Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6825,2,Mod(1,6825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6825, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("6825.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6825 = 3 \cdot 5^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6825.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: | \(54.4978993795\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.17428.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} - x^{3} - 6x^{2} + 4x + 6 \)
|
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 273) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2.10710\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6825.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.43986 | −1.01813 | −0.509066 | − | 0.860728i | \(-0.670009\pi\) | ||||
−0.509066 | + | 0.860728i | \(0.670009\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0.0731828 | 0.0365914 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.43986 | 0.587818 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 2.77434 | 0.980876 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.21419 | 1.27063 | 0.635313 | − | 0.772254i | \(-0.280871\pi\) | ||||
0.635313 | + | 0.772254i | \(0.280871\pi\) | |||||||
\(12\) | −0.0731828 | −0.0211261 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 1.43986 | 0.384817 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.14101 | −1.03525 | ||||||||
\(17\) | 2.87971 | 0.698432 | 0.349216 | − | 0.937042i | \(-0.386448\pi\) | ||||
0.349216 | + | 0.937042i | \(0.386448\pi\) | |||||||
\(18\) | −1.43986 | −0.339377 | ||||||||
\(19\) | −1.28738 | −0.295344 | −0.147672 | − | 0.989036i | \(-0.547178\pi\) | ||||
−0.147672 | + | 0.989036i | \(0.547178\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | −6.06783 | −1.29367 | ||||||||
\(23\) | 8.02072 | 1.67244 | 0.836218 | − | 0.548397i | \(-0.184762\pi\) | ||||
0.836218 | + | 0.548397i | \(0.184762\pi\) | |||||||
\(24\) | −2.77434 | −0.566309 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.43986 | 0.282379 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −0.0731828 | −0.0138303 | ||||||||
\(29\) | 3.28738 | 0.610450 | 0.305225 | − | 0.952280i | \(-0.401268\pi\) | ||||
0.305225 | + | 0.952280i | \(0.401268\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.04680 | −1.26564 | −0.632821 | − | 0.774298i | \(-0.718103\pi\) | ||||
−0.632821 | + | 0.774298i | \(0.718103\pi\) | |||||||
\(32\) | 0.413779 | 0.0731465 | ||||||||
\(33\) | −4.21419 | −0.733597 | ||||||||
\(34\) | −4.14637 | −0.711096 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.0731828 | 0.0121971 | ||||||||
\(37\) | −8.57475 | −1.40968 | −0.704840 | − | 0.709366i | \(-0.748981\pi\) | ||||
−0.704840 | + | 0.709366i | \(0.748981\pi\) | |||||||
\(38\) | 1.85363 | 0.300699 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −12.0678 | −1.88468 | −0.942339 | − | 0.334660i | \(-0.891379\pi\) | ||||
−0.942339 | + | 0.334660i | \(0.891379\pi\) | |||||||
\(42\) | −1.43986 | −0.222174 | ||||||||
\(43\) | −7.14101 | −1.08899 | −0.544497 | − | 0.838763i | \(-0.683279\pi\) | ||||
−0.544497 | + | 0.838763i | \(0.683279\pi\) | |||||||
\(44\) | 0.308407 | 0.0464940 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −11.5487 | −1.70276 | ||||||||
\(47\) | −1.95289 | −0.284859 | −0.142429 | − | 0.989805i | \(-0.545491\pi\) | ||||
−0.142429 | + | 0.989805i | \(0.545491\pi\) | |||||||
\(48\) | 4.14101 | 0.597703 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.87971 | −0.403240 | ||||||||
\(52\) | −0.0731828 | −0.0101486 | ||||||||
\(53\) | 5.14101 | 0.706172 | 0.353086 | − | 0.935591i | \(-0.385132\pi\) | ||||
0.353086 | + | 0.935591i | \(0.385132\pi\) | |||||||
\(54\) | 1.43986 | 0.195939 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.77434 | −0.370736 | ||||||||
\(57\) | 1.28738 | 0.170517 | ||||||||
\(58\) | −4.73334 | −0.621519 | ||||||||
\(59\) | −7.33448 | −0.954868 | −0.477434 | − | 0.878668i | \(-0.658433\pi\) | ||||
−0.477434 | + | 0.878668i | \(0.658433\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.75942 | 0.993492 | 0.496746 | − | 0.867896i | \(-0.334528\pi\) | ||||
0.496746 | + | 0.867896i | \(0.334528\pi\) | |||||||
\(62\) | 10.1464 | 1.28859 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 7.68624 | 0.960780 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 6.06783 | 0.746898 | ||||||||
\(67\) | −12.0414 | −1.47110 | −0.735548 | − | 0.677473i | \(-0.763075\pi\) | ||||
−0.735548 | + | 0.677473i | \(0.763075\pi\) | |||||||
\(68\) | 0.210745 | 0.0255566 | ||||||||
\(69\) | −8.02072 | −0.965581 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.7889 | 1.28041 | 0.640206 | − | 0.768203i | \(-0.278849\pi\) | ||||
0.640206 | + | 0.768203i | \(0.278849\pi\) | |||||||
\(72\) | 2.77434 | 0.326959 | ||||||||
\(73\) | 8.32568 | 0.974447 | 0.487224 | − | 0.873277i | \(-0.338010\pi\) | ||||
0.487224 | + | 0.873277i | \(0.338010\pi\) | |||||||
\(74\) | 12.3464 | 1.43524 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.0942138 | −0.0108071 | ||||||||
\(77\) | −4.21419 | −0.480252 | ||||||||
\(78\) | −1.43986 | −0.163031 | ||||||||
\(79\) | 4.47204 | 0.503144 | 0.251572 | − | 0.967839i | \(-0.419052\pi\) | ||||
0.251572 | + | 0.967839i | \(0.419052\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 17.3759 | 1.91885 | ||||||||
\(83\) | 3.80653 | 0.417821 | 0.208910 | − | 0.977935i | \(-0.433008\pi\) | ||||
0.208910 | + | 0.977935i | \(0.433008\pi\) | |||||||
\(84\) | 0.0731828 | 0.00798490 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 10.2820 | 1.10874 | ||||||||
\(87\) | −3.28738 | −0.352444 | ||||||||
\(88\) | 11.6916 | 1.24633 | ||||||||
\(89\) | −5.64793 | −0.598680 | −0.299340 | − | 0.954147i | \(-0.596766\pi\) | ||||
−0.299340 | + | 0.954147i | \(0.596766\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.00000 | 0.104828 | ||||||||
\(92\) | 0.586979 | 0.0611968 | ||||||||
\(93\) | 7.04680 | 0.730719 | ||||||||
\(94\) | 2.81188 | 0.290024 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.413779 | −0.0422312 | ||||||||
\(97\) | −6.90043 | −0.700633 | −0.350316 | − | 0.936631i | \(-0.613926\pi\) | ||||
−0.350316 | + | 0.936631i | \(0.613926\pi\) | |||||||
\(98\) | −1.43986 | −0.145447 | ||||||||
\(99\) | 4.21419 | 0.423542 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.9739 | −1.09195 | −0.545973 | − | 0.837803i | \(-0.683840\pi\) | ||||
−0.545973 | + | 0.837803i | \(0.683840\pi\) | |||||||
\(102\) | 4.14637 | 0.410551 | ||||||||
\(103\) | −16.4284 | −1.61874 | −0.809368 | − | 0.587301i | \(-0.800190\pi\) | ||||
−0.809368 | + | 0.587301i | \(0.800190\pi\) | |||||||
\(104\) | −2.77434 | −0.272046 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.40231 | −0.718976 | ||||||||
\(107\) | 3.45446 | 0.333955 | 0.166978 | − | 0.985961i | \(-0.446599\pi\) | ||||
0.166978 | + | 0.985961i | \(0.446599\pi\) | |||||||
\(108\) | −0.0731828 | −0.00704202 | ||||||||
