Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2601,2,Mod(1,2601)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2601, 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("2601.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2601 = 3^{2} \cdot 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2601.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: | \(20.7690895657\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{16})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 4x^{2} + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 153) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.765367\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2601.1 |
$q$-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 | −0.353553 | − | 0.935414i | \(-0.615027\pi\) | ||||
−0.353553 | + | 0.935414i | \(0.615027\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 2.93015 | 1.31040 | 0.655202 | − | 0.755454i | \(-0.272584\pi\) | ||||
0.655202 | + | 0.755454i | \(0.272584\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.53073 | 0.578563 | 0.289281 | − | 0.957244i | \(-0.406584\pi\) | ||||
0.289281 | + | 0.957244i | \(0.406584\pi\) | |||||||
\(8\) | 3.00000 | 1.06066 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.93015 | −0.926595 | ||||||||
\(11\) | 2.16478 | 0.652707 | 0.326354 | − | 0.945248i | \(-0.394180\pi\) | ||||
0.326354 | + | 0.945248i | \(0.394180\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.24264 | 1.17670 | 0.588348 | − | 0.808608i | \(-0.299778\pi\) | ||||
0.588348 | + | 0.808608i | \(0.299778\pi\) | |||||||
\(14\) | −1.53073 | −0.409106 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.82843 | −0.648886 | −0.324443 | − | 0.945905i | \(-0.605177\pi\) | ||||
−0.324443 | + | 0.945905i | \(0.605177\pi\) | |||||||
\(20\) | −2.93015 | −0.655202 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.16478 | −0.461534 | ||||||||
\(23\) | 8.92177 | 1.86032 | 0.930159 | − | 0.367157i | \(-0.119669\pi\) | ||||
0.930159 | + | 0.367157i | \(0.119669\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.58579 | 0.717157 | ||||||||
\(26\) | −4.24264 | −0.832050 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.53073 | −0.289281 | ||||||||
\(29\) | 0.317025 | 0.0588701 | 0.0294351 | − | 0.999567i | \(-0.490629\pi\) | ||||
0.0294351 | + | 0.999567i | \(0.490629\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.69552 | 0.663735 | 0.331867 | − | 0.943326i | \(-0.392321\pi\) | ||||
0.331867 | + | 0.943326i | \(0.392321\pi\) | |||||||
\(32\) | −5.00000 | −0.883883 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.48528 | 0.758151 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.68714 | 1.59256 | 0.796278 | − | 0.604931i | \(-0.206799\pi\) | ||||
0.796278 | + | 0.604931i | \(0.206799\pi\) | |||||||
\(38\) | 2.82843 | 0.458831 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 8.79045 | 1.38989 | ||||||||
\(41\) | 0.317025 | 0.0495110 | 0.0247555 | − | 0.999694i | \(-0.492119\pi\) | ||||
0.0247555 | + | 0.999694i | \(0.492119\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.65685 | 0.862662 | 0.431331 | − | 0.902194i | \(-0.358044\pi\) | ||||
0.431331 | + | 0.902194i | \(0.358044\pi\) | |||||||
\(44\) | −2.16478 | −0.326354 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −8.92177 | −1.31544 | ||||||||
\(47\) | −2.82843 | −0.412568 | −0.206284 | − | 0.978492i | \(-0.566137\pi\) | ||||
−0.206284 | + | 0.978492i | \(0.566137\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.65685 | −0.665265 | ||||||||
\(50\) | −3.58579 | −0.507107 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.24264 | −0.588348 | ||||||||
\(53\) | −8.24264 | −1.13221 | −0.566107 | − | 0.824332i | \(-0.691551\pi\) | ||||
−0.566107 | + | 0.824332i | \(0.691551\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.34315 | 0.855310 | ||||||||
\(56\) | 4.59220 | 0.613659 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.317025 | −0.0416275 | ||||||||
\(59\) | −12.4853 | −1.62545 | −0.812723 | − | 0.582651i | \(-0.802016\pi\) | ||||
−0.812723 | + | 0.582651i | \(0.802016\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.6662 | −1.49371 | −0.746853 | − | 0.664990i | \(-0.768436\pi\) | ||||
−0.746853 | + | 0.664990i | \(0.768436\pi\) | |||||||
\(62\) | −3.69552 | −0.469331 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.00000 | 0.875000 | ||||||||
\(65\) | 12.4316 | 1.54195 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.4853 | 1.52532 | 0.762660 | − | 0.646800i | \(-0.223893\pi\) | ||||
0.762660 | + | 0.646800i | \(0.223893\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −4.48528 | −0.536094 | ||||||||
\(71\) | −8.92177 | −1.05882 | −0.529410 | − | 0.848366i | \(-0.677587\pi\) | ||||
−0.529410 | + | 0.848366i | \(0.677587\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.82683 | 0.447897 | 0.223949 | − | 0.974601i | \(-0.428105\pi\) | ||||
0.223949 | + | 0.974601i | \(0.428105\pi\) | |||||||
\(74\) | −9.68714 | −1.12611 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.82843 | 0.324443 | ||||||||
\(77\) | 3.31371 | 0.377632 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.9832 | −1.34822 | −0.674110 | − | 0.738631i | \(-0.735473\pi\) | ||||
−0.674110 | + | 0.738631i | \(0.735473\pi\) | |||||||
\(80\) | −2.93015 | −0.327601 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.317025 | −0.0350096 | ||||||||
\(83\) | −4.48528 | −0.492324 | −0.246162 | − | 0.969229i | \(-0.579169\pi\) | ||||
−0.246162 | + | 0.969229i | \(0.579169\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −5.65685 | −0.609994 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 6.49435 | 0.692300 | ||||||||
\(89\) | −13.4142 | −1.42190 | −0.710952 | − | 0.703241i | \(-0.751736\pi\) | ||||
−0.710952 | + | 0.703241i | \(0.751736\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.49435 | 0.680793 | ||||||||
\(92\) | −8.92177 | −0.930159 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.82843 | 0.291730 | ||||||||
\(95\) | −8.28772 | −0.850302 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.48181 | −0.251990 | −0.125995 | − | 0.992031i | \(-0.540212\pi\) | ||||
−0.125995 | + | 0.992031i | \(0.540212\pi\) | |||||||
\(98\) | 4.65685 | 0.470413 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.58579 | −0.358579 | ||||||||
\(101\) | 16.2426 | 1.61620 | 0.808102 | − | 0.589043i | \(-0.200495\pi\) | ||||
0.808102 | + | 0.589043i | \(0.200495\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.4853 | 1.62434 | 0.812172 | − | 0.583419i | \(-0.198285\pi\) | ||||
0.812172 | + | 0.583419i | \(0.198285\pi\) | |||||||
