Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [169,4,Mod(1,169)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(169, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("169.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 169 = 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 169.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: | \(9.97132279097\) |
Analytic rank: | \(1\) |
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: | \( x^{9} - 4x^{8} - 46x^{7} + 145x^{6} + 680x^{5} - 1501x^{4} - 3203x^{3} + 4784x^{2} + 3584x - 4096 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 13^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(0.850942\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 169.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.149058 | −0.0527001 | −0.0263500 | − | 0.999653i | \(-0.508388\pi\) | ||||
−0.0263500 | + | 0.999653i | \(0.508388\pi\) | |||||||
\(3\) | −6.48858 | −1.24873 | −0.624364 | − | 0.781134i | \(-0.714642\pi\) | ||||
−0.624364 | + | 0.781134i | \(0.714642\pi\) | |||||||
\(4\) | −7.97778 | −0.997223 | ||||||||
\(5\) | 10.2526 | 0.917016 | 0.458508 | − | 0.888690i | \(-0.348384\pi\) | ||||
0.458508 | + | 0.888690i | \(0.348384\pi\) | |||||||
\(6\) | 0.967177 | 0.0658080 | ||||||||
\(7\) | 29.6743 | 1.60226 | 0.801131 | − | 0.598489i | \(-0.204232\pi\) | ||||
0.801131 | + | 0.598489i | \(0.204232\pi\) | |||||||
\(8\) | 2.38162 | 0.105254 | ||||||||
\(9\) | 15.1017 | 0.559321 | ||||||||
\(10\) | −1.52823 | −0.0483268 | ||||||||
\(11\) | −38.1011 | −1.04436 | −0.522178 | − | 0.852837i | \(-0.674880\pi\) | ||||
−0.522178 | + | 0.852837i | \(0.674880\pi\) | |||||||
\(12\) | 51.7645 | 1.24526 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −4.42320 | −0.0844394 | ||||||||
\(15\) | −66.5245 | −1.14510 | ||||||||
\(16\) | 63.4673 | 0.991676 | ||||||||
\(17\) | −71.3014 | −1.01724 | −0.508621 | − | 0.860990i | \(-0.669845\pi\) | ||||
−0.508621 | + | 0.860990i | \(0.669845\pi\) | |||||||
\(18\) | −2.25103 | −0.0294763 | ||||||||
\(19\) | −10.0947 | −0.121889 | −0.0609445 | − | 0.998141i | \(-0.519411\pi\) | ||||
−0.0609445 | + | 0.998141i | \(0.519411\pi\) | |||||||
\(20\) | −81.7926 | −0.914469 | ||||||||
\(21\) | −192.544 | −2.00079 | ||||||||
\(22\) | 5.67928 | 0.0550376 | ||||||||
\(23\) | −198.665 | −1.80107 | −0.900534 | − | 0.434786i | \(-0.856824\pi\) | ||||
−0.900534 | + | 0.434786i | \(0.856824\pi\) | |||||||
\(24\) | −15.4533 | −0.131433 | ||||||||
\(25\) | −19.8851 | −0.159081 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 77.2033 | 0.550288 | ||||||||
\(28\) | −236.735 | −1.59781 | ||||||||
\(29\) | 30.8164 | 0.197326 | 0.0986630 | − | 0.995121i | \(-0.468543\pi\) | ||||
0.0986630 | + | 0.995121i | \(0.468543\pi\) | |||||||
\(30\) | 9.91603 | 0.0603470 | ||||||||
\(31\) | −151.549 | −0.878031 | −0.439016 | − | 0.898479i | \(-0.644673\pi\) | ||||
−0.439016 | + | 0.898479i | \(0.644673\pi\) | |||||||
\(32\) | −28.5133 | −0.157515 | ||||||||
\(33\) | 247.222 | 1.30412 | ||||||||
\(34\) | 10.6281 | 0.0536088 | ||||||||
\(35\) | 304.238 | 1.46930 | ||||||||
\(36\) | −120.478 | −0.557768 | ||||||||
\(37\) | −151.381 | −0.672617 | −0.336308 | − | 0.941752i | \(-0.609178\pi\) | ||||
−0.336308 | + | 0.941752i | \(0.609178\pi\) | |||||||
\(38\) | 1.50470 | 0.00642356 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 24.4177 | 0.0965194 | ||||||||
\(41\) | 207.265 | 0.789495 | 0.394748 | − | 0.918790i | \(-0.370832\pi\) | ||||
0.394748 | + | 0.918790i | \(0.370832\pi\) | |||||||
\(42\) | 28.7003 | 0.105442 | ||||||||
\(43\) | −303.215 | −1.07534 | −0.537672 | − | 0.843154i | \(-0.680696\pi\) | ||||
−0.537672 | + | 0.843154i | \(0.680696\pi\) | |||||||
\(44\) | 303.962 | 1.04145 | ||||||||
\(45\) | 154.831 | 0.512906 | ||||||||
\(46\) | 29.6127 | 0.0949164 | ||||||||
\(47\) | −12.2241 | −0.0379377 | −0.0189689 | − | 0.999820i | \(-0.506038\pi\) | ||||
−0.0189689 | + | 0.999820i | \(0.506038\pi\) | |||||||
\(48\) | −411.812 | −1.23833 | ||||||||
\(49\) | 537.565 | 1.56725 | ||||||||
\(50\) | 2.96405 | 0.00838359 | ||||||||
\(51\) | 462.645 | 1.27026 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −250.726 | −0.649808 | −0.324904 | − | 0.945747i | \(-0.605332\pi\) | ||||
−0.324904 | + | 0.945747i | \(0.605332\pi\) | |||||||
\(54\) | −11.5078 | −0.0290002 | ||||||||
\(55\) | −390.633 | −0.957691 | ||||||||
\(56\) | 70.6730 | 0.168644 | ||||||||
\(57\) | 65.5005 | 0.152206 | ||||||||
\(58\) | −4.59343 | −0.0103991 | ||||||||
\(59\) | −390.502 | −0.861679 | −0.430840 | − | 0.902428i | \(-0.641783\pi\) | ||||
−0.430840 | + | 0.902428i | \(0.641783\pi\) | |||||||
\(60\) | 530.718 | 1.14192 | ||||||||
\(61\) | −156.528 | −0.328546 | −0.164273 | − | 0.986415i | \(-0.552528\pi\) | ||||
−0.164273 | + | 0.986415i | \(0.552528\pi\) | |||||||
\(62\) | 22.5896 | 0.0462723 | ||||||||
\(63\) | 448.132 | 0.896179 | ||||||||
\(64\) | −503.488 | −0.983375 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −36.8505 | −0.0687270 | ||||||||
\(67\) | 303.706 | 0.553786 | 0.276893 | − | 0.960901i | \(-0.410695\pi\) | ||||
0.276893 | + | 0.960901i | \(0.410695\pi\) | |||||||
\(68\) | 568.827 | 1.01442 | ||||||||
\(69\) | 1289.05 | 2.24904 | ||||||||
\(70\) | −45.3491 | −0.0774323 | ||||||||
\(71\) | −913.468 | −1.52688 | −0.763442 | − | 0.645876i | \(-0.776492\pi\) | ||||
−0.763442 | + | 0.645876i | \(0.776492\pi\) | |||||||
\(72\) | 35.9664 | 0.0588706 | ||||||||
\(73\) | 249.855 | 0.400594 | 0.200297 | − | 0.979735i | \(-0.435809\pi\) | ||||
0.200297 | + | 0.979735i | \(0.435809\pi\) | |||||||
\(74\) | 22.5645 | 0.0354469 | ||||||||
\(75\) | 129.026 | 0.198649 | ||||||||
\(76\) | 80.5336 | 0.121551 | ||||||||
\(77\) | −1130.62 | −1.67333 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −147.055 | −0.209430 | −0.104715 | − | 0.994502i | \(-0.533393\pi\) | ||||
−0.104715 | + | 0.994502i | \(0.533393\pi\) | |||||||
\(80\) | 650.701 | 0.909383 | ||||||||
\(81\) | −908.685 | −1.24648 | ||||||||
\(82\) | −30.8945 | −0.0416065 | ||||||||
\(83\) | −1020.16 | −1.34913 | −0.674564 | − | 0.738217i | \(-0.735668\pi\) | ||||
−0.674564 | + | 0.738217i | \(0.735668\pi\) | |||||||
\(84\) | 1536.08 | 1.99523 | ||||||||
\(85\) | −731.021 | −0.932828 | ||||||||
\(86\) | 45.1967 | 0.0566707 | ||||||||
\(87\) | −199.954 | −0.246406 | ||||||||
\(88\) | −90.7423 | −0.109922 | ||||||||
\(89\) | 946.062 | 1.12677 | 0.563384 | − | 0.826195i | \(-0.309499\pi\) | ||||
0.563384 | + | 0.826195i | \(0.309499\pi\) | |||||||
\(90\) | −23.0788 | −0.0270302 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1584.91 | 1.79607 | ||||||||
\(93\) | 983.337 | 1.09642 | ||||||||
\(94\) | 1.82211 | 0.00199932 | ||||||||
\(95\) | −103.497 | −0.111774 | ||||||||
\(96\) | 185.011 | 0.196694 | ||||||||
\(97\) | −417.680 | −0.437206 | −0.218603 | − | 0.975814i | \(-0.570150\pi\) | ||||
−0.218603 | + | 0.975814i | \(0.570150\pi\) | |||||||
\(98\) | −80.1286 | −0.0825939 | ||||||||
\(99\) | −575.390 | −0.584130 | ||||||||
\(100\) | 158.639 | 0.158639 | ||||||||
\(101\) | 850.691 | 0.838088 | 0.419044 | − | 0.907966i | \(-0.362365\pi\) | ||||
0.419044 | + | 0.907966i | \(0.362365\pi\) | |||||||
\(102\) | −68.9611 | −0.0669428 | ||||||||
\(103\) | 996.615 | 0.953392 | 0.476696 | − | 0.879068i | \(-0.341834\pi\) | ||||
