Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1470,2,Mod(1469,1470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1470, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1470.1469");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1470.d (of order \(2\), degree \(1\), 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: | \(11.7380090971\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-11})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 2x^{2} - 3x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1469.4 | ||
Root | \(-1.18614 - 1.26217i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1470.1469 |
Dual form | 1470.2.d.a.1469.3 |
$q$-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 \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).
\(n\) | \(491\) | \(1081\) | \(1177\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.18614 | + | 1.26217i | 0.684819 | + | 0.728714i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.686141 | − | 2.12819i | −0.306851 | − | 0.951757i | ||||
\(6\) | −1.18614 | − | 1.26217i | −0.484240 | − | 0.515278i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.186141 | + | 2.99422i | −0.0620469 | + | 0.998073i | ||||
\(10\) | 0.686141 | + | 2.12819i | 0.216977 | + | 0.672994i | ||||
\(11\) | − | 4.25639i | − | 1.28335i | −0.766977 | − | 0.641675i | \(-0.778240\pi\) | ||
0.766977 | − | 0.641675i | \(-0.221760\pi\) | |||||||
\(12\) | 1.18614 | + | 1.26217i | 0.342409 | + | 0.364357i | ||||
\(13\) | 2.00000 | 0.554700 | 0.277350 | − | 0.960769i | \(-0.410544\pi\) | ||||
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.87228 | − | 3.39036i | 0.483421 | − | 0.875388i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 6.63325i | − | 1.60880i | −0.594089 | − | 0.804400i | \(-0.702487\pi\) | ||
0.594089 | − | 0.804400i | \(-0.297513\pi\) | |||||||
\(18\) | 0.186141 | − | 2.99422i | 0.0438738 | − | 0.705744i | ||||
\(19\) | 3.46410i | 0.794719i | 0.917663 | + | 0.397360i | \(0.130073\pi\) | ||||
−0.917663 | + | 0.397360i | \(0.869927\pi\) | |||||||
\(20\) | −0.686141 | − | 2.12819i | −0.153426 | − | 0.475879i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.25639i | 0.907465i | ||||||||
\(23\) | −4.37228 | −0.911684 | −0.455842 | − | 0.890061i | \(-0.650662\pi\) | ||||
−0.455842 | + | 0.890061i | \(0.650662\pi\) | |||||||
\(24\) | −1.18614 | − | 1.26217i | −0.242120 | − | 0.257639i | ||||
\(25\) | −4.05842 | + | 2.92048i | −0.811684 | + | 0.584096i | ||||
\(26\) | −2.00000 | −0.392232 | ||||||||
\(27\) | −4.00000 | + | 3.31662i | −0.769800 | + | 0.638285i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.31662i | 0.615882i | 0.951405 | + | 0.307941i | \(0.0996399\pi\) | ||||
−0.951405 | + | 0.307941i | \(0.900360\pi\) | |||||||
\(30\) | −1.87228 | + | 3.39036i | −0.341830 | + | 0.618993i | ||||
\(31\) | − | 2.37686i | − | 0.426897i | −0.976954 | − | 0.213448i | \(-0.931530\pi\) | ||
0.976954 | − | 0.213448i | \(-0.0684695\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 5.37228 | − | 5.04868i | 0.935194 | − | 0.878862i | ||||
\(34\) | 6.63325i | 1.13759i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.186141 | + | 2.99422i | −0.0310234 | + | 0.499037i | ||||
\(37\) | − | 11.6819i | − | 1.92050i | −0.279147 | − | 0.960248i | \(-0.590052\pi\) | ||
0.279147 | − | 0.960248i | \(-0.409948\pi\) | |||||||
\(38\) | − | 3.46410i | − | 0.561951i | ||||||
\(39\) | 2.37228 | + | 2.52434i | 0.379869 | + | 0.404218i | ||||
\(40\) | 0.686141 | + | 2.12819i | 0.108488 | + | 0.336497i | ||||
\(41\) | −1.62772 | −0.254207 | −0.127103 | − | 0.991889i | \(-0.540568\pi\) | ||||
−0.127103 | + | 0.991889i | \(0.540568\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 11.0371i | − | 1.68314i | −0.540145 | − | 0.841572i | \(-0.681631\pi\) | ||
0.540145 | − | 0.841572i | \(-0.318369\pi\) | |||||||
\(44\) | − | 4.25639i | − | 0.641675i | ||||||
\(45\) | 6.50000 | − | 1.65831i | 0.968963 | − | 0.247207i | ||||
\(46\) | 4.37228 | 0.644658 | ||||||||
\(47\) | − | 1.87953i | − | 0.274157i | −0.990560 | − | 0.137079i | \(-0.956229\pi\) | ||
0.990560 | − | 0.137079i | \(-0.0437713\pi\) | |||||||
\(48\) | 1.18614 | + | 1.26217i | 0.171205 | + | 0.182178i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 4.05842 | − | 2.92048i | 0.573948 | − | 0.413018i | ||||
\(51\) | 8.37228 | − | 7.86797i | 1.17235 | − | 1.10174i | ||||
\(52\) | 2.00000 | 0.277350 | ||||||||
\(53\) | −1.37228 | −0.188497 | −0.0942487 | − | 0.995549i | \(-0.530045\pi\) | ||||
−0.0942487 | + | 0.995549i | \(0.530045\pi\) | |||||||
\(54\) | 4.00000 | − | 3.31662i | 0.544331 | − | 0.451335i | ||||
\(55\) | −9.05842 | + | 2.92048i | −1.22144 | + | 0.393798i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.37228 | + | 4.10891i | −0.579123 | + | 0.544239i | ||||
\(58\) | − | 3.31662i | − | 0.435494i | ||||||
\(59\) | 4.11684 | 0.535967 | 0.267984 | − | 0.963423i | \(-0.413643\pi\) | ||||
0.267984 | + | 0.963423i | \(0.413643\pi\) | |||||||
\(60\) | 1.87228 | − | 3.39036i | 0.241710 | − | 0.437694i | ||||
\(61\) | 2.81929i | 0.360973i | 0.983577 | + | 0.180487i | \(0.0577673\pi\) | ||||
−0.983577 | + | 0.180487i | \(0.942233\pi\) | |||||||
\(62\) | 2.37686i | 0.301862i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.37228 | − | 4.25639i | −0.170211 | − | 0.527940i | ||||
\(66\) | −5.37228 | + | 5.04868i | −0.661282 | + | 0.621449i | ||||
\(67\) | − | 7.57301i | − | 0.925191i | −0.886569 | − | 0.462595i | \(-0.846918\pi\) | ||
0.886569 | − | 0.462595i | \(-0.153082\pi\) | |||||||
\(68\) | − | 6.63325i | − | 0.804400i | ||||||
\(69\) | −5.18614 | − | 5.51856i | −0.624338 | − | 0.664356i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 1.87953i | − | 0.223059i | −0.993761 | − | 0.111529i | \(-0.964425\pi\) | ||
0.993761 | − | 0.111529i | \(-0.0355749\pi\) | |||||||
\(72\) | 0.186141 | − | 2.99422i | 0.0219369 | − | 0.352872i | ||||
\(73\) | 2.00000 | 0.234082 | 0.117041 | − | 0.993127i | \(-0.462659\pi\) | ||||
0.117041 | + | 0.993127i | \(0.462659\pi\) | |||||||
\(74\) | 11.6819i | 1.35800i | ||||||||
\(75\) | −8.50000 | − | 1.65831i | −0.981495 | − | 0.191485i | ||||
\(76\) | 3.46410i | 0.397360i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −2.37228 | − | 2.52434i | −0.268608 | − | 0.285825i | ||||
\(79\) | −8.11684 | −0.913216 | −0.456608 | − | 0.889668i | \(-0.650936\pi\) | ||||
−0.456608 | + | 0.889668i | \(0.650936\pi\) | |||||||
\(80\) | −0.686141 | − | 2.12819i | −0.0767129 | − | 0.237939i | ||||
\(81\) | −8.93070 | − | 1.11469i | −0.992300 | − | 0.123855i | ||||
\(82\) | 1.62772 | 0.179751 | ||||||||
\(83\) | − | 1.43710i | − | 0.157742i | −0.996885 | − | 0.0788710i | \(-0.974868\pi\) | ||
0.996885 | − | 0.0788710i | \(-0.0251315\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −14.1168 | + | 4.55134i | −1.53119 | + | 0.493662i | ||||
\(86\) | 11.0371i | 1.19016i | ||||||||
\(87\) | −4.18614 | + | 3.93398i | −0.448801 | + | 0.421767i | ||||
\(88\) | 4.25639i | 0.453733i | ||||||||
\(89\) | 4.37228 | 0.463461 | 0.231730 | − | 0.972780i | \(-0.425561\pi\) | ||||
0.231730 | + | 0.972780i | \(0.425561\pi\) | |||||||
\(90\) | −6.50000 | + | 1.65831i | −0.685160 | + | 0.174801i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −4.37228 | −0.455842 | ||||||||
\(93\) | 3.00000 | − | 2.81929i | 0.311086 | − | 0.292347i | ||||
\(94\) | 1.87953i | 0.193858i | ||||||||
\(95\) | 7.37228 | − | 2.37686i | 0.756380 | − | 0.243861i | ||||
\(96\) | −1.18614 | − | 1.26217i | −0.121060 | − | 0.128820i | ||||
\(97\) | −2.11684 | −0.214933 | −0.107466 | − | 0.994209i | \(-0.534274\pi\) | ||||
−0.107466 | + | 0.994209i | \(0.534274\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 12.7446 | + | 0.792287i | 1.28088 | + | 0.0796278i | ||||
\(100\) | −4.05842 | + | 2.92048i | −0.405842 | + | 0.292048i | ||||
\(101\) | 16.3723 | 1.62910 | 0.814551 | − | 0.580091i | \(-0.196983\pi\) | ||||
0.814551 | + | 0.580091i | \(0.196983\pi\) | |||||||
\(102\) | −8.37228 | + | 7.86797i | −0.828979 | + | 0.779045i | ||||
\(103\) | 15.1168 | 1.48951 | 0.744753 | − | 0.667340i | \(-0.232567\pi\) | ||||
0.744753 | + | 0.667340i | \(0.232567\pi\) | |||||||
\(104\) | −2.00000 | −0.196116 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.37228 | 0.133288 | ||||||||
\(107\) | −17.7446 | −1.71543 | −0.857716 | − | 0.514124i | \(-0.828117\pi\) | ||||
−0.857716 | + | 0.514124i | \(0.828117\pi\) | |||||||
\(108\) | −4.00000 | + | 3.31662i | −0.384900 | + | 0.319142i | ||||
\(109\) | 9.11684 | 0.873235 | 0.436618 | − | 0.899647i | \(-0.356176\pi\) | ||||
0.436618 | + | 0.899647i | \(0.356176\pi\) | |||||||
\(110\) | 9.05842 | − | 2.92048i | 0.863687 | − | 0.278457i | ||||
\(111\) | 14.7446 | − | 13.8564i | 1.39949 | − | 1.31519i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.25544 | 0.306246 | 0.153123 | − | 0.988207i | \(-0.451067\pi\) | ||||
