Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4008,2,Mod(1,4008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4008 = 2^{3} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4008.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: | \(32.0040411301\) |
Analytic rank: | \(1\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 3x^{8} - 16x^{7} + 45x^{6} + 67x^{5} - 166x^{4} - 83x^{3} + 152x^{2} + 51x - 10 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-3.17025\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4008.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.17025 | −1.86499 | −0.932496 | − | 0.361180i | \(-0.882374\pi\) | ||||
−0.932496 | + | 0.361180i | \(0.882374\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.78655 | −0.675251 | −0.337625 | − | 0.941281i | \(-0.609624\pi\) | ||||
−0.337625 | + | 0.941281i | \(0.609624\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.35038 | 1.31169 | 0.655844 | − | 0.754897i | \(-0.272313\pi\) | ||||
0.655844 | + | 0.754897i | \(0.272313\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.54982 | 0.707192 | 0.353596 | − | 0.935398i | \(-0.384959\pi\) | ||||
0.353596 | + | 0.935398i | \(0.384959\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.17025 | −1.07675 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.0716370 | 0.0173745 | 0.00868726 | − | 0.999962i | \(-0.497235\pi\) | ||||
0.00868726 | + | 0.999962i | \(0.497235\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.16710 | −1.64425 | −0.822123 | − | 0.569310i | \(-0.807211\pi\) | ||||
−0.822123 | + | 0.569310i | \(0.807211\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.78655 | −0.389856 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.75103 | −0.573630 | −0.286815 | − | 0.957986i | \(-0.592596\pi\) | ||||
−0.286815 | + | 0.957986i | \(0.592596\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 12.3910 | 2.47820 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.44140 | 1.01044 | 0.505222 | − | 0.862990i | \(-0.331411\pi\) | ||||
0.505222 | + | 0.862990i | \(0.331411\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.34520 | 0.600816 | 0.300408 | − | 0.953811i | \(-0.402877\pi\) | ||||
0.300408 | + | 0.953811i | \(0.402877\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.35038 | 0.757303 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 7.45034 | 1.25934 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.04022 | −0.993005 | −0.496503 | − | 0.868035i | \(-0.665383\pi\) | ||||
−0.496503 | + | 0.868035i | \(0.665383\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.54982 | 0.408298 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.33471 | 0.520794 | 0.260397 | − | 0.965502i | \(-0.416147\pi\) | ||||
0.260397 | + | 0.965502i | \(0.416147\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.47637 | 0.530142 | 0.265071 | − | 0.964229i | \(-0.414605\pi\) | ||||
0.265071 | + | 0.964229i | \(0.414605\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.17025 | −0.621664 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.84888 | 0.269687 | 0.134843 | − | 0.990867i | \(-0.456947\pi\) | ||||
0.134843 | + | 0.990867i | \(0.456947\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.80826 | −0.544036 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.0716370 | 0.0100312 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.4810 | −1.43968 | −0.719838 | − | 0.694142i | \(-0.755784\pi\) | ||||
−0.719838 | + | 0.694142i | \(0.755784\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −18.1422 | −2.44629 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.16710 | −0.949306 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.84697 | 1.02159 | 0.510794 | − | 0.859703i | \(-0.329351\pi\) | ||||
0.510794 | + | 0.859703i | \(0.329351\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.59987 | −0.845026 | −0.422513 | − | 0.906357i | \(-0.638852\pi\) | ||||
−0.422513 | + | 0.906357i | \(0.638852\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.78655 | −0.225084 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −10.6334 | −1.31891 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.06798 | 0.374814 | 0.187407 | − | 0.982282i | \(-0.439992\pi\) | ||||
0.187407 | + | 0.982282i | \(0.439992\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.75103 | −0.331185 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.41046 | −1.11682 | −0.558408 | − | 0.829566i | \(-0.688588\pi\) | ||||
−0.558408 | + | 0.829566i | \(0.688588\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.85175 | −1.03602 | −0.518009 | − | 0.855375i | \(-0.673327\pi\) | ||||
−0.518009 | + | 0.855375i | \(0.673327\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 12.3910 | 1.43079 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.77214 | −0.885718 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.0583476 | 0.00656462 | 0.00328231 | − | 0.999995i | \(-0.498955\pi\) | ||||
0.00328231 | + | 0.999995i | \(0.498955\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.584902 | 0.0642013 | 0.0321007 | − | 0.999485i | \(-0.489780\pi\) | ||||
0.0321007 | + | 0.999485i | \(0.489780\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.298744 | −0.0324033 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.44140 | 0.583380 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.61449 | −0.383135 | −0.191567 | − | 0.981479i | \(-0.561357\pi\) | ||||
−0.191567 | + | 0.981479i | \(0.561357\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.55536 | −0.477532 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.34520 | 0.346881 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 29.8886 | 3.06651 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.334815 | 0.0339953 | 0.0169976 | − | 0.999856i | \(-0.494589\pi\) | ||||
0.0169976 | + | 0.999856i | \(0.494589\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.35038 | 0.437229 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.71758 | 0.469416 | 0.234708 | − | 0.972066i | \(-0.424587\pi\) | ||||
0.234708 | + | 0.972066i | \(0.424587\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −20.2182 | −1.99216 | −0.996081 | − | 0.0884418i | \(-0.971811\pi\) | ||||
−0.996081 | + | 0.0884418i | \(0.971811\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 7.45034 | 0.727079 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.02095 | 0.388719 | 0.194360 | − | 0.980930i | \(-0.437737\pi\) | ||||
