Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [315,5,Mod(244,315)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(315, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("315.244");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 315 = 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 315.e (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: | \(32.5615383714\) |
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: | no (minimal twist has level 35) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 244.2 | ||
Root | \(2.44949i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 315.244 |
Dual form | 315.5.e.d.244.1 |
$q$-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 \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(136\) | \(281\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 | \(0.900947\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 10.0000 | 0.625000 | ||||||||
\(5\) | 5.00000 | + | 24.4949i | 0.200000 | + | 0.979796i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −35.0000 | − | 34.2929i | −0.714286 | − | 0.699854i | ||||
\(8\) | 63.6867i | 0.995105i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −60.0000 | + | 12.2474i | −0.600000 | + | 0.122474i | ||||
\(11\) | −89.0000 | −0.735537 | −0.367769 | − | 0.929917i | \(-0.619878\pi\) | ||||
−0.367769 | + | 0.929917i | \(0.619878\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.00000 | 0.0295858 | 0.0147929 | − | 0.999891i | \(-0.495291\pi\) | ||||
0.0147929 | + | 0.999891i | \(0.495291\pi\) | |||||||
\(14\) | 84.0000 | − | 85.7321i | 0.428571 | − | 0.437409i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.0156250 | ||||||||
\(17\) | −485.000 | −1.67820 | −0.839100 | − | 0.543977i | \(-0.816918\pi\) | ||||
−0.839100 | + | 0.543977i | \(0.816918\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 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 | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 218.005i | − | 0.450423i | ||||||
\(23\) | − | 700.554i | − | 1.32430i | −0.749372 | − | 0.662149i | \(-0.769644\pi\) | ||
0.749372 | − | 0.662149i | \(-0.230356\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −575.000 | + | 244.949i | −0.920000 | + | 0.391918i | ||||
\(26\) | 12.2474i | 0.0181175i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −350.000 | − | 342.929i | −0.446429 | − | 0.437409i | ||||
\(29\) | −191.000 | −0.227111 | −0.113555 | − | 0.993532i | \(-0.536224\pi\) | ||||
−0.113555 | + | 0.993532i | \(0.536224\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1053.28i | 1.09603i | 0.836470 | + | 0.548013i | \(0.184615\pi\) | ||||
−0.836470 | + | 0.548013i | \(0.815385\pi\) | |||||||
\(32\) | 1028.79i | 1.00467i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 1188.00i | − | 1.02768i | ||||||
\(35\) | 665.000 | − | 1028.79i | 0.542857 | − | 0.839825i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 1631.36i | − | 1.19164i | −0.803117 | − | 0.595822i | \(-0.796826\pi\) | ||
0.803117 | − | 0.595822i | \(-0.203174\pi\) | |||||||
\(38\) | 540.000 | 0.373961 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1560.00 | + | 318.434i | −0.975000 | + | 0.199021i | ||||
\(41\) | 2914.89i | 1.73402i | 0.498288 | + | 0.867012i | \(0.333962\pi\) | ||||
−0.498288 | + | 0.867012i | \(0.666038\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 377.221i | − | 0.204014i | −0.994784 | − | 0.102007i | \(-0.967474\pi\) | ||
0.994784 | − | 0.102007i | \(-0.0325264\pi\) | |||||||
\(44\) | −890.000 | −0.459711 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1716.00 | 0.810964 | ||||||||
\(47\) | −2195.00 | −0.993662 | −0.496831 | − | 0.867847i | \(-0.665503\pi\) | ||||
−0.496831 | + | 0.867847i | \(0.665503\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | + | 2400.50i | 0.0204082 | + | 0.999792i | ||||
\(50\) | −600.000 | − | 1408.46i | −0.240000 | − | 0.563383i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 50.0000 | 0.0184911 | ||||||||
\(53\) | − | 1587.27i | − | 0.565066i | −0.959258 | − | 0.282533i | \(-0.908825\pi\) | ||
0.959258 | − | 0.282533i | \(-0.0911746\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −445.000 | − | 2180.05i | −0.147107 | − | 0.720676i | ||||
\(56\) | 2184.00 | − | 2229.04i | 0.696429 | − | 0.710789i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 467.853i | − | 0.139076i | ||||||
\(59\) | − | 3625.24i | − | 1.04144i | −0.853728 | − | 0.520719i | \(-0.825664\pi\) | ||
0.853728 | − | 0.520719i | \(-0.174336\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 1935.10i | − | 0.520048i | −0.965602 | − | 0.260024i | \(-0.916270\pi\) | ||
0.965602 | − | 0.260024i | \(-0.0837304\pi\) | |||||||
\(62\) | −2580.00 | −0.671176 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2456.00 | −0.599609 | ||||||||
\(65\) | 25.0000 | + | 122.474i | 0.00591716 | + | 0.0289880i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 2047.77i | − | 0.456176i | −0.973641 | − | 0.228088i | \(-0.926753\pi\) | ||
0.973641 | − | 0.228088i | \(-0.0732474\pi\) | |||||||
\(68\) | −4850.00 | −1.04888 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2520.00 | + | 1628.91i | 0.514286 | + | 0.332431i | ||||
\(71\) | −4454.00 | −0.883555 | −0.441777 | − | 0.897125i | \(-0.645652\pi\) | ||||
−0.441777 | + | 0.897125i | \(0.645652\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8650.00 | −1.62319 | −0.811597 | − | 0.584218i | \(-0.801401\pi\) | ||||
−0.811597 | + | 0.584218i | \(0.801401\pi\) | |||||||
\(74\) | 3996.00 | 0.729730 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 2204.54i | − | 0.381673i | ||||||
\(77\) | 3115.00 | + | 3052.06i | 0.525384 | + | 0.514769i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 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 | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −7140.00 | −1.06187 | ||||||||
\(83\) | 1990.00 | 0.288866 | 0.144433 | − | 0.989515i | \(-0.453864\pi\) | ||||
0.144433 | + | 0.989515i | \(0.453864\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2425.00 | − | 11880.0i | −0.335640 | − | 1.64429i | ||||
\(86\) | 924.000 | 0.124932 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 5668.12i | − | 0.731937i | ||||||
\(89\) | − | 808.332i | − | 0.102049i | −0.998697 | − | 0.0510246i | \(-0.983751\pi\) | ||
0.998697 | − | 0.0510246i | \(-0.0162487\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −175.000 | − | 171.464i | −0.0211327 | − | 0.0207057i | ||||
\(92\) | − | 7005.54i | − | 0.827687i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 5376.63i | − | 0.608491i | ||||||
\(95\) | 5400.00 | − | 1102.27i | 0.598338 | − | 0.122135i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9235.00 | −0.981507 | −0.490754 | − | 0.871298i | \(-0.663278\pi\) | ||||
−0.490754 | + | 0.871298i | \(0.663278\pi\) | |||||||
\(98\) | −5880.00 | + | 120.025i | −0.612245 | + | 0.0124974i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −5750.00 | + | 2449.49i | −0.575000 | + | 0.244949i | ||||
\(101\) | − | 4825.49i | − | 0.473041i | −0.971626 | − | 0.236521i | \(-0.923993\pi\) | ||
0.971626 | − | 0.236521i | \(-0.0760071\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4715.00 | 0.444434 | 0.222217 | − | 0.974997i | \(-0.428671\pi\) | ||||
0.222217 | + | 0.974997i | \(0.428671\pi\) | |||||||
\(104\) | 318.434i | 0.0294410i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3888.00 | 0.346031 | ||||||||
\(107\) | − | 12668.8i | − | 1.10654i | −0.833002 | − | 0.553269i | \(-0.813380\pi\) | ||
