Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7800,2,Mod(1,7800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("7800.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7800 = 2^{3} \cdot 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7800.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: | \(62.2833135766\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.788.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 7x - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(3.35386\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7800.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.35386 | 1.26764 | 0.633819 | − | 0.773481i | \(-0.281486\pi\) | ||||
0.633819 | + | 0.773481i | \(0.281486\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.81322 | −1.14973 | −0.574864 | − | 0.818249i | \(-0.694945\pi\) | ||||
−0.574864 | + | 0.818249i | \(0.694945\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.00000 | −0.242536 | −0.121268 | − | 0.992620i | \(-0.538696\pi\) | ||||
−0.121268 | + | 0.992620i | \(0.538696\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.24835 | 0.974638 | 0.487319 | − | 0.873224i | \(-0.337975\pi\) | ||||
0.487319 | + | 0.873224i | \(0.337975\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.35386 | 0.731871 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.24835 | −1.30287 | −0.651435 | − | 0.758704i | \(-0.725833\pi\) | ||||
−0.651435 | + | 0.758704i | \(0.725833\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.78899 | −1.26068 | −0.630341 | − | 0.776318i | \(-0.717085\pi\) | ||||
−0.630341 | + | 0.776318i | \(0.717085\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.97577 | −1.07328 | −0.536640 | − | 0.843811i | \(-0.680307\pi\) | ||||
−0.536640 | + | 0.843811i | \(0.680307\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.81322 | −0.663796 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.45936 | −0.733115 | −0.366557 | − | 0.930395i | \(-0.619464\pi\) | ||||
−0.366557 | + | 0.930395i | \(0.619464\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.621911 | −0.0971262 | −0.0485631 | − | 0.998820i | \(-0.515464\pi\) | ||||
−0.0485631 | + | 0.998820i | \(0.515464\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.54064 | 0.234945 | 0.117472 | − | 0.993076i | \(-0.462521\pi\) | ||||
0.117472 | + | 0.993076i | \(0.462521\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.14284 | −1.33362 | −0.666810 | − | 0.745228i | \(-0.732341\pi\) | ||||
−0.666810 | + | 0.745228i | \(0.732341\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.24835 | 0.606907 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.08580 | −0.973310 | −0.486655 | − | 0.873594i | \(-0.661783\pi\) | ||||
−0.486655 | + | 0.873594i | \(0.661783\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.24835 | 0.562708 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.272582 | 0.0354871 | 0.0177436 | − | 0.999843i | \(-0.494352\pi\) | ||||
0.0177436 | + | 0.999843i | \(0.494352\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.78899 | 0.613167 | 0.306583 | − | 0.951844i | \(-0.400814\pi\) | ||||
0.306583 | + | 0.951844i | \(0.400814\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.35386 | 0.422546 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.81322 | 0.221520 | 0.110760 | − | 0.993847i | \(-0.464672\pi\) | ||||
0.110760 | + | 0.993847i | \(0.464672\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.24835 | −0.752213 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.16707 | −1.08793 | −0.543966 | − | 0.839107i | \(-0.683078\pi\) | ||||
−0.543966 | + | 0.839107i | \(0.683078\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.32962 | −0.389703 | −0.194851 | − | 0.980833i | \(-0.562422\pi\) | ||||
−0.194851 | + | 0.980833i | \(0.562422\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −12.7890 | −1.45744 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.54064 | −0.623370 | −0.311685 | − | 0.950185i | \(-0.600893\pi\) | ||||
−0.311685 | + | 0.950185i | \(0.600893\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.27258 | −0.688505 | −0.344253 | − | 0.938877i | \(-0.611868\pi\) | ||||
−0.344253 | + | 0.938877i | \(0.611868\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.78899 | −0.727856 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.78899 | 0.401632 | 0.200816 | − | 0.979629i | \(-0.435641\pi\) | ||||
0.200816 | + | 0.979629i | \(0.435641\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.35386 | −0.351580 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.97577 | −0.619658 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.7077 | −1.49334 | −0.746671 | − | 0.665194i | \(-0.768349\pi\) | ||||
−0.746671 | + | 0.665194i | \(0.768349\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.81322 | −0.383243 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.03733 | 0.700241 | 0.350120 | − | 0.936705i | \(-0.386141\pi\) | ||||
0.350120 | + | 0.936705i | \(0.386141\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 18.7935 | 1.85178 | 0.925890 | − | 0.377794i | \(-0.123317\pi\) | ||||
0.925890 | + | 0.377794i | \(0.123317\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.87026 | 0.470826 | 0.235413 | − | 0.971895i | \(-0.424356\pi\) | ||||
0.235413 | + | 0.971895i | \(0.424356\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.32962 | 0.127355 | 0.0636774 | − | 0.997971i | \(-0.479717\pi\) | ||||
