Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4014,2,Mod(1,4014)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4014, 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("4014.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4014 = 2 \cdot 3^{2} \cdot 223 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4014.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: | \(32.0519513713\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} - 12x^{6} + 46x^{5} + 54x^{4} - 148x^{3} - 98x^{2} + 126x + 69 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 446) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-1.07351\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4014.1 |
$q$-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 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.701327 | −0.313643 | −0.156821 | − | 0.987627i | \(-0.550125\pi\) | ||||
−0.156821 | + | 0.987627i | \(0.550125\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.38691 | 1.28013 | 0.640066 | − | 0.768320i | \(-0.278907\pi\) | ||||
0.640066 | + | 0.768320i | \(0.278907\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.701327 | −0.221779 | ||||||||
\(11\) | −3.84509 | −1.15934 | −0.579670 | − | 0.814852i | \(-0.696818\pi\) | ||||
−0.579670 | + | 0.814852i | \(0.696818\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.26701 | −1.18346 | −0.591728 | − | 0.806138i | \(-0.701554\pi\) | ||||
−0.591728 | + | 0.806138i | \(0.701554\pi\) | |||||||
\(14\) | 3.38691 | 0.905190 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.75189 | 1.63757 | 0.818787 | − | 0.574097i | \(-0.194647\pi\) | ||||
0.818787 | + | 0.574097i | \(0.194647\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.87608 | 1.80690 | 0.903448 | − | 0.428698i | \(-0.141028\pi\) | ||||
0.903448 | + | 0.428698i | \(0.141028\pi\) | |||||||
\(20\) | −0.701327 | −0.156821 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.84509 | −0.819777 | ||||||||
\(23\) | −1.63713 | −0.341365 | −0.170682 | − | 0.985326i | \(-0.554597\pi\) | ||||
−0.170682 | + | 0.985326i | \(0.554597\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.50814 | −0.901628 | ||||||||
\(26\) | −4.26701 | −0.836830 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3.38691 | 0.640066 | ||||||||
\(29\) | 2.14701 | 0.398691 | 0.199345 | − | 0.979929i | \(-0.436118\pi\) | ||||
0.199345 | + | 0.979929i | \(0.436118\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.31098 | −0.415064 | −0.207532 | − | 0.978228i | \(-0.566543\pi\) | ||||
−0.207532 | + | 0.978228i | \(0.566543\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.75189 | 1.15794 | ||||||||
\(35\) | −2.37533 | −0.401504 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.66056 | 0.930590 | 0.465295 | − | 0.885156i | \(-0.345948\pi\) | ||||
0.465295 | + | 0.885156i | \(0.345948\pi\) | |||||||
\(38\) | 7.87608 | 1.27767 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.701327 | −0.110889 | ||||||||
\(41\) | −1.47115 | −0.229756 | −0.114878 | − | 0.993380i | \(-0.536648\pi\) | ||||
−0.114878 | + | 0.993380i | \(0.536648\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.07202 | 0.925974 | 0.462987 | − | 0.886365i | \(-0.346778\pi\) | ||||
0.462987 | + | 0.886365i | \(0.346778\pi\) | |||||||
\(44\) | −3.84509 | −0.579670 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.63713 | −0.241381 | ||||||||
\(47\) | 10.2475 | 1.49476 | 0.747378 | − | 0.664400i | \(-0.231313\pi\) | ||||
0.747378 | + | 0.664400i | \(0.231313\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.47115 | 0.638736 | ||||||||
\(50\) | −4.50814 | −0.637547 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.26701 | −0.591728 | ||||||||
\(53\) | 7.27873 | 0.999810 | 0.499905 | − | 0.866080i | \(-0.333368\pi\) | ||||
0.499905 | + | 0.866080i | \(0.333368\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.69667 | 0.363618 | ||||||||
\(56\) | 3.38691 | 0.452595 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.14701 | 0.281917 | ||||||||
\(59\) | −8.21453 | −1.06944 | −0.534720 | − | 0.845029i | \(-0.679583\pi\) | ||||
−0.534720 | + | 0.845029i | \(0.679583\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.24775 | 0.927979 | 0.463989 | − | 0.885841i | \(-0.346418\pi\) | ||||
0.463989 | + | 0.885841i | \(0.346418\pi\) | |||||||
\(62\) | −2.31098 | −0.293495 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.99257 | 0.371183 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.74666 | 1.19074 | 0.595372 | − | 0.803450i | \(-0.297005\pi\) | ||||
0.595372 | + | 0.803450i | \(0.297005\pi\) | |||||||
\(68\) | 6.75189 | 0.818787 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.37533 | −0.283906 | ||||||||
\(71\) | −13.1548 | −1.56119 | −0.780594 | − | 0.625038i | \(-0.785083\pi\) | ||||
−0.780594 | + | 0.625038i | \(0.785083\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.79989 | −0.210661 | −0.105330 | − | 0.994437i | \(-0.533590\pi\) | ||||
−0.105330 | + | 0.994437i | \(0.533590\pi\) | |||||||
\(74\) | 5.66056 | 0.658027 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.87608 | 0.903448 | ||||||||
\(77\) | −13.0230 | −1.48411 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.88457 | −1.11210 | −0.556050 | − | 0.831149i | \(-0.687684\pi\) | ||||
−0.556050 | + | 0.831149i | \(0.687684\pi\) | |||||||
\(80\) | −0.701327 | −0.0784107 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.47115 | −0.162462 | ||||||||
\(83\) | 15.7196 | 1.72546 | 0.862728 | − | 0.505669i | \(-0.168754\pi\) | ||||
0.862728 | + | 0.505669i | \(0.168754\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.73528 | −0.513614 | ||||||||
\(86\) | 6.07202 | 0.654762 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.84509 | −0.409888 | ||||||||
\(89\) | 12.7445 | 1.35091 | 0.675456 | − | 0.737400i | \(-0.263947\pi\) | ||||
0.675456 | + | 0.737400i | \(0.263947\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −14.4520 | −1.51498 | ||||||||
\(92\) | −1.63713 | −0.170682 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 10.2475 | 1.05695 | ||||||||
\(95\) | −5.52370 | −0.566720 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.294371 | 0.0298888 | 0.0149444 | − | 0.999888i | \(-0.495243\pi\) | ||||
0.0149444 | + | 0.999888i | \(0.495243\pi\) | |||||||
\(98\) | 4.47115 | 0.451655 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.50814 | −0.450814 | ||||||||
\(101\) | 16.3182 | 1.62372 | 0.811859 | − | 0.583853i | \(-0.198456\pi\) | ||||
0.811859 | + | 0.583853i | \(0.198456\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.94961 | 0.783299 | 0.391649 | − | 0.920115i | \(-0.371905\pi\) | ||||
0.391649 | + | 0.920115i | \(0.371905\pi\) | |||||||
\(104\) | −4.26701 | −0.418415 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.27873 | 0.706973 | ||||||||
