Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [507,4,Mod(1,507)]
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, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("507.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 507 = 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 507.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(29.9139683729\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - x^{8} - 48x^{7} + 29x^{6} + 772x^{5} - 150x^{4} - 4745x^{3} - 966x^{2} + 9428x + 5144 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 13^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-2.37739\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 507.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.37739 | 1.19409 | 0.597044 | − | 0.802208i | \(-0.296342\pi\) | ||||
0.597044 | + | 0.802208i | \(0.296342\pi\) | |||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 3.40677 | 0.425846 | ||||||||
\(5\) | −15.7127 | −1.40538 | −0.702692 | − | 0.711494i | \(-0.748019\pi\) | ||||
−0.702692 | + | 0.711494i | \(0.748019\pi\) | |||||||
\(6\) | −10.1322 | −0.689407 | ||||||||
\(7\) | −17.1681 | −0.926992 | −0.463496 | − | 0.886099i | \(-0.653405\pi\) | ||||
−0.463496 | + | 0.886099i | \(0.653405\pi\) | |||||||
\(8\) | −15.5131 | −0.685590 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −53.0679 | −1.67815 | ||||||||
\(11\) | 52.8187 | 1.44777 | 0.723884 | − | 0.689922i | \(-0.242355\pi\) | ||||
0.723884 | + | 0.689922i | \(0.242355\pi\) | |||||||
\(12\) | −10.2203 | −0.245862 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −57.9835 | −1.10691 | ||||||||
\(15\) | 47.1380 | 0.811399 | ||||||||
\(16\) | −79.6481 | −1.24450 | ||||||||
\(17\) | −71.0654 | −1.01388 | −0.506938 | − | 0.861982i | \(-0.669223\pi\) | ||||
−0.506938 | + | 0.861982i | \(0.669223\pi\) | |||||||
\(18\) | 30.3965 | 0.398029 | ||||||||
\(19\) | 92.6916 | 1.11921 | 0.559603 | − | 0.828761i | \(-0.310954\pi\) | ||||
0.559603 | + | 0.828761i | \(0.310954\pi\) | |||||||
\(20\) | −53.5295 | −0.598478 | ||||||||
\(21\) | 51.5044 | 0.535199 | ||||||||
\(22\) | 178.390 | 1.72876 | ||||||||
\(23\) | 190.712 | 1.72896 | 0.864482 | − | 0.502663i | \(-0.167646\pi\) | ||||
0.864482 | + | 0.502663i | \(0.167646\pi\) | |||||||
\(24\) | 46.5394 | 0.395826 | ||||||||
\(25\) | 121.888 | 0.975106 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | −58.4878 | −0.394756 | ||||||||
\(29\) | −128.204 | −0.820927 | −0.410463 | − | 0.911877i | \(-0.634633\pi\) | ||||
−0.410463 | + | 0.911877i | \(0.634633\pi\) | |||||||
\(30\) | 159.204 | 0.968882 | ||||||||
\(31\) | 3.29674 | 0.0191004 | 0.00955020 | − | 0.999954i | \(-0.496960\pi\) | ||||
0.00955020 | + | 0.999954i | \(0.496960\pi\) | |||||||
\(32\) | −144.898 | −0.800454 | ||||||||
\(33\) | −158.456 | −0.835869 | ||||||||
\(34\) | −240.016 | −1.21066 | ||||||||
\(35\) | 269.757 | 1.30278 | ||||||||
\(36\) | 30.6609 | 0.141949 | ||||||||
\(37\) | 241.546 | 1.07324 | 0.536621 | − | 0.843823i | \(-0.319700\pi\) | ||||
0.536621 | + | 0.843823i | \(0.319700\pi\) | |||||||
\(38\) | 313.056 | 1.33643 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 243.753 | 0.963518 | ||||||||
\(41\) | −97.1824 | −0.370179 | −0.185090 | − | 0.982722i | \(-0.559258\pi\) | ||||
−0.185090 | + | 0.982722i | \(0.559258\pi\) | |||||||
\(42\) | 173.950 | 0.639075 | ||||||||
\(43\) | 376.151 | 1.33401 | 0.667006 | − | 0.745052i | \(-0.267575\pi\) | ||||
0.667006 | + | 0.745052i | \(0.267575\pi\) | |||||||
\(44\) | 179.941 | 0.616527 | ||||||||
\(45\) | −141.414 | −0.468462 | ||||||||
\(46\) | 644.109 | 2.06454 | ||||||||
\(47\) | 577.354 | 1.79182 | 0.895912 | − | 0.444231i | \(-0.146523\pi\) | ||||
0.895912 | + | 0.444231i | \(0.146523\pi\) | |||||||
\(48\) | 238.944 | 0.718513 | ||||||||
\(49\) | −48.2555 | −0.140686 | ||||||||
\(50\) | 411.664 | 1.16436 | ||||||||
\(51\) | 213.196 | 0.585362 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −307.686 | −0.797433 | −0.398716 | − | 0.917074i | \(-0.630544\pi\) | ||||
−0.398716 | + | 0.917074i | \(0.630544\pi\) | |||||||
\(54\) | −91.1896 | −0.229802 | ||||||||
\(55\) | −829.924 | −2.03467 | ||||||||
\(56\) | 266.331 | 0.635536 | ||||||||
\(57\) | −278.075 | −0.646174 | ||||||||
\(58\) | −432.995 | −0.980259 | ||||||||
\(59\) | 349.914 | 0.772117 | 0.386059 | − | 0.922474i | \(-0.373836\pi\) | ||||
0.386059 | + | 0.922474i | \(0.373836\pi\) | |||||||
\(60\) | 160.588 | 0.345531 | ||||||||
\(61\) | 127.467 | 0.267548 | 0.133774 | − | 0.991012i | \(-0.457290\pi\) | ||||
0.133774 | + | 0.991012i | \(0.457290\pi\) | |||||||
\(62\) | 11.1344 | 0.0228076 | ||||||||
\(63\) | −154.513 | −0.308997 | ||||||||
\(64\) | 147.809 | 0.288689 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −535.169 | −0.998102 | ||||||||
\(67\) | −903.564 | −1.64758 | −0.823791 | − | 0.566894i | \(-0.808145\pi\) | ||||
−0.823791 | + | 0.566894i | \(0.808145\pi\) | |||||||
\(68\) | −242.104 | −0.431755 | ||||||||
\(69\) | −572.136 | −0.998218 | ||||||||
\(70\) | 911.076 | 1.55563 | ||||||||
\(71\) | 826.106 | 1.38086 | 0.690428 | − | 0.723401i | \(-0.257422\pi\) | ||||
0.690428 | + | 0.723401i | \(0.257422\pi\) | |||||||
\(72\) | −139.618 | −0.228530 | ||||||||
\(73\) | −131.760 | −0.211252 | −0.105626 | − | 0.994406i | \(-0.533685\pi\) | ||||
−0.105626 | + | 0.994406i | \(0.533685\pi\) | |||||||
\(74\) | 815.796 | 1.28155 | ||||||||
\(75\) | −365.665 | −0.562978 | ||||||||
\(76\) | 315.779 | 0.476610 | ||||||||
\(77\) | −906.799 | −1.34207 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −556.244 | −0.792182 | −0.396091 | − | 0.918211i | \(-0.629633\pi\) | ||||
−0.396091 | + | 0.918211i | \(0.629633\pi\) | |||||||
\(80\) | 1251.48 | 1.74900 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −328.223 | −0.442026 | ||||||||
\(83\) | −254.664 | −0.336783 | −0.168391 | − | 0.985720i | \(-0.553857\pi\) | ||||
−0.168391 | + | 0.985720i | \(0.553857\pi\) | |||||||
\(84\) | 175.464 | 0.227912 | ||||||||
\(85\) | 1116.63 | 1.42489 | ||||||||
\(86\) | 1270.41 | 1.59293 | ||||||||
\(87\) | 384.612 | 0.473962 | ||||||||
\(88\) | −819.384 | −0.992576 | ||||||||
\(89\) | 183.410 | 0.218443 | 0.109222 | − | 0.994017i | \(-0.465164\pi\) | ||||
0.109222 | + | 0.994017i | \(0.465164\pi\) | |||||||
\(90\) | −477.611 | −0.559384 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 649.712 | 0.736273 | ||||||||
\(93\) | −9.89023 | −0.0110276 | ||||||||
\(94\) | 1949.95 | 2.13960 | ||||||||
\(95\) | −1456.43 | −1.57292 | ||||||||
\(96\) | 434.693 | 0.462142 | ||||||||
\(97\) | −780.498 | −0.816986 | −0.408493 | − | 0.912762i | \(-0.633946\pi\) | ||||
−0.408493 | + | 0.912762i | \(0.633946\pi\) | |||||||
\(98\) | −162.978 | −0.167992 | ||||||||
\(99\) | 475.369 | 0.482589 | ||||||||
\(100\) | 415.245 | 0.415245 | ||||||||
\(101\) | −1807.67 | −1.78089 | −0.890444 | − | 0.455093i | \(-0.849606\pi\) | ||||
−0.890444 | + | 0.455093i | \(0.849606\pi\) | |||||||
\(102\) | 720.047 | 0.698974 | ||||||||
\(103\) | 1560.78 | 1.49308 | 0.746542 | − | 0.665338i | \(-0.231712\pi\) | ||||
0.746542 | + | 0.665338i | \(0.231712\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −809.272 | −0.752160 | ||||||||
