Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2738,2,Mod(1,2738)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2738, 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("2738.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2738 = 2 \cdot 37^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2738.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: | \(21.8630400734\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | \(\Q(\zeta_{36})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 6x^{4} + 9x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 74) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-1.96962\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2738.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 1.53209 | 0.884552 | 0.442276 | − | 0.896879i | \(-0.354171\pi\) | ||||
0.442276 | + | 0.896879i | \(0.354171\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.384754 | 0.172067 | 0.0860337 | − | 0.996292i | \(-0.472581\pi\) | ||||
0.0860337 | + | 0.996292i | \(0.472581\pi\) | |||||||
\(6\) | 1.53209 | 0.625473 | ||||||||
\(7\) | −3.26414 | −1.23373 | −0.616864 | − | 0.787069i | \(-0.711597\pi\) | ||||
−0.616864 | + | 0.787069i | \(0.711597\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.652704 | −0.217568 | ||||||||
\(10\) | 0.384754 | 0.121670 | ||||||||
\(11\) | −2.58472 | −0.779321 | −0.389661 | − | 0.920959i | \(-0.627408\pi\) | ||||
−0.389661 | + | 0.920959i | \(0.627408\pi\) | |||||||
\(12\) | 1.53209 | 0.442276 | ||||||||
\(13\) | 1.36492 | 0.378561 | 0.189281 | − | 0.981923i | \(-0.439384\pi\) | ||||
0.189281 | + | 0.981923i | \(0.439384\pi\) | |||||||
\(14\) | −3.26414 | −0.872378 | ||||||||
\(15\) | 0.589478 | 0.152203 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.33213 | −0.808159 | −0.404080 | − | 0.914724i | \(-0.632408\pi\) | ||||
−0.404080 | + | 0.914724i | \(0.632408\pi\) | |||||||
\(18\) | −0.652704 | −0.153844 | ||||||||
\(19\) | −5.98578 | −1.37323 | −0.686616 | − | 0.727020i | \(-0.740905\pi\) | ||||
−0.686616 | + | 0.727020i | \(0.740905\pi\) | |||||||
\(20\) | 0.384754 | 0.0860337 | ||||||||
\(21\) | −5.00095 | −1.09130 | ||||||||
\(22\) | −2.58472 | −0.551063 | ||||||||
\(23\) | −7.54605 | −1.57346 | −0.786730 | − | 0.617297i | \(-0.788228\pi\) | ||||
−0.786730 | + | 0.617297i | \(0.788228\pi\) | |||||||
\(24\) | 1.53209 | 0.312736 | ||||||||
\(25\) | −4.85196 | −0.970393 | ||||||||
\(26\) | 1.36492 | 0.267683 | ||||||||
\(27\) | −5.59627 | −1.07700 | ||||||||
\(28\) | −3.26414 | −0.616864 | ||||||||
\(29\) | −3.21297 | −0.596634 | −0.298317 | − | 0.954467i | \(-0.596425\pi\) | ||||
−0.298317 | + | 0.954467i | \(0.596425\pi\) | |||||||
\(30\) | 0.589478 | 0.107623 | ||||||||
\(31\) | 2.53737 | 0.455726 | 0.227863 | − | 0.973693i | \(-0.426826\pi\) | ||||
0.227863 | + | 0.973693i | \(0.426826\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −3.96002 | −0.689350 | ||||||||
\(34\) | −3.33213 | −0.571455 | ||||||||
\(35\) | −1.25589 | −0.212285 | ||||||||
\(36\) | −0.652704 | −0.108784 | ||||||||
\(37\) | 0 | 0 | ||||||||
\(38\) | −5.98578 | −0.971022 | ||||||||
\(39\) | 2.09118 | 0.334857 | ||||||||
\(40\) | 0.384754 | 0.0608350 | ||||||||
\(41\) | 8.26915 | 1.29142 | 0.645712 | − | 0.763581i | \(-0.276561\pi\) | ||||
0.645712 | + | 0.763581i | \(0.276561\pi\) | |||||||
\(42\) | −5.00095 | −0.771664 | ||||||||
\(43\) | 4.33920 | 0.661722 | 0.330861 | − | 0.943680i | \(-0.392661\pi\) | ||||
0.330861 | + | 0.943680i | \(0.392661\pi\) | |||||||
\(44\) | −2.58472 | −0.389661 | ||||||||
\(45\) | −0.251131 | −0.0374363 | ||||||||
\(46\) | −7.54605 | −1.11260 | ||||||||
\(47\) | 5.22909 | 0.762742 | 0.381371 | − | 0.924422i | \(-0.375452\pi\) | ||||
0.381371 | + | 0.924422i | \(0.375452\pi\) | |||||||
\(48\) | 1.53209 | 0.221138 | ||||||||
\(49\) | 3.65461 | 0.522087 | ||||||||
\(50\) | −4.85196 | −0.686171 | ||||||||
\(51\) | −5.10511 | −0.714859 | ||||||||
\(52\) | 1.36492 | 0.189281 | ||||||||
\(53\) | −8.67122 | −1.19108 | −0.595542 | − | 0.803324i | \(-0.703063\pi\) | ||||
−0.595542 | + | 0.803324i | \(0.703063\pi\) | |||||||
\(54\) | −5.59627 | −0.761555 | ||||||||
\(55\) | −0.994481 | −0.134096 | ||||||||
\(56\) | −3.26414 | −0.436189 | ||||||||
\(57\) | −9.17075 | −1.21470 | ||||||||
\(58\) | −3.21297 | −0.421884 | ||||||||
\(59\) | 12.9674 | 1.68821 | 0.844107 | − | 0.536174i | \(-0.180131\pi\) | ||||
0.844107 | + | 0.536174i | \(0.180131\pi\) | |||||||
\(60\) | 0.589478 | 0.0761013 | ||||||||
\(61\) | −7.01264 | −0.897877 | −0.448938 | − | 0.893563i | \(-0.648198\pi\) | ||||
−0.448938 | + | 0.893563i | \(0.648198\pi\) | |||||||
\(62\) | 2.53737 | 0.322247 | ||||||||
\(63\) | 2.13052 | 0.268420 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.525160 | 0.0651381 | ||||||||
\(66\) | −3.96002 | −0.487444 | ||||||||
\(67\) | 11.2380 | 1.37294 | 0.686470 | − | 0.727158i | \(-0.259159\pi\) | ||||
0.686470 | + | 0.727158i | \(0.259159\pi\) | |||||||
\(68\) | −3.33213 | −0.404080 | ||||||||
\(69\) | −11.5612 | −1.39181 | ||||||||
\(70\) | −1.25589 | −0.150108 | ||||||||
\(71\) | 14.9995 | 1.78012 | 0.890059 | − | 0.455845i | \(-0.150663\pi\) | ||||
0.890059 | + | 0.455845i | \(0.150663\pi\) | |||||||
\(72\) | −0.652704 | −0.0769219 | ||||||||
\(73\) | 15.0792 | 1.76489 | 0.882445 | − | 0.470416i | \(-0.155896\pi\) | ||||
0.882445 | + | 0.470416i | \(0.155896\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −7.43364 | −0.858363 | ||||||||
\(76\) | −5.98578 | −0.686616 | ||||||||
\(77\) | 8.43688 | 0.961471 | ||||||||
\(78\) | 2.09118 | 0.236780 | ||||||||
\(79\) | −1.46329 | −0.164633 | −0.0823167 | − | 0.996606i | \(-0.526232\pi\) | ||||
−0.0823167 | + | 0.996606i | \(0.526232\pi\) | |||||||
\(80\) | 0.384754 | 0.0430169 | ||||||||
\(81\) | −6.61587 | −0.735096 | ||||||||
\(82\) | 8.26915 | 0.913175 | ||||||||
\(83\) | −0.0111178 | −0.00122034 | −0.000610170 | − | 1.00000i | \(-0.500194\pi\) | ||||
−0.000610170 | 1.00000i | \(0.500194\pi\) | ||||||||
\(84\) | −5.00095 | −0.545649 | ||||||||
\(85\) | −1.28205 | −0.139058 | ||||||||
\(86\) | 4.33920 | 0.467908 | ||||||||
\(87\) | −4.92256 | −0.527754 | ||||||||
\(88\) | −2.58472 | −0.275532 | ||||||||
\(89\) | 0.953262 | 0.101046 | 0.0505228 | − | 0.998723i | \(-0.483911\pi\) | ||||
0.0505228 | + | 0.998723i | \(0.483911\pi\) | |||||||
\(90\) | −0.251131 | −0.0264715 | ||||||||
\(91\) | −4.45530 | −0.467042 | ||||||||
\(92\) | −7.54605 | −0.786730 | ||||||||
\(93\) | 3.88748 | 0.403113 | ||||||||
\(94\) | 5.22909 | 0.539340 | ||||||||
\(95\) | −2.30306 | −0.236289 | ||||||||
\(96\) | 1.53209 | 0.156368 | ||||||||
\(97\) | −14.8185 | −1.50459 | −0.752297 | − | 0.658824i | \(-0.771054\pi\) | ||||
−0.752297 | + | 0.658824i | \(0.771054\pi\) | |||||||
\(98\) | 3.65461 | 0.369171 | ||||||||
\(99\) | 1.68705 | 0.169555 | ||||||||
\(100\) | −4.85196 | −0.485196 | ||||||||
\(101\) | −1.27252 | −0.126621 | −0.0633103 | − | 0.997994i | \(-0.520166\pi\) | ||||
−0.0633103 | + | 0.997994i | \(0.520166\pi\) | |||||||
\(102\) | −5.10511 | −0.505482 | ||||||||
\(103\) | −10.8461 | −1.06870 | −0.534350 | − | 0.845264i | \(-0.679443\pi\) | ||||
−0.534350 | + | 0.845264i | \(0.679443\pi\) | |||||||
\(104\) | 1.36492 | 0.133842 | ||||||||
\(105\) | −1.92414 | −0.187777 | ||||||||
\(106\) | −8.67122 | −0.842224 | ||||||||
