\) |
0.485687 | + | 0.874133i | \(0.338569\pi\) | |||||||
\(192\) | −2736.37 | −0.0742287 | ||||||||
\(193\) | −31829.7 | + | 31829.7i | −0.854511 | + | 0.854511i | −0.990685 | − | 0.136174i | \(-0.956519\pi\) |
0.136174 | + | 0.990685i | \(0.456519\pi\) | |||||||
\(194\) | −3782.78 | −0.100510 | ||||||||
\(195\) | 17084.5 | 0.449297 | ||||||||
\(196\) | 51625.0i | 1.34384i | ||||||||
\(197\) | 38635.1 | 0.995520 | 0.497760 | − | 0.867315i | \(-0.334156\pi\) | ||||
0.497760 | + | 0.867315i | \(0.334156\pi\) | |||||||
\(198\) | −10980.3 | + | 10980.3i | −0.280082 | + | 0.280082i | ||||
\(199\) | −42102.2 | − | 42102.2i | −1.06316 | − | 1.06316i | −0.997866 | − | 0.0652938i | \(-0.979202\pi\) |
−0.0652938 | − | 0.997866i | \(-0.520798\pi\) | |||||||
\(200\) | 6682.57 | + | 6682.57i | 0.167064 | + | 0.167064i | ||||
\(201\) | −14044.6 | −0.347629 | ||||||||
\(202\) | −36851.1 | + | 36851.1i | −0.903125 | + | 0.903125i | ||||
\(203\) | 5573.27 | + | 5573.27i | 0.135244 | + | 0.135244i | ||||
\(204\) | −12341.6 | + | 12341.6i | −0.296559 | + | 0.296559i | ||||
\(205\) | −18515.4 | − | 18515.4i | −0.440581 | − | 0.440581i | ||||
\(206\) | 2653.86i | 0.0625379i | ||||||||
\(207\) | 11887.9 | − | 11887.9i | 0.277438 | − | 0.277438i | ||||
\(208\) | 10046.7 | − | 10046.7i | 0.232218 | − | 0.232218i | ||||
\(209\) | 27012.5 | + | 27012.5i | 0.618404 | + | 0.618404i | ||||
\(210\) | − | 20481.6i | − | 0.464435i | ||||||
\(211\) | 3844.31 | 0.0863483 | 0.0431742 | − | 0.999068i | \(-0.486253\pi\) | ||||
0.0431742 | + | 0.999068i | \(0.486253\pi\) | |||||||
\(212\) | − | 1480.40i | − | 0.0329388i | ||||||
\(213\) | − | 30603.8i | − | 0.674553i | ||||||
\(214\) | 3125.87 | + | 3125.87i | 0.0682565 | + | 0.0682565i | ||||
\(215\) | − | 38481.1i | − | 0.832475i | ||||||
\(216\) | −11410.4 | − | 11410.4i | −0.244564 | − | 0.244564i | ||||
\(217\) | 57294.1 | + | 57294.1i | 1.21672 | + | 1.21672i | ||||
\(218\) | 42283.9 | 0.889738 | ||||||||
\(219\) | 42081.0 | 0.877400 | ||||||||
\(220\) | 8528.38 | − | 8528.38i | 0.176206 | − | 0.176206i | ||||
\(221\) | − | 90625.2i | − | 1.85552i | ||||||
\(222\) | 20663.4 | + | 1131.48i | 0.419273 | + | 0.0229584i | ||||
\(223\) | −61406.0 | −1.23481 | −0.617406 | − | 0.786644i | \(-0.711817\pi\) | ||||
−0.617406 | + | 0.786644i | \(0.711817\pi\) | |||||||
\(224\) | −12044.3 | − | 12044.3i | −0.240042 | − | 0.240042i | ||||
\(225\) | 21900.7i | 0.432607i | ||||||||
\(226\) | − | 18739.0i | − | 0.366886i | ||||||
\(227\) | 27233.3 | − | 27233.3i | 0.528504 | − | 0.528504i | −0.391622 | − | 0.920126i | \(-0.628086\pi\) |
0.920126 | + | 0.391622i | \(0.128086\pi\) | |||||||
\(228\) | −11030.8 | + | 11030.8i | −0.212197 | + | 0.212197i | ||||
\(229\) | 65938.4 | 1.25738 | 0.628691 | − | 0.777655i | \(-0.283591\pi\) | ||||
0.628691 | + | 0.777655i | \(0.283591\pi\) | |||||||
\(230\) | −9233.30 | + | 9233.30i | −0.174542 | + | 0.174542i | ||||
\(231\) | 52653.6 | 0.986742 | ||||||||
\(232\) | −1895.34 | −0.0352137 | ||||||||
\(233\) | − | 56189.5i | − | 1.03501i | −0.855681 | − | 0.517504i | \(-0.826861\pi\) | ||
0.855681 | − | 0.517504i | \(-0.173139\pi\) | |||||||
\(234\) | 32925.9 | 0.601320 | ||||||||
\(235\) | −25612.0 | + | 25612.0i | −0.463776 | + | 0.463776i | ||||
\(236\) | −15898.9 | − | 15898.9i | −0.285458 | − | 0.285458i | ||||
\(237\) | −17181.5 | − | 17181.5i | −0.305889 | − | 0.305889i | ||||
\(238\) | −108645. | −1.91803 | ||||||||
\(239\) | −79431.0 | + | 79431.0i | −1.39057 | + | 1.39057i | −0.566538 | + | 0.824036i | \(0.691718\pi\) |
−0.824036 | + | 0.566538i | \(0.808282\pi\) | |||||||
\(240\) | 3482.65 | + | 3482.65i | 0.0604627 | + | 0.0604627i | ||||
\(241\) | 21019.1 | − | 21019.1i | 0.361893 | − | 0.361893i | −0.502617 | − | 0.864509i | \(-0.667629\pi\) |
0.864509 | + | 0.502617i | \(0.167629\pi\) | |||||||
\(242\) | −7357.42 | − | 7357.42i | −0.125630 | − | 0.125630i | ||||
\(243\) | − | 60095.0i | − | 1.01771i | ||||||
\(244\) | 38445.4 | − | 38445.4i | 0.645750 | − | 0.645750i | ||||
\(245\) | 65704.6 | − | 65704.6i | 1.09462 | − | 1.09462i | ||||
\(246\) | 19437.5 | + | 19437.5i | 0.321197 | + | 0.321197i | ||||
\(247\) | − | 81000.2i | − | 1.32768i | ||||||
\(248\) | −19484.4 | −0.316799 | ||||||||
\(249\) | 52750.4i | 0.850800i | ||||||||
\(250\) | − | 42464.8i | − | 0.679437i | ||||||
\(251\) | 57975.7 | + | 57975.7i | 0.920235 | + | 0.920235i | 0.997046 | − | 0.0768107i | \(-0.0244737\pi\) |
−0.0768107 | + | 0.997046i | \(0.524474\pi\) | |||||||
\(252\) | − | 39472.8i | − | 0.621580i | ||||||
\(253\) | −23736.8 | − | 23736.8i | −0.370835 | − | 0.370835i | ||||
\(254\) | −1721.23 | − | 1721.23i | −0.0266792 | − | 0.0266792i | ||||
\(255\) | 31415.0 | 0.483122 | ||||||||
\(256\) | 4096.00 | 0.0625000 | ||||||||
\(257\) | −47329.8 | + | 47329.8i | −0.716586 | + | 0.716586i | −0.967904 | − | 0.251318i | \(-0.919136\pi\) |
0.251318 | + | 0.967904i | \(0.419136\pi\) | |||||||
\(258\) | 40397.7i | 0.606900i | ||||||||
\(259\) | 85971.5 | + | 95932.1i | 1.28161 | + | 1.43009i | ||||
\(260\) | −25573.4 | −0.378305 | ||||||||
\(261\) | −3105.79 | − | 3105.79i | −0.0455923 | − | 0.0455923i | ||||
\(262\) | − | 37059.4i | − | 0.539878i | ||||||
\(263\) | − | 75854.7i | − | 1.09666i | −0.836263 | − | 0.548329i | \(-0.815264\pi\) | ||
0.836263 | − | 0.548329i | \(-0.184736\pi\) | |||||||
\(264\) | −8953.13 | + | 8953.13i | −0.128460 | + | 0.128460i | ||||
\(265\) | −1884.15 | + | 1884.15i | −0.0268302 | + | 0.0268302i | ||||
\(266\) | −97106.2 | −1.37241 | ||||||||
\(267\) | 19560.2 | − | 19560.2i | 0.274378 | − | 0.274378i | ||||
\(268\) | 21023.0 | 0.292701 | ||||||||
\(269\) | 92814.4 | 1.28266 | 0.641329 | − | 0.767266i | \(-0.278384\pi\) | ||||
0.641329 | + | 0.767266i | \(0.278384\pi\) | |||||||
\(270\) | 29044.6i | 0.398417i | ||||||||
\(271\) | 3154.18 | 0.0429485 | 0.0214743 | − | 0.999769i | \(-0.493164\pi\) | ||||
0.0214743 | + | 0.999769i | \(0.493164\pi\) | |||||||
\(272\) | 18473.8 | − | 18473.8i | 0.249700 | − | 0.249700i | ||||
\(273\) | −78944.0 | − | 78944.0i | −1.05924 | − | 1.05924i | ||||
\(274\) | 25481.4 | + | 25481.4i | 0.339409 | + | 0.339409i | ||||
\(275\) | 43729.5 | 0.578241 | ||||||||
\(276\) | 9693.15 | − | 9693.15i | 0.127247 | − | 0.127247i | ||||
\(277\) | 64846.9 | + | 64846.9i | 0.845142 | + | 0.845142i | 0.989522 | − | 0.144380i | \(-0.0461188\pi\) |
−0.144380 | + | 0.989522i | \(0.546119\pi\) | |||||||
\(278\) | 5123.81 | − | 5123.81i | 0.0662984 | − | 0.0662984i | ||||
\(279\) | −31928.1 | − | 31928.1i | −0.410170 | − | 0.410170i | ||||
\(280\) | 30658.4i | 0.391050i | ||||||||
\(281\) | 65861.6 | − | 65861.6i | 0.834103 | − | 0.834103i | −0.153972 | − | 0.988075i | \(-0.549207\pi\) |
0.988075 | + | 0.153972i | \(0.0492066\pi\) | |||||||
\(282\) | 26887.6 | − | 26887.6i | 0.338107 | − | 0.338107i | ||||
\(283\) | 19240.4 | + | 19240.4i | 0.240238 | + | 0.240238i | 0.816948 | − | 0.576711i | \(-0.195664\pi\) |
−0.576711 | + | 0.816948i | \(0.695664\pi\) | |||||||
\(284\) | 45810.0i | 0.567968i | ||||||||
\(285\) | 28078.5 | 0.345688 | ||||||||
\(286\) | − | 65743.5i | − | 0.803750i | ||||||
\(287\) | 171112.i | 2.07738i | ||||||||
\(288\) | 6711.90 | + | 6711.90i | 0.0809208 | + | 0.0809208i | ||||
