Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [983,2,Mod(1,983)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(983, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("983.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 983 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 983.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(7.84929451869\) |
Analytic rank: | \(0\) |
Dimension: | \(54\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 983.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.13542 | −0.802861 | −0.401431 | − | 0.915889i | \(-0.631487\pi\) | ||||
−0.401431 | + | 0.915889i | \(0.631487\pi\) | |||||||
\(3\) | −1.73773 | −1.00328 | −0.501641 | − | 0.865076i | \(-0.667270\pi\) | ||||
−0.501641 | + | 0.865076i | \(0.667270\pi\) | |||||||
\(4\) | −0.710827 | −0.355414 | ||||||||
\(5\) | −4.00726 | −1.79210 | −0.896051 | − | 0.443952i | \(-0.853576\pi\) | ||||
−0.896051 | + | 0.443952i | \(0.853576\pi\) | |||||||
\(6\) | 1.97305 | 0.805496 | ||||||||
\(7\) | 3.34589 | 1.26463 | 0.632314 | − | 0.774712i | \(-0.282105\pi\) | ||||
0.632314 | + | 0.774712i | \(0.282105\pi\) | |||||||
\(8\) | 3.07792 | 1.08821 | ||||||||
\(9\) | 0.0197210 | 0.00657368 | ||||||||
\(10\) | 4.54991 | 1.43881 | ||||||||
\(11\) | −4.42673 | −1.33471 | −0.667354 | − | 0.744741i | \(-0.732573\pi\) | ||||
−0.667354 | + | 0.744741i | \(0.732573\pi\) | |||||||
\(12\) | 1.23523 | 0.356580 | ||||||||
\(13\) | −5.98120 | −1.65889 | −0.829444 | − | 0.558591i | \(-0.811342\pi\) | ||||
−0.829444 | + | 0.558591i | \(0.811342\pi\) | |||||||
\(14\) | −3.79899 | −1.01532 | ||||||||
\(15\) | 6.96355 | 1.79798 | ||||||||
\(16\) | −2.07307 | −0.518268 | ||||||||
\(17\) | −5.87490 | −1.42487 | −0.712436 | − | 0.701737i | \(-0.752408\pi\) | ||||
−0.712436 | + | 0.701737i | \(0.752408\pi\) | |||||||
\(18\) | −0.0223916 | −0.00527775 | ||||||||
\(19\) | −2.64412 | −0.606603 | −0.303302 | − | 0.952895i | \(-0.598089\pi\) | ||||
−0.303302 | + | 0.952895i | \(0.598089\pi\) | |||||||
\(20\) | 2.84847 | 0.636937 | ||||||||
\(21\) | −5.81427 | −1.26878 | ||||||||
\(22\) | 5.02618 | 1.07159 | ||||||||
\(23\) | −7.22232 | −1.50596 | −0.752979 | − | 0.658045i | \(-0.771384\pi\) | ||||
−0.752979 | + | 0.658045i | \(0.771384\pi\) | |||||||
\(24\) | −5.34861 | −1.09178 | ||||||||
\(25\) | 11.0581 | 2.21163 | ||||||||
\(26\) | 6.79116 | 1.33186 | ||||||||
\(27\) | 5.17893 | 0.996686 | ||||||||
\(28\) | −2.37835 | −0.449466 | ||||||||
\(29\) | −6.03703 | −1.12105 | −0.560524 | − | 0.828138i | \(-0.689400\pi\) | ||||
−0.560524 | + | 0.828138i | \(0.689400\pi\) | |||||||
\(30\) | −7.90654 | −1.44353 | ||||||||
\(31\) | 0.185465 | 0.0333105 | 0.0166553 | − | 0.999861i | \(-0.494698\pi\) | ||||
0.0166553 | + | 0.999861i | \(0.494698\pi\) | |||||||
\(32\) | −3.80204 | −0.672112 | ||||||||
\(33\) | 7.69248 | 1.33909 | ||||||||
\(34\) | 6.67046 | 1.14397 | ||||||||
\(35\) | −13.4079 | −2.26634 | ||||||||
\(36\) | −0.0140182 | −0.00233637 | ||||||||
\(37\) | −11.0285 | −1.81307 | −0.906537 | − | 0.422126i | \(-0.861284\pi\) | ||||
−0.906537 | + | 0.422126i | \(0.861284\pi\) | |||||||
\(38\) | 3.00218 | 0.487018 | ||||||||
\(39\) | 10.3937 | 1.66433 | ||||||||
\(40\) | −12.3340 | −1.95018 | ||||||||
\(41\) | 2.46853 | 0.385519 | 0.192759 | − | 0.981246i | \(-0.438256\pi\) | ||||
0.192759 | + | 0.981246i | \(0.438256\pi\) | |||||||
\(42\) | 6.60163 | 1.01865 | ||||||||
\(43\) | 6.27188 | 0.956453 | 0.478227 | − | 0.878236i | \(-0.341280\pi\) | ||||
0.478227 | + | 0.878236i | \(0.341280\pi\) | |||||||
\(44\) | 3.14664 | 0.474374 | ||||||||
\(45\) | −0.0790273 | −0.0117807 | ||||||||
\(46\) | 8.20035 | 1.20908 | ||||||||
\(47\) | 2.90363 | 0.423537 | 0.211769 | − | 0.977320i | \(-0.432078\pi\) | ||||
0.211769 | + | 0.977320i | \(0.432078\pi\) | |||||||
\(48\) | 3.60245 | 0.519968 | ||||||||
\(49\) | 4.19500 | 0.599286 | ||||||||
\(50\) | −12.5556 | −1.77563 | ||||||||
\(51\) | 10.2090 | 1.42955 | ||||||||
\(52\) | 4.25160 | 0.589591 | ||||||||
\(53\) | 0.991456 | 0.136187 | 0.0680935 | − | 0.997679i | \(-0.478308\pi\) | ||||
0.0680935 | + | 0.997679i | \(0.478308\pi\) | |||||||
\(54\) | −5.88025 | −0.800201 | ||||||||
\(55\) | 17.7390 | 2.39193 | ||||||||
\(56\) | 10.2984 | 1.37618 | ||||||||
\(57\) | 4.59478 | 0.608594 | ||||||||
\(58\) | 6.85455 | 0.900046 | ||||||||
\(59\) | 8.07947 | 1.05186 | 0.525929 | − | 0.850529i | \(-0.323718\pi\) | ||||
0.525929 | + | 0.850529i | \(0.323718\pi\) | |||||||
\(60\) | −4.94988 | −0.639027 | ||||||||
\(61\) | −14.0732 | −1.80189 | −0.900946 | − | 0.433932i | \(-0.857126\pi\) | ||||
−0.900946 | + | 0.433932i | \(0.857126\pi\) | |||||||
\(62\) | −0.210580 | −0.0267437 | ||||||||
\(63\) | 0.0659845 | 0.00831326 | ||||||||
\(64\) | 8.46304 | 1.05788 | ||||||||
\(65\) | 23.9682 | 2.97289 | ||||||||
\(66\) | −8.73417 | −1.07510 | ||||||||
\(67\) | 8.15799 | 0.996657 | 0.498328 | − | 0.866988i | \(-0.333947\pi\) | ||||
0.498328 | + | 0.866988i | \(0.333947\pi\) | |||||||
\(68\) | 4.17604 | 0.506419 | ||||||||
\(69\) | 12.5505 | 1.51090 | ||||||||
\(70\) | 15.2235 | 1.81956 | ||||||||
\(71\) | 1.43625 | 0.170452 | 0.0852259 | − | 0.996362i | \(-0.472839\pi\) | ||||
0.0852259 | + | 0.996362i | \(0.472839\pi\) | |||||||
\(72\) | 0.0606997 | 0.00715353 | ||||||||
\(73\) | −2.40711 | −0.281731 | −0.140865 | − | 0.990029i | \(-0.544988\pi\) | ||||
−0.140865 | + | 0.990029i | \(0.544988\pi\) | |||||||
\(74\) | 12.5220 | 1.45565 | ||||||||
\(75\) | −19.2161 | −2.21888 | ||||||||
\(76\) | 1.87951 | 0.215595 | ||||||||
\(77\) | −14.8114 | −1.68791 | ||||||||
\(78\) | −11.8012 | −1.33623 | ||||||||
\(79\) | 14.5102 | 1.63253 | 0.816265 | − | 0.577678i | \(-0.196041\pi\) | ||||
0.816265 | + | 0.577678i | \(0.196041\pi\) | |||||||
\(80\) | 8.30733 | 0.928788 | ||||||||
\(81\) | −9.05877 | −1.00653 | ||||||||
\(82\) | −2.80281 | −0.309518 | ||||||||
\(83\) | −14.6046 | −1.60306 | −0.801530 | − | 0.597955i | \(-0.795980\pi\) | ||||
−0.801530 | + | 0.597955i | \(0.795980\pi\) | |||||||
\(84\) | 4.13294 | 0.450941 | ||||||||
\(85\) | 23.5422 | 2.55351 | ||||||||
\(86\) | −7.12121 | −0.767900 | ||||||||
\(87\) | 10.4908 | 1.12473 | ||||||||
\(88\) | −13.6251 | −1.45244 | ||||||||
\(89\) | −10.3503 | −1.09713 | −0.548567 | − | 0.836106i | \(-0.684827\pi\) | ||||
−0.548567 | + | 0.836106i | \(0.684827\pi\) | |||||||
\(90\) | 0.0897289 | 0.00945826 | ||||||||
\(91\) | −20.0125 | −2.09788 | ||||||||
\(92\) | 5.13382 | 0.535238 | ||||||||
\(93\) | −0.322289 | −0.0334198 | ||||||||
\(94\) | −3.29683 | −0.340042 | ||||||||
\(95\) | 10.5957 | 1.08709 | ||||||||
\(96\) | 6.60694 | 0.674318 | ||||||||
\(97\) | 13.1320 | 1.33335 | 0.666677 | − | 0.745347i | \(-0.267716\pi\) | ||||
0.666677 | + | 0.745347i | \(0.267716\pi\) | |||||||
\(98\) | −4.76308 | −0.481144 | ||||||||
\(99\) | −0.0872996 | −0.00877394 | ||||||||
\(100\) | −7.86042 | −0.786042 | ||||||||
\(101\) | 4.54533 | 0.452277 | 0.226139 | − | 0.974095i | \(-0.427390\pi\) | ||||
0.226139 | + | 0.974095i | \(0.427390\pi\) | |||||||
\(102\) | −11.5915 | −1.14773 | ||||||||
\(103\) | −13.8304 | −1.36275 | −0.681374 | − | 0.731936i | \(-0.738617\pi\) | ||||
−0.681374 | + | 0.731936i | \(0.738617\pi\) | |||||||
\(104\) | −18.4097 | −1.80522 | ||||||||
