Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [11,5,Mod(10,11)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(11, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("11.10");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 11 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 11.b (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: | \(1.13706959392\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{-30}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 30 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 10.1 | ||
Root | \(-5.47723i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 11.10 |
Dual form | 11.5.b.b.10.2 |
$q$-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 \(\left(\mathbb{Z}/11\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 5.47723i | − | 1.36931i | −0.728869 | − | 0.684653i | \(-0.759954\pi\) | ||
0.728869 | − | 0.684653i | \(-0.240046\pi\) | |||||||
\(3\) | −3.00000 | −0.333333 | −0.166667 | − | 0.986013i | \(-0.553300\pi\) | ||||
−0.166667 | + | 0.986013i | \(0.553300\pi\) | |||||||
\(4\) | −14.0000 | −0.875000 | ||||||||
\(5\) | 31.0000 | 1.24000 | 0.620000 | − | 0.784602i | \(-0.287133\pi\) | ||||
0.620000 | + | 0.784602i | \(0.287133\pi\) | |||||||
\(6\) | 16.4317i | 0.456435i | ||||||||
\(7\) | 54.7723i | 1.11780i | 0.829235 | + | 0.558901i | \(0.188777\pi\) | ||||
−0.829235 | + | 0.558901i | \(0.811223\pi\) | |||||||
\(8\) | − | 10.9545i | − | 0.171163i | ||||||
\(9\) | −72.0000 | −0.888889 | ||||||||
\(10\) | − | 169.794i | − | 1.69794i | ||||||
\(11\) | 11.0000 | + | 120.499i | 0.0909091 | + | 0.995859i | ||||
\(12\) | 42.0000 | 0.291667 | ||||||||
\(13\) | − | 186.226i | − | 1.10193i | −0.834529 | − | 0.550964i | \(-0.814260\pi\) | ||
0.834529 | − | 0.550964i | \(-0.185740\pi\) | |||||||
\(14\) | 300.000 | 1.53061 | ||||||||
\(15\) | −93.0000 | −0.413333 | ||||||||
\(16\) | −284.000 | −1.10938 | ||||||||
\(17\) | 230.043i | 0.795998i | 0.917386 | + | 0.397999i | \(0.130295\pi\) | ||||
−0.917386 | + | 0.397999i | \(0.869705\pi\) | |||||||
\(18\) | 394.360i | 1.21716i | ||||||||
\(19\) | − | 98.5901i | − | 0.273103i | −0.990633 | − | 0.136551i | \(-0.956398\pi\) | ||
0.990633 | − | 0.136551i | \(-0.0436019\pi\) | |||||||
\(20\) | −434.000 | −1.08500 | ||||||||
\(21\) | − | 164.317i | − | 0.372600i | ||||||
\(22\) | 660.000 | − | 60.2495i | 1.36364 | − | 0.124482i | ||||
\(23\) | 277.000 | 0.523629 | 0.261815 | − | 0.965118i | \(-0.415679\pi\) | ||||
0.261815 | + | 0.965118i | \(0.415679\pi\) | |||||||
\(24\) | 32.8634i | 0.0570544i | ||||||||
\(25\) | 336.000 | 0.537600 | ||||||||
\(26\) | −1020.00 | −1.50888 | ||||||||
\(27\) | 459.000 | 0.629630 | ||||||||
\(28\) | − | 766.812i | − | 0.978076i | ||||||
\(29\) | − | 1270.72i | − | 1.51096i | −0.655172 | − | 0.755479i | \(-0.727404\pi\) | ||
0.655172 | − | 0.755479i | \(-0.272596\pi\) | |||||||
\(30\) | 509.382i | 0.565980i | ||||||||
\(31\) | −1363.00 | −1.41831 | −0.709157 | − | 0.705050i | \(-0.750924\pi\) | ||||
−0.709157 | + | 0.705050i | \(0.750924\pi\) | |||||||
\(32\) | 1380.26i | 1.34791i | ||||||||
\(33\) | −33.0000 | − | 361.497i | −0.0303030 | − | 0.331953i | ||||
\(34\) | 1260.00 | 1.08997 | ||||||||
\(35\) | 1697.94i | 1.38607i | ||||||||
\(36\) | 1008.00 | 0.777778 | ||||||||
\(37\) | 167.000 | 0.121987 | 0.0609934 | − | 0.998138i | \(-0.480573\pi\) | ||||
0.0609934 | + | 0.998138i | \(0.480573\pi\) | |||||||
\(38\) | −540.000 | −0.373961 | ||||||||
\(39\) | 558.677i | 0.367309i | ||||||||
\(40\) | − | 339.588i | − | 0.212242i | ||||||
\(41\) | − | 1062.58i | − | 0.632113i | −0.948740 | − | 0.316056i | \(-0.897641\pi\) | ||
0.948740 | − | 0.316056i | \(-0.102359\pi\) | |||||||
\(42\) | −900.000 | −0.510204 | ||||||||
\(43\) | 1204.99i | 0.651698i | 0.945422 | + | 0.325849i | \(0.105650\pi\) | ||||
−0.945422 | + | 0.325849i | \(0.894350\pi\) | |||||||
\(44\) | −154.000 | − | 1686.99i | −0.0795455 | − | 0.871377i | ||||
\(45\) | −2232.00 | −1.10222 | ||||||||
\(46\) | − | 1517.19i | − | 0.717009i | ||||||
\(47\) | 1702.00 | 0.770484 | 0.385242 | − | 0.922816i | \(-0.374118\pi\) | ||||
0.385242 | + | 0.922816i | \(0.374118\pi\) | |||||||
\(48\) | 852.000 | 0.369792 | ||||||||
\(49\) | −599.000 | −0.249479 | ||||||||
\(50\) | − | 1840.35i | − | 0.736139i | ||||||
\(51\) | − | 690.130i | − | 0.265333i | ||||||
\(52\) | 2607.16i | 0.964186i | ||||||||
\(53\) | 4522.00 | 1.60983 | 0.804913 | − | 0.593393i | \(-0.202212\pi\) | ||||
0.804913 | + | 0.593393i | \(0.202212\pi\) | |||||||
\(54\) | − | 2514.05i | − | 0.862156i | ||||||
\(55\) | 341.000 | + | 3735.47i | 0.112727 | + | 1.23487i | ||||
\(56\) | 600.000 | 0.191327 | ||||||||
\(57\) | 295.770i | 0.0910342i | ||||||||
\(58\) | −6960.00 | −2.06897 | ||||||||
\(59\) | −2363.00 | −0.678828 | −0.339414 | − | 0.940637i | \(-0.610229\pi\) | ||||
−0.339414 | + | 0.940637i | \(0.610229\pi\) | |||||||
\(60\) | 1302.00 | 0.361667 | ||||||||
\(61\) | 3965.51i | 1.06571i | 0.846206 | + | 0.532856i | \(0.178881\pi\) | ||||
−0.846206 | + | 0.532856i | \(0.821119\pi\) | |||||||
\(62\) | 7465.46i | 1.94211i | ||||||||
\(63\) | − | 3943.60i | − | 0.993601i | ||||||
\(64\) | 3016.00 | 0.736328 | ||||||||
\(65\) | − | 5773.00i | − | 1.36639i | ||||||
\(66\) | −1980.00 | + | 180.748i | −0.454545 | + | 0.0414941i | ||||
\(67\) | −2803.00 | −0.624415 | −0.312208 | − | 0.950014i | \(-0.601068\pi\) | ||||
−0.312208 | + | 0.950014i | \(0.601068\pi\) | |||||||
\(68\) | − | 3220.61i | − | 0.696498i | ||||||
\(69\) | −831.000 | −0.174543 | ||||||||
\(70\) | 9300.00 | 1.89796 | ||||||||
\(71\) | 3397.00 | 0.673874 | 0.336937 | − | 0.941527i | \(-0.390609\pi\) | ||||
0.336937 | + | 0.941527i | \(0.390609\pi\) | |||||||
\(72\) | 788.720i | 0.152145i | ||||||||
\(73\) | − | 3319.20i | − | 0.622856i | −0.950270 | − | 0.311428i | \(-0.899193\pi\) | ||
0.950270 | − | 0.311428i | \(-0.100807\pi\) | |||||||
\(74\) | − | 914.697i | − | 0.167037i | ||||||
\(75\) | −1008.00 | −0.179200 | ||||||||
\(76\) | 1380.26i | 0.238965i | ||||||||
\(77\) | −6600.00 | + | 602.495i | −1.11317 | + | 0.101618i | ||||
\(78\) | 3060.00 | 0.502959 | ||||||||
\(79\) | − | 6090.67i | − | 0.975913i | −0.872868 | − | 0.487957i | \(-0.837742\pi\) | ||
0.872868 | − | 0.487957i | \(-0.162258\pi\) | |||||||
\(80\) | −8804.00 | −1.37563 | ||||||||
\(81\) | 4455.00 | 0.679012 | ||||||||
\(82\) | −5820.00 | −0.865556 | ||||||||
\(83\) | 832.538i | 0.120850i | 0.998173 | + | 0.0604252i | \(0.0192457\pi\) | ||||
−0.998173 | + | 0.0604252i | \(0.980754\pi\) | |||||||
\(84\) | 2300.43i | 0.326025i | ||||||||
\(85\) | 7131.35i | 0.987038i | ||||||||
\(86\) | 6600.00 | 0.892374 | ||||||||
\(87\) | 3812.15i | 0.503653i | ||||||||
\(88\) | 1320.00 | − | 120.499i | 0.170455 | − | 0.0155603i | ||||
\(89\) | −4673.00 | −0.589951 | −0.294975 | − | 0.955505i | \(-0.595311\pi\) | ||||
−0.294975 | + | 0.955505i | \(0.595311\pi\) | |||||||
\(90\) | 12225.2i | 1.50928i | ||||||||
\(91\) | 10200.0 | 1.23174 | ||||||||
\(92\) | −3878.00 | −0.458176 | ||||||||
\(93\) | 4089.00 | 0.472771 | ||||||||
\(94\) | − | 9322.24i | − | 1.05503i | ||||||
\(95\) | − | 3056.29i | − | 0.338647i | ||||||
\(96\) | − | 4140.78i | − | 0.449304i | ||||||
\(97\) | 4247.00 | 0.451376 | 0.225688 | − | 0.974200i | \(-0.427537\pi\) | ||||
0.225688 | + | 0.974200i | \(0.427537\pi\) | |||||||
\(98\) | 3280.86i | 0.341614i | ||||||||
\(99\) | −792.000 | − | 8675.93i | −0.0808081 | − | 0.885208i | ||||
\(100\) | −4704.00 | −0.470400 | ||||||||
\(101\) | 12104.7i | 1.18662i | 0.804976 | + | 0.593308i | \(0.202178\pi\) | ||||
−0.804976 | + | 0.593308i | \(0.797822\pi\) | |||||||
\(102\) | −3780.00 | −0.363322 | ||||||||
\(103\) | −11218.0 | −1.05740 | −0.528702 | − | 0.848807i | \(-0.677321\pi\) | ||||
−0.528702 | + | 0.848807i | \(0.677321\pi\) | |||||||
\(104\) | −2040.00 | −0.188609 | ||||||||
\(105\) | − | 5093.82i | − | 0.462024i | ||||||
\(106\) | − | 24768.0i | − | 2.20434i | ||||||
\(107\) | − | 4436.55i | − | 0.387506i | −0.981050 | − | 0.193753i | \(-0.937934\pi\) | ||
