Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3696,2,Mod(1,3696)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3696, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3696.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3696 = 2^{4} \cdot 3 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3696.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: | \(29.5127085871\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.229.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 4x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 231) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-0.254102\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3696.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.18953 | 1.87362 | 0.936808 | − | 0.349843i | \(-0.113765\pi\) | ||||
0.936808 | + | 0.349843i | \(0.113765\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.17313 | −0.880067 | −0.440034 | − | 0.897981i | \(-0.645033\pi\) | ||||
−0.440034 | + | 0.897981i | \(0.645033\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.18953 | −1.08173 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.85446 | 1.66245 | 0.831225 | − | 0.555936i | \(-0.187640\pi\) | ||||
0.831225 | + | 0.555936i | \(0.187640\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.318669 | 0.0731078 | 0.0365539 | − | 0.999332i | \(-0.488362\pi\) | ||||
0.0365539 | + | 0.999332i | \(0.488362\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.87086 | 0.390102 | 0.195051 | − | 0.980793i | \(-0.437513\pi\) | ||||
0.195051 | + | 0.980793i | \(0.437513\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 12.5522 | 2.51044 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.17313 | −0.589235 | −0.294617 | − | 0.955615i | \(-0.595192\pi\) | ||||
−0.294617 | + | 0.955615i | \(0.595192\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.23353 | −1.65839 | −0.829195 | − | 0.558959i | \(-0.811201\pi\) | ||||
−0.829195 | + | 0.558959i | \(0.811201\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.18953 | 0.708161 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.55220 | −1.24157 | −0.620787 | − | 0.783980i | \(-0.713187\pi\) | ||||
−0.620787 | + | 0.783980i | \(0.713187\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.17313 | 0.508107 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.36266 | 1.46220 | 0.731101 | − | 0.682269i | \(-0.239007\pi\) | ||||
0.731101 | + | 0.682269i | \(0.239007\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.8873 | 1.66029 | 0.830147 | − | 0.557545i | \(-0.188257\pi\) | ||||
0.830147 | + | 0.557545i | \(0.188257\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.18953 | 0.624539 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.06040 | 1.17573 | 0.587865 | − | 0.808959i | \(-0.299969\pi\) | ||||
0.587865 | + | 0.808959i | \(0.299969\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.85446 | −0.959816 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.508203 | 0.0698071 | 0.0349036 | − | 0.999391i | \(-0.488888\pi\) | ||||
0.0349036 | + | 0.999391i | \(0.488888\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.18953 | 0.564917 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.318669 | −0.0422088 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.04399 | 0.917050 | 0.458525 | − | 0.888682i | \(-0.348378\pi\) | ||||
0.458525 | + | 0.888682i | \(0.348378\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.00000 | −0.256074 | −0.128037 | − | 0.991769i | \(-0.540868\pi\) | ||||
−0.128037 | + | 0.991769i | \(0.540868\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −13.2939 | −1.64891 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.66492 | 0.325572 | 0.162786 | − | 0.986661i | \(-0.447952\pi\) | ||||
0.162786 | + | 0.986661i | \(0.447952\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.87086 | −0.225226 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.01641 | 0.595338 | 0.297669 | − | 0.954669i | \(-0.403791\pi\) | ||||
0.297669 | + | 0.954669i | \(0.403791\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.82687 | −0.564943 | −0.282471 | − | 0.959276i | \(-0.591154\pi\) | ||||
−0.282471 | + | 0.959276i | \(0.591154\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −12.5522 | −1.44940 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.01641 | −0.564390 | −0.282195 | − | 0.959357i | \(-0.591062\pi\) | ||||
−0.282195 | + | 0.959357i | \(0.591062\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.52461 | −0.386876 | −0.193438 | − | 0.981112i | \(-0.561964\pi\) | ||||
−0.193438 | + | 0.981112i | \(0.561964\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 28.7170 | 3.11479 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.17313 | 0.340195 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.74173 | −0.184623 | −0.0923115 | − | 0.995730i | \(-0.529426\pi\) | ||||
−0.0923115 | + | 0.995730i | \(0.529426\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.17313 | −0.332634 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.23353 | 0.957472 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.33508 | 0.136976 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.2499 | −1.24379 | −0.621896 | − | 0.783100i | \(-0.713637\pi\) | ||||
−0.621896 | + | 0.783100i | \(0.713637\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.88727 | 0.486302 | 0.243151 | − | 0.969988i | \(-0.421819\pi\) | ||||
0.243151 | + | 0.969988i | \(0.421819\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.637339 | 0.0627988 | 0.0313994 | − | 0.999507i | \(-0.490004\pi\) | ||||
0.0313994 | + | 0.999507i | \(0.490004\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.18953 | −0.408857 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.956008 | −0.0924208 | −0.0462104 | − | 0.998932i | \(-0.514714\pi\) | ||||
−0.0462104 | + | 0.998932i | \(0.514714\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.61259 | −0.729154 | −0.364577 | − | 0.931173i | \(-0.618786\pi\) | ||||
−0.364577 | + | 0.931173i | \(0.618786\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.55220 | 0.716823 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.70892 | −0.725194 | −0.362597 | − | 0.931946i | \(-0.618110\pi\) | ||||