0.833002 | − | 0.553269i | \(-0.186620\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 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 | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −140.000 | − | 137.171i | −0.0111607 | − | 0.0109352i | ||||
\(113\) | 3120.65i | 0.244393i | 0.992506 | + | 0.122196i | \(0.0389938\pi\) | ||||
−0.992506 | + | 0.122196i | \(0.961006\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 17160.0 | − | 3502.77i | 1.29754 | − | 0.264860i | ||||
\(116\) | −1910.00 | −0.141944 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 8880.00 | 0.637748 | ||||||||
\(119\) | 16975.0 | + | 16632.0i | 1.19871 | + | 1.17450i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6720.00 | −0.458985 | ||||||||
\(122\) | 4740.00 | 0.318463 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 10532.8i | 0.685016i | ||||||||
\(125\) | −8875.00 | − | 12859.8i | −0.568000 | − | 0.823029i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 23867.8i | 1.47981i | 0.672712 | + | 0.739904i | \(0.265129\pi\) | ||||
−0.672712 | + | 0.739904i | \(0.734871\pi\) | |||||||
\(128\) | 10444.6i | 0.637489i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −300.000 | + | 61.2372i | −0.0177515 | + | 0.00362351i | ||||
\(131\) | 6736.10i | 0.392524i | 0.980552 | + | 0.196262i | \(0.0628802\pi\) | ||||
−0.980552 | + | 0.196262i | \(0.937120\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7560.00 | + | 7715.89i | −0.427384 | + | 0.436197i | ||||
\(134\) | 5016.00 | 0.279350 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 30888.1i | − | 1.66999i | ||||||
\(137\) | 23069.3i | 1.22912i | 0.788871 | + | 0.614558i | \(0.210666\pi\) | ||||
−0.788871 | + | 0.614558i | \(0.789334\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 29491.9i | 1.52641i | 0.646154 | + | 0.763207i | \(0.276376\pi\) | ||||
−0.646154 | + | 0.763207i | \(0.723624\pi\) | |||||||
\(140\) | 6650.00 | − | 10287.9i | 0.339286 | − | 0.524891i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 10910.0i | − | 0.541065i | ||||||
\(143\) | −445.000 | −0.0217615 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −955.000 | − | 4678.53i | −0.0454221 | − | 0.222522i | ||||
\(146\) | − | 21188.1i | − | 0.993999i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 16313.6i | − | 0.744777i | ||||||
\(149\) | −28346.0 | −1.27679 | −0.638395 | − | 0.769709i | \(-0.720401\pi\) | ||||
−0.638395 | + | 0.769709i | \(0.720401\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17551.0 | −0.769747 | −0.384873 | − | 0.922969i | \(-0.625755\pi\) | ||||
−0.384873 | + | 0.922969i | \(0.625755\pi\) | |||||||
\(152\) | 14040.0 | 0.607687 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −7476.00 | + | 7630.16i | −0.315230 | + | 0.321731i | ||||
\(155\) | −25800.0 | + | 5266.40i | −1.07388 | + | 0.219205i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 25790.0 | 1.04629 | 0.523145 | − | 0.852244i | \(-0.324759\pi\) | ||||
0.523145 | + | 0.852244i | \(0.324759\pi\) | |||||||
\(158\) | 13621.6i | 0.545650i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −25200.0 | + | 5143.93i | −0.984375 | + | 0.200935i | ||||
\(161\) | −24024.0 | + | 24519.4i | −0.926816 | + | 0.945928i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 37153.9i | 1.39839i | 0.714930 | + | 0.699196i | \(0.246458\pi\) | ||||
−0.714930 | + | 0.699196i | \(0.753542\pi\) | |||||||
\(164\) | 29148.9i | 1.08376i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4874.48i | 0.176894i | ||||||||
\(167\) | −20795.0 | −0.745634 | −0.372817 | − | 0.927905i | \(-0.621608\pi\) | ||||
−0.372817 | + | 0.927905i | \(0.621608\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −28536.0 | −0.999125 | ||||||||
\(170\) | 29100.0 | − | 5940.01i | 1.00692 | − | 0.205537i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 3772.21i | − | 0.127509i | ||||||
\(173\) | 115.000 | 0.00384243 | 0.00192121 | − | 0.999998i | \(-0.499388\pi\) | ||||
0.00192121 | + | 0.999998i | \(0.499388\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 28525.0 | + | 11145.2i | 0.931429 | + | 0.363924i | ||||
\(176\) | −356.000 | −0.0114928 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1980.00 | 0.0624921 | ||||||||
\(179\) | −5318.00 | −0.165975 | −0.0829874 | − | 0.996551i | \(-0.526446\pi\) | ||||
−0.0829874 | + | 0.996551i | \(0.526446\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 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 | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 44616.0 | 1.31782 | ||||||||
\(185\) | 39960.0 | − | 8156.80i | 1.16757 | − | 0.238329i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 43165.0 | 1.23438 | ||||||||
\(188\) | −21950.0 | −0.621039 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2700.00 | + | 13227.2i | 0.0747922 | + | 0.366406i | ||||
\(191\) | 14263.0 | 0.390971 | 0.195485 | − | 0.980707i | \(-0.437372\pi\) | ||||
0.195485 | + | 0.980707i | \(0.437372\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 32005.0i | 0.859219i | 0.903015 | + | 0.429609i | \(0.141349\pi\) | ||||
−0.903015 | + | 0.429609i | \(0.858651\pi\) | |||||||
\(194\) | − | 22621.0i | − | 0.601048i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 490.000 | + | 24005.0i | 0.0127551 | + | 0.624870i | ||||
\(197\) | 3394.99i | 0.0874795i | 0.999043 | + | 0.0437398i | \(0.0139272\pi\) | ||||
−0.999043 | + | 0.0437398i | \(0.986073\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 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 | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 11820.0 | 0.289677 | ||||||||
\(203\) | 6685.00 | + | 6549.94i | 0.162222 | + | 0.158944i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −71400.0 | + | 14574.5i | −1.69899 | + | 0.346805i | ||||
\(206\) | 11549.3i | 0.272159i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 20.0000 | 0.000462278 | ||||||||
\(209\) | 19620.4i | 0.449175i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 52817.0 | 1.18634 | 0.593170 | − | 0.805078i | \(-0.297876\pi\) | ||||
0.593170 | + | 0.805078i | \(0.297876\pi\) | |||||||
\(212\) | − | 15872.7i | − | 0.353166i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 31032.0 | 0.677614 | ||||||||
\(215\) | 9240.00 | − | 1886.11i | 0.199892 | − | 0.0408027i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 36120.0 | − | 36864.8i | 0.767058 | − | 0.782875i | ||||
\(218\) | 30155.7i | 0.634536i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −4450.00 | − | 21800.5i | −0.0919421 | − | 0.450423i | ||||
\(221\) | −2425.00 | −0.0496509 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13645.0 | −0.274387 | −0.137194 | − | 0.990544i | \(-0.543808\pi\) | ||||
−0.137194 | + | 0.990544i | \(0.543808\pi\) | |||||||
\(224\) | 35280.0 | − | 36007.5i | 0.703125 | − | 0.717624i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −7644.00 | −0.149659 | ||||||||
\(227\) | 74485.0 | 1.44550 | 0.722748 | − | 0.691111i | \(-0.242879\pi\) | ||||
0.722748 | + | 0.691111i | \(0.242879\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 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 | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 12164.2i | − | 0.225999i | ||||||
\(233\) | 60169.3i | 1.10831i | 0.832412 | + | 0.554157i | \(0.186959\pi\) | ||||
−0.832412 | + | 0.554157i | \(0.813041\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10975.0 | − | 53766.3i | −0.198732 | − | 0.973586i | ||||
\(236\) | − | 36252.4i | − | 0.650899i | ||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −40740.0 | + | 41580.1i | −0.719229 | + | 0.734060i | ||||
