Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [308,2,Mod(1,308)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(308, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("308.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 308 = 2^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 308.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: | \(2.45939238226\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.1016.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 6x + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.321637\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 308.1 |
$q$-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 | ||||||||
\(3\) | −0.321637 | −0.185697 | −0.0928487 | − | 0.995680i | \(-0.529597\pi\) | ||||
−0.0928487 | + | 0.995680i | \(0.529597\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.89655 | 1.74259 | 0.871295 | − | 0.490760i | \(-0.163281\pi\) | ||||
0.871295 | + | 0.490760i | \(0.163281\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.89655 | −0.965517 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.218187 | −0.0605141 | −0.0302571 | − | 0.999542i | \(-0.509633\pi\) | ||||
−0.0302571 | + | 0.999542i | \(0.509633\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.25328 | −0.323594 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.86146 | 1.17908 | 0.589539 | − | 0.807740i | \(-0.299310\pi\) | ||||
0.589539 | + | 0.807740i | \(0.299310\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.643274 | −0.147577 | −0.0737886 | − | 0.997274i | \(-0.523509\pi\) | ||||
−0.0737886 | + | 0.997274i | \(0.523509\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.321637 | −0.0701870 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.53982 | −1.36365 | −0.681824 | − | 0.731516i | \(-0.738813\pi\) | ||||
−0.681824 | + | 0.731516i | \(0.738813\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 10.1831 | 2.03662 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.89655 | 0.364991 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 10.4364 | 1.93799 | 0.968993 | − | 0.247088i | \(-0.0794738\pi\) | ||||
0.968993 | + | 0.247088i | \(0.0794738\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.03509 | −0.545118 | −0.272559 | − | 0.962139i | \(-0.587870\pi\) | ||||
−0.272559 | + | 0.962139i | \(0.587870\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.321637 | −0.0559898 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.89655 | 0.658637 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.89655 | −0.311791 | −0.155895 | − | 0.987774i | \(-0.549826\pi\) | ||||
−0.155895 | + | 0.987774i | \(0.549826\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.0701770 | 0.0112373 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.86146 | −0.759233 | −0.379616 | − | 0.925144i | \(-0.623944\pi\) | ||||
−0.379616 | + | 0.925144i | \(0.623944\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.35673 | −0.206899 | −0.103449 | − | 0.994635i | \(-0.532988\pi\) | ||||
−0.103449 | + | 0.994635i | \(0.532988\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −11.2865 | −1.68250 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.57491 | −0.813185 | −0.406592 | − | 0.913610i | \(-0.633283\pi\) | ||||
−0.406592 | + | 0.913610i | \(0.633283\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.56363 | −0.218952 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.79310 | −1.07046 | −0.535232 | − | 0.844705i | \(-0.679776\pi\) | ||||
−0.535232 | + | 0.844705i | \(0.679776\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.89655 | 0.525411 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.206901 | 0.0274047 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.67836 | −0.999638 | −0.499819 | − | 0.866130i | \(-0.666600\pi\) | ||||
−0.499819 | + | 0.866130i | \(0.666600\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.01129 | −1.02574 | −0.512870 | − | 0.858466i | \(-0.671418\pi\) | ||||
−0.512870 | + | 0.858466i | \(0.671418\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.89655 | −0.364931 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.850175 | −0.105451 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.53982 | 0.310289 | 0.155144 | − | 0.987892i | \(-0.450416\pi\) | ||||
0.155144 | + | 0.987892i | \(0.450416\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.10345 | 0.253226 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.3329 | −1.70101 | −0.850503 | − | 0.525971i | \(-0.823702\pi\) | ||||
−0.850503 | + | 0.525971i | \(0.823702\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.86146 | −1.03716 | −0.518578 | − | 0.855030i | \(-0.673538\pi\) | ||||
−0.518578 | + | 0.855030i | \(0.673538\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.27526 | −0.378195 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.1498 | 1.47947 | 0.739735 | − | 0.672898i | \(-0.234951\pi\) | ||||
0.739735 | + | 0.672898i | \(0.234951\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.07965 | 0.897739 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.72292 | 1.06723 | 0.533615 | − | 0.845728i | \(-0.320833\pi\) | ||||
0.533615 | + | 0.845728i | \(0.320833\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 18.9429 | 2.05465 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.35673 | −0.359879 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.6100 | −1.12466 | −0.562329 | − | 0.826914i | \(-0.690095\pi\) | ||||
−0.562329 | + | 0.826914i | \(0.690095\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.218187 | −0.0228722 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.976197 | 0.101227 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.50655 | −0.257167 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.746725 | 0.0758184 | 0.0379092 | − | 0.999281i | \(-0.487930\pi\) | ||||
0.0379092 | + | 0.999281i | \(0.487930\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.89655 | −0.291114 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.21819 | −0.817740 | −0.408870 | − | 0.912593i | \(-0.634077\pi\) | ||||
−0.408870 | + | 0.912593i | \(0.634077\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.86146 | 0.676080 | 0.338040 | − | 0.941132i | \(-0.390236\pi\) | ||||
0.338040 | + | 0.941132i | \(0.390236\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.25328 | −0.122307 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.79310 | −0.753387 | −0.376694 | − | 0.926338i | \(-0.622939\pi\) | ||||
−0.376694 | + | 0.926338i | \(0.622939\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.0701770 | 0.00672173 | 0.00336087 | − | 0.999994i | \(-0.498930\pi\) | ||||
