Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [507,4,Mod(337,507)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(507, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("507.337");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 507 = 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 507.b (of order \(2\), degree \(1\), not 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: | \(29.9139683729\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} + 97 x^{16} + 3906 x^{14} + 84743 x^{12} + 1077128 x^{10} + 8187552 x^{8} + 36483705 x^{6} + \cdots + 26460736 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 13^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 337.4 | ||
Root | \(-2.37739i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 507.337 |
Dual form | 507.4.b.j.337.15 |
$q$-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 \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).
\(n\) | \(170\) | \(340\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 3.37739i | − 1.19409i | −0.802208 | − | 0.597044i | \(-0.796342\pi\) | ||||
0.802208 | − | 0.597044i | \(-0.203658\pi\) | |||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | −3.40677 | −0.425846 | ||||||||
\(5\) | 15.7127i | 1.40538i | 0.711494 | + | 0.702692i | \(0.248019\pi\) | ||||
−0.711494 | + | 0.702692i | \(0.751981\pi\) | |||||||
\(6\) | 10.1322i | 0.689407i | ||||||||
\(7\) | − 17.1681i | − 0.926992i | −0.886099 | − | 0.463496i | \(-0.846595\pi\) | ||||
0.886099 | − | 0.463496i | \(-0.153405\pi\) | |||||||
\(8\) | − 15.5131i | − 0.685590i | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 53.0679 | 1.67815 | ||||||||
\(11\) | 52.8187i | 1.44777i | 0.689922 | + | 0.723884i | \(0.257645\pi\) | ||||
−0.689922 | + | 0.723884i | \(0.742355\pi\) | |||||||
\(12\) | 10.2203 | 0.245862 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −57.9835 | −1.10691 | ||||||||
\(15\) | − 47.1380i | − 0.811399i | ||||||||
\(16\) | −79.6481 | −1.24450 | ||||||||
\(17\) | 71.0654 | 1.01388 | 0.506938 | − | 0.861982i | \(-0.330777\pi\) | ||||
0.506938 | + | 0.861982i | \(0.330777\pi\) | |||||||
\(18\) | − 30.3965i | − 0.398029i | ||||||||
\(19\) | − 92.6916i | − 1.11921i | −0.828761 | − | 0.559603i | \(-0.810954\pi\) | ||||
0.828761 | − | 0.559603i | \(-0.189046\pi\) | |||||||
\(20\) | − 53.5295i | − 0.598478i | ||||||||
\(21\) | 51.5044i | 0.535199i | ||||||||
\(22\) | 178.390 | 1.72876 | ||||||||
\(23\) | −190.712 | −1.72896 | −0.864482 | − | 0.502663i | \(-0.832354\pi\) | ||||
−0.864482 | + | 0.502663i | \(0.832354\pi\) | |||||||
\(24\) | 46.5394i | 0.395826i | ||||||||
\(25\) | −121.888 | −0.975106 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 58.4878i | 0.394756i | ||||||||
\(29\) | −128.204 | −0.820927 | −0.410463 | − | 0.911877i | \(-0.634633\pi\) | ||||
−0.410463 | + | 0.911877i | \(0.634633\pi\) | |||||||
\(30\) | −159.204 | −0.968882 | ||||||||
\(31\) | − 3.29674i | − 0.0191004i | −0.999954 | − | 0.00955020i | \(-0.996960\pi\) | ||||
0.999954 | − | 0.00955020i | \(-0.00303997\pi\) | |||||||
\(32\) | 144.898i | 0.800454i | ||||||||
\(33\) | − 158.456i | − 0.835869i | ||||||||
\(34\) | − 240.016i | − 1.21066i | ||||||||
\(35\) | 269.757 | 1.30278 | ||||||||
\(36\) | −30.6609 | −0.141949 | ||||||||
\(37\) | 241.546i | 1.07324i | 0.843823 | + | 0.536621i | \(0.180300\pi\) | ||||
−0.843823 | + | 0.536621i | \(0.819700\pi\) | |||||||
\(38\) | −313.056 | −1.33643 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 243.753 | 0.963518 | ||||||||
\(41\) | 97.1824i | 0.370179i | 0.982722 | + | 0.185090i | \(0.0592575\pi\) | ||||
−0.982722 | + | 0.185090i | \(0.940742\pi\) | |||||||
\(42\) | 173.950 | 0.639075 | ||||||||
\(43\) | −376.151 | −1.33401 | −0.667006 | − | 0.745052i | \(-0.732425\pi\) | ||||
−0.667006 | + | 0.745052i | \(0.732425\pi\) | |||||||
\(44\) | − 179.941i | − 0.616527i | ||||||||
\(45\) | 141.414i | 0.468462i | ||||||||
\(46\) | 644.109i | 2.06454i | ||||||||
\(47\) | 577.354i | 1.79182i | 0.444231 | + | 0.895912i | \(0.353477\pi\) | ||||
−0.444231 | + | 0.895912i | \(0.646523\pi\) | |||||||
\(48\) | 238.944 | 0.718513 | ||||||||
\(49\) | 48.2555 | 0.140686 | ||||||||
\(50\) | 411.664i | 1.16436i | ||||||||
\(51\) | −213.196 | −0.585362 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −307.686 | −0.797433 | −0.398716 | − | 0.917074i | \(-0.630544\pi\) | ||||
−0.398716 | + | 0.917074i | \(0.630544\pi\) | |||||||
\(54\) | 91.1896i | 0.229802i | ||||||||
\(55\) | −829.924 | −2.03467 | ||||||||
\(56\) | −266.331 | −0.635536 | ||||||||
\(57\) | 278.075i | 0.646174i | ||||||||
\(58\) | 432.995i | 0.980259i | ||||||||
\(59\) | 349.914i | 0.772117i | 0.922474 | + | 0.386059i | \(0.126164\pi\) | ||||
−0.922474 | + | 0.386059i | \(0.873836\pi\) | |||||||
\(60\) | 160.588i | 0.345531i | ||||||||
\(61\) | 127.467 | 0.267548 | 0.133774 | − | 0.991012i | \(-0.457290\pi\) | ||||
0.133774 | + | 0.991012i | \(0.457290\pi\) | |||||||
\(62\) | −11.1344 | −0.0228076 | ||||||||
\(63\) | − 154.513i | − 0.308997i | ||||||||
\(64\) | −147.809 | −0.288689 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −535.169 | −0.998102 | ||||||||
\(67\) | 903.564i | 1.64758i | 0.566894 | + | 0.823791i | \(0.308145\pi\) | ||||
−0.566894 | + | 0.823791i | \(0.691855\pi\) | |||||||
\(68\) | −242.104 | −0.431755 | ||||||||
\(69\) | 572.136 | 0.998218 | ||||||||
\(70\) | − 911.076i | − 1.55563i | ||||||||
\(71\) | − 826.106i | − 1.38086i | −0.723401 | − | 0.690428i | \(-0.757422\pi\) | ||||
0.723401 | − | 0.690428i | \(-0.242578\pi\) | |||||||
\(72\) | − 139.618i | − 0.228530i | ||||||||
\(73\) | − 131.760i | − 0.211252i | −0.994406 | − | 0.105626i | \(-0.966315\pi\) | ||||
0.994406 | − | 0.105626i | \(-0.0336846\pi\) | |||||||
\(74\) | 815.796 | 1.28155 | ||||||||
\(75\) | 365.665 | 0.562978 | ||||||||
\(76\) | 315.779i | 0.476610i | ||||||||
\(77\) | 906.799 | 1.34207 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −556.244 | −0.792182 | −0.396091 | − | 0.918211i | \(-0.629633\pi\) | ||||
−0.396091 | + | 0.918211i | \(0.629633\pi\) | |||||||
\(80\) | − 1251.48i | − 1.74900i | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 328.223 | 0.442026 | ||||||||
\(83\) | 254.664i | 0.336783i | 0.985720 | + | 0.168391i | \(0.0538573\pi\) | ||||
−0.985720 | + | 0.168391i | \(0.946143\pi\) | |||||||
\(84\) | − 175.464i | − 0.227912i | ||||||||
\(85\) | 1116.63i | 1.42489i | ||||||||
\(86\) | 1270.41i | 1.59293i | ||||||||
\(87\) | 384.612 | 0.473962 | ||||||||
\(88\) | 819.384 | 0.992576 | ||||||||
\(89\) | 183.410i | 0.218443i | 0.994017 | + | 0.109222i | \(0.0348358\pi\) | ||||
−0.994017 | + | 0.109222i | \(0.965164\pi\) | |||||||
\(90\) | 477.611 | 0.559384 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 649.712 | 0.736273 | ||||||||
\(93\) | 9.89023i | 0.0110276i | ||||||||
\(94\) | 1949.95 | 2.13960 | ||||||||
\(95\) | 1456.43 | 1.57292 | ||||||||
\(96\) | − 434.693i | − 0.462142i | ||||||||
\(97\) | 780.498i | 0.816986i | 0.912762 | + | 0.408493i | \(0.133946\pi\) | ||||
−0.912762 | + | 0.408493i | \(0.866054\pi\) | |||||||
\(98\) | − 162.978i | − 0.167992i | ||||||||
\(99\) | 475.369i | 0.482589i | ||||||||
\(100\) | 415.245 | 0.415245 | ||||||||
\(101\) | 1807.67 | 1.78089 | 0.890444 | − | 0.455093i | \(-0.150394\pi\) | ||||
0.890444 | + | 0.455093i | \(0.150394\pi\) | |||||||
\(102\) | 720.047i | 0.698974i | ||||||||