0.981050 | − | 0.193753i | \(-0.0620660\pi\) | |||||||
\(108\) | −6426.00 | −0.550926 | ||||||||
\(109\) | 16628.9i | 1.39962i | 0.714330 | + | 0.699809i | \(0.246731\pi\) | ||||
−0.714330 | + | 0.699809i | \(0.753269\pi\) | |||||||
\(110\) | 20460.0 | − | 1867.73i | 1.69091 | − | 0.154358i | ||||
\(111\) | −501.000 | −0.0406623 | ||||||||
\(112\) | − | 15555.3i | − | 1.24006i | ||||||
\(113\) | 3847.00 | 0.301277 | 0.150638 | − | 0.988589i | \(-0.451867\pi\) | ||||
0.150638 | + | 0.988589i | \(0.451867\pi\) | |||||||
\(114\) | 1620.00 | 0.124654 | ||||||||
\(115\) | 8587.00 | 0.649301 | ||||||||
\(116\) | 17790.0i | 1.32209i | ||||||||
\(117\) | 13408.2i | 0.979491i | ||||||||
\(118\) | 12942.7i | 0.929523i | ||||||||
\(119\) | −12600.0 | −0.889768 | ||||||||
\(120\) | 1018.76i | 0.0707475i | ||||||||
\(121\) | −14399.0 | + | 2650.98i | −0.983471 | + | 0.181065i | ||||
\(122\) | 21720.0 | 1.45929 | ||||||||
\(123\) | 3187.75i | 0.210704i | ||||||||
\(124\) | 19082.0 | 1.24102 | ||||||||
\(125\) | −8959.00 | −0.573376 | ||||||||
\(126\) | −21600.0 | −1.36054 | ||||||||
\(127\) | − | 13506.8i | − | 0.837426i | −0.908119 | − | 0.418713i | \(-0.862481\pi\) | ||
0.908119 | − | 0.418713i | \(-0.137519\pi\) | |||||||
\(128\) | 5564.86i | 0.339652i | ||||||||
\(129\) | − | 3614.97i | − | 0.217233i | ||||||
\(130\) | −31620.0 | −1.87101 | ||||||||
\(131\) | − | 21569.3i | − | 1.25688i | −0.777858 | − | 0.628440i | \(-0.783694\pi\) | ||
0.777858 | − | 0.628440i | \(-0.216306\pi\) | |||||||
\(132\) | 462.000 | + | 5060.96i | 0.0265152 | + | 0.290459i | ||||
\(133\) | 5400.00 | 0.305274 | ||||||||
\(134\) | 15352.7i | 0.855016i | ||||||||
\(135\) | 14229.0 | 0.780741 | ||||||||
\(136\) | 2520.00 | 0.136246 | ||||||||
\(137\) | 11647.0 | 0.620545 | 0.310272 | − | 0.950648i | \(-0.399580\pi\) | ||||
0.310272 | + | 0.950648i | \(0.399580\pi\) | |||||||
\(138\) | 4551.57i | 0.239003i | ||||||||
\(139\) | 17165.6i | 0.888444i | 0.895917 | + | 0.444222i | \(0.146520\pi\) | ||||
−0.895917 | + | 0.444222i | \(0.853480\pi\) | |||||||
\(140\) | − | 23771.2i | − | 1.21281i | ||||||
\(141\) | −5106.00 | −0.256828 | ||||||||
\(142\) | − | 18606.1i | − | 0.922740i | ||||||
\(143\) | 22440.0 | − | 2048.48i | 1.09736 | − | 0.100175i | ||||
\(144\) | 20448.0 | 0.986111 | ||||||||
\(145\) | − | 39392.2i | − | 1.87359i | ||||||
\(146\) | −18180.0 | −0.852880 | ||||||||
\(147\) | 1797.00 | 0.0831598 | ||||||||
\(148\) | −2338.00 | −0.106738 | ||||||||
\(149\) | − | 6517.90i | − | 0.293586i | −0.989167 | − | 0.146793i | \(-0.953105\pi\) | ||
0.989167 | − | 0.146793i | \(-0.0468951\pi\) | |||||||
\(150\) | 5521.04i | 0.245380i | ||||||||
\(151\) | 34725.6i | 1.52299i | 0.648173 | + | 0.761493i | \(0.275533\pi\) | ||||
−0.648173 | + | 0.761493i | \(0.724467\pi\) | |||||||
\(152\) | −1080.00 | −0.0467452 | ||||||||
\(153\) | − | 16563.1i | − | 0.707554i | ||||||
\(154\) | 3300.00 | + | 36149.7i | 0.139147 | + | 1.52427i | ||||
\(155\) | −42253.0 | −1.75871 | ||||||||
\(156\) | − | 7821.48i | − | 0.321395i | ||||||
\(157\) | 23207.0 | 0.941499 | 0.470749 | − | 0.882267i | \(-0.343984\pi\) | ||||
0.470749 | + | 0.882267i | \(0.343984\pi\) | |||||||
\(158\) | −33360.0 | −1.33632 | ||||||||
\(159\) | −13566.0 | −0.536609 | ||||||||
\(160\) | 42788.1i | 1.67141i | ||||||||
\(161\) | 15171.9i | 0.585314i | ||||||||
\(162\) | − | 24401.0i | − | 0.929776i | ||||||
\(163\) | 25862.0 | 0.973390 | 0.486695 | − | 0.873572i | \(-0.338202\pi\) | ||||
0.486695 | + | 0.873572i | \(0.338202\pi\) | |||||||
\(164\) | 14876.1i | 0.553099i | ||||||||
\(165\) | −1023.00 | − | 11206.4i | −0.0375758 | − | 0.411622i | ||||
\(166\) | 4560.00 | 0.165481 | ||||||||
\(167\) | 777.766i | 0.0278879i | 0.999903 | + | 0.0139440i | \(0.00443864\pi\) | ||||
−0.999903 | + | 0.0139440i | \(0.995561\pi\) | |||||||
\(168\) | −1800.00 | −0.0637755 | ||||||||
\(169\) | −6119.00 | −0.214243 | ||||||||
\(170\) | 39060.0 | 1.35156 | ||||||||
\(171\) | 7098.48i | 0.242758i | ||||||||
\(172\) | − | 16869.9i | − | 0.570236i | ||||||
\(173\) | − | 2388.07i | − | 0.0797912i | −0.999204 | − | 0.0398956i | \(-0.987297\pi\) | ||
0.999204 | − | 0.0398956i | \(-0.0127025\pi\) | |||||||
\(174\) | 20880.0 | 0.689655 | ||||||||
\(175\) | 18403.5i | 0.600930i | ||||||||
\(176\) | −3124.00 | − | 34221.7i | −0.100852 | − | 1.10478i | ||||
\(177\) | 7089.00 | 0.226276 | ||||||||
\(178\) | 25595.1i | 0.807823i | ||||||||
\(179\) | −26843.0 | −0.837770 | −0.418885 | − | 0.908039i | \(-0.637579\pi\) | ||||
−0.418885 | + | 0.908039i | \(0.637579\pi\) | |||||||
\(180\) | 31248.0 | 0.964444 | ||||||||
\(181\) | −37633.0 | −1.14871 | −0.574357 | − | 0.818605i | \(-0.694748\pi\) | ||||
−0.574357 | + | 0.818605i | \(0.694748\pi\) | |||||||
\(182\) | − | 55867.7i | − | 1.68662i | ||||||
\(183\) | − | 11896.5i | − | 0.355237i | ||||||
\(184\) | − | 3034.38i | − | 0.0896262i | ||||||
\(185\) | 5177.00 | 0.151264 | ||||||||
\(186\) | − | 22396.4i | − | 0.647369i | ||||||
\(187\) | −27720.0 | + | 2530.48i | −0.792702 | + | 0.0723635i | ||||
\(188\) | −23828.0 | −0.674174 | ||||||||
\(189\) | 25140.5i | 0.703801i | ||||||||
\(190\) | −16740.0 | −0.463712 | ||||||||
\(191\) | 34597.0 | 0.948357 | 0.474178 | − | 0.880429i | \(-0.342745\pi\) | ||||
0.474178 | + | 0.880429i | \(0.342745\pi\) | |||||||
\(192\) | −9048.00 | −0.245443 | ||||||||
\(193\) | − | 28810.2i | − | 0.773449i | −0.922195 | − | 0.386725i | \(-0.873606\pi\) | ||
0.922195 | − | 0.386725i | \(-0.126394\pi\) | |||||||
\(194\) | − | 23261.8i | − | 0.618073i | ||||||
\(195\) | 17319.0i | 0.455463i | ||||||||
\(196\) | 8386.00 | 0.218294 | ||||||||
\(197\) | 53501.5i | 1.37859i | 0.724483 | + | 0.689293i | \(0.242079\pi\) | ||||
−0.724483 | + | 0.689293i | \(0.757921\pi\) | |||||||
\(198\) | −47520.0 | + | 4337.96i | −1.21212 | + | 0.110651i | ||||
\(199\) | 8582.00 | 0.216712 | 0.108356 | − | 0.994112i | \(-0.465441\pi\) | ||||
0.108356 | + | 0.994112i | \(0.465441\pi\) | |||||||
\(200\) | − | 3680.70i | − | 0.0920174i | ||||||
\(201\) | 8409.00 | 0.208138 | ||||||||
\(202\) | 66300.0 | 1.62484 | ||||||||
\(203\) | 69600.0 | 1.68895 | ||||||||
\(204\) | 9661.83i | 0.232166i | ||||||||
\(205\) | − | 32940.0i | − | 0.783820i | ||||||
\(206\) | 61443.5i | 1.44791i | ||||||||
\(207\) | −19944.0 | −0.465448 | ||||||||
\(208\) | 52888.1i | 1.22245i | ||||||||
\(209\) | 11880.0 | − | 1084.49i | 0.271972 | − | 0.0248275i | ||||
\(210\) | −27900.0 | −0.632653 | ||||||||
\(211\) | 22588.1i | 0.507358i | 0.967288 | + | 0.253679i | \(0.0816407\pi\) | ||||
−0.967288 | + | 0.253679i | \(0.918359\pi\) | |||||||
\(212\) | −63308.0 | −1.40860 | ||||||||
\(213\) | −10191.0 | −0.224625 | ||||||||
\(214\) | −24300.0 | −0.530614 | ||||||||
\(215\) | 37354.7i | 0.808106i | ||||||||
\(216\) | − | 5028.09i | − | 0.107769i | ||||||
\(217\) | − | 74654.6i | − | 1.58539i | ||||||
\(218\) | 91080.0 | 1.91651 | ||||||||
\(219\) | 9957.60i | 0.207619i | ||||||||
\(220\) | −4774.00 | − | 52296.5i | −0.0986364 | − | 1.08051i | ||||
\(221\) | 42840.0 | 0.877132 | ||||||||
\(222\) | 2744.09i | 0.0556791i | ||||||||
\(223\) | −86683.0 | −1.74311 | −0.871554 | − | 0.490300i | \(-0.836887\pi\) | ||||
−0.871554 | + | 0.490300i | \(0.836887\pi\) | |||||||
\(224\) | −75600.0 | −1.50670 | ||||||||
\(225\) | −24192.0 | −0.477867 | ||||||||
\(226\) | − | 21070.9i | − | 0.412540i | ||||||
\(227\) | − | 8139.16i | − | 0.157953i | −0.996876 | − | 0.0789765i | \(-0.974835\pi\) | ||
0.996876 | − | 0.0789765i | \(-0.0251652\pi\) | |||||||
\(228\) | − | 4140.78i | − | 0.0796549i | ||||||
\(229\) | 14807.0 | 0.282355 | 0.141178 | − | 0.989984i | \(-0.454911\pi\) | ||||
0.141178 | + | 0.989984i | \(0.454911\pi\) | |||||||
\(230\) | − | 47032.9i | − | 0.889091i | ||||||
\(231\) | 19800.0 | − | 1807.48i | 0.371058 | − | 0.0338728i | ||||
\(232\) | −13920.0 | −0.258621 | ||||||||
\(233\) | − | 9464.65i | − | 0.174338i | −0.996194 | − | 0.0871691i | \(-0.972218\pi\) | ||
0.996194 | − | 0.0871691i | \(-0.0277820\pi\) | |||||||
\(234\) | 73440.0 | 1.34122 | ||||||||
