Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9025,2,Mod(1,9025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9025, 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("9025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9025 = 5^{2} \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9025.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: | \(72.0649878242\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 32 x^{18} + 426 x^{16} - 3061 x^{14} + 12909 x^{12} - 32678 x^{10} + 49159 x^{8} - 42549 x^{6} + \cdots + 405 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Root | \(1.75426\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.75426 | 1.24045 | 0.620226 | − | 0.784424i | \(-0.287041\pi\) | ||||
0.620226 | + | 0.784424i | \(0.287041\pi\) | |||||||
\(3\) | 0.822481 | 0.474859 | 0.237430 | − | 0.971405i | \(-0.423695\pi\) | ||||
0.237430 | + | 0.971405i | \(0.423695\pi\) | |||||||
\(4\) | 1.07744 | 0.538719 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.44285 | 0.589040 | ||||||||
\(7\) | −3.28692 | −1.24234 | −0.621169 | − | 0.783677i | \(-0.713342\pi\) | ||||
−0.621169 | + | 0.783677i | \(0.713342\pi\) | |||||||
\(8\) | −1.61842 | −0.572197 | ||||||||
\(9\) | −2.32353 | −0.774509 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.18053 | 0.355942 | 0.177971 | − | 0.984036i | \(-0.443047\pi\) | ||||
0.177971 | + | 0.984036i | \(0.443047\pi\) | |||||||
\(12\) | 0.886172 | 0.255816 | ||||||||
\(13\) | −3.78272 | −1.04914 | −0.524569 | − | 0.851368i | \(-0.675774\pi\) | ||||
−0.524569 | + | 0.851368i | \(0.675774\pi\) | |||||||
\(14\) | −5.76611 | −1.54106 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.99400 | −1.24850 | ||||||||
\(17\) | 2.75438 | 0.668036 | 0.334018 | − | 0.942567i | \(-0.391595\pi\) | ||||
0.334018 | + | 0.942567i | \(0.391595\pi\) | |||||||
\(18\) | −4.07607 | −0.960740 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.70342 | −0.589936 | ||||||||
\(22\) | 2.07096 | 0.441529 | ||||||||
\(23\) | −3.31465 | −0.691152 | −0.345576 | − | 0.938391i | \(-0.612316\pi\) | ||||
−0.345576 | + | 0.938391i | \(0.612316\pi\) | |||||||
\(24\) | −1.33112 | −0.271713 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −6.63589 | −1.30141 | ||||||||
\(27\) | −4.37850 | −0.842642 | ||||||||
\(28\) | −3.54145 | −0.669271 | ||||||||
\(29\) | 9.75933 | 1.81226 | 0.906131 | − | 0.422996i | \(-0.139022\pi\) | ||||
0.906131 | + | 0.422996i | \(0.139022\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.66191 | −0.298488 | −0.149244 | − | 0.988800i | \(-0.547684\pi\) | ||||
−0.149244 | + | 0.988800i | \(0.547684\pi\) | |||||||
\(32\) | −5.52396 | −0.976508 | ||||||||
\(33\) | 0.970961 | 0.169023 | ||||||||
\(34\) | 4.83191 | 0.828665 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.50345 | −0.417242 | ||||||||
\(37\) | 8.47172 | 1.39274 | 0.696371 | − | 0.717682i | \(-0.254797\pi\) | ||||
0.696371 | + | 0.717682i | \(0.254797\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.11122 | −0.498193 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.81804 | −0.908624 | −0.454312 | − | 0.890843i | \(-0.650115\pi\) | ||||
−0.454312 | + | 0.890843i | \(0.650115\pi\) | |||||||
\(42\) | −4.74252 | −0.731786 | ||||||||
\(43\) | 4.63105 | 0.706229 | 0.353115 | − | 0.935580i | \(-0.385123\pi\) | ||||
0.353115 | + | 0.935580i | \(0.385123\pi\) | |||||||
\(44\) | 1.27195 | 0.191753 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.81477 | −0.857340 | ||||||||
\(47\) | 8.63909 | 1.26014 | 0.630071 | − | 0.776538i | \(-0.283026\pi\) | ||||
0.630071 | + | 0.776538i | \(0.283026\pi\) | |||||||
\(48\) | −4.10747 | −0.592862 | ||||||||
\(49\) | 3.80382 | 0.543403 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.26543 | 0.317223 | ||||||||
\(52\) | −4.07565 | −0.565191 | ||||||||
\(53\) | −0.0828551 | −0.0113810 | −0.00569051 | − | 0.999984i | \(-0.501811\pi\) | ||||
−0.00569051 | + | 0.999984i | \(0.501811\pi\) | |||||||
\(54\) | −7.68103 | −1.04526 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 5.31960 | 0.710861 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 17.1204 | 2.24802 | ||||||||
\(59\) | 4.80786 | 0.625930 | 0.312965 | − | 0.949765i | \(-0.398678\pi\) | ||||
0.312965 | + | 0.949765i | \(0.398678\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.01041 | 0.129370 | 0.0646850 | − | 0.997906i | \(-0.479396\pi\) | ||||
0.0646850 | + | 0.997906i | \(0.479396\pi\) | |||||||
\(62\) | −2.91542 | −0.370259 | ||||||||
\(63\) | 7.63723 | 0.962201 | ||||||||
\(64\) | 0.297527 | 0.0371909 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.70332 | 0.209664 | ||||||||
\(67\) | 8.59954 | 1.05060 | 0.525301 | − | 0.850917i | \(-0.323953\pi\) | ||||
0.525301 | + | 0.850917i | \(0.323953\pi\) | |||||||
\(68\) | 2.96767 | 0.359883 | ||||||||
\(69\) | −2.72623 | −0.328200 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.01790 | −0.595515 | −0.297758 | − | 0.954642i | \(-0.596239\pi\) | ||||
−0.297758 | + | 0.954642i | \(0.596239\pi\) | |||||||
\(72\) | 3.76043 | 0.443171 | ||||||||
\(73\) | 14.7801 | 1.72988 | 0.864940 | − | 0.501876i | \(-0.167356\pi\) | ||||
0.864940 | + | 0.501876i | \(0.167356\pi\) | |||||||
\(74\) | 14.8616 | 1.72763 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.88030 | −0.442201 | ||||||||
\(78\) | −5.45789 | −0.617984 | ||||||||
\(79\) | 13.9448 | 1.56891 | 0.784455 | − | 0.620185i | \(-0.212943\pi\) | ||||
0.784455 | + | 0.620185i | \(0.212943\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.36935 | 0.374372 | ||||||||
\(82\) | −10.2064 | −1.12710 | ||||||||
\(83\) | 11.8189 | 1.29729 | 0.648646 | − | 0.761090i | \(-0.275335\pi\) | ||||
0.648646 | + | 0.761090i | \(0.275335\pi\) | |||||||
\(84\) | −2.91277 | −0.317810 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 8.12409 | 0.876043 | ||||||||
\(87\) | 8.02686 | 0.860570 | ||||||||
\(88\) | −1.91059 | −0.203669 | ||||||||
\(89\) | 15.1049 | 1.60111 | 0.800556 | − | 0.599258i | \(-0.204538\pi\) | ||||
0.800556 | + | 0.599258i | \(0.204538\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.4335 | 1.30338 | ||||||||
\(92\) | −3.57133 | −0.372337 | ||||||||
\(93\) | −1.36689 | −0.141740 | ||||||||
\(94\) | 15.1552 | 1.56314 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −4.54335 | −0.463704 | ||||||||
\(97\) | −10.9874 | −1.11560 | −0.557802 | − | 0.829974i | \(-0.688355\pi\) | ||||
−0.557802 | + | 0.829974i | \(0.688355\pi\) | |||||||
\(98\) | 6.67290 | 0.674064 | ||||||||
\(99\) | −2.74299 | −0.275680 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.2361 | −1.21753 | −0.608767 | − | 0.793349i | \(-0.708336\pi\) | ||||
−0.608767 | + | 0.793349i | \(0.708336\pi\) | |||||||
\(102\) | 3.97415 | 0.393500 | ||||||||
\(103\) | −7.75916 | −0.764533 | −0.382266 | − | 0.924052i | \(-0.624856\pi\) | ||||
−0.382266 | + | 0.924052i | \(0.624856\pi\) | |||||||
