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: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.37902897.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 15x^{4} - x^{3} + 60x^{2} - 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
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 | 1.5 | ||
Root | \(-2.18117\) 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 | ||||||||
\(3\) | 2.18117 | 1.25930 | 0.629650 | − | 0.776879i | \(-0.283198\pi\) | ||||
0.629650 | + | 0.776879i | \(0.283198\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.87939 | −0.840487 | −0.420243 | − | 0.907411i | \(-0.638055\pi\) | ||||
−0.420243 | + | 0.907411i | \(0.638055\pi\) | |||||||
\(6\) | 2.18117 | 0.890460 | ||||||||
\(7\) | −4.09926 | −1.54938 | −0.774688 | − | 0.632344i | \(-0.782093\pi\) | ||||
−0.774688 | + | 0.632344i | \(0.782093\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.75751 | 0.585838 | ||||||||
\(10\) | −1.87939 | −0.594314 | ||||||||
\(11\) | 3.34175 | 1.00758 | 0.503788 | − | 0.863827i | \(-0.331939\pi\) | ||||
0.503788 | + | 0.863827i | \(0.331939\pi\) | |||||||
\(12\) | 2.18117 | 0.629650 | ||||||||
\(13\) | 1.93869 | 0.537695 | 0.268847 | − | 0.963183i | \(-0.413357\pi\) | ||||
0.268847 | + | 0.963183i | \(0.413357\pi\) | |||||||
\(14\) | −4.09926 | −1.09557 | ||||||||
\(15\) | −4.09926 | −1.05843 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.44656 | 1.07845 | 0.539225 | − | 0.842162i | \(-0.318717\pi\) | ||||
0.539225 | + | 0.842162i | \(0.318717\pi\) | |||||||
\(18\) | 1.75751 | 0.414250 | ||||||||
\(19\) | −0.0992633 | −0.0227726 | −0.0113863 | − | 0.999935i | \(-0.503624\pi\) | ||||
−0.0113863 | + | 0.999935i | \(0.503624\pi\) | |||||||
\(20\) | −1.87939 | −0.420243 | ||||||||
\(21\) | −8.94120 | −1.95113 | ||||||||
\(22\) | 3.34175 | 0.712464 | ||||||||
\(23\) | 9.52292 | 1.98567 | 0.992833 | − | 0.119507i | \(-0.0381315\pi\) | ||||
0.992833 | + | 0.119507i | \(0.0381315\pi\) | |||||||
\(24\) | 2.18117 | 0.445230 | ||||||||
\(25\) | −1.46791 | −0.293582 | ||||||||
\(26\) | 1.93869 | 0.380208 | ||||||||
\(27\) | −2.71008 | −0.521555 | ||||||||
\(28\) | −4.09926 | −0.774688 | ||||||||
\(29\) | 0.774576 | 0.143835 | 0.0719175 | − | 0.997411i | \(-0.477088\pi\) | ||||
0.0719175 | + | 0.997411i | \(0.477088\pi\) | |||||||
\(30\) | −4.09926 | −0.748420 | ||||||||
\(31\) | 10.3914 | 1.86636 | 0.933179 | − | 0.359413i | \(-0.117023\pi\) | ||||
0.933179 | + | 0.359413i | \(0.117023\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 7.28893 | 1.26884 | ||||||||
\(34\) | 4.44656 | 0.762579 | ||||||||
\(35\) | 7.70409 | 1.30223 | ||||||||
\(36\) | 1.75751 | 0.292919 | ||||||||
\(37\) | 0 | 0 | ||||||||
\(38\) | −0.0992633 | −0.0161026 | ||||||||
\(39\) | 4.22861 | 0.677119 | ||||||||
\(40\) | −1.87939 | −0.297157 | ||||||||
\(41\) | 5.69443 | 0.889320 | 0.444660 | − | 0.895699i | \(-0.353324\pi\) | ||||
0.444660 | + | 0.895699i | \(0.353324\pi\) | |||||||
\(42\) | −8.94120 | −1.37966 | ||||||||
\(43\) | −1.11986 | −0.170777 | −0.0853884 | − | 0.996348i | \(-0.527213\pi\) | ||||
−0.0853884 | + | 0.996348i | \(0.527213\pi\) | |||||||
\(44\) | 3.34175 | 0.503788 | ||||||||
\(45\) | −3.30304 | −0.492389 | ||||||||
\(46\) | 9.52292 | 1.40408 | ||||||||
\(47\) | −7.11448 | −1.03775 | −0.518877 | − | 0.854849i | \(-0.673650\pi\) | ||||
−0.518877 | + | 0.854849i | \(0.673650\pi\) | |||||||
\(48\) | 2.18117 | 0.314825 | ||||||||
\(49\) | 9.80396 | 1.40057 | ||||||||
\(50\) | −1.46791 | −0.207594 | ||||||||
\(51\) | 9.69871 | 1.35809 | ||||||||
\(52\) | 1.93869 | 0.268847 | ||||||||
\(53\) | 0.818828 | 0.112475 | 0.0562373 | − | 0.998417i | \(-0.482090\pi\) | ||||
0.0562373 | + | 0.998417i | \(0.482090\pi\) | |||||||
\(54\) | −2.71008 | −0.368795 | ||||||||
\(55\) | −6.28044 | −0.846854 | ||||||||
\(56\) | −4.09926 | −0.547787 | ||||||||
\(57\) | −0.216510 | −0.0286775 | ||||||||
\(58\) | 0.774576 | 0.101707 | ||||||||
\(59\) | 8.09926 | 1.05443 | 0.527217 | − | 0.849731i | \(-0.323235\pi\) | ||||
0.527217 | + | 0.849731i | \(0.323235\pi\) | |||||||
\(60\) | −4.09926 | −0.529213 | ||||||||
\(61\) | −10.7009 | −1.37011 | −0.685056 | − | 0.728491i | \(-0.740222\pi\) | ||||
−0.685056 | + | 0.728491i | \(0.740222\pi\) | |||||||
\(62\) | 10.3914 | 1.31971 | ||||||||
\(63\) | −7.20451 | −0.907683 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.64354 | −0.451925 | ||||||||
\(66\) | 7.28893 | 0.897206 | ||||||||
\(67\) | 13.1663 | 1.60852 | 0.804260 | − | 0.594278i | \(-0.202562\pi\) | ||||
0.804260 | + | 0.594278i | \(0.202562\pi\) | |||||||
\(68\) | 4.44656 | 0.539225 | ||||||||
\(69\) | 20.7711 | 2.50055 | ||||||||
\(70\) | 7.70409 | 0.920815 | ||||||||
\(71\) | −2.97316 | −0.352849 | −0.176425 | − | 0.984314i | \(-0.556453\pi\) | ||||
−0.176425 | + | 0.984314i | \(0.556453\pi\) | |||||||
\(72\) | 1.75751 | 0.207125 | ||||||||
\(73\) | −2.55740 | −0.299321 | −0.149660 | − | 0.988737i | \(-0.547818\pi\) | ||||
−0.149660 | + | 0.988737i | \(0.547818\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.20177 | −0.369708 | ||||||||
\(76\) | −0.0992633 | −0.0113863 | ||||||||
\(77\) | −13.6987 | −1.56111 | ||||||||
\(78\) | 4.22861 | 0.478796 | ||||||||
\(79\) | −5.43563 | −0.611556 | −0.305778 | − | 0.952103i | \(-0.598917\pi\) | ||||
−0.305778 | + | 0.952103i | \(0.598917\pi\) | |||||||
\(80\) | −1.87939 | −0.210122 | ||||||||
\(81\) | −11.1837 | −1.24263 | ||||||||
\(82\) | 5.69443 | 0.628844 | ||||||||
\(83\) | 0.658250 | 0.0722523 | 0.0361262 | − | 0.999347i | \(-0.488498\pi\) | ||||
0.0361262 | + | 0.999347i | \(0.488498\pi\) | |||||||
\(84\) | −8.94120 | −0.975565 | ||||||||
\(85\) | −8.35680 | −0.906422 | ||||||||
\(86\) | −1.11986 | −0.120757 | ||||||||
\(87\) | 1.68948 | 0.181132 | ||||||||
\(88\) | 3.34175 | 0.356232 | ||||||||
\(89\) | 3.52523 | 0.373673 | 0.186837 | − | 0.982391i | \(-0.440176\pi\) | ||||
0.186837 | + | 0.982391i | \(0.440176\pi\) | |||||||
\(90\) | −3.30304 | −0.348171 | ||||||||
\(91\) | −7.94718 | −0.833091 | ||||||||
\(92\) | 9.52292 | 0.992833 | ||||||||
\(93\) | 22.6655 | 2.35030 | ||||||||
\(94\) | −7.11448 | −0.733802 | ||||||||
\(95\) | 0.186554 | 0.0191400 | ||||||||
\(96\) | 2.18117 | 0.222615 | ||||||||
\(97\) | 3.62024 | 0.367580 | 0.183790 | − | 0.982966i | \(-0.441163\pi\) | ||||
0.183790 | + | 0.982966i | \(0.441163\pi\) | |||||||
\(98\) | 9.80396 | 0.990349 | ||||||||
\(99\) | 5.87317 | 0.590276 | ||||||||
\(100\) | −1.46791 | −0.146791 | ||||||||
\(101\) | 3.94811 | 0.392852 | 0.196426 | − | 0.980519i | \(-0.437066\pi\) | ||||
0.196426 | + | 0.980519i | \(0.437066\pi\) | |||||||
\(102\) | 9.69871 | 0.960316 | ||||||||
\(103\) | −1.97880 | −0.194977 | −0.0974887 | − | 0.995237i | \(-0.531081\pi\) | ||||
−0.0974887 | + | 0.995237i | \(0.531081\pi\) | |||||||
\(104\) | 1.93869 | 0.190104 | ||||||||
\(105\) | 16.8040 | 1.63990 | ||||||||
\(106\) | 0.818828 | 0.0795316 | ||||||||
\(107\) | 8.24882 | 0.797443 | 0.398722 | − | 0.917072i | \(-0.369454\pi\) | ||||
0.398722 | + | 0.917072i | \(0.369454\pi\) | |||||||
\(108\) | −2.71008 | −0.260777 | ||||||||
\(109\) | −8.78453 | −0.841406 | −0.420703 | − | 0.907198i | \(-0.638217\pi\) | ||||
−0.420703 | + | 0.907198i | \(0.638217\pi\) | |||||||
