Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6046,2,Mod(1,6046)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6046, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6046.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6046 = 2 \cdot 3023 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6046.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: | \(48.2775530621\) |
Analytic rank: | \(0\) |
Dimension: | \(69\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 6046.1 |
$q$-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 | ||||||||
\(3\) | −2.10025 | −1.21258 | −0.606290 | − | 0.795244i | \(-0.707343\pi\) | ||||
−0.606290 | + | 0.795244i | \(0.707343\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 4.19656 | 1.87676 | 0.938379 | − | 0.345609i | \(-0.112328\pi\) | ||||
0.938379 | + | 0.345609i | \(0.112328\pi\) | |||||||
\(6\) | 2.10025 | 0.857423 | ||||||||
\(7\) | 2.72635 | 1.03046 | 0.515232 | − | 0.857051i | \(-0.327706\pi\) | ||||
0.515232 | + | 0.857051i | \(0.327706\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.41104 | 0.470348 | ||||||||
\(10\) | −4.19656 | −1.32707 | ||||||||
\(11\) | 2.34795 | 0.707934 | 0.353967 | − | 0.935258i | \(-0.384833\pi\) | ||||
0.353967 | + | 0.935258i | \(0.384833\pi\) | |||||||
\(12\) | −2.10025 | −0.606290 | ||||||||
\(13\) | 4.28809 | 1.18930 | 0.594651 | − | 0.803984i | \(-0.297290\pi\) | ||||
0.594651 | + | 0.803984i | \(0.297290\pi\) | |||||||
\(14\) | −2.72635 | −0.728648 | ||||||||
\(15\) | −8.81381 | −2.27572 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.62658 | 1.12211 | 0.561055 | − | 0.827779i | \(-0.310396\pi\) | ||||
0.561055 | + | 0.827779i | \(0.310396\pi\) | |||||||
\(18\) | −1.41104 | −0.332586 | ||||||||
\(19\) | 1.86144 | 0.427043 | 0.213521 | − | 0.976938i | \(-0.431507\pi\) | ||||
0.213521 | + | 0.976938i | \(0.431507\pi\) | |||||||
\(20\) | 4.19656 | 0.938379 | ||||||||
\(21\) | −5.72601 | −1.24952 | ||||||||
\(22\) | −2.34795 | −0.500585 | ||||||||
\(23\) | −4.16667 | −0.868810 | −0.434405 | − | 0.900718i | \(-0.643041\pi\) | ||||
−0.434405 | + | 0.900718i | \(0.643041\pi\) | |||||||
\(24\) | 2.10025 | 0.428711 | ||||||||
\(25\) | 12.6111 | 2.52222 | ||||||||
\(26\) | −4.28809 | −0.840963 | ||||||||
\(27\) | 3.33720 | 0.642245 | ||||||||
\(28\) | 2.72635 | 0.515232 | ||||||||
\(29\) | −4.64041 | −0.861703 | −0.430851 | − | 0.902423i | \(-0.641787\pi\) | ||||
−0.430851 | + | 0.902423i | \(0.641787\pi\) | |||||||
\(30\) | 8.81381 | 1.60917 | ||||||||
\(31\) | −2.65007 | −0.475966 | −0.237983 | − | 0.971269i | \(-0.576486\pi\) | ||||
−0.237983 | + | 0.971269i | \(0.576486\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −4.93128 | −0.858426 | ||||||||
\(34\) | −4.62658 | −0.793451 | ||||||||
\(35\) | 11.4413 | 1.93393 | ||||||||
\(36\) | 1.41104 | 0.235174 | ||||||||
\(37\) | 8.00548 | 1.31609 | 0.658046 | − | 0.752977i | \(-0.271383\pi\) | ||||
0.658046 | + | 0.752977i | \(0.271383\pi\) | |||||||
\(38\) | −1.86144 | −0.301965 | ||||||||
\(39\) | −9.00605 | −1.44212 | ||||||||
\(40\) | −4.19656 | −0.663534 | ||||||||
\(41\) | 1.70811 | 0.266762 | 0.133381 | − | 0.991065i | \(-0.457417\pi\) | ||||
0.133381 | + | 0.991065i | \(0.457417\pi\) | |||||||
\(42\) | 5.72601 | 0.883543 | ||||||||
\(43\) | −5.72273 | −0.872708 | −0.436354 | − | 0.899775i | \(-0.643730\pi\) | ||||
−0.436354 | + | 0.899775i | \(0.643730\pi\) | |||||||
\(44\) | 2.34795 | 0.353967 | ||||||||
\(45\) | 5.92153 | 0.882729 | ||||||||
\(46\) | 4.16667 | 0.614341 | ||||||||
\(47\) | 5.21811 | 0.761139 | 0.380570 | − | 0.924752i | \(-0.375728\pi\) | ||||
0.380570 | + | 0.924752i | \(0.375728\pi\) | |||||||
\(48\) | −2.10025 | −0.303145 | ||||||||
\(49\) | 0.432985 | 0.0618551 | ||||||||
\(50\) | −12.6111 | −1.78348 | ||||||||
\(51\) | −9.71696 | −1.36065 | ||||||||
\(52\) | 4.28809 | 0.594651 | ||||||||
\(53\) | 13.6464 | 1.87448 | 0.937240 | − | 0.348685i | \(-0.113372\pi\) | ||||
0.937240 | + | 0.348685i | \(0.113372\pi\) | |||||||
\(54\) | −3.33720 | −0.454136 | ||||||||
\(55\) | 9.85331 | 1.32862 | ||||||||
\(56\) | −2.72635 | −0.364324 | ||||||||
\(57\) | −3.90948 | −0.517823 | ||||||||
\(58\) | 4.64041 | 0.609316 | ||||||||
\(59\) | −4.37714 | −0.569855 | −0.284928 | − | 0.958549i | \(-0.591970\pi\) | ||||
−0.284928 | + | 0.958549i | \(0.591970\pi\) | |||||||
\(60\) | −8.81381 | −1.13786 | ||||||||
\(61\) | −12.1769 | −1.55909 | −0.779545 | − | 0.626347i | \(-0.784549\pi\) | ||||
−0.779545 | + | 0.626347i | \(0.784549\pi\) | |||||||
\(62\) | 2.65007 | 0.336559 | ||||||||
\(63\) | 3.84700 | 0.484676 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 17.9952 | 2.23203 | ||||||||
\(66\) | 4.93128 | 0.606999 | ||||||||
\(67\) | 10.3490 | 1.26433 | 0.632165 | − | 0.774834i | \(-0.282167\pi\) | ||||
0.632165 | + | 0.774834i | \(0.282167\pi\) | |||||||
\(68\) | 4.62658 | 0.561055 | ||||||||
\(69\) | 8.75103 | 1.05350 | ||||||||
\(70\) | −11.4413 | −1.36749 | ||||||||
\(71\) | 7.91164 | 0.938939 | 0.469469 | − | 0.882949i | \(-0.344445\pi\) | ||||
0.469469 | + | 0.882949i | \(0.344445\pi\) | |||||||
\(72\) | −1.41104 | −0.166293 | ||||||||
\(73\) | −3.12735 | −0.366029 | −0.183014 | − | 0.983110i | \(-0.558586\pi\) | ||||
−0.183014 | + | 0.983110i | \(0.558586\pi\) | |||||||
\(74\) | −8.00548 | −0.930618 | ||||||||
\(75\) | −26.4864 | −3.05839 | ||||||||
\(76\) | 1.86144 | 0.213521 | ||||||||
\(77\) | 6.40134 | 0.729500 | ||||||||
\(78\) | 9.00605 | 1.01973 | ||||||||
\(79\) | 0.147439 | 0.0165882 | 0.00829411 | − | 0.999966i | \(-0.497360\pi\) | ||||
0.00829411 | + | 0.999966i | \(0.497360\pi\) | |||||||
\(80\) | 4.19656 | 0.469189 | ||||||||
\(81\) | −11.2421 | −1.24912 | ||||||||
\(82\) | −1.70811 | −0.188629 | ||||||||
\(83\) | −8.32890 | −0.914215 | −0.457108 | − | 0.889411i | \(-0.651115\pi\) | ||||
−0.457108 | + | 0.889411i | \(0.651115\pi\) | |||||||
\(84\) | −5.72601 | −0.624759 | ||||||||
\(85\) | 19.4157 | 2.10593 | ||||||||
\(86\) | 5.72273 | 0.617098 | ||||||||
\(87\) | 9.74602 | 1.04488 | ||||||||
\(88\) | −2.34795 | −0.250292 | ||||||||
\(89\) | 3.25753 | 0.345297 | 0.172649 | − | 0.984983i | \(-0.444767\pi\) | ||||
0.172649 | + | 0.984983i | \(0.444767\pi\) | |||||||
\(90\) | −5.92153 | −0.624184 | ||||||||
\(91\) | 11.6908 | 1.22553 | ||||||||
\(92\) | −4.16667 | −0.434405 | ||||||||
\(93\) | 5.56580 | 0.577147 | ||||||||
\(94\) | −5.21811 | −0.538207 | ||||||||
\(95\) | 7.81162 | 0.801456 | ||||||||
\(96\) | 2.10025 | 0.214356 | ||||||||
\(97\) | 3.43929 | 0.349207 | 0.174604 | − | 0.984639i | \(-0.444136\pi\) | ||||
0.174604 | + | 0.984639i | \(0.444136\pi\) | |||||||
\(98\) | −0.432985 | −0.0437381 | ||||||||
\(99\) | 3.31306 | 0.332975 | ||||||||
\(100\) | 12.6111 | 1.26111 | ||||||||
\(101\) | 17.9553 | 1.78662 | 0.893311 | − | 0.449439i | \(-0.148376\pi\) | ||||
0.893311 | + | 0.449439i | \(0.148376\pi\) | |||||||
\(102\) | 9.71696 | 0.962122 | ||||||||
\(103\) | 11.6765 | 1.15052 | 0.575258 | − | 0.817972i | \(-0.304902\pi\) | ||||
0.575258 | + | 0.817972i | \(0.304902\pi\) | |||||||
\(104\) | −4.28809 | −0.420482 | ||||||||
\(105\) | −24.0295 | −2.34504 | ||||||||
\(106\) | −13.6464 | −1.32546 | ||||||||
