Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [35,5,Mod(34,35)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(35, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("35.34");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 35 = 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 35.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.61794870793\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{-6}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 6 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 34.2 | ||
Root | \(2.44949i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 35.34 |
Dual form | 35.5.c.d.34.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/35\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.44949i | 0.612372i | 0.951972 | + | 0.306186i | \(0.0990530\pi\) | ||||
−0.951972 | + | 0.306186i | \(0.900947\pi\) | |||||||
\(3\) | 5.00000 | 0.555556 | 0.277778 | − | 0.960645i | \(-0.410402\pi\) | ||||
0.277778 | + | 0.960645i | \(0.410402\pi\) | |||||||
\(4\) | 10.0000 | 0.625000 | ||||||||
\(5\) | 5.00000 | − | 24.4949i | 0.200000 | − | 0.979796i | ||||
\(6\) | 12.2474i | 0.340207i | ||||||||
\(7\) | 35.0000 | + | 34.2929i | 0.714286 | + | 0.699854i | ||||
\(8\) | 63.6867i | 0.995105i | ||||||||
\(9\) | −56.0000 | −0.691358 | ||||||||
\(10\) | 60.0000 | + | 12.2474i | 0.600000 | + | 0.122474i | ||||
\(11\) | 89.0000 | 0.735537 | 0.367769 | − | 0.929917i | \(-0.380122\pi\) | ||||
0.367769 | + | 0.929917i | \(0.380122\pi\) | |||||||
\(12\) | 50.0000 | 0.347222 | ||||||||
\(13\) | −5.00000 | −0.0295858 | −0.0147929 | − | 0.999891i | \(-0.504709\pi\) | ||||
−0.0147929 | + | 0.999891i | \(0.504709\pi\) | |||||||
\(14\) | −84.0000 | + | 85.7321i | −0.428571 | + | 0.437409i | ||||
\(15\) | 25.0000 | − | 122.474i | 0.111111 | − | 0.544331i | ||||
\(16\) | 4.00000 | 0.0156250 | ||||||||
\(17\) | −485.000 | −1.67820 | −0.839100 | − | 0.543977i | \(-0.816918\pi\) | ||||
−0.839100 | + | 0.543977i | \(0.816918\pi\) | |||||||
\(18\) | − | 137.171i | − | 0.423369i | ||||||
\(19\) | − | 220.454i | − | 0.610676i | −0.952244 | − | 0.305338i | \(-0.901231\pi\) | ||
0.952244 | − | 0.305338i | \(-0.0987695\pi\) | |||||||
\(20\) | 50.0000 | − | 244.949i | 0.125000 | − | 0.612372i | ||||
\(21\) | 175.000 | + | 171.464i | 0.396825 | + | 0.388808i | ||||
\(22\) | 218.005i | 0.450423i | ||||||||
\(23\) | − | 700.554i | − | 1.32430i | −0.749372 | − | 0.662149i | \(-0.769644\pi\) | ||
0.749372 | − | 0.662149i | \(-0.230356\pi\) | |||||||
\(24\) | 318.434i | 0.552836i | ||||||||
\(25\) | −575.000 | − | 244.949i | −0.920000 | − | 0.391918i | ||||
\(26\) | − | 12.2474i | − | 0.0181175i | ||||||
\(27\) | −685.000 | −0.939643 | ||||||||
\(28\) | 350.000 | + | 342.929i | 0.446429 | + | 0.437409i | ||||
\(29\) | 191.000 | 0.227111 | 0.113555 | − | 0.993532i | \(-0.463776\pi\) | ||||
0.113555 | + | 0.993532i | \(0.463776\pi\) | |||||||
\(30\) | 300.000 | + | 61.2372i | 0.333333 | + | 0.0680414i | ||||
\(31\) | 1053.28i | 1.09603i | 0.836470 | + | 0.548013i | \(0.184615\pi\) | ||||
−0.836470 | + | 0.548013i | \(0.815385\pi\) | |||||||
\(32\) | 1028.79i | 1.00467i | ||||||||
\(33\) | 445.000 | 0.408632 | ||||||||
\(34\) | − | 1188.00i | − | 1.02768i | ||||||
\(35\) | 1015.00 | − | 685.857i | 0.828571 | − | 0.559883i | ||||
\(36\) | −560.000 | −0.432099 | ||||||||
\(37\) | 1631.36i | 1.19164i | 0.803117 | + | 0.595822i | \(0.203174\pi\) | ||||
−0.803117 | + | 0.595822i | \(0.796826\pi\) | |||||||
\(38\) | 540.000 | 0.373961 | ||||||||
\(39\) | −25.0000 | −0.0164366 | ||||||||
\(40\) | 1560.00 | + | 318.434i | 0.975000 | + | 0.199021i | ||||
\(41\) | − | 2914.89i | − | 1.73402i | −0.498288 | − | 0.867012i | \(-0.666038\pi\) | ||
0.498288 | − | 0.867012i | \(-0.333962\pi\) | |||||||
\(42\) | −420.000 | + | 428.661i | −0.238095 | + | 0.243005i | ||||
\(43\) | 377.221i | 0.204014i | 0.994784 | + | 0.102007i | \(0.0325264\pi\) | ||||
−0.994784 | + | 0.102007i | \(0.967474\pi\) | |||||||
\(44\) | 890.000 | 0.459711 | ||||||||
\(45\) | −280.000 | + | 1371.71i | −0.138272 | + | 0.677390i | ||||
\(46\) | 1716.00 | 0.810964 | ||||||||
\(47\) | −2195.00 | −0.993662 | −0.496831 | − | 0.867847i | \(-0.665503\pi\) | ||||
−0.496831 | + | 0.867847i | \(0.665503\pi\) | |||||||
\(48\) | 20.0000 | 0.00868056 | ||||||||
\(49\) | 49.0000 | + | 2400.50i | 0.0204082 | + | 0.999792i | ||||
\(50\) | 600.000 | − | 1408.46i | 0.240000 | − | 0.563383i | ||||
\(51\) | −2425.00 | −0.932334 | ||||||||
\(52\) | −50.0000 | −0.0184911 | ||||||||
\(53\) | − | 1587.27i | − | 0.565066i | −0.959258 | − | 0.282533i | \(-0.908825\pi\) | ||
0.959258 | − | 0.282533i | \(-0.0911746\pi\) | |||||||
\(54\) | − | 1677.90i | − | 0.575412i | ||||||
\(55\) | 445.000 | − | 2180.05i | 0.147107 | − | 0.720676i | ||||
\(56\) | −2184.00 | + | 2229.04i | −0.696429 | + | 0.710789i | ||||
\(57\) | − | 1102.27i | − | 0.339265i | ||||||
\(58\) | 467.853i | 0.139076i | ||||||||
\(59\) | 3625.24i | 1.04144i | 0.853728 | + | 0.520719i | \(0.174336\pi\) | ||||
−0.853728 | + | 0.520719i | \(0.825664\pi\) | |||||||
\(60\) | 250.000 | − | 1224.74i | 0.0694444 | − | 0.340207i | ||||
\(61\) | − | 1935.10i | − | 0.520048i | −0.965602 | − | 0.260024i | \(-0.916270\pi\) | ||
0.965602 | − | 0.260024i | \(-0.0837304\pi\) | |||||||
\(62\) | −2580.00 | −0.671176 | ||||||||
\(63\) | −1960.00 | − | 1920.40i | −0.493827 | − | 0.483850i | ||||
\(64\) | −2456.00 | −0.599609 | ||||||||
\(65\) | −25.0000 | + | 122.474i | −0.00591716 | + | 0.0289880i | ||||
\(66\) | 1090.02i | 0.250235i | ||||||||
\(67\) | 2047.77i | 0.456176i | 0.973641 | + | 0.228088i | \(0.0732474\pi\) | ||||
−0.973641 | + | 0.228088i | \(0.926753\pi\) | |||||||
\(68\) | −4850.00 | −1.04888 | ||||||||
\(69\) | − | 3502.77i | − | 0.735722i | ||||||
\(70\) | 1680.00 | + | 2486.23i | 0.342857 | + | 0.507394i | ||||
\(71\) | 4454.00 | 0.883555 | 0.441777 | − | 0.897125i | \(-0.354348\pi\) | ||||
0.441777 | + | 0.897125i | \(0.354348\pi\) | |||||||
\(72\) | − | 3566.46i | − | 0.687974i | ||||||
\(73\) | 8650.00 | 1.62319 | 0.811597 | − | 0.584218i | \(-0.198599\pi\) | ||||
0.811597 | + | 0.584218i | \(0.198599\pi\) | |||||||
\(74\) | −3996.00 | −0.729730 | ||||||||
\(75\) | −2875.00 | − | 1224.74i | −0.511111 | − | 0.217732i | ||||
\(76\) | − | 2204.54i | − | 0.381673i | ||||||
\(77\) | 3115.00 | + | 3052.06i | 0.525384 | + | 0.514769i | ||||
\(78\) | − | 61.2372i | − | 0.0100653i | ||||||
\(79\) | 5561.00 | 0.891043 | 0.445522 | − | 0.895271i | \(-0.353018\pi\) | ||||
0.445522 | + | 0.895271i | \(0.353018\pi\) | |||||||
\(80\) | 20.0000 | − | 97.9796i | 0.00312500 | − | 0.0153093i | ||||
\(81\) | 1111.00 | 0.169334 | ||||||||
\(82\) | 7140.00 | 1.06187 | ||||||||
\(83\) | 1990.00 | 0.288866 | 0.144433 | − | 0.989515i | \(-0.453864\pi\) | ||||
0.144433 | + | 0.989515i | \(0.453864\pi\) | |||||||
\(84\) | 1750.00 | + | 1714.64i | 0.248016 | + | 0.243005i | ||||
\(85\) | −2425.00 | + | 11880.0i | −0.335640 | + | 1.64429i | ||||
\(86\) | −924.000 | −0.124932 | ||||||||
\(87\) | 955.000 | 0.126173 | ||||||||
\(88\) | 5668.12i | 0.731937i | ||||||||
\(89\) | 808.332i | 0.102049i | 0.998697 | + | 0.0510246i | \(0.0162487\pi\) | ||||
−0.998697 | + | 0.0510246i | \(0.983751\pi\) | |||||||
\(90\) | −3360.00 | − | 685.857i | −0.414815 | − | 0.0846737i | ||||
\(91\) | −175.000 | − | 171.464i | −0.0211327 | − | 0.0207057i | ||||
\(92\) | − | 7005.54i | − | 0.827687i | ||||||
\(93\) | 5266.40i | 0.608903i | ||||||||
\(94\) | − | 5376.63i | − | 0.608491i | ||||||
\(95\) | −5400.00 | − | 1102.27i | −0.598338 | − | 0.122135i | ||||
\(96\) | 5143.93i | 0.558152i | ||||||||
\(97\) | 9235.00 | 0.981507 | 0.490754 | − | 0.871298i | \(-0.336722\pi\) | ||||
0.490754 | + | 0.871298i | \(0.336722\pi\) | |||||||
\(98\) | −5880.00 | + | 120.025i | −0.612245 | + | 0.0124974i | ||||
\(99\) | −4984.00 | −0.508520 | ||||||||
\(100\) | −5750.00 | − | 2449.49i | −0.575000 | − | 0.244949i | ||||
\(101\) | 4825.49i | 0.473041i | 0.971626 | + | 0.236521i | \(0.0760071\pi\) | ||||
−0.971626 | + | 0.236521i | \(0.923993\pi\) | |||||||
\(102\) | − | 5940.01i | − | 0.570935i | ||||||
\(103\) | −4715.00 | −0.444434 | −0.222217 | − | 0.974997i | \(-0.571329\pi\) | ||||
−0.222217 | + | 0.974997i | \(0.571329\pi\) | |||||||
\(104\) | − | 318.434i | − | 0.0294410i | ||||||
\(105\) | 5075.00 | − | 3429.29i | 0.460317 | − | 0.311046i | ||||
\(106\) | 3888.00 | 0.346031 | ||||||||
\(107\) | − | 12668.8i | − | 1.10654i | −0.833002 | − | 0.553269i | \(-0.813380\pi\) | ||
0.833002 | − | 0.553269i | \(-0.186620\pi\) | |||||||
\(108\) | −6850.00 | −0.587277 | ||||||||
\(109\) | 12311.0 | 1.03619 | 0.518096 | − | 0.855322i | \(-0.326641\pi\) | ||||