\(235\) | 52762.0 | 0.955401 | ||||||||
\(236\) | 33082.0 | 0.593974 | ||||||||
\(237\) | 18272.0i | 0.325304i | ||||||||
\(238\) | 69013.0i | 1.21836i | ||||||||
\(239\) | − | 36127.8i | − | 0.632478i | −0.948680 | − | 0.316239i | \(-0.897580\pi\) | ||
0.948680 | − | 0.316239i | \(-0.102420\pi\) | |||||||
\(240\) | 26412.0 | 0.458542 | ||||||||
\(241\) | − | 101460.i | − | 1.74687i | −0.486938 | − | 0.873436i | \(-0.661886\pi\) | ||
0.486938 | − | 0.873436i | \(-0.338114\pi\) | |||||||
\(242\) | 14520.0 | + | 78866.6i | 0.247934 | + | 1.34667i | ||||
\(243\) | −50544.0 | −0.855967 | ||||||||
\(244\) | − | 55517.2i | − | 0.932497i | ||||||
\(245\) | −18569.0 | −0.309354 | ||||||||
\(246\) | 17460.0 | 0.288519 | ||||||||
\(247\) | −18360.0 | −0.300939 | ||||||||
\(248\) | 14930.9i | 0.242763i | ||||||||
\(249\) | − | 2497.61i | − | 0.0402835i | ||||||
\(250\) | 49070.5i | 0.785127i | ||||||||
\(251\) | −6203.00 | −0.0984588 | −0.0492294 | − | 0.998787i | \(-0.515677\pi\) | ||||
−0.0492294 | + | 0.998787i | \(0.515677\pi\) | |||||||
\(252\) | 55210.4i | 0.869401i | ||||||||
\(253\) | 3047.00 | + | 33378.2i | 0.0476027 | + | 0.521461i | ||||
\(254\) | −73980.0 | −1.14669 | ||||||||
\(255\) | − | 21394.0i | − | 0.329013i | ||||||
\(256\) | 78736.0 | 1.20142 | ||||||||
\(257\) | −89318.0 | −1.35230 | −0.676150 | − | 0.736764i | \(-0.736353\pi\) | ||||
−0.676150 | + | 0.736764i | \(0.736353\pi\) | |||||||
\(258\) | −19800.0 | −0.297458 | ||||||||
\(259\) | 9146.97i | 0.136357i | ||||||||
\(260\) | 80821.9i | 1.19559i | ||||||||
\(261\) | 91491.6i | 1.34307i | ||||||||
\(262\) | −118140. | −1.72105 | ||||||||
\(263\) | − | 62298.0i | − | 0.900663i | −0.892861 | − | 0.450332i | \(-0.851306\pi\) | ||
0.892861 | − | 0.450332i | \(-0.148694\pi\) | |||||||
\(264\) | −3960.00 | + | 361.497i | −0.0568182 | + | 0.00518677i | ||||
\(265\) | 140182. | 1.99618 | ||||||||
\(266\) | − | 29577.0i | − | 0.418014i | ||||||
\(267\) | 14019.0 | 0.196650 | ||||||||
\(268\) | 39242.0 | 0.546363 | ||||||||
\(269\) | −38678.0 | −0.534514 | −0.267257 | − | 0.963625i | \(-0.586117\pi\) | ||||
−0.267257 | + | 0.963625i | \(0.586117\pi\) | |||||||
\(270\) | − | 77935.4i | − | 1.06907i | ||||||
\(271\) | 16201.6i | 0.220607i | 0.993898 | + | 0.110304i | \(0.0351824\pi\) | ||||
−0.993898 | + | 0.110304i | \(0.964818\pi\) | |||||||
\(272\) | − | 65332.3i | − | 0.883060i | ||||||
\(273\) | −30600.0 | −0.410578 | ||||||||
\(274\) | − | 63793.2i | − | 0.849716i | ||||||
\(275\) | 3696.00 | + | 40487.7i | 0.0488727 | + | 0.535374i | ||||
\(276\) | 11634.0 | 0.152725 | ||||||||
\(277\) | 68377.7i | 0.891158i | 0.895243 | + | 0.445579i | \(0.147002\pi\) | ||||
−0.895243 | + | 0.445579i | \(0.852998\pi\) | |||||||
\(278\) | 94020.0 | 1.21655 | ||||||||
\(279\) | 98136.0 | 1.26072 | ||||||||
\(280\) | 18600.0 | 0.237245 | ||||||||
\(281\) | 123741.i | 1.56712i | 0.621315 | + | 0.783561i | \(0.286599\pi\) | ||||
−0.621315 | + | 0.783561i | \(0.713401\pi\) | |||||||
\(282\) | 27966.7i | 0.351676i | ||||||||
\(283\) | − | 126020.i | − | 1.57350i | −0.617272 | − | 0.786750i | \(-0.711762\pi\) | ||
0.617272 | − | 0.786750i | \(-0.288238\pi\) | |||||||
\(284\) | −47558.0 | −0.589640 | ||||||||
\(285\) | 9168.88i | 0.112882i | ||||||||
\(286\) | −11220.0 | − | 122909.i | −0.137171 | − | 1.50263i | ||||
\(287\) | 58200.0 | 0.706577 | ||||||||
\(288\) | − | 99378.8i | − | 1.19814i | ||||||
\(289\) | 30601.0 | 0.366387 | ||||||||
\(290\) | −215760. | −2.56552 | ||||||||
\(291\) | −12741.0 | −0.150459 | ||||||||
\(292\) | 46468.8i | 0.544999i | ||||||||
\(293\) | − | 90319.4i | − | 1.05207i | −0.850462 | − | 0.526037i | \(-0.823677\pi\) | ||
0.850462 | − | 0.526037i | \(-0.176323\pi\) | |||||||
\(294\) | − | 9842.57i | − | 0.113871i | ||||||
\(295\) | −73253.0 | −0.841747 | ||||||||
\(296\) | − | 1829.39i | − | 0.0208797i | ||||||
\(297\) | 5049.00 | + | 55309.0i | 0.0572391 | + | 0.627022i | ||||
\(298\) | −35700.0 | −0.402009 | ||||||||
\(299\) | − | 51584.5i | − | 0.577001i | ||||||
\(300\) | 14112.0 | 0.156800 | ||||||||
\(301\) | −66000.0 | −0.728469 | ||||||||
\(302\) | 190200. | 2.08543 | ||||||||
\(303\) | − | 36314.0i | − | 0.395539i | ||||||
\(304\) | 27999.6i | 0.302973i | ||||||||
\(305\) | 122931.i | 1.32148i | ||||||||
\(306\) | −90720.0 | −0.968858 | ||||||||
\(307\) | 153636.i | 1.63011i | 0.579384 | + | 0.815055i | \(0.303293\pi\) | ||||
−0.579384 | + | 0.815055i | \(0.696707\pi\) | |||||||
\(308\) | 92400.0 | − | 8434.93i | 0.974026 | − | 0.0889160i | ||||
\(309\) | 33654.0 | 0.352468 | ||||||||
\(310\) | 231429.i | 2.40821i | ||||||||
\(311\) | −90698.0 | −0.937728 | −0.468864 | − | 0.883270i | \(-0.655337\pi\) | ||||
−0.468864 | + | 0.883270i | \(0.655337\pi\) | |||||||
\(312\) | 6120.00 | 0.0628698 | ||||||||
\(313\) | −104953. | −1.07129 | −0.535644 | − | 0.844444i | \(-0.679931\pi\) | ||||
−0.535644 | + | 0.844444i | \(0.679931\pi\) | |||||||
\(314\) | − | 127110.i | − | 1.28920i | ||||||
\(315\) | − | 122252.i | − | 1.23207i | ||||||
\(316\) | 85269.4i | 0.853924i | ||||||||
\(317\) | 77287.0 | 0.769109 | 0.384555 | − | 0.923102i | \(-0.374355\pi\) | ||||
0.384555 | + | 0.923102i | \(0.374355\pi\) | |||||||
\(318\) | 74304.0i | 0.734781i | ||||||||
\(319\) | 153120. | − | 13977.9i | 1.50470 | − | 0.137360i | ||||
\(320\) | 93496.0 | 0.913047 | ||||||||
\(321\) | 13309.7i | 0.129169i | ||||||||
\(322\) | 83100.0 | 0.801474 | ||||||||
\(323\) | 22680.0 | 0.217389 | ||||||||
\(324\) | −62370.0 | −0.594136 | ||||||||
\(325\) | − | 62571.8i | − | 0.592396i | ||||||
\(326\) | − | 141652.i | − | 1.33287i | ||||||
\(327\) | − | 49886.6i | − | 0.466539i | ||||||
\(328\) | −11640.0 | −0.108195 | ||||||||
\(329\) | 93222.4i | 0.861248i | ||||||||
\(330\) | −61380.0 | + | 5603.20i | −0.563636 | + | 0.0514527i | ||||
\(331\) | −174403. | −1.59183 | −0.795917 | − | 0.605405i | \(-0.793011\pi\) | ||||
−0.795917 | + | 0.605405i | \(0.793011\pi\) | |||||||
\(332\) | − | 11655.5i | − | 0.105744i | ||||||
\(333\) | −12024.0 | −0.108433 | ||||||||
\(334\) | 4260.00 | 0.0381871 | ||||||||
\(335\) | −86893.0 | −0.774275 | ||||||||
\(336\) | 46666.0i | 0.413354i | ||||||||
\(337\) | 115493.i | 1.01694i | 0.861080 | + | 0.508470i | \(0.169789\pi\) | ||||
−0.861080 | + | 0.508470i | \(0.830211\pi\) | |||||||
\(338\) | 33515.1i | 0.293365i | ||||||||
\(339\) | −11541.0 | −0.100426 | ||||||||
\(340\) | − | 99838.9i | − | 0.863658i | ||||||
\(341\) | −14993.0 | − | 164240.i | −0.128938 | − | 1.41244i | ||||
\(342\) | 38880.0 | 0.332410 | ||||||||
\(343\) | 98699.6i | 0.838933i | ||||||||
\(344\) | 13200.0 | 0.111547 | ||||||||
\(345\) | −25761.0 | −0.216434 | ||||||||
\(346\) | −13080.0 | −0.109259 | ||||||||
\(347\) | − | 137380.i | − | 1.14094i | −0.821317 | − | 0.570471i | \(-0.806761\pi\) | ||
0.821317 | − | 0.570471i | \(-0.193239\pi\) | |||||||
\(348\) | − | 53370.1i | − | 0.440696i | ||||||
\(349\) | − | 180365.i | − | 1.48082i | −0.672157 | − | 0.740409i | \(-0.734632\pi\) | ||
0.672157 | − | 0.740409i | \(-0.265368\pi\) | |||||||
\(350\) | 100800. | 0.822857 | ||||||||
\(351\) | − | 85477.6i | − | 0.693806i | ||||||
\(352\) | −166320. | + | 15182.9i | −1.34233 | + | 0.122537i | ||||
\(353\) | 107527. | 0.862915 | 0.431458 | − | 0.902133i | \(-0.357999\pi\) | ||||
0.431458 | + | 0.902133i | \(0.357999\pi\) | |||||||
\(354\) | − | 38828.1i | − | 0.309841i | ||||||
\(355\) | 105307. | 0.835604 | ||||||||
\(356\) | 65422.0 | 0.516207 | ||||||||
\(357\) | 37800.0 | 0.296589 | ||||||||
\(358\) | 147025.i | 1.14716i | ||||||||
\(359\) | 62473.2i | 0.484736i | 0.970184 | + | 0.242368i | \(0.0779241\pi\) | ||||
−0.970184 | + | 0.242368i | \(0.922076\pi\) | |||||||
\(360\) | 24450.3i | 0.188660i | ||||||||
\(361\) | 120601. | 0.925415 | ||||||||
\(362\) | 206124.i | 1.57294i | ||||||||
\(363\) | 43197.0 | − | 7952.93i | 0.327824 | − | 0.0603551i | ||||
\(364\) | −142800. | −1.07777 | ||||||||
\(365\) | − | 102895.i | − | 0.772341i | ||||||
\(366\) | −65160.0 | −0.486428 | ||||||||
\(367\) | 142397. | 1.05723 | 0.528614 | − | 0.848862i | \(-0.322712\pi\) | ||||
