Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1805,4,Mod(1,1805)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1805, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1805.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1805 = 5 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1805.a (trivial) |
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: | yes |
Analytic conductor: | \(106.498447560\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1805.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.00000 | 1.76777 | 0.883883 | − | 0.467707i | \(-0.154920\pi\) | ||||
0.883883 | + | 0.467707i | \(0.154920\pi\) | |||||||
\(3\) | −5.00000 | −0.962250 | −0.481125 | − | 0.876652i | \(-0.659772\pi\) | ||||
−0.481125 | + | 0.876652i | \(0.659772\pi\) | |||||||
\(4\) | 17.0000 | 2.12500 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | −25.0000 | −1.70103 | ||||||||
\(7\) | −19.0000 | −1.02590 | −0.512952 | − | 0.858417i | \(-0.671448\pi\) | ||||
−0.512952 | + | 0.858417i | \(0.671448\pi\) | |||||||
\(8\) | 45.0000 | 1.98874 | ||||||||
\(9\) | −2.00000 | −0.0740741 | ||||||||
\(10\) | 25.0000 | 0.790569 | ||||||||
\(11\) | 50.0000 | 1.37051 | 0.685253 | − | 0.728305i | \(-0.259692\pi\) | ||||
0.685253 | + | 0.728305i | \(0.259692\pi\) | |||||||
\(12\) | −85.0000 | −2.04478 | ||||||||
\(13\) | −55.0000 | −1.17340 | −0.586702 | − | 0.809803i | \(-0.699574\pi\) | ||||
−0.586702 | + | 0.809803i | \(0.699574\pi\) | |||||||
\(14\) | −95.0000 | −1.81356 | ||||||||
\(15\) | −25.0000 | −0.430331 | ||||||||
\(16\) | 89.0000 | 1.39062 | ||||||||
\(17\) | 51.0000 | 0.727607 | 0.363803 | − | 0.931476i | \(-0.381478\pi\) | ||||
0.363803 | + | 0.931476i | \(0.381478\pi\) | |||||||
\(18\) | −10.0000 | −0.130946 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 85.0000 | 0.950329 | ||||||||
\(21\) | 95.0000 | 0.987176 | ||||||||
\(22\) | 250.000 | 2.42274 | ||||||||
\(23\) | −147.000 | −1.33268 | −0.666340 | − | 0.745648i | \(-0.732140\pi\) | ||||
−0.666340 | + | 0.745648i | \(0.732140\pi\) | |||||||
\(24\) | −225.000 | −1.91366 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | −275.000 | −2.07431 | ||||||||
\(27\) | 145.000 | 1.03353 | ||||||||
\(28\) | −323.000 | −2.18005 | ||||||||
\(29\) | 165.000 | 1.05654 | 0.528271 | − | 0.849076i | \(-0.322840\pi\) | ||||
0.528271 | + | 0.849076i | \(0.322840\pi\) | |||||||
\(30\) | −125.000 | −0.760726 | ||||||||
\(31\) | 70.0000 | 0.405560 | 0.202780 | − | 0.979224i | \(-0.435002\pi\) | ||||
0.202780 | + | 0.979224i | \(0.435002\pi\) | |||||||
\(32\) | 85.0000 | 0.469563 | ||||||||
\(33\) | −250.000 | −1.31877 | ||||||||
\(34\) | 255.000 | 1.28624 | ||||||||
\(35\) | −95.0000 | −0.458798 | ||||||||
\(36\) | −34.0000 | −0.157407 | ||||||||
\(37\) | −210.000 | −0.933075 | −0.466538 | − | 0.884501i | \(-0.654499\pi\) | ||||
−0.466538 | + | 0.884501i | \(0.654499\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 275.000 | 1.12911 | ||||||||
\(40\) | 225.000 | 0.889391 | ||||||||
\(41\) | 80.0000 | 0.304729 | 0.152365 | − | 0.988324i | \(-0.451311\pi\) | ||||
0.152365 | + | 0.988324i | \(0.451311\pi\) | |||||||
\(42\) | 475.000 | 1.74510 | ||||||||
\(43\) | −558.000 | −1.97893 | −0.989467 | − | 0.144755i | \(-0.953760\pi\) | ||||
−0.989467 | + | 0.144755i | \(0.953760\pi\) | |||||||
\(44\) | 850.000 | 2.91233 | ||||||||
\(45\) | −10.0000 | −0.0331269 | ||||||||
\(46\) | −735.000 | −2.35587 | ||||||||
\(47\) | −464.000 | −1.44003 | −0.720014 | − | 0.693959i | \(-0.755865\pi\) | ||||
−0.720014 | + | 0.693959i | \(0.755865\pi\) | |||||||
\(48\) | −445.000 | −1.33813 | ||||||||
\(49\) | 18.0000 | 0.0524781 | ||||||||
\(50\) | 125.000 | 0.353553 | ||||||||
\(51\) | −255.000 | −0.700140 | ||||||||
\(52\) | −935.000 | −2.49348 | ||||||||
\(53\) | −455.000 | −1.17923 | −0.589614 | − | 0.807685i | \(-0.700720\pi\) | ||||
−0.589614 | + | 0.807685i | \(0.700720\pi\) | |||||||
\(54\) | 725.000 | 1.82704 | ||||||||
\(55\) | 250.000 | 0.612909 | ||||||||
\(56\) | −855.000 | −2.04025 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 825.000 | 1.86772 | ||||||||
\(59\) | −225.000 | −0.496483 | −0.248242 | − | 0.968698i | \(-0.579853\pi\) | ||||
−0.248242 | + | 0.968698i | \(0.579853\pi\) | |||||||
\(60\) | −425.000 | −0.914454 | ||||||||
\(61\) | 500.000 | 1.04948 | 0.524741 | − | 0.851262i | \(-0.324162\pi\) | ||||
0.524741 | + | 0.851262i | \(0.324162\pi\) | |||||||
\(62\) | 350.000 | 0.716936 | ||||||||
\(63\) | 38.0000 | 0.0759929 | ||||||||
\(64\) | −287.000 | −0.560547 | ||||||||
\(65\) | −275.000 | −0.524762 | ||||||||
\(66\) | −1250.00 | −2.33128 | ||||||||
\(67\) | −105.000 | −0.191460 | −0.0957298 | − | 0.995407i | \(-0.530518\pi\) | ||||
−0.0957298 | + | 0.995407i | \(0.530518\pi\) | |||||||
\(68\) | 867.000 | 1.54616 | ||||||||
\(69\) | 735.000 | 1.28237 | ||||||||
\(70\) | −475.000 | −0.811048 | ||||||||
\(71\) | 1140.00 | 1.90554 | 0.952768 | − | 0.303698i | \(-0.0982214\pi\) | ||||
0.952768 | + | 0.303698i | \(0.0982214\pi\) | |||||||
\(72\) | −90.0000 | −0.147314 | ||||||||
\(73\) | −703.000 | −1.12712 | −0.563561 | − | 0.826074i | \(-0.690569\pi\) | ||||
−0.563561 | + | 0.826074i | \(0.690569\pi\) | |||||||
\(74\) | −1050.00 | −1.64946 | ||||||||
\(75\) | −125.000 | −0.192450 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −950.000 | −1.40601 | ||||||||
\(78\) | 1375.00 | 1.99600 | ||||||||
\(79\) | −700.000 | −0.996913 | −0.498457 | − | 0.866915i | \(-0.666100\pi\) | ||||
−0.498457 | + | 0.866915i | \(0.666100\pi\) | |||||||
\(80\) | 445.000 | 0.621906 | ||||||||
\(81\) | −671.000 | −0.920439 | ||||||||
\(82\) | 400.000 | 0.538690 | ||||||||
\(83\) | −918.000 | −1.21402 | −0.607010 | − | 0.794695i | \(-0.707631\pi\) | ||||
−0.607010 | + | 0.794695i | \(0.707631\pi\) | |||||||
\(84\) | 1615.00 | 2.09775 | ||||||||
\(85\) | 255.000 | 0.325396 | ||||||||
\(86\) | −2790.00 | −3.49830 | ||||||||
\(87\) | −825.000 | −1.01666 | ||||||||
\(88\) | 2250.00 | 2.72558 | ||||||||
\(89\) | −870.000 | −1.03618 | −0.518089 | − | 0.855327i | \(-0.673356\pi\) | ||||
−0.518089 | + | 0.855327i | \(0.673356\pi\) | |||||||
\(90\) | −50.0000 | −0.0585607 | ||||||||
\(91\) | 1045.00 | 1.20380 | ||||||||
\(92\) | −2499.00 | −2.83194 | ||||||||
\(93\) | −350.000 | −0.390251 | ||||||||
\(94\) | −2320.00 | −2.54564 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −425.000 | −0.451837 | ||||||||
\(97\) | −1380.00 | −1.44451 | −0.722257 | − | 0.691625i | \(-0.756895\pi\) | ||||
−0.722257 | + | 0.691625i | \(0.756895\pi\) | |||||||
\(98\) | 90.0000 | 0.0927691 | ||||||||
\(99\) | −100.000 | −0.101519 | ||||||||
\(100\) | 425.000 | 0.425000 | ||||||||
\(101\) | 150.000 | 0.147778 | 0.0738889 | − | 0.997266i | \(-0.476459\pi\) | ||||
0.0738889 | + | 0.997266i | \(0.476459\pi\) | |||||||
\(102\) | −1275.00 | −1.23768 | ||||||||
\(103\) | 1250.00 | 1.19579 | 0.597894 | − | 0.801575i | \(-0.296004\pi\) | ||||
0.597894 | + | 0.801575i | \(0.296004\pi\) | |||||||
\(104\) | −2475.00 | −2.33359 | ||||||||
\(105\) | 475.000 | 0.441479 | ||||||||
\(106\) | −2275.00 | −2.08460 | ||||||||
