Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6525,2,Mod(1,6525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6525, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6525.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6525 = 3^{2} \cdot 5^{2} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6525.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: | \(52.1023873189\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{12} - 20x^{10} + 148x^{8} - 502x^{6} + 792x^{4} - 496x^{2} + 45 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 1305) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-1.35513\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6525.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.35513 | −0.958222 | −0.479111 | − | 0.877754i | \(-0.659041\pi\) | ||||
−0.479111 | + | 0.877754i | \(0.659041\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.163621 | −0.0818103 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.26969 | 0.479897 | 0.239949 | − | 0.970786i | \(-0.422869\pi\) | ||||
0.239949 | + | 0.970786i | \(0.422869\pi\) | |||||||
\(8\) | 2.93199 | 1.03661 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.474782 | 0.143152 | 0.0715761 | − | 0.997435i | \(-0.477197\pi\) | ||||
0.0715761 | + | 0.997435i | \(0.477197\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.407685 | 0.113071 | 0.0565357 | − | 0.998401i | \(-0.481995\pi\) | ||||
0.0565357 | + | 0.998401i | \(0.481995\pi\) | |||||||
\(14\) | −1.72060 | −0.459848 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.64599 | −0.911497 | ||||||||
\(17\) | −2.97132 | −0.720651 | −0.360326 | − | 0.932827i | \(-0.617334\pi\) | ||||
−0.360326 | + | 0.932827i | \(0.617334\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.80491 | 1.33174 | 0.665868 | − | 0.746069i | \(-0.268061\pi\) | ||||
0.665868 | + | 0.746069i | \(0.268061\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.643392 | −0.137172 | ||||||||
\(23\) | 3.06516 | 0.639130 | 0.319565 | − | 0.947564i | \(-0.396463\pi\) | ||||
0.319565 | + | 0.947564i | \(0.396463\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.552466 | −0.108348 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.207747 | −0.0392605 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.49210 | −0.806805 | −0.403403 | − | 0.915023i | \(-0.632173\pi\) | ||||
−0.403403 | + | 0.915023i | \(0.632173\pi\) | |||||||
\(32\) | −0.923188 | −0.163198 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.02653 | 0.690544 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.20325 | −1.18421 | −0.592103 | − | 0.805862i | \(-0.701702\pi\) | ||||
−0.592103 | + | 0.805862i | \(0.701702\pi\) | |||||||
\(38\) | −7.86641 | −1.27610 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −12.0668 | −1.88452 | −0.942259 | − | 0.334886i | \(-0.891302\pi\) | ||||
−0.942259 | + | 0.334886i | \(0.891302\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.03847 | 0.158365 | 0.0791827 | − | 0.996860i | \(-0.474769\pi\) | ||||
0.0791827 | + | 0.996860i | \(0.474769\pi\) | |||||||
\(44\) | −0.0776841 | −0.0117113 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.15369 | −0.612428 | ||||||||
\(47\) | −2.97132 | −0.433412 | −0.216706 | − | 0.976237i | \(-0.569531\pi\) | ||||
−0.216706 | + | 0.976237i | \(0.569531\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.38789 | −0.769698 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.0667056 | −0.00925040 | ||||||||
\(53\) | −7.87199 | −1.08130 | −0.540651 | − | 0.841247i | \(-0.681822\pi\) | ||||
−0.540651 | + | 0.841247i | \(0.681822\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.72271 | 0.497469 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.35513 | −0.177937 | ||||||||
\(59\) | 4.45891 | 0.580501 | 0.290250 | − | 0.956951i | \(-0.406261\pi\) | ||||
0.290250 | + | 0.956951i | \(0.406261\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.71609 | −0.219722 | −0.109861 | − | 0.993947i | \(-0.535041\pi\) | ||||
−0.109861 | + | 0.993947i | \(0.535041\pi\) | |||||||
\(62\) | 6.08739 | 0.773099 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.54301 | 1.06788 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 15.7754 | 1.92727 | 0.963636 | − | 0.267218i | \(-0.0861043\pi\) | ||||
0.963636 | + | 0.267218i | \(0.0861043\pi\) | |||||||
\(68\) | 0.486169 | 0.0589567 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.00806 | −1.06906 | −0.534530 | − | 0.845149i | \(-0.679511\pi\) | ||||
−0.534530 | + | 0.845149i | \(0.679511\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.677990 | 0.0793527 | 0.0396763 | − | 0.999213i | \(-0.487367\pi\) | ||||
0.0396763 | + | 0.999213i | \(0.487367\pi\) | |||||||
\(74\) | 9.76134 | 1.13473 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.949802 | −0.108950 | ||||||||
\(77\) | 0.602826 | 0.0686984 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.63957 | 0.184466 | 0.0922329 | − | 0.995737i | \(-0.470600\pi\) | ||||
0.0922329 | + | 0.995737i | \(0.470600\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 16.3521 | 1.80579 | ||||||||
\(83\) | 15.5423 | 1.70599 | 0.852995 | − | 0.521919i | \(-0.174784\pi\) | ||||
0.852995 | + | 0.521919i | \(0.174784\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.40726 | −0.151749 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.39206 | 0.148394 | ||||||||
\(89\) | −13.4175 | −1.42225 | −0.711126 | − | 0.703065i | \(-0.751814\pi\) | ||||
−0.711126 | + | 0.703065i | \(0.751814\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.517633 | 0.0542627 | ||||||||
\(92\) | −0.501523 | −0.0522874 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.02653 | 0.415305 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.10733 | −0.721640 | −0.360820 | − | 0.932636i | \(-0.617503\pi\) | ||||
−0.360820 | + | 0.932636i | \(0.617503\pi\) | |||||||
\(98\) | 7.30129 | 0.737542 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.68433 | −0.466108 | −0.233054 | − | 0.972464i | \(-0.574872\pi\) | ||||
−0.233054 | + | 0.972464i | \(0.574872\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.5180 | 1.52904 | 0.764519 | − | 0.644601i | \(-0.222976\pi\) | ||||
