Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [624,4,Mod(289,624)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(624, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("624.289");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 624 = 2^{4} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 624.q (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(36.8171918436\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 29x^{6} + 2x^{5} + 595x^{4} - 288x^{3} + 2526x^{2} + 1872x + 6084 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 39) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 289.1 | ||
Root | \(2.66520 - 4.61626i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 624.289 |
Dual form | 624.4.q.i.529.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/624\mathbb{Z}\right)^\times\).
\(n\) | \(79\) | \(145\) | \(209\) | \(469\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.50000 | − | 2.59808i | −0.288675 | − | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −16.4131 | −1.46803 | −0.734016 | − | 0.679132i | \(-0.762356\pi\) | ||||
−0.734016 | + | 0.679132i | \(0.762356\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.83984 | − | 8.38285i | 0.261327 | − | 0.452631i | −0.705268 | − | 0.708941i | \(-0.749173\pi\) |
0.966595 | + | 0.256309i | \(0.0825066\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.50000 | + | 7.79423i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 13.7941 | + | 23.8921i | 0.378098 | + | 0.654884i | 0.990785 | − | 0.135441i | \(-0.0432451\pi\) |
−0.612688 | + | 0.790325i | \(0.709912\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −37.3033 | − | 28.3807i | −0.795852 | − | 0.605491i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 24.6196 | + | 42.6425i | 0.423784 | + | 0.734016i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −53.9641 | + | 93.4685i | −0.769895 | + | 1.33350i | 0.167725 | + | 0.985834i | \(0.446358\pi\) |
−0.937619 | + | 0.347663i | \(0.886975\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.12362 | + | 1.94616i | −0.0135671 | + | 0.0234989i | −0.872729 | − | 0.488205i | \(-0.837652\pi\) |
0.859162 | + | 0.511703i | \(0.170985\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −29.0391 | −0.301754 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 20.9045 | + | 36.2077i | 0.189517 | + | 0.328253i | 0.945089 | − | 0.326812i | \(-0.105974\pi\) |
−0.755572 | + | 0.655065i | \(0.772641\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 144.390 | 1.15512 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −30.8106 | − | 53.3656i | −0.197289 | − | 0.341715i | 0.750359 | − | 0.661030i | \(-0.229881\pi\) |
−0.947649 | + | 0.319315i | \(0.896547\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −191.932 | −1.11200 | −0.556000 | − | 0.831182i | \(-0.687665\pi\) | ||||
−0.556000 | + | 0.831182i | \(0.687665\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 41.3822 | − | 71.6762i | 0.218295 | − | 0.378098i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −79.4368 | + | 137.589i | −0.383636 | + | 0.664477i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −49.2118 | − | 85.2373i | −0.218659 | − | 0.378728i | 0.735740 | − | 0.677265i | \(-0.236835\pi\) |
−0.954398 | + | 0.298537i | \(0.903501\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −17.7803 | + | 139.488i | −0.0730031 | + | 0.572716i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 15.3726 | + | 26.6261i | 0.0585561 | + | 0.101422i | 0.893817 | − | 0.448431i | \(-0.148017\pi\) |
−0.835261 | + | 0.549853i | \(0.814684\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 119.163 | − | 206.396i | 0.422608 | − | 0.731978i | −0.573586 | − | 0.819145i | \(-0.694448\pi\) |
0.996194 | + | 0.0871672i | \(0.0277814\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 73.8589 | − | 127.927i | 0.244672 | − | 0.423784i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 511.482 | 1.58739 | 0.793695 | − | 0.608316i | \(-0.208155\pi\) | ||||
0.793695 | + | 0.608316i | \(0.208155\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 124.652 | + | 215.903i | 0.363416 | + | 0.629456i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 323.785 | 0.888998 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 492.825 | 1.27726 | 0.638630 | − | 0.769514i | \(-0.279502\pi\) | ||||
0.638630 | + | 0.769514i | \(0.279502\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −226.404 | − | 392.142i | −0.555059 | − | 0.961390i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.74170 | 0.0156660 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 242.089 | − | 419.311i | 0.534192 | − | 0.925248i | −0.465010 | − | 0.885306i | \(-0.653949\pi\) |
0.999202 | − | 0.0399427i | \(-0.0127175\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 222.011 | − | 384.534i | 0.465993 | − | 0.807123i | −0.533253 | − | 0.845956i | \(-0.679031\pi\) |
0.999246 | + | 0.0388329i | \(0.0123640\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 43.5586 | + | 75.4457i | 0.0871090 | + | 0.150877i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 612.262 | + | 465.815i | 1.16834 | + | 0.888880i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 95.0568 | + | 164.643i | 0.173329 | + | 0.300215i | 0.939582 | − | 0.342325i | \(-0.111214\pi\) |
−0.766253 | + | 0.642539i | \(0.777881\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 62.7135 | − | 108.623i | 0.109418 | − | 0.189517i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 242.392 | − | 419.836i | 0.405164 | − | 0.701765i | −0.589176 | − | 0.808005i | \(-0.700548\pi\) |
0.994341 | + | 0.106239i | \(0.0338810\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −957.780 | −1.53561 | −0.767806 | − | 0.640683i | \(-0.778651\pi\) | ||||
−0.767806 | + | 0.640683i | \(0.778651\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −216.584 | − | 375.135i | −0.333453 | − | 0.577558i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 267.045 | 0.395228 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 375.216 | 0.534368 | 0.267184 | − | 0.963646i | \(-0.413907\pi\) | ||||
0.267184 | + | 0.963646i | \(0.413907\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −40.5000 | − | 70.1481i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 715.765 | 0.946571 | 0.473286 | − | 0.880909i | \(-0.343068\pi\) | ||||
0.473286 | + | 0.880909i | \(0.343068\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 885.717 | − | 1534.11i | 1.13023 | − | 1.95762i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −92.4319 | + | 160.097i | −0.113905 | + | 0.197289i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 519.076 | + | 899.066i | 0.618224 | + | 1.07080i | 0.989810 | + | 0.142397i | \(0.0454810\pi\) |
−0.371585 | + | 0.928399i | \(0.621186\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −418.453 | + | 175.350i | −0.482042 | + | 0.201996i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 287.898 | + | 498.654i | 0.321007 | + | 0.556000i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 18.4420 | − | 31.9425i | 0.0199169 | − | 0.0344972i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −32.7818 | + | 56.7797i | −0.0343143 | + | 0.0594341i | −0.882673 | − | 0.469989i | \(-0.844258\pi\) |
0.848358 | + | 0.529423i | \(0.177591\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −248.293 | −0.252065 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −265.899 | − | 460.551i | −0.261960 | − | 0.453728i | 0.704803 | − | 0.709403i | \(-0.251035\pi\) |
−0.966763 | + | 0.255676i | \(0.917702\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 735.984 | 0.704064 | 0.352032 | − | 0.935988i | \(-0.385491\pi\) | ||||
0.352032 | + | 0.935988i | \(0.385491\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 476.621 | 0.442985 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −391.632 | − | 678.327i | −0.353837 | − | 0.612863i | 0.633081 | − | 0.774085i | \(-0.281790\pi\) |
