Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5796,2,Mod(1,5796)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5796, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("5796.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5796 = 2^{2} \cdot 3^{2} \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5796.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: | \(46.2812930115\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1932) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5796.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.618034 | 0.276393 | 0.138197 | − | 0.990405i | \(-0.455869\pi\) | ||||
0.138197 | + | 0.990405i | \(0.455869\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.236068 | −0.0711772 | −0.0355886 | − | 0.999367i | \(-0.511331\pi\) | ||||
−0.0355886 | + | 0.999367i | \(0.511331\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.381966 | 0.105938 | 0.0529692 | − | 0.998596i | \(-0.483131\pi\) | ||||
0.0529692 | + | 0.998596i | \(0.483131\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.23607 | 0.542326 | 0.271163 | − | 0.962533i | \(-0.412592\pi\) | ||||
0.271163 | + | 0.962533i | \(0.412592\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.47214 | 0.796563 | 0.398281 | − | 0.917263i | \(-0.369607\pi\) | ||||
0.398281 | + | 0.917263i | \(0.369607\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.61803 | −0.923607 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.47214 | −1.01615 | −0.508075 | − | 0.861313i | \(-0.669643\pi\) | ||||
−0.508075 | + | 0.861313i | \(0.669643\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.76393 | −0.316812 | −0.158406 | − | 0.987374i | \(-0.550635\pi\) | ||||
−0.158406 | + | 0.987374i | \(0.550635\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.618034 | −0.104467 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.47214 | −0.899614 | −0.449807 | − | 0.893126i | \(-0.648507\pi\) | ||||
−0.449807 | + | 0.893126i | \(0.648507\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.47214 | −1.16695 | −0.583476 | − | 0.812131i | \(-0.698308\pi\) | ||||
−0.583476 | + | 0.812131i | \(0.698308\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −12.5623 | −1.91573 | −0.957867 | − | 0.287213i | \(-0.907271\pi\) | ||||
−0.957867 | + | 0.287213i | \(0.907271\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.763932 | 0.111431 | 0.0557155 | − | 0.998447i | \(-0.482256\pi\) | ||||
0.0557155 | + | 0.998447i | \(0.482256\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.09017 | 0.973910 | 0.486955 | − | 0.873427i | \(-0.338108\pi\) | ||||
0.486955 | + | 0.873427i | \(0.338108\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.145898 | −0.0196729 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.38197 | 0.440294 | 0.220147 | − | 0.975467i | \(-0.429346\pi\) | ||||
0.220147 | + | 0.975467i | \(0.429346\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.32624 | 0.681955 | 0.340977 | − | 0.940071i | \(-0.389242\pi\) | ||||
0.340977 | + | 0.940071i | \(0.389242\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.236068 | 0.0292806 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.38197 | −0.413173 | −0.206586 | − | 0.978428i | \(-0.566235\pi\) | ||||
−0.206586 | + | 0.978428i | \(0.566235\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.8541 | 1.28814 | 0.644072 | − | 0.764964i | \(-0.277244\pi\) | ||||
0.644072 | + | 0.764964i | \(0.277244\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.94427 | 0.227560 | 0.113780 | − | 0.993506i | \(-0.463704\pi\) | ||||
0.113780 | + | 0.993506i | \(0.463704\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.236068 | 0.0269024 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.23607 | −0.926630 | −0.463315 | − | 0.886194i | \(-0.653340\pi\) | ||||
−0.463315 | + | 0.886194i | \(0.653340\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.94427 | 0.871997 | 0.435999 | − | 0.899947i | \(-0.356395\pi\) | ||||
0.435999 | + | 0.899947i | \(0.356395\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.38197 | 0.149895 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.85410 | 0.302534 | 0.151267 | − | 0.988493i | \(-0.451665\pi\) | ||||
0.151267 | + | 0.988493i | \(0.451665\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.381966 | −0.0400409 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.14590 | 0.220164 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.236068 | −0.0239691 | −0.0119845 | − | 0.999928i | \(-0.503815\pi\) | ||||
−0.0119845 | + | 0.999928i | \(0.503815\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.38197 | 0.137511 | 0.0687554 | − | 0.997634i | \(-0.478097\pi\) | ||||
0.0687554 | + | 0.997634i | \(0.478097\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.94427 | −0.881305 | −0.440653 | − | 0.897678i | \(-0.645253\pi\) | ||||
−0.440653 | + | 0.897678i | \(0.645253\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.3820 | 1.00366 | 0.501831 | − | 0.864966i | \(-0.332660\pi\) | ||||
