Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2188,2,Mod(1,2188)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2188, 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("2188.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2188 = 2^{2} \cdot 547 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2188.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: | \(17.4712679623\) |
Analytic rank: | \(1\) |
Dimension: | \(19\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{19} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{19} - 8 x^{18} - 6 x^{17} + 187 x^{16} - 201 x^{15} - 1757 x^{14} + 3000 x^{13} + 8703 x^{12} + \cdots - 26 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 7 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.70555\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2188.1 |
$q$-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 | ||||||||
\(3\) | −2.70555 | −1.56205 | −0.781025 | − | 0.624500i | \(-0.785303\pi\) | ||||
−0.781025 | + | 0.624500i | \(0.785303\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.14706 | 0.960194 | 0.480097 | − | 0.877216i | \(-0.340602\pi\) | ||||
0.480097 | + | 0.877216i | \(0.340602\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.69407 | 1.77419 | 0.887095 | − | 0.461586i | \(-0.152720\pi\) | ||||
0.887095 | + | 0.461586i | \(0.152720\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.32000 | 1.44000 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.590837 | 0.178144 | 0.0890721 | − | 0.996025i | \(-0.471610\pi\) | ||||
0.0890721 | + | 0.996025i | \(0.471610\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.74905 | −1.59450 | −0.797250 | − | 0.603649i | \(-0.793713\pi\) | ||||
−0.797250 | + | 0.603649i | \(0.793713\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.80897 | −1.49987 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.15474 | −1.00767 | −0.503836 | − | 0.863799i | \(-0.668078\pi\) | ||||
−0.503836 | + | 0.863799i | \(0.668078\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.46951 | −0.337128 | −0.168564 | − | 0.985691i | \(-0.553913\pi\) | ||||
−0.168564 | + | 0.985691i | \(0.553913\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −12.7000 | −2.77137 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −9.20632 | −1.91965 | −0.959825 | − | 0.280598i | \(-0.909467\pi\) | ||||
−0.959825 | + | 0.280598i | \(0.909467\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.390142 | −0.0780284 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.57132 | −0.687301 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.19187 | 1.33550 | 0.667749 | − | 0.744387i | \(-0.267258\pi\) | ||||
0.667749 | + | 0.744387i | \(0.267258\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.61556 | −1.72701 | −0.863503 | − | 0.504344i | \(-0.831734\pi\) | ||||
−0.863503 | + | 0.504344i | \(0.831734\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.59854 | −0.278270 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 10.0784 | 1.70357 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.37912 | 0.226727 | 0.113363 | − | 0.993554i | \(-0.463838\pi\) | ||||
0.113363 | + | 0.993554i | \(0.463838\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 15.5544 | 2.49069 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.27885 | −0.199722 | −0.0998611 | − | 0.995001i | \(-0.531840\pi\) | ||||
−0.0998611 | + | 0.995001i | \(0.531840\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.14522 | −1.39463 | −0.697317 | − | 0.716763i | \(-0.745623\pi\) | ||||
−0.697317 | + | 0.716763i | \(0.745623\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 9.27529 | 1.38268 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.01716 | −1.16942 | −0.584711 | − | 0.811241i | \(-0.698792\pi\) | ||||
−0.584711 | + | 0.811241i | \(0.698792\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 15.0343 | 2.14775 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 11.2409 | 1.57403 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.13076 | 1.11685 | 0.558423 | − | 0.829557i | \(-0.311407\pi\) | ||||
0.558423 | + | 0.829557i | \(0.311407\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.26856 | 0.171053 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.97582 | 0.526610 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.91482 | −0.639855 | −0.319928 | − | 0.947442i | \(-0.603659\pi\) | ||||
−0.319928 | + | 0.947442i | \(0.603659\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.28465 | −0.676630 | −0.338315 | − | 0.941033i | \(-0.609857\pi\) | ||||
−0.338315 | + | 0.941033i | \(0.609857\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 20.2784 | 2.55483 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −12.3436 | −1.53103 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.67199 | 0.570774 | 0.285387 | − | 0.958412i | \(-0.407878\pi\) | ||||
0.285387 | + | 0.958412i | \(0.407878\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 24.9082 | 2.99859 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.33994 | −0.159021 | −0.0795107 | − | 0.996834i | \(-0.525336\pi\) | ||||
−0.0795107 | + | 0.996834i | \(0.525336\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.84901 | −0.450493 | −0.225246 | − | 0.974302i | \(-0.572319\pi\) | ||||
−0.225246 | + | 0.974302i | \(0.572319\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.05555 | 0.121884 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.77343 | 0.316062 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.7596 | 1.77310 | 0.886549 | − | 0.462634i | \(-0.153096\pi\) | ||||
0.886549 | + | 0.462634i | \(0.153096\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.29761 | −0.366401 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −14.8295 | −1.62775 | −0.813875 | − | 0.581040i | \(-0.802646\pi\) | ||||
−0.813875 | + | 0.581040i | \(0.802646\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.92047 | −0.967560 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −19.4580 | −2.08611 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.7019 | −1.34639 | −0.673197 | − | 0.739463i | \(-0.735080\pi\) | ||||
−0.673197 | + | 0.739463i | \(0.735080\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −26.9864 | −2.82895 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 26.0154 | 2.69767 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.15511 | −0.323708 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.39929 | 0.751284 | 0.375642 | − | 0.926765i | \(-0.377422\pi\) | ||||