\(104\) | 12.7279 | 1.24808 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.24264 | 0.800596 | ||||||||
\(107\) | −10.4525 | −1.01048 | −0.505241 | − | 0.862978i | \(-0.668596\pi\) | ||||
−0.505241 | + | 0.862978i | \(0.668596\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.6662 | 1.11742 | 0.558710 | − | 0.829363i | \(-0.311296\pi\) | ||||
0.558710 | + | 0.829363i | \(0.311296\pi\) | |||||||
\(110\) | −6.34315 | −0.604795 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.53073 | −0.144641 | ||||||||
\(113\) | −3.37849 | −0.317822 | −0.158911 | − | 0.987293i | \(-0.550798\pi\) | ||||
−0.158911 | + | 0.987293i | \(0.550798\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 26.1421 | 2.43777 | ||||||||
\(116\) | −0.317025 | −0.0294351 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 12.4853 | 1.14936 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.31371 | −0.573973 | ||||||||
\(122\) | 11.6662 | 1.05621 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3.69552 | −0.331867 | ||||||||
\(125\) | −4.14386 | −0.370638 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.34315 | 0.562863 | 0.281432 | − | 0.959581i | \(-0.409191\pi\) | ||||
0.281432 | + | 0.959581i | \(0.409191\pi\) | |||||||
\(128\) | 3.00000 | 0.265165 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −12.4316 | −1.09032 | ||||||||
\(131\) | 1.26810 | 0.110795 | 0.0553973 | − | 0.998464i | \(-0.482357\pi\) | ||||
0.0553973 | + | 0.998464i | \(0.482357\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.32957 | −0.375421 | ||||||||
\(134\) | −12.4853 | −1.07856 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.75736 | 0.662756 | 0.331378 | − | 0.943498i | \(-0.392486\pi\) | ||||
0.331378 | + | 0.943498i | \(0.392486\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.896683 | 0.0760557 | 0.0380278 | − | 0.999277i | \(-0.487892\pi\) | ||||
0.0380278 | + | 0.999277i | \(0.487892\pi\) | |||||||
\(140\) | −4.48528 | −0.379075 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 8.92177 | 0.748698 | ||||||||
\(143\) | 9.18440 | 0.768038 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.928932 | 0.0771436 | ||||||||
\(146\) | −3.82683 | −0.316711 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −9.68714 | −0.796278 | ||||||||
\(149\) | −17.3137 | −1.41839 | −0.709197 | − | 0.705010i | \(-0.750942\pi\) | ||||
−0.709197 | + | 0.705010i | \(0.750942\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.34315 | 0.516198 | 0.258099 | − | 0.966118i | \(-0.416904\pi\) | ||||
0.258099 | + | 0.966118i | \(0.416904\pi\) | |||||||
\(152\) | −8.48528 | −0.688247 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3.31371 | −0.267026 | ||||||||
\(155\) | 10.8284 | 0.869760 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(158\) | 11.9832 | 0.953335 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −14.6508 | −1.15824 | ||||||||
\(161\) | 13.6569 | 1.07631 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.6173 | −0.988262 | −0.494131 | − | 0.869387i | \(-0.664514\pi\) | ||||
−0.494131 | + | 0.869387i | \(0.664514\pi\) | |||||||
\(164\) | −0.317025 | −0.0247555 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.48528 | 0.348125 | ||||||||
\(167\) | −6.75699 | −0.522871 | −0.261436 | − | 0.965221i | \(-0.584196\pi\) | ||||
−0.261436 | + | 0.965221i | \(0.584196\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.00000 | 0.384615 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −5.65685 | −0.431331 | ||||||||
\(173\) | 4.46088 | 0.339155 | 0.169577 | − | 0.985517i | \(-0.445760\pi\) | ||||
0.169577 | + | 0.985517i | \(0.445760\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.48888 | 0.414921 | ||||||||
\(176\) | −2.16478 | −0.163177 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 13.4142 | 1.00544 | ||||||||
\(179\) | 16.0000 | 1.19590 | 0.597948 | − | 0.801535i | \(-0.295983\pi\) | ||||
0.597948 | + | 0.801535i | \(0.295983\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.09494 | −0.378704 | −0.189352 | − | 0.981909i | \(-0.560639\pi\) | ||||
−0.189352 | + | 0.981909i | \(0.560639\pi\) | |||||||
\(182\) | −6.49435 | −0.481393 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 26.7653 | 1.97316 | ||||||||
\(185\) | 28.3848 | 2.08689 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 2.82843 | 0.206284 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 8.28772 | 0.601254 | ||||||||
\(191\) | 14.8284 | 1.07295 | 0.536474 | − | 0.843917i | \(-0.319756\pi\) | ||||
0.536474 | + | 0.843917i | \(0.319756\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.9343 | 0.931032 | 0.465516 | − | 0.885039i | \(-0.345869\pi\) | ||||
0.465516 | + | 0.885039i | \(0.345869\pi\) | |||||||
\(194\) | 2.48181 | 0.178184 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.65685 | 0.332632 | ||||||||
\(197\) | 8.86738 | 0.631774 | 0.315887 | − | 0.948797i | \(-0.397698\pi\) | ||||
0.315887 | + | 0.948797i | \(0.397698\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.53073 | −0.108511 | −0.0542554 | − | 0.998527i | \(-0.517279\pi\) | ||||
−0.0542554 | + | 0.998527i | \(0.517279\pi\) | |||||||
\(200\) | 10.7574 | 0.760660 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −16.2426 | −1.14283 | ||||||||
\(203\) | 0.485281 | 0.0340601 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.928932 | 0.0648794 | ||||||||
\(206\) | −16.4853 | −1.14858 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4.24264 | −0.294174 | ||||||||
\(209\) | −6.12293 | −0.423532 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.43289 | 0.236330 | 0.118165 | − | 0.992994i | \(-0.462299\pi\) | ||||
0.118165 | + | 0.992994i | \(0.462299\pi\) | |||||||
\(212\) | 8.24264 | 0.566107 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 10.4525 | 0.714518 | ||||||||
\(215\) | 16.5754 | 1.13044 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.65685 | 0.384012 | ||||||||
\(218\) | −11.6662 | −0.790136 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −6.34315 | −0.427655 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.17157 | 0.614174 | 0.307087 | − | 0.951681i | \(-0.400646\pi\) | ||||
0.307087 | + | 0.951681i | \(0.400646\pi\) | |||||||
\(224\) | −7.65367 | −0.511382 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.37849 | 0.224734 | ||||||||
\(227\) | 13.5140 | 0.896954 | 0.448477 | − | 0.893794i | \(-0.351967\pi\) | ||||
0.448477 | + | 0.893794i | \(0.351967\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −22.6274 | −1.49526 | −0.747631 | − | 0.664114i | \(-0.768809\pi\) | ||||
−0.747631 | + | 0.664114i | \(0.768809\pi\) | |||||||
