Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [117,4,Mod(55,117)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(117, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([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("117.55");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 117 = 3^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 117.g (of order \(3\), degree \(2\), 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: | \(6.90322347067\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 39) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 55.4 | ||
Root | \(2.66520 + 4.61626i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 117.55 |
Dual form | 117.4.g.e.100.4 |
$q$-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 \(\left(\mathbb{Z}/117\mathbb{Z}\right)^\times\).
\(n\) | \(28\) | \(92\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.66520 | + | 4.61626i | 0.942289 | + | 1.63209i | 0.761090 | + | 0.648647i | \(0.224665\pi\) |
0.181199 | + | 0.983446i | \(0.442002\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −10.2065 | + | 17.6783i | −1.27582 | + | 2.20978i | ||||
\(5\) | 16.4131 | 1.46803 | 0.734016 | − | 0.679132i | \(-0.237644\pi\) | ||||
0.734016 | + | 0.679132i | \(0.237644\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.83984 | + | 8.38285i | −0.261327 | + | 0.452631i | −0.966595 | − | 0.256309i | \(-0.917493\pi\) |
0.705268 | + | 0.708941i | \(0.250827\pi\) | |||||||
\(8\) | −66.1667 | −2.92418 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 43.7441 | + | 75.7670i | 1.38331 | + | 2.39596i | ||||
\(11\) | 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 | ||||
\(14\) | −51.5965 | −0.984982 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −94.6948 | − | 164.016i | −1.47961 | − | 2.56275i | ||||
\(17\) | 53.9641 | − | 93.4685i | 0.769895 | − | 1.33350i | −0.167725 | − | 0.985834i | \(-0.553642\pi\) |
0.937619 | − | 0.347663i | \(-0.113025\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.12362 | − | 1.94616i | 0.0135671 | − | 0.0234989i | −0.859162 | − | 0.511703i | \(-0.829015\pi\) |
0.872729 | + | 0.488205i | \(0.162348\pi\) | |||||||
\(20\) | −167.521 | + | 290.155i | −1.87294 | + | 3.24403i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −73.5279 | + | 127.354i | −0.712554 | + | 1.23418i | ||||
\(23\) | 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 | ||||||||
\(26\) | 31.5919 | − | 247.842i | 0.238296 | − | 1.86945i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −98.7961 | − | 171.120i | −0.666811 | − | 1.15495i | ||||
\(29\) | 30.8106 | + | 53.3656i | 0.197289 | + | 0.341715i | 0.947649 | − | 0.319315i | \(-0.103453\pi\) |
−0.750359 | + | 0.661030i | \(0.770119\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 191.932 | 1.11200 | 0.556000 | − | 0.831182i | \(-0.312335\pi\) | ||||
0.556000 | + | 0.831182i | \(0.312335\pi\) | |||||||
\(32\) | 240.094 | − | 415.855i | 1.32634 | − | 2.29729i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 575.300 | 2.90185 | ||||||||
\(35\) | −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 | \(0.903501\pi\) | |||||||
\(38\) | 11.9786 | 0.0511366 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1086.00 | −4.29279 | ||||||||
\(41\) | −15.3726 | − | 26.6261i | −0.0585561 | − | 0.101422i | 0.835261 | − | 0.549853i | \(-0.185316\pi\) |
−0.893817 | + | 0.448431i | \(0.851983\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −119.163 | + | 206.396i | −0.422608 | + | 0.731978i | −0.996194 | − | 0.0871672i | \(-0.972219\pi\) |
0.573586 | + | 0.819145i | \(0.305552\pi\) | |||||||
\(44\) | −563.160 | −1.92953 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −111.429 | + | 193.001i | −0.357160 | + | 0.618618i | ||||
\(47\) | 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 | ||||
\(50\) | 384.826 | + | 666.539i | 1.08845 | + | 1.88526i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 882.459 | − | 369.788i | 2.35337 | − | 0.986162i | ||||
\(53\) | −492.825 | −1.27726 | −0.638630 | − | 0.769514i | \(-0.720498\pi\) | ||||
−0.638630 | + | 0.769514i | \(0.720498\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 226.404 | + | 392.142i | 0.555059 | + | 0.961390i | ||||
\(56\) | 320.236 | − | 554.665i | 0.764167 | − | 1.32358i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −164.233 | + | 284.460i | −0.371807 | + | 0.643989i | ||||
\(59\) | 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 | \(0.0123640\pi\) | |||||||
\(62\) | 511.536 | + | 886.007i | 1.04783 | + | 1.81489i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1044.47 | 2.03998 | ||||||||
\(65\) | −612.262 | − | 465.815i | −1.16834 | − | 0.888880i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −95.0568 | − | 164.643i | −0.173329 | − | 0.300215i | 0.766253 | − | 0.642539i | \(-0.222119\pi\) |
−0.939582 | + | 0.342325i | \(0.888786\pi\) | |||||||
\(68\) | 1101.57 | + | 1907.98i | 1.96449 | + | 3.40260i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −846.858 | −1.44598 | ||||||||
\(71\) | 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 | \(0.778651\pi\) | |||||||
\(74\) | 262.318 | − | 454.348i | 0.412079 | − | 0.713742i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 22.9365 | + | 39.7271i | 0.0346183 | + | 0.0599607i | ||||
\(77\) | −267.045 | −0.395228 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −375.216 | −0.534368 | −0.267184 | − | 0.963646i | \(-0.586093\pi\) | ||||
−0.267184 | + | 0.963646i | \(0.586093\pi\) | |||||||
\(80\) | −1554.23 | − | 2692.01i | −2.17211 | − | 3.76220i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 81.9421 | − | 141.928i | 0.110354 | − | 0.191138i | ||||
\(83\) | 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 | ||||
\(86\) | −1270.37 | −1.59288 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −912.708 | − | 1580.86i | −1.10563 | − | 1.91500i | ||||
\(89\) | −519.076 | − | 899.066i | −0.618224 | − | 1.07080i | −0.989810 | − | 0.142397i | \(-0.954519\pi\) |
0.371585 | − | 0.928399i | \(-0.378814\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 418.453 | − | 175.350i | 0.482042 | − | 0.201996i | ||||
\(92\) | −853.451 | −0.967157 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1363.20 | + | 2361.13i | 1.49578 | + | 2.59077i | ||||
\(95\) | 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 | \(0.177591\pi\) | |||||||
\(98\) | −664.443 | + | 1150.85i | −0.684887 | + | 1.18626i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1473.72 | + | 2552.56i | −1.47372 | + | 2.55256i | ||||
\(101\) | 265.899 | + | 460.551i | 0.261960 | + | 0.453728i | 0.966763 | − | 0.255676i | \(-0.0822979\pi\) |
−0.704803 | + | 0.709403i | \(0.748965\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −735.984 | −0.704064 | −0.352032 | − | 0.935988i | \(-0.614509\pi\) | ||||
−0.352032 | + | 0.935988i | \(0.614509\pi\) | |||||||
\(104\) | 2468.23 | + | 1877.86i | 2.32721 | + | 1.77057i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1313.48 | − | 2275.01i | −1.20355 | − | 2.08461i | ||||
\(107\) | −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 | \(0.575147\pi\) | |||||||
