Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [189,4,Mod(1,189)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(189, 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("189.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 189 = 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 189.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: | \(11.1513609911\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 189.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.73205 | −1.67303 | −0.836516 | − | 0.547942i | \(-0.815411\pi\) | ||||
−0.836516 | + | 0.547942i | \(0.815411\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 14.3923 | 1.79904 | ||||||||
\(5\) | −9.92820 | −0.888005 | −0.444003 | − | 0.896025i | \(-0.646442\pi\) | ||||
−0.444003 | + | 0.896025i | \(0.646442\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | −30.2487 | −1.33682 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 46.9808 | 1.48566 | ||||||||
\(11\) | 3.71281 | 0.101769 | 0.0508843 | − | 0.998705i | \(-0.483796\pi\) | ||||
0.0508843 | + | 0.998705i | \(0.483796\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −15.5692 | −0.332163 | −0.166082 | − | 0.986112i | \(-0.553112\pi\) | ||||
−0.166082 | + | 0.986112i | \(0.553112\pi\) | |||||||
\(14\) | −33.1244 | −0.632347 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 28.0000 | 0.437500 | ||||||||
\(17\) | 33.4974 | 0.477901 | 0.238951 | − | 0.971032i | \(-0.423197\pi\) | ||||
0.238951 | + | 0.971032i | \(0.423197\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 135.923 | 1.64120 | 0.820602 | − | 0.571500i | \(-0.193638\pi\) | ||||
0.820602 | + | 0.571500i | \(0.193638\pi\) | |||||||
\(20\) | −142.890 | −1.59756 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −17.5692 | −0.170262 | ||||||||
\(23\) | 87.7795 | 0.795795 | 0.397897 | − | 0.917430i | \(-0.369740\pi\) | ||||
0.397897 | + | 0.917430i | \(0.369740\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −26.4308 | −0.211446 | ||||||||
\(26\) | 73.6743 | 0.555720 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 100.746 | 0.679972 | ||||||||
\(29\) | −242.354 | −1.55186 | −0.775931 | − | 0.630818i | \(-0.782719\pi\) | ||||
−0.775931 | + | 0.630818i | \(0.782719\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −194.708 | −1.12808 | −0.564041 | − | 0.825747i | \(-0.690754\pi\) | ||||
−0.564041 | + | 0.825747i | \(0.690754\pi\) | |||||||
\(32\) | 109.492 | 0.604865 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −158.512 | −0.799544 | ||||||||
\(35\) | −69.4974 | −0.335635 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −239.708 | −1.06507 | −0.532536 | − | 0.846407i | \(-0.678761\pi\) | ||||
−0.532536 | + | 0.846407i | \(0.678761\pi\) | |||||||
\(38\) | −643.195 | −2.74579 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 300.315 | 1.18710 | ||||||||
\(41\) | −470.338 | −1.79157 | −0.895787 | − | 0.444484i | \(-0.853387\pi\) | ||||
−0.895787 | + | 0.444484i | \(0.853387\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −448.215 | −1.58959 | −0.794793 | − | 0.606880i | \(-0.792421\pi\) | ||||
−0.794793 | + | 0.606880i | \(0.792421\pi\) | |||||||
\(44\) | 53.4359 | 0.183086 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −415.377 | −1.33139 | ||||||||
\(47\) | −4.15906 | −0.0129077 | −0.00645384 | − | 0.999979i | \(-0.502054\pi\) | ||||
−0.00645384 | + | 0.999979i | \(0.502054\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 125.072 | 0.353756 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −224.077 | −0.597575 | ||||||||
\(53\) | 736.543 | 1.90891 | 0.954453 | − | 0.298361i | \(-0.0964400\pi\) | ||||
0.954453 | + | 0.298361i | \(0.0964400\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −36.8616 | −0.0903711 | ||||||||
\(56\) | −211.741 | −0.505269 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1146.83 | 2.59631 | ||||||||
\(59\) | −279.564 | −0.616884 | −0.308442 | − | 0.951243i | \(-0.599808\pi\) | ||||
−0.308442 | + | 0.951243i | \(0.599808\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −514.831 | −1.08061 | −0.540306 | − | 0.841469i | \(-0.681691\pi\) | ||||
−0.540306 | + | 0.841469i | \(0.681691\pi\) | |||||||
\(62\) | 921.367 | 1.88732 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −742.123 | −1.44946 | ||||||||
\(65\) | 154.574 | 0.294963 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −102.123 | −0.186214 | −0.0931068 | − | 0.995656i | \(-0.529680\pi\) | ||||
−0.0931068 | + | 0.995656i | \(0.529680\pi\) | |||||||
\(68\) | 482.105 | 0.859762 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 328.865 | 0.561528 | ||||||||
\(71\) | 44.1539 | 0.0738043 | 0.0369021 | − | 0.999319i | \(-0.488251\pi\) | ||||
0.0369021 | + | 0.999319i | \(0.488251\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −901.615 | −1.44556 | −0.722781 | − | 0.691077i | \(-0.757137\pi\) | ||||
−0.722781 | + | 0.691077i | \(0.757137\pi\) | |||||||
\(74\) | 1134.31 | 1.78190 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1956.25 | 2.95259 | ||||||||
\(77\) | 25.9897 | 0.0384649 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1054.31 | 1.50150 | 0.750752 | − | 0.660584i | \(-0.229691\pi\) | ||||
0.750752 | + | 0.660584i | \(0.229691\pi\) | |||||||
\(80\) | −277.990 | −0.388502 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2225.67 | 2.99736 | ||||||||
\(83\) | −487.246 | −0.644364 | −0.322182 | − | 0.946678i | \(-0.604416\pi\) | ||||
−0.322182 | + | 0.946678i | \(0.604416\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −332.569 | −0.424379 | ||||||||
\(86\) | 2120.98 | 2.65943 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −112.308 | −0.136046 | ||||||||
\(89\) | −963.682 | −1.14775 | −0.573877 | − | 0.818942i | \(-0.694561\pi\) | ||||
−0.573877 | + | 0.818942i | \(0.694561\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −108.985 | −0.125546 | ||||||||
\(92\) | 1263.35 | 1.43167 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 19.6809 | 0.0215950 | ||||||||
\(95\) | −1349.47 | −1.45740 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 726.908 | 0.760890 | 0.380445 | − | 0.924804i | \(-0.375771\pi\) | ||||
0.380445 | + | 0.924804i | \(0.375771\pi\) | |||||||
\(98\) | −231.870 | −0.239005 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −380.400 | −0.380400 | ||||||||
\(101\) | −268.872 | −0.264889 | −0.132444 | − | 0.991190i | \(-0.542283\pi\) | ||||
−0.132444 | + | 0.991190i | \(0.542283\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1108.35 | 1.06028 | 0.530142 | − | 0.847909i | \(-0.322138\pi\) | ||||
0.530142 | + | 0.847909i | \(0.322138\pi\) | |||||||
\(104\) | 470.949 | 0.444042 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3485.36 | −3.19366 | ||||||||
\(107\) | −84.4665 | −0.0763148 | −0.0381574 | − | 0.999272i | \(-0.512149\pi\) | ||||
