Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1150,2,Mod(1,1150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1150, 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("1150.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1150 = 2 \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1150.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: | \(9.18279623245\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.13448.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 7x^{2} + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 230) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.58874\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1150.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −3.25886 | −1.88150 | −0.940752 | − | 0.339095i | \(-0.889879\pi\) | ||||
−0.940752 | + | 0.339095i | \(0.889879\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 3.25886 | 1.33042 | ||||||||
\(7\) | −1.44270 | −0.545290 | −0.272645 | − | 0.962115i | \(-0.587898\pi\) | ||||
−0.272645 | + | 0.962115i | \(0.587898\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 7.62018 | 2.54006 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.03144 | −0.612502 | −0.306251 | − | 0.951951i | \(-0.599075\pi\) | ||||
−0.306251 | + | 0.951951i | \(0.599075\pi\) | |||||||
\(12\) | −3.25886 | −0.940752 | ||||||||
\(13\) | −0.557299 | −0.154567 | −0.0772835 | − | 0.997009i | \(-0.524625\pi\) | ||||
−0.0772835 | + | 0.997009i | \(0.524625\pi\) | |||||||
\(14\) | 1.44270 | 0.385578 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.91861 | 0.950403 | 0.475202 | − | 0.879877i | \(-0.342375\pi\) | ||||
0.475202 | + | 0.879877i | \(0.342375\pi\) | |||||||
\(18\) | −7.62018 | −1.79609 | ||||||||
\(19\) | −6.73300 | −1.54466 | −0.772328 | − | 0.635224i | \(-0.780908\pi\) | ||||
−0.772328 | + | 0.635224i | \(0.780908\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.70156 | 1.02596 | ||||||||
\(22\) | 2.03144 | 0.433104 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 3.25886 | 0.665212 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.557299 | 0.109295 | ||||||||
\(27\) | −15.0565 | −2.89763 | ||||||||
\(28\) | −1.44270 | −0.272645 | ||||||||
\(29\) | −9.69520 | −1.80035 | −0.900176 | − | 0.435525i | \(-0.856563\pi\) | ||||
−0.900176 | + | 0.435525i | \(0.856563\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.07502 | −0.552290 | −0.276145 | − | 0.961116i | \(-0.589057\pi\) | ||||
−0.276145 | + | 0.961116i | \(0.589057\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 6.62018 | 1.15242 | ||||||||
\(34\) | −3.91861 | −0.672037 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 7.62018 | 1.27003 | ||||||||
\(37\) | 3.65798 | 0.601368 | 0.300684 | − | 0.953724i | \(-0.402785\pi\) | ||||
0.300684 | + | 0.953724i | \(0.402785\pi\) | |||||||
\(38\) | 6.73300 | 1.09224 | ||||||||
\(39\) | 1.81616 | 0.290818 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.03321 | 1.09840 | 0.549202 | − | 0.835690i | \(-0.314932\pi\) | ||||
0.549202 | + | 0.835690i | \(0.314932\pi\) | |||||||
\(42\) | −4.70156 | −0.725467 | ||||||||
\(43\) | 5.06465 | 0.772352 | 0.386176 | − | 0.922425i | \(-0.373796\pi\) | ||||
0.386176 | + | 0.922425i | \(0.373796\pi\) | |||||||
\(44\) | −2.03144 | −0.306251 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | −0.659753 | −0.0962348 | −0.0481174 | − | 0.998842i | \(-0.515322\pi\) | ||||
−0.0481174 | + | 0.998842i | \(0.515322\pi\) | |||||||
\(48\) | −3.25886 | −0.470376 | ||||||||
\(49\) | −4.91861 | −0.702659 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −12.7702 | −1.78819 | ||||||||
\(52\) | −0.557299 | −0.0772835 | ||||||||
\(53\) | −11.1275 | −1.52848 | −0.764242 | − | 0.644930i | \(-0.776887\pi\) | ||||
−0.764242 | + | 0.644930i | \(0.776887\pi\) | |||||||
\(54\) | 15.0565 | 2.04893 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.44270 | 0.192789 | ||||||||
\(57\) | 21.9419 | 2.90628 | ||||||||
\(58\) | 9.69520 | 1.27304 | ||||||||
\(59\) | 10.7226 | 1.39597 | 0.697984 | − | 0.716114i | \(-0.254081\pi\) | ||||
0.697984 | + | 0.716114i | \(0.254081\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.73937 | 0.222703 | 0.111351 | − | 0.993781i | \(-0.464482\pi\) | ||||
0.111351 | + | 0.993781i | \(0.464482\pi\) | |||||||
\(62\) | 3.07502 | 0.390528 | ||||||||
\(63\) | −10.9936 | −1.38507 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −6.62018 | −0.814887 | ||||||||
\(67\) | −12.0129 | −1.46761 | −0.733806 | − | 0.679359i | \(-0.762258\pi\) | ||||
−0.733806 | + | 0.679359i | \(0.762258\pi\) | |||||||
\(68\) | 3.91861 | 0.475202 | ||||||||
\(69\) | 3.25886 | 0.392321 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.4363 | 1.47592 | 0.737961 | − | 0.674844i | \(-0.235789\pi\) | ||||
0.737961 | + | 0.674844i | \(0.235789\pi\) | |||||||
\(72\) | −7.62018 | −0.898046 | ||||||||
\(73\) | 9.26464 | 1.08434 | 0.542172 | − | 0.840267i | \(-0.317602\pi\) | ||||
0.542172 | + | 0.840267i | \(0.317602\pi\) | |||||||
\(74\) | −3.65798 | −0.425231 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.73300 | −0.772328 | ||||||||
\(77\) | 2.93076 | 0.333991 | ||||||||
\(78\) | −1.81616 | −0.205640 | ||||||||
\(79\) | 5.92439 | 0.666546 | 0.333273 | − | 0.942830i | \(-0.391847\pi\) | ||||
0.333273 | + | 0.942830i | \(0.391847\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 26.2066 | 2.91184 | ||||||||
\(82\) | −7.03321 | −0.776688 | ||||||||
\(83\) | 11.3775 | 1.24884 | 0.624420 | − | 0.781089i | \(-0.285336\pi\) | ||||
0.624420 | + | 0.781089i | \(0.285336\pi\) | |||||||
\(84\) | 4.70156 | 0.512982 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −5.06465 | −0.546135 | ||||||||
\(87\) | 31.5953 | 3.38737 | ||||||||
\(88\) | 2.03144 | 0.216552 | ||||||||
\(89\) | 5.25308 | 0.556826 | 0.278413 | − | 0.960462i | \(-0.410192\pi\) | ||||
0.278413 | + | 0.960462i | \(0.410192\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.804016 | 0.0842838 | ||||||||
\(92\) | −1.00000 | −0.104257 | ||||||||
\(93\) | 10.0211 | 1.03914 | ||||||||
\(94\) | 0.659753 | 0.0680483 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 3.25886 | 0.332606 | ||||||||
\(97\) | 0.0813861 | 0.00826350 | 0.00413175 | − | 0.999991i | \(-0.498685\pi\) | ||||
0.00413175 | + | 0.999991i | \(0.498685\pi\) | |||||||
\(98\) | 4.91861 | 0.496855 | ||||||||
\(99\) | −15.4799 | −1.55579 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.31281 | 0.827156 | 0.413578 | − | 0.910469i | \(-0.364279\pi\) | ||||
0.413578 | + | 0.910469i | \(0.364279\pi\) | |||||||
\(102\) | 12.7702 | 1.26444 | ||||||||
\(103\) | 6.36991 | 0.627646 | 0.313823 | − | 0.949481i | \(-0.398390\pi\) | ||||
0.313823 | + | 0.949481i | \(0.398390\pi\) | |||||||
\(104\) | 0.557299 | 0.0546477 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 11.1275 | 1.08080 | ||||||||
\(107\) | 16.9226 | 1.63597 | 0.817986 | − | 0.575239i | \(-0.195091\pi\) | ||||
0.817986 | + | 0.575239i | \(0.195091\pi\) | |||||||
\(108\) | −15.0565 | −1.44881 | ||||||||