\(105\) | 23.2993 | 2.27378 | ||||||||
\(106\) | −1.12572 | −0.109339 | ||||||||
\(107\) | 9.58532 | 0.926648 | 0.463324 | − | 0.886189i | \(-0.346657\pi\) | ||||
0.463324 | + | 0.886189i | \(0.346657\pi\) | |||||||
\(108\) | −3.68133 | −0.354236 | ||||||||
\(109\) | −6.83430 | −0.654607 | −0.327304 | − | 0.944919i | \(-0.606140\pi\) | ||||
−0.327304 | + | 0.944919i | \(0.606140\pi\) | |||||||
\(110\) | −20.1412 | −1.92039 | ||||||||
\(111\) | 19.1646 | 1.81902 | ||||||||
\(112\) | −6.93627 | −0.655416 | ||||||||
\(113\) | −10.2635 | −0.965509 | −0.482755 | − | 0.875756i | \(-0.660364\pi\) | ||||
−0.482755 | + | 0.875756i | \(0.660364\pi\) | |||||||
\(114\) | −5.21700 | −0.488617 | ||||||||
\(115\) | 28.9417 | 2.69883 | ||||||||
\(116\) | 4.29128 | 0.398436 | ||||||||
\(117\) | −0.117955 | −0.0109050 | ||||||||
\(118\) | −9.17357 | −0.844496 | ||||||||
\(119\) | −19.6568 | −1.80193 | ||||||||
\(120\) | 21.4333 | 1.95658 | ||||||||
\(121\) | 8.59591 | 0.781446 | ||||||||
\(122\) | 15.9790 | 1.44667 | ||||||||
\(123\) | −4.28964 | −0.386784 | ||||||||
\(124\) | −0.131834 | −0.0118390 | ||||||||
\(125\) | −24.2765 | −2.17136 | ||||||||
\(126\) | −0.0749199 | −0.00667439 | ||||||||
\(127\) | −5.93782 | −0.526896 | −0.263448 | − | 0.964674i | \(-0.584860\pi\) | ||||
−0.263448 | + | 0.964674i | \(0.584860\pi\) | |||||||
\(128\) | −2.00501 | −0.177219 | ||||||||
\(129\) | −10.8989 | −0.959592 | ||||||||
\(130\) | −27.2139 | −2.38682 | ||||||||
\(131\) | 2.42159 | 0.211576 | 0.105788 | − | 0.994389i | \(-0.466264\pi\) | ||||
0.105788 | + | 0.994389i | \(0.466264\pi\) | |||||||
\(132\) | −5.46802 | −0.475930 | ||||||||
\(133\) | −8.84696 | −0.767128 | ||||||||
\(134\) | −9.26272 | −0.800177 | ||||||||
\(135\) | −20.7533 | −1.78616 | ||||||||
\(136\) | −18.0825 | −1.55056 | ||||||||
\(137\) | 0.957836 | 0.0818335 | 0.0409167 | − | 0.999163i | \(-0.486972\pi\) | ||||
0.0409167 | + | 0.999163i | \(0.486972\pi\) | |||||||
\(138\) | −14.2500 | −1.21304 | ||||||||
\(139\) | 3.71094 | 0.314758 | 0.157379 | − | 0.987538i | \(-0.449696\pi\) | ||||
0.157379 | + | 0.987538i | \(0.449696\pi\) | |||||||
\(140\) | 9.53068 | 0.805489 | ||||||||
\(141\) | −5.04573 | −0.424927 | ||||||||
\(142\) | −1.63075 | −0.136849 | ||||||||
\(143\) | 26.4771 | 2.21413 | ||||||||
\(144\) | −0.0408831 | −0.00340692 | ||||||||
\(145\) | 24.1919 | 2.00903 | ||||||||
\(146\) | 2.73307 | 0.226191 | ||||||||
\(147\) | −7.28980 | −0.601253 | ||||||||
\(148\) | 7.83936 | 0.644391 | ||||||||
\(149\) | −8.61614 | −0.705862 | −0.352931 | − | 0.935649i | \(-0.614815\pi\) | ||||
−0.352931 | + | 0.935649i | \(0.614815\pi\) | |||||||
\(150\) | 21.8183 | 1.78146 | ||||||||
\(151\) | −9.01120 | −0.733321 | −0.366661 | − | 0.930355i | \(-0.619499\pi\) | ||||
−0.366661 | + | 0.930355i | \(0.619499\pi\) | |||||||
\(152\) | −8.13840 | −0.660112 | ||||||||
\(153\) | −0.115859 | −0.00936665 | ||||||||
\(154\) | 16.8171 | 1.35516 | ||||||||
\(155\) | −0.743207 | −0.0596958 | ||||||||
\(156\) | −7.38815 | −0.591526 | ||||||||
\(157\) | −2.92562 | −0.233490 | −0.116745 | − | 0.993162i | \(-0.537246\pi\) | ||||
−0.116745 | + | 0.993162i | \(0.537246\pi\) | |||||||
\(158\) | −16.4752 | −1.31070 | ||||||||
\(159\) | −1.72289 | −0.136634 | ||||||||
\(160\) | 15.2358 | 1.20449 | ||||||||
\(161\) | −24.1651 | −1.90448 | ||||||||
\(162\) | 10.2855 | 0.808104 | ||||||||
\(163\) | −1.40921 | −0.110378 | −0.0551890 | − | 0.998476i | \(-0.517576\pi\) | ||||
−0.0551890 | + | 0.998476i | \(0.517576\pi\) | |||||||
\(164\) | −1.75470 | −0.137019 | ||||||||
\(165\) | −30.8257 | −2.39978 | ||||||||
\(166\) | 16.5823 | 1.28703 | ||||||||
\(167\) | 2.86088 | 0.221382 | 0.110691 | − | 0.993855i | \(-0.464694\pi\) | ||||
0.110691 | + | 0.993855i | \(0.464694\pi\) | |||||||
\(168\) | −17.8959 | −1.38070 | ||||||||
\(169\) | 22.7748 | 1.75191 | ||||||||
\(170\) | −26.7303 | −2.05012 | ||||||||
\(171\) | −0.0521448 | −0.00398761 | ||||||||
\(172\) | −4.45823 | −0.339937 | ||||||||
\(173\) | 13.1930 | 1.00305 | 0.501524 | − | 0.865144i | \(-0.332773\pi\) | ||||
0.501524 | + | 0.865144i | \(0.332773\pi\) | |||||||
\(174\) | −11.9114 | −0.902999 | ||||||||
\(175\) | 36.9993 | 2.79689 | ||||||||
\(176\) | 9.17691 | 0.691736 | ||||||||
\(177\) | −14.0400 | −1.05531 | ||||||||
\(178\) | 11.7520 | 0.880847 | ||||||||
\(179\) | −8.13143 | −0.607771 | −0.303886 | − | 0.952709i | \(-0.598284\pi\) | ||||
−0.303886 | + | 0.952709i | \(0.598284\pi\) | |||||||
\(180\) | 0.0561747 | 0.00418702 | ||||||||
\(181\) | −10.9771 | −0.815924 | −0.407962 | − | 0.912999i | \(-0.633761\pi\) | ||||
−0.407962 | + | 0.912999i | \(0.633761\pi\) | |||||||
\(182\) | 22.7225 | 1.68430 | ||||||||
\(183\) | 24.4555 | 1.80780 | ||||||||
\(184\) | −22.2297 | −1.63880 | ||||||||
\(185\) | 44.1941 | 3.24921 | ||||||||
\(186\) | 0.365933 | 0.0268315 | ||||||||
\(187\) | 26.0066 | 1.90179 | ||||||||
\(188\) | −2.06398 | −0.150531 | ||||||||
\(189\) | 17.3282 | 1.26044 | ||||||||
\(190\) | −12.0305 | −0.872786 | ||||||||
\(191\) | −5.55812 | −0.402172 | −0.201086 | − | 0.979574i | \(-0.564447\pi\) | ||||
−0.201086 | + | 0.979574i | \(0.564447\pi\) | |||||||
\(192\) | −14.7065 | −1.06135 | ||||||||
\(193\) | 13.1531 | 0.946782 | 0.473391 | − | 0.880852i | \(-0.343030\pi\) | ||||
0.473391 | + | 0.880852i | \(0.343030\pi\) | |||||||
\(194\) | −14.9103 | −1.07050 | ||||||||
\(195\) | −41.6504 | −2.98265 | ||||||||
\(196\) | −2.98192 | −0.212995 | ||||||||
\(197\) | 16.6322 | 1.18500 | 0.592498 | − | 0.805572i | \(-0.298142\pi\) | ||||
0.592498 | + | 0.805572i | \(0.298142\pi\) | |||||||
\(198\) | 0.0991215 | 0.00704426 | ||||||||
\(199\) | 3.30876 | 0.234551 | 0.117276 | − | 0.993099i | \(-0.462584\pi\) | ||||
0.117276 | + | 0.993099i | \(0.462584\pi\) | |||||||
\(200\) | 34.0361 | 2.40671 | ||||||||
\(201\) | −14.1764 | −0.999927 | ||||||||
\(202\) | −5.16085 | −0.363116 | ||||||||
\(203\) | −20.1993 | −1.41771 | ||||||||
\(204\) | −7.25684 | −0.508081 | ||||||||
\(205\) | −9.89202 | −0.690889 | ||||||||
\(206\) | 15.7032 | 1.09410 | ||||||||
\(207\) | −0.142432 | −0.00989968 | ||||||||
\(208\) | 12.3995 | 0.859747 | ||||||||
\(209\) | 11.7048 | 0.809639 | ||||||||
\(210\) | −26.4544 | −1.82553 | ||||||||
\(211\) | 8.50878 | 0.585768 | 0.292884 | − | 0.956148i | \(-0.405385\pi\) | ||||
0.292884 | + | 0.956148i | \(0.405385\pi\) | |||||||
\(212\) | −0.704754 | −0.0484027 | ||||||||
\(213\) | −2.49582 | −0.171011 | ||||||||
\(214\) | −10.8833 | −0.743970 | ||||||||
\(215\) | −25.1331 | −1.71406 | ||||||||
\(216\) | 15.9403 | 1.08460 | ||||||||
\(217\) | 0.620547 | 0.0421255 | ||||||||
\(218\) | 7.75979 | 0.525559 | ||||||||
\(219\) | 4.18292 | 0.282655 | ||||||||
\(220\) | −12.6094 | −0.850125 | ||||||||
\(221\) | 35.1390 | 2.36370 | ||||||||
\(222\) | −21.7598 | −1.46042 | ||||||||
\(223\) | −7.38436 | −0.494493 | −0.247247 | − | 0.968953i | \(-0.579526\pi\) | ||||
−0.247247 | + | 0.968953i | \(0.579526\pi\) | |||||||
\(224\) | −12.7212 | −0.849973 | ||||||||
\(225\) | 0.218078 | 0.0145385 | ||||||||
\(226\) | 11.6534 | 0.775170 | ||||||||
\(227\) | 2.82859 | 0.187740 | 0.0938699 | − | 0.995584i | \(-0.470076\pi\) | ||||
0.0938699 | + | 0.995584i | \(0.470076\pi\) | |||||||
