Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2184,2,Mod(841,2184)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2184, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2184.841");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2184 = 2^{3} \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2184.bj (of order \(3\), degree \(2\), minimal) |
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: | no |
Analytic conductor: | \(17.4393278014\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.8248090761.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 7x^{6} - 2x^{5} + 41x^{4} - 7x^{3} + 57x^{2} + 8x + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 841.1 | ||
Root | \(-1.23409 + 2.13751i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2184.841 |
Dual form | 2184.2.bj.k.1849.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2184\mathbb{Z}\right)^\times\).
\(n\) | \(1093\) | \(1249\) | \(1457\) | \(1639\) | \(2017\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.46819 | −1.10381 | −0.551903 | − | 0.833908i | \(-0.686098\pi\) | ||||
−0.551903 | + | 0.833908i | \(0.686098\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.500000 | − | 0.866025i | −0.188982 | − | 0.327327i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.0102890 | − | 0.0178211i | 0.00310226 | − | 0.00537327i | −0.864470 | − | 0.502684i | \(-0.832346\pi\) |
0.867572 | + | 0.497311i | \(0.165679\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.0102890 | + | 3.60554i | −0.00285366 | + | 0.999996i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.23409 | + | 2.13751i | −0.318642 | + | 0.551903i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.198409 | − | 0.343655i | −0.0481213 | − | 0.0833485i | 0.840961 | − | 0.541095i | \(-0.181990\pi\) |
−0.889083 | + | 0.457746i | \(0.848657\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.96819 | + | 5.14105i | 0.680949 | + | 1.17944i | 0.974692 | + | 0.223553i | \(0.0717657\pi\) |
−0.293743 | + | 0.955884i | \(0.594901\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.93250 | − | 3.34719i | 0.402955 | − | 0.697938i | −0.591126 | − | 0.806579i | \(-0.701317\pi\) |
0.994081 | + | 0.108641i | \(0.0346499\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.09195 | 0.218389 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.01416 | − | 5.22068i | 0.559715 | − | 0.969456i | −0.437804 | − | 0.899070i | \(-0.644244\pi\) |
0.997520 | − | 0.0703854i | \(-0.0224229\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.22694 | −0.759181 | −0.379591 | − | 0.925155i | \(-0.623935\pi\) | ||||
−0.379591 | + | 0.925155i | \(0.623935\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.0102890 | − | 0.0178211i | −0.00179109 | − | 0.00310226i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.23409 | + | 2.13751i | 0.208600 | + | 0.361306i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.32604 | + | 9.22497i | −0.875596 | + | 1.51658i | −0.0194686 | + | 0.999810i | \(0.506197\pi\) |
−0.856127 | + | 0.516766i | \(0.827136\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.11734 | + | 1.81168i | 0.499174 | + | 0.290101i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.62062 | + | 4.53905i | −0.409273 | + | 0.708881i | −0.994808 | − | 0.101766i | \(-0.967551\pi\) |
0.585536 | + | 0.810646i | \(0.300884\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.15944 | + | 2.00822i | 0.176814 | + | 0.306250i | 0.940787 | − | 0.338997i | \(-0.110088\pi\) |
−0.763974 | + | 0.645247i | \(0.776754\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.23409 | + | 2.13751i | 0.183968 | + | 0.318642i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.1060 | 1.47411 | 0.737053 | − | 0.675835i | \(-0.236217\pi\) | ||||
0.737053 | + | 0.675835i | \(0.236217\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.500000 | + | 0.866025i | −0.0714286 | + | 0.123718i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.396818 | −0.0555657 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13.0566 | 1.79347 | 0.896734 | − | 0.442570i | \(-0.145933\pi\) | ||||
0.896734 | + | 0.442570i | \(0.145933\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.0253952 | + | 0.0439858i | −0.00342429 | + | 0.00593105i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.93637 | 0.786292 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.71958 | + | 11.6386i | 0.874814 | + | 1.51522i | 0.856960 | + | 0.515382i | \(0.172350\pi\) |
0.0178542 | + | 0.999841i | \(0.494317\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.06013 | − | 10.4965i | −0.775921 | − | 1.34393i | −0.934276 | − | 0.356552i | \(-0.883952\pi\) |
0.158355 | − | 0.987382i | \(-0.449381\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.500000 | + | 0.866025i | −0.0629941 | + | 0.109109i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.0253952 | − | 8.89914i | 0.00314989 | − | 1.10380i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.79036 | − | 8.29714i | 0.585235 | − | 1.01366i | −0.409611 | − | 0.912260i | \(-0.634336\pi\) |
0.994846 | − | 0.101397i | \(-0.0323311\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.93250 | − | 3.34719i | −0.232646 | − | 0.402955i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.79130 | + | 3.10263i | 0.212588 | + | 0.368214i | 0.952524 | − | 0.304464i | \(-0.0984773\pi\) |
−0.739935 | + | 0.672678i | \(0.765144\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.7029 | 1.72084 | 0.860420 | − | 0.509585i | \(-0.170201\pi\) | ||||
0.860420 | + | 0.509585i | \(0.170201\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.545973 | − | 0.945653i | 0.0630436 | − | 0.109195i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.0205780 | −0.00234509 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.50934 | 0.394832 | 0.197416 | − | 0.980320i | \(-0.436745\pi\) | ||||
0.197416 | + | 0.980320i | \(0.436745\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.0835 | 1.32634 | 0.663168 | − | 0.748471i | \(-0.269212\pi\) | ||||
0.663168 | + | 0.748471i | \(0.269212\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.489711 | + | 0.848204i | 0.0531166 | + | 0.0920007i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.01416 | − | 5.22068i | −0.323152 | − | 0.559715i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.81889 | − | 10.0786i | 0.616801 | − | 1.06833i | −0.373265 | − | 0.927725i | \(-0.621762\pi\) |
0.990066 | − | 0.140606i | \(-0.0449050\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.12763 | − | 1.79386i | 0.327865 | − | 0.188047i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.11347 | + | 3.66064i | −0.219157 | + | 0.379591i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −7.32604 | − | 12.6891i | −0.751636 | − | 1.30187i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.27679 | + | 9.13966i | 0.535776 | + | 0.927992i | 0.999125 | + | 0.0418160i | \(0.0133143\pi\) |
−0.463349 | + | 0.886176i | \(0.653352\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.0205780 | −0.00206817 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.13887 | − | 1.97257i | 0.113321 | − | 0.196278i | −0.803786 | − | 0.594918i | \(-0.797184\pi\) |
0.917107 | + | 0.398640i | \(0.130518\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −19.5454 | −1.92587 | −0.962933 | − | 0.269741i | \(-0.913062\pi\) | ||||
−0.962933 | + | 0.269741i | \(0.913062\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.46819 | 0.240870 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.59582 | + | 9.69224i | −0.540968 | + | 0.936984i | 0.457881 | + | 0.889014i | \(0.348609\pi\) |
−0.998849 | + | 0.0479706i | \(0.984725\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.03459 | 0.578009 | 0.289005 | − | 0.957328i | \(-0.406676\pi\) | ||||