0.764519 | + | 0.644601i | \(0.222976\pi\) | |||||||
\(104\) | 1.19533 | 0.117212 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 10.6676 | 1.03613 | ||||||||
\(107\) | −0.676108 | −0.0653618 | −0.0326809 | − | 0.999466i | \(-0.510405\pi\) | ||||
−0.0326809 | + | 0.999466i | \(0.510405\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.44734 | −0.713326 | −0.356663 | − | 0.934233i | \(-0.616086\pi\) | ||||
−0.356663 | + | 0.934233i | \(0.616086\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.62927 | −0.437425 | ||||||||
\(113\) | −14.1017 | −1.32658 | −0.663290 | − | 0.748363i | \(-0.730840\pi\) | ||||
−0.663290 | + | 0.748363i | \(0.730840\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.163621 | −0.0151918 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −6.04241 | −0.556249 | ||||||||
\(119\) | −3.77265 | −0.345839 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.7746 | −0.979507 | ||||||||
\(122\) | 2.32552 | 0.210543 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.735000 | 0.0660050 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.5508 | −1.02497 | −0.512486 | − | 0.858696i | \(-0.671275\pi\) | ||||
−0.512486 | + | 0.858696i | \(0.671275\pi\) | |||||||
\(128\) | −9.73053 | −0.860065 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.2432 | −0.894954 | −0.447477 | − | 0.894296i | \(-0.647677\pi\) | ||||
−0.447477 | + | 0.894296i | \(0.647677\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.37043 | 0.639097 | ||||||||
\(134\) | −21.3777 | −1.84676 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −8.71188 | −0.747038 | ||||||||
\(137\) | −2.06577 | −0.176491 | −0.0882455 | − | 0.996099i | \(-0.528126\pi\) | ||||
−0.0882455 | + | 0.996099i | \(0.528126\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.48237 | 0.295370 | 0.147685 | − | 0.989034i | \(-0.452818\pi\) | ||||
0.147685 | + | 0.989034i | \(0.452818\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 12.2071 | 1.02440 | ||||||||
\(143\) | 0.193562 | 0.0161864 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −0.918765 | −0.0760375 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.17860 | 0.0968802 | ||||||||
\(149\) | −10.8558 | −0.889343 | −0.444672 | − | 0.895694i | \(-0.646680\pi\) | ||||
−0.444672 | + | 0.895694i | \(0.646680\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.3555 | 0.924097 | 0.462048 | − | 0.886855i | \(-0.347115\pi\) | ||||
0.462048 | + | 0.886855i | \(0.347115\pi\) | |||||||
\(152\) | 17.0199 | 1.38050 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.816908 | −0.0658283 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.9813 | 1.35526 | 0.677628 | − | 0.735405i | \(-0.263008\pi\) | ||||
0.677628 | + | 0.735405i | \(0.263008\pi\) | |||||||
\(158\) | −2.22183 | −0.176759 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.89180 | 0.306717 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.78532 | 0.609793 | 0.304897 | − | 0.952385i | \(-0.401378\pi\) | ||||
0.304897 | + | 0.952385i | \(0.401378\pi\) | |||||||
\(164\) | 1.97438 | 0.154173 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −21.0619 | −1.63472 | ||||||||
\(167\) | 2.06389 | 0.159709 | 0.0798544 | − | 0.996807i | \(-0.474554\pi\) | ||||
0.0798544 | + | 0.996807i | \(0.474554\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.8338 | −0.987215 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.169915 | −0.0129559 | ||||||||
\(173\) | 0.522120 | 0.0396960 | 0.0198480 | − | 0.999803i | \(-0.493682\pi\) | ||||
0.0198480 | + | 0.999803i | \(0.493682\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.73105 | −0.130483 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 18.1825 | 1.36283 | ||||||||
\(179\) | −10.4805 | −0.783346 | −0.391673 | − | 0.920104i | \(-0.628104\pi\) | ||||
−0.391673 | + | 0.920104i | \(0.628104\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.2724 | 0.912197 | 0.456099 | − | 0.889929i | \(-0.349246\pi\) | ||||
0.456099 | + | 0.889929i | \(0.349246\pi\) | |||||||
\(182\) | −0.701461 | −0.0519957 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 8.98701 | 0.662531 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.41073 | −0.103163 | ||||||||
\(188\) | 0.486169 | 0.0354575 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.69478 | −0.701490 | −0.350745 | − | 0.936471i | \(-0.614072\pi\) | ||||
−0.350745 | + | 0.936471i | \(0.614072\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.0857 | 0.797963 | 0.398982 | − | 0.916959i | \(-0.369364\pi\) | ||||
0.398982 | + | 0.916959i | \(0.369364\pi\) | |||||||
\(194\) | 9.63136 | 0.691491 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.881569 | 0.0629692 | ||||||||
\(197\) | 2.00431 | 0.142801 | 0.0714007 | − | 0.997448i | \(-0.477253\pi\) | ||||
0.0714007 | + | 0.997448i | \(0.477253\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.1170 | −1.28428 | −0.642140 | − | 0.766588i | \(-0.721953\pi\) | ||||
−0.642140 | + | 0.766588i | \(0.721953\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 6.34788 | 0.446635 | ||||||||
\(203\) | 1.26969 | 0.0891147 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −21.0290 | −1.46516 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.48641 | −0.103064 | ||||||||
\(209\) | 2.75607 | 0.190641 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.4829 | 1.27241 | 0.636206 | − | 0.771519i | \(-0.280503\pi\) | ||||
0.636206 | + | 0.771519i | \(0.280503\pi\) | |||||||
\(212\) | 1.28802 | 0.0884615 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.916215 | 0.0626312 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.70357 | −0.387184 | ||||||||
\(218\) | 10.0921 | 0.683525 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.21136 | −0.0814851 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.6226 | 1.44796 | 0.723978 | − | 0.689823i | \(-0.242312\pi\) | ||||
0.723978 | + | 0.689823i | \(0.242312\pi\) | |||||||
\(224\) | −1.17216 | −0.0783184 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 19.1097 | 1.27116 | ||||||||
\(227\) | −19.5621 | −1.29838 | −0.649191 | − | 0.760625i | \(-0.724892\pi\) | ||||
