Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [228,2,Mod(25,228)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(228, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 0, 14]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("228.25");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 228 = 2^{2} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 228.q (of order \(9\), degree \(6\), 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: | \(1.82058916609\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{9})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} + 27 x^{10} + 309 x^{8} + 42 x^{7} + 2059 x^{6} + 1245 x^{5} + 8226 x^{4} + \cdots + 16129 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 73.2 | ||
Root | \(-0.629732 - 1.09073i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 228.73 |
Dual form | 228.2.q.b.25.2 |
$q$-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 \(\left(\mathbb{Z}/228\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(97\) | \(115\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{9}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 0.939693 | − | 0.342020i | 0.542532 | − | 0.197465i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.392352 | − | 2.22514i | 0.175465 | − | 0.995112i | −0.762141 | − | 0.647411i | \(-0.775852\pi\) |
0.937606 | − | 0.347700i | \(-0.113037\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.18351 | − | 3.78195i | −0.825289 | − | 1.42944i | −0.901699 | − | 0.432365i | \(-0.857679\pi\) |
0.0764099 | − | 0.997076i | \(-0.475654\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.766044 | − | 0.642788i | 0.255348 | − | 0.214263i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.08468 | + | 1.87871i | −0.327042 | + | 0.566454i | −0.981924 | − | 0.189278i | \(-0.939385\pi\) |
0.654881 | + | 0.755732i | \(0.272719\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.570168 | − | 0.207524i | −0.158136 | − | 0.0575568i | 0.261739 | − | 0.965139i | \(-0.415704\pi\) |
−0.419875 | + | 0.907582i | \(0.637926\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.392352 | − | 2.22514i | −0.101305 | − | 0.574528i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.25293 | + | 3.56863i | 1.03149 | + | 0.865521i | 0.991027 | − | 0.133660i | \(-0.0426731\pi\) |
0.0404605 | + | 0.999181i | \(0.487118\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.26937 | − | 0.878888i | 0.979462 | − | 0.201631i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.34533 | − | 2.80706i | −0.730011 | − | 0.612552i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.944939 | + | 5.35902i | 0.197033 | + | 1.11743i | 0.909493 | + | 0.415719i | \(0.136470\pi\) |
−0.712460 | + | 0.701713i | \(0.752419\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.0988321 | − | 0.0359720i | −0.0197664 | − | 0.00719439i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.500000 | − | 0.866025i | 0.0962250 | − | 0.166667i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.22757 | + | 1.03005i | −0.227954 | + | 0.191276i | −0.749610 | − | 0.661880i | \(-0.769759\pi\) |
0.521656 | + | 0.853156i | \(0.325314\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.37280 | − | 5.84187i | −0.605774 | − | 1.04923i | −0.991929 | − | 0.126797i | \(-0.959530\pi\) |
0.386155 | − | 0.922434i | \(-0.373803\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.376704 | + | 2.13640i | −0.0655758 | + | 0.371899i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −9.27206 | + | 3.37475i | −1.56726 | + | 0.570437i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.55866 | 1.07824 | 0.539118 | − | 0.842230i | \(-0.318758\pi\) | ||||
0.539118 | + | 0.842230i | \(0.318758\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.606760 | −0.0971593 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.77909 | − | 2.46739i | 1.05872 | − | 0.385341i | 0.246770 | − | 0.969074i | \(-0.420631\pi\) |
0.811946 | + | 0.583733i | \(0.198409\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.244654 | + | 1.38750i | −0.0373094 | + | 0.211592i | −0.997763 | − | 0.0668472i | \(-0.978706\pi\) |
0.960454 | + | 0.278439i | \(0.0898171\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.12973 | − | 1.95675i | −0.168410 | − | 0.291695i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.98289 | + | 6.69844i | −1.16442 | + | 0.977068i | −0.999957 | − | 0.00931405i | \(-0.997035\pi\) |
−0.164468 | + | 0.986382i | \(0.552591\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.03542 | + | 10.4537i | −0.862203 | + | 1.49338i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.21699 | + | 1.89883i | 0.730525 | + | 0.265889i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.95158 | + | 11.0680i | 0.268070 | + | 1.52030i | 0.760148 | + | 0.649750i | \(0.225126\pi\) |
−0.492078 | + | 0.870551i | \(0.663762\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.75482 | + | 3.15067i | 0.506300 | + | 0.424836i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.71130 | − | 2.28610i | 0.491574 | − | 0.302801i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.10210 | − | 4.28117i | −0.664237 | − | 0.557361i | 0.247116 | − | 0.968986i | \(-0.420517\pi\) |
−0.911354 | + | 0.411625i | \(0.864962\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.28393 | − | 7.28155i | −0.164391 | − | 0.932307i | −0.949690 | − | 0.313191i | \(-0.898602\pi\) |
0.785300 | − | 0.619116i | \(-0.212509\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.10365 | − | 1.49361i | −0.517012 | − | 0.188177i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.685476 | + | 1.18728i | −0.0850228 | + | 0.147264i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.37325 | + | 7.02599i | −1.02296 | + | 0.858361i | −0.989996 | − | 0.141095i | \(-0.954938\pi\) |
−0.0329593 | + | 0.999457i | \(0.510493\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.72084 | + | 4.71264i | 0.327551 | + | 0.567335i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.10032 | − | 11.9115i | 0.249263 | − | 1.41364i | −0.561119 | − | 0.827735i | \(-0.689629\pi\) |
0.810381 | − | 0.585903i | \(-0.199260\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.491424 | + | 0.178864i | −0.0575168 | + | 0.0209344i | −0.370618 | − | 0.928785i | \(-0.620854\pi\) |
0.313102 | + | 0.949720i | \(0.398632\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.105175 | −0.0121446 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 9.47360 | 1.07962 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.14536 | + | 3.32864i | −1.02893 | + | 0.374501i | −0.800675 | − | 0.599099i | \(-0.795525\pi\) |
−0.228259 | + | 0.973600i | \(0.573303\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.173648 | − | 0.984808i | 0.0192942 | − | 0.109423i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.51587 | + | 11.2858i | 0.715210 | + | 1.23878i | 0.962879 | + | 0.269935i | \(0.0870022\pi\) |
−0.247669 | + | 0.968845i | \(0.579664\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.60935 | − | 8.06320i | 1.04228 | − | 0.874577i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.801239 | + | 1.38779i | −0.0859019 | + | 0.148786i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.30653 | − | 1.56745i | −0.456491 | − | 0.166149i | 0.103532 | − | 0.994626i | \(-0.466986\pi\) |
−0.560023 | + | 0.828477i | \(0.689208\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.460121 | + | 2.60947i | 0.0482338 | + | 0.273547i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.16744 | − | 4.33599i | −0.535838 | − | 0.449622i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.280550 | − | 9.84478i | −0.0287839 | − | 1.01005i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.83934 | − | 6.57799i | −0.795964 | − | 0.667893i | 0.151250 | − | 0.988496i | \(-0.451670\pi\) |
−0.947214 | + | 0.320602i | \(0.896115\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.376704 | + | 2.13640i | 0.0378602 | + | 0.214716i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.4007 | + | 3.78553i | 1.03490 | + | 0.376674i | 0.802946 | − | 0.596051i | \(-0.203265\pi\) |
0.231958 | + | 0.972726i | \(0.425487\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.91284 | − | 13.7054i | 0.779675 | − | 1.35044i | −0.152454 | − | 0.988311i | \(-0.548718\pi\) |