\(289\) | − | 83120.7i | − | 0.995207i | ||||||
\(290\) | 2412.26 | + | 2412.26i | 0.0286832 | + | 0.0286832i | ||||
\(291\) | −5054.23 | − | 5054.23i | −0.0596855 | − | 0.0596855i | ||||
\(292\) | −62990.0 | −0.738764 | ||||||||
\(293\) | −79617.5 | −0.927413 | −0.463706 | − | 0.885989i | \(-0.653481\pi\) | ||||
−0.463706 | + | 0.885989i | \(0.653481\pi\) | |||||||
\(294\) | −68977.0 | + | 68977.0i | −0.798012 | + | 0.798012i | ||||
\(295\) | 40469.9i | 0.465038i | ||||||||
\(296\) | −30930.6 | − | 1693.69i | −0.353025 | − | 0.0193308i | ||||
\(297\) | −74667.3 | −0.846481 | ||||||||
\(298\) | 33026.8 | + | 33026.8i | 0.371907 | + | 0.371907i | ||||
\(299\) | 71177.5i | 0.796160i | ||||||||
\(300\) | 17857.4i | 0.198415i | ||||||||
\(301\) | −177814. | + | 177814.i | −1.96260 | + | 1.96260i | ||||
\(302\) | 7188.48 | − | 7188.48i | 0.0788176 | − | 0.0788176i | ||||
\(303\) | −98474.7 | −1.07260 | ||||||||
\(304\) | 16511.8 | − | 16511.8i | 0.178668 | − | 0.178668i | ||||
\(305\) | −97861.2 | −1.05199 | ||||||||
\(306\) | 60544.1 | 0.646590 | ||||||||
\(307\) | 65571.3i | 0.695725i | 0.937546 | + | 0.347862i | \(0.113092\pi\) | ||||
−0.937546 | + | 0.347862i | \(0.886908\pi\) | |||||||
\(308\) | −78815.8 | −0.830830 | ||||||||
\(309\) | −3545.86 | + | 3545.86i | −0.0371369 | + | 0.0371369i | ||||
\(310\) | 24798.4 | + | 24798.4i | 0.258048 | + | 0.258048i | ||||
\(311\) | 48552.1 | + | 48552.1i | 0.501981 | + | 0.501981i | 0.912053 | − | 0.410072i | \(-0.134497\pi\) |
−0.410072 | + | 0.912053i | \(0.634497\pi\) | |||||||
\(312\) | 26847.0 | 0.275796 | ||||||||
\(313\) | 16168.1 | − | 16168.1i | 0.165033 | − | 0.165033i | −0.619759 | − | 0.784792i | \(-0.712770\pi\) |
0.784792 | + | 0.619759i | \(0.212770\pi\) | |||||||
\(314\) | −2616.60 | − | 2616.60i | −0.0265386 | − | 0.0265386i | ||||
\(315\) | −50238.2 | + | 50238.2i | −0.506306 | + | 0.506306i | ||||
\(316\) | 25718.5 | + | 25718.5i | 0.257556 | + | 0.257556i | ||||
\(317\) | − | 93230.4i | − | 0.927767i | −0.885896 | − | 0.463884i | \(-0.846456\pi\) | ||
0.885896 | − | 0.463884i | \(-0.153544\pi\) | |||||||
\(318\) | 1977.99 | − | 1977.99i | 0.0195601 | − | 0.0195601i | ||||
\(319\) | −6201.38 | + | 6201.38i | −0.0609406 | + | 0.0609406i | ||||
\(320\) | −5213.10 | − | 5213.10i | −0.0509092 | − | 0.0509092i | ||||
\(321\) | 8353.07i | 0.0810655i | ||||||||
\(322\) | 85330.3 | 0.822985 | ||||||||
\(323\) | − | 148943.i | − | 1.42763i | ||||||
\(324\) | 3487.82i | 0.0332249i | ||||||||
\(325\) | −65564.0 | − | 65564.0i | −0.620725 | − | 0.620725i | ||||
\(326\) | 79425.1i | 0.747347i | ||||||||
\(327\) | 56496.2 | + | 56496.2i | 0.528353 | + | 0.528353i | ||||
\(328\) | −29095.6 | − | 29095.6i | −0.270445 | − | 0.270445i | ||||
\(329\) | 236696. | 2.18675 | ||||||||
\(330\) | 22789.8 | 0.209273 | ||||||||
\(331\) | −16551.9 | + | 16551.9i | −0.151075 | + | 0.151075i | −0.778598 | − | 0.627523i | \(-0.784069\pi\) |
0.627523 | + | 0.778598i | \(0.284069\pi\) | |||||||
\(332\) | − | 78960.8i | − | 0.716367i | ||||||
\(333\) | −47909.0 | − | 53459.7i | −0.432044 | − | 0.482101i | ||||
\(334\) | 65682.6 | 0.588786 | ||||||||
\(335\) | −26756.5 | − | 26756.5i | −0.238419 | − | 0.238419i | ||||
\(336\) | − | 32185.3i | − | 0.285088i | ||||||
\(337\) | − | 154951.i | − | 1.36437i | −0.731177 | − | 0.682187i | \(-0.761029\pi\) | ||
0.731177 | − | 0.682187i | \(-0.238971\pi\) | |||||||
\(338\) | −41447.9 | + | 41447.9i | −0.362802 | + | 0.362802i | ||||
\(339\) | 25037.6 | − | 25037.6i | 0.217868 | − | 0.217868i | ||||
\(340\) | −47024.4 | −0.406785 | ||||||||
\(341\) | −63751.1 | + | 63751.1i | −0.548251 | + | 0.548251i | ||||
\(342\) | 54114.0 | 0.462655 | ||||||||
\(343\) | −381290. | −3.24091 | ||||||||
\(344\) | − | 60470.3i | − | 0.511005i | ||||||
\(345\) | −24673.5 | −0.207297 | ||||||||
\(346\) | −2761.75 | + | 2761.75i | −0.0230692 | + | 0.0230692i | ||||
\(347\) | 78775.8 | + | 78775.8i | 0.654235 | + | 0.654235i | 0.954010 | − | 0.299775i | \(-0.0969116\pi\) |
−0.299775 | + | 0.954010i | \(0.596912\pi\) | |||||||
\(348\) | −2532.40 | − | 2532.40i | −0.0209109 | − | 0.0209109i | ||||
\(349\) | −85580.9 | −0.702629 | −0.351314 | − | 0.936258i | \(-0.614265\pi\) | ||||
−0.351314 | + | 0.936258i | \(0.614265\pi\) | |||||||
\(350\) | −78600.7 | + | 78600.7i | −0.641638 | + | 0.641638i | ||||
\(351\) | 111949. | + | 111949.i | 0.908673 | + | 0.908673i | ||||
\(352\) | 13401.7 | − | 13401.7i | 0.108162 | − | 0.108162i | ||||
\(353\) | 142011. | + | 142011.i | 1.13965 | + | 1.13965i | 0.988513 | + | 0.151136i | \(0.0482933\pi\) |
0.151136 | + | 0.988513i | \(0.451707\pi\) | |||||||
\(354\) | − | 42485.5i | − | 0.339027i | ||||||
\(355\) | 58303.8 | − | 58303.8i | 0.462637 | − | 0.462637i | ||||
\(356\) | −29279.1 | + | 29279.1i | −0.231025 | + | 0.231025i | ||||
\(357\) | −145162. | − | 145162.i | −1.13898 | − | 1.13898i | ||||
\(358\) | 44330.2i | 0.345886i | ||||||||
\(359\) | 8356.70 | 0.0648404 | 0.0324202 | − | 0.999474i | \(-0.489679\pi\) | ||||
0.0324202 | + | 0.999474i | \(0.489679\pi\) | |||||||
\(360\) | − | 17084.9i | − | 0.131828i | ||||||
\(361\) | − | 2803.52i | − | 0.0215124i | ||||||
\(362\) | −35622.1 | − | 35622.1i | −0.271833 | − | 0.271833i | ||||
\(363\) | − | 19660.7i | − | 0.149206i | ||||||
\(364\) | 118169. | + | 118169.i | 0.891872 | + | 0.891872i | ||||
\(365\) | 80169.2 | + | 80169.2i | 0.601758 | + | 0.601758i | ||||
\(366\) | 102735. | 0.766931 | ||||||||
\(367\) | 18123.6 | 0.134559 | 0.0672795 | − | 0.997734i | \(-0.478568\pi\) | ||||
0.0672795 | + | 0.997734i | \(0.478568\pi\) | |||||||
\(368\) | −14509.4 | + | 14509.4i | −0.107141 | + | 0.107141i | ||||
\(369\) | − | 95354.8i | − | 0.700309i | ||||||
\(370\) | 37210.7 | + | 41521.9i | 0.271809 | + | 0.303301i | ||||
\(371\) | 17412.6 | 0.126507 | ||||||||
\(372\) | −26033.4 | − | 26033.4i | −0.188125 | − | 0.188125i | ||||
\(373\) | − | 54554.8i | − | 0.392117i | −0.980592 | − | 0.196058i | \(-0.937186\pi\) | ||
0.980592 | − | 0.196058i | \(-0.0628142\pi\) | |||||||
\(374\) | − | 120889.i | − | 0.864260i | ||||||
\(375\) | 56737.9 | − | 56737.9i | 0.403470 | − | 0.403470i | ||||
\(376\) | −40247.4 | + | 40247.4i | −0.284683 | + | 0.284683i | ||||
\(377\) | 18595.6 | 0.130836 | ||||||||
\(378\) | 134209. | − | 134209.i | 0.939288 | − | 0.939288i | ||||
\(379\) | −217488. | −1.51411 | −0.757053 | − | 0.653354i | \(-0.773361\pi\) | ||||
−0.757053 | + | 0.653354i | \(0.773361\pi\) | |||||||
\(380\) | −42030.1 | −0.291067 | ||||||||
\(381\) | − | 4599.54i | − | 0.0316858i | ||||||
\(382\) | 56683.5 | 0.388446 | ||||||||
\(383\) | 114457. | − | 114457.i | 0.780269 | − | 0.780269i | −0.199607 | − | 0.979876i | \(-0.563967\pi\) |
0.979876 | + | 0.199607i | \(0.0639666\pi\) | |||||||
\(384\) | 5472.73 | + | 5472.73i | 0.0371143 | + | 0.0371143i | ||||
\(385\) | 100311. | + | 100311.i | 0.676750 | + | 0.676750i | ||||
\(386\) | 127319. | 0.854511 | ||||||||
\(387\) | 99089.4 | − | 99089.4i | 0.661615 | − | 0.661615i | ||||
\(388\) | 7565.56 | + | 7565.56i | 0.0502548 | + | 0.0502548i | ||||
\(389\) | −129419. | + | 129419.i | −0.855260 | + | 0.855260i | −0.990775 | − | 0.135515i | \(-0.956731\pi\) |
0.135515 | + | 0.990775i | \(0.456731\pi\) | |||||||
