Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6003,2,Mod(1,6003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6003, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("6003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6003 = 3^{2} \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6003.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: | \(47.9341963334\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 2 x^{13} - 18 x^{12} + 34 x^{11} + 124 x^{10} - 216 x^{9} - 420 x^{8} + 647 x^{7} + 750 x^{6} - 939 x^{5} - 717 x^{4} + 604 x^{3} + 352 x^{2} - 128 x - 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 2001) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Root | \(2.31598\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6003.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.31598 | 1.63764 | 0.818822 | − | 0.574047i | \(-0.194627\pi\) | ||||
0.818822 | + | 0.574047i | \(0.194627\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.36376 | 1.68188 | ||||||||
\(5\) | 2.86683 | 1.28209 | 0.641043 | − | 0.767505i | \(-0.278502\pi\) | ||||
0.641043 | + | 0.767505i | \(0.278502\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.60131 | 1.36117 | 0.680583 | − | 0.732671i | \(-0.261726\pi\) | ||||
0.680583 | + | 0.732671i | \(0.261726\pi\) | |||||||
\(8\) | 3.15843 | 1.11667 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 6.63952 | 2.09960 | ||||||||
\(11\) | −0.489865 | −0.147700 | −0.0738500 | − | 0.997269i | \(-0.523529\pi\) | ||||
−0.0738500 | + | 0.997269i | \(0.523529\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.88891 | 0.801238 | 0.400619 | − | 0.916245i | \(-0.368795\pi\) | ||||
0.400619 | + | 0.916245i | \(0.368795\pi\) | |||||||
\(14\) | 8.34055 | 2.22911 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.587346 | 0.146837 | ||||||||
\(17\) | 6.07526 | 1.47347 | 0.736733 | − | 0.676184i | \(-0.236368\pi\) | ||||
0.736733 | + | 0.676184i | \(0.236368\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.208958 | −0.0479383 | −0.0239692 | − | 0.999713i | \(-0.507630\pi\) | ||||
−0.0239692 | + | 0.999713i | \(0.507630\pi\) | |||||||
\(20\) | 9.64332 | 2.15631 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.13452 | −0.241880 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.21872 | 0.643743 | ||||||||
\(26\) | 6.69064 | 1.31214 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 12.1139 | 2.28932 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.93798 | −1.24610 | −0.623049 | − | 0.782183i | \(-0.714106\pi\) | ||||
−0.623049 | + | 0.782183i | \(0.714106\pi\) | |||||||
\(32\) | −4.95658 | −0.876208 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 14.0702 | 2.41301 | ||||||||
\(35\) | 10.3243 | 1.74513 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.06467 | −0.832627 | −0.416313 | − | 0.909221i | \(-0.636678\pi\) | ||||
−0.416313 | + | 0.909221i | \(0.636678\pi\) | |||||||
\(38\) | −0.483943 | −0.0785060 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 9.05469 | 1.43167 | ||||||||
\(41\) | −9.28334 | −1.44981 | −0.724907 | − | 0.688847i | \(-0.758117\pi\) | ||||
−0.724907 | + | 0.688847i | \(0.758117\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.52223 | 1.14713 | 0.573565 | − | 0.819160i | \(-0.305560\pi\) | ||||
0.573565 | + | 0.819160i | \(0.305560\pi\) | |||||||
\(44\) | −1.64779 | −0.248413 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.31598 | 0.341472 | ||||||||
\(47\) | 1.61063 | 0.234935 | 0.117468 | − | 0.993077i | \(-0.462522\pi\) | ||||
0.117468 | + | 0.993077i | \(0.462522\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.96943 | 0.852775 | ||||||||
\(50\) | 7.45448 | 1.05422 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 9.71758 | 1.34759 | ||||||||
\(53\) | −10.1414 | −1.39303 | −0.696516 | − | 0.717541i | \(-0.745267\pi\) | ||||
−0.696516 | + | 0.717541i | \(0.745267\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.40436 | −0.189364 | ||||||||
\(56\) | 11.3745 | 1.51998 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.31598 | 0.304103 | ||||||||
\(59\) | −10.2020 | −1.32818 | −0.664091 | − | 0.747652i | \(-0.731181\pi\) | ||||
−0.664091 | + | 0.747652i | \(0.731181\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.55359 | −1.22321 | −0.611606 | − | 0.791163i | \(-0.709476\pi\) | ||||
−0.611606 | + | 0.791163i | \(0.709476\pi\) | |||||||
\(62\) | −16.0682 | −2.04067 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −12.6540 | −1.58175 | ||||||||
\(65\) | 8.28200 | 1.02726 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.1104 | −1.47953 | −0.739763 | − | 0.672867i | \(-0.765062\pi\) | ||||
−0.739763 | + | 0.672867i | \(0.765062\pi\) | |||||||
\(68\) | 20.4357 | 2.47819 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 23.9110 | 2.85791 | ||||||||
\(71\) | −2.69908 | −0.320321 | −0.160161 | − | 0.987091i | \(-0.551201\pi\) | ||||
−0.160161 | + | 0.987091i | \(0.551201\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.65365 | −0.544668 | −0.272334 | − | 0.962203i | \(-0.587796\pi\) | ||||
−0.272334 | + | 0.962203i | \(0.587796\pi\) | |||||||
\(74\) | −11.7297 | −1.36355 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.702885 | −0.0806265 | ||||||||
\(77\) | −1.76416 | −0.201044 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.85970 | 0.884285 | 0.442142 | − | 0.896945i | \(-0.354219\pi\) | ||||
0.442142 | + | 0.896945i | \(0.354219\pi\) | |||||||
\(80\) | 1.68382 | 0.188257 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −21.5000 | −2.37428 | ||||||||
\(83\) | 1.79638 | 0.197178 | 0.0985889 | − | 0.995128i | \(-0.468567\pi\) | ||||
0.0985889 | + | 0.995128i | \(0.468567\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 17.4167 | 1.88911 | ||||||||
\(86\) | 17.4213 | 1.87859 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.54721 | −0.164933 | ||||||||
\(89\) | 7.62479 | 0.808227 | 0.404113 | − | 0.914709i | \(-0.367580\pi\) | ||||
0.404113 | + | 0.914709i | \(0.367580\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.4038 | 1.09062 | ||||||||
\(92\) | 3.36376 | 0.350696 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.73019 | 0.384740 | ||||||||
\(95\) | −0.599048 | −0.0614611 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.18136 | 0.526087 | 0.263044 | − | 0.964784i | \(-0.415274\pi\) | ||||
0.263044 | + | 0.964784i | \(0.415274\pi\) | |||||||
\(98\) | 13.8251 | 1.39654 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 10.8270 | 1.08270 | ||||||||
\(101\) | 13.7012 | 1.36332 | 0.681662 | − | 0.731667i | \(-0.261258\pi\) | ||||
0.681662 | + | 0.731667i | \(0.261258\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.5310 | 1.33325 | 0.666626 | − | 0.745393i | \(-0.267738\pi\) | ||||
0.666626 | + | 0.745393i | \(0.267738\pi\) | |||||||