\(104\) | 6.12202 | 0.600314 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.145350 | −0.0141176 | ||||||||
\(107\) | −6.28028 | −0.607138 | −0.303569 | − | 0.952809i | \(-0.598178\pi\) | ||||
−0.303569 | + | 0.952809i | \(0.598178\pi\) | |||||||
\(108\) | −4.71756 | −0.453947 | ||||||||
\(109\) | −20.2061 | −1.93539 | −0.967695 | − | 0.252125i | \(-0.918870\pi\) | ||||
−0.967695 | + | 0.252125i | \(0.918870\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.96783 | 0.661357 | ||||||||
\(112\) | 16.4149 | 1.55106 | ||||||||
\(113\) | 9.73195 | 0.915505 | 0.457752 | − | 0.889080i | \(-0.348655\pi\) | ||||
0.457752 | + | 0.889080i | \(0.348655\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 10.5151 | 0.976300 | ||||||||
\(117\) | 8.78925 | 0.812567 | ||||||||
\(118\) | 8.43424 | 0.776435 | ||||||||
\(119\) | −9.05342 | −0.829926 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.60635 | −0.873305 | ||||||||
\(122\) | 1.77253 | 0.160477 | ||||||||
\(123\) | −4.78522 | −0.431469 | ||||||||
\(124\) | −1.79060 | −0.160801 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 13.3977 | 1.19356 | ||||||||
\(127\) | 11.1672 | 0.990927 | 0.495464 | − | 0.868629i | \(-0.334998\pi\) | ||||
0.495464 | + | 0.868629i | \(0.334998\pi\) | |||||||
\(128\) | 11.5699 | 1.02264 | ||||||||
\(129\) | 3.80895 | 0.335360 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.2556 | −1.07077 | −0.535387 | − | 0.844607i | \(-0.679834\pi\) | ||||
−0.535387 | + | 0.844607i | \(0.679834\pi\) | |||||||
\(132\) | 1.04615 | 0.0910557 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 15.0859 | 1.30322 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.45774 | −0.382248 | ||||||||
\(137\) | 18.5506 | 1.58488 | 0.792440 | − | 0.609949i | \(-0.208810\pi\) | ||||
0.792440 | + | 0.609949i | \(0.208810\pi\) | |||||||
\(138\) | −4.78253 | −0.407116 | ||||||||
\(139\) | −11.1960 | −0.949635 | −0.474817 | − | 0.880084i | \(-0.657486\pi\) | ||||
−0.474817 | + | 0.880084i | \(0.657486\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.10549 | 0.598390 | ||||||||
\(142\) | −8.80271 | −0.738707 | ||||||||
\(143\) | −4.46561 | −0.373433 | ||||||||
\(144\) | 11.6037 | 0.966975 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 25.9282 | 2.14583 | ||||||||
\(147\) | 3.12857 | 0.258040 | ||||||||
\(148\) | 9.12775 | 0.750297 | ||||||||
\(149\) | −18.2403 | −1.49430 | −0.747150 | − | 0.664656i | \(-0.768578\pi\) | ||||
−0.747150 | + | 0.664656i | \(0.768578\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.19473 | −0.585499 | −0.292749 | − | 0.956189i | \(-0.594570\pi\) | ||||
−0.292749 | + | 0.956189i | \(0.594570\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.39988 | −0.517399 | ||||||||
\(154\) | −6.80706 | −0.548528 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −3.35214 | −0.268386 | ||||||||
\(157\) | −7.73363 | −0.617211 | −0.308605 | − | 0.951190i | \(-0.599862\pi\) | ||||
−0.308605 | + | 0.951190i | \(0.599862\pi\) | |||||||
\(158\) | 24.4628 | 1.94616 | ||||||||
\(159\) | −0.0681467 | −0.00540439 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.8950 | 0.858644 | ||||||||
\(162\) | 5.91072 | 0.464390 | ||||||||
\(163\) | −22.4050 | −1.75490 | −0.877448 | − | 0.479671i | \(-0.840756\pi\) | ||||
−0.877448 | + | 0.479671i | \(0.840756\pi\) | |||||||
\(164\) | −6.26857 | −0.489493 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 20.7335 | 1.60923 | ||||||||
\(167\) | 24.5234 | 1.89768 | 0.948839 | − | 0.315759i | \(-0.102259\pi\) | ||||
0.948839 | + | 0.315759i | \(0.102259\pi\) | |||||||
\(168\) | 4.37527 | 0.337559 | ||||||||
\(169\) | 1.30899 | 0.100692 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.98967 | 0.380459 | ||||||||
\(173\) | 14.0400 | 1.06744 | 0.533721 | − | 0.845661i | \(-0.320793\pi\) | ||||
0.533721 | + | 0.845661i | \(0.320793\pi\) | |||||||
\(174\) | 14.0812 | 1.06750 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −5.89556 | −0.444394 | ||||||||
\(177\) | 3.95437 | 0.297229 | ||||||||
\(178\) | 26.4979 | 1.98610 | ||||||||
\(179\) | −6.63809 | −0.496154 | −0.248077 | − | 0.968740i | \(-0.579799\pi\) | ||||
−0.248077 | + | 0.968740i | \(0.579799\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.7329 | 1.09509 | 0.547546 | − | 0.836776i | \(-0.315562\pi\) | ||||
0.547546 | + | 0.836776i | \(0.315562\pi\) | |||||||
\(182\) | 21.8116 | 1.61678 | ||||||||
\(183\) | 0.831044 | 0.0614325 | ||||||||
\(184\) | 5.36448 | 0.395475 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2.39788 | −0.175821 | ||||||||
\(187\) | 3.25162 | 0.237782 | ||||||||
\(188\) | 9.30809 | 0.678862 | ||||||||
\(189\) | 14.3918 | 1.04685 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.363561 | 0.0263064 | 0.0131532 | − | 0.999913i | \(-0.495813\pi\) | ||||
0.0131532 | + | 0.999913i | \(0.495813\pi\) | |||||||
\(192\) | 0.244710 | 0.0176604 | ||||||||
\(193\) | 4.06780 | 0.292807 | 0.146403 | − | 0.989225i | \(-0.453230\pi\) | ||||
0.146403 | + | 0.989225i | \(0.453230\pi\) | |||||||
\(194\) | −19.2748 | −1.38385 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.09838 | 0.292741 | ||||||||
\(197\) | −2.78703 | −0.198568 | −0.0992840 | − | 0.995059i | \(-0.531655\pi\) | ||||
−0.0992840 | + | 0.995059i | \(0.531655\pi\) | |||||||
\(198\) | −4.81192 | −0.341968 | ||||||||
\(199\) | 15.7467 | 1.11625 | 0.558126 | − | 0.829756i | \(-0.311521\pi\) | ||||
0.558126 | + | 0.829756i | \(0.311521\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.07296 | 0.498888 | ||||||||
\(202\) | −21.4653 | −1.51029 | ||||||||
\(203\) | −32.0781 | −2.25144 | ||||||||
\(204\) | 2.44085 | 0.170894 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −13.6116 | −0.948365 | ||||||||
\(207\) | 7.70167 | 0.535303 | ||||||||
\(208\) | 18.8909 | 1.30985 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.88685 | −0.129896 | −0.0649481 | − | 0.997889i | \(-0.520688\pi\) | ||||
−0.0649481 | + | 0.997889i | \(0.520688\pi\) | |||||||
\(212\) | −0.0892713 | −0.00613117 | ||||||||
\(213\) | −4.12712 | −0.282786 | ||||||||
\(214\) | −11.0173 | −0.753125 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 7.08623 | 0.482157 | ||||||||
\(217\) | 5.46255 | 0.370822 | ||||||||
\(218\) | −35.4467 | −2.40076 | ||||||||
\(219\) | 12.1563 | 0.821450 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.4191 | −0.700862 | ||||||||
\(222\) | 12.2234 | 0.820381 | ||||||||
\(223\) | −21.5427 | −1.44261 | −0.721305 | − | 0.692618i | \(-0.756457\pi\) | ||||
−0.721305 | + | 0.692618i | \(0.756457\pi\) | |||||||
\(224\) | 18.1568 | 1.21315 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 17.0724 | 1.13564 | ||||||||
\(227\) | 3.39937 | 0.225624 | 0.112812 | − | 0.993616i | \(-0.464014\pi\) | ||||
0.112812 | + | 0.993616i | \(0.464014\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.5113 | 1.42151 | 0.710753 | − | 0.703442i | \(-0.248355\pi\) | ||||