\(230\) | −26.1421 | −1.72376 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.951076 | 0.0624412 | ||||||||
\(233\) | 1.66205 | 0.108885 | 0.0544423 | − | 0.998517i | \(-0.482662\pi\) | ||||
0.0544423 | + | 0.998517i | \(0.482662\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.28772 | −0.540631 | ||||||||
\(236\) | 12.4853 | 0.812723 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −20.4853 | −1.32508 | −0.662541 | − | 0.749025i | \(-0.730522\pi\) | ||||
−0.662541 | + | 0.749025i | \(0.730522\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.9343 | 0.833172 | 0.416586 | − | 0.909096i | \(-0.363226\pi\) | ||||
0.416586 | + | 0.909096i | \(0.363226\pi\) | |||||||
\(242\) | 6.31371 | 0.405861 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 11.6662 | 0.746853 | ||||||||
\(245\) | −13.6453 | −0.871765 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −12.0000 | −0.763542 | ||||||||
\(248\) | 11.0866 | 0.703997 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 4.14386 | 0.262081 | ||||||||
\(251\) | 22.6274 | 1.42823 | 0.714115 | − | 0.700028i | \(-0.246829\pi\) | ||||
0.714115 | + | 0.700028i | \(0.246829\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 19.3137 | 1.21424 | ||||||||
\(254\) | −6.34315 | −0.398004 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −17.0000 | −1.06250 | ||||||||
\(257\) | −2.97056 | −0.185299 | −0.0926493 | − | 0.995699i | \(-0.529534\pi\) | ||||
−0.0926493 | + | 0.995699i | \(0.529534\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 14.8284 | 0.921394 | ||||||||
\(260\) | −12.4316 | −0.770974 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.26810 | −0.0783436 | ||||||||
\(263\) | 11.5147 | 0.710028 | 0.355014 | − | 0.934861i | \(-0.384476\pi\) | ||||
0.355014 | + | 0.934861i | \(0.384476\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −24.1522 | −1.48366 | ||||||||
\(266\) | 4.32957 | 0.265463 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −12.4853 | −0.762660 | ||||||||
\(269\) | −16.8925 | −1.02995 | −0.514976 | − | 0.857205i | \(-0.672199\pi\) | ||||
−0.514976 | + | 0.857205i | \(0.672199\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.00000 | 0.242983 | 0.121491 | − | 0.992592i | \(-0.461232\pi\) | ||||
0.121491 | + | 0.992592i | \(0.461232\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −7.75736 | −0.468639 | ||||||||
\(275\) | 7.76245 | 0.468094 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.35757 | −0.321905 | −0.160953 | − | 0.986962i | \(-0.551457\pi\) | ||||
−0.160953 | + | 0.986962i | \(0.551457\pi\) | |||||||
\(278\) | −0.896683 | −0.0537795 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 13.4558 | 0.804140 | ||||||||
\(281\) | −8.72792 | −0.520664 | −0.260332 | − | 0.965519i | \(-0.583832\pi\) | ||||
−0.260332 | + | 0.965519i | \(0.583832\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.7821 | 0.878703 | 0.439352 | − | 0.898315i | \(-0.355208\pi\) | ||||
0.439352 | + | 0.898315i | \(0.355208\pi\) | |||||||
\(284\) | 8.92177 | 0.529410 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −9.18440 | −0.543085 | ||||||||
\(287\) | 0.485281 | 0.0286453 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | −0.928932 | −0.0545488 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3.82683 | −0.223949 | ||||||||
\(293\) | 18.3431 | 1.07162 | 0.535809 | − | 0.844339i | \(-0.320007\pi\) | ||||
0.535809 | + | 0.844339i | \(0.320007\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −36.5838 | −2.12999 | ||||||||
\(296\) | 29.0614 | 1.68916 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 17.3137 | 1.00296 | ||||||||
\(299\) | 37.8519 | 2.18903 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.65914 | 0.499104 | ||||||||
\(302\) | −6.34315 | −0.365007 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.82843 | 0.162221 | ||||||||
\(305\) | −34.1838 | −1.95736 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 24.9706 | 1.42515 | 0.712573 | − | 0.701598i | \(-0.247530\pi\) | ||||
0.712573 | + | 0.701598i | \(0.247530\pi\) | |||||||
\(308\) | −3.31371 | −0.188816 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −10.8284 | −0.615013 | ||||||||
\(311\) | −5.86030 | −0.332307 | −0.166154 | − | 0.986100i | \(-0.553135\pi\) | ||||
−0.166154 | + | 0.986100i | \(0.553135\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.4077 | 1.21004 | 0.605019 | − | 0.796211i | \(-0.293166\pi\) | ||||
0.605019 | + | 0.796211i | \(0.293166\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 11.9832 | 0.674110 | ||||||||
\(317\) | −26.8966 | −1.51067 | −0.755333 | − | 0.655342i | \(-0.772525\pi\) | ||||
−0.755333 | + | 0.655342i | \(0.772525\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.686292 | 0.0384249 | ||||||||
\(320\) | 20.5111 | 1.14660 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −13.6569 | −0.761067 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 15.2132 | 0.843877 | ||||||||
\(326\) | 12.6173 | 0.698807 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.951076 | 0.0525144 | ||||||||
\(329\) | −4.32957 | −0.238697 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.686292 | −0.0377220 | −0.0188610 | − | 0.999822i | \(-0.506004\pi\) | ||||
−0.0188610 | + | 0.999822i | \(0.506004\pi\) | |||||||
\(332\) | 4.48528 | 0.246162 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 6.75699 | 0.369726 | ||||||||
\(335\) | 36.5838 | 1.99878 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.8365 | −0.808194 | −0.404097 | − | 0.914716i | \(-0.632414\pi\) | ||||
−0.404097 | + | 0.914716i | \(0.632414\pi\) | |||||||
\(338\) | −5.00000 | −0.271964 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.00000 | 0.433224 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.8435 | −0.963461 | ||||||||
\(344\) | 16.9706 | 0.914991 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.46088 | −0.239819 | ||||||||
\(347\) | −5.22625 | −0.280560 | −0.140280 | − | 0.990112i | \(-0.544800\pi\) | ||||
−0.140280 | + | 0.990112i | \(0.544800\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.07107 | −0.378506 | −0.189253 | − | 0.981928i | \(-0.560607\pi\) | ||||
−0.189253 | + | 0.981928i | \(0.560607\pi\) | |||||||
\(350\) | −5.48888 | −0.293393 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −10.8239 | −0.576917 | ||||||||
\(353\) | 5.65685 | 0.301084 | 0.150542 | − | 0.988604i | \(-0.451898\pi\) | ||||
0.150542 | + | 0.988604i | \(0.451898\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −26.1421 | −1.38748 | ||||||||
\(356\) | 13.4142 | 0.710952 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −16.0000 | −0.845626 | ||||||||