\(107\) | 1205.00 | 1.08871 | 0.544354 | − | 0.838856i | \(-0.316775\pi\) | ||||
0.544354 | + | 0.838856i | \(0.316775\pi\) | |||||||
\(108\) | 2465.00 | 2.19625 | ||||||||
\(109\) | −1245.00 | −1.09403 | −0.547015 | − | 0.837122i | \(-0.684236\pi\) | ||||
−0.547015 | + | 0.837122i | \(0.684236\pi\) | |||||||
\(110\) | 1250.00 | 1.08348 | ||||||||
\(111\) | 1050.00 | 0.897852 | ||||||||
\(112\) | −1691.00 | −1.42665 | ||||||||
\(113\) | 480.000 | 0.399598 | 0.199799 | − | 0.979837i | \(-0.435971\pi\) | ||||
0.199799 | + | 0.979837i | \(0.435971\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −735.000 | −0.595992 | ||||||||
\(116\) | 2805.00 | 2.24515 | ||||||||
\(117\) | 110.000 | 0.0869188 | ||||||||
\(118\) | −1125.00 | −0.877666 | ||||||||
\(119\) | −969.000 | −0.746454 | ||||||||
\(120\) | −1125.00 | −0.855816 | ||||||||
\(121\) | 1169.00 | 0.878287 | ||||||||
\(122\) | 2500.00 | 1.85524 | ||||||||
\(123\) | −400.000 | −0.293226 | ||||||||
\(124\) | 1190.00 | 0.861816 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 190.000 | 0.134338 | ||||||||
\(127\) | −100.000 | −0.0698706 | −0.0349353 | − | 0.999390i | \(-0.511123\pi\) | ||||
−0.0349353 | + | 0.999390i | \(0.511123\pi\) | |||||||
\(128\) | −2115.00 | −1.46048 | ||||||||
\(129\) | 2790.00 | 1.90423 | ||||||||
\(130\) | −1375.00 | −0.927658 | ||||||||
\(131\) | 1158.00 | 0.772328 | 0.386164 | − | 0.922430i | \(-0.373800\pi\) | ||||
0.386164 | + | 0.922430i | \(0.373800\pi\) | |||||||
\(132\) | −4250.00 | −2.80239 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −525.000 | −0.338456 | ||||||||
\(135\) | 725.000 | 0.462208 | ||||||||
\(136\) | 2295.00 | 1.44702 | ||||||||
\(137\) | 1759.00 | 1.09695 | 0.548473 | − | 0.836168i | \(-0.315209\pi\) | ||||
0.548473 | + | 0.836168i | \(0.315209\pi\) | |||||||
\(138\) | 3675.00 | 2.26693 | ||||||||
\(139\) | −2226.00 | −1.35832 | −0.679161 | − | 0.733989i | \(-0.737656\pi\) | ||||
−0.679161 | + | 0.733989i | \(0.737656\pi\) | |||||||
\(140\) | −1615.00 | −0.974946 | ||||||||
\(141\) | 2320.00 | 1.38567 | ||||||||
\(142\) | 5700.00 | 3.36854 | ||||||||
\(143\) | −2750.00 | −1.60816 | ||||||||
\(144\) | −178.000 | −0.103009 | ||||||||
\(145\) | 825.000 | 0.472500 | ||||||||
\(146\) | −3515.00 | −1.99249 | ||||||||
\(147\) | −90.0000 | −0.0504971 | ||||||||
\(148\) | −3570.00 | −1.98279 | ||||||||
\(149\) | 1736.00 | 0.954488 | 0.477244 | − | 0.878771i | \(-0.341636\pi\) | ||||
0.477244 | + | 0.878771i | \(0.341636\pi\) | |||||||
\(150\) | −625.000 | −0.340207 | ||||||||
\(151\) | 790.000 | 0.425757 | 0.212878 | − | 0.977079i | \(-0.431716\pi\) | ||||
0.212878 | + | 0.977079i | \(0.431716\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −102.000 | −0.0538968 | ||||||||
\(154\) | −4750.00 | −2.48549 | ||||||||
\(155\) | 350.000 | 0.181372 | ||||||||
\(156\) | 4675.00 | 2.39936 | ||||||||
\(157\) | −1944.00 | −0.988204 | −0.494102 | − | 0.869404i | \(-0.664503\pi\) | ||||
−0.494102 | + | 0.869404i | \(0.664503\pi\) | |||||||
\(158\) | −3500.00 | −1.76231 | ||||||||
\(159\) | 2275.00 | 1.13471 | ||||||||
\(160\) | 425.000 | 0.209995 | ||||||||
\(161\) | 2793.00 | 1.36720 | ||||||||
\(162\) | −3355.00 | −1.62712 | ||||||||
\(163\) | −3562.00 | −1.71164 | −0.855820 | − | 0.517273i | \(-0.826947\pi\) | ||||
−0.855820 | + | 0.517273i | \(0.826947\pi\) | |||||||
\(164\) | 1360.00 | 0.647550 | ||||||||
\(165\) | −1250.00 | −0.589772 | ||||||||
\(166\) | −4590.00 | −2.14610 | ||||||||
\(167\) | −3360.00 | −1.55691 | −0.778457 | − | 0.627698i | \(-0.783997\pi\) | ||||
−0.778457 | + | 0.627698i | \(0.783997\pi\) | |||||||
\(168\) | 4275.00 | 1.96323 | ||||||||
\(169\) | 828.000 | 0.376878 | ||||||||
\(170\) | 1275.00 | 0.575224 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −9486.00 | −4.20524 | ||||||||
\(173\) | 3870.00 | 1.70076 | 0.850378 | − | 0.526173i | \(-0.176374\pi\) | ||||
0.850378 | + | 0.526173i | \(0.176374\pi\) | |||||||
\(174\) | −4125.00 | −1.79722 | ||||||||
\(175\) | −475.000 | −0.205181 | ||||||||
\(176\) | 4450.00 | 1.90586 | ||||||||
\(177\) | 1125.00 | 0.477741 | ||||||||
\(178\) | −4350.00 | −1.83172 | ||||||||
\(179\) | −3340.00 | −1.39466 | −0.697328 | − | 0.716752i | \(-0.745628\pi\) | ||||
−0.697328 | + | 0.716752i | \(0.745628\pi\) | |||||||
\(180\) | −170.000 | −0.0703947 | ||||||||
\(181\) | −1790.00 | −0.735081 | −0.367540 | − | 0.930008i | \(-0.619800\pi\) | ||||
−0.367540 | + | 0.930008i | \(0.619800\pi\) | |||||||
\(182\) | 5225.00 | 2.12804 | ||||||||
\(183\) | −2500.00 | −1.00987 | ||||||||
\(184\) | −6615.00 | −2.65035 | ||||||||
\(185\) | −1050.00 | −0.417284 | ||||||||
\(186\) | −1750.00 | −0.689872 | ||||||||
\(187\) | 2550.00 | 0.997190 | ||||||||
\(188\) | −7888.00 | −3.06006 | ||||||||
\(189\) | −2755.00 | −1.06030 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1647.00 | −0.623941 | −0.311971 | − | 0.950092i | \(-0.600989\pi\) | ||||
−0.311971 | + | 0.950092i | \(0.600989\pi\) | |||||||
\(192\) | 1435.00 | 0.539386 | ||||||||
\(193\) | 1030.00 | 0.384150 | 0.192075 | − | 0.981380i | \(-0.438478\pi\) | ||||
0.192075 | + | 0.981380i | \(0.438478\pi\) | |||||||
\(194\) | −6900.00 | −2.55356 | ||||||||
\(195\) | 1375.00 | 0.504953 | ||||||||
\(196\) | 306.000 | 0.111516 | ||||||||
\(197\) | −336.000 | −0.121518 | −0.0607589 | − | 0.998152i | \(-0.519352\pi\) | ||||
−0.0607589 | + | 0.998152i | \(0.519352\pi\) | |||||||
\(198\) | −500.000 | −0.179462 | ||||||||
\(199\) | −875.000 | −0.311694 | −0.155847 | − | 0.987781i | \(-0.549811\pi\) | ||||
−0.155847 | + | 0.987781i | \(0.549811\pi\) | |||||||
\(200\) | 1125.00 | 0.397748 | ||||||||
\(201\) | 525.000 | 0.184232 | ||||||||
\(202\) | 750.000 | 0.261237 | ||||||||
\(203\) | −3135.00 | −1.08391 | ||||||||
\(204\) | −4335.00 | −1.48780 | ||||||||
\(205\) | 400.000 | 0.136279 | ||||||||
\(206\) | 6250.00 | 2.11387 | ||||||||
\(207\) | 294.000 | 0.0987170 | ||||||||
\(208\) | −4895.00 | −1.63177 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 2375.00 | 0.780431 | ||||||||
\(211\) | 3935.00 | 1.28387 | 0.641935 | − | 0.766759i | \(-0.278132\pi\) | ||||
0.641935 | + | 0.766759i | \(0.278132\pi\) | |||||||
\(212\) | −7735.00 | −2.50586 | ||||||||
\(213\) | −5700.00 | −1.83360 | ||||||||
\(214\) | 6025.00 | 1.92458 | ||||||||
\(215\) | −2790.00 | −0.885007 | ||||||||
\(216\) | 6525.00 | 2.05542 | ||||||||
\(217\) | −1330.00 | −0.416066 | ||||||||
\(218\) | −6225.00 | −1.93399 | ||||||||
\(219\) | 3515.00 | 1.08457 | ||||||||
\(220\) | 4250.00 | 1.30243 | ||||||||
\(221\) | −2805.00 | −0.853777 | ||||||||
\(222\) | 5250.00 | 1.58719 | ||||||||
\(223\) | 5690.00 | 1.70866 | 0.854329 | − | 0.519733i | \(-0.173969\pi\) | ||||
0.854329 | + | 0.519733i | \(0.173969\pi\) | |||||||
\(224\) | −1615.00 | −0.481726 | ||||||||
\(225\) | −50.0000 | −0.0148148 | ||||||||
\(226\) | 2400.00 | 0.706397 | ||||||||
\(227\) | 2715.00 | 0.793836 | 0.396918 | − | 0.917854i | \(-0.370080\pi\) | ||||
0.396918 | + | 0.917854i | \(0.370080\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −716.000 | −0.206614 | −0.103307 | − | 0.994650i | \(-0.532942\pi\) | ||||
−0.103307 | + | 0.994650i | \(0.532942\pi\) | |||||||