0.710753 | + | 0.703442i | \(0.248355\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.19147 | −0.209983 | ||||||||
\(232\) | −15.7947 | −1.03697 | ||||||||
\(233\) | −1.52013 | −0.0995871 | −0.0497935 | − | 0.998760i | \(-0.515856\pi\) | ||||
−0.0497935 | + | 0.998760i | \(0.515856\pi\) | |||||||
\(234\) | 15.4187 | 1.00795 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 5.18017 | 0.337200 | ||||||||
\(237\) | 11.4693 | 0.745012 | ||||||||
\(238\) | −15.8821 | −1.02948 | ||||||||
\(239\) | 24.8318 | 1.60624 | 0.803118 | − | 0.595820i | \(-0.203173\pi\) | ||||
0.803118 | + | 0.595820i | \(0.203173\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.3790 | 0.668572 | 0.334286 | − | 0.942472i | \(-0.391505\pi\) | ||||
0.334286 | + | 0.942472i | \(0.391505\pi\) | |||||||
\(242\) | −16.8521 | −1.08329 | ||||||||
\(243\) | 15.9067 | 1.02042 | ||||||||
\(244\) | 1.08866 | 0.0696940 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −8.39454 | −0.535216 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 2.68966 | 0.170794 | ||||||||
\(249\) | 9.72082 | 0.616032 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −22.3378 | −1.40995 | −0.704974 | − | 0.709233i | \(-0.749041\pi\) | ||||
−0.704974 | + | 0.709233i | \(0.749041\pi\) | |||||||
\(252\) | 8.22865 | 0.518356 | ||||||||
\(253\) | −3.91303 | −0.246010 | ||||||||
\(254\) | 19.5902 | 1.22920 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 19.7015 | 1.23135 | ||||||||
\(257\) | −16.4731 | −1.02756 | −0.513780 | − | 0.857922i | \(-0.671755\pi\) | ||||
−0.513780 | + | 0.857922i | \(0.671755\pi\) | |||||||
\(258\) | 6.68190 | 0.415997 | ||||||||
\(259\) | −27.8458 | −1.73026 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −22.6761 | −1.40361 | ||||||||
\(262\) | −21.4995 | −1.32824 | ||||||||
\(263\) | 6.76045 | 0.416867 | 0.208434 | − | 0.978037i | \(-0.433163\pi\) | ||||
0.208434 | + | 0.978037i | \(0.433163\pi\) | |||||||
\(264\) | −1.57142 | −0.0967142 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.4235 | 0.760303 | ||||||||
\(268\) | 9.26548 | 0.565979 | ||||||||
\(269\) | 13.1958 | 0.804562 | 0.402281 | − | 0.915516i | \(-0.368217\pi\) | ||||
0.402281 | + | 0.915516i | \(0.368217\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 31.0774 | 1.88782 | 0.943908 | − | 0.330209i | \(-0.107119\pi\) | ||||
0.943908 | + | 0.330209i | \(0.107119\pi\) | |||||||
\(272\) | −13.7554 | −0.834043 | ||||||||
\(273\) | 10.2263 | 0.618924 | ||||||||
\(274\) | 32.5425 | 1.96597 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2.93735 | −0.176808 | ||||||||
\(277\) | 10.8765 | 0.653505 | 0.326753 | − | 0.945110i | \(-0.394046\pi\) | ||||
0.326753 | + | 0.945110i | \(0.394046\pi\) | |||||||
\(278\) | −19.6408 | −1.17798 | ||||||||
\(279\) | 3.86149 | 0.231181 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.3306 | −0.616271 | −0.308135 | − | 0.951343i | \(-0.599705\pi\) | ||||
−0.308135 | + | 0.951343i | \(0.599705\pi\) | |||||||
\(282\) | 12.4649 | 0.742273 | ||||||||
\(283\) | −15.4014 | −0.915517 | −0.457758 | − | 0.889077i | \(-0.651347\pi\) | ||||
−0.457758 | + | 0.889077i | \(0.651347\pi\) | |||||||
\(284\) | −5.40647 | −0.320815 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −7.83385 | −0.463225 | ||||||||
\(287\) | 19.1234 | 1.12882 | ||||||||
\(288\) | 12.8351 | 0.756314 | ||||||||
\(289\) | −9.41338 | −0.553728 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.03695 | −0.529755 | ||||||||
\(292\) | 15.9246 | 0.931919 | ||||||||
\(293\) | −4.61862 | −0.269823 | −0.134911 | − | 0.990858i | \(-0.543075\pi\) | ||||
−0.134911 | + | 0.990858i | \(0.543075\pi\) | |||||||
\(294\) | 5.48833 | 0.320086 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −13.7108 | −0.796922 | ||||||||
\(297\) | −5.16894 | −0.299932 | ||||||||
\(298\) | −31.9982 | −1.85361 | ||||||||
\(299\) | 12.5384 | 0.725114 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −15.2219 | −0.877375 | ||||||||
\(302\) | −12.6215 | −0.726283 | ||||||||
\(303\) | −10.0639 | −0.578157 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −11.2271 | −0.641808 | ||||||||
\(307\) | 23.4626 | 1.33908 | 0.669541 | − | 0.742775i | \(-0.266491\pi\) | ||||
0.669541 | + | 0.742775i | \(0.266491\pi\) | |||||||
\(308\) | −4.18078 | −0.238222 | ||||||||
\(309\) | −6.38176 | −0.363045 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.7514 | −0.666363 | −0.333181 | − | 0.942863i | \(-0.608122\pi\) | ||||
−0.333181 | + | 0.942863i | \(0.608122\pi\) | |||||||
\(312\) | 5.03524 | 0.285065 | ||||||||
\(313\) | −10.6986 | −0.604722 | −0.302361 | − | 0.953193i | \(-0.597775\pi\) | ||||
−0.302361 | + | 0.953193i | \(0.597775\pi\) | |||||||
\(314\) | −13.5668 | −0.765620 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 15.0246 | 0.845202 | ||||||||
\(317\) | −0.144196 | −0.00809886 | −0.00404943 | − | 0.999992i | \(-0.501289\pi\) | ||||
−0.00404943 | + | 0.999992i | \(0.501289\pi\) | |||||||
\(318\) | −0.119547 | −0.00670388 | ||||||||
\(319\) | 11.5212 | 0.645061 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.16541 | −0.288305 | ||||||||
\(322\) | 19.1126 | 1.06511 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 3.63026 | 0.201681 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −39.3043 | −2.17686 | ||||||||
\(327\) | −16.6191 | −0.919038 | ||||||||
\(328\) | 9.41600 | 0.519912 | ||||||||
\(329\) | −28.3960 | −1.56552 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.5397 | 1.12896 | 0.564481 | − | 0.825446i | \(-0.309076\pi\) | ||||
0.564481 | + | 0.825446i | \(0.309076\pi\) | |||||||
\(332\) | 12.7341 | 0.698876 | ||||||||
\(333\) | −19.6843 | −1.07869 | ||||||||
\(334\) | 43.0205 | 2.35398 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 13.5009 | 0.736535 | ||||||||
\(337\) | −14.8076 | −0.806620 | −0.403310 | − | 0.915063i | \(-0.632140\pi\) | ||||
−0.403310 | + | 0.915063i | \(0.632140\pi\) | |||||||
\(338\) | 2.29632 | 0.124903 | ||||||||
\(339\) | 8.00434 | 0.434736 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.96193 | −0.106244 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.5056 | 0.567248 | ||||||||
\(344\) | −7.49498 | −0.404102 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 24.6298 | 1.32411 | ||||||||
\(347\) | −5.25982 | −0.282362 | −0.141181 | − | 0.989984i | \(-0.545090\pi\) | ||||
−0.141181 | + | 0.989984i | \(0.545090\pi\) | |||||||
\(348\) | 8.64845 | 0.463605 | ||||||||
\(349\) | 8.86326 | 0.474439 | 0.237220 | − | 0.971456i | \(-0.423764\pi\) | ||||
0.237220 | + | 0.971456i | \(0.423764\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 16.5626 | 0.884048 | ||||||||
\(352\) | −6.52119 | −0.347581 | ||||||||
\(353\) | 18.5459 | 0.987099 | 0.493550 | − | 0.869718i | \(-0.335699\pi\) | ||||
0.493550 | + | 0.869718i | \(0.335699\pi\) | |||||||