0.501831 | + | 0.864966i | \(0.332660\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.61803 | −0.633893 | −0.316946 | − | 0.948443i | \(-0.602658\pi\) | ||||
−0.316946 | + | 0.948443i | \(0.602658\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.56231 | −0.711402 | −0.355701 | − | 0.934600i | \(-0.615758\pi\) | ||||
−0.355701 | + | 0.934600i | \(0.615758\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.618034 | −0.0576320 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.23607 | −0.204980 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9443 | −0.994934 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.94427 | −0.531672 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.14590 | −0.634096 | −0.317048 | − | 0.948410i | \(-0.602692\pi\) | ||||
−0.317048 | + | 0.948410i | \(0.602692\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.0557281 | −0.00486899 | −0.00243449 | − | 0.999997i | \(-0.500775\pi\) | ||||
−0.00243449 | + | 0.999997i | \(0.500775\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.47214 | −0.301072 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.236068 | 0.0201686 | 0.0100843 | − | 0.999949i | \(-0.496790\pi\) | ||||
0.0100843 | + | 0.999949i | \(0.496790\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.0344 | −1.02075 | −0.510374 | − | 0.859953i | \(-0.670493\pi\) | ||||
−0.510374 | + | 0.859953i | \(0.670493\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.0901699 | −0.00754039 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.38197 | −0.280857 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −14.6525 | −1.20038 | −0.600189 | − | 0.799858i | \(-0.704908\pi\) | ||||
−0.600189 | + | 0.799858i | \(0.704908\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.29180 | −0.186504 | −0.0932519 | − | 0.995643i | \(-0.529726\pi\) | ||||
−0.0932519 | + | 0.995643i | \(0.529726\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.09017 | −0.0875646 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.2361 | −1.37559 | −0.687794 | − | 0.725906i | \(-0.741421\pi\) | ||||
−0.687794 | + | 0.725906i | \(0.741421\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.00000 | 0.0788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.56231 | 0.279021 | 0.139511 | − | 0.990221i | \(-0.455447\pi\) | ||||
0.139511 | + | 0.990221i | \(0.455447\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 14.8885 | 1.15211 | 0.576055 | − | 0.817411i | \(-0.304591\pi\) | ||||
0.576055 | + | 0.817411i | \(0.304591\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.8541 | −0.988777 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −19.9443 | −1.51633 | −0.758167 | − | 0.652060i | \(-0.773905\pi\) | ||||
−0.758167 | + | 0.652060i | \(0.773905\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.61803 | 0.349091 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.79837 | 0.209160 | 0.104580 | − | 0.994516i | \(-0.466650\pi\) | ||||
0.104580 | + | 0.994516i | \(0.466650\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.23607 | −0.314864 | −0.157432 | − | 0.987530i | \(-0.550322\pi\) | ||||
−0.157432 | + | 0.987530i | \(0.550322\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.38197 | −0.248647 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.527864 | −0.0386012 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −21.1246 | −1.52852 | −0.764262 | − | 0.644906i | \(-0.776896\pi\) | ||||
−0.764262 | + | 0.644906i | \(0.776896\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.29180 | −0.308930 | −0.154465 | − | 0.987998i | \(-0.549365\pi\) | ||||
−0.154465 | + | 0.987998i | \(0.549365\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.38197 | 0.454696 | 0.227348 | − | 0.973814i | \(-0.426994\pi\) | ||||
0.227348 | + | 0.973814i | \(0.426994\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.67376 | −0.402202 | −0.201101 | − | 0.979570i | \(-0.564452\pi\) | ||||
−0.201101 | + | 0.979570i | \(0.564452\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.47214 | 0.384069 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.61803 | −0.322537 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.819660 | −0.0566971 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.23607 | −0.153937 | −0.0769686 | − | 0.997034i | \(-0.524524\pi\) | ||||
−0.0769686 | + | 0.997034i | \(0.524524\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −7.76393 | −0.529496 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.76393 | 0.119744 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.854102 | 0.0574531 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 26.2148 | 1.75547 | 0.877736 | − | 0.479145i | \(-0.159053\pi\) | ||||
0.877736 | + | 0.479145i | \(0.159053\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.09017 | −0.0723571 | −0.0361786 | − | 0.999345i | \(-0.511519\pi\) | ||||
−0.0361786 | + | 0.999345i | \(0.511519\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.6180 | 0.965987 | 0.482993 | − | 0.875624i | \(-0.339549\pi\) | ||||