−0.986918 | + | 0.161222i | \(0.948456\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −532.339 | −0.467788 | −0.233894 | − | 0.972262i | \(-0.575147\pi\) | ||||
−0.233894 | + | 0.972262i | \(0.575147\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −147.635 | + | 255.712i | −0.126243 | + | 0.218659i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 90.2946 | − | 156.395i | 0.0751699 | − | 0.130198i | −0.825990 | − | 0.563684i | \(-0.809383\pi\) |
0.901160 | + | 0.433486i | \(0.142717\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −343.107 | − | 594.280i | −0.278217 | − | 0.481886i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 389.070 | − | 163.037i | 0.307432 | − | 0.128827i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 522.355 | + | 904.746i | 0.402389 | + | 0.696957i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 284.947 | − | 493.542i | 0.214085 | − | 0.370805i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 46.1178 | − | 79.8784i | 0.0338074 | − | 0.0585561i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −318.242 | −0.227716 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 715.817 | + | 1239.83i | 0.500146 | + | 0.866278i | 1.00000 | 0.000168331i | \(5.35814e-5\pi\) | |
−0.499854 | + | 0.866110i | \(0.666613\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −714.976 | −0.487986 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2067.32 | −1.37880 | −0.689400 | − | 0.724381i | \(-0.742126\pi\) | ||||
−0.689400 | + | 0.724381i | \(0.742126\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 10.8762 | + | 18.8382i | 0.00709090 | + | 0.0122818i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −443.153 | −0.282523 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 193.756 | − | 335.595i | 0.120830 | − | 0.209283i | −0.799265 | − | 0.600978i | \(-0.794778\pi\) |
0.920095 | + | 0.391695i | \(0.128111\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 376.284 | − | 651.743i | 0.229611 | − | 0.397699i | −0.728082 | − | 0.685491i | \(-0.759588\pi\) |
0.957693 | + | 0.287792i | \(0.0929211\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −767.223 | − | 1328.87i | −0.458240 | − | 0.793695i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 163.508 | − | 1282.74i | 0.0956171 | − | 0.750126i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 505.698 | + | 875.894i | 0.289627 | + | 0.501649i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 373.956 | − | 647.710i | 0.209819 | − | 0.363416i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1318.36 | − | 2283.47i | 0.724862 | − | 1.25550i | −0.234169 | − | 0.972196i | \(-0.575237\pi\) |
0.959031 | − | 0.283301i | \(-0.0914296\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3332.42 | 1.79595 | 0.897975 | − | 0.440046i | \(-0.145038\pi\) | ||||
0.897975 | + | 0.440046i | \(0.145038\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −485.677 | − | 841.217i | −0.256632 | − | 0.444499i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3150.20 | 1.63245 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1625.26 | −0.826179 | −0.413089 | − | 0.910690i | \(-0.635550\pi\) | ||||
−0.413089 | + | 0.910690i | \(0.635550\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −739.238 | − | 1280.40i | −0.368713 | − | 0.638630i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 404.698 | 0.198104 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −917.683 | + | 1589.47i | −0.440972 | + | 0.763786i | −0.997762 | − | 0.0668673i | \(-0.978700\pi\) |
0.556790 | + | 0.830653i | \(0.312033\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −679.211 | + | 1176.43i | −0.320463 | + | 0.555059i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 972.498 | + | 1684.42i | 0.450624 | + | 0.780503i | 0.998425 | − | 0.0561052i | \(-0.0178682\pi\) |
−0.547801 | + | 0.836609i | \(0.684535\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 586.072 | + | 2117.39i | 0.266760 | + | 0.963763i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −10.1125 | − | 17.5154i | −0.00452237 | − | 0.00783298i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1265.81 | + | 2192.45i | −0.556289 | + | 0.963522i | 0.441512 | + | 0.897255i | \(0.354442\pi\) |
−0.997802 | + | 0.0662666i | \(0.978891\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 698.823 | − | 1210.40i | 0.301863 | − | 0.522842i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1452.54 | −0.616832 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2131.51 | + | 3691.88i | 0.890035 | + | 1.54159i | 0.839831 | + | 0.542847i | \(0.182654\pi\) |
0.0502037 | + | 0.998739i | \(0.484013\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3944.61 | 1.61989 | 0.809946 | − | 0.586504i | \(-0.199496\pi\) | ||||
0.809946 | + | 0.586504i | \(0.199496\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1332.06 | −0.538082 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 807.717 | + | 1399.01i | 0.320998 | + | 0.555984i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2977.54 | −1.16438 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 130.676 | − | 226.337i | 0.0502924 | − | 0.0871090i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −107.054 | + | 185.424i | −0.0405559 | + | 0.0702449i | −0.885591 | − | 0.464466i | \(-0.846246\pi\) |
0.845035 | + | 0.534711i | \(0.179580\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 603.593 | + | 1045.45i | 0.225117 | + | 0.389914i | 0.956355 | − | 0.292209i | \(-0.0943902\pi\) |
−0.731238 | + | 0.682123i | \(0.761057\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 291.829 | − | 2289.43i | 0.107171 | − | 0.840765i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 463.816 | + | 803.352i | 0.167744 | + | 0.290541i | 0.937626 | − | 0.347645i | \(-0.113019\pi\) |
−0.769883 | + | 0.638186i | \(0.779685\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 239.476 | − | 414.784i | 0.0853064 | − | 0.147755i | −0.820215 | − | 0.572055i | \(-0.806146\pi\) |
0.905522 | + | 0.424300i | \(0.139480\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 285.170 | − | 493.930i | 0.100072 | − | 0.173329i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −596.474 | −0.206228 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −252.312 | − | 437.017i | −0.0859621 | − | 0.148891i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −376.281 | −0.126345 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −61.9970 | −0.0205188 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −725.477 | − | 1256.56i | −0.236701 | − | 0.409978i | 0.723065 | − | 0.690780i | \(-0.242733\pi\) |
−0.959766 | + | 0.280802i | \(0.909400\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1454.35 | −0.467843 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1955.83 | + | 3387.59i | −0.620402 | + | 1.07457i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −928.920 | + | 1608.94i | −0.290595 | + | 0.503326i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1436.67 | + | 2488.38i | 0.443293 | + | 0.767806i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4665.74 | − | 1955.15i | 1.42014 | − | 0.595101i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1029.89 | − | 1783.83i | −0.309268 | − | 0.535668i | 0.668935 | − | 0.743321i | \(-0.266751\pi\) |
−0.978202 | + | 0.207654i | \(0.933417\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −649.753 | + | 1125.41i | −0.192519 | + | 0.333453i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2241.23 | − | 3881.93i | 0.655311 | − | 1.13503i | −0.326504 | − | 0.945196i | \(-0.605871\pi\) |
0.981816 | − | 0.189837i | \(-0.0607959\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1630.39 | −0.470477 | −0.235239 | − | 0.971938i | \(-0.575587\pi\) | ||||
−0.235239 | + | 0.971938i | \(0.575587\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −400.567 | − | 693.803i | −0.114093 | − | 0.197614i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1903.69 | −0.535258 | −0.267629 | − | 0.963522i | \(-0.586240\pi\) | ||||
