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 | 1.9 | ||
Root | \(-4.48584\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.48584 | 1.93954 | 0.969769 | − | 0.244025i | \(-0.0784677\pi\) | ||||
0.969769 | + | 0.244025i | \(0.0784677\pi\) | |||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 22.0945 | 2.76181 | ||||||||
\(5\) | 13.3185 | 1.19125 | 0.595624 | − | 0.803264i | \(-0.296905\pi\) | ||||
0.595624 | + | 0.803264i | \(0.296905\pi\) | |||||||
\(6\) | −16.4575 | −1.11979 | ||||||||
\(7\) | 21.4234 | 1.15675 | 0.578377 | − | 0.815770i | \(-0.303686\pi\) | ||||
0.578377 | + | 0.815770i | \(0.303686\pi\) | |||||||
\(8\) | 77.3200 | 3.41709 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 73.0635 | 2.31047 | ||||||||
\(11\) | −19.0520 | −0.522217 | −0.261108 | − | 0.965310i | \(-0.584088\pi\) | ||||
−0.261108 | + | 0.965310i | \(0.584088\pi\) | |||||||
\(12\) | −66.2834 | −1.59453 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 117.525 | 2.24357 | ||||||||
\(15\) | −39.9556 | −0.687767 | ||||||||
\(16\) | 247.410 | 3.86578 | ||||||||
\(17\) | −71.7906 | −1.02422 | −0.512111 | − | 0.858919i | \(-0.671136\pi\) | ||||
−0.512111 | + | 0.858919i | \(0.671136\pi\) | |||||||
\(18\) | 49.3726 | 0.646513 | ||||||||
\(19\) | −102.134 | −1.23322 | −0.616611 | − | 0.787268i | \(-0.711495\pi\) | ||||
−0.616611 | + | 0.787268i | \(0.711495\pi\) | |||||||
\(20\) | 294.266 | 3.29000 | ||||||||
\(21\) | −64.2701 | −0.667852 | ||||||||
\(22\) | −104.516 | −1.01286 | ||||||||
\(23\) | −37.8302 | −0.342962 | −0.171481 | − | 0.985187i | \(-0.554855\pi\) | ||||
−0.171481 | + | 0.985187i | \(0.554855\pi\) | |||||||
\(24\) | −231.960 | −1.97286 | ||||||||
\(25\) | 52.3838 | 0.419070 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 473.338 | 3.19473 | ||||||||
\(29\) | 40.8605 | 0.261642 | 0.130821 | − | 0.991406i | \(-0.458239\pi\) | ||||
0.130821 | + | 0.991406i | \(0.458239\pi\) | |||||||
\(30\) | −219.190 | −1.33395 | ||||||||
\(31\) | −6.05542 | −0.0350834 | −0.0175417 | − | 0.999846i | \(-0.505584\pi\) | ||||
−0.0175417 | + | 0.999846i | \(0.505584\pi\) | |||||||
\(32\) | 738.690 | 4.08073 | ||||||||
\(33\) | 57.1559 | 0.301502 | ||||||||
\(34\) | −393.832 | −1.98652 | ||||||||
\(35\) | 285.328 | 1.37798 | ||||||||
\(36\) | 198.850 | 0.920603 | ||||||||
\(37\) | −285.682 | −1.26935 | −0.634673 | − | 0.772781i | \(-0.718865\pi\) | ||||
−0.634673 | + | 0.772781i | \(0.718865\pi\) | |||||||
\(38\) | −560.293 | −2.39188 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1029.79 | 4.07060 | ||||||||
\(41\) | −342.705 | −1.30540 | −0.652702 | − | 0.757615i | \(-0.726364\pi\) | ||||
−0.652702 | + | 0.757615i | \(0.726364\pi\) | |||||||
\(42\) | −352.576 | −1.29532 | ||||||||
\(43\) | 306.458 | 1.08685 | 0.543424 | − | 0.839458i | \(-0.317128\pi\) | ||||
0.543424 | + | 0.839458i | \(0.317128\pi\) | |||||||
\(44\) | −420.943 | −1.44226 | ||||||||
\(45\) | 119.867 | 0.397082 | ||||||||
\(46\) | −207.530 | −0.665188 | ||||||||
\(47\) | 346.863 | 1.07649 | 0.538246 | − | 0.842788i | \(-0.319087\pi\) | ||||
0.538246 | + | 0.842788i | \(0.319087\pi\) | |||||||
\(48\) | −742.229 | −2.23191 | ||||||||
\(49\) | 115.961 | 0.338079 | ||||||||
\(50\) | 287.369 | 0.812802 | ||||||||
\(51\) | 215.372 | 0.591335 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 398.219 | 1.03207 | 0.516034 | − | 0.856568i | \(-0.327408\pi\) | ||||
0.516034 | + | 0.856568i | \(0.327408\pi\) | |||||||
\(54\) | −148.118 | −0.373264 | ||||||||
\(55\) | −253.745 | −0.622089 | ||||||||
\(56\) | 1656.46 | 3.95274 | ||||||||
\(57\) | 306.403 | 0.712001 | ||||||||
\(58\) | 224.155 | 0.507464 | ||||||||
\(59\) | −208.497 | −0.460067 | −0.230034 | − | 0.973183i | \(-0.573884\pi\) | ||||
−0.230034 | + | 0.973183i | \(0.573884\pi\) | |||||||
\(60\) | −882.799 | −1.89948 | ||||||||
\(61\) | 546.936 | 1.14800 | 0.574000 | − | 0.818855i | \(-0.305391\pi\) | ||||
0.574000 | + | 0.818855i | \(0.305391\pi\) | |||||||
\(62\) | −33.2191 | −0.0680456 | ||||||||
\(63\) | 192.810 | 0.385585 | ||||||||
\(64\) | 2073.06 | 4.04895 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 313.548 | 0.584774 | ||||||||
\(67\) | −678.268 | −1.23677 | −0.618386 | − | 0.785875i | \(-0.712213\pi\) | ||||
−0.618386 | + | 0.785875i | \(0.712213\pi\) | |||||||
\(68\) | −1586.18 | −2.82871 | ||||||||
\(69\) | 113.490 | 0.198009 | ||||||||
\(70\) | 1565.27 | 2.67264 | ||||||||
\(71\) | 957.777 | 1.60095 | 0.800474 | − | 0.599368i | \(-0.204581\pi\) | ||||
0.800474 | + | 0.599368i | \(0.204581\pi\) | |||||||
\(72\) | 695.880 | 1.13903 | ||||||||
\(73\) | 270.360 | 0.433469 | 0.216734 | − | 0.976231i | \(-0.430459\pi\) | ||||
0.216734 | + | 0.976231i | \(0.430459\pi\) | |||||||
\(74\) | −1567.21 | −2.46195 | ||||||||
\(75\) | −157.151 | −0.241950 | ||||||||
\(76\) | −2256.60 | −3.40592 | ||||||||
\(77\) | −408.157 | −0.604076 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1032.86 | −1.47096 | −0.735482 | − | 0.677544i | \(-0.763044\pi\) | ||||
−0.735482 | + | 0.677544i | \(0.763044\pi\) | |||||||
\(80\) | 3295.14 | 4.60510 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −1880.03 | −2.53188 | ||||||||
\(83\) | −1065.90 | −1.40961 | −0.704806 | − | 0.709400i | \(-0.748966\pi\) | ||||
−0.704806 | + | 0.709400i | \(0.748966\pi\) | |||||||
\(84\) | −1420.01 | −1.84448 | ||||||||
\(85\) | −956.147 | −1.22010 | ||||||||
\(86\) | 1681.18 | 2.10798 | ||||||||
\(87\) | −122.582 | −0.151059 | ||||||||
\(88\) | −1473.10 | −1.78446 | ||||||||
\(89\) | 427.185 | 0.508782 | 0.254391 | − | 0.967101i | \(-0.418125\pi\) | ||||
0.254391 | + | 0.967101i | \(0.418125\pi\) | |||||||
\(90\) | 657.571 | 0.770156 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −835.837 | −0.947196 | ||||||||
\(93\) | 18.1663 | 0.0202554 | ||||||||
\(94\) | 1902.83 | 2.08790 | ||||||||
\(95\) | −1360.28 | −1.46907 | ||||||||
\(96\) | −2216.07 | −2.35601 | ||||||||
\(97\) | 698.084 | 0.730718 | 0.365359 | − | 0.930867i | \(-0.380946\pi\) | ||||
0.365359 | + | 0.930867i | \(0.380946\pi\) | |||||||
\(98\) | 636.144 | 0.655717 | ||||||||
\(99\) | −171.468 | −0.174072 | ||||||||
\(100\) | 1157.39 | 1.15739 | ||||||||
\(101\) | 88.7364 | 0.0874218 | 0.0437109 | − | 0.999044i | \(-0.486082\pi\) | ||||
0.0437109 | + | 0.999044i | \(0.486082\pi\) | |||||||
\(102\) | 1181.50 | 1.14692 | ||||||||
\(103\) | −1427.61 | −1.36570 | −0.682849 | − | 0.730560i | \(-0.739259\pi\) | ||||
−0.682849 | + | 0.730560i | \(0.739259\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −855.985 | −0.795577 | ||||||||
\(106\) | 2184.57 | 2.00173 | ||||||||
\(107\) | −15.0233 | −0.0135735 | −0.00678673 | − | 0.999977i | \(-0.502160\pi\) | ||||
−0.00678673 | + | 0.999977i | \(0.502160\pi\) | |||||||
\(108\) | −596.551 | −0.531510 | ||||||||
\(109\) | 2053.56 | 1.80455 | 0.902274 | − | 0.431163i | \(-0.141896\pi\) | ||||
0.902274 | + | 0.431163i | \(0.141896\pi\) | |||||||
\(110\) | −1392.00 | −1.20657 | ||||||||
\(111\) | 857.046 | 0.732857 | ||||||||
\(112\) | 5300.35 | 4.47175 | ||||||||