0.482993 | + | 0.875624i | \(0.339549\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.09017 | 0.595517 | 0.297758 | − | 0.954641i | \(-0.403761\pi\) | ||||
0.297758 | + | 0.954641i | \(0.403761\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.472136 | 0.0307988 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 22.0344 | 1.42529 | 0.712645 | − | 0.701525i | \(-0.247497\pi\) | ||||
0.712645 | + | 0.701525i | \(0.247497\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −24.7082 | −1.59160 | −0.795798 | − | 0.605563i | \(-0.792948\pi\) | ||||
−0.795798 | + | 0.605563i | \(0.792948\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.618034 | 0.0394847 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.32624 | 0.0843865 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −22.1803 | −1.40001 | −0.700005 | − | 0.714138i | \(-0.746819\pi\) | ||||
−0.700005 | + | 0.714138i | \(0.746819\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.236068 | 0.0148415 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −25.7082 | −1.60363 | −0.801817 | − | 0.597570i | \(-0.796133\pi\) | ||||
−0.801817 | + | 0.597570i | \(0.796133\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.47214 | 0.340022 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.94427 | 0.489865 | 0.244932 | − | 0.969540i | \(-0.421234\pi\) | ||||
0.244932 | + | 0.969540i | \(0.421234\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.38197 | 0.269182 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −11.9098 | −0.726155 | −0.363078 | − | 0.931759i | \(-0.618274\pi\) | ||||
−0.363078 | + | 0.931759i | \(0.618274\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.3607 | −0.811603 | −0.405802 | − | 0.913961i | \(-0.633008\pi\) | ||||
−0.405802 | + | 0.913961i | \(0.633008\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.09017 | 0.0657397 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.38197 | 0.383455 | 0.191728 | − | 0.981448i | \(-0.438591\pi\) | ||||
0.191728 | + | 0.981448i | \(0.438591\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.65248 | 0.516163 | 0.258082 | − | 0.966123i | \(-0.416910\pi\) | ||||
0.258082 | + | 0.966123i | \(0.416910\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −19.0902 | −1.13479 | −0.567396 | − | 0.823445i | \(-0.692049\pi\) | ||||
−0.567396 | + | 0.823445i | \(0.692049\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.47214 | 0.441066 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.0000 | −0.705882 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.05573 | −0.412200 | −0.206100 | − | 0.978531i | \(-0.566077\pi\) | ||||
−0.206100 | + | 0.978531i | \(0.566077\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.09017 | 0.121694 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.381966 | −0.0220897 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.5623 | 0.724079 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.29180 | 0.188488 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.76393 | 0.328965 | 0.164482 | − | 0.986380i | \(-0.447405\pi\) | ||||
0.164482 | + | 0.986380i | \(0.447405\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.9787 | 0.906070 | 0.453035 | − | 0.891493i | \(-0.350341\pi\) | ||||
0.453035 | + | 0.891493i | \(0.350341\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.47214 | 0.365827 | 0.182913 | − | 0.983129i | \(-0.441447\pi\) | ||||
0.182913 | + | 0.983129i | \(0.441447\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −34.0344 | −1.91156 | −0.955782 | − | 0.294075i | \(-0.904988\pi\) | ||||
−0.955782 | + | 0.294075i | \(0.904988\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.29180 | 0.0723267 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.76393 | 0.431997 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.76393 | −0.0978453 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.763932 | −0.0421169 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.05573 | 0.0580281 | 0.0290140 | − | 0.999579i | \(-0.490763\pi\) | ||||
0.0290140 | + | 0.999579i | \(0.490763\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.09017 | −0.114198 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.5623 | −0.793259 | −0.396630 | − | 0.917979i | \(-0.629820\pi\) | ||||
−0.396630 | + | 0.917979i | \(0.629820\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.416408 | 0.0225498 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −19.1803 | −1.02965 | −0.514827 | − | 0.857294i | \(-0.672144\pi\) | ||||
−0.514827 | + | 0.857294i | \(0.672144\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.0902 | 1.23599 | 0.617994 | − | 0.786183i | \(-0.287945\pi\) | ||||
0.617994 | + | 0.786183i | \(0.287945\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.05573 | −0.428763 | −0.214382 | − | 0.976750i | \(-0.568774\pi\) | ||||