\(230\) | −3675.00 | −1.05358 | ||||||||
\(231\) | 4750.00 | 1.35293 | ||||||||
\(232\) | 7425.00 | 2.10119 | ||||||||
\(233\) | 3182.00 | 0.894677 | 0.447339 | − | 0.894365i | \(-0.352372\pi\) | ||||
0.447339 | + | 0.894365i | \(0.352372\pi\) | |||||||
\(234\) | 550.000 | 0.153652 | ||||||||
\(235\) | −2320.00 | −0.644000 | ||||||||
\(236\) | −3825.00 | −1.05503 | ||||||||
\(237\) | 3500.00 | 0.959280 | ||||||||
\(238\) | −4845.00 | −1.31956 | ||||||||
\(239\) | −4275.00 | −1.15702 | −0.578508 | − | 0.815677i | \(-0.696365\pi\) | ||||
−0.578508 | + | 0.815677i | \(0.696365\pi\) | |||||||
\(240\) | −2225.00 | −0.598430 | ||||||||
\(241\) | 280.000 | 0.0748398 | 0.0374199 | − | 0.999300i | \(-0.488086\pi\) | ||||
0.0374199 | + | 0.999300i | \(0.488086\pi\) | |||||||
\(242\) | 5845.00 | 1.55261 | ||||||||
\(243\) | −560.000 | −0.147835 | ||||||||
\(244\) | 8500.00 | 2.23015 | ||||||||
\(245\) | 90.0000 | 0.0234689 | ||||||||
\(246\) | −2000.00 | −0.518355 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 3150.00 | 0.806553 | ||||||||
\(249\) | 4590.00 | 1.16819 | ||||||||
\(250\) | 625.000 | 0.158114 | ||||||||
\(251\) | 1152.00 | 0.289696 | 0.144848 | − | 0.989454i | \(-0.453731\pi\) | ||||
0.144848 | + | 0.989454i | \(0.453731\pi\) | |||||||
\(252\) | 646.000 | 0.161485 | ||||||||
\(253\) | −7350.00 | −1.82644 | ||||||||
\(254\) | −500.000 | −0.123515 | ||||||||
\(255\) | −1275.00 | −0.313112 | ||||||||
\(256\) | −8279.00 | −2.02124 | ||||||||
\(257\) | −870.000 | −0.211164 | −0.105582 | − | 0.994411i | \(-0.533671\pi\) | ||||
−0.105582 | + | 0.994411i | \(0.533671\pi\) | |||||||
\(258\) | 13950.0 | 3.36624 | ||||||||
\(259\) | 3990.00 | 0.957245 | ||||||||
\(260\) | −4675.00 | −1.11512 | ||||||||
\(261\) | −330.000 | −0.0782624 | ||||||||
\(262\) | 5790.00 | 1.36530 | ||||||||
\(263\) | −5688.00 | −1.33360 | −0.666801 | − | 0.745236i | \(-0.732337\pi\) | ||||
−0.666801 | + | 0.745236i | \(0.732337\pi\) | |||||||
\(264\) | −11250.0 | −2.62269 | ||||||||
\(265\) | −2275.00 | −0.527367 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4350.00 | 0.997062 | ||||||||
\(268\) | −1785.00 | −0.406852 | ||||||||
\(269\) | 1010.00 | 0.228925 | 0.114462 | − | 0.993428i | \(-0.463485\pi\) | ||||
0.114462 | + | 0.993428i | \(0.463485\pi\) | |||||||
\(270\) | 3625.00 | 0.817076 | ||||||||
\(271\) | 25.0000 | 0.00560384 | 0.00280192 | − | 0.999996i | \(-0.499108\pi\) | ||||
0.00280192 | + | 0.999996i | \(0.499108\pi\) | |||||||
\(272\) | 4539.00 | 1.01183 | ||||||||
\(273\) | −5225.00 | −1.15836 | ||||||||
\(274\) | 8795.00 | 1.93914 | ||||||||
\(275\) | 1250.00 | 0.274101 | ||||||||
\(276\) | 12495.0 | 2.72504 | ||||||||
\(277\) | 3646.00 | 0.790855 | 0.395428 | − | 0.918497i | \(-0.370596\pi\) | ||||
0.395428 | + | 0.918497i | \(0.370596\pi\) | |||||||
\(278\) | −11130.0 | −2.40120 | ||||||||
\(279\) | −140.000 | −0.0300415 | ||||||||
\(280\) | −4275.00 | −0.912429 | ||||||||
\(281\) | −6000.00 | −1.27377 | −0.636886 | − | 0.770958i | \(-0.719778\pi\) | ||||
−0.636886 | + | 0.770958i | \(0.719778\pi\) | |||||||
\(282\) | 11600.0 | 2.44954 | ||||||||
\(283\) | 5018.00 | 1.05403 | 0.527013 | − | 0.849857i | \(-0.323312\pi\) | ||||
0.527013 | + | 0.849857i | \(0.323312\pi\) | |||||||
\(284\) | 19380.0 | 4.04927 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −13750.0 | −2.84285 | ||||||||
\(287\) | −1520.00 | −0.312623 | ||||||||
\(288\) | −170.000 | −0.0347825 | ||||||||
\(289\) | −2312.00 | −0.470588 | ||||||||
\(290\) | 4125.00 | 0.835270 | ||||||||
\(291\) | 6900.00 | 1.38998 | ||||||||
\(292\) | −11951.0 | −2.39513 | ||||||||
\(293\) | 7035.00 | 1.40269 | 0.701347 | − | 0.712820i | \(-0.252583\pi\) | ||||
0.701347 | + | 0.712820i | \(0.252583\pi\) | |||||||
\(294\) | −450.000 | −0.0892671 | ||||||||
\(295\) | −1125.00 | −0.222034 | ||||||||
\(296\) | −9450.00 | −1.85564 | ||||||||
\(297\) | 7250.00 | 1.41646 | ||||||||
\(298\) | 8680.00 | 1.68731 | ||||||||
\(299\) | 8085.00 | 1.56377 | ||||||||
\(300\) | −2125.00 | −0.408956 | ||||||||
\(301\) | 10602.0 | 2.03020 | ||||||||
\(302\) | 3950.00 | 0.752639 | ||||||||
\(303\) | −750.000 | −0.142199 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2500.00 | 0.469343 | ||||||||
\(306\) | −510.000 | −0.0952770 | ||||||||
\(307\) | 4460.00 | 0.829139 | 0.414569 | − | 0.910018i | \(-0.363932\pi\) | ||||
0.414569 | + | 0.910018i | \(0.363932\pi\) | |||||||
\(308\) | −16150.0 | −2.98777 | ||||||||
\(309\) | −6250.00 | −1.15065 | ||||||||
\(310\) | 1750.00 | 0.320624 | ||||||||
\(311\) | 6825.00 | 1.24441 | 0.622203 | − | 0.782856i | \(-0.286238\pi\) | ||||
0.622203 | + | 0.782856i | \(0.286238\pi\) | |||||||
\(312\) | 12375.0 | 2.24550 | ||||||||
\(313\) | 4537.00 | 0.819318 | 0.409659 | − | 0.912239i | \(-0.365648\pi\) | ||||
0.409659 | + | 0.912239i | \(0.365648\pi\) | |||||||
\(314\) | −9720.00 | −1.74692 | ||||||||
\(315\) | 190.000 | 0.0339850 | ||||||||
\(316\) | −11900.0 | −2.11844 | ||||||||
\(317\) | −7845.00 | −1.38997 | −0.694983 | − | 0.719026i | \(-0.744588\pi\) | ||||
−0.694983 | + | 0.719026i | \(0.744588\pi\) | |||||||
\(318\) | 11375.0 | 2.00591 | ||||||||
\(319\) | 8250.00 | 1.44800 | ||||||||
\(320\) | −1435.00 | −0.250684 | ||||||||
\(321\) | −6025.00 | −1.04761 | ||||||||
\(322\) | 13965.0 | 2.41689 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −11407.0 | −1.95593 | ||||||||
\(325\) | −1375.00 | −0.234681 | ||||||||
\(326\) | −17810.0 | −3.02578 | ||||||||
\(327\) | 6225.00 | 1.05273 | ||||||||
\(328\) | 3600.00 | 0.606027 | ||||||||
\(329\) | 8816.00 | 1.47733 | ||||||||
\(330\) | −6250.00 | −1.04258 | ||||||||
\(331\) | −7075.00 | −1.17486 | −0.587428 | − | 0.809277i | \(-0.699859\pi\) | ||||
−0.587428 | + | 0.809277i | \(0.699859\pi\) | |||||||
\(332\) | −15606.0 | −2.57979 | ||||||||
\(333\) | 420.000 | 0.0691167 | ||||||||
\(334\) | −16800.0 | −2.75226 | ||||||||
\(335\) | −525.000 | −0.0856233 | ||||||||
\(336\) | 8455.00 | 1.37279 | ||||||||
\(337\) | 11710.0 | 1.89283 | 0.946416 | − | 0.322950i | \(-0.104675\pi\) | ||||
0.946416 | + | 0.322950i | \(0.104675\pi\) | |||||||
\(338\) | 4140.00 | 0.666232 | ||||||||
\(339\) | −2400.00 | −0.384514 | ||||||||
\(340\) | 4335.00 | 0.691466 | ||||||||
\(341\) | 3500.00 | 0.555823 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6175.00 | 0.972066 | ||||||||
\(344\) | −25110.0 | −3.93558 | ||||||||
\(345\) | 3675.00 | 0.573494 | ||||||||
\(346\) | 19350.0 | 3.00654 | ||||||||
\(347\) | −336.000 | −0.0519811 | −0.0259905 | − | 0.999662i | \(-0.508274\pi\) | ||||
−0.0259905 | + | 0.999662i | \(0.508274\pi\) | |||||||
\(348\) | −14025.0 | −2.16040 | ||||||||
\(349\) | −700.000 | −0.107364 | −0.0536822 | − | 0.998558i | \(-0.517096\pi\) | ||||
−0.0536822 | + | 0.998558i | \(0.517096\pi\) | |||||||
\(350\) | −2375.00 | −0.362712 | ||||||||
\(351\) | −7975.00 | −1.21275 | ||||||||
\(352\) | 4250.00 | 0.643539 | ||||||||
\(353\) | −8923.00 | −1.34539 | −0.672696 | − | 0.739919i | \(-0.734864\pi\) | ||||
−0.672696 | + | 0.739919i | \(0.734864\pi\) | |||||||
\(354\) | 5625.00 | 0.844535 | ||||||||
\(355\) | 5700.00 | 0.852182 | ||||||||