\(107\) | −4.75958 | −0.460126 | −0.230063 | − | 0.973176i | \(-0.573893\pi\) | ||||
−0.230063 | + | 0.973176i | \(0.573893\pi\) | |||||||
\(108\) | −5.59627 | −0.538501 | ||||||||
\(109\) | −9.63744 | −0.923099 | −0.461550 | − | 0.887114i | \(-0.652706\pi\) | ||||
−0.461550 | + | 0.887114i | \(0.652706\pi\) | |||||||
\(110\) | −0.994481 | −0.0948201 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.26414 | −0.308432 | ||||||||
\(113\) | −12.9549 | −1.21870 | −0.609348 | − | 0.792903i | \(-0.708569\pi\) | ||||
−0.609348 | + | 0.792903i | \(0.708569\pi\) | |||||||
\(114\) | −9.17075 | −0.858920 | ||||||||
\(115\) | −2.90338 | −0.270741 | ||||||||
\(116\) | −3.21297 | −0.298317 | ||||||||
\(117\) | −0.890890 | −0.0823628 | ||||||||
\(118\) | 12.9674 | 1.19375 | ||||||||
\(119\) | 10.8765 | 0.997050 | ||||||||
\(120\) | 0.589478 | 0.0538117 | ||||||||
\(121\) | −4.31924 | −0.392658 | ||||||||
\(122\) | −7.01264 | −0.634895 | ||||||||
\(123\) | 12.6691 | 1.14233 | ||||||||
\(124\) | 2.53737 | 0.227863 | ||||||||
\(125\) | −3.79059 | −0.339040 | ||||||||
\(126\) | 2.13052 | 0.189801 | ||||||||
\(127\) | 11.2408 | 0.997458 | 0.498729 | − | 0.866758i | \(-0.333800\pi\) | ||||
0.498729 | + | 0.866758i | \(0.333800\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 6.64804 | 0.585327 | ||||||||
\(130\) | 0.525160 | 0.0460596 | ||||||||
\(131\) | −8.36959 | −0.731254 | −0.365627 | − | 0.930761i | \(-0.619145\pi\) | ||||
−0.365627 | + | 0.930761i | \(0.619145\pi\) | |||||||
\(132\) | −3.96002 | −0.344675 | ||||||||
\(133\) | 19.5384 | 1.69420 | ||||||||
\(134\) | 11.2380 | 0.970815 | ||||||||
\(135\) | −2.15319 | −0.185317 | ||||||||
\(136\) | −3.33213 | −0.285728 | ||||||||
\(137\) | −3.98413 | −0.340387 | −0.170194 | − | 0.985411i | \(-0.554439\pi\) | ||||
−0.170194 | + | 0.985411i | \(0.554439\pi\) | |||||||
\(138\) | −11.5612 | −0.984156 | ||||||||
\(139\) | −5.11140 | −0.433543 | −0.216772 | − | 0.976222i | \(-0.569553\pi\) | ||||
−0.216772 | + | 0.976222i | \(0.569553\pi\) | |||||||
\(140\) | −1.25589 | −0.106142 | ||||||||
\(141\) | 8.01143 | 0.674684 | ||||||||
\(142\) | 14.9995 | 1.25873 | ||||||||
\(143\) | −3.52794 | −0.295021 | ||||||||
\(144\) | −0.652704 | −0.0543920 | ||||||||
\(145\) | −1.23620 | −0.102661 | ||||||||
\(146\) | 15.0792 | 1.24797 | ||||||||
\(147\) | 5.59918 | 0.461813 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.8700 | −1.30012 | −0.650060 | − | 0.759883i | \(-0.725256\pi\) | ||||
−0.650060 | + | 0.759883i | \(0.725256\pi\) | |||||||
\(150\) | −7.43364 | −0.606954 | ||||||||
\(151\) | 21.7680 | 1.77146 | 0.885729 | − | 0.464202i | \(-0.153659\pi\) | ||||
0.885729 | + | 0.464202i | \(0.153659\pi\) | |||||||
\(152\) | −5.98578 | −0.485511 | ||||||||
\(153\) | 2.17489 | 0.175830 | ||||||||
\(154\) | 8.43688 | 0.679863 | ||||||||
\(155\) | 0.976266 | 0.0784155 | ||||||||
\(156\) | 2.09118 | 0.167429 | ||||||||
\(157\) | −9.75142 | −0.778248 | −0.389124 | − | 0.921185i | \(-0.627222\pi\) | ||||
−0.389124 | + | 0.921185i | \(0.627222\pi\) | |||||||
\(158\) | −1.46329 | −0.116413 | ||||||||
\(159\) | −13.2851 | −1.05358 | ||||||||
\(160\) | 0.384754 | 0.0304175 | ||||||||
\(161\) | 24.6314 | 1.94122 | ||||||||
\(162\) | −6.61587 | −0.519792 | ||||||||
\(163\) | −13.1647 | −1.03114 | −0.515571 | − | 0.856847i | \(-0.672420\pi\) | ||||
−0.515571 | + | 0.856847i | \(0.672420\pi\) | |||||||
\(164\) | 8.26915 | 0.645712 | ||||||||
\(165\) | −1.52363 | −0.118615 | ||||||||
\(166\) | −0.0111178 | −0.000862910 0 | ||||||||
\(167\) | 5.60228 | 0.433518 | 0.216759 | − | 0.976225i | \(-0.430451\pi\) | ||||
0.216759 | + | 0.976225i | \(0.430451\pi\) | |||||||
\(168\) | −5.00095 | −0.385832 | ||||||||
\(169\) | −11.1370 | −0.856691 | ||||||||
\(170\) | −1.28205 | −0.0983288 | ||||||||
\(171\) | 3.90694 | 0.298771 | ||||||||
\(172\) | 4.33920 | 0.330861 | ||||||||
\(173\) | 10.8354 | 0.823800 | 0.411900 | − | 0.911229i | \(-0.364865\pi\) | ||||
0.411900 | + | 0.911229i | \(0.364865\pi\) | |||||||
\(174\) | −4.92256 | −0.373178 | ||||||||
\(175\) | 15.8375 | 1.19720 | ||||||||
\(176\) | −2.58472 | −0.194830 | ||||||||
\(177\) | 19.8672 | 1.49331 | ||||||||
\(178\) | 0.953262 | 0.0714500 | ||||||||
\(179\) | −6.07192 | −0.453837 | −0.226918 | − | 0.973914i | \(-0.572865\pi\) | ||||
−0.226918 | + | 0.973914i | \(0.572865\pi\) | |||||||
\(180\) | −0.251131 | −0.0187182 | ||||||||
\(181\) | 21.5538 | 1.60208 | 0.801042 | − | 0.598608i | \(-0.204279\pi\) | ||||
0.801042 | + | 0.598608i | \(0.204279\pi\) | |||||||
\(182\) | −4.45530 | −0.330249 | ||||||||
\(183\) | −10.7440 | −0.794219 | ||||||||
\(184\) | −7.54605 | −0.556302 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 3.88748 | 0.285044 | ||||||||
\(187\) | 8.61260 | 0.629816 | ||||||||
\(188\) | 5.22909 | 0.381371 | ||||||||
\(189\) | 18.2670 | 1.32873 | ||||||||
\(190\) | −2.30306 | −0.167081 | ||||||||
\(191\) | 6.62693 | 0.479508 | 0.239754 | − | 0.970834i | \(-0.422933\pi\) | ||||
0.239754 | + | 0.970834i | \(0.422933\pi\) | |||||||
\(192\) | 1.53209 | 0.110569 | ||||||||
\(193\) | −22.8544 | −1.64510 | −0.822548 | − | 0.568696i | \(-0.807448\pi\) | ||||
−0.822548 | + | 0.568696i | \(0.807448\pi\) | |||||||
\(194\) | −14.8185 | −1.06391 | ||||||||
\(195\) | 0.804592 | 0.0576180 | ||||||||
\(196\) | 3.65461 | 0.261043 | ||||||||
\(197\) | −14.7561 | −1.05133 | −0.525663 | − | 0.850693i | \(-0.676183\pi\) | ||||
−0.525663 | + | 0.850693i | \(0.676183\pi\) | |||||||
\(198\) | 1.68705 | 0.119894 | ||||||||
\(199\) | −1.47478 | −0.104544 | −0.0522721 | − | 0.998633i | \(-0.516646\pi\) | ||||
−0.0522721 | + | 0.998633i | \(0.516646\pi\) | |||||||
\(200\) | −4.85196 | −0.343086 | ||||||||
\(201\) | 17.2176 | 1.21444 | ||||||||
\(202\) | −1.27252 | −0.0895342 | ||||||||
\(203\) | 10.4876 | 0.736084 | ||||||||
\(204\) | −5.10511 | −0.357430 | ||||||||
\(205\) | 3.18159 | 0.222212 | ||||||||
\(206\) | −10.8461 | −0.755685 | ||||||||
\(207\) | 4.92533 | 0.342334 | ||||||||
\(208\) | 1.36492 | 0.0946403 | ||||||||
\(209\) | 15.4716 | 1.07019 | ||||||||
\(210\) | −1.92414 | −0.132778 | ||||||||
\(211\) | −2.41952 | −0.166567 | −0.0832835 | − | 0.996526i | \(-0.526541\pi\) | ||||
−0.0832835 | + | 0.996526i | \(0.526541\pi\) | |||||||
\(212\) | −8.67122 | −0.595542 | ||||||||
\(213\) | 22.9806 | 1.57461 | ||||||||
\(214\) | −4.75958 | −0.325358 | ||||||||
\(215\) | 1.66953 | 0.113861 | ||||||||
\(216\) | −5.59627 | −0.380778 | ||||||||
\(217\) | −8.28234 | −0.562242 | ||||||||
\(218\) | −9.63744 | −0.652730 | ||||||||
\(219\) | 23.1027 | 1.56114 | ||||||||
\(220\) | −0.994481 | −0.0670479 | ||||||||
\(221\) | −4.54809 | −0.305938 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.94726 | −0.465223 | −0.232611 | − | 0.972570i | \(-0.574727\pi\) | ||||
−0.232611 | + | 0.972570i | \(0.574727\pi\) | |||||||
\(224\) | −3.26414 | −0.218095 | ||||||||
\(225\) | 3.16689 | 0.211126 | ||||||||
\(226\) | −12.9549 | −0.861749 | ||||||||
\(227\) | 21.8490 | 1.45017 | 0.725084 | − | 0.688660i | \(-0.241801\pi\) | ||||
0.725084 | + | 0.688660i | \(0.241801\pi\) | |||||||
\(228\) | −9.17075 | −0.607348 | ||||||||
\(229\) | −4.25010 | −0.280854 | −0.140427 | − | 0.990091i | \(-0.544848\pi\) | ||||
−0.140427 | + | 0.990091i | \(0.544848\pi\) | |||||||
\(230\) | −2.90338 | −0.191443 | ||||||||