−0.362597 | + | 0.931946i | \(0.618110\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.83805 | 0.730902 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.17313 | −0.293356 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.85446 | 0.628347 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −9.36266 | −0.844203 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 31.6402 | 2.82998 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.49180 | 0.487318 | 0.243659 | − | 0.969861i | \(-0.421652\pi\) | ||||
0.243659 | + | 0.969861i | \(0.421652\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −10.8873 | −0.958571 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.00000 | −0.349482 | −0.174741 | − | 0.984614i | \(-0.555909\pi\) | ||||
−0.174741 | + | 0.984614i | \(0.555909\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.318669 | 0.0276321 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.18953 | −0.360578 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 15.6126 | 1.33387 | 0.666937 | − | 0.745114i | \(-0.267605\pi\) | ||||
0.666937 | + | 0.745114i | \(0.267605\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.01641 | 0.764762 | 0.382381 | − | 0.924005i | \(-0.375104\pi\) | ||||
0.382381 | + | 0.924005i | \(0.375104\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.06040 | −0.678808 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.17313 | −0.265350 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −13.2939 | −1.10400 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.20594 | −0.426487 | −0.213244 | − | 0.976999i | \(-0.568403\pi\) | ||||
−0.213244 | + | 0.976999i | \(0.568403\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.24993 | −0.508612 | −0.254306 | − | 0.967124i | \(-0.581847\pi\) | ||||
−0.254306 | + | 0.967124i | \(0.581847\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.85446 | 0.554150 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −38.6842 | −3.10719 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18.1208 | −1.44620 | −0.723099 | − | 0.690745i | \(-0.757283\pi\) | ||||
−0.723099 | + | 0.690745i | \(0.757283\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.508203 | −0.0403031 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.87086 | 0.147445 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.66492 | 0.208733 | 0.104366 | − | 0.994539i | \(-0.466719\pi\) | ||||
0.104366 | + | 0.994539i | \(0.466719\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.18953 | −0.326155 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.1455 | 0.862468 | 0.431234 | − | 0.902240i | \(-0.358078\pi\) | ||||
0.431234 | + | 0.902240i | \(0.358078\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.93126 | −0.225482 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.318669 | 0.0243693 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −24.8461 | −1.88902 | −0.944508 | − | 0.328489i | \(-0.893461\pi\) | ||||
−0.944508 | + | 0.328489i | \(0.893461\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 12.5522 | 0.948857 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −7.04399 | −0.529459 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.7581 | 0.953588 | 0.476794 | − | 0.879015i | \(-0.341799\pi\) | ||||
0.476794 | + | 0.879015i | \(0.341799\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.23353 | −0.240346 | −0.120173 | − | 0.992753i | \(-0.538345\pi\) | ||||
−0.120173 | + | 0.992753i | \(0.538345\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.00000 | 0.147844 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −31.6402 | −2.32623 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.85446 | 0.501248 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −20.9753 | −1.51772 | −0.758858 | − | 0.651256i | \(-0.774242\pi\) | ||||
−0.758858 | + | 0.651256i | \(0.774242\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.249933 | 0.0179905 | 0.00899527 | − | 0.999960i | \(-0.497137\pi\) | ||||
0.00899527 | + | 0.999960i | \(0.497137\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 13.2939 | 0.951998 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.4999 | 1.31806 | 0.659030 | − | 0.752116i | \(-0.270967\pi\) | ||||
0.659030 | + | 0.752116i | \(0.270967\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.87086 | −0.699727 | −0.349864 | − | 0.936801i | \(-0.613772\pi\) | ||||
−0.349864 | + | 0.936801i | \(0.613772\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.66492 | −0.187969 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.17313 | −0.222710 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 39.2252 | 2.73961 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.87086 | 0.130034 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.318669 | 0.0220428 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.63734 | 0.319248 | 0.159624 | − | 0.987178i | \(-0.448972\pi\) | ||||
0.159624 | + | 0.987178i | \(0.448972\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.01641 | −0.343719 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 45.6126 | 3.11075 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.23353 | −0.626813 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.82687 | 0.326170 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −21.7501 | −1.46307 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.3463 | 1.22856 | 0.614278 | − | 0.789090i | \(-0.289447\pi\) | ||||
0.614278 | + | 0.789090i | \(0.289447\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 12.5522 | 0.836813 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.379068 | −0.0251596 | −0.0125798 | − | 0.999921i | \(-0.504004\pi\) | ||||
−0.0125798 | + | 0.999921i | \(0.504004\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 24.9424 | 1.64824 | 0.824121 | − | 0.566413i | \(-0.191669\pi\) | ||||
0.824121 | + | 0.566413i | \(0.191669\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.00000 | −0.0657952 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 23.4506 | 1.53630 | 0.768151 | − | 0.640268i | \(-0.221177\pi\) | ||||
0.768151 | + | 0.640268i | \(0.221177\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 33.7693 | 2.20287 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.01641 | 0.325851 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.07681 | −0.328391 | −0.164196 | − | 0.986428i | \(-0.552503\pi\) | ||||
−0.164196 | + | 0.986428i | \(0.552503\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.2939 | 1.24283 | 0.621415 | − | 0.783481i | \(-0.286558\pi\) | ||||