\(359\) | 0.970563 | 0.0512243 | 0.0256122 | − | 0.999672i | \(-0.491847\pi\) | ||||
0.0256122 | + | 0.999672i | \(0.491847\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.0000 | −0.578947 | ||||||||
\(362\) | 5.09494 | 0.267784 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −6.49435 | −0.340397 | ||||||||
\(365\) | 11.2132 | 0.586926 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 20.6424 | 1.07752 | 0.538762 | − | 0.842458i | \(-0.318892\pi\) | ||||
0.538762 | + | 0.842458i | \(0.318892\pi\) | |||||||
\(368\) | −8.92177 | −0.465079 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −28.3848 | −1.47565 | ||||||||
\(371\) | −12.6173 | −0.655057 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.21320 | −0.269929 | −0.134965 | − | 0.990850i | \(-0.543092\pi\) | ||||
−0.134965 | + | 0.990850i | \(0.543092\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −8.48528 | −0.437595 | ||||||||
\(377\) | 1.34502 | 0.0692723 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.7402 | −0.962621 | −0.481310 | − | 0.876550i | \(-0.659839\pi\) | ||||
−0.481310 | + | 0.876550i | \(0.659839\pi\) | |||||||
\(380\) | 8.28772 | 0.425151 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −14.8284 | −0.758688 | ||||||||
\(383\) | 24.4853 | 1.25114 | 0.625570 | − | 0.780168i | \(-0.284867\pi\) | ||||
0.625570 | + | 0.780168i | \(0.284867\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.70967 | 0.494850 | ||||||||
\(386\) | −12.9343 | −0.658339 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.48181 | 0.125995 | ||||||||
\(389\) | 8.97056 | 0.454826 | 0.227413 | − | 0.973798i | \(-0.426973\pi\) | ||||
0.227413 | + | 0.973798i | \(0.426973\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −13.9706 | −0.705620 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −8.86738 | −0.446732 | ||||||||
\(395\) | −35.1127 | −1.76671 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −17.0782 | −0.857129 | −0.428564 | − | 0.903511i | \(-0.640981\pi\) | ||||
−0.428564 | + | 0.903511i | \(0.640981\pi\) | |||||||
\(398\) | 1.53073 | 0.0767287 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.58579 | −0.179289 | ||||||||
\(401\) | −22.4901 | −1.12310 | −0.561552 | − | 0.827442i | \(-0.689795\pi\) | ||||
−0.561552 | + | 0.827442i | \(0.689795\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 15.6788 | 0.781014 | ||||||||
\(404\) | −16.2426 | −0.808102 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.485281 | −0.0240841 | ||||||||
\(407\) | 20.9706 | 1.03947 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.970563 | 0.0479912 | 0.0239956 | − | 0.999712i | \(-0.492361\pi\) | ||||
0.0239956 | + | 0.999712i | \(0.492361\pi\) | |||||||
\(410\) | −0.928932 | −0.0458767 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −16.4853 | −0.812172 | ||||||||
\(413\) | −19.1116 | −0.940422 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13.1426 | −0.645143 | ||||||||
\(416\) | −21.2132 | −1.04006 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 6.12293 | 0.299483 | ||||||||
\(419\) | 27.0279 | 1.32040 | 0.660201 | − | 0.751089i | \(-0.270471\pi\) | ||||
0.660201 | + | 0.751089i | \(0.270471\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.2721 | −0.549367 | −0.274684 | − | 0.961535i | \(-0.588573\pi\) | ||||
−0.274684 | + | 0.961535i | \(0.588573\pi\) | |||||||
\(422\) | −3.43289 | −0.167110 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −24.7279 | −1.20089 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −17.8579 | −0.864203 | ||||||||
\(428\) | 10.4525 | 0.505241 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −16.5754 | −0.799339 | ||||||||
\(431\) | −31.6201 | −1.52309 | −0.761544 | − | 0.648113i | \(-0.775559\pi\) | ||||
−0.761544 | + | 0.648113i | \(0.775559\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.343146 | 0.0164905 | 0.00824527 | − | 0.999966i | \(-0.497375\pi\) | ||||
0.00824527 | + | 0.999966i | \(0.497375\pi\) | |||||||
\(434\) | −5.65685 | −0.271538 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −11.6662 | −0.558710 | ||||||||
\(437\) | −25.2346 | −1.20713 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.48888 | −0.261970 | −0.130985 | − | 0.991384i | \(-0.541814\pi\) | ||||
−0.130985 | + | 0.991384i | \(0.541814\pi\) | |||||||
\(440\) | 19.0294 | 0.907193 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.97056 | −0.236159 | −0.118079 | − | 0.993004i | \(-0.537674\pi\) | ||||
−0.118079 | + | 0.993004i | \(0.537674\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −39.3057 | −1.86327 | ||||||||
\(446\) | −9.17157 | −0.434287 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 10.7151 | 0.506243 | ||||||||
\(449\) | −20.5111 | −0.967977 | −0.483988 | − | 0.875074i | \(-0.660812\pi\) | ||||
−0.483988 | + | 0.875074i | \(0.660812\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.686292 | 0.0323162 | ||||||||
\(452\) | 3.37849 | 0.158911 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −13.5140 | −0.634242 | ||||||||
\(455\) | 19.0294 | 0.892114 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 28.2843 | 1.32308 | 0.661541 | − | 0.749909i | \(-0.269903\pi\) | ||||
0.661541 | + | 0.749909i | \(0.269903\pi\) | |||||||
\(458\) | 22.6274 | 1.05731 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −26.1421 | −1.21888 | ||||||||
\(461\) | 32.7279 | 1.52429 | 0.762146 | − | 0.647406i | \(-0.224146\pi\) | ||||
0.762146 | + | 0.647406i | \(0.224146\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.51472 | −0.163343 | −0.0816714 | − | 0.996659i | \(-0.526026\pi\) | ||||
−0.0816714 | + | 0.996659i | \(0.526026\pi\) | |||||||
\(464\) | −0.317025 | −0.0147175 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.66205 | −0.0769930 | ||||||||
\(467\) | 0.970563 | 0.0449123 | 0.0224561 | − | 0.999748i | \(-0.492851\pi\) | ||||
0.0224561 | + | 0.999748i | \(0.492851\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 19.1116 | 0.882494 | ||||||||
\(470\) | 8.28772 | 0.382284 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −37.4558 | −1.72404 | ||||||||
\(473\) | 12.2459 | 0.563066 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10.1421 | −0.465353 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 20.4853 | 0.936975 | ||||||||
\(479\) | −31.0949 | −1.42076 | −0.710381 | − | 0.703818i | \(-0.751477\pi\) | ||||
−0.710381 | + | 0.703818i | \(0.751477\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 41.0990 | 1.87395 | ||||||||
\(482\) | −12.9343 | −0.589142 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 6.31371 | 0.286987 | ||||||||