\(109\) | −0.218825 | −0.0209597 | −0.0104798 | − | 0.999945i | \(-0.503336\pi\) | ||||
−0.0104798 | + | 0.999945i | \(0.503336\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −11.9208 | −1.13148 | ||||||||
\(112\) | −1.44270 | −0.136322 | ||||||||
\(113\) | −0.580599 | −0.0546182 | −0.0273091 | − | 0.999627i | \(-0.508694\pi\) | ||||
−0.0273091 | + | 0.999627i | \(0.508694\pi\) | |||||||
\(114\) | −21.9419 | −2.05505 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −9.69520 | −0.900176 | ||||||||
\(117\) | −4.24672 | −0.392609 | ||||||||
\(118\) | −10.7226 | −0.987098 | ||||||||
\(119\) | −5.65339 | −0.518245 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.87326 | −0.624842 | ||||||||
\(122\) | −1.73937 | −0.157475 | ||||||||
\(123\) | −22.9203 | −2.06665 | ||||||||
\(124\) | −3.07502 | −0.276145 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 10.9936 | 0.979391 | ||||||||
\(127\) | −1.56944 | −0.139266 | −0.0696328 | − | 0.997573i | \(-0.522183\pi\) | ||||
−0.0696328 | + | 0.997573i | \(0.522183\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −16.5050 | −1.45318 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.9208 | 1.39101 | 0.695505 | − | 0.718521i | \(-0.255181\pi\) | ||||
0.695505 | + | 0.718521i | \(0.255181\pi\) | |||||||
\(132\) | 6.62018 | 0.576212 | ||||||||
\(133\) | 9.71371 | 0.842285 | ||||||||
\(134\) | 12.0129 | 1.03776 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.91861 | −0.336018 | ||||||||
\(137\) | 6.47013 | 0.552781 | 0.276390 | − | 0.961045i | \(-0.410862\pi\) | ||||
0.276390 | + | 0.961045i | \(0.410862\pi\) | |||||||
\(138\) | −3.25886 | −0.277413 | ||||||||
\(139\) | −0.656206 | −0.0556586 | −0.0278293 | − | 0.999613i | \(-0.508859\pi\) | ||||
−0.0278293 | + | 0.999613i | \(0.508859\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.15004 | 0.181066 | ||||||||
\(142\) | −12.4363 | −1.04363 | ||||||||
\(143\) | 1.13212 | 0.0946725 | ||||||||
\(144\) | 7.62018 | 0.635015 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −9.26464 | −0.766747 | ||||||||
\(147\) | 16.0291 | 1.32206 | ||||||||
\(148\) | 3.65798 | 0.300684 | ||||||||
\(149\) | 23.8349 | 1.95263 | 0.976314 | − | 0.216357i | \(-0.0694176\pi\) | ||||
0.976314 | + | 0.216357i | \(0.0694176\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.8669 | −1.20985 | −0.604925 | − | 0.796282i | \(-0.706797\pi\) | ||||
−0.604925 | + | 0.796282i | \(0.706797\pi\) | |||||||
\(152\) | 6.73300 | 0.546118 | ||||||||
\(153\) | 29.8605 | 2.41408 | ||||||||
\(154\) | −2.93076 | −0.236167 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.81616 | 0.145409 | ||||||||
\(157\) | −8.24213 | −0.657793 | −0.328897 | − | 0.944366i | \(-0.606677\pi\) | ||||
−0.328897 | + | 0.944366i | \(0.606677\pi\) | |||||||
\(158\) | −5.92439 | −0.471319 | ||||||||
\(159\) | 36.2631 | 2.87585 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.44270 | 0.113701 | ||||||||
\(162\) | −26.2066 | −2.05898 | ||||||||
\(163\) | 10.3154 | 0.807962 | 0.403981 | − | 0.914767i | \(-0.367626\pi\) | ||||
0.403981 | + | 0.914767i | \(0.367626\pi\) | |||||||
\(164\) | 7.03321 | 0.549202 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −11.3775 | −0.883063 | ||||||||
\(167\) | 4.65975 | 0.360582 | 0.180291 | − | 0.983613i | \(-0.442296\pi\) | ||||
0.180291 | + | 0.983613i | \(0.442296\pi\) | |||||||
\(168\) | −4.70156 | −0.362733 | ||||||||
\(169\) | −12.6894 | −0.976109 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −51.3067 | −3.92352 | ||||||||
\(172\) | 5.06465 | 0.386176 | ||||||||
\(173\) | −2.80402 | −0.213185 | −0.106593 | − | 0.994303i | \(-0.533994\pi\) | ||||
−0.106593 | + | 0.994303i | \(0.533994\pi\) | |||||||
\(174\) | −31.5953 | −2.39523 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.03144 | −0.153125 | ||||||||
\(177\) | −34.9436 | −2.62652 | ||||||||
\(178\) | −5.25308 | −0.393735 | ||||||||
\(179\) | −4.44212 | −0.332019 | −0.166010 | − | 0.986124i | \(-0.553088\pi\) | ||||
−0.166010 | + | 0.986124i | \(0.553088\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.42019 | 0.179891 | 0.0899455 | − | 0.995947i | \(-0.471331\pi\) | ||||
0.0899455 | + | 0.995947i | \(0.471331\pi\) | |||||||
\(182\) | −0.804016 | −0.0595976 | ||||||||
\(183\) | −5.66835 | −0.419016 | ||||||||
\(184\) | 1.00000 | 0.0737210 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −10.0211 | −0.734780 | ||||||||
\(187\) | −7.96042 | −0.582124 | ||||||||
\(188\) | −0.659753 | −0.0481174 | ||||||||
\(189\) | 21.7220 | 1.58005 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −20.8934 | −1.51179 | −0.755897 | − | 0.654690i | \(-0.772799\pi\) | ||||
−0.755897 | + | 0.654690i | \(0.772799\pi\) | |||||||
\(192\) | −3.25886 | −0.235188 | ||||||||
\(193\) | 2.88540 | 0.207696 | 0.103848 | − | 0.994593i | \(-0.466884\pi\) | ||||
0.103848 | + | 0.994593i | \(0.466884\pi\) | |||||||
\(194\) | −0.0813861 | −0.00584318 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.91861 | −0.351330 | ||||||||
\(197\) | −19.0925 | −1.36029 | −0.680144 | − | 0.733079i | \(-0.738083\pi\) | ||||
−0.680144 | + | 0.733079i | \(0.738083\pi\) | |||||||
\(198\) | 15.4799 | 1.10011 | ||||||||
\(199\) | 6.58060 | 0.466486 | 0.233243 | − | 0.972418i | \(-0.425066\pi\) | ||||
0.233243 | + | 0.972418i | \(0.425066\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 39.1485 | 2.76132 | ||||||||
\(202\) | −8.31281 | −0.584888 | ||||||||
\(203\) | 13.9873 | 0.981714 | ||||||||
\(204\) | −12.7702 | −0.894094 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −6.36991 | −0.443813 | ||||||||
\(207\) | −7.62018 | −0.529639 | ||||||||
\(208\) | −0.557299 | −0.0386417 | ||||||||
\(209\) | 13.6777 | 0.946105 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.55986 | 0.451599 | 0.225800 | − | 0.974174i | \(-0.427501\pi\) | ||||
0.225800 | + | 0.974174i | \(0.427501\pi\) | |||||||
\(212\) | −11.1275 | −0.764242 | ||||||||
\(213\) | −40.5283 | −2.77695 | ||||||||
\(214\) | −16.9226 | −1.15681 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 15.0565 | 1.02447 | ||||||||
\(217\) | 4.43634 | 0.301158 | ||||||||
\(218\) | 0.218825 | 0.0148207 | ||||||||
\(219\) | −30.1922 | −2.04020 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.18384 | −0.146901 | ||||||||
\(222\) | 11.9208 | 0.800075 | ||||||||
\(223\) | −20.2094 | −1.35332 | −0.676660 | − | 0.736296i | \(-0.736573\pi\) | ||||
−0.676660 | + | 0.736296i | \(0.736573\pi\) | |||||||
\(224\) | 1.44270 | 0.0963945 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.580599 | 0.0386209 | ||||||||
\(227\) | −15.0098 | −0.996234 | −0.498117 | − | 0.867110i | \(-0.665975\pi\) | ||||
−0.498117 | + | 0.867110i | \(0.665975\pi\) | |||||||
\(228\) | 21.9419 | 1.45314 | ||||||||
\(229\) | 13.7081 | 0.905859 | 0.452929 | − | 0.891546i | \(-0.350379\pi\) | ||||
0.452929 | + | 0.891546i | \(0.350379\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −9.55093 | −0.628405 | ||||||||
\(232\) | 9.69520 | 0.636521 | ||||||||
\(233\) | 9.19822 | 0.602595 | 0.301298 | − | 0.953530i | \(-0.402580\pi\) | ||||