−0.649191 | + | 0.760625i | \(0.724892\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.7779 | 0.712220 | 0.356110 | − | 0.934444i | \(-0.384103\pi\) | ||||
0.356110 | + | 0.934444i | \(0.384103\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.93199 | 0.192494 | ||||||||
\(233\) | 4.25222 | 0.278572 | 0.139286 | − | 0.990252i | \(-0.455519\pi\) | ||||
0.139286 | + | 0.990252i | \(0.455519\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −0.729569 | −0.0474909 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 5.11244 | 0.331390 | ||||||||
\(239\) | −16.8385 | −1.08919 | −0.544596 | − | 0.838699i | \(-0.683317\pi\) | ||||
−0.544596 | + | 0.838699i | \(0.683317\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 21.8396 | 1.40681 | 0.703405 | − | 0.710789i | \(-0.251662\pi\) | ||||
0.703405 | + | 0.710789i | \(0.251662\pi\) | |||||||
\(242\) | 14.6010 | 0.938586 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.280787 | 0.0179755 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.36657 | 0.150581 | ||||||||
\(248\) | −13.1708 | −0.836346 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.24264 | −0.141554 | −0.0707772 | − | 0.997492i | \(-0.522548\pi\) | ||||
−0.0707772 | + | 0.997492i | \(0.522548\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.45528 | 0.0914929 | ||||||||
\(254\) | 15.6529 | 0.982150 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3.89989 | −0.243743 | ||||||||
\(257\) | −1.27685 | −0.0796479 | −0.0398239 | − | 0.999207i | \(-0.512680\pi\) | ||||
−0.0398239 | + | 0.999207i | \(0.512680\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.14589 | −0.568298 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 13.8809 | 0.857564 | ||||||||
\(263\) | 19.6767 | 1.21332 | 0.606658 | − | 0.794963i | \(-0.292510\pi\) | ||||
0.606658 | + | 0.794963i | \(0.292510\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −9.98789 | −0.612397 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.58118 | −0.157671 | ||||||||
\(269\) | 11.7353 | 0.715516 | 0.357758 | − | 0.933814i | \(-0.383541\pi\) | ||||
0.357758 | + | 0.933814i | \(0.383541\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.92348 | −0.602809 | −0.301404 | − | 0.953496i | \(-0.597455\pi\) | ||||
−0.301404 | + | 0.953496i | \(0.597455\pi\) | |||||||
\(272\) | 10.8334 | 0.656871 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.79940 | 0.169118 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.50995 | −0.0907242 | −0.0453621 | − | 0.998971i | \(-0.514444\pi\) | ||||
−0.0453621 | + | 0.998971i | \(0.514444\pi\) | |||||||
\(278\) | −4.71906 | −0.283031 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −25.3285 | −1.51097 | −0.755487 | − | 0.655164i | \(-0.772600\pi\) | ||||
−0.755487 | + | 0.655164i | \(0.772600\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.09287 | −0.124408 | −0.0622041 | − | 0.998063i | \(-0.519813\pi\) | ||||
−0.0622041 | + | 0.998063i | \(0.519813\pi\) | |||||||
\(284\) | 1.47390 | 0.0874601 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.262301 | −0.0155102 | ||||||||
\(287\) | −15.3211 | −0.904375 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.17125 | −0.480662 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.110933 | −0.00649186 | ||||||||
\(293\) | 10.8526 | 0.634013 | 0.317007 | − | 0.948423i | \(-0.397322\pi\) | ||||
0.317007 | + | 0.948423i | \(0.397322\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −21.1198 | −1.22757 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 14.7111 | 0.852189 | ||||||||
\(299\) | 1.24962 | 0.0722674 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.31854 | 0.0759991 | ||||||||
\(302\) | −15.3882 | −0.885490 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −21.1646 | −1.21387 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.8956 | −0.964281 | −0.482141 | − | 0.876094i | \(-0.660141\pi\) | ||||
−0.482141 | + | 0.876094i | \(0.660141\pi\) | |||||||
\(308\) | −0.0986347 | −0.00562023 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.6643 | 0.604717 | 0.302359 | − | 0.953194i | \(-0.402226\pi\) | ||||
0.302359 | + | 0.953194i | \(0.402226\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.8702 | 0.783991 | 0.391995 | − | 0.919967i | \(-0.371785\pi\) | ||||
0.391995 | + | 0.919967i | \(0.371785\pi\) | |||||||
\(314\) | −23.0119 | −1.29864 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.268267 | −0.0150912 | ||||||||
\(317\) | 1.33953 | 0.0752355 | 0.0376178 | − | 0.999292i | \(-0.488023\pi\) | ||||
0.0376178 | + | 0.999292i | \(0.488023\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.474782 | 0.0265827 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −5.27390 | −0.293903 | ||||||||
\(323\) | −17.2482 | −0.959718 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −10.5501 | −0.584317 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −35.3797 | −1.95352 | ||||||||
\(329\) | −3.77265 | −0.207993 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.00072 | −0.164934 | −0.0824672 | − | 0.996594i | \(-0.526280\pi\) | ||||
−0.0824672 | + | 0.996594i | \(0.526280\pi\) | |||||||
\(332\) | −2.54304 | −0.139567 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.79685 | −0.153037 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −24.2763 | −1.32241 | −0.661207 | − | 0.750203i | \(-0.729956\pi\) | ||||
−0.661207 | + | 0.750203i | \(0.729956\pi\) | |||||||
\(338\) | 17.3915 | 0.945971 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.13277 | −0.115496 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.7288 | −0.849274 | ||||||||
\(344\) | 3.04479 | 0.164164 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.707540 | −0.0380376 | ||||||||
\(347\) | 14.0792 | 0.755809 | 0.377904 | − | 0.925845i | \(-0.376645\pi\) | ||||
0.377904 | + | 0.925845i | \(0.376645\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.9641 | −0.961597 | −0.480798 | − | 0.876831i | \(-0.659653\pi\) | ||||
−0.480798 | + | 0.876831i | \(0.659653\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.438313 | −0.0233622 | ||||||||
\(353\) | 9.49061 | 0.505134 | 0.252567 | − | 0.967579i | \(-0.418725\pi\) | ||||