\(356\) | −14790.0 | −2.20188 | ||||||||
\(357\) | 4845.00 | 0.718276 | ||||||||
\(358\) | −16700.0 | −2.46543 | ||||||||
\(359\) | −7521.00 | −1.10569 | −0.552846 | − | 0.833284i | \(-0.686458\pi\) | ||||
−0.552846 | + | 0.833284i | \(0.686458\pi\) | |||||||
\(360\) | −450.000 | −0.0658808 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | −8950.00 | −1.29945 | ||||||||
\(363\) | −5845.00 | −0.845132 | ||||||||
\(364\) | 17765.0 | 2.55807 | ||||||||
\(365\) | −3515.00 | −0.504064 | ||||||||
\(366\) | −12500.0 | −1.78521 | ||||||||
\(367\) | 4624.00 | 0.657686 | 0.328843 | − | 0.944385i | \(-0.393341\pi\) | ||||
0.328843 | + | 0.944385i | \(0.393341\pi\) | |||||||
\(368\) | −13083.0 | −1.85326 | ||||||||
\(369\) | −160.000 | −0.0225725 | ||||||||
\(370\) | −5250.00 | −0.737661 | ||||||||
\(371\) | 8645.00 | 1.20977 | ||||||||
\(372\) | −5950.00 | −0.829283 | ||||||||
\(373\) | 9015.00 | 1.25142 | 0.625709 | − | 0.780056i | \(-0.284810\pi\) | ||||
0.625709 | + | 0.780056i | \(0.284810\pi\) | |||||||
\(374\) | 12750.0 | 1.76280 | ||||||||
\(375\) | −625.000 | −0.0860663 | ||||||||
\(376\) | −20880.0 | −2.86384 | ||||||||
\(377\) | −9075.00 | −1.23975 | ||||||||
\(378\) | −13775.0 | −1.87436 | ||||||||
\(379\) | 3895.00 | 0.527896 | 0.263948 | − | 0.964537i | \(-0.414975\pi\) | ||||
0.263948 | + | 0.964537i | \(0.414975\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 500.000 | 0.0672330 | ||||||||
\(382\) | −8235.00 | −1.10298 | ||||||||
\(383\) | −9690.00 | −1.29278 | −0.646391 | − | 0.763006i | \(-0.723723\pi\) | ||||
−0.646391 | + | 0.763006i | \(0.723723\pi\) | |||||||
\(384\) | 10575.0 | 1.40535 | ||||||||
\(385\) | −4750.00 | −0.628785 | ||||||||
\(386\) | 5150.00 | 0.679088 | ||||||||
\(387\) | 1116.00 | 0.146588 | ||||||||
\(388\) | −23460.0 | −3.06959 | ||||||||
\(389\) | −5650.00 | −0.736417 | −0.368209 | − | 0.929743i | \(-0.620029\pi\) | ||||
−0.368209 | + | 0.929743i | \(0.620029\pi\) | |||||||
\(390\) | 6875.00 | 0.892639 | ||||||||
\(391\) | −7497.00 | −0.969666 | ||||||||
\(392\) | 810.000 | 0.104365 | ||||||||
\(393\) | −5790.00 | −0.743173 | ||||||||
\(394\) | −1680.00 | −0.214815 | ||||||||
\(395\) | −3500.00 | −0.445833 | ||||||||
\(396\) | −1700.00 | −0.215728 | ||||||||
\(397\) | 3386.00 | 0.428057 | 0.214028 | − | 0.976827i | \(-0.431342\pi\) | ||||
0.214028 | + | 0.976827i | \(0.431342\pi\) | |||||||
\(398\) | −4375.00 | −0.551002 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2225.00 | 0.278125 | ||||||||
\(401\) | 11840.0 | 1.47447 | 0.737234 | − | 0.675638i | \(-0.236132\pi\) | ||||
0.737234 | + | 0.675638i | \(0.236132\pi\) | |||||||
\(402\) | 2625.00 | 0.325679 | ||||||||
\(403\) | −3850.00 | −0.475886 | ||||||||
\(404\) | 2550.00 | 0.314028 | ||||||||
\(405\) | −3355.00 | −0.411633 | ||||||||
\(406\) | −15675.0 | −1.91610 | ||||||||
\(407\) | −10500.0 | −1.27879 | ||||||||
\(408\) | −11475.0 | −1.39239 | ||||||||
\(409\) | 6770.00 | 0.818472 | 0.409236 | − | 0.912429i | \(-0.365795\pi\) | ||||
0.409236 | + | 0.912429i | \(0.365795\pi\) | |||||||
\(410\) | 2000.00 | 0.240910 | ||||||||
\(411\) | −8795.00 | −1.05554 | ||||||||
\(412\) | 21250.0 | 2.54105 | ||||||||
\(413\) | 4275.00 | 0.509344 | ||||||||
\(414\) | 1470.00 | 0.174509 | ||||||||
\(415\) | −4590.00 | −0.542926 | ||||||||
\(416\) | −4675.00 | −0.550987 | ||||||||
\(417\) | 11130.0 | 1.30705 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4550.00 | 0.530506 | 0.265253 | − | 0.964179i | \(-0.414545\pi\) | ||||
0.265253 | + | 0.964179i | \(0.414545\pi\) | |||||||
\(420\) | 8075.00 | 0.938142 | ||||||||
\(421\) | 3085.00 | 0.357135 | 0.178567 | − | 0.983928i | \(-0.442854\pi\) | ||||
0.178567 | + | 0.983928i | \(0.442854\pi\) | |||||||
\(422\) | 19675.0 | 2.26958 | ||||||||
\(423\) | 928.000 | 0.106669 | ||||||||
\(424\) | −20475.0 | −2.34517 | ||||||||
\(425\) | 1275.00 | 0.145521 | ||||||||
\(426\) | −28500.0 | −3.24138 | ||||||||
\(427\) | −9500.00 | −1.07667 | ||||||||
\(428\) | 20485.0 | 2.31350 | ||||||||
\(429\) | 13750.0 | 1.54745 | ||||||||
\(430\) | −13950.0 | −1.56449 | ||||||||
\(431\) | −4780.00 | −0.534210 | −0.267105 | − | 0.963667i | \(-0.586067\pi\) | ||||
−0.267105 | + | 0.963667i | \(0.586067\pi\) | |||||||
\(432\) | 12905.0 | 1.43725 | ||||||||
\(433\) | 8570.00 | 0.951150 | 0.475575 | − | 0.879675i | \(-0.342240\pi\) | ||||
0.475575 | + | 0.879675i | \(0.342240\pi\) | |||||||
\(434\) | −6650.00 | −0.735507 | ||||||||
\(435\) | −4125.00 | −0.454663 | ||||||||
\(436\) | −21165.0 | −2.32482 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 17575.0 | 1.91727 | ||||||||
\(439\) | 7220.00 | 0.784947 | 0.392474 | − | 0.919763i | \(-0.371619\pi\) | ||||
0.392474 | + | 0.919763i | \(0.371619\pi\) | |||||||
\(440\) | 11250.0 | 1.21892 | ||||||||
\(441\) | −36.0000 | −0.00388727 | ||||||||
\(442\) | −14025.0 | −1.50928 | ||||||||
\(443\) | −10258.0 | −1.10016 | −0.550082 | − | 0.835111i | \(-0.685403\pi\) | ||||
−0.550082 | + | 0.835111i | \(0.685403\pi\) | |||||||
\(444\) | 17850.0 | 1.90794 | ||||||||
\(445\) | −4350.00 | −0.463393 | ||||||||
\(446\) | 28450.0 | 3.02051 | ||||||||
\(447\) | −8680.00 | −0.918456 | ||||||||
\(448\) | 5453.00 | 0.575067 | ||||||||
\(449\) | −7530.00 | −0.791454 | −0.395727 | − | 0.918368i | \(-0.629507\pi\) | ||||
−0.395727 | + | 0.918368i | \(0.629507\pi\) | |||||||
\(450\) | −250.000 | −0.0261891 | ||||||||
\(451\) | 4000.00 | 0.417633 | ||||||||
\(452\) | 8160.00 | 0.849146 | ||||||||
\(453\) | −3950.00 | −0.409685 | ||||||||
\(454\) | 13575.0 | 1.40332 | ||||||||
\(455\) | 5225.00 | 0.538356 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8819.00 | −0.902703 | −0.451352 | − | 0.892346i | \(-0.649058\pi\) | ||||
−0.451352 | + | 0.892346i | \(0.649058\pi\) | |||||||
\(458\) | −3580.00 | −0.365245 | ||||||||
\(459\) | 7395.00 | 0.752002 | ||||||||
\(460\) | −12495.0 | −1.26648 | ||||||||
\(461\) | 10232.0 | 1.03373 | 0.516867 | − | 0.856065i | \(-0.327098\pi\) | ||||
0.516867 | + | 0.856065i | \(0.327098\pi\) | |||||||
\(462\) | 23750.0 | 2.39167 | ||||||||
\(463\) | −12112.0 | −1.21575 | −0.607875 | − | 0.794033i | \(-0.707978\pi\) | ||||
−0.607875 | + | 0.794033i | \(0.707978\pi\) | |||||||
\(464\) | 14685.0 | 1.46925 | ||||||||
\(465\) | −1750.00 | −0.174525 | ||||||||
\(466\) | 15910.0 | 1.58158 | ||||||||
\(467\) | −5076.00 | −0.502975 | −0.251487 | − | 0.967861i | \(-0.580920\pi\) | ||||
−0.251487 | + | 0.967861i | \(0.580920\pi\) | |||||||
\(468\) | 1870.00 | 0.184703 | ||||||||
\(469\) | 1995.00 | 0.196419 | ||||||||
\(470\) | −11600.0 | −1.13844 | ||||||||
\(471\) | 9720.00 | 0.950900 | ||||||||
\(472\) | −10125.0 | −0.987375 | ||||||||
\(473\) | −27900.0 | −2.71214 | ||||||||
\(474\) | 17500.0 | 1.69578 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −16473.0 | −1.58622 | ||||||||
\(477\) | 910.000 | 0.0873502 | ||||||||
\(478\) | −21375.0 | −2.04533 | ||||||||
\(479\) | 15384.0 | 1.46746 | 0.733730 | − | 0.679442i | \(-0.237778\pi\) | ||||
0.733730 | + | 0.679442i | \(0.237778\pi\) | |||||||
\(480\) | −2125.00 | −0.202068 | ||||||||
\(481\) | 11550.0 | 1.09487 | ||||||||
\(482\) | 1400.00 | 0.132299 | ||||||||
