Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8036,2,Mod(1,8036)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8036, 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("8036.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8036 = 2^{2} \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8036.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: | \(64.1677830643\) |
Analytic rank: | \(0\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - x^{14} - 37 x^{13} + 39 x^{12} + 537 x^{11} - 616 x^{10} - 3853 x^{9} + 4929 x^{8} + \cdots + 3381 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 1148) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Root | \(-2.47735\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8036.1 |
$q$-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 | ||||||||
\(3\) | 2.47735 | 1.43030 | 0.715149 | − | 0.698973i | \(-0.246359\pi\) | ||||
0.715149 | + | 0.698973i | \(0.246359\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.49844 | −1.56455 | −0.782274 | − | 0.622935i | \(-0.785940\pi\) | ||||
−0.782274 | + | 0.622935i | \(0.785940\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.13725 | 1.04575 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.886832 | −0.267390 | −0.133695 | − | 0.991023i | \(-0.542684\pi\) | ||||
−0.133695 | + | 0.991023i | \(0.542684\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.85228 | −1.90048 | −0.950240 | − | 0.311519i | \(-0.899162\pi\) | ||||
−0.950240 | + | 0.311519i | \(0.899162\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −8.66684 | −2.23777 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.02899 | 0.734637 | 0.367318 | − | 0.930095i | \(-0.380276\pi\) | ||||
0.367318 | + | 0.930095i | \(0.380276\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.07400 | 1.39347 | 0.696735 | − | 0.717328i | \(-0.254635\pi\) | ||||
0.696735 | + | 0.717328i | \(0.254635\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.52270 | −0.943048 | −0.471524 | − | 0.881853i | \(-0.656296\pi\) | ||||
−0.471524 | + | 0.881853i | \(0.656296\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.23905 | 1.44781 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.340013 | 0.0654355 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.22633 | −1.34189 | −0.670947 | − | 0.741505i | \(-0.734112\pi\) | ||||
−0.670947 | + | 0.741505i | \(0.734112\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.72069 | 1.74589 | 0.872944 | − | 0.487821i | \(-0.162208\pi\) | ||||
0.872944 | + | 0.487821i | \(0.162208\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.19699 | −0.382447 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.05671 | 1.16012 | 0.580058 | − | 0.814575i | \(-0.303030\pi\) | ||||
0.580058 | + | 0.814575i | \(0.303030\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −16.9755 | −2.71825 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.25996 | 0.649638 | 0.324819 | − | 0.945776i | \(-0.394697\pi\) | ||||
0.324819 | + | 0.945776i | \(0.394697\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −10.9755 | −1.63613 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.7610 | −1.71551 | −0.857756 | − | 0.514056i | \(-0.828142\pi\) | ||||
−0.857756 | + | 0.514056i | \(0.828142\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.50385 | 1.05075 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.23725 | 0.856752 | 0.428376 | − | 0.903601i | \(-0.359086\pi\) | ||||
0.428376 | + | 0.903601i | \(0.359086\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.10252 | 0.418344 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 15.0474 | 1.99308 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.453451 | 0.0590343 | 0.0295171 | − | 0.999564i | \(-0.490603\pi\) | ||||
0.0295171 | + | 0.999564i | \(0.490603\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.80500 | −0.231106 | −0.115553 | − | 0.993301i | \(-0.536864\pi\) | ||||
−0.115553 | + | 0.993301i | \(0.536864\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 23.9722 | 2.97339 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.386390 | 0.0472050 | 0.0236025 | − | 0.999721i | \(-0.492486\pi\) | ||||
0.0236025 | + | 0.999721i | \(0.492486\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −11.2043 | −1.34884 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.406313 | 0.0482205 | 0.0241103 | − | 0.999709i | \(-0.492325\pi\) | ||||
0.0241103 | + | 0.999709i | \(0.492325\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.47266 | 0.289403 | 0.144701 | − | 0.989475i | \(-0.453778\pi\) | ||||
0.144701 | + | 0.989475i | \(0.453778\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 17.9336 | 2.07080 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.1588 | 1.59299 | 0.796497 | − | 0.604643i | \(-0.206684\pi\) | ||||
0.796497 | + | 0.604643i | \(0.206684\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.56942 | −0.952157 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.79158 | 0.855237 | 0.427618 | − | 0.903959i | \(-0.359353\pi\) | ||||
0.427618 | + | 0.903959i | \(0.359353\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.5967 | −1.14937 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −17.9021 | −1.91931 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.14645 | −0.545523 | −0.272761 | − | 0.962082i | \(-0.587937\pi\) | ||||
−0.272761 | + | 0.962082i | \(0.587937\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 24.0815 | 2.49714 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −21.2495 | −2.18015 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.4082 | −1.15833 | −0.579165 | − | 0.815211i | \(-0.696621\pi\) | ||||
−0.579165 | + | 0.815211i | \(0.696621\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.78221 | −0.279623 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.23469 | 0.719878 | 0.359939 | − | 0.932976i | \(-0.382797\pi\) | ||||