−0.214382 | + | 0.976750i | \(0.568774\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.70820 | 0.356034 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8.32624 | −0.439442 | −0.219721 | − | 0.975563i | \(-0.570515\pi\) | ||||
−0.219721 | + | 0.975563i | \(0.570515\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.94427 | −0.365488 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.20163 | 0.0628960 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.7984 | −0.615870 | −0.307935 | − | 0.951407i | \(-0.599638\pi\) | ||||
−0.307935 | + | 0.951407i | \(0.599638\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.09017 | −0.368103 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 25.9443 | 1.34334 | 0.671672 | − | 0.740849i | \(-0.265577\pi\) | ||||
0.671672 | + | 0.740849i | \(0.265577\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.09017 | −0.107649 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.8328 | 1.37831 | 0.689155 | − | 0.724614i | \(-0.257982\pi\) | ||||
0.689155 | + | 0.724614i | \(0.257982\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −0.527864 | −0.0269726 | −0.0134863 | − | 0.999909i | \(-0.504293\pi\) | ||||
−0.0134863 | + | 0.999909i | \(0.504293\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.145898 | 0.00743565 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.416408 | 0.0211127 | 0.0105564 | − | 0.999944i | \(-0.496640\pi\) | ||||
0.0105564 | + | 0.999944i | \(0.496640\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.23607 | −0.113083 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.09017 | −0.256114 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 28.1803 | 1.41433 | 0.707165 | − | 0.707048i | \(-0.249974\pi\) | ||||
0.707165 | + | 0.707048i | \(0.249974\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.3607 | 0.567325 | 0.283663 | − | 0.958924i | \(-0.408450\pi\) | ||||
0.283663 | + | 0.958924i | \(0.408450\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.673762 | −0.0335625 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.29180 | 0.0640320 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.23607 | −0.209460 | −0.104730 | − | 0.994501i | \(-0.533398\pi\) | ||||
−0.104730 | + | 0.994501i | \(0.533398\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.38197 | −0.166416 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.90983 | 0.241014 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −40.2148 | −1.96462 | −0.982310 | − | 0.187260i | \(-0.940039\pi\) | ||||
−0.982310 | + | 0.187260i | \(0.940039\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.5066 | 0.853218 | 0.426609 | − | 0.904436i | \(-0.359708\pi\) | ||||
0.426609 | + | 0.904436i | \(0.359708\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −10.3262 | −0.500896 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.32624 | −0.257755 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 22.5623 | 1.08679 | 0.543394 | − | 0.839478i | \(-0.317139\pi\) | ||||
0.543394 | + | 0.839478i | \(0.317139\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −23.7082 | −1.13934 | −0.569672 | − | 0.821872i | \(-0.692930\pi\) | ||||
−0.569672 | + | 0.821872i | \(0.692930\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.47214 | −0.166095 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.81966 | 0.325485 | 0.162742 | − | 0.986669i | \(-0.447966\pi\) | ||||
0.162742 | + | 0.986669i | \(0.447966\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13.8885 | 0.659865 | 0.329932 | − | 0.944005i | \(-0.392974\pi\) | ||||
0.329932 | + | 0.944005i | \(0.392974\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.76393 | 0.0836184 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9.09017 | −0.428992 | −0.214496 | − | 0.976725i | \(-0.568811\pi\) | ||||
−0.214496 | + | 0.976725i | \(0.568811\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.76393 | 0.0830603 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.236068 | −0.0110670 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.85410 | −0.180287 | −0.0901436 | − | 0.995929i | \(-0.528733\pi\) | ||||
−0.0901436 | + | 0.995929i | \(0.528733\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15.5623 | −0.724809 | −0.362404 | − | 0.932021i | \(-0.618044\pi\) | ||||
−0.362404 | + | 0.932021i | \(0.618044\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −36.8885 | −1.71436 | −0.857178 | − | 0.515020i | \(-0.827784\pi\) | ||||
−0.857178 | + | 0.515020i | \(0.827784\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −14.4164 | −0.667112 | −0.333556 | − | 0.942730i | \(-0.608249\pi\) | ||||
−0.333556 | + | 0.942730i | \(0.608249\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.38197 | 0.156165 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.96556 | 0.136357 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −16.0344 | −0.735711 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7.18034 | −0.328078 | −0.164039 | − | 0.986454i | \(-0.552452\pi\) | ||||