\(239\) | 75367.0 | 1.31943 | 0.659714 | − | 0.751517i | \(-0.270678\pi\) | ||||
0.659714 | + | 0.751517i | \(0.270678\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 77869.3i | 1.34070i | 0.742044 | + | 0.670351i | \(0.233856\pi\) | ||||
−0.742044 | + | 0.670351i | \(0.766144\pi\) | |||||||
\(242\) | − | 16460.6i | − | 0.281070i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 19351.0i | − | 0.325030i | ||||||
\(245\) | −58555.0 | + | 13202.7i | −0.975510 | + | 0.219954i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 1102.27i | − | 0.0180673i | ||||||
\(248\) | −67080.0 | −1.09066 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 31500.0 | − | 21739.2i | 0.504000 | − | 0.347828i | ||||
\(251\) | 50410.5i | 0.800154i | 0.916482 | + | 0.400077i | \(0.131017\pi\) | ||||
−0.916482 | + | 0.400077i | \(0.868983\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 62349.3i | 0.974071i | ||||||||
\(254\) | −58464.0 | −0.906194 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −64880.0 | −0.989990 | ||||||||
\(257\) | 3370.00 | 0.0510227 | 0.0255114 | − | 0.999675i | \(-0.491879\pi\) | ||||
0.0255114 | + | 0.999675i | \(0.491879\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −55944.0 | + | 57097.6i | −0.833977 | + | 0.851174i | ||||
\(260\) | 250.000 | + | 1224.74i | 0.00369822 | + | 0.0181175i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −16500.0 | −0.240371 | ||||||||
\(263\) | 59385.4i | 0.858556i | 0.903173 | + | 0.429278i | \(0.141232\pi\) | ||||
−0.903173 | + | 0.429278i | \(0.858768\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 38880.0 | − | 7936.35i | 0.553649 | − | 0.113013i | ||||
\(266\) | −18900.0 | − | 18518.1i | −0.267115 | − | 0.261718i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 20477.7i | − | 0.285110i | ||||||
\(269\) | − | 77012.0i | − | 1.06427i | −0.846658 | − | 0.532137i | \(-0.821389\pi\) | ||
0.846658 | − | 0.532137i | \(-0.178611\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 143222.i | − | 1.95016i | −0.221855 | − | 0.975080i | \(-0.571211\pi\) | ||
0.221855 | − | 0.975080i | \(-0.428789\pi\) | |||||||
\(272\) | −1940.00 | −0.0262219 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −56508.0 | −0.752677 | ||||||||
\(275\) | 51175.0 | − | 21800.5i | 0.676694 | − | 0.288271i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 101928.i | 1.32842i | 0.747547 | + | 0.664209i | \(0.231231\pi\) | ||||
−0.747547 | + | 0.664209i | \(0.768769\pi\) | |||||||
\(278\) | −72240.0 | −0.934734 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 65520.0 | + | 42351.7i | 0.835714 | + | 0.540200i | ||||
\(281\) | 47521.0 | 0.601829 | 0.300914 | − | 0.953651i | \(-0.402708\pi\) | ||||
0.300914 | + | 0.953651i | \(0.402708\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 43115.0 | 0.538339 | 0.269169 | − | 0.963093i | \(-0.413251\pi\) | ||||
0.269169 | + | 0.963093i | \(0.413251\pi\) | |||||||
\(284\) | −44540.0 | −0.552222 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 1090.02i | − | 0.0133261i | ||||||
\(287\) | 99960.0 | − | 102021.i | 1.21356 | − | 1.23859i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 151704. | 1.81636 | ||||||||
\(290\) | 11460.0 | − | 2339.26i | 0.136266 | − | 0.0278153i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −86500.0 | −1.01450 | ||||||||
\(293\) | −162125. | −1.88849 | −0.944245 | − | 0.329243i | \(-0.893206\pi\) | ||||
−0.944245 | + | 0.329243i | \(0.893206\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 88800.0 | − | 18126.2i | 1.02040 | − | 0.208288i | ||||
\(296\) | 103896. | 1.18581 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 69433.2i | − | 0.781871i | ||||||
\(299\) | − | 3502.77i | − | 0.0391804i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12936.0 | + | 13202.7i | −0.142780 | + | 0.145724i | ||||
\(302\) | − | 42991.0i | − | 0.471372i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 881.816i | − | 0.00954181i | ||||||
\(305\) | 47400.0 | − | 9675.48i | 0.509540 | − | 0.104010i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −33805.0 | −0.358678 | −0.179339 | − | 0.983787i | \(-0.557396\pi\) | ||||
−0.179339 | + | 0.983787i | \(0.557396\pi\) | |||||||
\(308\) | 31150.0 | + | 30520.6i | 0.328365 | + | 0.321731i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −12900.0 | − | 63196.8i | −0.134235 | − | 0.657615i | ||||
\(311\) | − | 50435.0i | − | 0.521448i | −0.965413 | − | 0.260724i | \(-0.916039\pi\) | ||
0.965413 | − | 0.260724i | \(-0.0839613\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −68155.0 | −0.695679 | −0.347840 | − | 0.937554i | \(-0.613085\pi\) | ||||
−0.347840 | + | 0.937554i | \(0.613085\pi\) | |||||||
\(314\) | 63172.3i | 0.640719i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 55610.0 | 0.556902 | ||||||||
\(317\) | − | 42435.0i | − | 0.422285i | −0.977455 | − | 0.211142i | \(-0.932282\pi\) | ||
0.977455 | − | 0.211142i | \(-0.0677184\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 16999.0 | 0.167048 | ||||||||
\(320\) | −12280.0 | − | 60159.5i | −0.119922 | − | 0.587495i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −60060.0 | − | 58846.5i | −0.579260 | − | 0.567557i | ||||
\(323\) | 106920.i | 1.02484i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2875.00 | + | 1224.74i | −0.0272189 | + | 0.0115952i | ||||
\(326\) | −91008.0 | −0.856336 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −185640. | −1.72554 | ||||||||
\(329\) | 76825.0 | + | 75272.8i | 0.709759 | + | 0.695419i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −114706. | −1.04696 | −0.523480 | − | 0.852038i | \(-0.675367\pi\) | ||||
−0.523480 | + | 0.852038i | \(0.675367\pi\) | |||||||
\(332\) | 19900.0 | 0.180541 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 50937.1i | − | 0.456606i | ||||||
\(335\) | 50160.0 | − | 10238.9i | 0.446959 | − | 0.0912352i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 117007.i | − | 1.03027i | −0.857108 | − | 0.515137i | \(-0.827741\pi\) | ||
0.857108 | − | 0.515137i | \(-0.172259\pi\) | |||||||
\(338\) | − | 69898.6i | − | 0.611836i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −24250.0 | − | 118800.i | −0.209775 | − | 1.02768i | ||||
\(341\) | − | 93742.0i | − | 0.806168i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 80605.0 | − | 85697.8i | 0.685131 | − | 0.728420i | ||||
\(344\) | 24024.0 | 0.203015 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 281.691i | 0.00235300i | ||||||||
\(347\) | − | 70481.6i | − | 0.585352i | −0.956212 | − | 0.292676i | \(-0.905454\pi\) | ||
0.956212 | − | 0.292676i | \(-0.0945457\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 91390.5i | 0.750326i | 0.926959 | + | 0.375163i | \(0.122413\pi\) | ||||
−0.926959 | + | 0.375163i | \(0.877587\pi\) | |||||||
\(350\) | −27300.0 | + | 69871.7i | −0.222857 | + | 0.570381i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 91561.9i | − | 0.738975i | ||||||
\(353\) | −11405.0 | −0.0915263 | −0.0457631 | − | 0.998952i | \(-0.514572\pi\) | ||||
−0.0457631 | + | 0.998952i | \(0.514572\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −22270.0 | − | 109100.i | −0.176711 | − | 0.865703i | ||||
\(356\) | − | 8083.32i | − | 0.0637807i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 13026.4i | − | 0.101638i | ||||||
\(359\) | −230366. | −1.78743 | −0.893716 | − | 0.448633i | \(-0.851911\pi\) | ||||
−0.893716 | + | 0.448633i | \(0.851911\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 81721.0 | 0.627075 | ||||||||
