Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6005,2,Mod(1,6005)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6005, 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("6005.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6005 = 5 \cdot 1201 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6005.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: | \(47.9501664138\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.2777.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 4x^{2} + x + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(0.825785\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6005.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.59615 | 1.83576 | 0.917879 | − | 0.396860i | \(-0.129900\pi\) | ||||
0.917879 | + | 0.396860i | \(0.129900\pi\) | |||||||
\(3\) | −0.452290 | −0.261130 | −0.130565 | − | 0.991440i | \(-0.541679\pi\) | ||||
−0.130565 | + | 0.991440i | \(0.541679\pi\) | |||||||
\(4\) | 4.74002 | 2.37001 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −1.17422 | −0.479371 | ||||||||
\(7\) | −1.17422 | −0.443812 | −0.221906 | − | 0.975068i | \(-0.571228\pi\) | ||||
−0.221906 | + | 0.975068i | \(0.571228\pi\) | |||||||
\(8\) | 7.11351 | 2.51501 | ||||||||
\(9\) | −2.79543 | −0.931811 | ||||||||
\(10\) | −2.59615 | −0.820976 | ||||||||
\(11\) | −0.904581 | −0.272741 | −0.136371 | − | 0.990658i | \(-0.543544\pi\) | ||||
−0.136371 | + | 0.990658i | \(0.543544\pi\) | |||||||
\(12\) | −2.14386 | −0.618880 | ||||||||
\(13\) | −1.59615 | −0.442694 | −0.221347 | − | 0.975195i | \(-0.571045\pi\) | ||||
−0.221347 | + | 0.975195i | \(0.571045\pi\) | |||||||
\(14\) | −3.04844 | −0.814731 | ||||||||
\(15\) | 0.452290 | 0.116781 | ||||||||
\(16\) | 8.98774 | 2.24694 | ||||||||
\(17\) | 1.22266 | 0.296539 | 0.148269 | − | 0.988947i | \(-0.452630\pi\) | ||||
0.148269 | + | 0.988947i | \(0.452630\pi\) | |||||||
\(18\) | −7.25738 | −1.71058 | ||||||||
\(19\) | 1.22963 | 0.282096 | 0.141048 | − | 0.990003i | \(-0.454953\pi\) | ||||
0.141048 | + | 0.990003i | \(0.454953\pi\) | |||||||
\(20\) | −4.74002 | −1.05990 | ||||||||
\(21\) | 0.531086 | 0.115893 | ||||||||
\(22\) | −2.34843 | −0.500687 | ||||||||
\(23\) | −2.82578 | −0.589217 | −0.294608 | − | 0.955618i | \(-0.595189\pi\) | ||||
−0.294608 | + | 0.955618i | \(0.595189\pi\) | |||||||
\(24\) | −3.21737 | −0.656743 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −4.14386 | −0.812679 | ||||||||
\(27\) | 2.62122 | 0.504454 | ||||||||
\(28\) | −5.56580 | −1.05184 | ||||||||
\(29\) | −5.34314 | −0.992197 | −0.496098 | − | 0.868266i | \(-0.665234\pi\) | ||||
−0.496098 | + | 0.868266i | \(0.665234\pi\) | |||||||
\(30\) | 1.17422 | 0.214381 | ||||||||
\(31\) | 2.36652 | 0.425040 | 0.212520 | − | 0.977157i | \(-0.431833\pi\) | ||||
0.212520 | + | 0.977157i | \(0.431833\pi\) | |||||||
\(32\) | 9.10654 | 1.60982 | ||||||||
\(33\) | 0.409133 | 0.0712209 | ||||||||
\(34\) | 3.17422 | 0.544373 | ||||||||
\(35\) | 1.17422 | 0.198479 | ||||||||
\(36\) | −13.2504 | −2.20840 | ||||||||
\(37\) | −8.52004 | −1.40069 | −0.700343 | − | 0.713806i | \(-0.746970\pi\) | ||||
−0.700343 | + | 0.713806i | \(0.746970\pi\) | |||||||
\(38\) | 3.19231 | 0.517861 | ||||||||
\(39\) | 0.721925 | 0.115601 | ||||||||
\(40\) | −7.11351 | −1.12475 | ||||||||
\(41\) | −3.00965 | −0.470029 | −0.235014 | − | 0.971992i | \(-0.575514\pi\) | ||||
−0.235014 | + | 0.971992i | \(0.575514\pi\) | |||||||
\(42\) | 1.37878 | 0.212751 | ||||||||
\(43\) | −0.990346 | −0.151026 | −0.0755132 | − | 0.997145i | \(-0.524059\pi\) | ||||
−0.0755132 | + | 0.997145i | \(0.524059\pi\) | |||||||
\(44\) | −4.28773 | −0.646399 | ||||||||
\(45\) | 2.79543 | 0.416719 | ||||||||
\(46\) | −7.33617 | −1.08166 | ||||||||
\(47\) | −9.52848 | −1.38987 | −0.694936 | − | 0.719072i | \(-0.744567\pi\) | ||||
−0.694936 | + | 0.719072i | \(0.744567\pi\) | |||||||
\(48\) | −4.06507 | −0.586742 | ||||||||
\(49\) | −5.62122 | −0.803031 | ||||||||
\(50\) | 2.59615 | 0.367152 | ||||||||
\(51\) | −0.552997 | −0.0774351 | ||||||||
\(52\) | −7.56580 | −1.04919 | ||||||||
\(53\) | 9.04844 | 1.24290 | 0.621450 | − | 0.783454i | \(-0.286544\pi\) | ||||
0.621450 | + | 0.783454i | \(0.286544\pi\) | |||||||
\(54\) | 6.80509 | 0.926055 | ||||||||
\(55\) | 0.904581 | 0.121974 | ||||||||
\(56\) | −8.35280 | −1.11619 | ||||||||
\(57\) | −0.556150 | −0.0736638 | ||||||||
\(58\) | −13.8716 | −1.82143 | ||||||||
\(59\) | −11.0511 | −1.43873 | −0.719367 | − | 0.694630i | \(-0.755568\pi\) | ||||
−0.719367 | + | 0.694630i | \(0.755568\pi\) | |||||||
\(60\) | 2.14386 | 0.276772 | ||||||||
\(61\) | 0.217373 | 0.0278317 | 0.0139159 | − | 0.999903i | \(-0.495570\pi\) | ||||
0.0139159 | + | 0.999903i | \(0.495570\pi\) | |||||||
\(62\) | 6.14386 | 0.780272 | ||||||||
\(63\) | 3.28244 | 0.413549 | ||||||||
\(64\) | 5.66651 | 0.708314 | ||||||||
\(65\) | 1.59615 | 0.197979 | ||||||||
\(66\) | 1.06217 | 0.130744 | ||||||||
\(67\) | −0.125771 | −0.0153653 | −0.00768266 | − | 0.999970i | \(-0.502445\pi\) | ||||
−0.00768266 | + | 0.999970i | \(0.502445\pi\) | |||||||
\(68\) | 5.79543 | 0.702800 | ||||||||
\(69\) | 1.27807 | 0.153862 | ||||||||
\(70\) | 3.04844 | 0.364359 | ||||||||
\(71\) | 3.18118 | 0.377537 | 0.188769 | − | 0.982022i | \(-0.439550\pi\) | ||||
0.188769 | + | 0.982022i | \(0.439550\pi\) | |||||||
\(72\) | −19.8854 | −2.34351 | ||||||||
\(73\) | −9.41934 | −1.10245 | −0.551225 | − | 0.834357i | \(-0.685839\pi\) | ||||
−0.551225 | + | 0.834357i | \(0.685839\pi\) | |||||||
\(74\) | −22.1194 | −2.57132 | ||||||||
\(75\) | −0.452290 | −0.0522260 | ||||||||
\(76\) | 5.82847 | 0.668571 | ||||||||
\(77\) | 1.06217 | 0.121046 | ||||||||
\(78\) | 1.87423 | 0.212215 | ||||||||
\(79\) | 6.36652 | 0.716290 | 0.358145 | − | 0.933666i | \(-0.383409\pi\) | ||||
0.358145 | + | 0.933666i | \(0.383409\pi\) | |||||||
\(80\) | −8.98774 | −1.00486 | ||||||||
\(81\) | 7.20075 | 0.800083 | ||||||||
\(82\) | −7.81353 | −0.862860 | ||||||||
\(83\) | −4.05013 | −0.444559 | −0.222280 | − | 0.974983i | \(-0.571350\pi\) | ||||
−0.222280 | + | 0.974983i | \(0.571350\pi\) | |||||||
\(84\) | 2.51736 | 0.274666 | ||||||||
\(85\) | −1.22266 | −0.132616 | ||||||||
\(86\) | −2.57109 | −0.277248 | ||||||||
\(87\) | 2.41665 | 0.259092 | ||||||||
\(88\) | −6.43475 | −0.685946 | ||||||||
\(89\) | 10.5690 | 1.12031 | 0.560154 | − | 0.828389i | \(-0.310742\pi\) | ||||
0.560154 | + | 0.828389i | \(0.310742\pi\) | |||||||
\(90\) | 7.25738 | 0.764995 | ||||||||
\(91\) | 1.87423 | 0.196473 | ||||||||
\(92\) | −13.3943 | −1.39645 | ||||||||
\(93\) | −1.07036 | −0.110991 | ||||||||
\(94\) | −24.7374 | −2.55147 | ||||||||
\(95\) | −1.22963 | −0.126157 | ||||||||
\(96\) | −4.11880 | −0.420373 | ||||||||
\(97\) | 6.19231 | 0.628734 | 0.314367 | − | 0.949302i | \(-0.398208\pi\) | ||||
0.314367 | + | 0.949302i | \(0.398208\pi\) | |||||||
\(98\) | −14.5936 | −1.47417 | ||||||||
\(99\) | 2.52869 | 0.254143 | ||||||||
\(100\) | 4.74002 | 0.474002 | ||||||||
\(101\) | −12.0261 | −1.19664 | −0.598319 | − | 0.801258i | \(-0.704165\pi\) | ||||
−0.598319 | + | 0.801258i | \(0.704165\pi\) | |||||||
\(102\) | −1.43567 | −0.142152 | ||||||||
\(103\) | −1.19231 | −0.117482 | −0.0587409 | − | 0.998273i | \(-0.518709\pi\) | ||||
