Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1140,2,Mod(1,1140)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1140, 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("1140.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1140 = 2^{2} \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1140.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: | \(9.10294583043\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.1524.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 7x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.140435\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1140.1 |
$q$-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 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.98028 | 1.88237 | 0.941184 | − | 0.337894i | \(-0.109715\pi\) | ||||
0.941184 | + | 0.337894i | \(0.109715\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.26115 | −1.58630 | −0.793148 | − | 0.609029i | \(-0.791559\pi\) | ||||
−0.793148 | + | 0.609029i | \(0.791559\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.98028 | 1.93598 | 0.967990 | − | 0.250987i | \(-0.0807552\pi\) | ||||
0.967990 | + | 0.250987i | \(0.0807552\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.280871 | 0.0681212 | 0.0340606 | − | 0.999420i | \(-0.489156\pi\) | ||||
0.0340606 | + | 0.999420i | \(0.489156\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.98028 | −1.08679 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.280871 | 0.0585656 | 0.0292828 | − | 0.999571i | \(-0.490678\pi\) | ||||
0.0292828 | + | 0.999571i | \(0.490678\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.26115 | −0.605580 | −0.302790 | − | 0.953057i | \(-0.597918\pi\) | ||||
−0.302790 | + | 0.953057i | \(0.597918\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.28087 | 0.409656 | 0.204828 | − | 0.978798i | \(-0.434336\pi\) | ||||
0.204828 | + | 0.978798i | \(0.434336\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.26115 | 0.915848 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.98028 | 0.841821 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.98028 | −0.489955 | −0.244977 | − | 0.969529i | \(-0.578781\pi\) | ||||
−0.244977 | + | 0.969529i | \(0.578781\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.98028 | −1.11774 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.738851 | 0.115389 | 0.0576946 | − | 0.998334i | \(-0.481625\pi\) | ||||
0.0576946 | + | 0.998334i | \(0.481625\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.54202 | −0.845150 | −0.422575 | − | 0.906328i | \(-0.638874\pi\) | ||||
−0.422575 | + | 0.906328i | \(0.638874\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.28087 | −0.624429 | −0.312215 | − | 0.950012i | \(-0.601071\pi\) | ||||
−0.312215 | + | 0.950012i | \(0.601071\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 17.8032 | 2.54331 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.280871 | −0.0393298 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.71913 | 0.785583 | 0.392791 | − | 0.919628i | \(-0.371509\pi\) | ||||
0.392791 | + | 0.919628i | \(0.371509\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.26115 | −0.709413 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.00000 | −0.132453 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.5223 | 1.36989 | 0.684943 | − | 0.728596i | \(-0.259827\pi\) | ||||
0.684943 | + | 0.728596i | \(0.259827\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.24143 | −0.286985 | −0.143493 | − | 0.989651i | \(-0.545833\pi\) | ||||
−0.143493 | + | 0.989651i | \(0.545833\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.98028 | 0.627456 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.98028 | 0.865797 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.280871 | −0.0338129 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.5223 | 1.72348 | 0.861740 | − | 0.507350i | \(-0.169375\pi\) | ||||
0.861740 | + | 0.507350i | \(0.169375\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.43826 | 0.636500 | 0.318250 | − | 0.948007i | \(-0.396905\pi\) | ||||
0.318250 | + | 0.948007i | \(0.396905\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −26.2020 | −2.98599 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −16.4829 | −1.85447 | −0.927233 | − | 0.374485i | \(-0.877819\pi\) | ||||
−0.927233 | + | 0.374485i | \(0.877819\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.8032 | 1.18580 | 0.592901 | − | 0.805275i | \(-0.297983\pi\) | ||||
0.592901 | + | 0.805275i | \(0.297983\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.280871 | 0.0304647 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.26115 | 0.349632 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 16.6600 | 1.76595 | 0.882976 | − | 0.469418i | \(-0.155536\pi\) | ||||
0.882976 | + | 0.469418i | \(0.155536\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 34.7637 | 3.64423 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.28087 | −0.236515 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.00000 | 0.102598 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.98028 | 0.302601 | 0.151301 | − | 0.988488i | \(-0.451654\pi\) | ||||
0.151301 | + | 0.988488i | \(0.451654\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.26115 | −0.528765 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.0840 | 1.30191 | 0.650955 | − | 0.759116i | \(-0.274369\pi\) | ||||
0.650955 | + | 0.759116i | \(0.274369\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.56174 | 0.449482 | 0.224741 | − | 0.974419i | \(-0.427846\pi\) | ||||
0.224741 | + | 0.974419i | \(0.427846\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.98028 | −0.486025 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −16.0000 | −1.54678 | −0.773389 | − | 0.633932i | \(-0.781440\pi\) | ||||
−0.773389 | + | 0.633932i | \(0.781440\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.52230 | −0.433158 | −0.216579 | − | 0.976265i | \(-0.569490\pi\) | ||||
−0.216579 | + | 0.976265i | \(0.569490\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.98028 | 0.282875 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.241427 | −0.0227115 | −0.0113557 | − | 0.999936i | \(-0.503615\pi\) | ||||