0.476696 | + | 0.879068i | \(0.341834\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1974.07 | −1.83476 | ||||||||
\(106\) | 37.3727 | 0.0342449 | ||||||||
\(107\) | 693.925 | 0.626956 | 0.313478 | − | 0.949596i | \(-0.398506\pi\) | ||||
0.313478 | + | 0.949596i | \(0.398506\pi\) | |||||||
\(108\) | −615.911 | −0.548760 | ||||||||
\(109\) | 1130.33 | 0.993267 | 0.496634 | − | 0.867960i | \(-0.334569\pi\) | ||||
0.496634 | + | 0.867960i | \(0.334569\pi\) | |||||||
\(110\) | 58.2271 | 0.0504704 | ||||||||
\(111\) | 982.245 | 0.839915 | ||||||||
\(112\) | 1883.35 | 1.58893 | ||||||||
\(113\) | −263.539 | −0.219395 | −0.109698 | − | 0.993965i | \(-0.534988\pi\) | ||||
−0.109698 | + | 0.993965i | \(0.534988\pi\) | |||||||
\(114\) | −9.76340 | −0.00802128 | ||||||||
\(115\) | −2036.83 | −1.65161 | ||||||||
\(116\) | −245.846 | −0.196778 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 58.2076 | 0.0454106 | ||||||||
\(119\) | −2115.82 | −1.62989 | ||||||||
\(120\) | −158.436 | −0.120526 | ||||||||
\(121\) | 120.692 | 0.0906774 | ||||||||
\(122\) | 23.3317 | 0.0173144 | ||||||||
\(123\) | −1344.85 | −0.985865 | ||||||||
\(124\) | 1209.02 | 0.875593 | ||||||||
\(125\) | −1485.44 | −1.06290 | ||||||||
\(126\) | −66.7977 | −0.0472287 | ||||||||
\(127\) | −101.762 | −0.0711019 | −0.0355510 | − | 0.999368i | \(-0.511319\pi\) | ||||
−0.0355510 | + | 0.999368i | \(0.511319\pi\) | |||||||
\(128\) | 303.155 | 0.209339 | ||||||||
\(129\) | 1967.43 | 1.34281 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −382.888 | −0.255367 | −0.127684 | − | 0.991815i | \(-0.540754\pi\) | ||||
−0.127684 | + | 0.991815i | \(0.540754\pi\) | |||||||
\(132\) | −1972.28 | −1.30049 | ||||||||
\(133\) | −299.554 | −0.195298 | ||||||||
\(134\) | −45.2700 | −0.0291845 | ||||||||
\(135\) | 791.531 | 0.504623 | ||||||||
\(136\) | −169.813 | −0.107069 | ||||||||
\(137\) | −1023.45 | −0.638243 | −0.319122 | − | 0.947714i | \(-0.603388\pi\) | ||||
−0.319122 | + | 0.947714i | \(0.603388\pi\) | |||||||
\(138\) | −192.144 | −0.118525 | ||||||||
\(139\) | 1018.95 | 0.621768 | 0.310884 | − | 0.950448i | \(-0.399375\pi\) | ||||
0.310884 | + | 0.950448i | \(0.399375\pi\) | |||||||
\(140\) | −2427.14 | −1.46522 | ||||||||
\(141\) | 79.3173 | 0.0473739 | ||||||||
\(142\) | 136.160 | 0.0804669 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 958.461 | 0.554665 | ||||||||
\(145\) | 315.946 | 0.180951 | ||||||||
\(146\) | −37.2430 | −0.0211113 | ||||||||
\(147\) | −3488.03 | −1.95706 | ||||||||
\(148\) | 1207.68 | 0.670749 | ||||||||
\(149\) | 1977.31 | 1.08716 | 0.543581 | − | 0.839357i | \(-0.317068\pi\) | ||||
0.543581 | + | 0.839357i | \(0.317068\pi\) | |||||||
\(150\) | −19.2325 | −0.0104688 | ||||||||
\(151\) | −3488.30 | −1.87996 | −0.939979 | − | 0.341234i | \(-0.889155\pi\) | ||||
−0.939979 | + | 0.341234i | \(0.889155\pi\) | |||||||
\(152\) | −24.0418 | −0.0128293 | ||||||||
\(153\) | −1076.77 | −0.568965 | ||||||||
\(154\) | 168.529 | 0.0881847 | ||||||||
\(155\) | −1553.76 | −0.805169 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1783.21 | 0.906471 | 0.453236 | − | 0.891391i | \(-0.350270\pi\) | ||||
0.453236 | + | 0.891391i | \(0.350270\pi\) | |||||||
\(158\) | 21.9197 | 0.0110370 | ||||||||
\(159\) | 1626.85 | 0.811433 | ||||||||
\(160\) | −292.334 | −0.144444 | ||||||||
\(161\) | −5895.25 | −2.88578 | ||||||||
\(162\) | 135.447 | 0.0656896 | ||||||||
\(163\) | 1643.40 | 0.789701 | 0.394851 | − | 0.918745i | \(-0.370796\pi\) | ||||
0.394851 | + | 0.918745i | \(0.370796\pi\) | |||||||
\(164\) | −1653.51 | −0.787303 | ||||||||
\(165\) | 2534.66 | 1.19589 | ||||||||
\(166\) | 152.064 | 0.0710991 | ||||||||
\(167\) | −2437.79 | −1.12959 | −0.564796 | − | 0.825231i | \(-0.691045\pi\) | ||||
−0.564796 | + | 0.825231i | \(0.691045\pi\) | |||||||
\(168\) | −458.567 | −0.210591 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 108.965 | 0.0491601 | ||||||||
\(171\) | −152.447 | −0.0681751 | ||||||||
\(172\) | 2418.98 | 1.07236 | ||||||||
\(173\) | 2986.64 | 1.31254 | 0.656271 | − | 0.754525i | \(-0.272133\pi\) | ||||
0.656271 | + | 0.754525i | \(0.272133\pi\) | |||||||
\(174\) | 29.8049 | 0.0129856 | ||||||||
\(175\) | −590.078 | −0.254890 | ||||||||
\(176\) | −2418.17 | −1.03566 | ||||||||
\(177\) | 2533.81 | 1.07600 | ||||||||
\(178\) | −141.018 | −0.0593808 | ||||||||
\(179\) | −3374.90 | −1.40923 | −0.704614 | − | 0.709591i | \(-0.748880\pi\) | ||||
−0.704614 | + | 0.709591i | \(0.748880\pi\) | |||||||
\(180\) | −1235.21 | −0.511482 | ||||||||
\(181\) | 2266.57 | 0.930790 | 0.465395 | − | 0.885103i | \(-0.345912\pi\) | ||||
0.465395 | + | 0.885103i | \(0.345912\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1015.64 | 0.410264 | ||||||||
\(184\) | −473.145 | −0.189569 | ||||||||
\(185\) | −1552.04 | −0.616800 | ||||||||
\(186\) | −146.574 | −0.0577815 | ||||||||
\(187\) | 2716.66 | 1.06236 | ||||||||
\(188\) | 97.5215 | 0.0378324 | ||||||||
\(189\) | 2290.95 | 0.881706 | ||||||||
\(190\) | 15.4271 | 0.00589051 | ||||||||
\(191\) | 670.719 | 0.254092 | 0.127046 | − | 0.991897i | \(-0.459450\pi\) | ||||
0.127046 | + | 0.991897i | \(0.459450\pi\) | |||||||
\(192\) | 3266.92 | 1.22797 | ||||||||
\(193\) | 4595.68 | 1.71401 | 0.857006 | − | 0.515307i | \(-0.172322\pi\) | ||||
0.857006 | + | 0.515307i | \(0.172322\pi\) | |||||||
\(194\) | 62.2586 | 0.0230408 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4288.58 | −1.56289 | ||||||||
\(197\) | −523.115 | −0.189190 | −0.0945949 | − | 0.995516i | \(-0.530156\pi\) | ||||
−0.0945949 | + | 0.995516i | \(0.530156\pi\) | |||||||
\(198\) | 85.7666 | 0.0307837 | ||||||||
\(199\) | −1573.25 | −0.560427 | −0.280213 | − | 0.959938i | \(-0.590405\pi\) | ||||
−0.280213 | + | 0.959938i | \(0.590405\pi\) | |||||||
\(200\) | −47.3589 | −0.0167439 | ||||||||
\(201\) | −1970.62 | −0.691527 | ||||||||
\(202\) | −126.803 | −0.0441673 | ||||||||
\(203\) | 914.454 | 0.316168 | ||||||||
\(204\) | −3690.88 | −1.26673 | ||||||||
\(205\) | 2124.99 | 0.723980 | ||||||||
\(206\) | −148.554 | −0.0502439 | ||||||||
\(207\) | −3000.17 | −1.00737 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 384.620 | 0.127295 | ||||||||
\(210\) | 294.251 | 0.0966918 | ||||||||
\(211\) | −4782.10 | −1.56025 | −0.780127 | − | 0.625622i | \(-0.784845\pi\) | ||||
−0.780127 | + | 0.625622i | \(0.784845\pi\) | |||||||
\(212\) | 2000.23 | 0.648003 | ||||||||
\(213\) | 5927.11 | 1.90666 | ||||||||
\(214\) | −103.435 | −0.0330406 | ||||||||
\(215\) | −3108.72 | −0.986108 | ||||||||
\(216\) | 183.869 | 0.0579199 | ||||||||
\(217\) | −4497.11 | −1.40684 | ||||||||
\(218\) | −168.485 | −0.0523452 | ||||||||
\(219\) | −1621.21 | −0.500233 | ||||||||
\(220\) | 3116.39 | 0.955031 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −146.412 | −0.0442636 | ||||||||
\(223\) | 2090.37 | 0.627721 | 0.313860 | − | 0.949469i | \(-0.398378\pi\) | ||||
0.313860 | + | 0.949469i | \(0.398378\pi\) | |||||||
\(224\) | −846.112 | −0.252381 | ||||||||
\(225\) | −300.299 | −0.0889774 | ||||||||
\(226\) | 39.2827 | 0.0115622 | ||||||||
\(227\) | 2174.16 | 0.635702 | 0.317851 | − | 0.948141i | \(-0.397039\pi\) | ||||
0.317851 | + | 0.948141i | \(0.397039\pi\) | |||||||
\(228\) | −522.549 | −0.151784 | ||||||||
\(229\) | 5997.16 | 1.73058 | 0.865291 | − | 0.501270i | \(-0.167134\pi\) | ||||
0.865291 | + | 0.501270i | \(0.167134\pi\) | |||||||
