Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [175,5,Mod(76,175)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(175, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("175.76");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 175 = 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 175.d (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: | \(18.0897435397\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2\cdot 5^{2} \) |
Twist minimal: | no (minimal twist has level 35) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 76.3 | ||
Root | \(-1.22474 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 175.76 |
Dual form | 175.5.d.e.76.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/175\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.44949 | 0.612372 | 0.306186 | − | 0.951972i | \(-0.400947\pi\) | ||||
0.306186 | + | 0.951972i | \(0.400947\pi\) | |||||||
\(3\) | − | 5.00000i | − | 0.555556i | −0.960645 | − | 0.277778i | \(-0.910402\pi\) | ||
0.960645 | − | 0.277778i | \(-0.0895979\pi\) | |||||||
\(4\) | −10.0000 | −0.625000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | − | 12.2474i | − | 0.340207i | ||||||
\(7\) | 34.2929 | + | 35.0000i | 0.699854 | + | 0.714286i | ||||
\(8\) | −63.6867 | −0.995105 | ||||||||
\(9\) | 56.0000 | 0.691358 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 89.0000 | 0.735537 | 0.367769 | − | 0.929917i | \(-0.380122\pi\) | ||||
0.367769 | + | 0.929917i | \(0.380122\pi\) | |||||||
\(12\) | 50.0000i | 0.347222i | ||||||||
\(13\) | 5.00000i | 0.0295858i | 0.999891 | + | 0.0147929i | \(0.00470890\pi\) | ||||
−0.999891 | + | 0.0147929i | \(0.995291\pi\) | |||||||
\(14\) | 84.0000 | + | 85.7321i | 0.428571 | + | 0.437409i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.0156250 | ||||||||
\(17\) | − | 485.000i | − | 1.67820i | −0.543977 | − | 0.839100i | \(-0.683082\pi\) | ||
0.543977 | − | 0.839100i | \(-0.316918\pi\) | |||||||
\(18\) | 137.171 | 0.423369 | ||||||||
\(19\) | − | 220.454i | − | 0.610676i | −0.952244 | − | 0.305338i | \(-0.901231\pi\) | ||
0.952244 | − | 0.305338i | \(-0.0987695\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 175.000 | − | 171.464i | 0.396825 | − | 0.388808i | ||||
\(22\) | 218.005 | 0.450423 | ||||||||
\(23\) | 700.554 | 1.32430 | 0.662149 | − | 0.749372i | \(-0.269644\pi\) | ||||
0.662149 | + | 0.749372i | \(0.269644\pi\) | |||||||
\(24\) | 318.434i | 0.552836i | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 12.2474i | 0.0181175i | ||||||||
\(27\) | − | 685.000i | − | 0.939643i | ||||||
\(28\) | −342.929 | − | 350.000i | −0.437409 | − | 0.446429i | ||||
\(29\) | −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 | \(-0.815385\pi\) | ||
0.836470 | − | 0.548013i | \(-0.184615\pi\) | |||||||
\(32\) | 1028.79 | 1.00467 | ||||||||
\(33\) | − | 445.000i | − | 0.408632i | ||||||
\(34\) | − | 1188.00i | − | 1.02768i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −560.000 | −0.432099 | ||||||||
\(37\) | 1631.36 | 1.19164 | 0.595822 | − | 0.803117i | \(-0.296826\pi\) | ||||
0.595822 | + | 0.803117i | \(0.296826\pi\) | |||||||
\(38\) | − | 540.000i | − | 0.373961i | ||||||
\(39\) | 25.0000 | 0.0164366 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2914.89i | 1.73402i | 0.498288 | + | 0.867012i | \(0.333962\pi\) | ||||
−0.498288 | + | 0.867012i | \(0.666038\pi\) | |||||||
\(42\) | 428.661 | − | 420.000i | 0.243005 | − | 0.238095i | ||||
\(43\) | −377.221 | −0.204014 | −0.102007 | − | 0.994784i | \(-0.532526\pi\) | ||||
−0.102007 | + | 0.994784i | \(0.532526\pi\) | |||||||
\(44\) | −890.000 | −0.459711 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1716.00 | 0.810964 | ||||||||
\(47\) | − | 2195.00i | − | 0.993662i | −0.867847 | − | 0.496831i | \(-0.834497\pi\) | ||
0.867847 | − | 0.496831i | \(-0.165503\pi\) | |||||||
\(48\) | − | 20.0000i | − | 0.00868056i | ||||||
\(49\) | −49.0000 | + | 2400.50i | −0.0204082 | + | 0.999792i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2425.00 | −0.932334 | ||||||||
\(52\) | − | 50.0000i | − | 0.0184911i | ||||||
\(53\) | 1587.27 | 0.565066 | 0.282533 | − | 0.959258i | \(-0.408825\pi\) | ||||
0.282533 | + | 0.959258i | \(0.408825\pi\) | |||||||
\(54\) | − | 1677.90i | − | 0.575412i | ||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2184.00 | − | 2229.04i | −0.696429 | − | 0.710789i | ||||
\(57\) | −1102.27 | −0.339265 | ||||||||
\(58\) | −467.853 | −0.139076 | ||||||||
\(59\) | 3625.24i | 1.04144i | 0.853728 | + | 0.520719i | \(0.174336\pi\) | ||||
−0.853728 | + | 0.520719i | \(0.825664\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1935.10i | 0.520048i | 0.965602 | + | 0.260024i | \(0.0837304\pi\) | ||||
−0.965602 | + | 0.260024i | \(0.916270\pi\) | |||||||
\(62\) | − | 2580.00i | − | 0.671176i | ||||||
\(63\) | 1920.40 | + | 1960.00i | 0.483850 | + | 0.493827i | ||||
\(64\) | 2456.00 | 0.599609 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | − | 1090.02i | − | 0.250235i | ||||||
\(67\) | 2047.77 | 0.456176 | 0.228088 | − | 0.973641i | \(-0.426753\pi\) | ||||
0.228088 | + | 0.973641i | \(0.426753\pi\) | |||||||
\(68\) | 4850.00i | 1.04888i | ||||||||
\(69\) | − | 3502.77i | − | 0.735722i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4454.00 | 0.883555 | 0.441777 | − | 0.897125i | \(-0.354348\pi\) | ||||
0.441777 | + | 0.897125i | \(0.354348\pi\) | |||||||
\(72\) | −3566.46 | −0.687974 | ||||||||
\(73\) | − | 8650.00i | − | 1.62319i | −0.584218 | − | 0.811597i | \(-0.698599\pi\) | ||
0.584218 | − | 0.811597i | \(-0.301401\pi\) | |||||||
\(74\) | 3996.00 | 0.729730 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2204.54i | 0.381673i | ||||||||
\(77\) | 3052.06 | + | 3115.00i | 0.514769 | + | 0.525384i | ||||
\(78\) | 61.2372 | 0.0100653 | ||||||||
\(79\) | −5561.00 | −0.891043 | −0.445522 | − | 0.895271i | \(-0.646982\pi\) | ||||
−0.445522 | + | 0.895271i | \(0.646982\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1111.00 | 0.169334 | ||||||||
\(82\) | 7140.00i | 1.06187i | ||||||||
\(83\) | − | 1990.00i | − | 0.288866i | −0.989515 | − | 0.144433i | \(-0.953864\pi\) | ||
0.989515 | − | 0.144433i | \(-0.0461359\pi\) | |||||||
\(84\) | −1750.00 | + | 1714.64i | −0.248016 | + | 0.243005i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −924.000 | −0.124932 | ||||||||
\(87\) | 955.000i | 0.126173i | ||||||||
\(88\) | −5668.12 | −0.731937 | ||||||||
\(89\) | 808.332i | 0.102049i | 0.998697 | + | 0.0510246i | \(0.0162487\pi\) | ||||
−0.998697 | + | 0.0510246i | \(0.983751\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −175.000 | + | 171.464i | −0.0211327 | + | 0.0207057i | ||||
\(92\) | −7005.54 | −0.827687 | ||||||||
\(93\) | −5266.40 | −0.608903 | ||||||||
\(94\) | − | 5376.63i | − | 0.608491i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | − | 5143.93i | − | 0.558152i | ||||||
\(97\) | 9235.00i | 0.981507i | 0.871298 | + | 0.490754i | \(0.163278\pi\) | ||||
−0.871298 | + | 0.490754i | \(0.836722\pi\) | |||||||
\(98\) | −120.025 | + | 5880.00i | −0.0124974 | + | 0.612245i | ||||
\(99\) | 4984.00 | 0.508520 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 4825.49i | − | 0.473041i | −0.971626 | − | 0.236521i | \(-0.923993\pi\) | ||
0.971626 | − | 0.236521i | \(-0.0760071\pi\) | |||||||
\(102\) | −5940.01 | −0.570935 | ||||||||
\(103\) | 4715.00i | 0.444434i | 0.974997 | + | 0.222217i | \(0.0713293\pi\) | ||||
−0.974997 | + | 0.222217i | \(0.928671\pi\) | |||||||