\(107\) | 6.96523 | 0.673354 | 0.336677 | − | 0.941620i | \(-0.390697\pi\) | ||||
0.336677 | + | 0.941620i | \(0.390697\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.3762 | −1.08964 | −0.544821 | − | 0.838552i | \(-0.683402\pi\) | ||||
−0.544821 | + | 0.838552i | \(0.683402\pi\) | |||||||
\(110\) | 2.69667 | 0.257117 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.38691 | 0.320033 | ||||||||
\(113\) | −1.07883 | −0.101487 | −0.0507437 | − | 0.998712i | \(-0.516159\pi\) | ||||
−0.0507437 | + | 0.998712i | \(0.516159\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.14816 | 0.107067 | ||||||||
\(116\) | 2.14701 | 0.199345 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −8.21453 | −0.756209 | ||||||||
\(119\) | 22.8680 | 2.09631 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.78474 | 0.344067 | ||||||||
\(122\) | 7.24775 | 0.656180 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.31098 | −0.207532 | ||||||||
\(125\) | 6.66831 | 0.596432 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −18.2481 | −1.61926 | −0.809631 | − | 0.586940i | \(-0.800333\pi\) | ||||
−0.809631 | + | 0.586940i | \(0.800333\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.99257 | 0.262466 | ||||||||
\(131\) | −5.09782 | −0.445398 | −0.222699 | − | 0.974887i | \(-0.571487\pi\) | ||||
−0.222699 | + | 0.974887i | \(0.571487\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 26.6756 | 2.31306 | ||||||||
\(134\) | 9.74666 | 0.841983 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.75189 | 0.578970 | ||||||||
\(137\) | −14.9155 | −1.27432 | −0.637159 | − | 0.770732i | \(-0.719891\pi\) | ||||
−0.637159 | + | 0.770732i | \(0.719891\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −17.6022 | −1.49300 | −0.746500 | − | 0.665385i | \(-0.768267\pi\) | ||||
−0.746500 | + | 0.665385i | \(0.768267\pi\) | |||||||
\(140\) | −2.37533 | −0.200752 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −13.1548 | −1.10393 | ||||||||
\(143\) | 16.4071 | 1.37203 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.50576 | −0.125046 | ||||||||
\(146\) | −1.79989 | −0.148960 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5.66056 | 0.465295 | ||||||||
\(149\) | 9.25428 | 0.758140 | 0.379070 | − | 0.925368i | \(-0.376244\pi\) | ||||
0.379070 | + | 0.925368i | \(0.376244\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.0326 | 1.63023 | 0.815116 | − | 0.579297i | \(-0.196673\pi\) | ||||
0.815116 | + | 0.579297i | \(0.196673\pi\) | |||||||
\(152\) | 7.87608 | 0.638834 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −13.0230 | −1.04942 | ||||||||
\(155\) | 1.62075 | 0.130182 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.5972 | −1.08518 | −0.542588 | − | 0.839999i | \(-0.682555\pi\) | ||||
−0.542588 | + | 0.839999i | \(0.682555\pi\) | |||||||
\(158\) | −9.88457 | −0.786374 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.701327 | −0.0554447 | ||||||||
\(161\) | −5.54480 | −0.436992 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.6768 | 1.38455 | 0.692277 | − | 0.721632i | \(-0.256608\pi\) | ||||
0.692277 | + | 0.721632i | \(0.256608\pi\) | |||||||
\(164\) | −1.47115 | −0.114878 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 15.7196 | 1.22008 | ||||||||
\(167\) | 6.94928 | 0.537752 | 0.268876 | − | 0.963175i | \(-0.413348\pi\) | ||||
0.268876 | + | 0.963175i | \(0.413348\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.20740 | 0.400569 | ||||||||
\(170\) | −4.73528 | −0.363180 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 6.07202 | 0.462987 | ||||||||
\(173\) | 2.88332 | 0.219215 | 0.109607 | − | 0.993975i | \(-0.465041\pi\) | ||||
0.109607 | + | 0.993975i | \(0.465041\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −15.2687 | −1.15420 | ||||||||
\(176\) | −3.84509 | −0.289835 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 12.7445 | 0.955239 | ||||||||
\(179\) | −26.3697 | −1.97096 | −0.985482 | − | 0.169779i | \(-0.945695\pi\) | ||||
−0.985482 | + | 0.169779i | \(0.945695\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.93387 | 0.515390 | 0.257695 | − | 0.966226i | \(-0.417037\pi\) | ||||
0.257695 | + | 0.966226i | \(0.417037\pi\) | |||||||
\(182\) | −14.4520 | −1.07125 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.63713 | −0.120691 | ||||||||
\(185\) | −3.96990 | −0.291873 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −25.9617 | −1.89850 | ||||||||
\(188\) | 10.2475 | 0.747378 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −5.52370 | −0.400731 | ||||||||
\(191\) | 4.44243 | 0.321443 | 0.160722 | − | 0.987000i | \(-0.448618\pi\) | ||||
0.160722 | + | 0.987000i | \(0.448618\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 23.6747 | 1.70414 | 0.852072 | − | 0.523424i | \(-0.175346\pi\) | ||||
0.852072 | + | 0.523424i | \(0.175346\pi\) | |||||||
\(194\) | 0.294371 | 0.0211346 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.47115 | 0.319368 | ||||||||
\(197\) | 1.49163 | 0.106274 | 0.0531372 | − | 0.998587i | \(-0.483078\pi\) | ||||
0.0531372 | + | 0.998587i | \(0.483078\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.62560 | 0.115235 | 0.0576177 | − | 0.998339i | \(-0.481650\pi\) | ||||
0.0576177 | + | 0.998339i | \(0.481650\pi\) | |||||||
\(200\) | −4.50814 | −0.318774 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 16.3182 | 1.14814 | ||||||||
\(203\) | 7.27175 | 0.510376 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.03176 | 0.0720613 | ||||||||
\(206\) | 7.94961 | 0.553876 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4.26701 | −0.295864 | ||||||||
\(209\) | −30.2842 | −2.09480 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.4293 | −0.786823 | −0.393411 | − | 0.919363i | \(-0.628705\pi\) | ||||
−0.393411 | + | 0.919363i | \(0.628705\pi\) | |||||||
\(212\) | 7.27873 | 0.499905 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 6.96523 | 0.476133 | ||||||||
\(215\) | −4.25847 | −0.290425 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.82707 | −0.531336 | ||||||||
\(218\) | −11.3762 | −0.770494 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.69667 | 0.181809 | ||||||||
\(221\) | −28.8104 | −1.93800 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.00000 | 0.0669650 | ||||||||
\(224\) | 3.38691 | 0.226297 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.07883 | −0.0717624 | ||||||||
\(227\) | −6.12257 | −0.406369 | −0.203185 | − | 0.979140i | \(-0.565129\pi\) | ||||
−0.203185 | + | 0.979140i | \(0.565129\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.84326 | 0.320052 | 0.160026 | − | 0.987113i | \(-0.448842\pi\) | ||||
0.160026 | + | 0.987113i | \(0.448842\pi\) | |||||||
\(230\) | 1.14816 | 0.0757075 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.14701 | 0.140958 | ||||||||