\(103\) | −1560.78 | −1.49308 | −0.746542 | − | 0.665338i | \(-0.768288\pi\) | ||||
−0.746542 | + | 0.665338i | \(0.768288\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −809.272 | −0.752160 | ||||||||
\(106\) | 1039.18i | 0.952205i | ||||||||
\(107\) | 322.266 | 0.291165 | 0.145582 | − | 0.989346i | \(-0.453494\pi\) | ||||
0.145582 | + | 0.989346i | \(0.453494\pi\) | |||||||
\(108\) | 91.9828 | 0.0819541 | ||||||||
\(109\) | − 1607.72i | − 1.41277i | −0.707827 | − | 0.706386i | \(-0.750324\pi\) | ||||
0.707827 | − | 0.706386i | \(-0.249676\pi\) | |||||||
\(110\) | 2802.98i | 2.42958i | ||||||||
\(111\) | − 724.639i | − 0.619637i | ||||||||
\(112\) | 1367.41i | 1.15364i | ||||||||
\(113\) | −429.905 | −0.357895 | −0.178947 | − | 0.983859i | \(-0.557269\pi\) | ||||
−0.178947 | + | 0.983859i | \(0.557269\pi\) | |||||||
\(114\) | 939.167 | 0.771589 | ||||||||
\(115\) | − 2996.60i | − 2.42986i | ||||||||
\(116\) | 436.761 | 0.349589 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1181.80 | 0.921976 | ||||||||
\(119\) | − 1220.06i | − 0.939855i | ||||||||
\(120\) | −731.259 | −0.556287 | ||||||||
\(121\) | −1458.82 | −1.09603 | ||||||||
\(122\) | − 430.505i | − 0.319476i | ||||||||
\(123\) | − 291.547i | − 0.213723i | ||||||||
\(124\) | 11.2312i | 0.00813383i | ||||||||
\(125\) | 48.8932i | 0.0349851i | ||||||||
\(126\) | −521.851 | −0.368970 | ||||||||
\(127\) | −2371.36 | −1.65688 | −0.828442 | − | 0.560076i | \(-0.810772\pi\) | ||||
−0.828442 | + | 0.560076i | \(0.810772\pi\) | |||||||
\(128\) | 1658.39i | 1.14517i | ||||||||
\(129\) | 1128.45 | 0.770193 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 169.200 | 0.112848 | 0.0564239 | − | 0.998407i | \(-0.482030\pi\) | ||||
0.0564239 | + | 0.998407i | \(0.482030\pi\) | |||||||
\(132\) | 539.824i | 0.355952i | ||||||||
\(133\) | −1591.34 | −1.03749 | ||||||||
\(134\) | 3051.69 | 1.96736 | ||||||||
\(135\) | − 424.242i | − 0.270466i | ||||||||
\(136\) | − 1102.45i | − 0.695104i | ||||||||
\(137\) | 2976.21i | 1.85602i | 0.372558 | + | 0.928009i | \(0.378481\pi\) | ||||
−0.372558 | + | 0.928009i | \(0.621519\pi\) | |||||||
\(138\) | − 1932.33i | − 1.19196i | ||||||||
\(139\) | −2555.15 | −1.55917 | −0.779585 | − | 0.626296i | \(-0.784570\pi\) | ||||
−0.779585 | + | 0.626296i | \(0.784570\pi\) | |||||||
\(140\) | −919.001 | −0.554784 | ||||||||
\(141\) | − 1732.06i | − 1.03451i | ||||||||
\(142\) | −2790.08 | −1.64886 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −716.833 | −0.414834 | ||||||||
\(145\) | − 2014.43i | − 1.15372i | ||||||||
\(146\) | −445.006 | −0.252253 | ||||||||
\(147\) | −144.766 | −0.0812254 | ||||||||
\(148\) | − 822.892i | − 0.457036i | ||||||||
\(149\) | − 424.529i | − 0.233415i | −0.993166 | − | 0.116707i | \(-0.962766\pi\) | ||||
0.993166 | − | 0.116707i | \(-0.0372339\pi\) | |||||||
\(150\) | − 1234.99i | − 0.672245i | ||||||||
\(151\) | 42.3232i | 0.0228093i | 0.999935 | + | 0.0114047i | \(0.00363030\pi\) | ||||
−0.999935 | + | 0.0114047i | \(0.996370\pi\) | |||||||
\(152\) | −1437.94 | −0.767317 | ||||||||
\(153\) | 639.589 | 0.337959 | ||||||||
\(154\) | − 3062.61i | − 1.60255i | ||||||||
\(155\) | 51.8007 | 0.0268434 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −990.187 | −0.503347 | −0.251674 | − | 0.967812i | \(-0.580981\pi\) | ||||
−0.251674 | + | 0.967812i | \(0.580981\pi\) | |||||||
\(158\) | 1878.65i | 0.945935i | ||||||||
\(159\) | 923.058 | 0.460398 | ||||||||
\(160\) | −2276.73 | −1.12495 | ||||||||
\(161\) | 3274.17i | 1.60274i | ||||||||
\(162\) | − 273.569i | − 0.132676i | ||||||||
\(163\) | 2645.82i | 1.27139i | 0.771940 | + | 0.635695i | \(0.219286\pi\) | ||||
−0.771940 | + | 0.635695i | \(0.780714\pi\) | |||||||
\(164\) | − 331.078i | − 0.157639i | ||||||||
\(165\) | 2489.77 | 1.17472 | ||||||||
\(166\) | 860.099 | 0.402148 | ||||||||
\(167\) | 295.428i | 0.136892i | 0.997655 | + | 0.0684458i | \(0.0218040\pi\) | ||||
−0.997655 | + | 0.0684458i | \(0.978196\pi\) | |||||||
\(168\) | 798.994 | 0.366927 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 3771.29 | 1.70144 | ||||||||
\(171\) | − 834.225i | − 0.373069i | ||||||||
\(172\) | 1281.46 | 0.568084 | ||||||||
\(173\) | −1495.46 | −0.657213 | −0.328606 | − | 0.944467i | \(-0.606579\pi\) | ||||
−0.328606 | + | 0.944467i | \(0.606579\pi\) | |||||||
\(174\) | − 1298.98i | − 0.565953i | ||||||||
\(175\) | 2092.59i | 0.903915i | ||||||||
\(176\) | − 4206.91i | − 1.80175i | ||||||||
\(177\) | − 1049.74i | − 0.445782i | ||||||||
\(178\) | 619.448 | 0.260840 | ||||||||
\(179\) | −785.097 | −0.327826 | −0.163913 | − | 0.986475i | \(-0.552412\pi\) | ||||
−0.163913 | + | 0.986475i | \(0.552412\pi\) | |||||||
\(180\) | − 481.765i | − 0.199493i | ||||||||
\(181\) | 1287.01 | 0.528522 | 0.264261 | − | 0.964451i | \(-0.414872\pi\) | ||||
0.264261 | + | 0.964451i | \(0.414872\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −382.400 | −0.154469 | ||||||||
\(184\) | 2958.54i | 1.18536i | ||||||||
\(185\) | −3795.34 | −1.50832 | ||||||||
\(186\) | 33.4032 | 0.0131680 | ||||||||
\(187\) | 3753.59i | 1.46786i | ||||||||
\(188\) | − 1966.91i | − 0.763042i | ||||||||
\(189\) | 463.539i | 0.178400i | ||||||||
\(190\) | − 4918.95i | − 1.87820i | ||||||||
\(191\) | 466.452 | 0.176708 | 0.0883542 | − | 0.996089i | \(-0.471839\pi\) | ||||
0.0883542 | + | 0.996089i | \(0.471839\pi\) | |||||||
\(192\) | 443.426 | 0.166675 | ||||||||
\(193\) | 2636.99i | 0.983495i | 0.870738 | + | 0.491747i | \(0.163642\pi\) | ||||
−0.870738 | + | 0.491747i | \(0.836358\pi\) | |||||||
\(194\) | 2636.05 | 0.975553 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −164.395 | −0.0599108 | ||||||||
\(197\) | − 3676.90i | − 1.32979i | −0.746937 | − | 0.664894i | \(-0.768477\pi\) | ||||
0.746937 | − | 0.664894i | \(-0.231523\pi\) | |||||||
\(198\) | 1605.51 | 0.576254 | ||||||||
\(199\) | −220.557 | −0.0785670 | −0.0392835 | − | 0.999228i | \(-0.512508\pi\) | ||||
−0.0392835 | + | 0.999228i | \(0.512508\pi\) | |||||||
\(200\) | 1890.87i | 0.668523i | ||||||||
\(201\) | − 2710.69i | − 0.951231i | ||||||||
\(202\) | − 6105.20i | − 2.12654i | ||||||||
\(203\) | 2201.02i | 0.760992i | ||||||||
\(204\) | 726.311 | 0.249274 | ||||||||
\(205\) | −1527.00 | −0.520244 | ||||||||
\(206\) | 5271.35i | 1.78287i | ||||||||
\(207\) | −1716.41 | −0.576322 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4895.85 | 1.62035 | ||||||||
\(210\) | 2733.23i | 0.898146i | ||||||||
\(211\) | 1385.93 | 0.452186 | 0.226093 | − | 0.974106i | \(-0.427405\pi\) | ||||
0.226093 | + | 0.974106i | \(0.427405\pi\) | |||||||
\(212\) | 1048.22 | 0.339584 | ||||||||
\(213\) | 2478.32i | 0.797237i | ||||||||
\(214\) | − 1088.42i | − 0.347676i | ||||||||
\(215\) | − 5910.35i | − 1.87480i | ||||||||
\(216\) | 418.855i | 0.131942i | ||||||||
\(217\) | −56.5989 | −0.0177059 | ||||||||
\(218\) | −5429.91 | −1.68697 | ||||||||
\(219\) | 395.281i | 0.121966i | ||||||||
\(220\) | 2827.36 | 0.866457 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −2447.39 | −0.739901 | ||||||||
\(223\) | 111.847i | 0.0335867i | 0.999859 | + | 0.0167933i | \(0.00534574\pi\) | ||||
−0.999859 | + | 0.0167933i | \(0.994654\pi\) | |||||||
\(224\) | 2487.62 | 0.742014 | ||||||||
\(225\) | −1096.99 | −0.325035 | ||||||||
\(226\) | 1451.96i | 0.427358i | ||||||||
\(227\) | − 4990.96i | − 1.45930i | −0.683819 | − | 0.729651i | \(-0.739682\pi\) | ||||