\(104\) | − | 318.434i | − | 0.0294410i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3888.00 | 0.346031 | ||||||||
\(107\) | −12668.8 | −1.10654 | −0.553269 | − | 0.833002i | \(-0.686620\pi\) | ||||
−0.553269 | + | 0.833002i | \(0.686620\pi\) | |||||||
\(108\) | 6850.00i | 0.587277i | ||||||||
\(109\) | −12311.0 | −1.03619 | −0.518096 | − | 0.855322i | \(-0.673359\pi\) | ||||
−0.518096 | + | 0.855322i | \(0.673359\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 8156.80i | − | 0.662024i | ||||||
\(112\) | 137.171 | + | 140.000i | 0.0109352 | + | 0.0111607i | ||||
\(113\) | −3120.65 | −0.244393 | −0.122196 | − | 0.992506i | \(-0.538994\pi\) | ||||
−0.122196 | + | 0.992506i | \(0.538994\pi\) | |||||||
\(114\) | −2700.00 | −0.207756 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1910.00 | 0.141944 | ||||||||
\(117\) | 280.000i | 0.0204544i | ||||||||
\(118\) | 8880.00i | 0.637748i | ||||||||
\(119\) | 16975.0 | − | 16632.0i | 1.19871 | − | 1.17450i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6720.00 | −0.458985 | ||||||||
\(122\) | 4740.00i | 0.318463i | ||||||||
\(123\) | 14574.5 | 0.963346 | ||||||||
\(124\) | 10532.8i | 0.685016i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 4704.00 | + | 4801.00i | 0.296296 | + | 0.302406i | ||||
\(127\) | −23867.8 | −1.47981 | −0.739904 | − | 0.672712i | \(-0.765129\pi\) | ||||
−0.739904 | + | 0.672712i | \(0.765129\pi\) | |||||||
\(128\) | −10444.6 | −0.637489 | ||||||||
\(129\) | 1886.11i | 0.113341i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6736.10i | 0.392524i | 0.980552 | + | 0.196262i | \(0.0628802\pi\) | ||||
−0.980552 | + | 0.196262i | \(0.937120\pi\) | |||||||
\(132\) | 4450.00i | 0.255395i | ||||||||
\(133\) | 7715.89 | − | 7560.00i | 0.436197 | − | 0.427384i | ||||
\(134\) | 5016.00 | 0.279350 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 30888.1i | 1.66999i | ||||||||
\(137\) | 23069.3 | 1.22912 | 0.614558 | − | 0.788871i | \(-0.289334\pi\) | ||||
0.614558 | + | 0.788871i | \(0.289334\pi\) | |||||||
\(138\) | − | 8580.00i | − | 0.450536i | ||||||
\(139\) | 29491.9i | 1.52641i | 0.646154 | + | 0.763207i | \(0.276376\pi\) | ||||
−0.646154 | + | 0.763207i | \(0.723624\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10975.0 | −0.552035 | ||||||||
\(142\) | 10910.0 | 0.541065 | ||||||||
\(143\) | 445.000i | 0.0217615i | ||||||||
\(144\) | 224.000 | 0.0108025 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 21188.1i | − | 0.993999i | ||||||
\(147\) | 12002.5 | + | 245.000i | 0.555440 | + | 0.0113379i | ||||
\(148\) | −16313.6 | −0.744777 | ||||||||
\(149\) | −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 | \(0.625755\pi\) | |||||||
\(152\) | 14040.0i | 0.607687i | ||||||||
\(153\) | − | 27160.0i | − | 1.16024i | ||||||
\(154\) | 7476.00 | + | 7630.16i | 0.315230 | + | 0.321731i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −250.000 | −0.0102728 | ||||||||
\(157\) | − | 25790.0i | − | 1.04629i | −0.852244 | − | 0.523145i | \(-0.824759\pi\) | ||
0.852244 | − | 0.523145i | \(-0.175241\pi\) | |||||||
\(158\) | −13621.6 | −0.545650 | ||||||||
\(159\) | − | 7936.35i | − | 0.313925i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 24024.0 | + | 24519.4i | 0.926816 | + | 0.945928i | ||||
\(162\) | 2721.38 | 0.103695 | ||||||||
\(163\) | 37153.9 | 1.39839 | 0.699196 | − | 0.714930i | \(-0.253542\pi\) | ||||
0.699196 | + | 0.714930i | \(0.253542\pi\) | |||||||
\(164\) | − | 29148.9i | − | 1.08376i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 4874.48i | − | 0.176894i | ||||||
\(167\) | − | 20795.0i | − | 0.745634i | −0.927905 | − | 0.372817i | \(-0.878392\pi\) | ||
0.927905 | − | 0.372817i | \(-0.121608\pi\) | |||||||
\(168\) | −11145.2 | + | 10920.0i | −0.394883 | + | 0.386905i | ||||
\(169\) | 28536.0 | 0.999125 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 12345.4i | − | 0.422196i | ||||||
\(172\) | 3772.21 | 0.127509 | ||||||||
\(173\) | − | 115.000i | − | 0.00384243i | −0.999998 | − | 0.00192121i | \(-0.999388\pi\) | ||
0.999998 | − | 0.00192121i | \(-0.000611542\pi\) | |||||||
\(174\) | 2339.26i | 0.0772646i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 356.000 | 0.0114928 | ||||||||
\(177\) | 18126.2 | 0.578577 | ||||||||
\(178\) | 1980.00i | 0.0624921i | ||||||||
\(179\) | −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 | \(-0.939665\pi\) | ||
0.982089 | − | 0.188417i | \(-0.0603355\pi\) | |||||||
\(182\) | −428.661 | + | 420.000i | −0.0129411 | + | 0.0126796i | ||||
\(183\) | 9675.48 | 0.288915 | ||||||||
\(184\) | −44616.0 | −1.31782 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −12900.0 | −0.372875 | ||||||||
\(187\) | − | 43165.0i | − | 1.23438i | ||||||
\(188\) | 21950.0i | 0.621039i | ||||||||
\(189\) | 23975.0 | − | 23490.6i | 0.671174 | − | 0.657613i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14263.0 | −0.390971 | −0.195485 | − | 0.980707i | \(-0.562628\pi\) | ||||
−0.195485 | + | 0.980707i | \(0.562628\pi\) | |||||||
\(192\) | − | 12280.0i | − | 0.333116i | ||||||
\(193\) | 32005.0 | 0.859219 | 0.429609 | − | 0.903015i | \(-0.358651\pi\) | ||||
0.429609 | + | 0.903015i | \(0.358651\pi\) | |||||||
\(194\) | 22621.0i | 0.601048i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 490.000 | − | 24005.0i | 0.0127551 | − | 0.624870i | ||||
\(197\) | 3394.99 | 0.0874795 | 0.0437398 | − | 0.999043i | \(-0.486073\pi\) | ||||
0.0437398 | + | 0.999043i | \(0.486073\pi\) | |||||||
\(198\) | 12208.3 | 0.311403 | ||||||||
\(199\) | 19400.0i | 0.489886i | 0.969538 | + | 0.244943i | \(0.0787692\pi\) | ||||
−0.969538 | + | 0.244943i | \(0.921231\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 10238.9i | − | 0.253431i | ||||||
\(202\) | − | 11820.0i | − | 0.289677i | ||||||
\(203\) | −6549.94 | − | 6685.00i | −0.158944 | − | 0.162222i | ||||
\(204\) | 24250.0 | 0.582709 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 11549.3i | 0.272159i | ||||||||
\(207\) | 39231.0 | 0.915565 | ||||||||
\(208\) | 20.0000i | 0.000462278i | ||||||||
\(209\) | − | 19620.4i | − | 0.449175i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 52817.0 | 1.18634 | 0.593170 | − | 0.805078i | \(-0.297876\pi\) | ||||
0.593170 | + | 0.805078i | \(0.297876\pi\) | |||||||
\(212\) | −15872.7 | −0.353166 | ||||||||
\(213\) | − | 22270.0i | − | 0.490864i | ||||||
\(214\) | −31032.0 | −0.677614 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 43625.4i | 0.935044i | ||||||||
\(217\) | 36864.8 | − | 36120.0i | 0.782875 | − | 0.767058i | ||||
\(218\) | −30155.7 | −0.634536 | ||||||||
\(219\) | −43250.0 | −0.901774 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2425.00 | 0.0496509 | ||||||||
\(222\) | − | 19980.0i | − | 0.405405i | ||||||
\(223\) | − | 13645.0i | − | 0.274387i | −0.990544 | − | 0.137194i | \(-0.956192\pi\) | ||
0.990544 | − | 0.137194i | \(-0.0438082\pi\) | |||||||
\(224\) | 35280.0 | + | 36007.5i | 0.703125 | + | 0.717624i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −7644.00 | −0.149659 | ||||||||
\(227\) | 74485.0i | 1.44550i | 0.691111 | + | 0.722748i | \(0.257121\pi\) | ||||
−0.691111 | + | 0.722748i | \(0.742879\pi\) | |||||||
\(228\) | 11022.7 | 0.212040 | ||||||||
\(229\) | − | 68463.2i | − | 1.30553i | −0.757561 | − | 0.652764i | \(-0.773609\pi\) | ||
0.757561 | − | 0.652764i | \(-0.226391\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 15575.0 | − | 15260.3i | 0.291880 | − | 0.285983i | ||||