\(483\) | −13965.0 | −1.31559 | ||||||||
\(484\) | 19873.0 | 1.86636 | ||||||||
\(485\) | −6900.00 | −0.646006 | ||||||||
\(486\) | −2800.00 | −0.261339 | ||||||||
\(487\) | 8350.00 | 0.776950 | 0.388475 | − | 0.921459i | \(-0.373002\pi\) | ||||
0.388475 | + | 0.921459i | \(0.373002\pi\) | |||||||
\(488\) | 22500.0 | 2.08715 | ||||||||
\(489\) | 17810.0 | 1.64703 | ||||||||
\(490\) | 450.000 | 0.0414876 | ||||||||
\(491\) | −8772.00 | −0.806262 | −0.403131 | − | 0.915142i | \(-0.632078\pi\) | ||||
−0.403131 | + | 0.915142i | \(0.632078\pi\) | |||||||
\(492\) | −6800.00 | −0.623105 | ||||||||
\(493\) | 8415.00 | 0.768748 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −500.000 | −0.0454007 | ||||||||
\(496\) | 6230.00 | 0.563982 | ||||||||
\(497\) | −21660.0 | −1.95490 | ||||||||
\(498\) | 22950.0 | 2.06509 | ||||||||
\(499\) | −2786.00 | −0.249937 | −0.124968 | − | 0.992161i | \(-0.539883\pi\) | ||||
−0.124968 | + | 0.992161i | \(0.539883\pi\) | |||||||
\(500\) | 2125.00 | 0.190066 | ||||||||
\(501\) | 16800.0 | 1.49814 | ||||||||
\(502\) | 5760.00 | 0.512114 | ||||||||
\(503\) | −727.000 | −0.0644440 | −0.0322220 | − | 0.999481i | \(-0.510258\pi\) | ||||
−0.0322220 | + | 0.999481i | \(0.510258\pi\) | |||||||
\(504\) | 1710.00 | 0.151130 | ||||||||
\(505\) | 750.000 | 0.0660882 | ||||||||
\(506\) | −36750.0 | −3.22873 | ||||||||
\(507\) | −4140.00 | −0.362651 | ||||||||
\(508\) | −1700.00 | −0.148475 | ||||||||
\(509\) | 2370.00 | 0.206382 | 0.103191 | − | 0.994662i | \(-0.467095\pi\) | ||||
0.103191 | + | 0.994662i | \(0.467095\pi\) | |||||||
\(510\) | −6375.00 | −0.553509 | ||||||||
\(511\) | 13357.0 | 1.15632 | ||||||||
\(512\) | −24475.0 | −2.11260 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4350.00 | −0.373288 | ||||||||
\(515\) | 6250.00 | 0.534773 | ||||||||
\(516\) | 47430.0 | 4.04649 | ||||||||
\(517\) | −23200.0 | −1.97357 | ||||||||
\(518\) | 19950.0 | 1.69219 | ||||||||
\(519\) | −19350.0 | −1.63655 | ||||||||
\(520\) | −12375.0 | −1.04361 | ||||||||
\(521\) | −12460.0 | −1.04776 | −0.523880 | − | 0.851792i | \(-0.675516\pi\) | ||||
−0.523880 | + | 0.851792i | \(0.675516\pi\) | |||||||
\(522\) | −1650.00 | −0.138350 | ||||||||
\(523\) | 14705.0 | 1.22945 | 0.614727 | − | 0.788740i | \(-0.289266\pi\) | ||||
0.614727 | + | 0.788740i | \(0.289266\pi\) | |||||||
\(524\) | 19686.0 | 1.64120 | ||||||||
\(525\) | 2375.00 | 0.197435 | ||||||||
\(526\) | −28440.0 | −2.35750 | ||||||||
\(527\) | 3570.00 | 0.295089 | ||||||||
\(528\) | −22250.0 | −1.83391 | ||||||||
\(529\) | 9442.00 | 0.776034 | ||||||||
\(530\) | −11375.0 | −0.932261 | ||||||||
\(531\) | 450.000 | 0.0367765 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4400.00 | −0.357571 | ||||||||
\(534\) | 21750.0 | 1.76257 | ||||||||
\(535\) | 6025.00 | 0.486885 | ||||||||
\(536\) | −4725.00 | −0.380763 | ||||||||
\(537\) | 16700.0 | 1.34201 | ||||||||
\(538\) | 5050.00 | 0.404686 | ||||||||
\(539\) | 900.000 | 0.0719216 | ||||||||
\(540\) | 12325.0 | 0.982192 | ||||||||
\(541\) | −11450.0 | −0.909933 | −0.454967 | − | 0.890508i | \(-0.650349\pi\) | ||||
−0.454967 | + | 0.890508i | \(0.650349\pi\) | |||||||
\(542\) | 125.000 | 0.00990629 | ||||||||
\(543\) | 8950.00 | 0.707332 | ||||||||
\(544\) | 4335.00 | 0.341657 | ||||||||
\(545\) | −6225.00 | −0.489266 | ||||||||
\(546\) | −26125.0 | −2.04770 | ||||||||
\(547\) | 12500.0 | 0.977078 | 0.488539 | − | 0.872542i | \(-0.337530\pi\) | ||||
0.488539 | + | 0.872542i | \(0.337530\pi\) | |||||||
\(548\) | 29903.0 | 2.33101 | ||||||||
\(549\) | −1000.00 | −0.0777395 | ||||||||
\(550\) | 6250.00 | 0.484547 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 33075.0 | 2.55030 | ||||||||
\(553\) | 13300.0 | 1.02274 | ||||||||
\(554\) | 18230.0 | 1.39805 | ||||||||
\(555\) | 5250.00 | 0.401532 | ||||||||
\(556\) | −37842.0 | −2.88644 | ||||||||
\(557\) | 8006.00 | 0.609022 | 0.304511 | − | 0.952509i | \(-0.401507\pi\) | ||||
0.304511 | + | 0.952509i | \(0.401507\pi\) | |||||||
\(558\) | −700.000 | −0.0531064 | ||||||||
\(559\) | 30690.0 | 2.32209 | ||||||||
\(560\) | −8455.00 | −0.638016 | ||||||||
\(561\) | −12750.0 | −0.959546 | ||||||||
\(562\) | −30000.0 | −2.25173 | ||||||||
\(563\) | 7280.00 | 0.544965 | 0.272483 | − | 0.962161i | \(-0.412155\pi\) | ||||
0.272483 | + | 0.962161i | \(0.412155\pi\) | |||||||
\(564\) | 39440.0 | 2.94455 | ||||||||
\(565\) | 2400.00 | 0.178706 | ||||||||
\(566\) | 25090.0 | 1.86327 | ||||||||
\(567\) | 12749.0 | 0.944282 | ||||||||
\(568\) | 51300.0 | 3.78961 | ||||||||
\(569\) | 2080.00 | 0.153248 | 0.0766240 | − | 0.997060i | \(-0.475586\pi\) | ||||
0.0766240 | + | 0.997060i | \(0.475586\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7700.00 | 0.564334 | 0.282167 | − | 0.959365i | \(-0.408947\pi\) | ||||
0.282167 | + | 0.959365i | \(0.408947\pi\) | |||||||
\(572\) | −46750.0 | −3.41734 | ||||||||
\(573\) | 8235.00 | 0.600388 | ||||||||
\(574\) | −7600.00 | −0.552644 | ||||||||
\(575\) | −3675.00 | −0.266536 | ||||||||
\(576\) | 574.000 | 0.0415220 | ||||||||
\(577\) | 23171.0 | 1.67179 | 0.835894 | − | 0.548891i | \(-0.184950\pi\) | ||||
0.835894 | + | 0.548891i | \(0.184950\pi\) | |||||||
\(578\) | −11560.0 | −0.831890 | ||||||||
\(579\) | −5150.00 | −0.369649 | ||||||||
\(580\) | 14025.0 | 1.00406 | ||||||||
\(581\) | 17442.0 | 1.24547 | ||||||||
\(582\) | 34500.0 | 2.45717 | ||||||||
\(583\) | −22750.0 | −1.61614 | ||||||||
\(584\) | −31635.0 | −2.24155 | ||||||||
\(585\) | 550.000 | 0.0388713 | ||||||||
\(586\) | 35175.0 | 2.47963 | ||||||||
\(587\) | −3984.00 | −0.280132 | −0.140066 | − | 0.990142i | \(-0.544731\pi\) | ||||
−0.140066 | + | 0.990142i | \(0.544731\pi\) | |||||||
\(588\) | −1530.00 | −0.107306 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −5625.00 | −0.392504 | ||||||||
\(591\) | 1680.00 | 0.116931 | ||||||||
\(592\) | −18690.0 | −1.29756 | ||||||||
\(593\) | −7458.00 | −0.516464 | −0.258232 | − | 0.966083i | \(-0.583140\pi\) | ||||
−0.258232 | + | 0.966083i | \(0.583140\pi\) | |||||||
\(594\) | 36250.0 | 2.50397 | ||||||||
\(595\) | −4845.00 | −0.333825 | ||||||||
\(596\) | 29512.0 | 2.02829 | ||||||||
\(597\) | 4375.00 | 0.299928 | ||||||||
\(598\) | 40425.0 | 2.76438 | ||||||||
\(599\) | −22000.0 | −1.50066 | −0.750330 | − | 0.661063i | \(-0.770106\pi\) | ||||
−0.750330 | + | 0.661063i | \(0.770106\pi\) | |||||||
\(600\) | −5625.00 | −0.382733 | ||||||||
\(601\) | 25270.0 | 1.71512 | 0.857558 | − | 0.514387i | \(-0.171981\pi\) | ||||
0.857558 | + | 0.514387i | \(0.171981\pi\) | |||||||
\(602\) | 53010.0 | 3.58891 | ||||||||
\(603\) | 210.000 | 0.0141822 | ||||||||
\(604\) | 13430.0 | 0.904733 | ||||||||
\(605\) | 5845.00 | 0.392782 | ||||||||
\(606\) | −3750.00 | −0.251375 | ||||||||
\(607\) | −780.000 | −0.0521569 | −0.0260784 | − | 0.999660i | \(-0.508302\pi\) | ||||
−0.0260784 | + | 0.999660i | \(0.508302\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 15675.0 | 1.04299 | ||||||||
\(610\) | 12500.0 | 0.829689 | ||||||||
\(611\) | 25520.0 | 1.68974 | ||||||||
\(612\) | −1734.00 | −0.114531 | ||||||||
\(613\) | −7162.00 | −0.471893 | −0.235947 | − | 0.971766i | \(-0.575819\pi\) | ||||
