Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9200,2,Mod(1,9200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9200, 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("9200.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9200 = 2^{4} \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9200.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: | \(73.4623698596\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.521397.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 9x^{3} - 3x^{2} + 18x + 12 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 4600) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-0.794805\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9200.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.794805 | 0.458881 | 0.229440 | − | 0.973323i | \(-0.426310\pi\) | ||||
0.229440 | + | 0.973323i | \(0.426310\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.47193 | −0.934303 | −0.467152 | − | 0.884177i | \(-0.654720\pi\) | ||||
−0.467152 | + | 0.884177i | \(0.654720\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.36829 | −0.789428 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.29993 | 0.693455 | 0.346728 | − | 0.937966i | \(-0.387293\pi\) | ||||
0.346728 | + | 0.937966i | \(0.387293\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.84022 | −1.06509 | −0.532543 | − | 0.846403i | \(-0.678763\pi\) | ||||
−0.532543 | + | 0.846403i | \(0.678763\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.74682 | −1.87888 | −0.939440 | − | 0.342713i | \(-0.888654\pi\) | ||||
−0.939440 | + | 0.342713i | \(0.888654\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.29993 | 0.527640 | 0.263820 | − | 0.964572i | \(-0.415017\pi\) | ||||
0.263820 | + | 0.964572i | \(0.415017\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.96471 | −0.428734 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.26674 | −0.821134 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.28380 | 0.981177 | 0.490589 | − | 0.871391i | \(-0.336782\pi\) | ||||
0.490589 | + | 0.871391i | \(0.336782\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.40148 | 1.14974 | 0.574870 | − | 0.818245i | \(-0.305053\pi\) | ||||
0.574870 | + | 0.818245i | \(0.305053\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.82800 | 0.318213 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.56457 | 1.40801 | 0.704003 | − | 0.710197i | \(-0.251394\pi\) | ||||
0.704003 | + | 0.710197i | \(0.251394\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.05223 | −0.488747 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.27699 | 0.667954 | 0.333977 | − | 0.942581i | \(-0.391609\pi\) | ||||
0.333977 | + | 0.942581i | \(0.391609\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.88954 | 0.288152 | 0.144076 | − | 0.989567i | \(-0.453979\pi\) | ||||
0.144076 | + | 0.989567i | \(0.453979\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −12.3432 | −1.80045 | −0.900223 | − | 0.435428i | \(-0.856597\pi\) | ||||
−0.900223 | + | 0.435428i | \(0.856597\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.889540 | −0.127077 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.15721 | −0.862182 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.57482 | −1.04048 | −0.520241 | − | 0.854020i | \(-0.674158\pi\) | ||||
−0.520241 | + | 0.854020i | \(0.674158\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.82800 | 0.242124 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.07180 | −0.790480 | −0.395240 | − | 0.918578i | \(-0.629339\pi\) | ||||
−0.395240 | + | 0.918578i | \(0.629339\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.635155 | −0.0813233 | −0.0406616 | − | 0.999173i | \(-0.512947\pi\) | ||||
−0.0406616 | + | 0.999173i | \(0.512947\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.85425 | 0.737566 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.1333 | −1.36015 | −0.680077 | − | 0.733141i | \(-0.738054\pi\) | ||||
−0.680077 | + | 0.733141i | \(0.738054\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.794805 | 0.0956833 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.58163 | −1.01845 | −0.509226 | − | 0.860633i | \(-0.670068\pi\) | ||||
−0.509226 | + | 0.860633i | \(0.670068\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 16.5849 | 1.94112 | 0.970560 | − | 0.240859i | \(-0.0774292\pi\) | ||||
0.970560 | + | 0.240859i | \(0.0774292\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.68528 | −0.647897 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.335225 | −0.0377157 | −0.0188579 | − | 0.999822i | \(-0.506003\pi\) | ||||
−0.0188579 | + | 0.999822i | \(0.506003\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.71363 | 0.412626 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −15.1937 | −1.66773 | −0.833863 | − | 0.551971i | \(-0.813876\pi\) | ||||
−0.833863 | + | 0.551971i | \(0.813876\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.19959 | 0.450243 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.55735 | 0.589078 | 0.294539 | − | 0.955639i | \(-0.404834\pi\) | ||||
0.294539 | + | 0.955639i | \(0.404834\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.49277 | 0.995113 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.08792 | 0.527593 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.42786 | 0.652650 | 0.326325 | − | 0.945258i | \(-0.394190\pi\) | ||||
0.326325 | + | 0.945258i | \(0.394190\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.44689 | −0.547433 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −14.6041 | −1.45316 | −0.726581 | − | 0.687081i | \(-0.758892\pi\) | ||||