0.252567 | + | 0.967579i | \(0.418725\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2.19538 | 0.116355 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 14.2024 | 0.750620 | ||||||||
\(359\) | 4.09130 | 0.215931 | 0.107965 | − | 0.994155i | \(-0.465566\pi\) | ||||
0.107965 | + | 0.994155i | \(0.465566\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.6969 | 0.773523 | ||||||||
\(362\) | −16.6307 | −0.874088 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.0846954 | −0.00443925 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −18.8383 | −0.983351 | −0.491676 | − | 0.870778i | \(-0.663615\pi\) | ||||
−0.491676 | + | 0.870778i | \(0.663615\pi\) | |||||||
\(368\) | −11.1755 | −0.582565 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9.99498 | −0.518914 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.23999 | −0.374872 | −0.187436 | − | 0.982277i | \(-0.560018\pi\) | ||||
−0.187436 | + | 0.982277i | \(0.560018\pi\) | |||||||
\(374\) | 1.91172 | 0.0988529 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −8.71188 | −0.449281 | ||||||||
\(377\) | 0.407685 | 0.0209968 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.2420 | 1.03976 | 0.519881 | − | 0.854239i | \(-0.325976\pi\) | ||||
0.519881 | + | 0.854239i | \(0.325976\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 13.1377 | 0.672183 | ||||||||
\(383\) | −4.34201 | −0.221866 | −0.110933 | − | 0.993828i | \(-0.535384\pi\) | ||||
−0.110933 | + | 0.993828i | \(0.535384\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −15.0225 | −0.764626 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.16290 | 0.0590375 | ||||||||
\(389\) | 0.508687 | 0.0257915 | 0.0128957 | − | 0.999917i | \(-0.495895\pi\) | ||||
0.0128957 | + | 0.999917i | \(0.495895\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.10757 | −0.460590 | ||||||||
\(392\) | −15.7972 | −0.797881 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.71611 | −0.136835 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −31.2135 | −1.56656 | −0.783280 | − | 0.621669i | \(-0.786455\pi\) | ||||
−0.783280 | + | 0.621669i | \(0.786455\pi\) | |||||||
\(398\) | 24.5509 | 1.23063 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.60957 | 0.280129 | 0.140064 | − | 0.990142i | \(-0.455269\pi\) | ||||
0.140064 | + | 0.990142i | \(0.455269\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.83136 | −0.0912267 | ||||||||
\(404\) | 0.766452 | 0.0381324 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.72060 | −0.0853917 | ||||||||
\(407\) | −3.41997 | −0.169522 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.68080 | −0.478685 | −0.239342 | − | 0.970935i | \(-0.576932\pi\) | ||||
−0.239342 | + | 0.970935i | \(0.576932\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2.53907 | −0.125091 | ||||||||
\(413\) | 5.66143 | 0.278581 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.376370 | −0.0184530 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3.73483 | −0.182677 | ||||||||
\(419\) | 18.2788 | 0.892979 | 0.446489 | − | 0.894789i | \(-0.352674\pi\) | ||||
0.446489 | + | 0.894789i | \(0.352674\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.0517 | 1.26968 | 0.634842 | − | 0.772642i | \(-0.281065\pi\) | ||||
0.634842 | + | 0.772642i | \(0.281065\pi\) | |||||||
\(422\) | −25.0467 | −1.21925 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −23.0806 | −1.12089 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.17890 | −0.105444 | ||||||||
\(428\) | 0.110625 | 0.00534727 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.19278 | −0.298296 | −0.149148 | − | 0.988815i | \(-0.547653\pi\) | ||||
−0.149148 | + | 0.988815i | \(0.547653\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −35.1538 | −1.68938 | −0.844692 | − | 0.535253i | \(-0.820216\pi\) | ||||
−0.844692 | + | 0.535253i | \(0.820216\pi\) | |||||||
\(434\) | 7.72909 | 0.371008 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.21854 | 0.0583574 | ||||||||
\(437\) | 17.7930 | 0.851153 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −20.1018 | −0.959408 | −0.479704 | − | 0.877430i | \(-0.659256\pi\) | ||||
−0.479704 | + | 0.877430i | \(0.659256\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.64156 | 0.0780808 | ||||||||
\(443\) | −20.8513 | −0.990676 | −0.495338 | − | 0.868700i | \(-0.664956\pi\) | ||||
−0.495338 | + | 0.868700i | \(0.664956\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −29.3014 | −1.38746 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 10.8470 | 0.512471 | ||||||||
\(449\) | −39.5199 | −1.86506 | −0.932529 | − | 0.361094i | \(-0.882403\pi\) | ||||
−0.932529 | + | 0.361094i | \(0.882403\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.72910 | −0.269773 | ||||||||
\(452\) | 2.30733 | 0.108528 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 26.5092 | 1.24414 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −25.6115 | −1.19806 | −0.599028 | − | 0.800728i | \(-0.704446\pi\) | ||||
−0.599028 | + | 0.800728i | \(0.704446\pi\) | |||||||
\(458\) | −14.6054 | −0.682465 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.911675 | 0.0424609 | 0.0212305 | − | 0.999775i | \(-0.493242\pi\) | ||||
0.0212305 | + | 0.999775i | \(0.493242\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −25.9744 | −1.20713 | −0.603567 | − | 0.797312i | \(-0.706254\pi\) | ||||
−0.603567 | + | 0.797312i | \(0.706254\pi\) | |||||||
\(464\) | −3.64599 | −0.169261 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5.76231 | −0.266934 | ||||||||
\(467\) | 15.8506 | 0.733479 | 0.366739 | − | 0.930324i | \(-0.380474\pi\) | ||||
0.366739 | + | 0.930324i | \(0.380474\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 20.0299 | 0.924893 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 13.0735 | 0.601756 | ||||||||
\(473\) | 0.493048 | 0.0226704 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.617284 | 0.0282932 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 22.8184 | 1.04369 | ||||||||
\(479\) | −16.3087 | −0.745162 | −0.372581 | − | 0.928000i | \(-0.621527\pi\) | ||||
−0.372581 | + | 0.928000i | \(0.621527\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.93666 | −0.133900 | ||||||||