\(230\) | 303.606 | 0.0870399 | ||||||||
\(231\) | 7336.14 | 2.08953 | ||||||||
\(232\) | 73.3929 | 0.0207693 | ||||||||
\(233\) | −1550.00 | −0.435810 | −0.217905 | − | 0.975970i | \(-0.569922\pi\) | ||||
−0.217905 | + | 0.975970i | \(0.569922\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −125.329 | −0.0347895 | ||||||||
\(236\) | 3115.34 | 0.859286 | ||||||||
\(237\) | 954.176 | 0.261521 | ||||||||
\(238\) | 315.381 | 0.0858953 | ||||||||
\(239\) | −3895.06 | −1.05419 | −0.527093 | − | 0.849807i | \(-0.676718\pi\) | ||||
−0.527093 | + | 0.849807i | \(0.676718\pi\) | |||||||
\(240\) | −4222.13 | −1.13557 | ||||||||
\(241\) | 4088.19 | 1.09271 | 0.546356 | − | 0.837553i | \(-0.316015\pi\) | ||||
0.546356 | + | 0.837553i | \(0.316015\pi\) | |||||||
\(242\) | −17.9901 | −0.00477870 | ||||||||
\(243\) | 3811.58 | 1.00623 | ||||||||
\(244\) | 1248.74 | 0.327633 | ||||||||
\(245\) | 5511.42 | 1.43719 | ||||||||
\(246\) | 200.462 | 0.0519551 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −360.932 | −0.0924161 | ||||||||
\(249\) | 6619.42 | 1.68469 | ||||||||
\(250\) | 221.418 | 0.0560147 | ||||||||
\(251\) | 5761.42 | 1.44883 | 0.724417 | − | 0.689362i | \(-0.242109\pi\) | ||||
0.724417 | + | 0.689362i | \(0.242109\pi\) | |||||||
\(252\) | −3575.10 | −0.893690 | ||||||||
\(253\) | 7569.36 | 1.88095 | ||||||||
\(254\) | 15.1685 | 0.00374708 | ||||||||
\(255\) | 4743.29 | 1.16485 | ||||||||
\(256\) | 3982.72 | 0.972343 | ||||||||
\(257\) | −4899.09 | −1.18909 | −0.594547 | − | 0.804061i | \(-0.702669\pi\) | ||||
−0.594547 | + | 0.804061i | \(0.702669\pi\) | |||||||
\(258\) | −293.262 | −0.0707663 | ||||||||
\(259\) | −4492.12 | −1.07771 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 465.378 | 0.110369 | ||||||||
\(262\) | 57.0727 | 0.0134579 | ||||||||
\(263\) | 7611.57 | 1.78460 | 0.892300 | − | 0.451444i | \(-0.149091\pi\) | ||||
0.892300 | + | 0.451444i | \(0.149091\pi\) | |||||||
\(264\) | 588.789 | 0.137263 | ||||||||
\(265\) | −2570.58 | −0.595884 | ||||||||
\(266\) | 44.6511 | 0.0102922 | ||||||||
\(267\) | −6138.60 | −1.40703 | ||||||||
\(268\) | −2422.90 | −0.552248 | ||||||||
\(269\) | −6596.55 | −1.49516 | −0.747582 | − | 0.664170i | \(-0.768785\pi\) | ||||
−0.747582 | + | 0.664170i | \(0.768785\pi\) | |||||||
\(270\) | −117.984 | −0.0265937 | ||||||||
\(271\) | −2904.72 | −0.651104 | −0.325552 | − | 0.945524i | \(-0.605550\pi\) | ||||
−0.325552 | + | 0.945524i | \(0.605550\pi\) | |||||||
\(272\) | −4525.30 | −1.00878 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 152.554 | 0.0336355 | ||||||||
\(275\) | 757.645 | 0.166137 | ||||||||
\(276\) | −10283.8 | −2.24280 | ||||||||
\(277\) | 1161.11 | 0.251857 | 0.125928 | − | 0.992039i | \(-0.459809\pi\) | ||||
0.125928 | + | 0.992039i | \(0.459809\pi\) | |||||||
\(278\) | −151.882 | −0.0327672 | ||||||||
\(279\) | −2288.64 | −0.491101 | ||||||||
\(280\) | 724.579 | 0.154649 | ||||||||
\(281\) | −8132.21 | −1.72643 | −0.863215 | − | 0.504836i | \(-0.831553\pi\) | ||||
−0.863215 | + | 0.504836i | \(0.831553\pi\) | |||||||
\(282\) | −11.8229 | −0.00249661 | ||||||||
\(283\) | 1131.86 | 0.237747 | 0.118873 | − | 0.992909i | \(-0.462072\pi\) | ||||
0.118873 | + | 0.992909i | \(0.462072\pi\) | |||||||
\(284\) | 7287.45 | 1.52264 | ||||||||
\(285\) | 671.548 | 0.139576 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6150.44 | 1.26498 | ||||||||
\(288\) | −430.598 | −0.0881015 | ||||||||
\(289\) | 170.889 | 0.0347830 | ||||||||
\(290\) | −47.0944 | −0.00953614 | ||||||||
\(291\) | 2710.15 | 0.545951 | ||||||||
\(292\) | −1993.29 | −0.399481 | ||||||||
\(293\) | −3834.34 | −0.764520 | −0.382260 | − | 0.924055i | \(-0.624854\pi\) | ||||
−0.382260 | + | 0.924055i | \(0.624854\pi\) | |||||||
\(294\) | 519.920 | 0.103137 | ||||||||
\(295\) | −4003.65 | −0.790174 | ||||||||
\(296\) | −360.531 | −0.0707954 | ||||||||
\(297\) | −2941.53 | −0.574696 | ||||||||
\(298\) | −294.734 | −0.0572935 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1029.34 | −0.198097 | ||||||||
\(301\) | −8997.69 | −1.72298 | ||||||||
\(302\) | 519.960 | 0.0990739 | ||||||||
\(303\) | −5519.78 | −1.04654 | ||||||||
\(304\) | −640.685 | −0.120874 | ||||||||
\(305\) | −1604.81 | −0.301282 | ||||||||
\(306\) | 160.501 | 0.0299845 | ||||||||
\(307\) | 6574.27 | 1.22219 | 0.611097 | − | 0.791556i | \(-0.290729\pi\) | ||||
0.611097 | + | 0.791556i | \(0.290729\pi\) | |||||||
\(308\) | 9019.87 | 1.66868 | ||||||||
\(309\) | −6466.62 | −1.19053 | ||||||||
\(310\) | 231.601 | 0.0424325 | ||||||||
\(311\) | 662.775 | 0.120844 | 0.0604220 | − | 0.998173i | \(-0.480755\pi\) | ||||
0.0604220 | + | 0.998173i | \(0.480755\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8353.04 | −1.50844 | −0.754220 | − | 0.656622i | \(-0.771985\pi\) | ||||
−0.754220 | + | 0.656622i | \(0.771985\pi\) | |||||||
\(314\) | −265.803 | −0.0477711 | ||||||||
\(315\) | 4594.49 | 0.821811 | ||||||||
\(316\) | 1173.17 | 0.208848 | ||||||||
\(317\) | 5258.80 | 0.931746 | 0.465873 | − | 0.884852i | \(-0.345740\pi\) | ||||
0.465873 | + | 0.884852i | \(0.345740\pi\) | |||||||
\(318\) | −242.496 | −0.0427626 | ||||||||
\(319\) | −1174.14 | −0.206078 | ||||||||
\(320\) | −5162.04 | −0.901771 | ||||||||
\(321\) | −4502.59 | −0.782897 | ||||||||
\(322\) | 878.737 | 0.152081 | ||||||||
\(323\) | 719.769 | 0.123991 | ||||||||
\(324\) | 7249.29 | 1.24302 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −244.963 | −0.0416173 | ||||||||
\(327\) | −7334.24 | −1.24032 | ||||||||
\(328\) | 493.626 | 0.0830974 | ||||||||
\(329\) | −362.743 | −0.0607862 | ||||||||
\(330\) | −377.811 | −0.0630237 | ||||||||
\(331\) | −2806.48 | −0.466036 | −0.233018 | − | 0.972472i | \(-0.574860\pi\) | ||||
−0.233018 | + | 0.972472i | \(0.574860\pi\) | |||||||
\(332\) | 8138.65 | 1.34538 | ||||||||
\(333\) | −2286.10 | −0.376209 | ||||||||
\(334\) | 363.373 | 0.0595296 | ||||||||
\(335\) | 3113.77 | 0.507830 | ||||||||
\(336\) | −12220.2 | −1.98413 | ||||||||
\(337\) | 10987.6 | 1.77607 | 0.888033 | − | 0.459780i | \(-0.152072\pi\) | ||||
0.888033 | + | 0.459780i | \(0.152072\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1709.99 | 0.273965 | ||||||||
\(340\) | 5831.93 | 0.930237 | ||||||||
\(341\) | 5774.17 | 0.916976 | ||||||||
\(342\) | 22.7235 | 0.00359283 | ||||||||
\(343\) | 5773.59 | 0.908876 | ||||||||
\(344\) | −722.142 | −0.113184 | ||||||||
\(345\) | 13216.1 | 2.06241 | ||||||||
\(346\) | −445.183 | −0.0691711 | ||||||||
\(347\) | 3976.96 | 0.615258 | 0.307629 | − | 0.951506i | \(-0.400464\pi\) | ||||
0.307629 | + | 0.951506i | \(0.400464\pi\) | |||||||
\(348\) | 1595.19 | 0.245722 | ||||||||
\(349\) | −9033.03 | −1.38546 | −0.692732 | − | 0.721195i | \(-0.743593\pi\) | ||||
−0.692732 | + | 0.721195i | \(0.743593\pi\) | |||||||
\(350\) | 87.9561 | 0.0134327 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1086.39 | 0.164502 | ||||||||
\(353\) | −5251.24 | −0.791772 | −0.395886 | − | 0.918300i | \(-0.629562\pi\) | ||||
−0.395886 | + | 0.918300i | \(0.629562\pi\) | |||||||
\(354\) | −377.685 | −0.0567054 | ||||||||
\(355\) | −9365.38 | −1.40018 | ||||||||
\(356\) | −7547.48 | −1.12364 | ||||||||
\(357\) | 13728.7 | 2.03529 | ||||||||
\(358\) | 503.057 | 0.0742664 | ||||||||
\(359\) | 3850.22 | 0.566035 | 0.283018 | − | 0.959115i | \(-0.408664\pi\) | ||||