0.194360 | + | 0.980930i | \(0.437737\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.32526 | 0.701633 | 0.350816 | − | 0.936444i | \(-0.385904\pi\) | ||||
0.350816 | + | 0.936444i | \(0.385904\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.04022 | −0.573312 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.8947 | −1.40118 | −0.700590 | − | 0.713564i | \(-0.747080\pi\) | ||||
−0.700590 | + | 0.713564i | \(0.747080\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 11.4725 | 1.06981 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.54982 | 0.235731 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.127983 | −0.0117322 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.92577 | 0.720525 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.33471 | 0.300681 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −30.8222 | −2.75683 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −18.8761 | −1.67498 | −0.837490 | − | 0.546453i | \(-0.815978\pi\) | ||||
−0.837490 | + | 0.546453i | \(0.815978\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.47637 | 0.306078 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.342949 | 0.0299636 | 0.0149818 | − | 0.999888i | \(-0.495231\pi\) | ||||
0.0149818 | + | 0.999888i | \(0.495231\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.8044 | 1.11028 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.17025 | −0.358918 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.5389 | 0.985833 | 0.492917 | − | 0.870077i | \(-0.335931\pi\) | ||||
0.492917 | + | 0.870077i | \(0.335931\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.7651 | −1.33718 | −0.668591 | − | 0.743630i | \(-0.733102\pi\) | ||||
−0.668591 | + | 0.743630i | \(0.733102\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.84888 | 0.155704 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 11.0927 | 0.927615 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −22.6920 | −1.88447 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.80826 | −0.314100 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.883298 | 0.0723626 | 0.0361813 | − | 0.999345i | \(-0.488481\pi\) | ||||
0.0361813 | + | 0.999345i | \(0.488481\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.06988 | −0.331202 | −0.165601 | − | 0.986193i | \(-0.552956\pi\) | ||||
−0.165601 | + | 0.986193i | \(0.552956\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.0716370 | 0.00579151 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −13.9503 | −1.12052 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.5877 | −1.00461 | −0.502304 | − | 0.864691i | \(-0.667514\pi\) | ||||
−0.502304 | + | 0.864691i | \(0.667514\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −10.4810 | −0.831198 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.91484 | 0.387344 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.2085 | −0.799593 | −0.399797 | − | 0.916604i | \(-0.630919\pi\) | ||||
−0.399797 | + | 0.916604i | \(0.630919\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −18.1422 | −1.41236 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.00000 | −0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.49843 | −0.499879 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.16710 | −0.548082 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −24.5779 | −1.86862 | −0.934310 | − | 0.356461i | \(-0.883983\pi\) | ||||
−0.934310 | + | 0.356461i | \(0.883983\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −22.1371 | −1.67340 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.84697 | 0.589814 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −14.2545 | −1.06543 | −0.532717 | − | 0.846293i | \(-0.678829\pi\) | ||||
−0.532717 | + | 0.846293i | \(0.678829\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.8429 | 1.69790 | 0.848948 | − | 0.528476i | \(-0.177236\pi\) | ||||
0.848948 | + | 0.528476i | \(0.177236\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.59987 | −0.487876 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 25.1892 | 1.85195 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.311648 | 0.0227899 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.78655 | −0.129952 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.42405 | 0.103041 | 0.0515203 | − | 0.998672i | \(-0.483593\pi\) | ||||
0.0515203 | + | 0.998672i | \(0.483593\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.9804 | −1.00633 | −0.503166 | − | 0.864190i | \(-0.667831\pi\) | ||||
−0.503166 | + | 0.864190i | \(0.667831\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −10.6334 | −0.761472 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.2442 | 1.01486 | 0.507428 | − | 0.861694i | \(-0.330596\pi\) | ||||
0.507428 | + | 0.861694i | \(0.330596\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.6866 | −1.18288 | −0.591441 | − | 0.806348i | \(-0.701441\pi\) | ||||
−0.591441 | + | 0.806348i | \(0.701441\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.06798 | 0.216399 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −9.72131 | −0.682302 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −13.9066 | −0.971277 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.75103 | −0.191210 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −31.1796 | −2.15674 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.11871 | −0.558915 | −0.279458 | − | 0.960158i | \(-0.590155\pi\) | ||||
−0.279458 | + | 0.960158i | \(0.590155\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −9.41046 | −0.644794 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −14.4973 | −0.988711 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.97636 | −0.405701 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −8.85175 | −0.598146 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.182661 | 0.0122871 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.7903 | −0.722574 | −0.361287 | − | 0.932455i | \(-0.617662\pi\) | ||||
−0.361287 | + | 0.932455i | \(0.617662\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 12.3910 | 0.826066 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.189331 | −0.0125664 | −0.00628318 | − | 0.999980i | \(-0.502000\pi\) | ||||
−0.00628318 | + | 0.999980i | \(0.502000\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.4062 | −0.951987 | −0.475993 | − | 0.879449i | \(-0.657911\pi\) | ||||
−0.475993 | + | 0.879449i | \(0.657911\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.77214 | −0.511370 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 29.7817 | 1.95107 | 0.975533 | − | 0.219854i | \(-0.0705582\pi\) | ||||