\(107\) | −8.37290 | −0.809439 | −0.404720 | − | 0.914441i | \(-0.632631\pi\) | ||||
−0.404720 | + | 0.914441i | \(0.632631\pi\) | |||||||
\(108\) | 3.33720 | 0.321123 | ||||||||
\(109\) | −7.43302 | −0.711954 | −0.355977 | − | 0.934495i | \(-0.615852\pi\) | ||||
−0.355977 | + | 0.934495i | \(0.615852\pi\) | |||||||
\(110\) | −9.85331 | −0.939476 | ||||||||
\(111\) | −16.8135 | −1.59587 | ||||||||
\(112\) | 2.72635 | 0.257616 | ||||||||
\(113\) | 9.43626 | 0.887689 | 0.443844 | − | 0.896104i | \(-0.353614\pi\) | ||||
0.443844 | + | 0.896104i | \(0.353614\pi\) | |||||||
\(114\) | 3.90948 | 0.366156 | ||||||||
\(115\) | −17.4856 | −1.63054 | ||||||||
\(116\) | −4.64041 | −0.430851 | ||||||||
\(117\) | 6.05068 | 0.559385 | ||||||||
\(118\) | 4.37714 | 0.402949 | ||||||||
\(119\) | 12.6137 | 1.15629 | ||||||||
\(120\) | 8.81381 | 0.804587 | ||||||||
\(121\) | −5.48713 | −0.498830 | ||||||||
\(122\) | 12.1769 | 1.10244 | ||||||||
\(123\) | −3.58746 | −0.323470 | ||||||||
\(124\) | −2.65007 | −0.237983 | ||||||||
\(125\) | 31.9404 | 2.85683 | ||||||||
\(126\) | −3.84700 | −0.342718 | ||||||||
\(127\) | −21.3319 | −1.89290 | −0.946452 | − | 0.322846i | \(-0.895361\pi\) | ||||
−0.946452 | + | 0.322846i | \(0.895361\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 12.0192 | 1.05823 | ||||||||
\(130\) | −17.9952 | −1.57828 | ||||||||
\(131\) | −10.5976 | −0.925919 | −0.462959 | − | 0.886379i | \(-0.653212\pi\) | ||||
−0.462959 | + | 0.886379i | \(0.653212\pi\) | |||||||
\(132\) | −4.93128 | −0.429213 | ||||||||
\(133\) | 5.07493 | 0.440052 | ||||||||
\(134\) | −10.3490 | −0.894016 | ||||||||
\(135\) | 14.0048 | 1.20534 | ||||||||
\(136\) | −4.62658 | −0.396726 | ||||||||
\(137\) | 6.57723 | 0.561931 | 0.280965 | − | 0.959718i | \(-0.409345\pi\) | ||||
0.280965 | + | 0.959718i | \(0.409345\pi\) | |||||||
\(138\) | −8.75103 | −0.744937 | ||||||||
\(139\) | 20.8114 | 1.76520 | 0.882600 | − | 0.470124i | \(-0.155791\pi\) | ||||
0.882600 | + | 0.470124i | \(0.155791\pi\) | |||||||
\(140\) | 11.4413 | 0.966965 | ||||||||
\(141\) | −10.9593 | −0.922941 | ||||||||
\(142\) | −7.91164 | −0.663930 | ||||||||
\(143\) | 10.0682 | 0.841947 | ||||||||
\(144\) | 1.41104 | 0.117587 | ||||||||
\(145\) | −19.4737 | −1.61721 | ||||||||
\(146\) | 3.12735 | 0.258821 | ||||||||
\(147\) | −0.909377 | −0.0750041 | ||||||||
\(148\) | 8.00548 | 0.658046 | ||||||||
\(149\) | 2.64225 | 0.216462 | 0.108231 | − | 0.994126i | \(-0.465481\pi\) | ||||
0.108231 | + | 0.994126i | \(0.465481\pi\) | |||||||
\(150\) | 26.4864 | 2.16261 | ||||||||
\(151\) | −17.0437 | −1.38700 | −0.693499 | − | 0.720458i | \(-0.743932\pi\) | ||||
−0.693499 | + | 0.720458i | \(0.743932\pi\) | |||||||
\(152\) | −1.86144 | −0.150982 | ||||||||
\(153\) | 6.52830 | 0.527782 | ||||||||
\(154\) | −6.40134 | −0.515834 | ||||||||
\(155\) | −11.1212 | −0.893273 | ||||||||
\(156\) | −9.00605 | −0.721061 | ||||||||
\(157\) | −20.1146 | −1.60532 | −0.802660 | − | 0.596437i | \(-0.796583\pi\) | ||||
−0.802660 | + | 0.596437i | \(0.796583\pi\) | |||||||
\(158\) | −0.147439 | −0.0117296 | ||||||||
\(159\) | −28.6609 | −2.27296 | ||||||||
\(160\) | −4.19656 | −0.331767 | ||||||||
\(161\) | −11.3598 | −0.895277 | ||||||||
\(162\) | 11.2421 | 0.883262 | ||||||||
\(163\) | 5.28295 | 0.413793 | 0.206896 | − | 0.978363i | \(-0.433664\pi\) | ||||
0.206896 | + | 0.978363i | \(0.433664\pi\) | |||||||
\(164\) | 1.70811 | 0.133381 | ||||||||
\(165\) | −20.6944 | −1.61106 | ||||||||
\(166\) | 8.32890 | 0.646448 | ||||||||
\(167\) | −18.7836 | −1.45352 | −0.726760 | − | 0.686891i | \(-0.758975\pi\) | ||||
−0.726760 | + | 0.686891i | \(0.758975\pi\) | |||||||
\(168\) | 5.72601 | 0.441771 | ||||||||
\(169\) | 5.38769 | 0.414438 | ||||||||
\(170\) | −19.4157 | −1.48912 | ||||||||
\(171\) | 2.62657 | 0.200859 | ||||||||
\(172\) | −5.72273 | −0.436354 | ||||||||
\(173\) | −15.7375 | −1.19650 | −0.598251 | − | 0.801308i | \(-0.704138\pi\) | ||||
−0.598251 | + | 0.801308i | \(0.704138\pi\) | |||||||
\(174\) | −9.74602 | −0.738844 | ||||||||
\(175\) | 34.3822 | 2.59905 | ||||||||
\(176\) | 2.34795 | 0.176983 | ||||||||
\(177\) | 9.19309 | 0.690995 | ||||||||
\(178\) | −3.25753 | −0.244162 | ||||||||
\(179\) | 19.4081 | 1.45063 | 0.725316 | − | 0.688417i | \(-0.241694\pi\) | ||||
0.725316 | + | 0.688417i | \(0.241694\pi\) | |||||||
\(180\) | 5.92153 | 0.441364 | ||||||||
\(181\) | 11.5761 | 0.860441 | 0.430221 | − | 0.902724i | \(-0.358436\pi\) | ||||
0.430221 | + | 0.902724i | \(0.358436\pi\) | |||||||
\(182\) | −11.6908 | −0.866582 | ||||||||
\(183\) | 25.5745 | 1.89052 | ||||||||
\(184\) | 4.16667 | 0.307171 | ||||||||
\(185\) | 33.5954 | 2.46999 | ||||||||
\(186\) | −5.56580 | −0.408104 | ||||||||
\(187\) | 10.8630 | 0.794379 | ||||||||
\(188\) | 5.21811 | 0.380570 | ||||||||
\(189\) | 9.09838 | 0.661810 | ||||||||
\(190\) | −7.81162 | −0.566715 | ||||||||
\(191\) | −17.4749 | −1.26444 | −0.632221 | − | 0.774788i | \(-0.717857\pi\) | ||||
−0.632221 | + | 0.774788i | \(0.717857\pi\) | |||||||
\(192\) | −2.10025 | −0.151572 | ||||||||
\(193\) | −4.30096 | −0.309590 | −0.154795 | − | 0.987947i | \(-0.549472\pi\) | ||||
−0.154795 | + | 0.987947i | \(0.549472\pi\) | |||||||
\(194\) | −3.43929 | −0.246927 | ||||||||
\(195\) | −37.7944 | −2.70651 | ||||||||
\(196\) | 0.432985 | 0.0309275 | ||||||||
\(197\) | −24.4924 | −1.74501 | −0.872506 | − | 0.488603i | \(-0.837507\pi\) | ||||
−0.872506 | + | 0.488603i | \(0.837507\pi\) | |||||||
\(198\) | −3.31306 | −0.235449 | ||||||||
\(199\) | −1.02679 | −0.0727875 | −0.0363937 | − | 0.999338i | \(-0.511587\pi\) | ||||
−0.0363937 | + | 0.999338i | \(0.511587\pi\) | |||||||
\(200\) | −12.6111 | −0.891739 | ||||||||
\(201\) | −21.7354 | −1.53310 | ||||||||
\(202\) | −17.9553 | −1.26333 | ||||||||
\(203\) | −12.6514 | −0.887953 | ||||||||
\(204\) | −9.71696 | −0.680323 | ||||||||
\(205\) | 7.16818 | 0.500648 | ||||||||
\(206\) | −11.6765 | −0.813538 | ||||||||
\(207\) | −5.87935 | −0.408643 | ||||||||
\(208\) | 4.28809 | 0.297325 | ||||||||
\(209\) | 4.37056 | 0.302318 | ||||||||
\(210\) | 24.0295 | 1.65820 | ||||||||
\(211\) | −13.9129 | −0.957805 | −0.478902 | − | 0.877868i | \(-0.658965\pi\) | ||||
−0.478902 | + | 0.877868i | \(0.658965\pi\) | |||||||
\(212\) | 13.6464 | 0.937240 | ||||||||
\(213\) | −16.6164 | −1.13854 | ||||||||
\(214\) | 8.37290 | 0.572360 | ||||||||
\(215\) | −24.0158 | −1.63786 | ||||||||
\(216\) | −3.33720 | −0.227068 | ||||||||
\(217\) | −7.22501 | −0.490466 | ||||||||
\(218\) | 7.43302 | 0.503428 | ||||||||
\(219\) | 6.56822 | 0.443839 | ||||||||
\(220\) | 9.85331 | 0.664310 | ||||||||
\(221\) | 19.8392 | 1.33453 | ||||||||
\(222\) | 16.8135 | 1.12845 | ||||||||
\(223\) | −14.2628 | −0.955105 | −0.477552 | − | 0.878603i | \(-0.658476\pi\) | ||||
−0.477552 | + | 0.878603i | \(0.658476\pi\) | |||||||
\(224\) | −2.72635 | −0.182162 | ||||||||
\(225\) | 17.7948 | 1.18632 | ||||||||
\(226\) | −9.43626 | −0.627691 | ||||||||
\(227\) | −27.4971 | −1.82505 | −0.912523 | − | 0.409026i | \(-0.865868\pi\) | ||||
−0.912523 | + | 0.409026i | \(0.865868\pi\) | |||||||
\(228\) | −3.90948 | −0.258912 | ||||||||
\(229\) | 1.83928 | 0.121543 | 0.0607716 | − | 0.998152i | \(-0.480644\pi\) | ||||