\(110\) | −6.28044 | −0.598816 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.09926 | −0.387344 | ||||||||
\(113\) | 9.97690 | 0.938548 | 0.469274 | − | 0.883053i | \(-0.344516\pi\) | ||||
0.469274 | + | 0.883053i | \(0.344516\pi\) | |||||||
\(114\) | −0.216510 | −0.0202781 | ||||||||
\(115\) | −17.8972 | −1.66893 | ||||||||
\(116\) | 0.774576 | 0.0719175 | ||||||||
\(117\) | 3.40727 | 0.315002 | ||||||||
\(118\) | 8.09926 | 0.745598 | ||||||||
\(119\) | −18.2276 | −1.67092 | ||||||||
\(120\) | −4.09926 | −0.374210 | ||||||||
\(121\) | 0.167293 | 0.0152085 | ||||||||
\(122\) | −10.7009 | −0.968815 | ||||||||
\(123\) | 12.4205 | 1.11992 | ||||||||
\(124\) | 10.3914 | 0.933179 | ||||||||
\(125\) | 12.1557 | 1.08724 | ||||||||
\(126\) | −7.20451 | −0.641829 | ||||||||
\(127\) | −16.7774 | −1.48875 | −0.744376 | − | 0.667761i | \(-0.767253\pi\) | ||||
−0.744376 | + | 0.667761i | \(0.767253\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −2.44260 | −0.215059 | ||||||||
\(130\) | −3.64354 | −0.319559 | ||||||||
\(131\) | 1.40367 | 0.122639 | 0.0613194 | − | 0.998118i | \(-0.480469\pi\) | ||||
0.0613194 | + | 0.998118i | \(0.480469\pi\) | |||||||
\(132\) | 7.28893 | 0.634420 | ||||||||
\(133\) | 0.406906 | 0.0352833 | ||||||||
\(134\) | 13.1663 | 1.13740 | ||||||||
\(135\) | 5.09328 | 0.438360 | ||||||||
\(136\) | 4.44656 | 0.381289 | ||||||||
\(137\) | 12.4193 | 1.06105 | 0.530525 | − | 0.847669i | \(-0.321995\pi\) | ||||
0.530525 | + | 0.847669i | \(0.321995\pi\) | |||||||
\(138\) | 20.7711 | 1.76816 | ||||||||
\(139\) | 18.3996 | 1.56063 | 0.780315 | − | 0.625386i | \(-0.215059\pi\) | ||||
0.780315 | + | 0.625386i | \(0.215059\pi\) | |||||||
\(140\) | 7.70409 | 0.651115 | ||||||||
\(141\) | −15.5179 | −1.30684 | ||||||||
\(142\) | −2.97316 | −0.249502 | ||||||||
\(143\) | 6.47860 | 0.541768 | ||||||||
\(144\) | 1.75751 | 0.146459 | ||||||||
\(145\) | −1.45573 | −0.120891 | ||||||||
\(146\) | −2.55740 | −0.211652 | ||||||||
\(147\) | 21.3841 | 1.76373 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.4068 | 1.01640 | 0.508201 | − | 0.861238i | \(-0.330311\pi\) | ||||
0.508201 | + | 0.861238i | \(0.330311\pi\) | |||||||
\(150\) | −3.20177 | −0.261423 | ||||||||
\(151\) | −12.5489 | −1.02121 | −0.510607 | − | 0.859814i | \(-0.670579\pi\) | ||||
−0.510607 | + | 0.859814i | \(0.670579\pi\) | |||||||
\(152\) | −0.0992633 | −0.00805132 | ||||||||
\(153\) | 7.81489 | 0.631796 | ||||||||
\(154\) | −13.6987 | −1.10387 | ||||||||
\(155\) | −19.5295 | −1.56865 | ||||||||
\(156\) | 4.22861 | 0.338560 | ||||||||
\(157\) | 3.51326 | 0.280388 | 0.140194 | − | 0.990124i | \(-0.455227\pi\) | ||||
0.140194 | + | 0.990124i | \(0.455227\pi\) | |||||||
\(158\) | −5.43563 | −0.432436 | ||||||||
\(159\) | 1.78600 | 0.141639 | ||||||||
\(160\) | −1.87939 | −0.148578 | ||||||||
\(161\) | −39.0370 | −3.07654 | ||||||||
\(162\) | −11.1837 | −0.878673 | ||||||||
\(163\) | −2.39144 | −0.187312 | −0.0936559 | − | 0.995605i | \(-0.529855\pi\) | ||||
−0.0936559 | + | 0.995605i | \(0.529855\pi\) | |||||||
\(164\) | 5.69443 | 0.444660 | ||||||||
\(165\) | −13.6987 | −1.06644 | ||||||||
\(166\) | 0.658250 | 0.0510901 | ||||||||
\(167\) | −15.5840 | −1.20592 | −0.602962 | − | 0.797770i | \(-0.706013\pi\) | ||||
−0.602962 | + | 0.797770i | \(0.706013\pi\) | |||||||
\(168\) | −8.94120 | −0.689829 | ||||||||
\(169\) | −9.24150 | −0.710884 | ||||||||
\(170\) | −8.35680 | −0.640937 | ||||||||
\(171\) | −0.174457 | −0.0133410 | ||||||||
\(172\) | −1.11986 | −0.0853884 | ||||||||
\(173\) | −17.8772 | −1.35918 | −0.679589 | − | 0.733593i | \(-0.737842\pi\) | ||||
−0.679589 | + | 0.733593i | \(0.737842\pi\) | |||||||
\(174\) | 1.68948 | 0.128079 | ||||||||
\(175\) | 6.01735 | 0.454869 | ||||||||
\(176\) | 3.34175 | 0.251894 | ||||||||
\(177\) | 17.6659 | 1.32785 | ||||||||
\(178\) | 3.52523 | 0.264227 | ||||||||
\(179\) | −20.4063 | −1.52524 | −0.762619 | − | 0.646848i | \(-0.776087\pi\) | ||||
−0.762619 | + | 0.646848i | \(0.776087\pi\) | |||||||
\(180\) | −3.30304 | −0.246194 | ||||||||
\(181\) | −18.2764 | −1.35848 | −0.679238 | − | 0.733918i | \(-0.737690\pi\) | ||||
−0.679238 | + | 0.733918i | \(0.737690\pi\) | |||||||
\(182\) | −7.94718 | −0.589084 | ||||||||
\(183\) | −23.3405 | −1.72538 | ||||||||
\(184\) | 9.52292 | 0.702039 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 22.6655 | 1.66192 | ||||||||
\(187\) | 14.8593 | 1.08662 | ||||||||
\(188\) | −7.11448 | −0.518877 | ||||||||
\(189\) | 11.1093 | 0.808084 | ||||||||
\(190\) | 0.186554 | 0.0135340 | ||||||||
\(191\) | 5.76567 | 0.417189 | 0.208595 | − | 0.978002i | \(-0.433111\pi\) | ||||
0.208595 | + | 0.978002i | \(0.433111\pi\) | |||||||
\(192\) | 2.18117 | 0.157413 | ||||||||
\(193\) | −0.359424 | −0.0258719 | −0.0129360 | − | 0.999916i | \(-0.504118\pi\) | ||||
−0.0129360 | + | 0.999916i | \(0.504118\pi\) | |||||||
\(194\) | 3.62024 | 0.259918 | ||||||||
\(195\) | −7.94718 | −0.569110 | ||||||||
\(196\) | 9.80396 | 0.700283 | ||||||||
\(197\) | 6.96601 | 0.496307 | 0.248154 | − | 0.968721i | \(-0.420176\pi\) | ||||
0.248154 | + | 0.968721i | \(0.420176\pi\) | |||||||
\(198\) | 5.87317 | 0.417388 | ||||||||
\(199\) | 11.1779 | 0.792383 | 0.396191 | − | 0.918168i | \(-0.370332\pi\) | ||||
0.396191 | + | 0.918168i | \(0.370332\pi\) | |||||||
\(200\) | −1.46791 | −0.103797 | ||||||||
\(201\) | 28.7180 | 2.02561 | ||||||||
\(202\) | 3.94811 | 0.277788 | ||||||||
\(203\) | −3.17519 | −0.222855 | ||||||||
\(204\) | 9.69871 | 0.679046 | ||||||||
\(205\) | −10.7020 | −0.747462 | ||||||||
\(206\) | −1.97880 | −0.137870 | ||||||||
\(207\) | 16.7367 | 1.16328 | ||||||||
\(208\) | 1.93869 | 0.134424 | ||||||||
\(209\) | −0.331713 | −0.0229451 | ||||||||
\(210\) | 16.8040 | 1.15958 | ||||||||
\(211\) | −12.2103 | −0.840589 | −0.420295 | − | 0.907388i | \(-0.638073\pi\) | ||||
−0.420295 | + | 0.907388i | \(0.638073\pi\) | |||||||
\(212\) | 0.818828 | 0.0562373 | ||||||||
\(213\) | −6.48497 | −0.444343 | ||||||||
\(214\) | 8.24882 | 0.563877 | ||||||||
\(215\) | 2.10464 | 0.143536 | ||||||||
\(216\) | −2.71008 | −0.184397 | ||||||||
\(217\) | −42.5972 | −2.89169 | ||||||||
\(218\) | −8.78453 | −0.594964 | ||||||||
\(219\) | −5.57812 | −0.376935 | ||||||||
\(220\) | −6.28044 | −0.423427 | ||||||||
\(221\) | 8.62048 | 0.579876 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.7545 | −0.720177 | −0.360088 | − | 0.932918i | \(-0.617253\pi\) | ||||
−0.360088 | + | 0.932918i | \(0.617253\pi\) | |||||||
\(224\) | −4.09926 | −0.273894 | ||||||||
\(225\) | −2.57987 | −0.171992 | ||||||||
\(226\) | 9.97690 | 0.663653 | ||||||||
\(227\) | −2.96526 | −0.196811 | −0.0984057 | − | 0.995146i | \(-0.531374\pi\) | ||||
−0.0984057 | + | 0.995146i | \(0.531374\pi\) | |||||||
\(228\) | −0.216510 | −0.0143388 | ||||||||
\(229\) | −3.03262 | −0.200401 | −0.100201 | − | 0.994967i | \(-0.531949\pi\) | ||||
−0.100201 | + | 0.994967i | \(0.531949\pi\) | |||||||
\(230\) | −17.8972 | −1.18011 | ||||||||
\(231\) | −29.8793 | −1.96591 | ||||||||
\(232\) | 0.774576 | 0.0508534 | ||||||||
\(233\) | −0.288806 | −0.0189203 | −0.00946016 | − | 0.999955i | \(-0.503011\pi\) | ||||
−0.00946016 | + | 0.999955i | \(0.503011\pi\) | |||||||
\(234\) | 3.40727 | 0.222740 | ||||||||
