Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6019,2,Mod(1,6019)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6019, 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("6019.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6019 = 13 \cdot 463 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6019.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: | \(48.0619569766\) |
Analytic rank: | \(1\) |
Dimension: | \(108\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 6019.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.25939 | −1.59763 | −0.798816 | − | 0.601576i | \(-0.794540\pi\) | ||||
−0.798816 | + | 0.601576i | \(0.794540\pi\) | |||||||
\(3\) | 2.42736 | 1.40144 | 0.700718 | − | 0.713439i | \(-0.252863\pi\) | ||||
0.700718 | + | 0.713439i | \(0.252863\pi\) | |||||||
\(4\) | 3.10485 | 1.55243 | ||||||||
\(5\) | −0.500622 | −0.223885 | −0.111942 | − | 0.993715i | \(-0.535707\pi\) | ||||
−0.111942 | + | 0.993715i | \(0.535707\pi\) | |||||||
\(6\) | −5.48435 | −2.23898 | ||||||||
\(7\) | 4.41326 | 1.66806 | 0.834028 | − | 0.551723i | \(-0.186029\pi\) | ||||
0.834028 | + | 0.551723i | \(0.186029\pi\) | |||||||
\(8\) | −2.49629 | −0.882574 | ||||||||
\(9\) | 2.89206 | 0.964021 | ||||||||
\(10\) | 1.13110 | 0.357686 | ||||||||
\(11\) | −1.42556 | −0.429823 | −0.214912 | − | 0.976633i | \(-0.568946\pi\) | ||||
−0.214912 | + | 0.976633i | \(0.568946\pi\) | |||||||
\(12\) | 7.53659 | 2.17562 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | −9.97128 | −2.66494 | ||||||||
\(15\) | −1.21519 | −0.313760 | ||||||||
\(16\) | −0.569596 | −0.142399 | ||||||||
\(17\) | 3.13782 | 0.761033 | 0.380517 | − | 0.924774i | \(-0.375746\pi\) | ||||
0.380517 | + | 0.924774i | \(0.375746\pi\) | |||||||
\(18\) | −6.53430 | −1.54015 | ||||||||
\(19\) | −7.27226 | −1.66837 | −0.834186 | − | 0.551484i | \(-0.814062\pi\) | ||||
−0.834186 | + | 0.551484i | \(0.814062\pi\) | |||||||
\(20\) | −1.55436 | −0.347565 | ||||||||
\(21\) | 10.7126 | 2.33767 | ||||||||
\(22\) | 3.22091 | 0.686700 | ||||||||
\(23\) | −8.26540 | −1.72345 | −0.861727 | − | 0.507372i | \(-0.830617\pi\) | ||||
−0.861727 | + | 0.507372i | \(0.830617\pi\) | |||||||
\(24\) | −6.05940 | −1.23687 | ||||||||
\(25\) | −4.74938 | −0.949876 | ||||||||
\(26\) | 2.25939 | 0.443103 | ||||||||
\(27\) | −0.262003 | −0.0504225 | ||||||||
\(28\) | 13.7025 | 2.58953 | ||||||||
\(29\) | −1.90070 | −0.352952 | −0.176476 | − | 0.984305i | \(-0.556470\pi\) | ||||
−0.176476 | + | 0.984305i | \(0.556470\pi\) | |||||||
\(30\) | 2.74559 | 0.501273 | ||||||||
\(31\) | 5.25956 | 0.944645 | 0.472322 | − | 0.881426i | \(-0.343416\pi\) | ||||
0.472322 | + | 0.881426i | \(0.343416\pi\) | |||||||
\(32\) | 6.27953 | 1.11007 | ||||||||
\(33\) | −3.46035 | −0.602370 | ||||||||
\(34\) | −7.08957 | −1.21585 | ||||||||
\(35\) | −2.20937 | −0.373452 | ||||||||
\(36\) | 8.97943 | 1.49657 | ||||||||
\(37\) | 6.75569 | 1.11063 | 0.555315 | − | 0.831640i | \(-0.312598\pi\) | ||||
0.555315 | + | 0.831640i | \(0.312598\pi\) | |||||||
\(38\) | 16.4309 | 2.66544 | ||||||||
\(39\) | −2.42736 | −0.388688 | ||||||||
\(40\) | 1.24970 | 0.197595 | ||||||||
\(41\) | −10.9114 | −1.70408 | −0.852041 | − | 0.523475i | \(-0.824635\pi\) | ||||
−0.852041 | + | 0.523475i | \(0.824635\pi\) | |||||||
\(42\) | −24.2039 | −3.73474 | ||||||||
\(43\) | −6.84316 | −1.04357 | −0.521786 | − | 0.853076i | \(-0.674734\pi\) | ||||
−0.521786 | + | 0.853076i | \(0.674734\pi\) | |||||||
\(44\) | −4.42616 | −0.667269 | ||||||||
\(45\) | −1.44783 | −0.215830 | ||||||||
\(46\) | 18.6748 | 2.75345 | ||||||||
\(47\) | −4.39465 | −0.641026 | −0.320513 | − | 0.947244i | \(-0.603855\pi\) | ||||
−0.320513 | + | 0.947244i | \(0.603855\pi\) | |||||||
\(48\) | −1.38261 | −0.199563 | ||||||||
\(49\) | 12.4769 | 1.78241 | ||||||||
\(50\) | 10.7307 | 1.51755 | ||||||||
\(51\) | 7.61661 | 1.06654 | ||||||||
\(52\) | −3.10485 | −0.430566 | ||||||||
\(53\) | 3.05136 | 0.419136 | 0.209568 | − | 0.977794i | \(-0.432794\pi\) | ||||
0.209568 | + | 0.977794i | \(0.432794\pi\) | |||||||
\(54\) | 0.591968 | 0.0805566 | ||||||||
\(55\) | 0.713668 | 0.0962310 | ||||||||
\(56\) | −11.0168 | −1.47218 | ||||||||
\(57\) | −17.6524 | −2.33811 | ||||||||
\(58\) | 4.29444 | 0.563887 | ||||||||
\(59\) | −11.4178 | −1.48647 | −0.743237 | − | 0.669028i | \(-0.766710\pi\) | ||||
−0.743237 | + | 0.669028i | \(0.766710\pi\) | |||||||
\(60\) | −3.77298 | −0.487090 | ||||||||
\(61\) | 12.7964 | 1.63841 | 0.819205 | − | 0.573501i | \(-0.194415\pi\) | ||||
0.819205 | + | 0.573501i | \(0.194415\pi\) | |||||||
\(62\) | −11.8834 | −1.50919 | ||||||||
\(63\) | 12.7634 | 1.60804 | ||||||||
\(64\) | −13.0487 | −1.63109 | ||||||||
\(65\) | 0.500622 | 0.0620945 | ||||||||
\(66\) | 7.81829 | 0.962365 | ||||||||
\(67\) | 1.26329 | 0.154336 | 0.0771679 | − | 0.997018i | \(-0.475412\pi\) | ||||
0.0771679 | + | 0.997018i | \(0.475412\pi\) | |||||||
\(68\) | 9.74247 | 1.18145 | ||||||||
\(69\) | −20.0631 | −2.41531 | ||||||||
\(70\) | 4.99184 | 0.596639 | ||||||||
\(71\) | −9.87557 | −1.17201 | −0.586007 | − | 0.810306i | \(-0.699301\pi\) | ||||
−0.586007 | + | 0.810306i | \(0.699301\pi\) | |||||||
\(72\) | −7.21944 | −0.850819 | ||||||||
\(73\) | −7.90176 | −0.924831 | −0.462416 | − | 0.886663i | \(-0.653017\pi\) | ||||
−0.462416 | + | 0.886663i | \(0.653017\pi\) | |||||||
\(74\) | −15.2638 | −1.77438 | ||||||||
\(75\) | −11.5284 | −1.33119 | ||||||||
\(76\) | −22.5793 | −2.59002 | ||||||||
\(77\) | −6.29138 | −0.716969 | ||||||||
\(78\) | 5.48435 | 0.620981 | ||||||||
\(79\) | −6.88388 | −0.774497 | −0.387249 | − | 0.921975i | \(-0.626574\pi\) | ||||
−0.387249 | + | 0.921975i | \(0.626574\pi\) | |||||||
\(80\) | 0.285152 | 0.0318810 | ||||||||
\(81\) | −9.31216 | −1.03468 | ||||||||
\(82\) | 24.6532 | 2.72250 | ||||||||
\(83\) | −2.36869 | −0.259997 | −0.129999 | − | 0.991514i | \(-0.541497\pi\) | ||||
−0.129999 | + | 0.991514i | \(0.541497\pi\) | |||||||
\(84\) | 33.2609 | 3.62906 | ||||||||
\(85\) | −1.57086 | −0.170384 | ||||||||
\(86\) | 15.4614 | 1.66724 | ||||||||
\(87\) | −4.61369 | −0.494639 | ||||||||
\(88\) | 3.55863 | 0.379351 | ||||||||
\(89\) | −3.70599 | −0.392834 | −0.196417 | − | 0.980520i | \(-0.562931\pi\) | ||||
−0.196417 | + | 0.980520i | \(0.562931\pi\) | |||||||
\(90\) | 3.27121 | 0.344816 | ||||||||
\(91\) | −4.41326 | −0.462635 | ||||||||
\(92\) | −25.6628 | −2.67554 | ||||||||
\(93\) | 12.7668 | 1.32386 | ||||||||
\(94\) | 9.92924 | 1.02412 | ||||||||
\(95\) | 3.64065 | 0.373523 | ||||||||
\(96\) | 15.2427 | 1.55570 | ||||||||
\(97\) | −15.1692 | −1.54020 | −0.770100 | − | 0.637923i | \(-0.779794\pi\) | ||||
−0.770100 | + | 0.637923i | \(0.779794\pi\) | |||||||
\(98\) | −28.1901 | −2.84763 | ||||||||
\(99\) | −4.12282 | −0.414359 | ||||||||
\(100\) | −14.7461 | −1.47461 | ||||||||
\(101\) | 8.31300 | 0.827175 | 0.413587 | − | 0.910464i | \(-0.364276\pi\) | ||||
0.413587 | + | 0.910464i | \(0.364276\pi\) | |||||||
\(102\) | −17.2089 | −1.70394 | ||||||||
\(103\) | 17.1535 | 1.69019 | 0.845095 | − | 0.534617i | \(-0.179544\pi\) | ||||
0.845095 | + | 0.534617i | \(0.179544\pi\) | |||||||
\(104\) | 2.49629 | 0.244782 | ||||||||
\(105\) | −5.36294 | −0.523369 | ||||||||
