Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8013,2,Mod(1,8013)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8013, 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("8013.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8013 = 3 \cdot 2671 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8013.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: | \(63.9841271397\) |
Analytic rank: | \(1\) |
Dimension: | \(116\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Character | \(\chi\) | \(=\) | 8013.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.74646 | −1.94204 | −0.971021 | − | 0.238996i | \(-0.923182\pi\) | ||||
−0.971021 | + | 0.238996i | \(0.923182\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 5.54305 | 2.77152 | ||||||||
\(5\) | −2.85945 | −1.27879 | −0.639393 | − | 0.768880i | \(-0.720814\pi\) | ||||
−0.639393 | + | 0.768880i | \(0.720814\pi\) | |||||||
\(6\) | 2.74646 | 1.12124 | ||||||||
\(7\) | 1.69114 | 0.639191 | 0.319596 | − | 0.947554i | \(-0.396453\pi\) | ||||
0.319596 | + | 0.947554i | \(0.396453\pi\) | |||||||
\(8\) | −9.73084 | −3.44037 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 7.85338 | 2.48346 | ||||||||
\(11\) | 2.11017 | 0.636240 | 0.318120 | − | 0.948050i | \(-0.396948\pi\) | ||||
0.318120 | + | 0.948050i | \(0.396948\pi\) | |||||||
\(12\) | −5.54305 | −1.60014 | ||||||||
\(13\) | 1.31830 | 0.365631 | 0.182816 | − | 0.983147i | \(-0.441479\pi\) | ||||
0.182816 | + | 0.983147i | \(0.441479\pi\) | |||||||
\(14\) | −4.64465 | −1.24134 | ||||||||
\(15\) | 2.85945 | 0.738308 | ||||||||
\(16\) | 15.6393 | 3.90982 | ||||||||
\(17\) | 4.38429 | 1.06335 | 0.531673 | − | 0.846950i | \(-0.321563\pi\) | ||||
0.531673 | + | 0.846950i | \(0.321563\pi\) | |||||||
\(18\) | −2.74646 | −0.647347 | ||||||||
\(19\) | −0.994689 | −0.228197 | −0.114099 | − | 0.993469i | \(-0.536398\pi\) | ||||
−0.114099 | + | 0.993469i | \(0.536398\pi\) | |||||||
\(20\) | −15.8501 | −3.54419 | ||||||||
\(21\) | −1.69114 | −0.369037 | ||||||||
\(22\) | −5.79550 | −1.23560 | ||||||||
\(23\) | −3.45019 | −0.719415 | −0.359707 | − | 0.933065i | \(-0.617123\pi\) | ||||
−0.359707 | + | 0.933065i | \(0.617123\pi\) | |||||||
\(24\) | 9.73084 | 1.98630 | ||||||||
\(25\) | 3.17647 | 0.635294 | ||||||||
\(26\) | −3.62067 | −0.710071 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 9.37407 | 1.77153 | ||||||||
\(29\) | −1.96936 | −0.365702 | −0.182851 | − | 0.983141i | \(-0.558533\pi\) | ||||
−0.182851 | + | 0.983141i | \(0.558533\pi\) | |||||||
\(30\) | −7.85338 | −1.43382 | ||||||||
\(31\) | 10.5424 | 1.89348 | 0.946740 | − | 0.322000i | \(-0.104355\pi\) | ||||
0.946740 | + | 0.322000i | \(0.104355\pi\) | |||||||
\(32\) | −23.4910 | −4.15266 | ||||||||
\(33\) | −2.11017 | −0.367333 | ||||||||
\(34\) | −12.0413 | −2.06506 | ||||||||
\(35\) | −4.83574 | −0.817389 | ||||||||
\(36\) | 5.54305 | 0.923841 | ||||||||
\(37\) | −6.94781 | −1.14221 | −0.571107 | − | 0.820876i | \(-0.693486\pi\) | ||||
−0.571107 | + | 0.820876i | \(0.693486\pi\) | |||||||
\(38\) | 2.73187 | 0.443169 | ||||||||
\(39\) | −1.31830 | −0.211097 | ||||||||
\(40\) | 27.8249 | 4.39950 | ||||||||
\(41\) | 8.37730 | 1.30832 | 0.654158 | − | 0.756358i | \(-0.273023\pi\) | ||||
0.654158 | + | 0.756358i | \(0.273023\pi\) | |||||||
\(42\) | 4.64465 | 0.716685 | ||||||||
\(43\) | 4.96606 | 0.757317 | 0.378658 | − | 0.925537i | \(-0.376386\pi\) | ||||
0.378658 | + | 0.925537i | \(0.376386\pi\) | |||||||
\(44\) | 11.6968 | 1.76335 | ||||||||
\(45\) | −2.85945 | −0.426262 | ||||||||
\(46\) | 9.47582 | 1.39713 | ||||||||
\(47\) | −6.26352 | −0.913629 | −0.456814 | − | 0.889562i | \(-0.651010\pi\) | ||||
−0.456814 | + | 0.889562i | \(0.651010\pi\) | |||||||
\(48\) | −15.6393 | −2.25734 | ||||||||
\(49\) | −4.14004 | −0.591435 | ||||||||
\(50\) | −8.72405 | −1.23377 | ||||||||
\(51\) | −4.38429 | −0.613923 | ||||||||
\(52\) | 7.30741 | 1.01336 | ||||||||
\(53\) | −1.58492 | −0.217705 | −0.108853 | − | 0.994058i | \(-0.534718\pi\) | ||||
−0.108853 | + | 0.994058i | \(0.534718\pi\) | |||||||
\(54\) | 2.74646 | 0.373746 | ||||||||
\(55\) | −6.03393 | −0.813615 | ||||||||
\(56\) | −16.4562 | −2.19905 | ||||||||
\(57\) | 0.994689 | 0.131750 | ||||||||
\(58\) | 5.40878 | 0.710208 | ||||||||
\(59\) | −9.41363 | −1.22555 | −0.612775 | − | 0.790257i | \(-0.709947\pi\) | ||||
−0.612775 | + | 0.790257i | \(0.709947\pi\) | |||||||
\(60\) | 15.8501 | 2.04624 | ||||||||
\(61\) | −5.77156 | −0.738973 | −0.369486 | − | 0.929236i | \(-0.620466\pi\) | ||||
−0.369486 | + | 0.929236i | \(0.620466\pi\) | |||||||
\(62\) | −28.9544 | −3.67721 | ||||||||
\(63\) | 1.69114 | 0.213064 | ||||||||
\(64\) | 33.2385 | 4.15482 | ||||||||
\(65\) | −3.76962 | −0.467564 | ||||||||
\(66\) | 5.79550 | 0.713377 | ||||||||
\(67\) | 7.36669 | 0.899984 | 0.449992 | − | 0.893033i | \(-0.351427\pi\) | ||||
0.449992 | + | 0.893033i | \(0.351427\pi\) | |||||||
\(68\) | 24.3023 | 2.94709 | ||||||||
\(69\) | 3.45019 | 0.415354 | ||||||||
\(70\) | 13.2812 | 1.58740 | ||||||||
\(71\) | −3.12053 | −0.370339 | −0.185170 | − | 0.982707i | \(-0.559283\pi\) | ||||
−0.185170 | + | 0.982707i | \(0.559283\pi\) | |||||||
\(72\) | −9.73084 | −1.14679 | ||||||||
\(73\) | −8.72593 | −1.02129 | −0.510646 | − | 0.859791i | \(-0.670594\pi\) | ||||
−0.510646 | + | 0.859791i | \(0.670594\pi\) | |||||||
\(74\) | 19.0819 | 2.21823 | ||||||||
\(75\) | −3.17647 | −0.366787 | ||||||||
\(76\) | −5.51361 | −0.632454 | ||||||||
\(77\) | 3.56859 | 0.406679 | ||||||||
\(78\) | 3.62067 | 0.409960 | ||||||||
\(79\) | 0.564522 | 0.0635137 | 0.0317568 | − | 0.999496i | \(-0.489890\pi\) | ||||
0.0317568 | + | 0.999496i | \(0.489890\pi\) | |||||||
\(80\) | −44.7198 | −4.99982 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −23.0079 | −2.54080 | ||||||||
\(83\) | −9.60777 | −1.05459 | −0.527295 | − | 0.849682i | \(-0.676794\pi\) | ||||
−0.527295 | + | 0.849682i | \(0.676794\pi\) | |||||||
\(84\) | −9.37407 | −1.02280 | ||||||||
\(85\) | −12.5367 | −1.35979 | ||||||||
\(86\) | −13.6391 | −1.47074 | ||||||||
\(87\) | 1.96936 | 0.211138 | ||||||||
\(88\) | −20.5337 | −2.18890 | ||||||||
\(89\) | −4.02539 | −0.426691 | −0.213345 | − | 0.976977i | \(-0.568436\pi\) | ||||
−0.213345 | + | 0.976977i | \(0.568436\pi\) | |||||||
\(90\) | 7.85338 | 0.827818 | ||||||||
\(91\) | 2.22943 | 0.233708 | ||||||||
\(92\) | −19.1246 | −1.99388 | ||||||||
\(93\) | −10.5424 | −1.09320 | ||||||||
\(94\) | 17.2025 | 1.77430 | ||||||||
\(95\) | 2.84427 | 0.291816 | ||||||||
\(96\) | 23.4910 | 2.39754 | ||||||||
\(97\) | −3.34692 | −0.339828 | −0.169914 | − | 0.985459i | \(-0.554349\pi\) | ||||
−0.169914 | + | 0.985459i | \(0.554349\pi\) | |||||||
\(98\) | 11.3705 | 1.14859 | ||||||||
\(99\) | 2.11017 | 0.212080 | ||||||||
\(100\) | 17.6073 | 1.76073 | ||||||||
\(101\) | 5.62201 | 0.559411 | 0.279706 | − | 0.960086i | \(-0.409763\pi\) | ||||
0.279706 | + | 0.960086i | \(0.409763\pi\) | |||||||
\(102\) | 12.0413 | 1.19226 | ||||||||
\(103\) | −9.64887 | −0.950731 | −0.475366 | − | 0.879788i | \(-0.657684\pi\) | ||||
−0.475366 | + | 0.879788i | \(0.657684\pi\) | |||||||
\(104\) | −12.8282 | −1.25791 | ||||||||
\(105\) | 4.83574 | 0.471920 | ||||||||
