Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4014,2,Mod(1,4014)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4014, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4014.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4014 = 2 \cdot 3^{2} \cdot 223 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4014.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: | \(32.0519513713\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.473.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 5x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1338) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.33006\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4014.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.42917 | 1.08636 | 0.543180 | − | 0.839616i | \(-0.317220\pi\) | ||||
0.543180 | + | 0.839616i | \(0.317220\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.669941 | 0.253214 | 0.126607 | − | 0.991953i | \(-0.459591\pi\) | ||||
0.126607 | + | 0.991953i | \(0.459591\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.42917 | 0.768172 | ||||||||
\(11\) | 0.330059 | 0.0995165 | 0.0497582 | − | 0.998761i | \(-0.484155\pi\) | ||||
0.0497582 | + | 0.998761i | \(0.484155\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.57083 | 0.435669 | 0.217834 | − | 0.975986i | \(-0.430101\pi\) | ||||
0.217834 | + | 0.975986i | \(0.430101\pi\) | |||||||
\(14\) | 0.669941 | 0.179049 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.23094 | 0.783619 | 0.391809 | − | 0.920046i | \(-0.371849\pi\) | ||||
0.391809 | + | 0.920046i | \(0.371849\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.90089 | 0.436093 | 0.218046 | − | 0.975938i | \(-0.430032\pi\) | ||||
0.218046 | + | 0.975938i | \(0.430032\pi\) | |||||||
\(20\) | 2.42917 | 0.543180 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.330059 | 0.0703688 | ||||||||
\(23\) | 2.52829 | 0.527185 | 0.263592 | − | 0.964634i | \(-0.415093\pi\) | ||||
0.263592 | + | 0.964634i | \(0.415093\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.900885 | 0.180177 | ||||||||
\(26\) | 1.57083 | 0.308064 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.669941 | 0.126607 | ||||||||
\(29\) | 5.33006 | 0.989767 | 0.494884 | − | 0.868959i | \(-0.335211\pi\) | ||||
0.494884 | + | 0.868959i | \(0.335211\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.56100 | −1.17839 | −0.589195 | − | 0.807991i | \(-0.700555\pi\) | ||||
−0.589195 | + | 0.807991i | \(0.700555\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.23094 | 0.554102 | ||||||||
\(35\) | 1.62740 | 0.275081 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.38664 | 1.21436 | 0.607178 | − | 0.794566i | \(-0.292302\pi\) | ||||
0.607178 | + | 0.794566i | \(0.292302\pi\) | |||||||
\(38\) | 1.90089 | 0.308364 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.42917 | 0.384086 | ||||||||
\(41\) | −12.2211 | −1.90862 | −0.954309 | − | 0.298821i | \(-0.903407\pi\) | ||||
−0.954309 | + | 0.298821i | \(0.903407\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.56100 | 0.848045 | 0.424022 | − | 0.905652i | \(-0.360618\pi\) | ||||
0.424022 | + | 0.905652i | \(0.360618\pi\) | |||||||
\(44\) | 0.330059 | 0.0497582 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.52829 | 0.372776 | ||||||||
\(47\) | −3.08929 | −0.450619 | −0.225310 | − | 0.974287i | \(-0.572339\pi\) | ||||
−0.225310 | + | 0.974287i | \(0.572339\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.55118 | −0.935883 | ||||||||
\(50\) | 0.900885 | 0.127404 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.57083 | 0.217834 | ||||||||
\(53\) | −4.95746 | −0.680960 | −0.340480 | − | 0.940252i | \(-0.610590\pi\) | ||||
−0.340480 | + | 0.940252i | \(0.610590\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.801770 | 0.108111 | ||||||||
\(56\) | 0.669941 | 0.0895247 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.33006 | 0.699871 | ||||||||
\(59\) | −4.28752 | −0.558188 | −0.279094 | − | 0.960264i | \(-0.590034\pi\) | ||||
−0.279094 | + | 0.960264i | \(0.590034\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.79195 | −0.997656 | −0.498828 | − | 0.866701i | \(-0.666236\pi\) | ||||
−0.498828 | + | 0.866701i | \(0.666236\pi\) | |||||||
\(62\) | −6.56100 | −0.833248 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.81581 | 0.473293 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.2875 | 1.37899 | 0.689495 | − | 0.724290i | \(-0.257832\pi\) | ||||
0.689495 | + | 0.724290i | \(0.257832\pi\) | |||||||
\(68\) | 3.23094 | 0.391809 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.62740 | 0.194512 | ||||||||
\(71\) | 9.66012 | 1.14645 | 0.573223 | − | 0.819400i | \(-0.305693\pi\) | ||||
0.573223 | + | 0.819400i | \(0.305693\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.5512 | 1.23492 | 0.617461 | − | 0.786601i | \(-0.288161\pi\) | ||||
0.617461 | + | 0.786601i | \(0.288161\pi\) | |||||||
\(74\) | 7.38664 | 0.858679 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.90089 | 0.218046 | ||||||||
\(77\) | 0.221120 | 0.0251990 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.7919 | 1.66422 | 0.832112 | − | 0.554608i | \(-0.187132\pi\) | ||||
0.832112 | + | 0.554608i | \(0.187132\pi\) | |||||||
\(80\) | 2.42917 | 0.271590 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −12.2211 | −1.34960 | ||||||||
\(83\) | 8.27770 | 0.908595 | 0.454298 | − | 0.890850i | \(-0.349890\pi\) | ||||
0.454298 | + | 0.890850i | \(0.349890\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.84852 | 0.851292 | ||||||||
\(86\) | 5.56100 | 0.599658 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.330059 | 0.0351844 | ||||||||
\(89\) | −11.2450 | −1.19197 | −0.595983 | − | 0.802997i | \(-0.703237\pi\) | ||||
−0.595983 | + | 0.802997i | \(0.703237\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.05236 | 0.110317 | ||||||||
\(92\) | 2.52829 | 0.263592 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.08929 | −0.318636 | ||||||||
\(95\) | 4.61758 | 0.473754 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.22112 | 0.936263 | 0.468131 | − | 0.883659i | \(-0.344927\pi\) | ||||
0.468131 | + | 0.883659i | \(0.344927\pi\) | |||||||
\(98\) | −6.55118 | −0.661769 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.900885 | 0.0900885 | ||||||||
\(101\) | −13.5086 | −1.34416 | −0.672080 | − | 0.740479i | \(-0.734599\pi\) | ||||
−0.672080 | + | 0.740479i | \(0.734599\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.0000 | 1.37946 | 0.689730 | − | 0.724066i | \(-0.257729\pi\) | ||||
0.689730 | + | 0.724066i | \(0.257729\pi\) | |||||||
\(104\) | 1.57083 | 0.154032 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.95746 | −0.481511 | ||||||||