0.0636774 | + | 0.997971i | \(0.479717\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.45936 | −0.423264 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.78899 | 0.544582 | 0.272291 | − | 0.962215i | \(-0.412219\pi\) | ||||
0.272291 | + | 0.962215i | \(0.412219\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.35386 | −0.307447 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.54064 | 0.321876 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.621911 | −0.0560758 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.16707 | −0.635975 | −0.317988 | − | 0.948095i | \(-0.603007\pi\) | ||||
−0.317988 | + | 0.948095i | \(0.603007\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.54064 | 0.135646 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.00453 | −0.611988 | −0.305994 | − | 0.952033i | \(-0.598989\pi\) | ||||
−0.305994 | + | 0.952033i | \(0.598989\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 14.2483 | 1.23549 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.12974 | −0.0965202 | −0.0482601 | − | 0.998835i | \(-0.515368\pi\) | ||||
−0.0482601 | + | 0.998835i | \(0.515368\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.16255 | −0.353063 | −0.176531 | − | 0.984295i | \(-0.556488\pi\) | ||||
−0.176531 | + | 0.984295i | \(0.556488\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.14284 | −0.769966 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.81322 | 0.318877 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.24835 | 0.350398 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 14.2857 | 1.17033 | 0.585164 | − | 0.810915i | \(-0.301030\pi\) | ||||
0.585164 | + | 0.810915i | \(0.301030\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.85055 | 0.801627 | 0.400813 | − | 0.916160i | \(-0.368728\pi\) | ||||
0.400813 | + | 0.916160i | \(0.368728\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.2483 | −1.37657 | −0.688284 | − | 0.725441i | \(-0.741636\pi\) | ||||
−0.688284 | + | 0.725441i | \(0.741636\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −7.08580 | −0.561941 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −20.9561 | −1.65157 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.4922 | 1.05679 | 0.528394 | − | 0.848999i | \(-0.322794\pi\) | ||||
0.528394 | + | 0.848999i | \(0.322794\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.54064 | −0.273983 | −0.136991 | − | 0.990572i | \(-0.543743\pi\) | ||||
−0.136991 | + | 0.990572i | \(0.543743\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.24835 | 0.324879 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.37809 | 0.180803 | 0.0904014 | − | 0.995905i | \(-0.471185\pi\) | ||||
0.0904014 | + | 0.995905i | \(0.471185\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.272582 | 0.0204885 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.7935 | −0.806745 | −0.403372 | − | 0.915036i | \(-0.632162\pi\) | ||||
−0.403372 | + | 0.915036i | \(0.632162\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.11861 | −0.603451 | −0.301726 | − | 0.953395i | \(-0.597563\pi\) | ||||
−0.301726 | + | 0.953395i | \(0.597563\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.78899 | 0.354012 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.81322 | 0.278850 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.35386 | 0.243957 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −25.5780 | −1.85076 | −0.925379 | − | 0.379044i | \(-0.876253\pi\) | ||||
−0.925379 | + | 0.379044i | \(0.876253\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19.1671 | 1.37968 | 0.689838 | − | 0.723964i | \(-0.257682\pi\) | ||||
0.689838 | + | 0.723964i | \(0.257682\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.04394 | −0.359366 | −0.179683 | − | 0.983725i | \(-0.557507\pi\) | ||||
−0.179683 | + | 0.983725i | \(0.557507\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.91873 | −0.206903 | −0.103451 | − | 0.994634i | \(-0.532989\pi\) | ||||
−0.103451 | + | 0.994634i | \(0.532989\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.81322 | 0.127895 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −22.7693 | −1.59809 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.24835 | −0.434290 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −16.1999 | −1.12057 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.1671 | −1.04414 | −0.522072 | − | 0.852901i | \(-0.674841\pi\) | ||||
−0.522072 | + | 0.852901i | \(0.674841\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −9.16707 | −0.628118 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −20.0419 | −1.36053 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.32962 | −0.224995 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.00000 | 0.0672673 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 28.4199 | 1.90314 | 0.951570 | − | 0.307431i | \(-0.0994694\pi\) | ||||
0.951570 | + | 0.307431i | \(0.0994694\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.4725 | 0.827827 | 0.413913 | − | 0.910316i | \(-0.364162\pi\) | ||||
0.413913 | + | 0.910316i | \(0.364162\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −29.1559 | −1.92668 | −0.963339 | − | 0.268285i | \(-0.913543\pi\) | ||||
−0.963339 | + | 0.268285i | \(0.913543\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −12.7890 | −0.841453 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.21101 | 0.144848 | 0.0724242 | − | 0.997374i | \(-0.476926\pi\) | ||||