\(113\) | 717.456 | 0.597280 | 0.298640 | − | 0.954366i | \(-0.403467\pi\) | ||||
0.298640 | + | 0.954366i | \(0.403467\pi\) | |||||||
\(114\) | 1680.88 | 1.38095 | ||||||||
\(115\) | −503.843 | −0.408553 | ||||||||
\(116\) | 902.792 | 0.722605 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1143.78 | −0.892318 | ||||||||
\(119\) | −1538.00 | −1.18477 | ||||||||
\(120\) | −3089.37 | −2.35016 | ||||||||
\(121\) | −968.023 | −0.727290 | ||||||||
\(122\) | 3000.41 | 2.22659 | ||||||||
\(123\) | 1028.12 | 0.753675 | ||||||||
\(124\) | −133.791 | −0.0968937 | ||||||||
\(125\) | −967.143 | −0.692031 | ||||||||
\(126\) | 1057.73 | 0.747856 | ||||||||
\(127\) | −117.640 | −0.0821955 | −0.0410978 | − | 0.999155i | \(-0.513086\pi\) | ||||
−0.0410978 | + | 0.999155i | \(0.513086\pi\) | |||||||
\(128\) | 5462.96 | 3.77236 | ||||||||
\(129\) | −919.375 | −0.627492 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −262.376 | −0.174991 | −0.0874957 | − | 0.996165i | \(-0.527886\pi\) | ||||
−0.0874957 | + | 0.996165i | \(0.527886\pi\) | |||||||
\(132\) | 1262.83 | 0.832690 | ||||||||
\(133\) | −2188.06 | −1.42653 | ||||||||
\(134\) | −3720.87 | −2.39876 | ||||||||
\(135\) | −359.601 | −0.229256 | ||||||||
\(136\) | −5550.85 | −3.49986 | ||||||||
\(137\) | −1317.41 | −0.821563 | −0.410782 | − | 0.911734i | \(-0.634744\pi\) | ||||
−0.410782 | + | 0.911734i | \(0.634744\pi\) | |||||||
\(138\) | 622.591 | 0.384047 | ||||||||
\(139\) | −6.43478 | −0.00392656 | −0.00196328 | − | 0.999998i | \(-0.500625\pi\) | ||||
−0.00196328 | + | 0.999998i | \(0.500625\pi\) | |||||||
\(140\) | 6304.18 | 3.80572 | ||||||||
\(141\) | −1040.59 | −0.621513 | ||||||||
\(142\) | 5254.22 | 3.10510 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 2226.69 | 1.28859 | ||||||||
\(145\) | 544.203 | 0.311680 | ||||||||
\(146\) | 1483.15 | 0.840729 | ||||||||
\(147\) | −347.883 | −0.195190 | ||||||||
\(148\) | −6311.99 | −3.50569 | ||||||||
\(149\) | 548.312 | 0.301473 | 0.150736 | − | 0.988574i | \(-0.451836\pi\) | ||||
0.150736 | + | 0.988574i | \(0.451836\pi\) | |||||||
\(150\) | −862.107 | −0.469272 | ||||||||
\(151\) | 1485.90 | 0.800799 | 0.400399 | − | 0.916341i | \(-0.368871\pi\) | ||||
0.400399 | + | 0.916341i | \(0.368871\pi\) | |||||||
\(152\) | −7897.03 | −4.21404 | ||||||||
\(153\) | −646.116 | −0.341408 | ||||||||
\(154\) | −2239.09 | −1.17163 | ||||||||
\(155\) | −80.6494 | −0.0417930 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2132.36 | 1.08396 | 0.541978 | − | 0.840393i | \(-0.317676\pi\) | ||||
0.541978 | + | 0.840393i | \(0.317676\pi\) | |||||||
\(158\) | −5666.13 | −2.85299 | ||||||||
\(159\) | −1194.66 | −0.595865 | ||||||||
\(160\) | 9838.28 | 4.86115 | ||||||||
\(161\) | −810.450 | −0.396723 | ||||||||
\(162\) | 444.353 | 0.215504 | ||||||||
\(163\) | 480.633 | 0.230957 | 0.115479 | − | 0.993310i | \(-0.463160\pi\) | ||||
0.115479 | + | 0.993310i | \(0.463160\pi\) | |||||||
\(164\) | −7571.88 | −3.60527 | ||||||||
\(165\) | 761.234 | 0.359163 | ||||||||
\(166\) | −5847.36 | −2.73400 | ||||||||
\(167\) | −2919.71 | −1.35290 | −0.676448 | − | 0.736490i | \(-0.736482\pi\) | ||||
−0.676448 | + | 0.736490i | \(0.736482\pi\) | |||||||
\(168\) | −4969.37 | −2.28211 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −5245.27 | −2.36643 | ||||||||
\(171\) | −919.209 | −0.411074 | ||||||||
\(172\) | 6771.04 | 3.00167 | ||||||||
\(173\) | −2339.62 | −1.02820 | −0.514098 | − | 0.857731i | \(-0.671873\pi\) | ||||
−0.514098 | + | 0.857731i | \(0.671873\pi\) | |||||||
\(174\) | −672.464 | −0.292985 | ||||||||
\(175\) | 1122.24 | 0.484761 | ||||||||
\(176\) | −4713.64 | −2.01877 | ||||||||
\(177\) | 625.490 | 0.265620 | ||||||||
\(178\) | 2343.47 | 0.986802 | ||||||||
\(179\) | −4558.71 | −1.90354 | −0.951772 | − | 0.306808i | \(-0.900739\pi\) | ||||
−0.951772 | + | 0.306808i | \(0.900739\pi\) | |||||||
\(180\) | 2648.40 | 1.09667 | ||||||||
\(181\) | −3524.56 | −1.44739 | −0.723696 | − | 0.690118i | \(-0.757558\pi\) | ||||
−0.723696 | + | 0.690118i | \(0.757558\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1640.81 | −0.662798 | ||||||||
\(184\) | −2925.03 | −1.17193 | ||||||||
\(185\) | −3804.87 | −1.51211 | ||||||||
\(186\) | 99.6573 | 0.0392862 | ||||||||
\(187\) | 1367.75 | 0.534866 | ||||||||
\(188\) | 7663.75 | 2.97306 | ||||||||
\(189\) | −578.431 | −0.222617 | ||||||||
\(190\) | −7462.29 | −2.84932 | ||||||||
\(191\) | 3343.27 | 1.26655 | 0.633273 | − | 0.773929i | \(-0.281711\pi\) | ||||
0.633273 | + | 0.773929i | \(0.281711\pi\) | |||||||
\(192\) | −6219.18 | −2.33766 | ||||||||
\(193\) | 3341.33 | 1.24619 | 0.623094 | − | 0.782147i | \(-0.285876\pi\) | ||||
0.623094 | + | 0.782147i | \(0.285876\pi\) | |||||||
\(194\) | 3829.58 | 1.41726 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2562.10 | 0.933709 | ||||||||
\(197\) | 3653.95 | 1.32149 | 0.660745 | − | 0.750611i | \(-0.270241\pi\) | ||||
0.660745 | + | 0.750611i | \(0.270241\pi\) | |||||||
\(198\) | −940.645 | −0.337620 | ||||||||
\(199\) | 1126.55 | 0.401301 | 0.200651 | − | 0.979663i | \(-0.435694\pi\) | ||||
0.200651 | + | 0.979663i | \(0.435694\pi\) | |||||||
\(200\) | 4050.31 | 1.43200 | ||||||||
\(201\) | 2034.81 | 0.714050 | ||||||||
\(202\) | 486.794 | 0.169558 | ||||||||
\(203\) | 875.371 | 0.302655 | ||||||||
\(204\) | 4758.53 | 1.63315 | ||||||||
\(205\) | −4564.33 | −1.55506 | ||||||||
\(206\) | −7831.66 | −2.64882 | ||||||||
\(207\) | −340.471 | −0.114321 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1945.86 | 0.644009 | ||||||||
\(210\) | −4695.80 | −1.54305 | ||||||||
\(211\) | −74.5243 | −0.0243150 | −0.0121575 | − | 0.999926i | \(-0.503870\pi\) | ||||
−0.0121575 | + | 0.999926i | \(0.503870\pi\) | |||||||
\(212\) | 8798.44 | 2.85037 | ||||||||
\(213\) | −2873.33 | −0.924307 | ||||||||
\(214\) | −82.4156 | −0.0263262 | ||||||||
\(215\) | 4081.58 | 1.29471 | ||||||||
\(216\) | −2087.64 | −0.657620 | ||||||||
\(217\) | −129.728 | −0.0405829 | ||||||||
\(218\) | 11265.5 | 3.49999 | ||||||||
\(219\) | −811.079 | −0.250263 | ||||||||
\(220\) | −5606.35 | −1.71809 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 4701.62 | 1.42140 | ||||||||
\(223\) | −3178.62 | −0.954512 | −0.477256 | − | 0.878764i | \(-0.658369\pi\) | ||||
−0.477256 | + | 0.878764i | \(0.658369\pi\) | |||||||
\(224\) | 15825.2 | 4.72039 | ||||||||
\(225\) | 471.454 | 0.139690 | ||||||||
\(226\) | 3935.85 | 1.15845 | ||||||||
\(227\) | 1349.76 | 0.394655 | 0.197327 | − | 0.980338i | \(-0.436774\pi\) | ||||
0.197327 | + | 0.980338i | \(0.436774\pi\) | |||||||
\(228\) | 6769.81 | 1.96641 | ||||||||
\(229\) | 4821.46 | 1.39131 | 0.695657 | − | 0.718374i | \(-0.255113\pi\) | ||||
0.695657 | + | 0.718374i | \(0.255113\pi\) | |||||||
\(230\) | −2764.00 | −0.792404 | ||||||||
\(231\) | 1224.47 | 0.348763 | ||||||||
\(232\) | 3159.34 | 0.894055 | ||||||||
\(233\) | −2400.88 | −0.675050 | −0.337525 | − | 0.941317i | \(-0.609590\pi\) | ||||
−0.337525 | + | 0.941317i | \(0.609590\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4619.71 | 1.28237 | ||||||||
\(236\) | −4606.63 | −1.27062 | ||||||||