−0.0113557 | + | 0.999936i | \(0.503615\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.280871 | 0.0261913 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.98028 | 0.645327 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.39881 | 0.128229 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 16.6797 | 1.51634 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.738851 | −0.0666200 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.00000 | 0.354943 | 0.177471 | − | 0.984126i | \(-0.443208\pi\) | ||||
0.177471 | + | 0.984126i | \(0.443208\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.54202 | 0.487948 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.7834 | −1.37901 | −0.689503 | − | 0.724283i | \(-0.742171\pi\) | ||||
−0.689503 | + | 0.724283i | \(0.742171\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.98028 | 0.431845 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.00000 | −0.512615 | −0.256307 | − | 0.966595i | \(-0.582506\pi\) | ||||
−0.256307 | + | 0.966595i | \(0.582506\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.5223 | −0.892490 | −0.446245 | − | 0.894911i | \(-0.647239\pi\) | ||||
−0.446245 | + | 0.894911i | \(0.647239\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.28087 | 0.360514 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −36.7243 | −3.07104 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.26115 | −0.270824 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −17.8032 | −1.46838 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.43826 | −0.445519 | −0.222760 | − | 0.974873i | \(-0.571507\pi\) | ||||
−0.222760 | + | 0.974873i | \(0.571507\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.2020 | −1.15574 | −0.577870 | − | 0.816128i | \(-0.696116\pi\) | ||||
−0.577870 | + | 0.816128i | \(0.696116\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.280871 | 0.0227071 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.28087 | 0.183204 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.3988 | −1.22896 | −0.614480 | − | 0.788933i | \(-0.710634\pi\) | ||||
−0.614480 | + | 0.788933i | \(0.710634\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.71913 | −0.453556 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.39881 | 0.110242 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −18.9408 | −1.48356 | −0.741780 | − | 0.670643i | \(-0.766018\pi\) | ||||
−0.741780 | + | 0.670643i | \(0.766018\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.26115 | 0.409580 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.6797 | 0.903801 | 0.451901 | − | 0.892068i | \(-0.350746\pi\) | ||||
0.451901 | + | 0.892068i | \(0.350746\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 35.7243 | 2.74802 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.00000 | 0.0764719 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −16.2414 | −1.23481 | −0.617406 | − | 0.786644i | \(-0.711817\pi\) | ||||
−0.617406 | + | 0.786644i | \(0.711817\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.98028 | 0.376474 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −10.5223 | −0.790904 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −21.9606 | −1.64141 | −0.820705 | − | 0.571353i | \(-0.806419\pi\) | ||||
−0.820705 | + | 0.571353i | \(0.806419\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19.9606 | 1.48366 | 0.741828 | − | 0.670590i | \(-0.233959\pi\) | ||||
0.741828 | + | 0.670590i | \(0.233959\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.24143 | 0.165691 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.98028 | −0.219114 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.47770 | −0.108060 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.98028 | −0.362262 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −19.2217 | −1.39083 | −0.695417 | − | 0.718607i | \(-0.744780\pi\) | ||||
−0.695417 | + | 0.718607i | \(0.744780\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.41854 | −0.462016 | −0.231008 | − | 0.972952i | \(-0.574202\pi\) | ||||
−0.231008 | + | 0.972952i | \(0.574202\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6.98028 | −0.499868 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −16.2809 | −1.15996 | −0.579982 | − | 0.814629i | \(-0.696940\pi\) | ||||
−0.579982 | + | 0.814629i | \(0.696940\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −25.3988 | −1.80047 | −0.900237 | − | 0.435400i | \(-0.856607\pi\) | ||||
−0.900237 | + | 0.435400i | \(0.856607\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −16.2414 | −1.13992 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.738851 | 0.0516036 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.280871 | 0.0195219 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.26115 | −0.363921 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 27.3594 | 1.88350 | 0.941748 | − | 0.336318i | \(-0.109182\pi\) | ||||
0.941748 | + | 0.336318i | \(0.109182\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −14.5223 | −0.995051 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.54202 | −0.377963 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 11.3594 | 0.771124 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.43826 | −0.367483 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.96056 | 0.131881 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.56174 | 0.305477 | 0.152738 | − | 0.988267i | \(-0.451191\pi\) | ||||
0.152738 | + | 0.988267i | \(0.451191\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 20.7243 | 1.37552 | 0.687759 | − | 0.725939i | \(-0.258594\pi\) | ||||
0.687759 | + | 0.725939i | \(0.258594\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.32031 | −0.153331 | −0.0766654 | − | 0.997057i | \(-0.524427\pi\) | ||||
−0.0766654 | + | 0.997057i | \(0.524427\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 26.2020 | 1.72396 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 23.6063 | 1.54650 | 0.773251 | − | 0.634100i | \(-0.218629\pi\) | ||||
0.773251 | + | 0.634100i | \(0.218629\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.28087 | −0.279253 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 16.4829 | 1.07068 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −16.6994 | −1.08019 | −0.540097 | − | 0.841603i | \(-0.681613\pi\) | ||||
−0.540097 | + | 0.841603i | \(0.681613\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.00000 | −0.128831 | −0.0644157 | − | 0.997923i | \(-0.520518\pi\) | ||||