−0.235947 | + | 0.971766i | \(0.575819\pi\) | |||||||
\(614\) | 22300.0 | 1.46572 | ||||||||
\(615\) | −2000.00 | −0.131135 | ||||||||
\(616\) | −42750.0 | −2.79618 | ||||||||
\(617\) | −14174.0 | −0.924836 | −0.462418 | − | 0.886662i | \(-0.653018\pi\) | ||||
−0.462418 | + | 0.886662i | \(0.653018\pi\) | |||||||
\(618\) | −31250.0 | −2.03408 | ||||||||
\(619\) | 10844.0 | 0.704131 | 0.352066 | − | 0.935975i | \(-0.385479\pi\) | ||||
0.352066 | + | 0.935975i | \(0.385479\pi\) | |||||||
\(620\) | 5950.00 | 0.385416 | ||||||||
\(621\) | −21315.0 | −1.37736 | ||||||||
\(622\) | 34125.0 | 2.19982 | ||||||||
\(623\) | 16530.0 | 1.06302 | ||||||||
\(624\) | 24475.0 | 1.57017 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 22685.0 | 1.44836 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −33048.0 | −2.09993 | ||||||||
\(629\) | −10710.0 | −0.678912 | ||||||||
\(630\) | 950.000 | 0.0600776 | ||||||||
\(631\) | −26200.0 | −1.65294 | −0.826470 | − | 0.562980i | \(-0.809655\pi\) | ||||
−0.826470 | + | 0.562980i | \(0.809655\pi\) | |||||||
\(632\) | −31500.0 | −1.98260 | ||||||||
\(633\) | −19675.0 | −1.23540 | ||||||||
\(634\) | −39225.0 | −2.45714 | ||||||||
\(635\) | −500.000 | −0.0312471 | ||||||||
\(636\) | 38675.0 | 2.41126 | ||||||||
\(637\) | −990.000 | −0.0615781 | ||||||||
\(638\) | 41250.0 | 2.55972 | ||||||||
\(639\) | −2280.00 | −0.141151 | ||||||||
\(640\) | −10575.0 | −0.653146 | ||||||||
\(641\) | −11970.0 | −0.737577 | −0.368788 | − | 0.929513i | \(-0.620227\pi\) | ||||
−0.368788 | + | 0.929513i | \(0.620227\pi\) | |||||||
\(642\) | −30125.0 | −1.85193 | ||||||||
\(643\) | −6792.00 | −0.416564 | −0.208282 | − | 0.978069i | \(-0.566787\pi\) | ||||
−0.208282 | + | 0.978069i | \(0.566787\pi\) | |||||||
\(644\) | 47481.0 | 2.90530 | ||||||||
\(645\) | 13950.0 | 0.851598 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 11561.0 | 0.702488 | 0.351244 | − | 0.936284i | \(-0.385759\pi\) | ||||
0.351244 | + | 0.936284i | \(0.385759\pi\) | |||||||
\(648\) | −30195.0 | −1.83051 | ||||||||
\(649\) | −11250.0 | −0.680433 | ||||||||
\(650\) | −6875.00 | −0.414861 | ||||||||
\(651\) | 6650.00 | 0.400360 | ||||||||
\(652\) | −60554.0 | −3.63724 | ||||||||
\(653\) | 20198.0 | 1.21043 | 0.605213 | − | 0.796063i | \(-0.293088\pi\) | ||||
0.605213 | + | 0.796063i | \(0.293088\pi\) | |||||||
\(654\) | 31125.0 | 1.86098 | ||||||||
\(655\) | 5790.00 | 0.345395 | ||||||||
\(656\) | 7120.00 | 0.423764 | ||||||||
\(657\) | 1406.00 | 0.0834905 | ||||||||
\(658\) | 44080.0 | 2.61158 | ||||||||
\(659\) | 8445.00 | 0.499197 | 0.249598 | − | 0.968349i | \(-0.419701\pi\) | ||||
0.249598 | + | 0.968349i | \(0.419701\pi\) | |||||||
\(660\) | −21250.0 | −1.25327 | ||||||||
\(661\) | 3095.00 | 0.182120 | 0.0910602 | − | 0.995845i | \(-0.470974\pi\) | ||||
0.0910602 | + | 0.995845i | \(0.470974\pi\) | |||||||
\(662\) | −35375.0 | −2.07687 | ||||||||
\(663\) | 14025.0 | 0.821547 | ||||||||
\(664\) | −41310.0 | −2.41437 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2100.00 | 0.122182 | ||||||||
\(667\) | −24255.0 | −1.40803 | ||||||||
\(668\) | −57120.0 | −3.30844 | ||||||||
\(669\) | −28450.0 | −1.64416 | ||||||||
\(670\) | −2625.00 | −0.151362 | ||||||||
\(671\) | 25000.0 | 1.43832 | ||||||||
\(672\) | 8075.00 | 0.463541 | ||||||||
\(673\) | 7880.00 | 0.451340 | 0.225670 | − | 0.974204i | \(-0.427543\pi\) | ||||
0.225670 | + | 0.974204i | \(0.427543\pi\) | |||||||
\(674\) | 58550.0 | 3.34609 | ||||||||
\(675\) | 3625.00 | 0.206706 | ||||||||
\(676\) | 14076.0 | 0.800865 | ||||||||
\(677\) | 3975.00 | 0.225660 | 0.112830 | − | 0.993614i | \(-0.464008\pi\) | ||||
0.112830 | + | 0.993614i | \(0.464008\pi\) | |||||||
\(678\) | −12000.0 | −0.679730 | ||||||||
\(679\) | 26220.0 | 1.48193 | ||||||||
\(680\) | 11475.0 | 0.647127 | ||||||||
\(681\) | −13575.0 | −0.763870 | ||||||||
\(682\) | 17500.0 | 0.982565 | ||||||||
\(683\) | −19140.0 | −1.07229 | −0.536143 | − | 0.844127i | \(-0.680119\pi\) | ||||
−0.536143 | + | 0.844127i | \(0.680119\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8795.00 | 0.490569 | ||||||||
\(686\) | 30875.0 | 1.71839 | ||||||||
\(687\) | 3580.00 | 0.198814 | ||||||||
\(688\) | −49662.0 | −2.75196 | ||||||||
\(689\) | 25025.0 | 1.38371 | ||||||||
\(690\) | 18375.0 | 1.01380 | ||||||||
\(691\) | −17200.0 | −0.946916 | −0.473458 | − | 0.880816i | \(-0.656994\pi\) | ||||
−0.473458 | + | 0.880816i | \(0.656994\pi\) | |||||||
\(692\) | 65790.0 | 3.61410 | ||||||||
\(693\) | 1900.00 | 0.104149 | ||||||||
\(694\) | −1680.00 | −0.0918904 | ||||||||
\(695\) | −11130.0 | −0.607460 | ||||||||
\(696\) | −37125.0 | −2.02187 | ||||||||
\(697\) | 4080.00 | 0.221723 | ||||||||
\(698\) | −3500.00 | −0.189795 | ||||||||
\(699\) | −15910.0 | −0.860903 | ||||||||
\(700\) | −8075.00 | −0.436009 | ||||||||
\(701\) | 10400.0 | 0.560346 | 0.280173 | − | 0.959950i | \(-0.409608\pi\) | ||||
0.280173 | + | 0.959950i | \(0.409608\pi\) | |||||||
\(702\) | −39875.0 | −2.14385 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −14350.0 | −0.768233 | ||||||||
\(705\) | 11600.0 | 0.619690 | ||||||||
\(706\) | −44615.0 | −2.37834 | ||||||||
\(707\) | −2850.00 | −0.151606 | ||||||||
\(708\) | 19125.0 | 1.01520 | ||||||||
\(709\) | 10800.0 | 0.572077 | 0.286038 | − | 0.958218i | \(-0.407661\pi\) | ||||
0.286038 | + | 0.958218i | \(0.407661\pi\) | |||||||
\(710\) | 28500.0 | 1.50646 | ||||||||
\(711\) | 1400.00 | 0.0738454 | ||||||||
\(712\) | −39150.0 | −2.06069 | ||||||||
\(713\) | −10290.0 | −0.540482 | ||||||||
\(714\) | 24225.0 | 1.26974 | ||||||||
\(715\) | −13750.0 | −0.719190 | ||||||||
\(716\) | −56780.0 | −2.96364 | ||||||||
\(717\) | 21375.0 | 1.11334 | ||||||||
\(718\) | −37605.0 | −1.95460 | ||||||||
\(719\) | 16569.0 | 0.859415 | 0.429708 | − | 0.902968i | \(-0.358617\pi\) | ||||
0.429708 | + | 0.902968i | \(0.358617\pi\) | |||||||
\(720\) | −890.000 | −0.0460671 | ||||||||
\(721\) | −23750.0 | −1.22676 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1400.00 | −0.0720146 | ||||||||
\(724\) | −30430.0 | −1.56205 | ||||||||
\(725\) | 4125.00 | 0.211308 | ||||||||
\(726\) | −29225.0 | −1.49400 | ||||||||
\(727\) | −371.000 | −0.0189266 | −0.00946329 | − | 0.999955i | \(-0.503012\pi\) | ||||
−0.00946329 | + | 0.999955i | \(0.503012\pi\) | |||||||
\(728\) | 47025.0 | 2.39404 | ||||||||
\(729\) | 20917.0 | 1.06269 | ||||||||
\(730\) | −17575.0 | −0.891068 | ||||||||
\(731\) | −28458.0 | −1.43989 | ||||||||
\(732\) | −42500.0 | −2.14596 | ||||||||
\(733\) | −35318.0 | −1.77967 | −0.889836 | − | 0.456280i | \(-0.849182\pi\) | ||||
−0.889836 | + | 0.456280i | \(0.849182\pi\) | |||||||
\(734\) | 23120.0 | 1.16264 | ||||||||
\(735\) | −450.000 | −0.0225830 | ||||||||
\(736\) | −12495.0 | −0.625777 | ||||||||
\(737\) | −5250.00 | −0.262397 | ||||||||
\(738\) | −800.000 | −0.0399030 | ||||||||
\(739\) | −8600.00 | −0.428087 | −0.214043 | − | 0.976824i | \(-0.568663\pi\) | ||||
−0.214043 | + | 0.976824i | \(0.568663\pi\) | |||||||
\(740\) | −17850.0 | −0.886728 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 43225.0 | 2.13860 | ||||||||