\(482\) | −29.5955 | −1.34804 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.76294 | 0.0801338 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.93950 | −0.450402 | −0.225201 | − | 0.974312i | \(-0.572304\pi\) | ||||
−0.225201 | + | 0.974312i | \(0.572304\pi\) | |||||||
\(488\) | −5.03155 | −0.227767 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −38.0638 | −1.71779 | −0.858897 | − | 0.512149i | \(-0.828850\pi\) | ||||
−0.858897 | + | 0.512149i | \(0.828850\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.97132 | −0.133822 | ||||||||
\(494\) | −3.20702 | −0.144290 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 16.3781 | 0.735401 | ||||||||
\(497\) | −11.4374 | −0.513039 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 44.3795 | 1.98670 | 0.993349 | − | 0.115143i | \(-0.0367327\pi\) | ||||
0.993349 | + | 0.115143i | \(0.0367327\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3.03908 | 0.135641 | ||||||||
\(503\) | 3.18073 | 0.141822 | 0.0709108 | − | 0.997483i | \(-0.477409\pi\) | ||||
0.0709108 | + | 0.997483i | \(0.477409\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.97210 | −0.0876705 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.88995 | 0.0838532 | ||||||||
\(509\) | −30.5882 | −1.35580 | −0.677899 | − | 0.735155i | \(-0.737109\pi\) | ||||
−0.677899 | + | 0.735155i | \(0.737109\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.860836 | 0.0380811 | ||||||||
\(512\) | 24.7459 | 1.09363 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.73030 | 0.0763203 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.41073 | −0.0620439 | ||||||||
\(518\) | 12.3939 | 0.544555 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −28.7858 | −1.26113 | −0.630564 | − | 0.776138i | \(-0.717176\pi\) | ||||
−0.630564 | + | 0.776138i | \(0.717176\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −27.2018 | −1.18945 | −0.594726 | − | 0.803928i | \(-0.702739\pi\) | ||||
−0.594726 | + | 0.803928i | \(0.702739\pi\) | |||||||
\(524\) | 1.67600 | 0.0732164 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −26.6645 | −1.16263 | ||||||||
\(527\) | 13.3475 | 0.581425 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.6048 | −0.591513 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.20595 | −0.0522847 | ||||||||
\(533\) | −4.91945 | −0.213085 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 46.2533 | 1.99784 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −15.9029 | −0.685623 | ||||||||
\(539\) | −2.55807 | −0.110184 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.84584 | 0.251332 | 0.125666 | − | 0.992073i | \(-0.459893\pi\) | ||||
0.125666 | + | 0.992073i | \(0.459893\pi\) | |||||||
\(542\) | 13.4476 | 0.577625 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.74309 | 0.117609 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.9324 | 0.809489 | 0.404745 | − | 0.914430i | \(-0.367360\pi\) | ||||
0.404745 | + | 0.914430i | \(0.367360\pi\) | |||||||
\(548\) | 0.338003 | 0.0144388 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.80491 | 0.247297 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.08174 | 0.0885247 | ||||||||
\(554\) | 2.04618 | 0.0869340 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.569787 | −0.0241643 | ||||||||
\(557\) | 29.6529 | 1.25643 | 0.628217 | − | 0.778038i | \(-0.283785\pi\) | ||||
0.628217 | + | 0.778038i | \(0.283785\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.423369 | 0.0179066 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 34.3235 | 1.44785 | ||||||||
\(563\) | −19.3966 | −0.817471 | −0.408736 | − | 0.912653i | \(-0.634030\pi\) | ||||
−0.408736 | + | 0.912653i | \(0.634030\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 2.83611 | 0.119211 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −26.4115 | −1.10820 | ||||||||
\(569\) | 6.00700 | 0.251826 | 0.125913 | − | 0.992041i | \(-0.459814\pi\) | ||||
0.125913 | + | 0.992041i | \(0.459814\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −28.1469 | −1.17791 | −0.588957 | − | 0.808165i | \(-0.700461\pi\) | ||||
−0.588957 | + | 0.808165i | \(0.700461\pi\) | |||||||
\(572\) | −0.0316706 | −0.00132422 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 20.7621 | 0.866592 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −32.9966 | −1.37367 | −0.686834 | − | 0.726815i | \(-0.741000\pi\) | ||||
−0.686834 | + | 0.726815i | \(0.741000\pi\) | |||||||
\(578\) | 11.0731 | 0.460581 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 19.7339 | 0.818700 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.73748 | −0.154791 | ||||||||
\(584\) | 1.98786 | 0.0822581 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −14.7066 | −0.607526 | ||||||||
\(587\) | 7.81241 | 0.322453 | 0.161226 | − | 0.986917i | \(-0.448455\pi\) | ||||
0.161226 | + | 0.986917i | \(0.448455\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −26.0762 | −1.07445 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 26.2629 | 1.07940 | ||||||||
\(593\) | −33.5131 | −1.37622 | −0.688108 | − | 0.725608i | \(-0.741559\pi\) | ||||
−0.688108 | + | 0.725608i | \(0.741559\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.77623 | 0.0727574 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.69340 | −0.0692482 | ||||||||
\(599\) | −27.1213 | −1.10815 | −0.554074 | − | 0.832468i | \(-0.686927\pi\) | ||||
−0.554074 | + | 0.832468i | \(0.686927\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17.4641 | −0.712376 | −0.356188 | − | 0.934414i | \(-0.615924\pi\) | ||||
−0.356188 | + | 0.934414i | \(0.615924\pi\) | |||||||
\(602\) | −1.78679 | −0.0728240 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.85799 | −0.0756006 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 32.9273 | 1.33648 | 0.668239 | − | 0.743947i | \(-0.267049\pi\) | ||||
0.668239 | + | 0.743947i | \(0.267049\pi\) | |||||||
\(608\) | −5.35902 | −0.217337 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.21136 | −0.0490065 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.97228 | 0.120049 | 0.0600245 | − | 0.998197i | \(-0.480882\pi\) | ||||
0.0600245 | + | 0.998197i | \(0.480882\pi\) | |||||||
\(614\) | 22.8957 | 0.923996 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.76748 | 0.0712138 | ||||||||