0.0724242 | + | 0.997374i | \(0.476926\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.54064 | −0.359903 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.8506 | −0.895918 | −0.447959 | − | 0.894054i | \(-0.647849\pi\) | ||||
−0.447959 | + | 0.894054i | \(0.647849\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.49217 | 0.482613 | 0.241307 | − | 0.970449i | \(-0.422424\pi\) | ||||
0.241307 | + | 0.970449i | \(0.422424\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.24835 | −0.270316 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.27258 | −0.397509 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.78446 | −0.301992 | −0.150996 | − | 0.988534i | \(-0.548248\pi\) | ||||
−0.150996 | + | 0.988534i | \(0.548248\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 23.8263 | 1.49795 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 15.4199 | 0.961870 | 0.480935 | − | 0.876756i | \(-0.340297\pi\) | ||||
0.480935 | + | 0.876756i | \(0.340297\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −14.9561 | −0.929324 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.78899 | −0.420228 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 29.8748 | 1.84216 | 0.921079 | − | 0.389375i | \(-0.127309\pi\) | ||||
0.921079 | + | 0.389375i | \(0.127309\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.78899 | 0.231882 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.16255 | 0.436708 | 0.218354 | − | 0.975870i | \(-0.429931\pi\) | ||||
0.218354 | + | 0.975870i | \(0.429931\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.1847 | 0.983151 | 0.491575 | − | 0.870835i | \(-0.336421\pi\) | ||||
0.491575 | + | 0.870835i | \(0.336421\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.35386 | −0.202985 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 25.5386 | 1.53446 | 0.767232 | − | 0.641370i | \(-0.221634\pi\) | ||||
0.767232 | + | 0.641370i | \(0.221634\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.97577 | −0.357760 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.65925 | 0.516567 | 0.258284 | − | 0.966069i | \(-0.416843\pi\) | ||||
0.258284 | + | 0.966069i | \(0.416843\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.9121 | −0.945877 | −0.472939 | − | 0.881095i | \(-0.656807\pi\) | ||||
−0.472939 | + | 0.881095i | \(0.656807\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.08580 | −0.123121 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.0000 | −0.941176 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −14.7077 | −0.862181 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 13.2529 | 0.774241 | 0.387121 | − | 0.922029i | \(-0.373470\pi\) | ||||
0.387121 | + | 0.922029i | \(0.373470\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.81322 | −0.221265 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.24835 | 0.361351 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.16707 | 0.297825 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7.03733 | 0.404284 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.12521 | 0.121292 | 0.0606462 | − | 0.998159i | \(-0.480684\pi\) | ||||
0.0606462 | + | 0.998159i | \(0.480684\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 18.7935 | 1.06913 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.9121 | 1.12911 | 0.564556 | − | 0.825395i | \(-0.309047\pi\) | ||||
0.564556 | + | 0.825395i | \(0.309047\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.50122 | −0.367471 | −0.183735 | − | 0.982976i | \(-0.558819\pi\) | ||||
−0.183735 | + | 0.982976i | \(0.558819\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −23.3296 | −1.31032 | −0.655161 | − | 0.755489i | \(-0.727399\pi\) | ||||
−0.655161 | + | 0.755489i | \(0.727399\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 25.8879 | 1.44944 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.87026 | 0.271831 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.24835 | −0.236384 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.32962 | 0.0735283 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −30.6638 | −1.69055 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.32962 | −0.402873 | −0.201436 | − | 0.979502i | \(-0.564561\pi\) | ||||
−0.201436 | + | 0.979502i | \(0.564561\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.45936 | −0.244372 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.03733 | −0.492295 | −0.246147 | − | 0.969232i | \(-0.579165\pi\) | ||||
−0.246147 | + | 0.969232i | \(0.579165\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.78899 | 0.314415 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 22.7869 | 1.23398 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.22864 | −0.498300 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −21.1559 | −1.13571 | −0.567855 | − | 0.823128i | \(-0.692227\pi\) | ||||
−0.567855 | + | 0.823128i | \(0.692227\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.956060 | 0.0511767 | 0.0255884 | − | 0.999673i | \(-0.491854\pi\) | ||||
0.0255884 | + | 0.999673i | \(0.491854\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 29.7869 | 1.58540 | 0.792699 | − | 0.609614i | \(-0.208675\pi\) | ||||
0.792699 | + | 0.609614i | \(0.208675\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.35386 | −0.177505 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 35.2660 | 1.86127 | 0.930634 | − | 0.365953i | \(-0.119257\pi\) | ||||
0.930634 | + | 0.365953i | \(0.119257\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.951534 | −0.0500807 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.54064 | 0.185835 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.8375 | 0.722309 | 0.361155 | − | 0.932506i | \(-0.382383\pi\) | ||||