\(110\) | −1206.82 | + | 2090.27i | −1.04605 | + | 1.81182i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1833.23 | 1.54664 | ||||||||
\(113\) | −90.2946 | + | 156.395i | −0.0751699 | + | 0.130198i | −0.901160 | − | 0.433486i | \(-0.857283\pi\) |
0.825990 | + | 0.563684i | \(0.190617\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 343.107 | + | 594.280i | 0.278217 | + | 0.481886i | ||||
\(116\) | −1257.88 | −1.00682 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2580.86 | 2.01346 | ||||||||
\(119\) | 522.355 | + | 904.746i | 0.402389 | + | 0.696957i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 284.947 | − | 493.542i | 0.214085 | − | 0.370805i | ||||
\(122\) | 2366.81 | 1.75640 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1958.96 | + | 3393.02i | −1.41871 | + | 2.45728i | ||||
\(125\) | 318.242 | 0.227716 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −715.817 | − | 1239.83i | −0.500146 | − | 0.866278i | −1.00000 | 0.000168331i | \(-0.999946\pi\) | |
0.499854 | − | 0.866110i | \(-0.333387\pi\) | |||||||
\(128\) | 862.972 | + | 1494.71i | 0.595912 | + | 1.03215i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 518.521 | − | 4067.85i | 0.349825 | − | 2.74441i | ||||
\(131\) | −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 | ||||
\(134\) | 506.690 | − | 877.613i | 0.326652 | − | 0.565778i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3570.62 | + | 6184.50i | −2.25131 | + | 3.89939i | ||||
\(137\) | −193.756 | + | 335.595i | −0.120830 | + | 0.209283i | −0.920095 | − | 0.391695i | \(-0.871889\pi\) |
0.799265 | + | 0.600978i | \(0.205222\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −376.284 | + | 651.743i | −0.229611 | + | 0.397699i | −0.957693 | − | 0.287792i | \(-0.907079\pi\) |
0.728082 | + | 0.685491i | \(0.240412\pi\) | |||||||
\(140\) | −1621.55 | − | 2808.61i | −0.978900 | − | 1.69550i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2584.09 | 1.52713 | ||||||||
\(143\) | 163.508 | − | 1282.74i | 0.0956171 | − | 0.750126i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 505.698 | + | 875.894i | 0.289627 | + | 0.501649i | ||||
\(146\) | −2552.67 | − | 4421.36i | −1.44699 | − | 2.50626i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2009.13 | 1.11587 | ||||||||
\(149\) | −1318.36 | + | 2283.47i | −0.724862 | + | 1.25550i | 0.234169 | + | 0.972196i | \(0.424763\pi\) |
−0.959031 | + | 0.283301i | \(0.908570\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3332.42 | −1.79595 | −0.897975 | − | 0.440046i | \(-0.854962\pi\) | ||||
−0.897975 | + | 0.440046i | \(0.854962\pi\) | |||||||
\(152\) | −74.3459 | + | 128.771i | −0.0396727 | + | 0.0687151i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −711.727 | − | 1232.75i | −0.372419 | − | 0.645049i | ||||
\(155\) | 3150.20 | 1.63245 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1625.26 | −0.826179 | −0.413089 | − | 0.910690i | \(-0.635550\pi\) | ||||
−0.413089 | + | 0.910690i | \(0.635550\pi\) | |||||||
\(158\) | −1000.02 | − | 1732.09i | −0.503529 | − | 0.872138i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3940.68 | − | 6825.46i | 1.94711 | − | 3.37250i | ||||
\(161\) | −404.698 | −0.198104 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 917.683 | − | 1589.47i | 0.440972 | − | 0.763786i | −0.556790 | − | 0.830653i | \(-0.687967\pi\) |
0.997762 | + | 0.0668673i | \(0.0213004\pi\) | |||||||
\(164\) | 627.605 | 0.298828 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1907.65 | + | 3304.15i | 0.891944 | + | 1.54489i | ||||
\(167\) | 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 | ||||
\(170\) | 9442.44 | 4.26001 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2432.48 | − | 4213.18i | −1.07834 | − | 1.86774i | ||||
\(173\) | 1265.81 | − | 2192.45i | 0.556289 | − | 0.963522i | −0.441512 | − | 0.897255i | \(-0.645558\pi\) |
0.997802 | − | 0.0662666i | \(-0.0211088\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −698.823 | + | 1210.40i | −0.301863 | + | 0.522842i | ||||
\(176\) | 2612.46 | − | 4524.90i | 1.11887 | − | 1.93794i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2766.88 | − | 4792.38i | 1.16509 | − | 2.01800i | ||||
\(179\) | 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 | \(0.199496\pi\) | |||||||
\(182\) | 1924.72 | + | 1464.35i | 0.783900 | + | 0.596398i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1383.18 | − | 2395.74i | −0.554182 | − | 0.959871i | ||||
\(185\) | −807.717 | − | 1399.01i | −0.320998 | − | 0.555984i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2977.54 | 1.16438 | ||||||||
\(188\) | −5220.46 | + | 9042.11i | −2.02522 | + | 3.50779i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 196.606 | 0.0750701 | ||||||||
\(191\) | −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 | \(0.761057\pi\) | |||||||
\(194\) | −349.480 | −0.129336 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5089.06 | −1.85461 | ||||||||
\(197\) | −463.816 | − | 803.352i | −0.167744 | − | 0.290541i | 0.769883 | − | 0.638186i | \(-0.220315\pi\) |
−0.937626 | + | 0.347645i | \(0.886981\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −239.476 | + | 414.784i | −0.0853064 | + | 0.147755i | −0.905522 | − | 0.424300i | \(-0.860520\pi\) |
0.820215 | + | 0.572055i | \(0.193854\pi\) | |||||||
\(200\) | −9553.77 | −3.37777 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1417.35 | + | 2454.92i | −0.493684 | + | 0.855086i | ||||
\(203\) | −596.474 | −0.206228 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −252.312 | − | 437.017i | −0.0859621 | − | 0.148891i | ||||
\(206\) | −1961.54 | − | 3397.49i | −0.663432 | − | 1.14910i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1122.46 | + | 8805.85i | −0.374178 | + | 2.93546i | ||||
\(209\) | 61.9970 | 0.0205188 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 725.477 | + | 1256.56i | 0.236701 | + | 0.409978i | 0.959766 | − | 0.280802i | \(-0.0906005\pi\) |
−0.723065 | + | 0.690780i | \(0.757267\pi\) | |||||||
\(212\) | 5030.04 | − | 8712.29i | 1.62955 | − | 2.82246i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2087.55 | − | 3615.75i | 0.666833 | − | 1.15499i | ||||
\(215\) | −1955.83 | + | 3387.59i | −0.620402 | + | 1.07457i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −928.920 | + | 1608.94i | −0.290595 | + | 0.503326i | ||||
\(218\) | −1418.79 | − | 2457.41i | −0.440791 | − | 0.763473i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −9243.19 | −2.83262 | ||||||||
\(221\) | −4665.74 | + | 1955.15i | −1.42014 | + | 0.595101i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1029.89 | + | 1783.83i | 0.309268 | + | 0.535668i | 0.978202 | − | 0.207654i | \(-0.0665827\pi\) |
−0.668935 | + | 0.743321i | \(0.733249\pi\) | |||||||
\(224\) | 2324.03 | + | 4025.34i | 0.693218 | + | 1.20069i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −962.612 | −0.283327 | ||||||||
\(227\) | 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 | \(0.575587\pi\) | |||||||
\(230\) | −1828.90 | + | 3167.74i | −0.524321 | + | 0.908151i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2038.64 | − | 3531.02i | −0.576910 | − | 0.999237i | ||||