\(104\) | 9.12441 | 0.894722 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −23.4873 | −2.28129 | ||||||||
\(107\) | −0.886283 | −0.0856802 | −0.0428401 | − | 0.999082i | \(-0.513641\pi\) | ||||
−0.0428401 | + | 0.999082i | \(0.513641\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.81821 | −0.269936 | −0.134968 | − | 0.990850i | \(-0.543093\pi\) | ||||
−0.134968 | + | 0.990850i | \(0.543093\pi\) | |||||||
\(110\) | −3.25247 | −0.310111 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.11521 | 0.199869 | ||||||||
\(113\) | 16.3262 | 1.53584 | 0.767920 | − | 0.640546i | \(-0.221292\pi\) | ||||
0.767920 | + | 0.640546i | \(0.221292\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.86683 | 0.267333 | ||||||||
\(116\) | 3.36376 | 0.312317 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −23.6275 | −2.17509 | ||||||||
\(119\) | 21.8789 | 2.00563 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.7600 | −0.978185 | ||||||||
\(122\) | −22.1259 | −2.00318 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −23.3377 | −2.09579 | ||||||||
\(125\) | −5.10664 | −0.456751 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.94903 | −0.527891 | −0.263945 | − | 0.964538i | \(-0.585024\pi\) | ||||
−0.263945 | + | 0.964538i | \(0.585024\pi\) | |||||||
\(128\) | −19.3933 | −1.71414 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 19.1809 | 1.68228 | ||||||||
\(131\) | −8.74603 | −0.764144 | −0.382072 | − | 0.924133i | \(-0.624789\pi\) | ||||
−0.382072 | + | 0.924133i | \(0.624789\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.752524 | −0.0652521 | ||||||||
\(134\) | −28.0475 | −2.42294 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 19.1883 | 1.64538 | ||||||||
\(137\) | 4.87871 | 0.416816 | 0.208408 | − | 0.978042i | \(-0.433172\pi\) | ||||
0.208408 | + | 0.978042i | \(0.433172\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.31445 | 0.705223 | 0.352611 | − | 0.935770i | \(-0.385294\pi\) | ||||
0.352611 | + | 0.935770i | \(0.385294\pi\) | |||||||
\(140\) | 34.7286 | 2.93510 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −6.25100 | −0.524573 | ||||||||
\(143\) | −1.41518 | −0.118343 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.86683 | 0.238077 | ||||||||
\(146\) | −10.7777 | −0.891973 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −17.0363 | −1.40038 | ||||||||
\(149\) | 22.8015 | 1.86797 | 0.933987 | − | 0.357307i | \(-0.116305\pi\) | ||||
0.933987 | + | 0.357307i | \(0.116305\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.4224 | −1.41782 | −0.708908 | − | 0.705301i | \(-0.750812\pi\) | ||||
−0.708908 | + | 0.705301i | \(0.750812\pi\) | |||||||
\(152\) | −0.659981 | −0.0535315 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.08575 | −0.329239 | ||||||||
\(155\) | −19.8900 | −1.59760 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.18382 | 0.732949 | 0.366474 | − | 0.930428i | \(-0.380565\pi\) | ||||
0.366474 | + | 0.930428i | \(0.380565\pi\) | |||||||
\(158\) | 18.2029 | 1.44814 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −14.2097 | −1.12337 | ||||||||
\(161\) | 3.60131 | 0.283823 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.9352 | 1.24814 | 0.624072 | − | 0.781367i | \(-0.285477\pi\) | ||||
0.624072 | + | 0.781367i | \(0.285477\pi\) | |||||||
\(164\) | −31.2269 | −2.43841 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.16037 | 0.322907 | ||||||||
\(167\) | −21.1433 | −1.63612 | −0.818058 | − | 0.575136i | \(-0.804949\pi\) | ||||
−0.818058 | + | 0.575136i | \(0.804949\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.65422 | −0.358017 | ||||||||
\(170\) | 40.3368 | 3.09369 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 25.3030 | 1.92933 | ||||||||
\(173\) | −13.5153 | −1.02755 | −0.513776 | − | 0.857924i | \(-0.671754\pi\) | ||||
−0.513776 | + | 0.857924i | \(0.671754\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 11.5916 | 0.876242 | ||||||||
\(176\) | −0.287721 | −0.0216877 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 17.6589 | 1.32359 | ||||||||
\(179\) | 7.42060 | 0.554641 | 0.277321 | − | 0.960777i | \(-0.410554\pi\) | ||||
0.277321 | + | 0.960777i | \(0.410554\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.32130 | 0.321200 | 0.160600 | − | 0.987020i | \(-0.448657\pi\) | ||||
0.160600 | + | 0.987020i | \(0.448657\pi\) | |||||||
\(182\) | 24.0951 | 1.78605 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.15843 | 0.232843 | ||||||||
\(185\) | −14.5196 | −1.06750 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.97606 | −0.217631 | ||||||||
\(188\) | 5.41778 | 0.395132 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.38738 | −0.100651 | ||||||||
\(191\) | 1.47681 | 0.106858 | 0.0534291 | − | 0.998572i | \(-0.482985\pi\) | ||||
0.0534291 | + | 0.998572i | \(0.482985\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −15.2102 | −1.09485 | −0.547427 | − | 0.836853i | \(-0.684393\pi\) | ||||
−0.547427 | + | 0.836853i | \(0.684393\pi\) | |||||||
\(194\) | 11.9999 | 0.861543 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 20.0797 | 1.43426 | ||||||||
\(197\) | 2.57123 | 0.183192 | 0.0915961 | − | 0.995796i | \(-0.470803\pi\) | ||||
0.0915961 | + | 0.995796i | \(0.470803\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15.7035 | −1.11319 | −0.556596 | − | 0.830783i | \(-0.687893\pi\) | ||||
−0.556596 | + | 0.830783i | \(0.687893\pi\) | |||||||
\(200\) | 10.1661 | 0.718852 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 31.7318 | 2.23264 | ||||||||
\(203\) | 3.60131 | 0.252762 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −26.6138 | −1.85879 | ||||||||
\(206\) | 31.3376 | 2.18339 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.69679 | 0.117651 | ||||||||
\(209\) | 0.102361 | 0.00708049 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.4076 | −1.61145 | −0.805723 | − | 0.592292i | \(-0.798223\pi\) | ||||
−0.805723 | + | 0.592292i | \(0.798223\pi\) | |||||||
\(212\) | −34.1133 | −2.34291 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.05261 | −0.140314 | ||||||||
\(215\) | 21.5650 | 1.47072 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −24.9858 | −1.69615 | ||||||||
\(218\) | −6.52692 | −0.442059 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −4.72393 | −0.318487 | ||||||||
\(221\) | 17.5508 | 1.18060 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −15.7410 | −1.05410 | −0.527048 | − | 0.849836i | \(-0.676701\pi\) | ||||
−0.527048 | + | 0.849836i | \(0.676701\pi\) | |||||||
\(224\) | −17.8502 | −1.19267 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 37.8111 | 2.51516 | ||||||||
\(227\) | 22.0224 | 1.46168 | 0.730840 | − | 0.682549i | \(-0.239129\pi\) | ||||