0.932129 | − | 0.362126i | \(-0.117949\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −7.55865 | + | 6.34246i | −0.737649 | + | 0.618961i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.51903 | − | 9.55924i | −0.533545 | − | 0.924126i | −0.999232 | − | 0.0391771i | \(-0.987526\pi\) |
0.465688 | − | 0.884949i | \(-0.345807\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.42162 | + | 8.06239i | −0.136166 | + | 0.772236i | 0.837874 | + | 0.545863i | \(0.183798\pi\) |
−0.974041 | + | 0.226373i | \(0.927313\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.16312 | − | 2.24319i | 0.584978 | − | 0.212914i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.70632 | −0.536806 | −0.268403 | − | 0.963307i | \(-0.586496\pi\) | ||||
−0.268403 | + | 0.963307i | \(0.586496\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.2953 | 1.14654 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.570168 | + | 0.207524i | −0.0527120 | + | 0.0191856i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.21007 | − | 23.8765i | 0.385937 | − | 2.18876i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.14695 | + | 5.45068i | 0.286087 | + | 0.495517i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.52636 | − | 4.63717i | 0.498295 | − | 0.418120i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.52984 | − | 9.57796i | 0.494604 | − | 0.856679i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.97448 | + | 2.90247i | 0.707621 | + | 0.257553i | 0.670661 | − | 0.741764i | \(-0.266010\pi\) |
0.0369596 | + | 0.999317i | \(0.488233\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.244654 | + | 1.38750i | 0.0215406 | + | 0.122163i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.46262 | − | 1.22728i | −0.127789 | − | 0.107228i | 0.576653 | − | 0.816989i | \(-0.304358\pi\) |
−0.704442 | + | 0.709761i | \(0.748803\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −12.6461 | − | 14.2275i | −1.09656 | − | 1.23368i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.73085 | − | 1.45236i | −0.148968 | − | 0.124999i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.32243 | − | 18.8425i | −0.283855 | − | 1.60982i | −0.709348 | − | 0.704859i | \(-0.751010\pi\) |
0.425493 | − | 0.904962i | \(-0.360101\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.3658 | + | 4.86476i | 1.13367 | + | 0.412624i | 0.839625 | − | 0.543167i | \(-0.182775\pi\) |
0.294049 | + | 0.955790i | \(0.404997\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.21046 | + | 9.02479i | −0.438800 | + | 0.760024i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.00833 | − | 0.846086i | 0.0843204 | − | 0.0707533i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.81037 | + | 3.13566i | 0.150343 | + | 0.260402i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.09608 | + | 11.8875i | −0.172882 | + | 0.980461i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −11.3128 | + | 4.11754i | −0.926785 | + | 0.337322i | −0.760934 | − | 0.648829i | \(-0.775259\pi\) |
−0.165850 | + | 0.986151i | \(0.553037\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.7491 | 0.874747 | 0.437373 | − | 0.899280i | \(-0.355909\pi\) | ||||
0.437373 | + | 0.899280i | \(0.355909\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.55181 | 0.448837 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −14.3223 | + | 5.21288i | −1.15039 | + | 0.418709i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.85893 | + | 16.2138i | −0.228167 | + | 1.29400i | 0.628369 | + | 0.777915i | \(0.283723\pi\) |
−0.856537 | + | 0.516086i | \(0.827388\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.61935 | + | 9.73300i | 0.445644 | + | 0.771877i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 18.2042 | − | 15.2752i | 1.43469 | − | 1.20385i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.01313 | + | 12.1471i | −0.549311 | + | 0.951434i | 0.449011 | + | 0.893526i | \(0.351776\pi\) |
−0.998322 | + | 0.0579082i | \(0.981557\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.60597 | + | 1.67644i | 0.358574 | + | 0.130510i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.75423 | + | 15.6200i | 0.213129 | + | 1.20871i | 0.884124 | + | 0.467253i | \(0.154756\pi\) |
−0.670995 | + | 0.741462i | \(0.734133\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.67655 | − | 8.11959i | −0.744350 | − | 0.624584i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.70559 | − | 3.41757i | 0.206902 | − | 0.261348i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −12.9943 | − | 10.9035i | −0.987935 | − | 0.828976i | −0.00266719 | − | 0.999996i | \(-0.500849\pi\) |
−0.985267 | + | 0.171021i | \(0.945293\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.0797567 | + | 0.452323i | 0.00602904 | + | 0.0341924i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.25866 | − | 2.27797i | −0.470430 | − | 0.171222i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.87345 | + | 15.3693i | −0.663233 | + | 1.14875i | 0.316528 | + | 0.948583i | \(0.397483\pi\) |
−0.979761 | + | 0.200170i | \(0.935851\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.70433 | + | 8.14290i | −0.721317 | + | 0.605257i | −0.927749 | − | 0.373204i | \(-0.878259\pi\) |
0.206432 | + | 0.978461i | \(0.433815\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.69694 | − | 6.40329i | −0.273286 | − | 0.473344i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.57330 | − | 14.5939i | 0.189193 | − | 1.07297i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −11.3175 | + | 4.11923i | −0.827618 | + | 0.301228i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.36702 | −0.317654 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.89322 | 0.571133 | 0.285567 | − | 0.958359i | \(-0.407818\pi\) | ||||
0.285567 | + | 0.958359i | \(0.407818\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.110620 | + | 0.0402626i | −0.00796263 | + | 0.00289816i | −0.345998 | − | 0.938235i | \(-0.612460\pi\) |
0.338036 | + | 0.941133i | \(0.390238\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.238063 | + | 1.35012i | −0.0170481 | + | 0.0966844i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.62847 | + | 13.2129i | 0.543506 | + | 0.941380i | 0.998699 | + | 0.0509872i | \(0.0162368\pi\) |
−0.455193 | + | 0.890393i | \(0.650430\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.15407 | − | 1.80748i | 0.152698 | − | 0.128129i | −0.563238 | − | 0.826295i | \(-0.690445\pi\) |
0.715936 | + | 0.698166i | \(0.246000\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.46525 | + | 9.46609i | −0.385489 | + | 0.667687i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.57602 | + | 2.39348i | 0.461546 | + | 0.167989i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.83049 | − | 16.0525i | −0.197690 | − | 1.12115i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.16857 | + | 3.49785i | 0.289736 | + | 0.243117i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.97971 | + | 8.97424i | −0.206111 | + | 0.620761i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.330119 | + | 0.277003i | 0.0227263 | + | 0.0190696i | 0.654080 | − | 0.756425i | \(-0.273056\pi\) |
−0.631354 | + | 0.775495i | \(0.717500\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.10032 | − | 11.9115i | −0.143912 | − | 0.816165i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.99139 | + | 1.08878i | 0.204011 | + | 0.0742540i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −14.7291 | + | 25.5115i | −0.999876 | + | 1.73184i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.400612 | + | 0.336154i | −0.0270709 | + | 0.0227152i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.68431 | − | 2.91731i | −0.113299 | − | 0.196239i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.422205 | + | 2.39445i | −0.0282730 | + | 0.160344i | −0.995675 | − | 0.0928998i | \(-0.970386\pi\) |
0.967402 | + | 0.253244i | \(0.0814975\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.0988321 | + | 0.0359720i | −0.00658881 | + | 0.00239813i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.4942 | 0.762896 | 0.381448 | − | 0.924390i | \(-0.375425\pi\) | ||||
0.381448 | + | 0.924390i | \(0.375425\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.13121 | 0.339080 | 0.169540 | − | 0.985523i | \(-0.445772\pi\) | ||||