−0.0644157 | + | 0.997923i | \(0.520518\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 17.8032 | 1.13740 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.98028 | 0.444144 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −10.8032 | −0.684623 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.1377 | −0.766123 | −0.383061 | − | 0.923723i | \(-0.625130\pi\) | ||||
−0.383061 | + | 0.923723i | \(0.625130\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.47770 | −0.0929024 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.280871 | −0.0175888 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.80317 | 0.549127 | 0.274563 | − | 0.961569i | \(-0.411467\pi\) | ||||
0.274563 | + | 0.961569i | \(0.411467\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −14.8426 | −0.922275 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.26115 | −0.201860 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.1179 | 0.808887 | 0.404444 | − | 0.914563i | \(-0.367465\pi\) | ||||
0.404444 | + | 0.914563i | \(0.367465\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.71913 | 0.351323 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −16.6600 | −1.01957 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.2217 | 0.806142 | 0.403071 | − | 0.915169i | \(-0.367943\pi\) | ||||
0.403071 | + | 0.915169i | \(0.367943\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.9606 | 1.33401 | 0.667004 | − | 0.745054i | \(-0.267576\pi\) | ||||
0.667004 | + | 0.745054i | \(0.267576\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −34.7637 | −2.10400 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.26115 | −0.317259 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −19.6063 | −1.17803 | −0.589015 | − | 0.808122i | \(-0.700484\pi\) | ||||
−0.589015 | + | 0.808122i | \(0.700484\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.28087 | 0.136552 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.78345 | −0.345011 | −0.172506 | − | 0.985009i | \(-0.555186\pi\) | ||||
−0.172506 | + | 0.985009i | \(0.555186\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.418536 | 0.0248794 | 0.0124397 | − | 0.999923i | \(-0.496040\pi\) | ||||
0.0124397 | + | 0.999923i | \(0.496040\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.00000 | −0.0592349 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.67969 | 0.217205 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9211 | −0.995360 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.98028 | −0.174707 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 24.2414 | 1.41620 | 0.708100 | − | 0.706113i | \(-0.249553\pi\) | ||||
0.708100 | + | 0.706113i | \(0.249553\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.5223 | 0.612632 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.26115 | 0.305283 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.96056 | 0.113382 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −27.6008 | −1.59088 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −13.0840 | −0.751658 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.24143 | −0.128344 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.39881 | −0.536419 | −0.268209 | − | 0.963361i | \(-0.586432\pi\) | ||||
−0.268209 | + | 0.963361i | \(0.586432\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.56174 | −0.259508 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −19.2217 | −1.08996 | −0.544981 | − | 0.838448i | \(-0.683463\pi\) | ||||
−0.544981 | + | 0.838448i | \(0.683463\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −31.9606 | −1.80652 | −0.903259 | − | 0.429096i | \(-0.858832\pi\) | ||||
−0.903259 | + | 0.429096i | \(0.858832\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.98028 | 0.280607 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.71913 | −0.545881 | −0.272940 | − | 0.962031i | \(-0.587996\pi\) | ||||
−0.272940 | + | 0.962031i | \(0.587996\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 17.1574 | 0.960629 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 16.0000 | 0.893033 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.280871 | 0.0156281 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.98028 | 0.387196 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.52230 | 0.250084 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −21.3199 | −1.17541 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.2020 | −1.00047 | −0.500236 | − | 0.865889i | \(-0.666753\pi\) | ||||
−0.500236 | + | 0.865889i | \(0.666753\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.98028 | −0.163318 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.37909 | −0.456438 | −0.228219 | − | 0.973610i | \(-0.573290\pi\) | ||||
−0.228219 | + | 0.973610i | \(0.573290\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.241427 | 0.0131125 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.0000 | −0.649836 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 53.8028 | 2.90508 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.280871 | −0.0151216 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −29.6008 | −1.58905 | −0.794527 | − | 0.607229i | \(-0.792281\pi\) | ||||
−0.794527 | + | 0.607229i | \(0.792281\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.0446 | 0.591204 | 0.295602 | − | 0.955311i | \(-0.404480\pi\) | ||||
0.295602 | + | 0.955311i | \(0.404480\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.98028 | −0.372580 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −19.0446 | −1.01364 | −0.506821 | − | 0.862051i | \(-0.669179\pi\) | ||||
−0.506821 | + | 0.862051i | \(0.669179\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 14.5223 | 0.770764 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.39881 | −0.0740331 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 29.7440 | 1.56983 | 0.784914 | − | 0.619604i | \(-0.212707\pi\) | ||||
0.784914 | + | 0.619604i | \(0.212707\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −16.6797 | −0.875456 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.43826 | 0.284651 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 27.5026 | 1.43562 | 0.717811 | − | 0.696238i | \(-0.245144\pi\) | ||||