0.730840 | + | 0.682549i | \(0.239129\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16.1546 | −1.06752 | −0.533762 | − | 0.845635i | \(-0.679222\pi\) | ||||
−0.533762 | + | 0.845635i | \(0.679222\pi\) | |||||||
\(230\) | 6.63952 | 0.437797 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.15843 | 0.207361 | ||||||||
\(233\) | 18.8801 | 1.23688 | 0.618440 | − | 0.785832i | \(-0.287765\pi\) | ||||
0.618440 | + | 0.785832i | \(0.287765\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.61741 | 0.301207 | ||||||||
\(236\) | −34.3169 | −2.23384 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 50.6710 | 3.28451 | ||||||||
\(239\) | 13.8197 | 0.893921 | 0.446960 | − | 0.894554i | \(-0.352507\pi\) | ||||
0.446960 | + | 0.894554i | \(0.352507\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.07448 | −0.262460 | −0.131230 | − | 0.991352i | \(-0.541893\pi\) | ||||
−0.131230 | + | 0.991352i | \(0.541893\pi\) | |||||||
\(242\) | −24.9200 | −1.60192 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −32.1359 | −2.05729 | ||||||||
\(245\) | 17.1133 | 1.09333 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.603661 | −0.0384100 | ||||||||
\(248\) | −21.9131 | −1.39149 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −11.8269 | −0.747996 | ||||||||
\(251\) | −6.49386 | −0.409889 | −0.204945 | − | 0.978774i | \(-0.565701\pi\) | ||||
−0.204945 | + | 0.978774i | \(0.565701\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.489865 | −0.0307976 | ||||||||
\(254\) | −13.7778 | −0.864498 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −19.6064 | −1.22540 | ||||||||
\(257\) | −15.0388 | −0.938097 | −0.469049 | − | 0.883172i | \(-0.655403\pi\) | ||||
−0.469049 | + | 0.883172i | \(0.655403\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −18.2394 | −1.13334 | ||||||||
\(260\) | 27.8586 | 1.72772 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −20.2556 | −1.25140 | ||||||||
\(263\) | 18.5844 | 1.14597 | 0.572983 | − | 0.819567i | \(-0.305786\pi\) | ||||
0.572983 | + | 0.819567i | \(0.305786\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −29.0737 | −1.78599 | ||||||||
\(266\) | −1.74283 | −0.106860 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −40.7366 | −2.48838 | ||||||||
\(269\) | 10.7377 | 0.654686 | 0.327343 | − | 0.944905i | \(-0.393847\pi\) | ||||
0.327343 | + | 0.944905i | \(0.393847\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.66418 | 0.161837 | 0.0809187 | − | 0.996721i | \(-0.474215\pi\) | ||||
0.0809187 | + | 0.996721i | \(0.474215\pi\) | |||||||
\(272\) | 3.56828 | 0.216359 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 11.2990 | 0.682597 | ||||||||
\(275\) | −1.57674 | −0.0950809 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 17.2762 | 1.03803 | 0.519013 | − | 0.854767i | \(-0.326300\pi\) | ||||
0.519013 | + | 0.854767i | \(0.326300\pi\) | |||||||
\(278\) | 19.2561 | 1.15490 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 32.6087 | 1.94874 | ||||||||
\(281\) | 26.7094 | 1.59335 | 0.796674 | − | 0.604409i | \(-0.206591\pi\) | ||||
0.796674 | + | 0.604409i | \(0.206591\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 25.3486 | 1.50682 | 0.753410 | − | 0.657551i | \(-0.228408\pi\) | ||||
0.753410 | + | 0.657551i | \(0.228408\pi\) | |||||||
\(284\) | −9.07904 | −0.538742 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.27752 | −0.193804 | ||||||||
\(287\) | −33.4322 | −1.97344 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 19.9087 | 1.17110 | ||||||||
\(290\) | 6.63952 | 0.389886 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −15.6537 | −0.916066 | ||||||||
\(293\) | 5.13931 | 0.300242 | 0.150121 | − | 0.988668i | \(-0.452034\pi\) | ||||
0.150121 | + | 0.988668i | \(0.452034\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −29.2473 | −1.70284 | ||||||||
\(296\) | −15.9964 | −0.929773 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 52.8079 | 3.05908 | ||||||||
\(299\) | 2.88891 | 0.167070 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 27.0899 | 1.56144 | ||||||||
\(302\) | −40.3500 | −2.32188 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.122731 | −0.00703910 | ||||||||
\(305\) | −27.3885 | −1.56826 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 19.5783 | 1.11739 | 0.558695 | − | 0.829373i | \(-0.311302\pi\) | ||||
0.558695 | + | 0.829373i | \(0.311302\pi\) | |||||||
\(308\) | −5.93419 | −0.338132 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −46.0648 | −2.61631 | ||||||||
\(311\) | 34.2429 | 1.94174 | 0.970868 | − | 0.239617i | \(-0.0770218\pi\) | ||||
0.970868 | + | 0.239617i | \(0.0770218\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.49992 | −0.367397 | −0.183699 | − | 0.982983i | \(-0.558807\pi\) | ||||
−0.183699 | + | 0.982983i | \(0.558807\pi\) | |||||||
\(314\) | 21.2695 | 1.20031 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 26.4381 | 1.48726 | ||||||||
\(317\) | 15.0420 | 0.844842 | 0.422421 | − | 0.906400i | \(-0.361180\pi\) | ||||
0.422421 | + | 0.906400i | \(0.361180\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.489865 | −0.0274272 | ||||||||
\(320\) | −36.2770 | −2.02794 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 8.34055 | 0.464801 | ||||||||
\(323\) | −1.26948 | −0.0706355 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.29857 | 0.515792 | ||||||||
\(326\) | 36.9057 | 2.04402 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −29.3208 | −1.61897 | ||||||||
\(329\) | 5.80039 | 0.319786 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.36598 | −0.130046 | −0.0650229 | − | 0.997884i | \(-0.520712\pi\) | ||||
−0.0650229 | + | 0.997884i | \(0.520712\pi\) | |||||||
\(332\) | 6.04257 | 0.331629 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −48.9674 | −2.67938 | ||||||||
\(335\) | −34.7186 | −1.89688 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.98588 | 0.543965 | 0.271983 | − | 0.962302i | \(-0.412321\pi\) | ||||
0.271983 | + | 0.962302i | \(0.412321\pi\) | |||||||
\(338\) | −10.7791 | −0.586304 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 58.5856 | 3.17725 | ||||||||
\(341\) | 3.39868 | 0.184049 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.71141 | −0.200397 | ||||||||
\(344\) | 23.7585 | 1.28097 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −31.3012 | −1.68277 | ||||||||
\(347\) | −6.98651 | −0.375055 | −0.187528 | − | 0.982259i | \(-0.560047\pi\) | ||||
−0.187528 | + | 0.982259i | \(0.560047\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 26.5857 | 1.42310 | 0.711550 | − | 0.702636i | \(-0.247994\pi\) | ||||
0.711550 | + | 0.702636i | \(0.247994\pi\) | |||||||
\(350\) | 26.8459 | 1.43497 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.42806 | 0.129416 | ||||||||
\(353\) | −7.02757 | −0.374040 | −0.187020 | − | 0.982356i | \(-0.559883\pi\) | ||||