\(106\) | 4.35292 | 0.422793 | ||||||||
\(107\) | 14.8604 | 1.43661 | 0.718306 | − | 0.695727i | \(-0.244918\pi\) | ||||
0.718306 | + | 0.695727i | \(0.244918\pi\) | |||||||
\(108\) | −5.54305 | −0.533380 | ||||||||
\(109\) | 8.27783 | 0.792872 | 0.396436 | − | 0.918062i | \(-0.370247\pi\) | ||||
0.396436 | + | 0.918062i | \(0.370247\pi\) | |||||||
\(110\) | 16.5720 | 1.58007 | ||||||||
\(111\) | 6.94781 | 0.659457 | ||||||||
\(112\) | 26.4482 | 2.49912 | ||||||||
\(113\) | −11.6422 | −1.09520 | −0.547602 | − | 0.836739i | \(-0.684459\pi\) | ||||
−0.547602 | + | 0.836739i | \(0.684459\pi\) | |||||||
\(114\) | −2.73187 | −0.255863 | ||||||||
\(115\) | 9.86566 | 0.919978 | ||||||||
\(116\) | −10.9163 | −1.01355 | ||||||||
\(117\) | 1.31830 | 0.121877 | ||||||||
\(118\) | 25.8542 | 2.38007 | ||||||||
\(119\) | 7.41445 | 0.679682 | ||||||||
\(120\) | −27.8249 | −2.54005 | ||||||||
\(121\) | −6.54718 | −0.595198 | ||||||||
\(122\) | 15.8514 | 1.43512 | ||||||||
\(123\) | −8.37730 | −0.755356 | ||||||||
\(124\) | 58.4373 | 5.24782 | ||||||||
\(125\) | 5.21430 | 0.466381 | ||||||||
\(126\) | −4.64465 | −0.413778 | ||||||||
\(127\) | 0.455510 | 0.0404200 | 0.0202100 | − | 0.999796i | \(-0.493567\pi\) | ||||
0.0202100 | + | 0.999796i | \(0.493567\pi\) | |||||||
\(128\) | −44.3063 | −3.91616 | ||||||||
\(129\) | −4.96606 | −0.437237 | ||||||||
\(130\) | 10.3531 | 0.908029 | ||||||||
\(131\) | −4.88141 | −0.426491 | −0.213245 | − | 0.976999i | \(-0.568403\pi\) | ||||
−0.213245 | + | 0.976999i | \(0.568403\pi\) | |||||||
\(132\) | −11.6968 | −1.01807 | ||||||||
\(133\) | −1.68216 | −0.145862 | ||||||||
\(134\) | −20.2323 | −1.74781 | ||||||||
\(135\) | 2.85945 | 0.246103 | ||||||||
\(136\) | −42.6628 | −3.65831 | ||||||||
\(137\) | −7.47667 | −0.638775 | −0.319388 | − | 0.947624i | \(-0.603477\pi\) | ||||
−0.319388 | + | 0.947624i | \(0.603477\pi\) | |||||||
\(138\) | −9.47582 | −0.806635 | ||||||||
\(139\) | 15.5388 | 1.31798 | 0.658992 | − | 0.752150i | \(-0.270983\pi\) | ||||
0.658992 | + | 0.752150i | \(0.270983\pi\) | |||||||
\(140\) | −26.8047 | −2.26541 | ||||||||
\(141\) | 6.26352 | 0.527484 | ||||||||
\(142\) | 8.57042 | 0.719214 | ||||||||
\(143\) | 2.78184 | 0.232629 | ||||||||
\(144\) | 15.6393 | 1.30327 | ||||||||
\(145\) | 5.63130 | 0.467654 | ||||||||
\(146\) | 23.9654 | 1.98339 | ||||||||
\(147\) | 4.14004 | 0.341465 | ||||||||
\(148\) | −38.5121 | −3.16567 | ||||||||
\(149\) | 4.52115 | 0.370387 | 0.185194 | − | 0.982702i | \(-0.440709\pi\) | ||||
0.185194 | + | 0.982702i | \(0.440709\pi\) | |||||||
\(150\) | 8.72405 | 0.712316 | ||||||||
\(151\) | −4.08267 | −0.332243 | −0.166122 | − | 0.986105i | \(-0.553124\pi\) | ||||
−0.166122 | + | 0.986105i | \(0.553124\pi\) | |||||||
\(152\) | 9.67916 | 0.785084 | ||||||||
\(153\) | 4.38429 | 0.354449 | ||||||||
\(154\) | −9.80100 | −0.789787 | ||||||||
\(155\) | −30.1456 | −2.42136 | ||||||||
\(156\) | −7.30741 | −0.585061 | ||||||||
\(157\) | −0.220306 | −0.0175823 | −0.00879117 | − | 0.999961i | \(-0.502798\pi\) | ||||
−0.00879117 | + | 0.999961i | \(0.502798\pi\) | |||||||
\(158\) | −1.55044 | −0.123346 | ||||||||
\(159\) | 1.58492 | 0.125692 | ||||||||
\(160\) | 67.1714 | 5.31036 | ||||||||
\(161\) | −5.83476 | −0.459844 | ||||||||
\(162\) | −2.74646 | −0.215782 | ||||||||
\(163\) | −9.65358 | −0.756126 | −0.378063 | − | 0.925780i | \(-0.623410\pi\) | ||||
−0.378063 | + | 0.925780i | \(0.623410\pi\) | |||||||
\(164\) | 46.4358 | 3.62603 | ||||||||
\(165\) | 6.03393 | 0.469741 | ||||||||
\(166\) | 26.3874 | 2.04806 | ||||||||
\(167\) | 9.54341 | 0.738491 | 0.369246 | − | 0.929332i | \(-0.379616\pi\) | ||||
0.369246 | + | 0.929332i | \(0.379616\pi\) | |||||||
\(168\) | 16.4562 | 1.26962 | ||||||||
\(169\) | −11.2621 | −0.866314 | ||||||||
\(170\) | 34.4315 | 2.64077 | ||||||||
\(171\) | −0.994689 | −0.0760658 | ||||||||
\(172\) | 27.5271 | 2.09892 | ||||||||
\(173\) | −2.24820 | −0.170928 | −0.0854639 | − | 0.996341i | \(-0.527237\pi\) | ||||
−0.0854639 | + | 0.996341i | \(0.527237\pi\) | |||||||
\(174\) | −5.40878 | −0.410039 | ||||||||
\(175\) | 5.37186 | 0.406074 | ||||||||
\(176\) | 33.0015 | 2.48758 | ||||||||
\(177\) | 9.41363 | 0.707572 | ||||||||
\(178\) | 11.0556 | 0.828651 | ||||||||
\(179\) | −22.6124 | −1.69013 | −0.845064 | − | 0.534665i | \(-0.820438\pi\) | ||||
−0.845064 | + | 0.534665i | \(0.820438\pi\) | |||||||
\(180\) | −15.8501 | −1.18140 | ||||||||
\(181\) | 5.51831 | 0.410173 | 0.205086 | − | 0.978744i | \(-0.434252\pi\) | ||||
0.205086 | + | 0.978744i | \(0.434252\pi\) | |||||||
\(182\) | −6.12305 | −0.453871 | ||||||||
\(183\) | 5.77156 | 0.426646 | ||||||||
\(184\) | 33.5733 | 2.47505 | ||||||||
\(185\) | 19.8669 | 1.46065 | ||||||||
\(186\) | 28.9544 | 2.12304 | ||||||||
\(187\) | 9.25160 | 0.676544 | ||||||||
\(188\) | −34.7190 | −2.53214 | ||||||||
\(189\) | −1.69114 | −0.123012 | ||||||||
\(190\) | −7.81167 | −0.566718 | ||||||||
\(191\) | 21.0522 | 1.52328 | 0.761642 | − | 0.647998i | \(-0.224394\pi\) | ||||
0.761642 | + | 0.647998i | \(0.224394\pi\) | |||||||
\(192\) | −33.2385 | −2.39878 | ||||||||
\(193\) | −0.181678 | −0.0130775 | −0.00653875 | − | 0.999979i | \(-0.502081\pi\) | ||||
−0.00653875 | + | 0.999979i | \(0.502081\pi\) | |||||||
\(194\) | 9.19218 | 0.659960 | ||||||||
\(195\) | 3.76962 | 0.269948 | ||||||||
\(196\) | −22.9485 | −1.63918 | ||||||||
\(197\) | −2.81430 | −0.200511 | −0.100255 | − | 0.994962i | \(-0.531966\pi\) | ||||
−0.100255 | + | 0.994962i | \(0.531966\pi\) | |||||||
\(198\) | −5.79550 | −0.411868 | ||||||||
\(199\) | −8.25008 | −0.584833 | −0.292416 | − | 0.956291i | \(-0.594459\pi\) | ||||
−0.292416 | + | 0.956291i | \(0.594459\pi\) | |||||||
\(200\) | −30.9097 | −2.18565 | ||||||||
\(201\) | −7.36669 | −0.519606 | ||||||||
\(202\) | −15.4406 | −1.08640 | ||||||||
\(203\) | −3.33047 | −0.233753 | ||||||||
\(204\) | −24.3023 | −1.70150 | ||||||||
\(205\) | −23.9545 | −1.67306 | ||||||||
\(206\) | 26.5002 | 1.84636 | ||||||||
\(207\) | −3.45019 | −0.239805 | ||||||||
\(208\) | 20.6173 | 1.42955 | ||||||||
\(209\) | −2.09896 | −0.145188 | ||||||||
\(210\) | −13.2812 | −0.916487 | ||||||||
\(211\) | −4.88830 | −0.336525 | −0.168262 | − | 0.985742i | \(-0.553816\pi\) | ||||
−0.168262 | + | 0.985742i | \(0.553816\pi\) | |||||||
\(212\) | −8.78528 | −0.603375 | ||||||||
\(213\) | 3.12053 | 0.213815 | ||||||||
\(214\) | −40.8136 | −2.78996 | ||||||||
\(215\) | −14.2002 | −0.968446 | ||||||||
\(216\) | 9.73084 | 0.662100 | ||||||||
\(217\) | 17.8288 | 1.21030 | ||||||||
\(218\) | −22.7347 | −1.53979 | ||||||||
\(219\) | 8.72593 | 0.589644 | ||||||||
\(220\) | −33.4464 | −2.25495 | ||||||||
\(221\) | 5.77982 | 0.388793 | ||||||||
\(222\) | −19.0819 | −1.28069 | ||||||||
\(223\) | −17.2666 | −1.15626 | −0.578130 | − | 0.815945i | \(-0.696217\pi\) | ||||
−0.578130 | + | 0.815945i | \(0.696217\pi\) | |||||||
\(224\) | −39.7266 | −2.65434 | ||||||||
\(225\) | 3.17647 | 0.211765 | ||||||||
\(226\) | 31.9748 | 2.12693 | ||||||||
\(227\) | −8.68134 | −0.576201 | −0.288100 | − | 0.957600i | \(-0.593024\pi\) | ||||
−0.288100 | + | 0.957600i | \(0.593024\pi\) | |||||||
\(228\) | 5.51361 | 0.365148 | ||||||||