0.301298 | + | 0.953530i | \(0.402580\pi\) | |||||||
\(234\) | 4.24672 | 0.277617 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 10.7226 | 0.697984 | ||||||||
\(237\) | −19.3068 | −1.25411 | ||||||||
\(238\) | 5.65339 | 0.366455 | ||||||||
\(239\) | −2.72618 | −0.176342 | −0.0881709 | − | 0.996105i | \(-0.528102\pi\) | ||||
−0.0881709 | + | 0.996105i | \(0.528102\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.26109 | 0.210066 | 0.105033 | − | 0.994469i | \(-0.466505\pi\) | ||||
0.105033 | + | 0.994469i | \(0.466505\pi\) | |||||||
\(242\) | 6.87326 | 0.441830 | ||||||||
\(243\) | −40.2340 | −2.58101 | ||||||||
\(244\) | 1.73937 | 0.111351 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 22.9203 | 1.46134 | ||||||||
\(247\) | 3.75229 | 0.238753 | ||||||||
\(248\) | 3.07502 | 0.195264 | ||||||||
\(249\) | −37.0776 | −2.34970 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 19.9941 | 1.26202 | 0.631008 | − | 0.775776i | \(-0.282641\pi\) | ||||
0.631008 | + | 0.775776i | \(0.282641\pi\) | |||||||
\(252\) | −10.9936 | −0.692534 | ||||||||
\(253\) | 2.03144 | 0.127715 | ||||||||
\(254\) | 1.56944 | 0.0984756 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 26.7935 | 1.67133 | 0.835667 | − | 0.549237i | \(-0.185081\pi\) | ||||
0.835667 | + | 0.549237i | \(0.185081\pi\) | |||||||
\(258\) | 16.5050 | 1.02756 | ||||||||
\(259\) | −5.27737 | −0.327920 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −73.8791 | −4.57300 | ||||||||
\(262\) | −15.9208 | −0.983593 | ||||||||
\(263\) | 15.8267 | 0.975918 | 0.487959 | − | 0.872867i | \(-0.337742\pi\) | ||||
0.487959 | + | 0.872867i | \(0.337742\pi\) | |||||||
\(264\) | −6.62018 | −0.407444 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −9.71371 | −0.595586 | ||||||||
\(267\) | −17.1191 | −1.04767 | ||||||||
\(268\) | −12.0129 | −0.733806 | ||||||||
\(269\) | 12.0872 | 0.736967 | 0.368484 | − | 0.929634i | \(-0.379877\pi\) | ||||
0.368484 | + | 0.929634i | \(0.379877\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.40254 | 0.510418 | 0.255209 | − | 0.966886i | \(-0.417856\pi\) | ||||
0.255209 | + | 0.966886i | \(0.417856\pi\) | |||||||
\(272\) | 3.91861 | 0.237601 | ||||||||
\(273\) | −2.62018 | −0.158580 | ||||||||
\(274\) | −6.47013 | −0.390875 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.25886 | 0.196160 | ||||||||
\(277\) | 13.8488 | 0.832093 | 0.416046 | − | 0.909343i | \(-0.363415\pi\) | ||||
0.416046 | + | 0.909343i | \(0.363415\pi\) | |||||||
\(278\) | 0.656206 | 0.0393566 | ||||||||
\(279\) | −23.4322 | −1.40285 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.15004 | −0.486191 | −0.243095 | − | 0.970002i | \(-0.578163\pi\) | ||||
−0.243095 | + | 0.970002i | \(0.578163\pi\) | |||||||
\(282\) | −2.15004 | −0.128033 | ||||||||
\(283\) | 17.3532 | 1.03154 | 0.515770 | − | 0.856727i | \(-0.327506\pi\) | ||||
0.515770 | + | 0.856727i | \(0.327506\pi\) | |||||||
\(284\) | 12.4363 | 0.737961 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.13212 | −0.0669436 | ||||||||
\(287\) | −10.1468 | −0.598948 | ||||||||
\(288\) | −7.62018 | −0.449023 | ||||||||
\(289\) | −1.64446 | −0.0967332 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.265226 | −0.0155478 | ||||||||
\(292\) | 9.26464 | 0.542172 | ||||||||
\(293\) | −7.02252 | −0.410260 | −0.205130 | − | 0.978735i | \(-0.565762\pi\) | ||||
−0.205130 | + | 0.978735i | \(0.565762\pi\) | |||||||
\(294\) | −16.0291 | −0.934835 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3.65798 | −0.212616 | ||||||||
\(297\) | 30.5864 | 1.77480 | ||||||||
\(298\) | −23.8349 | −1.38072 | ||||||||
\(299\) | 0.557299 | 0.0322294 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.30678 | −0.421156 | ||||||||
\(302\) | 14.8669 | 0.855494 | ||||||||
\(303\) | −27.0903 | −1.55630 | ||||||||
\(304\) | −6.73300 | −0.386164 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −29.8605 | −1.70701 | ||||||||
\(307\) | −16.4156 | −0.936887 | −0.468444 | − | 0.883493i | \(-0.655185\pi\) | ||||
−0.468444 | + | 0.883493i | \(0.655185\pi\) | |||||||
\(308\) | 2.93076 | 0.166995 | ||||||||
\(309\) | −20.7587 | −1.18092 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.35181 | 0.416883 | 0.208441 | − | 0.978035i | \(-0.433161\pi\) | ||||
0.208441 | + | 0.978035i | \(0.433161\pi\) | |||||||
\(312\) | −1.81616 | −0.102820 | ||||||||
\(313\) | −4.08972 | −0.231165 | −0.115582 | − | 0.993298i | \(-0.536873\pi\) | ||||
−0.115582 | + | 0.993298i | \(0.536873\pi\) | |||||||
\(314\) | 8.24213 | 0.465130 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.92439 | 0.333273 | ||||||||
\(317\) | −8.91580 | −0.500761 | −0.250381 | − | 0.968148i | \(-0.580556\pi\) | ||||
−0.250381 | + | 0.968148i | \(0.580556\pi\) | |||||||
\(318\) | −36.2631 | −2.03353 | ||||||||
\(319\) | 19.6952 | 1.10272 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −55.1485 | −3.07809 | ||||||||
\(322\) | −1.44270 | −0.0803986 | ||||||||
\(323\) | −26.3840 | −1.46805 | ||||||||
\(324\) | 26.2066 | 1.45592 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −10.3154 | −0.571316 | ||||||||
\(327\) | 0.713121 | 0.0394357 | ||||||||
\(328\) | −7.03321 | −0.388344 | ||||||||
\(329\) | 0.951826 | 0.0524759 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.3240 | 1.17207 | 0.586036 | − | 0.810285i | \(-0.300688\pi\) | ||||
0.586036 | + | 0.810285i | \(0.300688\pi\) | |||||||
\(332\) | 11.3775 | 0.624420 | ||||||||
\(333\) | 27.8744 | 1.52751 | ||||||||
\(334\) | −4.65975 | −0.254970 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 4.70156 | 0.256491 | ||||||||
\(337\) | 3.15417 | 0.171819 | 0.0859094 | − | 0.996303i | \(-0.472620\pi\) | ||||
0.0859094 | + | 0.996303i | \(0.472620\pi\) | |||||||
\(338\) | 12.6894 | 0.690213 | ||||||||
\(339\) | 1.89209 | 0.102764 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.24672 | 0.338279 | ||||||||
\(342\) | 51.3067 | 2.77435 | ||||||||
\(343\) | 17.1950 | 0.928443 | ||||||||
\(344\) | −5.06465 | −0.273068 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.80402 | 0.150745 | ||||||||
\(347\) | 3.54739 | 0.190434 | 0.0952169 | − | 0.995457i | \(-0.469646\pi\) | ||||
0.0952169 | + | 0.995457i | \(0.469646\pi\) | |||||||
\(348\) | 31.5953 | 1.69369 | ||||||||
\(349\) | −18.9726 | −1.01558 | −0.507789 | − | 0.861481i | \(-0.669537\pi\) | ||||
−0.507789 | + | 0.861481i | \(0.669537\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8.39098 | 0.447877 | ||||||||
\(352\) | 2.03144 | 0.108276 | ||||||||
\(353\) | 33.5710 | 1.78680 | 0.893402 | − | 0.449257i | \(-0.148311\pi\) | ||||
0.893402 | + | 0.449257i | \(0.148311\pi\) | |||||||
\(354\) | 34.9436 | 1.85723 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 5.25308 | 0.278413 | ||||||||
\(357\) | 18.4236 | 0.975081 | ||||||||
\(358\) | 4.44212 | 0.234773 | ||||||||
\(359\) | −3.53243 | −0.186434 | −0.0932171 | − | 0.995646i | \(-0.529715\pi\) | ||||
−0.0932171 | + | 0.995646i | \(0.529715\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 26.3333 | 1.38596 | ||||||||