0.00336087 | + | 0.999994i | \(0.498930\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.610001 | 0.0578987 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 18.4031 | 1.73122 | 0.865609 | − | 0.500721i | \(-0.166932\pi\) | ||||
0.865609 | + | 0.500721i | \(0.166932\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −25.4827 | −2.37628 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.631989 | 0.0584274 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.86146 | 0.445649 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.56363 | 0.140987 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 20.1962 | 1.80640 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 21.0796 | 1.87052 | 0.935258 | − | 0.353966i | \(-0.115167\pi\) | ||||
0.935258 | + | 0.353966i | \(0.115167\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.436373 | 0.0384205 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −19.7931 | −1.72933 | −0.864666 | − | 0.502348i | \(-0.832470\pi\) | ||||
−0.864666 | + | 0.502348i | \(0.832470\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.643274 | −0.0557790 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 7.39000 | 0.636030 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.9762 | −0.937760 | −0.468880 | − | 0.883262i | \(-0.655342\pi\) | ||||
−0.468880 | + | 0.883262i | \(0.655342\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.2295 | −1.37657 | −0.688283 | − | 0.725442i | \(-0.741635\pi\) | ||||
−0.688283 | + | 0.725442i | \(0.741635\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.79310 | 0.151006 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.218187 | −0.0182457 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 40.6658 | 3.37711 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.321637 | −0.0265282 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −14.8727 | −1.21842 | −0.609211 | − | 0.793008i | \(-0.708514\pi\) | ||||
−0.609211 | + | 0.793008i | \(0.708514\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.1498 | 1.07012 | 0.535059 | − | 0.844815i | \(-0.320289\pi\) | ||||
0.535059 | + | 0.844815i | \(0.320289\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −14.0815 | −1.13842 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −11.8264 | −0.949917 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.8965 | 0.949448 | 0.474724 | − | 0.880135i | \(-0.342548\pi\) | ||||
0.474724 | + | 0.880135i | \(0.342548\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.50655 | 0.198782 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.53982 | −0.515410 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.14982 | 0.560017 | 0.280009 | − | 0.959997i | \(-0.409663\pi\) | ||||
0.280009 | + | 0.959997i | \(0.409663\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.25328 | −0.0975673 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 25.0796 | 1.94072 | 0.970361 | − | 0.241661i | \(-0.0776922\pi\) | ||||
0.970361 | + | 0.241661i | \(0.0776922\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9524 | −0.996338 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.86328 | 0.142488 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.36801 | −0.560180 | −0.280090 | − | 0.959974i | \(-0.590364\pi\) | ||||
−0.280090 | + | 0.959974i | \(0.590364\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.1831 | 0.769770 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.46965 | 0.185630 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.81690 | 0.659006 | 0.329503 | − | 0.944154i | \(-0.393119\pi\) | ||||
0.329503 | + | 0.944154i | \(0.393119\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.4126 | 1.29427 | 0.647133 | − | 0.762377i | \(-0.275968\pi\) | ||||
0.647133 | + | 0.762377i | \(0.275968\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.57673 | 0.190477 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.39000 | −0.543324 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.86146 | 0.355505 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.89655 | 0.137954 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.89655 | −0.716089 | −0.358045 | − | 0.933704i | \(-0.616556\pi\) | ||||
−0.358045 | + | 0.933704i | \(0.616556\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.5862 | 1.26588 | 0.632941 | − | 0.774200i | \(-0.281848\pi\) | ||||
0.632941 | + | 0.774200i | \(0.281848\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.273448 | 0.0195820 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.00000 | −0.427482 | −0.213741 | − | 0.976890i | \(-0.568565\pi\) | ||||
−0.213741 | + | 0.976890i | \(0.568565\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 22.4477 | 1.59127 | 0.795636 | − | 0.605775i | \(-0.207137\pi\) | ||||
0.795636 | + | 0.605775i | \(0.207137\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.816902 | −0.0576198 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 10.4364 | 0.732490 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −18.9429 | −1.32303 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 18.9429 | 1.31662 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.643274 | −0.0444962 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.206901 | 0.0142436 | 0.00712182 | − | 0.999975i | \(-0.497733\pi\) | ||||
0.00712182 | + | 0.999975i | \(0.497733\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.61000 | 0.315872 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.28655 | −0.360540 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.03509 | −0.206035 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.85018 | 0.192597 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.06071 | −0.0713508 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −22.4809 | −1.50543 | −0.752717 | − | 0.658344i | \(-0.771257\pi\) | ||||
−0.752717 | + | 0.658344i | \(0.771257\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −29.4958 | −1.96639 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 15.5862 | 1.03449 | 0.517246 | − | 0.855837i | \(-0.326957\pi\) | ||||
0.517246 | + | 0.855837i | \(0.326957\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.04637 | −0.465638 | −0.232819 | − | 0.972520i | \(-0.574795\pi\) | ||||
−0.232819 | + | 0.972520i | \(0.574795\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.321637 | −0.0211622 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.56363 | −0.102437 | −0.0512183 | − | 0.998687i | \(-0.516310\pi\) | ||||
−0.0512183 | + | 0.998687i | \(0.516310\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −21.7229 | −1.41705 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.22947 | −0.274734 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 26.1593 | 1.69210 | 0.846052 | − | 0.533100i | \(-0.178973\pi\) | ||||