0.283018 | + | 0.959115i | \(0.408664\pi\) | |||||||
\(360\) | 368.748 | 0.0539853 | ||||||||
\(361\) | −6757.10 | −0.985143 | ||||||||
\(362\) | −337.851 | −0.0490527 | ||||||||
\(363\) | −783.117 | −0.113231 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2561.66 | 0.367351 | ||||||||
\(366\) | −151.390 | −0.0216210 | ||||||||
\(367\) | −7694.40 | −1.09440 | −0.547199 | − | 0.837002i | \(-0.684306\pi\) | ||||
−0.547199 | + | 0.837002i | \(0.684306\pi\) | |||||||
\(368\) | −12608.7 | −1.78608 | ||||||||
\(369\) | 3130.04 | 0.441581 | ||||||||
\(370\) | 231.344 | 0.0325054 | ||||||||
\(371\) | −7440.11 | −1.04116 | ||||||||
\(372\) | −7844.84 | −1.09338 | ||||||||
\(373\) | 8180.64 | 1.13560 | 0.567798 | − | 0.823168i | \(-0.307795\pi\) | ||||
0.567798 | + | 0.823168i | \(0.307795\pi\) | |||||||
\(374\) | −404.941 | −0.0559866 | ||||||||
\(375\) | 9638.41 | 1.32727 | ||||||||
\(376\) | −29.1133 | −0.00399309 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −341.486 | −0.0464660 | ||||||||
\(379\) | −1503.22 | −0.203733 | −0.101867 | − | 0.994798i | \(-0.532482\pi\) | ||||
−0.101867 | + | 0.994798i | \(0.532482\pi\) | |||||||
\(380\) | 825.675 | 0.111464 | ||||||||
\(381\) | 660.293 | 0.0887869 | ||||||||
\(382\) | −99.9762 | −0.0133906 | ||||||||
\(383\) | −12405.4 | −1.65506 | −0.827531 | − | 0.561420i | \(-0.810255\pi\) | ||||
−0.827531 | + | 0.561420i | \(0.810255\pi\) | |||||||
\(384\) | −1967.05 | −0.261408 | ||||||||
\(385\) | −11591.8 | −1.53447 | ||||||||
\(386\) | −685.024 | −0.0903285 | ||||||||
\(387\) | −4579.05 | −0.601463 | ||||||||
\(388\) | 3332.16 | 0.435991 | ||||||||
\(389\) | −3610.27 | −0.470560 | −0.235280 | − | 0.971928i | \(-0.575601\pi\) | ||||
−0.235280 | + | 0.971928i | \(0.575601\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14165.1 | 1.83212 | ||||||||
\(392\) | 1280.28 | 0.164958 | ||||||||
\(393\) | 2484.40 | 0.318884 | ||||||||
\(394\) | 77.9746 | 0.00997031 | ||||||||
\(395\) | −1507.69 | −0.192050 | ||||||||
\(396\) | 4590.33 | 0.582507 | ||||||||
\(397\) | 2381.37 | 0.301052 | 0.150526 | − | 0.988606i | \(-0.451903\pi\) | ||||
0.150526 | + | 0.988606i | \(0.451903\pi\) | |||||||
\(398\) | 234.506 | 0.0295345 | ||||||||
\(399\) | 1943.68 | 0.243874 | ||||||||
\(400\) | −1262.06 | −0.157757 | ||||||||
\(401\) | −3092.11 | −0.385069 | −0.192534 | − | 0.981290i | \(-0.561671\pi\) | ||||
−0.192534 | + | 0.981290i | \(0.561671\pi\) | |||||||
\(402\) | 293.738 | 0.0364435 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −6786.63 | −0.835761 | ||||||||
\(405\) | −9316.34 | −1.14304 | ||||||||
\(406\) | −136.307 | −0.0166621 | ||||||||
\(407\) | 5767.76 | 0.702451 | ||||||||
\(408\) | 1101.84 | 0.133700 | ||||||||
\(409\) | 341.312 | 0.0412635 | 0.0206318 | − | 0.999787i | \(-0.493432\pi\) | ||||
0.0206318 | + | 0.999787i | \(0.493432\pi\) | |||||||
\(410\) | −316.748 | −0.0381538 | ||||||||
\(411\) | 6640.74 | 0.796992 | ||||||||
\(412\) | −7950.78 | −0.950745 | ||||||||
\(413\) | −11587.9 | −1.38064 | ||||||||
\(414\) | 447.201 | 0.0530887 | ||||||||
\(415\) | −10459.3 | −1.23717 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6611.51 | −0.776419 | ||||||||
\(418\) | −57.3309 | −0.00670848 | ||||||||
\(419\) | −545.670 | −0.0636223 | −0.0318111 | − | 0.999494i | \(-0.510128\pi\) | ||||
−0.0318111 | + | 0.999494i | \(0.510128\pi\) | |||||||
\(420\) | 15748.7 | 1.82966 | ||||||||
\(421\) | −10508.0 | −1.21645 | −0.608226 | − | 0.793764i | \(-0.708119\pi\) | ||||
−0.608226 | + | 0.793764i | \(0.708119\pi\) | |||||||
\(422\) | 712.812 | 0.0822255 | ||||||||
\(423\) | −184.605 | −0.0212194 | ||||||||
\(424\) | −597.134 | −0.0683947 | ||||||||
\(425\) | 1417.84 | 0.161824 | ||||||||
\(426\) | −883.485 | −0.100481 | ||||||||
\(427\) | −4644.85 | −0.526417 | ||||||||
\(428\) | −5535.98 | −0.625214 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 463.381 | 0.0519680 | ||||||||
\(431\) | 5518.04 | 0.616693 | 0.308347 | − | 0.951274i | \(-0.400224\pi\) | ||||
0.308347 | + | 0.951274i | \(0.400224\pi\) | |||||||
\(432\) | 4899.88 | 0.545707 | ||||||||
\(433\) | 6072.31 | 0.673941 | 0.336971 | − | 0.941515i | \(-0.390598\pi\) | ||||
0.336971 | + | 0.941515i | \(0.390598\pi\) | |||||||
\(434\) | 670.331 | 0.0741404 | ||||||||
\(435\) | −2050.04 | −0.225959 | ||||||||
\(436\) | −9017.54 | −0.990508 | ||||||||
\(437\) | 2005.47 | 0.219530 | ||||||||
\(438\) | 241.654 | 0.0263623 | ||||||||
\(439\) | 14472.6 | 1.57343 | 0.786717 | − | 0.617314i | \(-0.211779\pi\) | ||||
0.786717 | + | 0.617314i | \(0.211779\pi\) | |||||||
\(440\) | −930.340 | −0.100801 | ||||||||
\(441\) | 8118.13 | 0.876593 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8593.87 | −0.921686 | −0.460843 | − | 0.887482i | \(-0.652453\pi\) | ||||
−0.460843 | + | 0.887482i | \(0.652453\pi\) | |||||||
\(444\) | −7836.14 | −0.837582 | ||||||||
\(445\) | 9699.55 | 1.03326 | ||||||||
\(446\) | −311.587 | −0.0330809 | ||||||||
\(447\) | −12829.9 | −1.35757 | ||||||||
\(448\) | −14940.7 | −1.57562 | ||||||||
\(449\) | −7695.65 | −0.808865 | −0.404432 | − | 0.914568i | \(-0.632531\pi\) | ||||
−0.404432 | + | 0.914568i | \(0.632531\pi\) | |||||||
\(450\) | 44.7620 | 0.00468912 | ||||||||
\(451\) | −7897.01 | −0.824513 | ||||||||
\(452\) | 2102.46 | 0.218786 | ||||||||
\(453\) | 22634.1 | 2.34755 | ||||||||
\(454\) | −324.077 | −0.0335015 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 155.997 | 0.0160203 | ||||||||
\(457\) | 13368.8 | 1.36841 | 0.684207 | − | 0.729288i | \(-0.260149\pi\) | ||||
0.684207 | + | 0.729288i | \(0.260149\pi\) | |||||||
\(458\) | −893.926 | −0.0912018 | ||||||||
\(459\) | −5504.70 | −0.559777 | ||||||||
\(460\) | 16249.3 | 1.64702 | ||||||||
\(461\) | 15502.1 | 1.56617 | 0.783086 | − | 0.621913i | \(-0.213644\pi\) | ||||
0.783086 | + | 0.621913i | \(0.213644\pi\) | |||||||
\(462\) | −1093.51 | −0.110119 | ||||||||
\(463\) | 9877.67 | 0.991478 | 0.495739 | − | 0.868472i | \(-0.334897\pi\) | ||||
0.495739 | + | 0.868472i | \(0.334897\pi\) | |||||||
\(464\) | 1955.83 | 0.195683 | ||||||||
\(465\) | 10081.7 | 1.00544 | ||||||||
\(466\) | 231.040 | 0.0229672 | ||||||||
\(467\) | 3509.82 | 0.347784 | 0.173892 | − | 0.984765i | \(-0.444366\pi\) | ||||
0.173892 | + | 0.984765i | \(0.444366\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9012.28 | 0.887310 | ||||||||
\(470\) | 18.6813 | 0.00183341 | ||||||||
\(471\) | −11570.5 | −1.13194 | ||||||||
\(472\) | −930.029 | −0.0906950 | ||||||||
\(473\) | 11552.8 | 1.12304 | ||||||||
\(474\) | −142.228 | −0.0137822 | ||||||||
\(475\) | 200.735 | 0.0193903 | ||||||||
\(476\) | 16879.6 | 1.62536 | ||||||||
\(477\) | −3786.38 | −0.363451 | ||||||||
\(478\) | 580.591 | 0.0555557 | ||||||||
\(479\) | −19882.2 | −1.89653 | −0.948266 | − | 0.317476i | \(-0.897165\pi\) | ||||
−0.948266 | + | 0.317476i | \(0.897165\pi\) | |||||||
\(480\) | 1896.83 | 0.180371 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −609.379 | −0.0575860 | ||||||||
\(483\) | 38251.8 | 3.60356 | ||||||||
\(484\) | −962.851 | −0.0904255 | ||||||||
\(485\) | −4282.28 | −0.400925 | ||||||||
\(486\) | −568.148 | −0.0530283 | ||||||||
\(487\) | 407.728 | 0.0379383 | 0.0189691 | − | 0.999820i | \(-0.493962\pi\) | ||||
0.0189691 | + | 0.999820i | \(0.493962\pi\) | |||||||
\(488\) | −372.789 | −0.0345807 | ||||||||