−0.267629 | + | 0.963522i | \(0.586240\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8395.00 | −2.33034 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −562.824 | − | 974.839i | −0.154259 | − | 0.267184i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3763.79 | −1.01866 | −0.509328 | − | 0.860572i | \(-0.670106\pi\) | ||||
−0.509328 | + | 0.860572i | \(0.670106\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1807.37 | − | 3130.46i | 0.483083 | − | 0.836724i | −0.516728 | − | 0.856149i | \(-0.672850\pi\) |
0.999811 | + | 0.0194250i | \(0.00618357\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −121.500 | + | 210.444i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2045.92 | − | 3543.64i | −0.533507 | − | 0.924061i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 97.1479 | − | 40.7092i | 0.0250258 | − | 0.0104869i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1073.65 | − | 1859.61i | −0.273252 | − | 0.473286i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2864.88 | + | 4962.12i | −0.720438 | + | 1.24783i | 0.240387 | + | 0.970677i | \(0.422726\pi\) |
−0.960824 | + | 0.277158i | \(0.910608\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −576.717 | + | 998.903i | −0.143312 | + | 0.248223i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5314.30 | −1.30508 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2762.89 | + | 4785.47i | 0.670602 | + | 1.16152i | 0.977734 | + | 0.209849i | \(0.0672974\pi\) |
−0.307132 | + | 0.951667i | \(0.599369\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −952.709 | −0.228565 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 554.591 | 0.131526 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2611.60 | + | 4523.43i | 0.612313 | + | 1.06056i | 0.990850 | + | 0.134971i | \(0.0430941\pi\) |
−0.378536 | + | 0.925586i | \(0.623573\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8088.78 | −1.87506 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1557.23 | − | 2697.20i | 0.356932 | − | 0.618224i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3601.94 | + | 6238.75i | −0.816410 | + | 1.41406i | 0.0919010 | + | 0.995768i | \(0.470706\pi\) |
−0.908311 | + | 0.418295i | \(0.862628\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4288.84 | − | 7428.49i | −0.961360 | − | 1.66512i | −0.719091 | − | 0.694916i | \(-0.755442\pi\) |
−0.242269 | − | 0.970209i | \(-0.577892\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1083.25 | + | 824.148i | 0.240152 | + | 0.182710i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1991.72 | + | 3449.76i | 0.436747 | + | 0.756467i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3584.60 | + | 6208.70i | −0.777536 | + | 1.34673i | 0.155822 | + | 0.987785i | \(0.450197\pi\) |
−0.933358 | + | 0.358947i | \(0.883136\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 863.694 | − | 1495.96i | 0.185333 | − | 0.321007i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 849.157 | 0.180272 | 0.0901360 | − | 0.995929i | \(-0.471270\pi\) | ||||
0.0901360 | + | 0.995929i | \(0.471270\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 557.686 | + | 965.941i | 0.117141 | + | 0.202895i | 0.918634 | − | 0.395110i | \(-0.129294\pi\) |
−0.801492 | + | 0.598005i | \(0.795960\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −110.652 | −0.0229981 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 297.604 | 0.0612091 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3367.75 | − | 5833.11i | −0.685476 | − | 1.18728i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 196.691 | 0.0396227 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 931.764 | − | 1613.86i | 0.185782 | − | 0.321784i | −0.758058 | − | 0.652188i | \(-0.773851\pi\) |
0.943840 | + | 0.330403i | \(0.107185\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3973.43 | + | 6882.19i | −0.784211 | + | 1.35829i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 372.440 | + | 645.085i | 0.0727649 | + | 0.126033i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 247.792 | − | 1943.95i | 0.0479269 | − | 0.375992i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1153.46 | − | 1997.85i | −0.220878 | − | 0.382571i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −797.697 | + | 1381.65i | −0.151243 | + | 0.261960i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3643.88 | + | 6311.39i | −0.684092 | + | 1.18488i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6387.50 | 1.18747 | 0.593736 | − | 0.804660i | \(-0.297652\pi\) | ||||
0.593736 | + | 0.804660i | \(0.297652\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1103.98 | − | 1912.14i | −0.203246 | − | 0.352032i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3492.59 | 0.636806 | 0.318403 | − | 0.947955i | \(-0.396853\pi\) | ||||
0.318403 | + | 0.947955i | \(0.396853\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5912.01 | −1.06762 | −0.533812 | − | 0.845603i | \(-0.679241\pi\) | ||||
−0.533812 | + | 0.845603i | \(0.679241\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −714.931 | − | 1238.30i | −0.127879 | − | 0.221492i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1677.54 | −0.297224 | −0.148612 | − | 0.988896i | \(-0.547481\pi\) | ||||
−0.148612 | + | 0.988896i | \(0.547481\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 850.009 | − | 1472.26i | 0.149189 | − | 0.258403i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1174.90 | + | 2034.98i | −0.204288 | + | 0.353837i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −121.270 | − | 210.045i | −0.0208905 | − | 0.0361834i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5386.21 | − | 4097.88i | −0.919301 | − | 0.699413i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 798.509 | + | 1383.06i | 0.135039 | + | 0.233894i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2475.49 | − | 4287.68i | 0.414828 | − | 0.718503i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1005.15 | − | 1740.98i | 0.166913 | − | 0.289102i | −0.770420 | − | 0.637537i | \(-0.779953\pi\) |
0.937333 | + | 0.348435i | \(0.113287\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 885.812 | 0.145772 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1560.18 | − | 2702.30i | −0.254452 | − | 0.440724i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7139.24 | 1.15400 | 0.577002 | − | 0.816743i | \(-0.304222\pi\) | ||||
0.577002 | + | 0.816743i | \(0.304222\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −541.768 | −0.0867988 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2647.53 | − | 4585.65i | −0.420444 | − | 0.728231i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5733.31 | 0.902536 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1029.32 | + | 1782.84i | −0.160629 | + | 0.278217i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.569949 | − | 0.987181i | 8.81743e−5 | − | 0.000152722i | −0.865981 | − | 0.500076i | \(-0.833305\pi\) |
0.866069 | + | 0.499924i | \(0.166639\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6099.55 | − | 10564.7i | −0.935535 | − | 1.62039i | −0.773678 | − | 0.633579i | \(-0.781585\pi\) |
−0.161857 | − | 0.986814i | \(-0.551748\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1007.19 | − | 766.279i | −0.153162 | − | 0.116527i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5446.15 | + | 9433.01i | 0.821160 | + | 1.42229i | 0.904819 | + | 0.425796i | \(0.140006\pi\) |
−0.0836595 | + | 0.996494i | \(0.526661\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3978.41 | + | 6890.80i | −0.594794 | + | 1.03021i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1567.07 | − | 2714.24i | 0.232319 | − | 0.402389i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3525.78 | 0.518339 | 0.259169 | − | 0.965832i | \(-0.416551\pi\) | ||||