0.621415 | + | 0.783481i | \(0.286558\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.18953 | 0.267660 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.01118 | −0.0643397 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.52461 | 0.223363 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −23.8021 | −1.50238 | −0.751188 | − | 0.660088i | \(-0.770519\pi\) | ||||
−0.751188 | + | 0.660088i | \(0.770519\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.87086 | 0.117620 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −28.7170 | −1.79833 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.9149 | 0.930363 | 0.465182 | − | 0.885215i | \(-0.345989\pi\) | ||||
0.465182 | + | 0.885215i | \(0.345989\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.55220 | −0.469271 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.17313 | −0.196412 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.92319 | −0.180252 | −0.0901259 | − | 0.995930i | \(-0.528727\pi\) | ||||
−0.0901259 | + | 0.995930i | \(0.528727\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.12914 | 0.130792 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.74173 | 0.106592 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.9672 | 0.729652 | 0.364826 | − | 0.931076i | \(-0.381128\pi\) | ||||
0.364826 | + | 0.931076i | \(0.381128\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.3187 | 1.23427 | 0.617136 | − | 0.786857i | \(-0.288293\pi\) | ||||
0.617136 | + | 0.786857i | \(0.288293\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.17313 | 0.192046 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 12.5522 | 0.756926 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.0552 | 1.08483 | 0.542415 | − | 0.840111i | \(-0.317510\pi\) | ||||
0.542415 | + | 0.840111i | \(0.317510\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −9.23353 | −0.552797 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 27.2939 | 1.62822 | 0.814110 | − | 0.580711i | \(-0.197226\pi\) | ||||
0.814110 | + | 0.580711i | \(0.197226\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −29.8901 | −1.77678 | −0.888391 | − | 0.459087i | \(-0.848177\pi\) | ||||
−0.888391 | + | 0.459087i | \(0.848177\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.33508 | −0.0790831 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.36266 | 0.552660 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 29.9836 | 1.76374 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.2499 | 0.718104 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4.34625 | −0.253911 | −0.126955 | − | 0.991908i | \(-0.540521\pi\) | ||||
−0.126955 | + | 0.991908i | \(0.540521\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 29.5110 | 1.71820 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.93649 | −0.343316 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.8873 | 0.627532 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.88727 | −0.280766 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8.37907 | −0.479784 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.7581 | 1.18473 | 0.592365 | − | 0.805670i | \(-0.298194\pi\) | ||||
0.592365 | + | 0.805670i | \(0.298194\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.637339 | −0.0362569 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.00000 | −0.453638 | −0.226819 | − | 0.973937i | \(-0.572833\pi\) | ||||
−0.226819 | + | 0.973937i | \(0.572833\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.12914 | 0.459486 | 0.229743 | − | 0.973251i | \(-0.426211\pi\) | ||||
0.229743 | + | 0.973251i | \(0.426211\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.18953 | 0.236054 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −19.9917 | −1.12284 | −0.561422 | − | 0.827530i | \(-0.689745\pi\) | ||||
−0.561422 | + | 0.827530i | \(0.689745\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.17313 | −0.177661 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.956008 | 0.0533592 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.18431 | 0.121538 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −39.8297 | −2.20935 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 7.61259 | 0.420977 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.06040 | 0.444384 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.0164 | −0.935306 | −0.467653 | − | 0.883912i | \(-0.654900\pi\) | ||||
−0.467653 | + | 0.883912i | \(0.654900\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7.55220 | −0.413858 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 11.1648 | 0.609998 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.52461 | 0.0830508 | 0.0415254 | − | 0.999137i | \(-0.486778\pi\) | ||||
0.0415254 | + | 0.999137i | \(0.486778\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.70892 | 0.418691 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.23353 | −0.500023 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −7.83805 | −0.421986 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −17.4506 | −0.936800 | −0.468400 | − | 0.883517i | \(-0.655169\pi\) | ||||
−0.468400 | + | 0.883517i | \(0.655169\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.85969 | 0.367191 | 0.183595 | − | 0.983002i | \(-0.441226\pi\) | ||||
0.183595 | + | 0.983002i | \(0.441226\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.17313 | 0.169369 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −31.9313 | −1.69953 | −0.849765 | − | 0.527162i | \(-0.823256\pi\) | ||||
−0.849765 | + | 0.527162i | \(0.823256\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 21.0164 | 1.11544 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.85446 | −0.362776 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 24.4342 | 1.28959 | 0.644795 | − | 0.764356i | \(-0.276943\pi\) | ||||
0.644795 | + | 0.764356i | \(0.276943\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.8984 | −0.994655 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −20.2223 | −1.05849 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −17.0716 | −0.891129 | −0.445565 | − | 0.895250i | \(-0.646997\pi\) | ||||
−0.445565 | + | 0.895250i | \(0.646997\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 9.36266 | 0.487401 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.508203 | 0.0263846 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.17836 | 0.164569 | 0.0822845 | − | 0.996609i | \(-0.473778\pi\) | ||||