\(362\) | −2.42019 | −0.127202 | ||||||||
\(363\) | 22.3990 | 1.17564 | ||||||||
\(364\) | 0.804016 | 0.0421419 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 5.66835 | 0.296289 | ||||||||
\(367\) | 8.07444 | 0.421482 | 0.210741 | − | 0.977542i | \(-0.432412\pi\) | ||||
0.210741 | + | 0.977542i | \(0.432412\pi\) | |||||||
\(368\) | −1.00000 | −0.0521286 | ||||||||
\(369\) | 53.5943 | 2.79001 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 16.0537 | 0.833466 | ||||||||
\(372\) | 10.0211 | 0.519568 | ||||||||
\(373\) | −1.31459 | −0.0680668 | −0.0340334 | − | 0.999421i | \(-0.510835\pi\) | ||||
−0.0340334 | + | 0.999421i | \(0.510835\pi\) | |||||||
\(374\) | 7.96042 | 0.411624 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.659753 | 0.0340242 | ||||||||
\(377\) | 5.40312 | 0.278275 | ||||||||
\(378\) | −21.7220 | −1.11726 | ||||||||
\(379\) | 0.311952 | 0.0160239 | 0.00801196 | − | 0.999968i | \(-0.497450\pi\) | ||||
0.00801196 | + | 0.999968i | \(0.497450\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.11460 | 0.262029 | ||||||||
\(382\) | 20.8934 | 1.06900 | ||||||||
\(383\) | 10.6805 | 0.545748 | 0.272874 | − | 0.962050i | \(-0.412026\pi\) | ||||
0.272874 | + | 0.962050i | \(0.412026\pi\) | |||||||
\(384\) | 3.25886 | 0.166303 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.88540 | −0.146863 | ||||||||
\(387\) | 38.5935 | 1.96182 | ||||||||
\(388\) | 0.0813861 | 0.00413175 | ||||||||
\(389\) | −7.86867 | −0.398957 | −0.199479 | − | 0.979902i | \(-0.563925\pi\) | ||||
−0.199479 | + | 0.979902i | \(0.563925\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.91861 | −0.198173 | ||||||||
\(392\) | 4.91861 | 0.248428 | ||||||||
\(393\) | −51.8838 | −2.61719 | ||||||||
\(394\) | 19.0925 | 0.961868 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −15.4799 | −0.777895 | ||||||||
\(397\) | 29.2334 | 1.46718 | 0.733591 | − | 0.679591i | \(-0.237843\pi\) | ||||
0.733591 | + | 0.679591i | \(0.237843\pi\) | |||||||
\(398\) | −6.58060 | −0.329856 | ||||||||
\(399\) | −31.6556 | −1.58476 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 23.7130 | 1.18417 | 0.592086 | − | 0.805874i | \(-0.298304\pi\) | ||||
0.592086 | + | 0.805874i | \(0.298304\pi\) | |||||||
\(402\) | −39.1485 | −1.95255 | ||||||||
\(403\) | 1.71371 | 0.0853658 | ||||||||
\(404\) | 8.31281 | 0.413578 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −13.9873 | −0.694177 | ||||||||
\(407\) | −7.43096 | −0.368339 | ||||||||
\(408\) | 12.7702 | 0.632220 | ||||||||
\(409\) | −33.2509 | −1.64415 | −0.822076 | − | 0.569378i | \(-0.807184\pi\) | ||||
−0.822076 | + | 0.569378i | \(0.807184\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −21.0853 | −1.04006 | ||||||||
\(412\) | 6.36991 | 0.313823 | ||||||||
\(413\) | −15.4695 | −0.761207 | ||||||||
\(414\) | 7.62018 | 0.374511 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.557299 | 0.0273238 | ||||||||
\(417\) | 2.13848 | 0.104722 | ||||||||
\(418\) | −13.6777 | −0.668997 | ||||||||
\(419\) | 7.28229 | 0.355763 | 0.177882 | − | 0.984052i | \(-0.443076\pi\) | ||||
0.177882 | + | 0.984052i | \(0.443076\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.71515 | −0.132329 | −0.0661643 | − | 0.997809i | \(-0.521076\pi\) | ||||
−0.0661643 | + | 0.997809i | \(0.521076\pi\) | |||||||
\(422\) | −6.55986 | −0.319329 | ||||||||
\(423\) | −5.02743 | −0.244442 | ||||||||
\(424\) | 11.1275 | 0.540401 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 40.5283 | 1.96360 | ||||||||
\(427\) | −2.50938 | −0.121438 | ||||||||
\(428\) | 16.9226 | 0.817986 | ||||||||
\(429\) | −3.68942 | −0.178127 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.3336 | 0.497750 | 0.248875 | − | 0.968536i | \(-0.419939\pi\) | ||||
0.248875 | + | 0.968536i | \(0.419939\pi\) | |||||||
\(432\) | −15.0565 | −0.724407 | ||||||||
\(433\) | 28.4153 | 1.36555 | 0.682775 | − | 0.730628i | \(-0.260773\pi\) | ||||
0.682775 | + | 0.730628i | \(0.260773\pi\) | |||||||
\(434\) | −4.43634 | −0.212951 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.218825 | −0.0104798 | ||||||||
\(437\) | 6.73300 | 0.322083 | ||||||||
\(438\) | 30.1922 | 1.44264 | ||||||||
\(439\) | 6.37313 | 0.304173 | 0.152087 | − | 0.988367i | \(-0.451401\pi\) | ||||
0.152087 | + | 0.988367i | \(0.451401\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −37.4807 | −1.78480 | ||||||||
\(442\) | 2.18384 | 0.103875 | ||||||||
\(443\) | −9.43114 | −0.448087 | −0.224044 | − | 0.974579i | \(-0.571926\pi\) | ||||
−0.224044 | + | 0.974579i | \(0.571926\pi\) | |||||||
\(444\) | −11.9208 | −0.565738 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 20.2094 | 0.956942 | ||||||||
\(447\) | −77.6745 | −3.67388 | ||||||||
\(448\) | −1.44270 | −0.0681612 | ||||||||
\(449\) | 11.3185 | 0.534154 | 0.267077 | − | 0.963675i | \(-0.413942\pi\) | ||||
0.267077 | + | 0.963675i | \(0.413942\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −14.2875 | −0.672774 | ||||||||
\(452\) | −0.580599 | −0.0273091 | ||||||||
\(453\) | 48.4491 | 2.27634 | ||||||||
\(454\) | 15.0098 | 0.704444 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −21.9419 | −1.02752 | ||||||||
\(457\) | 4.96456 | 0.232232 | 0.116116 | − | 0.993236i | \(-0.462956\pi\) | ||||
0.116116 | + | 0.993236i | \(0.462956\pi\) | |||||||
\(458\) | −13.7081 | −0.640539 | ||||||||
\(459\) | −59.0007 | −2.75391 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 19.9128 | 0.927433 | 0.463717 | − | 0.885984i | \(-0.346516\pi\) | ||||
0.463717 | + | 0.885984i | \(0.346516\pi\) | |||||||
\(462\) | 9.55093 | 0.444350 | ||||||||
\(463\) | −29.9046 | −1.38978 | −0.694892 | − | 0.719114i | \(-0.744548\pi\) | ||||
−0.694892 | + | 0.719114i | \(0.744548\pi\) | |||||||
\(464\) | −9.69520 | −0.450088 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −9.19822 | −0.426099 | ||||||||
\(467\) | 15.1032 | 0.698895 | 0.349447 | − | 0.936956i | \(-0.386369\pi\) | ||||
0.349447 | + | 0.936956i | \(0.386369\pi\) | |||||||
\(468\) | −4.24672 | −0.196305 | ||||||||
\(469\) | 17.3311 | 0.800274 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 26.8599 | 1.23764 | ||||||||
\(472\) | −10.7226 | −0.493549 | ||||||||
\(473\) | −10.2885 | −0.473067 | ||||||||
\(474\) | 19.3068 | 0.886790 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −5.65339 | −0.259123 | ||||||||
\(477\) | −84.7937 | −3.88244 | ||||||||
\(478\) | 2.72618 | 0.124692 | ||||||||
\(479\) | 28.6678 | 1.30986 | 0.654932 | − | 0.755688i | \(-0.272697\pi\) | ||||
0.654932 | + | 0.755688i | \(0.272697\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.03859 | −0.0929516 | ||||||||
\(482\) | −3.26109 | −0.148539 | ||||||||
\(483\) | −4.70156 | −0.213928 | ||||||||
\(484\) | −6.87326 | −0.312421 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 40.2340 | 1.82505 | ||||||||
\(487\) | 9.15319 | 0.414770 | 0.207385 | − | 0.978259i | \(-0.433505\pi\) | ||||
0.207385 | + | 0.978259i | \(0.433505\pi\) | |||||||
\(488\) | −1.73937 | −0.0787374 | ||||||||
