Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2842,2,Mod(1,2842)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2842, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("2842.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2842 = 2 \cdot 7^{2} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2842.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: | \(22.6934842544\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.373409792.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 13x^{4} + 48x^{2} - 50 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(1.33784\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2842.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0.833497 | 0.481220 | 0.240610 | − | 0.970622i | \(-0.422653\pi\) | ||||
0.240610 | + | 0.970622i | \(0.422653\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.96556 | −1.77345 | −0.886726 | − | 0.462296i | \(-0.847026\pi\) | ||||
−0.886726 | + | 0.462296i | \(0.847026\pi\) | |||||||
\(6\) | 0.833497 | 0.340274 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.30528 | −0.768427 | ||||||||
\(10\) | −3.96556 | −1.25402 | ||||||||
\(11\) | −1.11509 | −0.336211 | −0.168106 | − | 0.985769i | \(-0.553765\pi\) | ||||
−0.168106 | + | 0.985769i | \(0.553765\pi\) | |||||||
\(12\) | 0.833497 | 0.240610 | ||||||||
\(13\) | −3.96556 | −1.09985 | −0.549924 | − | 0.835215i | \(-0.685343\pi\) | ||||
−0.549924 | + | 0.835215i | \(0.685343\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.30528 | −0.853420 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.79906 | 1.16394 | 0.581971 | − | 0.813210i | \(-0.302282\pi\) | ||||
0.581971 | + | 0.813210i | \(0.302282\pi\) | |||||||
\(18\) | −2.30528 | −0.543360 | ||||||||
\(19\) | 2.67568 | 0.613843 | 0.306922 | − | 0.951735i | \(-0.400701\pi\) | ||||
0.306922 | + | 0.951735i | \(0.400701\pi\) | |||||||
\(20\) | −3.96556 | −0.886726 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.11509 | −0.237737 | ||||||||
\(23\) | 8.42037 | 1.75577 | 0.877884 | − | 0.478873i | \(-0.158955\pi\) | ||||
0.877884 | + | 0.478873i | \(0.158955\pi\) | |||||||
\(24\) | 0.833497 | 0.170137 | ||||||||
\(25\) | 10.7257 | 2.14513 | ||||||||
\(26\) | −3.96556 | −0.777710 | ||||||||
\(27\) | −4.42194 | −0.851002 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | −3.30528 | −0.603459 | ||||||||
\(31\) | 2.95687 | 0.531070 | 0.265535 | − | 0.964101i | \(-0.414451\pi\) | ||||
0.265535 | + | 0.964101i | \(0.414451\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −0.929421 | −0.161791 | ||||||||
\(34\) | 4.79906 | 0.823031 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.30528 | −0.384214 | ||||||||
\(37\) | 8.19020 | 1.34646 | 0.673230 | − | 0.739433i | \(-0.264906\pi\) | ||||
0.673230 | + | 0.739433i | \(0.264906\pi\) | |||||||
\(38\) | 2.67568 | 0.434053 | ||||||||
\(39\) | −3.30528 | −0.529269 | ||||||||
\(40\) | −3.96556 | −0.627010 | ||||||||
\(41\) | −10.1504 | −1.58523 | −0.792614 | − | 0.609723i | \(-0.791281\pi\) | ||||
−0.792614 | + | 0.609723i | \(0.791281\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.30528 | 0.504051 | 0.252025 | − | 0.967721i | \(-0.418903\pi\) | ||||
0.252025 | + | 0.967721i | \(0.418903\pi\) | |||||||
\(44\) | −1.11509 | −0.168106 | ||||||||
\(45\) | 9.14173 | 1.36277 | ||||||||
\(46\) | 8.42037 | 1.24152 | ||||||||
\(47\) | 4.97424 | 0.725568 | 0.362784 | − | 0.931873i | \(-0.381826\pi\) | ||||
0.362784 | + | 0.931873i | \(0.381826\pi\) | |||||||
\(48\) | 0.833497 | 0.120305 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 10.7257 | 1.51684 | ||||||||
\(51\) | 4.00000 | 0.560112 | ||||||||
\(52\) | −3.96556 | −0.549924 | ||||||||
\(53\) | 5.30528 | 0.728737 | 0.364368 | − | 0.931255i | \(-0.381285\pi\) | ||||
0.364368 | + | 0.931255i | \(0.381285\pi\) | |||||||
\(54\) | −4.42194 | −0.601750 | ||||||||
\(55\) | 4.42194 | 0.596254 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.23017 | 0.295394 | ||||||||
\(58\) | 1.00000 | 0.131306 | ||||||||
\(59\) | 9.14173 | 1.19015 | 0.595076 | − | 0.803669i | \(-0.297122\pi\) | ||||
0.595076 | + | 0.803669i | \(0.297122\pi\) | |||||||
\(60\) | −3.30528 | −0.426710 | ||||||||
\(61\) | −6.92243 | −0.886326 | −0.443163 | − | 0.896441i | \(-0.646144\pi\) | ||||
−0.443163 | + | 0.896441i | \(0.646144\pi\) | |||||||
\(62\) | 2.95687 | 0.375523 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 15.7257 | 1.95053 | ||||||||
\(66\) | −0.929421 | −0.114404 | ||||||||
\(67\) | −6.61056 | −0.807609 | −0.403804 | − | 0.914845i | \(-0.632312\pi\) | ||||
−0.403804 | + | 0.914845i | \(0.632312\pi\) | |||||||
\(68\) | 4.79906 | 0.581971 | ||||||||
\(69\) | 7.01835 | 0.844911 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15.0309 | 1.78384 | 0.891922 | − | 0.452190i | \(-0.149357\pi\) | ||||
0.891922 | + | 0.452190i | \(0.149357\pi\) | |||||||
\(72\) | −2.30528 | −0.271680 | ||||||||
\(73\) | −4.79906 | −0.561687 | −0.280843 | − | 0.959754i | \(-0.590614\pi\) | ||||
−0.280843 | + | 0.959754i | \(0.590614\pi\) | |||||||
\(74\) | 8.19020 | 0.952091 | ||||||||
\(75\) | 8.93980 | 1.03228 | ||||||||
\(76\) | 2.67568 | 0.306922 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −3.30528 | −0.374250 | ||||||||
\(79\) | 7.30528 | 0.821908 | 0.410954 | − | 0.911656i | \(-0.365196\pi\) | ||||
0.410954 | + | 0.911656i | \(0.365196\pi\) | |||||||
\(80\) | −3.96556 | −0.443363 | ||||||||
\(81\) | 3.23017 | 0.358908 | ||||||||
\(82\) | −10.1504 | −1.12093 | ||||||||
\(83\) | 4.89498 | 0.537294 | 0.268647 | − | 0.963239i | \(-0.413424\pi\) | ||||
0.268647 | + | 0.963239i | \(0.413424\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −19.0309 | −2.06419 | ||||||||
\(86\) | 3.30528 | 0.356418 | ||||||||
\(87\) | 0.833497 | 0.0893603 | ||||||||
\(88\) | −1.11509 | −0.118869 | ||||||||
\(89\) | −1.11469 | −0.118157 | −0.0590785 | − | 0.998253i | \(-0.518816\pi\) | ||||
−0.0590785 | + | 0.998253i | \(0.518816\pi\) | |||||||
\(90\) | 9.14173 | 0.963623 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 8.42037 | 0.877884 | ||||||||
\(93\) | 2.46455 | 0.255561 | ||||||||
\(94\) | 4.97424 | 0.513054 | ||||||||
\(95\) | −10.6106 | −1.08862 | ||||||||
\(96\) | 0.833497 | 0.0850685 | ||||||||
\(97\) | 17.3273 | 1.75932 | 0.879660 | − | 0.475603i | \(-0.157770\pi\) | ||||
0.879660 | + | 0.475603i | \(0.157770\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.57059 | 0.258354 | ||||||||
\(100\) | 10.7257 | 1.07257 | ||||||||
\(101\) | 1.92145 | 0.191191 | 0.0955955 | − | 0.995420i | \(-0.469524\pi\) | ||||
0.0955955 | + | 0.995420i | \(0.469524\pi\) | |||||||
\(102\) | 4.00000 | 0.396059 | ||||||||
\(103\) | 0.912761 | 0.0899370 | 0.0449685 | − | 0.998988i | \(-0.485681\pi\) | ||||
0.0449685 | + | 0.998988i | \(0.485681\pi\) | |||||||
\(104\) | −3.96556 | −0.388855 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.30528 | 0.515295 | ||||||||
\(107\) | −2.61056 | −0.252373 | −0.126186 | − | 0.992007i | \(-0.540274\pi\) | ||||
−0.126186 | + | 0.992007i | \(0.540274\pi\) | |||||||