\(354\) | 6.93700 | 0.368698 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 16.2745 | 0.862549 | ||||||||
\(357\) | −7.44626 | −0.394098 | ||||||||
\(358\) | −11.6450 | −0.615455 | ||||||||
\(359\) | 21.6459 | 1.14243 | 0.571214 | − | 0.820801i | \(-0.306473\pi\) | ||||
0.571214 | + | 0.820801i | \(0.306473\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 25.8455 | 1.35841 | ||||||||
\(363\) | −7.90104 | −0.414697 | ||||||||
\(364\) | 13.3963 | 0.702158 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.45787 | 0.0762041 | ||||||||
\(367\) | 18.0042 | 0.939813 | 0.469907 | − | 0.882716i | \(-0.344288\pi\) | ||||
0.469907 | + | 0.882716i | \(0.344288\pi\) | |||||||
\(368\) | 16.5534 | 0.862904 | ||||||||
\(369\) | 13.5184 | 0.703737 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.272338 | 0.0141391 | ||||||||
\(372\) | −1.47274 | −0.0763578 | ||||||||
\(373\) | −15.5878 | −0.807104 | −0.403552 | − | 0.914957i | \(-0.632225\pi\) | ||||
−0.403552 | + | 0.914957i | \(0.632225\pi\) | |||||||
\(374\) | 5.70420 | 0.294957 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −13.9817 | −0.721049 | ||||||||
\(377\) | −36.9169 | −1.90131 | ||||||||
\(378\) | 25.2469 | 1.29856 | ||||||||
\(379\) | 19.1906 | 0.985753 | 0.492876 | − | 0.870099i | \(-0.335945\pi\) | ||||
0.492876 | + | 0.870099i | \(0.335945\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.18479 | 0.470551 | ||||||||
\(382\) | 0.637782 | 0.0326317 | ||||||||
\(383\) | −1.19446 | −0.0610343 | −0.0305171 | − | 0.999534i | \(-0.509715\pi\) | ||||
−0.0305171 | + | 0.999534i | \(0.509715\pi\) | |||||||
\(384\) | 9.51599 | 0.485611 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 7.13599 | 0.363212 | ||||||||
\(387\) | −10.7604 | −0.546981 | ||||||||
\(388\) | −11.8383 | −0.600997 | ||||||||
\(389\) | −18.9387 | −0.960232 | −0.480116 | − | 0.877205i | \(-0.659405\pi\) | ||||
−0.480116 | + | 0.877205i | \(0.659405\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.12981 | −0.461714 | ||||||||
\(392\) | −6.15616 | −0.310933 | ||||||||
\(393\) | −10.0800 | −0.508467 | ||||||||
\(394\) | −4.88919 | −0.246314 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −2.95540 | −0.148514 | ||||||||
\(397\) | 7.08835 | 0.355754 | 0.177877 | − | 0.984053i | \(-0.443077\pi\) | ||||
0.177877 | + | 0.984053i | \(0.443077\pi\) | |||||||
\(398\) | 27.6238 | 1.38466 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −17.6177 | −0.879786 | −0.439893 | − | 0.898050i | \(-0.644984\pi\) | ||||
−0.439893 | + | 0.898050i | \(0.644984\pi\) | |||||||
\(402\) | 12.4078 | 0.618846 | ||||||||
\(403\) | 6.28654 | 0.313155 | ||||||||
\(404\) | −13.1836 | −0.655909 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −56.2734 | −2.79280 | ||||||||
\(407\) | 10.0011 | 0.495736 | ||||||||
\(408\) | −3.66640 | −0.181514 | ||||||||
\(409\) | 6.28149 | 0.310600 | 0.155300 | − | 0.987867i | \(-0.450366\pi\) | ||||
0.155300 | + | 0.987867i | \(0.450366\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 15.2575 | 0.752596 | ||||||||
\(412\) | −8.36001 | −0.411868 | ||||||||
\(413\) | −15.8030 | −0.777616 | ||||||||
\(414\) | 13.5108 | 0.664017 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 20.8956 | 1.02449 | ||||||||
\(417\) | −9.20851 | −0.450943 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 26.7472 | 1.30669 | 0.653343 | − | 0.757062i | \(-0.273366\pi\) | ||||
0.653343 | + | 0.757062i | \(0.273366\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 35.1919 | 1.71515 | 0.857573 | − | 0.514362i | \(-0.171971\pi\) | ||||
0.857573 | + | 0.514362i | \(0.171971\pi\) | |||||||
\(422\) | −3.31003 | −0.161130 | ||||||||
\(423\) | −20.0732 | −0.975990 | ||||||||
\(424\) | 0.134094 | 0.00651219 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −7.24006 | −0.350782 | ||||||||
\(427\) | −3.32114 | −0.160721 | ||||||||
\(428\) | −6.76661 | −0.327077 | ||||||||
\(429\) | −3.67288 | −0.177328 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.4602 | −0.792860 | −0.396430 | − | 0.918065i | \(-0.629751\pi\) | ||||
−0.396430 | + | 0.918065i | \(0.629751\pi\) | |||||||
\(432\) | 21.8662 | 1.05204 | ||||||||
\(433\) | 13.3712 | 0.642579 | 0.321289 | − | 0.946981i | \(-0.395884\pi\) | ||||
0.321289 | + | 0.946981i | \(0.395884\pi\) | |||||||
\(434\) | 9.58275 | 0.459987 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −21.7708 | −1.04263 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 21.3254 | 1.01897 | ||||||||
\(439\) | −18.1159 | −0.864623 | −0.432312 | − | 0.901724i | \(-0.642302\pi\) | ||||
−0.432312 | + | 0.901724i | \(0.642302\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −8.83827 | −0.420870 | ||||||||
\(442\) | −18.2778 | −0.869385 | ||||||||
\(443\) | −0.868020 | −0.0412409 | −0.0206204 | − | 0.999787i | \(-0.506564\pi\) | ||||
−0.0206204 | + | 0.999787i | \(0.506564\pi\) | |||||||
\(444\) | 7.50740 | 0.356285 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −37.7916 | −1.78949 | ||||||||
\(447\) | −15.0023 | −0.709582 | ||||||||
\(448\) | −0.977946 | −0.0462036 | ||||||||
\(449\) | −16.9428 | −0.799578 | −0.399789 | − | 0.916607i | \(-0.630917\pi\) | ||||
−0.399789 | + | 0.916607i | \(0.630917\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.86835 | −0.323418 | ||||||||
\(452\) | 10.4856 | 0.493200 | ||||||||
\(453\) | −5.91753 | −0.278030 | ||||||||
\(454\) | 5.96339 | 0.279876 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −22.8692 | −1.06977 | −0.534887 | − | 0.844924i | \(-0.679646\pi\) | ||||
−0.534887 | + | 0.844924i | \(0.679646\pi\) | |||||||
\(458\) | 37.7364 | 1.76331 | ||||||||
\(459\) | −12.0600 | −0.562915 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −30.5780 | −1.42416 | −0.712079 | − | 0.702100i | \(-0.752246\pi\) | ||||
−0.712079 | + | 0.702100i | \(0.752246\pi\) | |||||||
\(462\) | −5.59867 | −0.260474 | ||||||||
\(463\) | 22.5471 | 1.04785 | 0.523927 | − | 0.851763i | \(-0.324467\pi\) | ||||
0.523927 | + | 0.851763i | \(0.324467\pi\) | |||||||
\(464\) | −48.7381 | −2.26261 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.66671 | −0.123533 | ||||||||
\(467\) | 8.45394 | 0.391202 | 0.195601 | − | 0.980684i | \(-0.437334\pi\) | ||||
0.195601 | + | 0.980684i | \(0.437334\pi\) | |||||||
\(468\) | 9.46987 | 0.437745 | ||||||||
\(469\) | −28.2660 | −1.30520 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.36076 | −0.293088 | ||||||||
\(472\) | −7.78112 | −0.358155 | ||||||||
\(473\) | 5.46709 | 0.251377 | ||||||||
\(474\) | 20.1202 | 0.924151 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −9.75450 | −0.447097 | ||||||||
\(477\) | 0.192516 | 0.00881470 | ||||||||
\(478\) | 43.5615 | 1.99246 | ||||||||
\(479\) | 9.94732 | 0.454505 | 0.227252 | − | 0.973836i | \(-0.427026\pi\) | ||||
0.227252 | + | 0.973836i | \(0.427026\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −32.0462 | −1.46118 | ||||||||
\(482\) | 18.2075 | 0.829331 | ||||||||