\(489\) | −33.6164 | −1.52018 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −20.8098 | −0.939133 | −0.469566 | − | 0.882897i | \(-0.655590\pi\) | ||||
−0.469566 | + | 0.882897i | \(0.655590\pi\) | |||||||
\(492\) | −22.9203 | −1.03333 | ||||||||
\(493\) | −37.9917 | −1.71106 | ||||||||
\(494\) | −3.75229 | −0.168824 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.07502 | −0.138073 | ||||||||
\(497\) | −17.9419 | −0.804805 | ||||||||
\(498\) | 37.0776 | 1.66149 | ||||||||
\(499\) | −18.1293 | −0.811579 | −0.405789 | − | 0.913967i | \(-0.633003\pi\) | ||||
−0.405789 | + | 0.913967i | \(0.633003\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −15.1855 | −0.678438 | ||||||||
\(502\) | −19.9941 | −0.892380 | ||||||||
\(503\) | −26.4296 | −1.17844 | −0.589218 | − | 0.807974i | \(-0.700564\pi\) | ||||
−0.589218 | + | 0.807974i | \(0.700564\pi\) | |||||||
\(504\) | 10.9936 | 0.489695 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −2.03144 | −0.0903085 | ||||||||
\(507\) | 41.3531 | 1.83655 | ||||||||
\(508\) | −1.56944 | −0.0696328 | ||||||||
\(509\) | −12.0501 | −0.534113 | −0.267057 | − | 0.963681i | \(-0.586051\pi\) | ||||
−0.267057 | + | 0.963681i | \(0.586051\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13.3661 | −0.591282 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 101.376 | 4.47584 | ||||||||
\(514\) | −26.7935 | −1.18181 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −16.5050 | −0.726592 | ||||||||
\(517\) | 1.34025 | 0.0589440 | ||||||||
\(518\) | 5.27737 | 0.231874 | ||||||||
\(519\) | 9.13790 | 0.401109 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −25.3697 | −1.11146 | −0.555732 | − | 0.831361i | \(-0.687562\pi\) | ||||
−0.555732 | + | 0.831361i | \(0.687562\pi\) | |||||||
\(522\) | 73.8791 | 3.23360 | ||||||||
\(523\) | −25.0018 | −1.09325 | −0.546626 | − | 0.837377i | \(-0.684088\pi\) | ||||
−0.546626 | + | 0.837377i | \(0.684088\pi\) | |||||||
\(524\) | 15.9208 | 0.695505 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −15.8267 | −0.690078 | ||||||||
\(527\) | −12.0498 | −0.524898 | ||||||||
\(528\) | 6.62018 | 0.288106 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 81.7083 | 3.54584 | ||||||||
\(532\) | 9.71371 | 0.421143 | ||||||||
\(533\) | −3.91960 | −0.169777 | ||||||||
\(534\) | 17.1191 | 0.740814 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 12.0129 | 0.518880 | ||||||||
\(537\) | 14.4762 | 0.624696 | ||||||||
\(538\) | −12.0872 | −0.521115 | ||||||||
\(539\) | 9.99186 | 0.430380 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 24.7900 | 1.06580 | 0.532902 | − | 0.846177i | \(-0.321101\pi\) | ||||
0.532902 | + | 0.846177i | \(0.321101\pi\) | |||||||
\(542\) | −8.40254 | −0.360920 | ||||||||
\(543\) | −7.88705 | −0.338466 | ||||||||
\(544\) | −3.91861 | −0.168009 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 2.62018 | 0.112133 | ||||||||
\(547\) | −30.9508 | −1.32336 | −0.661681 | − | 0.749785i | \(-0.730157\pi\) | ||||
−0.661681 | + | 0.749785i | \(0.730157\pi\) | |||||||
\(548\) | 6.47013 | 0.276390 | ||||||||
\(549\) | 13.2543 | 0.565678 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 65.2778 | 2.78093 | ||||||||
\(552\) | −3.25886 | −0.138706 | ||||||||
\(553\) | −8.54713 | −0.363461 | ||||||||
\(554\) | −13.8488 | −0.588379 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.656206 | −0.0278293 | ||||||||
\(557\) | −7.45307 | −0.315797 | −0.157898 | − | 0.987455i | \(-0.550472\pi\) | ||||
−0.157898 | + | 0.987455i | \(0.550472\pi\) | |||||||
\(558\) | 23.4322 | 0.991964 | ||||||||
\(559\) | −2.82252 | −0.119380 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 25.9419 | 1.09527 | ||||||||
\(562\) | 8.15004 | 0.343789 | ||||||||
\(563\) | −7.96161 | −0.335542 | −0.167771 | − | 0.985826i | \(-0.553657\pi\) | ||||
−0.167771 | + | 0.985826i | \(0.553657\pi\) | |||||||
\(564\) | 2.15004 | 0.0905331 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −17.3532 | −0.729408 | ||||||||
\(567\) | −37.8082 | −1.58780 | ||||||||
\(568\) | −12.4363 | −0.521817 | ||||||||
\(569\) | 32.3873 | 1.35774 | 0.678872 | − | 0.734257i | \(-0.262469\pi\) | ||||
0.678872 | + | 0.734257i | \(0.262469\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.38994 | −0.267410 | −0.133705 | − | 0.991021i | \(-0.542688\pi\) | ||||
−0.133705 | + | 0.991021i | \(0.542688\pi\) | |||||||
\(572\) | 1.13212 | 0.0473363 | ||||||||
\(573\) | 68.0887 | 2.84445 | ||||||||
\(574\) | 10.1468 | 0.423520 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 7.62018 | 0.317507 | ||||||||
\(577\) | −39.1728 | −1.63078 | −0.815392 | − | 0.578910i | \(-0.803478\pi\) | ||||
−0.815392 | + | 0.578910i | \(0.803478\pi\) | |||||||
\(578\) | 1.64446 | 0.0684007 | ||||||||
\(579\) | −9.40312 | −0.390781 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −16.4143 | −0.680979 | ||||||||
\(582\) | 0.265226 | 0.0109940 | ||||||||
\(583\) | 22.6049 | 0.936199 | ||||||||
\(584\) | −9.26464 | −0.383374 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7.02252 | 0.290097 | ||||||||
\(587\) | −21.3811 | −0.882491 | −0.441246 | − | 0.897386i | \(-0.645463\pi\) | ||||
−0.441246 | + | 0.897386i | \(0.645463\pi\) | |||||||
\(588\) | 16.0291 | 0.661028 | ||||||||
\(589\) | 20.7041 | 0.853098 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 62.2199 | 2.55939 | ||||||||
\(592\) | 3.65798 | 0.150342 | ||||||||
\(593\) | −2.45130 | −0.100663 | −0.0503314 | − | 0.998733i | \(-0.516028\pi\) | ||||
−0.0503314 | + | 0.998733i | \(0.516028\pi\) | |||||||
\(594\) | −30.5864 | −1.25497 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 23.8349 | 0.976314 | ||||||||
\(597\) | −21.4453 | −0.877696 | ||||||||
\(598\) | −0.557299 | −0.0227897 | ||||||||
\(599\) | 38.5828 | 1.57645 | 0.788226 | − | 0.615386i | \(-0.211000\pi\) | ||||
0.788226 | + | 0.615386i | \(0.211000\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −35.3416 | −1.44162 | −0.720808 | − | 0.693135i | \(-0.756229\pi\) | ||||
−0.720808 | + | 0.693135i | \(0.756229\pi\) | |||||||
\(602\) | 7.30678 | 0.297802 | ||||||||
\(603\) | −91.5406 | −3.72782 | ||||||||
\(604\) | −14.8669 | −0.604925 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 27.0903 | 1.10047 | ||||||||
\(607\) | −17.8129 | −0.723005 | −0.361502 | − | 0.932371i | \(-0.617736\pi\) | ||||
−0.361502 | + | 0.932371i | \(0.617736\pi\) | |||||||
\(608\) | 6.73300 | 0.273059 | ||||||||
\(609\) | −45.5826 | −1.84710 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.367680 | 0.0148747 | ||||||||
\(612\) | 29.8605 | 1.20704 | ||||||||
\(613\) | −37.7547 | −1.52490 | −0.762450 | − | 0.647048i | \(-0.776003\pi\) | ||||
−0.762450 | + | 0.647048i | \(0.776003\pi\) | |||||||
\(614\) | 16.4156 | 0.662479 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.93076 | −0.118084 | ||||||||
\(617\) | 23.1248 | 0.930971 | 0.465486 | − | 0.885055i | \(-0.345880\pi\) | ||||
0.465486 | + | 0.885055i | \(0.345880\pi\) | |||||||
\(618\) | 20.7587 | 0.835036 | ||||||||
\(619\) | 19.5428 | 0.785491 | 0.392746 | − | 0.919647i | \(-0.371525\pi\) | ||||