0.169540 | + | 0.985523i | \(0.445772\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.90227 | − | 3.24016i | 0.585727 | − | 0.213187i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.59200 | − | 9.02868i | 0.104295 | − | 0.591489i | −0.887204 | − | 0.461377i | \(-0.847355\pi\) |
0.991499 | − | 0.130111i | \(-0.0415335\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.7729 | + | 20.3912i | 0.767976 | + | 1.33017i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.45537 | + | 6.25580i | −0.484278 | + | 0.406358i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.22469 | + | 2.12123i | −0.0792188 | + | 0.137211i | −0.902913 | − | 0.429823i | \(-0.858576\pi\) |
0.823694 | + | 0.567034i | \(0.191909\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.21239 | − | 0.805242i | −0.142512 | − | 0.0518702i | 0.269779 | − | 0.962922i | \(-0.413049\pi\) |
−0.412292 | + | 0.911052i | \(0.635271\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.173648 | − | 0.984808i | −0.0111395 | − | 0.0631754i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 20.8928 | + | 17.5311i | 1.33479 | + | 1.12002i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.61665 | − | 0.384884i | −0.166493 | − | 0.0244896i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 9.98289 | + | 8.37664i | 0.632640 | + | 0.530848i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.28777 | + | 12.9746i | 0.144402 | + | 0.818947i | 0.967845 | + | 0.251547i | \(0.0809394\pi\) |
−0.823443 | + | 0.567400i | \(0.807949\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −11.0930 | − | 4.03753i | −0.697412 | − | 0.253837i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.27206 | − | 10.8635i | 0.392771 | − | 0.680300i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −14.9008 | + | 12.5033i | −0.929488 | + | 0.779933i | −0.975725 | − | 0.218998i | \(-0.929721\pi\) |
0.0462378 | + | 0.998930i | \(0.485277\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −14.3209 | − | 24.8045i | −0.889857 | − | 1.54128i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.278268 | + | 1.57813i | −0.0172243 | + | 0.0976840i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7.36433 | + | 2.68040i | −0.454104 | + | 0.165280i | −0.558938 | − | 0.829209i | \(-0.688791\pi\) |
0.104834 | + | 0.994490i | \(0.466569\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 25.3934 | 1.55991 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.58292 | −0.280470 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −15.7423 | + | 5.72974i | −0.959826 | + | 0.349348i | −0.773965 | − | 0.633228i | \(-0.781730\pi\) |
−0.185861 | + | 0.982576i | \(0.559507\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.70011 | − | 26.6557i | 0.285512 | − | 1.61922i | −0.417941 | − | 0.908474i | \(-0.637248\pi\) |
0.703453 | − | 0.710742i | \(-0.251641\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.32487 | + | 2.29473i | 0.0801845 | + | 0.138884i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.174782 | − | 0.146659i | 0.0105397 | − | 0.00884390i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.41553 | + | 4.18382i | −0.145135 | + | 0.251382i | −0.929423 | − | 0.369015i | \(-0.879695\pi\) |
0.784288 | + | 0.620397i | \(0.213028\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.33880 | − | 2.30713i | −0.379494 | − | 0.138124i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.86633 | − | 21.9270i | −0.230646 | − | 1.30806i | −0.851592 | − | 0.524205i | \(-0.824363\pi\) |
0.620946 | − | 0.783853i | \(-0.286749\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.31905 | + | 3.62411i | 0.256741 | + | 0.215431i | 0.762068 | − | 0.647497i | \(-0.224184\pi\) |
−0.505328 | + | 0.862927i | \(0.668628\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.63074 | − | 9.15511i | −0.215067 | − | 0.542302i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −24.1337 | − | 20.2506i | −1.42457 | − | 1.19536i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.40027 | + | 13.6126i | 0.141192 | + | 0.800741i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.61637 | − | 3.50007i | −0.563722 | − | 0.205178i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −11.6997 | + | 20.2646i | −0.683507 | + | 1.18387i | 0.290397 | + | 0.956906i | \(0.406213\pi\) |
−0.973904 | + | 0.226962i | \(0.927121\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.5280 | + | 9.67316i | −0.671187 | + | 0.563193i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.08468 | + | 1.87871i | 0.0629393 | + | 0.109014i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.573351 | − | 3.25164i | 0.0331577 | − | 0.188047i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.78166 | − | 2.10435i | 0.333249 | − | 0.121293i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 11.0682 | 0.635849 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −16.7062 | −0.956594 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 31.3120 | − | 11.3967i | 1.78707 | − | 0.650441i | 0.787663 | − | 0.616107i | \(-0.211291\pi\) |
0.999410 | − | 0.0343346i | \(-0.0109312\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.74810 | − | 15.5852i | 0.156334 | − | 0.886614i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.4338 | − | 21.5360i | −0.705057 | − | 1.22119i | −0.966671 | − | 0.256021i | \(-0.917588\pi\) |
0.261614 | − | 0.965172i | \(-0.415745\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.85375 | − | 6.59008i | 0.443920 | − | 0.372493i | −0.393254 | − | 0.919430i | \(-0.628651\pi\) |
0.837174 | + | 0.546937i | \(0.184206\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.93356 | + | 8.54517i | −0.277974 | + | 0.481466i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.14865 | − | 3.32983i | −0.513839 | − | 0.187022i | 0.0720689 | − | 0.997400i | \(-0.477040\pi\) |
−0.585908 | + | 0.810377i | \(0.699262\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.603660 | − | 3.42353i | −0.0337985 | − | 0.191681i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.45564 | − | 7.09513i | −0.471948 | − | 0.396011i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 21.2938 | + | 11.4980i | 1.18482 | + | 0.639765i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.0488858 | + | 0.0410201i | 0.00271170 | + | 0.00227539i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.42162 | + | 8.06239i | 0.0786155 | + | 0.445851i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 42.7639 | + | 15.5648i | 2.35765 | + | 0.858114i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.4709 | − | 21.6002i | 0.685460 | − | 1.18725i | −0.287832 | − | 0.957681i | \(-0.592934\pi\) |
0.973292 | − | 0.229571i | \(-0.0737322\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.02422 | − | 4.21582i | 0.275326 | − | 0.231026i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12.3485 | + | 21.3883i | 0.674673 | + | 1.16857i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.60846 | − | 14.7933i | 0.142092 | − | 0.805843i | −0.827564 | − | 0.561371i | \(-0.810274\pi\) |
0.969656 | − | 0.244472i | \(-0.0786147\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.36219 | + | 1.95168i | −0.291234 | + | 0.106001i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 14.6336 | 0.792454 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 22.1444 | 1.19569 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 11.5538 | − | 4.20524i | 0.622036 | − | 0.226402i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.78358 | + | 10.1152i | −0.0957476 | + | 0.543011i | 0.898768 | + | 0.438424i | \(0.144463\pi\) |
−0.994516 | + | 0.104587i | \(0.966648\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.01578 | + | 1.75939i | 0.0543736 | + | 0.0941779i | 0.891931 | − | 0.452171i | \(-0.149350\pi\) |
−0.837557 | + | 0.546349i | \(0.816017\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.464805 | + | 0.390018i | −0.0248095 | + | 0.0208176i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.5203 | + | 18.2216i | −0.559937 | + | 0.969839i | 0.437564 | + | 0.899187i | \(0.355841\pi\) |
−0.997501 | + | 0.0706522i | \(0.977492\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −25.6807 | − | 9.34702i | −1.36299 | − | 0.496088i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.21007 | − | 23.8765i | −0.222821 | − | 1.26368i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.93581 | + | 4.98074i | 0.313280 | + | 0.262873i | 0.785846 | − | 0.618422i | \(-0.212228\pi\) |