−0.0381574 | + | 0.999272i | \(0.512149\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −174.169 | −0.153050 | −0.0765248 | − | 0.997068i | \(-0.524382\pi\) | ||||
−0.0765248 | + | 0.997068i | \(0.524382\pi\) | |||||||
\(110\) | 174.431 | 0.151194 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 196.000 | 0.165359 | ||||||||
\(113\) | −1049.77 | −0.873929 | −0.436964 | − | 0.899479i | \(-0.643946\pi\) | ||||
−0.436964 | + | 0.899479i | \(0.643946\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −871.492 | −0.706670 | ||||||||
\(116\) | −3488.03 | −2.79186 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1322.91 | 1.03207 | ||||||||
\(119\) | 234.482 | 0.180630 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1317.22 | −0.989643 | ||||||||
\(122\) | 2436.20 | 1.80790 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2802.29 | −2.02946 | ||||||||
\(125\) | 1503.44 | 1.07577 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −293.969 | −0.205398 | −0.102699 | − | 0.994712i | \(-0.532748\pi\) | ||||
−0.102699 | + | 0.994712i | \(0.532748\pi\) | |||||||
\(128\) | 2635.83 | 1.82013 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −731.454 | −0.493483 | ||||||||
\(131\) | −1110.76 | −0.740820 | −0.370410 | − | 0.928868i | \(-0.620783\pi\) | ||||
−0.370410 | + | 0.928868i | \(0.620783\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 951.461 | 0.620317 | ||||||||
\(134\) | 483.251 | 0.311541 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1013.25 | −0.638866 | ||||||||
\(137\) | 238.113 | 0.148492 | 0.0742458 | − | 0.997240i | \(-0.476345\pi\) | ||||
0.0742458 | + | 0.997240i | \(0.476345\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −189.108 | −0.115395 | −0.0576974 | − | 0.998334i | \(-0.518376\pi\) | ||||
−0.0576974 | + | 0.998334i | \(0.518376\pi\) | |||||||
\(140\) | −1000.23 | −0.603819 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −208.939 | −0.123477 | ||||||||
\(143\) | −57.8056 | −0.0338038 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2406.14 | 1.37806 | ||||||||
\(146\) | 4266.49 | 2.41847 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3449.95 | −1.91611 | ||||||||
\(149\) | −1107.59 | −0.608975 | −0.304487 | − | 0.952516i | \(-0.598485\pi\) | ||||
−0.304487 | + | 0.952516i | \(0.598485\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3512.55 | 1.89303 | 0.946515 | − | 0.322660i | \(-0.104577\pi\) | ||||
0.946515 | + | 0.322660i | \(0.104577\pi\) | |||||||
\(152\) | −4111.50 | −2.19399 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −122.985 | −0.0643531 | ||||||||
\(155\) | 1933.10 | 1.00174 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 524.169 | 0.266454 | 0.133227 | − | 0.991086i | \(-0.457466\pi\) | ||||
0.133227 | + | 0.991086i | \(0.457466\pi\) | |||||||
\(158\) | −4989.04 | −2.51207 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1087.06 | −0.537123 | ||||||||
\(161\) | 614.456 | 0.300782 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 245.693 | 0.118062 | 0.0590311 | − | 0.998256i | \(-0.481199\pi\) | ||||
0.0590311 | + | 0.998256i | \(0.481199\pi\) | |||||||
\(164\) | −6769.25 | −3.22311 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2305.67 | 1.07804 | ||||||||
\(167\) | −586.785 | −0.271897 | −0.135948 | − | 0.990716i | \(-0.543408\pi\) | ||||
−0.135948 | + | 0.990716i | \(0.543408\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1954.60 | −0.889667 | ||||||||
\(170\) | 1573.73 | 0.710000 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −6450.85 | −2.85973 | ||||||||
\(173\) | −2957.80 | −1.29987 | −0.649936 | − | 0.759989i | \(-0.725204\pi\) | ||||
−0.649936 | + | 0.759989i | \(0.725204\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −185.015 | −0.0799192 | ||||||||
\(176\) | 103.959 | 0.0445238 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 4560.19 | 1.92023 | ||||||||
\(179\) | −2724.73 | −1.13774 | −0.568872 | − | 0.822426i | \(-0.692620\pi\) | ||||
−0.568872 | + | 0.822426i | \(0.692620\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 446.138 | 0.183211 | 0.0916055 | − | 0.995795i | \(-0.470800\pi\) | ||||
0.0916055 | + | 0.995795i | \(0.470800\pi\) | |||||||
\(182\) | 515.720 | 0.210043 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2655.22 | −1.06383 | ||||||||
\(185\) | 2379.87 | 0.945791 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 124.370 | 0.0486354 | ||||||||
\(188\) | −59.8584 | −0.0232214 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6385.77 | 2.43828 | ||||||||
\(191\) | −3517.90 | −1.33270 | −0.666351 | − | 0.745638i | \(-0.732145\pi\) | ||||
−0.666351 | + | 0.745638i | \(0.732145\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4869.61 | 1.81618 | 0.908090 | − | 0.418776i | \(-0.137541\pi\) | ||||
0.908090 | + | 0.418776i | \(0.137541\pi\) | |||||||
\(194\) | −3439.76 | −1.27299 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 705.223 | 0.257005 | ||||||||
\(197\) | 3427.46 | 1.23958 | 0.619788 | − | 0.784769i | \(-0.287219\pi\) | ||||
0.619788 | + | 0.784769i | \(0.287219\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4012.51 | −1.42934 | −0.714671 | − | 0.699461i | \(-0.753424\pi\) | ||||
−0.714671 | + | 0.699461i | \(0.753424\pi\) | |||||||
\(200\) | 799.497 | 0.282665 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1272.32 | 0.443167 | ||||||||
\(203\) | −1696.48 | −0.586548 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4669.61 | 1.59093 | ||||||||
\(206\) | −5244.79 | −1.77389 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −435.938 | −0.145321 | ||||||||
\(209\) | 504.657 | 0.167023 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4281.08 | 1.39678 | 0.698392 | − | 0.715715i | \(-0.253899\pi\) | ||||
0.698392 | + | 0.715715i | \(0.253899\pi\) | |||||||
\(212\) | 10600.6 | 3.43419 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 399.700 | 0.127677 | ||||||||
\(215\) | 4449.97 | 1.41156 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1362.95 | −0.426375 | ||||||||
\(218\) | 824.178 | 0.256057 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −530.523 | −0.162581 | ||||||||
\(221\) | −521.529 | −0.158741 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −764.153 | −0.229469 | −0.114734 | − | 0.993396i | \(-0.536602\pi\) | ||||
−0.114734 | + | 0.993396i | \(0.536602\pi\) | |||||||
\(224\) | 766.446 | 0.228617 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4967.56 | 1.46211 | ||||||||
\(227\) | −3872.35 | −1.13223 | −0.566116 | − | 0.824325i | \(-0.691555\pi\) | ||||
−0.566116 | + | 0.824325i | \(0.691555\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3866.11 | −1.11563 | −0.557816 | − | 0.829965i | \(-0.688360\pi\) | ||||
−0.557816 | + | 0.829965i | \(0.688360\pi\) | |||||||