\(108\) | −4.42194 | −0.425501 | ||||||||
\(109\) | −7.91585 | −0.758201 | −0.379100 | − | 0.925356i | \(-0.623766\pi\) | ||||
−0.379100 | + | 0.925356i | \(0.623766\pi\) | |||||||
\(110\) | 4.42194 | 0.421615 | ||||||||
\(111\) | 6.82651 | 0.647943 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −17.4513 | −1.64168 | −0.820840 | − | 0.571158i | \(-0.806494\pi\) | ||||
−0.820840 | + | 0.571158i | \(0.806494\pi\) | |||||||
\(114\) | 2.23017 | 0.208875 | ||||||||
\(115\) | −33.3915 | −3.11377 | ||||||||
\(116\) | 1.00000 | 0.0928477 | ||||||||
\(117\) | 9.14173 | 0.845153 | ||||||||
\(118\) | 9.14173 | 0.841564 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −3.30528 | −0.301730 | ||||||||
\(121\) | −9.75658 | −0.886962 | ||||||||
\(122\) | −6.92243 | −0.626727 | ||||||||
\(123\) | −8.46034 | −0.762844 | ||||||||
\(124\) | 2.95687 | 0.265535 | ||||||||
\(125\) | −22.7054 | −2.03083 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −20.8407 | −1.84932 | −0.924658 | − | 0.380798i | \(-0.875649\pi\) | ||||
−0.924658 | + | 0.380798i | \(0.875649\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 2.75494 | 0.242559 | ||||||||
\(130\) | 15.7257 | 1.37923 | ||||||||
\(131\) | 7.83519 | 0.684564 | 0.342282 | − | 0.939597i | \(-0.388800\pi\) | ||||
0.342282 | + | 0.939597i | \(0.388800\pi\) | |||||||
\(132\) | −0.929421 | −0.0808957 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −6.61056 | −0.571066 | ||||||||
\(135\) | 17.5355 | 1.50921 | ||||||||
\(136\) | 4.79906 | 0.411516 | ||||||||
\(137\) | −2.00000 | −0.170872 | −0.0854358 | − | 0.996344i | \(-0.527228\pi\) | ||||
−0.0854358 | + | 0.996344i | \(0.527228\pi\) | |||||||
\(138\) | 7.01835 | 0.597442 | ||||||||
\(139\) | 8.38750 | 0.711418 | 0.355709 | − | 0.934597i | \(-0.384239\pi\) | ||||
0.355709 | + | 0.934597i | \(0.384239\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.14602 | 0.349158 | ||||||||
\(142\) | 15.0309 | 1.26137 | ||||||||
\(143\) | 4.42194 | 0.369781 | ||||||||
\(144\) | −2.30528 | −0.192107 | ||||||||
\(145\) | −3.96556 | −0.329322 | ||||||||
\(146\) | −4.79906 | −0.397173 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 8.19020 | 0.673230 | ||||||||
\(149\) | 4.92489 | 0.403463 | 0.201731 | − | 0.979441i | \(-0.435343\pi\) | ||||
0.201731 | + | 0.979441i | \(0.435343\pi\) | |||||||
\(150\) | 8.93980 | 0.729932 | ||||||||
\(151\) | 21.6415 | 1.76116 | 0.880580 | − | 0.473897i | \(-0.157153\pi\) | ||||
0.880580 | + | 0.473897i | \(0.157153\pi\) | |||||||
\(152\) | 2.67568 | 0.217026 | ||||||||
\(153\) | −11.0632 | −0.894405 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −11.7257 | −0.941827 | ||||||||
\(156\) | −3.30528 | −0.264634 | ||||||||
\(157\) | −14.8535 | −1.18544 | −0.592721 | − | 0.805408i | \(-0.701946\pi\) | ||||
−0.592721 | + | 0.805408i | \(0.701946\pi\) | |||||||
\(158\) | 7.30528 | 0.581177 | ||||||||
\(159\) | 4.42194 | 0.350683 | ||||||||
\(160\) | −3.96556 | −0.313505 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 3.23017 | 0.253786 | ||||||||
\(163\) | −9.95582 | −0.779800 | −0.389900 | − | 0.920857i | \(-0.627490\pi\) | ||||
−0.389900 | + | 0.920857i | \(0.627490\pi\) | |||||||
\(164\) | −10.1504 | −0.792614 | ||||||||
\(165\) | 3.68567 | 0.286929 | ||||||||
\(166\) | 4.89498 | 0.379924 | ||||||||
\(167\) | 2.01737 | 0.156109 | 0.0780544 | − | 0.996949i | \(-0.475129\pi\) | ||||
0.0780544 | + | 0.996949i | \(0.475129\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.72565 | 0.209665 | ||||||||
\(170\) | −19.0309 | −1.45961 | ||||||||
\(171\) | −6.16820 | −0.471694 | ||||||||
\(172\) | 3.30528 | 0.252025 | ||||||||
\(173\) | −6.72050 | −0.510950 | −0.255475 | − | 0.966816i | \(-0.582232\pi\) | ||||
−0.255475 | + | 0.966816i | \(0.582232\pi\) | |||||||
\(174\) | 0.833497 | 0.0631873 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.11509 | −0.0840528 | ||||||||
\(177\) | 7.61961 | 0.572725 | ||||||||
\(178\) | −1.11469 | −0.0835496 | ||||||||
\(179\) | 25.6815 | 1.91952 | 0.959762 | − | 0.280816i | \(-0.0906050\pi\) | ||||
0.959762 | + | 0.280816i | \(0.0906050\pi\) | |||||||
\(180\) | 9.14173 | 0.681384 | ||||||||
\(181\) | −19.4774 | −1.44774 | −0.723872 | − | 0.689934i | \(-0.757640\pi\) | ||||
−0.723872 | + | 0.689934i | \(0.757640\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.76983 | −0.426518 | ||||||||
\(184\) | 8.42037 | 0.620758 | ||||||||
\(185\) | −32.4787 | −2.38788 | ||||||||
\(186\) | 2.46455 | 0.180709 | ||||||||
\(187\) | −5.35136 | −0.391330 | ||||||||
\(188\) | 4.97424 | 0.362784 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −10.6106 | −0.769771 | ||||||||
\(191\) | 4.38039 | 0.316954 | 0.158477 | − | 0.987363i | \(-0.449342\pi\) | ||||
0.158477 | + | 0.987363i | \(0.449342\pi\) | |||||||
\(192\) | 0.833497 | 0.0601525 | ||||||||
\(193\) | 3.76983 | 0.271358 | 0.135679 | − | 0.990753i | \(-0.456678\pi\) | ||||
0.135679 | + | 0.990753i | \(0.456678\pi\) | |||||||
\(194\) | 17.3273 | 1.24403 | ||||||||
\(195\) | 13.1073 | 0.938632 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.38039 | −0.169596 | −0.0847980 | − | 0.996398i | \(-0.527024\pi\) | ||||
−0.0847980 | + | 0.996398i | \(0.527024\pi\) | |||||||
\(198\) | 2.57059 | 0.182684 | ||||||||
\(199\) | 20.1090 | 1.42549 | 0.712744 | − | 0.701424i | \(-0.247452\pi\) | ||||
0.712744 | + | 0.701424i | \(0.247452\pi\) | |||||||
\(200\) | 10.7257 | 0.758418 | ||||||||
\(201\) | −5.50989 | −0.388638 | ||||||||
\(202\) | 1.92145 | 0.135193 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 4.00000 | 0.280056 | ||||||||
\(205\) | 40.2521 | 2.81133 | ||||||||
\(206\) | 0.912761 | 0.0635951 | ||||||||
\(207\) | −19.4113 | −1.34918 | ||||||||
\(208\) | −3.96556 | −0.274962 | ||||||||
\(209\) | −2.98361 | −0.206381 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.7566 | 1.29126 | 0.645628 | − | 0.763652i | \(-0.276596\pi\) | ||||
0.645628 | + | 0.763652i | \(0.276596\pi\) | |||||||
\(212\) | 5.30528 | 0.364368 | ||||||||
\(213\) | 12.5282 | 0.858421 | ||||||||
\(214\) | −2.61056 | −0.178455 | ||||||||
\(215\) | −13.1073 | −0.893910 | ||||||||
\(216\) | −4.42194 | −0.300875 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −7.91585 | −0.536129 | ||||||||
\(219\) | −4.00000 | −0.270295 | ||||||||
\(220\) | 4.42194 | 0.298127 | ||||||||
\(221\) | −19.0309 | −1.28016 | ||||||||
\(222\) | 6.82651 | 0.458165 | ||||||||
\(223\) | 25.4603 | 1.70495 | 0.852475 | − | 0.522767i | \(-0.175100\pi\) | ||||
0.852475 | + | 0.522767i | \(0.175100\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −24.7257 | −1.64838 | ||||||||
\(226\) | −17.4513 | −1.16084 | ||||||||
\(227\) | 20.0030 | 1.32764 | 0.663822 | − | 0.747890i | \(-0.268933\pi\) | ||||
0.663822 | + | 0.747890i | \(0.268933\pi\) | |||||||
\(228\) | 2.23017 | 0.147697 | ||||||||
\(229\) | −15.2039 | −1.00470 | −0.502352 | − | 0.864663i | \(-0.667532\pi\) | ||||
−0.502352 | + | 0.864663i | \(0.667532\pi\) | |||||||
\(230\) | −33.3915 | −2.20177 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.00000 | 0.0656532 | ||||||||