\(235\) | 13.3708 | 0.872218 | ||||||||
\(236\) | 8.09926 | 0.527217 | ||||||||
\(237\) | −11.8561 | −0.770133 | ||||||||
\(238\) | −18.2276 | −1.18152 | ||||||||
\(239\) | −5.03510 | −0.325693 | −0.162847 | − | 0.986651i | \(-0.552068\pi\) | ||||
−0.162847 | + | 0.986651i | \(0.552068\pi\) | |||||||
\(240\) | −4.09926 | −0.264606 | ||||||||
\(241\) | −17.3760 | −1.11928 | −0.559642 | − | 0.828734i | \(-0.689061\pi\) | ||||
−0.559642 | + | 0.828734i | \(0.689061\pi\) | |||||||
\(242\) | 0.167293 | 0.0107540 | ||||||||
\(243\) | −16.2633 | −1.04329 | ||||||||
\(244\) | −10.7009 | −0.685056 | ||||||||
\(245\) | −18.4254 | −1.17716 | ||||||||
\(246\) | 12.4205 | 0.791904 | ||||||||
\(247\) | −0.192440 | −0.0122447 | ||||||||
\(248\) | 10.3914 | 0.659857 | ||||||||
\(249\) | 1.43576 | 0.0909874 | ||||||||
\(250\) | 12.1557 | 0.768794 | ||||||||
\(251\) | −1.75569 | −0.110818 | −0.0554090 | − | 0.998464i | \(-0.517646\pi\) | ||||
−0.0554090 | + | 0.998464i | \(0.517646\pi\) | |||||||
\(252\) | −7.20451 | −0.453841 | ||||||||
\(253\) | 31.8232 | 2.00071 | ||||||||
\(254\) | −16.7774 | −1.05271 | ||||||||
\(255\) | −18.2276 | −1.14146 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −12.7541 | −0.795577 | −0.397789 | − | 0.917477i | \(-0.630222\pi\) | ||||
−0.397789 | + | 0.917477i | \(0.630222\pi\) | |||||||
\(258\) | −2.44260 | −0.152070 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −3.64354 | −0.225963 | ||||||||
\(261\) | 1.36133 | 0.0842640 | ||||||||
\(262\) | 1.40367 | 0.0867188 | ||||||||
\(263\) | −26.3651 | −1.62574 | −0.812871 | − | 0.582444i | \(-0.802096\pi\) | ||||
−0.812871 | + | 0.582444i | \(0.802096\pi\) | |||||||
\(264\) | 7.28893 | 0.448603 | ||||||||
\(265\) | −1.53889 | −0.0945334 | ||||||||
\(266\) | 0.406906 | 0.0249490 | ||||||||
\(267\) | 7.68913 | 0.470567 | ||||||||
\(268\) | 13.1663 | 0.804260 | ||||||||
\(269\) | 13.6058 | 0.829559 | 0.414779 | − | 0.909922i | \(-0.363859\pi\) | ||||
0.414779 | + | 0.909922i | \(0.363859\pi\) | |||||||
\(270\) | 5.09328 | 0.309967 | ||||||||
\(271\) | −4.31590 | −0.262172 | −0.131086 | − | 0.991371i | \(-0.541846\pi\) | ||||
−0.131086 | + | 0.991371i | \(0.541846\pi\) | |||||||
\(272\) | 4.44656 | 0.269612 | ||||||||
\(273\) | −17.3342 | −1.04911 | ||||||||
\(274\) | 12.4193 | 0.750275 | ||||||||
\(275\) | −4.90539 | −0.295806 | ||||||||
\(276\) | 20.7711 | 1.25028 | ||||||||
\(277\) | −3.49344 | −0.209900 | −0.104950 | − | 0.994477i | \(-0.533468\pi\) | ||||
−0.104950 | + | 0.994477i | \(0.533468\pi\) | |||||||
\(278\) | 18.3996 | 1.10353 | ||||||||
\(279\) | 18.2631 | 1.09338 | ||||||||
\(280\) | 7.70409 | 0.460408 | ||||||||
\(281\) | −7.33775 | −0.437734 | −0.218867 | − | 0.975755i | \(-0.570236\pi\) | ||||
−0.218867 | + | 0.975755i | \(0.570236\pi\) | |||||||
\(282\) | −15.5179 | −0.924078 | ||||||||
\(283\) | 14.0029 | 0.832384 | 0.416192 | − | 0.909277i | \(-0.363364\pi\) | ||||
0.416192 | + | 0.909277i | \(0.363364\pi\) | |||||||
\(284\) | −2.97316 | −0.176425 | ||||||||
\(285\) | 0.406906 | 0.0241031 | ||||||||
\(286\) | 6.47860 | 0.383088 | ||||||||
\(287\) | −23.3430 | −1.37789 | ||||||||
\(288\) | 1.75751 | 0.103562 | ||||||||
\(289\) | 2.77189 | 0.163053 | ||||||||
\(290\) | −1.45573 | −0.0854832 | ||||||||
\(291\) | 7.89638 | 0.462894 | ||||||||
\(292\) | −2.55740 | −0.149660 | ||||||||
\(293\) | −25.2747 | −1.47657 | −0.738283 | − | 0.674491i | \(-0.764363\pi\) | ||||
−0.738283 | + | 0.674491i | \(0.764363\pi\) | |||||||
\(294\) | 21.3841 | 1.24715 | ||||||||
\(295\) | −15.2216 | −0.886238 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −9.05640 | −0.525506 | ||||||||
\(298\) | 12.4068 | 0.718705 | ||||||||
\(299\) | 18.4620 | 1.06768 | ||||||||
\(300\) | −3.20177 | −0.184854 | ||||||||
\(301\) | 4.59059 | 0.264597 | ||||||||
\(302\) | −12.5489 | −0.722108 | ||||||||
\(303\) | 8.61152 | 0.494719 | ||||||||
\(304\) | −0.0992633 | −0.00569314 | ||||||||
\(305\) | 20.1111 | 1.15156 | ||||||||
\(306\) | 7.81489 | 0.446747 | ||||||||
\(307\) | −24.5991 | −1.40394 | −0.701972 | − | 0.712205i | \(-0.747697\pi\) | ||||
−0.701972 | + | 0.712205i | \(0.747697\pi\) | |||||||
\(308\) | −13.6987 | −0.780557 | ||||||||
\(309\) | −4.31611 | −0.245535 | ||||||||
\(310\) | −19.5295 | −1.10920 | ||||||||
\(311\) | 5.20715 | 0.295270 | 0.147635 | − | 0.989042i | \(-0.452834\pi\) | ||||
0.147635 | + | 0.989042i | \(0.452834\pi\) | |||||||
\(312\) | 4.22861 | 0.239398 | ||||||||
\(313\) | 7.23640 | 0.409025 | 0.204513 | − | 0.978864i | \(-0.434439\pi\) | ||||
0.204513 | + | 0.978864i | \(0.434439\pi\) | |||||||
\(314\) | 3.51326 | 0.198264 | ||||||||
\(315\) | 13.5400 | 0.762895 | ||||||||
\(316\) | −5.43563 | −0.305778 | ||||||||
\(317\) | −13.3490 | −0.749755 | −0.374878 | − | 0.927074i | \(-0.622315\pi\) | ||||
−0.374878 | + | 0.927074i | \(0.622315\pi\) | |||||||
\(318\) | 1.78600 | 0.100154 | ||||||||
\(319\) | 2.58844 | 0.144925 | ||||||||
\(320\) | −1.87939 | −0.105061 | ||||||||
\(321\) | 17.9921 | 1.00422 | ||||||||
\(322\) | −39.0370 | −2.17545 | ||||||||
\(323\) | −0.441380 | −0.0245591 | ||||||||
\(324\) | −11.1837 | −0.621316 | ||||||||
\(325\) | −2.84582 | −0.157858 | ||||||||
\(326\) | −2.39144 | −0.132449 | ||||||||
\(327\) | −19.1606 | −1.05958 | ||||||||
\(328\) | 5.69443 | 0.314422 | ||||||||
\(329\) | 29.1641 | 1.60787 | ||||||||
\(330\) | −13.6987 | −0.754089 | ||||||||
\(331\) | −4.57313 | −0.251362 | −0.125681 | − | 0.992071i | \(-0.540112\pi\) | ||||
−0.125681 | + | 0.992071i | \(0.540112\pi\) | |||||||
\(332\) | 0.658250 | 0.0361262 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −15.5840 | −0.852717 | ||||||||
\(335\) | −24.7446 | −1.35194 | ||||||||
\(336\) | −8.94120 | −0.487782 | ||||||||
\(337\) | 3.25330 | 0.177219 | 0.0886094 | − | 0.996066i | \(-0.471758\pi\) | ||||
0.0886094 | + | 0.996066i | \(0.471758\pi\) | |||||||
\(338\) | −9.24150 | −0.502671 | ||||||||
\(339\) | 21.7613 | 1.18191 | ||||||||
\(340\) | −8.35680 | −0.453211 | ||||||||
\(341\) | 34.7256 | 1.88050 | ||||||||
\(342\) | −0.174457 | −0.00943353 | ||||||||
\(343\) | −11.4942 | −0.620627 | ||||||||
\(344\) | −1.11986 | −0.0603787 | ||||||||
\(345\) | −39.0370 | −2.10168 | ||||||||
\(346\) | −17.8772 | −0.961084 | ||||||||
\(347\) | 24.4774 | 1.31402 | 0.657008 | − | 0.753884i | \(-0.271822\pi\) | ||||
0.657008 | + | 0.753884i | \(0.271822\pi\) | |||||||
\(348\) | 1.68948 | 0.0905658 | ||||||||
\(349\) | 5.70239 | 0.305242 | 0.152621 | − | 0.988285i | \(-0.451229\pi\) | ||||
0.152621 | + | 0.988285i | \(0.451229\pi\) | |||||||
\(350\) | 6.01735 | 0.321641 | ||||||||
\(351\) | −5.25399 | −0.280437 | ||||||||
\(352\) | 3.34175 | 0.178116 | ||||||||
\(353\) | 24.4340 | 1.30049 | 0.650245 | − | 0.759725i | \(-0.274666\pi\) | ||||
0.650245 | + | 0.759725i | \(0.274666\pi\) | |||||||
\(354\) | 17.6659 | 0.938931 | ||||||||
\(355\) | 5.58771 | 0.296565 | ||||||||
\(356\) | 3.52523 | 0.186837 | ||||||||
\(357\) | −39.7576 | −2.10419 | ||||||||
\(358\) | −20.4063 | −1.07851 | ||||||||
\(359\) | 18.7092 | 0.987435 | 0.493717 | − | 0.869622i | \(-0.335638\pi\) | ||||
0.493717 | + | 0.869622i | \(0.335638\pi\) | |||||||
\(360\) | −3.30304 | −0.174086 | ||||||||
\(361\) | −18.9901 | −0.999481 | ||||||||
\(362\) | −18.2764 | −0.960588 | ||||||||
