Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6025,2,Mod(1,6025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6025, 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("6025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6025 = 5^{2} \cdot 241 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6025.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: | \(48.1098672178\) |
Analytic rank: | \(1\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 6025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.98624 | −1.40449 | −0.702243 | − | 0.711937i | \(-0.747818\pi\) | ||||
−0.702243 | + | 0.711937i | \(0.747818\pi\) | |||||||
\(3\) | 2.93351 | 1.69366 | 0.846831 | − | 0.531863i | \(-0.178508\pi\) | ||||
0.846831 | + | 0.531863i | \(0.178508\pi\) | |||||||
\(4\) | 1.94516 | 0.972582 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −5.82666 | −2.37872 | ||||||||
\(7\) | −3.87755 | −1.46558 | −0.732789 | − | 0.680456i | \(-0.761782\pi\) | ||||
−0.732789 | + | 0.680456i | \(0.761782\pi\) | |||||||
\(8\) | 0.108919 | 0.0385087 | ||||||||
\(9\) | 5.60547 | 1.86849 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.43632 | 1.63911 | 0.819556 | − | 0.572999i | \(-0.194220\pi\) | ||||
0.819556 | + | 0.572999i | \(0.194220\pi\) | |||||||
\(12\) | 5.70615 | 1.64722 | ||||||||
\(13\) | 4.51589 | 1.25248 | 0.626242 | − | 0.779629i | \(-0.284592\pi\) | ||||
0.626242 | + | 0.779629i | \(0.284592\pi\) | |||||||
\(14\) | 7.70177 | 2.05838 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.10667 | −1.02667 | ||||||||
\(17\) | −3.56474 | −0.864577 | −0.432289 | − | 0.901735i | \(-0.642294\pi\) | ||||
−0.432289 | + | 0.901735i | \(0.642294\pi\) | |||||||
\(18\) | −11.1338 | −2.62427 | ||||||||
\(19\) | −4.95200 | −1.13607 | −0.568034 | − | 0.823005i | \(-0.692296\pi\) | ||||
−0.568034 | + | 0.823005i | \(0.692296\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −11.3748 | −2.48219 | ||||||||
\(22\) | −10.7979 | −2.30211 | ||||||||
\(23\) | −8.91648 | −1.85922 | −0.929608 | − | 0.368551i | \(-0.879854\pi\) | ||||
−0.929608 | + | 0.368551i | \(0.879854\pi\) | |||||||
\(24\) | 0.319515 | 0.0652208 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −8.96966 | −1.75910 | ||||||||
\(27\) | 7.64316 | 1.47093 | ||||||||
\(28\) | −7.54248 | −1.42539 | ||||||||
\(29\) | 2.56121 | 0.475605 | 0.237802 | − | 0.971314i | \(-0.423573\pi\) | ||||
0.237802 | + | 0.971314i | \(0.423573\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.87389 | −0.336561 | −0.168281 | − | 0.985739i | \(-0.553822\pi\) | ||||
−0.168281 | + | 0.985739i | \(0.553822\pi\) | |||||||
\(32\) | 7.93900 | 1.40343 | ||||||||
\(33\) | 15.9475 | 2.77610 | ||||||||
\(34\) | 7.08045 | 1.21429 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 10.9035 | 1.81726 | ||||||||
\(37\) | −8.26816 | −1.35928 | −0.679639 | − | 0.733547i | \(-0.737863\pi\) | ||||
−0.679639 | + | 0.733547i | \(0.737863\pi\) | |||||||
\(38\) | 9.83588 | 1.59559 | ||||||||
\(39\) | 13.2474 | 2.12128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.60127 | 0.250076 | 0.125038 | − | 0.992152i | \(-0.460095\pi\) | ||||
0.125038 | + | 0.992152i | \(0.460095\pi\) | |||||||
\(42\) | 22.5932 | 3.48620 | ||||||||
\(43\) | −10.9508 | −1.66998 | −0.834991 | − | 0.550263i | \(-0.814527\pi\) | ||||
−0.834991 | + | 0.550263i | \(0.814527\pi\) | |||||||
\(44\) | 10.5745 | 1.59417 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 17.7103 | 2.61124 | ||||||||
\(47\) | −0.538956 | −0.0786148 | −0.0393074 | − | 0.999227i | \(-0.512515\pi\) | ||||
−0.0393074 | + | 0.999227i | \(0.512515\pi\) | |||||||
\(48\) | −12.0469 | −1.73883 | ||||||||
\(49\) | 8.03542 | 1.14792 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −10.4572 | −1.46430 | ||||||||
\(52\) | 8.78415 | 1.21814 | ||||||||
\(53\) | 6.76785 | 0.929636 | 0.464818 | − | 0.885406i | \(-0.346120\pi\) | ||||
0.464818 | + | 0.885406i | \(0.346120\pi\) | |||||||
\(54\) | −15.1812 | −2.06590 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.422340 | −0.0564376 | ||||||||
\(57\) | −14.5267 | −1.92411 | ||||||||
\(58\) | −5.08719 | −0.667980 | ||||||||
\(59\) | −7.99400 | −1.04073 | −0.520365 | − | 0.853944i | \(-0.674204\pi\) | ||||
−0.520365 | + | 0.853944i | \(0.674204\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.30204 | −0.806894 | −0.403447 | − | 0.915003i | \(-0.632188\pi\) | ||||
−0.403447 | + | 0.915003i | \(0.632188\pi\) | |||||||
\(62\) | 3.72201 | 0.472696 | ||||||||
\(63\) | −21.7355 | −2.73842 | ||||||||
\(64\) | −7.55546 | −0.944432 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −31.6756 | −3.89900 | ||||||||
\(67\) | 6.40319 | 0.782274 | 0.391137 | − | 0.920332i | \(-0.372082\pi\) | ||||
0.391137 | + | 0.920332i | \(0.372082\pi\) | |||||||
\(68\) | −6.93401 | −0.840872 | ||||||||
\(69\) | −26.1566 | −3.14888 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −15.2258 | −1.80698 | −0.903488 | − | 0.428614i | \(-0.859002\pi\) | ||||
−0.903488 | + | 0.428614i | \(0.859002\pi\) | |||||||
\(72\) | 0.610543 | 0.0719532 | ||||||||
\(73\) | −8.98213 | −1.05128 | −0.525640 | − | 0.850707i | \(-0.676174\pi\) | ||||
−0.525640 | + | 0.850707i | \(0.676174\pi\) | |||||||
\(74\) | 16.4226 | 1.90909 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −9.63245 | −1.10492 | ||||||||
\(77\) | −21.0796 | −2.40225 | ||||||||
\(78\) | −26.3126 | −2.97931 | ||||||||
\(79\) | −5.39894 | −0.607428 | −0.303714 | − | 0.952763i | \(-0.598227\pi\) | ||||
−0.303714 | + | 0.952763i | \(0.598227\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.60486 | 0.622762 | ||||||||
\(82\) | −3.18051 | −0.351229 | ||||||||
\(83\) | 10.5577 | 1.15886 | 0.579428 | − | 0.815024i | \(-0.303276\pi\) | ||||
0.579428 | + | 0.815024i | \(0.303276\pi\) | |||||||
\(84\) | −22.1259 | −2.41413 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 21.7510 | 2.34547 | ||||||||
\(87\) | 7.51333 | 0.805513 | ||||||||
\(88\) | 0.592120 | 0.0631202 | ||||||||
\(89\) | 10.9001 | 1.15541 | 0.577704 | − | 0.816246i | \(-0.303949\pi\) | ||||
0.577704 | + | 0.816246i | \(0.303949\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −17.5106 | −1.83561 | ||||||||
\(92\) | −17.3440 | −1.80824 | ||||||||
\(93\) | −5.49708 | −0.570021 | ||||||||
\(94\) | 1.07050 | 0.110413 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 23.2891 | 2.37694 | ||||||||
\(97\) | −3.42286 | −0.347539 | −0.173769 | − | 0.984786i | \(-0.555595\pi\) | ||||
−0.173769 | + | 0.984786i | \(0.555595\pi\) | |||||||
\(98\) | −15.9603 | −1.61223 | ||||||||
\(99\) | 30.4731 | 3.06266 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.970244 | 0.0965429 | 0.0482715 | − | 0.998834i | \(-0.484629\pi\) | ||||
0.0482715 | + | 0.998834i | \(0.484629\pi\) | |||||||
\(102\) | 20.7705 | 2.05659 | ||||||||
\(103\) | −17.2509 | −1.69978 | −0.849890 | − | 0.526960i | \(-0.823332\pi\) | ||||
−0.849890 | + | 0.526960i | \(0.823332\pi\) | |||||||