\(617\) | −0.0642578 | −0.00258692 | −0.00129346 | − | 0.999999i | \(-0.500412\pi\) | ||||
−0.00129346 | + | 0.999999i | \(0.500412\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.45588 | 0.299677 | 0.149839 | − | 0.988710i | \(-0.452125\pi\) | ||||
0.149839 | + | 0.988710i | \(0.452125\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −14.4515 | −0.579454 | ||||||||
\(623\) | −17.0360 | −0.682535 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −18.7960 | −0.751237 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.77849 | −0.110874 | ||||||||
\(629\) | 21.4032 | 0.853400 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −38.0735 | −1.51568 | −0.757841 | − | 0.652439i | \(-0.773746\pi\) | ||||
−0.757841 | + | 0.652439i | \(0.773746\pi\) | |||||||
\(632\) | 4.80720 | 0.191220 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.81524 | −0.0720924 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.19656 | −0.0870309 | ||||||||
\(638\) | −0.643392 | −0.0254721 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.49665 | 0.177607 | 0.0888035 | − | 0.996049i | \(-0.471696\pi\) | ||||
0.0888035 | + | 0.996049i | \(0.471696\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20.9607 | −0.826610 | −0.413305 | − | 0.910593i | \(-0.635626\pi\) | ||||
−0.413305 | + | 0.910593i | \(0.635626\pi\) | |||||||
\(644\) | −0.636778 | −0.0250926 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 23.3736 | 0.919623 | ||||||||
\(647\) | 37.8398 | 1.48764 | 0.743819 | − | 0.668381i | \(-0.233013\pi\) | ||||
0.743819 | + | 0.668381i | \(0.233013\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.11701 | 0.0831000 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.27384 | −0.0498873 | ||||||||
\(653\) | −48.0703 | −1.88114 | −0.940568 | − | 0.339606i | \(-0.889706\pi\) | ||||
−0.940568 | + | 0.339606i | \(0.889706\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 43.9954 | 1.71773 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 5.11244 | 0.199304 | ||||||||
\(659\) | −26.0861 | −1.01617 | −0.508084 | − | 0.861307i | \(-0.669646\pi\) | ||||
−0.508084 | + | 0.861307i | \(0.669646\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.00120 | 0.194524 | 0.0972620 | − | 0.995259i | \(-0.468992\pi\) | ||||
0.0972620 | + | 0.995259i | \(0.468992\pi\) | |||||||
\(662\) | 4.06636 | 0.158044 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 45.5699 | 1.76845 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.06516 | 0.118683 | ||||||||
\(668\) | −0.337695 | −0.0130658 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.814768 | −0.0314538 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 26.1113 | 1.00652 | 0.503258 | − | 0.864136i | \(-0.332134\pi\) | ||||
0.503258 | + | 0.864136i | \(0.332134\pi\) | |||||||
\(674\) | 32.8976 | 1.26717 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.09987 | 0.0807643 | ||||||||
\(677\) | −32.0992 | −1.23367 | −0.616836 | − | 0.787092i | \(-0.711586\pi\) | ||||
−0.616836 | + | 0.787092i | \(0.711586\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.02410 | −0.346313 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2.89018 | 0.110671 | ||||||||
\(683\) | 4.70468 | 0.180020 | 0.0900098 | − | 0.995941i | \(-0.471310\pi\) | ||||
0.0900098 | + | 0.995941i | \(0.471310\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 21.3145 | 0.813793 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3.78625 | −0.144349 | ||||||||
\(689\) | −3.20929 | −0.122264 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.881335 | 0.0335276 | 0.0167638 | − | 0.999859i | \(-0.494664\pi\) | ||||
0.0167638 | + | 0.999859i | \(0.494664\pi\) | |||||||
\(692\) | −0.0854295 | −0.00324754 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −19.0791 | −0.724233 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 35.8543 | 1.35808 | ||||||||
\(698\) | 24.3437 | 0.921423 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 45.1606 | 1.70569 | 0.852847 | − | 0.522161i | \(-0.174874\pi\) | ||||
0.852847 | + | 0.522161i | \(0.174874\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −41.8142 | −1.57705 | ||||||||
\(704\) | 4.05607 | 0.152869 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −12.8610 | −0.484031 | ||||||||
\(707\) | −5.94764 | −0.223684 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.8061 | 0.706277 | 0.353139 | − | 0.935571i | \(-0.385114\pi\) | ||||
0.353139 | + | 0.935571i | \(0.385114\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −39.3399 | −1.47433 | ||||||||
\(713\) | −13.7690 | −0.515653 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.71482 | 0.0640857 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −5.54425 | −0.206910 | ||||||||
\(719\) | 18.7384 | 0.698824 | 0.349412 | − | 0.936969i | \(-0.386381\pi\) | ||||
0.349412 | + | 0.936969i | \(0.386381\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 19.7031 | 0.733782 | ||||||||
\(722\) | −19.9163 | −0.741207 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2.00801 | −0.0746271 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20.2155 | 0.749752 | 0.374876 | − | 0.927075i | \(-0.377685\pi\) | ||||
0.374876 | + | 0.927075i | \(0.377685\pi\) | |||||||
\(728\) | 1.51769 | 0.0562495 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.08563 | −0.114126 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −45.1963 | −1.66936 | −0.834682 | − | 0.550732i | \(-0.814349\pi\) | ||||
−0.834682 | + | 0.550732i | \(0.814349\pi\) | |||||||
\(734\) | 25.5284 | 0.942269 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.82972 | −0.104305 | ||||||||
\(737\) | 7.48988 | 0.275893 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 42.2473 | 1.55409 | 0.777046 | − | 0.629443i | \(-0.216717\pi\) | ||||
0.777046 | + | 0.629443i | \(0.216717\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 13.5445 | 0.497235 | ||||||||
\(743\) | 38.5919 | 1.41580 | 0.707900 | − | 0.706313i | \(-0.249643\pi\) | ||||
0.707900 | + | 0.706313i | \(0.249643\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 9.81113 | 0.359211 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.230825 | 0.00843978 | ||||||||