0.375642 | + | 0.926765i | \(0.377422\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.55242 | 0.256528 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.9619 | 1.58827 | 0.794135 | − | 0.607741i | \(-0.207924\pi\) | ||||
0.794135 | + | 0.607741i | \(0.207924\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.8375 | −1.36345 | −0.681725 | − | 0.731609i | \(-0.738770\pi\) | ||||
−0.681725 | + | 0.731609i | \(0.738770\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −27.2677 | −2.66106 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.31245 | 0.513574 | 0.256787 | − | 0.966468i | \(-0.417336\pi\) | ||||
0.256787 | + | 0.966468i | \(0.417336\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.15861 | 0.877236 | 0.438618 | − | 0.898674i | \(-0.355468\pi\) | ||||
0.438618 | + | 0.898674i | \(0.355468\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.73129 | −0.354158 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.84691 | −0.361886 | −0.180943 | − | 0.983494i | \(-0.557915\pi\) | ||||
−0.180943 | + | 0.983494i | \(0.557915\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −19.7665 | −1.84324 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −24.8359 | −2.29608 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −19.5026 | −1.78780 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.6509 | −0.968265 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.45998 | 0.311976 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.5729 | −1.03512 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.37675 | −0.743317 | −0.371658 | − | 0.928370i | \(-0.621211\pi\) | ||||
−0.371658 | + | 0.928370i | \(0.621211\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 24.7428 | 2.17849 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.70641 | 0.848053 | 0.424027 | − | 0.905650i | \(-0.360616\pi\) | ||||
0.424027 | + | 0.905650i | \(0.360616\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.89796 | −0.598129 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −7.66783 | −0.659942 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.99461 | 0.170411 | 0.0852055 | − | 0.996363i | \(-0.472845\pi\) | ||||
0.0852055 | + | 0.996363i | \(0.472845\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.6719 | 0.905181 | 0.452590 | − | 0.891718i | \(-0.350500\pi\) | ||||
0.452590 | + | 0.891718i | \(0.350500\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 21.6908 | 1.82670 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.39676 | −0.284051 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 15.4414 | 1.28234 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −40.6759 | −3.35489 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.88883 | −0.728201 | −0.364101 | − | 0.931360i | \(-0.618624\pi\) | ||||
−0.364101 | + | 0.931360i | \(0.618624\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.8575 | −1.12771 | −0.563855 | − | 0.825874i | \(-0.690682\pi\) | ||||
−0.563855 | + | 0.825874i | \(0.690682\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −17.9485 | −1.45105 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −20.6452 | −1.65826 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 19.6167 | 1.56558 | 0.782791 | − | 0.622285i | \(-0.213796\pi\) | ||||
0.782791 | + | 0.622285i | \(0.213796\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −21.9982 | −1.74457 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −43.2151 | −3.40583 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.86906 | 0.538027 | 0.269013 | − | 0.963136i | \(-0.413302\pi\) | ||||
0.269013 | + | 0.963136i | \(0.413302\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.43216 | −0.267193 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.02765 | −0.311669 | −0.155834 | − | 0.987783i | \(-0.549807\pi\) | ||||
−0.155834 | + | 0.987783i | \(0.549807\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 20.0516 | 1.54243 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.34826 | −0.485464 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −16.9875 | −1.29154 | −0.645769 | − | 0.763533i | \(-0.723463\pi\) | ||||
−0.645769 | + | 0.763533i | \(0.723463\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.83135 | −0.138437 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 13.2973 | 0.999485 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −13.1553 | −0.983276 | −0.491638 | − | 0.870800i | \(-0.663602\pi\) | ||||
−0.491638 | + | 0.870800i | \(0.663602\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.47748 | 0.630126 | 0.315063 | − | 0.949071i | \(-0.397974\pi\) | ||||
0.315063 | + | 0.949071i | \(0.397974\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 14.2979 | 1.05693 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.96106 | 0.217701 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.45478 | −0.179511 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −16.7640 | −1.21940 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.26070 | −0.308293 | −0.154147 | − | 0.988048i | \(-0.549263\pi\) | ||||
−0.154147 | + | 0.988048i | \(0.549263\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.0626 | 0.724319 | 0.362160 | − | 0.932116i | \(-0.382040\pi\) | ||||
0.362160 | + | 0.932116i | \(0.382040\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 33.3961 | 2.39154 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.79741 | 0.484296 | 0.242148 | − | 0.970239i | \(-0.422148\pi\) | ||||
0.242148 | + | 0.970239i | \(0.422148\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.42106 | −0.171624 | −0.0858122 | − | 0.996311i | \(-0.527348\pi\) | ||||
−0.0858122 | + | 0.996311i | \(0.527348\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −12.6403 | −0.891578 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 33.7591 | 2.36943 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.74576 | −0.191772 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −39.7713 | −2.76430 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.868239 | −0.0600573 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.79643 | −0.261357 | −0.130679 | − | 0.991425i | \(-0.541716\pi\) | ||||
−0.130679 | + | 0.991425i | \(0.541716\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.62527 | 0.248399 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −19.6353 | −1.33912 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −45.1361 | −3.06404 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 10.4137 | 0.703692 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 23.8858 | 1.60673 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.2596 | 0.820966 | 0.410483 | − | 0.911868i | \(-0.365360\pi\) | ||||