0.153123 | + | 0.988207i | \(0.451067\pi\) | |||||||
\(114\) | 4.37228 | − | 4.10891i | 0.409502 | − | 0.384835i | ||||
\(115\) | 3.00000 | + | 9.30506i | 0.279751 | + | 0.867702i | ||||
\(116\) | 3.31662i | 0.307941i | ||||||||
\(117\) | −0.372281 | + | 5.98844i | −0.0344174 | + | 0.553631i | ||||
\(118\) | −4.11684 | −0.378986 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.87228 | + | 3.39036i | −0.170915 | + | 0.309496i | ||||
\(121\) | −7.11684 | −0.646986 | ||||||||
\(122\) | − | 2.81929i | − | 0.255247i | ||||||
\(123\) | −1.93070 | − | 2.05446i | −0.174086 | − | 0.185244i | ||||
\(124\) | − | 2.37686i | − | 0.213448i | ||||||
\(125\) | 9.00000 | + | 6.63325i | 0.804984 | + | 0.593296i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 2.37686i | − | 0.210912i | −0.994424 | − | 0.105456i | \(-0.966370\pi\) | ||
0.994424 | − | 0.105456i | \(-0.0336303\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 13.9307 | − | 13.0916i | 1.22653 | − | 1.15265i | ||||
\(130\) | 1.37228 | + | 4.25639i | 0.120357 | + | 0.373310i | ||||
\(131\) | 4.62772 | 0.404326 | 0.202163 | − | 0.979352i | \(-0.435203\pi\) | ||||
0.202163 | + | 0.979352i | \(0.435203\pi\) | |||||||
\(132\) | 5.37228 | − | 5.04868i | 0.467597 | − | 0.439431i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 7.57301i | 0.654209i | ||||||||
\(135\) | 9.80298 | + | 6.23711i | 0.843707 | + | 0.536805i | ||||
\(136\) | 6.63325i | 0.568796i | ||||||||
\(137\) | −2.74456 | −0.234484 | −0.117242 | − | 0.993103i | \(-0.537405\pi\) | ||||
−0.117242 | + | 0.993103i | \(0.537405\pi\) | |||||||
\(138\) | 5.18614 | + | 5.51856i | 0.441474 | + | 0.469771i | ||||
\(139\) | − | 11.6819i | − | 0.990848i | −0.868651 | − | 0.495424i | \(-0.835013\pi\) | ||
0.868651 | − | 0.495424i | \(-0.164987\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.37228 | − | 2.22938i | 0.199782 | − | 0.187748i | ||||
\(142\) | 1.87953i | 0.157726i | ||||||||
\(143\) | − | 8.51278i | − | 0.711874i | ||||||
\(144\) | −0.186141 | + | 2.99422i | −0.0155117 | + | 0.249518i | ||||
\(145\) | 7.05842 | − | 2.27567i | 0.586170 | − | 0.188984i | ||||
\(146\) | −2.00000 | −0.165521 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 11.6819i | − | 0.960248i | ||||||
\(149\) | − | 14.2063i | − | 1.16382i | −0.813252 | − | 0.581911i | \(-0.802305\pi\) | ||
0.813252 | − | 0.581911i | \(-0.197695\pi\) | |||||||
\(150\) | 8.50000 | + | 1.65831i | 0.694022 | + | 0.135401i | ||||
\(151\) | −8.11684 | −0.660539 | −0.330270 | − | 0.943887i | \(-0.607140\pi\) | ||||
−0.330270 | + | 0.943887i | \(0.607140\pi\) | |||||||
\(152\) | − | 3.46410i | − | 0.280976i | ||||||
\(153\) | 19.8614 | + | 1.23472i | 1.60570 | + | 0.0998210i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.05842 | + | 1.63086i | −0.406302 | + | 0.130994i | ||||
\(156\) | 2.37228 | + | 2.52434i | 0.189935 | + | 0.202109i | ||||
\(157\) | 8.00000 | 0.638470 | 0.319235 | − | 0.947676i | \(-0.396574\pi\) | ||||
0.319235 | + | 0.947676i | \(0.396574\pi\) | |||||||
\(158\) | 8.11684 | 0.645741 | ||||||||
\(159\) | −1.62772 | − | 1.73205i | −0.129086 | − | 0.137361i | ||||
\(160\) | 0.686141 | + | 2.12819i | 0.0542442 | + | 0.168249i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 8.93070 | + | 1.11469i | 0.701662 | + | 0.0875785i | ||||
\(163\) | 3.46410i | 0.271329i | 0.990755 | + | 0.135665i | \(0.0433170\pi\) | ||||
−0.990755 | + | 0.135665i | \(0.956683\pi\) | |||||||
\(164\) | −1.62772 | −0.127103 | ||||||||
\(165\) | −14.4307 | − | 7.96916i | −1.12343 | − | 0.620398i | ||||
\(166\) | 1.43710i | 0.111540i | ||||||||
\(167\) | 11.3321i | 0.876902i | 0.898755 | + | 0.438451i | \(0.144473\pi\) | ||||
−0.898755 | + | 0.438451i | \(0.855527\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 14.1168 | − | 4.55134i | 1.08271 | − | 0.349072i | ||||
\(171\) | −10.3723 | − | 0.644810i | −0.793188 | − | 0.0493099i | ||||
\(172\) | − | 11.0371i | − | 0.841572i | ||||||
\(173\) | 3.75906i | 0.285796i | 0.989737 | + | 0.142898i | \(0.0456420\pi\) | ||||
−0.989737 | + | 0.142898i | \(0.954358\pi\) | |||||||
\(174\) | 4.18614 | − | 3.93398i | 0.317351 | − | 0.298235i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 4.25639i | − | 0.320837i | ||||||
\(177\) | 4.88316 | + | 5.19615i | 0.367040 | + | 0.390567i | ||||
\(178\) | −4.37228 | −0.327716 | ||||||||
\(179\) | 2.87419i | 0.214827i | 0.994214 | + | 0.107414i | \(0.0342569\pi\) | ||||
−0.994214 | + | 0.107414i | \(0.965743\pi\) | |||||||
\(180\) | 6.50000 | − | 1.65831i | 0.484481 | − | 0.123603i | ||||
\(181\) | 17.9653i | 1.33535i | 0.744452 | + | 0.667676i | \(0.232711\pi\) | ||||
−0.744452 | + | 0.667676i | \(0.767289\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.55842 | + | 3.34408i | −0.263046 | + | 0.247201i | ||||
\(184\) | 4.37228 | 0.322329 | ||||||||
\(185\) | −24.8614 | + | 8.01544i | −1.82785 | + | 0.589307i | ||||
\(186\) | −3.00000 | + | 2.81929i | −0.219971 | + | 0.206720i | ||||
\(187\) | −28.2337 | −2.06465 | ||||||||
\(188\) | − | 1.87953i | − | 0.137079i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −7.37228 | + | 2.37686i | −0.534842 | + | 0.172436i | ||||
\(191\) | 3.75906i | 0.271996i | 0.990709 | + | 0.135998i | \(0.0434240\pi\) | ||||
−0.990709 | + | 0.135998i | \(0.956576\pi\) | |||||||
\(192\) | 1.18614 | + | 1.26217i | 0.0856023 | + | 0.0910892i | ||||
\(193\) | − | 8.01544i | − | 0.576964i | −0.957485 | − | 0.288482i | \(-0.906849\pi\) | ||
0.957485 | − | 0.288482i | \(-0.0931506\pi\) | |||||||
\(194\) | 2.11684 | 0.151981 | ||||||||
\(195\) | 3.74456 | − | 6.78073i | 0.268154 | − | 0.485578i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 20.2337 | 1.44159 | 0.720795 | − | 0.693148i | \(-0.243777\pi\) | ||||
0.720795 | + | 0.693148i | \(0.243777\pi\) | |||||||
\(198\) | −12.7446 | − | 0.792287i | −0.905717 | − | 0.0563054i | ||||
\(199\) | − | 18.6101i | − | 1.31924i | −0.751601 | − | 0.659619i | \(-0.770718\pi\) | ||
0.751601 | − | 0.659619i | \(-0.229282\pi\) | |||||||
\(200\) | 4.05842 | − | 2.92048i | 0.286974 | − | 0.206509i | ||||
\(201\) | 9.55842 | − | 8.98266i | 0.674199 | − | 0.633588i | ||||
\(202\) | −16.3723 | −1.15195 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 8.37228 | − | 7.86797i | 0.586177 | − | 0.550868i | ||||
\(205\) | 1.11684 | + | 3.46410i | 0.0780038 | + | 0.241943i | ||||
\(206\) | −15.1168 | −1.05324 | ||||||||
\(207\) | 0.813859 | − | 13.0916i | 0.0565671 | − | 0.909927i | ||||
\(208\) | 2.00000 | 0.138675 | ||||||||
\(209\) | 14.7446 | 1.01990 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.2337 | −1.25526 | −0.627629 | − | 0.778512i | \(-0.715975\pi\) | ||||
−0.627629 | + | 0.778512i | \(0.715975\pi\) | |||||||
\(212\) | −1.37228 | −0.0942487 | ||||||||
\(213\) | 2.37228 | − | 2.22938i | 0.162546 | − | 0.152755i | ||||
\(214\) | 17.7446 | 1.21299 | ||||||||
\(215\) | −23.4891 | + | 7.57301i | −1.60195 | + | 0.516475i | ||||
\(216\) | 4.00000 | − | 3.31662i | 0.272166 | − | 0.225668i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −9.11684 | −0.617471 | ||||||||
\(219\) | 2.37228 | + | 2.52434i | 0.160304 | + | 0.170579i | ||||
\(220\) | −9.05842 | + | 2.92048i | −0.610719 | + | 0.196899i | ||||
\(221\) | − | 13.2665i | − | 0.892401i | ||||||
\(222\) | −14.7446 | + | 13.8564i | −0.989590 | + | 0.929981i | ||||
\(223\) | 18.1168 | 1.21319 | 0.606597 | − | 0.795010i | \(-0.292534\pi\) | ||||
0.606597 | + | 0.795010i | \(0.292534\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −7.98913 | − | 12.6954i | −0.532608 | − | 0.846362i | ||||
\(226\) | −3.25544 | −0.216548 | ||||||||
\(227\) | 15.6434i | 1.03829i | 0.854687 | + | 0.519143i | \(0.173749\pi\) | ||||
−0.854687 | + | 0.519143i | \(0.826251\pi\) | |||||||
\(228\) | −4.37228 | + | 4.10891i | −0.289561 | + | 0.272119i | ||||
\(229\) | − | 13.8564i | − | 0.915657i | −0.889041 | − | 0.457829i | \(-0.848627\pi\) | ||
0.889041 | − | 0.457829i | \(-0.151373\pi\) | |||||||
\(230\) | −3.00000 | − | 9.30506i | −0.197814 | − | 0.613558i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 3.31662i | − | 0.217747i | ||||||
\(233\) | 23.4891 | 1.53882 | 0.769412 | − | 0.638753i | \(-0.220549\pi\) | ||||
0.769412 | + | 0.638753i | \(0.220549\pi\) | |||||||
\(234\) | 0.372281 | − | 5.98844i | 0.0243368 | − | 0.391477i | ||||
\(235\) | −4.00000 | + | 1.28962i | −0.260931 | + | 0.0841256i | ||||
\(236\) | 4.11684 | 0.267984 | ||||||||
\(237\) | −9.62772 | − | 10.2448i | −0.625388 | − | 0.665473i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.87419i | 0.185916i | 0.995670 | + | 0.0929581i | \(0.0296323\pi\) | ||||
−0.995670 | + | 0.0929581i | \(0.970368\pi\) | |||||||
\(240\) | 1.87228 | − | 3.39036i | 0.120855 | − | 0.218847i | ||||