\(485\) | −7.27208 | −0.330208 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 41.5474 | 1.88269 | 0.941346 | − | 0.337443i | \(-0.109562\pi\) | ||||
0.941346 | + | 0.337443i | \(0.109562\pi\) | |||||||
\(488\) | −34.9986 | −1.58431 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 13.6453 | 0.616431 | ||||||||
\(491\) | −29.9411 | −1.35122 | −0.675612 | − | 0.737257i | \(-0.736121\pi\) | ||||
−0.675612 | + | 0.737257i | \(0.736121\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 12.0000 | 0.539906 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.69552 | −0.165934 | ||||||||
\(497\) | −13.6569 | −0.612594 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −27.7708 | −1.24319 | −0.621595 | − | 0.783338i | \(-0.713515\pi\) | ||||
−0.621595 | + | 0.783338i | \(0.713515\pi\) | |||||||
\(500\) | 4.14386 | 0.185319 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −22.6274 | −1.00991 | ||||||||
\(503\) | −43.7122 | −1.94903 | −0.974515 | − | 0.224324i | \(-0.927983\pi\) | ||||
−0.974515 | + | 0.224324i | \(0.927983\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 47.5934 | 2.11788 | ||||||||
\(506\) | −19.3137 | −0.858599 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −6.34315 | −0.281432 | ||||||||
\(509\) | −6.00000 | −0.265945 | −0.132973 | − | 0.991120i | \(-0.542452\pi\) | ||||
−0.132973 | + | 0.991120i | \(0.542452\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.85786 | 0.259137 | ||||||||
\(512\) | 11.0000 | 0.486136 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2.97056 | 0.131026 | ||||||||
\(515\) | 48.3044 | 2.12854 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.12293 | −0.269286 | ||||||||
\(518\) | −14.8284 | −0.651524 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 37.2947 | 1.63548 | ||||||||
\(521\) | −8.52782 | −0.373611 | −0.186805 | − | 0.982397i | \(-0.559813\pi\) | ||||
−0.186805 | + | 0.982397i | \(0.559813\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.48528 | −0.371035 | −0.185518 | − | 0.982641i | \(-0.559396\pi\) | ||||
−0.185518 | + | 0.982641i | \(0.559396\pi\) | |||||||
\(524\) | −1.26810 | −0.0553973 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −11.5147 | −0.502066 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 56.5980 | 2.46078 | ||||||||
\(530\) | 24.1522 | 1.04910 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4.32957 | 0.187711 | ||||||||
\(533\) | 1.34502 | 0.0582595 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −30.6274 | −1.32414 | ||||||||
\(536\) | 37.4558 | 1.61785 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 16.8925 | 0.728286 | ||||||||
\(539\) | −10.0811 | −0.434223 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.8715 | −0.811351 | −0.405675 | − | 0.914017i | \(-0.632964\pi\) | ||||
−0.405675 | + | 0.914017i | \(0.632964\pi\) | |||||||
\(542\) | −4.00000 | −0.171815 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 34.1838 | 1.46427 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 32.2542 | 1.37909 | 0.689545 | − | 0.724243i | \(-0.257811\pi\) | ||||
0.689545 | + | 0.724243i | \(0.257811\pi\) | |||||||
\(548\) | −7.75736 | −0.331378 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −7.76245 | −0.330992 | ||||||||
\(551\) | −0.896683 | −0.0382000 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −18.3431 | −0.780030 | ||||||||
\(554\) | 5.35757 | 0.227621 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.896683 | −0.0380278 | ||||||||
\(557\) | −36.0416 | −1.52713 | −0.763566 | − | 0.645729i | \(-0.776553\pi\) | ||||
−0.763566 | + | 0.645729i | \(0.776553\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 24.0000 | 1.01509 | ||||||||
\(560\) | −4.48528 | −0.189538 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 8.72792 | 0.368165 | ||||||||
\(563\) | 4.48528 | 0.189032 | 0.0945160 | − | 0.995523i | \(-0.469870\pi\) | ||||
0.0945160 | + | 0.995523i | \(0.469870\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.89949 | −0.416475 | ||||||||
\(566\) | −14.7821 | −0.621337 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −26.7653 | −1.12305 | ||||||||
\(569\) | 0.242641 | 0.0101720 | 0.00508601 | − | 0.999987i | \(-0.498381\pi\) | ||||
0.00508601 | + | 0.999987i | \(0.498381\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.1116 | −0.799797 | −0.399899 | − | 0.916559i | \(-0.630955\pi\) | ||||
−0.399899 | + | 0.916559i | \(0.630955\pi\) | |||||||
\(572\) | −9.18440 | −0.384019 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.485281 | −0.0202553 | ||||||||
\(575\) | 31.9916 | 1.33414 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.72792 | 0.196826 | 0.0984130 | − | 0.995146i | \(-0.468623\pi\) | ||||
0.0984130 | + | 0.995146i | \(0.468623\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.928932 | −0.0385718 | ||||||||
\(581\) | −6.86577 | −0.284840 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −17.8435 | −0.739004 | ||||||||
\(584\) | 11.4805 | 0.475067 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −18.3431 | −0.757748 | ||||||||
\(587\) | −12.9706 | −0.535352 | −0.267676 | − | 0.963509i | \(-0.586256\pi\) | ||||
−0.267676 | + | 0.963509i | \(0.586256\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.4525 | −0.430688 | ||||||||
\(590\) | 36.5838 | 1.50613 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −9.68714 | −0.398139 | ||||||||
\(593\) | −32.7279 | −1.34397 | −0.671987 | − | 0.740563i | \(-0.734559\pi\) | ||||
−0.671987 | + | 0.740563i | \(0.734559\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 17.3137 | 0.709197 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −37.8519 | −1.54788 | ||||||||
\(599\) | 16.2843 | 0.665357 | 0.332679 | − | 0.943040i | \(-0.392048\pi\) | ||||
0.332679 | + | 0.943040i | \(0.392048\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −33.3141 | −1.35891 | −0.679454 | − | 0.733718i | \(-0.737783\pi\) | ||||
−0.679454 | + | 0.733718i | \(0.737783\pi\) | |||||||
\(602\) | −8.65914 | −0.352920 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −6.34315 | −0.258099 | ||||||||
\(605\) | −18.5001 | −0.752137 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 45.5055 | 1.84701 | 0.923506 | − | 0.383583i | \(-0.125310\pi\) | ||||
0.923506 | + | 0.383583i | \(0.125310\pi\) | |||||||
\(608\) | 14.1421 | 0.573539 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 34.1838 | 1.38406 | ||||||||
\(611\) | −12.0000 | −0.485468 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.00000 | 0.0807792 | 0.0403896 | − | 0.999184i | \(-0.487140\pi\) | ||||
0.0403896 | + | 0.999184i | \(0.487140\pi\) | |||||||
\(614\) | −24.9706 | −1.00773 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 9.94113 | 0.400539 | ||||||||
