Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6034,2,Mod(1,6034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6034, 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("6034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6034 = 2 \cdot 7 \cdot 431 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6034.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: | \(48.1817325796\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 6034.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −0.797155 | −0.460238 | −0.230119 | − | 0.973163i | \(-0.573912\pi\) | ||||
−0.230119 | + | 0.973163i | \(0.573912\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.40867 | 0.629976 | 0.314988 | − | 0.949096i | \(-0.397999\pi\) | ||||
0.314988 | + | 0.949096i | \(0.397999\pi\) | |||||||
\(6\) | 0.797155 | 0.325437 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.36454 | −0.788181 | ||||||||
\(10\) | −1.40867 | −0.445460 | ||||||||
\(11\) | −4.26652 | −1.28640 | −0.643202 | − | 0.765696i | \(-0.722394\pi\) | ||||
−0.643202 | + | 0.765696i | \(0.722394\pi\) | |||||||
\(12\) | −0.797155 | −0.230119 | ||||||||
\(13\) | 0.799192 | 0.221656 | 0.110828 | − | 0.993840i | \(-0.464650\pi\) | ||||
0.110828 | + | 0.993840i | \(0.464650\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | −1.12293 | −0.289939 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.62976 | −0.880345 | −0.440173 | − | 0.897913i | \(-0.645083\pi\) | ||||
−0.440173 | + | 0.897913i | \(0.645083\pi\) | |||||||
\(18\) | 2.36454 | 0.557328 | ||||||||
\(19\) | −6.70269 | −1.53770 | −0.768851 | − | 0.639427i | \(-0.779171\pi\) | ||||
−0.768851 | + | 0.639427i | \(0.779171\pi\) | |||||||
\(20\) | 1.40867 | 0.314988 | ||||||||
\(21\) | 0.797155 | 0.173954 | ||||||||
\(22\) | 4.26652 | 0.909625 | ||||||||
\(23\) | −4.59211 | −0.957522 | −0.478761 | − | 0.877945i | \(-0.658914\pi\) | ||||
−0.478761 | + | 0.877945i | \(0.658914\pi\) | |||||||
\(24\) | 0.797155 | 0.162719 | ||||||||
\(25\) | −3.01565 | −0.603130 | ||||||||
\(26\) | −0.799192 | −0.156734 | ||||||||
\(27\) | 4.27637 | 0.822989 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | −6.21178 | −1.15350 | −0.576749 | − | 0.816921i | \(-0.695679\pi\) | ||||
−0.576749 | + | 0.816921i | \(0.695679\pi\) | |||||||
\(30\) | 1.12293 | 0.205018 | ||||||||
\(31\) | −6.61866 | −1.18875 | −0.594373 | − | 0.804189i | \(-0.702600\pi\) | ||||
−0.594373 | + | 0.804189i | \(0.702600\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 3.40108 | 0.592052 | ||||||||
\(34\) | 3.62976 | 0.622498 | ||||||||
\(35\) | −1.40867 | −0.238109 | ||||||||
\(36\) | −2.36454 | −0.394091 | ||||||||
\(37\) | 5.42018 | 0.891072 | 0.445536 | − | 0.895264i | \(-0.353013\pi\) | ||||
0.445536 | + | 0.895264i | \(0.353013\pi\) | |||||||
\(38\) | 6.70269 | 1.08732 | ||||||||
\(39\) | −0.637080 | −0.102014 | ||||||||
\(40\) | −1.40867 | −0.222730 | ||||||||
\(41\) | −4.51614 | −0.705303 | −0.352652 | − | 0.935755i | \(-0.614720\pi\) | ||||
−0.352652 | + | 0.935755i | \(0.614720\pi\) | |||||||
\(42\) | −0.797155 | −0.123004 | ||||||||
\(43\) | 0.780925 | 0.119090 | 0.0595450 | − | 0.998226i | \(-0.481035\pi\) | ||||
0.0595450 | + | 0.998226i | \(0.481035\pi\) | |||||||
\(44\) | −4.26652 | −0.643202 | ||||||||
\(45\) | −3.33086 | −0.496535 | ||||||||
\(46\) | 4.59211 | 0.677070 | ||||||||
\(47\) | 11.1285 | 1.62325 | 0.811627 | − | 0.584176i | \(-0.198582\pi\) | ||||
0.811627 | + | 0.584176i | \(0.198582\pi\) | |||||||
\(48\) | −0.797155 | −0.115059 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 3.01565 | 0.426477 | ||||||||
\(51\) | 2.89348 | 0.405168 | ||||||||
\(52\) | 0.799192 | 0.110828 | ||||||||
\(53\) | −3.36589 | −0.462341 | −0.231170 | − | 0.972913i | \(-0.574255\pi\) | ||||
−0.231170 | + | 0.972913i | \(0.574255\pi\) | |||||||
\(54\) | −4.27637 | −0.581941 | ||||||||
\(55\) | −6.01012 | −0.810404 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 5.34309 | 0.707709 | ||||||||
\(58\) | 6.21178 | 0.815646 | ||||||||
\(59\) | 5.39532 | 0.702410 | 0.351205 | − | 0.936298i | \(-0.385772\pi\) | ||||
0.351205 | + | 0.936298i | \(0.385772\pi\) | |||||||
\(60\) | −1.12293 | −0.144969 | ||||||||
\(61\) | −5.80734 | −0.743554 | −0.371777 | − | 0.928322i | \(-0.621251\pi\) | ||||
−0.371777 | + | 0.928322i | \(0.621251\pi\) | |||||||
\(62\) | 6.61866 | 0.840571 | ||||||||
\(63\) | 2.36454 | 0.297904 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.12580 | 0.139638 | ||||||||
\(66\) | −3.40108 | −0.418644 | ||||||||
\(67\) | −4.88292 | −0.596543 | −0.298272 | − | 0.954481i | \(-0.596410\pi\) | ||||
−0.298272 | + | 0.954481i | \(0.596410\pi\) | |||||||
\(68\) | −3.62976 | −0.440173 | ||||||||
\(69\) | 3.66063 | 0.440688 | ||||||||
\(70\) | 1.40867 | 0.168368 | ||||||||
\(71\) | 9.37398 | 1.11249 | 0.556243 | − | 0.831020i | \(-0.312242\pi\) | ||||
0.556243 | + | 0.831020i | \(0.312242\pi\) | |||||||
\(72\) | 2.36454 | 0.278664 | ||||||||
\(73\) | −3.99440 | −0.467510 | −0.233755 | − | 0.972296i | \(-0.575101\pi\) | ||||
−0.233755 | + | 0.972296i | \(0.575101\pi\) | |||||||
\(74\) | −5.42018 | −0.630083 | ||||||||
\(75\) | 2.40394 | 0.277583 | ||||||||
\(76\) | −6.70269 | −0.768851 | ||||||||
\(77\) | 4.26652 | 0.486215 | ||||||||
\(78\) | 0.637080 | 0.0721351 | ||||||||
\(79\) | 5.28980 | 0.595149 | 0.297575 | − | 0.954699i | \(-0.403822\pi\) | ||||
0.297575 | + | 0.954699i | \(0.403822\pi\) | |||||||
\(80\) | 1.40867 | 0.157494 | ||||||||
\(81\) | 3.68470 | 0.409411 | ||||||||
\(82\) | 4.51614 | 0.498725 | ||||||||
\(83\) | 14.1032 | 1.54803 | 0.774015 | − | 0.633168i | \(-0.218246\pi\) | ||||
0.774015 | + | 0.633168i | \(0.218246\pi\) | |||||||
\(84\) | 0.797155 | 0.0869768 | ||||||||
\(85\) | −5.11313 | −0.554596 | ||||||||
\(86\) | −0.780925 | −0.0842093 | ||||||||
\(87\) | 4.95175 | 0.530883 | ||||||||
\(88\) | 4.26652 | 0.454813 | ||||||||
\(89\) | −13.9685 | −1.48066 | −0.740328 | − | 0.672246i | \(-0.765330\pi\) | ||||
−0.740328 | + | 0.672246i | \(0.765330\pi\) | |||||||
\(90\) | 3.33086 | 0.351104 | ||||||||
\(91\) | −0.799192 | −0.0837781 | ||||||||
\(92\) | −4.59211 | −0.478761 | ||||||||
\(93\) | 5.27610 | 0.547106 | ||||||||
\(94\) | −11.1285 | −1.14781 | ||||||||
\(95\) | −9.44188 | −0.968716 | ||||||||
\(96\) | 0.797155 | 0.0813593 | ||||||||
\(97\) | −3.54831 | −0.360277 | −0.180138 | − | 0.983641i | \(-0.557655\pi\) | ||||
−0.180138 | + | 0.983641i | \(0.557655\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 10.0884 | 1.01392 | ||||||||
\(100\) | −3.01565 | −0.301565 | ||||||||
\(101\) | 9.29483 | 0.924870 | 0.462435 | − | 0.886653i | \(-0.346976\pi\) | ||||
0.462435 | + | 0.886653i | \(0.346976\pi\) | |||||||
\(102\) | −2.89348 | −0.286497 | ||||||||
\(103\) | 8.45408 | 0.833005 | 0.416503 | − | 0.909134i | \(-0.363256\pi\) | ||||
0.416503 | + | 0.909134i | \(0.363256\pi\) | |||||||
\(104\) | −0.799192 | −0.0783672 | ||||||||
\(105\) | 1.12293 | 0.109587 | ||||||||
\(106\) | 3.36589 | 0.326924 | ||||||||
\(107\) | 12.0908 | 1.16886 | 0.584430 | − | 0.811444i | \(-0.301318\pi\) | ||||
0.584430 | + | 0.811444i | \(0.301318\pi\) | |||||||
\(108\) | 4.27637 | 0.411494 | ||||||||