\(363\) | 0.364896 | 0.0191521 | ||||||||
\(364\) | −7.94718 | −0.416546 | ||||||||
\(365\) | 4.80633 | 0.251575 | ||||||||
\(366\) | −23.3405 | −1.22003 | ||||||||
\(367\) | 33.7230 | 1.76032 | 0.880162 | − | 0.474673i | \(-0.157434\pi\) | ||||
0.880162 | + | 0.474673i | \(0.157434\pi\) | |||||||
\(368\) | 9.52292 | 0.496417 | ||||||||
\(369\) | 10.0080 | 0.520997 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.35659 | −0.174265 | ||||||||
\(372\) | 22.6655 | 1.17515 | ||||||||
\(373\) | 31.4347 | 1.62763 | 0.813813 | − | 0.581127i | \(-0.197388\pi\) | ||||
0.813813 | + | 0.581127i | \(0.197388\pi\) | |||||||
\(374\) | 14.8593 | 0.768356 | ||||||||
\(375\) | 26.5137 | 1.36916 | ||||||||
\(376\) | −7.11448 | −0.366901 | ||||||||
\(377\) | 1.50166 | 0.0773394 | ||||||||
\(378\) | 11.1093 | 0.571402 | ||||||||
\(379\) | 6.96691 | 0.357866 | 0.178933 | − | 0.983861i | \(-0.442735\pi\) | ||||
0.178933 | + | 0.983861i | \(0.442735\pi\) | |||||||
\(380\) | 0.186554 | 0.00957002 | ||||||||
\(381\) | −36.5944 | −1.87479 | ||||||||
\(382\) | 5.76567 | 0.294997 | ||||||||
\(383\) | −2.87727 | −0.147022 | −0.0735109 | − | 0.997294i | \(-0.523420\pi\) | ||||
−0.0735109 | + | 0.997294i | \(0.523420\pi\) | |||||||
\(384\) | 2.18117 | 0.111307 | ||||||||
\(385\) | 25.7452 | 1.31209 | ||||||||
\(386\) | −0.359424 | −0.0182942 | ||||||||
\(387\) | −1.96817 | −0.100047 | ||||||||
\(388\) | 3.62024 | 0.183790 | ||||||||
\(389\) | −11.8116 | −0.598873 | −0.299436 | − | 0.954116i | \(-0.596799\pi\) | ||||
−0.299436 | + | 0.954116i | \(0.596799\pi\) | |||||||
\(390\) | −7.94718 | −0.402421 | ||||||||
\(391\) | 42.3442 | 2.14144 | ||||||||
\(392\) | 9.80396 | 0.495175 | ||||||||
\(393\) | 3.06164 | 0.154439 | ||||||||
\(394\) | 6.96601 | 0.350942 | ||||||||
\(395\) | 10.2156 | 0.514005 | ||||||||
\(396\) | 5.87317 | 0.295138 | ||||||||
\(397\) | −31.3125 | −1.57153 | −0.785765 | − | 0.618525i | \(-0.787730\pi\) | ||||
−0.785765 | + | 0.618525i | \(0.787730\pi\) | |||||||
\(398\) | 11.1779 | 0.560299 | ||||||||
\(399\) | 0.887533 | 0.0444322 | ||||||||
\(400\) | −1.46791 | −0.0733956 | ||||||||
\(401\) | −14.0281 | −0.700531 | −0.350266 | − | 0.936650i | \(-0.613909\pi\) | ||||
−0.350266 | + | 0.936650i | \(0.613909\pi\) | |||||||
\(402\) | 28.7180 | 1.43232 | ||||||||
\(403\) | 20.1457 | 1.00353 | ||||||||
\(404\) | 3.94811 | 0.196426 | ||||||||
\(405\) | 21.0185 | 1.04442 | ||||||||
\(406\) | −3.17519 | −0.157582 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 9.69871 | 0.480158 | ||||||||
\(409\) | −0.0810699 | −0.00400865 | −0.00200432 | − | 0.999998i | \(-0.500638\pi\) | ||||
−0.00200432 | + | 0.999998i | \(0.500638\pi\) | |||||||
\(410\) | −10.7020 | −0.528535 | ||||||||
\(411\) | 27.0886 | 1.33618 | ||||||||
\(412\) | −1.97880 | −0.0974887 | ||||||||
\(413\) | −33.2010 | −1.63372 | ||||||||
\(414\) | 16.7367 | 0.822562 | ||||||||
\(415\) | −1.23711 | −0.0607271 | ||||||||
\(416\) | 1.93869 | 0.0950519 | ||||||||
\(417\) | 40.1326 | 1.96530 | ||||||||
\(418\) | −0.331713 | −0.0162246 | ||||||||
\(419\) | 4.63611 | 0.226489 | 0.113244 | − | 0.993567i | \(-0.463876\pi\) | ||||
0.113244 | + | 0.993567i | \(0.463876\pi\) | |||||||
\(420\) | 16.8040 | 0.819949 | ||||||||
\(421\) | −19.3222 | −0.941706 | −0.470853 | − | 0.882212i | \(-0.656054\pi\) | ||||
−0.470853 | + | 0.882212i | \(0.656054\pi\) | |||||||
\(422\) | −12.2103 | −0.594386 | ||||||||
\(423\) | −12.5038 | −0.607955 | ||||||||
\(424\) | 0.818828 | 0.0397658 | ||||||||
\(425\) | −6.52715 | −0.316613 | ||||||||
\(426\) | −6.48497 | −0.314198 | ||||||||
\(427\) | 43.8659 | 2.12282 | ||||||||
\(428\) | 8.24882 | 0.398722 | ||||||||
\(429\) | 14.1310 | 0.682249 | ||||||||
\(430\) | 2.10464 | 0.101495 | ||||||||
\(431\) | 7.54172 | 0.363272 | 0.181636 | − | 0.983366i | \(-0.441861\pi\) | ||||
0.181636 | + | 0.983366i | \(0.441861\pi\) | |||||||
\(432\) | −2.71008 | −0.130389 | ||||||||
\(433\) | 29.8339 | 1.43373 | 0.716863 | − | 0.697214i | \(-0.245577\pi\) | ||||
0.716863 | + | 0.697214i | \(0.245577\pi\) | |||||||
\(434\) | −42.5972 | −2.04473 | ||||||||
\(435\) | −3.17519 | −0.152239 | ||||||||
\(436\) | −8.78453 | −0.420703 | ||||||||
\(437\) | −0.945277 | −0.0452187 | ||||||||
\(438\) | −5.57812 | −0.266533 | ||||||||
\(439\) | 21.9541 | 1.04781 | 0.523906 | − | 0.851776i | \(-0.324474\pi\) | ||||
0.523906 | + | 0.851776i | \(0.324474\pi\) | |||||||
\(440\) | −6.28044 | −0.299408 | ||||||||
\(441\) | 17.2306 | 0.820504 | ||||||||
\(442\) | 8.62048 | 0.410034 | ||||||||
\(443\) | −34.6241 | −1.64504 | −0.822520 | − | 0.568736i | \(-0.807433\pi\) | ||||
−0.822520 | + | 0.568736i | \(0.807433\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.62526 | −0.314068 | ||||||||
\(446\) | −10.7545 | −0.509242 | ||||||||
\(447\) | 27.0613 | 1.27996 | ||||||||
\(448\) | −4.09926 | −0.193672 | ||||||||
\(449\) | −19.9414 | −0.941093 | −0.470547 | − | 0.882375i | \(-0.655943\pi\) | ||||
−0.470547 | + | 0.882375i | \(0.655943\pi\) | |||||||
\(450\) | −2.57987 | −0.121616 | ||||||||
\(451\) | 19.0294 | 0.896057 | ||||||||
\(452\) | 9.97690 | 0.469274 | ||||||||
\(453\) | −27.3713 | −1.28602 | ||||||||
\(454\) | −2.96526 | −0.139167 | ||||||||
\(455\) | 14.9358 | 0.700202 | ||||||||
\(456\) | −0.216510 | −0.0101390 | ||||||||
\(457\) | 32.2388 | 1.50807 | 0.754034 | − | 0.656835i | \(-0.228105\pi\) | ||||
0.754034 | + | 0.656835i | \(0.228105\pi\) | |||||||
\(458\) | −3.03262 | −0.141705 | ||||||||
\(459\) | −12.0505 | −0.562470 | ||||||||
\(460\) | −17.8972 | −0.834463 | ||||||||
\(461\) | 7.32821 | 0.341309 | 0.170654 | − | 0.985331i | \(-0.445412\pi\) | ||||
0.170654 | + | 0.985331i | \(0.445412\pi\) | |||||||
\(462\) | −29.8793 | −1.39011 | ||||||||
\(463\) | 6.48631 | 0.301444 | 0.150722 | − | 0.988576i | \(-0.451840\pi\) | ||||
0.150722 | + | 0.988576i | \(0.451840\pi\) | |||||||
\(464\) | 0.774576 | 0.0359588 | ||||||||
\(465\) | −42.5972 | −1.97540 | ||||||||
\(466\) | −0.288806 | −0.0133787 | ||||||||
\(467\) | −11.9858 | −0.554635 | −0.277317 | − | 0.960778i | \(-0.589445\pi\) | ||||
−0.277317 | + | 0.960778i | \(0.589445\pi\) | |||||||
\(468\) | 3.40727 | 0.157501 | ||||||||
\(469\) | −53.9721 | −2.49220 | ||||||||
\(470\) | 13.3708 | 0.616751 | ||||||||
\(471\) | 7.66302 | 0.353093 | ||||||||
\(472\) | 8.09926 | 0.372799 | ||||||||
\(473\) | −3.74229 | −0.172070 | ||||||||
\(474\) | −11.8561 | −0.544566 | ||||||||
\(475\) | 0.145710 | 0.00668562 | ||||||||
\(476\) | −18.2276 | −0.835462 | ||||||||
\(477\) | 1.43910 | 0.0658919 | ||||||||
\(478\) | −5.03510 | −0.230300 | ||||||||
\(479\) | 22.6922 | 1.03683 | 0.518417 | − | 0.855128i | \(-0.326522\pi\) | ||||
0.518417 | + | 0.855128i | \(0.326522\pi\) | |||||||
\(480\) | −4.09926 | −0.187105 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −17.3760 | −0.791454 | ||||||||
\(483\) | −85.1464 | −3.87429 | ||||||||
\(484\) | 0.167293 | 0.00760425 | ||||||||
\(485\) | −6.80383 | −0.308946 | ||||||||
\(486\) | −16.2633 | −0.737719 | ||||||||
\(487\) | 12.3108 | 0.557856 | 0.278928 | − | 0.960312i | \(-0.410021\pi\) | ||||
0.278928 | + | 0.960312i | \(0.410021\pi\) | |||||||
\(488\) | −10.7009 | −0.484408 | ||||||||
\(489\) | −5.21614 | −0.235882 | ||||||||