\(390\) | −34169.0 | − | 34169.0i | −0.224648 | − | 0.224648i | ||||
\(391\) | 130881.i | 0.856099i | ||||||||
\(392\) | 103250. | − | 103250.i | 0.671920 | − | 0.671920i | ||||
\(393\) | 49515.6 | − | 49515.6i | 0.320595 | − | 0.320595i | ||||
\(394\) | −77270.2 | − | 77270.2i | −0.497760 | − | 0.497760i | ||||
\(395\) | − | 65465.4i | − | 0.419583i | ||||||
\(396\) | 43921.4 | 0.280082 | ||||||||
\(397\) | 89391.0i | 0.567170i | 0.958947 | + | 0.283585i | \(0.0915237\pi\) | ||||
−0.958947 | + | 0.283585i | \(0.908476\pi\) | |||||||
\(398\) | 168409.i | 1.06316i | ||||||||
\(399\) | −129745. | − | 129745.i | −0.814977 | − | 0.814977i | ||||
\(400\) | − | 26730.3i | − | 0.167064i | ||||||
\(401\) | −11590.6 | − | 11590.6i | −0.0720807 | − | 0.0720807i | 0.670147 | − | 0.742228i | \(-0.266231\pi\) |
−0.742228 | + | 0.670147i | \(0.766231\pi\) | |||||||
\(402\) | 28089.1 | + | 28089.1i | 0.173814 | + | 0.173814i | ||||
\(403\) | 191165. | 1.17706 | ||||||||
\(404\) | 147404. | 0.903125 | ||||||||
\(405\) | 4439.05 | − | 4439.05i | 0.0270633 | − | 0.0270633i | ||||
\(406\) | − | 22293.1i | − | 0.135244i | ||||||
\(407\) | −106744. | + | 95660.4i | −0.644396 | + | 0.577489i | ||||
\(408\) | 49366.4 | 0.296559 | ||||||||
\(409\) | −158731. | − | 158731.i | −0.948890 | − | 0.948890i | 0.0498664 | − | 0.998756i | \(-0.484120\pi\) |
−0.998756 | + | 0.0498664i | \(0.984120\pi\) | |||||||
\(410\) | 74061.6i | 0.440581i | ||||||||
\(411\) | 68092.3i | 0.403102i | ||||||||
\(412\) | 5307.72 | − | 5307.72i | 0.0312690 | − | 0.0312690i | ||||
\(413\) | 187003. | − | 187003.i | 1.09635 | − | 1.09635i | ||||
\(414\) | −47551.7 | −0.277438 | ||||||||
\(415\) | −100496. | + | 100496.i | −0.583514 | + | 0.583514i | ||||
\(416\) | −40186.7 | −0.232218 | ||||||||
\(417\) | 13692.0 | 0.0787399 | ||||||||
\(418\) | − | 108050.i | − | 0.618404i | ||||||
\(419\) | −53640.6 | −0.305538 | −0.152769 | − | 0.988262i | \(-0.548819\pi\) | ||||
−0.152769 | + | 0.988262i | \(0.548819\pi\) | |||||||
\(420\) | −40963.1 | + | 40963.1i | −0.232217 | + | 0.232217i | ||||
\(421\) | −113029. | − | 113029.i | −0.637716 | − | 0.637716i | 0.312276 | − | 0.949992i | \(-0.398909\pi\) |
−0.949992 | + | 0.312276i | \(0.898909\pi\) | |||||||
\(422\) | −7688.63 | − | 7688.63i | −0.0431742 | − | 0.0431742i | ||||
\(423\) | −131903. | −0.737178 | ||||||||
\(424\) | −2960.81 | + | 2960.81i | −0.0164694 | + | 0.0164694i | ||||
\(425\) | −120559. | − | 120559.i | −0.667456 | − | 0.667456i | ||||
\(426\) | −61207.6 | + | 61207.6i | −0.337276 | + | 0.337276i | ||||
\(427\) | 452196. | + | 452196.i | 2.48011 | + | 2.48011i | ||||
\(428\) | − | 12503.5i | − | 0.0682565i | ||||||
\(429\) | 87841.0 | − | 87841.0i | 0.477290 | − | 0.477290i | ||||
\(430\) | −76962.3 | + | 76962.3i | −0.416237 | + | 0.416237i | ||||
\(431\) | 208728. | + | 208728.i | 1.12364 | + | 1.12364i | 0.991190 | + | 0.132448i | \(0.0422839\pi\) |
0.132448 | + | 0.991190i | \(0.457716\pi\) | |||||||
\(432\) | 45641.5i | 0.244564i | ||||||||
\(433\) | −75452.6 | −0.402437 | −0.201219 | − | 0.979546i | \(-0.564490\pi\) | ||||
−0.201219 | + | 0.979546i | \(0.564490\pi\) | |||||||
\(434\) | − | 229176.i | − | 1.21672i | ||||||
\(435\) | 6446.11i | 0.0340658i | ||||||||
\(436\) | −84567.9 | − | 84567.9i | −0.444869 | − | 0.444869i | ||||
\(437\) | 116981.i | 0.612565i | ||||||||
\(438\) | −84162.0 | − | 84162.0i | −0.438700 | − | 0.438700i | ||||
\(439\) | −246708. | − | 246708.i | −1.28013 | − | 1.28013i | −0.940593 | − | 0.339535i | \(-0.889730\pi\) |
−0.339535 | − | 0.940593i | \(-0.610270\pi\) | |||||||
\(440\) | −34113.5 | −0.176206 | ||||||||
\(441\) | 338380. | 1.73992 | ||||||||
\(442\) | −181250. | + | 181250.i | −0.927758 | + | 0.927758i | ||||
\(443\) | − | 68941.1i | − | 0.351294i | −0.984453 | − | 0.175647i | \(-0.943798\pi\) | ||
0.984453 | − | 0.175647i | \(-0.0562017\pi\) | |||||||
\(444\) | −39063.9 | − | 43589.8i | −0.198157 | − | 0.221116i | ||||
\(445\) | 74528.8 | 0.376361 | ||||||||
\(446\) | 122812. | + | 122812.i | 0.617406 | + | 0.617406i | ||||
\(447\) | 88255.4i | 0.441699i | ||||||||
\(448\) | 48177.3i | 0.240042i | ||||||||
\(449\) | 143056. | − | 143056.i | 0.709600 | − | 0.709600i | −0.256851 | − | 0.966451i | \(-0.582685\pi\) |
0.966451 | + | 0.256851i | \(0.0826849\pi\) | |||||||
\(450\) | 43801.5 | − | 43801.5i | 0.216304 | − | 0.216304i | ||||
\(451\) | −190396. | −0.936062 | ||||||||
\(452\) | −37478.1 | + | 37478.1i | −0.183443 | + | 0.183443i | ||||
\(453\) | 19209.3 | 0.0936085 | ||||||||
\(454\) | −108933. | −0.528504 | ||||||||
\(455\) | − | 300795.i | − | 1.45294i | ||||||
\(456\) | 44123.3 | 0.212197 | ||||||||
\(457\) | 133820. | − | 133820.i | 0.640752 | − | 0.640752i | −0.309988 | − | 0.950740i | \(-0.600325\pi\) |
0.950740 | + | 0.309988i | \(0.100325\pi\) | |||||||
\(458\) | −131877. | − | 131877.i | −0.628691 | − | 0.628691i | ||||
\(459\) | 205853. | + | 205853.i | 0.977082 | + | 0.977082i | ||||
\(460\) | 36933.2 | 0.174542 | ||||||||
\(461\) | 40084.3 | − | 40084.3i | 0.188613 | − | 0.188613i | −0.606483 | − | 0.795096i | \(-0.707420\pi\) |
0.795096 | + | 0.606483i | \(0.207420\pi\) | |||||||
\(462\) | −105307. | − | 105307.i | −0.493371 | − | 0.493371i | ||||
\(463\) | −230400. | + | 230400.i | −1.07478 | + | 1.07478i | −0.0778161 | + | 0.996968i | \(0.524795\pi\) |
−0.996968 | + | 0.0778161i | \(0.975205\pi\) | |||||||
\(464\) | 3790.68 | + | 3790.68i | 0.0176068 | + | 0.0176068i | ||||
\(465\) | 66267.0i | 0.306473i | ||||||||
\(466\) | −112379. | + | 112379.i | −0.517504 | + | 0.517504i | ||||
\(467\) | 106600. | − | 106600.i | 0.488790 | − | 0.488790i | −0.419134 | − | 0.907924i | \(-0.637666\pi\) |
0.907924 | + | 0.419134i | \(0.137666\pi\) | |||||||
\(468\) | −65851.8 | − | 65851.8i | −0.300660 | − | 0.300660i | ||||
\(469\) | 247273.i | 1.12417i | ||||||||
\(470\) | 102448. | 0.463776 | ||||||||
\(471\) | − | 6992.16i | − | 0.0315188i | ||||||
\(472\) | 63595.5i | 0.285458i | ||||||||
\(473\) | −197853. | − | 197853.i | −0.884342 | − | 0.884342i | ||||
\(474\) | 68725.8i | 0.305889i | ||||||||
\(475\) | −107755. | − | 107755.i | −0.477584 | − | 0.477584i | ||||
\(476\) | 217290. | + | 217290.i | 0.959016 | + | 0.959016i | ||||
\(477\) | −9703.43 | −0.0426470 | ||||||||
\(478\) | 317724. | 1.39057 | ||||||||
\(479\) | −142463. | + | 142463.i | −0.620913 | + | 0.620913i | −0.945765 | − | 0.324852i | \(-0.894685\pi\) |
0.324852 | + | 0.945765i | \(0.394685\pi\) | |||||||
\(480\) | − | 13930.6i | − | 0.0604627i | ||||||
\(481\) | 303466. | + | 16617.1i | 1.31166 | + | 0.0718232i | ||||
\(482\) | −84076.4 | −0.361893 | ||||||||
\(483\) | 114011. | + | 114011.i | 0.488713 | + | 0.488713i | ||||
\(484\) | 29429.7i | 0.125630i | ||||||||
\(485\) | − | 19257.8i | − | 0.0818697i | ||||||
\(486\) | −120190. | + | 120190.i | −0.508857 | + | 0.508857i | ||||
\(487\) | 22476.6 | − | 22476.6i | 0.0947706 | − | 0.0947706i | −0.658132 | − | 0.752903i | \(-0.728653\pi\) |
0.752903 | + | 0.658132i | \(0.228653\pi\) | |||||||
\(488\) | −153782. | −0.645750 | ||||||||
\(489\) | −106121. | + | 106121.i | −0.443797 | + | 0.443797i | ||||
\(490\) | −262819. | −1.09462 | ||||||||