0.0822845 | + | 0.996609i | \(0.473778\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −31.6402 | −1.63389 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10.0687 | 0.518566 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.93960 | −0.202364 | −0.101182 | − | 0.994868i | \(-0.532262\pi\) | ||||
−0.101182 | + | 0.994868i | \(0.532262\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.49180 | −0.281353 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 24.7581 | 1.26508 | 0.632541 | − | 0.774527i | \(-0.282012\pi\) | ||||
0.632541 | + | 0.774527i | \(0.282012\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.18953 | 0.213518 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 10.8873 | 0.553431 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.65375 | 0.185252 | 0.0926261 | − | 0.995701i | \(-0.470474\pi\) | ||||
0.0926261 | + | 0.995701i | \(0.470474\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.8238 | 0.648526 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.00000 | 0.201773 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −21.0164 | −1.05745 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.56337 | 0.229029 | 0.114515 | − | 0.993422i | \(-0.463469\pi\) | ||||
0.114515 | + | 0.993422i | \(0.463469\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.318669 | −0.0159534 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.23353 | −0.361225 | −0.180613 | − | 0.983554i | \(-0.557808\pi\) | ||||
−0.180613 | + | 0.983554i | \(0.557808\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 29.2992 | 1.45949 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.18953 | 0.208180 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.55220 | −0.374348 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.30749 | 0.262439 | 0.131219 | − | 0.991353i | \(-0.458111\pi\) | ||||
0.131219 | + | 0.991353i | \(0.458111\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −15.6126 | −0.770112 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.04399 | 0.346612 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −14.7665 | −0.724858 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9.01641 | −0.441535 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 11.4231 | 0.558053 | 0.279026 | − | 0.960283i | \(-0.409988\pi\) | ||||
0.279026 | + | 0.960283i | \(0.409988\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −27.4147 | −1.33611 | −0.668056 | − | 0.744111i | \(-0.732873\pi\) | ||||
−0.668056 | + | 0.744111i | \(0.732873\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8.06040 | 0.391910 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 86.0385 | 4.17348 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.00000 | −0.0967868 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.17313 | 0.153200 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.28586 | 0.110106 | 0.0550529 | − | 0.998483i | \(-0.482467\pi\) | ||||
0.0550529 | + | 0.998483i | \(0.482467\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 31.5714 | 1.51723 | 0.758613 | − | 0.651541i | \(-0.225877\pi\) | ||||
0.758613 | + | 0.651541i | \(0.225877\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 13.2939 | 0.637395 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.596187 | 0.0285195 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.5275 | 0.884267 | 0.442133 | − | 0.896949i | \(-0.354222\pi\) | ||||
0.442133 | + | 0.896949i | \(0.354222\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −28.4342 | −1.35095 | −0.675476 | − | 0.737382i | \(-0.736062\pi\) | ||||
−0.675476 | + | 0.737382i | \(0.736062\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.29703 | −0.345913 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.20594 | 0.246233 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.68656 | −0.268365 | −0.134183 | − | 0.990957i | \(-0.542841\pi\) | ||||
−0.134183 | + | 0.990957i | \(0.542841\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.36266 | 0.440871 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.24993 | 0.293647 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −13.2939 | −0.623229 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.0081 | −0.608492 | −0.304246 | − | 0.952594i | \(-0.598404\pi\) | ||||
−0.304246 | + | 0.952594i | \(0.598404\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.85446 | −0.319939 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.37907 | −0.297103 | −0.148551 | − | 0.988905i | \(-0.547461\pi\) | ||||
−0.148551 | + | 0.988905i | \(0.547461\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −34.0932 | −1.58445 | −0.792223 | − | 0.610232i | \(-0.791076\pi\) | ||||
−0.792223 | + | 0.610232i | \(0.791076\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 38.6842 | 1.79394 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −18.1484 | −0.839807 | −0.419903 | − | 0.907569i | \(-0.637936\pi\) | ||||
−0.419903 | + | 0.907569i | \(0.637936\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.66492 | 0.123055 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 18.1208 | 0.834962 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10.8873 | 0.500597 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.00000 | 0.183533 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.508203 | 0.0232690 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 42.7498 | 1.95329 | 0.976644 | − | 0.214864i | \(-0.0689307\pi\) | ||||
0.976644 | + | 0.214864i | \(0.0689307\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 23.9641 | 1.09267 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.87086 | −0.0851273 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −51.3215 | −2.33039 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −26.7909 | −1.21401 | −0.607007 | − | 0.794697i | \(-0.707630\pi\) | ||||
−0.607007 | + | 0.794697i | \(0.707630\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.66492 | −0.120512 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −31.6813 | −1.42976 | −0.714879 | − | 0.699248i | \(-0.753518\pi\) | ||||
−0.714879 | + | 0.699248i | \(0.753518\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −21.7501 | −0.979574 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.18953 | 0.188306 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.01641 | 0.225017 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.1260 | 1.08003 | 0.540015 | − | 0.841656i | \(-0.318419\pi\) | ||||