\(104\) | 0.491867 | 0.0482316 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −13.4426 | −1.30566 | ||||||||
\(107\) | 1.63982 | 0.158527 | 0.0792636 | − | 0.996854i | \(-0.474743\pi\) | ||||
0.0792636 | + | 0.996854i | \(0.474743\pi\) | |||||||
\(108\) | 14.8672 | 1.43060 | ||||||||
\(109\) | 6.29189 | 0.602653 | 0.301327 | − | 0.953521i | \(-0.402571\pi\) | ||||
0.301327 | + | 0.953521i | \(0.402571\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −24.2547 | −2.30216 | ||||||||
\(112\) | 15.9238 | 1.50466 | ||||||||
\(113\) | −9.81404 | −0.923228 | −0.461614 | − | 0.887081i | \(-0.652729\pi\) | ||||
−0.461614 | + | 0.887081i | \(0.652729\pi\) | |||||||
\(114\) | 28.8536 | 2.70239 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 4.98197 | 0.462564 | ||||||||
\(117\) | 25.3137 | 2.34025 | ||||||||
\(118\) | 15.8780 | 1.46169 | ||||||||
\(119\) | 13.8225 | 1.26710 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 18.5536 | 1.68669 | ||||||||
\(122\) | 12.5174 | 1.13327 | ||||||||
\(123\) | 4.69733 | 0.423544 | ||||||||
\(124\) | −3.64503 | −0.327333 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 43.1720 | 3.84607 | ||||||||
\(127\) | −0.747436 | −0.0663242 | −0.0331621 | − | 0.999450i | \(-0.510558\pi\) | ||||
−0.0331621 | + | 0.999450i | \(0.510558\pi\) | |||||||
\(128\) | −0.871026 | −0.0769885 | ||||||||
\(129\) | −32.1243 | −2.82838 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.06461 | −0.617238 | −0.308619 | − | 0.951186i | \(-0.599867\pi\) | ||||
−0.308619 | + | 0.951186i | \(0.599867\pi\) | |||||||
\(132\) | 31.0205 | 2.69999 | ||||||||
\(133\) | 19.2017 | 1.66499 | ||||||||
\(134\) | −12.7183 | −1.09869 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.388269 | −0.0332938 | ||||||||
\(137\) | −8.32374 | −0.711145 | −0.355573 | − | 0.934649i | \(-0.615714\pi\) | ||||
−0.355573 | + | 0.934649i | \(0.615714\pi\) | |||||||
\(138\) | 51.9533 | 4.42256 | ||||||||
\(139\) | −4.03004 | −0.341823 | −0.170912 | − | 0.985286i | \(-0.554671\pi\) | ||||
−0.170912 | + | 0.985286i | \(0.554671\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.58103 | −0.133147 | ||||||||
\(142\) | 30.2422 | 2.53787 | ||||||||
\(143\) | 24.5498 | 2.05296 | ||||||||
\(144\) | −23.0198 | −1.91832 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 17.8407 | 1.47651 | ||||||||
\(147\) | 23.5720 | 1.94418 | ||||||||
\(148\) | −16.0829 | −1.32201 | ||||||||
\(149\) | 13.5027 | 1.10618 | 0.553091 | − | 0.833121i | \(-0.313448\pi\) | ||||
0.553091 | + | 0.833121i | \(0.313448\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.4658 | 1.17721 | 0.588607 | − | 0.808420i | \(-0.299677\pi\) | ||||
0.588607 | + | 0.808420i | \(0.299677\pi\) | |||||||
\(152\) | −0.539368 | −0.0437485 | ||||||||
\(153\) | −19.9820 | −1.61545 | ||||||||
\(154\) | 41.8693 | 3.37392 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 25.7684 | 2.06312 | ||||||||
\(157\) | −1.44367 | −0.115218 | −0.0576089 | − | 0.998339i | \(-0.518348\pi\) | ||||
−0.0576089 | + | 0.998339i | \(0.518348\pi\) | |||||||
\(158\) | 10.7236 | 0.853124 | ||||||||
\(159\) | 19.8535 | 1.57449 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 34.5741 | 2.72482 | ||||||||
\(162\) | −11.1326 | −0.874661 | ||||||||
\(163\) | −10.3677 | −0.812064 | −0.406032 | − | 0.913859i | \(-0.633088\pi\) | ||||
−0.406032 | + | 0.913859i | \(0.633088\pi\) | |||||||
\(164\) | 3.11473 | 0.243219 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −20.9701 | −1.62760 | ||||||||
\(167\) | −20.8554 | −1.61384 | −0.806920 | − | 0.590661i | \(-0.798867\pi\) | ||||
−0.806920 | + | 0.590661i | \(0.798867\pi\) | |||||||
\(168\) | −1.23894 | −0.0955861 | ||||||||
\(169\) | 7.39329 | 0.568715 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −27.7583 | −2.12273 | ||||||||
\(172\) | −21.3011 | −1.62419 | ||||||||
\(173\) | 17.8780 | 1.35924 | 0.679621 | − | 0.733563i | \(-0.262144\pi\) | ||||
0.679621 | + | 0.733563i | \(0.262144\pi\) | |||||||
\(174\) | −14.9233 | −1.13133 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −22.3252 | −1.68282 | ||||||||
\(177\) | −23.4505 | −1.76265 | ||||||||
\(178\) | −21.6502 | −1.62275 | ||||||||
\(179\) | 9.33051 | 0.697395 | 0.348698 | − | 0.937235i | \(-0.386624\pi\) | ||||
0.348698 | + | 0.937235i | \(0.386624\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.0060 | 1.11539 | 0.557695 | − | 0.830046i | \(-0.311686\pi\) | ||||
0.557695 | + | 0.830046i | \(0.311686\pi\) | |||||||
\(182\) | 34.7804 | 2.57809 | ||||||||
\(183\) | −18.4871 | −1.36661 | ||||||||
\(184\) | −0.971176 | −0.0715960 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 10.9185 | 0.800587 | ||||||||
\(187\) | −19.3791 | −1.41714 | ||||||||
\(188\) | −1.04836 | −0.0764593 | ||||||||
\(189\) | −29.6368 | −2.15576 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.3478 | 0.893453 | 0.446726 | − | 0.894671i | \(-0.352590\pi\) | ||||
0.446726 | + | 0.894671i | \(0.352590\pi\) | |||||||
\(192\) | −22.1640 | −1.59955 | ||||||||
\(193\) | 5.16306 | 0.371645 | 0.185823 | − | 0.982583i | \(-0.440505\pi\) | ||||
0.185823 | + | 0.982583i | \(0.440505\pi\) | |||||||
\(194\) | 6.79863 | 0.488113 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 15.6302 | 1.11644 | ||||||||
\(197\) | −2.21283 | −0.157658 | −0.0788289 | − | 0.996888i | \(-0.525118\pi\) | ||||
−0.0788289 | + | 0.996888i | \(0.525118\pi\) | |||||||
\(198\) | −60.5270 | −4.30147 | ||||||||
\(199\) | 8.99087 | 0.637346 | 0.318673 | − | 0.947865i | \(-0.396763\pi\) | ||||
0.318673 | + | 0.947865i | \(0.396763\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 18.7838 | 1.32491 | ||||||||
\(202\) | −1.92714 | −0.135593 | ||||||||
\(203\) | −9.93123 | −0.697036 | ||||||||
\(204\) | −20.3410 | −1.42415 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 34.2644 | 2.38732 | ||||||||
\(207\) | −49.9811 | −3.47392 | ||||||||
\(208\) | −18.5453 | −1.28588 | ||||||||
\(209\) | −26.9207 | −1.86214 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.78841 | −0.398490 | −0.199245 | − | 0.979950i | \(-0.563849\pi\) | ||||
−0.199245 | + | 0.979950i | \(0.563849\pi\) | |||||||
\(212\) | 13.1646 | 0.904147 | ||||||||
\(213\) | −44.6651 | −3.06040 | ||||||||
\(214\) | −3.25708 | −0.222649 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0.832486 | 0.0566435 | ||||||||
\(217\) | 7.26613 | 0.493257 | ||||||||
\(218\) | −12.4972 | −0.846418 | ||||||||
\(219\) | −26.3492 | −1.78051 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −16.0980 | −1.08287 | ||||||||
\(222\) | 48.1758 | 3.23335 | ||||||||
\(223\) | 4.23873 | 0.283847 | 0.141923 | − | 0.989878i | \(-0.454671\pi\) | ||||
0.141923 | + | 0.989878i | \(0.454671\pi\) | |||||||
\(224\) | −30.7839 | −2.05684 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 19.4931 | 1.29666 | ||||||||
\(227\) | −13.5718 | −0.900792 | −0.450396 | − | 0.892829i | \(-0.648717\pi\) | ||||
−0.450396 | + | 0.892829i | \(0.648717\pi\) | |||||||