\(489\) | −10663.4 | −0.986122 | ||||||||
\(490\) | −821.522 | −0.0757400 | ||||||||
\(491\) | 20130.1 | 1.85022 | 0.925109 | − | 0.379701i | \(-0.123973\pi\) | ||||
0.925109 | + | 0.379701i | \(0.123973\pi\) | |||||||
\(492\) | 10728.9 | 0.983127 | ||||||||
\(493\) | −2197.25 | −0.200728 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5899.21 | −0.535656 | ||||||||
\(496\) | −9618.39 | −0.870722 | ||||||||
\(497\) | −27106.6 | −2.44647 | ||||||||
\(498\) | −986.679 | −0.0887834 | ||||||||
\(499\) | −772.760 | −0.0693256 | −0.0346628 | − | 0.999399i | \(-0.511036\pi\) | ||||
−0.0346628 | + | 0.999399i | \(0.511036\pi\) | |||||||
\(500\) | 11850.5 | 1.05994 | ||||||||
\(501\) | 15817.8 | 1.41055 | ||||||||
\(502\) | −858.787 | −0.0763537 | ||||||||
\(503\) | −7444.25 | −0.659886 | −0.329943 | − | 0.944001i | \(-0.607030\pi\) | ||||
−0.329943 | + | 0.944001i | \(0.607030\pi\) | |||||||
\(504\) | 1067.28 | 0.0943262 | ||||||||
\(505\) | 8721.76 | 0.768541 | ||||||||
\(506\) | −1128.28 | −0.0991264 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 811.837 | 0.0709044 | ||||||||
\(509\) | −3591.47 | −0.312748 | −0.156374 | − | 0.987698i | \(-0.549981\pi\) | ||||
−0.156374 | + | 0.987698i | \(0.549981\pi\) | |||||||
\(510\) | −707.027 | −0.0613876 | ||||||||
\(511\) | 7414.29 | 0.641857 | ||||||||
\(512\) | −3018.90 | −0.260582 | ||||||||
\(513\) | −779.347 | −0.0670741 | ||||||||
\(514\) | 730.251 | 0.0626653 | ||||||||
\(515\) | 10217.9 | 0.874276 | ||||||||
\(516\) | −15695.7 | −1.33908 | ||||||||
\(517\) | 465.753 | 0.0396205 | ||||||||
\(518\) | 669.587 | 0.0567953 | ||||||||
\(519\) | −19379.0 | −1.63901 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1822.89 | 0.153286 | 0.0766432 | − | 0.997059i | \(-0.475580\pi\) | ||||
0.0766432 | + | 0.997059i | \(0.475580\pi\) | |||||||
\(522\) | −69.3685 | −0.00581643 | ||||||||
\(523\) | 12203.2 | 1.02028 | 0.510140 | − | 0.860091i | \(-0.329594\pi\) | ||||
0.510140 | + | 0.860091i | \(0.329594\pi\) | |||||||
\(524\) | 3054.60 | 0.254658 | ||||||||
\(525\) | 3828.77 | 0.318288 | ||||||||
\(526\) | −1134.57 | −0.0940485 | ||||||||
\(527\) | 10805.6 | 0.893171 | ||||||||
\(528\) | 15690.5 | 1.29326 | ||||||||
\(529\) | 27300.8 | 2.24384 | ||||||||
\(530\) | 383.166 | 0.0314032 | ||||||||
\(531\) | −5897.24 | −0.481955 | ||||||||
\(532\) | 2389.78 | 0.194756 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 915.009 | 0.0741504 | ||||||||
\(535\) | 7114.50 | 0.574928 | ||||||||
\(536\) | 723.313 | 0.0582880 | ||||||||
\(537\) | 21898.3 | 1.75974 | ||||||||
\(538\) | 983.271 | 0.0787952 | ||||||||
\(539\) | −20481.8 | −1.63676 | ||||||||
\(540\) | −6314.66 | −0.503222 | ||||||||
\(541\) | 6728.89 | 0.534746 | 0.267373 | − | 0.963593i | \(-0.413844\pi\) | ||||
0.267373 | + | 0.963593i | \(0.413844\pi\) | |||||||
\(542\) | 432.973 | 0.0343132 | ||||||||
\(543\) | −14706.8 | −1.16230 | ||||||||
\(544\) | 2033.04 | 0.160231 | ||||||||
\(545\) | 11588.8 | 0.910842 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14650.8 | −1.14519 | −0.572597 | − | 0.819837i | \(-0.694064\pi\) | ||||
−0.572597 | + | 0.819837i | \(0.694064\pi\) | |||||||
\(548\) | 8164.87 | 0.636471 | ||||||||
\(549\) | −2363.83 | −0.183763 | ||||||||
\(550\) | −112.933 | −0.00875544 | ||||||||
\(551\) | −311.083 | −0.0240519 | ||||||||
\(552\) | 3070.04 | 0.236720 | ||||||||
\(553\) | −4363.75 | −0.335561 | ||||||||
\(554\) | −173.073 | −0.0132729 | ||||||||
\(555\) | 10070.5 | 0.770216 | ||||||||
\(556\) | −8128.92 | −0.620042 | ||||||||
\(557\) | 4208.91 | 0.320175 | 0.160087 | − | 0.987103i | \(-0.448822\pi\) | ||||
0.160087 | + | 0.987103i | \(0.448822\pi\) | |||||||
\(558\) | 341.141 | 0.0258811 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 19309.1 | 1.45707 | ||||||||
\(561\) | −17627.3 | −1.32660 | ||||||||
\(562\) | 1212.17 | 0.0909830 | ||||||||
\(563\) | −9224.28 | −0.690510 | −0.345255 | − | 0.938509i | \(-0.612208\pi\) | ||||
−0.345255 | + | 0.938509i | \(0.612208\pi\) | |||||||
\(564\) | −632.776 | −0.0472423 | ||||||||
\(565\) | −2701.95 | −0.201189 | ||||||||
\(566\) | −168.714 | −0.0125293 | ||||||||
\(567\) | −26964.6 | −1.99719 | ||||||||
\(568\) | −2175.54 | −0.160710 | ||||||||
\(569\) | 14132.9 | 1.04127 | 0.520634 | − | 0.853780i | \(-0.325696\pi\) | ||||
0.520634 | + | 0.853780i | \(0.325696\pi\) | |||||||
\(570\) | −100.100 | −0.00735564 | ||||||||
\(571\) | −17983.4 | −1.31801 | −0.659003 | − | 0.752140i | \(-0.729022\pi\) | ||||
−0.659003 | + | 0.752140i | \(0.729022\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4352.01 | −0.317291 | ||||||||
\(574\) | −916.774 | −0.0666645 | ||||||||
\(575\) | 3950.49 | 0.286516 | ||||||||
\(576\) | −7603.51 | −0.550022 | ||||||||
\(577\) | −24401.8 | −1.76059 | −0.880295 | − | 0.474427i | \(-0.842655\pi\) | ||||
−0.880295 | + | 0.474427i | \(0.842655\pi\) | |||||||
\(578\) | −25.4724 | −0.00183307 | ||||||||
\(579\) | −29819.4 | −2.14033 | ||||||||
\(580\) | −2520.55 | −0.180449 | ||||||||
\(581\) | −30272.7 | −2.16166 | ||||||||
\(582\) | −403.970 | −0.0287717 | ||||||||
\(583\) | 9552.92 | 0.678630 | ||||||||
\(584\) | 595.061 | 0.0421640 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 571.540 | 0.0402902 | ||||||||
\(587\) | −20586.5 | −1.44753 | −0.723763 | − | 0.690049i | \(-0.757589\pi\) | ||||
−0.723763 | + | 0.690049i | \(0.757589\pi\) | |||||||
\(588\) | 27826.8 | 1.95163 | ||||||||
\(589\) | 1529.85 | 0.107022 | ||||||||
\(590\) | 596.777 | 0.0416422 | ||||||||
\(591\) | 3394.27 | 0.236246 | ||||||||
\(592\) | −9607.71 | −0.667018 | ||||||||
\(593\) | −19701.5 | −1.36432 | −0.682162 | − | 0.731201i | \(-0.738960\pi\) | ||||
−0.682162 | + | 0.731201i | \(0.738960\pi\) | |||||||
\(594\) | 438.459 | 0.0302865 | ||||||||
\(595\) | −21692.6 | −1.49464 | ||||||||
\(596\) | −15774.5 | −1.08414 | ||||||||
\(597\) | 10208.2 | 0.699821 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3645.91 | −0.248694 | −0.124347 | − | 0.992239i | \(-0.539684\pi\) | ||||
−0.124347 | + | 0.992239i | \(0.539684\pi\) | |||||||
\(600\) | 307.292 | 0.0209086 | ||||||||
\(601\) | −6285.73 | −0.426623 | −0.213311 | − | 0.976984i | \(-0.568425\pi\) | ||||
−0.213311 | + | 0.976984i | \(0.568425\pi\) | |||||||
\(602\) | 1341.18 | 0.0908014 | ||||||||
\(603\) | 4586.47 | 0.309744 | ||||||||
\(604\) | 27828.9 | 1.87474 | ||||||||
\(605\) | 1237.40 | 0.0831526 | ||||||||
\(606\) | 822.769 | 0.0551530 | ||||||||
\(607\) | −1831.87 | −0.122493 | −0.0612466 | − | 0.998123i | \(-0.519508\pi\) | ||||
−0.0612466 | + | 0.998123i | \(0.519508\pi\) | |||||||
\(608\) | 287.834 | 0.0191994 | ||||||||
\(609\) | −5933.51 | −0.394808 | ||||||||
\(610\) | 239.210 | 0.0158776 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 8590.23 | 0.567385 | ||||||||
\(613\) | 4396.09 | 0.289651 | 0.144826 | − | 0.989457i | \(-0.453738\pi\) | ||||
0.144826 | + | 0.989457i | \(0.453738\pi\) | |||||||
\(614\) | −979.950 | −0.0644097 | ||||||||
\(615\) | −13788.2 | −0.904054 | ||||||||
\(616\) | −2692.72 | −0.176124 | ||||||||
\(617\) | −15140.8 | −0.987917 | −0.493959 | − | 0.869485i | \(-0.664451\pi\) | ||||
−0.493959 | + | 0.869485i | \(0.664451\pi\) | |||||||
\(618\) | 963.903 | 0.0627409 | ||||||||
\(619\) | −20913.0 | −1.35794 | −0.678971 | − | 0.734165i | \(-0.737574\pi\) | ||||
−0.678971 | + | 0.734165i | \(0.737574\pi\) | |||||||
