Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [370,2,Mod(269,370)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(370, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("370.269");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 370 = 2 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 370.n (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.95446487479\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.303595776.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 5x^{6} + 16x^{4} + 45x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 269.2 | ||
Root | \(0.396143 + 1.68614i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 370.269 |
Dual form | 370.2.n.e.359.2 |
$q$-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 \(\left(\mathbb{Z}/370\mathbb{Z}\right)^\times\).
\(n\) | \(261\) | \(297\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | − | 0.500000i | −0.612372 | − | 0.353553i | ||||
\(3\) | 1.73205 | − | 1.00000i | 1.00000 | − | 0.577350i | 0.0917517 | − | 0.995782i | \(-0.470753\pi\) |
0.908248 | + | 0.418432i | \(0.137420\pi\) | |||||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | −0.469882 | + | 2.18614i | −0.210138 | + | 0.977672i | ||||
\(6\) | −2.00000 | −0.816497 | ||||||||
\(7\) | −2.00626 | + | 1.15831i | −0.758293 | + | 0.437801i | −0.828683 | − | 0.559719i | \(-0.810909\pi\) |
0.0703892 | + | 0.997520i | \(0.477576\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | 1.50000 | − | 1.65831i | 0.474342 | − | 0.524404i | ||||
\(11\) | 4.31662 | 1.30151 | 0.650756 | − | 0.759287i | \(-0.274452\pi\) | ||||
0.650756 | + | 0.759287i | \(0.274452\pi\) | |||||||
\(12\) | 1.73205 | + | 1.00000i | 0.500000 | + | 0.288675i | ||||
\(13\) | 3.46410 | − | 2.00000i | 0.960769 | − | 0.554700i | 0.0643593 | − | 0.997927i | \(-0.479500\pi\) |
0.896410 | + | 0.443227i | \(0.146166\pi\) | |||||||
\(14\) | 2.31662 | 0.619144 | ||||||||
\(15\) | 1.37228 | + | 4.25639i | 0.354322 | + | 1.09899i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 4.60433 | + | 2.65831i | 1.11671 | + | 0.644735i | 0.940560 | − | 0.339627i | \(-0.110301\pi\) |
0.176154 | + | 0.984363i | \(0.443634\pi\) | |||||||
\(18\) | −0.866025 | + | 0.500000i | −0.204124 | + | 0.117851i | ||||
\(19\) | 2.15831 | + | 3.73831i | 0.495151 | + | 0.857626i | 0.999984 | − | 0.00559033i | \(-0.00177947\pi\) |
−0.504834 | + | 0.863217i | \(0.668446\pi\) | |||||||
\(20\) | −2.12819 | + | 0.686141i | −0.475879 | + | 0.153426i | ||||
\(21\) | −2.31662 | + | 4.01251i | −0.505529 | + | 0.875602i | ||||
\(22\) | −3.73831 | − | 2.15831i | −0.797010 | − | 0.460154i | ||||
\(23\) | − | 6.00000i | − | 1.25109i | −0.780189 | − | 0.625543i | \(-0.784877\pi\) | ||
0.780189 | − | 0.625543i | \(-0.215123\pi\) | |||||||
\(24\) | −1.00000 | − | 1.73205i | −0.204124 | − | 0.353553i | ||||
\(25\) | −4.55842 | − | 2.05446i | −0.911684 | − | 0.410891i | ||||
\(26\) | −4.00000 | −0.784465 | ||||||||
\(27\) | 4.00000i | 0.769800i | ||||||||
\(28\) | −2.00626 | − | 1.15831i | −0.379147 | − | 0.218900i | ||||
\(29\) | −3.31662 | −0.615882 | −0.307941 | − | 0.951405i | \(-0.599640\pi\) | ||||
−0.307941 | + | 0.951405i | \(0.599640\pi\) | |||||||