−0.187020 | + | 0.982356i | \(0.559883\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.73780 | −0.410680 | ||||||||
\(356\) | 25.6480 | 1.35934 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 17.1859 | 0.908305 | ||||||||
\(359\) | 26.5303 | 1.40022 | 0.700108 | − | 0.714037i | \(-0.253135\pi\) | ||||
0.700108 | + | 0.714037i | \(0.253135\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9563 | −0.997702 | ||||||||
\(362\) | 10.0080 | 0.526011 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 34.9960 | 1.83429 | ||||||||
\(365\) | −13.3412 | −0.698311 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −34.2926 | −1.79006 | −0.895029 | − | 0.446007i | \(-0.852845\pi\) | ||||
−0.895029 | + | 0.446007i | \(0.852845\pi\) | |||||||
\(368\) | 0.587346 | 0.0306175 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −33.6270 | −1.74818 | ||||||||
\(371\) | −36.5224 | −1.89615 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.1764 | −0.734028 | −0.367014 | − | 0.930215i | \(-0.619620\pi\) | ||||
−0.367014 | + | 0.930215i | \(0.619620\pi\) | |||||||
\(374\) | −6.89249 | −0.356402 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.08707 | 0.262346 | ||||||||
\(377\) | 2.88891 | 0.148786 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −25.6733 | −1.31875 | −0.659374 | − | 0.751815i | \(-0.729178\pi\) | ||||
−0.659374 | + | 0.751815i | \(0.729178\pi\) | |||||||
\(380\) | −2.01505 | −0.103370 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3.42026 | 0.174996 | ||||||||
\(383\) | −17.9881 | −0.919147 | −0.459573 | − | 0.888140i | \(-0.651998\pi\) | ||||
−0.459573 | + | 0.888140i | \(0.651998\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.05754 | −0.257756 | ||||||||
\(386\) | −35.2265 | −1.79298 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 17.4288 | 0.884814 | ||||||||
\(389\) | 23.3777 | 1.18530 | 0.592648 | − | 0.805462i | \(-0.298083\pi\) | ||||
0.592648 | + | 0.805462i | \(0.298083\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.07526 | 0.307239 | ||||||||
\(392\) | 18.8540 | 0.952272 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 5.95491 | 0.300004 | ||||||||
\(395\) | 22.5324 | 1.13373 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 34.1121 | 1.71204 | 0.856018 | − | 0.516945i | \(-0.172931\pi\) | ||||
0.856018 | + | 0.516945i | \(0.172931\pi\) | |||||||
\(398\) | −36.3690 | −1.82301 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.89050 | 0.0945250 | ||||||||
\(401\) | 4.90447 | 0.244918 | 0.122459 | − | 0.992474i | \(-0.460922\pi\) | ||||
0.122459 | + | 0.992474i | \(0.460922\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −20.0432 | −0.998422 | ||||||||
\(404\) | 46.0876 | 2.29294 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.34055 | 0.413935 | ||||||||
\(407\) | 2.48101 | 0.122979 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.13942 | −0.303575 | −0.151787 | − | 0.988413i | \(-0.548503\pi\) | ||||
−0.151787 | + | 0.988413i | \(0.548503\pi\) | |||||||
\(410\) | −61.6369 | −3.04403 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 45.5151 | 2.24237 | ||||||||
\(413\) | −36.7404 | −1.80788 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.14990 | 0.252799 | ||||||||
\(416\) | −14.3191 | −0.702052 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.237067 | 0.0115953 | ||||||||
\(419\) | −1.46153 | −0.0714006 | −0.0357003 | − | 0.999363i | \(-0.511366\pi\) | ||||
−0.0357003 | + | 0.999363i | \(0.511366\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 32.7873 | 1.59796 | 0.798978 | − | 0.601360i | \(-0.205374\pi\) | ||||
0.798978 | + | 0.601360i | \(0.205374\pi\) | |||||||
\(422\) | −54.2115 | −2.63898 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −32.0310 | −1.55556 | ||||||||
\(425\) | 19.5545 | 0.948534 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −34.4054 | −1.66499 | ||||||||
\(428\) | −2.98124 | −0.144104 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 49.9440 | 2.40851 | ||||||||
\(431\) | 27.1771 | 1.30908 | 0.654539 | − | 0.756029i | \(-0.272863\pi\) | ||||
0.654539 | + | 0.756029i | \(0.272863\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 30.6675 | 1.47379 | 0.736893 | − | 0.676009i | \(-0.236292\pi\) | ||||
0.736893 | + | 0.676009i | \(0.236292\pi\) | |||||||
\(434\) | −57.8666 | −2.77769 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9.47978 | −0.453999 | ||||||||
\(437\) | −0.208958 | −0.00999584 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.50454 | 0.167263 | 0.0836313 | − | 0.996497i | \(-0.473348\pi\) | ||||
0.0836313 | + | 0.996497i | \(0.473348\pi\) | |||||||
\(440\) | −4.43558 | −0.211458 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 40.6474 | 1.93340 | ||||||||
\(443\) | 5.91295 | 0.280933 | 0.140466 | − | 0.990085i | \(-0.455140\pi\) | ||||
0.140466 | + | 0.990085i | \(0.455140\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 21.8590 | 1.03622 | ||||||||
\(446\) | −36.4558 | −1.72623 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −45.5711 | −2.15303 | ||||||||
\(449\) | −22.8726 | −1.07942 | −0.539711 | − | 0.841850i | \(-0.681467\pi\) | ||||
−0.539711 | + | 0.841850i | \(0.681467\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.54759 | 0.214137 | ||||||||
\(452\) | 54.9174 | 2.58310 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 51.0035 | 2.39371 | ||||||||
\(455\) | 29.8261 | 1.39827 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16.5249 | 0.773001 | 0.386500 | − | 0.922289i | \(-0.373684\pi\) | ||||
0.386500 | + | 0.922289i | \(0.373684\pi\) | |||||||
\(458\) | −37.4136 | −1.74822 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 9.64332 | 0.449622 | ||||||||
\(461\) | 6.64056 | 0.309282 | 0.154641 | − | 0.987971i | \(-0.450578\pi\) | ||||
0.154641 | + | 0.987971i | \(0.450578\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −18.7173 | −0.869868 | −0.434934 | − | 0.900462i | \(-0.643228\pi\) | ||||
−0.434934 | + | 0.900462i | \(0.643228\pi\) | |||||||
\(464\) | 0.587346 | 0.0272669 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 43.7260 | 2.02557 | ||||||||
\(467\) | −7.74364 | −0.358333 | −0.179167 | − | 0.983819i | \(-0.557340\pi\) | ||||
−0.179167 | + | 0.983819i | \(0.557340\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −43.6135 | −2.01388 | ||||||||
\(470\) | 10.6938 | 0.493270 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −32.2222 | −1.48315 | ||||||||
\(473\) | −3.68488 | −0.169431 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.672578 | −0.0308600 | ||||||||
\(476\) | 73.5952 | 3.37323 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 32.0061 | 1.46392 | ||||||||
\(479\) | −19.4249 | −0.887547 | −0.443773 | − | 0.896139i | \(-0.646360\pi\) | ||||