0.683819 | − | 0.729651i | \(-0.260318\pi\) | |||||||
\(228\) | − 947.337i | − 0.275171i | ||||||||
\(229\) | − 5787.56i | − 1.67010i | −0.550174 | − | 0.835050i | \(-0.685439\pi\) | ||||
0.550174 | − | 0.835050i | \(-0.314561\pi\) | |||||||
\(230\) | −10120.7 | −2.90147 | ||||||||
\(231\) | −2720.40 | −0.774844 | ||||||||
\(232\) | 1988.85i | 0.562819i | ||||||||
\(233\) | 723.707 | 0.203483 | 0.101742 | − | 0.994811i | \(-0.467559\pi\) | ||||
0.101742 | + | 0.994811i | \(0.467559\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9071.78 | −2.51820 | ||||||||
\(236\) | − 1192.08i | − 0.328803i | ||||||||
\(237\) | 1668.73 | 0.457366 | ||||||||
\(238\) | −4120.62 | −1.12227 | ||||||||
\(239\) | 1239.74i | 0.335531i | 0.985827 | + | 0.167766i | \(0.0536552\pi\) | ||||
−0.985827 | + | 0.167766i | \(0.946345\pi\) | |||||||
\(240\) | 3754.45i | 1.00979i | ||||||||
\(241\) | − 755.393i | − 0.201905i | −0.994891 | − | 0.100953i | \(-0.967811\pi\) | ||||
0.994891 | − | 0.100953i | \(-0.0321890\pi\) | |||||||
\(242\) | 4927.00i | 1.30876i | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | −434.249 | −0.113934 | ||||||||
\(245\) | 758.222i | 0.197719i | ||||||||
\(246\) | −984.669 | −0.255204 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −51.1428 | −0.0130950 | ||||||||
\(249\) | − 763.991i | − 0.194442i | ||||||||
\(250\) | 165.131 | 0.0417753 | ||||||||
\(251\) | −2252.06 | −0.566330 | −0.283165 | − | 0.959071i | \(-0.591384\pi\) | ||||
−0.283165 | + | 0.959071i | \(0.591384\pi\) | |||||||
\(252\) | 526.391i | 0.131585i | ||||||||
\(253\) | − 10073.2i | − 2.50314i | ||||||||
\(254\) | 8009.01i | 1.97846i | ||||||||
\(255\) | − 3349.89i | − 0.822659i | ||||||||
\(256\) | 4418.56 | 1.07875 | ||||||||
\(257\) | −3716.75 | −0.902118 | −0.451059 | − | 0.892494i | \(-0.648954\pi\) | ||||
−0.451059 | + | 0.892494i | \(0.648954\pi\) | |||||||
\(258\) | − 3811.23i | − 0.919678i | ||||||||
\(259\) | 4146.90 | 0.994887 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1153.84 | −0.273642 | ||||||||
\(262\) | − 571.454i | − 0.134750i | ||||||||
\(263\) | −49.9521 | −0.0117117 | −0.00585585 | − | 0.999983i | \(-0.501864\pi\) | ||||
−0.00585585 | + | 0.999983i | \(0.501864\pi\) | |||||||
\(264\) | −2458.15 | −0.573064 | ||||||||
\(265\) | − 4834.57i | − 1.12070i | ||||||||
\(266\) | 5374.58i | 1.23886i | ||||||||
\(267\) | − 550.231i | − 0.126118i | ||||||||
\(268\) | − 3078.23i | − 0.701616i | ||||||||
\(269\) | 3421.44 | 0.775497 | 0.387748 | − | 0.921765i | \(-0.373253\pi\) | ||||
0.387748 | + | 0.921765i | \(0.373253\pi\) | |||||||
\(270\) | −1432.83 | −0.322961 | ||||||||
\(271\) | − 2958.89i | − 0.663247i | −0.943412 | − | 0.331624i | \(-0.892404\pi\) | ||||
0.943412 | − | 0.331624i | \(-0.107596\pi\) | |||||||
\(272\) | −5660.23 | −1.26177 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 10051.8 | 2.21625 | ||||||||
\(275\) | − 6437.99i | − 1.41173i | ||||||||
\(276\) | −1949.13 | −0.425087 | ||||||||
\(277\) | 7461.08 | 1.61839 | 0.809193 | − | 0.587543i | \(-0.199905\pi\) | ||||
0.809193 | + | 0.587543i | \(0.199905\pi\) | |||||||
\(278\) | 8629.73i | 1.86179i | ||||||||
\(279\) | − 29.6707i | − 0.00636680i | ||||||||
\(280\) | − 4184.78i | − 0.893173i | ||||||||
\(281\) | − 4728.04i | − 1.00374i | −0.864943 | − | 0.501871i | \(-0.832645\pi\) | ||||
0.864943 | − | 0.501871i | \(-0.167355\pi\) | |||||||
\(282\) | −5849.85 | −1.23530 | ||||||||
\(283\) | 2879.69 | 0.604876 | 0.302438 | − | 0.953169i | \(-0.402199\pi\) | ||||
0.302438 | + | 0.953169i | \(0.402199\pi\) | |||||||
\(284\) | 2814.35i | 0.588032i | ||||||||
\(285\) | −4369.30 | −0.908123 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1668.44 | 0.343153 | ||||||||
\(288\) | 1304.08i | 0.266818i | ||||||||
\(289\) | 137.298 | 0.0279458 | ||||||||
\(290\) | −6803.51 | −1.37764 | ||||||||
\(291\) | − 2341.50i | − 0.471687i | ||||||||
\(292\) | 448.877i | 0.0899607i | ||||||||
\(293\) | 8200.94i | 1.63517i | 0.575810 | + | 0.817583i | \(0.304687\pi\) | ||||
−0.575810 | + | 0.817583i | \(0.695313\pi\) | |||||||
\(294\) | 488.933i | 0.0969902i | ||||||||
\(295\) | −5498.09 | −1.08512 | ||||||||
\(296\) | 3747.14 | 0.735804 | ||||||||
\(297\) | − 1426.11i | − 0.278623i | ||||||||
\(298\) | −1433.80 | −0.278718 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1245.74 | −0.239742 | ||||||||
\(301\) | 6457.81i | 1.23662i | ||||||||
\(302\) | 142.942 | 0.0272364 | ||||||||
\(303\) | −5423.00 | −1.02820 | ||||||||
\(304\) | 7382.71i | 1.39285i | ||||||||
\(305\) | 2002.84i | 0.376008i | ||||||||
\(306\) | − 2160.14i | − 0.403553i | ||||||||
\(307\) | 2058.82i | 0.382747i | 0.981517 | + | 0.191374i | \(0.0612942\pi\) | ||||
−0.981517 | + | 0.191374i | \(0.938706\pi\) | |||||||
\(308\) | −3089.25 | −0.571515 | ||||||||
\(309\) | 4682.33 | 0.862033 | ||||||||
\(310\) | − 174.951i | − 0.0320534i | ||||||||
\(311\) | −1862.08 | −0.339514 | −0.169757 | − | 0.985486i | \(-0.554298\pi\) | ||||
−0.169757 | + | 0.985486i | \(0.554298\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −255.896 | −0.0462112 | −0.0231056 | − | 0.999733i | \(-0.507355\pi\) | ||||
−0.0231056 | + | 0.999733i | \(0.507355\pi\) | |||||||
\(314\) | 3344.25i | 0.601041i | ||||||||
\(315\) | 2427.82 | 0.434260 | ||||||||
\(316\) | 1895.00 | 0.337348 | ||||||||
\(317\) | − 6265.68i | − 1.11014i | −0.831802 | − | 0.555072i | \(-0.812691\pi\) | ||||
0.831802 | − | 0.555072i | \(-0.187309\pi\) | |||||||
\(318\) | − 3117.53i | − 0.549756i | ||||||||
\(319\) | − 6771.57i | − 1.18851i | ||||||||
\(320\) | − 2322.47i | − 0.405719i | ||||||||
\(321\) | −966.798 | −0.168104 | ||||||||
\(322\) | 11058.1 | 1.91381 | ||||||||
\(323\) | − 6587.17i | − 1.13474i | ||||||||
\(324\) | −275.948 | −0.0473162 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 8935.96 | 1.51815 | ||||||||
\(327\) | 4823.17i | 0.815664i | ||||||||
\(328\) | 1507.60 | 0.253791 | ||||||||
\(329\) | 9912.09 | 1.66101 | ||||||||
\(330\) | − 8408.93i | − 1.40272i | ||||||||
\(331\) | − 1071.93i | − 0.178002i | −0.996032 | − | 0.0890011i | \(-0.971633\pi\) | ||||
0.996032 | − | 0.0890011i | \(-0.0283674\pi\) | |||||||
\(332\) | − 867.581i | − 0.143418i | ||||||||
\(333\) | 2173.92i | 0.357747i | ||||||||
\(334\) | 997.775 | 0.163461 | ||||||||
\(335\) | −14197.4 | −2.31549 | ||||||||
\(336\) | − 4102.22i | − 0.666056i | ||||||||
\(337\) | 5572.02 | 0.900675 | 0.450337 | − | 0.892858i | \(-0.351304\pi\) | ||||
0.450337 | + | 0.892858i | \(0.351304\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1289.72 | 0.206631 | ||||||||
\(340\) | − 3804.10i | − 0.606783i | ||||||||
\(341\) | 174.130 | 0.0276530 | ||||||||
\(342\) | −2817.50 | −0.445477 | ||||||||
\(343\) | − 6717.12i | − 1.05741i | ||||||||
\(344\) | 5835.29i | 0.914586i | ||||||||
\(345\) | 8989.79i | 1.40288i | ||||||||
\(346\) | 5050.76i | 0.784770i | ||||||||
\(347\) | −1903.44 | −0.294472 | −0.147236 | − | 0.989101i | \(-0.547038\pi\) | ||||
−0.147236 | + | 0.989101i | \(0.547038\pi\) | |||||||
\(348\) | −1310.28 | −0.201835 | ||||||||
\(349\) | 1097.17i | 0.168282i | 0.996454 | + | 0.0841409i | \(0.0268146\pi\) | ||||
−0.996454 | + | 0.0841409i | \(0.973185\pi\) | |||||||
\(350\) | 7067.51 | 1.07935 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −7653.31 | −1.15887 | ||||||||
\(353\) | − 5420.90i | − 0.817352i | −0.912679 | − | 0.408676i | \(-0.865991\pi\) | ||||