\(109\) | 4.66896 | 0.447206 | 0.223603 | − | 0.974680i | \(-0.428218\pi\) | ||||
0.223603 | + | 0.974680i | \(0.428218\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.57475 | 0.813879 | ||||||||
\(112\) | 4.14101 | 0.391289 | ||||||||
\(113\) | 3.28738 | 0.309250 | 0.154625 | − | 0.987973i | \(-0.450583\pi\) | ||||
0.154625 | + | 0.987973i | \(0.450583\pi\) | |||||||
\(114\) | −1.85363 | −0.173609 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.240579 | 0.0223372 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | 10.5606 | 0.972181 | ||||||||
\(119\) | −2.87971 | −0.263983 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.75942 | 0.614493 | ||||||||
\(122\) | −11.1724 | −1.01151 | ||||||||
\(123\) | 12.0678 | 1.08812 | ||||||||
\(124\) | −0.515704 | −0.0463116 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.43986 | 0.128272 | ||||||||
\(127\) | 0.428386 | 0.0380131 | 0.0190065 | − | 0.999819i | \(-0.493950\pi\) | ||||
0.0190065 | + | 0.999819i | \(0.493950\pi\) | |||||||
\(128\) | −11.8946 | −1.05135 | ||||||||
\(129\) | 7.14101 | 0.628731 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.1878 | 1.23959 | 0.619797 | − | 0.784762i | \(-0.287215\pi\) | ||||
0.619797 | + | 0.784762i | \(0.287215\pi\) | |||||||
\(132\) | −0.308407 | −0.0268433 | ||||||||
\(133\) | 1.28738 | 0.111630 | ||||||||
\(134\) | 17.3379 | 1.49777 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.98929 | 0.685076 | ||||||||
\(137\) | −14.7070 | −1.25650 | −0.628250 | − | 0.778011i | \(-0.716229\pi\) | ||||
−0.628250 | + | 0.778011i | \(0.716229\pi\) | |||||||
\(138\) | 11.5487 | 0.983089 | ||||||||
\(139\) | 9.85363 | 0.835774 | 0.417887 | − | 0.908499i | \(-0.362771\pi\) | ||||
0.417887 | + | 0.908499i | \(0.362771\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.95289 | 0.164463 | ||||||||
\(142\) | −15.5345 | −1.30363 | ||||||||
\(143\) | −4.21419 | −0.352409 | ||||||||
\(144\) | −4.14101 | −0.345084 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −11.9878 | −0.992115 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | −0.627525 | −0.0515822 | ||||||||
\(149\) | −3.38663 | −0.277444 | −0.138722 | − | 0.990331i | \(-0.544299\pi\) | ||||
−0.138722 | + | 0.990331i | \(0.544299\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −21.8951 | −1.78180 | −0.890898 | − | 0.454204i | \(-0.849924\pi\) | ||||
−0.890898 | + | 0.454204i | \(0.849924\pi\) | |||||||
\(152\) | −3.57161 | −0.289696 | ||||||||
\(153\) | 2.87971 | 0.232811 | ||||||||
\(154\) | 6.06783 | 0.488959 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.0731828 | 0.00585932 | ||||||||
\(157\) | 0.867482 | 0.0692326 | 0.0346163 | − | 0.999401i | \(-0.488979\pi\) | ||||
0.0346163 | + | 0.999401i | \(0.488979\pi\) | |||||||
\(158\) | −6.43910 | −0.512267 | ||||||||
\(159\) | −5.14101 | −0.407709 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.02072 | −0.632121 | ||||||||
\(162\) | −1.43986 | −0.113126 | ||||||||
\(163\) | −4.42839 | −0.346858 | −0.173429 | − | 0.984846i | \(-0.555485\pi\) | ||||
−0.173429 | + | 0.984846i | \(0.555485\pi\) | |||||||
\(164\) | −0.883158 | −0.0689630 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.48085 | −0.425396 | ||||||||
\(167\) | −20.5276 | −1.58848 | −0.794238 | − | 0.607606i | \(-0.792130\pi\) | ||||
−0.794238 | + | 0.607606i | \(0.792130\pi\) | |||||||
\(168\) | 2.77434 | 0.214045 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.28738 | −0.0984481 | ||||||||
\(172\) | −0.522599 | −0.0398478 | ||||||||
\(173\) | −15.0154 | −1.14160 | −0.570799 | − | 0.821090i | \(-0.693366\pi\) | ||||
−0.570799 | + | 0.821090i | \(0.693366\pi\) | |||||||
\(174\) | 4.73334 | 0.358834 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −17.4510 | −1.31542 | ||||||||
\(177\) | 7.33448 | 0.551293 | ||||||||
\(178\) | 8.13221 | 0.609535 | ||||||||
\(179\) | −5.35176 | −0.400009 | −0.200004 | − | 0.979795i | \(-0.564096\pi\) | ||||
−0.200004 | + | 0.979795i | \(0.564096\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.4667 | 0.852312 | 0.426156 | − | 0.904650i | \(-0.359867\pi\) | ||||
0.426156 | + | 0.904650i | \(0.359867\pi\) | |||||||
\(182\) | −1.43986 | −0.106729 | ||||||||
\(183\) | −7.75942 | −0.573593 | ||||||||
\(184\) | 22.2522 | 1.64045 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −10.1464 | −0.743968 | ||||||||
\(187\) | 12.1357 | 0.887447 | ||||||||
\(188\) | −0.142918 | −0.0104234 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 20.1756 | 1.45985 | 0.729927 | − | 0.683525i | \(-0.239554\pi\) | ||||
0.729927 | + | 0.683525i | \(0.239554\pi\) | |||||||
\(192\) | −7.68624 | −0.554706 | ||||||||
\(193\) | 26.3756 | 1.89856 | 0.949279 | − | 0.314435i | \(-0.101815\pi\) | ||||
0.949279 | + | 0.314435i | \(0.101815\pi\) | |||||||
\(194\) | 9.93562 | 0.713336 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.0731828 | 0.00522734 | ||||||||
\(197\) | 20.1322 | 1.43436 | 0.717180 | − | 0.696888i | \(-0.245432\pi\) | ||||
0.717180 | + | 0.696888i | \(0.245432\pi\) | |||||||
\(198\) | −6.06783 | −0.431222 | ||||||||
\(199\) | 1.75942 | 0.124722 | 0.0623610 | − | 0.998054i | \(-0.480137\pi\) | ||||
0.0623610 | + | 0.998054i | \(0.480137\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.0414 | 0.849338 | ||||||||
\(202\) | 15.8009 | 1.11174 | ||||||||
\(203\) | −3.28738 | −0.230729 | ||||||||
\(204\) | −0.210745 | −0.0147551 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 23.6545 | 1.64809 | ||||||||
\(207\) | 8.02072 | 0.557479 | ||||||||
\(208\) | 4.14101 | 0.287127 | ||||||||
\(209\) | −5.42525 | −0.375272 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.5694 | 1.07184 | 0.535921 | − | 0.844268i | \(-0.319965\pi\) | ||||
0.535921 | + | 0.844268i | \(0.319965\pi\) | |||||||
\(212\) | 0.376234 | 0.0258398 | ||||||||
\(213\) | −10.7889 | −0.739246 | ||||||||
\(214\) | −4.97392 | −0.340010 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.77434 | −0.188770 | ||||||||
\(217\) | 7.04680 | 0.478368 | ||||||||
\(218\) | −6.72263 | −0.455314 | ||||||||
\(219\) | −8.32568 | −0.562597 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.87971 | −0.193710 | ||||||||
\(222\) | −12.3464 | −0.828636 | ||||||||
\(223\) | 11.5694 | 0.774744 | 0.387372 | − | 0.921923i | \(-0.373383\pi\) | ||||
0.387372 | + | 0.921923i | \(0.373383\pi\) | |||||||
\(224\) | −0.413779 | −0.0276468 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.73334 | −0.314857 | ||||||||
\(227\) | 11.0418 | 0.732867 | 0.366433 | − | 0.930444i | \(-0.380579\pi\) | ||||
0.366433 | + | 0.930444i | \(0.380579\pi\) | |||||||
\(228\) | 0.0942138 | 0.00623946 | ||||||||
\(229\) | −13.7073 | −0.905802 | −0.452901 | − | 0.891561i | \(-0.649611\pi\) | ||||
−0.452901 | + | 0.891561i | \(0.649611\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.21419 | 0.277274 | ||||||||
\(232\) | 9.12029 | 0.598776 | ||||||||
\(233\) | −1.23522 | −0.0809222 | −0.0404611 | − | 0.999181i | \(-0.512883\pi\) | ||||
−0.0404611 | + | 0.999181i | \(0.512883\pi\) | |||||||