\(233\) | 7.53545 | 0.493664 | 0.246832 | − | 0.969058i | \(-0.420610\pi\) | ||||
0.246832 | + | 0.969058i | \(0.420610\pi\) | |||||||
\(234\) | 9.14173 | 0.597614 | ||||||||
\(235\) | −19.7257 | −1.28676 | ||||||||
\(236\) | 9.14173 | 0.595076 | ||||||||
\(237\) | 6.08893 | 0.395519 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.84074 | −0.571860 | −0.285930 | − | 0.958251i | \(-0.592302\pi\) | ||||
−0.285930 | + | 0.958251i | \(0.592302\pi\) | |||||||
\(240\) | −3.30528 | −0.213355 | ||||||||
\(241\) | 11.4403 | 0.736934 | 0.368467 | − | 0.929641i | \(-0.379883\pi\) | ||||
0.368467 | + | 0.929641i | \(0.379883\pi\) | |||||||
\(242\) | −9.75658 | −0.627177 | ||||||||
\(243\) | 15.9582 | 1.02372 | ||||||||
\(244\) | −6.92243 | −0.443163 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −8.46034 | −0.539412 | ||||||||
\(247\) | −10.6106 | −0.675134 | ||||||||
\(248\) | 2.95687 | 0.187762 | ||||||||
\(249\) | 4.07995 | 0.258556 | ||||||||
\(250\) | −22.7054 | −1.43602 | ||||||||
\(251\) | −15.7830 | −0.996212 | −0.498106 | − | 0.867116i | \(-0.665971\pi\) | ||||
−0.498106 | + | 0.867116i | \(0.665971\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.38944 | −0.590309 | ||||||||
\(254\) | −20.8407 | −1.30766 | ||||||||
\(255\) | −15.8622 | −0.993332 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −16.0374 | −1.00039 | −0.500193 | − | 0.865914i | \(-0.666738\pi\) | ||||
−0.500193 | + | 0.865914i | \(0.666738\pi\) | |||||||
\(258\) | 2.75494 | 0.171515 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 15.7257 | 0.975263 | ||||||||
\(261\) | −2.30528 | −0.142693 | ||||||||
\(262\) | 7.83519 | 0.484060 | ||||||||
\(263\) | 0.694718 | 0.0428381 | 0.0214191 | − | 0.999771i | \(-0.493182\pi\) | ||||
0.0214191 | + | 0.999771i | \(0.493182\pi\) | |||||||
\(264\) | −0.929421 | −0.0572019 | ||||||||
\(265\) | −21.0384 | −1.29238 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.929091 | −0.0568595 | ||||||||
\(268\) | −6.61056 | −0.403804 | ||||||||
\(269\) | 24.6435 | 1.50254 | 0.751271 | − | 0.659994i | \(-0.229441\pi\) | ||||
0.751271 | + | 0.659994i | \(0.229441\pi\) | |||||||
\(270\) | 17.5355 | 1.06717 | ||||||||
\(271\) | 26.5917 | 1.61533 | 0.807665 | − | 0.589641i | \(-0.200731\pi\) | ||||
0.807665 | + | 0.589641i | \(0.200731\pi\) | |||||||
\(272\) | 4.79906 | 0.290985 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.00000 | −0.120824 | ||||||||
\(275\) | −11.9600 | −0.721217 | ||||||||
\(276\) | 7.01835 | 0.422455 | ||||||||
\(277\) | 1.15926 | 0.0696534 | 0.0348267 | − | 0.999393i | \(-0.488912\pi\) | ||||
0.0348267 | + | 0.999393i | \(0.488912\pi\) | |||||||
\(278\) | 8.38750 | 0.503049 | ||||||||
\(279\) | −6.81643 | −0.408089 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.11509 | 0.424450 | 0.212225 | − | 0.977221i | \(-0.431929\pi\) | ||||
0.212225 | + | 0.977221i | \(0.431929\pi\) | |||||||
\(282\) | 4.14602 | 0.246892 | ||||||||
\(283\) | −13.7389 | −0.816690 | −0.408345 | − | 0.912828i | \(-0.633894\pi\) | ||||
−0.408345 | + | 0.912828i | \(0.633894\pi\) | |||||||
\(284\) | 15.0309 | 0.891922 | ||||||||
\(285\) | −8.84388 | −0.523866 | ||||||||
\(286\) | 4.42194 | 0.261475 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −2.30528 | −0.135840 | ||||||||
\(289\) | 6.03093 | 0.354761 | ||||||||
\(290\) | −3.96556 | −0.232866 | ||||||||
\(291\) | 14.4423 | 0.846620 | ||||||||
\(292\) | −4.79906 | −0.280843 | ||||||||
\(293\) | 27.0314 | 1.57919 | 0.789596 | − | 0.613627i | \(-0.210290\pi\) | ||||
0.789596 | + | 0.613627i | \(0.210290\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −36.2521 | −2.11068 | ||||||||
\(296\) | 8.19020 | 0.476045 | ||||||||
\(297\) | 4.93084 | 0.286116 | ||||||||
\(298\) | 4.92489 | 0.285291 | ||||||||
\(299\) | −33.3915 | −1.93108 | ||||||||
\(300\) | 8.93980 | 0.516140 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 21.6415 | 1.24533 | ||||||||
\(303\) | 1.60152 | 0.0920050 | ||||||||
\(304\) | 2.67568 | 0.153461 | ||||||||
\(305\) | 27.4513 | 1.57186 | ||||||||
\(306\) | −11.0632 | −0.632440 | ||||||||
\(307\) | −20.0297 | −1.14316 | −0.571578 | − | 0.820548i | \(-0.693669\pi\) | ||||
−0.571578 | + | 0.820548i | \(0.693669\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.760784 | 0.0432795 | ||||||||
\(310\) | −11.7257 | −0.665972 | ||||||||
\(311\) | 28.9963 | 1.64423 | 0.822114 | − | 0.569324i | \(-0.192795\pi\) | ||||
0.822114 | + | 0.569324i | \(0.192795\pi\) | |||||||
\(312\) | −3.30528 | −0.187125 | ||||||||
\(313\) | −4.07156 | −0.230138 | −0.115069 | − | 0.993357i | \(-0.536709\pi\) | ||||
−0.115069 | + | 0.993357i | \(0.536709\pi\) | |||||||
\(314\) | −14.8535 | −0.838234 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.30528 | 0.410954 | ||||||||
\(317\) | −15.6815 | −0.880759 | −0.440380 | − | 0.897812i | \(-0.645156\pi\) | ||||
−0.440380 | + | 0.897812i | \(0.645156\pi\) | |||||||
\(318\) | 4.42194 | 0.247970 | ||||||||
\(319\) | −1.11509 | −0.0624328 | ||||||||
\(320\) | −3.96556 | −0.221681 | ||||||||
\(321\) | −2.17590 | −0.121447 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.8407 | 0.714478 | ||||||||
\(324\) | 3.23017 | 0.179454 | ||||||||
\(325\) | −42.5332 | −2.35932 | ||||||||
\(326\) | −9.95582 | −0.551402 | ||||||||
\(327\) | −6.59784 | −0.364861 | ||||||||
\(328\) | −10.1504 | −0.560463 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 3.68567 | 0.202890 | ||||||||
\(331\) | −17.0751 | −0.938533 | −0.469266 | − | 0.883057i | \(-0.655482\pi\) | ||||
−0.469266 | + | 0.883057i | \(0.655482\pi\) | |||||||
\(332\) | 4.89498 | 0.268647 | ||||||||
\(333\) | −18.8807 | −1.03466 | ||||||||
\(334\) | 2.01737 | 0.110386 | ||||||||
\(335\) | 26.2146 | 1.43226 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.00000 | −0.326841 | −0.163420 | − | 0.986557i | \(-0.552253\pi\) | ||||
−0.163420 | + | 0.986557i | \(0.552253\pi\) | |||||||
\(338\) | 2.72565 | 0.148256 | ||||||||
\(339\) | −14.5456 | −0.790009 | ||||||||
\(340\) | −19.0309 | −1.03210 | ||||||||
\(341\) | −3.29717 | −0.178552 | ||||||||
\(342\) | −6.16820 | −0.333538 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 3.30528 | 0.178209 | ||||||||
\(345\) | −27.8317 | −1.49841 | ||||||||
\(346\) | −6.72050 | −0.361296 | ||||||||
\(347\) | 7.07091 | 0.379586 | 0.189793 | − | 0.981824i | \(-0.439218\pi\) | ||||
0.189793 | + | 0.981824i | \(0.439218\pi\) | |||||||
\(348\) | 0.833497 | 0.0446801 | ||||||||
\(349\) | −30.7425 | −1.64561 | −0.822805 | − | 0.568324i | \(-0.807592\pi\) | ||||
−0.822805 | + | 0.568324i | \(0.807592\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 17.5355 | 0.935973 | ||||||||
\(352\) | −1.11509 | −0.0594343 | ||||||||
\(353\) | 9.19425 | 0.489361 | 0.244680 | − | 0.969604i | \(-0.421317\pi\) | ||||
0.244680 | + | 0.969604i | \(0.421317\pi\) | |||||||
\(354\) | 7.61961 | 0.404978 | ||||||||
\(355\) | −59.6060 | −3.16356 | ||||||||
\(356\) | −1.11469 | −0.0590785 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 25.6815 | 1.35731 | ||||||||