\(233\) | 1903.69 | 0.535258 | 0.267629 | − | 0.963522i | \(-0.413760\pi\) | ||||
0.267629 | + | 0.963522i | \(0.413760\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8395.00 | 2.33034 | ||||||||
\(236\) | 4941.79 | + | 8559.44i | 1.36306 | + | 2.36090i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2784.36 | + | 4822.65i | −0.758333 | + | 1.31347i | ||||
\(239\) | −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 | \(0.00618357\pi\) | |||||||
\(242\) | 3037.75 | 0.806918 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 4531.92 | + | 7849.52i | 1.18904 | + | 2.05948i | ||||
\(245\) | 2045.92 | + | 3543.64i | 0.533507 | + | 0.924061i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −97.1479 | + | 40.7092i | −0.0250258 | + | 0.0104869i | ||||
\(248\) | −12699.5 | −3.25169 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 848.178 | + | 1469.09i | 0.214574 | + | 0.371653i | ||||
\(251\) | −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 | ||||
\(254\) | 3815.59 | − | 6608.79i | 0.942564 | − | 1.63257i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −422.095 | + | 731.091i | −0.103051 | + | 0.178489i | ||||
\(257\) | −2762.89 | − | 4785.47i | −0.670602 | − | 1.16152i | −0.977734 | − | 0.209849i | \(-0.932703\pi\) |
0.307132 | − | 0.951667i | \(-0.400631\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 952.709 | 0.228565 | ||||||||
\(260\) | 14483.9 | − | 6069.37i | 3.45482 | − | 1.44772i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −5509.82 | − | 9543.28i | −1.29923 | − | 2.25033i | ||||
\(263\) | 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 | ||||||||
\(266\) | −57.9747 | + | 100.415i | −0.0133634 | + | 0.0231460i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3880.81 | 0.884545 | ||||||||
\(269\) | 3601.94 | − | 6238.75i | 0.816410 | − | 1.41406i | −0.0919010 | − | 0.995768i | \(-0.529294\pi\) |
0.908311 | − | 0.418295i | \(-0.137372\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4288.84 | + | 7428.49i | 0.961360 | + | 1.66512i | 0.719091 | + | 0.694916i | \(0.244558\pi\) |
0.242269 | + | 0.970209i | \(0.422108\pi\) | |||||||
\(272\) | −20440.5 | −4.55656 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2065.59 | −0.455427 | ||||||||
\(275\) | 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 | \(0.883136\pi\) | |||||||
\(278\) | −4011.48 | −0.865442 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 5256.06 | − | 9103.77i | 1.12182 | − | 1.94305i | ||||
\(281\) | −849.157 | −0.180272 | −0.0901360 | − | 0.995929i | \(-0.528730\pi\) | ||||
−0.0901360 | + | 0.995929i | \(0.528730\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −557.686 | − | 965.941i | −0.117141 | − | 0.202895i | 0.801492 | − | 0.598005i | \(-0.204040\pi\) |
−0.918634 | + | 0.395110i | \(0.870706\pi\) | |||||||
\(284\) | 4947.97 | + | 8570.14i | 1.03383 | + | 1.79065i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6357.23 | − | 2663.95i | 1.31437 | − | 0.550779i | ||||
\(287\) | 297.604 | 0.0612091 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3367.75 | − | 5833.11i | −0.685476 | − | 1.18728i | ||||
\(290\) | −2695.57 | + | 4668.86i | −0.545825 | + | 0.945396i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 9775.62 | − | 16931.9i | 1.95916 | − | 3.39337i | ||||
\(293\) | −931.764 | + | 1613.86i | −0.185782 | + | 0.321784i | −0.943840 | − | 0.330403i | \(-0.892815\pi\) |
0.758058 | + | 0.652188i | \(0.226149\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3973.43 | − | 6882.19i | 0.784211 | − | 1.35829i | ||||
\(296\) | 3256.18 | + | 5639.87i | 0.639397 | + | 1.10747i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −14054.8 | −2.73212 | ||||||||
\(299\) | 247.792 | − | 1943.95i | 0.0479269 | − | 0.375992i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1153.46 | − | 1997.85i | −0.220878 | − | 0.382571i | ||||
\(302\) | −8881.55 | − | 15383.3i | −1.69230 | − | 2.93116i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −425.602 | −0.0802959 | ||||||||
\(305\) | 3643.88 | − | 6311.39i | 0.684092 | − | 1.18488i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6387.50 | −1.18747 | −0.593736 | − | 0.804660i | \(-0.702348\pi\) | ||||
−0.593736 | + | 0.804660i | \(0.702348\pi\) | |||||||
\(308\) | 2725.60 | − | 4720.89i | 0.504239 | − | 0.873368i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 8395.89 | + | 14542.1i | 1.53824 | + | 2.66431i | ||||
\(311\) | 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 | \(0.679241\pi\) | |||||||
\(314\) | −4331.64 | − | 7502.63i | −0.778499 | − | 1.34840i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3829.66 | − | 6633.16i | 0.681756 | − | 1.18084i | ||||
\(317\) | 1677.54 | 0.297224 | 0.148612 | − | 0.988896i | \(-0.452519\pi\) | ||||
0.148612 | + | 0.988896i | \(0.452519\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −850.009 | + | 1472.26i | −0.149189 | + | 0.258403i | ||||
\(320\) | 17143.0 | 2.99476 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1078.60 | − | 1868.19i | −0.186671 | − | 0.323323i | ||||
\(323\) | −121.270 | − | 210.045i | −0.0208905 | − | 0.0361834i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5386.21 | − | 4097.88i | −0.919301 | − | 0.699413i | ||||
\(326\) | 9783.22 | 1.66209 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1017.15 | + | 1761.76i | 0.171228 | + | 0.296576i | ||||
\(329\) | −2475.49 | + | 4287.68i | −0.414828 | + | 0.718503i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1005.15 | + | 1740.98i | −0.166913 | + | 0.289102i | −0.937333 | − | 0.348435i | \(-0.886713\pi\) |
0.770420 | + | 0.637537i | \(0.220047\pi\) | |||||||
\(332\) | −7305.49 | + | 12653.5i | −1.20765 | + | 2.09172i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −5183.80 | + | 8978.60i | −0.849236 | + | 1.47092i | ||||
\(335\) | −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 | \(0.304222\pi\) | |||||||
\(338\) | −8212.40 | + | 8348.71i | −1.32159 | + | 1.34352i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 18080.2 | + | 31315.9i | 2.88394 | + | 4.99512i | ||||
\(341\) | 2647.53 | + | 4585.65i | 0.420444 | + | 0.728231i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5733.31 | −0.902536 | ||||||||
\(344\) | 7884.60 | − | 13656.5i | 1.23578 | − | 2.14044i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 13494.6 | 2.09674 | ||||||||
\(347\) | 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 | \(-0.551748\pi\) | |||||||
\(350\) | −7450.00 | −1.13777 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 13247.5 | 2.00595 | ||||||||
\(353\) | −5446.15 | − | 9433.01i | −0.821160 | − | 1.42229i | −0.904819 | − | 0.425796i | \(-0.859994\pi\) |
0.0836595 | − | 0.996494i | \(-0.473339\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3978.41 | − | 6890.80i | 0.594794 | − | 1.03021i | ||||
\(356\) | 21191.9 | 3.15497 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −11361.8 | + | 19679.2i | −1.67734 | + | 2.90524i | ||||
\(359\) | 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 | ||||
\(362\) | 10513.2 | + | 18209.3i | 1.52641 | + | 2.64382i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1171.08 | + | 9187.24i | −0.168630 | + | 1.32292i | ||||