\(234\) | 1.43986 | 0.0941263 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −0.536758 | −0.0349400 | ||||||||
\(237\) | −4.47204 | −0.290491 | ||||||||
\(238\) | 4.14637 | 0.268769 | ||||||||
\(239\) | 19.1061 | 1.23587 | 0.617936 | − | 0.786228i | \(-0.287969\pi\) | ||||
0.617936 | + | 0.786228i | \(0.287969\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.0329 | −0.775110 | −0.387555 | − | 0.921847i | \(-0.626680\pi\) | ||||
−0.387555 | + | 0.921847i | \(0.626680\pi\) | |||||||
\(242\) | −9.73259 | −0.625634 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0.567856 | 0.0363533 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −17.3759 | −1.10785 | ||||||||
\(247\) | 1.28738 | 0.0819137 | ||||||||
\(248\) | −19.5502 | −1.24144 | ||||||||
\(249\) | −3.80653 | −0.241229 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.0031 | −0.946990 | −0.473495 | − | 0.880797i | \(-0.657008\pi\) | ||||
−0.473495 | + | 0.880797i | \(0.657008\pi\) | |||||||
\(252\) | −0.0731828 | −0.00461008 | ||||||||
\(253\) | 33.8009 | 2.12504 | ||||||||
\(254\) | −0.616813 | −0.0387023 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.75406 | 0.109629 | ||||||||
\(257\) | 13.0261 | 0.812544 | 0.406272 | − | 0.913752i | \(-0.366828\pi\) | ||||
0.406272 | + | 0.913752i | \(0.366828\pi\) | |||||||
\(258\) | −10.2820 | −0.640131 | ||||||||
\(259\) | 8.57475 | 0.532809 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.28738 | 0.203483 | ||||||||
\(262\) | −20.4284 | −1.26207 | ||||||||
\(263\) | 2.59547 | 0.160044 | 0.0800218 | − | 0.996793i | \(-0.474501\pi\) | ||||
0.0800218 | + | 0.996793i | \(0.474501\pi\) | |||||||
\(264\) | −11.6916 | −0.719568 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1.85363 | −0.113654 | ||||||||
\(267\) | 5.64793 | 0.345648 | ||||||||
\(268\) | −0.881227 | −0.0538295 | ||||||||
\(269\) | −23.3081 | −1.42112 | −0.710560 | − | 0.703637i | \(-0.751558\pi\) | ||||
−0.710560 | + | 0.703637i | \(0.751558\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.05215 | −0.367642 | −0.183821 | − | 0.982960i | \(-0.558847\pi\) | ||||
−0.183821 | + | 0.982960i | \(0.558847\pi\) | |||||||
\(272\) | −11.9249 | −0.723054 | ||||||||
\(273\) | −1.00000 | −0.0605228 | ||||||||
\(274\) | 21.1759 | 1.27928 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.586979 | −0.0353320 | ||||||||
\(277\) | −15.1932 | −0.912869 | −0.456434 | − | 0.889757i | \(-0.650874\pi\) | ||||
−0.456434 | + | 0.889757i | \(0.650874\pi\) | |||||||
\(278\) | −14.1878 | −0.850928 | ||||||||
\(279\) | −7.04680 | −0.421881 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.57506 | −0.451890 | −0.225945 | − | 0.974140i | \(-0.572547\pi\) | ||||
−0.225945 | + | 0.974140i | \(0.572547\pi\) | |||||||
\(282\) | −2.81188 | −0.167445 | ||||||||
\(283\) | −19.0974 | −1.13522 | −0.567610 | − | 0.823298i | \(-0.692132\pi\) | ||||
−0.567610 | + | 0.823298i | \(0.692132\pi\) | |||||||
\(284\) | 0.789565 | 0.0468521 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6.06783 | 0.358798 | ||||||||
\(287\) | 12.0678 | 0.712341 | ||||||||
\(288\) | 0.413779 | 0.0243822 | ||||||||
\(289\) | −8.70727 | −0.512192 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.90043 | 0.404510 | ||||||||
\(292\) | 0.609297 | 0.0356564 | ||||||||
\(293\) | 3.79430 | 0.221665 | 0.110833 | − | 0.993839i | \(-0.464648\pi\) | ||||
0.110833 | + | 0.993839i | \(0.464648\pi\) | |||||||
\(294\) | 1.43986 | 0.0839741 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −23.7893 | −1.38272 | ||||||||
\(297\) | −4.21419 | −0.244532 | ||||||||
\(298\) | 4.87626 | 0.282474 | ||||||||
\(299\) | −8.02072 | −0.463850 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.14101 | 0.411601 | ||||||||
\(302\) | 31.5257 | 1.81410 | ||||||||
\(303\) | 10.9739 | 0.630435 | ||||||||
\(304\) | 5.33104 | 0.305756 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −4.14637 | −0.237032 | ||||||||
\(307\) | 5.19316 | 0.296389 | 0.148195 | − | 0.988958i | \(-0.452654\pi\) | ||||
0.148195 | + | 0.988958i | \(0.452654\pi\) | |||||||
\(308\) | −0.308407 | −0.0175731 | ||||||||
\(309\) | 16.4284 | 0.934578 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.8536 | −0.785568 | −0.392784 | − | 0.919631i | \(-0.628488\pi\) | ||||
−0.392784 | + | 0.919631i | \(0.628488\pi\) | |||||||
\(312\) | 2.77434 | 0.157066 | ||||||||
\(313\) | 32.6162 | 1.84358 | 0.921788 | − | 0.387694i | \(-0.126728\pi\) | ||||
0.921788 | + | 0.387694i | \(0.126728\pi\) | |||||||
\(314\) | −1.24905 | −0.0704879 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.327277 | 0.0184108 | ||||||||
\(317\) | −12.0380 | −0.676121 | −0.338061 | − | 0.941124i | \(-0.609771\pi\) | ||||
−0.338061 | + | 0.941124i | \(0.609771\pi\) | |||||||
\(318\) | 7.40231 | 0.415101 | ||||||||
\(319\) | 13.8536 | 0.775655 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.45446 | −0.192809 | ||||||||
\(322\) | 11.5487 | 0.643583 | ||||||||
\(323\) | −3.70727 | −0.206278 | ||||||||
\(324\) | 0.0731828 | 0.00406571 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 6.37623 | 0.353147 | ||||||||
\(327\) | −4.66896 | −0.258194 | ||||||||
\(328\) | −33.4802 | −1.84864 | ||||||||
\(329\) | 1.95289 | 0.107666 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −26.2820 | −1.44459 | −0.722295 | − | 0.691585i | \(-0.756913\pi\) | ||||
−0.722295 | + | 0.691585i | \(0.756913\pi\) | |||||||
\(332\) | 0.278572 | 0.0152886 | ||||||||
\(333\) | −8.57475 | −0.469893 | ||||||||
\(334\) | 29.5568 | 1.61728 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −4.14101 | −0.225911 | ||||||||
\(337\) | −26.2905 | −1.43214 | −0.716068 | − | 0.698031i | \(-0.754060\pi\) | ||||
−0.716068 | + | 0.698031i | \(0.754060\pi\) | |||||||
\(338\) | −1.43986 | −0.0783178 | ||||||||
\(339\) | −3.28738 | −0.178546 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −29.6966 | −1.60816 | ||||||||
\(342\) | 1.85363 | 0.100233 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −19.8116 | −1.06817 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 21.6199 | 1.16230 | ||||||||
\(347\) | −16.4928 | −0.885378 | −0.442689 | − | 0.896675i | \(-0.645975\pi\) | ||||
−0.442689 | + | 0.896675i | \(0.645975\pi\) | |||||||
\(348\) | −0.240579 | −0.0128964 | ||||||||
\(349\) | 14.1793 | 0.759001 | 0.379501 | − | 0.925191i | \(-0.376096\pi\) | ||||
0.379501 | + | 0.925191i | \(0.376096\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 1.74375 | 0.0929419 | ||||||||
\(353\) | 29.8272 | 1.58754 | 0.793772 | − | 0.608215i | \(-0.208114\pi\) | ||||
0.793772 | + | 0.608215i | \(0.208114\pi\) | |||||||
\(354\) | −10.5606 | −0.561289 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −0.413332 | −0.0219065 | ||||||||
\(357\) | 2.87971 | 0.152410 | ||||||||
\(358\) | 7.70575 | 0.407262 | ||||||||
\(359\) | 1.34671 | 0.0710767 | 0.0355383 | − | 0.999368i | \(-0.488685\pi\) | ||||
0.0355383 | + | 0.999368i | \(0.488685\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.3427 | −0.912772 | ||||||||