−0.0587409 | + | 0.998273i | \(0.518709\pi\) | |||||||
\(104\) | −11.3543 | −1.11338 | ||||||||
\(105\) | −0.531086 | −0.0518287 | ||||||||
\(106\) | 23.4912 | 2.28166 | ||||||||
\(107\) | 0.246253 | 0.0238062 | 0.0119031 | − | 0.999929i | \(-0.496211\pi\) | ||||
0.0119031 | + | 0.999929i | \(0.496211\pi\) | |||||||
\(108\) | 12.4246 | 1.19556 | ||||||||
\(109\) | −9.75283 | −0.934151 | −0.467076 | − | 0.884217i | \(-0.654692\pi\) | ||||
−0.467076 | + | 0.884217i | \(0.654692\pi\) | |||||||
\(110\) | 2.34843 | 0.223914 | ||||||||
\(111\) | 3.85353 | 0.365761 | ||||||||
\(112\) | −10.5535 | −0.997216 | ||||||||
\(113\) | 10.7981 | 1.01580 | 0.507901 | − | 0.861416i | \(-0.330422\pi\) | ||||
0.507901 | + | 0.861416i | \(0.330422\pi\) | |||||||
\(114\) | −1.44385 | −0.135229 | ||||||||
\(115\) | 2.82578 | 0.263506 | ||||||||
\(116\) | −25.3266 | −2.35152 | ||||||||
\(117\) | 4.46194 | 0.412507 | ||||||||
\(118\) | −28.6904 | −2.64117 | ||||||||
\(119\) | −1.43567 | −0.131607 | ||||||||
\(120\) | 3.21737 | 0.293705 | ||||||||
\(121\) | −10.1817 | −0.925612 | ||||||||
\(122\) | 0.564333 | 0.0510923 | ||||||||
\(123\) | 1.36124 | 0.122739 | ||||||||
\(124\) | 11.2174 | 1.00735 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 8.52173 | 0.759176 | ||||||||
\(127\) | −15.3878 | −1.36544 | −0.682722 | − | 0.730678i | \(-0.739204\pi\) | ||||
−0.682722 | + | 0.730678i | \(0.739204\pi\) | |||||||
\(128\) | −3.50195 | −0.309532 | ||||||||
\(129\) | 0.447924 | 0.0394375 | ||||||||
\(130\) | 4.14386 | 0.363441 | ||||||||
\(131\) | −15.4769 | −1.35222 | −0.676111 | − | 0.736800i | \(-0.736336\pi\) | ||||
−0.676111 | + | 0.736800i | \(0.736336\pi\) | |||||||
\(132\) | 1.93930 | 0.168794 | ||||||||
\(133\) | −1.44385 | −0.125198 | ||||||||
\(134\) | −0.326520 | −0.0282070 | ||||||||
\(135\) | −2.62122 | −0.225599 | ||||||||
\(136\) | 8.69741 | 0.745797 | ||||||||
\(137\) | −9.04966 | −0.773165 | −0.386582 | − | 0.922255i | \(-0.626344\pi\) | ||||
−0.386582 | + | 0.922255i | \(0.626344\pi\) | |||||||
\(138\) | 3.31808 | 0.282454 | ||||||||
\(139\) | −0.303138 | −0.0257118 | −0.0128559 | − | 0.999917i | \(-0.504092\pi\) | ||||
−0.0128559 | + | 0.999917i | \(0.504092\pi\) | |||||||
\(140\) | 5.56580 | 0.470396 | ||||||||
\(141\) | 4.30964 | 0.362937 | ||||||||
\(142\) | 8.25885 | 0.693067 | ||||||||
\(143\) | 1.44385 | 0.120741 | ||||||||
\(144\) | −25.1246 | −2.09372 | ||||||||
\(145\) | 5.34314 | 0.443724 | ||||||||
\(146\) | −24.4541 | −2.02383 | ||||||||
\(147\) | 2.54242 | 0.209695 | ||||||||
\(148\) | −40.3852 | −3.31964 | ||||||||
\(149\) | −2.82532 | −0.231459 | −0.115729 | − | 0.993281i | \(-0.536921\pi\) | ||||
−0.115729 | + | 0.993281i | \(0.536921\pi\) | |||||||
\(150\) | −1.17422 | −0.0958743 | ||||||||
\(151\) | 9.01234 | 0.733414 | 0.366707 | − | 0.930337i | \(-0.380485\pi\) | ||||
0.366707 | + | 0.930337i | \(0.380485\pi\) | |||||||
\(152\) | 8.74699 | 0.709474 | ||||||||
\(153\) | −3.41787 | −0.276318 | ||||||||
\(154\) | 2.75756 | 0.222211 | ||||||||
\(155\) | −2.36652 | −0.190084 | ||||||||
\(156\) | 3.42194 | 0.273974 | ||||||||
\(157\) | 10.6277 | 0.848184 | 0.424092 | − | 0.905619i | \(-0.360593\pi\) | ||||
0.424092 | + | 0.905619i | \(0.360593\pi\) | |||||||
\(158\) | 16.5285 | 1.31494 | ||||||||
\(159\) | −4.09252 | −0.324558 | ||||||||
\(160\) | −9.10654 | −0.719936 | ||||||||
\(161\) | 3.31808 | 0.261501 | ||||||||
\(162\) | 18.6943 | 1.46876 | ||||||||
\(163\) | 0.206505 | 0.0161747 | 0.00808734 | − | 0.999967i | \(-0.497426\pi\) | ||||
0.00808734 | + | 0.999967i | \(0.497426\pi\) | |||||||
\(164\) | −14.2658 | −1.11397 | ||||||||
\(165\) | −0.409133 | −0.0318510 | ||||||||
\(166\) | −10.5148 | −0.816103 | ||||||||
\(167\) | 7.43306 | 0.575188 | 0.287594 | − | 0.957752i | \(-0.407145\pi\) | ||||
0.287594 | + | 0.957752i | \(0.407145\pi\) | |||||||
\(168\) | 3.77789 | 0.291470 | ||||||||
\(169\) | −10.4523 | −0.804022 | ||||||||
\(170\) | −3.17422 | −0.243451 | ||||||||
\(171\) | −3.43735 | −0.262861 | ||||||||
\(172\) | −4.69426 | −0.357934 | ||||||||
\(173\) | 21.3097 | 1.62015 | 0.810074 | − | 0.586328i | \(-0.199427\pi\) | ||||
0.810074 | + | 0.586328i | \(0.199427\pi\) | |||||||
\(174\) | 6.27400 | 0.475631 | ||||||||
\(175\) | −1.17422 | −0.0887623 | ||||||||
\(176\) | −8.13014 | −0.612832 | ||||||||
\(177\) | 4.99832 | 0.375697 | ||||||||
\(178\) | 27.4386 | 2.05661 | ||||||||
\(179\) | 10.0569 | 0.751687 | 0.375843 | − | 0.926683i | \(-0.377353\pi\) | ||||
0.375843 | + | 0.926683i | \(0.377353\pi\) | |||||||
\(180\) | 13.2504 | 0.987627 | ||||||||
\(181\) | −19.1205 | −1.42121 | −0.710607 | − | 0.703589i | \(-0.751580\pi\) | ||||
−0.710607 | + | 0.703589i | \(0.751580\pi\) | |||||||
\(182\) | 4.86579 | 0.360676 | ||||||||
\(183\) | −0.0983156 | −0.00726770 | ||||||||
\(184\) | −20.1013 | −1.48188 | ||||||||
\(185\) | 8.52004 | 0.626406 | ||||||||
\(186\) | −2.77881 | −0.203752 | ||||||||
\(187\) | −1.10599 | −0.0808783 | ||||||||
\(188\) | −45.1652 | −3.29401 | ||||||||
\(189\) | −3.07787 | −0.223882 | ||||||||
\(190\) | −3.19231 | −0.231594 | ||||||||
\(191\) | −2.21209 | −0.160061 | −0.0800304 | − | 0.996792i | \(-0.525502\pi\) | ||||
−0.0800304 | + | 0.996792i | \(0.525502\pi\) | |||||||
\(192\) | −2.56291 | −0.184962 | ||||||||
\(193\) | −0.709587 | −0.0510772 | −0.0255386 | − | 0.999674i | \(-0.508130\pi\) | ||||
−0.0255386 | + | 0.999674i | \(0.508130\pi\) | |||||||
\(194\) | 16.0762 | 1.15420 | ||||||||
\(195\) | −0.721925 | −0.0516981 | ||||||||
\(196\) | −26.6447 | −1.90319 | ||||||||
\(197\) | −18.8174 | −1.34069 | −0.670343 | − | 0.742051i | \(-0.733853\pi\) | ||||
−0.670343 | + | 0.742051i | \(0.733853\pi\) | |||||||
\(198\) | 6.56488 | 0.466546 | ||||||||
\(199\) | 26.4524 | 1.87516 | 0.937579 | − | 0.347771i | \(-0.113061\pi\) | ||||
0.937579 | + | 0.347771i | \(0.113061\pi\) | |||||||
\(200\) | 7.11351 | 0.503001 | ||||||||
\(201\) | 0.0568848 | 0.00401234 | ||||||||
\(202\) | −31.2215 | −2.19674 | ||||||||
\(203\) | 6.27400 | 0.440349 | ||||||||
\(204\) | −2.62122 | −0.183522 | ||||||||
\(205\) | 3.00965 | 0.210203 | ||||||||
\(206\) | −3.09542 | −0.215668 | ||||||||
\(207\) | 7.89929 | 0.549039 | ||||||||
\(208\) | −14.3458 | −0.994704 | ||||||||
\(209\) | −1.11230 | −0.0769393 | ||||||||
\(210\) | −1.37878 | −0.0951450 | ||||||||
\(211\) | 23.1967 | 1.59693 | 0.798463 | − | 0.602045i | \(-0.205647\pi\) | ||||
0.798463 | + | 0.602045i | \(0.205647\pi\) | |||||||
\(212\) | 42.8898 | 2.94568 | ||||||||
\(213\) | −1.43882 | −0.0985862 | ||||||||
\(214\) | 0.639312 | 0.0437025 | ||||||||
\(215\) | 0.990346 | 0.0675410 | ||||||||
\(216\) | 18.6461 | 1.26870 | ||||||||
\(217\) | −2.77881 | −0.188638 | ||||||||
\(218\) | −25.3198 | −1.71488 | ||||||||
\(219\) | 4.26027 | 0.287883 | ||||||||
\(220\) | 4.28773 | 0.289079 | ||||||||
\(221\) | −1.95156 | −0.131276 | ||||||||
\(222\) | 10.0044 | 0.671449 | ||||||||
\(223\) | 5.80341 | 0.388625 | 0.194312 | − | 0.980940i | \(-0.437752\pi\) | ||||
0.194312 | + | 0.980940i | \(0.437752\pi\) | |||||||
\(224\) | −10.6930 | −0.714459 | ||||||||
\(225\) | −2.79543 | −0.186362 | ||||||||
\(226\) | 28.0336 | 1.86477 | ||||||||
\(227\) | 6.42916 | 0.426719 | 0.213359 | − | 0.976974i | \(-0.431559\pi\) | ||||
0.213359 | + | 0.976974i | \(0.431559\pi\) | |||||||