0.846052 | + | 0.533100i | \(0.178973\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.6546 | −1.07281 | −0.536407 | − | 0.843959i | \(-0.680219\pi\) | ||||
−0.536407 | + | 0.843959i | \(0.680219\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −8.28836 | −0.531699 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.89655 | 0.248941 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.140354 | 0.00893051 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.12725 | −0.198182 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −29.4013 | −1.85579 | −0.927896 | − | 0.372838i | \(-0.878385\pi\) | ||||
−0.927896 | + | 0.372838i | \(0.878385\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.53982 | −0.411155 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −6.09275 | −0.381543 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 12.7135 | 0.793043 | 0.396522 | − | 0.918025i | \(-0.370217\pi\) | ||||
0.396522 | + | 0.918025i | \(0.370217\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.89655 | −0.117846 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −30.2295 | −1.87116 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.20690 | 0.259409 | 0.129704 | − | 0.991553i | \(-0.458597\pi\) | ||||
0.129704 | + | 0.991553i | \(0.458597\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −30.3662 | −1.86538 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.41257 | 0.208846 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.72292 | 0.226991 | 0.113495 | − | 0.993539i | \(-0.463795\pi\) | ||||
0.113495 | + | 0.993539i | \(0.463795\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.72292 | 0.347643 | 0.173821 | − | 0.984777i | \(-0.444388\pi\) | ||||
0.173821 | + | 0.984777i | \(0.444388\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.0701770 | 0.00424730 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 10.1831 | 0.614064 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −12.5066 | −0.751446 | −0.375723 | − | 0.926732i | \(-0.622606\pi\) | ||||
−0.375723 | + | 0.926732i | \(0.622606\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.79128 | 0.526320 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.22947 | 0.371619 | 0.185810 | − | 0.982586i | \(-0.440509\pi\) | ||||
0.185810 | + | 0.982586i | \(0.440509\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.8727 | 1.00298 | 0.501490 | − | 0.865163i | \(-0.332785\pi\) | ||||
0.501490 | + | 0.865163i | \(0.332785\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.806200 | 0.0477552 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.86146 | −0.286963 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.63380 | 0.390224 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.240174 | −0.0140793 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 13.0018 | 0.759574 | 0.379787 | − | 0.925074i | \(-0.375997\pi\) | ||||
0.379787 | + | 0.925074i | \(0.375997\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −29.9191 | −1.74196 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.89655 | 0.110049 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.42690 | 0.0825199 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.35673 | −0.0782004 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.64327 | 0.151852 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −31.2164 | −1.78744 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −0.413802 | −0.0236169 | −0.0118085 | − | 0.999930i | \(-0.503759\pi\) | ||||
−0.0118085 | + | 0.999930i | \(0.503759\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.20690 | −0.125546 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 27.8746 | 1.58062 | 0.790311 | − | 0.612706i | \(-0.209919\pi\) | ||||
0.790311 | + | 0.612706i | \(0.209919\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.4031 | 0.814111 | 0.407056 | − | 0.913403i | \(-0.366555\pi\) | ||||
0.407056 | + | 0.913403i | \(0.366555\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −11.2865 | −0.635925 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.97620 | 0.279491 | 0.139746 | − | 0.990187i | \(-0.455372\pi\) | ||||
0.139746 | + | 0.990187i | \(0.455372\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.4364 | 0.584325 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.50655 | 0.139902 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.12725 | −0.174005 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.22182 | −0.123244 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.0225715 | −0.00124821 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.57491 | −0.307355 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.40310 | −0.242016 | −0.121008 | − | 0.992652i | \(-0.538613\pi\) | ||||
−0.121008 | + | 0.992652i | \(0.538613\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.49345 | 0.301039 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9.89655 | 0.540706 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 25.1498 | 1.37000 | 0.684999 | − | 0.728544i | \(-0.259803\pi\) | ||||
0.684999 | + | 0.728544i | \(0.259803\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.91912 | −0.321483 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.03509 | −0.164359 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 8.19620 | 0.441269 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.72292 | −0.199857 | −0.0999285 | − | 0.994995i | \(-0.531861\pi\) | ||||
−0.0999285 | + | 0.994995i | \(0.531861\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.73421 | 0.521060 | 0.260530 | − | 0.965466i | \(-0.416103\pi\) | ||||
0.260530 | + | 0.965466i | \(0.416103\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.413802 | −0.0220871 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −28.3555 | −1.50921 | −0.754605 | − | 0.656179i | \(-0.772172\pi\) | ||||
−0.754605 | + | 0.656179i | \(0.772172\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −55.8489 | −2.96415 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.56363 | −0.0827559 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.07018 | 0.214816 | 0.107408 | − | 0.994215i | \(-0.465745\pi\) | ||||
0.107408 | + | 0.994215i | \(0.465745\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.5862 | −0.978221 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.321637 | −0.0168816 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −34.5291 | −1.80734 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.3442 | −0.853161 | −0.426580 | − | 0.904450i | \(-0.640282\pi\) | ||||