\(106\) | −1039.18 | −0.952205 | ||||||||
\(107\) | 322.266 | 0.291165 | 0.145582 | − | 0.989346i | \(-0.453494\pi\) | ||||
0.145582 | + | 0.989346i | \(0.453494\pi\) | |||||||
\(108\) | −91.9828 | −0.0819541 | ||||||||
\(109\) | 1607.72 | 1.41277 | 0.706386 | − | 0.707827i | \(-0.250324\pi\) | ||||
0.706386 | + | 0.707827i | \(0.250324\pi\) | |||||||
\(110\) | −2802.98 | −2.42958 | ||||||||
\(111\) | −724.639 | −0.619637 | ||||||||
\(112\) | 1367.41 | 1.15364 | ||||||||
\(113\) | −429.905 | −0.357895 | −0.178947 | − | 0.983859i | \(-0.557269\pi\) | ||||
−0.178947 | + | 0.983859i | \(0.557269\pi\) | |||||||
\(114\) | −939.167 | −0.771589 | ||||||||
\(115\) | −2996.60 | −2.42986 | ||||||||
\(116\) | −436.761 | −0.349589 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1181.80 | 0.921976 | ||||||||
\(119\) | 1220.06 | 0.939855 | ||||||||
\(120\) | −731.259 | −0.556287 | ||||||||
\(121\) | 1458.82 | 1.09603 | ||||||||
\(122\) | 430.505 | 0.319476 | ||||||||
\(123\) | 291.547 | 0.213723 | ||||||||
\(124\) | 11.2312 | 0.00813383 | ||||||||
\(125\) | 48.8932 | 0.0349851 | ||||||||
\(126\) | −521.851 | −0.368970 | ||||||||
\(127\) | 2371.36 | 1.65688 | 0.828442 | − | 0.560076i | \(-0.189228\pi\) | ||||
0.828442 | + | 0.560076i | \(0.189228\pi\) | |||||||
\(128\) | 1658.39 | 1.14517 | ||||||||
\(129\) | −1128.45 | −0.770193 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 169.200 | 0.112848 | 0.0564239 | − | 0.998407i | \(-0.482030\pi\) | ||||
0.0564239 | + | 0.998407i | \(0.482030\pi\) | |||||||
\(132\) | −539.824 | −0.355952 | ||||||||
\(133\) | −1591.34 | −1.03749 | ||||||||
\(134\) | −3051.69 | −1.96736 | ||||||||
\(135\) | 424.242 | 0.270466 | ||||||||
\(136\) | 1102.45 | 0.695104 | ||||||||
\(137\) | 2976.21 | 1.85602 | 0.928009 | − | 0.372558i | \(-0.121519\pi\) | ||||
0.928009 | + | 0.372558i | \(0.121519\pi\) | |||||||
\(138\) | −1932.33 | −1.19196 | ||||||||
\(139\) | −2555.15 | −1.55917 | −0.779585 | − | 0.626296i | \(-0.784570\pi\) | ||||
−0.779585 | + | 0.626296i | \(0.784570\pi\) | |||||||
\(140\) | 919.001 | 0.554784 | ||||||||
\(141\) | −1732.06 | −1.03451 | ||||||||
\(142\) | 2790.08 | 1.64886 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −716.833 | −0.414834 | ||||||||
\(145\) | 2014.43 | 1.15372 | ||||||||
\(146\) | −445.006 | −0.252253 | ||||||||
\(147\) | 144.766 | 0.0812254 | ||||||||
\(148\) | 822.892 | 0.457036 | ||||||||
\(149\) | 424.529 | 0.233415 | 0.116707 | − | 0.993166i | \(-0.462766\pi\) | ||||
0.116707 | + | 0.993166i | \(0.462766\pi\) | |||||||
\(150\) | −1234.99 | −0.672245 | ||||||||
\(151\) | 42.3232 | 0.0228093 | 0.0114047 | − | 0.999935i | \(-0.496370\pi\) | ||||
0.0114047 | + | 0.999935i | \(0.496370\pi\) | |||||||
\(152\) | −1437.94 | −0.767317 | ||||||||
\(153\) | −639.589 | −0.337959 | ||||||||
\(154\) | −3062.61 | −1.60255 | ||||||||
\(155\) | −51.8007 | −0.0268434 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −990.187 | −0.503347 | −0.251674 | − | 0.967812i | \(-0.580981\pi\) | ||||
−0.251674 | + | 0.967812i | \(0.580981\pi\) | |||||||
\(158\) | −1878.65 | −0.945935 | ||||||||
\(159\) | 923.058 | 0.460398 | ||||||||
\(160\) | 2276.73 | 1.12495 | ||||||||
\(161\) | −3274.17 | −1.60274 | ||||||||
\(162\) | 273.569 | 0.132676 | ||||||||
\(163\) | 2645.82 | 1.27139 | 0.635695 | − | 0.771940i | \(-0.280714\pi\) | ||||
0.635695 | + | 0.771940i | \(0.280714\pi\) | |||||||
\(164\) | −331.078 | −0.157639 | ||||||||
\(165\) | 2489.77 | 1.17472 | ||||||||
\(166\) | −860.099 | −0.402148 | ||||||||
\(167\) | 295.428 | 0.136892 | 0.0684458 | − | 0.997655i | \(-0.478196\pi\) | ||||
0.0684458 | + | 0.997655i | \(0.478196\pi\) | |||||||
\(168\) | −798.994 | −0.366927 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 3771.29 | 1.70144 | ||||||||
\(171\) | 834.225 | 0.373069 | ||||||||
\(172\) | 1281.46 | 0.568084 | ||||||||
\(173\) | 1495.46 | 0.657213 | 0.328606 | − | 0.944467i | \(-0.393421\pi\) | ||||
0.328606 | + | 0.944467i | \(0.393421\pi\) | |||||||
\(174\) | 1298.98 | 0.565953 | ||||||||
\(175\) | −2092.59 | −0.903915 | ||||||||
\(176\) | −4206.91 | −1.80175 | ||||||||
\(177\) | −1049.74 | −0.445782 | ||||||||
\(178\) | 619.448 | 0.260840 | ||||||||
\(179\) | 785.097 | 0.327826 | 0.163913 | − | 0.986475i | \(-0.447588\pi\) | ||||
0.163913 | + | 0.986475i | \(0.447588\pi\) | |||||||
\(180\) | −481.765 | −0.199493 | ||||||||
\(181\) | −1287.01 | −0.528522 | −0.264261 | − | 0.964451i | \(-0.585128\pi\) | ||||
−0.264261 | + | 0.964451i | \(0.585128\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −382.400 | −0.154469 | ||||||||
\(184\) | −2958.54 | −1.18536 | ||||||||
\(185\) | −3795.34 | −1.50832 | ||||||||
\(186\) | −33.4032 | −0.0131680 | ||||||||
\(187\) | −3753.59 | −1.46786 | ||||||||
\(188\) | 1966.91 | 0.763042 | ||||||||
\(189\) | 463.539 | 0.178400 | ||||||||
\(190\) | −4918.95 | −1.87820 | ||||||||
\(191\) | 466.452 | 0.176708 | 0.0883542 | − | 0.996089i | \(-0.471839\pi\) | ||||
0.0883542 | + | 0.996089i | \(0.471839\pi\) | |||||||
\(192\) | −443.426 | −0.166675 | ||||||||
\(193\) | 2636.99 | 0.983495 | 0.491747 | − | 0.870738i | \(-0.336358\pi\) | ||||
0.491747 | + | 0.870738i | \(0.336358\pi\) | |||||||
\(194\) | −2636.05 | −0.975553 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −164.395 | −0.0599108 | ||||||||
\(197\) | 3676.90 | 1.32979 | 0.664894 | − | 0.746937i | \(-0.268477\pi\) | ||||
0.664894 | + | 0.746937i | \(0.268477\pi\) | |||||||
\(198\) | 1605.51 | 0.576254 | ||||||||
\(199\) | 220.557 | 0.0785670 | 0.0392835 | − | 0.999228i | \(-0.487492\pi\) | ||||
0.0392835 | + | 0.999228i | \(0.487492\pi\) | |||||||
\(200\) | −1890.87 | −0.668523 | ||||||||
\(201\) | 2710.69 | 0.951231 | ||||||||
\(202\) | −6105.20 | −2.12654 | ||||||||
\(203\) | 2201.02 | 0.760992 | ||||||||
\(204\) | 726.311 | 0.249274 | ||||||||
\(205\) | 1527.00 | 0.520244 | ||||||||
\(206\) | 5271.35 | 1.78287 | ||||||||
\(207\) | 1716.41 | 0.576322 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4895.85 | 1.62035 | ||||||||
\(210\) | −2733.23 | −0.898146 | ||||||||
\(211\) | 1385.93 | 0.452186 | 0.226093 | − | 0.974106i | \(-0.427405\pi\) | ||||
0.226093 | + | 0.974106i | \(0.427405\pi\) | |||||||
\(212\) | −1048.22 | −0.339584 | ||||||||
\(213\) | −2478.32 | −0.797237 | ||||||||
\(214\) | 1088.42 | 0.347676 | ||||||||
\(215\) | −5910.35 | −1.87480 | ||||||||
\(216\) | 418.855 | 0.131942 | ||||||||
\(217\) | −56.5989 | −0.0177059 | ||||||||
\(218\) | 5429.91 | 1.68697 | ||||||||
\(219\) | 395.281 | 0.121966 | ||||||||
\(220\) | −2827.36 | −0.866457 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −2447.39 | −0.739901 | ||||||||
\(223\) | −111.847 | −0.0335867 | −0.0167933 | − | 0.999859i | \(-0.505346\pi\) | ||||
−0.0167933 | + | 0.999859i | \(0.505346\pi\) | |||||||
\(224\) | 2487.62 | 0.742014 | ||||||||
\(225\) | 1096.99 | 0.325035 | ||||||||
\(226\) | −1451.96 | −0.427358 | ||||||||
\(227\) | 4990.96 | 1.45930 | 0.729651 | − | 0.683819i | \(-0.239682\pi\) | ||||
0.729651 | + | 0.683819i | \(0.239682\pi\) | |||||||
\(228\) | −947.337 | −0.275171 | ||||||||
\(229\) | −5787.56 | −1.67010 | −0.835050 | − | 0.550174i | \(-0.814561\pi\) | ||||