\(106\) | −6.89422 | −0.669625 | ||||||||
\(107\) | −17.1940 | −1.66221 | −0.831105 | − | 0.556116i | \(-0.812291\pi\) | ||||
−0.831105 | + | 0.556116i | \(0.812291\pi\) | |||||||
\(108\) | −0.813481 | −0.0782773 | ||||||||
\(109\) | −17.0135 | −1.62959 | −0.814797 | − | 0.579746i | \(-0.803152\pi\) | ||||
−0.814797 | + | 0.579746i | \(0.803152\pi\) | |||||||
\(110\) | −1.61246 | −0.153742 | ||||||||
\(111\) | 16.3985 | 1.55647 | ||||||||
\(112\) | −2.51378 | −0.237529 | ||||||||
\(113\) | 4.53839 | 0.426936 | 0.213468 | − | 0.976950i | \(-0.431524\pi\) | ||||
0.213468 | + | 0.976950i | \(0.431524\pi\) | |||||||
\(114\) | 39.8836 | 3.73545 | ||||||||
\(115\) | 4.13784 | 0.385855 | ||||||||
\(116\) | −5.90141 | −0.547932 | ||||||||
\(117\) | −2.89206 | −0.267371 | ||||||||
\(118\) | 25.7973 | 2.37484 | ||||||||
\(119\) | 13.8480 | 1.26945 | ||||||||
\(120\) | 3.03347 | 0.276916 | ||||||||
\(121\) | −8.96777 | −0.815252 | ||||||||
\(122\) | −28.9121 | −2.61757 | ||||||||
\(123\) | −26.4860 | −2.38816 | ||||||||
\(124\) | 16.3302 | 1.46649 | ||||||||
\(125\) | 4.88075 | 0.436548 | ||||||||
\(126\) | −28.8376 | −2.56905 | ||||||||
\(127\) | 11.3985 | 1.01145 | 0.505726 | − | 0.862694i | \(-0.331225\pi\) | ||||
0.505726 | + | 0.862694i | \(0.331225\pi\) | |||||||
\(128\) | 16.9231 | 1.49581 | ||||||||
\(129\) | −16.6108 | −1.46250 | ||||||||
\(130\) | −1.13110 | −0.0992041 | ||||||||
\(131\) | 8.05120 | 0.703437 | 0.351719 | − | 0.936106i | \(-0.385597\pi\) | ||||
0.351719 | + | 0.936106i | \(0.385597\pi\) | |||||||
\(132\) | −10.7439 | −0.935135 | ||||||||
\(133\) | −32.0944 | −2.78294 | ||||||||
\(134\) | −2.85428 | −0.246572 | ||||||||
\(135\) | 0.131165 | 0.0112888 | ||||||||
\(136\) | −7.83293 | −0.671668 | ||||||||
\(137\) | −10.4214 | −0.890361 | −0.445181 | − | 0.895441i | \(-0.646861\pi\) | ||||
−0.445181 | + | 0.895441i | \(0.646861\pi\) | |||||||
\(138\) | 45.3303 | 3.85877 | ||||||||
\(139\) | −8.35576 | −0.708727 | −0.354363 | − | 0.935108i | \(-0.615302\pi\) | ||||
−0.354363 | + | 0.935108i | \(0.615302\pi\) | |||||||
\(140\) | −6.85978 | −0.579757 | ||||||||
\(141\) | −10.6674 | −0.898356 | ||||||||
\(142\) | 22.3128 | 1.87245 | ||||||||
\(143\) | 1.42556 | 0.119212 | ||||||||
\(144\) | −1.64731 | −0.137276 | ||||||||
\(145\) | 0.951534 | 0.0790206 | ||||||||
\(146\) | 17.8532 | 1.47754 | ||||||||
\(147\) | 30.2858 | 2.49793 | ||||||||
\(148\) | 20.9754 | 1.72417 | ||||||||
\(149\) | 3.81003 | 0.312130 | 0.156065 | − | 0.987747i | \(-0.450119\pi\) | ||||
0.156065 | + | 0.987747i | \(0.450119\pi\) | |||||||
\(150\) | 26.0473 | 2.12675 | ||||||||
\(151\) | 14.3357 | 1.16663 | 0.583313 | − | 0.812247i | \(-0.301756\pi\) | ||||
0.583313 | + | 0.812247i | \(0.301756\pi\) | |||||||
\(152\) | 18.1537 | 1.47246 | ||||||||
\(153\) | 9.07477 | 0.733652 | ||||||||
\(154\) | 14.2147 | 1.14545 | ||||||||
\(155\) | −2.63305 | −0.211492 | ||||||||
\(156\) | −7.53659 | −0.603410 | ||||||||
\(157\) | 2.13284 | 0.170219 | 0.0851094 | − | 0.996372i | \(-0.472876\pi\) | ||||
0.0851094 | + | 0.996372i | \(0.472876\pi\) | |||||||
\(158\) | 15.5534 | 1.23736 | ||||||||
\(159\) | 7.40674 | 0.587393 | ||||||||
\(160\) | −3.14367 | −0.248529 | ||||||||
\(161\) | −36.4773 | −2.87482 | ||||||||
\(162\) | 21.0398 | 1.65304 | ||||||||
\(163\) | −0.398816 | −0.0312377 | −0.0156188 | − | 0.999878i | \(-0.504972\pi\) | ||||
−0.0156188 | + | 0.999878i | \(0.504972\pi\) | |||||||
\(164\) | −33.8784 | −2.64546 | ||||||||
\(165\) | 1.73233 | 0.134861 | ||||||||
\(166\) | 5.35180 | 0.415380 | ||||||||
\(167\) | −2.36092 | −0.182693 | −0.0913467 | − | 0.995819i | \(-0.529117\pi\) | ||||
−0.0913467 | + | 0.995819i | \(0.529117\pi\) | |||||||
\(168\) | −26.7417 | −2.06317 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 3.54919 | 0.272211 | ||||||||
\(171\) | −21.0318 | −1.60834 | ||||||||
\(172\) | −21.2470 | −1.62007 | ||||||||
\(173\) | −0.260989 | −0.0198426 | −0.00992132 | − | 0.999951i | \(-0.503158\pi\) | ||||
−0.00992132 | + | 0.999951i | \(0.503158\pi\) | |||||||
\(174\) | 10.4241 | 0.790251 | ||||||||
\(175\) | −20.9602 | −1.58444 | ||||||||
\(176\) | 0.811995 | 0.0612064 | ||||||||
\(177\) | −27.7151 | −2.08320 | ||||||||
\(178\) | 8.37329 | 0.627604 | ||||||||
\(179\) | 22.3568 | 1.67102 | 0.835512 | − | 0.549473i | \(-0.185171\pi\) | ||||
0.835512 | + | 0.549473i | \(0.185171\pi\) | |||||||
\(180\) | −4.49530 | −0.335060 | ||||||||
\(181\) | 13.5208 | 1.00499 | 0.502496 | − | 0.864580i | \(-0.332415\pi\) | ||||
0.502496 | + | 0.864580i | \(0.332415\pi\) | |||||||
\(182\) | 9.97128 | 0.739121 | ||||||||
\(183\) | 31.0614 | 2.29613 | ||||||||
\(184\) | 20.6329 | 1.52108 | ||||||||
\(185\) | −3.38205 | −0.248653 | ||||||||
\(186\) | −28.8453 | −2.11504 | ||||||||
\(187\) | −4.47316 | −0.327110 | ||||||||
\(188\) | −13.6447 | −0.995146 | ||||||||
\(189\) | −1.15629 | −0.0841076 | ||||||||
\(190\) | −8.22566 | −0.596752 | ||||||||
\(191\) | 9.04166 | 0.654231 | 0.327116 | − | 0.944984i | \(-0.393923\pi\) | ||||
0.327116 | + | 0.944984i | \(0.393923\pi\) | |||||||
\(192\) | −31.6739 | −2.28587 | ||||||||
\(193\) | −5.67409 | −0.408430 | −0.204215 | − | 0.978926i | \(-0.565464\pi\) | ||||
−0.204215 | + | 0.978926i | \(0.565464\pi\) | |||||||
\(194\) | 34.2732 | 2.46067 | ||||||||
\(195\) | 1.21519 | 0.0870214 | ||||||||
\(196\) | 38.7388 | 2.76706 | ||||||||
\(197\) | −3.63596 | −0.259051 | −0.129526 | − | 0.991576i | \(-0.541345\pi\) | ||||
−0.129526 | + | 0.991576i | \(0.541345\pi\) | |||||||
\(198\) | 9.31506 | 0.661993 | ||||||||
\(199\) | −8.68652 | −0.615771 | −0.307886 | − | 0.951423i | \(-0.599621\pi\) | ||||
−0.307886 | + | 0.951423i | \(0.599621\pi\) | |||||||
\(200\) | 11.8558 | 0.838335 | ||||||||
\(201\) | 3.06646 | 0.216292 | ||||||||
\(202\) | −18.7823 | −1.32152 | ||||||||
\(203\) | −8.38830 | −0.588743 | ||||||||
\(204\) | 23.6485 | 1.65572 | ||||||||
\(205\) | 5.46251 | 0.381518 | ||||||||
\(206\) | −38.7566 | −2.70030 | ||||||||
\(207\) | −23.9040 | −1.66145 | ||||||||
\(208\) | 0.569596 | 0.0394944 | ||||||||
\(209\) | 10.3671 | 0.717105 | ||||||||
\(210\) | 12.1170 | 0.836151 | ||||||||
\(211\) | 13.1202 | 0.903230 | 0.451615 | − | 0.892213i | \(-0.350848\pi\) | ||||
0.451615 | + | 0.892213i | \(0.350848\pi\) | |||||||
\(212\) | 9.47402 | 0.650678 | ||||||||
\(213\) | −23.9715 | −1.64250 | ||||||||
\(214\) | 38.8481 | 2.65560 | ||||||||
\(215\) | 3.42583 | 0.233640 | ||||||||
\(216\) | 0.654037 | 0.0445016 | ||||||||
\(217\) | 23.2118 | 1.57572 | ||||||||
\(218\) | 38.4401 | 2.60349 | ||||||||
\(219\) | −19.1804 | −1.29609 | ||||||||
\(220\) | 2.21583 | 0.149392 | ||||||||
\(221\) | −3.13782 | −0.211073 | ||||||||
\(222\) | −37.0506 | −2.48667 | ||||||||
\(223\) | 7.26442 | 0.486461 | 0.243231 | − | 0.969968i | \(-0.421793\pi\) | ||||
0.243231 | + | 0.969968i | \(0.421793\pi\) | |||||||
\(224\) | 27.7132 | 1.85167 | ||||||||
\(225\) | −13.7355 | −0.915700 | ||||||||
\(226\) | −10.2540 | −0.682086 | ||||||||
\(227\) | −17.1791 | −1.14022 | −0.570108 | − | 0.821570i | \(-0.693098\pi\) | ||||
−0.570108 | + | 0.821570i | \(0.693098\pi\) | |||||||
\(228\) | −54.8080 | −3.62975 | ||||||||