\(490\) | −18.4254 | −0.832375 | ||||||||
\(491\) | 1.15080 | 0.0519347 | 0.0259674 | − | 0.999663i | \(-0.491733\pi\) | ||||
0.0259674 | + | 0.999663i | \(0.491733\pi\) | |||||||
\(492\) | 12.4205 | 0.559961 | ||||||||
\(493\) | 3.44420 | 0.155119 | ||||||||
\(494\) | −0.192440 | −0.00865830 | ||||||||
\(495\) | −11.0379 | −0.496119 | ||||||||
\(496\) | 10.3914 | 0.466589 | ||||||||
\(497\) | 12.1878 | 0.546696 | ||||||||
\(498\) | 1.43576 | 0.0643378 | ||||||||
\(499\) | 27.9156 | 1.24967 | 0.624837 | − | 0.780755i | \(-0.285166\pi\) | ||||
0.624837 | + | 0.780755i | \(0.285166\pi\) | |||||||
\(500\) | 12.1557 | 0.543619 | ||||||||
\(501\) | −33.9913 | −1.51862 | ||||||||
\(502\) | −1.75569 | −0.0783602 | ||||||||
\(503\) | −16.3677 | −0.729800 | −0.364900 | − | 0.931047i | \(-0.618897\pi\) | ||||
−0.364900 | + | 0.931047i | \(0.618897\pi\) | |||||||
\(504\) | −7.20451 | −0.320914 | ||||||||
\(505\) | −7.42003 | −0.330187 | ||||||||
\(506\) | 31.8232 | 1.41471 | ||||||||
\(507\) | −20.1573 | −0.895217 | ||||||||
\(508\) | −16.7774 | −0.744376 | ||||||||
\(509\) | 4.33404 | 0.192103 | 0.0960514 | − | 0.995376i | \(-0.469379\pi\) | ||||
0.0960514 | + | 0.995376i | \(0.469379\pi\) | |||||||
\(510\) | −18.2276 | −0.807133 | ||||||||
\(511\) | 10.4834 | 0.463760 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0.269011 | 0.0118771 | ||||||||
\(514\) | −12.7541 | −0.562558 | ||||||||
\(515\) | 3.71893 | 0.163876 | ||||||||
\(516\) | −2.44260 | −0.107530 | ||||||||
\(517\) | −23.7748 | −1.04561 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −38.9932 | −1.71161 | ||||||||
\(520\) | −3.64354 | −0.159780 | ||||||||
\(521\) | 1.87292 | 0.0820542 | 0.0410271 | − | 0.999158i | \(-0.486937\pi\) | ||||
0.0410271 | + | 0.999158i | \(0.486937\pi\) | |||||||
\(522\) | 1.36133 | 0.0595837 | ||||||||
\(523\) | 37.0562 | 1.62035 | 0.810177 | − | 0.586186i | \(-0.199371\pi\) | ||||
0.810177 | + | 0.586186i | \(0.199371\pi\) | |||||||
\(524\) | 1.40367 | 0.0613194 | ||||||||
\(525\) | 13.1249 | 0.572817 | ||||||||
\(526\) | −26.3651 | −1.14957 | ||||||||
\(527\) | 46.2061 | 2.01277 | ||||||||
\(528\) | 7.28893 | 0.317210 | ||||||||
\(529\) | 67.6861 | 2.94287 | ||||||||
\(530\) | −1.53889 | −0.0668452 | ||||||||
\(531\) | 14.2346 | 0.617727 | ||||||||
\(532\) | 0.406906 | 0.0176416 | ||||||||
\(533\) | 11.0397 | 0.478183 | ||||||||
\(534\) | 7.68913 | 0.332741 | ||||||||
\(535\) | −15.5027 | −0.670240 | ||||||||
\(536\) | 13.1663 | 0.568698 | ||||||||
\(537\) | −44.5096 | −1.92073 | ||||||||
\(538\) | 13.6058 | 0.586587 | ||||||||
\(539\) | 32.7624 | 1.41118 | ||||||||
\(540\) | 5.09328 | 0.219180 | ||||||||
\(541\) | 15.5062 | 0.666665 | 0.333332 | − | 0.942809i | \(-0.391827\pi\) | ||||
0.333332 | + | 0.942809i | \(0.391827\pi\) | |||||||
\(542\) | −4.31590 | −0.185384 | ||||||||
\(543\) | −39.8641 | −1.71073 | ||||||||
\(544\) | 4.44656 | 0.190645 | ||||||||
\(545\) | 16.5095 | 0.707190 | ||||||||
\(546\) | −17.3342 | −0.741834 | ||||||||
\(547\) | −41.1850 | −1.76094 | −0.880472 | − | 0.474099i | \(-0.842774\pi\) | ||||
−0.880472 | + | 0.474099i | \(0.842774\pi\) | |||||||
\(548\) | 12.4193 | 0.530525 | ||||||||
\(549\) | −18.8070 | −0.802663 | ||||||||
\(550\) | −4.90539 | −0.209167 | ||||||||
\(551\) | −0.0768869 | −0.00327549 | ||||||||
\(552\) | 20.7711 | 0.884078 | ||||||||
\(553\) | 22.2821 | 0.947531 | ||||||||
\(554\) | −3.49344 | −0.148422 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 18.3996 | 0.780315 | ||||||||
\(557\) | −12.2046 | −0.517126 | −0.258563 | − | 0.965994i | \(-0.583249\pi\) | ||||
−0.258563 | + | 0.965994i | \(0.583249\pi\) | |||||||
\(558\) | 18.2631 | 0.773138 | ||||||||
\(559\) | −2.17105 | −0.0918258 | ||||||||
\(560\) | 7.70409 | 0.325557 | ||||||||
\(561\) | 32.4107 | 1.36838 | ||||||||
\(562\) | −7.33775 | −0.309524 | ||||||||
\(563\) | −11.4193 | −0.481266 | −0.240633 | − | 0.970616i | \(-0.577355\pi\) | ||||
−0.240633 | + | 0.970616i | \(0.577355\pi\) | |||||||
\(564\) | −15.5179 | −0.653421 | ||||||||
\(565\) | −18.7504 | −0.788837 | ||||||||
\(566\) | 14.0029 | 0.588585 | ||||||||
\(567\) | 45.8449 | 1.92530 | ||||||||
\(568\) | −2.97316 | −0.124751 | ||||||||
\(569\) | −22.3465 | −0.936812 | −0.468406 | − | 0.883513i | \(-0.655172\pi\) | ||||
−0.468406 | + | 0.883513i | \(0.655172\pi\) | |||||||
\(570\) | 0.406906 | 0.0170434 | ||||||||
\(571\) | −13.2022 | −0.552494 | −0.276247 | − | 0.961087i | \(-0.589091\pi\) | ||||
−0.276247 | + | 0.961087i | \(0.589091\pi\) | |||||||
\(572\) | 6.47860 | 0.270884 | ||||||||
\(573\) | 12.5759 | 0.525367 | ||||||||
\(574\) | −23.3430 | −0.974316 | ||||||||
\(575\) | −13.9788 | −0.582956 | ||||||||
\(576\) | 1.75751 | 0.0732297 | ||||||||
\(577\) | 29.3529 | 1.22198 | 0.610989 | − | 0.791639i | \(-0.290772\pi\) | ||||
0.610989 | + | 0.791639i | \(0.290772\pi\) | |||||||
\(578\) | 2.77189 | 0.115296 | ||||||||
\(579\) | −0.783966 | −0.0325805 | ||||||||
\(580\) | −1.45573 | −0.0604457 | ||||||||
\(581\) | −2.69834 | −0.111946 | ||||||||
\(582\) | 7.89638 | 0.327315 | ||||||||
\(583\) | 2.73632 | 0.113327 | ||||||||
\(584\) | −2.55740 | −0.105826 | ||||||||
\(585\) | −6.40356 | −0.264755 | ||||||||
\(586\) | −25.2747 | −1.04409 | ||||||||
\(587\) | −21.2405 | −0.876690 | −0.438345 | − | 0.898807i | \(-0.644435\pi\) | ||||
−0.438345 | + | 0.898807i | \(0.644435\pi\) | |||||||
\(588\) | 21.3841 | 0.881867 | ||||||||
\(589\) | −1.03149 | −0.0425017 | ||||||||
\(590\) | −15.2216 | −0.626665 | ||||||||
\(591\) | 15.1941 | 0.625000 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 31.4119 | 1.28993 | 0.644965 | − | 0.764212i | \(-0.276872\pi\) | ||||
0.644965 | + | 0.764212i | \(0.276872\pi\) | |||||||
\(594\) | −9.05640 | −0.371589 | ||||||||
\(595\) | 34.2567 | 1.40439 | ||||||||
\(596\) | 12.4068 | 0.508201 | ||||||||
\(597\) | 24.3810 | 0.997848 | ||||||||
\(598\) | 18.4620 | 0.754965 | ||||||||
\(599\) | −20.3033 | −0.829570 | −0.414785 | − | 0.909919i | \(-0.636143\pi\) | ||||
−0.414785 | + | 0.909919i | \(0.636143\pi\) | |||||||
\(600\) | −3.20177 | −0.130712 | ||||||||
\(601\) | −44.5828 | −1.81857 | −0.909286 | − | 0.416171i | \(-0.863372\pi\) | ||||
−0.909286 | + | 0.416171i | \(0.863372\pi\) | |||||||
\(602\) | 4.59059 | 0.187099 | ||||||||
\(603\) | 23.1400 | 0.942332 | ||||||||
\(604\) | −12.5489 | −0.510607 | ||||||||
\(605\) | −0.314409 | −0.0127825 | ||||||||
\(606\) | 8.61152 | 0.349819 | ||||||||
\(607\) | −20.1087 | −0.816188 | −0.408094 | − | 0.912940i | \(-0.633806\pi\) | ||||
−0.408094 | + | 0.912940i | \(0.633806\pi\) | |||||||
\(608\) | −0.0992633 | −0.00402566 | ||||||||
\(609\) | −6.92564 | −0.280641 | ||||||||
\(610\) | 20.1111 | 0.814276 | ||||||||
\(611\) | −13.7927 | −0.557994 | ||||||||
\(612\) | 7.81489 | 0.315898 | ||||||||
\(613\) | 32.2195 | 1.30133 | 0.650667 | − | 0.759363i | \(-0.274489\pi\) | ||||
0.650667 | + | 0.759363i | \(0.274489\pi\) | |||||||
\(614\) | −24.5991 | −0.992738 | ||||||||
\(615\) | −23.3430 | −0.941279 | ||||||||
\(616\) | −13.6987 | −0.551937 | ||||||||
\(617\) | 38.9312 | 1.56731 | 0.783656 | − | 0.621195i | \(-0.213353\pi\) | ||||
0.783656 | + | 0.621195i | \(0.213353\pi\) | |||||||
\(618\) | −4.31611 | −0.173619 | ||||||||