−0.726581 | + | 0.687081i | \(0.758892\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.3980 | 1.32014 | 0.660071 | − | 0.751203i | \(-0.270526\pi\) | ||||
0.660071 | + | 0.751203i | \(0.270526\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.63549 | −0.158109 | −0.0790544 | − | 0.996870i | \(-0.525190\pi\) | ||||
−0.0790544 | + | 0.996870i | \(0.525190\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.50182 | 0.143848 | 0.0719239 | − | 0.997410i | \(-0.477086\pi\) | ||||
0.0719239 | + | 0.997410i | \(0.477086\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.80716 | 0.646107 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.6451 | 1.65992 | 0.829958 | − | 0.557826i | \(-0.188364\pi\) | ||||
0.829958 | + | 0.557826i | \(0.188364\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9.09474 | 0.840809 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 19.1496 | 1.75544 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.71032 | −0.519120 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.39937 | 0.306511 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.97362 | −0.352602 | −0.176301 | − | 0.984336i | \(-0.556413\pi\) | ||||
−0.176301 | + | 0.984336i | \(0.556413\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.50182 | 0.132228 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.3032 | 1.24968 | 0.624840 | − | 0.780753i | \(-0.285164\pi\) | ||||
0.624840 | + | 0.780753i | \(0.285164\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.68528 | −0.492976 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.25585 | 0.363602 | 0.181801 | − | 0.983335i | \(-0.441807\pi\) | ||||
0.181801 | + | 0.983335i | \(0.441807\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.86950 | 0.837120 | 0.418560 | − | 0.908189i | \(-0.362535\pi\) | ||||
0.418560 | + | 0.908189i | \(0.362535\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.81047 | −0.826191 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8.83224 | −0.738589 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.707011 | −0.0583133 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.55735 | 0.782969 | 0.391484 | − | 0.920185i | \(-0.371962\pi\) | ||||
0.391484 | + | 0.920185i | \(0.371962\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 24.4557 | 1.99018 | 0.995090 | − | 0.0989730i | \(-0.0315557\pi\) | ||||
0.995090 | + | 0.0989730i | \(0.0315557\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 18.3467 | 1.48324 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.1922 | 0.973047 | 0.486524 | − | 0.873667i | \(-0.338265\pi\) | ||||
0.486524 | + | 0.873667i | \(0.338265\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.02050 | −0.477457 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.47193 | −0.194816 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.5762 | 1.45500 | 0.727498 | − | 0.686109i | \(-0.240683\pi\) | ||||
0.727498 | + | 0.686109i | \(0.240683\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 16.8639 | 1.30497 | 0.652484 | − | 0.757803i | \(-0.273727\pi\) | ||||
0.652484 | + | 0.757803i | \(0.273727\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.74729 | 0.134407 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.44689 | −0.416534 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 24.4626 | 1.85985 | 0.929927 | − | 0.367745i | \(-0.119870\pi\) | ||||
0.929927 | + | 0.367745i | \(0.119870\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.82589 | −0.362736 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.26173 | −0.169050 | −0.0845249 | − | 0.996421i | \(-0.526937\pi\) | ||||
−0.0845249 | + | 0.996421i | \(0.526937\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.7187 | 1.09404 | 0.547018 | − | 0.837121i | \(-0.315763\pi\) | ||||
0.547018 | + | 0.837121i | \(0.315763\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.504824 | −0.0373177 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −17.8171 | −1.30292 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 10.5471 | 0.767189 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 23.7055 | 1.71527 | 0.857636 | − | 0.514258i | \(-0.171933\pi\) | ||||
0.857636 | + | 0.514258i | \(0.171933\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −20.4146 | −1.46947 | −0.734736 | − | 0.678353i | \(-0.762694\pi\) | ||||
−0.734736 | + | 0.678353i | \(0.762694\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 17.7607 | 1.26540 | 0.632699 | − | 0.774398i | \(-0.281947\pi\) | ||||
0.632699 | + | 0.774398i | \(0.281947\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.1379 | −0.789546 | −0.394773 | − | 0.918779i | \(-0.629177\pi\) | ||||
−0.394773 | + | 0.918779i | \(0.629177\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.84883 | −0.624149 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −13.0612 | −0.916717 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.36829 | −0.164607 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.28968 | 0.365895 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.17347 | −0.287314 | −0.143657 | − | 0.989628i | \(-0.545886\pi\) | ||||
−0.143657 | + | 0.989628i | \(0.545886\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.82072 | −0.467348 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −15.8240 | −1.07421 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 13.1818 | 0.890743 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 29.7495 | 2.00117 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.4218 | −0.764863 | −0.382432 | − | 0.923984i | \(-0.624913\pi\) | ||||
−0.382432 | + | 0.923984i | \(0.624913\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.40014 | −0.358420 | −0.179210 | − | 0.983811i | \(-0.557354\pi\) | ||||