0.528614 | + | 0.848862i | \(0.322712\pi\) | |||||||
\(368\) | −78668.0 | −0.580901 | ||||||||
\(369\) | 76505.9i | 0.561878i | ||||||||
\(370\) | − | 28355.6i | − | 0.207126i | ||||||
\(371\) | 247680.i | 1.79946i | ||||||||
\(372\) | −57246.0 | −0.413675 | ||||||||
\(373\) | − | 59406.0i | − | 0.426985i | −0.976945 | − | 0.213492i | \(-0.931516\pi\) | ||
0.976945 | − | 0.213492i | \(-0.0684839\pi\) | |||||||
\(374\) | 13860.0 | + | 151829.i | 0.0990878 | + | 1.08545i | ||||
\(375\) | 26877.0 | 0.191125 | ||||||||
\(376\) | − | 18644.5i | − | 0.131879i | ||||||
\(377\) | −236640. | −1.66497 | ||||||||
\(378\) | 137700. | 0.963719 | ||||||||
\(379\) | 123077. | 0.856838 | 0.428419 | − | 0.903580i | \(-0.359071\pi\) | ||||
0.428419 | + | 0.903580i | \(0.359071\pi\) | |||||||
\(380\) | 42788.1i | 0.296316i | ||||||||
\(381\) | 40520.5i | 0.279142i | ||||||||
\(382\) | − | 189496.i | − | 1.29859i | ||||||
\(383\) | −155363. | −1.05913 | −0.529566 | − | 0.848269i | \(-0.677645\pi\) | ||||
−0.529566 | + | 0.848269i | \(0.677645\pi\) | |||||||
\(384\) | − | 16694.6i | − | 0.113217i | ||||||
\(385\) | −204600. | + | 18677.3i | −1.38033 | + | 0.126007i | ||||
\(386\) | −157800. | −1.05909 | ||||||||
\(387\) | − | 86759.3i | − | 0.579287i | ||||||
\(388\) | −59458.0 | −0.394954 | ||||||||
\(389\) | −41633.0 | −0.275130 | −0.137565 | − | 0.990493i | \(-0.543928\pi\) | ||||
−0.137565 | + | 0.990493i | \(0.543928\pi\) | |||||||
\(390\) | 94860.0 | 0.623669 | ||||||||
\(391\) | 63722.0i | 0.416808i | ||||||||
\(392\) | 6561.72i | 0.0427017i | ||||||||
\(393\) | 64707.9i | 0.418960i | ||||||||
\(394\) | 293040. | 1.88771 | ||||||||
\(395\) | − | 188811.i | − | 1.21013i | ||||||
\(396\) | 11088.0 | + | 121463.i | 0.0707071 | + | 0.774557i | ||||
\(397\) | 77882.0 | 0.494147 | 0.247073 | − | 0.968997i | \(-0.420531\pi\) | ||||
0.247073 | + | 0.968997i | \(0.420531\pi\) | |||||||
\(398\) | − | 47005.5i | − | 0.296745i | ||||||
\(399\) | −16200.0 | −0.101758 | ||||||||
\(400\) | −95424.0 | −0.596400 | ||||||||
\(401\) | 198922. | 1.23707 | 0.618535 | − | 0.785757i | \(-0.287727\pi\) | ||||
0.618535 | + | 0.785757i | \(0.287727\pi\) | |||||||
\(402\) | − | 46058.0i | − | 0.285005i | ||||||
\(403\) | 253826.i | 1.56288i | ||||||||
\(404\) | − | 169465.i | − | 1.03829i | ||||||
\(405\) | 138105. | 0.841975 | ||||||||
\(406\) | − | 381215.i | − | 2.31269i | ||||||
\(407\) | 1837.00 | + | 20123.3i | 0.0110897 | + | 0.121482i | ||||
\(408\) | −7560.00 | −0.0454152 | ||||||||
\(409\) | − | 30913.5i | − | 0.184800i | −0.995722 | − | 0.0923998i | \(-0.970546\pi\) | ||
0.995722 | − | 0.0923998i | \(-0.0294538\pi\) | |||||||
\(410\) | −180420. | −1.07329 | ||||||||
\(411\) | −34941.0 | −0.206848 | ||||||||
\(412\) | 157052. | 0.925229 | ||||||||
\(413\) | − | 129427.i | − | 0.758795i | ||||||
\(414\) | 109238.i | 0.637342i | ||||||||
\(415\) | 25808.7i | 0.149854i | ||||||||
\(416\) | 257040. | 1.48530 | ||||||||
\(417\) | − | 51496.9i | − | 0.296148i | ||||||
\(418\) | −5940.00 | − | 65069.4i | −0.0339965 | − | 0.372413i | ||||
\(419\) | −232538. | −1.32454 | −0.662271 | − | 0.749264i | \(-0.730407\pi\) | ||||
−0.662271 | + | 0.749264i | \(0.730407\pi\) | |||||||
\(420\) | 71313.5i | 0.404271i | ||||||||
\(421\) | −46918.0 | −0.264713 | −0.132357 | − | 0.991202i | \(-0.542254\pi\) | ||||
−0.132357 | + | 0.991202i | \(0.542254\pi\) | |||||||
\(422\) | 123720. | 0.694728 | ||||||||
\(423\) | −122544. | −0.684875 | ||||||||
\(424\) | − | 49536.0i | − | 0.275543i | ||||||
\(425\) | 77294.6i | 0.427929i | ||||||||
\(426\) | 55818.4i | 0.307580i | ||||||||
\(427\) | −217200. | −1.19125 | ||||||||
\(428\) | 62111.7i | 0.339067i | ||||||||
\(429\) | −67320.0 | + | 6145.45i | −0.365788 | + | 0.0333917i | ||||
\(430\) | 204600. | 1.10654 | ||||||||
\(431\) | 57412.3i | 0.309065i | 0.987988 | + | 0.154533i | \(0.0493872\pi\) | ||||
−0.987988 | + | 0.154533i | \(0.950613\pi\) | |||||||
\(432\) | −130356. | −0.698495 | ||||||||
\(433\) | 33167.0 | 0.176901 | 0.0884505 | − | 0.996081i | \(-0.471808\pi\) | ||||
0.0884505 | + | 0.996081i | \(0.471808\pi\) | |||||||
\(434\) | −408900. | −2.17089 | ||||||||
\(435\) | 118177.i | 0.624530i | ||||||||
\(436\) | − | 232804.i | − | 1.22467i | ||||||
\(437\) | − | 27309.4i | − | 0.143005i | ||||||
\(438\) | 54540.0 | 0.284293 | ||||||||
\(439\) | 353303.i | 1.83324i | 0.399765 | + | 0.916618i | \(0.369092\pi\) | ||||
−0.399765 | + | 0.916618i | \(0.630908\pi\) | |||||||
\(440\) | 40920.0 | − | 3735.47i | 0.211364 | − | 0.0192948i | ||||
\(441\) | 43128.0 | 0.221759 | ||||||||
\(442\) | − | 234644.i | − | 1.20106i | ||||||
\(443\) | 279397. | 1.42369 | 0.711843 | − | 0.702339i | \(-0.247861\pi\) | ||||
0.711843 | + | 0.702339i | \(0.247861\pi\) | |||||||
\(444\) | 7014.00 | 0.0355795 | ||||||||
\(445\) | −144863. | −0.731539 | ||||||||
\(446\) | 474782.i | 2.38685i | ||||||||
\(447\) | 19553.7i | 0.0978619i | ||||||||
\(448\) | 165193.i | 0.823068i | ||||||||
\(449\) | 144607. | 0.717293 | 0.358647 | − | 0.933473i | \(-0.383238\pi\) | ||||
0.358647 | + | 0.933473i | \(0.383238\pi\) | |||||||
\(450\) | 132505.i | 0.654346i | ||||||||
\(451\) | 128040. | − | 11688.4i | 0.629495 | − | 0.0574648i | ||||
\(452\) | −53858.0 | −0.263617 | ||||||||
\(453\) | − | 104177.i | − | 0.507662i | ||||||
\(454\) | −44580.0 | −0.216286 | ||||||||
\(455\) | 316200. | 1.52735 | ||||||||
\(456\) | 3240.00 | 0.0155817 | ||||||||
\(457\) | − | 384282.i | − | 1.84000i | −0.391918 | − | 0.920000i | \(-0.628188\pi\) | ||
0.391918 | − | 0.920000i | \(-0.371812\pi\) | |||||||
\(458\) | − | 81101.3i | − | 0.386631i | ||||||
\(459\) | 105590.i | 0.501184i | ||||||||
\(460\) | −120218. | −0.568138 | ||||||||
\(461\) | − | 6988.94i | − | 0.0328859i | −0.999865 | − | 0.0164429i | \(-0.994766\pi\) | ||
0.999865 | − | 0.0164429i | \(-0.00523419\pi\) | |||||||
\(462\) | −9900.00 | − | 108449.i | −0.0463822 | − | 0.508091i | ||||
\(463\) | −227203. | −1.05987 | −0.529934 | − | 0.848039i | \(-0.677783\pi\) | ||||
−0.529934 | + | 0.848039i | \(0.677783\pi\) | |||||||
\(464\) | 360883.i | 1.67622i | ||||||||
\(465\) | 126759. | 0.586237 | ||||||||
\(466\) | −51840.0 | −0.238722 | ||||||||
\(467\) | 328117. | 1.50451 | 0.752255 | − | 0.658872i | \(-0.228966\pi\) | ||||
0.752255 | + | 0.658872i | \(0.228966\pi\) | |||||||
\(468\) | − | 187715.i | − | 0.857054i | ||||||
\(469\) | − | 153527.i | − | 0.697972i | ||||||
\(470\) | − | 288989.i | − | 1.30824i | ||||||
\(471\) | −69621.0 | −0.313833 | ||||||||
\(472\) | 25885.4i | 0.116190i | ||||||||
\(473\) | −145200. | + | 13254.9i | −0.648999 | + | 0.0592453i | ||||
\(474\) | 100080. | 0.445441 | ||||||||
\(475\) | − | 33126.3i | − | 0.146820i | ||||||
\(476\) | 176400. | 0.778547 | ||||||||
\(477\) | −325584. | −1.43096 | ||||||||
\(478\) | −197880. | −0.866056 | ||||||||
\(479\) | − | 132560.i | − | 0.577751i | −0.957367 | − | 0.288876i | \(-0.906719\pi\) | ||
0.957367 | − | 0.288876i | \(-0.0932814\pi\) | |||||||
\(480\) | − | 128364.i | − | 0.557137i | ||||||
\(481\) | − | 31099.7i | − | 0.134421i | ||||||
\(482\) | −555720. | −2.39200 | ||||||||
\(483\) | − | 45515.7i | − | 0.195105i | ||||||
\(484\) | 201586. | − | 37113.7i | 0.860537 | − | 0.158432i | ||||
\(485\) | 131657. | 0.559707 | ||||||||
\(486\) | 276841.i | 1.17208i | ||||||||
\(487\) | −106483. | −0.448975 | −0.224488 | − | 0.974477i | \(-0.572071\pi\) | ||||
−0.224488 | + | 0.974477i | \(0.572071\pi\) | |||||||
\(488\) | 43440.0 | 0.182411 | ||||||||
\(489\) | −77586.0 | −0.324463 | ||||||||
\(490\) | 101707.i | 0.423601i | ||||||||
\(491\) | − | 234557.i | − | 0.972937i | −0.873698 | − | 0.486469i | \(-0.838285\pi\) | ||
0.873698 | − | 0.486469i | \(-0.161715\pi\) | |||||||
\(492\) | − | 44628.4i | − | 0.184366i | ||||||
\(493\) | 292320. | 1.20272 | ||||||||
\(494\) | 100562.i | 0.412078i | ||||||||
\(495\) | −24552.0 | − | 268954.i | −0.100202 | − | 1.09766i | ||||
\(496\) | 387092. | 1.57344 | ||||||||
\(497\) | 186061.i | 0.753257i | ||||||||