\(228\) | −28.2569 | −1.87136 | ||||||||
\(229\) | −5.88333 | −0.388781 | −0.194391 | − | 0.980924i | \(-0.562273\pi\) | ||||
−0.194391 | + | 0.980924i | \(0.562273\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −61.8373 | −4.06859 | ||||||||
\(232\) | 0.278965 | 0.0183149 | ||||||||
\(233\) | 12.0619 | 0.790199 | 0.395099 | − | 0.918638i | \(-0.370710\pi\) | ||||
0.395099 | + | 0.918638i | \(0.370710\pi\) | |||||||
\(234\) | −50.2792 | −3.28685 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −15.5496 | −1.01220 | ||||||||
\(237\) | −15.8378 | −1.02878 | ||||||||
\(238\) | −27.4548 | −1.77963 | ||||||||
\(239\) | −26.8308 | −1.73554 | −0.867769 | − | 0.496967i | \(-0.834447\pi\) | ||||
−0.867769 | + | 0.496967i | \(0.834447\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.00000 | 0.0644157 | ||||||||
\(242\) | −36.8520 | −2.36893 | ||||||||
\(243\) | −6.48757 | −0.416178 | ||||||||
\(244\) | −12.2585 | −0.784770 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −9.33005 | −0.594862 | ||||||||
\(247\) | −22.3627 | −1.42291 | ||||||||
\(248\) | −0.204103 | −0.0129606 | ||||||||
\(249\) | 30.9710 | 1.96271 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14.0119 | 0.884421 | 0.442210 | − | 0.896911i | \(-0.354194\pi\) | ||||
0.442210 | + | 0.896911i | \(0.354194\pi\) | |||||||
\(252\) | −42.2791 | −2.66333 | ||||||||
\(253\) | −48.4729 | −3.04746 | ||||||||
\(254\) | 1.48459 | 0.0931514 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.8410 | 1.05256 | ||||||||
\(257\) | 3.14158 | 0.195966 | 0.0979831 | − | 0.995188i | \(-0.468761\pi\) | ||||
0.0979831 | + | 0.995188i | \(0.468761\pi\) | |||||||
\(258\) | 63.8066 | 3.97243 | ||||||||
\(259\) | 32.0602 | 1.99213 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 14.3568 | 0.888662 | ||||||||
\(262\) | 14.0320 | 0.866902 | ||||||||
\(263\) | −20.4977 | −1.26394 | −0.631970 | − | 0.774993i | \(-0.717753\pi\) | ||||
−0.631970 | + | 0.774993i | \(0.717753\pi\) | |||||||
\(264\) | 1.73699 | 0.106904 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −38.1392 | −2.33846 | ||||||||
\(267\) | 31.9755 | 1.95687 | ||||||||
\(268\) | 12.4552 | 0.760825 | ||||||||
\(269\) | 21.5895 | 1.31633 | 0.658166 | − | 0.752873i | \(-0.271332\pi\) | ||||
0.658166 | + | 0.752873i | \(0.271332\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 30.3487 | 1.84355 | 0.921777 | − | 0.387721i | \(-0.126737\pi\) | ||||
0.921777 | + | 0.387721i | \(0.126737\pi\) | |||||||
\(272\) | 14.6392 | 0.887632 | ||||||||
\(273\) | −51.3675 | −3.10890 | ||||||||
\(274\) | 16.5330 | 0.998794 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −50.8788 | −3.06254 | ||||||||
\(277\) | −28.3808 | −1.70523 | −0.852617 | − | 0.522536i | \(-0.824986\pi\) | ||||
−0.852617 | + | 0.522536i | \(0.824986\pi\) | |||||||
\(278\) | 8.00464 | 0.480086 | ||||||||
\(279\) | −10.5041 | −0.628861 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.5214 | 1.10489 | 0.552446 | − | 0.833549i | \(-0.313695\pi\) | ||||
0.552446 | + | 0.833549i | \(0.313695\pi\) | |||||||
\(282\) | 3.14031 | 0.187003 | ||||||||
\(283\) | 15.6962 | 0.933045 | 0.466523 | − | 0.884509i | \(-0.345507\pi\) | ||||
0.466523 | + | 0.884509i | \(0.345507\pi\) | |||||||
\(284\) | −29.6168 | −1.75743 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −48.7620 | −2.88336 | ||||||||
\(287\) | −6.20901 | −0.366506 | ||||||||
\(288\) | 44.5018 | 2.62229 | ||||||||
\(289\) | −4.29261 | −0.252507 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −10.0410 | −0.588613 | ||||||||
\(292\) | −17.4717 | −1.02245 | ||||||||
\(293\) | 19.4528 | 1.13644 | 0.568221 | − | 0.822876i | \(-0.307632\pi\) | ||||
0.568221 | + | 0.822876i | \(0.307632\pi\) | |||||||
\(294\) | −46.8197 | −2.73058 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −0.900561 | −0.0523441 | ||||||||
\(297\) | 41.5507 | 2.41101 | ||||||||
\(298\) | −26.8196 | −1.55362 | ||||||||
\(299\) | −40.2659 | −2.32864 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 42.4623 | 2.44749 | ||||||||
\(302\) | −28.7327 | −1.65338 | ||||||||
\(303\) | 2.84622 | 0.163511 | ||||||||
\(304\) | 20.3362 | 1.16636 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 39.6892 | 2.26888 | ||||||||
\(307\) | −18.5628 | −1.05944 | −0.529718 | − | 0.848174i | \(-0.677702\pi\) | ||||
−0.529718 | + | 0.848174i | \(0.677702\pi\) | |||||||
\(308\) | −41.0033 | −2.33638 | ||||||||
\(309\) | −50.6056 | −2.87885 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −25.1593 | −1.42665 | −0.713326 | − | 0.700833i | \(-0.752812\pi\) | ||||
−0.713326 | + | 0.700833i | \(0.752812\pi\) | |||||||
\(312\) | 1.44290 | 0.0816879 | ||||||||
\(313\) | 22.7874 | 1.28802 | 0.644010 | − | 0.765017i | \(-0.277269\pi\) | ||||
0.644010 | + | 0.765017i | \(0.277269\pi\) | |||||||
\(314\) | 2.86749 | 0.161822 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −10.5018 | −0.590773 | ||||||||
\(317\) | −16.8654 | −0.947253 | −0.473627 | − | 0.880726i | \(-0.657055\pi\) | ||||
−0.473627 | + | 0.880726i | \(0.657055\pi\) | |||||||
\(318\) | −39.4340 | −2.21135 | ||||||||
\(319\) | 13.9236 | 0.779570 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.81042 | 0.268492 | ||||||||
\(322\) | −68.6727 | −3.82698 | ||||||||
\(323\) | 17.6526 | 0.982218 | ||||||||
\(324\) | 10.9024 | 0.605687 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 20.5929 | 1.14053 | ||||||||
\(327\) | 18.4573 | 1.02069 | ||||||||
\(328\) | 0.174409 | 0.00963012 | ||||||||
\(329\) | 2.08983 | 0.115216 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 34.9055 | 1.91858 | 0.959289 | − | 0.282425i | \(-0.0911388\pi\) | ||||
0.959289 | + | 0.282425i | \(0.0911388\pi\) | |||||||
\(332\) | 20.5364 | 1.12708 | ||||||||
\(333\) | −46.3469 | −2.53979 | ||||||||
\(334\) | 41.4239 | 2.26662 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 46.7127 | 2.54838 | ||||||||
\(337\) | 7.07149 | 0.385208 | 0.192604 | − | 0.981277i | \(-0.438307\pi\) | ||||
0.192604 | + | 0.981277i | \(0.438307\pi\) | |||||||
\(338\) | −14.6849 | −0.798752 | ||||||||
\(339\) | −28.7896 | −1.56363 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.1871 | −0.551662 | ||||||||
\(342\) | 55.1347 | 2.98134 | ||||||||
\(343\) | −4.01492 | −0.216785 | ||||||||
\(344\) | −1.19275 | −0.0643089 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −35.5101 | −1.90904 | ||||||||
\(347\) | 33.0795 | 1.77580 | 0.887901 | − | 0.460035i | \(-0.152163\pi\) | ||||
0.887901 | + | 0.460035i | \(0.152163\pi\) | |||||||
\(348\) | 14.6147 | 0.783427 | ||||||||
\(349\) | −22.7013 | −1.21517 | −0.607587 | − | 0.794253i | \(-0.707862\pi\) | ||||
−0.607587 | + | 0.794253i | \(0.707862\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 34.5157 | 1.84231 | ||||||||
\(352\) | 43.1590 | 2.30038 | ||||||||
\(353\) | −20.3867 | −1.08508 | −0.542538 | − | 0.840031i | \(-0.682536\pi\) | ||||
−0.542538 | + | 0.840031i | \(0.682536\pi\) | |||||||