\(231\) | 12.9260 | 0.850471 | ||||||||
\(232\) | −3.21297 | −0.210942 | ||||||||
\(233\) | −17.3443 | −1.13626 | −0.568131 | − | 0.822938i | \(-0.692333\pi\) | ||||
−0.568131 | + | 0.822938i | \(0.692333\pi\) | |||||||
\(234\) | −0.890890 | −0.0582393 | ||||||||
\(235\) | 2.01192 | 0.131243 | ||||||||
\(236\) | 12.9674 | 0.844107 | ||||||||
\(237\) | −2.24190 | −0.145627 | ||||||||
\(238\) | 10.8765 | 0.705021 | ||||||||
\(239\) | −18.3584 | −1.18750 | −0.593752 | − | 0.804648i | \(-0.702354\pi\) | ||||
−0.593752 | + | 0.804648i | \(0.702354\pi\) | |||||||
\(240\) | 0.589478 | 0.0380506 | ||||||||
\(241\) | 23.4661 | 1.51158 | 0.755792 | − | 0.654811i | \(-0.227252\pi\) | ||||
0.755792 | + | 0.654811i | \(0.227252\pi\) | |||||||
\(242\) | −4.31924 | −0.277651 | ||||||||
\(243\) | 6.65270 | 0.426771 | ||||||||
\(244\) | −7.01264 | −0.448938 | ||||||||
\(245\) | 1.40613 | 0.0898341 | ||||||||
\(246\) | 12.6691 | 0.807751 | ||||||||
\(247\) | −8.17013 | −0.519853 | ||||||||
\(248\) | 2.53737 | 0.161123 | ||||||||
\(249\) | −0.0170335 | −0.00107945 | ||||||||
\(250\) | −3.79059 | −0.239738 | ||||||||
\(251\) | −6.10149 | −0.385123 | −0.192561 | − | 0.981285i | \(-0.561679\pi\) | ||||
−0.192561 | + | 0.981285i | \(0.561679\pi\) | |||||||
\(252\) | 2.13052 | 0.134210 | ||||||||
\(253\) | 19.5044 | 1.22623 | ||||||||
\(254\) | 11.2408 | 0.705309 | ||||||||
\(255\) | −1.96422 | −0.123004 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −4.34710 | −0.271165 | −0.135582 | − | 0.990766i | \(-0.543291\pi\) | ||||
−0.135582 | + | 0.990766i | \(0.543291\pi\) | |||||||
\(258\) | 6.64804 | 0.413889 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0.525160 | 0.0325690 | ||||||||
\(261\) | 2.09712 | 0.129808 | ||||||||
\(262\) | −8.36959 | −0.517075 | ||||||||
\(263\) | 4.05485 | 0.250033 | 0.125016 | − | 0.992155i | \(-0.460102\pi\) | ||||
0.125016 | + | 0.992155i | \(0.460102\pi\) | |||||||
\(264\) | −3.96002 | −0.243722 | ||||||||
\(265\) | −3.33629 | −0.204947 | ||||||||
\(266\) | 19.5384 | 1.19798 | ||||||||
\(267\) | 1.46048 | 0.0893801 | ||||||||
\(268\) | 11.2380 | 0.686470 | ||||||||
\(269\) | 8.79337 | 0.536141 | 0.268071 | − | 0.963399i | \(-0.413614\pi\) | ||||
0.268071 | + | 0.963399i | \(0.413614\pi\) | |||||||
\(270\) | −2.15319 | −0.131039 | ||||||||
\(271\) | −12.9122 | −0.784361 | −0.392180 | − | 0.919888i | \(-0.628279\pi\) | ||||
−0.392180 | + | 0.919888i | \(0.628279\pi\) | |||||||
\(272\) | −3.33213 | −0.202040 | ||||||||
\(273\) | −6.82591 | −0.413123 | ||||||||
\(274\) | −3.98413 | −0.240690 | ||||||||
\(275\) | 12.5410 | 0.756248 | ||||||||
\(276\) | −11.5612 | −0.695904 | ||||||||
\(277\) | −7.77643 | −0.467240 | −0.233620 | − | 0.972328i | \(-0.575057\pi\) | ||||
−0.233620 | + | 0.972328i | \(0.575057\pi\) | |||||||
\(278\) | −5.11140 | −0.306561 | ||||||||
\(279\) | −1.65615 | −0.0991513 | ||||||||
\(280\) | −1.25589 | −0.0750539 | ||||||||
\(281\) | 0.232510 | 0.0138704 | 0.00693518 | − | 0.999976i | \(-0.497792\pi\) | ||||
0.00693518 | + | 0.999976i | \(0.497792\pi\) | |||||||
\(282\) | 8.01143 | 0.477074 | ||||||||
\(283\) | −12.8330 | −0.762843 | −0.381421 | − | 0.924401i | \(-0.624565\pi\) | ||||
−0.381421 | + | 0.924401i | \(0.624565\pi\) | |||||||
\(284\) | 14.9995 | 0.890059 | ||||||||
\(285\) | −3.52849 | −0.209010 | ||||||||
\(286\) | −3.52794 | −0.208611 | ||||||||
\(287\) | −26.9917 | −1.59327 | ||||||||
\(288\) | −0.652704 | −0.0384609 | ||||||||
\(289\) | −5.89693 | −0.346878 | ||||||||
\(290\) | −1.23620 | −0.0725925 | ||||||||
\(291\) | −22.7033 | −1.33089 | ||||||||
\(292\) | 15.0792 | 0.882445 | ||||||||
\(293\) | −24.6443 | −1.43974 | −0.719868 | − | 0.694111i | \(-0.755797\pi\) | ||||
−0.719868 | + | 0.694111i | \(0.755797\pi\) | |||||||
\(294\) | 5.59918 | 0.326551 | ||||||||
\(295\) | 4.98927 | 0.290487 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 14.4648 | 0.839331 | ||||||||
\(298\) | −15.8700 | −0.919324 | ||||||||
\(299\) | −10.2998 | −0.595651 | ||||||||
\(300\) | −7.43364 | −0.429181 | ||||||||
\(301\) | −14.1638 | −0.816385 | ||||||||
\(302\) | 21.7680 | 1.25261 | ||||||||
\(303\) | −1.94961 | −0.112002 | ||||||||
\(304\) | −5.98578 | −0.343308 | ||||||||
\(305\) | −2.69815 | −0.154495 | ||||||||
\(306\) | 2.17489 | 0.124330 | ||||||||
\(307\) | −6.91132 | −0.394450 | −0.197225 | − | 0.980358i | \(-0.563193\pi\) | ||||
−0.197225 | + | 0.980358i | \(0.563193\pi\) | |||||||
\(308\) | 8.43688 | 0.480736 | ||||||||
\(309\) | −16.6172 | −0.945320 | ||||||||
\(310\) | 0.976266 | 0.0554482 | ||||||||
\(311\) | −1.65859 | −0.0940501 | −0.0470251 | − | 0.998894i | \(-0.514974\pi\) | ||||
−0.0470251 | + | 0.998894i | \(0.514974\pi\) | |||||||
\(312\) | 2.09118 | 0.118390 | ||||||||
\(313\) | 25.9509 | 1.46683 | 0.733416 | − | 0.679780i | \(-0.237925\pi\) | ||||
0.733416 | + | 0.679780i | \(0.237925\pi\) | |||||||
\(314\) | −9.75142 | −0.550304 | ||||||||
\(315\) | 0.819725 | 0.0461863 | ||||||||
\(316\) | −1.46329 | −0.0823167 | ||||||||
\(317\) | 11.3498 | 0.637470 | 0.318735 | − | 0.947844i | \(-0.396742\pi\) | ||||
0.318735 | + | 0.947844i | \(0.396742\pi\) | |||||||
\(318\) | −13.2851 | −0.744991 | ||||||||
\(319\) | 8.30462 | 0.464969 | ||||||||
\(320\) | 0.384754 | 0.0215084 | ||||||||
\(321\) | −7.29210 | −0.407006 | ||||||||
\(322\) | 24.6314 | 1.37265 | ||||||||
\(323\) | 19.9454 | 1.10979 | ||||||||
\(324\) | −6.61587 | −0.367548 | ||||||||
\(325\) | −6.62255 | −0.367353 | ||||||||
\(326\) | −13.1647 | −0.729127 | ||||||||
\(327\) | −14.7654 | −0.816529 | ||||||||
\(328\) | 8.26915 | 0.456588 | ||||||||
\(329\) | −17.0685 | −0.941016 | ||||||||
\(330\) | −1.52363 | −0.0838733 | ||||||||
\(331\) | 12.8377 | 0.705623 | 0.352811 | − | 0.935694i | \(-0.385226\pi\) | ||||
0.352811 | + | 0.935694i | \(0.385226\pi\) | |||||||
\(332\) | −0.0111178 | −0.000610170 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 5.60228 | 0.306543 | ||||||||
\(335\) | 4.32387 | 0.236238 | ||||||||
\(336\) | −5.00095 | −0.272824 | ||||||||
\(337\) | −5.71183 | −0.311143 | −0.155572 | − | 0.987825i | \(-0.549722\pi\) | ||||
−0.155572 | + | 0.987825i | \(0.549722\pi\) | |||||||
\(338\) | −11.1370 | −0.605772 | ||||||||
\(339\) | −19.8481 | −1.07800 | ||||||||
\(340\) | −1.28205 | −0.0695290 | ||||||||
\(341\) | −6.55839 | −0.355157 | ||||||||
\(342\) | 3.90694 | 0.211263 | ||||||||
\(343\) | 10.9198 | 0.589615 | ||||||||
\(344\) | 4.33920 | 0.233954 | ||||||||
\(345\) | −4.44823 | −0.239485 | ||||||||
\(346\) | 10.8354 | 0.582515 | ||||||||
\(347\) | 32.3416 | 1.73619 | 0.868095 | − | 0.496398i | \(-0.165344\pi\) | ||||
0.868095 | + | 0.496398i | \(0.165344\pi\) | |||||||
\(348\) | −4.92256 | −0.263877 | ||||||||
\(349\) | −24.9320 | −1.33458 | −0.667290 | − | 0.744798i | \(-0.732546\pi\) | ||||
−0.667290 | + | 0.744798i | \(0.732546\pi\) | |||||||
\(350\) | 15.8375 | 0.846549 | ||||||||
\(351\) | −7.63847 | −0.407711 | ||||||||
\(352\) | −2.58472 | −0.137766 | ||||||||
\(353\) | −8.64114 | −0.459921 | −0.229961 | − | 0.973200i | \(-0.573860\pi\) | ||||
−0.229961 | + | 0.973200i | \(0.573860\pi\) | |||||||
\(354\) | 19.8672 | 1.05593 | ||||||||
\(355\) | 5.77114 | 0.306300 | ||||||||
\(356\) | 0.953262 | 0.0505228 | ||||||||
\(357\) | 16.6638 | 0.881942 | ||||||||
\(358\) | −6.07192 | −0.320911 | ||||||||