\(498\) | −13680.0 | −0.0551604 | ||||||||
\(499\) | −292378. | −1.17420 | −0.587102 | − | 0.809513i | \(-0.699731\pi\) | ||||
−0.587102 | + | 0.809513i | \(0.699731\pi\) | |||||||
\(500\) | 125426. | 0.501704 | ||||||||
\(501\) | − | 2333.30i | − | 0.00929597i | ||||||
\(502\) | 33975.2i | 0.134820i | ||||||||
\(503\) | 25567.7i | 0.101054i | 0.998723 | + | 0.0505272i | \(0.0160902\pi\) | ||||
−0.998723 | + | 0.0505272i | \(0.983910\pi\) | |||||||
\(504\) | −43200.0 | −0.170068 | ||||||||
\(505\) | 375245.i | 1.47140i | ||||||||
\(506\) | 182820. | − | 16689.1i | 0.714040 | − | 0.0651827i | ||||
\(507\) | 18357.0 | 0.0714144 | ||||||||
\(508\) | 189096.i | 0.732747i | ||||||||
\(509\) | 307447. | 1.18668 | 0.593341 | − | 0.804951i | \(-0.297808\pi\) | ||||
0.593341 | + | 0.804951i | \(0.297808\pi\) | |||||||
\(510\) | −117180. | −0.450519 | ||||||||
\(511\) | 181800. | 0.696229 | ||||||||
\(512\) | − | 342217.i | − | 1.30545i | ||||||
\(513\) | − | 45252.8i | − | 0.171954i | ||||||
\(514\) | 489215.i | 1.85171i | ||||||||
\(515\) | −347758. | −1.31118 | ||||||||
\(516\) | 50609.6i | 0.190079i | ||||||||
\(517\) | 18722.0 | + | 205089.i | 0.0700440 | + | 0.767294i | ||||
\(518\) | 50100.0 | 0.186715 | ||||||||
\(519\) | 7164.21i | 0.0265971i | ||||||||
\(520\) | −63240.0 | −0.233876 | ||||||||
\(521\) | −375593. | −1.38370 | −0.691850 | − | 0.722041i | \(-0.743204\pi\) | ||||
−0.691850 | + | 0.722041i | \(0.743204\pi\) | |||||||
\(522\) | 501120. | 1.83908 | ||||||||
\(523\) | 272076.i | 0.994687i | 0.867554 | + | 0.497343i | \(0.165691\pi\) | ||||
−0.867554 | + | 0.497343i | \(0.834309\pi\) | |||||||
\(524\) | 301970.i | 1.09977i | ||||||||
\(525\) | − | 55210.4i | − | 0.200310i | ||||||
\(526\) | −341220. | −1.23328 | ||||||||
\(527\) | − | 313549.i | − | 1.12898i | ||||||
\(528\) | 9372.00 | + | 102665.i | 0.0336174 | + | 0.368260i | ||||
\(529\) | −203112. | −0.725812 | ||||||||
\(530\) | − | 767808.i | − | 2.73339i | ||||||
\(531\) | 170136. | 0.603403 | ||||||||
\(532\) | −75600.0 | −0.267115 | ||||||||
\(533\) | −197880. | −0.696542 | ||||||||
\(534\) | − | 76785.2i | − | 0.269274i | ||||||
\(535\) | − | 137533.i | − | 0.480507i | ||||||
\(536\) | 30705.3i | 0.106877i | ||||||||
\(537\) | 80529.0 | 0.279257 | ||||||||
\(538\) | 211848.i | 0.731914i | ||||||||
\(539\) | −6589.00 | − | 72178.9i | −0.0226799 | − | 0.248446i | ||||
\(540\) | −199206. | −0.683148 | ||||||||
\(541\) | − | 150810.i | − | 0.515271i | −0.966242 | − | 0.257635i | \(-0.917057\pi\) | ||
0.966242 | − | 0.257635i | \(-0.0829433\pi\) | |||||||
\(542\) | 88740.0 | 0.302079 | ||||||||
\(543\) | 112899. | 0.382904 | ||||||||
\(544\) | −317520. | −1.07293 | ||||||||
\(545\) | 515495.i | 1.73553i | ||||||||
\(546\) | 167603.i | 0.562208i | ||||||||
\(547\) | − | 215430.i | − | 0.719999i | −0.932952 | − | 0.360000i | \(-0.882777\pi\) | ||
0.932952 | − | 0.360000i | \(-0.117223\pi\) | |||||||
\(548\) | −163058. | −0.542976 | ||||||||
\(549\) | − | 285517.i | − | 0.947299i | ||||||
\(550\) | 221760. | − | 20243.8i | 0.733091 | − | 0.0669217i | ||||
\(551\) | −125280. | −0.412647 | ||||||||
\(552\) | 9103.15i | 0.0298754i | ||||||||
\(553\) | 333600. | 1.09088 | ||||||||
\(554\) | 374520. | 1.22027 | ||||||||
\(555\) | −15531.0 | −0.0504212 | ||||||||
\(556\) | − | 240319.i | − | 0.777388i | ||||||
\(557\) | 298892.i | 0.963395i | 0.876338 | + | 0.481697i | \(0.159980\pi\) | ||||
−0.876338 | + | 0.481697i | \(0.840020\pi\) | |||||||
\(558\) | − | 537513.i | − | 1.72632i | ||||||
\(559\) | 224400. | 0.718124 | ||||||||
\(560\) | − | 482215.i | − | 1.53768i | ||||||
\(561\) | 83160.0 | − | 7591.43i | 0.264234 | − | 0.0241212i | ||||
\(562\) | 677760. | 2.14587 | ||||||||
\(563\) | 257079.i | 0.811054i | 0.914083 | + | 0.405527i | \(0.132912\pi\) | ||||
−0.914083 | + | 0.405527i | \(0.867088\pi\) | |||||||
\(564\) | 71484.0 | 0.224725 | ||||||||
\(565\) | 119257. | 0.373583 | ||||||||
\(566\) | −690240. | −2.15460 | ||||||||
\(567\) | 244010.i | 0.759001i | ||||||||
\(568\) | − | 37212.3i | − | 0.115343i | ||||||
\(569\) | − | 133250.i | − | 0.411569i | −0.978597 | − | 0.205784i | \(-0.934025\pi\) | ||
0.978597 | − | 0.205784i | \(-0.0659746\pi\) | |||||||
\(570\) | 50220.0 | 0.154571 | ||||||||
\(571\) | − | 171832.i | − | 0.527024i | −0.964656 | − | 0.263512i | \(-0.915119\pi\) | ||
0.964656 | − | 0.263512i | \(-0.0848809\pi\) | |||||||
\(572\) | −314160. | + | 28678.8i | −0.960194 | + | 0.0876533i | ||||
\(573\) | −103791. | −0.316119 | ||||||||
\(574\) | − | 318775.i | − | 0.967520i | ||||||
\(575\) | 93072.0 | 0.281503 | ||||||||
\(576\) | −217152. | −0.654514 | ||||||||
\(577\) | 41567.0 | 0.124852 | 0.0624262 | − | 0.998050i | \(-0.480116\pi\) | ||||
0.0624262 | + | 0.998050i | \(0.480116\pi\) | |||||||
\(578\) | − | 167609.i | − | 0.501696i | ||||||
\(579\) | 86430.6i | 0.257816i | ||||||||
\(580\) | 551491.i | 1.63939i | ||||||||
\(581\) | −45600.0 | −0.135087 | ||||||||
\(582\) | 69785.3i | 0.206024i | ||||||||
\(583\) | 49742.0 | + | 544896.i | 0.146348 | + | 1.60316i | ||||
\(584\) | −36360.0 | −0.106610 | ||||||||
\(585\) | 415656.i | 1.21457i | ||||||||
\(586\) | −494700. | −1.44061 | ||||||||
\(587\) | 236062. | 0.685094 | 0.342547 | − | 0.939501i | \(-0.388710\pi\) | ||||
0.342547 | + | 0.939501i | \(0.388710\pi\) | |||||||
\(588\) | −25158.0 | −0.0727648 | ||||||||
\(589\) | 134378.i | 0.387345i | ||||||||
\(590\) | 401223.i | 1.15261i | ||||||||
\(591\) | − | 160505.i | − | 0.459529i | ||||||
\(592\) | −47428.0 | −0.135329 | ||||||||
\(593\) | − | 39764.7i | − | 0.113081i | −0.998400 | − | 0.0565403i | \(-0.981993\pi\) | ||
0.998400 | − | 0.0565403i | \(-0.0180069\pi\) | |||||||
\(594\) | 302940. | − | 27654.5i | 0.858586 | − | 0.0783778i | ||||
\(595\) | −390600. | −1.10331 | ||||||||
\(596\) | 91250.6i | 0.256888i | ||||||||
\(597\) | −25746.0 | −0.0722372 | ||||||||
\(598\) | −282540. | −0.790092 | ||||||||
\(599\) | −2378.00 | −0.00662763 | −0.00331381 | − | 0.999995i | \(-0.501055\pi\) | ||||
−0.00331381 | + | 0.999995i | \(0.501055\pi\) | |||||||
\(600\) | 11042.1i | 0.0306725i | ||||||||
\(601\) | − | 184309.i | − | 0.510266i | −0.966906 | − | 0.255133i | \(-0.917881\pi\) | ||
0.966906 | − | 0.255133i | \(-0.0821193\pi\) | |||||||
\(602\) | 361497.i | 0.997497i | ||||||||
\(603\) | 201816. | 0.555036 | ||||||||
\(604\) | − | 486159.i | − | 1.33261i | ||||||
\(605\) | −446369. | + | 82180.3i | −1.21950 | + | 0.224521i | ||||
\(606\) | −198900. | −0.541614 | ||||||||
\(607\) | − | 640397.i | − | 1.73809i | −0.494734 | − | 0.869045i | \(-0.664734\pi\) | ||
0.494734 | − | 0.869045i | \(-0.335266\pi\) | |||||||
\(608\) | 136080. | 0.368118 | ||||||||
\(609\) | −208800. | −0.562984 | ||||||||
\(610\) | 673320. | 1.80951 | ||||||||
\(611\) | − | 316956.i | − | 0.849018i | ||||||
\(612\) | 231884.i | 0.619110i | ||||||||
\(613\) | 144139.i | 0.383583i | 0.981436 | + | 0.191792i | \(0.0614298\pi\) | ||||
−0.981436 | + | 0.191792i | \(0.938570\pi\) | |||||||
\(614\) | 841500. | 2.23212 | ||||||||
\(615\) | 98820.1i | 0.261273i | ||||||||
\(616\) | 6600.00 | + | 72299.4i | 0.0173933 | + | 0.190534i | ||||
\(617\) | 707962. | 1.85969 | 0.929843 | − | 0.367957i | \(-0.119942\pi\) | ||||
0.929843 | + | 0.367957i | \(0.119942\pi\) | |||||||
\(618\) | − | 184331.i | − | 0.482637i | ||||||
\(619\) | −487963. | −1.27352 | −0.636760 | − | 0.771062i | \(-0.719726\pi\) | ||||
−0.636760 | + | 0.771062i | \(0.719726\pi\) | |||||||
\(620\) | 591542. | 1.53887 | ||||||||
\(621\) | 127143. | 0.329693 | ||||||||
\(622\) | 496773.i | 1.28404i | ||||||||
\(623\) | − | 255951.i | − | 0.659448i | ||||||
\(624\) | − | 158664.i | − | 0.407483i | ||||||
\(625\) | −487729. | −1.24859 | ||||||||
\(626\) | 574851.i | 1.46692i | ||||||||
\(627\) | −35640.0 | + | 3253.47i | −0.0906573 | + | 0.00827584i | ||||
\(628\) | −324898. | −0.823811 | ||||||||
\(629\) | 38417.3i | 0.0971013i | ||||||||
\(630\) | −669600. | −1.68707 | ||||||||
\(631\) | 274397. | 0.689161 | 0.344580 | − | 0.938757i | \(-0.388021\pi\) | ||||