−0.835050 | + | 0.550174i | \(0.814561\pi\) | |||||||
\(230\) | −10120.7 | −2.90147 | ||||||||
\(231\) | 2720.40 | 0.774844 | ||||||||
\(232\) | 1988.85 | 0.562819 | ||||||||
\(233\) | −723.707 | −0.203483 | −0.101742 | − | 0.994811i | \(-0.532441\pi\) | ||||
−0.101742 | + | 0.994811i | \(0.532441\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9071.78 | −2.51820 | ||||||||
\(236\) | 1192.08 | 0.328803 | ||||||||
\(237\) | 1668.73 | 0.457366 | ||||||||
\(238\) | 4120.62 | 1.12227 | ||||||||
\(239\) | −1239.74 | −0.335531 | −0.167766 | − | 0.985827i | \(-0.553655\pi\) | ||||
−0.167766 | + | 0.985827i | \(0.553655\pi\) | |||||||
\(240\) | −3754.45 | −1.00979 | ||||||||
\(241\) | −755.393 | −0.201905 | −0.100953 | − | 0.994891i | \(-0.532189\pi\) | ||||
−0.100953 | + | 0.994891i | \(0.532189\pi\) | |||||||
\(242\) | 4927.00 | 1.30876 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 434.249 | 0.113934 | ||||||||
\(245\) | 758.222 | 0.197719 | ||||||||
\(246\) | 984.669 | 0.255204 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −51.1428 | −0.0130950 | ||||||||
\(249\) | 763.991 | 0.194442 | ||||||||
\(250\) | 165.131 | 0.0417753 | ||||||||
\(251\) | 2252.06 | 0.566330 | 0.283165 | − | 0.959071i | \(-0.408616\pi\) | ||||
0.283165 | + | 0.959071i | \(0.408616\pi\) | |||||||
\(252\) | −526.391 | −0.131585 | ||||||||
\(253\) | 10073.2 | 2.50314 | ||||||||
\(254\) | 8009.01 | 1.97846 | ||||||||
\(255\) | −3349.89 | −0.822659 | ||||||||
\(256\) | 4418.56 | 1.07875 | ||||||||
\(257\) | 3716.75 | 0.902118 | 0.451059 | − | 0.892494i | \(-0.351046\pi\) | ||||
0.451059 | + | 0.892494i | \(0.351046\pi\) | |||||||
\(258\) | −3811.23 | −0.919678 | ||||||||
\(259\) | −4146.90 | −0.994887 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1153.84 | −0.273642 | ||||||||
\(262\) | 571.454 | 0.134750 | ||||||||
\(263\) | −49.9521 | −0.0117117 | −0.00585585 | − | 0.999983i | \(-0.501864\pi\) | ||||
−0.00585585 | + | 0.999983i | \(0.501864\pi\) | |||||||
\(264\) | 2458.15 | 0.573064 | ||||||||
\(265\) | 4834.57 | 1.12070 | ||||||||
\(266\) | −5374.58 | −1.23886 | ||||||||
\(267\) | −550.231 | −0.126118 | ||||||||
\(268\) | −3078.23 | −0.701616 | ||||||||
\(269\) | 3421.44 | 0.775497 | 0.387748 | − | 0.921765i | \(-0.373253\pi\) | ||||
0.387748 | + | 0.921765i | \(0.373253\pi\) | |||||||
\(270\) | 1432.83 | 0.322961 | ||||||||
\(271\) | −2958.89 | −0.663247 | −0.331624 | − | 0.943412i | \(-0.607596\pi\) | ||||
−0.331624 | + | 0.943412i | \(0.607596\pi\) | |||||||
\(272\) | 5660.23 | 1.26177 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 10051.8 | 2.21625 | ||||||||
\(275\) | 6437.99 | 1.41173 | ||||||||
\(276\) | −1949.13 | −0.425087 | ||||||||
\(277\) | −7461.08 | −1.61839 | −0.809193 | − | 0.587543i | \(-0.800095\pi\) | ||||
−0.809193 | + | 0.587543i | \(0.800095\pi\) | |||||||
\(278\) | −8629.73 | −1.86179 | ||||||||
\(279\) | 29.6707 | 0.00636680 | ||||||||
\(280\) | −4184.78 | −0.893173 | ||||||||
\(281\) | −4728.04 | −1.00374 | −0.501871 | − | 0.864943i | \(-0.667355\pi\) | ||||
−0.501871 | + | 0.864943i | \(0.667355\pi\) | |||||||
\(282\) | −5849.85 | −1.23530 | ||||||||
\(283\) | −2879.69 | −0.604876 | −0.302438 | − | 0.953169i | \(-0.597801\pi\) | ||||
−0.302438 | + | 0.953169i | \(0.597801\pi\) | |||||||
\(284\) | 2814.35 | 0.588032 | ||||||||
\(285\) | 4369.30 | 0.908123 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1668.44 | 0.343153 | ||||||||
\(288\) | −1304.08 | −0.266818 | ||||||||
\(289\) | 137.298 | 0.0279458 | ||||||||
\(290\) | 6803.51 | 1.37764 | ||||||||
\(291\) | 2341.50 | 0.471687 | ||||||||
\(292\) | −448.877 | −0.0899607 | ||||||||
\(293\) | 8200.94 | 1.63517 | 0.817583 | − | 0.575810i | \(-0.195313\pi\) | ||||
0.817583 | + | 0.575810i | \(0.195313\pi\) | |||||||
\(294\) | 488.933 | 0.0969902 | ||||||||
\(295\) | −5498.09 | −1.08512 | ||||||||
\(296\) | −3747.14 | −0.735804 | ||||||||
\(297\) | −1426.11 | −0.278623 | ||||||||
\(298\) | 1433.80 | 0.278718 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1245.74 | −0.239742 | ||||||||
\(301\) | −6457.81 | −1.23662 | ||||||||
\(302\) | 142.942 | 0.0272364 | ||||||||
\(303\) | 5423.00 | 1.02820 | ||||||||
\(304\) | −7382.71 | −1.39285 | ||||||||
\(305\) | −2002.84 | −0.376008 | ||||||||
\(306\) | −2160.14 | −0.403553 | ||||||||
\(307\) | 2058.82 | 0.382747 | 0.191374 | − | 0.981517i | \(-0.438706\pi\) | ||||
0.191374 | + | 0.981517i | \(0.438706\pi\) | |||||||
\(308\) | −3089.25 | −0.571515 | ||||||||
\(309\) | −4682.33 | −0.862033 | ||||||||
\(310\) | −174.951 | −0.0320534 | ||||||||
\(311\) | 1862.08 | 0.339514 | 0.169757 | − | 0.985486i | \(-0.445702\pi\) | ||||
0.169757 | + | 0.985486i | \(0.445702\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −255.896 | −0.0462112 | −0.0231056 | − | 0.999733i | \(-0.507355\pi\) | ||||
−0.0231056 | + | 0.999733i | \(0.507355\pi\) | |||||||
\(314\) | −3344.25 | −0.601041 | ||||||||
\(315\) | 2427.82 | 0.434260 | ||||||||
\(316\) | −1895.00 | −0.337348 | ||||||||
\(317\) | 6265.68 | 1.11014 | 0.555072 | − | 0.831802i | \(-0.312691\pi\) | ||||
0.555072 | + | 0.831802i | \(0.312691\pi\) | |||||||
\(318\) | 3117.53 | 0.549756 | ||||||||
\(319\) | −6771.57 | −1.18851 | ||||||||
\(320\) | −2322.47 | −0.405719 | ||||||||
\(321\) | −966.798 | −0.168104 | ||||||||
\(322\) | −11058.1 | −1.91381 | ||||||||
\(323\) | −6587.17 | −1.13474 | ||||||||
\(324\) | 275.948 | 0.0473162 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 8935.96 | 1.51815 | ||||||||
\(327\) | −4823.17 | −0.815664 | ||||||||
\(328\) | 1507.60 | 0.253791 | ||||||||
\(329\) | −9912.09 | −1.66101 | ||||||||
\(330\) | 8408.93 | 1.40272 | ||||||||
\(331\) | 1071.93 | 0.178002 | 0.0890011 | − | 0.996032i | \(-0.471633\pi\) | ||||
0.0890011 | + | 0.996032i | \(0.471633\pi\) | |||||||
\(332\) | −867.581 | −0.143418 | ||||||||
\(333\) | 2173.92 | 0.357747 | ||||||||
\(334\) | 997.775 | 0.163461 | ||||||||
\(335\) | 14197.4 | 2.31549 | ||||||||
\(336\) | −4102.22 | −0.666056 | ||||||||
\(337\) | −5572.02 | −0.900675 | −0.450337 | − | 0.892858i | \(-0.648696\pi\) | ||||
−0.450337 | + | 0.892858i | \(0.648696\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1289.72 | 0.206631 | ||||||||
\(340\) | 3804.10 | 0.606783 | ||||||||
\(341\) | 174.130 | 0.0276530 | ||||||||
\(342\) | 2817.50 | 0.445477 | ||||||||
\(343\) | 6717.12 | 1.05741 | ||||||||
\(344\) | −5835.29 | −0.914586 | ||||||||
\(345\) | 8989.79 | 1.40288 | ||||||||
\(346\) | 5050.76 | 0.784770 | ||||||||
\(347\) | −1903.44 | −0.294472 | −0.147236 | − | 0.989101i | \(-0.547038\pi\) | ||||
−0.147236 | + | 0.989101i | \(0.547038\pi\) | |||||||
\(348\) | 1310.28 | 0.201835 | ||||||||
\(349\) | 1097.17 | 0.168282 | 0.0841409 | − | 0.996454i | \(-0.473185\pi\) | ||||
0.0841409 | + | 0.996454i | \(0.473185\pi\) | |||||||
\(350\) | −7067.51 | −1.07935 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −7653.31 | −1.15887 | ||||||||
\(353\) | 5420.90 | 0.817352 | 0.408676 | − | 0.912679i | \(-0.365991\pi\) | ||||
0.408676 | + | 0.912679i | \(0.365991\pi\) | |||||||
\(354\) | −3545.39 | −0.532303 | ||||||||
\(355\) | −12980.3 | −1.94063 | ||||||||
\(356\) | 624.836 | 0.0930232 | ||||||||