\(107\) | −11.8158 | −1.14228 | −0.571139 | − | 0.820854i | \(-0.693498\pi\) | ||||
−0.571139 | + | 0.820854i | \(0.693498\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.2777 | −1.17599 | −0.587995 | − | 0.808865i | \(-0.700083\pi\) | ||||
−0.587995 | + | 0.808865i | \(0.700083\pi\) | |||||||
\(110\) | 0.801770 | 0.0764458 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.669941 | 0.0633035 | ||||||||
\(113\) | −3.99018 | −0.375364 | −0.187682 | − | 0.982230i | \(-0.560097\pi\) | ||||
−0.187682 | + | 0.982230i | \(0.560097\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.14165 | 0.572712 | ||||||||
\(116\) | 5.33006 | 0.494884 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.28752 | −0.394698 | ||||||||
\(119\) | 2.16454 | 0.198423 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.8911 | −0.990096 | ||||||||
\(122\) | −7.79195 | −0.705450 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −6.56100 | −0.589195 | ||||||||
\(125\) | −9.95746 | −0.890623 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.50443 | 0.222232 | 0.111116 | − | 0.993807i | \(-0.464558\pi\) | ||||
0.111116 | + | 0.993807i | \(0.464558\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 3.81581 | 0.334669 | ||||||||
\(131\) | −7.85835 | −0.686587 | −0.343294 | − | 0.939228i | \(-0.611543\pi\) | ||||
−0.343294 | + | 0.939228i | \(0.611543\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.27348 | 0.110425 | ||||||||
\(134\) | 11.2875 | 0.975093 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.23094 | 0.277051 | ||||||||
\(137\) | 22.5979 | 1.93067 | 0.965336 | − | 0.261011i | \(-0.0840559\pi\) | ||||
0.965336 | + | 0.261011i | \(0.0840559\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.91071 | 0.501340 | 0.250670 | − | 0.968073i | \(-0.419349\pi\) | ||||
0.250670 | + | 0.968073i | \(0.419349\pi\) | |||||||
\(140\) | 1.62740 | 0.137541 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 9.66012 | 0.810659 | ||||||||
\(143\) | 0.518465 | 0.0433562 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 12.9476 | 1.07524 | ||||||||
\(146\) | 10.5512 | 0.873222 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 7.38664 | 0.607178 | ||||||||
\(149\) | 2.75923 | 0.226045 | 0.113023 | − | 0.993592i | \(-0.463947\pi\) | ||||
0.113023 | + | 0.993592i | \(0.463947\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.07947 | 0.331982 | 0.165991 | − | 0.986127i | \(-0.446918\pi\) | ||||
0.165991 | + | 0.986127i | \(0.446918\pi\) | |||||||
\(152\) | 1.90089 | 0.154182 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.221120 | 0.0178184 | ||||||||
\(155\) | −15.9378 | −1.28016 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.1688 | −1.05098 | −0.525491 | − | 0.850799i | \(-0.676118\pi\) | ||||
−0.525491 | + | 0.850799i | \(0.676118\pi\) | |||||||
\(158\) | 14.7919 | 1.17678 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.42917 | 0.192043 | ||||||||
\(161\) | 1.69380 | 0.133491 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.1132 | 0.792123 | 0.396062 | − | 0.918224i | \(-0.370377\pi\) | ||||
0.396062 | + | 0.918224i | \(0.370377\pi\) | |||||||
\(164\) | −12.2211 | −0.954309 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8.27770 | 0.642474 | ||||||||
\(167\) | −19.9575 | −1.54435 | −0.772177 | − | 0.635407i | \(-0.780832\pi\) | ||||
−0.772177 | + | 0.635407i | \(0.780832\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.5325 | −0.810193 | ||||||||
\(170\) | 7.84852 | 0.601954 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5.56100 | 0.424022 | ||||||||
\(173\) | −13.4095 | −1.01951 | −0.509754 | − | 0.860320i | \(-0.670263\pi\) | ||||
−0.509754 | + | 0.860320i | \(0.670263\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.603540 | 0.0456233 | ||||||||
\(176\) | 0.330059 | 0.0248791 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −11.2450 | −0.842847 | ||||||||
\(179\) | −1.59372 | −0.119120 | −0.0595600 | − | 0.998225i | \(-0.518970\pi\) | ||||
−0.0595600 | + | 0.998225i | \(0.518970\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.08929 | 0.229625 | 0.114813 | − | 0.993387i | \(-0.463373\pi\) | ||||
0.114813 | + | 0.993387i | \(0.463373\pi\) | |||||||
\(182\) | 1.05236 | 0.0780062 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.52829 | 0.186388 | ||||||||
\(185\) | 17.9434 | 1.31923 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.06640 | 0.0779830 | ||||||||
\(188\) | −3.08929 | −0.225310 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.61758 | 0.334994 | ||||||||
\(191\) | −7.50443 | −0.543001 | −0.271501 | − | 0.962438i | \(-0.587520\pi\) | ||||
−0.271501 | + | 0.962438i | \(0.587520\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.7069 | 1.27457 | 0.637284 | − | 0.770629i | \(-0.280058\pi\) | ||||
0.637284 | + | 0.770629i | \(0.280058\pi\) | |||||||
\(194\) | 9.22112 | 0.662038 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.55118 | −0.467941 | ||||||||
\(197\) | −5.42917 | −0.386813 | −0.193406 | − | 0.981119i | \(-0.561954\pi\) | ||||
−0.193406 | + | 0.981119i | \(0.561954\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.00982 | −0.142473 | −0.0712363 | − | 0.997459i | \(-0.522694\pi\) | ||||
−0.0712363 | + | 0.997459i | \(0.522694\pi\) | |||||||
\(200\) | 0.900885 | 0.0637022 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −13.5086 | −0.950465 | ||||||||
\(203\) | 3.57083 | 0.250623 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −29.6872 | −2.07345 | ||||||||
\(206\) | 14.0000 | 0.975426 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.57083 | 0.108917 | ||||||||
\(209\) | 0.627404 | 0.0433984 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.19823 | 0.0824896 | 0.0412448 | − | 0.999149i | \(-0.486868\pi\) | ||||
0.0412448 | + | 0.999149i | \(0.486868\pi\) | |||||||
\(212\) | −4.95746 | −0.340480 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −11.8158 | −0.807712 | ||||||||
\(215\) | 13.5086 | 0.921282 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.39549 | −0.298385 | ||||||||
\(218\) | −12.2777 | −0.831551 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.801770 | 0.0540553 | ||||||||
\(221\) | 5.07525 | 0.341398 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.00000 | 0.0669650 | ||||||||
\(224\) | 0.669941 | 0.0447623 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.99018 | −0.265423 | ||||||||
\(227\) | 1.93360 | 0.128337 | 0.0641687 | − | 0.997939i | \(-0.479560\pi\) | ||||
0.0641687 | + | 0.997939i | \(0.479560\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.4563 | 1.08746 | 0.543731 | − | 0.839260i | \(-0.317011\pi\) | ||||
0.543731 | + | 0.839260i | \(0.317011\pi\) | |||||||
\(230\) | 6.14165 | 0.404969 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.33006 | 0.349936 | ||||||||