−0.179210 | + | 0.983811i | \(0.557354\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.4333 | −1.21811 | −0.609054 | − | 0.793129i | \(-0.708451\pi\) | ||||
−0.609054 | + | 0.793129i | \(0.708451\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.51869 | −0.297308 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.82122 | −0.512385 | −0.256193 | − | 0.966626i | \(-0.582468\pi\) | ||||
−0.256193 | + | 0.966626i | \(0.582468\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.266438 | −0.0173070 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.26133 | 0.146273 | 0.0731365 | − | 0.997322i | \(-0.476699\pi\) | ||||
0.0731365 | + | 0.997322i | \(0.476699\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.4906 | 0.869006 | 0.434503 | − | 0.900670i | \(-0.356924\pi\) | ||||
0.434503 | + | 0.900670i | \(0.356924\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.7518 | 1.01048 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.83224 | −0.561982 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −12.0760 | −0.765288 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.5642 | −0.982406 | −0.491203 | − | 0.871045i | \(-0.663443\pi\) | ||||
−0.491203 | + | 0.871045i | \(0.663443\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.29993 | 0.144595 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 25.2354 | 1.57414 | 0.787069 | − | 0.616865i | \(-0.211598\pi\) | ||||
0.787069 | + | 0.616865i | \(0.211598\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −21.1710 | −1.31550 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −12.5135 | −0.774569 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.6243 | 0.778448 | 0.389224 | − | 0.921143i | \(-0.372743\pi\) | ||||
0.389224 | + | 0.921143i | \(0.372743\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.41701 | 0.270317 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 25.0644 | 1.52820 | 0.764101 | − | 0.645096i | \(-0.223183\pi\) | ||||
0.764101 | + | 0.645096i | \(0.223183\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.6777 | 1.07384 | 0.536922 | − | 0.843632i | \(-0.319587\pi\) | ||||
0.536922 | + | 0.843632i | \(0.319587\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 7.54490 | 0.456638 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.22724 | −0.434243 | −0.217121 | − | 0.976145i | \(-0.569667\pi\) | ||||
−0.217121 | + | 0.976145i | \(0.569667\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −15.1605 | −0.907637 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.61315 | −0.334852 | −0.167426 | − | 0.985885i | \(-0.553546\pi\) | ||||
−0.167426 | + | 0.985885i | \(0.553546\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.873541 | 0.0519266 | 0.0259633 | − | 0.999663i | \(-0.491735\pi\) | ||||
0.0259633 | + | 0.999663i | \(0.491735\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.5724 | −0.624071 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 43.0132 | 2.53019 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.10889 | 0.299489 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.2737 | 0.600195 | 0.300097 | − | 0.953909i | \(-0.402981\pi\) | ||||
0.300097 | + | 0.953909i | \(0.402981\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −9.81320 | −0.569420 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.84022 | −0.222086 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.67082 | −0.269222 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −11.6074 | −0.666828 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −26.3994 | −1.50670 | −0.753348 | − | 0.657622i | \(-0.771562\pi\) | ||||
−0.753348 | + | 0.657622i | \(0.771562\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.6488 | 0.605788 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −31.6429 | −1.79430 | −0.897151 | − | 0.441725i | \(-0.854367\pi\) | ||||
−0.897151 | + | 0.441725i | \(0.854367\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −24.1327 | −1.36406 | −0.682032 | − | 0.731323i | \(-0.738903\pi\) | ||||
−0.682032 | + | 0.731323i | \(0.738903\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.973154 | −0.0546578 | −0.0273289 | − | 0.999626i | \(-0.508700\pi\) | ||||
−0.0273289 | + | 0.999626i | \(0.508700\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.1524 | 0.680402 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.29990 | −0.0725531 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −17.8171 | −0.991373 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.19365 | 0.0660090 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 30.5117 | 1.68216 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.10352 | −0.0606549 | −0.0303274 | − | 0.999540i | \(-0.509655\pi\) | ||||
−0.0303274 | + | 0.999540i | \(0.509655\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −20.2833 | −1.11152 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.33526 | −0.508524 | −0.254262 | − | 0.967135i | \(-0.581833\pi\) | ||||
−0.254262 | + | 0.967135i | \(0.581833\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 14.0244 | 0.761703 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 14.7229 | 0.797292 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.5024 | 1.05303 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −19.4052 | −1.04173 | −0.520863 | − | 0.853641i | \(-0.674390\pi\) | ||||
−0.520863 | + | 0.853641i | \(0.674390\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 26.0825 | 1.39616 | 0.698081 | − | 0.716019i | \(-0.254038\pi\) | ||||
0.698081 | + | 0.716019i | \(0.254038\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 16.3852 | 0.874578 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 24.5504 | 1.30669 | 0.653343 | − | 0.757062i | \(-0.273366\pi\) | ||||