\(359\) | 8.52641 | 0.450007 | 0.225003 | − | 0.974358i | \(-0.427761\pi\) | ||||
0.225003 | + | 0.974358i | \(0.427761\pi\) | |||||||
\(360\) | 9.14173 | 0.481811 | ||||||||
\(361\) | −11.8407 | −0.623197 | ||||||||
\(362\) | −19.4774 | −1.02371 | ||||||||
\(363\) | −8.13209 | −0.426824 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 19.0309 | 0.996125 | ||||||||
\(366\) | −5.76983 | −0.301594 | ||||||||
\(367\) | −2.02745 | −0.105832 | −0.0529161 | − | 0.998599i | \(-0.516852\pi\) | ||||
−0.0529161 | + | 0.998599i | \(0.516852\pi\) | |||||||
\(368\) | 8.42037 | 0.438942 | ||||||||
\(369\) | 23.3996 | 1.21813 | ||||||||
\(370\) | −32.4787 | −1.68849 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 2.46455 | 0.127781 | ||||||||
\(373\) | 22.5264 | 1.16637 | 0.583187 | − | 0.812338i | \(-0.301806\pi\) | ||||
0.583187 | + | 0.812338i | \(0.301806\pi\) | |||||||
\(374\) | −5.35136 | −0.276712 | ||||||||
\(375\) | −18.9249 | −0.977277 | ||||||||
\(376\) | 4.97424 | 0.256527 | ||||||||
\(377\) | −3.96556 | −0.204237 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −24.3804 | −1.25234 | −0.626168 | − | 0.779688i | \(-0.715378\pi\) | ||||
−0.626168 | + | 0.779688i | \(0.715378\pi\) | |||||||
\(380\) | −10.6106 | −0.544310 | ||||||||
\(381\) | −17.3707 | −0.889928 | ||||||||
\(382\) | 4.38039 | 0.224120 | ||||||||
\(383\) | 30.0575 | 1.53586 | 0.767932 | − | 0.640531i | \(-0.221286\pi\) | ||||
0.767932 | + | 0.640531i | \(0.221286\pi\) | |||||||
\(384\) | 0.833497 | 0.0425342 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.76983 | 0.191879 | ||||||||
\(387\) | −7.61961 | −0.387326 | ||||||||
\(388\) | 17.3273 | 0.879660 | ||||||||
\(389\) | −7.26110 | −0.368153 | −0.184076 | − | 0.982912i | \(-0.558929\pi\) | ||||
−0.184076 | + | 0.982912i | \(0.558929\pi\) | |||||||
\(390\) | 13.1073 | 0.663713 | ||||||||
\(391\) | 40.4098 | 2.04361 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.53061 | 0.329426 | ||||||||
\(394\) | −2.38039 | −0.119922 | ||||||||
\(395\) | −28.9695 | −1.45761 | ||||||||
\(396\) | 2.57059 | 0.129177 | ||||||||
\(397\) | 9.87930 | 0.495828 | 0.247914 | − | 0.968782i | \(-0.420255\pi\) | ||||
0.247914 | + | 0.968782i | \(0.420255\pi\) | |||||||
\(398\) | 20.1090 | 1.00797 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 10.7257 | 0.536283 | ||||||||
\(401\) | −2.69472 | −0.134568 | −0.0672839 | − | 0.997734i | \(-0.521433\pi\) | ||||
−0.0672839 | + | 0.997734i | \(0.521433\pi\) | |||||||
\(402\) | −5.50989 | −0.274808 | ||||||||
\(403\) | −11.7257 | −0.584096 | ||||||||
\(404\) | 1.92145 | 0.0955955 | ||||||||
\(405\) | −12.8094 | −0.636506 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9.13277 | −0.452695 | ||||||||
\(408\) | 4.00000 | 0.198030 | ||||||||
\(409\) | 2.97353 | 0.147032 | 0.0735159 | − | 0.997294i | \(-0.476578\pi\) | ||||
0.0735159 | + | 0.997294i | \(0.476578\pi\) | |||||||
\(410\) | 40.2521 | 1.98791 | ||||||||
\(411\) | −1.66699 | −0.0822268 | ||||||||
\(412\) | 0.912761 | 0.0449685 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −19.4113 | −0.954015 | ||||||||
\(415\) | −19.4113 | −0.952864 | ||||||||
\(416\) | −3.96556 | −0.194427 | ||||||||
\(417\) | 6.99096 | 0.342349 | ||||||||
\(418\) | −2.98361 | −0.145933 | ||||||||
\(419\) | −0.648229 | −0.0316680 | −0.0158340 | − | 0.999875i | \(-0.505040\pi\) | ||||
−0.0158340 | + | 0.999875i | \(0.505040\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −21.4113 | −1.04352 | −0.521762 | − | 0.853091i | \(-0.674725\pi\) | ||||
−0.521762 | + | 0.853091i | \(0.674725\pi\) | |||||||
\(422\) | 18.7566 | 0.913056 | ||||||||
\(423\) | −11.4670 | −0.557546 | ||||||||
\(424\) | 5.30528 | 0.257647 | ||||||||
\(425\) | 51.4730 | 2.49681 | ||||||||
\(426\) | 12.5282 | 0.606995 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −2.61056 | −0.126186 | ||||||||
\(429\) | 3.68567 | 0.177946 | ||||||||
\(430\) | −13.1073 | −0.632090 | ||||||||
\(431\) | −29.2211 | −1.40753 | −0.703766 | − | 0.710432i | \(-0.748500\pi\) | ||||
−0.703766 | + | 0.710432i | \(0.748500\pi\) | |||||||
\(432\) | −4.42194 | −0.212751 | ||||||||
\(433\) | −26.3630 | −1.26693 | −0.633463 | − | 0.773773i | \(-0.718367\pi\) | ||||
−0.633463 | + | 0.773773i | \(0.718367\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.30528 | −0.158476 | ||||||||
\(436\) | −7.91585 | −0.379100 | ||||||||
\(437\) | 22.5302 | 1.07777 | ||||||||
\(438\) | −4.00000 | −0.191127 | ||||||||
\(439\) | 17.7211 | 0.845781 | 0.422890 | − | 0.906181i | \(-0.361016\pi\) | ||||
0.422890 | + | 0.906181i | \(0.361016\pi\) | |||||||
\(440\) | 4.42194 | 0.210808 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −19.0309 | −0.905209 | ||||||||
\(443\) | −1.80980 | −0.0859864 | −0.0429932 | − | 0.999075i | \(-0.513689\pi\) | ||||
−0.0429932 | + | 0.999075i | \(0.513689\pi\) | |||||||
\(444\) | 6.82651 | 0.323972 | ||||||||
\(445\) | 4.42037 | 0.209546 | ||||||||
\(446\) | 25.4603 | 1.20558 | ||||||||
\(447\) | 4.10488 | 0.194154 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.99096 | −0.424309 | −0.212155 | − | 0.977236i | \(-0.568048\pi\) | ||||
−0.212155 | + | 0.977236i | \(0.568048\pi\) | |||||||
\(450\) | −24.7257 | −1.16558 | ||||||||
\(451\) | 11.3186 | 0.532971 | ||||||||
\(452\) | −17.4513 | −0.820840 | ||||||||
\(453\) | 18.0381 | 0.847505 | ||||||||
\(454\) | 20.0030 | 0.938786 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.23017 | 0.104437 | ||||||||
\(457\) | 21.4913 | 1.00532 | 0.502660 | − | 0.864484i | \(-0.332355\pi\) | ||||
0.502660 | + | 0.864484i | \(0.332355\pi\) | |||||||
\(458\) | −15.2039 | −0.710433 | ||||||||
\(459\) | −21.2211 | −0.990517 | ||||||||
\(460\) | −33.3915 | −1.55688 | ||||||||
\(461\) | 26.4690 | 1.23279 | 0.616393 | − | 0.787439i | \(-0.288593\pi\) | ||||
0.616393 | + | 0.787439i | \(0.288593\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.80980 | 0.455900 | 0.227950 | − | 0.973673i | \(-0.426798\pi\) | ||||
0.227950 | + | 0.973673i | \(0.426798\pi\) | |||||||
\(464\) | 1.00000 | 0.0464238 | ||||||||
\(465\) | −9.77330 | −0.453226 | ||||||||
\(466\) | 7.53545 | 0.349073 | ||||||||
\(467\) | 5.78100 | 0.267513 | 0.133756 | − | 0.991014i | \(-0.457296\pi\) | ||||
0.133756 | + | 0.991014i | \(0.457296\pi\) | |||||||
\(468\) | 9.14173 | 0.422577 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −19.7257 | −0.909876 | ||||||||
\(471\) | −12.3804 | −0.570458 | ||||||||
\(472\) | 9.14173 | 0.420782 | ||||||||
\(473\) | −3.68567 | −0.169467 | ||||||||
\(474\) | 6.08893 | 0.279674 | ||||||||
\(475\) | 28.6984 | 1.31677 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −12.2302 | −0.559981 | ||||||||
\(478\) | −8.84074 | −0.404366 | ||||||||
\(479\) | 28.8211 | 1.31687 | 0.658434 | − | 0.752638i | \(-0.271219\pi\) | ||||
0.658434 | + | 0.752638i | \(0.271219\pi\) | |||||||
\(480\) | −3.30528 | −0.150865 | ||||||||
\(481\) | −32.4787 | −1.48090 | ||||||||
\(482\) | 11.4403 | 0.521091 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −9.75658 | −0.443481 | ||||||||