\(109\) | −5.51476 | −0.528218 | −0.264109 | − | 0.964493i | \(-0.585078\pi\) | ||||
−0.264109 | + | 0.964493i | \(0.585078\pi\) | |||||||
\(110\) | 6.01012 | 0.573042 | ||||||||
\(111\) | −4.32072 | −0.410105 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | 5.38250 | 0.506343 | 0.253171 | − | 0.967421i | \(-0.418526\pi\) | ||||
0.253171 | + | 0.967421i | \(0.418526\pi\) | |||||||
\(114\) | −5.34309 | −0.500426 | ||||||||
\(115\) | −6.46877 | −0.603216 | ||||||||
\(116\) | −6.21178 | −0.576749 | ||||||||
\(117\) | −1.88972 | −0.174705 | ||||||||
\(118\) | −5.39532 | −0.496679 | ||||||||
\(119\) | 3.62976 | 0.332739 | ||||||||
\(120\) | 1.12293 | 0.102509 | ||||||||
\(121\) | 7.20319 | 0.654836 | ||||||||
\(122\) | 5.80734 | 0.525772 | ||||||||
\(123\) | 3.60007 | 0.324607 | ||||||||
\(124\) | −6.61866 | −0.594373 | ||||||||
\(125\) | −11.2914 | −1.00993 | ||||||||
\(126\) | −2.36454 | −0.210650 | ||||||||
\(127\) | 13.0689 | 1.15968 | 0.579839 | − | 0.814731i | \(-0.303115\pi\) | ||||
0.579839 | + | 0.814731i | \(0.303115\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −0.622518 | −0.0548097 | ||||||||
\(130\) | −1.12580 | −0.0987390 | ||||||||
\(131\) | 5.75249 | 0.502597 | 0.251299 | − | 0.967910i | \(-0.419142\pi\) | ||||
0.251299 | + | 0.967910i | \(0.419142\pi\) | |||||||
\(132\) | 3.40108 | 0.296026 | ||||||||
\(133\) | 6.70269 | 0.581197 | ||||||||
\(134\) | 4.88292 | 0.421820 | ||||||||
\(135\) | 6.02400 | 0.518463 | ||||||||
\(136\) | 3.62976 | 0.311249 | ||||||||
\(137\) | 7.21273 | 0.616225 | 0.308113 | − | 0.951350i | \(-0.400303\pi\) | ||||
0.308113 | + | 0.951350i | \(0.400303\pi\) | |||||||
\(138\) | −3.66063 | −0.311613 | ||||||||
\(139\) | −3.15380 | −0.267502 | −0.133751 | − | 0.991015i | \(-0.542702\pi\) | ||||
−0.133751 | + | 0.991015i | \(0.542702\pi\) | |||||||
\(140\) | −1.40867 | −0.119054 | ||||||||
\(141\) | −8.87112 | −0.747083 | ||||||||
\(142\) | −9.37398 | −0.786647 | ||||||||
\(143\) | −3.40977 | −0.285139 | ||||||||
\(144\) | −2.36454 | −0.197045 | ||||||||
\(145\) | −8.75034 | −0.726676 | ||||||||
\(146\) | 3.99440 | 0.330579 | ||||||||
\(147\) | −0.797155 | −0.0657483 | ||||||||
\(148\) | 5.42018 | 0.445536 | ||||||||
\(149\) | 16.0083 | 1.31145 | 0.655726 | − | 0.754999i | \(-0.272363\pi\) | ||||
0.655726 | + | 0.754999i | \(0.272363\pi\) | |||||||
\(150\) | −2.40394 | −0.196281 | ||||||||
\(151\) | 9.62444 | 0.783226 | 0.391613 | − | 0.920130i | \(-0.371917\pi\) | ||||
0.391613 | + | 0.920130i | \(0.371917\pi\) | |||||||
\(152\) | 6.70269 | 0.543660 | ||||||||
\(153\) | 8.58272 | 0.693871 | ||||||||
\(154\) | −4.26652 | −0.343806 | ||||||||
\(155\) | −9.32351 | −0.748882 | ||||||||
\(156\) | −0.637080 | −0.0510072 | ||||||||
\(157\) | −2.78528 | −0.222289 | −0.111145 | − | 0.993804i | \(-0.535452\pi\) | ||||
−0.111145 | + | 0.993804i | \(0.535452\pi\) | |||||||
\(158\) | −5.28980 | −0.420834 | ||||||||
\(159\) | 2.68314 | 0.212787 | ||||||||
\(160\) | −1.40867 | −0.111365 | ||||||||
\(161\) | 4.59211 | 0.361909 | ||||||||
\(162\) | −3.68470 | −0.289497 | ||||||||
\(163\) | 7.65399 | 0.599507 | 0.299753 | − | 0.954017i | \(-0.403096\pi\) | ||||
0.299753 | + | 0.954017i | \(0.403096\pi\) | |||||||
\(164\) | −4.51614 | −0.352652 | ||||||||
\(165\) | 4.79100 | 0.372979 | ||||||||
\(166\) | −14.1032 | −1.09462 | ||||||||
\(167\) | 8.70855 | 0.673888 | 0.336944 | − | 0.941525i | \(-0.390607\pi\) | ||||
0.336944 | + | 0.941525i | \(0.390607\pi\) | |||||||
\(168\) | −0.797155 | −0.0615019 | ||||||||
\(169\) | −12.3613 | −0.950869 | ||||||||
\(170\) | 5.11313 | 0.392159 | ||||||||
\(171\) | 15.8488 | 1.21199 | ||||||||
\(172\) | 0.780925 | 0.0595450 | ||||||||
\(173\) | 0.799481 | 0.0607834 | 0.0303917 | − | 0.999538i | \(-0.490325\pi\) | ||||
0.0303917 | + | 0.999538i | \(0.490325\pi\) | |||||||
\(174\) | −4.95175 | −0.375391 | ||||||||
\(175\) | 3.01565 | 0.227962 | ||||||||
\(176\) | −4.26652 | −0.321601 | ||||||||
\(177\) | −4.30091 | −0.323276 | ||||||||
\(178\) | 13.9685 | 1.04698 | ||||||||
\(179\) | −7.40805 | −0.553704 | −0.276852 | − | 0.960913i | \(-0.589291\pi\) | ||||
−0.276852 | + | 0.960913i | \(0.589291\pi\) | |||||||
\(180\) | −3.33086 | −0.248268 | ||||||||
\(181\) | −11.7333 | −0.872126 | −0.436063 | − | 0.899916i | \(-0.643628\pi\) | ||||
−0.436063 | + | 0.899916i | \(0.643628\pi\) | |||||||
\(182\) | 0.799192 | 0.0592400 | ||||||||
\(183\) | 4.62935 | 0.342211 | ||||||||
\(184\) | 4.59211 | 0.338535 | ||||||||
\(185\) | 7.63524 | 0.561354 | ||||||||
\(186\) | −5.27610 | −0.386863 | ||||||||
\(187\) | 15.4864 | 1.13248 | ||||||||
\(188\) | 11.1285 | 0.811627 | ||||||||
\(189\) | −4.27637 | −0.311060 | ||||||||
\(190\) | 9.44188 | 0.684986 | ||||||||
\(191\) | 8.22734 | 0.595309 | 0.297655 | − | 0.954674i | \(-0.403796\pi\) | ||||
0.297655 | + | 0.954674i | \(0.403796\pi\) | |||||||
\(192\) | −0.797155 | −0.0575297 | ||||||||
\(193\) | −18.7582 | −1.35024 | −0.675121 | − | 0.737707i | \(-0.735909\pi\) | ||||
−0.675121 | + | 0.737707i | \(0.735909\pi\) | |||||||
\(194\) | 3.54831 | 0.254754 | ||||||||
\(195\) | −0.897435 | −0.0642667 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −20.4237 | −1.45512 | −0.727562 | − | 0.686041i | \(-0.759347\pi\) | ||||
−0.727562 | + | 0.686041i | \(0.759347\pi\) | |||||||
\(198\) | −10.0884 | −0.716949 | ||||||||
\(199\) | −13.8409 | −0.981152 | −0.490576 | − | 0.871398i | \(-0.663214\pi\) | ||||
−0.490576 | + | 0.871398i | \(0.663214\pi\) | |||||||
\(200\) | 3.01565 | 0.213239 | ||||||||
\(201\) | 3.89244 | 0.274552 | ||||||||
\(202\) | −9.29483 | −0.653982 | ||||||||
\(203\) | 6.21178 | 0.435981 | ||||||||
\(204\) | 2.89348 | 0.202584 | ||||||||
\(205\) | −6.36175 | −0.444324 | ||||||||
\(206\) | −8.45408 | −0.589024 | ||||||||
\(207\) | 10.8582 | 0.754701 | ||||||||
\(208\) | 0.799192 | 0.0554140 | ||||||||
\(209\) | 28.5972 | 1.97811 | ||||||||
\(210\) | −1.12293 | −0.0774894 | ||||||||
\(211\) | 22.7593 | 1.56681 | 0.783407 | − | 0.621509i | \(-0.213480\pi\) | ||||
0.783407 | + | 0.621509i | \(0.213480\pi\) | |||||||
\(212\) | −3.36589 | −0.231170 | ||||||||
\(213\) | −7.47251 | −0.512008 | ||||||||
\(214\) | −12.0908 | −0.826509 | ||||||||
\(215\) | 1.10007 | 0.0750238 | ||||||||
\(216\) | −4.27637 | −0.290970 | ||||||||
\(217\) | 6.61866 | 0.449304 | ||||||||
\(218\) | 5.51476 | 0.373507 | ||||||||
\(219\) | 3.18416 | 0.215166 | ||||||||
\(220\) | −6.01012 | −0.405202 | ||||||||
\(221\) | −2.90087 | −0.195134 | ||||||||
\(222\) | 4.32072 | 0.289988 | ||||||||
\(223\) | −8.70757 | −0.583102 | −0.291551 | − | 0.956555i | \(-0.594171\pi\) | ||||
−0.291551 | + | 0.956555i | \(0.594171\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 7.13063 | 0.475376 | ||||||||
\(226\) | −5.38250 | −0.358038 | ||||||||
\(227\) | −16.8011 | −1.11513 | −0.557564 | − | 0.830134i | \(-0.688264\pi\) | ||||
−0.557564 | + | 0.830134i | \(0.688264\pi\) | |||||||
\(228\) | 5.34309 | 0.353854 | ||||||||
\(229\) | 24.0920 | 1.59205 | 0.796023 | − | 0.605267i | \(-0.206934\pi\) | ||||
0.796023 | + | 0.605267i | \(0.206934\pi\) | |||||||
\(230\) | 6.46877 | 0.426538 | ||||||||
\(231\) | −3.40108 | −0.223775 | ||||||||
\(232\) | 6.21178 | 0.407823 | ||||||||