\(228\) | −2.63616 | −0.174584 | ||||||||
\(229\) | 16.9105 | 1.11748 | 0.558739 | − | 0.829344i | \(-0.311286\pi\) | ||||
0.558739 | + | 0.829344i | \(0.311286\pi\) | |||||||
\(230\) | 7.33617 | 0.483733 | ||||||||
\(231\) | −0.480410 | −0.0316087 | ||||||||
\(232\) | −38.0085 | −2.49538 | ||||||||
\(233\) | 22.3637 | 1.46510 | 0.732548 | − | 0.680716i | \(-0.238331\pi\) | ||||
0.732548 | + | 0.680716i | \(0.238331\pi\) | |||||||
\(234\) | 11.5839 | 0.757263 | ||||||||
\(235\) | 9.52848 | 0.621570 | ||||||||
\(236\) | −52.3826 | −3.40981 | ||||||||
\(237\) | −2.87952 | −0.187045 | ||||||||
\(238\) | −3.72721 | −0.241599 | ||||||||
\(239\) | 17.6425 | 1.14120 | 0.570598 | − | 0.821229i | \(-0.306711\pi\) | ||||
0.570598 | + | 0.821229i | \(0.306711\pi\) | |||||||
\(240\) | 4.06507 | 0.262399 | ||||||||
\(241\) | −25.6723 | −1.65370 | −0.826851 | − | 0.562422i | \(-0.809870\pi\) | ||||
−0.826851 | + | 0.562422i | \(0.809870\pi\) | |||||||
\(242\) | −26.4334 | −1.69920 | ||||||||
\(243\) | −11.1205 | −0.713379 | ||||||||
\(244\) | 1.03035 | 0.0659615 | ||||||||
\(245\) | 5.62122 | 0.359126 | ||||||||
\(246\) | 3.53398 | 0.225318 | ||||||||
\(247\) | −1.96268 | −0.124882 | ||||||||
\(248\) | 16.8343 | 1.06898 | ||||||||
\(249\) | 1.83183 | 0.116088 | ||||||||
\(250\) | −2.59615 | −0.164195 | ||||||||
\(251\) | 11.1715 | 0.705141 | 0.352570 | − | 0.935785i | \(-0.385308\pi\) | ||||
0.352570 | + | 0.935785i | \(0.385308\pi\) | |||||||
\(252\) | 15.5588 | 0.980114 | ||||||||
\(253\) | 2.55615 | 0.160704 | ||||||||
\(254\) | −39.9490 | −2.50663 | ||||||||
\(255\) | 0.552997 | 0.0346300 | ||||||||
\(256\) | −20.4246 | −1.27654 | ||||||||
\(257\) | 9.73573 | 0.607298 | 0.303649 | − | 0.952784i | \(-0.401795\pi\) | ||||
0.303649 | + | 0.952784i | \(0.401795\pi\) | |||||||
\(258\) | 1.16288 | 0.0723977 | ||||||||
\(259\) | 10.0044 | 0.621641 | ||||||||
\(260\) | 7.56580 | 0.469211 | ||||||||
\(261\) | 14.9364 | 0.924540 | ||||||||
\(262\) | −40.1804 | −2.48235 | ||||||||
\(263\) | 1.14970 | 0.0708936 | 0.0354468 | − | 0.999372i | \(-0.488715\pi\) | ||||
0.0354468 | + | 0.999372i | \(0.488715\pi\) | |||||||
\(264\) | 2.91037 | 0.179121 | ||||||||
\(265\) | −9.04844 | −0.555842 | ||||||||
\(266\) | −3.74846 | −0.229833 | ||||||||
\(267\) | −4.78024 | −0.292546 | ||||||||
\(268\) | −0.596155 | −0.0364159 | ||||||||
\(269\) | 1.90076 | 0.115892 | 0.0579458 | − | 0.998320i | \(-0.481545\pi\) | ||||
0.0579458 | + | 0.998320i | \(0.481545\pi\) | |||||||
\(270\) | −6.80509 | −0.414144 | ||||||||
\(271\) | −13.4412 | −0.816498 | −0.408249 | − | 0.912871i | \(-0.633860\pi\) | ||||
−0.408249 | + | 0.912871i | \(0.633860\pi\) | |||||||
\(272\) | 10.9890 | 0.666303 | ||||||||
\(273\) | −0.847696 | −0.0513049 | ||||||||
\(274\) | −23.4943 | −1.41934 | ||||||||
\(275\) | −0.904581 | −0.0545483 | ||||||||
\(276\) | 6.05810 | 0.364655 | ||||||||
\(277\) | −2.23177 | −0.134094 | −0.0670469 | − | 0.997750i | \(-0.521358\pi\) | ||||
−0.0670469 | + | 0.997750i | \(0.521358\pi\) | |||||||
\(278\) | −0.786994 | −0.0472007 | ||||||||
\(279\) | −6.61546 | −0.396057 | ||||||||
\(280\) | 8.35280 | 0.499175 | ||||||||
\(281\) | 18.4789 | 1.10236 | 0.551180 | − | 0.834387i | \(-0.314178\pi\) | ||||
0.551180 | + | 0.834387i | \(0.314178\pi\) | |||||||
\(282\) | 11.1885 | 0.666265 | ||||||||
\(283\) | 30.6493 | 1.82191 | 0.910956 | − | 0.412504i | \(-0.135346\pi\) | ||||
0.910956 | + | 0.412504i | \(0.135346\pi\) | |||||||
\(284\) | 15.0789 | 0.894767 | ||||||||
\(285\) | 0.556150 | 0.0329435 | ||||||||
\(286\) | 3.74846 | 0.221651 | ||||||||
\(287\) | 3.53398 | 0.208604 | ||||||||
\(288\) | −25.4567 | −1.50005 | ||||||||
\(289\) | −15.5051 | −0.912065 | ||||||||
\(290\) | 13.8716 | 0.814570 | ||||||||
\(291\) | −2.80072 | −0.164181 | ||||||||
\(292\) | −44.6478 | −2.61282 | ||||||||
\(293\) | 4.29617 | 0.250985 | 0.125492 | − | 0.992095i | \(-0.459949\pi\) | ||||
0.125492 | + | 0.992095i | \(0.459949\pi\) | |||||||
\(294\) | 6.60052 | 0.384950 | ||||||||
\(295\) | 11.0511 | 0.643422 | ||||||||
\(296\) | −60.6074 | −3.52274 | ||||||||
\(297\) | −2.37110 | −0.137585 | ||||||||
\(298\) | −7.33496 | −0.424903 | ||||||||
\(299\) | 4.51039 | 0.260843 | ||||||||
\(300\) | −2.14386 | −0.123776 | ||||||||
\(301\) | 1.16288 | 0.0670273 | ||||||||
\(302\) | 23.3974 | 1.34637 | ||||||||
\(303\) | 5.43927 | 0.312478 | ||||||||
\(304\) | 11.0516 | 0.633853 | ||||||||
\(305\) | −0.217373 | −0.0124467 | ||||||||
\(306\) | −8.87331 | −0.507253 | ||||||||
\(307\) | −31.6878 | −1.80852 | −0.904258 | − | 0.426987i | \(-0.859575\pi\) | ||||
−0.904258 | + | 0.426987i | \(0.859575\pi\) | |||||||
\(308\) | 5.03472 | 0.286880 | ||||||||
\(309\) | 0.539270 | 0.0306780 | ||||||||
\(310\) | −6.14386 | −0.348948 | ||||||||
\(311\) | 2.64942 | 0.150235 | 0.0751174 | − | 0.997175i | \(-0.476067\pi\) | ||||
0.0751174 | + | 0.997175i | \(0.476067\pi\) | |||||||
\(312\) | 5.13542 | 0.290736 | ||||||||
\(313\) | 2.59729 | 0.146807 | 0.0734037 | − | 0.997302i | \(-0.476614\pi\) | ||||
0.0734037 | + | 0.997302i | \(0.476614\pi\) | |||||||
\(314\) | 27.5912 | 1.55706 | ||||||||
\(315\) | −3.28244 | −0.184945 | ||||||||
\(316\) | 30.1774 | 1.69761 | ||||||||
\(317\) | −2.56727 | −0.144192 | −0.0720962 | − | 0.997398i | \(-0.522969\pi\) | ||||
−0.0720962 | + | 0.997398i | \(0.522969\pi\) | |||||||
\(318\) | −10.6248 | −0.595811 | ||||||||
\(319\) | 4.83330 | 0.270613 | ||||||||
\(320\) | −5.66651 | −0.316768 | ||||||||
\(321\) | −0.111378 | −0.00621652 | ||||||||
\(322\) | 8.61425 | 0.480053 | ||||||||
\(323\) | 1.50342 | 0.0836525 | ||||||||
\(324\) | 34.1317 | 1.89620 | ||||||||
\(325\) | −1.59615 | −0.0885387 | ||||||||
\(326\) | 0.536118 | 0.0296928 | ||||||||
\(327\) | 4.41111 | 0.243935 | ||||||||
\(328\) | −21.4092 | −1.18213 | ||||||||
\(329\) | 11.1885 | 0.616842 | ||||||||
\(330\) | −1.06217 | −0.0584707 | ||||||||
\(331\) | 11.5907 | 0.637080 | 0.318540 | − | 0.947909i | \(-0.396807\pi\) | ||||
0.318540 | + | 0.947909i | \(0.396807\pi\) | |||||||
\(332\) | −19.1977 | −1.05361 | ||||||||
\(333\) | 23.8172 | 1.30518 | ||||||||
\(334\) | 19.2974 | 1.05591 | ||||||||
\(335\) | 0.125771 | 0.00687158 | ||||||||
\(336\) | 4.77327 | 0.260403 | ||||||||
\(337\) | −18.8186 | −1.02512 | −0.512558 | − | 0.858652i | \(-0.671302\pi\) | ||||
−0.512558 | + | 0.858652i | \(0.671302\pi\) | |||||||
\(338\) | −27.1358 | −1.47599 | ||||||||
\(339\) | −4.88388 | −0.265256 | ||||||||
\(340\) | −5.79543 | −0.314302 | ||||||||
\(341\) | −2.14071 | −0.115926 | ||||||||
\(342\) | −8.92389 | −0.482549 | ||||||||
\(343\) | 14.8200 | 0.800206 | ||||||||
\(344\) | −7.04484 | −0.379832 | ||||||||
\(345\) | −1.27807 | −0.0688092 | ||||||||
\(346\) | 55.3233 | 2.97420 | ||||||||
\(347\) | −15.3441 | −0.823717 | −0.411858 | − | 0.911248i | \(-0.635120\pi\) | ||||
−0.411858 | + | 0.911248i | \(0.635120\pi\) | |||||||
\(348\) | 11.4550 | 0.614051 | ||||||||
\(349\) | 28.5259 | 1.52696 | 0.763478 | − | 0.645834i | \(-0.223490\pi\) | ||||
0.763478 | + | 0.645834i | \(0.223490\pi\) | |||||||
\(350\) | −3.04844 | −0.162946 | ||||||||
\(351\) | −4.18387 | −0.223318 | ||||||||
\(352\) | −8.23760 | −0.439066 | ||||||||
\(353\) | 18.0353 | 0.959920 | 0.479960 | − | 0.877290i | \(-0.340651\pi\) | ||||