\(362\) | −30240.0 | −0.230762 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1750.00 | − | 1714.64i | −0.0132079 | − | 0.0129411i | ||||
\(365\) | −43250.0 | − | 211881.i | −0.324639 | − | 1.59040i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −74485.0 | −0.553015 | −0.276507 | − | 0.961012i | \(-0.589177\pi\) | ||||
−0.276507 | + | 0.961012i | \(0.589177\pi\) | |||||||
\(368\) | − | 2802.22i | − | 0.0206922i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 19980.0 | + | 97881.6i | 0.145946 | + | 0.714986i | ||||
\(371\) | −54432.0 | + | 55554.4i | −0.395464 | + | 0.403618i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 102550.i | 0.737088i | 0.929610 | + | 0.368544i | \(0.120144\pi\) | ||||
−0.929610 | + | 0.368544i | \(0.879856\pi\) | |||||||
\(374\) | 105732.i | 0.755900i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 139792.i | − | 0.988799i | ||||||
\(377\) | −955.000 | −0.00671925 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −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 | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 34937.1i | 0.239420i | ||||||||
\(383\) | −144050. | −0.982010 | −0.491005 | − | 0.871157i | \(-0.663370\pi\) | ||||
−0.491005 | + | 0.871157i | \(0.663370\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −59185.0 | + | 91561.9i | −0.399292 | + | 0.617723i | ||||
\(386\) | −78396.0 | −0.526162 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −92350.0 | −0.613442 | ||||||||
\(389\) | 148969. | 0.984457 | 0.492228 | − | 0.870466i | \(-0.336182\pi\) | ||||
0.492228 | + | 0.870466i | \(0.336182\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 339769.i | 2.22244i | ||||||||
\(392\) | −152880. | + | 3120.65i | −0.994898 | + | 0.0203083i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −8316.00 | −0.0535700 | ||||||||
\(395\) | 27805.0 | + | 136216.i | 0.178209 | + | 0.873040i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 256925. | 1.63014 | 0.815071 | − | 0.579361i | \(-0.196698\pi\) | ||||
0.815071 | + | 0.579361i | \(0.196698\pi\) | |||||||
\(398\) | −47520.0 | −0.299992 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2300.00 | + | 979.796i | −0.0143750 | + | 0.00612372i | ||||
\(401\) | 35641.0 | 0.221647 | 0.110823 | − | 0.993840i | \(-0.464651\pi\) | ||||
0.110823 | + | 0.993840i | \(0.464651\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5266.40i | 0.0324268i | ||||||||
\(404\) | − | 48254.9i | − | 0.295651i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −16044.0 | + | 16374.8i | −0.0973331 | + | 0.0993402i | ||||
\(407\) | 145191.i | 0.876498i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 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 | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 47150.0 | 0.277771 | ||||||||
\(413\) | −124320. | + | 126884.i | −0.728855 | + | 0.743884i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9950.00 | + | 48744.8i | 0.0577733 | + | 0.283030i | ||||
\(416\) | 5143.93i | 0.0297241i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −48060.0 | −0.275062 | ||||||||
\(419\) | − | 150889.i | − | 0.859465i | −0.902956 | − | 0.429733i | \(-0.858608\pi\) | ||
0.902956 | − | 0.429733i | \(-0.141392\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4681.00 | −0.0264104 | −0.0132052 | − | 0.999913i | \(-0.504203\pi\) | ||||
−0.0132052 | + | 0.999913i | \(0.504203\pi\) | |||||||
\(422\) | 129375.i | 0.726481i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 101088. | 0.562300 | ||||||||
\(425\) | 278875. | − | 118800.i | 1.54394 | − | 0.657718i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −66360.0 | + | 67728.4i | −0.363957 | + | 0.371463i | ||||
\(428\) | − | 126688.i | − | 0.691587i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4620.00 | + | 22633.3i | 0.0249865 | + | 0.122408i | ||||
\(431\) | 87103.0 | 0.468898 | 0.234449 | − | 0.972128i | \(-0.424671\pi\) | ||||
0.234449 | + | 0.972128i | \(0.424671\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −231730. | −1.23597 | −0.617983 | − | 0.786192i | \(-0.712050\pi\) | ||||
−0.617983 | + | 0.786192i | \(0.712050\pi\) | |||||||
\(434\) | 90300.0 | + | 88475.6i | 0.479411 | + | 0.469725i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 123110. | 0.647620 | ||||||||
\(437\) | −154440. | −0.808718 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 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 | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 5940.01i | − | 0.0304048i | ||||||
\(443\) | 349841.i | 1.78264i | 0.453376 | + | 0.891319i | \(0.350219\pi\) | ||||
−0.453376 | + | 0.891319i | \(0.649781\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 19800.0 | − | 4041.66i | 0.0999874 | − | 0.0204098i | ||||
\(446\) | − | 33423.3i | − | 0.168027i | ||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 85960.0 | + | 84223.3i | 0.428292 | + | 0.419639i | ||||
\(449\) | −254711. | −1.26344 | −0.631721 | − | 0.775196i | \(-0.717651\pi\) | ||||
−0.631721 | + | 0.775196i | \(0.717651\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 259425.i | − | 1.27544i | ||||||
\(452\) | 31206.5i | 0.152745i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 182450.i | 0.885182i | ||||||||
\(455\) | 3325.00 | − | 5143.93i | 0.0160609 | − | 0.0248469i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 263629.i | − | 1.26229i | −0.775663 | − | 0.631147i | \(-0.782585\pi\) | ||
0.775663 | − | 0.631147i | \(-0.217415\pi\) | |||||||
\(458\) | 167700. | 0.799470 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 171600. | − | 35027.7i | 0.810964 | − | 0.165537i | ||||
\(461\) | 128255.i | 0.603495i | 0.953388 | + | 0.301747i | \(0.0975699\pi\) | ||||
−0.953388 | + | 0.301747i | \(0.902430\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 81857.0i | 0.381851i | 0.981605 | + | 0.190926i | \(0.0611489\pi\) | ||||
−0.981605 | + | 0.190926i | \(0.938851\pi\) | |||||||
\(464\) | −764.000 | −0.00354860 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −147384. | −0.678701 | ||||||||
\(467\) | 204445. | 0.937438 | 0.468719 | − | 0.883347i | \(-0.344716\pi\) | ||||
0.468719 | + | 0.883347i | \(0.344716\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −70224.0 | + | 71672.1i | −0.319257 | + | 0.325840i | ||||
\(470\) | 131700. | − | 26883.1i | 0.596197 | − | 0.121698i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 230880. | 1.03634 | ||||||||
\(473\) | 33572.7i | 0.150060i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 54000.0 | + | 126761.i | 0.239335 | + | 0.561822i | ||||
\(476\) | 169750. | + | 166320.i | 0.749197 | + | 0.734060i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 184611.i | 0.807981i | ||||||||
\(479\) | 79534.9i | 0.346647i | 0.984865 | + | 0.173323i | \(0.0554505\pi\) | ||||
−0.984865 | + | 0.173323i | \(0.944549\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 8156.80i | − | 0.0352557i | ||||||
\(482\) | −190740. | −0.821009 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −67200.0 | −0.286866 | ||||||||
\(485\) | −46175.0 | − | 226210.i | −0.196301 | − | 0.961677i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 164958.i | 0.695531i | 0.937582 | + | 0.347766i | \(0.113059\pi\) | ||||
−0.937582 | + | 0.347766i | \(0.886941\pi\) | |||||||
\(488\) | 123240. | 0.517502 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −32340.0 | − | 143430.i | −0.134694 | − | 0.597376i | ||||
\(491\) | 74191.0 | 0.307743 | 0.153872 | − | 0.988091i | \(-0.450826\pi\) | ||||
0.153872 | + | 0.988091i | \(0.450826\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 92635.0 | 0.381137 | ||||||||