\(354\) | 46.5783 | 2.47561 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 21.2025 | 1.12373 | ||||||||
\(357\) | 40.5484 | 2.14605 | ||||||||
\(358\) | −18.5327 | −0.979482 | ||||||||
\(359\) | −24.8228 | −1.31010 | −0.655049 | − | 0.755586i | \(-0.727352\pi\) | ||||
−0.655049 | + | 0.755586i | \(0.727352\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.52233 | 0.290649 | ||||||||
\(362\) | −29.8056 | −1.56655 | ||||||||
\(363\) | 54.4271 | 2.85668 | ||||||||
\(364\) | −34.0610 | −1.78528 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 36.7199 | 1.91938 | ||||||||
\(367\) | −18.2538 | −0.952843 | −0.476422 | − | 0.879217i | \(-0.658066\pi\) | ||||
−0.476422 | + | 0.879217i | \(0.658066\pi\) | |||||||
\(368\) | 36.6170 | 1.90879 | ||||||||
\(369\) | 8.97586 | 0.467265 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −26.2427 | −1.36245 | ||||||||
\(372\) | −10.6927 | −0.554392 | ||||||||
\(373\) | 33.2495 | 1.72159 | 0.860796 | − | 0.508951i | \(-0.169966\pi\) | ||||
0.860796 | + | 0.508951i | \(0.169966\pi\) | |||||||
\(374\) | 38.4916 | 1.99035 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.0587026 | −0.00302736 | ||||||||
\(377\) | 11.5661 | 0.595687 | ||||||||
\(378\) | 58.8658 | 3.02773 | ||||||||
\(379\) | 6.47197 | 0.332443 | 0.166221 | − | 0.986088i | \(-0.446843\pi\) | ||||
0.166221 | + | 0.986088i | \(0.446843\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.19261 | −0.112331 | ||||||||
\(382\) | −24.5257 | −1.25484 | ||||||||
\(383\) | 8.33312 | 0.425802 | 0.212901 | − | 0.977074i | \(-0.431709\pi\) | ||||
0.212901 | + | 0.977074i | \(0.431709\pi\) | |||||||
\(384\) | −2.55516 | −0.130393 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −10.2551 | −0.521971 | ||||||||
\(387\) | −61.3844 | −3.12034 | ||||||||
\(388\) | −6.65802 | −0.338010 | ||||||||
\(389\) | −4.68009 | −0.237290 | −0.118645 | − | 0.992937i | \(-0.537855\pi\) | ||||
−0.118645 | + | 0.992937i | \(0.537855\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 31.7850 | 1.60743 | ||||||||
\(392\) | 0.875212 | 0.0442049 | ||||||||
\(393\) | −20.7241 | −1.04539 | ||||||||
\(394\) | 4.39522 | 0.221428 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 59.2752 | 2.97869 | ||||||||
\(397\) | −28.7097 | −1.44090 | −0.720449 | − | 0.693508i | \(-0.756064\pi\) | ||||
−0.720449 | + | 0.693508i | \(0.756064\pi\) | |||||||
\(398\) | −17.8581 | −0.895144 | ||||||||
\(399\) | 56.3282 | 2.81994 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.7554 | −0.936600 | −0.468300 | − | 0.883570i | \(-0.655133\pi\) | ||||
−0.468300 | + | 0.883570i | \(0.655133\pi\) | |||||||
\(402\) | −37.3092 | −1.86081 | ||||||||
\(403\) | −8.46231 | −0.421538 | ||||||||
\(404\) | 1.88728 | 0.0938959 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 19.7258 | 0.978977 | ||||||||
\(407\) | −44.9484 | −2.22801 | ||||||||
\(408\) | −1.13899 | −0.0563884 | ||||||||
\(409\) | −11.8347 | −0.585186 | −0.292593 | − | 0.956237i | \(-0.594518\pi\) | ||||
−0.292593 | + | 0.956237i | \(0.594518\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −24.4178 | −1.20444 | ||||||||
\(412\) | −33.5558 | −1.65317 | ||||||||
\(413\) | 30.9972 | 1.52527 | ||||||||
\(414\) | 99.2745 | 4.87908 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 35.8517 | 1.75777 | ||||||||
\(417\) | −11.8221 | −0.578933 | ||||||||
\(418\) | 53.4710 | 2.61535 | ||||||||
\(419\) | 24.9971 | 1.22119 | 0.610593 | − | 0.791944i | \(-0.290931\pi\) | ||||
0.610593 | + | 0.791944i | \(0.290931\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −40.3191 | −1.96503 | −0.982515 | − | 0.186182i | \(-0.940388\pi\) | ||||
−0.982515 | + | 0.186182i | \(0.940388\pi\) | |||||||
\(422\) | 11.4972 | 0.559674 | ||||||||
\(423\) | −3.02110 | −0.146891 | ||||||||
\(424\) | 0.737149 | 0.0357991 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 88.7158 | 4.29830 | ||||||||
\(427\) | 24.4365 | 1.18257 | ||||||||
\(428\) | 3.18972 | 0.154181 | ||||||||
\(429\) | 72.0172 | 3.47702 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −38.3225 | −1.84593 | −0.922965 | − | 0.384883i | \(-0.874242\pi\) | ||||
−0.922965 | + | 0.384883i | \(0.874242\pi\) | |||||||
\(432\) | −31.3879 | −1.51015 | ||||||||
\(433\) | −11.7086 | −0.562677 | −0.281339 | − | 0.959609i | \(-0.590778\pi\) | ||||
−0.281339 | + | 0.959609i | \(0.590778\pi\) | |||||||
\(434\) | −14.4323 | −0.692772 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 12.2387 | 0.586130 | ||||||||
\(437\) | 44.1544 | 2.11219 | ||||||||
\(438\) | 52.3358 | 2.50070 | ||||||||
\(439\) | −21.0713 | −1.00568 | −0.502840 | − | 0.864379i | \(-0.667712\pi\) | ||||
−0.502840 | + | 0.864379i | \(0.667712\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 45.0423 | 2.14487 | ||||||||
\(442\) | 31.9745 | 1.52087 | ||||||||
\(443\) | −35.7235 | −1.69728 | −0.848638 | − | 0.528974i | \(-0.822577\pi\) | ||||
−0.848638 | + | 0.528974i | \(0.822577\pi\) | |||||||
\(444\) | −47.1794 | −2.23903 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −8.41915 | −0.398659 | ||||||||
\(447\) | 39.6102 | 1.87350 | ||||||||
\(448\) | 29.2967 | 1.38414 | ||||||||
\(449\) | 16.5801 | 0.782462 | 0.391231 | − | 0.920293i | \(-0.372049\pi\) | ||||
0.391231 | + | 0.920293i | \(0.372049\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.70501 | 0.409903 | ||||||||
\(452\) | −19.0899 | −0.897914 | ||||||||
\(453\) | 42.4356 | 1.99380 | ||||||||
\(454\) | 26.9569 | 1.26515 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.58224 | −0.0740952 | ||||||||
\(457\) | 14.2167 | 0.665029 | 0.332515 | − | 0.943098i | \(-0.392103\pi\) | ||||
0.332515 | + | 0.943098i | \(0.392103\pi\) | |||||||
\(458\) | 11.6857 | 0.546038 | ||||||||
\(459\) | −27.2459 | −1.27173 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −29.7262 | −1.38449 | −0.692245 | − | 0.721663i | \(-0.743378\pi\) | ||||
−0.692245 | + | 0.721663i | \(0.743378\pi\) | |||||||
\(462\) | 122.824 | 5.71428 | ||||||||
\(463\) | −16.6345 | −0.773069 | −0.386535 | − | 0.922275i | \(-0.626328\pi\) | ||||
−0.386535 | + | 0.922275i | \(0.626328\pi\) | |||||||
\(464\) | −10.5180 | −0.488287 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −23.9578 | −1.10982 | ||||||||
\(467\) | −14.0306 | −0.649260 | −0.324630 | − | 0.945841i | \(-0.605240\pi\) | ||||
−0.324630 | + | 0.945841i | \(0.605240\pi\) | |||||||
\(468\) | 49.2393 | 2.27609 | ||||||||
\(469\) | −24.8287 | −1.14648 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.23503 | −0.195140 | ||||||||
\(472\) | −0.870700 | −0.0400772 | ||||||||
\(473\) | −59.5321 | −2.73729 | ||||||||
\(474\) | 31.4578 | 1.44490 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 26.8870 | 1.23236 | ||||||||
\(477\) | 37.9370 | 1.73701 | ||||||||
\(478\) | 53.2924 | 2.43754 | ||||||||
\(479\) | 7.38971 | 0.337645 | 0.168822 | − | 0.985647i | \(-0.446004\pi\) | ||||
0.168822 | + | 0.985647i | \(0.446004\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −37.3381 | −1.70247 | ||||||||