0.0607716 | + | 0.998152i | \(0.480644\pi\) | |||||||
\(230\) | 17.4856 | 1.15297 | ||||||||
\(231\) | −13.4444 | −0.884576 | ||||||||
\(232\) | 4.64041 | 0.304658 | ||||||||
\(233\) | −9.08508 | −0.595183 | −0.297592 | − | 0.954693i | \(-0.596183\pi\) | ||||
−0.297592 | + | 0.954693i | \(0.596183\pi\) | |||||||
\(234\) | −6.05068 | −0.395545 | ||||||||
\(235\) | 21.8981 | 1.42847 | ||||||||
\(236\) | −4.37714 | −0.284928 | ||||||||
\(237\) | −0.309659 | −0.0201145 | ||||||||
\(238\) | −12.6137 | −0.817622 | ||||||||
\(239\) | 4.75495 | 0.307572 | 0.153786 | − | 0.988104i | \(-0.450853\pi\) | ||||
0.153786 | + | 0.988104i | \(0.450853\pi\) | |||||||
\(240\) | −8.81381 | −0.568929 | ||||||||
\(241\) | −3.30036 | −0.212595 | −0.106297 | − | 0.994334i | \(-0.533900\pi\) | ||||
−0.106297 | + | 0.994334i | \(0.533900\pi\) | |||||||
\(242\) | 5.48713 | 0.352726 | ||||||||
\(243\) | 13.5996 | 0.872413 | ||||||||
\(244\) | −12.1769 | −0.779545 | ||||||||
\(245\) | 1.81705 | 0.116087 | ||||||||
\(246\) | 3.58746 | 0.228728 | ||||||||
\(247\) | 7.98200 | 0.507883 | ||||||||
\(248\) | 2.65007 | 0.168279 | ||||||||
\(249\) | 17.4928 | 1.10856 | ||||||||
\(250\) | −31.9404 | −2.02009 | ||||||||
\(251\) | −24.0193 | −1.51608 | −0.758041 | − | 0.652207i | \(-0.773843\pi\) | ||||
−0.758041 | + | 0.652207i | \(0.773843\pi\) | |||||||
\(252\) | 3.84700 | 0.242338 | ||||||||
\(253\) | −9.78312 | −0.615060 | ||||||||
\(254\) | 21.3319 | 1.33848 | ||||||||
\(255\) | −40.7778 | −2.55360 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −16.3421 | −1.01939 | −0.509696 | − | 0.860354i | \(-0.670242\pi\) | ||||
−0.509696 | + | 0.860354i | \(0.670242\pi\) | |||||||
\(258\) | −12.0192 | −0.748280 | ||||||||
\(259\) | 21.8257 | 1.35619 | ||||||||
\(260\) | 17.9952 | 1.11602 | ||||||||
\(261\) | −6.54782 | −0.405300 | ||||||||
\(262\) | 10.5976 | 0.654724 | ||||||||
\(263\) | −27.7339 | −1.71015 | −0.855073 | − | 0.518507i | \(-0.826488\pi\) | ||||
−0.855073 | + | 0.518507i | \(0.826488\pi\) | |||||||
\(264\) | 4.93128 | 0.303499 | ||||||||
\(265\) | 57.2680 | 3.51794 | ||||||||
\(266\) | −5.07493 | −0.311164 | ||||||||
\(267\) | −6.84162 | −0.418700 | ||||||||
\(268\) | 10.3490 | 0.632165 | ||||||||
\(269\) | 25.0318 | 1.52621 | 0.763107 | − | 0.646272i | \(-0.223673\pi\) | ||||
0.763107 | + | 0.646272i | \(0.223673\pi\) | |||||||
\(270\) | −14.0048 | −0.852303 | ||||||||
\(271\) | 18.7328 | 1.13794 | 0.568969 | − | 0.822359i | \(-0.307342\pi\) | ||||
0.568969 | + | 0.822359i | \(0.307342\pi\) | |||||||
\(272\) | 4.62658 | 0.280527 | ||||||||
\(273\) | −24.5536 | −1.48605 | ||||||||
\(274\) | −6.57723 | −0.397345 | ||||||||
\(275\) | 29.6102 | 1.78556 | ||||||||
\(276\) | 8.75103 | 0.526750 | ||||||||
\(277\) | 1.97682 | 0.118775 | 0.0593877 | − | 0.998235i | \(-0.481085\pi\) | ||||
0.0593877 | + | 0.998235i | \(0.481085\pi\) | |||||||
\(278\) | −20.8114 | −1.24819 | ||||||||
\(279\) | −3.73936 | −0.223870 | ||||||||
\(280\) | −11.4413 | −0.683747 | ||||||||
\(281\) | −6.89170 | −0.411124 | −0.205562 | − | 0.978644i | \(-0.565902\pi\) | ||||
−0.205562 | + | 0.978644i | \(0.565902\pi\) | |||||||
\(282\) | 10.9593 | 0.652618 | ||||||||
\(283\) | −22.1297 | −1.31547 | −0.657737 | − | 0.753247i | \(-0.728486\pi\) | ||||
−0.657737 | + | 0.753247i | \(0.728486\pi\) | |||||||
\(284\) | 7.91164 | 0.469469 | ||||||||
\(285\) | −16.4063 | −0.971828 | ||||||||
\(286\) | −10.0682 | −0.595346 | ||||||||
\(287\) | 4.65691 | 0.274889 | ||||||||
\(288\) | −1.41104 | −0.0831465 | ||||||||
\(289\) | 4.40520 | 0.259129 | ||||||||
\(290\) | 19.4737 | 1.14354 | ||||||||
\(291\) | −7.22337 | −0.423441 | ||||||||
\(292\) | −3.12735 | −0.183014 | ||||||||
\(293\) | 25.5694 | 1.49378 | 0.746889 | − | 0.664948i | \(-0.231546\pi\) | ||||
0.746889 | + | 0.664948i | \(0.231546\pi\) | |||||||
\(294\) | 0.909377 | 0.0530359 | ||||||||
\(295\) | −18.3689 | −1.06948 | ||||||||
\(296\) | −8.00548 | −0.465309 | ||||||||
\(297\) | 7.83559 | 0.454667 | ||||||||
\(298\) | −2.64225 | −0.153062 | ||||||||
\(299\) | −17.8670 | −1.03328 | ||||||||
\(300\) | −26.4864 | −1.52919 | ||||||||
\(301\) | −15.6022 | −0.899294 | ||||||||
\(302\) | 17.0437 | 0.980755 | ||||||||
\(303\) | −37.7106 | −2.16642 | ||||||||
\(304\) | 1.86144 | 0.106761 | ||||||||
\(305\) | −51.1009 | −2.92603 | ||||||||
\(306\) | −6.52830 | −0.373198 | ||||||||
\(307\) | 20.1772 | 1.15157 | 0.575786 | − | 0.817600i | \(-0.304696\pi\) | ||||
0.575786 | + | 0.817600i | \(0.304696\pi\) | |||||||
\(308\) | 6.40134 | 0.364750 | ||||||||
\(309\) | −24.5235 | −1.39509 | ||||||||
\(310\) | 11.1212 | 0.631639 | ||||||||
\(311\) | −3.56956 | −0.202411 | −0.101205 | − | 0.994866i | \(-0.532270\pi\) | ||||
−0.101205 | + | 0.994866i | \(0.532270\pi\) | |||||||
\(312\) | 9.00605 | 0.509867 | ||||||||
\(313\) | −13.4653 | −0.761102 | −0.380551 | − | 0.924760i | \(-0.624266\pi\) | ||||
−0.380551 | + | 0.924760i | \(0.624266\pi\) | |||||||
\(314\) | 20.1146 | 1.13513 | ||||||||
\(315\) | 16.1442 | 0.909620 | ||||||||
\(316\) | 0.147439 | 0.00829411 | ||||||||
\(317\) | 24.2502 | 1.36203 | 0.681014 | − | 0.732271i | \(-0.261539\pi\) | ||||
0.681014 | + | 0.732271i | \(0.261539\pi\) | |||||||
\(318\) | 28.6609 | 1.60722 | ||||||||
\(319\) | −10.8955 | −0.610028 | ||||||||
\(320\) | 4.19656 | 0.234595 | ||||||||
\(321\) | 17.5852 | 0.981509 | ||||||||
\(322\) | 11.3598 | 0.633056 | ||||||||
\(323\) | 8.61207 | 0.479189 | ||||||||
\(324\) | −11.2421 | −0.624560 | ||||||||
\(325\) | 54.0775 | 2.99968 | ||||||||
\(326\) | −5.28295 | −0.292596 | ||||||||
\(327\) | 15.6112 | 0.863301 | ||||||||
\(328\) | −1.70811 | −0.0943146 | ||||||||
\(329\) | 14.2264 | 0.784326 | ||||||||
\(330\) | 20.6944 | 1.13919 | ||||||||
\(331\) | 18.6103 | 1.02292 | 0.511458 | − | 0.859308i | \(-0.329106\pi\) | ||||
0.511458 | + | 0.859308i | \(0.329106\pi\) | |||||||
\(332\) | −8.32890 | −0.457108 | ||||||||
\(333\) | 11.2961 | 0.619021 | ||||||||
\(334\) | 18.7836 | 1.02779 | ||||||||
\(335\) | 43.4301 | 2.37284 | ||||||||
\(336\) | −5.72601 | −0.312380 | ||||||||
\(337\) | 25.7371 | 1.40199 | 0.700993 | − | 0.713168i | \(-0.252740\pi\) | ||||
0.700993 | + | 0.713168i | \(0.252740\pi\) | |||||||
\(338\) | −5.38769 | −0.293052 | ||||||||
\(339\) | −19.8185 | −1.07639 | ||||||||
\(340\) | 19.4157 | 1.05296 | ||||||||
\(341\) | −6.22223 | −0.336952 | ||||||||
\(342\) | −2.62657 | −0.142029 | ||||||||
\(343\) | −17.9040 | −0.966724 | ||||||||
\(344\) | 5.72273 | 0.308549 | ||||||||
\(345\) | 36.7242 | 1.97716 | ||||||||
\(346\) | 15.7375 | 0.846055 | ||||||||
\(347\) | −6.68163 | −0.358688 | −0.179344 | − | 0.983786i | \(-0.557398\pi\) | ||||
−0.179344 | + | 0.983786i | \(0.557398\pi\) | |||||||
\(348\) | 9.74602 | 0.522441 | ||||||||
\(349\) | −14.7538 | −0.789755 | −0.394878 | − | 0.918734i | \(-0.629213\pi\) | ||||
−0.394878 | + | 0.918734i | \(0.629213\pi\) | |||||||
\(350\) | −34.3822 | −1.83781 | ||||||||
\(351\) | 14.3102 | 0.763823 | ||||||||
\(352\) | −2.34795 | −0.125146 | ||||||||
\(353\) | 21.0243 | 1.11901 | 0.559505 | − | 0.828827i | \(-0.310991\pi\) | ||||
0.559505 | + | 0.828827i | \(0.310991\pi\) | |||||||
\(354\) | −9.19309 | −0.488607 | ||||||||