−0.472566 | + | 0.881295i | \(0.656672\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.4551 | − | 7.50461i | 0.918690 | − | 0.394979i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4.82141 | + | 4.04565i | 0.253059 | + | 0.212341i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.205185 | + | 1.16366i | 0.0107399 | + | 0.0609089i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −33.9531 | − | 12.3579i | −1.77234 | − | 0.645077i | −0.999951 | − | 0.00992253i | \(-0.996842\pi\) |
−0.772385 | − | 0.635155i | \(-0.780936\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.60708 | − | 6.24764i | 0.187777 | − | 0.325239i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 37.5972 | − | 31.5478i | 1.95195 | − | 1.63788i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9.97590 | − | 17.2788i | −0.516533 | − | 0.894661i | −0.999816 | − | 0.0191965i | \(-0.993889\pi\) |
0.483283 | − | 0.875464i | \(-0.339444\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.92049 | − | 10.8917i | 0.0991738 | − | 0.562443i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.913682 | − | 0.332553i | 0.0470570 | − | 0.0171273i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −34.1329 | −1.75329 | −0.876645 | − | 0.481138i | \(-0.840224\pi\) | ||||
−0.876645 | + | 0.481138i | \(0.840224\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.48627 | 0.434765 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −23.4883 | + | 8.54903i | −1.20019 | + | 0.436835i | −0.863292 | − | 0.504705i | \(-0.831601\pi\) |
−0.336902 | + | 0.941540i | \(0.609379\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.71698 | − | 21.0801i | 0.189435 | − | 1.07434i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.704453 | + | 1.22015i | 0.0358094 | + | 0.0620236i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 22.0835 | − | 18.5303i | 1.11968 | − | 0.939521i | 0.121090 | − | 0.992642i | \(-0.461361\pi\) |
0.998588 | + | 0.0531205i | \(0.0169167\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −15.1056 | + | 26.1637i | −0.763923 | + | 1.32315i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.79416 | − | 0.653022i | −0.0905036 | − | 0.0329406i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.81848 | + | 21.6557i | 0.192129 | + | 1.08962i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.65047 | − | 1.38491i | −0.0828348 | − | 0.0695066i | 0.600430 | − | 0.799677i | \(-0.294996\pi\) |
−0.683265 | + | 0.730171i | \(0.739441\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −16.7496 | − | 9.04424i | −0.838527 | − | 0.452778i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −22.9070 | − | 19.2213i | −1.14392 | − | 0.959865i | −0.144362 | − | 0.989525i | \(-0.546113\pi\) |
−0.999560 | + | 0.0296600i | \(0.990558\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.710736 | + | 4.03078i | 0.0354043 | + | 0.200788i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.12320 | − | 0.772782i | −0.105503 | − | 0.0383998i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.11402 | + | 12.3218i | −0.352629 | + | 0.610771i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.27041 | − | 5.26150i | 0.310052 | − | 0.260165i | −0.474462 | − | 0.880276i | \(-0.657357\pi\) |
0.784513 | + | 0.620112i | \(0.212913\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.56657 | − | 16.5698i | −0.471884 | − | 0.817327i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5.05069 | + | 28.6439i | −0.248528 | + | 1.40947i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 27.6690 | − | 10.0707i | 1.35822 | − | 0.494351i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 14.2236 | 0.696533 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.29279 | 0.307423 | 0.153712 | − | 0.988116i | \(-0.450877\pi\) | ||||
0.153712 | + | 0.988116i | \(0.450877\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.2411 | − | 5.91129i | 0.791544 | − | 0.288099i | 0.0855664 | − | 0.996332i | \(-0.472730\pi\) |
0.705978 | + | 0.708234i | \(0.250508\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.80958 | + | 10.2626i | −0.0879846 | + | 0.498985i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.291956 | − | 0.505682i | −0.0141619 | − | 0.0245292i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −24.7350 | + | 20.7551i | −1.19701 | + | 1.00441i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.658138 | − | 1.13993i | 0.0317752 | − | 0.0550363i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.08293 | − | 3.30592i | −0.437509 | − | 0.159240i | 0.113869 | − | 0.993496i | \(-0.463676\pi\) |
−0.551378 | + | 0.834255i | \(0.685898\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.67942 | + | 20.8670i | 0.176822 | + | 1.00281i | 0.936020 | + | 0.351946i | \(0.114480\pi\) |
−0.759199 | + | 0.650859i | \(0.774409\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.77365 | + | 2.32737i | 0.132986 | + | 0.111589i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.74428 | + | 22.0492i | 0.418295 | + | 1.05475i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.92619 | − | 3.29446i | −0.187387 | − | 0.157236i | 0.544268 | − | 0.838911i | \(-0.316807\pi\) |
−0.731655 | + | 0.681675i | \(0.761252\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.09608 | + | 11.8875i | 0.0998133 | + | 0.566069i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.70577 | − | 0.620849i | −0.0810436 | − | 0.0294974i | 0.301180 | − | 0.953567i | \(-0.402619\pi\) |
−0.382224 | + | 0.924070i | \(0.624842\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.17746 | + | 8.96763i | −0.245435 | + | 0.425107i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9.22232 | + | 7.73844i | −0.436201 | + | 0.366016i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.63865 | − | 14.9626i | −0.407683 | − | 0.706128i | 0.586947 | − | 0.809626i | \(-0.300330\pi\) |
−0.994630 | + | 0.103498i | \(0.966996\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.71760 | + | 15.4123i | −0.127967 | + | 0.725736i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 10.1008 | − | 3.67640i | 0.474578 | − | 0.172732i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.98697 | 0.280673 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −28.8598 | −1.35001 | −0.675003 | − | 0.737815i | \(-0.735858\pi\) | ||||
−0.675003 | + | 0.737815i | \(0.735858\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.21699 | − | 1.89883i | 0.243508 | − | 0.0886298i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.75107 | + | 21.2734i | −0.174705 | + | 0.990800i | 0.763779 | + | 0.645478i | \(0.223342\pi\) |
−0.938484 | + | 0.345323i | \(0.887769\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.81671 | − | 6.61074i | −0.177378 | − | 0.307227i | 0.763604 | − | 0.645685i | \(-0.223428\pi\) |
−0.940982 | + | 0.338458i | \(0.890095\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −11.6756 | + | 9.79702i | −0.541444 | + | 0.454326i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.8773 | − | 22.3042i | 0.595891 | − | 1.03211i | −0.397529 | − | 0.917590i | \(-0.630132\pi\) |
0.993420 | − | 0.114524i | \(-0.0365344\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 44.8550 | + | 16.3259i | 2.07121 | + | 0.753859i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.85893 | + | 16.2138i | 0.131732 | + | 0.747092i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.34135 | − | 1.96463i | −0.107655 | − | 0.0903336i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.453567 | − | 0.0667153i | −0.0208111 | − | 0.00306111i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.60935 | + | 7.22410i | 0.394195 | + | 0.330769i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.81928 | + | 27.3315i | 0.220198 | + | 1.24881i | 0.871655 | + | 0.490121i | \(0.163047\pi\) |
−0.651456 | + | 0.758686i | \(0.725842\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.73954 | − | 1.36108i | −0.170508 | − | 0.0620599i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 11.8820 | − | 20.5802i | 0.540648 | − | 0.936431i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −17.7127 | + | 14.8627i | −0.804292 | + | 0.674881i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.7231 | + | 30.6973i | 0.803110 | + | 1.39103i | 0.917559 | + | 0.397599i | \(0.130156\pi\) |