\(359\) | 3.85848 | 0.203643 | 0.101821 | − | 0.994803i | \(-0.467533\pi\) | ||||
0.101821 | + | 0.994803i | \(0.467533\pi\) | |||||||
\(360\) | −0.251131 | −0.0132357 | ||||||||
\(361\) | 16.8296 | 0.885768 | ||||||||
\(362\) | 21.5538 | 1.13284 | ||||||||
\(363\) | −6.61746 | −0.347327 | ||||||||
\(364\) | −4.45530 | −0.233521 | ||||||||
\(365\) | 5.80180 | 0.303680 | ||||||||
\(366\) | −10.7440 | −0.561597 | ||||||||
\(367\) | 10.4563 | 0.545813 | 0.272906 | − | 0.962041i | \(-0.412015\pi\) | ||||
0.272906 | + | 0.962041i | \(0.412015\pi\) | |||||||
\(368\) | −7.54605 | −0.393365 | ||||||||
\(369\) | −5.39731 | −0.280973 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 28.3041 | 1.46947 | ||||||||
\(372\) | 3.88748 | 0.201557 | ||||||||
\(373\) | −9.86566 | −0.510825 | −0.255412 | − | 0.966832i | \(-0.582211\pi\) | ||||
−0.255412 | + | 0.966832i | \(0.582211\pi\) | |||||||
\(374\) | 8.61260 | 0.445347 | ||||||||
\(375\) | −5.80752 | −0.299899 | ||||||||
\(376\) | 5.22909 | 0.269670 | ||||||||
\(377\) | −4.38546 | −0.225862 | ||||||||
\(378\) | 18.2670 | 0.939553 | ||||||||
\(379\) | 2.48121 | 0.127451 | 0.0637255 | − | 0.997967i | \(-0.479702\pi\) | ||||
0.0637255 | + | 0.997967i | \(0.479702\pi\) | |||||||
\(380\) | −2.30306 | −0.118144 | ||||||||
\(381\) | 17.2219 | 0.882303 | ||||||||
\(382\) | 6.62693 | 0.339063 | ||||||||
\(383\) | −25.5639 | −1.30625 | −0.653127 | − | 0.757249i | \(-0.726543\pi\) | ||||
−0.653127 | + | 0.757249i | \(0.726543\pi\) | |||||||
\(384\) | 1.53209 | 0.0781841 | ||||||||
\(385\) | 3.24613 | 0.165438 | ||||||||
\(386\) | −22.8544 | −1.16326 | ||||||||
\(387\) | −2.83221 | −0.143969 | ||||||||
\(388\) | −14.8185 | −0.752297 | ||||||||
\(389\) | −6.37509 | −0.323230 | −0.161615 | − | 0.986854i | \(-0.551670\pi\) | ||||
−0.161615 | + | 0.986854i | \(0.551670\pi\) | |||||||
\(390\) | 0.804592 | 0.0407421 | ||||||||
\(391\) | 25.1444 | 1.27161 | ||||||||
\(392\) | 3.65461 | 0.184586 | ||||||||
\(393\) | −12.8229 | −0.646832 | ||||||||
\(394\) | −14.7561 | −0.743400 | ||||||||
\(395\) | −0.563009 | −0.0283281 | ||||||||
\(396\) | 1.68705 | 0.0847776 | ||||||||
\(397\) | 37.4977 | 1.88196 | 0.940979 | − | 0.338465i | \(-0.109908\pi\) | ||||
0.940979 | + | 0.338465i | \(0.109908\pi\) | |||||||
\(398\) | −1.47478 | −0.0739240 | ||||||||
\(399\) | 29.9346 | 1.49861 | ||||||||
\(400\) | −4.85196 | −0.242598 | ||||||||
\(401\) | −35.1464 | −1.75513 | −0.877563 | − | 0.479462i | \(-0.840832\pi\) | ||||
−0.877563 | + | 0.479462i | \(0.840832\pi\) | |||||||
\(402\) | 17.2176 | 0.858737 | ||||||||
\(403\) | 3.46332 | 0.172520 | ||||||||
\(404\) | −1.27252 | −0.0633103 | ||||||||
\(405\) | −2.54548 | −0.126486 | ||||||||
\(406\) | 10.4876 | 0.520490 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −5.10511 | −0.252741 | ||||||||
\(409\) | 0.450741 | 0.0222877 | 0.0111439 | − | 0.999938i | \(-0.496453\pi\) | ||||
0.0111439 | + | 0.999938i | \(0.496453\pi\) | |||||||
\(410\) | 3.18159 | 0.157128 | ||||||||
\(411\) | −6.10404 | −0.301090 | ||||||||
\(412\) | −10.8461 | −0.534350 | ||||||||
\(413\) | −42.3275 | −2.08280 | ||||||||
\(414\) | 4.92533 | 0.242067 | ||||||||
\(415\) | −0.00427763 | −0.000209981 0 | ||||||||
\(416\) | 1.36492 | 0.0669208 | ||||||||
\(417\) | −7.83112 | −0.383492 | ||||||||
\(418\) | 15.4716 | 0.756738 | ||||||||
\(419\) | −15.3113 | −0.748006 | −0.374003 | − | 0.927428i | \(-0.622015\pi\) | ||||
−0.374003 | + | 0.927428i | \(0.622015\pi\) | |||||||
\(420\) | −1.92414 | −0.0938884 | ||||||||
\(421\) | −22.3965 | −1.09154 | −0.545769 | − | 0.837936i | \(-0.683762\pi\) | ||||
−0.545769 | + | 0.837936i | \(0.683762\pi\) | |||||||
\(422\) | −2.41952 | −0.117781 | ||||||||
\(423\) | −3.41305 | −0.165948 | ||||||||
\(424\) | −8.67122 | −0.421112 | ||||||||
\(425\) | 16.1674 | 0.784232 | ||||||||
\(426\) | 22.9806 | 1.11342 | ||||||||
\(427\) | 22.8902 | 1.10774 | ||||||||
\(428\) | −4.75958 | −0.230063 | ||||||||
\(429\) | −5.40511 | −0.260961 | ||||||||
\(430\) | 1.66953 | 0.0805117 | ||||||||
\(431\) | −0.102080 | −0.00491701 | −0.00245851 | − | 0.999997i | \(-0.500783\pi\) | ||||
−0.00245851 | + | 0.999997i | \(0.500783\pi\) | |||||||
\(432\) | −5.59627 | −0.269251 | ||||||||
\(433\) | 7.92714 | 0.380954 | 0.190477 | − | 0.981692i | \(-0.438997\pi\) | ||||
0.190477 | + | 0.981692i | \(0.438997\pi\) | |||||||
\(434\) | −8.28234 | −0.397565 | ||||||||
\(435\) | −1.89398 | −0.0908092 | ||||||||
\(436\) | −9.63744 | −0.461550 | ||||||||
\(437\) | 45.1690 | 2.16073 | ||||||||
\(438\) | 23.1027 | 1.10389 | ||||||||
\(439\) | 7.57063 | 0.361326 | 0.180663 | − | 0.983545i | \(-0.442176\pi\) | ||||
0.180663 | + | 0.983545i | \(0.442176\pi\) | |||||||
\(440\) | −0.994481 | −0.0474100 | ||||||||
\(441\) | −2.38538 | −0.113589 | ||||||||
\(442\) | −4.54809 | −0.216331 | ||||||||
\(443\) | −15.9856 | −0.759499 | −0.379749 | − | 0.925089i | \(-0.623990\pi\) | ||||
−0.379749 | + | 0.925089i | \(0.623990\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.366772 | 0.0173867 | ||||||||
\(446\) | −6.94726 | −0.328962 | ||||||||
\(447\) | −24.3142 | −1.15002 | ||||||||
\(448\) | −3.26414 | −0.154216 | ||||||||
\(449\) | 28.6753 | 1.35327 | 0.676636 | − | 0.736318i | \(-0.263437\pi\) | ||||
0.676636 | + | 0.736318i | \(0.263437\pi\) | |||||||
\(450\) | 3.16689 | 0.149289 | ||||||||
\(451\) | −21.3734 | −1.00643 | ||||||||
\(452\) | −12.9549 | −0.609348 | ||||||||
\(453\) | 33.3506 | 1.56695 | ||||||||
\(454\) | 21.8490 | 1.02542 | ||||||||
\(455\) | −1.71420 | −0.0803627 | ||||||||
\(456\) | −9.17075 | −0.429460 | ||||||||
\(457\) | −0.105116 | −0.00491713 | −0.00245857 | − | 0.999997i | \(-0.500783\pi\) | ||||
−0.00245857 | + | 0.999997i | \(0.500783\pi\) | |||||||
\(458\) | −4.25010 | −0.198594 | ||||||||
\(459\) | 18.6475 | 0.870389 | ||||||||
\(460\) | −2.90338 | −0.135371 | ||||||||
\(461\) | 23.9701 | 1.11640 | 0.558199 | − | 0.829707i | \(-0.311493\pi\) | ||||
0.558199 | + | 0.829707i | \(0.311493\pi\) | |||||||
\(462\) | 12.9260 | 0.601374 | ||||||||
\(463\) | −20.7514 | −0.964398 | −0.482199 | − | 0.876062i | \(-0.660162\pi\) | ||||
−0.482199 | + | 0.876062i | \(0.660162\pi\) | |||||||
\(464\) | −3.21297 | −0.149158 | ||||||||
\(465\) | 1.49573 | 0.0693626 | ||||||||
\(466\) | −17.3443 | −0.803459 | ||||||||
\(467\) | −17.4928 | −0.809472 | −0.404736 | − | 0.914434i | \(-0.632637\pi\) | ||||
−0.404736 | + | 0.914434i | \(0.632637\pi\) | |||||||
\(468\) | −0.890890 | −0.0411814 | ||||||||
\(469\) | −36.6824 | −1.69384 | ||||||||
\(470\) | 2.01192 | 0.0928028 | ||||||||
\(471\) | −14.9400 | −0.688401 | ||||||||
\(472\) | 12.9674 | 0.596874 | ||||||||
\(473\) | −11.2156 | −0.515694 | ||||||||
\(474\) | −2.24190 | −0.102974 | ||||||||
\(475\) | 29.0428 | 1.33258 | ||||||||
\(476\) | 10.8765 | 0.498525 | ||||||||
\(477\) | 5.65974 | 0.259142 | ||||||||
\(478\) | −18.3584 | −0.839692 | ||||||||
\(479\) | 6.88046 | 0.314376 | 0.157188 | − | 0.987569i | \(-0.449757\pi\) | ||||
0.157188 | + | 0.987569i | \(0.449757\pi\) | |||||||
\(480\) | 0.589478 | 0.0269059 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 23.4661 | 1.06885 | ||||||||
\(483\) | 37.7374 | 1.71711 | ||||||||
\(484\) | −4.31924 | −0.196329 | ||||||||
\(485\) | −5.70150 | −0.258892 | ||||||||
\(486\) | 6.65270 | 0.301773 | ||||||||