−0.426580 | + | 0.904450i | \(0.640282\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 14.0815 | 0.733052 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.79310 | −0.404598 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 27.0796 | 1.40213 | 0.701066 | − | 0.713097i | \(-0.252708\pi\) | ||||
0.701066 | + | 0.713097i | \(0.252708\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.49585 | −0.335444 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.27708 | −0.117275 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.90602 | 0.457472 | 0.228736 | − | 0.973489i | \(-0.426541\pi\) | ||||
0.228736 | + | 0.973489i | \(0.426541\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.78000 | −0.347350 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11.6118 | −0.593336 | −0.296668 | − | 0.954981i | \(-0.595875\pi\) | ||||
−0.296668 | + | 0.954981i | \(0.595875\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.89655 | 0.198587 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.92982 | 0.199764 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −12.7693 | −0.647429 | −0.323715 | − | 0.946155i | \(-0.604932\pi\) | ||||
−0.323715 | + | 0.946155i | \(0.604932\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −31.7931 | −1.60785 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.36620 | 0.321132 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 51.2389 | 2.57811 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 24.2996 | 1.21956 | 0.609782 | − | 0.792569i | \(-0.291257\pi\) | ||||
0.609782 | + | 0.792569i | \(0.291257\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.206901 | 0.0103580 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.7135 | 0.634879 | 0.317440 | − | 0.948278i | \(-0.397177\pi\) | ||||
0.317440 | + | 0.948278i | \(0.397177\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.662216 | 0.0329873 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 31.4827 | 1.56439 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.89655 | −0.0940085 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.72474 | 0.332517 | 0.166258 | − | 0.986082i | \(-0.446831\pi\) | ||||
0.166258 | + | 0.986082i | \(0.446831\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.53035 | 0.174139 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.67836 | −0.377828 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 37.8858 | 1.85974 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.22000 | 0.255625 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 24.2884 | 1.18656 | 0.593282 | − | 0.804995i | \(-0.297832\pi\) | ||||
0.593282 | + | 0.804995i | \(0.297832\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.7931 | −0.574760 | −0.287380 | − | 0.957817i | \(-0.592784\pi\) | ||||
−0.287380 | + | 0.957817i | \(0.592784\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 16.1480 | 0.785143 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 49.5047 | 2.40133 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.01129 | −0.387693 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.0701770 | 0.00338818 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.7836 | −0.519429 | −0.259715 | − | 0.965685i | \(-0.583628\pi\) | ||||
−0.259715 | + | 0.965685i | \(0.583628\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −25.4126 | −1.22125 | −0.610625 | − | 0.791920i | \(-0.709082\pi\) | ||||
−0.610625 | + | 0.791920i | \(0.709082\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −13.0796 | −0.627121 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.20690 | 0.201243 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −19.3567 | −0.923846 | −0.461923 | − | 0.886920i | \(-0.652840\pi\) | ||||
−0.461923 | + | 0.886920i | \(0.652840\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.89655 | −0.137931 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 22.9762 | 1.09163 | 0.545816 | − | 0.837905i | \(-0.316220\pi\) | ||||
0.545816 | + | 0.837905i | \(0.316220\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −41.3424 | −1.95982 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.78363 | 0.226258 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.26275 | 0.201171 | 0.100586 | − | 0.994928i | \(-0.467928\pi\) | ||||
0.100586 | + | 0.994928i | \(0.467928\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.86146 | −0.228917 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.22947 | −0.198718 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.850175 | −0.0398568 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 32.0927 | 1.50124 | 0.750618 | − | 0.660737i | \(-0.229756\pi\) | ||||
0.750618 | + | 0.660737i | \(0.229756\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 9.22000 | 0.430353 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.7116 | 0.824913 | 0.412457 | − | 0.910977i | \(-0.364671\pi\) | ||||
0.412457 | + | 0.910977i | \(0.364671\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 23.4126 | 1.08807 | 0.544037 | − | 0.839061i | \(-0.316895\pi\) | ||||
0.544037 | + | 0.839061i | \(0.316895\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.80380 | 0.176397 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 25.1944 | 1.16586 | 0.582929 | − | 0.812523i | \(-0.301907\pi\) | ||||
0.582929 | + | 0.812523i | \(0.301907\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.53982 | 0.117278 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.82637 | −0.176310 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.35673 | −0.0623823 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.55053 | −0.300559 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 22.5731 | 1.03355 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 33.7229 | 1.54084 | 0.770420 | − | 0.637537i | \(-0.220047\pi\) | ||||
0.770420 | + | 0.637537i | \(0.220047\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.413802 | 0.0188677 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.10345 | 0.0957103 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.90965 | 0.132120 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 24.4922 | 1.10985 | 0.554924 | − | 0.831901i | \(-0.312747\pi\) | ||||
0.554924 | + | 0.831901i | \(0.312747\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.29965 | −0.103994 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.136724 | 0.00617027 | 0.00308513 | − | 0.999995i | \(-0.499018\pi\) | ||||
0.00308513 | + | 0.999995i | \(0.499018\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 50.7360 | 2.28504 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −11.2865 | −0.507293 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −14.3329 | −0.642919 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.29602 | 0.192316 | 0.0961581 | − | 0.995366i | \(-0.469345\pi\) | ||||