0.359939 | + | 0.932976i | \(0.382797\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.81614 | −0.967213 | −0.483606 | − | 0.875286i | \(-0.660673\pi\) | ||||
−0.483606 | + | 0.875286i | \(0.660673\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.91514 | 0.958533 | 0.479266 | − | 0.877669i | \(-0.340903\pi\) | ||||
0.479266 | + | 0.877669i | \(0.340903\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.44277 | 0.425540 | 0.212770 | − | 0.977102i | \(-0.431751\pi\) | ||||
0.212770 | + | 0.977102i | \(0.431751\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 17.4819 | 1.65931 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.0359 | 1.22631 | 0.613157 | − | 0.789961i | \(-0.289899\pi\) | ||||
0.613157 | + | 0.789961i | \(0.289899\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 15.8224 | 1.47544 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −21.4973 | −1.98743 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.2135 | −0.928503 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.47735 | −0.223375 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7.83317 | −0.700620 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 21.6259 | 1.91899 | 0.959496 | − | 0.281722i | \(-0.0909057\pi\) | ||||
0.959496 | + | 0.281722i | \(0.0909057\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 10.5534 | 0.929175 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.13139 | 0.186221 | 0.0931104 | − | 0.995656i | \(-0.470319\pi\) | ||||
0.0931104 | + | 0.995656i | \(0.470319\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.18951 | −0.102377 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.35667 | 0.201344 | 0.100672 | − | 0.994920i | \(-0.467901\pi\) | ||||
0.100672 | + | 0.994920i | \(0.467901\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.9520 | 1.09858 | 0.549288 | − | 0.835633i | \(-0.314899\pi\) | ||||
0.549288 | + | 0.835633i | \(0.314899\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −29.1360 | −2.45369 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.07682 | 0.508169 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 25.2808 | 2.09946 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −14.5047 | −1.18827 | −0.594137 | − | 0.804364i | \(-0.702506\pi\) | ||||
−0.594137 | + | 0.804364i | \(0.702506\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.6316 | 0.946569 | 0.473285 | − | 0.880910i | \(-0.343068\pi\) | ||||
0.473285 | + | 0.880910i | \(0.343068\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 9.50268 | 0.768246 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −34.0072 | −2.73152 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.60289 | 0.447160 | 0.223580 | − | 0.974686i | \(-0.428226\pi\) | ||||
0.223580 | + | 0.974686i | \(0.428226\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 15.4518 | 1.22541 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.42331 | 0.581439 | 0.290719 | − | 0.956808i | \(-0.406105\pi\) | ||||
0.290719 | + | 0.956808i | \(0.406105\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7.68603 | 0.598356 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 17.5163 | 1.35545 | 0.677726 | − | 0.735314i | \(-0.262965\pi\) | ||||
0.677726 | + | 0.735314i | \(0.262965\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 33.9537 | 2.61182 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 19.0556 | 1.45722 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.59063 | 0.729162 | 0.364581 | − | 0.931172i | \(-0.381212\pi\) | ||||
0.364581 | + | 0.931172i | \(0.381212\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.12336 | 0.0844366 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 24.6408 | 1.84174 | 0.920870 | − | 0.389871i | \(-0.127480\pi\) | ||||
0.920870 | + | 0.389871i | \(0.127480\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.27455 | −0.243395 | −0.121698 | − | 0.992567i | \(-0.538834\pi\) | ||||
−0.121698 | + | 0.992567i | \(0.538834\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.47160 | −0.330551 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −24.6874 | −1.81506 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.68620 | −0.196434 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.00730 | 0.0728855 | 0.0364428 | − | 0.999336i | \(-0.488397\pi\) | ||||
0.0364428 | + | 0.999336i | \(0.488397\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19.9178 | 1.43371 | 0.716857 | − | 0.697220i | \(-0.245580\pi\) | ||||
0.716857 | + | 0.697220i | \(0.245580\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 59.3876 | 4.25283 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.96044 | 0.567158 | 0.283579 | − | 0.958949i | \(-0.408478\pi\) | ||||
0.283579 | + | 0.958949i | \(0.408478\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.1963 | −1.14813 | −0.574064 | − | 0.818811i | \(-0.694634\pi\) | ||||
−0.574064 | + | 0.818811i | \(0.694634\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.957221 | 0.0675172 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.49844 | 0.244341 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −14.1888 | −0.986193 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.38661 | −0.372600 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.1084 | 0.695894 | 0.347947 | − | 0.937514i | \(-0.386879\pi\) | ||||
0.347947 | + | 0.937514i | \(0.386879\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.00658 | 0.0689696 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −14.9032 | −1.01639 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.12564 | 0.413932 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −20.7554 | −1.39616 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.60799 | 0.375539 | 0.187770 | − | 0.982213i | \(-0.439874\pi\) | ||||
0.187770 | + | 0.982213i | \(0.439874\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 22.7107 | 1.51405 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.16589 | −0.342872 | −0.171436 | − | 0.985195i | \(-0.554841\pi\) | ||||