−0.443773 | + | 0.896139i | \(0.646360\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −14.6314 | −0.667133 | ||||||||
\(482\) | −9.43640 | −0.429816 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −36.1941 | −1.64519 | ||||||||
\(485\) | 14.8541 | 0.674489 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.6818 | 0.484040 | 0.242020 | − | 0.970271i | \(-0.422190\pi\) | ||||
0.242020 | + | 0.970271i | \(0.422190\pi\) | |||||||
\(488\) | −30.1743 | −1.36593 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 39.6341 | 1.79049 | ||||||||
\(491\) | −1.90753 | −0.0860855 | −0.0430427 | − | 0.999073i | \(-0.513705\pi\) | ||||
−0.0430427 | + | 0.999073i | \(0.513705\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.07526 | 0.273616 | ||||||||
\(494\) | −1.39807 | −0.0629020 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.07499 | −0.182973 | ||||||||
\(497\) | −9.72021 | −0.436011 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.2192 | −0.591774 | −0.295887 | − | 0.955223i | \(-0.595615\pi\) | ||||
−0.295887 | + | 0.955223i | \(0.595615\pi\) | |||||||
\(500\) | −17.1775 | −0.768200 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −15.0397 | −0.671253 | ||||||||
\(503\) | −27.6893 | −1.23460 | −0.617302 | − | 0.786726i | \(-0.711774\pi\) | ||||
−0.617302 | + | 0.786726i | \(0.711774\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 39.2791 | 1.74790 | ||||||||
\(506\) | −1.13452 | −0.0504355 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −20.0111 | −0.887848 | ||||||||
\(509\) | −9.69520 | −0.429732 | −0.214866 | − | 0.976644i | \(-0.568931\pi\) | ||||
−0.214866 | + | 0.976644i | \(0.568931\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16.7592 | −0.741384 | ||||||||
\(512\) | −6.62141 | −0.292628 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −34.8296 | −1.53627 | ||||||||
\(515\) | 38.7911 | 1.70934 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.788994 | −0.0346999 | ||||||||
\(518\) | −42.2422 | −1.85601 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 26.1581 | 1.14711 | ||||||||
\(521\) | −24.2177 | −1.06100 | −0.530498 | − | 0.847686i | \(-0.677995\pi\) | ||||
−0.530498 | + | 0.847686i | \(0.677995\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −32.5030 | −1.42126 | −0.710629 | − | 0.703567i | \(-0.751590\pi\) | ||||
−0.710629 | + | 0.703567i | \(0.751590\pi\) | |||||||
\(524\) | −29.4195 | −1.28520 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 43.0412 | 1.87668 | ||||||||
\(527\) | −42.1500 | −1.83608 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −67.3342 | −2.92481 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.53131 | −0.109746 | ||||||||
\(533\) | −26.8187 | −1.16165 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.54082 | −0.109849 | ||||||||
\(536\) | −38.2500 | −1.65215 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 24.8682 | 1.07214 | ||||||||
\(539\) | −2.92422 | −0.125955 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.49329 | −0.107195 | −0.0535974 | − | 0.998563i | \(-0.517069\pi\) | ||||
−0.0535974 | + | 0.998563i | \(0.517069\pi\) | |||||||
\(542\) | 6.17019 | 0.265032 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −30.1125 | −1.29106 | ||||||||
\(545\) | −8.07934 | −0.346081 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −44.0449 | −1.88322 | −0.941612 | − | 0.336699i | \(-0.890690\pi\) | ||||
−0.941612 | + | 0.336699i | \(0.890690\pi\) | |||||||
\(548\) | 16.4108 | 0.701035 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −3.65169 | −0.155709 | ||||||||
\(551\) | −0.208958 | −0.00890193 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 28.3052 | 1.20366 | ||||||||
\(554\) | 40.0113 | 1.69992 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 27.9678 | 1.18610 | ||||||||
\(557\) | −1.56699 | −0.0663954 | −0.0331977 | − | 0.999449i | \(-0.510569\pi\) | ||||
−0.0331977 | + | 0.999449i | \(0.510569\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 21.7310 | 0.919124 | ||||||||
\(560\) | 6.06396 | 0.256249 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 61.8584 | 2.60934 | ||||||||
\(563\) | 24.2279 | 1.02109 | 0.510543 | − | 0.859852i | \(-0.329444\pi\) | ||||
0.510543 | + | 0.859852i | \(0.329444\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 46.8045 | 1.96908 | ||||||||
\(566\) | 58.7069 | 2.46763 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −8.52485 | −0.357695 | ||||||||
\(569\) | 14.7118 | 0.616753 | 0.308376 | − | 0.951264i | \(-0.400214\pi\) | ||||
0.308376 | + | 0.951264i | \(0.400214\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.6613 | 0.739103 | 0.369551 | − | 0.929210i | \(-0.379511\pi\) | ||||
0.369551 | + | 0.929210i | \(0.379511\pi\) | |||||||
\(572\) | −4.76031 | −0.199038 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −77.4282 | −3.23179 | ||||||||
\(575\) | 3.21872 | 0.134230 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.7470 | 0.530665 | 0.265333 | − | 0.964157i | \(-0.414518\pi\) | ||||
0.265333 | + | 0.964157i | \(0.414518\pi\) | |||||||
\(578\) | 46.1082 | 1.91785 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 9.64332 | 0.400417 | ||||||||
\(581\) | 6.46930 | 0.268392 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.96793 | 0.205751 | ||||||||
\(584\) | −14.6982 | −0.608217 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 11.9025 | 0.491689 | ||||||||
\(587\) | 0.658885 | 0.0271951 | 0.0135976 | − | 0.999908i | \(-0.495672\pi\) | ||||
0.0135976 | + | 0.999908i | \(0.495672\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.44975 | 0.0597359 | ||||||||
\(590\) | −67.7361 | −2.78865 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.97471 | −0.122260 | ||||||||
\(593\) | 34.1532 | 1.40250 | 0.701251 | − | 0.712914i | \(-0.252625\pi\) | ||||
0.701251 | + | 0.712914i | \(0.252625\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 62.7230 | 2.57139 | ||||||||
\(596\) | 76.6988 | 3.14171 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 6.69064 | 0.273601 | ||||||||
\(599\) | 11.7324 | 0.479373 | 0.239687 | − | 0.970850i | \(-0.422955\pi\) | ||||
0.239687 | + | 0.970850i | \(0.422955\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.1962 | −0.905400 | −0.452700 | − | 0.891663i | \(-0.649539\pi\) | ||||
−0.452700 | + | 0.891663i | \(0.649539\pi\) | |||||||
\(602\) | 62.7396 | 2.55707 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −58.6048 | −2.38460 | ||||||||
\(605\) | −30.8472 | −1.25412 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −48.0676 | −1.95100 | −0.975501 | − | 0.219995i | \(-0.929396\pi\) | ||||
−0.975501 | + | 0.219995i | \(0.929396\pi\) | |||||||
\(608\) | 1.03572 | 0.0420040 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −63.4312 | −2.56825 | ||||||||