0.259169 | + | 0.965832i | \(0.416551\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3426.97 | + | 5935.69i | 0.499632 | + | 0.865388i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1709.68 | −0.247204 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15720.1 | 2.25433 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1191.88 | + | 2064.39i | 0.169525 | + | 0.293625i | 0.938253 | − | 0.345950i | \(-0.112443\pi\) |
−0.768728 | + | 0.639576i | \(0.779110\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −276.707 | −0.0390374 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2385.20 | − | 4131.28i | 0.333782 | − | 0.578128i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6641.10 | − | 11502.7i | 0.921885 | − | 1.59675i | 0.125390 | − | 0.992108i | \(-0.459982\pi\) |
0.796495 | − | 0.604645i | \(-0.206685\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 477.363 | + | 826.818i | 0.0657358 | + | 0.113858i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −365.214 | + | 2865.14i | −0.0498925 | + | 0.391412i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2218.36 | − | 3842.32i | −0.300659 | − | 0.520756i | 0.675627 | − | 0.737244i | \(-0.263873\pi\) |
−0.976285 | + | 0.216488i | \(0.930540\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2147.45 | − | 3719.50i | 0.288759 | − | 0.500146i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −405.206 | + | 701.838i | −0.0540602 | + | 0.0936351i | −0.891789 | − | 0.452451i | \(-0.850550\pi\) |
0.837729 | + | 0.546086i | \(0.183883\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4383.03 | −0.580207 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1072.46 | + | 1857.56i | 0.140869 | + | 0.243993i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3463.79 | 0.451469 | 0.225734 | − | 0.974189i | \(-0.427522\pi\) | ||||
0.225734 | + | 0.974189i | \(0.427522\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4512.37 | −0.583633 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3100.98 | + | 5371.06i | 0.398025 | + | 0.689400i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6158.45 | −0.784469 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −212.703 | + | 368.412i | −0.0268898 | + | 0.0465745i | −0.879157 | − | 0.476532i | \(-0.841894\pi\) |
0.852267 | + | 0.523106i | \(0.175227\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 32.6287 | − | 56.5146i | 0.00409394 | − | 0.00709090i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 593.424 | + | 1027.84i | 0.0739007 | + | 0.128000i | 0.900608 | − | 0.434633i | \(-0.143122\pi\) |
−0.826707 | + | 0.562633i | \(0.809789\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7159.70 | + | 5447.16i | 0.884987 | + | 0.673306i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 664.730 | + | 1151.35i | 0.0815573 | + | 0.141261i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1357.66 | − | 2351.54i | 0.165349 | − | 0.286392i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4003.71 | + | 6934.63i | −0.484036 | + | 0.838375i | −0.999832 | − | 0.0183369i | \(-0.994163\pi\) |
0.515796 | + | 0.856711i | \(0.327496\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1162.54 | −0.139522 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2343.35 | − | 4058.80i | −0.279198 | − | 0.483585i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −11747.9 | −1.38960 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2257.70 | −0.265132 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3416.23 | + | 5917.08i | 0.398314 | + | 0.689901i | 0.993518 | − | 0.113674i | \(-0.0362620\pi\) |
−0.595204 | + | 0.803575i | \(0.702929\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10739.6 | 1.24326 | 0.621632 | − | 0.783309i | \(-0.286470\pi\) | ||||
0.621632 | + | 0.783309i | \(0.286470\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2301.67 | + | 3986.61i | −0.264565 | + | 0.458240i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7791.85 | + | 13495.9i | −0.889318 | + | 1.54034i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2148.99 | − | 3722.16i | −0.243553 | − | 0.421846i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3577.91 | + | 1499.30i | −0.402665 | + | 0.168734i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2607.22 | + | 4515.84i | 0.291382 | + | 0.504688i | 0.974137 | − | 0.225959i | \(-0.0725517\pi\) |
−0.682755 | + | 0.730647i | \(0.739218\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4321.12 | + | 7484.40i | −0.479584 | + | 0.830664i | −0.999726 | − | 0.0234161i | \(-0.992546\pi\) |
0.520142 | + | 0.854080i | \(0.325879\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1517.09 | − | 2627.68i | 0.167216 | − | 0.289627i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −93.9545 | −0.0102848 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6513.12 | − | 11281.1i | −0.708097 | − | 1.22646i | −0.965562 | − | 0.260172i | \(-0.916221\pi\) |
0.257466 | − | 0.966287i | \(-0.417113\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2243.73 | −0.242278 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11533.0 | 1.23690 | 0.618450 | − | 0.785824i | \(-0.287761\pi\) | ||||
0.618450 | + | 0.785824i | \(0.287761\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8519.64 | − | 14756.5i | −0.907573 | − | 1.57196i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −7910.17 | −0.836998 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4941.37 | + | 8558.71i | −0.519372 | + | 0.899578i | 0.480375 | + | 0.877063i | \(0.340501\pi\) |
−0.999747 | + | 0.0225149i | \(0.992833\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −424.102 | + | 734.566i | −0.0442798 | + | 0.0766949i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4998.63 | − | 8657.88i | −0.518446 | − | 0.897975i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6868.11 | − | 2878.04i | 0.707653 | − | 0.296537i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7814.04 | + | 13534.3i | 0.799836 | + | 1.38536i | 0.919722 | + | 0.392569i | \(0.128414\pi\) |
−0.119886 | + | 0.992788i | \(0.538253\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1457.03 | + | 2523.65i | −0.148166 | + | 0.256632i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3873.73 | − | 6709.50i | 0.391361 | − | 0.677858i | −0.601268 | − | 0.799047i | \(-0.705338\pi\) |
0.992629 | + | 0.121190i | \(0.0386709\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 333.422 | 0.0334675 | 0.0167337 | − | 0.999860i | \(-0.494673\pi\) | ||||
0.0167337 | + | 0.999860i | \(0.494673\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4725.29 | − | 8184.45i | −0.471248 | − | 0.816225i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8198.33 | −0.812363 | −0.406182 | − | 0.913792i | \(-0.633140\pi\) | ||||
−0.406182 | + | 0.913792i | \(0.633140\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1840.24 | 0.181182 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2437.89 | + | 4222.56i | 0.238497 | + | 0.413089i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6574.96 | 0.639148 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −162.238 | + | 281.005i | −0.0156716 | + | 0.0271440i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2217.71 | + | 3841.19i | −0.212877 | + | 0.368713i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3217.94 | − | 5573.64i | −0.306955 | − | 0.531662i | 0.670740 | − | 0.741693i | \(-0.265977\pi\) |
−0.977695 | + | 0.210031i | \(0.932643\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −583.332 | + | 4576.30i | −0.0552966 | + | 0.433807i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −607.047 | − | 1051.44i | −0.0571876 | − | 0.0990518i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 538.050 | − | 931.931i | 0.0503745 | − | 0.0872511i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4047.69 | − | 7010.80i | 0.376629 | − | 0.652340i | −0.613941 | − | 0.789352i | \(-0.710417\pi\) |