0.518096 | + | 0.855322i | \(0.326641\pi\) | |||||||
\(110\) | 5340.00 | + | 1090.02i | 0.441322 | + | 0.0900845i | ||||
\(111\) | 8156.80i | 0.662024i | ||||||||
\(112\) | 140.000 | + | 137.171i | 0.0111607 | + | 0.0109352i | ||||
\(113\) | 3120.65i | 0.244393i | 0.992506 | + | 0.122196i | \(0.0389938\pi\) | ||||
−0.992506 | + | 0.122196i | \(0.961006\pi\) | |||||||
\(114\) | 2700.00 | 0.207756 | ||||||||
\(115\) | −17160.0 | − | 3502.77i | −1.29754 | − | 0.264860i | ||||
\(116\) | 1910.00 | 0.141944 | ||||||||
\(117\) | 280.000 | 0.0204544 | ||||||||
\(118\) | −8880.00 | −0.637748 | ||||||||
\(119\) | −16975.0 | − | 16632.0i | −1.19871 | − | 1.17450i | ||||
\(120\) | 7800.00 | + | 1592.17i | 0.541667 | + | 0.110567i | ||||
\(121\) | −6720.00 | −0.458985 | ||||||||
\(122\) | 4740.00 | 0.318463 | ||||||||
\(123\) | − | 14574.5i | − | 0.963346i | ||||||
\(124\) | 10532.8i | 0.685016i | ||||||||
\(125\) | −8875.00 | + | 12859.8i | −0.568000 | + | 0.823029i | ||||
\(126\) | 4704.00 | − | 4801.00i | 0.296296 | − | 0.302406i | ||||
\(127\) | − | 23867.8i | − | 1.47981i | −0.672712 | − | 0.739904i | \(-0.734871\pi\) | ||
0.672712 | − | 0.739904i | \(-0.265129\pi\) | |||||||
\(128\) | 10444.6i | 0.637489i | ||||||||
\(129\) | 1886.11i | 0.113341i | ||||||||
\(130\) | −300.000 | − | 61.2372i | −0.0177515 | − | 0.00362351i | ||||
\(131\) | − | 6736.10i | − | 0.392524i | −0.980552 | − | 0.196262i | \(-0.937120\pi\) | ||
0.980552 | − | 0.196262i | \(-0.0628802\pi\) | |||||||
\(132\) | 4450.00 | 0.255395 | ||||||||
\(133\) | 7560.00 | − | 7715.89i | 0.427384 | − | 0.436197i | ||||
\(134\) | −5016.00 | −0.279350 | ||||||||
\(135\) | −3425.00 | + | 16779.0i | −0.187929 | + | 0.920659i | ||||
\(136\) | − | 30888.1i | − | 1.66999i | ||||||
\(137\) | 23069.3i | 1.22912i | 0.788871 | + | 0.614558i | \(0.210666\pi\) | ||||
−0.788871 | + | 0.614558i | \(0.789334\pi\) | |||||||
\(138\) | 8580.00 | 0.450536 | ||||||||
\(139\) | 29491.9i | 1.52641i | 0.646154 | + | 0.763207i | \(0.276376\pi\) | ||||
−0.646154 | + | 0.763207i | \(0.723624\pi\) | |||||||
\(140\) | 10150.0 | − | 6858.57i | 0.517857 | − | 0.349927i | ||||
\(141\) | −10975.0 | −0.552035 | ||||||||
\(142\) | 10910.0i | 0.541065i | ||||||||
\(143\) | −445.000 | −0.0217615 | ||||||||
\(144\) | −224.000 | −0.0108025 | ||||||||
\(145\) | 955.000 | − | 4678.53i | 0.0454221 | − | 0.222522i | ||||
\(146\) | 21188.1i | 0.993999i | ||||||||
\(147\) | 245.000 | + | 12002.5i | 0.0113379 | + | 0.555440i | ||||
\(148\) | 16313.6i | 0.744777i | ||||||||
\(149\) | 28346.0 | 1.27679 | 0.638395 | − | 0.769709i | \(-0.279599\pi\) | ||||
0.638395 | + | 0.769709i | \(0.279599\pi\) | |||||||
\(150\) | 3000.00 | − | 7042.28i | 0.133333 | − | 0.312990i | ||||
\(151\) | −17551.0 | −0.769747 | −0.384873 | − | 0.922969i | \(-0.625755\pi\) | ||||
−0.384873 | + | 0.922969i | \(0.625755\pi\) | |||||||
\(152\) | 14040.0 | 0.607687 | ||||||||
\(153\) | 27160.0 | 1.16024 | ||||||||
\(154\) | −7476.00 | + | 7630.16i | −0.315230 | + | 0.321731i | ||||
\(155\) | 25800.0 | + | 5266.40i | 1.07388 | + | 0.219205i | ||||
\(156\) | −250.000 | −0.0102728 | ||||||||
\(157\) | −25790.0 | −1.04629 | −0.523145 | − | 0.852244i | \(-0.675241\pi\) | ||||
−0.523145 | + | 0.852244i | \(0.675241\pi\) | |||||||
\(158\) | 13621.6i | 0.545650i | ||||||||
\(159\) | − | 7936.35i | − | 0.313925i | ||||||
\(160\) | 25200.0 | + | 5143.93i | 0.984375 | + | 0.200935i | ||||
\(161\) | 24024.0 | − | 24519.4i | 0.926816 | − | 0.945928i | ||||
\(162\) | 2721.38i | 0.103695i | ||||||||
\(163\) | − | 37153.9i | − | 1.39839i | −0.714930 | − | 0.699196i | \(-0.753542\pi\) | ||
0.714930 | − | 0.699196i | \(-0.246458\pi\) | |||||||
\(164\) | − | 29148.9i | − | 1.08376i | ||||||
\(165\) | 2225.00 | − | 10900.2i | 0.0817264 | − | 0.400376i | ||||
\(166\) | 4874.48i | 0.176894i | ||||||||
\(167\) | −20795.0 | −0.745634 | −0.372817 | − | 0.927905i | \(-0.621608\pi\) | ||||
−0.372817 | + | 0.927905i | \(0.621608\pi\) | |||||||
\(168\) | −10920.0 | + | 11145.2i | −0.386905 | + | 0.394883i | ||||
\(169\) | −28536.0 | −0.999125 | ||||||||
\(170\) | −29100.0 | − | 5940.01i | −1.00692 | − | 0.205537i | ||||
\(171\) | 12345.4i | 0.422196i | ||||||||
\(172\) | 3772.21i | 0.127509i | ||||||||
\(173\) | 115.000 | 0.00384243 | 0.00192121 | − | 0.999998i | \(-0.499388\pi\) | ||||
0.00192121 | + | 0.999998i | \(0.499388\pi\) | |||||||
\(174\) | 2339.26i | 0.0772646i | ||||||||
\(175\) | −11725.0 | − | 28291.6i | −0.382857 | − | 0.923808i | ||||
\(176\) | 356.000 | 0.0114928 | ||||||||
\(177\) | 18126.2i | 0.578577i | ||||||||
\(178\) | −1980.00 | −0.0624921 | ||||||||
\(179\) | 5318.00 | 0.165975 | 0.0829874 | − | 0.996551i | \(-0.473554\pi\) | ||||
0.0829874 | + | 0.996551i | \(0.473554\pi\) | |||||||
\(180\) | −2800.00 | + | 13717.1i | −0.0864198 | + | 0.423369i | ||||
\(181\) | 12345.4i | 0.376833i | 0.982089 | + | 0.188417i | \(0.0603355\pi\) | ||||
−0.982089 | + | 0.188417i | \(0.939665\pi\) | |||||||
\(182\) | 420.000 | − | 428.661i | 0.0126796 | − | 0.0129411i | ||||
\(183\) | − | 9675.48i | − | 0.288915i | ||||||
\(184\) | 44616.0 | 1.31782 | ||||||||
\(185\) | 39960.0 | + | 8156.80i | 1.16757 | + | 0.238329i | ||||
\(186\) | −12900.0 | −0.372875 | ||||||||
\(187\) | −43165.0 | −1.23438 | ||||||||
\(188\) | −21950.0 | −0.621039 | ||||||||
\(189\) | −23975.0 | − | 23490.6i | −0.671174 | − | 0.657613i | ||||
\(190\) | 2700.00 | − | 13227.2i | 0.0747922 | − | 0.366406i | ||||
\(191\) | −14263.0 | −0.390971 | −0.195485 | − | 0.980707i | \(-0.562628\pi\) | ||||
−0.195485 | + | 0.980707i | \(0.562628\pi\) | |||||||
\(192\) | −12280.0 | −0.333116 | ||||||||
\(193\) | − | 32005.0i | − | 0.859219i | −0.903015 | − | 0.429609i | \(-0.858651\pi\) | ||
0.903015 | − | 0.429609i | \(-0.141349\pi\) | |||||||
\(194\) | 22621.0i | 0.601048i | ||||||||
\(195\) | −125.000 | + | 612.372i | −0.00328731 | + | 0.0161045i | ||||
\(196\) | 490.000 | + | 24005.0i | 0.0127551 | + | 0.624870i | ||||
\(197\) | 3394.99i | 0.0874795i | 0.999043 | + | 0.0437398i | \(0.0139272\pi\) | ||||
−0.999043 | + | 0.0437398i | \(0.986073\pi\) | |||||||
\(198\) | − | 12208.3i | − | 0.311403i | ||||||
\(199\) | 19400.0i | 0.489886i | 0.969538 | + | 0.244943i | \(0.0787692\pi\) | ||||
−0.969538 | + | 0.244943i | \(0.921231\pi\) | |||||||
\(200\) | 15600.0 | − | 36619.9i | 0.390000 | − | 0.915497i | ||||
\(201\) | 10238.9i | 0.253431i | ||||||||
\(202\) | −11820.0 | −0.289677 | ||||||||
\(203\) | 6685.00 | + | 6549.94i | 0.162222 | + | 0.158944i | ||||
\(204\) | −24250.0 | −0.582709 | ||||||||
\(205\) | −71400.0 | − | 14574.5i | −1.69899 | − | 0.346805i | ||||
\(206\) | − | 11549.3i | − | 0.272159i | ||||||
\(207\) | 39231.0i | 0.915565i | ||||||||
\(208\) | −20.0000 | −0.000462278 | ||||||||
\(209\) | − | 19620.4i | − | 0.449175i | ||||||
\(210\) | 8400.00 | + | 12431.2i | 0.190476 | + | 0.281886i | ||||
\(211\) | 52817.0 | 1.18634 | 0.593170 | − | 0.805078i | \(-0.297876\pi\) | ||||
0.593170 | + | 0.805078i | \(0.297876\pi\) | |||||||
\(212\) | − | 15872.7i | − | 0.353166i | ||||||
\(213\) | 22270.0 | 0.490864 | ||||||||
\(214\) | 31032.0 | 0.677614 | ||||||||
\(215\) | 9240.00 | + | 1886.11i | 0.199892 | + | 0.0408027i | ||||
\(216\) | − | 43625.4i | − | 0.935044i | ||||||
\(217\) | −36120.0 | + | 36864.8i | −0.767058 | + | 0.782875i | ||||
\(218\) | 30155.7i | 0.634536i | ||||||||
\(219\) | 43250.0 | 0.901774 | ||||||||
\(220\) | 4450.00 | − | 21800.5i | 0.0919421 | − | 0.450423i | ||||
\(221\) | 2425.00 | 0.0496509 | ||||||||
\(222\) | −19980.0 | −0.405405 | ||||||||
\(223\) | 13645.0 | 0.274387 | 0.137194 | − | 0.990544i | \(-0.456192\pi\) | ||||
0.137194 | + | 0.990544i | \(0.456192\pi\) | |||||||
\(224\) | −35280.0 | + | 36007.5i | −0.703125 | + | 0.717624i | ||||
\(225\) | 32200.0 | + | 13717.1i | 0.636049 | + | 0.270956i | ||||
\(226\) | −7644.00 | −0.149659 | ||||||||
\(227\) | 74485.0 | 1.44550 | 0.722748 | − | 0.691111i | \(-0.242879\pi\) | ||||
0.722748 | + | 0.691111i | \(0.242879\pi\) | |||||||
\(228\) | − | 11022.7i | − | 0.212040i | ||||||
\(229\) | − | 68463.2i | − | 1.30553i | −0.757561 | − | 0.652764i | \(-0.773609\pi\) | ||
0.757561 | − | 0.652764i | \(-0.226391\pi\) | |||||||
\(230\) | 8580.00 | − | 42033.2i | 0.162193 | − | 0.794579i | ||||
\(231\) | 15575.0 | + | 15260.3i | 0.291880 | + | 0.285983i | ||||
\(232\) | 12164.2i | 0.225999i | ||||||||
\(233\) | 60169.3i | 1.10831i | 0.832412 | + | 0.554157i | \(0.186959\pi\) | ||||
−0.832412 | + | 0.554157i | \(0.813041\pi\) | |||||||
\(234\) | 685.857i | 0.0125257i | ||||||||
\(235\) | −10975.0 | + | 53766.3i | −0.198732 | + | 0.973586i | ||||