0.410483 | + | 0.911868i | \(0.365360\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.68541 | −0.112361 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −18.5387 | −1.23045 | −0.615227 | − | 0.788350i | \(-0.710936\pi\) | ||||
−0.615227 | + | 0.788350i | \(0.710936\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.50004 | 0.165207 | 0.0826036 | − | 0.996582i | \(-0.473676\pi\) | ||||
0.0826036 | + | 0.996582i | \(0.473676\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.50365 | −0.493704 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.32097 | −0.217564 | −0.108782 | − | 0.994066i | \(-0.534695\pi\) | ||||
−0.108782 | + | 0.994066i | \(0.534695\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −17.2133 | −1.12287 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −42.6385 | −2.76967 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.26627 | 0.0819080 | 0.0409540 | − | 0.999161i | \(-0.486960\pi\) | ||||
0.0409540 | + | 0.999161i | \(0.486960\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.3866 | 1.11997 | 0.559986 | − | 0.828502i | \(-0.310806\pi\) | ||||
0.559986 | + | 0.828502i | \(0.310806\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 19.6358 | 1.25964 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 32.2794 | 2.06226 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.44827 | 0.537550 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 40.1220 | 2.54263 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.6180 | 1.55388 | 0.776938 | − | 0.629577i | \(-0.216772\pi\) | ||||
0.776938 | + | 0.629577i | \(0.216772\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.43944 | −0.341975 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 24.1348 | 1.51138 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 15.1970 | 0.947961 | 0.473981 | − | 0.880535i | \(-0.342817\pi\) | ||||
0.473981 | + | 0.880535i | \(0.342817\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.47370 | 0.402256 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 31.0689 | 1.92312 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −11.4014 | −0.703038 | −0.351519 | − | 0.936181i | \(-0.614335\pi\) | ||||
−0.351519 | + | 0.936181i | \(0.614335\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 17.4572 | 1.07239 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 34.3655 | 2.10314 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −18.2805 | −1.11458 | −0.557291 | − | 0.830317i | \(-0.688159\pi\) | ||||
−0.557291 | + | 0.830317i | \(0.688159\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −24.6033 | −1.49454 | −0.747272 | − | 0.664518i | \(-0.768637\pi\) | ||||
−0.747272 | + | 0.664518i | \(0.768637\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 73.0132 | 4.41896 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.230511 | −0.0139003 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.8532 | −0.832360 | −0.416180 | − | 0.909282i | \(-0.636631\pi\) | ||||
−0.416180 | + | 0.909282i | \(0.636631\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −41.5392 | −2.48689 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.38849 | 0.0828304 | 0.0414152 | − | 0.999142i | \(-0.486813\pi\) | ||||
0.0414152 | + | 0.999142i | \(0.486813\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.99481 | −0.356355 | −0.178177 | − | 0.983998i | \(-0.557020\pi\) | ||||
−0.178177 | + | 0.983998i | \(0.557020\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 8.53632 | 0.505648 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.00299 | −0.354345 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.261861 | 0.0154036 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −20.0192 | −1.17354 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.9440 | 0.639356 | 0.319678 | − | 0.947526i | \(-0.396425\pi\) | ||||
0.319678 | + | 0.947526i | \(0.396425\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.5524 | −0.614385 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.11007 | −0.122439 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 52.9276 | 3.06088 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −42.9283 | −2.47434 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −43.1858 | −2.48096 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −11.3465 | −0.649696 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.3830 | 0.592588 | 0.296294 | − | 0.955097i | \(-0.404249\pi\) | ||||
0.296294 | + | 0.955097i | \(0.404249\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 37.4381 | 2.12978 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.4132 | 0.590477 | 0.295239 | − | 0.955424i | \(-0.404601\pi\) | ||||
0.295239 | + | 0.955424i | \(0.404601\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −23.1140 | −1.30648 | −0.653240 | − | 0.757151i | \(-0.726591\pi\) | ||||
−0.653240 | + | 0.757151i | \(0.726591\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 43.5388 | 2.45313 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 17.9414 | 1.00769 | 0.503846 | − | 0.863794i | \(-0.331918\pi\) | ||||
0.503846 | + | 0.863794i | \(0.331918\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.24923 | 0.237911 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −14.3731 | −0.802228 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.10541 | 0.339714 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.24295 | 0.124416 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −24.7791 | −1.37029 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −37.6331 | −2.07478 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.6507 | 0.695347 | 0.347674 | − | 0.937616i | \(-0.386972\pi\) | ||||
0.347674 | + | 0.937616i | \(0.386972\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.95781 | 0.326486 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 10.0310 | 0.548054 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 34.9183 | 1.90212 | 0.951061 | − | 0.309002i | \(-0.0999951\pi\) | ||||
0.951061 | + | 0.309002i | \(0.0999951\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 10.4080 | 0.565285 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.68123 | −0.307656 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 37.7134 | 2.03633 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 53.4793 | 2.87923 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −30.8185 | −1.65442 | −0.827212 | − | 0.561890i | \(-0.810074\pi\) | ||||
−0.827212 | + | 0.561890i | \(0.810074\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.68565 | −0.464932 | −0.232466 | − | 0.972605i | \(-0.574679\pi\) | ||||