\(233\) | 7.17437 | 0.470008 | 0.235004 | − | 0.971994i | \(-0.424490\pi\) | ||||
0.235004 | + | 0.971994i | \(0.424490\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.50443 | −0.489535 | ||||||||
\(236\) | −4.28752 | −0.279094 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.16454 | 0.140306 | ||||||||
\(239\) | 16.3997 | 1.06081 | 0.530404 | − | 0.847745i | \(-0.322040\pi\) | ||||
0.530404 | + | 0.847745i | \(0.322040\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.82142 | −0.181743 | −0.0908717 | − | 0.995863i | \(-0.528965\pi\) | ||||
−0.0908717 | + | 0.995863i | \(0.528965\pi\) | |||||||
\(242\) | −10.8911 | −0.700104 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −7.79195 | −0.498828 | ||||||||
\(245\) | −15.9140 | −1.01671 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.98596 | 0.189992 | ||||||||
\(248\) | −6.56100 | −0.416624 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −9.95746 | −0.629765 | ||||||||
\(251\) | −22.4661 | −1.41805 | −0.709024 | − | 0.705184i | \(-0.750864\pi\) | ||||
−0.709024 | + | 0.705184i | \(0.750864\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.834484 | 0.0524635 | ||||||||
\(254\) | 2.50443 | 0.157142 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 15.7494 | 0.982421 | 0.491211 | − | 0.871041i | \(-0.336555\pi\) | ||||
0.491211 | + | 0.871041i | \(0.336555\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.94861 | 0.307492 | ||||||||
\(260\) | 3.81581 | 0.236646 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −7.85835 | −0.485490 | ||||||||
\(263\) | 9.13183 | 0.563093 | 0.281546 | − | 0.959548i | \(-0.409153\pi\) | ||||
0.281546 | + | 0.959548i | \(0.409153\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.0425 | −0.739767 | ||||||||
\(266\) | 1.27348 | 0.0780821 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 11.2875 | 0.689495 | ||||||||
\(269\) | −7.56100 | −0.461002 | −0.230501 | − | 0.973072i | \(-0.574037\pi\) | ||||
−0.230501 | + | 0.973072i | \(0.574037\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.40531 | −0.328349 | −0.164175 | − | 0.986431i | \(-0.552496\pi\) | ||||
−0.164175 | + | 0.986431i | \(0.552496\pi\) | |||||||
\(272\) | 3.23094 | 0.195905 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 22.5979 | 1.36519 | ||||||||
\(275\) | 0.297345 | 0.0179306 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.6035 | 0.757273 | 0.378637 | − | 0.925545i | \(-0.376393\pi\) | ||||
0.378637 | + | 0.925545i | \(0.376393\pi\) | |||||||
\(278\) | 5.91071 | 0.354501 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.62740 | 0.0972560 | ||||||||
\(281\) | 20.9705 | 1.25100 | 0.625498 | − | 0.780225i | \(-0.284896\pi\) | ||||
0.625498 | + | 0.780225i | \(0.284896\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.71669 | −0.339822 | −0.169911 | − | 0.985459i | \(-0.554348\pi\) | ||||
−0.169911 | + | 0.985459i | \(0.554348\pi\) | |||||||
\(284\) | 9.66012 | 0.573223 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.518465 | 0.0306575 | ||||||||
\(287\) | −8.18743 | −0.483289 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.56100 | −0.385941 | ||||||||
\(290\) | 12.9476 | 0.760312 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 10.5512 | 0.617461 | ||||||||
\(293\) | 9.68398 | 0.565744 | 0.282872 | − | 0.959158i | \(-0.408713\pi\) | ||||
0.282872 | + | 0.959158i | \(0.408713\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.4151 | −0.606393 | ||||||||
\(296\) | 7.38664 | 0.429340 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.75923 | 0.159838 | ||||||||
\(299\) | 3.97150 | 0.229678 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.72555 | 0.214737 | ||||||||
\(302\) | 4.07947 | 0.234747 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.90089 | 0.109023 | ||||||||
\(305\) | −18.9280 | −1.08381 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.00000 | 0.399511 | 0.199756 | − | 0.979846i | \(-0.435985\pi\) | ||||
0.199756 | + | 0.979846i | \(0.435985\pi\) | |||||||
\(308\) | 0.221120 | 0.0125995 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −15.9378 | −0.905207 | ||||||||
\(311\) | 28.1262 | 1.59489 | 0.797446 | − | 0.603391i | \(-0.206184\pi\) | ||||
0.797446 | + | 0.603391i | \(0.206184\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.27770 | −0.524406 | −0.262203 | − | 0.965013i | \(-0.584449\pi\) | ||||
−0.262203 | + | 0.965013i | \(0.584449\pi\) | |||||||
\(314\) | −13.1688 | −0.743156 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 14.7919 | 0.832112 | ||||||||
\(317\) | −10.4151 | −0.584972 | −0.292486 | − | 0.956270i | \(-0.594483\pi\) | ||||
−0.292486 | + | 0.956270i | \(0.594483\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.75923 | 0.0984981 | ||||||||
\(320\) | 2.42917 | 0.135795 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.69380 | 0.0943921 | ||||||||
\(323\) | 6.14165 | 0.341731 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.41513 | 0.0784975 | ||||||||
\(326\) | 10.1132 | 0.560116 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −12.2211 | −0.674798 | ||||||||
\(329\) | −2.06964 | −0.114103 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.40628 | −0.132261 | −0.0661307 | − | 0.997811i | \(-0.521065\pi\) | ||||
−0.0661307 | + | 0.997811i | \(0.521065\pi\) | |||||||
\(332\) | 8.27770 | 0.454298 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −19.9575 | −1.09202 | ||||||||
\(335\) | 27.4193 | 1.49808 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −27.2875 | −1.48645 | −0.743223 | − | 0.669044i | \(-0.766704\pi\) | ||||
−0.743223 | + | 0.669044i | \(0.766704\pi\) | |||||||
\(338\) | −10.5325 | −0.572893 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 7.84852 | 0.425646 | ||||||||
\(341\) | −2.16552 | −0.117269 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.07849 | −0.490193 | ||||||||
\(344\) | 5.56100 | 0.299829 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −13.4095 | −0.720901 | ||||||||
\(347\) | −30.2538 | −1.62411 | −0.812055 | − | 0.583580i | \(-0.801651\pi\) | ||||
−0.812055 | + | 0.583580i | \(0.801651\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −24.3866 | −1.30539 | −0.652693 | − | 0.757622i | \(-0.726361\pi\) | ||||
−0.652693 | + | 0.757622i | \(0.726361\pi\) | |||||||
\(350\) | 0.603540 | 0.0322606 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.330059 | 0.0175922 | ||||||||
\(353\) | 8.18841 | 0.435825 | 0.217912 | − | 0.975968i | \(-0.430075\pi\) | ||||
0.217912 | + | 0.975968i | \(0.430075\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 23.4661 | 1.24545 | ||||||||
\(356\) | −11.2450 | −0.595983 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.59372 | −0.0842305 | ||||||||