0.540015 | + | 0.841656i | \(0.318419\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −11.1455 | −0.497946 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −30.8873 | −1.37720 | −0.688598 | − | 0.725144i | \(-0.741773\pi\) | ||||
−0.688598 | + | 0.725144i | \(0.741773\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 20.4754 | 0.911143 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.93126 | 0.130182 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 28.2088 | 1.25033 | 0.625166 | − | 0.780492i | \(-0.285031\pi\) | ||||
0.625166 | + | 0.780492i | \(0.285031\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.82687 | −0.213528 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.318669 | −0.0140696 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.67015 | 0.117661 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.06040 | 0.354496 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 24.8461 | 1.09062 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −33.7610 | −1.47910 | −0.739548 | − | 0.673104i | \(-0.764961\pi\) | ||||
−0.739548 | + | 0.673104i | \(0.764961\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.8185 | −0.560515 | −0.280258 | − | 0.959925i | \(-0.590420\pi\) | ||||
−0.280258 | + | 0.959925i | \(0.590420\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −12.5522 | −0.547823 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −63.2908 | −2.75699 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.4999 | −0.847820 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.04399 | 0.305683 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −29.7089 | −1.28684 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.00523 | −0.173161 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −12.7581 | −0.550554 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21.8625 | −0.939943 | −0.469972 | − | 0.882681i | \(-0.655736\pi\) | ||||
−0.469972 | + | 0.882681i | \(0.655736\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.23353 | 0.138764 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −31.8932 | −1.36616 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −23.4178 | −1.00127 | −0.500637 | − | 0.865657i | \(-0.666901\pi\) | ||||
−0.500637 | + | 0.865657i | \(0.666901\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.00000 | −0.0853579 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.01118 | −0.0430776 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.01641 | −0.213319 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 31.6402 | 1.34305 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.91486 | −0.292992 | −0.146496 | − | 0.989211i | \(-0.546800\pi\) | ||||
−0.146496 | + | 0.989211i | \(0.546800\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −34.5467 | −1.46117 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.85446 | −0.289395 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −11.8381 | −0.498914 | −0.249457 | − | 0.968386i | \(-0.580252\pi\) | ||||
−0.249457 | + | 0.968386i | \(0.580252\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −32.2968 | −1.35874 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10.0000 | 0.419222 | 0.209611 | − | 0.977785i | \(-0.432780\pi\) | ||||
0.209611 | + | 0.977785i | \(0.432780\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.2252 | 0.637154 | 0.318577 | − | 0.947897i | \(-0.396795\pi\) | ||||
0.318577 | + | 0.947897i | \(0.396795\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 20.9753 | 0.876254 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 23.4835 | 0.979328 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.3215 | 0.721104 | 0.360552 | − | 0.932739i | \(-0.382588\pi\) | ||||
0.360552 | + | 0.932739i | \(0.382588\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.249933 | −0.0103868 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.52461 | −0.146225 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.508203 | 0.0210476 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −13.2939 | −0.549636 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −27.8678 | −1.15023 | −0.575113 | − | 0.818074i | \(-0.695042\pi\) | ||||
−0.575113 | + | 0.818074i | \(0.695042\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.94244 | −0.121241 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −18.4999 | −0.760983 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −24.3463 | −0.999781 | −0.499890 | − | 0.866089i | \(-0.666626\pi\) | ||||
−0.499890 | + | 0.866089i | \(0.666626\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 28.7170 | 1.17728 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 9.87086 | 0.403988 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −21.0164 | −0.858707 | −0.429354 | − | 0.903136i | \(-0.641259\pi\) | ||||
−0.429354 | + | 0.903136i | \(0.641259\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 40.9477 | 1.67029 | 0.835145 | − | 0.550030i | \(-0.185384\pi\) | ||||
0.835145 | + | 0.550030i | \(0.185384\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.66492 | 0.108524 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.18953 | 0.170329 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.0276 | 0.569362 | 0.284681 | − | 0.958622i | \(-0.408112\pi\) | ||||
0.284681 | + | 0.958622i | \(0.408112\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.17313 | 0.128582 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −25.5767 | −1.03472 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18.5306 | 0.748442 | 0.374221 | − | 0.927339i | \(-0.377910\pi\) | ||||
0.374221 | + | 0.927339i | \(0.377910\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −39.2252 | −1.58171 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.43424 | 0.0979987 | 0.0489994 | − | 0.998799i | \(-0.484397\pi\) | ||||
0.0489994 | + | 0.998799i | \(0.484397\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 30.4259 | 1.22292 | 0.611460 | − | 0.791275i | \(-0.290582\pi\) | ||||
0.611460 | + | 0.791275i | \(0.290582\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.87086 | −0.0750752 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.74173 | −0.0697809 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 69.7966 | 2.79187 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.318669 | −0.0127264 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −51.7662 | −2.06405 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −34.9836 | −1.39267 | −0.696337 | − | 0.717715i | \(-0.745188\pi\) | ||||