\(485\) | −68.7124 | −3.12007 | ||||||||
\(486\) | 15.9582 | 0.723877 | ||||||||
\(487\) | 17.6815 | 0.801224 | 0.400612 | − | 0.916248i | \(-0.368798\pi\) | ||||
0.400612 | + | 0.916248i | \(0.368798\pi\) | |||||||
\(488\) | −6.92243 | −0.313364 | ||||||||
\(489\) | −8.29815 | −0.375255 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 23.6857 | 1.06892 | 0.534460 | − | 0.845194i | \(-0.320515\pi\) | ||||
0.534460 | + | 0.845194i | \(0.320515\pi\) | |||||||
\(492\) | −8.46034 | −0.381422 | ||||||||
\(493\) | 4.79906 | 0.216139 | ||||||||
\(494\) | −10.6106 | −0.477392 | ||||||||
\(495\) | −10.1938 | −0.458178 | ||||||||
\(496\) | 2.95687 | 0.132768 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 4.07995 | 0.182827 | ||||||||
\(499\) | −14.9910 | −0.671087 | −0.335544 | − | 0.942025i | \(-0.608920\pi\) | ||||
−0.335544 | + | 0.942025i | \(0.608920\pi\) | |||||||
\(500\) | −22.7054 | −1.01542 | ||||||||
\(501\) | 1.68147 | 0.0751227 | ||||||||
\(502\) | −15.7830 | −0.704428 | ||||||||
\(503\) | 35.7859 | 1.59562 | 0.797808 | − | 0.602911i | \(-0.205993\pi\) | ||||
0.797808 | + | 0.602911i | \(0.205993\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.61961 | −0.339068 | ||||||||
\(506\) | −9.38944 | −0.417411 | ||||||||
\(507\) | 2.27182 | 0.100895 | ||||||||
\(508\) | −20.8407 | −0.924658 | ||||||||
\(509\) | 0.473041 | 0.0209672 | 0.0104836 | − | 0.999945i | \(-0.496663\pi\) | ||||
0.0104836 | + | 0.999945i | \(0.496663\pi\) | |||||||
\(510\) | −15.8622 | −0.702391 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −11.8317 | −0.522382 | ||||||||
\(514\) | −16.0374 | −0.707380 | ||||||||
\(515\) | −3.61961 | −0.159499 | ||||||||
\(516\) | 2.75494 | 0.121280 | ||||||||
\(517\) | −5.54671 | −0.243944 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.60152 | −0.245879 | ||||||||
\(520\) | 15.7257 | 0.689615 | ||||||||
\(521\) | −13.6697 | −0.598879 | −0.299440 | − | 0.954115i | \(-0.596800\pi\) | ||||
−0.299440 | + | 0.954115i | \(0.596800\pi\) | |||||||
\(522\) | −2.30528 | −0.100899 | ||||||||
\(523\) | 1.21061 | 0.0529365 | 0.0264682 | − | 0.999650i | \(-0.491574\pi\) | ||||
0.0264682 | + | 0.999650i | \(0.491574\pi\) | |||||||
\(524\) | 7.83519 | 0.342282 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.694718 | 0.0302911 | ||||||||
\(527\) | 14.1902 | 0.618135 | ||||||||
\(528\) | −0.929421 | −0.0404479 | ||||||||
\(529\) | 47.9026 | 2.08272 | ||||||||
\(530\) | −21.0384 | −0.913850 | ||||||||
\(531\) | −21.0743 | −0.914545 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 40.2521 | 1.74351 | ||||||||
\(534\) | −0.929091 | −0.0402057 | ||||||||
\(535\) | 10.3523 | 0.447571 | ||||||||
\(536\) | −6.61056 | −0.285533 | ||||||||
\(537\) | 21.4054 | 0.923713 | ||||||||
\(538\) | 24.6435 | 1.06246 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 17.5355 | 0.754606 | ||||||||
\(541\) | 40.6106 | 1.74598 | 0.872992 | − | 0.487734i | \(-0.162176\pi\) | ||||
0.872992 | + | 0.487734i | \(0.162176\pi\) | |||||||
\(542\) | 26.5917 | 1.14221 | ||||||||
\(543\) | −16.2344 | −0.696684 | ||||||||
\(544\) | 4.79906 | 0.205758 | ||||||||
\(545\) | 31.3907 | 1.34463 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −43.4513 | −1.85784 | −0.928922 | − | 0.370276i | \(-0.879263\pi\) | ||||
−0.928922 | + | 0.370276i | \(0.879263\pi\) | |||||||
\(548\) | −2.00000 | −0.0854358 | ||||||||
\(549\) | 15.9582 | 0.681078 | ||||||||
\(550\) | −11.9600 | −0.509977 | ||||||||
\(551\) | 2.67568 | 0.113988 | ||||||||
\(552\) | 7.01835 | 0.298721 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 1.15926 | 0.0492524 | ||||||||
\(555\) | −27.0709 | −1.14910 | ||||||||
\(556\) | 8.38750 | 0.355709 | ||||||||
\(557\) | 5.15926 | 0.218605 | 0.109303 | − | 0.994009i | \(-0.465138\pi\) | ||||
0.109303 | + | 0.994009i | \(0.465138\pi\) | |||||||
\(558\) | −6.81643 | −0.288562 | ||||||||
\(559\) | −13.1073 | −0.554379 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.46034 | −0.188316 | ||||||||
\(562\) | 7.11509 | 0.300132 | ||||||||
\(563\) | −10.6235 | −0.447725 | −0.223863 | − | 0.974621i | \(-0.571867\pi\) | ||||
−0.223863 | + | 0.974621i | \(0.571867\pi\) | |||||||
\(564\) | 4.14602 | 0.174579 | ||||||||
\(565\) | 69.2041 | 2.91144 | ||||||||
\(566\) | −13.7389 | −0.577487 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 15.0309 | 0.630684 | ||||||||
\(569\) | −1.53966 | −0.0645457 | −0.0322729 | − | 0.999479i | \(-0.510275\pi\) | ||||
−0.0322729 | + | 0.999479i | \(0.510275\pi\) | |||||||
\(570\) | −8.84388 | −0.370429 | ||||||||
\(571\) | −42.9910 | −1.79912 | −0.899558 | − | 0.436802i | \(-0.856111\pi\) | ||||
−0.899558 | + | 0.436802i | \(0.856111\pi\) | |||||||
\(572\) | 4.42194 | 0.184891 | ||||||||
\(573\) | 3.65105 | 0.152525 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 90.3139 | 3.76635 | ||||||||
\(576\) | −2.30528 | −0.0960534 | ||||||||
\(577\) | −3.32391 | −0.138376 | −0.0691881 | − | 0.997604i | \(-0.522041\pi\) | ||||
−0.0691881 | + | 0.997604i | \(0.522041\pi\) | |||||||
\(578\) | 6.03093 | 0.250854 | ||||||||
\(579\) | 3.14214 | 0.130583 | ||||||||
\(580\) | −3.96556 | −0.164661 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 14.4423 | 0.598651 | ||||||||
\(583\) | −5.91585 | −0.245009 | ||||||||
\(584\) | −4.79906 | −0.198586 | ||||||||
\(585\) | −36.2521 | −1.49884 | ||||||||
\(586\) | 27.0314 | 1.11666 | ||||||||
\(587\) | −36.4609 | −1.50490 | −0.752452 | − | 0.658648i | \(-0.771129\pi\) | ||||
−0.752452 | + | 0.658648i | \(0.771129\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.91165 | 0.325994 | ||||||||
\(590\) | −36.2521 | −1.49247 | ||||||||
\(591\) | −1.98405 | −0.0816129 | ||||||||
\(592\) | 8.19020 | 0.336615 | ||||||||
\(593\) | −30.4447 | −1.25021 | −0.625106 | − | 0.780540i | \(-0.714944\pi\) | ||||
−0.625106 | + | 0.780540i | \(0.714944\pi\) | |||||||
\(594\) | 4.93084 | 0.202315 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4.92489 | 0.201731 | ||||||||
\(597\) | 16.7608 | 0.685973 | ||||||||
\(598\) | −33.3915 | −1.36548 | ||||||||
\(599\) | −35.9777 | −1.47001 | −0.735005 | − | 0.678062i | \(-0.762820\pi\) | ||||
−0.735005 | + | 0.678062i | \(0.762820\pi\) | |||||||
\(600\) | 8.93980 | 0.364966 | ||||||||
\(601\) | 9.04581 | 0.368986 | 0.184493 | − | 0.982834i | \(-0.440936\pi\) | ||||
0.184493 | + | 0.982834i | \(0.440936\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 15.2392 | 0.620589 | ||||||||
\(604\) | 21.6415 | 0.880580 | ||||||||
\(605\) | 38.6903 | 1.57298 | ||||||||
\(606\) | 1.60152 | 0.0650573 | ||||||||
\(607\) | −22.6953 | −0.921175 | −0.460587 | − | 0.887614i | \(-0.652361\pi\) | ||||
−0.460587 | + | 0.887614i | \(0.652361\pi\) | |||||||
\(608\) | 2.67568 | 0.108513 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 27.4513 | 1.11147 | ||||||||
\(611\) | −19.7257 | −0.798014 | ||||||||
\(612\) | −11.0632 | −0.447202 | ||||||||
\(613\) | 27.5355 | 1.11215 | 0.556073 | − | 0.831133i | \(-0.312307\pi\) | ||||