\(743\) | 29730.0 | 1.46795 | 0.733976 | − | 0.679176i | \(-0.237663\pi\) | ||||
0.733976 | + | 0.679176i | \(0.237663\pi\) | |||||||
\(744\) | −15750.0 | −0.776106 | ||||||||
\(745\) | 8680.00 | 0.426860 | ||||||||
\(746\) | 45075.0 | 2.21222 | ||||||||
\(747\) | 1836.00 | 0.0899273 | ||||||||
\(748\) | 43350.0 | 2.11903 | ||||||||
\(749\) | −22895.0 | −1.11691 | ||||||||
\(750\) | −3125.00 | −0.152145 | ||||||||
\(751\) | −10680.0 | −0.518933 | −0.259467 | − | 0.965752i | \(-0.583547\pi\) | ||||
−0.259467 | + | 0.965752i | \(0.583547\pi\) | |||||||
\(752\) | −41296.0 | −2.00254 | ||||||||
\(753\) | −5760.00 | −0.278760 | ||||||||
\(754\) | −45375.0 | −2.19159 | ||||||||
\(755\) | 3950.00 | 0.190404 | ||||||||
\(756\) | −46835.0 | −2.25314 | ||||||||
\(757\) | 35444.0 | 1.70176 | 0.850881 | − | 0.525358i | \(-0.176069\pi\) | ||||
0.850881 | + | 0.525358i | \(0.176069\pi\) | |||||||
\(758\) | 19475.0 | 0.933198 | ||||||||
\(759\) | 36750.0 | 1.75750 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −14525.0 | −0.691893 | −0.345947 | − | 0.938254i | \(-0.612442\pi\) | ||||
−0.345947 | + | 0.938254i | \(0.612442\pi\) | |||||||
\(762\) | 2500.00 | 0.118852 | ||||||||
\(763\) | 23655.0 | 1.12237 | ||||||||
\(764\) | −27999.0 | −1.32587 | ||||||||
\(765\) | −510.000 | −0.0241034 | ||||||||
\(766\) | −48450.0 | −2.28534 | ||||||||
\(767\) | 12375.0 | 0.582575 | ||||||||
\(768\) | 41395.0 | 1.94494 | ||||||||
\(769\) | 22169.0 | 1.03958 | 0.519788 | − | 0.854295i | \(-0.326011\pi\) | ||||
0.519788 | + | 0.854295i | \(0.326011\pi\) | |||||||
\(770\) | −23750.0 | −1.11155 | ||||||||
\(771\) | 4350.00 | 0.203193 | ||||||||
\(772\) | 17510.0 | 0.816320 | ||||||||
\(773\) | 26435.0 | 1.23001 | 0.615007 | − | 0.788522i | \(-0.289153\pi\) | ||||
0.615007 | + | 0.788522i | \(0.289153\pi\) | |||||||
\(774\) | 5580.00 | 0.259133 | ||||||||
\(775\) | 1750.00 | 0.0811121 | ||||||||
\(776\) | −62100.0 | −2.87276 | ||||||||
\(777\) | −19950.0 | −0.921110 | ||||||||
\(778\) | −28250.0 | −1.30181 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 23375.0 | 1.07302 | ||||||||
\(781\) | 57000.0 | 2.61155 | ||||||||
\(782\) | −37485.0 | −1.71414 | ||||||||
\(783\) | 23925.0 | 1.09197 | ||||||||
\(784\) | 1602.00 | 0.0729774 | ||||||||
\(785\) | −9720.00 | −0.441938 | ||||||||
\(786\) | −28950.0 | −1.31376 | ||||||||
\(787\) | 37175.0 | 1.68379 | 0.841897 | − | 0.539638i | \(-0.181439\pi\) | ||||
0.841897 | + | 0.539638i | \(0.181439\pi\) | |||||||
\(788\) | −5712.00 | −0.258225 | ||||||||
\(789\) | 28440.0 | 1.28326 | ||||||||
\(790\) | −17500.0 | −0.788129 | ||||||||
\(791\) | −9120.00 | −0.409949 | ||||||||
\(792\) | −4500.00 | −0.201895 | ||||||||
\(793\) | −27500.0 | −1.23147 | ||||||||
\(794\) | 16930.0 | 0.756704 | ||||||||
\(795\) | 11375.0 | 0.507459 | ||||||||
\(796\) | −14875.0 | −0.662350 | ||||||||
\(797\) | 16205.0 | 0.720214 | 0.360107 | − | 0.932911i | \(-0.382740\pi\) | ||||
0.360107 | + | 0.932911i | \(0.382740\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −23664.0 | −1.04777 | ||||||||
\(800\) | 2125.00 | 0.0939126 | ||||||||
\(801\) | 1740.00 | 0.0767539 | ||||||||
\(802\) | 59200.0 | 2.60651 | ||||||||
\(803\) | −35150.0 | −1.54473 | ||||||||
\(804\) | 8925.00 | 0.391493 | ||||||||
\(805\) | 13965.0 | 0.611431 | ||||||||
\(806\) | −19250.0 | −0.841256 | ||||||||
\(807\) | −5050.00 | −0.220283 | ||||||||
\(808\) | 6750.00 | 0.293891 | ||||||||
\(809\) | −13675.0 | −0.594298 | −0.297149 | − | 0.954831i | \(-0.596036\pi\) | ||||
−0.297149 | + | 0.954831i | \(0.596036\pi\) | |||||||
\(810\) | −16775.0 | −0.727671 | ||||||||
\(811\) | −9275.00 | −0.401590 | −0.200795 | − | 0.979633i | \(-0.564352\pi\) | ||||
−0.200795 | + | 0.979633i | \(0.564352\pi\) | |||||||
\(812\) | −53295.0 | −2.30331 | ||||||||
\(813\) | −125.000 | −0.00539230 | ||||||||
\(814\) | −52500.0 | −2.26059 | ||||||||
\(815\) | −17810.0 | −0.765469 | ||||||||
\(816\) | −22695.0 | −0.973632 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 33850.0 | 1.44687 | ||||||||
\(819\) | −2090.00 | −0.0891703 | ||||||||
\(820\) | 6800.00 | 0.289593 | ||||||||
\(821\) | 9938.00 | 0.422459 | 0.211229 | − | 0.977437i | \(-0.432253\pi\) | ||||
0.211229 | + | 0.977437i | \(0.432253\pi\) | |||||||
\(822\) | −43975.0 | −1.86594 | ||||||||
\(823\) | 8203.00 | 0.347435 | 0.173717 | − | 0.984796i | \(-0.444422\pi\) | ||||
0.173717 | + | 0.984796i | \(0.444422\pi\) | |||||||
\(824\) | 56250.0 | 2.37811 | ||||||||
\(825\) | −6250.00 | −0.263754 | ||||||||
\(826\) | 21375.0 | 0.900401 | ||||||||
\(827\) | −31905.0 | −1.34153 | −0.670765 | − | 0.741670i | \(-0.734034\pi\) | ||||
−0.670765 | + | 0.741670i | \(0.734034\pi\) | |||||||
\(828\) | 4998.00 | 0.209774 | ||||||||
\(829\) | −7325.00 | −0.306885 | −0.153443 | − | 0.988158i | \(-0.549036\pi\) | ||||
−0.153443 | + | 0.988158i | \(0.549036\pi\) | |||||||
\(830\) | −22950.0 | −0.959766 | ||||||||
\(831\) | −18230.0 | −0.761001 | ||||||||
\(832\) | 15785.0 | 0.657748 | ||||||||
\(833\) | 918.000 | 0.0381835 | ||||||||
\(834\) | 55650.0 | 2.31055 | ||||||||
\(835\) | −16800.0 | −0.696273 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 10150.0 | 0.419158 | ||||||||
\(838\) | 22750.0 | 0.937811 | ||||||||
\(839\) | −26370.0 | −1.08509 | −0.542547 | − | 0.840026i | \(-0.682540\pi\) | ||||
−0.542547 | + | 0.840026i | \(0.682540\pi\) | |||||||
\(840\) | 21375.0 | 0.877985 | ||||||||
\(841\) | 2836.00 | 0.116282 | ||||||||
\(842\) | 15425.0 | 0.631331 | ||||||||
\(843\) | 30000.0 | 1.22569 | ||||||||
\(844\) | 66895.0 | 2.72822 | ||||||||
\(845\) | 4140.00 | 0.168545 | ||||||||
\(846\) | 4640.00 | 0.188566 | ||||||||
\(847\) | −22211.0 | −0.901038 | ||||||||
\(848\) | −40495.0 | −1.63986 | ||||||||
\(849\) | −25090.0 | −1.01424 | ||||||||
\(850\) | 6375.00 | 0.257248 | ||||||||
\(851\) | 30870.0 | 1.24349 | ||||||||
\(852\) | −96900.0 | −3.89641 | ||||||||
\(853\) | −8898.00 | −0.357165 | −0.178582 | − | 0.983925i | \(-0.557151\pi\) | ||||
−0.178582 | + | 0.983925i | \(0.557151\pi\) | |||||||
\(854\) | −47500.0 | −1.90330 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 54225.0 | 2.16515 | ||||||||
\(857\) | 33200.0 | 1.32333 | 0.661663 | − | 0.749801i | \(-0.269851\pi\) | ||||
0.661663 | + | 0.749801i | \(0.269851\pi\) | |||||||
\(858\) | 68750.0 | 2.73553 | ||||||||
\(859\) | 15450.0 | 0.613675 | 0.306838 | − | 0.951762i | \(-0.400729\pi\) | ||||
0.306838 | + | 0.951762i | \(0.400729\pi\) | |||||||
\(860\) | −47430.0 | −1.88064 | ||||||||
\(861\) | 7600.00 | 0.300821 | ||||||||
\(862\) | −23900.0 | −0.944359 | ||||||||
\(863\) | −18140.0 | −0.715519 | −0.357759 | − | 0.933814i | \(-0.616459\pi\) | ||||
−0.357759 | + | 0.933814i | \(0.616459\pi\) | |||||||
\(864\) | 12325.0 | 0.485307 | ||||||||
\(865\) | 19350.0 | 0.760601 | ||||||||
\(866\) | 42850.0 | 1.68141 | ||||||||
\(867\) | 11560.0 | 0.452824 | ||||||||
\(868\) | −22610.0 | −0.884140 | ||||||||
\(869\) | −35000.0 | −1.36628 | ||||||||
\(870\) | −20625.0 | −0.803739 | ||||||||
\(871\) | 5775.00 | 0.224659 | ||||||||
\(872\) | −56025.0 | −2.17574 | ||||||||