−0.164039 | + | 0.986454i | \(0.552452\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.09017 | −0.0953035 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.145898 | −0.00662489 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.5279 | 0.930206 | 0.465103 | − | 0.885256i | \(-0.346017\pi\) | ||||
0.465103 | + | 0.885256i | \(0.346017\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.854102 | 0.0385451 | 0.0192725 | − | 0.999814i | \(-0.493865\pi\) | ||||
0.0192725 | + | 0.999814i | \(0.493865\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12.2361 | −0.551085 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −10.8541 | −0.486873 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.27051 | −0.0568758 | −0.0284379 | − | 0.999596i | \(-0.509053\pi\) | ||||
−0.0284379 | + | 0.999596i | \(0.509053\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.43769 | 0.197867 | 0.0989335 | − | 0.995094i | \(-0.468457\pi\) | ||||
0.0989335 | + | 0.995094i | \(0.468457\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.854102 | 0.0380070 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.29180 | −0.101582 | −0.0507910 | − | 0.998709i | \(-0.516174\pi\) | ||||
−0.0507910 | + | 0.998709i | \(0.516174\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.94427 | −0.0860095 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.52786 | −0.243587 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.180340 | −0.00793134 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.47214 | −0.371171 | −0.185586 | − | 0.982628i | \(-0.559418\pi\) | ||||
−0.185586 | + | 0.982628i | \(0.559418\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17.4164 | −0.761566 | −0.380783 | − | 0.924664i | \(-0.624346\pi\) | ||||
−0.380783 | + | 0.924664i | \(0.624346\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.94427 | −0.171815 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.85410 | −0.123625 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.41641 | 0.277406 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.236068 | −0.0101682 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.29180 | −0.0985320 | −0.0492660 | − | 0.998786i | \(-0.515688\pi\) | ||||
−0.0492660 | + | 0.998786i | \(0.515688\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.09017 | −0.175204 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.09017 | 0.132126 | 0.0660631 | − | 0.997815i | \(-0.478956\pi\) | ||||
0.0660631 | + | 0.997815i | \(0.478956\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −19.0000 | −0.809427 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.23607 | 0.350233 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4.65248 | −0.197132 | −0.0985659 | − | 0.995131i | \(-0.531426\pi\) | ||||
−0.0985659 | + | 0.995131i | \(0.531426\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.79837 | −0.202950 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 37.5066 | 1.58071 | 0.790357 | − | 0.612647i | \(-0.209895\pi\) | ||||
0.790357 | + | 0.612647i | \(0.209895\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.67376 | −0.196627 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −26.4721 | −1.10977 | −0.554885 | − | 0.831927i | \(-0.687238\pi\) | ||||
−0.554885 | + | 0.831927i | \(0.687238\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.29180 | 0.137757 | 0.0688787 | − | 0.997625i | \(-0.478058\pi\) | ||||
0.0688787 | + | 0.997625i | \(0.478058\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.61803 | 0.192585 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −30.9443 | −1.28823 | −0.644113 | − | 0.764930i | \(-0.722774\pi\) | ||||
−0.644113 | + | 0.764930i | \(0.722774\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.94427 | −0.329584 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.67376 | −0.0693201 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 17.0344 | 0.703087 | 0.351543 | − | 0.936172i | \(-0.385657\pi\) | ||||
0.351543 | + | 0.936172i | \(0.385657\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.12461 | −0.252360 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.76393 | −0.113501 | −0.0567505 | − | 0.998388i | \(-0.518074\pi\) | ||||
−0.0567505 | + | 0.998388i | \(0.518074\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.38197 | −0.0566551 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −37.3951 | −1.52792 | −0.763962 | − | 0.645262i | \(-0.776748\pi\) | ||||
−0.763962 | + | 0.645262i | \(0.776748\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 34.6869 | 1.41491 | 0.707454 | − | 0.706759i | \(-0.249843\pi\) | ||||
0.707454 | + | 0.706759i | \(0.249843\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6.76393 | −0.274993 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 40.6312 | 1.64917 | 0.824585 | − | 0.565739i | \(-0.191409\pi\) | ||||
0.824585 | + | 0.565739i | \(0.191409\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.291796 | 0.0118048 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17.7639 | −0.717478 | −0.358739 | − | 0.933438i | \(-0.616793\pi\) | ||||