\(483\) | 8.96091 | 0.407735 | ||||||||
\(484\) | −10.3503 | −0.470466 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 27.9046 | 1.26578 | ||||||||
\(487\) | 30.2632 | 1.37136 | 0.685679 | − | 0.727904i | \(-0.259506\pi\) | ||||
0.685679 | + | 0.727904i | \(0.259506\pi\) | |||||||
\(488\) | −1.63527 | −0.0740251 | ||||||||
\(489\) | −18.4277 | −0.833329 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.7209 | 0.799732 | 0.399866 | − | 0.916574i | \(-0.369057\pi\) | ||||
0.399866 | + | 0.916574i | \(0.369057\pi\) | |||||||
\(492\) | −5.15578 | −0.232440 | ||||||||
\(493\) | 26.8809 | 1.21066 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.29958 | 0.372662 | ||||||||
\(497\) | 16.4934 | 0.739831 | ||||||||
\(498\) | 17.0529 | 0.764157 | ||||||||
\(499\) | 38.8961 | 1.74123 | 0.870614 | − | 0.491967i | \(-0.163722\pi\) | ||||
0.870614 | + | 0.491967i | \(0.163722\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 20.1700 | 0.901131 | ||||||||
\(502\) | −39.1863 | −1.74897 | ||||||||
\(503\) | −18.7202 | −0.834692 | −0.417346 | − | 0.908748i | \(-0.637040\pi\) | ||||
−0.417346 | + | 0.908748i | \(0.637040\pi\) | |||||||
\(504\) | −12.3602 | −0.550568 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −6.86449 | −0.305164 | ||||||||
\(507\) | 1.07662 | 0.0478144 | ||||||||
\(508\) | 12.0319 | 0.533831 | ||||||||
\(509\) | −9.43885 | −0.418370 | −0.209185 | − | 0.977876i | \(-0.567081\pi\) | ||||
−0.209185 | + | 0.977876i | \(0.567081\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −48.5809 | −2.14909 | ||||||||
\(512\) | 11.4219 | 0.504783 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −28.8981 | −1.27464 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 4.10391 | 0.180665 | ||||||||
\(517\) | 10.1987 | 0.448538 | ||||||||
\(518\) | −48.8489 | −2.14630 | ||||||||
\(519\) | 11.5476 | 0.506884 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.91656 | 0.171587 | 0.0857937 | − | 0.996313i | \(-0.472657\pi\) | ||||
0.0857937 | + | 0.996313i | \(0.472657\pi\) | |||||||
\(522\) | −39.7798 | −1.74111 | ||||||||
\(523\) | 11.9016 | 0.520419 | 0.260210 | − | 0.965552i | \(-0.416208\pi\) | ||||
0.260210 | + | 0.965552i | \(0.416208\pi\) | |||||||
\(524\) | −13.2046 | −0.576847 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 11.8596 | 0.517103 | ||||||||
\(527\) | −4.57753 | −0.199400 | ||||||||
\(528\) | −4.84898 | −0.211025 | ||||||||
\(529\) | −12.0131 | −0.522309 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −11.1712 | −0.484788 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 22.0080 | 0.953273 | ||||||||
\(534\) | 21.7940 | 0.943118 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −13.9176 | −0.601151 | ||||||||
\(537\) | −5.45970 | −0.235604 | ||||||||
\(538\) | 23.1489 | 0.998020 | ||||||||
\(539\) | 4.49051 | 0.193420 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21.7564 | 0.935381 | 0.467691 | − | 0.883892i | \(-0.345086\pi\) | ||||
0.467691 | + | 0.883892i | \(0.345086\pi\) | |||||||
\(542\) | 54.5179 | 2.34174 | ||||||||
\(543\) | 12.1176 | 0.520014 | ||||||||
\(544\) | −15.2151 | −0.652342 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 17.9396 | 0.767745 | ||||||||
\(547\) | 22.2776 | 0.952521 | 0.476261 | − | 0.879304i | \(-0.341992\pi\) | ||||
0.476261 | + | 0.879304i | \(0.341992\pi\) | |||||||
\(548\) | 19.9871 | 0.853805 | ||||||||
\(549\) | −2.34772 | −0.100198 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 4.41218 | 0.187795 | ||||||||
\(553\) | −45.8353 | −1.94912 | ||||||||
\(554\) | 19.0802 | 0.810641 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −12.0630 | −0.511586 | ||||||||
\(557\) | 43.9900 | 1.86392 | 0.931958 | − | 0.362566i | \(-0.118099\pi\) | ||||
0.931958 | + | 0.362566i | \(0.118099\pi\) | |||||||
\(558\) | 6.77406 | 0.286769 | ||||||||
\(559\) | −17.5180 | −0.740932 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.67440 | 0.112913 | ||||||||
\(562\) | −18.1226 | −0.764454 | ||||||||
\(563\) | 4.06538 | 0.171335 | 0.0856677 | − | 0.996324i | \(-0.472698\pi\) | ||||
0.0856677 | + | 0.996324i | \(0.472698\pi\) | |||||||
\(564\) | 7.65572 | 0.322364 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −27.0181 | −1.13565 | ||||||||
\(567\) | −11.0748 | −0.465096 | ||||||||
\(568\) | 8.12105 | 0.340752 | ||||||||
\(569\) | 12.6422 | 0.529988 | 0.264994 | − | 0.964250i | \(-0.414630\pi\) | ||||
0.264994 | + | 0.964250i | \(0.414630\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −28.4993 | −1.19266 | −0.596329 | − | 0.802740i | \(-0.703375\pi\) | ||||
−0.596329 | + | 0.802740i | \(0.703375\pi\) | |||||||
\(572\) | −4.81142 | −0.201175 | ||||||||
\(573\) | 0.299022 | 0.0124918 | ||||||||
\(574\) | 33.5475 | 1.40024 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.691312 | −0.0288047 | ||||||||
\(577\) | 35.2404 | 1.46708 | 0.733538 | − | 0.679649i | \(-0.237868\pi\) | ||||
0.733538 | + | 0.679649i | \(0.237868\pi\) | |||||||
\(578\) | −16.5135 | −0.686873 | ||||||||
\(579\) | 3.34569 | 0.139042 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −38.8477 | −1.61168 | ||||||||
\(582\) | −15.8532 | −0.657135 | ||||||||
\(583\) | −0.0978128 | −0.00405099 | ||||||||
\(584\) | −23.9204 | −0.989831 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −8.10227 | −0.334702 | ||||||||
\(587\) | −3.38822 | −0.139847 | −0.0699235 | − | 0.997552i | \(-0.522276\pi\) | ||||
−0.0699235 | + | 0.997552i | \(0.522276\pi\) | |||||||
\(588\) | 3.37084 | 0.139011 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.29228 | −0.0942919 | ||||||||
\(592\) | −42.3078 | −1.73884 | ||||||||
\(593\) | 10.8479 | 0.445471 | 0.222735 | − | 0.974879i | \(-0.428501\pi\) | ||||
0.222735 | + | 0.974879i | \(0.428501\pi\) | |||||||
\(594\) | −9.06767 | −0.372051 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −19.6527 | −0.805007 | ||||||||
\(597\) | 12.9513 | 0.530063 | ||||||||
\(598\) | 21.9956 | 0.899469 | ||||||||
\(599\) | −13.3422 | −0.545148 | −0.272574 | − | 0.962135i | \(-0.587875\pi\) | ||||
−0.272574 | + | 0.962135i | \(0.587875\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.4985 | 0.917734 | 0.458867 | − | 0.888505i | \(-0.348256\pi\) | ||||
0.458867 | + | 0.888505i | \(0.348256\pi\) | |||||||
\(602\) | −26.7032 | −1.08834 | ||||||||
\(603\) | −19.9813 | −0.813700 | ||||||||
\(604\) | −7.75188 | −0.315419 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −17.6548 | −0.717176 | ||||||||
\(607\) | −10.0129 | −0.406411 | −0.203206 | − | 0.979136i | \(-0.565136\pi\) | ||||
−0.203206 | + | 0.979136i | \(0.565136\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −26.3836 | −1.06912 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −32.6793 | −1.32206 | ||||||||
\(612\) | −6.89547 | −0.278733 | ||||||||
\(613\) | 17.0655 | 0.689268 | 0.344634 | − | 0.938737i | \(-0.388003\pi\) | ||||