\(228\) | −3.26610 | −0.216303 | ||||||||
\(229\) | −18.8778 | −1.24748 | −0.623739 | − | 0.781633i | \(-0.714387\pi\) | ||||
−0.623739 | + | 0.781633i | \(0.714387\pi\) | |||||||
\(230\) | −32.8609 | −2.16679 | ||||||||
\(231\) | 25.7382 | 1.69345 | ||||||||
\(232\) | −18.5815 | −1.21993 | ||||||||
\(233\) | 11.3943 | 0.746463 | 0.373231 | − | 0.927738i | \(-0.378250\pi\) | ||||
0.373231 | + | 0.927738i | \(0.378250\pi\) | |||||||
\(234\) | 0.133929 | 0.00875519 | ||||||||
\(235\) | −11.6356 | −0.759022 | ||||||||
\(236\) | −5.74311 | −0.373845 | ||||||||
\(237\) | −25.2150 | −1.63789 | ||||||||
\(238\) | 22.3187 | 1.44670 | ||||||||
\(239\) | −6.61371 | −0.427805 | −0.213903 | − | 0.976855i | \(-0.568618\pi\) | ||||
−0.213903 | + | 0.976855i | \(0.568618\pi\) | |||||||
\(240\) | −14.4359 | −0.931836 | ||||||||
\(241\) | −27.0082 | −1.73975 | −0.869875 | − | 0.493273i | \(-0.835801\pi\) | ||||
−0.869875 | + | 0.493273i | \(0.835801\pi\) | |||||||
\(242\) | −9.75995 | −0.627393 | ||||||||
\(243\) | 0.204944 | 0.0131471 | ||||||||
\(244\) | 10.0036 | 0.640417 | ||||||||
\(245\) | −16.8105 | −1.07398 | ||||||||
\(246\) | 4.87053 | 0.310534 | ||||||||
\(247\) | 15.8150 | 1.00629 | ||||||||
\(248\) | 0.570847 | 0.0362488 | ||||||||
\(249\) | 25.3789 | 1.60832 | ||||||||
\(250\) | 27.5640 | 1.74330 | ||||||||
\(251\) | −21.0115 | −1.32624 | −0.663118 | − | 0.748515i | \(-0.730767\pi\) | ||||
−0.663118 | + | 0.748515i | \(0.730767\pi\) | |||||||
\(252\) | −0.0469035 | −0.00295465 | ||||||||
\(253\) | 31.9712 | 2.01001 | ||||||||
\(254\) | 6.74190 | 0.423025 | ||||||||
\(255\) | −40.9102 | −2.56189 | ||||||||
\(256\) | −14.6496 | −0.915598 | ||||||||
\(257\) | −15.3646 | −0.958419 | −0.479209 | − | 0.877701i | \(-0.659077\pi\) | ||||
−0.479209 | + | 0.877701i | \(0.659077\pi\) | |||||||
\(258\) | 12.3748 | 0.770419 | ||||||||
\(259\) | −36.9002 | −2.29287 | ||||||||
\(260\) | −17.0373 | −1.05661 | ||||||||
\(261\) | −0.119056 | −0.00736940 | ||||||||
\(262\) | −2.74952 | −0.169866 | ||||||||
\(263\) | −20.3976 | −1.25777 | −0.628884 | − | 0.777499i | \(-0.716488\pi\) | ||||
−0.628884 | + | 0.777499i | \(0.716488\pi\) | |||||||
\(264\) | 23.6768 | 1.45721 | ||||||||
\(265\) | −3.97302 | −0.244061 | ||||||||
\(266\) | 10.0450 | 0.615898 | ||||||||
\(267\) | 17.9862 | 1.10073 | ||||||||
\(268\) | −5.79892 | −0.354225 | ||||||||
\(269\) | 12.7051 | 0.774642 | 0.387321 | − | 0.921945i | \(-0.373400\pi\) | ||||
0.387321 | + | 0.921945i | \(0.373400\pi\) | |||||||
\(270\) | 23.5637 | 1.43404 | ||||||||
\(271\) | −8.76714 | −0.532566 | −0.266283 | − | 0.963895i | \(-0.585796\pi\) | ||||
−0.266283 | + | 0.963895i | \(0.585796\pi\) | |||||||
\(272\) | 12.1791 | 0.738465 | ||||||||
\(273\) | 34.7764 | 2.10476 | ||||||||
\(274\) | −1.08754 | −0.0657009 | ||||||||
\(275\) | −48.9513 | −2.95188 | ||||||||
\(276\) | −8.92122 | −0.536994 | ||||||||
\(277\) | 30.1590 | 1.81208 | 0.906040 | − | 0.423193i | \(-0.139091\pi\) | ||||
0.906040 | + | 0.423193i | \(0.139091\pi\) | |||||||
\(278\) | −4.21347 | −0.252707 | ||||||||
\(279\) | 0.00365756 | 0.000218973 0 | ||||||||
\(280\) | −41.2683 | −2.46626 | ||||||||
\(281\) | −12.3546 | −0.737015 | −0.368508 | − | 0.929625i | \(-0.620131\pi\) | ||||
−0.368508 | + | 0.929625i | \(0.620131\pi\) | |||||||
\(282\) | 5.72901 | 0.341158 | ||||||||
\(283\) | 6.38400 | 0.379489 | 0.189745 | − | 0.981833i | \(-0.439234\pi\) | ||||
0.189745 | + | 0.981833i | \(0.439234\pi\) | |||||||
\(284\) | −1.02093 | −0.0605809 | ||||||||
\(285\) | −18.4125 | −1.09066 | ||||||||
\(286\) | −30.0626 | −1.77764 | ||||||||
\(287\) | 8.25942 | 0.487538 | ||||||||
\(288\) | −0.0749802 | −0.00441825 | ||||||||
\(289\) | 17.5144 | 1.03026 | ||||||||
\(290\) | −27.4679 | −1.61297 | ||||||||
\(291\) | −22.8200 | −1.33773 | ||||||||
\(292\) | 1.71104 | 0.100131 | ||||||||
\(293\) | 8.15051 | 0.476158 | 0.238079 | − | 0.971246i | \(-0.423482\pi\) | ||||
0.238079 | + | 0.971246i | \(0.423482\pi\) | |||||||
\(294\) | 8.27697 | 0.482723 | ||||||||
\(295\) | −32.3765 | −1.88504 | ||||||||
\(296\) | −33.9449 | −1.97300 | ||||||||
\(297\) | −22.9257 | −1.33029 | ||||||||
\(298\) | 9.78292 | 0.566709 | ||||||||
\(299\) | 43.1982 | 2.49821 | ||||||||
\(300\) | 13.6593 | 0.788622 | ||||||||
\(301\) | 20.9851 | 1.20956 | ||||||||
\(302\) | 10.2315 | 0.588755 | ||||||||
\(303\) | −7.89858 | −0.453761 | ||||||||
\(304\) | 5.48145 | 0.314383 | ||||||||
\(305\) | 56.3950 | 3.22917 | ||||||||
\(306\) | 0.131548 | 0.00752012 | ||||||||
\(307\) | −25.4382 | −1.45183 | −0.725917 | − | 0.687783i | \(-0.758584\pi\) | ||||
−0.725917 | + | 0.687783i | \(0.758584\pi\) | |||||||
\(308\) | 10.5283 | 0.599906 | ||||||||
\(309\) | 24.0335 | 1.36722 | ||||||||
\(310\) | 0.843850 | 0.0479275 | ||||||||
\(311\) | −7.39618 | −0.419399 | −0.209700 | − | 0.977766i | \(-0.567249\pi\) | ||||
−0.209700 | + | 0.977766i | \(0.567249\pi\) | |||||||
\(312\) | 31.9911 | 1.81114 | ||||||||
\(313\) | −11.5734 | −0.654168 | −0.327084 | − | 0.944995i | \(-0.606066\pi\) | ||||
−0.327084 | + | 0.944995i | \(0.606066\pi\) | |||||||
\(314\) | 3.32180 | 0.187460 | ||||||||
\(315\) | −0.264417 | −0.0148982 | ||||||||
\(316\) | −10.3143 | −0.580223 | ||||||||
\(317\) | 15.1402 | 0.850358 | 0.425179 | − | 0.905109i | \(-0.360211\pi\) | ||||
0.425179 | + | 0.905109i | \(0.360211\pi\) | |||||||
\(318\) | 1.95620 | 0.109698 | ||||||||
\(319\) | 26.7243 | 1.49627 | ||||||||
\(320\) | −33.9136 | −1.89583 | ||||||||
\(321\) | −16.6567 | −0.929689 | ||||||||
\(322\) | 27.4375 | 1.52903 | ||||||||
\(323\) | 15.5340 | 0.864332 | ||||||||
\(324\) | 6.43922 | 0.357735 | ||||||||
\(325\) | −66.1409 | −3.66884 | ||||||||
\(326\) | 1.60004 | 0.0886183 | ||||||||
\(327\) | 11.8762 | 0.656756 | ||||||||
\(328\) | 7.59793 | 0.419525 | ||||||||
\(329\) | 9.71522 | 0.535617 | ||||||||
\(330\) | 35.0001 | 1.92669 | ||||||||
\(331\) | 3.53220 | 0.194147 | 0.0970735 | − | 0.995277i | \(-0.469052\pi\) | ||||
0.0970735 | + | 0.995277i | \(0.469052\pi\) | |||||||
\(332\) | 10.3813 | 0.569749 | ||||||||
\(333\) | −0.217493 | −0.0119186 | ||||||||
\(334\) | −3.24830 | −0.177739 | ||||||||
\(335\) | −32.6912 | −1.78611 | ||||||||
\(336\) | 12.0534 | 0.657567 | ||||||||
\(337\) | 8.06868 | 0.439529 | 0.219764 | − | 0.975553i | \(-0.429471\pi\) | ||||
0.219764 | + | 0.975553i | \(0.429471\pi\) | |||||||
\(338\) | −25.8589 | −1.40654 | ||||||||
\(339\) | 17.8352 | 0.968678 | ||||||||
\(340\) | −16.7345 | −0.907554 | ||||||||
\(341\) | −0.821004 | −0.0444598 | ||||||||
\(342\) | 0.0592061 | 0.00320150 | ||||||||
\(343\) | −9.38522 | −0.506754 | ||||||||
\(344\) | 19.3044 | 1.04082 | ||||||||
\(345\) | −50.2930 | −2.70768 | ||||||||
\(346\) | −14.9796 | −0.805309 | ||||||||
\(347\) | −5.99108 | −0.321618 | −0.160809 | − | 0.986986i | \(-0.551410\pi\) | ||||
−0.160809 | + | 0.986986i | \(0.551410\pi\) | |||||||
\(348\) | −7.45711 | −0.399743 | ||||||||
\(349\) | −17.1178 | −0.916295 | −0.458147 | − | 0.888876i | \(-0.651487\pi\) | ||||
−0.458147 | + | 0.888876i | \(0.651487\pi\) | |||||||
\(350\) | −42.0097 | −2.24551 | ||||||||
\(351\) | −30.9762 | −1.65339 | ||||||||
\(352\) | 16.8306 | 0.897074 | ||||||||
\(353\) | 9.77501 | 0.520271 | 0.260136 | − | 0.965572i | \(-0.416233\pi\) | ||||