\(359\) | −23.9149 | −1.26218 | −0.631091 | − | 0.775709i | \(-0.717392\pi\) | ||||
−0.631091 | + | 0.775709i | \(0.717392\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.3866 | −0.809823 | ||||||||
\(362\) | 3.08929 | 0.162370 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.05236 | 0.0551587 | ||||||||
\(365\) | 25.6306 | 1.34157 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.54794 | 0.341799 | 0.170900 | − | 0.985288i | \(-0.445333\pi\) | ||||
0.170900 | + | 0.985288i | \(0.445333\pi\) | |||||||
\(368\) | 2.52829 | 0.131796 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 17.9434 | 0.932834 | ||||||||
\(371\) | −3.32121 | −0.172429 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −21.7396 | −1.12563 | −0.562817 | − | 0.826582i | \(-0.690282\pi\) | ||||
−0.562817 | + | 0.826582i | \(0.690282\pi\) | |||||||
\(374\) | 1.06640 | 0.0551423 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.08929 | −0.159318 | ||||||||
\(377\) | 8.37260 | 0.431211 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.514249 | 0.0264152 | 0.0132076 | − | 0.999913i | \(-0.495796\pi\) | ||||
0.0132076 | + | 0.999913i | \(0.495796\pi\) | |||||||
\(380\) | 4.61758 | 0.236877 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −7.50443 | −0.383960 | ||||||||
\(383\) | 9.90089 | 0.505912 | 0.252956 | − | 0.967478i | \(-0.418597\pi\) | ||||
0.252956 | + | 0.967478i | \(0.418597\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.537139 | 0.0273751 | ||||||||
\(386\) | 17.7069 | 0.901256 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 9.22112 | 0.468131 | ||||||||
\(389\) | 18.1515 | 0.920316 | 0.460158 | − | 0.887837i | \(-0.347793\pi\) | ||||
0.460158 | + | 0.887837i | \(0.347793\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.16876 | 0.413112 | ||||||||
\(392\) | −6.55118 | −0.330884 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −5.42917 | −0.273518 | ||||||||
\(395\) | 35.9322 | 1.80795 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 24.4848 | 1.22886 | 0.614428 | − | 0.788973i | \(-0.289387\pi\) | ||||
0.614428 | + | 0.788973i | \(0.289387\pi\) | |||||||
\(398\) | −2.00982 | −0.100743 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.900885 | 0.0450443 | ||||||||
\(401\) | 12.2309 | 0.610784 | 0.305392 | − | 0.952227i | \(-0.401212\pi\) | ||||
0.305392 | + | 0.952227i | \(0.401212\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.3062 | −0.513388 | ||||||||
\(404\) | −13.5086 | −0.672080 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.57083 | 0.177217 | ||||||||
\(407\) | 2.43802 | 0.120848 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.6643 | 0.725105 | 0.362552 | − | 0.931963i | \(-0.381905\pi\) | ||||
0.362552 | + | 0.931963i | \(0.381905\pi\) | |||||||
\(410\) | −29.6872 | −1.46615 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 14.0000 | 0.689730 | ||||||||
\(413\) | −2.87239 | −0.141341 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 20.1080 | 0.987061 | ||||||||
\(416\) | 1.57083 | 0.0770161 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.627404 | 0.0306873 | ||||||||
\(419\) | −17.6166 | −0.860628 | −0.430314 | − | 0.902679i | \(-0.641597\pi\) | ||||
−0.430314 | + | 0.902679i | \(0.641597\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −27.0369 | −1.31770 | −0.658850 | − | 0.752275i | \(-0.728957\pi\) | ||||
−0.658850 | + | 0.752275i | \(0.728957\pi\) | |||||||
\(422\) | 1.19823 | 0.0583289 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4.95746 | −0.240756 | ||||||||
\(425\) | 2.91071 | 0.141190 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.22015 | −0.252621 | ||||||||
\(428\) | −11.8158 | −0.571139 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 13.5086 | 0.651445 | ||||||||
\(431\) | −4.15472 | −0.200126 | −0.100063 | − | 0.994981i | \(-0.531904\pi\) | ||||
−0.100063 | + | 0.994981i | \(0.531904\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −32.7438 | −1.57357 | −0.786783 | − | 0.617229i | \(-0.788255\pi\) | ||||
−0.786783 | + | 0.617229i | \(0.788255\pi\) | |||||||
\(434\) | −4.39549 | −0.210990 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −12.2777 | −0.587995 | ||||||||
\(437\) | 4.80599 | 0.229901 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.29313 | −0.109445 | −0.0547225 | − | 0.998502i | \(-0.517427\pi\) | ||||
−0.0547225 | + | 0.998502i | \(0.517427\pi\) | |||||||
\(440\) | 0.801770 | 0.0382229 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 5.07525 | 0.241405 | ||||||||
\(443\) | −17.2113 | −0.817733 | −0.408867 | − | 0.912594i | \(-0.634076\pi\) | ||||
−0.408867 | + | 0.912594i | \(0.634076\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −27.3160 | −1.29490 | ||||||||
\(446\) | 1.00000 | 0.0473514 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.669941 | 0.0316517 | ||||||||
\(449\) | −28.3202 | −1.33651 | −0.668257 | − | 0.743930i | \(-0.732959\pi\) | ||||
−0.668257 | + | 0.743930i | \(0.732959\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.03369 | −0.189939 | ||||||||
\(452\) | −3.99018 | −0.187682 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.93360 | 0.0907483 | ||||||||
\(455\) | 2.55637 | 0.119844 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 27.5357 | 1.28807 | 0.644034 | − | 0.764997i | \(-0.277260\pi\) | ||||
0.644034 | + | 0.764997i | \(0.277260\pi\) | |||||||
\(458\) | 16.4563 | 0.768951 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 6.14165 | 0.286356 | ||||||||
\(461\) | 6.35295 | 0.295886 | 0.147943 | − | 0.988996i | \(-0.452735\pi\) | ||||
0.147943 | + | 0.988996i | \(0.452735\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.6928 | −0.496938 | −0.248469 | − | 0.968640i | \(-0.579927\pi\) | ||||
−0.248469 | + | 0.968640i | \(0.579927\pi\) | |||||||
\(464\) | 5.33006 | 0.247442 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7.17437 | 0.332346 | ||||||||
\(467\) | −28.2113 | −1.30546 | −0.652732 | − | 0.757589i | \(-0.726377\pi\) | ||||
−0.652732 | + | 0.757589i | \(0.726377\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.56198 | 0.349180 | ||||||||
\(470\) | −7.50443 | −0.346153 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −4.28752 | −0.197349 | ||||||||
\(473\) | 1.83546 | 0.0843944 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.71248 | 0.0785739 | ||||||||
\(476\) | 2.16454 | 0.0992116 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 16.3997 | 0.750105 | ||||||||
\(479\) | −2.27770 | −0.104071 | −0.0520353 | − | 0.998645i | \(-0.516571\pi\) | ||||
−0.0520353 | + | 0.998645i | \(0.516571\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.6031 | 0.529057 | ||||||||
\(482\) | −2.82142 | −0.128512 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.8911 | −0.495048 | ||||||||