\(229\) | −29.9412 | −1.97857 | −0.989285 | − | 0.145995i | \(-0.953362\pi\) | ||||
−0.989285 | + | 0.145995i | \(0.953362\pi\) | |||||||
\(230\) | −27.0957 | −1.78663 | ||||||||
\(231\) | −3.56859 | −0.234796 | ||||||||
\(232\) | 19.1636 | 1.25815 | ||||||||
\(233\) | 20.9419 | 1.37195 | 0.685974 | − | 0.727626i | \(-0.259376\pi\) | ||||
0.685974 | + | 0.727626i | \(0.259376\pi\) | |||||||
\(234\) | −3.62067 | −0.236690 | ||||||||
\(235\) | 17.9102 | 1.16834 | ||||||||
\(236\) | −52.1802 | −3.39664 | ||||||||
\(237\) | −0.564522 | −0.0366697 | ||||||||
\(238\) | −20.3635 | −1.31997 | ||||||||
\(239\) | 6.72716 | 0.435144 | 0.217572 | − | 0.976044i | \(-0.430186\pi\) | ||||
0.217572 | + | 0.976044i | \(0.430186\pi\) | |||||||
\(240\) | 44.7198 | 2.88665 | ||||||||
\(241\) | 27.1333 | 1.74781 | 0.873906 | − | 0.486095i | \(-0.161579\pi\) | ||||
0.873906 | + | 0.486095i | \(0.161579\pi\) | |||||||
\(242\) | 17.9816 | 1.15590 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −31.9920 | −2.04808 | ||||||||
\(245\) | 11.8383 | 0.756319 | ||||||||
\(246\) | 23.0079 | 1.46693 | ||||||||
\(247\) | −1.31130 | −0.0834361 | ||||||||
\(248\) | −102.587 | −6.51427 | ||||||||
\(249\) | 9.60777 | 0.608868 | ||||||||
\(250\) | −14.3209 | −0.905731 | ||||||||
\(251\) | −16.7055 | −1.05444 | −0.527221 | − | 0.849728i | \(-0.676766\pi\) | ||||
−0.527221 | + | 0.849728i | \(0.676766\pi\) | |||||||
\(252\) | 9.37407 | 0.590511 | ||||||||
\(253\) | −7.28049 | −0.457721 | ||||||||
\(254\) | −1.25104 | −0.0784973 | ||||||||
\(255\) | 12.5367 | 0.785077 | ||||||||
\(256\) | 55.2086 | 3.45053 | ||||||||
\(257\) | −7.13776 | −0.445241 | −0.222621 | − | 0.974905i | \(-0.571461\pi\) | ||||
−0.222621 | + | 0.974905i | \(0.571461\pi\) | |||||||
\(258\) | 13.6391 | 0.849132 | ||||||||
\(259\) | −11.7497 | −0.730092 | ||||||||
\(260\) | −20.8952 | −1.29587 | ||||||||
\(261\) | −1.96936 | −0.121901 | ||||||||
\(262\) | 13.4066 | 0.828262 | ||||||||
\(263\) | −5.37160 | −0.331227 | −0.165613 | − | 0.986191i | \(-0.552960\pi\) | ||||
−0.165613 | + | 0.986191i | \(0.552960\pi\) | |||||||
\(264\) | 20.5337 | 1.26376 | ||||||||
\(265\) | 4.53200 | 0.278399 | ||||||||
\(266\) | 4.61998 | 0.283269 | ||||||||
\(267\) | 4.02539 | 0.246350 | ||||||||
\(268\) | 40.8339 | 2.49433 | ||||||||
\(269\) | 25.7170 | 1.56799 | 0.783997 | − | 0.620764i | \(-0.213178\pi\) | ||||
0.783997 | + | 0.620764i | \(0.213178\pi\) | |||||||
\(270\) | −7.85338 | −0.477941 | ||||||||
\(271\) | 16.9470 | 1.02945 | 0.514727 | − | 0.857354i | \(-0.327893\pi\) | ||||
0.514727 | + | 0.857354i | \(0.327893\pi\) | |||||||
\(272\) | 68.5671 | 4.15749 | ||||||||
\(273\) | −2.22943 | −0.134932 | ||||||||
\(274\) | 20.5344 | 1.24053 | ||||||||
\(275\) | 6.70289 | 0.404200 | ||||||||
\(276\) | 19.1246 | 1.15116 | ||||||||
\(277\) | −7.64851 | −0.459555 | −0.229777 | − | 0.973243i | \(-0.573800\pi\) | ||||
−0.229777 | + | 0.973243i | \(0.573800\pi\) | |||||||
\(278\) | −42.6767 | −2.55958 | ||||||||
\(279\) | 10.5424 | 0.631160 | ||||||||
\(280\) | 47.0558 | 2.81212 | ||||||||
\(281\) | 3.16013 | 0.188518 | 0.0942588 | − | 0.995548i | \(-0.469952\pi\) | ||||
0.0942588 | + | 0.995548i | \(0.469952\pi\) | |||||||
\(282\) | −17.2025 | −1.02440 | ||||||||
\(283\) | 21.4093 | 1.27265 | 0.636325 | − | 0.771421i | \(-0.280454\pi\) | ||||
0.636325 | + | 0.771421i | \(0.280454\pi\) | |||||||
\(284\) | −17.2973 | −1.02640 | ||||||||
\(285\) | −2.84427 | −0.168480 | ||||||||
\(286\) | −7.64022 | −0.451776 | ||||||||
\(287\) | 14.1672 | 0.836263 | ||||||||
\(288\) | −23.4910 | −1.38422 | ||||||||
\(289\) | 2.22200 | 0.130706 | ||||||||
\(290\) | −15.4662 | −0.908204 | ||||||||
\(291\) | 3.34692 | 0.196200 | ||||||||
\(292\) | −48.3682 | −2.83054 | ||||||||
\(293\) | −27.5891 | −1.61177 | −0.805887 | − | 0.592069i | \(-0.798311\pi\) | ||||
−0.805887 | + | 0.592069i | \(0.798311\pi\) | |||||||
\(294\) | −11.3705 | −0.663139 | ||||||||
\(295\) | 26.9178 | 1.56722 | ||||||||
\(296\) | 67.6081 | 3.92964 | ||||||||
\(297\) | −2.11017 | −0.122444 | ||||||||
\(298\) | −12.4172 | −0.719307 | ||||||||
\(299\) | −4.54840 | −0.263041 | ||||||||
\(300\) | −17.6073 | −1.01656 | ||||||||
\(301\) | 8.39830 | 0.484070 | ||||||||
\(302\) | 11.2129 | 0.645230 | ||||||||
\(303\) | −5.62201 | −0.322976 | ||||||||
\(304\) | −15.5562 | −0.892210 | ||||||||
\(305\) | 16.5035 | 0.944988 | ||||||||
\(306\) | −12.0413 | −0.688354 | ||||||||
\(307\) | −23.3751 | −1.33409 | −0.667044 | − | 0.745019i | \(-0.732441\pi\) | ||||
−0.667044 | + | 0.745019i | \(0.732441\pi\) | |||||||
\(308\) | 19.7809 | 1.12712 | ||||||||
\(309\) | 9.64887 | 0.548905 | ||||||||
\(310\) | 82.7938 | 4.70237 | ||||||||
\(311\) | 11.3883 | 0.645770 | 0.322885 | − | 0.946438i | \(-0.395347\pi\) | ||||
0.322885 | + | 0.946438i | \(0.395347\pi\) | |||||||
\(312\) | 12.8282 | 0.726253 | ||||||||
\(313\) | 31.5987 | 1.78606 | 0.893031 | − | 0.449995i | \(-0.148574\pi\) | ||||
0.893031 | + | 0.449995i | \(0.148574\pi\) | |||||||
\(314\) | 0.605062 | 0.0341456 | ||||||||
\(315\) | −4.83574 | −0.272463 | ||||||||
\(316\) | 3.12917 | 0.176030 | ||||||||
\(317\) | 3.45277 | 0.193927 | 0.0969634 | − | 0.995288i | \(-0.469087\pi\) | ||||
0.0969634 | + | 0.995288i | \(0.469087\pi\) | |||||||
\(318\) | −4.35292 | −0.244099 | ||||||||
\(319\) | −4.15569 | −0.232674 | ||||||||
\(320\) | −95.0440 | −5.31312 | ||||||||
\(321\) | −14.8604 | −0.829428 | ||||||||
\(322\) | 16.0249 | 0.893035 | ||||||||
\(323\) | −4.36100 | −0.242653 | ||||||||
\(324\) | 5.54305 | 0.307947 | ||||||||
\(325\) | 4.18755 | 0.232283 | ||||||||
\(326\) | 26.5132 | 1.46843 | ||||||||
\(327\) | −8.27783 | −0.457765 | ||||||||
\(328\) | −81.5182 | −4.50109 | ||||||||
\(329\) | −10.5925 | −0.583983 | ||||||||
\(330\) | −16.5720 | −0.912256 | ||||||||
\(331\) | 14.4247 | 0.792856 | 0.396428 | − | 0.918066i | \(-0.370250\pi\) | ||||
0.396428 | + | 0.918066i | \(0.370250\pi\) | |||||||
\(332\) | −53.2563 | −2.92282 | ||||||||
\(333\) | −6.94781 | −0.380738 | ||||||||
\(334\) | −26.2106 | −1.43418 | ||||||||
\(335\) | −21.0647 | −1.15089 | ||||||||
\(336\) | −26.4482 | −1.44287 | ||||||||
\(337\) | 19.4647 | 1.06031 | 0.530154 | − | 0.847901i | \(-0.322134\pi\) | ||||
0.530154 | + | 0.847901i | \(0.322134\pi\) | |||||||
\(338\) | 30.9309 | 1.68242 | ||||||||
\(339\) | 11.6422 | 0.632317 | ||||||||
\(340\) | −69.4914 | −3.76870 | ||||||||
\(341\) | 22.2464 | 1.20471 | ||||||||
\(342\) | 2.73187 | 0.147723 | ||||||||
\(343\) | −18.8394 | −1.01723 | ||||||||
\(344\) | −48.3239 | −2.60545 | ||||||||
\(345\) | −9.86566 | −0.531149 | ||||||||
\(346\) | 6.17460 | 0.331949 | ||||||||
\(347\) | 11.9970 | 0.644032 | 0.322016 | − | 0.946734i | \(-0.395639\pi\) | ||||
0.322016 | + | 0.946734i | \(0.395639\pi\) | |||||||
\(348\) | 10.9163 | 0.585174 | ||||||||
\(349\) | 0.0640178 | 0.00342679 | 0.00171340 | − | 0.999999i | \(-0.499455\pi\) | ||||
0.00171340 | + | 0.999999i | \(0.499455\pi\) | |||||||
\(350\) | −14.7536 | −0.788613 | ||||||||
\(351\) | −1.31830 | −0.0703658 | ||||||||
\(352\) | −49.5700 | −2.64209 | ||||||||
\(353\) | −8.53915 | −0.454493 | −0.227246 | − | 0.973837i | \(-0.572972\pi\) | ||||
−0.227246 | + | 0.973837i | \(0.572972\pi\) | |||||||