0.556073 | + | 0.831133i | \(0.312307\pi\) | |||||||
\(614\) | −20.0297 | −0.808334 | ||||||||
\(615\) | 33.5500 | 1.35287 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 29.0709 | 1.17035 | 0.585175 | − | 0.810907i | \(-0.301026\pi\) | ||||
0.585175 | + | 0.810907i | \(0.301026\pi\) | |||||||
\(618\) | 0.760784 | 0.0306032 | ||||||||
\(619\) | 14.2745 | 0.573741 | 0.286870 | − | 0.957969i | \(-0.407385\pi\) | ||||
0.286870 | + | 0.957969i | \(0.407385\pi\) | |||||||
\(620\) | −11.7257 | −0.470913 | ||||||||
\(621\) | −37.2344 | −1.49416 | ||||||||
\(622\) | 28.9963 | 1.16264 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −3.30528 | −0.132317 | ||||||||
\(625\) | 36.4113 | 1.45645 | ||||||||
\(626\) | −4.07156 | −0.162732 | ||||||||
\(627\) | −2.48683 | −0.0993146 | ||||||||
\(628\) | −14.8535 | −0.592721 | ||||||||
\(629\) | 39.3052 | 1.56720 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 39.7433 | 1.58216 | 0.791079 | − | 0.611714i | \(-0.209520\pi\) | ||||
0.791079 | + | 0.611714i | \(0.209520\pi\) | |||||||
\(632\) | 7.30528 | 0.290589 | ||||||||
\(633\) | 15.6336 | 0.621378 | ||||||||
\(634\) | −15.6815 | −0.622791 | ||||||||
\(635\) | 82.6451 | 3.27967 | ||||||||
\(636\) | 4.42194 | 0.175341 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.11509 | −0.0441467 | ||||||||
\(639\) | −34.6505 | −1.37075 | ||||||||
\(640\) | −3.96556 | −0.156752 | ||||||||
\(641\) | −33.0709 | −1.30622 | −0.653111 | − | 0.757262i | \(-0.726537\pi\) | ||||
−0.653111 | + | 0.757262i | \(0.726537\pi\) | |||||||
\(642\) | −2.17590 | −0.0858759 | ||||||||
\(643\) | −16.3186 | −0.643543 | −0.321772 | − | 0.946817i | \(-0.604278\pi\) | ||||
−0.321772 | + | 0.946817i | \(0.604278\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −10.9249 | −0.430167 | ||||||||
\(646\) | 12.8407 | 0.505212 | ||||||||
\(647\) | 26.7770 | 1.05271 | 0.526355 | − | 0.850265i | \(-0.323558\pi\) | ||||
0.526355 | + | 0.850265i | \(0.323558\pi\) | |||||||
\(648\) | 3.23017 | 0.126893 | ||||||||
\(649\) | −10.1938 | −0.400142 | ||||||||
\(650\) | −42.5332 | −1.66829 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −9.95582 | −0.389900 | ||||||||
\(653\) | −25.3713 | −0.992858 | −0.496429 | − | 0.868077i | \(-0.665356\pi\) | ||||
−0.496429 | + | 0.868077i | \(0.665356\pi\) | |||||||
\(654\) | −6.59784 | −0.257996 | ||||||||
\(655\) | −31.0709 | −1.21404 | ||||||||
\(656\) | −10.1504 | −0.396307 | ||||||||
\(657\) | 11.0632 | 0.431616 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.34526 | −0.130313 | −0.0651564 | − | 0.997875i | \(-0.520755\pi\) | ||||
−0.0651564 | + | 0.997875i | \(0.520755\pi\) | |||||||
\(660\) | 3.68567 | 0.143465 | ||||||||
\(661\) | 36.8315 | 1.43258 | 0.716289 | − | 0.697804i | \(-0.245839\pi\) | ||||
0.716289 | + | 0.697804i | \(0.245839\pi\) | |||||||
\(662\) | −17.0751 | −0.663643 | ||||||||
\(663\) | −15.8622 | −0.616038 | ||||||||
\(664\) | 4.89498 | 0.189962 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −18.8807 | −0.731613 | ||||||||
\(667\) | 8.42037 | 0.326038 | ||||||||
\(668\) | 2.01737 | 0.0780544 | ||||||||
\(669\) | 21.2211 | 0.820456 | ||||||||
\(670\) | 26.2146 | 1.01276 | ||||||||
\(671\) | 7.71911 | 0.297993 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −27.9558 | −1.07762 | −0.538809 | − | 0.842428i | \(-0.681126\pi\) | ||||
−0.538809 | + | 0.842428i | \(0.681126\pi\) | |||||||
\(674\) | −6.00000 | −0.231111 | ||||||||
\(675\) | −47.4282 | −1.82551 | ||||||||
\(676\) | 2.72565 | 0.104833 | ||||||||
\(677\) | 51.2286 | 1.96888 | 0.984438 | − | 0.175733i | \(-0.0562295\pi\) | ||||
0.984438 | + | 0.175733i | \(0.0562295\pi\) | |||||||
\(678\) | −14.5456 | −0.558621 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −19.0309 | −0.729803 | ||||||||
\(681\) | 16.6724 | 0.638889 | ||||||||
\(682\) | −3.29717 | −0.126255 | ||||||||
\(683\) | 45.2211 | 1.73034 | 0.865169 | − | 0.501480i | \(-0.167211\pi\) | ||||
0.865169 | + | 0.501480i | \(0.167211\pi\) | |||||||
\(684\) | −6.16820 | −0.235847 | ||||||||
\(685\) | 7.93112 | 0.303032 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −12.6724 | −0.483483 | ||||||||
\(688\) | 3.30528 | 0.126013 | ||||||||
\(689\) | −21.0384 | −0.801499 | ||||||||
\(690\) | −27.8317 | −1.05953 | ||||||||
\(691\) | 4.70313 | 0.178916 | 0.0894578 | − | 0.995991i | \(-0.471487\pi\) | ||||
0.0894578 | + | 0.995991i | \(0.471487\pi\) | |||||||
\(692\) | −6.72050 | −0.255475 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7.07091 | 0.268408 | ||||||||
\(695\) | −33.2611 | −1.26167 | ||||||||
\(696\) | 0.833497 | 0.0315936 | ||||||||
\(697\) | −48.7124 | −1.84511 | ||||||||
\(698\) | −30.7425 | −1.16362 | ||||||||
\(699\) | 6.28078 | 0.237561 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −0.376191 | −0.0142085 | −0.00710427 | − | 0.999975i | \(-0.502261\pi\) | ||||
−0.00710427 | + | 0.999975i | \(0.502261\pi\) | |||||||
\(702\) | 17.5355 | 0.661833 | ||||||||
\(703\) | 21.9143 | 0.826515 | ||||||||
\(704\) | −1.11509 | −0.0420264 | ||||||||
\(705\) | −16.4413 | −0.619214 | ||||||||
\(706\) | 9.19425 | 0.346030 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 7.61961 | 0.286362 | ||||||||
\(709\) | −42.0661 | −1.57982 | −0.789912 | − | 0.613220i | \(-0.789874\pi\) | ||||
−0.789912 | + | 0.613220i | \(0.789874\pi\) | |||||||
\(710\) | −59.6060 | −2.23697 | ||||||||
\(711\) | −16.8407 | −0.631577 | ||||||||
\(712\) | −1.11469 | −0.0417748 | ||||||||
\(713\) | 24.8980 | 0.932436 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −17.5355 | −0.655789 | ||||||||
\(716\) | 25.6815 | 0.959762 | ||||||||
\(717\) | −7.36873 | −0.275190 | ||||||||
\(718\) | 8.52641 | 0.318203 | ||||||||
\(719\) | −39.6556 | −1.47890 | −0.739452 | − | 0.673210i | \(-0.764915\pi\) | ||||
−0.739452 | + | 0.673210i | \(0.764915\pi\) | |||||||
\(720\) | 9.14173 | 0.340692 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −11.8407 | −0.440667 | ||||||||
\(723\) | 9.53545 | 0.354627 | ||||||||
\(724\) | −19.4774 | −0.723872 | ||||||||
\(725\) | 10.7257 | 0.398341 | ||||||||
\(726\) | −8.13209 | −0.301810 | ||||||||
\(727\) | −16.7649 | −0.621776 | −0.310888 | − | 0.950447i | \(-0.600626\pi\) | ||||
−0.310888 | + | 0.950447i | \(0.600626\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3.61056 | 0.133725 | ||||||||
\(730\) | 19.0309 | 0.704366 | ||||||||
\(731\) | 15.8622 | 0.586686 | ||||||||
\(732\) | −5.76983 | −0.213259 | ||||||||
\(733\) | −4.28919 | −0.158425 | −0.0792125 | − | 0.996858i | \(-0.525241\pi\) | ||||
−0.0792125 | + | 0.996858i | \(0.525241\pi\) | |||||||
\(734\) | −2.02745 | −0.0748346 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 8.42037 | 0.310379 | ||||||||
\(737\) | 7.37135 | 0.271527 | ||||||||
\(738\) | 23.3996 | 0.861350 | ||||||||
\(739\) | −23.7656 | −0.874233 | −0.437116 | − | 0.899405i | \(-0.644000\pi\) | ||||
−0.437116 | + | 0.899405i | \(0.644000\pi\) | |||||||
\(740\) | −32.4787 | −1.19394 | ||||||||
\(741\) | −8.84388 | −0.324888 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 32.3804 | 1.18792 | 0.593961 | − | 0.804494i | \(-0.297563\pi\) | ||||