0.653343 | + | 0.757062i | \(0.273366\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 15.2202 | 0.805540 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10.2809 | 0.542607 | 0.271303 | − | 0.962494i | \(-0.412545\pi\) | ||||
0.271303 | + | 0.962494i | \(0.412545\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.7103 | −0.721596 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4.53859 | −0.238214 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.2290 | 0.690549 | 0.345274 | − | 0.938502i | \(-0.387786\pi\) | ||||
0.345274 | + | 0.938502i | \(0.387786\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −10.1291 | −0.527302 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 18.7245 | 0.972125 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 34.2573 | 1.77378 | 0.886889 | − | 0.461983i | \(-0.152862\pi\) | ||||
0.886889 | + | 0.461983i | \(0.152862\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −20.2910 | −1.04504 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.2939 | 0.528763 | 0.264382 | − | 0.964418i | \(-0.414832\pi\) | ||||
0.264382 | + | 0.964418i | \(0.414832\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.15825 | −0.161802 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 26.2028 | 1.33890 | 0.669450 | − | 0.742857i | \(-0.266530\pi\) | ||||
0.669450 | + | 0.742857i | \(0.266530\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.47497 | −0.227476 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.59078 | 0.283464 | 0.141732 | − | 0.989905i | \(-0.454733\pi\) | ||||
0.141732 | + | 0.989905i | \(0.454733\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.74682 | −0.391774 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 11.3683 | 0.573454 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.98084 | −0.149604 | −0.0748019 | − | 0.997198i | \(-0.523832\pi\) | ||||
−0.0748019 | + | 0.997198i | \(0.523832\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.51869 | −0.226217 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −19.8229 | −0.989906 | −0.494953 | − | 0.868920i | \(-0.664815\pi\) | ||||
−0.494953 | + | 0.868920i | \(0.664815\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −24.5831 | −1.22457 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 19.6979 | 0.976389 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.8521 | 0.635498 | 0.317749 | − | 0.948175i | \(-0.397073\pi\) | ||||
0.317749 | + | 0.948175i | \(0.397073\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.38257 | 0.166850 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 15.0091 | 0.738549 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.84433 | 0.384139 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.42665 | 0.265109 | 0.132555 | − | 0.991176i | \(-0.457682\pi\) | ||||
0.132555 | + | 0.991176i | \(0.457682\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.2456 | 0.937973 | 0.468987 | − | 0.883205i | \(-0.344619\pi\) | ||||
0.468987 | + | 0.883205i | \(0.344619\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 29.2323 | 1.42132 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.57006 | 0.0759806 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −7.01991 | −0.338924 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.53348 | −0.411043 | −0.205522 | − | 0.978653i | \(-0.565889\pi\) | ||||
−0.205522 | + | 0.978653i | \(0.565889\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 22.7745 | 1.09447 | 0.547237 | − | 0.836978i | \(-0.315680\pi\) | ||||
0.547237 | + | 0.836978i | \(0.315680\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.29993 | 0.110021 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.67135 | −0.222952 | −0.111476 | − | 0.993767i | \(-0.535558\pi\) | ||||
−0.111476 | + | 0.993767i | \(0.535558\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.10668 | 0.100318 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.00378 | −0.142714 | −0.0713568 | − | 0.997451i | \(-0.522733\pi\) | ||||
−0.0713568 | + | 0.997451i | \(0.522733\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7.59623 | 0.359289 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.56914 | 0.262824 | 0.131412 | − | 0.991328i | \(-0.458049\pi\) | ||||
0.131412 | + | 0.991328i | \(0.458049\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.83678 | 0.463196 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 19.4375 | 0.913256 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −31.0180 | −1.45096 | −0.725481 | − | 0.688242i | \(-0.758383\pi\) | ||||
−0.725481 | + | 0.688242i | \(0.758383\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 33.0537 | 1.54281 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.92290 | −0.462155 | −0.231078 | − | 0.972935i | \(-0.574225\pi\) | ||||
−0.231078 | + | 0.972935i | \(0.574225\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.0111 | −0.465256 | −0.232628 | − | 0.972566i | \(-0.574733\pi\) | ||||
−0.232628 | + | 0.972566i | \(0.574733\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −36.9345 | −1.70912 | −0.854562 | − | 0.519350i | \(-0.826174\pi\) | ||||
−0.854562 | + | 0.519350i | \(0.826174\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 27.5209 | 1.27080 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.69046 | 0.446513 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.34581 | 0.199821 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 17.9393 | 0.821385 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16.7734 | 0.766396 | 0.383198 | − | 0.923666i | \(-0.374823\pi\) | ||||