\(229\) | 13.1285 | 0.867553 | 0.433776 | − | 0.901021i | \(-0.357181\pi\) | ||||
0.433776 | + | 0.901021i | \(0.357181\pi\) | |||||||
\(230\) | −9.34900 | −0.616455 | ||||||||
\(231\) | −15.2714 | −1.00479 | ||||||||
\(232\) | 4.74472 | 0.311506 | ||||||||
\(233\) | 8.50600 | 0.557247 | 0.278623 | − | 0.960400i | \(-0.410122\pi\) | ||||
0.278623 | + | 0.960400i | \(0.410122\pi\) | |||||||
\(234\) | 6.53430 | 0.427161 | ||||||||
\(235\) | 2.20006 | 0.143516 | ||||||||
\(236\) | −35.4506 | −2.30764 | ||||||||
\(237\) | −16.7096 | −1.08541 | ||||||||
\(238\) | −31.2881 | −2.02811 | ||||||||
\(239\) | −16.1972 | −1.04771 | −0.523854 | − | 0.851808i | \(-0.675506\pi\) | ||||
−0.523854 | + | 0.851808i | \(0.675506\pi\) | |||||||
\(240\) | 0.692166 | 0.0446791 | ||||||||
\(241\) | −12.8332 | −0.826657 | −0.413328 | − | 0.910582i | \(-0.635634\pi\) | ||||
−0.413328 | + | 0.910582i | \(0.635634\pi\) | |||||||
\(242\) | 20.2617 | 1.30247 | ||||||||
\(243\) | −21.8179 | −1.39962 | ||||||||
\(244\) | 39.7309 | 2.54351 | ||||||||
\(245\) | −6.24619 | −0.399054 | ||||||||
\(246\) | 59.8422 | 3.81540 | ||||||||
\(247\) | 7.27226 | 0.462723 | ||||||||
\(248\) | −13.1294 | −0.833719 | ||||||||
\(249\) | −5.74965 | −0.364370 | ||||||||
\(250\) | −11.0275 | −0.697442 | ||||||||
\(251\) | −0.126202 | −0.00796582 | −0.00398291 | − | 0.999992i | \(-0.501268\pi\) | ||||
−0.00398291 | + | 0.999992i | \(0.501268\pi\) | |||||||
\(252\) | 39.6285 | 2.49636 | ||||||||
\(253\) | 11.7828 | 0.740781 | ||||||||
\(254\) | −25.7536 | −1.61593 | ||||||||
\(255\) | −3.81304 | −0.238782 | ||||||||
\(256\) | −12.1385 | −0.758659 | ||||||||
\(257\) | 8.29401 | 0.517366 | 0.258683 | − | 0.965962i | \(-0.416711\pi\) | ||||
0.258683 | + | 0.965962i | \(0.416711\pi\) | |||||||
\(258\) | 37.5303 | 2.33653 | ||||||||
\(259\) | 29.8146 | 1.85259 | ||||||||
\(260\) | 1.55436 | 0.0963971 | ||||||||
\(261\) | −5.49696 | −0.340253 | ||||||||
\(262\) | −18.1908 | −1.12383 | ||||||||
\(263\) | 16.7730 | 1.03427 | 0.517133 | − | 0.855905i | \(-0.326999\pi\) | ||||
0.517133 | + | 0.855905i | \(0.326999\pi\) | |||||||
\(264\) | 8.63806 | 0.531636 | ||||||||
\(265\) | −1.52758 | −0.0938383 | ||||||||
\(266\) | 72.5138 | 4.44611 | ||||||||
\(267\) | −8.99576 | −0.550532 | ||||||||
\(268\) | 3.92234 | 0.239595 | ||||||||
\(269\) | −20.5132 | −1.25071 | −0.625355 | − | 0.780341i | \(-0.715046\pi\) | ||||
−0.625355 | + | 0.780341i | \(0.715046\pi\) | |||||||
\(270\) | −0.296352 | −0.0180354 | ||||||||
\(271\) | 24.7716 | 1.50477 | 0.752385 | − | 0.658723i | \(-0.228903\pi\) | ||||
0.752385 | + | 0.658723i | \(0.228903\pi\) | |||||||
\(272\) | −1.78729 | −0.108370 | ||||||||
\(273\) | −10.7126 | −0.648353 | ||||||||
\(274\) | 23.5461 | 1.42247 | ||||||||
\(275\) | 6.77054 | 0.408279 | ||||||||
\(276\) | −62.2929 | −3.74959 | ||||||||
\(277\) | 18.8033 | 1.12978 | 0.564890 | − | 0.825166i | \(-0.308918\pi\) | ||||
0.564890 | + | 0.825166i | \(0.308918\pi\) | |||||||
\(278\) | 18.8789 | 1.13228 | ||||||||
\(279\) | 15.2110 | 0.910657 | ||||||||
\(280\) | 5.51525 | 0.329599 | ||||||||
\(281\) | 29.7889 | 1.77705 | 0.888527 | − | 0.458824i | \(-0.151729\pi\) | ||||
0.888527 | + | 0.458824i | \(0.151729\pi\) | |||||||
\(282\) | 24.1018 | 1.43524 | ||||||||
\(283\) | 19.0897 | 1.13476 | 0.567381 | − | 0.823455i | \(-0.307957\pi\) | ||||
0.567381 | + | 0.823455i | \(0.307957\pi\) | |||||||
\(284\) | −30.6622 | −1.81947 | ||||||||
\(285\) | 8.83717 | 0.523469 | ||||||||
\(286\) | −3.22091 | −0.190456 | ||||||||
\(287\) | −48.1551 | −2.84250 | ||||||||
\(288\) | 18.1608 | 1.07014 | ||||||||
\(289\) | −7.15408 | −0.420828 | ||||||||
\(290\) | −2.14989 | −0.126246 | ||||||||
\(291\) | −36.8211 | −2.15849 | ||||||||
\(292\) | −24.5338 | −1.43573 | ||||||||
\(293\) | −20.1293 | −1.17597 | −0.587983 | − | 0.808873i | \(-0.700078\pi\) | ||||
−0.587983 | + | 0.808873i | \(0.700078\pi\) | |||||||
\(294\) | −68.4275 | −3.99077 | ||||||||
\(295\) | 5.71601 | 0.332799 | ||||||||
\(296\) | −16.8642 | −0.980212 | ||||||||
\(297\) | 0.373502 | 0.0216728 | ||||||||
\(298\) | −8.60836 | −0.498669 | ||||||||
\(299\) | 8.26540 | 0.478000 | ||||||||
\(300\) | −35.7941 | −2.06657 | ||||||||
\(301\) | −30.2006 | −1.74074 | ||||||||
\(302\) | −32.3901 | −1.86384 | ||||||||
\(303\) | 20.1786 | 1.15923 | ||||||||
\(304\) | 4.14225 | 0.237574 | ||||||||
\(305\) | −6.40615 | −0.366815 | ||||||||
\(306\) | −20.5035 | −1.17211 | ||||||||
\(307\) | −21.2467 | −1.21261 | −0.606307 | − | 0.795231i | \(-0.707350\pi\) | ||||
−0.606307 | + | 0.795231i | \(0.707350\pi\) | |||||||
\(308\) | −19.5338 | −1.11304 | ||||||||
\(309\) | 41.6378 | 2.36869 | ||||||||
\(310\) | 5.94909 | 0.337886 | ||||||||
\(311\) | −10.1016 | −0.572808 | −0.286404 | − | 0.958109i | \(-0.592460\pi\) | ||||
−0.286404 | + | 0.958109i | \(0.592460\pi\) | |||||||
\(312\) | 6.05940 | 0.343046 | ||||||||
\(313\) | −21.9204 | −1.23901 | −0.619507 | − | 0.784991i | \(-0.712667\pi\) | ||||
−0.619507 | + | 0.784991i | \(0.712667\pi\) | |||||||
\(314\) | −4.81891 | −0.271947 | ||||||||
\(315\) | −6.38965 | −0.360016 | ||||||||
\(316\) | −21.3734 | −1.20235 | ||||||||
\(317\) | −24.1933 | −1.35883 | −0.679416 | − | 0.733753i | \(-0.737767\pi\) | ||||
−0.679416 | + | 0.733753i | \(0.737767\pi\) | |||||||
\(318\) | −16.7347 | −0.938437 | ||||||||
\(319\) | 2.70957 | 0.151707 | ||||||||
\(320\) | 6.53248 | 0.365177 | ||||||||
\(321\) | −41.7361 | −2.32948 | ||||||||
\(322\) | 82.4166 | 4.59290 | ||||||||
\(323\) | −22.8191 | −1.26969 | ||||||||
\(324\) | −28.9129 | −1.60627 | ||||||||
\(325\) | 4.74938 | 0.263448 | ||||||||
\(326\) | 0.901081 | 0.0499063 | ||||||||
\(327\) | −41.2978 | −2.28377 | ||||||||
\(328\) | 27.2382 | 1.50398 | ||||||||
\(329\) | −19.3947 | −1.06927 | ||||||||
\(330\) | −3.91401 | −0.215459 | ||||||||
\(331\) | 9.01493 | 0.495505 | 0.247753 | − | 0.968823i | \(-0.420308\pi\) | ||||
0.247753 | + | 0.968823i | \(0.420308\pi\) | |||||||
\(332\) | −7.35443 | −0.403627 | ||||||||
\(333\) | 19.5379 | 1.07067 | ||||||||
\(334\) | 5.33424 | 0.291877 | ||||||||
\(335\) | −0.632432 | −0.0345535 | ||||||||
\(336\) | −6.10183 | −0.332882 | ||||||||
\(337\) | −21.9916 | −1.19796 | −0.598980 | − | 0.800764i | \(-0.704427\pi\) | ||||
−0.598980 | + | 0.800764i | \(0.704427\pi\) | |||||||
\(338\) | −2.25939 | −0.122895 | ||||||||
\(339\) | 11.0163 | 0.598323 | ||||||||
\(340\) | −4.87729 | −0.264508 | ||||||||
\(341\) | −7.49784 | −0.406031 | ||||||||
\(342\) | 47.5192 | 2.56954 | ||||||||
\(343\) | 24.1708 | 1.30510 | ||||||||
\(344\) | 17.0825 | 0.921029 | ||||||||
\(345\) | 10.0440 | 0.540751 | ||||||||
\(346\) | 0.589677 | 0.0317012 | ||||||||
\(347\) | −13.8394 | −0.742939 | −0.371469 | − | 0.928445i | \(-0.621146\pi\) | ||||
−0.371469 | + | 0.928445i | \(0.621146\pi\) | |||||||
\(348\) | −14.3248 | −0.767891 | ||||||||
\(349\) | 3.59936 | 0.192669 | 0.0963347 | − | 0.995349i | \(-0.469288\pi\) | ||||
0.0963347 | + | 0.995349i | \(0.469288\pi\) | |||||||
\(350\) | 47.3574 | 2.53136 | ||||||||
\(351\) | 0.262003 | 0.0139847 | ||||||||
\(352\) | −8.95187 | −0.477136 | ||||||||
\(353\) | −3.85925 | −0.205407 | −0.102704 | − | 0.994712i | \(-0.532749\pi\) | ||||