\(749\) | −0.858447 | −0.0313670 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.50634 | −0.0549670 | −0.0274835 | − | 0.999622i | \(-0.508749\pi\) | ||||
−0.0274835 | + | 0.999622i | \(0.508749\pi\) | |||||||
\(752\) | 10.8334 | 0.395053 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −0.552466 | −0.0201196 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17.3890 | −0.632016 | −0.316008 | − | 0.948757i | \(-0.602343\pi\) | ||||
−0.316008 | + | 0.948757i | \(0.602343\pi\) | |||||||
\(758\) | −27.4306 | −0.996324 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.21457 | −0.334028 | −0.167014 | − | 0.985955i | \(-0.553413\pi\) | ||||
−0.167014 | + | 0.985955i | \(0.553413\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.45581 | −0.342323 | ||||||||
\(764\) | 1.58626 | 0.0573890 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5.88399 | 0.212597 | ||||||||
\(767\) | 1.81783 | 0.0656381 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 25.6939 | 0.926547 | 0.463273 | − | 0.886215i | \(-0.346675\pi\) | ||||
0.463273 | + | 0.886215i | \(0.346675\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.81384 | −0.0652816 | ||||||||
\(773\) | 42.9070 | 1.54326 | 0.771628 | − | 0.636074i | \(-0.219443\pi\) | ||||
0.771628 | + | 0.636074i | \(0.219443\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −20.8386 | −0.748062 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −0.689338 | −0.0247140 | ||||||||
\(779\) | −70.0466 | −2.50968 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.27687 | −0.153038 | ||||||||
\(782\) | 12.3420 | 0.441347 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 19.6442 | 0.701578 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22.2120 | −0.791772 | −0.395886 | − | 0.918300i | \(-0.629562\pi\) | ||||
−0.395886 | + | 0.918300i | \(0.629562\pi\) | |||||||
\(788\) | −0.327947 | −0.0116826 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −17.9048 | −0.636622 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.699623 | −0.0248443 | ||||||||
\(794\) | 42.2984 | 1.50111 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.96431 | 0.105067 | ||||||||
\(797\) | −46.2386 | −1.63785 | −0.818927 | − | 0.573897i | \(-0.805431\pi\) | ||||
−0.818927 | + | 0.573897i | \(0.805431\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.82875 | 0.312339 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −7.60171 | −0.268426 | ||||||||
\(803\) | 0.321897 | 0.0113595 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.48174 | 0.0874154 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −13.7344 | −0.483175 | ||||||||
\(809\) | −23.9257 | −0.841184 | −0.420592 | − | 0.907250i | \(-0.638178\pi\) | ||||
−0.420592 | + | 0.907250i | \(0.638178\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −52.0210 | −1.82670 | −0.913352 | − | 0.407170i | \(-0.866516\pi\) | ||||
−0.913352 | + | 0.407170i | \(0.866516\pi\) | |||||||
\(812\) | −0.207747 | −0.00729050 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4.63451 | 0.162440 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.02823 | 0.210901 | ||||||||
\(818\) | 13.1188 | 0.458686 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.0444 | −0.525052 | −0.262526 | − | 0.964925i | \(-0.584556\pi\) | ||||
−0.262526 | + | 0.964925i | \(0.584556\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 44.8652 | 1.56390 | 0.781952 | − | 0.623339i | \(-0.214224\pi\) | ||||
0.781952 | + | 0.623339i | \(0.214224\pi\) | |||||||
\(824\) | 45.4987 | 1.58502 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.67198 | −0.266942 | ||||||||
\(827\) | −41.5569 | −1.44508 | −0.722538 | − | 0.691331i | \(-0.757025\pi\) | ||||
−0.722538 | + | 0.691331i | \(0.757025\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −25.3645 | −0.880946 | −0.440473 | − | 0.897766i | \(-0.645189\pi\) | ||||
−0.440473 | + | 0.897766i | \(0.645189\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.48286 | 0.120746 | ||||||||
\(833\) | 16.0092 | 0.554684 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −0.450949 | −0.0155964 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −24.7702 | −0.855672 | ||||||||
\(839\) | 3.34480 | 0.115475 | 0.0577376 | − | 0.998332i | \(-0.481611\pi\) | ||||
0.0577376 | + | 0.998332i | \(0.481611\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −35.3035 | −1.21664 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −3.02417 | −0.104096 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −13.6804 | −0.470063 | ||||||||
\(848\) | 28.7012 | 0.985603 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −22.0791 | −0.756862 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −45.8873 | −1.57115 | −0.785575 | − | 0.618766i | \(-0.787633\pi\) | ||||
−0.785575 | + | 0.618766i | \(0.787633\pi\) | |||||||
\(854\) | 2.95269 | 0.101039 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.98234 | −0.0677550 | ||||||||
\(857\) | 51.8755 | 1.77203 | 0.886017 | − | 0.463652i | \(-0.153461\pi\) | ||||
0.886017 | + | 0.463652i | \(0.153461\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 31.7698 | 1.08397 | 0.541987 | − | 0.840387i | \(-0.317672\pi\) | ||||
0.541987 | + | 0.840387i | \(0.317672\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 8.39203 | 0.285834 | ||||||||
\(863\) | 39.9472 | 1.35982 | 0.679909 | − | 0.733296i | \(-0.262019\pi\) | ||||
0.679909 | + | 0.733296i | \(0.262019\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 47.6380 | 1.61880 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0.933222 | 0.0316756 | ||||||||
\(869\) | 0.778438 | 0.0264067 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.43139 | 0.217920 | ||||||||
\(872\) | −21.8355 | −0.739444 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −24.1118 | −0.815594 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 44.8875 | 1.51574 | 0.757872 | − | 0.652403i | \(-0.226239\pi\) | ||||
0.757872 | + | 0.652403i | \(0.226239\pi\) | |||||||
\(878\) | 27.2406 | 0.919326 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.90189 | 0.131458 | 0.0657290 | − | 0.997838i | \(-0.479063\pi\) | ||||