\(233\) | −12.7964 | −0.838321 | −0.419160 | − | 0.907912i | \(-0.637676\pi\) | ||||
−0.419160 | + | 0.907912i | \(0.637676\pi\) | |||||||
\(234\) | 1.88972 | 0.123535 | ||||||||
\(235\) | 15.6763 | 1.02261 | ||||||||
\(236\) | 5.39532 | 0.351205 | ||||||||
\(237\) | −4.21680 | −0.273910 | ||||||||
\(238\) | −3.62976 | −0.235282 | ||||||||
\(239\) | 2.87318 | 0.185851 | 0.0929253 | − | 0.995673i | \(-0.470378\pi\) | ||||
0.0929253 | + | 0.995673i | \(0.470378\pi\) | |||||||
\(240\) | −1.12293 | −0.0724847 | ||||||||
\(241\) | −8.19163 | −0.527669 | −0.263835 | − | 0.964568i | \(-0.584987\pi\) | ||||
−0.263835 | + | 0.964568i | \(0.584987\pi\) | |||||||
\(242\) | −7.20319 | −0.463039 | ||||||||
\(243\) | −15.7664 | −1.01141 | ||||||||
\(244\) | −5.80734 | −0.371777 | ||||||||
\(245\) | 1.40867 | 0.0899966 | ||||||||
\(246\) | −3.60007 | −0.229532 | ||||||||
\(247\) | −5.35674 | −0.340841 | ||||||||
\(248\) | 6.61866 | 0.420285 | ||||||||
\(249\) | −11.2425 | −0.712462 | ||||||||
\(250\) | 11.2914 | 0.714131 | ||||||||
\(251\) | −14.2956 | −0.902332 | −0.451166 | − | 0.892440i | \(-0.648992\pi\) | ||||
−0.451166 | + | 0.892440i | \(0.648992\pi\) | |||||||
\(252\) | 2.36454 | 0.148952 | ||||||||
\(253\) | 19.5923 | 1.23176 | ||||||||
\(254\) | −13.0689 | −0.820017 | ||||||||
\(255\) | 4.07596 | 0.255246 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 8.61994 | 0.537697 | 0.268849 | − | 0.963182i | \(-0.413357\pi\) | ||||
0.268849 | + | 0.963182i | \(0.413357\pi\) | |||||||
\(258\) | 0.622518 | 0.0387563 | ||||||||
\(259\) | −5.42018 | −0.336793 | ||||||||
\(260\) | 1.12580 | 0.0698190 | ||||||||
\(261\) | 14.6880 | 0.909165 | ||||||||
\(262\) | −5.75249 | −0.355390 | ||||||||
\(263\) | −22.6467 | −1.39646 | −0.698228 | − | 0.715875i | \(-0.746028\pi\) | ||||
−0.698228 | + | 0.715875i | \(0.746028\pi\) | |||||||
\(264\) | −3.40108 | −0.209322 | ||||||||
\(265\) | −4.74143 | −0.291264 | ||||||||
\(266\) | −6.70269 | −0.410968 | ||||||||
\(267\) | 11.1350 | 0.681454 | ||||||||
\(268\) | −4.88292 | −0.298272 | ||||||||
\(269\) | −1.14346 | −0.0697182 | −0.0348591 | − | 0.999392i | \(-0.511098\pi\) | ||||
−0.0348591 | + | 0.999392i | \(0.511098\pi\) | |||||||
\(270\) | −6.02400 | −0.366609 | ||||||||
\(271\) | −26.5613 | −1.61349 | −0.806743 | − | 0.590903i | \(-0.798772\pi\) | ||||
−0.806743 | + | 0.590903i | \(0.798772\pi\) | |||||||
\(272\) | −3.62976 | −0.220086 | ||||||||
\(273\) | 0.637080 | 0.0385578 | ||||||||
\(274\) | −7.21273 | −0.435737 | ||||||||
\(275\) | 12.8663 | 0.775869 | ||||||||
\(276\) | 3.66063 | 0.220344 | ||||||||
\(277\) | −17.7413 | −1.06597 | −0.532987 | − | 0.846124i | \(-0.678930\pi\) | ||||
−0.532987 | + | 0.846124i | \(0.678930\pi\) | |||||||
\(278\) | 3.15380 | 0.189152 | ||||||||
\(279\) | 15.6501 | 0.936948 | ||||||||
\(280\) | 1.40867 | 0.0841841 | ||||||||
\(281\) | 3.28356 | 0.195881 | 0.0979404 | − | 0.995192i | \(-0.468775\pi\) | ||||
0.0979404 | + | 0.995192i | \(0.468775\pi\) | |||||||
\(282\) | 8.87112 | 0.528267 | ||||||||
\(283\) | 15.1321 | 0.899508 | 0.449754 | − | 0.893152i | \(-0.351512\pi\) | ||||
0.449754 | + | 0.893152i | \(0.351512\pi\) | |||||||
\(284\) | 9.37398 | 0.556243 | ||||||||
\(285\) | 7.52664 | 0.445840 | ||||||||
\(286\) | 3.40977 | 0.201624 | ||||||||
\(287\) | 4.51614 | 0.266580 | ||||||||
\(288\) | 2.36454 | 0.139332 | ||||||||
\(289\) | −3.82487 | −0.224993 | ||||||||
\(290\) | 8.75034 | 0.513838 | ||||||||
\(291\) | 2.82856 | 0.165813 | ||||||||
\(292\) | −3.99440 | −0.233755 | ||||||||
\(293\) | 3.09226 | 0.180652 | 0.0903259 | − | 0.995912i | \(-0.471209\pi\) | ||||
0.0903259 | + | 0.995912i | \(0.471209\pi\) | |||||||
\(294\) | 0.797155 | 0.0464910 | ||||||||
\(295\) | 7.60022 | 0.442502 | ||||||||
\(296\) | −5.42018 | −0.315041 | ||||||||
\(297\) | −18.2452 | −1.05870 | ||||||||
\(298\) | −16.0083 | −0.927337 | ||||||||
\(299\) | −3.66998 | −0.212240 | ||||||||
\(300\) | 2.40394 | 0.138792 | ||||||||
\(301\) | −0.780925 | −0.0450118 | ||||||||
\(302\) | −9.62444 | −0.553825 | ||||||||
\(303\) | −7.40942 | −0.425660 | ||||||||
\(304\) | −6.70269 | −0.384426 | ||||||||
\(305\) | −8.18062 | −0.468421 | ||||||||
\(306\) | −8.58272 | −0.490641 | ||||||||
\(307\) | 12.4885 | 0.712754 | 0.356377 | − | 0.934342i | \(-0.384012\pi\) | ||||
0.356377 | + | 0.934342i | \(0.384012\pi\) | |||||||
\(308\) | 4.26652 | 0.243108 | ||||||||
\(309\) | −6.73922 | −0.383381 | ||||||||
\(310\) | 9.32351 | 0.529540 | ||||||||
\(311\) | −17.8336 | −1.01125 | −0.505624 | − | 0.862754i | \(-0.668738\pi\) | ||||
−0.505624 | + | 0.862754i | \(0.668738\pi\) | |||||||
\(312\) | 0.637080 | 0.0360676 | ||||||||
\(313\) | −28.9134 | −1.63428 | −0.817142 | − | 0.576437i | \(-0.804443\pi\) | ||||
−0.817142 | + | 0.576437i | \(0.804443\pi\) | |||||||
\(314\) | 2.78528 | 0.157182 | ||||||||
\(315\) | 3.33086 | 0.187673 | ||||||||
\(316\) | 5.28980 | 0.297575 | ||||||||
\(317\) | −7.35728 | −0.413226 | −0.206613 | − | 0.978423i | \(-0.566244\pi\) | ||||
−0.206613 | + | 0.978423i | \(0.566244\pi\) | |||||||
\(318\) | −2.68314 | −0.150463 | ||||||||
\(319\) | 26.5027 | 1.48386 | ||||||||
\(320\) | 1.40867 | 0.0787470 | ||||||||
\(321\) | −9.63823 | −0.537954 | ||||||||
\(322\) | −4.59211 | −0.255908 | ||||||||
\(323\) | 24.3291 | 1.35371 | ||||||||
\(324\) | 3.68470 | 0.204705 | ||||||||
\(325\) | −2.41008 | −0.133687 | ||||||||
\(326\) | −7.65399 | −0.423915 | ||||||||
\(327\) | 4.39612 | 0.243106 | ||||||||
\(328\) | 4.51614 | 0.249362 | ||||||||
\(329\) | −11.1285 | −0.613532 | ||||||||
\(330\) | −4.79100 | −0.263736 | ||||||||
\(331\) | −6.60868 | −0.363246 | −0.181623 | − | 0.983368i | \(-0.558135\pi\) | ||||
−0.181623 | + | 0.983368i | \(0.558135\pi\) | |||||||
\(332\) | 14.1032 | 0.774015 | ||||||||
\(333\) | −12.8162 | −0.702326 | ||||||||
\(334\) | −8.70855 | −0.476511 | ||||||||
\(335\) | −6.87841 | −0.375808 | ||||||||
\(336\) | 0.797155 | 0.0434884 | ||||||||
\(337\) | −13.4528 | −0.732821 | −0.366411 | − | 0.930453i | \(-0.619413\pi\) | ||||
−0.366411 | + | 0.930453i | \(0.619413\pi\) | |||||||
\(338\) | 12.3613 | 0.672366 | ||||||||
\(339\) | −4.29069 | −0.233038 | ||||||||
\(340\) | −5.11313 | −0.277298 | ||||||||
\(341\) | 28.2387 | 1.52921 | ||||||||
\(342\) | −15.8488 | −0.857005 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −0.780925 | −0.0421046 | ||||||||
\(345\) | 5.15661 | 0.277623 | ||||||||
\(346\) | −0.799481 | −0.0429803 | ||||||||
\(347\) | −13.0592 | −0.701052 | −0.350526 | − | 0.936553i | \(-0.613997\pi\) | ||||
−0.350526 | + | 0.936553i | \(0.613997\pi\) | |||||||
\(348\) | 4.95175 | 0.265442 | ||||||||
\(349\) | −32.8893 | −1.76052 | −0.880262 | − | 0.474488i | \(-0.842633\pi\) | ||||
−0.880262 | + | 0.474488i | \(0.842633\pi\) | |||||||
\(350\) | −3.01565 | −0.161193 | ||||||||
\(351\) | 3.41764 | 0.182420 | ||||||||
\(352\) | 4.26652 | 0.227406 | ||||||||
\(353\) | 33.8962 | 1.80411 | 0.902056 | − | 0.431620i | \(-0.142058\pi\) | ||||
0.902056 | + | 0.431620i | \(0.142058\pi\) | |||||||
\(354\) | 4.30091 | 0.228591 | ||||||||
\(355\) | 13.2048 | 0.700840 | ||||||||
\(356\) | −13.9685 | −0.740328 | ||||||||
\(357\) | −2.89348 | −0.153139 | ||||||||