\(241\) | 10.5947i | 0.682464i | 0.939979 | + | 0.341232i | \(0.110844\pi\) | ||||
−0.939979 | + | 0.341232i | \(0.889156\pi\) | |||||||
\(242\) | 7.11684 | 0.457488 | ||||||||
\(243\) | −9.18614 | − | 12.5942i | −0.589291 | − | 0.807921i | ||||
\(244\) | 2.81929i | 0.180487i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.93070 | + | 2.05446i | 0.123097 | + | 0.130987i | ||||
\(247\) | 6.92820i | 0.440831i | ||||||||
\(248\) | 2.37686i | 0.150931i | ||||||||
\(249\) | 1.81386 | − | 1.70460i | 0.114949 | − | 0.108025i | ||||
\(250\) | −9.00000 | − | 6.63325i | −0.569210 | − | 0.419524i | ||||
\(251\) | −16.1168 | −1.01729 | −0.508643 | − | 0.860977i | \(-0.669853\pi\) | ||||
−0.508643 | + | 0.860977i | \(0.669853\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 18.6101i | 1.17001i | ||||||||
\(254\) | 2.37686i | 0.149138i | ||||||||
\(255\) | −22.4891 | − | 12.4193i | −1.40832 | − | 0.777727i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 8.51278i | 0.531012i | 0.964109 | + | 0.265506i | \(0.0855391\pi\) | ||||
−0.964109 | + | 0.265506i | \(0.914461\pi\) | |||||||
\(258\) | −13.9307 | + | 13.0916i | −0.867288 | + | 0.815046i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −1.37228 | − | 4.25639i | −0.0851053 | − | 0.263970i | ||||
\(261\) | −9.93070 | − | 0.617359i | −0.614695 | − | 0.0382135i | ||||
\(262\) | −4.62772 | −0.285901 | ||||||||
\(263\) | −1.62772 | −0.100369 | −0.0501847 | − | 0.998740i | \(-0.515981\pi\) | ||||
−0.0501847 | + | 0.998740i | \(0.515981\pi\) | |||||||
\(264\) | −5.37228 | + | 5.04868i | −0.330641 | + | 0.310725i | ||||
\(265\) | 0.941578 | + | 2.92048i | 0.0578407 | + | 0.179404i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.18614 | + | 5.51856i | 0.317387 | + | 0.337730i | ||||
\(268\) | − | 7.57301i | − | 0.462595i | ||||||
\(269\) | 19.9783 | 1.21810 | 0.609048 | − | 0.793134i | \(-0.291552\pi\) | ||||
0.609048 | + | 0.793134i | \(0.291552\pi\) | |||||||
\(270\) | −9.80298 | − | 6.23711i | −0.596591 | − | 0.379578i | ||||
\(271\) | 20.9870i | 1.27487i | 0.770505 | + | 0.637434i | \(0.220004\pi\) | ||||
−0.770505 | + | 0.637434i | \(0.779996\pi\) | |||||||
\(272\) | − | 6.63325i | − | 0.402200i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.74456 | 0.165805 | ||||||||
\(275\) | 12.4307 | + | 17.2742i | 0.749600 | + | 1.04167i | ||||
\(276\) | −5.18614 | − | 5.51856i | −0.312169 | − | 0.332178i | ||||
\(277\) | 29.0024i | 1.74259i | 0.490762 | + | 0.871294i | \(0.336718\pi\) | ||||
−0.490762 | + | 0.871294i | \(0.663282\pi\) | |||||||
\(278\) | 11.6819i | 0.700635i | ||||||||
\(279\) | 7.11684 | + | 0.442430i | 0.426074 | + | 0.0264876i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 21.7793i | − | 1.29924i | −0.760258 | − | 0.649621i | \(-0.774927\pi\) | ||
0.760258 | − | 0.649621i | \(-0.225073\pi\) | |||||||
\(282\) | −2.37228 | + | 2.22938i | −0.141267 | + | 0.132758i | ||||
\(283\) | −16.0000 | −0.951101 | −0.475551 | − | 0.879688i | \(-0.657751\pi\) | ||||
−0.475551 | + | 0.879688i | \(0.657751\pi\) | |||||||
\(284\) | − | 1.87953i | − | 0.111529i | ||||||
\(285\) | 11.7446 | + | 6.48577i | 0.695688 | + | 0.384184i | ||||
\(286\) | 8.51278i | 0.503371i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.186141 | − | 2.99422i | 0.0109684 | − | 0.176436i | ||||
\(289\) | −27.0000 | −1.58824 | ||||||||
\(290\) | −7.05842 | + | 2.27567i | −0.414485 | + | 0.133632i | ||||
\(291\) | −2.51087 | − | 2.67181i | −0.147190 | − | 0.156625i | ||||
\(292\) | 2.00000 | 0.117041 | ||||||||
\(293\) | − | 25.0410i | − | 1.46291i | −0.681889 | − | 0.731455i | \(-0.738841\pi\) | ||
0.681889 | − | 0.731455i | \(-0.261159\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.82473 | − | 8.76144i | −0.164462 | − | 0.510111i | ||||
\(296\) | 11.6819i | 0.678998i | ||||||||
\(297\) | 14.1168 | + | 17.0256i | 0.819142 | + | 0.987923i | ||||
\(298\) | 14.2063i | 0.822947i | ||||||||
\(299\) | −8.74456 | −0.505711 | ||||||||
\(300\) | −8.50000 | − | 1.65831i | −0.490748 | − | 0.0957427i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 8.11684 | 0.467072 | ||||||||
\(303\) | 19.4198 | + | 20.6646i | 1.11564 | + | 1.18715i | ||||
\(304\) | 3.46410i | 0.198680i | ||||||||
\(305\) | 6.00000 | − | 1.93443i | 0.343559 | − | 0.110765i | ||||
\(306\) | −19.8614 | − | 1.23472i | −1.13540 | − | 0.0705841i | ||||
\(307\) | 6.88316 | 0.392842 | 0.196421 | − | 0.980520i | \(-0.437068\pi\) | ||||
0.196421 | + | 0.980520i | \(0.437068\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 17.9307 | + | 19.0800i | 1.02004 | + | 1.08542i | ||||
\(310\) | 5.05842 | − | 1.63086i | 0.287299 | − | 0.0926267i | ||||
\(311\) | −14.2337 | −0.807118 | −0.403559 | − | 0.914954i | \(-0.632227\pi\) | ||||
−0.403559 | + | 0.914954i | \(0.632227\pi\) | |||||||
\(312\) | −2.37228 | − | 2.52434i | −0.134304 | − | 0.142912i | ||||
\(313\) | −14.1168 | −0.797931 | −0.398966 | − | 0.916966i | \(-0.630631\pi\) | ||||
−0.398966 | + | 0.916966i | \(0.630631\pi\) | |||||||
\(314\) | −8.00000 | −0.451466 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.11684 | −0.456608 | ||||||||
\(317\) | −16.1168 | −0.905212 | −0.452606 | − | 0.891711i | \(-0.649506\pi\) | ||||
−0.452606 | + | 0.891711i | \(0.649506\pi\) | |||||||
\(318\) | 1.62772 | + | 1.73205i | 0.0912779 | + | 0.0971286i | ||||
\(319\) | 14.1168 | 0.790392 | ||||||||
\(320\) | −0.686141 | − | 2.12819i | −0.0383564 | − | 0.118970i | ||||
\(321\) | −21.0475 | − | 22.3966i | −1.17476 | − | 1.25006i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 22.9783 | 1.27854 | ||||||||
\(324\) | −8.93070 | − | 1.11469i | −0.496150 | − | 0.0619273i | ||||
\(325\) | −8.11684 | + | 5.84096i | −0.450241 | + | 0.323998i | ||||
\(326\) | − | 3.46410i | − | 0.191859i | ||||||
\(327\) | 10.8139 | + | 11.5070i | 0.598008 | + | 0.636338i | ||||
\(328\) | 1.62772 | 0.0898757 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 14.4307 | + | 7.96916i | 0.794384 | + | 0.438688i | ||||
\(331\) | 10.2337 | 0.562494 | 0.281247 | − | 0.959635i | \(-0.409252\pi\) | ||||
0.281247 | + | 0.959635i | \(0.409252\pi\) | |||||||
\(332\) | − | 1.43710i | − | 0.0788710i | ||||||
\(333\) | 34.9783 | + | 2.17448i | 1.91680 | + | 0.119161i | ||||
\(334\) | − | 11.3321i | − | 0.620063i | ||||||
\(335\) | −16.1168 | + | 5.19615i | −0.880557 | + | 0.283896i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 9.30506i | − | 0.506879i | −0.967351 | − | 0.253440i | \(-0.918438\pi\) | ||
0.967351 | − | 0.253440i | \(-0.0815619\pi\) | |||||||
\(338\) | 9.00000 | 0.489535 | ||||||||
\(339\) | 3.86141 | + | 4.10891i | 0.209723 | + | 0.223165i | ||||
\(340\) | −14.1168 | + | 4.55134i | −0.765593 | + | 0.246831i | ||||
\(341\) | −10.1168 | −0.547858 | ||||||||
\(342\) | 10.3723 | + | 0.644810i | 0.560869 | + | 0.0348673i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 11.0371i | 0.595081i | ||||||||
\(345\) | −8.18614 | + | 14.8236i | −0.440727 | + | 0.798077i | ||||
\(346\) | − | 3.75906i | − | 0.202088i | ||||||
\(347\) | −19.1168 | −1.02625 | −0.513123 | − | 0.858315i | \(-0.671512\pi\) | ||||
−0.513123 | + | 0.858315i | \(0.671512\pi\) | |||||||
\(348\) | −4.18614 | + | 3.93398i | −0.224401 | + | 0.210884i | ||||
\(349\) | 24.0087i | 1.28515i | 0.766221 | + | 0.642577i | \(0.222135\pi\) | ||||
−0.766221 | + | 0.642577i | \(0.777865\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.00000 | + | 6.63325i | −0.427008 | + | 0.354057i | ||||
\(352\) | 4.25639i | 0.226866i | ||||||||
\(353\) | 18.9051i | 1.00622i | 0.864224 | + | 0.503108i | \(0.167810\pi\) | ||||
−0.864224 | + | 0.503108i | \(0.832190\pi\) | |||||||
\(354\) | −4.88316 | − | 5.19615i | −0.259537 | − | 0.276172i | ||||
\(355\) | −4.00000 | + | 1.28962i | −0.212298 | + | 0.0684459i | ||||
\(356\) | 4.37228 | 0.231730 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 2.87419i | − | 0.151906i | ||||||
\(359\) | 14.1514i | 0.746880i | 0.927654 | + | 0.373440i | \(0.121822\pi\) | ||||
−0.927654 | + | 0.373440i | \(0.878178\pi\) | |||||||
\(360\) | −6.50000 | + | 1.65831i | −0.342580 | + | 0.0874007i | ||||
\(361\) | 7.00000 | 0.368421 | ||||||||
\(362\) | − | 17.9653i | − | 0.944236i | ||||||
\(363\) | −8.44158 | − | 8.98266i | −0.443068 | − | 0.471467i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.37228 | − | 4.25639i | −0.0718285 | − | 0.222790i | ||||
\(366\) | 3.55842 | − | 3.34408i | 0.186002 | − | 0.174798i | ||||
\(367\) | −21.2337 | −1.10839 | −0.554195 | − | 0.832387i | \(-0.686974\pi\) | ||||
−0.554195 | + | 0.832387i | \(0.686974\pi\) | |||||||
\(368\) | −4.37228 | −0.227921 | ||||||||
\(369\) | 0.302985 | − | 4.87375i | 0.0157727 | − | 0.253717i | ||||
\(370\) | 24.8614 | − | 8.01544i | 1.29248 | − | 0.416703i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 3.00000 | − | 2.81929i | 0.155543 | − | 0.146173i | ||||