0.0657290 | + | 0.997838i | \(0.479063\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −52.7256 | −1.77436 | −0.887178 | − | 0.461427i | \(-0.847338\pi\) | ||||
−0.887178 | + | 0.461427i | \(0.847338\pi\) | |||||||
\(884\) | 0.198204 | 0.00666632 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 28.2563 | 0.949288 | ||||||||
\(887\) | 20.7833 | 0.697834 | 0.348917 | − | 0.937154i | \(-0.386550\pi\) | ||||
0.348917 | + | 0.937154i | \(0.386550\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −14.6660 | −0.491881 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −3.53790 | −0.118458 | ||||||||
\(893\) | −17.2482 | −0.577190 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −12.3547 | −0.412743 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 53.5546 | 1.78714 | ||||||||
\(899\) | −4.49210 | −0.149820 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 23.3902 | 0.779241 | ||||||||
\(902\) | 7.76368 | 0.258502 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −41.3461 | −1.37515 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 26.2116 | 0.870342 | 0.435171 | − | 0.900348i | \(-0.356688\pi\) | ||||
0.435171 | + | 0.900348i | \(0.356688\pi\) | |||||||
\(908\) | 3.20076 | 0.106221 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −31.4264 | −1.04120 | −0.520601 | − | 0.853800i | \(-0.674292\pi\) | ||||
−0.520601 | + | 0.853800i | \(0.674292\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.37921 | 0.244216 | ||||||||
\(914\) | 34.7070 | 1.14800 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.76348 | −0.0582669 | ||||||||
\(917\) | −13.0057 | −0.429486 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −21.0083 | −0.693000 | −0.346500 | − | 0.938050i | \(-0.612630\pi\) | ||||
−0.346500 | + | 0.938050i | \(0.612630\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1.23544 | −0.0406870 | ||||||||
\(923\) | −3.67245 | −0.120880 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 35.1988 | 1.15670 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.923188 | −0.0303051 | ||||||||
\(929\) | −37.3920 | −1.22679 | −0.613395 | − | 0.789776i | \(-0.710197\pi\) | ||||
−0.613395 | + | 0.789776i | \(0.710197\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −31.2762 | −1.02504 | ||||||||
\(932\) | −0.695750 | −0.0227901 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −21.4796 | −0.702836 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 13.8377 | 0.452057 | 0.226029 | − | 0.974121i | \(-0.427426\pi\) | ||||
0.226029 | + | 0.974121i | \(0.427426\pi\) | |||||||
\(938\) | −27.1431 | −0.886253 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14.5708 | −0.474995 | −0.237497 | − | 0.971388i | \(-0.576327\pi\) | ||||
−0.237497 | + | 0.971388i | \(0.576327\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −36.9867 | −1.20445 | ||||||||
\(944\) | −16.2571 | −0.529125 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.668144 | −0.0217232 | ||||||||
\(947\) | 43.4267 | 1.41118 | 0.705589 | − | 0.708622i | \(-0.250683\pi\) | ||||
0.705589 | + | 0.708622i | \(0.250683\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.276406 | 0.00897252 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −11.0614 | −0.358501 | ||||||||
\(953\) | 51.0500 | 1.65367 | 0.826836 | − | 0.562442i | \(-0.190138\pi\) | ||||
0.826836 | + | 0.562442i | \(0.190138\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 2.75512 | 0.0891071 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 22.1004 | 0.714030 | ||||||||
\(959\) | −2.62289 | −0.0846976 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10.8210 | −0.349065 | ||||||||
\(962\) | 3.97955 | 0.128306 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −3.57340 | −0.115091 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −56.0658 | −1.80295 | −0.901477 | − | 0.432828i | \(-0.857516\pi\) | ||||
−0.901477 | + | 0.432828i | \(0.857516\pi\) | |||||||
\(968\) | −31.5910 | −1.01537 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 6.58898 | 0.211450 | 0.105725 | − | 0.994395i | \(-0.466284\pi\) | ||||
0.105725 | + | 0.994395i | \(0.466284\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.42152 | 0.141748 | ||||||||
\(974\) | 13.4693 | 0.431585 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.25683 | 0.200276 | ||||||||
\(977\) | 29.3327 | 0.938437 | 0.469218 | − | 0.883082i | \(-0.344536\pi\) | ||||
0.469218 | + | 0.883082i | \(0.344536\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.37039 | −0.203599 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 51.5814 | 1.64603 | ||||||||
\(983\) | 13.6719 | 0.436064 | 0.218032 | − | 0.975942i | \(-0.430036\pi\) | ||||
0.218032 | + | 0.975942i | \(0.430036\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 4.02653 | 0.128231 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.387220 | −0.0123191 | ||||||||
\(989\) | 3.18308 | 0.101216 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.7210 | 0.626459 | 0.313230 | − | 0.949677i | \(-0.398589\pi\) | ||||
0.313230 | + | 0.949677i | \(0.398589\pi\) | |||||||
\(992\) | 4.14705 | 0.131669 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 15.4992 | 0.491606 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −53.4618 | −1.69315 | −0.846576 | − | 0.532268i | \(-0.821340\pi\) | ||||
−0.846576 | + | 0.532268i | \(0.821340\pi\) | |||||||
\(998\) | −60.1400 | −1.90370 | ||||||||
\(999\) | 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 | 6525.2.a.ce.1.4 | 12 | ||
3.2 | odd | 2 | 6525.2.a.cf.1.9 | 12 | |||
5.2 | odd | 4 | 1305.2.c.k.784.4 | ✓ | 12 | ||
5.3 | odd | 4 | 1305.2.c.k.784.9 | yes | 12 | ||
5.4 | even | 2 | inner | 6525.2.a.ce.1.9 | 12 | ||
15.2 | even | 4 | 1305.2.c.l.784.9 | yes | 12 | ||
15.8 | even | 4 | 1305.2.c.l.784.4 | yes | 12 | ||
15.14 | odd | 2 | 6525.2.a.cf.1.4 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1305.2.c.k.784.4 | ✓ | 12 | 5.2 | odd | 4 | ||
1305.2.c.k.784.9 | yes | 12 | 5.3 | odd | 4 | ||
1305.2.c.l.784.4 | yes | 12 | 15.8 | even | 4 | ||
1305.2.c.l.784.9 | yes | 12 | 15.2 | even | 4 | ||
6525.2.a.ce.1.4 | 12 | 1.1 | even | 1 | trivial | ||
6525.2.a.ce.1.9 | 12 | 5.4 | even | 2 | inner | ||
6525.2.a.cf.1.4 | 12 | 15.14 | odd | 2 | |||
6525.2.a.cf.1.9 | 12 | 3.2 | odd | 2 |