0.0961581 | + | 0.995366i | \(0.469345\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.06655 | −0.360387 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −39.4684 | −1.75981 | −0.879905 | − | 0.475150i | \(-0.842394\pi\) | ||||
−0.879905 | + | 0.475150i | \(0.842394\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −32.0226 | −1.42499 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.16597 | 0.185017 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −39.0464 | −1.73070 | −0.865350 | − | 0.501168i | \(-0.832904\pi\) | ||||
−0.865350 | + | 0.501168i | \(0.832904\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.86146 | −0.392008 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.22000 | −0.0538644 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 26.7360 | 1.17813 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.57491 | −0.245184 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.36983 | 0.104024 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.39363 | −0.148678 | −0.0743388 | − | 0.997233i | \(-0.523685\pi\) | ||||
−0.0743388 | + | 0.997233i | \(0.523685\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −30.1593 | −1.31877 | −0.659387 | − | 0.751804i | \(-0.729184\pi\) | ||||
−0.659387 | + | 0.751804i | \(0.729184\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.27526 | −0.142944 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −14.7550 | −0.642736 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.7693 | 0.859535 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 22.2408 | 0.965167 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.06071 | 0.0459443 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −30.3662 | −1.31285 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.83584 | −0.122376 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.7931 | −0.764985 | −0.382493 | − | 0.923959i | \(-0.624934\pi\) | ||||
−0.382493 | + | 0.923959i | \(0.624934\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5.60053 | −0.240342 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.273448 | 0.0117132 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.7324 | −0.715425 | −0.357713 | − | 0.933832i | \(-0.616443\pi\) | ||||
−0.357713 | + | 0.933832i | \(0.616443\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 23.2051 | 0.990369 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.71345 | −0.286003 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.1498 | 0.559187 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.37690 | 0.100894 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −16.2996 | −0.690638 | −0.345319 | − | 0.938485i | \(-0.612229\pi\) | ||||
−0.345319 | + | 0.938485i | \(0.612229\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.296019 | 0.0125203 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.56363 | −0.0660164 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6.13672 | −0.258632 | −0.129316 | − | 0.991603i | \(-0.541278\pi\) | ||||
−0.129316 | + | 0.991603i | \(0.541278\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 71.7086 | 3.01680 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 8.07965 | 0.339313 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −29.1498 | −1.22202 | −0.611012 | − | 0.791621i | \(-0.709237\pi\) | ||||
−0.611012 | + | 0.791621i | \(0.709237\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12.8727 | −0.538708 | −0.269354 | − | 0.963041i | \(-0.586810\pi\) | ||||
−0.269354 | + | 0.963041i | \(0.586810\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.18310 | 0.132976 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −66.5957 | −2.77723 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16.3329 | 0.679948 | 0.339974 | − | 0.940435i | \(-0.389582\pi\) | ||||
0.339974 | + | 0.940435i | \(0.389582\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5.65638 | −0.235071 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.72292 | 0.403375 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.79310 | −0.322757 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.46257 | 0.101815 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −26.4477 | −1.09161 | −0.545806 | − | 0.837912i | \(-0.683776\pi\) | ||||
−0.545806 | + | 0.837912i | \(0.683776\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.95239 | 0.0804470 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.92982 | 0.0793823 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −26.5844 | −1.09169 | −0.545845 | − | 0.837886i | \(-0.683791\pi\) | ||||
−0.545845 | + | 0.837886i | \(0.683791\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 18.9429 | 0.776584 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −7.22000 | −0.295495 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 38.7360 | 1.58271 | 0.791355 | − | 0.611356i | \(-0.209376\pi\) | ||||
0.791355 | + | 0.611356i | \(0.209376\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14.4953 | −0.591274 | −0.295637 | − | 0.955300i | \(-0.595532\pi\) | ||||
−0.295637 | + | 0.955300i | \(0.595532\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.35673 | −0.299589 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.89655 | 0.158417 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10.7800 | 0.437547 | 0.218773 | − | 0.975776i | \(-0.429794\pi\) | ||||
0.218773 | + | 0.975776i | \(0.429794\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.35673 | −0.136021 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.21637 | 0.0492091 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −43.1022 | −1.74088 | −0.870441 | − | 0.492273i | \(-0.836166\pi\) | ||||
−0.870441 | + | 0.492273i | \(0.836166\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 6.09275 | 0.245683 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.93929 | −0.198848 | −0.0994242 | − | 0.995045i | \(-0.531700\pi\) | ||||
−0.0994242 | + | 0.995045i | \(0.531700\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.88526 | −0.156162 | −0.0780810 | − | 0.996947i | \(-0.524879\pi\) | ||||
−0.0780810 | + | 0.996947i | \(0.524879\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −12.4031 | −0.497719 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −10.6100 | −0.425081 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 27.7800 | 1.11120 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.206901 | 0.00826283 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −9.22000 | −0.367626 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.9097 | 0.434306 | 0.217153 | − | 0.976138i | \(-0.430323\pi\) | ||||