\(355\) | 33.2016 | 1.76216 | ||||||||
\(356\) | 3.25753 | 0.172649 | ||||||||
\(357\) | −26.4918 | −1.40210 | ||||||||
\(358\) | −19.4081 | −1.02575 | ||||||||
\(359\) | −8.26515 | −0.436218 | −0.218109 | − | 0.975924i | \(-0.569989\pi\) | ||||
−0.218109 | + | 0.975924i | \(0.569989\pi\) | |||||||
\(360\) | −5.92153 | −0.312092 | ||||||||
\(361\) | −15.5351 | −0.817635 | ||||||||
\(362\) | −11.5761 | −0.608424 | ||||||||
\(363\) | 11.5243 | 0.604871 | ||||||||
\(364\) | 11.6908 | 0.612766 | ||||||||
\(365\) | −13.1241 | −0.686947 | ||||||||
\(366\) | −25.5745 | −1.33680 | ||||||||
\(367\) | −11.9739 | −0.625032 | −0.312516 | − | 0.949913i | \(-0.601172\pi\) | ||||
−0.312516 | + | 0.949913i | \(0.601172\pi\) | |||||||
\(368\) | −4.16667 | −0.217202 | ||||||||
\(369\) | 2.41022 | 0.125471 | ||||||||
\(370\) | −33.5954 | −1.74654 | ||||||||
\(371\) | 37.2049 | 1.93158 | ||||||||
\(372\) | 5.56580 | 0.288573 | ||||||||
\(373\) | −26.4342 | −1.36871 | −0.684354 | − | 0.729149i | \(-0.739916\pi\) | ||||
−0.684354 | + | 0.729149i | \(0.739916\pi\) | |||||||
\(374\) | −10.8630 | −0.561711 | ||||||||
\(375\) | −67.0827 | −3.46414 | ||||||||
\(376\) | −5.21811 | −0.269103 | ||||||||
\(377\) | −19.8985 | −1.02482 | ||||||||
\(378\) | −9.09838 | −0.467970 | ||||||||
\(379\) | 16.0303 | 0.823423 | 0.411712 | − | 0.911314i | \(-0.364931\pi\) | ||||
0.411712 | + | 0.911314i | \(0.364931\pi\) | |||||||
\(380\) | 7.81162 | 0.400728 | ||||||||
\(381\) | 44.8024 | 2.29529 | ||||||||
\(382\) | 17.4749 | 0.894096 | ||||||||
\(383\) | 12.0712 | 0.616808 | 0.308404 | − | 0.951255i | \(-0.400205\pi\) | ||||
0.308404 | + | 0.951255i | \(0.400205\pi\) | |||||||
\(384\) | 2.10025 | 0.107178 | ||||||||
\(385\) | 26.8636 | 1.36909 | ||||||||
\(386\) | 4.30096 | 0.218913 | ||||||||
\(387\) | −8.07502 | −0.410476 | ||||||||
\(388\) | 3.43929 | 0.174604 | ||||||||
\(389\) | 19.4306 | 0.985171 | 0.492585 | − | 0.870264i | \(-0.336052\pi\) | ||||
0.492585 | + | 0.870264i | \(0.336052\pi\) | |||||||
\(390\) | 37.7944 | 1.91379 | ||||||||
\(391\) | −19.2774 | −0.974899 | ||||||||
\(392\) | −0.432985 | −0.0218691 | ||||||||
\(393\) | 22.2577 | 1.12275 | ||||||||
\(394\) | 24.4924 | 1.23391 | ||||||||
\(395\) | 0.618737 | 0.0311321 | ||||||||
\(396\) | 3.31306 | 0.166488 | ||||||||
\(397\) | −33.4445 | −1.67853 | −0.839266 | − | 0.543721i | \(-0.817015\pi\) | ||||
−0.839266 | + | 0.543721i | \(0.817015\pi\) | |||||||
\(398\) | 1.02679 | 0.0514685 | ||||||||
\(399\) | −10.6586 | −0.533598 | ||||||||
\(400\) | 12.6111 | 0.630554 | ||||||||
\(401\) | 10.5349 | 0.526090 | 0.263045 | − | 0.964784i | \(-0.415273\pi\) | ||||
0.263045 | + | 0.964784i | \(0.415273\pi\) | |||||||
\(402\) | 21.7354 | 1.08406 | ||||||||
\(403\) | −11.3637 | −0.566067 | ||||||||
\(404\) | 17.9553 | 0.893311 | ||||||||
\(405\) | −47.1781 | −2.34430 | ||||||||
\(406\) | 12.6514 | 0.627878 | ||||||||
\(407\) | 18.7965 | 0.931706 | ||||||||
\(408\) | 9.71696 | 0.481061 | ||||||||
\(409\) | 18.5593 | 0.917699 | 0.458849 | − | 0.888514i | \(-0.348262\pi\) | ||||
0.458849 | + | 0.888514i | \(0.348262\pi\) | |||||||
\(410\) | −7.16818 | −0.354011 | ||||||||
\(411\) | −13.8138 | −0.681385 | ||||||||
\(412\) | 11.6765 | 0.575258 | ||||||||
\(413\) | −11.9336 | −0.587215 | ||||||||
\(414\) | 5.87935 | 0.288954 | ||||||||
\(415\) | −34.9527 | −1.71576 | ||||||||
\(416\) | −4.28809 | −0.210241 | ||||||||
\(417\) | −43.7091 | −2.14045 | ||||||||
\(418\) | −4.37056 | −0.213771 | ||||||||
\(419\) | 5.76487 | 0.281633 | 0.140816 | − | 0.990036i | \(-0.455027\pi\) | ||||
0.140816 | + | 0.990036i | \(0.455027\pi\) | |||||||
\(420\) | −24.0295 | −1.17252 | ||||||||
\(421\) | −4.18467 | −0.203948 | −0.101974 | − | 0.994787i | \(-0.532516\pi\) | ||||
−0.101974 | + | 0.994787i | \(0.532516\pi\) | |||||||
\(422\) | 13.9129 | 0.677270 | ||||||||
\(423\) | 7.36298 | 0.358000 | ||||||||
\(424\) | −13.6464 | −0.662729 | ||||||||
\(425\) | 58.3462 | 2.83020 | ||||||||
\(426\) | 16.6164 | 0.805068 | ||||||||
\(427\) | −33.1984 | −1.60658 | ||||||||
\(428\) | −8.37290 | −0.404720 | ||||||||
\(429\) | −21.1458 | −1.02093 | ||||||||
\(430\) | 24.0158 | 1.15814 | ||||||||
\(431\) | −5.80236 | −0.279490 | −0.139745 | − | 0.990188i | \(-0.544628\pi\) | ||||
−0.139745 | + | 0.990188i | \(0.544628\pi\) | |||||||
\(432\) | 3.33720 | 0.160561 | ||||||||
\(433\) | 32.6204 | 1.56764 | 0.783819 | − | 0.620989i | \(-0.213269\pi\) | ||||
0.783819 | + | 0.620989i | \(0.213269\pi\) | |||||||
\(434\) | 7.22501 | 0.346812 | ||||||||
\(435\) | 40.8997 | 1.96099 | ||||||||
\(436\) | −7.43302 | −0.355977 | ||||||||
\(437\) | −7.75598 | −0.371019 | ||||||||
\(438\) | −6.56822 | −0.313842 | ||||||||
\(439\) | 22.7808 | 1.08727 | 0.543635 | − | 0.839322i | \(-0.317048\pi\) | ||||
0.543635 | + | 0.839322i | \(0.317048\pi\) | |||||||
\(440\) | −9.85331 | −0.469738 | ||||||||
\(441\) | 0.610961 | 0.0290934 | ||||||||
\(442\) | −19.8392 | −0.943653 | ||||||||
\(443\) | 22.9851 | 1.09206 | 0.546028 | − | 0.837767i | \(-0.316139\pi\) | ||||
0.546028 | + | 0.837767i | \(0.316139\pi\) | |||||||
\(444\) | −16.8135 | −0.797933 | ||||||||
\(445\) | 13.6704 | 0.648039 | ||||||||
\(446\) | 14.2628 | 0.675361 | ||||||||
\(447\) | −5.54939 | −0.262477 | ||||||||
\(448\) | 2.72635 | 0.128808 | ||||||||
\(449\) | −18.3512 | −0.866047 | −0.433024 | − | 0.901383i | \(-0.642553\pi\) | ||||
−0.433024 | + | 0.901383i | \(0.642553\pi\) | |||||||
\(450\) | −17.7948 | −0.838855 | ||||||||
\(451\) | 4.01056 | 0.188850 | ||||||||
\(452\) | 9.43626 | 0.443844 | ||||||||
\(453\) | 35.7960 | 1.68184 | ||||||||
\(454\) | 27.4971 | 1.29050 | ||||||||
\(455\) | 49.0612 | 2.30003 | ||||||||
\(456\) | 3.90948 | 0.183078 | ||||||||
\(457\) | −11.9075 | −0.557009 | −0.278504 | − | 0.960435i | \(-0.589839\pi\) | ||||
−0.278504 | + | 0.960435i | \(0.589839\pi\) | |||||||
\(458\) | −1.83928 | −0.0859440 | ||||||||
\(459\) | 15.4398 | 0.720669 | ||||||||
\(460\) | −17.4856 | −0.815272 | ||||||||
\(461\) | 0.191347 | 0.00891190 | 0.00445595 | − | 0.999990i | \(-0.498582\pi\) | ||||
0.00445595 | + | 0.999990i | \(0.498582\pi\) | |||||||
\(462\) | 13.4444 | 0.625490 | ||||||||
\(463\) | 0.344055 | 0.0159896 | 0.00799479 | − | 0.999968i | \(-0.497455\pi\) | ||||
0.00799479 | + | 0.999968i | \(0.497455\pi\) | |||||||
\(464\) | −4.64041 | −0.215426 | ||||||||
\(465\) | 23.3572 | 1.08316 | ||||||||
\(466\) | 9.08508 | 0.420858 | ||||||||
\(467\) | −0.403713 | −0.0186816 | −0.00934082 | − | 0.999956i | \(-0.502973\pi\) | ||||
−0.00934082 | + | 0.999956i | \(0.502973\pi\) | |||||||
\(468\) | 6.05068 | 0.279693 | ||||||||
\(469\) | 28.2149 | 1.30285 | ||||||||
\(470\) | −21.8981 | −1.01008 | ||||||||
\(471\) | 42.2457 | 1.94658 | ||||||||
\(472\) | 4.37714 | 0.201474 | ||||||||
\(473\) | −13.4367 | −0.617819 | ||||||||
\(474\) | 0.309659 | 0.0142231 | ||||||||
\(475\) | 23.4747 | 1.07709 | ||||||||
\(476\) | 12.6137 | 0.578146 | ||||||||
\(477\) | 19.2557 | 0.881658 | ||||||||
\(478\) | −4.75495 | −0.217487 | ||||||||
\(479\) | 12.3751 | 0.565431 | 0.282716 | − | 0.959204i | \(-0.408765\pi\) | ||||
0.282716 | + | 0.959204i | \(0.408765\pi\) | |||||||
\(480\) | 8.81381 | 0.402294 | ||||||||