\(620\) | 12395.6 | 0.802933 | ||||||||
\(621\) | −15337.6 | −0.991106 | ||||||||
\(622\) | −98.7921 | −0.00636849 | ||||||||
\(623\) | 28073.7 | 1.80538 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12743.9 | −0.815612 | ||||||||
\(626\) | 1245.09 | 0.0794949 | ||||||||
\(627\) | −2495.64 | −0.158957 | ||||||||
\(628\) | −14226.1 | −0.903954 | ||||||||
\(629\) | 10793.6 | 0.684215 | ||||||||
\(630\) | −684.847 | −0.0433095 | ||||||||
\(631\) | 7104.58 | 0.448223 | 0.224112 | − | 0.974563i | \(-0.428052\pi\) | ||||
0.224112 | + | 0.974563i | \(0.428052\pi\) | |||||||
\(632\) | −350.228 | −0.0220433 | ||||||||
\(633\) | 31029.0 | 1.94833 | ||||||||
\(634\) | −783.867 | −0.0491031 | ||||||||
\(635\) | −1043.32 | −0.0652016 | ||||||||
\(636\) | −12978.7 | −0.809180 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 175.015 | 0.0108603 | ||||||||
\(639\) | −13794.9 | −0.854018 | ||||||||
\(640\) | 3108.12 | 0.191967 | ||||||||
\(641\) | −2696.10 | −0.166131 | −0.0830653 | − | 0.996544i | \(-0.526471\pi\) | ||||
−0.0830653 | + | 0.996544i | \(0.526471\pi\) | |||||||
\(642\) | 671.148 | 0.0412587 | ||||||||
\(643\) | −11994.7 | −0.735653 | −0.367826 | − | 0.929894i | \(-0.619898\pi\) | ||||
−0.367826 | + | 0.929894i | \(0.619898\pi\) | |||||||
\(644\) | 47031.0 | 2.87777 | ||||||||
\(645\) | 20171.2 | 1.23138 | ||||||||
\(646\) | −107.288 | −0.00653432 | ||||||||
\(647\) | 16239.8 | 0.986788 | 0.493394 | − | 0.869806i | \(-0.335756\pi\) | ||||
0.493394 | + | 0.869806i | \(0.335756\pi\) | |||||||
\(648\) | −2164.14 | −0.131197 | ||||||||
\(649\) | 14878.6 | 0.899899 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 29179.8 | 1.75676 | ||||||||
\(652\) | −13110.7 | −0.787508 | ||||||||
\(653\) | 7316.99 | 0.438493 | 0.219246 | − | 0.975670i | \(-0.429640\pi\) | ||||
0.219246 | + | 0.975670i | \(0.429640\pi\) | |||||||
\(654\) | 1093.23 | 0.0653650 | ||||||||
\(655\) | −3925.58 | −0.234176 | ||||||||
\(656\) | 13154.5 | 0.782923 | ||||||||
\(657\) | 3773.23 | 0.224061 | ||||||||
\(658\) | 54.0699 | 0.00320344 | ||||||||
\(659\) | 8573.39 | 0.506786 | 0.253393 | − | 0.967363i | \(-0.418453\pi\) | ||||
0.253393 | + | 0.967363i | \(0.418453\pi\) | |||||||
\(660\) | −20220.9 | −1.19257 | ||||||||
\(661\) | −14262.5 | −0.839255 | −0.419628 | − | 0.907696i | \(-0.637839\pi\) | ||||
−0.419628 | + | 0.907696i | \(0.637839\pi\) | |||||||
\(662\) | 418.329 | 0.0245601 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2429.64 | −0.142001 | ||||||||
\(665\) | −3071.20 | −0.179092 | ||||||||
\(666\) | 340.762 | 0.0198262 | ||||||||
\(667\) | −6122.14 | −0.355397 | ||||||||
\(668\) | 19448.2 | 1.12645 | ||||||||
\(669\) | −13563.5 | −0.783852 | ||||||||
\(670\) | −464.133 | −0.0267627 | ||||||||
\(671\) | 5963.87 | 0.343119 | ||||||||
\(672\) | 5490.07 | 0.315155 | ||||||||
\(673\) | −2690.08 | −0.154079 | −0.0770394 | − | 0.997028i | \(-0.524547\pi\) | ||||
−0.0770394 | + | 0.997028i | \(0.524547\pi\) | |||||||
\(674\) | −1637.80 | −0.0935988 | ||||||||
\(675\) | −1535.20 | −0.0875405 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −25288.0 | −1.43559 | −0.717795 | − | 0.696254i | \(-0.754849\pi\) | ||||
−0.717795 | + | 0.696254i | \(0.754849\pi\) | |||||||
\(678\) | −254.889 | −0.0144380 | ||||||||
\(679\) | −12394.4 | −0.700518 | ||||||||
\(680\) | −1741.02 | −0.0981837 | ||||||||
\(681\) | −14107.2 | −0.793818 | ||||||||
\(682\) | −860.688 | −0.0483247 | ||||||||
\(683\) | 28981.5 | 1.62364 | 0.811821 | − | 0.583906i | \(-0.198476\pi\) | ||||
0.811821 | + | 0.583906i | \(0.198476\pi\) | |||||||
\(684\) | 1216.19 | 0.0679858 | ||||||||
\(685\) | −10493.0 | −0.585279 | ||||||||
\(686\) | −860.601 | −0.0478978 | ||||||||
\(687\) | −38913.0 | −2.16103 | ||||||||
\(688\) | −19244.2 | −1.06639 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −1969.97 | −0.108689 | ||||||||
\(691\) | −31243.3 | −1.72005 | −0.860023 | − | 0.510255i | \(-0.829551\pi\) | ||||
−0.860023 | + | 0.510255i | \(0.829551\pi\) | |||||||
\(692\) | −23826.7 | −1.30890 | ||||||||
\(693\) | −17074.3 | −0.935929 | ||||||||
\(694\) | −592.799 | −0.0324241 | ||||||||
\(695\) | 10446.8 | 0.570172 | ||||||||
\(696\) | −476.216 | −0.0259352 | ||||||||
\(697\) | −14778.3 | −0.803108 | ||||||||
\(698\) | 1346.45 | 0.0730141 | ||||||||
\(699\) | 10057.3 | 0.544208 | ||||||||
\(700\) | 4707.51 | 0.254182 | ||||||||
\(701\) | 25077.1 | 1.35114 | 0.675570 | − | 0.737296i | \(-0.263898\pi\) | ||||
0.675570 | + | 0.737296i | \(0.263898\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1528.15 | 0.0819846 | ||||||||
\(704\) | 19183.4 | 1.02699 | ||||||||
\(705\) | 813.205 | 0.0434426 | ||||||||
\(706\) | 782.741 | 0.0417264 | ||||||||
\(707\) | 25243.7 | 1.34284 | ||||||||
\(708\) | −20214.1 | −1.07301 | ||||||||
\(709\) | −5894.38 | −0.312226 | −0.156113 | − | 0.987739i | \(-0.549896\pi\) | ||||
−0.156113 | + | 0.987739i | \(0.549896\pi\) | |||||||
\(710\) | 1395.99 | 0.0737894 | ||||||||
\(711\) | −2220.77 | −0.117138 | ||||||||
\(712\) | 2253.16 | 0.118597 | ||||||||
\(713\) | 30107.5 | 1.58139 | ||||||||
\(714\) | −2046.37 | −0.107260 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 26924.2 | 1.40531 | ||||||||
\(717\) | 25273.4 | 1.31639 | ||||||||
\(718\) | −573.907 | −0.0298301 | ||||||||
\(719\) | −5430.64 | −0.281681 | −0.140841 | − | 0.990032i | \(-0.544980\pi\) | ||||
−0.140841 | + | 0.990032i | \(0.544980\pi\) | |||||||
\(720\) | 9826.68 | 0.508637 | ||||||||
\(721\) | 29573.9 | 1.52759 | ||||||||
\(722\) | 1007.20 | 0.0519171 | ||||||||
\(723\) | −26526.6 | −1.36450 | ||||||||
\(724\) | −18082.2 | −0.928205 | ||||||||
\(725\) | −612.788 | −0.0313908 | ||||||||
\(726\) | 116.730 | 0.00596730 | ||||||||
\(727\) | 17033.7 | 0.868974 | 0.434487 | − | 0.900678i | \(-0.356930\pi\) | ||||
0.434487 | + | 0.900678i | \(0.356930\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −197.281 | −0.0100229 | ||||||||
\(730\) | −381.836 | −0.0193594 | ||||||||
\(731\) | 21619.6 | 1.09389 | ||||||||
\(732\) | −8102.57 | −0.409125 | ||||||||
\(733\) | 7130.74 | 0.359318 | 0.179659 | − | 0.983729i | \(-0.442501\pi\) | ||||
0.179659 | + | 0.983729i | \(0.442501\pi\) | |||||||
\(734\) | 1146.91 | 0.0576749 | ||||||||
\(735\) | −35761.3 | −1.79466 | ||||||||
\(736\) | 5664.60 | 0.283695 | ||||||||
\(737\) | −11571.5 | −0.578349 | ||||||||
\(738\) | −466.559 | −0.0232714 | ||||||||
\(739\) | 27531.1 | 1.37043 | 0.685215 | − | 0.728341i | \(-0.259708\pi\) | ||||
0.685215 | + | 0.728341i | \(0.259708\pi\) | |||||||
\(740\) | 12381.8 | 0.615087 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1109.01 | 0.0548694 | ||||||||
\(743\) | −11915.0 | −0.588314 | −0.294157 | − | 0.955757i | \(-0.595039\pi\) | ||||
−0.294157 | + | 0.955757i | \(0.595039\pi\) | |||||||
\(744\) | 2341.94 | 0.115403 | ||||||||
\(745\) | 20272.4 | 0.996946 | ||||||||
\(746\) | −1219.39 | −0.0598460 | ||||||||
\(747\) | −15406.2 | −0.754595 | ||||||||
\(748\) | −21672.9 | −1.05941 | ||||||||
\(749\) | 20591.7 | 1.00455 | ||||||||
\(750\) | −1436.69 | −0.0699471 | ||||||||
\(751\) | −4730.41 | −0.229847 | −0.114923 | − | 0.993374i | \(-0.536662\pi\) | ||||
−0.114923 | + | 0.993374i | \(0.536662\pi\) | |||||||
\(752\) | −775.832 | −0.0376219 | ||||||||
\(753\) | −37383.4 | −1.80920 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −35763.9 | −1.72395 | ||||||||
