Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8004,2,Mod(1,8004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8004, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8004.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8004 = 2^{2} \cdot 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8004.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: | \(63.9122617778\) |
Analytic rank: | \(0\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 5 x^{12} - 27 x^{11} + 158 x^{10} + 180 x^{9} - 1652 x^{8} + 65 x^{7} + 7388 x^{6} + \cdots - 5832 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-4.03097\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8004.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.03097 | −1.80270 | −0.901352 | − | 0.433087i | \(-0.857424\pi\) | ||||
−0.901352 | + | 0.433087i | \(0.857424\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.90486 | −1.47590 | −0.737950 | − | 0.674856i | \(-0.764206\pi\) | ||||
−0.737950 | + | 0.674856i | \(0.764206\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.96079 | 1.49573 | 0.747867 | − | 0.663849i | \(-0.231078\pi\) | ||||
0.747867 | + | 0.663849i | \(0.231078\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.829895 | 0.230172 | 0.115086 | − | 0.993356i | \(-0.463286\pi\) | ||||
0.115086 | + | 0.993356i | \(0.463286\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.03097 | 1.04079 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.147001 | 0.0356530 | 0.0178265 | − | 0.999841i | \(-0.494325\pi\) | ||||
0.0178265 | + | 0.999841i | \(0.494325\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.16848 | −0.497482 | −0.248741 | − | 0.968570i | \(-0.580017\pi\) | ||||
−0.248741 | + | 0.968570i | \(0.580017\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.90486 | 0.852111 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 11.2487 | 2.24974 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.11610 | −1.63730 | −0.818650 | − | 0.574293i | \(-0.805277\pi\) | ||||
−0.818650 | + | 0.574293i | \(0.805277\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.96079 | −0.863562 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 15.7404 | 2.66061 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.18358 | 1.01657 | 0.508287 | − | 0.861188i | \(-0.330279\pi\) | ||||
0.508287 | + | 0.861188i | \(0.330279\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.829895 | −0.132890 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.10485 | −0.641071 | −0.320535 | − | 0.947237i | \(-0.603863\pi\) | ||||
−0.320535 | + | 0.947237i | \(0.603863\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.53731 | 0.234438 | 0.117219 | − | 0.993106i | \(-0.462602\pi\) | ||||
0.117219 | + | 0.993106i | \(0.462602\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.03097 | −0.600901 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.98483 | −1.01884 | −0.509421 | − | 0.860517i | \(-0.670140\pi\) | ||||
−0.509421 | + | 0.860517i | \(0.670140\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 8.24795 | 1.17828 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.147001 | −0.0205843 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.48267 | −1.30254 | −0.651272 | − | 0.758844i | \(-0.725764\pi\) | ||||
−0.651272 | + | 0.758844i | \(0.725764\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −19.9968 | −2.69636 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.16848 | 0.287222 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.01956 | −0.523302 | −0.261651 | − | 0.965163i | \(-0.584267\pi\) | ||||
−0.261651 | + | 0.965163i | \(0.584267\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.6833 | −1.75197 | −0.875985 | − | 0.482338i | \(-0.839788\pi\) | ||||
−0.875985 | + | 0.482338i | \(0.839788\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.90486 | −0.491966 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.34528 | −0.414931 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.37725 | −0.779105 | −0.389553 | − | 0.921004i | \(-0.627370\pi\) | ||||
−0.389553 | + | 0.921004i | \(0.627370\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.54807 | −0.895792 | −0.447896 | − | 0.894086i | \(-0.647826\pi\) | ||||
−0.447896 | + | 0.894086i | \(0.647826\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.99373 | −0.233348 | −0.116674 | − | 0.993170i | \(-0.537223\pi\) | ||||
−0.116674 | + | 0.993170i | \(0.537223\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −11.2487 | −1.29889 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −19.3712 | −2.20755 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.3147 | 1.49802 | 0.749008 | − | 0.662561i | \(-0.230531\pi\) | ||||
0.749008 | + | 0.662561i | \(0.230531\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −15.7448 | −1.72822 | −0.864110 | − | 0.503303i | \(-0.832118\pi\) | ||||
−0.864110 | + | 0.503303i | \(0.832118\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.592557 | −0.0642719 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.00000 | 0.107211 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.4691 | 1.42772 | 0.713861 | − | 0.700287i | \(-0.246945\pi\) | ||||
0.713861 | + | 0.700287i | \(0.246945\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.24063 | −0.339710 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.11610 | 0.945296 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 8.74106 | 0.896813 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.85389 | −0.492838 | −0.246419 | − | 0.969163i | \(-0.579254\pi\) | ||||
−0.246419 | + | 0.969163i | \(0.579254\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.96079 | 0.498578 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.52395 | −0.151638 | −0.0758192 | − | 0.997122i | \(-0.524157\pi\) | ||||
−0.0758192 | + | 0.997122i | \(0.524157\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.81435 | 0.671438 | 0.335719 | − | 0.941962i | \(-0.391021\pi\) | ||||
0.335719 | + | 0.941962i | \(0.391021\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −15.7404 | −1.53610 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.19721 | 0.309086 | 0.154543 | − | 0.987986i | \(-0.450609\pi\) | ||||
0.154543 | + | 0.987986i | \(0.450609\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.08806 | −0.583130 | −0.291565 | − | 0.956551i | \(-0.594176\pi\) | ||||