\(365\) | −15720.1 | −2.25433 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1191.88 | − | 2064.39i | −0.169525 | − | 0.293625i | 0.768728 | − | 0.639576i | \(-0.220890\pi\) |
−0.938253 | + | 0.345950i | \(0.887557\pi\) | |||||||
\(368\) | 3959.09 | − | 6857.35i | 0.560821 | − | 0.971370i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 4305.45 | − | 7457.26i | 0.604945 | − | 1.04780i | ||||
\(371\) | 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 | \(-0.206685\pi\) | |||||||
\(374\) | 7935.73 | + | 13745.1i | 1.09718 | + | 1.90038i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −33843.1 | −4.64181 | ||||||||
\(377\) | 365.214 | − | 2865.14i | 0.0498925 | − | 0.391412i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2218.36 | + | 3842.32i | 0.300659 | + | 0.520756i | 0.976285 | − | 0.216488i | \(-0.0694601\pi\) |
−0.675627 | + | 0.737244i | \(0.736127\pi\) | |||||||
\(380\) | 376.458 | + | 652.045i | 0.0508208 | + | 0.0880242i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1141.28 | −0.152862 | ||||||||
\(383\) | −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 | ||||||||
\(386\) | −3217.39 | + | 5572.68i | −0.424251 | + | 0.734824i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −669.177 | − | 1159.05i | −0.0875576 | − | 0.151654i | ||||
\(389\) | −3463.79 | −0.451469 | −0.225734 | − | 0.974189i | \(-0.572478\pi\) | ||||
−0.225734 | + | 0.974189i | \(0.572478\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4512.37 | 0.583633 | ||||||||
\(392\) | −8247.80 | − | 14285.6i | −1.06270 | − | 1.84064i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2472.32 | − | 4282.18i | 0.316126 | − | 0.547546i | ||||
\(395\) | −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 | \(0.175227\pi\) | |||||||
\(398\) | −2553.00 | −0.321533 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −13672.9 | − | 23682.2i | −1.70912 | − | 2.96028i | ||||
\(401\) | −593.424 | − | 1027.84i | −0.0739007 | − | 0.128000i | 0.826707 | − | 0.562633i | \(-0.190211\pi\) |
−0.900608 | + | 0.434633i | \(0.856878\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7159.70 | − | 5447.16i | −0.884987 | − | 0.673306i | ||||
\(404\) | −10855.6 | −1.33685 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1589.72 | − | 2753.48i | −0.194327 | − | 0.336583i | ||||
\(407\) | 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 | \(0.327496\pi\) | |||||||
\(410\) | 1344.92 | − | 2329.47i | 0.162002 | − | 0.280596i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 7511.85 | − | 13010.9i | 0.898258 | − | 1.55583i | ||||
\(413\) | 2343.35 | + | 4058.80i | 0.279198 | + | 0.483585i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11747.9 | 1.38960 | ||||||||
\(416\) | −20758.5 | + | 8698.72i | −2.44656 | + | 1.02522i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 165.234 | + | 286.194i | 0.0193346 | + | 0.0334885i | ||||
\(419\) | 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 | \(0.286470\pi\) | |||||||
\(422\) | −3867.08 | + | 6697.98i | −0.446082 | + | 0.772636i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 32608.6 | 3.73494 | ||||||||
\(425\) | 7791.85 | − | 13495.9i | 0.889318 | − | 1.54034i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2148.99 | + | 3722.16i | 0.243553 | + | 0.421846i | ||||
\(428\) | 15988.9 | 1.80573 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −20850.7 | −2.33839 | ||||||||
\(431\) | 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 | \(0.325879\pi\) | |||||||
\(434\) | −9903.02 | −1.09530 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5433.34 | − | 9410.83i | 0.596812 | − | 1.03371i | ||||
\(437\) | 93.9545 | 0.0102848 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6513.12 | + | 11281.1i | 0.708097 | + | 1.22646i | 0.965562 | + | 0.260172i | \(0.0837793\pi\) |
−0.257466 | + | 0.966287i | \(0.582887\pi\) | |||||||
\(440\) | −14980.4 | − | 25946.8i | −1.62309 | − | 2.81128i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −21460.6 | − | 16327.4i | −2.30945 | − | 1.75705i | ||||
\(443\) | 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 | ||||
\(446\) | −5489.74 | + | 9508.50i | −0.582840 | + | 1.00951i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −5055.08 | + | 8755.65i | −0.533103 | + | 0.923361i | ||||
\(449\) | 4941.37 | − | 8558.71i | 0.519372 | − | 0.899578i | −0.480375 | − | 0.877063i | \(-0.659499\pi\) |
0.999747 | − | 0.0225149i | \(-0.00716731\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 424.102 | − | 734.566i | 0.0442798 | − | 0.0766949i | ||||
\(452\) | −1843.19 | − | 3192.50i | −0.191806 | − | 0.332218i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 23893.3 | 2.46997 | ||||||||
\(455\) | 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 | \(0.538253\pi\) | |||||||
\(458\) | −4345.31 | − | 7526.31i | −0.443326 | − | 0.767863i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −14007.8 | −1.41982 | ||||||||
\(461\) | −3873.73 | + | 6709.50i | −0.391361 | + | 0.677858i | −0.992629 | − | 0.121190i | \(-0.961329\pi\) |
0.601268 | + | 0.799047i | \(0.294662\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −333.422 | −0.0334675 | −0.0167337 | − | 0.999860i | \(-0.505327\pi\) | ||||
−0.0167337 | + | 0.999860i | \(0.505327\pi\) | |||||||
\(464\) | 5835.21 | − | 10106.9i | 0.583821 | − | 1.01121i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5073.71 | + | 8787.93i | 0.504368 | + | 0.873590i | ||||
\(467\) | −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 | ||||||||
\(470\) | 22374.3 | + | 38753.5i | 2.19585 | + | 3.80333i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −16018.2 | + | 27744.4i | −1.56208 | + | 2.70559i | ||||
\(473\) | −6574.96 | −0.639148 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 162.238 | − | 281.005i | 0.0156716 | − | 0.0271440i | ||||
\(476\) | −21325.8 | −2.05350 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −10031.2 | − | 17374.6i | −0.959870 | − | 1.66254i | ||||
\(479\) | −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 | ||||
\(482\) | 19268.0 | 1.82082 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5816.64 | + | 10074.7i | 0.546266 | + | 0.946160i | ||||
\(485\) | −538.050 | + | 931.931i | −0.0503745 | + | 0.0872511i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4047.69 | + | 7010.80i | −0.376629 | + | 0.652340i | −0.990569 | − | 0.137012i | \(-0.956250\pi\) |
0.613941 | + | 0.789352i | \(0.289583\pi\) | |||||||
\(488\) | −14689.7 | + | 25443.3i | −1.36265 | + | 2.36017i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −10905.6 | + | 18889.0i | −1.00544 | + | 1.74147i | ||||
\(491\) | 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 | ||||||||
\(494\) | −446.842 | − | 339.962i | −0.0406971 | − | 0.0309628i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −18175.0 | − | 31479.9i | −1.64532 | − | 2.84978i | ||||
\(497\) | 2346.28 | + | 4063.88i | 0.211761 | + | 0.366780i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18050.7 | −1.61936 | −0.809682 | − | 0.586870i | \(-0.800360\pi\) | ||||