\(373\) | 16.4356i | 0.851006i | 0.904957 | + | 0.425503i | \(0.139903\pi\) | ||||
−0.904957 | + | 0.425503i | \(0.860097\pi\) | |||||||
\(374\) | 28.2337 | 1.45993 | ||||||||
\(375\) | 2.30298 | + | 19.2275i | 0.118926 | + | 0.992903i | ||||
\(376\) | 1.87953i | 0.0969292i | ||||||||
\(377\) | 6.63325i | 0.341630i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 22.2337 | 1.14207 | 0.571034 | − | 0.820926i | \(-0.306542\pi\) | ||||
0.571034 | + | 0.820926i | \(0.306542\pi\) | |||||||
\(380\) | 7.37228 | − | 2.37686i | 0.378190 | − | 0.121930i | ||||
\(381\) | 3.00000 | − | 2.81929i | 0.153695 | − | 0.144437i | ||||
\(382\) | − | 3.75906i | − | 0.192330i | ||||||
\(383\) | 20.8395i | 1.06485i | 0.846477 | + | 0.532425i | \(0.178719\pi\) | ||||
−0.846477 | + | 0.532425i | \(0.821281\pi\) | |||||||
\(384\) | −1.18614 | − | 1.26217i | −0.0605300 | − | 0.0644098i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.01544i | 0.407975i | ||||||||
\(387\) | 33.0475 | + | 2.05446i | 1.67990 | + | 0.104434i | ||||
\(388\) | −2.11684 | −0.107466 | ||||||||
\(389\) | 34.0511i | 1.72646i | 0.504811 | + | 0.863230i | \(0.331562\pi\) | ||||
−0.504811 | + | 0.863230i | \(0.668438\pi\) | |||||||
\(390\) | −3.74456 | + | 6.78073i | −0.189613 | + | 0.343355i | ||||
\(391\) | 29.0024i | 1.46672i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.48913 | + | 5.84096i | 0.276890 | + | 0.294638i | ||||
\(394\) | −20.2337 | −1.01936 | ||||||||
\(395\) | 5.56930 | + | 17.2742i | 0.280222 | + | 0.869160i | ||||
\(396\) | 12.7446 | + | 0.792287i | 0.640438 | + | 0.0398139i | ||||
\(397\) | 8.00000 | 0.401508 | 0.200754 | − | 0.979642i | \(-0.435661\pi\) | ||||
0.200754 | + | 0.979642i | \(0.435661\pi\) | |||||||
\(398\) | 18.6101i | 0.932841i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.05842 | + | 2.92048i | −0.202921 | + | 0.146024i | ||||
\(401\) | − | 19.8448i | − | 0.991004i | −0.868607 | − | 0.495502i | \(-0.834984\pi\) | ||
0.868607 | − | 0.495502i | \(-0.165016\pi\) | |||||||
\(402\) | −9.55842 | + | 8.98266i | −0.476731 | + | 0.448014i | ||||
\(403\) | − | 4.75372i | − | 0.236800i | ||||||
\(404\) | 16.3723 | 0.814551 | ||||||||
\(405\) | 3.75544 | + | 19.7711i | 0.186609 | + | 0.982434i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −49.7228 | −2.46467 | ||||||||
\(408\) | −8.37228 | + | 7.86797i | −0.414490 | + | 0.389522i | ||||
\(409\) | − | 35.4882i | − | 1.75478i | −0.479779 | − | 0.877389i | \(-0.659283\pi\) | ||
0.479779 | − | 0.877389i | \(-0.340717\pi\) | |||||||
\(410\) | −1.11684 | − | 3.46410i | −0.0551570 | − | 0.171080i | ||||
\(411\) | −3.25544 | − | 3.46410i | −0.160579 | − | 0.170872i | ||||
\(412\) | 15.1168 | 0.744753 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −0.813859 | + | 13.0916i | −0.0399990 | + | 0.643416i | ||||
\(415\) | −3.05842 | + | 0.986051i | −0.150132 | + | 0.0484033i | ||||
\(416\) | −2.00000 | −0.0980581 | ||||||||
\(417\) | 14.7446 | − | 13.8564i | 0.722044 | − | 0.678551i | ||||
\(418\) | −14.7446 | −0.721180 | ||||||||
\(419\) | 29.4891 | 1.44064 | 0.720319 | − | 0.693643i | \(-0.243995\pi\) | ||||
0.720319 | + | 0.693643i | \(0.243995\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.1168 | 0.736750 | 0.368375 | − | 0.929677i | \(-0.379914\pi\) | ||||
0.368375 | + | 0.929677i | \(0.379914\pi\) | |||||||
\(422\) | 18.2337 | 0.887602 | ||||||||
\(423\) | 5.62772 | + | 0.349857i | 0.273629 | + | 0.0170106i | ||||
\(424\) | 1.37228 | 0.0666439 | ||||||||
\(425\) | 19.3723 | + | 26.9205i | 0.939694 | + | 1.30584i | ||||
\(426\) | −2.37228 | + | 2.22938i | −0.114937 | + | 0.108014i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −17.7446 | −0.857716 | ||||||||
\(429\) | 10.7446 | − | 10.0974i | 0.518752 | − | 0.487505i | ||||
\(430\) | 23.4891 | − | 7.57301i | 1.13275 | − | 0.365203i | ||||
\(431\) | 3.75906i | 0.181067i | 0.995893 | + | 0.0905337i | \(0.0288573\pi\) | ||||
−0.995893 | + | 0.0905337i | \(0.971143\pi\) | |||||||
\(432\) | −4.00000 | + | 3.31662i | −0.192450 | + | 0.159571i | ||||
\(433\) | −34.0000 | −1.63394 | −0.816968 | − | 0.576683i | \(-0.804347\pi\) | ||||
−0.816968 | + | 0.576683i | \(0.804347\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 11.2446 | + | 6.20965i | 0.539136 | + | 0.297730i | ||||
\(436\) | 9.11684 | 0.436618 | ||||||||
\(437\) | − | 15.1460i | − | 0.724533i | ||||||
\(438\) | −2.37228 | − | 2.52434i | −0.113352 | − | 0.120618i | ||||
\(439\) | 12.7692i | 0.609439i | 0.952442 | + | 0.304720i | \(0.0985627\pi\) | ||||
−0.952442 | + | 0.304720i | \(0.901437\pi\) | |||||||
\(440\) | 9.05842 | − | 2.92048i | 0.431843 | − | 0.139228i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 13.2665i | 0.631023i | ||||||||
\(443\) | −9.00000 | −0.427603 | −0.213801 | − | 0.976877i | \(-0.568585\pi\) | ||||
−0.213801 | + | 0.976877i | \(0.568585\pi\) | |||||||
\(444\) | 14.7446 | − | 13.8564i | 0.699746 | − | 0.657596i | ||||
\(445\) | −3.00000 | − | 9.30506i | −0.142214 | − | 0.441102i | ||||
\(446\) | −18.1168 | −0.857857 | ||||||||
\(447\) | 17.9307 | − | 16.8506i | 0.848093 | − | 0.797007i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 35.9855i | 1.69826i | 0.528182 | + | 0.849131i | \(0.322874\pi\) | ||||
−0.528182 | + | 0.849131i | \(0.677126\pi\) | |||||||
\(450\) | 7.98913 | + | 12.6954i | 0.376611 | + | 0.598468i | ||||
\(451\) | 6.92820i | 0.326236i | ||||||||
\(452\) | 3.25544 | 0.153123 | ||||||||
\(453\) | −9.62772 | − | 10.2448i | −0.452350 | − | 0.481344i | ||||
\(454\) | − | 15.6434i | − | 0.734179i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4.37228 | − | 4.10891i | 0.204751 | − | 0.192417i | ||||
\(457\) | − | 12.7692i | − | 0.597316i | −0.954360 | − | 0.298658i | \(-0.903461\pi\) | ||
0.954360 | − | 0.298658i | \(-0.0965390\pi\) | |||||||
\(458\) | 13.8564i | 0.647467i | ||||||||
\(459\) | 22.0000 | + | 26.5330i | 1.02687 | + | 1.23845i | ||||
\(460\) | 3.00000 | + | 9.30506i | 0.139876 | + | 0.433851i | ||||
\(461\) | 0.510875 | 0.0237938 | 0.0118969 | − | 0.999929i | \(-0.496213\pi\) | ||||
0.0118969 | + | 0.999929i | \(0.496213\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 36.5754i | 1.69981i | 0.526940 | + | 0.849903i | \(0.323339\pi\) | ||||
−0.526940 | + | 0.849903i | \(0.676661\pi\) | |||||||
\(464\) | 3.31662i | 0.153970i | ||||||||
\(465\) | −8.05842 | − | 4.45015i | −0.373700 | − | 0.206371i | ||||
\(466\) | −23.4891 | −1.08811 | ||||||||
\(467\) | 0.0549029i | 0.00254060i | 0.999999 | + | 0.00127030i | \(0.000404349\pi\) | ||||
−0.999999 | + | 0.00127030i | \(0.999596\pi\) | |||||||
\(468\) | −0.372281 | + | 5.98844i | −0.0172087 | + | 0.276816i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 4.00000 | − | 1.28962i | 0.184506 | − | 0.0594858i | ||||
\(471\) | 9.48913 | + | 10.0974i | 0.437236 | + | 0.465261i | ||||
\(472\) | −4.11684 | −0.189493 | ||||||||
\(473\) | −46.9783 | −2.16006 | ||||||||
\(474\) | 9.62772 | + | 10.2448i | 0.442216 | + | 0.470561i | ||||
\(475\) | −10.1168 | − | 14.0588i | −0.464193 | − | 0.645061i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.255437 | − | 4.10891i | 0.0116957 | − | 0.188134i | ||||
\(478\) | − | 2.87419i | − | 0.131463i | ||||||
\(479\) | −8.74456 | −0.399549 | −0.199775 | − | 0.979842i | \(-0.564021\pi\) | ||||
−0.199775 | + | 0.979842i | \(0.564021\pi\) | |||||||
\(480\) | −1.87228 | + | 3.39036i | −0.0854576 | + | 0.154748i | ||||
\(481\) | − | 23.3639i | − | 1.06530i | ||||||
\(482\) | − | 10.5947i | − | 0.482575i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7.11684 | −0.323493 | ||||||||
\(485\) | 1.45245 | + | 4.50506i | 0.0659525 | + | 0.204564i | ||||
\(486\) | 9.18614 | + | 12.5942i | 0.416692 | + | 0.571286i | ||||
\(487\) | 4.55134i | 0.206241i | 0.994669 | + | 0.103121i | \(0.0328827\pi\) | ||||
−0.994669 | + | 0.103121i | \(0.967117\pi\) | |||||||
\(488\) | − | 2.81929i | − | 0.127623i | ||||||
\(489\) | −4.37228 | + | 4.10891i | −0.197721 | + | 0.185811i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 26.9205i | 1.21491i | 0.794355 | + | 0.607453i | \(0.207809\pi\) | ||||
−0.794355 | + | 0.607453i | \(0.792191\pi\) | |||||||
\(492\) | −1.93070 | − | 2.05446i | −0.0870428 | − | 0.0926220i | ||||
\(493\) | 22.0000 | 0.990830 | ||||||||
\(494\) | − | 6.92820i | − | 0.311715i | ||||||
\(495\) | −7.05842 | − | 27.6665i | −0.317252 | − | 1.24352i | ||||
\(496\) | − | 2.37686i | − | 0.106724i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −1.81386 | + | 1.70460i | −0.0812810 | + | 0.0763849i | ||||
\(499\) | 28.2337 | 1.26391 | 0.631957 | − | 0.775004i | \(-0.282252\pi\) | ||||
0.631957 | + | 0.775004i | \(0.282252\pi\) | |||||||
\(500\) | 9.00000 | + | 6.63325i | 0.402492 | + | 0.296648i | ||||
\(501\) | −14.3030 | + | 13.4414i | −0.639010 | + | 0.600519i | ||||