−0.358739 | + | 0.933438i | \(0.616793\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.9098 | 0.640506 | 0.320253 | − | 0.947332i | \(-0.396232\pi\) | ||||
0.320253 | + | 0.947332i | \(0.396232\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.03444 | 0.282738 | 0.141369 | − | 0.989957i | \(-0.454850\pi\) | ||||
0.141369 | + | 0.989957i | \(0.454850\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.85410 | −0.114347 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.4164 | 0.776656 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −12.2361 | −0.487884 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.47214 | −0.377080 | −0.188540 | − | 0.982066i | \(-0.560375\pi\) | ||||
−0.188540 | + | 0.982066i | \(0.560375\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.41641 | −0.175260 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.381966 | 0.0151340 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 34.8541 | 1.37665 | 0.688327 | − | 0.725400i | \(-0.258345\pi\) | ||||
0.688327 | + | 0.725400i | \(0.258345\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.9787 | 0.787884 | 0.393942 | − | 0.919135i | \(-0.371111\pi\) | ||||
0.393942 | + | 0.919135i | \(0.371111\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 30.9098 | 1.21519 | 0.607595 | − | 0.794247i | \(-0.292134\pi\) | ||||
0.607595 | + | 0.794247i | \(0.292134\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.798374 | −0.0313389 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10.0344 | 0.392678 | 0.196339 | − | 0.980536i | \(-0.437095\pi\) | ||||
0.196339 | + | 0.980536i | \(0.437095\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.0344419 | −0.00134575 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 41.0689 | 1.59982 | 0.799908 | − | 0.600122i | \(-0.204881\pi\) | ||||
0.799908 | + | 0.600122i | \(0.204881\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.81966 | −0.343045 | −0.171523 | − | 0.985180i | \(-0.554869\pi\) | ||||
−0.171523 | + | 0.985180i | \(0.554869\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.14590 | −0.0832144 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.47214 | 0.211882 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.25735 | −0.0485396 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −34.4164 | −1.32666 | −0.663328 | − | 0.748329i | \(-0.730856\pi\) | ||||
−0.663328 | + | 0.748329i | \(0.730856\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 21.9787 | 0.844711 | 0.422355 | − | 0.906430i | \(-0.361203\pi\) | ||||
0.422355 | + | 0.906430i | \(0.361203\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.236068 | 0.00905946 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15.7639 | 0.603190 | 0.301595 | − | 0.953436i | \(-0.402481\pi\) | ||||
0.301595 | + | 0.953436i | \(0.402481\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.145898 | 0.00557448 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.70820 | 0.103174 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.56231 | 0.0974747 | 0.0487374 | − | 0.998812i | \(-0.484480\pi\) | ||||
0.0487374 | + | 0.998812i | \(0.484480\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.43769 | −0.282128 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −16.7082 | −0.632868 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 46.2148 | 1.74551 | 0.872754 | − | 0.488160i | \(-0.162332\pi\) | ||||
0.872754 | + | 0.488160i | \(0.162332\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −19.0000 | −0.716599 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.38197 | −0.0519742 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.27051 | 0.310606 | 0.155303 | − | 0.987867i | \(-0.450365\pi\) | ||||
0.155303 | + | 0.987867i | \(0.450365\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.76393 | 0.0660598 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.0557281 | −0.00208411 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.76393 | 0.0657836 | 0.0328918 | − | 0.999459i | \(-0.489528\pi\) | ||||
0.0328918 | + | 0.999459i | \(0.489528\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.94427 | 0.333102 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 25.2705 | 0.938523 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 45.4721 | 1.68647 | 0.843234 | − | 0.537547i | \(-0.180649\pi\) | ||||
0.843234 | + | 0.537547i | \(0.180649\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −28.0902 | −1.03895 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −41.5967 | −1.53641 | −0.768205 | − | 0.640203i | \(-0.778850\pi\) | ||||
−0.768205 | + | 0.640203i | \(0.778850\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.798374 | 0.0294085 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24.5967 | 0.904806 | 0.452403 | − | 0.891814i | \(-0.350567\pi\) | ||||
0.452403 | + | 0.891814i | \(0.350567\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 29.2016 | 1.07130 | 0.535652 | − | 0.844439i | \(-0.320066\pi\) | ||||