\(485\) | 22.3997 | 1.01712 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.46610 | −0.293007 | −0.146504 | − | 0.989210i | \(-0.546802\pi\) | ||||
−0.146504 | + | 0.989210i | \(0.546802\pi\) | |||||||
\(488\) | −7.79195 | −0.352725 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −15.9140 | −0.718919 | ||||||||
\(491\) | 6.00885 | 0.271176 | 0.135588 | − | 0.990765i | \(-0.456708\pi\) | ||||
0.135588 | + | 0.990765i | \(0.456708\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 17.2211 | 0.775600 | ||||||||
\(494\) | 2.98596 | 0.134345 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.56100 | −0.294598 | ||||||||
\(497\) | 6.47171 | 0.290296 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 39.8616 | 1.78445 | 0.892225 | − | 0.451591i | \(-0.149143\pi\) | ||||
0.892225 | + | 0.451591i | \(0.149143\pi\) | |||||||
\(500\) | −9.95746 | −0.445311 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −22.4661 | −1.00271 | ||||||||
\(503\) | −19.1655 | −0.854548 | −0.427274 | − | 0.904122i | \(-0.640526\pi\) | ||||
−0.427274 | + | 0.904122i | \(0.640526\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −32.8148 | −1.46024 | ||||||||
\(506\) | 0.834484 | 0.0370973 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.50443 | 0.111116 | ||||||||
\(509\) | −18.0000 | −0.797836 | −0.398918 | − | 0.916987i | \(-0.630614\pi\) | ||||
−0.398918 | + | 0.916987i | \(0.630614\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.06867 | 0.312700 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 15.7494 | 0.694677 | ||||||||
\(515\) | 34.0084 | 1.49859 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.01965 | −0.0448440 | ||||||||
\(518\) | 4.94861 | 0.217430 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 3.81581 | 0.167334 | ||||||||
\(521\) | −29.2777 | −1.28268 | −0.641340 | − | 0.767257i | \(-0.721621\pi\) | ||||
−0.641340 | + | 0.767257i | \(0.721621\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 23.4661 | 1.02610 | 0.513051 | − | 0.858358i | \(-0.328515\pi\) | ||||
0.513051 | + | 0.858358i | \(0.328515\pi\) | |||||||
\(524\) | −7.85835 | −0.343294 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.13183 | 0.398167 | ||||||||
\(527\) | −21.1982 | −0.923409 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.6078 | −0.722076 | ||||||||
\(530\) | −12.0425 | −0.523094 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.27348 | 0.0552124 | ||||||||
\(533\) | −19.1973 | −0.831525 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −28.7027 | −1.24092 | ||||||||
\(536\) | 11.2875 | 0.487547 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −7.56100 | −0.325978 | ||||||||
\(539\) | −2.16227 | −0.0931357 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 28.3768 | 1.22001 | 0.610007 | − | 0.792396i | \(-0.291167\pi\) | ||||
0.610007 | + | 0.792396i | \(0.291167\pi\) | |||||||
\(542\) | −5.40531 | −0.232178 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.23094 | 0.138526 | ||||||||
\(545\) | −29.8247 | −1.27755 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.11779 | 0.347092 | 0.173546 | − | 0.984826i | \(-0.444478\pi\) | ||||
0.173546 | + | 0.984826i | \(0.444478\pi\) | |||||||
\(548\) | 22.5979 | 0.965336 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.297345 | 0.0126788 | ||||||||
\(551\) | 10.1318 | 0.431630 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.90974 | 0.421405 | ||||||||
\(554\) | 12.6035 | 0.535473 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.91071 | 0.250670 | ||||||||
\(557\) | −8.25059 | −0.349589 | −0.174794 | − | 0.984605i | \(-0.555926\pi\) | ||||
−0.174794 | + | 0.984605i | \(0.555926\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.73537 | 0.369467 | ||||||||
\(560\) | 1.62740 | 0.0687704 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 20.9705 | 0.884588 | ||||||||
\(563\) | −28.1220 | −1.18520 | −0.592601 | − | 0.805496i | \(-0.701899\pi\) | ||||
−0.592601 | + | 0.805496i | \(0.701899\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.69283 | −0.407780 | ||||||||
\(566\) | −5.71669 | −0.240291 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9.66012 | 0.405330 | ||||||||
\(569\) | −5.70266 | −0.239068 | −0.119534 | − | 0.992830i | \(-0.538140\pi\) | ||||
−0.119534 | + | 0.992830i | \(0.538140\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23.1884 | 0.970405 | 0.485202 | − | 0.874402i | \(-0.338746\pi\) | ||||
0.485202 | + | 0.874402i | \(0.338746\pi\) | |||||||
\(572\) | 0.518465 | 0.0216781 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −8.18743 | −0.341737 | ||||||||
\(575\) | 2.27770 | 0.0949865 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.39970 | −0.183162 | −0.0915810 | − | 0.995798i | \(-0.529192\pi\) | ||||
−0.0915810 | + | 0.995798i | \(0.529192\pi\) | |||||||
\(578\) | −6.56100 | −0.272902 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 12.9476 | 0.537621 | ||||||||
\(581\) | 5.54557 | 0.230069 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.63625 | −0.0677667 | ||||||||
\(584\) | 10.5512 | 0.436611 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9.68398 | 0.400042 | ||||||||
\(587\) | 5.19726 | 0.214514 | 0.107257 | − | 0.994231i | \(-0.465793\pi\) | ||||
0.107257 | + | 0.994231i | \(0.465793\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12.4717 | −0.513888 | ||||||||
\(590\) | −10.4151 | −0.428784 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 7.38664 | 0.303589 | ||||||||
\(593\) | −8.91071 | −0.365919 | −0.182959 | − | 0.983120i | \(-0.558568\pi\) | ||||
−0.182959 | + | 0.983120i | \(0.558568\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.25805 | 0.215559 | ||||||||
\(596\) | 2.75923 | 0.113023 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 3.97150 | 0.162407 | ||||||||
\(599\) | 14.1080 | 0.576436 | 0.288218 | − | 0.957565i | \(-0.406937\pi\) | ||||
0.288218 | + | 0.957565i | \(0.406937\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.2538 | −0.907753 | −0.453876 | − | 0.891065i | \(-0.649959\pi\) | ||||
−0.453876 | + | 0.891065i | \(0.649959\pi\) | |||||||
\(602\) | 3.72555 | 0.151842 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4.07947 | 0.165991 | ||||||||
\(605\) | −26.4563 | −1.07560 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21.1491 | 0.858416 | 0.429208 | − | 0.903206i | \(-0.358793\pi\) | ||||
0.429208 | + | 0.903206i | \(0.358793\pi\) | |||||||
\(608\) | 1.90089 | 0.0770911 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −18.9280 | −0.766372 | ||||||||
\(611\) | −4.85274 | −0.196321 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −20.5750 | −0.831018 | −0.415509 | − | 0.909589i | \(-0.636397\pi\) | ||||
−0.415509 | + | 0.909589i | \(0.636397\pi\) | |||||||