0.912679 | − | 0.408676i | \(-0.134009\pi\) | |||||||
\(354\) | −3545.39 | −0.532303 | ||||||||
\(355\) | 12980.3 | 1.94063 | ||||||||
\(356\) | − 624.836i | − 0.0930232i | ||||||||
\(357\) | 3660.18i | 0.542626i | ||||||||
\(358\) | 2651.58i | 0.391453i | ||||||||
\(359\) | 3885.40i | 0.571208i | 0.958348 | + | 0.285604i | \(0.0921942\pi\) | ||||
−0.958348 | + | 0.285604i | \(0.907806\pi\) | |||||||
\(360\) | 2193.78 | 0.321173 | ||||||||
\(361\) | −1732.74 | −0.252622 | ||||||||
\(362\) | − 4346.72i | − 0.631102i | ||||||||
\(363\) | 4376.46 | 0.632795 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2070.31 | 0.296890 | ||||||||
\(366\) | 1291.51i | 0.184450i | ||||||||
\(367\) | −3888.26 | −0.553039 | −0.276520 | − | 0.961008i | \(-0.589181\pi\) | ||||
−0.276520 | + | 0.961008i | \(0.589181\pi\) | |||||||
\(368\) | 15189.8 | 2.15170 | ||||||||
\(369\) | 874.642i | 0.123393i | ||||||||
\(370\) | 12818.3i | 1.80106i | ||||||||
\(371\) | 5282.39i | 0.739213i | ||||||||
\(372\) | − 33.6937i | − 0.00469607i | ||||||||
\(373\) | 9960.88 | 1.38272 | 0.691361 | − | 0.722510i | \(-0.257012\pi\) | ||||
0.691361 | + | 0.722510i | \(0.257012\pi\) | |||||||
\(374\) | 12677.3 | 1.75275 | ||||||||
\(375\) | − 146.680i | − 0.0201987i | ||||||||
\(376\) | 8956.57 | 1.22846 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 1565.55 | 0.213025 | ||||||||
\(379\) | − 5288.25i | − 0.716726i | −0.933582 | − | 0.358363i | \(-0.883335\pi\) | ||||
0.933582 | − | 0.358363i | \(-0.116665\pi\) | |||||||
\(380\) | −4961.73 | −0.669820 | ||||||||
\(381\) | 7114.08 | 0.956602 | ||||||||
\(382\) | − 1575.39i | − 0.211005i | ||||||||
\(383\) | − 688.944i | − 0.0919149i | −0.998943 | − | 0.0459575i | \(-0.985366\pi\) | ||||
0.998943 | − | 0.0459575i | \(-0.0146339\pi\) | |||||||
\(384\) | − 4975.17i | − 0.661166i | ||||||||
\(385\) | 14248.2i | 1.88612i | ||||||||
\(386\) | 8906.14 | 1.17438 | ||||||||
\(387\) | −3385.36 | −0.444671 | ||||||||
\(388\) | − 2658.98i | − 0.347910i | ||||||||
\(389\) | −2102.57 | −0.274048 | −0.137024 | − | 0.990568i | \(-0.543754\pi\) | ||||
−0.137024 | + | 0.990568i | \(0.543754\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13553.0 | −1.75296 | ||||||||
\(392\) | − 748.593i | − 0.0964533i | ||||||||
\(393\) | −507.599 | −0.0651527 | ||||||||
\(394\) | −12418.3 | −1.58788 | ||||||||
\(395\) | − 8740.09i | − 1.11332i | ||||||||
\(396\) | − 1619.47i | − 0.205509i | ||||||||
\(397\) | − 11254.8i | − 1.42283i | −0.702774 | − | 0.711413i | \(-0.748056\pi\) | ||||
0.702774 | − | 0.711413i | \(-0.251944\pi\) | |||||||
\(398\) | 744.906i | 0.0938159i | ||||||||
\(399\) | 4774.02 | 0.598998 | ||||||||
\(400\) | 9708.17 | 1.21352 | ||||||||
\(401\) | − 3523.22i | − 0.438756i | −0.975640 | − | 0.219378i | \(-0.929597\pi\) | ||||
0.975640 | − | 0.219378i | \(-0.0704028\pi\) | |||||||
\(402\) | −9155.07 | −1.13585 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −6158.31 | −0.758384 | ||||||||
\(405\) | 1272.73i | 0.156154i | ||||||||
\(406\) | 7433.71 | 0.908692 | ||||||||
\(407\) | −12758.2 | −1.55381 | ||||||||
\(408\) | 3307.34i | 0.401318i | ||||||||
\(409\) | 6366.65i | 0.769708i | 0.922978 | + | 0.384854i | \(0.125748\pi\) | ||||
−0.922978 | + | 0.384854i | \(0.874252\pi\) | |||||||
\(410\) | 5157.26i | 0.621217i | ||||||||
\(411\) | − 8928.62i | − 1.07157i | ||||||||
\(412\) | 5317.20 | 0.635824 | ||||||||
\(413\) | 6007.37 | 0.715746 | ||||||||
\(414\) | 5796.98i | 0.688179i | ||||||||
\(415\) | −4001.45 | −0.473310 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7665.44 | 0.900187 | ||||||||
\(418\) | − 16535.2i | − 1.93484i | ||||||||
\(419\) | 8919.77 | 1.04000 | 0.519999 | − | 0.854167i | \(-0.325932\pi\) | ||||
0.519999 | + | 0.854167i | \(0.325932\pi\) | |||||||
\(420\) | 2757.00 | 0.320305 | ||||||||
\(421\) | 1090.71i | 0.126266i | 0.998005 | + | 0.0631328i | \(0.0201092\pi\) | ||||
−0.998005 | + | 0.0631328i | \(0.979891\pi\) | |||||||
\(422\) | − 4680.82i | − 0.539949i | ||||||||
\(423\) | 5196.19i | 0.597275i | ||||||||
\(424\) | 4773.17i | 0.546712i | ||||||||
\(425\) | −8662.05 | −0.988638 | ||||||||
\(426\) | 8370.25 | 0.951971 | ||||||||
\(427\) | − 2188.36i | − 0.248015i | ||||||||
\(428\) | −1097.89 | −0.123991 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −19961.5 | −2.23868 | ||||||||
\(431\) | 3760.43i | 0.420263i | 0.977673 | + | 0.210132i | \(0.0673892\pi\) | ||||
−0.977673 | + | 0.210132i | \(0.932611\pi\) | |||||||
\(432\) | 2150.50 | 0.239504 | ||||||||
\(433\) | 4085.06 | 0.453384 | 0.226692 | − | 0.973967i | \(-0.427209\pi\) | ||||
0.226692 | + | 0.973967i | \(0.427209\pi\) | |||||||
\(434\) | 191.157i | 0.0211424i | ||||||||
\(435\) | 6043.28i | 0.666099i | ||||||||
\(436\) | 5477.15i | 0.601623i | ||||||||
\(437\) | 17677.4i | 1.93507i | ||||||||
\(438\) | 1335.02 | 0.145638 | ||||||||
\(439\) | −9385.35 | −1.02036 | −0.510180 | − | 0.860068i | \(-0.670421\pi\) | ||||
−0.510180 | + | 0.860068i | \(0.670421\pi\) | |||||||
\(440\) | 12874.7i | 1.39495i | ||||||||
\(441\) | 434.299 | 0.0468955 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5755.41 | 0.617264 | 0.308632 | − | 0.951182i | \(-0.400129\pi\) | ||||
0.308632 | + | 0.951182i | \(0.400129\pi\) | |||||||
\(444\) | 2468.68i | 0.263870i | ||||||||
\(445\) | −2881.87 | −0.306997 | ||||||||
\(446\) | 377.751 | 0.0401055 | ||||||||
\(447\) | 1273.59i | 0.134762i | ||||||||
\(448\) | 2537.60i | 0.267612i | ||||||||
\(449\) | 1104.67i | 0.116108i | 0.998313 | + | 0.0580541i | \(0.0184896\pi\) | ||||
−0.998313 | + | 0.0580541i | \(0.981510\pi\) | |||||||
\(450\) | 3704.98i | 0.388121i | ||||||||
\(451\) | −5133.05 | −0.535934 | ||||||||
\(452\) | 1464.59 | 0.152408 | ||||||||
\(453\) | − 126.969i | − 0.0131690i | ||||||||
\(454\) | −16856.4 | −1.74254 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4313.81 | 0.443011 | ||||||||
\(457\) | 13548.5i | 1.38681i | 0.720548 | + | 0.693405i | \(0.243890\pi\) | ||||
−0.720548 | + | 0.693405i | \(0.756110\pi\) | |||||||
\(458\) | −19546.9 | −1.99425 | ||||||||
\(459\) | −1918.77 | −0.195121 | ||||||||
\(460\) | 10208.7i | 1.03475i | ||||||||
\(461\) | − 2996.03i | − 0.302688i | −0.988481 | − | 0.151344i | \(-0.951640\pi\) | ||||
0.988481 | − | 0.151344i | \(-0.0483601\pi\) | |||||||
\(462\) | 9187.84i | 0.925232i | ||||||||
\(463\) | − 2026.10i | − 0.203371i | −0.994817 | − | 0.101686i | \(-0.967576\pi\) | ||||
0.994817 | − | 0.101686i | \(-0.0324236\pi\) | |||||||
\(464\) | 10211.2 | 1.02164 | ||||||||
\(465\) | −155.402 | −0.0154981 | ||||||||
\(466\) | − 2444.24i | − 0.242977i | ||||||||
\(467\) | 3284.20 | 0.325428 | 0.162714 | − | 0.986673i | \(-0.447975\pi\) | ||||
0.162714 | + | 0.986673i | \(0.447975\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 15512.5 | 1.52729 | ||||||||
\(470\) | 30638.9i | 3.00696i | ||||||||
\(471\) | 2970.56 | 0.290608 | ||||||||
\(472\) | 5428.26 | 0.529356 | ||||||||
\(473\) | − 19867.8i | − 1.93134i | ||||||||
\(474\) | − 5635.96i | − 0.546136i | ||||||||
\(475\) | 11298.0i | 1.09134i | ||||||||
\(476\) | 4156.46i | 0.400234i | ||||||||
\(477\) | −2769.17 | −0.265811 | ||||||||
\(478\) | 4187.08 | 0.400654 | ||||||||
\(479\) | 13208.5i | 1.25994i | 0.776621 | + | 0.629969i | \(0.216932\pi\) | ||||
−0.776621 | + | 0.629969i | \(0.783068\pi\) | |||||||
\(480\) | 6830.19 | 0.649488 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −2551.26 | −0.241092 | ||||||||