\(233\) | −9.65575 | −0.632569 | −0.316285 | − | 0.948664i | \(-0.602435\pi\) | ||||
−0.316285 | + | 0.948664i | \(0.602435\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.18686 | −0.468819 | ||||||||
\(236\) | −8.21453 | −0.534720 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 22.8680 | 1.48232 | ||||||||
\(239\) | 10.3110 | 0.666962 | 0.333481 | − | 0.942757i | \(-0.391777\pi\) | ||||
0.333481 | + | 0.942757i | \(0.391777\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.6947 | −1.01099 | −0.505493 | − | 0.862831i | \(-0.668689\pi\) | ||||
−0.505493 | + | 0.862831i | \(0.668689\pi\) | |||||||
\(242\) | 3.78474 | 0.243292 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 7.24775 | 0.463989 | ||||||||
\(245\) | −3.13574 | −0.200335 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −33.6073 | −2.13838 | ||||||||
\(248\) | −2.31098 | −0.146747 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 6.66831 | 0.421741 | ||||||||
\(251\) | −25.9448 | −1.63762 | −0.818812 | − | 0.574062i | \(-0.805367\pi\) | ||||
−0.818812 | + | 0.574062i | \(0.805367\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.29491 | 0.395758 | ||||||||
\(254\) | −18.2481 | −1.14499 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 1.15869 | 0.0722769 | 0.0361385 | − | 0.999347i | \(-0.488494\pi\) | ||||
0.0361385 | + | 0.999347i | \(0.488494\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 19.1718 | 1.19128 | ||||||||
\(260\) | 2.99257 | 0.185591 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −5.09782 | −0.314944 | ||||||||
\(263\) | 13.0580 | 0.805192 | 0.402596 | − | 0.915378i | \(-0.368108\pi\) | ||||
0.402596 | + | 0.915378i | \(0.368108\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.10477 | −0.313583 | ||||||||
\(266\) | 26.6756 | 1.63558 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 9.74666 | 0.595372 | ||||||||
\(269\) | 2.49787 | 0.152298 | 0.0761490 | − | 0.997096i | \(-0.475738\pi\) | ||||
0.0761490 | + | 0.997096i | \(0.475738\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.4578 | 1.30347 | 0.651734 | − | 0.758448i | \(-0.274042\pi\) | ||||
0.651734 | + | 0.758448i | \(0.274042\pi\) | |||||||
\(272\) | 6.75189 | 0.409394 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −14.9155 | −0.901079 | ||||||||
\(275\) | 17.3342 | 1.04529 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.158364 | −0.00951516 | −0.00475758 | − | 0.999989i | \(-0.501514\pi\) | ||||
−0.00475758 | + | 0.999989i | \(0.501514\pi\) | |||||||
\(278\) | −17.6022 | −1.05571 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.37533 | −0.141953 | ||||||||
\(281\) | −23.0387 | −1.37437 | −0.687186 | − | 0.726482i | \(-0.741154\pi\) | ||||
−0.687186 | + | 0.726482i | \(0.741154\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 23.3254 | 1.38655 | 0.693276 | − | 0.720672i | \(-0.256167\pi\) | ||||
0.693276 | + | 0.720672i | \(0.256167\pi\) | |||||||
\(284\) | −13.1548 | −0.780594 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 16.4071 | 0.970170 | ||||||||
\(287\) | −4.98267 | −0.294118 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 28.5881 | 1.68165 | ||||||||
\(290\) | −1.50576 | −0.0884212 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.79989 | −0.105330 | ||||||||
\(293\) | −8.40583 | −0.491074 | −0.245537 | − | 0.969387i | \(-0.578964\pi\) | ||||
−0.245537 | + | 0.969387i | \(0.578964\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.76107 | 0.335422 | ||||||||
\(296\) | 5.66056 | 0.329013 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 9.25428 | 0.536086 | ||||||||
\(299\) | 6.98565 | 0.403990 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 20.5654 | 1.18537 | ||||||||
\(302\) | 20.0326 | 1.15275 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 7.87608 | 0.451724 | ||||||||
\(305\) | −5.08304 | −0.291054 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.38356 | 0.478475 | 0.239237 | − | 0.970961i | \(-0.423103\pi\) | ||||
0.239237 | + | 0.970961i | \(0.423103\pi\) | |||||||
\(308\) | −13.0230 | −0.742053 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.62075 | 0.0920525 | ||||||||
\(311\) | −26.7140 | −1.51481 | −0.757406 | − | 0.652944i | \(-0.773534\pi\) | ||||
−0.757406 | + | 0.652944i | \(0.773534\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.6102 | −0.769292 | −0.384646 | − | 0.923064i | \(-0.625677\pi\) | ||||
−0.384646 | + | 0.923064i | \(0.625677\pi\) | |||||||
\(314\) | −13.5972 | −0.767335 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −9.88457 | −0.556050 | ||||||||
\(317\) | 16.8160 | 0.944479 | 0.472239 | − | 0.881470i | \(-0.343446\pi\) | ||||
0.472239 | + | 0.881470i | \(0.343446\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.25547 | −0.462218 | ||||||||
\(320\) | −0.701327 | −0.0392054 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −5.54480 | −0.309000 | ||||||||
\(323\) | 53.1784 | 2.95893 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 19.2363 | 1.06704 | ||||||||
\(326\) | 17.6768 | 0.979028 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.47115 | −0.0812309 | ||||||||
\(329\) | 34.7074 | 1.91348 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.3521 | 1.06369 | 0.531845 | − | 0.846842i | \(-0.321499\pi\) | ||||
0.531845 | + | 0.846842i | \(0.321499\pi\) | |||||||
\(332\) | 15.7196 | 0.862728 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 6.94928 | 0.380248 | ||||||||
\(335\) | −6.83559 | −0.373468 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.23068 | 0.121513 | 0.0607563 | − | 0.998153i | \(-0.480649\pi\) | ||||
0.0607563 | + | 0.998153i | \(0.480649\pi\) | |||||||
\(338\) | 5.20740 | 0.283245 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −4.73528 | −0.256807 | ||||||||
\(341\) | 8.88593 | 0.481200 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.56497 | −0.462465 | ||||||||
\(344\) | 6.07202 | 0.327381 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.88332 | 0.155008 | ||||||||
\(347\) | −1.31333 | −0.0705034 | −0.0352517 | − | 0.999378i | \(-0.511223\pi\) | ||||
−0.0352517 | + | 0.999378i | \(0.511223\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.42077 | 0.183109 | 0.0915547 | − | 0.995800i | \(-0.470816\pi\) | ||||
0.0915547 | + | 0.995800i | \(0.470816\pi\) | |||||||
\(350\) | −15.2687 | −0.816144 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.84509 | −0.204944 | ||||||||
\(353\) | 21.3404 | 1.13583 | 0.567916 | − | 0.823086i | \(-0.307750\pi\) | ||||
0.567916 | + | 0.823086i | \(0.307750\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.22582 | 0.489655 | ||||||||
\(356\) | 12.7445 | 0.675456 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −26.3697 | −1.39368 | ||||||||