\(357\) | −3660.18 | −0.542626 | ||||||||
\(358\) | 2651.58 | 0.391453 | ||||||||
\(359\) | 3885.40 | 0.571208 | 0.285604 | − | 0.958348i | \(-0.407806\pi\) | ||||
0.285604 | + | 0.958348i | \(0.407806\pi\) | |||||||
\(360\) | 2193.78 | 0.321173 | ||||||||
\(361\) | 1732.74 | 0.252622 | ||||||||
\(362\) | −4346.72 | −0.631102 | ||||||||
\(363\) | −4376.46 | −0.632795 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2070.31 | 0.296890 | ||||||||
\(366\) | −1291.51 | −0.184450 | ||||||||
\(367\) | −3888.26 | −0.553039 | −0.276520 | − | 0.961008i | \(-0.589181\pi\) | ||||
−0.276520 | + | 0.961008i | \(0.589181\pi\) | |||||||
\(368\) | −15189.8 | −2.15170 | ||||||||
\(369\) | −874.642 | −0.123393 | ||||||||
\(370\) | −12818.3 | −1.80106 | ||||||||
\(371\) | 5282.39 | 0.739213 | ||||||||
\(372\) | −33.6937 | −0.00469607 | ||||||||
\(373\) | 9960.88 | 1.38272 | 0.691361 | − | 0.722510i | \(-0.257012\pi\) | ||||
0.691361 | + | 0.722510i | \(0.257012\pi\) | |||||||
\(374\) | −12677.3 | −1.75275 | ||||||||
\(375\) | −146.680 | −0.0201987 | ||||||||
\(376\) | −8956.57 | −1.22846 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 1565.55 | 0.213025 | ||||||||
\(379\) | 5288.25 | 0.716726 | 0.358363 | − | 0.933582i | \(-0.383335\pi\) | ||||
0.358363 | + | 0.933582i | \(0.383335\pi\) | |||||||
\(380\) | −4961.73 | −0.669820 | ||||||||
\(381\) | −7114.08 | −0.956602 | ||||||||
\(382\) | 1575.39 | 0.211005 | ||||||||
\(383\) | 688.944 | 0.0919149 | 0.0459575 | − | 0.998943i | \(-0.485366\pi\) | ||||
0.0459575 | + | 0.998943i | \(0.485366\pi\) | |||||||
\(384\) | −4975.17 | −0.661166 | ||||||||
\(385\) | 14248.2 | 1.88612 | ||||||||
\(386\) | 8906.14 | 1.17438 | ||||||||
\(387\) | 3385.36 | 0.444671 | ||||||||
\(388\) | −2658.98 | −0.347910 | ||||||||
\(389\) | 2102.57 | 0.274048 | 0.137024 | − | 0.990568i | \(-0.456246\pi\) | ||||
0.137024 | + | 0.990568i | \(0.456246\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13553.0 | −1.75296 | ||||||||
\(392\) | 748.593 | 0.0964533 | ||||||||
\(393\) | −507.599 | −0.0651527 | ||||||||
\(394\) | 12418.3 | 1.58788 | ||||||||
\(395\) | 8740.09 | 1.11332 | ||||||||
\(396\) | 1619.47 | 0.205509 | ||||||||
\(397\) | −11254.8 | −1.42283 | −0.711413 | − | 0.702774i | \(-0.751944\pi\) | ||||
−0.711413 | + | 0.702774i | \(0.751944\pi\) | |||||||
\(398\) | 744.906 | 0.0938159 | ||||||||
\(399\) | 4774.02 | 0.598998 | ||||||||
\(400\) | −9708.17 | −1.21352 | ||||||||
\(401\) | −3523.22 | −0.438756 | −0.219378 | − | 0.975640i | \(-0.570403\pi\) | ||||
−0.219378 | + | 0.975640i | \(0.570403\pi\) | |||||||
\(402\) | 9155.07 | 1.13585 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −6158.31 | −0.758384 | ||||||||
\(405\) | −1272.73 | −0.156154 | ||||||||
\(406\) | 7433.71 | 0.908692 | ||||||||
\(407\) | 12758.2 | 1.55381 | ||||||||
\(408\) | −3307.34 | −0.401318 | ||||||||
\(409\) | −6366.65 | −0.769708 | −0.384854 | − | 0.922978i | \(-0.625748\pi\) | ||||
−0.384854 | + | 0.922978i | \(0.625748\pi\) | |||||||
\(410\) | 5157.26 | 0.621217 | ||||||||
\(411\) | −8928.62 | −1.07157 | ||||||||
\(412\) | 5317.20 | 0.635824 | ||||||||
\(413\) | −6007.37 | −0.715746 | ||||||||
\(414\) | 5796.98 | 0.688179 | ||||||||
\(415\) | 4001.45 | 0.473310 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7665.44 | 0.900187 | ||||||||
\(418\) | 16535.2 | 1.93484 | ||||||||
\(419\) | 8919.77 | 1.04000 | 0.519999 | − | 0.854167i | \(-0.325932\pi\) | ||||
0.519999 | + | 0.854167i | \(0.325932\pi\) | |||||||
\(420\) | −2757.00 | −0.320305 | ||||||||
\(421\) | −1090.71 | −0.126266 | −0.0631328 | − | 0.998005i | \(-0.520109\pi\) | ||||
−0.0631328 | + | 0.998005i | \(0.520109\pi\) | |||||||
\(422\) | 4680.82 | 0.539949 | ||||||||
\(423\) | 5196.19 | 0.597275 | ||||||||
\(424\) | 4773.17 | 0.546712 | ||||||||
\(425\) | −8662.05 | −0.988638 | ||||||||
\(426\) | −8370.25 | −0.951971 | ||||||||
\(427\) | −2188.36 | −0.248015 | ||||||||
\(428\) | 1097.89 | 0.123991 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −19961.5 | −2.23868 | ||||||||
\(431\) | −3760.43 | −0.420263 | −0.210132 | − | 0.977673i | \(-0.567389\pi\) | ||||
−0.210132 | + | 0.977673i | \(0.567389\pi\) | |||||||
\(432\) | 2150.50 | 0.239504 | ||||||||
\(433\) | −4085.06 | −0.453384 | −0.226692 | − | 0.973967i | \(-0.572791\pi\) | ||||
−0.226692 | + | 0.973967i | \(0.572791\pi\) | |||||||
\(434\) | −191.157 | −0.0211424 | ||||||||
\(435\) | −6043.28 | −0.666099 | ||||||||
\(436\) | 5477.15 | 0.601623 | ||||||||
\(437\) | 17677.4 | 1.93507 | ||||||||
\(438\) | 1335.02 | 0.145638 | ||||||||
\(439\) | 9385.35 | 1.02036 | 0.510180 | − | 0.860068i | \(-0.329579\pi\) | ||||
0.510180 | + | 0.860068i | \(0.329579\pi\) | |||||||
\(440\) | 12874.7 | 1.39495 | ||||||||
\(441\) | −434.299 | −0.0468955 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5755.41 | 0.617264 | 0.308632 | − | 0.951182i | \(-0.400129\pi\) | ||||
0.308632 | + | 0.951182i | \(0.400129\pi\) | |||||||
\(444\) | −2468.68 | −0.263870 | ||||||||
\(445\) | −2881.87 | −0.306997 | ||||||||
\(446\) | −377.751 | −0.0401055 | ||||||||
\(447\) | −1273.59 | −0.134762 | ||||||||
\(448\) | −2537.60 | −0.267612 | ||||||||
\(449\) | 1104.67 | 0.116108 | 0.0580541 | − | 0.998313i | \(-0.481510\pi\) | ||||
0.0580541 | + | 0.998313i | \(0.481510\pi\) | |||||||
\(450\) | 3704.98 | 0.388121 | ||||||||
\(451\) | −5133.05 | −0.535934 | ||||||||
\(452\) | −1464.59 | −0.152408 | ||||||||
\(453\) | −126.969 | −0.0131690 | ||||||||
\(454\) | 16856.4 | 1.74254 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4313.81 | 0.443011 | ||||||||
\(457\) | −13548.5 | −1.38681 | −0.693405 | − | 0.720548i | \(-0.743890\pi\) | ||||
−0.693405 | + | 0.720548i | \(0.743890\pi\) | |||||||
\(458\) | −19546.9 | −1.99425 | ||||||||
\(459\) | 1918.77 | 0.195121 | ||||||||
\(460\) | −10208.7 | −1.03475 | ||||||||
\(461\) | 2996.03 | 0.302688 | 0.151344 | − | 0.988481i | \(-0.451640\pi\) | ||||
0.151344 | + | 0.988481i | \(0.451640\pi\) | |||||||
\(462\) | 9187.84 | 0.925232 | ||||||||
\(463\) | −2026.10 | −0.203371 | −0.101686 | − | 0.994817i | \(-0.532424\pi\) | ||||
−0.101686 | + | 0.994817i | \(0.532424\pi\) | |||||||
\(464\) | 10211.2 | 1.02164 | ||||||||
\(465\) | 155.402 | 0.0154981 | ||||||||
\(466\) | −2444.24 | −0.242977 | ||||||||
\(467\) | −3284.20 | −0.325428 | −0.162714 | − | 0.986673i | \(-0.552025\pi\) | ||||
−0.162714 | + | 0.986673i | \(0.552025\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 15512.5 | 1.52729 | ||||||||
\(470\) | −30638.9 | −3.00696 | ||||||||
\(471\) | 2970.56 | 0.290608 | ||||||||
\(472\) | −5428.26 | −0.529356 | ||||||||
\(473\) | 19867.8 | 1.93134 | ||||||||
\(474\) | 5635.96 | 0.546136 | ||||||||
\(475\) | 11298.0 | 1.09134 | ||||||||
\(476\) | 4156.46 | 0.400234 | ||||||||
\(477\) | −2769.17 | −0.265811 | ||||||||
\(478\) | −4187.08 | −0.400654 | ||||||||
\(479\) | 13208.5 | 1.25994 | 0.629969 | − | 0.776621i | \(-0.283068\pi\) | ||||
0.629969 | + | 0.776621i | \(0.283068\pi\) | |||||||
\(480\) | −6830.19 | −0.649488 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −2551.26 | −0.241092 | ||||||||
\(483\) | 9822.50 | 0.925340 | ||||||||
\(484\) | 4969.86 | 0.466741 | ||||||||