\(756\) | −18276.7 | −0.879257 | ||||||||
\(757\) | 15910.3 | 0.763895 | 0.381948 | − | 0.924184i | \(-0.375253\pi\) | ||||
0.381948 | + | 0.924184i | \(0.375253\pi\) | |||||||
\(758\) | 224.067 | 0.0107368 | ||||||||
\(759\) | −49114.4 | −2.34880 | ||||||||
\(760\) | −246.490 | −0.0117647 | ||||||||
\(761\) | −33817.2 | −1.61087 | −0.805436 | − | 0.592683i | \(-0.798069\pi\) | ||||
−0.805436 | + | 0.592683i | \(0.798069\pi\) | |||||||
\(762\) | −98.4221 | −0.00467908 | ||||||||
\(763\) | 33541.8 | 1.59147 | ||||||||
\(764\) | −5350.85 | −0.253386 | ||||||||
\(765\) | −11039.6 | −0.521750 | ||||||||
\(766\) | 1849.13 | 0.0872219 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −25842.2 | −1.21419 | ||||||||
\(769\) | 36061.0 | 1.69102 | 0.845510 | − | 0.533960i | \(-0.179297\pi\) | ||||
0.845510 | + | 0.533960i | \(0.179297\pi\) | |||||||
\(770\) | 1727.85 | 0.0808668 | ||||||||
\(771\) | 31788.2 | 1.48485 | ||||||||
\(772\) | −36663.3 | −1.70925 | ||||||||
\(773\) | 463.749 | 0.0215781 | 0.0107891 | − | 0.999942i | \(-0.496566\pi\) | ||||
0.0107891 | + | 0.999942i | \(0.496566\pi\) | |||||||
\(774\) | 682.545 | 0.0316971 | ||||||||
\(775\) | 3013.57 | 0.139678 | ||||||||
\(776\) | −994.755 | −0.0460176 | ||||||||
\(777\) | 29147.5 | 1.34576 | ||||||||
\(778\) | 538.140 | 0.0247985 | ||||||||
\(779\) | −2092.28 | −0.0962308 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 34804.1 | 1.59461 | ||||||||
\(782\) | −2111.43 | −0.0965530 | ||||||||
\(783\) | 2379.12 | 0.108586 | ||||||||
\(784\) | 34117.8 | 1.55420 | ||||||||
\(785\) | 18282.5 | 0.831249 | ||||||||
\(786\) | −370.321 | −0.0168052 | ||||||||
\(787\) | 13712.8 | 0.621101 | 0.310551 | − | 0.950557i | \(-0.399487\pi\) | ||||
0.310551 | + | 0.950557i | \(0.399487\pi\) | |||||||
\(788\) | 4173.29 | 0.188664 | ||||||||
\(789\) | −49388.3 | −2.22848 | ||||||||
\(790\) | 224.733 | 0.0101211 | ||||||||
\(791\) | −7820.34 | −0.351529 | ||||||||
\(792\) | −1370.36 | −0.0614819 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −354.963 | −0.0158655 | ||||||||
\(795\) | 16679.4 | 0.744097 | ||||||||
\(796\) | 12551.1 | 0.558870 | ||||||||
\(797\) | 4005.41 | 0.178016 | 0.0890081 | − | 0.996031i | \(-0.471630\pi\) | ||||
0.0890081 | + | 0.996031i | \(0.471630\pi\) | |||||||
\(798\) | −289.722 | −0.0128522 | ||||||||
\(799\) | 871.598 | 0.0385919 | ||||||||
\(800\) | 566.991 | 0.0250577 | ||||||||
\(801\) | 14287.1 | 0.630225 | ||||||||
\(802\) | 460.904 | 0.0202931 | ||||||||
\(803\) | −9519.76 | −0.418362 | ||||||||
\(804\) | 15721.2 | 0.689607 | ||||||||
\(805\) | −60441.4 | −2.64631 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 42802.3 | 1.86705 | ||||||||
\(808\) | 2026.02 | 0.0882120 | ||||||||
\(809\) | −22419.9 | −0.974342 | −0.487171 | − | 0.873307i | \(-0.661971\pi\) | ||||
−0.487171 | + | 0.873307i | \(0.661971\pi\) | |||||||
\(810\) | 1388.68 | 0.0602385 | ||||||||
\(811\) | 14185.7 | 0.614213 | 0.307107 | − | 0.951675i | \(-0.400639\pi\) | ||||
0.307107 | + | 0.951675i | \(0.400639\pi\) | |||||||
\(812\) | −7295.32 | −0.315290 | ||||||||
\(813\) | 18847.5 | 0.813051 | ||||||||
\(814\) | −859.733 | −0.0370192 | ||||||||
\(815\) | 16849.1 | 0.724169 | ||||||||
\(816\) | 29362.8 | 1.25969 | ||||||||
\(817\) | 3060.87 | 0.131073 | ||||||||
\(818\) | −50.8754 | −0.00217459 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −16952.7 | −0.721969 | ||||||||
\(821\) | 30014.4 | 1.27590 | 0.637949 | − | 0.770079i | \(-0.279783\pi\) | ||||
0.637949 | + | 0.770079i | \(0.279783\pi\) | |||||||
\(822\) | −989.858 | −0.0420015 | ||||||||
\(823\) | 11791.4 | 0.499418 | 0.249709 | − | 0.968321i | \(-0.419665\pi\) | ||||
0.249709 | + | 0.968321i | \(0.419665\pi\) | |||||||
\(824\) | 2373.56 | 0.100348 | ||||||||
\(825\) | −4916.04 | −0.207460 | ||||||||
\(826\) | 1727.27 | 0.0727596 | ||||||||
\(827\) | 26657.2 | 1.12087 | 0.560436 | − | 0.828198i | \(-0.310634\pi\) | ||||
0.560436 | + | 0.828198i | \(0.310634\pi\) | |||||||
\(828\) | 23934.7 | 1.00458 | ||||||||
\(829\) | −23450.6 | −0.982475 | −0.491238 | − | 0.871026i | \(-0.663455\pi\) | ||||
−0.491238 | + | 0.871026i | \(0.663455\pi\) | |||||||
\(830\) | 1559.04 | 0.0651990 | ||||||||
\(831\) | −7533.96 | −0.314501 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −38329.1 | −1.59427 | ||||||||
\(834\) | 985.500 | 0.0409174 | ||||||||
\(835\) | −24993.6 | −1.03585 | ||||||||
\(836\) | −3068.42 | −0.126942 | ||||||||
\(837\) | −11700.1 | −0.483170 | ||||||||
\(838\) | 81.3367 | 0.00335290 | ||||||||
\(839\) | 11212.1 | 0.461362 | 0.230681 | − | 0.973029i | \(-0.425905\pi\) | ||||
0.230681 | + | 0.973029i | \(0.425905\pi\) | |||||||
\(840\) | −4701.49 | −0.193115 | ||||||||
\(841\) | −23439.4 | −0.961062 | ||||||||
\(842\) | 1566.30 | 0.0641071 | ||||||||
\(843\) | 52766.5 | 2.15584 | ||||||||
\(844\) | 38150.6 | 1.55592 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 27.5169 | 0.00111826 | ||||||||
\(847\) | 3581.44 | 0.145289 | ||||||||
\(848\) | −15912.9 | −0.644399 | ||||||||
\(849\) | −7344.18 | −0.296881 | ||||||||
\(850\) | −211.341 | −0.00852815 | ||||||||
\(851\) | 30074.1 | 1.21143 | ||||||||
\(852\) | −47285.2 | −1.90137 | ||||||||
\(853\) | 10447.0 | 0.419342 | 0.209671 | − | 0.977772i | \(-0.432761\pi\) | ||||
0.209671 | + | 0.977772i | \(0.432761\pi\) | |||||||
\(854\) | 692.353 | 0.0277422 | ||||||||
\(855\) | −1562.97 | −0.0625177 | ||||||||
\(856\) | 1652.67 | 0.0659894 | ||||||||
\(857\) | −37041.9 | −1.47646 | −0.738230 | − | 0.674549i | \(-0.764338\pi\) | ||||
−0.738230 | + | 0.674549i | \(0.764338\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15972.0 | 0.634409 | 0.317204 | − | 0.948357i | \(-0.397256\pi\) | ||||
0.317204 | + | 0.948357i | \(0.397256\pi\) | |||||||
\(860\) | 24800.7 | 0.983369 | ||||||||
\(861\) | −39907.6 | −1.57961 | ||||||||
\(862\) | −822.510 | −0.0324998 | ||||||||
\(863\) | 32985.8 | 1.30110 | 0.650549 | − | 0.759464i | \(-0.274539\pi\) | ||||
0.650549 | + | 0.759464i | \(0.274539\pi\) | |||||||
\(864\) | −2201.32 | −0.0866787 | ||||||||
\(865\) | 30620.7 | 1.20362 | ||||||||
\(866\) | −905.128 | −0.0355167 | ||||||||
\(867\) | −1108.83 | −0.0434345 | ||||||||
\(868\) | 35876.9 | 1.40293 | ||||||||
\(869\) | 5602.94 | 0.218719 | ||||||||
\(870\) | 305.576 | 0.0119080 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 2692.02 | 0.104545 | ||||||||
\(873\) | −6307.66 | −0.244538 | ||||||||
\(874\) | −298.932 | −0.0115693 | ||||||||
\(875\) | −44079.5 | −1.70304 | ||||||||
\(876\) | 12933.6 | 0.498843 | ||||||||
\(877\) | −12279.5 | −0.472804 | −0.236402 | − | 0.971655i | \(-0.575968\pi\) | ||||
−0.236402 | + | 0.971655i | \(0.575968\pi\) | |||||||
\(878\) | −2157.26 | −0.0829201 | ||||||||
\(879\) | 24879.4 | 0.954677 | ||||||||
\(880\) | −24792.4 | −0.949719 | ||||||||
\(881\) | 30939.0 | 1.18316 | 0.591579 | − | 0.806247i | \(-0.298505\pi\) | ||||
0.591579 | + | 0.806247i | \(0.298505\pi\) | |||||||
\(882\) | −1210.07 | −0.0461965 | ||||||||
\(883\) | 31309.8 | 1.19327 | 0.596636 | − | 0.802512i | \(-0.296503\pi\) | ||||
0.596636 | + | 0.802512i | \(0.296503\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 25978.0 | 0.986712 | ||||||||
\(886\) | 1280.99 | 0.0485729 | ||||||||
\(887\) | −4033.26 | −0.152676 | −0.0763380 | − | 0.997082i | \(-0.524323\pi\) | ||||