\(359\) | 15.3455 | 0.809903 | 0.404951 | − | 0.914338i | \(-0.367288\pi\) | ||||
0.404951 | + | 0.914338i | \(0.367288\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 43.0326 | 2.26487 | ||||||||
\(362\) | 6.93387 | 0.364436 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −14.4520 | −0.757490 | ||||||||
\(365\) | 1.26231 | 0.0660723 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −27.1605 | −1.41777 | −0.708883 | − | 0.705326i | \(-0.750800\pi\) | ||||
−0.708883 | + | 0.705326i | \(0.750800\pi\) | |||||||
\(368\) | −1.63713 | −0.0853412 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −3.96990 | −0.206385 | ||||||||
\(371\) | 24.6524 | 1.27989 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.9138 | −0.772208 | −0.386104 | − | 0.922455i | \(-0.626179\pi\) | ||||
−0.386104 | + | 0.922455i | \(0.626179\pi\) | |||||||
\(374\) | −25.9617 | −1.34245 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10.2475 | 0.528476 | ||||||||
\(377\) | −9.16134 | −0.471833 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.04923 | −0.0538954 | −0.0269477 | − | 0.999637i | \(-0.508579\pi\) | ||||
−0.0269477 | + | 0.999637i | \(0.508579\pi\) | |||||||
\(380\) | −5.52370 | −0.283360 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4.44243 | 0.227295 | ||||||||
\(383\) | −2.71233 | −0.138593 | −0.0692967 | − | 0.997596i | \(-0.522076\pi\) | ||||
−0.0692967 | + | 0.997596i | \(0.522076\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.13337 | 0.465479 | ||||||||
\(386\) | 23.6747 | 1.20501 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0.294371 | 0.0149444 | ||||||||
\(389\) | 3.46935 | 0.175903 | 0.0879516 | − | 0.996125i | \(-0.471968\pi\) | ||||
0.0879516 | + | 0.996125i | \(0.471968\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.0537 | −0.559010 | ||||||||
\(392\) | 4.47115 | 0.225827 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.49163 | 0.0751474 | ||||||||
\(395\) | 6.93231 | 0.348802 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.9785 | −0.651373 | −0.325687 | − | 0.945478i | \(-0.605595\pi\) | ||||
−0.325687 | + | 0.945478i | \(0.605595\pi\) | |||||||
\(398\) | 1.62560 | 0.0814838 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.50814 | −0.225407 | ||||||||
\(401\) | −24.6893 | −1.23292 | −0.616462 | − | 0.787385i | \(-0.711435\pi\) | ||||
−0.616462 | + | 0.787385i | \(0.711435\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.86098 | 0.491210 | ||||||||
\(404\) | 16.3182 | 0.811859 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7.27175 | 0.360891 | ||||||||
\(407\) | −21.7654 | −1.07887 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.79617 | −0.138262 | −0.0691309 | − | 0.997608i | \(-0.522023\pi\) | ||||
−0.0691309 | + | 0.997608i | \(0.522023\pi\) | |||||||
\(410\) | 1.03176 | 0.0509550 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 7.94961 | 0.391649 | ||||||||
\(413\) | −27.8219 | −1.36902 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −11.0246 | −0.541177 | ||||||||
\(416\) | −4.26701 | −0.209208 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −30.2842 | −1.48125 | ||||||||
\(419\) | −31.0300 | −1.51591 | −0.757956 | − | 0.652305i | \(-0.773802\pi\) | ||||
−0.757956 | + | 0.652305i | \(0.773802\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.5370 | 0.708492 | 0.354246 | − | 0.935152i | \(-0.384738\pi\) | ||||
0.354246 | + | 0.935152i | \(0.384738\pi\) | |||||||
\(422\) | −11.4293 | −0.556368 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 7.27873 | 0.353486 | ||||||||
\(425\) | −30.4385 | −1.47648 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 24.5475 | 1.18793 | ||||||||
\(428\) | 6.96523 | 0.336677 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −4.25847 | −0.205362 | ||||||||
\(431\) | 13.6708 | 0.658499 | 0.329249 | − | 0.944243i | \(-0.393204\pi\) | ||||
0.329249 | + | 0.944243i | \(0.393204\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.5748 | 0.748478 | 0.374239 | − | 0.927332i | \(-0.377904\pi\) | ||||
0.374239 | + | 0.927332i | \(0.377904\pi\) | |||||||
\(434\) | −7.82707 | −0.375712 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −11.3762 | −0.544821 | ||||||||
\(437\) | −12.8941 | −0.616810 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.0983 | 0.481964 | 0.240982 | − | 0.970530i | \(-0.422531\pi\) | ||||
0.240982 | + | 0.970530i | \(0.422531\pi\) | |||||||
\(440\) | 2.69667 | 0.128559 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −28.8104 | −1.37037 | ||||||||
\(443\) | −17.6094 | −0.836646 | −0.418323 | − | 0.908298i | \(-0.637382\pi\) | ||||
−0.418323 | + | 0.908298i | \(0.637382\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.93804 | −0.423704 | ||||||||
\(446\) | 1.00000 | 0.0473514 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3.38691 | 0.160016 | ||||||||
\(449\) | 0.274840 | 0.0129705 | 0.00648525 | − | 0.999979i | \(-0.497936\pi\) | ||||
0.00648525 | + | 0.999979i | \(0.497936\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.65673 | 0.266365 | ||||||||
\(452\) | −1.07883 | −0.0507437 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −6.12257 | −0.287346 | ||||||||
\(455\) | 10.1356 | 0.475163 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −37.0426 | −1.73278 | −0.866389 | − | 0.499370i | \(-0.833565\pi\) | ||||
−0.866389 | + | 0.499370i | \(0.833565\pi\) | |||||||
\(458\) | 4.84326 | 0.226311 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.14816 | 0.0535333 | ||||||||
\(461\) | −12.2641 | −0.571194 | −0.285597 | − | 0.958350i | \(-0.592192\pi\) | ||||
−0.285597 | + | 0.958350i | \(0.592192\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.156445 | 0.00727060 | 0.00363530 | − | 0.999993i | \(-0.498843\pi\) | ||||
0.00363530 | + | 0.999993i | \(0.498843\pi\) | |||||||
\(464\) | 2.14701 | 0.0996727 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −9.65575 | −0.447294 | ||||||||
\(467\) | 15.7563 | 0.729116 | 0.364558 | − | 0.931181i | \(-0.381220\pi\) | ||||
0.364558 | + | 0.931181i | \(0.381220\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 33.0111 | 1.52431 | ||||||||
\(470\) | −7.18686 | −0.331505 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −8.21453 | −0.378104 | ||||||||
\(473\) | −23.3475 | −1.07352 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −35.5065 | −1.62915 | ||||||||
\(476\) | 22.8680 | 1.04816 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 10.3110 | 0.471613 | ||||||||
\(479\) | −31.9259 | −1.45873 | −0.729365 | − | 0.684125i | \(-0.760184\pi\) | ||||
−0.729365 | + | 0.684125i | \(0.760184\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −24.1537 | −1.10131 | ||||||||
\(482\) | −15.6947 | −0.714874 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.78474 | 0.172034 | ||||||||