0.289005 | + | 0.957328i | \(0.406676\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.32604 | + | 9.22497i | 0.505525 | + | 0.875596i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.22600 | + | 9.05169i | 0.491620 | + | 0.851511i | 0.999953 | − | 0.00964919i | \(-0.00307148\pi\) |
−0.508333 | + | 0.861160i | \(0.669738\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.76978 | + | 8.26150i | −0.444784 | + | 0.770389i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.12763 | − | 1.79386i | 0.289150 | − | 0.165842i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.198409 | + | 0.343655i | −0.0181881 | + | 0.0315028i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.49979 | + | 9.52591i | 0.499981 | + | 0.865992i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.62062 | + | 4.53905i | 0.236294 | + | 0.409273i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.64581 | 0.862747 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.79423 | + | 3.10769i | −0.159212 | + | 0.275763i | −0.934585 | − | 0.355741i | \(-0.884229\pi\) |
0.775373 | + | 0.631504i | \(0.217562\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.31889 | 0.204167 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.5473 | 1.18363 | 0.591816 | − | 0.806073i | \(-0.298411\pi\) | ||||
0.591816 | + | 0.806073i | \(0.298411\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.96819 | − | 5.14105i | 0.257374 | − | 0.445786i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.46819 | 0.212428 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.85691 | − | 11.8765i | −0.585825 | − | 1.01468i | −0.994772 | − | 0.102121i | \(-0.967437\pi\) |
0.408947 | − | 0.912558i | \(-0.365896\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.42499 | + | 16.3246i | 0.799418 | + | 1.38463i | 0.919996 | + | 0.391928i | \(0.128192\pi\) |
−0.120578 | + | 0.992704i | \(0.538475\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.05298 | − | 8.75202i | 0.425538 | − | 0.737053i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.0641488 | + | 0.0372808i | 0.00536439 | + | 0.00311758i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.43951 | + | 12.8856i | −0.617818 | + | 1.07009i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.500000 | + | 0.866025i | 0.0412393 | + | 0.0714286i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.04175 | − | 7.00051i | −0.331113 | − | 0.573504i | 0.651618 | − | 0.758548i | \(-0.274091\pi\) |
−0.982730 | + | 0.185044i | \(0.940757\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.26928 | −0.591565 | −0.295783 | − | 0.955255i | \(-0.595580\pi\) | ||||
−0.295783 | + | 0.955255i | \(0.595580\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.198409 | + | 0.343655i | −0.0160404 | + | 0.0277828i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.4329 | 0.837989 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.27802 | −0.261614 | −0.130807 | − | 0.991408i | \(-0.541757\pi\) | ||||
−0.130807 | + | 0.991408i | \(0.541757\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.52832 | − | 11.3074i | 0.517729 | − | 0.896734i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.86501 | −0.304605 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.2203 | − | 19.4341i | −0.878843 | − | 1.52220i | −0.852612 | − | 0.522544i | \(-0.824983\pi\) |
−0.0262304 | − | 0.999656i | \(-0.508350\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.0253952 | + | 0.0439858i | 0.00197702 | + | 0.00342429i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.53920 | + | 16.5224i | −0.738165 | + | 1.27854i | 0.215155 | + | 0.976580i | \(0.430974\pi\) |
−0.953321 | + | 0.301960i | \(0.902359\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9998 | − | 0.0741949i | −0.999984 | − | 0.00570730i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.96819 | − | 5.14105i | 0.226983 | − | 0.393146i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.64821 | − | 2.85478i | −0.125311 | − | 0.217045i | 0.796543 | − | 0.604581i | \(-0.206660\pi\) |
−0.921854 | + | 0.387536i | \(0.873326\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.545973 | − | 0.945653i | −0.0412717 | − | 0.0714847i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 13.4392 | 1.01015 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.70615 | + | 16.8115i | −0.725472 | + | 1.25655i | 0.233308 | + | 0.972403i | \(0.425045\pi\) |
−0.958780 | + | 0.284151i | \(0.908288\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.60129 | 0.416341 | 0.208170 | − | 0.978093i | \(-0.433249\pi\) | ||||
0.208170 | + | 0.978093i | \(0.433249\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −12.1203 | −0.895956 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 13.1457 | − | 22.7690i | 0.966488 | − | 1.67401i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.00816575 | −0.000597139 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.500000 | + | 0.866025i | 0.0363696 | + | 0.0629941i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.60705 | − | 6.24760i | −0.260997 | − | 0.452060i | 0.705510 | − | 0.708700i | \(-0.250718\pi\) |
−0.966507 | + | 0.256640i | \(0.917385\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.10552 | − | 3.64686i | 0.151558 | − | 0.262507i | −0.780242 | − | 0.625478i | \(-0.784904\pi\) |
0.931801 | + | 0.362971i | \(0.118238\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −7.69418 | − | 4.47156i | −0.550992 | − | 0.320215i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.87355 | − | 8.44124i | 0.347226 | − | 0.601413i | −0.638530 | − | 0.769597i | \(-0.720457\pi\) |
0.985756 | + | 0.168184i | \(0.0537903\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.61326 | + | 11.4545i | 0.468801 | + | 0.811988i | 0.999364 | − | 0.0356578i | \(-0.0113526\pi\) |
−0.530563 | + | 0.847646i | \(0.678019\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.79036 | − | 8.29714i | −0.337886 | − | 0.585235i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.02832 | −0.423105 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.46819 | − | 11.2032i | 0.451758 | − | 0.782467i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.86501 | −0.268636 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.122159 | 0.00844991 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.38011 | + | 5.85452i | −0.232696 | + | 0.403042i | −0.958601 | − | 0.284754i | \(-0.908088\pi\) |
0.725904 | + | 0.687796i | \(0.241422\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.58260 | 0.245476 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.86172 | − | 4.95665i | −0.195168 | − | 0.338041i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.11347 | + | 3.66064i | 0.143472 | + | 0.248500i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 7.35144 | − | 12.7331i | 0.496764 | − | 0.860420i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.24110 | − | 0.711836i | 0.0834855 | − | 0.0478833i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.2980 | + | 19.5686i | −0.756567 | + | 1.31041i | 0.188025 | + | 0.982164i | \(0.439792\pi\) |
−0.944592 | + | 0.328248i | \(0.893542\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.545973 | − | 0.945653i | −0.0363982 | − | 0.0630436i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.319834 | + | 0.553968i | 0.0212281 | + | 0.0367682i | 0.876444 | − | 0.481503i | \(-0.159909\pi\) |
−0.855216 | + | 0.518271i | \(0.826576\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.8587 | 1.04797 | 0.523987 | − | 0.851726i | \(-0.324444\pi\) | ||||
0.523987 | + | 0.851726i | \(0.324444\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.0102890 | + | 0.0178211i | −0.000676968 | + | 0.00117254i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −21.0504 | −1.37906 | −0.689528 | − | 0.724259i | \(-0.742182\pi\) | ||||