−0.102704 | + | 0.994712i | \(0.532749\pi\) | |||||||
\(354\) | 62.6193 | 3.32818 | ||||||||
\(355\) | 4.94393 | 0.262396 | ||||||||
\(356\) | −11.5066 | −0.609846 | ||||||||
\(357\) | 33.6141 | 1.77905 | ||||||||
\(358\) | −50.5127 | −2.66968 | ||||||||
\(359\) | 8.30954 | 0.438561 | 0.219280 | − | 0.975662i | \(-0.429629\pi\) | ||||
0.219280 | + | 0.975662i | \(0.429629\pi\) | |||||||
\(360\) | 3.61421 | 0.190486 | ||||||||
\(361\) | 33.8858 | 1.78346 | ||||||||
\(362\) | −30.5488 | −1.60561 | ||||||||
\(363\) | −21.7680 | −1.14252 | ||||||||
\(364\) | −13.7025 | −0.718207 | ||||||||
\(365\) | 3.95580 | 0.207056 | ||||||||
\(366\) | −70.1799 | −3.66836 | ||||||||
\(367\) | 18.5090 | 0.966162 | 0.483081 | − | 0.875576i | \(-0.339518\pi\) | ||||
0.483081 | + | 0.875576i | \(0.339518\pi\) | |||||||
\(368\) | 4.70794 | 0.245418 | ||||||||
\(369\) | −31.5566 | −1.64277 | ||||||||
\(370\) | 7.64137 | 0.397256 | ||||||||
\(371\) | 13.4664 | 0.699143 | ||||||||
\(372\) | 39.6391 | 2.05519 | ||||||||
\(373\) | −8.31567 | −0.430569 | −0.215284 | − | 0.976551i | \(-0.569068\pi\) | ||||
−0.215284 | + | 0.976551i | \(0.569068\pi\) | |||||||
\(374\) | 10.1066 | 0.522601 | ||||||||
\(375\) | 11.8473 | 0.611793 | ||||||||
\(376\) | 10.9703 | 0.565753 | ||||||||
\(377\) | 1.90070 | 0.0978913 | ||||||||
\(378\) | 2.61251 | 0.134373 | ||||||||
\(379\) | 25.1001 | 1.28930 | 0.644652 | − | 0.764476i | \(-0.277002\pi\) | ||||
0.644652 | + | 0.764476i | \(0.277002\pi\) | |||||||
\(380\) | 11.3037 | 0.579867 | ||||||||
\(381\) | 27.6682 | 1.41748 | ||||||||
\(382\) | −20.4286 | −1.04522 | ||||||||
\(383\) | 19.9566 | 1.01973 | 0.509867 | − | 0.860253i | \(-0.329694\pi\) | ||||
0.509867 | + | 0.860253i | \(0.329694\pi\) | |||||||
\(384\) | 41.0785 | 2.09628 | ||||||||
\(385\) | 3.14960 | 0.160519 | ||||||||
\(386\) | 12.8200 | 0.652521 | ||||||||
\(387\) | −19.7908 | −1.00603 | ||||||||
\(388\) | −47.0982 | −2.39105 | ||||||||
\(389\) | −2.93457 | −0.148788 | −0.0743942 | − | 0.997229i | \(-0.523702\pi\) | ||||
−0.0743942 | + | 0.997229i | \(0.523702\pi\) | |||||||
\(390\) | −2.74559 | −0.139028 | ||||||||
\(391\) | −25.9353 | −1.31161 | ||||||||
\(392\) | −31.1459 | −1.57311 | ||||||||
\(393\) | 19.5431 | 0.985821 | ||||||||
\(394\) | 8.21505 | 0.413868 | ||||||||
\(395\) | 3.44622 | 0.173398 | ||||||||
\(396\) | −12.8007 | −0.643261 | ||||||||
\(397\) | 9.31463 | 0.467488 | 0.233744 | − | 0.972298i | \(-0.424902\pi\) | ||||
0.233744 | + | 0.972298i | \(0.424902\pi\) | |||||||
\(398\) | 19.6263 | 0.983776 | ||||||||
\(399\) | −77.9045 | −3.90010 | ||||||||
\(400\) | 2.70523 | 0.135261 | ||||||||
\(401\) | 3.11165 | 0.155389 | 0.0776943 | − | 0.996977i | \(-0.475244\pi\) | ||||
0.0776943 | + | 0.996977i | \(0.475244\pi\) | |||||||
\(402\) | −6.92835 | −0.345554 | ||||||||
\(403\) | −5.25956 | −0.261997 | ||||||||
\(404\) | 25.8106 | 1.28413 | ||||||||
\(405\) | 4.66187 | 0.231650 | ||||||||
\(406\) | 18.9525 | 0.940595 | ||||||||
\(407\) | −9.63067 | −0.477374 | ||||||||
\(408\) | −19.0133 | −0.941299 | ||||||||
\(409\) | 3.93964 | 0.194802 | 0.0974012 | − | 0.995245i | \(-0.468947\pi\) | ||||
0.0974012 | + | 0.995245i | \(0.468947\pi\) | |||||||
\(410\) | −12.3420 | −0.609526 | ||||||||
\(411\) | −25.2965 | −1.24778 | ||||||||
\(412\) | 53.2592 | 2.62389 | ||||||||
\(413\) | −50.3898 | −2.47952 | ||||||||
\(414\) | 54.0086 | 2.65438 | ||||||||
\(415\) | 1.18582 | 0.0582095 | ||||||||
\(416\) | −6.27953 | −0.307879 | ||||||||
\(417\) | −20.2824 | −0.993234 | ||||||||
\(418\) | −23.4233 | −1.14567 | ||||||||
\(419\) | 13.7535 | 0.671905 | 0.335952 | − | 0.941879i | \(-0.390942\pi\) | ||||
0.335952 | + | 0.941879i | \(0.390942\pi\) | |||||||
\(420\) | −16.6511 | −0.812492 | ||||||||
\(421\) | 28.7304 | 1.40024 | 0.700118 | − | 0.714028i | \(-0.253131\pi\) | ||||
0.700118 | + | 0.714028i | \(0.253131\pi\) | |||||||
\(422\) | −29.6436 | −1.44303 | ||||||||
\(423\) | −12.7096 | −0.617962 | ||||||||
\(424\) | −7.61709 | −0.369919 | ||||||||
\(425\) | −14.9027 | −0.722887 | ||||||||
\(426\) | 54.1611 | 2.62411 | ||||||||
\(427\) | 56.4738 | 2.73296 | ||||||||
\(428\) | −53.3849 | −2.58046 | ||||||||
\(429\) | 3.46035 | 0.167067 | ||||||||
\(430\) | −7.74030 | −0.373271 | ||||||||
\(431\) | −4.37709 | −0.210837 | −0.105419 | − | 0.994428i | \(-0.533618\pi\) | ||||
−0.105419 | + | 0.994428i | \(0.533618\pi\) | |||||||
\(432\) | 0.149236 | 0.00718012 | ||||||||
\(433\) | 29.8842 | 1.43614 | 0.718071 | − | 0.695970i | \(-0.245025\pi\) | ||||
0.718071 | + | 0.695970i | \(0.245025\pi\) | |||||||
\(434\) | −52.4446 | −2.51742 | ||||||||
\(435\) | 2.30971 | 0.110742 | ||||||||
\(436\) | −52.8243 | −2.52983 | ||||||||
\(437\) | 60.1081 | 2.87536 | ||||||||
\(438\) | 43.3360 | 2.07068 | ||||||||
\(439\) | 15.6911 | 0.748896 | 0.374448 | − | 0.927248i | \(-0.377832\pi\) | ||||
0.374448 | + | 0.927248i | \(0.377832\pi\) | |||||||
\(440\) | −1.78153 | −0.0849309 | ||||||||
\(441\) | 36.0838 | 1.71828 | ||||||||
\(442\) | 7.08957 | 0.337216 | ||||||||
\(443\) | −22.0329 | −1.04682 | −0.523408 | − | 0.852082i | \(-0.675340\pi\) | ||||
−0.523408 | + | 0.852082i | \(0.675340\pi\) | |||||||
\(444\) | 50.9149 | 2.41631 | ||||||||
\(445\) | 1.85530 | 0.0879497 | ||||||||
\(446\) | −16.4132 | −0.777186 | ||||||||
\(447\) | 9.24831 | 0.437430 | ||||||||
\(448\) | −57.5874 | −2.72075 | ||||||||
\(449\) | 12.5016 | 0.589985 | 0.294992 | − | 0.955500i | \(-0.404683\pi\) | ||||
0.294992 | + | 0.955500i | \(0.404683\pi\) | |||||||
\(450\) | 31.0339 | 1.46295 | ||||||||
\(451\) | 15.5550 | 0.732455 | ||||||||
\(452\) | 14.0910 | 0.662787 | ||||||||
\(453\) | 34.7980 | 1.63495 | ||||||||
\(454\) | 38.8143 | 1.82164 | ||||||||
\(455\) | 2.20937 | 0.103577 | ||||||||
\(456\) | 44.0655 | 2.06356 | ||||||||
\(457\) | 31.6221 | 1.47922 | 0.739611 | − | 0.673035i | \(-0.235010\pi\) | ||||
0.739611 | + | 0.673035i | \(0.235010\pi\) | |||||||
\(458\) | −29.6623 | −1.38603 | ||||||||
\(459\) | −0.822119 | −0.0383732 | ||||||||
\(460\) | 12.8474 | 0.599012 | ||||||||
\(461\) | 15.7316 | 0.732695 | 0.366348 | − | 0.930478i | \(-0.380608\pi\) | ||||
0.366348 | + | 0.930478i | \(0.380608\pi\) | |||||||
\(462\) | 34.5041 | 1.60528 | ||||||||
\(463\) | −1.00000 | −0.0464739 | ||||||||
\(464\) | 1.08263 | 0.0502600 | ||||||||
\(465\) | −6.39135 | −0.296392 | ||||||||
\(466\) | −19.2184 | −0.890275 | ||||||||
\(467\) | 35.0632 | 1.62253 | 0.811265 | − | 0.584679i | \(-0.198779\pi\) | ||||
0.811265 | + | 0.584679i | \(0.198779\pi\) | |||||||
\(468\) | −8.97943 | −0.415074 | ||||||||
\(469\) | 5.57524 | 0.257441 | ||||||||
\(470\) | −4.97080 | −0.229286 | ||||||||
\(471\) | 5.17716 | 0.238551 | ||||||||
\(472\) | 28.5022 | 1.31192 | ||||||||
\(473\) | 9.75536 | 0.448552 | ||||||||
\(474\) | 37.7536 | 1.73408 | ||||||||
\(475\) | 34.5387 | 1.58475 | ||||||||
\(476\) | 42.9960 | 1.97072 | ||||||||
\(477\) | 8.82472 | 0.404056 | ||||||||
\(478\) | 36.5957 | 1.67385 | ||||||||
\(479\) | 12.9719 | 0.592701 | 0.296350 | − | 0.955079i | \(-0.404230\pi\) | ||||
0.296350 | + | 0.955079i | \(0.404230\pi\) | |||||||
\(480\) | −7.63081 | −0.348297 | ||||||||
\(481\) | −6.75569 | −0.308033 | ||||||||
\(482\) | 28.9952 | 1.32069 | ||||||||