0.361155 | + | 0.932506i | \(0.382383\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.621911 | −0.0323754 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −23.7648 | −1.23380 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.2812 | −0.946562 | −0.473281 | − | 0.880911i | \(-0.656931\pi\) | ||||
−0.473281 | + | 0.880911i | \(0.656931\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.78899 | 0.349651 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.0086 | 0.770939 | 0.385469 | − | 0.922721i | \(-0.374040\pi\) | ||||
0.385469 | + | 0.922721i | \(0.374040\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.16707 | −0.367180 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −15.5012 | −0.792076 | −0.396038 | − | 0.918234i | \(-0.629615\pi\) | ||||
−0.396038 | + | 0.918234i | \(0.629615\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.54064 | 0.0783150 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −17.0419 | −0.864057 | −0.432028 | − | 0.901860i | \(-0.642202\pi\) | ||||
−0.432028 | + | 0.901860i | \(0.642202\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.24835 | 0.315993 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7.00453 | −0.353332 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −23.2044 | −1.16460 | −0.582298 | − | 0.812975i | \(-0.697846\pi\) | ||||
−0.582298 | + | 0.812975i | \(0.697846\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 14.2483 | 0.713310 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −11.1186 | −0.555237 | −0.277618 | − | 0.960691i | \(-0.589545\pi\) | ||||
−0.277618 | + | 0.960691i | \(0.589545\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.97577 | 0.297674 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 17.0045 | 0.842883 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.87479 | 0.191596 | 0.0957979 | − | 0.995401i | \(-0.469460\pi\) | ||||
0.0957979 | + | 0.995401i | \(0.469460\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.12974 | −0.0557260 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.914200 | 0.0449848 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.16255 | −0.203841 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13.8748 | 0.677828 | 0.338914 | − | 0.940817i | \(-0.389940\pi\) | ||||
0.338914 | + | 0.940817i | \(0.389940\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −37.5870 | −1.83188 | −0.915940 | − | 0.401316i | \(-0.868553\pi\) | ||||
−0.915940 | + | 0.401316i | \(0.868553\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −9.14284 | −0.444540 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 16.0616 | 0.777274 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.81322 | 0.184104 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.58250 | 0.317068 | 0.158534 | − | 0.987354i | \(-0.449323\pi\) | ||||
0.158534 | + | 0.987354i | \(0.449323\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 20.5452 | 0.987338 | 0.493669 | − | 0.869650i | \(-0.335656\pi\) | ||||
0.493669 | + | 0.869650i | \(0.335656\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −26.5452 | −1.26983 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −23.4922 | −1.12122 | −0.560610 | − | 0.828080i | \(-0.689433\pi\) | ||||
−0.560610 | + | 0.828080i | \(0.689433\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.24835 | 0.202302 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.04394 | −0.239645 | −0.119822 | − | 0.992795i | \(-0.538233\pi\) | ||||
−0.119822 | + | 0.992795i | \(0.538233\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 14.2857 | 0.675690 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.3341 | 0.865242 | 0.432621 | − | 0.901576i | \(-0.357589\pi\) | ||||
0.432621 | + | 0.901576i | \(0.357589\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.37148 | 0.111669 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 9.85055 | 0.462819 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 26.2089 | 1.22600 | 0.613001 | − | 0.790082i | \(-0.289962\pi\) | ||||
0.613001 | + | 0.790082i | \(0.289962\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −34.4967 | −1.60667 | −0.803336 | − | 0.595526i | \(-0.796943\pi\) | ||||
−0.803336 | + | 0.595526i | \(0.796943\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.43060 | 0.252382 | 0.126191 | − | 0.992006i | \(-0.459725\pi\) | ||||
0.126191 | + | 0.992006i | \(0.459725\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 35.0419 | 1.62154 | 0.810772 | − | 0.585362i | \(-0.199048\pi\) | ||||
0.810772 | + | 0.585362i | \(0.199048\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.08127 | 0.280807 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −17.2483 | −0.794762 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.87479 | −0.270123 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.08580 | −0.324437 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 24.0989 | 1.10111 | 0.550553 | − | 0.834800i | \(-0.314417\pi\) | ||||
0.550553 | + | 0.834800i | \(0.314417\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.45936 | 0.203329 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −20.9561 | −0.953534 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −31.2286 | −1.41510 | −0.707552 | − | 0.706661i | \(-0.750201\pi\) | ||||