\(614\) | 7.00000 | 0.282497 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.221120 | 0.00890918 | ||||||||
\(617\) | −16.7069 | −0.672593 | −0.336297 | − | 0.941756i | \(-0.609174\pi\) | ||||
−0.336297 | + | 0.941756i | \(0.609174\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 29.6742 | 1.19271 | 0.596353 | − | 0.802723i | \(-0.296616\pi\) | ||||
0.596353 | + | 0.802723i | \(0.296616\pi\) | |||||||
\(620\) | −15.9378 | −0.640078 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 28.1262 | 1.12776 | ||||||||
\(623\) | −7.53348 | −0.301822 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −28.6928 | −1.14771 | ||||||||
\(626\) | −9.27770 | −0.370811 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −13.1688 | −0.525491 | ||||||||
\(629\) | 23.8658 | 0.951592 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −44.7340 | −1.78083 | −0.890416 | − | 0.455148i | \(-0.849586\pi\) | ||||
−0.890416 | + | 0.455148i | \(0.849586\pi\) | |||||||
\(632\) | 14.7919 | 0.588392 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −10.4151 | −0.413638 | ||||||||
\(635\) | 6.08368 | 0.241424 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −10.2908 | −0.407735 | ||||||||
\(638\) | 1.75923 | 0.0696487 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.42917 | 0.0960215 | ||||||||
\(641\) | 18.3441 | 0.724548 | 0.362274 | − | 0.932072i | \(-0.382000\pi\) | ||||
0.362274 | + | 0.932072i | \(0.382000\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.49557 | 0.177288 | 0.0886441 | − | 0.996063i | \(-0.471747\pi\) | ||||
0.0886441 | + | 0.996063i | \(0.471747\pi\) | |||||||
\(644\) | 1.69380 | 0.0667453 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.14165 | 0.241640 | ||||||||
\(647\) | −6.75923 | −0.265733 | −0.132866 | − | 0.991134i | \(-0.542418\pi\) | ||||
−0.132866 | + | 0.991134i | \(0.542418\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.41513 | −0.0555489 | ||||||||
\(650\) | 1.41513 | 0.0555061 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 10.1132 | 0.396062 | ||||||||
\(653\) | −46.3146 | −1.81243 | −0.906216 | − | 0.422816i | \(-0.861042\pi\) | ||||
−0.906216 | + | 0.422816i | \(0.861042\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −19.0893 | −0.745880 | ||||||||
\(656\) | −12.2211 | −0.477155 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2.06964 | −0.0806831 | ||||||||
\(659\) | −9.36277 | −0.364722 | −0.182361 | − | 0.983232i | \(-0.558374\pi\) | ||||
−0.182361 | + | 0.983232i | \(0.558374\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −25.8626 | −1.00594 | −0.502969 | − | 0.864305i | \(-0.667759\pi\) | ||||
−0.502969 | + | 0.864305i | \(0.667759\pi\) | |||||||
\(662\) | −2.40628 | −0.0935229 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 8.27770 | 0.321237 | ||||||||
\(665\) | 3.09351 | 0.119961 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 13.4759 | 0.521790 | ||||||||
\(668\) | −19.9575 | −0.772177 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 27.4193 | 1.05930 | ||||||||
\(671\) | −2.57180 | −0.0992832 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 37.1818 | 1.43325 | 0.716627 | − | 0.697457i | \(-0.245685\pi\) | ||||
0.716627 | + | 0.697457i | \(0.245685\pi\) | |||||||
\(674\) | −27.2875 | −1.05108 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −10.5325 | −0.405096 | ||||||||
\(677\) | −9.18280 | −0.352924 | −0.176462 | − | 0.984307i | \(-0.556465\pi\) | ||||
−0.176462 | + | 0.984307i | \(0.556465\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.17761 | 0.237075 | ||||||||
\(680\) | 7.84852 | 0.300977 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2.16552 | −0.0829219 | ||||||||
\(683\) | −26.0131 | −0.995362 | −0.497681 | − | 0.867360i | \(-0.665815\pi\) | ||||
−0.497681 | + | 0.867360i | \(0.665815\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 54.8943 | 2.09740 | ||||||||
\(686\) | −9.07849 | −0.346619 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5.56100 | 0.212011 | ||||||||
\(689\) | −7.78731 | −0.296673 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.6840 | 0.482521 | 0.241261 | − | 0.970460i | \(-0.422439\pi\) | ||||
0.241261 | + | 0.970460i | \(0.422439\pi\) | |||||||
\(692\) | −13.4095 | −0.509754 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −30.2538 | −1.14842 | ||||||||
\(695\) | 14.3581 | 0.544635 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −39.4858 | −1.49563 | ||||||||
\(698\) | −24.3866 | −0.923048 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.603540 | 0.0228117 | ||||||||
\(701\) | −39.8092 | −1.50357 | −0.751787 | − | 0.659406i | \(-0.770808\pi\) | ||||
−0.751787 | + | 0.659406i | \(0.770808\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 14.0411 | 0.529572 | ||||||||
\(704\) | 0.330059 | 0.0124396 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.18841 | 0.308175 | ||||||||
\(707\) | −9.05000 | −0.340360 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −28.7494 | −1.07971 | −0.539853 | − | 0.841759i | \(-0.681520\pi\) | ||||
−0.539853 | + | 0.841759i | \(0.681520\pi\) | |||||||
\(710\) | 23.4661 | 0.880667 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −11.2450 | −0.421424 | ||||||||
\(713\) | −16.5881 | −0.621230 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.25944 | 0.0471004 | ||||||||
\(716\) | −1.59372 | −0.0595600 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −23.9149 | −0.892497 | ||||||||
\(719\) | 1.88545 | 0.0703156 | 0.0351578 | − | 0.999382i | \(-0.488807\pi\) | ||||
0.0351578 | + | 0.999382i | \(0.488807\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.37918 | 0.349299 | ||||||||
\(722\) | −15.3866 | −0.572631 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 3.08929 | 0.114813 | ||||||||
\(725\) | 4.80177 | 0.178333 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −32.3670 | −1.20043 | −0.600213 | − | 0.799841i | \(-0.704917\pi\) | ||||
−0.600213 | + | 0.799841i | \(0.704917\pi\) | |||||||
\(728\) | 1.05236 | 0.0390031 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 25.6306 | 0.948633 | ||||||||
\(731\) | 17.9673 | 0.664544 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −22.4801 | −0.830323 | −0.415162 | − | 0.909748i | \(-0.636275\pi\) | ||||
−0.415162 | + | 0.909748i | \(0.636275\pi\) | |||||||
\(734\) | 6.54794 | 0.241689 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.52829 | 0.0931940 | ||||||||
\(737\) | 3.72555 | 0.137232 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.82044 | 0.361251 | 0.180625 | − | 0.983552i | \(-0.442188\pi\) | ||||
0.180625 | + | 0.983552i | \(0.442188\pi\) | |||||||
\(740\) | 17.9434 | 0.659613 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.32121 | −0.121925 | ||||||||