−0.291565 | + | 0.956551i | \(0.594176\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.18358 | −0.586919 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.0154 | 1.60068 | 0.800339 | − | 0.599547i | \(-0.204653\pi\) | ||||
0.800339 | + | 0.599547i | \(0.204653\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.03097 | 0.375890 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.829895 | 0.0767239 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.574020 | −0.0526203 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 13.6094 | 1.23722 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.10485 | 0.370122 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −25.1883 | −2.25291 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.07441 | −0.450281 | −0.225141 | − | 0.974326i | \(-0.572284\pi\) | ||||
−0.225141 | + | 0.974326i | \(0.572284\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.53731 | −0.135353 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.2269 | 1.33038 | 0.665192 | − | 0.746672i | \(-0.268350\pi\) | ||||
0.665192 | + | 0.746672i | \(0.268350\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.46760 | 0.734234 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.03097 | 0.346931 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −18.7628 | −1.60302 | −0.801509 | − | 0.597983i | \(-0.795969\pi\) | ||||
−0.801509 | + | 0.597983i | \(0.795969\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.21984 | 0.442741 | 0.221370 | − | 0.975190i | \(-0.428947\pi\) | ||||
0.221370 | + | 0.975190i | \(0.428947\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.98483 | 0.588229 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.11693 | 0.344275 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.03097 | 0.334754 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −8.24795 | −0.680279 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.87639 | 0.563336 | 0.281668 | − | 0.959512i | \(-0.409112\pi\) | ||||
0.281668 | + | 0.959512i | \(0.409112\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.3390 | −1.49241 | −0.746203 | − | 0.665718i | \(-0.768125\pi\) | ||||
−0.746203 | + | 0.665718i | \(0.768125\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.147001 | 0.0118843 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 36.7467 | 2.95157 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.9650 | −0.875105 | −0.437553 | − | 0.899193i | \(-0.644155\pi\) | ||||
−0.437553 | + | 0.899193i | \(0.644155\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9.48267 | 0.752025 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.90486 | 0.307746 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.9769 | −1.09476 | −0.547379 | − | 0.836885i | \(-0.684374\pi\) | ||||
−0.547379 | + | 0.836885i | \(0.684374\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 19.9968 | 1.55675 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.64616 | 0.359531 | 0.179765 | − | 0.983710i | \(-0.442466\pi\) | ||||
0.179765 | + | 0.983710i | \(0.442466\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.3113 | −0.947021 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.16848 | −0.165827 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.16388 | −0.696717 | −0.348358 | − | 0.937361i | \(-0.613261\pi\) | ||||
−0.348358 | + | 0.937361i | \(0.613261\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −43.9246 | −3.32039 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.01956 | 0.302129 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.7124 | 0.875426 | 0.437713 | − | 0.899115i | \(-0.355789\pi\) | ||||
0.437713 | + | 0.899115i | \(0.355789\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.52725 | −0.485167 | −0.242583 | − | 0.970131i | \(-0.577995\pi\) | ||||
−0.242583 | + | 0.970131i | \(0.577995\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 13.6833 | 1.01150 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −24.9258 | −1.83258 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.729242 | 0.0533275 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.90486 | 0.284037 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.40460 | −0.318706 | −0.159353 | − | 0.987222i | \(-0.550941\pi\) | ||||
−0.159353 | + | 0.987222i | \(0.550941\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.96239 | 0.717108 | 0.358554 | − | 0.933509i | \(-0.383270\pi\) | ||||
0.358554 | + | 0.933509i | \(0.383270\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.34528 | 0.239561 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.93648 | 0.565451 | 0.282725 | − | 0.959201i | \(-0.408762\pi\) | ||||
0.282725 | + | 0.959201i | \(0.408762\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.76032 | −0.266562 | −0.133281 | − | 0.991078i | \(-0.542551\pi\) | ||||
−0.133281 | + | 0.991078i | \(0.542551\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.37725 | 0.449817 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.90486 | 0.274068 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 16.5465 | 1.15566 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −10.7573 | −0.744101 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.2194 | 0.703533 | 0.351766 | − | 0.936088i | \(-0.385581\pi\) | ||||
0.351766 | + | 0.936088i | \(0.385581\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.54807 | 0.517186 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.19685 | −0.422622 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 35.5971 | 2.41649 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.99373 | 0.134724 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.121996 | 0.00820632 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.1127 | −0.811126 | −0.405563 | − | 0.914067i | \(-0.632925\pi\) | ||||
−0.405563 | + | 0.914067i | \(0.632925\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 11.2487 | 0.749914 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −14.9527 | −0.992447 | −0.496224 | − | 0.868195i | \(-0.665280\pi\) | ||||
−0.496224 | + | 0.868195i | \(0.665280\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.53624 | −0.564090 | −0.282045 | − | 0.959401i | \(-0.591013\pi\) | ||||
−0.282045 | + | 0.959401i | \(0.591013\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 19.3712 | 1.27453 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −25.5531 | −1.67404 | −0.837020 | − | 0.547172i | \(-0.815704\pi\) | ||||