−0.171436 | + | 0.985195i | \(0.554841\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.39496 | 0.422591 | 0.211296 | − | 0.977422i | \(-0.432232\pi\) | ||||
0.211296 | + | 0.977422i | \(0.432232\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.1923 | 0.929771 | 0.464885 | − | 0.885371i | \(-0.346096\pi\) | ||||
0.464885 | + | 0.885371i | \(0.346096\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 41.1450 | 2.68400 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 35.0763 | 2.27845 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.2318 | −0.985266 | −0.492633 | − | 0.870237i | \(-0.663966\pi\) | ||||
−0.492633 | + | 0.870237i | \(0.663966\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.90521 | −0.444804 | −0.222402 | − | 0.974955i | \(-0.571390\pi\) | ||||
−0.222402 | + | 0.974955i | \(0.571390\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −22.2495 | −1.42730 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −41.6207 | −2.64826 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 19.3024 | 1.22324 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −21.2459 | −1.34103 | −0.670515 | − | 0.741896i | \(-0.733927\pi\) | ||||
−0.670515 | + | 0.741896i | \(0.733927\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.01088 | 0.252162 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −26.2517 | −1.64395 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.06200 | −0.378137 | −0.189068 | − | 0.981964i | \(-0.560547\pi\) | ||||
−0.189068 | + | 0.981964i | \(0.560547\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −22.6708 | −1.40329 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −15.1984 | −0.937171 | −0.468586 | − | 0.883418i | \(-0.655236\pi\) | ||||
−0.468586 | + | 0.883418i | \(0.655236\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −21.8206 | −1.34043 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −12.7495 | −0.780260 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 18.8933 | 1.15195 | 0.575973 | − | 0.817469i | \(-0.304623\pi\) | ||||
0.575973 | + | 0.817469i | \(0.304623\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.9578 | 0.908621 | 0.454310 | − | 0.890843i | \(-0.349886\pi\) | ||||
0.454310 | + | 0.890843i | \(0.349886\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.41982 | −0.387130 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.0971 | −0.786931 | −0.393465 | − | 0.919339i | \(-0.628724\pi\) | ||||
−0.393465 | + | 0.919339i | \(0.628724\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 30.4962 | 1.82576 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −21.2844 | −1.26972 | −0.634860 | − | 0.772627i | \(-0.718942\pi\) | ||||
−0.634860 | + | 0.772627i | \(0.718942\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 22.7683 | 1.35343 | 0.676717 | − | 0.736243i | \(-0.263402\pi\) | ||||
0.676717 | + | 0.736243i | \(0.263402\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −52.6424 | −3.11826 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.82525 | −0.460309 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −28.2621 | −1.65675 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.51752 | 0.263916 | 0.131958 | − | 0.991255i | \(-0.457874\pi\) | ||||
0.131958 | + | 0.991255i | \(0.457874\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.58637 | −0.0923620 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.301534 | −0.0174968 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 30.9908 | 1.79224 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 17.9228 | 1.02964 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.31467 | 0.361577 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.60882 | 0.263039 | 0.131520 | − | 0.991314i | \(-0.458014\pi\) | ||||
0.131520 | + | 0.991314i | \(0.458014\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −24.3180 | −1.38340 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.9788 | −0.906077 | −0.453039 | − | 0.891491i | \(-0.649660\pi\) | ||||
−0.453039 | + | 0.891491i | \(0.649660\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −32.4129 | −1.83208 | −0.916042 | − | 0.401082i | \(-0.868634\pi\) | ||||
−0.916042 | + | 0.401082i | \(0.868634\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −13.1162 | −0.736679 | −0.368340 | − | 0.929691i | \(-0.620074\pi\) | ||||
−0.368340 | + | 0.929691i | \(0.620074\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.40854 | 0.358809 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 24.5632 | 1.37099 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 18.3981 | 1.02370 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −49.6040 | −2.75153 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 11.0063 | 0.608649 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 26.6358 | 1.46403 | 0.732017 | − | 0.681286i | \(-0.238579\pi\) | ||||
0.732017 | + | 0.681286i | \(0.238579\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 22.1387 | 1.21319 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.35176 | −0.0738545 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −22.0648 | −1.20194 | −0.600972 | − | 0.799270i | \(-0.705220\pi\) | ||||
−0.600972 | + | 0.799270i | \(0.705220\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 32.2945 | 1.75399 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.62062 | −0.466833 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 39.1975 | 2.11032 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 29.4858 | 1.58288 | 0.791440 | − | 0.611246i | \(-0.209332\pi\) | ||||
0.791440 | + | 0.611246i | \(0.209332\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.9842 | −0.802084 | −0.401042 | − | 0.916060i | \(-0.631352\pi\) | ||||
−0.401042 | + | 0.916060i | \(0.631352\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.32986 | −0.124359 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.2650 | 0.972149 | 0.486075 | − | 0.873917i | \(-0.338428\pi\) | ||||