\(483\) | −88.5435 | −4.02887 | ||||||||
\(484\) | −27.8436 | −1.26562 | ||||||||
\(485\) | 7.59404 | 0.344828 | ||||||||
\(486\) | 49.2953 | 2.23608 | ||||||||
\(487\) | 15.8936 | 0.720207 | 0.360103 | − | 0.932912i | \(-0.382741\pi\) | ||||
0.360103 | + | 0.932912i | \(0.382741\pi\) | |||||||
\(488\) | −31.9436 | −1.44602 | ||||||||
\(489\) | −0.968068 | −0.0437776 | ||||||||
\(490\) | 14.1126 | 0.637542 | ||||||||
\(491\) | −2.49045 | −0.112392 | −0.0561962 | − | 0.998420i | \(-0.517897\pi\) | ||||
−0.0561962 | + | 0.998420i | \(0.517897\pi\) | |||||||
\(492\) | −82.2351 | −3.70744 | ||||||||
\(493\) | −5.96407 | −0.268608 | ||||||||
\(494\) | −16.4309 | −0.739261 | ||||||||
\(495\) | 2.06397 | 0.0927687 | ||||||||
\(496\) | −2.99583 | −0.134517 | ||||||||
\(497\) | −43.5834 | −1.95498 | ||||||||
\(498\) | 12.9907 | 0.582128 | ||||||||
\(499\) | −14.9183 | −0.667837 | −0.333918 | − | 0.942602i | \(-0.608371\pi\) | ||||
−0.333918 | + | 0.942602i | \(0.608371\pi\) | |||||||
\(500\) | 15.1540 | 0.677708 | ||||||||
\(501\) | −5.73079 | −0.256033 | ||||||||
\(502\) | 0.285141 | 0.0127265 | ||||||||
\(503\) | 4.68926 | 0.209084 | 0.104542 | − | 0.994520i | \(-0.466662\pi\) | ||||
0.104542 | + | 0.994520i | \(0.466662\pi\) | |||||||
\(504\) | −31.8613 | −1.41921 | ||||||||
\(505\) | −4.16167 | −0.185192 | ||||||||
\(506\) | −26.6221 | −1.18350 | ||||||||
\(507\) | 2.42736 | 0.107803 | ||||||||
\(508\) | 35.3906 | 1.57020 | ||||||||
\(509\) | −1.28176 | −0.0568131 | −0.0284065 | − | 0.999596i | \(-0.509043\pi\) | ||||
−0.0284065 | + | 0.999596i | \(0.509043\pi\) | |||||||
\(510\) | 8.61516 | 0.381486 | ||||||||
\(511\) | −34.8725 | −1.54267 | ||||||||
\(512\) | −6.42056 | −0.283751 | ||||||||
\(513\) | 1.90536 | 0.0841235 | ||||||||
\(514\) | −18.7394 | −0.826560 | ||||||||
\(515\) | −8.58744 | −0.378408 | ||||||||
\(516\) | −51.5741 | −2.27042 | ||||||||
\(517\) | 6.26486 | 0.275528 | ||||||||
\(518\) | −67.3629 | −2.95976 | ||||||||
\(519\) | −0.633514 | −0.0278082 | ||||||||
\(520\) | −1.24970 | −0.0548030 | ||||||||
\(521\) | 9.27993 | 0.406561 | 0.203281 | − | 0.979121i | \(-0.434840\pi\) | ||||
0.203281 | + | 0.979121i | \(0.434840\pi\) | |||||||
\(522\) | 12.4198 | 0.543599 | ||||||||
\(523\) | 42.2067 | 1.84557 | 0.922786 | − | 0.385313i | \(-0.125907\pi\) | ||||
0.922786 | + | 0.385313i | \(0.125907\pi\) | |||||||
\(524\) | 24.9978 | 1.09203 | ||||||||
\(525\) | −50.8780 | −2.22050 | ||||||||
\(526\) | −37.8967 | −1.65237 | ||||||||
\(527\) | 16.5036 | 0.718906 | ||||||||
\(528\) | 1.97100 | 0.0857769 | ||||||||
\(529\) | 45.3168 | 1.97030 | ||||||||
\(530\) | 3.45140 | 0.149919 | ||||||||
\(531\) | −33.0210 | −1.43299 | ||||||||
\(532\) | −99.6483 | −4.32030 | ||||||||
\(533\) | 10.9114 | 0.472627 | ||||||||
\(534\) | 20.3250 | 0.879547 | ||||||||
\(535\) | 8.60771 | 0.372144 | ||||||||
\(536\) | −3.15355 | −0.136213 | ||||||||
\(537\) | 54.2679 | 2.34183 | ||||||||
\(538\) | 46.3473 | 1.99817 | ||||||||
\(539\) | −17.7865 | −0.766121 | ||||||||
\(540\) | 0.407247 | 0.0175251 | ||||||||
\(541\) | −42.4956 | −1.82703 | −0.913514 | − | 0.406807i | \(-0.866642\pi\) | ||||
−0.913514 | + | 0.406807i | \(0.866642\pi\) | |||||||
\(542\) | −55.9689 | −2.40407 | ||||||||
\(543\) | 32.8198 | 1.40843 | ||||||||
\(544\) | 19.7040 | 0.844804 | ||||||||
\(545\) | 8.51731 | 0.364842 | ||||||||
\(546\) | 24.2039 | 1.03583 | ||||||||
\(547\) | 23.0202 | 0.984273 | 0.492136 | − | 0.870518i | \(-0.336216\pi\) | ||||
0.492136 | + | 0.870518i | \(0.336216\pi\) | |||||||
\(548\) | −32.3569 | −1.38222 | ||||||||
\(549\) | 37.0080 | 1.57946 | ||||||||
\(550\) | −15.2973 | −0.652279 | ||||||||
\(551\) | 13.8224 | 0.588855 | ||||||||
\(552\) | 50.0833 | 2.13169 | ||||||||
\(553\) | −30.3804 | −1.29190 | ||||||||
\(554\) | −42.4840 | −1.80497 | ||||||||
\(555\) | −8.20944 | −0.348471 | ||||||||
\(556\) | −25.9434 | −1.10025 | ||||||||
\(557\) | −33.1487 | −1.40456 | −0.702279 | − | 0.711902i | \(-0.747834\pi\) | ||||
−0.702279 | + | 0.711902i | \(0.747834\pi\) | |||||||
\(558\) | −34.3676 | −1.45489 | ||||||||
\(559\) | 6.84316 | 0.289435 | ||||||||
\(560\) | 1.25845 | 0.0531793 | ||||||||
\(561\) | −10.8580 | −0.458423 | ||||||||
\(562\) | −67.3047 | −2.83908 | ||||||||
\(563\) | −32.9532 | −1.38881 | −0.694406 | − | 0.719583i | \(-0.744333\pi\) | ||||
−0.694406 | + | 0.719583i | \(0.744333\pi\) | |||||||
\(564\) | −33.1207 | −1.39463 | ||||||||
\(565\) | −2.27202 | −0.0955845 | ||||||||
\(566\) | −43.1310 | −1.81293 | ||||||||
\(567\) | −41.0970 | −1.72591 | ||||||||
\(568\) | 24.6523 | 1.03439 | ||||||||
\(569\) | −3.53665 | −0.148264 | −0.0741320 | − | 0.997248i | \(-0.523619\pi\) | ||||
−0.0741320 | + | 0.997248i | \(0.523619\pi\) | |||||||
\(570\) | −19.9666 | −0.836310 | ||||||||
\(571\) | −9.42884 | −0.394585 | −0.197292 | − | 0.980345i | \(-0.563215\pi\) | ||||
−0.197292 | + | 0.980345i | \(0.563215\pi\) | |||||||
\(572\) | 4.42616 | 0.185067 | ||||||||
\(573\) | 21.9473 | 0.916863 | ||||||||
\(574\) | 108.801 | 4.54127 | ||||||||
\(575\) | 39.2555 | 1.63707 | ||||||||
\(576\) | −37.7377 | −1.57241 | ||||||||
\(577\) | −44.3051 | −1.84445 | −0.922223 | − | 0.386659i | \(-0.873629\pi\) | ||||
−0.922223 | + | 0.386659i | \(0.873629\pi\) | |||||||
\(578\) | 16.1639 | 0.672329 | ||||||||
\(579\) | −13.7730 | −0.572388 | ||||||||
\(580\) | 2.95437 | 0.122674 | ||||||||
\(581\) | −10.4536 | −0.433690 | ||||||||
\(582\) | 83.1933 | 3.44847 | ||||||||
\(583\) | −4.34991 | −0.180155 | ||||||||
\(584\) | 19.7251 | 0.816232 | ||||||||
\(585\) | 1.44783 | 0.0598604 | ||||||||
\(586\) | 45.4800 | 1.87876 | ||||||||
\(587\) | −4.45810 | −0.184006 | −0.0920028 | − | 0.995759i | \(-0.529327\pi\) | ||||
−0.0920028 | + | 0.995759i | \(0.529327\pi\) | |||||||
\(588\) | 94.0329 | 3.87785 | ||||||||
\(589\) | −38.2489 | −1.57602 | ||||||||
\(590\) | −12.9147 | −0.531690 | ||||||||
\(591\) | −8.82577 | −0.363044 | ||||||||
\(592\) | −3.84802 | −0.158152 | ||||||||
\(593\) | −34.5096 | −1.41714 | −0.708571 | − | 0.705640i | \(-0.750660\pi\) | ||||
−0.708571 | + | 0.705640i | \(0.750660\pi\) | |||||||
\(594\) | −0.843888 | −0.0346251 | ||||||||
\(595\) | −6.93262 | −0.284210 | ||||||||
\(596\) | 11.8296 | 0.484559 | ||||||||
\(597\) | −21.0853 | −0.862964 | ||||||||
\(598\) | −18.6748 | −0.763668 | ||||||||
\(599\) | −41.1084 | −1.67965 | −0.839823 | − | 0.542861i | \(-0.817341\pi\) | ||||
−0.839823 | + | 0.542861i | \(0.817341\pi\) | |||||||
\(600\) | 28.7784 | 1.17487 | ||||||||
\(601\) | −12.3698 | −0.504573 | −0.252286 | − | 0.967653i | \(-0.581182\pi\) | ||||
−0.252286 | + | 0.967653i | \(0.581182\pi\) | |||||||
\(602\) | 68.2351 | 2.78105 | ||||||||
\(603\) | 3.65352 | 0.148783 | ||||||||
\(604\) | 44.5104 | 1.81110 | ||||||||
\(605\) | 4.48946 | 0.182523 | ||||||||
\(606\) | −45.5914 | −1.85203 | ||||||||
\(607\) | −17.4467 | −0.708139 | −0.354070 | − | 0.935219i | \(-0.615202\pi\) | ||||
−0.354070 | + | 0.935219i | \(0.615202\pi\) | |||||||
\(608\) | −45.6664 | −1.85202 | ||||||||
\(609\) | −20.3614 | −0.825086 | ||||||||
\(610\) | 14.4740 | 0.586035 | ||||||||
\(611\) | 4.39465 | 0.177789 | ||||||||
\(612\) | 28.1758 | 1.13894 | ||||||||