−0.232466 | + | 0.972605i | \(0.574679\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 20.5317 | 1.09590 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −29.0976 | −1.54871 | −0.774356 | − | 0.632751i | \(-0.781926\pi\) | ||||
−0.774356 | + | 0.632751i | \(0.781926\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.87692 | −0.152691 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 52.7653 | 2.79264 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −22.5265 | −1.18890 | −0.594452 | − | 0.804131i | \(-0.702631\pi\) | ||||
−0.594452 | + | 0.804131i | \(0.702631\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.8406 | −0.886345 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 28.8166 | 1.51248 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.26405 | −0.432560 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.4363 | 0.701370 | 0.350685 | − | 0.936493i | \(-0.385949\pi\) | ||||
0.350685 | + | 0.936493i | \(0.385949\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.52461 | −0.287600 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 38.1663 | 1.98150 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.0426 | −0.623541 | −0.311771 | − | 0.950157i | \(-0.600922\pi\) | ||||
−0.311771 | + | 0.950157i | \(0.600922\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 31.3112 | 1.61690 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −41.3465 | −2.12945 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −28.4063 | −1.45913 | −0.729567 | − | 0.683909i | \(-0.760279\pi\) | ||||
−0.729567 | + | 0.683909i | \(0.760279\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 22.6637 | 1.16110 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.299679 | 0.0153129 | 0.00765645 | − | 0.999971i | \(-0.497563\pi\) | ||||
0.00765645 | + | 0.999971i | \(0.497563\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.95472 | 0.303480 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −39.5073 | −2.00827 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −21.8178 | −1.10621 | −0.553103 | − | 0.833113i | \(-0.686556\pi\) | ||||
−0.553103 | + | 0.833113i | \(0.686556\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 38.2499 | 1.93438 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −26.2612 | −1.32470 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 33.8369 | 1.70252 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.00401 | 0.351521 | 0.175760 | − | 0.984433i | \(-0.443762\pi\) | ||||
0.175760 | + | 0.984433i | \(0.443762\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 18.6628 | 0.934307 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.06453 | −0.402723 | −0.201362 | − | 0.979517i | \(-0.564537\pi\) | ||||
−0.201362 | + | 0.979517i | \(0.564537\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 55.2804 | 2.75371 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −7.08016 | −0.351816 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.814838 | 0.0403900 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.3853 | 0.958544 | 0.479272 | − | 0.877666i | \(-0.340901\pi\) | ||||
0.479272 | + | 0.877666i | \(0.340901\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.39651 | −0.266190 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −23.0705 | −1.13522 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −31.8398 | −1.56295 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −28.8734 | −1.41394 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −21.0266 | −1.02722 | −0.513609 | − | 0.858024i | \(-0.671692\pi\) | ||||
−0.513609 | + | 0.858024i | \(0.671692\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 36.2193 | 1.76522 | 0.882611 | − | 0.470105i | \(-0.155784\pi\) | ||||
0.882611 | + | 0.470105i | \(0.155784\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −34.6341 | −1.68397 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.62094 | 0.0786271 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −24.8065 | −1.20047 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 9.19009 | 0.443702 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 23.9972 | 1.15591 | 0.577953 | − | 0.816070i | \(-0.303852\pi\) | ||||
0.577953 | + | 0.816070i | \(0.303852\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 22.2587 | 1.06969 | 0.534843 | − | 0.844952i | \(-0.320371\pi\) | ||||
0.534843 | + | 0.844952i | \(0.320371\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −41.7774 | −2.00307 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 13.5287 | 0.647167 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −35.9300 | −1.71485 | −0.857423 | − | 0.514612i | \(-0.827936\pi\) | ||||
−0.857423 | + | 0.514612i | \(0.827936\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 64.9480 | 3.09276 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 18.0219 | 0.856245 | 0.428122 | − | 0.903721i | \(-0.359175\pi\) | ||||
0.428122 | + | 0.903721i | \(0.359175\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −27.2716 | −1.29280 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 24.0492 | 1.13749 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15.4794 | 0.730517 | 0.365258 | − | 0.930906i | \(-0.380981\pi\) | ||||
0.365258 | + | 0.930906i | \(0.380981\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.755590 | −0.0355794 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 37.4922 | 1.76154 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −57.9415 | −2.71634 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.50970 | 0.398067 | 0.199033 | − | 0.979993i | \(-0.436220\pi\) | ||||
0.199033 | + | 0.979993i | \(0.436220\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 14.8379 | 0.692574 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −28.9586 | −1.34873 | −0.674367 | − | 0.738396i | \(-0.735584\pi\) | ||||
−0.674367 | + | 0.738396i | \(0.735584\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.09061 | 0.0506850 | 0.0253425 | − | 0.999679i | \(-0.491932\pi\) | ||||
0.0253425 | + | 0.999679i | \(0.491932\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 55.8565 | 2.59028 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13.3623 | 0.618333 | 0.309167 | − | 0.951008i | \(-0.399950\pi\) | ||||
0.309167 | + | 0.951008i | \(0.399950\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 21.9306 | 1.01266 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −53.0739 | −2.44552 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.40334 | −0.248446 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.573316 | 0.0263055 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 35.1249 | 1.60826 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.84759 | 0.267183 | 0.133592 | − | 0.991036i | \(-0.457349\pi\) | ||||