0.344580 | + | 0.938757i | \(0.388021\pi\) | |||||||
\(632\) | −66720.0 | −0.167041 | ||||||||
\(633\) | − | 67764.2i | − | 0.169119i | ||||||
\(634\) | − | 423318.i | − | 1.05315i | ||||||
\(635\) | − | 418712.i | − | 1.03841i | ||||||
\(636\) | 189924. | 0.469532 | ||||||||
\(637\) | 111549.i | 0.274908i | ||||||||
\(638\) | −76560.0 | − | 838673.i | −0.188088 | − | 2.06040i | ||||
\(639\) | −244584. | −0.598999 | ||||||||
\(640\) | 172511.i | 0.421169i | ||||||||
\(641\) | −99113.0 | −0.241221 | −0.120610 | − | 0.992700i | \(-0.538485\pi\) | ||||
−0.120610 | + | 0.992700i | \(0.538485\pi\) | |||||||
\(642\) | 72900.0 | 0.176871 | ||||||||
\(643\) | 526997. | 1.27464 | 0.637318 | − | 0.770601i | \(-0.280044\pi\) | ||||
0.637318 | + | 0.770601i | \(0.280044\pi\) | |||||||
\(644\) | − | 212407.i | − | 0.512149i | ||||||
\(645\) | − | 112064.i | − | 0.269369i | ||||||
\(646\) | − | 124223.i | − | 0.297672i | ||||||
\(647\) | −140843. | −0.336455 | −0.168227 | − | 0.985748i | \(-0.553804\pi\) | ||||
−0.168227 | + | 0.985748i | \(0.553804\pi\) | |||||||
\(648\) | − | 48802.1i | − | 0.116222i | ||||||
\(649\) | −25993.0 | − | 284739.i | −0.0617116 | − | 0.676017i | ||||
\(650\) | −342720. | −0.811172 | ||||||||
\(651\) | 223964.i | 0.528464i | ||||||||
\(652\) | −362068. | −0.851716 | ||||||||
\(653\) | −240953. | −0.565075 | −0.282537 | − | 0.959256i | \(-0.591176\pi\) | ||||
−0.282537 | + | 0.959256i | \(0.591176\pi\) | |||||||
\(654\) | −273240. | −0.638835 | ||||||||
\(655\) | − | 668649.i | − | 1.55853i | ||||||
\(656\) | 301773.i | 0.701250i | ||||||||
\(657\) | 238982.i | 0.553650i | ||||||||
\(658\) | 510600. | 1.17931 | ||||||||
\(659\) | 499830.i | 1.15094i | 0.817824 | + | 0.575468i | \(0.195180\pi\) | ||||
−0.817824 | + | 0.575468i | \(0.804820\pi\) | |||||||
\(660\) | 14322.0 | + | 156890.i | 0.0328788 | + | 0.360169i | ||||
\(661\) | 122927. | 0.281348 | 0.140674 | − | 0.990056i | \(-0.455073\pi\) | ||||
0.140674 | + | 0.990056i | \(0.455073\pi\) | |||||||
\(662\) | 955245.i | 2.17971i | ||||||||
\(663\) | −128520. | −0.292377 | ||||||||
\(664\) | 9120.00 | 0.0206852 | ||||||||
\(665\) | 167400. | 0.378540 | ||||||||
\(666\) | 65858.2i | 0.148478i | ||||||||
\(667\) | − | 351988.i | − | 0.791183i | ||||||
\(668\) | − | 10888.7i | − | 0.0244019i | ||||||
\(669\) | 260049. | 0.581036 | ||||||||
\(670\) | 475933.i | 1.06022i | ||||||||
\(671\) | −477840. | + | 43620.6i | −1.06130 | + | 0.0968828i | ||||
\(672\) | 226800. | 0.502232 | ||||||||
\(673\) | − | 202745.i | − | 0.447631i | −0.974632 | − | 0.223815i | \(-0.928149\pi\) | ||
0.974632 | − | 0.223815i | \(-0.0718513\pi\) | |||||||
\(674\) | 632580. | 1.39250 | ||||||||
\(675\) | 154224. | 0.338489 | ||||||||
\(676\) | 85666.0 | 0.187463 | ||||||||
\(677\) | 776966.i | 1.69522i | 0.530623 | + | 0.847608i | \(0.321958\pi\) | ||||
−0.530623 | + | 0.847608i | \(0.678042\pi\) | |||||||
\(678\) | 63212.7i | 0.137513i | ||||||||
\(679\) | 232618.i | 0.504549i | ||||||||
\(680\) | 78120.0 | 0.168945 | ||||||||
\(681\) | 24417.5i | 0.0526510i | ||||||||
\(682\) | −899580. | + | 82120.0i | −1.93406 | + | 0.176555i | ||||
\(683\) | 68422.0 | 0.146674 | 0.0733372 | − | 0.997307i | \(-0.476635\pi\) | ||||
0.0733372 | + | 0.997307i | \(0.476635\pi\) | |||||||
\(684\) | − | 99378.8i | − | 0.212413i | ||||||
\(685\) | 361057. | 0.769475 | ||||||||
\(686\) | 540600. | 1.14876 | ||||||||
\(687\) | −44421.0 | −0.0941185 | ||||||||
\(688\) | − | 342217.i | − | 0.722977i | ||||||
\(689\) | − | 842112.i | − | 1.77391i | ||||||
\(690\) | 141099.i | 0.296364i | ||||||||
\(691\) | 662597. | 1.38769 | 0.693846 | − | 0.720123i | \(-0.255915\pi\) | ||||
0.693846 | + | 0.720123i | \(0.255915\pi\) | |||||||
\(692\) | 33433.0i | 0.0698173i | ||||||||
\(693\) | 475200. | − | 43379.6i | 0.989487 | − | 0.0903274i | ||||
\(694\) | −752460. | −1.56230 | ||||||||
\(695\) | 532134.i | 1.10167i | ||||||||
\(696\) | 41760.0 | 0.0862069 | ||||||||
\(697\) | 244440. | 0.503161 | ||||||||
\(698\) | −987900. | −2.02769 | ||||||||
\(699\) | 28393.9i | 0.0581127i | ||||||||
\(700\) | − | 257649.i | − | 0.525814i | ||||||
\(701\) | 64247.9i | 0.130744i | 0.997861 | + | 0.0653721i | \(0.0208234\pi\) | ||||
−0.997861 | + | 0.0653721i | \(0.979177\pi\) | |||||||
\(702\) | −468180. | −0.950033 | ||||||||
\(703\) | − | 16464.5i | − | 0.0333149i | ||||||
\(704\) | 33176.0 | + | 363425.i | 0.0669389 | + | 0.733279i | ||||
\(705\) | −158286. | −0.318467 | ||||||||
\(706\) | − | 588950.i | − | 1.18160i | ||||||
\(707\) | −663000. | −1.32640 | ||||||||
\(708\) | −99246.0 | −0.197991 | ||||||||
\(709\) | −656713. | −1.30642 | −0.653210 | − | 0.757176i | \(-0.726578\pi\) | ||||
−0.653210 | + | 0.757176i | \(0.726578\pi\) | |||||||
\(710\) | − | 576790.i | − | 1.14420i | ||||||
\(711\) | 438529.i | 0.867478i | ||||||||
\(712\) | 51190.2i | 0.100978i | ||||||||
\(713\) | −377551. | −0.742671 | ||||||||
\(714\) | − | 207039.i | − | 0.406122i | ||||||
\(715\) | 695640. | − | 63503.0i | 1.36073 | − | 0.124217i | ||||
\(716\) | 375802. | 0.733049 | ||||||||
\(717\) | 108383.i | 0.210826i | ||||||||
\(718\) | 342180. | 0.663752 | ||||||||
\(719\) | 278797. | 0.539300 | 0.269650 | − | 0.962958i | \(-0.413092\pi\) | ||||
0.269650 | + | 0.962958i | \(0.413092\pi\) | |||||||
\(720\) | 633888. | 1.22278 | ||||||||
\(721\) | − | 614435.i | − | 1.18197i | ||||||
\(722\) | − | 660559.i | − | 1.26718i | ||||||
\(723\) | 304380.i | 0.582291i | ||||||||
\(724\) | 526862. | 1.00512 | ||||||||
\(725\) | − | 426961.i | − | 0.812291i | ||||||
\(726\) | −43560.0 | − | 236600.i | −0.0826446 | − | 0.448891i | ||||
\(727\) | −384283. | −0.727080 | −0.363540 | − | 0.931579i | \(-0.618432\pi\) | ||||
−0.363540 | + | 0.931579i | \(0.618432\pi\) | |||||||
\(728\) | − | 111735.i | − | 0.210828i | ||||||
\(729\) | −209223. | −0.393690 | ||||||||
\(730\) | −563580. | −1.05757 | ||||||||
\(731\) | −277200. | −0.518750 | ||||||||
\(732\) | 166551.i | 0.310832i | ||||||||
\(733\) | 900303.i | 1.67564i | 0.545947 | + | 0.837820i | \(0.316170\pi\) | ||||
−0.545947 | + | 0.837820i | \(0.683830\pi\) | |||||||
\(734\) | − | 779940.i | − | 1.44767i | ||||||
\(735\) | 55707.0 | 0.103118 | ||||||||
\(736\) | 382332.i | 0.705806i | ||||||||
\(737\) | −30833.0 | − | 337759.i | −0.0567650 | − | 0.621830i | ||||
\(738\) | 419040. | 0.769383 | ||||||||
\(739\) | 179237.i | 0.328200i | 0.986444 | + | 0.164100i | \(0.0524719\pi\) | ||||
−0.986444 | + | 0.164100i | \(0.947528\pi\) | |||||||
\(740\) | −72478.0 | −0.132356 | ||||||||
\(741\) | 55080.0 | 0.100313 | ||||||||
\(742\) | 1.35660e6 | 2.46402 | ||||||||
\(743\) | 815888.i | 1.47793i | 0.673746 | + | 0.738963i | \(0.264684\pi\) | ||||
−0.673746 | + | 0.738963i | \(0.735316\pi\) | |||||||
\(744\) | − | 44792.8i | − | 0.0809211i | ||||||
\(745\) | − | 202055.i | − | 0.364046i | ||||||
\(746\) | −325380. | −0.584673 | ||||||||
\(747\) | − | 59942.8i | − | 0.107423i | ||||||
\(748\) | 388080. | − | 35426.7i | 0.693614 | − | 0.0633180i | ||||
\(749\) | 243000. | 0.433154 | ||||||||
\(750\) | − | 147211.i | − | 0.261709i | ||||||
\(751\) | 463757. | 0.822263 | 0.411131 | − | 0.911576i | \(-0.365134\pi\) | ||||
0.411131 | + | 0.911576i | \(0.365134\pi\) | |||||||
\(752\) | −483368. | −0.854756 | ||||||||
\(753\) | 18609.0 | 0.0328196 | ||||||||
\(754\) | 1.29613e6i | 2.27985i | ||||||||
\(755\) | 1.07649e6i | 1.88850i | ||||||||
\(756\) | − | 351967.i | − | 0.615826i | ||||||
\(757\) | −593878. | −1.03635 | −0.518174 | − | 0.855275i | \(-0.673388\pi\) | ||||
−0.518174 | + | 0.855275i | \(0.673388\pi\) | |||||||
\(758\) | − | 674120.i | − | 1.17327i | ||||||
\(759\) | −9141.00 | − | 100135.i | −0.0158676 | − | 0.173820i | ||||
\(760\) | −33480.0 | −0.0579640 | ||||||||
\(761\) | − | 1.06130e6i | − | 1.83261i | −0.400487 | − | 0.916303i | \(-0.631159\pi\) | ||
0.400487 | − | 0.916303i | \(-0.368841\pi\) | |||||||
\(762\) | 221940. | 0.382231 | ||||||||
\(763\) | −910800. | −1.56449 | ||||||||
\(764\) | −484358. | −0.829812 | ||||||||