0.593961 | + | 0.804494i | \(0.297563\pi\) | |||||||
\(744\) | 2.46455 | 0.0903546 | ||||||||
\(745\) | −19.5299 | −0.715522 | ||||||||
\(746\) | 22.5264 | 0.824750 | ||||||||
\(747\) | −11.2843 | −0.412871 | ||||||||
\(748\) | −5.35136 | −0.195665 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −18.9249 | −0.691039 | ||||||||
\(751\) | −20.8407 | −0.760489 | −0.380245 | − | 0.924886i | \(-0.624160\pi\) | ||||
−0.380245 | + | 0.924886i | \(0.624160\pi\) | |||||||
\(752\) | 4.97424 | 0.181392 | ||||||||
\(753\) | −13.1551 | −0.479397 | ||||||||
\(754\) | −3.96556 | −0.144417 | ||||||||
\(755\) | −85.8206 | −3.12333 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −45.3230 | −1.64729 | −0.823646 | − | 0.567105i | \(-0.808063\pi\) | ||||
−0.823646 | + | 0.567105i | \(0.808063\pi\) | |||||||
\(758\) | −24.3804 | −0.885536 | ||||||||
\(759\) | −7.82607 | −0.284068 | ||||||||
\(760\) | −10.6106 | −0.384886 | ||||||||
\(761\) | −31.5326 | −1.14306 | −0.571528 | − | 0.820582i | \(-0.693649\pi\) | ||||
−0.571528 | + | 0.820582i | \(0.693649\pi\) | |||||||
\(762\) | −17.3707 | −0.629274 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 4.38039 | 0.158477 | ||||||||
\(765\) | 43.8717 | 1.58618 | ||||||||
\(766\) | 30.0575 | 1.08602 | ||||||||
\(767\) | −36.2521 | −1.30899 | ||||||||
\(768\) | 0.833497 | 0.0300762 | ||||||||
\(769\) | 2.97353 | 0.107228 | 0.0536142 | − | 0.998562i | \(-0.482926\pi\) | ||||
0.0536142 | + | 0.998562i | \(0.482926\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13.3671 | −0.481406 | ||||||||
\(772\) | 3.76983 | 0.135679 | ||||||||
\(773\) | −36.0671 | −1.29724 | −0.648622 | − | 0.761110i | \(-0.724655\pi\) | ||||
−0.648622 | + | 0.761110i | \(0.724655\pi\) | |||||||
\(774\) | −7.61961 | −0.273881 | ||||||||
\(775\) | 31.7144 | 1.13921 | ||||||||
\(776\) | 17.3273 | 0.622014 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −7.26110 | −0.260323 | ||||||||
\(779\) | −27.1593 | −0.973082 | ||||||||
\(780\) | 13.1073 | 0.469316 | ||||||||
\(781\) | −16.7608 | −0.599748 | ||||||||
\(782\) | 40.4098 | 1.44505 | ||||||||
\(783\) | −4.42194 | −0.158027 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 58.9026 | 2.10232 | ||||||||
\(786\) | 6.53061 | 0.232939 | ||||||||
\(787\) | −31.0762 | −1.10775 | −0.553874 | − | 0.832600i | \(-0.686851\pi\) | ||||
−0.553874 | + | 0.832600i | \(0.686851\pi\) | |||||||
\(788\) | −2.38039 | −0.0847980 | ||||||||
\(789\) | 0.579045 | 0.0206146 | ||||||||
\(790\) | −28.9695 | −1.03069 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 2.57059 | 0.0913419 | ||||||||
\(793\) | 27.4513 | 0.974824 | ||||||||
\(794\) | 9.87930 | 0.350603 | ||||||||
\(795\) | −17.5355 | −0.621918 | ||||||||
\(796\) | 20.1090 | 0.712744 | ||||||||
\(797\) | −32.2242 | −1.14144 | −0.570721 | − | 0.821144i | \(-0.693336\pi\) | ||||
−0.570721 | + | 0.821144i | \(0.693336\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 23.8717 | 0.844519 | ||||||||
\(800\) | 10.7257 | 0.379209 | ||||||||
\(801\) | 2.56968 | 0.0907950 | ||||||||
\(802\) | −2.69472 | −0.0951538 | ||||||||
\(803\) | 5.35136 | 0.188845 | ||||||||
\(804\) | −5.50989 | −0.194319 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −11.7257 | −0.413018 | ||||||||
\(807\) | 20.5403 | 0.723053 | ||||||||
\(808\) | 1.92145 | 0.0675963 | ||||||||
\(809\) | 22.0000 | 0.773479 | 0.386739 | − | 0.922189i | \(-0.373601\pi\) | ||||
0.386739 | + | 0.922189i | \(0.373601\pi\) | |||||||
\(810\) | −12.8094 | −0.450078 | ||||||||
\(811\) | −27.0748 | −0.950725 | −0.475363 | − | 0.879790i | \(-0.657683\pi\) | ||||
−0.475363 | + | 0.879790i | \(0.657683\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 22.1641 | 0.777329 | ||||||||
\(814\) | −9.13277 | −0.320104 | ||||||||
\(815\) | 39.4804 | 1.38294 | ||||||||
\(816\) | 4.00000 | 0.140028 | ||||||||
\(817\) | 8.84388 | 0.309408 | ||||||||
\(818\) | 2.97353 | 0.103967 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 40.2521 | 1.40566 | ||||||||
\(821\) | 24.2962 | 0.847945 | 0.423972 | − | 0.905675i | \(-0.360635\pi\) | ||||
0.423972 | + | 0.905675i | \(0.360635\pi\) | |||||||
\(822\) | −1.66699 | −0.0581431 | ||||||||
\(823\) | −12.3804 | −0.431553 | −0.215777 | − | 0.976443i | \(-0.569228\pi\) | ||||
−0.215777 | + | 0.976443i | \(0.569228\pi\) | |||||||
\(824\) | 0.912761 | 0.0317975 | ||||||||
\(825\) | −9.96865 | −0.347064 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 30.3362 | 1.05489 | 0.527447 | − | 0.849588i | \(-0.323149\pi\) | ||||
0.527447 | + | 0.849588i | \(0.323149\pi\) | |||||||
\(828\) | −19.4113 | −0.674590 | ||||||||
\(829\) | −10.6068 | −0.368389 | −0.184195 | − | 0.982890i | \(-0.558968\pi\) | ||||
−0.184195 | + | 0.982890i | \(0.558968\pi\) | |||||||
\(830\) | −19.4113 | −0.673777 | ||||||||
\(831\) | 0.966243 | 0.0335186 | ||||||||
\(832\) | −3.96556 | −0.137481 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 6.99096 | 0.242077 | ||||||||
\(835\) | −8.00000 | −0.276851 | ||||||||
\(836\) | −2.98361 | −0.103190 | ||||||||
\(837\) | −13.0751 | −0.451942 | ||||||||
\(838\) | −0.648229 | −0.0223927 | ||||||||
\(839\) | −22.1531 | −0.764810 | −0.382405 | − | 0.923995i | \(-0.624904\pi\) | ||||
−0.382405 | + | 0.923995i | \(0.624904\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −21.4113 | −0.737883 | ||||||||
\(843\) | 5.93041 | 0.204254 | ||||||||
\(844\) | 18.7566 | 0.645628 | ||||||||
\(845\) | −10.8087 | −0.371831 | ||||||||
\(846\) | −11.4670 | −0.394245 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 5.30528 | 0.182184 | ||||||||
\(849\) | −11.4513 | −0.393008 | ||||||||
\(850\) | 51.4730 | 1.76551 | ||||||||
\(851\) | 68.9645 | 2.36407 | ||||||||
\(852\) | 12.5282 | 0.429211 | ||||||||
\(853\) | −0.446300 | −0.0152810 | −0.00764051 | − | 0.999971i | \(-0.502432\pi\) | ||||
−0.00764051 | + | 0.999971i | \(0.502432\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 24.4603 | 0.836526 | ||||||||
\(856\) | −2.61056 | −0.0892273 | ||||||||
\(857\) | 23.2678 | 0.794812 | 0.397406 | − | 0.917643i | \(-0.369910\pi\) | ||||
0.397406 | + | 0.917643i | \(0.369910\pi\) | |||||||
\(858\) | 3.68567 | 0.125827 | ||||||||
\(859\) | 36.5927 | 1.24853 | 0.624263 | − | 0.781214i | \(-0.285399\pi\) | ||||
0.624263 | + | 0.781214i | \(0.285399\pi\) | |||||||
\(860\) | −13.1073 | −0.446955 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −29.2211 | −0.995276 | ||||||||
\(863\) | −34.0219 | −1.15812 | −0.579059 | − | 0.815285i | \(-0.696580\pi\) | ||||
−0.579059 | + | 0.815285i | \(0.696580\pi\) | |||||||
\(864\) | −4.42194 | −0.150437 | ||||||||
\(865\) | 26.6505 | 0.906146 | ||||||||
\(866\) | −26.3630 | −0.895852 | ||||||||
\(867\) | 5.02677 | 0.170718 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.14602 | −0.276335 | ||||||||
\(870\) | −3.30528 | −0.112060 | ||||||||
\(871\) | 26.2146 | 0.888247 | ||||||||
\(872\) | −7.91585 | −0.268064 | ||||||||
\(873\) | −39.9443 | −1.35191 | ||||||||