\(237\) | 3098.59 | 0.849262 | ||||||||
\(238\) | −8437.21 | −2.29791 | ||||||||
\(239\) | 1880.85 | 0.509047 | 0.254523 | − | 0.967067i | \(-0.418081\pi\) | ||||
0.254523 | + | 0.967067i | \(0.418081\pi\) | |||||||
\(240\) | −9885.41 | −2.65875 | ||||||||
\(241\) | −5435.01 | −1.45270 | −0.726349 | − | 0.687327i | \(-0.758784\pi\) | ||||
−0.726349 | + | 0.687327i | \(0.758784\pi\) | |||||||
\(242\) | −5310.42 | −1.41061 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 12084.3 | 3.17056 | ||||||||
\(245\) | 1544.43 | 0.402736 | ||||||||
\(246\) | 5640.08 | 1.46178 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −468.205 | −0.119883 | ||||||||
\(249\) | 3197.70 | 0.813840 | ||||||||
\(250\) | −5305.59 | −1.34222 | ||||||||
\(251\) | 1256.70 | 0.316024 | 0.158012 | − | 0.987437i | \(-0.449492\pi\) | ||||
0.158012 | + | 0.987437i | \(0.449492\pi\) | |||||||
\(252\) | 4260.04 | 1.06491 | ||||||||
\(253\) | 720.739 | 0.179101 | ||||||||
\(254\) | −645.353 | −0.159421 | ||||||||
\(255\) | 2868.44 | 0.704426 | ||||||||
\(256\) | 13384.5 | 3.26769 | ||||||||
\(257\) | 5504.87 | 1.33612 | 0.668062 | − | 0.744105i | \(-0.267124\pi\) | ||||
0.668062 | + | 0.744105i | \(0.267124\pi\) | |||||||
\(258\) | −5043.55 | −1.21705 | ||||||||
\(259\) | −6120.27 | −1.46832 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 367.745 | 0.0872139 | ||||||||
\(262\) | −1439.35 | −0.339402 | ||||||||
\(263\) | 2032.44 | 0.476522 | 0.238261 | − | 0.971201i | \(-0.423423\pi\) | ||||
0.238261 | + | 0.971201i | \(0.423423\pi\) | |||||||
\(264\) | 4419.29 | 1.03026 | ||||||||
\(265\) | 5303.70 | 1.22945 | ||||||||
\(266\) | −12003.4 | −2.76682 | ||||||||
\(267\) | −1281.56 | −0.293745 | ||||||||
\(268\) | −14986.0 | −3.41572 | ||||||||
\(269\) | 5523.82 | 1.25202 | 0.626009 | − | 0.779816i | \(-0.284687\pi\) | ||||
0.626009 | + | 0.779816i | \(0.284687\pi\) | |||||||
\(270\) | −1972.71 | −0.444650 | ||||||||
\(271\) | −3918.69 | −0.878389 | −0.439194 | − | 0.898392i | \(-0.644736\pi\) | ||||
−0.439194 | + | 0.898392i | \(0.644736\pi\) | |||||||
\(272\) | −17761.7 | −3.95941 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −7227.12 | −1.59345 | ||||||||
\(275\) | −998.013 | −0.218845 | ||||||||
\(276\) | 2507.51 | 0.546864 | ||||||||
\(277\) | −2944.56 | −0.638705 | −0.319353 | − | 0.947636i | \(-0.603465\pi\) | ||||
−0.319353 | + | 0.947636i | \(0.603465\pi\) | |||||||
\(278\) | −35.3002 | −0.00761570 | ||||||||
\(279\) | −54.4988 | −0.0116945 | ||||||||
\(280\) | 22061.6 | 4.70869 | ||||||||
\(281\) | 5048.76 | 1.07183 | 0.535914 | − | 0.844273i | \(-0.319967\pi\) | ||||
0.535914 | + | 0.844273i | \(0.319967\pi\) | |||||||
\(282\) | −5708.50 | −1.20545 | ||||||||
\(283\) | 4491.66 | 0.943469 | 0.471734 | − | 0.881741i | \(-0.343628\pi\) | ||||
0.471734 | + | 0.881741i | \(0.343628\pi\) | |||||||
\(284\) | 21161.6 | 4.42151 | ||||||||
\(285\) | 4080.84 | 0.848169 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7341.90 | −1.51003 | ||||||||
\(288\) | 6648.21 | 1.36024 | ||||||||
\(289\) | 240.893 | 0.0490318 | ||||||||
\(290\) | 2985.41 | 0.604515 | ||||||||
\(291\) | −2094.25 | −0.421880 | ||||||||
\(292\) | 5973.45 | 1.19716 | ||||||||
\(293\) | 4754.86 | 0.948061 | 0.474031 | − | 0.880508i | \(-0.342799\pi\) | ||||
0.474031 | + | 0.880508i | \(0.342799\pi\) | |||||||
\(294\) | −1908.43 | −0.378578 | ||||||||
\(295\) | −2776.88 | −0.548054 | ||||||||
\(296\) | −22088.9 | −4.33747 | ||||||||
\(297\) | 514.403 | 0.100501 | ||||||||
\(298\) | 3007.95 | 0.584718 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −3472.17 | −0.668220 | ||||||||
\(301\) | 6565.38 | 1.25722 | ||||||||
\(302\) | 8151.40 | 1.55318 | ||||||||
\(303\) | −266.209 | −0.0504730 | ||||||||
\(304\) | −25269.0 | −4.76736 | ||||||||
\(305\) | 7284.40 | 1.36755 | ||||||||
\(306\) | −3544.49 | −0.662173 | ||||||||
\(307\) | 1623.31 | 0.301783 | 0.150891 | − | 0.988550i | \(-0.451786\pi\) | ||||
0.150891 | + | 0.988550i | \(0.451786\pi\) | |||||||
\(308\) | −9018.02 | −1.66834 | ||||||||
\(309\) | 4282.84 | 0.788486 | ||||||||
\(310\) | −442.430 | −0.0810592 | ||||||||
\(311\) | 6683.49 | 1.21860 | 0.609302 | − | 0.792938i | \(-0.291450\pi\) | ||||
0.609302 | + | 0.792938i | \(0.291450\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1584.55 | 0.286147 | 0.143073 | − | 0.989712i | \(-0.454301\pi\) | ||||
0.143073 | + | 0.989712i | \(0.454301\pi\) | |||||||
\(314\) | 11697.8 | 2.10237 | ||||||||
\(315\) | 2567.95 | 0.459327 | ||||||||
\(316\) | −22820.6 | −4.06252 | ||||||||
\(317\) | 787.932 | 0.139605 | 0.0698023 | − | 0.997561i | \(-0.477763\pi\) | ||||
0.0698023 | + | 0.997561i | \(0.477763\pi\) | |||||||
\(318\) | −6553.70 | −1.15570 | ||||||||
\(319\) | −778.474 | −0.136634 | ||||||||
\(320\) | 27610.2 | 4.82330 | ||||||||
\(321\) | 45.0700 | 0.00783664 | ||||||||
\(322\) | −4446.00 | −0.769459 | ||||||||
\(323\) | 7332.28 | 1.26309 | ||||||||
\(324\) | 1789.65 | 0.306868 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2636.67 | 0.447951 | ||||||||
\(327\) | −6160.69 | −1.04186 | ||||||||
\(328\) | −26498.0 | −4.46069 | ||||||||
\(329\) | 7430.97 | 1.24524 | ||||||||
\(330\) | 4176.01 | 0.696611 | ||||||||
\(331\) | −9493.56 | −1.57647 | −0.788237 | − | 0.615371i | \(-0.789006\pi\) | ||||
−0.788237 | + | 0.615371i | \(0.789006\pi\) | |||||||
\(332\) | −23550.5 | −3.89308 | ||||||||
\(333\) | −2571.14 | −0.423115 | ||||||||
\(334\) | −16017.1 | −2.62399 | ||||||||
\(335\) | −9033.55 | −1.47330 | ||||||||
\(336\) | −15901.1 | −2.58177 | ||||||||
\(337\) | −4123.06 | −0.666461 | −0.333230 | − | 0.942845i | \(-0.608139\pi\) | ||||
−0.333230 | + | 0.942845i | \(0.608139\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2152.37 | −0.344840 | ||||||||
\(340\) | −21125.6 | −3.36969 | ||||||||
\(341\) | 115.368 | 0.0183211 | ||||||||
\(342\) | −5042.63 | −0.797294 | ||||||||
\(343\) | −4863.94 | −0.765680 | ||||||||
\(344\) | 23695.4 | 3.71386 | ||||||||
\(345\) | 1511.53 | 0.235878 | ||||||||
\(346\) | −12834.8 | −1.99423 | ||||||||
\(347\) | 2320.76 | 0.359034 | 0.179517 | − | 0.983755i | \(-0.442546\pi\) | ||||
0.179517 | + | 0.983755i | \(0.442546\pi\) | |||||||
\(348\) | −2708.38 | −0.417196 | ||||||||
\(349\) | 3818.85 | 0.585726 | 0.292863 | − | 0.956154i | \(-0.405392\pi\) | ||||
0.292863 | + | 0.956154i | \(0.405392\pi\) | |||||||
\(350\) | 6156.41 | 0.940212 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −14073.5 | −2.13102 | ||||||||
\(353\) | −6065.53 | −0.914549 | −0.457274 | − | 0.889326i | \(-0.651174\pi\) | ||||
−0.457274 | + | 0.889326i | \(0.651174\pi\) | |||||||
\(354\) | 3431.34 | 0.515180 | ||||||||
\(355\) | 12756.2 | 1.90712 | ||||||||
\(356\) | 9438.43 | 1.40516 | ||||||||
\(357\) | 4613.99 | 0.684029 | ||||||||
\(358\) | −25008.4 | −3.69199 | ||||||||
\(359\) | 7406.02 | 1.08879 | 0.544394 | − | 0.838830i | \(-0.316760\pi\) | ||||
0.544394 | + | 0.838830i | \(0.316760\pi\) | |||||||
\(360\) | 9268.11 | 1.35687 | ||||||||
\(361\) | 3572.42 | 0.520836 | ||||||||
\(362\) | −19335.2 | −2.80727 | ||||||||