\(358\) | 7.40805 | 0.391528 | ||||||||
\(359\) | −20.3577 | −1.07444 | −0.537219 | − | 0.843442i | \(-0.680525\pi\) | ||||
−0.537219 | + | 0.843442i | \(0.680525\pi\) | |||||||
\(360\) | 3.33086 | 0.175552 | ||||||||
\(361\) | 25.9261 | 1.36453 | ||||||||
\(362\) | 11.7333 | 0.616686 | ||||||||
\(363\) | −5.74206 | −0.301380 | ||||||||
\(364\) | −0.799192 | −0.0418890 | ||||||||
\(365\) | −5.62680 | −0.294520 | ||||||||
\(366\) | −4.62935 | −0.241980 | ||||||||
\(367\) | 23.4757 | 1.22542 | 0.612710 | − | 0.790308i | \(-0.290079\pi\) | ||||
0.612710 | + | 0.790308i | \(0.290079\pi\) | |||||||
\(368\) | −4.59211 | −0.239380 | ||||||||
\(369\) | 10.6786 | 0.555907 | ||||||||
\(370\) | −7.63524 | −0.396937 | ||||||||
\(371\) | 3.36589 | 0.174748 | ||||||||
\(372\) | 5.27610 | 0.273553 | ||||||||
\(373\) | 7.31132 | 0.378566 | 0.189283 | − | 0.981923i | \(-0.439384\pi\) | ||||
0.189283 | + | 0.981923i | \(0.439384\pi\) | |||||||
\(374\) | −15.4864 | −0.800784 | ||||||||
\(375\) | 9.00100 | 0.464810 | ||||||||
\(376\) | −11.1285 | −0.573907 | ||||||||
\(377\) | −4.96440 | −0.255680 | ||||||||
\(378\) | 4.27637 | 0.219953 | ||||||||
\(379\) | −15.8034 | −0.811766 | −0.405883 | − | 0.913925i | \(-0.633036\pi\) | ||||
−0.405883 | + | 0.913925i | \(0.633036\pi\) | |||||||
\(380\) | −9.44188 | −0.484358 | ||||||||
\(381\) | −10.4180 | −0.533728 | ||||||||
\(382\) | −8.22734 | −0.420947 | ||||||||
\(383\) | 13.1987 | 0.674424 | 0.337212 | − | 0.941429i | \(-0.390516\pi\) | ||||
0.337212 | + | 0.941429i | \(0.390516\pi\) | |||||||
\(384\) | 0.797155 | 0.0406797 | ||||||||
\(385\) | 6.01012 | 0.306304 | ||||||||
\(386\) | 18.7582 | 0.954765 | ||||||||
\(387\) | −1.84653 | −0.0938644 | ||||||||
\(388\) | −3.54831 | −0.180138 | ||||||||
\(389\) | 33.1194 | 1.67922 | 0.839609 | − | 0.543191i | \(-0.182784\pi\) | ||||
0.839609 | + | 0.543191i | \(0.182784\pi\) | |||||||
\(390\) | 0.897435 | 0.0454434 | ||||||||
\(391\) | 16.6682 | 0.842949 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | −4.58563 | −0.231314 | ||||||||
\(394\) | 20.4237 | 1.02893 | ||||||||
\(395\) | 7.45159 | 0.374930 | ||||||||
\(396\) | 10.0884 | 0.506960 | ||||||||
\(397\) | −17.0911 | −0.857777 | −0.428888 | − | 0.903358i | \(-0.641095\pi\) | ||||
−0.428888 | + | 0.903358i | \(0.641095\pi\) | |||||||
\(398\) | 13.8409 | 0.693779 | ||||||||
\(399\) | −5.34309 | −0.267489 | ||||||||
\(400\) | −3.01565 | −0.150782 | ||||||||
\(401\) | −20.1721 | −1.00735 | −0.503673 | − | 0.863894i | \(-0.668018\pi\) | ||||
−0.503673 | + | 0.863894i | \(0.668018\pi\) | |||||||
\(402\) | −3.89244 | −0.194137 | ||||||||
\(403\) | −5.28958 | −0.263493 | ||||||||
\(404\) | 9.29483 | 0.462435 | ||||||||
\(405\) | 5.19052 | 0.257919 | ||||||||
\(406\) | −6.21178 | −0.308285 | ||||||||
\(407\) | −23.1253 | −1.14628 | ||||||||
\(408\) | −2.89348 | −0.143249 | ||||||||
\(409\) | 32.3193 | 1.59809 | 0.799043 | − | 0.601274i | \(-0.205340\pi\) | ||||
0.799043 | + | 0.601274i | \(0.205340\pi\) | |||||||
\(410\) | 6.36175 | 0.314185 | ||||||||
\(411\) | −5.74967 | −0.283610 | ||||||||
\(412\) | 8.45408 | 0.416503 | ||||||||
\(413\) | −5.39532 | −0.265486 | ||||||||
\(414\) | −10.8582 | −0.533654 | ||||||||
\(415\) | 19.8668 | 0.975222 | ||||||||
\(416\) | −0.799192 | −0.0391836 | ||||||||
\(417\) | 2.51407 | 0.123114 | ||||||||
\(418\) | −28.5972 | −1.39873 | ||||||||
\(419\) | −22.7045 | −1.10919 | −0.554594 | − | 0.832121i | \(-0.687126\pi\) | ||||
−0.554594 | + | 0.832121i | \(0.687126\pi\) | |||||||
\(420\) | 1.12293 | 0.0547933 | ||||||||
\(421\) | 16.2815 | 0.793513 | 0.396756 | − | 0.917924i | \(-0.370136\pi\) | ||||
0.396756 | + | 0.917924i | \(0.370136\pi\) | |||||||
\(422\) | −22.7593 | −1.10790 | ||||||||
\(423\) | −26.3137 | −1.27942 | ||||||||
\(424\) | 3.36589 | 0.163462 | ||||||||
\(425\) | 10.9461 | 0.530962 | ||||||||
\(426\) | 7.47251 | 0.362044 | ||||||||
\(427\) | 5.80734 | 0.281037 | ||||||||
\(428\) | 12.0908 | 0.584430 | ||||||||
\(429\) | 2.71811 | 0.131232 | ||||||||
\(430\) | −1.10007 | −0.0530499 | ||||||||
\(431\) | 1.00000 | 0.0481683 | ||||||||
\(432\) | 4.27637 | 0.205747 | ||||||||
\(433\) | 5.04478 | 0.242437 | 0.121218 | − | 0.992626i | \(-0.461320\pi\) | ||||
0.121218 | + | 0.992626i | \(0.461320\pi\) | |||||||
\(434\) | −6.61866 | −0.317706 | ||||||||
\(435\) | 6.97538 | 0.334444 | ||||||||
\(436\) | −5.51476 | −0.264109 | ||||||||
\(437\) | 30.7795 | 1.47238 | ||||||||
\(438\) | −3.18416 | −0.152145 | ||||||||
\(439\) | 12.8675 | 0.614132 | 0.307066 | − | 0.951688i | \(-0.400653\pi\) | ||||
0.307066 | + | 0.951688i | \(0.400653\pi\) | |||||||
\(440\) | 6.01012 | 0.286521 | ||||||||
\(441\) | −2.36454 | −0.112597 | ||||||||
\(442\) | 2.90087 | 0.137980 | ||||||||
\(443\) | 7.97797 | 0.379045 | 0.189522 | − | 0.981876i | \(-0.439306\pi\) | ||||
0.189522 | + | 0.981876i | \(0.439306\pi\) | |||||||
\(444\) | −4.32072 | −0.205052 | ||||||||
\(445\) | −19.6770 | −0.932778 | ||||||||
\(446\) | 8.70757 | 0.412315 | ||||||||
\(447\) | −12.7611 | −0.603580 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | 33.4115 | 1.57679 | 0.788394 | − | 0.615171i | \(-0.210913\pi\) | ||||
0.788394 | + | 0.615171i | \(0.210913\pi\) | |||||||
\(450\) | −7.13063 | −0.336141 | ||||||||
\(451\) | 19.2682 | 0.907305 | ||||||||
\(452\) | 5.38250 | 0.253171 | ||||||||
\(453\) | −7.67218 | −0.360470 | ||||||||
\(454\) | 16.8011 | 0.788515 | ||||||||
\(455\) | −1.12580 | −0.0527782 | ||||||||
\(456\) | −5.34309 | −0.250213 | ||||||||
\(457\) | 14.1064 | 0.659871 | 0.329935 | − | 0.944004i | \(-0.392973\pi\) | ||||
0.329935 | + | 0.944004i | \(0.392973\pi\) | |||||||
\(458\) | −24.0920 | −1.12575 | ||||||||
\(459\) | −15.5222 | −0.724514 | ||||||||
\(460\) | −6.46877 | −0.301608 | ||||||||
\(461\) | 12.0170 | 0.559688 | 0.279844 | − | 0.960046i | \(-0.409717\pi\) | ||||
0.279844 | + | 0.960046i | \(0.409717\pi\) | |||||||
\(462\) | 3.40108 | 0.158233 | ||||||||
\(463\) | −11.9976 | −0.557575 | −0.278787 | − | 0.960353i | \(-0.589932\pi\) | ||||
−0.278787 | + | 0.960353i | \(0.589932\pi\) | |||||||
\(464\) | −6.21178 | −0.288375 | ||||||||
\(465\) | 7.43228 | 0.344664 | ||||||||
\(466\) | 12.7964 | 0.592782 | ||||||||
\(467\) | 11.6270 | 0.538035 | 0.269018 | − | 0.963135i | \(-0.413301\pi\) | ||||
0.269018 | + | 0.963135i | \(0.413301\pi\) | |||||||
\(468\) | −1.88972 | −0.0873525 | ||||||||
\(469\) | 4.88292 | 0.225472 | ||||||||
\(470\) | −15.6763 | −0.723095 | ||||||||
\(471\) | 2.22030 | 0.102306 | ||||||||
\(472\) | −5.39532 | −0.248340 | ||||||||
\(473\) | −3.33183 | −0.153198 | ||||||||
\(474\) | 4.21680 | 0.193684 | ||||||||
\(475\) | 20.2130 | 0.927435 | ||||||||
\(476\) | 3.62976 | 0.166370 | ||||||||
\(477\) | 7.95880 | 0.364408 | ||||||||
\(478\) | −2.87318 | −0.131416 | ||||||||
\(479\) | 2.99665 | 0.136921 | 0.0684603 | − | 0.997654i | \(-0.478191\pi\) | ||||
0.0684603 | + | 0.997654i | \(0.478191\pi\) | |||||||
\(480\) | 1.12293 | 0.0512544 | ||||||||
\(481\) | 4.33176 | 0.197511 | ||||||||
\(482\) | 8.19163 | 0.373118 | ||||||||
\(483\) | −3.66063 | −0.166564 | ||||||||
\(484\) | 7.20319 | 0.327418 | ||||||||
\(485\) | −4.99840 | −0.226966 | ||||||||