−0.114449 | + | 0.993429i | \(0.536510\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.43564 | + | 13.8132i | −0.110143 | + | 0.624653i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16.4863 | + | 6.00052i | −0.744016 | + | 0.270800i | −0.686085 | − | 0.727521i | \(-0.740672\pi\) |
−0.0579303 | + | 0.998321i | \(0.518450\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.89666 | −0.400685 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.90157 | 0.220309 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −49.6349 | + | 18.0656i | −2.22643 | + | 0.810353i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.62329 | + | 20.5487i | −0.162201 | + | 0.919886i | 0.789703 | + | 0.613489i | \(0.210235\pi\) |
−0.951904 | + | 0.306397i | \(0.900876\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7.93050 | + | 13.7360i | 0.354309 | + | 0.613681i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.17161 | − | 3.50040i | 0.186003 | − | 0.156075i | −0.545031 | − | 0.838416i | \(-0.683482\pi\) |
0.731035 | + | 0.682340i | \(0.239038\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.5040 | − | 21.6576i | 0.556423 | − | 0.963752i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −11.8700 | − | 4.32034i | −0.527167 | − | 0.191873i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.40893 | + | 13.6617i | 0.106774 | + | 0.605545i | 0.990497 | + | 0.137534i | \(0.0439178\pi\) |
−0.883723 | + | 0.468010i | \(0.844971\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.74948 | + | 1.46799i | 0.0773925 | + | 0.0649400i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.37355 | − | 4.13683i | 0.0606436 | − | 0.182646i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −27.3919 | − | 22.9845i | −1.20703 | − | 1.01282i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.92561 | − | 22.2632i | −0.172648 | − | 0.979135i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −15.9398 | − | 5.80162i | −0.699680 | − | 0.254663i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.0703 | − | 29.5666i | 0.747863 | − | 1.29534i | −0.200982 | − | 0.979595i | \(-0.564413\pi\) |
0.948845 | − | 0.315741i | \(-0.102253\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.0575 | − | 14.3129i | 0.745872 | − | 0.625861i | −0.188535 | − | 0.982066i | \(-0.560374\pi\) |
0.934408 | + | 0.356205i | \(0.115930\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.229650 | + | 0.397766i | 0.0100228 | + | 0.0173599i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.50318 | − | 36.8814i | 0.283283 | − | 1.60658i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.21322 | + | 2.26143i | −0.270140 | + | 0.0983229i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.66032 | −0.289033 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.37726 | −0.189600 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −23.4360 | + | 8.53001i | −1.01323 | + | 0.368785i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.08172 | + | 17.4773i | −0.132986 | + | 0.754201i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −13.0930 | − | 22.6777i | −0.563953 | − | 0.976796i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −24.3976 | + | 20.4720i | −1.04893 | + | 0.880160i | −0.992981 | − | 0.118273i | \(-0.962264\pi\) |
−0.0559529 | + | 0.998433i | \(0.517820\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6.33405 | + | 10.9709i | −0.271820 | + | 0.470806i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 17.3821 | + | 6.32658i | 0.744569 | + | 0.271001i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.03033 | − | 5.84330i | −0.0440538 | − | 0.249842i | 0.954826 | − | 0.297166i | \(-0.0960416\pi\) |
−0.998880 | + | 0.0473247i | \(0.984930\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.66404 | − | 4.75269i | −0.241735 | − | 0.202840i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.33565 | + | 5.47658i | −0.184705 | + | 0.233310i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 32.5577 | + | 27.3192i | 1.38450 | + | 1.16173i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.57330 | − | 14.5939i | −0.109231 | − | 0.619477i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 23.6477 | + | 8.60705i | 1.00198 | + | 0.364693i | 0.790350 | − | 0.612656i | \(-0.209899\pi\) |
0.211635 | + | 0.977349i | \(0.432121\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.427434 | − | 0.740337i | 0.0180785 | − | 0.0313129i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.22611 | + | 7.74163i | −0.389527 | + | 0.326852i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 14.8587 | + | 25.7361i | 0.626221 | + | 1.08465i | 0.988303 | + | 0.152501i | \(0.0487326\pi\) |
−0.362082 | + | 0.932146i | \(0.617934\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.23889 | + | 12.6974i | −0.0941906 | + | 0.534182i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.10365 | + | 1.49361i | −0.172337 | + | 0.0627256i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −26.6200 | −1.11597 | −0.557985 | − | 0.829851i | \(-0.688425\pi\) | ||||
−0.557985 | + | 0.829851i | \(0.688425\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 35.6248 | 1.49085 | 0.745425 | − | 0.666589i | \(-0.232246\pi\) | ||||
0.745425 | + | 0.666589i | \(0.232246\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7.41720 | − | 2.69964i | 0.309858 | − | 0.112779i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.0993839 | − | 0.563634i | 0.00414460 | − | 0.0235052i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 21.6806 | + | 37.5520i | 0.902577 | + | 1.56331i | 0.824138 | + | 0.566390i | \(0.191660\pi\) |
0.0784390 | + | 0.996919i | \(0.475006\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.0901786 | + | 0.0756689i | −0.00374770 | + | 0.00314469i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 28.4549 | − | 49.2854i | 1.18051 | − | 2.04470i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −22.9104 | − | 8.33869i | −0.948851 | − | 0.345353i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.238063 | + | 1.35012i | 0.00984270 | + | 0.0558207i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.27986 | + | 6.10852i | 0.300472 | + | 0.252126i | 0.780541 | − | 0.625105i | \(-0.214944\pi\) |
−0.480069 | + | 0.877231i | \(0.659388\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −19.5341 | − | 21.9768i | −0.804889 | − | 0.905538i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11.6875 | + | 9.80697i | 0.480759 | + | 0.403405i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.49910 | − | 19.8444i | −0.143691 | − | 0.814910i | −0.968409 | − | 0.249367i | \(-0.919778\pi\) |
0.824719 | − | 0.565543i | \(-0.191334\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −51.4767 | − | 18.7360i | −2.11034 | − | 0.768100i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.40597 | − | 2.43521i | 0.0575424 | − | 0.0996663i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10.6487 | − | 8.93534i | 0.435095 | − | 0.365088i | −0.398775 | − | 0.917049i | \(-0.630565\pi\) |
0.833870 | + | 0.551961i | \(0.186120\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.6544 | + | 32.3104i | 0.760931 | + | 1.31797i | 0.942371 | + | 0.334569i | \(0.108591\pi\) |
−0.181441 | + | 0.983402i | \(0.558076\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.89806 | + | 10.7644i | −0.0772950 | + | 0.438362i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 13.3632 | − | 4.86382i | 0.543293 | − | 0.197742i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18.1639 | 0.737249 | 0.368624 | − | 0.929578i | \(-0.379829\pi\) | ||||
0.368624 | + | 0.929578i | \(0.379829\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6.99805 | 0.283575 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.94168 | − | 2.16259i | 0.240374 | − | 0.0874892i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.64117 | − | 26.3214i | 0.187455 | − | 1.06311i | −0.735305 | − | 0.677736i | \(-0.762961\pi\) |
0.922760 | − | 0.385375i | \(-0.125928\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8.15006 | − | 14.1163i | −0.328642 | − | 0.569225i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.330289 | − | 0.277145i | 0.0132969 | − | 0.0111574i | −0.636115 | − | 0.771594i | \(-0.719460\pi\) |