\(482\) | −1.98624 | −0.0904709 | ||||||||
\(483\) | 101.424 | 4.61493 | ||||||||
\(484\) | 36.0898 | 1.64044 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 12.8859 | 0.584516 | ||||||||
\(487\) | −37.6880 | −1.70780 | −0.853902 | − | 0.520433i | \(-0.825770\pi\) | ||||
−0.853902 | + | 0.520433i | \(0.825770\pi\) | |||||||
\(488\) | −0.686414 | −0.0310725 | ||||||||
\(489\) | −30.4139 | −1.37536 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.9491 | 0.855162 | 0.427581 | − | 0.903977i | \(-0.359366\pi\) | ||||
0.427581 | + | 0.903977i | \(0.359366\pi\) | |||||||
\(492\) | 9.13708 | 0.411931 | ||||||||
\(493\) | −9.13005 | −0.411197 | ||||||||
\(494\) | 44.4178 | 1.99845 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.69546 | 0.345536 | ||||||||
\(497\) | 59.0390 | 2.64826 | ||||||||
\(498\) | −61.5160 | −2.75660 | ||||||||
\(499\) | −0.653039 | −0.0292340 | −0.0146170 | − | 0.999893i | \(-0.504653\pi\) | ||||
−0.0146170 | + | 0.999893i | \(0.504653\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −61.1795 | −2.73330 | ||||||||
\(502\) | −27.8310 | −1.24216 | ||||||||
\(503\) | −18.2091 | −0.811905 | −0.405953 | − | 0.913894i | \(-0.633060\pi\) | ||||
−0.405953 | + | 0.913894i | \(0.633060\pi\) | |||||||
\(504\) | −2.36741 | −0.105453 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 96.2789 | 4.28012 | ||||||||
\(507\) | 21.6883 | 0.963210 | ||||||||
\(508\) | −1.45388 | −0.0645057 | ||||||||
\(509\) | −30.1462 | −1.33621 | −0.668104 | − | 0.744068i | \(-0.732894\pi\) | ||||
−0.668104 | + | 0.744068i | \(0.732894\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 34.8287 | 1.54073 | ||||||||
\(512\) | −31.7082 | −1.40132 | ||||||||
\(513\) | −37.8489 | −1.67107 | ||||||||
\(514\) | −6.23994 | −0.275232 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −62.4870 | −2.75084 | ||||||||
\(517\) | −2.92994 | −0.128858 | ||||||||
\(518\) | −63.6794 | −2.79791 | ||||||||
\(519\) | 52.4454 | 2.30210 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.89716 | −0.170738 | −0.0853688 | − | 0.996349i | \(-0.527207\pi\) | ||||
−0.0853688 | + | 0.996349i | \(0.527207\pi\) | |||||||
\(522\) | −28.5161 | −1.24811 | ||||||||
\(523\) | 32.4111 | 1.41724 | 0.708620 | − | 0.705591i | \(-0.249318\pi\) | ||||
0.708620 | + | 0.705591i | \(0.249318\pi\) | |||||||
\(524\) | −13.7418 | −0.600314 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 40.7133 | 1.77519 | ||||||||
\(527\) | 6.67995 | 0.290983 | ||||||||
\(528\) | −65.4910 | −2.85013 | ||||||||
\(529\) | 56.5037 | 2.45668 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −44.8101 | −1.94459 | ||||||||
\(532\) | 37.3504 | 1.61934 | ||||||||
\(533\) | 7.23116 | 0.313216 | ||||||||
\(534\) | −63.5112 | −2.74840 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0.697430 | 0.0301244 | ||||||||
\(537\) | 27.3711 | 1.18115 | ||||||||
\(538\) | −42.8819 | −1.84877 | ||||||||
\(539\) | 43.6832 | 1.88157 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.5981 | −0.756603 | −0.378301 | − | 0.925682i | \(-0.623492\pi\) | ||||
−0.378301 | + | 0.925682i | \(0.623492\pi\) | |||||||
\(542\) | −60.2800 | −2.58925 | ||||||||
\(543\) | 44.0203 | 1.88909 | ||||||||
\(544\) | −28.3005 | −1.21337 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 102.028 | 4.36641 | ||||||||
\(547\) | 34.2404 | 1.46401 | 0.732006 | − | 0.681298i | \(-0.238584\pi\) | ||||
0.732006 | + | 0.681298i | \(0.238584\pi\) | |||||||
\(548\) | −16.1910 | −0.691647 | ||||||||
\(549\) | −35.3259 | −1.50767 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12.6831 | −0.540319 | ||||||||
\(552\) | −2.84895 | −0.121259 | ||||||||
\(553\) | 20.9347 | 0.890233 | ||||||||
\(554\) | 56.3711 | 2.39498 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7.83908 | −0.332451 | ||||||||
\(557\) | 6.43152 | 0.272512 | 0.136256 | − | 0.990674i | \(-0.456493\pi\) | ||||
0.136256 | + | 0.990674i | \(0.456493\pi\) | |||||||
\(558\) | 20.8636 | 0.883227 | ||||||||
\(559\) | −49.4527 | −2.09163 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −56.8487 | −2.40015 | ||||||||
\(562\) | −36.7879 | −1.55181 | ||||||||
\(563\) | −14.0474 | −0.592026 | −0.296013 | − | 0.955184i | \(-0.595657\pi\) | ||||
−0.296013 | + | 0.955184i | \(0.595657\pi\) | |||||||
\(564\) | −3.07536 | −0.129496 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −31.1766 | −1.31045 | ||||||||
\(567\) | −21.7331 | −0.912706 | ||||||||
\(568\) | −1.65839 | −0.0695844 | ||||||||
\(569\) | −21.2540 | −0.891015 | −0.445508 | − | 0.895278i | \(-0.646977\pi\) | ||||
−0.445508 | + | 0.895278i | \(0.646977\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.79489 | −0.409903 | −0.204952 | − | 0.978772i | \(-0.565704\pi\) | ||||
−0.204952 | + | 0.978772i | \(0.565704\pi\) | |||||||
\(572\) | 47.7535 | 1.99667 | ||||||||
\(573\) | 36.2223 | 1.51321 | ||||||||
\(574\) | 12.3326 | 0.514753 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −42.3519 | −1.76466 | ||||||||
\(577\) | 2.46709 | 0.102706 | 0.0513532 | − | 0.998681i | \(-0.483647\pi\) | ||||
0.0513532 | + | 0.998681i | \(0.483647\pi\) | |||||||
\(578\) | 8.52617 | 0.354642 | ||||||||
\(579\) | 15.1459 | 0.629441 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −40.9380 | −1.69839 | ||||||||
\(582\) | 19.9438 | 0.826699 | ||||||||
\(583\) | 36.7922 | 1.52378 | ||||||||
\(584\) | −0.978327 | −0.0404834 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −38.6379 | −1.59612 | ||||||||
\(587\) | −31.4948 | −1.29993 | −0.649965 | − | 0.759964i | \(-0.725216\pi\) | ||||
−0.649965 | + | 0.759964i | \(0.725216\pi\) | |||||||
\(588\) | 45.8513 | 1.89088 | ||||||||
\(589\) | 9.27953 | 0.382356 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.49136 | −0.267019 | ||||||||
\(592\) | 33.9546 | 1.39552 | ||||||||
\(593\) | 21.8589 | 0.897637 | 0.448818 | − | 0.893623i | \(-0.351845\pi\) | ||||
0.448818 | + | 0.893623i | \(0.351845\pi\) | |||||||
\(594\) | −82.5297 | −3.38624 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 26.2649 | 1.07585 | ||||||||
\(597\) | 26.3748 | 1.07945 | ||||||||
\(598\) | 79.9778 | 3.27054 | ||||||||
\(599\) | −33.0013 | −1.34840 | −0.674199 | − | 0.738550i | \(-0.735511\pi\) | ||||
−0.674199 | + | 0.738550i | \(0.735511\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.9772 | 0.978051 | 0.489025 | − | 0.872270i | \(-0.337353\pi\) | ||||
0.489025 | + | 0.872270i | \(0.337353\pi\) | |||||||
\(602\) | −84.3406 | −3.43746 | ||||||||
\(603\) | 35.8929 | 1.46167 | ||||||||
\(604\) | 28.1384 | 1.14494 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −5.65328 | −0.229649 | ||||||||
\(607\) | 0.694914 | 0.0282057 | 0.0141028 | − | 0.999901i | \(-0.495511\pi\) | ||||
0.0141028 | + | 0.999901i | \(0.495511\pi\) | |||||||
\(608\) | −39.3140 | −1.59439 | ||||||||
\(609\) | −29.1333 | −1.18054 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.43387 | −0.0984637 | ||||||||
\(612\) | −38.8683 | −1.57116 | ||||||||