\(481\) | 34.3282 | 1.56523 | ||||||||
\(482\) | 3.30036 | 0.150327 | ||||||||
\(483\) | 23.8584 | 1.08559 | ||||||||
\(484\) | −5.48713 | −0.249415 | ||||||||
\(485\) | 14.4332 | 0.655377 | ||||||||
\(486\) | −13.5996 | −0.616889 | ||||||||
\(487\) | −35.6262 | −1.61438 | −0.807188 | − | 0.590294i | \(-0.799012\pi\) | ||||
−0.807188 | + | 0.590294i | \(0.799012\pi\) | |||||||
\(488\) | 12.1769 | 0.551221 | ||||||||
\(489\) | −11.0955 | −0.501756 | ||||||||
\(490\) | −1.81705 | −0.0820859 | ||||||||
\(491\) | 21.8556 | 0.986327 | 0.493164 | − | 0.869937i | \(-0.335840\pi\) | ||||
0.493164 | + | 0.869937i | \(0.335840\pi\) | |||||||
\(492\) | −3.58746 | −0.161735 | ||||||||
\(493\) | −21.4692 | −0.966925 | ||||||||
\(494\) | −7.98200 | −0.359127 | ||||||||
\(495\) | 13.9034 | 0.624914 | ||||||||
\(496\) | −2.65007 | −0.118992 | ||||||||
\(497\) | 21.5699 | 0.967542 | ||||||||
\(498\) | −17.4928 | −0.783869 | ||||||||
\(499\) | 2.53687 | 0.113566 | 0.0567830 | − | 0.998387i | \(-0.481916\pi\) | ||||
0.0567830 | + | 0.998387i | \(0.481916\pi\) | |||||||
\(500\) | 31.9404 | 1.42842 | ||||||||
\(501\) | 39.4503 | 1.76251 | ||||||||
\(502\) | 24.0193 | 1.07203 | ||||||||
\(503\) | −20.7392 | −0.924716 | −0.462358 | − | 0.886693i | \(-0.652997\pi\) | ||||
−0.462358 | + | 0.886693i | \(0.652997\pi\) | |||||||
\(504\) | −3.84700 | −0.171359 | ||||||||
\(505\) | 75.3505 | 3.35306 | ||||||||
\(506\) | 9.78312 | 0.434913 | ||||||||
\(507\) | −11.3155 | −0.502539 | ||||||||
\(508\) | −21.3319 | −0.946452 | ||||||||
\(509\) | −27.1126 | −1.20175 | −0.600873 | − | 0.799345i | \(-0.705180\pi\) | ||||
−0.600873 | + | 0.799345i | \(0.705180\pi\) | |||||||
\(510\) | 40.7778 | 1.80567 | ||||||||
\(511\) | −8.52626 | −0.377179 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 6.21199 | 0.274266 | ||||||||
\(514\) | 16.3421 | 0.720820 | ||||||||
\(515\) | 49.0010 | 2.15924 | ||||||||
\(516\) | 12.0192 | 0.529114 | ||||||||
\(517\) | 12.2519 | 0.538836 | ||||||||
\(518\) | −21.8257 | −0.958968 | ||||||||
\(519\) | 33.0527 | 1.45085 | ||||||||
\(520\) | −17.9952 | −0.789142 | ||||||||
\(521\) | 9.40566 | 0.412069 | 0.206035 | − | 0.978545i | \(-0.433944\pi\) | ||||
0.206035 | + | 0.978545i | \(0.433944\pi\) | |||||||
\(522\) | 6.54782 | 0.286590 | ||||||||
\(523\) | −7.41472 | −0.324223 | −0.162112 | − | 0.986772i | \(-0.551830\pi\) | ||||
−0.162112 | + | 0.986772i | \(0.551830\pi\) | |||||||
\(524\) | −10.5976 | −0.462959 | ||||||||
\(525\) | −72.2113 | −3.15156 | ||||||||
\(526\) | 27.7339 | 1.20926 | ||||||||
\(527\) | −12.2607 | −0.534086 | ||||||||
\(528\) | −4.93128 | −0.214606 | ||||||||
\(529\) | −5.63890 | −0.245170 | ||||||||
\(530\) | −57.2680 | −2.48756 | ||||||||
\(531\) | −6.17634 | −0.268030 | ||||||||
\(532\) | 5.07493 | 0.220026 | ||||||||
\(533\) | 7.32453 | 0.317261 | ||||||||
\(534\) | 6.84162 | 0.296066 | ||||||||
\(535\) | −35.1374 | −1.51912 | ||||||||
\(536\) | −10.3490 | −0.447008 | ||||||||
\(537\) | −40.7619 | −1.75900 | ||||||||
\(538\) | −25.0318 | −1.07920 | ||||||||
\(539\) | 1.01663 | 0.0437893 | ||||||||
\(540\) | 14.0048 | 0.602669 | ||||||||
\(541\) | 22.0332 | 0.947282 | 0.473641 | − | 0.880718i | \(-0.342939\pi\) | ||||
0.473641 | + | 0.880718i | \(0.342939\pi\) | |||||||
\(542\) | −18.7328 | −0.804644 | ||||||||
\(543\) | −24.3126 | −1.04335 | ||||||||
\(544\) | −4.62658 | −0.198363 | ||||||||
\(545\) | −31.1931 | −1.33617 | ||||||||
\(546\) | 24.5536 | 1.05080 | ||||||||
\(547\) | 8.33944 | 0.356569 | 0.178284 | − | 0.983979i | \(-0.442945\pi\) | ||||
0.178284 | + | 0.983979i | \(0.442945\pi\) | |||||||
\(548\) | 6.57723 | 0.280965 | ||||||||
\(549\) | −17.1821 | −0.733314 | ||||||||
\(550\) | −29.6102 | −1.26258 | ||||||||
\(551\) | −8.63783 | −0.367984 | ||||||||
\(552\) | −8.75103 | −0.372469 | ||||||||
\(553\) | 0.401971 | 0.0170936 | ||||||||
\(554\) | −1.97682 | −0.0839869 | ||||||||
\(555\) | −70.5588 | −2.99505 | ||||||||
\(556\) | 20.8114 | 0.882600 | ||||||||
\(557\) | 2.79343 | 0.118361 | 0.0591807 | − | 0.998247i | \(-0.481151\pi\) | ||||
0.0591807 | + | 0.998247i | \(0.481151\pi\) | |||||||
\(558\) | 3.73936 | 0.158300 | ||||||||
\(559\) | −24.5396 | −1.03791 | ||||||||
\(560\) | 11.4413 | 0.483482 | ||||||||
\(561\) | −22.8149 | −0.963247 | ||||||||
\(562\) | 6.89170 | 0.290709 | ||||||||
\(563\) | 0.482130 | 0.0203194 | 0.0101597 | − | 0.999948i | \(-0.496766\pi\) | ||||
0.0101597 | + | 0.999948i | \(0.496766\pi\) | |||||||
\(564\) | −10.9593 | −0.461471 | ||||||||
\(565\) | 39.5998 | 1.66598 | ||||||||
\(566\) | 22.1297 | 0.930181 | ||||||||
\(567\) | −30.6499 | −1.28717 | ||||||||
\(568\) | −7.91164 | −0.331965 | ||||||||
\(569\) | 5.31075 | 0.222638 | 0.111319 | − | 0.993785i | \(-0.464492\pi\) | ||||
0.111319 | + | 0.993785i | \(0.464492\pi\) | |||||||
\(570\) | 16.4063 | 0.687186 | ||||||||
\(571\) | −6.78172 | −0.283806 | −0.141903 | − | 0.989881i | \(-0.545322\pi\) | ||||
−0.141903 | + | 0.989881i | \(0.545322\pi\) | |||||||
\(572\) | 10.0682 | 0.420973 | ||||||||
\(573\) | 36.7017 | 1.53324 | ||||||||
\(574\) | −4.65691 | −0.194376 | ||||||||
\(575\) | −52.5462 | −2.19133 | ||||||||
\(576\) | 1.41104 | 0.0587935 | ||||||||
\(577\) | 6.01415 | 0.250373 | 0.125186 | − | 0.992133i | \(-0.460047\pi\) | ||||
0.125186 | + | 0.992133i | \(0.460047\pi\) | |||||||
\(578\) | −4.40520 | −0.183232 | ||||||||
\(579\) | 9.03309 | 0.375403 | ||||||||
\(580\) | −19.4737 | −0.808603 | ||||||||
\(581\) | −22.7075 | −0.942065 | ||||||||
\(582\) | 7.22337 | 0.299418 | ||||||||
\(583\) | 32.0411 | 1.32701 | ||||||||
\(584\) | 3.12735 | 0.129411 | ||||||||
\(585\) | 25.3920 | 1.04983 | ||||||||
\(586\) | −25.5694 | −1.05626 | ||||||||
\(587\) | 30.9975 | 1.27940 | 0.639701 | − | 0.768623i | \(-0.279058\pi\) | ||||
0.639701 | + | 0.768623i | \(0.279058\pi\) | |||||||
\(588\) | −0.909377 | −0.0375021 | ||||||||
\(589\) | −4.93293 | −0.203258 | ||||||||
\(590\) | 18.3689 | 0.756237 | ||||||||
\(591\) | 51.4402 | 2.11597 | ||||||||
\(592\) | 8.00548 | 0.329023 | ||||||||
\(593\) | 27.4988 | 1.12924 | 0.564620 | − | 0.825351i | \(-0.309023\pi\) | ||||
0.564620 | + | 0.825351i | \(0.309023\pi\) | |||||||
\(594\) | −7.83559 | −0.321498 | ||||||||
\(595\) | 52.9340 | 2.17008 | ||||||||
\(596\) | 2.64225 | 0.108231 | ||||||||
\(597\) | 2.15652 | 0.0882606 | ||||||||
\(598\) | 17.8670 | 0.730637 | ||||||||
\(599\) | 11.5512 | 0.471968 | 0.235984 | − | 0.971757i | \(-0.424169\pi\) | ||||
0.235984 | + | 0.971757i | \(0.424169\pi\) | |||||||
\(600\) | 26.4864 | 1.08130 | ||||||||
\(601\) | 31.1016 | 1.26866 | 0.634330 | − | 0.773062i | \(-0.281276\pi\) | ||||
0.634330 | + | 0.773062i | \(0.281276\pi\) | |||||||
\(602\) | 15.6022 | 0.635897 | ||||||||
\(603\) | 14.6029 | 0.594675 | ||||||||
\(604\) | −17.0437 | −0.693499 | ||||||||
\(605\) | −23.0270 | −0.936183 | ||||||||
\(606\) | 37.7106 | 1.53189 | ||||||||
\(607\) | 3.08921 | 0.125387 | 0.0626936 | − | 0.998033i | \(-0.480031\pi\) | ||||
0.0626936 | + | 0.998033i | \(0.480031\pi\) | |||||||
\(608\) | −1.86144 | −0.0754912 | ||||||||
\(609\) | 26.5711 | 1.07671 | ||||||||
\(610\) | 51.1009 | 2.06902 | ||||||||
\(611\) | 22.3757 | 0.905224 | ||||||||
\(612\) | 6.52830 | 0.263891 | ||||||||