−0.689528 | + | 0.724259i | \(0.742182\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −24.9434 | −1.62713 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.75467 | − | 3.03918i | 0.113978 | − | 0.197416i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −19.5741 | −1.26615 | −0.633073 | − | 0.774092i | \(-0.718207\pi\) | ||||
−0.633073 | + | 0.774092i | \(0.718207\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.0576 | + | 26.0805i | 0.969944 | + | 1.67999i | 0.695699 | + | 0.718333i | \(0.255095\pi\) |
0.274245 | + | 0.961660i | \(0.411572\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.23409 | − | 2.13751i | 0.0788433 | − | 0.136561i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −18.5668 | + | 10.6490i | −1.18138 | + | 0.677580i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.04175 | − | 10.4646i | 0.382880 | − | 0.663168i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.30511 | + | 16.1169i | 0.587333 | + | 1.01729i | 0.994580 | + | 0.103973i | \(0.0331555\pi\) |
−0.407247 | + | 0.913318i | \(0.633511\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.0397671 | − | 0.0688787i | −0.00250014 | − | 0.00433037i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.979422 | 0.0613338 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 12.5322 | − | 21.7064i | 0.781737 | − | 1.35401i | −0.149193 | − | 0.988808i | \(-0.547667\pi\) |
0.930929 | − | 0.365199i | \(-0.118999\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.6521 | 0.661888 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.02832 | −0.373144 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.67689 | + | 4.63650i | −0.165064 | + | 0.285899i | −0.936678 | − | 0.350192i | \(-0.886116\pi\) |
0.771614 | + | 0.636091i | \(0.219450\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −32.2262 | −1.97964 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.81889 | − | 10.0786i | −0.356110 | − | 0.616801i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.31794 | − | 12.6750i | −0.446183 | − | 0.772811i | 0.551951 | − | 0.833877i | \(-0.313884\pi\) |
−0.998134 | + | 0.0610653i | \(0.980550\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.1173 | − | 17.5237i | 0.614585 | − | 1.06449i | −0.375872 | − | 0.926671i | \(-0.622657\pi\) |
0.990457 | − | 0.137821i | \(-0.0440097\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.0102890 | − | 3.60554i | 0.000622720 | − | 0.218217i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.0112351 | − | 0.0194597i | 0.000677500 | − | 0.00117346i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.31889 | + | 2.28438i | 0.0792443 | + | 0.137255i | 0.902924 | − | 0.429800i | \(-0.141416\pi\) |
−0.823680 | + | 0.567055i | \(0.808083\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.11347 | + | 3.66064i | 0.126530 | + | 0.219157i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.8933 | 1.12708 | 0.563541 | − | 0.826088i | \(-0.309439\pi\) | ||||
0.563541 | + | 0.826088i | \(0.309439\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.32991 | + | 5.76758i | −0.197943 | + | 0.342847i | −0.947861 | − | 0.318683i | \(-0.896759\pi\) |
0.749919 | + | 0.661530i | \(0.230093\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −14.6521 | −0.867914 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.24125 | 0.309381 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.42127 | − | 14.5861i | 0.495369 | − | 0.858004i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.5536 | 0.618661 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.54671 | − | 4.41103i | −0.148780 | − | 0.257695i | 0.781997 | − | 0.623283i | \(-0.214201\pi\) |
−0.930777 | + | 0.365588i | \(0.880868\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −16.5852 | − | 28.7264i | −0.965626 | − | 1.67251i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.0102890 | + | 0.0178211i | −0.000597030 | + | 0.00103409i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12.0485 | + | 7.00215i | 0.696785 | + | 0.404945i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.15944 | − | 2.00822i | 0.0668292 | − | 0.115752i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.13887 | − | 1.97257i | −0.0654261 | − | 0.113321i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 14.9575 | + | 25.9072i | 0.856466 | + | 1.48344i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.7484 | 1.18417 | 0.592087 | − | 0.805874i | \(-0.298304\pi\) | ||||
0.592087 | + | 0.805874i | \(0.298304\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.77270 | + | 16.9268i | −0.555950 | + | 0.962933i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −30.0151 | −1.70200 | −0.850999 | − | 0.525167i | \(-0.824003\pi\) | ||||
−0.850999 | + | 0.525167i | \(0.824003\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −28.9376 | −1.63565 | −0.817824 | − | 0.575469i | \(-0.804820\pi\) | ||||
−0.817824 | + | 0.575469i | \(0.804820\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.23409 | − | 2.13751i | 0.0695333 | − | 0.120435i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.39989 | 0.527950 | 0.263975 | − | 0.964529i | \(-0.414966\pi\) | ||||
0.263975 | + | 0.964529i | \(0.414966\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.0620255 | − | 0.107431i | −0.00347276 | − | 0.00601500i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.59582 | + | 9.69224i | 0.312328 | + | 0.540968i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.17783 | − | 2.04006i | 0.0655363 | − | 0.113512i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.0112351 | + | 3.93705i | −0.000623209 | + | 0.218388i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.01730 | − | 5.22611i | 0.166857 | − | 0.289005i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.05298 | − | 8.75202i | −0.278580 | − | 0.482514i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.2302 | + | 17.7193i | 0.562304 | + | 0.973939i | 0.997295 | + | 0.0735041i | \(0.0234182\pi\) |
−0.434991 | + | 0.900435i | \(0.643248\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 10.6521 | 0.583730 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.8235 | + | 20.4789i | −0.645986 | + | 1.11888i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.7032 | 0.800932 | 0.400466 | − | 0.916312i | \(-0.368848\pi\) | ||||
0.400466 | + | 0.916312i | \(0.368848\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 10.4520 | 0.567674 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.0434911 | + | 0.0753288i | −0.00235517 | + | 0.00407928i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.76978 | + | 8.26150i | 0.256796 | + | 0.444784i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −11.5029 | − | 19.9237i | −0.617509 | − | 1.06956i | −0.989939 | − | 0.141497i | \(-0.954808\pi\) |
0.372429 | − | 0.928061i | \(-0.378525\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.77752 | + | 6.54286i | −0.202206 | + | 0.350231i | −0.949239 | − | 0.314556i | \(-0.898144\pi\) |
0.747033 | + | 0.664787i | \(0.231478\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.0102890 | − | 3.60554i | 0.000549187 | − | 0.192449i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −16.7450 | + | 29.0031i | −0.891245 | + | 1.54368i | −0.0528607 | + | 0.998602i | \(0.516834\pi\) |
−0.838384 | + | 0.545080i | \(0.816499\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.42127 | − | 7.65786i | −0.234657 | − | 0.406437i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.198409 | + | 0.343655i | 0.0105009 | + | 0.0181881i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −12.1708 | −0.642349 | −0.321174 | − | 0.947020i | \(-0.604078\pi\) | ||||