\(483\) | − 9822.50i | − 0.925340i | ||||||||
\(484\) | 4969.86 | 0.466741 | ||||||||
\(485\) | −12263.7 | −1.14818 | ||||||||
\(486\) | 820.706i | 0.0766008i | ||||||||
\(487\) | − 8974.09i | − 0.835020i | −0.908672 | − | 0.417510i | \(-0.862903\pi\) | ||||
0.908672 | − | 0.417510i | \(-0.137097\pi\) | |||||||
\(488\) | − 1977.41i | − 0.183428i | ||||||||
\(489\) | − 7937.46i | − 0.734037i | ||||||||
\(490\) | 2560.81 | 0.236093 | ||||||||
\(491\) | 12889.8 | 1.18474 | 0.592370 | − | 0.805666i | \(-0.298192\pi\) | ||||
0.592370 | + | 0.805666i | \(0.298192\pi\) | |||||||
\(492\) | 993.234i | 0.0910131i | ||||||||
\(493\) | −9110.87 | −0.832319 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7469.32 | −0.678224 | ||||||||
\(496\) | 262.579i | 0.0237705i | ||||||||
\(497\) | −14182.7 | −1.28004 | ||||||||
\(498\) | −2580.30 | −0.232181 | ||||||||
\(499\) | − 7371.92i | − 0.661348i | −0.943745 | − | 0.330674i | \(-0.892724\pi\) | ||||
0.943745 | − | 0.330674i | \(-0.107276\pi\) | |||||||
\(500\) | − 166.568i | − 0.0148983i | ||||||||
\(501\) | − 886.284i | − 0.0790344i | ||||||||
\(502\) | 7606.09i | 0.676248i | ||||||||
\(503\) | 19788.2 | 1.75410 | 0.877049 | − | 0.480400i | \(-0.159509\pi\) | ||||
0.877049 | + | 0.480400i | \(0.159509\pi\) | |||||||
\(504\) | −2396.98 | −0.211845 | ||||||||
\(505\) | 28403.3i | 2.50283i | ||||||||
\(506\) | −34021.0 | −2.98897 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 8078.67 | 0.705577 | ||||||||
\(509\) | − 11682.4i | − 1.01732i | −0.860968 | − | 0.508658i | \(-0.830142\pi\) | ||||
0.860968 | − | 0.508658i | \(-0.169858\pi\) | |||||||
\(510\) | −11313.9 | −0.982327 | ||||||||
\(511\) | −2262.08 | −0.195829 | ||||||||
\(512\) | − 1656.08i | − 0.142948i | ||||||||
\(513\) | 2502.67i | 0.215391i | ||||||||
\(514\) | 12552.9i | 1.07721i | ||||||||
\(515\) | − 24524.0i | − 2.09836i | ||||||||
\(516\) | −3844.38 | −0.327984 | ||||||||
\(517\) | −30495.1 | −2.59415 | ||||||||
\(518\) | − 14005.7i | − 1.18798i | ||||||||
\(519\) | 4486.38 | 0.379442 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −19025.1 | −1.59982 | −0.799908 | − | 0.600122i | \(-0.795119\pi\) | ||||
−0.799908 | + | 0.600122i | \(0.795119\pi\) | |||||||
\(522\) | 3896.95i | 0.326753i | ||||||||
\(523\) | 5345.69 | 0.446942 | 0.223471 | − | 0.974711i | \(-0.428261\pi\) | ||||
0.223471 | + | 0.974711i | \(0.428261\pi\) | |||||||
\(524\) | −576.425 | −0.0480558 | ||||||||
\(525\) | − 6277.78i | − 0.521876i | ||||||||
\(526\) | 168.708i | 0.0139848i | ||||||||
\(527\) | − 234.284i | − 0.0193655i | ||||||||
\(528\) | 12620.7i | 1.04024i | ||||||||
\(529\) | 24204.0 | 1.98932 | ||||||||
\(530\) | −16328.2 | −1.33821 | ||||||||
\(531\) | 3149.23i | 0.257372i | ||||||||
\(532\) | 5421.33 | 0.441813 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −1858.34 | −0.150596 | ||||||||
\(535\) | 5063.66i | 0.409199i | ||||||||
\(536\) | 14017.1 | 1.12957 | ||||||||
\(537\) | 2355.29 | 0.189271 | ||||||||
\(538\) | − 11555.5i | − 0.926012i | ||||||||
\(539\) | 2548.79i | 0.203681i | ||||||||
\(540\) | 1445.30i | 0.115177i | ||||||||
\(541\) | − 3058.01i | − 0.243021i | −0.992590 | − | 0.121510i | \(-0.961226\pi\) | ||||
0.992590 | − | 0.121510i | \(-0.0387737\pi\) | |||||||
\(542\) | −9993.34 | −0.791975 | ||||||||
\(543\) | −3861.02 | −0.305142 | ||||||||
\(544\) | 10297.2i | 0.811561i | ||||||||
\(545\) | 25261.7 | 1.98549 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17921.1 | 1.40082 | 0.700410 | − | 0.713740i | \(-0.253000\pi\) | ||||
0.700410 | + | 0.713740i | \(0.253000\pi\) | |||||||
\(548\) | − 10139.2i | − 0.790378i | ||||||||
\(549\) | 1147.20 | 0.0891827 | ||||||||
\(550\) | −21743.6 | −1.68573 | ||||||||
\(551\) | 11883.4i | 0.918786i | ||||||||
\(552\) | − 8875.62i | − 0.684369i | ||||||||
\(553\) | 9549.67i | 0.734346i | ||||||||
\(554\) | − 25199.0i | − 1.93250i | ||||||||
\(555\) | 11386.0 | 0.870828 | ||||||||
\(556\) | 8704.79 | 0.663967 | ||||||||
\(557\) | 9106.04i | 0.692702i | 0.938105 | + | 0.346351i | \(0.112579\pi\) | ||||
−0.938105 | + | 0.346351i | \(0.887421\pi\) | |||||||
\(558\) | −100.209 | −0.00760252 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −21485.6 | −1.62131 | ||||||||
\(561\) | − 11260.8i | − 0.847468i | ||||||||
\(562\) | −15968.4 | −1.19856 | ||||||||
\(563\) | −11327.9 | −0.847985 | −0.423992 | − | 0.905666i | \(-0.639372\pi\) | ||||
−0.423992 | + | 0.905666i | \(0.639372\pi\) | |||||||
\(564\) | 5900.74i | 0.440542i | ||||||||
\(565\) | − 6754.97i | − 0.502980i | ||||||||
\(566\) | − 9725.84i | − 0.722275i | ||||||||
\(567\) | − 1390.62i | − 0.102999i | ||||||||
\(568\) | −12815.5 | −0.946701 | ||||||||
\(569\) | −1963.27 | −0.144647 | −0.0723237 | − | 0.997381i | \(-0.523041\pi\) | ||||
−0.0723237 | + | 0.997381i | \(0.523041\pi\) | |||||||
\(570\) | 14756.8i | 1.08438i | ||||||||
\(571\) | 2270.35 | 0.166394 | 0.0831971 | − | 0.996533i | \(-0.473487\pi\) | ||||
0.0831971 | + | 0.996533i | \(0.473487\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1399.36 | −0.102023 | ||||||||
\(574\) | − 5634.97i | − 0.409755i | ||||||||
\(575\) | 23245.6 | 1.68592 | ||||||||
\(576\) | −1330.28 | −0.0962297 | ||||||||
\(577\) | 13949.6i | 1.00646i | 0.864152 | + | 0.503231i | \(0.167855\pi\) | ||||
−0.864152 | + | 0.503231i | \(0.832145\pi\) | |||||||
\(578\) | − 463.708i | − 0.0333697i | ||||||||
\(579\) | − 7910.96i | − 0.567821i | ||||||||
\(580\) | 6862.69i | 0.491306i | ||||||||
\(581\) | 4372.10 | 0.312195 | ||||||||
\(582\) | −7908.14 | −0.563236 | ||||||||
\(583\) | − 16251.6i | − 1.15450i | ||||||||
\(584\) | −2044.02 | −0.144832 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 27697.8 | 1.95253 | ||||||||
\(587\) | 26731.4i | 1.87960i | 0.341727 | + | 0.939799i | \(0.388988\pi\) | ||||
−0.341727 | + | 0.939799i | \(0.611012\pi\) | |||||||
\(588\) | 493.186 | 0.0345895 | ||||||||
\(589\) | −305.580 | −0.0213773 | ||||||||
\(590\) | 18569.2i | 1.29573i | ||||||||
\(591\) | 11030.7i | 0.767754i | ||||||||
\(592\) | − 19238.7i | − 1.33565i | ||||||||
\(593\) | 10508.6i | 0.727715i | 0.931455 | + | 0.363858i | \(0.118541\pi\) | ||||
−0.931455 | + | 0.363858i | \(0.881459\pi\) | |||||||
\(594\) | −4816.52 | −0.332701 | ||||||||
\(595\) | 19170.4 | 1.32086 | ||||||||
\(596\) | 1446.27i | 0.0993987i | ||||||||
\(597\) | 661.670 | 0.0453607 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1935.87 | −0.132049 | −0.0660246 | − | 0.997818i | \(-0.521032\pi\) | ||||
−0.0660246 | + | 0.997818i | \(0.521032\pi\) | |||||||
\(600\) | − 5672.61i | − 0.385972i | ||||||||
\(601\) | −16155.5 | −1.09650 | −0.548249 | − | 0.836315i | \(-0.684705\pi\) | ||||
−0.548249 | + | 0.836315i | \(0.684705\pi\) | |||||||
\(602\) | 21810.6 | 1.47663 | ||||||||
\(603\) | 8132.08i | 0.549194i | ||||||||
\(604\) | − 144.185i | − 0.00971327i | ||||||||
\(605\) | − 22922.0i | − 1.54035i | ||||||||
\(606\) | 18315.6i | 1.22776i | ||||||||
\(607\) | −1698.75 | −0.113592 | −0.0567959 | − | 0.998386i | \(-0.518088\pi\) | ||||
−0.0567959 | + | 0.998386i | \(0.518088\pi\) | |||||||
\(608\) | 13430.8 | 0.895873 | ||||||||
\(609\) | − 6603.07i | − 0.439359i | ||||||||
\(610\) | 6764.38 | 0.448987 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −2178.93 | −0.143918 | ||||||||
\(613\) | 8627.42i | 0.568448i | 0.958758 | + | 0.284224i | \(0.0917359\pi\) | ||||