\(487\) | 1.70810 | 0.0774014 | 0.0387007 | − | 0.999251i | \(-0.487678\pi\) | ||||
0.0387007 | + | 0.999251i | \(0.487678\pi\) | |||||||
\(488\) | −7.01264 | −0.317447 | ||||||||
\(489\) | −20.1696 | −0.912099 | ||||||||
\(490\) | 1.40613 | 0.0635223 | ||||||||
\(491\) | 10.6231 | 0.479412 | 0.239706 | − | 0.970846i | \(-0.422949\pi\) | ||||
0.239706 | + | 0.970846i | \(0.422949\pi\) | |||||||
\(492\) | 12.6691 | 0.571166 | ||||||||
\(493\) | 10.7060 | 0.482175 | ||||||||
\(494\) | −8.17013 | −0.367591 | ||||||||
\(495\) | 0.649101 | 0.0291749 | ||||||||
\(496\) | 2.53737 | 0.113931 | ||||||||
\(497\) | −48.9606 | −2.19618 | ||||||||
\(498\) | −0.0170335 | −0.000763289 0 | ||||||||
\(499\) | −35.4707 | −1.58789 | −0.793944 | − | 0.607991i | \(-0.791976\pi\) | ||||
−0.793944 | + | 0.607991i | \(0.791976\pi\) | |||||||
\(500\) | −3.79059 | −0.169520 | ||||||||
\(501\) | 8.58320 | 0.383469 | ||||||||
\(502\) | −6.10149 | −0.272323 | ||||||||
\(503\) | −30.0880 | −1.34156 | −0.670778 | − | 0.741658i | \(-0.734040\pi\) | ||||
−0.670778 | + | 0.741658i | \(0.734040\pi\) | |||||||
\(504\) | 2.13052 | 0.0949007 | ||||||||
\(505\) | −0.489608 | −0.0217873 | ||||||||
\(506\) | 19.5044 | 0.867076 | ||||||||
\(507\) | −17.0629 | −0.757788 | ||||||||
\(508\) | 11.2408 | 0.498729 | ||||||||
\(509\) | 24.0909 | 1.06781 | 0.533905 | − | 0.845544i | \(-0.320724\pi\) | ||||
0.533905 | + | 0.845544i | \(0.320724\pi\) | |||||||
\(510\) | −1.96422 | −0.0869769 | ||||||||
\(511\) | −49.2207 | −2.17740 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 33.4980 | 1.47897 | ||||||||
\(514\) | −4.34710 | −0.191742 | ||||||||
\(515\) | −4.17309 | −0.183888 | ||||||||
\(516\) | 6.64804 | 0.292664 | ||||||||
\(517\) | −13.5157 | −0.594421 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 16.6008 | 0.728694 | ||||||||
\(520\) | 0.525160 | 0.0230298 | ||||||||
\(521\) | 0.749547 | 0.0328383 | 0.0164191 | − | 0.999865i | \(-0.494773\pi\) | ||||
0.0164191 | + | 0.999865i | \(0.494773\pi\) | |||||||
\(522\) | 2.09712 | 0.0917884 | ||||||||
\(523\) | −2.03859 | −0.0891413 | −0.0445706 | − | 0.999006i | \(-0.514192\pi\) | ||||
−0.0445706 | + | 0.999006i | \(0.514192\pi\) | |||||||
\(524\) | −8.36959 | −0.365627 | ||||||||
\(525\) | 24.2644 | 1.05899 | ||||||||
\(526\) | 4.05485 | 0.176800 | ||||||||
\(527\) | −8.45485 | −0.368299 | ||||||||
\(528\) | −3.96002 | −0.172338 | ||||||||
\(529\) | 33.9429 | 1.47578 | ||||||||
\(530\) | −3.33629 | −0.144919 | ||||||||
\(531\) | −8.46389 | −0.367301 | ||||||||
\(532\) | 19.5384 | 0.847098 | ||||||||
\(533\) | 11.2868 | 0.488883 | ||||||||
\(534\) | 1.46048 | 0.0632013 | ||||||||
\(535\) | −1.83127 | −0.0791727 | ||||||||
\(536\) | 11.2380 | 0.485408 | ||||||||
\(537\) | −9.30273 | −0.401442 | ||||||||
\(538\) | 8.79337 | 0.379109 | ||||||||
\(539\) | −9.44612 | −0.406873 | ||||||||
\(540\) | −2.15319 | −0.0926585 | ||||||||
\(541\) | 31.3434 | 1.34756 | 0.673778 | − | 0.738934i | \(-0.264670\pi\) | ||||
0.673778 | + | 0.738934i | \(0.264670\pi\) | |||||||
\(542\) | −12.9122 | −0.554627 | ||||||||
\(543\) | 33.0224 | 1.41713 | ||||||||
\(544\) | −3.33213 | −0.142864 | ||||||||
\(545\) | −3.70805 | −0.158835 | ||||||||
\(546\) | −6.82591 | −0.292122 | ||||||||
\(547\) | −18.1663 | −0.776737 | −0.388368 | − | 0.921504i | \(-0.626961\pi\) | ||||
−0.388368 | + | 0.921504i | \(0.626961\pi\) | |||||||
\(548\) | −3.98413 | −0.170194 | ||||||||
\(549\) | 4.57718 | 0.195349 | ||||||||
\(550\) | 12.5410 | 0.534748 | ||||||||
\(551\) | 19.2321 | 0.819317 | ||||||||
\(552\) | −11.5612 | −0.492078 | ||||||||
\(553\) | 4.77640 | 0.203113 | ||||||||
\(554\) | −7.77643 | −0.330389 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.11140 | −0.216772 | ||||||||
\(557\) | 32.9061 | 1.39427 | 0.697137 | − | 0.716938i | \(-0.254457\pi\) | ||||
0.697137 | + | 0.716938i | \(0.254457\pi\) | |||||||
\(558\) | −1.65615 | −0.0701105 | ||||||||
\(559\) | 5.92267 | 0.250502 | ||||||||
\(560\) | −1.25589 | −0.0530711 | ||||||||
\(561\) | 13.1953 | 0.557105 | ||||||||
\(562\) | 0.232510 | 0.00980782 | ||||||||
\(563\) | 34.3008 | 1.44561 | 0.722804 | − | 0.691053i | \(-0.242853\pi\) | ||||
0.722804 | + | 0.691053i | \(0.242853\pi\) | |||||||
\(564\) | 8.01143 | 0.337342 | ||||||||
\(565\) | −4.98446 | −0.209698 | ||||||||
\(566\) | −12.8330 | −0.539411 | ||||||||
\(567\) | 21.5951 | 0.906910 | ||||||||
\(568\) | 14.9995 | 0.629367 | ||||||||
\(569\) | 21.2198 | 0.889579 | 0.444789 | − | 0.895635i | \(-0.353278\pi\) | ||||
0.444789 | + | 0.895635i | \(0.353278\pi\) | |||||||
\(570\) | −3.52849 | −0.147792 | ||||||||
\(571\) | 16.4467 | 0.688272 | 0.344136 | − | 0.938920i | \(-0.388172\pi\) | ||||
0.344136 | + | 0.938920i | \(0.388172\pi\) | |||||||
\(572\) | −3.52794 | −0.147510 | ||||||||
\(573\) | 10.1530 | 0.424150 | ||||||||
\(574\) | −26.9917 | −1.12661 | ||||||||
\(575\) | 36.6132 | 1.52687 | ||||||||
\(576\) | −0.652704 | −0.0271960 | ||||||||
\(577\) | −36.3216 | −1.51209 | −0.756044 | − | 0.654521i | \(-0.772870\pi\) | ||||
−0.756044 | + | 0.654521i | \(0.772870\pi\) | |||||||
\(578\) | −5.89693 | −0.245280 | ||||||||
\(579\) | −35.0150 | −1.45517 | ||||||||
\(580\) | −1.23620 | −0.0513306 | ||||||||
\(581\) | 0.0362901 | 0.00150557 | ||||||||
\(582\) | −22.7033 | −0.941083 | ||||||||
\(583\) | 22.4127 | 0.928237 | ||||||||
\(584\) | 15.0792 | 0.623983 | ||||||||
\(585\) | −0.342774 | −0.0141720 | ||||||||
\(586\) | −24.6443 | −1.01805 | ||||||||
\(587\) | 37.5244 | 1.54880 | 0.774398 | − | 0.632699i | \(-0.218053\pi\) | ||||
0.774398 | + | 0.632699i | \(0.218053\pi\) | |||||||
\(588\) | 5.59918 | 0.230906 | ||||||||
\(589\) | −15.1882 | −0.625817 | ||||||||
\(590\) | 4.98927 | 0.205405 | ||||||||
\(591\) | −22.6076 | −0.929953 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −10.0159 | −0.411302 | −0.205651 | − | 0.978625i | \(-0.565931\pi\) | ||||
−0.205651 | + | 0.978625i | \(0.565931\pi\) | |||||||
\(594\) | 14.4648 | 0.593496 | ||||||||
\(595\) | 4.18479 | 0.171560 | ||||||||
\(596\) | −15.8700 | −0.650060 | ||||||||
\(597\) | −2.25949 | −0.0924748 | ||||||||
\(598\) | −10.2998 | −0.421189 | ||||||||
\(599\) | −33.6544 | −1.37508 | −0.687541 | − | 0.726145i | \(-0.741310\pi\) | ||||
−0.687541 | + | 0.726145i | \(0.741310\pi\) | |||||||
\(600\) | −7.43364 | −0.303477 | ||||||||
\(601\) | −42.8067 | −1.74612 | −0.873061 | − | 0.487610i | \(-0.837869\pi\) | ||||
−0.873061 | + | 0.487610i | \(0.837869\pi\) | |||||||
\(602\) | −14.1638 | −0.577272 | ||||||||
\(603\) | −7.33508 | −0.298708 | ||||||||
\(604\) | 21.7680 | 0.885729 | ||||||||
\(605\) | −1.66185 | −0.0675637 | ||||||||
\(606\) | −1.94961 | −0.0791977 | ||||||||
\(607\) | −5.37572 | −0.218194 | −0.109097 | − | 0.994031i | \(-0.534796\pi\) | ||||
−0.109097 | + | 0.994031i | \(0.534796\pi\) | |||||||
\(608\) | −5.98578 | −0.242756 | ||||||||
\(609\) | 16.0679 | 0.651105 | ||||||||
\(610\) | −2.69815 | −0.109245 | ||||||||
\(611\) | 7.13731 | 0.288744 | ||||||||
\(612\) | 2.17489 | 0.0879148 | ||||||||
\(613\) | 33.4187 | 1.34977 | 0.674884 | − | 0.737924i | \(-0.264194\pi\) | ||||
0.674884 | + | 0.737924i | \(0.264194\pi\) | |||||||
\(614\) | −6.91132 | −0.278918 | ||||||||
\(615\) | 4.87448 | 0.196558 | ||||||||
\(616\) | 8.43688 | 0.339931 | ||||||||
\(617\) | 5.05959 | 0.203691 | 0.101846 | − | 0.994800i | \(-0.467525\pi\) | ||||