0.479960 | + | 0.877290i | \(0.340651\pi\) | |||||||
\(354\) | 12.9764 | 0.689688 | ||||||||
\(355\) | −3.18118 | −0.168840 | ||||||||
\(356\) | 50.0971 | 2.65514 | ||||||||
\(357\) | 0.649338 | 0.0343666 | ||||||||
\(358\) | 26.1092 | 1.37992 | ||||||||
\(359\) | −8.96965 | −0.473400 | −0.236700 | − | 0.971583i | \(-0.576066\pi\) | ||||
−0.236700 | + | 0.971583i | \(0.576066\pi\) | |||||||
\(360\) | 19.8854 | 1.04805 | ||||||||
\(361\) | −17.4880 | −0.920422 | ||||||||
\(362\) | −49.6397 | −2.60901 | ||||||||
\(363\) | 4.60510 | 0.241705 | ||||||||
\(364\) | 8.88388 | 0.465642 | ||||||||
\(365\) | 9.41934 | 0.493031 | ||||||||
\(366\) | −0.255242 | −0.0133417 | ||||||||
\(367\) | 10.8470 | 0.566210 | 0.283105 | − | 0.959089i | \(-0.408635\pi\) | ||||
0.283105 | + | 0.959089i | \(0.408635\pi\) | |||||||
\(368\) | −25.3974 | −1.32393 | ||||||||
\(369\) | 8.41329 | 0.437978 | ||||||||
\(370\) | 22.1194 | 1.14993 | ||||||||
\(371\) | −10.6248 | −0.551613 | ||||||||
\(372\) | −5.07351 | −0.263049 | ||||||||
\(373\) | −16.8259 | −0.871210 | −0.435605 | − | 0.900138i | \(-0.643466\pi\) | ||||
−0.435605 | + | 0.900138i | \(0.643466\pi\) | |||||||
\(374\) | −2.87133 | −0.148473 | ||||||||
\(375\) | 0.452290 | 0.0233562 | ||||||||
\(376\) | −67.7810 | −3.49554 | ||||||||
\(377\) | 8.52848 | 0.439239 | ||||||||
\(378\) | −7.99064 | −0.410994 | ||||||||
\(379\) | 20.9415 | 1.07569 | 0.537847 | − | 0.843043i | \(-0.319238\pi\) | ||||
0.537847 | + | 0.843043i | \(0.319238\pi\) | |||||||
\(380\) | −5.82847 | −0.298994 | ||||||||
\(381\) | 6.95974 | 0.356558 | ||||||||
\(382\) | −5.74292 | −0.293833 | ||||||||
\(383\) | 15.2974 | 0.781660 | 0.390830 | − | 0.920463i | \(-0.372188\pi\) | ||||
0.390830 | + | 0.920463i | \(0.372188\pi\) | |||||||
\(384\) | 1.58390 | 0.0808279 | ||||||||
\(385\) | −1.06217 | −0.0541333 | ||||||||
\(386\) | −1.84220 | −0.0937653 | ||||||||
\(387\) | 2.76845 | 0.140728 | ||||||||
\(388\) | 29.3517 | 1.49011 | ||||||||
\(389\) | −6.50984 | −0.330062 | −0.165031 | − | 0.986288i | \(-0.552772\pi\) | ||||
−0.165031 | + | 0.986288i | \(0.552772\pi\) | |||||||
\(390\) | −1.87423 | −0.0949053 | ||||||||
\(391\) | −3.45497 | −0.174726 | ||||||||
\(392\) | −39.9866 | −2.01963 | ||||||||
\(393\) | 7.00004 | 0.353106 | ||||||||
\(394\) | −48.8529 | −2.46118 | ||||||||
\(395\) | −6.36652 | −0.320335 | ||||||||
\(396\) | 11.9861 | 0.602322 | ||||||||
\(397\) | 15.5893 | 0.782403 | 0.391201 | − | 0.920305i | \(-0.372060\pi\) | ||||
0.391201 | + | 0.920305i | \(0.372060\pi\) | |||||||
\(398\) | 68.6744 | 3.44234 | ||||||||
\(399\) | 0.653039 | 0.0326929 | ||||||||
\(400\) | 8.98774 | 0.449387 | ||||||||
\(401\) | 8.82847 | 0.440873 | 0.220436 | − | 0.975401i | \(-0.429252\pi\) | ||||
0.220436 | + | 0.975401i | \(0.429252\pi\) | |||||||
\(402\) | 0.147682 | 0.00736569 | ||||||||
\(403\) | −3.77734 | −0.188163 | ||||||||
\(404\) | −57.0038 | −2.83604 | ||||||||
\(405\) | −7.20075 | −0.357808 | ||||||||
\(406\) | 16.2883 | 0.808374 | ||||||||
\(407\) | 7.70707 | 0.382025 | ||||||||
\(408\) | −3.93375 | −0.194750 | ||||||||
\(409\) | 20.7329 | 1.02517 | 0.512587 | − | 0.858635i | \(-0.328687\pi\) | ||||
0.512587 | + | 0.858635i | \(0.328687\pi\) | |||||||
\(410\) | 7.81353 | 0.385883 | ||||||||
\(411\) | 4.09307 | 0.201896 | ||||||||
\(412\) | −5.65157 | −0.278433 | ||||||||
\(413\) | 12.9764 | 0.638527 | ||||||||
\(414\) | 20.5078 | 1.00790 | ||||||||
\(415\) | 4.05013 | 0.198813 | ||||||||
\(416\) | −14.5355 | −0.712659 | ||||||||
\(417\) | 0.137106 | 0.00671413 | ||||||||
\(418\) | −2.88770 | −0.141242 | ||||||||
\(419\) | −16.5755 | −0.809764 | −0.404882 | − | 0.914369i | \(-0.632687\pi\) | ||||
−0.404882 | + | 0.914369i | \(0.632687\pi\) | |||||||
\(420\) | −2.51736 | −0.122835 | ||||||||
\(421\) | −4.19063 | −0.204239 | −0.102119 | − | 0.994772i | \(-0.532562\pi\) | ||||
−0.102119 | + | 0.994772i | \(0.532562\pi\) | |||||||
\(422\) | 60.2222 | 2.93157 | ||||||||
\(423\) | 26.6362 | 1.29510 | ||||||||
\(424\) | 64.3662 | 3.12590 | ||||||||
\(425\) | 1.22266 | 0.0593077 | ||||||||
\(426\) | −3.73540 | −0.180981 | ||||||||
\(427\) | −0.255242 | −0.0123520 | ||||||||
\(428\) | 1.16725 | 0.0564210 | ||||||||
\(429\) | −0.653039 | −0.0315290 | ||||||||
\(430\) | 2.57109 | 0.123989 | ||||||||
\(431\) | 7.76240 | 0.373902 | 0.186951 | − | 0.982369i | \(-0.440140\pi\) | ||||
0.186951 | + | 0.982369i | \(0.440140\pi\) | |||||||
\(432\) | 23.5588 | 1.13347 | ||||||||
\(433\) | −4.56727 | −0.219489 | −0.109745 | − | 0.993960i | \(-0.535003\pi\) | ||||
−0.109745 | + | 0.993960i | \(0.535003\pi\) | |||||||
\(434\) | −7.21422 | −0.346294 | ||||||||
\(435\) | −2.41665 | −0.115870 | ||||||||
\(436\) | −46.2286 | −2.21395 | ||||||||
\(437\) | −3.47467 | −0.166216 | ||||||||
\(438\) | 11.0603 | 0.528483 | ||||||||
\(439\) | −20.5919 | −0.982797 | −0.491398 | − | 0.870935i | \(-0.663514\pi\) | ||||
−0.491398 | + | 0.870935i | \(0.663514\pi\) | |||||||
\(440\) | 6.43475 | 0.306764 | ||||||||
\(441\) | 15.7137 | 0.748273 | ||||||||
\(442\) | −5.06654 | −0.240991 | ||||||||
\(443\) | −30.7294 | −1.46000 | −0.730000 | − | 0.683447i | \(-0.760480\pi\) | ||||
−0.730000 | + | 0.683447i | \(0.760480\pi\) | |||||||
\(444\) | 18.2658 | 0.866857 | ||||||||
\(445\) | −10.5690 | −0.501017 | ||||||||
\(446\) | 15.0665 | 0.713421 | ||||||||
\(447\) | 1.27786 | 0.0604409 | ||||||||
\(448\) | −6.65370 | −0.314358 | ||||||||
\(449\) | −8.15953 | −0.385072 | −0.192536 | − | 0.981290i | \(-0.561671\pi\) | ||||
−0.192536 | + | 0.981290i | \(0.561671\pi\) | |||||||
\(450\) | −7.25738 | −0.342116 | ||||||||
\(451\) | 2.72247 | 0.128196 | ||||||||
\(452\) | 51.1833 | 2.40746 | ||||||||
\(453\) | −4.07619 | −0.191516 | ||||||||
\(454\) | 16.6911 | 0.783352 | ||||||||
\(455\) | −1.87423 | −0.0878652 | ||||||||
\(456\) | −3.95618 | −0.185265 | ||||||||
\(457\) | −21.6435 | −1.01244 | −0.506219 | − | 0.862405i | \(-0.668957\pi\) | ||||
−0.506219 | + | 0.862405i | \(0.668957\pi\) | |||||||
\(458\) | 43.9023 | 2.05142 | ||||||||
\(459\) | 3.20486 | 0.149590 | ||||||||
\(460\) | 13.3943 | 0.624511 | ||||||||
\(461\) | −11.5152 | −0.536317 | −0.268159 | − | 0.963375i | \(-0.586415\pi\) | ||||
−0.268159 | + | 0.963375i | \(0.586415\pi\) | |||||||
\(462\) | −1.24722 | −0.0580259 | ||||||||
\(463\) | −30.6684 | −1.42528 | −0.712642 | − | 0.701528i | \(-0.752502\pi\) | ||||
−0.712642 | + | 0.701528i | \(0.752502\pi\) | |||||||
\(464\) | −48.0228 | −2.22940 | ||||||||
\(465\) | 1.07036 | 0.0496366 | ||||||||
\(466\) | 58.0597 | 2.68956 | ||||||||
\(467\) | −23.2541 | −1.07607 | −0.538036 | − | 0.842922i | \(-0.680834\pi\) | ||||
−0.538036 | + | 0.842922i | \(0.680834\pi\) | |||||||
\(468\) | 21.1497 | 0.977645 | ||||||||
\(469\) | 0.147682 | 0.00681931 | ||||||||
\(470\) | 24.7374 | 1.14105 | ||||||||
\(471\) | −4.80681 | −0.221486 | ||||||||
\(472\) | −78.6124 | −3.61843 | ||||||||
\(473\) | 0.895848 | 0.0411911 | ||||||||
\(474\) | −7.47567 | −0.343369 | ||||||||
\(475\) | 1.22963 | 0.0564193 | ||||||||
\(476\) | −6.80509 | −0.311911 | ||||||||
\(477\) | −25.2943 | −1.15815 | ||||||||
\(478\) | 45.8026 | 2.09496 | ||||||||
\(479\) | 29.5772 | 1.35142 | 0.675709 | − | 0.737169i | \(-0.263838\pi\) | ||||