0.535652 | + | 0.844439i | \(0.320066\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.05573 | −0.331776 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −10.3820 | −0.379349 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −38.0344 | −1.38790 | −0.693948 | − | 0.720025i | \(-0.744130\pi\) | ||||
−0.693948 | + | 0.720025i | \(0.744130\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.41641 | −0.0515484 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 35.0000 | 1.27210 | 0.636048 | − | 0.771649i | \(-0.280568\pi\) | ||||
0.636048 | + | 0.771649i | \(0.280568\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10.8328 | −0.392689 | −0.196345 | − | 0.980535i | \(-0.562907\pi\) | ||||
−0.196345 | + | 0.980535i | \(0.562907\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.61803 | 0.239589 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.29180 | 0.0466441 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 30.1803 | 1.08833 | 0.544165 | − | 0.838978i | \(-0.316846\pi\) | ||||
0.544165 | + | 0.838978i | \(0.316846\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −6.52786 | −0.234791 | −0.117395 | − | 0.993085i | \(-0.537455\pi\) | ||||
−0.117395 | + | 0.993085i | \(0.537455\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.14590 | 0.292609 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −25.9443 | −0.929550 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.56231 | −0.0916865 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −10.6525 | −0.380203 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17.4508 | −0.622056 | −0.311028 | − | 0.950401i | \(-0.600673\pi\) | ||||
−0.311028 | + | 0.950401i | \(0.600673\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.56231 | 0.268885 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.03444 | 0.0722451 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −28.5410 | −1.01097 | −0.505487 | − | 0.862834i | \(-0.668687\pi\) | ||||
−0.505487 | + | 0.862834i | \(0.668687\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.70820 | 0.0604319 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.458980 | −0.0161971 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.618034 | 0.0217828 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −16.3820 | −0.575959 | −0.287980 | − | 0.957637i | \(-0.592984\pi\) | ||||
−0.287980 | + | 0.957637i | \(0.592984\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.58359 | 0.196066 | 0.0980332 | − | 0.995183i | \(-0.468745\pi\) | ||||
0.0980332 | + | 0.995183i | \(0.468745\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.20163 | 0.0771196 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −43.6180 | −1.52600 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −41.1246 | −1.43526 | −0.717629 | − | 0.696425i | \(-0.754773\pi\) | ||||
−0.717629 | + | 0.696425i | \(0.754773\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 49.2705 | 1.71746 | 0.858731 | − | 0.512427i | \(-0.171253\pi\) | ||||
0.858731 | + | 0.512427i | \(0.171253\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 23.5623 | 0.819342 | 0.409671 | − | 0.912233i | \(-0.365644\pi\) | ||||
0.409671 | + | 0.912233i | \(0.365644\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.1246 | −0.698957 | −0.349478 | − | 0.936944i | \(-0.613641\pi\) | ||||
−0.349478 | + | 0.936944i | \(0.613641\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.23607 | 0.0774752 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.20163 | 0.318435 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 34.9230 | 1.20568 | 0.602838 | − | 0.797864i | \(-0.294037\pi\) | ||||
0.602838 | + | 0.797864i | \(0.294037\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.944272 | 0.0325611 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7.94427 | −0.273291 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.9443 | 0.376050 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.47214 | 0.187582 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −28.6525 | −0.981042 | −0.490521 | − | 0.871429i | \(-0.663194\pi\) | ||||
−0.490521 | + | 0.871429i | \(0.663194\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −0.875388 | −0.0299027 | −0.0149513 | − | 0.999888i | \(-0.504759\pi\) | ||||
−0.0149513 | + | 0.999888i | \(0.504759\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14.9443 | −0.509892 | −0.254946 | − | 0.966955i | \(-0.582058\pi\) | ||||
−0.254946 | + | 0.966955i | \(0.582058\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.12461 | −0.106363 | −0.0531815 | − | 0.998585i | \(-0.516936\pi\) | ||||
−0.0531815 | + | 0.998585i | \(0.516936\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12.3262 | −0.419105 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.94427 | 0.0659549 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.29180 | −0.0437708 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5.94427 | 0.200953 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −47.1935 | −1.59361 | −0.796806 | − | 0.604236i | \(-0.793478\pi\) | ||||