\(486\) | 15.7664 | 0.715178 | ||||||||
\(487\) | −18.3844 | −0.833079 | −0.416539 | − | 0.909118i | \(-0.636757\pi\) | ||||
−0.416539 | + | 0.909118i | \(0.636757\pi\) | |||||||
\(488\) | 5.80734 | 0.262886 | ||||||||
\(489\) | −6.10142 | −0.275916 | ||||||||
\(490\) | −1.40867 | −0.0636372 | ||||||||
\(491\) | 21.2906 | 0.960832 | 0.480416 | − | 0.877041i | \(-0.340486\pi\) | ||||
0.480416 | + | 0.877041i | \(0.340486\pi\) | |||||||
\(492\) | 3.60007 | 0.162304 | ||||||||
\(493\) | 22.5472 | 1.01548 | ||||||||
\(494\) | 5.35674 | 0.241011 | ||||||||
\(495\) | 14.2112 | 0.638745 | ||||||||
\(496\) | −6.61866 | −0.297187 | ||||||||
\(497\) | −9.37398 | −0.420480 | ||||||||
\(498\) | 11.2425 | 0.503787 | ||||||||
\(499\) | 39.7003 | 1.77723 | 0.888614 | − | 0.458655i | \(-0.151669\pi\) | ||||
0.888614 | + | 0.458655i | \(0.151669\pi\) | |||||||
\(500\) | −11.2914 | −0.504967 | ||||||||
\(501\) | −6.94207 | −0.310149 | ||||||||
\(502\) | 14.2956 | 0.638045 | ||||||||
\(503\) | −24.7499 | −1.10354 | −0.551772 | − | 0.833995i | \(-0.686048\pi\) | ||||
−0.551772 | + | 0.833995i | \(0.686048\pi\) | |||||||
\(504\) | −2.36454 | −0.105325 | ||||||||
\(505\) | 13.0933 | 0.582646 | ||||||||
\(506\) | −19.5923 | −0.870986 | ||||||||
\(507\) | 9.85387 | 0.437626 | ||||||||
\(508\) | 13.0689 | 0.579839 | ||||||||
\(509\) | 16.9879 | 0.752977 | 0.376489 | − | 0.926421i | \(-0.377131\pi\) | ||||
0.376489 | + | 0.926421i | \(0.377131\pi\) | |||||||
\(510\) | −4.07596 | −0.180486 | ||||||||
\(511\) | 3.99440 | 0.176702 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −28.6632 | −1.26551 | ||||||||
\(514\) | −8.61994 | −0.380209 | ||||||||
\(515\) | 11.9090 | 0.524774 | ||||||||
\(516\) | −0.622518 | −0.0274048 | ||||||||
\(517\) | −47.4798 | −2.08816 | ||||||||
\(518\) | 5.42018 | 0.238149 | ||||||||
\(519\) | −0.637310 | −0.0279748 | ||||||||
\(520\) | −1.12580 | −0.0493695 | ||||||||
\(521\) | −0.356556 | −0.0156210 | −0.00781050 | − | 0.999969i | \(-0.502486\pi\) | ||||
−0.00781050 | + | 0.999969i | \(0.502486\pi\) | |||||||
\(522\) | −14.6880 | −0.642877 | ||||||||
\(523\) | 0.463689 | 0.0202757 | 0.0101379 | − | 0.999949i | \(-0.496773\pi\) | ||||
0.0101379 | + | 0.999949i | \(0.496773\pi\) | |||||||
\(524\) | 5.75249 | 0.251299 | ||||||||
\(525\) | −2.40394 | −0.104917 | ||||||||
\(526\) | 22.6467 | 0.987444 | ||||||||
\(527\) | 24.0241 | 1.04651 | ||||||||
\(528\) | 3.40108 | 0.148013 | ||||||||
\(529\) | −1.91250 | −0.0831523 | ||||||||
\(530\) | 4.74143 | 0.205955 | ||||||||
\(531\) | −12.7575 | −0.553627 | ||||||||
\(532\) | 6.70269 | 0.290599 | ||||||||
\(533\) | −3.60927 | −0.156335 | ||||||||
\(534\) | −11.1350 | −0.481861 | ||||||||
\(535\) | 17.0319 | 0.736354 | ||||||||
\(536\) | 4.88292 | 0.210910 | ||||||||
\(537\) | 5.90537 | 0.254835 | ||||||||
\(538\) | 1.14346 | 0.0492982 | ||||||||
\(539\) | −4.26652 | −0.183772 | ||||||||
\(540\) | 6.02400 | 0.259232 | ||||||||
\(541\) | −18.7910 | −0.807888 | −0.403944 | − | 0.914784i | \(-0.632361\pi\) | ||||
−0.403944 | + | 0.914784i | \(0.632361\pi\) | |||||||
\(542\) | 26.5613 | 1.14091 | ||||||||
\(543\) | 9.35323 | 0.401385 | ||||||||
\(544\) | 3.62976 | 0.155624 | ||||||||
\(545\) | −7.76848 | −0.332765 | ||||||||
\(546\) | −0.637080 | −0.0272645 | ||||||||
\(547\) | 22.4507 | 0.959923 | 0.479962 | − | 0.877290i | \(-0.340651\pi\) | ||||
0.479962 | + | 0.877290i | \(0.340651\pi\) | |||||||
\(548\) | 7.21273 | 0.308113 | ||||||||
\(549\) | 13.7317 | 0.586055 | ||||||||
\(550\) | −12.8663 | −0.548622 | ||||||||
\(551\) | 41.6356 | 1.77374 | ||||||||
\(552\) | −3.66063 | −0.155807 | ||||||||
\(553\) | −5.28980 | −0.224945 | ||||||||
\(554\) | 17.7413 | 0.753757 | ||||||||
\(555\) | −6.08647 | −0.258356 | ||||||||
\(556\) | −3.15380 | −0.133751 | ||||||||
\(557\) | 26.9804 | 1.14320 | 0.571599 | − | 0.820533i | \(-0.306323\pi\) | ||||
0.571599 | + | 0.820533i | \(0.306323\pi\) | |||||||
\(558\) | −15.6501 | −0.662522 | ||||||||
\(559\) | 0.624109 | 0.0263970 | ||||||||
\(560\) | −1.40867 | −0.0595272 | ||||||||
\(561\) | −12.3451 | −0.521210 | ||||||||
\(562\) | −3.28356 | −0.138509 | ||||||||
\(563\) | 9.44939 | 0.398244 | 0.199122 | − | 0.979975i | \(-0.436191\pi\) | ||||
0.199122 | + | 0.979975i | \(0.436191\pi\) | |||||||
\(564\) | −8.87112 | −0.373541 | ||||||||
\(565\) | 7.58216 | 0.318984 | ||||||||
\(566\) | −15.1321 | −0.636048 | ||||||||
\(567\) | −3.68470 | −0.154743 | ||||||||
\(568\) | −9.37398 | −0.393323 | ||||||||
\(569\) | −22.8688 | −0.958710 | −0.479355 | − | 0.877621i | \(-0.659129\pi\) | ||||
−0.479355 | + | 0.877621i | \(0.659129\pi\) | |||||||
\(570\) | −7.52664 | −0.315256 | ||||||||
\(571\) | 33.7728 | 1.41335 | 0.706674 | − | 0.707539i | \(-0.250195\pi\) | ||||
0.706674 | + | 0.707539i | \(0.250195\pi\) | |||||||
\(572\) | −3.40977 | −0.142570 | ||||||||
\(573\) | −6.55847 | −0.273984 | ||||||||
\(574\) | −4.51614 | −0.188500 | ||||||||
\(575\) | 13.8482 | 0.577510 | ||||||||
\(576\) | −2.36454 | −0.0985226 | ||||||||
\(577\) | 30.0463 | 1.25084 | 0.625422 | − | 0.780286i | \(-0.284927\pi\) | ||||
0.625422 | + | 0.780286i | \(0.284927\pi\) | |||||||
\(578\) | 3.82487 | 0.159094 | ||||||||
\(579\) | 14.9532 | 0.621432 | ||||||||
\(580\) | −8.75034 | −0.363338 | ||||||||
\(581\) | −14.1032 | −0.585100 | ||||||||
\(582\) | −2.82856 | −0.117247 | ||||||||
\(583\) | 14.3606 | 0.594757 | ||||||||
\(584\) | 3.99440 | 0.165290 | ||||||||
\(585\) | −2.66200 | −0.110060 | ||||||||
\(586\) | −3.09226 | −0.127740 | ||||||||
\(587\) | −3.46068 | −0.142838 | −0.0714189 | − | 0.997446i | \(-0.522753\pi\) | ||||
−0.0714189 | + | 0.997446i | \(0.522753\pi\) | |||||||
\(588\) | −0.797155 | −0.0328741 | ||||||||
\(589\) | 44.3628 | 1.82794 | ||||||||
\(590\) | −7.60022 | −0.312896 | ||||||||
\(591\) | 16.2808 | 0.669703 | ||||||||
\(592\) | 5.42018 | 0.222768 | ||||||||
\(593\) | 10.4962 | 0.431029 | 0.215514 | − | 0.976501i | \(-0.430857\pi\) | ||||
0.215514 | + | 0.976501i | \(0.430857\pi\) | |||||||
\(594\) | 18.2452 | 0.748611 | ||||||||
\(595\) | 5.11313 | 0.209618 | ||||||||
\(596\) | 16.0083 | 0.655726 | ||||||||
\(597\) | 11.0333 | 0.451563 | ||||||||
\(598\) | 3.66998 | 0.150077 | ||||||||
\(599\) | 6.44694 | 0.263415 | 0.131707 | − | 0.991289i | \(-0.457954\pi\) | ||||
0.131707 | + | 0.991289i | \(0.457954\pi\) | |||||||
\(600\) | −2.40394 | −0.0981405 | ||||||||
\(601\) | −8.45631 | −0.344940 | −0.172470 | − | 0.985015i | \(-0.555175\pi\) | ||||
−0.172470 | + | 0.985015i | \(0.555175\pi\) | |||||||
\(602\) | 0.780925 | 0.0318281 | ||||||||
\(603\) | 11.5459 | 0.470184 | ||||||||
\(604\) | 9.62444 | 0.391613 | ||||||||
\(605\) | 10.1469 | 0.412531 | ||||||||
\(606\) | 7.40942 | 0.300987 | ||||||||
\(607\) | −25.4777 | −1.03411 | −0.517053 | − | 0.855953i | \(-0.672971\pi\) | ||||
−0.517053 | + | 0.855953i | \(0.672971\pi\) | |||||||
\(608\) | 6.70269 | 0.271830 | ||||||||
\(609\) | −4.95175 | −0.200655 | ||||||||
\(610\) | 8.18062 | 0.331224 | ||||||||
\(611\) | 8.89378 | 0.359804 | ||||||||
\(612\) | 8.58272 | 0.346936 | ||||||||
\(613\) | −37.4831 | −1.51393 | −0.756964 | − | 0.653456i | \(-0.773318\pi\) | ||||