−0.837020 | + | 0.547172i | \(0.815704\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 28.1556 | 1.83667 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −13.3147 | −0.864880 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.3948 | 1.31923 | 0.659614 | − | 0.751604i | \(-0.270720\pi\) | ||||
0.659614 | + | 0.751604i | \(0.270720\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 26.1445 | 1.68412 | 0.842058 | − | 0.539388i | \(-0.181344\pi\) | ||||
0.842058 | + | 0.539388i | \(0.181344\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −33.2472 | −2.12409 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.79961 | −0.114506 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 15.7448 | 0.997788 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 17.1143 | 1.08024 | 0.540122 | − | 0.841587i | \(-0.318378\pi\) | ||||
0.540122 | + | 0.841587i | \(0.318378\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.96079 | −0.311882 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.592557 | 0.0371074 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 25.1527 | 1.56898 | 0.784490 | − | 0.620141i | \(-0.212925\pi\) | ||||
0.784490 | + | 0.620141i | \(0.212925\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −24.1460 | −1.50036 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.00000 | −0.0618984 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.4949 | 0.832130 | 0.416065 | − | 0.909335i | \(-0.363409\pi\) | ||||
0.416065 | + | 0.909335i | \(0.363409\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 38.2243 | 2.34810 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −13.4691 | −0.824296 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 29.9542 | 1.82634 | 0.913169 | − | 0.407581i | \(-0.133628\pi\) | ||||
0.913169 | + | 0.407581i | \(0.133628\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.86261 | −0.113146 | −0.0565729 | − | 0.998398i | \(-0.518017\pi\) | ||||
−0.0565729 | + | 0.998398i | \(0.518017\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.24063 | 0.196132 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 55.8024 | 3.36501 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 29.8432 | 1.79310 | 0.896551 | − | 0.442941i | \(-0.146065\pi\) | ||||
0.896551 | + | 0.442941i | \(0.146065\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −9.11610 | −0.545767 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.73980 | 0.521373 | 0.260686 | − | 0.965424i | \(-0.416051\pi\) | ||||
0.260686 | + | 0.965424i | \(0.416051\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 17.0153 | 1.01146 | 0.505728 | − | 0.862693i | \(-0.331224\pi\) | ||||
0.505728 | + | 0.862693i | \(0.331224\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −8.74106 | −0.517775 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 16.0289 | 0.946155 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9784 | −0.998729 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.85389 | 0.284540 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.4295 | 0.609300 | 0.304650 | − | 0.952464i | \(-0.401461\pi\) | ||||
0.304650 | + | 0.952464i | \(0.401461\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 16.2027 | 0.943359 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.96079 | −0.287854 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.829895 | −0.0479941 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.00299 | −0.346006 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.52395 | 0.0875484 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 55.1571 | 3.15828 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −32.9207 | −1.87889 | −0.939443 | − | 0.342706i | \(-0.888657\pi\) | ||||
−0.939443 | + | 0.342706i | \(0.888657\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.81435 | −0.387655 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.5860 | 0.600279 | 0.300139 | − | 0.953895i | \(-0.402967\pi\) | ||||
0.300139 | + | 0.953895i | \(0.402967\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.05323 | −0.342149 | −0.171075 | − | 0.985258i | \(-0.554724\pi\) | ||||
−0.171075 | + | 0.985258i | \(0.554724\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 15.7404 | 0.886870 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.74177 | −0.434821 | −0.217410 | − | 0.976080i | \(-0.569761\pi\) | ||||
−0.217410 | + | 0.976080i | \(0.569761\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.96079 | −0.277751 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.19721 | −0.178451 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.318769 | −0.0177368 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.33525 | 0.517826 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.08806 | 0.336670 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 27.2748 | 1.50371 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.41328 | 0.187611 | 0.0938053 | − | 0.995591i | \(-0.470097\pi\) | ||||
0.0938053 | + | 0.995591i | \(0.470097\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.18358 | 0.338858 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 25.7065 | 1.40450 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.64344 | 0.0895237 | 0.0447618 | − | 0.998998i | \(-0.485747\pi\) | ||||
0.0447618 | + | 0.998998i | \(0.485747\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −17.0154 | −0.924152 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −45.2230 | −2.44897 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.87307 | −0.263121 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.03097 | −0.217020 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11.7854 | 0.632674 | 0.316337 | − | 0.948647i | \(-0.397547\pi\) | ||||
0.316337 | + | 0.948647i | \(0.397547\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.26298 | −0.281721 | −0.140860 | − | 0.990029i | \(-0.544987\pi\) | ||||
−0.140860 | + | 0.990029i | \(0.544987\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.829895 | −0.0442965 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.2153 | 0.596932 | 0.298466 | − | 0.954420i | \(-0.403525\pi\) | ||||
0.298466 | + | 0.954420i | \(0.403525\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 30.4260 | 1.61485 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.574020 | 0.0303803 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 20.7645 | 1.09591 | 0.547953 | − | 0.836509i | \(-0.315407\pi\) | ||||