\(613\) | −21.9841 | −0.887931 | −0.443966 | − | 0.896044i | \(-0.646429\pi\) | ||||
−0.443966 | + | 0.896044i | \(0.646429\pi\) | |||||||
\(614\) | 48.0046 | 1.93731 | ||||||||
\(615\) | 13.2595 | 0.534673 | ||||||||
\(616\) | 15.7051 | 0.632778 | ||||||||
\(617\) | −17.1761 | −0.691485 | −0.345743 | − | 0.938329i | \(-0.612373\pi\) | ||||
−0.345743 | + | 0.938329i | \(0.612373\pi\) | |||||||
\(618\) | −94.0761 | −3.78430 | ||||||||
\(619\) | 12.1978 | 0.490273 | 0.245136 | − | 0.969489i | \(-0.421167\pi\) | ||||
0.245136 | + | 0.969489i | \(0.421167\pi\) | |||||||
\(620\) | −8.17523 | −0.328325 | ||||||||
\(621\) | 2.16556 | 0.0869010 | ||||||||
\(622\) | 22.8234 | 0.915136 | ||||||||
\(623\) | −16.3555 | −0.655269 | ||||||||
\(624\) | 1.38261 | 0.0553488 | ||||||||
\(625\) | 21.3035 | 0.852139 | ||||||||
\(626\) | 49.5267 | 1.97949 | ||||||||
\(627\) | 25.1646 | 1.00498 | ||||||||
\(628\) | 6.62214 | 0.264252 | ||||||||
\(629\) | 21.1981 | 0.845226 | ||||||||
\(630\) | 14.4367 | 0.575173 | ||||||||
\(631\) | 24.4143 | 0.971918 | 0.485959 | − | 0.873982i | \(-0.338470\pi\) | ||||
0.485959 | + | 0.873982i | \(0.338470\pi\) | |||||||
\(632\) | 17.1842 | 0.683551 | ||||||||
\(633\) | 31.8473 | 1.26582 | ||||||||
\(634\) | 54.6622 | 2.17091 | ||||||||
\(635\) | −5.70633 | −0.226449 | ||||||||
\(636\) | 22.9968 | 0.911884 | ||||||||
\(637\) | −12.4769 | −0.494351 | ||||||||
\(638\) | −6.12199 | −0.242372 | ||||||||
\(639\) | −28.5608 | −1.12985 | ||||||||
\(640\) | −8.47209 | −0.334889 | ||||||||
\(641\) | −37.7005 | −1.48908 | −0.744540 | − | 0.667578i | \(-0.767331\pi\) | ||||
−0.744540 | + | 0.667578i | \(0.767331\pi\) | |||||||
\(642\) | 94.2981 | 3.72165 | ||||||||
\(643\) | −47.1181 | −1.85816 | −0.929079 | − | 0.369882i | \(-0.879398\pi\) | ||||
−0.929079 | + | 0.369882i | \(0.879398\pi\) | |||||||
\(644\) | −113.257 | −4.46294 | ||||||||
\(645\) | 8.31572 | 0.327431 | ||||||||
\(646\) | 51.5572 | 2.02849 | ||||||||
\(647\) | −19.8341 | −0.779760 | −0.389880 | − | 0.920866i | \(-0.627483\pi\) | ||||
−0.389880 | + | 0.920866i | \(0.627483\pi\) | |||||||
\(648\) | 23.2459 | 0.913185 | ||||||||
\(649\) | 16.2768 | 0.638921 | ||||||||
\(650\) | −10.7307 | −0.420893 | ||||||||
\(651\) | 56.3433 | 2.20827 | ||||||||
\(652\) | −1.23826 | −0.0484942 | ||||||||
\(653\) | 17.5247 | 0.685796 | 0.342898 | − | 0.939373i | \(-0.388592\pi\) | ||||
0.342898 | + | 0.939373i | \(0.388592\pi\) | |||||||
\(654\) | 93.3078 | 3.64863 | ||||||||
\(655\) | −4.03061 | −0.157489 | ||||||||
\(656\) | 6.21512 | 0.242660 | ||||||||
\(657\) | −22.8524 | −0.891557 | ||||||||
\(658\) | 43.8203 | 1.70829 | ||||||||
\(659\) | 19.2598 | 0.750254 | 0.375127 | − | 0.926973i | \(-0.377599\pi\) | ||||
0.375127 | + | 0.926973i | \(0.377599\pi\) | |||||||
\(660\) | 5.37862 | 0.209363 | ||||||||
\(661\) | 33.1412 | 1.28904 | 0.644521 | − | 0.764586i | \(-0.277057\pi\) | ||||
0.644521 | + | 0.764586i | \(0.277057\pi\) | |||||||
\(662\) | −20.3683 | −0.791635 | ||||||||
\(663\) | −7.61661 | −0.295805 | ||||||||
\(664\) | 5.91295 | 0.229467 | ||||||||
\(665\) | 16.0671 | 0.623057 | ||||||||
\(666\) | −44.1437 | −1.71054 | ||||||||
\(667\) | 15.7101 | 0.608297 | ||||||||
\(668\) | −7.33030 | −0.283618 | ||||||||
\(669\) | 17.6333 | 0.681744 | ||||||||
\(670\) | 1.42891 | 0.0552037 | ||||||||
\(671\) | −18.2421 | −0.704227 | ||||||||
\(672\) | 67.2698 | 2.59499 | ||||||||
\(673\) | −41.3761 | −1.59493 | −0.797466 | − | 0.603363i | \(-0.793827\pi\) | ||||
−0.797466 | + | 0.603363i | \(0.793827\pi\) | |||||||
\(674\) | 49.6877 | 1.91390 | ||||||||
\(675\) | 1.24435 | 0.0478951 | ||||||||
\(676\) | 3.10485 | 0.119417 | ||||||||
\(677\) | −0.406026 | −0.0156048 | −0.00780242 | − | 0.999970i | \(-0.502484\pi\) | ||||
−0.00780242 | + | 0.999970i | \(0.502484\pi\) | |||||||
\(678\) | −24.8901 | −0.955900 | ||||||||
\(679\) | −66.9457 | −2.56914 | ||||||||
\(680\) | 3.92133 | 0.150376 | ||||||||
\(681\) | −41.6997 | −1.59794 | ||||||||
\(682\) | 16.9406 | 0.648687 | ||||||||
\(683\) | −21.2673 | −0.813771 | −0.406885 | − | 0.913479i | \(-0.633385\pi\) | ||||
−0.406885 | + | 0.913479i | \(0.633385\pi\) | |||||||
\(684\) | −65.3008 | −2.49684 | ||||||||
\(685\) | 5.21719 | 0.199338 | ||||||||
\(686\) | −54.6113 | −2.08507 | ||||||||
\(687\) | 31.8675 | 1.21582 | ||||||||
\(688\) | 3.89784 | 0.148604 | ||||||||
\(689\) | −3.05136 | −0.116248 | ||||||||
\(690\) | −22.6934 | −0.863921 | ||||||||
\(691\) | −25.6566 | −0.976023 | −0.488011 | − | 0.872837i | \(-0.662278\pi\) | ||||
−0.488011 | + | 0.872837i | \(0.662278\pi\) | |||||||
\(692\) | −0.810333 | −0.0308042 | ||||||||
\(693\) | −18.1951 | −0.691173 | ||||||||
\(694\) | 31.2687 | 1.18694 | ||||||||
\(695\) | 4.18308 | 0.158673 | ||||||||
\(696\) | 11.5171 | 0.436556 | ||||||||
\(697\) | −34.2382 | −1.29686 | ||||||||
\(698\) | −8.13237 | −0.307815 | ||||||||
\(699\) | 20.6471 | 0.780945 | ||||||||
\(700\) | −65.0784 | −2.45973 | ||||||||
\(701\) | −20.3870 | −0.770007 | −0.385003 | − | 0.922915i | \(-0.625800\pi\) | ||||
−0.385003 | + | 0.922915i | \(0.625800\pi\) | |||||||
\(702\) | −0.591968 | −0.0223424 | ||||||||
\(703\) | −49.1292 | −1.85294 | ||||||||
\(704\) | 18.6018 | 0.701081 | ||||||||
\(705\) | 5.34033 | 0.201128 | ||||||||
\(706\) | 8.71956 | 0.328165 | ||||||||
\(707\) | 36.6874 | 1.37977 | ||||||||
\(708\) | −86.0514 | −3.23401 | ||||||||
\(709\) | −14.8967 | −0.559456 | −0.279728 | − | 0.960079i | \(-0.590244\pi\) | ||||
−0.279728 | + | 0.960079i | \(0.590244\pi\) | |||||||
\(710\) | −11.1703 | −0.419213 | ||||||||
\(711\) | −19.9086 | −0.746631 | ||||||||
\(712\) | 9.25125 | 0.346705 | ||||||||
\(713\) | −43.4724 | −1.62805 | ||||||||
\(714\) | −75.9474 | −2.84226 | ||||||||
\(715\) | −0.713668 | −0.0266897 | ||||||||
\(716\) | 69.4145 | 2.59414 | ||||||||
\(717\) | −39.3163 | −1.46829 | ||||||||
\(718\) | −18.7745 | −0.700658 | ||||||||
\(719\) | −15.0128 | −0.559881 | −0.279941 | − | 0.960017i | \(-0.590315\pi\) | ||||
−0.279941 | + | 0.960017i | \(0.590315\pi\) | |||||||
\(720\) | 0.824678 | 0.0307339 | ||||||||
\(721\) | 75.7031 | 2.81933 | ||||||||
\(722\) | −76.5613 | −2.84932 | ||||||||
\(723\) | −31.1507 | −1.15851 | ||||||||
\(724\) | 41.9800 | 1.56018 | ||||||||
\(725\) | 9.02717 | 0.335261 | ||||||||
\(726\) | 49.1824 | 1.82533 | ||||||||
\(727\) | −6.05656 | −0.224625 | −0.112313 | − | 0.993673i | \(-0.535826\pi\) | ||||
−0.112313 | + | 0.993673i | \(0.535826\pi\) | |||||||
\(728\) | 11.0168 | 0.408310 | ||||||||
\(729\) | −25.0234 | −0.926794 | ||||||||
\(730\) | −8.93769 | −0.330799 | ||||||||
\(731\) | −21.4726 | −0.794193 | ||||||||
\(732\) | 96.4411 | 3.56456 | ||||||||
\(733\) | 3.08414 | 0.113915 | 0.0569577 | − | 0.998377i | \(-0.481860\pi\) | ||||
0.0569577 | + | 0.998377i | \(0.481860\pi\) | |||||||
\(734\) | −41.8191 | −1.54357 | ||||||||
\(735\) | −15.1617 | −0.559249 | ||||||||
\(736\) | −51.9028 | −1.91316 | ||||||||
\(737\) | −1.80090 | −0.0663372 | ||||||||
\(738\) | 71.2987 | 2.62454 | ||||||||
\(739\) | 20.5392 | 0.755548 | 0.377774 | − | 0.925898i | \(-0.376690\pi\) | ||||
0.377774 | + | 0.925898i | \(0.376690\pi\) | |||||||
\(740\) | −10.5008 | −0.386016 | ||||||||