\(363\) | 2904.07 | 0.419901 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3600.80 | 0.516368 | ||||||||
\(366\) | −9001.22 | −1.28552 | ||||||||
\(367\) | −4754.23 | −0.676209 | −0.338105 | − | 0.941109i | \(-0.609786\pi\) | ||||
−0.338105 | + | 0.941109i | \(0.609786\pi\) | |||||||
\(368\) | −9359.55 | −1.32582 | ||||||||
\(369\) | −3084.35 | −0.435134 | ||||||||
\(370\) | −20872.9 | −2.93279 | ||||||||
\(371\) | 8531.20 | 1.19385 | ||||||||
\(372\) | 401.374 | 0.0559416 | ||||||||
\(373\) | −4684.13 | −0.650229 | −0.325114 | − | 0.945675i | \(-0.605403\pi\) | ||||
−0.325114 | + | 0.945675i | \(0.605403\pi\) | |||||||
\(374\) | 7503.27 | 1.03739 | ||||||||
\(375\) | 2901.43 | 0.399544 | ||||||||
\(376\) | 26819.4 | 3.67847 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −3173.18 | −0.431775 | ||||||||
\(379\) | 12103.9 | 1.64047 | 0.820233 | − | 0.572030i | \(-0.193844\pi\) | ||||
0.820233 | + | 0.572030i | \(0.193844\pi\) | |||||||
\(380\) | −30054.7 | −4.05730 | ||||||||
\(381\) | 352.919 | 0.0474556 | ||||||||
\(382\) | 18340.6 | 2.45651 | ||||||||
\(383\) | −5601.56 | −0.747327 | −0.373663 | − | 0.927564i | \(-0.621898\pi\) | ||||
−0.373663 | + | 0.927564i | \(0.621898\pi\) | |||||||
\(384\) | −16388.9 | −2.17797 | ||||||||
\(385\) | −5436.06 | −0.719604 | ||||||||
\(386\) | 18330.0 | 2.41703 | ||||||||
\(387\) | 2758.13 | 0.362283 | ||||||||
\(388\) | 15423.8 | 2.01810 | ||||||||
\(389\) | 9450.46 | 1.23177 | 0.615883 | − | 0.787837i | \(-0.288799\pi\) | ||||
0.615883 | + | 0.787837i | \(0.288799\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2715.85 | 0.351270 | ||||||||
\(392\) | 8966.11 | 1.15525 | ||||||||
\(393\) | 787.127 | 0.101031 | ||||||||
\(394\) | 20045.0 | 2.56308 | ||||||||
\(395\) | −13756.2 | −1.75228 | ||||||||
\(396\) | −3788.49 | −0.480754 | ||||||||
\(397\) | −2723.98 | −0.344364 | −0.172182 | − | 0.985065i | \(-0.555082\pi\) | ||||
−0.172182 | + | 0.985065i | \(0.555082\pi\) | |||||||
\(398\) | 6180.07 | 0.778339 | ||||||||
\(399\) | 6564.18 | 0.823610 | ||||||||
\(400\) | 12960.2 | 1.62003 | ||||||||
\(401\) | 4680.46 | 0.582870 | 0.291435 | − | 0.956591i | \(-0.405867\pi\) | ||||
0.291435 | + | 0.956591i | \(0.405867\pi\) | |||||||
\(402\) | 11162.6 | 1.38493 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 1960.58 | 0.241442 | ||||||||
\(405\) | 1078.80 | 0.132361 | ||||||||
\(406\) | 4802.15 | 0.587011 | ||||||||
\(407\) | 5442.80 | 0.662874 | ||||||||
\(408\) | 16652.6 | 2.02065 | ||||||||
\(409\) | −3272.70 | −0.395659 | −0.197830 | − | 0.980236i | \(-0.563389\pi\) | ||||
−0.197830 | + | 0.980236i | \(0.563389\pi\) | |||||||
\(410\) | −25039.2 | −3.01609 | ||||||||
\(411\) | 3952.24 | 0.474330 | ||||||||
\(412\) | −31542.3 | −3.77179 | ||||||||
\(413\) | −4466.71 | −0.532185 | ||||||||
\(414\) | −1867.77 | −0.221729 | ||||||||
\(415\) | −14196.2 | −1.67920 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 19.3043 | 0.00226700 | ||||||||
\(418\) | 10674.7 | 1.24908 | ||||||||
\(419\) | 1501.48 | 0.175065 | 0.0875323 | − | 0.996162i | \(-0.472102\pi\) | ||||
0.0875323 | + | 0.996162i | \(0.472102\pi\) | |||||||
\(420\) | −18912.5 | −2.19723 | ||||||||
\(421\) | −16578.1 | −1.91916 | −0.959580 | − | 0.281436i | \(-0.909189\pi\) | ||||
−0.959580 | + | 0.281436i | \(0.909189\pi\) | |||||||
\(422\) | −408.828 | −0.0471598 | ||||||||
\(423\) | 3121.76 | 0.358831 | ||||||||
\(424\) | 30790.3 | 3.52667 | ||||||||
\(425\) | −3760.66 | −0.429221 | ||||||||
\(426\) | −15762.6 | −1.79273 | ||||||||
\(427\) | 11717.2 | 1.32795 | ||||||||
\(428\) | −331.933 | −0.0374873 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 22390.9 | 2.51113 | ||||||||
\(431\) | −3776.55 | −0.422065 | −0.211032 | − | 0.977479i | \(-0.567683\pi\) | ||||
−0.211032 | + | 0.977479i | \(0.567683\pi\) | |||||||
\(432\) | −6680.06 | −0.743969 | ||||||||
\(433\) | −709.953 | −0.0787948 | −0.0393974 | − | 0.999224i | \(-0.512544\pi\) | ||||
−0.0393974 | + | 0.999224i | \(0.512544\pi\) | |||||||
\(434\) | −711.665 | −0.0787120 | ||||||||
\(435\) | −1632.61 | −0.179949 | ||||||||
\(436\) | 45372.4 | 4.98382 | ||||||||
\(437\) | 3863.76 | 0.422949 | ||||||||
\(438\) | −4449.45 | −0.485395 | ||||||||
\(439\) | −16262.2 | −1.76800 | −0.884002 | − | 0.467484i | \(-0.845161\pi\) | ||||
−0.884002 | + | 0.467484i | \(0.845161\pi\) | |||||||
\(440\) | −19619.5 | −2.12574 | ||||||||
\(441\) | 1043.65 | 0.112693 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2899.45 | 0.310964 | 0.155482 | − | 0.987839i | \(-0.450307\pi\) | ||||
0.155482 | + | 0.987839i | \(0.450307\pi\) | |||||||
\(444\) | 18936.0 | 2.02401 | ||||||||
\(445\) | 5689.49 | 0.606085 | ||||||||
\(446\) | −17437.4 | −1.85131 | ||||||||
\(447\) | −1644.94 | −0.174055 | ||||||||
\(448\) | 44412.0 | 4.68363 | ||||||||
\(449\) | 7817.78 | 0.821701 | 0.410851 | − | 0.911703i | \(-0.365232\pi\) | ||||
0.410851 | + | 0.911703i | \(0.365232\pi\) | |||||||
\(450\) | 2586.32 | 0.270934 | ||||||||
\(451\) | 6529.20 | 0.681703 | ||||||||
\(452\) | 15851.8 | 1.64957 | ||||||||
\(453\) | −4457.69 | −0.462341 | ||||||||
\(454\) | 7404.57 | 0.765448 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 23691.1 | 2.43297 | ||||||||
\(457\) | 14452.9 | 1.47939 | 0.739694 | − | 0.672943i | \(-0.234970\pi\) | ||||
0.739694 | + | 0.672943i | \(0.234970\pi\) | |||||||
\(458\) | 26449.8 | 2.69851 | ||||||||
\(459\) | 1938.35 | 0.197112 | ||||||||
\(460\) | −11132.1 | −1.12834 | ||||||||
\(461\) | −2891.46 | −0.292123 | −0.146061 | − | 0.989276i | \(-0.546660\pi\) | ||||
−0.146061 | + | 0.989276i | \(0.546660\pi\) | |||||||
\(462\) | 6717.26 | 0.676440 | ||||||||
\(463\) | −9223.83 | −0.925848 | −0.462924 | − | 0.886398i | \(-0.653200\pi\) | ||||
−0.462924 | + | 0.886398i | \(0.653200\pi\) | |||||||
\(464\) | 10109.3 | 1.01145 | ||||||||
\(465\) | 241.948 | 0.0241292 | ||||||||
\(466\) | −13170.8 | −1.30929 | ||||||||
\(467\) | −7988.25 | −0.791546 | −0.395773 | − | 0.918348i | \(-0.629523\pi\) | ||||
−0.395773 | + | 0.918348i | \(0.629523\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14530.8 | −1.43064 | ||||||||
\(470\) | 25343.0 | 2.48720 | ||||||||
\(471\) | −6397.09 | −0.625822 | ||||||||
\(472\) | −16121.0 | −1.57209 | ||||||||
\(473\) | −5838.64 | −0.567570 | ||||||||
\(474\) | 16998.4 | 1.64718 | ||||||||
\(475\) | −5350.18 | −0.516806 | ||||||||
\(476\) | −33981.2 | −3.27212 | ||||||||
\(477\) | 3583.97 | 0.344023 | ||||||||
\(478\) | 10318.1 | 0.987315 | ||||||||
\(479\) | 6908.64 | 0.659006 | 0.329503 | − | 0.944155i | \(-0.393119\pi\) | ||||
0.329503 | + | 0.944155i | \(0.393119\pi\) | |||||||
\(480\) | −29514.8 | −2.80659 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −29815.6 | −2.81756 | ||||||||
\(483\) | 2431.35 | 0.229048 | ||||||||
\(484\) | −21387.9 | −2.00863 | ||||||||
\(485\) | 9297.47 | 0.870466 | ||||||||
\(486\) | −1333.06 | −0.124421 | ||||||||
\(487\) | −13455.0 | −1.25196 | −0.625978 | − | 0.779841i | \(-0.715300\pi\) | ||||
−0.625978 | + | 0.779841i | \(0.715300\pi\) | |||||||
\(488\) | 42289.1 | 3.92282 | ||||||||
\(489\) | −1441.90 | −0.133343 | ||||||||