\(765\) | − | 513457.i | − | 0.877367i | ||||||
\(766\) | 850958.i | 1.45028i | ||||||||
\(767\) | 440051.i | 0.748019i | ||||||||
\(768\) | −236208. | −0.400472 | ||||||||
\(769\) | − | 219188.i | − | 0.370649i | −0.982677 | − | 0.185325i | \(-0.940666\pi\) | ||
0.982677 | − | 0.185325i | \(-0.0593337\pi\) | |||||||
\(770\) | 102300. | + | 1.12064e6i | 0.172542 | + | 1.89010i | ||||
\(771\) | 267954. | 0.450766 | ||||||||
\(772\) | 403343.i | 0.676768i | ||||||||
\(773\) | −315758. | −0.528440 | −0.264220 | − | 0.964462i | \(-0.585114\pi\) | ||||
−0.264220 | + | 0.964462i | \(0.585114\pi\) | |||||||
\(774\) | −475200. | −0.793222 | ||||||||
\(775\) | −457968. | −0.762486 | ||||||||
\(776\) | − | 46523.6i | − | 0.0772591i | ||||||
\(777\) | − | 27440.9i | − | 0.0454523i | ||||||
\(778\) | 228033.i | 0.376738i | ||||||||
\(779\) | −104760. | −0.172632 | ||||||||
\(780\) | − | 242466.i | − | 0.398530i | ||||||
\(781\) | 37367.0 | + | 409335.i | 0.0612613 | + | 0.671084i | ||||
\(782\) | 349020. | 0.570738 | ||||||||
\(783\) | − | 583259.i | − | 0.951344i | ||||||
\(784\) | 170116. | 0.276766 | ||||||||
\(785\) | 719417. | 1.16746 | ||||||||
\(786\) | 354420. | 0.573685 | ||||||||
\(787\) | − | 15796.3i | − | 0.0255039i | −0.999919 | − | 0.0127519i | \(-0.995941\pi\) | ||
0.999919 | − | 0.0127519i | \(-0.00405918\pi\) | |||||||
\(788\) | − | 749022.i | − | 1.20626i | ||||||
\(789\) | 186894.i | 0.300221i | ||||||||
\(790\) | −1.03416e6 | −1.65704 | ||||||||
\(791\) | 210709.i | 0.336767i | ||||||||
\(792\) | −95040.0 | + | 8675.93i | −0.151515 | + | 0.0138314i | ||||
\(793\) | 738480. | 1.17434 | ||||||||
\(794\) | − | 426577.i | − | 0.676639i | ||||||
\(795\) | −420546. | −0.665395 | ||||||||
\(796\) | −120148. | −0.189623 | ||||||||
\(797\) | 378607. | 0.596035 | 0.298018 | − | 0.954560i | \(-0.403675\pi\) | ||||
0.298018 | + | 0.954560i | \(0.403675\pi\) | |||||||
\(798\) | 88731.1i | 0.139338i | ||||||||
\(799\) | 391534.i | 0.613304i | ||||||||
\(800\) | 463768.i | 0.724637i | ||||||||
\(801\) | 336456. | 0.524401 | ||||||||
\(802\) | − | 1.08954e6i | − | 1.69393i | ||||||
\(803\) | 399960. | − | 36511.2i | 0.620277 | − | 0.0566233i | ||||
\(804\) | −117726. | −0.182121 | ||||||||
\(805\) | 470329.i | 0.725789i | ||||||||
\(806\) | 1.39026e6 | 2.14006 | ||||||||
\(807\) | 116034. | 0.178171 | ||||||||
\(808\) | 132600. | 0.203105 | ||||||||
\(809\) | − | 891221.i | − | 1.36172i | −0.732413 | − | 0.680861i | \(-0.761606\pi\) | ||
0.732413 | − | 0.680861i | \(-0.238394\pi\) | |||||||
\(810\) | − | 756432.i | − | 1.15292i | ||||||
\(811\) | − | 944690.i | − | 1.43631i | −0.695884 | − | 0.718154i | \(-0.744987\pi\) | ||
0.695884 | − | 0.718154i | \(-0.255013\pi\) | |||||||
\(812\) | −974400. | −1.47783 | ||||||||
\(813\) | − | 48604.9i | − | 0.0735358i | ||||||
\(814\) | 110220. | − | 10061.7i | 0.166346 | − | 0.0151852i | ||||
\(815\) | 801722. | 1.20700 | ||||||||
\(816\) | 195997.i | 0.294353i | ||||||||
\(817\) | 118800. | 0.177980 | ||||||||
\(818\) | −169320. | −0.253047 | ||||||||
\(819\) | −734400. | −1.09488 | ||||||||
\(820\) | 461160.i | 0.685842i | ||||||||
\(821\) | 551820.i | 0.818674i | 0.912383 | + | 0.409337i | \(0.134240\pi\) | ||||
−0.912383 | + | 0.409337i | \(0.865760\pi\) | |||||||
\(822\) | 191380.i | 0.283239i | ||||||||
\(823\) | −55483.0 | −0.0819144 | −0.0409572 | − | 0.999161i | \(-0.513041\pi\) | ||||
−0.0409572 | + | 0.999161i | \(0.513041\pi\) | |||||||
\(824\) | 122887.i | 0.180989i | ||||||||
\(825\) | −11088.0 | − | 121463.i | −0.0162909 | − | 0.178458i | ||||
\(826\) | −708900. | −1.03902 | ||||||||
\(827\) | − | 581714.i | − | 0.850548i | −0.905065 | − | 0.425274i | \(-0.860178\pi\) | ||
0.905065 | − | 0.425274i | \(-0.139822\pi\) | |||||||
\(828\) | 279216. | 0.407267 | ||||||||
\(829\) | −86953.0 | −0.126525 | −0.0632624 | − | 0.997997i | \(-0.520150\pi\) | ||||
−0.0632624 | + | 0.997997i | \(0.520150\pi\) | |||||||
\(830\) | 141360. | 0.205197 | ||||||||
\(831\) | − | 205133.i | − | 0.297053i | ||||||
\(832\) | − | 561657.i | − | 0.811380i | ||||||
\(833\) | − | 137796.i | − | 0.198585i | ||||||
\(834\) | −282060. | −0.405517 | ||||||||
\(835\) | 24110.7i | 0.0345810i | ||||||||
\(836\) | −166320. | + | 15182.9i | −0.237975 | + | 0.0217241i | ||||
\(837\) | −625617. | −0.893013 | ||||||||
\(838\) | 1.27366e6i | 1.81370i | ||||||||
\(839\) | 1.03048e6 | 1.46391 | 0.731955 | − | 0.681353i | \(-0.238608\pi\) | ||||
0.731955 | + | 0.681353i | \(0.238608\pi\) | |||||||
\(840\) | −55800.0 | −0.0790816 | ||||||||
\(841\) | −907439. | −1.28300 | ||||||||
\(842\) | 256980.i | 0.362473i | ||||||||
\(843\) | − | 371224.i | − | 0.522374i | ||||||
\(844\) | − | 316233.i | − | 0.443938i | ||||||
\(845\) | −189689. | −0.265662 | ||||||||
\(846\) | 671201.i | 0.937804i | ||||||||
\(847\) | −145200. | − | 788666.i | −0.202395 | − | 1.09933i | ||||
\(848\) | −1.28425e6 | −1.78590 | ||||||||
\(849\) | 378060.i | 0.524500i | ||||||||
\(850\) | 423360. | 0.585965 | ||||||||
\(851\) | 46259.0 | 0.0638759 | ||||||||
\(852\) | 142674. | 0.196547 | ||||||||
\(853\) | 225925.i | 0.310503i | 0.987875 | + | 0.155251i | \(0.0496188\pi\) | ||||
−0.987875 | + | 0.155251i | \(0.950381\pi\) | |||||||
\(854\) | 1.18965e6i | 1.63119i | ||||||||
\(855\) | 220053.i | 0.301020i | ||||||||
\(856\) | −48600.0 | −0.0663268 | ||||||||
\(857\) | 49404.6i | 0.0672675i | 0.999434 | + | 0.0336338i | \(0.0107080\pi\) | ||||
−0.999434 | + | 0.0336338i | \(0.989292\pi\) | |||||||
\(858\) | 33660.0 | + | 368727.i | 0.0457235 | + | 0.500876i | ||||
\(859\) | 1.08224e6 | 1.46668 | 0.733341 | − | 0.679861i | \(-0.237960\pi\) | ||||
0.733341 | + | 0.679861i | \(0.237960\pi\) | |||||||
\(860\) | − | 522965.i | − | 0.707092i | ||||||
\(861\) | −174600. | −0.235526 | ||||||||
\(862\) | 314460. | 0.423205 | ||||||||
\(863\) | 132262. | 0.177588 | 0.0887940 | − | 0.996050i | \(-0.471699\pi\) | ||||
0.0887940 | + | 0.996050i | \(0.471699\pi\) | |||||||
\(864\) | 633540.i | 0.848685i | ||||||||
\(865\) | − | 74030.2i | − | 0.0989411i | ||||||
\(866\) | − | 181663.i | − | 0.242232i | ||||||
\(867\) | −91803.0 | −0.122129 | ||||||||
\(868\) | 1.04516e6i | 1.38722i | ||||||||
\(869\) | 733920. | − | 66997.4i | 0.971872 | − | 0.0887194i | ||||
\(870\) | 647280. | 0.855172 | ||||||||
\(871\) | 521991.i | 0.688060i | ||||||||
\(872\) | 182160. | 0.239563 | ||||||||
\(873\) | −305784. | −0.401223 | ||||||||
\(874\) | −149580. | −0.195817 | ||||||||
\(875\) | − | 490705.i | − | 0.640920i | ||||||
\(876\) | − | 139406.i | − | 0.181666i | ||||||
\(877\) | 679034.i | 0.882860i | 0.897296 | + | 0.441430i | \(0.145529\pi\) | ||||
−0.897296 | + | 0.441430i | \(0.854471\pi\) | |||||||
\(878\) | 1.93512e6 | 2.51026 | ||||||||
\(879\) | 270958.i | 0.350691i | ||||||||
\(880\) | −96844.0 | − | 1.06087e6i | −0.125057 | − | 1.36993i | ||||
\(881\) | −1.01711e6 | −1.31044 | −0.655220 | − | 0.755438i | \(-0.727424\pi\) | ||||
−0.655220 | + | 0.755438i | \(0.727424\pi\) | |||||||
\(882\) | − | 236222.i | − | 0.303657i | ||||||
\(883\) | −1.51674e6 | −1.94531 | −0.972656 | − | 0.232252i | \(-0.925391\pi\) | ||||
−0.972656 | + | 0.232252i | \(0.925391\pi\) | |||||||
\(884\) | −599760. | −0.767490 | ||||||||
\(885\) | 219759. | 0.280582 | ||||||||
\(886\) | − | 1.53032e6i | − | 1.94946i | ||||||
\(887\) | − | 1.30820e6i | − | 1.66275i | −0.555710 | − | 0.831376i | \(-0.687553\pi\) | ||
0.555710 | − | 0.831376i | \(-0.312447\pi\) | |||||||
\(888\) | 5488.18i | 0.00695989i | ||||||||
\(889\) | 739800. | 0.936075 | ||||||||
\(890\) | 793447.i | 1.00170i | ||||||||
\(891\) | 49005.0 | + | 536823.i | 0.0617284 | + | 0.676201i | ||||
\(892\) | 1.21356e6 | 1.52522 | ||||||||
\(893\) | − | 167800.i | − | 0.210421i | ||||||
\(894\) | 107100. | 0.134003 | ||||||||
\(895\) | −832133. | −1.03884 | ||||||||
\(896\) | −304800. | −0.379664 | ||||||||
\(897\) | 154754.i | 0.192334i | ||||||||
\(898\) | − | 792045.i | − | 0.982194i | ||||||
\(899\) | 1.73199e6i | 2.14301i | ||||||||
\(900\) | 338688. | 0.418133 | ||||||||
\(901\) | 1.04026e6i | 1.28142i | ||||||||