0.990569 | + | 0.137012i | \(0.0437500\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5506.10 | 0.509191 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2558.23 | + | 4430.99i | 0.235135 | + | 0.407266i | 0.959312 | − | 0.282348i | \(-0.0911134\pi\) |
−0.724177 | + | 0.689614i | \(0.757780\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6650.67 | 0.607568 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4075.26 | 0.370039 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2346.28 | − | 4063.88i | −0.211761 | − | 0.366780i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18050.7 | 1.61936 | 0.809682 | − | 0.586870i | \(-0.199640\pi\) | ||||
0.809682 | + | 0.586870i | \(0.199640\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2917.50 | − | 5053.25i | 0.260168 | − | 0.450624i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5265.53 | − | 9120.16i | 0.466756 | − | 0.808445i | −0.532523 | − | 0.846416i | \(-0.678756\pi\) |
0.999279 | + | 0.0379705i | \(0.0120893\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4364.22 | + | 7559.06i | 0.384565 | + | 0.666087i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4622.02 | − | 4698.74i | 0.404874 | − | 0.411595i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 981.654 | + | 1700.27i | 0.0854834 | + | 0.148062i | 0.905597 | − | 0.424139i | \(-0.139423\pi\) |
−0.820114 | + | 0.572201i | \(0.806090\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4635.50 | + | 8028.93i | −0.401297 | + | 0.695066i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −30.3376 | + | 52.5463i | −0.00261099 | + | 0.00452237i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −12079.8 | −1.03359 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7055.43 | + | 12220.4i | 0.600188 | + | 1.03956i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7594.89 | 0.642348 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7044.93 | −0.592407 | −0.296203 | − | 0.955125i | \(-0.595721\pi\) | ||||
−0.296203 | + | 0.955125i | \(0.595721\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1606.65 | − | 2782.79i | −0.134328 | − | 0.232664i | 0.791012 | − | 0.611800i | \(-0.209554\pi\) |
−0.925341 | + | 0.379137i | \(0.876221\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4192.94 | −0.348561 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10357.4 | − | 17939.6i | 0.856123 | − | 1.48285i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5209.50 | − | 9023.13i | 0.428167 | − | 0.741606i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2178.80 | + | 3773.80i | 0.178064 | + | 0.308416i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 182.219 | − | 1429.53i | 0.0148082 | − | 0.116172i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6427.90 | + | 11133.4i | 0.519443 | + | 0.899702i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6394.52 | − | 11075.6i | 0.513862 | − | 0.890035i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3438.92 | + | 5956.38i | −0.274814 | + | 0.475991i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11251.4 | 0.894150 | 0.447075 | − | 0.894497i | \(-0.352466\pi\) | ||||
0.447075 | + | 0.894497i | \(0.352466\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5916.91 | − | 10248.4i | −0.467623 | − | 0.809946i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8737.33 | 0.686727 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1533.54 | −0.119871 | −0.0599353 | − | 0.998202i | \(-0.519089\pi\) | ||||
−0.0599353 | + | 0.998202i | \(0.519089\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1998.10 | + | 3460.80i | 0.155331 | + | 0.269041i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 138.477 | 0.0107066 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1815.98 | − | 3145.38i | 0.139645 | − | 0.241872i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2423.15 | − | 4197.02i | 0.185328 | − | 0.320998i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8422.84 | − | 14588.8i | −0.640731 | − | 1.10978i | −0.985270 | − | 0.171006i | \(-0.945298\pi\) |
0.344539 | − | 0.938772i | \(-0.388035\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10302.8 | + | 4317.33i | −0.779540 | + | 0.326661i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4466.31 | + | 7735.88i | 0.336128 | + | 0.582191i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −10410.0 | + | 18030.7i | −0.779273 | + | 1.34974i | 0.153089 | + | 0.988212i | \(0.451078\pi\) |
−0.932361 | + | 0.361528i | \(0.882255\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1482.01 | + | 2566.92i | −0.110352 | + | 0.191135i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −784.054 | −0.0580726 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −11818.3 | − | 20469.9i | −0.870735 | − | 1.50816i | −0.861237 | − | 0.508203i | \(-0.830310\pi\) |
−0.00949803 | − | 0.999955i | \(-0.503023\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26955.1 | 1.97554 | 0.987771 | − | 0.155913i | \(-0.0498319\pi\) | ||||
0.987771 | + | 0.155913i | \(0.0498319\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 642.326 | 0.0468300 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3018.39 | + | 5228.01i | 0.218914 | + | 0.379170i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 23499.8 | 1.69551 | 0.847755 | − | 0.530388i | \(-0.177954\pi\) | ||||
0.847755 | + | 0.530388i | \(0.177954\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1810.78 | − | 3136.36i | 0.129971 | − | 0.225117i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3464.19 | − | 6000.15i | 0.247365 | − | 0.428448i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6798.07 | + | 11774.6i | 0.482929 | + | 0.836457i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6385.85 | + | 2675.95i | −0.451320 | + | 0.189123i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2318.75 | + | 4016.19i | 0.163041 | + | 0.282395i | 0.935958 | − | 0.352112i | \(-0.114536\pi\) |
−0.772917 | + | 0.634507i | \(0.781203\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 215.658 | − | 373.530i | 0.0150866 | − | 0.0261308i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1391.45 | − | 2410.06i | 0.0968468 | − | 0.167744i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 12633.5 | 0.874869 | 0.437434 | − | 0.899250i | \(-0.355887\pi\) | ||||
0.437434 | + | 0.899250i | \(0.355887\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8573.47 | − | 14849.7i | −0.590719 | − | 1.02316i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1436.85 | −0.0985033 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18757.1 | 1.27946 | 0.639730 | − | 0.768600i | \(-0.279046\pi\) | ||||
0.639730 | + | 0.768600i | \(0.279046\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1816.49 | + | 3146.25i | 0.123288 | + | 0.213541i | 0.921062 | − | 0.389415i | \(-0.127323\pi\) |
−0.797774 | + | 0.602956i | \(0.793989\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1711.02 | −0.115553 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4676.85 | + | 8100.55i | −0.314283 | + | 0.544354i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6349.99 | + | 10998.5i | −0.424610 | + | 0.735445i | −0.996384 | − | 0.0849656i | \(-0.972922\pi\) |
0.571774 | + | 0.820411i | \(0.306255\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 894.712 | + | 1549.69i | 0.0595329 | + | 0.103114i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −19080.0 | − | 14516.2i | −1.26333 | − | 0.961151i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10820.1 | − | 18740.9i | −0.712918 | − | 1.23481i | −0.963757 | − | 0.266781i | \(-0.914040\pi\) |
0.250839 | − | 0.968029i | \(-0.419293\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −756.936 | + | 1311.05i | −0.0496303 | + | 0.0859621i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8270.85 | − | 14325.5i | 0.539663 | − | 0.934723i | −0.459259 | − | 0.888302i | \(-0.651885\pi\) |
0.998922 | − | 0.0464208i | \(-0.0147815\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21138.9 | 1.37261 | 0.686303 | − | 0.727316i | \(-0.259233\pi\) | ||||