0.344634 | + | 0.938737i | \(0.388003\pi\) | |||||||
\(614\) | 41.1596 | 1.66106 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.27993 | 0.253026 | ||||||||
\(617\) | −9.23533 | −0.371800 | −0.185900 | − | 0.982569i | \(-0.559520\pi\) | ||||
−0.185900 | + | 0.982569i | \(0.559520\pi\) | |||||||
\(618\) | −11.1953 | −0.450340 | ||||||||
\(619\) | −43.9538 | −1.76665 | −0.883325 | − | 0.468761i | \(-0.844701\pi\) | ||||
−0.883325 | + | 0.468761i | \(0.844701\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 14.5132 | 0.582394 | ||||||||
\(622\) | −20.6151 | −0.826591 | ||||||||
\(623\) | −49.6484 | −1.98912 | ||||||||
\(624\) | 15.5374 | 0.621995 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −18.7682 | −0.750128 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −8.33250 | −0.332503 | ||||||||
\(629\) | 23.3343 | 0.930401 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 49.7923 | 1.98220 | 0.991101 | − | 0.133114i | \(-0.0424975\pi\) | ||||
0.991101 | + | 0.133114i | \(0.0424975\pi\) | |||||||
\(632\) | −22.5685 | −0.897725 | ||||||||
\(633\) | −1.55190 | −0.0616824 | ||||||||
\(634\) | −0.252958 | −0.0100462 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.0734239 | −0.00291145 | ||||||||
\(637\) | −14.3888 | −0.570105 | ||||||||
\(638\) | 20.2111 | 0.800167 | ||||||||
\(639\) | 11.6592 | 0.461232 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −29.5597 | −1.16754 | −0.583769 | − | 0.811920i | \(-0.698423\pi\) | ||||
−0.583769 | + | 0.811920i | \(0.698423\pi\) | |||||||
\(642\) | −9.06149 | −0.357628 | ||||||||
\(643\) | −3.65094 | −0.143979 | −0.0719895 | − | 0.997405i | \(-0.522935\pi\) | ||||
−0.0719895 | + | 0.997405i | \(0.522935\pi\) | |||||||
\(644\) | 11.7387 | 0.462568 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 11.2901 | 0.443858 | 0.221929 | − | 0.975063i | \(-0.428765\pi\) | ||||
0.221929 | + | 0.975063i | \(0.428765\pi\) | |||||||
\(648\) | −5.45301 | −0.214214 | ||||||||
\(649\) | 5.67581 | 0.222795 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.49284 | 0.176088 | ||||||||
\(652\) | −24.1400 | −0.945396 | ||||||||
\(653\) | 28.5362 | 1.11671 | 0.558353 | − | 0.829603i | \(-0.311433\pi\) | ||||
0.558353 | + | 0.829603i | \(0.311433\pi\) | |||||||
\(654\) | −29.1542 | −1.14002 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 29.0553 | 1.13442 | ||||||||
\(657\) | −34.3419 | −1.33981 | ||||||||
\(658\) | −49.8140 | −1.94195 | ||||||||
\(659\) | −42.7200 | −1.66413 | −0.832067 | − | 0.554675i | \(-0.812843\pi\) | ||||
−0.832067 | + | 0.554675i | \(0.812843\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15.0393 | −0.584961 | −0.292480 | − | 0.956271i | \(-0.594481\pi\) | ||||
−0.292480 | + | 0.956271i | \(0.594481\pi\) | |||||||
\(662\) | 36.0320 | 1.40042 | ||||||||
\(663\) | −8.56948 | −0.332811 | ||||||||
\(664\) | −19.1279 | −0.742307 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −34.5314 | −1.33806 | ||||||||
\(667\) | −32.3488 | −1.25255 | ||||||||
\(668\) | 26.4225 | 1.02232 | ||||||||
\(669\) | −17.7185 | −0.685037 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.19282 | 0.0460483 | ||||||||
\(672\) | 14.9336 | 0.576077 | ||||||||
\(673\) | 16.0734 | 0.619584 | 0.309792 | − | 0.950804i | \(-0.399741\pi\) | ||||
0.309792 | + | 0.950804i | \(0.399741\pi\) | |||||||
\(674\) | −25.9764 | −1.00057 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.41036 | 0.0542445 | ||||||||
\(677\) | 41.6435 | 1.60049 | 0.800244 | − | 0.599674i | \(-0.204703\pi\) | ||||
0.800244 | + | 0.599674i | \(0.204703\pi\) | |||||||
\(678\) | 14.0417 | 0.539269 | ||||||||
\(679\) | 36.1148 | 1.38596 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.79591 | 0.107140 | ||||||||
\(682\) | −3.44174 | −0.131791 | ||||||||
\(683\) | −13.5982 | −0.520322 | −0.260161 | − | 0.965565i | \(-0.583776\pi\) | ||||
−0.260161 | + | 0.965565i | \(0.583776\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 18.4295 | 0.703643 | ||||||||
\(687\) | 17.6926 | 0.675015 | ||||||||
\(688\) | −23.1275 | −0.881728 | ||||||||
\(689\) | 0.313418 | 0.0119403 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 40.7185 | 1.54900 | 0.774502 | − | 0.632571i | \(-0.218000\pi\) | ||||
0.774502 | + | 0.632571i | \(0.218000\pi\) | |||||||
\(692\) | 15.1272 | 0.575051 | ||||||||
\(693\) | 9.01597 | 0.342488 | ||||||||
\(694\) | −9.22711 | −0.350256 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −12.9908 | −0.492415 | ||||||||
\(697\) | −16.0251 | −0.606993 | ||||||||
\(698\) | 15.5485 | 0.588519 | ||||||||
\(699\) | −1.25028 | −0.0472899 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.66455 | −0.138408 | −0.0692040 | − | 0.997603i | \(-0.522046\pi\) | ||||
−0.0692040 | + | 0.997603i | \(0.522046\pi\) | |||||||
\(702\) | 29.0552 | 1.09662 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0.351239 | 0.0132378 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 32.5344 | 1.22445 | ||||||||
\(707\) | 40.2189 | 1.51259 | ||||||||
\(708\) | 4.26059 | 0.160123 | ||||||||
\(709\) | 10.2722 | 0.385779 | 0.192890 | − | 0.981220i | \(-0.438214\pi\) | ||||
0.192890 | + | 0.981220i | \(0.438214\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −32.4011 | −1.21513 | ||||||||
\(712\) | −24.4459 | −0.916151 | ||||||||
\(713\) | 5.50864 | 0.206300 | ||||||||
\(714\) | −13.0627 | −0.488859 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −7.15213 | −0.267288 | ||||||||
\(717\) | 20.4237 | 0.762737 | ||||||||
\(718\) | 37.9726 | 1.41713 | ||||||||
\(719\) | 31.4259 | 1.17199 | 0.585995 | − | 0.810315i | \(-0.300704\pi\) | ||||
0.585995 | + | 0.810315i | \(0.300704\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 25.5037 | 0.949807 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 8.53655 | 0.317478 | ||||||||
\(724\) | 15.8738 | 0.589947 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −13.8605 | −0.514411 | ||||||||
\(727\) | 15.0853 | 0.559484 | 0.279742 | − | 0.960075i | \(-0.409751\pi\) | ||||
0.279742 | + | 0.960075i | \(0.409751\pi\) | |||||||
\(728\) | −20.1226 | −0.745792 | ||||||||
\(729\) | 2.97492 | 0.110182 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12.7557 | 0.471786 | ||||||||
\(732\) | 0.895398 | 0.0330949 | ||||||||
\(733\) | 23.6607 | 0.873930 | 0.436965 | − | 0.899479i | \(-0.356053\pi\) | ||||
0.436965 | + | 0.899479i | \(0.356053\pi\) | |||||||
\(734\) | 31.5841 | 1.16579 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 18.3100 | 0.674915 | ||||||||
\(737\) | 10.1520 | 0.373954 | ||||||||
\(738\) | 23.7147 | 0.872952 | ||||||||
\(739\) | 15.4199 | 0.567231 | 0.283615 | − | 0.958938i | \(-0.408466\pi\) | ||||
0.283615 | + | 0.958938i | \(0.408466\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.477752 | 0.0175388 | ||||||||
\(743\) | −25.9872 | −0.953378 | −0.476689 | − | 0.879072i | \(-0.658163\pi\) | ||||
−0.476689 | + | 0.879072i | \(0.658163\pi\) | |||||||