−0.958758 | + | 0.284224i | \(0.908264\pi\) | |||||||
\(614\) | 6953.46 | 0.457034 | ||||||||
\(615\) | 4580.99 | 0.300363 | ||||||||
\(616\) | − 14067.3i | − 0.920109i | ||||||||
\(617\) | 21415.4i | 1.39733i | 0.715450 | + | 0.698664i | \(0.246222\pi\) | ||||
−0.715450 | + | 0.698664i | \(0.753778\pi\) | |||||||
\(618\) | − 15814.0i | − 1.02934i | ||||||||
\(619\) | − 17396.0i | − 1.12957i | −0.825238 | − | 0.564784i | \(-0.808959\pi\) | ||||
0.825238 | − | 0.564784i | \(-0.191041\pi\) | |||||||
\(620\) | −176.473 | −0.0114312 | ||||||||
\(621\) | 5149.22 | 0.332739 | ||||||||
\(622\) | 6288.96i | 0.405409i | ||||||||
\(623\) | 3148.81 | 0.202495 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16004.3 | −1.02427 | ||||||||
\(626\) | 864.261i | 0.0551802i | ||||||||
\(627\) | −14687.6 | −0.935510 | ||||||||
\(628\) | 3373.34 | 0.214349 | ||||||||
\(629\) | 17165.6i | 1.08814i | ||||||||
\(630\) | − 8199.68i | − 0.518545i | ||||||||
\(631\) | − 13059.2i | − 0.823898i | −0.911207 | − | 0.411949i | \(-0.864848\pi\) | ||||
0.911207 | − | 0.411949i | \(-0.135152\pi\) | |||||||
\(632\) | 8629.09i | 0.543112i | ||||||||
\(633\) | −4157.78 | −0.261070 | ||||||||
\(634\) | −21161.6 | −1.32561 | ||||||||
\(635\) | − 37260.4i | − 2.32856i | ||||||||
\(636\) | −3144.65 | −0.196059 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −22870.2 | −1.41919 | ||||||||
\(639\) | − 7434.95i | − 0.460285i | ||||||||
\(640\) | −26057.7 | −1.60941 | ||||||||
\(641\) | −22397.7 | −1.38012 | −0.690060 | − | 0.723752i | \(-0.742416\pi\) | ||||
−0.690060 | + | 0.723752i | \(0.742416\pi\) | |||||||
\(642\) | 3265.26i | 0.200731i | ||||||||
\(643\) | − 5878.08i | − 0.360511i | −0.983620 | − | 0.180256i | \(-0.942307\pi\) | ||||
0.983620 | − | 0.180256i | \(-0.0576925\pi\) | |||||||
\(644\) | − 11154.3i | − 0.682519i | ||||||||
\(645\) | 17731.0i | 1.08242i | ||||||||
\(646\) | −22247.5 | −1.35498 | ||||||||
\(647\) | 20768.3 | 1.26196 | 0.630979 | − | 0.775800i | \(-0.282653\pi\) | ||||
0.630979 | + | 0.775800i | \(0.282653\pi\) | |||||||
\(648\) | − 1256.56i | − 0.0761767i | ||||||||
\(649\) | −18482.0 | −1.11785 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 169.797 | 0.0102225 | ||||||||
\(652\) | − 9013.69i | − 0.541416i | ||||||||
\(653\) | 15516.4 | 0.929865 | 0.464933 | − | 0.885346i | \(-0.346079\pi\) | ||||
0.464933 | + | 0.885346i | \(0.346079\pi\) | |||||||
\(654\) | 16289.7 | 0.973975 | ||||||||
\(655\) | 2658.58i | 0.158594i | ||||||||
\(656\) | − 7740.39i | − 0.460688i | ||||||||
\(657\) | − 1185.84i | − 0.0704172i | ||||||||
\(658\) | − 33477.0i | − 1.98339i | ||||||||
\(659\) | 24025.0 | 1.42015 | 0.710077 | − | 0.704124i | \(-0.248660\pi\) | ||||
0.710077 | + | 0.704124i | \(0.248660\pi\) | |||||||
\(660\) | −8482.08 | −0.500249 | ||||||||
\(661\) | − 10778.8i | − 0.634262i | −0.948382 | − | 0.317131i | \(-0.897281\pi\) | ||||
0.948382 | − | 0.317131i | \(-0.102719\pi\) | |||||||
\(662\) | −3620.33 | −0.212550 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3950.63 | 0.230895 | ||||||||
\(665\) | − 25004.2i | − 1.45808i | ||||||||
\(666\) | 7342.17 | 0.427182 | ||||||||
\(667\) | 24450.0 | 1.41935 | ||||||||
\(668\) | − 1006.45i | − 0.0582948i | ||||||||
\(669\) | − 335.541i | − 0.0193913i | ||||||||
\(670\) | 47950.2i | 2.76489i | ||||||||
\(671\) | 6732.63i | 0.387348i | ||||||||
\(672\) | −7462.86 | −0.428402 | ||||||||
\(673\) | −22345.9 | −1.27990 | −0.639950 | − | 0.768417i | \(-0.721045\pi\) | ||||
−0.639950 | + | 0.768417i | \(0.721045\pi\) | |||||||
\(674\) | − 18818.9i | − 1.07549i | ||||||||
\(675\) | 3290.98 | 0.187659 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12326.7 | 0.699782 | 0.349891 | − | 0.936790i | \(-0.386219\pi\) | ||||
0.349891 | + | 0.936790i | \(0.386219\pi\) | |||||||
\(678\) | − 4355.88i | − 0.246735i | ||||||||
\(679\) | 13399.7 | 0.757339 | ||||||||
\(680\) | 17322.4 | 0.976888 | ||||||||
\(681\) | 14972.9i | 0.842529i | ||||||||
\(682\) | − 588.104i | − 0.0330201i | ||||||||
\(683\) | − 27452.5i | − 1.53798i | −0.639262 | − | 0.768989i | \(-0.720760\pi\) | ||||
0.639262 | − | 0.768989i | \(-0.279240\pi\) | |||||||
\(684\) | 2842.01i | 0.158870i | ||||||||
\(685\) | −46764.2 | −2.60842 | ||||||||
\(686\) | −22686.3 | −1.26264 | ||||||||
\(687\) | 17362.7i | 0.964232i | ||||||||
\(688\) | 29959.7 | 1.66018 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 30362.0 | 1.67516 | ||||||||
\(691\) | 18663.6i | 1.02749i | 0.857942 | + | 0.513746i | \(0.171743\pi\) | ||||
−0.857942 | + | 0.513746i | \(0.828257\pi\) | |||||||
\(692\) | 5094.69 | 0.279871 | ||||||||
\(693\) | 8161.19 | 0.447356 | ||||||||
\(694\) | 6428.65i | 0.351626i | ||||||||
\(695\) | − 40148.2i | − 2.19123i | ||||||||
\(696\) | − 5966.54i | − 0.324944i | ||||||||
\(697\) | 6906.31i | 0.375316i | ||||||||
\(698\) | 3705.59 | 0.200943 | ||||||||
\(699\) | −2171.12 | −0.117481 | ||||||||
\(700\) | − 7128.98i | − 0.384929i | ||||||||
\(701\) | 4131.00 | 0.222576 | 0.111288 | − | 0.993788i | \(-0.464502\pi\) | ||||
0.111288 | + | 0.993788i | \(0.464502\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 22389.3 | 1.20118 | ||||||||
\(704\) | − 7807.07i | − 0.417955i | ||||||||
\(705\) | 27215.3 | 1.45389 | ||||||||
\(706\) | −18308.5 | −0.975990 | ||||||||
\(707\) | − 31034.3i | − 1.65087i | ||||||||
\(708\) | 3576.23i | 0.189835i | ||||||||
\(709\) | 33578.1i | 1.77863i | 0.457291 | + | 0.889317i | \(0.348820\pi\) | ||||
−0.457291 | + | 0.889317i | \(0.651180\pi\) | |||||||
\(710\) | − 43839.7i | − 2.31729i | ||||||||
\(711\) | −5006.20 | −0.264061 | ||||||||
\(712\) | 2845.27 | 0.149762 | ||||||||
\(713\) | 628.728i | 0.0330239i | ||||||||
\(714\) | 12361.9 | 0.647943 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2674.64 | 0.139603 | ||||||||
\(717\) | − 3719.21i | − 0.193719i | ||||||||
\(718\) | 13122.5 | 0.682073 | ||||||||
\(719\) | −22527.2 | −1.16846 | −0.584229 | − | 0.811589i | \(-0.698603\pi\) | ||||
−0.584229 | + | 0.811589i | \(0.698603\pi\) | |||||||
\(720\) | − 11263.4i | − 0.583001i | ||||||||
\(721\) | 26795.6i | 1.38408i | ||||||||
\(722\) | 5852.12i | 0.301653i | ||||||||
\(723\) | 2266.18i | 0.116570i | ||||||||
\(724\) | −4384.53 | −0.225069 | ||||||||
\(725\) | 15626.6 | 0.800491 | ||||||||
\(726\) | − 14781.0i | − 0.755613i | ||||||||
\(727\) | −241.718 | −0.0123312 | −0.00616562 | − | 0.999981i | \(-0.501963\pi\) | ||||
−0.00616562 | + | 0.999981i | \(0.501963\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | − 6992.24i | − 0.354513i | ||||||||
\(731\) | −26731.4 | −1.35252 | ||||||||
\(732\) | 1302.75 | 0.0657800 | ||||||||
\(733\) | 17235.4i | 0.868490i | 0.900795 | + | 0.434245i | \(0.142985\pi\) | ||||
−0.900795 | + | 0.434245i | \(0.857015\pi\) | |||||||
\(734\) | 13132.2i | 0.660377i | ||||||||
\(735\) | − 2274.67i | − 0.114153i | ||||||||
\(736\) | − 27633.7i | − 1.38396i | ||||||||
\(737\) | −47725.1 | −2.38532 | ||||||||
\(738\) | 2954.01 | 0.147342 | ||||||||
\(739\) | − 34304.3i | − 1.70758i | −0.520615 | − | 0.853792i | \(-0.674297\pi\) | ||||
0.520615 | − | 0.853792i | \(-0.325703\pi\) | |||||||
\(740\) | 12929.8 | 0.642312 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 17840.7 | 0.882686 | ||||||||
\(743\) | − 2114.59i | − 0.104410i | −0.998636 | − | 0.0522052i | \(-0.983375\pi\) | ||||
0.998636 | − | 0.0522052i | \(-0.0166250\pi\) | |||||||
\(744\) | 153.428 | 0.00756043 | ||||||||