\(230\) | 4123.95 | 1.18228 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7330.89 | 2.07455 | ||||||||
\(233\) | 5378.29 | 1.51220 | 0.756102 | − | 0.654454i | \(-0.227102\pi\) | ||||
0.756102 | + | 0.654454i | \(0.227102\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 41.2920 | 0.0114621 | ||||||||
\(236\) | −4023.57 | −1.10980 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1109.58 | −0.302199 | ||||||||
\(239\) | −4763.15 | −1.28913 | −0.644566 | − | 0.764548i | \(-0.722962\pi\) | ||||
−0.644566 | + | 0.764548i | \(0.722962\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −318.030 | −0.0850047 | −0.0425023 | − | 0.999096i | \(-0.513533\pi\) | ||||
−0.0425023 | + | 0.999096i | \(0.513533\pi\) | |||||||
\(242\) | 6233.13 | 1.65571 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −7409.60 | −1.94406 | ||||||||
\(245\) | −486.482 | −0.126858 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2116.22 | −0.545148 | ||||||||
\(248\) | 5889.66 | 1.50804 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −7114.33 | −1.79980 | ||||||||
\(251\) | −1577.00 | −0.396571 | −0.198285 | − | 0.980144i | \(-0.563537\pi\) | ||||
−0.198285 | + | 0.980144i | \(0.563537\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 325.909 | 0.0809870 | ||||||||
\(254\) | 1391.08 | 0.343638 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −6535.88 | −1.59567 | ||||||||
\(257\) | 6069.46 | 1.47316 | 0.736580 | − | 0.676350i | \(-0.236439\pi\) | ||||
0.736580 | + | 0.676350i | \(0.236439\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1677.95 | −0.402560 | ||||||||
\(260\) | 2224.68 | 0.530650 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 5256.17 | 1.23942 | ||||||||
\(263\) | 3654.73 | 0.856883 | 0.428441 | − | 0.903570i | \(-0.359063\pi\) | ||||
0.428441 | + | 0.903570i | \(0.359063\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7312.55 | −1.69512 | ||||||||
\(266\) | −4502.36 | −1.03781 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1469.78 | −0.335005 | ||||||||
\(269\) | 435.652 | 0.0987441 | 0.0493721 | − | 0.998780i | \(-0.484278\pi\) | ||||
0.0493721 | + | 0.998780i | \(0.484278\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1230.98 | 0.275930 | 0.137965 | − | 0.990437i | \(-0.455944\pi\) | ||||
0.137965 | + | 0.990437i | \(0.455944\pi\) | |||||||
\(272\) | 937.928 | 0.209082 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1126.76 | −0.248431 | ||||||||
\(275\) | −98.1325 | −0.0215186 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3994.17 | 0.866377 | 0.433188 | − | 0.901303i | \(-0.357388\pi\) | ||||
0.433188 | + | 0.901303i | \(0.357388\pi\) | |||||||
\(278\) | 894.866 | 0.193059 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2102.21 | 0.448682 | ||||||||
\(281\) | 3615.71 | 0.767598 | 0.383799 | − | 0.923417i | \(-0.374616\pi\) | ||||
0.383799 | + | 0.923417i | \(0.374616\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2353.42 | −0.494332 | −0.247166 | − | 0.968973i | \(-0.579499\pi\) | ||||
−0.247166 | + | 0.968973i | \(0.579499\pi\) | |||||||
\(284\) | 635.476 | 0.132777 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 273.539 | 0.0565549 | ||||||||
\(287\) | −3292.37 | −0.677151 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3790.92 | −0.771611 | ||||||||
\(290\) | −11386.0 | −2.30554 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −12976.3 | −2.60062 | ||||||||
\(293\) | −3580.68 | −0.713943 | −0.356972 | − | 0.934115i | \(-0.616191\pi\) | ||||
−0.356972 | + | 0.934115i | \(0.616191\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2775.57 | 0.547796 | ||||||||
\(296\) | 7250.85 | 1.42381 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5241.17 | 1.01883 | ||||||||
\(299\) | −1366.66 | −0.264334 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3137.51 | −0.600807 | ||||||||
\(302\) | −16621.6 | −3.16710 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3805.85 | 0.718027 | ||||||||
\(305\) | 5111.34 | 0.959589 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9077.92 | −1.68764 | −0.843818 | − | 0.536629i | \(-0.819697\pi\) | ||||
−0.843818 | + | 0.536629i | \(0.819697\pi\) | |||||||
\(308\) | 374.052 | 0.0691999 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −9147.51 | −1.67595 | ||||||||
\(311\) | 8966.68 | 1.63490 | 0.817450 | − | 0.576000i | \(-0.195387\pi\) | ||||
0.817450 | + | 0.576000i | \(0.195387\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7191.74 | 1.29873 | 0.649363 | − | 0.760479i | \(-0.275036\pi\) | ||||
0.649363 | + | 0.760479i | \(0.275036\pi\) | |||||||
\(314\) | −2480.39 | −0.445786 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 15173.9 | 2.70126 | ||||||||
\(317\) | 2288.95 | 0.405553 | 0.202776 | − | 0.979225i | \(-0.435004\pi\) | ||||
0.202776 | + | 0.979225i | \(0.435004\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −899.814 | −0.157931 | ||||||||
\(320\) | 7367.95 | 1.28713 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2907.64 | −0.503218 | ||||||||
\(323\) | 4553.07 | 0.784333 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 411.507 | 0.0702347 | ||||||||
\(326\) | −1162.63 | −0.197522 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 14227.1 | 2.39501 | ||||||||
\(329\) | −29.1134 | −0.00487864 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6298.61 | −1.04593 | −0.522965 | − | 0.852354i | \(-0.675174\pi\) | ||||
−0.522965 | + | 0.852354i | \(0.675174\pi\) | |||||||
\(332\) | −7012.59 | −1.15923 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2776.70 | 0.454892 | ||||||||
\(335\) | 1013.90 | 0.165359 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 189.615 | 0.0306498 | 0.0153249 | − | 0.999883i | \(-0.495122\pi\) | ||||
0.0153249 | + | 0.999883i | \(0.495122\pi\) | |||||||
\(338\) | 9249.26 | 1.48844 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −4786.44 | −0.763474 | ||||||||
\(341\) | −722.913 | −0.114803 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | 13557.9 | 2.12499 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 13996.5 | 2.17473 | ||||||||
\(347\) | −50.4728 | −0.00780841 | −0.00390421 | − | 0.999992i | \(-0.501243\pi\) | ||||
−0.00390421 | + | 0.999992i | \(0.501243\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1338.71 | −0.205328 | −0.102664 | − | 0.994716i | \(-0.532737\pi\) | ||||
−0.102664 | + | 0.994716i | \(0.532737\pi\) | |||||||
\(350\) | 875.503 | 0.133707 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 406.524 | 0.0615563 | ||||||||
\(353\) | −3192.99 | −0.481433 | −0.240717 | − | 0.970595i | \(-0.577382\pi\) | ||||
−0.240717 | + | 0.970595i | \(0.577382\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −438.369 | −0.0655386 | ||||||||
\(356\) | −13869.6 | −2.06485 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 12893.6 | 1.90348 | ||||||||