0.717811 | + | 0.696238i | \(0.245144\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.738851 | 0.0384631 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 28.4829 | 1.47876 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.4580 | −0.852162 | −0.426081 | − | 0.904685i | \(-0.640106\pi\) | ||||
−0.426081 | + | 0.904685i | \(0.640106\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −22.7637 | −1.17239 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.84261 | 0.146015 | 0.0730076 | − | 0.997331i | \(-0.476740\pi\) | ||||
0.0730076 | + | 0.997331i | \(0.476740\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.00000 | −0.204926 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 15.4383 | 0.788858 | 0.394429 | − | 0.918926i | \(-0.370942\pi\) | ||||
0.394429 | + | 0.918926i | \(0.370942\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −26.2020 | −1.33538 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.54202 | −0.281717 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.4829 | −0.937118 | −0.468559 | − | 0.883432i | \(-0.655227\pi\) | ||||
−0.468559 | + | 0.883432i | \(0.655227\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.0788884 | 0.00398956 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 15.7834 | 0.796170 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −16.4829 | −0.829342 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −34.9657 | −1.75488 | −0.877439 | − | 0.479688i | \(-0.840750\pi\) | ||||
−0.877439 | + | 0.479688i | \(0.840750\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.98028 | −0.249326 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 19.8229 | 0.989908 | 0.494954 | − | 0.868919i | \(-0.335185\pi\) | ||||
0.494954 | + | 0.868919i | \(0.335185\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 15.9211 | 0.793087 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 15.6797 | 0.777213 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.64578 | −0.476953 | −0.238477 | − | 0.971148i | \(-0.576648\pi\) | ||||
−0.238477 | + | 0.971148i | \(0.576648\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.00000 | 0.295958 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 52.4040 | 2.57863 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.8032 | 0.530307 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 10.5223 | 0.515279 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.65996 | 0.325360 | 0.162680 | − | 0.986679i | \(-0.447986\pi\) | ||||
0.162680 | + | 0.986679i | \(0.447986\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.0000 | 0.487370 | 0.243685 | − | 0.969854i | \(-0.421644\pi\) | ||||
0.243685 | + | 0.969854i | \(0.421644\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.28087 | −0.208143 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.280871 | 0.0136242 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −11.1629 | −0.540212 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 36.7243 | 1.77306 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −20.8371 | −1.00369 | −0.501843 | − | 0.864959i | \(-0.667345\pi\) | ||||
−0.501843 | + | 0.864959i | \(0.667345\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.58146 | 0.460456 | 0.230228 | − | 0.973137i | \(-0.426053\pi\) | ||||
0.230228 | + | 0.973137i | \(0.426053\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.26115 | 0.156360 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.280871 | 0.0134359 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.04459 | 0.240765 | 0.120383 | − | 0.992728i | \(-0.461588\pi\) | ||||
0.120383 | + | 0.992728i | \(0.461588\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 17.8032 | 0.847770 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 31.6402 | 1.50327 | 0.751637 | − | 0.659577i | \(-0.229265\pi\) | ||||
0.751637 | + | 0.659577i | \(0.229265\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 16.6600 | 0.789758 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.43826 | 0.257221 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7.82289 | −0.369185 | −0.184593 | − | 0.982815i | \(-0.559097\pi\) | ||||
−0.184593 | + | 0.982815i | \(0.559097\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.88721 | −0.183041 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 14.2020 | 0.667267 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 34.7637 | 1.62975 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.4777 | −0.724016 | −0.362008 | − | 0.932175i | \(-0.617909\pi\) | ||||
−0.362008 | + | 0.932175i | \(0.617909\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.280871 | −0.0131099 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.92111 | 0.462072 | 0.231036 | − | 0.972945i | \(-0.425788\pi\) | ||||
0.231036 | + | 0.972945i | \(0.425788\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −21.4631 | −0.997476 | −0.498738 | − | 0.866753i | \(-0.666203\pi\) | ||||
−0.498738 | + | 0.866753i | \(0.666203\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.28087 | −0.105773 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −32.7637 | −1.51612 | −0.758062 | − | 0.652182i | \(-0.773854\pi\) | ||||
−0.758062 | + | 0.652182i | \(0.773854\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 15.3988 | 0.709540 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 29.1574 | 1.34066 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.00000 | 0.0458831 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.71913 | 0.261861 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −27.7834 | −1.26946 | −0.634729 | − | 0.772735i | \(-0.718888\pi\) | ||||
−0.634729 | + | 0.772735i | \(0.718888\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20.8032 | −0.948543 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.39881 | −0.0636483 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.98028 | 0.135327 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −29.3199 | −1.32861 | −0.664306 | − | 0.747460i | \(-0.731273\pi\) | ||||
−0.664306 | + | 0.747460i | \(0.731273\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 18.9408 | 0.856534 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.69941 | 0.212081 | 0.106041 | − | 0.994362i | \(-0.466183\pi\) | ||||
0.106041 | + | 0.994362i | \(0.466183\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.915961 | −0.0412528 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.26115 | −0.236471 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 72.3251 | 3.24422 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 30.4434 | 1.36283 | 0.681417 | − | 0.731895i | \(-0.261364\pi\) | ||||