\(362\) | −16.5104 | −0.867766 | ||||||||
\(363\) | −6.75942 | −0.354778 | ||||||||
\(364\) | 0.0731828 | 0.00383582 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 11.1724 | 0.583993 | ||||||||
\(367\) | −36.1771 | −1.88843 | −0.944214 | − | 0.329331i | \(-0.893177\pi\) | ||||
−0.944214 | + | 0.329331i | \(0.893177\pi\) | |||||||
\(368\) | −33.2139 | −1.73139 | ||||||||
\(369\) | −12.0678 | −0.628226 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.14101 | −0.266908 | ||||||||
\(372\) | 0.515704 | 0.0267380 | ||||||||
\(373\) | 16.9089 | 0.875511 | 0.437755 | − | 0.899094i | \(-0.355774\pi\) | ||||
0.437755 | + | 0.899094i | \(0.355774\pi\) | |||||||
\(374\) | −17.4736 | −0.903538 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.41798 | −0.279411 | ||||||||
\(377\) | −3.28738 | −0.169308 | ||||||||
\(378\) | −1.43986 | −0.0740582 | ||||||||
\(379\) | −11.6131 | −0.596523 | −0.298261 | − | 0.954484i | \(-0.596407\pi\) | ||||
−0.298261 | + | 0.954484i | \(0.596407\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.428386 | −0.0219469 | ||||||||
\(382\) | −29.0499 | −1.48632 | ||||||||
\(383\) | −14.6134 | −0.746708 | −0.373354 | − | 0.927689i | \(-0.621792\pi\) | ||||
−0.373354 | + | 0.927689i | \(0.621792\pi\) | |||||||
\(384\) | 11.8946 | 0.606995 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −37.9771 | −1.93298 | ||||||||
\(387\) | −7.14101 | −0.362998 | ||||||||
\(388\) | −0.504993 | −0.0256371 | ||||||||
\(389\) | 6.00000 | 0.304212 | 0.152106 | − | 0.988364i | \(-0.451394\pi\) | ||||
0.152106 | + | 0.988364i | \(0.451394\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 23.0974 | 1.16808 | ||||||||
\(392\) | 2.77434 | 0.140125 | ||||||||
\(393\) | −14.1878 | −0.715680 | ||||||||
\(394\) | −28.9875 | −1.46037 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.308407 | 0.0154980 | ||||||||
\(397\) | −25.6982 | −1.28975 | −0.644877 | − | 0.764287i | \(-0.723091\pi\) | ||||
−0.644877 | + | 0.764287i | \(0.723091\pi\) | |||||||
\(398\) | −2.53331 | −0.126983 | ||||||||
\(399\) | −1.28738 | −0.0644494 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −19.5637 | −0.976966 | −0.488483 | − | 0.872573i | \(-0.662450\pi\) | ||||
−0.488483 | + | 0.872573i | \(0.662450\pi\) | |||||||
\(402\) | −17.3379 | −0.864737 | ||||||||
\(403\) | 7.04680 | 0.351026 | ||||||||
\(404\) | −0.803103 | −0.0399559 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.73334 | 0.234912 | ||||||||
\(407\) | −36.1357 | −1.79118 | ||||||||
\(408\) | −7.98929 | −0.395529 | ||||||||
\(409\) | 3.19316 | 0.157892 | 0.0789458 | − | 0.996879i | \(-0.474845\pi\) | ||||
0.0789458 | + | 0.996879i | \(0.474845\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 14.7070 | 0.725441 | ||||||||
\(412\) | −1.20228 | −0.0592319 | ||||||||
\(413\) | 7.33448 | 0.360906 | ||||||||
\(414\) | −11.5487 | −0.567586 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.413779 | −0.0202872 | ||||||||
\(417\) | −9.85363 | −0.482535 | ||||||||
\(418\) | 7.81157 | 0.382076 | ||||||||
\(419\) | 30.2292 | 1.47680 | 0.738398 | − | 0.674366i | \(-0.235583\pi\) | ||||
0.738398 | + | 0.674366i | \(0.235583\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.9510 | 1.31351 | 0.656755 | − | 0.754104i | \(-0.271928\pi\) | ||||
0.656755 | + | 0.754104i | \(0.271928\pi\) | |||||||
\(422\) | −22.4177 | −1.09128 | ||||||||
\(423\) | −1.95289 | −0.0949529 | ||||||||
\(424\) | 14.2629 | 0.692668 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 15.5345 | 0.752650 | ||||||||
\(427\) | −7.75942 | −0.375505 | ||||||||
\(428\) | 0.252807 | 0.0122199 | ||||||||
\(429\) | 4.21419 | 0.203463 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.7713 | 0.807847 | 0.403923 | − | 0.914793i | \(-0.367646\pi\) | ||||
0.403923 | + | 0.914793i | \(0.367646\pi\) | |||||||
\(432\) | 4.14101 | 0.199234 | ||||||||
\(433\) | −25.8530 | −1.24242 | −0.621208 | − | 0.783646i | \(-0.713358\pi\) | ||||
−0.621208 | + | 0.783646i | \(0.713358\pi\) | |||||||
\(434\) | −10.1464 | −0.487041 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.341688 | 0.0163639 | ||||||||
\(437\) | −10.3257 | −0.493944 | ||||||||
\(438\) | 11.9878 | 0.572798 | ||||||||
\(439\) | 25.0553 | 1.19582 | 0.597912 | − | 0.801562i | \(-0.295997\pi\) | ||||
0.597912 | + | 0.801562i | \(0.295997\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 4.14637 | 0.197223 | ||||||||
\(443\) | −4.64762 | −0.220815 | −0.110408 | − | 0.993886i | \(-0.535216\pi\) | ||||
−0.110408 | + | 0.993886i | \(0.535216\pi\) | |||||||
\(444\) | 0.627525 | 0.0297810 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −16.6583 | −0.788791 | ||||||||
\(447\) | 3.38663 | 0.160182 | ||||||||
\(448\) | −7.68624 | −0.363141 | ||||||||
\(449\) | 0.494696 | 0.0233462 | 0.0116731 | − | 0.999932i | \(-0.496284\pi\) | ||||
0.0116731 | + | 0.999932i | \(0.496284\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −50.8561 | −2.39472 | ||||||||
\(452\) | 0.240579 | 0.0113159 | ||||||||
\(453\) | 21.8951 | 1.02872 | ||||||||
\(454\) | −15.8985 | −0.746155 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.57161 | 0.167256 | ||||||||
\(457\) | −26.4698 | −1.23821 | −0.619103 | − | 0.785310i | \(-0.712504\pi\) | ||||
−0.619103 | + | 0.785310i | \(0.712504\pi\) | |||||||
\(458\) | 19.7365 | 0.922225 | ||||||||
\(459\) | −2.87971 | −0.134413 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.08168 | −0.0503786 | −0.0251893 | − | 0.999683i | \(-0.508019\pi\) | ||||
−0.0251893 | + | 0.999683i | \(0.508019\pi\) | |||||||
\(462\) | −6.06783 | −0.282301 | ||||||||
\(463\) | 32.7098 | 1.52015 | 0.760076 | − | 0.649834i | \(-0.225162\pi\) | ||||
0.760076 | + | 0.649834i | \(0.225162\pi\) | |||||||
\(464\) | −13.6131 | −0.631970 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.77854 | 0.0823894 | ||||||||
\(467\) | 17.0797 | 0.790356 | 0.395178 | − | 0.918605i | \(-0.370683\pi\) | ||||
0.395178 | + | 0.918605i | \(0.370683\pi\) | |||||||
\(468\) | −0.0731828 | −0.00338288 | ||||||||
\(469\) | 12.0414 | 0.556022 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.867482 | −0.0399715 | ||||||||
\(472\) | −20.3483 | −0.936608 | ||||||||
\(473\) | −30.0936 | −1.38370 | ||||||||
\(474\) | 6.43910 | 0.295758 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −0.210745 | −0.00965950 | ||||||||
\(477\) | 5.14101 | 0.235391 | ||||||||
\(478\) | −27.5101 | −1.25828 | ||||||||
\(479\) | −17.1790 | −0.784929 | −0.392464 | − | 0.919767i | \(-0.628377\pi\) | ||||
−0.392464 | + | 0.919767i | \(0.628377\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.57475 | 0.390975 | ||||||||
\(482\) | 17.3257 | 0.789164 | ||||||||
\(483\) | 8.02072 | 0.364955 | ||||||||
\(484\) | 0.494674 | 0.0224852 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.43986 | 0.0653132 | ||||||||
\(487\) | 4.28264 | 0.194065 | 0.0970325 | − | 0.995281i | \(-0.469065\pi\) | ||||
0.0970325 | + | 0.995281i | \(0.469065\pi\) | |||||||
\(488\) | 21.5273 | 0.974493 | ||||||||