−0.321174 | + | 0.947020i | \(0.604078\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.12027 | + | 14.0647i | −0.427382 | + | 0.740248i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.9996 | 0.577328 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −36.2894 | −1.89948 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.5272 | + | 18.2337i | −0.549517 | + | 0.951791i | 0.448791 | + | 0.893637i | \(0.351855\pi\) |
−0.998308 | + | 0.0581543i | \(0.981478\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.24125 | 0.272848 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.52832 | − | 11.3074i | −0.338934 | − | 0.587050i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.96272 | − | 8.59567i | −0.256960 | − | 0.445067i | 0.708466 | − | 0.705745i | \(-0.249387\pi\) |
−0.965426 | + | 0.260677i | \(0.916054\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.82290 | − | 8.35351i | 0.249054 | − | 0.431374i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 18.7923 | + | 10.9214i | 0.967854 | + | 0.562480i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.09195 | − | 1.89131i | 0.0560895 | − | 0.0971499i | −0.836617 | − | 0.547788i | \(-0.815470\pi\) |
0.892707 | + | 0.450638i | \(0.148803\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.79423 | + | 3.10769i | 0.0919210 | + | 0.159212i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 14.5982 | + | 25.2847i | 0.745931 | + | 1.29199i | 0.949759 | + | 0.312983i | \(0.101328\pi\) |
−0.203828 | + | 0.979007i | \(0.565338\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.0507905 | 0.00258852 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.15944 | − | 2.00822i | 0.0589378 | − | 0.102083i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10.4694 | 0.530818 | 0.265409 | − | 0.964136i | \(-0.414493\pi\) | ||||
0.265409 | + | 0.964136i | \(0.414493\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.53371 | −0.0775628 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.77365 | − | 11.7323i | 0.341685 | − | 0.591816i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8.66171 | −0.435818 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.87529 | + | 11.9084i | 0.345061 | + | 0.597663i | 0.985365 | − | 0.170458i | \(-0.0545248\pi\) |
−0.640304 | + | 0.768122i | \(0.721192\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.96819 | − | 5.14105i | −0.148595 | − | 0.257374i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.14602 | − | 7.18111i | 0.207042 | − | 0.358608i | −0.743739 | − | 0.668470i | \(-0.766950\pi\) |
0.950781 | + | 0.309862i | \(0.100283\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.0434911 | − | 15.2404i | 0.00216645 | − | 0.759178i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.23409 | − | 2.13751i | 0.0613226 | − | 0.106214i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.109599 | + | 0.189832i | 0.00543264 | + | 0.00940962i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.4156 | − | 23.2365i | −0.663358 | − | 1.14897i | −0.979728 | − | 0.200334i | \(-0.935797\pi\) |
0.316370 | − | 0.948636i | \(-0.397536\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −13.7138 | −0.676453 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.71958 | − | 11.6386i | 0.330649 | − | 0.572700i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −29.8243 | −1.46402 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 18.8500 | 0.923088 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.603772 | + | 1.04576i | −0.0294962 | + | 0.0510889i | −0.880397 | − | 0.474238i | \(-0.842724\pi\) |
0.850901 | + | 0.525327i | \(0.176057\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.20447 | −0.0587023 | −0.0293512 | − | 0.999569i | \(-0.509344\pi\) | ||||
−0.0293512 | + | 0.999569i | \(0.509344\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.05298 | − | 8.75202i | −0.245684 | − | 0.425538i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.216652 | − | 0.375253i | −0.0105092 | − | 0.0182024i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.06013 | + | 10.4965i | −0.293270 | + | 0.507959i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.0643605 | − | 0.0369141i | 0.00310736 | − | 0.00178223i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.50373 | + | 14.7289i | −0.409610 | + | 0.709466i | −0.994846 | − | 0.101398i | \(-0.967669\pi\) |
0.585236 | + | 0.810863i | \(0.301002\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.92828 | + | 6.80397i | 0.188781 | + | 0.326978i | 0.944844 | − | 0.327521i | \(-0.106213\pi\) |
−0.756063 | + | 0.654499i | \(0.772880\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.43951 | + | 12.8856i | 0.356697 | + | 0.617818i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 22.9441 | 1.09757 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.627041 | + | 1.08607i | −0.0299270 | + | 0.0518351i | −0.880601 | − | 0.473858i | \(-0.842861\pi\) |
0.850674 | + | 0.525694i | \(0.176194\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 19.0155 | 0.903453 | 0.451726 | − | 0.892156i | \(-0.350808\pi\) | ||||
0.451726 | + | 0.892156i | \(0.350808\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.3621 | + | 24.8759i | −0.680829 | + | 1.17923i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −8.08349 | −0.382336 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.7325 | − | 18.5892i | −0.506498 | − | 0.877280i | −0.999972 | − | 0.00751916i | \(-0.997607\pi\) |
0.493474 | − | 0.869761i | \(-0.335727\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.0539273 | + | 0.0934048i | 0.00253934 | + | 0.00439826i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.63464 | + | 6.29538i | −0.170770 | + | 0.295783i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −7.71958 | + | 4.42758i | −0.361899 | + | 0.207568i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.98329 | + | 17.2916i | −0.466999 | + | 0.808866i | −0.999289 | − | 0.0376962i | \(-0.987998\pi\) |
0.532290 | + | 0.846562i | \(0.321331\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.198409 | + | 0.343655i | 0.00926095 | + | 0.0160404i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.354716 | + | 0.614387i | 0.0165208 | + | 0.0286148i | 0.874168 | − | 0.485624i | \(-0.161408\pi\) |
−0.857647 | + | 0.514239i | \(0.828074\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.94803 | 0.137007 | 0.0685033 | − | 0.997651i | \(-0.478178\pi\) | ||||
0.0685033 | + | 0.997651i | \(0.478178\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5.21644 | − | 9.03514i | 0.241907 | − | 0.418995i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −7.02903 | −0.325265 | −0.162632 | − | 0.986687i | \(-0.551998\pi\) | ||||
−0.162632 | + | 0.986687i | \(0.551998\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.58071 | −0.442396 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.63901 | + | 2.83885i | −0.0755216 | + | 0.130807i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.0477182 | 0.00219408 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.24110 | + | 5.61375i | 0.148712 | + | 0.257577i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.52832 | − | 11.3074i | −0.298911 | − | 0.517729i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12.5244 | − | 21.6930i | 0.572257 | − | 0.991178i | −0.424077 | − | 0.905626i | \(-0.639401\pi\) |
0.996334 | − | 0.0855516i | \(-0.0272652\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −33.2062 | − | 19.2981i | −1.51407 | − | 0.879920i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.93250 | + | 3.34719i | −0.0879319 | + | 0.152303i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −13.0241 | − | 22.5584i | −0.591394 | − | 1.02432i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.9409 | + | 25.8784i | 0.677037 | + | 1.17266i | 0.975869 | + | 0.218356i | \(0.0700695\pi\) |