\(491\) | −132795. | −0.550831 | −0.275416 | − | 0.961325i | \(-0.588815\pi\) | ||||
−0.275416 | + | 0.961325i | \(0.588815\pi\) | |||||||
\(492\) | − | 77750.2i | − | 0.321197i | ||||||
\(493\) | 34193.6 | 0.140686 | ||||||||
\(494\) | −162000. | + | 162000.i | −0.663838 | + | 0.663838i | ||||
\(495\) | −55900.0 | − | 55900.0i | −0.228140 | − | 0.228140i | ||||
\(496\) | 38968.8 | + | 38968.8i | 0.158399 | + | 0.158399i | ||||
\(497\) | −538820. | −2.18138 | ||||||||
\(498\) | 105501. | − | 105501.i | 0.425400 | − | 0.425400i | ||||
\(499\) | 206696. | + | 206696.i | 0.830101 | + | 0.830101i | 0.987530 | − | 0.157430i | \(-0.0503207\pi\) |
−0.157430 | + | 0.987530i | \(0.550321\pi\) | |||||||
\(500\) | −84929.6 | + | 84929.6i | −0.339718 | + | 0.339718i | ||||
\(501\) | 87759.6 | + | 87759.6i | 0.349638 | + | 0.349638i | ||||
\(502\) | − | 231903.i | − | 0.920235i | ||||||
\(503\) | −119635. | + | 119635.i | −0.472849 | + | 0.472849i | −0.902835 | − | 0.429987i | \(-0.858518\pi\) |
0.429987 | + | 0.902835i | \(0.358518\pi\) | |||||||
\(504\) | −78945.6 | + | 78945.6i | −0.310790 | + | 0.310790i | ||||
\(505\) | −187606. | − | 187606.i | −0.735637 | − | 0.735637i | ||||
\(506\) | 94947.0i | 0.370835i | ||||||||
\(507\) | −110759. | −0.430885 | ||||||||
\(508\) | 6884.94i | 0.0266792i | ||||||||
\(509\) | 78749.6i | 0.303957i | 0.988384 | + | 0.151979i | \(0.0485645\pi\) | ||||
−0.988384 | + | 0.151979i | \(0.951435\pi\) | |||||||
\(510\) | −62830.0 | − | 62830.0i | −0.241561 | − | 0.241561i | ||||
\(511\) | − | 740891.i | − | 2.83735i | ||||||
\(512\) | −8192.00 | − | 8192.00i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | 183990. | + | 183990.i | 0.699131 | + | 0.699131i | ||||
\(514\) | 189319. | 0.716586 | ||||||||
\(515\) | −13510.6 | −0.0509401 | ||||||||
\(516\) | 80795.3 | − | 80795.3i | 0.303450 | − | 0.303450i | ||||
\(517\) | 263371.i | 0.985343i | ||||||||
\(518\) | 19921.2 | − | 363807.i | 0.0742431 | − | 1.35585i | ||||
\(519\) | −7380.05 | −0.0273984 | ||||||||
\(520\) | 51146.8 | + | 51146.8i | 0.189152 | + | 0.189152i | ||||
\(521\) | 283986.i | 1.04622i | 0.852266 | + | 0.523109i | \(0.175228\pi\) | ||||
−0.852266 | + | 0.523109i | \(0.824772\pi\) | |||||||
\(522\) | 12423.2i | 0.0455923i | ||||||||
\(523\) | 173621. | − | 173621.i | 0.634746 | − | 0.634746i | −0.314508 | − | 0.949255i | \(-0.601840\pi\) |
0.949255 | + | 0.314508i | \(0.101840\pi\) | |||||||
\(524\) | −74118.7 | + | 74118.7i | −0.269939 | + | 0.269939i | ||||
\(525\) | −210039. | −0.762047 | ||||||||
\(526\) | −151709. | + | 151709.i | −0.548329 | + | 0.548329i | ||||
\(527\) | 351515. | 1.26568 | ||||||||
\(528\) | 35812.5 | 0.128460 | ||||||||
\(529\) | 177046.i | 0.632667i | ||||||||
\(530\) | 7536.61 | 0.0268302 | ||||||||
\(531\) | −104210. | + | 104210.i | −0.369592 | + | 0.369592i | ||||
\(532\) | 194212. | + | 194212.i | 0.686204 | + | 0.686204i | ||||
\(533\) | 285463. | + | 285463.i | 1.00484 | + | 1.00484i | ||||
\(534\) | −78240.6 | −0.274378 | ||||||||
\(535\) | −15913.6 | + | 15913.6i | −0.0555981 | + | 0.0555981i | ||||
\(536\) | −42045.9 | − | 42045.9i | −0.146350 | − | 0.146350i | ||||
\(537\) | −59230.3 | + | 59230.3i | −0.205398 | + | 0.205398i | ||||
\(538\) | −185629. | − | 185629.i | −0.641329 | − | 0.641329i | ||||
\(539\) | − | 675648.i | − | 2.32564i | ||||||
\(540\) | 58089.2 | − | 58089.2i | 0.199209 | − | 0.199209i | ||||
\(541\) | 207308. | − | 207308.i | 0.708308 | − | 0.708308i | −0.257871 | − | 0.966179i | \(-0.583021\pi\) |
0.966179 | + | 0.257871i | \(0.0830210\pi\) | |||||||
\(542\) | −6308.37 | − | 6308.37i | −0.0214743 | − | 0.0214743i | ||||
\(543\) | − | 95190.7i | − | 0.322845i | ||||||
\(544\) | −73895.3 | −0.249700 | ||||||||
\(545\) | 215264.i | 0.724734i | ||||||||
\(546\) | 315776.i | 1.05924i | ||||||||
\(547\) | 150439. | + | 150439.i | 0.502790 | + | 0.502790i | 0.912304 | − | 0.409514i | \(-0.134302\pi\) |
−0.409514 | + | 0.912304i | \(0.634302\pi\) | |||||||
\(548\) | − | 101926.i | − | 0.339409i | ||||||
\(549\) | −251994. | − | 251994.i | −0.836074 | − | 0.836074i | ||||
\(550\) | −87458.9 | − | 87458.9i | −0.289120 | − | 0.289120i | ||||
\(551\) | 30562.0 | 0.100665 | ||||||||
\(552\) | −38772.6 | −0.127247 | ||||||||
\(553\) | −302502. | + | 302502.i | −0.989187 | + | 0.989187i | ||||
\(554\) | − | 259388.i | − | 0.845142i | ||||||
\(555\) | −5760.27 | + | 105196.i | −0.0187007 | + | 0.341517i | ||||
\(556\) | −20495.2 | −0.0662984 | ||||||||
\(557\) | −38740.6 | − | 38740.6i | −0.124869 | − | 0.124869i | 0.641910 | − | 0.766780i | \(-0.278142\pi\) |
−0.766780 | + | 0.641910i | \(0.778142\pi\) | |||||||
\(558\) | 127712.i | 0.410170i | ||||||||
\(559\) | 593286.i | 1.89863i | ||||||||
\(560\) | 61316.7 | − | 61316.7i | 0.195525 | − | 0.195525i | ||||
\(561\) | 161522. | − | 161522.i | 0.513223 | − | 0.513223i | ||||
\(562\) | −263446. | −0.834103 | ||||||||
\(563\) | 124572. | − | 124572.i | 0.393011 | − | 0.393011i | −0.482748 | − | 0.875759i | \(-0.660361\pi\) |
0.875759 | + | 0.482748i | \(0.160361\pi\) | |||||||
\(564\) | −107550. | −0.338107 | ||||||||
\(565\) | 95399.0 | 0.298845 | ||||||||
\(566\) | − | 76961.6i | − | 0.240238i | ||||||
\(567\) | −41023.9 | −0.127606 | ||||||||
\(568\) | 91620.1 | − | 91620.1i | 0.283984 | − | 0.283984i | ||||
\(569\) | 101858. | + | 101858.i | 0.314609 | + | 0.314609i | 0.846692 | − | 0.532083i | \(-0.178591\pi\) |
−0.532083 | + | 0.846692i | \(0.678591\pi\) | |||||||
\(570\) | −56157.1 | − | 56157.1i | −0.172844 | − | 0.172844i | ||||
\(571\) | −110278. | −0.338234 | −0.169117 | − | 0.985596i | \(-0.554092\pi\) | ||||
−0.169117 | + | 0.985596i | \(0.554092\pi\) | |||||||
\(572\) | −131487. | + | 131487.i | −0.401875 | + | 0.401875i | ||||
\(573\) | 75735.8 | + | 75735.8i | 0.230670 | + | 0.230670i | ||||
\(574\) | 342224. | − | 342224.i | 1.03869 | − | 1.03869i | ||||
\(575\) | 94687.8 | + | 94687.8i | 0.286390 | + | 0.286390i | ||||
\(576\) | − | 26847.6i | − | 0.0809208i | ||||||
\(577\) | 196203. | − | 196203.i | 0.589324 | − | 0.589324i | −0.348124 | − | 0.937448i | \(-0.613181\pi\) |
0.937448 | + | 0.348124i | \(0.113181\pi\) | |||||||
\(578\) | −166241. | + | 166241.i | −0.497603 | + | 0.497603i | ||||
\(579\) | 170113. | + | 170113.i | 0.507434 | + | 0.507434i | ||||
\(580\) | − | 9649.02i | − | 0.0286832i | ||||||
\(581\) | 928741. | 2.75133 | ||||||||
\(582\) | 20216.9i | 0.0596855i | ||||||||
\(583\) | 19375.0i | 0.0570038i | ||||||||
\(584\) | 125980. | + | 125980.i | 0.369382 | + | 0.369382i | ||||
\(585\) | 167623.i | 0.489803i | ||||||||
\(586\) | 159235. | + | 159235.i | 0.463706 | + | 0.463706i | ||||
\(587\) | −189138. | − | 189138.i | −0.548913 | − | 0.548913i | 0.377213 | − | 0.926126i | \(-0.376882\pi\) |
−0.926126 | + | 0.377213i | \(0.876882\pi\) | |||||||
\(588\) | 275908. | 0.798012 | ||||||||
\(589\) | 314182. | 0.905630 | ||||||||
\(590\) | 80939.8 | − | 80939.8i | 0.232519 | − | 0.232519i | ||||
\(591\) | − | 206484.i | − | 0.591169i | ||||||
\(592\) | 58473.8 | + | 65248.6i | 0.166847 | + | 0.186178i | ||||
\(593\) | −477286. | −1.35728 | −0.678640 | − | 0.734471i | \(-0.737430\pi\) | ||||
−0.678640 | + | 0.734471i | \(0.737430\pi\) | |||||||