0.486075 | + | 0.873917i | \(0.338428\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.42146 | −0.0754433 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 20.1774 | 1.06492 | 0.532462 | − | 0.846454i | \(-0.321267\pi\) | ||||
0.532462 | + | 0.846454i | \(0.321267\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.8935 | 0.941761 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −25.3025 | −1.32803 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.65044 | −0.452785 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.2336 | 0.899585 | 0.449792 | − | 0.893133i | \(-0.351498\pi\) | ||||
0.449792 | + | 0.893133i | \(0.351498\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.13725 | −0.163319 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.7019 | −0.554125 | −0.277062 | − | 0.960852i | \(-0.589361\pi\) | ||||
−0.277062 | + | 0.960852i | \(0.589361\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −19.4055 | −1.00209 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 49.5168 | 2.55024 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.9770 | 1.28298 | 0.641492 | − | 0.767130i | \(-0.278316\pi\) | ||||
0.641492 | + | 0.767130i | \(0.278316\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 53.5750 | 2.74473 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.22751 | −0.216016 | −0.108008 | − | 0.994150i | \(-0.534447\pi\) | ||||
−0.108008 | + | 0.994150i | \(0.534447\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 13.3646 | 0.679359 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 25.5041 | 1.29311 | 0.646555 | − | 0.762867i | \(-0.276209\pi\) | ||||
0.646555 | + | 0.762867i | \(0.276209\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13.6992 | −0.692798 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.28020 | 0.266351 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −49.5338 | −2.49231 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −30.2426 | −1.51783 | −0.758917 | − | 0.651187i | \(-0.774271\pi\) | ||||
−0.758917 | + | 0.651187i | \(0.774271\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.81709 | 0.290491 | 0.145246 | − | 0.989396i | \(-0.453603\pi\) | ||||
0.145246 | + | 0.989396i | \(0.453603\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −66.6089 | −3.31802 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 29.9796 | 1.48970 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.25812 | −0.310203 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.436763 | −0.0215965 | −0.0107983 | − | 0.999942i | \(-0.503437\pi\) | ||||
−0.0107983 | + | 0.999942i | \(0.503437\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.83829 | 0.287982 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −27.2583 | −1.33806 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 32.0867 | 1.57129 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.44035 | −0.363485 | −0.181743 | − | 0.983346i | \(-0.558174\pi\) | ||||
−0.181743 | + | 0.983346i | \(0.558174\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.7010 | 1.10638 | 0.553189 | − | 0.833056i | \(-0.313411\pi\) | ||||
0.553189 | + | 0.833056i | \(0.313411\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −36.8971 | −1.79400 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 21.9270 | 1.06361 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 15.0544 | 0.726833 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 33.3117 | 1.60457 | 0.802285 | − | 0.596942i | \(-0.203618\pi\) | ||||
0.802285 | + | 0.596942i | \(0.203618\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13.8756 | −0.666816 | −0.333408 | − | 0.942783i | \(-0.608199\pi\) | ||||
−0.333408 | + | 0.942783i | \(0.608199\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 62.6294 | 3.00285 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −27.4709 | −1.31411 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 25.0594 | 1.19602 | 0.598010 | − | 0.801488i | \(-0.295958\pi\) | ||||
0.598010 | + | 0.801488i | \(0.295958\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.6739 | 0.602154 | 0.301077 | − | 0.953600i | \(-0.402654\pi\) | ||||
0.301077 | + | 0.953600i | \(0.402654\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 18.0045 | 0.853497 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −35.9333 | −1.69959 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −35.8184 | −1.69037 | −0.845187 | − | 0.534470i | \(-0.820511\pi\) | ||||
−0.845187 | + | 0.534470i | \(0.820511\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.886832 | 0.0417593 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 28.8156 | 1.35388 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −21.1037 | −0.987190 | −0.493595 | − | 0.869692i | \(-0.664318\pi\) | ||||
−0.493595 | + | 0.869692i | \(0.664318\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.02989 | 0.0480713 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −33.8364 | −1.57592 | −0.787958 | − | 0.615729i | \(-0.788862\pi\) | ||||
−0.787958 | + | 0.615729i | \(0.788862\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 31.5226 | 1.46498 | 0.732490 | − | 0.680778i | \(-0.238358\pi\) | ||||
0.732490 | + | 0.680778i | \(0.238358\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −84.2477 | −3.90689 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 33.1549 | 1.53422 | 0.767112 | − | 0.641513i | \(-0.221693\pi\) | ||||
0.767112 | + | 0.641513i | \(0.221693\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 13.8803 | 0.639571 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.77787 | −0.173707 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 43.9700 | 2.01748 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 19.5678 | 0.895948 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7.80316 | −0.356536 | −0.178268 | − | 0.983982i | \(-0.557049\pi\) | ||||