−0.298832 | + | 0.954306i | \(0.596597\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −22.4406 | −1.01480 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.44244 | − | 14.6227i | 0.381002 | − | 0.659914i | −0.610204 | − | 0.792244i | \(-0.708913\pi\) |
0.991206 | + | 0.132330i | \(0.0422458\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.39215 | −0.107737 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.0507905 | 0.00228286 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.79130 | − | 3.10263i | 0.0803509 | − | 0.139172i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −22.5420 | −1.00912 | −0.504560 | − | 0.863376i | \(-0.668345\pi\) | ||||
−0.504560 | + | 0.863376i | \(0.668345\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9.53920 | + | 16.5224i | 0.426180 | + | 0.738165i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −10.8603 | − | 18.8105i | −0.484235 | − | 0.838720i | 0.515601 | − | 0.856829i | \(-0.327569\pi\) |
−0.999836 | + | 0.0181087i | \(0.994236\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.81093 | + | 4.86868i | −0.125085 | + | 0.216653i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.56415 | + | 11.2210i | −0.291524 | + | 0.498344i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.57297 | + | 4.45651i | −0.114045 | + | 0.197531i | −0.917398 | − | 0.397972i | \(-0.869714\pi\) |
0.803353 | + | 0.595504i | \(0.203047\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.35144 | − | 12.7331i | −0.325208 | − | 0.563277i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.96819 | − | 5.14105i | −0.131049 | − | 0.226983i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 48.2417 | 2.12578 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.103980 | − | 0.180099i | 0.00457306 | − | 0.00792077i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.29642 | −0.144697 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.7709 | −0.515692 | −0.257846 | − | 0.966186i | \(-0.583013\pi\) | ||||
−0.257846 | + | 0.966186i | \(0.583013\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.13280 | − | 5.42618i | 0.136988 | − | 0.237270i | −0.789367 | − | 0.613921i | \(-0.789591\pi\) |
0.926355 | + | 0.376651i | \(0.122925\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.09195 | −0.0476565 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.838664 | + | 1.45261i | 0.0365328 | + | 0.0632766i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.03087 | + | 6.98167i | 0.175255 | + | 0.303551i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.71958 | − | 11.6386i | 0.291605 | − | 0.505074i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −16.3388 | − | 9.49545i | −0.707710 | − | 0.411294i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13.8115 | − | 23.9223i | 0.597124 | − | 1.03425i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.70615 | + | 16.8115i | 0.418851 | + | 0.725472i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.0102890 | + | 0.0178211i | 0.000443180 | + | 0.000767609i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.93680 | 0.255243 | 0.127621 | − | 0.991823i | \(-0.459266\pi\) | ||||
0.127621 | + | 0.991823i | \(0.459266\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.80064 | − | 4.85086i | 0.120187 | − | 0.208170i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −14.8945 | −0.638011 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.11762 | −0.0905428 | −0.0452714 | − | 0.998975i | \(-0.514415\pi\) | ||||
−0.0452714 | + | 0.998975i | \(0.514415\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.06013 | + | 10.4965i | −0.258640 | + | 0.447978i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 35.7864 | 1.52455 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.75467 | − | 3.03918i | −0.0746162 | − | 0.129239i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −13.1457 | − | 22.7690i | −0.558002 | − | 0.966488i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −16.6394 | + | 28.8203i | −0.705034 | + | 1.22115i | 0.261646 | + | 0.965164i | \(0.415735\pi\) |
−0.966679 | + | 0.255990i | \(0.917599\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.25262 | + | 4.15975i | −0.306753 | + | 0.175939i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.00408287 | + | 0.00707174i | −0.000172379 | + | 0.000298569i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.25861 | − | 2.17998i | −0.0530441 | − | 0.0918751i | 0.838284 | − | 0.545234i | \(-0.183559\pi\) |
−0.891328 | + | 0.453359i | \(0.850226\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12.8987 | − | 22.3413i | −0.542654 | − | 0.939904i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.57684 | + | 7.92732i | −0.191871 | + | 0.332331i | −0.945870 | − | 0.324545i | \(-0.894789\pi\) |
0.753999 | + | 0.656875i | \(0.228122\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24.6436 | −1.03130 | −0.515652 | − | 0.856798i | \(-0.672450\pi\) | ||||
−0.515652 | + | 0.856798i | \(0.672450\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.21411 | −0.301374 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.11019 | − | 3.65496i | 0.0880010 | − | 0.152422i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 33.2384 | 1.38373 | 0.691865 | − | 0.722027i | \(-0.256789\pi\) | ||||
0.691865 | + | 0.722027i | \(0.256789\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.10552 | − | 3.64686i | −0.0875023 | − | 0.151558i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.04175 | − | 10.4646i | −0.250654 | − | 0.434145i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.134340 | − | 0.232684i | 0.00556380 | − | 0.00963678i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −7.71958 | + | 4.42758i | −0.319165 | + | 0.183058i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.45630 | + | 11.1826i | −0.266480 | + | 0.461557i | −0.967950 | − | 0.251142i | \(-0.919194\pi\) |
0.701470 | + | 0.712699i | \(0.252527\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12.5464 | − | 21.7309i | −0.516963 | − | 0.895407i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.87355 | − | 8.44124i | −0.200471 | − | 0.347226i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −27.6591 | −1.13582 | −0.567912 | − | 0.823089i | \(-0.692249\pi\) | ||||
−0.567912 | + | 0.823089i | \(0.692249\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.489711 | − | 0.848204i | 0.0200762 | − | 0.0347730i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 13.2265 | 0.541325 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18.6826 | 0.763350 | 0.381675 | − | 0.924297i | \(-0.375347\pi\) | ||||
0.381675 | + | 0.924297i | \(0.375347\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.93578 | − | 17.2093i | 0.405289 | − | 0.701981i | −0.589066 | − | 0.808085i | \(-0.700504\pi\) |
0.994355 | + | 0.106104i | \(0.0338375\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9.58071 | −0.390157 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −13.5745 | − | 23.5117i | −0.551882 | − | 0.955888i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.47739 | − | 7.75506i | −0.181731 | − | 0.314768i | 0.760739 | − | 0.649058i | \(-0.224837\pi\) |
−0.942470 | + | 0.334290i | \(0.891503\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.01416 | + | 5.22068i | −0.122140 | + | 0.211553i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.103980 | + | 36.4374i | −0.00420660 | + | 1.47410i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17.6795 | + | 30.6218i | −0.714069 | + | 1.23680i | 0.249248 | + | 0.968440i | \(0.419816\pi\) |
−0.963317 | + | 0.268364i | \(0.913517\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6.46819 | − | 11.2032i | −0.260822 | − | 0.451758i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14.1922 | − | 24.5817i | −0.571357 | − | 0.989620i | −0.996427 | − | 0.0844594i | \(-0.973084\pi\) |