\(613\) | 36.3876 | 1.46968 | 0.734840 | − | 0.678240i | \(-0.237257\pi\) | ||||
0.734840 | + | 0.678240i | \(0.237257\pi\) | |||||||
\(614\) | −20.1772 | −0.814284 | ||||||||
\(615\) | −15.0550 | −0.607075 | ||||||||
\(616\) | −6.40134 | −0.257917 | ||||||||
\(617\) | 7.35811 | 0.296226 | 0.148113 | − | 0.988970i | \(-0.452680\pi\) | ||||
0.148113 | + | 0.988970i | \(0.452680\pi\) | |||||||
\(618\) | 24.5235 | 0.986479 | ||||||||
\(619\) | 16.5856 | 0.666631 | 0.333315 | − | 0.942815i | \(-0.391833\pi\) | ||||
0.333315 | + | 0.942815i | \(0.391833\pi\) | |||||||
\(620\) | −11.1212 | −0.446636 | ||||||||
\(621\) | −13.9050 | −0.557989 | ||||||||
\(622\) | 3.56956 | 0.143126 | ||||||||
\(623\) | 8.88116 | 0.355816 | ||||||||
\(624\) | −9.00605 | −0.360531 | ||||||||
\(625\) | 70.9841 | 2.83937 | ||||||||
\(626\) | 13.4653 | 0.538181 | ||||||||
\(627\) | −9.17926 | −0.366584 | ||||||||
\(628\) | −20.1146 | −0.802660 | ||||||||
\(629\) | 37.0379 | 1.47680 | ||||||||
\(630\) | −16.1442 | −0.643198 | ||||||||
\(631\) | 5.82222 | 0.231779 | 0.115889 | − | 0.993262i | \(-0.463028\pi\) | ||||
0.115889 | + | 0.993262i | \(0.463028\pi\) | |||||||
\(632\) | −0.147439 | −0.00586482 | ||||||||
\(633\) | 29.2206 | 1.16141 | ||||||||
\(634\) | −24.2502 | −0.963099 | ||||||||
\(635\) | −89.5207 | −3.55252 | ||||||||
\(636\) | −28.6609 | −1.13648 | ||||||||
\(637\) | 1.85668 | 0.0735643 | ||||||||
\(638\) | 10.8955 | 0.431355 | ||||||||
\(639\) | 11.1637 | 0.441628 | ||||||||
\(640\) | −4.19656 | −0.165883 | ||||||||
\(641\) | −39.3312 | −1.55349 | −0.776744 | − | 0.629817i | \(-0.783130\pi\) | ||||
−0.776744 | + | 0.629817i | \(0.783130\pi\) | |||||||
\(642\) | −17.5852 | −0.694032 | ||||||||
\(643\) | 4.80588 | 0.189525 | 0.0947627 | − | 0.995500i | \(-0.469791\pi\) | ||||
0.0947627 | + | 0.995500i | \(0.469791\pi\) | |||||||
\(644\) | −11.3598 | −0.447638 | ||||||||
\(645\) | 50.4391 | 1.98604 | ||||||||
\(646\) | −8.61207 | −0.338838 | ||||||||
\(647\) | −14.5215 | −0.570900 | −0.285450 | − | 0.958394i | \(-0.592143\pi\) | ||||
−0.285450 | + | 0.958394i | \(0.592143\pi\) | |||||||
\(648\) | 11.2421 | 0.441631 | ||||||||
\(649\) | −10.2773 | −0.403420 | ||||||||
\(650\) | −54.0775 | −2.12109 | ||||||||
\(651\) | 15.1743 | 0.594728 | ||||||||
\(652\) | 5.28295 | 0.206896 | ||||||||
\(653\) | −32.8222 | −1.28443 | −0.642216 | − | 0.766524i | \(-0.721985\pi\) | ||||
−0.642216 | + | 0.766524i | \(0.721985\pi\) | |||||||
\(654\) | −15.6112 | −0.610446 | ||||||||
\(655\) | −44.4735 | −1.73773 | ||||||||
\(656\) | 1.70811 | 0.0666905 | ||||||||
\(657\) | −4.41283 | −0.172161 | ||||||||
\(658\) | −14.2264 | −0.554602 | ||||||||
\(659\) | 38.2114 | 1.48850 | 0.744252 | − | 0.667899i | \(-0.232806\pi\) | ||||
0.744252 | + | 0.667899i | \(0.232806\pi\) | |||||||
\(660\) | −20.6944 | −0.805528 | ||||||||
\(661\) | 16.0617 | 0.624726 | 0.312363 | − | 0.949963i | \(-0.398879\pi\) | ||||
0.312363 | + | 0.949963i | \(0.398879\pi\) | |||||||
\(662\) | −18.6103 | −0.723310 | ||||||||
\(663\) | −41.6672 | −1.61822 | ||||||||
\(664\) | 8.32890 | 0.323224 | ||||||||
\(665\) | 21.2972 | 0.825871 | ||||||||
\(666\) | −11.2961 | −0.437714 | ||||||||
\(667\) | 19.3350 | 0.748656 | ||||||||
\(668\) | −18.7836 | −0.726760 | ||||||||
\(669\) | 29.9553 | 1.15814 | ||||||||
\(670\) | −43.4301 | −1.67785 | ||||||||
\(671\) | −28.5907 | −1.10373 | ||||||||
\(672\) | 5.72601 | 0.220886 | ||||||||
\(673\) | −36.6337 | −1.41212 | −0.706062 | − | 0.708150i | \(-0.749530\pi\) | ||||
−0.706062 | + | 0.708150i | \(0.749530\pi\) | |||||||
\(674\) | −25.7371 | −0.991355 | ||||||||
\(675\) | 42.0858 | 1.61988 | ||||||||
\(676\) | 5.38769 | 0.207219 | ||||||||
\(677\) | 33.5506 | 1.28946 | 0.644728 | − | 0.764412i | \(-0.276971\pi\) | ||||
0.644728 | + | 0.764412i | \(0.276971\pi\) | |||||||
\(678\) | 19.8185 | 0.761125 | ||||||||
\(679\) | 9.37671 | 0.359845 | ||||||||
\(680\) | −19.4157 | −0.744558 | ||||||||
\(681\) | 57.7507 | 2.21301 | ||||||||
\(682\) | 6.22223 | 0.238261 | ||||||||
\(683\) | 26.9587 | 1.03154 | 0.515772 | − | 0.856726i | \(-0.327505\pi\) | ||||
0.515772 | + | 0.856726i | \(0.327505\pi\) | |||||||
\(684\) | 2.62657 | 0.100429 | ||||||||
\(685\) | 27.6017 | 1.05461 | ||||||||
\(686\) | 17.9040 | 0.683577 | ||||||||
\(687\) | −3.86295 | −0.147381 | ||||||||
\(688\) | −5.72273 | −0.218177 | ||||||||
\(689\) | 58.5171 | 2.22932 | ||||||||
\(690\) | −36.7242 | −1.39807 | ||||||||
\(691\) | −25.7477 | −0.979487 | −0.489743 | − | 0.871867i | \(-0.662910\pi\) | ||||
−0.489743 | + | 0.871867i | \(0.662910\pi\) | |||||||
\(692\) | −15.7375 | −0.598251 | ||||||||
\(693\) | 9.03256 | 0.343119 | ||||||||
\(694\) | 6.68163 | 0.253631 | ||||||||
\(695\) | 87.3363 | 3.31285 | ||||||||
\(696\) | −9.74602 | −0.369422 | ||||||||
\(697\) | 7.90270 | 0.299336 | ||||||||
\(698\) | 14.7538 | 0.558441 | ||||||||
\(699\) | 19.0809 | 0.721706 | ||||||||
\(700\) | 34.3822 | 1.29953 | ||||||||
\(701\) | −29.3989 | −1.11038 | −0.555191 | − | 0.831723i | \(-0.687355\pi\) | ||||
−0.555191 | + | 0.831723i | \(0.687355\pi\) | |||||||
\(702\) | −14.3102 | −0.540104 | ||||||||
\(703\) | 14.9017 | 0.562028 | ||||||||
\(704\) | 2.34795 | 0.0884917 | ||||||||
\(705\) | −45.9914 | −1.73214 | ||||||||
\(706\) | −21.0243 | −0.791260 | ||||||||
\(707\) | 48.9525 | 1.84105 | ||||||||
\(708\) | 9.19309 | 0.345497 | ||||||||
\(709\) | −31.8895 | −1.19764 | −0.598818 | − | 0.800885i | \(-0.704363\pi\) | ||||
−0.598818 | + | 0.800885i | \(0.704363\pi\) | |||||||
\(710\) | −33.2016 | −1.24604 | ||||||||
\(711\) | 0.208043 | 0.00780223 | ||||||||
\(712\) | −3.25753 | −0.122081 | ||||||||
\(713\) | 11.0419 | 0.413524 | ||||||||
\(714\) | 26.4918 | 0.991432 | ||||||||
\(715\) | 42.2518 | 1.58013 | ||||||||
\(716\) | 19.4081 | 0.725316 | ||||||||
\(717\) | −9.98658 | −0.372956 | ||||||||
\(718\) | 8.26515 | 0.308453 | ||||||||
\(719\) | 12.7218 | 0.474444 | 0.237222 | − | 0.971455i | \(-0.423763\pi\) | ||||
0.237222 | + | 0.971455i | \(0.423763\pi\) | |||||||
\(720\) | 5.92153 | 0.220682 | ||||||||
\(721\) | 31.8341 | 1.18557 | ||||||||
\(722\) | 15.5351 | 0.578155 | ||||||||
\(723\) | 6.93157 | 0.257788 | ||||||||
\(724\) | 11.5761 | 0.430221 | ||||||||
\(725\) | −58.5206 | −2.17340 | ||||||||
\(726\) | −11.5243 | −0.427708 | ||||||||
\(727\) | 45.0305 | 1.67009 | 0.835044 | − | 0.550184i | \(-0.185442\pi\) | ||||
0.835044 | + | 0.550184i | \(0.185442\pi\) | |||||||
\(728\) | −11.6908 | −0.433291 | ||||||||
\(729\) | 5.16379 | 0.191252 | ||||||||
\(730\) | 13.1241 | 0.485745 | ||||||||
\(731\) | −26.4766 | −0.979274 | ||||||||
\(732\) | 25.5745 | 0.945259 | ||||||||
\(733\) | −24.6880 | −0.911873 | −0.455937 | − | 0.890012i | \(-0.650696\pi\) | ||||
−0.455937 | + | 0.890012i | \(0.650696\pi\) | |||||||
\(734\) | 11.9739 | 0.441964 | ||||||||
\(735\) | −3.81625 | −0.140765 | ||||||||
\(736\) | 4.16667 | 0.153585 | ||||||||
\(737\) | 24.2989 | 0.895061 | ||||||||
\(738\) | −2.41022 | −0.0887214 | ||||||||
\(739\) | −48.2684 | −1.77558 | −0.887792 | − | 0.460245i | \(-0.847761\pi\) | ||||
−0.887792 | + | 0.460245i | \(0.847761\pi\) | |||||||
\(740\) | 33.5954 | 1.23499 | ||||||||
\(741\) | −16.7642 | −0.615848 | ||||||||