\(611\) | 4.65297 | 0.188239 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.40933 | 0.299260 | 0.149630 | − | 0.988742i | \(-0.452192\pi\) | ||||
0.149630 | + | 0.988742i | \(0.452192\pi\) | |||||||
\(614\) | 45.3428 | 1.82989 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5.57197 | −0.224501 | ||||||||
\(617\) | 13.8020 | 0.555649 | 0.277824 | − | 0.960632i | \(-0.410387\pi\) | ||||
0.277824 | + | 0.960632i | \(0.410387\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15.4327 | −0.620294 | −0.310147 | − | 0.950689i | \(-0.600378\pi\) | ||||
−0.310147 | + | 0.950689i | \(0.600378\pi\) | |||||||
\(620\) | −66.9052 | −2.68698 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 79.3058 | 3.17987 | ||||||||
\(623\) | 27.4592 | 1.10013 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.7334 | −1.22934 | ||||||||
\(626\) | −15.0537 | −0.601666 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 30.8921 | 1.23273 | ||||||||
\(629\) | −30.7692 | −1.22685 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.3091 | 1.16678 | 0.583388 | − | 0.812193i | \(-0.301727\pi\) | ||||
0.583388 | + | 0.812193i | \(0.301727\pi\) | |||||||
\(632\) | 24.8243 | 0.987458 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 34.8369 | 1.38355 | ||||||||
\(635\) | −17.0549 | −0.676801 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 17.2451 | 0.683276 | ||||||||
\(638\) | −1.13452 | −0.0449160 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −55.5973 | −2.19768 | ||||||||
\(641\) | −1.75725 | −0.0694071 | −0.0347035 | − | 0.999398i | \(-0.511049\pi\) | ||||
−0.0347035 | + | 0.999398i | \(0.511049\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −33.6057 | −1.32528 | −0.662639 | − | 0.748939i | \(-0.730564\pi\) | ||||
−0.662639 | + | 0.748939i | \(0.730564\pi\) | |||||||
\(644\) | 12.1139 | 0.477356 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.94008 | −0.115676 | ||||||||
\(647\) | −20.4559 | −0.804204 | −0.402102 | − | 0.915595i | \(-0.631720\pi\) | ||||
−0.402102 | + | 0.915595i | \(0.631720\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.99759 | 0.196172 | ||||||||
\(650\) | 21.5353 | 0.844684 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 53.6022 | 2.09923 | ||||||||
\(653\) | −11.8457 | −0.463559 | −0.231780 | − | 0.972768i | \(-0.574455\pi\) | ||||
−0.231780 | + | 0.972768i | \(0.574455\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −25.0734 | −0.979698 | ||||||||
\(656\) | −5.45253 | −0.212886 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 13.4336 | 0.523695 | ||||||||
\(659\) | −1.45749 | −0.0567757 | −0.0283878 | − | 0.999597i | \(-0.509037\pi\) | ||||
−0.0283878 | + | 0.999597i | \(0.509037\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.17925 | −0.123659 | −0.0618293 | − | 0.998087i | \(-0.519693\pi\) | ||||
−0.0618293 | + | 0.998087i | \(0.519693\pi\) | |||||||
\(662\) | −5.47955 | −0.212969 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5.67373 | 0.220183 | ||||||||
\(665\) | −2.15736 | −0.0836588 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.00000 | 0.0387202 | ||||||||
\(668\) | −71.1208 | −2.75175 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −80.4075 | −3.10641 | ||||||||
\(671\) | 4.67997 | 0.180668 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −35.6189 | −1.37301 | −0.686503 | − | 0.727127i | \(-0.740855\pi\) | ||||
−0.686503 | + | 0.727127i | \(0.740855\pi\) | |||||||
\(674\) | 23.1271 | 0.890822 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −15.6557 | −0.602141 | ||||||||
\(677\) | 34.7094 | 1.33399 | 0.666994 | − | 0.745063i | \(-0.267580\pi\) | ||||
0.666994 | + | 0.745063i | \(0.267580\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 18.6597 | 0.716092 | ||||||||
\(680\) | 55.0095 | 2.10952 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 7.87126 | 0.301406 | ||||||||
\(683\) | −38.2453 | −1.46342 | −0.731708 | − | 0.681618i | \(-0.761277\pi\) | ||||
−0.731708 | + | 0.681618i | \(0.761277\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13.9864 | 0.534394 | ||||||||
\(686\) | −8.59555 | −0.328179 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4.41815 | 0.168441 | ||||||||
\(689\) | −29.2976 | −1.11615 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.9352 | −0.720331 | −0.360165 | − | 0.932888i | \(-0.617280\pi\) | ||||
−0.360165 | + | 0.932888i | \(0.617280\pi\) | |||||||
\(692\) | −45.4623 | −1.72822 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −16.1806 | −0.614207 | ||||||||
\(695\) | 23.8361 | 0.904156 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −56.3987 | −2.13625 | ||||||||
\(698\) | 61.5719 | 2.33053 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 38.9913 | 1.47373 | ||||||||
\(701\) | −23.3256 | −0.880995 | −0.440498 | − | 0.897754i | \(-0.645198\pi\) | ||||
−0.440498 | + | 0.897754i | \(0.645198\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.05831 | 0.0399148 | ||||||||
\(704\) | 6.19877 | 0.233625 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −16.2757 | −0.612544 | ||||||||
\(707\) | 49.3424 | 1.85571 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −24.5991 | −0.923839 | −0.461919 | − | 0.886922i | \(-0.652839\pi\) | ||||
−0.461919 | + | 0.886922i | \(0.652839\pi\) | |||||||
\(710\) | −17.9206 | −0.672547 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 24.0824 | 0.902526 | ||||||||
\(713\) | −6.93798 | −0.259829 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.05707 | −0.151726 | ||||||||
\(716\) | 24.9611 | 0.932839 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 61.4437 | 2.29306 | ||||||||
\(719\) | −23.4718 | −0.875352 | −0.437676 | − | 0.899133i | \(-0.644198\pi\) | ||||
−0.437676 | + | 0.899133i | \(0.644198\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 48.7294 | 1.81478 | ||||||||
\(722\) | −43.9025 | −1.63388 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 14.5358 | 0.540219 | ||||||||
\(725\) | 3.21872 | 0.119540 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −22.5482 | −0.836266 | −0.418133 | − | 0.908386i | \(-0.637315\pi\) | ||||
−0.418133 | + | 0.908386i | \(0.637315\pi\) | |||||||
\(728\) | 32.8598 | 1.21787 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −30.8980 | −1.14359 | ||||||||
\(731\) | 45.6995 | 1.69026 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18.3331 | −0.677149 | −0.338574 | − | 0.940940i | \(-0.609945\pi\) | ||||
−0.338574 | + | 0.940940i | \(0.609945\pi\) | |||||||
\(734\) | −79.4209 | −2.93148 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.95658 | −0.182702 | ||||||||
\(737\) | 5.93249 | 0.218526 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 33.6701 | 1.23858 | 0.619288 | − | 0.785164i | \(-0.287421\pi\) | ||||
0.619288 | + | 0.785164i | \(0.287421\pi\) | |||||||