\(236\) | 36252.4i | 0.650899i | ||||||||
\(237\) | 27805.0 | 0.495024 | ||||||||
\(238\) | 40740.0 | − | 41580.1i | 0.719229 | − | 0.734060i | ||||
\(239\) | −75367.0 | −1.31943 | −0.659714 | − | 0.751517i | \(-0.729322\pi\) | ||||
−0.659714 | + | 0.751517i | \(0.729322\pi\) | |||||||
\(240\) | 100.000 | − | 489.898i | 0.00173611 | − | 0.00850517i | ||||
\(241\) | 77869.3i | 1.34070i | 0.742044 | + | 0.670351i | \(0.233856\pi\) | ||||
−0.742044 | + | 0.670351i | \(0.766144\pi\) | |||||||
\(242\) | − | 16460.6i | − | 0.281070i | ||||||
\(243\) | 61040.0 | 1.03372 | ||||||||
\(244\) | − | 19351.0i | − | 0.325030i | ||||||
\(245\) | 59045.0 | + | 10802.2i | 0.983673 | + | 0.179963i | ||||
\(246\) | 35700.0 | 0.589927 | ||||||||
\(247\) | 1102.27i | 0.0180673i | ||||||||
\(248\) | −67080.0 | −1.09066 | ||||||||
\(249\) | 9950.00 | 0.160481 | ||||||||
\(250\) | −31500.0 | − | 21739.2i | −0.504000 | − | 0.347828i | ||||
\(251\) | − | 50410.5i | − | 0.800154i | −0.916482 | − | 0.400077i | \(-0.868983\pi\) | ||
0.916482 | − | 0.400077i | \(-0.131017\pi\) | |||||||
\(252\) | −19600.0 | − | 19204.0i | −0.308642 | − | 0.302406i | ||||
\(253\) | − | 62349.3i | − | 0.974071i | ||||||
\(254\) | 58464.0 | 0.906194 | ||||||||
\(255\) | −12125.0 | + | 59400.1i | −0.186467 | + | 0.913497i | ||||
\(256\) | −64880.0 | −0.989990 | ||||||||
\(257\) | 3370.00 | 0.0510227 | 0.0255114 | − | 0.999675i | \(-0.491879\pi\) | ||||
0.0255114 | + | 0.999675i | \(0.491879\pi\) | |||||||
\(258\) | −4620.00 | −0.0694069 | ||||||||
\(259\) | −55944.0 | + | 57097.6i | −0.833977 | + | 0.851174i | ||||
\(260\) | −250.000 | + | 1224.74i | −0.00369822 | + | 0.0181175i | ||||
\(261\) | −10696.0 | −0.157015 | ||||||||
\(262\) | 16500.0 | 0.240371 | ||||||||
\(263\) | 59385.4i | 0.858556i | 0.903173 | + | 0.429278i | \(0.141232\pi\) | ||||
−0.903173 | + | 0.429278i | \(0.858768\pi\) | |||||||
\(264\) | 28340.6i | 0.406632i | ||||||||
\(265\) | −38880.0 | − | 7936.35i | −0.553649 | − | 0.113013i | ||||
\(266\) | 18900.0 | + | 18518.1i | 0.267115 | + | 0.261718i | ||||
\(267\) | 4041.66i | 0.0566940i | ||||||||
\(268\) | 20477.7i | 0.285110i | ||||||||
\(269\) | 77012.0i | 1.06427i | 0.846658 | + | 0.532137i | \(0.178611\pi\) | ||||
−0.846658 | + | 0.532137i | \(0.821389\pi\) | |||||||
\(270\) | −41100.0 | − | 8389.50i | −0.563786 | − | 0.115082i | ||||
\(271\) | − | 143222.i | − | 1.95016i | −0.221855 | − | 0.975080i | \(-0.571211\pi\) | ||
0.221855 | − | 0.975080i | \(-0.428789\pi\) | |||||||
\(272\) | −1940.00 | −0.0262219 | ||||||||
\(273\) | −875.000 | − | 857.321i | −0.0117404 | − | 0.0115032i | ||||
\(274\) | −56508.0 | −0.752677 | ||||||||
\(275\) | −51175.0 | − | 21800.5i | −0.676694 | − | 0.288271i | ||||
\(276\) | − | 35027.7i | − | 0.459826i | ||||||
\(277\) | − | 101928.i | − | 1.32842i | −0.747547 | − | 0.664209i | \(-0.768769\pi\) | ||
0.747547 | − | 0.664209i | \(-0.231231\pi\) | |||||||
\(278\) | −72240.0 | −0.934734 | ||||||||
\(279\) | − | 58983.7i | − | 0.757746i | ||||||
\(280\) | 43680.0 | + | 64642.0i | 0.557143 | + | 0.824516i | ||||
\(281\) | −47521.0 | −0.601829 | −0.300914 | − | 0.953651i | \(-0.597292\pi\) | ||||
−0.300914 | + | 0.953651i | \(0.597292\pi\) | |||||||
\(282\) | − | 26883.1i | − | 0.338051i | ||||||
\(283\) | −43115.0 | −0.538339 | −0.269169 | − | 0.963093i | \(-0.586749\pi\) | ||||
−0.269169 | + | 0.963093i | \(0.586749\pi\) | |||||||
\(284\) | 44540.0 | 0.552222 | ||||||||
\(285\) | −27000.0 | − | 5511.35i | −0.332410 | − | 0.0678529i | ||||
\(286\) | − | 1090.02i | − | 0.0133261i | ||||||
\(287\) | 99960.0 | − | 102021.i | 1.21356 | − | 1.23859i | ||||
\(288\) | − | 57612.0i | − | 0.694589i | ||||||
\(289\) | 151704. | 1.81636 | ||||||||
\(290\) | 11460.0 | + | 2339.26i | 0.136266 | + | 0.0278153i | ||||
\(291\) | 46175.0 | 0.545282 | ||||||||
\(292\) | 86500.0 | 1.01450 | ||||||||
\(293\) | −162125. | −1.88849 | −0.944245 | − | 0.329243i | \(-0.893206\pi\) | ||||
−0.944245 | + | 0.329243i | \(0.893206\pi\) | |||||||
\(294\) | −29400.0 | + | 600.125i | −0.340136 | + | 0.00694300i | ||||
\(295\) | 88800.0 | + | 18126.2i | 1.02040 | + | 0.208288i | ||||
\(296\) | −103896. | −1.18581 | ||||||||
\(297\) | −60965.0 | −0.691143 | ||||||||
\(298\) | 69433.2i | 0.781871i | ||||||||
\(299\) | 3502.77i | 0.0391804i | ||||||||
\(300\) | −28750.0 | − | 12247.4i | −0.319444 | − | 0.136083i | ||||
\(301\) | −12936.0 | + | 13202.7i | −0.142780 | + | 0.145724i | ||||
\(302\) | − | 42991.0i | − | 0.471372i | ||||||
\(303\) | 24127.5i | 0.262801i | ||||||||
\(304\) | − | 881.816i | − | 0.00954181i | ||||||
\(305\) | −47400.0 | − | 9675.48i | −0.509540 | − | 0.104010i | ||||
\(306\) | 66528.1i | 0.710497i | ||||||||
\(307\) | 33805.0 | 0.358678 | 0.179339 | − | 0.983787i | \(-0.442604\pi\) | ||||
0.179339 | + | 0.983787i | \(0.442604\pi\) | |||||||
\(308\) | 31150.0 | + | 30520.6i | 0.328365 | + | 0.321731i | ||||
\(309\) | −23575.0 | −0.246908 | ||||||||
\(310\) | −12900.0 | + | 63196.8i | −0.134235 | + | 0.657615i | ||||
\(311\) | 50435.0i | 0.521448i | 0.965413 | + | 0.260724i | \(0.0839613\pi\) | ||||
−0.965413 | + | 0.260724i | \(0.916039\pi\) | |||||||
\(312\) | − | 1592.17i | − | 0.0163561i | ||||||
\(313\) | 68155.0 | 0.695679 | 0.347840 | − | 0.937554i | \(-0.386915\pi\) | ||||
0.347840 | + | 0.937554i | \(0.386915\pi\) | |||||||
\(314\) | − | 63172.3i | − | 0.640719i | ||||||
\(315\) | −56840.0 | + | 38408.0i | −0.572840 | + | 0.387080i | ||||
\(316\) | 55610.0 | 0.556902 | ||||||||
\(317\) | − | 42435.0i | − | 0.422285i | −0.977455 | − | 0.211142i | \(-0.932282\pi\) | ||
0.977455 | − | 0.211142i | \(-0.0677184\pi\) | |||||||
\(318\) | 19440.0 | 0.192239 | ||||||||
\(319\) | 16999.0 | 0.167048 | ||||||||
\(320\) | −12280.0 | + | 60159.5i | −0.119922 | + | 0.587495i | ||||
\(321\) | − | 63343.8i | − | 0.614744i | ||||||
\(322\) | 60060.0 | + | 58846.5i | 0.579260 | + | 0.567557i | ||||
\(323\) | 106920.i | 1.02484i | ||||||||
\(324\) | 11110.0 | 0.105834 | ||||||||
\(325\) | 2875.00 | + | 1224.74i | 0.0272189 | + | 0.0115952i | ||||
\(326\) | 91008.0 | 0.856336 | ||||||||
\(327\) | 61555.0 | 0.575662 | ||||||||
\(328\) | 185640. | 1.72554 | ||||||||
\(329\) | −76825.0 | − | 75272.8i | −0.709759 | − | 0.695419i | ||||
\(330\) | 26700.0 | + | 5450.11i | 0.245179 | + | 0.0500470i | ||||
\(331\) | −114706. | −1.04696 | −0.523480 | − | 0.852038i | \(-0.675367\pi\) | ||||
−0.523480 | + | 0.852038i | \(0.675367\pi\) | |||||||
\(332\) | 19900.0 | 0.180541 | ||||||||
\(333\) | − | 91356.2i | − | 0.823852i | ||||||
\(334\) | − | 50937.1i | − | 0.456606i | ||||||
\(335\) | 50160.0 | + | 10238.9i | 0.446959 | + | 0.0912352i | ||||
\(336\) | 700.000 | + | 685.857i | 0.00620040 | + | 0.00607512i | ||||
\(337\) | 117007.i | 1.03027i | 0.857108 | + | 0.515137i | \(0.172259\pi\) | ||||
−0.857108 | + | 0.515137i | \(0.827741\pi\) | |||||||
\(338\) | − | 69898.6i | − | 0.611836i | ||||||
\(339\) | 15603.2i | 0.135774i | ||||||||
\(340\) | −24250.0 | + | 118800.i | −0.209775 | + | 1.02768i | ||||
\(341\) | 93742.0i | 0.806168i | ||||||||
\(342\) | −30240.0 | −0.258541 | ||||||||
\(343\) | −80605.0 | + | 85697.8i | −0.685131 | + | 0.728420i | ||||
\(344\) | −24024.0 | −0.203015 | ||||||||
\(345\) | −85800.0 | − | 17513.9i | −0.720857 | − | 0.147144i | ||||
\(346\) | 281.691i | 0.00235300i | ||||||||
\(347\) | − | 70481.6i | − | 0.585352i | −0.956212 | − | 0.292676i | \(-0.905454\pi\) | ||
0.956212 | − | 0.292676i | \(-0.0945457\pi\) | |||||||
\(348\) | 9550.00 | 0.0788578 | ||||||||
\(349\) | 91390.5i | 0.750326i | 0.926959 | + | 0.375163i | \(0.122413\pi\) | ||||
−0.926959 | + | 0.375163i | \(0.877587\pi\) | |||||||
\(350\) | 69300.0 | − | 28720.3i | 0.565714 | − | 0.234451i | ||||
\(351\) | 3425.00 | 0.0278001 | ||||||||
\(352\) | 91561.9i | 0.738975i | ||||||||
\(353\) | −11405.0 | −0.0915263 | −0.0457631 | − | 0.998952i | \(-0.514572\pi\) | ||||
−0.0457631 | + | 0.998952i | \(0.514572\pi\) | |||||||
\(354\) | −44400.0 | −0.354304 | ||||||||
\(355\) | 22270.0 | − | 109100.i | 0.176711 | − | 0.865703i | ||||
\(356\) | 8083.32i | 0.0637807i | ||||||||
\(357\) | −84875.0 | − | 83160.2i | −0.665953 | − | 0.652498i | ||||
\(358\) | 13026.4i | 0.101638i | ||||||||
\(359\) | 230366. | 1.78743 | 0.893716 | − | 0.448633i | \(-0.148089\pi\) | ||||
0.893716 | + | 0.448633i | \(0.148089\pi\) | |||||||
\(360\) | −87360.0 | − | 17832.3i | −0.674074 | − | 0.137595i | ||||
\(361\) | 81721.0 | 0.627075 | ||||||||
\(362\) | −30240.0 | −0.230762 | ||||||||
\(363\) | −33600.0 | −0.254992 | ||||||||
\(364\) | −1750.00 | − | 1714.64i | −0.0132079 | − | 0.0129411i | ||||
\(365\) | 43250.0 | − | 211881.i | 0.324639 | − | 1.59040i | ||||