0.547953 | + | 0.836509i | \(0.315407\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.2977 | −0.752511 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −13.6094 | −0.714309 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.03665 | 0.420657 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −22.6854 | −1.18417 | −0.592085 | − | 0.805875i | \(-0.701695\pi\) | ||||
−0.592085 | + | 0.805875i | \(0.701695\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.10485 | −0.213690 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 37.0285 | 1.92243 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.31491 | 0.378751 | 0.189376 | − | 0.981905i | \(-0.439354\pi\) | ||||
0.189376 | + | 0.981905i | \(0.439354\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 25.1883 | 1.30072 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.829895 | −0.0427418 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −24.9633 | −1.28228 | −0.641140 | − | 0.767424i | \(-0.721538\pi\) | ||||
−0.641140 | + | 0.767424i | \(0.721538\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.07441 | 0.259970 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.87282 | −0.300087 | −0.150043 | − | 0.988679i | \(-0.547941\pi\) | ||||
−0.150043 | + | 0.988679i | \(0.547941\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 78.0847 | 3.97956 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.53731 | 0.0781459 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.89909 | −0.0962878 | −0.0481439 | − | 0.998840i | \(-0.515331\pi\) | ||||
−0.0481439 | + | 0.998840i | \(0.515331\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.147001 | −0.00743417 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −15.2269 | −0.768098 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −53.6709 | −2.70048 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.774834 | 0.0388878 | 0.0194439 | − | 0.999811i | \(-0.493810\pi\) | ||||
0.0194439 | + | 0.999811i | \(0.493810\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −8.46760 | −0.423910 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.41544 | 0.120621 | 0.0603106 | − | 0.998180i | \(-0.480791\pi\) | ||||
0.0603106 | + | 0.998180i | \(0.480791\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.56541 | −0.376860 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.03097 | −0.200300 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 30.6754 | 1.52052 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.8714 | 0.587004 | 0.293502 | − | 0.955959i | \(-0.405179\pi\) | ||||
0.293502 | + | 0.955959i | \(0.405179\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 18.7628 | 0.925502 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 15.6958 | 0.772341 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 63.4669 | 3.11547 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.21984 | −0.255617 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 18.3072 | 0.894364 | 0.447182 | − | 0.894443i | \(-0.352428\pi\) | ||||
0.447182 | + | 0.894443i | \(0.352428\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.5315 | 0.610749 | 0.305375 | − | 0.952232i | \(-0.401218\pi\) | ||||
0.305375 | + | 0.952232i | \(0.401218\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.98483 | −0.339614 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.65357 | 0.0802101 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 53.4315 | 2.58573 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.11693 | −0.198767 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.6824 | 0.514555 | 0.257277 | − | 0.966338i | \(-0.417175\pi\) | ||||
0.257277 | + | 0.966338i | \(0.417175\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.573366 | 0.0275542 | 0.0137771 | − | 0.999905i | \(-0.495614\pi\) | ||||
0.0137771 | + | 0.999905i | \(0.495614\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.03097 | −0.193270 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.16848 | 0.103732 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −38.2927 | −1.82761 | −0.913805 | − | 0.406153i | \(-0.866870\pi\) | ||||
−0.913805 | + | 0.406153i | \(0.866870\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8.24795 | 0.392759 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −21.2516 | −1.00969 | −0.504847 | − | 0.863209i | \(-0.668451\pi\) | ||||
−0.504847 | + | 0.863209i | \(0.668451\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −54.2935 | −2.57376 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −6.87639 | −0.325242 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −15.1730 | −0.716060 | −0.358030 | − | 0.933710i | \(-0.616552\pi\) | ||||
−0.358030 | + | 0.933710i | \(0.616552\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −20.3633 | −0.958871 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 18.3390 | 0.861641 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 13.0629 | 0.612397 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −30.8406 | −1.44266 | −0.721331 | − | 0.692591i | \(-0.756469\pi\) | ||||
−0.721331 | + | 0.692591i | \(0.756469\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.147001 | −0.00686143 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 21.2697 | 0.990630 | 0.495315 | − | 0.868714i | \(-0.335053\pi\) | ||||
0.495315 | + | 0.868714i | \(0.335053\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.24681 | 0.0579441 | 0.0289721 | − | 0.999580i | \(-0.490777\pi\) | ||||
0.0289721 | + | 0.999580i | \(0.490777\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −36.7467 | −1.70409 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 30.2601 | 1.40027 | 0.700134 | − | 0.714011i | \(-0.253123\pi\) | ||||
0.700134 | + | 0.714011i | \(0.253123\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 24.9023 | 1.14988 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10.9650 | 0.505242 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.62627 | 0.350656 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −24.3925 | −1.11921 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9.48267 | −0.434182 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −36.2396 | −1.65583 | −0.827915 | − | 0.560854i | \(-0.810473\pi\) | ||||
−0.827915 | + | 0.560854i | \(0.810473\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.13172 | 0.233986 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.90486 | −0.177677 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 19.5659 | 0.888441 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.03406 | −0.137487 | −0.0687433 | − | 0.997634i | \(-0.521899\pi\) | ||||