0.686303 | + | 0.727316i | \(0.259233\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 564.421 | + | 977.607i | 0.0364726 | + | 0.0631723i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 10049.0 | 0.646235 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12825.4 | −0.820823 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 92.9955 | + | 161.073i | 0.00592326 | + | 0.0102594i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 10622.7 | 0.673377 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2744.90 | − | 4754.31i | 0.173174 | − | 0.299946i | −0.766354 | − | 0.642419i | \(-0.777931\pi\) |
0.939528 | + | 0.342473i | \(0.111264\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2176.43 | + | 3769.69i | −0.136659 | + | 0.236701i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −11748.8 | − | 20349.5i | −0.734230 | − | 1.27172i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1477.56 | − | 11591.6i | 0.0919044 | − | 0.720999i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2181.53 | + | 3778.52i | 0.135055 | + | 0.233922i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2148.52 | + | 3721.35i | −0.132389 | + | 0.229305i | −0.924597 | − | 0.380946i | \(-0.875598\pi\) |
0.792208 | + | 0.610251i | \(0.208932\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12848.5 | − | 22254.2i | 0.788016 | − | 1.36488i | −0.139164 | − | 0.990269i | \(-0.544442\pi\) |
0.927181 | − | 0.374615i | \(-0.122225\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 11735.0 | 0.716378 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1087.49 | + | 1883.59i | 0.0660798 | + | 0.114454i | 0.897172 | − | 0.441680i | \(-0.145617\pi\) |
−0.831093 | + | 0.556134i | \(0.812284\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13357.6 | 0.807907 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5573.52 | 0.335551 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7727.27 | + | 13384.0i | 0.463080 | + | 0.802078i | 0.999113 | − | 0.0421191i | \(-0.0134109\pi\) |
−0.536032 | + | 0.844197i | \(0.680078\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 33931.1 | 2.02412 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4310.01 | − | 7465.15i | 0.255935 | − | 0.443293i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1574.39 | + | 2726.92i | −0.0930643 | + | 0.161192i | −0.908799 | − | 0.417234i | \(-0.863000\pi\) |
0.815735 | + | 0.578426i | \(0.196333\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1049.85 | + | 1818.39i | 0.0617767 | + | 0.107000i | 0.895260 | − | 0.445545i | \(-0.146990\pi\) |
−0.833483 | + | 0.552545i | \(0.813657\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −12078.2 | − | 9189.23i | −0.707511 | − | 0.538281i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −178.513 | − | 309.193i | −0.0104097 | − | 0.0180301i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1288.16 | − | 2231.16i | 0.0747794 | − | 0.129522i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3089.68 | + | 5351.48i | −0.178556 | + | 0.309268i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12249.7 | 0.704763 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15485.4 | − | 26821.5i | −0.886950 | − | 1.53624i | −0.843462 | − | 0.537189i | \(-0.819486\pi\) |
−0.0434884 | − | 0.999054i | \(-0.513847\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3898.52 | 0.222302 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 14640.6 | 0.831141 | 0.415570 | − | 0.909561i | \(-0.363582\pi\) | ||||
0.415570 | + | 0.909561i | \(0.363582\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 317.317 | + | 549.610i | 0.0179345 | + | 0.0310635i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −13447.4 | −0.756688 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3342.92 | + | 5790.10i | −0.187281 | + | 0.324381i | −0.944343 | − | 0.328963i | \(-0.893301\pi\) |
0.757062 | + | 0.653343i | \(0.226634\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3180.13 | + | 5508.15i | −0.177382 | + | 0.307235i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2445.59 | + | 4235.88i | 0.135815 | + | 0.235239i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −18384.0 | − | 13986.7i | −1.01651 | − | 0.773370i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15097.0 | − | 26148.8i | −0.831141 | − | 1.43958i | −0.897134 | − | 0.441758i | \(-0.854355\pi\) |
0.0659934 | − | 0.997820i | \(-0.478978\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1201.70 | + | 2081.41i | −0.0658714 | + | 0.114093i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6175.98 | + | 10697.1i | −0.337077 | + | 0.583834i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3318.28 | −0.180328 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2855.54 | + | 4945.94i | 0.154516 | + | 0.267629i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −30300.9 | −1.63260 | −0.816298 | − | 0.577631i | \(-0.803977\pi\) | ||||
−0.816298 | + | 0.577631i | \(0.803977\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 221.181 | 0.0118663 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 12592.5 | + | 21810.9i | 0.672711 | + | 1.16517i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5147.64 | −0.273829 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13061.6 | + | 22623.4i | −0.691875 | + | 1.19836i | 0.279348 | + | 0.960190i | \(0.409882\pi\) |
−0.971223 | + | 0.238173i | \(0.923452\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1688.47 | + | 2924.52i | −0.0890613 | + | 0.154259i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4012.24 | − | 6949.41i | −0.210743 | − | 0.365017i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2683.68 | + | 21053.7i | −0.140369 | + | 1.10121i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5645.68 | + | 9778.60i | 0.294061 | + | 0.509328i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9662.83 | − | 16736.5i | 0.501200 | − | 0.868104i | −0.498799 | − | 0.866718i | \(-0.666225\pi\) |
0.999999 | − | 0.00138631i | \(-0.000441276\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3562.05 | − | 6169.64i | 0.183991 | − | 0.318682i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −10844.2 | −0.557816 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4448.73 | − | 7705.43i | −0.227892 | − | 0.394721i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −26065.8 | −1.32975 | −0.664875 | − | 0.746954i | \(-0.731515\pi\) | ||||
−0.664875 | + | 0.746954i | \(0.731515\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12861.0 | + | 22275.9i | 0.650727 | + | 1.12709i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1055.45 | 0.0531843 | 0.0265921 | − | 0.999646i | \(-0.491534\pi\) | ||||
0.0265921 | + | 0.999646i | \(0.491534\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6137.77 | + | 10630.9i | −0.308020 | + | 0.533507i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2622.44 | + | 4542.21i | −0.131070 | + | 0.227021i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4705.20 | + | 8149.64i | 0.234213 | + | 0.405669i | 0.959044 | − | 0.283258i | \(-0.0914153\pi\) |
−0.724831 | + | 0.688927i | \(0.758082\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −251.487 | − | 191.334i | −0.0124678 | − | 0.00948560i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3761.85 | − | 6515.72i | −0.185746 | − | 0.321721i | 0.758082 | − | 0.652159i | \(-0.226137\pi\) |
−0.943827 | + | 0.330439i | \(0.892803\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −21638.4 | + | 37478.8i | −1.06412 | + | 1.84311i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3220.94 | + | 5578.84i | −0.157762 | + | 0.273252i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7581.76 | −0.369868 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6492.03 | − | 11244.5i | −0.315443 | − | 0.546363i | 0.664089 | − | 0.747654i | \(-0.268820\pi\) |