\(354\) | −25.8542 | −1.37413 | ||||||||
\(355\) | 8.92302 | 0.473584 | ||||||||
\(356\) | −22.3130 | −1.18258 | ||||||||
\(357\) | −7.41445 | −0.392414 | ||||||||
\(358\) | 62.1040 | 3.28230 | ||||||||
\(359\) | 8.62463 | 0.455191 | 0.227595 | − | 0.973756i | \(-0.426914\pi\) | ||||
0.227595 | + | 0.973756i | \(0.426914\pi\) | |||||||
\(360\) | 27.8249 | 1.46650 | ||||||||
\(361\) | −18.0106 | −0.947926 | ||||||||
\(362\) | −15.1558 | −0.796572 | ||||||||
\(363\) | 6.54718 | 0.343638 | ||||||||
\(364\) | 12.3579 | 0.647728 | ||||||||
\(365\) | 24.9514 | 1.30601 | ||||||||
\(366\) | −15.8514 | −0.828564 | ||||||||
\(367\) | 2.84408 | 0.148460 | 0.0742299 | − | 0.997241i | \(-0.476350\pi\) | ||||
0.0742299 | + | 0.997241i | \(0.476350\pi\) | |||||||
\(368\) | −53.9585 | −2.81278 | ||||||||
\(369\) | 8.37730 | 0.436105 | ||||||||
\(370\) | −54.5638 | −2.83664 | ||||||||
\(371\) | −2.68032 | −0.139155 | ||||||||
\(372\) | −58.4373 | −3.02983 | ||||||||
\(373\) | −20.4244 | −1.05754 | −0.528768 | − | 0.848766i | \(-0.677346\pi\) | ||||
−0.528768 | + | 0.848766i | \(0.677346\pi\) | |||||||
\(374\) | −25.4091 | −1.31388 | ||||||||
\(375\) | −5.21430 | −0.269265 | ||||||||
\(376\) | 60.9493 | 3.14322 | ||||||||
\(377\) | −2.59622 | −0.133712 | ||||||||
\(378\) | 4.64465 | 0.238895 | ||||||||
\(379\) | −1.47694 | −0.0758652 | −0.0379326 | − | 0.999280i | \(-0.512077\pi\) | ||||
−0.0379326 | + | 0.999280i | \(0.512077\pi\) | |||||||
\(380\) | 15.7659 | 0.808774 | ||||||||
\(381\) | −0.455510 | −0.0233365 | ||||||||
\(382\) | −57.8191 | −2.95828 | ||||||||
\(383\) | −12.4669 | −0.637030 | −0.318515 | − | 0.947918i | \(-0.603184\pi\) | ||||
−0.318515 | + | 0.947918i | \(0.603184\pi\) | |||||||
\(384\) | 44.3063 | 2.26100 | ||||||||
\(385\) | −10.2042 | −0.520055 | ||||||||
\(386\) | 0.498973 | 0.0253970 | ||||||||
\(387\) | 4.96606 | 0.252439 | ||||||||
\(388\) | −18.5521 | −0.941841 | ||||||||
\(389\) | 14.1089 | 0.715351 | 0.357676 | − | 0.933846i | \(-0.383569\pi\) | ||||
0.357676 | + | 0.933846i | \(0.383569\pi\) | |||||||
\(390\) | −10.3531 | −0.524251 | ||||||||
\(391\) | −15.1266 | −0.764987 | ||||||||
\(392\) | 40.2861 | 2.03476 | ||||||||
\(393\) | 4.88141 | 0.246235 | ||||||||
\(394\) | 7.72937 | 0.389400 | ||||||||
\(395\) | −1.61422 | −0.0812204 | ||||||||
\(396\) | 11.6968 | 0.587785 | ||||||||
\(397\) | 9.46892 | 0.475232 | 0.237616 | − | 0.971359i | \(-0.423634\pi\) | ||||
0.237616 | + | 0.971359i | \(0.423634\pi\) | |||||||
\(398\) | 22.6585 | 1.13577 | ||||||||
\(399\) | 1.68216 | 0.0842133 | ||||||||
\(400\) | 49.6777 | 2.48389 | ||||||||
\(401\) | 29.6367 | 1.47999 | 0.739993 | − | 0.672614i | \(-0.234829\pi\) | ||||
0.739993 | + | 0.672614i | \(0.234829\pi\) | |||||||
\(402\) | 20.2323 | 1.00910 | ||||||||
\(403\) | 13.8981 | 0.692315 | ||||||||
\(404\) | 31.1631 | 1.55042 | ||||||||
\(405\) | −2.85945 | −0.142087 | ||||||||
\(406\) | 9.14701 | 0.453959 | ||||||||
\(407\) | −14.6611 | −0.726722 | ||||||||
\(408\) | 42.6628 | 2.11212 | ||||||||
\(409\) | −20.5317 | −1.01523 | −0.507614 | − | 0.861585i | \(-0.669472\pi\) | ||||
−0.507614 | + | 0.861585i | \(0.669472\pi\) | |||||||
\(410\) | 65.7901 | 3.24914 | ||||||||
\(411\) | 7.47667 | 0.368797 | ||||||||
\(412\) | −53.4842 | −2.63497 | ||||||||
\(413\) | −15.9198 | −0.783361 | ||||||||
\(414\) | 9.47582 | 0.465711 | ||||||||
\(415\) | 27.4730 | 1.34859 | ||||||||
\(416\) | −30.9682 | −1.51834 | ||||||||
\(417\) | −15.5388 | −0.760938 | ||||||||
\(418\) | 5.76472 | 0.281962 | ||||||||
\(419\) | 4.17894 | 0.204154 | 0.102077 | − | 0.994776i | \(-0.467451\pi\) | ||||
0.102077 | + | 0.994776i | \(0.467451\pi\) | |||||||
\(420\) | 26.8047 | 1.30794 | ||||||||
\(421\) | 28.9145 | 1.40920 | 0.704602 | − | 0.709603i | \(-0.251125\pi\) | ||||
0.704602 | + | 0.709603i | \(0.251125\pi\) | |||||||
\(422\) | 13.4255 | 0.653545 | ||||||||
\(423\) | −6.26352 | −0.304543 | ||||||||
\(424\) | 15.4226 | 0.748987 | ||||||||
\(425\) | 13.9266 | 0.675538 | ||||||||
\(426\) | −8.57042 | −0.415238 | ||||||||
\(427\) | −9.76052 | −0.472345 | ||||||||
\(428\) | 82.3721 | 3.98160 | ||||||||
\(429\) | −2.78184 | −0.134309 | ||||||||
\(430\) | 39.0003 | 1.88076 | ||||||||
\(431\) | 38.3283 | 1.84621 | 0.923105 | − | 0.384547i | \(-0.125642\pi\) | ||||
0.923105 | + | 0.384547i | \(0.125642\pi\) | |||||||
\(432\) | −15.6393 | −0.752445 | ||||||||
\(433\) | −8.93861 | −0.429562 | −0.214781 | − | 0.976662i | \(-0.568904\pi\) | ||||
−0.214781 | + | 0.976662i | \(0.568904\pi\) | |||||||
\(434\) | −48.9660 | −2.35044 | ||||||||
\(435\) | −5.63130 | −0.270000 | ||||||||
\(436\) | 45.8844 | 2.19746 | ||||||||
\(437\) | 3.43187 | 0.164169 | ||||||||
\(438\) | −23.9654 | −1.14511 | ||||||||
\(439\) | −23.7305 | −1.13260 | −0.566298 | − | 0.824201i | \(-0.691625\pi\) | ||||
−0.566298 | + | 0.824201i | \(0.691625\pi\) | |||||||
\(440\) | 58.7152 | 2.79914 | ||||||||
\(441\) | −4.14004 | −0.197145 | ||||||||
\(442\) | −15.8740 | −0.755052 | ||||||||
\(443\) | −10.6949 | −0.508128 | −0.254064 | − | 0.967187i | \(-0.581767\pi\) | ||||
−0.254064 | + | 0.967187i | \(0.581767\pi\) | |||||||
\(444\) | 38.5121 | 1.82770 | ||||||||
\(445\) | 11.5104 | 0.545646 | ||||||||
\(446\) | 47.4222 | 2.24551 | ||||||||
\(447\) | −4.52115 | −0.213843 | ||||||||
\(448\) | 56.2110 | 2.65572 | ||||||||
\(449\) | 13.9203 | 0.656942 | 0.328471 | − | 0.944514i | \(-0.393467\pi\) | ||||
0.328471 | + | 0.944514i | \(0.393467\pi\) | |||||||
\(450\) | −8.72405 | −0.411256 | ||||||||
\(451\) | 17.6775 | 0.832403 | ||||||||
\(452\) | −64.5332 | −3.03539 | ||||||||
\(453\) | 4.08267 | 0.191821 | ||||||||
\(454\) | 23.8430 | 1.11901 | ||||||||
\(455\) | −6.37496 | −0.298863 | ||||||||
\(456\) | −9.67916 | −0.453268 | ||||||||
\(457\) | −13.9019 | −0.650303 | −0.325152 | − | 0.945662i | \(-0.605415\pi\) | ||||
−0.325152 | + | 0.945662i | \(0.605415\pi\) | |||||||
\(458\) | 82.2324 | 3.84247 | ||||||||
\(459\) | −4.38429 | −0.204641 | ||||||||
\(460\) | 54.6858 | 2.54974 | ||||||||
\(461\) | −10.8670 | −0.506125 | −0.253062 | − | 0.967450i | \(-0.581438\pi\) | ||||
−0.253062 | + | 0.967450i | \(0.581438\pi\) | |||||||
\(462\) | 9.80100 | 0.455984 | ||||||||
\(463\) | 1.70025 | 0.0790172 | 0.0395086 | − | 0.999219i | \(-0.487421\pi\) | ||||
0.0395086 | + | 0.999219i | \(0.487421\pi\) | |||||||
\(464\) | −30.7994 | −1.42983 | ||||||||
\(465\) | 30.1456 | 1.39797 | ||||||||
\(466\) | −57.5161 | −2.66438 | ||||||||
\(467\) | 13.4312 | 0.621520 | 0.310760 | − | 0.950488i | \(-0.399416\pi\) | ||||
0.310760 | + | 0.950488i | \(0.399416\pi\) | |||||||
\(468\) | 7.30741 | 0.337785 | ||||||||
\(469\) | 12.4581 | 0.575262 | ||||||||
\(470\) | −49.1898 | −2.26896 | ||||||||
\(471\) | 0.220306 | 0.0101512 | ||||||||
\(472\) | 91.6026 | 4.21635 | ||||||||
\(473\) | 10.4792 | 0.481835 | ||||||||
\(474\) | 1.55044 | 0.0712140 | ||||||||
\(475\) | −3.15960 | −0.144972 | ||||||||
\(476\) | 41.0986 | 1.88375 | ||||||||
\(477\) | −1.58492 | −0.0725684 | ||||||||
\(478\) | −18.4759 | −0.845067 | ||||||||
\(479\) | 22.3516 | 1.02127 | 0.510636 | − | 0.859797i | \(-0.329410\pi\) | ||||
0.510636 | + | 0.859797i | \(0.329410\pi\) | |||||||
\(480\) | −67.1714 | −3.06594 | ||||||||