0.681417 | + | 0.731895i | \(0.261364\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −11.6797 | −0.521810 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −13.6797 | −0.609947 | −0.304974 | − | 0.952361i | \(-0.598648\pi\) | ||||
−0.304974 | + | 0.952361i | \(0.598648\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.0840 | 0.582232 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −35.7243 | −1.58657 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −17.7046 | −0.784741 | −0.392370 | − | 0.919807i | \(-0.628345\pi\) | ||||
−0.392370 | + | 0.919807i | \(0.628345\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 27.0840 | 1.19813 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.00000 | −0.0441511 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.56174 | 0.201014 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 22.5223 | 0.990530 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 16.2414 | 0.712919 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.30059 | −0.407466 | −0.203733 | − | 0.979026i | \(-0.565308\pi\) | ||||
−0.203733 | + | 0.979026i | \(0.565308\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.64578 | 0.334327 | 0.167163 | − | 0.985929i | \(-0.446539\pi\) | ||||
0.167163 | + | 0.985929i | \(0.446539\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.98028 | −0.217357 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.640630 | 0.0279063 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9211 | −0.996570 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.5223 | 0.456629 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.15739 | 0.223391 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −16.0000 | −0.691740 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 21.9606 | 0.947668 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −93.6651 | −4.03444 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.8765 | −0.553605 | −0.276802 | − | 0.960927i | \(-0.589275\pi\) | ||||
−0.276802 | + | 0.960927i | \(0.589275\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −19.9606 | −0.856589 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.52230 | −0.193714 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.4777 | 0.576265 | 0.288132 | − | 0.957591i | \(-0.406966\pi\) | ||||
0.288132 | + | 0.957591i | \(0.406966\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.24143 | −0.0956618 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.26115 | −0.138930 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −82.0892 | −3.49079 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.98028 | 0.126506 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.68522 | −0.156148 | −0.0780740 | − | 0.996948i | \(-0.524877\pi\) | ||||
−0.0780740 | + | 0.996948i | \(0.524877\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −38.6848 | −1.63619 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.47770 | 0.0623887 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12.7243 | 0.536264 | 0.268132 | − | 0.963382i | \(-0.413594\pi\) | ||||
0.268132 | + | 0.963382i | \(0.413594\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.241427 | −0.0101569 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.98028 | 0.209152 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 25.3006 | 1.06066 | 0.530328 | − | 0.847793i | \(-0.322069\pi\) | ||||
0.530328 | + | 0.847793i | \(0.322069\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23.0052 | 0.962736 | 0.481368 | − | 0.876519i | \(-0.340140\pi\) | ||||
0.481368 | + | 0.876519i | \(0.340140\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 19.2217 | 0.802998 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.280871 | 0.0117131 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −25.0840 | −1.04426 | −0.522131 | − | 0.852865i | \(-0.674863\pi\) | ||||
−0.522131 | + | 0.852865i | \(0.674863\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.41854 | 0.266745 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 53.8028 | 2.23212 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −30.0892 | −1.24617 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6.98028 | 0.288599 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −28.6848 | −1.18395 | −0.591975 | − | 0.805956i | \(-0.701652\pi\) | ||||
−0.591975 | + | 0.805956i | \(0.701652\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.28087 | 0.0939816 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 16.2809 | 0.669706 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.56174 | 0.105198 | 0.0525991 | − | 0.998616i | \(-0.483249\pi\) | ||||
0.0525991 | + | 0.998616i | \(0.483249\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.39881 | 0.0573458 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 25.3988 | 1.03950 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 33.0446 | 1.35017 | 0.675083 | − | 0.737742i | \(-0.264108\pi\) | ||||
0.675083 | + | 0.737742i | \(0.264108\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.8371 | −0.931544 | −0.465772 | − | 0.884905i | \(-0.654223\pi\) | ||||
−0.465772 | + | 0.884905i | \(0.654223\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 16.6797 | 0.678126 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −28.1286 | −1.14171 | −0.570853 | − | 0.821052i | \(-0.693387\pi\) | ||||
−0.570853 | + | 0.821052i | \(0.693387\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 16.2414 | 0.658136 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −29.8817 | −1.20888 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.9606 | 0.644641 | 0.322320 | − | 0.946631i | \(-0.395537\pi\) | ||||
0.322320 | + | 0.946631i | \(0.395537\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.738851 | −0.0297934 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.59565 | −0.265531 | −0.132765 | − | 0.991147i | \(-0.542386\pi\) | ||||
−0.132765 | + | 0.991147i | \(0.542386\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 33.8817 | 1.36182 | 0.680910 | − | 0.732367i | \(-0.261585\pi\) | ||||