−0.809682 | + | 0.586870i | \(0.800360\pi\) | |||||||
\(500\) | −3248.15 | + | 5625.97i | −0.290524 | + | 0.503202i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −30541.9 | −2.71544 | ||||||||
\(503\) | 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 | ||||
\(506\) | −6148.25 | −0.540165 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 29224.1 | 2.55238 | ||||||||
\(509\) | −981.654 | − | 1700.27i | −0.0854834 | − | 0.148062i | 0.820114 | − | 0.572201i | \(-0.193910\pi\) |
−0.905597 | + | 0.424139i | \(0.860577\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4635.50 | − | 8028.93i | 0.401297 | − | 0.695066i | ||||
\(512\) | 9307.69 | 0.803409 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 14727.3 | − | 25508.5i | 1.26380 | − | 2.18897i | ||||
\(515\) | −12079.8 | −1.03359 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7055.43 | + | 12220.4i | 0.600188 | + | 1.03956i | ||||
\(518\) | 2539.16 | + | 4397.95i | 0.215375 | + | 0.373040i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 40511.4 | + | 30821.4i | 3.41642 | + | 2.59925i | ||||
\(521\) | 7044.93 | 0.592407 | 0.296203 | − | 0.955125i | \(-0.404279\pi\) | ||||
0.296203 | + | 0.955125i | \(0.404279\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1606.65 | + | 2782.79i | 0.134328 | + | 0.232664i | 0.925341 | − | 0.379137i | \(-0.123779\pi\) |
−0.791012 | + | 0.611800i | \(0.790446\pi\) | |||||||
\(524\) | 21100.2 | − | 36546.6i | 1.75910 | − | 3.04685i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −13920.9 | + | 24111.7i | −1.15395 | + | 1.99870i | ||||
\(527\) | 10357.4 | − | 17939.6i | 0.856123 | − | 1.48285i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5209.50 | − | 9023.13i | 0.428167 | − | 0.741606i | ||||
\(530\) | −21558.2 | − | 37339.9i | −1.76685 | − | 3.06027i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −444.036 | −0.0361868 | ||||||||
\(533\) | −182.219 | + | 1429.53i | −0.0148082 | + | 0.116172i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6427.90 | − | 11133.4i | −0.519443 | − | 0.899702i | ||||
\(536\) | 6289.59 | + | 10893.9i | 0.506845 | + | 0.877882i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 38399.5 | 3.07718 | ||||||||
\(539\) | −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 | \(0.352466\pi\) | |||||||
\(542\) | −22861.2 | + | 39596.8i | −1.81176 | + | 3.13806i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −25912.9 | − | 44882.4i | −2.04229 | − | 3.53735i | ||||
\(545\) | −8737.33 | −0.686727 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1533.54 | 0.119871 | 0.0599353 | − | 0.998202i | \(-0.480911\pi\) | ||||
0.0599353 | + | 0.998202i | \(0.480911\pi\) | |||||||
\(548\) | −3955.16 | − | 6850.53i | −0.308314 | − | 0.534015i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −10616.7 | + | 18388.6i | −0.823083 | + | 1.42562i | ||||
\(551\) | 138.477 | 0.0107066 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1815.98 | − | 3145.38i | 0.139645 | − | 0.241872i | ||||
\(554\) | −38214.6 | −2.93066 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7681.12 | − | 13304.1i | −0.585885 | − | 1.01478i | ||||
\(557\) | 8422.84 | + | 14588.8i | 0.640731 | + | 1.10978i | 0.985270 | + | 0.171006i | \(0.0547019\pi\) |
−0.344539 | + | 0.938772i | \(0.611965\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10302.8 | − | 4317.33i | 0.779540 | − | 0.326661i | ||||
\(560\) | 30089.0 | 2.27052 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2263.17 | − | 3919.92i | −0.169868 | − | 0.294221i | ||||
\(563\) | −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 | ||||
\(566\) | 2972.69 | − | 5148.84i | 0.220762 | − | 0.382371i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −16038.3 | + | 27779.1i | −1.18477 | + | 2.05209i | ||||
\(569\) | 11818.3 | + | 20469.9i | 0.870735 | + | 1.50816i | 0.861237 | + | 0.508203i | \(0.169690\pi\) |
0.00949803 | + | 0.999955i | \(0.496977\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −26955.1 | −1.97554 | −0.987771 | − | 0.155913i | \(-0.950168\pi\) | ||||
−0.987771 | + | 0.155913i | \(0.950168\pi\) | |||||||
\(572\) | 21007.7 | + | 15982.9i | 1.53562 | + | 1.16832i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 793.173 | + | 1373.82i | 0.0576767 | + | 0.0998989i | ||||
\(575\) | 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 | \(0.177954\pi\) | |||||||
\(578\) | 17951.4 | − | 31092.8i | 1.29183 | − | 2.23752i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −20645.7 | −1.47805 | ||||||||
\(581\) | −3464.19 | + | 6000.15i | −0.247365 | + | 0.428448i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6798.07 | − | 11774.6i | −0.482929 | − | 0.836457i | ||||
\(584\) | 63373.1 | 4.49040 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −9933.33 | −0.700243 | ||||||||
\(587\) | 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 | ||||
\(590\) | 42359.9 | 2.95582 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −9320.20 | + | 16143.1i | −0.647057 | + | 1.12074i | ||||
\(593\) | −12633.5 | −0.874869 | −0.437434 | − | 0.899250i | \(-0.644113\pi\) | ||||
−0.437434 | + | 0.899250i | \(0.644113\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8573.47 | + | 14849.7i | 0.590719 | + | 1.02316i | ||||
\(596\) | −26911.8 | − | 46612.7i | −1.84958 | − | 3.20357i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 9634.18 | − | 4037.14i | 0.658814 | − | 0.276072i | ||||
\(599\) | 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 | \(0.793989\pi\) | |||||||
\(602\) | 6148.38 | − | 10649.3i | 0.416261 | − | 0.720986i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 34012.5 | − | 58911.4i | 2.29131 | − | 3.96866i | ||||
\(605\) | 4676.85 | − | 8100.55i | 0.314283 | − | 0.544354i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6349.99 | − | 10998.5i | 0.424610 | − | 0.735445i | −0.571774 | − | 0.820411i | \(-0.693745\pi\) |
0.996384 | + | 0.0849656i | \(0.0270781\pi\) | |||||||
\(608\) | −539.546 | − | 934.522i | −0.0359893 | − | 0.0623353i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 38846.6 | 2.57845 | ||||||||
\(611\) | −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 | \(-0.419293\pi\) | |||||||
\(614\) | −17023.9 | − | 29486.3i | −1.11894 | − | 1.93806i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 17669.5 | 1.15572 | ||||||||
\(617\) | −8270.85 | + | 14325.5i | −0.539663 | + | 0.934723i | 0.459259 | + | 0.888302i | \(0.348115\pi\) |
−0.998922 | + | 0.0464208i | \(0.985219\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −21138.9 | −1.37261 | −0.686303 | − | 0.727316i | \(-0.740767\pi\) | ||||
−0.686303 | + | 0.727316i | \(0.740767\pi\) | |||||||
\(620\) | −32152.6 | + | 55690.0i | −2.08271 | + | 3.60736i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 9308.44 | + | 16122.7i | 0.600055 | + | 1.03933i | ||||
\(623\) | 10049.0 | 0.646235 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12825.4 | −0.820823 | ||||||||
\(626\) | −15756.7 | − | 27291.3i | −1.00601 | − | 1.74246i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 16588.3 | − | 28731.8i | 1.05405 | − | 1.82568i | ||||