0.101846 | + | 0.994800i | \(0.467525\pi\) | |||||||
\(618\) | −16.6172 | −0.668442 | ||||||||
\(619\) | −35.7818 | −1.43819 | −0.719096 | − | 0.694911i | \(-0.755444\pi\) | ||||
−0.719096 | + | 0.694911i | \(0.755444\pi\) | |||||||
\(620\) | 0.976266 | 0.0392078 | ||||||||
\(621\) | 42.2297 | 1.69462 | ||||||||
\(622\) | −1.65859 | −0.0665035 | ||||||||
\(623\) | −3.11158 | −0.124663 | ||||||||
\(624\) | 2.09118 | 0.0837143 | ||||||||
\(625\) | 22.8014 | 0.912055 | ||||||||
\(626\) | 25.9509 | 1.03721 | ||||||||
\(627\) | 23.7038 | 0.946638 | ||||||||
\(628\) | −9.75142 | −0.389124 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0.819725 | 0.0326586 | ||||||||
\(631\) | 6.62105 | 0.263580 | 0.131790 | − | 0.991278i | \(-0.457928\pi\) | ||||
0.131790 | + | 0.991278i | \(0.457928\pi\) | |||||||
\(632\) | −1.46329 | −0.0582067 | ||||||||
\(633\) | −3.70693 | −0.147337 | ||||||||
\(634\) | 11.3498 | 0.450759 | ||||||||
\(635\) | 4.32494 | 0.171630 | ||||||||
\(636\) | −13.2851 | −0.526788 | ||||||||
\(637\) | 4.98826 | 0.197642 | ||||||||
\(638\) | 8.30462 | 0.328783 | ||||||||
\(639\) | −9.79025 | −0.387296 | ||||||||
\(640\) | 0.384754 | 0.0152088 | ||||||||
\(641\) | −35.5949 | −1.40591 | −0.702956 | − | 0.711233i | \(-0.748137\pi\) | ||||
−0.702956 | + | 0.711233i | \(0.748137\pi\) | |||||||
\(642\) | −7.29210 | −0.287796 | ||||||||
\(643\) | 5.01240 | 0.197670 | 0.0988350 | − | 0.995104i | \(-0.468488\pi\) | ||||
0.0988350 | + | 0.995104i | \(0.468488\pi\) | |||||||
\(644\) | 24.6314 | 0.970612 | ||||||||
\(645\) | 2.55786 | 0.100716 | ||||||||
\(646\) | 19.9454 | 0.784741 | ||||||||
\(647\) | 35.2707 | 1.38663 | 0.693317 | − | 0.720633i | \(-0.256149\pi\) | ||||
0.693317 | + | 0.720633i | \(0.256149\pi\) | |||||||
\(648\) | −6.61587 | −0.259896 | ||||||||
\(649\) | −33.5171 | −1.31566 | ||||||||
\(650\) | −6.62255 | −0.259758 | ||||||||
\(651\) | −12.6893 | −0.497332 | ||||||||
\(652\) | −13.1647 | −0.515571 | ||||||||
\(653\) | 2.70516 | 0.105861 | 0.0529305 | − | 0.998598i | \(-0.483144\pi\) | ||||
0.0529305 | + | 0.998598i | \(0.483144\pi\) | |||||||
\(654\) | −14.7654 | −0.577373 | ||||||||
\(655\) | −3.22024 | −0.125825 | ||||||||
\(656\) | 8.26915 | 0.322856 | ||||||||
\(657\) | −9.84227 | −0.383983 | ||||||||
\(658\) | −17.0685 | −0.665399 | ||||||||
\(659\) | −27.8599 | −1.08527 | −0.542634 | − | 0.839969i | \(-0.682573\pi\) | ||||
−0.542634 | + | 0.839969i | \(0.682573\pi\) | |||||||
\(660\) | −1.52363 | −0.0593074 | ||||||||
\(661\) | −10.6125 | −0.412777 | −0.206388 | − | 0.978470i | \(-0.566171\pi\) | ||||
−0.206388 | + | 0.978470i | \(0.566171\pi\) | |||||||
\(662\) | 12.8377 | 0.498951 | ||||||||
\(663\) | −6.96809 | −0.270618 | ||||||||
\(664\) | −0.0111178 | −0.000431455 0 | ||||||||
\(665\) | 7.51750 | 0.291516 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 24.2452 | 0.938779 | ||||||||
\(668\) | 5.60228 | 0.216759 | ||||||||
\(669\) | −10.6438 | −0.411514 | ||||||||
\(670\) | 4.32387 | 0.167046 | ||||||||
\(671\) | 18.1257 | 0.699735 | ||||||||
\(672\) | −5.00095 | −0.192916 | ||||||||
\(673\) | −0.657395 | −0.0253407 | −0.0126704 | − | 0.999920i | \(-0.504033\pi\) | ||||
−0.0126704 | + | 0.999920i | \(0.504033\pi\) | |||||||
\(674\) | −5.71183 | −0.220011 | ||||||||
\(675\) | 27.1529 | 1.04512 | ||||||||
\(676\) | −11.1370 | −0.428346 | ||||||||
\(677\) | 32.0071 | 1.23013 | 0.615067 | − | 0.788475i | \(-0.289129\pi\) | ||||
0.615067 | + | 0.788475i | \(0.289129\pi\) | |||||||
\(678\) | −19.8481 | −0.762261 | ||||||||
\(679\) | 48.3698 | 1.85626 | ||||||||
\(680\) | −1.28205 | −0.0491644 | ||||||||
\(681\) | 33.4746 | 1.28275 | ||||||||
\(682\) | −6.55839 | −0.251134 | ||||||||
\(683\) | −3.99530 | −0.152876 | −0.0764379 | − | 0.997074i | \(-0.524355\pi\) | ||||
−0.0764379 | + | 0.997074i | \(0.524355\pi\) | |||||||
\(684\) | 3.90694 | 0.149386 | ||||||||
\(685\) | −1.53291 | −0.0585695 | ||||||||
\(686\) | 10.9198 | 0.416921 | ||||||||
\(687\) | −6.51153 | −0.248430 | ||||||||
\(688\) | 4.33920 | 0.165430 | ||||||||
\(689\) | −11.8355 | −0.450898 | ||||||||
\(690\) | −4.44823 | −0.169341 | ||||||||
\(691\) | 4.39613 | 0.167237 | 0.0836184 | − | 0.996498i | \(-0.473352\pi\) | ||||
0.0836184 | + | 0.996498i | \(0.473352\pi\) | |||||||
\(692\) | 10.8354 | 0.411900 | ||||||||
\(693\) | −5.50678 | −0.209185 | ||||||||
\(694\) | 32.3416 | 1.22767 | ||||||||
\(695\) | −1.96663 | −0.0745987 | ||||||||
\(696\) | −4.92256 | −0.186589 | ||||||||
\(697\) | −27.5539 | −1.04368 | ||||||||
\(698\) | −24.9320 | −0.943691 | ||||||||
\(699\) | −26.5730 | −1.00508 | ||||||||
\(700\) | 15.8375 | 0.598601 | ||||||||
\(701\) | −14.3530 | −0.542106 | −0.271053 | − | 0.962564i | \(-0.587372\pi\) | ||||
−0.271053 | + | 0.962564i | \(0.587372\pi\) | |||||||
\(702\) | −7.63847 | −0.288295 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −2.58472 | −0.0974152 | ||||||||
\(705\) | 3.08244 | 0.116091 | ||||||||
\(706\) | −8.64114 | −0.325214 | ||||||||
\(707\) | 4.15368 | 0.156215 | ||||||||
\(708\) | 19.8672 | 0.746657 | ||||||||
\(709\) | 6.87475 | 0.258187 | 0.129093 | − | 0.991632i | \(-0.458793\pi\) | ||||
0.129093 | + | 0.991632i | \(0.458793\pi\) | |||||||
\(710\) | 5.77114 | 0.216587 | ||||||||
\(711\) | 0.955097 | 0.0358190 | ||||||||
\(712\) | 0.953262 | 0.0357250 | ||||||||
\(713\) | −19.1471 | −0.717066 | ||||||||
\(714\) | 16.6638 | 0.623627 | ||||||||
\(715\) | −1.35739 | −0.0507635 | ||||||||
\(716\) | −6.07192 | −0.226918 | ||||||||
\(717\) | −28.1266 | −1.05041 | ||||||||
\(718\) | 3.85848 | 0.143997 | ||||||||
\(719\) | −17.0965 | −0.637592 | −0.318796 | − | 0.947823i | \(-0.603279\pi\) | ||||
−0.318796 | + | 0.947823i | \(0.603279\pi\) | |||||||
\(720\) | −0.251131 | −0.00935909 | ||||||||
\(721\) | 35.4032 | 1.31849 | ||||||||
\(722\) | 16.8296 | 0.626333 | ||||||||
\(723\) | 35.9522 | 1.33708 | ||||||||
\(724\) | 21.5538 | 0.801042 | ||||||||
\(725\) | 15.5892 | 0.578969 | ||||||||
\(726\) | −6.61746 | −0.245597 | ||||||||
\(727\) | −42.6268 | −1.58094 | −0.790470 | − | 0.612501i | \(-0.790163\pi\) | ||||
−0.790470 | + | 0.612501i | \(0.790163\pi\) | |||||||
\(728\) | −4.45530 | −0.165124 | ||||||||
\(729\) | 30.0401 | 1.11260 | ||||||||
\(730\) | 5.80180 | 0.214734 | ||||||||
\(731\) | −14.4588 | −0.534777 | ||||||||
\(732\) | −10.7440 | −0.397109 | ||||||||
\(733\) | −42.6192 | −1.57418 | −0.787088 | − | 0.616841i | \(-0.788412\pi\) | ||||
−0.787088 | + | 0.616841i | \(0.788412\pi\) | |||||||
\(734\) | 10.4563 | 0.385948 | ||||||||
\(735\) | 2.15431 | 0.0794630 | ||||||||
\(736\) | −7.54605 | −0.278151 | ||||||||
\(737\) | −29.0470 | −1.06996 | ||||||||
\(738\) | −5.39731 | −0.198678 | ||||||||
\(739\) | −1.69175 | −0.0622321 | −0.0311161 | − | 0.999516i | \(-0.509906\pi\) | ||||
−0.0311161 | + | 0.999516i | \(0.509906\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −12.5174 | −0.459837 | ||||||||
\(742\) | 28.3041 | 1.03908 | ||||||||
\(743\) | 12.8065 | 0.469823 | 0.234912 | − | 0.972017i | \(-0.424520\pi\) | ||||
0.234912 | + | 0.972017i | \(0.424520\pi\) | |||||||
\(744\) | 3.88748 | 0.142522 | ||||||||
\(745\) | −6.10605 | −0.223708 | ||||||||
\(746\) | −9.86566 | −0.361208 | ||||||||
\(747\) | 0.00725664 | 0.000265507 0 | ||||||||
\(748\) | 8.61260 | 0.314908 | ||||||||