\(490\) | 8472.52 | 0.781121 | ||||||||
\(491\) | −1044.02 | −0.0959589 | −0.0479795 | − | 0.998848i | \(-0.515278\pi\) | ||||
−0.0479795 | + | 0.998848i | \(0.515278\pi\) | |||||||
\(492\) | 22715.7 | 2.08151 | ||||||||
\(493\) | −2933.40 | −0.267979 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2283.70 | −0.207363 | ||||||||
\(496\) | −1498.17 | −0.135625 | ||||||||
\(497\) | 20518.8 | 1.85190 | ||||||||
\(498\) | 17542.1 | 1.57847 | ||||||||
\(499\) | 16190.7 | 1.45249 | 0.726246 | − | 0.687435i | \(-0.241263\pi\) | ||||
0.726246 | + | 0.687435i | \(0.241263\pi\) | |||||||
\(500\) | −21368.5 | −1.91126 | ||||||||
\(501\) | 8759.12 | 0.781095 | ||||||||
\(502\) | 6894.04 | 0.612940 | ||||||||
\(503\) | −11854.8 | −1.05086 | −0.525429 | − | 0.850838i | \(-0.676095\pi\) | ||||
−0.525429 | + | 0.850838i | \(0.676095\pi\) | |||||||
\(504\) | 14908.1 | 1.31758 | ||||||||
\(505\) | 1181.84 | 0.104141 | ||||||||
\(506\) | 3953.86 | 0.347372 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2599.19 | −0.227008 | ||||||||
\(509\) | −6647.07 | −0.578834 | −0.289417 | − | 0.957203i | \(-0.593461\pi\) | ||||
−0.289417 | + | 0.957203i | \(0.593461\pi\) | |||||||
\(510\) | 15735.8 | 1.36626 | ||||||||
\(511\) | 5792.02 | 0.501416 | ||||||||
\(512\) | 29721.4 | 2.56545 | ||||||||
\(513\) | 2757.63 | 0.237334 | ||||||||
\(514\) | 30198.8 | 2.59146 | ||||||||
\(515\) | −19013.7 | −1.62688 | ||||||||
\(516\) | −20313.1 | −1.73301 | ||||||||
\(517\) | −6608.42 | −0.562162 | ||||||||
\(518\) | −33574.8 | −2.84786 | ||||||||
\(519\) | 7018.86 | 0.593630 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16839.6 | 1.41604 | 0.708019 | − | 0.706193i | \(-0.249589\pi\) | ||||
0.708019 | + | 0.706193i | \(0.249589\pi\) | |||||||
\(522\) | 2017.39 | 0.169155 | ||||||||
\(523\) | 10414.1 | 0.870701 | 0.435351 | − | 0.900261i | \(-0.356624\pi\) | ||||
0.435351 | + | 0.900261i | \(0.356624\pi\) | |||||||
\(524\) | −5797.05 | −0.483293 | ||||||||
\(525\) | −3366.71 | −0.279877 | ||||||||
\(526\) | 11149.6 | 0.924233 | ||||||||
\(527\) | 434.723 | 0.0359332 | ||||||||
\(528\) | 14140.9 | 1.16554 | ||||||||
\(529\) | −10735.9 | −0.882377 | ||||||||
\(530\) | 29095.3 | 2.38456 | ||||||||
\(531\) | −1876.47 | −0.153356 | ||||||||
\(532\) | −48344.1 | −3.93981 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −7030.42 | −0.569730 | ||||||||
\(535\) | −200.089 | −0.0161694 | ||||||||
\(536\) | −52443.7 | −4.22616 | ||||||||
\(537\) | 13676.1 | 1.09901 | ||||||||
\(538\) | 30302.8 | 2.42834 | ||||||||
\(539\) | −2209.29 | −0.176550 | ||||||||
\(540\) | −7945.19 | −0.633160 | ||||||||
\(541\) | 5464.03 | 0.434227 | 0.217114 | − | 0.976146i | \(-0.430336\pi\) | ||||
0.217114 | + | 0.976146i | \(0.430336\pi\) | |||||||
\(542\) | −21497.3 | −1.70367 | ||||||||
\(543\) | 10573.7 | 0.835653 | ||||||||
\(544\) | −53031.0 | −4.17957 | ||||||||
\(545\) | 27350.5 | 2.14966 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24902.3 | 1.94652 | 0.973261 | − | 0.229702i | \(-0.0737753\pi\) | ||||
0.973261 | + | 0.229702i | \(0.0737753\pi\) | |||||||
\(548\) | −29107.5 | −2.26900 | ||||||||
\(549\) | 4922.43 | 0.382667 | ||||||||
\(550\) | −5474.94 | −0.424459 | ||||||||
\(551\) | −4173.26 | −0.322662 | ||||||||
\(552\) | 8775.08 | 0.676617 | ||||||||
\(553\) | −22127.4 | −1.70154 | ||||||||
\(554\) | −16153.4 | −1.23879 | ||||||||
\(555\) | 11414.6 | 0.873014 | ||||||||
\(556\) | −142.173 | −0.0108444 | ||||||||
\(557\) | 9817.71 | 0.746840 | 0.373420 | − | 0.927662i | \(-0.378185\pi\) | ||||
0.373420 | + | 0.927662i | \(0.378185\pi\) | |||||||
\(558\) | −298.972 | −0.0226819 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 70593.0 | 5.32696 | ||||||||
\(561\) | −4103.26 | −0.308805 | ||||||||
\(562\) | 27696.7 | 2.07885 | ||||||||
\(563\) | −23333.7 | −1.74671 | −0.873356 | − | 0.487083i | \(-0.838061\pi\) | ||||
−0.873356 | + | 0.487083i | \(0.838061\pi\) | |||||||
\(564\) | −22991.2 | −1.71650 | ||||||||
\(565\) | 9555.48 | 0.711508 | ||||||||
\(566\) | 24640.6 | 1.82989 | ||||||||
\(567\) | 1735.29 | 0.128528 | ||||||||
\(568\) | 74055.4 | 5.47059 | ||||||||
\(569\) | 24543.9 | 1.80832 | 0.904160 | − | 0.427194i | \(-0.140498\pi\) | ||||
0.904160 | + | 0.427194i | \(0.140498\pi\) | |||||||
\(570\) | 22386.9 | 1.64506 | ||||||||
\(571\) | −10562.5 | −0.774126 | −0.387063 | − | 0.922053i | \(-0.626510\pi\) | ||||
−0.387063 | + | 0.922053i | \(0.626510\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −10029.8 | −0.731241 | ||||||||
\(574\) | −40276.5 | −2.92876 | ||||||||
\(575\) | −1981.69 | −0.143725 | ||||||||
\(576\) | 18657.5 | 1.34965 | ||||||||
\(577\) | 18922.5 | 1.36526 | 0.682629 | − | 0.730765i | \(-0.260837\pi\) | ||||
0.682629 | + | 0.730765i | \(0.260837\pi\) | |||||||
\(578\) | 1321.50 | 0.0950991 | ||||||||
\(579\) | −10024.0 | −0.719486 | ||||||||
\(580\) | 12023.9 | 0.860801 | ||||||||
\(581\) | −22835.2 | −1.63057 | ||||||||
\(582\) | −11488.7 | −0.818253 | ||||||||
\(583\) | −7586.85 | −0.538963 | ||||||||
\(584\) | 20904.2 | 1.48120 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 26084.4 | 1.83880 | ||||||||
\(587\) | 7989.65 | 0.561786 | 0.280893 | − | 0.959739i | \(-0.409369\pi\) | ||||
0.280893 | + | 0.959739i | \(0.409369\pi\) | |||||||
\(588\) | −7686.29 | −0.539077 | ||||||||
\(589\) | 618.466 | 0.0432656 | ||||||||
\(590\) | −15233.5 | −1.06297 | ||||||||
\(591\) | −10961.9 | −0.762962 | ||||||||
\(592\) | −70680.4 | −4.90701 | ||||||||
\(593\) | 25239.2 | 1.74781 | 0.873905 | − | 0.486097i | \(-0.161580\pi\) | ||||
0.873905 | + | 0.486097i | \(0.161580\pi\) | |||||||
\(594\) | 2821.93 | 0.194925 | ||||||||
\(595\) | −20483.9 | −1.41136 | ||||||||
\(596\) | 12114.7 | 0.832610 | ||||||||
\(597\) | −3379.65 | −0.231691 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7412.19 | −0.505599 | −0.252800 | − | 0.967519i | \(-0.581351\pi\) | ||||
−0.252800 | + | 0.967519i | \(0.581351\pi\) | |||||||
\(600\) | −12150.9 | −0.826767 | ||||||||
\(601\) | −21459.2 | −1.45647 | −0.728236 | − | 0.685327i | \(-0.759659\pi\) | ||||
−0.728236 | + | 0.685327i | \(0.759659\pi\) | |||||||
\(602\) | 36016.6 | 2.43842 | ||||||||
\(603\) | −6104.42 | −0.412257 | ||||||||
\(604\) | 32830.1 | 2.21165 | ||||||||
\(605\) | −12892.7 | −0.866382 | ||||||||
\(606\) | −1460.38 | −0.0978944 | ||||||||
\(607\) | −18246.7 | −1.22011 | −0.610057 | − | 0.792358i | \(-0.708853\pi\) | ||||
−0.610057 | + | 0.792358i | \(0.708853\pi\) | |||||||
\(608\) | −75445.6 | −5.03244 | ||||||||
\(609\) | −2626.11 | −0.174738 | ||||||||
\(610\) | 39961.1 | 2.65242 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −14275.6 | −0.942902 | ||||||||
\(613\) | 24087.5 | 1.58709 | 0.793545 | − | 0.608512i | \(-0.208233\pi\) | ||||
0.793545 | + | 0.608512i | \(0.208233\pi\) | |||||||
\(614\) | 8905.23 | 0.585319 | ||||||||
\(615\) | 13693.0 | 0.897813 | ||||||||
\(616\) | −31558.7 | −2.06418 | ||||||||
\(617\) | 14400.6 | 0.939621 | 0.469811 | − | 0.882767i | \(-0.344322\pi\) | ||||
0.469811 | + | 0.882767i | \(0.344322\pi\) | |||||||