\(30\) | 0.939764 | − | 4.37228i | 0.171577 | − | 0.798266i | ||||
\(31\) | 2.31662 | 0.416078 | 0.208039 | − | 0.978121i | \(-0.433292\pi\) | ||||
0.208039 | + | 0.978121i | \(0.433292\pi\) | |||||||
\(32\) | 0.866025 | − | 0.500000i | 0.153093 | − | 0.0883883i | ||||
\(33\) | 7.47661 | − | 4.31662i | 1.30151 | − | 0.751428i | ||||
\(34\) | −2.65831 | − | 4.60433i | −0.455897 | − | 0.789636i | ||||
\(35\) | −1.58953 | − | 4.93023i | −0.268680 | − | 0.833361i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −2.59808 | + | 5.50000i | −0.427121 | + | 0.904194i | ||||
\(38\) | − | 4.31662i | − | 0.700249i | ||||||
\(39\) | 4.00000 | − | 6.92820i | 0.640513 | − | 1.10940i | ||||
\(40\) | 2.18614 | + | 0.469882i | 0.345659 | + | 0.0742949i | ||||
\(41\) | −3.81662 | − | 6.61059i | −0.596057 | − | 1.03240i | −0.993397 | − | 0.114729i | \(-0.963400\pi\) |
0.397340 | − | 0.917671i | \(-0.369933\pi\) | |||||||
\(42\) | 4.01251 | − | 2.31662i | 0.619144 | − | 0.357463i | ||||
\(43\) | 8.94987i | 1.36484i | 0.730959 | + | 0.682422i | \(0.239073\pi\) | ||||
−0.730959 | + | 0.682422i | \(0.760927\pi\) | |||||||
\(44\) | 2.15831 | + | 3.73831i | 0.325378 | + | 0.563571i | ||||
\(45\) | 1.65831 | + | 1.50000i | 0.247207 | + | 0.223607i | ||||
\(46\) | −3.00000 | + | 5.19615i | −0.442326 | + | 0.766131i | ||||
\(47\) | − | 4.31662i | − | 0.629644i | −0.949151 | − | 0.314822i | \(-0.898055\pi\) | ||
0.949151 | − | 0.314822i | \(-0.101945\pi\) | |||||||
\(48\) | 2.00000i | 0.288675i | ||||||||
\(49\) | −0.816625 | + | 1.41444i | −0.116661 | + | 0.202062i | ||||
\(50\) | 2.92048 | + | 4.05842i | 0.413018 | + | 0.573948i | ||||
\(51\) | 10.6332 | 1.48895 | ||||||||
\(52\) | 3.46410 | + | 2.00000i | 0.480384 | + | 0.277350i | ||||
\(53\) | −7.47661 | − | 4.31662i | −1.02699 | − | 0.592934i | −0.110870 | − | 0.993835i | \(-0.535364\pi\) |
−0.916121 | + | 0.400901i | \(0.868697\pi\) | |||||||
\(54\) | 2.00000 | − | 3.46410i | 0.272166 | − | 0.471405i | ||||
\(55\) | −2.02830 | + | 9.43675i | −0.273496 | + | 1.27245i | ||||
\(56\) | 1.15831 | + | 2.00626i | 0.154786 | + | 0.268097i | ||||
\(57\) | 7.47661 | + | 4.31662i | 0.990302 | + | 0.571751i | ||||
\(58\) | 2.87228 | + | 1.65831i | 0.377149 | + | 0.217747i | ||||
\(59\) | 6.31662 | − | 10.9407i | 0.822355 | − | 1.42436i | −0.0815699 | − | 0.996668i | \(-0.525993\pi\) |
0.903924 | − | 0.427692i | \(-0.140673\pi\) | |||||||
\(60\) | −3.00000 | + | 3.31662i | −0.387298 | + | 0.428174i | ||||
\(61\) | −5.97494 | − | 10.3489i | −0.765012 | − | 1.32504i | −0.940240 | − | 0.340512i | \(-0.889400\pi\) |
0.175228 | − | 0.984528i | \(-0.443934\pi\) | |||||||
\(62\) | −2.00626 | − | 1.15831i | −0.254795 | − | 0.147106i | ||||
\(63\) | 2.31662i | 0.291867i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 2.74456 | + | 8.51278i | 0.340421 | + | 1.05588i | ||||
\(66\) | −8.63325 | −1.06268 | ||||||||
\(67\) | −1.45785 | + | 0.841688i | −0.178104 | + | 0.102829i | −0.586402 | − | 0.810020i | \(-0.699456\pi\) |
0.408297 | + | 0.912849i | \(0.366123\pi\) | |||||||
\(68\) | 5.31662i | 0.644735i | ||||||||
\(69\) | −6.00000 | − | 10.3923i | −0.722315 | − | 1.25109i | ||||
\(70\) | −1.08854 | + | 5.06447i | −0.130105 | + | 0.605320i | ||||