\(617\) | −14.6508 | −0.589817 | −0.294909 | − | 0.955525i | \(-0.595289\pi\) | ||||
−0.294909 | + | 0.955525i | \(0.595289\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 25.6060 | 1.02919 | 0.514596 | − | 0.857433i | \(-0.327942\pi\) | ||||
0.514596 | + | 0.857433i | \(0.327942\pi\) | |||||||
\(620\) | −10.8284 | −0.434880 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 5.86030 | 0.234977 | ||||||||
\(623\) | −20.5336 | −0.822661 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.0711 | −1.20284 | ||||||||
\(626\) | −21.4077 | −0.855625 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.17157 | 0.365115 | 0.182557 | − | 0.983195i | \(-0.441563\pi\) | ||||
0.182557 | + | 0.983195i | \(0.441563\pi\) | |||||||
\(632\) | −35.9497 | −1.43000 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 26.8966 | 1.06820 | ||||||||
\(635\) | 18.5864 | 0.737578 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −19.7574 | −0.782815 | ||||||||
\(638\) | −0.686292 | −0.0271705 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 8.79045 | 0.347473 | ||||||||
\(641\) | 23.8352 | 0.941432 | 0.470716 | − | 0.882285i | \(-0.343996\pi\) | ||||
0.470716 | + | 0.882285i | \(0.343996\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.9665 | 0.945146 | 0.472573 | − | 0.881292i | \(-0.343325\pi\) | ||||
0.472573 | + | 0.881292i | \(0.343325\pi\) | |||||||
\(644\) | −13.6569 | −0.538155 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −44.4853 | −1.74890 | −0.874448 | − | 0.485118i | \(-0.838776\pi\) | ||||
−0.874448 | + | 0.485118i | \(0.838776\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −27.0279 | −1.06094 | ||||||||
\(650\) | −15.2132 | −0.596711 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 12.6173 | 0.494131 | ||||||||
\(653\) | −10.7695 | −0.421444 | −0.210722 | − | 0.977546i | \(-0.567582\pi\) | ||||
−0.210722 | + | 0.977546i | \(0.567582\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.71573 | 0.145186 | ||||||||
\(656\) | −0.317025 | −0.0123778 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 4.32957 | 0.168784 | ||||||||
\(659\) | 2.14214 | 0.0834458 | 0.0417229 | − | 0.999129i | \(-0.486715\pi\) | ||||
0.0417229 | + | 0.999129i | \(0.486715\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.89949 | −0.385046 | −0.192523 | − | 0.981292i | \(-0.561667\pi\) | ||||
−0.192523 | + | 0.981292i | \(0.561667\pi\) | |||||||
\(662\) | 0.686292 | 0.0266735 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −13.4558 | −0.522188 | ||||||||
\(665\) | −12.6863 | −0.491953 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.82843 | 0.109517 | ||||||||
\(668\) | 6.75699 | 0.261436 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −36.5838 | −1.41335 | ||||||||
\(671\) | −25.2548 | −0.974952 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 41.8644 | 1.61375 | 0.806877 | − | 0.590719i | \(-0.201156\pi\) | ||||
0.806877 | + | 0.590719i | \(0.201156\pi\) | |||||||
\(674\) | 14.8365 | 0.571479 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.00000 | −0.192308 | ||||||||
\(677\) | 17.7122 | 0.680736 | 0.340368 | − | 0.940292i | \(-0.389448\pi\) | ||||
0.340368 | + | 0.940292i | \(0.389448\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.79899 | −0.145792 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −8.00000 | −0.306336 | ||||||||
\(683\) | 2.16478 | 0.0828332 | 0.0414166 | − | 0.999142i | \(-0.486813\pi\) | ||||
0.0414166 | + | 0.999142i | \(0.486813\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 22.7302 | 0.868478 | ||||||||
\(686\) | 17.8435 | 0.681270 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5.65685 | −0.215666 | ||||||||
\(689\) | −34.9706 | −1.33227 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.4721 | 0.664671 | 0.332335 | − | 0.943161i | \(-0.392163\pi\) | ||||
0.332335 | + | 0.943161i | \(0.392163\pi\) | |||||||
\(692\) | −4.46088 | −0.169577 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5.22625 | 0.198386 | ||||||||
\(695\) | 2.62742 | 0.0996636 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 7.07107 | 0.267644 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −5.48888 | −0.207460 | ||||||||
\(701\) | 10.5858 | 0.399820 | 0.199910 | − | 0.979814i | \(-0.435935\pi\) | ||||
0.199910 | + | 0.979814i | \(0.435935\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −27.3994 | −1.03339 | ||||||||
\(704\) | 15.1535 | 0.571119 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −5.65685 | −0.212899 | ||||||||
\(707\) | 24.8632 | 0.935075 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12.2233 | −0.459057 | −0.229529 | − | 0.973302i | \(-0.573718\pi\) | ||||
−0.229529 | + | 0.973302i | \(0.573718\pi\) | |||||||
\(710\) | 26.1421 | 0.981097 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −40.2426 | −1.50816 | ||||||||
\(713\) | 32.9706 | 1.23476 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 26.9117 | 1.00644 | ||||||||
\(716\) | −16.0000 | −0.597948 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −0.970563 | −0.0362211 | ||||||||
\(719\) | 31.9916 | 1.19308 | 0.596542 | − | 0.802582i | \(-0.296541\pi\) | ||||
0.596542 | + | 0.802582i | \(0.296541\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 25.2346 | 0.939785 | ||||||||
\(722\) | 11.0000 | 0.409378 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5.09494 | 0.189352 | ||||||||
\(725\) | 1.13679 | 0.0422191 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −16.9706 | −0.629403 | −0.314702 | − | 0.949191i | \(-0.601904\pi\) | ||||
−0.314702 | + | 0.949191i | \(0.601904\pi\) | |||||||
\(728\) | 19.4831 | 0.722090 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −11.2132 | −0.415019 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.61522 | −0.207403 | −0.103702 | − | 0.994608i | \(-0.533069\pi\) | ||||
−0.103702 | + | 0.994608i | \(0.533069\pi\) | |||||||
\(734\) | −20.6424 | −0.761924 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −44.6088 | −1.64430 | ||||||||
\(737\) | 27.0279 | 0.995587 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 26.8284 | 0.986900 | 0.493450 | − | 0.869774i | \(-0.335736\pi\) | ||||
0.493450 | + | 0.869774i | \(0.335736\pi\) | |||||||
\(740\) | −28.3848 | −1.04345 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 12.6173 | 0.463195 | ||||||||
\(743\) | −22.8072 | −0.836714 | −0.418357 | − | 0.908283i | \(-0.637394\pi\) | ||||
−0.418357 | + | 0.908283i | \(0.637394\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −50.7318 | −1.85867 | ||||||||