0.260136 | + | 0.965572i | \(0.416233\pi\) | |||||||
\(354\) | 15.9412 | 0.847267 | ||||||||
\(355\) | −5.75544 | −0.305467 | ||||||||
\(356\) | 7.35731 | 0.389937 | ||||||||
\(357\) | 34.1583 | 1.80785 | ||||||||
\(358\) | 9.23256 | 0.487956 | ||||||||
\(359\) | −24.0383 | −1.26869 | −0.634347 | − | 0.773048i | \(-0.718731\pi\) | ||||
−0.634347 | + | 0.773048i | \(0.718731\pi\) | |||||||
\(360\) | −0.243240 | −0.0128199 | ||||||||
\(361\) | −12.0086 | −0.632032 | ||||||||
\(362\) | 12.4636 | 0.655074 | ||||||||
\(363\) | −14.9374 | −0.784011 | ||||||||
\(364\) | 14.2254 | 0.745614 | ||||||||
\(365\) | 9.64591 | 0.504890 | ||||||||
\(366\) | −27.7672 | −1.45142 | ||||||||
\(367\) | −11.4894 | −0.599743 | −0.299872 | − | 0.953980i | \(-0.596944\pi\) | ||||
−0.299872 | + | 0.953980i | \(0.596944\pi\) | |||||||
\(368\) | 14.9724 | 0.780489 | ||||||||
\(369\) | 0.0486819 | 0.00253428 | ||||||||
\(370\) | −50.1787 | −2.60867 | ||||||||
\(371\) | 3.31731 | 0.172226 | ||||||||
\(372\) | 0.229092 | 0.0118779 | ||||||||
\(373\) | 28.3635 | 1.46860 | 0.734302 | − | 0.678823i | \(-0.237510\pi\) | ||||
0.734302 | + | 0.678823i | \(0.237510\pi\) | |||||||
\(374\) | −29.5283 | −1.52687 | ||||||||
\(375\) | 42.1861 | 2.17848 | ||||||||
\(376\) | 8.93713 | 0.460897 | ||||||||
\(377\) | 36.1087 | 1.85969 | ||||||||
\(378\) | −19.6747 | −1.01196 | ||||||||
\(379\) | 26.1006 | 1.34070 | 0.670350 | − | 0.742045i | \(-0.266144\pi\) | ||||
0.670350 | + | 0.742045i | \(0.266144\pi\) | |||||||
\(380\) | −7.53170 | −0.386368 | ||||||||
\(381\) | 10.3184 | 0.528625 | ||||||||
\(382\) | 6.31079 | 0.322888 | ||||||||
\(383\) | 32.3936 | 1.65524 | 0.827619 | − | 0.561291i | \(-0.189695\pi\) | ||||
0.827619 | + | 0.561291i | \(0.189695\pi\) | |||||||
\(384\) | 3.48417 | 0.177801 | ||||||||
\(385\) | 59.3530 | 3.02491 | ||||||||
\(386\) | −14.9343 | −0.760135 | ||||||||
\(387\) | 0.123688 | 0.00628741 | ||||||||
\(388\) | −9.33459 | −0.473892 | ||||||||
\(389\) | 7.66199 | 0.388478 | 0.194239 | − | 0.980954i | \(-0.437776\pi\) | ||||
0.194239 | + | 0.980954i | \(0.437776\pi\) | |||||||
\(390\) | 47.2906 | 2.39465 | ||||||||
\(391\) | 42.4304 | 2.14580 | ||||||||
\(392\) | 12.9119 | 0.652149 | ||||||||
\(393\) | −4.20809 | −0.212270 | ||||||||
\(394\) | −18.8845 | −0.951388 | ||||||||
\(395\) | −58.1463 | −2.92566 | ||||||||
\(396\) | 0.0620549 | 0.00311838 | ||||||||
\(397\) | −16.9437 | −0.850379 | −0.425189 | − | 0.905104i | \(-0.639792\pi\) | ||||
−0.425189 | + | 0.905104i | \(0.639792\pi\) | |||||||
\(398\) | −3.75682 | −0.188312 | ||||||||
\(399\) | 15.3737 | 0.769646 | ||||||||
\(400\) | −22.9243 | −1.14621 | ||||||||
\(401\) | −9.87337 | −0.493053 | −0.246526 | − | 0.969136i | \(-0.579289\pi\) | ||||
−0.246526 | + | 0.969136i | \(0.579289\pi\) | |||||||
\(402\) | 16.0962 | 0.802803 | ||||||||
\(403\) | −1.10930 | −0.0552584 | ||||||||
\(404\) | −3.23094 | −0.160746 | ||||||||
\(405\) | 36.3009 | 1.80380 | ||||||||
\(406\) | 22.9346 | 1.13822 | ||||||||
\(407\) | 48.8202 | 2.41993 | ||||||||
\(408\) | 31.4225 | 1.55565 | ||||||||
\(409\) | 13.2558 | 0.655458 | 0.327729 | − | 0.944772i | \(-0.393717\pi\) | ||||
0.327729 | + | 0.944772i | \(0.393717\pi\) | |||||||
\(410\) | 11.2316 | 0.554688 | ||||||||
\(411\) | −1.66446 | −0.0821020 | ||||||||
\(412\) | 9.83101 | 0.484339 | ||||||||
\(413\) | 27.0331 | 1.33021 | ||||||||
\(414\) | 0.161719 | 0.00794807 | ||||||||
\(415\) | 58.5243 | 2.87284 | ||||||||
\(416\) | 22.7408 | 1.11496 | ||||||||
\(417\) | −6.44863 | −0.315791 | ||||||||
\(418\) | −13.2898 | −0.650028 | ||||||||
\(419\) | −25.2387 | −1.23299 | −0.616496 | − | 0.787358i | \(-0.711448\pi\) | ||||
−0.616496 | + | 0.787358i | \(0.711448\pi\) | |||||||
\(420\) | −16.5618 | −0.808132 | ||||||||
\(421\) | 14.4226 | 0.702916 | 0.351458 | − | 0.936204i | \(-0.385686\pi\) | ||||
0.351458 | + | 0.936204i | \(0.385686\pi\) | |||||||
\(422\) | −9.66101 | −0.470291 | ||||||||
\(423\) | 0.0572625 | 0.00278420 | ||||||||
\(424\) | 3.05162 | 0.148200 | ||||||||
\(425\) | −64.9654 | −3.15128 | ||||||||
\(426\) | 2.83380 | 0.137298 | ||||||||
\(427\) | −47.0875 | −2.27872 | ||||||||
\(428\) | −6.81351 | −0.329343 | ||||||||
\(429\) | −46.0103 | −2.22140 | ||||||||
\(430\) | 28.5365 | 1.37615 | ||||||||
\(431\) | −14.4106 | −0.694136 | −0.347068 | − | 0.937840i | \(-0.612823\pi\) | ||||
−0.347068 | + | 0.937840i | \(0.612823\pi\) | |||||||
\(432\) | −10.7363 | −0.516550 | ||||||||
\(433\) | −24.6812 | −1.18610 | −0.593051 | − | 0.805165i | \(-0.702077\pi\) | ||||
−0.593051 | + | 0.805165i | \(0.702077\pi\) | |||||||
\(434\) | −0.704580 | −0.0338209 | ||||||||
\(435\) | −42.0392 | −2.01562 | ||||||||
\(436\) | 4.85801 | 0.232656 | ||||||||
\(437\) | 19.0967 | 0.913519 | ||||||||
\(438\) | −4.74936 | −0.226933 | ||||||||
\(439\) | −29.4671 | −1.40639 | −0.703194 | − | 0.710998i | \(-0.748244\pi\) | ||||
−0.703194 | + | 0.710998i | \(0.748244\pi\) | |||||||
\(440\) | 54.5994 | 2.60292 | ||||||||
\(441\) | 0.0827298 | 0.00393951 | ||||||||
\(442\) | −39.8974 | −1.89772 | ||||||||
\(443\) | 4.51884 | 0.214697 | 0.107348 | − | 0.994221i | \(-0.465764\pi\) | ||||
0.107348 | + | 0.994221i | \(0.465764\pi\) | |||||||
\(444\) | −13.6227 | −0.646506 | ||||||||
\(445\) | 41.4765 | 1.96618 | ||||||||
\(446\) | 8.38433 | 0.397010 | ||||||||
\(447\) | 14.9726 | 0.708178 | ||||||||
\(448\) | 28.3164 | 1.33783 | ||||||||
\(449\) | 6.82816 | 0.322241 | 0.161120 | − | 0.986935i | \(-0.448489\pi\) | ||||
0.161120 | + | 0.986935i | \(0.448489\pi\) | |||||||
\(450\) | −0.247609 | −0.0116724 | ||||||||
\(451\) | −10.9275 | −0.514555 | ||||||||
\(452\) | 7.29558 | 0.343155 | ||||||||
\(453\) | 15.6591 | 0.735727 | ||||||||
\(454\) | −3.21162 | −0.150729 | ||||||||
\(455\) | 80.1952 | 3.75961 | ||||||||
\(456\) | 14.1424 | 0.662278 | ||||||||
\(457\) | −18.3271 | −0.857304 | −0.428652 | − | 0.903470i | \(-0.641011\pi\) | ||||
−0.428652 | + | 0.903470i | \(0.641011\pi\) | |||||||
\(458\) | 21.4341 | 1.00155 | ||||||||
\(459\) | −30.4257 | −1.42015 | ||||||||
\(460\) | −20.5726 | −0.959201 | ||||||||
\(461\) | −30.0207 | −1.39820 | −0.699101 | − | 0.715023i | \(-0.746416\pi\) | ||||
−0.699101 | + | 0.715023i | \(0.746416\pi\) | |||||||
\(462\) | −29.2236 | −1.35961 | ||||||||
\(463\) | 27.1507 | 1.26180 | 0.630901 | − | 0.775864i | \(-0.282686\pi\) | ||||
0.630901 | + | 0.775864i | \(0.282686\pi\) | |||||||
\(464\) | 12.5152 | 0.581003 | ||||||||
\(465\) | 1.29150 | 0.0598917 | ||||||||
\(466\) | −12.9372 | −0.599306 | ||||||||
\(467\) | 2.08061 | 0.0962791 | 0.0481396 | − | 0.998841i | \(-0.484671\pi\) | ||||
0.0481396 | + | 0.998841i | \(0.484671\pi\) | |||||||
\(468\) | 0.0838459 | 0.00387578 | ||||||||
\(469\) | 27.2958 | 1.26040 | ||||||||
\(470\) | 13.2112 | 0.609389 | ||||||||
\(471\) | 5.08394 | 0.234256 | ||||||||
\(472\) | 24.8680 | 1.14464 | ||||||||
\(473\) | −27.7639 | −1.27659 | ||||||||
\(474\) | 28.6295 | 1.31500 | ||||||||
\(475\) | −29.2391 | −1.34158 | ||||||||
\(476\) | 13.9726 | 0.640432 | ||||||||
\(477\) | 0.0195525 | 0.000895249 0 | ||||||||
\(478\) | 7.50932 | 0.343468 | ||||||||
\(479\) | −2.25809 | −0.103175 | −0.0515873 | − | 0.998668i | \(-0.516428\pi\) | ||||
−0.0515873 | + | 0.998668i | \(0.516428\pi\) | |||||||