0.680910 | + | 0.732367i | \(0.261585\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.280871 | −0.0112710 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 82.9712 | 3.32417 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.26115 | 0.210110 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.837073 | −0.0333763 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.7976 | 1.06680 | 0.533398 | − | 0.845864i | \(-0.320915\pi\) | ||||
0.533398 | + | 0.845864i | \(0.320915\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −27.3594 | −1.08744 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.00000 | 0.158735 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 124.271 | 4.92380 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 14.5223 | 0.574493 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 25.7834 | 1.01838 | 0.509192 | − | 0.860653i | \(-0.329944\pi\) | ||||
0.509192 | + | 0.860653i | \(0.329944\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −19.4237 | −0.765995 | −0.382998 | − | 0.923749i | \(-0.625108\pi\) | ||||
−0.382998 | + | 0.923749i | \(0.625108\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.54202 | 0.218217 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8.55620 | −0.336379 | −0.168190 | − | 0.985755i | \(-0.553792\pi\) | ||||
−0.168190 | + | 0.985755i | \(0.553792\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −55.3594 | −2.17305 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −11.3594 | −0.445209 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −0.842612 | −0.0329740 | −0.0164870 | − | 0.999864i | \(-0.505248\pi\) | ||||
−0.0164870 | + | 0.999864i | \(0.505248\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −15.7834 | −0.616710 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5.43826 | 0.212167 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.43826 | −0.133936 | −0.0669678 | − | 0.997755i | \(-0.521332\pi\) | ||||
−0.0669678 | + | 0.997755i | \(0.521332\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.08404 | 0.353328 | 0.176664 | − | 0.984271i | \(-0.443469\pi\) | ||||
0.176664 | + | 0.984271i | \(0.443469\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.96056 | −0.0761417 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.98028 | 0.193127 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.915961 | −0.0354662 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4.56174 | −0.176367 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.7925 | 0.455244 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.98028 | 0.114881 | 0.0574406 | − | 0.998349i | \(-0.481706\pi\) | ||||
0.0574406 | + | 0.998349i | \(0.481706\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −48.9996 | −1.88321 | −0.941604 | − | 0.336722i | \(-0.890682\pi\) | ||||
−0.941604 | + | 0.336722i | \(0.890682\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 14.8426 | 0.569607 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −20.7243 | −0.794156 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 27.9211 | 1.06837 | 0.534186 | − | 0.845367i | \(-0.320618\pi\) | ||||
0.534186 | + | 0.845367i | \(0.320618\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.00000 | −0.229248 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.32031 | 0.0885255 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 39.9211 | 1.52087 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.96056 | −0.378917 | −0.189459 | − | 0.981889i | \(-0.560673\pi\) | ||||
−0.189459 | + | 0.981889i | \(0.560673\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −26.2020 | −0.995331 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −10.5223 | −0.399133 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.207522 | 0.00786045 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −23.6063 | −0.892874 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10.4829 | −0.395932 | −0.197966 | − | 0.980209i | \(-0.563434\pi\) | ||||
−0.197966 | + | 0.980209i | \(0.563434\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.98028 | −0.112403 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.28087 | 0.161227 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 65.1621 | 2.45067 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.5562 | 0.621781 | 0.310891 | − | 0.950446i | \(-0.399373\pi\) | ||||
0.310891 | + | 0.950446i | \(0.399373\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −16.4829 | −0.618155 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.640630 | 0.0239918 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −36.7243 | −1.37341 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 16.6994 | 0.623651 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4.21655 | −0.157251 | −0.0786255 | − | 0.996904i | \(-0.525053\pi\) | ||||
−0.0786255 | + | 0.996904i | \(0.525053\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 22.7187 | 0.846090 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.00000 | 0.0743808 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.26115 | −0.121116 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26.4580 | 0.981272 | 0.490636 | − | 0.871365i | \(-0.336764\pi\) | ||||
0.490636 | + | 0.871365i | \(0.336764\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.55659 | −0.0575726 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.56174 | −0.242363 | −0.121182 | − | 0.992630i | \(-0.538668\pi\) | ||||
−0.121182 | + | 0.992630i | \(0.538668\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −17.8032 | −0.656680 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 44.9657 | 1.65409 | 0.827045 | − | 0.562136i | \(-0.190020\pi\) | ||||
0.827045 | + | 0.562136i | \(0.190020\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.98028 | −0.256427 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −24.4040 | −0.895295 | −0.447647 | − | 0.894210i | \(-0.647738\pi\) | ||||
−0.447647 | + | 0.894210i | \(0.647738\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.43826 | −0.199242 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 10.8032 | 0.395267 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −79.6844 | −2.91161 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.23628 | 0.191074 | 0.0955372 | − | 0.995426i | \(-0.469543\pi\) | ||||
0.0955372 | + | 0.995426i | \(0.469543\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 12.1377 | 0.442321 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −14.2020 | −0.516863 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20.5223 | 0.745896 | 0.372948 | − | 0.927852i | \(-0.378347\pi\) | ||||