0.383198 | + | 0.923666i | \(0.374823\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −32.8898 | −1.49965 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.96471 | −0.0893972 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.47391 | −0.248046 | −0.124023 | − | 0.992279i | \(-0.539580\pi\) | ||||
−0.124023 | + | 0.992279i | \(0.539580\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 14.7644 | 0.667670 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −35.4536 | −1.60000 | −0.800000 | − | 0.600001i | \(-0.795167\pi\) | ||||
−0.800000 | + | 0.600001i | \(0.795167\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −40.9327 | −1.84351 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 21.2132 | 0.951543 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 33.4110 | 1.49568 | 0.747840 | − | 0.663879i | \(-0.231091\pi\) | ||||
0.747840 | + | 0.663879i | \(0.231091\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 13.4035 | 0.598825 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.97733 | 0.0881650 | 0.0440825 | − | 0.999028i | \(-0.485964\pi\) | ||||
0.0440825 | + | 0.999028i | \(0.485964\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.38875 | 0.0616766 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −23.0984 | −1.02382 | −0.511909 | − | 0.859040i | \(-0.671061\pi\) | ||||
−0.511909 | + | 0.859040i | \(0.671061\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −40.9969 | −1.81360 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −9.81320 | −0.433264 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −28.3886 | −1.24853 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 19.4430 | 0.853451 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.2867 | 0.932588 | 0.466294 | − | 0.884630i | \(-0.345589\pi\) | ||||
0.466294 | + | 0.884630i | \(0.345589\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −28.1943 | −1.23285 | −0.616425 | − | 0.787414i | \(-0.711420\pi\) | ||||
−0.616425 | + | 0.787414i | \(0.711420\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −49.5911 | −2.16022 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 14.3797 | 0.624028 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −16.4246 | −0.711428 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.79763 | −0.0775737 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.04588 | −0.0881223 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.8271 | 0.637468 | 0.318734 | − | 0.947844i | \(-0.396742\pi\) | ||||
0.318734 | + | 0.947844i | \(0.396742\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 11.6985 | 0.502032 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.09950 | 0.389067 | 0.194533 | − | 0.980896i | \(-0.437681\pi\) | ||||
0.194533 | + | 0.980896i | \(0.437681\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.50423 | 0.0641989 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.1524 | 0.517709 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.828654 | 0.0352379 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −32.9824 | −1.39751 | −0.698754 | − | 0.715362i | \(-0.746262\pi\) | ||||
−0.698754 | + | 0.715362i | \(0.746262\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.25625 | −0.306907 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −14.1612 | −0.597885 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 21.9384 | 0.924595 | 0.462297 | − | 0.886725i | \(-0.347025\pi\) | ||||
0.462297 | + | 0.886725i | \(0.347025\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −9.17985 | −0.385517 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −28.2664 | −1.18499 | −0.592495 | − | 0.805574i | \(-0.701857\pi\) | ||||
−0.592495 | + | 0.805574i | \(0.701857\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.13671 | 0.173116 | 0.0865580 | − | 0.996247i | \(-0.472413\pi\) | ||||
0.0865580 | + | 0.996247i | \(0.472413\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 18.8413 | 0.787105 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 13.8146 | 0.575111 | 0.287556 | − | 0.957764i | \(-0.407157\pi\) | ||||
0.287556 | + | 0.957764i | \(0.407157\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −16.2256 | −0.674313 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 37.5579 | 1.55816 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −17.4216 | −0.721527 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 17.2506 | 0.712010 | 0.356005 | − | 0.934484i | \(-0.384139\pi\) | ||||
0.356005 | + | 0.934484i | \(0.384139\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14.7229 | 0.606649 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 14.1163 | 0.580667 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 27.0042 | 1.10893 | 0.554466 | − | 0.832207i | \(-0.312923\pi\) | ||||
0.554466 | + | 0.832207i | \(0.312923\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8.85247 | −0.362307 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11.5259 | 0.470934 | 0.235467 | − | 0.971882i | \(-0.424338\pi\) | ||||
0.235467 | + | 0.971882i | \(0.424338\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.8541 | −0.442750 | −0.221375 | − | 0.975189i | \(-0.571054\pi\) | ||||
−0.221375 | + | 0.975189i | \(0.571054\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 26.3669 | 1.07374 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.16930 | 0.209816 | 0.104908 | − | 0.994482i | \(-0.466545\pi\) | ||||
0.104908 | + | 0.994482i | \(0.466545\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −10.3811 | −0.420664 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 47.4008 | 1.91763 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −27.3190 | −1.10340 | −0.551701 | − | 0.834042i | \(-0.686021\pi\) | ||||