0.217153 | + | 0.976138i | \(0.430323\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.0665470 | −0.00264501 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 82.1379 | 3.25954 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.218187 | −0.00864487 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 41.5160 | 1.64235 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14.1035 | 0.557053 | 0.278526 | − | 0.960429i | \(-0.410154\pi\) | ||||
0.278526 | + | 0.960429i | \(0.410154\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −43.7009 | −1.72340 | −0.861698 | − | 0.507421i | \(-0.830599\pi\) | ||||
−0.861698 | + | 0.507421i | \(0.830599\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.70035 | 0.0669512 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.04456 | 0.0803799 | 0.0401900 | − | 0.999192i | \(-0.487204\pi\) | ||||
0.0401900 | + | 0.999192i | \(0.487204\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.67836 | −0.301402 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.976197 | 0.0382602 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.67655 | −0.261274 | −0.130637 | − | 0.991430i | \(-0.541702\pi\) | ||||
−0.130637 | + | 0.991430i | \(0.541702\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −77.1248 | −3.01351 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 25.6677 | 1.00139 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −15.4495 | −0.601826 | −0.300913 | − | 0.953652i | \(-0.597291\pi\) | ||||
−0.300913 | + | 0.953652i | \(0.597291\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 31.0689 | 1.20844 | 0.604221 | − | 0.796817i | \(-0.293484\pi\) | ||||
0.604221 | + | 0.796817i | \(0.293484\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.341163 | 0.0132497 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.50655 | −0.0971999 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −68.2520 | −2.64273 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7.23070 | 0.279555 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.01129 | −0.309272 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.8026 | 0.956069 | 0.478034 | − | 0.878341i | \(-0.341349\pi\) | ||||
0.478034 | + | 0.878341i | \(0.341349\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 19.3128 | 0.743348 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 31.0208 | 1.19222 | 0.596112 | − | 0.802901i | \(-0.296711\pi\) | ||||
0.596112 | + | 0.802901i | \(0.296711\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.746725 | 0.0286567 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.01310 | −0.192102 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 20.8727 | 0.798673 | 0.399337 | − | 0.916804i | \(-0.369240\pi\) | ||||
0.399337 | + | 0.916804i | \(0.369240\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −42.7693 | −1.63413 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.26638 | 0.0864676 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.70035 | 0.0647782 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.05766 | 0.116319 | 0.0581594 | − | 0.998307i | \(-0.481477\pi\) | ||||
0.0581594 | + | 0.998307i | \(0.481477\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.89655 | −0.110031 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −63.2389 | −2.39879 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −23.6338 | −0.895194 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0.502920 | 0.0190222 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −23.5160 | −0.888188 | −0.444094 | − | 0.895980i | \(-0.646474\pi\) | ||||
−0.444094 | + | 0.895980i | \(0.646474\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.22000 | 0.0460132 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.98690 | 0.263142 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −8.21819 | −0.309077 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12.1035 | −0.454555 | −0.227277 | − | 0.973830i | \(-0.572982\pi\) | ||||
−0.227277 | + | 0.973830i | \(0.572982\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −38.0891 | −1.42845 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 19.8489 | 0.743349 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.850175 | −0.0317948 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −8.41380 | −0.314219 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −26.0446 | −0.971298 | −0.485649 | − | 0.874154i | \(-0.661417\pi\) | ||||
−0.485649 | + | 0.874154i | \(0.661417\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.86146 | 0.255534 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.35673 | 0.199219 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 106.275 | 3.94694 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.19438 | −0.192649 | −0.0963245 | − | 0.995350i | \(-0.530709\pi\) | ||||
−0.0963245 | + | 0.995350i | \(0.530709\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −21.5731 | −0.799004 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.59567 | −0.243950 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 40.7949 | 1.50679 | 0.753397 | − | 0.657566i | \(-0.228414\pi\) | ||||
0.753397 | + | 0.657566i | \(0.228414\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.25328 | −0.0462278 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.53982 | 0.0935556 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −43.2389 | −1.59057 | −0.795285 | − | 0.606236i | \(-0.792679\pi\) | ||||
−0.795285 | + | 0.606236i | \(0.792679\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.0451430 | −0.00165837 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −31.1724 | −1.14360 | −0.571802 | − | 0.820392i | \(-0.693756\pi\) | ||||
−0.571802 | + | 0.820392i | \(0.693756\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −57.9524 | −2.12321 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −28.1629 | −1.03043 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7.79310 | −0.284754 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.33292 | −0.231092 | −0.115546 | − | 0.993302i | \(-0.536862\pi\) | ||||
−0.115546 | + | 0.993302i | \(0.536862\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 9.45655 | 0.344616 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 51.2389 | 1.86478 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 31.0131 | 1.12719 | 0.563595 | − | 0.826051i | \(-0.309418\pi\) | ||||
0.563595 | + | 0.826051i | \(0.309418\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.10345 | 0.0763504 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −14.3549 | −0.520365 | −0.260183 | − | 0.965559i | \(-0.583783\pi\) | ||||