0.975533 | + | 0.219854i | \(0.0705582\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.71029 | −0.502964 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.0583476 | 0.00379008 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.50122 | 0.485213 | 0.242607 | − | 0.970125i | \(-0.421998\pi\) | ||||
0.242607 | + | 0.970125i | \(0.421998\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.6609 | 1.00881 | 0.504404 | − | 0.863468i | \(-0.331712\pi\) | ||||
0.504404 | + | 0.863468i | \(0.331712\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 15.8814 | 1.01462 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −18.2748 | −1.16280 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.584902 | 0.0370667 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.02486 | −0.443405 | −0.221703 | − | 0.975114i | \(-0.571161\pi\) | ||||
−0.221703 | + | 0.975114i | \(0.571161\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −11.9680 | −0.752423 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.298744 | −0.0187081 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.17803 | 0.510132 | 0.255066 | − | 0.966924i | \(-0.417903\pi\) | ||||
0.255066 | + | 0.966924i | \(0.417903\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.7911 | 0.670528 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.44140 | 0.336814 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 22.1033 | 1.36295 | 0.681473 | − | 0.731843i | \(-0.261340\pi\) | ||||
0.681473 | + | 0.731843i | \(0.261340\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 43.7084 | 2.68499 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.61449 | −0.221203 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.4088 | −0.878519 | −0.439259 | − | 0.898360i | \(-0.644759\pi\) | ||||
−0.439259 | + | 0.898360i | \(0.644759\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.72029 | −0.286737 | −0.143369 | − | 0.989669i | \(-0.545793\pi\) | ||||
−0.143369 | + | 0.989669i | \(0.545793\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.55536 | −0.275703 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 53.9054 | 3.25062 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −27.9962 | −1.68213 | −0.841063 | − | 0.540937i | \(-0.818070\pi\) | ||||
−0.841063 | + | 0.540937i | \(0.818070\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.34520 | 0.200272 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −21.2473 | −1.26751 | −0.633755 | − | 0.773534i | \(-0.718487\pi\) | ||||
−0.633755 | + | 0.773534i | \(0.718487\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.07839 | −0.361322 | −0.180661 | − | 0.983545i | \(-0.557824\pi\) | ||||
−0.180661 | + | 0.983545i | \(0.557824\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 29.8886 | 1.77045 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.95761 | −0.351666 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9949 | −0.999698 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.334815 | 0.0196272 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 15.5348 | 0.907553 | 0.453777 | − | 0.891115i | \(-0.350076\pi\) | ||||
0.453777 | + | 0.891115i | \(0.350076\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −32.7238 | −1.90525 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.35038 | 0.252434 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −7.01463 | −0.405666 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.21070 | −0.357979 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.71758 | 0.271018 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 27.5231 | 1.57597 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.05233 | −0.402498 | −0.201249 | − | 0.979540i | \(-0.564500\pi\) | ||||
−0.201249 | + | 0.979540i | \(0.564500\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −20.2182 | −1.15018 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 26.0059 | 1.47466 | 0.737330 | − | 0.675532i | \(-0.236086\pi\) | ||||
0.737330 | + | 0.675532i | \(0.236086\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.5377 | 0.991287 | 0.495644 | − | 0.868526i | \(-0.334932\pi\) | ||||
0.495644 | + | 0.868526i | \(0.334932\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 7.45034 | 0.419779 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 20.8460 | 1.17083 | 0.585413 | − | 0.810735i | \(-0.300932\pi\) | ||||
0.585413 | + | 0.810735i | \(0.300932\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 23.6721 | 1.32539 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.02095 | 0.224427 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.513430 | −0.0285680 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 31.5947 | 1.75256 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 7.32526 | 0.405088 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.30311 | −0.182106 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 27.8470 | 1.53061 | 0.765305 | − | 0.643667i | \(-0.222588\pi\) | ||||
0.765305 | + | 0.643667i | \(0.222588\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.04022 | −0.331002 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −12.7943 | −0.699025 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.22298 | 0.393461 | 0.196731 | − | 0.980458i | \(-0.436968\pi\) | ||||
0.196731 | + | 0.980458i | \(0.436968\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −14.8947 | −0.808971 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 14.5529 | 0.788083 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.3094 | 1.04261 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 11.4725 | 0.617658 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 14.7990 | 0.794452 | 0.397226 | − | 0.917721i | \(-0.369973\pi\) | ||||
0.397226 | + | 0.917721i | \(0.369973\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.40557 | −0.0752384 | −0.0376192 | − | 0.999292i | \(-0.511977\pi\) | ||||
−0.0376192 | + | 0.999292i | \(0.511977\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.54982 | 0.136099 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −11.8156 | −0.628883 | −0.314442 | − | 0.949277i | \(-0.601817\pi\) | ||||
−0.314442 | + | 0.949277i | \(0.601817\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 39.2440 | 2.08285 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.127983 | −0.00677356 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.61217 | −0.296199 | −0.148099 | − | 0.988972i | \(-0.547316\pi\) | ||||