\(619\) | −26.3624 | −1.05959 | −0.529796 | − | 0.848125i | \(-0.677732\pi\) | ||||
−0.529796 | + | 0.848125i | \(0.677732\pi\) | |||||||
\(620\) | −19.5295 | −0.784324 | ||||||||
\(621\) | −25.8079 | −1.03563 | ||||||||
\(622\) | 5.20715 | 0.208788 | ||||||||
\(623\) | −14.4508 | −0.578961 | ||||||||
\(624\) | 4.22861 | 0.169280 | ||||||||
\(625\) | −15.5057 | −0.620227 | ||||||||
\(626\) | 7.23640 | 0.289225 | ||||||||
\(627\) | −0.723524 | −0.0288947 | ||||||||
\(628\) | 3.51326 | 0.140194 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 13.5400 | 0.539448 | ||||||||
\(631\) | 41.3133 | 1.64466 | 0.822328 | − | 0.569013i | \(-0.192675\pi\) | ||||
0.822328 | + | 0.569013i | \(0.192675\pi\) | |||||||
\(632\) | −5.43563 | −0.216218 | ||||||||
\(633\) | −26.6327 | −1.05855 | ||||||||
\(634\) | −13.3490 | −0.530157 | ||||||||
\(635\) | 31.5312 | 1.25128 | ||||||||
\(636\) | 1.78600 | 0.0708197 | ||||||||
\(637\) | 19.0068 | 0.753077 | ||||||||
\(638\) | 2.58844 | 0.102477 | ||||||||
\(639\) | −5.22537 | −0.206712 | ||||||||
\(640\) | −1.87939 | −0.0742892 | ||||||||
\(641\) | −43.7391 | −1.72759 | −0.863795 | − | 0.503844i | \(-0.831919\pi\) | ||||
−0.863795 | + | 0.503844i | \(0.831919\pi\) | |||||||
\(642\) | 17.9921 | 0.710091 | ||||||||
\(643\) | −3.31553 | −0.130752 | −0.0653759 | − | 0.997861i | \(-0.520825\pi\) | ||||
−0.0653759 | + | 0.997861i | \(0.520825\pi\) | |||||||
\(644\) | −39.0370 | −1.53827 | ||||||||
\(645\) | 4.59059 | 0.180754 | ||||||||
\(646\) | −0.441380 | −0.0173659 | ||||||||
\(647\) | −22.8404 | −0.897950 | −0.448975 | − | 0.893544i | \(-0.648211\pi\) | ||||
−0.448975 | + | 0.893544i | \(0.648211\pi\) | |||||||
\(648\) | −11.1837 | −0.439337 | ||||||||
\(649\) | 27.0657 | 1.06242 | ||||||||
\(650\) | −2.84582 | −0.111622 | ||||||||
\(651\) | −92.9119 | −3.64151 | ||||||||
\(652\) | −2.39144 | −0.0936559 | ||||||||
\(653\) | 2.12737 | 0.0832505 | 0.0416252 | − | 0.999133i | \(-0.486746\pi\) | ||||
0.0416252 | + | 0.999133i | \(0.486746\pi\) | |||||||
\(654\) | −19.1606 | −0.749238 | ||||||||
\(655\) | −2.63803 | −0.103076 | ||||||||
\(656\) | 5.69443 | 0.222330 | ||||||||
\(657\) | −4.49466 | −0.175353 | ||||||||
\(658\) | 29.1641 | 1.13694 | ||||||||
\(659\) | −8.56624 | −0.333693 | −0.166847 | − | 0.985983i | \(-0.553358\pi\) | ||||
−0.166847 | + | 0.985983i | \(0.553358\pi\) | |||||||
\(660\) | −13.6987 | −0.533222 | ||||||||
\(661\) | 0.801614 | 0.0311792 | 0.0155896 | − | 0.999878i | \(-0.495037\pi\) | ||||
0.0155896 | + | 0.999878i | \(0.495037\pi\) | |||||||
\(662\) | −4.57313 | −0.177740 | ||||||||
\(663\) | 18.8028 | 0.730239 | ||||||||
\(664\) | 0.658250 | 0.0255451 | ||||||||
\(665\) | −0.764734 | −0.0296551 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.37622 | 0.285609 | ||||||||
\(668\) | −15.5840 | −0.602962 | ||||||||
\(669\) | −23.4575 | −0.906919 | ||||||||
\(670\) | −24.7446 | −0.955966 | ||||||||
\(671\) | −35.7598 | −1.38049 | ||||||||
\(672\) | −8.94120 | −0.344914 | ||||||||
\(673\) | 43.0383 | 1.65901 | 0.829503 | − | 0.558502i | \(-0.188624\pi\) | ||||
0.829503 | + | 0.558502i | \(0.188624\pi\) | |||||||
\(674\) | 3.25330 | 0.125313 | ||||||||
\(675\) | 3.97815 | 0.153119 | ||||||||
\(676\) | −9.24150 | −0.355442 | ||||||||
\(677\) | 19.9943 | 0.768444 | 0.384222 | − | 0.923241i | \(-0.374470\pi\) | ||||
0.384222 | + | 0.923241i | \(0.374470\pi\) | |||||||
\(678\) | 21.7613 | 0.835739 | ||||||||
\(679\) | −14.8403 | −0.569520 | ||||||||
\(680\) | −8.35680 | −0.320469 | ||||||||
\(681\) | −6.46775 | −0.247845 | ||||||||
\(682\) | 34.7256 | 1.32971 | ||||||||
\(683\) | 36.8290 | 1.40922 | 0.704611 | − | 0.709594i | \(-0.251122\pi\) | ||||
0.704611 | + | 0.709594i | \(0.251122\pi\) | |||||||
\(684\) | −0.174457 | −0.00667051 | ||||||||
\(685\) | −23.3406 | −0.891798 | ||||||||
\(686\) | −11.4942 | −0.438849 | ||||||||
\(687\) | −6.61468 | −0.252366 | ||||||||
\(688\) | −1.11986 | −0.0426942 | ||||||||
\(689\) | 1.58745 | 0.0604770 | ||||||||
\(690\) | −39.0370 | −1.48611 | ||||||||
\(691\) | 0.878837 | 0.0334325 | 0.0167163 | − | 0.999860i | \(-0.494679\pi\) | ||||
0.0167163 | + | 0.999860i | \(0.494679\pi\) | |||||||
\(692\) | −17.8772 | −0.679589 | ||||||||
\(693\) | −24.0757 | −0.914559 | ||||||||
\(694\) | 24.4774 | 0.929149 | ||||||||
\(695\) | −34.5799 | −1.31169 | ||||||||
\(696\) | 1.68948 | 0.0640397 | ||||||||
\(697\) | 25.3206 | 0.959087 | ||||||||
\(698\) | 5.70239 | 0.215839 | ||||||||
\(699\) | −0.629936 | −0.0238264 | ||||||||
\(700\) | 6.01735 | 0.227435 | ||||||||
\(701\) | −20.8420 | −0.787193 | −0.393596 | − | 0.919283i | \(-0.628769\pi\) | ||||
−0.393596 | + | 0.919283i | \(0.628769\pi\) | |||||||
\(702\) | −5.25399 | −0.198299 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 3.34175 | 0.125947 | ||||||||
\(705\) | 29.1641 | 1.09838 | ||||||||
\(706\) | 24.4340 | 0.919585 | ||||||||
\(707\) | −16.1844 | −0.608676 | ||||||||
\(708\) | 17.6659 | 0.663925 | ||||||||
\(709\) | −21.6348 | −0.812512 | −0.406256 | − | 0.913759i | \(-0.633166\pi\) | ||||
−0.406256 | + | 0.913759i | \(0.633166\pi\) | |||||||
\(710\) | 5.58771 | 0.209703 | ||||||||
\(711\) | −9.55319 | −0.358273 | ||||||||
\(712\) | 3.52523 | 0.132114 | ||||||||
\(713\) | 98.9569 | 3.70596 | ||||||||
\(714\) | −39.7576 | −1.48789 | ||||||||
\(715\) | −12.1758 | −0.455349 | ||||||||
\(716\) | −20.4063 | −0.762619 | ||||||||
\(717\) | −10.9824 | −0.410146 | ||||||||
\(718\) | 18.7092 | 0.698222 | ||||||||
\(719\) | 25.6877 | 0.957991 | 0.478996 | − | 0.877817i | \(-0.341001\pi\) | ||||
0.478996 | + | 0.877817i | \(0.341001\pi\) | |||||||
\(720\) | −3.30304 | −0.123097 | ||||||||
\(721\) | 8.11164 | 0.302093 | ||||||||
\(722\) | −18.9901 | −0.706740 | ||||||||
\(723\) | −37.9000 | −1.40952 | ||||||||
\(724\) | −18.2764 | −0.679238 | ||||||||
\(725\) | −1.13701 | −0.0422274 | ||||||||
\(726\) | 0.364896 | 0.0135426 | ||||||||
\(727\) | 26.6751 | 0.989326 | 0.494663 | − | 0.869085i | \(-0.335291\pi\) | ||||
0.494663 | + | 0.869085i | \(0.335291\pi\) | |||||||
\(728\) | −7.94718 | −0.294542 | ||||||||
\(729\) | −1.92204 | −0.0711865 | ||||||||
\(730\) | 4.80633 | 0.177890 | ||||||||
\(731\) | −4.97952 | −0.184174 | ||||||||
\(732\) | −23.3405 | −0.862691 | ||||||||
\(733\) | −11.3802 | −0.420336 | −0.210168 | − | 0.977665i | \(-0.567401\pi\) | ||||
−0.210168 | + | 0.977665i | \(0.567401\pi\) | |||||||
\(734\) | 33.7230 | 1.24474 | ||||||||
\(735\) | −40.1890 | −1.48239 | ||||||||
\(736\) | 9.52292 | 0.351020 | ||||||||
\(737\) | 43.9985 | 1.62071 | ||||||||
\(738\) | 10.0080 | 0.368401 | ||||||||
\(739\) | 3.18059 | 0.117000 | 0.0584999 | − | 0.998287i | \(-0.481368\pi\) | ||||
0.0584999 | + | 0.998287i | \(0.481368\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.419746 | −0.0154197 | ||||||||
\(742\) | −3.35659 | −0.123224 | ||||||||
\(743\) | −52.9609 | −1.94295 | −0.971473 | − | 0.237151i | \(-0.923786\pi\) | ||||
−0.971473 | + | 0.237151i | \(0.923786\pi\) | |||||||
\(744\) | 22.6655 | 0.830958 | ||||||||
\(745\) | −23.3171 | −0.854273 | ||||||||
\(746\) | 31.4347 | 1.15091 | ||||||||
\(747\) | 1.15688 | 0.0423281 | ||||||||
\(748\) | 14.8593 | 0.543309 | ||||||||
\(749\) | −33.8141 | −1.23554 | ||||||||
\(750\) | 26.5137 | 0.968142 | ||||||||