\(232\) | 12164.2 | 0.225999 | ||||||||
\(233\) | −60169.3 | −1.10831 | −0.554157 | − | 0.832412i | \(-0.686959\pi\) | ||||
−0.554157 | + | 0.832412i | \(0.686959\pi\) | |||||||
\(234\) | 685.857i | 0.0125257i | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 36252.4i | − | 0.650899i | ||||||
\(237\) | 27805.0i | 0.495024i | ||||||||
\(238\) | 41580.1 | − | 40740.0i | 0.734060 | − | 0.719229i | ||||
\(239\) | 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 | \(-0.766144\pi\) | ||
0.742044 | − | 0.670351i | \(-0.233856\pi\) | |||||||
\(242\) | −16460.6 | −0.281070 | ||||||||
\(243\) | − | 61040.0i | − | 1.03372i | ||||||
\(244\) | − | 19351.0i | − | 0.325030i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 35700.0 | 0.589927 | ||||||||
\(247\) | 1102.27 | 0.0180673 | ||||||||
\(248\) | 67080.0i | 1.09066i | ||||||||
\(249\) | −9950.00 | −0.160481 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 50410.5i | 0.800154i | 0.916482 | + | 0.400077i | \(0.131017\pi\) | ||||
−0.916482 | + | 0.400077i | \(0.868983\pi\) | |||||||
\(252\) | −19204.0 | − | 19600.0i | −0.302406 | − | 0.308642i | ||||
\(253\) | 62349.3 | 0.974071 | ||||||||
\(254\) | −58464.0 | −0.906194 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −64880.0 | −0.989990 | ||||||||
\(257\) | 3370.00i | 0.0510227i | 0.999675 | + | 0.0255114i | \(0.00812140\pi\) | ||||
−0.999675 | + | 0.0255114i | \(0.991879\pi\) | |||||||
\(258\) | 4620.00i | 0.0694069i | ||||||||
\(259\) | 55944.0 | + | 57097.6i | 0.833977 | + | 0.851174i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −10696.0 | −0.157015 | ||||||||
\(262\) | 16500.0i | 0.240371i | ||||||||
\(263\) | −59385.4 | −0.858556 | −0.429278 | − | 0.903173i | \(-0.641232\pi\) | ||||
−0.429278 | + | 0.903173i | \(0.641232\pi\) | |||||||
\(264\) | 28340.6i | 0.406632i | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 18900.0 | − | 18518.1i | 0.267115 | − | 0.261718i | ||||
\(267\) | 4041.66 | 0.0566940 | ||||||||
\(268\) | −20477.7 | −0.285110 | ||||||||
\(269\) | 77012.0i | 1.06427i | 0.846658 | + | 0.532137i | \(0.178611\pi\) | ||||
−0.846658 | + | 0.532137i | \(0.821389\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 143222.i | 1.95016i | 0.221855 | + | 0.975080i | \(0.428789\pi\) | ||||
−0.221855 | + | 0.975080i | \(0.571211\pi\) | |||||||
\(272\) | − | 1940.00i | − | 0.0262219i | ||||||
\(273\) | 857.321 | + | 875.000i | 0.0115032 | + | 0.0117404i | ||||
\(274\) | 56508.0 | 0.752677 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 35027.7i | 0.459826i | ||||||||
\(277\) | −101928. | −1.32842 | −0.664209 | − | 0.747547i | \(-0.731231\pi\) | ||||
−0.664209 | + | 0.747547i | \(0.731231\pi\) | |||||||
\(278\) | 72240.0i | 0.934734i | ||||||||
\(279\) | − | 58983.7i | − | 0.757746i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −47521.0 | −0.601829 | −0.300914 | − | 0.953651i | \(-0.597292\pi\) | ||||
−0.300914 | + | 0.953651i | \(0.597292\pi\) | |||||||
\(282\) | −26883.1 | −0.338051 | ||||||||
\(283\) | 43115.0i | 0.538339i | 0.963093 | + | 0.269169i | \(0.0867491\pi\) | ||||
−0.963093 | + | 0.269169i | \(0.913251\pi\) | |||||||
\(284\) | −44540.0 | −0.552222 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1090.02i | 0.0133261i | ||||||||
\(287\) | −102021. | + | 99960.0i | −1.23859 | + | 1.21356i | ||||
\(288\) | 57612.0 | 0.694589 | ||||||||
\(289\) | −151704. | −1.81636 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 46175.0 | 0.545282 | ||||||||
\(292\) | 86500.0i | 1.01450i | ||||||||
\(293\) | 162125.i | 1.88849i | 0.329243 | + | 0.944245i | \(0.393206\pi\) | ||||
−0.329243 | + | 0.944245i | \(0.606794\pi\) | |||||||
\(294\) | 29400.0 | + | 600.125i | 0.340136 | + | 0.00694300i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −103896. | −1.18581 | ||||||||
\(297\) | − | 60965.0i | − | 0.691143i | ||||||
\(298\) | −69433.2 | −0.781871 | ||||||||
\(299\) | 3502.77i | 0.0391804i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12936.0 | − | 13202.7i | −0.142780 | − | 0.145724i | ||||
\(302\) | −42991.0 | −0.471372 | ||||||||
\(303\) | −24127.5 | −0.262801 | ||||||||
\(304\) | − | 881.816i | − | 0.00954181i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | − | 66528.1i | − | 0.710497i | ||||||
\(307\) | 33805.0i | 0.358678i | 0.983787 | + | 0.179339i | \(0.0573958\pi\) | ||||
−0.983787 | + | 0.179339i | \(0.942604\pi\) | |||||||
\(308\) | −30520.6 | − | 31150.0i | −0.321731 | − | 0.328365i | ||||
\(309\) | 23575.0 | 0.246908 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 50435.0i | − | 0.521448i | −0.965413 | − | 0.260724i | \(-0.916039\pi\) | ||
0.965413 | − | 0.260724i | \(-0.0839613\pi\) | |||||||
\(312\) | −1592.17 | −0.0163561 | ||||||||
\(313\) | − | 68155.0i | − | 0.695679i | −0.937554 | − | 0.347840i | \(-0.886915\pi\) | ||
0.937554 | − | 0.347840i | \(-0.113085\pi\) | |||||||
\(314\) | − | 63172.3i | − | 0.640719i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 55610.0 | 0.556902 | ||||||||
\(317\) | −42435.0 | −0.422285 | −0.211142 | − | 0.977455i | \(-0.567718\pi\) | ||||
−0.211142 | + | 0.977455i | \(0.567718\pi\) | |||||||
\(318\) | − | 19440.0i | − | 0.192239i | ||||||
\(319\) | −16999.0 | −0.167048 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 63343.8i | 0.614744i | ||||||||
\(322\) | 58846.5 | + | 60060.0i | 0.567557 | + | 0.579260i | ||||
\(323\) | −106920. | −1.02484 | ||||||||
\(324\) | −11110.0 | −0.105834 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 91008.0 | 0.856336 | ||||||||
\(327\) | 61555.0i | 0.575662i | ||||||||
\(328\) | − | 185640.i | − | 1.72554i | ||||||
\(329\) | 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 | \(0.675367\pi\) | |||||||
\(332\) | 19900.0i | 0.180541i | ||||||||
\(333\) | 91356.2 | 0.823852 | ||||||||
\(334\) | − | 50937.1i | − | 0.456606i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 700.000 | − | 685.857i | 0.00620040 | − | 0.00607512i | ||||
\(337\) | 117007. | 1.03027 | 0.515137 | − | 0.857108i | \(-0.327741\pi\) | ||||
0.515137 | + | 0.857108i | \(0.327741\pi\) | |||||||
\(338\) | 69898.6 | 0.611836 | ||||||||
\(339\) | 15603.2i | 0.135774i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 93742.0i | − | 0.806168i | ||||||
\(342\) | − | 30240.0i | − | 0.258541i | ||||||
\(343\) | −85697.8 | + | 80605.0i | −0.728420 | + | 0.685131i | ||||
\(344\) | 24024.0 | 0.203015 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 281.691i | − | 0.00235300i | ||||||
\(347\) | −70481.6 | −0.585352 | −0.292676 | − | 0.956212i | \(-0.594546\pi\) | ||||
−0.292676 | + | 0.956212i | \(0.594546\pi\) | |||||||
\(348\) | − | 9550.00i | − | 0.0788578i | ||||||
\(349\) | 91390.5i | 0.750326i | 0.926959 | + | 0.375163i | \(0.122413\pi\) | ||||
−0.926959 | + | 0.375163i | \(0.877587\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3425.00 | 0.0278001 | ||||||||
\(352\) | 91561.9 | 0.738975 | ||||||||
\(353\) | 11405.0i | 0.0915263i | 0.998952 | + | 0.0457631i | \(0.0145720\pi\) | ||||
−0.998952 | + | 0.0457631i | \(0.985428\pi\) | |||||||
\(354\) | 44400.0 | 0.354304 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 8083.32i | − | 0.0637807i | ||||||
\(357\) | −83160.2 | − | 84875.0i | −0.652498 | − | 0.665953i | ||||
\(358\) | −13026.4 | −0.101638 | ||||||||
\(359\) | −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 | ||||||||
\(362\) | − | 30240.0i | − | 0.230762i | ||||||
\(363\) | 33600.0i | 0.254992i | ||||||||