−0.696337 | + | 0.717715i | \(0.745188\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.63734 | −0.184318 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 23.0081 | 0.913047 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.17313 | −0.125724 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.01641 | 0.198446 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.56337 | 0.338233 | 0.169116 | − | 0.985596i | \(-0.445909\pi\) | ||||
0.169116 | + | 0.985596i | \(0.445909\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.11273 | 0.201626 | 0.100813 | − | 0.994905i | \(-0.467856\pi\) | ||||
0.100813 | + | 0.994905i | \(0.467856\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −45.6126 | −1.79599 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −25.7693 | −1.01310 | −0.506548 | − | 0.862212i | \(-0.669079\pi\) | ||||
−0.506548 | + | 0.862212i | \(0.669079\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.04399 | 0.276501 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9.23353 | 0.361890 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −47.8953 | −1.87429 | −0.937145 | − | 0.348941i | \(-0.886541\pi\) | ||||
−0.937145 | + | 0.348941i | \(0.886541\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −16.7581 | −0.654795 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.82687 | −0.188314 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.95601 | −0.348877 | −0.174438 | − | 0.984668i | \(-0.555811\pi\) | ||||
−0.174438 | + | 0.984668i | \(0.555811\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.7993 | −0.420044 | −0.210022 | − | 0.977697i | \(-0.567353\pi\) | ||||
−0.210022 | + | 0.977697i | \(0.567353\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 21.7501 | 0.844703 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.33508 | 0.0517720 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.93649 | −0.229862 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −18.3463 | −0.709307 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.00000 | −0.0772091 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 32.2499 | 1.24314 | 0.621572 | − | 0.783357i | \(-0.286494\pi\) | ||||
0.621572 | + | 0.783357i | \(0.286494\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −12.5522 | −0.483134 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −27.7089 | −1.06494 | −0.532470 | − | 0.846449i | \(-0.678736\pi\) | ||||
−0.532470 | + | 0.846449i | \(0.678736\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.2499 | −0.470109 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.379068 | 0.0145259 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −22.3156 | −0.853881 | −0.426941 | − | 0.904280i | \(-0.640409\pi\) | ||||
−0.426941 | + | 0.904280i | \(0.640409\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 65.4095 | 2.49917 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −24.9424 | −0.951614 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.61259 | −0.0614349 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.1372 | −0.956264 | −0.478132 | − | 0.878288i | \(-0.658686\pi\) | ||||
−0.478132 | + | 0.878288i | \(0.658686\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.00000 | 0.0379869 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 37.7745 | 1.43287 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 64.1760 | 2.43084 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −23.4506 | −0.886985 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19.2747 | −0.727995 | −0.363997 | − | 0.931400i | \(-0.618588\pi\) | ||||
−0.363997 | + | 0.931400i | \(0.618588\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.40665 | −0.0907686 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −33.7693 | −1.27183 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.88727 | 0.183805 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.76098 | 0.366581 | 0.183291 | − | 0.983059i | \(-0.441325\pi\) | ||||
0.183291 | + | 0.983059i | \(0.441325\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.01641 | −0.188130 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −17.2747 | −0.646942 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −13.2939 | −0.497165 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5.07681 | 0.189597 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −14.0276 | −0.523141 | −0.261570 | − | 0.965184i | \(-0.584240\pi\) | ||||
−0.261570 | + | 0.965184i | \(0.584240\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.637339 | 0.0237357 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −19.2939 | −0.717549 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −39.8297 | −1.47924 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 34.3051 | 1.27231 | 0.636153 | − | 0.771563i | \(-0.280525\pi\) | ||||
0.636153 | + | 0.771563i | \(0.280525\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 74.6263 | 2.76016 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10.7581 | −0.397361 | −0.198680 | − | 0.980064i | \(-0.563666\pi\) | ||||
−0.198680 | + | 0.980064i | \(0.563666\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4.18953 | −0.154533 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.66492 | 0.0981637 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.38741 | 0.234965 | 0.117482 | − | 0.993075i | \(-0.462518\pi\) | ||||
0.117482 | + | 0.993075i | \(0.462518\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.01118 | 0.0371466 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 23.1096 | 0.847810 | 0.423905 | − | 0.905707i | \(-0.360659\pi\) | ||||
0.423905 | + | 0.905707i | \(0.360659\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −21.8105 | −0.799074 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.52461 | −0.128959 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.956008 | −0.0349318 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −31.8678 | −1.16287 | −0.581435 | − | 0.813593i | \(-0.697509\pi\) | ||||
−0.581435 | + | 0.813593i | \(0.697509\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 23.8021 | 0.867398 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −26.1843 | −0.952944 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −48.3103 | −1.75587 | −0.877934 | − | 0.478781i | \(-0.841079\pi\) | ||||