\(502\) | 16.1168 | 0.719330 | ||||||||
\(503\) | − | 9.45254i | − | 0.421468i | −0.977543 | − | 0.210734i | \(-0.932415\pi\) | ||
0.977543 | − | 0.210734i | \(-0.0675854\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11.2337 | − | 34.8434i | −0.499893 | − | 1.55051i | ||||
\(506\) | − | 18.6101i | − | 0.827321i | ||||||
\(507\) | −10.6753 | − | 11.3595i | −0.474105 | − | 0.504494i | ||||
\(508\) | − | 2.37686i | − | 0.105456i | ||||||
\(509\) | −0.255437 | −0.0113221 | −0.00566103 | − | 0.999984i | \(-0.501802\pi\) | ||||
−0.00566103 | + | 0.999984i | \(0.501802\pi\) | |||||||
\(510\) | 22.4891 | + | 12.4193i | 0.995835 | + | 0.549936i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −11.4891 | − | 13.8564i | −0.507257 | − | 0.611775i | ||||
\(514\) | − | 8.51278i | − | 0.375483i | ||||||
\(515\) | −10.3723 | − | 32.1716i | −0.457057 | − | 1.41765i | ||||
\(516\) | 13.9307 | − | 13.0916i | 0.613265 | − | 0.576324i | ||||
\(517\) | −8.00000 | −0.351840 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.74456 | + | 4.45877i | −0.208263 | + | 0.195718i | ||||
\(520\) | 1.37228 | + | 4.25639i | 0.0601785 | + | 0.186655i | ||||
\(521\) | −3.25544 | −0.142623 | −0.0713116 | − | 0.997454i | \(-0.522718\pi\) | ||||
−0.0713116 | + | 0.997454i | \(0.522718\pi\) | |||||||
\(522\) | 9.93070 | + | 0.617359i | 0.434655 | + | 0.0270211i | ||||
\(523\) | −24.2337 | −1.05967 | −0.529833 | − | 0.848102i | \(-0.677745\pi\) | ||||
−0.529833 | + | 0.848102i | \(0.677745\pi\) | |||||||
\(524\) | 4.62772 | 0.202163 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.62772 | 0.0709719 | ||||||||
\(527\) | −15.7663 | −0.686791 | ||||||||
\(528\) | 5.37228 | − | 5.04868i | 0.233799 | − | 0.219715i | ||||
\(529\) | −3.88316 | −0.168833 | ||||||||
\(530\) | −0.941578 | − | 2.92048i | −0.0408995 | − | 0.126858i | ||||
\(531\) | −0.766312 | + | 12.3267i | −0.0332551 | + | 0.534935i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.25544 | −0.141009 | ||||||||
\(534\) | −5.18614 | − | 5.51856i | −0.224426 | − | 0.238811i | ||||
\(535\) | 12.1753 | + | 37.7639i | 0.526383 | + | 1.63267i | ||||
\(536\) | 7.57301i | 0.327104i | ||||||||
\(537\) | −3.62772 | + | 3.40920i | −0.156548 | + | 0.147118i | ||||
\(538\) | −19.9783 | −0.861324 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 9.80298 | + | 6.23711i | 0.421853 | + | 0.268402i | ||||
\(541\) | −13.3505 | −0.573984 | −0.286992 | − | 0.957933i | \(-0.592655\pi\) | ||||
−0.286992 | + | 0.957933i | \(0.592655\pi\) | |||||||
\(542\) | − | 20.9870i | − | 0.901468i | ||||||
\(543\) | −22.6753 | + | 21.3094i | −0.973089 | + | 0.914474i | ||||
\(544\) | 6.63325i | 0.284398i | ||||||||
\(545\) | −6.25544 | − | 19.4024i | −0.267953 | − | 0.831108i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 0.644810i | − | 0.0275701i | −0.999905 | − | 0.0137850i | \(-0.995612\pi\) | ||
0.999905 | − | 0.0137850i | \(-0.00438806\pi\) | |||||||
\(548\) | −2.74456 | −0.117242 | ||||||||
\(549\) | −8.44158 | − | 0.524785i | −0.360278 | − | 0.0223973i | ||||
\(550\) | −12.4307 | − | 17.2742i | −0.530047 | − | 0.736575i | ||||
\(551\) | −11.4891 | −0.489453 | ||||||||
\(552\) | 5.18614 | + | 5.51856i | 0.220737 | + | 0.234885i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 29.0024i | − | 1.23220i | ||||||
\(555\) | −39.6060 | − | 21.8719i | −1.68118 | − | 0.928408i | ||||
\(556\) | − | 11.6819i | − | 0.495424i | ||||||
\(557\) | 0.861407 | 0.0364990 | 0.0182495 | − | 0.999833i | \(-0.494191\pi\) | ||||
0.0182495 | + | 0.999833i | \(0.494191\pi\) | |||||||
\(558\) | −7.11684 | − | 0.442430i | −0.301280 | − | 0.0187296i | ||||
\(559\) | − | 22.0742i | − | 0.933640i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −33.4891 | − | 35.6357i | −1.41391 | − | 1.50454i | ||||
\(562\) | 21.7793i | 0.918703i | ||||||||
\(563\) | − | 11.8294i | − | 0.498550i | −0.968433 | − | 0.249275i | \(-0.919808\pi\) | ||
0.968433 | − | 0.249275i | \(-0.0801923\pi\) | |||||||
\(564\) | 2.37228 | − | 2.22938i | 0.0998911 | − | 0.0938740i | ||||
\(565\) | −2.23369 | − | 6.92820i | −0.0939720 | − | 0.291472i | ||||
\(566\) | 16.0000 | 0.672530 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.87953i | 0.0788632i | ||||||||
\(569\) | − | 21.7793i | − | 0.913035i | −0.889714 | − | 0.456517i | \(-0.849097\pi\) | ||
0.889714 | − | 0.456517i | \(-0.150903\pi\) | |||||||
\(570\) | −11.7446 | − | 6.48577i | −0.491926 | − | 0.271659i | ||||
\(571\) | 34.2337 | 1.43264 | 0.716318 | − | 0.697774i | \(-0.245826\pi\) | ||||
0.716318 | + | 0.697774i | \(0.245826\pi\) | |||||||
\(572\) | − | 8.51278i | − | 0.355937i | ||||||
\(573\) | −4.74456 | + | 4.45877i | −0.198207 | + | 0.186268i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 17.7446 | − | 12.7692i | 0.739999 | − | 0.532511i | ||||
\(576\) | −0.186141 | + | 2.99422i | −0.00775586 | + | 0.124759i | ||||
\(577\) | −17.8832 | −0.744486 | −0.372243 | − | 0.928135i | \(-0.621411\pi\) | ||||
−0.372243 | + | 0.928135i | \(0.621411\pi\) | |||||||
\(578\) | 27.0000 | 1.12305 | ||||||||
\(579\) | 10.1168 | − | 9.50744i | 0.420442 | − | 0.395116i | ||||
\(580\) | 7.05842 | − | 2.27567i | 0.293085 | − | 0.0944921i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 2.51087 | + | 2.67181i | 0.104079 | + | 0.110750i | ||||
\(583\) | 5.84096i | 0.241908i | ||||||||
\(584\) | −2.00000 | −0.0827606 | ||||||||
\(585\) | 13.0000 | − | 3.31662i | 0.537484 | − | 0.137126i | ||||
\(586\) | 25.0410i | 1.03443i | ||||||||
\(587\) | 36.4280i | 1.50354i | 0.659424 | + | 0.751772i | \(0.270800\pi\) | ||||
−0.659424 | + | 0.751772i | \(0.729200\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.23369 | 0.339263 | ||||||||
\(590\) | 2.82473 | + | 8.76144i | 0.116292 | + | 0.360703i | ||||
\(591\) | 24.0000 | + | 25.5383i | 0.987228 | + | 1.05051i | ||||
\(592\) | − | 11.6819i | − | 0.480124i | ||||||
\(593\) | 14.1514i | 0.581127i | 0.956856 | + | 0.290563i | \(0.0938427\pi\) | ||||
−0.956856 | + | 0.290563i | \(0.906157\pi\) | |||||||
\(594\) | −14.1168 | − | 17.0256i | −0.579221 | − | 0.698567i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 14.2063i | − | 0.581911i | ||||||
\(597\) | 23.4891 | − | 22.0742i | 0.961346 | − | 0.903438i | ||||
\(598\) | 8.74456 | 0.357592 | ||||||||
\(599\) | 8.51278i | 0.347823i | 0.984761 | + | 0.173911i | \(0.0556406\pi\) | ||||
−0.984761 | + | 0.173911i | \(0.944359\pi\) | |||||||
\(600\) | 8.50000 | + | 1.65831i | 0.347011 | + | 0.0677003i | ||||
\(601\) | − | 10.5947i | − | 0.432166i | −0.976375 | − | 0.216083i | \(-0.930672\pi\) | ||
0.976375 | − | 0.216083i | \(-0.0693282\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 22.6753 | + | 1.40965i | 0.923408 | + | 0.0574052i | ||||
\(604\) | −8.11684 | −0.330270 | ||||||||
\(605\) | 4.88316 | + | 15.1460i | 0.198529 | + | 0.615774i | ||||
\(606\) | −19.4198 | − | 20.6646i | −0.788877 | − | 0.839441i | ||||
\(607\) | 27.4674 | 1.11487 | 0.557433 | − | 0.830222i | \(-0.311786\pi\) | ||||
0.557433 | + | 0.830222i | \(0.311786\pi\) | |||||||
\(608\) | − | 3.46410i | − | 0.140488i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −6.00000 | + | 1.93443i | −0.242933 | + | 0.0783228i | ||||
\(611\) | − | 3.75906i | − | 0.152075i | ||||||
\(612\) | 19.8614 | + | 1.23472i | 0.802850 | + | 0.0499105i | ||||
\(613\) | − | 12.9715i | − | 0.523916i | −0.965079 | − | 0.261958i | \(-0.915632\pi\) | ||
0.965079 | − | 0.261958i | \(-0.0843682\pi\) | |||||||
\(614\) | −6.88316 | −0.277782 | ||||||||
\(615\) | −3.04755 | + | 5.51856i | −0.122889 | + | 0.222530i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.02175 | 0.0411341 | 0.0205670 | − | 0.999788i | \(-0.493453\pi\) | ||||
0.0205670 | + | 0.999788i | \(0.493453\pi\) | |||||||
\(618\) | −17.9307 | − | 19.0800i | −0.721279 | − | 0.767511i | ||||
\(619\) | 23.3639i | 0.939072i | 0.882913 | + | 0.469536i | \(0.155579\pi\) | ||||
−0.882913 | + | 0.469536i | \(0.844421\pi\) | |||||||
\(620\) | −5.05842 | + | 1.63086i | −0.203151 | + | 0.0654970i | ||||
\(621\) | 17.4891 | − | 14.5012i | 0.701814 | − | 0.581914i | ||||
\(622\) | 14.2337 | 0.570719 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 2.37228 | + | 2.52434i | 0.0949673 | + | 0.101054i | ||||
\(625\) | 7.94158 | − | 23.7051i | 0.317663 | − | 0.948204i | ||||
\(626\) | 14.1168 | 0.564223 | ||||||||
\(627\) | 17.4891 | + | 18.6101i | 0.698448 | + | 0.743217i | ||||
\(628\) | 8.00000 | 0.319235 | ||||||||
\(629\) | −77.4891 | −3.08969 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 30.1168 | 1.19893 | 0.599466 | − | 0.800400i | \(-0.295380\pi\) | ||||
0.599466 | + | 0.800400i | \(0.295380\pi\) | |||||||
\(632\) | 8.11684 | 0.322871 | ||||||||
\(633\) | −21.6277 | − | 23.0140i | −0.859625 | − | 0.914724i | ||||
\(634\) | 16.1168 | 0.640082 | ||||||||
\(635\) | −5.05842 | + | 1.63086i | −0.200737 | + | 0.0647187i | ||||