\(359\) | −6661.22 | −0.979292 | −0.489646 | − | 0.871921i | \(-0.662874\pi\) | ||||
−0.489646 | + | 0.871921i | \(0.662874\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11616.1 | 1.69355 | ||||||||
\(362\) | −2111.15 | −0.306518 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1568.54 | −0.225862 | ||||||||
\(365\) | 8951.42 | 1.28367 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4592.77 | 0.653244 | 0.326622 | − | 0.945155i | \(-0.394090\pi\) | ||||
0.326622 | + | 0.945155i | \(0.394090\pi\) | |||||||
\(368\) | 2457.82 | 0.348160 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −11261.6 | −1.58234 | ||||||||
\(371\) | 5155.80 | 0.721499 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6982.57 | 0.969286 | 0.484643 | − | 0.874712i | \(-0.338950\pi\) | ||||
0.484643 | + | 0.874712i | \(0.338950\pi\) | |||||||
\(374\) | −588.524 | −0.0813685 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 125.806 | 0.0172552 | ||||||||
\(377\) | 3773.26 | 0.515472 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12060.4 | −1.63457 | −0.817286 | − | 0.576233i | \(-0.804522\pi\) | ||||
−0.817286 | + | 0.576233i | \(0.804522\pi\) | |||||||
\(380\) | −19422.0 | −2.62192 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 16646.9 | 2.22965 | ||||||||
\(383\) | −9674.46 | −1.29071 | −0.645355 | − | 0.763883i | \(-0.723291\pi\) | ||||
−0.645355 | + | 0.763883i | \(0.723291\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −258.031 | −0.0341571 | ||||||||
\(386\) | −23043.3 | −3.03853 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 10461.9 | 1.36887 | ||||||||
\(389\) | 11377.9 | 1.48299 | 0.741496 | − | 0.670957i | \(-0.234117\pi\) | ||||
0.741496 | + | 0.670957i | \(0.234117\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2940.39 | 0.380311 | ||||||||
\(392\) | −1482.19 | −0.190974 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −16218.9 | −2.07385 | ||||||||
\(395\) | −10467.4 | −1.33334 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15202.7 | −1.92192 | −0.960958 | − | 0.276693i | \(-0.910762\pi\) | ||||
−0.960958 | + | 0.276693i | \(0.910762\pi\) | |||||||
\(398\) | 18987.4 | 2.39134 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −740.062 | −0.0925077 | ||||||||
\(401\) | 1396.02 | 0.173851 | 0.0869254 | − | 0.996215i | \(-0.472296\pi\) | ||||
0.0869254 | + | 0.996215i | \(0.472296\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3031.45 | 0.374707 | ||||||||
\(404\) | −3869.69 | −0.476545 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8027.81 | 0.981315 | ||||||||
\(407\) | −889.990 | −0.108391 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8673.54 | −1.04860 | −0.524302 | − | 0.851533i | \(-0.675674\pi\) | ||||
−0.524302 | + | 0.851533i | \(0.675674\pi\) | |||||||
\(410\) | −22096.9 | −2.66167 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 15951.8 | 1.90749 | ||||||||
\(413\) | −1956.95 | −0.233160 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4837.48 | 0.572199 | ||||||||
\(416\) | −1704.71 | −0.200914 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2388.06 | −0.279435 | ||||||||
\(419\) | −7313.92 | −0.852765 | −0.426382 | − | 0.904543i | \(-0.640212\pi\) | ||||
−0.426382 | + | 0.904543i | \(0.640212\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7695.26 | −0.890841 | −0.445420 | − | 0.895322i | \(-0.646946\pi\) | ||||
−0.445420 | + | 0.895322i | \(0.646946\pi\) | |||||||
\(422\) | −20258.3 | −2.33687 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −22279.5 | −2.55186 | ||||||||
\(425\) | −885.363 | −0.101050 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3603.81 | −0.408433 | ||||||||
\(428\) | −1215.67 | −0.137293 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −21057.5 | −2.36159 | ||||||||
\(431\) | −6258.10 | −0.699402 | −0.349701 | − | 0.936861i | \(-0.613717\pi\) | ||||
−0.349701 | + | 0.936861i | \(0.613717\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11923.3 | −1.32332 | −0.661660 | − | 0.749804i | \(-0.730148\pi\) | ||||
−0.661660 | + | 0.749804i | \(0.730148\pi\) | |||||||
\(434\) | 6449.57 | 0.713339 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2506.70 | −0.275342 | ||||||||
\(437\) | 11931.3 | 1.30606 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17115.6 | 1.86079 | 0.930393 | − | 0.366564i | \(-0.119466\pi\) | ||||
0.930393 | + | 0.366564i | \(0.119466\pi\) | |||||||
\(440\) | 1115.01 | 0.120810 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2467.90 | 0.265579 | ||||||||
\(443\) | 8095.04 | 0.868187 | 0.434094 | − | 0.900868i | \(-0.357069\pi\) | ||||
0.434094 | + | 0.900868i | \(0.357069\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9567.63 | 1.01921 | ||||||||
\(446\) | 3616.01 | 0.383908 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −5194.86 | −0.547844 | ||||||||
\(449\) | 6156.71 | 0.647111 | 0.323556 | − | 0.946209i | \(-0.395122\pi\) | ||||
0.323556 | + | 0.946209i | \(0.395122\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1746.28 | −0.182326 | ||||||||
\(452\) | −15108.6 | −1.57223 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 18324.2 | 1.89426 | ||||||||
\(455\) | 1082.02 | 0.111486 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5657.23 | 0.579068 | 0.289534 | − | 0.957168i | \(-0.406500\pi\) | ||||
0.289534 | + | 0.957168i | \(0.406500\pi\) | |||||||
\(458\) | 18294.6 | 1.86649 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −12542.8 | −1.27133 | ||||||||
\(461\) | 1414.61 | 0.142918 | 0.0714589 | − | 0.997444i | \(-0.477235\pi\) | ||||
0.0714589 | + | 0.997444i | \(0.477235\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5404.92 | −0.542523 | −0.271261 | − | 0.962506i | \(-0.587441\pi\) | ||||
−0.271261 | + | 0.962506i | \(0.587441\pi\) | |||||||
\(464\) | −6785.91 | −0.678939 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −25450.3 | −2.52996 | ||||||||
\(467\) | −16952.8 | −1.67983 | −0.839916 | − | 0.542717i | \(-0.817396\pi\) | ||||
−0.839916 | + | 0.542717i | \(0.817396\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −714.861 | −0.0703821 | ||||||||
\(470\) | −195.396 | −0.0191765 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 8456.45 | 0.824661 | ||||||||
\(473\) | −1664.14 | −0.161770 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3592.55 | −0.347027 | ||||||||
\(476\) | 3374.74 | 0.324960 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 22539.5 | 2.15676 | ||||||||
\(479\) | 18372.7 | 1.75255 | 0.876276 | − | 0.481810i | \(-0.160021\pi\) | ||||
0.876276 | + | 0.481810i | \(0.160021\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3732.06 | 0.353778 | ||||||||
\(482\) | 1504.94 | 0.142216 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −18957.8 | −1.78041 | ||||||||