−0.0687433 | + | 0.997634i | \(0.521899\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 13.9769 | 0.632059 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.9779 | −0.540554 | −0.270277 | − | 0.962783i | \(-0.587115\pi\) | ||||
−0.270277 | + | 0.962783i | \(0.587115\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.147001 | −0.00662060 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −19.9968 | −0.898788 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 29.4742 | 1.32210 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −22.4638 | −1.00562 | −0.502809 | − | 0.864398i | \(-0.667700\pi\) | ||||
−0.502809 | + | 0.864398i | \(0.667700\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.64616 | −0.207575 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 10.4505 | 0.465967 | 0.232983 | − | 0.972481i | \(-0.425151\pi\) | ||||
0.232983 | + | 0.972481i | \(0.425151\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.14298 | 0.273359 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.3113 | 0.546763 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 28.5002 | 1.26325 | 0.631624 | − | 0.775275i | \(-0.282389\pi\) | ||||
0.631624 | + | 0.775275i | \(0.282389\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.78523 | 0.344398 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.16848 | 0.0957405 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −27.4684 | −1.21040 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −34.6503 | −1.52392 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.16388 | 0.402250 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 38.9395 | 1.70597 | 0.852985 | − | 0.521935i | \(-0.174790\pi\) | ||||
0.852985 | + | 0.521935i | \(0.174790\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.9394 | −0.478348 | −0.239174 | − | 0.970977i | \(-0.576877\pi\) | ||||
−0.239174 | + | 0.970977i | \(0.576877\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 43.9246 | 1.91703 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.34008 | −0.0583747 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.01956 | −0.174434 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.40660 | −0.147556 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.8879 | −0.557191 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −11.7124 | −0.505427 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 40.9163 | 1.76239 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.2251 | 0.955532 | 0.477766 | − | 0.878487i | \(-0.341447\pi\) | ||||
0.477766 | + | 0.878487i | \(0.341447\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.52725 | 0.280111 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 24.5408 | 1.05121 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.560610 | −0.0239700 | −0.0119850 | − | 0.999928i | \(-0.503815\pi\) | ||||
−0.0119850 | + | 0.999928i | \(0.503815\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −13.6833 | −0.583990 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.16848 | 0.0923802 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −51.9919 | −2.21092 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 24.9258 | 1.05804 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 37.7776 | 1.60069 | 0.800344 | − | 0.599542i | \(-0.204650\pi\) | ||||
0.800344 | + | 0.599542i | \(0.204650\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.27581 | 0.0539609 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.729242 | −0.0307886 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −32.6315 | −1.37525 | −0.687627 | − | 0.726064i | \(-0.741348\pi\) | ||||
−0.687627 | + | 0.726064i | \(0.741348\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −68.5887 | −2.88555 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.90486 | −0.163989 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14.7589 | −0.618724 | −0.309362 | − | 0.950944i | \(-0.600115\pi\) | ||||
−0.309362 | + | 0.950944i | \(0.600115\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 42.5411 | 1.78029 | 0.890146 | − | 0.455676i | \(-0.150602\pi\) | ||||
0.890146 | + | 0.455676i | \(0.150602\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.40460 | 0.184005 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −11.2487 | −0.469103 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15.6892 | −0.653148 | −0.326574 | − | 0.945172i | \(-0.605894\pi\) | ||||
−0.326574 | + | 0.945172i | \(0.605894\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −9.96239 | −0.414023 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 61.4814 | 2.55068 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −47.0415 | −1.94826 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.34528 | −0.138310 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 23.8218 | 0.983229 | 0.491615 | − | 0.870813i | \(-0.336407\pi\) | ||||
0.491615 | + | 0.870813i | \(0.336407\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 19.7680 | 0.814528 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.93648 | −0.326463 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −34.8866 | −1.43262 | −0.716310 | − | 0.697782i | \(-0.754171\pi\) | ||||
−0.716310 | + | 0.697782i | \(0.754171\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.31385 | 0.0948588 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.76032 | 0.153900 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15.3555 | 0.627409 | 0.313705 | − | 0.949521i | \(-0.398430\pi\) | ||||
0.313705 | + | 0.949521i | \(0.398430\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.80170 | 0.236656 | 0.118328 | − | 0.992975i | \(-0.462247\pi\) | ||||
0.118328 | + | 0.992975i | \(0.462247\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.37725 | −0.259702 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −54.8591 | −2.23034 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −28.0828 | −1.13985 | −0.569923 | − | 0.821698i | \(-0.693027\pi\) | ||||
−0.569923 | + | 0.821698i | \(0.693027\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.90486 | −0.158233 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.79668 | −0.234509 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.45164 | 0.381748 | 0.190874 | − | 0.981615i | \(-0.438868\pi\) | ||||