0.133592 | + | 0.991036i | \(0.457349\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.92866 | −0.361516 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 116.921 | 5.32007 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 15.8867 | 0.721378 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.40839 | −0.426335 | −0.213168 | − | 0.977016i | \(-0.568378\pi\) | ||||
−0.213168 | + | 0.977016i | \(0.568378\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −18.5846 | −0.840424 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 23.8787 | 1.07763 | 0.538814 | − | 0.842425i | \(-0.318872\pi\) | ||||
0.538814 | + | 0.842425i | \(0.318872\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −29.8804 | −1.34574 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.48019 | 0.246316 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.28976 | −0.282134 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 29.2196 | 1.30805 | 0.654025 | − | 0.756473i | \(-0.273079\pi\) | ||||
0.654025 | + | 0.756473i | \(0.273079\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.8970 | 0.486842 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 38.9542 | 1.73688 | 0.868440 | − | 0.495794i | \(-0.165123\pi\) | ||||
0.868440 | + | 0.495794i | \(0.165123\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 34.2712 | 1.52505 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −54.2507 | −2.40936 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.811469 | −0.0359677 | −0.0179839 | − | 0.999838i | \(-0.505725\pi\) | ||||
−0.0179839 | + | 0.999838i | \(0.505725\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −18.0675 | −0.799260 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.24807 | 0.231708 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −29.7099 | −1.30918 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.73684 | −0.208326 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 45.9606 | 2.01745 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17.3710 | −0.761038 | −0.380519 | − | 0.924773i | \(-0.624255\pi\) | ||||
−0.380519 | + | 0.924773i | \(0.624255\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −37.4711 | −1.63850 | −0.819249 | − | 0.573438i | \(-0.805609\pi\) | ||||
−0.819249 | + | 0.573438i | \(0.805609\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.95482 | 0.216246 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 39.9501 | 1.74026 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 61.7563 | 2.68506 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −21.2320 | −0.921391 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.35216 | 0.318457 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11.4061 | 0.493130 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 35.5924 | 1.53593 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 8.88280 | 0.382609 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.9974 | −0.687780 | −0.343890 | − | 0.939010i | \(-0.611745\pi\) | ||||
−0.343890 | + | 0.939010i | \(0.611745\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −22.9362 | −0.984289 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 19.6641 | 0.842316 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.00000 | 0.0427569 | ||||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −22.8297 | −0.974347 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.5685 | −0.450233 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 73.9768 | 3.14581 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −8.01129 | −0.340060 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −39.9182 | −1.69139 | −0.845695 | − | 0.533667i | \(-0.820814\pi\) | ||||
−0.845695 | + | 0.533667i | \(0.820814\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 52.5764 | 2.22374 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.64152 | 0.280405 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −31.8813 | −1.34363 | −0.671817 | − | 0.740717i | \(-0.734486\pi\) | ||||
−0.671817 | + | 0.740717i | \(0.734486\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.25953 | −0.347481 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −15.4792 | −0.650065 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.19999 | −0.176073 | −0.0880363 | − | 0.996117i | \(-0.528059\pi\) | ||||
−0.0880363 | + | 0.996117i | \(0.528059\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.3317 | 0.641611 | 0.320805 | − | 0.947145i | \(-0.396046\pi\) | ||||
0.320805 | + | 0.947145i | \(0.396046\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 11.5275 | 0.481570 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.59177 | 0.149787 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −44.1755 | −1.83905 | −0.919526 | − | 0.393030i | \(-0.871427\pi\) | ||||
−0.919526 | + | 0.393030i | \(0.871427\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −27.2248 | −1.13142 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −69.6107 | −2.88794 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.80396 | 0.198960 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −53.3241 | −2.20468 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7.59967 | −0.313672 | −0.156836 | − | 0.987625i | \(-0.550129\pi\) | ||||
−0.156836 | + | 0.987625i | \(0.550129\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14.1301 | 0.582221 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −18.3907 | −0.756494 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −37.1183 | −1.52426 | −0.762132 | − | 0.647422i | \(-0.775847\pi\) | ||||
−0.762132 | + | 0.647422i | \(0.775847\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −41.8733 | −1.71664 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.55029 | 0.268086 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5.78766 | −0.236477 | −0.118239 | − | 0.992985i | \(-0.537725\pi\) | ||||
−0.118239 | + | 0.992985i | \(0.537725\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 40.0019 | 1.63171 | 0.815856 | − | 0.578255i | \(-0.196266\pi\) | ||||
0.815856 | + | 0.578255i | \(0.196266\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 20.1830 | 0.821915 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −22.8681 | −0.929721 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.15068 | −0.371415 | −0.185707 | − | 0.982605i | \(-0.559458\pi\) | ||||