−0.756964 | + | 0.653456i | \(0.773318\pi\) | |||||||
\(614\) | −12.4885 | −0.503993 | ||||||||
\(615\) | 5.07131 | 0.204495 | ||||||||
\(616\) | −4.26652 | −0.171903 | ||||||||
\(617\) | 44.3768 | 1.78654 | 0.893271 | − | 0.449518i | \(-0.148404\pi\) | ||||
0.893271 | + | 0.449518i | \(0.148404\pi\) | |||||||
\(618\) | 6.73922 | 0.271091 | ||||||||
\(619\) | 23.0916 | 0.928131 | 0.464066 | − | 0.885801i | \(-0.346390\pi\) | ||||
0.464066 | + | 0.885801i | \(0.346390\pi\) | |||||||
\(620\) | −9.32351 | −0.374441 | ||||||||
\(621\) | −19.6376 | −0.788029 | ||||||||
\(622\) | 17.8336 | 0.715060 | ||||||||
\(623\) | 13.9685 | 0.559635 | ||||||||
\(624\) | −0.637080 | −0.0255036 | ||||||||
\(625\) | −0.827608 | −0.0331043 | ||||||||
\(626\) | 28.9134 | 1.15561 | ||||||||
\(627\) | −22.7964 | −0.910400 | ||||||||
\(628\) | −2.78528 | −0.111145 | ||||||||
\(629\) | −19.6739 | −0.784451 | ||||||||
\(630\) | −3.33086 | −0.132705 | ||||||||
\(631\) | −0.164653 | −0.00655472 | −0.00327736 | − | 0.999995i | \(-0.501043\pi\) | ||||
−0.00327736 | + | 0.999995i | \(0.501043\pi\) | |||||||
\(632\) | −5.28980 | −0.210417 | ||||||||
\(633\) | −18.1427 | −0.721107 | ||||||||
\(634\) | 7.35728 | 0.292195 | ||||||||
\(635\) | 18.4098 | 0.730570 | ||||||||
\(636\) | 2.68314 | 0.106393 | ||||||||
\(637\) | 0.799192 | 0.0316651 | ||||||||
\(638\) | −26.5027 | −1.04925 | ||||||||
\(639\) | −22.1652 | −0.876841 | ||||||||
\(640\) | −1.40867 | −0.0556826 | ||||||||
\(641\) | 5.09320 | 0.201169 | 0.100585 | − | 0.994928i | \(-0.467929\pi\) | ||||
0.100585 | + | 0.994928i | \(0.467929\pi\) | |||||||
\(642\) | 9.63823 | 0.380391 | ||||||||
\(643\) | −27.0878 | −1.06824 | −0.534119 | − | 0.845409i | \(-0.679357\pi\) | ||||
−0.534119 | + | 0.845409i | \(0.679357\pi\) | |||||||
\(644\) | 4.59211 | 0.180955 | ||||||||
\(645\) | −0.876923 | −0.0345288 | ||||||||
\(646\) | −24.3291 | −0.957217 | ||||||||
\(647\) | 9.90929 | 0.389574 | 0.194787 | − | 0.980846i | \(-0.437598\pi\) | ||||
0.194787 | + | 0.980846i | \(0.437598\pi\) | |||||||
\(648\) | −3.68470 | −0.144749 | ||||||||
\(649\) | −23.0192 | −0.903584 | ||||||||
\(650\) | 2.41008 | 0.0945312 | ||||||||
\(651\) | −5.27610 | −0.206787 | ||||||||
\(652\) | 7.65399 | 0.299753 | ||||||||
\(653\) | 10.1183 | 0.395961 | 0.197980 | − | 0.980206i | \(-0.436562\pi\) | ||||
0.197980 | + | 0.980206i | \(0.436562\pi\) | |||||||
\(654\) | −4.39612 | −0.171902 | ||||||||
\(655\) | 8.10335 | 0.316624 | ||||||||
\(656\) | −4.51614 | −0.176326 | ||||||||
\(657\) | 9.44494 | 0.368482 | ||||||||
\(658\) | 11.1285 | 0.433833 | ||||||||
\(659\) | −22.7802 | −0.887392 | −0.443696 | − | 0.896177i | \(-0.646333\pi\) | ||||
−0.443696 | + | 0.896177i | \(0.646333\pi\) | |||||||
\(660\) | 4.79100 | 0.186489 | ||||||||
\(661\) | −29.7642 | −1.15769 | −0.578846 | − | 0.815437i | \(-0.696497\pi\) | ||||
−0.578846 | + | 0.815437i | \(0.696497\pi\) | |||||||
\(662\) | 6.60868 | 0.256854 | ||||||||
\(663\) | 2.31244 | 0.0898079 | ||||||||
\(664\) | −14.1032 | −0.547311 | ||||||||
\(665\) | 9.44188 | 0.366140 | ||||||||
\(666\) | 12.8162 | 0.496619 | ||||||||
\(667\) | 28.5252 | 1.10450 | ||||||||
\(668\) | 8.70855 | 0.336944 | ||||||||
\(669\) | 6.94128 | 0.268365 | ||||||||
\(670\) | 6.87841 | 0.265736 | ||||||||
\(671\) | 24.7771 | 0.956510 | ||||||||
\(672\) | −0.797155 | −0.0307509 | ||||||||
\(673\) | 5.64016 | 0.217412 | 0.108706 | − | 0.994074i | \(-0.465329\pi\) | ||||
0.108706 | + | 0.994074i | \(0.465329\pi\) | |||||||
\(674\) | 13.4528 | 0.518183 | ||||||||
\(675\) | −12.8960 | −0.496369 | ||||||||
\(676\) | −12.3613 | −0.475434 | ||||||||
\(677\) | −31.1155 | −1.19586 | −0.597932 | − | 0.801547i | \(-0.704011\pi\) | ||||
−0.597932 | + | 0.801547i | \(0.704011\pi\) | |||||||
\(678\) | 4.29069 | 0.164783 | ||||||||
\(679\) | 3.54831 | 0.136172 | ||||||||
\(680\) | 5.11313 | 0.196079 | ||||||||
\(681\) | 13.3931 | 0.513224 | ||||||||
\(682\) | −28.2387 | −1.08131 | ||||||||
\(683\) | −0.451659 | −0.0172822 | −0.00864112 | − | 0.999963i | \(-0.502751\pi\) | ||||
−0.00864112 | + | 0.999963i | \(0.502751\pi\) | |||||||
\(684\) | 15.8488 | 0.605994 | ||||||||
\(685\) | 10.1604 | 0.388207 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | −19.2051 | −0.732719 | ||||||||
\(688\) | 0.780925 | 0.0297725 | ||||||||
\(689\) | −2.68999 | −0.102481 | ||||||||
\(690\) | −5.15661 | −0.196309 | ||||||||
\(691\) | −40.4771 | −1.53982 | −0.769910 | − | 0.638152i | \(-0.779699\pi\) | ||||
−0.769910 | + | 0.638152i | \(0.779699\pi\) | |||||||
\(692\) | 0.799481 | 0.0303917 | ||||||||
\(693\) | −10.0884 | −0.383226 | ||||||||
\(694\) | 13.0592 | 0.495719 | ||||||||
\(695\) | −4.44266 | −0.168520 | ||||||||
\(696\) | −4.95175 | −0.187696 | ||||||||
\(697\) | 16.3925 | 0.620910 | ||||||||
\(698\) | 32.8893 | 1.24488 | ||||||||
\(699\) | 10.2007 | 0.385827 | ||||||||
\(700\) | 3.01565 | 0.113981 | ||||||||
\(701\) | 9.36340 | 0.353651 | 0.176825 | − | 0.984242i | \(-0.443417\pi\) | ||||
0.176825 | + | 0.984242i | \(0.443417\pi\) | |||||||
\(702\) | −3.41764 | −0.128991 | ||||||||
\(703\) | −36.3298 | −1.37020 | ||||||||
\(704\) | −4.26652 | −0.160801 | ||||||||
\(705\) | −12.4965 | −0.470644 | ||||||||
\(706\) | −33.8962 | −1.27570 | ||||||||
\(707\) | −9.29483 | −0.349568 | ||||||||
\(708\) | −4.30091 | −0.161638 | ||||||||
\(709\) | 42.8899 | 1.61076 | 0.805381 | − | 0.592757i | \(-0.201961\pi\) | ||||
0.805381 | + | 0.592757i | \(0.201961\pi\) | |||||||
\(710\) | −13.2048 | −0.495569 | ||||||||
\(711\) | −12.5080 | −0.469086 | ||||||||
\(712\) | 13.9685 | 0.523491 | ||||||||
\(713\) | 30.3936 | 1.13825 | ||||||||
\(714\) | 2.89348 | 0.108286 | ||||||||
\(715\) | −4.80324 | −0.179631 | ||||||||
\(716\) | −7.40805 | −0.276852 | ||||||||
\(717\) | −2.29037 | −0.0855354 | ||||||||
\(718\) | 20.3577 | 0.759743 | ||||||||
\(719\) | 42.3347 | 1.57882 | 0.789409 | − | 0.613867i | \(-0.210387\pi\) | ||||
0.789409 | + | 0.613867i | \(0.210387\pi\) | |||||||
\(720\) | −3.33086 | −0.124134 | ||||||||
\(721\) | −8.45408 | −0.314846 | ||||||||
\(722\) | −25.9261 | −0.964869 | ||||||||
\(723\) | 6.53000 | 0.242853 | ||||||||
\(724\) | −11.7333 | −0.436063 | ||||||||
\(725\) | 18.7325 | 0.695709 | ||||||||
\(726\) | 5.74206 | 0.213108 | ||||||||
\(727\) | 50.0598 | 1.85661 | 0.928307 | − | 0.371814i | \(-0.121264\pi\) | ||||
0.928307 | + | 0.371814i | \(0.121264\pi\) | |||||||
\(728\) | 0.799192 | 0.0296200 | ||||||||
\(729\) | 1.51418 | 0.0560806 | ||||||||
\(730\) | 5.62680 | 0.208257 | ||||||||
\(731\) | −2.83457 | −0.104840 | ||||||||
\(732\) | 4.62935 | 0.171106 | ||||||||
\(733\) | −42.7236 | −1.57803 | −0.789016 | − | 0.614372i | \(-0.789409\pi\) | ||||
−0.789016 | + | 0.614372i | \(0.789409\pi\) | |||||||
\(734\) | −23.4757 | −0.866503 | ||||||||
\(735\) | −1.12293 | −0.0414198 | ||||||||
\(736\) | 4.59211 | 0.169268 | ||||||||
\(737\) | 20.8331 | 0.767395 | ||||||||
\(738\) | −10.6786 | −0.393085 | ||||||||
\(739\) | −17.5227 | −0.644583 | −0.322292 | − | 0.946640i | \(-0.604453\pi\) | ||||
−0.322292 | + | 0.946640i | \(0.604453\pi\) | |||||||
\(740\) | 7.63524 | 0.280677 | ||||||||
\(741\) | 4.27015 | 0.156868 | ||||||||
\(742\) | −3.36589 | −0.123566 | ||||||||