0.190874 | + | 0.981615i | \(0.438868\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −16.5465 | −0.667221 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 34.7059 | 1.39721 | 0.698603 | − | 0.715510i | \(-0.253806\pi\) | ||||
0.698603 | + | 0.715510i | \(0.253806\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −40.7134 | −1.63641 | −0.818206 | − | 0.574926i | \(-0.805031\pi\) | ||||
−0.818206 | + | 0.574926i | \(0.805031\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −52.5950 | −2.10717 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 45.2898 | 1.81159 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 10.7573 | 0.429607 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.908993 | 0.0362439 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.5231 | 1.33453 | 0.667267 | − | 0.744818i | \(-0.267464\pi\) | ||||
0.667267 | + | 0.744818i | \(0.267464\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −10.2194 | −0.406185 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 20.4548 | 0.811724 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.84494 | 0.271206 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7.54807 | −0.298597 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.84476 | 0.270352 | 0.135176 | − | 0.990822i | \(-0.456840\pi\) | ||||
0.135176 | + | 0.990822i | \(0.456840\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 32.8310 | 1.29473 | 0.647363 | − | 0.762181i | \(-0.275872\pi\) | ||||
0.647363 | + | 0.762181i | \(0.275872\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.19685 | 0.244001 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 15.0945 | 0.593427 | 0.296714 | − | 0.954966i | \(-0.404109\pi\) | ||||
0.296714 | + | 0.954966i | \(0.404109\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −19.9402 | −0.782721 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −35.5971 | −1.39516 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 40.5264 | 1.58592 | 0.792961 | − | 0.609272i | \(-0.208538\pi\) | ||||
0.792961 | + | 0.609272i | \(0.208538\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −61.3793 | −2.39829 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.99373 | −0.0777827 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22.2279 | 0.865875 | 0.432938 | − | 0.901424i | \(-0.357477\pi\) | ||||
0.432938 | + | 0.901424i | \(0.357477\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.2576 | −0.632348 | −0.316174 | − | 0.948701i | \(-0.602398\pi\) | ||||
−0.316174 | + | 0.948701i | \(0.602398\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.121996 | −0.00473792 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −34.1326 | −1.32361 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.00000 | 0.0387202 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 12.1127 | 0.468304 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −67.8801 | −2.62048 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18.4106 | −0.709675 | −0.354838 | − | 0.934928i | \(-0.615464\pi\) | ||||
−0.354838 | + | 0.934928i | \(0.615464\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −11.2487 | −0.432963 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 34.3896 | 1.32170 | 0.660850 | − | 0.750518i | \(-0.270196\pi\) | ||||
0.660850 | + | 0.750518i | \(0.270196\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 18.9538 | 0.727379 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 14.9527 | 0.572990 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −34.5638 | −1.32255 | −0.661274 | − | 0.750144i | \(-0.729984\pi\) | ||||
−0.661274 | + | 0.750144i | \(0.729984\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 75.6324 | 2.88976 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8.53624 | 0.325678 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −7.86962 | −0.299809 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.08087 | 0.0411181 | 0.0205591 | − | 0.999789i | \(-0.493455\pi\) | ||||
0.0205591 | + | 0.999789i | \(0.493455\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −19.3712 | −0.735851 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −21.0410 | −0.798131 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.603419 | −0.0228561 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 25.5531 | 0.966508 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −41.2475 | −1.55790 | −0.778948 | − | 0.627088i | \(-0.784247\pi\) | ||||
−0.778948 | + | 0.627088i | \(0.784247\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −13.4089 | −0.505727 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −28.1556 | −1.06040 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.95080 | 0.223803 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 41.4970 | 1.55845 | 0.779227 | − | 0.626742i | \(-0.215612\pi\) | ||||
0.779227 | + | 0.626742i | \(0.215612\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13.3147 | 0.499339 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.11610 | 0.341401 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −16.5952 | −0.620627 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −20.3948 | −0.761657 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −26.6451 | −0.993696 | −0.496848 | − | 0.867838i | \(-0.665509\pi\) | ||||
−0.496848 | + | 0.867838i | \(0.665509\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −26.6091 | −0.990975 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −26.1445 | −0.972324 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −11.2487 | −0.417766 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.12096 | −0.0415742 | −0.0207871 | − | 0.999784i | \(-0.506617\pi\) | ||||
−0.0207871 | + | 0.999784i | \(0.506617\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.225987 | 0.00835842 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21.9912 | 0.812265 | 0.406132 | − | 0.913814i | \(-0.366877\pi\) | ||||
0.406132 | + | 0.913814i | \(0.366877\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 33.2472 | 1.22634 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −31.6362 | −1.16533 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.0801 | −0.591515 | −0.295757 | − | 0.955263i | \(-0.595572\pi\) | ||||
−0.295757 | + | 0.955263i | \(0.595572\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.79961 | 0.0661103 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −16.2773 | −0.597156 | −0.298578 | − | 0.954385i | \(-0.596512\pi\) | ||||