\(489\) | 4.42839 | 0.200259 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 27.4545 | 1.23900 | 0.619501 | − | 0.784996i | \(-0.287335\pi\) | ||||
0.619501 | + | 0.784996i | \(0.287335\pi\) | |||||||
\(492\) | 0.883158 | 0.0398158 | ||||||||
\(493\) | 9.46669 | 0.426358 | ||||||||
\(494\) | −1.85363 | −0.0833990 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 29.1809 | 1.31026 | ||||||||
\(497\) | −10.7889 | −0.483950 | ||||||||
\(498\) | 5.48085 | 0.245603 | ||||||||
\(499\) | −37.0452 | −1.65837 | −0.829185 | − | 0.558974i | \(-0.811195\pi\) | ||||
−0.829185 | + | 0.558974i | \(0.811195\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 20.5276 | 0.917108 | ||||||||
\(502\) | 21.6023 | 0.964160 | ||||||||
\(503\) | −3.23744 | −0.144350 | −0.0721752 | − | 0.997392i | \(-0.522994\pi\) | ||||
−0.0721752 | + | 0.997392i | \(0.522994\pi\) | |||||||
\(504\) | −2.77434 | −0.123579 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −48.6683 | −2.16357 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | 0.0313505 | 0.00139095 | ||||||||
\(509\) | −30.4877 | −1.35134 | −0.675672 | − | 0.737202i | \(-0.736147\pi\) | ||||
−0.675672 | + | 0.737202i | \(0.736147\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.32568 | −0.368306 | ||||||||
\(512\) | 21.2637 | 0.939730 | ||||||||
\(513\) | 1.28738 | 0.0568390 | ||||||||
\(514\) | −18.7557 | −0.827277 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.522599 | 0.0230062 | ||||||||
\(517\) | −8.22987 | −0.361949 | ||||||||
\(518\) | −12.3464 | −0.542470 | ||||||||
\(519\) | 15.0154 | 0.659101 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −25.3602 | −1.11105 | −0.555526 | − | 0.831499i | \(-0.687483\pi\) | ||||
−0.555526 | + | 0.831499i | \(0.687483\pi\) | |||||||
\(522\) | −4.73334 | −0.207173 | ||||||||
\(523\) | 7.00314 | 0.306226 | 0.153113 | − | 0.988209i | \(-0.451070\pi\) | ||||
0.153113 | + | 0.988209i | \(0.451070\pi\) | |||||||
\(524\) | 1.03830 | 0.0453585 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.73710 | −0.162945 | ||||||||
\(527\) | −20.2927 | −0.883965 | ||||||||
\(528\) | 17.4510 | 0.759458 | ||||||||
\(529\) | 41.3320 | 1.79704 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.33448 | −0.318289 | ||||||||
\(532\) | 0.0942138 | 0.00408469 | ||||||||
\(533\) | 12.0678 | 0.522716 | ||||||||
\(534\) | −8.13221 | −0.351915 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −33.4070 | −1.44296 | ||||||||
\(537\) | 5.35176 | 0.230945 | ||||||||
\(538\) | 33.5603 | 1.44689 | ||||||||
\(539\) | 4.21419 | 0.181518 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.42463 | −0.0612495 | −0.0306248 | − | 0.999531i | \(-0.509750\pi\) | ||||
−0.0306248 | + | 0.999531i | \(0.509750\pi\) | |||||||
\(542\) | 8.71422 | 0.374308 | ||||||||
\(543\) | −11.4667 | −0.492083 | ||||||||
\(544\) | 1.19156 | 0.0510879 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.43986 | 0.0616201 | ||||||||
\(547\) | 22.0499 | 0.942787 | 0.471394 | − | 0.881923i | \(-0.343751\pi\) | ||||
0.471394 | + | 0.881923i | \(0.343751\pi\) | |||||||
\(548\) | −1.07630 | −0.0459771 | ||||||||
\(549\) | 7.75942 | 0.331164 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.23209 | −0.180293 | ||||||||
\(552\) | −22.2522 | −0.947116 | ||||||||
\(553\) | −4.47204 | −0.190171 | ||||||||
\(554\) | 21.8760 | 0.929420 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.721117 | 0.0305822 | ||||||||
\(557\) | 9.08319 | 0.384867 | 0.192434 | − | 0.981310i | \(-0.438362\pi\) | ||||
0.192434 | + | 0.981310i | \(0.438362\pi\) | |||||||
\(558\) | 10.1464 | 0.429530 | ||||||||
\(559\) | 7.14101 | 0.302033 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12.1357 | −0.512368 | ||||||||
\(562\) | 10.9070 | 0.460084 | ||||||||
\(563\) | −34.1350 | −1.43862 | −0.719310 | − | 0.694689i | \(-0.755542\pi\) | ||||
−0.719310 | + | 0.694689i | \(0.755542\pi\) | |||||||
\(564\) | 0.142918 | 0.00601794 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 27.4974 | 1.15580 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 29.9322 | 1.25593 | ||||||||
\(569\) | 1.23522 | 0.0517833 | 0.0258916 | − | 0.999665i | \(-0.491758\pi\) | ||||
0.0258916 | + | 0.999665i | \(0.491758\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −26.4613 | −1.10737 | −0.553686 | − | 0.832725i | \(-0.686779\pi\) | ||||
−0.553686 | + | 0.832725i | \(0.686779\pi\) | |||||||
\(572\) | −0.308407 | −0.0128951 | ||||||||
\(573\) | −20.1756 | −0.842847 | ||||||||
\(574\) | −17.3759 | −0.725257 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 7.68624 | 0.320260 | ||||||||
\(577\) | 23.2852 | 0.969374 | 0.484687 | − | 0.874688i | \(-0.338934\pi\) | ||||
0.484687 | + | 0.874688i | \(0.338934\pi\) | |||||||
\(578\) | 12.5372 | 0.521479 | ||||||||
\(579\) | −26.3756 | −1.09613 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.80653 | −0.157921 | ||||||||
\(582\) | −9.93562 | −0.411845 | ||||||||
\(583\) | 21.6652 | 0.897281 | ||||||||
\(584\) | 23.0982 | 0.955812 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5.46324 | −0.225684 | ||||||||
\(587\) | 10.7155 | 0.442274 | 0.221137 | − | 0.975243i | \(-0.429023\pi\) | ||||
0.221137 | + | 0.975243i | \(0.429023\pi\) | |||||||
\(588\) | −0.0731828 | −0.00301801 | ||||||||
\(589\) | 9.07187 | 0.373800 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −20.1322 | −0.828128 | ||||||||
\(592\) | 35.5081 | 1.45938 | ||||||||
\(593\) | −14.1008 | −0.579049 | −0.289525 | − | 0.957171i | \(-0.593497\pi\) | ||||
−0.289525 | + | 0.957171i | \(0.593497\pi\) | |||||||
\(594\) | 6.06783 | 0.248966 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.247843 | −0.0101521 | ||||||||
\(597\) | −1.75942 | −0.0720083 | ||||||||
\(598\) | 11.5487 | 0.472260 | ||||||||
\(599\) | −38.9296 | −1.59062 | −0.795311 | − | 0.606202i | \(-0.792692\pi\) | ||||
−0.795311 | + | 0.606202i | \(0.792692\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −32.6162 | −1.33044 | −0.665221 | − | 0.746646i | \(-0.731663\pi\) | ||||
−0.665221 | + | 0.746646i | \(0.731663\pi\) | |||||||
\(602\) | −10.2820 | −0.419064 | ||||||||
\(603\) | −12.0414 | −0.490365 | ||||||||
\(604\) | −1.60234 | −0.0651984 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −15.8009 | −0.641866 | ||||||||
\(607\) | −19.3203 | −0.784188 | −0.392094 | − | 0.919925i | \(-0.628249\pi\) | ||||
−0.392094 | + | 0.919925i | \(0.628249\pi\) | |||||||
\(608\) | −0.532689 | −0.0216034 | ||||||||
\(609\) | 3.28738 | 0.133211 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.95289 | 0.0790056 | ||||||||
\(612\) | 0.210745 | 0.00851888 | ||||||||
\(613\) | −35.3197 | −1.42655 | −0.713275 | − | 0.700885i | \(-0.752789\pi\) | ||||
−0.713275 | + | 0.700885i | \(0.752789\pi\) | |||||||
\(614\) | −7.47740 | −0.301763 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −11.6916 | −0.471068 | ||||||||
\(617\) | 24.4318 | 0.983589 | 0.491794 | − | 0.870711i | \(-0.336341\pi\) | ||||
0.491794 | + | 0.870711i | \(0.336341\pi\) | |||||||