\(636\) | −1.62772 | − | 1.73205i | −0.0645432 | − | 0.0686803i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −14.1168 | −0.558891 | ||||||||
\(639\) | 5.62772 | + | 0.349857i | 0.222629 | + | 0.0138401i | ||||
\(640\) | 0.686141 | + | 2.12819i | 0.0271221 | + | 0.0841243i | ||||
\(641\) | − | 14.2063i | − | 0.561114i | −0.959837 | − | 0.280557i | \(-0.909481\pi\) | ||
0.959837 | − | 0.280557i | \(-0.0905191\pi\) | |||||||
\(642\) | 21.0475 | + | 22.3966i | 0.830680 | + | 0.883925i | ||||
\(643\) | 16.2337 | 0.640194 | 0.320097 | − | 0.947385i | \(-0.396284\pi\) | ||||
0.320097 | + | 0.947385i | \(0.396284\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −37.4198 | − | 20.6646i | −1.47340 | − | 0.813667i | ||||
\(646\) | −22.9783 | −0.904067 | ||||||||
\(647\) | − | 25.4834i | − | 1.00186i | −0.865489 | − | 0.500928i | \(-0.832992\pi\) | ||
0.865489 | − | 0.500928i | \(-0.167008\pi\) | |||||||
\(648\) | 8.93070 | + | 1.11469i | 0.350831 | + | 0.0437892i | ||||
\(649\) | − | 17.5229i | − | 0.687834i | ||||||
\(650\) | 8.11684 | − | 5.84096i | 0.318369 | − | 0.229101i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.46410i | 0.135665i | ||||||||
\(653\) | 10.6277 | 0.415895 | 0.207947 | − | 0.978140i | \(-0.433322\pi\) | ||||
0.207947 | + | 0.978140i | \(0.433322\pi\) | |||||||
\(654\) | −10.8139 | − | 11.5070i | −0.422855 | − | 0.449959i | ||||
\(655\) | −3.17527 | − | 9.84868i | −0.124068 | − | 0.384820i | ||||
\(656\) | −1.62772 | −0.0635517 | ||||||||
\(657\) | −0.372281 | + | 5.98844i | −0.0145241 | + | 0.233631i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 36.9253i | − | 1.43841i | −0.694800 | − | 0.719203i | \(-0.744507\pi\) | ||
0.694800 | − | 0.719203i | \(-0.255493\pi\) | |||||||
\(660\) | −14.4307 | − | 7.96916i | −0.561714 | − | 0.310199i | ||||
\(661\) | 2.81929i | 0.109658i | 0.998496 | + | 0.0548289i | \(0.0174613\pi\) | ||||
−0.998496 | + | 0.0548289i | \(0.982539\pi\) | |||||||
\(662\) | −10.2337 | −0.397744 | ||||||||
\(663\) | 16.7446 | − | 15.7359i | 0.650305 | − | 0.611133i | ||||
\(664\) | 1.43710i | 0.0557702i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −34.9783 | − | 2.17448i | −1.35538 | − | 0.0842594i | ||||
\(667\) | − | 14.5012i | − | 0.561489i | ||||||
\(668\) | 11.3321i | 0.438451i | ||||||||
\(669\) | 21.4891 | + | 22.8665i | 0.830818 | + | 0.884071i | ||||
\(670\) | 16.1168 | − | 5.19615i | 0.622648 | − | 0.200745i | ||||
\(671\) | 12.0000 | 0.463255 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 17.1181i | − | 0.659855i | −0.944006 | − | 0.329928i | \(-0.892976\pi\) | ||
0.944006 | − | 0.329928i | \(-0.107024\pi\) | |||||||
\(674\) | 9.30506i | 0.358418i | ||||||||
\(675\) | 6.54755 | − | 25.1422i | 0.252015 | − | 0.967723i | ||||
\(676\) | −9.00000 | −0.346154 | ||||||||
\(677\) | − | 44.9407i | − | 1.72721i | −0.504166 | − | 0.863607i | \(-0.668200\pi\) | ||
0.504166 | − | 0.863607i | \(-0.331800\pi\) | |||||||
\(678\) | −3.86141 | − | 4.10891i | −0.148296 | − | 0.157802i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 14.1168 | − | 4.55134i | 0.541356 | − | 0.174536i | ||||
\(681\) | −19.7446 | + | 18.5552i | −0.756613 | + | 0.711038i | ||||
\(682\) | 10.1168 | 0.387394 | ||||||||
\(683\) | 13.9783 | 0.534863 | 0.267431 | − | 0.963577i | \(-0.413825\pi\) | ||||
0.267431 | + | 0.963577i | \(0.413825\pi\) | |||||||
\(684\) | −10.3723 | − | 0.644810i | −0.396594 | − | 0.0246549i | ||||
\(685\) | 1.88316 | + | 5.84096i | 0.0719517 | + | 0.223172i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 17.4891 | − | 16.4356i | 0.667252 | − | 0.627059i | ||||
\(688\) | − | 11.0371i | − | 0.420786i | ||||||
\(689\) | −2.74456 | −0.104560 | ||||||||
\(690\) | 8.18614 | − | 14.8236i | 0.311641 | − | 0.564326i | ||||
\(691\) | 30.2921i | 1.15236i | 0.817321 | + | 0.576182i | \(0.195458\pi\) | ||||
−0.817321 | + | 0.576182i | \(0.804542\pi\) | |||||||
\(692\) | 3.75906i | 0.142898i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 19.1168 | 0.725665 | ||||||||
\(695\) | −24.8614 | + | 8.01544i | −0.943047 | + | 0.304043i | ||||
\(696\) | 4.18614 | − | 3.93398i | 0.158675 | − | 0.149117i | ||||
\(697\) | 10.7971i | 0.408968i | ||||||||
\(698\) | − | 24.0087i | − | 0.908741i | ||||||
\(699\) | 27.8614 | + | 29.6472i | 1.05382 | + | 1.12136i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 12.7143i | − | 0.480211i | −0.970747 | − | 0.240106i | \(-0.922818\pi\) | ||
0.970747 | − | 0.240106i | \(-0.0771821\pi\) | |||||||
\(702\) | 8.00000 | − | 6.63325i | 0.301941 | − | 0.250356i | ||||
\(703\) | 40.4674 | 1.52626 | ||||||||
\(704\) | − | 4.25639i | − | 0.160419i | ||||||
\(705\) | −6.37228 | − | 3.51900i | −0.239994 | − | 0.132533i | ||||
\(706\) | − | 18.9051i | − | 0.711502i | ||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 4.88316 | + | 5.19615i | 0.183520 | + | 0.195283i | ||||
\(709\) | −5.11684 | −0.192167 | −0.0960836 | − | 0.995373i | \(-0.530632\pi\) | ||||
−0.0960836 | + | 0.995373i | \(0.530632\pi\) | |||||||
\(710\) | 4.00000 | − | 1.28962i | 0.150117 | − | 0.0483986i | ||||
\(711\) | 1.51087 | − | 24.3036i | 0.0566622 | − | 0.911457i | ||||
\(712\) | −4.37228 | −0.163858 | ||||||||
\(713\) | 10.3923i | 0.389195i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −18.1168 | + | 5.84096i | −0.677532 | + | 0.218440i | ||||
\(716\) | 2.87419i | 0.107414i | ||||||||
\(717\) | −3.62772 | + | 3.40920i | −0.135480 | + | 0.127319i | ||||
\(718\) | − | 14.1514i | − | 0.528124i | ||||||
\(719\) | 33.2554 | 1.24022 | 0.620109 | − | 0.784515i | \(-0.287088\pi\) | ||||
0.620109 | + | 0.784515i | \(0.287088\pi\) | |||||||
\(720\) | 6.50000 | − | 1.65831i | 0.242241 | − | 0.0618017i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −7.00000 | −0.260513 | ||||||||
\(723\) | −13.3723 | + | 12.5668i | −0.497320 | + | 0.467364i | ||||
\(724\) | 17.9653i | 0.667676i | ||||||||
\(725\) | −9.68614 | − | 13.4603i | −0.359734 | − | 0.499902i | ||||
\(726\) | 8.44158 | + | 8.98266i | 0.313296 | + | 0.333378i | ||||
\(727\) | −19.0000 | −0.704671 | −0.352335 | − | 0.935874i | \(-0.614612\pi\) | ||||
−0.352335 | + | 0.935874i | \(0.614612\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 5.00000 | − | 26.5330i | 0.185185 | − | 0.982704i | ||||
\(730\) | 1.37228 | + | 4.25639i | 0.0507904 | + | 0.157536i | ||||
\(731\) | −73.2119 | −2.70784 | ||||||||
\(732\) | −3.55842 | + | 3.34408i | −0.131523 | + | 0.123601i | ||||
\(733\) | 36.4674 | 1.34695 | 0.673477 | − | 0.739209i | \(-0.264800\pi\) | ||||
0.673477 | + | 0.739209i | \(0.264800\pi\) | |||||||
\(734\) | 21.2337 | 0.783750 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.37228 | 0.161164 | ||||||||
\(737\) | −32.2337 | −1.18734 | ||||||||
\(738\) | −0.302985 | + | 4.87375i | −0.0111530 | + | 0.179405i | ||||
\(739\) | −36.2337 | −1.33288 | −0.666439 | − | 0.745560i | \(-0.732182\pi\) | ||||
−0.666439 | + | 0.745560i | \(0.732182\pi\) | |||||||
\(740\) | −24.8614 | + | 8.01544i | −0.913923 | + | 0.294654i | ||||
\(741\) | −8.74456 | + | 8.21782i | −0.321240 | + | 0.301889i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18.6060 | 0.682587 | 0.341293 | − | 0.939957i | \(-0.389135\pi\) | ||||
0.341293 | + | 0.939957i | \(0.389135\pi\) | |||||||
\(744\) | −3.00000 | + | 2.81929i | −0.109985 | + | 0.103360i | ||||
\(745\) | −30.2337 | + | 9.74749i | −1.10768 | + | 0.357121i | ||||
\(746\) | − | 16.4356i | − | 0.601752i | ||||||
\(747\) | 4.30298 | + | 0.267502i | 0.157438 | + | 0.00978739i | ||||
\(748\) | −28.2337 | −1.03233 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −2.30298 | − | 19.2275i | −0.0840931 | − | 0.702089i | ||||
\(751\) | 42.1168 | 1.53687 | 0.768433 | − | 0.639931i | \(-0.221037\pi\) | ||||
0.768433 | + | 0.639931i | \(0.221037\pi\) | |||||||
\(752\) | − | 1.87953i | − | 0.0685393i | ||||||
\(753\) | −19.1168 | − | 20.3422i | −0.696657 | − | 0.741310i | ||||
\(754\) | − | 6.63325i | − | 0.241569i | ||||||
\(755\) | 5.56930 | + | 17.2742i | 0.202687 | + | 0.628673i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 5.63858i | − | 0.204938i | −0.994736 | − | 0.102469i | \(-0.967326\pi\) | ||
0.994736 | − | 0.102469i | \(-0.0326742\pi\) | |||||||
\(758\) | −22.2337 | −0.807564 | ||||||||
\(759\) | −23.4891 | + | 22.0742i | −0.852601 | + | 0.801244i | ||||
\(760\) | −7.37228 | + | 2.37686i | −0.267421 | + | 0.0862178i | ||||
\(761\) | 52.9783 | 1.92046 | 0.960230 | − | 0.279210i | \(-0.0900726\pi\) | ||||
0.960230 | + | 0.279210i | \(0.0900726\pi\) | |||||||
\(762\) | −3.00000 | + | 2.81929i | −0.108679 | + | 0.102132i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 3.75906i | 0.135998i | ||||||||
\(765\) | −11.0000 | − | 43.1161i | −0.397706 | − | 1.55887i | ||||
\(766\) | − | 20.8395i | − | 0.752962i | ||||||