0.392746 | + | 0.919647i | \(0.371525\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 15.0565 | 0.604197 | ||||||||
\(622\) | −7.35181 | −0.294781 | ||||||||
\(623\) | −7.57863 | −0.303631 | ||||||||
\(624\) | 1.81616 | 0.0727046 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 4.08972 | 0.163458 | ||||||||
\(627\) | −44.5736 | −1.78010 | ||||||||
\(628\) | −8.24213 | −0.328897 | ||||||||
\(629\) | 14.3342 | 0.571542 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26.4807 | −1.05418 | −0.527090 | − | 0.849809i | \(-0.676717\pi\) | ||||
−0.527090 | + | 0.849809i | \(0.676717\pi\) | |||||||
\(632\) | −5.92439 | −0.235660 | ||||||||
\(633\) | −21.3777 | −0.849686 | ||||||||
\(634\) | 8.91580 | 0.354092 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 36.2631 | 1.43792 | ||||||||
\(637\) | 2.74114 | 0.108608 | ||||||||
\(638\) | −19.6952 | −0.779740 | ||||||||
\(639\) | 94.7671 | 3.74893 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −35.9594 | −1.42031 | −0.710156 | − | 0.704044i | \(-0.751376\pi\) | ||||
−0.710156 | + | 0.704044i | \(0.751376\pi\) | |||||||
\(642\) | 55.1485 | 2.17654 | ||||||||
\(643\) | 14.6934 | 0.579452 | 0.289726 | − | 0.957110i | \(-0.406436\pi\) | ||||
0.289726 | + | 0.957110i | \(0.406436\pi\) | |||||||
\(644\) | 1.44270 | 0.0568504 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 26.3840 | 1.03807 | ||||||||
\(647\) | 26.7763 | 1.05269 | 0.526343 | − | 0.850272i | \(-0.323563\pi\) | ||||
0.526343 | + | 0.850272i | \(0.323563\pi\) | |||||||
\(648\) | −26.2066 | −1.02949 | ||||||||
\(649\) | −21.7824 | −0.855033 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −14.4574 | −0.566630 | ||||||||
\(652\) | 10.3154 | 0.403981 | ||||||||
\(653\) | 18.8331 | 0.736996 | 0.368498 | − | 0.929629i | \(-0.379872\pi\) | ||||
0.368498 | + | 0.929629i | \(0.379872\pi\) | |||||||
\(654\) | −0.713121 | −0.0278853 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 7.03321 | 0.274601 | ||||||||
\(657\) | 70.5982 | 2.75430 | ||||||||
\(658\) | −0.951826 | −0.0371060 | ||||||||
\(659\) | −18.0885 | −0.704629 | −0.352315 | − | 0.935882i | \(-0.614605\pi\) | ||||
−0.352315 | + | 0.935882i | \(0.614605\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30.3235 | 1.17945 | 0.589724 | − | 0.807605i | \(-0.299237\pi\) | ||||
0.589724 | + | 0.807605i | \(0.299237\pi\) | |||||||
\(662\) | −21.3240 | −0.828780 | ||||||||
\(663\) | 7.11683 | 0.276395 | ||||||||
\(664\) | −11.3775 | −0.441531 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −27.8744 | −1.08011 | ||||||||
\(667\) | 9.69520 | 0.375400 | ||||||||
\(668\) | 4.65975 | 0.180291 | ||||||||
\(669\) | 65.8595 | 2.54628 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.53341 | −0.136406 | ||||||||
\(672\) | −4.70156 | −0.181367 | ||||||||
\(673\) | 11.1496 | 0.429787 | 0.214894 | − | 0.976637i | \(-0.431060\pi\) | ||||
0.214894 | + | 0.976637i | \(0.431060\pi\) | |||||||
\(674\) | −3.15417 | −0.121494 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.6894 | −0.488055 | ||||||||
\(677\) | −43.5275 | −1.67290 | −0.836449 | − | 0.548045i | \(-0.815372\pi\) | ||||
−0.836449 | + | 0.548045i | \(0.815372\pi\) | |||||||
\(678\) | −1.89209 | −0.0726654 | ||||||||
\(679\) | −0.117416 | −0.00450600 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 48.9148 | 1.87442 | ||||||||
\(682\) | −6.24672 | −0.239199 | ||||||||
\(683\) | 24.1375 | 0.923596 | 0.461798 | − | 0.886985i | \(-0.347205\pi\) | ||||
0.461798 | + | 0.886985i | \(0.347205\pi\) | |||||||
\(684\) | −51.3067 | −1.96176 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −17.1950 | −0.656508 | ||||||||
\(687\) | −44.6729 | −1.70438 | ||||||||
\(688\) | 5.06465 | 0.193088 | ||||||||
\(689\) | 6.20136 | 0.236253 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20.8241 | −0.792186 | −0.396093 | − | 0.918210i | \(-0.629634\pi\) | ||||
−0.396093 | + | 0.918210i | \(0.629634\pi\) | |||||||
\(692\) | −2.80402 | −0.106593 | ||||||||
\(693\) | 22.3329 | 0.848356 | ||||||||
\(694\) | −3.54739 | −0.134657 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −31.5953 | −1.19762 | ||||||||
\(697\) | 27.5604 | 1.04393 | ||||||||
\(698\) | 18.9726 | 0.718122 | ||||||||
\(699\) | −29.9757 | −1.13379 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −31.5301 | −1.19087 | −0.595437 | − | 0.803402i | \(-0.703021\pi\) | ||||
−0.595437 | + | 0.803402i | \(0.703021\pi\) | |||||||
\(702\) | −8.39098 | −0.316697 | ||||||||
\(703\) | −24.6292 | −0.928907 | ||||||||
\(704\) | −2.03144 | −0.0765627 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −33.5710 | −1.26346 | ||||||||
\(707\) | −11.9929 | −0.451040 | ||||||||
\(708\) | −34.9436 | −1.31326 | ||||||||
\(709\) | 3.12175 | 0.117240 | 0.0586199 | − | 0.998280i | \(-0.481330\pi\) | ||||
0.0586199 | + | 0.998280i | \(0.481330\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 45.1449 | 1.69307 | ||||||||
\(712\) | −5.25308 | −0.196868 | ||||||||
\(713\) | 3.07502 | 0.115160 | ||||||||
\(714\) | −18.4236 | −0.689486 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −4.44212 | −0.166010 | ||||||||
\(717\) | 8.88423 | 0.331788 | ||||||||
\(718\) | 3.53243 | 0.131829 | ||||||||
\(719\) | 20.3945 | 0.760588 | 0.380294 | − | 0.924866i | \(-0.375823\pi\) | ||||
0.380294 | + | 0.924866i | \(0.375823\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.18988 | −0.342249 | ||||||||
\(722\) | −26.3333 | −0.980024 | ||||||||
\(723\) | −10.6275 | −0.395239 | ||||||||
\(724\) | 2.42019 | 0.0899455 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −22.3990 | −0.831305 | ||||||||
\(727\) | 39.8896 | 1.47942 | 0.739712 | − | 0.672924i | \(-0.234962\pi\) | ||||
0.739712 | + | 0.672924i | \(0.234962\pi\) | |||||||
\(728\) | −0.804016 | −0.0297988 | ||||||||
\(729\) | 52.4973 | 1.94434 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 19.8464 | 0.734046 | ||||||||
\(732\) | −5.66835 | −0.209508 | ||||||||
\(733\) | 22.7761 | 0.841255 | 0.420628 | − | 0.907233i | \(-0.361810\pi\) | ||||
0.420628 | + | 0.907233i | \(0.361810\pi\) | |||||||
\(734\) | −8.07444 | −0.298033 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | 24.4035 | 0.898915 | ||||||||
\(738\) | −53.5943 | −1.97283 | ||||||||
\(739\) | 33.7661 | 1.24211 | 0.621053 | − | 0.783769i | \(-0.286705\pi\) | ||||
0.621053 | + | 0.783769i | \(0.286705\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −12.2282 | −0.449214 | ||||||||
\(742\) | −16.0537 | −0.589350 | ||||||||
\(743\) | −47.5880 | −1.74584 | −0.872918 | − | 0.487868i | \(-0.837775\pi\) | ||||
−0.872918 | + | 0.487868i | \(0.837775\pi\) | |||||||
\(744\) | −10.0211 | −0.367390 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1.31459 | 0.0481305 | ||||||||
\(747\) | 86.6983 | 3.17212 | ||||||||
\(748\) | −7.96042 | −0.291062 | ||||||||
\(749\) | −24.4143 | −0.892078 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 51.2698 | 1.87086 | 0.935430 | − | 0.353512i | \(-0.115013\pi\) | ||||
0.935430 | + | 0.353512i | \(0.115013\pi\) | |||||||
\(752\) | −0.659753 | −0.0240587 | ||||||||