\(481\) | −9.15932 | −0.417629 | ||||||||
\(482\) | −74.5206 | −3.39432 | ||||||||
\(483\) | 5.83476 | 0.265491 | ||||||||
\(484\) | −36.2913 | −1.64961 | ||||||||
\(485\) | 9.57035 | 0.434567 | ||||||||
\(486\) | 2.74646 | 0.124582 | ||||||||
\(487\) | 21.9576 | 0.994995 | 0.497497 | − | 0.867466i | \(-0.334252\pi\) | ||||
0.497497 | + | 0.867466i | \(0.334252\pi\) | |||||||
\(488\) | 56.1622 | 2.54234 | ||||||||
\(489\) | 9.65358 | 0.436550 | ||||||||
\(490\) | −32.5133 | −1.46880 | ||||||||
\(491\) | −25.8543 | −1.16679 | −0.583393 | − | 0.812190i | \(-0.698275\pi\) | ||||
−0.583393 | + | 0.812190i | \(0.698275\pi\) | |||||||
\(492\) | −46.4358 | −2.09349 | ||||||||
\(493\) | −8.63426 | −0.388868 | ||||||||
\(494\) | 3.60144 | 0.162036 | ||||||||
\(495\) | −6.03393 | −0.271205 | ||||||||
\(496\) | 164.876 | 7.40316 | ||||||||
\(497\) | −5.27726 | −0.236717 | ||||||||
\(498\) | −26.3874 | −1.18245 | ||||||||
\(499\) | −3.55903 | −0.159324 | −0.0796620 | − | 0.996822i | \(-0.525384\pi\) | ||||
−0.0796620 | + | 0.996822i | \(0.525384\pi\) | |||||||
\(500\) | 28.9031 | 1.29259 | ||||||||
\(501\) | −9.54341 | −0.426368 | ||||||||
\(502\) | 45.8810 | 2.04777 | ||||||||
\(503\) | 10.8578 | 0.484126 | 0.242063 | − | 0.970261i | \(-0.422176\pi\) | ||||
0.242063 | + | 0.970261i | \(0.422176\pi\) | |||||||
\(504\) | −16.4562 | −0.733018 | ||||||||
\(505\) | −16.0759 | −0.715368 | ||||||||
\(506\) | 19.9956 | 0.888912 | ||||||||
\(507\) | 11.2621 | 0.500166 | ||||||||
\(508\) | 2.52492 | 0.112025 | ||||||||
\(509\) | −33.6865 | −1.49313 | −0.746565 | − | 0.665313i | \(-0.768298\pi\) | ||||
−0.746565 | + | 0.665313i | \(0.768298\pi\) | |||||||
\(510\) | −34.4315 | −1.52465 | ||||||||
\(511\) | −14.7568 | −0.652801 | ||||||||
\(512\) | −63.0155 | −2.78492 | ||||||||
\(513\) | 0.994689 | 0.0439166 | ||||||||
\(514\) | 19.6036 | 0.864677 | ||||||||
\(515\) | 27.5905 | 1.21578 | ||||||||
\(516\) | −27.5271 | −1.21181 | ||||||||
\(517\) | −13.2171 | −0.581287 | ||||||||
\(518\) | 32.2702 | 1.41787 | ||||||||
\(519\) | 2.24820 | 0.0986852 | ||||||||
\(520\) | 36.6816 | 1.60859 | ||||||||
\(521\) | 17.9861 | 0.787987 | 0.393993 | − | 0.919113i | \(-0.371093\pi\) | ||||
0.393993 | + | 0.919113i | \(0.371093\pi\) | |||||||
\(522\) | 5.40878 | 0.236736 | ||||||||
\(523\) | −3.35948 | −0.146900 | −0.0734500 | − | 0.997299i | \(-0.523401\pi\) | ||||
−0.0734500 | + | 0.997299i | \(0.523401\pi\) | |||||||
\(524\) | −27.0579 | −1.18203 | ||||||||
\(525\) | −5.37186 | −0.234447 | ||||||||
\(526\) | 14.7529 | 0.643256 | ||||||||
\(527\) | 46.2211 | 2.01342 | ||||||||
\(528\) | −33.0015 | −1.43621 | ||||||||
\(529\) | −11.0962 | −0.482442 | ||||||||
\(530\) | −12.4470 | −0.540661 | ||||||||
\(531\) | −9.41363 | −0.408517 | ||||||||
\(532\) | −9.32429 | −0.404259 | ||||||||
\(533\) | 11.0438 | 0.478361 | ||||||||
\(534\) | −11.0556 | −0.478422 | ||||||||
\(535\) | −42.4927 | −1.83712 | ||||||||
\(536\) | −71.6841 | −3.09628 | ||||||||
\(537\) | 22.6124 | 0.975796 | ||||||||
\(538\) | −70.6308 | −3.04511 | ||||||||
\(539\) | −8.73620 | −0.376295 | ||||||||
\(540\) | 15.8501 | 0.682079 | ||||||||
\(541\) | −27.3714 | −1.17679 | −0.588393 | − | 0.808575i | \(-0.700239\pi\) | ||||
−0.588393 | + | 0.808575i | \(0.700239\pi\) | |||||||
\(542\) | −46.5442 | −1.99924 | ||||||||
\(543\) | −5.51831 | −0.236813 | ||||||||
\(544\) | −102.991 | −4.41572 | ||||||||
\(545\) | −23.6701 | −1.01391 | ||||||||
\(546\) | 6.12305 | 0.262043 | ||||||||
\(547\) | 13.4961 | 0.577053 | 0.288527 | − | 0.957472i | \(-0.406835\pi\) | ||||
0.288527 | + | 0.957472i | \(0.406835\pi\) | |||||||
\(548\) | −41.4435 | −1.77038 | ||||||||
\(549\) | −5.77156 | −0.246324 | ||||||||
\(550\) | −18.4092 | −0.784972 | ||||||||
\(551\) | 1.95891 | 0.0834522 | ||||||||
\(552\) | −33.5733 | −1.42897 | ||||||||
\(553\) | 0.954686 | 0.0405974 | ||||||||
\(554\) | 21.0063 | 0.892474 | ||||||||
\(555\) | −19.8669 | −0.843305 | ||||||||
\(556\) | 86.1323 | 3.65282 | ||||||||
\(557\) | 4.55033 | 0.192804 | 0.0964019 | − | 0.995342i | \(-0.469267\pi\) | ||||
0.0964019 | + | 0.995342i | \(0.469267\pi\) | |||||||
\(558\) | −28.9544 | −1.22574 | ||||||||
\(559\) | 6.54676 | 0.276899 | ||||||||
\(560\) | −75.6274 | −3.19584 | ||||||||
\(561\) | −9.25160 | −0.390603 | ||||||||
\(562\) | −8.67917 | −0.366109 | ||||||||
\(563\) | −5.64962 | −0.238103 | −0.119052 | − | 0.992888i | \(-0.537985\pi\) | ||||
−0.119052 | + | 0.992888i | \(0.537985\pi\) | |||||||
\(564\) | 34.7190 | 1.46193 | ||||||||
\(565\) | 33.2903 | 1.40053 | ||||||||
\(566\) | −58.7998 | −2.47154 | ||||||||
\(567\) | 1.69114 | 0.0710212 | ||||||||
\(568\) | 30.3654 | 1.27410 | ||||||||
\(569\) | 6.76448 | 0.283582 | 0.141791 | − | 0.989897i | \(-0.454714\pi\) | ||||
0.141791 | + | 0.989897i | \(0.454714\pi\) | |||||||
\(570\) | 7.81167 | 0.327195 | ||||||||
\(571\) | 29.5683 | 1.23739 | 0.618697 | − | 0.785630i | \(-0.287661\pi\) | ||||
0.618697 | + | 0.785630i | \(0.287661\pi\) | |||||||
\(572\) | 15.4199 | 0.644738 | ||||||||
\(573\) | −21.0522 | −0.879468 | ||||||||
\(574\) | −38.9097 | −1.62406 | ||||||||
\(575\) | −10.9594 | −0.457040 | ||||||||
\(576\) | 33.2385 | 1.38494 | ||||||||
\(577\) | −16.1569 | −0.672622 | −0.336311 | − | 0.941751i | \(-0.609179\pi\) | ||||
−0.336311 | + | 0.941751i | \(0.609179\pi\) | |||||||
\(578\) | −6.10263 | −0.253836 | ||||||||
\(579\) | 0.181678 | 0.00755030 | ||||||||
\(580\) | 31.2146 | 1.29612 | ||||||||
\(581\) | −16.2481 | −0.674084 | ||||||||
\(582\) | −9.19218 | −0.381028 | ||||||||
\(583\) | −3.34445 | −0.138513 | ||||||||
\(584\) | 84.9106 | 3.51363 | ||||||||
\(585\) | −3.76962 | −0.155855 | ||||||||
\(586\) | 75.7725 | 3.13013 | ||||||||
\(587\) | −29.0886 | −1.20061 | −0.600307 | − | 0.799770i | \(-0.704955\pi\) | ||||
−0.600307 | + | 0.799770i | \(0.704955\pi\) | |||||||
\(588\) | 22.9485 | 0.946379 | ||||||||
\(589\) | −10.4865 | −0.432087 | ||||||||
\(590\) | −73.9288 | −3.04360 | ||||||||
\(591\) | 2.81430 | 0.115765 | ||||||||
\(592\) | −108.659 | −4.46585 | ||||||||
\(593\) | 14.8646 | 0.610415 | 0.305207 | − | 0.952286i | \(-0.401274\pi\) | ||||
0.305207 | + | 0.952286i | \(0.401274\pi\) | |||||||
\(594\) | 5.79550 | 0.237792 | ||||||||
\(595\) | −21.2013 | −0.869167 | ||||||||
\(596\) | 25.0610 | 1.02654 | ||||||||
\(597\) | 8.25008 | 0.337653 | ||||||||
\(598\) | 12.4920 | 0.510836 | ||||||||
\(599\) | 15.7234 | 0.642442 | 0.321221 | − | 0.947004i | \(-0.395907\pi\) | ||||
0.321221 | + | 0.947004i | \(0.395907\pi\) | |||||||
\(600\) | 30.9097 | 1.26188 | ||||||||
\(601\) | −3.56659 | −0.145484 | −0.0727421 | − | 0.997351i | \(-0.523175\pi\) | ||||
−0.0727421 | + | 0.997351i | \(0.523175\pi\) | |||||||
\(602\) | −23.0656 | −0.940084 | ||||||||
\(603\) | 7.36669 | 0.299995 | ||||||||
\(604\) | −22.6304 | −0.920820 | ||||||||
\(605\) | 18.7214 | 0.761132 | ||||||||
\(606\) | 15.4406 | 0.627233 | ||||||||
\(607\) | 5.63249 | 0.228616 | 0.114308 | − | 0.993445i | \(-0.463535\pi\) | ||||
0.114308 | + | 0.993445i | \(0.463535\pi\) | |||||||
\(608\) | 23.3662 | 0.947626 | ||||||||
\(609\) | 3.33047 | 0.134958 | ||||||||
\(610\) | −45.3263 | −1.83521 | ||||||||
\(611\) | −8.25722 | −0.334051 | ||||||||