\(741\) | 17.6524 | 0.648476 | ||||||||
\(742\) | −30.4260 | −1.11697 | ||||||||
\(743\) | 8.00492 | 0.293672 | 0.146836 | − | 0.989161i | \(-0.453091\pi\) | ||||
0.146836 | + | 0.989161i | \(0.453091\pi\) | |||||||
\(744\) | −31.8698 | −1.16840 | ||||||||
\(745\) | −1.90739 | −0.0698812 | ||||||||
\(746\) | 18.7884 | 0.687890 | ||||||||
\(747\) | −6.85040 | −0.250643 | ||||||||
\(748\) | −13.8885 | −0.507814 | ||||||||
\(749\) | −75.8817 | −2.77266 | ||||||||
\(750\) | −26.7678 | −0.977420 | ||||||||
\(751\) | 8.36300 | 0.305170 | 0.152585 | − | 0.988290i | \(-0.451240\pi\) | ||||
0.152585 | + | 0.988290i | \(0.451240\pi\) | |||||||
\(752\) | 2.50318 | 0.0912815 | ||||||||
\(753\) | −0.306338 | −0.0111636 | ||||||||
\(754\) | −4.29444 | −0.156394 | ||||||||
\(755\) | −7.17679 | −0.261190 | ||||||||
\(756\) | −3.59010 | −0.130571 | ||||||||
\(757\) | −33.9896 | −1.23537 | −0.617686 | − | 0.786425i | \(-0.711930\pi\) | ||||
−0.617686 | + | 0.786425i | \(0.711930\pi\) | |||||||
\(758\) | −56.7109 | −2.05983 | ||||||||
\(759\) | 28.6012 | 1.03816 | ||||||||
\(760\) | −9.08815 | −0.329662 | ||||||||
\(761\) | 44.7848 | 1.62345 | 0.811724 | − | 0.584041i | \(-0.198529\pi\) | ||||
0.811724 | + | 0.584041i | \(0.198529\pi\) | |||||||
\(762\) | −62.5133 | −2.26462 | ||||||||
\(763\) | −75.0849 | −2.71825 | ||||||||
\(764\) | 28.0730 | 1.01565 | ||||||||
\(765\) | −4.54303 | −0.164254 | ||||||||
\(766\) | −45.0898 | −1.62916 | ||||||||
\(767\) | 11.4178 | 0.412274 | ||||||||
\(768\) | −29.4646 | −1.06321 | ||||||||
\(769\) | −55.0355 | −1.98463 | −0.992315 | − | 0.123734i | \(-0.960513\pi\) | ||||
−0.992315 | + | 0.123734i | \(0.960513\pi\) | |||||||
\(770\) | −7.11619 | −0.256450 | ||||||||
\(771\) | 20.1325 | 0.725055 | ||||||||
\(772\) | −17.6172 | −0.634058 | ||||||||
\(773\) | −26.2196 | −0.943052 | −0.471526 | − | 0.881852i | \(-0.656297\pi\) | ||||
−0.471526 | + | 0.881852i | \(0.656297\pi\) | |||||||
\(774\) | 44.7153 | 1.60726 | ||||||||
\(775\) | −24.9796 | −0.897295 | ||||||||
\(776\) | 37.8668 | 1.35934 | ||||||||
\(777\) | 72.3707 | 2.59629 | ||||||||
\(778\) | 6.63033 | 0.237709 | ||||||||
\(779\) | 79.3509 | 2.84304 | ||||||||
\(780\) | 3.77298 | 0.135094 | ||||||||
\(781\) | 14.0782 | 0.503759 | ||||||||
\(782\) | 58.5981 | 2.09546 | ||||||||
\(783\) | 0.497991 | 0.0177967 | ||||||||
\(784\) | −7.10677 | −0.253813 | ||||||||
\(785\) | −1.06774 | −0.0381094 | ||||||||
\(786\) | −44.1556 | −1.57498 | ||||||||
\(787\) | −11.8062 | −0.420845 | −0.210423 | − | 0.977610i | \(-0.567484\pi\) | ||||
−0.210423 | + | 0.977610i | \(0.567484\pi\) | |||||||
\(788\) | −11.2891 | −0.402158 | ||||||||
\(789\) | 40.7140 | 1.44946 | ||||||||
\(790\) | −7.78637 | −0.277026 | ||||||||
\(791\) | 20.0291 | 0.712153 | ||||||||
\(792\) | 10.2918 | 0.365702 | ||||||||
\(793\) | −12.7964 | −0.454413 | ||||||||
\(794\) | −21.0454 | −0.746873 | ||||||||
\(795\) | −3.70797 | −0.131508 | ||||||||
\(796\) | −26.9704 | −0.955940 | ||||||||
\(797\) | −23.6726 | −0.838528 | −0.419264 | − | 0.907864i | \(-0.637712\pi\) | ||||
−0.419264 | + | 0.907864i | \(0.637712\pi\) | |||||||
\(798\) | 176.017 | 6.23093 | ||||||||
\(799\) | −13.7896 | −0.487842 | ||||||||
\(800\) | −29.8239 | −1.05443 | ||||||||
\(801\) | −10.7180 | −0.378700 | ||||||||
\(802\) | −7.03045 | −0.248254 | ||||||||
\(803\) | 11.2645 | 0.397514 | ||||||||
\(804\) | 9.52092 | 0.335777 | ||||||||
\(805\) | 18.2614 | 0.643628 | ||||||||
\(806\) | 11.8834 | 0.418575 | ||||||||
\(807\) | −49.7928 | −1.75279 | ||||||||
\(808\) | −20.7517 | −0.730042 | ||||||||
\(809\) | 12.4371 | 0.437265 | 0.218633 | − | 0.975807i | \(-0.429840\pi\) | ||||
0.218633 | + | 0.975807i | \(0.429840\pi\) | |||||||
\(810\) | −10.5330 | −0.370092 | ||||||||
\(811\) | 28.5505 | 1.00254 | 0.501271 | − | 0.865290i | \(-0.332866\pi\) | ||||
0.501271 | + | 0.865290i | \(0.332866\pi\) | |||||||
\(812\) | −26.0444 | −0.913981 | ||||||||
\(813\) | 60.1296 | 2.10884 | ||||||||
\(814\) | 21.7595 | 0.762668 | ||||||||
\(815\) | 0.199656 | 0.00699364 | ||||||||
\(816\) | −4.33839 | −0.151874 | ||||||||
\(817\) | 49.7653 | 1.74107 | ||||||||
\(818\) | −8.90118 | −0.311223 | ||||||||
\(819\) | −12.7634 | −0.445990 | ||||||||
\(820\) | 16.9603 | 0.592279 | ||||||||
\(821\) | 28.5283 | 0.995643 | 0.497822 | − | 0.867279i | \(-0.334133\pi\) | ||||
0.497822 | + | 0.867279i | \(0.334133\pi\) | |||||||
\(822\) | 57.1547 | 1.99350 | ||||||||
\(823\) | 0.611865 | 0.0213283 | 0.0106641 | − | 0.999943i | \(-0.496605\pi\) | ||||
0.0106641 | + | 0.999943i | \(0.496605\pi\) | |||||||
\(824\) | −42.8203 | −1.49172 | ||||||||
\(825\) | 16.4345 | 0.572176 | ||||||||
\(826\) | 113.850 | 3.96136 | ||||||||
\(827\) | −1.39672 | −0.0485688 | −0.0242844 | − | 0.999705i | \(-0.507731\pi\) | ||||
−0.0242844 | + | 0.999705i | \(0.507731\pi\) | |||||||
\(828\) | −74.2185 | −2.57927 | ||||||||
\(829\) | 19.8978 | 0.691079 | 0.345540 | − | 0.938404i | \(-0.387696\pi\) | ||||
0.345540 | + | 0.938404i | \(0.387696\pi\) | |||||||
\(830\) | −2.67923 | −0.0929973 | ||||||||
\(831\) | 45.6423 | 1.58331 | ||||||||
\(832\) | 13.0487 | 0.452383 | ||||||||
\(833\) | 39.1501 | 1.35647 | ||||||||
\(834\) | 45.8259 | 1.58682 | ||||||||
\(835\) | 1.18193 | 0.0409023 | ||||||||
\(836\) | 32.1882 | 1.11325 | ||||||||
\(837\) | −1.37802 | −0.0476314 | ||||||||
\(838\) | −31.0747 | −1.07346 | ||||||||
\(839\) | −46.8515 | −1.61749 | −0.808747 | − | 0.588156i | \(-0.799854\pi\) | ||||
−0.808747 | + | 0.588156i | \(0.799854\pi\) | |||||||
\(840\) | 13.3875 | 0.461912 | ||||||||
\(841\) | −25.3873 | −0.875425 | ||||||||
\(842\) | −64.9133 | −2.23706 | ||||||||
\(843\) | 72.3082 | 2.49043 | ||||||||
\(844\) | 40.7362 | 1.40220 | ||||||||
\(845\) | −0.500622 | −0.0172219 | ||||||||
\(846\) | 28.7160 | 0.987276 | ||||||||
\(847\) | −39.5771 | −1.35988 | ||||||||
\(848\) | −1.73804 | −0.0596846 | ||||||||
\(849\) | 46.3374 | 1.59030 | ||||||||
\(850\) | 33.6710 | 1.15491 | ||||||||
\(851\) | −55.8385 | −1.91412 | ||||||||
\(852\) | −74.4281 | −2.54986 | ||||||||
\(853\) | −2.82819 | −0.0968352 | −0.0484176 | − | 0.998827i | \(-0.515418\pi\) | ||||
−0.0484176 | + | 0.998827i | \(0.515418\pi\) | |||||||
\(854\) | −127.596 | −4.36626 | ||||||||
\(855\) | 10.5290 | 0.360084 | ||||||||
\(856\) | 42.9214 | 1.46702 | ||||||||
\(857\) | 47.7385 | 1.63072 | 0.815358 | − | 0.578958i | \(-0.196540\pi\) | ||||
0.815358 | + | 0.578958i | \(0.196540\pi\) | |||||||
\(858\) | −7.81829 | −0.266912 | ||||||||
\(859\) | −22.4413 | −0.765689 | −0.382844 | − | 0.923813i | \(-0.625055\pi\) | ||||
−0.382844 | + | 0.923813i | \(0.625055\pi\) | |||||||
\(860\) | 10.6367 | 0.362709 | ||||||||
\(861\) | −116.890 | −3.98358 | ||||||||
\(862\) | 9.88956 | 0.336840 | ||||||||
\(863\) | −26.3657 | −0.897498 | −0.448749 | − | 0.893658i | \(-0.648130\pi\) | ||||
−0.448749 | + | 0.893658i | \(0.648130\pi\) | |||||||
\(864\) | −1.64526 | −0.0559728 | ||||||||
\(865\) | 0.130657 | 0.00444247 | ||||||||
\(866\) | −67.5200 | −2.29442 | ||||||||
\(867\) | −17.3655 | −0.589764 | ||||||||
\(868\) | 72.0692 | 2.44619 | ||||||||
\(869\) | 9.81341 | 0.332897 | ||||||||
\(870\) | −5.21855 | −0.176925 | ||||||||