\(594\) | 149335. | + | 149335.i | 0.423241 | + | 0.423241i | ||||
\(595\) | − | 553103.i | − | 1.56233i | ||||||
\(596\) | − | 132107.i | − | 0.371907i | ||||||
\(597\) | −225014. | + | 225014.i | −0.631336 | + | 0.631336i | ||||
\(598\) | 142355. | − | 142355.i | 0.398080 | − | 0.398080i | ||||
\(599\) | −693204. | −1.93200 | −0.966000 | − | 0.258540i | \(-0.916758\pi\) | ||||
−0.966000 | + | 0.258540i | \(0.916758\pi\) | |||||||
\(600\) | 35714.8 | − | 35714.8i | 0.0992077 | − | 0.0992077i | ||||
\(601\) | −450318. | −1.24672 | −0.623362 | − | 0.781933i | \(-0.714234\pi\) | ||||
−0.623362 | + | 0.781933i | \(0.714234\pi\) | |||||||
\(602\) | 711254. | 1.96260 | ||||||||
\(603\) | − | 137797.i | − | 0.378970i | ||||||
\(604\) | −28753.9 | −0.0788176 | ||||||||
\(605\) | 37456.0 | − | 37456.0i | 0.102332 | − | 0.102332i | ||||
\(606\) | 196949. | + | 196949.i | 0.536302 | + | 0.536302i | ||||
\(607\) | −80454.7 | − | 80454.7i | −0.218360 | − | 0.218360i | 0.589447 | − | 0.807807i | \(-0.299346\pi\) |
−0.807807 | + | 0.589447i | \(0.799346\pi\) | |||||||
\(608\) | −66047.1 | −0.178668 | ||||||||
\(609\) | 29786.2 | − | 29786.2i | 0.0803119 | − | 0.0803119i | ||||
\(610\) | 195722. | + | 195722.i | 0.525994 | + | 0.525994i | ||||
\(611\) | 394875. | − | 394875.i | 1.05774 | − | 1.05774i | ||||
\(612\) | −121088. | − | 121088.i | −0.323295 | − | 0.323295i | ||||
\(613\) | − | 427684.i | − | 1.13816i | −0.822283 | − | 0.569078i | \(-0.807300\pi\) | ||
0.822283 | − | 0.569078i | \(-0.192700\pi\) | |||||||
\(614\) | 131143. | − | 131143.i | 0.347862 | − | 0.347862i | ||||
\(615\) | −98955.0 | + | 98955.0i | −0.261630 | + | 0.261630i | ||||
\(616\) | 157632. | + | 157632.i | 0.415415 | + | 0.415415i | ||||
\(617\) | − | 423563.i | − | 1.11262i | −0.830974 | − | 0.556311i | \(-0.812216\pi\) | ||
0.830974 | − | 0.556311i | \(-0.187784\pi\) | |||||||
\(618\) | 14183.5 | 0.0371369 | ||||||||
\(619\) | − | 704207.i | − | 1.83789i | −0.394389 | − | 0.918944i | \(-0.629044\pi\) | ||
0.394389 | − | 0.918944i | \(-0.370956\pi\) | |||||||
\(620\) | − | 99193.5i | − | 0.258048i | ||||||
\(621\) | −161678. | − | 161678.i | −0.419244 | − | 0.419244i | ||||
\(622\) | − | 194208.i | − | 0.501981i | ||||||
\(623\) | −344382. | − | 344382.i | −0.887288 | − | 0.887288i | ||||
\(624\) | −53694.1 | − | 53694.1i | −0.137898 | − | 0.137898i | ||||
\(625\) | −44853.1 | −0.114824 | ||||||||
\(626\) | −64672.5 | −0.165033 | ||||||||
\(627\) | 144367. | − | 144367.i | 0.367226 | − | 0.367226i | ||||
\(628\) | 10466.4i | 0.0265386i | ||||||||
\(629\) | 558014. | + | 30555.5i | 1.41041 | + | 0.0772304i | ||||
\(630\) | 200953. | 0.506306 | ||||||||
\(631\) | 187320. | + | 187320.i | 0.470462 | + | 0.470462i | 0.902064 | − | 0.431602i | \(-0.142051\pi\) |
−0.431602 | + | 0.902064i | \(0.642051\pi\) | |||||||
\(632\) | − | 102874.i | − | 0.257556i | ||||||
\(633\) | − | 20545.8i | − | 0.0512762i | ||||||
\(634\) | −186461. | + | 186461.i | −0.463884 | + | 0.463884i | ||||
\(635\) | 8762.66 | − | 8762.66i | 0.0217315 | − | 0.0217315i | ||||
\(636\) | −7911.96 | −0.0195601 | ||||||||
\(637\) | −1.01301e6 | + | 1.01301e6i | −2.49651 | + | 2.49651i | ||||
\(638\) | 24805.5 | 0.0609406 | ||||||||
\(639\) | 300266. | 0.735367 | ||||||||
\(640\) | 20852.4i | 0.0509092i | ||||||||
\(641\) | −709193. | −1.72603 | −0.863015 | − | 0.505178i | \(-0.831427\pi\) | ||||
−0.863015 | + | 0.505178i | \(0.831427\pi\) | |||||||
\(642\) | 16706.1 | − | 16706.1i | 0.0405327 | − | 0.0405327i | ||||
\(643\) | 217277. | + | 217277.i | 0.525522 | + | 0.525522i | 0.919234 | − | 0.393712i | \(-0.128809\pi\) |
−0.393712 | + | 0.919234i | \(0.628809\pi\) | |||||||
\(644\) | −170661. | − | 170661.i | −0.411492 | − | 0.411492i | ||||
\(645\) | −205661. | −0.494348 | ||||||||
\(646\) | −297887. | + | 297887.i | −0.713815 | + | 0.713815i | ||||
\(647\) | 110695. | + | 110695.i | 0.264435 | + | 0.264435i | 0.826853 | − | 0.562418i | \(-0.190129\pi\) |
−0.562418 | + | 0.826853i | \(0.690129\pi\) | |||||||
\(648\) | 6975.64 | − | 6975.64i | 0.0166125 | − | 0.0166125i | ||||
\(649\) | 208078. | + | 208078.i | 0.494012 | + | 0.494012i | ||||
\(650\) | 262256.i | 0.620725i | ||||||||
\(651\) | 306206. | − | 306206.i | 0.722524 | − | 0.722524i | ||||
\(652\) | 158850. | − | 158850.i | 0.373674 | − | 0.373674i | ||||
\(653\) | −239393. | − | 239393.i | −0.561417 | − | 0.561417i | 0.368292 | − | 0.929710i | \(-0.379943\pi\) |
−0.929710 | + | 0.368292i | \(0.879943\pi\) | |||||||
\(654\) | − | 225985.i | − | 0.528353i | ||||||
\(655\) | 188666. | 0.439756 | ||||||||
\(656\) | 116382.i | 0.270445i | ||||||||
\(657\) | 412873.i | 0.956502i | ||||||||
\(658\) | −473392. | − | 473392.i | −1.09337 | − | 1.09337i | ||||
\(659\) | 597265.i | 1.37530i | 0.726044 | + | 0.687648i | \(0.241357\pi\) | ||||
−0.726044 | + | 0.687648i | \(0.758643\pi\) | |||||||
\(660\) | −45579.7 | − | 45579.7i | −0.104636 | − | 0.104636i | ||||
\(661\) | −38924.4 | − | 38924.4i | −0.0890881 | − | 0.0890881i | 0.661158 | − | 0.750246i | \(-0.270065\pi\) |
−0.750246 | + | 0.661158i | \(0.770065\pi\) | |||||||
\(662\) | 66207.6 | 0.151075 | ||||||||
\(663\) | −484343. | −1.10186 | ||||||||
\(664\) | −157922. | + | 157922.i | −0.358183 | + | 0.358183i | ||||
\(665\) | − | 494359.i | − | 1.11789i | ||||||
\(666\) | −11101.4 | + | 202737.i | −0.0250282 | + | 0.457073i | ||||
\(667\) | −26855.8 | −0.0603652 | ||||||||
\(668\) | −131365. | − | 131365.i | −0.294393 | − | 0.294393i | ||||
\(669\) | 328182.i | 0.733268i | ||||||||
\(670\) | 107026.i | 0.238419i | ||||||||
\(671\) | −503159. | + | 503159.i | −1.11753 | + | 1.11753i | ||||
\(672\) | −64370.5 | + | 64370.5i | −0.142544 | + | 0.142544i | ||||
\(673\) | 528423. | 1.16668 | 0.583340 | − | 0.812228i | \(-0.301745\pi\) | ||||
0.583340 | + | 0.812228i | \(0.301745\pi\) | |||||||
\(674\) | −309901. | + | 309901.i | −0.682187 | + | 0.682187i | ||||
\(675\) | 297854. | 0.653725 | ||||||||
\(676\) | 165792. | 0.362802 | ||||||||
\(677\) | − | 504764.i | − | 1.10131i | −0.834732 | − | 0.550657i | \(-0.814377\pi\) | ||
0.834732 | − | 0.550657i | \(-0.185623\pi\) | |||||||
\(678\) | −100150. | −0.217868 | ||||||||
\(679\) | −88986.4 | + | 88986.4i | −0.193012 | + | 0.193012i | ||||
\(680\) | 94048.7 | + | 94048.7i | 0.203393 | + | 0.203393i | ||||
\(681\) | −145547. | − | 145547.i | −0.313841 | − | 0.313841i | ||||
\(682\) | 255004. | 0.548251 | ||||||||
\(683\) | −360139. | + | 360139.i | −0.772020 | + | 0.772020i | −0.978459 | − | 0.206440i | \(-0.933812\pi\) |
0.206440 | + | 0.978459i | \(0.433812\pi\) | |||||||
\(684\) | −108228. | − | 108228.i | −0.231327 | − | 0.231327i | ||||
\(685\) | −129724. | + | 129724.i | −0.276464 | + | 0.276464i | ||||
\(686\) | 762580. | + | 762580.i | 1.62046 | + | 1.62046i | ||||
\(687\) | − | 352406.i | − | 0.746671i | ||||||
\(688\) | −120941. | + | 120941.i | −0.255502 | + | 0.255502i | ||||
\(689\) | 29049.1 | − | 29049.1i | 0.0611919 | − | 0.0611919i | ||||
\(690\) | 49347.0 | + | 49347.0i | 0.103648 | + | 0.103648i | ||||
\(691\) | − | 850032.i | − | 1.78024i | −0.455723 | − | 0.890122i | \(-0.650619\pi\) | ||
0.455723 | − | 0.890122i | \(-0.349381\pi\) | |||||||
\(692\) | 11047.0 | 0.0230692 | ||||||||