\(613\) | 31.6306 | 1.27755 | 0.638775 | − | 0.769394i | \(-0.279442\pi\) | ||||
0.638775 | + | 0.769394i | \(0.279442\pi\) | |||||||
\(614\) | 36.8703 | 1.48796 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.29598 | −0.0925075 | ||||||||
\(617\) | 14.8903 | 0.599462 | 0.299731 | − | 0.954024i | \(-0.403103\pi\) | ||||
0.299731 | + | 0.954024i | \(0.403103\pi\) | |||||||
\(618\) | 100.515 | 4.04331 | ||||||||
\(619\) | 33.9882 | 1.36610 | 0.683051 | − | 0.730371i | \(-0.260653\pi\) | ||||
0.683051 | + | 0.730371i | \(0.260653\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −68.1501 | −2.73477 | ||||||||
\(622\) | 49.9724 | 2.00371 | ||||||||
\(623\) | −42.2657 | −1.69334 | ||||||||
\(624\) | −54.4027 | −2.17785 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −45.2613 | −1.80901 | ||||||||
\(627\) | −78.9720 | −3.15384 | ||||||||
\(628\) | −2.80818 | −0.112059 | ||||||||
\(629\) | 29.4739 | 1.17520 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14.1877 | −0.564803 | −0.282402 | − | 0.959296i | \(-0.591131\pi\) | ||||
−0.282402 | + | 0.959296i | \(0.591131\pi\) | |||||||
\(632\) | −0.588048 | −0.0233913 | ||||||||
\(633\) | −16.9803 | −0.674908 | ||||||||
\(634\) | 33.4987 | 1.33040 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 38.6184 | 1.53132 | ||||||||
\(637\) | 36.2871 | 1.43775 | ||||||||
\(638\) | −27.6556 | −1.09489 | ||||||||
\(639\) | −85.3480 | −3.37631 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.661663 | 0.0261341 | 0.0130671 | − | 0.999915i | \(-0.495841\pi\) | ||||
0.0130671 | + | 0.999915i | \(0.495841\pi\) | |||||||
\(642\) | −9.55467 | −0.377093 | ||||||||
\(643\) | 8.27801 | 0.326453 | 0.163226 | − | 0.986589i | \(-0.447810\pi\) | ||||
0.163226 | + | 0.986589i | \(0.447810\pi\) | |||||||
\(644\) | 67.2524 | 2.65011 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −35.0624 | −1.37951 | ||||||||
\(647\) | −11.5359 | −0.453522 | −0.226761 | − | 0.973950i | \(-0.572814\pi\) | ||||
−0.226761 | + | 0.973950i | \(0.572814\pi\) | |||||||
\(648\) | 0.610477 | 0.0239818 | ||||||||
\(649\) | −43.4580 | −1.70587 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 21.3152 | 0.835410 | ||||||||
\(652\) | −20.1670 | −0.789799 | ||||||||
\(653\) | 15.7264 | 0.615422 | 0.307711 | − | 0.951480i | \(-0.400437\pi\) | ||||
0.307711 | + | 0.951480i | \(0.400437\pi\) | |||||||
\(654\) | −36.6607 | −1.43355 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −6.57588 | −0.256745 | ||||||||
\(657\) | −50.3490 | −1.96430 | ||||||||
\(658\) | −4.15091 | −0.161819 | ||||||||
\(659\) | −2.84552 | −0.110846 | −0.0554228 | − | 0.998463i | \(-0.517651\pi\) | ||||
−0.0554228 | + | 0.998463i | \(0.517651\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 48.6598 | 1.89265 | 0.946323 | − | 0.323222i | \(-0.104766\pi\) | ||||
0.946323 | + | 0.323222i | \(0.104766\pi\) | |||||||
\(662\) | −69.3308 | −2.69462 | ||||||||
\(663\) | −47.2236 | −1.83401 | ||||||||
\(664\) | 1.14993 | 0.0446261 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 92.0562 | 3.56711 | ||||||||
\(667\) | −22.8370 | −0.884251 | ||||||||
\(668\) | −40.5672 | −1.56959 | ||||||||
\(669\) | 12.4344 | 0.480740 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −34.2599 | −1.32259 | ||||||||
\(672\) | −90.3048 | −3.48358 | ||||||||
\(673\) | 38.8479 | 1.49748 | 0.748738 | − | 0.662866i | \(-0.230660\pi\) | ||||
0.748738 | + | 0.662866i | \(0.230660\pi\) | |||||||
\(674\) | −14.0457 | −0.541020 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 14.3812 | 0.553121 | ||||||||
\(677\) | 43.1514 | 1.65844 | 0.829222 | − | 0.558919i | \(-0.188784\pi\) | ||||
0.829222 | + | 0.558919i | \(0.188784\pi\) | |||||||
\(678\) | 57.1831 | 2.19610 | ||||||||
\(679\) | 13.2723 | 0.509345 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −39.8130 | −1.52564 | ||||||||
\(682\) | 20.2341 | 0.774802 | ||||||||
\(683\) | 5.62695 | 0.215309 | 0.107655 | − | 0.994188i | \(-0.465666\pi\) | ||||
0.107655 | + | 0.994188i | \(0.465666\pi\) | |||||||
\(684\) | −53.9944 | −2.06453 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 7.97460 | 0.304472 | ||||||||
\(687\) | −17.2588 | −0.658464 | ||||||||
\(688\) | 44.9713 | 1.71452 | ||||||||
\(689\) | 30.5629 | 1.16435 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15.1423 | −0.576041 | −0.288020 | − | 0.957624i | \(-0.592997\pi\) | ||||
−0.288020 | + | 0.957624i | \(0.592997\pi\) | |||||||
\(692\) | 34.7757 | 1.32197 | ||||||||
\(693\) | −118.161 | −4.48857 | ||||||||
\(694\) | −65.7040 | −2.49409 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0.818346 | 0.0310193 | ||||||||
\(697\) | −5.70811 | −0.216210 | ||||||||
\(698\) | 45.0903 | 1.70669 | ||||||||
\(699\) | 35.3836 | 1.33833 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −26.7358 | −1.00980 | −0.504899 | − | 0.863178i | \(-0.668470\pi\) | ||||
−0.504899 | + | 0.863178i | \(0.668470\pi\) | |||||||
\(702\) | −68.5566 | −2.58750 | ||||||||
\(703\) | 40.9440 | 1.54423 | ||||||||
\(704\) | −41.0739 | −1.54803 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 40.4930 | 1.52397 | ||||||||
\(707\) | −3.76218 | −0.141491 | ||||||||
\(708\) | −45.6150 | −1.71432 | ||||||||
\(709\) | 19.3807 | 0.727857 | 0.363929 | − | 0.931427i | \(-0.381435\pi\) | ||||
0.363929 | + | 0.931427i | \(0.381435\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −30.2636 | −1.13497 | ||||||||
\(712\) | 1.18723 | 0.0444933 | ||||||||
\(713\) | 16.7085 | 0.625740 | ||||||||
\(714\) | −80.5389 | −3.01409 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 18.1494 | 0.678274 | ||||||||
\(717\) | −78.7083 | −2.93941 | ||||||||
\(718\) | 49.3042 | 1.84002 | ||||||||
\(719\) | −39.6526 | −1.47879 | −0.739396 | − | 0.673271i | \(-0.764889\pi\) | ||||
−0.739396 | + | 0.673271i | \(0.764889\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 66.8912 | 2.49116 | ||||||||
\(722\) | −10.9687 | −0.408212 | ||||||||
\(723\) | 2.93351 | 0.109098 | ||||||||
\(724\) | 29.1892 | 1.08481 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −108.106 | −4.01217 | ||||||||
\(727\) | −45.2495 | −1.67821 | −0.839105 | − | 0.543970i | \(-0.816921\pi\) | ||||
−0.839105 | + | 0.543970i | \(0.816921\pi\) | |||||||
\(728\) | −1.90724 | −0.0706871 | ||||||||
\(729\) | −35.8459 | −1.32763 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 39.0368 | 1.44383 | ||||||||
\(732\) | −35.9604 | −1.32914 | ||||||||
\(733\) | −18.5883 | −0.686574 | −0.343287 | − | 0.939231i | \(-0.611540\pi\) | ||||
−0.343287 | + | 0.939231i | \(0.611540\pi\) | |||||||
\(734\) | 36.2566 | 1.33826 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −70.7880 | −2.60928 | ||||||||
\(737\) | 34.8098 | 1.28224 | ||||||||
\(738\) | −17.8282 | −0.656267 | ||||||||
\(739\) | 5.85210 | 0.215273 | 0.107637 | − | 0.994190i | \(-0.465672\pi\) | ||||
0.107637 | + | 0.994190i | \(0.465672\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −65.6012 | −2.40992 | ||||||||