\(746\) | 5.21320 | 0.190869 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −16.0000 | −0.584627 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −38.8573 | −1.41792 | −0.708962 | − | 0.705247i | \(-0.750836\pi\) | ||||
−0.708962 | + | 0.705247i | \(0.750836\pi\) | |||||||
\(752\) | 2.82843 | 0.103142 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.34502 | −0.0489829 | ||||||||
\(755\) | 18.5864 | 0.676428 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −35.3137 | −1.28350 | −0.641749 | − | 0.766915i | \(-0.721791\pi\) | ||||
−0.641749 | + | 0.766915i | \(0.721791\pi\) | |||||||
\(758\) | 18.7402 | 0.680676 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −24.8632 | −0.901882 | ||||||||
\(761\) | 14.8701 | 0.539039 | 0.269520 | − | 0.962995i | \(-0.413135\pi\) | ||||
0.269520 | + | 0.962995i | \(0.413135\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 17.8579 | 0.646498 | ||||||||
\(764\) | −14.8284 | −0.536474 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −24.4853 | −0.884689 | ||||||||
\(767\) | −52.9706 | −1.91266 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −45.2132 | −1.63043 | −0.815215 | − | 0.579159i | \(-0.803381\pi\) | ||||
−0.815215 | + | 0.579159i | \(0.803381\pi\) | |||||||
\(770\) | −9.70967 | −0.349912 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −12.9343 | −0.465516 | ||||||||
\(773\) | −8.97056 | −0.322649 | −0.161324 | − | 0.986901i | \(-0.551577\pi\) | ||||
−0.161324 | + | 0.986901i | \(0.551577\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 13.2513 | 0.476002 | ||||||||
\(776\) | −7.44543 | −0.267275 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −8.97056 | −0.321610 | ||||||||
\(779\) | −0.896683 | −0.0321270 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19.3137 | −0.691099 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 4.65685 | 0.166316 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.43289 | 0.122369 | 0.0611846 | − | 0.998126i | \(-0.480512\pi\) | ||||
0.0611846 | + | 0.998126i | \(0.480512\pi\) | |||||||
\(788\) | −8.86738 | −0.315887 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 35.1127 | 1.24925 | ||||||||
\(791\) | −5.17157 | −0.183880 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −49.4955 | −1.75764 | ||||||||
\(794\) | 17.0782 | 0.606082 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.53073 | 0.0542554 | ||||||||
\(797\) | −17.2132 | −0.609723 | −0.304861 | − | 0.952397i | \(-0.598610\pi\) | ||||
−0.304861 | + | 0.952397i | \(0.598610\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −17.9289 | −0.633883 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 22.4901 | 0.794154 | ||||||||
\(803\) | 8.28427 | 0.292346 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 40.0166 | 1.41040 | ||||||||
\(806\) | −15.6788 | −0.552261 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 48.7279 | 1.71424 | ||||||||
\(809\) | 16.7068 | 0.587378 | 0.293689 | − | 0.955901i | \(-0.405117\pi\) | ||||
0.293689 | + | 0.955901i | \(0.405117\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −19.1116 | −0.671100 | −0.335550 | − | 0.942022i | \(-0.608922\pi\) | ||||
−0.335550 | + | 0.942022i | \(0.608922\pi\) | |||||||
\(812\) | −0.485281 | −0.0170300 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −20.9706 | −0.735018 | ||||||||
\(815\) | −36.9706 | −1.29502 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16.0000 | −0.559769 | ||||||||
\(818\) | −0.970563 | −0.0339349 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.928932 | −0.0324397 | ||||||||
\(821\) | 32.9426 | 1.14971 | 0.574853 | − | 0.818257i | \(-0.305059\pi\) | ||||
0.574853 | + | 0.818257i | \(0.305059\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14.1480 | −0.493169 | −0.246585 | − | 0.969121i | \(-0.579308\pi\) | ||||
−0.246585 | + | 0.969121i | \(0.579308\pi\) | |||||||
\(824\) | 49.4558 | 1.72288 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 19.1116 | 0.664979 | ||||||||
\(827\) | 37.3266 | 1.29797 | 0.648987 | − | 0.760800i | \(-0.275193\pi\) | ||||
0.648987 | + | 0.760800i | \(0.275193\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(830\) | 13.1426 | 0.456185 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 29.6985 | 1.02961 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −19.7990 | −0.685172 | ||||||||
\(836\) | 6.12293 | 0.211766 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −27.0279 | −0.933665 | ||||||||
\(839\) | 11.6118 | 0.400885 | 0.200442 | − | 0.979706i | \(-0.435762\pi\) | ||||
0.200442 | + | 0.979706i | \(0.435762\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.8995 | −0.996534 | ||||||||
\(842\) | 11.2721 | 0.388461 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −3.43289 | −0.118165 | ||||||||
\(845\) | 14.6508 | 0.504001 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.66461 | −0.332080 | ||||||||
\(848\) | 8.24264 | 0.283053 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 86.4264 | 2.96266 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.09494 | 0.174447 | 0.0872236 | − | 0.996189i | \(-0.472201\pi\) | ||||
0.0872236 | + | 0.996189i | \(0.472201\pi\) | |||||||
\(854\) | 17.8579 | 0.611084 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −31.3575 | −1.07178 | ||||||||
\(857\) | 7.59928 | 0.259586 | 0.129793 | − | 0.991541i | \(-0.458569\pi\) | ||||
0.129793 | + | 0.991541i | \(0.458569\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 34.6274 | 1.18147 | 0.590736 | − | 0.806865i | \(-0.298837\pi\) | ||||
0.590736 | + | 0.806865i | \(0.298837\pi\) | |||||||
\(860\) | −16.5754 | −0.565218 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 31.6201 | 1.07699 | ||||||||
\(863\) | −40.2843 | −1.37129 | −0.685646 | − | 0.727935i | \(-0.740480\pi\) | ||||
−0.685646 | + | 0.727935i | \(0.740480\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13.0711 | 0.444430 | ||||||||
\(866\) | −0.343146 | −0.0116606 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −5.65685 | −0.192006 | ||||||||
\(869\) | −25.9411 | −0.879992 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 52.9706 | 1.79484 | ||||||||
\(872\) | 34.9986 | 1.18520 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 25.2346 | 0.853572 | ||||||||
\(875\) | −6.34315 | −0.214437 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −43.0237 | −1.45281 | −0.726404 | − | 0.687268i | \(-0.758810\pi\) | ||||
−0.726404 | + | 0.687268i | \(0.758810\pi\) | |||||||
\(878\) | 5.48888 | 0.185241 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −6.34315 | −0.213827 | ||||||||
\(881\) | −45.0028 | −1.51618 | −0.758091 | − | 0.652148i | \(-0.773868\pi\) | ||||