\(494\) | 2700.00 | 0.0110639 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4213.12i | 0.0171254i | ||||||||
\(497\) | 155890. | + | 152740.i | 0.631111 | + | 0.618360i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −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 | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −123480. | −0.489992 | ||||||||
\(503\) | −60275.0 | −0.238233 | −0.119116 | − | 0.992880i | \(-0.538006\pi\) | ||||
−0.119116 | + | 0.992880i | \(0.538006\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 118200. | − | 24127.5i | 0.463484 | − | 0.0946083i | ||||
\(506\) | −152724. | −0.596494 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 238678.i | 0.924880i | ||||||||
\(509\) | − | 348709.i | − | 1.34595i | −0.739666 | − | 0.672974i | \(-0.765017\pi\) | ||
0.739666 | − | 0.672974i | \(-0.234983\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 302750. | + | 296633.i | 1.15942 | + | 1.13600i | ||||
\(512\) | 8191.09i | 0.0312465i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 8254.78i | 0.0312449i | ||||||||
\(515\) | 23575.0 | + | 115493.i | 0.0888868 | + | 0.435455i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 195355. | 0.730876 | ||||||||
\(518\) | −139860. | − | 137034.i | −0.521236 | − | 0.510704i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −7800.00 | + | 1592.17i | −0.0288462 | + | 0.00588820i | ||||
\(521\) | − | 84727.9i | − | 0.312141i | −0.987746 | − | 0.156070i | \(-0.950117\pi\) | ||
0.987746 | − | 0.156070i | \(-0.0498827\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 235610. | 0.861371 | 0.430686 | − | 0.902502i | \(-0.358272\pi\) | ||||
0.430686 | + | 0.902502i | \(0.358272\pi\) | |||||||
\(524\) | 67361.0i | 0.245327i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −145464. | −0.525756 | ||||||||
\(527\) | − | 510841.i | − | 1.83935i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −210935. | −0.753767 | ||||||||
\(530\) | 19440.0 | + | 95236.2i | 0.0692061 | + | 0.339039i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −75600.0 | + | 77158.9i | −0.267115 | + | 0.272623i | ||||
\(533\) | 14574.5i | 0.0513025i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 310320. | − | 63343.8i | 1.08418 | − | 0.221308i | ||||
\(536\) | 130416. | 0.453943 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 188640. | 0.651732 | ||||||||
\(539\) | −4361.00 | − | 213644.i | −0.0150110 | − | 0.735384i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 259199. | 0.885602 | 0.442801 | − | 0.896620i | \(-0.353985\pi\) | ||||
0.442801 | + | 0.896620i | \(0.353985\pi\) | |||||||
\(542\) | 350820. | 1.19422 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 498961.i | − | 1.68604i | ||||||
\(545\) | 61555.0 | + | 301557.i | 0.207238 | + | 1.01526i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 423894.i | 1.41672i | 0.705854 | + | 0.708358i | \(0.250564\pi\) | ||||
−0.705854 | + | 0.708358i | \(0.749436\pi\) | |||||||
\(548\) | 230693.i | 0.768198i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 53400.0 | + | 125353.i | 0.176529 | + | 0.414389i | ||||
\(551\) | 42106.7i | 0.138691i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −194635. | − | 190703.i | −0.636459 | − | 0.623600i | ||||
\(554\) | −249672. | −0.813486 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 294919.i | 0.954009i | ||||||||
\(557\) | 133389.i | 0.429943i | 0.976620 | + | 0.214972i | \(0.0689659\pi\) | ||||
−0.976620 | + | 0.214972i | \(0.931034\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 1886.11i | − | 0.00603591i | ||||||
\(560\) | 2660.00 | − | 4115.14i | 0.00848214 | − | 0.0131223i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 116402.i | 0.368543i | ||||||||
\(563\) | −369770. | −1.16658 | −0.583290 | − | 0.812264i | \(-0.698235\pi\) | ||||
−0.583290 | + | 0.812264i | \(0.698235\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −76440.0 | + | 15603.2i | −0.239455 | + | 0.0488785i | ||||
\(566\) | 105610.i | 0.329664i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 283661.i | − | 0.879230i | ||||||
\(569\) | 326134. | 1.00733 | 0.503665 | − | 0.863899i | \(-0.331985\pi\) | ||||
0.503665 | + | 0.863899i | \(0.331985\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 306374. | 0.939679 | 0.469840 | − | 0.882752i | \(-0.344312\pi\) | ||||
0.469840 | + | 0.882752i | \(0.344312\pi\) | |||||||
\(572\) | −4450.00 | −0.0136009 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 249900. | + | 244851.i | 0.758477 | + | 0.743153i | ||||
\(575\) | 171600. | + | 402819.i | 0.519017 | + | 1.21835i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −387595. | −1.16420 | −0.582099 | − | 0.813118i | \(-0.697768\pi\) | ||||
−0.582099 | + | 0.813118i | \(0.697768\pi\) | |||||||
\(578\) | 371597.i | 1.11229i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −9550.00 | − | 46785.3i | −0.0283888 | − | 0.139076i | ||||
\(581\) | −69650.0 | − | 68242.8i | −0.206333 | − | 0.202164i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 141267.i | 0.415627i | ||||||||
\(584\) | − | 550890.i | − | 1.61525i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 397124.i | − | 1.15646i | ||||||
\(587\) | 467350. | 1.35633 | 0.678166 | − | 0.734909i | \(-0.262775\pi\) | ||||
0.678166 | + | 0.734909i | \(0.262775\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 232200. | 0.669317 | ||||||||
\(590\) | 44400.0 | + | 217515.i | 0.127550 | + | 0.624863i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 6525.44i | − | 0.0186194i | ||||||
\(593\) | 214315. | 0.609457 | 0.304729 | − | 0.952439i | \(-0.401434\pi\) | ||||
0.304729 | + | 0.952439i | \(0.401434\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −322525. | + | 498961.i | −0.911023 | + | 1.40939i | ||||
\(596\) | −283460. | −0.797993 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 8580.00 | 0.0239930 | ||||||||
\(599\) | 283999. | 0.791522 | 0.395761 | − | 0.918353i | \(-0.370481\pi\) | ||||
0.395761 | + | 0.918353i | \(0.370481\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 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 | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −175510. | −0.481092 | ||||||||
\(605\) | −33600.0 | − | 164606.i | −0.0917970 | − | 0.449712i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 193715. | 0.525758 | 0.262879 | − | 0.964829i | \(-0.415328\pi\) | ||||
0.262879 | + | 0.964829i | \(0.415328\pi\) | |||||||
\(608\) | 226800. | 0.613530 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 23700.0 | + | 116106.i | 0.0636926 | + | 0.312029i | ||||
\(611\) | −10975.0 | −0.0293983 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 296231.i | 0.788334i | 0.919039 | + | 0.394167i | \(0.128967\pi\) | ||||
−0.919039 | + | 0.394167i | \(0.871033\pi\) | |||||||
\(614\) | − | 82805.0i | − | 0.219644i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −194376. | + | 198384.i | −0.512249 | + | 0.522812i | ||||
\(617\) | − | 424751.i | − | 1.11574i | −0.829927 | − | 0.557872i | \(-0.811618\pi\) | ||
0.829927 | − | 0.557872i | \(-0.188382\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 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 | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 123540. | 0.319321 | ||||||||
\(623\) | −27720.0 | + | 28291.6i | −0.0714196 | + | 0.0728923i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 270625. | − | 281691.i | 0.692800 | − | 0.721130i | ||||
\(626\) | − | 166945.i | − | 0.426015i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 257900. | 0.653931 | ||||||||