−0.178268 | + | 0.983982i | \(0.557049\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −48.3545 | −2.20478 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 39.9109 | 1.81226 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.9654 | 0.542202 | 0.271101 | − | 0.962551i | \(-0.412612\pi\) | ||||
0.271101 | + | 0.962551i | \(0.412612\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 18.3901 | 0.831630 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.00762 | 0.180861 | 0.0904307 | − | 0.995903i | \(-0.471176\pi\) | ||||
0.0904307 | + | 0.995903i | \(0.471176\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −21.8884 | −0.985806 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 9.73339 | 0.437483 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11.7405 | −0.525578 | −0.262789 | − | 0.964853i | \(-0.584642\pi\) | ||||
−0.262789 | + | 0.964853i | \(0.584642\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 43.3940 | 1.93870 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.10200 | −0.227487 | −0.113743 | − | 0.993510i | \(-0.536284\pi\) | ||||
−0.113743 | + | 0.993510i | \(0.536284\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −25.3101 | −1.12628 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 84.1151 | 3.73568 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −22.1952 | −0.983784 | −0.491892 | − | 0.870656i | \(-0.663695\pi\) | ||||
−0.491892 | + | 0.870656i | \(0.663695\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.06524 | 0.0911824 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 34.3411 | 1.51325 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.4300 | 0.458711 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 23.7593 | 1.04292 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −26.9053 | −1.17874 | −0.589370 | − | 0.807863i | \(-0.700624\pi\) | ||||
−0.589370 | + | 0.807863i | \(0.700624\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 28.5119 | 1.24674 | 0.623369 | − | 0.781928i | \(-0.285764\pi\) | ||||
0.623369 | + | 0.781928i | \(0.285764\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 29.4438 | 1.28259 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.54517 | −0.110660 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.42259 | 0.0617351 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.85228 | 0.296805 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −34.6875 | −1.49967 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 61.0438 | 2.63423 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.1630 | −0.565920 | −0.282960 | − | 0.959132i | \(-0.591316\pi\) | ||||
−0.282960 | + | 0.959132i | \(0.591316\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8.11220 | −0.348128 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −15.5427 | −0.665778 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.8254 | −0.591133 | −0.295567 | − | 0.955322i | \(-0.595508\pi\) | ||||
−0.295567 | + | 0.955322i | \(0.595508\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.66273 | −0.241679 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −43.8927 | −1.86989 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −61.1594 | −2.59607 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −34.3090 | −1.45372 | −0.726861 | − | 0.686785i | \(-0.759021\pi\) | ||||
−0.726861 | + | 0.686785i | \(0.759021\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −29.1904 | −1.23462 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.65465 | −0.280960 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −13.4964 | −0.568806 | −0.284403 | − | 0.958705i | \(-0.591795\pi\) | ||||
−0.284403 | + | 0.958705i | \(0.591795\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −45.6053 | −1.91863 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7.21418 | −0.302434 | −0.151217 | − | 0.988501i | \(-0.548319\pi\) | ||||
−0.151217 | + | 0.988501i | \(0.548319\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.09658 | −0.380680 | −0.190340 | − | 0.981718i | \(-0.560959\pi\) | ||||
−0.190340 | + | 0.981718i | \(0.560959\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.49543 | 0.104248 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −32.7401 | −1.36536 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −25.5931 | −1.06545 | −0.532727 | − | 0.846287i | \(-0.678833\pi\) | ||||
−0.532727 | + | 0.846287i | \(0.678833\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 49.3433 | 2.05064 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.53139 | −0.229087 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 75.2069 | 3.10942 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 14.8861 | 0.614416 | 0.307208 | − | 0.951642i | \(-0.400605\pi\) | ||||
0.307208 | + | 0.951642i | \(0.400605\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 59.0435 | 2.43284 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 19.7208 | 0.811204 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9.85853 | 0.404841 | 0.202421 | − | 0.979299i | \(-0.435119\pi\) | ||||
0.202421 | + | 0.979299i | \(0.435119\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −40.1239 | −1.64216 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11.2816 | 0.460953 | 0.230476 | − | 0.973078i | \(-0.425972\pi\) | ||||
0.230476 | + | 0.973078i | \(0.425972\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.84169 | 0.197497 | 0.0987483 | − | 0.995112i | \(-0.468516\pi\) | ||||
0.0987483 | + | 0.995112i | \(0.468516\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.21220 | 0.0493646 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 35.7314 | 1.45269 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −28.9727 | −1.17596 | −0.587982 | − | 0.808874i | \(-0.700077\pi\) | ||||
−0.587982 | + | 0.808874i | \(0.700077\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 80.5894 | 3.26030 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.05986 | 0.163976 | 0.0819881 | − | 0.996633i | \(-0.473873\pi\) | ||||