\(485\) | −7216.89 | −0.675674 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −42.5560 | −0.00395974 | −0.00197987 | − | 0.999998i | \(-0.500630\pi\) | ||||
−0.00197987 | + | 0.999998i | \(0.500630\pi\) | |||||||
\(488\) | 15573.0 | 1.44458 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2302.06 | 0.212237 | ||||||||
\(491\) | 6092.09 | 0.559943 | 0.279972 | − | 0.960008i | \(-0.409675\pi\) | ||||
0.279972 | + | 0.960008i | \(0.409675\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8118.23 | −0.741636 | ||||||||
\(494\) | 10014.0 | 0.912051 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5451.81 | −0.493536 | ||||||||
\(497\) | 309.077 | 0.0278954 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6128.64 | 0.549811 | 0.274906 | − | 0.961471i | \(-0.411353\pi\) | ||||
0.274906 | + | 0.961471i | \(0.411353\pi\) | |||||||
\(500\) | 21637.9 | 1.93535 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 7462.44 | 0.663476 | ||||||||
\(503\) | 3606.14 | 0.319661 | 0.159831 | − | 0.987144i | \(-0.448905\pi\) | ||||
0.159831 | + | 0.987144i | \(0.448905\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2669.41 | 0.235223 | ||||||||
\(506\) | −1542.22 | −0.135494 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4230.90 | −0.369519 | ||||||||
\(509\) | 15207.2 | 1.32426 | 0.662128 | − | 0.749391i | \(-0.269654\pi\) | ||||
0.662128 | + | 0.749391i | \(0.269654\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6311.31 | −0.546371 | ||||||||
\(512\) | 9841.49 | 0.849486 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −28721.0 | −2.46465 | ||||||||
\(515\) | −11004.0 | −0.941539 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −15.4418 | −0.00131360 | ||||||||
\(518\) | 7940.16 | 0.673496 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4675.68 | −0.394311 | ||||||||
\(521\) | 5497.74 | 0.462304 | 0.231152 | − | 0.972918i | \(-0.425750\pi\) | ||||
0.231152 | + | 0.972918i | \(0.425750\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15158.7 | 1.26739 | 0.633693 | − | 0.773584i | \(-0.281538\pi\) | ||||
0.633693 | + | 0.773584i | \(0.281538\pi\) | |||||||
\(524\) | −15986.4 | −1.33276 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −17294.4 | −1.43359 | ||||||||
\(527\) | −6522.20 | −0.539111 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4461.77 | −0.366711 | ||||||||
\(530\) | 34603.4 | 2.83599 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 13693.7 | 1.11597 | ||||||||
\(533\) | 7322.80 | 0.595095 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 838.601 | 0.0677680 | ||||||||
\(536\) | 3089.09 | 0.248933 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −2061.53 | −0.165202 | ||||||||
\(539\) | 181.928 | 0.0145384 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21418.8 | 1.70216 | 0.851080 | − | 0.525037i | \(-0.175948\pi\) | ||||
0.851080 | + | 0.525037i | \(0.175948\pi\) | |||||||
\(542\) | −5825.08 | −0.461639 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3667.71 | 0.289066 | ||||||||
\(545\) | 1729.19 | 0.135909 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15536.1 | 1.21439 | 0.607197 | − | 0.794551i | \(-0.292294\pi\) | ||||
0.607197 | + | 0.794551i | \(0.292294\pi\) | |||||||
\(548\) | 3426.99 | 0.267142 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 464.368 | 0.0360013 | ||||||||
\(551\) | −32941.5 | −2.54692 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7380.15 | 0.567515 | ||||||||
\(554\) | −18900.6 | −1.44948 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2721.69 | −0.207600 | ||||||||
\(557\) | −13975.1 | −1.06309 | −0.531547 | − | 0.847029i | \(-0.678389\pi\) | ||||
−0.531547 | + | 0.847029i | \(0.678389\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6978.36 | 0.528002 | ||||||||
\(560\) | −1945.93 | −0.146840 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −17109.7 | −1.28422 | ||||||||
\(563\) | −1117.89 | −0.0836825 | −0.0418412 | − | 0.999124i | \(-0.513322\pi\) | ||||
−0.0418412 | + | 0.999124i | \(0.513322\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10422.3 | 0.776054 | ||||||||
\(566\) | 11136.5 | 0.827034 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1335.60 | −0.0986628 | ||||||||
\(569\) | −14452.1 | −1.06478 | −0.532392 | − | 0.846498i | \(-0.678707\pi\) | ||||
−0.532392 | + | 0.846498i | \(0.678707\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17396.8 | 1.27501 | 0.637506 | − | 0.770445i | \(-0.279966\pi\) | ||||
0.637506 | + | 0.770445i | \(0.279966\pi\) | |||||||
\(572\) | −831.956 | −0.0608144 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 15579.7 | 1.13290 | ||||||||
\(575\) | −2320.08 | −0.168268 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12251.2 | 0.883923 | 0.441961 | − | 0.897034i | \(-0.354283\pi\) | ||||
0.441961 | + | 0.897034i | \(0.354283\pi\) | |||||||
\(578\) | 17938.8 | 1.29093 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 34629.9 | 2.47918 | ||||||||
\(581\) | −3410.72 | −0.243547 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2734.65 | 0.194267 | ||||||||
\(584\) | 27272.7 | 1.93245 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 16943.9 | 1.19445 | ||||||||
\(587\) | −24620.6 | −1.73118 | −0.865589 | − | 0.500755i | \(-0.833056\pi\) | ||||
−0.865589 | + | 0.500755i | \(0.833056\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −26465.3 | −1.85141 | ||||||||
\(590\) | −13134.1 | −0.916481 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −6711.81 | −0.465969 | ||||||||
\(593\) | 3020.20 | 0.209148 | 0.104574 | − | 0.994517i | \(-0.466652\pi\) | ||||
0.104574 | + | 0.994517i | \(0.466652\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2327.98 | −0.160400 | ||||||||
\(596\) | −15940.8 | −1.09557 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 6467.09 | 0.442239 | ||||||||
\(599\) | 16830.3 | 1.14803 | 0.574013 | − | 0.818846i | \(-0.305386\pi\) | ||||
0.574013 | + | 0.818846i | \(0.305386\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8783.94 | 0.596180 | 0.298090 | − | 0.954538i | \(-0.403650\pi\) | ||||
0.298090 | + | 0.954538i | \(0.403650\pi\) | |||||||
\(602\) | 14846.8 | 1.00517 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 50553.7 | 3.40563 | ||||||||
\(605\) | 13077.6 | 0.878809 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16803.3 | 1.12360 | 0.561799 | − | 0.827274i | \(-0.310109\pi\) | ||||
0.561799 | + | 0.827274i | \(0.310109\pi\) | |||||||
\(608\) | 14882.5 | 0.992707 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −24187.1 | −1.60542 | ||||||||
\(611\) | 64.7533 | 0.00428746 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1319.88 | 0.0869647 | 0.0434823 | − | 0.999054i | \(-0.486155\pi\) | ||||
0.0434823 | + | 0.999054i | \(0.486155\pi\) | |||||||