\(744\) | 2.21219 | 0.0811029 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −27.3450 | −1.00117 | ||||||||
\(747\) | −27.4615 | −1.00476 | ||||||||
\(748\) | 3.50342 | 0.128098 | ||||||||
\(749\) | 20.6428 | 0.754270 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.25003 | −0.228067 | −0.114033 | − | 0.993477i | \(-0.536377\pi\) | ||||
−0.114033 | + | 0.993477i | \(0.536377\pi\) | |||||||
\(752\) | −43.1437 | −1.57329 | ||||||||
\(753\) | −18.3724 | −0.669527 | ||||||||
\(754\) | −64.7619 | −2.35849 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 15.5062 | 0.563956 | ||||||||
\(757\) | 1.86179 | 0.0676678 | 0.0338339 | − | 0.999427i | \(-0.489228\pi\) | ||||
0.0338339 | + | 0.999427i | \(0.489228\pi\) | |||||||
\(758\) | 33.6653 | 1.22278 | ||||||||
\(759\) | −3.21840 | −0.116820 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −21.8059 | −0.790463 | −0.395231 | − | 0.918582i | \(-0.629336\pi\) | ||||
−0.395231 | + | 0.918582i | \(0.629336\pi\) | |||||||
\(762\) | 16.1125 | 0.583696 | ||||||||
\(763\) | 66.4156 | 2.40441 | ||||||||
\(764\) | 0.391714 | 0.0141717 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.09540 | −0.0757100 | ||||||||
\(767\) | −18.1868 | −0.656687 | ||||||||
\(768\) | 16.2041 | 0.584716 | ||||||||
\(769\) | −30.2405 | −1.09050 | −0.545250 | − | 0.838273i | \(-0.683565\pi\) | ||||
−0.545250 | + | 0.838273i | \(0.683565\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13.5488 | −0.487947 | ||||||||
\(772\) | 4.38280 | 0.157740 | ||||||||
\(773\) | 23.8034 | 0.856149 | 0.428074 | − | 0.903744i | \(-0.359192\pi\) | ||||
0.428074 | + | 0.903744i | \(0.359192\pi\) | |||||||
\(774\) | −18.8765 | −0.678503 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 17.7822 | 0.638345 | ||||||||
\(777\) | −22.9027 | −0.821628 | ||||||||
\(778\) | −33.2235 | −1.19112 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.92377 | −0.211969 | ||||||||
\(782\) | −16.0161 | −0.572734 | ||||||||
\(783\) | −42.7312 | −1.52709 | ||||||||
\(784\) | −18.9963 | −0.678439 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −17.6829 | −0.630729 | ||||||||
\(787\) | −0.635412 | −0.0226500 | −0.0113250 | − | 0.999936i | \(-0.503605\pi\) | ||||
−0.0113250 | + | 0.999936i | \(0.503605\pi\) | |||||||
\(788\) | −3.00286 | −0.106972 | ||||||||
\(789\) | 5.56034 | 0.197953 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −31.9881 | −1.13737 | ||||||||
\(792\) | 4.43929 | 0.157743 | ||||||||
\(793\) | −3.82211 | −0.135727 | ||||||||
\(794\) | 12.4348 | 0.441295 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 16.9661 | 0.601346 | ||||||||
\(797\) | −29.6702 | −1.05097 | −0.525486 | − | 0.850802i | \(-0.676117\pi\) | ||||
−0.525486 | + | 0.850802i | \(0.676117\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 23.7954 | 0.841819 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −35.0965 | −1.24007 | ||||||||
\(802\) | −30.9061 | −1.09133 | ||||||||
\(803\) | 17.4483 | 0.615738 | ||||||||
\(804\) | 7.62067 | 0.268760 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 11.0282 | 0.388453 | ||||||||
\(807\) | 10.8533 | 0.382054 | ||||||||
\(808\) | 19.8030 | 0.696669 | ||||||||
\(809\) | −23.2880 | −0.818764 | −0.409382 | − | 0.912363i | \(-0.634256\pi\) | ||||
−0.409382 | + | 0.912363i | \(0.634256\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −52.6829 | −1.84995 | −0.924974 | − | 0.380031i | \(-0.875913\pi\) | ||||
−0.924974 | + | 0.380031i | \(0.875913\pi\) | |||||||
\(812\) | −34.5622 | −1.21289 | ||||||||
\(813\) | 25.5605 | 0.896447 | ||||||||
\(814\) | 17.5446 | 0.614936 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −11.3135 | −0.396053 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 11.0194 | 0.385284 | ||||||||
\(819\) | −28.8895 | −1.00948 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25.2205 | 0.880202 | 0.440101 | − | 0.897948i | \(-0.354943\pi\) | ||||
0.440101 | + | 0.897948i | \(0.354943\pi\) | |||||||
\(822\) | 26.7656 | 0.933558 | ||||||||
\(823\) | 4.78467 | 0.166783 | 0.0833916 | − | 0.996517i | \(-0.473425\pi\) | ||||
0.0833916 | + | 0.996517i | \(0.473425\pi\) | |||||||
\(824\) | 12.5575 | 0.437463 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −27.7227 | −0.964595 | ||||||||
\(827\) | −11.2608 | −0.391578 | −0.195789 | − | 0.980646i | \(-0.562727\pi\) | ||||
−0.195789 | + | 0.980646i | \(0.562727\pi\) | |||||||
\(828\) | 8.29807 | 0.288378 | ||||||||
\(829\) | −11.7132 | −0.406816 | −0.203408 | − | 0.979094i | \(-0.565202\pi\) | ||||
−0.203408 | + | 0.979094i | \(0.565202\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.94570 | 0.310323 | ||||||||
\(832\) | −1.12546 | −0.0390184 | ||||||||
\(833\) | 10.4772 | 0.363012 | ||||||||
\(834\) | −16.1542 | −0.559373 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.27666 | 0.251518 | ||||||||
\(838\) | 46.9216 | 1.62088 | ||||||||
\(839\) | −51.9732 | −1.79431 | −0.897157 | − | 0.441712i | \(-0.854371\pi\) | ||||
−0.897157 | + | 0.441712i | \(0.854371\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 66.2446 | 2.28430 | ||||||||
\(842\) | 61.7358 | 2.12755 | ||||||||
\(843\) | −8.49670 | −0.292642 | ||||||||
\(844\) | −2.03297 | −0.0699775 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −35.2136 | −1.21067 | ||||||||
\(847\) | 31.5753 | 1.08494 | ||||||||
\(848\) | 0.413779 | 0.0142092 | ||||||||
\(849\) | −12.6673 | −0.434742 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −28.0808 | −0.962597 | ||||||||
\(852\) | −4.44672 | −0.152342 | ||||||||
\(853\) | 2.23758 | 0.0766132 | 0.0383066 | − | 0.999266i | \(-0.487804\pi\) | ||||
0.0383066 | + | 0.999266i | \(0.487804\pi\) | |||||||
\(854\) | −5.82615 | −0.199367 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 10.1641 | 0.347402 | ||||||||
\(857\) | 49.8445 | 1.70266 | 0.851328 | − | 0.524634i | \(-0.175798\pi\) | ||||
0.851328 | + | 0.524634i | \(0.175798\pi\) | |||||||
\(858\) | −6.44319 | −0.219967 | ||||||||
\(859\) | 13.4945 | 0.460426 | 0.230213 | − | 0.973140i | \(-0.426058\pi\) | ||||
0.230213 | + | 0.973140i | \(0.426058\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 15.7286 | 0.536030 | ||||||||
\(862\) | −28.8755 | −0.983504 | ||||||||
\(863\) | −15.7231 | −0.535221 | −0.267610 | − | 0.963527i | \(-0.586234\pi\) | ||||
−0.267610 | + | 0.963527i | \(0.586234\pi\) | |||||||
\(864\) | 24.1866 | 0.822846 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 23.4566 | 0.797087 | ||||||||
\(867\) | −7.74233 | −0.262943 | ||||||||
\(868\) | 5.88556 | 0.199769 | ||||||||
\(869\) | 16.4622 | 0.558442 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −32.5297 | −1.10223 | ||||||||
\(872\) | 32.7018 | 1.10742 | ||||||||
\(873\) | 25.5296 | 0.864045 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 13.0977 | 0.442530 | ||||||||
\(877\) | −5.92134 | −0.199949 | −0.0999747 | − | 0.994990i | \(-0.531876\pi\) | ||||