0.649412 | + | 0.760437i | \(0.275015\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.40534 | − | 14.5585i | 0.337839 | − | 0.585154i | −0.646187 | − | 0.763179i | \(-0.723637\pi\) |
0.984026 | + | 0.178025i | \(0.0569707\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.11351 | + | 1.86117i | 0.205198 | + | 0.0746861i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.47534 | + | 19.7096i | 0.139236 | + | 0.789649i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.5455 | − | 16.4006i | −0.781819 | − | 0.656024i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.269362 | + | 9.45215i | 0.0107573 | + | 0.377483i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 27.8935 | + | 23.4055i | 1.11219 | + | 0.933237i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.87914 | − | 10.6571i | −0.0748073 | − | 0.424253i | −0.999094 | − | 0.0425545i | \(-0.986450\pi\) |
0.924287 | − | 0.381698i | \(-0.124661\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.404951 | + | 0.147390i | 0.0160953 | + | 0.00585823i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9.58720 | − | 16.6055i | 0.380457 | − | 0.658970i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.61058 | − | 4.70784i | 0.222299 | − | 0.186531i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.04764 | − | 10.4748i | −0.239241 | − | 0.414378i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.44930 | − | 42.2471i | 0.294230 | − | 1.66866i | −0.376087 | − | 0.926585i | \(-0.622730\pi\) |
0.670316 | − | 0.742075i | \(-0.266158\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.50831 | + | 3.09677i | −0.335535 | + | 0.122125i | −0.504293 | − | 0.863533i | \(-0.668247\pi\) |
0.168758 | + | 0.985658i | \(0.446024\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.18337 | 0.125345 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 23.3186 | 0.916748 | 0.458374 | − | 0.888759i | \(-0.348432\pi\) | ||||
0.458374 | + | 0.888759i | \(0.348432\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.5772 | − | 4.94171i | 0.532953 | − | 0.193979i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.11536 | + | 29.0107i | −0.200487 | + | 1.13702i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −22.8315 | − | 39.5453i | −0.893466 | − | 1.54753i | −0.835692 | − | 0.549198i | \(-0.814933\pi\) |
−0.0577733 | − | 0.998330i | \(-0.518400\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.30473 | + | 2.77299i | −0.129126 | + | 0.108350i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.261481 | + | 0.452899i | −0.0102013 | + | 0.0176693i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.24846 | − | 2.63822i | −0.282360 | − | 0.102771i | 0.196958 | − | 0.980412i | \(-0.436894\pi\) |
−0.479318 | + | 0.877641i | \(0.659116\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.80015 | − | 10.2091i | −0.0700176 | − | 0.397089i | −0.999595 | − | 0.0284622i | \(-0.990939\pi\) |
0.929577 | − | 0.368627i | \(-0.120172\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.58051 | − | 2.16530i | −0.100219 | − | 0.0840934i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −36.6198 | + | 22.5572i | −1.42006 | + | 0.874730i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.68005 | − | 5.60523i | −0.258653 | − | 0.217035i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.422205 | + | 2.39445i | 0.0163234 | + | 0.0925746i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 15.0726 | + | 5.48598i | 0.581871 | + | 0.211784i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.63202 | − | 14.9511i | 0.332740 | − | 0.576322i | −0.650308 | − | 0.759670i | \(-0.725360\pi\) |
0.983048 | + | 0.183348i | \(0.0586936\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.0805687 | + | 0.0676052i | −0.00310109 | + | 0.00260212i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −16.5624 | − | 28.6869i | −0.636544 | − | 1.10253i | −0.986186 | − | 0.165643i | \(-0.947030\pi\) |
0.349642 | − | 0.936883i | \(-0.386303\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.76034 | + | 44.0111i | −0.297814 | + | 1.68899i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10.8010 | − | 3.93124i | 0.413895 | − | 0.150646i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −32.6531 | −1.24944 | −0.624718 | − | 0.780851i | \(-0.714786\pi\) | ||||
−0.624718 | + | 0.780851i | \(0.714786\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −43.2306 | −1.65176 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.82176 | − | 1.75498i | 0.183962 | − | 0.0669565i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.18414 | − | 6.71559i | 0.0451122 | − | 0.255844i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.40650 | − | 2.43613i | −0.0535058 | − | 0.0926748i | 0.838032 | − | 0.545621i | \(-0.183706\pi\) |
−0.891538 | + | 0.452946i | \(0.850373\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 7.25720 | − | 6.08951i | 0.275678 | − | 0.231321i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 16.0689 | − | 27.8321i | 0.609527 | − | 1.05573i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 37.6362 | + | 13.6985i | 1.42557 | + | 0.518866i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.59200 | − | 9.02868i | −0.0602150 | − | 0.341496i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.28484 | − | 4.43451i | −0.199606 | − | 0.167489i | 0.537506 | − | 0.843260i | \(-0.319366\pi\) |
−0.737112 | + | 0.675771i | \(0.763811\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 28.0014 | − | 5.76433i | 1.05609 | − | 0.217406i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 18.0371 | + | 15.1349i | 0.679315 | + | 0.570013i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −8.39325 | − | 47.6005i | −0.315661 | − | 1.79020i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 32.9972 | + | 12.0100i | 1.23923 | + | 0.451044i | 0.876750 | − | 0.480946i | \(-0.159707\pi\) |
0.362484 | + | 0.931990i | \(0.381929\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.86615 | + | 8.42841i | −0.182495 | + | 0.316090i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 28.1196 | − | 23.5951i | 1.05309 | − | 0.883644i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.48704 | − | 2.57563i | −0.0556121 | − | 0.0963230i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −0.425332 | + | 2.41218i | −0.0158843 | + | 0.0900843i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 12.8274 | − | 4.66880i | 0.478382 | − | 0.174117i | −0.0915638 | − | 0.995799i | \(-0.529187\pi\) |
0.569945 | + | 0.821683i | \(0.306964\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −69.1110 | −2.57383 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.35437 | −0.0875600 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.158376 | − | 0.0576443i | 0.00588195 | − | 0.00214086i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.59150 | + | 37.3823i | −0.244465 | + | 1.38643i | 0.577266 | + | 0.816556i | \(0.304120\pi\) |
−0.821731 | + | 0.569875i | \(0.806992\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.500000 | − | 0.866025i | −0.0185185 | − | 0.0320750i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.99198 | + | 5.02787i | −0.221621 | + | 0.185963i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.64378 | − | 6.31122i | 0.134586 | − | 0.233110i | −0.790853 | − | 0.612006i | \(-0.790363\pi\) |
0.925439 | + | 0.378896i | \(0.123696\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 25.6288 | + | 9.32813i | 0.945333 | + | 0.344073i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.11757 | − | 23.3519i | −0.151672 | − | 0.860177i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10.7726 | − | 9.03929i | −0.396277 | − | 0.332516i | 0.422776 | − | 0.906234i | \(-0.361056\pi\) |
−0.819052 | + | 0.573719i | \(0.805500\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.59048 | + | 0.533274i | −0.0951638 | + | 0.0195903i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 19.6806 | + | 16.5140i | 0.722011 | + | 0.605839i | 0.927941 | − | 0.372728i | \(-0.121578\pi\) |
−0.205930 | + | 0.978567i | \(0.566022\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.72348 | + | 26.7882i | 0.173055 | + | 0.981442i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 12.2458 | + | 4.45712i | 0.448052 | + | 0.163077i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −24.1017 | + | 41.7453i | −0.880656 | + | 1.52534i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.84443 | + | 7.42136i | −0.322738 | + | 0.270809i | −0.789733 | − | 0.613451i | \(-0.789781\pi\) |