\(480\) | −26.4757 | −1.20845 | ||||||||
\(481\) | 65.9637 | 3.00769 | ||||||||
\(482\) | 30.6656 | 1.39678 | ||||||||
\(483\) | 41.9926 | 1.91073 | ||||||||
\(484\) | −6.11021 | −0.277737 | ||||||||
\(485\) | −52.6234 | −2.38951 | ||||||||
\(486\) | −0.232697 | −0.0105553 | ||||||||
\(487\) | 5.19372 | 0.235350 | 0.117675 | − | 0.993052i | \(-0.462456\pi\) | ||||
0.117675 | + | 0.993052i | \(0.462456\pi\) | |||||||
\(488\) | −43.3163 | −1.96083 | ||||||||
\(489\) | 2.44884 | 0.110740 | ||||||||
\(490\) | 19.0869 | 0.862258 | ||||||||
\(491\) | 1.50929 | 0.0681135 | 0.0340567 | − | 0.999420i | \(-0.489157\pi\) | ||||
0.0340567 | + | 0.999420i | \(0.489157\pi\) | |||||||
\(492\) | 3.04919 | 0.137468 | ||||||||
\(493\) | 35.4669 | 1.59735 | ||||||||
\(494\) | −17.9567 | −0.807909 | ||||||||
\(495\) | 0.349832 | 0.0157238 | ||||||||
\(496\) | −0.384482 | −0.0172638 | ||||||||
\(497\) | 4.80555 | 0.215558 | ||||||||
\(498\) | −28.8156 | −1.29126 | ||||||||
\(499\) | 16.7473 | 0.749714 | 0.374857 | − | 0.927083i | \(-0.377692\pi\) | ||||
0.374857 | + | 0.927083i | \(0.377692\pi\) | |||||||
\(500\) | 17.2564 | 0.771730 | ||||||||
\(501\) | −4.97145 | −0.222108 | ||||||||
\(502\) | 23.8569 | 1.06478 | ||||||||
\(503\) | 16.8253 | 0.750204 | 0.375102 | − | 0.926984i | \(-0.377608\pi\) | ||||
0.375102 | + | 0.926984i | \(0.377608\pi\) | |||||||
\(504\) | 0.203095 | 0.00904657 | ||||||||
\(505\) | −18.2143 | −0.810527 | ||||||||
\(506\) | −36.3007 | −1.61376 | ||||||||
\(507\) | −39.5765 | −1.75766 | ||||||||
\(508\) | 4.22076 | 0.187266 | ||||||||
\(509\) | −11.7317 | −0.519999 | −0.259999 | − | 0.965609i | \(-0.583722\pi\) | ||||
−0.259999 | + | 0.965609i | \(0.583722\pi\) | |||||||
\(510\) | 46.4501 | 2.05685 | ||||||||
\(511\) | −8.05393 | −0.356285 | ||||||||
\(512\) | 20.6434 | 0.912317 | ||||||||
\(513\) | −13.6937 | −0.604593 | ||||||||
\(514\) | 17.4453 | 0.769477 | ||||||||
\(515\) | 55.4219 | 2.44218 | ||||||||
\(516\) | 7.74721 | 0.341052 | ||||||||
\(517\) | −12.8536 | −0.565299 | ||||||||
\(518\) | 41.8971 | 1.84085 | ||||||||
\(519\) | −22.9260 | −1.00634 | ||||||||
\(520\) | 73.7723 | 3.23513 | ||||||||
\(521\) | −35.9580 | −1.57535 | −0.787675 | − | 0.616091i | \(-0.788715\pi\) | ||||
−0.787675 | + | 0.616091i | \(0.788715\pi\) | |||||||
\(522\) | 0.135179 | 0.00591661 | ||||||||
\(523\) | 6.13225 | 0.268145 | 0.134072 | − | 0.990972i | \(-0.457195\pi\) | ||||
0.134072 | + | 0.990972i | \(0.457195\pi\) | |||||||
\(524\) | −1.72133 | −0.0751968 | ||||||||
\(525\) | −64.2950 | −2.80606 | ||||||||
\(526\) | 23.1597 | 1.00981 | ||||||||
\(527\) | −1.08959 | −0.0474632 | ||||||||
\(528\) | −15.9470 | −0.694006 | ||||||||
\(529\) | 29.1619 | 1.26791 | ||||||||
\(530\) | 4.51104 | 0.195947 | ||||||||
\(531\) | 0.159335 | 0.00691457 | ||||||||
\(532\) | 6.28866 | 0.272648 | ||||||||
\(533\) | −14.7648 | −0.639532 | ||||||||
\(534\) | −20.4218 | −0.883738 | ||||||||
\(535\) | −38.4109 | −1.66065 | ||||||||
\(536\) | 25.1096 | 1.08457 | ||||||||
\(537\) | 14.1303 | 0.609766 | ||||||||
\(538\) | −14.4256 | −0.621930 | ||||||||
\(539\) | −18.5701 | −0.799872 | ||||||||
\(540\) | 14.7520 | 0.634826 | ||||||||
\(541\) | −29.5854 | −1.27197 | −0.635987 | − | 0.771700i | \(-0.719407\pi\) | ||||
−0.635987 | + | 0.771700i | \(0.719407\pi\) | |||||||
\(542\) | 9.95436 | 0.427577 | ||||||||
\(543\) | 19.0754 | 0.818602 | ||||||||
\(544\) | 22.3366 | 0.957674 | ||||||||
\(545\) | 27.3868 | 1.17312 | ||||||||
\(546\) | −39.4857 | −1.68983 | ||||||||
\(547\) | 36.6644 | 1.56765 | 0.783827 | − | 0.620979i | \(-0.213265\pi\) | ||||
0.783827 | + | 0.620979i | \(0.213265\pi\) | |||||||
\(548\) | −0.680856 | −0.0290847 | ||||||||
\(549\) | −0.277538 | −0.0118450 | ||||||||
\(550\) | 55.5802 | 2.36995 | ||||||||
\(551\) | 15.9626 | 0.680032 | ||||||||
\(552\) | 38.6294 | 1.64417 | ||||||||
\(553\) | 48.5497 | 2.06454 | ||||||||
\(554\) | −34.2431 | −1.45485 | ||||||||
\(555\) | −76.7976 | −3.25987 | ||||||||
\(556\) | −2.63784 | −0.111869 | ||||||||
\(557\) | −13.0289 | −0.552052 | −0.276026 | − | 0.961150i | \(-0.589018\pi\) | ||||
−0.276026 | + | 0.961150i | \(0.589018\pi\) | |||||||
\(558\) | −0.00415286 | −0.000175805 0 | ||||||||
\(559\) | −37.5134 | −1.58665 | ||||||||
\(560\) | 27.7954 | 1.17457 | ||||||||
\(561\) | −45.1925 | −1.90803 | ||||||||
\(562\) | 14.0277 | 0.591721 | ||||||||
\(563\) | −29.6497 | −1.24959 | −0.624793 | − | 0.780790i | \(-0.714817\pi\) | ||||
−0.624793 | + | 0.780790i | \(0.714817\pi\) | |||||||
\(564\) | 3.58664 | 0.151025 | ||||||||
\(565\) | 41.1285 | 1.73029 | ||||||||
\(566\) | −7.24850 | −0.304677 | ||||||||
\(567\) | −30.3097 | −1.27289 | ||||||||
\(568\) | 4.42067 | 0.185487 | ||||||||
\(569\) | −26.5214 | −1.11183 | −0.555916 | − | 0.831238i | \(-0.687633\pi\) | ||||
−0.555916 | + | 0.831238i | \(0.687633\pi\) | |||||||
\(570\) | 20.9059 | 0.875650 | ||||||||
\(571\) | −37.2859 | −1.56037 | −0.780183 | − | 0.625552i | \(-0.784874\pi\) | ||||
−0.780183 | + | 0.625552i | \(0.784874\pi\) | |||||||
\(572\) | −18.8207 | −0.786932 | ||||||||
\(573\) | 9.65854 | 0.403491 | ||||||||
\(574\) | −9.37789 | −0.391426 | ||||||||
\(575\) | −79.8654 | −3.33062 | ||||||||
\(576\) | 0.166900 | 0.00695416 | ||||||||
\(577\) | 1.03258 | 0.0429868 | 0.0214934 | − | 0.999769i | \(-0.493158\pi\) | ||||
0.0214934 | + | 0.999769i | \(0.493158\pi\) | |||||||
\(578\) | −19.8862 | −0.827156 | ||||||||
\(579\) | −22.8566 | −0.949889 | ||||||||
\(580\) | −17.1963 | −0.714037 | ||||||||
\(581\) | −48.8653 | −2.02727 | ||||||||
\(582\) | 25.9102 | 1.07401 | ||||||||
\(583\) | −4.38891 | −0.181770 | ||||||||
\(584\) | −7.40889 | −0.306582 | ||||||||
\(585\) | 0.472678 | 0.0195428 | ||||||||
\(586\) | −9.25423 | −0.382289 | ||||||||
\(587\) | −29.6501 | −1.22379 | −0.611895 | − | 0.790939i | \(-0.709593\pi\) | ||||
−0.611895 | + | 0.790939i | \(0.709593\pi\) | |||||||
\(588\) | 5.18179 | 0.213693 | ||||||||
\(589\) | −0.490393 | −0.0202063 | ||||||||
\(590\) | 36.7609 | 1.51342 | ||||||||
\(591\) | −28.9024 | −1.18888 | ||||||||
\(592\) | 22.8629 | 0.939658 | ||||||||
\(593\) | −3.38488 | −0.139000 | −0.0695002 | − | 0.997582i | \(-0.522140\pi\) | ||||
−0.0695002 | + | 0.997582i | \(0.522140\pi\) | |||||||
\(594\) | 26.0303 | 1.06803 | ||||||||
\(595\) | 78.7698 | 3.22925 | ||||||||
\(596\) | 6.12459 | 0.250873 | ||||||||
\(597\) | −5.74974 | −0.235321 | ||||||||
\(598\) | −49.0479 | −2.00572 | ||||||||
\(599\) | 3.31033 | 0.135256 | 0.0676281 | − | 0.997711i | \(-0.478457\pi\) | ||||
0.0676281 | + | 0.997711i | \(0.478457\pi\) | |||||||
\(600\) | −59.1456 | −2.41461 | ||||||||
\(601\) | 38.6413 | 1.57621 | 0.788107 | − | 0.615539i | \(-0.211061\pi\) | ||||
0.788107 | + | 0.615539i | \(0.211061\pi\) | |||||||
\(602\) | −23.8268 | −0.971108 | ||||||||
\(603\) | 0.160884 | 0.00655170 | ||||||||
\(604\) | 6.40541 | 0.260632 | ||||||||
\(605\) | −34.4460 | −1.40043 | ||||||||
\(606\) | 8.96818 | 0.364307 | ||||||||
\(607\) | −42.5467 | −1.72692 | −0.863458 | − | 0.504420i | \(-0.831706\pi\) | ||||
−0.863458 | + | 0.504420i | \(0.831706\pi\) | |||||||
\(608\) | 10.0531 | 0.407706 | ||||||||
\(609\) | 35.1009 | 1.42236 | ||||||||
\(610\) | −64.0319 | −2.59258 | ||||||||