\(485\) | 12263.7 | 1.14818 | ||||||||
\(486\) | −820.706 | −0.0766008 | ||||||||
\(487\) | 8974.09 | 0.835020 | 0.417510 | − | 0.908672i | \(-0.362903\pi\) | ||||
0.417510 | + | 0.908672i | \(0.362903\pi\) | |||||||
\(488\) | −1977.41 | −0.183428 | ||||||||
\(489\) | −7937.46 | −0.734037 | ||||||||
\(490\) | 2560.81 | 0.236093 | ||||||||
\(491\) | −12889.8 | −1.18474 | −0.592370 | − | 0.805666i | \(-0.701808\pi\) | ||||
−0.592370 | + | 0.805666i | \(0.701808\pi\) | |||||||
\(492\) | 993.234 | 0.0910131 | ||||||||
\(493\) | 9110.87 | 0.832319 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7469.32 | −0.678224 | ||||||||
\(496\) | −262.579 | −0.0237705 | ||||||||
\(497\) | −14182.7 | −1.28004 | ||||||||
\(498\) | 2580.30 | 0.232181 | ||||||||
\(499\) | 7371.92 | 0.661348 | 0.330674 | − | 0.943745i | \(-0.392724\pi\) | ||||
0.330674 | + | 0.943745i | \(0.392724\pi\) | |||||||
\(500\) | 166.568 | 0.0148983 | ||||||||
\(501\) | −886.284 | −0.0790344 | ||||||||
\(502\) | 7606.09 | 0.676248 | ||||||||
\(503\) | 19788.2 | 1.75410 | 0.877049 | − | 0.480400i | \(-0.159509\pi\) | ||||
0.877049 | + | 0.480400i | \(0.159509\pi\) | |||||||
\(504\) | 2396.98 | 0.211845 | ||||||||
\(505\) | 28403.3 | 2.50283 | ||||||||
\(506\) | 34021.0 | 2.98897 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 8078.67 | 0.705577 | ||||||||
\(509\) | 11682.4 | 1.01732 | 0.508658 | − | 0.860968i | \(-0.330142\pi\) | ||||
0.508658 | + | 0.860968i | \(0.330142\pi\) | |||||||
\(510\) | −11313.9 | −0.982327 | ||||||||
\(511\) | 2262.08 | 0.195829 | ||||||||
\(512\) | 1656.08 | 0.142948 | ||||||||
\(513\) | −2502.67 | −0.215391 | ||||||||
\(514\) | 12552.9 | 1.07721 | ||||||||
\(515\) | −24524.0 | −2.09836 | ||||||||
\(516\) | −3844.38 | −0.327984 | ||||||||
\(517\) | 30495.1 | 2.59415 | ||||||||
\(518\) | −14005.7 | −1.18798 | ||||||||
\(519\) | −4486.38 | −0.379442 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −19025.1 | −1.59982 | −0.799908 | − | 0.600122i | \(-0.795119\pi\) | ||||
−0.799908 | + | 0.600122i | \(0.795119\pi\) | |||||||
\(522\) | −3896.95 | −0.326753 | ||||||||
\(523\) | 5345.69 | 0.446942 | 0.223471 | − | 0.974711i | \(-0.428261\pi\) | ||||
0.223471 | + | 0.974711i | \(0.428261\pi\) | |||||||
\(524\) | 576.425 | 0.0480558 | ||||||||
\(525\) | 6277.78 | 0.521876 | ||||||||
\(526\) | −168.708 | −0.0139848 | ||||||||
\(527\) | −234.284 | −0.0193655 | ||||||||
\(528\) | 12620.7 | 1.04024 | ||||||||
\(529\) | 24204.0 | 1.98932 | ||||||||
\(530\) | 16328.2 | 1.33821 | ||||||||
\(531\) | 3149.23 | 0.257372 | ||||||||
\(532\) | −5421.33 | −0.441813 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −1858.34 | −0.150596 | ||||||||
\(535\) | −5063.66 | −0.409199 | ||||||||
\(536\) | 14017.1 | 1.12957 | ||||||||
\(537\) | −2355.29 | −0.189271 | ||||||||
\(538\) | 11555.5 | 0.926012 | ||||||||
\(539\) | −2548.79 | −0.203681 | ||||||||
\(540\) | 1445.30 | 0.115177 | ||||||||
\(541\) | −3058.01 | −0.243021 | −0.121510 | − | 0.992590i | \(-0.538774\pi\) | ||||
−0.121510 | + | 0.992590i | \(0.538774\pi\) | |||||||
\(542\) | −9993.34 | −0.791975 | ||||||||
\(543\) | 3861.02 | 0.305142 | ||||||||
\(544\) | 10297.2 | 0.811561 | ||||||||
\(545\) | −25261.7 | −1.98549 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17921.1 | 1.40082 | 0.700410 | − | 0.713740i | \(-0.253000\pi\) | ||||
0.700410 | + | 0.713740i | \(0.253000\pi\) | |||||||
\(548\) | 10139.2 | 0.790378 | ||||||||
\(549\) | 1147.20 | 0.0891827 | ||||||||
\(550\) | 21743.6 | 1.68573 | ||||||||
\(551\) | −11883.4 | −0.918786 | ||||||||
\(552\) | 8875.62 | 0.684369 | ||||||||
\(553\) | 9549.67 | 0.734346 | ||||||||
\(554\) | −25199.0 | −1.93250 | ||||||||
\(555\) | 11386.0 | 0.870828 | ||||||||
\(556\) | −8704.79 | −0.663967 | ||||||||
\(557\) | 9106.04 | 0.692702 | 0.346351 | − | 0.938105i | \(-0.387421\pi\) | ||||
0.346351 | + | 0.938105i | \(0.387421\pi\) | |||||||
\(558\) | 100.209 | 0.00760252 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −21485.6 | −1.62131 | ||||||||
\(561\) | 11260.8 | 0.847468 | ||||||||
\(562\) | −15968.4 | −1.19856 | ||||||||
\(563\) | 11327.9 | 0.847985 | 0.423992 | − | 0.905666i | \(-0.360628\pi\) | ||||
0.423992 | + | 0.905666i | \(0.360628\pi\) | |||||||
\(564\) | −5900.74 | −0.440542 | ||||||||
\(565\) | 6754.97 | 0.502980 | ||||||||
\(566\) | −9725.84 | −0.722275 | ||||||||
\(567\) | −1390.62 | −0.102999 | ||||||||
\(568\) | −12815.5 | −0.946701 | ||||||||
\(569\) | 1963.27 | 0.144647 | 0.0723237 | − | 0.997381i | \(-0.476959\pi\) | ||||
0.0723237 | + | 0.997381i | \(0.476959\pi\) | |||||||
\(570\) | 14756.8 | 1.08438 | ||||||||
\(571\) | −2270.35 | −0.166394 | −0.0831971 | − | 0.996533i | \(-0.526513\pi\) | ||||
−0.0831971 | + | 0.996533i | \(0.526513\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1399.36 | −0.102023 | ||||||||
\(574\) | 5634.97 | 0.409755 | ||||||||
\(575\) | 23245.6 | 1.68592 | ||||||||
\(576\) | 1330.28 | 0.0962297 | ||||||||
\(577\) | −13949.6 | −1.00646 | −0.503231 | − | 0.864152i | \(-0.667855\pi\) | ||||
−0.503231 | + | 0.864152i | \(0.667855\pi\) | |||||||
\(578\) | 463.708 | 0.0333697 | ||||||||
\(579\) | −7910.96 | −0.567821 | ||||||||
\(580\) | 6862.69 | 0.491306 | ||||||||
\(581\) | 4372.10 | 0.312195 | ||||||||
\(582\) | 7908.14 | 0.563236 | ||||||||
\(583\) | −16251.6 | −1.15450 | ||||||||
\(584\) | 2044.02 | 0.144832 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 27697.8 | 1.95253 | ||||||||
\(587\) | −26731.4 | −1.87960 | −0.939799 | − | 0.341727i | \(-0.888988\pi\) | ||||
−0.939799 | + | 0.341727i | \(0.888988\pi\) | |||||||
\(588\) | 493.186 | 0.0345895 | ||||||||
\(589\) | 305.580 | 0.0213773 | ||||||||
\(590\) | −18569.2 | −1.29573 | ||||||||
\(591\) | −11030.7 | −0.767754 | ||||||||
\(592\) | −19238.7 | −1.33565 | ||||||||
\(593\) | 10508.6 | 0.727715 | 0.363858 | − | 0.931455i | \(-0.381459\pi\) | ||||
0.363858 | + | 0.931455i | \(0.381459\pi\) | |||||||
\(594\) | −4816.52 | −0.332701 | ||||||||
\(595\) | −19170.4 | −1.32086 | ||||||||
\(596\) | 1446.27 | 0.0993987 | ||||||||
\(597\) | −661.670 | −0.0453607 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1935.87 | −0.132049 | −0.0660246 | − | 0.997818i | \(-0.521032\pi\) | ||||
−0.0660246 | + | 0.997818i | \(0.521032\pi\) | |||||||
\(600\) | 5672.61 | 0.385972 | ||||||||
\(601\) | −16155.5 | −1.09650 | −0.548249 | − | 0.836315i | \(-0.684705\pi\) | ||||
−0.548249 | + | 0.836315i | \(0.684705\pi\) | |||||||
\(602\) | −21810.6 | −1.47663 | ||||||||
\(603\) | −8132.08 | −0.549194 | ||||||||
\(604\) | 144.185 | 0.00971327 | ||||||||
\(605\) | −22922.0 | −1.54035 | ||||||||
\(606\) | 18315.6 | 1.22776 | ||||||||
\(607\) | −1698.75 | −0.113592 | −0.0567959 | − | 0.998386i | \(-0.518088\pi\) | ||||
−0.0567959 | + | 0.998386i | \(0.518088\pi\) | |||||||
\(608\) | −13430.8 | −0.895873 | ||||||||
\(609\) | −6603.07 | −0.439359 | ||||||||
\(610\) | −6764.38 | −0.448987 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −2178.93 | −0.143918 | ||||||||
\(613\) | −8627.42 | −0.568448 | −0.284224 | − | 0.958758i | \(-0.591736\pi\) | ||||
−0.284224 | + | 0.958758i | \(0.591736\pi\) | |||||||
\(614\) | 6953.46 | 0.457034 | ||||||||