0.0819881 | + | 0.996633i | \(0.473873\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 8.66684 | 0.349481 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 31.0323 | 1.24931 | 0.624657 | − | 0.780900i | \(-0.285239\pi\) | ||||
0.624657 | + | 0.780900i | \(0.285239\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12.8594 | −0.516862 | −0.258431 | − | 0.966030i | \(-0.583206\pi\) | ||||
−0.258431 | + | 0.966030i | \(0.583206\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.53778 | −0.0617088 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.79140 | −0.351656 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −13.3445 | −0.532929 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 21.3747 | 0.852264 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28.0819 | −1.11792 | −0.558961 | − | 0.829194i | \(-0.688800\pi\) | ||||
−0.558961 | + | 0.829194i | \(0.688800\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 25.0421 | 0.995335 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −75.6570 | −3.00235 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.27471 | 0.0504266 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −29.1285 | −1.15051 | −0.575253 | − | 0.817976i | \(-0.695096\pi\) | ||||
−0.575253 | + | 0.817976i | \(0.695096\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −34.0791 | −1.34395 | −0.671974 | − | 0.740575i | \(-0.734553\pi\) | ||||
−0.671974 | + | 0.740575i | \(0.734553\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −36.9204 | −1.45374 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.04612 | 0.277012 | 0.138506 | − | 0.990362i | \(-0.455770\pi\) | ||||
0.138506 | + | 0.990362i | \(0.455770\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.402135 | −0.0157852 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 13.5790 | 0.531388 | 0.265694 | − | 0.964057i | \(-0.414399\pi\) | ||||
0.265694 | + | 0.964057i | \(0.414399\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.45654 | −0.291351 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.75735 | 0.302643 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 38.7358 | 1.50893 | 0.754466 | − | 0.656339i | \(-0.227896\pi\) | ||||
0.754466 | + | 0.656339i | \(0.227896\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26.6698 | 1.03734 | 0.518668 | − | 0.854976i | \(-0.326428\pi\) | ||||
0.518668 | + | 0.854976i | \(0.326428\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −51.4184 | −1.99693 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 32.6825 | 1.26547 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 13.8929 | 0.537132 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.60073 | 0.0617955 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −43.4682 | −1.67558 | −0.837789 | − | 0.545995i | \(-0.816152\pi\) | ||||
−0.837789 | + | 0.545995i | \(0.816152\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.46137 | 0.0947381 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −37.2749 | −1.43259 | −0.716296 | − | 0.697797i | \(-0.754164\pi\) | ||||
−0.716296 | + | 0.697797i | \(0.754164\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12.7977 | −0.490409 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −27.7986 | −1.06368 | −0.531842 | − | 0.846844i | \(-0.678500\pi\) | ||||
−0.531842 | + | 0.846844i | \(0.678500\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.24466 | −0.315012 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 15.8425 | 0.604431 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −42.7394 | −1.62824 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 31.1281 | 1.18417 | 0.592084 | − | 0.805876i | \(-0.298305\pi\) | ||||
0.592084 | + | 0.805876i | \(0.298305\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −45.3118 | −1.71877 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.02899 | −0.114731 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 35.1593 | 1.32985 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12.0547 | −0.455301 | −0.227651 | − | 0.973743i | \(-0.573104\pi\) | ||||
−0.227651 | + | 0.973743i | \(0.573104\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 42.8625 | 1.61659 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 101.930 | 3.83892 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 46.4903 | 1.74598 | 0.872989 | − | 0.487739i | \(-0.162178\pi\) | ||||
0.872989 | + | 0.487739i | \(0.162178\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 44.4198 | 1.66587 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −43.9638 | −1.64646 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −21.2594 | −0.795055 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −37.7346 | −1.40922 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 12.5884 | 0.469467 | 0.234734 | − | 0.972060i | \(-0.424578\pi\) | ||||
0.234734 | + | 0.972060i | \(0.424578\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −17.1066 | −0.636201 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −52.3117 | −1.94281 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.55299 | −0.243037 | −0.121519 | − | 0.992589i | \(-0.538776\pi\) | ||||
−0.121519 | + | 0.992589i | \(0.538776\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −29.4114 | −1.08931 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12.9034 | 0.477248 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.10776 | 0.225595 | 0.112798 | − | 0.993618i | \(-0.464019\pi\) | ||||
0.112798 | + | 0.993618i | \(0.464019\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.342663 | −0.0126221 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 22.0038 | 0.809421 | 0.404711 | − | 0.914445i | \(-0.367372\pi\) | ||||
0.404711 | + | 0.914445i | \(0.367372\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −103.109 | −3.78780 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 34.6353 | 1.27065 | 0.635323 | − | 0.772247i | \(-0.280867\pi\) | ||||