\(743\) | 6.42032 | 0.235539 | 0.117769 | − | 0.993041i | \(-0.462426\pi\) | ||||
0.117769 | + | 0.993041i | \(0.462426\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.70266 | 0.245566 | ||||||||
\(746\) | −21.7396 | −0.795943 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.06640 | 0.0389915 | ||||||||
\(749\) | −7.91590 | −0.289241 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25.6601 | −0.936351 | −0.468175 | − | 0.883636i | \(-0.655088\pi\) | ||||
−0.468175 | + | 0.883636i | \(0.655088\pi\) | |||||||
\(752\) | −3.08929 | −0.112655 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 8.37260 | 0.304912 | ||||||||
\(755\) | 9.90974 | 0.360652 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.17858 | 0.115528 | 0.0577638 | − | 0.998330i | \(-0.481603\pi\) | ||||
0.0577638 | + | 0.998330i | \(0.481603\pi\) | |||||||
\(758\) | 0.514249 | 0.0186784 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.61758 | 0.167497 | ||||||||
\(761\) | 43.1533 | 1.56431 | 0.782153 | − | 0.623086i | \(-0.214121\pi\) | ||||
0.782153 | + | 0.623086i | \(0.214121\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.22534 | −0.297777 | ||||||||
\(764\) | −7.50443 | −0.271501 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9.90089 | 0.357734 | ||||||||
\(767\) | −6.73495 | −0.243185 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −48.4890 | −1.74856 | −0.874279 | − | 0.485424i | \(-0.838665\pi\) | ||||
−0.874279 | + | 0.485424i | \(0.838665\pi\) | |||||||
\(770\) | 0.537139 | 0.0193571 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 17.7069 | 0.637284 | ||||||||
\(773\) | 35.0925 | 1.26219 | 0.631095 | − | 0.775705i | \(-0.282606\pi\) | ||||
0.631095 | + | 0.775705i | \(0.282606\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.91071 | −0.212319 | ||||||||
\(776\) | 9.22112 | 0.331019 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 18.1515 | 0.650762 | ||||||||
\(779\) | −23.2309 | −0.832335 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.18841 | 0.114090 | ||||||||
\(782\) | 8.16876 | 0.292114 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.55118 | −0.233971 | ||||||||
\(785\) | −31.9892 | −1.14174 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19.3104 | −0.688342 | −0.344171 | − | 0.938907i | \(-0.611840\pi\) | ||||
−0.344171 | + | 0.938907i | \(0.611840\pi\) | |||||||
\(788\) | −5.42917 | −0.193406 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 35.9322 | 1.27841 | ||||||||
\(791\) | −2.67318 | −0.0950475 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12.2398 | −0.434648 | ||||||||
\(794\) | 24.4848 | 0.868932 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.00982 | −0.0712363 | ||||||||
\(797\) | 27.4376 | 0.971890 | 0.485945 | − | 0.873989i | \(-0.338476\pi\) | ||||
0.485945 | + | 0.873989i | \(0.338476\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.98133 | −0.353114 | ||||||||
\(800\) | 0.900885 | 0.0318511 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 12.2309 | 0.431890 | ||||||||
\(803\) | 3.48251 | 0.122895 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.11455 | 0.145019 | ||||||||
\(806\) | −10.3062 | −0.363020 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −13.5086 | −0.475232 | ||||||||
\(809\) | −9.94666 | −0.349706 | −0.174853 | − | 0.984595i | \(-0.555945\pi\) | ||||
−0.174853 | + | 0.984595i | \(0.555945\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.14587 | 0.286040 | 0.143020 | − | 0.989720i | \(-0.454319\pi\) | ||||
0.143020 | + | 0.989720i | \(0.454319\pi\) | |||||||
\(812\) | 3.57083 | 0.125311 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.43802 | 0.0854527 | ||||||||
\(815\) | 24.5666 | 0.860531 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.5708 | 0.369826 | ||||||||
\(818\) | 14.6643 | 0.512726 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −29.6872 | −1.03672 | ||||||||
\(821\) | 31.3343 | 1.09357 | 0.546787 | − | 0.837272i | \(-0.315851\pi\) | ||||
0.546787 | + | 0.837272i | \(0.315851\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −55.5685 | −1.93699 | −0.968497 | − | 0.249024i | \(-0.919890\pi\) | ||||
−0.968497 | + | 0.249024i | \(0.919890\pi\) | |||||||
\(824\) | 14.0000 | 0.487713 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.87239 | −0.0999431 | ||||||||
\(827\) | 32.2024 | 1.11979 | 0.559894 | − | 0.828564i | \(-0.310842\pi\) | ||||
0.559894 | + | 0.828564i | \(0.310842\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.37681 | 0.186744 | 0.0933722 | − | 0.995631i | \(-0.470235\pi\) | ||||
0.0933722 | + | 0.995631i | \(0.470235\pi\) | |||||||
\(830\) | 20.1080 | 0.697958 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.57083 | 0.0544586 | ||||||||
\(833\) | −21.1665 | −0.733375 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −48.4801 | −1.67772 | ||||||||
\(836\) | 0.627404 | 0.0216992 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −17.6166 | −0.608556 | ||||||||
\(839\) | −10.0042 | −0.345384 | −0.172692 | − | 0.984976i | \(-0.555247\pi\) | ||||
−0.172692 | + | 0.984976i | \(0.555247\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.590474 | −0.0203612 | ||||||||
\(842\) | −27.0369 | −0.931754 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.19823 | 0.0412448 | ||||||||
\(845\) | −25.5853 | −0.880161 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.29637 | −0.250706 | ||||||||
\(848\) | −4.95746 | −0.170240 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.91071 | 0.0998365 | ||||||||
\(851\) | 18.6755 | 0.640190 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −22.9519 | −0.785857 | −0.392928 | − | 0.919569i | \(-0.628538\pi\) | ||||
−0.392928 | + | 0.919569i | \(0.628538\pi\) | |||||||
\(854\) | −5.22015 | −0.178630 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −11.8158 | −0.403856 | ||||||||
\(857\) | 28.2908 | 0.966394 | 0.483197 | − | 0.875512i | \(-0.339475\pi\) | ||||
0.483197 | + | 0.875512i | \(0.339475\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18.5849 | 0.634107 | 0.317054 | − | 0.948408i | \(-0.397306\pi\) | ||||
0.317054 | + | 0.948408i | \(0.397306\pi\) | |||||||
\(860\) | 13.5086 | 0.460641 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −4.15472 | −0.141510 | ||||||||
\(863\) | −44.1818 | −1.50397 | −0.751983 | − | 0.659182i | \(-0.770903\pi\) | ||||
−0.751983 | + | 0.659182i | \(0.770903\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −32.5741 | −1.10755 | ||||||||
\(866\) | −32.7438 | −1.11268 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4.39549 | −0.149193 | ||||||||
\(869\) | 4.88221 | 0.165618 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17.7307 | 0.600783 | ||||||||
\(872\) | −12.2777 | −0.415775 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 4.80599 | 0.162565 | ||||||||