\(902\) | −64020.0 | − | 701304.i | −0.0786869 | − | 0.861972i | ||||
\(903\) | 198000. | 0.242823 | ||||||||
\(904\) | − | 42141.8i | − | 0.0515675i | ||||||
\(905\) | −1.16662e6 | −1.42440 | ||||||||
\(906\) | −570600. | −0.695145 | ||||||||
\(907\) | 711302. | 0.864648 | 0.432324 | − | 0.901718i | \(-0.357694\pi\) | ||||
0.432324 | + | 0.901718i | \(0.357694\pi\) | |||||||
\(908\) | 113948.i | 0.138209i | ||||||||
\(909\) | − | 871536.i | − | 1.05477i | ||||||
\(910\) | − | 1.73190e6i | − | 2.09141i | ||||||
\(911\) | −1.48510e6 | −1.78945 | −0.894723 | − | 0.446622i | \(-0.852627\pi\) | ||||
−0.894723 | + | 0.446622i | \(0.852627\pi\) | |||||||
\(912\) | − | 83998.7i | − | 0.100991i | ||||||
\(913\) | −100320. | + | 9157.92i | −0.120350 | + | 0.0109864i | ||||
\(914\) | −2.10480e6 | −2.51952 | ||||||||
\(915\) | − | 368793.i | − | 0.440494i | ||||||
\(916\) | −207298. | −0.247061 | ||||||||
\(917\) | 1.18140e6 | 1.40494 | ||||||||
\(918\) | 578340. | 0.686275 | ||||||||
\(919\) | 143021.i | 0.169344i | 0.996409 | + | 0.0846720i | \(0.0269842\pi\) | ||||
−0.996409 | + | 0.0846720i | \(0.973016\pi\) | |||||||
\(920\) | − | 94065.9i | − | 0.111136i | ||||||
\(921\) | − | 460909.i | − | 0.543370i | ||||||
\(922\) | −38280.0 | −0.0450308 | ||||||||
\(923\) | − | 632609.i | − | 0.742560i | ||||||
\(924\) | −277200. | + | 25304.8i | −0.324675 | + | 0.0296387i | ||||
\(925\) | 56112.0 | 0.0655801 | ||||||||
\(926\) | 1.24444e6i | 1.45129i | ||||||||
\(927\) | 807696. | 0.939915 | ||||||||
\(928\) | 1.75392e6 | 2.03664 | ||||||||
\(929\) | 1.18628e6 | 1.37454 | 0.687269 | − | 0.726403i | \(-0.258810\pi\) | ||||
0.687269 | + | 0.726403i | \(0.258810\pi\) | |||||||
\(930\) | − | 694288.i | − | 0.802737i | ||||||
\(931\) | 59055.4i | 0.0681335i | ||||||||
\(932\) | 132505.i | 0.152546i | ||||||||
\(933\) | 272094. | 0.312576 | ||||||||
\(934\) | − | 1.79717e6i | − | 2.06013i | ||||||
\(935\) | −859320. | + | 78444.8i | −0.982951 | + | 0.0897307i | ||||
\(936\) | 146880. | 0.167653 | ||||||||
\(937\) | 1.16865e6i | 1.33109i | 0.746359 | + | 0.665544i | \(0.231800\pi\) | ||||
−0.746359 | + | 0.665544i | \(0.768200\pi\) | |||||||
\(938\) | −840900. | −0.955738 | ||||||||
\(939\) | 314859. | 0.357096 | ||||||||
\(940\) | −738668. | −0.835976 | ||||||||
\(941\) | 40838.2i | 0.0461198i | 0.999734 | + | 0.0230599i | \(0.00734084\pi\) | ||||
−0.999734 | + | 0.0230599i | \(0.992659\pi\) | |||||||
\(942\) | 381330.i | 0.429733i | ||||||||
\(943\) | − | 294335.i | − | 0.330993i | ||||||
\(944\) | 671092. | 0.753075 | ||||||||
\(945\) | 779354.i | 0.872713i | ||||||||
\(946\) | 72600.0 | + | 795293.i | 0.0811249 | + | 0.888679i | ||||
\(947\) | 1.40080e6 | 1.56198 | 0.780990 | − | 0.624544i | \(-0.214715\pi\) | ||||
0.780990 | + | 0.624544i | \(0.214715\pi\) | |||||||
\(948\) | − | 255808.i | − | 0.284641i | ||||||
\(949\) | −618120. | −0.686342 | ||||||||
\(950\) | −181440. | −0.201042 | ||||||||
\(951\) | −231861. | −0.256370 | ||||||||
\(952\) | 138026.i | 0.152296i | ||||||||
\(953\) | 1.12238e6i | 1.23582i | 0.786249 | + | 0.617910i | \(0.212020\pi\) | ||||
−0.786249 | + | 0.617910i | \(0.787980\pi\) | |||||||
\(954\) | 1.78330e6i | 1.95942i | ||||||||
\(955\) | 1.07251e6 | 1.17596 | ||||||||
\(956\) | 505789.i | 0.553418i | ||||||||
\(957\) | −459360. | + | 41933.6i | −0.501567 | + | 0.0457866i | ||||
\(958\) | −726060. | −0.791118 | ||||||||
\(959\) | 637932.i | 0.693645i | ||||||||
\(960\) | −280488. | −0.304349 | ||||||||
\(961\) | 934248. | 1.01162 | ||||||||
\(962\) | −170340. | −0.184063 | ||||||||
\(963\) | 319432.i | 0.344450i | ||||||||
\(964\) | 1.42044e6i | 1.52851i | ||||||||
\(965\) | − | 893116.i | − | 0.959077i | ||||||
\(966\) | −249300. | −0.267158 | ||||||||
\(967\) | − | 1.64168e6i | − | 1.75564i | −0.478992 | − | 0.877819i | \(-0.658998\pi\) | ||
0.478992 | − | 0.877819i | \(-0.341002\pi\) | |||||||
\(968\) | 29040.0 | + | 157733.i | 0.0309917 | + | 0.168334i | ||||
\(969\) | −68040.0 | −0.0724631 | ||||||||
\(970\) | − | 721115.i | − | 0.766410i | ||||||
\(971\) | −677603. | −0.718682 | −0.359341 | − | 0.933206i | \(-0.616999\pi\) | ||||
−0.359341 | + | 0.933206i | \(0.616999\pi\) | |||||||
\(972\) | 707616. | 0.748971 | ||||||||
\(973\) | −940200. | −0.993104 | ||||||||
\(974\) | 583231.i | 0.614785i | ||||||||
\(975\) | 187715.i | 0.197465i | ||||||||
\(976\) | − | 1.12621e6i | − | 1.18227i | ||||||
\(977\) | −486353. | −0.509521 | −0.254761 | − | 0.967004i | \(-0.581997\pi\) | ||||
−0.254761 | + | 0.967004i | \(0.581997\pi\) | |||||||
\(978\) | 424956.i | 0.444290i | ||||||||
\(979\) | −51403.0 | − | 563092.i | −0.0536319 | − | 0.587508i | ||||
\(980\) | 259966. | 0.270685 | ||||||||
\(981\) | − | 1.19728e6i | − | 1.24410i | ||||||
\(982\) | −1.28472e6 | −1.33225 | ||||||||
\(983\) | −618803. | −0.640391 | −0.320196 | − | 0.947351i | \(-0.603749\pi\) | ||||
−0.320196 | + | 0.947351i | \(0.603749\pi\) | |||||||
\(984\) | 34920.0 | 0.0360648 | ||||||||
\(985\) | 1.65855e6i | 1.70945i | ||||||||
\(986\) | − | 1.60110e6i | − | 1.64689i | ||||||
\(987\) | − | 279667.i | − | 0.287083i | ||||||
\(988\) | 257040. | 0.263322 | ||||||||
\(989\) | 333782.i | 0.341248i | ||||||||
\(990\) | −1.47312e6 | + | 134477.i | −1.50303 | + | 0.137207i | ||||
\(991\) | 53462.0 | 0.0544375 | 0.0272187 | − | 0.999630i | \(-0.491335\pi\) | ||||
0.0272187 | + | 0.999630i | \(0.491335\pi\) | |||||||
\(992\) | − | 1.88130e6i | − | 1.91176i | ||||||
\(993\) | 523209. | 0.530612 | ||||||||
\(994\) | 1.01910e6 | 1.03144 | ||||||||
\(995\) | 266042. | 0.268723 | ||||||||
\(996\) | 34966.6i | 0.0352480i | ||||||||
\(997\) | 393363.i | 0.395734i | 0.980229 | + | 0.197867i | \(0.0634015\pi\) | ||||
−0.980229 | + | 0.197867i | \(0.936599\pi\) | |||||||
\(998\) | 1.60142e6i | 1.60785i | ||||||||
\(999\) | 76653.0 | 0.0768065 |
(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 | 11.5.b.b.10.1 | ✓ | 2 | |
3.2 | odd | 2 | 99.5.c.b.10.2 | 2 | |||
4.3 | odd | 2 | 176.5.h.c.65.1 | 2 | |||
5.2 | odd | 4 | 275.5.d.b.274.4 | 4 | |||
5.3 | odd | 4 | 275.5.d.b.274.1 | 4 | |||
5.4 | even | 2 | 275.5.c.e.76.2 | 2 | |||
8.3 | odd | 2 | 704.5.h.d.65.1 | 2 | |||
8.5 | even | 2 | 704.5.h.f.65.2 | 2 | |||
11.2 | odd | 10 | 121.5.d.b.40.2 | 8 | |||
11.3 | even | 5 | 121.5.d.b.112.1 | 8 | |||
11.4 | even | 5 | 121.5.d.b.94.2 | 8 | |||
11.5 | even | 5 | 121.5.d.b.118.2 | 8 | |||
11.6 | odd | 10 | 121.5.d.b.118.1 | 8 | |||
11.7 | odd | 10 | 121.5.d.b.94.1 | 8 | |||
11.8 | odd | 10 | 121.5.d.b.112.2 | 8 | |||
11.9 | even | 5 | 121.5.d.b.40.1 | 8 | |||
11.10 | odd | 2 | inner | 11.5.b.b.10.2 | yes | 2 | |
33.32 | even | 2 | 99.5.c.b.10.1 | 2 | |||
44.43 | even | 2 | 176.5.h.c.65.2 | 2 | |||
55.32 | even | 4 | 275.5.d.b.274.2 | 4 | |||
55.43 | even | 4 | 275.5.d.b.274.3 | 4 | |||
55.54 | odd | 2 | 275.5.c.e.76.1 | 2 | |||
88.21 | odd | 2 | 704.5.h.f.65.1 | 2 | |||
88.43 | even | 2 | 704.5.h.d.65.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
11.5.b.b.10.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
11.5.b.b.10.2 | yes | 2 | 11.10 | odd | 2 | inner | |
99.5.c.b.10.1 | 2 | 33.32 | even | 2 | |||
99.5.c.b.10.2 | 2 | 3.2 | odd | 2 | |||
121.5.d.b.40.1 | 8 | 11.9 | even | 5 | |||
121.5.d.b.40.2 | 8 | 11.2 | odd | 10 | |||
121.5.d.b.94.1 | 8 | 11.7 | odd | 10 | |||
121.5.d.b.94.2 | 8 | 11.4 | even | 5 | |||
121.5.d.b.112.1 | 8 | 11.3 | even | 5 | |||
121.5.d.b.112.2 | 8 | 11.8 | odd | 10 | |||
121.5.d.b.118.1 | 8 | 11.6 | odd | 10 | |||
121.5.d.b.118.2 | 8 | 11.5 | even | 5 | |||
176.5.h.c.65.1 | 2 | 4.3 | odd | 2 | |||
176.5.h.c.65.2 | 2 | 44.43 | even | 2 | |||
275.5.c.e.76.1 | 2 | 55.54 | odd | 2 | |||
275.5.c.e.76.2 | 2 | 5.4 | even | 2 | |||
275.5.d.b.274.1 | 4 | 5.3 | odd | 4 | |||
275.5.d.b.274.2 | 4 | 55.32 | even | 4 | |||
275.5.d.b.274.3 | 4 | 55.43 | even | 4 | |||
275.5.d.b.274.4 | 4 | 5.2 | odd | 4 | |||
704.5.h.d.65.1 | 2 | 8.3 | odd | 2 | |||
704.5.h.d.65.2 | 2 | 88.43 | even | 2 | |||
704.5.h.f.65.1 | 2 | 88.21 | odd | 2 | |||
704.5.h.f.65.2 | 2 | 8.5 | even | 2 |