\(753\) | −65.1580 | −2.37449 | ||||||||
\(754\) | −5.40312 | −0.196770 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 21.7220 | 0.790023 | ||||||||
\(757\) | 26.2807 | 0.955189 | 0.477594 | − | 0.878580i | \(-0.341509\pi\) | ||||
0.477594 | + | 0.878580i | \(0.341509\pi\) | |||||||
\(758\) | −0.311952 | −0.0113306 | ||||||||
\(759\) | −6.62018 | −0.240297 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.18003 | −0.260276 | −0.130138 | − | 0.991496i | \(-0.541542\pi\) | ||||
−0.130138 | + | 0.991496i | \(0.541542\pi\) | |||||||
\(762\) | −5.11460 | −0.185282 | ||||||||
\(763\) | 0.315700 | 0.0114291 | ||||||||
\(764\) | −20.8934 | −0.755897 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −10.6805 | −0.385902 | ||||||||
\(767\) | −5.97571 | −0.215770 | ||||||||
\(768\) | −3.25886 | −0.117594 | ||||||||
\(769\) | −32.2666 | −1.16356 | −0.581782 | − | 0.813345i | \(-0.697644\pi\) | ||||
−0.581782 | + | 0.813345i | \(0.697644\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −87.3164 | −3.14462 | ||||||||
\(772\) | 2.88540 | 0.103848 | ||||||||
\(773\) | −3.75316 | −0.134992 | −0.0674958 | − | 0.997720i | \(-0.521501\pi\) | ||||
−0.0674958 | + | 0.997720i | \(0.521501\pi\) | |||||||
\(774\) | −38.5935 | −1.38722 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −0.0813861 | −0.00292159 | ||||||||
\(777\) | 17.1982 | 0.616983 | ||||||||
\(778\) | 7.86867 | 0.282105 | ||||||||
\(779\) | −47.3546 | −1.69666 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −25.2637 | −0.904005 | ||||||||
\(782\) | 3.91861 | 0.140129 | ||||||||
\(783\) | 145.976 | 5.21675 | ||||||||
\(784\) | −4.91861 | −0.175665 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 51.8838 | 1.85063 | ||||||||
\(787\) | 21.9373 | 0.781981 | 0.390991 | − | 0.920395i | \(-0.372133\pi\) | ||||
0.390991 | + | 0.920395i | \(0.372133\pi\) | |||||||
\(788\) | −19.0925 | −0.680144 | ||||||||
\(789\) | −51.5771 | −1.83619 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.837631 | 0.0297827 | ||||||||
\(792\) | 15.4799 | 0.550055 | ||||||||
\(793\) | −0.969347 | −0.0344225 | ||||||||
\(794\) | −29.2334 | −1.03745 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6.58060 | 0.233243 | ||||||||
\(797\) | 7.57883 | 0.268456 | 0.134228 | − | 0.990950i | \(-0.457145\pi\) | ||||
0.134228 | + | 0.990950i | \(0.457145\pi\) | |||||||
\(798\) | 31.6556 | 1.12060 | ||||||||
\(799\) | −2.58532 | −0.0914619 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 40.0294 | 1.41437 | ||||||||
\(802\) | −23.7130 | −0.837337 | ||||||||
\(803\) | −18.8205 | −0.664163 | ||||||||
\(804\) | 39.1485 | 1.38066 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.71371 | −0.0603627 | ||||||||
\(807\) | −39.3904 | −1.38661 | ||||||||
\(808\) | −8.31281 | −0.292444 | ||||||||
\(809\) | 18.9835 | 0.667423 | 0.333712 | − | 0.942675i | \(-0.391699\pi\) | ||||
0.333712 | + | 0.942675i | \(0.391699\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14.1851 | 0.498106 | 0.249053 | − | 0.968490i | \(-0.419881\pi\) | ||||
0.249053 | + | 0.968490i | \(0.419881\pi\) | |||||||
\(812\) | 13.9873 | 0.490857 | ||||||||
\(813\) | −27.3827 | −0.960354 | ||||||||
\(814\) | 7.43096 | 0.260455 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −12.7702 | −0.447047 | ||||||||
\(817\) | −34.1003 | −1.19302 | ||||||||
\(818\) | 33.2509 | 1.16259 | ||||||||
\(819\) | 6.12674 | 0.214086 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −44.8294 | −1.56456 | −0.782278 | − | 0.622930i | \(-0.785942\pi\) | ||||
−0.782278 | + | 0.622930i | \(0.785942\pi\) | |||||||
\(822\) | 21.0853 | 0.735433 | ||||||||
\(823\) | −15.7652 | −0.549539 | −0.274770 | − | 0.961510i | \(-0.588602\pi\) | ||||
−0.274770 | + | 0.961510i | \(0.588602\pi\) | |||||||
\(824\) | −6.36991 | −0.221906 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 15.4695 | 0.538254 | ||||||||
\(827\) | 11.4332 | 0.397573 | 0.198786 | − | 0.980043i | \(-0.436300\pi\) | ||||
0.198786 | + | 0.980043i | \(0.436300\pi\) | |||||||
\(828\) | −7.62018 | −0.264819 | ||||||||
\(829\) | −28.3924 | −0.986108 | −0.493054 | − | 0.869999i | \(-0.664119\pi\) | ||||
−0.493054 | + | 0.869999i | \(0.664119\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −45.1313 | −1.56559 | ||||||||
\(832\) | −0.557299 | −0.0193209 | ||||||||
\(833\) | −19.2741 | −0.667810 | ||||||||
\(834\) | −2.13848 | −0.0740496 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 13.6777 | 0.473052 | ||||||||
\(837\) | 46.2991 | 1.60033 | ||||||||
\(838\) | −7.28229 | −0.251562 | ||||||||
\(839\) | 54.3340 | 1.87582 | 0.937908 | − | 0.346883i | \(-0.112760\pi\) | ||||
0.937908 | + | 0.346883i | \(0.112760\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 64.9969 | 2.24127 | ||||||||
\(842\) | 2.71515 | 0.0935704 | ||||||||
\(843\) | 26.5599 | 0.914770 | ||||||||
\(844\) | 6.55986 | 0.225800 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 5.02743 | 0.172847 | ||||||||
\(847\) | 9.91606 | 0.340720 | ||||||||
\(848\) | −11.1275 | −0.382121 | ||||||||
\(849\) | −56.5516 | −1.94085 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.65798 | −0.125394 | ||||||||
\(852\) | −40.5283 | −1.38848 | ||||||||
\(853\) | 46.8542 | 1.60426 | 0.802129 | − | 0.597150i | \(-0.203700\pi\) | ||||
0.802129 | + | 0.597150i | \(0.203700\pi\) | |||||||
\(854\) | 2.50938 | 0.0858694 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −16.9226 | −0.578403 | ||||||||
\(857\) | −28.5356 | −0.974756 | −0.487378 | − | 0.873191i | \(-0.662047\pi\) | ||||
−0.487378 | + | 0.873191i | \(0.662047\pi\) | |||||||
\(858\) | 3.68942 | 0.125955 | ||||||||
\(859\) | 19.4417 | 0.663343 | 0.331671 | − | 0.943395i | \(-0.392387\pi\) | ||||
0.331671 | + | 0.943395i | \(0.392387\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 33.0671 | 1.12692 | ||||||||
\(862\) | −10.3336 | −0.351962 | ||||||||
\(863\) | −1.94514 | −0.0662132 | −0.0331066 | − | 0.999452i | \(-0.510540\pi\) | ||||
−0.0331066 | + | 0.999452i | \(0.510540\pi\) | |||||||
\(864\) | 15.0565 | 0.512233 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −28.4153 | −0.965590 | ||||||||
\(867\) | 5.35908 | 0.182004 | ||||||||
\(868\) | 4.43634 | 0.150579 | ||||||||
\(869\) | −12.0350 | −0.408261 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.69479 | 0.226844 | ||||||||
\(872\) | 0.218825 | 0.00741036 | ||||||||
\(873\) | 0.620176 | 0.0209898 | ||||||||
\(874\) | −6.73300 | −0.227747 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −30.1922 | −1.02010 | ||||||||
\(877\) | 38.6457 | 1.30497 | 0.652486 | − | 0.757800i | \(-0.273726\pi\) | ||||
0.652486 | + | 0.757800i | \(0.273726\pi\) | |||||||
\(878\) | −6.37313 | −0.215083 | ||||||||
\(879\) | 22.8854 | 0.771905 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −54.6889 | −1.84252 | −0.921258 | − | 0.388952i | \(-0.872837\pi\) | ||||
−0.921258 | + | 0.388952i | \(0.872837\pi\) | |||||||
\(882\) | 37.4807 | 1.26204 | ||||||||
\(883\) | 14.6273 | 0.492247 | 0.246123 | − | 0.969238i | \(-0.420843\pi\) | ||||