\(693\) | 516605.i | 1.07570i | ||||||||
\(694\) | − | 315103.i | − | 0.654235i | ||||||
\(695\) | 26084.9 | + | 26084.9i | 0.0540032 | + | 0.0540032i | ||||
\(696\) | 10129.6i | 0.0209109i | ||||||||
\(697\) | 524909. | + | 524909.i | 1.08048 | + | 1.08048i | ||||
\(698\) | 171162. | + | 171162.i | 0.351314 | + | 0.351314i | ||||
\(699\) | −300303. | −0.614618 | ||||||||
\(700\) | 314403. | 0.641638 | ||||||||
\(701\) | −67567.6 | + | 67567.6i | −0.137500 | + | 0.137500i | −0.772507 | − | 0.635007i | \(-0.780997\pi\) |
0.635007 | + | 0.772507i | \(0.280997\pi\) | |||||||
\(702\) | − | 447798.i | − | 0.908673i | ||||||
\(703\) | 498749. | + | 27310.3i | 1.00919 | + | 0.0552607i | ||||
\(704\) | −53606.9 | −0.108162 | ||||||||
\(705\) | 136883. | + | 136883.i | 0.275404 | + | 0.275404i | ||||
\(706\) | − | 568042.i | − | 1.13965i | ||||||
\(707\) | 1.73378e6i | 3.46860i | ||||||||
\(708\) | −84971.0 | + | 84971.0i | −0.169513 | + | 0.169513i | ||||
\(709\) | −223391. | + | 223391.i | −0.444399 | + | 0.444399i | −0.893487 | − | 0.449089i | \(-0.851749\pi\) |
0.449089 | + | 0.893487i | \(0.351749\pi\) | |||||||
\(710\) | −233215. | −0.462637 | ||||||||
\(711\) | 168574. | − | 168574.i | 0.333466 | − | 0.333466i | ||||
\(712\) | 117117. | 0.231025 | ||||||||
\(713\) | −276082. | −0.543074 | ||||||||
\(714\) | 580649.i | 1.13898i | ||||||||
\(715\) | 334695. | 0.654692 | ||||||||
\(716\) | 88660.4 | − | 88660.4i | 0.172943 | − | 0.172943i | ||||
\(717\) | 424516. | + | 424516.i | 0.825764 | + | 0.825764i | ||||
\(718\) | −16713.4 | − | 16713.4i | −0.0324202 | − | 0.0324202i | ||||
\(719\) | −964220. | −1.86517 | −0.932585 | − | 0.360950i | \(-0.882452\pi\) | ||||
−0.932585 | + | 0.360950i | \(0.882452\pi\) | |||||||
\(720\) | −34169.7 | + | 34169.7i | −0.0659138 | + | 0.0659138i | ||||
\(721\) | 62429.6 | + | 62429.6i | 0.120094 | + | 0.120094i | ||||
\(722\) | −5607.04 | + | 5607.04i | −0.0107562 | + | 0.0107562i | ||||
\(723\) | −112336. | − | 112336.i | −0.214903 | − | 0.214903i | ||||
\(724\) | 142489.i | 0.271833i | ||||||||
\(725\) | 24737.8 | − | 24737.8i | 0.0470636 | − | 0.0470636i | ||||
\(726\) | −39321.5 | + | 39321.5i | −0.0746030 | + | 0.0746030i | ||||
\(727\) | −223895. | − | 223895.i | −0.423620 | − | 0.423620i | 0.462828 | − | 0.886448i | \(-0.346835\pi\) |
−0.886448 | + | 0.462828i | \(0.846835\pi\) | |||||||
\(728\) | − | 472678.i | − | 0.891872i | ||||||
\(729\) | −285862. | −0.537899 | ||||||||
\(730\) | − | 320677.i | − | 0.601758i | ||||||
\(731\) | 1.09093e6i | 2.04157i | ||||||||
\(732\) | −205470. | − | 205470.i | −0.383466 | − | 0.383466i | ||||
\(733\) | − | 551842.i | − | 1.02709i | −0.858064 | − | 0.513543i | \(-0.828333\pi\) | ||
0.858064 | − | 0.513543i | \(-0.171667\pi\) | |||||||
\(734\) | −36247.2 | − | 36247.2i | −0.0672795 | − | 0.0672795i | ||||
\(735\) | −351156. | − | 351156.i | −0.650018 | − | 0.650018i | ||||
\(736\) | 58037.8 | 0.107141 | ||||||||
\(737\) | −275140. | −0.506547 | ||||||||
\(738\) | −190710. | + | 190710.i | −0.350155 | + | 0.350155i | ||||
\(739\) | 137775.i | 0.252278i | 0.992013 | + | 0.126139i | \(0.0402586\pi\) | ||||
−0.992013 | + | 0.126139i | \(0.959741\pi\) | |||||||
\(740\) | 8622.41 | − | 157465.i | 0.0157458 | − | 0.287555i | ||||
\(741\) | −432903. | −0.788414 | ||||||||
\(742\) | −34825.1 | − | 34825.1i | −0.0632536 | − | 0.0632536i | ||||
\(743\) | 352194.i | 0.637977i | 0.947759 | + | 0.318988i | \(0.103343\pi\) | ||||
−0.947759 | + | 0.318988i | \(0.896657\pi\) | |||||||
\(744\) | 104134.i | 0.188125i | ||||||||
\(745\) | −168137. | + | 168137.i | −0.302936 | + | 0.302936i | ||||
\(746\) | −109110. | + | 109110.i | −0.196058 | + | 0.196058i | ||||
\(747\) | −517555. | −0.927504 | ||||||||
\(748\) | −241778. | + | 241778.i | −0.432130 | + | 0.432130i | ||||
\(749\) | 147067. | 0.262151 | ||||||||
\(750\) | −226952. | −0.403470 | ||||||||
\(751\) | − | 1.08959e6i | − | 1.93190i | −0.258737 | − | 0.965948i | \(-0.583306\pi\) | ||
0.258737 | − | 0.965948i | \(-0.416694\pi\) | |||||||
\(752\) | 160990. | 0.284683 | ||||||||
\(753\) | 309849. | − | 309849.i | 0.546463 | − | 0.546463i | ||||
\(754\) | −37191.2 | − | 37191.2i | −0.0654180 | − | 0.0654180i | ||||
\(755\) | 36596.0 | + | 36596.0i | 0.0642006 | + | 0.0642006i | ||||
\(756\) | −536837. | −0.939288 | ||||||||
\(757\) | 103856. | − | 103856.i | 0.181233 | − | 0.181233i | −0.610660 | − | 0.791893i | \(-0.709096\pi\) |
0.791893 | + | 0.610660i | \(0.209096\pi\) | |||||||
\(758\) | 434975. | + | 434975.i | 0.757053 | + | 0.757053i | ||||
\(759\) | −126860. | + | 126860.i | −0.220213 | + | 0.220213i | ||||
\(760\) | 84060.1 | + | 84060.1i | 0.145533 | + | 0.145533i | ||||
\(761\) | − | 357264.i | − | 0.616908i | −0.951239 | − | 0.308454i | \(-0.900188\pi\) | ||
0.951239 | − | 0.308454i | \(-0.0998116\pi\) | |||||||
\(762\) | −9199.08 | + | 9199.08i | −0.0158429 | + | 0.0158429i | ||||
\(763\) | 994691. | − | 994691.i | 1.70859 | − | 1.70859i | ||||
\(764\) | −113367. | − | 113367.i | −0.194223 | − | 0.194223i | ||||
\(765\) | 308225.i | 0.526678i | ||||||||
\(766\) | −457827. | −0.780269 | ||||||||
\(767\) | − | 623948.i | − | 1.06061i | ||||||
\(768\) | − | 21890.9i | − | 0.0371143i | ||||||
\(769\) | 305401. | + | 305401.i | 0.516438 | + | 0.516438i | 0.916492 | − | 0.400054i | \(-0.131009\pi\) |
−0.400054 | + | 0.916492i | \(0.631009\pi\) | |||||||
\(770\) | − | 401245.i | − | 0.676750i | ||||||
\(771\) | 252952. | + | 252952.i | 0.425530 | + | 0.425530i | ||||
\(772\) | −254637. | − | 254637.i | −0.427255 | − | 0.427255i | ||||
\(773\) | −199611. | −0.334060 | −0.167030 | − | 0.985952i | \(-0.553418\pi\) | ||||
−0.167030 | + | 0.985952i | \(0.553418\pi\) | |||||||
\(774\) | −396358. | −0.661615 | ||||||||
\(775\) | 254308. | − | 254308.i | 0.423406 | − | 0.423406i | ||||
\(776\) | − | 30262.2i | − | 0.0502548i | ||||||
\(777\) | 512706. | − | 459472.i | 0.849231 | − | 0.761056i | ||||
\(778\) | 517675. | 0.855260 | ||||||||
\(779\) | 469160. | + | 469160.i | 0.773119 | + | 0.773119i | ||||
\(780\) | 136676.i | 0.224648i | ||||||||
\(781\) | − | 599545.i | − | 0.982923i | ||||||
\(782\) | 261763. | − | 261763.i | 0.428049 | − | 0.428049i | ||||
\(783\) | −42239.3 | + | 42239.3i | −0.0688959 | + | 0.0688959i | ||||
\(784\) | −413000. | −0.671920 | ||||||||
\(785\) | 13320.9 | − | 13320.9i | 0.0216169 | − | 0.0216169i | ||||
\(786\) | −198063. | −0.320595 | ||||||||
\(787\) | 397114. | 0.641158 | 0.320579 | − | 0.947222i | \(-0.396122\pi\) | ||||
0.320579 | + | 0.947222i | \(0.396122\pi\) | |||||||
\(788\) | 309081.i | 0.497760i | ||||||||
\(789\) | −405403. | −0.651228 | ||||||||
\(790\) | −130931. | + | 130931.i | −0.209791 | + | 0.209791i | ||||
\(791\) | −440819. | − | 440819.i | −0.704543 | − | 0.704543i | ||||
\(792\) | −87842.7 | − | 87842.7i | −0.140041 | − | 0.140041i | ||||
\(793\) | 1.50878e6 | 2.39928 | ||||||||
\(794\) | 178782. | − | 178782.i | 0.283585 | − | 0.283585i | ||||
\(795\) | 10069.8 | + | 10069.8i | 0.0159326 | + | 0.0159326i | ||||
\(796\) | 336818. | − | 336818.i | 0.531580 | − | 0.531580i | ||||
\(797\) | −521684. | − | 521684.i | −0.821280 | − | 0.821280i | 0.165012 | − | 0.986292i | \(-0.447234\pi\) |