−0.551701 | + | 0.834042i | \(0.686021\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.08325 | 0.204644 | 0.102322 | − | 0.994751i | \(-0.467373\pi\) | ||||
0.102322 | + | 0.994751i | \(0.467373\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.207299 | 0.00833203 | 0.00416602 | − | 0.999991i | \(-0.498674\pi\) | ||||
0.00416602 | + | 0.999991i | \(0.498674\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.26674 | −0.171218 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −13.7374 | −0.550378 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.20426 | 0.167902 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −66.3482 | −2.64547 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −40.7410 | −1.62187 | −0.810937 | − | 0.585133i | \(-0.801042\pi\) | ||||
−0.810937 | + | 0.585133i | \(0.801042\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.31710 | −0.131843 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.41603 | 0.135348 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 20.3237 | 0.803995 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −29.7426 | −1.17476 | −0.587381 | − | 0.809310i | \(-0.699841\pi\) | ||||
−0.587381 | + | 0.809310i | \(0.699841\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 34.3329 | 1.35396 | 0.676978 | − | 0.736003i | \(-0.263289\pi\) | ||||
0.676978 | + | 0.736003i | \(0.263289\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 15.0002 | 0.589717 | 0.294859 | − | 0.955541i | \(-0.404727\pi\) | ||||
0.294859 | + | 0.955541i | \(0.404727\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.9647 | −0.548163 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −12.5770 | −0.492932 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −14.2038 | −0.555837 | −0.277918 | − | 0.960605i | \(-0.589644\pi\) | ||||
−0.277918 | + | 0.960605i | \(0.589644\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −39.2779 | −1.53238 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −47.9718 | −1.86872 | −0.934359 | − | 0.356334i | \(-0.884027\pi\) | ||||
−0.934359 | + | 0.356334i | \(0.884027\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 43.6518 | 1.69786 | 0.848928 | − | 0.528508i | \(-0.177248\pi\) | ||||
0.848928 | + | 0.528508i | \(0.177248\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 23.6450 | 0.918297 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.28380 | 0.204590 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9.07814 | −0.350981 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.46081 | −0.0563940 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.9330 | −0.459983 | −0.229991 | − | 0.973193i | \(-0.573870\pi\) | ||||
−0.229991 | + | 0.973193i | \(0.573870\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −18.7598 | −0.720999 | −0.360500 | − | 0.932759i | \(-0.617394\pi\) | ||||
−0.360500 | + | 0.932759i | \(0.617394\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −15.8892 | −0.609773 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.29206 | −0.164472 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −10.4542 | −0.400020 | −0.200010 | − | 0.979794i | \(-0.564098\pi\) | ||||
−0.200010 | + | 0.979794i | \(0.564098\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14.6509 | −0.558966 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 29.0890 | 1.10820 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.8518 | 0.793240 | 0.396620 | − | 0.917983i | \(-0.370183\pi\) | ||||
0.396620 | + | 0.917983i | \(0.370183\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 13.4644 | 0.511469 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −33.1331 | −1.25500 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −6.21634 | −0.235124 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22.1231 | 0.835578 | 0.417789 | − | 0.908544i | \(-0.362805\pi\) | ||||
0.417789 | + | 0.908544i | \(0.362805\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 19.6979 | 0.742921 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 36.1004 | 1.35769 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14.1669 | 0.532049 | 0.266024 | − | 0.963966i | \(-0.414290\pi\) | ||||
0.266024 | + | 0.963966i | \(0.414290\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.793908 | 0.0297739 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.40148 | 0.239737 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.79731 | 0.0671219 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.86389 | 0.255980 | 0.127990 | − | 0.991775i | \(-0.459147\pi\) | ||||
0.127990 | + | 0.991775i | \(0.459147\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −33.1189 | −1.23341 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 10.7224 | 0.398770 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.72298 | 0.0639016 | 0.0319508 | − | 0.999489i | \(-0.489828\pi\) | ||||
0.0319508 | + | 0.999489i | \(0.489828\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.37874 | 0.0510645 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −14.6379 | −0.541403 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.2855 | 0.490712 | 0.245356 | − | 0.969433i | \(-0.421095\pi\) | ||||
0.245356 | + | 0.969433i | \(0.421095\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −25.6059 | −0.943206 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 28.8043 | 1.05958 | 0.529791 | − | 0.848128i | \(-0.322270\pi\) | ||||
0.529791 | + | 0.848128i | \(0.322270\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.01991 | −0.257883 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15.7966 | −0.579521 | −0.289761 | − | 0.957099i | \(-0.593576\pi\) | ||||