\(612\) | 24.3023 | 0.982363 | ||||||||
\(613\) | −33.3570 | −1.34728 | −0.673638 | − | 0.739062i | \(-0.735269\pi\) | ||||
−0.673638 | + | 0.739062i | \(0.735269\pi\) | |||||||
\(614\) | 64.1988 | 2.59085 | ||||||||
\(615\) | 23.9545 | 0.965939 | ||||||||
\(616\) | −34.7254 | −1.39913 | ||||||||
\(617\) | −34.0842 | −1.37218 | −0.686088 | − | 0.727518i | \(-0.740674\pi\) | ||||
−0.686088 | + | 0.727518i | \(0.740674\pi\) | |||||||
\(618\) | −26.5002 | −1.06600 | ||||||||
\(619\) | −22.6527 | −0.910488 | −0.455244 | − | 0.890367i | \(-0.650448\pi\) | ||||
−0.455244 | + | 0.890367i | \(0.650448\pi\) | |||||||
\(620\) | −167.099 | −6.71084 | ||||||||
\(621\) | 3.45019 | 0.138451 | ||||||||
\(622\) | −31.2775 | −1.25411 | ||||||||
\(623\) | −6.80751 | −0.272737 | ||||||||
\(624\) | −20.6173 | −0.825353 | ||||||||
\(625\) | −30.7924 | −1.23170 | ||||||||
\(626\) | −86.7845 | −3.46861 | ||||||||
\(627\) | 2.09896 | 0.0838245 | ||||||||
\(628\) | −1.22117 | −0.0487299 | ||||||||
\(629\) | −30.4612 | −1.21457 | ||||||||
\(630\) | 13.2812 | 0.529134 | ||||||||
\(631\) | 11.7492 | 0.467730 | 0.233865 | − | 0.972269i | \(-0.424863\pi\) | ||||
0.233865 | + | 0.972269i | \(0.424863\pi\) | |||||||
\(632\) | −5.49328 | −0.218511 | ||||||||
\(633\) | 4.88830 | 0.194293 | ||||||||
\(634\) | −9.48289 | −0.376614 | ||||||||
\(635\) | −1.30251 | −0.0516885 | ||||||||
\(636\) | 8.78528 | 0.348359 | ||||||||
\(637\) | −5.45783 | −0.216247 | ||||||||
\(638\) | 11.4134 | 0.451863 | ||||||||
\(639\) | −3.12053 | −0.123446 | ||||||||
\(640\) | 126.692 | 5.00794 | ||||||||
\(641\) | −29.9914 | −1.18459 | −0.592294 | − | 0.805722i | \(-0.701778\pi\) | ||||
−0.592294 | + | 0.805722i | \(0.701778\pi\) | |||||||
\(642\) | 40.8136 | 1.61078 | ||||||||
\(643\) | −43.3144 | −1.70815 | −0.854076 | − | 0.520148i | \(-0.825877\pi\) | ||||
−0.854076 | + | 0.520148i | \(0.825877\pi\) | |||||||
\(644\) | −32.3424 | −1.27447 | ||||||||
\(645\) | 14.2002 | 0.559132 | ||||||||
\(646\) | 11.9773 | 0.471242 | ||||||||
\(647\) | 33.9303 | 1.33394 | 0.666968 | − | 0.745086i | \(-0.267592\pi\) | ||||
0.666968 | + | 0.745086i | \(0.267592\pi\) | |||||||
\(648\) | −9.73084 | −0.382264 | ||||||||
\(649\) | −19.8644 | −0.779745 | ||||||||
\(650\) | −11.5009 | −0.451104 | ||||||||
\(651\) | −17.8288 | −0.698764 | ||||||||
\(652\) | −53.5102 | −2.09562 | ||||||||
\(653\) | 31.4945 | 1.23248 | 0.616238 | − | 0.787560i | \(-0.288656\pi\) | ||||
0.616238 | + | 0.787560i | \(0.288656\pi\) | |||||||
\(654\) | 22.7347 | 0.888999 | ||||||||
\(655\) | 13.9582 | 0.545390 | ||||||||
\(656\) | 131.015 | 5.11528 | ||||||||
\(657\) | −8.72593 | −0.340431 | ||||||||
\(658\) | 29.0919 | 1.13412 | ||||||||
\(659\) | −31.6154 | −1.23156 | −0.615780 | − | 0.787918i | \(-0.711159\pi\) | ||||
−0.615780 | + | 0.787918i | \(0.711159\pi\) | |||||||
\(660\) | 33.4464 | 1.30190 | ||||||||
\(661\) | −5.75734 | −0.223935 | −0.111967 | − | 0.993712i | \(-0.535715\pi\) | ||||
−0.111967 | + | 0.993712i | \(0.535715\pi\) | |||||||
\(662\) | −39.6170 | −1.53976 | ||||||||
\(663\) | −5.77982 | −0.224470 | ||||||||
\(664\) | 93.4917 | 3.62818 | ||||||||
\(665\) | 4.81005 | 0.186526 | ||||||||
\(666\) | 19.0819 | 0.739408 | ||||||||
\(667\) | 6.79469 | 0.263091 | ||||||||
\(668\) | 52.8996 | 2.04675 | ||||||||
\(669\) | 17.2666 | 0.667567 | ||||||||
\(670\) | 57.8534 | 2.23507 | ||||||||
\(671\) | −12.1790 | −0.470164 | ||||||||
\(672\) | 39.7266 | 1.53249 | ||||||||
\(673\) | −38.2613 | −1.47486 | −0.737432 | − | 0.675421i | \(-0.763962\pi\) | ||||
−0.737432 | + | 0.675421i | \(0.763962\pi\) | |||||||
\(674\) | −53.4590 | −2.05916 | ||||||||
\(675\) | −3.17647 | −0.122262 | ||||||||
\(676\) | −62.4262 | −2.40101 | ||||||||
\(677\) | −5.06528 | −0.194674 | −0.0973372 | − | 0.995251i | \(-0.531033\pi\) | ||||
−0.0973372 | + | 0.995251i | \(0.531033\pi\) | |||||||
\(678\) | −31.9748 | −1.22799 | ||||||||
\(679\) | −5.66011 | −0.217215 | ||||||||
\(680\) | 121.992 | 4.67819 | ||||||||
\(681\) | 8.68134 | 0.332670 | ||||||||
\(682\) | −61.0987 | −2.33959 | ||||||||
\(683\) | −13.3896 | −0.512337 | −0.256169 | − | 0.966632i | \(-0.582460\pi\) | ||||
−0.256169 | + | 0.966632i | \(0.582460\pi\) | |||||||
\(684\) | −5.51361 | −0.210818 | ||||||||
\(685\) | 21.3792 | 0.816857 | ||||||||
\(686\) | 51.7416 | 1.97550 | ||||||||
\(687\) | 29.9412 | 1.14233 | ||||||||
\(688\) | 77.6656 | 2.96097 | ||||||||
\(689\) | −2.08940 | −0.0795999 | ||||||||
\(690\) | 27.0957 | 1.03151 | ||||||||
\(691\) | 3.29591 | 0.125382 | 0.0626912 | − | 0.998033i | \(-0.480032\pi\) | ||||
0.0626912 | + | 0.998033i | \(0.480032\pi\) | |||||||
\(692\) | −12.4619 | −0.473730 | ||||||||
\(693\) | 3.56859 | 0.135560 | ||||||||
\(694\) | −32.9493 | −1.25074 | ||||||||
\(695\) | −44.4324 | −1.68542 | ||||||||
\(696\) | −19.1636 | −0.726393 | ||||||||
\(697\) | 36.7285 | 1.39119 | ||||||||
\(698\) | −0.175822 | −0.00665497 | ||||||||
\(699\) | −20.9419 | −0.792095 | ||||||||
\(700\) | 29.7765 | 1.12544 | ||||||||
\(701\) | −43.1251 | −1.62881 | −0.814406 | − | 0.580295i | \(-0.802937\pi\) | ||||
−0.814406 | + | 0.580295i | \(0.802937\pi\) | |||||||
\(702\) | 3.62067 | 0.136653 | ||||||||
\(703\) | 6.91091 | 0.260650 | ||||||||
\(704\) | 70.1389 | 2.64346 | ||||||||
\(705\) | −17.9102 | −0.674539 | ||||||||
\(706\) | 23.4524 | 0.882644 | ||||||||
\(707\) | 9.50762 | 0.357571 | ||||||||
\(708\) | 52.1802 | 1.96105 | ||||||||
\(709\) | −9.46629 | −0.355514 | −0.177757 | − | 0.984074i | \(-0.556884\pi\) | ||||
−0.177757 | + | 0.984074i | \(0.556884\pi\) | |||||||
\(710\) | −24.5067 | −0.919721 | ||||||||
\(711\) | 0.564522 | 0.0211712 | ||||||||
\(712\) | 39.1705 | 1.46798 | ||||||||
\(713\) | −36.3735 | −1.36220 | ||||||||
\(714\) | 20.3635 | 0.762085 | ||||||||
\(715\) | −7.95455 | −0.297483 | ||||||||
\(716\) | −125.341 | −4.68423 | ||||||||
\(717\) | −6.72716 | −0.251230 | ||||||||
\(718\) | −23.6872 | −0.883999 | ||||||||
\(719\) | 28.9236 | 1.07867 | 0.539335 | − | 0.842091i | \(-0.318676\pi\) | ||||
0.539335 | + | 0.842091i | \(0.318676\pi\) | |||||||
\(720\) | −44.7198 | −1.66661 | ||||||||
\(721\) | −16.3176 | −0.607699 | ||||||||
\(722\) | 49.4654 | 1.84091 | ||||||||
\(723\) | −27.1333 | −1.00910 | ||||||||
\(724\) | 30.5883 | 1.13680 | ||||||||
\(725\) | −6.25563 | −0.232328 | ||||||||
\(726\) | −17.9816 | −0.667359 | ||||||||
\(727\) | 15.6425 | 0.580148 | 0.290074 | − | 0.957004i | \(-0.406320\pi\) | ||||
0.290074 | + | 0.957004i | \(0.406320\pi\) | |||||||
\(728\) | −21.6943 | −0.804043 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −68.5280 | −2.53633 | ||||||||
\(731\) | 21.7726 | 0.805290 | ||||||||
\(732\) | 31.9920 | 1.18246 | ||||||||
\(733\) | −19.2180 | −0.709834 | −0.354917 | − | 0.934898i | \(-0.615491\pi\) | ||||
−0.354917 | + | 0.934898i | \(0.615491\pi\) | |||||||
\(734\) | −7.81116 | −0.288315 | ||||||||
\(735\) | −11.8383 | −0.436661 | ||||||||
\(736\) | 81.0484 | 2.98749 | ||||||||
\(737\) | 15.5450 | 0.572606 | ||||||||
\(738\) | −23.0079 | −0.846934 | ||||||||
\(739\) | 12.5164 | 0.460424 | 0.230212 | − | 0.973140i | \(-0.426058\pi\) | ||||
0.230212 | + | 0.973140i | \(0.426058\pi\) | |||||||
\(740\) | 110.123 | 4.04822 | ||||||||