\(366\) | 23700.0 | 0.176924 | ||||||||
\(367\) | 74485.0 | 0.553015 | 0.276507 | − | 0.961012i | \(-0.410823\pi\) | ||||
0.276507 | + | 0.961012i | \(0.410823\pi\) | |||||||
\(368\) | − | 2802.22i | − | 0.0206922i | ||||||
\(369\) | 163234.i | 1.19883i | ||||||||
\(370\) | −19980.0 | + | 97881.6i | −0.145946 | + | 0.714986i | ||||
\(371\) | 54432.0 | − | 55554.4i | 0.395464 | − | 0.403618i | ||||
\(372\) | 52664.0i | 0.380564i | ||||||||
\(373\) | − | 102550.i | − | 0.737088i | −0.929610 | − | 0.368544i | \(-0.879856\pi\) | ||
0.929610 | − | 0.368544i | \(-0.120144\pi\) | |||||||
\(374\) | − | 105732.i | − | 0.755900i | ||||||
\(375\) | −44375.0 | + | 64299.1i | −0.315556 | + | 0.457238i | ||||
\(376\) | − | 139792.i | − | 0.988799i | ||||||
\(377\) | −955.000 | −0.00671925 | ||||||||
\(378\) | 57540.0 | − | 58726.5i | 0.402704 | − | 0.411008i | ||||
\(379\) | −172954. | −1.20407 | −0.602036 | − | 0.798469i | \(-0.705643\pi\) | ||||
−0.602036 | + | 0.798469i | \(0.705643\pi\) | |||||||
\(380\) | −54000.0 | − | 11022.7i | −0.373961 | − | 0.0763345i | ||||
\(381\) | − | 119339.i | − | 0.822116i | ||||||
\(382\) | − | 34937.1i | − | 0.239420i | ||||||
\(383\) | −144050. | −0.982010 | −0.491005 | − | 0.871157i | \(-0.663370\pi\) | ||||
−0.491005 | + | 0.871157i | \(0.663370\pi\) | |||||||
\(384\) | 52223.1i | 0.354161i | ||||||||
\(385\) | 90335.0 | − | 61041.3i | 0.609445 | − | 0.411815i | ||||
\(386\) | 78396.0 | 0.526162 | ||||||||
\(387\) | − | 21124.4i | − | 0.141047i | ||||||
\(388\) | 92350.0 | 0.613442 | ||||||||
\(389\) | −148969. | −0.984457 | −0.492228 | − | 0.870466i | \(-0.663818\pi\) | ||||
−0.492228 | + | 0.870466i | \(0.663818\pi\) | |||||||
\(390\) | −1500.00 | − | 306.186i | −0.00986193 | − | 0.00201306i | ||||
\(391\) | 339769.i | 2.22244i | ||||||||
\(392\) | −152880. | + | 3120.65i | −0.994898 | + | 0.0203083i | ||||
\(393\) | − | 33680.5i | − | 0.218069i | ||||||
\(394\) | −8316.00 | −0.0535700 | ||||||||
\(395\) | 27805.0 | − | 136216.i | 0.178209 | − | 0.873040i | ||||
\(396\) | −49840.0 | −0.317825 | ||||||||
\(397\) | −256925. | −1.63014 | −0.815071 | − | 0.579361i | \(-0.803302\pi\) | ||||
−0.815071 | + | 0.579361i | \(0.803302\pi\) | |||||||
\(398\) | −47520.0 | −0.299992 | ||||||||
\(399\) | 37800.0 | − | 38579.5i | 0.237436 | − | 0.242332i | ||||
\(400\) | −2300.00 | − | 979.796i | −0.0143750 | − | 0.00612372i | ||||
\(401\) | −35641.0 | −0.221647 | −0.110823 | − | 0.993840i | \(-0.535349\pi\) | ||||
−0.110823 | + | 0.993840i | \(0.535349\pi\) | |||||||
\(402\) | −25080.0 | −0.155194 | ||||||||
\(403\) | − | 5266.40i | − | 0.0324268i | ||||||
\(404\) | 48254.9i | 0.295651i | ||||||||
\(405\) | 5555.00 | − | 27213.8i | 0.0338668 | − | 0.165913i | ||||
\(406\) | −16044.0 | + | 16374.8i | −0.0973331 | + | 0.0993402i | ||||
\(407\) | 145191.i | 0.876498i | ||||||||
\(408\) | − | 154440.i | − | 0.927770i | ||||||
\(409\) | − | 151721.i | − | 0.906985i | −0.891260 | − | 0.453493i | \(-0.850178\pi\) | ||
0.891260 | − | 0.453493i | \(-0.149822\pi\) | |||||||
\(410\) | 35700.0 | − | 174894.i | 0.212374 | − | 1.04041i | ||||
\(411\) | 115346.i | 0.682843i | ||||||||
\(412\) | −47150.0 | −0.277771 | ||||||||
\(413\) | −124320. | + | 126884.i | −0.728855 | + | 0.743884i | ||||
\(414\) | −96096.0 | −0.560667 | ||||||||
\(415\) | 9950.00 | − | 48744.8i | 0.0577733 | − | 0.283030i | ||||
\(416\) | − | 5143.93i | − | 0.0297241i | ||||||
\(417\) | 147459.i | 0.848008i | ||||||||
\(418\) | 48060.0 | 0.275062 | ||||||||
\(419\) | 150889.i | 0.859465i | 0.902956 | + | 0.429733i | \(0.141392\pi\) | ||||
−0.902956 | + | 0.429733i | \(0.858608\pi\) | |||||||
\(420\) | 50750.0 | − | 34292.9i | 0.287698 | − | 0.194404i | ||||
\(421\) | −4681.00 | −0.0264104 | −0.0132052 | − | 0.999913i | \(-0.504203\pi\) | ||||
−0.0132052 | + | 0.999913i | \(0.504203\pi\) | |||||||
\(422\) | 129375.i | 0.726481i | ||||||||
\(423\) | 122920. | 0.686976 | ||||||||
\(424\) | 101088. | 0.562300 | ||||||||
\(425\) | 278875. | + | 118800.i | 1.54394 | + | 0.657718i | ||||
\(426\) | 54550.1i | 0.300591i | ||||||||
\(427\) | 66360.0 | − | 67728.4i | 0.363957 | − | 0.371463i | ||||
\(428\) | − | 126688.i | − | 0.691587i | ||||||
\(429\) | −2225.00 | −0.0120897 | ||||||||
\(430\) | −4620.00 | + | 22633.3i | −0.0249865 | + | 0.122408i | ||||
\(431\) | −87103.0 | −0.468898 | −0.234449 | − | 0.972128i | \(-0.575329\pi\) | ||||
−0.234449 | + | 0.972128i | \(0.575329\pi\) | |||||||
\(432\) | −2740.00 | −0.0146819 | ||||||||
\(433\) | 231730. | 1.23597 | 0.617983 | − | 0.786192i | \(-0.287950\pi\) | ||||
0.617983 | + | 0.786192i | \(0.287950\pi\) | |||||||
\(434\) | −90300.0 | − | 88475.6i | −0.479411 | − | 0.469725i | ||||
\(435\) | 4775.00 | − | 23392.6i | 0.0252345 | − | 0.123623i | ||||
\(436\) | 123110. | 0.647620 | ||||||||
\(437\) | −154440. | −0.808718 | ||||||||
\(438\) | 105940.i | 0.552222i | ||||||||
\(439\) | − | 246272.i | − | 1.27787i | −0.769262 | − | 0.638933i | \(-0.779376\pi\) | ||
0.769262 | − | 0.638933i | \(-0.220624\pi\) | |||||||
\(440\) | 138840. | + | 28340.6i | 0.717149 | + | 0.146387i | ||||
\(441\) | −2744.00 | − | 134428.i | −0.0141093 | − | 0.691214i | ||||
\(442\) | 5940.01i | 0.0304048i | ||||||||
\(443\) | 349841.i | 1.78264i | 0.453376 | + | 0.891319i | \(0.350219\pi\) | ||||
−0.453376 | + | 0.891319i | \(0.649781\pi\) | |||||||
\(444\) | 81568.0i | 0.413765i | ||||||||
\(445\) | 19800.0 | + | 4041.66i | 0.0999874 | + | 0.0204098i | ||||
\(446\) | 33423.3i | 0.168027i | ||||||||
\(447\) | 141730. | 0.709327 | ||||||||
\(448\) | −85960.0 | − | 84223.3i | −0.428292 | − | 0.419639i | ||||
\(449\) | 254711. | 1.26344 | 0.631721 | − | 0.775196i | \(-0.282349\pi\) | ||||
0.631721 | + | 0.775196i | \(0.282349\pi\) | |||||||
\(450\) | −33600.0 | + | 78873.6i | −0.165926 | + | 0.389499i | ||||
\(451\) | − | 259425.i | − | 1.27544i | ||||||
\(452\) | 31206.5i | 0.152745i | ||||||||
\(453\) | −87755.0 | −0.427637 | ||||||||
\(454\) | 182450.i | 0.885182i | ||||||||
\(455\) | −5075.00 | + | 3429.29i | −0.0245139 | + | 0.0165646i | ||||
\(456\) | 70200.0 | 0.337604 | ||||||||
\(457\) | 263629.i | 1.26229i | 0.775663 | + | 0.631147i | \(0.217415\pi\) | ||||
−0.775663 | + | 0.631147i | \(0.782585\pi\) | |||||||
\(458\) | 167700. | 0.799470 | ||||||||
\(459\) | 332225. | 1.57691 | ||||||||
\(460\) | −171600. | − | 35027.7i | −0.810964 | − | 0.165537i | ||||
\(461\) | − | 128255.i | − | 0.603495i | −0.953388 | − | 0.301747i | \(-0.902430\pi\) | ||
0.953388 | − | 0.301747i | \(-0.0975699\pi\) | |||||||
\(462\) | −37380.0 | + | 38150.8i | −0.175128 | + | 0.178739i | ||||
\(463\) | − | 81857.0i | − | 0.381851i | −0.981605 | − | 0.190926i | \(-0.938851\pi\) | ||
0.981605 | − | 0.190926i | \(-0.0611489\pi\) | |||||||
\(464\) | 764.000 | 0.00354860 | ||||||||
\(465\) | 129000. | + | 26332.0i | 0.596601 | + | 0.121781i | ||||
\(466\) | −147384. | −0.678701 | ||||||||
\(467\) | 204445. | 0.937438 | 0.468719 | − | 0.883347i | \(-0.344716\pi\) | ||||
0.468719 | + | 0.883347i | \(0.344716\pi\) | |||||||
\(468\) | 2800.00 | 0.0127840 | ||||||||
\(469\) | −70224.0 | + | 71672.1i | −0.319257 | + | 0.325840i | ||||
\(470\) | −131700. | − | 26883.1i | −0.596197 | − | 0.121698i | ||||
\(471\) | −128950. | −0.581272 | ||||||||
\(472\) | −230880. | −1.03634 | ||||||||
\(473\) | 33572.7i | 0.150060i | ||||||||
\(474\) | 68108.1i | 0.303139i | ||||||||
\(475\) | −54000.0 | + | 126761.i | −0.239335 | + | 0.561822i | ||||
\(476\) | −169750. | − | 166320.i | −0.749197 | − | 0.734060i | ||||
\(477\) | 88887.1i | 0.390663i | ||||||||
\(478\) | − | 184611.i | − | 0.807981i | ||||||
\(479\) | − | 79534.9i | − | 0.346647i | −0.984865 | − | 0.173323i | \(-0.944549\pi\) | ||
0.984865 | − | 0.173323i | \(-0.0554505\pi\) | |||||||
\(480\) | 126000. | + | 25719.6i | 0.546875 | + | 0.111630i | ||||
\(481\) | − | 8156.80i | − | 0.0352557i | ||||||
\(482\) | −190740. | −0.821009 | ||||||||
\(483\) | 120120. | − | 122597.i | 0.514898 | − | 0.525515i | ||||
\(484\) | −67200.0 | −0.286866 | ||||||||
\(485\) | 46175.0 | − | 226210.i | 0.196301 | − | 0.961677i | ||||
\(486\) | 149517.i | 0.633020i | ||||||||
\(487\) | − | 164958.i | − | 0.695531i | −0.937582 | − | 0.347766i | \(-0.886941\pi\) | ||
0.937582 | − | 0.347766i | \(-0.113059\pi\) | |||||||
\(488\) | 123240. | 0.517502 | ||||||||
\(489\) | − | 185769.i | − | 0.776884i | ||||||
\(490\) | −26460.0 | + | 144630.i | −0.110204 | + | 0.602375i | ||||
\(491\) | −74191.0 | −0.307743 | −0.153872 | − | 0.988091i | \(-0.549174\pi\) | ||||
−0.153872 | + | 0.988091i | \(0.549174\pi\) | |||||||
\(492\) | − | 145745.i | − | 0.602091i | ||||||