−0.758091 | + | 0.652148i | \(0.773868\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −21.4558 | −0.722047 | −0.361023 | − | 0.932557i | \(-0.617573\pi\) | ||||
−0.361023 | + | 0.932557i | \(0.617573\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.97056 | 0.166989 | ||||||||
\(887\) | −11.6118 | −0.389887 | −0.194943 | − | 0.980815i | \(-0.562452\pi\) | ||||
−0.194943 | + | 0.980815i | \(0.562452\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.70967 | 0.325652 | ||||||||
\(890\) | 39.3057 | 1.31753 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −9.17157 | −0.307087 | ||||||||
\(893\) | 8.00000 | 0.267710 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 46.8824 | 1.56711 | ||||||||
\(896\) | 4.59220 | 0.153415 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 20.5111 | 0.684463 | ||||||||
\(899\) | 1.17157 | 0.0390741 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −0.686292 | −0.0228510 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −10.1355 | −0.337101 | ||||||||
\(905\) | −14.9289 | −0.496254 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −33.1509 | −1.10076 | −0.550378 | − | 0.834915i | \(-0.685517\pi\) | ||||
−0.550378 | + | 0.834915i | \(0.685517\pi\) | |||||||
\(908\) | −13.5140 | −0.448477 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −19.0294 | −0.630820 | ||||||||
\(911\) | −8.55035 | −0.283286 | −0.141643 | − | 0.989918i | \(-0.545238\pi\) | ||||
−0.141643 | + | 0.989918i | \(0.545238\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.70967 | −0.321343 | ||||||||
\(914\) | −28.2843 | −0.935561 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 22.6274 | 0.747631 | ||||||||
\(917\) | 1.94113 | 0.0641016 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.9706 | 0.427859 | 0.213930 | − | 0.976849i | \(-0.431374\pi\) | ||||
0.213930 | + | 0.976849i | \(0.431374\pi\) | |||||||
\(920\) | 78.4264 | 2.58564 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −32.7279 | −1.07784 | ||||||||
\(923\) | −37.8519 | −1.24591 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 34.7360 | 1.14211 | ||||||||
\(926\) | 3.51472 | 0.115501 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.58513 | −0.0520343 | ||||||||
\(929\) | −22.3044 | −0.731784 | −0.365892 | − | 0.930657i | \(-0.619236\pi\) | ||||
−0.365892 | + | 0.930657i | \(0.619236\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13.1716 | 0.431681 | ||||||||
\(932\) | −1.66205 | −0.0544423 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −0.970563 | −0.0317578 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −24.0416 | −0.785406 | −0.392703 | − | 0.919665i | \(-0.628460\pi\) | ||||
−0.392703 | + | 0.919665i | \(0.628460\pi\) | |||||||
\(938\) | −19.1116 | −0.624017 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 8.28772 | 0.270316 | ||||||||
\(941\) | −12.8574 | −0.419139 | −0.209569 | − | 0.977794i | \(-0.567206\pi\) | ||||
−0.209569 | + | 0.977794i | \(0.567206\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.82843 | 0.0921063 | ||||||||
\(944\) | 12.4853 | 0.406361 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −12.2459 | −0.398148 | ||||||||
\(947\) | −45.7682 | −1.48727 | −0.743633 | − | 0.668588i | \(-0.766899\pi\) | ||||
−0.743633 | + | 0.668588i | \(0.766899\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 16.2359 | 0.527039 | ||||||||
\(950\) | 10.1421 | 0.329054 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −33.2132 | −1.07588 | −0.537941 | − | 0.842983i | \(-0.680798\pi\) | ||||
−0.537941 | + | 0.842983i | \(0.680798\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 43.4495 | 1.40599 | ||||||||
\(956\) | 20.4853 | 0.662541 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 31.0949 | 1.00463 | ||||||||
\(959\) | 11.8745 | 0.383446 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17.3431 | −0.559456 | ||||||||
\(962\) | −41.0990 | −1.32509 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −12.9343 | −0.416586 | ||||||||
\(965\) | 37.8995 | 1.22003 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −55.1127 | −1.77230 | −0.886152 | − | 0.463394i | \(-0.846632\pi\) | ||||
−0.886152 | + | 0.463394i | \(0.846632\pi\) | |||||||
\(968\) | −18.9411 | −0.608791 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 7.27208 | 0.233492 | ||||||||
\(971\) | 40.4853 | 1.29923 | 0.649617 | − | 0.760261i | \(-0.274929\pi\) | ||||
0.649617 | + | 0.760261i | \(0.274929\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.37258 | 0.0440030 | ||||||||
\(974\) | −41.5474 | −1.33126 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 11.6662 | 0.373426 | ||||||||
\(977\) | 8.72792 | 0.279231 | 0.139615 | − | 0.990206i | \(-0.455413\pi\) | ||||
0.139615 | + | 0.990206i | \(0.455413\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −29.0389 | −0.928087 | ||||||||
\(980\) | 13.6453 | 0.435883 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 29.9411 | 0.955460 | ||||||||
\(983\) | −41.9188 | −1.33700 | −0.668501 | − | 0.743711i | \(-0.733064\pi\) | ||||
−0.668501 | + | 0.743711i | \(0.733064\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 25.9828 | 0.827879 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 12.0000 | 0.381771 | ||||||||
\(989\) | 50.4692 | 1.60483 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.96362 | −0.157675 | −0.0788373 | − | 0.996887i | \(-0.525121\pi\) | ||||
−0.0788373 | + | 0.996887i | \(0.525121\pi\) | |||||||
\(992\) | −18.4776 | −0.586664 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 13.6569 | 0.433169 | ||||||||
\(995\) | −4.48528 | −0.142193 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.84776 | −0.0585191 | −0.0292596 | − | 0.999572i | \(-0.509315\pi\) | ||||
−0.0292596 | + | 0.999572i | \(0.509315\pi\) | |||||||
\(998\) | 27.7708 | 0.879069 | ||||||||
\(999\) | 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 | 2601.2.a.ba.1.3 | 4 | ||
3.2 | odd | 2 | 2601.2.a.bg.1.2 | 4 | |||
17.3 | odd | 16 | 153.2.l.b.145.1 | yes | 4 | ||
17.6 | odd | 16 | 153.2.l.b.19.1 | yes | 4 | ||
17.16 | even | 2 | inner | 2601.2.a.ba.1.2 | 4 | ||
51.20 | even | 16 | 153.2.l.a.145.1 | yes | 4 | ||
51.23 | even | 16 | 153.2.l.a.19.1 | ✓ | 4 | ||
51.50 | odd | 2 | 2601.2.a.bg.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
153.2.l.a.19.1 | ✓ | 4 | 51.23 | even | 16 | ||
153.2.l.a.145.1 | yes | 4 | 51.20 | even | 16 | ||
153.2.l.b.19.1 | yes | 4 | 17.6 | odd | 16 | ||
153.2.l.b.145.1 | yes | 4 | 17.3 | odd | 16 | ||
2601.2.a.ba.1.2 | 4 | 17.16 | even | 2 | inner | ||
2601.2.a.ba.1.3 | 4 | 1.1 | even | 1 | trivial | ||
2601.2.a.bg.1.2 | 4 | 3.2 | odd | 2 | |||
2601.2.a.bg.1.3 | 4 | 51.50 | odd | 2 |