−0.148099 | + | 0.988972i | \(0.547316\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 32.3674 | 1.70355 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7.92577 | 0.415995 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 36.9140 | 1.93217 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −31.0874 | −1.62275 | −0.811374 | − | 0.584527i | \(-0.801280\pi\) | ||||
−0.811374 | + | 0.584527i | \(0.801280\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.33471 | 0.173598 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 18.7248 | 0.972143 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.78421 | −0.0923828 | −0.0461914 | − | 0.998933i | \(-0.514708\pi\) | ||||
−0.0461914 | + | 0.998933i | \(0.514708\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −30.8222 | −1.59165 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 13.8746 | 0.714577 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.79107 | 0.451567 | 0.225783 | − | 0.974178i | \(-0.427506\pi\) | ||||
0.225783 | + | 0.974178i | \(0.427506\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −18.8761 | −0.967050 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −19.5651 | −0.999729 | −0.499865 | − | 0.866103i | \(-0.666617\pi\) | ||||
−0.499865 | + | 0.866103i | \(0.666617\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 32.4118 | 1.65186 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.47637 | 0.176714 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −19.6033 | −0.993927 | −0.496963 | − | 0.867772i | \(-0.665552\pi\) | ||||
−0.496963 | + | 0.867772i | \(0.665552\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.197075 | −0.00996654 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.342949 | 0.0172995 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.243324 | −0.0122430 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.41521 | −0.422347 | −0.211174 | − | 0.977449i | \(-0.567729\pi\) | ||||
−0.211174 | + | 0.977449i | \(0.567729\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 12.8044 | 0.641020 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.30360 | 0.0650989 | 0.0325494 | − | 0.999470i | \(-0.489637\pi\) | ||||
0.0325494 | + | 0.999470i | \(0.489637\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.52965 | 0.424892 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.17025 | −0.207221 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −26.2772 | −1.30251 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.4075 | 0.514616 | 0.257308 | − | 0.966329i | \(-0.417165\pi\) | ||||
0.257308 | + | 0.966329i | \(0.417165\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11.5389 | 0.569171 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −14.0190 | −0.689828 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.43919 | −0.119735 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −15.7651 | −0.772022 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.00995 | 0.391312 | 0.195656 | − | 0.980673i | \(-0.437316\pi\) | ||||
0.195656 | + | 0.980673i | \(0.437316\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.1739 | 1.12943 | 0.564714 | − | 0.825287i | \(-0.308986\pi\) | ||||
0.564714 | + | 0.825287i | \(0.308986\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.84888 | 0.0898956 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.887653 | 0.0430575 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11.7910 | 0.570605 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 11.0927 | 0.535559 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −36.5254 | −1.75937 | −0.879684 | − | 0.475559i | \(-0.842246\pi\) | ||||
−0.879684 | + | 0.475559i | \(0.842246\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.3450 | −0.545207 | −0.272603 | − | 0.962127i | \(-0.587885\pi\) | ||||
−0.272603 | + | 0.962127i | \(0.587885\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −22.6920 | −1.08800 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 19.7169 | 0.943188 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.47796 | 0.0705391 | 0.0352696 | − | 0.999378i | \(-0.488771\pi\) | ||||
0.0352696 | + | 0.999378i | \(0.488771\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.80826 | −0.181345 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −30.7173 | −1.45943 | −0.729713 | − | 0.683754i | \(-0.760346\pi\) | ||||
−0.729713 | + | 0.683754i | \(0.760346\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 15.0733 | 0.714544 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.883298 | 0.0417786 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13.5252 | 0.638292 | 0.319146 | − | 0.947705i | \(-0.396604\pi\) | ||||
0.319146 | + | 0.947705i | \(0.396604\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14.5072 | 0.683119 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.06988 | −0.191220 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 18.9970 | 0.890593 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.2676 | 0.854523 | 0.427262 | − | 0.904128i | \(-0.359478\pi\) | ||||
0.427262 | + | 0.904128i | \(0.359478\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.0716370 | 0.00334373 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 21.1705 | 0.986007 | 0.493003 | − | 0.870027i | \(-0.335899\pi\) | ||||
0.493003 | + | 0.870027i | \(0.335899\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −25.4679 | −1.18359 | −0.591796 | − | 0.806088i | \(-0.701581\pi\) | ||||
−0.591796 | + | 0.806088i | \(0.701581\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −13.9503 | −0.646931 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −18.1847 | −0.841488 | −0.420744 | − | 0.907179i | \(-0.638231\pi\) | ||||
−0.420744 | + | 0.907179i | \(0.638231\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.48109 | −0.253093 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −12.5877 | −0.580010 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 15.1235 | 0.695381 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −88.8075 | −4.07477 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −10.4810 | −0.479892 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −31.4363 | −1.43636 | −0.718182 | − | 0.695856i | \(-0.755025\pi\) | ||||
−0.718182 | + | 0.695856i | \(0.755025\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15.4014 | −0.702246 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.91484 | 0.223633 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.39626 | −0.0634009 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.63846 | 0.346132 | 0.173066 | − | 0.984910i | \(-0.444633\pi\) | ||||