−0.185707 | + | 0.982605i | \(0.559458\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −91.3370 | −3.70116 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 46.0911 | 1.86465 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −38.0698 | −1.53763 | −0.768813 | − | 0.639474i | \(-0.779152\pi\) | ||||
−0.768813 | + | 0.639474i | \(0.779152\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7.42878 | 0.299557 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −24.2439 | −0.976023 | −0.488011 | − | 0.872837i | \(-0.662278\pi\) | ||||
−0.488011 | + | 0.872837i | \(0.662278\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.304762 | 0.0122494 | 0.00612471 | − | 0.999981i | \(-0.498050\pi\) | ||||
0.00612471 | + | 0.999981i | \(0.498050\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 32.8787 | 1.31938 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −59.6234 | −2.38876 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −22.8971 | −0.915883 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.34906 | 0.0938125 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5.72990 | −0.228466 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.9553 | 0.475935 | 0.237967 | − | 0.971273i | \(-0.423519\pi\) | ||||
0.237967 | + | 0.971273i | \(0.423519\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 10.2714 | 0.408253 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −17.9854 | −0.713728 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −86.4328 | −3.42459 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.78853 | −0.228991 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.7547 | 0.503782 | 0.251891 | − | 0.967756i | \(-0.418948\pi\) | ||||
0.251891 | + | 0.967756i | \(0.418948\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22.1093 | 0.871907 | 0.435954 | − | 0.899969i | \(-0.356411\pi\) | ||||
0.435954 | + | 0.899969i | \(0.356411\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 53.1243 | 2.09177 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −42.8684 | −1.68533 | −0.842666 | − | 0.538436i | \(-0.819015\pi\) | ||||
−0.842666 | + | 0.538436i | \(0.819015\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.90386 | −0.113986 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 122.118 | 4.78618 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −23.0620 | −0.902484 | −0.451242 | − | 0.892402i | \(-0.649019\pi\) | ||||
−0.451242 | + | 0.892402i | \(0.649019\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 20.8402 | 0.814295 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −16.6277 | −0.648709 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24.7761 | 0.965138 | 0.482569 | − | 0.875858i | \(-0.339704\pi\) | ||||
0.482569 | + | 0.875858i | \(0.339704\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29.6199 | 1.15208 | 0.576039 | − | 0.817422i | \(-0.304597\pi\) | ||||
0.576039 | + | 0.817422i | \(0.304597\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −64.6243 | −2.50980 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −14.8103 | −0.574319 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −66.2107 | −2.56369 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −33.1690 | −1.28239 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.12237 | −0.120538 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −27.5103 | −1.06045 | −0.530223 | − | 0.847858i | \(-0.677892\pi\) | ||||
−0.530223 | + | 0.847858i | \(0.677892\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.39332 | 0.0536290 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 43.7448 | 1.68125 | 0.840624 | − | 0.541619i | \(-0.182188\pi\) | ||||
0.840624 | + | 0.541619i | \(0.182188\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 34.7328 | 1.33292 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 50.1573 | 1.92203 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 34.9503 | 1.33734 | 0.668668 | − | 0.743561i | \(-0.266865\pi\) | ||||
0.668668 | + | 0.743561i | \(0.266865\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.28254 | 0.163627 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.76398 | −0.258062 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −46.7442 | −1.78081 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 35.4820 | 1.34980 | 0.674899 | − | 0.737910i | \(-0.264187\pi\) | ||||
0.674899 | + | 0.737910i | \(0.264187\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 11.9812 | 0.455129 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 22.9132 | 0.869149 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.31327 | 0.201255 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8.98505 | 0.339846 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −45.8462 | −1.73159 | −0.865794 | − | 0.500400i | \(-0.833186\pi\) | ||||
−0.865794 | + | 0.500400i | \(0.833186\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.02663 | −0.0764358 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 46.5714 | 1.75398 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 74.9263 | 2.81789 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19.1166 | 0.717939 | 0.358969 | − | 0.933349i | \(-0.383128\pi\) | ||||
0.358969 | + | 0.933349i | \(0.383128\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 68.0816 | 2.55326 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 88.5239 | 3.31525 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.29303 | −0.272744 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.42595 | −0.127944 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 10.4573 | 0.389993 | 0.194997 | − | 0.980804i | \(-0.437530\pi\) | ||||
0.194997 | + | 0.980804i | \(0.437530\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −64.9542 | −2.41902 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −47.0404 | −1.74945 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.80585 | −0.104207 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13.4503 | −0.498844 | −0.249422 | − | 0.968395i | \(-0.580241\pi\) | ||||
−0.249422 | + | 0.968395i | \(0.580241\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −43.2328 | −1.60122 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 37.9960 | 1.40533 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −40.8592 | −1.50917 | −0.754584 | − | 0.656203i | \(-0.772161\pi\) | ||||
−0.754584 | + | 0.656203i | \(0.772161\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −87.3336 | −3.22135 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.76039 | 0.101680 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 32.2376 | 1.18588 | 0.592939 | − | 0.805247i | \(-0.297967\pi\) | ||||