\(364\) | 1750.00 | − | 1714.64i | 0.0132079 | − | 0.0129411i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 23700.0 | 0.176924 | ||||||||
\(367\) | 74485.0i | 0.553015i | 0.961012 | + | 0.276507i | \(0.0891770\pi\) | ||||
−0.961012 | + | 0.276507i | \(0.910823\pi\) | |||||||
\(368\) | 2802.22 | 0.0206922 | ||||||||
\(369\) | 163234.i | 1.19883i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 54432.0 | + | 55554.4i | 0.395464 | + | 0.403618i | ||||
\(372\) | 52664.0 | 0.380564 | ||||||||
\(373\) | 102550. | 0.737088 | 0.368544 | − | 0.929610i | \(-0.379856\pi\) | ||||
0.368544 | + | 0.929610i | \(0.379856\pi\) | |||||||
\(374\) | − | 105732.i | − | 0.755900i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 139792.i | 0.988799i | ||||||||
\(377\) | − | 955.000i | − | 0.00671925i | ||||||
\(378\) | 58726.5 | − | 57540.0i | 0.411008 | − | 0.402704i | ||||
\(379\) | 172954. | 1.20407 | 0.602036 | − | 0.798469i | \(-0.294357\pi\) | ||||
0.602036 | + | 0.798469i | \(0.294357\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 119339.i | 0.822116i | ||||||||
\(382\) | −34937.1 | −0.239420 | ||||||||
\(383\) | 144050.i | 0.982010i | 0.871157 | + | 0.491005i | \(0.163370\pi\) | ||||
−0.871157 | + | 0.491005i | \(0.836630\pi\) | |||||||
\(384\) | 52223.1i | 0.354161i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 78396.0 | 0.526162 | ||||||||
\(387\) | −21124.4 | −0.141047 | ||||||||
\(388\) | − | 92350.0i | − | 0.613442i | ||||||
\(389\) | 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 | ||||||
\(392\) | 3120.65 | − | 152880.i | 0.0203083 | − | 0.994898i | ||||
\(393\) | 33680.5 | 0.218069 | ||||||||
\(394\) | 8316.00 | 0.0535700 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −49840.0 | −0.317825 | ||||||||
\(397\) | − | 256925.i | − | 1.63014i | −0.579361 | − | 0.815071i | \(-0.696698\pi\) | ||
0.579361 | − | 0.815071i | \(-0.303302\pi\) | |||||||
\(398\) | 47520.0i | 0.299992i | ||||||||
\(399\) | −37800.0 | − | 38579.5i | −0.237436 | − | 0.242332i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −35641.0 | −0.221647 | −0.110823 | − | 0.993840i | \(-0.535349\pi\) | ||||
−0.110823 | + | 0.993840i | \(0.535349\pi\) | |||||||
\(402\) | − | 25080.0i | − | 0.155194i | ||||||
\(403\) | 5266.40 | 0.0324268 | ||||||||
\(404\) | 48254.9i | 0.295651i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −16044.0 | − | 16374.8i | −0.0973331 | − | 0.0993402i | ||||
\(407\) | 145191. | 0.876498 | ||||||||
\(408\) | 154440. | 0.927770 | ||||||||
\(409\) | − | 151721.i | − | 0.906985i | −0.891260 | − | 0.453493i | \(-0.850178\pi\) | ||
0.891260 | − | 0.453493i | \(-0.149822\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 115346.i | − | 0.682843i | ||||||
\(412\) | − | 47150.0i | − | 0.277771i | ||||||
\(413\) | −126884. | + | 124320.i | −0.743884 | + | 0.728855i | ||||
\(414\) | 96096.0 | 0.560667 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 5143.93i | 0.0297241i | ||||||||
\(417\) | 147459. | 0.848008 | ||||||||
\(418\) | − | 48060.0i | − | 0.275062i | ||||||
\(419\) | 150889.i | 0.859465i | 0.902956 | + | 0.429733i | \(0.141392\pi\) | ||||
−0.902956 | + | 0.429733i | \(0.858608\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4681.00 | −0.0264104 | −0.0132052 | − | 0.999913i | \(-0.504203\pi\) | ||||
−0.0132052 | + | 0.999913i | \(0.504203\pi\) | |||||||
\(422\) | 129375. | 0.726481 | ||||||||
\(423\) | − | 122920.i | − | 0.686976i | ||||||
\(424\) | −101088. | −0.562300 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | − | 54550.1i | − | 0.300591i | ||||||
\(427\) | −67728.4 | + | 66360.0i | −0.371463 | + | 0.363957i | ||||
\(428\) | 126688. | 0.691587 | ||||||||
\(429\) | 2225.00 | 0.0120897 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −87103.0 | −0.468898 | −0.234449 | − | 0.972128i | \(-0.575329\pi\) | ||||
−0.234449 | + | 0.972128i | \(0.575329\pi\) | |||||||
\(432\) | − | 2740.00i | − | 0.0146819i | ||||||
\(433\) | − | 231730.i | − | 1.23597i | −0.786192 | − | 0.617983i | \(-0.787950\pi\) | ||
0.786192 | − | 0.617983i | \(-0.212050\pi\) | |||||||
\(434\) | 90300.0 | − | 88475.6i | 0.479411 | − | 0.469725i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 123110. | 0.647620 | ||||||||
\(437\) | − | 154440.i | − | 0.808718i | ||||||
\(438\) | −105940. | −0.552222 | ||||||||
\(439\) | − | 246272.i | − | 1.27787i | −0.769262 | − | 0.638933i | \(-0.779376\pi\) | ||
0.769262 | − | 0.638933i | \(-0.220624\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2744.00 | + | 134428.i | −0.0141093 | + | 0.691214i | ||||
\(442\) | 5940.01 | 0.0304048 | ||||||||
\(443\) | −349841. | −1.78264 | −0.891319 | − | 0.453376i | \(-0.850219\pi\) | ||||
−0.891319 | + | 0.453376i | \(0.850219\pi\) | |||||||
\(444\) | 81568.0i | 0.413765i | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 33423.3i | − | 0.168027i | ||||||
\(447\) | 141730.i | 0.709327i | ||||||||
\(448\) | 84223.3 | + | 85960.0i | 0.419639 | + | 0.428292i | ||||
\(449\) | −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 | ||||||||
\(452\) | 31206.5 | 0.152745 | ||||||||
\(453\) | 87755.0i | 0.427637i | ||||||||
\(454\) | 182450.i | 0.885182i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 70200.0 | 0.337604 | ||||||||
\(457\) | 263629. | 1.26229 | 0.631147 | − | 0.775663i | \(-0.282585\pi\) | ||||
0.631147 | + | 0.775663i | \(0.282585\pi\) | |||||||
\(458\) | − | 167700.i | − | 0.799470i | ||||||
\(459\) | −332225. | −1.57691 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 128255.i | 0.603495i | 0.953388 | + | 0.301747i | \(0.0975699\pi\) | ||||
−0.953388 | + | 0.301747i | \(0.902430\pi\) | |||||||
\(462\) | 38150.8 | − | 37380.0i | 0.178739 | − | 0.175128i | ||||
\(463\) | 81857.0 | 0.381851 | 0.190926 | − | 0.981605i | \(-0.438851\pi\) | ||||
0.190926 | + | 0.981605i | \(0.438851\pi\) | |||||||
\(464\) | −764.000 | −0.00354860 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −147384. | −0.678701 | ||||||||
\(467\) | 204445.i | 0.937438i | 0.883347 | + | 0.468719i | \(0.155284\pi\) | ||||
−0.883347 | + | 0.468719i | \(0.844716\pi\) | |||||||
\(468\) | − | 2800.00i | − | 0.0127840i | ||||||
\(469\) | 70224.0 | + | 71672.1i | 0.319257 | + | 0.325840i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −128950. | −0.581272 | ||||||||
\(472\) | − | 230880.i | − | 1.03634i | ||||||
\(473\) | −33572.7 | −0.150060 | ||||||||
\(474\) | 68108.1i | 0.303139i | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −169750. | + | 166320.i | −0.749197 | + | 0.734060i | ||||
\(477\) | 88887.1 | 0.390663 | ||||||||
\(478\) | 184611. | 0.807981 | ||||||||
\(479\) | − | 79534.9i | − | 0.346647i | −0.984865 | − | 0.173323i | \(-0.944549\pi\) | ||
0.984865 | − | 0.173323i | \(-0.0554505\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8156.80i | 0.0352557i | ||||||||
\(482\) | − | 190740.i | − | 0.821009i | ||||||
\(483\) | 122597. | − | 120120.i | 0.525515 | − | 0.514898i | ||||
\(484\) | 67200.0 | 0.286866 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | − | 149517.i | − | 0.633020i | ||||||
\(487\) | −164958. | −0.695531 | −0.347766 | − | 0.937582i | \(-0.613059\pi\) | ||||
−0.347766 | + | 0.937582i | \(0.613059\pi\) | |||||||
\(488\) | − | 123240.i | − | 0.517502i | ||||||
\(489\) | − | 185769.i | − | 0.776884i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −74191.0 | −0.307743 | −0.153872 | − | 0.988091i | \(-0.549174\pi\) | ||||