−0.986292 | + | 0.165012i | \(0.947234\pi\) | |||||||
\(798\) | 518981.i | 0.814977i | ||||||||
\(799\) | 726097. | − | 726097.i | 1.13737 | − | 1.13737i | ||||
\(800\) | −53460.5 | + | 53460.5i | −0.0835321 | + | 0.0835321i | ||||
\(801\) | 191913. | + | 191913.i | 0.299115 | + | 0.299115i | ||||
\(802\) | 46362.6i | 0.0720807i | ||||||||
\(803\) | 824389. | 1.27850 | ||||||||
\(804\) | − | 112356.i | − | 0.173814i | ||||||
\(805\) | 434410.i | 0.670359i | ||||||||
\(806\) | −382331. | − | 382331.i | −0.588531 | − | 0.588531i | ||||
\(807\) | − | 496043.i | − | 0.761680i | ||||||
\(808\) | −294809. | − | 294809.i | −0.451562 | − | 0.451562i | ||||
\(809\) | 609373. | + | 609373.i | 0.931078 | + | 0.931078i | 0.997773 | − | 0.0666958i | \(-0.0212457\pi\) |
−0.0666958 | + | 0.997773i | \(0.521246\pi\) | |||||||
\(810\) | −17756.2 | −0.0270633 | ||||||||
\(811\) | 390914. | 0.594346 | 0.297173 | − | 0.954824i | \(-0.403956\pi\) | ||||
0.297173 | + | 0.954824i | \(0.403956\pi\) | |||||||
\(812\) | −44586.2 | + | 44586.2i | −0.0676220 | + | 0.0676220i | ||||
\(813\) | − | 16857.4i | − | 0.0255041i | ||||||
\(814\) | 404808. | + | 22166.3i | 0.610942 | + | 0.0334537i | ||||
\(815\) | −404346. | −0.608749 | ||||||||
\(816\) | −98732.7 | − | 98732.7i | −0.148279 | − | 0.148279i | ||||
\(817\) | 975070.i | 1.46080i | ||||||||
\(818\) | 634925.i | 0.948890i | ||||||||
\(819\) | 774552. | − | 774552.i | 1.15474 | − | 1.15474i | ||||
\(820\) | 148123. | − | 148123.i | 0.220290 | − | 0.220290i | ||||
\(821\) | 1.07295e6 | 1.59181 | 0.795906 | − | 0.605421i | \(-0.206995\pi\) | ||||
0.795906 | + | 0.605421i | \(0.206995\pi\) | |||||||
\(822\) | 136185. | − | 136185.i | 0.201551 | − | 0.201551i | ||||
\(823\) | −932897. | −1.37732 | −0.688658 | − | 0.725086i | \(-0.741800\pi\) | ||||
−0.688658 | + | 0.725086i | \(0.741800\pi\) | |||||||
\(824\) | −21230.9 | −0.0312690 | ||||||||
\(825\) | − | 233711.i | − | 0.343376i | ||||||
\(826\) | −748013. | −1.09635 | ||||||||
\(827\) | 610170. | − | 610170.i | 0.892153 | − | 0.892153i | −0.102572 | − | 0.994726i | \(-0.532707\pi\) |
0.994726 | + | 0.102572i | \(0.0327072\pi\) | |||||||
\(828\) | 95103.4 | + | 95103.4i | 0.138719 | + | 0.138719i | ||||
\(829\) | −576887. | − | 576887.i | −0.839425 | − | 0.839425i | 0.149359 | − | 0.988783i | \(-0.452279\pi\) |
−0.988783 | + | 0.149359i | \(0.952279\pi\) | |||||||
\(830\) | 401983. | 0.583514 | ||||||||
\(831\) | 346572. | − | 346572.i | 0.501870 | − | 0.501870i | ||||
\(832\) | 80373.4 | + | 80373.4i | 0.116109 | + | 0.116109i | ||||
\(833\) | −1.86272e6 | + | 1.86272e6i | −2.68446 | + | 2.68446i | ||||
\(834\) | −27384.0 | − | 27384.0i | −0.0393700 | − | 0.0393700i | ||||
\(835\) | 334385.i | 0.479594i | ||||||||
\(836\) | −216100. | + | 216100.i | −0.309202 | + | 0.309202i | ||||
\(837\) | −434227. | + | 434227.i | −0.619820 | + | 0.619820i | ||||
\(838\) | 107281. | + | 107281.i | 0.152769 | + | 0.152769i | ||||
\(839\) | 1.04170e6i | 1.47985i | 0.672691 | + | 0.739924i | \(0.265139\pi\) | ||||
−0.672691 | + | 0.739924i | \(0.734861\pi\) | |||||||
\(840\) | 163853. | 0.232217 | ||||||||
\(841\) | − | 700265.i | − | 0.990080i | ||||||
\(842\) | 452118.i | 0.637716i | ||||||||
\(843\) | −351995. | − | 351995.i | −0.495315 | − | 0.495315i | ||||
\(844\) | 30754.5i | 0.0431742i | ||||||||
\(845\) | −211008. | − | 211008.i | −0.295519 | − | 0.295519i | ||||
\(846\) | 263805. | + | 263805.i | 0.368589 | + | 0.368589i | ||||
\(847\) | −346153. | −0.482504 | ||||||||
\(848\) | 11843.2 | 0.0164694 | ||||||||
\(849\) | 102830. | − | 102830.i | 0.142660 | − | 0.142660i | ||||
\(850\) | 482237.i | 0.667456i | ||||||||
\(851\) | −438267. | − | 23998.5i | −0.605173 | − | 0.0331378i | ||||
\(852\) | 244830. | 0.337276 | ||||||||
\(853\) | 732648. | + | 732648.i | 1.00693 | + | 1.00693i | 0.999976 | + | 0.00695022i | \(0.00221234\pi\) |
0.00695022 | + | 0.999976i | \(0.497788\pi\) | |||||||
\(854\) | − | 1.80879e6i | − | 2.48011i | ||||||
\(855\) | 275490.i | 0.376854i | ||||||||
\(856\) | −25007.0 | + | 25007.0i | −0.0341283 | + | 0.0341283i | ||||
\(857\) | 683980. | − | 683980.i | 0.931283 | − | 0.931283i | −0.0665034 | − | 0.997786i | \(-0.521184\pi\) |
0.997786 | + | 0.0665034i | \(0.0211843\pi\) | |||||||
\(858\) | −351364. | −0.477290 | ||||||||
\(859\) | −134430. | + | 134430.i | −0.182184 | + | 0.182184i | −0.792307 | − | 0.610123i | \(-0.791120\pi\) |
0.610123 | + | 0.792307i | \(0.291120\pi\) | |||||||
\(860\) | 307849. | 0.416237 | ||||||||
\(861\) | 914501. | 1.23361 | ||||||||
\(862\) | − | 834913.i | − | 1.12364i | ||||||
\(863\) | 913704. | 1.22683 | 0.613414 | − | 0.789761i | \(-0.289796\pi\) | ||||
0.613414 | + | 0.789761i | \(0.289796\pi\) | |||||||
\(864\) | 91282.9 | − | 91282.9i | 0.122282 | − | 0.122282i | ||||
\(865\) | −14059.9 | − | 14059.9i | −0.0187910 | − | 0.0187910i | ||||
\(866\) | 150905. | + | 150905.i | 0.201219 | + | 0.201219i | ||||
\(867\) | −444236. | −0.590983 | ||||||||
\(868\) | −458353. | + | 458353.i | −0.608360 | + | 0.608360i | ||||
\(869\) | −336594. | − | 336594.i | −0.445725 | − | 0.445725i | ||||
\(870\) | 12892.2 | − | 12892.2i | 0.0170329 | − | 0.0170329i | ||||
\(871\) | 412521. | + | 412521.i | 0.543763 | + | 0.543763i | ||||
\(872\) | 338271.i | 0.444869i | ||||||||
\(873\) | 49589.1 | − | 49589.1i | 0.0650665 | − | 0.0650665i | ||||
\(874\) | 233962. | − | 233962.i | 0.306282 | − | 0.306282i | ||||
\(875\) | −998945. | − | 998945.i | −1.30475 | − | 1.30475i | ||||
\(876\) | 336648.i | 0.438700i | ||||||||
\(877\) | −102923. | −0.133818 | −0.0669091 | − | 0.997759i | \(-0.521314\pi\) | ||||
−0.0669091 | + | 0.997759i | \(0.521314\pi\) | |||||||
\(878\) | 986830.i | 1.28013i | ||||||||
\(879\) | 425513.i | 0.550725i | ||||||||
\(880\) | 68227.1 | + | 68227.1i | 0.0881031 | + | 0.0881031i | ||||
\(881\) | − | 751242.i | − | 0.967895i | −0.875097 | − | 0.483947i | \(-0.839203\pi\) | ||
0.875097 | − | 0.483947i | \(-0.160797\pi\) | |||||||
\(882\) | −676761. | − | 676761.i | −0.869958 | − | 0.869958i | ||||
\(883\) | −477447. | − | 477447.i | −0.612356 | − | 0.612356i | 0.331204 | − | 0.943559i | \(-0.392545\pi\) |
−0.943559 | + | 0.331204i | \(0.892545\pi\) | |||||||
\(884\) | 725002. | 0.927758 | ||||||||
\(885\) | 216290. | 0.276153 | ||||||||
\(886\) | −137882. | + | 137882.i | −0.175647 | + | 0.175647i | ||||
\(887\) | 1.05408e6i | 1.33976i | 0.742471 | + | 0.669879i | \(0.233654\pi\) | ||||
−0.742471 | + | 0.669879i | \(0.766346\pi\) | |||||||
\(888\) | −9051.84 | + | 165308.i | −0.0114792 | + | 0.209636i | ||||
\(889\) | −80981.0 | −0.102466 | ||||||||
\(890\) | −149058. | − | 149058.i | −0.188180 | − | 0.188180i | ||||
\(891\) | − | 45647.3i | − | 0.0574989i | ||||||
\(892\) | − | 491248.i | − | 0.617406i | ||||||
\(893\) | 648981. | − | 648981.i | 0.813821 | − | 0.813821i | ||||
\(894\) | 176511. | − | 176511.i | 0.220849 | − | 0.220849i | ||||
\(895\) | −225681. | −0.281741 | ||||||||
\(896\) | 96354.7 | − | 96354.7i | 0.120021 | − | 0.120021i | ||||
\(897\) | 380406. | 0.472784 | ||||||||
\(898\) | −572224. | −0.709600 | ||||||||
\(899\) | 72128.1i | 0.0892453i | ||||||||
\(900\) | −175206. | −0.216304 | ||||||||
\(901\) | 53415.4 | − | 53415.4i | 0.0657987 | − | 0.0657987i | ||||