0.635323 | + | 0.772247i | \(0.280867\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 50.7439 | 1.85911 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 24.4441 | 0.894363 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.3539 | −0.742725 | −0.371363 | − | 0.928488i | \(-0.621109\pi\) | ||||
−0.371363 | + | 0.928488i | \(0.621109\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −52.6335 | −1.91807 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −40.6925 | −1.48095 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29.9426 | 1.08828 | 0.544141 | − | 0.838994i | \(-0.316856\pi\) | ||||
0.544141 | + | 0.838994i | \(0.316856\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 9.93633 | 0.360666 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 53.3438 | 1.93371 | 0.966855 | − | 0.255326i | \(-0.0821830\pi\) | ||||
0.966855 | + | 0.255326i | \(0.0821830\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −33.2445 | −1.20196 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.10717 | −0.112193 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.577705 | 0.0208326 | 0.0104163 | − | 0.999946i | \(-0.496684\pi\) | ||||
0.0104163 | + | 0.999946i | \(0.496684\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −15.0177 | −0.540848 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7.91026 | −0.284512 | −0.142256 | − | 0.989830i | \(-0.545436\pi\) | ||||
−0.142256 | + | 0.989830i | \(0.545436\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 70.3686 | 2.52771 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.07400 | −0.217624 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.360331 | −0.0128937 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.45704 | −0.0878075 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −19.6014 | −0.699603 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −24.6891 | −0.880072 | −0.440036 | − | 0.897980i | \(-0.645034\pi\) | ||||
−0.440036 | + | 0.897980i | \(0.645034\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −37.6516 | −1.34043 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.3683 | 0.439213 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −54.0572 | −1.91721 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −11.1868 | −0.396258 | −0.198129 | − | 0.980176i | \(-0.563486\pi\) | ||||
−0.198129 | + | 0.980176i | \(0.563486\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −35.6238 | −1.26028 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −16.1457 | −0.570480 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.19283 | −0.0773834 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 46.8053 | 1.64763 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.29964 | 0.151167 | 0.0755836 | − | 0.997139i | \(-0.475918\pi\) | ||||
0.0755836 | + | 0.997139i | \(0.475918\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19.4277 | 0.682199 | 0.341100 | − | 0.940027i | \(-0.389201\pi\) | ||||
0.341100 | + | 0.940027i | \(0.389201\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 37.0556 | 1.29960 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −25.9700 | −0.909689 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 25.8750 | 0.905252 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 47.1341 | 1.64499 | 0.822495 | − | 0.568772i | \(-0.192581\pi\) | ||||
0.822495 | + | 0.568772i | \(0.192581\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.94967 | 0.207392 | 0.103696 | − | 0.994609i | \(-0.466933\pi\) | ||||
0.103696 | + | 0.994609i | \(0.466933\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −15.9041 | −0.553710 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.01224 | 0.139519 | 0.0697596 | − | 0.997564i | \(-0.477777\pi\) | ||||
0.0697596 | + | 0.997564i | \(0.477777\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.09097 | 0.107354 | 0.0536769 | − | 0.998558i | \(-0.482906\pi\) | ||||
0.0536769 | + | 0.998558i | \(0.482906\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −32.4462 | −1.12555 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −61.2797 | −2.12067 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.30516 | 0.114243 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 35.1218 | 1.21254 | 0.606270 | − | 0.795259i | \(-0.292665\pi\) | ||||
0.606270 | + | 0.795259i | \(0.292665\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23.2198 | 0.800682 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −52.7288 | −1.81608 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −118.785 | −4.08632 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 56.4050 | 1.93581 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −31.9154 | −1.09405 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −21.6536 | −0.741405 | −0.370702 | − | 0.928752i | \(-0.620883\pi\) | ||||
−0.370702 | + | 0.928752i | \(0.620883\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −66.6649 | −2.27989 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −54.7616 | −1.87062 | −0.935310 | − | 0.353828i | \(-0.884880\pi\) | ||||
−0.935310 | + | 0.353828i | \(0.884880\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.263155 | 0.00897874 | 0.00448937 | − | 0.999990i | \(-0.498571\pi\) | ||||
0.00448937 | + | 0.999990i | \(0.498571\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −54.0124 | −1.83860 | −0.919302 | − | 0.393552i | \(-0.871246\pi\) | ||||
−0.919302 | + | 0.393552i | \(0.871246\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −33.5522 | −1.14081 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −19.3859 | −0.658378 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12.5565 | −0.425950 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.64765 | −0.0897122 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −35.7904 | −1.21132 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.54025 | 0.0520105 | 0.0260053 | − | 0.999662i | \(-0.491721\pi\) | ||||