\(741\) | 1.31130 | 0.0481718 | ||||||||
\(742\) | 7.36139 | 0.270245 | ||||||||
\(743\) | 15.1423 | 0.555516 | 0.277758 | − | 0.960651i | \(-0.410409\pi\) | ||||
0.277758 | + | 0.960651i | \(0.410409\pi\) | |||||||
\(744\) | 102.587 | 3.76102 | ||||||||
\(745\) | −12.9280 | −0.473646 | ||||||||
\(746\) | 56.0949 | 2.05378 | ||||||||
\(747\) | −9.60777 | −0.351530 | ||||||||
\(748\) | 51.2820 | 1.87506 | ||||||||
\(749\) | 25.1311 | 0.918269 | ||||||||
\(750\) | 14.3209 | 0.522924 | ||||||||
\(751\) | −4.84471 | −0.176786 | −0.0883929 | − | 0.996086i | \(-0.528173\pi\) | ||||
−0.0883929 | + | 0.996086i | \(0.528173\pi\) | |||||||
\(752\) | −97.9570 | −3.57212 | ||||||||
\(753\) | 16.7055 | 0.608782 | ||||||||
\(754\) | 7.13041 | 0.259674 | ||||||||
\(755\) | 11.6742 | 0.424868 | ||||||||
\(756\) | −9.37407 | −0.340932 | ||||||||
\(757\) | −47.8734 | −1.73999 | −0.869994 | − | 0.493062i | \(-0.835877\pi\) | ||||
−0.869994 | + | 0.493062i | \(0.835877\pi\) | |||||||
\(758\) | 4.05635 | 0.147333 | ||||||||
\(759\) | 7.28049 | 0.264265 | ||||||||
\(760\) | −27.6771 | −1.00395 | ||||||||
\(761\) | −5.82382 | −0.211113 | −0.105557 | − | 0.994413i | \(-0.533662\pi\) | ||||
−0.105557 | + | 0.994413i | \(0.533662\pi\) | |||||||
\(762\) | 1.25104 | 0.0453204 | ||||||||
\(763\) | 13.9990 | 0.506797 | ||||||||
\(764\) | 116.693 | 4.22182 | ||||||||
\(765\) | −12.5367 | −0.453264 | ||||||||
\(766\) | 34.2399 | 1.23714 | ||||||||
\(767\) | −12.4100 | −0.448100 | ||||||||
\(768\) | −55.2086 | −1.99217 | ||||||||
\(769\) | 42.0154 | 1.51512 | 0.757558 | − | 0.652768i | \(-0.226392\pi\) | ||||
0.757558 | + | 0.652768i | \(0.226392\pi\) | |||||||
\(770\) | 28.0255 | 1.00997 | ||||||||
\(771\) | 7.13776 | 0.257060 | ||||||||
\(772\) | −1.00705 | −0.0362446 | ||||||||
\(773\) | 14.8121 | 0.532755 | 0.266377 | − | 0.963869i | \(-0.414173\pi\) | ||||
0.266377 | + | 0.963869i | \(0.414173\pi\) | |||||||
\(774\) | −13.6391 | −0.490247 | ||||||||
\(775\) | 33.4878 | 1.20292 | ||||||||
\(776\) | 32.5683 | 1.16913 | ||||||||
\(777\) | 11.7497 | 0.421519 | ||||||||
\(778\) | −38.7496 | −1.38924 | ||||||||
\(779\) | −8.33281 | −0.298554 | ||||||||
\(780\) | 20.8952 | 0.748168 | ||||||||
\(781\) | −6.58485 | −0.235625 | ||||||||
\(782\) | 41.5447 | 1.48564 | ||||||||
\(783\) | 1.96936 | 0.0703793 | ||||||||
\(784\) | −64.7473 | −2.31240 | ||||||||
\(785\) | 0.629955 | 0.0224841 | ||||||||
\(786\) | −13.4066 | −0.478198 | ||||||||
\(787\) | 0.437405 | 0.0155918 | 0.00779590 | − | 0.999970i | \(-0.497518\pi\) | ||||
0.00779590 | + | 0.999970i | \(0.497518\pi\) | |||||||
\(788\) | −15.5998 | −0.555720 | ||||||||
\(789\) | 5.37160 | 0.191234 | ||||||||
\(790\) | 4.43340 | 0.157733 | ||||||||
\(791\) | −19.6886 | −0.700045 | ||||||||
\(792\) | −20.5337 | −0.729634 | ||||||||
\(793\) | −7.60867 | −0.270192 | ||||||||
\(794\) | −26.0060 | −0.922919 | ||||||||
\(795\) | −4.53200 | −0.160733 | ||||||||
\(796\) | −45.7306 | −1.62088 | ||||||||
\(797\) | 55.9640 | 1.98235 | 0.991173 | − | 0.132573i | \(-0.0423238\pi\) | ||||
0.991173 | + | 0.132573i | \(0.0423238\pi\) | |||||||
\(798\) | −4.61998 | −0.163546 | ||||||||
\(799\) | −27.4611 | −0.971504 | ||||||||
\(800\) | −74.6184 | −2.63816 | ||||||||
\(801\) | −4.02539 | −0.142230 | ||||||||
\(802\) | −81.3961 | −2.87419 | ||||||||
\(803\) | −18.4132 | −0.649787 | ||||||||
\(804\) | −40.8339 | −1.44010 | ||||||||
\(805\) | 16.6842 | 0.588042 | ||||||||
\(806\) | −38.1707 | −1.34450 | ||||||||
\(807\) | −25.7170 | −0.905282 | ||||||||
\(808\) | −54.7069 | −1.92458 | ||||||||
\(809\) | −32.7203 | −1.15038 | −0.575192 | − | 0.818018i | \(-0.695073\pi\) | ||||
−0.575192 | + | 0.818018i | \(0.695073\pi\) | |||||||
\(810\) | 7.85338 | 0.275939 | ||||||||
\(811\) | −25.7291 | −0.903471 | −0.451736 | − | 0.892152i | \(-0.649195\pi\) | ||||
−0.451736 | + | 0.892152i | \(0.649195\pi\) | |||||||
\(812\) | −18.4610 | −0.647853 | ||||||||
\(813\) | −16.9470 | −0.594356 | ||||||||
\(814\) | 40.2660 | 1.41132 | ||||||||
\(815\) | 27.6039 | 0.966924 | ||||||||
\(816\) | −68.5671 | −2.40033 | ||||||||
\(817\) | −4.93968 | −0.172818 | ||||||||
\(818\) | 56.3895 | 1.97161 | ||||||||
\(819\) | 2.22943 | 0.0779027 | ||||||||
\(820\) | −132.781 | −4.63691 | ||||||||
\(821\) | −21.5467 | −0.751986 | −0.375993 | − | 0.926622i | \(-0.622698\pi\) | ||||
−0.375993 | + | 0.926622i | \(0.622698\pi\) | |||||||
\(822\) | −20.5344 | −0.716219 | ||||||||
\(823\) | −37.4937 | −1.30695 | −0.653475 | − | 0.756948i | \(-0.726689\pi\) | ||||
−0.653475 | + | 0.756948i | \(0.726689\pi\) | |||||||
\(824\) | 93.8916 | 3.27087 | ||||||||
\(825\) | −6.70289 | −0.233365 | ||||||||
\(826\) | 43.7230 | 1.52132 | ||||||||
\(827\) | −29.9469 | −1.04136 | −0.520678 | − | 0.853753i | \(-0.674321\pi\) | ||||
−0.520678 | + | 0.853753i | \(0.674321\pi\) | |||||||
\(828\) | −19.1246 | −0.664625 | ||||||||
\(829\) | −53.8651 | −1.87081 | −0.935407 | − | 0.353574i | \(-0.884966\pi\) | ||||
−0.935407 | + | 0.353574i | \(0.884966\pi\) | |||||||
\(830\) | −75.4534 | −2.61903 | ||||||||
\(831\) | 7.64851 | 0.265324 | ||||||||
\(832\) | 43.8184 | 1.51913 | ||||||||
\(833\) | −18.1512 | −0.628900 | ||||||||
\(834\) | 42.6767 | 1.47777 | ||||||||
\(835\) | −27.2889 | −0.944372 | ||||||||
\(836\) | −11.6347 | −0.402393 | ||||||||
\(837\) | −10.5424 | −0.364400 | ||||||||
\(838\) | −11.4773 | −0.396476 | ||||||||
\(839\) | 3.17579 | 0.109641 | 0.0548203 | − | 0.998496i | \(-0.482541\pi\) | ||||
0.0548203 | + | 0.998496i | \(0.482541\pi\) | |||||||
\(840\) | −47.0558 | −1.62358 | ||||||||
\(841\) | −25.1216 | −0.866262 | ||||||||
\(842\) | −79.4124 | −2.73673 | ||||||||
\(843\) | −3.16013 | −0.108841 | ||||||||
\(844\) | −27.0961 | −0.932686 | ||||||||
\(845\) | 32.2034 | 1.10783 | ||||||||
\(846\) | 17.2025 | 0.591435 | ||||||||
\(847\) | −11.0722 | −0.380446 | ||||||||
\(848\) | −24.7870 | −0.851189 | ||||||||
\(849\) | −21.4093 | −0.734765 | ||||||||
\(850\) | −38.2488 | −1.31192 | ||||||||
\(851\) | 23.9713 | 0.821725 | ||||||||
\(852\) | 17.2973 | 0.592594 | ||||||||
\(853\) | −6.22163 | −0.213025 | −0.106512 | − | 0.994311i | \(-0.533968\pi\) | ||||
−0.106512 | + | 0.994311i | \(0.533968\pi\) | |||||||
\(854\) | 26.8069 | 0.917313 | ||||||||
\(855\) | 2.84427 | 0.0972719 | ||||||||
\(856\) | −144.604 | −4.94248 | ||||||||
\(857\) | 43.6096 | 1.48967 | 0.744837 | − | 0.667246i | \(-0.232527\pi\) | ||||
0.744837 | + | 0.667246i | \(0.232527\pi\) | |||||||
\(858\) | 7.64022 | 0.260833 | ||||||||
\(859\) | 30.3020 | 1.03389 | 0.516945 | − | 0.856019i | \(-0.327069\pi\) | ||||
0.516945 | + | 0.856019i | \(0.327069\pi\) | |||||||
\(860\) | −78.7124 | −2.68407 | ||||||||
\(861\) | −14.1672 | −0.482817 | ||||||||
\(862\) | −105.267 | −3.58542 | ||||||||
\(863\) | −3.10315 | −0.105633 | −0.0528163 | − | 0.998604i | \(-0.516820\pi\) | ||||
−0.0528163 | + | 0.998604i | \(0.516820\pi\) | |||||||
\(864\) | 23.4910 | 0.799180 | ||||||||
\(865\) | 6.42863 | 0.218580 | ||||||||
\(866\) | 24.5495 | 0.834227 | ||||||||
\(867\) | −2.22200 | −0.0754630 | ||||||||
\(868\) | 98.8257 | 3.35436 | ||||||||
\(869\) | 1.19124 | 0.0404100 | ||||||||
\(870\) | 15.4662 | 0.524352 | ||||||||