−0.707552 | + | 0.706661i | \(0.750201\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 13.4922 | 0.610137 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.2529 | −0.598094 | −0.299047 | − | 0.954238i | \(-0.596669\pi\) | ||||
−0.299047 | + | 0.954238i | \(0.596669\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.78899 | 0.305761 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −30.7450 | −1.37910 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −40.6329 | −1.81898 | −0.909490 | − | 0.415726i | \(-0.863528\pi\) | ||||
−0.909490 | + | 0.415726i | \(0.863528\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.54064 | −0.158184 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 31.0792 | 1.38575 | 0.692876 | − | 0.721056i | \(-0.256343\pi\) | ||||
0.692876 | + | 0.721056i | \(0.256343\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −20.4109 | −0.904697 | −0.452349 | − | 0.891841i | \(-0.649414\pi\) | ||||
−0.452349 | + | 0.891841i | \(0.649414\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.1671 | −0.494002 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.24835 | 0.187569 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 34.8637 | 1.53330 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.37809 | 0.104387 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.57797 | −0.419619 | −0.209809 | − | 0.977742i | \(-0.567284\pi\) | ||||
−0.209809 | + | 0.977742i | \(0.567284\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19.1297 | 0.836485 | 0.418243 | − | 0.908335i | \(-0.362646\pi\) | ||||
0.418243 | + | 0.908335i | \(0.362646\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.97577 | 0.260308 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 16.0419 | 0.697472 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.272582 | 0.0118290 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.621911 | 0.0269380 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −10.7935 | −0.465774 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −16.1999 | −0.697778 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −26.6572 | −1.14608 | −0.573041 | − | 0.819527i | \(-0.694236\pi\) | ||||
−0.573041 | + | 0.819527i | \(0.694236\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8.11861 | −0.348403 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.9561 | 0.724989 | 0.362494 | − | 0.931986i | \(-0.381925\pi\) | ||||
0.362494 | + | 0.931986i | \(0.381925\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.78899 | 0.204389 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −28.8420 | −1.22871 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −18.5825 | −0.790208 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −29.5012 | −1.25001 | −0.625003 | − | 0.780622i | \(-0.714902\pi\) | ||||
−0.625003 | + | 0.780622i | \(0.714902\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.54064 | −0.0651620 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.81322 | 0.160994 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −41.4043 | −1.74498 | −0.872491 | − | 0.488629i | \(-0.837497\pi\) | ||||
−0.872491 | + | 0.488629i | \(0.837497\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.35386 | 0.140849 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −46.4618 | −1.94778 | −0.973890 | − | 0.227020i | \(-0.927102\pi\) | ||||
−0.973890 | + | 0.227020i | \(0.927102\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.82632 | −0.0764291 | −0.0382146 | − | 0.999270i | \(-0.512167\pi\) | ||||
−0.0382146 | + | 0.999270i | \(0.512167\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −25.5780 | −1.06854 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −35.7980 | −1.49029 | −0.745146 | − | 0.666901i | \(-0.767620\pi\) | ||||
−0.745146 | + | 0.666901i | \(0.767620\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 19.1671 | 0.796556 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −21.0373 | −0.872776 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 27.0197 | 1.11904 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −34.9297 | −1.44170 | −0.720852 | − | 0.693089i | \(-0.756249\pi\) | ||||
−0.720852 | + | 0.693089i | \(0.756249\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −25.3871 | −1.04606 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.04394 | −0.207480 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 22.4967 | 0.923829 | 0.461914 | − | 0.886925i | \(-0.347163\pi\) | ||||
0.461914 | + | 0.886925i | \(0.347163\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.91873 | −0.119455 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 24.7450 | 1.01106 | 0.505528 | − | 0.862810i | \(-0.331298\pi\) | ||||
0.505528 | + | 0.862810i | \(0.331298\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.57345 | −0.0641822 | −0.0320911 | − | 0.999485i | \(-0.510217\pi\) | ||||
−0.0320911 | + | 0.999485i | \(0.510217\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.81322 | 0.0738400 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 36.9449 | 1.49955 | 0.749774 | − | 0.661694i | \(-0.230162\pi\) | ||||
0.749774 | + | 0.661694i | \(0.230162\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −22.7693 | −0.922658 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.14284 | 0.369880 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17.2529 | −0.696837 | −0.348419 | − | 0.937339i | \(-0.613281\pi\) | ||||
−0.348419 | + | 0.937339i | \(0.613281\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15.9515 | −0.642185 | −0.321092 | − | 0.947048i | \(-0.604050\pi\) | ||||