0.425069 | − | 0.905161i | \(-0.360250\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.9301 | 0.519705 | 0.259852 | − | 0.965648i | \(-0.416326\pi\) | ||||
0.259852 | + | 0.965648i | \(0.416326\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.93250 | + | 3.34719i | −0.0775487 | + | 0.134318i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −11.6378 | −0.466258 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.2674 | −1.17070 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.0610795 | − | 0.105793i | 0.00243928 | − | 0.00422496i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.22694 | 0.168539 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.04911 | + | 7.01326i | 0.161193 | + | 0.279194i | 0.935297 | − | 0.353865i | \(-0.115133\pi\) |
−0.774104 | + | 0.633058i | \(0.781799\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.38011 | + | 5.85452i | 0.134347 | + | 0.232696i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.42849 | − | 7.67036i | 0.175739 | − | 0.304389i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.11734 | − | 1.81168i | −0.123514 | − | 0.0717813i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.79130 | − | 3.10263i | 0.0708628 | − | 0.122738i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.14543 | − | 8.91214i | −0.203232 | − | 0.352008i | 0.746336 | − | 0.665570i | \(-0.231811\pi\) |
−0.949568 | + | 0.313561i | \(0.898478\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.8506 | + | 36.1142i | 0.822266 | + | 1.42421i | 0.903991 | + | 0.427552i | \(0.140624\pi\) |
−0.0817247 | + | 0.996655i | \(0.526043\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.72345 | −0.225361 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17.3474 | − | 30.0465i | 0.681995 | − | 1.18125i | −0.292376 | − | 0.956303i | \(-0.594446\pi\) |
0.974371 | − | 0.224946i | \(-0.0722207\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.276552 | 0.0108556 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.22694 | 0.165667 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 13.4011 | − | 23.2113i | 0.524424 | − | 0.908330i | −0.475171 | − | 0.879893i | \(-0.657614\pi\) |
0.999596 | − | 0.0284362i | \(-0.00905276\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −33.4373 | −1.30650 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −7.35144 | − | 12.7331i | −0.286807 | − | 0.496764i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.25307 | + | 9.09859i | 0.204631 | + | 0.354431i | 0.950015 | − | 0.312204i | \(-0.101067\pi\) |
−0.745384 | + | 0.666635i | \(0.767734\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16.0557 | − | 27.8093i | 0.624494 | − | 1.08166i | −0.364144 | − | 0.931343i | \(-0.618639\pi\) |
0.988638 | − | 0.150313i | \(-0.0480282\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.00408287 | − | 1.43074i | 0.000158566 | − | 0.0555655i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7.32604 | + | 12.6891i | −0.284092 | + | 0.492061i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −11.6497 | − | 20.1780i | −0.451080 | − | 0.781293i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 11.2980 | + | 19.5686i | 0.436804 | + | 0.756567i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.249411 | −0.00962842 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.27030 | + | 14.3246i | −0.318797 | + | 0.552172i | −0.980237 | − | 0.197826i | \(-0.936612\pi\) |
0.661441 | + | 0.749998i | \(0.269945\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.09195 | −0.0420290 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −17.2129 | −0.661546 | −0.330773 | − | 0.943710i | \(-0.607310\pi\) | ||||
−0.330773 | + | 0.943710i | \(0.607310\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.27679 | − | 9.13966i | 0.202504 | − | 0.350748i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.639668 | 0.0245121 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −16.9957 | − | 29.4374i | −0.650323 | − | 1.12639i | −0.983045 | − | 0.183367i | \(-0.941300\pi\) |
0.332722 | − | 0.943025i | \(-0.392033\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 16.9241 | + | 29.3134i | 0.646638 | + | 1.12001i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.92937 | − | 13.7341i | 0.302524 | − | 0.523987i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.134340 | + | 47.0762i | −0.00511795 | + | 1.79346i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.99731 | − | 6.92354i | 0.152065 | − | 0.263384i | −0.779922 | − | 0.625877i | \(-0.784741\pi\) |
0.931986 | + | 0.362493i | \(0.118074\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.0102890 | + | 0.0178211i | 0.000390848 | + | 0.000676968i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −23.2626 | − | 40.2921i | −0.882403 | − | 1.52837i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.07982 | 0.0787789 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −10.5252 | + | 18.2302i | −0.398099 | + | 0.689528i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 28.6792 | 1.08320 | 0.541600 | − | 0.840637i | \(-0.317819\pi\) | ||||
0.541600 | + | 0.840637i | \(0.317819\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −63.2347 | −2.38494 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −12.4717 | + | 21.6016i | −0.469711 | + | 0.813564i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.27773 | −0.0856629 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.47987 | − | 11.2235i | −0.243357 | − | 0.421506i | 0.718312 | − | 0.695721i | \(-0.244915\pi\) |
−0.961668 | + | 0.274216i | \(0.911582\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.75467 | − | 3.03918i | −0.0658053 | − | 0.113978i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8.16858 | + | 14.1484i | −0.305916 | + | 0.529861i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.158331 | − | 0.0920160i | −0.00592125 | − | 0.00344120i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −9.78707 | + | 16.9517i | −0.365505 | + | 0.633073i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0.319690 | + | 0.553719i | 0.0119224 | + | 0.0206502i | 0.871925 | − | 0.489639i | \(-0.162872\pi\) |
−0.860003 | + | 0.510290i | \(0.829538\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.77270 | + | 16.9268i | 0.363954 | + | 0.630388i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 30.1152 | 1.12000 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.29130 | − | 5.70070i | 0.122236 | − | 0.211719i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26.2751 | 0.974491 | 0.487245 | − | 0.873265i | \(-0.338002\pi\) | ||||
0.487245 | + | 0.873265i | \(0.338002\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.460089 | − | 0.796897i | 0.0170170 | − | 0.0294743i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −47.9027 | −1.76933 | −0.884664 | − | 0.466230i | \(-0.845612\pi\) | ||||
−0.884664 | + | 0.466230i | \(0.845612\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.23409 | − | 2.13751i | −0.0455202 | − | 0.0788433i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.0985762 | − | 0.170739i | −0.00363110 | − | 0.00628925i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10.5703 | + | 18.3083i | −0.388834 | + | 0.673480i | −0.992293 | − | 0.123914i | \(-0.960455\pi\) |
0.603459 | + | 0.797394i | \(0.293789\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.0610795 | + | 21.4038i | −0.00224381 | + | 0.786289i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.51570 | − | 16.4817i | 0.349097 | − | 0.604654i | −0.636992 | − | 0.770870i | \(-0.719822\pi\) |