0.675709 | + | 0.737169i | \(0.263838\pi\) | |||||||
\(480\) | 4.11880 | 0.187997 | ||||||||
\(481\) | 13.5993 | 0.620075 | ||||||||
\(482\) | −66.6494 | −3.03580 | ||||||||
\(483\) | −1.50074 | −0.0682858 | ||||||||
\(484\) | −48.2616 | −2.19371 | ||||||||
\(485\) | −6.19231 | −0.281178 | ||||||||
\(486\) | −28.8705 | −1.30959 | ||||||||
\(487\) | −27.1780 | −1.23155 | −0.615776 | − | 0.787921i | \(-0.711158\pi\) | ||||
−0.615776 | + | 0.787921i | \(0.711158\pi\) | |||||||
\(488\) | 1.54628 | 0.0699970 | ||||||||
\(489\) | −0.0934000 | −0.00422369 | ||||||||
\(490\) | 14.5936 | 0.659269 | ||||||||
\(491\) | −30.8639 | −1.39287 | −0.696434 | − | 0.717620i | \(-0.745231\pi\) | ||||
−0.696434 | + | 0.717620i | \(0.745231\pi\) | |||||||
\(492\) | 6.45229 | 0.290892 | ||||||||
\(493\) | −6.53285 | −0.294225 | ||||||||
\(494\) | −5.09542 | −0.229254 | ||||||||
\(495\) | −2.52869 | −0.113656 | ||||||||
\(496\) | 21.2697 | 0.955038 | ||||||||
\(497\) | −3.73540 | −0.167555 | ||||||||
\(498\) | 4.75572 | 0.213109 | ||||||||
\(499\) | −24.5066 | −1.09706 | −0.548532 | − | 0.836129i | \(-0.684813\pi\) | ||||
−0.548532 | + | 0.836129i | \(0.684813\pi\) | |||||||
\(500\) | −4.74002 | −0.211980 | ||||||||
\(501\) | −3.36190 | −0.150199 | ||||||||
\(502\) | 29.0030 | 1.29447 | ||||||||
\(503\) | 9.54846 | 0.425745 | 0.212872 | − | 0.977080i | \(-0.431718\pi\) | ||||
0.212872 | + | 0.977080i | \(0.431718\pi\) | |||||||
\(504\) | 23.3497 | 1.04008 | ||||||||
\(505\) | 12.0261 | 0.535153 | ||||||||
\(506\) | 6.63616 | 0.295013 | ||||||||
\(507\) | 4.72747 | 0.209954 | ||||||||
\(508\) | −72.9383 | −3.23612 | ||||||||
\(509\) | −1.13413 | −0.0502694 | −0.0251347 | − | 0.999684i | \(-0.508001\pi\) | ||||
−0.0251347 | + | 0.999684i | \(0.508001\pi\) | |||||||
\(510\) | 1.43567 | 0.0635724 | ||||||||
\(511\) | 11.0603 | 0.489280 | ||||||||
\(512\) | −46.0216 | −2.03389 | ||||||||
\(513\) | 3.22313 | 0.142305 | ||||||||
\(514\) | 25.2755 | 1.11485 | ||||||||
\(515\) | 1.19231 | 0.0525394 | ||||||||
\(516\) | 2.12317 | 0.0934672 | ||||||||
\(517\) | 8.61928 | 0.379076 | ||||||||
\(518\) | 25.9729 | 1.14118 | ||||||||
\(519\) | −9.63818 | −0.423069 | ||||||||
\(520\) | 11.3543 | 0.497918 | ||||||||
\(521\) | 27.0866 | 1.18668 | 0.593342 | − | 0.804950i | \(-0.297808\pi\) | ||||
0.593342 | + | 0.804950i | \(0.297808\pi\) | |||||||
\(522\) | 38.7772 | 1.69723 | ||||||||
\(523\) | 6.02636 | 0.263514 | 0.131757 | − | 0.991282i | \(-0.457938\pi\) | ||||
0.131757 | + | 0.991282i | \(0.457938\pi\) | |||||||
\(524\) | −73.3607 | −3.20478 | ||||||||
\(525\) | 0.531086 | 0.0231785 | ||||||||
\(526\) | 2.98480 | 0.130144 | ||||||||
\(527\) | 2.89346 | 0.126041 | ||||||||
\(528\) | 3.67718 | 0.160029 | ||||||||
\(529\) | −15.0149 | −0.652824 | ||||||||
\(530\) | −23.4912 | −1.02039 | ||||||||
\(531\) | 30.8927 | 1.34063 | ||||||||
\(532\) | −6.84388 | −0.296720 | ||||||||
\(533\) | 4.80387 | 0.208079 | ||||||||
\(534\) | −12.4102 | −0.537043 | ||||||||
\(535\) | −0.246253 | −0.0106465 | ||||||||
\(536\) | −0.894670 | −0.0386439 | ||||||||
\(537\) | −4.54863 | −0.196288 | ||||||||
\(538\) | 4.93468 | 0.212749 | ||||||||
\(539\) | 5.08484 | 0.219020 | ||||||||
\(540\) | −12.4246 | −0.534671 | ||||||||
\(541\) | 9.54544 | 0.410391 | 0.205195 | − | 0.978721i | \(-0.434217\pi\) | ||||
0.205195 | + | 0.978721i | \(0.434217\pi\) | |||||||
\(542\) | −34.8956 | −1.49889 | ||||||||
\(543\) | 8.64801 | 0.371122 | ||||||||
\(544\) | 11.1342 | 0.477375 | ||||||||
\(545\) | 9.75283 | 0.417765 | ||||||||
\(546\) | −2.20075 | −0.0941834 | ||||||||
\(547\) | 25.5774 | 1.09361 | 0.546805 | − | 0.837260i | \(-0.315844\pi\) | ||||
0.546805 | + | 0.837260i | \(0.315844\pi\) | |||||||
\(548\) | −42.8956 | −1.83241 | ||||||||
\(549\) | −0.607651 | −0.0259339 | ||||||||
\(550\) | −2.34843 | −0.100137 | ||||||||
\(551\) | −6.57009 | −0.279895 | ||||||||
\(552\) | 9.09160 | 0.386964 | ||||||||
\(553\) | −7.47567 | −0.317898 | ||||||||
\(554\) | −5.79401 | −0.246164 | ||||||||
\(555\) | −3.85353 | −0.163573 | ||||||||
\(556\) | −1.43688 | −0.0609373 | ||||||||
\(557\) | −1.72802 | −0.0732185 | −0.0366092 | − | 0.999330i | \(-0.511656\pi\) | ||||
−0.0366092 | + | 0.999330i | \(0.511656\pi\) | |||||||
\(558\) | −17.1748 | −0.727066 | ||||||||
\(559\) | 1.58075 | 0.0668584 | ||||||||
\(560\) | 10.5535 | 0.445969 | ||||||||
\(561\) | 0.500231 | 0.0211198 | ||||||||
\(562\) | 47.9741 | 2.02367 | ||||||||
\(563\) | −29.4710 | −1.24206 | −0.621028 | − | 0.783789i | \(-0.713285\pi\) | ||||
−0.621028 | + | 0.783789i | \(0.713285\pi\) | |||||||
\(564\) | 20.4278 | 0.860165 | ||||||||
\(565\) | −10.7981 | −0.454280 | ||||||||
\(566\) | 79.5703 | 3.34459 | ||||||||
\(567\) | −8.45523 | −0.355086 | ||||||||
\(568\) | 22.6294 | 0.949509 | ||||||||
\(569\) | −27.5541 | −1.15513 | −0.577564 | − | 0.816345i | \(-0.695997\pi\) | ||||
−0.577564 | + | 0.816345i | \(0.695997\pi\) | |||||||
\(570\) | 1.44385 | 0.0604762 | ||||||||
\(571\) | 30.1035 | 1.25979 | 0.629895 | − | 0.776680i | \(-0.283098\pi\) | ||||
0.629895 | + | 0.776680i | \(0.283098\pi\) | |||||||
\(572\) | 6.84388 | 0.286157 | ||||||||
\(573\) | 1.00050 | 0.0417967 | ||||||||
\(574\) | 9.17476 | 0.382947 | ||||||||
\(575\) | −2.82578 | −0.117843 | ||||||||
\(576\) | −15.8404 | −0.660015 | ||||||||
\(577\) | 11.1776 | 0.465331 | 0.232665 | − | 0.972557i | \(-0.425255\pi\) | ||||
0.232665 | + | 0.972557i | \(0.425255\pi\) | |||||||
\(578\) | −40.2536 | −1.67433 | ||||||||
\(579\) | 0.320939 | 0.0133378 | ||||||||
\(580\) | 25.3266 | 1.05163 | ||||||||
\(581\) | 4.75572 | 0.197301 | ||||||||
\(582\) | −7.27111 | −0.301397 | ||||||||
\(583\) | −8.18505 | −0.338990 | ||||||||
\(584\) | −67.0046 | −2.77267 | ||||||||
\(585\) | −4.46194 | −0.184479 | ||||||||
\(586\) | 11.1535 | 0.460748 | ||||||||
\(587\) | −6.26603 | −0.258627 | −0.129313 | − | 0.991604i | \(-0.541277\pi\) | ||||
−0.129313 | + | 0.991604i | \(0.541277\pi\) | |||||||
\(588\) | 12.0511 | 0.496980 | ||||||||
\(589\) | 2.90995 | 0.119902 | ||||||||
\(590\) | 28.6904 | 1.18117 | ||||||||
\(591\) | 8.51094 | 0.350093 | ||||||||
\(592\) | −76.5760 | −3.14725 | ||||||||
\(593\) | 32.8762 | 1.35007 | 0.675033 | − | 0.737788i | \(-0.264129\pi\) | ||||
0.675033 | + | 0.737788i | \(0.264129\pi\) | |||||||
\(594\) | −6.15575 | −0.252573 | ||||||||
\(595\) | 1.43567 | 0.0588566 | ||||||||
\(596\) | −13.3921 | −0.548560 | ||||||||
\(597\) | −11.9641 | −0.489660 | ||||||||
\(598\) | 11.7097 | 0.478844 | ||||||||
\(599\) | −14.6940 | −0.600382 | −0.300191 | − | 0.953879i | \(-0.597051\pi\) | ||||
−0.300191 | + | 0.953879i | \(0.597051\pi\) | |||||||
\(600\) | −3.21737 | −0.131349 | ||||||||
\(601\) | 12.9725 | 0.529161 | 0.264581 | − | 0.964364i | \(-0.414766\pi\) | ||||
0.264581 | + | 0.964364i | \(0.414766\pi\) | |||||||
\(602\) | 3.01902 | 0.123046 | ||||||||
\(603\) | 0.351583 | 0.0143176 | ||||||||
\(604\) | 42.7187 | 1.73820 | ||||||||
\(605\) | 10.1817 | 0.413946 | ||||||||
\(606\) | 14.1212 | 0.573634 | ||||||||
\(607\) | 16.7592 | 0.680237 | 0.340118 | − | 0.940383i | \(-0.389533\pi\) | ||||
0.340118 | + | 0.940383i | \(0.389533\pi\) | |||||||
\(608\) | 11.1977 | 0.454126 | ||||||||
\(609\) | −2.83767 | −0.114988 | ||||||||
\(610\) | −0.564333 | −0.0228492 | ||||||||