\(875\) | −6.67091 | −0.225518 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −21.0098 | −0.709451 | −0.354726 | − | 0.934970i | \(-0.615426\pi\) | ||||
−0.354726 | + | 0.934970i | \(0.615426\pi\) | |||||||
\(878\) | −2.29313 | −0.0773894 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.801770 | 0.0270277 | ||||||||
\(881\) | −30.3660 | −1.02306 | −0.511529 | − | 0.859266i | \(-0.670921\pi\) | ||||
−0.511529 | + | 0.859266i | \(0.670921\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 51.6535 | 1.73828 | 0.869140 | − | 0.494566i | \(-0.164673\pi\) | ||||
0.869140 | + | 0.494566i | \(0.164673\pi\) | |||||||
\(884\) | 5.07525 | 0.170699 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −17.2113 | −0.578225 | ||||||||
\(887\) | −12.2725 | −0.412070 | −0.206035 | − | 0.978545i | \(-0.566056\pi\) | ||||
−0.206035 | + | 0.978545i | \(0.566056\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.67782 | 0.0562722 | ||||||||
\(890\) | −27.3160 | −0.915635 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.00000 | 0.0334825 | ||||||||
\(893\) | −5.87239 | −0.196512 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.87141 | −0.129407 | ||||||||
\(896\) | 0.669941 | 0.0223812 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −28.3202 | −0.945058 | ||||||||
\(899\) | −34.9705 | −1.16633 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −16.0173 | −0.533613 | ||||||||
\(902\) | −4.03369 | −0.134307 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3.99018 | −0.132711 | ||||||||
\(905\) | 7.50443 | 0.249456 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.68862 | −0.188887 | −0.0944437 | − | 0.995530i | \(-0.530107\pi\) | ||||
−0.0944437 | + | 0.995530i | \(0.530107\pi\) | |||||||
\(908\) | 1.93360 | 0.0641687 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2.55637 | 0.0847428 | ||||||||
\(911\) | 28.4007 | 0.940956 | 0.470478 | − | 0.882412i | \(-0.344081\pi\) | ||||
0.470478 | + | 0.882412i | \(0.344081\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.73213 | 0.0904202 | ||||||||
\(914\) | 27.5357 | 0.910802 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 16.4563 | 0.543731 | ||||||||
\(917\) | −5.26463 | −0.173853 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11.2342 | 0.370582 | 0.185291 | − | 0.982684i | \(-0.440677\pi\) | ||||
0.185291 | + | 0.982684i | \(0.440677\pi\) | |||||||
\(920\) | 6.14165 | 0.202484 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 6.35295 | 0.209223 | ||||||||
\(923\) | 15.1744 | 0.499470 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.65451 | 0.218799 | ||||||||
\(926\) | −10.6928 | −0.351388 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 5.33006 | 0.174968 | ||||||||
\(929\) | −48.3048 | −1.58483 | −0.792415 | − | 0.609983i | \(-0.791176\pi\) | ||||
−0.792415 | + | 0.609983i | \(0.791176\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −12.4530 | −0.408132 | ||||||||
\(932\) | 7.17437 | 0.235004 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −28.2113 | −0.923102 | ||||||||
\(935\) | 2.59047 | 0.0847176 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 32.0215 | 1.04610 | 0.523048 | − | 0.852303i | \(-0.324795\pi\) | ||||
0.523048 | + | 0.852303i | \(0.324795\pi\) | |||||||
\(938\) | 7.56198 | 0.246907 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −7.50443 | −0.244767 | ||||||||
\(941\) | 19.1599 | 0.624595 | 0.312298 | − | 0.949984i | \(-0.398901\pi\) | ||||
0.312298 | + | 0.949984i | \(0.398901\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −30.8985 | −1.00619 | ||||||||
\(944\) | −4.28752 | −0.139547 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.83546 | 0.0596759 | ||||||||
\(947\) | 20.8397 | 0.677198 | 0.338599 | − | 0.940931i | \(-0.390047\pi\) | ||||
0.338599 | + | 0.940931i | \(0.390047\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 16.5741 | 0.538017 | ||||||||
\(950\) | 1.71248 | 0.0555601 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.16454 | 0.0701532 | ||||||||
\(953\) | −48.9280 | −1.58493 | −0.792467 | − | 0.609915i | \(-0.791203\pi\) | ||||
−0.792467 | + | 0.609915i | \(0.791203\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −18.2296 | −0.589894 | ||||||||
\(956\) | 16.3997 | 0.530404 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −2.27770 | −0.0735891 | ||||||||
\(959\) | 15.1393 | 0.488873 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.0468 | 0.388605 | ||||||||
\(962\) | 11.6031 | 0.374100 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2.82142 | −0.0908717 | ||||||||
\(965\) | 43.0131 | 1.38464 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.88221 | 0.189159 | 0.0945796 | − | 0.995517i | \(-0.469849\pi\) | ||||
0.0945796 | + | 0.995517i | \(0.469849\pi\) | |||||||
\(968\) | −10.8911 | −0.350052 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 22.3997 | 0.719211 | ||||||||
\(971\) | 3.95227 | 0.126834 | 0.0634172 | − | 0.997987i | \(-0.479800\pi\) | ||||
0.0634172 | + | 0.997987i | \(0.479800\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.95983 | 0.126946 | ||||||||
\(974\) | −6.46610 | −0.207187 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7.79195 | −0.249414 | ||||||||
\(977\) | −6.39085 | −0.204461 | −0.102231 | − | 0.994761i | \(-0.532598\pi\) | ||||
−0.102231 | + | 0.994761i | \(0.532598\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.71151 | −0.118620 | ||||||||
\(980\) | −15.9140 | −0.508353 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 6.00885 | 0.191750 | ||||||||
\(983\) | −43.0650 | −1.37356 | −0.686780 | − | 0.726865i | \(-0.740977\pi\) | ||||
−0.686780 | + | 0.726865i | \(0.740977\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −13.1884 | −0.420218 | ||||||||
\(986\) | 17.2211 | 0.548432 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.98596 | 0.0949960 | ||||||||
\(989\) | 14.0598 | 0.447076 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −61.2057 | −1.94426 | −0.972131 | − | 0.234437i | \(-0.924675\pi\) | ||||
−0.972131 | + | 0.234437i | \(0.924675\pi\) | |||||||
\(992\) | −6.56100 | −0.208312 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 6.47171 | 0.205270 | ||||||||
\(995\) | −4.88221 | −0.154776 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 32.5119 | 1.02966 | 0.514831 | − | 0.857292i | \(-0.327855\pi\) | ||||
0.514831 | + | 0.857292i | \(0.327855\pi\) | |||||||
\(998\) | 39.8616 | 1.26180 | ||||||||
\(999\) | 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 | 4014.2.a.p.1.3 | 3 | ||
3.2 | odd | 2 | 1338.2.a.c.1.1 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1338.2.a.c.1.1 | ✓ | 3 | 3.2 | odd | 2 | ||
4014.2.a.p.1.3 | 3 | 1.1 | even | 1 | trivial |