\(629\) | 791210.i | 1.99982i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −471511. | −1.18422 | −0.592111 | − | 0.805856i | \(-0.701705\pi\) | ||||
−0.592111 | + | 0.805856i | \(0.701705\pi\) | |||||||
\(632\) | 354162.i | 0.886682i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 103944. | 0.258595 | ||||||||
\(635\) | −584640. | + | 119339.i | −1.44991 | + | 0.295962i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 245.000 | + | 12002.5i | 0.000603792 | + | 0.0295796i | ||||
\(638\) | 41638.9i | 0.102296i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −255840. | + | 52223.1i | −0.624609 | + | 0.127498i | ||||
\(641\) | −558794. | −1.35999 | −0.679995 | − | 0.733217i | \(-0.738018\pi\) | ||||
−0.679995 | + | 0.733217i | \(0.738018\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 454235. | 1.09865 | 0.549324 | − | 0.835609i | \(-0.314885\pi\) | ||||
0.549324 | + | 0.835609i | \(0.314885\pi\) | |||||||
\(644\) | −240240. | + | 245194.i | −0.579260 | + | 0.591205i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −261900. | −0.627582 | ||||||||
\(647\) | −129530. | −0.309430 | −0.154715 | − | 0.987959i | \(-0.549446\pi\) | ||||
−0.154715 | + | 0.987959i | \(0.549446\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 322647.i | 0.766016i | ||||||||
\(650\) | −3000.00 | − | 7042.28i | −0.00710059 | − | 0.0166681i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 371539.i | 0.873995i | ||||||||
\(653\) | − | 343903.i | − | 0.806511i | −0.915087 | − | 0.403255i | \(-0.867879\pi\) | ||
0.915087 | − | 0.403255i | \(-0.132121\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −165000. | + | 33680.5i | −0.384593 | + | 0.0785047i | ||||
\(656\) | 11659.6i | 0.0270941i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −184380. | + | 188182.i | −0.425855 | + | 0.434637i | ||||
\(659\) | −526913. | −1.21330 | −0.606650 | − | 0.794969i | \(-0.707487\pi\) | ||||
−0.606650 | + | 0.794969i | \(0.707487\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 191844.i | − | 0.439082i | −0.975603 | − | 0.219541i | \(-0.929544\pi\) | ||
0.975603 | − | 0.219541i | \(-0.0704559\pi\) | |||||||
\(662\) | − | 280971.i | − | 0.641130i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 126737.i | 0.287452i | ||||||||
\(665\) | −226800. | − | 146602.i | −0.512861 | − | 0.331510i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 133806.i | 0.300762i | ||||||||
\(668\) | −207950. | −0.466022 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 25080.0 | + | 122866.i | 0.0558699 | + | 0.273706i | ||||
\(671\) | 172224.i | 0.382514i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 429792.i | − | 0.948918i | −0.880278 | − | 0.474459i | \(-0.842644\pi\) | ||
0.880278 | − | 0.474459i | \(-0.157356\pi\) | |||||||
\(674\) | 286608. | 0.630912 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −285360. | −0.624453 | ||||||||
\(677\) | −79685.0 | −0.173860 | −0.0869299 | − | 0.996214i | \(-0.527706\pi\) | ||||
−0.0869299 | + | 0.996214i | \(0.527706\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 323225. | + | 316695.i | 0.701076 | + | 0.686912i | ||||
\(680\) | 756600. | − | 154440.i | 1.63625 | − | 0.333997i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 229620. | 0.493675 | ||||||||
\(683\) | − | 719577.i | − | 1.54254i | −0.636510 | − | 0.771269i | \(-0.719622\pi\) | ||
0.636510 | − | 0.771269i | \(-0.280378\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −565080. | + | 115346.i | −1.20428 | + | 0.245823i | ||||
\(686\) | 209916. | + | 197441.i | 0.446064 | + | 0.419555i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 1508.89i | − | 0.00318771i | ||||||
\(689\) | − | 7936.35i | − | 0.0167179i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 398532.i | − | 0.834655i | −0.908756 | − | 0.417328i | \(-0.862967\pi\) | ||
0.908756 | − | 0.417328i | \(-0.137033\pi\) | |||||||
\(692\) | 1150.00 | 0.00240152 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 172644. | 0.358453 | ||||||||
\(695\) | −722400. | + | 147459.i | −1.49557 | + | 0.305283i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 1.41372e6i | − | 2.91004i | ||||||
\(698\) | −223860. | −0.459479 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 285250. | + | 111452.i | 0.582143 | + | 0.227453i | ||||
\(701\) | 658873. | 1.34081 | 0.670403 | − | 0.741998i | \(-0.266121\pi\) | ||||
0.670403 | + | 0.741998i | \(0.266121\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −359640. | −0.727708 | ||||||||
\(704\) | 218584. | 0.441035 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 27936.4i | − | 0.0560482i | ||||||
\(707\) | −165480. | + | 168892.i | −0.331060 | + | 0.337887i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −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 | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 51480.0 | 0.101550 | ||||||||
\(713\) | 737880. | 1.45147 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2225.00 | − | 10900.2i | −0.00435229 | − | 0.0213218i | ||||
\(716\) | −53180.0 | −0.103734 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 564279.i | − | 1.09457i | ||||||
\(719\) | 75321.8i | 0.145701i | 0.997343 | + | 0.0728506i | \(0.0232096\pi\) | ||||
−0.997343 | + | 0.0728506i | \(0.976790\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −165025. | − | 161691.i | −0.317453 | − | 0.311039i | ||||
\(722\) | 200175.i | 0.384003i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 123454.i | 0.235521i | ||||||||
\(725\) | 109825. | − | 46785.3i | 0.208942 | − | 0.0890088i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −342190. | −0.647438 | −0.323719 | − | 0.946153i | \(-0.604933\pi\) | ||||
−0.323719 | + | 0.946153i | \(0.604933\pi\) | |||||||
\(728\) | 10920.0 | − | 11145.2i | 0.0206044 | − | 0.0210293i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 519000. | − | 105940.i | 0.973916 | − | 0.198800i | ||||
\(731\) | 182952.i | 0.342376i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −958555. | −1.78406 | −0.892029 | − | 0.451978i | \(-0.850719\pi\) | ||||
−0.892029 | + | 0.451978i | \(0.850719\pi\) | |||||||
\(734\) | − | 182450.i | − | 0.338651i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 720720. | 1.33049 | ||||||||
\(737\) | 182252.i | 0.335534i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −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 | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −136080. | − | 133331.i | −0.247165 | − | 0.242171i | ||||
\(743\) | − | 97803.2i | − | 0.177164i | −0.996069 | − | 0.0885820i | \(-0.971766\pi\) | ||
0.996069 | − | 0.0885820i | \(-0.0282335\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −141730. | − | 694332.i | −0.255358 | − | 1.25099i | ||||
\(746\) | −251196. | −0.451372 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 431650. | 0.771487 | ||||||||
\(749\) | −434448. | + | 443407.i | −0.774416 | + | 0.790385i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 246977. | 0.437902 | 0.218951 | − | 0.975736i | \(-0.429737\pi\) | ||||
0.218951 | + | 0.975736i | \(0.429737\pi\) | |||||||
\(752\) | −8780.00 | −0.0155260 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 2339.26i | − | 0.00411468i | ||||||
\(755\) | −87755.0 | − | 429910.i | −0.153949 | − | 0.754195i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 1.05636e6i | − | 1.84340i | −0.387906 | − | 0.921699i | \(-0.626802\pi\) | ||
0.387906 | − | 0.921699i | \(-0.373198\pi\) | |||||||