\(611\) | 15.2089 | 0.615288 | ||||||||
\(612\) | −16.2007 | −0.654876 | ||||||||
\(613\) | −13.2791 | −0.536338 | −0.268169 | − | 0.963372i | \(-0.586419\pi\) | ||||
−0.268169 | + | 0.963372i | \(0.586419\pi\) | |||||||
\(614\) | −82.2663 | −3.32000 | ||||||||
\(615\) | −1.36124 | −0.0548904 | ||||||||
\(616\) | 7.55578 | 0.304431 | ||||||||
\(617\) | −10.4731 | −0.421630 | −0.210815 | − | 0.977526i | \(-0.567612\pi\) | ||||
−0.210815 | + | 0.977526i | \(0.567612\pi\) | |||||||
\(618\) | 1.40003 | 0.0563174 | ||||||||
\(619\) | −35.3334 | −1.42017 | −0.710085 | − | 0.704116i | \(-0.751343\pi\) | ||||
−0.710085 | + | 0.704116i | \(0.751343\pi\) | |||||||
\(620\) | −11.2174 | −0.450501 | ||||||||
\(621\) | −7.40700 | −0.297233 | ||||||||
\(622\) | 6.87830 | 0.275795 | ||||||||
\(623\) | −12.4102 | −0.497205 | ||||||||
\(624\) | 6.48848 | 0.259747 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 6.74296 | 0.269503 | ||||||||
\(627\) | 0.503082 | 0.0200912 | ||||||||
\(628\) | 50.3756 | 2.01021 | ||||||||
\(629\) | −10.4171 | −0.415358 | ||||||||
\(630\) | −8.52173 | −0.339514 | ||||||||
\(631\) | −42.3389 | −1.68549 | −0.842743 | − | 0.538316i | \(-0.819061\pi\) | ||||
−0.842743 | + | 0.538316i | \(0.819061\pi\) | |||||||
\(632\) | 45.2884 | 1.80147 | ||||||||
\(633\) | −10.4916 | −0.417005 | ||||||||
\(634\) | −6.66504 | −0.264703 | ||||||||
\(635\) | 15.3878 | 0.610645 | ||||||||
\(636\) | −19.3986 | −0.769206 | ||||||||
\(637\) | 8.97233 | 0.355497 | ||||||||
\(638\) | 12.5480 | 0.496780 | ||||||||
\(639\) | −8.89279 | −0.351793 | ||||||||
\(640\) | 3.50195 | 0.138427 | ||||||||
\(641\) | −36.3728 | −1.43664 | −0.718320 | − | 0.695713i | \(-0.755089\pi\) | ||||
−0.718320 | + | 0.695713i | \(0.755089\pi\) | |||||||
\(642\) | −0.289155 | −0.0114120 | ||||||||
\(643\) | 11.1027 | 0.437849 | 0.218924 | − | 0.975742i | \(-0.429745\pi\) | ||||
0.218924 | + | 0.975742i | \(0.429745\pi\) | |||||||
\(644\) | 15.7278 | 0.619761 | ||||||||
\(645\) | −0.447924 | −0.0176370 | ||||||||
\(646\) | 3.90311 | 0.153566 | ||||||||
\(647\) | 14.5536 | 0.572162 | 0.286081 | − | 0.958205i | \(-0.407647\pi\) | ||||
0.286081 | + | 0.958205i | \(0.407647\pi\) | |||||||
\(648\) | 51.2226 | 2.01221 | ||||||||
\(649\) | 9.99664 | 0.392402 | ||||||||
\(650\) | −4.14386 | −0.162536 | ||||||||
\(651\) | 1.25683 | 0.0492590 | ||||||||
\(652\) | 0.978835 | 0.0383342 | ||||||||
\(653\) | −40.4031 | −1.58109 | −0.790547 | − | 0.612401i | \(-0.790204\pi\) | ||||
−0.790547 | + | 0.612401i | \(0.790204\pi\) | |||||||
\(654\) | 11.4519 | 0.447805 | ||||||||
\(655\) | 15.4769 | 0.604732 | ||||||||
\(656\) | −27.0500 | −1.05612 | ||||||||
\(657\) | 26.3311 | 1.02728 | ||||||||
\(658\) | 29.0471 | 1.13237 | ||||||||
\(659\) | −17.9447 | −0.699025 | −0.349512 | − | 0.936932i | \(-0.613653\pi\) | ||||
−0.349512 | + | 0.936932i | \(0.613653\pi\) | |||||||
\(660\) | −1.93930 | −0.0754871 | ||||||||
\(661\) | 3.43856 | 0.133745 | 0.0668723 | − | 0.997762i | \(-0.478698\pi\) | ||||
0.0668723 | + | 0.997762i | \(0.478698\pi\) | |||||||
\(662\) | 30.0911 | 1.16953 | ||||||||
\(663\) | 0.882669 | 0.0342800 | ||||||||
\(664\) | −28.8106 | −1.11807 | ||||||||
\(665\) | 1.44385 | 0.0559901 | ||||||||
\(666\) | 61.8332 | 2.39599 | ||||||||
\(667\) | 15.0986 | 0.584619 | ||||||||
\(668\) | 35.2329 | 1.36320 | ||||||||
\(669\) | −2.62482 | −0.101482 | ||||||||
\(670\) | 0.326520 | 0.0126146 | ||||||||
\(671\) | −0.196631 | −0.00759086 | ||||||||
\(672\) | 4.83636 | 0.186567 | ||||||||
\(673\) | 24.0825 | 0.928312 | 0.464156 | − | 0.885754i | \(-0.346358\pi\) | ||||
0.464156 | + | 0.885754i | \(0.346358\pi\) | |||||||
\(674\) | −48.8561 | −1.88187 | ||||||||
\(675\) | 2.62122 | 0.100891 | ||||||||
\(676\) | −49.5441 | −1.90554 | ||||||||
\(677\) | −2.61480 | −0.100495 | −0.0502474 | − | 0.998737i | \(-0.516001\pi\) | ||||
−0.0502474 | + | 0.998737i | \(0.516001\pi\) | |||||||
\(678\) | −12.6793 | −0.486946 | ||||||||
\(679\) | −7.27111 | −0.279039 | ||||||||
\(680\) | −8.69741 | −0.333530 | ||||||||
\(681\) | −2.90785 | −0.111429 | ||||||||
\(682\) | −5.55762 | −0.212812 | ||||||||
\(683\) | 27.4169 | 1.04908 | 0.524540 | − | 0.851386i | \(-0.324237\pi\) | ||||
0.524540 | + | 0.851386i | \(0.324237\pi\) | |||||||
\(684\) | −16.2931 | −0.622982 | ||||||||
\(685\) | 9.04966 | 0.345770 | ||||||||
\(686\) | 38.4751 | 1.46899 | ||||||||
\(687\) | −7.64845 | −0.291807 | ||||||||
\(688\) | −8.90097 | −0.339346 | ||||||||
\(689\) | −14.4427 | −0.550224 | ||||||||
\(690\) | −3.31808 | −0.126317 | ||||||||
\(691\) | 4.15666 | 0.158127 | 0.0790633 | − | 0.996870i | \(-0.474807\pi\) | ||||
0.0790633 | + | 0.996870i | \(0.474807\pi\) | |||||||
\(692\) | 101.008 | 3.83977 | ||||||||
\(693\) | −2.96923 | −0.112792 | ||||||||
\(694\) | −39.8358 | −1.51215 | ||||||||
\(695\) | 0.303138 | 0.0114987 | ||||||||
\(696\) | 17.1909 | 0.651619 | ||||||||
\(697\) | −3.67978 | −0.139382 | ||||||||
\(698\) | 74.0576 | 2.80312 | ||||||||
\(699\) | −10.1149 | −0.382580 | ||||||||
\(700\) | −5.56580 | −0.210368 | ||||||||
\(701\) | 25.3609 | 0.957866 | 0.478933 | − | 0.877851i | \(-0.341024\pi\) | ||||
0.478933 | + | 0.877851i | \(0.341024\pi\) | |||||||
\(702\) | −10.8620 | −0.409959 | ||||||||
\(703\) | −10.4765 | −0.395129 | ||||||||
\(704\) | −5.12582 | −0.193186 | ||||||||
\(705\) | −4.30964 | −0.162310 | ||||||||
\(706\) | 46.8223 | 1.76218 | ||||||||
\(707\) | 14.1212 | 0.531082 | ||||||||
\(708\) | 23.6921 | 0.890405 | ||||||||
\(709\) | 23.6181 | 0.886998 | 0.443499 | − | 0.896275i | \(-0.353737\pi\) | ||||
0.443499 | + | 0.896275i | \(0.353737\pi\) | |||||||
\(710\) | −8.25885 | −0.309949 | ||||||||
\(711\) | −17.7972 | −0.667447 | ||||||||
\(712\) | 75.1824 | 2.81758 | ||||||||
\(713\) | −6.68729 | −0.250441 | ||||||||
\(714\) | 1.68578 | 0.0630888 | ||||||||
\(715\) | −1.44385 | −0.0539969 | ||||||||
\(716\) | 47.6698 | 1.78151 | ||||||||
\(717\) | −7.97951 | −0.298000 | ||||||||
\(718\) | −23.2866 | −0.869048 | ||||||||
\(719\) | −0.0337594 | −0.00125901 | −0.000629507 | − | 1.00000i | \(-0.500200\pi\) | ||||
−0.000629507 | 1.00000i | \(0.500200\pi\) | ||||||||
\(720\) | 25.1246 | 0.936340 | ||||||||
\(721\) | 1.40003 | 0.0521398 | ||||||||
\(722\) | −45.4016 | −1.68967 | ||||||||
\(723\) | 11.6114 | 0.431831 | ||||||||
\(724\) | −90.6315 | −3.36829 | ||||||||
\(725\) | −5.34314 | −0.198439 | ||||||||
\(726\) | 11.9555 | 0.443712 | ||||||||
\(727\) | −36.1204 | −1.33963 | −0.669815 | − | 0.742528i | \(-0.733627\pi\) | ||||
−0.669815 | + | 0.742528i | \(0.733627\pi\) | |||||||
\(728\) | 13.3324 | 0.494130 | ||||||||
\(729\) | −16.5726 | −0.613799 | ||||||||
\(730\) | 24.4541 | 0.905085 | ||||||||
\(731\) | −1.21086 | −0.0447852 | ||||||||
\(732\) | −0.466018 | −0.0172245 | ||||||||
\(733\) | 37.4642 | 1.38377 | 0.691885 | − | 0.722007i | \(-0.256780\pi\) | ||||
0.691885 | + | 0.722007i | \(0.256780\pi\) | |||||||
\(734\) | 28.1606 | 1.03943 | ||||||||
\(735\) | −2.54242 | −0.0937787 | ||||||||
\(736\) | −25.7331 | −0.948536 | ||||||||
\(737\) | 0.113770 | 0.00419076 | ||||||||
\(738\) | 21.8422 | 0.804022 | ||||||||
\(739\) | 15.5868 | 0.573371 | 0.286686 | − | 0.958025i | \(-0.407447\pi\) | ||||
0.286686 | + | 0.958025i | \(0.407447\pi\) | |||||||