0.246123 | + | 0.969238i | \(0.420843\pi\) | |||||||
\(884\) | −2.18384 | −0.0734505 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 9.43114 | 0.316845 | ||||||||
\(887\) | −40.2666 | −1.35202 | −0.676010 | − | 0.736892i | \(-0.736293\pi\) | ||||
−0.676010 | + | 0.736892i | \(0.736293\pi\) | |||||||
\(888\) | 11.9208 | 0.400037 | ||||||||
\(889\) | 2.26424 | 0.0759401 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −53.2370 | −1.78351 | ||||||||
\(892\) | −20.2094 | −0.676660 | ||||||||
\(893\) | 4.44212 | 0.148650 | ||||||||
\(894\) | 77.6745 | 2.59782 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.44270 | 0.0481973 | ||||||||
\(897\) | −1.81616 | −0.0606398 | ||||||||
\(898\) | −11.3185 | −0.377704 | ||||||||
\(899\) | 29.8129 | 0.994317 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −43.6045 | −1.45268 | ||||||||
\(902\) | 14.2875 | 0.475723 | ||||||||
\(903\) | 23.8118 | 0.792406 | ||||||||
\(904\) | 0.580599 | 0.0193104 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −48.4491 | −1.60961 | ||||||||
\(907\) | −7.87090 | −0.261349 | −0.130674 | − | 0.991425i | \(-0.541714\pi\) | ||||
−0.130674 | + | 0.991425i | \(0.541714\pi\) | |||||||
\(908\) | −15.0098 | −0.498117 | ||||||||
\(909\) | 63.3451 | 2.10102 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.586235 | 0.0194228 | 0.00971141 | − | 0.999953i | \(-0.496909\pi\) | ||||
0.00971141 | + | 0.999953i | \(0.496909\pi\) | |||||||
\(912\) | 21.9419 | 0.726569 | ||||||||
\(913\) | −23.1126 | −0.764916 | ||||||||
\(914\) | −4.96456 | −0.164213 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 13.7081 | 0.452929 | ||||||||
\(917\) | −22.9690 | −0.758504 | ||||||||
\(918\) | 59.0007 | 1.94731 | ||||||||
\(919\) | −27.9422 | −0.921729 | −0.460865 | − | 0.887470i | \(-0.652461\pi\) | ||||
−0.460865 | + | 0.887470i | \(0.652461\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 53.4961 | 1.76276 | ||||||||
\(922\) | −19.9128 | −0.655794 | ||||||||
\(923\) | −6.93076 | −0.228129 | ||||||||
\(924\) | −9.55093 | −0.314203 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 29.9046 | 0.982725 | ||||||||
\(927\) | 48.5399 | 1.59426 | ||||||||
\(928\) | 9.69520 | 0.318260 | ||||||||
\(929\) | −4.79352 | −0.157270 | −0.0786351 | − | 0.996903i | \(-0.525056\pi\) | ||||
−0.0786351 | + | 0.996903i | \(0.525056\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 33.1170 | 1.08537 | ||||||||
\(932\) | 9.19822 | 0.301298 | ||||||||
\(933\) | −23.9585 | −0.784367 | ||||||||
\(934\) | −15.1032 | −0.494193 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 4.24672 | 0.138808 | ||||||||
\(937\) | −0.110466 | −0.00360877 | −0.00180438 | − | 0.999998i | \(-0.500574\pi\) | ||||
−0.00180438 | + | 0.999998i | \(0.500574\pi\) | |||||||
\(938\) | −17.3311 | −0.565879 | ||||||||
\(939\) | 13.3278 | 0.434938 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 19.2077 | 0.626155 | 0.313077 | − | 0.949728i | \(-0.398640\pi\) | ||||
0.313077 | + | 0.949728i | \(0.398640\pi\) | |||||||
\(942\) | −26.8599 | −0.875144 | ||||||||
\(943\) | −7.03321 | −0.229033 | ||||||||
\(944\) | 10.7226 | 0.348992 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 10.2885 | 0.334509 | ||||||||
\(947\) | −20.0933 | −0.652944 | −0.326472 | − | 0.945207i | \(-0.605860\pi\) | ||||
−0.326472 | + | 0.945207i | \(0.605860\pi\) | |||||||
\(948\) | −19.3068 | −0.627055 | ||||||||
\(949\) | −5.16318 | −0.167604 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 29.0553 | 0.942184 | ||||||||
\(952\) | 5.65339 | 0.183227 | ||||||||
\(953\) | −55.4762 | −1.79705 | −0.898526 | − | 0.438920i | \(-0.855361\pi\) | ||||
−0.898526 | + | 0.438920i | \(0.855361\pi\) | |||||||
\(954\) | 84.7937 | 2.74530 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −2.72618 | −0.0881709 | ||||||||
\(957\) | −64.1839 | −2.07477 | ||||||||
\(958\) | −28.6678 | −0.926213 | ||||||||
\(959\) | −9.33447 | −0.301426 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.5442 | −0.694976 | ||||||||
\(962\) | 2.03859 | 0.0657267 | ||||||||
\(963\) | 128.953 | 4.15546 | ||||||||
\(964\) | 3.26109 | 0.105033 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 4.70156 | 0.151270 | ||||||||
\(967\) | 2.86228 | 0.0920448 | 0.0460224 | − | 0.998940i | \(-0.485345\pi\) | ||||
0.0460224 | + | 0.998940i | \(0.485345\pi\) | |||||||
\(968\) | 6.87326 | 0.220915 | ||||||||
\(969\) | 85.9819 | 2.76214 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 42.5901 | 1.36678 | 0.683391 | − | 0.730052i | \(-0.260504\pi\) | ||||
0.683391 | + | 0.730052i | \(0.260504\pi\) | |||||||
\(972\) | −40.2340 | −1.29051 | ||||||||
\(973\) | 0.946709 | 0.0303501 | ||||||||
\(974\) | −9.15319 | −0.293287 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.73937 | 0.0556757 | ||||||||
\(977\) | −42.5633 | −1.36172 | −0.680861 | − | 0.732413i | \(-0.738394\pi\) | ||||
−0.680861 | + | 0.732413i | \(0.738394\pi\) | |||||||
\(978\) | 33.6164 | 1.07493 | ||||||||
\(979\) | −10.6713 | −0.341057 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.66749 | −0.0532388 | ||||||||
\(982\) | 20.8098 | 0.664067 | ||||||||
\(983\) | −32.6691 | −1.04198 | −0.520991 | − | 0.853562i | \(-0.674437\pi\) | ||||
−0.520991 | + | 0.853562i | \(0.674437\pi\) | |||||||
\(984\) | 22.9203 | 0.730671 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 37.9917 | 1.20990 | ||||||||
\(987\) | −3.10187 | −0.0987336 | ||||||||
\(988\) | 3.75229 | 0.119376 | ||||||||
\(989\) | −5.06465 | −0.161047 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.39775 | −0.139699 | −0.0698495 | − | 0.997558i | \(-0.522252\pi\) | ||||
−0.0698495 | + | 0.997558i | \(0.522252\pi\) | |||||||
\(992\) | 3.07502 | 0.0976320 | ||||||||
\(993\) | −69.4919 | −2.20526 | ||||||||
\(994\) | 17.9419 | 0.569083 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −37.0776 | −1.17485 | ||||||||
\(997\) | −33.4135 | −1.05822 | −0.529108 | − | 0.848554i | \(-0.677473\pi\) | ||||
−0.529108 | + | 0.848554i | \(0.677473\pi\) | |||||||
\(998\) | 18.1293 | 0.573873 | ||||||||
\(999\) | −55.0764 | −1.74254 |
(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 | 1150.2.a.r.1.1 | 4 | ||
4.3 | odd | 2 | 9200.2.a.cr.1.4 | 4 | |||
5.2 | odd | 4 | 230.2.b.b.139.4 | ✓ | 8 | ||
5.3 | odd | 4 | 230.2.b.b.139.5 | yes | 8 | ||
5.4 | even | 2 | 1150.2.a.s.1.4 | 4 | |||
15.2 | even | 4 | 2070.2.d.f.829.6 | 8 | |||
15.8 | even | 4 | 2070.2.d.f.829.2 | 8 | |||
20.3 | even | 4 | 1840.2.e.e.369.8 | 8 | |||
20.7 | even | 4 | 1840.2.e.e.369.1 | 8 | |||
20.19 | odd | 2 | 9200.2.a.cj.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.2.b.b.139.4 | ✓ | 8 | 5.2 | odd | 4 | ||
230.2.b.b.139.5 | yes | 8 | 5.3 | odd | 4 | ||
1150.2.a.r.1.1 | 4 | 1.1 | even | 1 | trivial | ||
1150.2.a.s.1.4 | 4 | 5.4 | even | 2 | |||
1840.2.e.e.369.1 | 8 | 20.7 | even | 4 | |||
1840.2.e.e.369.8 | 8 | 20.3 | even | 4 | |||
2070.2.d.f.829.2 | 8 | 15.8 | even | 4 | |||
2070.2.d.f.829.6 | 8 | 15.2 | even | 4 | |||
9200.2.a.cj.1.1 | 4 | 20.19 | odd | 2 | |||
9200.2.a.cr.1.4 | 4 | 4.3 | odd | 2 |