\(767\) | 8.23369 | 0.297301 | ||||||||
\(768\) | 1.18614 | + | 1.26217i | 0.0428012 | + | 0.0455446i | ||||
\(769\) | − | 40.4820i | − | 1.45982i | −0.683545 | − | 0.729909i | \(-0.739563\pi\) | ||
0.683545 | − | 0.729909i | \(-0.260437\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10.7446 | + | 10.0974i | −0.386956 | + | 0.363647i | ||||
\(772\) | − | 8.01544i | − | 0.288482i | ||||||
\(773\) | − | 1.87953i | − | 0.0676019i | −0.999429 | − | 0.0338010i | \(-0.989239\pi\) | ||
0.999429 | − | 0.0338010i | \(-0.0107612\pi\) | |||||||
\(774\) | −33.0475 | − | 2.05446i | −1.18787 | − | 0.0738459i | ||||
\(775\) | 6.94158 | + | 9.64630i | 0.249349 | + | 0.346505i | ||||
\(776\) | 2.11684 | 0.0759903 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 34.0511i | − | 1.22079i | ||||||
\(779\) | − | 5.63858i | − | 0.202023i | ||||||
\(780\) | 3.74456 | − | 6.78073i | 0.134077 | − | 0.242789i | ||||
\(781\) | −8.00000 | −0.286263 | ||||||||
\(782\) | − | 29.0024i | − | 1.03712i | ||||||
\(783\) | −11.0000 | − | 13.2665i | −0.393108 | − | 0.474106i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.48913 | − | 17.0256i | −0.195915 | − | 0.607668i | ||||
\(786\) | −5.48913 | − | 5.84096i | −0.195791 | − | 0.208340i | ||||
\(787\) | 27.1168 | 0.966611 | 0.483306 | − | 0.875452i | \(-0.339436\pi\) | ||||
0.483306 | + | 0.875452i | \(0.339436\pi\) | |||||||
\(788\) | 20.2337 | 0.720795 | ||||||||
\(789\) | −1.93070 | − | 2.05446i | −0.0687349 | − | 0.0731406i | ||||
\(790\) | −5.56930 | − | 17.2742i | −0.198147 | − | 0.614589i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −12.7446 | − | 0.792287i | −0.452858 | − | 0.0281527i | ||||
\(793\) | 5.63858i | 0.200232i | ||||||||
\(794\) | −8.00000 | −0.283909 | ||||||||
\(795\) | −2.56930 | + | 4.65253i | −0.0911236 | + | 0.165008i | ||||
\(796\) | − | 18.6101i | − | 0.659619i | ||||||
\(797\) | − | 4.25639i | − | 0.150769i | −0.997155 | − | 0.0753845i | \(-0.975982\pi\) | ||
0.997155 | − | 0.0753845i | \(-0.0240184\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12.4674 | −0.441064 | ||||||||
\(800\) | 4.05842 | − | 2.92048i | 0.143487 | − | 0.103255i | ||||
\(801\) | −0.813859 | + | 13.0916i | −0.0287563 | + | 0.462568i | ||||
\(802\) | 19.8448i | 0.700746i | ||||||||
\(803\) | − | 8.51278i | − | 0.300409i | ||||||
\(804\) | 9.55842 | − | 8.98266i | 0.337100 | − | 0.316794i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 4.75372i | 0.167443i | ||||||||
\(807\) | 23.6970 | + | 25.2159i | 0.834174 | + | 0.887643i | ||||
\(808\) | −16.3723 | −0.575975 | ||||||||
\(809\) | − | 25.4834i | − | 0.895950i | −0.894046 | − | 0.447975i | \(-0.852145\pi\) | ||
0.894046 | − | 0.447975i | \(-0.147855\pi\) | |||||||
\(810\) | −3.75544 | − | 19.7711i | −0.131953 | − | 0.694686i | ||||
\(811\) | − | 10.3923i | − | 0.364923i | −0.983213 | − | 0.182462i | \(-0.941593\pi\) | ||
0.983213 | − | 0.182462i | \(-0.0584065\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −26.4891 | + | 24.8935i | −0.929014 | + | 0.873054i | ||||
\(814\) | 49.7228 | 1.74278 | ||||||||
\(815\) | 7.37228 | − | 2.37686i | 0.258240 | − | 0.0832578i | ||||
\(816\) | 8.37228 | − | 7.86797i | 0.293088 | − | 0.275434i | ||||
\(817\) | 38.2337 | 1.33763 | ||||||||
\(818\) | 35.4882i | 1.24082i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.11684 | + | 3.46410i | 0.0390019 | + | 0.120972i | ||||
\(821\) | 21.2819i | 0.742745i | 0.928484 | + | 0.371372i | \(0.121113\pi\) | ||||
−0.928484 | + | 0.371372i | \(0.878887\pi\) | |||||||
\(822\) | 3.25544 | + | 3.46410i | 0.113546 | + | 0.120824i | ||||
\(823\) | 43.5036i | 1.51644i | 0.651998 | + | 0.758221i | \(0.273931\pi\) | ||||
−0.651998 | + | 0.758221i | \(0.726069\pi\) | |||||||
\(824\) | −15.1168 | −0.526620 | ||||||||
\(825\) | −7.05842 | + | 36.1793i | −0.245743 | + | 1.25960i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −33.0000 | −1.14752 | −0.573761 | − | 0.819023i | \(-0.694516\pi\) | ||||
−0.573761 | + | 0.819023i | \(0.694516\pi\) | |||||||
\(828\) | 0.813859 | − | 13.0916i | 0.0282836 | − | 0.454964i | ||||
\(829\) | − | 18.6101i | − | 0.646356i | −0.946338 | − | 0.323178i | \(-0.895249\pi\) | ||
0.946338 | − | 0.323178i | \(-0.104751\pi\) | |||||||
\(830\) | 3.05842 | − | 0.986051i | 0.106159 | − | 0.0342263i | ||||
\(831\) | −36.6060 | + | 34.4010i | −1.26985 | + | 1.19336i | ||||
\(832\) | 2.00000 | 0.0693375 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −14.7446 | + | 13.8564i | −0.510562 | + | 0.479808i | ||||
\(835\) | 24.1168 | − | 7.77539i | 0.834598 | − | 0.269079i | ||||
\(836\) | 14.7446 | 0.509951 | ||||||||
\(837\) | 7.88316 | + | 9.50744i | 0.272482 | + | 0.328625i | ||||
\(838\) | −29.4891 | −1.01868 | ||||||||
\(839\) | −1.72281 | −0.0594781 | −0.0297391 | − | 0.999558i | \(-0.509468\pi\) | ||||
−0.0297391 | + | 0.999558i | \(0.509468\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 18.0000 | 0.620690 | ||||||||
\(842\) | −15.1168 | −0.520961 | ||||||||
\(843\) | 27.4891 | − | 25.8333i | 0.946776 | − | 0.889746i | ||||
\(844\) | −18.2337 | −0.627629 | ||||||||
\(845\) | 6.17527 | + | 19.1537i | 0.212436 | + | 0.658909i | ||||
\(846\) | −5.62772 | − | 0.349857i | −0.193485 | − | 0.0120283i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −1.37228 | −0.0471243 | ||||||||
\(849\) | −18.9783 | − | 20.1947i | −0.651332 | − | 0.693080i | ||||
\(850\) | −19.3723 | − | 26.9205i | −0.664464 | − | 0.923366i | ||||
\(851\) | 51.0767i | 1.75089i | ||||||||
\(852\) | 2.37228 | − | 2.22938i | 0.0812730 | − | 0.0763774i | ||||
\(853\) | 30.4674 | 1.04318 | 0.521592 | − | 0.853195i | \(-0.325339\pi\) | ||||
0.521592 | + | 0.853195i | \(0.325339\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.74456 | + | 22.5167i | 0.196460 | + | 0.770054i | ||||
\(856\) | 17.7446 | 0.606497 | ||||||||
\(857\) | − | 37.8102i | − | 1.29157i | −0.763519 | − | 0.645785i | \(-0.776530\pi\) | ||
0.763519 | − | 0.645785i | \(-0.223470\pi\) | |||||||
\(858\) | −10.7446 | + | 10.0974i | −0.366813 | + | 0.344718i | ||||
\(859\) | − | 32.8713i | − | 1.12155i | −0.827967 | − | 0.560777i | \(-0.810502\pi\) | ||
0.827967 | − | 0.560777i | \(-0.189498\pi\) | |||||||
\(860\) | −23.4891 | + | 7.57301i | −0.800973 | + | 0.258238i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 3.75906i | − | 0.128034i | ||||||
\(863\) | −7.62772 | −0.259651 | −0.129825 | − | 0.991537i | \(-0.541442\pi\) | ||||
−0.129825 | + | 0.991537i | \(0.541442\pi\) | |||||||
\(864\) | 4.00000 | − | 3.31662i | 0.136083 | − | 0.112834i | ||||
\(865\) | 8.00000 | − | 2.57924i | 0.272008 | − | 0.0876968i | ||||
\(866\) | 34.0000 | 1.15537 | ||||||||
\(867\) | −32.0258 | − | 34.0786i | −1.08765 | − | 1.15737i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 34.5484i | 1.17198i | ||||||||
\(870\) | −11.2446 | − | 6.20965i | −0.381226 | − | 0.210527i | ||||
\(871\) | − | 15.1460i | − | 0.513204i | ||||||
\(872\) | −9.11684 | −0.308735 | ||||||||
\(873\) | 0.394031 | − | 6.33830i | 0.0133359 | − | 0.214519i | ||||
\(874\) | 15.1460i | 0.512322i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.37228 | + | 2.52434i | 0.0801520 | + | 0.0852895i | ||||
\(877\) | 31.5817i | 1.06644i | 0.845977 | + | 0.533219i | \(0.179018\pi\) | ||||
−0.845977 | + | 0.533219i | \(0.820982\pi\) | |||||||
\(878\) | − | 12.7692i | − | 0.430938i | ||||||
\(879\) | 31.6060 | − | 29.7021i | 1.06604 | − | 1.00183i | ||||
\(880\) | −9.05842 | + | 2.92048i | −0.305359 | + | 0.0984494i | ||||
\(881\) | 51.3505 | 1.73004 | 0.865022 | − | 0.501734i | \(-0.167305\pi\) | ||||
0.865022 | + | 0.501734i | \(0.167305\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 54.9455i | 1.84906i | 0.381104 | + | 0.924532i | \(0.375544\pi\) | ||||
−0.381104 | + | 0.924532i | \(0.624456\pi\) | |||||||
\(884\) | − | 13.2665i | − | 0.446201i | ||||||
\(885\) | 7.70789 | − | 13.9576i | 0.259098 | − | 0.469179i | ||||
\(886\) | 9.00000 | 0.302361 | ||||||||
\(887\) | − | 54.8906i | − | 1.84305i | −0.388323 | − | 0.921523i | \(-0.626945\pi\) | ||
0.388323 | − | 0.921523i | \(-0.373055\pi\) | |||||||
\(888\) | −14.7446 | + | 13.8564i | −0.494795 | + | 0.464991i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 3.00000 | + | 9.30506i | 0.100560 | + | 0.311906i | ||||
\(891\) | −4.74456 | + | 38.0125i | −0.158949 | + | 1.27347i | ||||
\(892\) | 18.1168 | 0.606597 | ||||||||
\(893\) | 6.51087 | 0.217878 | ||||||||
\(894\) | −17.9307 | + | 16.8506i | −0.599692 | + | 0.563569i | ||||
\(895\) | 6.11684 | − | 1.97210i | 0.204464 | − | 0.0659201i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −10.3723 | − | 11.0371i | −0.346320 | − | 0.368519i | ||||
\(898\) | − | 35.9855i | − | 1.20085i | ||||||
\(899\) | 7.88316 | 0.262918 | ||||||||
\(900\) | −7.98913 | − | 12.6954i | −0.266304 | − | 0.423181i | ||||