−0.260183 | + | 0.965559i | \(0.583783\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.0701770 | 0.00254058 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −54.8691 | −1.98380 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.67532 | 0.0604922 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −25.6451 | −0.924786 | −0.462393 | − | 0.886675i | \(-0.653009\pi\) | ||||
−0.462393 | + | 0.886675i | \(0.653009\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.08912 | −0.147266 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −23.1688 | −0.833323 | −0.416661 | − | 0.909062i | \(-0.636800\pi\) | ||||
−0.416661 | + | 0.909062i | \(0.636800\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −30.9066 | −1.11020 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.610001 | 0.0218837 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.12725 | 0.112045 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14.3329 | −0.512872 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 19.7931 | 0.707348 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 46.3555 | 1.65450 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −41.6564 | −1.48489 | −0.742445 | − | 0.669907i | \(-0.766334\pi\) | ||||
−0.742445 | + | 0.669907i | \(0.766334\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.35310 | −0.0481715 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 18.4031 | 0.654339 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.74796 | 0.0620717 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 9.76690 | 0.346396 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 19.0238 | 0.673858 | 0.336929 | − | 0.941530i | \(-0.390612\pi\) | ||||
0.336929 | + | 0.941530i | \(0.390612\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −27.1022 | −0.958808 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 30.7324 | 1.08588 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8.86146 | −0.312714 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −25.4827 | −0.898149 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.19743 | −0.0421515 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 23.0131 | 0.809098 | 0.404549 | − | 0.914516i | \(-0.367429\pi\) | ||||
0.404549 | + | 0.914516i | \(0.367429\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24.6658 | 0.866135 | 0.433067 | − | 0.901361i | \(-0.357431\pi\) | ||||
0.433067 | + | 0.901361i | \(0.357431\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.84070 | −0.0645563 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 27.8596 | 0.975881 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.872747 | 0.0305335 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.631989 | 0.0220835 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 44.6182 | 1.55719 | 0.778594 | − | 0.627528i | \(-0.215933\pi\) | ||||
0.778594 | + | 0.627528i | \(0.215933\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 38.7693 | 1.35141 | 0.675706 | − | 0.737171i | \(-0.263839\pi\) | ||||
0.675706 | + | 0.737171i | \(0.263839\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.27526 | −0.114030 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 39.1022 | 1.35972 | 0.679859 | − | 0.733343i | \(-0.262041\pi\) | ||||
0.679859 | + | 0.733343i | \(0.262041\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.68965 | −0.128147 | −0.0640734 | − | 0.997945i | \(-0.520409\pi\) | ||||
−0.0640734 | + | 0.997945i | \(0.520409\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.02257 | 0.139541 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.86146 | 0.168440 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 97.7241 | 3.38188 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.75620 | −0.198963 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −26.0446 | −0.899158 | −0.449579 | − | 0.893241i | \(-0.648426\pi\) | ||||
−0.449579 | + | 0.893241i | \(0.648426\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 79.9179 | 2.75579 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.00363 | −0.0690087 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −50.4696 | −1.73621 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.00000 | 0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5.42690 | −0.186251 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.4031 | 0.425173 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 40.1742 | 1.37554 | 0.687769 | − | 0.725929i | \(-0.258590\pi\) | ||||
0.687769 | + | 0.725929i | \(0.258590\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.26035 | 0.248299 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −7.64146 | −0.261027 | −0.130514 | − | 0.991447i | \(-0.541663\pi\) | ||||
−0.130514 | + | 0.991447i | \(0.541663\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.11474 | −0.140393 | −0.0701965 | − | 0.997533i | \(-0.522363\pi\) | ||||
−0.0701965 | + | 0.997533i | \(0.522363\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.56363 | 0.0532883 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.15930 | 0.0735033 | 0.0367516 | − | 0.999324i | \(-0.488299\pi\) | ||||
0.0367516 | + | 0.999324i | \(0.488299\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −28.7098 | −0.976163 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.13368 | −0.0724635 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13.1498 | 0.446077 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.554156 | −0.0187769 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.16293 | −0.0732039 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 20.1962 | 0.682756 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −27.8633 | −0.940876 | −0.470438 | − | 0.882433i | \(-0.655904\pi\) | ||||
−0.470438 | + | 0.882433i | \(0.655904\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4.18187 | −0.141051 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −26.6991 | −0.899516 | −0.449758 | − | 0.893150i | \(-0.648490\pi\) | ||||
−0.449758 | + | 0.893150i | \(0.648490\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −26.2996 | −0.885054 | −0.442527 | − | 0.896755i | \(-0.645918\pi\) | ||||
−0.442527 | + | 0.896755i | \(0.645918\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 9.62310 | 0.323477 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 51.3567 | 1.72439 | 0.862195 | − | 0.506576i | \(-0.169089\pi\) | ||||