\(871\) | 9.71152 | 0.329062 | ||||||||
\(872\) | −80.5503 | −2.72778 | ||||||||
\(873\) | −3.34692 | −0.113276 | ||||||||
\(874\) | −9.42549 | −0.318822 | ||||||||
\(875\) | 8.81811 | 0.298106 | ||||||||
\(876\) | 48.3682 | 1.63421 | ||||||||
\(877\) | −24.8936 | −0.840598 | −0.420299 | − | 0.907386i | \(-0.638075\pi\) | ||||
−0.420299 | + | 0.907386i | \(0.638075\pi\) | |||||||
\(878\) | 65.1749 | 2.19955 | ||||||||
\(879\) | 27.5891 | 0.930558 | ||||||||
\(880\) | −94.3663 | −3.18109 | ||||||||
\(881\) | −46.1780 | −1.55578 | −0.777888 | − | 0.628403i | \(-0.783709\pi\) | ||||
−0.777888 | + | 0.628403i | \(0.783709\pi\) | |||||||
\(882\) | 11.3705 | 0.382864 | ||||||||
\(883\) | −46.5572 | −1.56677 | −0.783387 | − | 0.621534i | \(-0.786510\pi\) | ||||
−0.783387 | + | 0.621534i | \(0.786510\pi\) | |||||||
\(884\) | 32.0378 | 1.07755 | ||||||||
\(885\) | −26.9178 | −0.904833 | ||||||||
\(886\) | 29.3730 | 0.986806 | ||||||||
\(887\) | −44.5558 | −1.49604 | −0.748019 | − | 0.663677i | \(-0.768995\pi\) | ||||
−0.748019 | + | 0.663677i | \(0.768995\pi\) | |||||||
\(888\) | −67.6081 | −2.26878 | ||||||||
\(889\) | 0.770332 | 0.0258361 | ||||||||
\(890\) | −31.6129 | −1.05967 | ||||||||
\(891\) | 2.11017 | 0.0706934 | ||||||||
\(892\) | −95.7099 | −3.20460 | ||||||||
\(893\) | 6.23026 | 0.208488 | ||||||||
\(894\) | 12.4172 | 0.415292 | ||||||||
\(895\) | 64.6590 | 2.16131 | ||||||||
\(896\) | −74.9282 | −2.50318 | ||||||||
\(897\) | 4.54840 | 0.151867 | ||||||||
\(898\) | −38.2317 | −1.27581 | ||||||||
\(899\) | −20.7619 | −0.692449 | ||||||||
\(900\) | 17.6073 | 0.586911 | ||||||||
\(901\) | −6.94874 | −0.231496 | ||||||||
\(902\) | −48.5507 | −1.61656 | ||||||||
\(903\) | −8.39830 | −0.279478 | ||||||||
\(904\) | 113.288 | 3.76791 | ||||||||
\(905\) | −15.7793 | −0.524523 | ||||||||
\(906\) | −11.2129 | −0.372524 | ||||||||
\(907\) | −27.9534 | −0.928178 | −0.464089 | − | 0.885789i | \(-0.653618\pi\) | ||||
−0.464089 | + | 0.885789i | \(0.653618\pi\) | |||||||
\(908\) | −48.1211 | −1.59695 | ||||||||
\(909\) | 5.62201 | 0.186470 | ||||||||
\(910\) | 17.5086 | 0.580404 | ||||||||
\(911\) | 40.1941 | 1.33169 | 0.665845 | − | 0.746090i | \(-0.268071\pi\) | ||||
0.665845 | + | 0.746090i | \(0.268071\pi\) | |||||||
\(912\) | 15.5562 | 0.515118 | ||||||||
\(913\) | −20.2740 | −0.670972 | ||||||||
\(914\) | 38.1810 | 1.26292 | ||||||||
\(915\) | −16.5035 | −0.545589 | ||||||||
\(916\) | −165.966 | −5.48366 | ||||||||
\(917\) | −8.25515 | −0.272609 | ||||||||
\(918\) | 12.0413 | 0.397421 | ||||||||
\(919\) | 19.2051 | 0.633518 | 0.316759 | − | 0.948506i | \(-0.397405\pi\) | ||||
0.316759 | + | 0.948506i | \(0.397405\pi\) | |||||||
\(920\) | −96.0012 | −3.16507 | ||||||||
\(921\) | 23.3751 | 0.770236 | ||||||||
\(922\) | 29.8457 | 0.982915 | ||||||||
\(923\) | −4.11381 | −0.135408 | ||||||||
\(924\) | −19.7809 | −0.650743 | ||||||||
\(925\) | −22.0695 | −0.725641 | ||||||||
\(926\) | −4.66967 | −0.153455 | ||||||||
\(927\) | −9.64887 | −0.316910 | ||||||||
\(928\) | 46.2623 | 1.51864 | ||||||||
\(929\) | −35.9039 | −1.17797 | −0.588985 | − | 0.808144i | \(-0.700472\pi\) | ||||
−0.588985 | + | 0.808144i | \(0.700472\pi\) | |||||||
\(930\) | −82.7938 | −2.71492 | ||||||||
\(931\) | 4.11806 | 0.134964 | ||||||||
\(932\) | 116.082 | 3.80239 | ||||||||
\(933\) | −11.3883 | −0.372835 | ||||||||
\(934\) | −36.8882 | −1.20702 | ||||||||
\(935\) | −26.4545 | −0.865155 | ||||||||
\(936\) | −12.8282 | −0.419303 | ||||||||
\(937\) | −42.9330 | −1.40256 | −0.701279 | − | 0.712887i | \(-0.747387\pi\) | ||||
−0.701279 | + | 0.712887i | \(0.747387\pi\) | |||||||
\(938\) | −34.2157 | −1.11718 | ||||||||
\(939\) | −31.5987 | −1.03118 | ||||||||
\(940\) | 99.2773 | 3.23807 | ||||||||
\(941\) | 60.2836 | 1.96519 | 0.982595 | − | 0.185761i | \(-0.0594749\pi\) | ||||
0.982595 | + | 0.185761i | \(0.0594749\pi\) | |||||||
\(942\) | −0.605062 | −0.0197140 | ||||||||
\(943\) | −28.9033 | −0.941221 | ||||||||
\(944\) | −147.222 | −4.79168 | ||||||||
\(945\) | 4.83574 | 0.157307 | ||||||||
\(946\) | −28.7808 | −0.935744 | ||||||||
\(947\) | −60.8483 | −1.97730 | −0.988652 | − | 0.150221i | \(-0.952001\pi\) | ||||
−0.988652 | + | 0.150221i | \(0.952001\pi\) | |||||||
\(948\) | −3.12917 | −0.101631 | ||||||||
\(949\) | −11.5034 | −0.373417 | ||||||||
\(950\) | 8.67772 | 0.281542 | ||||||||
\(951\) | −3.45277 | −0.111964 | ||||||||
\(952\) | −72.1488 | −2.33836 | ||||||||
\(953\) | −14.1760 | −0.459206 | −0.229603 | − | 0.973284i | \(-0.573743\pi\) | ||||
−0.229603 | + | 0.973284i | \(0.573743\pi\) | |||||||
\(954\) | 4.35292 | 0.140931 | ||||||||
\(955\) | −60.1978 | −1.94795 | ||||||||
\(956\) | 37.2889 | 1.20601 | ||||||||
\(957\) | 4.15569 | 0.134334 | ||||||||
\(958\) | −61.3879 | −1.98335 | ||||||||
\(959\) | −12.6441 | −0.408299 | ||||||||
\(960\) | 95.0440 | 3.06753 | ||||||||
\(961\) | 80.1432 | 2.58526 | ||||||||
\(962\) | 25.1557 | 0.811052 | ||||||||
\(963\) | 14.8604 | 0.478871 | ||||||||
\(964\) | 150.401 | 4.84410 | ||||||||
\(965\) | 0.519501 | 0.0167233 | ||||||||
\(966\) | −16.0249 | −0.515594 | ||||||||
\(967\) | −12.3841 | −0.398247 | −0.199124 | − | 0.979974i | \(-0.563809\pi\) | ||||
−0.199124 | + | 0.979974i | \(0.563809\pi\) | |||||||
\(968\) | 63.7096 | 2.04770 | ||||||||
\(969\) | 4.36100 | 0.140096 | ||||||||
\(970\) | −26.2846 | −0.843947 | ||||||||
\(971\) | −12.1908 | −0.391220 | −0.195610 | − | 0.980682i | \(-0.562669\pi\) | ||||
−0.195610 | + | 0.980682i | \(0.562669\pi\) | |||||||
\(972\) | −5.54305 | −0.177793 | ||||||||
\(973\) | 26.2783 | 0.842443 | ||||||||
\(974\) | −60.3057 | −1.93232 | ||||||||
\(975\) | −4.18755 | −0.134109 | ||||||||
\(976\) | −90.2631 | −2.88925 | ||||||||
\(977\) | −40.0697 | −1.28194 | −0.640971 | − | 0.767565i | \(-0.721468\pi\) | ||||
−0.640971 | + | 0.767565i | \(0.721468\pi\) | |||||||
\(978\) | −26.5132 | −0.847798 | ||||||||
\(979\) | −8.49427 | −0.271478 | ||||||||
\(980\) | 65.6200 | 2.09616 | ||||||||
\(981\) | 8.27783 | 0.264291 | ||||||||
\(982\) | 71.0077 | 2.26595 | ||||||||
\(983\) | −3.57628 | −0.114066 | −0.0570329 | − | 0.998372i | \(-0.518164\pi\) | ||||
−0.0570329 | + | 0.998372i | \(0.518164\pi\) | |||||||
\(984\) | 81.5182 | 2.59871 | ||||||||
\(985\) | 8.04736 | 0.256410 | ||||||||
\(986\) | 23.7137 | 0.755197 | ||||||||
\(987\) | 10.5925 | 0.337163 | ||||||||
\(988\) | −7.26860 | −0.231245 | ||||||||
\(989\) | −17.1339 | −0.544825 | ||||||||
\(990\) | 16.5720 | 0.526691 | ||||||||
\(991\) | 9.72926 | 0.309060 | 0.154530 | − | 0.987988i | \(-0.450614\pi\) | ||||
0.154530 | + | 0.987988i | \(0.450614\pi\) | |||||||
\(992\) | −247.653 | −7.86298 | ||||||||
\(993\) | −14.4247 | −0.457755 | ||||||||
\(994\) | 14.4938 | 0.459715 | ||||||||
\(995\) | 23.5907 | 0.747876 | ||||||||
\(996\) | 53.2563 | 1.68749 | ||||||||
\(997\) | 59.0473 | 1.87005 | 0.935023 | − | 0.354586i | \(-0.115378\pi\) | ||||
0.935023 | + | 0.354586i | \(0.115378\pi\) | |||||||
\(998\) | 9.77473 | 0.309414 | ||||||||
\(999\) | 6.94781 | 0.219819 |
(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 | 8013.2.a.c.1.3 | ✓ | 116 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8013.2.a.c.1.3 | ✓ | 116 | 1.1 | even | 1 | trivial |