\(871\) | −1.26329 | −0.0428051 | ||||||||
\(872\) | 42.4706 | 1.43824 | ||||||||
\(873\) | −43.8703 | −1.48479 | ||||||||
\(874\) | −135.808 | −4.59377 | ||||||||
\(875\) | 21.5400 | 0.728186 | ||||||||
\(876\) | −59.5523 | −2.01209 | ||||||||
\(877\) | 20.4596 | 0.690872 | 0.345436 | − | 0.938442i | \(-0.387731\pi\) | ||||
0.345436 | + | 0.938442i | \(0.387731\pi\) | |||||||
\(878\) | −35.4524 | −1.19646 | ||||||||
\(879\) | −48.8610 | −1.64804 | ||||||||
\(880\) | −0.406503 | −0.0137032 | ||||||||
\(881\) | −44.1552 | −1.48763 | −0.743813 | − | 0.668388i | \(-0.766985\pi\) | ||||
−0.743813 | + | 0.668388i | \(0.766985\pi\) | |||||||
\(882\) | −81.5276 | −2.74518 | ||||||||
\(883\) | −20.4976 | −0.689800 | −0.344900 | − | 0.938640i | \(-0.612087\pi\) | ||||
−0.344900 | + | 0.938640i | \(0.612087\pi\) | |||||||
\(884\) | −9.74247 | −0.327675 | ||||||||
\(885\) | 13.8748 | 0.466396 | ||||||||
\(886\) | 49.7811 | 1.67243 | ||||||||
\(887\) | −51.8347 | −1.74044 | −0.870219 | − | 0.492665i | \(-0.836023\pi\) | ||||
−0.870219 | + | 0.492665i | \(0.836023\pi\) | |||||||
\(888\) | −40.9354 | −1.37370 | ||||||||
\(889\) | 50.3044 | 1.68716 | ||||||||
\(890\) | −4.19185 | −0.140511 | ||||||||
\(891\) | 13.2751 | 0.444732 | ||||||||
\(892\) | 22.5549 | 0.755195 | ||||||||
\(893\) | 31.9591 | 1.06947 | ||||||||
\(894\) | −20.8956 | −0.698852 | ||||||||
\(895\) | −11.1923 | −0.374117 | ||||||||
\(896\) | 74.6862 | 2.49509 | ||||||||
\(897\) | 20.0631 | 0.669886 | ||||||||
\(898\) | −28.2459 | −0.942578 | ||||||||
\(899\) | −9.99687 | −0.333414 | ||||||||
\(900\) | −42.6467 | −1.42156 | ||||||||
\(901\) | 9.57462 | 0.318977 | ||||||||
\(902\) | −35.1448 | −1.17019 | ||||||||
\(903\) | −73.3077 | −2.43953 | ||||||||
\(904\) | −11.3292 | −0.376802 | ||||||||
\(905\) | −6.76880 | −0.225003 | ||||||||
\(906\) | −78.6223 | −2.61205 | ||||||||
\(907\) | −6.46458 | −0.214653 | −0.107326 | − | 0.994224i | \(-0.534229\pi\) | ||||
−0.107326 | + | 0.994224i | \(0.534229\pi\) | |||||||
\(908\) | −53.3385 | −1.77010 | ||||||||
\(909\) | 24.0417 | 0.797414 | ||||||||
\(910\) | −4.99184 | −0.165478 | ||||||||
\(911\) | 9.59642 | 0.317943 | 0.158972 | − | 0.987283i | \(-0.449182\pi\) | ||||
0.158972 | + | 0.987283i | \(0.449182\pi\) | |||||||
\(912\) | 10.0547 | 0.332945 | ||||||||
\(913\) | 3.37672 | 0.111753 | ||||||||
\(914\) | −71.4468 | −2.36325 | ||||||||
\(915\) | −15.5500 | −0.514068 | ||||||||
\(916\) | 40.7619 | 1.34681 | ||||||||
\(917\) | 35.5321 | 1.17337 | ||||||||
\(918\) | 1.85749 | 0.0613063 | ||||||||
\(919\) | −6.55296 | −0.216162 | −0.108081 | − | 0.994142i | \(-0.534471\pi\) | ||||
−0.108081 | + | 0.994142i | \(0.534471\pi\) | |||||||
\(920\) | −10.3293 | −0.340546 | ||||||||
\(921\) | −51.5734 | −1.69940 | ||||||||
\(922\) | −35.5439 | −1.17058 | ||||||||
\(923\) | 9.87557 | 0.325058 | ||||||||
\(924\) | −47.4155 | −1.55986 | ||||||||
\(925\) | −32.0853 | −1.05496 | ||||||||
\(926\) | 2.25939 | 0.0742482 | ||||||||
\(927\) | 49.6091 | 1.62938 | ||||||||
\(928\) | −11.9355 | −0.391803 | ||||||||
\(929\) | −3.94686 | −0.129492 | −0.0647462 | − | 0.997902i | \(-0.520624\pi\) | ||||
−0.0647462 | + | 0.997902i | \(0.520624\pi\) | |||||||
\(930\) | 14.4406 | 0.473525 | ||||||||
\(931\) | −90.7350 | −2.97372 | ||||||||
\(932\) | 26.4099 | 0.865084 | ||||||||
\(933\) | −24.5201 | −0.802753 | ||||||||
\(934\) | −79.2214 | −2.59220 | ||||||||
\(935\) | 2.23936 | 0.0732350 | ||||||||
\(936\) | 7.21944 | 0.235975 | ||||||||
\(937\) | −21.9296 | −0.716408 | −0.358204 | − | 0.933643i | \(-0.616611\pi\) | ||||
−0.358204 | + | 0.933643i | \(0.616611\pi\) | |||||||
\(938\) | −12.5967 | −0.411295 | ||||||||
\(939\) | −53.2086 | −1.73640 | ||||||||
\(940\) | 6.83086 | 0.222798 | ||||||||
\(941\) | 13.0132 | 0.424219 | 0.212109 | − | 0.977246i | \(-0.431967\pi\) | ||||
0.212109 | + | 0.977246i | \(0.431967\pi\) | |||||||
\(942\) | −11.6972 | −0.381116 | ||||||||
\(943\) | 90.1875 | 2.93691 | ||||||||
\(944\) | 6.50355 | 0.211672 | ||||||||
\(945\) | 0.578863 | 0.0188304 | ||||||||
\(946\) | −22.0412 | −0.716620 | ||||||||
\(947\) | −21.2379 | −0.690139 | −0.345070 | − | 0.938577i | \(-0.612145\pi\) | ||||
−0.345070 | + | 0.938577i | \(0.612145\pi\) | |||||||
\(948\) | −51.8810 | −1.68502 | ||||||||
\(949\) | 7.90176 | 0.256502 | ||||||||
\(950\) | −78.0365 | −2.53184 | ||||||||
\(951\) | −58.7258 | −1.90431 | ||||||||
\(952\) | −34.5687 | −1.12038 | ||||||||
\(953\) | 47.9556 | 1.55343 | 0.776717 | − | 0.629850i | \(-0.216883\pi\) | ||||
0.776717 | + | 0.629850i | \(0.216883\pi\) | |||||||
\(954\) | −19.9385 | −0.645533 | ||||||||
\(955\) | −4.52645 | −0.146473 | ||||||||
\(956\) | −50.2898 | −1.62649 | ||||||||
\(957\) | 6.57711 | 0.212608 | ||||||||
\(958\) | −29.3086 | −0.946917 | ||||||||
\(959\) | −45.9924 | −1.48517 | ||||||||
\(960\) | 15.8567 | 0.511771 | ||||||||
\(961\) | −3.33702 | −0.107646 | ||||||||
\(962\) | 15.2638 | 0.492123 | ||||||||
\(963\) | −49.7262 | −1.60240 | ||||||||
\(964\) | −39.8451 | −1.28332 | ||||||||
\(965\) | 2.84057 | 0.0914413 | ||||||||
\(966\) | 200.055 | 6.43665 | ||||||||
\(967\) | 29.2656 | 0.941119 | 0.470560 | − | 0.882368i | \(-0.344052\pi\) | ||||
0.470560 | + | 0.882368i | \(0.344052\pi\) | |||||||
\(968\) | 22.3862 | 0.719520 | ||||||||
\(969\) | −55.3900 | −1.77938 | ||||||||
\(970\) | −17.1579 | −0.550908 | ||||||||
\(971\) | 4.15655 | 0.133390 | 0.0666951 | − | 0.997773i | \(-0.478755\pi\) | ||||
0.0666951 | + | 0.997773i | \(0.478755\pi\) | |||||||
\(972\) | −67.7415 | −2.17281 | ||||||||
\(973\) | −36.8761 | −1.18220 | ||||||||
\(974\) | −35.9098 | −1.15062 | ||||||||
\(975\) | 11.5284 | 0.369205 | ||||||||
\(976\) | −7.28877 | −0.233308 | ||||||||
\(977\) | 27.3819 | 0.876025 | 0.438012 | − | 0.898969i | \(-0.355683\pi\) | ||||
0.438012 | + | 0.898969i | \(0.355683\pi\) | |||||||
\(978\) | 2.18725 | 0.0699404 | ||||||||
\(979\) | 5.28312 | 0.168849 | ||||||||
\(980\) | −19.3935 | −0.619502 | ||||||||
\(981\) | −49.2040 | −1.57096 | ||||||||
\(982\) | 5.62691 | 0.179562 | ||||||||
\(983\) | 37.8216 | 1.20632 | 0.603161 | − | 0.797620i | \(-0.293908\pi\) | ||||
0.603161 | + | 0.797620i | \(0.293908\pi\) | |||||||
\(984\) | 66.1168 | 2.10773 | ||||||||
\(985\) | 1.82024 | 0.0579977 | ||||||||
\(986\) | 13.4752 | 0.429137 | ||||||||
\(987\) | −47.0780 | −1.49851 | ||||||||
\(988\) | 22.5793 | 0.718343 | ||||||||
\(989\) | 56.5614 | 1.79855 | ||||||||
\(990\) | −4.66332 | −0.148210 | ||||||||
\(991\) | 21.0434 | 0.668466 | 0.334233 | − | 0.942491i | \(-0.391523\pi\) | ||||
0.334233 | + | 0.942491i | \(0.391523\pi\) | |||||||
\(992\) | 33.0276 | 1.04863 | ||||||||
\(993\) | 21.8824 | 0.694419 | ||||||||
\(994\) | 98.4721 | 3.12335 | ||||||||
\(995\) | 4.34866 | 0.137862 | ||||||||
\(996\) | −17.8518 | −0.565657 | ||||||||
\(997\) | 12.1203 | 0.383853 | 0.191927 | − | 0.981409i | \(-0.438526\pi\) | ||||
0.191927 | + | 0.981409i | \(0.438526\pi\) | |||||||
\(998\) | 33.7064 | 1.06696 | ||||||||
\(999\) | −1.77001 | −0.0560007 |
(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 | 6019.2.a.c.1.15 | ✓ | 108 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6019.2.a.c.1.15 | ✓ | 108 | 1.1 | even | 1 | trivial |