\(758\) | − | 423649.i | − | 0.737340i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 70200.0 | + | 343908.i | 0.121537 | + | 0.595409i | ||||
\(761\) | − | 406836.i | − | 0.702506i | −0.936281 | − | 0.351253i | \(-0.885756\pi\) | ||
0.936281 | − | 0.351253i | \(-0.114244\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −430885. | − | 422179.i | −0.740137 | − | 0.725184i | ||||
\(764\) | 142630. | 0.244357 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 352849.i | − | 0.601356i | ||||||
\(767\) | − | 18126.2i | − | 0.0308118i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 592238.i | 1.00148i | 0.865597 | + | 0.500741i | \(0.166939\pi\) | ||||
−0.865597 | + | 0.500741i | \(0.833061\pi\) | |||||||
\(770\) | −224280. | − | 144973.i | −0.378276 | − | 0.244515i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 320050.i | 0.537012i | ||||||||
\(773\) | −401165. | −0.671373 | −0.335687 | − | 0.941974i | \(-0.608968\pi\) | ||||
−0.335687 | + | 0.941974i | \(0.608968\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −258000. | − | 605636.i | −0.429553 | − | 1.00834i | ||||
\(776\) | − | 588147.i | − | 0.976703i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 364898.i | 0.602854i | ||||||||
\(779\) | 642600. | 1.05893 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 396406. | 0.649887 | ||||||||
\(782\) | −832260. | −1.36096 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 196.000 | + | 9602.00i | 0.000318878 | + | 0.0156217i | ||||
\(785\) | 128950. | + | 631723.i | 0.209258 | + | 1.02515i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −357565. | −0.577305 | −0.288653 | − | 0.957434i | \(-0.593207\pi\) | ||||
−0.288653 | + | 0.957434i | \(0.593207\pi\) | |||||||
\(788\) | 33949.9i | 0.0546747i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −333660. | + | 68108.1i | −0.534626 | + | 0.109130i | ||||
\(791\) | 107016. | − | 109223.i | 0.171039 | − | 0.174566i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 9675.48i | − | 0.0153860i | ||||||
\(794\) | 629335.i | 0.998254i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 194000.i | 0.306178i | ||||||||
\(797\) | −1.18188e6 | −1.86062 | −0.930312 | − | 0.366769i | \(-0.880464\pi\) | ||||
−0.930312 | + | 0.366769i | \(0.880464\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.06458e6 | 1.66756 | ||||||||
\(800\) | −252000. | − | 591552.i | −0.393750 | − | 0.924300i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 87302.3i | 0.135730i | ||||||||
\(803\) | 769850. | 1.19392 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −720720. | − | 465868.i | −1.11218 | − | 0.718905i | ||||
\(806\) | −12900.0 | −0.0198573 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 307320. | 0.470726 | ||||||||
\(809\) | 272449. | 0.416283 | 0.208141 | − | 0.978099i | \(-0.433259\pi\) | ||||
0.208141 | + | 0.978099i | \(0.433259\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 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 | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −355644. | −0.536743 | ||||||||
\(815\) | −910080. | + | 185769.i | −1.37014 | + | 0.279678i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −83160.0 | −0.124586 | ||||||||
\(818\) | 371640. | 0.555413 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −714000. | + | 145745.i | −1.06187 | + | 0.216753i | ||||
\(821\) | 621793. | 0.922485 | 0.461243 | − | 0.887274i | \(-0.347404\pi\) | ||||
0.461243 | + | 0.887274i | \(0.347404\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 117394.i | 0.173319i | 0.996238 | + | 0.0866597i | \(0.0276193\pi\) | ||||
−0.996238 | + | 0.0866597i | \(0.972381\pi\) | |||||||
\(824\) | 300283.i | 0.442259i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −310800. | − | 304521.i | −0.455534 | − | 0.446330i | ||||
\(827\) | − | 199790.i | − | 0.292121i | −0.989276 | − | 0.146061i | \(-0.953341\pi\) | ||
0.989276 | − | 0.146061i | \(-0.0466595\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 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 | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −12280.0 | −0.0177399 | ||||||||
\(833\) | −23765.0 | − | 1.16424e6i | −0.0342490 | − | 1.67785i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −103975. | − | 509371.i | −0.149127 | − | 0.730570i | ||||
\(836\) | 196204.i | 0.280734i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 369600. | 0.526313 | ||||||||
\(839\) | − | 826972.i | − | 1.17481i | −0.809294 | − | 0.587404i | \(-0.800150\pi\) | ||
0.809294 | − | 0.587404i | \(-0.199850\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −670800. | −0.948421 | ||||||||
\(842\) | − | 11466.1i | − | 0.0161730i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 528170. | 0.741462 | ||||||||
\(845\) | −142680. | − | 698986.i | −0.199825 | − | 0.978938i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 235200. | + | 230448.i | 0.327846 | + | 0.321223i | ||||
\(848\) | − | 6349.08i | − | 0.00882915i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 291000. | + | 683101.i | 0.402768 | + | 0.945469i | ||||
\(851\) | −1.14286e6 | −1.57809 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −385450. | −0.529749 | −0.264874 | − | 0.964283i | \(-0.585330\pi\) | ||||
−0.264874 | + | 0.964283i | \(0.585330\pi\) | |||||||
\(854\) | −165900. | − | 162548.i | −0.227473 | − | 0.222878i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 806832. | 1.10112 | ||||||||
\(857\) | −356750. | −0.485738 | −0.242869 | − | 0.970059i | \(-0.578089\pi\) | ||||
−0.242869 | + | 0.970059i | \(0.578089\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 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 | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 213358.i | 0.287140i | ||||||||
\(863\) | 151217.i | 0.203039i | 0.994834 | + | 0.101519i | \(0.0323704\pi\) | ||||
−0.994834 | + | 0.101519i | \(0.967630\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 575.000 | + | 2816.91i | 0.000768485 | + | 0.00376479i | ||||
\(866\) | − | 567620.i | − | 0.756871i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 361200. | − | 368648.i | 0.479411 | − | 0.489297i | ||||
\(869\) | −494929. | −0.655395 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 10238.9i | − | 0.0134963i | ||||||
\(872\) | 784047.i | 1.03112i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 378299.i | − | 0.495236i | ||||||
\(875\) | −130375. | + | 754443.i | −0.170286 | + | 0.985395i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 553981.i | 0.720271i | 0.932900 | + | 0.360136i | \(0.117270\pi\) | ||||
−0.932900 | + | 0.360136i | \(0.882730\pi\) | |||||||
\(878\) | 603240. | 0.782530 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1780.00 | − | 8720.18i | −0.00229855 | − | 0.0112606i | ||||
\(881\) | 531882.i | 0.685273i | 0.939468 | + | 0.342637i | \(0.111320\pi\) | ||||
−0.939468 | + | 0.342637i | \(0.888680\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 606675.i | − | 0.778099i | −0.921217 | − | 0.389049i | \(-0.872804\pi\) | ||
0.921217 | − | 0.389049i | \(-0.127196\pi\) | |||||||
\(884\) | −24250.0 | −0.0310318 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −856932. | −1.09164 | ||||||||
\(887\) | 1.35703e6 | 1.72481 | 0.862407 | − | 0.506216i | \(-0.168956\pi\) | ||||
0.862407 | + | 0.506216i | \(0.168956\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 818496. | − | 835374.i | 1.03565 | − | 1.05701i | ||||
\(890\) | 9900.00 | + | 48499.9i | 0.0124984 | + | 0.0612295i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −136450. | −0.171492 | ||||||||