−0.796806 | + | 0.604236i | \(0.793478\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 35.7082 | 1.20304 | 0.601520 | − | 0.798858i | \(-0.294562\pi\) | ||||
0.601520 | + | 0.798858i | \(0.294562\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −32.7426 | −1.10188 | −0.550939 | − | 0.834546i | \(-0.685730\pi\) | ||||
−0.550939 | + | 0.834546i | \(0.685730\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 20.5623 | 0.690415 | 0.345207 | − | 0.938526i | \(-0.387809\pi\) | ||||
0.345207 | + | 0.938526i | \(0.387809\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.14590 | 0.239666 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.65248 | 0.0887617 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.72949 | 0.0578105 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.65248 | 0.321928 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15.8541 | 0.528177 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.61803 | −0.0870264 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17.9656 | 0.596537 | 0.298268 | − | 0.954482i | \(-0.403591\pi\) | ||||
0.298268 | + | 0.954482i | \(0.403591\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −32.5410 | −1.07813 | −0.539066 | − | 0.842264i | \(-0.681223\pi\) | ||||
−0.539066 | + | 0.842264i | \(0.681223\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.87539 | −0.0620663 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.0557281 | 0.00184030 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.41641 | −0.211658 | −0.105829 | − | 0.994384i | \(-0.533750\pi\) | ||||
−0.105829 | + | 0.994384i | \(0.533750\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.14590 | 0.136464 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 25.2705 | 0.830889 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 30.5066 | 1.00089 | 0.500444 | − | 0.865769i | \(-0.333170\pi\) | ||||
0.500444 | + | 0.865769i | \(0.333170\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.47214 | 0.113795 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.326238 | −0.0106691 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 31.4721 | 1.02815 | 0.514075 | − | 0.857745i | \(-0.328135\pi\) | ||||
0.514075 | + | 0.857745i | \(0.328135\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −28.0000 | −0.912774 | −0.456387 | − | 0.889781i | \(-0.650857\pi\) | ||||
−0.456387 | + | 0.889781i | \(0.650857\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.47214 | 0.243326 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −24.1115 | −0.783517 | −0.391759 | − | 0.920068i | \(-0.628133\pi\) | ||||
−0.391759 | + | 0.920068i | \(0.628133\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.742646 | 0.0241073 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 13.4377 | 0.435290 | 0.217645 | − | 0.976028i | \(-0.430163\pi\) | ||||
0.217645 | + | 0.976028i | \(0.430163\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −13.0557 | −0.422473 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.236068 | −0.00762303 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.8885 | −0.899630 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.65248 | −0.0853862 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.4721 | 0.529708 | 0.264854 | − | 0.964288i | \(-0.414676\pi\) | ||||
0.264854 | + | 0.964288i | \(0.414676\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 29.3262 | 0.941124 | 0.470562 | − | 0.882367i | \(-0.344051\pi\) | ||||
0.470562 | + | 0.882367i | \(0.344051\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12.0344 | 0.385806 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 45.9098 | 1.46879 | 0.734393 | − | 0.678725i | \(-0.237467\pi\) | ||||
0.734393 | + | 0.678725i | \(0.237467\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.673762 | −0.0215335 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −22.7771 | −0.726476 | −0.363238 | − | 0.931696i | \(-0.618329\pi\) | ||||
−0.363238 | + | 0.931696i | \(0.618329\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.94427 | 0.125675 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12.5623 | 0.399458 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10.1591 | −0.322713 | −0.161356 | − | 0.986896i | \(-0.551587\pi\) | ||||
−0.161356 | + | 0.986896i | \(0.551587\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.50658 | −0.111166 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −12.1246 | −0.383990 | −0.191995 | − | 0.981396i | \(-0.561496\pi\) | ||||
−0.191995 | + | 0.981396i | \(0.561496\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 5796.2.a.i.1.2 | 2 | ||
3.2 | odd | 2 | 1932.2.a.d.1.1 | ✓ | 2 | ||
12.11 | even | 2 | 7728.2.a.bo.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1932.2.a.d.1.1 | ✓ | 2 | 3.2 | odd | 2 | ||
5796.2.a.i.1.2 | 2 | 1.1 | even | 1 | trivial | ||
7728.2.a.bo.1.1 | 2 | 12.11 | even | 2 |