\(749\) | 15.5359 | 0.567671 | ||||||||
\(750\) | −5.80752 | −0.212061 | ||||||||
\(751\) | 48.4720 | 1.76877 | 0.884384 | − | 0.466759i | \(-0.154579\pi\) | ||||
0.884384 | + | 0.466759i | \(0.154579\pi\) | |||||||
\(752\) | 5.22909 | 0.190685 | ||||||||
\(753\) | −9.34802 | −0.340661 | ||||||||
\(754\) | −4.38546 | −0.159709 | ||||||||
\(755\) | 8.37535 | 0.304810 | ||||||||
\(756\) | 18.2670 | 0.664364 | ||||||||
\(757\) | 32.1365 | 1.16802 | 0.584010 | − | 0.811746i | \(-0.301483\pi\) | ||||
0.584010 | + | 0.811746i | \(0.301483\pi\) | |||||||
\(758\) | 2.48121 | 0.0901215 | ||||||||
\(759\) | 29.8825 | 1.08467 | ||||||||
\(760\) | −2.30306 | −0.0835406 | ||||||||
\(761\) | −10.3730 | −0.376022 | −0.188011 | − | 0.982167i | \(-0.560204\pi\) | ||||
−0.188011 | + | 0.982167i | \(0.560204\pi\) | |||||||
\(762\) | 17.2219 | 0.623883 | ||||||||
\(763\) | 31.4579 | 1.13885 | ||||||||
\(764\) | 6.62693 | 0.239754 | ||||||||
\(765\) | 0.836799 | 0.0302545 | ||||||||
\(766\) | −25.5639 | −0.923661 | ||||||||
\(767\) | 17.6995 | 0.639093 | ||||||||
\(768\) | 1.53209 | 0.0552845 | ||||||||
\(769\) | −33.9273 | −1.22345 | −0.611725 | − | 0.791070i | \(-0.709524\pi\) | ||||
−0.611725 | + | 0.791070i | \(0.709524\pi\) | |||||||
\(770\) | 3.24613 | 0.116982 | ||||||||
\(771\) | −6.66015 | −0.239859 | ||||||||
\(772\) | −22.8544 | −0.822548 | ||||||||
\(773\) | −28.9843 | −1.04249 | −0.521247 | − | 0.853406i | \(-0.674533\pi\) | ||||
−0.521247 | + | 0.853406i | \(0.674533\pi\) | |||||||
\(774\) | −2.83221 | −0.101802 | ||||||||
\(775\) | −12.3112 | −0.442233 | ||||||||
\(776\) | −14.8185 | −0.531954 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −6.37509 | −0.228558 | ||||||||
\(779\) | −49.4973 | −1.77343 | ||||||||
\(780\) | 0.804592 | 0.0288090 | ||||||||
\(781\) | −38.7696 | −1.38728 | ||||||||
\(782\) | 25.1444 | 0.899162 | ||||||||
\(783\) | 17.9806 | 0.642576 | ||||||||
\(784\) | 3.65461 | 0.130522 | ||||||||
\(785\) | −3.75190 | −0.133911 | ||||||||
\(786\) | −12.8229 | −0.457379 | ||||||||
\(787\) | −16.7100 | −0.595647 | −0.297823 | − | 0.954621i | \(-0.596261\pi\) | ||||
−0.297823 | + | 0.954621i | \(0.596261\pi\) | |||||||
\(788\) | −14.7561 | −0.525663 | ||||||||
\(789\) | 6.21239 | 0.221167 | ||||||||
\(790\) | −0.563009 | −0.0200310 | ||||||||
\(791\) | 42.2867 | 1.50354 | ||||||||
\(792\) | 1.68705 | 0.0599468 | ||||||||
\(793\) | −9.57171 | −0.339901 | ||||||||
\(794\) | 37.4977 | 1.33075 | ||||||||
\(795\) | −5.11150 | −0.181286 | ||||||||
\(796\) | −1.47478 | −0.0522721 | ||||||||
\(797\) | −5.21454 | −0.184709 | −0.0923543 | − | 0.995726i | \(-0.529439\pi\) | ||||
−0.0923543 | + | 0.995726i | \(0.529439\pi\) | |||||||
\(798\) | 29.9346 | 1.05967 | ||||||||
\(799\) | −17.4240 | −0.616417 | ||||||||
\(800\) | −4.85196 | −0.171543 | ||||||||
\(801\) | −0.622198 | −0.0219843 | ||||||||
\(802\) | −35.1464 | −1.24106 | ||||||||
\(803\) | −38.9755 | −1.37542 | ||||||||
\(804\) | 17.2176 | 0.607219 | ||||||||
\(805\) | 9.47703 | 0.334021 | ||||||||
\(806\) | 3.46332 | 0.121990 | ||||||||
\(807\) | 13.4722 | 0.474245 | ||||||||
\(808\) | −1.27252 | −0.0447671 | ||||||||
\(809\) | 50.5612 | 1.77764 | 0.888818 | − | 0.458260i | \(-0.151527\pi\) | ||||
0.888818 | + | 0.458260i | \(0.151527\pi\) | |||||||
\(810\) | −2.54548 | −0.0894392 | ||||||||
\(811\) | 36.0684 | 1.26653 | 0.633267 | − | 0.773934i | \(-0.281714\pi\) | ||||
0.633267 | + | 0.773934i | \(0.281714\pi\) | |||||||
\(812\) | 10.4876 | 0.368042 | ||||||||
\(813\) | −19.7826 | −0.693808 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.06519 | −0.177426 | ||||||||
\(816\) | −5.10511 | −0.178715 | ||||||||
\(817\) | −25.9735 | −0.908698 | ||||||||
\(818\) | 0.450741 | 0.0157598 | ||||||||
\(819\) | 2.90799 | 0.101613 | ||||||||
\(820\) | 3.18159 | 0.111106 | ||||||||
\(821\) | 51.1334 | 1.78457 | 0.892285 | − | 0.451473i | \(-0.149101\pi\) | ||||
0.892285 | + | 0.451473i | \(0.149101\pi\) | |||||||
\(822\) | −6.10404 | −0.212903 | ||||||||
\(823\) | 8.08213 | 0.281725 | 0.140863 | − | 0.990029i | \(-0.455012\pi\) | ||||
0.140863 | + | 0.990029i | \(0.455012\pi\) | |||||||
\(824\) | −10.8461 | −0.377842 | ||||||||
\(825\) | 19.2139 | 0.668940 | ||||||||
\(826\) | −42.3275 | −1.47276 | ||||||||
\(827\) | −25.8525 | −0.898981 | −0.449490 | − | 0.893285i | \(-0.648394\pi\) | ||||
−0.449490 | + | 0.893285i | \(0.648394\pi\) | |||||||
\(828\) | 4.92533 | 0.171167 | ||||||||
\(829\) | −8.19775 | −0.284720 | −0.142360 | − | 0.989815i | \(-0.545469\pi\) | ||||
−0.142360 | + | 0.989815i | \(0.545469\pi\) | |||||||
\(830\) | −0.00427763 | −0.000148479 0 | ||||||||
\(831\) | −11.9142 | −0.413298 | ||||||||
\(832\) | 1.36492 | 0.0473202 | ||||||||
\(833\) | −12.1776 | −0.421929 | ||||||||
\(834\) | −7.83112 | −0.271170 | ||||||||
\(835\) | 2.15550 | 0.0745943 | ||||||||
\(836\) | 15.4716 | 0.535095 | ||||||||
\(837\) | −14.1998 | −0.490817 | ||||||||
\(838\) | −15.3113 | −0.528920 | ||||||||
\(839\) | 52.8482 | 1.82452 | 0.912261 | − | 0.409610i | \(-0.134335\pi\) | ||||
0.912261 | + | 0.409610i | \(0.134335\pi\) | |||||||
\(840\) | −1.92414 | −0.0663891 | ||||||||
\(841\) | −18.6768 | −0.644028 | ||||||||
\(842\) | −22.3965 | −0.771833 | ||||||||
\(843\) | 0.356225 | 0.0122691 | ||||||||
\(844\) | −2.41952 | −0.0832835 | ||||||||
\(845\) | −4.28501 | −0.147409 | ||||||||
\(846\) | −3.41305 | −0.117343 | ||||||||
\(847\) | 14.0986 | 0.484434 | ||||||||
\(848\) | −8.67122 | −0.297771 | ||||||||
\(849\) | −19.6613 | −0.674774 | ||||||||
\(850\) | 16.1674 | 0.554536 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 22.9806 | 0.787303 | ||||||||
\(853\) | −32.9906 | −1.12958 | −0.564788 | − | 0.825236i | \(-0.691042\pi\) | ||||
−0.564788 | + | 0.825236i | \(0.691042\pi\) | |||||||
\(854\) | 22.8902 | 0.783288 | ||||||||
\(855\) | 1.50321 | 0.0514088 | ||||||||
\(856\) | −4.75958 | −0.162679 | ||||||||
\(857\) | 38.4078 | 1.31199 | 0.655993 | − | 0.754767i | \(-0.272250\pi\) | ||||
0.655993 | + | 0.754767i | \(0.272250\pi\) | |||||||
\(858\) | −5.40511 | −0.184528 | ||||||||
\(859\) | −20.7158 | −0.706814 | −0.353407 | − | 0.935470i | \(-0.614977\pi\) | ||||
−0.353407 | + | 0.935470i | \(0.614977\pi\) | |||||||
\(860\) | 1.66953 | 0.0569304 | ||||||||
\(861\) | −41.3536 | −1.40933 | ||||||||
\(862\) | −0.102080 | −0.00347685 | ||||||||
\(863\) | 35.3661 | 1.20388 | 0.601938 | − | 0.798543i | \(-0.294396\pi\) | ||||
0.601938 | + | 0.798543i | \(0.294396\pi\) | |||||||
\(864\) | −5.59627 | −0.190389 | ||||||||
\(865\) | 4.16897 | 0.141749 | ||||||||
\(866\) | 7.92714 | 0.269375 | ||||||||
\(867\) | −9.03462 | −0.306832 | ||||||||
\(868\) | −8.28234 | −0.281121 | ||||||||
\(869\) | 3.78220 | 0.128302 | ||||||||
\(870\) | −1.89398 | −0.0642118 | ||||||||
\(871\) | 15.3390 | 0.519742 | ||||||||
\(872\) | −9.63744 | −0.326365 | ||||||||
\(873\) | 9.67211 | 0.327351 | ||||||||
\(874\) | 45.1690 | 1.52786 | ||||||||
\(875\) | 12.3730 | 0.418284 | ||||||||
\(876\) | 23.1027 | 0.780568 | ||||||||
\(877\) | 26.3702 | 0.890459 | 0.445230 | − | 0.895416i | \(-0.353122\pi\) | ||||
0.445230 | + | 0.895416i | \(0.353122\pi\) | |||||||
\(878\) | 7.57063 | 0.255496 | ||||||||
\(879\) | −37.7573 | −1.27352 | ||||||||
\(880\) | −0.994481 | −0.0335240 | ||||||||