\(742\) | 52.1244 | 1.91355 | ||||||||
\(743\) | −10.0765 | −0.369672 | −0.184836 | − | 0.982769i | \(-0.559175\pi\) | ||||
−0.184836 | + | 0.982769i | \(0.559175\pi\) | |||||||
\(744\) | −0.598738 | −0.0219508 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −66.0415 | −2.41795 | ||||||||
\(747\) | 59.1807 | 2.16531 | ||||||||
\(748\) | −37.6955 | −1.37828 | ||||||||
\(749\) | −6.35849 | −0.232334 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.62585 | −0.0593280 | −0.0296640 | − | 0.999560i | \(-0.509444\pi\) | ||||
−0.0296640 | + | 0.999560i | \(0.509444\pi\) | |||||||
\(752\) | 2.21331 | 0.0807112 | ||||||||
\(753\) | 41.1039 | 1.49791 | ||||||||
\(754\) | −22.9732 | −0.836634 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −57.6483 | −2.09665 | ||||||||
\(757\) | 3.59438 | 0.130640 | 0.0653200 | − | 0.997864i | \(-0.479193\pi\) | ||||
0.0653200 | + | 0.997864i | \(0.479193\pi\) | |||||||
\(758\) | −12.8549 | −0.466911 | ||||||||
\(759\) | −142.196 | −5.16137 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 35.8363 | 1.29906 | 0.649532 | − | 0.760335i | \(-0.274965\pi\) | ||||
0.649532 | + | 0.760335i | \(0.274965\pi\) | |||||||
\(762\) | 4.35506 | 0.157767 | ||||||||
\(763\) | −24.3971 | −0.883235 | ||||||||
\(764\) | 24.0184 | 0.868956 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −16.5516 | −0.598034 | ||||||||
\(767\) | −36.1001 | −1.30350 | ||||||||
\(768\) | 49.4032 | 1.78268 | ||||||||
\(769\) | −45.5522 | −1.64265 | −0.821327 | − | 0.570457i | \(-0.806766\pi\) | ||||
−0.821327 | + | 0.570457i | \(0.806766\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.21584 | 0.331900 | ||||||||
\(772\) | 10.0430 | 0.361455 | ||||||||
\(773\) | −21.4939 | −0.773082 | −0.386541 | − | 0.922272i | \(-0.626330\pi\) | ||||
−0.386541 | + | 0.922272i | \(0.626330\pi\) | |||||||
\(774\) | 121.924 | 4.38248 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −0.372815 | −0.0133833 | ||||||||
\(777\) | 94.0490 | 3.37399 | ||||||||
\(778\) | 9.29579 | 0.333270 | ||||||||
\(779\) | −7.92949 | −0.284103 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −82.7726 | −2.96184 | ||||||||
\(782\) | −63.1327 | −2.25762 | ||||||||
\(783\) | 19.5757 | 0.699580 | ||||||||
\(784\) | −32.9988 | −1.17853 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 41.1631 | 1.46824 | ||||||||
\(787\) | 39.0117 | 1.39062 | 0.695309 | − | 0.718711i | \(-0.255268\pi\) | ||||
0.695309 | + | 0.718711i | \(0.255268\pi\) | |||||||
\(788\) | −4.30432 | −0.153335 | ||||||||
\(789\) | −60.1300 | −2.14069 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 38.0545 | 1.35306 | ||||||||
\(792\) | 3.31911 | 0.117939 | ||||||||
\(793\) | −28.4594 | −1.01062 | ||||||||
\(794\) | 57.0244 | 2.02372 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 17.4887 | 0.619871 | ||||||||
\(797\) | −27.0551 | −0.958340 | −0.479170 | − | 0.877722i | \(-0.659062\pi\) | ||||
−0.479170 | + | 0.877722i | \(0.659062\pi\) | |||||||
\(798\) | −111.882 | −3.96056 | ||||||||
\(799\) | 1.92124 | 0.0679685 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 61.1001 | 2.15887 | ||||||||
\(802\) | 37.2528 | 1.31544 | ||||||||
\(803\) | −48.8298 | −1.72317 | ||||||||
\(804\) | 36.5376 | 1.28858 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 16.8082 | 0.592044 | ||||||||
\(807\) | 63.3328 | 2.22942 | ||||||||
\(808\) | 0.105678 | 0.00371775 | ||||||||
\(809\) | −3.74501 | −0.131667 | −0.0658337 | − | 0.997831i | \(-0.520971\pi\) | ||||
−0.0658337 | + | 0.997831i | \(0.520971\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23.8097 | 0.836073 | 0.418036 | − | 0.908430i | \(-0.362718\pi\) | ||||
0.418036 | + | 0.908430i | \(0.362718\pi\) | |||||||
\(812\) | −19.3179 | −0.677924 | ||||||||
\(813\) | 89.0282 | 3.12236 | ||||||||
\(814\) | 89.2784 | 3.12921 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 42.9442 | 1.50335 | ||||||||
\(817\) | 54.2284 | 1.89721 | ||||||||
\(818\) | 23.5065 | 0.821886 | ||||||||
\(819\) | −98.1552 | −3.42982 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.44339 | 0.329577 | 0.164788 | − | 0.986329i | \(-0.447306\pi\) | ||||
0.164788 | + | 0.986329i | \(0.447306\pi\) | |||||||
\(822\) | 48.4996 | 1.69162 | ||||||||
\(823\) | −22.6151 | −0.788314 | −0.394157 | − | 0.919043i | \(-0.628963\pi\) | ||||
−0.394157 | + | 0.919043i | \(0.628963\pi\) | |||||||
\(824\) | −1.87895 | −0.0654564 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −61.5679 | −2.14222 | ||||||||
\(827\) | 30.2635 | 1.05237 | 0.526183 | − | 0.850372i | \(-0.323623\pi\) | ||||
0.526183 | + | 0.850372i | \(0.323623\pi\) | |||||||
\(828\) | −97.2213 | −3.37867 | ||||||||
\(829\) | 29.8682 | 1.03736 | 0.518682 | − | 0.854967i | \(-0.326423\pi\) | ||||
0.518682 | + | 0.854967i | \(0.326423\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −83.2552 | −2.88809 | ||||||||
\(832\) | −34.1196 | −1.18289 | ||||||||
\(833\) | −28.6442 | −0.992463 | ||||||||
\(834\) | 23.4817 | 0.813104 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −52.3651 | −1.81109 | ||||||||
\(837\) | −14.3225 | −0.495057 | ||||||||
\(838\) | −49.6503 | −1.71514 | ||||||||
\(839\) | 6.20080 | 0.214075 | 0.107038 | − | 0.994255i | \(-0.465863\pi\) | ||||
0.107038 | + | 0.994255i | \(0.465863\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.4402 | −0.773800 | ||||||||
\(842\) | 80.0835 | 2.75986 | ||||||||
\(843\) | 54.3326 | 1.87131 | ||||||||
\(844\) | −11.2594 | −0.387564 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 6.00064 | 0.206306 | ||||||||
\(847\) | −71.9426 | −2.47198 | ||||||||
\(848\) | −27.7933 | −0.954426 | ||||||||
\(849\) | 46.0451 | 1.58026 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 73.7229 | 2.52719 | ||||||||
\(852\) | −86.8810 | −2.97649 | ||||||||
\(853\) | −6.31693 | −0.216288 | −0.108144 | − | 0.994135i | \(-0.534491\pi\) | ||||
−0.108144 | + | 0.994135i | \(0.534491\pi\) | |||||||
\(854\) | −48.5369 | −1.66090 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.178608 | 0.00610469 | ||||||||
\(857\) | −37.5338 | −1.28213 | −0.641065 | − | 0.767486i | \(-0.721507\pi\) | ||||
−0.641065 | + | 0.767486i | \(0.721507\pi\) | |||||||
\(858\) | −143.044 | −4.88343 | ||||||||
\(859\) | −0.322062 | −0.0109886 | −0.00549432 | − | 0.999985i | \(-0.501749\pi\) | ||||
−0.00549432 | + | 0.999985i | \(0.501749\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −18.2142 | −0.620737 | ||||||||
\(862\) | 76.1178 | 2.59258 | ||||||||
\(863\) | −27.0433 | −0.920566 | −0.460283 | − | 0.887772i | \(-0.652252\pi\) | ||||
−0.460283 | + | 0.887772i | \(0.652252\pi\) | |||||||
\(864\) | 60.6790 | 2.06434 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 23.2560 | 0.790273 | ||||||||
\(867\) | −12.5924 | −0.427661 | ||||||||
\(868\) | 14.1338 | 0.479733 | ||||||||
\(869\) | −29.3504 | −0.995643 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 28.9161 | 0.979785 | ||||||||
\(872\) | 0.685307 | 0.0232074 | ||||||||