0.173066 | + | 0.984910i | \(0.444633\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −10.2085 | −0.461645 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.60219 | 0.117435 | 0.0587176 | − | 0.998275i | \(-0.481299\pi\) | ||||
0.0587176 | + | 0.998275i | \(0.481299\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.389806 | 0.0175560 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −18.1422 | −0.815429 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 16.8122 | 0.754131 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11.7781 | −0.527261 | −0.263631 | − | 0.964624i | \(-0.584920\pi\) | ||||
−0.263631 | + | 0.964624i | \(0.584920\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.00000 | −0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 19.8128 | 0.883410 | 0.441705 | − | 0.897160i | \(-0.354374\pi\) | ||||
0.441705 | + | 0.897160i | \(0.354374\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −19.6735 | −0.875458 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.49843 | −0.288606 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 41.0164 | 1.81802 | 0.909010 | − | 0.416774i | \(-0.136839\pi\) | ||||
0.909010 | + | 0.416774i | \(0.136839\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 15.8140 | 0.699572 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7.16710 | −0.316435 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 84.3151 | 3.71537 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.04332 | 0.353745 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −24.5779 | −1.07885 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −24.5419 | −1.07520 | −0.537599 | − | 0.843201i | \(-0.680669\pi\) | ||||
−0.537599 | + | 0.843201i | \(0.680669\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 42.2257 | 1.84640 | 0.923201 | − | 0.384318i | \(-0.125563\pi\) | ||||
0.923201 | + | 0.384318i | \(0.125563\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −22.1371 | −0.966140 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.239640 | 0.0104389 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.4318 | −0.670949 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.84697 | 0.340530 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.50290 | 0.368301 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −16.7683 | −0.724959 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −14.2545 | −0.615129 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −16.5673 | −0.713606 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 39.1790 | 1.68444 | 0.842219 | − | 0.539135i | \(-0.181249\pi\) | ||||
0.842219 | + | 0.539135i | \(0.181249\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 22.8429 | 0.980281 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −30.5482 | −1.30854 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 30.0775 | 1.28602 | 0.643010 | − | 0.765858i | \(-0.277685\pi\) | ||||
0.643010 | + | 0.765858i | \(0.277685\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.59987 | −0.281675 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −38.9991 | −1.66142 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.104241 | −0.00443276 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 25.1892 | 1.06922 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 37.0920 | 1.57164 | 0.785819 | − | 0.618456i | \(-0.212242\pi\) | ||||
0.785819 | + | 0.618456i | \(0.212242\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.86412 | 0.374912 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.311648 | 0.0131578 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −41.1589 | −1.73464 | −0.867321 | − | 0.497749i | \(-0.834160\pi\) | ||||
−0.867321 | + | 0.497749i | \(0.834160\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 62.1148 | 2.61319 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.78655 | −0.0750279 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 14.7976 | 0.620347 | 0.310173 | − | 0.950680i | \(-0.399613\pi\) | ||||
0.310173 | + | 0.950680i | \(0.399613\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.6533 | −0.822464 | −0.411232 | − | 0.911531i | \(-0.634901\pi\) | ||||
−0.411232 | + | 0.911531i | \(0.634901\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.42405 | 0.0594906 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −34.0880 | −1.42157 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 34.3832 | 1.43139 | 0.715696 | − | 0.698412i | \(-0.246109\pi\) | ||||
0.715696 | + | 0.698412i | \(0.246109\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −13.9804 | −0.581006 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.04495 | −0.0433520 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −45.5963 | −1.88841 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −10.6334 | −0.439636 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −11.7539 | −0.485135 | −0.242567 | − | 0.970135i | \(-0.577990\pi\) | ||||
−0.242567 | + | 0.970135i | \(0.577990\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −23.9754 | −0.987889 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 14.2442 | 0.585928 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −30.1475 | −1.23801 | −0.619005 | − | 0.785387i | \(-0.712464\pi\) | ||||
−0.619005 | + | 0.785387i | \(0.712464\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.533720 | 0.0218804 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −16.6866 | −0.682938 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 39.4902 | 1.61353 | 0.806764 | − | 0.590874i | \(-0.201217\pi\) | ||||
0.806764 | + | 0.590874i | \(0.201217\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.04132 | −0.328012 | −0.164006 | − | 0.986459i | \(-0.552442\pi\) | ||||
−0.164006 | + | 0.986459i | \(0.552442\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.06798 | 0.124938 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −33.0524 | −1.34377 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.36619 | 0.0960408 | 0.0480204 | − | 0.998846i | \(-0.484709\pi\) | ||||
0.0480204 | + | 0.998846i | \(0.484709\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −9.72131 | −0.393927 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.71430 | 0.190720 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 38.3389 | 1.54849 | 0.774247 | − | 0.632884i | \(-0.218129\pi\) | ||||