\(618\) | 23495.0 | 1.52930 | ||||||||
\(619\) | −25635.8 | −1.66460 | −0.832302 | − | 0.554322i | \(-0.812978\pi\) | ||||
−0.832302 | + | 0.554322i | \(0.812978\pi\) | |||||||
\(620\) | −1781.91 | −0.115424 | ||||||||
\(621\) | 1021.41 | 0.0660031 | ||||||||
\(622\) | 36664.6 | 2.36353 | ||||||||
\(623\) | 9151.76 | 0.588535 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19428.9 | −1.24345 | ||||||||
\(626\) | 8692.58 | 0.554993 | ||||||||
\(627\) | −5837.58 | −0.371819 | ||||||||
\(628\) | 47113.4 | 2.99368 | ||||||||
\(629\) | 20509.3 | 1.30009 | ||||||||
\(630\) | 14087.4 | 0.890881 | ||||||||
\(631\) | 2757.17 | 0.173948 | 0.0869741 | − | 0.996211i | \(-0.472280\pi\) | ||||
0.0869741 | + | 0.996211i | \(0.472280\pi\) | |||||||
\(632\) | −79861.0 | −5.02643 | ||||||||
\(633\) | 223.573 | 0.0140383 | ||||||||
\(634\) | 4322.47 | 0.270768 | ||||||||
\(635\) | −1566.79 | −0.0979152 | ||||||||
\(636\) | −26395.3 | −1.64566 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −4270.58 | −0.265006 | ||||||||
\(639\) | 8620.00 | 0.533649 | ||||||||
\(640\) | 72758.7 | 4.49382 | ||||||||
\(641\) | 14317.0 | 0.882196 | 0.441098 | − | 0.897459i | \(-0.354589\pi\) | ||||
0.441098 | + | 0.897459i | \(0.354589\pi\) | |||||||
\(642\) | 247.247 | 0.0151995 | ||||||||
\(643\) | 51.9171 | 0.00318415 | 0.00159208 | − | 0.999999i | \(-0.499493\pi\) | ||||
0.00159208 | + | 0.999999i | \(0.499493\pi\) | |||||||
\(644\) | −17906.5 | −1.09567 | ||||||||
\(645\) | −12244.7 | −0.747498 | ||||||||
\(646\) | 40223.8 | 2.44982 | ||||||||
\(647\) | −9735.07 | −0.591538 | −0.295769 | − | 0.955260i | \(-0.595576\pi\) | ||||
−0.295769 | + | 0.955260i | \(0.595576\pi\) | |||||||
\(648\) | 6262.92 | 0.379677 | ||||||||
\(649\) | 3972.27 | 0.240255 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 389.183 | 0.0234305 | ||||||||
\(652\) | 10619.3 | 0.637860 | ||||||||
\(653\) | 10842.6 | 0.649778 | 0.324889 | − | 0.945752i | \(-0.394673\pi\) | ||||
0.324889 | + | 0.945752i | \(0.394673\pi\) | |||||||
\(654\) | −33796.6 | −2.02072 | ||||||||
\(655\) | −3494.46 | −0.208458 | ||||||||
\(656\) | −84788.5 | −5.04640 | ||||||||
\(657\) | 2433.24 | 0.144490 | ||||||||
\(658\) | 40765.1 | 2.41518 | ||||||||
\(659\) | 28940.9 | 1.71074 | 0.855369 | − | 0.518020i | \(-0.173331\pi\) | ||||
0.855369 | + | 0.518020i | \(0.173331\pi\) | |||||||
\(660\) | 16819.0 | 0.991940 | ||||||||
\(661\) | 3108.58 | 0.182919 | 0.0914597 | − | 0.995809i | \(-0.470847\pi\) | ||||
0.0914597 | + | 0.995809i | \(0.470847\pi\) | |||||||
\(662\) | −52080.2 | −3.05763 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −82415.4 | −4.81677 | ||||||||
\(665\) | −29141.8 | −1.69935 | ||||||||
\(666\) | −14104.8 | −0.820648 | ||||||||
\(667\) | −1545.76 | −0.0897333 | ||||||||
\(668\) | −64509.4 | −3.73644 | ||||||||
\(669\) | 9535.86 | 0.551088 | ||||||||
\(670\) | −49556.6 | −2.85752 | ||||||||
\(671\) | −10420.2 | −0.599505 | ||||||||
\(672\) | −47475.7 | −2.72532 | ||||||||
\(673\) | −9950.09 | −0.569908 | −0.284954 | − | 0.958541i | \(-0.591978\pi\) | ||||
−0.284954 | + | 0.958541i | \(0.591978\pi\) | |||||||
\(674\) | −22618.4 | −1.29263 | ||||||||
\(675\) | −1414.36 | −0.0806501 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3483.60 | −0.197763 | −0.0988816 | − | 0.995099i | \(-0.531527\pi\) | ||||
−0.0988816 | + | 0.995099i | \(0.531527\pi\) | |||||||
\(678\) | −11807.6 | −0.668830 | ||||||||
\(679\) | 14955.3 | 0.845261 | ||||||||
\(680\) | −73929.3 | −4.16920 | ||||||||
\(681\) | −4049.28 | −0.227854 | ||||||||
\(682\) | 632.889 | 0.0355346 | ||||||||
\(683\) | −16811.4 | −0.941829 | −0.470915 | − | 0.882179i | \(-0.656076\pi\) | ||||
−0.470915 | + | 0.882179i | \(0.656076\pi\) | |||||||
\(684\) | −20309.4 | −1.13531 | ||||||||
\(685\) | −17546.0 | −0.978685 | ||||||||
\(686\) | −26682.8 | −1.48506 | ||||||||
\(687\) | −14464.4 | −0.803276 | ||||||||
\(688\) | 75820.8 | 4.20151 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 8292.01 | 0.457495 | ||||||||
\(691\) | −3078.78 | −0.169497 | −0.0847484 | − | 0.996402i | \(-0.527009\pi\) | ||||
−0.0847484 | + | 0.996402i | \(0.527009\pi\) | |||||||
\(692\) | −51692.6 | −2.83968 | ||||||||
\(693\) | −3673.42 | −0.201359 | ||||||||
\(694\) | 12731.3 | 0.696361 | ||||||||
\(695\) | −85.7020 | −0.00467750 | ||||||||
\(696\) | −9478.01 | −0.516183 | ||||||||
\(697\) | 24603.0 | 1.33702 | ||||||||
\(698\) | 20949.6 | 1.13604 | ||||||||
\(699\) | 7202.63 | 0.389740 | ||||||||
\(700\) | 24795.2 | 1.33882 | ||||||||
\(701\) | −18608.6 | −1.00262 | −0.501311 | − | 0.865267i | \(-0.667149\pi\) | ||||
−0.501311 | + | 0.865267i | \(0.667149\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 29177.9 | 1.56539 | ||||||||
\(704\) | −39495.9 | −2.11443 | ||||||||
\(705\) | −13859.1 | −0.740376 | ||||||||
\(706\) | −33274.5 | −1.77380 | ||||||||
\(707\) | 1901.03 | 0.101126 | ||||||||
\(708\) | 13819.9 | 0.733591 | ||||||||
\(709\) | 19046.2 | 1.00888 | 0.504439 | − | 0.863448i | \(-0.331699\pi\) | ||||
0.504439 | + | 0.863448i | \(0.331699\pi\) | |||||||
\(710\) | 69978.5 | 3.69894 | ||||||||
\(711\) | −9295.77 | −0.490322 | ||||||||
\(712\) | 33030.0 | 1.73855 | ||||||||
\(713\) | 229.078 | 0.0120323 | ||||||||
\(714\) | 25311.6 | 1.32670 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −100722. | −5.25722 | ||||||||
\(717\) | −5642.55 | −0.293898 | ||||||||
\(718\) | 40628.2 | 2.11174 | ||||||||
\(719\) | −14013.4 | −0.726859 | −0.363430 | − | 0.931622i | \(-0.618394\pi\) | ||||
−0.363430 | + | 0.931622i | \(0.618394\pi\) | |||||||
\(720\) | 29656.2 | 1.53503 | ||||||||
\(721\) | −30584.3 | −1.57978 | ||||||||
\(722\) | 19597.7 | 1.01018 | ||||||||
\(723\) | 16305.0 | 0.838715 | ||||||||
\(724\) | −77873.2 | −3.99742 | ||||||||
\(725\) | 2140.43 | 0.109646 | ||||||||
\(726\) | 15931.3 | 0.814414 | ||||||||
\(727\) | 2578.98 | 0.131567 | 0.0657834 | − | 0.997834i | \(-0.479045\pi\) | ||||
0.0657834 | + | 0.997834i | \(0.479045\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 19753.4 | 1.00152 | ||||||||
\(731\) | −22000.8 | −1.11317 | ||||||||
\(732\) | −36252.8 | −1.83052 | ||||||||
\(733\) | 5029.12 | 0.253417 | 0.126709 | − | 0.991940i | \(-0.459559\pi\) | ||||
0.126709 | + | 0.991940i | \(0.459559\pi\) | |||||||
\(734\) | −26081.0 | −1.31153 | ||||||||
\(735\) | −4633.30 | −0.232520 | ||||||||
\(736\) | −27944.8 | −1.39954 | ||||||||
\(737\) | 12922.3 | 0.645863 | ||||||||
\(738\) | −16920.2 | −0.843960 | ||||||||
\(739\) | −23856.4 | −1.18751 | −0.593757 | − | 0.804644i | \(-0.702356\pi\) | ||||
−0.593757 | + | 0.804644i | \(0.702356\pi\) | |||||||
\(740\) | −84066.5 | −4.17614 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 46800.8 | 2.31551 | ||||||||
\(743\) | 4887.62 | 0.241332 | 0.120666 | − | 0.992693i | \(-0.461497\pi\) | ||||
0.120666 | + | 0.992693i | \(0.461497\pi\) | |||||||
\(744\) | 1404.62 | 0.0692147 | ||||||||
\(745\) | 7302.72 | 0.359129 | ||||||||
\(746\) | −25696.4 | −1.26114 | ||||||||
\(747\) | −9593.10 | −0.469870 | ||||||||
\(748\) | 30219.8 | 1.47720 | ||||||||
\(749\) | −321.851 | −0.0157012 | ||||||||