\(493\) | −92635.0 | −0.381137 | ||||||||
\(494\) | −2700.00 | −0.0110639 | ||||||||
\(495\) | −24920.0 | + | 122083.i | −0.101704 | + | 0.498245i | ||||
\(496\) | 4213.12i | 0.0171254i | ||||||||
\(497\) | 155890. | + | 152740.i | 0.631111 | + | 0.618360i | ||||
\(498\) | 24372.4i | 0.0982743i | ||||||||
\(499\) | −278527. | −1.11858 | −0.559289 | − | 0.828973i | \(-0.688926\pi\) | ||||
−0.559289 | + | 0.828973i | \(0.688926\pi\) | |||||||
\(500\) | −88750.0 | + | 128598.i | −0.355000 | + | 0.514393i | ||||
\(501\) | −103975. | −0.414241 | ||||||||
\(502\) | 123480. | 0.489992 | ||||||||
\(503\) | −60275.0 | −0.238233 | −0.119116 | − | 0.992880i | \(-0.538006\pi\) | ||||
−0.119116 | + | 0.992880i | \(0.538006\pi\) | |||||||
\(504\) | 122304. | − | 124826.i | 0.481481 | − | 0.491410i | ||||
\(505\) | 118200. | + | 24127.5i | 0.463484 | + | 0.0946083i | ||||
\(506\) | 152724. | 0.596494 | ||||||||
\(507\) | −142680. | −0.555069 | ||||||||
\(508\) | − | 238678.i | − | 0.924880i | ||||||
\(509\) | 348709.i | 1.34595i | 0.739666 | + | 0.672974i | \(0.234983\pi\) | ||||
−0.739666 | + | 0.672974i | \(0.765017\pi\) | |||||||
\(510\) | −145500. | − | 29700.1i | −0.559400 | − | 0.114187i | ||||
\(511\) | 302750. | + | 296633.i | 1.15942 | + | 1.13600i | ||||
\(512\) | 8191.09i | 0.0312465i | ||||||||
\(513\) | 151011.i | 0.573818i | ||||||||
\(514\) | 8254.78i | 0.0312449i | ||||||||
\(515\) | −23575.0 | + | 115493.i | −0.0888868 | + | 0.435455i | ||||
\(516\) | 18861.1i | 0.0708381i | ||||||||
\(517\) | −195355. | −0.730876 | ||||||||
\(518\) | −139860. | − | 137034.i | −0.521236 | − | 0.510704i | ||||
\(519\) | 575.000 | 0.00213468 | ||||||||
\(520\) | −7800.00 | − | 1592.17i | −0.0288462 | − | 0.00588820i | ||||
\(521\) | 84727.9i | 0.312141i | 0.987746 | + | 0.156070i | \(0.0498827\pi\) | ||||
−0.987746 | + | 0.156070i | \(0.950117\pi\) | |||||||
\(522\) | − | 26199.7i | − | 0.0961515i | ||||||
\(523\) | −235610. | −0.861371 | −0.430686 | − | 0.902502i | \(-0.641728\pi\) | ||||
−0.430686 | + | 0.902502i | \(0.641728\pi\) | |||||||
\(524\) | − | 67361.0i | − | 0.245327i | ||||||
\(525\) | −58625.0 | − | 141458.i | −0.212698 | − | 0.513226i | ||||
\(526\) | −145464. | −0.525756 | ||||||||
\(527\) | − | 510841.i | − | 1.83935i | ||||||
\(528\) | 1780.00 | 0.00638487 | ||||||||
\(529\) | −210935. | −0.753767 | ||||||||
\(530\) | 19440.0 | − | 95236.2i | 0.0692061 | − | 0.339039i | ||||
\(531\) | − | 203014.i | − | 0.720006i | ||||||
\(532\) | 75600.0 | − | 77158.9i | 0.267115 | − | 0.272623i | ||||
\(533\) | 14574.5i | 0.0513025i | ||||||||
\(534\) | −9900.00 | −0.0347178 | ||||||||
\(535\) | −310320. | − | 63343.8i | −1.08418 | − | 0.221308i | ||||
\(536\) | −130416. | −0.453943 | ||||||||
\(537\) | 26590.0 | 0.0922082 | ||||||||
\(538\) | −188640. | −0.651732 | ||||||||
\(539\) | 4361.00 | + | 213644.i | 0.0150110 | + | 0.735384i | ||||
\(540\) | −34250.0 | + | 167790.i | −0.117455 | + | 0.575412i | ||||
\(541\) | 259199. | 0.885602 | 0.442801 | − | 0.896620i | \(-0.353985\pi\) | ||||
0.442801 | + | 0.896620i | \(0.353985\pi\) | |||||||
\(542\) | 350820. | 1.19422 | ||||||||
\(543\) | 61727.1i | 0.209352i | ||||||||
\(544\) | − | 498961.i | − | 1.68604i | ||||||
\(545\) | 61555.0 | − | 301557.i | 0.207238 | − | 1.01526i | ||||
\(546\) | 2100.00 | − | 2143.30i | 0.00704424 | − | 0.00718950i | ||||
\(547\) | − | 423894.i | − | 1.41672i | −0.705854 | − | 0.708358i | \(-0.749436\pi\) | ||
0.705854 | − | 0.708358i | \(-0.250564\pi\) | |||||||
\(548\) | 230693.i | 0.768198i | ||||||||
\(549\) | 108365.i | 0.359539i | ||||||||
\(550\) | 53400.0 | − | 125353.i | 0.176529 | − | 0.414389i | ||||
\(551\) | − | 42106.7i | − | 0.138691i | ||||||
\(552\) | 223080. | 0.732120 | ||||||||
\(553\) | 194635. | + | 190703.i | 0.636459 | + | 0.623600i | ||||
\(554\) | 249672. | 0.813486 | ||||||||
\(555\) | 199800. | + | 40784.0i | 0.648649 | + | 0.132405i | ||||
\(556\) | 294919.i | 0.954009i | ||||||||
\(557\) | 133389.i | 0.429943i | 0.976620 | + | 0.214972i | \(0.0689659\pi\) | ||||
−0.976620 | + | 0.214972i | \(0.931034\pi\) | |||||||
\(558\) | 144480. | 0.464023 | ||||||||
\(559\) | − | 1886.11i | − | 0.00603591i | ||||||
\(560\) | 4060.00 | − | 2743.43i | 0.0129464 | − | 0.00874818i | ||||
\(561\) | −215825. | −0.685766 | ||||||||
\(562\) | − | 116402.i | − | 0.368543i | ||||||
\(563\) | −369770. | −1.16658 | −0.583290 | − | 0.812264i | \(-0.698235\pi\) | ||||
−0.583290 | + | 0.812264i | \(0.698235\pi\) | |||||||
\(564\) | −109750. | −0.345022 | ||||||||
\(565\) | 76440.0 | + | 15603.2i | 0.239455 | + | 0.0488785i | ||||
\(566\) | − | 105610.i | − | 0.329664i | ||||||
\(567\) | 38885.0 | + | 38099.4i | 0.120953 | + | 0.118509i | ||||
\(568\) | 283661.i | 0.879230i | ||||||||
\(569\) | −326134. | −1.00733 | −0.503665 | − | 0.863899i | \(-0.668015\pi\) | ||||
−0.503665 | + | 0.863899i | \(0.668015\pi\) | |||||||
\(570\) | 13500.0 | − | 66136.2i | 0.0415512 | − | 0.203559i | ||||
\(571\) | 306374. | 0.939679 | 0.469840 | − | 0.882752i | \(-0.344312\pi\) | ||||
0.469840 | + | 0.882752i | \(0.344312\pi\) | |||||||
\(572\) | −4450.00 | −0.0136009 | ||||||||
\(573\) | −71315.0 | −0.217206 | ||||||||
\(574\) | 249900. | + | 244851.i | 0.758477 | + | 0.743153i | ||||
\(575\) | −171600. | + | 402819.i | −0.519017 | + | 1.21835i | ||||
\(576\) | 137536. | 0.414545 | ||||||||
\(577\) | 387595. | 1.16420 | 0.582099 | − | 0.813118i | \(-0.302232\pi\) | ||||
0.582099 | + | 0.813118i | \(0.302232\pi\) | |||||||
\(578\) | 371597.i | 1.11229i | ||||||||
\(579\) | − | 160025.i | − | 0.477344i | ||||||
\(580\) | 9550.00 | − | 46785.3i | 0.0283888 | − | 0.139076i | ||||
\(581\) | 69650.0 | + | 68242.8i | 0.206333 | + | 0.202164i | ||||
\(582\) | 113105.i | 0.333915i | ||||||||
\(583\) | − | 141267.i | − | 0.415627i | ||||||
\(584\) | 550890.i | 1.61525i | ||||||||
\(585\) | 1400.00 | − | 6858.57i | 0.00409088 | − | 0.0200411i | ||||
\(586\) | − | 397124.i | − | 1.15646i | ||||||
\(587\) | 467350. | 1.35633 | 0.678166 | − | 0.734909i | \(-0.262775\pi\) | ||||
0.678166 | + | 0.734909i | \(0.262775\pi\) | |||||||
\(588\) | 2450.00 | + | 120025.i | 0.00708617 | + | 0.347150i | ||||
\(589\) | 232200. | 0.669317 | ||||||||
\(590\) | −44400.0 | + | 217515.i | −0.127550 | + | 0.624863i | ||||
\(591\) | 16975.0i | 0.0485997i | ||||||||
\(592\) | 6525.44i | 0.0186194i | ||||||||
\(593\) | 214315. | 0.609457 | 0.304729 | − | 0.952439i | \(-0.401434\pi\) | ||||
0.304729 | + | 0.952439i | \(0.401434\pi\) | |||||||
\(594\) | − | 149333.i | − | 0.423237i | ||||||
\(595\) | −492275. | + | 332641.i | −1.39051 | + | 0.939597i | ||||
\(596\) | 283460. | 0.797993 | ||||||||
\(597\) | 96999.8i | 0.272159i | ||||||||
\(598\) | −8580.00 | −0.0239930 | ||||||||
\(599\) | −283999. | −0.791522 | −0.395761 | − | 0.918353i | \(-0.629519\pi\) | ||||
−0.395761 | + | 0.918353i | \(0.629519\pi\) | |||||||
\(600\) | 78000.0 | − | 183099.i | 0.216667 | − | 0.508609i | ||||
\(601\) | − | 91219.0i | − | 0.252544i | −0.991996 | − | 0.126272i | \(-0.959699\pi\) | ||
0.991996 | − | 0.126272i | \(-0.0403011\pi\) | |||||||
\(602\) | −32340.0 | − | 31686.6i | −0.0892374 | − | 0.0874345i | ||||
\(603\) | − | 114675.i | − | 0.315381i | ||||||
\(604\) | −175510. | −0.481092 | ||||||||
\(605\) | −33600.0 | + | 164606.i | −0.0917970 | + | 0.449712i | ||||
\(606\) | −59100.0 | −0.160932 | ||||||||
\(607\) | −193715. | −0.525758 | −0.262879 | − | 0.964829i | \(-0.584672\pi\) | ||||
−0.262879 | + | 0.964829i | \(0.584672\pi\) | |||||||
\(608\) | 226800. | 0.613530 | ||||||||
\(609\) | 33425.0 | + | 32749.7i | 0.0901232 | + | 0.0883024i | ||||
\(610\) | 23700.0 | − | 116106.i | 0.0636926 | − | 0.312029i | ||||
\(611\) | 10975.0 | 0.0293983 | ||||||||
\(612\) | 271600. | 0.725148 | ||||||||
\(613\) | − | 296231.i | − | 0.788334i | −0.919039 | − | 0.394167i | \(-0.871033\pi\) | ||
0.919039 | − | 0.394167i | \(-0.128967\pi\) | |||||||
\(614\) | 82805.0i | 0.219644i | ||||||||
\(615\) | −357000. | − | 72872.3i | −0.943883 | − | 0.192669i | ||||
\(616\) | −194376. | + | 198384.i | −0.512249 | + | 0.522812i | ||||
\(617\) | − | 424751.i | − | 1.11574i | −0.829927 | − | 0.557872i | \(-0.811618\pi\) | ||
0.829927 | − | 0.557872i | \(-0.188382\pi\) | |||||||
\(618\) | − | 57746.7i | − | 0.151200i | ||||||
\(619\) | − | 375825.i | − | 0.980855i | −0.871482 | − | 0.490427i | \(-0.836841\pi\) | ||
0.871482 | − | 0.490427i | \(-0.163159\pi\) | |||||||
\(620\) | 258000. | + | 52664.0i | 0.671176 | + | 0.137003i | ||||
\(621\) | 479880.i | 1.24437i | ||||||||
\(622\) | −123540. | −0.319321 | ||||||||
\(623\) | −27720.0 | + | 28291.6i | −0.0714196 | + | 0.0728923i | ||||