0.986089 | + | 0.166216i | \(0.0531550\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.97578 | + | 17.2786i | 0.365484 | + | 0.633038i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.04175 | − | 10.4646i | −0.221056 | − | 0.382880i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 11.1916 | 0.408933 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.6902 | − | 28.9082i | 0.609033 | − | 1.05488i | −0.382367 | − | 0.924011i | \(-0.624891\pi\) |
0.991400 | − | 0.130866i | \(-0.0417758\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 18.6102 | 0.678194 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 17.9419 | 0.652974 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16.1319 | − | 27.9412i | 0.586323 | − | 1.01554i | −0.408386 | − | 0.912809i | \(-0.633908\pi\) |
0.994709 | − | 0.102732i | \(-0.0327584\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.0795342 | −0.00288691 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13.9160 | − | 24.1033i | −0.504456 | − | 0.873743i | −0.999987 | − | 0.00515265i | \(-0.998360\pi\) |
0.495531 | − | 0.868590i | \(-0.334973\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.01730 | − | 5.22611i | −0.109233 | − | 0.189198i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.489711 | − | 0.848204i | 0.0177055 | − | 0.0306669i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −42.0327 | + | 24.1079i | −1.51771 | + | 0.870487i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −25.1346 | + | 43.5344i | −0.906376 | + | 1.56989i | −0.0873161 | + | 0.996181i | \(0.527829\pi\) |
−0.819060 | + | 0.573708i | \(0.805504\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12.5322 | − | 21.7064i | −0.451336 | − | 0.781737i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.11107 | − | 3.65648i | −0.0759298 | − | 0.131514i | 0.825560 | − | 0.564314i | \(-0.190859\pi\) |
−0.901490 | + | 0.432799i | \(0.857526\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.61559 | −0.165797 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5.32604 | − | 9.22497i | 0.191071 | − | 0.330944i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −31.1140 | −1.11477 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.0737230 | 0.00263802 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.01416 | + | 5.22068i | −0.107717 | + | 0.186572i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8.09077 | 0.288772 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.406309 | + | 0.703747i | 0.0144833 | + | 0.0250859i | 0.873176 | − | 0.487405i | \(-0.162056\pi\) |
−0.858693 | + | 0.512490i | \(0.828723\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.67689 | + | 4.63650i | 0.0952996 | + | 0.165064i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.22600 | − | 9.05169i | 0.185815 | − | 0.321841i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 37.9077 | − | 21.7420i | 1.34614 | − | 0.772082i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −16.1131 | + | 27.9087i | −0.571473 | + | 0.989821i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −8.87697 | − | 15.3754i | −0.314439 | − | 0.544624i | 0.664879 | − | 0.746951i | \(-0.268483\pi\) |
−0.979318 | + | 0.202327i | \(0.935150\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.00512 | − | 3.47296i | −0.0709359 | − | 0.122865i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −11.6378 | −0.411201 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.151278 | − | 0.262021i | 0.00533849 | − | 0.00924654i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.53956 | 0.336225 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −14.6359 | −0.515208 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 22.5266 | − | 39.0172i | 0.791992 | − | 1.37177i | −0.132740 | − | 0.991151i | \(-0.542377\pi\) |
0.924732 | − | 0.380620i | \(-0.124289\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 43.6533 | 1.53287 | 0.766437 | − | 0.642319i | \(-0.222028\pi\) | ||||
0.766437 | + | 0.642319i | \(0.222028\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −10.1173 | − | 17.5237i | −0.354831 | − | 0.614585i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 27.6938 | + | 47.9671i | 0.970072 | + | 1.68021i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.88289 | + | 11.9215i | −0.240802 | + | 0.417081i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.11734 | − | 1.81168i | −0.108929 | − | 0.0633052i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16.2308 | − | 28.1126i | 0.566460 | − | 0.981138i | −0.430452 | − | 0.902613i | \(-0.641646\pi\) |
0.996912 | − | 0.0785242i | \(-0.0250208\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.78861 | − | 4.83002i | −0.0972049 | − | 0.168364i | 0.813322 | − | 0.581814i | \(-0.197657\pi\) |
−0.910527 | + | 0.413450i | \(0.864324\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.0112351 | − | 0.0194597i | −0.000391155 | − | 0.000677500i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 36.9740 | 1.28571 | 0.642857 | − | 0.765986i | \(-0.277749\pi\) | ||||
0.642857 | + | 0.765986i | \(0.277749\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17.2708 | − | 29.9139i | 0.599840 | − | 1.03895i | −0.393004 | − | 0.919537i | \(-0.628564\pi\) |
0.992844 | − | 0.119417i | \(-0.0381025\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.63778 | 0.0915034 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.396818 | 0.0137489 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 23.5445 | − | 40.7803i | 0.814792 | − | 1.41126i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.22694 | 0.146104 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 13.1472 | + | 22.7716i | 0.453892 | + | 0.786163i | 0.998624 | − | 0.0524467i | \(-0.0167020\pi\) |
−0.544732 | + | 0.838610i | \(0.683369\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.67032 | − | 6.35719i | −0.126563 | − | 0.219213i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 9.44666 | − | 16.3621i | 0.325360 | − | 0.563541i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 32.0859 | + | 0.183127i | 1.10379 | + | 0.00629976i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.49979 | − | 9.52591i | 0.188975 | − | 0.327314i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.32991 | + | 5.76758i | 0.114282 | + | 0.197943i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 20.5852 | + | 35.6546i | 0.705651 | + | 1.22222i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −35.1534 | −1.20363 | −0.601815 | − | 0.798636i | \(-0.705556\pi\) | ||||
−0.601815 | + | 0.798636i | \(0.705556\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −7.32604 | + | 12.6891i | −0.250545 | + | 0.433957i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −16.8437 | −0.575370 | −0.287685 | − | 0.957725i | \(-0.592886\pi\) | ||||
−0.287685 | + | 0.957725i | \(0.592886\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 23.0292 | 0.785747 | 0.392873 | − | 0.919593i | \(-0.371481\pi\) | ||||
0.392873 | + | 0.919593i | \(0.371481\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.62062 | − | 4.53905i | 0.0893106 | − | 0.154690i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −0.585093 | −0.0199168 | −0.00995840 | − | 0.999950i | \(-0.503170\pi\) | ||||
−0.00995840 | + | 0.999950i | \(0.503170\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.06809 | + | 7.04613i | 0.138319 | + | 0.239576i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −8.42127 | − | 14.5861i | −0.286001 | − | 0.495369i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.0361077 | − | 0.0625404i | 0.00122487 | − | 0.00212154i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 29.8664 | + | 17.3572i | 1.01198 | + | 0.588125i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.27679 | − | 9.13966i | 0.178592 | − | 0.309331i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.82290 | − | 8.35351i | −0.163044 | − | 0.282400i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 12.6565 | + | 21.9218i | 0.427381 | + | 0.740246i | 0.996639 | − | 0.0819130i | \(-0.0261030\pi\) |