\(615\) | −4580.99 | −0.300363 | ||||||||
\(616\) | 14067.3 | 0.920109 | ||||||||
\(617\) | −21415.4 | −1.39733 | −0.698664 | − | 0.715450i | \(-0.746222\pi\) | ||||
−0.698664 | + | 0.715450i | \(0.746222\pi\) | |||||||
\(618\) | −15814.0 | −1.02934 | ||||||||
\(619\) | −17396.0 | −1.12957 | −0.564784 | − | 0.825238i | \(-0.691041\pi\) | ||||
−0.564784 | + | 0.825238i | \(0.691041\pi\) | |||||||
\(620\) | −176.473 | −0.0114312 | ||||||||
\(621\) | −5149.22 | −0.332739 | ||||||||
\(622\) | 6288.96 | 0.405409 | ||||||||
\(623\) | −3148.81 | −0.202495 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16004.3 | −1.02427 | ||||||||
\(626\) | −864.261 | −0.0551802 | ||||||||
\(627\) | −14687.6 | −0.935510 | ||||||||
\(628\) | −3373.34 | −0.214349 | ||||||||
\(629\) | −17165.6 | −1.08814 | ||||||||
\(630\) | 8199.68 | 0.518545 | ||||||||
\(631\) | −13059.2 | −0.823898 | −0.411949 | − | 0.911207i | \(-0.635152\pi\) | ||||
−0.411949 | + | 0.911207i | \(0.635152\pi\) | |||||||
\(632\) | 8629.09 | 0.543112 | ||||||||
\(633\) | −4157.78 | −0.261070 | ||||||||
\(634\) | 21161.6 | 1.32561 | ||||||||
\(635\) | −37260.4 | −2.32856 | ||||||||
\(636\) | 3144.65 | 0.196059 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −22870.2 | −1.41919 | ||||||||
\(639\) | 7434.95 | 0.460285 | ||||||||
\(640\) | −26057.7 | −1.60941 | ||||||||
\(641\) | 22397.7 | 1.38012 | 0.690060 | − | 0.723752i | \(-0.257584\pi\) | ||||
0.690060 | + | 0.723752i | \(0.257584\pi\) | |||||||
\(642\) | −3265.26 | −0.200731 | ||||||||
\(643\) | 5878.08 | 0.360511 | 0.180256 | − | 0.983620i | \(-0.442307\pi\) | ||||
0.180256 | + | 0.983620i | \(0.442307\pi\) | |||||||
\(644\) | −11154.3 | −0.682519 | ||||||||
\(645\) | 17731.0 | 1.08242 | ||||||||
\(646\) | −22247.5 | −1.35498 | ||||||||
\(647\) | −20768.3 | −1.26196 | −0.630979 | − | 0.775800i | \(-0.717347\pi\) | ||||
−0.630979 | + | 0.775800i | \(0.717347\pi\) | |||||||
\(648\) | −1256.56 | −0.0761767 | ||||||||
\(649\) | 18482.0 | 1.11785 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 169.797 | 0.0102225 | ||||||||
\(652\) | 9013.69 | 0.541416 | ||||||||
\(653\) | 15516.4 | 0.929865 | 0.464933 | − | 0.885346i | \(-0.346079\pi\) | ||||
0.464933 | + | 0.885346i | \(0.346079\pi\) | |||||||
\(654\) | −16289.7 | −0.973975 | ||||||||
\(655\) | −2658.58 | −0.158594 | ||||||||
\(656\) | 7740.39 | 0.460688 | ||||||||
\(657\) | −1185.84 | −0.0704172 | ||||||||
\(658\) | −33477.0 | −1.98339 | ||||||||
\(659\) | 24025.0 | 1.42015 | 0.710077 | − | 0.704124i | \(-0.248660\pi\) | ||||
0.710077 | + | 0.704124i | \(0.248660\pi\) | |||||||
\(660\) | 8482.08 | 0.500249 | ||||||||
\(661\) | −10778.8 | −0.634262 | −0.317131 | − | 0.948382i | \(-0.602719\pi\) | ||||
−0.317131 | + | 0.948382i | \(0.602719\pi\) | |||||||
\(662\) | 3620.33 | 0.212550 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3950.63 | 0.230895 | ||||||||
\(665\) | 25004.2 | 1.45808 | ||||||||
\(666\) | 7342.17 | 0.427182 | ||||||||
\(667\) | −24450.0 | −1.41935 | ||||||||
\(668\) | 1006.45 | 0.0582948 | ||||||||
\(669\) | 335.541 | 0.0193913 | ||||||||
\(670\) | 47950.2 | 2.76489 | ||||||||
\(671\) | 6732.63 | 0.387348 | ||||||||
\(672\) | −7462.86 | −0.428402 | ||||||||
\(673\) | 22345.9 | 1.27990 | 0.639950 | − | 0.768417i | \(-0.278955\pi\) | ||||
0.639950 | + | 0.768417i | \(0.278955\pi\) | |||||||
\(674\) | −18818.9 | −1.07549 | ||||||||
\(675\) | −3290.98 | −0.187659 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12326.7 | 0.699782 | 0.349891 | − | 0.936790i | \(-0.386219\pi\) | ||||
0.349891 | + | 0.936790i | \(0.386219\pi\) | |||||||
\(678\) | 4355.88 | 0.246735 | ||||||||
\(679\) | 13399.7 | 0.757339 | ||||||||
\(680\) | −17322.4 | −0.976888 | ||||||||
\(681\) | −14972.9 | −0.842529 | ||||||||
\(682\) | 588.104 | 0.0330201 | ||||||||
\(683\) | −27452.5 | −1.53798 | −0.768989 | − | 0.639262i | \(-0.779240\pi\) | ||||
−0.768989 | + | 0.639262i | \(0.779240\pi\) | |||||||
\(684\) | 2842.01 | 0.158870 | ||||||||
\(685\) | −46764.2 | −2.60842 | ||||||||
\(686\) | 22686.3 | 1.26264 | ||||||||
\(687\) | 17362.7 | 0.964232 | ||||||||
\(688\) | −29959.7 | −1.66018 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 30362.0 | 1.67516 | ||||||||
\(691\) | −18663.6 | −1.02749 | −0.513746 | − | 0.857942i | \(-0.671743\pi\) | ||||
−0.513746 | + | 0.857942i | \(0.671743\pi\) | |||||||
\(692\) | 5094.69 | 0.279871 | ||||||||
\(693\) | −8161.19 | −0.447356 | ||||||||
\(694\) | −6428.65 | −0.351626 | ||||||||
\(695\) | 40148.2 | 2.19123 | ||||||||
\(696\) | −5966.54 | −0.324944 | ||||||||
\(697\) | 6906.31 | 0.375316 | ||||||||
\(698\) | 3705.59 | 0.200943 | ||||||||
\(699\) | 2171.12 | 0.117481 | ||||||||
\(700\) | −7128.98 | −0.384929 | ||||||||
\(701\) | −4131.00 | −0.222576 | −0.111288 | − | 0.993788i | \(-0.535498\pi\) | ||||
−0.111288 | + | 0.993788i | \(0.535498\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 22389.3 | 1.20118 | ||||||||
\(704\) | 7807.07 | 0.417955 | ||||||||
\(705\) | 27215.3 | 1.45389 | ||||||||
\(706\) | 18308.5 | 0.975990 | ||||||||
\(707\) | 31034.3 | 1.65087 | ||||||||
\(708\) | −3576.23 | −0.189835 | ||||||||
\(709\) | 33578.1 | 1.77863 | 0.889317 | − | 0.457291i | \(-0.151180\pi\) | ||||
0.889317 | + | 0.457291i | \(0.151180\pi\) | |||||||
\(710\) | −43839.7 | −2.31729 | ||||||||
\(711\) | −5006.20 | −0.264061 | ||||||||
\(712\) | −2845.27 | −0.149762 | ||||||||
\(713\) | 628.728 | 0.0330239 | ||||||||
\(714\) | −12361.9 | −0.647943 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2674.64 | 0.139603 | ||||||||
\(717\) | 3719.21 | 0.193719 | ||||||||
\(718\) | 13122.5 | 0.682073 | ||||||||
\(719\) | 22527.2 | 1.16846 | 0.584229 | − | 0.811589i | \(-0.301397\pi\) | ||||
0.584229 | + | 0.811589i | \(0.301397\pi\) | |||||||
\(720\) | 11263.4 | 0.583001 | ||||||||
\(721\) | −26795.6 | −1.38408 | ||||||||
\(722\) | 5852.12 | 0.301653 | ||||||||
\(723\) | 2266.18 | 0.116570 | ||||||||
\(724\) | −4384.53 | −0.225069 | ||||||||
\(725\) | −15626.6 | −0.800491 | ||||||||
\(726\) | −14781.0 | −0.755613 | ||||||||
\(727\) | 241.718 | 0.0123312 | 0.00616562 | − | 0.999981i | \(-0.498037\pi\) | ||||
0.00616562 | + | 0.999981i | \(0.498037\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 6992.24 | 0.354513 | ||||||||
\(731\) | −26731.4 | −1.35252 | ||||||||
\(732\) | −1302.75 | −0.0657800 | ||||||||
\(733\) | −17235.4 | −0.868490 | −0.434245 | − | 0.900795i | \(-0.642985\pi\) | ||||
−0.434245 | + | 0.900795i | \(0.642985\pi\) | |||||||
\(734\) | −13132.2 | −0.660377 | ||||||||
\(735\) | −2274.67 | −0.114153 | ||||||||
\(736\) | −27633.7 | −1.38396 | ||||||||
\(737\) | −47725.1 | −2.38532 | ||||||||
\(738\) | −2954.01 | −0.147342 | ||||||||
\(739\) | −34304.3 | −1.70758 | −0.853792 | − | 0.520615i | \(-0.825703\pi\) | ||||
−0.853792 | + | 0.520615i | \(0.825703\pi\) | |||||||
\(740\) | −12929.8 | −0.642312 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 17840.7 | 0.882686 | ||||||||
\(743\) | 2114.59 | 0.104410 | 0.0522052 | − | 0.998636i | \(-0.483375\pi\) | ||||
0.0522052 | + | 0.998636i | \(0.483375\pi\) | |||||||
\(744\) | 153.428 | 0.00756043 | ||||||||
\(745\) | −6670.49 | −0.328037 | ||||||||