\(751\) | −6.42966 | −0.234621 | −0.117311 | − | 0.993095i | \(-0.537427\pi\) | ||||
−0.117311 | + | 0.993095i | \(0.537427\pi\) | |||||||
\(752\) | −7.11448 | −0.259438 | ||||||||
\(753\) | −3.82946 | −0.139553 | ||||||||
\(754\) | 1.50166 | 0.0546872 | ||||||||
\(755\) | 23.5842 | 0.858317 | ||||||||
\(756\) | 11.1093 | 0.404042 | ||||||||
\(757\) | −31.7443 | −1.15377 | −0.576883 | − | 0.816827i | \(-0.695731\pi\) | ||||
−0.576883 | + | 0.816827i | \(0.695731\pi\) | |||||||
\(758\) | 6.96691 | 0.253050 | ||||||||
\(759\) | 69.4119 | 2.51949 | ||||||||
\(760\) | 0.186554 | 0.00676702 | ||||||||
\(761\) | −23.0835 | −0.836778 | −0.418389 | − | 0.908268i | \(-0.637405\pi\) | ||||
−0.418389 | + | 0.908268i | \(0.637405\pi\) | |||||||
\(762\) | −36.5944 | −1.32567 | ||||||||
\(763\) | 36.0101 | 1.30365 | ||||||||
\(764\) | 5.76567 | 0.208595 | ||||||||
\(765\) | −14.6872 | −0.531016 | ||||||||
\(766\) | −2.87727 | −0.103960 | ||||||||
\(767\) | 15.7019 | 0.566964 | ||||||||
\(768\) | 2.18117 | 0.0787063 | ||||||||
\(769\) | 47.1598 | 1.70062 | 0.850312 | − | 0.526278i | \(-0.176413\pi\) | ||||
0.850312 | + | 0.526278i | \(0.176413\pi\) | |||||||
\(770\) | 25.7452 | 0.927791 | ||||||||
\(771\) | −27.8188 | −1.00187 | ||||||||
\(772\) | −0.359424 | −0.0129360 | ||||||||
\(773\) | −4.00160 | −0.143927 | −0.0719637 | − | 0.997407i | \(-0.522927\pi\) | ||||
−0.0719637 | + | 0.997407i | \(0.522927\pi\) | |||||||
\(774\) | −1.96817 | −0.0707442 | ||||||||
\(775\) | −15.2537 | −0.547929 | ||||||||
\(776\) | 3.62024 | 0.129959 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −11.8116 | −0.423467 | ||||||||
\(779\) | −0.565248 | −0.0202521 | ||||||||
\(780\) | −7.94718 | −0.284555 | ||||||||
\(781\) | −9.93556 | −0.355522 | ||||||||
\(782\) | 42.3442 | 1.51423 | ||||||||
\(783\) | −2.09916 | −0.0750179 | ||||||||
\(784\) | 9.80396 | 0.350141 | ||||||||
\(785\) | −6.60276 | −0.235663 | ||||||||
\(786\) | 3.06164 | 0.109205 | ||||||||
\(787\) | 11.5669 | 0.412315 | 0.206157 | − | 0.978519i | \(-0.433904\pi\) | ||||
0.206157 | + | 0.978519i | \(0.433904\pi\) | |||||||
\(788\) | 6.96601 | 0.248154 | ||||||||
\(789\) | −57.5068 | −2.04730 | ||||||||
\(790\) | 10.2156 | 0.363456 | ||||||||
\(791\) | −40.8979 | −1.45416 | ||||||||
\(792\) | 5.87317 | 0.208694 | ||||||||
\(793\) | −20.7457 | −0.736702 | ||||||||
\(794\) | −31.3125 | −1.11124 | ||||||||
\(795\) | −3.35659 | −0.119046 | ||||||||
\(796\) | 11.1779 | 0.396191 | ||||||||
\(797\) | −36.6547 | −1.29838 | −0.649189 | − | 0.760627i | \(-0.724891\pi\) | ||||
−0.649189 | + | 0.760627i | \(0.724891\pi\) | |||||||
\(798\) | 0.887533 | 0.0314183 | ||||||||
\(799\) | −31.6349 | −1.11916 | ||||||||
\(800\) | −1.46791 | −0.0518985 | ||||||||
\(801\) | 6.19564 | 0.218912 | ||||||||
\(802\) | −14.0281 | −0.495351 | ||||||||
\(803\) | −8.54618 | −0.301588 | ||||||||
\(804\) | 28.7180 | 1.01281 | ||||||||
\(805\) | 73.3655 | 2.58579 | ||||||||
\(806\) | 20.1457 | 0.709603 | ||||||||
\(807\) | 29.6765 | 1.04466 | ||||||||
\(808\) | 3.94811 | 0.138894 | ||||||||
\(809\) | −7.79653 | −0.274112 | −0.137056 | − | 0.990563i | \(-0.543764\pi\) | ||||
−0.137056 | + | 0.990563i | \(0.543764\pi\) | |||||||
\(810\) | 21.0185 | 0.738513 | ||||||||
\(811\) | −29.7682 | −1.04530 | −0.522652 | − | 0.852546i | \(-0.675057\pi\) | ||||
−0.522652 | + | 0.852546i | \(0.675057\pi\) | |||||||
\(812\) | −3.17519 | −0.111427 | ||||||||
\(813\) | −9.41372 | −0.330154 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.49443 | 0.157433 | ||||||||
\(816\) | 9.69871 | 0.339523 | ||||||||
\(817\) | 0.111161 | 0.00388902 | ||||||||
\(818\) | −0.0810699 | −0.00283454 | ||||||||
\(819\) | −13.9673 | −0.488056 | ||||||||
\(820\) | −10.7020 | −0.373731 | ||||||||
\(821\) | 39.2154 | 1.36863 | 0.684313 | − | 0.729188i | \(-0.260102\pi\) | ||||
0.684313 | + | 0.729188i | \(0.260102\pi\) | |||||||
\(822\) | 27.0886 | 0.944822 | ||||||||
\(823\) | −12.1146 | −0.422288 | −0.211144 | − | 0.977455i | \(-0.567719\pi\) | ||||
−0.211144 | + | 0.977455i | \(0.567719\pi\) | |||||||
\(824\) | −1.97880 | −0.0689349 | ||||||||
\(825\) | −10.6995 | −0.372509 | ||||||||
\(826\) | −33.2010 | −1.15521 | ||||||||
\(827\) | −14.0447 | −0.488384 | −0.244192 | − | 0.969727i | \(-0.578523\pi\) | ||||
−0.244192 | + | 0.969727i | \(0.578523\pi\) | |||||||
\(828\) | 16.7367 | 0.581639 | ||||||||
\(829\) | 32.0629 | 1.11359 | 0.556796 | − | 0.830649i | \(-0.312031\pi\) | ||||
0.556796 | + | 0.830649i | \(0.312031\pi\) | |||||||
\(830\) | −1.23711 | −0.0429405 | ||||||||
\(831\) | −7.61980 | −0.264328 | ||||||||
\(832\) | 1.93869 | 0.0672118 | ||||||||
\(833\) | 43.5939 | 1.51044 | ||||||||
\(834\) | 40.1326 | 1.38968 | ||||||||
\(835\) | 29.2883 | 1.01356 | ||||||||
\(836\) | −0.331713 | −0.0114725 | ||||||||
\(837\) | −28.1616 | −0.973407 | ||||||||
\(838\) | 4.63611 | 0.160152 | ||||||||
\(839\) | −11.0541 | −0.381631 | −0.190815 | − | 0.981626i | \(-0.561113\pi\) | ||||
−0.190815 | + | 0.981626i | \(0.561113\pi\) | |||||||
\(840\) | 16.8040 | 0.579792 | ||||||||
\(841\) | −28.4000 | −0.979311 | ||||||||
\(842\) | −19.3222 | −0.665887 | ||||||||
\(843\) | −16.0049 | −0.551238 | ||||||||
\(844\) | −12.2103 | −0.420295 | ||||||||
\(845\) | 17.3683 | 0.597489 | ||||||||
\(846\) | −12.5038 | −0.429889 | ||||||||
\(847\) | −0.685780 | −0.0235637 | ||||||||
\(848\) | 0.818828 | 0.0281187 | ||||||||
\(849\) | 30.5427 | 1.04822 | ||||||||
\(850\) | −6.52715 | −0.223880 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | −6.48497 | −0.222172 | ||||||||
\(853\) | 51.1448 | 1.75116 | 0.875582 | − | 0.483070i | \(-0.160478\pi\) | ||||
0.875582 | + | 0.483070i | \(0.160478\pi\) | |||||||
\(854\) | 43.8659 | 1.50106 | ||||||||
\(855\) | 0.327871 | 0.0112130 | ||||||||
\(856\) | 8.24882 | 0.281939 | ||||||||
\(857\) | −11.4315 | −0.390493 | −0.195246 | − | 0.980754i | \(-0.562551\pi\) | ||||
−0.195246 | + | 0.980754i | \(0.562551\pi\) | |||||||
\(858\) | 14.1310 | 0.482423 | ||||||||
\(859\) | −10.9927 | −0.375066 | −0.187533 | − | 0.982258i | \(-0.560049\pi\) | ||||
−0.187533 | + | 0.982258i | \(0.560049\pi\) | |||||||
\(860\) | 2.10464 | 0.0717678 | ||||||||
\(861\) | −50.9150 | −1.73518 | ||||||||
\(862\) | 7.54172 | 0.256872 | ||||||||
\(863\) | −15.0332 | −0.511737 | −0.255869 | − | 0.966712i | \(-0.582361\pi\) | ||||
−0.255869 | + | 0.966712i | \(0.582361\pi\) | |||||||
\(864\) | −2.71008 | −0.0921987 | ||||||||
\(865\) | 33.5981 | 1.14237 | ||||||||
\(866\) | 29.8339 | 1.01380 | ||||||||
\(867\) | 6.04598 | 0.205332 | ||||||||
\(868\) | −42.5972 | −1.44584 | ||||||||
\(869\) | −18.1645 | −0.616189 | ||||||||
\(870\) | −3.17519 | −0.107649 | ||||||||
\(871\) | 25.5253 | 0.864893 | ||||||||
\(872\) | −8.78453 | −0.297482 | ||||||||
\(873\) | 6.36263 | 0.215342 | ||||||||
\(874\) | −0.945277 | −0.0319745 | ||||||||
\(875\) | −49.8294 | −1.68454 | ||||||||
\(876\) | −5.57812 | −0.188467 | ||||||||
\(877\) | −29.4471 | −0.994360 | −0.497180 | − | 0.867648i | \(-0.665631\pi\) | ||||
−0.497180 | + | 0.867648i | \(0.665631\pi\) | |||||||
\(878\) | 21.9541 | 0.740915 | ||||||||
\(879\) | −55.1286 | −1.85944 | ||||||||
\(880\) | −6.28044 | −0.211713 | ||||||||
\(881\) | 18.3789 | 0.619200 | 0.309600 | − | 0.950867i | \(-0.399805\pi\) | ||||