−0.569258 | + | 0.822159i | \(0.692770\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5.09342 | −0.171797 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20.0742 | − | 34.7696i | 0.676318 | − | 1.17142i | −0.299764 | − | 0.954013i | \(-0.596908\pi\) |
0.976082 | − | 0.217403i | \(-0.0697587\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 25.4319 | 0.855851 | 0.427925 | − | 0.903814i | \(-0.359245\pi\) | ||||
0.427925 | + | 0.903814i | \(0.359245\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −33.1703 | −1.11501 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.07451 | − | 8.78930i | 0.170385 | − | 0.295116i | −0.768169 | − | 0.640247i | \(-0.778832\pi\) |
0.938555 | + | 0.345131i | \(0.112165\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.58845 | 0.120353 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.0102890 | + | 0.0178211i | 0.000344695 | + | 0.000597030i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 29.9964 | + | 51.9553i | 1.00379 | + | 1.73862i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 23.9566 | − | 41.4940i | 0.800781 | − | 1.38699i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 12.0883 | − | 6.93327i | 0.403617 | − | 0.231495i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −12.7407 | + | 22.0675i | −0.424925 | + | 0.735992i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.59056 | − | 4.48698i | −0.0863040 | − | 0.149483i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.15944 | − | 2.00822i | −0.0385839 | − | 0.0668292i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −13.8250 | −0.459560 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.97185 | + | 10.3435i | −0.198292 | + | 0.343452i | −0.947975 | − | 0.318346i | \(-0.896873\pi\) |
0.749683 | + | 0.661797i | \(0.230206\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.27773 | −0.0755476 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 27.3764 | 0.907021 | 0.453511 | − | 0.891251i | \(-0.350171\pi\) | ||||
0.453511 | + | 0.891251i | \(0.350171\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.124327 | − | 0.215341i | 0.00411463 | − | 0.00712675i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 29.9151 | 0.988962 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.77365 | − | 11.7323i | −0.223686 | − | 0.387435i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24.4068 | + | 42.2737i | 0.805104 | + | 1.39448i | 0.916221 | + | 0.400674i | \(0.131224\pi\) |
−0.111116 | + | 0.993807i | \(0.535443\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.3742 | − | 17.9686i | 0.341842 | − | 0.592087i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −11.2051 | + | 6.42668i | −0.368819 | + | 0.211537i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.81575 | + | 10.0732i | −0.191221 | + | 0.331204i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 9.77270 | + | 16.9268i | 0.320978 | + | 0.555950i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 20.5528 | + | 35.5984i | 0.674314 | + | 1.16795i | 0.976669 | + | 0.214751i | \(0.0688941\pi\) |
−0.302354 | + | 0.953196i | \(0.597773\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.93637 | −0.194557 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −15.0075 | + | 25.9938i | −0.491324 | + | 0.850999i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.0201546 | 0.000659126 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26.7099 | 0.872574 | 0.436287 | − | 0.899807i | \(-0.356293\pi\) | ||||
0.436287 | + | 0.899807i | \(0.356293\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −14.4688 | + | 25.0607i | −0.472171 | + | 0.817824i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −59.7172 | −1.94673 | −0.973363 | − | 0.229270i | \(-0.926366\pi\) | ||||
−0.973363 | + | 0.229270i | \(0.926366\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.1287 | + | 17.5435i | 0.329837 | + | 0.571294i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.23409 | − | 2.13751i | −0.0401451 | − | 0.0695333i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 12.0956 | − | 20.9502i | 0.393054 | − | 0.680790i | −0.599796 | − | 0.800153i | \(-0.704752\pi\) |
0.992851 | + | 0.119363i | \(0.0380851\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.151278 | + | 53.0117i | −0.00491070 | + | 1.72083i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.69995 | − | 8.14054i | 0.152406 | − | 0.263975i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −21.6992 | − | 37.5842i | −0.702907 | − | 1.21747i | −0.967442 | − | 0.253095i | \(-0.918552\pi\) |
0.264534 | − | 0.964376i | \(-0.414782\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.90288 | + | 15.4202i | 0.288090 | + | 0.498987i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.124051 | −0.00401000 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.85691 | + | 11.8765i | −0.221421 | + | 0.383513i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.1330 | −0.423644 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 11.1916 | 0.360645 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −5.19681 | + | 9.00114i | −0.167291 | + | 0.289757i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 19.9001 | 0.639943 | 0.319972 | − | 0.947427i | \(-0.396327\pi\) | ||||
0.319972 | + | 0.947427i | \(0.396327\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.17783 | − | 2.04006i | −0.0378374 | − | 0.0655363i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 19.8960 | + | 34.4610i | 0.638494 | + | 1.10590i | 0.985763 | + | 0.168139i | \(0.0537758\pi\) |
−0.347269 | + | 0.937766i | \(0.612891\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.42499 | − | 16.3246i | 0.302151 | − | 0.523342i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.40397 | + | 1.97826i | 0.109014 | + | 0.0633549i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −14.7152 | + | 25.4875i | −0.470781 | + | 0.815416i | −0.999441 | − | 0.0334170i | \(-0.989361\pi\) |
0.528661 | + | 0.848833i | \(0.322694\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.119741 | − | 0.207398i | −0.00382695 | − | 0.00662847i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.01730 | − | 5.22611i | −0.0963349 | − | 0.166857i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −21.1327 | −0.674028 | −0.337014 | − | 0.941500i | \(-0.609417\pi\) | ||||
−0.337014 | + | 0.941500i | \(0.609417\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12.0288 | + | 20.8345i | −0.383270 | + | 0.663844i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −10.1060 | −0.321676 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.96251 | 0.284991 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21.5982 | − | 37.4092i | 0.686090 | − | 1.18834i | −0.287002 | − | 0.957930i | \(-0.592659\pi\) |
0.973093 | − | 0.230414i | \(-0.0740079\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 20.4604 | 0.649293 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −16.3228 | − | 28.2718i | −0.517466 | − | 0.896278i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14.5439 | + | 25.1907i | 0.460609 | + | 0.797798i | 0.998991 | − | 0.0449024i | \(-0.0142977\pi\) |
−0.538382 | + | 0.842701i | \(0.680964\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.32604 | − | 9.22497i | 0.168508 | − | 0.291865i |
(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 | 2184.2.bj.k.841.1 | ✓ | 8 | |
13.3 | even | 3 | inner | 2184.2.bj.k.1849.1 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2184.2.bj.k.841.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
2184.2.bj.k.1849.1 | yes | 8 | 13.3 | even | 3 | inner |