−0.289761 | + | 0.957099i | \(0.593576\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 35.9830 | 1.31655 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.04282 | 0.147722 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.7384 | 0.464829 | 0.232415 | − | 0.972617i | \(-0.425337\pi\) | ||||
0.232415 | + | 0.972617i | \(0.425337\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −12.3705 | −0.450807 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.07420 | −0.111734 | −0.0558668 | − | 0.998438i | \(-0.517792\pi\) | ||||
−0.0558668 | + | 0.998438i | \(0.517792\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.82800 | 0.0663520 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 30.6818 | 1.11222 | 0.556108 | − | 0.831110i | \(-0.312294\pi\) | ||||
0.556108 | + | 0.831110i | \(0.312294\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.71239 | −0.134398 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 23.3170 | 0.841929 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −34.5153 | −1.24465 | −0.622327 | − | 0.782758i | \(-0.713812\pi\) | ||||
−0.622327 | + | 0.782758i | \(0.713812\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 20.0572 | 0.722342 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −36.6662 | −1.31879 | −0.659396 | − | 0.751796i | \(-0.729188\pi\) | ||||
−0.659396 | + | 0.751796i | \(0.729188\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −16.8269 | −0.603660 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.83678 | 0.352439 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19.7371 | −0.706251 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −22.5446 | −0.805678 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17.6991 | −0.630906 | −0.315453 | − | 0.948941i | \(-0.602156\pi\) | ||||
−0.315453 | + | 0.948941i | \(0.602156\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 10.0339 | 0.357215 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −43.6176 | −1.55086 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.43913 | 0.0866162 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 26.6535 | 0.944117 | 0.472058 | − | 0.881567i | \(-0.343511\pi\) | ||||
0.472058 | + | 0.881567i | \(0.343511\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 95.6209 | 3.38282 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −13.1614 | −0.465035 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 38.1442 | 1.34608 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 19.9213 | 0.701263 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −24.1080 | −0.847591 | −0.423795 | − | 0.905758i | \(-0.639302\pi\) | ||||
−0.423795 | + | 0.905758i | \(0.639302\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.3363 | 0.398071 | 0.199035 | − | 0.979992i | \(-0.436219\pi\) | ||||
0.199035 | + | 0.979992i | \(0.436219\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 14.0503 | 0.492766 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.34581 | 0.152041 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −22.4816 | −0.785570 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.95739 | −0.138114 | −0.0690569 | − | 0.997613i | \(-0.521999\pi\) | ||||
−0.0690569 | + | 0.997613i | \(0.521999\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −46.5023 | −1.62097 | −0.810484 | − | 0.585761i | \(-0.800796\pi\) | ||||
−0.810484 | + | 0.585761i | \(0.800796\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −27.7619 | −0.965375 | −0.482687 | − | 0.875793i | \(-0.660339\pi\) | ||||
−0.482687 | + | 0.875793i | \(0.660339\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 37.8234 | 1.31366 | 0.656831 | − | 0.754038i | \(-0.271896\pi\) | ||||
0.656831 | + | 0.754038i | \(0.271896\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.74424 | −0.199266 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.89111 | 0.238763 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −27.3134 | −0.944090 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −20.0661 | −0.692758 | −0.346379 | − | 0.938095i | \(-0.612589\pi\) | ||||
−0.346379 | + | 0.938095i | \(0.612589\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.08145 | −0.0372913 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −4.46136 | −0.153657 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 14.1155 | 0.485016 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.694295 | 0.0238281 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.56457 | 0.293590 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8.35933 | −0.286218 | −0.143109 | − | 0.989707i | \(-0.545710\pi\) | ||||
−0.143109 | + | 0.989707i | \(0.545710\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −17.0931 | −0.583889 | −0.291945 | − | 0.956435i | \(-0.594302\pi\) | ||||
−0.291945 | + | 0.956435i | \(0.594302\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −23.0254 | −0.785617 | −0.392809 | − | 0.919620i | \(-0.628497\pi\) | ||||
−0.392809 | + | 0.919620i | \(0.628497\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.40303 | −0.286374 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −5.49197 | −0.186949 | −0.0934745 | − | 0.995622i | \(-0.529797\pi\) | ||||
−0.0934745 | + | 0.995622i | \(0.529797\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 34.1871 | 1.16106 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.770994 | −0.0261542 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 42.7545 | 1.44868 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −15.2230 | −0.515220 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.98307 | 0.269569 | 0.134785 | − | 0.990875i | \(-0.456966\pi\) | ||||
0.134785 | + | 0.990875i | \(0.456966\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 8.16557 | 0.275418 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 44.5925 | 1.50236 | 0.751180 | − | 0.660098i | \(-0.229485\pi\) | ||||