\(745\) | 6670.49 | 0.328037 | ||||||||
\(746\) | − 33641.8i | − 1.65109i | ||||||||
\(747\) | 2291.97i | 0.112261i | ||||||||
\(748\) | − 12787.6i | − 0.625082i | ||||||||
\(749\) | − 5532.70i | − 0.269907i | ||||||||
\(750\) | −495.394 | −0.0241190 | ||||||||
\(751\) | 40958.7 | 1.99015 | 0.995077 | − | 0.0991024i | \(-0.0315971\pi\) | ||||
0.995077 | + | 0.0991024i | \(0.0315971\pi\) | |||||||
\(752\) | − 45985.1i | − 2.22993i | ||||||||
\(753\) | 6756.18 | 0.326971 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −665.010 | −0.0320559 | ||||||||
\(756\) | − 1579.17i | − 0.0759708i | ||||||||
\(757\) | 10530.8 | 0.505613 | 0.252807 | − | 0.967517i | \(-0.418646\pi\) | ||||
0.252807 | + | 0.967517i | \(0.418646\pi\) | |||||||
\(758\) | −17860.5 | −0.855834 | ||||||||
\(759\) | 30219.5i | 1.44519i | ||||||||
\(760\) | − 22593.9i | − 1.07838i | ||||||||
\(761\) | − 787.955i | − 0.0375340i | −0.999824 | − | 0.0187670i | \(-0.994026\pi\) | ||||
0.999824 | − | 0.0187670i | \(-0.00597407\pi\) | |||||||
\(762\) | − 24027.0i | − 1.14227i | ||||||||
\(763\) | −27601.6 | −1.30963 | ||||||||
\(764\) | −1589.10 | −0.0752506 | ||||||||
\(765\) | 10049.7i | 0.474962i | ||||||||
\(766\) | −2326.83 | −0.109755 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −13255.7 | −0.622816 | ||||||||
\(769\) | − 5227.62i | − 0.245140i | −0.992460 | − | 0.122570i | \(-0.960886\pi\) | ||||
0.992460 | − | 0.122570i | \(-0.0391136\pi\) | |||||||
\(770\) | 48121.9 | 2.25220 | ||||||||
\(771\) | 11150.2 | 0.520838 | ||||||||
\(772\) | − 8983.61i | − 0.418818i | ||||||||
\(773\) | − 4516.79i | − 0.210165i | −0.994464 | − | 0.105082i | \(-0.966489\pi\) | ||||
0.994464 | − | 0.105082i | \(-0.0335107\pi\) | |||||||
\(774\) | 11433.7i | 0.530976i | ||||||||
\(775\) | 401.834i | 0.0186249i | ||||||||
\(776\) | 12108.0 | 0.560117 | ||||||||
\(777\) | −12440.7 | −0.574398 | ||||||||
\(778\) | 7101.21i | 0.327237i | ||||||||
\(779\) | 9008.00 | 0.414307 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 43633.9 | 1.99916 | ||||||||
\(782\) | 45773.9i | 2.09318i | ||||||||
\(783\) | 3461.51 | 0.157987 | ||||||||
\(784\) | −3843.45 | −0.175084 | ||||||||
\(785\) | − 15558.5i | − 0.707397i | ||||||||
\(786\) | 1714.36i | 0.0777980i | ||||||||
\(787\) | 6800.09i | 0.308001i | 0.988071 | + | 0.154001i | \(0.0492158\pi\) | ||||
−0.988071 | + | 0.154001i | \(0.950784\pi\) | |||||||
\(788\) | 12526.4i | 0.566285i | ||||||||
\(789\) | 149.856 | 0.00676176 | ||||||||
\(790\) | −29518.7 | −1.32940 | ||||||||
\(791\) | 7380.67i | 0.331765i | ||||||||
\(792\) | 7374.46 | 0.330859 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −38011.8 | −1.69898 | ||||||||
\(795\) | 14503.7i | 0.647036i | ||||||||
\(796\) | 751.385 | 0.0334575 | ||||||||
\(797\) | 40553.3 | 1.80235 | 0.901174 | − | 0.433457i | \(-0.142707\pi\) | ||||
0.901174 | + | 0.433457i | \(0.142707\pi\) | |||||||
\(798\) | − 16123.7i | − 0.715256i | ||||||||
\(799\) | 41029.9i | 1.81669i | ||||||||
\(800\) | − 17661.3i | − 0.780528i | ||||||||
\(801\) | 1650.69i | 0.0728144i | ||||||||
\(802\) | −11899.3 | −0.523913 | ||||||||
\(803\) | 6959.41 | 0.305844 | ||||||||
\(804\) | 9234.70i | 0.405078i | ||||||||
\(805\) | −51445.9 | −2.25246 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −10264.3 | −0.447733 | ||||||||
\(808\) | − 28042.6i | − 1.22096i | ||||||||
\(809\) | −6517.83 | −0.283257 | −0.141628 | − | 0.989920i | \(-0.545234\pi\) | ||||
−0.141628 | + | 0.989920i | \(0.545234\pi\) | |||||||
\(810\) | 4298.50 | 0.186461 | ||||||||
\(811\) | − 2898.99i | − 0.125521i | −0.998029 | − | 0.0627603i | \(-0.980010\pi\) | ||||
0.998029 | − | 0.0627603i | \(-0.0199903\pi\) | |||||||
\(812\) | − 7498.37i | − 0.324066i | ||||||||
\(813\) | 8876.68i | 0.382926i | ||||||||
\(814\) | 43089.3i | 1.85538i | ||||||||
\(815\) | −41572.9 | −1.78679 | ||||||||
\(816\) | 16980.7 | 0.728484 | ||||||||
\(817\) | 34866.1i | 1.49303i | ||||||||
\(818\) | 21502.7 | 0.919099 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5202.12 | 0.221544 | ||||||||
\(821\) | − 716.621i | − 0.0304632i | −0.999884 | − | 0.0152316i | \(-0.995151\pi\) | ||||
0.999884 | − | 0.0152316i | \(-0.00484855\pi\) | |||||||
\(822\) | −30155.4 | −1.27955 | ||||||||
\(823\) | −15510.0 | −0.656920 | −0.328460 | − | 0.944518i | \(-0.606530\pi\) | ||||
−0.328460 | + | 0.944518i | \(0.606530\pi\) | |||||||
\(824\) | 24212.5i | 1.02364i | ||||||||
\(825\) | 19314.0i | 0.815062i | ||||||||
\(826\) | − 20289.2i | − 0.854664i | ||||||||
\(827\) | − 24063.2i | − 1.01180i | −0.862591 | − | 0.505901i | \(-0.831160\pi\) | ||||
0.862591 | − | 0.505901i | \(-0.168840\pi\) | |||||||
\(828\) | 5847.40 | 0.245424 | ||||||||
\(829\) | −10037.8 | −0.420540 | −0.210270 | − | 0.977643i | \(-0.567434\pi\) | ||||
−0.210270 | + | 0.977643i | \(0.567434\pi\) | |||||||
\(830\) | 13514.5i | 0.565173i | ||||||||
\(831\) | −22383.2 | −0.934376 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3429.30 | 0.142639 | ||||||||
\(834\) | − 25889.2i | − 1.07490i | ||||||||
\(835\) | −4641.96 | −0.192385 | ||||||||
\(836\) | −16679.0 | −0.690020 | ||||||||
\(837\) | 89.0121i | 0.00367587i | ||||||||
\(838\) | − 30125.6i | − 1.24185i | ||||||||
\(839\) | − 4005.19i | − 0.164809i | −0.996599 | − | 0.0824044i | \(-0.973740\pi\) | ||||
0.996599 | − | 0.0824044i | \(-0.0262599\pi\) | |||||||
\(840\) | 12554.3i | 0.515674i | ||||||||
\(841\) | −7952.74 | −0.326079 | ||||||||
\(842\) | 3683.74 | 0.150772 | ||||||||
\(843\) | 14184.1i | 0.579510i | ||||||||
\(844\) | −4721.53 | −0.192562 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 17549.6 | 0.713199 | ||||||||
\(847\) | 25045.2i | 1.01601i | ||||||||
\(848\) | 24506.6 | 0.992406 | ||||||||
\(849\) | −8639.08 | −0.349225 | ||||||||
\(850\) | 29255.1i | 1.18052i | ||||||||
\(851\) | − 46065.8i | − 1.85560i | ||||||||
\(852\) | − 8443.06i | − 0.339500i | ||||||||
\(853\) | 44062.6i | 1.76867i | 0.466856 | + | 0.884334i | \(0.345387\pi\) | ||||
−0.466856 | + | 0.884334i | \(0.654613\pi\) | |||||||
\(854\) | −7390.96 | −0.296152 | ||||||||
\(855\) | 13107.9 | 0.524305 | ||||||||
\(856\) | − 4999.36i | − 0.199620i | ||||||||
\(857\) | −3365.44 | −0.134144 | −0.0670718 | − | 0.997748i | \(-0.521366\pi\) | ||||
−0.0670718 | + | 0.997748i | \(0.521366\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −40969.3 | −1.62731 | −0.813653 | − | 0.581351i | \(-0.802524\pi\) | ||||
−0.813653 | + | 0.581351i | \(0.802524\pi\) | |||||||
\(860\) | 20135.2i | 0.798377i | ||||||||
\(861\) | −5005.32 | −0.198119 | ||||||||
\(862\) | 12700.4 | 0.501831 | ||||||||
\(863\) | 18132.8i | 0.715236i | 0.933868 | + | 0.357618i | \(0.116411\pi\) | ||||
−0.933868 | + | 0.357618i | \(0.883589\pi\) | |||||||
\(864\) | − 3912.24i | − 0.154047i | ||||||||
\(865\) | − 23497.7i | − 0.923637i | ||||||||
\(866\) | − 13796.8i | − 0.541380i | ||||||||
\(867\) | −411.893 | −0.0161345 | ||||||||
\(868\) | 192.819 | 0.00753999 | ||||||||
\(869\) | − 29380.1i | − 1.14690i | ||||||||
\(870\) | 20410.5 | 0.795381 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −24940.9 | −0.968582 | ||||||||
\(873\) | 7024.49i | 0.272329i | ||||||||
\(874\) | 59703.5 | 2.31064 | ||||||||
\(875\) | 839.404 | 0.0324309 | ||||||||
\(876\) | − 1346.63i | − 0.0519388i | ||||||||
\(877\) | − 33047.6i | − 1.27245i | −0.771503 | − | 0.636226i | \(-0.780495\pi\) | ||||
0.771503 | − | 0.636226i | \(-0.219505\pi\) | |||||||