\(746\) | 33641.8 | 1.65109 | ||||||||
\(747\) | −2291.97 | −0.112261 | ||||||||
\(748\) | −12787.6 | −0.625082 | ||||||||
\(749\) | −5532.70 | −0.269907 | ||||||||
\(750\) | −495.394 | −0.0241190 | ||||||||
\(751\) | −40958.7 | −1.99015 | −0.995077 | − | 0.0991024i | \(-0.968403\pi\) | ||||
−0.995077 | + | 0.0991024i | \(0.968403\pi\) | |||||||
\(752\) | −45985.1 | −2.22993 | ||||||||
\(753\) | −6756.18 | −0.326971 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −665.010 | −0.0320559 | ||||||||
\(756\) | 1579.17 | 0.0759708 | ||||||||
\(757\) | 10530.8 | 0.505613 | 0.252807 | − | 0.967517i | \(-0.418646\pi\) | ||||
0.252807 | + | 0.967517i | \(0.418646\pi\) | |||||||
\(758\) | 17860.5 | 0.855834 | ||||||||
\(759\) | −30219.5 | −1.44519 | ||||||||
\(760\) | 22593.9 | 1.07838 | ||||||||
\(761\) | −787.955 | −0.0375340 | −0.0187670 | − | 0.999824i | \(-0.505974\pi\) | ||||
−0.0187670 | + | 0.999824i | \(0.505974\pi\) | |||||||
\(762\) | −24027.0 | −1.14227 | ||||||||
\(763\) | −27601.6 | −1.30963 | ||||||||
\(764\) | 1589.10 | 0.0752506 | ||||||||
\(765\) | 10049.7 | 0.474962 | ||||||||
\(766\) | 2326.83 | 0.109755 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −13255.7 | −0.622816 | ||||||||
\(769\) | 5227.62 | 0.245140 | 0.122570 | − | 0.992460i | \(-0.460886\pi\) | ||||
0.122570 | + | 0.992460i | \(0.460886\pi\) | |||||||
\(770\) | 48121.9 | 2.25220 | ||||||||
\(771\) | −11150.2 | −0.520838 | ||||||||
\(772\) | 8983.61 | 0.418818 | ||||||||
\(773\) | 4516.79 | 0.210165 | 0.105082 | − | 0.994464i | \(-0.466489\pi\) | ||||
0.105082 | + | 0.994464i | \(0.466489\pi\) | |||||||
\(774\) | 11433.7 | 0.530976 | ||||||||
\(775\) | 401.834 | 0.0186249 | ||||||||
\(776\) | 12108.0 | 0.560117 | ||||||||
\(777\) | 12440.7 | 0.574398 | ||||||||
\(778\) | 7101.21 | 0.327237 | ||||||||
\(779\) | −9008.00 | −0.414307 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 43633.9 | 1.99916 | ||||||||
\(782\) | −45773.9 | −2.09318 | ||||||||
\(783\) | 3461.51 | 0.157987 | ||||||||
\(784\) | 3843.45 | 0.175084 | ||||||||
\(785\) | 15558.5 | 0.707397 | ||||||||
\(786\) | −1714.36 | −0.0777980 | ||||||||
\(787\) | 6800.09 | 0.308001 | 0.154001 | − | 0.988071i | \(-0.450784\pi\) | ||||
0.154001 | + | 0.988071i | \(0.450784\pi\) | |||||||
\(788\) | 12526.4 | 0.566285 | ||||||||
\(789\) | 149.856 | 0.00676176 | ||||||||
\(790\) | 29518.7 | 1.32940 | ||||||||
\(791\) | 7380.67 | 0.331765 | ||||||||
\(792\) | −7374.46 | −0.330859 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −38011.8 | −1.69898 | ||||||||
\(795\) | −14503.7 | −0.647036 | ||||||||
\(796\) | 751.385 | 0.0334575 | ||||||||
\(797\) | −40553.3 | −1.80235 | −0.901174 | − | 0.433457i | \(-0.857293\pi\) | ||||
−0.901174 | + | 0.433457i | \(0.857293\pi\) | |||||||
\(798\) | 16123.7 | 0.715256 | ||||||||
\(799\) | −41029.9 | −1.81669 | ||||||||
\(800\) | −17661.3 | −0.780528 | ||||||||
\(801\) | 1650.69 | 0.0728144 | ||||||||
\(802\) | −11899.3 | −0.523913 | ||||||||
\(803\) | −6959.41 | −0.305844 | ||||||||
\(804\) | 9234.70 | 0.405078 | ||||||||
\(805\) | 51445.9 | 2.25246 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −10264.3 | −0.447733 | ||||||||
\(808\) | 28042.6 | 1.22096 | ||||||||
\(809\) | −6517.83 | −0.283257 | −0.141628 | − | 0.989920i | \(-0.545234\pi\) | ||||
−0.141628 | + | 0.989920i | \(0.545234\pi\) | |||||||
\(810\) | −4298.50 | −0.186461 | ||||||||
\(811\) | 2898.99 | 0.125521 | 0.0627603 | − | 0.998029i | \(-0.480010\pi\) | ||||
0.0627603 | + | 0.998029i | \(0.480010\pi\) | |||||||
\(812\) | 7498.37 | 0.324066 | ||||||||
\(813\) | 8876.68 | 0.382926 | ||||||||
\(814\) | 43089.3 | 1.85538 | ||||||||
\(815\) | −41572.9 | −1.78679 | ||||||||
\(816\) | −16980.7 | −0.728484 | ||||||||
\(817\) | 34866.1 | 1.49303 | ||||||||
\(818\) | −21502.7 | −0.919099 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5202.12 | 0.221544 | ||||||||
\(821\) | 716.621 | 0.0304632 | 0.0152316 | − | 0.999884i | \(-0.495151\pi\) | ||||
0.0152316 | + | 0.999884i | \(0.495151\pi\) | |||||||
\(822\) | −30155.4 | −1.27955 | ||||||||
\(823\) | 15510.0 | 0.656920 | 0.328460 | − | 0.944518i | \(-0.393470\pi\) | ||||
0.328460 | + | 0.944518i | \(0.393470\pi\) | |||||||
\(824\) | −24212.5 | −1.02364 | ||||||||
\(825\) | −19314.0 | −0.815062 | ||||||||
\(826\) | −20289.2 | −0.854664 | ||||||||
\(827\) | −24063.2 | −1.01180 | −0.505901 | − | 0.862591i | \(-0.668840\pi\) | ||||
−0.505901 | + | 0.862591i | \(0.668840\pi\) | |||||||
\(828\) | 5847.40 | 0.245424 | ||||||||
\(829\) | 10037.8 | 0.420540 | 0.210270 | − | 0.977643i | \(-0.432566\pi\) | ||||
0.210270 | + | 0.977643i | \(0.432566\pi\) | |||||||
\(830\) | 13514.5 | 0.565173 | ||||||||
\(831\) | 22383.2 | 0.934376 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3429.30 | 0.142639 | ||||||||
\(834\) | 25889.2 | 1.07490 | ||||||||
\(835\) | −4641.96 | −0.192385 | ||||||||
\(836\) | 16679.0 | 0.690020 | ||||||||
\(837\) | −89.0121 | −0.00367587 | ||||||||
\(838\) | 30125.6 | 1.24185 | ||||||||
\(839\) | −4005.19 | −0.164809 | −0.0824044 | − | 0.996599i | \(-0.526260\pi\) | ||||
−0.0824044 | + | 0.996599i | \(0.526260\pi\) | |||||||
\(840\) | 12554.3 | 0.515674 | ||||||||
\(841\) | −7952.74 | −0.326079 | ||||||||
\(842\) | −3683.74 | −0.150772 | ||||||||
\(843\) | 14184.1 | 0.579510 | ||||||||
\(844\) | 4721.53 | 0.192562 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 17549.6 | 0.713199 | ||||||||
\(847\) | −25045.2 | −1.01601 | ||||||||
\(848\) | 24506.6 | 0.992406 | ||||||||
\(849\) | 8639.08 | 0.349225 | ||||||||
\(850\) | −29255.1 | −1.18052 | ||||||||
\(851\) | 46065.8 | 1.85560 | ||||||||
\(852\) | −8443.06 | −0.339500 | ||||||||
\(853\) | 44062.6 | 1.76867 | 0.884334 | − | 0.466856i | \(-0.154613\pi\) | ||||
0.884334 | + | 0.466856i | \(0.154613\pi\) | |||||||
\(854\) | −7390.96 | −0.296152 | ||||||||
\(855\) | −13107.9 | −0.524305 | ||||||||
\(856\) | −4999.36 | −0.199620 | ||||||||
\(857\) | 3365.44 | 0.134144 | 0.0670718 | − | 0.997748i | \(-0.478634\pi\) | ||||
0.0670718 | + | 0.997748i | \(0.478634\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −40969.3 | −1.62731 | −0.813653 | − | 0.581351i | \(-0.802524\pi\) | ||||
−0.813653 | + | 0.581351i | \(0.802524\pi\) | |||||||
\(860\) | −20135.2 | −0.798377 | ||||||||
\(861\) | −5005.32 | −0.198119 | ||||||||
\(862\) | −12700.4 | −0.501831 | ||||||||
\(863\) | −18132.8 | −0.715236 | −0.357618 | − | 0.933868i | \(-0.616411\pi\) | ||||
−0.357618 | + | 0.933868i | \(0.616411\pi\) | |||||||
\(864\) | 3912.24 | 0.154047 | ||||||||
\(865\) | −23497.7 | −0.923637 | ||||||||
\(866\) | −13796.8 | −0.541380 | ||||||||
\(867\) | −411.893 | −0.0161345 | ||||||||
\(868\) | −192.819 | −0.00753999 | ||||||||
\(869\) | −29380.1 | −1.14690 | ||||||||
\(870\) | −20410.5 | −0.795381 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −24940.9 | −0.968582 | ||||||||
\(873\) | −7024.49 | −0.272329 | ||||||||
\(874\) | 59703.5 | 2.31064 | ||||||||
\(875\) | −839.404 | −0.0324309 | ||||||||
\(876\) | 1346.63 | 0.0519388 | ||||||||
\(877\) | 33047.6 | 1.27245 | 0.636226 | − | 0.771503i | \(-0.280495\pi\) | ||||
0.636226 | + | 0.771503i | \(0.280495\pi\) | |||||||