−0.153872 | + | 0.988091i | \(0.549174\pi\) | |||||||
\(492\) | −145745. | −0.602091 | ||||||||
\(493\) | 92635.0i | 0.381137i | ||||||||
\(494\) | 2700.00 | 0.0110639 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 4213.12i | − | 0.0171254i | ||||||
\(497\) | 152740. | + | 155890.i | 0.618360 | + | 0.631111i | ||||
\(498\) | −24372.4 | −0.0982743 | ||||||||
\(499\) | 278527. | 1.11858 | 0.559289 | − | 0.828973i | \(-0.311074\pi\) | ||||
0.559289 | + | 0.828973i | \(0.311074\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −103975. | −0.414241 | ||||||||
\(502\) | 123480.i | 0.489992i | ||||||||
\(503\) | 60275.0i | 0.238233i | 0.992880 | + | 0.119116i | \(0.0380061\pi\) | ||||
−0.992880 | + | 0.119116i | \(0.961994\pi\) | |||||||
\(504\) | −122304. | − | 124826.i | −0.481481 | − | 0.491410i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 152724. | 0.596494 | ||||||||
\(507\) | − | 142680.i | − | 0.555069i | ||||||
\(508\) | 238678. | 0.924880 | ||||||||
\(509\) | 348709.i | 1.34595i | 0.739666 | + | 0.672974i | \(0.234983\pi\) | ||||
−0.739666 | + | 0.672974i | \(0.765017\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 302750. | − | 296633.i | 1.15942 | − | 1.13600i | ||||
\(512\) | 8191.09 | 0.0312465 | ||||||||
\(513\) | −151011. | −0.573818 | ||||||||
\(514\) | 8254.78i | 0.0312449i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | − | 18861.1i | − | 0.0708381i | ||||||
\(517\) | − | 195355.i | − | 0.730876i | ||||||
\(518\) | 137034. | + | 139860.i | 0.510704 | + | 0.521236i | ||||
\(519\) | −575.000 | −0.00213468 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 84727.9i | − | 0.312141i | −0.987746 | − | 0.156070i | \(-0.950117\pi\) | ||
0.987746 | − | 0.156070i | \(-0.0498827\pi\) | |||||||
\(522\) | −26199.7 | −0.0961515 | ||||||||
\(523\) | 235610.i | 0.861371i | 0.902502 | + | 0.430686i | \(0.141728\pi\) | ||||
−0.902502 | + | 0.430686i | \(0.858272\pi\) | |||||||
\(524\) | − | 67361.0i | − | 0.245327i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −145464. | −0.525756 | ||||||||
\(527\) | −510841. | −1.83935 | ||||||||
\(528\) | − | 1780.00i | − | 0.00638487i | ||||||
\(529\) | 210935. | 0.753767 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 203014.i | 0.720006i | ||||||||
\(532\) | −77158.9 | + | 75600.0i | −0.272623 | + | 0.267115i | ||||
\(533\) | −14574.5 | −0.0513025 | ||||||||
\(534\) | 9900.00 | 0.0347178 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −130416. | −0.453943 | ||||||||
\(537\) | 26590.0i | 0.0922082i | ||||||||
\(538\) | 188640.i | 0.651732i | ||||||||
\(539\) | −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.i | 1.19422i | ||||||||
\(543\) | −61727.1 | −0.209352 | ||||||||
\(544\) | − | 498961.i | − | 1.68604i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 2100.00 | + | 2143.30i | 0.00704424 | + | 0.00718950i | ||||
\(547\) | −423894. | −1.41672 | −0.708358 | − | 0.705854i | \(-0.750564\pi\) | ||||
−0.708358 | + | 0.705854i | \(0.750564\pi\) | |||||||
\(548\) | −230693. | −0.768198 | ||||||||
\(549\) | 108365.i | 0.359539i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 42106.7i | 0.138691i | ||||||||
\(552\) | 223080.i | 0.732120i | ||||||||
\(553\) | −190703. | − | 194635.i | −0.623600 | − | 0.636459i | ||||
\(554\) | −249672. | −0.813486 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 294919.i | − | 0.954009i | ||||||
\(557\) | 133389. | 0.429943 | 0.214972 | − | 0.976620i | \(-0.431034\pi\) | ||||
0.214972 | + | 0.976620i | \(0.431034\pi\) | |||||||
\(558\) | − | 144480.i | − | 0.464023i | ||||||
\(559\) | − | 1886.11i | − | 0.00603591i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −215825. | −0.685766 | ||||||||
\(562\) | −116402. | −0.368543 | ||||||||
\(563\) | 369770.i | 1.16658i | 0.812264 | + | 0.583290i | \(0.198235\pi\) | ||||
−0.812264 | + | 0.583290i | \(0.801765\pi\) | |||||||
\(564\) | 109750. | 0.345022 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 105610.i | 0.329664i | ||||||||
\(567\) | 38099.4 | + | 38885.0i | 0.118509 | + | 0.120953i | ||||
\(568\) | −283661. | −0.879230 | ||||||||
\(569\) | 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 | \(0.344312\pi\) | |||||||
\(572\) | − | 4450.00i | − | 0.0136009i | ||||||
\(573\) | 71315.0i | 0.217206i | ||||||||
\(574\) | −249900. | + | 244851.i | −0.758477 | + | 0.743153i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 137536. | 0.414545 | ||||||||
\(577\) | 387595.i | 1.16420i | 0.813118 | + | 0.582099i | \(0.197768\pi\) | ||||
−0.813118 | + | 0.582099i | \(0.802232\pi\) | |||||||
\(578\) | −371597. | −1.11229 | ||||||||
\(579\) | − | 160025.i | − | 0.477344i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 69650.0 | − | 68242.8i | 0.206333 | − | 0.202164i | ||||
\(582\) | 113105. | 0.333915 | ||||||||
\(583\) | 141267. | 0.415627 | ||||||||
\(584\) | 550890.i | 1.61525i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 397124.i | 1.15646i | ||||||||
\(587\) | 467350.i | 1.35633i | 0.734909 | + | 0.678166i | \(0.237225\pi\) | ||||
−0.734909 | + | 0.678166i | \(0.762775\pi\) | |||||||
\(588\) | −120025. | − | 2450.00i | −0.347150 | − | 0.00708617i | ||||
\(589\) | −232200. | −0.669317 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 16975.0i | − | 0.0485997i | ||||||
\(592\) | 6525.44 | 0.0186194 | ||||||||
\(593\) | − | 214315.i | − | 0.609457i | −0.952439 | − | 0.304729i | \(-0.901434\pi\) | ||
0.952439 | − | 0.304729i | \(-0.0985658\pi\) | |||||||
\(594\) | − | 149333.i | − | 0.423237i | ||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 283460. | 0.797993 | ||||||||
\(597\) | 96999.8 | 0.272159 | ||||||||
\(598\) | 8580.00i | 0.0239930i | ||||||||
\(599\) | 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 | \(0.0403011\pi\) | ||||
−0.991996 | + | 0.126272i | \(0.959699\pi\) | |||||||
\(602\) | −31686.6 | − | 32340.0i | −0.0874345 | − | 0.0892374i | ||||
\(603\) | 114675. | 0.315381 | ||||||||
\(604\) | 175510. | 0.481092 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −59100.0 | −0.160932 | ||||||||
\(607\) | − | 193715.i | − | 0.525758i | −0.964829 | − | 0.262879i | \(-0.915328\pi\) | ||
0.964829 | − | 0.262879i | \(-0.0846720\pi\) | |||||||
\(608\) | − | 226800.i | − | 0.613530i | ||||||
\(609\) | −33425.0 | + | 32749.7i | −0.0901232 | + | 0.0883024i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10975.0 | 0.0293983 | ||||||||
\(612\) | 271600.i | 0.725148i | ||||||||
\(613\) | 296231. | 0.788334 | 0.394167 | − | 0.919039i | \(-0.371033\pi\) | ||||
0.394167 | + | 0.919039i | \(0.371033\pi\) | |||||||
\(614\) | 82805.0i | 0.219644i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −194376. | − | 198384.i | −0.512249 | − | 0.522812i | ||||
\(617\) | −424751. | −1.11574 | −0.557872 | − | 0.829927i | \(-0.688382\pi\) | ||||
−0.557872 | + | 0.829927i | \(0.688382\pi\) | |||||||
\(618\) | 57746.7 | 0.151200 | ||||||||
\(619\) | − | 375825.i | − | 0.980855i | −0.871482 | − | 0.490427i | \(-0.836841\pi\) | ||
0.871482 | − | 0.490427i | \(-0.163159\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 479880.i | − | 1.24437i | ||||||
\(622\) | − | 123540.i | − | 0.319321i | ||||||
\(623\) | −28291.6 | + | 27720.0i | −0.0728923 | + | 0.0714196i | ||||
\(624\) | 100.000 | 0.000256821 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 166945.i | − | 0.426015i | ||||||
\(627\) | −98102.1 | −0.249542 | ||||||||
\(628\) | 257900.i | 0.653931i | ||||||||