\(485\) | −0.206450 | −0.00937442 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.42661 | −0.0646461 | −0.0323230 | − | 0.999477i | \(-0.510291\pi\) | ||||
−0.0323230 | + | 0.999477i | \(0.510291\pi\) | |||||||
\(488\) | 7.24775 | 0.328090 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −3.13574 | −0.141658 | ||||||||
\(491\) | 2.95757 | 0.133473 | 0.0667366 | − | 0.997771i | \(-0.478741\pi\) | ||||
0.0667366 | + | 0.997771i | \(0.478741\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 14.4964 | 0.652886 | ||||||||
\(494\) | −33.6073 | −1.51206 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.31098 | −0.103766 | ||||||||
\(497\) | −44.5541 | −1.99853 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −33.8099 | −1.51354 | −0.756769 | − | 0.653683i | \(-0.773223\pi\) | ||||
−0.756769 | + | 0.653683i | \(0.773223\pi\) | |||||||
\(500\) | 6.66831 | 0.298216 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −25.9448 | −1.15797 | ||||||||
\(503\) | −31.5723 | −1.40774 | −0.703870 | − | 0.710329i | \(-0.748546\pi\) | ||||
−0.703870 | + | 0.710329i | \(0.748546\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11.4444 | −0.509268 | ||||||||
\(506\) | 6.29491 | 0.279843 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −18.2481 | −0.809631 | ||||||||
\(509\) | 1.20420 | 0.0533753 | 0.0266877 | − | 0.999644i | \(-0.491504\pi\) | ||||
0.0266877 | + | 0.999644i | \(0.491504\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.09605 | −0.269674 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.15869 | 0.0511075 | ||||||||
\(515\) | −5.57528 | −0.245676 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −39.4027 | −1.73293 | ||||||||
\(518\) | 19.1718 | 0.842361 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.99257 | 0.131233 | ||||||||
\(521\) | −32.4362 | −1.42106 | −0.710528 | − | 0.703669i | \(-0.751544\pi\) | ||||
−0.710528 | + | 0.703669i | \(0.751544\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 22.4618 | 0.982186 | 0.491093 | − | 0.871107i | \(-0.336597\pi\) | ||||
0.491093 | + | 0.871107i | \(0.336597\pi\) | |||||||
\(524\) | −5.09782 | −0.222699 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 13.0580 | 0.569357 | ||||||||
\(527\) | −15.6035 | −0.679698 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.3198 | −0.883470 | ||||||||
\(530\) | −5.10477 | −0.221737 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 26.6756 | 1.15653 | ||||||||
\(533\) | 6.27744 | 0.271906 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.88490 | −0.211193 | ||||||||
\(536\) | 9.74666 | 0.420992 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 2.49787 | 0.107691 | ||||||||
\(539\) | −17.1920 | −0.740512 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22.9994 | −0.988821 | −0.494410 | − | 0.869229i | \(-0.664616\pi\) | ||||
−0.494410 | + | 0.869229i | \(0.664616\pi\) | |||||||
\(542\) | 21.4578 | 0.921691 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 6.75189 | 0.289485 | ||||||||
\(545\) | 7.97843 | 0.341759 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.8746 | 0.635991 | 0.317996 | − | 0.948092i | \(-0.396990\pi\) | ||||
0.317996 | + | 0.948092i | \(0.396990\pi\) | |||||||
\(548\) | −14.9155 | −0.637159 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 17.3342 | 0.739134 | ||||||||
\(551\) | 16.9101 | 0.720392 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −33.4781 | −1.42364 | ||||||||
\(554\) | −0.158364 | −0.00672824 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −17.6022 | −0.746500 | ||||||||
\(557\) | −24.1336 | −1.02257 | −0.511287 | − | 0.859410i | \(-0.670831\pi\) | ||||
−0.511287 | + | 0.859410i | \(0.670831\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −25.9094 | −1.09585 | ||||||||
\(560\) | −2.37533 | −0.100376 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −23.0387 | −0.971828 | ||||||||
\(563\) | 14.6662 | 0.618107 | 0.309054 | − | 0.951045i | \(-0.399988\pi\) | ||||
0.309054 | + | 0.951045i | \(0.399988\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.756609 | 0.0318308 | ||||||||
\(566\) | 23.3254 | 0.980440 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −13.1548 | −0.551963 | ||||||||
\(569\) | 2.57588 | 0.107987 | 0.0539933 | − | 0.998541i | \(-0.482805\pi\) | ||||
0.0539933 | + | 0.998541i | \(0.482805\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13.2168 | −0.553107 | −0.276554 | − | 0.960998i | \(-0.589192\pi\) | ||||
−0.276554 | + | 0.960998i | \(0.589192\pi\) | |||||||
\(572\) | 16.4071 | 0.686014 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −4.98267 | −0.207973 | ||||||||
\(575\) | 7.38040 | 0.307784 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.0810 | 0.502938 | 0.251469 | − | 0.967865i | \(-0.419086\pi\) | ||||
0.251469 | + | 0.967865i | \(0.419086\pi\) | |||||||
\(578\) | 28.5881 | 1.18911 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.50576 | −0.0625232 | ||||||||
\(581\) | 53.2410 | 2.20881 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −27.9874 | −1.15912 | ||||||||
\(584\) | −1.79989 | −0.0744798 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −8.40583 | −0.347241 | ||||||||
\(587\) | −23.7403 | −0.979865 | −0.489933 | − | 0.871760i | \(-0.662979\pi\) | ||||
−0.489933 | + | 0.871760i | \(0.662979\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −18.2014 | −0.749977 | ||||||||
\(590\) | 5.76107 | 0.237179 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 5.66056 | 0.232648 | ||||||||
\(593\) | −19.0061 | −0.780488 | −0.390244 | − | 0.920711i | \(-0.627609\pi\) | ||||
−0.390244 | + | 0.920711i | \(0.627609\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −16.0380 | −0.657493 | ||||||||
\(596\) | 9.25428 | 0.379070 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 6.98565 | 0.285664 | ||||||||
\(599\) | −22.5395 | −0.920937 | −0.460469 | − | 0.887676i | \(-0.652319\pi\) | ||||
−0.460469 | + | 0.887676i | \(0.652319\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14.5353 | −0.592908 | −0.296454 | − | 0.955047i | \(-0.595804\pi\) | ||||
−0.296454 | + | 0.955047i | \(0.595804\pi\) | |||||||
\(602\) | 20.5654 | 0.838182 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 20.0326 | 0.815116 | ||||||||
\(605\) | −2.65434 | −0.107914 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 27.5040 | 1.11635 | 0.558176 | − | 0.829723i | \(-0.311502\pi\) | ||||
0.558176 | + | 0.829723i | \(0.311502\pi\) | |||||||
\(608\) | 7.87608 | 0.319417 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5.08304 | −0.205806 | ||||||||
\(611\) | −43.7263 | −1.76898 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.1418 | 0.611570 | 0.305785 | − | 0.952101i | \(-0.401081\pi\) | ||||
0.305785 | + | 0.952101i | \(0.401081\pi\) | |||||||