\(71\) | 3.84169 | + | 6.65400i | 0.455924 | + | 0.789684i | 0.998741 | − | 0.0501671i | \(-0.0159754\pi\) |
−0.542816 | + | 0.839851i | \(0.682642\pi\) | |||||||
\(72\) | −0.866025 | − | 0.500000i | −0.102062 | − | 0.0589256i | ||||
\(73\) | 2.63325i | 0.308199i | 0.988055 | + | 0.154099i | \(0.0492476\pi\) | ||||
−0.988055 | + | 0.154099i | \(0.950752\pi\) | |||||||
\(74\) | 5.00000 | − | 3.46410i | 0.581238 | − | 0.402694i | ||||
\(75\) | −9.94987 | + | 1.00000i | −1.14891 | + | 0.115470i | ||||
\(76\) | −2.15831 | + | 3.73831i | −0.247575 | + | 0.428813i | ||||
\(77\) | −8.66025 | + | 5.00000i | −0.986928 | + | 0.569803i | ||||
\(78\) | −6.92820 | + | 4.00000i | −0.784465 | + | 0.452911i | ||||
\(79\) | −5.47494 | − | 9.48287i | −0.615979 | − | 1.06691i | −0.990212 | − | 0.139572i | \(-0.955427\pi\) |
0.374233 | − | 0.927335i | \(-0.377906\pi\) | |||||||
\(80\) | −1.65831 | − | 1.50000i | −0.185405 | − | 0.167705i | ||||
\(81\) | 5.50000 | + | 9.52628i | 0.611111 | + | 1.05848i | ||||
\(82\) | 7.63325i | 0.842951i | ||||||||
\(83\) | −5.74456 | − | 3.31662i | −0.630548 | − | 0.364047i | 0.150416 | − | 0.988623i | \(-0.451939\pi\) |
−0.780964 | + | 0.624576i | \(0.785272\pi\) | |||||||
\(84\) | −4.63325 | −0.505529 | ||||||||
\(85\) | −7.97494 | + | 8.81662i | −0.865003 | + | 0.956297i | ||||
\(86\) | 4.47494 | − | 7.75082i | 0.482545 | − | 0.835792i | ||||
\(87\) | −5.74456 | + | 3.31662i | −0.615882 | + | 0.355580i | ||||
\(88\) | − | 4.31662i | − | 0.460154i | ||||||
\(89\) | 5.81662 | − | 10.0747i | 0.616561 | − | 1.06791i | −0.373547 | − | 0.927611i | \(-0.621859\pi\) |
0.990108 | − | 0.140304i | \(-0.0448080\pi\) | |||||||
\(90\) | −0.686141 | − | 2.12819i | −0.0723256 | − | 0.224331i | ||||
\(91\) | −4.63325 | + | 8.02502i | −0.485697 | + | 0.841251i | ||||
\(92\) | 5.19615 | − | 3.00000i | 0.541736 | − | 0.312772i | ||||
\(93\) | 4.01251 | − | 2.31662i | 0.416078 | − | 0.240223i | ||||
\(94\) | −2.15831 | + | 3.73831i | −0.222613 | + | 0.385577i | ||||
\(95\) | −9.18662 | + | 2.96181i | −0.942527 | + | 0.303875i | ||||
\(96\) | 1.00000 | − | 1.73205i | 0.102062 | − | 0.176777i | ||||
\(97\) | − | 9.94987i | − | 1.01026i | −0.863044 | − | 0.505128i | \(-0.831445\pi\) | ||
0.863044 | − | 0.505128i | \(-0.168555\pi\) | |||||||
\(98\) | 1.41444 | − | 0.816625i | 0.142880 | − | 0.0824916i | ||||
\(99\) | 2.15831 | − | 3.73831i | 0.216919 | − | 0.375714i | ||||
\(100\) | −0.500000 | − | 4.97494i | −0.0500000 | − | 0.497494i | ||||
\(101\) | −15.3166 | −1.52406 | −0.762031 | − | 0.647541i | \(-0.775797\pi\) | ||||
−0.762031 | + | 0.647541i | \(0.775797\pi\) | |||||||
\(102\) | −9.20866 | − | 5.31662i | −0.911794 | − | 0.526424i | ||||
\(103\) | 9.68338i | 0.954131i | 0.878868 | + | 0.477066i | \(0.158300\pi\) | ||||
−0.878868 | + | 0.477066i | \(0.841700\pi\) | |||||||
\(104\) | −2.00000 | − | 3.46410i | −0.196116 | − | 0.339683i | ||||
\(105\) | −7.68338 | − | 6.94987i | −0.749821 | − | 0.678238i | ||||
\(106\) | 4.31662 | + | 7.47661i | 0.419268 | + | 0.726193i | ||||
\(107\) | −0.274205 | + | 0.158312i | −0.0265084 | + | 0.0153046i | −0.513196 | − | 0.858272i | \(-0.671538\pi\) |
0.486687 | + | 0.873576i | \(0.338205\pi\) | |||||||