0.774247 | + | 0.632884i | \(0.218129\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −13.9066 | −0.560767 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23.7019 | 0.954201 | 0.477100 | − | 0.878849i | \(-0.341688\pi\) | ||||
0.477100 | + | 0.878849i | \(0.341688\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21.6224 | 0.869078 | 0.434539 | − | 0.900653i | \(-0.356911\pi\) | ||||
0.434539 | + | 0.900653i | \(0.356911\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.75103 | −0.110395 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.45745 | 0.258712 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 66.5816 | 2.66326 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −31.1796 | −1.24519 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.432703 | −0.0172530 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22.0461 | −0.877643 | −0.438822 | − | 0.898574i | \(-0.644604\pi\) | ||||
−0.438822 | + | 0.898574i | \(0.644604\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8.11871 | −0.322690 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 78.7179 | 3.12383 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9.71036 | −0.384738 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.41046 | −0.372272 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.39872 | −0.0947438 | −0.0473719 | − | 0.998877i | \(-0.515085\pi\) | ||||
−0.0473719 | + | 0.998877i | \(0.515085\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.16347 | 0.164191 | 0.0820957 | − | 0.996624i | \(-0.473839\pi\) | ||||
0.0820957 | + | 0.996624i | \(0.473839\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −14.4973 | −0.570832 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −18.0107 | −0.708072 | −0.354036 | − | 0.935232i | \(-0.615191\pi\) | ||||
−0.354036 | + | 0.935232i | \(0.615191\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 34.1373 | 1.34001 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.97636 | −0.234232 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −12.0581 | −0.471871 | −0.235935 | − | 0.971769i | \(-0.575815\pi\) | ||||
−0.235935 | + | 0.971769i | \(0.575815\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.43018 | −0.0558819 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −8.85175 | −0.345340 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.11754 | 0.121442 | 0.0607211 | − | 0.998155i | \(-0.480660\pi\) | ||||
0.0607211 | + | 0.998155i | \(0.480660\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.44996 | 0.250874 | 0.125437 | − | 0.992102i | \(-0.459967\pi\) | ||||
0.125437 | + | 0.992102i | \(0.459967\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.182661 | 0.00709397 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −53.3974 | −2.07066 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −14.9695 | −0.579620 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −10.7903 | −0.417178 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −28.7119 | −1.10841 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −49.1326 | −1.89392 | −0.946960 | − | 0.321350i | \(-0.895863\pi\) | ||||
−0.946960 | + | 0.321350i | \(0.895863\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 12.3910 | 0.476929 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −12.1529 | −0.467074 | −0.233537 | − | 0.972348i | \(-0.575030\pi\) | ||||
−0.233537 | + | 0.972348i | \(0.575030\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.598161 | −0.0229553 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.189331 | −0.00725519 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 34.4616 | 1.31863 | 0.659317 | − | 0.751865i | \(-0.270845\pi\) | ||||
0.659317 | + | 0.751865i | \(0.270845\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −48.1200 | −1.83857 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14.4062 | −0.549630 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −26.7247 | −1.01813 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.60365 | −0.137089 | −0.0685446 | − | 0.997648i | \(-0.521836\pi\) | ||||
−0.0685446 | + | 0.997648i | \(0.521836\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −7.77214 | −0.295239 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 65.7446 | 2.49383 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.238888 | 0.00904854 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 29.7817 | 1.12645 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 40.8273 | 1.54203 | 0.771013 | − | 0.636819i | \(-0.219750\pi\) | ||||
0.771013 | + | 0.636819i | \(0.219750\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 43.2909 | 1.63275 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7.71029 | −0.290386 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −8.42816 | −0.316974 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 29.4473 | 1.10592 | 0.552959 | − | 0.833209i | \(-0.313499\pi\) | ||||
0.552959 | + | 0.833209i | \(0.313499\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.0583476 | 0.00218821 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.20275 | −0.344646 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −46.2592 | −1.73000 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7.50122 | 0.280138 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −15.9152 | −0.593535 | −0.296768 | − | 0.954950i | \(-0.595909\pi\) | ||||
−0.296768 | + | 0.954950i | \(0.595909\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 36.1208 | 1.34521 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 15.6609 | 0.582435 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 67.4243 | 2.50408 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −52.3345 | −1.94098 | −0.970490 | − | 0.241142i | \(-0.922478\pi\) | ||||
−0.970490 | + | 0.241142i | \(0.922478\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.249037 | 0.00921096 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −25.8494 | −0.954771 | −0.477385 | − | 0.878694i | \(-0.658415\pi\) | ||||
−0.477385 | + | 0.878694i | \(0.658415\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 15.8814 | 0.585793 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13.3469 | 0.491639 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15.9750 | −0.587650 | −0.293825 | − | 0.955859i | \(-0.594928\pi\) | ||||
−0.293825 | + | 0.955859i | \(0.594928\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −18.2748 | −0.671342 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −23.6409 | −0.867302 | −0.433651 | − | 0.901081i | \(-0.642775\pi\) | ||||