−0.298578 | + | 0.954385i | \(0.596512\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −27.7185 | −1.01553 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −15.7448 | −0.576073 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −12.4847 | −0.456180 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −35.5283 | −1.29645 | −0.648223 | − | 0.761450i | \(-0.724488\pi\) | ||||
−0.648223 | + | 0.761450i | \(0.724488\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −17.1143 | −0.623679 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 73.9239 | 2.69037 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 35.3643 | 1.28534 | 0.642669 | − | 0.766144i | \(-0.277827\pi\) | ||||
0.642669 | + | 0.766144i | \(0.277827\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.96079 | 0.180065 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.67008 | −0.241790 | −0.120895 | − | 0.992665i | \(-0.538576\pi\) | ||||
−0.120895 | + | 0.992665i | \(0.538576\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 23.7730 | 0.860641 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.592557 | −0.0214240 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.33582 | −0.120449 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.37674 | −0.193890 | −0.0969451 | − | 0.995290i | \(-0.530907\pi\) | ||||
−0.0969451 | + | 0.995290i | \(0.530907\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −25.1527 | −0.905852 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −53.1000 | −1.90988 | −0.954938 | − | 0.296805i | \(-0.904079\pi\) | ||||
−0.954938 | + | 0.296805i | \(0.904079\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −102.544 | −3.68350 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 24.1460 | 0.866233 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8.90128 | 0.318921 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −37.4444 | −1.33987 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.00000 | 0.0357371 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 44.1997 | 1.57756 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.33014 | 0.332584 | 0.166292 | − | 0.986077i | \(-0.446821\pi\) | ||||
0.166292 | + | 0.986077i | \(0.446821\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −13.4949 | −0.480431 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −66.4430 | −2.36244 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −11.3557 | −0.403254 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −38.2243 | −1.35568 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 34.2215 | 1.21219 | 0.606094 | − | 0.795393i | \(-0.292735\pi\) | ||||
0.606094 | + | 0.795393i | \(0.292735\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.02678 | −0.0363248 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 13.4691 | 0.475908 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.89045 | −0.349027 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −15.7404 | −0.554775 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −29.9542 | −1.05444 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −28.8744 | −1.01517 | −0.507585 | − | 0.861601i | \(-0.669462\pi\) | ||||
−0.507585 | + | 0.861601i | \(0.669462\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24.1457 | 0.847871 | 0.423935 | − | 0.905692i | \(-0.360648\pi\) | ||||
0.423935 | + | 0.905692i | \(0.360648\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.86261 | 0.0653247 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 56.3406 | 1.97352 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.33362 | −0.116629 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.24063 | −0.113237 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 37.2427 | 1.29978 | 0.649889 | − | 0.760029i | \(-0.274815\pi\) | ||||
0.649889 | + | 0.760029i | \(0.274815\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.8654 | 0.378745 | 0.189372 | − | 0.981905i | \(-0.439355\pi\) | ||||
0.189372 | + | 0.981905i | \(0.439355\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −55.8024 | −1.94279 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −38.2007 | −1.32837 | −0.664183 | − | 0.747570i | \(-0.731221\pi\) | ||||
−0.664183 | + | 0.747570i | \(0.731221\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12.2516 | 0.425516 | 0.212758 | − | 0.977105i | \(-0.431755\pi\) | ||||
0.212758 | + | 0.977105i | \(0.431755\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −29.8432 | −1.03525 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.21246 | 0.0420092 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −18.7285 | −0.648127 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 9.11610 | 0.315099 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 35.6628 | 1.23121 | 0.615607 | − | 0.788053i | \(-0.288911\pi\) | ||||
0.615607 | + | 0.788053i | \(0.288911\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −8.73980 | −0.301015 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 49.6264 | 1.70720 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −53.1429 | −1.82601 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −17.0153 | −0.583965 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.18358 | −0.211970 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13.9763 | 0.478540 | 0.239270 | − | 0.970953i | \(-0.423092\pi\) | ||||
0.239270 | + | 0.970953i | \(0.423092\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.74106 | 0.298938 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −13.7131 | −0.468432 | −0.234216 | − | 0.972185i | \(-0.575252\pi\) | ||||
−0.234216 | + | 0.972185i | \(0.575252\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −38.0918 | −1.29968 | −0.649838 | − | 0.760073i | \(-0.725163\pi\) | ||||
−0.649838 | + | 0.760073i | \(0.725163\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −16.0289 | −0.546263 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −39.0177 | −1.32818 | −0.664089 | − | 0.747654i | \(-0.731180\pi\) | ||||
−0.664089 | + | 0.747654i | \(0.731180\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 36.9393 | 1.25597 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 16.9784 | 0.576616 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 66.0512 | 2.24063 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.29245 | −0.179328 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.85389 | −0.164279 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 98.3570 | 3.32507 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 45.9512 | 1.55166 | 0.775831 | − | 0.630941i | \(-0.217331\pi\) | ||||