\(611\) | −17.3672 | −0.702600 | ||||||||
\(612\) | 0.0823557 | 0.00332903 | ||||||||
\(613\) | −31.8355 | −1.28583 | −0.642913 | − | 0.765939i | \(-0.722274\pi\) | ||||
−0.642913 | + | 0.765939i | \(0.722274\pi\) | |||||||
\(614\) | 28.8830 | 1.16562 | ||||||||
\(615\) | 17.1897 | 0.693156 | ||||||||
\(616\) | −45.5882 | −1.83680 | ||||||||
\(617\) | −4.30232 | −0.173205 | −0.0866024 | − | 0.996243i | \(-0.527601\pi\) | ||||
−0.0866024 | + | 0.996243i | \(0.527601\pi\) | |||||||
\(618\) | −27.2881 | −1.09769 | ||||||||
\(619\) | 28.5222 | 1.14641 | 0.573203 | − | 0.819413i | \(-0.305701\pi\) | ||||
0.573203 | + | 0.819413i | \(0.305701\pi\) | |||||||
\(620\) | 0.528292 | 0.0212167 | ||||||||
\(621\) | −37.4039 | −1.50097 | ||||||||
\(622\) | 8.39776 | 0.336719 | ||||||||
\(623\) | −34.6312 | −1.38747 | ||||||||
\(624\) | −21.5470 | −0.862568 | ||||||||
\(625\) | 41.9916 | 1.67966 | ||||||||
\(626\) | 13.1407 | 0.525206 | ||||||||
\(627\) | −20.3399 | −0.812296 | ||||||||
\(628\) | 2.07961 | 0.0829854 | ||||||||
\(629\) | 64.7913 | 2.58340 | ||||||||
\(630\) | 0.300223 | 0.0119612 | ||||||||
\(631\) | 12.2527 | 0.487773 | 0.243887 | − | 0.969804i | \(-0.421578\pi\) | ||||
0.243887 | + | 0.969804i | \(0.421578\pi\) | |||||||
\(632\) | 44.6614 | 1.77653 | ||||||||
\(633\) | −14.7860 | −0.587691 | ||||||||
\(634\) | −17.1904 | −0.682720 | ||||||||
\(635\) | 23.7944 | 0.944252 | ||||||||
\(636\) | 1.22468 | 0.0485615 | ||||||||
\(637\) | −25.0912 | −0.994148 | ||||||||
\(638\) | −30.3432 | −1.20130 | ||||||||
\(639\) | 0.0283244 | 0.00112049 | ||||||||
\(640\) | 8.03458 | 0.317595 | ||||||||
\(641\) | 10.4682 | 0.413468 | 0.206734 | − | 0.978397i | \(-0.433716\pi\) | ||||
0.206734 | + | 0.978397i | \(0.433716\pi\) | |||||||
\(642\) | 18.9124 | 0.746411 | ||||||||
\(643\) | −29.7777 | −1.17432 | −0.587159 | − | 0.809471i | \(-0.699754\pi\) | ||||
−0.587159 | + | 0.809471i | \(0.699754\pi\) | |||||||
\(644\) | 17.1772 | 0.676877 | ||||||||
\(645\) | 43.6746 | 1.71969 | ||||||||
\(646\) | −17.6375 | −0.693939 | ||||||||
\(647\) | 36.4269 | 1.43209 | 0.716045 | − | 0.698054i | \(-0.245951\pi\) | ||||
0.716045 | + | 0.698054i | \(0.245951\pi\) | |||||||
\(648\) | −27.8822 | −1.09532 | ||||||||
\(649\) | −35.7656 | −1.40392 | ||||||||
\(650\) | 75.0976 | 2.94557 | ||||||||
\(651\) | −1.07835 | −0.0422637 | ||||||||
\(652\) | 1.00171 | 0.0392299 | ||||||||
\(653\) | 43.7870 | 1.71352 | 0.856759 | − | 0.515717i | \(-0.172474\pi\) | ||||
0.856759 | + | 0.515717i | \(0.172474\pi\) | |||||||
\(654\) | −13.4844 | −0.527284 | ||||||||
\(655\) | −9.70395 | −0.379165 | ||||||||
\(656\) | −5.11743 | −0.199802 | ||||||||
\(657\) | −0.0474707 | −0.00185201 | ||||||||
\(658\) | −11.0308 | −0.430027 | ||||||||
\(659\) | 47.6225 | 1.85511 | 0.927554 | − | 0.373690i | \(-0.121907\pi\) | ||||
0.927554 | + | 0.373690i | \(0.121907\pi\) | |||||||
\(660\) | 21.9118 | 0.852915 | ||||||||
\(661\) | −40.4025 | −1.57147 | −0.785737 | − | 0.618560i | \(-0.787716\pi\) | ||||
−0.785737 | + | 0.618560i | \(0.787716\pi\) | |||||||
\(662\) | −4.01052 | −0.155873 | ||||||||
\(663\) | −61.0622 | −2.37146 | ||||||||
\(664\) | −44.9517 | −1.74446 | ||||||||
\(665\) | 35.4520 | 1.37477 | ||||||||
\(666\) | 0.246946 | 0.00956895 | ||||||||
\(667\) | 43.6013 | 1.68825 | ||||||||
\(668\) | −2.03359 | −0.0786821 | ||||||||
\(669\) | 12.8321 | 0.496116 | ||||||||
\(670\) | 37.1181 | 1.43400 | ||||||||
\(671\) | 62.2983 | 2.40500 | ||||||||
\(672\) | 22.1061 | 0.852762 | ||||||||
\(673\) | 50.1686 | 1.93386 | 0.966928 | − | 0.255048i | \(-0.0820913\pi\) | ||||
0.966928 | + | 0.255048i | \(0.0820913\pi\) | |||||||
\(674\) | −9.16132 | −0.352881 | ||||||||
\(675\) | 57.2693 | 2.20430 | ||||||||
\(676\) | −16.1889 | −0.622651 | ||||||||
\(677\) | −29.5797 | −1.13684 | −0.568421 | − | 0.822738i | \(-0.692445\pi\) | ||||
−0.568421 | + | 0.822738i | \(0.692445\pi\) | |||||||
\(678\) | −20.2505 | −0.777714 | ||||||||
\(679\) | 43.9383 | 1.68620 | ||||||||
\(680\) | 72.4612 | 2.77876 | ||||||||
\(681\) | −4.91533 | −0.188356 | ||||||||
\(682\) | 0.932182 | 0.0356951 | ||||||||
\(683\) | −21.1259 | −0.808359 | −0.404179 | − | 0.914680i | \(-0.632443\pi\) | ||||
−0.404179 | + | 0.914680i | \(0.632443\pi\) | |||||||
\(684\) | 0.0370660 | 0.00141725 | ||||||||
\(685\) | −3.83830 | −0.146654 | ||||||||
\(686\) | 10.6561 | 0.406853 | ||||||||
\(687\) | 32.8045 | 1.25157 | ||||||||
\(688\) | −13.0021 | −0.495699 | ||||||||
\(689\) | −5.93010 | −0.225919 | ||||||||
\(690\) | 57.1036 | 2.17390 | ||||||||
\(691\) | 8.14572 | 0.309878 | 0.154939 | − | 0.987924i | \(-0.450482\pi\) | ||||
0.154939 | + | 0.987924i | \(0.450482\pi\) | |||||||
\(692\) | −9.37798 | −0.356497 | ||||||||
\(693\) | −0.292095 | −0.0110958 | ||||||||
\(694\) | 6.80238 | 0.258215 | ||||||||
\(695\) | −14.8707 | −0.564078 | ||||||||
\(696\) | 32.2897 | 1.22394 | ||||||||
\(697\) | −14.5023 | −0.549315 | ||||||||
\(698\) | 19.4358 | 0.735657 | ||||||||
\(699\) | −19.8002 | −0.748912 | ||||||||
\(700\) | −26.3001 | −0.994052 | ||||||||
\(701\) | 24.2564 | 0.916152 | 0.458076 | − | 0.888913i | \(-0.348539\pi\) | ||||
0.458076 | + | 0.888913i | \(0.348539\pi\) | |||||||
\(702\) | 35.1710 | 1.32744 | ||||||||
\(703\) | 29.1607 | 1.09982 | ||||||||
\(704\) | −37.4636 | −1.41196 | ||||||||
\(705\) | 20.2195 | 0.761512 | ||||||||
\(706\) | −11.0987 | −0.417706 | ||||||||
\(707\) | 15.2082 | 0.571963 | ||||||||
\(708\) | 9.98000 | 0.375071 | ||||||||
\(709\) | 32.2235 | 1.21018 | 0.605089 | − | 0.796158i | \(-0.293138\pi\) | ||||
0.605089 | + | 0.796158i | \(0.293138\pi\) | |||||||
\(710\) | 6.53482 | 0.245247 | ||||||||
\(711\) | 0.286157 | 0.0107317 | ||||||||
\(712\) | −31.8575 | −1.19391 | ||||||||
\(713\) | −1.33949 | −0.0501643 | ||||||||
\(714\) | −38.7839 | −1.45145 | ||||||||
\(715\) | −106.101 | −3.96795 | ||||||||
\(716\) | 5.78004 | 0.216010 | ||||||||
\(717\) | 11.4929 | 0.429209 | ||||||||
\(718\) | 27.2935 | 1.01859 | ||||||||
\(719\) | 38.1364 | 1.42225 | 0.711124 | − | 0.703066i | \(-0.248186\pi\) | ||||
0.711124 | + | 0.703066i | \(0.248186\pi\) | |||||||
\(720\) | 0.163829 | 0.00610555 | ||||||||
\(721\) | −46.2750 | −1.72337 | ||||||||
\(722\) | 13.6348 | 0.507434 | ||||||||
\(723\) | 46.9330 | 1.74546 | ||||||||
\(724\) | 7.80285 | 0.289991 | ||||||||
\(725\) | −66.7582 | −2.47934 | ||||||||
\(726\) | 16.9602 | 0.629452 | ||||||||
\(727\) | 3.55446 | 0.131828 | 0.0659138 | − | 0.997825i | \(-0.479004\pi\) | ||||
0.0659138 | + | 0.997825i | \(0.479004\pi\) | |||||||
\(728\) | −61.5968 | −2.28293 | ||||||||
\(729\) | 26.8202 | 0.993340 | ||||||||
\(730\) | −10.9521 | −0.405357 | ||||||||
\(731\) | −36.8467 | −1.36282 | ||||||||
\(732\) | −17.3836 | −0.642518 | ||||||||
\(733\) | −2.38315 | −0.0880236 | −0.0440118 | − | 0.999031i | \(-0.514014\pi\) | ||||
−0.0440118 | + | 0.999031i | \(0.514014\pi\) | |||||||
\(734\) | 13.0453 | 0.481511 | ||||||||
\(735\) | 29.2121 | 1.07751 | ||||||||
\(736\) | 27.4596 | 1.01217 | ||||||||
\(737\) | −36.1132 | −1.33025 | ||||||||
\(738\) | −0.0552742 | −0.00203467 | ||||||||
\(739\) | −45.3722 | −1.66904 | −0.834522 | − | 0.550974i | \(-0.814256\pi\) | ||||
−0.834522 | + | 0.550974i | \(0.814256\pi\) | |||||||