−0.979532 | + | 0.201291i | \(0.935486\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 17189.3 | 0.831890 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −54695.3 | −2.63651 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13967.3 | + | 24192.1i | 0.670609 | + | 1.16153i | 0.977732 | + | 0.209859i | \(0.0673004\pi\) |
−0.307123 | + | 0.951670i | \(0.599366\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3460.30 | 0.165482 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7759.63 | − | 13440.1i | 0.369627 | − | 0.640214i | −0.619880 | − | 0.784697i | \(-0.712819\pi\) |
0.989507 | + | 0.144483i | \(0.0461520\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2576.44 | + | 4462.52i | −0.122246 | + | 0.211735i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 7971.46 | + | 13807.0i | 0.376743 | + | 0.652539i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −20931.1 | + | 8771.02i | −0.985368 | + | 0.412912i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6442.59 | − | 11158.9i | −0.302114 | − | 0.523277i | 0.674501 | − | 0.738274i | \(-0.264359\pi\) |
−0.976615 | + | 0.214997i | \(0.931026\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8288.68 | − | 14356.4i | 0.387172 | − | 0.670602i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2946.02 | + | 5102.66i | −0.137078 | + | 0.237425i | −0.926389 | − | 0.376567i | \(-0.877104\pi\) |
0.789312 | + | 0.613993i | \(0.210438\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −27713.0 | −1.28449 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1429.06 | + | 2475.21i | 0.0659812 | + | 0.114283i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −69.0916 | −0.00317775 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13374.3 | 0.612766 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −831.887 | − | 1440.87i | −0.0379684 | − | 0.0657631i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 26675.6 | 1.21286 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10510.2 | + | 18204.2i | −0.476045 | + | 0.824535i | −0.999623 | − | 0.0274430i | \(-0.991264\pi\) |
0.523578 | + | 0.851978i | \(0.324597\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 7834.81 | − | 13570.3i | 0.353519 | − | 0.612313i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −874.023 | − | 1513.85i | −0.0392879 | − | 0.0680486i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −19195.1 | + | 8043.56i | −0.859567 | + | 0.360196i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 12133.2 | + | 21015.3i | 0.541282 | + | 0.937528i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −15677.8 | + | 27154.7i | −0.696782 | + | 1.20686i | 0.272794 | + | 0.962073i | \(0.412052\pi\) |
−0.969576 | + | 0.244790i | \(0.921281\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −27601.7 | + | 47807.5i | −1.22212 | + | 2.11678i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9343.37 | −0.412150 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −13211.7 | − | 22883.3i | −0.580611 | − | 1.00565i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6642.34 | −0.290822 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 21611.7 | 0.942709 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9066.27 | + | 15703.2i | 0.394009 | + | 0.682443i | 0.992974 | − | 0.118332i | \(-0.0377546\pi\) |
−0.598965 | + | 0.800775i | \(0.704421\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24755.3 | 1.07186 | 0.535928 | − | 0.844263i | \(-0.319962\pi\) | ||||
0.535928 | + | 0.844263i | \(0.319962\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −12866.5 | + | 22285.5i | −0.555042 | + | 0.961360i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 15062.0 | − | 26088.2i | 0.647361 | − | 1.12126i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 267.786 | + | 463.819i | 0.0114671 | + | 0.0198617i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 516.322 | − | 4050.60i | 0.0220290 | − | 0.172820i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2041.32 | − | 3535.67i | −0.0867755 | − | 0.150300i | 0.819371 | − | 0.573264i | \(-0.194323\pi\) |
−0.906146 | + | 0.422964i | \(0.860990\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17163.5 | + | 29728.1i | −0.726954 | + | 1.25912i | 0.231211 | + | 0.972904i | \(0.425731\pi\) |
−0.958165 | + | 0.286217i | \(0.907602\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5975.16 | − | 10349.3i | 0.252156 | − | 0.436747i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3228.87 | −0.135767 | −0.0678833 | − | 0.997693i | \(-0.521625\pi\) | ||||
−0.0678833 | + | 0.997693i | \(0.521625\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5226.19 | + | 9052.03i | 0.218954 | + | 0.379240i | 0.954489 | − | 0.298248i | \(-0.0964021\pi\) |
−0.735534 | + | 0.677487i | \(0.763069\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 21507.6 | 0.897821 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −26906.9 | −1.11917 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −15961.7 | − | 27646.5i | −0.661530 | − | 1.14580i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5182.16 | −0.214004 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −14144.5 | + | 24499.0i | −0.582028 | + | 1.00810i | 0.413211 | + | 0.910635i | \(0.364407\pi\) |
−0.995239 | + | 0.0974668i | \(0.968926\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10295.9 | − | 17833.0i | 0.422154 | − | 0.731192i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1273.73 | − | 2206.17i | −0.0520400 | − | 0.0901360i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −9619.26 | − | 34752.9i | −0.391613 | − | 1.41483i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2758.19 | − | 4777.33i | −0.111892 | − | 0.193803i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1673.06 | − | 2897.82i | 0.0676316 | − | 0.117141i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2057.50 | − | 3563.69i | 0.0828790 | − | 0.143551i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −26631.8 | −1.06900 | −0.534498 | − | 0.845170i | \(-0.679499\pi\) | ||||
−0.534498 | + | 0.845170i | \(0.679499\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 165.978 | + | 287.482i | 0.00663898 | + | 0.0114991i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 11796.7 | 0.470209 | 0.235104 | − | 0.971970i | \(-0.424457\pi\) | ||||
0.235104 | + | 0.971970i | \(0.424457\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22672.8 | 0.900567 | 0.450283 | − | 0.892886i | \(-0.351323\pi\) | ||||
0.450283 | + | 0.892886i | \(0.351323\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −446.406 | − | 773.198i | −0.0176695 | − | 0.0306046i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −21421.1 | −0.844940 | −0.422470 | − | 0.906377i | \(-0.638837\pi\) | ||||
−0.422470 | + | 0.906377i | \(0.638837\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 20775.9 | − | 35985.0i | 0.816650 | − | 1.41448i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −10103.2 | + | 17499.3i | −0.395760 | + | 0.685476i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5175.76 | + | 8964.67i | 0.202043 | + | 0.349949i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1126.76 | − | 8839.52i | 0.0438332 | − | 0.343875i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −295.036 | − | 511.017i | −0.0114381 | − | 0.0198114i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1540.24 | + | 2667.78i | −0.0595082 | + | 0.103071i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2577.60 | − | 4464.53i | 0.0992466 | − | 0.171900i | −0.812126 | − | 0.583482i | \(-0.801690\pi\) |
0.911373 | + | 0.411581i | \(0.135023\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5590.58 | −0.214523 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −11846.1 | − | 20518.0i | −0.453013 | − | 0.784642i | 0.545558 | − | 0.838073i | \(-0.316318\pi\) |
−0.998572 | + | 0.0534309i | \(0.982984\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14591.5 | 0.556108 | 0.278054 | − | 0.960565i | \(-0.410311\pi\) | ||||