\(902\) | 380792. | + | 380792.i | 0.468031 | + | 0.468031i | ||||
\(903\) | 950318. | + | 950318.i | 1.16545 | + | 1.16545i | ||||
\(904\) | 149912. | 0.183443 | ||||||||
\(905\) | 181349. | − | 181349.i | 0.221421 | − | 0.221421i | ||||
\(906\) | −38418.6 | − | 38418.6i | −0.0468042 | − | 0.0468042i | ||||
\(907\) | −698673. | + | 698673.i | −0.849296 | + | 0.849296i | −0.990045 | − | 0.140749i | \(-0.955049\pi\) |
0.140749 | + | 0.990045i | \(0.455049\pi\) | |||||||
\(908\) | 217866. | + | 217866.i | 0.264252 | + | 0.264252i | ||||
\(909\) | − | 966175.i | − | 1.16931i | ||||||
\(910\) | −601591. | + | 601591.i | −0.726471 | + | 0.726471i | ||||
\(911\) | −739565. | + | 739565.i | −0.891127 | + | 0.891127i | −0.994629 | − | 0.103502i | \(-0.966995\pi\) |
0.103502 | + | 0.994629i | \(0.466995\pi\) | |||||||
\(912\) | −88246.7 | − | 88246.7i | −0.106098 | − | 0.106098i | ||||
\(913\) | 1.03341e6i | 1.23974i | ||||||||
\(914\) | −535282. | −0.640752 | ||||||||
\(915\) | 523016.i | 0.624701i | ||||||||
\(916\) | 527507.i | 0.628691i | ||||||||
\(917\) | −871788. | − | 871788.i | −1.03675 | − | 1.03675i | ||||
\(918\) | − | 823410.i | − | 0.977082i | ||||||
\(919\) | 206120. | + | 206120.i | 0.244055 | + | 0.244055i | 0.818526 | − | 0.574470i | \(-0.194792\pi\) |
−0.574470 | + | 0.818526i | \(0.694792\pi\) | |||||||
\(920\) | −73866.4 | − | 73866.4i | −0.0872712 | − | 0.0872712i | ||||
\(921\) | 350444. | 0.413142 | ||||||||
\(922\) | −160337. | −0.188613 | ||||||||
\(923\) | −898903. | + | 898903.i | −1.05514 | + | 1.05514i | ||||
\(924\) | 421229.i | 0.493371i | ||||||||
\(925\) | 425809. | − | 381597.i | 0.497658 | − | 0.445986i | ||||
\(926\) | 921601. | 1.07478 | ||||||||
\(927\) | −34789.9 | − | 34789.9i | −0.0404850 | − | 0.0404850i | ||||
\(928\) | − | 15162.7i | − | 0.0176068i | ||||||
\(929\) | − | 1.26493e6i | − | 1.46567i | −0.680406 | − | 0.732835i | \(-0.738196\pi\) | ||
0.680406 | − | 0.732835i | \(-0.261804\pi\) | |||||||
\(930\) | 132534. | − | 132534.i | 0.153236 | − | 0.153236i | ||||
\(931\) | −1.66488e6 | + | 1.66488e6i | −1.92081 | + | 1.92081i | ||||
\(932\) | 449516. | 0.517504 | ||||||||
\(933\) | 259485. | − | 259485.i | 0.298091 | − | 0.298091i | ||||
\(934\) | −426399. | −0.488790 | ||||||||
\(935\) | 615437. | 0.703980 | ||||||||
\(936\) | 263407.i | 0.300660i | ||||||||
\(937\) | −238720. | −0.271900 | −0.135950 | − | 0.990716i | \(-0.543409\pi\) | ||||
−0.135950 | + | 0.990716i | \(0.543409\pi\) | |||||||
\(938\) | 494546. | − | 494546.i | 0.562083 | − | 0.562083i | ||||
\(939\) | −86410.0 | − | 86410.0i | −0.0980015 | − | 0.0980015i | ||||
\(940\) | −204896. | − | 204896.i | −0.231888 | − | 0.231888i | ||||
\(941\) | −1.43551e6 | −1.62117 | −0.810584 | − | 0.585623i | \(-0.800850\pi\) | ||||
−0.810584 | + | 0.585623i | \(0.800850\pi\) | |||||||
\(942\) | −13984.3 | + | 13984.3i | −0.0157594 | + | 0.0157594i | ||||
\(943\) | −412266. | − | 412266.i | −0.463612 | − | 0.463612i | ||||
\(944\) | 127191. | − | 127191.i | 0.142729 | − | 0.142729i | ||||
\(945\) | 683248. | + | 683248.i | 0.765094 | + | 0.765094i | ||||
\(946\) | 791412.i | 0.884342i | ||||||||
\(947\) | −650178. | + | 650178.i | −0.724990 | + | 0.724990i | −0.969617 | − | 0.244627i | \(-0.921334\pi\) |
0.244627 | + | 0.969617i | \(0.421334\pi\) | |||||||
\(948\) | 137452. | − | 137452.i | 0.152944 | − | 0.152944i | ||||
\(949\) | −1.23602e6 | − | 1.23602e6i | −1.37243 | − | 1.37243i | ||||
\(950\) | 431020.i | 0.477584i | ||||||||
\(951\) | −498267. | −0.550936 | ||||||||
\(952\) | − | 869160.i | − | 0.959016i | ||||||
\(953\) | 421638.i | 0.464253i | 0.972686 | + | 0.232126i | \(0.0745683\pi\) | ||||
−0.972686 | + | 0.232126i | \(0.925432\pi\) | |||||||
\(954\) | 19406.9 | + | 19406.9i | 0.0213235 | + | 0.0213235i | ||||
\(955\) | 288571.i | 0.316407i | ||||||||
\(956\) | −635448. | − | 635448.i | −0.695287 | − | 0.695287i | ||||
\(957\) | 33143.0 | + | 33143.0i | 0.0361883 | + | 0.0361883i | ||||
\(958\) | 569851. | 0.620913 | ||||||||
\(959\) | 1.19886e6 | 1.30356 | ||||||||
\(960\) | −27861.2 | + | 27861.2i | −0.0302314 | + | 0.0302314i | ||||
\(961\) | − | 182033.i | − | 0.197107i | ||||||
\(962\) | −573699. | − | 640167.i | −0.619917 | − | 0.691740i | ||||
\(963\) | −81955.3 | −0.0883739 | ||||||||
\(964\) | 168153. | + | 168153.i | 0.180946 | + | 0.180946i | ||||
\(965\) | 648169.i | 0.696039i | ||||||||
\(966\) | − | 456045.i | − | 0.488713i | ||||||
\(967\) | −59980.1 | + | 59980.1i | −0.0641437 | + | 0.0641437i | −0.738451 | − | 0.674307i | \(-0.764442\pi\) |
0.674307 | + | 0.738451i | \(0.264442\pi\) | |||||||
\(968\) | 58859.3 | − | 58859.3i | 0.0628152 | − | 0.0628152i | ||||
\(969\) | −796022. | −0.847769 | ||||||||
\(970\) | −38515.6 | + | 38515.6i | −0.0409349 | + | 0.0409349i | ||||
\(971\) | 1.05017e6 | 1.11383 | 0.556916 | − | 0.830569i | \(-0.311985\pi\) | ||||
0.556916 | + | 0.830569i | \(0.311985\pi\) | |||||||
\(972\) | 480760. | 0.508857 | ||||||||
\(973\) | − | 241066.i | − | 0.254630i | ||||||
\(974\) | −89906.6 | −0.0947706 | ||||||||
\(975\) | −350405. | + | 350405.i | −0.368605 | + | 0.368605i | ||||
\(976\) | 307563. | + | 307563.i | 0.322875 | + | 0.322875i | ||||
\(977\) | −540645. | − | 540645.i | −0.566400 | − | 0.566400i | 0.364718 | − | 0.931118i | \(-0.381165\pi\) |
−0.931118 | + | 0.364718i | \(0.881165\pi\) | |||||||
\(978\) | 424485. | 0.443797 | ||||||||
\(979\) | 383194. | − | 383194.i | 0.399810 | − | 0.399810i | ||||
\(980\) | 525637. | + | 525637.i | 0.547311 | + | 0.547311i | ||||
\(981\) | −554307. | + | 554307.i | −0.575987 | + | 0.575987i | ||||
\(982\) | 265590. | + | 265590.i | 0.275416 | + | 0.275416i | ||||
\(983\) | 906557.i | 0.938184i | 0.883149 | + | 0.469092i | \(0.155419\pi\) | ||||
−0.883149 | + | 0.469092i | \(0.844581\pi\) | |||||||
\(984\) | −155500. | + | 155500.i | −0.160598 | + | 0.160598i | ||||
\(985\) | 393376. | − | 393376.i | 0.405449 | − | 0.405449i | ||||
\(986\) | −68387.1 | − | 68387.1i | −0.0703429 | − | 0.0703429i | ||||
\(987\) | − | 1.26501e6i | − | 1.29856i | ||||||
\(988\) | 648002. | 0.663838 | ||||||||
\(989\) | − | 856826.i | − | 0.875992i | ||||||
\(990\) | 223600.i | 0.228140i | ||||||||
\(991\) | 452537. | + | 452537.i | 0.460794 | + | 0.460794i | 0.898916 | − | 0.438122i | \(-0.144356\pi\) |
−0.438122 | + | 0.898916i | \(0.644356\pi\) | |||||||
\(992\) | − | 155875.i | − | 0.158399i | ||||||
\(993\) | 88461.1 | + | 88461.1i | 0.0897127 | + | 0.0897127i | ||||
\(994\) | 1.07764e6 | + | 1.07764e6i | 1.09069 | + | 1.09069i | ||||
\(995\) | −857355. | −0.865993 | ||||||||
\(996\) | −422003. | −0.425400 | ||||||||
\(997\) | −34077.1 | + | 34077.1i | −0.0342825 | + | 0.0342825i | −0.724040 | − | 0.689758i | \(-0.757717\pi\) |
0.689758 | + | 0.724040i | \(0.257717\pi\) | |||||||
\(998\) | − | 826784.i | − | 0.830101i | ||||||
\(999\) | −727060. | + | 651570.i | −0.728517 | + | 0.652875i |
(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 | 74.5.d.a.31.3 | ✓ | 14 | |
37.6 | odd | 4 | inner | 74.5.d.a.43.5 | yes | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
74.5.d.a.31.3 | ✓ | 14 | 1.1 | even | 1 | trivial | |
74.5.d.a.43.5 | yes | 14 | 37.6 | odd | 4 | inner |