\(624\) | −100.000 | −0.000256821 | ||||||||
\(625\) | 270625. | + | 281691.i | 0.692800 | + | 0.721130i | ||||
\(626\) | 166945.i | 0.426015i | ||||||||
\(627\) | − | 98102.1i | − | 0.249542i | ||||||
\(628\) | −257900. | −0.653931 | ||||||||
\(629\) | − | 791210.i | − | 1.99982i | ||||||
\(630\) | −94080.0 | − | 139229.i | −0.237037 | − | 0.350791i | ||||
\(631\) | −471511. | −1.18422 | −0.592111 | − | 0.805856i | \(-0.701705\pi\) | ||||
−0.592111 | + | 0.805856i | \(0.701705\pi\) | |||||||
\(632\) | 354162.i | 0.886682i | ||||||||
\(633\) | 264085. | 0.659077 | ||||||||
\(634\) | 103944. | 0.258595 | ||||||||
\(635\) | −584640. | − | 119339.i | −1.44991 | − | 0.295962i | ||||
\(636\) | − | 79363.5i | − | 0.196203i | ||||||
\(637\) | −245.000 | − | 12002.5i | −0.000603792 | − | 0.0295796i | ||||
\(638\) | 41638.9i | 0.102296i | ||||||||
\(639\) | −249424. | −0.610853 | ||||||||
\(640\) | 255840. | + | 52223.1i | 0.624609 | + | 0.127498i | ||||
\(641\) | 558794. | 1.35999 | 0.679995 | − | 0.733217i | \(-0.261982\pi\) | ||||
0.679995 | + | 0.733217i | \(0.261982\pi\) | |||||||
\(642\) | 155160. | 0.376452 | ||||||||
\(643\) | −454235. | −1.09865 | −0.549324 | − | 0.835609i | \(-0.685115\pi\) | ||||
−0.549324 | + | 0.835609i | \(0.685115\pi\) | |||||||
\(644\) | 240240. | − | 245194.i | 0.579260 | − | 0.591205i | ||||
\(645\) | 46200.0 | + | 9430.54i | 0.111051 | + | 0.0226682i | ||||
\(646\) | −261900. | −0.627582 | ||||||||
\(647\) | −129530. | −0.309430 | −0.154715 | − | 0.987959i | \(-0.549446\pi\) | ||||
−0.154715 | + | 0.987959i | \(0.549446\pi\) | |||||||
\(648\) | 70756.0i | 0.168505i | ||||||||
\(649\) | 322647.i | 0.766016i | ||||||||
\(650\) | −3000.00 | + | 7042.28i | −0.00710059 | + | 0.0166681i | ||||
\(651\) | −180600. | + | 184324.i | −0.426143 | + | 0.434931i | ||||
\(652\) | − | 371539.i | − | 0.873995i | ||||||
\(653\) | − | 343903.i | − | 0.806511i | −0.915087 | − | 0.403255i | \(-0.867879\pi\) | ||
0.915087 | − | 0.403255i | \(-0.132121\pi\) | |||||||
\(654\) | 150778.i | 0.352520i | ||||||||
\(655\) | −165000. | − | 33680.5i | −0.384593 | − | 0.0785047i | ||||
\(656\) | − | 11659.6i | − | 0.0270941i | ||||||
\(657\) | −484400. | −1.12221 | ||||||||
\(658\) | 184380. | − | 188182.i | 0.425855 | − | 0.434637i | ||||
\(659\) | 526913. | 1.21330 | 0.606650 | − | 0.794969i | \(-0.292513\pi\) | ||||
0.606650 | + | 0.794969i | \(0.292513\pi\) | |||||||
\(660\) | 22250.0 | − | 109002.i | 0.0510790 | − | 0.250235i | ||||
\(661\) | − | 191844.i | − | 0.439082i | −0.975603 | − | 0.219541i | \(-0.929544\pi\) | ||
0.975603 | − | 0.219541i | \(-0.0704559\pi\) | |||||||
\(662\) | − | 280971.i | − | 0.641130i | ||||||
\(663\) | 12125.0 | 0.0275838 | ||||||||
\(664\) | 126737.i | 0.287452i | ||||||||
\(665\) | −151200. | − | 223761.i | −0.341907 | − | 0.505989i | ||||
\(666\) | 223776. | 0.504505 | ||||||||
\(667\) | − | 133806.i | − | 0.300762i | ||||||
\(668\) | −207950. | −0.466022 | ||||||||
\(669\) | 68225.0 | 0.152437 | ||||||||
\(670\) | −25080.0 | + | 122866.i | −0.0558699 | + | 0.273706i | ||||
\(671\) | − | 172224.i | − | 0.382514i | ||||||
\(672\) | −176400. | + | 180037.i | −0.390625 | + | 0.398680i | ||||
\(673\) | 429792.i | 0.948918i | 0.880278 | + | 0.474459i | \(0.157356\pi\) | ||||
−0.880278 | + | 0.474459i | \(0.842644\pi\) | |||||||
\(674\) | −286608. | −0.630912 | ||||||||
\(675\) | 393875. | + | 167790.i | 0.864472 | + | 0.368263i | ||||
\(676\) | −285360. | −0.624453 | ||||||||
\(677\) | −79685.0 | −0.173860 | −0.0869299 | − | 0.996214i | \(-0.527706\pi\) | ||||
−0.0869299 | + | 0.996214i | \(0.527706\pi\) | |||||||
\(678\) | −38220.0 | −0.0831441 | ||||||||
\(679\) | 323225. | + | 316695.i | 0.701076 | + | 0.686912i | ||||
\(680\) | −756600. | − | 154440.i | −1.63625 | − | 0.333997i | ||||
\(681\) | 372425. | 0.803054 | ||||||||
\(682\) | −229620. | −0.493675 | ||||||||
\(683\) | − | 719577.i | − | 1.54254i | −0.636510 | − | 0.771269i | \(-0.719622\pi\) | ||
0.636510 | − | 0.771269i | \(-0.280378\pi\) | |||||||
\(684\) | 123454.i | 0.263872i | ||||||||
\(685\) | 565080. | + | 115346.i | 1.20428 | + | 0.245823i | ||||
\(686\) | −209916. | − | 197441.i | −0.446064 | − | 0.419555i | ||||
\(687\) | − | 342316.i | − | 0.725294i | ||||||
\(688\) | 1508.89i | 0.00318771i | ||||||||
\(689\) | 7936.35i | 0.0167179i | ||||||||
\(690\) | 42900.0 | − | 210166.i | 0.0901071 | − | 0.441433i | ||||
\(691\) | − | 398532.i | − | 0.834655i | −0.908756 | − | 0.417328i | \(-0.862967\pi\) | ||
0.908756 | − | 0.417328i | \(-0.137033\pi\) | |||||||
\(692\) | 1150.00 | 0.00240152 | ||||||||
\(693\) | −174440. | − | 170916.i | −0.363228 | − | 0.355890i | ||||
\(694\) | 172644. | 0.358453 | ||||||||
\(695\) | 722400. | + | 147459.i | 1.49557 | + | 0.305283i | ||||
\(696\) | 60820.8i | 0.125555i | ||||||||
\(697\) | 1.41372e6i | 2.91004i | ||||||||
\(698\) | −223860. | −0.459479 | ||||||||
\(699\) | 300846.i | 0.615730i | ||||||||
\(700\) | −117250. | − | 282916.i | −0.239286 | − | 0.577380i | ||||
\(701\) | −658873. | −1.34081 | −0.670403 | − | 0.741998i | \(-0.733879\pi\) | ||||
−0.670403 | + | 0.741998i | \(0.733879\pi\) | |||||||
\(702\) | 8389.50i | 0.0170240i | ||||||||
\(703\) | 359640. | 0.727708 | ||||||||
\(704\) | −218584. | −0.441035 | ||||||||
\(705\) | −54875.0 | + | 268831.i | −0.110407 | + | 0.540881i | ||||
\(706\) | − | 27936.4i | − | 0.0560482i | ||||||
\(707\) | −165480. | + | 168892.i | −0.331060 | + | 0.337887i | ||||
\(708\) | 181262.i | 0.361610i | ||||||||
\(709\) | −593737. | −1.18114 | −0.590570 | − | 0.806986i | \(-0.701097\pi\) | ||||
−0.590570 | + | 0.806986i | \(0.701097\pi\) | |||||||
\(710\) | 267240. | + | 54550.1i | 0.530133 | + | 0.108213i | ||||
\(711\) | −311416. | −0.616030 | ||||||||
\(712\) | −51480.0 | −0.101550 | ||||||||
\(713\) | 737880. | 1.45147 | ||||||||
\(714\) | 203700. | − | 207900.i | 0.399572 | − | 0.407811i | ||||
\(715\) | −2225.00 | + | 10900.2i | −0.00435229 | + | 0.0213218i | ||||
\(716\) | 53180.0 | 0.103734 | ||||||||
\(717\) | −376835. | −0.733015 | ||||||||
\(718\) | 564279.i | 1.09457i | ||||||||
\(719\) | − | 75321.8i | − | 0.145701i | −0.997343 | − | 0.0728506i | \(-0.976790\pi\) | ||
0.997343 | − | 0.0728506i | \(-0.0232096\pi\) | |||||||
\(720\) | −1120.00 | + | 5486.86i | −0.00216049 | + | 0.0105842i | ||||
\(721\) | −165025. | − | 161691.i | −0.317453 | − | 0.311039i | ||||
\(722\) | 200175.i | 0.384003i | ||||||||
\(723\) | 389346.i | 0.744834i | ||||||||
\(724\) | 123454.i | 0.235521i | ||||||||
\(725\) | −109825. | − | 46785.3i | −0.208942 | − | 0.0890088i | ||||
\(726\) | − | 82302.9i | − | 0.156150i | ||||||
\(727\) | 342190. | 0.647438 | 0.323719 | − | 0.946153i | \(-0.395067\pi\) | ||||
0.323719 | + | 0.946153i | \(0.395067\pi\) | |||||||
\(728\) | 10920.0 | − | 11145.2i | 0.0206044 | − | 0.0210293i | ||||
\(729\) | 215209. | 0.404954 | ||||||||
\(730\) | 519000. | + | 105940.i | 0.973916 | + | 0.198800i | ||||
\(731\) | − | 182952.i | − | 0.342376i | ||||||
\(732\) | − | 96754.8i | − | 0.180572i | ||||||
\(733\) | 958555. | 1.78406 | 0.892029 | − | 0.451978i | \(-0.149281\pi\) | ||||
0.892029 | + | 0.451978i | \(0.149281\pi\) | |||||||
\(734\) | 182450.i | 0.338651i | ||||||||
\(735\) | 295225. | + | 54011.2i | 0.546485 | + | 0.0999792i | ||||
\(736\) | 720720. | 1.33049 | ||||||||
\(737\) | 182252.i | 0.335534i | ||||||||
\(738\) | −399840. | −0.734131 | ||||||||
\(739\) | −229399. | −0.420052 | −0.210026 | − | 0.977696i | \(-0.567355\pi\) | ||||
−0.210026 | + | 0.977696i | \(0.567355\pi\) | |||||||
\(740\) | 399600. | + | 81568.0i | 0.729730 | + | 0.148955i | ||||
\(741\) | 5511.35i | 0.0100374i | ||||||||
\(742\) | 136080. | + | 133331.i | 0.247165 | + | 0.242171i | ||||
\(743\) | − | 97803.2i | − | 0.177164i | −0.996069 | − | 0.0885820i | \(-0.971766\pi\) | ||
0.996069 | − | 0.0885820i | \(-0.0282335\pi\) | |||||||
\(744\) | −335400. | −0.605923 | ||||||||
\(745\) | 141730. | − | 694332.i | 0.255358 | − | 1.25099i | ||||
\(746\) | 251196. | 0.451372 | ||||||||
\(747\) | −111440. | −0.199710 | ||||||||
\(748\) | −431650. | −0.771487 | ||||||||
\(749\) | 434448. | − | 443407.i | 0.774416 | − | 0.790385i | ||||
\(750\) | −157500. | − | 108696.i | −0.280000 | − | 0.193238i | ||||
\(751\) | 246977. | 0.437902 | 0.218951 | − | 0.975736i | \(-0.429737\pi\) | ||||
0.218951 | + | 0.975736i | \(0.429737\pi\) | |||||||
\(752\) | −8780.00 | −0.0155260 | ||||||||
\(753\) | − | 252052.i | − | 0.444530i | ||||||
\(754\) | − | 2339.26i | − | 0.00411468i | ||||||
\(755\) | −87755.0 | + | 429910.i | −0.153949 | + | 0.754195i | ||||
\(756\) | −239750. | − | 234906.i | −0.419484 | − | 0.411008i | ||||