\(629\) | −10622.7 | −0.673377 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2744.90 | + | 4754.31i | −0.173174 | + | 0.299946i | −0.939528 | − | 0.342473i | \(-0.888736\pi\) |
0.766354 | + | 0.642419i | \(0.222069\pi\) | |||||||
\(632\) | 24826.8 | 1.56259 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 4470.97 | + | 7743.94i | 0.280071 | + | 0.485097i | ||||
\(635\) | −11748.8 | − | 20349.5i | −0.734230 | − | 1.27172i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1477.56 | − | 11591.6i | 0.0919044 | − | 0.720999i | ||||
\(638\) | −9061.76 | −0.562318 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 14164.0 | + | 24532.8i | 0.874817 | + | 1.51523i | ||||
\(641\) | 2148.52 | − | 3721.35i | 0.132389 | − | 0.229305i | −0.792208 | − | 0.610251i | \(-0.791068\pi\) |
0.924597 | + | 0.380946i | \(0.124402\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12848.5 | + | 22254.2i | −0.788016 | + | 1.36488i | 0.139164 | + | 0.990269i | \(0.455558\pi\) |
−0.927181 | + | 0.374615i | \(0.877775\pi\) | |||||||
\(644\) | 4130.57 | − | 7154.35i | 0.252744 | − | 0.437766i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 646.416 | − | 1119.62i | 0.0393698 | − | 0.0681905i | ||||
\(647\) | 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 | ||||||||
\(650\) | 4561.54 | − | 35785.7i | 0.275259 | − | 2.15943i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 18732.7 | + | 32446.1i | 1.12520 | + | 1.94890i | ||||
\(653\) | −7727.27 | − | 13384.0i | −0.463080 | − | 0.802078i | 0.536032 | − | 0.844197i | \(-0.319922\pi\) |
−0.999113 | + | 0.0421191i | \(0.986589\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −33931.1 | −2.02412 | ||||||||
\(656\) | −2911.41 | + | 5042.71i | −0.173280 | + | 0.300129i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −26390.7 | −1.56355 | ||||||||
\(659\) | −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 | \(0.813657\pi\) | |||||||
\(662\) | −10715.7 | −0.629122 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −47359.8 | −2.76795 | ||||||||
\(665\) | 178.513 | + | 309.193i | 0.0104097 | + | 0.0180301i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1288.16 | + | 2231.16i | −0.0747794 | + | 0.129522i | ||||
\(668\) | −39703.4 | −2.29966 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 8316.35 | − | 14404.3i | 0.479535 | − | 0.830580i | ||||
\(671\) | 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 | \(-0.513847\pi\) | |||||||
\(674\) | 19027.5 | + | 32956.6i | 1.08741 | + | 1.88344i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −43413.5 | − | 11250.5i | −2.47004 | − | 0.640104i | ||||
\(677\) | −14640.6 | −0.831141 | −0.415570 | − | 0.909561i | \(-0.636418\pi\) | ||||
−0.415570 | + | 0.909561i | \(0.636418\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −317.317 | − | 549.610i | −0.0179345 | − | 0.0310635i | ||||
\(680\) | −58605.0 | + | 101507.i | −3.30500 | + | 5.72442i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −14112.4 | + | 24443.3i | −0.792360 | + | 1.37241i | ||||
\(683\) | −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 | ||||
\(686\) | −15280.4 | − | 26466.4i | −0.850450 | − | 1.47302i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 45136.3 | 2.50117 | ||||||||
\(689\) | 18384.0 | + | 13986.7i | 1.01651 | + | 0.773370i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15097.0 | + | 26148.8i | 0.831141 | + | 1.43958i | 0.897134 | + | 0.441758i | \(0.145645\pi\) |
−0.0659934 | + | 0.997820i | \(0.521022\pi\) | |||||||
\(692\) | 25839.2 | + | 44754.8i | 1.41945 | + | 2.45856i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6.07611 | 0.000332343 | ||||||||
\(695\) | −6175.98 | + | 10697.1i | −0.337077 | + | 0.583834i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3318.28 | −0.180328 | ||||||||
\(698\) | 32513.0 | − | 56314.2i | 1.76309 | − | 3.05376i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −14265.1 | − | 24707.9i | −0.770245 | − | 1.33410i | ||||
\(701\) | 30300.9 | 1.63260 | 0.816298 | − | 0.577631i | \(-0.196023\pi\) | ||||
0.816298 | + | 0.577631i | \(0.196023\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −221.181 | −0.0118663 | ||||||||
\(704\) | 14407.5 | + | 24954.6i | 0.771313 | + | 1.33595i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 29030.1 | − | 50281.7i | 1.54754 | − | 2.68042i | ||||
\(707\) | −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 | \(0.923452\pi\) | |||||||
\(710\) | 42412.9 | 2.24187 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 34345.5 | + | 59488.2i | 1.80780 | + | 3.13120i | ||||
\(713\) | 4012.24 | + | 6949.41i | 0.210743 | + | 0.365017i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2683.68 | − | 21053.7i | 0.140369 | − | 1.10121i | ||||
\(716\) | −87021.3 | −4.54209 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 9396.90 | + | 16275.9i | 0.488425 | + | 0.845977i | ||||
\(719\) | 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 | ||||
\(722\) | −18267.1 | + | 31639.6i | −0.941595 | + | 1.63089i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −40260.8 | + | 69733.8i | −2.06669 | + | 3.57961i | ||||
\(725\) | 4448.73 | + | 7705.43i | 0.227892 | + | 0.394721i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26065.8 | 1.32975 | 0.664875 | − | 0.746954i | \(-0.268485\pi\) | ||||
0.664875 | + | 0.746954i | \(0.268485\pi\) | |||||||
\(728\) | −27687.7 | + | 11602.3i | −1.40958 | + | 0.590674i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −41897.2 | − | 72568.1i | −2.12423 | − | 3.67927i | ||||
\(731\) | 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 | \(0.491534\pi\) | |||||||
\(734\) | 6353.18 | − | 11004.0i | 0.319482 | − | 0.553359i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 20076.2 | 1.00546 | ||||||||
\(737\) | 2622.44 | − | 4542.21i | 0.131070 | − | 0.227021i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4705.20 | − | 8149.64i | −0.234213 | − | 0.405669i | 0.724831 | − | 0.688927i | \(-0.241918\pi\) |
−0.959044 | + | 0.283258i | \(0.908585\pi\) | |||||||
\(740\) | 32976.0 | 1.63814 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 25428.1 | 1.25808 | ||||||||
\(743\) | −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 | ||||
\(746\) | 70799.4 | 3.47473 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −30390.4 | + | 52637.7i | −1.48554 | + | 2.57303i | ||||
\(749\) | 7581.76 | 0.369868 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6492.03 | + | 11244.5i | 0.315443 | + | 0.546363i | 0.979532 | − | 0.201291i | \(-0.0645136\pi\) |
−0.664089 | + | 0.747654i | \(0.731180\pi\) | |||||||
\(752\) | −48434.7 | − | 83891.3i | −2.34871 | − | 4.06809i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 14199.6 | − | 5950.24i | 0.685833 | − | 0.287394i | ||||
\(755\) | −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 | \(0.599366\pi\) | |||||||
\(758\) | −11824.7 | + | 20481.1i | −0.566615 | + | 0.981406i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1220.25 | + | 2113.53i | −0.0582408 | + | 0.100876i | ||||
\(761\) | −7759.63 | + | 13440.1i | −0.369627 | + | 0.640214i | −0.989507 | − | 0.144483i | \(-0.953848\pi\) |