\(614\) | 42957.2 | 2.82347 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −786.155 | −0.0514206 | ||||||||
\(617\) | 2586.39 | 0.168759 | 0.0843793 | − | 0.996434i | \(-0.473109\pi\) | ||||
0.0843793 | + | 0.996434i | \(0.473109\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5296.63 | 0.343925 | 0.171962 | − | 0.985104i | \(-0.444989\pi\) | ||||
0.171962 | + | 0.985104i | \(0.444989\pi\) | |||||||
\(620\) | 27821.7 | 1.80217 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −42430.8 | −2.73524 | ||||||||
\(623\) | −6745.77 | −0.433810 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11622.6 | −0.743844 | ||||||||
\(626\) | −34031.7 | −2.17281 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 7544.00 | 0.479360 | ||||||||
\(629\) | −8029.59 | −0.508999 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15857.8 | −1.00046 | −0.500228 | − | 0.865894i | \(-0.666751\pi\) | ||||
−0.500228 | + | 0.865894i | \(0.666751\pi\) | |||||||
\(632\) | −31891.4 | −2.00724 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −10831.4 | −0.678503 | ||||||||
\(635\) | 2918.59 | 0.182395 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −762.892 | −0.0474519 | ||||||||
\(638\) | 4257.97 | 0.264223 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −26169.0 | −1.61628 | ||||||||
\(641\) | 30365.3 | 1.87107 | 0.935537 | − | 0.353228i | \(-0.114916\pi\) | ||||
0.935537 | + | 0.353228i | \(0.114916\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3746.71 | 0.229791 | 0.114896 | − | 0.993378i | \(-0.463347\pi\) | ||||
0.114896 | + | 0.993378i | \(0.463347\pi\) | |||||||
\(644\) | 8843.44 | 0.541119 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −21545.4 | −1.31222 | ||||||||
\(647\) | −13032.7 | −0.791915 | −0.395957 | − | 0.918269i | \(-0.629587\pi\) | ||||
−0.395957 | + | 0.918269i | \(0.629587\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1037.97 | −0.0627794 | ||||||||
\(650\) | −1947.27 | −0.117505 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3536.08 | 0.212398 | ||||||||
\(653\) | 3096.91 | 0.185592 | 0.0927960 | − | 0.995685i | \(-0.470420\pi\) | ||||
0.0927960 | + | 0.995685i | \(0.470420\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11027.8 | 0.657853 | ||||||||
\(656\) | −13169.5 | −0.783813 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 137.766 | 0.00816213 | ||||||||
\(659\) | −11759.2 | −0.695103 | −0.347551 | − | 0.937661i | \(-0.612987\pi\) | ||||
−0.347551 | + | 0.937661i | \(0.612987\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2363.12 | 0.139054 | 0.0695270 | − | 0.997580i | \(-0.477851\pi\) | ||||
0.0695270 | + | 0.997580i | \(0.477851\pi\) | |||||||
\(662\) | 29805.4 | 1.74988 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 14738.6 | 0.861396 | ||||||||
\(665\) | −9446.30 | −0.550845 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −21273.7 | −1.23496 | ||||||||
\(668\) | −8445.19 | −0.489153 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −4797.82 | −0.276650 | ||||||||
\(671\) | −1911.47 | −0.109972 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19358.2 | −1.10877 | −0.554387 | − | 0.832259i | \(-0.687047\pi\) | ||||
−0.554387 | + | 0.832259i | \(0.687047\pi\) | |||||||
\(674\) | −897.267 | −0.0512781 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −28131.2 | −1.60055 | ||||||||
\(677\) | −7931.13 | −0.450248 | −0.225124 | − | 0.974330i | \(-0.572279\pi\) | ||||
−0.225124 | + | 0.974330i | \(0.572279\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5088.35 | 0.287589 | ||||||||
\(680\) | 10059.8 | 0.567317 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 3420.86 | 0.192070 | ||||||||
\(683\) | −7289.89 | −0.408404 | −0.204202 | − | 0.978929i | \(-0.565460\pi\) | ||||
−0.204202 | + | 0.978929i | \(0.565460\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2364.03 | −0.131861 | ||||||||
\(686\) | −1623.09 | −0.0903353 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −12550.0 | −0.695444 | ||||||||
\(689\) | −11467.4 | −0.634069 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13338.6 | −0.734335 | −0.367167 | − | 0.930155i | \(-0.619672\pi\) | ||||
−0.367167 | + | 0.930155i | \(0.619672\pi\) | |||||||
\(692\) | −42569.6 | −2.33852 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 238.840 | 0.0130637 | ||||||||
\(695\) | 1877.50 | 0.102471 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −15755.1 | −0.856195 | ||||||||
\(698\) | 6334.84 | 0.343520 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2662.80 | −0.143778 | ||||||||
\(701\) | 12918.5 | 0.696042 | 0.348021 | − | 0.937487i | \(-0.386854\pi\) | ||||
0.348021 | + | 0.937487i | \(0.386854\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −32581.8 | −1.74800 | ||||||||
\(704\) | −2755.36 | −0.147509 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 15109.4 | 0.805453 | ||||||||
\(707\) | −1882.10 | −0.100118 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2282.78 | 0.120919 | 0.0604596 | − | 0.998171i | \(-0.480743\pi\) | ||||
0.0604596 | + | 0.998171i | \(0.480743\pi\) | |||||||
\(710\) | 2074.38 | 0.109648 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 29150.1 | 1.53434 | ||||||||
\(713\) | −17091.3 | −0.897721 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 573.906 | 0.0300180 | ||||||||
\(716\) | −39215.2 | −2.04684 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 31521.2 | 1.63839 | ||||||||
\(719\) | 29360.8 | 1.52291 | 0.761456 | − | 0.648217i | \(-0.224485\pi\) | ||||
0.761456 | + | 0.648217i | \(0.224485\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7758.48 | 0.400750 | ||||||||
\(722\) | −54967.9 | −2.83337 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 6420.96 | 0.329603 | ||||||||
\(725\) | 6405.60 | 0.328135 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18139.1 | −0.925368 | −0.462684 | − | 0.886523i | \(-0.653114\pi\) | ||||
−0.462684 | + | 0.886523i | \(0.653114\pi\) | |||||||
\(728\) | 3296.64 | 0.167832 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −42358.6 | −2.14762 | ||||||||
\(731\) | −15014.1 | −0.759665 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5292.54 | −0.266691 | −0.133345 | − | 0.991070i | \(-0.542572\pi\) | ||||
−0.133345 | + | 0.991070i | \(0.542572\pi\) | |||||||
\(734\) | −21733.2 | −1.09290 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 9611.17 | 0.481348 | ||||||||
\(737\) | −379.163 | −0.0189507 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −25955.7 | −1.29201 | −0.646007 | − | 0.763332i | \(-0.723562\pi\) | ||||
−0.646007 | + | 0.763332i | \(0.723562\pi\) | |||||||
\(740\) | 34251.8 | 1.70151 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −24397.5 | −1.20709 | ||||||||
\(743\) | 25972.0 | 1.28240 | 0.641199 | − | 0.767375i | \(-0.278437\pi\) | ||||