\(881\) | −33.7205 | −1.13607 | −0.568037 | − | 0.823003i | \(-0.692297\pi\) | ||||
−0.568037 | + | 0.823003i | \(0.692297\pi\) | |||||||
\(882\) | −2.38538 | −0.0803198 | ||||||||
\(883\) | −57.8576 | −1.94706 | −0.973531 | − | 0.228555i | \(-0.926600\pi\) | ||||
−0.973531 | + | 0.228555i | \(0.926600\pi\) | |||||||
\(884\) | −4.54809 | −0.152969 | ||||||||
\(885\) | 7.64401 | 0.256951 | ||||||||
\(886\) | −15.9856 | −0.537047 | ||||||||
\(887\) | 44.4679 | 1.49309 | 0.746544 | − | 0.665336i | \(-0.231712\pi\) | ||||
0.746544 | + | 0.665336i | \(0.231712\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −36.6915 | −1.23059 | ||||||||
\(890\) | 0.366772 | 0.0122942 | ||||||||
\(891\) | 17.1001 | 0.572876 | ||||||||
\(892\) | −6.94726 | −0.232611 | ||||||||
\(893\) | −31.3002 | −1.04742 | ||||||||
\(894\) | −24.3142 | −0.813190 | ||||||||
\(895\) | −2.33620 | −0.0780905 | ||||||||
\(896\) | −3.26414 | −0.109047 | ||||||||
\(897\) | −15.7802 | −0.526884 | ||||||||
\(898\) | 28.6753 | 0.956908 | ||||||||
\(899\) | −8.15251 | −0.271901 | ||||||||
\(900\) | 3.16689 | 0.105563 | ||||||||
\(901\) | 28.8936 | 0.962586 | ||||||||
\(902\) | −21.3734 | −0.711657 | ||||||||
\(903\) | −21.7001 | −0.722135 | ||||||||
\(904\) | −12.9549 | −0.430874 | ||||||||
\(905\) | 8.29294 | 0.275667 | ||||||||
\(906\) | 33.3506 | 1.10800 | ||||||||
\(907\) | −13.0951 | −0.434815 | −0.217407 | − | 0.976081i | \(-0.569760\pi\) | ||||
−0.217407 | + | 0.976081i | \(0.569760\pi\) | |||||||
\(908\) | 21.8490 | 0.725084 | ||||||||
\(909\) | 0.830579 | 0.0275486 | ||||||||
\(910\) | −1.71420 | −0.0568250 | ||||||||
\(911\) | 38.4466 | 1.27379 | 0.636896 | − | 0.770950i | \(-0.280218\pi\) | ||||
0.636896 | + | 0.770950i | \(0.280218\pi\) | |||||||
\(912\) | −9.17075 | −0.303674 | ||||||||
\(913\) | 0.0287364 | 0.000951036 0 | ||||||||
\(914\) | −0.105116 | −0.00347694 | ||||||||
\(915\) | −4.13380 | −0.136659 | ||||||||
\(916\) | −4.25010 | −0.140427 | ||||||||
\(917\) | 27.3195 | 0.902169 | ||||||||
\(918\) | 18.6475 | 0.615458 | ||||||||
\(919\) | 14.8613 | 0.490229 | 0.245115 | − | 0.969494i | \(-0.421174\pi\) | ||||
0.245115 | + | 0.969494i | \(0.421174\pi\) | |||||||
\(920\) | −2.90338 | −0.0957215 | ||||||||
\(921\) | −10.5888 | −0.348911 | ||||||||
\(922\) | 23.9701 | 0.789413 | ||||||||
\(923\) | 20.4732 | 0.673884 | ||||||||
\(924\) | 12.9260 | 0.425236 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −20.7514 | −0.681933 | ||||||||
\(927\) | 7.07930 | 0.232515 | ||||||||
\(928\) | −3.21297 | −0.105471 | ||||||||
\(929\) | −7.26526 | −0.238366 | −0.119183 | − | 0.992872i | \(-0.538027\pi\) | ||||
−0.119183 | + | 0.992872i | \(0.538027\pi\) | |||||||
\(930\) | 1.49573 | 0.0490468 | ||||||||
\(931\) | −21.8757 | −0.716947 | ||||||||
\(932\) | −17.3443 | −0.568131 | ||||||||
\(933\) | −2.54111 | −0.0831922 | ||||||||
\(934\) | −17.4928 | −0.572383 | ||||||||
\(935\) | 3.31374 | 0.108371 | ||||||||
\(936\) | −0.890890 | −0.0291196 | ||||||||
\(937\) | −26.3830 | −0.861897 | −0.430948 | − | 0.902377i | \(-0.641821\pi\) | ||||
−0.430948 | + | 0.902377i | \(0.641821\pi\) | |||||||
\(938\) | −36.6824 | −1.19772 | ||||||||
\(939\) | 39.7591 | 1.29749 | ||||||||
\(940\) | 2.01192 | 0.0656215 | ||||||||
\(941\) | 36.1584 | 1.17873 | 0.589366 | − | 0.807866i | \(-0.299378\pi\) | ||||
0.589366 | + | 0.807866i | \(0.299378\pi\) | |||||||
\(942\) | −14.9400 | −0.486773 | ||||||||
\(943\) | −62.3994 | −2.03201 | ||||||||
\(944\) | 12.9674 | 0.422054 | ||||||||
\(945\) | 7.02831 | 0.228631 | ||||||||
\(946\) | −11.2156 | −0.364651 | ||||||||
\(947\) | −47.1144 | −1.53101 | −0.765506 | − | 0.643428i | \(-0.777511\pi\) | ||||
−0.765506 | + | 0.643428i | \(0.777511\pi\) | |||||||
\(948\) | −2.24190 | −0.0728134 | ||||||||
\(949\) | 20.5820 | 0.668119 | ||||||||
\(950\) | 29.0428 | 0.942273 | ||||||||
\(951\) | 17.3889 | 0.563875 | ||||||||
\(952\) | 10.8765 | 0.352510 | ||||||||
\(953\) | −9.35174 | −0.302933 | −0.151466 | − | 0.988462i | \(-0.548399\pi\) | ||||
−0.151466 | + | 0.988462i | \(0.548399\pi\) | |||||||
\(954\) | 5.65974 | 0.183241 | ||||||||
\(955\) | 2.54974 | 0.0825077 | ||||||||
\(956\) | −18.3584 | −0.593752 | ||||||||
\(957\) | 12.7234 | 0.411290 | ||||||||
\(958\) | 6.88046 | 0.222298 | ||||||||
\(959\) | 13.0048 | 0.419945 | ||||||||
\(960\) | 0.589478 | 0.0190253 | ||||||||
\(961\) | −24.5617 | −0.792314 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.10660 | 0.100109 | ||||||||
\(964\) | 23.4661 | 0.755792 | ||||||||
\(965\) | −8.79333 | −0.283067 | ||||||||
\(966\) | 37.7374 | 1.21418 | ||||||||
\(967\) | −49.9460 | −1.60615 | −0.803077 | − | 0.595875i | \(-0.796805\pi\) | ||||
−0.803077 | + | 0.595875i | \(0.796805\pi\) | |||||||
\(968\) | −4.31924 | −0.138826 | ||||||||
\(969\) | 30.5581 | 0.981668 | ||||||||
\(970\) | −5.70150 | −0.183064 | ||||||||
\(971\) | 37.6187 | 1.20724 | 0.603621 | − | 0.797271i | \(-0.293724\pi\) | ||||
0.603621 | + | 0.797271i | \(0.293724\pi\) | |||||||
\(972\) | 6.65270 | 0.213386 | ||||||||
\(973\) | 16.6843 | 0.534875 | ||||||||
\(974\) | 1.70810 | 0.0547311 | ||||||||
\(975\) | −10.1463 | −0.324943 | ||||||||
\(976\) | −7.01264 | −0.224469 | ||||||||
\(977\) | −28.1356 | −0.900136 | −0.450068 | − | 0.892994i | \(-0.648600\pi\) | ||||
−0.450068 | + | 0.892994i | \(0.648600\pi\) | |||||||
\(978\) | −20.1696 | −0.644951 | ||||||||
\(979\) | −2.46391 | −0.0787470 | ||||||||
\(980\) | 1.40613 | 0.0449171 | ||||||||
\(981\) | 6.29039 | 0.200837 | ||||||||
\(982\) | 10.6231 | 0.338995 | ||||||||
\(983\) | 32.9418 | 1.05068 | 0.525340 | − | 0.850893i | \(-0.323938\pi\) | ||||
0.525340 | + | 0.850893i | \(0.323938\pi\) | |||||||
\(984\) | 12.6691 | 0.403875 | ||||||||
\(985\) | −5.67746 | −0.180899 | ||||||||
\(986\) | 10.7060 | 0.340949 | ||||||||
\(987\) | −26.1504 | −0.832378 | ||||||||
\(988\) | −8.17013 | −0.259926 | ||||||||
\(989\) | −32.7438 | −1.04119 | ||||||||
\(990\) | 0.649101 | 0.0206298 | ||||||||
\(991\) | −38.9993 | −1.23885 | −0.619426 | − | 0.785055i | \(-0.712635\pi\) | ||||
−0.619426 | + | 0.785055i | \(0.712635\pi\) | |||||||
\(992\) | 2.53737 | 0.0805617 | ||||||||
\(993\) | 19.6685 | 0.624160 | ||||||||
\(994\) | −48.9606 | −1.55294 | ||||||||
\(995\) | −0.567428 | −0.0179887 | ||||||||
\(996\) | −0.0170335 | −0.000539727 0 | ||||||||
\(997\) | 7.98046 | 0.252744 | 0.126372 | − | 0.991983i | \(-0.459667\pi\) | ||||
0.126372 | + | 0.991983i | \(0.459667\pi\) | |||||||
\(998\) | −35.4707 | −1.12281 | ||||||||
\(999\) | 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 | 2738.2.a.s.1.6 | 6 | ||
37.2 | odd | 36 | 74.2.h.a.41.2 | ✓ | 12 | ||
37.19 | odd | 36 | 74.2.h.a.65.2 | yes | 12 | ||
37.36 | even | 2 | 2738.2.a.r.1.5 | 6 | |||
111.2 | even | 36 | 666.2.bj.c.559.1 | 12 | |||
111.56 | even | 36 | 666.2.bj.c.361.1 | 12 | |||
148.19 | even | 36 | 592.2.bq.b.65.2 | 12 | |||
148.39 | even | 36 | 592.2.bq.b.337.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
74.2.h.a.41.2 | ✓ | 12 | 37.2 | odd | 36 | ||
74.2.h.a.65.2 | yes | 12 | 37.19 | odd | 36 | ||
592.2.bq.b.65.2 | 12 | 148.19 | even | 36 | |||
592.2.bq.b.337.2 | 12 | 148.39 | even | 36 | |||
666.2.bj.c.361.1 | 12 | 111.56 | even | 36 | |||
666.2.bj.c.559.1 | 12 | 111.2 | even | 36 | |||
2738.2.a.r.1.5 | 6 | 37.36 | even | 2 | |||
2738.2.a.s.1.6 | 6 | 1.1 | even | 1 | trivial |