\(878\) | 31698.0i | 1.21840i | ||||||||
\(879\) | − 24602.8i | − 0.944064i | ||||||||
\(880\) | 66101.9 | 2.53215 | ||||||||
\(881\) | −1349.22 | −0.0515965 | −0.0257982 | − | 0.999667i | \(-0.508213\pi\) | ||||
−0.0257982 | + | 0.999667i | \(0.508213\pi\) | |||||||
\(882\) | − 1466.80i | − 0.0559973i | ||||||||
\(883\) | 33934.5 | 1.29330 | 0.646651 | − | 0.762786i | \(-0.276169\pi\) | ||||
0.646651 | + | 0.762786i | \(0.276169\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 16494.3 | 0.626495 | ||||||||
\(886\) | − 19438.3i | − 0.737067i | ||||||||
\(887\) | −45609.5 | −1.72651 | −0.863256 | − | 0.504766i | \(-0.831579\pi\) | ||||
−0.863256 | + | 0.504766i | \(0.831579\pi\) | |||||||
\(888\) | −11241.4 | −0.424817 | ||||||||
\(889\) | 40711.8i | 1.53592i | ||||||||
\(890\) | 9733.19i | 0.366581i | ||||||||
\(891\) | 4278.32i | 0.160863i | ||||||||
\(892\) | − 381.037i | − 0.0143028i | ||||||||
\(893\) | 53515.9 | 2.00542 | ||||||||
\(894\) | 4301.40 | 0.160918 | ||||||||
\(895\) | − 12336.0i | − 0.460722i | ||||||||
\(896\) | 28471.4 | 1.06157 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3730.90 | 0.138643 | ||||||||
\(899\) | 422.655i | 0.0156800i | ||||||||
\(900\) | 3737.21 | 0.138415 | ||||||||
\(901\) | −21865.8 | −0.808498 | ||||||||
\(902\) | 17336.3i | 0.639952i | ||||||||
\(903\) | − 19373.4i | − 0.713962i | ||||||||
\(904\) | 6669.18i | 0.245369i | ||||||||
\(905\) | 20222.3i | 0.742777i | ||||||||
\(906\) | −428.826 | −0.0157249 | ||||||||
\(907\) | −8620.99 | −0.315607 | −0.157803 | − | 0.987471i | \(-0.550441\pi\) | ||||
−0.157803 | + | 0.987471i | \(0.550441\pi\) | |||||||
\(908\) | 17003.1i | 0.621438i | ||||||||
\(909\) | 16269.0 | 0.593629 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −43993.6 | −1.59997 | −0.799986 | − | 0.600019i | \(-0.795160\pi\) | ||||
−0.799986 | + | 0.600019i | \(0.795160\pi\) | |||||||
\(912\) | − 22148.1i | − 0.804164i | ||||||||
\(913\) | −13451.0 | −0.487584 | ||||||||
\(914\) | 45758.6 | 1.65597 | ||||||||
\(915\) | − 6008.53i | − 0.217088i | ||||||||
\(916\) | 19716.9i | 0.711205i | ||||||||
\(917\) | − 2904.84i | − 0.104609i | ||||||||
\(918\) | 6480.43i | 0.232991i | ||||||||
\(919\) | 15176.0 | 0.544733 | 0.272366 | − | 0.962194i | \(-0.412194\pi\) | ||||
0.272366 | + | 0.962194i | \(0.412194\pi\) | |||||||
\(920\) | −46486.6 | −1.66589 | ||||||||
\(921\) | − 6176.47i | − 0.220979i | ||||||||
\(922\) | −10118.8 | −0.361436 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 9267.76 | 0.329964 | ||||||||
\(925\) | − 29441.7i | − 1.04653i | ||||||||
\(926\) | −6842.94 | −0.242843 | ||||||||
\(927\) | −14047.0 | −0.497695 | ||||||||
\(928\) | − 18576.4i | − 0.657114i | ||||||||
\(929\) | 29749.7i | 1.05065i | 0.850901 | + | 0.525326i | \(0.176057\pi\) | ||||
−0.850901 | + | 0.525326i | \(0.823943\pi\) | |||||||
\(930\) | 524.853i | 0.0185060i | ||||||||
\(931\) | − 4472.88i | − 0.157457i | ||||||||
\(932\) | −2465.50 | −0.0866526 | ||||||||
\(933\) | 5586.23 | 0.196018 | ||||||||
\(934\) | − 11092.0i | − 0.388589i | ||||||||
\(935\) | −58978.9 | −2.06291 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −46456.0 | −1.61969 | −0.809846 | − | 0.586643i | \(-0.800449\pi\) | ||||
−0.809846 | + | 0.586643i | \(0.800449\pi\) | |||||||
\(938\) | − 52391.8i | − 1.82372i | ||||||||
\(939\) | 767.688 | 0.0266800 | ||||||||
\(940\) | 30905.5 | 1.07237 | ||||||||
\(941\) | − 3243.36i | − 0.112360i | −0.998421 | − | 0.0561799i | \(-0.982108\pi\) | ||||
0.998421 | − | 0.0561799i | \(-0.0178920\pi\) | |||||||
\(942\) | − 10032.7i | − 0.347011i | ||||||||
\(943\) | − 18533.9i | − 0.640027i | ||||||||
\(944\) | − 27870.0i | − 0.960901i | ||||||||
\(945\) | −7283.45 | −0.250720 | ||||||||
\(946\) | −67101.5 | −2.30619 | ||||||||
\(947\) | 53344.1i | 1.83047i | 0.402926 | + | 0.915233i | \(0.367993\pi\) | ||||
−0.402926 | + | 0.915233i | \(0.632007\pi\) | |||||||
\(948\) | −5684.99 | −0.194768 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 38157.8 | 1.30316 | ||||||||
\(951\) | 18797.0i | 0.640942i | ||||||||
\(952\) | −18927.0 | −0.644356 | ||||||||
\(953\) | −53496.9 | −1.81840 | −0.909200 | − | 0.416360i | \(-0.863306\pi\) | ||||
−0.909200 | + | 0.416360i | \(0.863306\pi\) | |||||||
\(954\) | 9352.58i | 0.317402i | ||||||||
\(955\) | 7329.22i | 0.248343i | ||||||||
\(956\) | − 4223.50i | − 0.142885i | ||||||||
\(957\) | 20314.7i | 0.686188i | ||||||||
\(958\) | 44610.1 | 1.50448 | ||||||||
\(959\) | 51095.9 | 1.72051 | ||||||||
\(960\) | 6967.42i | 0.234242i | ||||||||
\(961\) | 29780.1 | 0.999635 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2900.39 | 0.0970549 | ||||||||
\(964\) | 2573.45i | 0.0859805i | ||||||||
\(965\) | −41434.1 | −1.38219 | ||||||||
\(966\) | −33174.4 | −1.10494 | ||||||||
\(967\) | − 48822.0i | − 1.62359i | −0.583944 | − | 0.811794i | \(-0.698491\pi\) | ||||
0.583944 | − | 0.811794i | \(-0.301509\pi\) | |||||||
\(968\) | 22630.9i | 0.751429i | ||||||||
\(969\) | 19761.5i | 0.655141i | ||||||||
\(970\) | 41419.4i | 1.37103i | ||||||||
\(971\) | 36228.1 | 1.19734 | 0.598670 | − | 0.800996i | \(-0.295696\pi\) | ||||
0.598670 | + | 0.800996i | \(0.295696\pi\) | |||||||
\(972\) | 827.845 | 0.0273180 | ||||||||
\(973\) | 43867.1i | 1.44534i | ||||||||
\(974\) | −30309.0 | −0.997087 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −10152.5 | −0.332964 | ||||||||
\(977\) | 46689.8i | 1.52890i | 0.644681 | + | 0.764451i | \(0.276990\pi\) | ||||
−0.644681 | + | 0.764451i | \(0.723010\pi\) | |||||||
\(978\) | −26807.9 | −0.876505 | ||||||||
\(979\) | −9687.50 | −0.316255 | ||||||||
\(980\) | − 2583.09i | − 0.0841977i | ||||||||
\(981\) | − 14469.5i | − 0.470924i | ||||||||
\(982\) | − 43533.8i | − 1.41468i | ||||||||
\(983\) | − 11501.9i | − 0.373197i | −0.982436 | − | 0.186598i | \(-0.940254\pi\) | ||||
0.982436 | − | 0.186598i | \(-0.0597463\pi\) | |||||||
\(984\) | −4522.81 | −0.146526 | ||||||||
\(985\) | 57774.0 | 1.86886 | ||||||||
\(986\) | 30771.0i | 0.993862i | ||||||||
\(987\) | −29736.3 | −0.958983 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 71736.6 | 2.30646 | ||||||||
\(990\) | 25226.8i | 0.809859i | ||||||||
\(991\) | 7137.46 | 0.228788 | 0.114394 | − | 0.993435i | \(-0.463507\pi\) | ||||
0.114394 | + | 0.993435i | \(0.463507\pi\) | |||||||
\(992\) | 477.690 | 0.0152890 | ||||||||
\(993\) | 3215.80i | 0.102770i | ||||||||
\(994\) | 47900.5i | 1.52848i | ||||||||
\(995\) | − 3465.53i | − 0.110417i | ||||||||
\(996\) | 2602.74i | 0.0828022i | ||||||||
\(997\) | −18389.5 | −0.584152 | −0.292076 | − | 0.956395i | \(-0.594346\pi\) | ||||
−0.292076 | + | 0.956395i | \(0.594346\pi\) | |||||||
\(998\) | −24897.9 | −0.789708 | ||||||||
\(999\) | − 6521.75i | − 0.206546i |
(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 | 507.4.b.j.337.4 | 18 | ||
13.5 | odd | 4 | 507.4.a.n.1.3 | ✓ | 9 | ||
13.8 | odd | 4 | 507.4.a.q.1.7 | yes | 9 | ||
13.12 | even | 2 | inner | 507.4.b.j.337.15 | 18 | ||
39.5 | even | 4 | 1521.4.a.bj.1.7 | 9 | |||
39.8 | even | 4 | 1521.4.a.be.1.3 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
507.4.a.n.1.3 | ✓ | 9 | 13.5 | odd | 4 | ||
507.4.a.q.1.7 | yes | 9 | 13.8 | odd | 4 | ||
507.4.b.j.337.4 | 18 | 1.1 | even | 1 | trivial | ||
507.4.b.j.337.15 | 18 | 13.12 | even | 2 | inner | ||
1521.4.a.be.1.3 | 9 | 39.8 | even | 4 | |||
1521.4.a.bj.1.7 | 9 | 39.5 | even | 4 |