\(742\) | −37.2049 | −1.36584 | ||||||||
\(743\) | 47.6956 | 1.74978 | 0.874890 | − | 0.484321i | \(-0.160933\pi\) | ||||
0.874890 | + | 0.484321i | \(0.160933\pi\) | |||||||
\(744\) | −5.56580 | −0.204052 | ||||||||
\(745\) | 11.0884 | 0.406246 | ||||||||
\(746\) | 26.4342 | 0.967823 | ||||||||
\(747\) | −11.7524 | −0.429999 | ||||||||
\(748\) | 10.8630 | 0.397190 | ||||||||
\(749\) | −22.8275 | −0.834098 | ||||||||
\(750\) | 67.0827 | 2.44951 | ||||||||
\(751\) | −23.5969 | −0.861064 | −0.430532 | − | 0.902575i | \(-0.641674\pi\) | ||||
−0.430532 | + | 0.902575i | \(0.641674\pi\) | |||||||
\(752\) | 5.21811 | 0.190285 | ||||||||
\(753\) | 50.4464 | 1.83837 | ||||||||
\(754\) | 19.8985 | 0.724660 | ||||||||
\(755\) | −71.5249 | −2.60306 | ||||||||
\(756\) | 9.09838 | 0.330905 | ||||||||
\(757\) | −43.7178 | −1.58895 | −0.794475 | − | 0.607297i | \(-0.792254\pi\) | ||||
−0.794475 | + | 0.607297i | \(0.792254\pi\) | |||||||
\(758\) | −16.0303 | −0.582248 | ||||||||
\(759\) | 20.5470 | 0.745808 | ||||||||
\(760\) | −7.81162 | −0.283357 | ||||||||
\(761\) | −25.2780 | −0.916328 | −0.458164 | − | 0.888868i | \(-0.651493\pi\) | ||||
−0.458164 | + | 0.888868i | \(0.651493\pi\) | |||||||
\(762\) | −44.8024 | −1.62302 | ||||||||
\(763\) | −20.2650 | −0.733643 | ||||||||
\(764\) | −17.4749 | −0.632221 | ||||||||
\(765\) | 27.3964 | 0.990518 | ||||||||
\(766\) | −12.0712 | −0.436149 | ||||||||
\(767\) | −18.7696 | −0.677730 | ||||||||
\(768\) | −2.10025 | −0.0757862 | ||||||||
\(769\) | −4.76921 | −0.171982 | −0.0859910 | − | 0.996296i | \(-0.527406\pi\) | ||||
−0.0859910 | + | 0.996296i | \(0.527406\pi\) | |||||||
\(770\) | −26.8636 | −0.968096 | ||||||||
\(771\) | 34.3225 | 1.23609 | ||||||||
\(772\) | −4.30096 | −0.154795 | ||||||||
\(773\) | 31.9420 | 1.14887 | 0.574437 | − | 0.818549i | \(-0.305221\pi\) | ||||
0.574437 | + | 0.818549i | \(0.305221\pi\) | |||||||
\(774\) | 8.07502 | 0.290251 | ||||||||
\(775\) | −33.4202 | −1.20049 | ||||||||
\(776\) | −3.43929 | −0.123463 | ||||||||
\(777\) | −45.8395 | −1.64448 | ||||||||
\(778\) | −19.4306 | −0.696621 | ||||||||
\(779\) | 3.17954 | 0.113919 | ||||||||
\(780\) | −37.7944 | −1.35326 | ||||||||
\(781\) | 18.5761 | 0.664707 | ||||||||
\(782\) | 19.2774 | 0.689358 | ||||||||
\(783\) | −15.4860 | −0.553424 | ||||||||
\(784\) | 0.432985 | 0.0154638 | ||||||||
\(785\) | −84.4121 | −3.01280 | ||||||||
\(786\) | −22.2577 | −0.793904 | ||||||||
\(787\) | 30.9627 | 1.10370 | 0.551850 | − | 0.833943i | \(-0.313922\pi\) | ||||
0.551850 | + | 0.833943i | \(0.313922\pi\) | |||||||
\(788\) | −24.4924 | −0.872506 | ||||||||
\(789\) | 58.2481 | 2.07369 | ||||||||
\(790\) | −0.618737 | −0.0220137 | ||||||||
\(791\) | 25.7265 | 0.914731 | ||||||||
\(792\) | −3.31306 | −0.117724 | ||||||||
\(793\) | −52.2155 | −1.85423 | ||||||||
\(794\) | 33.4445 | 1.18690 | ||||||||
\(795\) | −120.277 | −4.26579 | ||||||||
\(796\) | −1.02679 | −0.0363937 | ||||||||
\(797\) | 11.4900 | 0.406997 | 0.203498 | − | 0.979075i | \(-0.434769\pi\) | ||||
0.203498 | + | 0.979075i | \(0.434769\pi\) | |||||||
\(798\) | 10.6586 | 0.377311 | ||||||||
\(799\) | 24.1420 | 0.854081 | ||||||||
\(800\) | −12.6111 | −0.445869 | ||||||||
\(801\) | 4.59651 | 0.162410 | ||||||||
\(802\) | −10.5349 | −0.372001 | ||||||||
\(803\) | −7.34287 | −0.259124 | ||||||||
\(804\) | −21.7354 | −0.766550 | ||||||||
\(805\) | −47.6720 | −1.68022 | ||||||||
\(806\) | 11.3637 | 0.400270 | ||||||||
\(807\) | −52.5729 | −1.85065 | ||||||||
\(808\) | −17.9553 | −0.631666 | ||||||||
\(809\) | 34.9288 | 1.22803 | 0.614016 | − | 0.789293i | \(-0.289553\pi\) | ||||
0.614016 | + | 0.789293i | \(0.289553\pi\) | |||||||
\(810\) | 47.1781 | 1.65767 | ||||||||
\(811\) | −36.0547 | −1.26605 | −0.633026 | − | 0.774131i | \(-0.718187\pi\) | ||||
−0.633026 | + | 0.774131i | \(0.718187\pi\) | |||||||
\(812\) | −12.6514 | −0.443977 | ||||||||
\(813\) | −39.3436 | −1.37984 | ||||||||
\(814\) | −18.7965 | −0.658816 | ||||||||
\(815\) | 22.1702 | 0.776588 | ||||||||
\(816\) | −9.71696 | −0.340162 | ||||||||
\(817\) | −10.6525 | −0.372684 | ||||||||
\(818\) | −18.5593 | −0.648911 | ||||||||
\(819\) | 16.4963 | 0.576426 | ||||||||
\(820\) | 7.16818 | 0.250324 | ||||||||
\(821\) | −1.28425 | −0.0448207 | −0.0224103 | − | 0.999749i | \(-0.507134\pi\) | ||||
−0.0224103 | + | 0.999749i | \(0.507134\pi\) | |||||||
\(822\) | 13.8138 | 0.481812 | ||||||||
\(823\) | 6.04580 | 0.210743 | 0.105372 | − | 0.994433i | \(-0.466397\pi\) | ||||
0.105372 | + | 0.994433i | \(0.466397\pi\) | |||||||
\(824\) | −11.6765 | −0.406769 | ||||||||
\(825\) | −62.1888 | −2.16514 | ||||||||
\(826\) | 11.9336 | 0.415224 | ||||||||
\(827\) | 16.8031 | 0.584301 | 0.292150 | − | 0.956372i | \(-0.405629\pi\) | ||||
0.292150 | + | 0.956372i | \(0.405629\pi\) | |||||||
\(828\) | −5.87935 | −0.204321 | ||||||||
\(829\) | −19.7056 | −0.684403 | −0.342202 | − | 0.939627i | \(-0.611173\pi\) | ||||
−0.342202 | + | 0.939627i | \(0.611173\pi\) | |||||||
\(830\) | 34.9527 | 1.21323 | ||||||||
\(831\) | −4.15181 | −0.144025 | ||||||||
\(832\) | 4.28809 | 0.148663 | ||||||||
\(833\) | 2.00324 | 0.0694081 | ||||||||
\(834\) | 43.7091 | 1.51352 | ||||||||
\(835\) | −78.8265 | −2.72790 | ||||||||
\(836\) | 4.37056 | 0.151159 | ||||||||
\(837\) | −8.84381 | −0.305687 | ||||||||
\(838\) | −5.76487 | −0.199144 | ||||||||
\(839\) | −27.7956 | −0.959611 | −0.479806 | − | 0.877375i | \(-0.659293\pi\) | ||||
−0.479806 | + | 0.877375i | \(0.659293\pi\) | |||||||
\(840\) | 24.0295 | 0.829098 | ||||||||
\(841\) | −7.46659 | −0.257469 | ||||||||
\(842\) | 4.18467 | 0.144213 | ||||||||
\(843\) | 14.4743 | 0.498521 | ||||||||
\(844\) | −13.9129 | −0.478902 | ||||||||
\(845\) | 22.6098 | 0.777800 | ||||||||
\(846\) | −7.36298 | −0.253144 | ||||||||
\(847\) | −14.9598 | −0.514026 | ||||||||
\(848\) | 13.6464 | 0.468620 | ||||||||
\(849\) | 46.4779 | 1.59512 | ||||||||
\(850\) | −58.3462 | −2.00126 | ||||||||
\(851\) | −33.3561 | −1.14343 | ||||||||
\(852\) | −16.6164 | −0.569269 | ||||||||
\(853\) | −45.8249 | −1.56901 | −0.784507 | − | 0.620121i | \(-0.787084\pi\) | ||||
−0.784507 | + | 0.620121i | \(0.787084\pi\) | |||||||
\(854\) | 33.1984 | 1.13603 | ||||||||
\(855\) | 11.0225 | 0.376963 | ||||||||
\(856\) | 8.37290 | 0.286180 | ||||||||
\(857\) | 33.4509 | 1.14266 | 0.571330 | − | 0.820721i | \(-0.306428\pi\) | ||||
0.571330 | + | 0.820721i | \(0.306428\pi\) | |||||||
\(858\) | 21.1458 | 0.721904 | ||||||||
\(859\) | 30.8890 | 1.05392 | 0.526959 | − | 0.849891i | \(-0.323332\pi\) | ||||
0.526959 | + | 0.849891i | \(0.323332\pi\) | |||||||
\(860\) | −24.0158 | −0.818930 | ||||||||
\(861\) | −9.78066 | −0.333324 | ||||||||
\(862\) | 5.80236 | 0.197629 | ||||||||
\(863\) | −32.6839 | −1.11257 | −0.556287 | − | 0.830990i | \(-0.687774\pi\) | ||||
−0.556287 | + | 0.830990i | \(0.687774\pi\) | |||||||
\(864\) | −3.33720 | −0.113534 | ||||||||
\(865\) | −66.0435 | −2.24555 | ||||||||
\(866\) | −32.6204 | −1.10849 | ||||||||
\(867\) | −9.25201 | −0.314215 | ||||||||
\(868\) | −7.22501 | −0.245233 | ||||||||
\(869\) | 0.346180 | 0.0117434 | ||||||||
\(870\) | −40.8997 | −1.38663 | ||||||||
\(871\) | 44.3773 | 1.50367 | ||||||||