0.592939 | + | 0.805247i | \(0.297967\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −22.8572 | −0.839680 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 15.5927 | 0.572040 | 0.286020 | − | 0.958224i | \(-0.407668\pi\) | ||||
0.286020 | + | 0.958224i | \(0.407668\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −19.0848 | −0.699214 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −64.0634 | −2.34396 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 24.9370 | 0.911178 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 43.8336 | 1.59951 | 0.799755 | − | 0.600327i | \(-0.204963\pi\) | ||||
0.799755 | + | 0.600327i | \(0.204963\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −66.6053 | −2.42723 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −29.7529 | −1.08282 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.28134 | −0.337336 | −0.168668 | − | 0.985673i | \(-0.553947\pi\) | ||||
−0.168668 | + | 0.985673i | \(0.553947\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 14.7167 | 0.534181 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −42.5353 | −1.54190 | −0.770952 | − | 0.636893i | \(-0.780219\pi\) | ||||
−0.770952 | + | 0.636893i | \(0.780219\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 42.9911 | 1.55638 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −38.5364 | −1.39329 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 28.2556 | 1.02025 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 40.0893 | 1.44566 | 0.722829 | − | 0.691027i | \(-0.242842\pi\) | ||||
0.722829 | + | 0.691027i | \(0.242842\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −41.1162 | −1.48076 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −19.6626 | −0.707216 | −0.353608 | − | 0.935394i | \(-0.615045\pi\) | ||||
−0.353608 | + | 0.935394i | \(0.615045\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.75143 | 0.134756 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −17.5149 | −0.628344 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.87927 | 0.0673319 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.791686 | −0.0283287 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −25.6845 | −0.917889 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 42.1181 | 1.50326 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23.6239 | 0.842103 | 0.421051 | − | 0.907037i | \(-0.361661\pi\) | ||||
0.421051 | + | 0.907037i | \(0.361661\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 30.8470 | 1.09818 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −18.0576 | −0.642055 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 30.3818 | 1.07889 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −47.2313 | −1.67512 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9.45081 | 0.334765 | 0.167382 | − | 0.985892i | \(-0.446469\pi\) | ||||
0.167382 | + | 0.985892i | \(0.446469\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 33.3092 | 1.17839 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −54.8720 | −1.93881 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.27414 | −0.0802527 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −92.7853 | −3.27025 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 49.4588 | 1.74103 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 31.8431 | 1.11955 | 0.559773 | − | 0.828646i | \(-0.310888\pi\) | ||||
0.559773 | + | 0.828646i | \(0.310888\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28.3073 | 0.994003 | 0.497001 | − | 0.867750i | \(-0.334434\pi\) | ||||
0.497001 | + | 0.867750i | \(0.334434\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 66.5655 | 2.33455 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 14.7483 | 0.516610 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 13.4390 | 0.470169 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −116.581 | −4.07368 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −42.9066 | −1.49745 | −0.748726 | − | 0.662880i | \(-0.769334\pi\) | ||||
−0.748726 | + | 0.662880i | \(0.769334\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 18.5656 | 0.647157 | 0.323579 | − | 0.946201i | \(-0.395114\pi\) | ||||
0.323579 | + | 0.946201i | \(0.395114\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.623658 | 0.0217130 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.00267 | 0.208733 | 0.104367 | − | 0.994539i | \(-0.466718\pi\) | ||||
0.104367 | + | 0.994539i | \(0.466718\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.15215 | 0.0400159 | 0.0200080 | − | 0.999800i | \(-0.493631\pi\) | ||||
0.0200080 | + | 0.999800i | \(0.493631\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 37.4806 | 1.30019 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −62.4634 | −2.16423 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.64759 | −0.299262 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 34.3402 | 1.18697 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 13.7860 | 0.475947 | 0.237973 | − | 0.971272i | \(-0.423517\pi\) | ||||
0.237973 | + | 0.971272i | \(0.423517\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.7231 | 0.783554 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.75663 | −0.129385 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 43.0520 | 1.48103 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −49.9961 | −1.71789 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 16.2193 | 0.556644 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −12.6967 | −0.435236 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 42.9006 | 1.46889 | 0.734445 | − | 0.678668i | \(-0.237443\pi\) | ||||
0.734445 | + | 0.678668i | \(0.237443\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −13.6301 | −0.466139 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 14.4266 | 0.492802 | 0.246401 | − | 0.969168i | \(-0.420752\pi\) | ||||
0.246401 | + | 0.969168i | \(0.420752\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −29.6901 | −1.01301 | −0.506506 | − | 0.862236i | \(-0.669063\pi\) | ||||
−0.506506 | + | 0.862236i | \(0.669063\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 16.2414 | 0.553505 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −17.9177 | −0.609925 | −0.304963 | − | 0.952364i | \(-0.598644\pi\) | ||||
−0.304963 | + | 0.952364i | \(0.598644\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −36.4732 | −1.24013 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.708479 | −0.0240612 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.31139 | 0.315867 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −26.8595 | −0.910100 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 31.9649 | 1.08185 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −54.3242 | −1.83649 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 40.1479 | 1.35570 | 0.677849 | − | 0.735201i | \(-0.262912\pi\) | ||||