\(629\) | − | 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. | 0.886682 | ||||||||
\(633\) | − | 264085.i | − | 0.659077i | ||||||
\(634\) | −103944. | −0.258595 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 79363.5i | 0.196203i | ||||||||
\(637\) | −12002.5 | − | 245.000i | −0.0295796 | − | 0.000603792i | ||||
\(638\) | −41638.9 | −0.102296 | ||||||||
\(639\) | 249424. | 0.610853 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 558794. | 1.35999 | 0.679995 | − | 0.733217i | \(-0.261982\pi\) | ||||
0.679995 | + | 0.733217i | \(0.261982\pi\) | |||||||
\(642\) | 155160.i | 0.376452i | ||||||||
\(643\) | 454235.i | 1.09865i | 0.835609 | + | 0.549324i | \(0.185115\pi\) | ||||
−0.835609 | + | 0.549324i | \(0.814885\pi\) | |||||||
\(644\) | −240240. | − | 245194.i | −0.579260 | − | 0.591205i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −261900. | −0.627582 | ||||||||
\(647\) | − | 129530.i | − | 0.309430i | −0.987959 | − | 0.154715i | \(-0.950554\pi\) | ||
0.987959 | − | 0.154715i | \(-0.0494459\pi\) | |||||||
\(648\) | −70756.0 | −0.168505 | ||||||||
\(649\) | 322647.i | 0.766016i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −180600. | − | 184324.i | −0.426143 | − | 0.434931i | ||||
\(652\) | −371539. | −0.873995 | ||||||||
\(653\) | 343903. | 0.806511 | 0.403255 | − | 0.915087i | \(-0.367879\pi\) | ||||
0.403255 | + | 0.915087i | \(0.367879\pi\) | |||||||
\(654\) | 150778.i | 0.352520i | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 11659.6i | 0.0270941i | ||||||||
\(657\) | − | 484400.i | − | 1.12221i | ||||||
\(658\) | 188182. | − | 184380.i | 0.434637 | − | 0.425855i | ||||
\(659\) | −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 | \(0.0704559\pi\) | ||||
−0.975603 | + | 0.219541i | \(0.929544\pi\) | |||||||
\(662\) | −280971. | −0.641130 | ||||||||
\(663\) | − | 12125.0i | − | 0.0275838i | ||||||
\(664\) | 126737.i | 0.287452i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 223776. | 0.504505 | ||||||||
\(667\) | −133806. | −0.300762 | ||||||||
\(668\) | 207950.i | 0.466022i | ||||||||
\(669\) | −68225.0 | −0.152437 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 172224.i | 0.382514i | ||||||||
\(672\) | 180037. | − | 176400.i | 0.398680 | − | 0.390625i | ||||
\(673\) | −429792. | −0.948918 | −0.474459 | − | 0.880278i | \(-0.657356\pi\) | ||||
−0.474459 | + | 0.880278i | \(0.657356\pi\) | |||||||
\(674\) | 286608. | 0.630912 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −285360. | −0.624453 | ||||||||
\(677\) | − | 79685.0i | − | 0.173860i | −0.996214 | − | 0.0869299i | \(-0.972294\pi\) | ||
0.996214 | − | 0.0869299i | \(-0.0277056\pi\) | |||||||
\(678\) | 38220.0i | 0.0831441i | ||||||||
\(679\) | −323225. | + | 316695.i | −0.701076 | + | 0.686912i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 372425. | 0.803054 | ||||||||
\(682\) | − | 229620.i | − | 0.493675i | ||||||
\(683\) | 719577. | 1.54254 | 0.771269 | − | 0.636510i | \(-0.219622\pi\) | ||||
0.771269 | + | 0.636510i | \(0.219622\pi\) | |||||||
\(684\) | 123454.i | 0.263872i | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −209916. | + | 197441.i | −0.446064 | + | 0.419555i | ||||
\(687\) | −342316. | −0.725294 | ||||||||
\(688\) | −1508.89 | −0.00318771 | ||||||||
\(689\) | 7936.35i | 0.0167179i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 398532.i | 0.834655i | 0.908756 | + | 0.417328i | \(0.137033\pi\) | ||||
−0.908756 | + | 0.417328i | \(0.862967\pi\) | |||||||
\(692\) | 1150.00i | 0.00240152i | ||||||||
\(693\) | 170916. | + | 174440.i | 0.355890 | + | 0.363228i | ||||
\(694\) | −172644. | −0.358453 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | − | 60820.8i | − | 0.125555i | ||||||
\(697\) | 1.41372e6 | 2.91004 | ||||||||
\(698\) | 223860.i | 0.459479i | ||||||||
\(699\) | 300846.i | 0.615730i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −658873. | −1.34081 | −0.670403 | − | 0.741998i | \(-0.733879\pi\) | ||||
−0.670403 | + | 0.741998i | \(0.733879\pi\) | |||||||
\(702\) | 8389.50 | 0.0170240 | ||||||||
\(703\) | − | 359640.i | − | 0.727708i | ||||||
\(704\) | 218584. | 0.441035 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 27936.4i | 0.0560482i | ||||||||
\(707\) | 168892. | − | 165480.i | 0.337887 | − | 0.331060i | ||||
\(708\) | −181262. | −0.361610 | ||||||||
\(709\) | 593737. | 1.18114 | 0.590570 | − | 0.806986i | \(-0.298903\pi\) | ||||
0.590570 | + | 0.806986i | \(0.298903\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −311416. | −0.616030 | ||||||||
\(712\) | − | 51480.0i | − | 0.101550i | ||||||
\(713\) | − | 737880.i | − | 1.45147i | ||||||
\(714\) | −203700. | − | 207900.i | −0.399572 | − | 0.407811i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 53180.0 | 0.103734 | ||||||||
\(717\) | − | 376835.i | − | 0.733015i | ||||||
\(718\) | −564279. | −1.09457 | ||||||||
\(719\) | − | 75321.8i | − | 0.145701i | −0.997343 | − | 0.0728506i | \(-0.976790\pi\) | ||
0.997343 | − | 0.0728506i | \(-0.0232096\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −165025. | + | 161691.i | −0.317453 | + | 0.311039i | ||||
\(722\) | 200175. | 0.384003 | ||||||||
\(723\) | −389346. | −0.744834 | ||||||||
\(724\) | 123454.i | 0.235521i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 82302.9i | 0.156150i | ||||||||
\(727\) | 342190.i | 0.647438i | 0.946153 | + | 0.323719i | \(0.104933\pi\) | ||||
−0.946153 | + | 0.323719i | \(0.895067\pi\) | |||||||
\(728\) | 11145.2 | − | 10920.0i | 0.0210293 | − | 0.0206044i | ||||
\(729\) | −215209. | −0.404954 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 182952.i | 0.342376i | ||||||||
\(732\) | −96754.8 | −0.180572 | ||||||||
\(733\) | − | 958555.i | − | 1.78406i | −0.451978 | − | 0.892029i | \(-0.649281\pi\) | ||
0.451978 | − | 0.892029i | \(-0.350719\pi\) | |||||||
\(734\) | 182450.i | 0.338651i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 720720. | 1.33049 | ||||||||
\(737\) | 182252. | 0.335534 | ||||||||
\(738\) | 399840.i | 0.734131i | ||||||||
\(739\) | 229399. | 0.420052 | 0.210026 | − | 0.977696i | \(-0.432645\pi\) | ||||
0.210026 | + | 0.977696i | \(0.432645\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 5511.35i | − | 0.0100374i | ||||||
\(742\) | 133331. | + | 136080.i | 0.242171 | + | 0.247165i | ||||
\(743\) | 97803.2 | 0.177164 | 0.0885820 | − | 0.996069i | \(-0.471766\pi\) | ||||
0.0885820 | + | 0.996069i | \(0.471766\pi\) | |||||||
\(744\) | 335400. | 0.605923 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 251196. | 0.451372 | ||||||||
\(747\) | − | 111440.i | − | 0.199710i | ||||||
\(748\) | 431650.i | 0.771487i | ||||||||
\(749\) | −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 | \(0.429737\pi\) | |||||||
\(752\) | − | 8780.00i | − | 0.0155260i | ||||||
\(753\) | 252052. | 0.444530 | ||||||||
\(754\) | − | 2339.26i | − | 0.00411468i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −239750. | + | 234906.i | −0.419484 | + | 0.411008i | ||||
\(757\) | 1.05636e6 | 1.84340 | 0.921699 | − | 0.387906i | \(-0.126802\pi\) | ||||
0.921699 | + | 0.387906i | \(0.126802\pi\) | |||||||
\(758\) | 423649. | 0.737340 | ||||||||
\(759\) | − | 311747.i | − | 0.541151i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 406836.i | − | 0.702506i | −0.936281 | − | 0.351253i | \(-0.885756\pi\) | ||
0.936281 | − | 0.351253i | \(-0.114244\pi\) | |||||||
\(762\) | 292320.i | 0.503441i | ||||||||
\(763\) | −422179. | − | 430885.i | −0.725184 | − | 0.740137i | ||||