0.641199 | + | 0.767375i | \(0.278437\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10996.4 | 0.540773 | ||||||||
\(746\) | −33041.9 | −1.62165 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1789.97 | 0.0874968 | ||||||||
\(749\) | −591.265 | −0.0288443 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6487.01 | 0.315199 | 0.157599 | − | 0.987503i | \(-0.449625\pi\) | ||||
0.157599 | + | 0.987503i | \(0.449625\pi\) | |||||||
\(752\) | −116.454 | −0.00564711 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −17855.3 | −0.862401 | ||||||||
\(755\) | −34873.3 | −1.68102 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22221.6 | 1.06692 | 0.533459 | − | 0.845826i | \(-0.320892\pi\) | ||||
0.533459 | + | 0.845826i | \(0.320892\pi\) | |||||||
\(758\) | 57070.6 | 2.73469 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 40819.8 | 1.94827 | ||||||||
\(761\) | −19820.0 | −0.944120 | −0.472060 | − | 0.881567i | \(-0.656489\pi\) | ||||
−0.472060 | + | 0.881567i | \(0.656489\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1219.19 | −0.0578473 | ||||||||
\(764\) | −50630.6 | −2.39758 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 45780.1 | 2.15940 | ||||||||
\(767\) | 4352.59 | 0.204906 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3307.64 | −0.155106 | −0.0775531 | − | 0.996988i | \(-0.524711\pi\) | ||||
−0.0775531 | + | 0.996988i | \(0.524711\pi\) | |||||||
\(770\) | 1221.02 | 0.0571459 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 70085.0 | 3.26738 | ||||||||
\(773\) | −15964.0 | −0.742801 | −0.371401 | − | 0.928473i | \(-0.621122\pi\) | ||||
−0.371401 | + | 0.928473i | \(0.621122\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5146.28 | 0.238529 | ||||||||
\(776\) | −21988.0 | −1.01717 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −53840.9 | −2.48109 | ||||||||
\(779\) | −63929.8 | −2.94034 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 163.935 | 0.00751096 | ||||||||
\(782\) | −13914.1 | −0.636273 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1372.00 | 0.0625000 | ||||||||
\(785\) | −5204.06 | −0.236612 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −36394.0 | −1.64842 | −0.824210 | − | 0.566284i | \(-0.808381\pi\) | ||||
−0.824210 | + | 0.566284i | \(0.808381\pi\) | |||||||
\(788\) | 49329.1 | 2.23004 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 49532.2 | 2.23073 | ||||||||
\(791\) | −7348.38 | −0.330314 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8015.51 | 0.358940 | ||||||||
\(794\) | 71939.9 | 3.21543 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −57749.2 | −2.57144 | ||||||||
\(797\) | 13384.0 | 0.594836 | 0.297418 | − | 0.954747i | \(-0.403874\pi\) | ||||
0.297418 | + | 0.954747i | \(0.403874\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −139.318 | −0.00616859 | ||||||||
\(800\) | −2893.97 | −0.127896 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −6606.06 | −0.290858 | ||||||||
\(803\) | −3347.53 | −0.147113 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6100.45 | −0.267096 | ||||||||
\(806\) | −14345.0 | −0.626898 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 8133.03 | 0.354108 | ||||||||
\(809\) | −13971.0 | −0.607161 | −0.303580 | − | 0.952806i | \(-0.598182\pi\) | ||||
−0.303580 | + | 0.952806i | \(0.598182\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18471.8 | 0.799793 | 0.399897 | − | 0.916560i | \(-0.369046\pi\) | ||||
0.399897 | + | 0.916560i | \(0.369046\pi\) | |||||||
\(812\) | −24416.2 | −1.05522 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4211.48 | 0.181342 | ||||||||
\(815\) | −2439.29 | −0.104840 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −60922.8 | −2.60884 | ||||||||
\(818\) | 41043.6 | 1.75435 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 67206.5 | 2.86214 | ||||||||
\(821\) | 28188.3 | 1.19827 | 0.599135 | − | 0.800648i | \(-0.295511\pi\) | ||||
0.599135 | + | 0.800648i | \(0.295511\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8071.14 | −0.341849 | −0.170925 | − | 0.985284i | \(-0.554675\pi\) | ||||
−0.170925 | + | 0.985284i | \(0.554675\pi\) | |||||||
\(824\) | −33526.3 | −1.41741 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 9260.38 | 0.390085 | ||||||||
\(827\) | 41952.8 | 1.76402 | 0.882009 | − | 0.471233i | \(-0.156191\pi\) | ||||
0.882009 | + | 0.471233i | \(0.156191\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14443.2 | 0.605108 | 0.302554 | − | 0.953132i | \(-0.402161\pi\) | ||||
0.302554 | + | 0.953132i | \(0.402161\pi\) | |||||||
\(830\) | −22891.2 | −0.957307 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 11554.3 | 0.481457 | ||||||||
\(833\) | 1641.37 | 0.0682716 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5825.72 | 0.241446 | ||||||||
\(836\) | 7263.18 | 0.300481 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 34609.9 | 1.42670 | ||||||||
\(839\) | 26360.6 | 1.08471 | 0.542353 | − | 0.840151i | \(-0.317534\pi\) | ||||
0.542353 | + | 0.840151i | \(0.317534\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 34346.4 | 1.40827 | ||||||||
\(842\) | 36414.4 | 1.49041 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 61614.5 | 2.51287 | ||||||||
\(845\) | 19405.7 | 0.790030 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9220.51 | −0.374050 | ||||||||
\(848\) | 20623.2 | 0.835146 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 4189.58 | 0.169061 | ||||||||
\(851\) | −21041.4 | −0.847580 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −18939.8 | −0.760241 | −0.380120 | − | 0.924937i | \(-0.624117\pi\) | ||||
−0.380120 | + | 0.924937i | \(0.624117\pi\) | |||||||
\(854\) | 17053.4 | 0.683321 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2555.00 | 0.102019 | ||||||||
\(857\) | 44583.6 | 1.77707 | 0.888533 | − | 0.458812i | \(-0.151725\pi\) | ||||
0.888533 | + | 0.458812i | \(0.151725\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7975.35 | 0.316782 | 0.158391 | − | 0.987376i | \(-0.449369\pi\) | ||||
0.158391 | + | 0.987376i | \(0.449369\pi\) | |||||||
\(860\) | 64045.4 | 2.53945 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 29613.7 | 1.17012 | ||||||||
\(863\) | −8258.42 | −0.325747 | −0.162874 | − | 0.986647i | \(-0.552076\pi\) | ||||
−0.162874 | + | 0.986647i | \(0.552076\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 29365.7 | 1.15429 | ||||||||
\(866\) | 56421.7 | 2.21396 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −19616.0 | −0.767064 | ||||||||
\(869\) | 3914.45 | 0.152806 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1589.97 | 0.0618533 | ||||||||
\(872\) | 5268.40 | 0.204599 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −56459.3 | −2.18508 | ||||||||
\(875\) | 10524.0 | 0.406603 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −43106.2 | −1.65974 | −0.829871 | − | 0.557956i | \(-0.811586\pi\) | ||||