0.309600 | + | 0.950867i | \(0.399805\pi\) | |||||||
\(882\) | 17.2306 | 0.580184 | ||||||||
\(883\) | 29.1969 | 0.982555 | 0.491278 | − | 0.871003i | \(-0.336530\pi\) | ||||
0.491278 | + | 0.871003i | \(0.336530\pi\) | |||||||
\(884\) | 8.62048 | 0.289938 | ||||||||
\(885\) | −33.2010 | −1.11604 | ||||||||
\(886\) | −34.6241 | −1.16322 | ||||||||
\(887\) | −36.5446 | −1.22705 | −0.613524 | − | 0.789676i | \(-0.710249\pi\) | ||||
−0.613524 | + | 0.789676i | \(0.710249\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 68.7749 | 2.30664 | ||||||||
\(890\) | −6.62526 | −0.222079 | ||||||||
\(891\) | −37.3731 | −1.25205 | ||||||||
\(892\) | −10.7545 | −0.360088 | ||||||||
\(893\) | 0.706206 | 0.0236323 | ||||||||
\(894\) | 27.0613 | 0.905066 | ||||||||
\(895\) | 38.3513 | 1.28194 | ||||||||
\(896\) | −4.09926 | −0.136947 | ||||||||
\(897\) | 40.2687 | 1.34453 | ||||||||
\(898\) | −19.9414 | −0.665453 | ||||||||
\(899\) | 8.04895 | 0.268448 | ||||||||
\(900\) | −2.57987 | −0.0859958 | ||||||||
\(901\) | 3.64097 | 0.121298 | ||||||||
\(902\) | 19.0294 | 0.633608 | ||||||||
\(903\) | 10.0129 | 0.333208 | ||||||||
\(904\) | 9.97690 | 0.331827 | ||||||||
\(905\) | 34.3485 | 1.14178 | ||||||||
\(906\) | −27.3713 | −0.909351 | ||||||||
\(907\) | 18.2228 | 0.605080 | 0.302540 | − | 0.953137i | \(-0.402165\pi\) | ||||
0.302540 | + | 0.953137i | \(0.402165\pi\) | |||||||
\(908\) | −2.96526 | −0.0984057 | ||||||||
\(909\) | 6.93886 | 0.230148 | ||||||||
\(910\) | 14.9358 | 0.495118 | ||||||||
\(911\) | −52.4746 | −1.73856 | −0.869280 | − | 0.494319i | \(-0.835417\pi\) | ||||
−0.869280 | + | 0.494319i | \(0.835417\pi\) | |||||||
\(912\) | −0.216510 | −0.00716938 | ||||||||
\(913\) | 2.19971 | 0.0727997 | ||||||||
\(914\) | 32.2388 | 1.06637 | ||||||||
\(915\) | 43.8659 | 1.45016 | ||||||||
\(916\) | −3.03262 | −0.100201 | ||||||||
\(917\) | −5.75400 | −0.190014 | ||||||||
\(918\) | −12.0505 | −0.397727 | ||||||||
\(919\) | −44.3955 | −1.46447 | −0.732236 | − | 0.681051i | \(-0.761523\pi\) | ||||
−0.732236 | + | 0.681051i | \(0.761523\pi\) | |||||||
\(920\) | −17.8972 | −0.590055 | ||||||||
\(921\) | −53.6548 | −1.76799 | ||||||||
\(922\) | 7.32821 | 0.241342 | ||||||||
\(923\) | −5.76402 | −0.189725 | ||||||||
\(924\) | −29.8793 | −0.982955 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 6.48631 | 0.213153 | ||||||||
\(927\) | −3.47777 | −0.114225 | ||||||||
\(928\) | 0.774576 | 0.0254267 | ||||||||
\(929\) | 29.9244 | 0.981787 | 0.490893 | − | 0.871220i | \(-0.336670\pi\) | ||||
0.490893 | + | 0.871220i | \(0.336670\pi\) | |||||||
\(930\) | −42.5972 | −1.39682 | ||||||||
\(931\) | −0.973173 | −0.0318945 | ||||||||
\(932\) | −0.288806 | −0.00946016 | ||||||||
\(933\) | 11.3577 | 0.371834 | ||||||||
\(934\) | −11.9858 | −0.392186 | ||||||||
\(935\) | −27.9263 | −0.913289 | ||||||||
\(936\) | 3.40727 | 0.111370 | ||||||||
\(937\) | 9.94451 | 0.324873 | 0.162436 | − | 0.986719i | \(-0.448065\pi\) | ||||
0.162436 | + | 0.986719i | \(0.448065\pi\) | |||||||
\(938\) | −53.9721 | −1.76225 | ||||||||
\(939\) | 15.7838 | 0.515086 | ||||||||
\(940\) | 13.3708 | 0.436109 | ||||||||
\(941\) | 12.3569 | 0.402824 | 0.201412 | − | 0.979507i | \(-0.435447\pi\) | ||||
0.201412 | + | 0.979507i | \(0.435447\pi\) | |||||||
\(942\) | 7.66302 | 0.249675 | ||||||||
\(943\) | 54.2276 | 1.76589 | ||||||||
\(944\) | 8.09926 | 0.263609 | ||||||||
\(945\) | −20.8787 | −0.679184 | ||||||||
\(946\) | −3.74229 | −0.121672 | ||||||||
\(947\) | −27.9971 | −0.909784 | −0.454892 | − | 0.890547i | \(-0.650322\pi\) | ||||
−0.454892 | + | 0.890547i | \(0.650322\pi\) | |||||||
\(948\) | −11.8561 | −0.385067 | ||||||||
\(949\) | −4.95799 | −0.160943 | ||||||||
\(950\) | 0.145710 | 0.00472745 | ||||||||
\(951\) | −29.1165 | −0.944167 | ||||||||
\(952\) | −18.2276 | −0.590761 | ||||||||
\(953\) | 43.8032 | 1.41893 | 0.709463 | − | 0.704743i | \(-0.248938\pi\) | ||||
0.709463 | + | 0.704743i | \(0.248938\pi\) | |||||||
\(954\) | 1.43910 | 0.0465926 | ||||||||
\(955\) | −10.8359 | −0.350642 | ||||||||
\(956\) | −5.03510 | −0.162847 | ||||||||
\(957\) | 5.64583 | 0.182504 | ||||||||
\(958\) | 22.6922 | 0.733152 | ||||||||
\(959\) | −50.9099 | −1.64396 | ||||||||
\(960\) | −4.09926 | −0.132303 | ||||||||
\(961\) | 76.9820 | 2.48329 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 14.4974 | 0.467172 | ||||||||
\(964\) | −17.3760 | −0.559642 | ||||||||
\(965\) | 0.675497 | 0.0217450 | ||||||||
\(966\) | −85.1464 | −2.73954 | ||||||||
\(967\) | −55.3082 | −1.77859 | −0.889295 | − | 0.457334i | \(-0.848805\pi\) | ||||
−0.889295 | + | 0.457334i | \(0.848805\pi\) | |||||||
\(968\) | 0.167293 | 0.00537702 | ||||||||
\(969\) | −0.962726 | −0.0309272 | ||||||||
\(970\) | −6.80383 | −0.218458 | ||||||||
\(971\) | −55.1799 | −1.77081 | −0.885404 | − | 0.464822i | \(-0.846118\pi\) | ||||
−0.885404 | + | 0.464822i | \(0.846118\pi\) | |||||||
\(972\) | −16.2633 | −0.521646 | ||||||||
\(973\) | −75.4247 | −2.41800 | ||||||||
\(974\) | 12.3108 | 0.394464 | ||||||||
\(975\) | −6.20722 | −0.198790 | ||||||||
\(976\) | −10.7009 | −0.342528 | ||||||||
\(977\) | −25.5345 | −0.816920 | −0.408460 | − | 0.912776i | \(-0.633934\pi\) | ||||
−0.408460 | + | 0.912776i | \(0.633934\pi\) | |||||||
\(978\) | −5.21614 | −0.166794 | ||||||||
\(979\) | 11.7804 | 0.376504 | ||||||||
\(980\) | −18.4254 | −0.588578 | ||||||||
\(981\) | −15.4389 | −0.492927 | ||||||||
\(982\) | 1.15080 | 0.0367234 | ||||||||
\(983\) | −31.2734 | −0.997465 | −0.498733 | − | 0.866756i | \(-0.666201\pi\) | ||||
−0.498733 | + | 0.866756i | \(0.666201\pi\) | |||||||
\(984\) | 12.4205 | 0.395952 | ||||||||
\(985\) | −13.0918 | −0.417140 | ||||||||
\(986\) | 3.44420 | 0.109686 | ||||||||
\(987\) | 63.6120 | 2.02479 | ||||||||
\(988\) | −0.192440 | −0.00612234 | ||||||||
\(989\) | −10.6643 | −0.339106 | ||||||||
\(990\) | −11.0379 | −0.350809 | ||||||||
\(991\) | −7.61348 | −0.241850 | −0.120925 | − | 0.992662i | \(-0.538586\pi\) | ||||
−0.120925 | + | 0.992662i | \(0.538586\pi\) | |||||||
\(992\) | 10.3914 | 0.329928 | ||||||||
\(993\) | −9.97478 | −0.316540 | ||||||||
\(994\) | 12.1878 | 0.386572 | ||||||||
\(995\) | −21.0076 | −0.665987 | ||||||||
\(996\) | 1.43576 | 0.0454937 | ||||||||
\(997\) | 15.6027 | 0.494143 | 0.247071 | − | 0.968997i | \(-0.420532\pi\) | ||||
0.247071 | + | 0.968997i | \(0.420532\pi\) | |||||||
\(998\) | 27.9156 | 0.883653 | ||||||||
\(999\) | 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.t.1.5 | 6 | ||
37.9 | even | 9 | 74.2.f.b.7.1 | ✓ | 12 | ||
37.33 | even | 9 | 74.2.f.b.53.1 | yes | 12 | ||
37.36 | even | 2 | 2738.2.a.q.1.5 | 6 | |||
111.83 | odd | 18 | 666.2.x.g.451.1 | 12 | |||
111.107 | odd | 18 | 666.2.x.g.127.1 | 12 | |||
148.83 | odd | 18 | 592.2.bc.d.81.2 | 12 | |||
148.107 | odd | 18 | 592.2.bc.d.497.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
74.2.f.b.7.1 | ✓ | 12 | 37.9 | even | 9 | ||
74.2.f.b.53.1 | yes | 12 | 37.33 | even | 9 | ||
592.2.bc.d.81.2 | 12 | 148.83 | odd | 18 | |||
592.2.bc.d.497.2 | 12 | 148.107 | odd | 18 | |||
666.2.x.g.127.1 | 12 | 111.107 | odd | 18 | |||
666.2.x.g.451.1 | 12 | 111.83 | odd | 18 | |||
2738.2.a.q.1.5 | 6 | 37.36 | even | 2 | |||
2738.2.a.t.1.5 | 6 | 1.1 | even | 1 | trivial |