0.278054 | + | 0.960565i | \(0.410311\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 23840.6 | 0.905529 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4861.13 | − | 8419.72i | −0.184014 | − | 0.318722i | 0.759230 | − | 0.650823i | \(-0.225576\pi\) |
−0.943244 | + | 0.332101i | \(0.892243\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13857.8 | 0.522806 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1117.32 | − | 1935.26i | 0.0420108 | − | 0.0727649i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −574.709 | + | 995.426i | −0.0215363 | + | 0.0373020i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −34984.6 | − | 60595.1i | −1.30660 | − | 2.26310i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5422.22 | + | 2272.14i | −0.201831 | + | 0.0845760i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5913.55 | + | 10242.6i | 0.219386 | + | 0.379987i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −26594.9 | + | 46063.7i | −0.983355 | + | 1.70322i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3460.37 | + | 5993.54i | −0.127524 | + | 0.220878i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −64743.2 | −2.37805 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5899.50 | + | 10218.2i | 0.215975 | + | 0.374080i | 0.953574 | − | 0.301159i | \(-0.0973736\pi\) |
−0.737599 | + | 0.675239i | \(0.764040\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4786.18 | 0.174640 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 43012.4 | 1.56429 | 0.782143 | − | 0.623099i | \(-0.214127\pi\) | ||||
0.782143 | + | 0.623099i | \(0.214127\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9873.32 | + | 17101.1i | 0.357896 | + | 0.619895i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 21863.3 | 0.789921 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −10005.5 | + | 17330.1i | −0.360317 | + | 0.624088i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2475.70 | + | 4288.04i | −0.0888639 | + | 0.153917i | −0.907031 | − | 0.421063i | \(-0.861657\pi\) |
0.818167 | + | 0.574980i | \(0.194990\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9581.25 | − | 16595.2i | −0.342793 | − | 0.593736i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −20957.3 | + | 8782.00i | −0.747364 | + | 0.313178i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7105.67 | − | 12307.4i | −0.252576 | − | 0.437475i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3311.93 | + | 5736.43i | −0.117344 | + | 0.203246i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4467.43 | − | 7737.82i | 0.157774 | − | 0.273272i | −0.776292 | − | 0.630374i | \(-0.782902\pi\) |
0.934065 | + | 0.357102i | \(0.116235\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −560.243 | −0.0197221 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5238.89 | − | 9074.02i | −0.183830 | − | 0.318403i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 48870.6 | 1.70935 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13182.8 | −0.459620 | −0.229810 | − | 0.973235i | \(-0.573811\pi\) | ||||
−0.229810 | + | 0.973235i | \(0.573811\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 8868.01 | + | 15359.8i | 0.308197 | + | 0.533812i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −21693.7 | −0.751536 | −0.375768 | − | 0.926714i | \(-0.622621\pi\) | ||||
−0.375768 | + | 0.926714i | \(0.622621\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −642.714 | + | 1113.21i | −0.0221947 | + | 0.0384424i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2144.79 | + | 3714.89i | −0.0738308 | + | 0.127879i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −24895.0 | − | 43119.4i | −0.854254 | − | 1.47961i | −0.877335 | − | 0.479878i | \(-0.840681\pi\) |
0.0230813 | − | 0.999734i | \(-0.492652\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 35728.3 | + | 27182.4i | 1.22212 | + | 0.929799i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2516.31 | + | 4358.37i | 0.0858011 | + | 0.148612i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2108.96 | + | 3652.83i | −0.0716853 | + | 0.124162i | −0.899640 | − | 0.436632i | \(-0.856171\pi\) |
0.827955 | + | 0.560795i | \(0.189504\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1757.09 | − | 3043.37i | 0.0595374 | − | 0.103122i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −5100.05 | −0.172269 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1875.50 | − | 3248.45i | −0.0631522 | − | 0.109383i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7046.87 | 0.236544 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7049.38 | 0.235891 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −9906.83 | − | 17159.1i | −0.330479 | − | 0.572406i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 40927.9 | 1.36107 | 0.680534 | − | 0.732717i | \(-0.261748\pi\) | ||||
0.680534 | + | 0.732717i | \(0.261748\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −363.809 | + | 630.136i | −0.0120611 | + | 0.0208905i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −8557.42 | + | 14821.9i | −0.282822 | + | 0.489863i | −0.972079 | − | 0.234655i | \(-0.924604\pi\) |
0.689256 | + | 0.724518i | \(0.257937\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3642.31 | − | 6308.67i | −0.120007 | − | 0.207859i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2567.28 | + | 20140.6i | −0.0843270 | + | 0.661554i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 59.2348 | + | 102.598i | 0.00193970 | + | 0.00335966i | 0.866994 | − | 0.498319i | \(-0.166049\pi\) |
−0.865054 | + | 0.501679i | \(0.832716\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14320.4 | + | 24803.6i | −0.467498 | + | 0.809731i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2395.53 | − | 4149.17i | 0.0779646 | − | 0.135039i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −26002.8 | −0.843705 | −0.421852 | − | 0.906665i | \(-0.638620\pi\) | ||||
−0.421852 | + | 0.906665i | \(0.638620\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7612.65 | − | 13185.5i | −0.246253 | − | 0.426523i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −14853.0 | −0.479002 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9964.14 | 0.320365 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8031.00 | − | 13910.1i | −0.257430 | − | 0.445882i | 0.708123 | − | 0.706089i | \(-0.249542\pi\) |
−0.965553 | + | 0.260208i | \(0.916209\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6030.93 | −0.192735 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3930.53 | + | 6807.88i | −0.125232 | + | 0.216909i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −680.772 | + | 1179.13i | −0.0216251 | + | 0.0374558i | −0.876635 | − | 0.481155i | \(-0.840217\pi\) |
0.855010 | + | 0.518611i | \(0.173551\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1328.72 | − | 2301.41i | −0.0420809 | − | 0.0728862i |
(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 | 624.4.q.i.289.1 | 8 | ||
4.3 | odd | 2 | 39.4.e.c.16.1 | ✓ | 8 | ||
12.11 | even | 2 | 117.4.g.e.55.4 | 8 | |||
13.9 | even | 3 | inner | 624.4.q.i.529.1 | 8 | ||
52.3 | odd | 6 | 507.4.a.m.1.4 | 4 | |||
52.11 | even | 12 | 507.4.b.h.337.8 | 8 | |||
52.15 | even | 12 | 507.4.b.h.337.1 | 8 | |||
52.23 | odd | 6 | 507.4.a.i.1.1 | 4 | |||
52.35 | odd | 6 | 39.4.e.c.22.1 | yes | 8 | ||
156.23 | even | 6 | 1521.4.a.bb.1.4 | 4 | |||
156.35 | even | 6 | 117.4.g.e.100.4 | 8 | |||
156.107 | even | 6 | 1521.4.a.v.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.4.e.c.16.1 | ✓ | 8 | 4.3 | odd | 2 | ||
39.4.e.c.22.1 | yes | 8 | 52.35 | odd | 6 | ||
117.4.g.e.55.4 | 8 | 12.11 | even | 2 | |||
117.4.g.e.100.4 | 8 | 156.35 | even | 6 | |||
507.4.a.i.1.1 | 4 | 52.23 | odd | 6 | |||
507.4.a.m.1.4 | 4 | 52.3 | odd | 6 | |||
507.4.b.h.337.1 | 8 | 52.15 | even | 12 | |||
507.4.b.h.337.8 | 8 | 52.11 | even | 12 | |||
624.4.q.i.289.1 | 8 | 1.1 | even | 1 | trivial | ||
624.4.q.i.529.1 | 8 | 13.9 | even | 3 | inner | ||
1521.4.a.v.1.1 | 4 | 156.107 | even | 6 | |||
1521.4.a.bb.1.4 | 4 | 156.23 | even | 6 |