\(893\) | 483897.i | 0.606806i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −26590.0 | − | 130264.i | −0.0331950 | − | 0.162621i | ||||
\(896\) | 358176. | − | 365562.i | 0.446150 | − | 0.455349i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 623912.i | − | 0.773697i | ||||||
\(899\) | − | 201177.i | − | 0.248919i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 769826.i | 0.948294i | ||||||||
\(902\) | 635460. | 0.781043 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −198744. | −0.243196 | ||||||||
\(905\) | −302400. | + | 61727.1i | −0.369219 | + | 0.0753666i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 452230.i | 0.549724i | 0.961484 | + | 0.274862i | \(0.0886321\pi\) | ||||
−0.961484 | + | 0.274862i | \(0.911368\pi\) | |||||||
\(908\) | 744850. | 0.903435 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 12600.0 | + | 8144.55i | 0.0152156 | + | 0.00983523i | ||||
\(911\) | 948106. | 1.14241 | 0.571203 | − | 0.820809i | \(-0.306477\pi\) | ||||
0.571203 | + | 0.820809i | \(0.306477\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −177110. | −0.212472 | ||||||||
\(914\) | 645756. | 0.772994 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 684632.i | − | 0.815956i | ||||||
\(917\) | 231000. | − | 235763.i | 0.274709 | − | 0.280374i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 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 | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −314160. | −0.369563 | ||||||||
\(923\) | −22270.0 | −0.0261407 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 399600. | + | 938032.i | 0.467027 | + | 1.09631i | ||||
\(926\) | −200508. | −0.233835 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 196498.i | − | 0.228172i | ||||||
\(929\) | − | 139523.i | − | 0.161664i | −0.996728 | − | 0.0808322i | \(-0.974242\pi\) | ||
0.996728 | − | 0.0808322i | \(-0.0257578\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 529200. | − | 10802.2i | 0.610549 | − | 0.0124628i | ||||
\(932\) | 601693.i | 0.692696i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 500786.i | 0.574061i | ||||||||
\(935\) | 215825. | + | 1.05732e6i | 0.246876 | + | 1.20944i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 434285. | 0.494647 | 0.247324 | − | 0.968933i | \(-0.420449\pi\) | ||||
0.247324 | + | 0.968933i | \(0.420449\pi\) | |||||||
\(938\) | −175560. | − | 172013.i | −0.199535 | − | 0.195504i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −109750. | − | 537663.i | −0.124208 | − | 0.608491i | ||||
\(941\) | − | 539108.i | − | 0.608831i | −0.952539 | − | 0.304415i | \(-0.901539\pi\) | ||
0.952539 | − | 0.304415i | \(-0.0984611\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.04204e6 | 2.29636 | ||||||||
\(944\) | − | 14501.0i | − | 0.0162725i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −82236.0 | −0.0918924 | ||||||||
\(947\) | 167540.i | 0.186818i | 0.995628 | + | 0.0934091i | \(0.0297764\pi\) | ||||
−0.995628 | + | 0.0934091i | \(0.970224\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −43250.0 | −0.0480235 | ||||||||
\(950\) | −310500. | + | 132272.i | −0.344044 | + | 0.146562i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.05924e6 | + | 1.08108e6i | −1.16875 | + | 1.19285i | ||||
\(953\) | − | 1.31304e6i | − | 1.44575i | −0.690981 | − | 0.722873i | \(-0.742821\pi\) | ||
0.690981 | − | 0.722873i | \(-0.257179\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 71315.0 | + | 349371.i | 0.0781941 | + | 0.383071i | ||||
\(956\) | 753670. | 0.824642 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −194820. | −0.212277 | ||||||||
\(959\) | 791112. | − | 807425.i | 0.860203 | − | 0.877941i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −185879. | −0.201272 | ||||||||
\(962\) | 19980.0 | 0.0215896 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 778693.i | 0.837938i | ||||||||
\(965\) | −783960. | + | 160025.i | −0.841859 | + | 0.171844i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 338745.i | 0.362259i | 0.983459 | + | 0.181130i | \(0.0579754\pi\) | ||||
−0.983459 | + | 0.181130i | \(0.942025\pi\) | |||||||
\(968\) | − | 427975.i | − | 0.456738i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 554100. | − | 113105.i | 0.588904 | − | 0.120210i | ||||
\(971\) | 1.60718e6i | 1.70462i | 0.523039 | + | 0.852309i | \(0.324798\pi\) | ||||
−0.523039 | + | 0.852309i | \(0.675202\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.01136e6 | − | 1.03221e6i | 1.06827 | − | 1.09030i | ||||
\(974\) | −404064. | −0.425924 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 7740.39i | − | 0.00812574i | ||||||
\(977\) | − | 1.40070e6i | − | 1.46743i | −0.679459 | − | 0.733713i | \(-0.737785\pi\) | ||
0.679459 | − | 0.733713i | \(-0.262215\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 71941.5i | 0.0750610i | ||||||||
\(980\) | −585550. | + | 132027.i | −0.609694 | + | 0.137471i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 181730.i | 0.188453i | ||||||||
\(983\) | 1.73768e6 | 1.79831 | 0.899154 | − | 0.437633i | \(-0.144183\pi\) | ||||
0.899154 | + | 0.437633i | \(0.144183\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −83160.0 | + | 16975.0i | −0.0857121 | + | 0.0174959i | ||||
\(986\) | 226908.i | 0.233398i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 11022.7i | − | 0.0112921i | ||||||
\(989\) | −264264. | −0.270175 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −423586. | −0.431315 | −0.215657 | − | 0.976469i | \(-0.569189\pi\) | ||||
−0.215657 | + | 0.976469i | \(0.569189\pi\) | |||||||
\(992\) | −1.08360e6 | −1.10115 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −374136. | + | 381851.i | −0.378666 | + | 0.386475i | ||||
\(995\) | −475200. | + | 96999.8i | −0.479988 | + | 0.0979771i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −548035. | −0.551338 | −0.275669 | − | 0.961253i | \(-0.588899\pi\) | ||||
−0.275669 | + | 0.961253i | \(0.588899\pi\) | |||||||
\(998\) | − | 682249.i | − | 0.684986i | ||||||
\(999\) | 0 | 0 |
(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 | 315.5.e.d.244.2 | 2 | ||
3.2 | odd | 2 | 35.5.c.c.34.1 | ✓ | 2 | ||
5.4 | even | 2 | 315.5.e.c.244.1 | 2 | |||
7.6 | odd | 2 | 315.5.e.c.244.2 | 2 | |||
12.11 | even | 2 | 560.5.p.e.209.1 | 2 | |||
15.2 | even | 4 | 175.5.d.e.76.4 | 4 | |||
15.8 | even | 4 | 175.5.d.e.76.1 | 4 | |||
15.14 | odd | 2 | 35.5.c.d.34.2 | yes | 2 | ||
21.20 | even | 2 | 35.5.c.d.34.1 | yes | 2 | ||
35.34 | odd | 2 | inner | 315.5.e.d.244.1 | 2 | ||
60.59 | even | 2 | 560.5.p.d.209.1 | 2 | |||
84.83 | odd | 2 | 560.5.p.d.209.2 | 2 | |||
105.62 | odd | 4 | 175.5.d.e.76.3 | 4 | |||
105.83 | odd | 4 | 175.5.d.e.76.2 | 4 | |||
105.104 | even | 2 | 35.5.c.c.34.2 | yes | 2 | ||
420.419 | odd | 2 | 560.5.p.e.209.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.5.c.c.34.1 | ✓ | 2 | 3.2 | odd | 2 | ||
35.5.c.c.34.2 | yes | 2 | 105.104 | even | 2 | ||
35.5.c.d.34.1 | yes | 2 | 21.20 | even | 2 | ||
35.5.c.d.34.2 | yes | 2 | 15.14 | odd | 2 | ||
175.5.d.e.76.1 | 4 | 15.8 | even | 4 | |||
175.5.d.e.76.2 | 4 | 105.83 | odd | 4 | |||
175.5.d.e.76.3 | 4 | 105.62 | odd | 4 | |||
175.5.d.e.76.4 | 4 | 15.2 | even | 4 | |||
315.5.e.c.244.1 | 2 | 5.4 | even | 2 | |||
315.5.e.c.244.2 | 2 | 7.6 | odd | 2 | |||
315.5.e.d.244.1 | 2 | 35.34 | odd | 2 | inner | ||
315.5.e.d.244.2 | 2 | 1.1 | even | 1 | trivial | ||
560.5.p.d.209.1 | 2 | 60.59 | even | 2 | |||
560.5.p.d.209.2 | 2 | 84.83 | odd | 2 | |||
560.5.p.e.209.1 | 2 | 12.11 | even | 2 | |||
560.5.p.e.209.2 | 2 | 420.419 | odd | 2 |