\(757\) | 1.05636e6i | 1.84340i | 0.387906 | + | 0.921699i | \(0.373198\pi\) | ||||
−0.387906 | + | 0.921699i | \(0.626802\pi\) | |||||||
\(758\) | − | 423649.i | − | 0.737340i | ||||||
\(759\) | − | 311747.i | − | 0.541151i | ||||||
\(760\) | 70200.0 | − | 343908.i | 0.121537 | − | 0.595409i | ||||
\(761\) | 406836.i | 0.702506i | 0.936281 | + | 0.351253i | \(0.114244\pi\) | ||||
−0.936281 | + | 0.351253i | \(0.885756\pi\) | |||||||
\(762\) | 292320. | 0.503441 | ||||||||
\(763\) | 430885. | + | 422179.i | 0.740137 | + | 0.725184i | ||||
\(764\) | −142630. | −0.244357 | ||||||||
\(765\) | 135800. | − | 665281.i | 0.232048 | − | 1.13680i | ||||
\(766\) | − | 352849.i | − | 0.601356i | ||||||
\(767\) | − | 18126.2i | − | 0.0308118i | ||||||
\(768\) | −324400. | −0.549995 | ||||||||
\(769\) | 592238.i | 1.00148i | 0.865597 | + | 0.500741i | \(0.166939\pi\) | ||||
−0.865597 | + | 0.500741i | \(0.833061\pi\) | |||||||
\(770\) | 149520. | + | 221275.i | 0.252184 | + | 0.373207i | ||||
\(771\) | 16850.0 | 0.0283460 | ||||||||
\(772\) | − | 320050.i | − | 0.537012i | ||||||
\(773\) | −401165. | −0.671373 | −0.335687 | − | 0.941974i | \(-0.608968\pi\) | ||||
−0.335687 | + | 0.941974i | \(0.608968\pi\) | |||||||
\(774\) | 51744.0 | 0.0863730 | ||||||||
\(775\) | 258000. | − | 605636.i | 0.429553 | − | 1.00834i | ||||
\(776\) | 588147.i | 0.976703i | ||||||||
\(777\) | −279720. | + | 285488.i | −0.463320 | + | 0.472874i | ||||
\(778\) | − | 364898.i | − | 0.602854i | ||||||
\(779\) | −642600. | −1.05893 | ||||||||
\(780\) | −1250.00 | + | 6123.72i | −0.00205457 | + | 0.0100653i | ||||
\(781\) | 396406. | 0.649887 | ||||||||
\(782\) | −832260. | −1.36096 | ||||||||
\(783\) | −130835. | −0.213403 | ||||||||
\(784\) | 196.000 | + | 9602.00i | 0.000318878 | + | 0.0156217i | ||||
\(785\) | −128950. | + | 631723.i | −0.209258 | + | 1.02515i | ||||
\(786\) | 82500.0 | 0.133539 | ||||||||
\(787\) | 357565. | 0.577305 | 0.288653 | − | 0.957434i | \(-0.406793\pi\) | ||||
0.288653 | + | 0.957434i | \(0.406793\pi\) | |||||||
\(788\) | 33949.9i | 0.0546747i | ||||||||
\(789\) | 296927.i | 0.476975i | ||||||||
\(790\) | 333660. | + | 68108.1i | 0.534626 | + | 0.109130i | ||||
\(791\) | −107016. | + | 109223.i | −0.171039 | + | 0.174566i | ||||
\(792\) | − | 317415.i | − | 0.506030i | ||||||
\(793\) | 9675.48i | 0.0153860i | ||||||||
\(794\) | − | 629335.i | − | 0.998254i | ||||||
\(795\) | −194400. | − | 39681.7i | −0.307583 | − | 0.0627851i | ||||
\(796\) | 194000.i | 0.306178i | ||||||||
\(797\) | −1.18188e6 | −1.86062 | −0.930312 | − | 0.366769i | \(-0.880464\pi\) | ||||
−0.930312 | + | 0.366769i | \(0.880464\pi\) | |||||||
\(798\) | 94500.0 | + | 92590.7i | 0.148397 | + | 0.145399i | ||||
\(799\) | 1.06458e6 | 1.66756 | ||||||||
\(800\) | 252000. | − | 591552.i | 0.393750 | − | 0.924300i | ||||
\(801\) | − | 45266.6i | − | 0.0705525i | ||||||
\(802\) | − | 87302.3i | − | 0.135730i | ||||||
\(803\) | 769850. | 1.19392 | ||||||||
\(804\) | 102389.i | 0.158394i | ||||||||
\(805\) | −480480. | − | 711062.i | −0.741453 | − | 1.09728i | ||||
\(806\) | 12900.0 | 0.0198573 | ||||||||
\(807\) | 385060.i | 0.591264i | ||||||||
\(808\) | −307320. | −0.470726 | ||||||||
\(809\) | −272449. | −0.416283 | −0.208141 | − | 0.978099i | \(-0.566741\pi\) | ||||
−0.208141 | + | 0.978099i | \(0.566741\pi\) | |||||||
\(810\) | 66660.0 | + | 13606.9i | 0.101600 | + | 0.0207391i | ||||
\(811\) | 1.22117e6i | 1.85667i | 0.371749 | + | 0.928333i | \(0.378758\pi\) | ||||
−0.371749 | + | 0.928333i | \(0.621242\pi\) | |||||||
\(812\) | 66850.0 | + | 65499.4i | 0.101389 | + | 0.0993402i | ||||
\(813\) | − | 716108.i | − | 1.08342i | ||||||
\(814\) | −355644. | −0.536743 | ||||||||
\(815\) | −910080. | − | 185769.i | −1.37014 | − | 0.279678i | ||||
\(816\) | −9700.00 | −0.0145677 | ||||||||
\(817\) | 83160.0 | 0.124586 | ||||||||
\(818\) | 371640. | 0.555413 | ||||||||
\(819\) | 9800.00 | + | 9602.00i | 0.0146103 | + | 0.0143151i | ||||
\(820\) | −714000. | − | 145745.i | −1.06187 | − | 0.216753i | ||||
\(821\) | −621793. | −0.922485 | −0.461243 | − | 0.887274i | \(-0.652596\pi\) | ||||
−0.461243 | + | 0.887274i | \(0.652596\pi\) | |||||||
\(822\) | −282540. | −0.418154 | ||||||||
\(823\) | − | 117394.i | − | 0.173319i | −0.996238 | − | 0.0866597i | \(-0.972381\pi\) | ||
0.996238 | − | 0.0866597i | \(-0.0276193\pi\) | |||||||
\(824\) | − | 300283.i | − | 0.442259i | ||||||
\(825\) | −255875. | − | 109002.i | −0.375941 | − | 0.160150i | ||||
\(826\) | −310800. | − | 304521.i | −0.455534 | − | 0.446330i | ||||
\(827\) | − | 199790.i | − | 0.292121i | −0.989276 | − | 0.146061i | \(-0.953341\pi\) | ||
0.989276 | − | 0.146061i | \(-0.0466595\pi\) | |||||||
\(828\) | 392310.i | 0.572228i | ||||||||
\(829\) | 197894.i | 0.287955i | 0.989581 | + | 0.143977i | \(0.0459892\pi\) | ||||
−0.989581 | + | 0.143977i | \(0.954011\pi\) | |||||||
\(830\) | 119400. | + | 24372.4i | 0.173320 | + | 0.0353788i | ||||
\(831\) | − | 509641.i | − | 0.738010i | ||||||
\(832\) | 12280.0 | 0.0177399 | ||||||||
\(833\) | −23765.0 | − | 1.16424e6i | −0.0342490 | − | 1.67785i | ||||
\(834\) | −361200. | −0.519297 | ||||||||
\(835\) | −103975. | + | 509371.i | −0.149127 | + | 0.730570i | ||||
\(836\) | − | 196204.i | − | 0.280734i | ||||||
\(837\) | − | 721497.i | − | 1.02987i | ||||||
\(838\) | −369600. | −0.526313 | ||||||||
\(839\) | 826972.i | 1.17481i | 0.809294 | + | 0.587404i | \(0.199850\pi\) | ||||
−0.809294 | + | 0.587404i | \(0.800150\pi\) | |||||||
\(840\) | 218400. | + | 323210.i | 0.309524 | + | 0.458064i | ||||
\(841\) | −670800. | −0.948421 | ||||||||
\(842\) | − | 11466.1i | − | 0.0161730i | ||||||
\(843\) | −237605. | −0.334349 | ||||||||
\(844\) | 528170. | 0.741462 | ||||||||
\(845\) | −142680. | + | 698986.i | −0.199825 | + | 0.978938i | ||||
\(846\) | 301091.i | 0.420685i | ||||||||
\(847\) | −235200. | − | 230448.i | −0.327846 | − | 0.321223i | ||||
\(848\) | − | 6349.08i | − | 0.00882915i | ||||||
\(849\) | −215575. | −0.299077 | ||||||||
\(850\) | −291000. | + | 683101.i | −0.402768 | + | 0.945469i | ||||
\(851\) | 1.14286e6 | 1.57809 | ||||||||
\(852\) | 222700. | 0.306790 | ||||||||
\(853\) | 385450. | 0.529749 | 0.264874 | − | 0.964283i | \(-0.414670\pi\) | ||||
0.264874 | + | 0.964283i | \(0.414670\pi\) | |||||||
\(854\) | 165900. | + | 162548.i | 0.227473 | + | 0.222878i | ||||
\(855\) | 302400. | + | 61727.1i | 0.413666 | + | 0.0844392i | ||||
\(856\) | 806832. | 1.10112 | ||||||||
\(857\) | −356750. | −0.485738 | −0.242869 | − | 0.970059i | \(-0.578089\pi\) | ||||
−0.242869 | + | 0.970059i | \(0.578089\pi\) | |||||||
\(858\) | − | 5450.11i | − | 0.00740340i | ||||||
\(859\) | − | 578227.i | − | 0.783631i | −0.920044 | − | 0.391816i | \(-0.871847\pi\) | ||
0.920044 | − | 0.391816i | \(-0.128153\pi\) | |||||||
\(860\) | 92400.0 | + | 18861.1i | 0.124932 | + | 0.0255017i | ||||
\(861\) | 499800. | − | 510106.i | 0.674202 | − | 0.688104i | ||||
\(862\) | − | 213358.i | − | 0.287140i | ||||||
\(863\) | 151217.i | 0.203039i | 0.994834 | + | 0.101519i | \(0.0323704\pi\) | ||||
−0.994834 | + | 0.101519i | \(0.967630\pi\) | |||||||
\(864\) | − | 704718.i | − | 0.944035i | ||||||
\(865\) | 575.000 | − | 2816.91i | 0.000768485 | − | 0.00376479i | ||||
\(866\) | 567620.i | 0.756871i | ||||||||
\(867\) | 758520. | 1.00909 | ||||||||
\(868\) | −361200. | + | 368648.i | −0.479411 | + | 0.489297i | ||||
\(869\) | 494929. | 0.655395 | ||||||||
\(870\) | 57300.0 | + | 11696.3i | 0.0757035 | + | 0.0154529i | ||||
\(871\) | − | 10238.9i | − | 0.0134963i | ||||||
\(872\) | 784047.i | 1.03112i | ||||||||
\(873\) | −517160. | −0.678573 | ||||||||
\(874\) | − | 378299.i | − | 0.495236i | ||||||
\(875\) | −751625. | + | 145745.i | −0.981714 | + | 0.190360i | ||||
\(876\) | 432500. | 0.563609 | ||||||||
\(877\) | − | 553981.i | − | 0.720271i | −0.932900 | − | 0.360136i | \(-0.882730\pi\) | ||
0.932900 | − | 0.360136i | \(-0.117270\pi\) | |||||||
\(878\) | 603240. | 0.782530 | ||||||||
\(879\) | −810625. | −1.04916 | ||||||||
\(880\) | 1780.00 | − | 8720.18i | 0.00229855 | − | 0.0112606i | ||||
\(881\) | − | 531882.i | − | 0.685273i | −0.939468 | − | 0.342637i | \(-0.888680\pi\) | ||
0.939468 | − | 0.342637i | \(-0.111320\pi\) | |||||||
\(882\) | 329280. | − | 6721.40i | 0.423280 | − | 0.00864018i | ||||
\(883\) | 606675.i | 0.778099i | 0.921217 | + | 0.389049i | \(0.127196\pi\) | ||||
−0.921217 | + | 0.389049i | \(0.872804\pi\) | |||||||
\(884\) | 24250.0 | 0.0310318 | ||||||||
\(885\) | 444000. | + | 90631.1i | 0.566887 | + | 0.115715i | ||||
\(886\) | −856932. | −1.09164 | ||||||||
\(887\) | 1.35703e6 | 1.72481 | 0.862407 | − | 0.506216i | \(-0.168956\pi\) | ||||