0.0260053 | + | 0.999662i | \(0.491721\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 11.1915 | 0.377478 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.28992 | 0.211913 | 0.105956 | − | 0.994371i | \(-0.466210\pi\) | ||||
0.105956 | + | 0.994371i | \(0.466210\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.57266 | −0.221188 | −0.110594 | − | 0.993866i | \(-0.535275\pi\) | ||||
−0.110594 | + | 0.993866i | \(0.535275\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.92999 | −0.132105 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −24.6143 | −0.826468 | −0.413234 | − | 0.910625i | \(-0.635601\pi\) | ||||
−0.413234 | + | 0.910625i | \(0.635601\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 7.59963 | 0.254597 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −71.4361 | −2.39052 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −86.2042 | −2.88149 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 76.7750 | 2.56344 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −70.2449 | −2.34280 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 18.8925 | 0.629402 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 11.4558 | 0.380804 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −21.4285 | −0.711522 | −0.355761 | − | 0.934577i | \(-0.615778\pi\) | ||||
−0.355761 | + | 0.934577i | \(0.615778\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 22.6970 | 0.752812 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 20.6989 | 0.685786 | 0.342893 | − | 0.939374i | \(-0.388593\pi\) | ||||
0.342893 | + | 0.939374i | \(0.388593\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.90982 | −0.228682 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 15.6436 | 0.517162 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −13.5900 | −0.448292 | −0.224146 | − | 0.974556i | \(-0.571959\pi\) | ||||
−0.224146 | + | 0.974556i | \(0.571959\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 11.4176 | 0.376224 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.78417 | −0.0916421 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 51.0839 | 1.67963 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −30.7957 | −1.01146 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −42.8414 | −1.40558 | −0.702790 | − | 0.711398i | \(-0.748063\pi\) | ||||
−0.702790 | + | 0.711398i | \(0.748063\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −39.5852 | −1.29596 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 9.39750 | 0.307331 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −17.0062 | −0.555568 | −0.277784 | − | 0.960644i | \(-0.589600\pi\) | ||||
−0.277784 | + | 0.960644i | \(0.589600\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −80.2979 | −2.62042 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 43.8180 | 1.42843 | 0.714213 | − | 0.699928i | \(-0.246785\pi\) | ||||
0.714213 | + | 0.699928i | \(0.246785\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.52270 | 0.147279 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15.2023 | −0.494008 | −0.247004 | − | 0.969014i | \(-0.579446\pi\) | ||||
−0.247004 | + | 0.969014i | \(0.579446\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −16.9434 | −0.550004 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −32.4934 | −1.05367 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 19.0486 | 0.617044 | 0.308522 | − | 0.951217i | \(-0.400166\pi\) | ||||
0.308522 | + | 0.951217i | \(0.400166\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.52397 | −0.114033 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 15.8762 | 0.513204 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 63.4918 | 2.04812 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 31.1063 | 1.00239 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −69.6812 | −2.24312 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12.3278 | −0.396435 | −0.198218 | − | 0.980158i | \(-0.563515\pi\) | ||||
−0.198218 | + | 0.980158i | \(0.563515\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 45.5784 | 1.46419 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −0.959044 | −0.0307772 | −0.0153886 | − | 0.999882i | \(-0.504899\pi\) | ||||
−0.0153886 | + | 0.999882i | \(0.504899\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −122.886 | −3.93551 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −37.7183 | −1.20672 | −0.603358 | − | 0.797471i | \(-0.706171\pi\) | ||||
−0.603358 | + | 0.797471i | \(0.706171\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.56404 | 0.145867 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 13.9381 | 0.445008 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −32.2162 | −1.02754 | −0.513768 | − | 0.857929i | \(-0.671751\pi\) | ||||
−0.513768 | + | 0.857929i | \(0.671751\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −27.8491 | −0.887345 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −19.2665 | −0.612640 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.3658 | 0.361048 | 0.180524 | − | 0.983571i | \(-0.442221\pi\) | ||||
0.180524 | + | 0.983571i | \(0.442221\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 65.9861 | 2.09400 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 56.6618 | 1.79630 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −10.3504 | −0.327799 | −0.163900 | − | 0.986477i | \(-0.552407\pi\) | ||||
−0.163900 | + | 0.986477i | \(0.552407\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.39937 | 0.0759127 |
(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 | 8036.2.a.q.1.12 | 15 | ||
7.2 | even | 3 | 1148.2.i.e.165.4 | ✓ | 30 | ||
7.4 | even | 3 | 1148.2.i.e.821.4 | yes | 30 | ||
7.6 | odd | 2 | 8036.2.a.r.1.4 | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1148.2.i.e.165.4 | ✓ | 30 | 7.2 | even | 3 | ||
1148.2.i.e.821.4 | yes | 30 | 7.4 | even | 3 | ||
8036.2.a.q.1.12 | 15 | 1.1 | even | 1 | trivial | ||
8036.2.a.r.1.4 | 15 | 7.6 | odd | 2 |