0.466995 | + | 0.884260i | \(0.345337\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.58736 | + | 11.4096i | 0.240057 | + | 0.415790i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.21742 | − | 23.9182i | 0.153487 | − | 0.870471i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.71337 | − | 1.71553i | 0.171310 | − | 0.0623519i | −0.254941 | − | 0.966957i | \(-0.582056\pi\) |
0.426252 | + | 0.904605i | \(0.359834\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −11.8049 | −0.428492 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −41.7464 | −1.51331 | −0.756653 | − | 0.653816i | \(-0.773167\pi\) | ||||
−0.756653 | + | 0.653816i | \(0.773167\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 33.5956 | − | 12.2278i | 1.21624 | − | 0.442676i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.17826 | − | 12.3535i | 0.0787552 | − | 0.446643i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.02061 | + | 3.49980i | 0.0729599 | + | 0.126370i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 34.4563 | − | 28.9123i | 1.24253 | − | 1.04260i | 0.245204 | − | 0.969471i | \(-0.421145\pi\) |
0.997322 | − | 0.0731323i | \(-0.0232995\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.72582 | + | 16.8456i | −0.350267 | + | 0.606680i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −45.2766 | − | 16.4793i | −1.62849 | − | 0.592720i | −0.643513 | − | 0.765435i | \(-0.722524\pi\) |
−0.984972 | + | 0.172715i | \(0.944746\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.123198 | + | 0.698691i | 0.00442540 | + | 0.0250977i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −21.9409 | − | 18.4106i | −0.787124 | − | 0.660476i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 26.7739 | − | 16.4923i | 0.959275 | − | 0.590896i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 20.1002 | + | 16.8661i | 0.719241 | + | 0.603515i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.278268 | + | 1.57813i | 0.00994447 | + | 0.0563979i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 34.9562 | + | 12.7230i | 1.24764 | + | 0.454104i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19.3475 | − | 33.5108i | 0.689663 | − | 1.19453i | −0.282284 | − | 0.959331i | \(-0.591092\pi\) |
0.971947 | − | 0.235200i | \(-0.0755745\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6.00346 | + | 5.03750i | −0.213729 | + | 0.179340i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 12.4598 | + | 21.5810i | 0.443020 | + | 0.767333i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.779039 | + | 4.41815i | −0.0276645 | + | 0.156893i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 23.8620 | − | 8.68507i | 0.846299 | − | 0.308028i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5.37913 | −0.190538 | −0.0952692 | − | 0.995452i | \(-0.530371\pi\) | ||||
−0.0952692 | + | 0.995452i | \(0.530371\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −57.8550 | −2.04676 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.30653 | + | 1.56745i | −0.152164 | + | 0.0553831i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.197002 | − | 1.11725i | 0.00695205 | − | 0.0394270i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −26.8469 | − | 46.5002i | −0.946228 | − | 1.63892i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −12.8333 | + | 10.7684i | −0.451752 | + | 0.379065i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.18762 | + | 3.78907i | −0.0769126 | + | 0.133217i | −0.901916 | − | 0.431911i | \(-0.857840\pi\) |
0.825004 | + | 0.565127i | \(0.191173\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.53177 | − | 2.37737i | −0.229361 | − | 0.0834807i | 0.224783 | − | 0.974409i | \(-0.427833\pi\) |
−0.454144 | + | 0.890928i | \(0.650055\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.70011 | − | 26.6557i | −0.164840 | − | 0.934855i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 24.2774 | + | 20.3711i | 0.850399 | + | 0.713569i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.174939 | + | 6.13879i | 0.00612036 | + | 0.214769i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.02981 | + | 1.70321i | 0.0709273 | + | 0.0595151i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.60348 | + | 26.1076i | 0.160662 | + | 0.911162i | 0.953425 | + | 0.301631i | \(0.0975311\pi\) |
−0.792762 | + | 0.609531i | \(0.791358\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.6911 | + | 4.25523i | 0.407528 | + | 0.148328i | 0.537646 | − | 0.843171i | \(-0.319314\pi\) |
−0.130119 | + | 0.991498i | \(0.541536\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.114081 | − | 0.197594i | 0.00397178 | − | 0.00687933i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 18.4462 | − | 15.4782i | 0.641439 | − | 0.538231i | −0.263021 | − | 0.964790i | \(-0.584719\pi\) |
0.904460 | + | 0.426559i | \(0.140274\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.2182 | + | 17.6984i | 0.354893 | + | 0.614692i | 0.987100 | − | 0.160108i | \(-0.0511841\pi\) |
−0.632207 | + | 0.774800i | \(0.717851\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.838905 | + | 4.75767i | −0.0291013 | + | 0.165042i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −62.9735 | + | 22.9205i | −2.18190 | + | 0.794147i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 35.8374 | 1.24020 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.74561 | −0.233162 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 31.4323 | − | 11.4404i | 1.08516 | − | 0.394968i | 0.263337 | − | 0.964704i | \(-0.415177\pi\) |
0.821828 | + | 0.569736i | \(0.192955\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.58988 | + | 26.0305i | −0.158272 | + | 0.897603i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −11.1327 | − | 19.2823i | −0.383429 | − | 0.664118i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −21.8638 | + | 18.3459i | −0.752138 | + | 0.631119i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 13.7428 | − | 23.8032i | 0.472208 | − | 0.817889i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.29809 | + | 1.92835i | 0.181830 | + | 0.0661808i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.19753 | + | 35.1480i | 0.212449 | + | 1.20486i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.500291 | + | 0.419794i | 0.0171297 | + | 0.0143735i | 0.651312 | − | 0.758810i | \(-0.274219\pi\) |
−0.634183 | + | 0.773183i | \(0.718663\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6.54301 | − | 7.36120i | −0.223766 | − | 0.251748i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 41.0839 | + | 34.4735i | 1.40340 | + | 1.17759i | 0.959566 | + | 0.281485i | \(0.0908269\pi\) |
0.443835 | + | 0.896108i | \(0.353618\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.79974 | + | 21.5494i | 0.129646 | + | 0.735256i | 0.978440 | + | 0.206533i | \(0.0662180\pi\) |
−0.848794 | + | 0.528723i | \(0.822671\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −29.6044 | − | 10.7751i | −1.00892 | − | 0.367215i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −13.3479 | + | 23.1192i | −0.454366 | + | 0.786985i | −0.998652 | − | 0.0519148i | \(-0.983468\pi\) |
0.544285 | + | 0.838900i | \(0.316801\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −29.3600 | + | 24.6360i | −0.998271 | + | 0.837649i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6.91129 | + | 11.9707i | 0.234720 | + | 0.406547i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.66619 | − | 20.7920i | 0.124367 | − | 0.705321i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.23222 | − | 2.26834i | 0.211171 | − | 0.0768598i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −10.2335 | −0.346353 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −48.2978 | −1.63276 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 25.7568 | − | 9.37471i | 0.869746 | − | 0.316562i | 0.131681 | − | 0.991292i | \(-0.457962\pi\) |
0.738064 | + | 0.674731i | \(0.235740\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4.06328 | + | 23.0440i | −0.137051 | + | 0.777255i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.53145 | + | 14.7769i | 0.287432 | + | 0.497847i | 0.973196 | − | 0.229977i | \(-0.0738652\pi\) |