\(750\) | 15916.8 | 0.774932 | ||||||||
\(751\) | 24814.3 | 1.20571 | 0.602854 | − | 0.797851i | \(-0.294030\pi\) | ||||
0.602854 | + | 0.797851i | \(0.294030\pi\) | |||||||
\(752\) | 85817.2 | 4.16148 | ||||||||
\(753\) | −3770.09 | −0.182456 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 19790.0 | 0.953949 | ||||||||
\(756\) | −12780.1 | −0.614826 | ||||||||
\(757\) | −6552.91 | −0.314623 | −0.157311 | − | 0.987549i | \(-0.550283\pi\) | ||||
−0.157311 | + | 0.987549i | \(0.550283\pi\) | |||||||
\(758\) | 66400.2 | 3.18175 | ||||||||
\(759\) | −2162.22 | −0.103404 | ||||||||
\(760\) | −105177. | −5.01996 | ||||||||
\(761\) | 20351.4 | 0.969431 | 0.484715 | − | 0.874672i | \(-0.338923\pi\) | ||||
0.484715 | + | 0.874672i | \(0.338923\pi\) | |||||||
\(762\) | 1936.06 | 0.0920420 | ||||||||
\(763\) | 43994.3 | 2.08742 | ||||||||
\(764\) | 73867.7 | 3.49796 | ||||||||
\(765\) | −8605.32 | −0.406701 | ||||||||
\(766\) | −30729.3 | −1.44947 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −40153.4 | −1.88660 | ||||||||
\(769\) | −22209.7 | −1.04148 | −0.520742 | − | 0.853714i | \(-0.674345\pi\) | ||||
−0.520742 | + | 0.853714i | \(0.674345\pi\) | |||||||
\(770\) | −29821.4 | −1.39570 | ||||||||
\(771\) | −16514.6 | −0.771412 | ||||||||
\(772\) | 73824.9 | 3.44173 | ||||||||
\(773\) | 28496.6 | 1.32594 | 0.662971 | − | 0.748645i | \(-0.269295\pi\) | ||||
0.662971 | + | 0.748645i | \(0.269295\pi\) | |||||||
\(774\) | 15130.6 | 0.702661 | ||||||||
\(775\) | −317.206 | −0.0147024 | ||||||||
\(776\) | 53975.9 | 2.49693 | ||||||||
\(777\) | 18360.8 | 0.847735 | ||||||||
\(778\) | 51843.7 | 2.38906 | ||||||||
\(779\) | 35001.9 | 1.60985 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18247.5 | −0.836041 | ||||||||
\(782\) | 14898.7 | 0.681301 | ||||||||
\(783\) | −1103.23 | −0.0503530 | ||||||||
\(784\) | 28689.9 | 1.30694 | ||||||||
\(785\) | 28400.0 | 1.29126 | ||||||||
\(786\) | 4318.05 | 0.195954 | ||||||||
\(787\) | −2394.07 | −0.108436 | −0.0542181 | − | 0.998529i | \(-0.517267\pi\) | ||||
−0.0542181 | + | 0.998529i | \(0.517267\pi\) | |||||||
\(788\) | 80732.2 | 3.64970 | ||||||||
\(789\) | −6097.31 | −0.275120 | ||||||||
\(790\) | −75464.6 | −3.39862 | ||||||||
\(791\) | 15370.3 | 0.690906 | ||||||||
\(792\) | −13257.9 | −0.594821 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −14943.3 | −0.667907 | ||||||||
\(795\) | −15911.1 | −0.709822 | ||||||||
\(796\) | 24890.5 | 1.10832 | ||||||||
\(797\) | −37996.7 | −1.68872 | −0.844362 | − | 0.535773i | \(-0.820020\pi\) | ||||
−0.844362 | + | 0.535773i | \(0.820020\pi\) | |||||||
\(798\) | 36010.1 | 1.59742 | ||||||||
\(799\) | −24901.5 | −1.10257 | ||||||||
\(800\) | 38695.4 | 1.71011 | ||||||||
\(801\) | 3844.67 | 0.169594 | ||||||||
\(802\) | 25676.3 | 1.13050 | ||||||||
\(803\) | −5150.88 | −0.226364 | ||||||||
\(804\) | 44957.9 | 1.97207 | ||||||||
\(805\) | −10794.0 | −0.472595 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −16571.4 | −0.722853 | ||||||||
\(808\) | 6861.10 | 0.298729 | ||||||||
\(809\) | −25993.4 | −1.12964 | −0.564821 | − | 0.825213i | \(-0.691055\pi\) | ||||
−0.564821 | + | 0.825213i | \(0.691055\pi\) | |||||||
\(810\) | 5918.14 | 0.256719 | ||||||||
\(811\) | −15524.4 | −0.672176 | −0.336088 | − | 0.941831i | \(-0.609104\pi\) | ||||
−0.336088 | + | 0.941831i | \(0.609104\pi\) | |||||||
\(812\) | 19340.9 | 0.835875 | ||||||||
\(813\) | 11756.1 | 0.507138 | ||||||||
\(814\) | 29858.3 | 1.28567 | ||||||||
\(815\) | 6401.33 | 0.275127 | ||||||||
\(816\) | 53285.1 | 2.28597 | ||||||||
\(817\) | −31299.9 | −1.34033 | ||||||||
\(818\) | −17953.5 | −0.767396 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −100847. | −4.29477 | ||||||||
\(821\) | −2029.40 | −0.0862684 | −0.0431342 | − | 0.999069i | \(-0.513734\pi\) | ||||
−0.0431342 | + | 0.999069i | \(0.513734\pi\) | |||||||
\(822\) | 21681.3 | 0.919980 | ||||||||
\(823\) | −42010.4 | −1.77933 | −0.889667 | − | 0.456610i | \(-0.849064\pi\) | ||||
−0.889667 | + | 0.456610i | \(0.849064\pi\) | |||||||
\(824\) | −110383. | −4.66672 | ||||||||
\(825\) | 2994.04 | 0.126350 | ||||||||
\(826\) | −24503.6 | −1.03219 | ||||||||
\(827\) | 3941.24 | 0.165720 | 0.0828599 | − | 0.996561i | \(-0.473595\pi\) | ||||
0.0828599 | + | 0.996561i | \(0.473595\pi\) | |||||||
\(828\) | −7522.53 | −0.315732 | ||||||||
\(829\) | 11264.7 | 0.471941 | 0.235970 | − | 0.971760i | \(-0.424173\pi\) | ||||
0.235970 | + | 0.971760i | \(0.424173\pi\) | |||||||
\(830\) | −77878.4 | −3.25686 | ||||||||
\(831\) | 8833.68 | 0.368757 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −8324.92 | −0.346268 | ||||||||
\(834\) | 105.901 | 0.00439693 | ||||||||
\(835\) | −38886.3 | −1.61163 | ||||||||
\(836\) | 42992.7 | 1.77863 | ||||||||
\(837\) | 163.496 | 0.00675181 | ||||||||
\(838\) | 8236.88 | 0.339544 | ||||||||
\(839\) | 35221.1 | 1.44931 | 0.724653 | − | 0.689114i | \(-0.242000\pi\) | ||||
0.724653 | + | 0.689114i | \(0.242000\pi\) | |||||||
\(840\) | −66184.8 | −2.71856 | ||||||||
\(841\) | −22719.4 | −0.931544 | ||||||||
\(842\) | −90944.8 | −3.72228 | ||||||||
\(843\) | −15146.3 | −0.618820 | ||||||||
\(844\) | −1646.57 | −0.0671533 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 17125.5 | 0.695966 | ||||||||
\(847\) | −20738.3 | −0.841295 | ||||||||
\(848\) | 98523.2 | 3.98974 | ||||||||
\(849\) | −13475.0 | −0.544712 | ||||||||
\(850\) | −20630.4 | −0.832490 | ||||||||
\(851\) | 10807.4 | 0.435338 | ||||||||
\(852\) | −63484.7 | −2.55276 | ||||||||
\(853\) | −37662.7 | −1.51178 | −0.755888 | − | 0.654701i | \(-0.772795\pi\) | ||||
−0.755888 | + | 0.654701i | \(0.772795\pi\) | |||||||
\(854\) | 64278.8 | 2.57562 | ||||||||
\(855\) | −12242.5 | −0.489691 | ||||||||
\(856\) | −1161.60 | −0.0463818 | ||||||||
\(857\) | 800.368 | 0.0319020 | 0.0159510 | − | 0.999873i | \(-0.494922\pi\) | ||||
0.0159510 | + | 0.999873i | \(0.494922\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8800.69 | −0.349564 | −0.174782 | − | 0.984607i | \(-0.555922\pi\) | ||||
−0.174782 | + | 0.984607i | \(0.555922\pi\) | |||||||
\(860\) | 90180.4 | 3.57573 | ||||||||
\(861\) | 22025.7 | 0.871816 | ||||||||
\(862\) | −20717.6 | −0.818611 | ||||||||
\(863\) | 17991.0 | 0.709641 | 0.354821 | − | 0.934934i | \(-0.384542\pi\) | ||||
0.354821 | + | 0.934934i | \(0.384542\pi\) | |||||||
\(864\) | −19944.6 | −0.785336 | ||||||||
\(865\) | −31160.3 | −1.22484 | ||||||||
\(866\) | −3894.69 | −0.152826 | ||||||||
\(867\) | −722.680 | −0.0283085 | ||||||||
\(868\) | −2866.26 | −0.112082 | ||||||||
\(869\) | 19678.1 | 0.768162 | ||||||||
\(870\) | −8956.24 | −0.349017 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 158782. | 6.16631 | ||||||||
\(873\) | 6282.76 | 0.243573 | ||||||||
\(874\) | 21196.0 | 0.820325 | ||||||||
\(875\) | −20719.5 | −0.800510 | ||||||||
\(876\) | −17920.4 | −0.691179 | ||||||||
\(877\) | 44304.5 | 1.70588 | 0.852940 | − | 0.522008i | \(-0.174817\pi\) | ||||
0.852940 | + | 0.522008i | \(0.174817\pi\) | |||||||
\(878\) | −89212.0 | −3.42911 | ||||||||
\(879\) | −14264.6 | −0.547363 | ||||||||