0.751180 | + | 0.660098i | \(0.229485\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −45.9134 | −1.54511 | −0.772554 | − | 0.634949i | \(-0.781021\pi\) | ||||
−0.772554 | + | 0.634949i | \(0.781021\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −53.6109 | −1.80008 | −0.900039 | − | 0.435810i | \(-0.856462\pi\) | ||||
−0.900039 | + | 0.435810i | \(0.856462\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.82253 | 0.329437 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 8.54109 | 0.286137 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −28.3886 | −0.949988 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.05223 | −0.101911 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 33.8241 | 1.12810 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 58.6808 | 1.95494 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.71239 | −0.123541 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −45.1277 | −1.49844 | −0.749220 | − | 0.662322i | \(-0.769571\pi\) | ||||
−0.749220 | + | 0.662322i | \(0.769571\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 34.5867 | 1.14717 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.06248 | −0.200859 | −0.100429 | − | 0.994944i | \(-0.532022\pi\) | ||||
−0.100429 | + | 0.994944i | \(0.532022\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −34.9445 | −1.15649 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −35.3567 | −1.16758 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −38.8692 | −1.28218 | −0.641089 | − | 0.767467i | \(-0.721517\pi\) | ||||
−0.641089 | + | 0.767467i | \(0.721517\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −20.9824 | −0.691394 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 32.9553 | 1.08474 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −31.7302 | −1.04216 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −43.4632 | −1.42598 | −0.712991 | − | 0.701173i | \(-0.752660\pi\) | ||||
−0.712991 | + | 0.701173i | \(0.752660\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.04588 | −0.0670510 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −25.1499 | −0.823371 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 19.7812 | 0.646223 | 0.323112 | − | 0.946361i | \(-0.395271\pi\) | ||||
0.323112 | + | 0.946361i | \(0.395271\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −19.1808 | −0.625942 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 31.1805 | 1.01645 | 0.508227 | − | 0.861223i | \(-0.330301\pi\) | ||||
0.508227 | + | 0.861223i | \(0.330301\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.27699 | 0.139278 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3.65195 | −0.118673 | −0.0593363 | − | 0.998238i | \(-0.518898\pi\) | ||||
−0.0593363 | + | 0.998238i | \(0.518898\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −63.6898 | −2.06746 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.773468 | −0.0250814 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.81987 | 0.156131 | 0.0780655 | − | 0.996948i | \(-0.475126\pi\) | ||||
0.0780655 | + | 0.996948i | \(0.475126\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.65877 | 0.312224 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −10.5202 | −0.339715 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9.97890 | 0.321900 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.87331 | 0.124816 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 28.9718 | 0.931670 | 0.465835 | − | 0.884872i | \(-0.345754\pi\) | ||||
0.465835 | + | 0.884872i | \(0.345754\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −14.1612 | −0.454922 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −32.8376 | −1.05381 | −0.526905 | − | 0.849924i | \(-0.676648\pi\) | ||||
−0.526905 | + | 0.849924i | \(0.676648\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −24.3968 | −0.782125 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 58.0091 | 1.85587 | 0.927937 | − | 0.372737i | \(-0.121581\pi\) | ||||
0.927937 | + | 0.372737i | \(0.121581\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.7815 | 0.408499 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.55673 | −0.113558 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.41757 | −0.140899 | −0.0704493 | − | 0.997515i | \(-0.522443\pi\) | ||||
−0.0704493 | + | 0.997515i | \(0.522443\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 24.2508 | 0.771913 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.88954 | 0.0600839 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −36.1617 | −1.14871 | −0.574357 | − | 0.818605i | \(-0.694748\pi\) | ||||
−0.574357 | + | 0.818605i | \(0.694748\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −0.877082 | −0.0278334 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.6357 | 0.368506 | 0.184253 | − | 0.982879i | \(-0.441013\pi\) | ||||
0.184253 | + | 0.982879i | \(0.441013\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −36.5428 | −1.15616 |
(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 | 9200.2.a.ct.1.3 | 5 | ||
4.3 | odd | 2 | 4600.2.a.bf.1.3 | yes | 5 | ||
5.4 | even | 2 | 9200.2.a.cv.1.3 | 5 | |||
20.3 | even | 4 | 4600.2.e.w.4049.5 | 10 | |||
20.7 | even | 4 | 4600.2.e.w.4049.6 | 10 | |||
20.19 | odd | 2 | 4600.2.a.bd.1.3 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4600.2.a.bd.1.3 | ✓ | 5 | 20.19 | odd | 2 | ||
4600.2.a.bf.1.3 | yes | 5 | 4.3 | odd | 2 | ||
4600.2.e.w.4049.5 | 10 | 20.3 | even | 4 | |||
4600.2.e.w.4049.6 | 10 | 20.7 | even | 4 | |||
9200.2.a.ct.1.3 | 5 | 1.1 | even | 1 | trivial | ||
9200.2.a.cv.1.3 | 5 | 5.4 | even | 2 |