0.619880 | + | 0.784697i | \(0.287181\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2576.44 | − | 4462.52i | 0.122246 | − | 0.211735i | ||||
\(764\) | −2185.31 | − | 3785.07i | −0.103484 | − | 0.179240i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4319.82 | −0.203761 | ||||||||
\(767\) | −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 | \(0.931026\pi\) | |||||||
\(770\) | −11681.6 | − | 20233.2i | −0.546723 | − | 0.946952i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −24642.4 | −1.14883 | ||||||||
\(773\) | 2946.02 | − | 5102.66i | 0.137078 | − | 0.237425i | −0.789312 | − | 0.613993i | \(-0.789562\pi\) |
0.926389 | + | 0.376567i | \(0.122896\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 27713.0 | 1.28449 | ||||||||
\(776\) | 2169.06 | − | 3756.92i | 0.100341 | − | 0.173796i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −9231.69 | − | 15989.8i | −0.425414 | − | 0.736839i | ||||
\(779\) | −69.0916 | −0.00317775 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13374.3 | 0.612766 | ||||||||
\(782\) | 12026.4 | + | 20830.2i | 0.549951 | + | 0.952542i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 23607.8 | − | 40889.8i | 1.07543 | − | 1.86269i | ||||
\(785\) | −26675.6 | −1.21286 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10510.2 | − | 18204.2i | 0.476045 | − | 0.824535i | −0.523578 | − | 0.851978i | \(-0.675403\pi\) |
0.999623 | + | 0.0274430i | \(0.00873649\pi\) | |||||||
\(788\) | 18935.8 | 0.856042 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −16413.5 | − | 28429.0i | −0.739197 | − | 1.28033i | ||||
\(791\) | −874.023 | − | 1513.85i | −0.0392879 | − | 0.0680486i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −19195.1 | + | 8043.56i | −0.859567 | + | 0.360196i | ||||
\(794\) | −2267.58 | −0.101352 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4888.44 | − | 8467.02i | −0.217671 | − | 0.377017i | ||||
\(797\) | 15677.8 | − | 27154.7i | 0.696782 | − | 1.20686i | −0.272794 | − | 0.962073i | \(-0.587948\pi\) |
0.969576 | − | 0.244790i | \(-0.0787190\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 27601.7 | − | 47807.5i | 1.22212 | − | 2.11678i | ||||
\(800\) | 34667.0 | − | 60045.0i | 1.53208 | − | 2.65364i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 3163.18 | − | 5478.80i | 0.139272 | − | 0.241226i | ||||
\(803\) | −13211.7 | − | 22883.3i | −0.580611 | − | 1.00565i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6642.34 | −0.290822 | ||||||||
\(806\) | 6063.50 | − | 47568.7i | 0.264985 | − | 2.07883i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −17593.6 | − | 30473.1i | −0.766018 | − | 1.32678i | ||||
\(809\) | −9066.27 | − | 15703.2i | −0.394009 | − | 0.682443i | 0.598965 | − | 0.800775i | \(-0.295579\pi\) |
−0.992974 | + | 0.118332i | \(0.962245\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −24755.3 | −1.07186 | −0.535928 | − | 0.844263i | \(-0.680038\pi\) | ||||
−0.535928 | + | 0.844263i | \(0.680038\pi\) | |||||||
\(812\) | 6087.94 | − | 10544.6i | 0.263110 | − | 0.455719i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 14473.8 | 0.623225 | ||||||||
\(815\) | 15062.0 | − | 26088.2i | 0.647361 | − | 1.12126i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 267.786 | + | 463.819i | 0.0114671 | + | 0.0198617i | ||||
\(818\) | −42682.7 | −1.82441 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 10300.9 | 0.438688 | ||||||||
\(821\) | 2041.32 | + | 3535.67i | 0.0867755 | + | 0.150300i | 0.906146 | − | 0.422964i | \(-0.139010\pi\) |
−0.819371 | + | 0.573264i | \(0.805677\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17163.5 | − | 29728.1i | 0.726954 | − | 1.25912i | −0.231211 | − | 0.972904i | \(-0.574269\pi\) |
0.958165 | − | 0.286217i | \(-0.0923978\pi\) | |||||||
\(824\) | 48697.6 | 2.05881 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −12491.0 | + | 21635.0i | −0.526170 | + | 0.911353i | ||||
\(827\) | −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 | \(0.763069\pi\) | |||||||
\(830\) | 31310.5 | + | 54231.4i | 1.30940 | + | 2.26795i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −38962.2 | − | 29642.8i | −1.62352 | − | 1.23519i | ||||
\(833\) | 26906.9 | 1.11917 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 15961.7 | + | 27646.5i | 0.661530 | + | 1.14580i | ||||
\(836\) | −632.775 | + | 1096.00i | −0.0261782 | + | 0.0453420i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −18209.8 | + | 31540.4i | −0.750655 | + | 1.30017i | ||||
\(839\) | −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 | ||||
\(842\) | 28623.0 | + | 49576.6i | 1.17151 | + | 2.02912i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −29618.5 | −1.20795 | ||||||||
\(845\) | 9619.26 | + | 34752.9i | 0.391613 | + | 1.41483i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2758.19 | + | 4777.33i | 0.111892 | + | 0.193803i | ||||
\(848\) | 46668.0 | + | 80831.3i | 1.88984 | + | 3.27330i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 83067.2 | 3.35198 | ||||||||
\(851\) | 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 | \(0.679499\pi\) | |||||||
\(854\) | −11455.0 | + | 19840.6i | −0.458994 | + | 0.795002i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 25913.0 | + | 44882.6i | 1.03468 | + | 1.79212i | ||||
\(857\) | −11796.7 | −0.470209 | −0.235104 | − | 0.971970i | \(-0.575543\pi\) | ||||
−0.235104 | + | 0.971970i | \(0.575543\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −22672.8 | −0.900567 | −0.450283 | − | 0.892886i | \(-0.648677\pi\) | ||||
−0.450283 | + | 0.892886i | \(0.648677\pi\) | |||||||
\(860\) | −39924.5 | − | 69151.2i | −1.58304 | − | 2.74190i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −13897.5 | + | 24071.2i | −0.549132 | + | 0.951124i | ||||
\(863\) | −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 | ||||
\(866\) | −46066.6 | −1.80763 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −18962.1 | − | 32843.4i | −0.741494 | − | 1.28431i | ||||
\(869\) | −5175.76 | − | 8964.67i | −0.202043 | − | 0.349949i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1126.76 | + | 8839.52i | −0.0438332 | + | 0.343875i | ||||
\(872\) | 35223.1 | 1.36790 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 250.407 | + | 433.718i | 0.00969125 | + | 0.0167857i | ||||
\(875\) | −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 | \(0.135023\pi\) | |||||||
\(878\) | −34717.5 | + | 60132.5i | −1.33446 | + | 2.31136i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 42878.5 | − | 74267.7i | 1.64254 | − | 2.84496i | ||||
\(881\) | 11846.1 | + | 20518.0i | 0.453013 | + | 0.784642i | 0.998572 | − | 0.0534309i | \(-0.0170157\pi\) |
−0.545558 | + | 0.838073i | \(0.683682\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −14591.5 | −0.556108 | −0.278054 | − | 0.960565i | \(-0.589689\pi\) | ||||
−0.278054 | + | 0.960565i | \(0.589689\pi\) | |||||||
\(884\) | 13057.5 | − | 102437.i | 0.496800 | − | 3.89745i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 30737.6 | + | 53239.1i | 1.16552 | + | 2.01874i | ||||
\(887\) | −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 | ||||||||