\(764\) | 142630. | 0.244357 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 352849.i | 0.601356i | ||||||||
\(767\) | −18126.2 | −0.0308118 | ||||||||
\(768\) | 324400.i | 0.549995i | ||||||||
\(769\) | 592238.i | 1.00148i | 0.865597 | + | 0.500741i | \(0.166939\pi\) | ||||
−0.865597 | + | 0.500741i | \(0.833061\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 16850.0 | 0.0283460 | ||||||||
\(772\) | −320050. | −0.537012 | ||||||||
\(773\) | 401165.i | 0.671373i | 0.941974 | + | 0.335687i | \(0.108968\pi\) | ||||
−0.941974 | + | 0.335687i | \(0.891032\pi\) | |||||||
\(774\) | −51744.0 | −0.0863730 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 588147.i | − | 0.976703i | ||||||
\(777\) | 285488. | − | 279720.i | 0.472874 | − | 0.463320i | ||||
\(778\) | 364898. | 0.602854 | ||||||||
\(779\) | 642600. | 1.05893 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 396406. | 0.649887 | ||||||||
\(782\) | − | 832260.i | − | 1.36096i | ||||||
\(783\) | 130835.i | 0.213403i | ||||||||
\(784\) | −196.000 | + | 9602.00i | −0.000318878 | + | 0.0156217i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 82500.0 | 0.133539 | ||||||||
\(787\) | 357565.i | 0.577305i | 0.957434 | + | 0.288653i | \(0.0932073\pi\) | ||||
−0.957434 | + | 0.288653i | \(0.906793\pi\) | |||||||
\(788\) | −33949.9 | −0.0546747 | ||||||||
\(789\) | 296927.i | 0.476975i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −107016. | − | 109223.i | −0.171039 | − | 0.174566i | ||||
\(792\) | −317415. | −0.506030 | ||||||||
\(793\) | −9675.48 | −0.0153860 | ||||||||
\(794\) | − | 629335.i | − | 0.998254i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 194000.i | − | 0.306178i | ||||||
\(797\) | − | 1.18188e6i | − | 1.86062i | −0.366769 | − | 0.930312i | \(-0.619536\pi\) | ||
0.366769 | − | 0.930312i | \(-0.380464\pi\) | |||||||
\(798\) | −92590.7 | − | 94500.0i | −0.145399 | − | 0.148397i | ||||
\(799\) | −1.06458e6 | −1.66756 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 45266.6i | 0.0705525i | ||||||||
\(802\) | −87302.3 | −0.135730 | ||||||||
\(803\) | − | 769850.i | − | 1.19392i | ||||||
\(804\) | 102389.i | 0.158394i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 12900.0 | 0.0198573 | ||||||||
\(807\) | 385060. | 0.591264 | ||||||||
\(808\) | 307320.i | 0.470726i | ||||||||
\(809\) | 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 | \(-0.621242\pi\) | ||
0.371749 | − | 0.928333i | \(-0.378758\pi\) | |||||||
\(812\) | 65499.4 | + | 66850.0i | 0.0993402 | + | 0.101389i | ||||
\(813\) | 716108. | 1.08342 | ||||||||
\(814\) | 355644. | 0.536743 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −9700.00 | −0.0145677 | ||||||||
\(817\) | 83160.0i | 0.124586i | ||||||||
\(818\) | − | 371640.i | − | 0.555413i | ||||||
\(819\) | −9800.00 | + | 9602.00i | −0.0146103 | + | 0.0143151i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −621793. | −0.922485 | −0.461243 | − | 0.887274i | \(-0.652596\pi\) | ||||
−0.461243 | + | 0.887274i | \(0.652596\pi\) | |||||||
\(822\) | − | 282540.i | − | 0.418154i | ||||||
\(823\) | 117394. | 0.173319 | 0.0866597 | − | 0.996238i | \(-0.472381\pi\) | ||||
0.0866597 | + | 0.996238i | \(0.472381\pi\) | |||||||
\(824\) | − | 300283.i | − | 0.442259i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −310800. | + | 304521.i | −0.455534 | + | 0.446330i | ||||
\(827\) | −199790. | −0.292121 | −0.146061 | − | 0.989276i | \(-0.546659\pi\) | ||||
−0.146061 | + | 0.989276i | \(0.546659\pi\) | |||||||
\(828\) | −392310. | −0.572228 | ||||||||
\(829\) | 197894.i | 0.287955i | 0.989581 | + | 0.143977i | \(0.0459892\pi\) | ||||
−0.989581 | + | 0.143977i | \(0.954011\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 509641.i | 0.738010i | ||||||||
\(832\) | 12280.0i | 0.0177399i | ||||||||
\(833\) | 1.16424e6 | + | 23765.0i | 1.67785 | + | 0.0342490i | ||||
\(834\) | 361200. | 0.519297 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 196204.i | 0.280734i | ||||||||
\(837\) | −721497. | −1.02987 | ||||||||
\(838\) | 369600.i | 0.526313i | ||||||||
\(839\) | 826972.i | 1.17481i | 0.809294 | + | 0.587404i | \(0.199850\pi\) | ||||
−0.809294 | + | 0.587404i | \(0.800150\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −670800. | −0.948421 | ||||||||
\(842\) | −11466.1 | −0.0161730 | ||||||||
\(843\) | 237605.i | 0.334349i | ||||||||
\(844\) | −528170. | −0.741462 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | − | 301091.i | − | 0.420685i | ||||||
\(847\) | −230448. | − | 235200.i | −0.321223 | − | 0.327846i | ||||
\(848\) | 6349.08 | 0.00882915 | ||||||||
\(849\) | 215575. | 0.299077 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.14286e6 | 1.57809 | ||||||||
\(852\) | 222700.i | 0.306790i | ||||||||
\(853\) | − | 385450.i | − | 0.529749i | −0.964283 | − | 0.264874i | \(-0.914670\pi\) | ||
0.964283 | − | 0.264874i | \(-0.0853305\pi\) | |||||||
\(854\) | −165900. | + | 162548.i | −0.227473 | + | 0.222878i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 806832. | 1.10112 | ||||||||
\(857\) | − | 356750.i | − | 0.485738i | −0.970059 | − | 0.242869i | \(-0.921911\pi\) | ||
0.970059 | − | 0.242869i | \(-0.0780886\pi\) | |||||||
\(858\) | 5450.11 | 0.00740340 | ||||||||
\(859\) | − | 578227.i | − | 0.783631i | −0.920044 | − | 0.391816i | \(-0.871847\pi\) | ||
0.920044 | − | 0.391816i | \(-0.128153\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 499800. | + | 510106.i | 0.674202 | + | 0.688104i | ||||
\(862\) | −213358. | −0.287140 | ||||||||
\(863\) | −151217. | −0.203039 | −0.101519 | − | 0.994834i | \(-0.532370\pi\) | ||||
−0.101519 | + | 0.994834i | \(0.532370\pi\) | |||||||
\(864\) | − | 704718.i | − | 0.944035i | ||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 567620.i | − | 0.756871i | ||||||
\(867\) | 758520.i | 1.00909i | ||||||||
\(868\) | −368648. | + | 361200.i | −0.489297 | + | 0.479411i | ||||
\(869\) | −494929. | −0.655395 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10238.9i | 0.0134963i | ||||||||
\(872\) | 784047. | 1.03112 | ||||||||
\(873\) | 517160.i | 0.678573i | ||||||||
\(874\) | − | 378299.i | − | 0.495236i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 432500. | 0.563609 | ||||||||
\(877\) | −553981. | −0.720271 | −0.360136 | − | 0.932900i | \(-0.617270\pi\) | ||||
−0.360136 | + | 0.932900i | \(0.617270\pi\) | |||||||
\(878\) | − | 603240.i | − | 0.782530i | ||||||
\(879\) | 810625. | 1.04916 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 531882.i | 0.685273i | 0.939468 | + | 0.342637i | \(0.111320\pi\) | ||||
−0.939468 | + | 0.342637i | \(0.888680\pi\) | |||||||
\(882\) | −6721.40 | + | 329280.i | −0.00864018 | + | 0.423280i | ||||
\(883\) | −606675. | −0.778099 | −0.389049 | − | 0.921217i | \(-0.627196\pi\) | ||||
−0.389049 | + | 0.921217i | \(0.627196\pi\) | |||||||
\(884\) | −24250.0 | −0.0310318 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −856932. | −1.09164 | ||||||||
\(887\) | 1.35703e6i | 1.72481i | 0.506216 | + | 0.862407i | \(0.331044\pi\) | ||||
−0.506216 | + | 0.862407i | \(0.668956\pi\) | |||||||
\(888\) | 519480.i | 0.658784i | ||||||||
\(889\) | −818496. | − | 835374.i | −1.03565 | − | 1.05701i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 98879.0 | 0.124551 | ||||||||
\(892\) | 136450.i | 0.171492i | ||||||||
\(893\) | −483897. | −0.606806 | ||||||||
\(894\) | 347166.i | 0.434373i | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −358176. | − | 365562.i | −0.446150 | − | 0.455349i | ||||