\(873\) | −19.1867 | −0.649372 | ||||||||
\(874\) | −87.7015 | −2.96655 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −51.2534 | −1.73169 | ||||||||
\(877\) | −9.62045 | −0.324859 | −0.162430 | − | 0.986720i | \(-0.551933\pi\) | ||||
−0.162430 | + | 0.986720i | \(0.551933\pi\) | |||||||
\(878\) | 41.8528 | 1.41246 | ||||||||
\(879\) | 57.0648 | 1.92475 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0.517032 | 0.0174193 | 0.00870963 | − | 0.999962i | \(-0.497228\pi\) | ||||
0.00870963 | + | 0.999962i | \(0.497228\pi\) | |||||||
\(882\) | −89.4650 | −3.01244 | ||||||||
\(883\) | 19.8807 | 0.669037 | 0.334519 | − | 0.942389i | \(-0.391426\pi\) | ||||
0.334519 | + | 0.942389i | \(0.391426\pi\) | |||||||
\(884\) | −31.3132 | −1.05318 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 70.9556 | 2.38380 | ||||||||
\(887\) | 17.2279 | 0.578456 | 0.289228 | − | 0.957260i | \(-0.406601\pi\) | ||||
0.289228 | + | 0.957260i | \(0.406601\pi\) | |||||||
\(888\) | −2.64180 | −0.0886531 | ||||||||
\(889\) | 2.89822 | 0.0972033 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 30.4698 | 1.02078 | ||||||||
\(892\) | 8.24503 | 0.276064 | ||||||||
\(893\) | 2.66891 | 0.0893117 | ||||||||
\(894\) | −78.6755 | −2.63130 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 3.37745 | 0.112833 | ||||||||
\(897\) | −118.120 | −3.94392 | ||||||||
\(898\) | −32.9321 | −1.09896 | ||||||||
\(899\) | −4.79944 | −0.160070 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −24.1256 | −0.803742 | ||||||||
\(902\) | −17.2903 | −0.575703 | ||||||||
\(903\) | 124.564 | 4.14522 | ||||||||
\(904\) | −1.06894 | −0.0355523 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −84.2875 | −2.80027 | ||||||||
\(907\) | −16.6575 | −0.553104 | −0.276552 | − | 0.960999i | \(-0.589192\pi\) | ||||
−0.276552 | + | 0.960999i | \(0.589192\pi\) | |||||||
\(908\) | −26.3994 | −0.876094 | ||||||||
\(909\) | 5.43867 | 0.180389 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 27.5693 | 0.913411 | 0.456706 | − | 0.889618i | \(-0.349029\pi\) | ||||
0.456706 | + | 0.889618i | \(0.349029\pi\) | |||||||
\(912\) | 59.6565 | 1.97542 | ||||||||
\(913\) | 57.3949 | 1.89949 | ||||||||
\(914\) | −28.2378 | −0.934024 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −11.4440 | −0.378121 | ||||||||
\(917\) | 27.3934 | 0.904610 | ||||||||
\(918\) | 54.1170 | 1.78613 | ||||||||
\(919\) | 28.4662 | 0.939012 | 0.469506 | − | 0.882929i | \(-0.344432\pi\) | ||||
0.469506 | + | 0.882929i | \(0.344432\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −54.4542 | −1.79433 | ||||||||
\(922\) | 59.0436 | 1.94450 | ||||||||
\(923\) | −68.7583 | −2.26321 | ||||||||
\(924\) | −120.284 | −3.95704 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 33.0401 | 1.08577 | ||||||||
\(927\) | −96.6992 | −3.17602 | ||||||||
\(928\) | 20.3334 | 0.667478 | ||||||||
\(929\) | −40.8486 | −1.34020 | −0.670100 | − | 0.742271i | \(-0.733749\pi\) | ||||
−0.670100 | + | 0.742271i | \(0.733749\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −39.7914 | −1.30411 | ||||||||
\(932\) | 23.4623 | 0.768533 | ||||||||
\(933\) | −73.8049 | −2.41626 | ||||||||
\(934\) | 27.8682 | 0.911877 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.75715 | 0.0901202 | ||||||||
\(937\) | 11.1714 | 0.364953 | 0.182476 | − | 0.983210i | \(-0.441589\pi\) | ||||
0.182476 | + | 0.983210i | \(0.441589\pi\) | |||||||
\(938\) | 49.3159 | 1.61022 | ||||||||
\(939\) | 66.8470 | 2.18147 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 43.0290 | 1.40271 | 0.701353 | − | 0.712814i | \(-0.252580\pi\) | ||||
0.701353 | + | 0.712814i | \(0.252580\pi\) | |||||||
\(942\) | 8.41180 | 0.274071 | ||||||||
\(943\) | −14.2777 | −0.464945 | ||||||||
\(944\) | 32.8287 | 1.06848 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 118.245 | 3.84449 | ||||||||
\(947\) | −12.2469 | −0.397970 | −0.198985 | − | 0.980003i | \(-0.563764\pi\) | ||||
−0.198985 | + | 0.980003i | \(0.563764\pi\) | |||||||
\(948\) | −30.8071 | −1.00057 | ||||||||
\(949\) | −40.5624 | −1.31671 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −49.4747 | −1.60433 | ||||||||
\(952\) | 1.50553 | 0.0487946 | ||||||||
\(953\) | −3.64133 | −0.117954 | −0.0589771 | − | 0.998259i | \(-0.518784\pi\) | ||||
−0.0589771 | + | 0.998259i | \(0.518784\pi\) | |||||||
\(954\) | −75.3521 | −2.43961 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −52.1902 | −1.68795 | ||||||||
\(957\) | 40.8449 | 1.32033 | ||||||||
\(958\) | −14.6778 | −0.474217 | ||||||||
\(959\) | 32.2758 | 1.04224 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.4885 | −0.886726 | ||||||||
\(962\) | 74.1626 | 2.39110 | ||||||||
\(963\) | 9.19195 | 0.296206 | ||||||||
\(964\) | 1.94516 | 0.0626495 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −201.452 | −6.48161 | ||||||||
\(967\) | 58.7347 | 1.88878 | 0.944390 | − | 0.328828i | \(-0.106654\pi\) | ||||
0.944390 | + | 0.328828i | \(0.106654\pi\) | |||||||
\(968\) | 2.02084 | 0.0649523 | ||||||||
\(969\) | 51.7841 | 1.66354 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 31.9698 | 1.02596 | 0.512980 | − | 0.858400i | \(-0.328541\pi\) | ||||
0.512980 | + | 0.858400i | \(0.328541\pi\) | |||||||
\(972\) | −12.6194 | −0.404767 | ||||||||
\(973\) | 15.6267 | 0.500969 | ||||||||
\(974\) | 74.8575 | 2.39859 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 25.8804 | 0.828411 | ||||||||
\(977\) | 55.9385 | 1.78963 | 0.894816 | − | 0.446436i | \(-0.147307\pi\) | ||||
0.894816 | + | 0.446436i | \(0.147307\pi\) | |||||||
\(978\) | 60.4093 | 1.93168 | ||||||||
\(979\) | 59.2564 | 1.89384 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 35.2690 | 1.12605 | ||||||||
\(982\) | −37.6376 | −1.20106 | ||||||||
\(983\) | −17.5972 | −0.561264 | −0.280632 | − | 0.959815i | \(-0.590544\pi\) | ||||
−0.280632 | + | 0.959815i | \(0.590544\pi\) | |||||||
\(984\) | 0.511630 | 0.0163102 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 18.1345 | 0.577520 | ||||||||
\(987\) | 6.13053 | 0.195137 | ||||||||
\(988\) | −43.4991 | −1.38389 | ||||||||
\(989\) | 97.6427 | 3.10486 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21.5494 | 0.684539 | 0.342269 | − | 0.939602i | \(-0.388804\pi\) | ||||
0.342269 | + | 0.939602i | \(0.388804\pi\) | |||||||
\(992\) | −14.8769 | −0.472341 | ||||||||
\(993\) | 102.395 | 3.24942 | ||||||||
\(994\) | −117.266 | −3.71945 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 60.2437 | 1.90889 | ||||||||
\(997\) | 24.2979 | 0.769522 | 0.384761 | − | 0.923016i | \(-0.374284\pi\) | ||||
0.384761 | + | 0.923016i | \(0.374284\pi\) | |||||||
\(998\) | 1.29709 | 0.0410588 | ||||||||
\(999\) | −63.1949 | −1.99940 |
(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 | 6025.2.a.m.1.10 | ✓ | 40 | |
5.4 | even | 2 | 6025.2.a.n.1.31 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6025.2.a.m.1.10 | ✓ | 40 | 1.1 | even | 1 | trivial | |
6025.2.a.n.1.31 | yes | 40 | 5.4 | even | 2 |