\(614\) | 8.38356 | 0.338333 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −13.0230 | −0.524711 | ||||||||
\(617\) | −27.1620 | −1.09350 | −0.546751 | − | 0.837295i | \(-0.684136\pi\) | ||||
−0.546751 | + | 0.837295i | \(0.684136\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −34.2116 | −1.37508 | −0.687540 | − | 0.726147i | \(-0.741309\pi\) | ||||
−0.687540 | + | 0.726147i | \(0.741309\pi\) | |||||||
\(620\) | 1.62075 | 0.0650909 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −26.7140 | −1.07113 | ||||||||
\(623\) | 43.1644 | 1.72935 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.8640 | 0.714562 | ||||||||
\(626\) | −13.6102 | −0.543972 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −13.5972 | −0.542588 | ||||||||
\(629\) | 38.2195 | 1.52391 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 41.5717 | 1.65494 | 0.827472 | − | 0.561507i | \(-0.189778\pi\) | ||||
0.827472 | + | 0.561507i | \(0.189778\pi\) | |||||||
\(632\) | −9.88457 | −0.393187 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 16.8160 | 0.667847 | ||||||||
\(635\) | 12.7979 | 0.507870 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −19.0785 | −0.755917 | ||||||||
\(638\) | −8.25547 | −0.326837 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.701327 | −0.0277224 | ||||||||
\(641\) | −29.3818 | −1.16051 | −0.580256 | − | 0.814434i | \(-0.697048\pi\) | ||||
−0.580256 | + | 0.814434i | \(0.697048\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.71200 | 0.343568 | 0.171784 | − | 0.985135i | \(-0.445047\pi\) | ||||
0.171784 | + | 0.985135i | \(0.445047\pi\) | |||||||
\(644\) | −5.54480 | −0.218496 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 53.1784 | 2.09228 | ||||||||
\(647\) | −15.3152 | −0.602102 | −0.301051 | − | 0.953608i | \(-0.597337\pi\) | ||||
−0.301051 | + | 0.953608i | \(0.597337\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 31.5856 | 1.23984 | ||||||||
\(650\) | 19.2363 | 0.754510 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 17.6768 | 0.692277 | ||||||||
\(653\) | 25.7650 | 1.00826 | 0.504131 | − | 0.863627i | \(-0.331813\pi\) | ||||
0.504131 | + | 0.863627i | \(0.331813\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.57524 | 0.139696 | ||||||||
\(656\) | −1.47115 | −0.0574389 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 34.7074 | 1.35304 | ||||||||
\(659\) | 34.9731 | 1.36236 | 0.681180 | − | 0.732116i | \(-0.261467\pi\) | ||||
0.681180 | + | 0.732116i | \(0.261467\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −42.0894 | −1.63709 | −0.818544 | − | 0.574444i | \(-0.805218\pi\) | ||||
−0.818544 | + | 0.574444i | \(0.805218\pi\) | |||||||
\(662\) | 19.3521 | 0.752142 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 15.7196 | 0.610040 | ||||||||
\(665\) | −18.7083 | −0.725476 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.51494 | −0.136099 | ||||||||
\(668\) | 6.94928 | 0.268876 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −6.83559 | −0.264082 | ||||||||
\(671\) | −27.8683 | −1.07584 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.05744 | −0.156403 | −0.0782014 | − | 0.996938i | \(-0.524918\pi\) | ||||
−0.0782014 | + | 0.996938i | \(0.524918\pi\) | |||||||
\(674\) | 2.23068 | 0.0859224 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.20740 | 0.200285 | ||||||||
\(677\) | 19.3432 | 0.743421 | 0.371710 | − | 0.928349i | \(-0.378771\pi\) | ||||
0.371710 | + | 0.928349i | \(0.378771\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.997008 | 0.0382617 | ||||||||
\(680\) | −4.73528 | −0.181590 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 8.88593 | 0.340260 | ||||||||
\(683\) | −25.3201 | −0.968847 | −0.484423 | − | 0.874834i | \(-0.660971\pi\) | ||||
−0.484423 | + | 0.874834i | \(0.660971\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.4606 | 0.399681 | ||||||||
\(686\) | −8.56497 | −0.327012 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 6.07202 | 0.231493 | ||||||||
\(689\) | −31.0584 | −1.18323 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14.5336 | 0.552886 | 0.276443 | − | 0.961030i | \(-0.410844\pi\) | ||||
0.276443 | + | 0.961030i | \(0.410844\pi\) | |||||||
\(692\) | 2.88332 | 0.109607 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.31333 | −0.0498534 | ||||||||
\(695\) | 12.3449 | 0.468269 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.93308 | −0.376242 | ||||||||
\(698\) | 3.42077 | 0.129478 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −15.2687 | −0.577101 | ||||||||
\(701\) | 28.6997 | 1.08397 | 0.541986 | − | 0.840388i | \(-0.317673\pi\) | ||||
0.541986 | + | 0.840388i | \(0.317673\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 44.5830 | 1.68148 | ||||||||
\(704\) | −3.84509 | −0.144917 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 21.3404 | 0.803155 | ||||||||
\(707\) | 55.2682 | 2.07857 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −46.4505 | −1.74449 | −0.872243 | − | 0.489073i | \(-0.837335\pi\) | ||||
−0.872243 | + | 0.489073i | \(0.837335\pi\) | |||||||
\(710\) | 9.22582 | 0.346239 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 12.7445 | 0.477620 | ||||||||
\(713\) | 3.78337 | 0.141688 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11.5067 | −0.430327 | ||||||||
\(716\) | −26.3697 | −0.985482 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 15.3455 | 0.572688 | ||||||||
\(719\) | −43.6929 | −1.62947 | −0.814734 | − | 0.579835i | \(-0.803117\pi\) | ||||
−0.814734 | + | 0.579835i | \(0.803117\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 26.9246 | 1.00273 | ||||||||
\(722\) | 43.0326 | 1.60151 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 6.93387 | 0.257695 | ||||||||
\(725\) | −9.67905 | −0.359471 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −52.8123 | −1.95870 | −0.979350 | − | 0.202172i | \(-0.935200\pi\) | ||||
−0.979350 | + | 0.202172i | \(0.935200\pi\) | |||||||
\(728\) | −14.4520 | −0.535626 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.26231 | 0.0467201 | ||||||||
\(731\) | 40.9976 | 1.51635 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −34.2947 | −1.26670 | −0.633352 | − | 0.773864i | \(-0.718321\pi\) | ||||
−0.633352 | + | 0.773864i | \(0.718321\pi\) | |||||||
\(734\) | −27.1605 | −1.00251 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.63713 | −0.0603453 | ||||||||
\(737\) | −37.4768 | −1.38048 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.66709 | 0.0613250 | 0.0306625 | − | 0.999530i | \(-0.490238\pi\) | ||||
0.0306625 | + | 0.999530i | \(0.490238\pi\) | |||||||
\(740\) | −3.96990 | −0.145936 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 24.6524 | 0.905018 | ||||||||
\(743\) | −15.5597 | −0.570831 | −0.285416 | − | 0.958404i | \(-0.592132\pi\) | ||||