0.372948 | + | 0.927852i | \(0.378347\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.47770 | 0.0536372 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13.5171 | −0.489996 | −0.244998 | − | 0.969524i | \(-0.578787\pi\) | ||||
−0.244998 | + | 0.969524i | \(0.578787\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −22.5223 | −0.815362 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.280871 | 0.0101549 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 73.4486 | 2.65207 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 33.9211 | 1.22323 | 0.611613 | − | 0.791157i | \(-0.290521\pi\) | ||||
0.611613 | + | 0.791157i | \(0.290521\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.80317 | −0.317038 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −5.79802 | −0.208540 | −0.104270 | − | 0.994549i | \(-0.533251\pi\) | ||||
−0.104270 | + | 0.994549i | \(0.533251\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.28087 | 0.0819313 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 14.8426 | 0.532476 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.738851 | 0.0264721 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −76.4040 | −2.73395 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.26115 | 0.116544 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −15.3988 | −0.549607 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.5669 | 0.412315 | 0.206158 | − | 0.978519i | \(-0.433904\pi\) | ||||
0.206158 | + | 0.978519i | \(0.433904\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −13.1179 | −0.467011 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.20237 | −0.0427514 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −15.6458 | −0.555598 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.71913 | −0.202837 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −17.3649 | −0.615097 | −0.307548 | − | 0.951532i | \(-0.599509\pi\) | ||||
−0.307548 | + | 0.951532i | \(0.599509\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.20237 | −0.0425368 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 16.6600 | 0.588651 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −28.6115 | −1.00968 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.39881 | 0.0493017 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −13.2217 | −0.465426 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 26.4829 | 0.931088 | 0.465544 | − | 0.885025i | \(-0.345859\pi\) | ||||
0.465544 | + | 0.885025i | \(0.345859\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 35.8422 | 1.25859 | 0.629295 | − | 0.777166i | \(-0.283344\pi\) | ||||
0.629295 | + | 0.777166i | \(0.283344\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −21.9606 | −0.770190 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −18.9408 | −0.663468 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.54202 | −0.193891 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 34.7637 | 1.21474 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12.5223 | −0.437031 | −0.218516 | − | 0.975833i | \(-0.570121\pi\) | ||||
−0.218516 | + | 0.975833i | \(0.570121\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.06432 | 0.141673 | 0.0708366 | − | 0.997488i | \(-0.477433\pi\) | ||||
0.0708366 | + | 0.997488i | \(0.477433\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5.26115 | 0.183170 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −33.8478 | −1.17700 | −0.588501 | − | 0.808496i | \(-0.700282\pi\) | ||||
−0.588501 | + | 0.808496i | \(0.700282\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.08404 | −0.315502 | −0.157751 | − | 0.987479i | \(-0.550424\pi\) | ||||
−0.157751 | + | 0.987479i | \(0.550424\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 19.6063 | 0.680136 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.00039 | 0.173253 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 11.6797 | 0.404192 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.28087 | −0.0788384 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 12.2753 | 0.423792 | 0.211896 | − | 0.977292i | \(-0.432036\pi\) | ||||
0.211896 | + | 0.977292i | \(0.432036\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.3649 | −0.633273 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.78345 | 0.199192 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 35.7243 | 1.22895 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 83.0695 | 2.85430 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.418536 | −0.0143641 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.837073 | −0.0286945 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −11.4777 | −0.392989 | −0.196495 | − | 0.980505i | \(-0.562956\pi\) | ||||
−0.196495 | + | 0.980505i | \(0.562956\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.00000 | 0.0341993 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −46.7637 | −1.59742 | −0.798709 | − | 0.601717i | \(-0.794483\pi\) | ||||
−0.798709 | + | 0.601717i | \(0.794483\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 30.7298 | 1.04849 | 0.524244 | − | 0.851568i | \(-0.324348\pi\) | ||||
0.524244 | + | 0.851568i | \(0.324348\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.67969 | −0.125403 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 44.0000 | 1.49778 | 0.748889 | − | 0.662696i | \(-0.230588\pi\) | ||||
0.748889 | + | 0.662696i | \(0.230588\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −16.2414 | −0.552225 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 16.9211 | 0.574671 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 86.7187 | 2.94173 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.98028 | 0.100867 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.98028 | 0.168364 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −31.1878 | −1.05314 | −0.526569 | − | 0.850133i | \(-0.676522\pi\) | ||||
−0.526569 | + | 0.850133i | \(0.676522\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −24.2414 | −0.817643 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.56689 | 0.0527899 | 0.0263950 | − | 0.999652i | \(-0.491597\pi\) | ||||
0.0263950 | + | 0.999652i | \(0.491597\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −36.0643 | −1.21366 | −0.606830 | − | 0.794831i | \(-0.707559\pi\) | ||||