\(880\) | −62778.8 | −2.40486 | ||||||||
\(881\) | 10814.6 | 0.413567 | 0.206783 | − | 0.978387i | \(-0.433700\pi\) | ||||
0.206783 | + | 0.978387i | \(0.433700\pi\) | |||||||
\(882\) | 5725.30 | 0.218572 | ||||||||
\(883\) | 14530.8 | 0.553793 | 0.276897 | − | 0.960900i | \(-0.410694\pi\) | ||||
0.276897 | + | 0.960900i | \(0.410694\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8330.63 | 0.316419 | ||||||||
\(886\) | 15905.9 | 0.603126 | ||||||||
\(887\) | −3385.82 | −0.128168 | −0.0640838 | − | 0.997945i | \(-0.520412\pi\) | ||||
−0.0640838 | + | 0.997945i | \(0.520412\pi\) | |||||||
\(888\) | 66266.8 | 2.50424 | ||||||||
\(889\) | −2520.24 | −0.0950800 | ||||||||
\(890\) | 31211.7 | 1.17552 | ||||||||
\(891\) | −1543.21 | −0.0580241 | ||||||||
\(892\) | −70229.9 | −2.63618 | ||||||||
\(893\) | −35426.6 | −1.32755 | ||||||||
\(894\) | −9023.86 | −0.337587 | ||||||||
\(895\) | −60715.4 | −2.26759 | ||||||||
\(896\) | 117035. | 4.36369 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 42887.1 | 1.59372 | ||||||||
\(899\) | −247.428 | −0.00917929 | ||||||||
\(900\) | 10416.5 | 0.385797 | ||||||||
\(901\) | −28588.4 | −1.05707 | ||||||||
\(902\) | 35818.2 | 1.32219 | ||||||||
\(903\) | −19696.1 | −0.725854 | ||||||||
\(904\) | 55473.7 | 2.04096 | ||||||||
\(905\) | −46942.0 | −1.72420 | ||||||||
\(906\) | −24454.2 | −0.896729 | ||||||||
\(907\) | 38174.2 | 1.39752 | 0.698762 | − | 0.715354i | \(-0.253735\pi\) | ||||
0.698762 | + | 0.715354i | \(0.253735\pi\) | |||||||
\(908\) | 29822.2 | 1.08996 | ||||||||
\(909\) | 798.628 | 0.0291406 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11699.5 | −0.425489 | −0.212745 | − | 0.977108i | \(-0.568240\pi\) | ||||
−0.212745 | + | 0.977108i | \(0.568240\pi\) | |||||||
\(912\) | 75807.0 | 2.75244 | ||||||||
\(913\) | 20307.5 | 0.736123 | ||||||||
\(914\) | 79286.6 | 2.86933 | ||||||||
\(915\) | −21853.2 | −0.789557 | ||||||||
\(916\) | 106528. | 3.84254 | ||||||||
\(917\) | −5620.97 | −0.202422 | ||||||||
\(918\) | 10633.5 | 0.382306 | ||||||||
\(919\) | 21615.6 | 0.775879 | 0.387939 | − | 0.921685i | \(-0.373187\pi\) | ||||
0.387939 | + | 0.921685i | \(0.373187\pi\) | |||||||
\(920\) | −38957.1 | −1.39606 | ||||||||
\(921\) | −4869.93 | −0.174234 | ||||||||
\(922\) | −15862.1 | −0.566583 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 27054.1 | 0.963218 | ||||||||
\(925\) | −14965.1 | −0.531945 | ||||||||
\(926\) | −50600.5 | −1.79572 | ||||||||
\(927\) | −12848.5 | −0.455232 | ||||||||
\(928\) | 30183.3 | 1.06769 | ||||||||
\(929\) | 22325.9 | 0.788471 | 0.394236 | − | 0.919009i | \(-0.371009\pi\) | ||||
0.394236 | + | 0.919009i | \(0.371009\pi\) | |||||||
\(930\) | 1327.29 | 0.0467995 | ||||||||
\(931\) | −11843.6 | −0.416926 | ||||||||
\(932\) | −53046.1 | −1.86436 | ||||||||
\(933\) | −20050.5 | −0.703561 | ||||||||
\(934\) | −43822.3 | −1.53523 | ||||||||
\(935\) | 18216.5 | 0.637158 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −29401.5 | −1.02509 | −0.512543 | − | 0.858661i | \(-0.671297\pi\) | ||||
−0.512543 | + | 0.858661i | \(0.671297\pi\) | |||||||
\(938\) | −79713.7 | −2.77478 | ||||||||
\(939\) | −4753.65 | −0.165207 | ||||||||
\(940\) | 102070. | 3.54166 | ||||||||
\(941\) | 30280.7 | 1.04902 | 0.524508 | − | 0.851406i | \(-0.324249\pi\) | ||||
0.524508 | + | 0.851406i | \(0.324249\pi\) | |||||||
\(942\) | −35093.4 | −1.21381 | ||||||||
\(943\) | 12964.6 | 0.447704 | ||||||||
\(944\) | −51584.1 | −1.77852 | ||||||||
\(945\) | −7703.86 | −0.265192 | ||||||||
\(946\) | −32029.8 | −1.10082 | ||||||||
\(947\) | 25226.1 | 0.865617 | 0.432809 | − | 0.901486i | \(-0.357523\pi\) | ||||
0.432809 | + | 0.901486i | \(0.357523\pi\) | |||||||
\(948\) | 68461.7 | 2.34550 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −29350.2 | −1.00237 | ||||||||
\(951\) | −2363.80 | −0.0806008 | ||||||||
\(952\) | −118918. | −4.04848 | ||||||||
\(953\) | −11893.7 | −0.404275 | −0.202137 | − | 0.979357i | \(-0.564789\pi\) | ||||
−0.202137 | + | 0.979357i | \(0.564789\pi\) | |||||||
\(954\) | 19661.1 | 0.667245 | ||||||||
\(955\) | 44527.5 | 1.50877 | ||||||||
\(956\) | 41556.4 | 1.40589 | ||||||||
\(957\) | 2335.42 | 0.0788855 | ||||||||
\(958\) | 37899.7 | 1.27817 | ||||||||
\(959\) | −28223.4 | −0.950346 | ||||||||
\(960\) | −82830.5 | −2.78473 | ||||||||
\(961\) | −29754.3 | −0.998769 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −135.210 | −0.00452449 | ||||||||
\(964\) | −120084. | −4.01207 | ||||||||
\(965\) | 44501.7 | 1.48452 | ||||||||
\(966\) | 13338.0 | 0.444247 | ||||||||
\(967\) | 8534.72 | 0.283824 | 0.141912 | − | 0.989879i | \(-0.454675\pi\) | ||||
0.141912 | + | 0.989879i | \(0.454675\pi\) | |||||||
\(968\) | −74847.5 | −2.48522 | ||||||||
\(969\) | −21996.9 | −0.729247 | ||||||||
\(970\) | 51004.4 | 1.68830 | ||||||||
\(971\) | 25615.3 | 0.846585 | 0.423292 | − | 0.905993i | \(-0.360874\pi\) | ||||
0.423292 | + | 0.905993i | \(0.360874\pi\) | |||||||
\(972\) | −5368.95 | −0.177170 | ||||||||
\(973\) | −137.855 | −0.00454206 | ||||||||
\(974\) | −73811.8 | −2.42822 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 135317. | 4.43791 | ||||||||
\(977\) | −22995.5 | −0.753011 | −0.376506 | − | 0.926414i | \(-0.622874\pi\) | ||||
−0.376506 | + | 0.926414i | \(0.622874\pi\) | |||||||
\(978\) | −7910.02 | −0.258624 | ||||||||
\(979\) | −8138.72 | −0.265694 | ||||||||
\(980\) | 34123.4 | 1.11228 | ||||||||
\(981\) | 18482.1 | 0.601516 | ||||||||
\(982\) | −5727.31 | −0.186116 | ||||||||
\(983\) | −20592.1 | −0.668144 | −0.334072 | − | 0.942548i | \(-0.608423\pi\) | ||||
−0.334072 | + | 0.942548i | \(0.608423\pi\) | |||||||
\(984\) | 79493.9 | 2.57538 | ||||||||
\(985\) | 48665.4 | 1.57422 | ||||||||
\(986\) | −16092.2 | −0.519756 | ||||||||
\(987\) | −22292.9 | −0.718937 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −11593.4 | −0.372748 | ||||||||
\(990\) | −12528.0 | −0.402189 | ||||||||
\(991\) | −11557.9 | −0.370485 | −0.185242 | − | 0.982693i | \(-0.559307\pi\) | ||||
−0.185242 | + | 0.982693i | \(0.559307\pi\) | |||||||
\(992\) | −4473.08 | −0.143166 | ||||||||
\(993\) | 28480.7 | 0.910178 | ||||||||
\(994\) | 112563. | 3.59183 | ||||||||
\(995\) | 15004.0 | 0.478049 | ||||||||
\(996\) | 70651.5 | 2.24767 | ||||||||
\(997\) | −15481.5 | −0.491778 | −0.245889 | − | 0.969298i | \(-0.579080\pi\) | ||||
−0.245889 | + | 0.969298i | \(0.579080\pi\) | |||||||
\(998\) | 88819.4 | 2.81716 | ||||||||
\(999\) | 7713.41 | 0.244286 |
(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.1.9 | yes | 9 | |
3.2 | odd | 2 | 1521.4.a.be.1.1 | 9 | |||
13.5 | odd | 4 | 507.4.b.j.337.1 | 18 | |||
13.8 | odd | 4 | 507.4.b.j.337.18 | 18 | |||
13.12 | even | 2 | 507.4.a.n.1.1 | ✓ | 9 | ||
39.38 | odd | 2 | 1521.4.a.bj.1.9 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
507.4.a.n.1.1 | ✓ | 9 | 13.12 | even | 2 | ||
507.4.a.q.1.9 | yes | 9 | 1.1 | even | 1 | trivial | |
507.4.b.j.337.1 | 18 | 13.5 | odd | 4 | |||
507.4.b.j.337.18 | 18 | 13.8 | odd | 4 | |||
1521.4.a.be.1.1 | 9 | 3.2 | odd | 2 | |||
1521.4.a.bj.1.9 | 9 | 39.38 | odd | 2 |