−0.285416 | + | 0.958404i | \(0.592132\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.49027 | −0.237785 | ||||||||
\(746\) | −14.9138 | −0.546034 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −25.9617 | −0.949252 | ||||||||
\(749\) | 23.5906 | 0.861981 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 44.1995 | 1.61286 | 0.806431 | − | 0.591328i | \(-0.201396\pi\) | ||||
0.806431 | + | 0.591328i | \(0.201396\pi\) | |||||||
\(752\) | 10.2475 | 0.373689 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −9.16134 | −0.333636 | ||||||||
\(755\) | −14.0494 | −0.511311 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −31.4100 | −1.14162 | −0.570808 | − | 0.821083i | \(-0.693370\pi\) | ||||
−0.570808 | + | 0.821083i | \(0.693370\pi\) | |||||||
\(758\) | −1.04923 | −0.0381098 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −5.52370 | −0.200366 | ||||||||
\(761\) | 40.2142 | 1.45776 | 0.728881 | − | 0.684640i | \(-0.240041\pi\) | ||||
0.728881 | + | 0.684640i | \(0.240041\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −38.5302 | −1.39489 | ||||||||
\(764\) | 4.44243 | 0.160722 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.71233 | −0.0980003 | ||||||||
\(767\) | 35.0515 | 1.26564 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −24.4812 | −0.882815 | −0.441408 | − | 0.897307i | \(-0.645521\pi\) | ||||
−0.441408 | + | 0.897307i | \(0.645521\pi\) | |||||||
\(770\) | 9.13337 | 0.329144 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 23.6747 | 0.852072 | ||||||||
\(773\) | −0.486252 | −0.0174893 | −0.00874464 | − | 0.999962i | \(-0.502784\pi\) | ||||
−0.00874464 | + | 0.999962i | \(0.502784\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.4182 | 0.374233 | ||||||||
\(776\) | 0.294371 | 0.0105673 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.46935 | 0.124382 | ||||||||
\(779\) | −11.5869 | −0.415145 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 50.5814 | 1.80995 | ||||||||
\(782\) | −11.0537 | −0.395280 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 4.47115 | 0.159684 | ||||||||
\(785\) | 9.53609 | 0.340358 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 31.7144 | 1.13050 | 0.565248 | − | 0.824921i | \(-0.308780\pi\) | ||||
0.565248 | + | 0.824921i | \(0.308780\pi\) | |||||||
\(788\) | 1.49163 | 0.0531372 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 6.93231 | 0.246641 | ||||||||
\(791\) | −3.65388 | −0.129917 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −30.9262 | −1.09822 | ||||||||
\(794\) | −12.9785 | −0.460591 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.62560 | 0.0576177 | ||||||||
\(797\) | 23.9711 | 0.849101 | 0.424551 | − | 0.905404i | \(-0.360432\pi\) | ||||
0.424551 | + | 0.905404i | \(0.360432\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 69.1902 | 2.44777 | ||||||||
\(800\) | −4.50814 | −0.159387 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −24.6893 | −0.871809 | ||||||||
\(803\) | 6.92073 | 0.244227 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.88872 | 0.137059 | ||||||||
\(806\) | 9.86098 | 0.347338 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 16.3182 | 0.574071 | ||||||||
\(809\) | −22.6055 | −0.794766 | −0.397383 | − | 0.917653i | \(-0.630082\pi\) | ||||
−0.397383 | + | 0.917653i | \(0.630082\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18.6409 | −0.654572 | −0.327286 | − | 0.944925i | \(-0.606134\pi\) | ||||
−0.327286 | + | 0.944925i | \(0.606134\pi\) | |||||||
\(812\) | 7.27175 | 0.255188 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −21.7654 | −0.762876 | ||||||||
\(815\) | −12.3972 | −0.434256 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 47.8237 | 1.67314 | ||||||||
\(818\) | −2.79617 | −0.0977659 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.03176 | 0.0360306 | ||||||||
\(821\) | −40.3808 | −1.40930 | −0.704650 | − | 0.709555i | \(-0.748896\pi\) | ||||
−0.704650 | + | 0.709555i | \(0.748896\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −30.8413 | −1.07506 | −0.537529 | − | 0.843245i | \(-0.680642\pi\) | ||||
−0.537529 | + | 0.843245i | \(0.680642\pi\) | |||||||
\(824\) | 7.94961 | 0.276938 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −27.8219 | −0.968047 | ||||||||
\(827\) | 39.7181 | 1.38113 | 0.690567 | − | 0.723268i | \(-0.257361\pi\) | ||||
0.690567 | + | 0.723268i | \(0.257361\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.4476 | −0.501784 | −0.250892 | − | 0.968015i | \(-0.580724\pi\) | ||||
−0.250892 | + | 0.968015i | \(0.580724\pi\) | |||||||
\(830\) | −11.0246 | −0.382670 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −4.26701 | −0.147932 | ||||||||
\(833\) | 30.1888 | 1.04598 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.87372 | −0.168662 | ||||||||
\(836\) | −30.2842 | −1.04740 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −31.0300 | −1.07191 | ||||||||
\(839\) | −12.2534 | −0.423035 | −0.211518 | − | 0.977374i | \(-0.567841\pi\) | ||||
−0.211518 | + | 0.977374i | \(0.567841\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.3903 | −0.841046 | ||||||||
\(842\) | 14.5370 | 0.500979 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −11.4293 | −0.393411 | ||||||||
\(845\) | −3.65209 | −0.125636 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 12.8186 | 0.440451 | ||||||||
\(848\) | 7.27873 | 0.249953 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −30.4385 | −1.04403 | ||||||||
\(851\) | −9.26706 | −0.317671 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −19.2084 | −0.657684 | −0.328842 | − | 0.944385i | \(-0.606658\pi\) | ||||
−0.328842 | + | 0.944385i | \(0.606658\pi\) | |||||||
\(854\) | 24.5475 | 0.839997 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.96523 | 0.238066 | ||||||||
\(857\) | −23.6792 | −0.808865 | −0.404433 | − | 0.914568i | \(-0.632531\pi\) | ||||
−0.404433 | + | 0.914568i | \(0.632531\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17.3459 | 0.591834 | 0.295917 | − | 0.955214i | \(-0.404375\pi\) | ||||
0.295917 | + | 0.955214i | \(0.404375\pi\) | |||||||
\(860\) | −4.25847 | −0.145213 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 13.6708 | 0.465629 | ||||||||
\(863\) | 3.48179 | 0.118522 | 0.0592608 | − | 0.998243i | \(-0.481126\pi\) | ||||
0.0592608 | + | 0.998243i | \(0.481126\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.02215 | −0.0687551 | ||||||||
\(866\) | 15.5748 | 0.529254 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −7.82707 | −0.265668 | ||||||||
\(869\) | 38.0071 | 1.28930 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −41.5891 | −1.40919 | ||||||||
\(872\) | −11.3762 | −0.385247 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −12.8941 | −0.436151 | ||||||||