\(618\) | −23.6545 | −0.951523 | ||||||||
\(619\) | 2.90892 | 0.116919 | 0.0584597 | − | 0.998290i | \(-0.481381\pi\) | ||||
0.0584597 | + | 0.998290i | \(0.481381\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.02072 | −0.321860 | ||||||||
\(622\) | 19.9472 | 0.799811 | ||||||||
\(623\) | 5.64793 | 0.226280 | ||||||||
\(624\) | −4.14101 | −0.165773 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −46.9626 | −1.87700 | ||||||||
\(627\) | 5.42525 | 0.216664 | ||||||||
\(628\) | 0.0634848 | 0.00253332 | ||||||||
\(629\) | −24.6928 | −0.984566 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.66521 | 0.225528 | 0.112764 | − | 0.993622i | \(-0.464030\pi\) | ||||
0.112764 | + | 0.993622i | \(0.464030\pi\) | |||||||
\(632\) | 12.4070 | 0.493522 | ||||||||
\(633\) | −15.5694 | −0.618828 | ||||||||
\(634\) | 17.3330 | 0.688380 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.376234 | −0.0149186 | ||||||||
\(637\) | −1.00000 | −0.0396214 | ||||||||
\(638\) | −19.9472 | −0.789718 | ||||||||
\(639\) | 10.7889 | 0.426804 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.2842 | 0.485198 | 0.242599 | − | 0.970127i | \(-0.422000\pi\) | ||||
0.242599 | + | 0.970127i | \(0.422000\pi\) | |||||||
\(642\) | 4.97392 | 0.196305 | ||||||||
\(643\) | −9.14950 | −0.360821 | −0.180411 | − | 0.983591i | \(-0.557743\pi\) | ||||
−0.180411 | + | 0.983591i | \(0.557743\pi\) | |||||||
\(644\) | −0.586979 | −0.0231302 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.33793 | 0.210018 | ||||||||
\(647\) | −38.4108 | −1.51008 | −0.755042 | − | 0.655677i | \(-0.772383\pi\) | ||||
−0.755042 | + | 0.655677i | \(0.772383\pi\) | |||||||
\(648\) | 2.77434 | 0.108986 | ||||||||
\(649\) | −30.9089 | −1.21328 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.04680 | −0.276186 | ||||||||
\(652\) | −0.324082 | −0.0126920 | ||||||||
\(653\) | −28.4805 | −1.11453 | −0.557265 | − | 0.830335i | \(-0.688149\pi\) | ||||
−0.557265 | + | 0.830335i | \(0.688149\pi\) | |||||||
\(654\) | 6.72263 | 0.262876 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 49.9730 | 1.95112 | ||||||||
\(657\) | 8.32568 | 0.324816 | ||||||||
\(658\) | −2.81188 | −0.109619 | ||||||||
\(659\) | −30.4384 | −1.18571 | −0.592856 | − | 0.805309i | \(-0.702000\pi\) | ||||
−0.592856 | + | 0.805309i | \(0.702000\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 36.7710 | 1.43023 | 0.715114 | − | 0.699008i | \(-0.246375\pi\) | ||||
0.715114 | + | 0.699008i | \(0.246375\pi\) | |||||||
\(662\) | 37.8423 | 1.47078 | ||||||||
\(663\) | 2.87971 | 0.111839 | ||||||||
\(664\) | 10.5606 | 0.409830 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 12.3464 | 0.478413 | ||||||||
\(667\) | 26.3671 | 1.02094 | ||||||||
\(668\) | −1.50227 | −0.0581246 | ||||||||
\(669\) | −11.5694 | −0.447299 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 32.6997 | 1.26236 | ||||||||
\(672\) | 0.413779 | 0.0159619 | ||||||||
\(673\) | −26.7961 | −1.03291 | −0.516457 | − | 0.856313i | \(-0.672750\pi\) | ||||
−0.516457 | + | 0.856313i | \(0.672750\pi\) | |||||||
\(674\) | 37.8545 | 1.45810 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.0731828 | 0.00281472 | ||||||||
\(677\) | 20.3050 | 0.780383 | 0.390191 | − | 0.920734i | \(-0.372409\pi\) | ||||
0.390191 | + | 0.920734i | \(0.372409\pi\) | |||||||
\(678\) | 4.73334 | 0.181783 | ||||||||
\(679\) | 6.90043 | 0.264814 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11.0418 | −0.423121 | ||||||||
\(682\) | 42.7587 | 1.63732 | ||||||||
\(683\) | −44.9240 | −1.71897 | −0.859484 | − | 0.511162i | \(-0.829215\pi\) | ||||
−0.859484 | + | 0.511162i | \(0.829215\pi\) | |||||||
\(684\) | −0.0942138 | −0.00360235 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.43986 | 0.0549739 | ||||||||
\(687\) | 13.7073 | 0.522965 | ||||||||
\(688\) | 29.5710 | 1.12738 | ||||||||
\(689\) | −5.14101 | −0.195857 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.0085 | 0.837243 | 0.418621 | − | 0.908161i | \(-0.362513\pi\) | ||||
0.418621 | + | 0.908161i | \(0.362513\pi\) | |||||||
\(692\) | −1.09887 | −0.0417726 | ||||||||
\(693\) | −4.21419 | −0.160084 | ||||||||
\(694\) | 23.7472 | 0.901431 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −9.12029 | −0.345704 | ||||||||
\(697\) | −34.7518 | −1.31632 | ||||||||
\(698\) | −20.4162 | −0.772763 | ||||||||
\(699\) | 1.23522 | 0.0467205 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 31.4645 | 1.18840 | 0.594198 | − | 0.804319i | \(-0.297469\pi\) | ||||
0.594198 | + | 0.804319i | \(0.297469\pi\) | |||||||
\(702\) | −1.43986 | −0.0543438 | ||||||||
\(703\) | 11.0389 | 0.416341 | ||||||||
\(704\) | 32.3913 | 1.22079 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −42.9469 | −1.61633 | ||||||||
\(707\) | 10.9739 | 0.412717 | ||||||||
\(708\) | 0.536758 | 0.0201726 | ||||||||
\(709\) | −25.3373 | −0.951563 | −0.475781 | − | 0.879564i | \(-0.657835\pi\) | ||||
−0.475781 | + | 0.879564i | \(0.657835\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.47204 | 0.167715 | ||||||||
\(712\) | −15.6693 | −0.587231 | ||||||||
\(713\) | −56.5204 | −2.11670 | ||||||||
\(714\) | −4.14637 | −0.155174 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −0.391657 | −0.0146369 | ||||||||
\(717\) | −19.1061 | −0.713532 | ||||||||
\(718\) | −1.93907 | −0.0723654 | ||||||||
\(719\) | −43.8002 | −1.63347 | −0.816737 | − | 0.577011i | \(-0.804219\pi\) | ||||
−0.816737 | + | 0.577011i | \(0.804219\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16.4284 | 0.611825 | ||||||||
\(722\) | 24.9709 | 0.929322 | ||||||||
\(723\) | 12.0329 | 0.447510 | ||||||||
\(724\) | 0.839165 | 0.0311873 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 9.73259 | 0.361210 | ||||||||
\(727\) | −0.944090 | −0.0350144 | −0.0175072 | − | 0.999847i | \(-0.505573\pi\) | ||||
−0.0175072 | + | 0.999847i | \(0.505573\pi\) | |||||||
\(728\) | 2.77434 | 0.102824 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −20.5640 | −0.760588 | ||||||||
\(732\) | −0.567856 | −0.0209886 | ||||||||
\(733\) | 5.09957 | 0.188357 | 0.0941784 | − | 0.995555i | \(-0.469978\pi\) | ||||
0.0941784 | + | 0.995555i | \(0.469978\pi\) | |||||||
\(734\) | 52.0898 | 1.92267 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.31881 | 0.122333 | ||||||||
\(737\) | −50.7450 | −1.86921 | ||||||||
\(738\) | 17.3759 | 0.639617 | ||||||||
\(739\) | −8.25129 | −0.303529 | −0.151764 | − | 0.988417i | \(-0.548495\pi\) | ||||
−0.151764 | + | 0.988417i | \(0.548495\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.28738 | −0.0472929 | ||||||||
\(742\) | 7.40231 | 0.271747 | ||||||||
\(743\) | −38.4962 | −1.41229 | −0.706145 | − | 0.708068i | \(-0.749567\pi\) | ||||
−0.706145 | + | 0.708068i | \(0.749567\pi\) | |||||||
\(744\) | 19.5502 | 0.716745 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −24.3464 | −0.891385 | ||||||||
\(747\) | 3.80653 | 0.139274 | ||||||||
\(748\) | 0.888121 | 0.0324729 | ||||||||