−0.321092 | + | 0.947048i | \(0.604050\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.7122 | 0.470755 | 0.235377 | − | 0.971904i | \(-0.424367\pi\) | ||||
0.235377 | + | 0.971904i | \(0.424367\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.24835 | −0.250738 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 12.7077 | 0.509124 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −16.1999 | −0.646961 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.45936 | 0.177806 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28.0373 | −1.11615 | −0.558074 | − | 0.829791i | \(-0.688460\pi\) | ||||
−0.558074 | + | 0.829791i | \(0.688460\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −15.1671 | −0.602837 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.24835 | −0.168326 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.16707 | −0.362644 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −35.6683 | −1.40881 | −0.704407 | − | 0.709797i | \(-0.748787\pi\) | ||||
−0.704407 | + | 0.709797i | \(0.748787\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 34.0858 | 1.34421 | 0.672106 | − | 0.740455i | \(-0.265390\pi\) | ||||
0.672106 | + | 0.740455i | \(0.265390\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 15.7890 | 0.620729 | 0.310365 | − | 0.950618i | \(-0.399549\pi\) | ||||
0.310365 | + | 0.950618i | \(0.399549\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.03941 | −0.0408005 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −20.0419 | −0.785502 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −16.9031 | −0.661468 | −0.330734 | − | 0.943724i | \(-0.607296\pi\) | ||||
−0.330734 | + | 0.943724i | \(0.607296\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.32962 | −0.129901 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16.1252 | 0.628149 | 0.314075 | − | 0.949398i | \(-0.398306\pi\) | ||||
0.314075 | + | 0.949398i | \(0.398306\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.5250 | 0.798329 | 0.399165 | − | 0.916879i | \(-0.369300\pi\) | ||||
0.399165 | + | 0.916879i | \(0.369300\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.00000 | 0.0388368 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 42.4199 | 1.64251 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 28.4199 | 1.09878 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −18.2614 | −0.704975 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 39.9561 | 1.54019 | 0.770096 | − | 0.637927i | \(-0.220208\pi\) | ||||
0.770096 | + | 0.637927i | \(0.220208\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.49670 | 0.0959559 | 0.0479779 | − | 0.998848i | \(-0.484722\pi\) | ||||
0.0479779 | + | 0.998848i | \(0.484722\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −49.3275 | −1.89302 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.4725 | 0.477946 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −30.3099 | −1.15978 | −0.579888 | − | 0.814696i | \(-0.696904\pi\) | ||||
−0.579888 | + | 0.814696i | \(0.696904\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −29.1559 | −1.11237 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.08580 | 0.269947 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −50.3563 | −1.91564 | −0.957822 | − | 0.287362i | \(-0.907222\pi\) | ||||
−0.957822 | + | 0.287362i | \(0.907222\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −12.7890 | −0.485813 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.621911 | 0.0235566 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.21101 | 0.0836282 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10.3670 | 0.391555 | 0.195777 | − | 0.980648i | \(-0.437277\pi\) | ||||
0.195777 | + | 0.980648i | \(0.437277\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −18.9449 | −0.714522 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 23.6022 | 0.887652 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.87479 | −0.295744 | −0.147872 | − | 0.989007i | \(-0.547242\pi\) | ||||
−0.147872 | + | 0.989007i | \(0.547242\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.54064 | −0.207790 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 37.3387 | 1.39834 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −13.8506 | −0.517258 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 18.1252 | 0.675956 | 0.337978 | − | 0.941154i | \(-0.390257\pi\) | ||||
0.337978 | + | 0.941154i | \(0.390257\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 63.0307 | 2.34739 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.49217 | 0.278637 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28.5340 | 1.05827 | 0.529134 | − | 0.848538i | \(-0.322517\pi\) | ||||
0.529134 | + | 0.848538i | \(0.322517\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.54064 | −0.0569825 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −27.4245 | −1.01295 | −0.506473 | − | 0.862256i | \(-0.669051\pi\) | ||||
−0.506473 | + | 0.862256i | \(0.669051\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.91420 | −0.254688 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.52093 | 0.0927339 | 0.0463670 | − | 0.998924i | \(-0.485236\pi\) | ||||
0.0463670 | + | 0.998924i | \(0.485236\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.24835 | −0.156067 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13.9364 | 0.511275 | 0.255638 | − | 0.966773i | \(-0.417715\pi\) | ||||