\(740\) | 40.3852 | 1.48459 | ||||||||
\(741\) | 0.887701 | 0.0326105 | ||||||||
\(742\) | −27.5837 | −1.01263 | ||||||||
\(743\) | −6.63688 | −0.243484 | −0.121742 | − | 0.992562i | \(-0.538848\pi\) | ||||
−0.121742 | + | 0.992562i | \(0.538848\pi\) | |||||||
\(744\) | −7.61399 | −0.279143 | ||||||||
\(745\) | 2.82532 | 0.103512 | ||||||||
\(746\) | −43.6826 | −1.59933 | ||||||||
\(747\) | 11.3219 | 0.414245 | ||||||||
\(748\) | −5.24244 | −0.191682 | ||||||||
\(749\) | −0.289155 | −0.0105655 | ||||||||
\(750\) | 1.17422 | 0.0428763 | ||||||||
\(751\) | 9.63335 | 0.351526 | 0.175763 | − | 0.984433i | \(-0.443761\pi\) | ||||
0.175763 | + | 0.984433i | \(0.443761\pi\) | |||||||
\(752\) | −85.6396 | −3.12295 | ||||||||
\(753\) | −5.05277 | −0.184133 | ||||||||
\(754\) | 22.1413 | 0.806337 | ||||||||
\(755\) | −9.01234 | −0.327993 | ||||||||
\(756\) | −14.5892 | −0.530604 | ||||||||
\(757\) | 2.90728 | 0.105667 | 0.0528334 | − | 0.998603i | \(-0.483175\pi\) | ||||
0.0528334 | + | 0.998603i | \(0.483175\pi\) | |||||||
\(758\) | 54.3674 | 1.97471 | ||||||||
\(759\) | −1.15612 | −0.0419646 | ||||||||
\(760\) | −8.74699 | −0.317287 | ||||||||
\(761\) | 14.0584 | 0.509618 | 0.254809 | − | 0.966991i | \(-0.417987\pi\) | ||||
0.254809 | + | 0.966991i | \(0.417987\pi\) | |||||||
\(762\) | 18.0686 | 0.654555 | ||||||||
\(763\) | 11.4519 | 0.414587 | ||||||||
\(764\) | −10.4853 | −0.379346 | ||||||||
\(765\) | 3.41787 | 0.123573 | ||||||||
\(766\) | 39.7144 | 1.43494 | ||||||||
\(767\) | 17.6393 | 0.636919 | ||||||||
\(768\) | 9.23786 | 0.333342 | ||||||||
\(769\) | −11.5598 | −0.416857 | −0.208428 | − | 0.978038i | \(-0.566835\pi\) | ||||
−0.208428 | + | 0.978038i | \(0.566835\pi\) | |||||||
\(770\) | −2.75756 | −0.0993757 | ||||||||
\(771\) | −4.40338 | −0.158584 | ||||||||
\(772\) | −3.36345 | −0.121053 | ||||||||
\(773\) | 20.7860 | 0.747620 | 0.373810 | − | 0.927505i | \(-0.378051\pi\) | ||||
0.373810 | + | 0.927505i | \(0.378051\pi\) | |||||||
\(774\) | 7.18731 | 0.258343 | ||||||||
\(775\) | 2.36652 | 0.0850081 | ||||||||
\(776\) | 44.0491 | 1.58127 | ||||||||
\(777\) | −4.52488 | −0.162329 | ||||||||
\(778\) | −16.9006 | −0.605914 | ||||||||
\(779\) | −3.70076 | −0.132594 | ||||||||
\(780\) | −3.42194 | −0.122525 | ||||||||
\(781\) | −2.87764 | −0.102970 | ||||||||
\(782\) | −8.96965 | −0.320754 | ||||||||
\(783\) | −14.0055 | −0.500517 | ||||||||
\(784\) | −50.5221 | −1.80436 | ||||||||
\(785\) | −10.6277 | −0.379320 | ||||||||
\(786\) | 18.1732 | 0.648217 | ||||||||
\(787\) | 9.07355 | 0.323437 | 0.161719 | − | 0.986837i | \(-0.448296\pi\) | ||||
0.161719 | + | 0.986837i | \(0.448296\pi\) | |||||||
\(788\) | −89.1950 | −3.17744 | ||||||||
\(789\) | −0.519999 | −0.0185124 | ||||||||
\(790\) | −16.5285 | −0.588057 | ||||||||
\(791\) | −12.6793 | −0.450825 | ||||||||
\(792\) | 17.9879 | 0.639172 | ||||||||
\(793\) | −0.346961 | −0.0123209 | ||||||||
\(794\) | 40.4721 | 1.43630 | ||||||||
\(795\) | 4.09252 | 0.145147 | ||||||||
\(796\) | 125.385 | 4.44414 | ||||||||
\(797\) | 43.4476 | 1.53899 | 0.769496 | − | 0.638652i | \(-0.220508\pi\) | ||||
0.769496 | + | 0.638652i | \(0.220508\pi\) | |||||||
\(798\) | 1.69539 | 0.0600162 | ||||||||
\(799\) | −11.6501 | −0.412151 | ||||||||
\(800\) | 9.10654 | 0.321965 | ||||||||
\(801\) | −29.5448 | −1.04391 | ||||||||
\(802\) | 22.9201 | 0.809336 | ||||||||
\(803\) | 8.52055 | 0.300684 | ||||||||
\(804\) | 0.269635 | 0.00950929 | ||||||||
\(805\) | −3.31808 | −0.116947 | ||||||||
\(806\) | −9.80656 | −0.345421 | ||||||||
\(807\) | −0.859697 | −0.0302628 | ||||||||
\(808\) | −85.5476 | −3.00955 | ||||||||
\(809\) | −33.3100 | −1.17112 | −0.585558 | − | 0.810630i | \(-0.699125\pi\) | ||||
−0.585558 | + | 0.810630i | \(0.699125\pi\) | |||||||
\(810\) | −18.6943 | −0.656849 | ||||||||
\(811\) | −21.6565 | −0.760462 | −0.380231 | − | 0.924892i | \(-0.624156\pi\) | ||||
−0.380231 | + | 0.924892i | \(0.624156\pi\) | |||||||
\(812\) | 29.7389 | 1.04363 | ||||||||
\(813\) | 6.07935 | 0.213212 | ||||||||
\(814\) | 20.0087 | 0.701306 | ||||||||
\(815\) | −0.206505 | −0.00723354 | ||||||||
\(816\) | −4.97020 | −0.173992 | ||||||||
\(817\) | −1.21776 | −0.0426040 | ||||||||
\(818\) | 53.8258 | 1.88197 | ||||||||
\(819\) | −5.23928 | −0.183075 | ||||||||
\(820\) | 14.2658 | 0.498184 | ||||||||
\(821\) | 20.6996 | 0.722422 | 0.361211 | − | 0.932484i | \(-0.382363\pi\) | ||||
0.361211 | + | 0.932484i | \(0.382363\pi\) | |||||||
\(822\) | 10.6262 | 0.370633 | ||||||||
\(823\) | 0.177112 | 0.00617372 | 0.00308686 | − | 0.999995i | \(-0.499017\pi\) | ||||
0.00308686 | + | 0.999995i | \(0.499017\pi\) | |||||||
\(824\) | −8.48151 | −0.295467 | ||||||||
\(825\) | 0.409133 | 0.0142442 | ||||||||
\(826\) | 33.6888 | 1.17218 | ||||||||
\(827\) | −10.6057 | −0.368796 | −0.184398 | − | 0.982852i | \(-0.559033\pi\) | ||||
−0.184398 | + | 0.982852i | \(0.559033\pi\) | |||||||
\(828\) | 37.4428 | 1.30123 | ||||||||
\(829\) | −7.04429 | −0.244658 | −0.122329 | − | 0.992490i | \(-0.539036\pi\) | ||||
−0.122329 | + | 0.992490i | \(0.539036\pi\) | |||||||
\(830\) | 10.5148 | 0.364972 | ||||||||
\(831\) | 1.00941 | 0.0350159 | ||||||||
\(832\) | −9.04463 | −0.313566 | ||||||||
\(833\) | −6.87284 | −0.238130 | ||||||||
\(834\) | 0.355950 | 0.0123255 | ||||||||
\(835\) | −7.43306 | −0.257232 | ||||||||
\(836\) | −5.27232 | −0.182347 | ||||||||
\(837\) | 6.20318 | 0.214413 | ||||||||
\(838\) | −43.0325 | −1.48653 | ||||||||
\(839\) | 1.90848 | 0.0658880 | 0.0329440 | − | 0.999457i | \(-0.489512\pi\) | ||||
0.0329440 | + | 0.999457i | \(0.489512\pi\) | |||||||
\(840\) | −3.77789 | −0.130350 | ||||||||
\(841\) | −0.450820 | −0.0155455 | ||||||||
\(842\) | −10.8795 | −0.374933 | ||||||||
\(843\) | −8.35783 | −0.287859 | ||||||||
\(844\) | 109.953 | 3.78473 | ||||||||
\(845\) | 10.4523 | 0.359570 | ||||||||
\(846\) | 69.1518 | 2.37749 | ||||||||
\(847\) | 11.9555 | 0.410798 | ||||||||
\(848\) | 81.3251 | 2.79272 | ||||||||
\(849\) | −13.8624 | −0.475756 | ||||||||
\(850\) | 3.17422 | 0.108875 | ||||||||
\(851\) | 24.0758 | 0.825308 | ||||||||
\(852\) | −6.82003 | −0.233650 | ||||||||
\(853\) | 24.4557 | 0.837348 | 0.418674 | − | 0.908137i | \(-0.362495\pi\) | ||||
0.418674 | + | 0.908137i | \(0.362495\pi\) | |||||||
\(854\) | −0.662649 | −0.0226754 | ||||||||
\(855\) | 3.43735 | 0.117555 | ||||||||
\(856\) | 1.75173 | 0.0598728 | ||||||||
\(857\) | 37.4047 | 1.27772 | 0.638861 | − | 0.769322i | \(-0.279406\pi\) | ||||
0.638861 | + | 0.769322i | \(0.279406\pi\) | |||||||
\(858\) | −1.69539 | −0.0578797 | ||||||||
\(859\) | −21.0744 | −0.719050 | −0.359525 | − | 0.933135i | \(-0.617061\pi\) | ||||
−0.359525 | + | 0.933135i | \(0.617061\pi\) | |||||||
\(860\) | 4.69426 | 0.160073 | ||||||||
\(861\) | −1.59839 | −0.0544728 | ||||||||
\(862\) | 20.1524 | 0.686393 | ||||||||
\(863\) | −33.2821 | −1.13293 | −0.566467 | − | 0.824084i | \(-0.691690\pi\) | ||||
−0.566467 | + | 0.824084i | \(0.691690\pi\) | |||||||
\(864\) | 23.8702 | 0.812082 | ||||||||
\(865\) | −21.3097 | −0.724552 | ||||||||
\(866\) | −11.8573 | −0.402929 | ||||||||
\(867\) | 7.01281 | 0.238167 | ||||||||
\(868\) | −13.1716 | −0.447074 | ||||||||
\(869\) | −5.75903 | −0.195362 | ||||||||
\(870\) | −6.27400 | −0.212709 | ||||||||