\(743\) | −19.0604 | −0.699259 | −0.349629 | − | 0.936888i | \(-0.613693\pi\) | ||||
−0.349629 | + | 0.936888i | \(0.613693\pi\) | |||||||
\(744\) | −5.27610 | −0.193431 | ||||||||
\(745\) | 22.5504 | 0.826184 | ||||||||
\(746\) | −7.31132 | −0.267686 | ||||||||
\(747\) | −33.3477 | −1.22013 | ||||||||
\(748\) | 15.4864 | 0.566240 | ||||||||
\(749\) | −12.0908 | −0.441788 | ||||||||
\(750\) | −9.00100 | −0.328670 | ||||||||
\(751\) | 39.7034 | 1.44880 | 0.724398 | − | 0.689382i | \(-0.242118\pi\) | ||||
0.724398 | + | 0.689382i | \(0.242118\pi\) | |||||||
\(752\) | 11.1285 | 0.405813 | ||||||||
\(753\) | 11.3958 | 0.415287 | ||||||||
\(754\) | 4.96440 | 0.180793 | ||||||||
\(755\) | 13.5577 | 0.493414 | ||||||||
\(756\) | −4.27637 | −0.155530 | ||||||||
\(757\) | 29.3432 | 1.06650 | 0.533248 | − | 0.845959i | \(-0.320971\pi\) | ||||
0.533248 | + | 0.845959i | \(0.320971\pi\) | |||||||
\(758\) | 15.8034 | 0.574005 | ||||||||
\(759\) | −15.6181 | −0.566902 | ||||||||
\(760\) | 9.44188 | 0.342493 | ||||||||
\(761\) | 8.77351 | 0.318039 | 0.159020 | − | 0.987275i | \(-0.449167\pi\) | ||||
0.159020 | + | 0.987275i | \(0.449167\pi\) | |||||||
\(762\) | 10.4180 | 0.377403 | ||||||||
\(763\) | 5.51476 | 0.199648 | ||||||||
\(764\) | 8.22734 | 0.297655 | ||||||||
\(765\) | 12.0902 | 0.437122 | ||||||||
\(766\) | −13.1987 | −0.476890 | ||||||||
\(767\) | 4.31189 | 0.155693 | ||||||||
\(768\) | −0.797155 | −0.0287649 | ||||||||
\(769\) | −2.17784 | −0.0785349 | −0.0392675 | − | 0.999229i | \(-0.512502\pi\) | ||||
−0.0392675 | + | 0.999229i | \(0.512502\pi\) | |||||||
\(770\) | −6.01012 | −0.216590 | ||||||||
\(771\) | −6.87143 | −0.247469 | ||||||||
\(772\) | −18.7582 | −0.675121 | ||||||||
\(773\) | 16.9098 | 0.608204 | 0.304102 | − | 0.952639i | \(-0.401644\pi\) | ||||
0.304102 | + | 0.952639i | \(0.401644\pi\) | |||||||
\(774\) | 1.84653 | 0.0663722 | ||||||||
\(775\) | 19.9596 | 0.716969 | ||||||||
\(776\) | 3.54831 | 0.127377 | ||||||||
\(777\) | 4.32072 | 0.155005 | ||||||||
\(778\) | −33.1194 | −1.18739 | ||||||||
\(779\) | 30.2703 | 1.08455 | ||||||||
\(780\) | −0.897435 | −0.0321333 | ||||||||
\(781\) | −39.9943 | −1.43111 | ||||||||
\(782\) | −16.6682 | −0.596055 | ||||||||
\(783\) | −26.5639 | −0.949316 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −3.92354 | −0.140037 | ||||||||
\(786\) | 4.58563 | 0.163564 | ||||||||
\(787\) | −0.623669 | −0.0222314 | −0.0111157 | − | 0.999938i | \(-0.503538\pi\) | ||||
−0.0111157 | + | 0.999938i | \(0.503538\pi\) | |||||||
\(788\) | −20.4237 | −0.727562 | ||||||||
\(789\) | 18.0530 | 0.642702 | ||||||||
\(790\) | −7.45159 | −0.265116 | ||||||||
\(791\) | −5.38250 | −0.191380 | ||||||||
\(792\) | −10.0884 | −0.358475 | ||||||||
\(793\) | −4.64118 | −0.164813 | ||||||||
\(794\) | 17.0911 | 0.606540 | ||||||||
\(795\) | 3.77966 | 0.134051 | ||||||||
\(796\) | −13.8409 | −0.490576 | ||||||||
\(797\) | 35.5372 | 1.25879 | 0.629396 | − | 0.777084i | \(-0.283302\pi\) | ||||
0.629396 | + | 0.777084i | \(0.283302\pi\) | |||||||
\(798\) | 5.34309 | 0.189143 | ||||||||
\(799\) | −40.3936 | −1.42902 | ||||||||
\(800\) | 3.01565 | 0.106619 | ||||||||
\(801\) | 33.0291 | 1.16702 | ||||||||
\(802\) | 20.1721 | 0.712301 | ||||||||
\(803\) | 17.0422 | 0.601406 | ||||||||
\(804\) | 3.89244 | 0.137276 | ||||||||
\(805\) | 6.46877 | 0.227994 | ||||||||
\(806\) | 5.28958 | 0.186318 | ||||||||
\(807\) | 0.911518 | 0.0320870 | ||||||||
\(808\) | −9.29483 | −0.326991 | ||||||||
\(809\) | 15.9061 | 0.559227 | 0.279614 | − | 0.960113i | \(-0.409794\pi\) | ||||
0.279614 | + | 0.960113i | \(0.409794\pi\) | |||||||
\(810\) | −5.19052 | −0.182376 | ||||||||
\(811\) | 21.1041 | 0.741064 | 0.370532 | − | 0.928820i | \(-0.379175\pi\) | ||||
0.370532 | + | 0.928820i | \(0.379175\pi\) | |||||||
\(812\) | 6.21178 | 0.217991 | ||||||||
\(813\) | 21.1735 | 0.742587 | ||||||||
\(814\) | 23.1253 | 0.810541 | ||||||||
\(815\) | 10.7819 | 0.377675 | ||||||||
\(816\) | 2.89348 | 0.101292 | ||||||||
\(817\) | −5.23430 | −0.183125 | ||||||||
\(818\) | −32.3193 | −1.13002 | ||||||||
\(819\) | 1.88972 | 0.0660323 | ||||||||
\(820\) | −6.36175 | −0.222162 | ||||||||
\(821\) | 14.3095 | 0.499405 | 0.249702 | − | 0.968323i | \(-0.419667\pi\) | ||||
0.249702 | + | 0.968323i | \(0.419667\pi\) | |||||||
\(822\) | 5.74967 | 0.200543 | ||||||||
\(823\) | −45.2039 | −1.57571 | −0.787854 | − | 0.615862i | \(-0.788808\pi\) | ||||
−0.787854 | + | 0.615862i | \(0.788808\pi\) | |||||||
\(824\) | −8.45408 | −0.294512 | ||||||||
\(825\) | −10.2565 | −0.357084 | ||||||||
\(826\) | 5.39532 | 0.187727 | ||||||||
\(827\) | −1.63444 | −0.0568352 | −0.0284176 | − | 0.999596i | \(-0.509047\pi\) | ||||
−0.0284176 | + | 0.999596i | \(0.509047\pi\) | |||||||
\(828\) | 10.8582 | 0.377350 | ||||||||
\(829\) | −6.78874 | −0.235783 | −0.117891 | − | 0.993026i | \(-0.537613\pi\) | ||||
−0.117891 | + | 0.993026i | \(0.537613\pi\) | |||||||
\(830\) | −19.8668 | −0.689586 | ||||||||
\(831\) | 14.1426 | 0.490601 | ||||||||
\(832\) | 0.799192 | 0.0277070 | ||||||||
\(833\) | −3.62976 | −0.125764 | ||||||||
\(834\) | −2.51407 | −0.0870550 | ||||||||
\(835\) | 12.2675 | 0.424533 | ||||||||
\(836\) | 28.5972 | 0.989054 | ||||||||
\(837\) | −28.3039 | −0.978325 | ||||||||
\(838\) | 22.7045 | 0.784314 | ||||||||
\(839\) | −13.8355 | −0.477656 | −0.238828 | − | 0.971062i | \(-0.576763\pi\) | ||||
−0.238828 | + | 0.971062i | \(0.576763\pi\) | |||||||
\(840\) | −1.12293 | −0.0387447 | ||||||||
\(841\) | 9.58617 | 0.330558 | ||||||||
\(842\) | −16.2815 | −0.561098 | ||||||||
\(843\) | −2.61751 | −0.0901518 | ||||||||
\(844\) | 22.7593 | 0.783407 | ||||||||
\(845\) | −17.4130 | −0.599025 | ||||||||
\(846\) | 26.3137 | 0.904685 | ||||||||
\(847\) | −7.20319 | −0.247505 | ||||||||
\(848\) | −3.36589 | −0.115585 | ||||||||
\(849\) | −12.0626 | −0.413988 | ||||||||
\(850\) | −10.9461 | −0.375447 | ||||||||
\(851\) | −24.8901 | −0.853221 | ||||||||
\(852\) | −7.47251 | −0.256004 | ||||||||
\(853\) | −34.3220 | −1.17516 | −0.587582 | − | 0.809165i | \(-0.699920\pi\) | ||||
−0.587582 | + | 0.809165i | \(0.699920\pi\) | |||||||
\(854\) | −5.80734 | −0.198723 | ||||||||
\(855\) | 22.3257 | 0.763524 | ||||||||
\(856\) | −12.0908 | −0.413254 | ||||||||
\(857\) | 1.08984 | 0.0372282 | 0.0186141 | − | 0.999827i | \(-0.494075\pi\) | ||||
0.0186141 | + | 0.999827i | \(0.494075\pi\) | |||||||
\(858\) | −2.71811 | −0.0927949 | ||||||||
\(859\) | 54.4606 | 1.85817 | 0.929086 | − | 0.369863i | \(-0.120595\pi\) | ||||
0.929086 | + | 0.369863i | \(0.120595\pi\) | |||||||
\(860\) | 1.10007 | 0.0375119 | ||||||||
\(861\) | −3.60007 | −0.122690 | ||||||||
\(862\) | −1.00000 | −0.0340601 | ||||||||
\(863\) | 1.23710 | 0.0421113 | 0.0210557 | − | 0.999778i | \(-0.493297\pi\) | ||||
0.0210557 | + | 0.999778i | \(0.493297\pi\) | |||||||
\(864\) | −4.27637 | −0.145485 | ||||||||
\(865\) | 1.12620 | 0.0382921 | ||||||||
\(866\) | −5.04478 | −0.171429 | ||||||||
\(867\) | 3.04902 | 0.103550 | ||||||||
\(868\) | 6.61866 | 0.224652 | ||||||||
\(869\) | −22.5691 | −0.765603 | ||||||||
\(870\) | −6.97538 | −0.236488 | ||||||||
\(871\) | −3.90239 | −0.132227 | ||||||||