0.255638 | + | 0.966773i | \(0.417715\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.27258 | −0.229502 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 16.3341 | 0.596837 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −24.2574 | −0.885165 | −0.442583 | − | 0.896728i | \(-0.645938\pi\) | ||||
−0.442583 | + | 0.896728i | \(0.645938\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.78446 | −0.174355 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.32510 | −0.0481615 | −0.0240807 | − | 0.999710i | \(-0.507666\pi\) | ||||
−0.0240807 | + | 0.999710i | \(0.507666\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 23.8263 | 0.864841 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.32962 | −0.265699 | −0.132849 | − | 0.991136i | \(-0.542413\pi\) | ||||
−0.132849 | + | 0.991136i | \(0.542413\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.45936 | 0.161440 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.272582 | −0.00984235 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.70771 | 0.169764 | 0.0848822 | − | 0.996391i | \(-0.472949\pi\) | ||||
0.0848822 | + | 0.996391i | \(0.472949\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15.4199 | 0.555336 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −18.7077 | −0.672870 | −0.336435 | − | 0.941707i | \(-0.609221\pi\) | ||||
−0.336435 | + | 0.941707i | \(0.609221\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −14.9561 | −0.536546 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.64210 | −0.0946629 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 34.9561 | 1.25083 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.78899 | −0.242619 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15.0176 | −0.535321 | −0.267660 | − | 0.963513i | \(-0.586250\pi\) | ||||
−0.267660 | + | 0.963513i | \(0.586250\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 29.8748 | 1.06357 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 19.4154 | 0.690333 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.78899 | −0.170062 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −50.2135 | −1.77865 | −0.889326 | − | 0.457274i | \(-0.848826\pi\) | ||||
−0.889326 | + | 0.457274i | \(0.848826\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.14284 | 0.323450 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.78899 | 0.133877 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 12.6966 | 0.448053 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7.16255 | 0.252134 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −13.7143 | −0.482170 | −0.241085 | − | 0.970504i | \(-0.577503\pi\) | ||||
−0.241085 | + | 0.970504i | \(0.577503\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30.3473 | 1.06564 | 0.532818 | − | 0.846230i | \(-0.321133\pi\) | ||||
0.532818 | + | 0.846230i | \(0.321133\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 16.1847 | 0.567622 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.54516 | 0.228986 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.35386 | −0.117193 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −0.287762 | −0.0100430 | −0.00502148 | − | 0.999987i | \(-0.501598\pi\) | ||||
−0.00502148 | + | 0.999987i | \(0.501598\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 41.1075 | 1.43292 | 0.716458 | − | 0.697630i | \(-0.245762\pi\) | ||||
0.716458 | + | 0.697630i | \(0.245762\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 37.0176 | 1.28723 | 0.643615 | − | 0.765350i | \(-0.277434\pi\) | ||||
0.643615 | + | 0.765350i | \(0.277434\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −50.7011 | −1.76092 | −0.880461 | − | 0.474118i | \(-0.842767\pi\) | ||||
−0.880461 | + | 0.474118i | \(0.842767\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 25.5386 | 0.885923 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.24835 | −0.147197 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.97577 | −0.206553 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 44.4199 | 1.53355 | 0.766773 | − | 0.641918i | \(-0.221861\pi\) | ||||
0.766773 | + | 0.641918i | \(0.221861\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17.0903 | 0.589322 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 8.65925 | 0.298240 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11.8748 | 0.408022 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −15.9121 | −0.546103 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 27.8637 | 0.955154 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.4088 | 0.493349 | 0.246674 | − | 0.969098i | \(-0.420662\pi\) | ||||
0.246674 | + | 0.969098i | \(0.420662\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 45.1559 | 1.54250 | 0.771249 | − | 0.636534i | \(-0.219632\pi\) | ||||
0.771249 | + | 0.636534i | \(0.219632\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.54969 | −0.257592 | −0.128796 | − | 0.991671i | \(-0.541111\pi\) | ||||
−0.128796 | + | 0.991671i | \(0.541111\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.08580 | −0.0710839 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −28.8551 | −0.982238 | −0.491119 | − | 0.871092i | \(-0.663412\pi\) | ||||
−0.491119 | + | 0.871092i | \(0.663412\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −16.0000 | −0.543388 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 21.1277 | 0.716707 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.81322 | −0.0614386 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −14.7077 | −0.497781 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −25.7011 | −0.867865 | −0.433932 | − | 0.900945i | \(-0.642874\pi\) | ||||