\(871\) | 0.200749 | 0.00680213 | ||||||||
\(872\) | −69.3769 | −2.34940 | ||||||||
\(873\) | −17.3102 | −0.585861 | ||||||||
\(874\) | −9.02078 | −0.305132 | ||||||||
\(875\) | 1.17422 | 0.0396957 | ||||||||
\(876\) | 20.1938 | 0.682285 | ||||||||
\(877\) | 18.9012 | 0.638248 | 0.319124 | − | 0.947713i | \(-0.396611\pi\) | ||||
0.319124 | + | 0.947713i | \(0.396611\pi\) | |||||||
\(878\) | −53.4597 | −1.80418 | ||||||||
\(879\) | −1.94312 | −0.0655396 | ||||||||
\(880\) | 8.13014 | 0.274067 | ||||||||
\(881\) | −57.0309 | −1.92142 | −0.960709 | − | 0.277557i | \(-0.910475\pi\) | ||||
−0.960709 | + | 0.277557i | \(0.910475\pi\) | |||||||
\(882\) | 40.7953 | 1.37365 | ||||||||
\(883\) | −2.19873 | −0.0739931 | −0.0369966 | − | 0.999315i | \(-0.511779\pi\) | ||||
−0.0369966 | + | 0.999315i | \(0.511779\pi\) | |||||||
\(884\) | −9.25041 | −0.311125 | ||||||||
\(885\) | −4.99832 | −0.168017 | ||||||||
\(886\) | −79.7784 | −2.68021 | ||||||||
\(887\) | 47.3960 | 1.59140 | 0.795702 | − | 0.605689i | \(-0.207102\pi\) | ||||
0.795702 | + | 0.605689i | \(0.207102\pi\) | |||||||
\(888\) | 27.4122 | 0.919892 | ||||||||
\(889\) | 18.0686 | 0.606000 | ||||||||
\(890\) | −27.4386 | −0.919745 | ||||||||
\(891\) | −6.51366 | −0.218216 | ||||||||
\(892\) | 27.5083 | 0.921044 | ||||||||
\(893\) | −11.7165 | −0.392078 | ||||||||
\(894\) | 3.31753 | 0.110955 | ||||||||
\(895\) | −10.0569 | −0.336165 | ||||||||
\(896\) | 4.11204 | 0.137374 | ||||||||
\(897\) | −2.04001 | −0.0681138 | ||||||||
\(898\) | −21.1834 | −0.706899 | ||||||||
\(899\) | −12.6447 | −0.421724 | ||||||||
\(900\) | −13.2504 | −0.441680 | ||||||||
\(901\) | 11.0632 | 0.368568 | ||||||||
\(902\) | 7.06796 | 0.235337 | ||||||||
\(903\) | −0.525959 | −0.0175028 | ||||||||
\(904\) | 76.8126 | 2.55475 | ||||||||
\(905\) | 19.1205 | 0.635586 | ||||||||
\(906\) | −10.5824 | −0.351578 | ||||||||
\(907\) | −15.0409 | −0.499426 | −0.249713 | − | 0.968320i | \(-0.580336\pi\) | ||||
−0.249713 | + | 0.968320i | \(0.580336\pi\) | |||||||
\(908\) | 30.4744 | 1.01133 | ||||||||
\(909\) | 33.6181 | 1.11504 | ||||||||
\(910\) | −4.86579 | −0.161299 | ||||||||
\(911\) | −22.1298 | −0.733193 | −0.366597 | − | 0.930380i | \(-0.619477\pi\) | ||||
−0.366597 | + | 0.930380i | \(0.619477\pi\) | |||||||
\(912\) | −4.99853 | −0.165518 | ||||||||
\(913\) | 3.66367 | 0.121250 | ||||||||
\(914\) | −56.1898 | −1.85859 | ||||||||
\(915\) | 0.0983156 | 0.00325021 | ||||||||
\(916\) | 80.1561 | 2.64843 | ||||||||
\(917\) | 18.1732 | 0.600132 | ||||||||
\(918\) | 8.32031 | 0.274611 | ||||||||
\(919\) | −46.0521 | −1.51912 | −0.759559 | − | 0.650438i | \(-0.774585\pi\) | ||||
−0.759559 | + | 0.650438i | \(0.774585\pi\) | |||||||
\(920\) | 20.1013 | 0.662719 | ||||||||
\(921\) | 14.3321 | 0.472258 | ||||||||
\(922\) | −29.8953 | −0.984549 | ||||||||
\(923\) | −5.07766 | −0.167133 | ||||||||
\(924\) | −2.27715 | −0.0749129 | ||||||||
\(925\) | −8.52004 | −0.280137 | ||||||||
\(926\) | −79.6200 | −2.61648 | ||||||||
\(927\) | 3.33302 | 0.109471 | ||||||||
\(928\) | −48.6576 | −1.59726 | ||||||||
\(929\) | 1.19407 | 0.0391763 | 0.0195881 | − | 0.999808i | \(-0.493765\pi\) | ||||
0.0195881 | + | 0.999808i | \(0.493765\pi\) | |||||||
\(930\) | 2.77881 | 0.0911208 | ||||||||
\(931\) | −6.91202 | −0.226532 | ||||||||
\(932\) | 106.004 | 3.47229 | ||||||||
\(933\) | −1.19831 | −0.0392308 | ||||||||
\(934\) | −60.3713 | −1.97541 | ||||||||
\(935\) | 1.10599 | 0.0361699 | ||||||||
\(936\) | 31.7401 | 1.03746 | ||||||||
\(937\) | −0.426436 | −0.0139310 | −0.00696552 | − | 0.999976i | \(-0.502217\pi\) | ||||
−0.00696552 | + | 0.999976i | \(0.502217\pi\) | |||||||
\(938\) | 0.383405 | 0.0125186 | ||||||||
\(939\) | −1.17473 | −0.0383358 | ||||||||
\(940\) | 45.1652 | 1.47313 | ||||||||
\(941\) | 21.5391 | 0.702154 | 0.351077 | − | 0.936347i | \(-0.385816\pi\) | ||||
0.351077 | + | 0.936347i | \(0.385816\pi\) | |||||||
\(942\) | −12.4792 | −0.406595 | ||||||||
\(943\) | 8.50463 | 0.276949 | ||||||||
\(944\) | −99.3247 | −3.23274 | ||||||||
\(945\) | 3.07787 | 0.100123 | ||||||||
\(946\) | 2.32576 | 0.0756169 | ||||||||
\(947\) | −16.3233 | −0.530436 | −0.265218 | − | 0.964189i | \(-0.585444\pi\) | ||||
−0.265218 | + | 0.964189i | \(0.585444\pi\) | |||||||
\(948\) | −13.6490 | −0.443298 | ||||||||
\(949\) | 15.0347 | 0.488048 | ||||||||
\(950\) | 3.19231 | 0.103572 | ||||||||
\(951\) | 1.16115 | 0.0376530 | ||||||||
\(952\) | −10.2126 | −0.330993 | ||||||||
\(953\) | 50.2552 | 1.62793 | 0.813963 | − | 0.580916i | \(-0.197306\pi\) | ||||
0.813963 | + | 0.580916i | \(0.197306\pi\) | |||||||
\(954\) | −65.6680 | −2.12608 | ||||||||
\(955\) | 2.21209 | 0.0715814 | ||||||||
\(956\) | 83.6256 | 2.70465 | ||||||||
\(957\) | −2.18606 | −0.0706652 | ||||||||
\(958\) | 76.7870 | 2.48088 | ||||||||
\(959\) | 10.6262 | 0.343139 | ||||||||
\(960\) | 2.56291 | 0.0827175 | ||||||||
\(961\) | −25.3996 | −0.819341 | ||||||||
\(962\) | 35.3059 | 1.13831 | ||||||||
\(963\) | −0.688385 | −0.0221829 | ||||||||
\(964\) | −121.687 | −3.91929 | ||||||||
\(965\) | 0.709587 | 0.0228424 | ||||||||
\(966\) | −3.89614 | −0.125356 | ||||||||
\(967\) | 17.0631 | 0.548713 | 0.274357 | − | 0.961628i | \(-0.411535\pi\) | ||||
0.274357 | + | 0.961628i | \(0.411535\pi\) | |||||||
\(968\) | −72.4279 | −2.32792 | ||||||||
\(969\) | −0.679982 | −0.0218442 | ||||||||
\(970\) | −16.0762 | −0.516175 | ||||||||
\(971\) | −45.1473 | −1.44884 | −0.724422 | − | 0.689356i | \(-0.757893\pi\) | ||||
−0.724422 | + | 0.689356i | \(0.757893\pi\) | |||||||
\(972\) | −52.7113 | −1.69072 | ||||||||
\(973\) | 0.355950 | 0.0114112 | ||||||||
\(974\) | −70.5583 | −2.26083 | ||||||||
\(975\) | 0.721925 | 0.0231201 | ||||||||
\(976\) | 1.95369 | 0.0625361 | ||||||||
\(977\) | −22.9284 | −0.733544 | −0.366772 | − | 0.930311i | \(-0.619537\pi\) | ||||
−0.366772 | + | 0.930311i | \(0.619537\pi\) | |||||||
\(978\) | −0.242481 | −0.00775368 | ||||||||
\(979\) | −9.56047 | −0.305554 | ||||||||
\(980\) | 26.6447 | 0.851133 | ||||||||
\(981\) | 27.2634 | 0.870453 | ||||||||
\(982\) | −80.1275 | −2.55697 | ||||||||
\(983\) | −58.6824 | −1.87168 | −0.935839 | − | 0.352429i | \(-0.885356\pi\) | ||||
−0.935839 | + | 0.352429i | \(0.885356\pi\) | |||||||
\(984\) | 9.68318 | 0.308688 | ||||||||
\(985\) | 18.8174 | 0.599573 | ||||||||
\(986\) | −16.9603 | −0.540126 | ||||||||
\(987\) | −5.06045 | −0.161076 | ||||||||
\(988\) | −9.30314 | −0.295972 | ||||||||
\(989\) | 2.79850 | 0.0889873 | ||||||||
\(990\) | −6.56488 | −0.208646 | ||||||||
\(991\) | 46.8097 | 1.48696 | 0.743480 | − | 0.668758i | \(-0.233174\pi\) | ||||
0.743480 | + | 0.668758i | \(0.233174\pi\) | |||||||
\(992\) | 21.5509 | 0.684241 | ||||||||
\(993\) | −5.24234 | −0.166361 | ||||||||
\(994\) | −9.69767 | −0.307591 | ||||||||
\(995\) | −26.4524 | −0.838597 | ||||||||
\(996\) | 8.68292 | 0.275129 | ||||||||
\(997\) | −45.1216 | −1.42902 | −0.714508 | − | 0.699627i | \(-0.753350\pi\) | ||||
−0.714508 | + | 0.699627i | \(0.753350\pi\) | |||||||
\(998\) | −63.6229 | −2.01395 | ||||||||
\(999\) | −22.3329 | −0.706581 |
(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 | 6005.2.a.c.1.4 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6005.2.a.c.1.4 | ✓ | 4 | 1.1 | even | 1 | trivial |