\(872\) | 7.43302 | 0.251714 | ||||||||
\(873\) | 4.85299 | 0.164249 | ||||||||
\(874\) | 7.75598 | 0.262350 | ||||||||
\(875\) | 87.0806 | 2.94386 | ||||||||
\(876\) | 6.56822 | 0.221919 | ||||||||
\(877\) | −30.1155 | −1.01693 | −0.508463 | − | 0.861084i | \(-0.669786\pi\) | ||||
−0.508463 | + | 0.861084i | \(0.669786\pi\) | |||||||
\(878\) | −22.7808 | −0.768816 | ||||||||
\(879\) | −53.7020 | −1.81132 | ||||||||
\(880\) | 9.85331 | 0.332155 | ||||||||
\(881\) | −3.62693 | −0.122194 | −0.0610971 | − | 0.998132i | \(-0.519460\pi\) | ||||
−0.0610971 | + | 0.998132i | \(0.519460\pi\) | |||||||
\(882\) | −0.610961 | −0.0205721 | ||||||||
\(883\) | −5.41120 | −0.182101 | −0.0910507 | − | 0.995846i | \(-0.529023\pi\) | ||||
−0.0910507 | + | 0.995846i | \(0.529023\pi\) | |||||||
\(884\) | 19.8392 | 0.667263 | ||||||||
\(885\) | 38.5793 | 1.29683 | ||||||||
\(886\) | −22.9851 | −0.772200 | ||||||||
\(887\) | −4.22032 | −0.141705 | −0.0708523 | − | 0.997487i | \(-0.522572\pi\) | ||||
−0.0708523 | + | 0.997487i | \(0.522572\pi\) | |||||||
\(888\) | 16.8135 | 0.564224 | ||||||||
\(889\) | −58.1583 | −1.95057 | ||||||||
\(890\) | −13.6704 | −0.458233 | ||||||||
\(891\) | −26.3959 | −0.884295 | ||||||||
\(892\) | −14.2628 | −0.477552 | ||||||||
\(893\) | 9.71317 | 0.325039 | ||||||||
\(894\) | 5.54939 | 0.185599 | ||||||||
\(895\) | 81.4473 | 2.72248 | ||||||||
\(896\) | −2.72635 | −0.0910810 | ||||||||
\(897\) | 37.5252 | 1.25293 | ||||||||
\(898\) | 18.3512 | 0.612388 | ||||||||
\(899\) | 12.2974 | 0.410141 | ||||||||
\(900\) | 17.7948 | 0.593160 | ||||||||
\(901\) | 63.1362 | 2.10337 | ||||||||
\(902\) | −4.01056 | −0.133537 | ||||||||
\(903\) | 32.7684 | 1.09046 | ||||||||
\(904\) | −9.43626 | −0.313845 | ||||||||
\(905\) | 48.5796 | 1.61484 | ||||||||
\(906\) | −35.7960 | −1.18924 | ||||||||
\(907\) | 10.9447 | 0.363414 | 0.181707 | − | 0.983353i | \(-0.441838\pi\) | ||||
0.181707 | + | 0.983353i | \(0.441838\pi\) | |||||||
\(908\) | −27.4971 | −0.912523 | ||||||||
\(909\) | 25.3358 | 0.840334 | ||||||||
\(910\) | −49.0612 | −1.62636 | ||||||||
\(911\) | −24.2244 | −0.802591 | −0.401296 | − | 0.915949i | \(-0.631440\pi\) | ||||
−0.401296 | + | 0.915949i | \(0.631440\pi\) | |||||||
\(912\) | −3.90948 | −0.129456 | ||||||||
\(913\) | −19.5558 | −0.647204 | ||||||||
\(914\) | 11.9075 | 0.393865 | ||||||||
\(915\) | 107.325 | 3.54804 | ||||||||
\(916\) | 1.83928 | 0.0607716 | ||||||||
\(917\) | −28.8928 | −0.954126 | ||||||||
\(918\) | −15.4398 | −0.509590 | ||||||||
\(919\) | −2.68405 | −0.0885388 | −0.0442694 | − | 0.999020i | \(-0.514096\pi\) | ||||
−0.0442694 | + | 0.999020i | \(0.514096\pi\) | |||||||
\(920\) | 17.4856 | 0.576485 | ||||||||
\(921\) | −42.3771 | −1.39637 | ||||||||
\(922\) | −0.191347 | −0.00630167 | ||||||||
\(923\) | 33.9258 | 1.11668 | ||||||||
\(924\) | −13.4444 | −0.442288 | ||||||||
\(925\) | 100.958 | 3.31947 | ||||||||
\(926\) | −0.344055 | −0.0113063 | ||||||||
\(927\) | 16.4760 | 0.541143 | ||||||||
\(928\) | 4.64041 | 0.152329 | ||||||||
\(929\) | 37.4174 | 1.22762 | 0.613812 | − | 0.789452i | \(-0.289635\pi\) | ||||
0.613812 | + | 0.789452i | \(0.289635\pi\) | |||||||
\(930\) | −23.3572 | −0.765913 | ||||||||
\(931\) | 0.805975 | 0.0264148 | ||||||||
\(932\) | −9.08508 | −0.297592 | ||||||||
\(933\) | 7.49696 | 0.245439 | ||||||||
\(934\) | 0.403713 | 0.0132099 | ||||||||
\(935\) | 45.5871 | 1.49086 | ||||||||
\(936\) | −6.05068 | −0.197773 | ||||||||
\(937\) | −35.7845 | −1.16903 | −0.584514 | − | 0.811384i | \(-0.698715\pi\) | ||||
−0.584514 | + | 0.811384i | \(0.698715\pi\) | |||||||
\(938\) | −28.2149 | −0.921251 | ||||||||
\(939\) | 28.2804 | 0.922897 | ||||||||
\(940\) | 21.8981 | 0.714237 | ||||||||
\(941\) | 55.5362 | 1.81043 | 0.905215 | − | 0.424954i | \(-0.139710\pi\) | ||||
0.905215 | + | 0.424954i | \(0.139710\pi\) | |||||||
\(942\) | −42.2457 | −1.37644 | ||||||||
\(943\) | −7.11712 | −0.231765 | ||||||||
\(944\) | −4.37714 | −0.142464 | ||||||||
\(945\) | 38.1819 | 1.24206 | ||||||||
\(946\) | 13.4367 | 0.436864 | ||||||||
\(947\) | 31.4831 | 1.02306 | 0.511531 | − | 0.859265i | \(-0.329078\pi\) | ||||
0.511531 | + | 0.859265i | \(0.329078\pi\) | |||||||
\(948\) | −0.309659 | −0.0100573 | ||||||||
\(949\) | −13.4104 | −0.435319 | ||||||||
\(950\) | −23.4747 | −0.761621 | ||||||||
\(951\) | −50.9315 | −1.65157 | ||||||||
\(952\) | −12.6137 | −0.408811 | ||||||||
\(953\) | −34.6687 | −1.12303 | −0.561515 | − | 0.827466i | \(-0.689781\pi\) | ||||
−0.561515 | + | 0.827466i | \(0.689781\pi\) | |||||||
\(954\) | −19.2557 | −0.623426 | ||||||||
\(955\) | −73.3346 | −2.37305 | ||||||||
\(956\) | 4.75495 | 0.153786 | ||||||||
\(957\) | 22.8832 | 0.739708 | ||||||||
\(958\) | −12.3751 | −0.399820 | ||||||||
\(959\) | 17.9318 | 0.579049 | ||||||||
\(960\) | −8.81381 | −0.284465 | ||||||||
\(961\) | −23.9771 | −0.773456 | ||||||||
\(962\) | −34.3282 | −1.10679 | ||||||||
\(963\) | −11.8145 | −0.380718 | ||||||||
\(964\) | −3.30036 | −0.106297 | ||||||||
\(965\) | −18.0492 | −0.581026 | ||||||||
\(966\) | −23.8584 | −0.767631 | ||||||||
\(967\) | −39.4697 | −1.26926 | −0.634629 | − | 0.772817i | \(-0.718847\pi\) | ||||
−0.634629 | + | 0.772817i | \(0.718847\pi\) | |||||||
\(968\) | 5.48713 | 0.176363 | ||||||||
\(969\) | −18.0875 | −0.581054 | ||||||||
\(970\) | −14.4332 | −0.463422 | ||||||||
\(971\) | 45.5251 | 1.46097 | 0.730485 | − | 0.682928i | \(-0.239294\pi\) | ||||
0.730485 | + | 0.682928i | \(0.239294\pi\) | |||||||
\(972\) | 13.5996 | 0.436206 | ||||||||
\(973\) | 56.7392 | 1.81897 | ||||||||
\(974\) | 35.6262 | 1.14154 | ||||||||
\(975\) | −113.576 | −3.63735 | ||||||||
\(976\) | −12.1769 | −0.389772 | ||||||||
\(977\) | −1.48194 | −0.0474113 | −0.0237057 | − | 0.999719i | \(-0.507546\pi\) | ||||
−0.0237057 | + | 0.999719i | \(0.507546\pi\) | |||||||
\(978\) | 11.0955 | 0.354795 | ||||||||
\(979\) | 7.64851 | 0.244448 | ||||||||
\(980\) | 1.81705 | 0.0580435 | ||||||||
\(981\) | −10.4883 | −0.334866 | ||||||||
\(982\) | −21.8556 | −0.697439 | ||||||||
\(983\) | −35.7828 | −1.14129 | −0.570647 | − | 0.821195i | \(-0.693308\pi\) | ||||
−0.570647 | + | 0.821195i | \(0.693308\pi\) | |||||||
\(984\) | 3.58746 | 0.114364 | ||||||||
\(985\) | −102.784 | −3.27497 | ||||||||
\(986\) | 21.4692 | 0.683719 | ||||||||
\(987\) | −29.8790 | −0.951057 | ||||||||
\(988\) | 7.98200 | 0.253941 | ||||||||
\(989\) | 23.8447 | 0.758217 | ||||||||
\(990\) | −13.9034 | −0.441881 | ||||||||
\(991\) | 38.0912 | 1.21001 | 0.605004 | − | 0.796223i | \(-0.293172\pi\) | ||||
0.605004 | + | 0.796223i | \(0.293172\pi\) | |||||||
\(992\) | 2.65007 | 0.0841397 | ||||||||
\(993\) | −39.0863 | −1.24037 | ||||||||
\(994\) | −21.5699 | −0.684156 | ||||||||
\(995\) | −4.30900 | −0.136604 | ||||||||
\(996\) | 17.4928 | 0.554279 | ||||||||
\(997\) | 23.5263 | 0.745087 | 0.372543 | − | 0.928015i | \(-0.378486\pi\) | ||||
0.372543 | + | 0.928015i | \(0.378486\pi\) | |||||||
\(998\) | −2.53687 | −0.0803032 | ||||||||
\(999\) | 26.7159 | 0.845254 |
(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 | 6046.2.a.g.1.16 | ✓ | 69 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6046.2.a.g.1.16 | ✓ | 69 | 1.1 | even | 1 | trivial |