\(890\) | 45413.1 | − | 78657.7i | 1.71039 | − | 2.96249i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −42046.6 | −1.57828 | ||||||||
\(893\) | 574.709 | − | 995.426i | 0.0215363 | − | 0.0373020i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 34984.6 | + | 60595.1i | 1.30660 | + | 2.26310i | ||||
\(896\) | −16706.6 | −0.622911 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 52678.9 | 1.95759 | ||||||||
\(899\) | 5913.55 | + | 10242.6i | 0.219386 | + | 0.379987i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −26594.9 | + | 46063.7i | −0.983355 | + | 1.70322i | ||||
\(902\) | 4521.26 | 0.166898 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5974.49 | − | 10348.1i | 0.219810 | − | 0.380723i | ||||
\(905\) | 64743.2 | 2.37805 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5899.50 | − | 10218.2i | −0.215975 | − | 0.374080i | 0.737599 | − | 0.675239i | \(-0.235960\pi\) |
−0.953574 | + | 0.301159i | \(0.902626\pi\) | |||||||
\(908\) | 45750.4 | + | 79242.1i | 1.67212 | + | 2.89619i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 31590.6 | + | 24034.4i | 1.15079 | + | 0.875531i | ||||
\(911\) | 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 | ||||
\(914\) | −41651.9 | + | 72143.2i | −1.50735 | + | 2.61081i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 16640.7 | − | 28822.5i | 0.600244 | − | 1.03965i | ||||
\(917\) | 10005.5 | − | 17330.1i | 0.360317 | − | 0.624088i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2475.70 | − | 4288.04i | 0.0888639 | − | 0.153917i | −0.818167 | − | 0.574980i | \(-0.805010\pi\) |
0.907031 | + | 0.421063i | \(0.138343\pi\) | |||||||
\(920\) | −22702.3 | − | 39321.5i | −0.813556 | − | 1.40912i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −41297.0 | −1.47510 | ||||||||
\(923\) | −20957.3 | + | 8782.00i | −0.747364 | + | 0.313178i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7105.67 | − | 12307.4i | −0.252576 | − | 0.437475i | ||||
\(926\) | −888.635 | − | 1539.16i | −0.0315360 | − | 0.0546220i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 29589.8 | 1.04669 | ||||||||
\(929\) | −4467.43 | + | 7737.82i | −0.157774 | + | 0.273272i | −0.934065 | − | 0.357102i | \(-0.883765\pi\) |
0.776292 | + | 0.630374i | \(0.217098\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 560.243 | 0.0197221 | ||||||||
\(932\) | −19430.1 | + | 33654.0i | −0.682891 | + | 1.18280i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −21850.2 | − | 37845.6i | −0.765481 | − | 1.32585i | ||||
\(935\) | 48870.6 | 1.70935 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13182.8 | −0.459620 | −0.229810 | − | 0.973235i | \(-0.573811\pi\) | ||||
−0.229810 | + | 0.973235i | \(0.573811\pi\) | |||||||
\(938\) | 4904.60 | + | 8495.02i | 0.170726 | + | 0.295706i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −85684.0 | + | 148409.i | −2.97309 | + | 5.14954i | ||||
\(941\) | 21693.7 | 0.751536 | 0.375768 | − | 0.926714i | \(-0.377379\pi\) | ||||
0.375768 | + | 0.926714i | \(0.377379\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 642.714 | − | 1113.21i | 0.0221947 | − | 0.0384424i | ||||
\(944\) | −91698.4 | −3.16158 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −17523.6 | − | 30351.7i | −0.602262 | − | 1.04315i | ||||
\(947\) | −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 | ||||
\(950\) | 1729.59 | 0.0590687 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −34562.5 | − | 59864.0i | −1.17666 | − | 2.03803i | ||||
\(953\) | 2108.96 | − | 3652.83i | 0.0716853 | − | 0.124162i | −0.827955 | − | 0.560795i | \(-0.810496\pi\) |
0.899640 | + | 0.436632i | \(0.143829\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1757.09 | + | 3043.37i | −0.0595374 | + | 0.103122i | ||||
\(956\) | 38415.2 | − | 66537.2i | 1.29962 | − | 2.25101i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 17152.9 | − | 29709.7i | 0.578481 | − | 1.00196i | ||||
\(959\) | −1875.50 | − | 3248.45i | −0.0631522 | − | 0.109383i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7046.87 | 0.236544 | ||||||||
\(962\) | −22680.1 | + | 9503.92i | −0.760119 | + | 0.318523i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 36894.0 | + | 63902.3i | 1.23265 | + | 2.13502i | ||||
\(965\) | 9906.83 | + | 17159.1i | 0.330479 | + | 0.572406i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −40927.9 | −1.36107 | −0.680534 | − | 0.732717i | \(-0.738252\pi\) | ||||
−0.680534 | + | 0.732717i | \(0.738252\pi\) | |||||||
\(968\) | −18854.0 | + | 32656.0i | −0.626022 | + | 1.08430i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −5736.04 | −0.189869 | ||||||||
\(971\) | −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 | ||||
\(974\) | −43151.5 | −1.41957 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −84093.0 | −2.75794 | ||||||||
\(977\) | −59.2348 | − | 102.598i | −0.00193970 | − | 0.00335966i | 0.865054 | − | 0.501679i | \(-0.167284\pi\) |
−0.866994 | + | 0.498319i | \(0.833951\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14320.4 | − | 24803.6i | 0.467498 | − | 0.809731i | ||||
\(980\) | −83527.2 | −2.72263 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −13636.4 | + | 23618.9i | −0.443131 | + | 0.767525i | ||||
\(983\) | −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 | ||||
\(986\) | 17725.3 | + | 30701.2i | 0.572505 | + | 0.991608i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 271.878 | − | 2132.91i | 0.00875463 | − | 0.0686810i | ||||
\(989\) | −9964.14 | −0.320365 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8031.00 | + | 13910.1i | 0.257430 | + | 0.445882i | 0.965553 | − | 0.260208i | \(-0.0837910\pi\) |
−0.708123 | + | 0.706089i | \(0.750458\pi\) | |||||||
\(992\) | 46081.7 | − | 79815.8i | 1.47489 | − | 2.55459i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −12506.6 | + | 21662.1i | −0.399080 | + | 0.691226i | ||||
\(995\) | −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 | \(0.173551\pi\) | |||||||
\(998\) | −48108.8 | − | 83326.8i | −1.52591 | − | 2.64295i | ||||
\(999\) | 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 | 117.4.g.e.55.4 | 8 | ||
3.2 | odd | 2 | 39.4.e.c.16.1 | ✓ | 8 | ||
12.11 | even | 2 | 624.4.q.i.289.1 | 8 | |||
13.3 | even | 3 | 1521.4.a.v.1.1 | 4 | |||
13.9 | even | 3 | inner | 117.4.g.e.100.4 | 8 | ||
13.10 | even | 6 | 1521.4.a.bb.1.4 | 4 | |||
39.2 | even | 12 | 507.4.b.h.337.1 | 8 | |||
39.11 | even | 12 | 507.4.b.h.337.8 | 8 | |||
39.23 | odd | 6 | 507.4.a.i.1.1 | 4 | |||
39.29 | odd | 6 | 507.4.a.m.1.4 | 4 | |||
39.35 | odd | 6 | 39.4.e.c.22.1 | yes | 8 | ||
156.35 | even | 6 | 624.4.q.i.529.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.4.e.c.16.1 | ✓ | 8 | 3.2 | odd | 2 | ||
39.4.e.c.22.1 | yes | 8 | 39.35 | odd | 6 | ||
117.4.g.e.55.4 | 8 | 1.1 | even | 1 | trivial | ||
117.4.g.e.100.4 | 8 | 13.9 | even | 3 | inner | ||
507.4.a.i.1.1 | 4 | 39.23 | odd | 6 | |||
507.4.a.m.1.4 | 4 | 39.29 | odd | 6 | |||
507.4.b.h.337.1 | 8 | 39.2 | even | 12 | |||
507.4.b.h.337.8 | 8 | 39.11 | even | 12 | |||
624.4.q.i.289.1 | 8 | 12.11 | even | 2 | |||
624.4.q.i.529.1 | 8 | 156.35 | even | 6 | |||
1521.4.a.v.1.1 | 4 | 13.3 | even | 3 | |||
1521.4.a.bb.1.4 | 4 | 13.10 | even | 6 |