\(740\) | −31.4144 | −1.15481 | ||||||||
\(741\) | −27.4823 | −1.00959 | ||||||||
\(742\) | −3.76653 | −0.138274 | ||||||||
\(743\) | −7.70430 | −0.282643 | −0.141322 | − | 0.989964i | \(-0.545135\pi\) | ||||
−0.141322 | + | 0.989964i | \(0.545135\pi\) | |||||||
\(744\) | −0.991981 | −0.0363678 | ||||||||
\(745\) | 34.5271 | 1.26498 | ||||||||
\(746\) | −32.2044 | −1.17909 | ||||||||
\(747\) | −0.288017 | −0.0105380 | ||||||||
\(748\) | −18.4862 | −0.675922 | ||||||||
\(749\) | 32.0715 | 1.17187 | ||||||||
\(750\) | −47.8989 | −1.74902 | ||||||||
\(751\) | −44.9613 | −1.64066 | −0.820331 | − | 0.571889i | \(-0.806211\pi\) | ||||
−0.820331 | + | 0.571889i | \(0.806211\pi\) | |||||||
\(752\) | −6.01942 | −0.219506 | ||||||||
\(753\) | 36.5125 | 1.33059 | ||||||||
\(754\) | −40.9984 | −1.49307 | ||||||||
\(755\) | 36.1102 | 1.31419 | ||||||||
\(756\) | −12.3173 | −0.447977 | ||||||||
\(757\) | 4.92035 | 0.178833 | 0.0894165 | − | 0.995994i | \(-0.471500\pi\) | ||||
0.0894165 | + | 0.995994i | \(0.471500\pi\) | |||||||
\(758\) | −29.6351 | −1.07640 | ||||||||
\(759\) | −55.5575 | −2.01661 | ||||||||
\(760\) | 32.6127 | 1.18299 | ||||||||
\(761\) | −15.7194 | −0.569828 | −0.284914 | − | 0.958553i | \(-0.591965\pi\) | ||||
−0.284914 | + | 0.958553i | \(0.591965\pi\) | |||||||
\(762\) | −11.7156 | −0.424413 | ||||||||
\(763\) | −22.8669 | −0.827836 | ||||||||
\(764\) | 3.95086 | 0.142937 | ||||||||
\(765\) | 0.464277 | 0.0167860 | ||||||||
\(766\) | −36.7803 | −1.32893 | ||||||||
\(767\) | −48.3250 | −1.74491 | ||||||||
\(768\) | 25.4571 | 0.918603 | ||||||||
\(769\) | 45.1212 | 1.62711 | 0.813556 | − | 0.581487i | \(-0.197529\pi\) | ||||
0.813556 | + | 0.581487i | \(0.197529\pi\) | |||||||
\(770\) | −67.3904 | −2.42858 | ||||||||
\(771\) | 26.6996 | 0.961564 | ||||||||
\(772\) | −9.34960 | −0.336499 | ||||||||
\(773\) | 21.3169 | 0.766716 | 0.383358 | − | 0.923600i | \(-0.374768\pi\) | ||||
0.383358 | + | 0.923600i | \(0.374768\pi\) | |||||||
\(774\) | −0.140438 | −0.00504792 | ||||||||
\(775\) | 2.05090 | 0.0736704 | ||||||||
\(776\) | 40.4193 | 1.45097 | ||||||||
\(777\) | 64.1227 | 2.30039 | ||||||||
\(778\) | −8.69955 | −0.311894 | ||||||||
\(779\) | −6.52709 | −0.233857 | ||||||||
\(780\) | 29.6063 | 1.06007 | ||||||||
\(781\) | −6.35790 | −0.227503 | ||||||||
\(782\) | −48.1762 | −1.72278 | ||||||||
\(783\) | −31.2654 | −1.11733 | ||||||||
\(784\) | −8.69654 | −0.310591 | ||||||||
\(785\) | 11.7237 | 0.418437 | ||||||||
\(786\) | 4.77793 | 0.170423 | ||||||||
\(787\) | 27.4495 | 0.978470 | 0.489235 | − | 0.872152i | \(-0.337276\pi\) | ||||
0.489235 | + | 0.872152i | \(0.337276\pi\) | |||||||
\(788\) | −11.8226 | −0.421164 | ||||||||
\(789\) | 35.4455 | 1.26189 | ||||||||
\(790\) | 66.0203 | 2.34890 | ||||||||
\(791\) | −34.3406 | −1.22101 | ||||||||
\(792\) | −0.268701 | −0.00954788 | ||||||||
\(793\) | 84.1748 | 2.98913 | ||||||||
\(794\) | 19.2381 | 0.682736 | ||||||||
\(795\) | 6.90406 | 0.244862 | ||||||||
\(796\) | −2.35195 | −0.0833628 | ||||||||
\(797\) | 6.11326 | 0.216543 | 0.108271 | − | 0.994121i | \(-0.465468\pi\) | ||||
0.108271 | + | 0.994121i | \(0.465468\pi\) | |||||||
\(798\) | −17.4555 | −0.617919 | ||||||||
\(799\) | −17.0585 | −0.603486 | ||||||||
\(800\) | −42.0435 | −1.48646 | ||||||||
\(801\) | −0.204119 | −0.00721221 | ||||||||
\(802\) | 11.2104 | 0.395853 | ||||||||
\(803\) | 10.6556 | 0.376029 | ||||||||
\(804\) | 10.0770 | 0.355388 | ||||||||
\(805\) | 96.8359 | 3.41302 | ||||||||
\(806\) | 1.25952 | 0.0443648 | ||||||||
\(807\) | −22.0780 | −0.777184 | ||||||||
\(808\) | 13.9902 | 0.492172 | ||||||||
\(809\) | −15.9722 | −0.561551 | −0.280776 | − | 0.959773i | \(-0.590592\pi\) | ||||
−0.280776 | + | 0.959773i | \(0.590592\pi\) | |||||||
\(810\) | −41.2166 | −1.44820 | ||||||||
\(811\) | −22.7644 | −0.799367 | −0.399684 | − | 0.916653i | \(-0.630880\pi\) | ||||
−0.399684 | + | 0.916653i | \(0.630880\pi\) | |||||||
\(812\) | 14.3582 | 0.503873 | ||||||||
\(813\) | 15.2350 | 0.534313 | ||||||||
\(814\) | −55.4313 | −1.94286 | ||||||||
\(815\) | 5.64708 | 0.197809 | ||||||||
\(816\) | −21.1640 | −0.740888 | ||||||||
\(817\) | −16.5836 | −0.580188 | ||||||||
\(818\) | −15.0509 | −0.526242 | ||||||||
\(819\) | −0.394666 | −0.0137908 | ||||||||
\(820\) | 7.03152 | 0.245551 | ||||||||
\(821\) | −17.5222 | −0.611528 | −0.305764 | − | 0.952107i | \(-0.598912\pi\) | ||||
−0.305764 | + | 0.952107i | \(0.598912\pi\) | |||||||
\(822\) | 1.88986 | 0.0659165 | ||||||||
\(823\) | −5.85303 | −0.204024 | −0.102012 | − | 0.994783i | \(-0.532528\pi\) | ||||
−0.102012 | + | 0.994783i | \(0.532528\pi\) | |||||||
\(824\) | −42.5688 | −1.48295 | ||||||||
\(825\) | 85.0644 | 2.96156 | ||||||||
\(826\) | −30.6938 | −1.06797 | ||||||||
\(827\) | 47.7861 | 1.66168 | 0.830842 | − | 0.556508i | \(-0.187859\pi\) | ||||
0.830842 | + | 0.556508i | \(0.187859\pi\) | |||||||
\(828\) | 0.101244 | 0.00351848 | ||||||||
\(829\) | −28.5195 | −0.990523 | −0.495261 | − | 0.868744i | \(-0.664928\pi\) | ||||
−0.495261 | + | 0.868744i | \(0.664928\pi\) | |||||||
\(830\) | −66.4495 | −2.30650 | ||||||||
\(831\) | −52.4083 | −1.81803 | ||||||||
\(832\) | −50.6192 | −1.75490 | ||||||||
\(833\) | −24.6452 | −0.853906 | ||||||||
\(834\) | 7.32189 | 0.253536 | ||||||||
\(835\) | −11.4643 | −0.396738 | ||||||||
\(836\) | −8.32010 | −0.287757 | ||||||||
\(837\) | 0.960512 | 0.0332001 | ||||||||
\(838\) | 28.6565 | 0.989921 | ||||||||
\(839\) | 8.65980 | 0.298970 | 0.149485 | − | 0.988764i | \(-0.452238\pi\) | ||||
0.149485 | + | 0.988764i | \(0.452238\pi\) | |||||||
\(840\) | 71.7134 | 2.47435 | ||||||||
\(841\) | 7.44570 | 0.256748 | ||||||||
\(842\) | −16.3757 | −0.564344 | ||||||||
\(843\) | 21.4691 | 0.739434 | ||||||||
\(844\) | −6.04827 | −0.208190 | ||||||||
\(845\) | −91.2645 | −3.13959 | ||||||||
\(846\) | −0.0650168 | −0.00223532 | ||||||||
\(847\) | 28.7610 | 0.988240 | ||||||||
\(848\) | −2.05536 | −0.0705813 | ||||||||
\(849\) | −11.0937 | −0.380735 | ||||||||
\(850\) | 73.7628 | 2.53004 | ||||||||
\(851\) | 79.6514 | 2.73041 | ||||||||
\(852\) | 1.77410 | 0.0607797 | ||||||||
\(853\) | 6.46300 | 0.221289 | 0.110644 | − | 0.993860i | \(-0.464709\pi\) | ||||
0.110644 | + | 0.993860i | \(0.464709\pi\) | |||||||
\(854\) | 53.4640 | 1.82950 | ||||||||
\(855\) | 0.208958 | 0.00714621 | ||||||||
\(856\) | 29.5029 | 1.00839 | ||||||||
\(857\) | 28.1294 | 0.960881 | 0.480441 | − | 0.877027i | \(-0.340477\pi\) | ||||
0.480441 | + | 0.877027i | \(0.340477\pi\) | |||||||
\(858\) | 52.2408 | 1.78347 | ||||||||
\(859\) | −12.9481 | −0.441785 | −0.220893 | − | 0.975298i | \(-0.570897\pi\) | ||||
−0.220893 | + | 0.975298i | \(0.570897\pi\) | |||||||
\(860\) | 17.8653 | 0.609201 | ||||||||
\(861\) | −14.3527 | −0.489138 | ||||||||
\(862\) | 16.3621 | 0.557295 | ||||||||
\(863\) | −7.32424 | −0.249320 | −0.124660 | − | 0.992200i | \(-0.539784\pi\) | ||||
−0.124660 | + | 0.992200i | \(0.539784\pi\) | |||||||
\(864\) | −19.6905 | −0.669885 | ||||||||
\(865\) | −52.8680 | −1.79756 | ||||||||
\(866\) | 28.0235 | 0.952276 | ||||||||
\(867\) | −30.4354 | −1.03364 | ||||||||
\(868\) | −0.441102 | −0.0149720 | ||||||||
\(869\) | −64.2329 | −2.17895 | ||||||||
\(870\) | 47.7320 | 1.61827 | ||||||||