\(740\) | −48.8402 | −1.79540 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −84.5851 | −3.10522 | ||||||||
\(743\) | 18.9673 | 0.695843 | 0.347921 | − | 0.937524i | \(-0.386888\pi\) | ||||
0.347921 | + | 0.937524i | \(0.386888\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 65.3681 | 2.39490 | ||||||||
\(746\) | −32.8323 | −1.20208 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −10.0107 | −0.366029 | ||||||||
\(749\) | −3.19178 | −0.116625 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.06184 | −0.0387470 | −0.0193735 | − | 0.999812i | \(-0.506167\pi\) | ||||
−0.0193735 | + | 0.999812i | \(0.506167\pi\) | |||||||
\(752\) | 0.945999 | 0.0344970 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 6.69064 | 0.243659 | ||||||||
\(755\) | −49.9471 | −1.81776 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.5206 | −0.527761 | −0.263880 | − | 0.964555i | \(-0.585002\pi\) | ||||
−0.263880 | + | 0.964555i | \(0.585002\pi\) | |||||||
\(758\) | −59.4587 | −2.15964 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.89205 | −0.0686320 | ||||||||
\(761\) | 40.3345 | 1.46213 | 0.731063 | − | 0.682310i | \(-0.239025\pi\) | ||||
0.731063 | + | 0.682310i | \(0.239025\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.1493 | −0.367428 | ||||||||
\(764\) | 4.96763 | 0.179723 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −41.6600 | −1.50524 | ||||||||
\(767\) | −29.4725 | −1.06419 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10.0707 | −0.363158 | −0.181579 | − | 0.983376i | \(-0.558121\pi\) | ||||
−0.181579 | + | 0.983376i | \(0.558121\pi\) | |||||||
\(770\) | −11.7132 | −0.422113 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −51.1634 | −1.84141 | ||||||||
\(773\) | −40.1438 | −1.44387 | −0.721937 | − | 0.691959i | \(-0.756748\pi\) | ||||
−0.721937 | + | 0.691959i | \(0.756748\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −22.3314 | −0.802167 | ||||||||
\(776\) | 16.3650 | 0.587468 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 54.1422 | 1.94109 | ||||||||
\(779\) | 1.93983 | 0.0695017 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.32218 | 0.0473115 | ||||||||
\(782\) | 14.0702 | 0.503148 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.50612 | 0.125219 | ||||||||
\(785\) | 26.3285 | 0.939703 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.18087 | −0.0420933 | −0.0210467 | − | 0.999778i | \(-0.506700\pi\) | ||||
−0.0210467 | + | 0.999778i | \(0.506700\pi\) | |||||||
\(788\) | 8.64898 | 0.308107 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 52.1846 | 1.85664 | ||||||||
\(791\) | 58.7957 | 2.09053 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −27.5994 | −0.980084 | ||||||||
\(794\) | 79.0029 | 2.80371 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −52.8228 | −1.87225 | ||||||||
\(797\) | 27.8099 | 0.985077 | 0.492538 | − | 0.870291i | \(-0.336069\pi\) | ||||
0.492538 | + | 0.870291i | \(0.336069\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.78501 | 0.346169 | ||||||||
\(800\) | −15.9538 | −0.564053 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 11.3586 | 0.401088 | ||||||||
\(803\) | 2.27966 | 0.0804475 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10.3243 | 0.363885 | ||||||||
\(806\) | −46.4196 | −1.63506 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 43.2744 | 1.52239 | ||||||||
\(809\) | −1.32667 | −0.0466432 | −0.0233216 | − | 0.999728i | \(-0.507424\pi\) | ||||
−0.0233216 | + | 0.999728i | \(0.507424\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −17.3003 | −0.607497 | −0.303748 | − | 0.952752i | \(-0.598238\pi\) | ||||
−0.303748 | + | 0.952752i | \(0.598238\pi\) | |||||||
\(812\) | 12.1139 | 0.425116 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 5.74596 | 0.201396 | ||||||||
\(815\) | 45.6836 | 1.60023 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.57183 | −0.0549915 | ||||||||
\(818\) | −14.2188 | −0.497147 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −89.5222 | −3.12625 | ||||||||
\(821\) | −6.86557 | −0.239610 | −0.119805 | − | 0.992797i | \(-0.538227\pi\) | ||||
−0.119805 | + | 0.992797i | \(0.538227\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.8510 | 0.447959 | 0.223980 | − | 0.974594i | \(-0.428095\pi\) | ||||
0.223980 | + | 0.974594i | \(0.428095\pi\) | |||||||
\(824\) | 42.7368 | 1.48881 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −85.0900 | −2.96066 | ||||||||
\(827\) | −26.4853 | −0.920983 | −0.460491 | − | 0.887664i | \(-0.652327\pi\) | ||||
−0.460491 | + | 0.887664i | \(0.652327\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 29.5767 | 1.02724 | 0.513621 | − | 0.858017i | \(-0.328304\pi\) | ||||
0.513621 | + | 0.858017i | \(0.328304\pi\) | |||||||
\(830\) | 11.9271 | 0.413994 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −36.5563 | −1.26736 | ||||||||
\(833\) | 36.2658 | 1.25654 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −60.6142 | −2.09764 | ||||||||
\(836\) | 0.344319 | 0.0119085 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −3.38488 | −0.116929 | ||||||||
\(839\) | −18.3216 | −0.632531 | −0.316265 | − | 0.948671i | \(-0.602429\pi\) | ||||
−0.316265 | + | 0.948671i | \(0.602429\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 75.9348 | 2.61688 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −78.7375 | −2.71026 | ||||||||
\(845\) | −13.3429 | −0.459008 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −38.7502 | −1.33147 | ||||||||
\(848\) | −5.95653 | −0.204548 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 45.2879 | 1.55336 | ||||||||
\(851\) | −5.06467 | −0.173615 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 36.3737 | 1.24541 | 0.622706 | − | 0.782456i | \(-0.286033\pi\) | ||||
0.622706 | + | 0.782456i | \(0.286033\pi\) | |||||||
\(854\) | −79.6822 | −2.72667 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.79927 | −0.0956769 | ||||||||
\(857\) | −12.8909 | −0.440344 | −0.220172 | − | 0.975461i | \(-0.570662\pi\) | ||||
−0.220172 | + | 0.975461i | \(0.570662\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13.1919 | 0.450102 | 0.225051 | − | 0.974347i | \(-0.427745\pi\) | ||||
0.225051 | + | 0.974347i | \(0.427745\pi\) | |||||||
\(860\) | 72.5393 | 2.47357 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 62.9417 | 2.14380 | ||||||||
\(863\) | 22.4029 | 0.762603 | 0.381302 | − | 0.924451i | \(-0.375476\pi\) | ||||
0.381302 | + | 0.924451i | \(0.375476\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −38.7462 | −1.31741 | ||||||||
\(866\) | 71.0253 | 2.41354 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −84.0462 | −2.85271 | ||||||||
\(869\) | −3.85019 | −0.130609 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −34.9859 | −1.18545 | ||||||||