\(874\) | 22.5302 | 0.762096 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4.00000 | −0.135147 | ||||||||
\(877\) | −53.0486 | −1.79132 | −0.895662 | − | 0.444735i | \(-0.853298\pi\) | ||||
−0.895662 | + | 0.444735i | \(0.853298\pi\) | |||||||
\(878\) | 17.7211 | 0.598057 | ||||||||
\(879\) | 22.5306 | 0.759939 | ||||||||
\(880\) | 4.42194 | 0.149064 | ||||||||
\(881\) | 54.0527 | 1.82108 | 0.910542 | − | 0.413417i | \(-0.135665\pi\) | ||||
0.910542 | + | 0.413417i | \(0.135665\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.31012 | −0.0777419 | −0.0388709 | − | 0.999244i | \(-0.512376\pi\) | ||||
−0.0388709 | + | 0.999244i | \(0.512376\pi\) | |||||||
\(884\) | −19.0309 | −0.640080 | ||||||||
\(885\) | −30.2160 | −1.01570 | ||||||||
\(886\) | −1.80980 | −0.0608016 | ||||||||
\(887\) | −21.5907 | −0.724945 | −0.362473 | − | 0.931994i | \(-0.618067\pi\) | ||||
−0.362473 | + | 0.931994i | \(0.618067\pi\) | |||||||
\(888\) | 6.82651 | 0.229083 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 4.42037 | 0.148171 | ||||||||
\(891\) | −3.60192 | −0.120669 | ||||||||
\(892\) | 25.4603 | 0.852475 | ||||||||
\(893\) | 13.3095 | 0.445385 | ||||||||
\(894\) | 4.10488 | 0.137288 | ||||||||
\(895\) | −101.841 | −3.40418 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −27.8317 | −0.929273 | ||||||||
\(898\) | −8.99096 | −0.300032 | ||||||||
\(899\) | 2.95687 | 0.0986172 | ||||||||
\(900\) | −24.7257 | −0.824188 | ||||||||
\(901\) | 25.4603 | 0.848207 | ||||||||
\(902\) | 11.3186 | 0.376868 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −17.4513 | −0.580422 | ||||||||
\(905\) | 77.2388 | 2.56751 | ||||||||
\(906\) | 18.0381 | 0.599277 | ||||||||
\(907\) | −30.1902 | −1.00245 | −0.501225 | − | 0.865317i | \(-0.667117\pi\) | ||||
−0.501225 | + | 0.865317i | \(0.667117\pi\) | |||||||
\(908\) | 20.0030 | 0.663822 | ||||||||
\(909\) | −4.42948 | −0.146916 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 13.2434 | 0.438774 | 0.219387 | − | 0.975638i | \(-0.429594\pi\) | ||||
0.219387 | + | 0.975638i | \(0.429594\pi\) | |||||||
\(912\) | 2.23017 | 0.0738484 | ||||||||
\(913\) | −5.45832 | −0.180644 | ||||||||
\(914\) | 21.4913 | 0.710868 | ||||||||
\(915\) | 22.8806 | 0.756409 | ||||||||
\(916\) | −15.2039 | −0.502352 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −21.2211 | −0.700402 | ||||||||
\(919\) | −7.57963 | −0.250029 | −0.125014 | − | 0.992155i | \(-0.539898\pi\) | ||||
−0.125014 | + | 0.992155i | \(0.539898\pi\) | |||||||
\(920\) | −33.3915 | −1.10088 | ||||||||
\(921\) | −16.6947 | −0.550110 | ||||||||
\(922\) | 26.4690 | 0.871711 | ||||||||
\(923\) | −59.6060 | −1.96196 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 87.8452 | 2.88833 | ||||||||
\(926\) | 9.80980 | 0.322370 | ||||||||
\(927\) | −2.10417 | −0.0691101 | ||||||||
\(928\) | 1.00000 | 0.0328266 | ||||||||
\(929\) | −51.1125 | −1.67695 | −0.838474 | − | 0.544942i | \(-0.816552\pi\) | ||||
−0.838474 | + | 0.544942i | \(0.816552\pi\) | |||||||
\(930\) | −9.77330 | −0.320479 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 7.53545 | 0.246832 | ||||||||
\(933\) | 24.1683 | 0.791235 | ||||||||
\(934\) | 5.78100 | 0.189160 | ||||||||
\(935\) | 21.2211 | 0.694005 | ||||||||
\(936\) | 9.14173 | 0.298807 | ||||||||
\(937\) | −33.9337 | −1.10857 | −0.554283 | − | 0.832329i | \(-0.687007\pi\) | ||||
−0.554283 | + | 0.832329i | \(0.687007\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.39364 | −0.110747 | ||||||||
\(940\) | −19.7257 | −0.643380 | ||||||||
\(941\) | −38.0578 | −1.24065 | −0.620324 | − | 0.784346i | \(-0.712999\pi\) | ||||
−0.620324 | + | 0.784346i | \(0.712999\pi\) | |||||||
\(942\) | −12.3804 | −0.403375 | ||||||||
\(943\) | −85.4702 | −2.78329 | ||||||||
\(944\) | 9.14173 | 0.297538 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.68567 | −0.119832 | ||||||||
\(947\) | −6.37619 | −0.207198 | −0.103599 | − | 0.994619i | \(-0.533036\pi\) | ||||
−0.103599 | + | 0.994619i | \(0.533036\pi\) | |||||||
\(948\) | 6.08893 | 0.197759 | ||||||||
\(949\) | 19.0309 | 0.617770 | ||||||||
\(950\) | 28.6984 | 0.931099 | ||||||||
\(951\) | −13.0705 | −0.423839 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −20.2563 | −0.656165 | −0.328082 | − | 0.944649i | \(-0.606402\pi\) | ||||
−0.328082 | + | 0.944649i | \(0.606402\pi\) | |||||||
\(954\) | −12.2302 | −0.395966 | ||||||||
\(955\) | −17.3707 | −0.562103 | ||||||||
\(956\) | −8.84074 | −0.285930 | ||||||||
\(957\) | −0.929421 | −0.0300439 | ||||||||
\(958\) | 28.8211 | 0.931167 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −3.30528 | −0.106678 | ||||||||
\(961\) | −22.2569 | −0.717965 | ||||||||
\(962\) | −32.4787 | −1.04716 | ||||||||
\(963\) | 6.01809 | 0.193930 | ||||||||
\(964\) | 11.4403 | 0.368467 | ||||||||
\(965\) | −14.9495 | −0.481240 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 29.8275 | 0.959187 | 0.479594 | − | 0.877491i | \(-0.340784\pi\) | ||||
0.479594 | + | 0.877491i | \(0.340784\pi\) | |||||||
\(968\) | −9.75658 | −0.313588 | ||||||||
\(969\) | 10.7027 | 0.343821 | ||||||||
\(970\) | −68.7124 | −2.20622 | ||||||||
\(971\) | 17.8372 | 0.572422 | 0.286211 | − | 0.958167i | \(-0.407604\pi\) | ||||
0.286211 | + | 0.958167i | \(0.407604\pi\) | |||||||
\(972\) | 15.9582 | 0.511858 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 17.6815 | 0.566551 | ||||||||
\(975\) | −35.4513 | −1.13535 | ||||||||
\(976\) | −6.92243 | −0.221582 | ||||||||
\(977\) | 21.7257 | 0.695065 | 0.347533 | − | 0.937668i | \(-0.387020\pi\) | ||||
0.347533 | + | 0.937668i | \(0.387020\pi\) | |||||||
\(978\) | −8.29815 | −0.265346 | ||||||||
\(979\) | 1.24298 | 0.0397257 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 18.2483 | 0.582622 | ||||||||
\(982\) | 23.6857 | 0.755840 | ||||||||
\(983\) | 6.23738 | 0.198942 | 0.0994708 | − | 0.995040i | \(-0.468285\pi\) | ||||
0.0994708 | + | 0.995040i | \(0.468285\pi\) | |||||||
\(984\) | −8.46034 | −0.269706 | ||||||||
\(985\) | 9.43958 | 0.300770 | ||||||||
\(986\) | 4.79906 | 0.152833 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −10.6106 | −0.337567 | ||||||||
\(989\) | 27.8317 | 0.884996 | ||||||||
\(990\) | −10.1938 | −0.323981 | ||||||||
\(991\) | 18.1502 | 0.576561 | 0.288280 | − | 0.957546i | \(-0.406916\pi\) | ||||
0.288280 | + | 0.957546i | \(0.406916\pi\) | |||||||
\(992\) | 2.95687 | 0.0938808 | ||||||||
\(993\) | −14.2321 | −0.451641 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −79.7433 | −2.52803 | ||||||||
\(996\) | 4.07995 | 0.129278 | ||||||||
\(997\) | 29.2608 | 0.926699 | 0.463349 | − | 0.886176i | \(-0.346648\pi\) | ||||
0.463349 | + | 0.886176i | \(0.346648\pi\) | |||||||
\(998\) | −14.9910 | −0.474530 | ||||||||
\(999\) | −36.2165 | −1.14584 |
(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 | 2842.2.a.bc.1.4 | yes | 6 | |
7.6 | odd | 2 | inner | 2842.2.a.bc.1.3 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2842.2.a.bc.1.3 | ✓ | 6 | 7.6 | odd | 2 | inner | |
2842.2.a.bc.1.4 | yes | 6 | 1.1 | even | 1 | trivial |