−0.0763380 | + | 0.997082i | \(0.524323\pi\) | |||||||
\(888\) | 2339.34 | 0.0884042 | ||||||||
\(889\) | −3019.73 | −0.113924 | ||||||||
\(890\) | −1445.80 | −0.0544531 | ||||||||
\(891\) | 34621.9 | 1.30177 | ||||||||
\(892\) | −16676.5 | −0.625977 | ||||||||
\(893\) | 123.399 | 0.00462419 | ||||||||
\(894\) | 1912.40 | 0.0715440 | ||||||||
\(895\) | −34601.3 | −1.29229 | ||||||||
\(896\) | 8995.93 | 0.335416 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1147.10 | 0.0426272 | ||||||||
\(899\) | −4670.18 | −0.173258 | ||||||||
\(900\) | 2395.72 | 0.0887303 | ||||||||
\(901\) | 17877.1 | 0.661012 | ||||||||
\(902\) | 1177.11 | 0.0434519 | ||||||||
\(903\) | 58382.2 | 2.15154 | ||||||||
\(904\) | −627.650 | −0.0230922 | ||||||||
\(905\) | 23238.2 | 0.853550 | ||||||||
\(906\) | −3373.80 | −0.123716 | ||||||||
\(907\) | 8809.38 | 0.322504 | 0.161252 | − | 0.986913i | \(-0.448447\pi\) | ||||
0.161252 | + | 0.986913i | \(0.448447\pi\) | |||||||
\(908\) | −17345.0 | −0.633936 | ||||||||
\(909\) | 12846.9 | 0.468760 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −33046.9 | −1.20186 | −0.600930 | − | 0.799302i | \(-0.705203\pi\) | ||||
−0.600930 | + | 0.799302i | \(0.705203\pi\) | |||||||
\(912\) | 4157.14 | 0.150939 | ||||||||
\(913\) | 38869.3 | 1.40897 | ||||||||
\(914\) | −1992.73 | −0.0721155 | ||||||||
\(915\) | 10412.9 | 0.376219 | ||||||||
\(916\) | −47844.0 | −1.72578 | ||||||||
\(917\) | −11362.0 | −0.409165 | ||||||||
\(918\) | 820.522 | 0.0295003 | ||||||||
\(919\) | −4512.85 | −0.161986 | −0.0809930 | − | 0.996715i | \(-0.525809\pi\) | ||||
−0.0809930 | + | 0.996715i | \(0.525809\pi\) | |||||||
\(920\) | −4850.95 | −0.173838 | ||||||||
\(921\) | −42657.7 | −1.52619 | ||||||||
\(922\) | −2310.72 | −0.0825374 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −58526.1 | −2.08373 | ||||||||
\(925\) | 3010.23 | 0.107001 | ||||||||
\(926\) | −1472.35 | −0.0522510 | ||||||||
\(927\) | 15050.6 | 0.533252 | ||||||||
\(928\) | −878.676 | −0.0310818 | ||||||||
\(929\) | −33818.5 | −1.19435 | −0.597174 | − | 0.802111i | \(-0.703710\pi\) | ||||
−0.597174 | + | 0.802111i | \(0.703710\pi\) | |||||||
\(930\) | −1502.76 | −0.0529866 | ||||||||
\(931\) | −5426.58 | −0.191030 | ||||||||
\(932\) | 12365.5 | 0.434600 | ||||||||
\(933\) | −4300.47 | −0.150901 | ||||||||
\(934\) | −523.168 | −0.0183282 | ||||||||
\(935\) | 27852.7 | 0.974204 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 19737.5 | 0.688150 | 0.344075 | − | 0.938942i | \(-0.388193\pi\) | ||||
0.344075 | + | 0.938942i | \(0.388193\pi\) | |||||||
\(938\) | −1343.35 | −0.0467613 | ||||||||
\(939\) | 54199.3 | 1.88363 | ||||||||
\(940\) | 999.844 | 0.0346929 | ||||||||
\(941\) | −21587.6 | −0.747860 | −0.373930 | − | 0.927457i | \(-0.621990\pi\) | ||||
−0.373930 | + | 0.927457i | \(0.621990\pi\) | |||||||
\(942\) | 1724.68 | 0.0596531 | ||||||||
\(943\) | −41176.3 | −1.42193 | ||||||||
\(944\) | −24784.1 | −0.854507 | ||||||||
\(945\) | 23488.1 | 0.808539 | ||||||||
\(946\) | −1722.04 | −0.0591843 | ||||||||
\(947\) | 5830.13 | 0.200057 | 0.100028 | − | 0.994985i | \(-0.468107\pi\) | ||||
0.100028 | + | 0.994985i | \(0.468107\pi\) | |||||||
\(948\) | −7612.20 | −0.260794 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −29.9213 | −0.00102187 | ||||||||
\(951\) | −34122.1 | −1.16350 | ||||||||
\(952\) | −5039.08 | −0.171552 | ||||||||
\(953\) | 8839.77 | 0.300470 | 0.150235 | − | 0.988650i | \(-0.451997\pi\) | ||||
0.150235 | + | 0.988650i | \(0.451997\pi\) | |||||||
\(954\) | 564.391 | 0.0191539 | ||||||||
\(955\) | 6876.58 | 0.233006 | ||||||||
\(956\) | 31073.9 | 1.05126 | ||||||||
\(957\) | 7618.47 | 0.257336 | ||||||||
\(958\) | 2963.60 | 0.0999474 | ||||||||
\(959\) | −30370.2 | −1.02263 | ||||||||
\(960\) | 33494.3 | 1.12607 | ||||||||
\(961\) | −6823.95 | −0.229061 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 10479.4 | 0.350669 | ||||||||
\(964\) | −32614.7 | −1.08968 | ||||||||
\(965\) | 47117.4 | 1.57178 | ||||||||
\(966\) | −5701.75 | −0.189908 | ||||||||
\(967\) | 10346.1 | 0.344063 | 0.172032 | − | 0.985091i | \(-0.444967\pi\) | ||||
0.172032 | + | 0.985091i | \(0.444967\pi\) | |||||||
\(968\) | 287.442 | 0.00954414 | ||||||||
\(969\) | −4670.28 | −0.154831 | ||||||||
\(970\) | 638.310 | 0.0211288 | ||||||||
\(971\) | −17420.0 | −0.575730 | −0.287865 | − | 0.957671i | \(-0.592945\pi\) | ||||
−0.287865 | + | 0.957671i | \(0.592945\pi\) | |||||||
\(972\) | −30408.0 | −1.00343 | ||||||||
\(973\) | 30236.5 | 0.996236 | ||||||||
\(974\) | −60.7753 | −0.00199935 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9934.37 | −0.325811 | ||||||||
\(977\) | −41735.0 | −1.36665 | −0.683327 | − | 0.730113i | \(-0.739468\pi\) | ||||
−0.683327 | + | 0.730113i | \(0.739468\pi\) | |||||||
\(978\) | 1589.46 | 0.0519687 | ||||||||
\(979\) | −36046.0 | −1.17675 | ||||||||
\(980\) | −43968.9 | −1.43320 | ||||||||
\(981\) | 17069.9 | 0.555555 | ||||||||
\(982\) | −3000.55 | −0.0975067 | ||||||||
\(983\) | −34123.8 | −1.10720 | −0.553602 | − | 0.832781i | \(-0.686747\pi\) | ||||
−0.553602 | + | 0.832781i | \(0.686747\pi\) | |||||||
\(984\) | −3202.93 | −0.103766 | ||||||||
\(985\) | −5363.26 | −0.173490 | ||||||||
\(986\) | 327.518 | 0.0105784 | ||||||||
\(987\) | 2353.69 | 0.0759054 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 60238.2 | 1.93677 | ||||||||
\(990\) | 879.327 | 0.0282291 | ||||||||
\(991\) | −54296.7 | −1.74046 | −0.870228 | − | 0.492649i | \(-0.836029\pi\) | ||||
−0.870228 | + | 0.492649i | \(0.836029\pi\) | |||||||
\(992\) | 4321.16 | 0.138303 | ||||||||
\(993\) | 18210.1 | 0.581952 | ||||||||
\(994\) | 4040.46 | 0.128929 | ||||||||
\(995\) | −16129.9 | −0.513921 | ||||||||
\(996\) | −52808.3 | −1.68001 | ||||||||
\(997\) | 46879.3 | 1.48915 | 0.744575 | − | 0.667538i | \(-0.232652\pi\) | ||||
0.744575 | + | 0.667538i | \(0.232652\pi\) | |||||||
\(998\) | 115.186 | 0.00365347 | ||||||||
\(999\) | −11687.1 | −0.370133 |
(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 | 169.4.a.k.1.5 | ✓ | 9 | |
3.2 | odd | 2 | 1521.4.a.bh.1.5 | 9 | |||
13.2 | odd | 12 | 169.4.e.h.147.9 | 36 | |||
13.3 | even | 3 | 169.4.c.l.22.5 | 18 | |||
13.4 | even | 6 | 169.4.c.k.146.5 | 18 | |||
13.5 | odd | 4 | 169.4.b.g.168.10 | 18 | |||
13.6 | odd | 12 | 169.4.e.h.23.10 | 36 | |||
13.7 | odd | 12 | 169.4.e.h.23.9 | 36 | |||
13.8 | odd | 4 | 169.4.b.g.168.9 | 18 | |||
13.9 | even | 3 | 169.4.c.l.146.5 | 18 | |||
13.10 | even | 6 | 169.4.c.k.22.5 | 18 | |||
13.11 | odd | 12 | 169.4.e.h.147.10 | 36 | |||
13.12 | even | 2 | 169.4.a.l.1.5 | yes | 9 | ||
39.38 | odd | 2 | 1521.4.a.bg.1.5 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
169.4.a.k.1.5 | ✓ | 9 | 1.1 | even | 1 | trivial | |
169.4.a.l.1.5 | yes | 9 | 13.12 | even | 2 | ||
169.4.b.g.168.9 | 18 | 13.8 | odd | 4 | |||
169.4.b.g.168.10 | 18 | 13.5 | odd | 4 | |||
169.4.c.k.22.5 | 18 | 13.10 | even | 6 | |||
169.4.c.k.146.5 | 18 | 13.4 | even | 6 | |||
169.4.c.l.22.5 | 18 | 13.3 | even | 3 | |||
169.4.c.l.146.5 | 18 | 13.9 | even | 3 | |||
169.4.e.h.23.9 | 36 | 13.7 | odd | 12 | |||
169.4.e.h.23.10 | 36 | 13.6 | odd | 12 | |||
169.4.e.h.147.9 | 36 | 13.2 | odd | 12 | |||
169.4.e.h.147.10 | 36 | 13.11 | odd | 12 | |||
1521.4.a.bg.1.5 | 9 | 39.38 | odd | 2 | |||
1521.4.a.bh.1.5 | 9 | 3.2 | odd | 2 |