\(873\) | 2760.00 | 0.107001 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2375.00 | −0.0917596 | ||||||||
\(876\) | 59755.0 | 2.30472 | ||||||||
\(877\) | 22655.0 | 0.872298 | 0.436149 | − | 0.899875i | \(-0.356342\pi\) | ||||
0.436149 | + | 0.899875i | \(0.356342\pi\) | |||||||
\(878\) | 36100.0 | 1.38760 | ||||||||
\(879\) | −35175.0 | −1.34974 | ||||||||
\(880\) | 22250.0 | 0.852327 | ||||||||
\(881\) | −43350.0 | −1.65777 | −0.828887 | − | 0.559416i | \(-0.811025\pi\) | ||||
−0.828887 | + | 0.559416i | \(0.811025\pi\) | |||||||
\(882\) | −180.000 | −0.00687179 | ||||||||
\(883\) | 24568.0 | 0.936330 | 0.468165 | − | 0.883641i | \(-0.344915\pi\) | ||||
0.468165 | + | 0.883641i | \(0.344915\pi\) | |||||||
\(884\) | −47685.0 | −1.81428 | ||||||||
\(885\) | 5625.00 | 0.213652 | ||||||||
\(886\) | −51290.0 | −1.94483 | ||||||||
\(887\) | −32060.0 | −1.21361 | −0.606804 | − | 0.794852i | \(-0.707549\pi\) | ||||
−0.606804 | + | 0.794852i | \(0.707549\pi\) | |||||||
\(888\) | 47250.0 | 1.78559 | ||||||||
\(889\) | 1900.00 | 0.0716805 | ||||||||
\(890\) | −21750.0 | −0.819170 | ||||||||
\(891\) | −33550.0 | −1.26147 | ||||||||
\(892\) | 96730.0 | 3.63090 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −43400.0 | −1.62362 | ||||||||
\(895\) | −16700.0 | −0.623709 | ||||||||
\(896\) | 40185.0 | 1.49831 | ||||||||
\(897\) | −40425.0 | −1.50474 | ||||||||
\(898\) | −37650.0 | −1.39911 | ||||||||
\(899\) | 11550.0 | 0.428492 | ||||||||
\(900\) | −850.000 | −0.0314815 | ||||||||
\(901\) | −23205.0 | −0.858014 | ||||||||
\(902\) | 20000.0 | 0.738278 | ||||||||
\(903\) | −53010.0 | −1.95356 | ||||||||
\(904\) | 21600.0 | 0.794696 | ||||||||
\(905\) | −8950.00 | −0.328738 | ||||||||
\(906\) | −19750.0 | −0.724227 | ||||||||
\(907\) | −13295.0 | −0.486718 | −0.243359 | − | 0.969936i | \(-0.578249\pi\) | ||||
−0.243359 | + | 0.969936i | \(0.578249\pi\) | |||||||
\(908\) | 46155.0 | 1.68690 | ||||||||
\(909\) | −300.000 | −0.0109465 | ||||||||
\(910\) | 26125.0 | 0.951687 | ||||||||
\(911\) | −190.000 | −0.00690997 | −0.00345498 | − | 0.999994i | \(-0.501100\pi\) | ||||
−0.00345498 | + | 0.999994i | \(0.501100\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −45900.0 | −1.66382 | ||||||||
\(914\) | −44095.0 | −1.59577 | ||||||||
\(915\) | −12500.0 | −0.451625 | ||||||||
\(916\) | −12172.0 | −0.439055 | ||||||||
\(917\) | −22002.0 | −0.792334 | ||||||||
\(918\) | 36975.0 | 1.32936 | ||||||||
\(919\) | −2725.00 | −0.0978122 | −0.0489061 | − | 0.998803i | \(-0.515574\pi\) | ||||
−0.0489061 | + | 0.998803i | \(0.515574\pi\) | |||||||
\(920\) | −33075.0 | −1.18527 | ||||||||
\(921\) | −22300.0 | −0.797839 | ||||||||
\(922\) | 51160.0 | 1.82740 | ||||||||
\(923\) | −62700.0 | −2.23596 | ||||||||
\(924\) | 80750.0 | 2.87498 | ||||||||
\(925\) | −5250.00 | −0.186615 | ||||||||
\(926\) | −60560.0 | −2.14916 | ||||||||
\(927\) | −2500.00 | −0.0885769 | ||||||||
\(928\) | 14025.0 | 0.496113 | ||||||||
\(929\) | 16825.0 | 0.594198 | 0.297099 | − | 0.954847i | \(-0.403981\pi\) | ||||
0.297099 | + | 0.954847i | \(0.403981\pi\) | |||||||
\(930\) | −8750.00 | −0.308520 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 54094.0 | 1.90119 | ||||||||
\(933\) | −34125.0 | −1.19743 | ||||||||
\(934\) | −25380.0 | −0.889142 | ||||||||
\(935\) | 12750.0 | 0.445957 | ||||||||
\(936\) | 4950.00 | 0.172859 | ||||||||
\(937\) | −19259.0 | −0.671466 | −0.335733 | − | 0.941957i | \(-0.608984\pi\) | ||||
−0.335733 | + | 0.941957i | \(0.608984\pi\) | |||||||
\(938\) | 9975.00 | 0.347223 | ||||||||
\(939\) | −22685.0 | −0.788389 | ||||||||
\(940\) | −39440.0 | −1.36850 | ||||||||
\(941\) | −11435.0 | −0.396143 | −0.198071 | − | 0.980188i | \(-0.563468\pi\) | ||||
−0.198071 | + | 0.980188i | \(0.563468\pi\) | |||||||
\(942\) | 48600.0 | 1.68097 | ||||||||
\(943\) | −11760.0 | −0.406106 | ||||||||
\(944\) | −20025.0 | −0.690422 | ||||||||
\(945\) | −13775.0 | −0.474181 | ||||||||
\(946\) | −139500. | −4.79444 | ||||||||
\(947\) | −20014.0 | −0.686766 | −0.343383 | − | 0.939195i | \(-0.611573\pi\) | ||||
−0.343383 | + | 0.939195i | \(0.611573\pi\) | |||||||
\(948\) | 59500.0 | 2.03847 | ||||||||
\(949\) | 38665.0 | 1.32257 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 39225.0 | 1.33750 | ||||||||
\(952\) | −43605.0 | −1.48450 | ||||||||
\(953\) | −26970.0 | −0.916730 | −0.458365 | − | 0.888764i | \(-0.651565\pi\) | ||||
−0.458365 | + | 0.888764i | \(0.651565\pi\) | |||||||
\(954\) | 4550.00 | 0.154415 | ||||||||
\(955\) | −8235.00 | −0.279035 | ||||||||
\(956\) | −72675.0 | −2.45866 | ||||||||
\(957\) | −41250.0 | −1.39334 | ||||||||
\(958\) | 76920.0 | 2.59413 | ||||||||
\(959\) | −33421.0 | −1.12536 | ||||||||
\(960\) | 7175.00 | 0.241221 | ||||||||
\(961\) | −24891.0 | −0.835521 | ||||||||
\(962\) | 57750.0 | 1.93548 | ||||||||
\(963\) | −2410.00 | −0.0806450 | ||||||||
\(964\) | 4760.00 | 0.159035 | ||||||||
\(965\) | 5150.00 | 0.171797 | ||||||||
\(966\) | −69825.0 | −2.32565 | ||||||||
\(967\) | 7024.00 | 0.233585 | 0.116792 | − | 0.993156i | \(-0.462739\pi\) | ||||
0.116792 | + | 0.993156i | \(0.462739\pi\) | |||||||
\(968\) | 52605.0 | 1.74668 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −34500.0 | −1.14199 | ||||||||
\(971\) | 12960.0 | 0.428328 | 0.214164 | − | 0.976798i | \(-0.431297\pi\) | ||||
0.214164 | + | 0.976798i | \(0.431297\pi\) | |||||||
\(972\) | −9520.00 | −0.314150 | ||||||||
\(973\) | 42294.0 | 1.39351 | ||||||||
\(974\) | 41750.0 | 1.37347 | ||||||||
\(975\) | 6875.00 | 0.225822 | ||||||||
\(976\) | 44500.0 | 1.45944 | ||||||||
\(977\) | 5550.00 | 0.181740 | 0.0908701 | − | 0.995863i | \(-0.471035\pi\) | ||||
0.0908701 | + | 0.995863i | \(0.471035\pi\) | |||||||
\(978\) | 89050.0 | 2.91156 | ||||||||
\(979\) | −43500.0 | −1.42009 | ||||||||
\(980\) | 1530.00 | 0.0498715 | ||||||||
\(981\) | 2490.00 | 0.0810393 | ||||||||
\(982\) | −43860.0 | −1.42528 | ||||||||
\(983\) | 14480.0 | 0.469827 | 0.234914 | − | 0.972016i | \(-0.424519\pi\) | ||||
0.234914 | + | 0.972016i | \(0.424519\pi\) | |||||||
\(984\) | −18000.0 | −0.583149 | ||||||||
\(985\) | −1680.00 | −0.0543444 | ||||||||
\(986\) | 42075.0 | 1.35897 | ||||||||
\(987\) | −44080.0 | −1.42156 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 82026.0 | 2.63729 | ||||||||
\(990\) | −2500.00 | −0.0802578 | ||||||||
\(991\) | −21670.0 | −0.694622 | −0.347311 | − | 0.937750i | \(-0.612905\pi\) | ||||
−0.347311 | + | 0.937750i | \(0.612905\pi\) | |||||||
\(992\) | 5950.00 | 0.190436 | ||||||||
\(993\) | 35375.0 | 1.13051 | ||||||||
\(994\) | −108300. | −3.45580 | ||||||||
\(995\) | −4375.00 | −0.139394 | ||||||||
\(996\) | 78030.0 | 2.48240 | ||||||||
\(997\) | −40686.0 | −1.29242 | −0.646208 | − | 0.763161i | \(-0.723646\pi\) | ||||
−0.646208 | + | 0.763161i | \(0.723646\pi\) | |||||||
\(998\) | −13930.0 | −0.441830 | ||||||||
\(999\) | −30450.0 | −0.964360 |
(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 | 1805.4.a.i.1.1 | yes | 1 | |
19.18 | odd | 2 | 1805.4.a.b.1.1 | ✓ | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1805.4.a.b.1.1 | ✓ | 1 | 19.18 | odd | 2 | ||
1805.4.a.i.1.1 | yes | 1 | 1.1 | even | 1 | trivial |