\(897\) | 17513.9 | 0.0217669 | ||||||||
\(898\) | −623912. | −0.773697 | ||||||||
\(899\) | 201177.i | 0.248919i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 769826.i | − | 0.948294i | ||||||
\(902\) | 635460.i | 0.781043i | ||||||||
\(903\) | −66013.7 | + | 64680.0i | −0.0809578 | + | 0.0793222i | ||||
\(904\) | 198744. | 0.243196 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 214955.i | 0.261873i | ||||||||
\(907\) | −452230. | −0.549724 | −0.274862 | − | 0.961484i | \(-0.588632\pi\) | ||||
−0.274862 | + | 0.961484i | \(0.588632\pi\) | |||||||
\(908\) | − | 744850.i | − | 0.903435i | ||||||
\(909\) | − | 270228.i | − | 0.327041i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −948106. | −1.14241 | −0.571203 | − | 0.820809i | \(-0.693523\pi\) | ||||
−0.571203 | + | 0.820809i | \(0.693523\pi\) | |||||||
\(912\) | −4409.08 | −0.00530101 | ||||||||
\(913\) | − | 177110.i | − | 0.212472i | ||||||
\(914\) | 645756. | 0.772994 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 684632.i | 0.815956i | ||||||||
\(917\) | −235763. | + | 231000.i | −0.280374 | + | 0.274709i | ||||
\(918\) | −813782. | −0.965656 | ||||||||
\(919\) | −394481. | −0.467084 | −0.233542 | − | 0.972347i | \(-0.575032\pi\) | ||||
−0.233542 | + | 0.972347i | \(0.575032\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 169025. | 0.199265 | ||||||||
\(922\) | 314160.i | 0.369563i | ||||||||
\(923\) | 22270.0i | 0.0261407i | ||||||||
\(924\) | −155750. | + | 152603.i | −0.182425 | + | 0.178739i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 200508. | 0.233835 | ||||||||
\(927\) | 264040.i | 0.307263i | ||||||||
\(928\) | −196498. | −0.228172 | ||||||||
\(929\) | 139523.i | 0.161664i | 0.996728 | + | 0.0808322i | \(0.0257578\pi\) | ||||
−0.996728 | + | 0.0808322i | \(0.974242\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 529200. | + | 10802.2i | 0.610549 | + | 0.0124628i | ||||
\(932\) | 601693. | 0.692696 | ||||||||
\(933\) | −252175. | −0.289693 | ||||||||
\(934\) | 500786.i | 0.574061i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | − | 17832.3i | − | 0.0203543i | ||||||
\(937\) | − | 434285.i | − | 0.494647i | −0.968933 | − | 0.247324i | \(-0.920449\pi\) | ||
0.968933 | − | 0.247324i | \(-0.0795511\pi\) | |||||||
\(938\) | 172013. | + | 175560.i | 0.195504 | + | 0.199535i | ||||
\(939\) | −340775. | −0.386488 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 539108.i | − | 0.608831i | −0.952539 | − | 0.304415i | \(-0.901539\pi\) | ||
0.952539 | − | 0.304415i | \(-0.0984611\pi\) | |||||||
\(942\) | −315862. | −0.355955 | ||||||||
\(943\) | 2.04204e6i | 2.29636i | ||||||||
\(944\) | 14501.0i | 0.0162725i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −82236.0 | −0.0918924 | ||||||||
\(947\) | 167540. | 0.186818 | 0.0934091 | − | 0.995628i | \(-0.470224\pi\) | ||||
0.0934091 | + | 0.995628i | \(0.470224\pi\) | |||||||
\(948\) | − | 278050.i | − | 0.309390i | ||||||
\(949\) | 43250.0 | 0.0480235 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 212175.i | 0.234603i | ||||||||
\(952\) | −1.08108e6 | + | 1.05924e6i | −1.19285 | + | 1.16875i | ||||
\(953\) | 1.31304e6 | 1.44575 | 0.722873 | − | 0.690981i | \(-0.242821\pi\) | ||||
0.722873 | + | 0.690981i | \(0.242821\pi\) | |||||||
\(954\) | 217728. | 0.239231 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −753670. | −0.824642 | ||||||||
\(957\) | 84995.0i | 0.0928046i | ||||||||
\(958\) | − | 194820.i | − | 0.212277i | ||||||
\(959\) | 791112. | + | 807425.i | 0.860203 | + | 0.877941i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −185879. | −0.201272 | ||||||||
\(962\) | 19980.0i | 0.0215896i | ||||||||
\(963\) | −709451. | −0.765014 | ||||||||
\(964\) | 778693.i | 0.837938i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 300300. | − | 294233.i | 0.321811 | − | 0.315309i | ||||
\(967\) | −338745. | −0.362259 | −0.181130 | − | 0.983459i | \(-0.557975\pi\) | ||||
−0.181130 | + | 0.983459i | \(0.557975\pi\) | |||||||
\(968\) | 427975. | 0.456738 | ||||||||
\(969\) | 534601.i | 0.569354i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.60718e6i | 1.70462i | 0.523039 | + | 0.852309i | \(0.324798\pi\) | ||||
−0.523039 | + | 0.852309i | \(0.675202\pi\) | |||||||
\(972\) | 610400.i | 0.646074i | ||||||||
\(973\) | −1.03221e6 | + | 1.01136e6i | −1.09030 | + | 1.06827i | ||||
\(974\) | −404064. | −0.425924 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7740.39i | 0.00812574i | ||||||||
\(977\) | −1.40070e6 | −1.46743 | −0.733713 | − | 0.679459i | \(-0.762215\pi\) | ||||
−0.733713 | + | 0.679459i | \(0.762215\pi\) | |||||||
\(978\) | − | 455040.i | − | 0.475742i | ||||||
\(979\) | 71941.5i | 0.0750610i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −689416. | −0.716380 | ||||||||
\(982\) | −181730. | −0.188453 | ||||||||
\(983\) | − | 1.73768e6i | − | 1.79831i | −0.437633 | − | 0.899154i | \(-0.644183\pi\) | ||
0.437633 | − | 0.899154i | \(-0.355817\pi\) | |||||||
\(984\) | −928200. | −0.958631 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 226908.i | 0.233398i | ||||||||
\(987\) | −376364. | − | 384125.i | −0.386344 | − | 0.394310i | ||||
\(988\) | −11022.7 | −0.0112921 | ||||||||
\(989\) | −264264. | −0.270175 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −423586. | −0.431315 | −0.215657 | − | 0.976469i | \(-0.569189\pi\) | ||||
−0.215657 | + | 0.976469i | \(0.569189\pi\) | |||||||
\(992\) | − | 1.08360e6i | − | 1.10115i | ||||||
\(993\) | 573530.i | 0.581645i | ||||||||
\(994\) | 374136. | + | 381851.i | 0.378666 | + | 0.386475i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 99500.0 | 0.100301 | ||||||||
\(997\) | 548035.i | 0.551338i | 0.961253 | + | 0.275669i | \(0.0888994\pi\) | ||||
−0.961253 | + | 0.275669i | \(0.911101\pi\) | |||||||
\(998\) | 682249. | 0.684986 | ||||||||
\(999\) | − | 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 | 175.5.d.e.76.3 | 4 | ||
5.2 | odd | 4 | 35.5.c.c.34.2 | yes | 2 | ||
5.3 | odd | 4 | 35.5.c.d.34.1 | yes | 2 | ||
5.4 | even | 2 | inner | 175.5.d.e.76.2 | 4 | ||
7.6 | odd | 2 | inner | 175.5.d.e.76.4 | 4 | ||
15.2 | even | 4 | 315.5.e.d.244.1 | 2 | |||
15.8 | even | 4 | 315.5.e.c.244.2 | 2 | |||
20.3 | even | 4 | 560.5.p.d.209.2 | 2 | |||
20.7 | even | 4 | 560.5.p.e.209.2 | 2 | |||
35.13 | even | 4 | 35.5.c.c.34.1 | ✓ | 2 | ||
35.27 | even | 4 | 35.5.c.d.34.2 | yes | 2 | ||
35.34 | odd | 2 | inner | 175.5.d.e.76.1 | 4 | ||
105.62 | odd | 4 | 315.5.e.c.244.1 | 2 | |||
105.83 | odd | 4 | 315.5.e.d.244.2 | 2 | |||
140.27 | odd | 4 | 560.5.p.d.209.1 | 2 | |||
140.83 | odd | 4 | 560.5.p.e.209.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.5.c.c.34.1 | ✓ | 2 | 35.13 | even | 4 | ||
35.5.c.c.34.2 | yes | 2 | 5.2 | odd | 4 | ||
35.5.c.d.34.1 | yes | 2 | 5.3 | odd | 4 | ||
35.5.c.d.34.2 | yes | 2 | 35.27 | even | 4 | ||
175.5.d.e.76.1 | 4 | 35.34 | odd | 2 | inner | ||
175.5.d.e.76.2 | 4 | 5.4 | even | 2 | inner | ||
175.5.d.e.76.3 | 4 | 1.1 | even | 1 | trivial | ||
175.5.d.e.76.4 | 4 | 7.6 | odd | 2 | inner | ||
315.5.e.c.244.1 | 2 | 105.62 | odd | 4 | |||
315.5.e.c.244.2 | 2 | 15.8 | even | 4 | |||
315.5.e.d.244.1 | 2 | 15.2 | even | 4 | |||
315.5.e.d.244.2 | 2 | 105.83 | odd | 4 | |||
560.5.p.d.209.1 | 2 | 140.27 | odd | 4 | |||
560.5.p.d.209.2 | 2 | 20.3 | even | 4 | |||
560.5.p.e.209.1 | 2 | 140.83 | odd | 4 | |||
560.5.p.e.209.2 | 2 | 20.7 | even | 4 |