−0.685764 | + | 0.727824i | \(0.740532\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.61617 | + | 2.19523i | −0.0880413 | + | 0.0738754i | −0.685746 | − | 0.727841i | \(-0.740524\pi\) |
0.597705 | + | 0.801716i | \(0.296079\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −7.52438 | + | 13.0326i | −0.252929 | + | 0.438086i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12.9915 | + | 4.72854i | 0.436213 | + | 0.158769i | 0.550787 | − | 0.834646i | \(-0.314328\pi\) |
−0.114573 | + | 0.993415i | \(0.536550\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.43534 | − | 36.4966i | −0.215834 | − | 1.22406i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.66182 | + | 1.39443i | 0.0556731 | + | 0.0467153i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −28.1948 | + | 35.6142i | −0.943502 | + | 1.19178i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 30.7172 | + | 25.7748i | 1.02676 | + | 0.861557i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.573351 | − | 3.25164i | −0.0191436 | − | 0.108569i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 10.1578 | + | 3.69713i | 0.338781 | + | 0.123306i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −31.1976 | + | 54.0358i | −1.03934 | + | 1.80019i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.71325 | − | 3.95489i | 0.156847 | − | 0.131610i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 14.3116 | + | 24.7883i | 0.475732 | + | 0.823992i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.460472 | + | 2.61146i | −0.0152897 | + | 0.0867123i | −0.991498 | − | 0.130124i | \(-0.958463\pi\) |
0.976208 | + | 0.216836i | \(0.0695737\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 10.4007 | − | 3.78553i | 0.344968 | − | 0.125558i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.443526 | 0.0146947 | 0.00734733 | − | 0.999973i | \(-0.497661\pi\) | ||||
0.00734733 | + | 0.999973i | \(0.497661\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −28.2704 | −0.935615 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −15.6987 | + | 5.71385i | −0.518983 | + | 0.188894i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.44788 | + | 8.21131i | −0.0478131 | + | 0.271161i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −28.0481 | − | 48.5807i | −0.925220 | − | 1.60253i | −0.791207 | − | 0.611548i | \(-0.790547\pi\) |
−0.134013 | − | 0.990980i | \(-0.542786\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 25.5258 | − | 21.4187i | 0.841104 | − | 0.705770i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.66947 | + | 6.35570i | −0.120782 | + | 0.209200i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.648206 | − | 0.235928i | −0.0213129 | − | 0.00775726i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.74810 | − | 15.5852i | −0.0902594 | − | 0.511887i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −14.5755 | − | 12.2303i | −0.478206 | − | 0.401263i | 0.371571 | − | 0.928405i | \(-0.378819\pi\) |
−0.849777 | + | 0.527142i | \(0.823264\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −16.5799 | + | 49.9350i | −0.543383 | + | 1.63655i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −19.0497 | − | 15.9846i | −0.623659 | − | 0.523312i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.72542 | + | 26.7992i | 0.154538 | + | 0.876427i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −46.5000 | − | 16.9246i | −1.51909 | − | 0.552903i | −0.558168 | − | 0.829728i | \(-0.688495\pi\) |
−0.960920 | + | 0.276825i | \(0.910718\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.12617 | − | 8.87879i | 0.167286 | − | 0.289748i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.17706 | + | 0.987675i | −0.0383712 | + | 0.0321973i | −0.661772 | − | 0.749706i | \(-0.730195\pi\) |
0.623400 | + | 0.781903i | \(0.285751\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 19.6286 | + | 33.9977i | 0.639195 | + | 1.10712i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.71341 | + | 9.71721i | −0.0557371 | + | 0.316101i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 14.8158 | − | 5.39253i | 0.481450 | − | 0.175234i | −0.0898820 | − | 0.995952i | \(-0.528649\pi\) |
0.571332 | + | 0.820719i | \(0.306427\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.317312 | 0.0103004 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −9.73579 | −0.315704 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.89211 | − | 2.50852i | 0.223257 | − | 0.0812590i | −0.227970 | − | 0.973668i | \(-0.573209\pi\) |
0.451227 | + | 0.892409i | \(0.350986\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.09692 | − | 17.5635i | 0.100214 | − | 0.568341i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.73817 | − | 3.01060i | −0.0561871 | − | 0.0973189i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −64.0066 | + | 53.7079i | −2.06688 | + | 1.73432i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.25162 | + | 12.5602i | −0.233923 | + | 0.405167i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −10.3724 | − | 3.77524i | −0.334245 | − | 0.121655i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.0461876 | + | 0.261943i | 0.00148683 | + | 0.00843224i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.143324 | − | 0.120263i | −0.00460899 | − | 0.00386740i | 0.640480 | − | 0.767975i | \(-0.278735\pi\) |
−0.645089 | + | 0.764107i | \(0.723180\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 23.9422 | + | 3.52166i | 0.769133 | + | 0.113132i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −17.6661 | − | 14.8236i | −0.566931 | − | 0.475712i | 0.313695 | − | 0.949524i | \(-0.398433\pi\) |
−0.880626 | + | 0.473812i | \(0.842878\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.7861 | − | 61.1711i | −0.345787 | − | 1.96105i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.0599674 | + | 0.0218263i | 0.00192049 | + | 0.000699002i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 15.4121 | − | 26.6946i | 0.493077 | − | 0.854035i | −0.506891 | − | 0.862010i | \(-0.669205\pi\) |
0.999968 | + | 0.00797538i | \(0.00253867\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.61598 | − | 6.39057i | 0.243408 | − | 0.204243i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.09338 | + | 7.08994i | 0.130692 | + | 0.226364i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.11074 | + | 6.29933i | −0.0354272 | + | 0.200917i | −0.997384 | − | 0.0722836i | \(-0.976971\pi\) |
0.961957 | + | 0.273201i | \(0.0880824\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 32.3935 | − | 11.7903i | 1.03214 | − | 0.375670i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 45.5084 | 1.44855 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.66683 | −0.243791 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.19218 | + | 3.34568i | −0.291999 | + | 0.106279i | −0.483866 | − | 0.875142i | \(-0.660768\pi\) |
0.191867 | + | 0.981421i | \(0.438546\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.33108 | − | 24.5628i | 0.137443 | − | 0.779476i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.17673 | − | 5.50226i | −0.100709 | − | 0.174433i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7.13937 | + | 5.99065i | −0.226106 | + | 0.189726i | −0.748802 | − | 0.662793i | \(-0.769371\pi\) |
0.522696 | + | 0.852519i | \(0.324926\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.27933 | − | 5.67996i | 0.103753 | − | 0.179706i |
(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 | 228.2.q.b.73.2 | yes | 12 | |
3.2 | odd | 2 | 684.2.bo.e.73.1 | 12 | |||
4.3 | odd | 2 | 912.2.bo.g.529.2 | 12 | |||
19.5 | even | 9 | 4332.2.a.t.1.4 | 6 | |||
19.6 | even | 9 | inner | 228.2.q.b.25.2 | ✓ | 12 | |
19.14 | odd | 18 | 4332.2.a.u.1.4 | 6 | |||
57.44 | odd | 18 | 684.2.bo.e.253.1 | 12 | |||
76.63 | odd | 18 | 912.2.bo.g.481.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
228.2.q.b.25.2 | ✓ | 12 | 19.6 | even | 9 | inner | |
228.2.q.b.73.2 | yes | 12 | 1.1 | even | 1 | trivial | |
684.2.bo.e.73.1 | 12 | 3.2 | odd | 2 | |||
684.2.bo.e.253.1 | 12 | 57.44 | odd | 18 | |||
912.2.bo.g.481.2 | 12 | 76.63 | odd | 18 | |||
912.2.bo.g.529.2 | 12 | 4.3 | odd | 2 | |||
4332.2.a.t.1.4 | 6 | 19.5 | even | 9 | |||
4332.2.a.u.1.4 | 6 | 19.14 | odd | 18 |