\(901\) | 9.10268i | 0.303254i | ||||||||
\(902\) | − | 6.92820i | − | 0.230684i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3.25544 | −0.108274 | ||||||||
\(905\) | 38.2337 | − | 12.3267i | 1.27093 | − | 0.409755i | ||||
\(906\) | 9.62772 | + | 10.2448i | 0.319860 | + | 0.340362i | ||||
\(907\) | − | 44.7933i | − | 1.48734i | −0.668549 | − | 0.743668i | \(-0.733084\pi\) | ||
0.668549 | − | 0.743668i | \(-0.266916\pi\) | |||||||
\(908\) | 15.6434i | 0.519143i | ||||||||
\(909\) | −3.04755 | + | 49.0222i | −0.101081 | + | 1.62596i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.5437i | 0.813168i | 0.913613 | + | 0.406584i | \(0.133280\pi\) | ||||
−0.913613 | + | 0.406584i | \(0.866720\pi\) | |||||||
\(912\) | −4.37228 | + | 4.10891i | −0.144781 | + | 0.136060i | ||||
\(913\) | −6.11684 | −0.202438 | ||||||||
\(914\) | 12.7692i | 0.422366i | ||||||||
\(915\) | 9.55842 | + | 5.27851i | 0.315992 | + | 0.174502i | ||||
\(916\) | − | 13.8564i | − | 0.457829i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −22.0000 | − | 26.5330i | −0.726108 | − | 0.875719i | ||||
\(919\) | −18.2337 | −0.601474 | −0.300737 | − | 0.953707i | \(-0.597233\pi\) | ||||
−0.300737 | + | 0.953707i | \(0.597233\pi\) | |||||||
\(920\) | −3.00000 | − | 9.30506i | −0.0989071 | − | 0.306779i | ||||
\(921\) | 8.16439 | + | 8.68771i | 0.269026 | + | 0.286270i | ||||
\(922\) | −0.510875 | −0.0168248 | ||||||||
\(923\) | − | 3.75906i | − | 0.123731i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 34.1168 | + | 47.4102i | 1.12175 | + | 1.55884i | ||||
\(926\) | − | 36.5754i | − | 1.20194i | ||||||
\(927\) | −2.81386 | + | 45.2632i | −0.0924193 | + | 1.48664i | ||||
\(928\) | − | 3.31662i | − | 0.108874i | ||||||
\(929\) | −16.8832 | −0.553918 | −0.276959 | − | 0.960882i | \(-0.589327\pi\) | ||||
−0.276959 | + | 0.960882i | \(0.589327\pi\) | |||||||
\(930\) | 8.05842 | + | 4.45015i | 0.264246 | + | 0.145926i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 23.4891 | 0.769412 | ||||||||
\(933\) | −16.8832 | − | 17.9653i | −0.552730 | − | 0.588158i | ||||
\(934\) | − | 0.0549029i | − | 0.00179648i | ||||||
\(935\) | 19.3723 | + | 60.0868i | 0.633541 | + | 1.96505i | ||||
\(936\) | 0.372281 | − | 5.98844i | 0.0121684 | − | 0.195738i | ||||
\(937\) | 50.3505 | 1.64488 | 0.822440 | − | 0.568852i | \(-0.192612\pi\) | ||||
0.822440 | + | 0.568852i | \(0.192612\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −16.7446 | − | 17.8178i | −0.546438 | − | 0.581463i | ||||
\(940\) | −4.00000 | + | 1.28962i | −0.130466 | + | 0.0420628i | ||||
\(941\) | 24.3505 | 0.793805 | 0.396902 | − | 0.917861i | \(-0.370085\pi\) | ||||
0.396902 | + | 0.917861i | \(0.370085\pi\) | |||||||
\(942\) | −9.48913 | − | 10.0974i | −0.309172 | − | 0.328989i | ||||
\(943\) | 7.11684 | 0.231756 | ||||||||
\(944\) | 4.11684 | 0.133992 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 46.9783 | 1.52739 | ||||||||
\(947\) | −43.1168 | −1.40111 | −0.700555 | − | 0.713599i | \(-0.747064\pi\) | ||||
−0.700555 | + | 0.713599i | \(0.747064\pi\) | |||||||
\(948\) | −9.62772 | − | 10.2448i | −0.312694 | − | 0.332737i | ||||
\(949\) | 4.00000 | 0.129845 | ||||||||
\(950\) | 10.1168 | + | 14.0588i | 0.328234 | + | 0.456127i | ||||
\(951\) | −19.1168 | − | 20.3422i | −0.619906 | − | 0.659640i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 48.0000 | 1.55487 | 0.777436 | − | 0.628962i | \(-0.216520\pi\) | ||||
0.777436 | + | 0.628962i | \(0.216520\pi\) | |||||||
\(954\) | −0.255437 | + | 4.10891i | −0.00827009 | + | 0.133031i | ||||
\(955\) | 8.00000 | − | 2.57924i | 0.258874 | − | 0.0834623i | ||||
\(956\) | 2.87419i | 0.0929581i | ||||||||
\(957\) | 16.7446 | + | 17.8178i | 0.541275 | + | 0.575969i | ||||
\(958\) | 8.74456 | 0.282524 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 1.87228 | − | 3.39036i | 0.0604276 | − | 0.109424i | ||||
\(961\) | 25.3505 | 0.817759 | ||||||||
\(962\) | 23.3639i | 0.753281i | ||||||||
\(963\) | 3.30298 | − | 53.1311i | 0.106437 | − | 1.71213i | ||||
\(964\) | 10.5947i | 0.341232i | ||||||||
\(965\) | −17.0584 | + | 5.49972i | −0.549130 | + | 0.177042i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 51.9239i | − | 1.66976i | −0.550433 | − | 0.834879i | \(-0.685537\pi\) | ||
0.550433 | − | 0.834879i | \(-0.314463\pi\) | |||||||
\(968\) | 7.11684 | 0.228744 | ||||||||
\(969\) | 27.2554 | + | 29.0024i | 0.875571 | + | 0.931692i | ||||
\(970\) | −1.45245 | − | 4.50506i | −0.0466354 | − | 0.144649i | ||||
\(971\) | −28.6277 | −0.918707 | −0.459354 | − | 0.888253i | \(-0.651919\pi\) | ||||
−0.459354 | + | 0.888253i | \(0.651919\pi\) | |||||||
\(972\) | −9.18614 | − | 12.5942i | −0.294646 | − | 0.403960i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 4.55134i | − | 0.145834i | ||||||
\(975\) | −17.0000 | − | 3.31662i | −0.544436 | − | 0.106217i | ||||
\(976\) | 2.81929i | 0.0902433i | ||||||||
\(977\) | 40.4674 | 1.29467 | 0.647333 | − | 0.762207i | \(-0.275884\pi\) | ||||
0.647333 | + | 0.762207i | \(0.275884\pi\) | |||||||
\(978\) | 4.37228 | − | 4.10891i | 0.139810 | − | 0.131389i | ||||
\(979\) | − | 18.6101i | − | 0.594782i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.69702 | + | 27.2978i | −0.0541815 | + | 0.871553i | ||||
\(982\) | − | 26.9205i | − | 0.859069i | ||||||
\(983\) | 21.7244i | 0.692900i | 0.938068 | + | 0.346450i | \(0.112613\pi\) | ||||
−0.938068 | + | 0.346450i | \(0.887387\pi\) | |||||||
\(984\) | 1.93070 | + | 2.05446i | 0.0615486 | + | 0.0654937i | ||||
\(985\) | −13.8832 | − | 43.0612i | −0.442354 | − | 1.37204i | ||||
\(986\) | −22.0000 | −0.700623 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6.92820i | 0.220416i | ||||||||
\(989\) | 48.2574i | 1.53450i | ||||||||
\(990\) | 7.05842 | + | 27.6665i | 0.224331 | + | 0.879300i | ||||
\(991\) | −28.3505 | −0.900584 | −0.450292 | − | 0.892881i | \(-0.648680\pi\) | ||||
−0.450292 | + | 0.892881i | \(0.648680\pi\) | |||||||
\(992\) | 2.37686i | 0.0754654i | ||||||||
\(993\) | 12.1386 | + | 12.9166i | 0.385207 | + | 0.409897i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −39.6060 | + | 12.7692i | −1.25559 | + | 0.404810i | ||||
\(996\) | 1.81386 | − | 1.70460i | 0.0574743 | − | 0.0540123i | ||||
\(997\) | 30.4674 | 0.964911 | 0.482456 | − | 0.875920i | \(-0.339745\pi\) | ||||
0.482456 | + | 0.875920i | \(0.339745\pi\) | |||||||
\(998\) | −28.2337 | −0.893722 | ||||||||
\(999\) | 38.7446 | + | 46.7277i | 1.22582 | + | 1.47840i |
(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 | 1470.2.d.a.1469.4 | 4 | ||
3.2 | odd | 2 | 1470.2.d.c.1469.3 | 4 | |||
5.4 | even | 2 | 1470.2.d.d.1469.1 | 4 | |||
7.4 | even | 3 | 210.2.t.d.89.1 | yes | 4 | ||
7.5 | odd | 6 | 210.2.t.c.59.2 | yes | 4 | ||
7.6 | odd | 2 | 1470.2.d.b.1469.1 | 4 | |||
15.14 | odd | 2 | 1470.2.d.b.1469.2 | 4 | |||
21.5 | even | 6 | 210.2.t.a.59.1 | ✓ | 4 | ||
21.11 | odd | 6 | 210.2.t.b.89.1 | yes | 4 | ||
21.20 | even | 2 | 1470.2.d.d.1469.2 | 4 | |||
35.4 | even | 6 | 210.2.t.a.89.2 | yes | 4 | ||
35.12 | even | 12 | 1050.2.s.d.101.1 | 8 | |||
35.18 | odd | 12 | 1050.2.s.e.551.2 | 8 | |||
35.19 | odd | 6 | 210.2.t.b.59.1 | yes | 4 | ||
35.32 | odd | 12 | 1050.2.s.e.551.3 | 8 | |||
35.33 | even | 12 | 1050.2.s.d.101.4 | 8 | |||
35.34 | odd | 2 | 1470.2.d.c.1469.4 | 4 | |||
105.32 | even | 12 | 1050.2.s.d.551.1 | 8 | |||
105.47 | odd | 12 | 1050.2.s.e.101.3 | 8 | |||
105.53 | even | 12 | 1050.2.s.d.551.4 | 8 | |||
105.68 | odd | 12 | 1050.2.s.e.101.2 | 8 | |||
105.74 | odd | 6 | 210.2.t.c.89.2 | yes | 4 | ||
105.89 | even | 6 | 210.2.t.d.59.2 | yes | 4 | ||
105.104 | even | 2 | inner | 1470.2.d.a.1469.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.t.a.59.1 | ✓ | 4 | 21.5 | even | 6 | ||
210.2.t.a.89.2 | yes | 4 | 35.4 | even | 6 | ||
210.2.t.b.59.1 | yes | 4 | 35.19 | odd | 6 | ||
210.2.t.b.89.1 | yes | 4 | 21.11 | odd | 6 | ||
210.2.t.c.59.2 | yes | 4 | 7.5 | odd | 6 | ||
210.2.t.c.89.2 | yes | 4 | 105.74 | odd | 6 | ||
210.2.t.d.59.2 | yes | 4 | 105.89 | even | 6 | ||
210.2.t.d.89.1 | yes | 4 | 7.4 | even | 3 | ||
1050.2.s.d.101.1 | 8 | 35.12 | even | 12 | |||
1050.2.s.d.101.4 | 8 | 35.33 | even | 12 | |||
1050.2.s.d.551.1 | 8 | 105.32 | even | 12 | |||
1050.2.s.d.551.4 | 8 | 105.53 | even | 12 | |||
1050.2.s.e.101.2 | 8 | 105.68 | odd | 12 | |||
1050.2.s.e.101.3 | 8 | 105.47 | odd | 12 | |||
1050.2.s.e.551.2 | 8 | 35.18 | odd | 12 | |||
1050.2.s.e.551.3 | 8 | 35.32 | odd | 12 | |||
1470.2.d.a.1469.3 | 4 | 105.104 | even | 2 | inner | ||
1470.2.d.a.1469.4 | 4 | 1.1 | even | 1 | trivial | ||
1470.2.d.b.1469.1 | 4 | 7.6 | odd | 2 | |||
1470.2.d.b.1469.2 | 4 | 15.14 | odd | 2 | |||
1470.2.d.c.1469.3 | 4 | 3.2 | odd | 2 | |||
1470.2.d.c.1469.4 | 4 | 35.34 | odd | 2 | |||
1470.2.d.d.1469.1 | 4 | 5.4 | even | 2 | |||
1470.2.d.d.1469.2 | 4 | 21.20 | even | 2 |