\(872\) | −8.90113 | −0.301430 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.483943 | −0.0163696 | ||||||||
\(875\) | −18.3906 | −0.621715 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 24.5509 | 0.829024 | 0.414512 | − | 0.910044i | \(-0.363952\pi\) | ||||
0.414512 | + | 0.910044i | \(0.363952\pi\) | |||||||
\(878\) | 8.11644 | 0.273917 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.824846 | −0.0278056 | ||||||||
\(881\) | 31.0084 | 1.04470 | 0.522350 | − | 0.852731i | \(-0.325056\pi\) | ||||
0.522350 | + | 0.852731i | \(0.325056\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 38.3023 | 1.28898 | 0.644488 | − | 0.764615i | \(-0.277071\pi\) | ||||
0.644488 | + | 0.764615i | \(0.277071\pi\) | |||||||
\(884\) | 59.0368 | 1.98562 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 13.6943 | 0.460068 | ||||||||
\(887\) | 1.22792 | 0.0412294 | 0.0206147 | − | 0.999787i | \(-0.493438\pi\) | ||||
0.0206147 | + | 0.999787i | \(0.493438\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −21.4243 | −0.718548 | ||||||||
\(890\) | 50.6250 | 1.69695 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −52.9489 | −1.77286 | ||||||||
\(893\) | −0.336555 | −0.0112624 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 21.2736 | 0.711098 | ||||||||
\(896\) | −69.8413 | −2.33323 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −52.9723 | −1.76771 | ||||||||
\(899\) | −6.93798 | −0.231395 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −61.6117 | −2.05258 | ||||||||
\(902\) | 10.5321 | 0.350681 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 51.5652 | 1.71503 | ||||||||
\(905\) | 12.3884 | 0.411806 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −46.6379 | −1.54859 | −0.774293 | − | 0.632828i | \(-0.781894\pi\) | ||||
−0.774293 | + | 0.632828i | \(0.781894\pi\) | |||||||
\(908\) | 74.0781 | 2.45837 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 69.0765 | 2.28986 | ||||||||
\(911\) | −14.2047 | −0.470623 | −0.235311 | − | 0.971920i | \(-0.575611\pi\) | ||||
−0.235311 | + | 0.971920i | \(0.575611\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.879982 | −0.0291232 | ||||||||
\(914\) | 38.2712 | 1.26590 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −54.3400 | −1.79544 | ||||||||
\(917\) | −31.4971 | −1.04013 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 27.6942 | 0.913546 | 0.456773 | − | 0.889583i | \(-0.349005\pi\) | ||||
0.456773 | + | 0.889583i | \(0.349005\pi\) | |||||||
\(920\) | 9.05469 | 0.298524 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 15.3794 | 0.506493 | ||||||||
\(923\) | −7.79738 | −0.256654 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −16.3017 | −0.535998 | ||||||||
\(926\) | −43.3489 | −1.42453 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.95658 | −0.162708 | ||||||||
\(929\) | 31.4646 | 1.03232 | 0.516160 | − | 0.856492i | \(-0.327361\pi\) | ||||
0.516160 | + | 0.856492i | \(0.327361\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.24736 | −0.0408806 | ||||||||
\(932\) | 63.5082 | 2.08028 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −17.9341 | −0.586822 | ||||||||
\(935\) | −8.53185 | −0.279021 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −42.5528 | −1.39014 | −0.695070 | − | 0.718942i | \(-0.744627\pi\) | ||||
−0.695070 | + | 0.718942i | \(0.744627\pi\) | |||||||
\(938\) | −101.008 | −3.29802 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 15.5319 | 0.506593 | ||||||||
\(941\) | 53.6015 | 1.74736 | 0.873680 | − | 0.486501i | \(-0.161727\pi\) | ||||
0.873680 | + | 0.486501i | \(0.161727\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.28334 | −0.302307 | ||||||||
\(944\) | −5.99208 | −0.195026 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.53411 | −0.277468 | ||||||||
\(947\) | −6.75896 | −0.219637 | −0.109818 | − | 0.993952i | \(-0.535027\pi\) | ||||
−0.109818 | + | 0.993952i | \(0.535027\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13.4440 | −0.436409 | ||||||||
\(950\) | −1.55768 | −0.0505377 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 69.1029 | 2.23964 | ||||||||
\(953\) | 2.12857 | 0.0689513 | 0.0344756 | − | 0.999406i | \(-0.489024\pi\) | ||||
0.0344756 | + | 0.999406i | \(0.489024\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.23377 | 0.137001 | ||||||||
\(956\) | 46.4860 | 1.50347 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −44.9877 | −1.45349 | ||||||||
\(959\) | 17.5697 | 0.567357 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 17.1356 | 0.552760 | ||||||||
\(962\) | −33.8859 | −1.09253 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −13.7056 | −0.441426 | ||||||||
\(965\) | −43.6051 | −1.40370 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 49.9771 | 1.60715 | 0.803577 | − | 0.595201i | \(-0.202928\pi\) | ||||
0.803577 | + | 0.595201i | \(0.202928\pi\) | |||||||
\(968\) | −33.9848 | −1.09231 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 34.4017 | 1.10457 | ||||||||
\(971\) | −3.70618 | −0.118937 | −0.0594684 | − | 0.998230i | \(-0.518941\pi\) | ||||
−0.0594684 | + | 0.998230i | \(0.518941\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 29.9429 | 0.959926 | ||||||||
\(974\) | 24.7389 | 0.792685 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.61126 | −0.179612 | ||||||||
\(977\) | −36.6110 | −1.17129 | −0.585645 | − | 0.810568i | \(-0.699159\pi\) | ||||
−0.585645 | + | 0.810568i | \(0.699159\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.73512 | −0.119375 | ||||||||
\(980\) | 57.5651 | 1.83885 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −4.41779 | −0.140977 | ||||||||
\(983\) | 2.20529 | 0.0703378 | 0.0351689 | − | 0.999381i | \(-0.488803\pi\) | ||||
0.0351689 | + | 0.999381i | \(0.488803\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.37127 | 0.234868 | ||||||||
\(986\) | 14.0702 | 0.448085 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.03057 | −0.0646010 | ||||||||
\(989\) | 7.52223 | 0.239193 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −29.6667 | −0.942394 | −0.471197 | − | 0.882028i | \(-0.656178\pi\) | ||||
−0.471197 | + | 0.882028i | \(0.656178\pi\) | |||||||
\(992\) | 34.3887 | 1.09184 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −22.5118 | −0.714031 | ||||||||
\(995\) | −45.0193 | −1.42721 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 26.9367 | 0.853094 | 0.426547 | − | 0.904465i | \(-0.359730\pi\) | ||||
0.426547 | + | 0.904465i | \(0.359730\pi\) | |||||||
\(998\) | −30.6155 | −0.969116 | ||||||||
\(999\) | 0 | 0 |
(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 | 6003.2.a.p.1.13 | 14 | ||
3.2 | odd | 2 | 2001.2.a.m.1.2 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2001.2.a.m.1.2 | ✓ | 14 | 3.2 | odd | 2 | ||
6003.2.a.p.1.13 | 14 | 1.1 | even | 1 | trivial |