\(878\) | 31698.0 | 1.21840 | ||||||||
\(879\) | −24602.8 | −0.944064 | ||||||||
\(880\) | 66101.9 | 2.53215 | ||||||||
\(881\) | 1349.22 | 0.0515965 | 0.0257982 | − | 0.999667i | \(-0.491787\pi\) | ||||
0.0257982 | + | 0.999667i | \(0.491787\pi\) | |||||||
\(882\) | −1466.80 | −0.0559973 | ||||||||
\(883\) | −33934.5 | −1.29330 | −0.646651 | − | 0.762786i | \(-0.723831\pi\) | ||||
−0.646651 | + | 0.762786i | \(0.723831\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 16494.3 | 0.626495 | ||||||||
\(886\) | 19438.3 | 0.737067 | ||||||||
\(887\) | −45609.5 | −1.72651 | −0.863256 | − | 0.504766i | \(-0.831579\pi\) | ||||
−0.863256 | + | 0.504766i | \(0.831579\pi\) | |||||||
\(888\) | 11241.4 | 0.424817 | ||||||||
\(889\) | −40711.8 | −1.53592 | ||||||||
\(890\) | −9733.19 | −0.366581 | ||||||||
\(891\) | 4278.32 | 0.160863 | ||||||||
\(892\) | −381.037 | −0.0143028 | ||||||||
\(893\) | 53515.9 | 2.00542 | ||||||||
\(894\) | −4301.40 | −0.160918 | ||||||||
\(895\) | −12336.0 | −0.460722 | ||||||||
\(896\) | −28471.4 | −1.06157 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3730.90 | 0.138643 | ||||||||
\(899\) | −422.655 | −0.0156800 | ||||||||
\(900\) | 3737.21 | 0.138415 | ||||||||
\(901\) | 21865.8 | 0.808498 | ||||||||
\(902\) | −17336.3 | −0.639952 | ||||||||
\(903\) | 19373.4 | 0.713962 | ||||||||
\(904\) | 6669.18 | 0.245369 | ||||||||
\(905\) | 20222.3 | 0.742777 | ||||||||
\(906\) | −428.826 | −0.0157249 | ||||||||
\(907\) | 8620.99 | 0.315607 | 0.157803 | − | 0.987471i | \(-0.449559\pi\) | ||||
0.157803 | + | 0.987471i | \(0.449559\pi\) | |||||||
\(908\) | 17003.1 | 0.621438 | ||||||||
\(909\) | −16269.0 | −0.593629 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −43993.6 | −1.59997 | −0.799986 | − | 0.600019i | \(-0.795160\pi\) | ||||
−0.799986 | + | 0.600019i | \(0.795160\pi\) | |||||||
\(912\) | 22148.1 | 0.804164 | ||||||||
\(913\) | −13451.0 | −0.487584 | ||||||||
\(914\) | −45758.6 | −1.65597 | ||||||||
\(915\) | 6008.53 | 0.217088 | ||||||||
\(916\) | −19716.9 | −0.711205 | ||||||||
\(917\) | −2904.84 | −0.104609 | ||||||||
\(918\) | 6480.43 | 0.232991 | ||||||||
\(919\) | 15176.0 | 0.544733 | 0.272366 | − | 0.962194i | \(-0.412194\pi\) | ||||
0.272366 | + | 0.962194i | \(0.412194\pi\) | |||||||
\(920\) | 46486.6 | 1.66589 | ||||||||
\(921\) | −6176.47 | −0.220979 | ||||||||
\(922\) | 10118.8 | 0.361436 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 9267.76 | 0.329964 | ||||||||
\(925\) | 29441.7 | 1.04653 | ||||||||
\(926\) | −6842.94 | −0.242843 | ||||||||
\(927\) | 14047.0 | 0.497695 | ||||||||
\(928\) | 18576.4 | 0.657114 | ||||||||
\(929\) | −29749.7 | −1.05065 | −0.525326 | − | 0.850901i | \(-0.676057\pi\) | ||||
−0.525326 | + | 0.850901i | \(0.676057\pi\) | |||||||
\(930\) | 524.853 | 0.0185060 | ||||||||
\(931\) | −4472.88 | −0.157457 | ||||||||
\(932\) | −2465.50 | −0.0866526 | ||||||||
\(933\) | −5586.23 | −0.196018 | ||||||||
\(934\) | −11092.0 | −0.388589 | ||||||||
\(935\) | 58978.9 | 2.06291 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −46456.0 | −1.61969 | −0.809846 | − | 0.586643i | \(-0.800449\pi\) | ||||
−0.809846 | + | 0.586643i | \(0.800449\pi\) | |||||||
\(938\) | 52391.8 | 1.82372 | ||||||||
\(939\) | 767.688 | 0.0266800 | ||||||||
\(940\) | −30905.5 | −1.07237 | ||||||||
\(941\) | 3243.36 | 0.112360 | 0.0561799 | − | 0.998421i | \(-0.482108\pi\) | ||||
0.0561799 | + | 0.998421i | \(0.482108\pi\) | |||||||
\(942\) | 10032.7 | 0.347011 | ||||||||
\(943\) | −18533.9 | −0.640027 | ||||||||
\(944\) | −27870.0 | −0.960901 | ||||||||
\(945\) | −7283.45 | −0.250720 | ||||||||
\(946\) | 67101.5 | 2.30619 | ||||||||
\(947\) | 53344.1 | 1.83047 | 0.915233 | − | 0.402926i | \(-0.132007\pi\) | ||||
0.915233 | + | 0.402926i | \(0.132007\pi\) | |||||||
\(948\) | 5684.99 | 0.194768 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 38157.8 | 1.30316 | ||||||||
\(951\) | −18797.0 | −0.640942 | ||||||||
\(952\) | −18927.0 | −0.644356 | ||||||||
\(953\) | 53496.9 | 1.81840 | 0.909200 | − | 0.416360i | \(-0.136694\pi\) | ||||
0.909200 | + | 0.416360i | \(0.136694\pi\) | |||||||
\(954\) | −9352.58 | −0.317402 | ||||||||
\(955\) | −7329.22 | −0.248343 | ||||||||
\(956\) | −4223.50 | −0.142885 | ||||||||
\(957\) | 20314.7 | 0.686188 | ||||||||
\(958\) | 44610.1 | 1.50448 | ||||||||
\(959\) | −51095.9 | −1.72051 | ||||||||
\(960\) | 6967.42 | 0.234242 | ||||||||
\(961\) | −29780.1 | −0.999635 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2900.39 | 0.0970549 | ||||||||
\(964\) | −2573.45 | −0.0859805 | ||||||||
\(965\) | −41434.1 | −1.38219 | ||||||||
\(966\) | 33174.4 | 1.10494 | ||||||||
\(967\) | 48822.0 | 1.62359 | 0.811794 | − | 0.583944i | \(-0.198491\pi\) | ||||
0.811794 | + | 0.583944i | \(0.198491\pi\) | |||||||
\(968\) | −22630.9 | −0.751429 | ||||||||
\(969\) | 19761.5 | 0.655141 | ||||||||
\(970\) | 41419.4 | 1.37103 | ||||||||
\(971\) | 36228.1 | 1.19734 | 0.598670 | − | 0.800996i | \(-0.295696\pi\) | ||||
0.598670 | + | 0.800996i | \(0.295696\pi\) | |||||||
\(972\) | −827.845 | −0.0273180 | ||||||||
\(973\) | 43867.1 | 1.44534 | ||||||||
\(974\) | 30309.0 | 0.997087 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −10152.5 | −0.332964 | ||||||||
\(977\) | −46689.8 | −1.52890 | −0.764451 | − | 0.644681i | \(-0.776990\pi\) | ||||
−0.764451 | + | 0.644681i | \(0.776990\pi\) | |||||||
\(978\) | −26807.9 | −0.876505 | ||||||||
\(979\) | 9687.50 | 0.316255 | ||||||||
\(980\) | 2583.09 | 0.0841977 | ||||||||
\(981\) | 14469.5 | 0.470924 | ||||||||
\(982\) | −43533.8 | −1.41468 | ||||||||
\(983\) | −11501.9 | −0.373197 | −0.186598 | − | 0.982436i | \(-0.559746\pi\) | ||||
−0.186598 | + | 0.982436i | \(0.559746\pi\) | |||||||
\(984\) | −4522.81 | −0.146526 | ||||||||
\(985\) | −57774.0 | −1.86886 | ||||||||
\(986\) | 30771.0 | 0.993862 | ||||||||
\(987\) | 29736.3 | 0.958983 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 71736.6 | 2.30646 | ||||||||
\(990\) | −25226.8 | −0.809859 | ||||||||
\(991\) | 7137.46 | 0.228788 | 0.114394 | − | 0.993435i | \(-0.463507\pi\) | ||||
0.114394 | + | 0.993435i | \(0.463507\pi\) | |||||||
\(992\) | −477.690 | −0.0152890 | ||||||||
\(993\) | −3215.80 | −0.102770 | ||||||||
\(994\) | −47900.5 | −1.52848 | ||||||||
\(995\) | −3465.53 | −0.110417 | ||||||||
\(996\) | 2602.74 | 0.0828022 | ||||||||
\(997\) | −18389.5 | −0.584152 | −0.292076 | − | 0.956395i | \(-0.594346\pi\) | ||||
−0.292076 | + | 0.956395i | \(0.594346\pi\) | |||||||
\(998\) | 24897.9 | 0.789708 | ||||||||
\(999\) | −6521.75 | −0.206546 |
(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.a.q.1.7 | yes | 9 | |
3.2 | odd | 2 | 1521.4.a.be.1.3 | 9 | |||
13.5 | odd | 4 | 507.4.b.j.337.4 | 18 | |||
13.8 | odd | 4 | 507.4.b.j.337.15 | 18 | |||
13.12 | even | 2 | 507.4.a.n.1.3 | ✓ | 9 | ||
39.38 | odd | 2 | 1521.4.a.bj.1.7 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
507.4.a.n.1.3 | ✓ | 9 | 13.12 | even | 2 | ||
507.4.a.q.1.7 | yes | 9 | 1.1 | even | 1 | trivial | |
507.4.b.j.337.4 | 18 | 13.5 | odd | 4 | |||
507.4.b.j.337.15 | 18 | 13.8 | odd | 4 | |||
1521.4.a.be.1.3 | 9 | 3.2 | odd | 2 | |||
1521.4.a.bj.1.7 | 9 | 39.38 | odd | 2 |