0.677849 | + | 0.735201i | \(0.262912\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −29.6096 | −0.998706 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 32.1429 | 1.08292 | 0.541461 | − | 0.840726i | \(-0.317871\pi\) | ||||
0.541461 | + | 0.840726i | \(0.317871\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −43.7505 | −1.47232 | −0.736161 | − | 0.676807i | \(-0.763363\pi\) | ||||
−0.736161 | + | 0.676807i | \(0.763363\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 28.5500 | 0.959699 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 26.7741 | 0.898986 | 0.449493 | − | 0.893284i | \(-0.351605\pi\) | ||||
0.449493 | + | 0.893284i | \(0.351605\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −39.3210 | −1.31879 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.94835 | −0.0652722 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 11.7813 | 0.394245 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −28.2453 | −0.944136 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −143.198 | −4.78125 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −69.1539 | −2.30641 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −33.7812 | −1.12541 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 116.145 | 3.86505 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 18.2016 | 0.605043 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −17.6942 | −0.587525 | −0.293762 | − | 0.955878i | \(-0.594907\pi\) | ||||
−0.293762 | + | 0.955878i | \(0.594907\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 68.9555 | 2.28711 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −41.8408 | −1.38625 | −0.693124 | − | 0.720818i | \(-0.743766\pi\) | ||||
−0.693124 | + | 0.720818i | \(0.743766\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.76183 | −0.289974 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 30.6984 | 1.01486 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 45.5626 | 1.50461 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.91865 | 0.0632905 | 0.0316452 | − | 0.999499i | \(-0.489925\pi\) | ||||
0.0316452 | + | 0.999499i | \(0.489925\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −28.0917 | −0.925652 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7.70338 | 0.253560 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.538055 | −0.0176911 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −59.7780 | −1.96337 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 52.9575 | 1.73748 | 0.868740 | − | 0.495268i | \(-0.164930\pi\) | ||||
0.868740 | + | 0.495268i | \(0.164930\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −22.0929 | −0.724067 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −28.1734 | −0.922355 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.27055 | −0.172365 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17.6093 | 0.575270 | 0.287635 | − | 0.957740i | \(-0.407131\pi\) | ||||
0.287635 | + | 0.957740i | \(0.407131\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 62.5361 | 2.04079 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −21.4295 | −0.698583 | −0.349292 | − | 0.937014i | \(-0.613578\pi\) | ||||
−0.349292 | + | 0.937014i | \(0.613578\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 11.7735 | 0.383397 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −35.9933 | −1.17086 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −35.2679 | −1.14605 | −0.573027 | − | 0.819537i | \(-0.694231\pi\) | ||||
−0.573027 | + | 0.819537i | \(0.694231\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 22.1282 | 0.718311 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −48.5414 | −1.57406 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 36.9565 | 1.19714 | 0.598570 | − | 0.801071i | \(-0.295736\pi\) | ||||
0.598570 | + | 0.801071i | \(0.295736\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9.14797 | −0.296021 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −11.4965 | −0.371629 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9.36283 | 0.302341 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 61.4590 | 1.98255 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 22.9498 | 0.739546 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 21.6049 | 0.695486 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 18.3859 | 0.591250 | 0.295625 | − | 0.955304i | \(-0.404472\pi\) | ||||
0.295625 | + | 0.955304i | \(0.404472\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −16.5185 | −0.530651 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −0.173527 | −0.00556874 | −0.00278437 | − | 0.999996i | \(-0.500886\pi\) | ||||
−0.00278437 | + | 0.999996i | \(0.500886\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 50.0947 | 1.60596 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6.06841 | −0.194345 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 9.78931 | 0.313188 | 0.156594 | − | 0.987663i | \(-0.449949\pi\) | ||||
0.156594 | + | 0.987663i | \(0.449949\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.50474 | −0.239852 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 39.5652 | 1.26322 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 47.3555 | 1.51040 | 0.755202 | − | 0.655492i | \(-0.227539\pi\) | ||||
0.755202 | + | 0.655492i | \(0.227539\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14.5944 | 0.465018 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 101.818 | 3.24091 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 84.1938 | 2.67721 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −34.1753 | −1.08562 | −0.542808 | − | 0.839857i | \(-0.682639\pi\) | ||||
−0.542808 | + | 0.839857i | \(0.682639\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −34.2272 | −1.08617 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.19815 | −0.164793 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 53.5988 | 1.69749 | 0.848746 | − | 0.528800i | \(-0.177358\pi\) | ||||
0.848746 | + | 0.528800i | \(0.177358\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.92529 | −0.155829 |
(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 | 2188.2.a.d.1.3 | ✓ | 19 | |
4.3 | odd | 2 | 8752.2.a.t.1.17 | 19 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2188.2.a.d.1.3 | ✓ | 19 | 1.1 | even | 1 | trivial | |
8752.2.a.t.1.17 | 19 | 4.3 | odd | 2 |