−0.877934 | + | 0.478781i | \(0.841079\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.87086 | −0.0679081 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17.8625 | −0.647516 | −0.323758 | − | 0.946140i | \(-0.604946\pi\) | ||||
−0.323758 | + | 0.946140i | \(0.604946\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.61259 | −0.275594 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 28.7170 | 1.03826 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −22.3515 | −0.807065 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −24.8820 | −0.897269 | −0.448635 | − | 0.893715i | \(-0.648090\pi\) | ||||
−0.448635 | + | 0.893715i | \(0.648090\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14.9149 | −0.537145 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −34.9700 | −1.25778 | −0.628892 | − | 0.777492i | \(-0.716491\pi\) | ||||
−0.628892 | + | 0.777492i | \(0.716491\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −115.901 | −4.16329 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.55220 | 0.270933 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.98359 | 0.106898 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.01641 | 0.179501 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.17313 | 0.113398 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −75.9177 | −2.70962 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.1648 | 0.540566 | 0.270283 | − | 0.962781i | \(-0.412883\pi\) | ||||
0.270283 | + | 0.962781i | \(0.412883\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.92319 | 0.104068 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.70892 | −0.274097 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.34625 | 0.225362 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.12914 | −0.0755126 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 8.24470 | 0.292042 | 0.146021 | − | 0.989281i | \(-0.453353\pi\) | ||||
0.146021 | + | 0.989281i | \(0.453353\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 55.2497 | 1.95459 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.74173 | −0.0615410 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.82687 | −0.170337 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.83805 | 0.276255 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −11.9672 | −0.421265 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 29.8433 | 1.04923 | 0.524617 | − | 0.851338i | \(-0.324209\pi\) | ||||
0.524617 | + | 0.851338i | \(0.324209\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16.6321 | 0.584032 | 0.292016 | − | 0.956413i | \(-0.405674\pi\) | ||||
0.292016 | + | 0.956413i | \(0.405674\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −20.3187 | −0.712607 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 11.1648 | 0.391086 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.46944 | 0.121380 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.17313 | −0.110878 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 30.3327 | 1.05862 | 0.529309 | − | 0.848429i | \(-0.322451\pi\) | ||||
0.529309 | + | 0.848429i | \(0.322451\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 18.4067 | 0.641616 | 0.320808 | − | 0.947144i | \(-0.396046\pi\) | ||||
0.320808 | + | 0.947144i | \(0.396046\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −12.5522 | −0.437011 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −45.4559 | −1.58066 | −0.790328 | − | 0.612684i | \(-0.790090\pi\) | ||||
−0.790328 | + | 0.612684i | \(0.790090\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.3463 | −0.706655 | −0.353327 | − | 0.935500i | \(-0.614950\pi\) | ||||
−0.353327 | + | 0.935500i | \(0.614950\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −18.0552 | −0.626327 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.85446 | 0.237493 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 46.6946 | 1.61593 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 9.23353 | 0.319157 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −16.1812 | −0.558637 | −0.279318 | − | 0.960199i | \(-0.590109\pi\) | ||||
−0.279318 | + | 0.960199i | \(0.590109\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.9313 | −0.652802 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −27.2939 | −0.940053 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −12.2806 | −0.422466 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.00000 | 0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 29.8901 | 1.02583 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −14.1291 | −0.484341 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −20.9836 | −0.718465 | −0.359232 | − | 0.933248i | \(-0.616961\pi\) | ||||
−0.359232 | + | 0.933248i | \(0.616961\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.33508 | 0.0456586 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.79095 | 0.163656 | 0.0818279 | − | 0.996646i | \(-0.473924\pi\) | ||||
0.0818279 | + | 0.996646i | \(0.473924\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.96719 | 0.340076 | 0.170038 | − | 0.985438i | \(-0.445611\pi\) | ||||
0.170038 | + | 0.985438i | \(0.445611\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −9.36266 | −0.319079 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −25.5470 | −0.869629 | −0.434814 | − | 0.900520i | \(-0.643186\pi\) | ||||
−0.434814 | + | 0.900520i | \(0.643186\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −104.094 | −3.53929 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −29.9836 | −1.01830 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.01641 | −0.170170 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.45614 | −0.286525 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −12.2499 | −0.414597 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 31.6402 | 1.06963 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −50.9893 | −1.72179 | −0.860893 | − | 0.508787i | \(-0.830094\pi\) | ||||
−0.860893 | + | 0.508787i | \(0.830094\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.34625 | 0.146596 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 32.1895 | 1.08449 | 0.542246 | − | 0.840219i | \(-0.317574\pi\) | ||||
0.542246 | + | 0.840219i | \(0.317574\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −36.6154 | −1.23221 | −0.616104 | − | 0.787665i | \(-0.711290\pi\) | ||||