\(749\) | −3.45446 | −0.126223 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −41.3175 | −1.50770 | −0.753848 | − | 0.657049i | \(-0.771805\pi\) | ||||
−0.753848 | + | 0.657049i | \(0.771805\pi\) | |||||||
\(752\) | 8.08695 | 0.294901 | ||||||||
\(753\) | 15.0031 | 0.546745 | ||||||||
\(754\) | 4.73334 | 0.172378 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.0731828 | 0.00266163 | ||||||||
\(757\) | 39.7158 | 1.44349 | 0.721747 | − | 0.692157i | \(-0.243339\pi\) | ||||
0.721747 | + | 0.692157i | \(0.243339\pi\) | |||||||
\(758\) | 16.7211 | 0.607338 | ||||||||
\(759\) | −33.8009 | −1.22689 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.7390 | 0.389289 | 0.194644 | − | 0.980874i | \(-0.437645\pi\) | ||||
0.194644 | + | 0.980874i | \(0.437645\pi\) | |||||||
\(762\) | 0.616813 | 0.0223448 | ||||||||
\(763\) | −4.66896 | −0.169028 | ||||||||
\(764\) | 1.47651 | 0.0534181 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 21.0411 | 0.760247 | ||||||||
\(767\) | 7.33448 | 0.264833 | ||||||||
\(768\) | −1.75406 | −0.0632944 | ||||||||
\(769\) | −50.5549 | −1.82306 | −0.911529 | − | 0.411237i | \(-0.865097\pi\) | ||||
−0.911529 | + | 0.411237i | \(0.865097\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13.0261 | −0.469123 | ||||||||
\(772\) | 1.93024 | 0.0694709 | ||||||||
\(773\) | −8.91770 | −0.320747 | −0.160374 | − | 0.987056i | \(-0.551270\pi\) | ||||
−0.160374 | + | 0.987056i | \(0.551270\pi\) | |||||||
\(774\) | 10.2820 | 0.369580 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −19.1441 | −0.687234 | ||||||||
\(777\) | −8.57475 | −0.307617 | ||||||||
\(778\) | −8.63913 | −0.309728 | ||||||||
\(779\) | 15.5358 | 0.556629 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 45.4667 | 1.62693 | ||||||||
\(782\) | −33.2568 | −1.18926 | ||||||||
\(783\) | −3.28738 | −0.117481 | ||||||||
\(784\) | −4.14101 | −0.147893 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 20.4284 | 0.728656 | ||||||||
\(787\) | −22.3671 | −0.797302 | −0.398651 | − | 0.917103i | \(-0.630521\pi\) | ||||
−0.398651 | + | 0.917103i | \(0.630521\pi\) | |||||||
\(788\) | 1.47333 | 0.0524853 | ||||||||
\(789\) | −2.59547 | −0.0924012 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.28738 | −0.116886 | ||||||||
\(792\) | 11.6916 | 0.415443 | ||||||||
\(793\) | −7.75942 | −0.275545 | ||||||||
\(794\) | 37.0016 | 1.31314 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0.128759 | 0.00456375 | ||||||||
\(797\) | −20.5518 | −0.727983 | −0.363991 | − | 0.931402i | \(-0.618586\pi\) | ||||
−0.363991 | + | 0.931402i | \(0.618586\pi\) | |||||||
\(798\) | 1.85363 | 0.0656179 | ||||||||
\(799\) | −5.62377 | −0.198955 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.64793 | −0.199560 | ||||||||
\(802\) | 28.1689 | 0.994680 | ||||||||
\(803\) | 35.0860 | 1.23816 | ||||||||
\(804\) | 0.881227 | 0.0310785 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −10.1464 | −0.357390 | ||||||||
\(807\) | 23.3081 | 0.820484 | ||||||||
\(808\) | −30.4454 | −1.07106 | ||||||||
\(809\) | 7.83443 | 0.275444 | 0.137722 | − | 0.990471i | \(-0.456022\pi\) | ||||
0.137722 | + | 0.990471i | \(0.456022\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −47.5502 | −1.66971 | −0.834857 | − | 0.550468i | \(-0.814449\pi\) | ||||
−0.834857 | + | 0.550468i | \(0.814449\pi\) | |||||||
\(812\) | −0.240579 | −0.00844268 | ||||||||
\(813\) | 6.05215 | 0.212258 | ||||||||
\(814\) | 52.0301 | 1.82365 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 11.9249 | 0.417455 | ||||||||
\(817\) | 9.19316 | 0.321628 | ||||||||
\(818\) | −4.59769 | −0.160754 | ||||||||
\(819\) | 1.00000 | 0.0349428 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.42494 | 0.154431 | 0.0772157 | − | 0.997014i | \(-0.475397\pi\) | ||||
0.0772157 | + | 0.997014i | \(0.475397\pi\) | |||||||
\(822\) | −21.1759 | −0.738594 | ||||||||
\(823\) | 28.7525 | 1.00225 | 0.501124 | − | 0.865375i | \(-0.332920\pi\) | ||||
0.501124 | + | 0.865375i | \(0.332920\pi\) | |||||||
\(824\) | −45.5779 | −1.58778 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −10.5606 | −0.367450 | ||||||||
\(827\) | 5.58667 | 0.194267 | 0.0971337 | − | 0.995271i | \(-0.469033\pi\) | ||||
0.0971337 | + | 0.995271i | \(0.469033\pi\) | |||||||
\(828\) | 0.586979 | 0.0203989 | ||||||||
\(829\) | 53.4974 | 1.85804 | 0.929021 | − | 0.370027i | \(-0.120652\pi\) | ||||
0.929021 | + | 0.370027i | \(0.120652\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 15.1932 | 0.527045 | ||||||||
\(832\) | −7.68624 | −0.266472 | ||||||||
\(833\) | 2.87971 | 0.0997760 | ||||||||
\(834\) | 14.1878 | 0.491284 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −0.397035 | −0.0137317 | ||||||||
\(837\) | 7.04680 | 0.243573 | ||||||||
\(838\) | −43.5257 | −1.50357 | ||||||||
\(839\) | −43.0405 | −1.48592 | −0.742962 | − | 0.669334i | \(-0.766580\pi\) | ||||
−0.742962 | + | 0.669334i | \(0.766580\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.1932 | −0.627350 | ||||||||
\(842\) | −38.8055 | −1.33733 | ||||||||
\(843\) | 7.57506 | 0.260899 | ||||||||
\(844\) | 1.13941 | 0.0392202 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 2.81188 | 0.0966745 | ||||||||
\(847\) | −6.75942 | −0.232256 | ||||||||
\(848\) | −21.2890 | −0.731066 | ||||||||
\(849\) | 19.0974 | 0.655419 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −68.7757 | −2.35760 | ||||||||
\(852\) | −0.789565 | −0.0270501 | ||||||||
\(853\) | 30.7434 | 1.05263 | 0.526316 | − | 0.850289i | \(-0.323573\pi\) | ||||
0.526316 | + | 0.850289i | \(0.323573\pi\) | |||||||
\(854\) | 11.1724 | 0.382313 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9.58384 | 0.327569 | ||||||||
\(857\) | 24.5449 | 0.838438 | 0.419219 | − | 0.907885i | \(-0.362304\pi\) | ||||
0.419219 | + | 0.907885i | \(0.362304\pi\) | |||||||
\(858\) | −6.06783 | −0.207152 | ||||||||
\(859\) | −52.1243 | −1.77846 | −0.889229 | − | 0.457461i | \(-0.848759\pi\) | ||||
−0.889229 | + | 0.457461i | \(0.848759\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −12.0678 | −0.411270 | ||||||||
\(862\) | −24.1483 | −0.822494 | ||||||||
\(863\) | −22.2563 | −0.757612 | −0.378806 | − | 0.925476i | \(-0.623665\pi\) | ||||
−0.378806 | + | 0.925476i | \(0.623665\pi\) | |||||||
\(864\) | −0.413779 | −0.0140771 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 37.2246 | 1.26494 | ||||||||
\(867\) | 8.70727 | 0.295714 | ||||||||
\(868\) | 0.515704 | 0.0175041 | ||||||||
\(869\) | 18.8461 | 0.639309 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.0414 | 0.408009 | ||||||||
\(872\) | 12.9533 | 0.438654 | ||||||||
\(873\) | −6.90043 | −0.233544 | ||||||||
\(874\) | 14.8675 | 0.502900 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −0.609297 | −0.0205862 | ||||||||
\(877\) | −41.0547 | −1.38632 | −0.693159 | − | 0.720785i | \(-0.743782\pi\) | ||||
−0.693159 | + | 0.720785i | \(0.743782\pi\) | |||||||
\(878\) | −36.0760 | −1.21751 | ||||||||
\(879\) | −3.79430 | −0.127979 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −31.0568 | −1.04633 | −0.523165 | − | 0.852231i | \(-0.675249\pi\) | ||||