−0.433932 | + | 0.900945i | \(0.642874\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 13.2529 | 0.447008 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.32962 | 0.145869 | 0.0729343 | − | 0.997337i | \(-0.476764\pi\) | ||||
0.0729343 | + | 0.997337i | \(0.476764\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 53.3760 | 1.79625 | 0.898123 | − | 0.439745i | \(-0.144931\pi\) | ||||
0.898123 | + | 0.439745i | \(0.144931\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 8.19988 | 0.275325 | 0.137663 | − | 0.990479i | \(-0.456041\pi\) | ||||
0.137663 | + | 0.990479i | \(0.456041\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −24.0373 | −0.806186 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.81322 | −0.127748 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −38.8420 | −1.29980 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.24835 | 0.208626 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 40.5694 | 1.35307 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.08580 | 0.236062 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.16707 | 0.171949 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22.4088 | −0.744073 | −0.372036 | − | 0.928218i | \(-0.621340\pi\) | ||||
−0.372036 | + | 0.928218i | \(0.621340\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7.03733 | 0.233414 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.57345 | −0.0852620 | −0.0426310 | − | 0.999091i | \(-0.513574\pi\) | ||||
−0.0426310 | + | 0.999091i | \(0.513574\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 23.9187 | 0.791594 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −23.4922 | −0.775780 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 22.7824 | 0.751521 | 0.375761 | − | 0.926717i | \(-0.377381\pi\) | ||||
0.375761 | + | 0.926717i | \(0.377381\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.12521 | 0.0700282 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9.16707 | 0.301738 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 18.7935 | 0.617260 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −14.5936 | −0.478801 | −0.239401 | − | 0.970921i | \(-0.576951\pi\) | ||||
−0.239401 | + | 0.970921i | \(0.576951\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 18.0485 | 0.591515 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 19.9121 | 0.651894 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.11408 | 0.167070 | 0.0835349 | − | 0.996505i | \(-0.473379\pi\) | ||||
0.0835349 | + | 0.996505i | \(0.473379\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.50122 | −0.212159 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −44.5734 | −1.45305 | −0.726526 | − | 0.687139i | \(-0.758867\pi\) | ||||
−0.726526 | + | 0.687139i | \(0.758867\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.88592 | 0.126543 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 28.3493 | 0.921229 | 0.460615 | − | 0.887600i | \(-0.347629\pi\) | ||||
0.460615 | + | 0.887600i | \(0.347629\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.32962 | 0.108084 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −23.3296 | −0.756515 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −49.7056 | −1.61012 | −0.805062 | − | 0.593191i | \(-0.797868\pi\) | ||||
−0.805062 | + | 0.593191i | \(0.797868\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 25.8879 | 0.836837 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.78899 | −0.122353 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.70979 | 0.151929 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.87026 | 0.156942 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.21959 | −0.167851 | −0.0839253 | − | 0.996472i | \(-0.526746\pi\) | ||||
−0.0839253 | + | 0.996472i | \(0.526746\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.24835 | −0.136477 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 48.1978 | 1.54674 | 0.773371 | − | 0.633954i | \(-0.218569\pi\) | ||||
0.773371 | + | 0.633954i | \(0.218569\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −13.9606 | −0.447556 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −24.9187 | −0.797221 | −0.398610 | − | 0.917120i | \(-0.630507\pi\) | ||||
−0.398610 | + | 0.917120i | \(0.630507\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14.4482 | −0.461767 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.32962 | 0.0424516 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −37.5537 | −1.19778 | −0.598889 | − | 0.800832i | \(-0.704391\pi\) | ||||
−0.598889 | + | 0.800832i | \(0.704391\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −30.6638 | −0.976039 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.62644 | −0.306103 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −47.8354 | −1.51954 | −0.759770 | − | 0.650192i | \(-0.774689\pi\) | ||||
−0.759770 | + | 0.650192i | \(0.774689\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −7.32962 | −0.232599 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 40.0509 | 1.26843 | 0.634213 | − | 0.773159i | \(-0.281324\pi\) | ||||
0.634213 | + | 0.773159i | \(0.281324\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.45936 | −0.141088 |
(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 | 7800.2.a.br.1.3 | yes | 3 | |
5.4 | even | 2 | 7800.2.a.bg.1.1 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7800.2.a.bg.1.1 | ✓ | 3 | 5.4 | even | 2 | ||
7800.2.a.br.1.3 | yes | 3 | 1.1 | even | 1 | trivial |