\(875\) | 22.5850 | 0.763511 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 43.1141 | 1.45586 | 0.727929 | − | 0.685652i | \(-0.240483\pi\) | ||||
0.727929 | + | 0.685652i | \(0.240483\pi\) | |||||||
\(878\) | 10.0983 | 0.340800 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2.69667 | 0.0909046 | ||||||||
\(881\) | −37.3841 | −1.25950 | −0.629752 | − | 0.776796i | \(-0.716843\pi\) | ||||
−0.629752 | + | 0.776796i | \(0.716843\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.74579 | −0.0924031 | −0.0462016 | − | 0.998932i | \(-0.514712\pi\) | ||||
−0.0462016 | + | 0.998932i | \(0.514712\pi\) | |||||||
\(884\) | −28.8104 | −0.968999 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −17.6094 | −0.591598 | ||||||||
\(887\) | 17.6940 | 0.594107 | 0.297054 | − | 0.954861i | \(-0.403996\pi\) | ||||
0.297054 | + | 0.954861i | \(0.403996\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −61.8048 | −2.07287 | ||||||||
\(890\) | −8.93804 | −0.299604 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.00000 | 0.0334825 | ||||||||
\(893\) | 80.7103 | 2.70087 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 18.4938 | 0.618179 | ||||||||
\(896\) | 3.38691 | 0.113149 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0.274840 | 0.00917153 | ||||||||
\(899\) | −4.96171 | −0.165482 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 49.1452 | 1.63726 | ||||||||
\(902\) | 5.65673 | 0.188348 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.07883 | −0.0358812 | ||||||||
\(905\) | −4.86291 | −0.161648 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 36.2527 | 1.20375 | 0.601876 | − | 0.798590i | \(-0.294420\pi\) | ||||
0.601876 | + | 0.798590i | \(0.294420\pi\) | |||||||
\(908\) | −6.12257 | −0.203185 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 10.1356 | 0.335991 | ||||||||
\(911\) | −37.4246 | −1.23993 | −0.619965 | − | 0.784629i | \(-0.712853\pi\) | ||||
−0.619965 | + | 0.784629i | \(0.712853\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −60.4435 | −2.00039 | ||||||||
\(914\) | −37.0426 | −1.22526 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4.84326 | 0.160026 | ||||||||
\(917\) | −17.2658 | −0.570168 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.95028 | 0.0973208 | 0.0486604 | − | 0.998815i | \(-0.484505\pi\) | ||||
0.0486604 | + | 0.998815i | \(0.484505\pi\) | |||||||
\(920\) | 1.14816 | 0.0378538 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −12.2641 | −0.403895 | ||||||||
\(923\) | 56.1317 | 1.84760 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −25.5186 | −0.839046 | ||||||||
\(926\) | 0.156445 | 0.00514109 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.14701 | 0.0704792 | ||||||||
\(929\) | 28.6871 | 0.941194 | 0.470597 | − | 0.882348i | \(-0.344039\pi\) | ||||
0.470597 | + | 0.882348i | \(0.344039\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 35.2152 | 1.15413 | ||||||||
\(932\) | −9.65575 | −0.316285 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 15.7563 | 0.515563 | ||||||||
\(935\) | 18.2076 | 0.595452 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −37.2160 | −1.21579 | −0.607897 | − | 0.794016i | \(-0.707986\pi\) | ||||
−0.607897 | + | 0.794016i | \(0.707986\pi\) | |||||||
\(938\) | 33.0111 | 1.07785 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −7.18686 | −0.234410 | ||||||||
\(941\) | 10.7583 | 0.350711 | 0.175355 | − | 0.984505i | \(-0.443893\pi\) | ||||
0.175355 | + | 0.984505i | \(0.443893\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.40847 | 0.0784305 | ||||||||
\(944\) | −8.21453 | −0.267360 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −23.3475 | −0.759092 | ||||||||
\(947\) | −21.7826 | −0.707840 | −0.353920 | − | 0.935276i | \(-0.615151\pi\) | ||||
−0.353920 | + | 0.935276i | \(0.615151\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.68014 | 0.249308 | ||||||||
\(950\) | −35.5065 | −1.15198 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 22.8680 | 0.741158 | ||||||||
\(953\) | −53.2874 | −1.72615 | −0.863074 | − | 0.505078i | \(-0.831464\pi\) | ||||
−0.863074 | + | 0.505078i | \(0.831464\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.11560 | −0.100818 | ||||||||
\(956\) | 10.3110 | 0.333481 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −31.9259 | −1.03148 | ||||||||
\(959\) | −50.5175 | −1.63130 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.6594 | −0.827722 | ||||||||
\(962\) | −24.1537 | −0.778746 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −15.6947 | −0.505493 | ||||||||
\(965\) | −16.6037 | −0.534493 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −29.3472 | −0.943743 | −0.471872 | − | 0.881667i | \(-0.656421\pi\) | ||||
−0.471872 | + | 0.881667i | \(0.656421\pi\) | |||||||
\(968\) | 3.78474 | 0.121646 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −0.206450 | −0.00662872 | ||||||||
\(971\) | 33.0902 | 1.06192 | 0.530958 | − | 0.847398i | \(-0.321832\pi\) | ||||
0.530958 | + | 0.847398i | \(0.321832\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −59.6171 | −1.91124 | ||||||||
\(974\) | −1.42661 | −0.0457117 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.24775 | 0.231995 | ||||||||
\(977\) | 10.1556 | 0.324908 | 0.162454 | − | 0.986716i | \(-0.448059\pi\) | ||||
0.162454 | + | 0.986716i | \(0.448059\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −49.0037 | −1.56617 | ||||||||
\(980\) | −3.13574 | −0.100168 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2.95757 | 0.0943799 | ||||||||
\(983\) | −1.81725 | −0.0579611 | −0.0289806 | − | 0.999580i | \(-0.509226\pi\) | ||||
−0.0289806 | + | 0.999580i | \(0.509226\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.04612 | −0.0333322 | ||||||||
\(986\) | 14.4964 | 0.461660 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −33.6073 | −1.06919 | ||||||||
\(989\) | −9.94067 | −0.316095 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.50467 | −0.0477974 | −0.0238987 | − | 0.999714i | \(-0.507608\pi\) | ||||
−0.0238987 | + | 0.999714i | \(0.507608\pi\) | |||||||
\(992\) | −2.31098 | −0.0733736 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −44.5541 | −1.41317 | ||||||||
\(995\) | −1.14007 | −0.0361428 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 59.3196 | 1.87867 | 0.939336 | − | 0.342999i | \(-0.111443\pi\) | ||||
0.939336 | + | 0.342999i | \(0.111443\pi\) | |||||||
\(998\) | −33.8099 | −1.07023 | ||||||||
\(999\) | 0 | 0 |
(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 | 4014.2.a.z.1.5 | 8 | ||
3.2 | odd | 2 | 446.2.a.f.1.6 | ✓ | 8 | ||
12.11 | even | 2 | 3568.2.a.n.1.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
446.2.a.f.1.6 | ✓ | 8 | 3.2 | odd | 2 | ||
3568.2.a.n.1.3 | 8 | 12.11 | even | 2 | |||
4014.2.a.z.1.5 | 8 | 1.1 | even | 1 | trivial |