\(871\) | −48.7946 | −1.65334 | ||||||||
\(872\) | −21.0354 | −0.712350 | ||||||||
\(873\) | 0.258977 | 0.00876504 | ||||||||
\(874\) | −21.6827 | −0.733429 | ||||||||
\(875\) | −81.2266 | −2.74596 | ||||||||
\(876\) | −2.97333 | −0.100460 | ||||||||
\(877\) | 7.11657 | 0.240310 | 0.120155 | − | 0.992755i | \(-0.461661\pi\) | ||||
0.120155 | + | 0.992755i | \(0.461661\pi\) | |||||||
\(878\) | 33.4575 | 1.12914 | ||||||||
\(879\) | −14.1634 | −0.477720 | ||||||||
\(880\) | −36.7743 | −1.23966 | ||||||||
\(881\) | 4.35498 | 0.146723 | 0.0733615 | − | 0.997305i | \(-0.476627\pi\) | ||||
0.0733615 | + | 0.997305i | \(0.476627\pi\) | |||||||
\(882\) | −0.0939328 | −0.00316288 | ||||||||
\(883\) | −9.97198 | −0.335584 | −0.167792 | − | 0.985822i | \(-0.553664\pi\) | ||||
−0.167792 | + | 0.985822i | \(0.553664\pi\) | |||||||
\(884\) | −24.9777 | −0.840092 | ||||||||
\(885\) | 56.2618 | 1.89122 | ||||||||
\(886\) | −5.13077 | −0.172372 | ||||||||
\(887\) | 34.5329 | 1.15950 | 0.579751 | − | 0.814794i | \(-0.303150\pi\) | ||||
0.579751 | + | 0.814794i | \(0.303150\pi\) | |||||||
\(888\) | 58.9871 | 1.97948 | ||||||||
\(889\) | −19.8673 | −0.666328 | ||||||||
\(890\) | −47.0932 | −1.57857 | ||||||||
\(891\) | 40.1007 | 1.34342 | ||||||||
\(892\) | 5.24901 | 0.175750 | ||||||||
\(893\) | −7.67754 | −0.256919 | ||||||||
\(894\) | −17.0001 | −0.568569 | ||||||||
\(895\) | 32.5847 | 1.08919 | ||||||||
\(896\) | −6.70853 | −0.224116 | ||||||||
\(897\) | −75.0669 | −2.50641 | ||||||||
\(898\) | −7.75281 | −0.258715 | ||||||||
\(899\) | −1.11966 | −0.0373427 | ||||||||
\(900\) | −0.155016 | −0.00516719 | ||||||||
\(901\) | −5.82470 | −0.194049 | ||||||||
\(902\) | 12.4073 | 0.413117 | ||||||||
\(903\) | −36.4665 | −1.21353 | ||||||||
\(904\) | −31.5903 | −1.05068 | ||||||||
\(905\) | 43.9883 | 1.46222 | ||||||||
\(906\) | −17.7796 | −0.590687 | ||||||||
\(907\) | −40.9405 | −1.35941 | −0.679703 | − | 0.733487i | \(-0.737891\pi\) | ||||
−0.679703 | + | 0.733487i | \(0.737891\pi\) | |||||||
\(908\) | −2.01064 | −0.0667253 | ||||||||
\(909\) | 0.0896386 | 0.00297312 | ||||||||
\(910\) | −91.0550 | −3.01844 | ||||||||
\(911\) | −3.82522 | −0.126735 | −0.0633676 | − | 0.997990i | \(-0.520184\pi\) | ||||
−0.0633676 | + | 0.997990i | \(0.520184\pi\) | |||||||
\(912\) | −9.52531 | −0.315415 | ||||||||
\(913\) | 64.6504 | 2.13962 | ||||||||
\(914\) | 20.8089 | 0.688296 | ||||||||
\(915\) | −97.9996 | −3.23977 | ||||||||
\(916\) | 13.4188 | 0.443371 | ||||||||
\(917\) | 8.10239 | 0.267565 | ||||||||
\(918\) | 34.5459 | 1.14018 | ||||||||
\(919\) | 7.29380 | 0.240600 | 0.120300 | − | 0.992738i | \(-0.461614\pi\) | ||||
0.120300 | + | 0.992738i | \(0.461614\pi\) | |||||||
\(920\) | 89.0803 | 2.93689 | ||||||||
\(921\) | 44.2048 | 1.45660 | ||||||||
\(922\) | 34.0860 | 1.12256 | ||||||||
\(923\) | −8.59051 | −0.282760 | ||||||||
\(924\) | −18.2954 | −0.601875 | ||||||||
\(925\) | −121.955 | −4.00984 | ||||||||
\(926\) | −30.8274 | −1.01305 | ||||||||
\(927\) | −0.272749 | −0.00895826 | ||||||||
\(928\) | 22.9530 | 0.753470 | ||||||||
\(929\) | 8.47518 | 0.278062 | 0.139031 | − | 0.990288i | \(-0.455601\pi\) | ||||
0.139031 | + | 0.990288i | \(0.455601\pi\) | |||||||
\(930\) | −1.46639 | −0.0480848 | ||||||||
\(931\) | −11.0921 | −0.363529 | ||||||||
\(932\) | −8.09935 | −0.265303 | ||||||||
\(933\) | 12.8526 | 0.420775 | ||||||||
\(934\) | −2.36236 | −0.0772988 | ||||||||
\(935\) | −104.215 | −3.40820 | ||||||||
\(936\) | −0.363057 | −0.0118669 | ||||||||
\(937\) | −24.0951 | −0.787152 | −0.393576 | − | 0.919292i | \(-0.628762\pi\) | ||||
−0.393576 | + | 0.919292i | \(0.628762\pi\) | |||||||
\(938\) | −30.9921 | −1.01193 | ||||||||
\(939\) | 20.1115 | 0.656315 | ||||||||
\(940\) | 8.27089 | 0.269767 | ||||||||
\(941\) | 41.4426 | 1.35099 | 0.675494 | − | 0.737365i | \(-0.263930\pi\) | ||||
0.675494 | + | 0.737365i | \(0.263930\pi\) | |||||||
\(942\) | −5.77240 | −0.188075 | ||||||||
\(943\) | −17.8285 | −0.580575 | ||||||||
\(944\) | −16.7493 | −0.545144 | ||||||||
\(945\) | −69.4384 | −2.25883 | ||||||||
\(946\) | 31.5236 | 1.02492 | ||||||||
\(947\) | 32.9840 | 1.07184 | 0.535919 | − | 0.844270i | \(-0.319965\pi\) | ||||
0.535919 | + | 0.844270i | \(0.319965\pi\) | |||||||
\(948\) | 17.9235 | 0.582127 | ||||||||
\(949\) | 14.3974 | 0.467360 | ||||||||
\(950\) | 33.1985 | 1.07710 | ||||||||
\(951\) | −26.3096 | −0.853149 | ||||||||
\(952\) | −60.5020 | −1.96088 | ||||||||
\(953\) | −18.1979 | −0.589488 | −0.294744 | − | 0.955576i | \(-0.595234\pi\) | ||||
−0.294744 | + | 0.955576i | \(0.595234\pi\) | |||||||
\(954\) | −0.0222003 | −0.000718761 0 | ||||||||
\(955\) | 22.2728 | 0.720732 | ||||||||
\(956\) | 4.70121 | 0.152048 | ||||||||
\(957\) | −46.4397 | −1.50118 | ||||||||
\(958\) | 2.56387 | 0.0828349 | ||||||||
\(959\) | 3.20482 | 0.103489 | ||||||||
\(960\) | 58.9329 | 1.90205 | ||||||||
\(961\) | −30.9656 | −0.998890 | ||||||||
\(962\) | −74.8963 | −2.41475 | ||||||||
\(963\) | 0.189032 | 0.00609148 | ||||||||
\(964\) | 19.1981 | 0.618331 | ||||||||
\(965\) | −52.7080 | −1.69673 | ||||||||
\(966\) | −47.6791 | −1.53405 | ||||||||
\(967\) | 33.2473 | 1.06916 | 0.534580 | − | 0.845118i | \(-0.320470\pi\) | ||||
0.534580 | + | 0.845118i | \(0.320470\pi\) | |||||||
\(968\) | 26.4575 | 0.850377 | ||||||||
\(969\) | −26.9939 | −0.867169 | ||||||||
\(970\) | 59.7495 | 1.91844 | ||||||||
\(971\) | 37.0654 | 1.18949 | 0.594743 | − | 0.803916i | \(-0.297254\pi\) | ||||
0.594743 | + | 0.803916i | \(0.297254\pi\) | |||||||
\(972\) | −0.145679 | −0.00467267 | ||||||||
\(973\) | 12.4164 | 0.398052 | ||||||||
\(974\) | −5.89704 | −0.188953 | ||||||||
\(975\) | 114.935 | 3.68088 | ||||||||
\(976\) | 29.1748 | 0.933862 | ||||||||
\(977\) | 13.9196 | 0.445328 | 0.222664 | − | 0.974895i | \(-0.428525\pi\) | ||||
0.222664 | + | 0.974895i | \(0.428525\pi\) | |||||||
\(978\) | −2.78045 | −0.0889091 | ||||||||
\(979\) | 45.8182 | 1.46435 | ||||||||
\(980\) | 11.9493 | 0.381708 | ||||||||
\(981\) | −0.134779 | −0.00430318 | ||||||||
\(982\) | −1.71368 | −0.0546857 | ||||||||
\(983\) | 1.00000 | 0.0318950 | ||||||||
\(984\) | −13.2032 | −0.420902 | ||||||||
\(985\) | −66.6496 | −2.12363 | ||||||||
\(986\) | −40.2698 | −1.28245 | ||||||||
\(987\) | −16.8825 | −0.537375 | ||||||||
\(988\) | −11.2418 | −0.357648 | ||||||||
\(989\) | −45.2976 | −1.44038 | ||||||||
\(990\) | −0.397206 | −0.0126240 | ||||||||
\(991\) | 2.58781 | 0.0822045 | 0.0411023 | − | 0.999155i | \(-0.486913\pi\) | ||||
0.0411023 | + | 0.999155i | \(0.486913\pi\) | |||||||
\(992\) | −0.705146 | −0.0223884 | ||||||||
\(993\) | −6.13802 | −0.194784 | ||||||||
\(994\) | −5.45630 | −0.173063 | ||||||||
\(995\) | −13.2590 | −0.420340 | ||||||||
\(996\) | −18.0400 | −0.571619 | ||||||||
\(997\) | 0.514953 | 0.0163087 | 0.00815436 | − | 0.999967i | \(-0.497404\pi\) | ||||
0.00815436 | + | 0.999967i | \(0.497404\pi\) | |||||||
\(998\) | −19.0152 | −0.601917 | ||||||||
\(999\) | −57.1159 | −1.80707 |
(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 | 983.2.a.b.1.17 | ✓ | 54 | |
3.2 | odd | 2 | 8847.2.a.g.1.38 | 54 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
983.2.a.b.1.17 | ✓ | 54 | 1.1 | even | 1 | trivial | |
8847.2.a.g.1.38 | 54 | 3.2 | odd | 2 |