−0.0999747 | + | 0.994990i | \(0.531876\pi\) | |||||||
\(878\) | −31.7800 | −1.07252 | ||||||||
\(879\) | −3.79872 | −0.128128 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −11.9843 | −0.403761 | −0.201880 | − | 0.979410i | \(-0.564705\pi\) | ||||
−0.201880 | + | 0.979410i | \(0.564705\pi\) | |||||||
\(882\) | −15.5046 | −0.522069 | ||||||||
\(883\) | 42.2882 | 1.42311 | 0.711556 | − | 0.702630i | \(-0.247991\pi\) | ||||
0.711556 | + | 0.702630i | \(0.247991\pi\) | |||||||
\(884\) | −11.2259 | −0.377568 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.52274 | −0.0511573 | ||||||||
\(887\) | −54.7820 | −1.83940 | −0.919700 | − | 0.392622i | \(-0.871568\pi\) | ||||
−0.919700 | + | 0.392622i | \(0.871568\pi\) | |||||||
\(888\) | −11.2768 | −0.378426 | ||||||||
\(889\) | −36.7056 | −1.23107 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.97761 | 0.133255 | ||||||||
\(892\) | −23.2110 | −0.777161 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −26.3179 | −0.880202 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −38.0292 | −1.27047 | ||||||||
\(897\) | 10.3126 | 0.344327 | ||||||||
\(898\) | −29.7220 | −0.991838 | ||||||||
\(899\) | −16.2191 | −0.540938 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.228215 | −0.00760293 | ||||||||
\(902\) | −12.0489 | −0.401184 | ||||||||
\(903\) | −12.5197 | −0.416630 | ||||||||
\(904\) | −15.7504 | −0.523849 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −10.3809 | −0.344882 | ||||||||
\(907\) | 10.4933 | 0.348424 | 0.174212 | − | 0.984708i | \(-0.444262\pi\) | ||||
0.174212 | + | 0.984708i | \(0.444262\pi\) | |||||||
\(908\) | 3.66261 | 0.121548 | ||||||||
\(909\) | 28.4308 | 0.942990 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18.3295 | 0.607282 | 0.303641 | − | 0.952786i | \(-0.401798\pi\) | ||||
0.303641 | + | 0.952786i | \(0.401798\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 13.9525 | 0.461762 | ||||||||
\(914\) | −40.1185 | −1.32700 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 23.1771 | 0.765792 | ||||||||
\(917\) | 40.2831 | 1.33026 | ||||||||
\(918\) | −21.1565 | −0.698268 | ||||||||
\(919\) | 9.34747 | 0.308345 | 0.154172 | − | 0.988044i | \(-0.450729\pi\) | ||||
0.154172 | + | 0.988044i | \(0.450729\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 19.2975 | 0.635875 | ||||||||
\(922\) | −53.6418 | −1.76660 | ||||||||
\(923\) | 18.9813 | 0.624778 | ||||||||
\(924\) | −3.43861 | −0.113122 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 39.5536 | 1.29981 | ||||||||
\(927\) | 18.0286 | 0.592137 | ||||||||
\(928\) | −53.9102 | −1.76969 | ||||||||
\(929\) | −49.4310 | −1.62178 | −0.810889 | − | 0.585199i | \(-0.801016\pi\) | ||||
−0.810889 | + | 0.585199i | \(0.801016\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −1.63785 | −0.0536495 | ||||||||
\(933\) | −9.66533 | −0.316429 | ||||||||
\(934\) | 14.8304 | 0.485267 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −14.2247 | −0.464948 | ||||||||
\(937\) | 47.5613 | 1.55376 | 0.776879 | − | 0.629649i | \(-0.216801\pi\) | ||||
0.776879 | + | 0.629649i | \(0.216801\pi\) | |||||||
\(938\) | −49.5860 | −1.61904 | ||||||||
\(939\) | −8.79941 | −0.287158 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −29.3057 | −0.955338 | −0.477669 | − | 0.878540i | \(-0.658518\pi\) | ||||
−0.477669 | + | 0.878540i | \(0.658518\pi\) | |||||||
\(942\) | −11.1584 | −0.363562 | ||||||||
\(943\) | 19.2847 | 0.627998 | ||||||||
\(944\) | −24.0105 | −0.781474 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 9.59071 | 0.311821 | ||||||||
\(947\) | 51.1324 | 1.66158 | 0.830790 | − | 0.556586i | \(-0.187889\pi\) | ||||
0.830790 | + | 0.556586i | \(0.187889\pi\) | |||||||
\(948\) | 12.3575 | 0.401352 | ||||||||
\(949\) | −55.9090 | −1.81488 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.118598 | −0.00384582 | ||||||||
\(952\) | 14.6522 | 0.474881 | ||||||||
\(953\) | −46.8750 | −1.51843 | −0.759214 | − | 0.650841i | \(-0.774417\pi\) | ||||
−0.759214 | + | 0.650841i | \(0.774417\pi\) | |||||||
\(954\) | 0.337724 | 0.0109342 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 26.7547 | 0.865310 | ||||||||
\(957\) | 9.47593 | 0.306313 | ||||||||
\(958\) | 17.4502 | 0.563791 | ||||||||
\(959\) | −60.9741 | −1.96896 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.2381 | −0.910905 | ||||||||
\(962\) | −56.2174 | −1.81252 | ||||||||
\(963\) | 14.5924 | 0.470233 | ||||||||
\(964\) | 11.1828 | 0.360172 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 15.7198 | 0.505776 | ||||||||
\(967\) | 16.2364 | 0.522127 | 0.261064 | − | 0.965322i | \(-0.415927\pi\) | ||||
0.261064 | + | 0.965322i | \(0.415927\pi\) | |||||||
\(968\) | 15.5471 | 0.499702 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −42.0596 | −1.34976 | −0.674879 | − | 0.737928i | \(-0.735804\pi\) | ||||
−0.674879 | + | 0.737928i | \(0.735804\pi\) | |||||||
\(972\) | 17.1385 | 0.549717 | ||||||||
\(973\) | 36.8004 | 1.17977 | ||||||||
\(974\) | 53.0896 | 1.70110 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.04600 | −0.161519 | ||||||||
\(977\) | −21.1766 | −0.677498 | −0.338749 | − | 0.940877i | \(-0.610004\pi\) | ||||
−0.338749 | + | 0.940877i | \(0.610004\pi\) | |||||||
\(978\) | −32.3270 | −1.03370 | ||||||||
\(979\) | 17.8317 | 0.569904 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 46.9493 | 1.49898 | ||||||||
\(982\) | 31.0871 | 0.992028 | ||||||||
\(983\) | −57.8160 | −1.84404 | −0.922022 | − | 0.387138i | \(-0.873464\pi\) | ||||
−0.922022 | + | 0.387138i | \(0.873464\pi\) | |||||||
\(984\) | 7.74448 | 0.246885 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 47.1562 | 1.50176 | ||||||||
\(987\) | −23.3551 | −0.743402 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −15.3503 | −0.488112 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.78874 | 0.0885872 | 0.0442936 | − | 0.999019i | \(-0.485896\pi\) | ||||
0.0442936 | + | 0.999019i | \(0.485896\pi\) | |||||||
\(992\) | 9.18032 | 0.291475 | ||||||||
\(993\) | 16.8935 | 0.536098 | ||||||||
\(994\) | 28.9338 | 0.917724 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 10.4736 | 0.331868 | ||||||||
\(997\) | −11.9770 | −0.379316 | −0.189658 | − | 0.981850i | \(-0.560738\pi\) | ||||
−0.189658 | + | 0.981850i | \(0.560738\pi\) | |||||||
\(998\) | 68.2339 | 2.15991 | ||||||||
\(999\) | −37.0934 | −1.17358 |
(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 | 9025.2.a.co.1.16 | yes | 20 | |
5.4 | even | 2 | 9025.2.a.cn.1.5 | ✓ | 20 | ||
19.18 | odd | 2 | inner | 9025.2.a.co.1.5 | yes | 20 | |
95.94 | odd | 2 | 9025.2.a.cn.1.16 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
9025.2.a.cn.1.5 | ✓ | 20 | 5.4 | even | 2 | ||
9025.2.a.cn.1.16 | yes | 20 | 95.94 | odd | 2 | ||
9025.2.a.co.1.5 | yes | 20 | 19.18 | odd | 2 | inner | |
9025.2.a.co.1.16 | yes | 20 | 1.1 | even | 1 | trivial |