0.775831 | + | 0.630941i | \(0.217331\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −10.4295 | −0.351779 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 30.2706 | 1.01984 | 0.509920 | − | 0.860222i | \(-0.329675\pi\) | ||||
0.509920 | + | 0.860222i | \(0.329675\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.95233 | −0.0657010 | −0.0328505 | − | 0.999460i | \(-0.510459\pi\) | ||||
−0.0328505 | + | 0.999460i | \(0.510459\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −16.2027 | −0.544649 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 11.5661 | 0.388351 | 0.194176 | − | 0.980967i | \(-0.437797\pi\) | ||||
0.194176 | + | 0.980967i | \(0.437797\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 19.8149 | 0.664570 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.96079 | 0.166193 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 15.1464 | 0.506856 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −47.2123 | −1.57813 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.829895 | 0.0277094 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.11610 | 0.304039 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.39396 | −0.0464397 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.00299 | 0.199767 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 26.3111 | 0.874612 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 34.6836 | 1.15165 | 0.575825 | − | 0.817573i | \(-0.304681\pi\) | ||||
0.575825 | + | 0.817573i | \(0.304681\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.52395 | −0.0505461 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25.5610 | −0.846873 | −0.423436 | − | 0.905926i | \(-0.639176\pi\) | ||||
−0.423436 | + | 0.905926i | \(0.639176\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −78.1068 | −2.58496 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −55.1571 | −1.82344 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −59.4591 | −1.96351 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.95660 | 0.130516 | 0.0652581 | − | 0.997868i | \(-0.479213\pi\) | ||||
0.0652581 | + | 0.997868i | \(0.479213\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 32.9207 | 1.08478 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −6.26411 | −0.206186 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 69.5572 | 2.28703 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.81435 | 0.223813 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.48452 | −0.0487055 | −0.0243527 | − | 0.999703i | \(-0.507752\pi\) | ||||
−0.0243527 | + | 0.999703i | \(0.507752\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −17.8855 | −0.586173 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −10.5860 | −0.346571 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.93955 | −0.0961336 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 54.2332 | 1.77172 | 0.885860 | − | 0.463952i | \(-0.153569\pi\) | ||||
0.885860 | + | 0.463952i | \(0.153569\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.05323 | 0.197540 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 39.8925 | 1.30046 | 0.650230 | − | 0.759738i | \(-0.274673\pi\) | ||||
0.650230 | + | 0.759738i | \(0.274673\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.10485 | 0.133672 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −15.7404 | −0.512034 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −5.94190 | −0.193086 | −0.0965429 | − | 0.995329i | \(-0.530778\pi\) | ||||
−0.0965429 | + | 0.995329i | \(0.530778\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.65458 | −0.0537101 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.74177 | 0.251044 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12.7427 | 0.412775 | 0.206388 | − | 0.978470i | \(-0.433829\pi\) | ||||
0.206388 | + | 0.978470i | \(0.433829\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 17.7548 | 0.574532 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.96079 | 0.160359 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 73.2663 | 2.36589 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 52.1033 | 1.68075 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.19721 | 0.103029 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −40.1581 | −1.29273 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.67016 | 0.118025 | 0.0590123 | − | 0.998257i | \(-0.481205\pi\) | ||||
0.0590123 | + | 0.998257i | \(0.481205\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.318769 | 0.0102403 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.44430 | 0.174716 | 0.0873580 | − | 0.996177i | \(-0.472158\pi\) | ||||
0.0873580 | + | 0.996177i | \(0.472158\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −20.3828 | −0.653441 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −9.33525 | −0.298967 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −23.3595 | −0.747336 | −0.373668 | − | 0.927563i | \(-0.621900\pi\) | ||||
−0.373668 | + | 0.927563i | \(0.621900\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 66.8174 | 2.13549 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.08806 | −0.194377 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 22.9356 | 0.731534 | 0.365767 | − | 0.930707i | \(-0.380807\pi\) | ||||
0.365767 | + | 0.930707i | \(0.380807\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −31.9917 | −1.01934 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −27.2748 | −0.868166 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.53731 | −0.0488836 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 36.2226 | 1.15065 | 0.575325 | − | 0.817925i | \(-0.304876\pi\) | ||||
0.575325 | + | 0.817925i | \(0.304876\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3.41328 | −0.108317 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 15.1577 | 0.480532 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.15952 | 0.0367224 | 0.0183612 | − | 0.999831i | \(-0.494155\pi\) | ||||
0.0183612 | + | 0.999831i | \(0.494155\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.18358 | −0.195640 |
(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 | 8004.2.a.h.1.1 | ✓ | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8004.2.a.h.1.1 | ✓ | 13 | 1.1 | even | 1 | trivial |