−0.523165 | + | 0.852231i | \(0.675249\pi\) | |||||||
\(882\) | −1.43986 | −0.0484824 | ||||||||
\(883\) | 56.5357 | 1.90258 | 0.951289 | − | 0.308300i | \(-0.0997600\pi\) | ||||
0.951289 | + | 0.308300i | \(0.0997600\pi\) | |||||||
\(884\) | −0.210745 | −0.00708813 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.69190 | 0.224819 | ||||||||
\(887\) | −9.94785 | −0.334016 | −0.167008 | − | 0.985956i | \(-0.553411\pi\) | ||||
−0.167008 | + | 0.985956i | \(0.553411\pi\) | |||||||
\(888\) | 23.7893 | 0.798315 | ||||||||
\(889\) | −0.428386 | −0.0143676 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.21419 | 0.141181 | ||||||||
\(892\) | 0.846681 | 0.0283490 | ||||||||
\(893\) | 2.51411 | 0.0841314 | ||||||||
\(894\) | −4.87626 | −0.163087 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 11.8946 | 0.397372 | ||||||||
\(897\) | 8.02072 | 0.267804 | ||||||||
\(898\) | −0.712291 | −0.0237695 | ||||||||
\(899\) | −23.1655 | −0.772612 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14.8046 | 0.493213 | ||||||||
\(902\) | 73.2255 | 2.43814 | ||||||||
\(903\) | −7.14101 | −0.237638 | ||||||||
\(904\) | 9.12029 | 0.303336 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −31.5257 | −1.04737 | ||||||||
\(907\) | 31.2936 | 1.03909 | 0.519544 | − | 0.854444i | \(-0.326102\pi\) | ||||
0.519544 | + | 0.854444i | \(0.326102\pi\) | |||||||
\(908\) | 0.808067 | 0.0268166 | ||||||||
\(909\) | −10.9739 | −0.363982 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.39320 | −0.311210 | −0.155605 | − | 0.987819i | \(-0.549733\pi\) | ||||
−0.155605 | + | 0.987819i | \(0.549733\pi\) | |||||||
\(912\) | −5.33104 | −0.176528 | ||||||||
\(913\) | 16.0414 | 0.530894 | ||||||||
\(914\) | 38.1127 | 1.26066 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.00314 | −0.0331446 | ||||||||
\(917\) | −14.1878 | −0.468523 | ||||||||
\(918\) | 4.14637 | 0.136850 | ||||||||
\(919\) | 21.7066 | 0.716036 | 0.358018 | − | 0.933715i | \(-0.383453\pi\) | ||||
0.358018 | + | 0.933715i | \(0.383453\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.19316 | −0.171120 | ||||||||
\(922\) | 1.55746 | 0.0512921 | ||||||||
\(923\) | −10.7889 | −0.355122 | ||||||||
\(924\) | 0.308407 | 0.0101458 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −47.0974 | −1.54771 | ||||||||
\(927\) | −16.4284 | −0.539579 | ||||||||
\(928\) | 1.36025 | 0.0446523 | ||||||||
\(929\) | 35.6787 | 1.17058 | 0.585289 | − | 0.810824i | \(-0.300981\pi\) | ||||
0.585289 | + | 0.810824i | \(0.300981\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.28738 | −0.0421920 | ||||||||
\(932\) | −0.0903972 | −0.00296106 | ||||||||
\(933\) | 13.8536 | 0.453548 | ||||||||
\(934\) | −24.5924 | −0.804687 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.77434 | −0.0906821 | ||||||||
\(937\) | 47.0866 | 1.53825 | 0.769127 | − | 0.639096i | \(-0.220691\pi\) | ||||
0.769127 | + | 0.639096i | \(0.220691\pi\) | |||||||
\(938\) | −17.3379 | −0.566103 | ||||||||
\(939\) | −32.6162 | −1.06439 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 45.2923 | 1.47649 | 0.738244 | − | 0.674534i | \(-0.235655\pi\) | ||||
0.738244 | + | 0.674534i | \(0.235655\pi\) | |||||||
\(942\) | 1.24905 | 0.0406962 | ||||||||
\(943\) | −96.7927 | −3.15200 | ||||||||
\(944\) | 30.3722 | 0.988530 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 43.3304 | 1.40879 | ||||||||
\(947\) | −4.77134 | −0.155048 | −0.0775238 | − | 0.996991i | \(-0.524701\pi\) | ||||
−0.0775238 | + | 0.996991i | \(0.524701\pi\) | |||||||
\(948\) | −0.327277 | −0.0106295 | ||||||||
\(949\) | −8.32568 | −0.270263 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 12.0380 | 0.390359 | ||||||||
\(952\) | −7.98929 | −0.258934 | ||||||||
\(953\) | 3.95572 | 0.128138 | 0.0640692 | − | 0.997945i | \(-0.479592\pi\) | ||||
0.0640692 | + | 0.997945i | \(0.479592\pi\) | |||||||
\(954\) | −7.40231 | −0.239659 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.39824 | 0.0452223 | ||||||||
\(957\) | −13.8536 | −0.447824 | ||||||||
\(958\) | 24.7353 | 0.799160 | ||||||||
\(959\) | 14.7070 | 0.474912 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18.6573 | 0.601850 | ||||||||
\(962\) | −12.3464 | −0.398064 | ||||||||
\(963\) | 3.45446 | 0.111318 | ||||||||
\(964\) | −0.880605 | −0.0283624 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −11.5487 | −0.371573 | ||||||||
\(967\) | −50.2292 | −1.61526 | −0.807632 | − | 0.589687i | \(-0.799251\pi\) | ||||
−0.807632 | + | 0.589687i | \(0.799251\pi\) | |||||||
\(968\) | 18.7529 | 0.602742 | ||||||||
\(969\) | 3.70727 | 0.119095 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 38.6576 | 1.24058 | 0.620291 | − | 0.784372i | \(-0.287014\pi\) | ||||
0.620291 | + | 0.784372i | \(0.287014\pi\) | |||||||
\(972\) | −0.0731828 | −0.00234734 | ||||||||
\(973\) | −9.85363 | −0.315893 | ||||||||
\(974\) | −6.16638 | −0.197584 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −32.1318 | −1.02852 | ||||||||
\(977\) | 20.6134 | 0.659480 | 0.329740 | − | 0.944072i | \(-0.393039\pi\) | ||||
0.329740 | + | 0.944072i | \(0.393039\pi\) | |||||||
\(978\) | −6.37623 | −0.203889 | ||||||||
\(979\) | −23.8015 | −0.760699 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.66896 | 0.149069 | ||||||||
\(982\) | −39.5304 | −1.26147 | ||||||||
\(983\) | 4.48620 | 0.143088 | 0.0715438 | − | 0.997437i | \(-0.477207\pi\) | ||||
0.0715438 | + | 0.997437i | \(0.477207\pi\) | |||||||
\(984\) | 33.4802 | 1.06731 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −13.6307 | −0.434089 | ||||||||
\(987\) | −1.95289 | −0.0621613 | ||||||||
\(988\) | 0.0942138 | 0.00299734 | ||||||||
\(989\) | −57.2760 | −1.82127 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −32.7971 | −1.04183 | −0.520917 | − | 0.853607i | \(-0.674410\pi\) | ||||
−0.520917 | + | 0.853607i | \(0.674410\pi\) | |||||||
\(992\) | −2.91582 | −0.0925773 | ||||||||
\(993\) | 26.2820 | 0.834035 | ||||||||
\(994\) | 15.5345 | 0.492725 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −0.278572 | −0.00882691 | ||||||||
\(997\) | −0.491870 | −0.0155777 | −0.00778884 | − | 0.999970i | \(-0.502479\pi\) | ||||
−0.00778884 | + | 0.999970i | \(0.502479\pi\) | |||||||
\(998\) | 53.3397 | 1.68844 | ||||||||
\(999\) | 8.57475 | 0.271293 |
(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 | 6825.2.a.bg.1.2 | 4 | ||
5.4 | even | 2 | 273.2.a.e.1.3 | ✓ | 4 | ||
15.14 | odd | 2 | 819.2.a.k.1.2 | 4 | |||
20.19 | odd | 2 | 4368.2.a.br.1.3 | 4 | |||
35.34 | odd | 2 | 1911.2.a.s.1.3 | 4 | |||
65.64 | even | 2 | 3549.2.a.w.1.2 | 4 | |||
105.104 | even | 2 | 5733.2.a.bf.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.a.e.1.3 | ✓ | 4 | 5.4 | even | 2 | ||
819.2.a.k.1.2 | 4 | 15.14 | odd | 2 | |||
1911.2.a.s.1.3 | 4 | 35.34 | odd | 2 | |||
3549.2.a.w.1.2 | 4 | 65.64 | even | 2 | |||
4368.2.a.br.1.3 | 4 | 20.19 | odd | 2 | |||
5733.2.a.bf.1.2 | 4 | 105.104 | even | 2 | |||
6825.2.a.bg.1.2 | 4 | 1.1 | even | 1 | trivial |