−0.829871 | + | 0.557956i | \(0.811586\pi\) | |||||||
\(878\) | −80992.1 | −3.11316 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1032.12 | −0.0395374 | ||||||||
\(881\) | −662.616 | −0.0253395 | −0.0126697 | − | 0.999920i | \(-0.504033\pi\) | ||||
−0.0126697 | + | 0.999920i | \(0.504033\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 32497.0 | 1.23852 | 0.619258 | − | 0.785187i | \(-0.287433\pi\) | ||||
0.619258 | + | 0.785187i | \(0.287433\pi\) | |||||||
\(884\) | −7506.00 | −0.285582 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −38306.1 | −1.45251 | ||||||||
\(887\) | −3176.34 | −0.120238 | −0.0601190 | − | 0.998191i | \(-0.519148\pi\) | ||||
−0.0601190 | + | 0.998191i | \(0.519148\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2057.79 | −0.0776332 | ||||||||
\(890\) | −45274.5 | −1.70517 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −10997.9 | −0.412823 | ||||||||
\(893\) | −565.312 | −0.0211841 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 27051.7 | 1.01032 | ||||||||
\(896\) | 18450.8 | 0.687943 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −29133.8 | −1.08264 | ||||||||
\(899\) | 47188.1 | 1.75063 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 24672.3 | 0.912268 | ||||||||
\(902\) | 8263.48 | 0.305037 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 31754.2 | 1.16828 | ||||||||
\(905\) | −4429.35 | −0.162692 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −31726.2 | −1.16147 | −0.580733 | − | 0.814094i | \(-0.697234\pi\) | ||||
−0.580733 | + | 0.814094i | \(0.697234\pi\) | |||||||
\(908\) | −55732.0 | −2.03693 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −5120.18 | −0.186519 | ||||||||
\(911\) | 10882.3 | 0.395772 | 0.197886 | − | 0.980225i | \(-0.436592\pi\) | ||||
0.197886 | + | 0.980225i | \(0.436592\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1809.05 | −0.0655760 | ||||||||
\(914\) | −26770.3 | −0.968799 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −55642.2 | −2.00706 | ||||||||
\(917\) | −7775.31 | −0.280004 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −29610.9 | −1.06286 | −0.531432 | − | 0.847101i | \(-0.678346\pi\) | ||||
−0.531432 | + | 0.847101i | \(0.678346\pi\) | |||||||
\(920\) | 26361.5 | 0.944689 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −6694.02 | −0.239106 | ||||||||
\(923\) | −687.442 | −0.0245151 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6335.66 | 0.225206 | ||||||||
\(926\) | 25576.4 | 0.907658 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −26535.9 | −0.938667 | ||||||||
\(929\) | −52496.6 | −1.85399 | −0.926995 | − | 0.375074i | \(-0.877617\pi\) | ||||
−0.926995 | + | 0.375074i | \(0.877617\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6660.23 | 0.234458 | ||||||||
\(932\) | 77405.9 | 2.72051 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 80221.5 | 2.81041 | ||||||||
\(935\) | −1234.77 | −0.0431885 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1661.46 | −0.0579269 | −0.0289634 | − | 0.999580i | \(-0.509221\pi\) | ||||
−0.0289634 | + | 0.999580i | \(0.509221\pi\) | |||||||
\(938\) | 3382.76 | 0.117752 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 594.287 | 0.0206207 | ||||||||
\(941\) | −43066.9 | −1.49197 | −0.745983 | − | 0.665965i | \(-0.768020\pi\) | ||||
−0.745983 | + | 0.665965i | \(0.768020\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −41286.0 | −1.42572 | ||||||||
\(944\) | −7827.79 | −0.269887 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7874.79 | 0.270647 | ||||||||
\(947\) | 10024.6 | 0.343986 | 0.171993 | − | 0.985098i | \(-0.444979\pi\) | ||||
0.171993 | + | 0.985098i | \(0.444979\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 14037.4 | 0.480163 | ||||||||
\(950\) | 17000.1 | 0.580587 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −7092.78 | −0.241469 | ||||||||
\(953\) | 36134.8 | 1.22825 | 0.614125 | − | 0.789209i | \(-0.289509\pi\) | ||||
0.614125 | + | 0.789209i | \(0.289509\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 34926.4 | 1.18345 | ||||||||
\(956\) | −68552.7 | −2.31920 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −86940.7 | −2.93208 | ||||||||
\(959\) | 1666.79 | 0.0561245 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8120.07 | 0.272568 | ||||||||
\(962\) | −17660.3 | −0.591883 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −4577.19 | −0.152927 | ||||||||
\(965\) | −48346.5 | −1.61278 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 22016.7 | 0.732171 | 0.366086 | − | 0.930581i | \(-0.380698\pi\) | ||||
0.366086 | + | 0.930581i | \(0.380698\pi\) | |||||||
\(968\) | 39844.1 | 1.32297 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 34150.7 | 1.13042 | ||||||||
\(971\) | −8087.76 | −0.267300 | −0.133650 | − | 0.991029i | \(-0.542670\pi\) | ||||
−0.133650 | + | 0.991029i | \(0.542670\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1323.75 | −0.0436152 | ||||||||
\(974\) | 201.377 | 0.00662478 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −14415.3 | −0.472768 | ||||||||
\(977\) | 19050.6 | 0.623830 | 0.311915 | − | 0.950110i | \(-0.399030\pi\) | ||||
0.311915 | + | 0.950110i | \(0.399030\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3577.97 | −0.116805 | ||||||||
\(980\) | −7001.60 | −0.228222 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −28828.1 | −0.936803 | ||||||||
\(983\) | 35176.7 | 1.14136 | 0.570682 | − | 0.821171i | \(-0.306679\pi\) | ||||
0.570682 | + | 0.821171i | \(0.306679\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −34028.5 | −1.10075 | ||||||||
\(986\) | 38415.9 | 1.24078 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −30457.2 | −0.980742 | ||||||||
\(989\) | −39344.1 | −1.26498 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26830.6 | −0.860041 | −0.430021 | − | 0.902819i | \(-0.641494\pi\) | ||||
−0.430021 | + | 0.902819i | \(0.641494\pi\) | |||||||
\(992\) | −21319.0 | −0.682337 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1462.57 | −0.0466699 | ||||||||
\(995\) | 39837.0 | 1.26926 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 27316.3 | 0.867721 | 0.433860 | − | 0.900980i | \(-0.357151\pi\) | ||||
0.433860 | + | 0.900980i | \(0.357151\pi\) | |||||||
\(998\) | −29001.1 | −0.919852 | ||||||||
\(999\) | 0 | 0 |
(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 | 189.4.a.e.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 189.4.a.i.1.2 | yes | 2 | ||
7.6 | odd | 2 | 1323.4.a.o.1.1 | 2 | |||
21.20 | even | 2 | 1323.4.a.x.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
189.4.a.e.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
189.4.a.i.1.2 | yes | 2 | 3.2 | odd | 2 | ||
1323.4.a.o.1.1 | 2 | 7.6 | odd | 2 | |||
1323.4.a.x.1.2 | 2 | 21.20 | even | 2 |