−0.616104 | + | 0.787665i | \(0.711290\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −29.5110 | −0.992003 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 48.2004 | 1.61841 | 0.809206 | − | 0.587525i | \(-0.199897\pi\) | ||||
0.809206 | + | 0.587525i | \(0.199897\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.49180 | 0.184189 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.56860 | 0.0859550 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 53.4506 | 1.78666 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.93649 | 0.198214 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 29.2992 | 0.977181 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.48346 | 0.116051 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −10.8873 | −0.362306 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −13.5470 | −0.450316 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22.9013 | −0.760425 | −0.380212 | − | 0.924899i | \(-0.624149\pi\) | ||||
−0.380212 | + | 0.924899i | \(0.624149\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.88727 | 0.162101 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 36.0552 | 1.19456 | 0.597281 | − | 0.802032i | \(-0.296248\pi\) | ||||
0.597281 | + | 0.802032i | \(0.296248\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.52461 | −0.116648 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 8.37907 | 0.277003 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.00000 | −0.132092 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 28.3379 | 0.934782 | 0.467391 | − | 0.884051i | \(-0.345194\pi\) | ||||
0.467391 | + | 0.884051i | \(0.345194\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −20.7581 | −0.684004 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −15.9177 | −0.523937 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −94.7966 | −3.11689 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.637339 | 0.0209329 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.08514 | 0.166838 | 0.0834191 | − | 0.996515i | \(-0.473416\pi\) | ||||
0.0834191 | + | 0.996515i | \(0.473416\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.318669 | 0.0104440 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8.00000 | 0.261908 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 28.7170 | 0.939146 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 32.2088 | 1.05222 | 0.526108 | − | 0.850418i | \(-0.323651\pi\) | ||||
0.526108 | + | 0.850418i | \(0.323651\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −8.12914 | −0.265284 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 32.7805 | 1.06861 | 0.534307 | − | 0.845291i | \(-0.320573\pi\) | ||||
0.534307 | + | 0.845291i | \(0.320573\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 17.5163 | 0.570408 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.18953 | −0.136286 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 27.3627 | 0.889167 | 0.444584 | − | 0.895737i | \(-0.353352\pi\) | ||||
0.444584 | + | 0.895737i | \(0.353352\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 15.3163 | 0.497188 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 19.9917 | 0.648274 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −24.6894 | −0.799768 | −0.399884 | − | 0.916566i | \(-0.630950\pi\) | ||||
−0.399884 | + | 0.916566i | \(0.630950\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −87.8765 | −2.84362 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.17313 | 0.102573 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 15.6126 | 0.504157 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 54.2580 | 1.75026 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.956008 | −0.0308069 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.04710 | 0.0337074 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −21.3298 | −0.685922 | −0.342961 | − | 0.939350i | \(-0.611430\pi\) | ||||
−0.342961 | + | 0.939350i | \(0.611430\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.18431 | −0.0701700 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −28.4946 | −0.914436 | −0.457218 | − | 0.889355i | \(-0.651154\pi\) | ||||
−0.457218 | + | 0.889355i | \(0.651154\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.01641 | 0.289053 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 39.8297 | 1.27557 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −19.8157 | −0.633960 | −0.316980 | − | 0.948432i | \(-0.602669\pi\) | ||||
−0.316980 | + | 0.948432i | \(0.602669\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.74173 | −0.0556659 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.61259 | −0.243051 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 53.7745 | 1.71514 | 0.857571 | − | 0.514366i | \(-0.171973\pi\) | ||||
0.857571 | + | 0.514366i | \(0.171973\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 77.5058 | 2.46954 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −8.06040 | −0.256565 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 20.3686 | 0.647684 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −49.7693 | −1.58097 | −0.790487 | − | 0.612479i | \(-0.790173\pi\) | ||||
−0.790487 | + | 0.612479i | \(0.790173\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 17.0164 | 0.539999 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −41.3543 | −1.31102 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.659696 | 0.0208928 | 0.0104464 | − | 0.999945i | \(-0.496675\pi\) | ||||
0.0104464 | + | 0.999945i | \(0.496675\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.55220 | 0.238941 |
(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 | 3696.2.a.bo.1.3 | 3 | ||
4.3 | odd | 2 | 231.2.a.e.1.1 | ✓ | 3 | ||
12.11 | even | 2 | 693.2.a.l.1.3 | 3 | |||
20.19 | odd | 2 | 5775.2.a.bp.1.3 | 3 | |||
28.27 | even | 2 | 1617.2.a.t.1.1 | 3 | |||
44.43 | even | 2 | 2541.2.a.bg.1.3 | 3 | |||
84.83 | odd | 2 | 4851.2.a.bi.1.3 | 3 | |||
132.131 | odd | 2 | 7623.2.a.cd.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
231.2.a.e.1.1 | ✓ | 3 | 4.3 | odd | 2 | ||
693.2.a.l.1.3 | 3 | 12.11 | even | 2 | |||
1617.2.a.t.1.1 | 3 | 28.27 | even | 2 | |||
2541.2.a.bg.1.3 | 3 | 44.43 | even | 2 | |||
3696.2.a.bo.1.3 | 3 | 1.1 | even | 1 | trivial | ||
4851.2.a.bi.1.3 | 3 | 84.83 | odd | 2 | |||
5775.2.a.bp.1.3 | 3 | 20.19 | odd | 2 | |||
7623.2.a.cd.1.1 | 3 | 132.131 | odd | 2 |