0.862195 | + | 0.506576i | \(0.169089\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 21.0796 | 0.706989 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 8.07965 | 0.270678 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.58620 | 0.120008 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 34.3555 | 1.14838 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.458945 | −0.0153237 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −31.6753 | −1.05643 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −37.8858 | −1.26216 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.436373 | 0.0145216 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 67.8489 | 2.25538 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14.5957 | 0.484641 | 0.242321 | − | 0.970196i | \(-0.422091\pi\) | ||||
0.242321 | + | 0.970196i | \(0.422091\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 23.8044 | 0.789542 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −27.0095 | −0.894864 | −0.447432 | − | 0.894318i | \(-0.647661\pi\) | ||||
−0.447432 | + | 0.894318i | \(0.647661\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.72292 | 0.321782 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 10.0403 | 0.331924 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −19.7931 | −0.653626 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 49.7455 | 1.64095 | 0.820476 | − | 0.571681i | \(-0.193708\pi\) | ||||
0.820476 | + | 0.571681i | \(0.193708\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.133094 | 0.00438560 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.12725 | 0.102935 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −19.3128 | −0.634999 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −19.8746 | −0.652766 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −7.30912 | −0.239804 | −0.119902 | − | 0.992786i | \(-0.538258\pi\) | ||||
−0.119902 | + | 0.992786i | \(0.538258\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.643274 | −0.0210825 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8.96550 | −0.293517 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 18.9429 | 0.619500 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −39.5309 | −1.29142 | −0.645710 | − | 0.763583i | \(-0.723438\pi\) | ||||
−0.645710 | + | 0.763583i | \(0.723438\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.63257 | −0.151178 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −53.8971 | −1.75700 | −0.878498 | − | 0.477746i | \(-0.841454\pi\) | ||||
−0.878498 | + | 0.477746i | \(0.841454\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 31.7931 | 1.03533 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 7.39000 | 0.240397 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 28.7217 | 0.933330 | 0.466665 | − | 0.884434i | \(-0.345455\pi\) | ||||
0.466665 | + | 0.884434i | \(0.345455\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.93345 | 0.0627625 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.60053 | −0.0519007 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 21.9335 | 0.710494 | 0.355247 | − | 0.934772i | \(-0.384397\pi\) | ||||
0.355247 | + | 0.934772i | \(0.384397\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −38.5624 | −1.24785 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.35673 | −0.108508 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −10.9762 | −0.354440 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.7882 | −0.702846 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 22.5731 | 0.727408 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 68.5255 | 2.20591 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 40.7360 | 1.30998 | 0.654991 | − | 0.755637i | \(-0.272672\pi\) | ||||
0.654991 | + | 0.755637i | \(0.272672\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.00584 | 0.0323123 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −38.0446 | −1.22091 | −0.610454 | − | 0.792052i | \(-0.709013\pi\) | ||||
−0.610454 | + | 0.792052i | \(0.709013\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −16.2295 | −0.520293 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.714619 | 0.0228861 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −37.2282 | −1.19104 | −0.595518 | − | 0.803342i | \(-0.703053\pi\) | ||||
−0.595518 | + | 0.803342i | \(0.703053\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10.6100 | −0.339097 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.203271 | −0.00648994 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −50.0446 | −1.59617 | −0.798087 | − | 0.602543i | \(-0.794154\pi\) | ||||
−0.798087 | + | 0.602543i | \(0.794154\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −23.3793 | −0.744926 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.79310 | 0.0570750 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.87275 | 0.282137 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.9774 | 0.380476 | 0.190238 | − | 0.981738i | \(-0.439074\pi\) | ||||
0.190238 | + | 0.981738i | \(0.439074\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.41620 | 0.0449418 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 87.4684 | 2.77294 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 23.3906 | 0.740787 | 0.370394 | − | 0.928875i | \(-0.379223\pi\) | ||||
0.370394 | + | 0.928875i | \(0.379223\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.59690 | −0.113801 |
(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 | 308.2.a.c.1.2 | ✓ | 3 | |
3.2 | odd | 2 | 2772.2.a.s.1.1 | 3 | |||
4.3 | odd | 2 | 1232.2.a.r.1.2 | 3 | |||
5.2 | odd | 4 | 7700.2.e.p.1849.4 | 6 | |||
5.3 | odd | 4 | 7700.2.e.p.1849.3 | 6 | |||
5.4 | even | 2 | 7700.2.a.y.1.2 | 3 | |||
7.2 | even | 3 | 2156.2.i.m.1145.2 | 6 | |||
7.3 | odd | 6 | 2156.2.i.k.177.2 | 6 | |||
7.4 | even | 3 | 2156.2.i.m.177.2 | 6 | |||
7.5 | odd | 6 | 2156.2.i.k.1145.2 | 6 | |||
7.6 | odd | 2 | 2156.2.a.j.1.2 | 3 | |||
8.3 | odd | 2 | 4928.2.a.bx.1.2 | 3 | |||
8.5 | even | 2 | 4928.2.a.ca.1.2 | 3 | |||
11.10 | odd | 2 | 3388.2.a.o.1.2 | 3 | |||
28.27 | even | 2 | 8624.2.a.cj.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
308.2.a.c.1.2 | ✓ | 3 | 1.1 | even | 1 | trivial | |
1232.2.a.r.1.2 | 3 | 4.3 | odd | 2 | |||
2156.2.a.j.1.2 | 3 | 7.6 | odd | 2 | |||
2156.2.i.k.177.2 | 6 | 7.3 | odd | 6 | |||
2156.2.i.k.1145.2 | 6 | 7.5 | odd | 6 | |||
2156.2.i.m.177.2 | 6 | 7.4 | even | 3 | |||
2156.2.i.m.1145.2 | 6 | 7.2 | even | 3 | |||
2772.2.a.s.1.1 | 3 | 3.2 | odd | 2 | |||
3388.2.a.o.1.2 | 3 | 11.10 | odd | 2 | |||
4928.2.a.bx.1.2 | 3 | 8.3 | odd | 2 | |||
4928.2.a.ca.1.2 | 3 | 8.5 | even | 2 | |||
7700.2.a.y.1.2 | 3 | 5.4 | even | 2 | |||
7700.2.e.p.1849.3 | 6 | 5.3 | odd | 4 | |||
7700.2.e.p.1849.4 | 6 | 5.2 | odd | 4 | |||
8624.2.a.cj.1.2 | 3 | 28.27 | even | 2 |