\(872\) | 5.51476 | 0.186753 | ||||||||
\(873\) | 8.39014 | 0.283963 | ||||||||
\(874\) | −30.7795 | −1.04113 | ||||||||
\(875\) | 11.2914 | 0.381719 | ||||||||
\(876\) | 3.18416 | 0.107583 | ||||||||
\(877\) | −55.8532 | −1.88603 | −0.943014 | − | 0.332753i | \(-0.892022\pi\) | ||||
−0.943014 | + | 0.332753i | \(0.892022\pi\) | |||||||
\(878\) | −12.8675 | −0.434257 | ||||||||
\(879\) | −2.46501 | −0.0831428 | ||||||||
\(880\) | −6.01012 | −0.202601 | ||||||||
\(881\) | 3.74474 | 0.126164 | 0.0630818 | − | 0.998008i | \(-0.479907\pi\) | ||||
0.0630818 | + | 0.998008i | \(0.479907\pi\) | |||||||
\(882\) | 2.36454 | 0.0796183 | ||||||||
\(883\) | 31.3669 | 1.05558 | 0.527789 | − | 0.849375i | \(-0.323021\pi\) | ||||
0.527789 | + | 0.849375i | \(0.323021\pi\) | |||||||
\(884\) | −2.90087 | −0.0975669 | ||||||||
\(885\) | −6.05856 | −0.203656 | ||||||||
\(886\) | −7.97797 | −0.268025 | ||||||||
\(887\) | −9.21818 | −0.309516 | −0.154758 | − | 0.987952i | \(-0.549460\pi\) | ||||
−0.154758 | + | 0.987952i | \(0.549460\pi\) | |||||||
\(888\) | 4.32072 | 0.144994 | ||||||||
\(889\) | −13.0689 | −0.438317 | ||||||||
\(890\) | 19.6770 | 0.659574 | ||||||||
\(891\) | −15.7208 | −0.526668 | ||||||||
\(892\) | −8.70757 | −0.291551 | ||||||||
\(893\) | −74.5907 | −2.49608 | ||||||||
\(894\) | 12.7611 | 0.426796 | ||||||||
\(895\) | −10.4355 | −0.348820 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 2.92554 | 0.0976810 | ||||||||
\(898\) | −33.4115 | −1.11496 | ||||||||
\(899\) | 41.1137 | 1.37122 | ||||||||
\(900\) | 7.13063 | 0.237688 | ||||||||
\(901\) | 12.2174 | 0.407019 | ||||||||
\(902\) | −19.2682 | −0.641561 | ||||||||
\(903\) | 0.622518 | 0.0207161 | ||||||||
\(904\) | −5.38250 | −0.179019 | ||||||||
\(905\) | −16.5283 | −0.549419 | ||||||||
\(906\) | 7.67218 | 0.254891 | ||||||||
\(907\) | −55.8219 | −1.85353 | −0.926767 | − | 0.375637i | \(-0.877424\pi\) | ||||
−0.926767 | + | 0.375637i | \(0.877424\pi\) | |||||||
\(908\) | −16.8011 | −0.557564 | ||||||||
\(909\) | −21.9780 | −0.728965 | ||||||||
\(910\) | 1.12580 | 0.0373198 | ||||||||
\(911\) | −52.2580 | −1.73139 | −0.865693 | − | 0.500576i | \(-0.833122\pi\) | ||||
−0.865693 | + | 0.500576i | \(0.833122\pi\) | |||||||
\(912\) | 5.34309 | 0.176927 | ||||||||
\(913\) | −60.1717 | −1.99139 | ||||||||
\(914\) | −14.1064 | −0.466599 | ||||||||
\(915\) | 6.52123 | 0.215585 | ||||||||
\(916\) | 24.0920 | 0.796023 | ||||||||
\(917\) | −5.75249 | −0.189964 | ||||||||
\(918\) | 15.5222 | 0.512309 | ||||||||
\(919\) | −26.2785 | −0.866847 | −0.433423 | − | 0.901190i | \(-0.642694\pi\) | ||||
−0.433423 | + | 0.901190i | \(0.642694\pi\) | |||||||
\(920\) | 6.46877 | 0.213269 | ||||||||
\(921\) | −9.95524 | −0.328036 | ||||||||
\(922\) | −12.0170 | −0.395759 | ||||||||
\(923\) | 7.49161 | 0.246589 | ||||||||
\(924\) | −3.40108 | −0.111887 | ||||||||
\(925\) | −16.3454 | −0.537432 | ||||||||
\(926\) | 11.9976 | 0.394265 | ||||||||
\(927\) | −19.9900 | −0.656559 | ||||||||
\(928\) | 6.21178 | 0.203912 | ||||||||
\(929\) | 59.5011 | 1.95217 | 0.976084 | − | 0.217396i | \(-0.0697561\pi\) | ||||
0.976084 | + | 0.217396i | \(0.0697561\pi\) | |||||||
\(930\) | −7.43228 | −0.243714 | ||||||||
\(931\) | −6.70269 | −0.219672 | ||||||||
\(932\) | −12.7964 | −0.419160 | ||||||||
\(933\) | 14.2161 | 0.465415 | ||||||||
\(934\) | −11.6270 | −0.380448 | ||||||||
\(935\) | 21.8153 | 0.713435 | ||||||||
\(936\) | 1.88972 | 0.0617676 | ||||||||
\(937\) | 28.4226 | 0.928527 | 0.464263 | − | 0.885697i | \(-0.346319\pi\) | ||||
0.464263 | + | 0.885697i | \(0.346319\pi\) | |||||||
\(938\) | −4.88292 | −0.159433 | ||||||||
\(939\) | 23.0485 | 0.752159 | ||||||||
\(940\) | 15.6763 | 0.511306 | ||||||||
\(941\) | −5.91289 | −0.192755 | −0.0963773 | − | 0.995345i | \(-0.530726\pi\) | ||||
−0.0963773 | + | 0.995345i | \(0.530726\pi\) | |||||||
\(942\) | −2.22030 | −0.0723413 | ||||||||
\(943\) | 20.7386 | 0.675343 | ||||||||
\(944\) | 5.39532 | 0.175603 | ||||||||
\(945\) | −6.02400 | −0.195961 | ||||||||
\(946\) | 3.33183 | 0.108327 | ||||||||
\(947\) | 10.4490 | 0.339547 | 0.169774 | − | 0.985483i | \(-0.445696\pi\) | ||||
0.169774 | + | 0.985483i | \(0.445696\pi\) | |||||||
\(948\) | −4.21680 | −0.136955 | ||||||||
\(949\) | −3.19229 | −0.103626 | ||||||||
\(950\) | −20.2130 | −0.655795 | ||||||||
\(951\) | 5.86490 | 0.190182 | ||||||||
\(952\) | −3.62976 | −0.117641 | ||||||||
\(953\) | 22.5565 | 0.730677 | 0.365338 | − | 0.930875i | \(-0.380953\pi\) | ||||
0.365338 | + | 0.930875i | \(0.380953\pi\) | |||||||
\(954\) | −7.95880 | −0.257676 | ||||||||
\(955\) | 11.5896 | 0.375031 | ||||||||
\(956\) | 2.87318 | 0.0929253 | ||||||||
\(957\) | −21.1267 | −0.682931 | ||||||||
\(958\) | −2.99665 | −0.0968174 | ||||||||
\(959\) | −7.21273 | −0.232911 | ||||||||
\(960\) | −1.12293 | −0.0362424 | ||||||||
\(961\) | 12.8067 | 0.413119 | ||||||||
\(962\) | −4.33176 | −0.139662 | ||||||||
\(963\) | −28.5892 | −0.921274 | ||||||||
\(964\) | −8.19163 | −0.263835 | ||||||||
\(965\) | −26.4241 | −0.850620 | ||||||||
\(966\) | 3.66063 | 0.117779 | ||||||||
\(967\) | −55.7314 | −1.79220 | −0.896101 | − | 0.443851i | \(-0.853612\pi\) | ||||
−0.896101 | + | 0.443851i | \(0.853612\pi\) | |||||||
\(968\) | −7.20319 | −0.231519 | ||||||||
\(969\) | −19.3941 | −0.623028 | ||||||||
\(970\) | 4.99840 | 0.160489 | ||||||||
\(971\) | 9.35061 | 0.300075 | 0.150038 | − | 0.988680i | \(-0.452061\pi\) | ||||
0.150038 | + | 0.988680i | \(0.452061\pi\) | |||||||
\(972\) | −15.7664 | −0.505707 | ||||||||
\(973\) | 3.15380 | 0.101106 | ||||||||
\(974\) | 18.3844 | 0.589076 | ||||||||
\(975\) | 1.92121 | 0.0615280 | ||||||||
\(976\) | −5.80734 | −0.185888 | ||||||||
\(977\) | −59.4553 | −1.90214 | −0.951072 | − | 0.308969i | \(-0.900016\pi\) | ||||
−0.951072 | + | 0.308969i | \(0.900016\pi\) | |||||||
\(978\) | 6.10142 | 0.195102 | ||||||||
\(979\) | 59.5968 | 1.90472 | ||||||||
\(980\) | 1.40867 | 0.0449983 | ||||||||
\(981\) | 13.0399 | 0.416332 | ||||||||
\(982\) | −21.2906 | −0.679411 | ||||||||
\(983\) | −4.33086 | −0.138133 | −0.0690665 | − | 0.997612i | \(-0.522002\pi\) | ||||
−0.0690665 | + | 0.997612i | \(0.522002\pi\) | |||||||
\(984\) | −3.60007 | −0.114766 | ||||||||
\(985\) | −28.7702 | −0.916694 | ||||||||
\(986\) | −22.5472 | −0.718050 | ||||||||
\(987\) | 8.87112 | 0.282371 | ||||||||
\(988\) | −5.35674 | −0.170420 | ||||||||
\(989\) | −3.58609 | −0.114031 | ||||||||
\(990\) | −14.2112 | −0.451661 | ||||||||
\(991\) | −50.8695 | −1.61592 | −0.807961 | − | 0.589236i | \(-0.799429\pi\) | ||||
−0.807961 | + | 0.589236i | \(0.799429\pi\) | |||||||
\(992\) | 6.61866 | 0.210143 | ||||||||
\(993\) | 5.26814 | 0.167179 | ||||||||
\(994\) | 9.37398 | 0.297324 | ||||||||
\(995\) | −19.4972 | −0.618103 | ||||||||
\(996\) | −11.2425 | −0.356231 | ||||||||
\(997\) | −34.9720 | −1.10757 | −0.553787 | − | 0.832658i | \(-0.686818\pi\) | ||||
−0.553787 | + | 0.832658i | \(0.686818\pi\) | |||||||
\(998\) | −39.7003 | −1.25669 | ||||||||
\(999\) | 23.1787 | 0.733342 |
(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 | 6034.2.a.n.1.9 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6034.2.a.n.1.9 | ✓ | 24 | 1.1 | even | 1 | trivial |