0.862407 | + | 0.506216i | \(0.168956\pi\) | |||||||
\(888\) | −519480. | −0.658784 | ||||||||
\(889\) | 818496. | − | 835374.i | 1.03565 | − | 1.05701i | ||||
\(890\) | −9900.00 | + | 48499.9i | −0.0124984 | + | 0.0612295i | ||||
\(891\) | 98879.0 | 0.124551 | ||||||||
\(892\) | 136450. | 0.171492 | ||||||||
\(893\) | 483897.i | 0.606806i | ||||||||
\(894\) | 347166.i | 0.434373i | ||||||||
\(895\) | 26590.0 | − | 130264.i | 0.0331950 | − | 0.162621i | ||||
\(896\) | −358176. | + | 365562.i | −0.446150 | + | 0.455349i | ||||
\(897\) | 17513.9i | 0.0217669i | ||||||||
\(898\) | 623912.i | 0.773697i | ||||||||
\(899\) | 201177.i | 0.248919i | ||||||||
\(900\) | 322000. | + | 137171.i | 0.397531 | + | 0.169347i | ||||
\(901\) | 769826.i | 0.948294i | ||||||||
\(902\) | 635460. | 0.781043 | ||||||||
\(903\) | −64680.0 | + | 66013.7i | −0.0793222 | + | 0.0809578i | ||||
\(904\) | −198744. | −0.243196 | ||||||||
\(905\) | 302400. | + | 61727.1i | 0.369219 | + | 0.0753666i | ||||
\(906\) | − | 214955.i | − | 0.261873i | ||||||
\(907\) | − | 452230.i | − | 0.549724i | −0.961484 | − | 0.274862i | \(-0.911368\pi\) | ||
0.961484 | − | 0.274862i | \(-0.0886321\pi\) | |||||||
\(908\) | 744850. | 0.903435 | ||||||||
\(909\) | − | 270228.i | − | 0.327041i | ||||||
\(910\) | −8400.00 | − | 12431.2i | −0.0101437 | − | 0.0150117i | ||||
\(911\) | −948106. | −1.14241 | −0.571203 | − | 0.820809i | \(-0.693523\pi\) | ||||
−0.571203 | + | 0.820809i | \(0.693523\pi\) | |||||||
\(912\) | − | 4409.08i | − | 0.00530101i | ||||||
\(913\) | 177110. | 0.212472 | ||||||||
\(914\) | −645756. | −0.772994 | ||||||||
\(915\) | −237000. | − | 48377.4i | −0.283078 | − | 0.0577831i | ||||
\(916\) | − | 684632.i | − | 0.815956i | ||||||
\(917\) | 231000. | − | 235763.i | 0.274709 | − | 0.280374i | ||||
\(918\) | 813782.i | 0.965656i | ||||||||
\(919\) | 394481. | 0.467084 | 0.233542 | − | 0.972347i | \(-0.424968\pi\) | ||||
0.233542 | + | 0.972347i | \(0.424968\pi\) | |||||||
\(920\) | 223080. | − | 1.09286e6i | 0.263563 | − | 1.29119i | ||||
\(921\) | 169025. | 0.199265 | ||||||||
\(922\) | 314160. | 0.369563 | ||||||||
\(923\) | −22270.0 | −0.0261407 | ||||||||
\(924\) | 155750. | + | 152603.i | 0.182425 | + | 0.178739i | ||||
\(925\) | 399600. | − | 938032.i | 0.467027 | − | 1.09631i | ||||
\(926\) | 200508. | 0.233835 | ||||||||
\(927\) | 264040. | 0.307263 | ||||||||
\(928\) | 196498.i | 0.228172i | ||||||||
\(929\) | 139523.i | 0.161664i | 0.996728 | + | 0.0808322i | \(0.0257578\pi\) | ||||
−0.996728 | + | 0.0808322i | \(0.974242\pi\) | |||||||
\(930\) | −64500.0 | + | 315984.i | −0.0745751 | + | 0.365342i | ||||
\(931\) | 529200. | − | 10802.2i | 0.610549 | − | 0.0124628i | ||||
\(932\) | 601693.i | 0.692696i | ||||||||
\(933\) | 252175.i | 0.289693i | ||||||||
\(934\) | 500786.i | 0.574061i | ||||||||
\(935\) | −215825. | + | 1.05732e6i | −0.246876 | + | 1.20944i | ||||
\(936\) | 17832.3i | 0.0203543i | ||||||||
\(937\) | −434285. | −0.494647 | −0.247324 | − | 0.968933i | \(-0.579551\pi\) | ||||
−0.247324 | + | 0.968933i | \(0.579551\pi\) | |||||||
\(938\) | −175560. | − | 172013.i | −0.199535 | − | 0.195504i | ||||
\(939\) | 340775. | 0.386488 | ||||||||
\(940\) | −109750. | + | 537663.i | −0.124208 | + | 0.608491i | ||||
\(941\) | 539108.i | 0.608831i | 0.952539 | + | 0.304415i | \(0.0984611\pi\) | ||||
−0.952539 | + | 0.304415i | \(0.901539\pi\) | |||||||
\(942\) | − | 315862.i | − | 0.355955i | ||||||
\(943\) | −2.04204e6 | −2.29636 | ||||||||
\(944\) | 14501.0i | 0.0162725i | ||||||||
\(945\) | −695275. | + | 469812.i | −0.778562 | + | 0.526091i | ||||
\(946\) | −82236.0 | −0.0918924 | ||||||||
\(947\) | 167540.i | 0.186818i | 0.995628 | + | 0.0934091i | \(0.0297764\pi\) | ||||
−0.995628 | + | 0.0934091i | \(0.970224\pi\) | |||||||
\(948\) | 278050. | 0.309390 | ||||||||
\(949\) | −43250.0 | −0.0480235 | ||||||||
\(950\) | −310500. | − | 132272.i | −0.344044 | − | 0.146562i | ||||
\(951\) | − | 212175.i | − | 0.234603i | ||||||
\(952\) | 1.05924e6 | − | 1.08108e6i | 1.16875 | − | 1.19285i | ||||
\(953\) | − | 1.31304e6i | − | 1.44575i | −0.690981 | − | 0.722873i | \(-0.742821\pi\) | ||
0.690981 | − | 0.722873i | \(-0.257179\pi\) | |||||||
\(954\) | −217728. | −0.239231 | ||||||||
\(955\) | −71315.0 | + | 349371.i | −0.0781941 | + | 0.383071i | ||||
\(956\) | −753670. | −0.824642 | ||||||||
\(957\) | 84995.0 | 0.0928046 | ||||||||
\(958\) | 194820. | 0.212277 | ||||||||
\(959\) | −791112. | + | 807425.i | −0.860203 | + | 0.877941i | ||||
\(960\) | −61400.0 | + | 300797.i | −0.0666233 | + | 0.326386i | ||||
\(961\) | −185879. | −0.201272 | ||||||||
\(962\) | 19980.0 | 0.0215896 | ||||||||
\(963\) | 709451.i | 0.765014i | ||||||||
\(964\) | 778693.i | 0.837938i | ||||||||
\(965\) | −783960. | − | 160025.i | −0.841859 | − | 0.171844i | ||||
\(966\) | 300300. | + | 294233.i | 0.321811 | + | 0.315309i | ||||
\(967\) | − | 338745.i | − | 0.362259i | −0.983459 | − | 0.181130i | \(-0.942025\pi\) | ||
0.983459 | − | 0.181130i | \(-0.0579754\pi\) | |||||||
\(968\) | − | 427975.i | − | 0.456738i | ||||||
\(969\) | 534601.i | 0.569354i | ||||||||
\(970\) | 554100. | + | 113105.i | 0.588904 | + | 0.120210i | ||||
\(971\) | − | 1.60718e6i | − | 1.70462i | −0.523039 | − | 0.852309i | \(-0.675202\pi\) | ||
0.523039 | − | 0.852309i | \(-0.324798\pi\) | |||||||
\(972\) | 610400. | 0.646074 | ||||||||
\(973\) | −1.01136e6 | + | 1.03221e6i | −1.06827 | + | 1.09030i | ||||
\(974\) | 404064. | 0.425924 | ||||||||
\(975\) | 14375.0 | + | 6123.72i | 0.0151216 | + | 0.00644179i | ||||
\(976\) | − | 7740.39i | − | 0.00812574i | ||||||
\(977\) | − | 1.40070e6i | − | 1.46743i | −0.679459 | − | 0.733713i | \(-0.737785\pi\) | ||
0.679459 | − | 0.733713i | \(-0.262215\pi\) | |||||||
\(978\) | 455040. | 0.475742 | ||||||||
\(979\) | 71941.5i | 0.0750610i | ||||||||
\(980\) | 590450. | + | 108022.i | 0.614796 | + | 0.112477i | ||||
\(981\) | −689416. | −0.716380 | ||||||||
\(982\) | − | 181730.i | − | 0.188453i | ||||||
\(983\) | 1.73768e6 | 1.79831 | 0.899154 | − | 0.437633i | \(-0.144183\pi\) | ||||
0.899154 | + | 0.437633i | \(0.144183\pi\) | |||||||
\(984\) | 928200. | 0.958631 | ||||||||
\(985\) | 83160.0 | + | 16975.0i | 0.0857121 | + | 0.0174959i | ||||
\(986\) | − | 226908.i | − | 0.233398i | ||||||
\(987\) | −384125. | − | 376364.i | −0.394310 | − | 0.386344i | ||||
\(988\) | 11022.7i | 0.0112921i | ||||||||
\(989\) | 264264. | 0.270175 | ||||||||
\(990\) | −299040. | − | 61041.3i | −0.305112 | − | 0.0622807i | ||||
\(991\) | −423586. | −0.431315 | −0.215657 | − | 0.976469i | \(-0.569189\pi\) | ||||
−0.215657 | + | 0.976469i | \(0.569189\pi\) | |||||||
\(992\) | −1.08360e6 | −1.10115 | ||||||||
\(993\) | −573530. | −0.581645 | ||||||||
\(994\) | −374136. | + | 381851.i | −0.378666 | + | 0.386475i | ||||
\(995\) | 475200. | + | 96999.8i | 0.479988 | + | 0.0979771i | ||||
\(996\) | 99500.0 | 0.100301 | ||||||||
\(997\) | 548035. | 0.551338 | 0.275669 | − | 0.961253i | \(-0.411101\pi\) | ||||
0.275669 | + | 0.961253i | \(0.411101\pi\) | |||||||
\(998\) | − | 682249.i | − | 0.684986i | ||||||
\(999\) | − | 1.11748e6i | − | 1.11972i |
(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 | 35.5.c.d.34.2 | yes | 2 | |
3.2 | odd | 2 | 315.5.e.c.244.1 | 2 | |||
4.3 | odd | 2 | 560.5.p.d.209.1 | 2 | |||
5.2 | odd | 4 | 175.5.d.e.76.1 | 4 | |||
5.3 | odd | 4 | 175.5.d.e.76.4 | 4 | |||
5.4 | even | 2 | 35.5.c.c.34.1 | ✓ | 2 | ||
7.6 | odd | 2 | 35.5.c.c.34.2 | yes | 2 | ||
15.14 | odd | 2 | 315.5.e.d.244.2 | 2 | |||
20.19 | odd | 2 | 560.5.p.e.209.1 | 2 | |||
21.20 | even | 2 | 315.5.e.d.244.1 | 2 | |||
28.27 | even | 2 | 560.5.p.e.209.2 | 2 | |||
35.13 | even | 4 | 175.5.d.e.76.3 | 4 | |||
35.27 | even | 4 | 175.5.d.e.76.2 | 4 | |||
35.34 | odd | 2 | inner | 35.5.c.d.34.1 | yes | 2 | |
105.104 | even | 2 | 315.5.e.c.244.2 | 2 | |||
140.139 | even | 2 | 560.5.p.d.209.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.5.c.c.34.1 | ✓ | 2 | 5.4 | even | 2 | ||
35.5.c.c.34.2 | yes | 2 | 7.6 | odd | 2 | ||
35.5.c.d.34.1 | yes | 2 | 35.34 | odd | 2 | inner | |
35.5.c.d.34.2 | yes | 2 | 1.1 | even | 1 | trivial | |
175.5.d.e.76.1 | 4 | 5.2 | odd | 4 | |||
175.5.d.e.76.2 | 4 | 35.27 | even | 4 | |||
175.5.d.e.76.3 | 4 | 35.13 | even | 4 | |||
175.5.d.e.76.4 | 4 | 5.3 | odd | 4 | |||
315.5.e.c.244.1 | 2 | 3.2 | odd | 2 | |||
315.5.e.c.244.2 | 2 | 105.104 | even | 2 | |||
315.5.e.d.244.1 | 2 | 21.20 | even | 2 | |||
315.5.e.d.244.2 | 2 | 15.14 | odd | 2 | |||
560.5.p.d.209.1 | 2 | 4.3 | odd | 2 | |||
560.5.p.d.209.2 | 2 | 140.139 | even | 2 | |||
560.5.p.e.209.1 | 2 | 20.19 | odd | 2 | |||
560.5.p.e.209.2 | 2 | 28.27 | even | 2 |