−0.433651 | + | 0.901081i | \(0.642775\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.68357 | −0.134956 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.584902 | 0.0214004 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7.18360 | −0.262483 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.1018 | −0.733526 | −0.366763 | − | 0.930314i | \(-0.619534\pi\) | ||||
−0.366763 | + | 0.930314i | \(0.619534\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −7.02486 | −0.256000 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 16.9724 | 0.617689 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.43011 | 0.161015 | 0.0805075 | − | 0.996754i | \(-0.474346\pi\) | ||||
0.0805075 | + | 0.996754i | \(0.474346\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −11.9680 | −0.434412 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12.1245 | 0.439512 | 0.219756 | − | 0.975555i | \(-0.429474\pi\) | ||||
0.219756 | + | 0.975555i | \(0.429474\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −13.0869 | −0.473778 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.298744 | −0.0108011 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 20.0083 | 0.722459 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −27.8010 | −1.00253 | −0.501265 | − | 0.865294i | \(-0.667132\pi\) | ||||
−0.501265 | + | 0.865294i | \(0.667132\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.17803 | 0.294525 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 23.2674 | 0.836869 | 0.418435 | − | 0.908247i | \(-0.362579\pi\) | ||||
0.418435 | + | 0.908247i | \(0.362579\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 41.4503 | 1.48894 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 10.7911 | 0.387129 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −23.9002 | −0.856313 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −40.9390 | −1.46491 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.44140 | 0.194460 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 52.4938 | 1.87358 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −51.5377 | −1.83712 | −0.918560 | − | 0.395282i | \(-0.870647\pi\) | ||||
−0.918560 | + | 0.395282i | \(0.870647\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 22.1033 | 0.786897 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 26.6101 | 0.946148 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16.8285 | −0.597596 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 43.7084 | 1.55018 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5.11408 | −0.181150 | −0.0905750 | − | 0.995890i | \(-0.528870\pi\) | ||||
−0.0905750 | + | 0.995890i | \(0.528870\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.132448 | 0.00468568 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.61449 | −0.127712 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −38.5084 | −1.35893 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −20.4961 | −0.722393 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −14.4088 | −0.507213 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 36.7775 | 1.29303 | 0.646514 | − | 0.762902i | \(-0.276226\pi\) | ||||
0.646514 | + | 0.762902i | \(0.276226\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 38.7923 | 1.36218 | 0.681090 | − | 0.732200i | \(-0.261506\pi\) | ||||
0.681090 | + | 0.732200i | \(0.261506\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.72029 | −0.165548 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 42.5721 | 1.49124 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −24.9155 | −0.871684 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.55536 | −0.159177 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −26.0951 | −0.910725 | −0.455363 | − | 0.890306i | \(-0.650490\pi\) | ||||
−0.455363 | + | 0.890306i | \(0.650490\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 41.9826 | 1.46342 | 0.731710 | − | 0.681616i | \(-0.238723\pi\) | ||||
0.731710 | + | 0.681616i | \(0.238723\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 53.9054 | 1.87675 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.82167 | −0.306759 | −0.153380 | − | 0.988167i | \(-0.549016\pi\) | ||||
−0.153380 | + | 0.988167i | \(0.549016\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −27.5764 | −0.957768 | −0.478884 | − | 0.877878i | \(-0.658959\pi\) | ||||
−0.478884 | + | 0.877878i | \(0.658959\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −27.9962 | −0.971176 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.272812 | −0.00945237 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.17025 | 0.144317 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.34520 | 0.115627 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −35.2189 | −1.21589 | −0.607945 | − | 0.793979i | \(-0.708006\pi\) | ||||
−0.607945 | + | 0.793979i | \(0.708006\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.608865 | 0.0209953 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −21.2473 | −0.731797 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 27.1001 | 0.932271 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −14.1598 | −0.486535 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6.07839 | −0.208610 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 16.6168 | 0.569617 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −0.579339 | −0.0198362 | −0.00991810 | − | 0.999951i | \(-0.503157\pi\) | ||||
−0.00991810 | + | 0.999951i | \(0.503157\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 29.8886 | 1.02217 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −11.0178 | −0.376359 | −0.188180 | − | 0.982135i | \(-0.560259\pi\) | ||||
−0.188180 | + | 0.982135i | \(0.560259\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −18.7589 | −0.640045 | −0.320022 | − | 0.947410i | \(-0.603690\pi\) | ||||
−0.320022 | + | 0.947410i | \(0.603690\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.95761 | −0.203035 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −5.38140 | −0.183185 | −0.0915925 | − | 0.995797i | \(-0.529196\pi\) | ||||
−0.0915925 | + | 0.995797i | \(0.529196\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 102.496 | 3.48496 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −16.9949 | −0.577176 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.253834 | 0.00861073 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.82280 | 0.265065 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.334815 | 0.0113318 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 55.0653 | 1.86155 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.93120 | −0.267818 | −0.133909 | − | 0.990994i | \(-0.542753\pi\) | ||||