−0.606830 | + | 0.794831i | \(0.707559\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −10.5223 | −0.353703 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −9.12348 | −0.306337 | −0.153168 | − | 0.988200i | \(-0.548948\pi\) | ||||
−0.153168 | + | 0.988200i | \(0.548948\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 19.9211 | 0.668133 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.26115 | −0.176255 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.28087 | −0.143254 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −21.9606 | −0.734060 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.96056 | −0.0654611 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7.43826 | −0.248080 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.60634 | 0.0535148 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 27.6008 | 0.918497 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 19.9606 | 0.663511 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −15.7136 | −0.521761 | −0.260881 | − | 0.965371i | \(-0.584013\pi\) | ||||
−0.260881 | + | 0.965371i | \(0.584013\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 13.0840 | 0.433970 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −47.3594 | −1.56909 | −0.784543 | − | 0.620074i | \(-0.787102\pi\) | ||||
−0.784543 | + | 0.620074i | \(0.787102\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −56.8371 | −1.88103 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.24143 | 0.0740993 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −78.6059 | −2.59580 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24.4829 | 0.807615 | 0.403807 | − | 0.914844i | \(-0.367687\pi\) | ||||
0.403807 | + | 0.914844i | \(0.367687\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.39881 | 0.309701 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 101.370 | 3.33662 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.98028 | −0.0979909 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.56174 | 0.149827 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 51.3988 | 1.68634 | 0.843170 | − | 0.537647i | \(-0.180687\pi\) | ||||
0.843170 | + | 0.537647i | \(0.180687\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 17.8032 | 0.583475 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 19.2217 | 0.629290 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.47770 | −0.0483260 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21.5669 | 0.704560 | 0.352280 | − | 0.935895i | \(-0.385407\pi\) | ||||
0.352280 | + | 0.935895i | \(0.385407\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 31.9606 | 1.04299 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −28.8675 | −0.941053 | −0.470527 | − | 0.882386i | \(-0.655936\pi\) | ||||
−0.470527 | + | 0.882386i | \(0.655936\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.207522 | 0.00675784 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.98028 | −0.162008 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 26.2414 | 0.852732 | 0.426366 | − | 0.904551i | \(-0.359794\pi\) | ||||
0.426366 | + | 0.904551i | \(0.359794\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 37.9606 | 1.23225 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.71913 | 0.315164 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −47.0391 | −1.52374 | −0.761872 | − | 0.647727i | \(-0.775720\pi\) | ||||
−0.761872 | + | 0.647727i | \(0.775720\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −19.2217 | −0.622000 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −17.1574 | −0.554620 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −29.8817 | −0.964929 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.7976 | −0.832182 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −16.0000 | −0.515593 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −6.41854 | −0.206620 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −53.9460 | −1.73479 | −0.867393 | − | 0.497624i | \(-0.834206\pi\) | ||||
−0.867393 | + | 0.497624i | \(0.834206\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.280871 | −0.00902287 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −13.6852 | −0.439180 | −0.219590 | − | 0.975592i | \(-0.570472\pi\) | ||||
−0.219590 | + | 0.975592i | \(0.570472\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −52.4040 | −1.67999 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6.98028 | −0.223548 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 50.6848 | 1.62155 | 0.810776 | − | 0.585357i | \(-0.199046\pi\) | ||||
0.810776 | + | 0.585357i | \(0.199046\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −87.6505 | −2.80132 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.52230 | −0.144386 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.19683 | 0.101963 | 0.0509816 | − | 0.998700i | \(-0.483765\pi\) | ||||
0.0509816 | + | 0.998700i | \(0.483765\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −16.2809 | −0.518752 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 21.3199 | 0.678621 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.55659 | −0.0494967 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.04459 | 0.160247 | 0.0801234 | − | 0.996785i | \(-0.474469\pi\) | ||||
0.0801234 | + | 0.996785i | \(0.474469\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 18.2020 | 0.577622 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −25.3988 | −0.805197 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.64578 | −0.0521224 | −0.0260612 | − | 0.999660i | \(-0.508296\pi\) | ||||
−0.0260612 | + | 0.999660i | \(0.508296\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.98028 | 0.0942918 |
(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 | 1140.2.a.f.1.3 | ✓ | 3 | |
3.2 | odd | 2 | 3420.2.a.k.1.3 | 3 | |||
4.3 | odd | 2 | 4560.2.a.bu.1.1 | 3 | |||
5.2 | odd | 4 | 5700.2.f.p.3649.6 | 6 | |||
5.3 | odd | 4 | 5700.2.f.p.3649.1 | 6 | |||
5.4 | even | 2 | 5700.2.a.z.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1140.2.a.f.1.3 | ✓ | 3 | 1.1 | even | 1 | trivial | |
3420.2.a.k.1.3 | 3 | 3.2 | odd | 2 | |||
4560.2.a.bu.1.1 | 3 | 4.3 | odd | 2 | |||
5700.2.a.z.1.1 | 3 | 5.4 | even | 2 | |||
5700.2.f.p.3649.1 | 6 | 5.3 | odd | 4 | |||
5700.2.f.p.3649.6 | 6 | 5.2 | odd | 4 |