−0.133909 | + | 0.990994i | \(0.542753\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 15.5348 | 0.523976 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −27.7441 | −0.934721 | −0.467361 | − | 0.884067i | \(-0.654795\pi\) | ||||
−0.467361 | + | 0.884067i | \(0.654795\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10.6482 | 0.358340 | 0.179170 | − | 0.983818i | \(-0.442659\pi\) | ||||
0.179170 | + | 0.983818i | \(0.442659\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −32.7238 | −1.10000 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −41.5610 | −1.39548 | −0.697741 | − | 0.716350i | \(-0.745811\pi\) | ||||
−0.697741 | + | 0.716350i | \(0.745811\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 33.7230 | 1.13103 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.35038 | 0.145743 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −13.2511 | −0.443431 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 59.4450 | 1.98703 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7.01463 | −0.234212 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 18.2026 | 0.607090 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.750828 | −0.0250137 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6.21070 | −0.206679 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −95.2604 | −3.16656 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 58.4184 | 1.93975 | 0.969876 | − | 0.243599i | \(-0.0783280\pi\) | ||||
0.969876 | + | 0.243599i | \(0.0783280\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.71758 | 0.156472 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −21.0024 | −0.695840 | −0.347920 | − | 0.937524i | \(-0.613112\pi\) | ||||
−0.347920 | + | 0.937524i | \(0.613112\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.54454 | 0.0842121 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 27.5231 | 0.909885 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.612695 | −0.0202330 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10.2975 | −0.339683 | −0.169842 | − | 0.985471i | \(-0.554326\pi\) | ||||
−0.169842 | + | 0.985471i | \(0.554326\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.05233 | −0.232382 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −23.9950 | −0.789804 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −74.8442 | −2.46086 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −20.2182 | −0.664054 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −47.3424 | −1.55325 | −0.776627 | − | 0.629960i | \(-0.783071\pi\) | ||||
−0.776627 | + | 0.629960i | \(0.783071\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 27.2942 | 0.894530 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 26.0059 | 0.851396 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.29965 | −0.0425031 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 33.2393 | 1.08588 | 0.542941 | − | 0.839771i | \(-0.317311\pi\) | ||||
0.542941 | + | 0.839771i | \(0.317311\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 17.5377 | 0.572320 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 50.1401 | 1.63452 | 0.817260 | − | 0.576270i | \(-0.195492\pi\) | ||||
0.817260 | + | 0.576270i | \(0.195492\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.17388 | −0.298743 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 7.45034 | 0.242360 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 16.5748 | 0.538609 | 0.269304 | − | 0.963055i | \(-0.413206\pi\) | ||||
0.269304 | + | 0.963055i | \(0.413206\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −22.5703 | −0.732664 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 20.8460 | 0.675977 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −26.0587 | −0.844123 | −0.422062 | − | 0.906567i | \(-0.638693\pi\) | ||||
−0.422062 | + | 0.906567i | \(0.638693\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.93865 | −0.192170 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 23.6721 | 0.765212 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −20.6147 | −0.665685 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.8096 | −0.639020 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.02095 | 0.129573 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 58.3018 | 1.87680 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12.6689 | −0.407403 | −0.203702 | − | 0.979033i | \(-0.565297\pi\) | ||||
−0.203702 | + | 0.979033i | \(0.565297\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.513430 | −0.0164937 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −49.9738 | −1.60373 | −0.801867 | − | 0.597502i | \(-0.796160\pi\) | ||||
−0.801867 | + | 0.597502i | \(0.796160\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 28.1651 | 0.902933 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 31.5947 | 1.01184 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 33.0974 | 1.05888 | 0.529440 | − | 0.848347i | \(-0.322402\pi\) | ||||
0.529440 | + | 0.848347i | \(0.322402\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −15.7244 | −0.502553 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.32526 | 0.233878 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −39.4423 | −1.25801 | −0.629007 | − | 0.777400i | \(-0.716538\pi\) | ||||
−0.629007 | + | 0.777400i | \(0.716538\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −59.4018 | −1.89270 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.30311 | −0.105139 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.56361 | −0.304105 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 53.1881 | 1.68957 | 0.844787 | − | 0.535102i | \(-0.179727\pi\) | ||||
0.844787 | + | 0.535102i | \(0.179727\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 27.8470 | 0.883698 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 69.5874 | 2.20607 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −30.5032 | −0.966046 | −0.483023 | − | 0.875608i | \(-0.660461\pi\) | ||||
−0.483023 | + | 0.875608i | \(0.660461\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.04022 | −0.191104 |
(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 | 4008.2.a.i.1.1 | ✓ | 9 | |
4.3 | odd | 2 | 8016.2.a.ba.1.1 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4008.2.a.i.1.1 | ✓ | 9 | 1.1 | even | 1 | trivial | |
8016.2.a.ba.1.1 | 9 | 4.3 | odd | 2 |