\(108\) | −3.46410 | + | 2.00000i | −0.333333 | + | 0.192450i | ||||
\(109\) | 1.97494 | − | 3.42069i | 0.189165 | − | 0.327643i | −0.755807 | − | 0.654794i | \(-0.772755\pi\) |
0.944972 | + | 0.327151i | \(0.106089\pi\) | |||||||
\(110\) | 6.47494 | − | 7.15831i | 0.617361 | − | 0.682518i | ||||
\(111\) | 1.00000 | + | 12.1244i | 0.0949158 | + | 1.15079i | ||||
\(112\) | − | 2.31662i | − | 0.218900i | ||||||
\(113\) | 4.64774 | + | 2.68338i | 0.437223 | + | 0.252431i | 0.702419 | − | 0.711764i | \(-0.252103\pi\) |
−0.265196 | + | 0.964195i | \(0.585437\pi\) | |||||||
\(114\) | −4.31662 | − | 7.47661i | −0.404289 | − | 0.700249i | ||||
\(115\) | 13.1168 | + | 2.81929i | 1.22315 | + | 0.262900i | ||||
\(116\) | −1.65831 | − | 2.87228i | −0.153970 | − | 0.266685i | ||||
\(117\) | − | 4.00000i | − | 0.369800i | ||||||
\(118\) | −10.9407 | + | 6.31662i | −1.00717 | + | 0.581492i | ||||
\(119\) | −12.3166 | −1.12906 | ||||||||
\(120\) | 4.25639 | − | 1.37228i | 0.388553 | − | 0.125272i | ||||
\(121\) | 7.63325 | 0.693932 | ||||||||
\(122\) | 11.9499i | 1.08189i | ||||||||
\(123\) | −13.2212 | − | 7.63325i | −1.19211 | − | 0.688267i | ||||
\(124\) | 1.15831 | + | 2.00626i | 0.104020 | + | 0.180167i | ||||
\(125\) | 6.63325 | − | 9.00000i | 0.593296 | − | 0.804984i | ||||
\(126\) | 1.15831 | − | 2.00626i | 0.103191 | − | 0.178731i | ||||
\(127\) | 1.18364 | + | 0.683375i | 0.105031 | + | 0.0606397i | 0.551595 | − | 0.834112i | \(-0.314019\pi\) |
−0.446564 | + | 0.894752i | \(0.647353\pi\) | |||||||
\(128\) | 0.866025 | + | 0.500000i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | 8.94987 | + | 15.5016i | 0.787993 | + | 1.36484i | ||||
\(130\) | 1.87953 | − | 8.74456i | 0.164845 | − | 0.766949i | ||||
\(131\) | 0.683375 | − | 1.18364i | 0.0597068 | − | 0.103415i | −0.834627 | − | 0.550816i | \(-0.814317\pi\) |
0.894334 | + | 0.447400i | \(0.147650\pi\) | |||||||
\(132\) | 7.47661 | + | 4.31662i | 0.650756 | + | 0.375714i | ||||
\(133\) | −8.66025 | − | 5.00000i | −0.750939 | − | 0.433555i | ||||
\(134\) | 1.68338 | 0.145421 | ||||||||
\(135\) | −8.74456 | − | 1.87953i | −0.752612 | − | 0.161764i | ||||
\(136\) | 2.65831 | − | 4.60433i | 0.227948 | − | 0.394818i | ||||
\(137\) | − | 11.3166i | − | 0.966845i | −0.875387 | − | 0.483422i | \(-0.839394\pi\) | ||
0.875387 | − | 0.483422i | \(-0.160606\pi\) | |||||||
\(138\) | 12.0000i | 1.02151i | ||||||||
\(139\) | −9.94987 | + | 17.2337i | −0.843937 | + | 1.46174i | 0.0426035 | + | 0.999092i | \(0.486435\pi\) |
−0.886541 | + | 0.462650i | \(0.846899\pi\) | |||||||
\(140\) | 3.47494 | − | 3.84169i | 0.293686 | − | 0.324682i | ||||
\(141\) | −4.31662 | − | 7.47661i | −0.363525 | − | 0.629644i | ||||
\(142\) | − | 7.68338i | − | 0.644775i | ||||||
\(143\) | 14.9532 | − | 8.63325i | 1.25045 | − | 0.721949i | ||||
\(144\) | 0.500000 | + | 0.866025i | 0.0416667 | + | 0.0721688i | ||||
\(145\) | 1.55842 | − | 7.25061i | 0.129420 | − | 0.602130i | ||||
\(146\) | 1.31662 | − | 2.28046i | 0.108965 | − | 0.188732i | ||||
\(147\) | 3.26650i | 0.269416i | ||||||||
\(148\) | −6.06218 | + | 0.500000i | −0.498308 | + | 0.0410997i | ||||
\(149\) | 15.9499 | 1.30666 | 0.653332 | − | 0.757071i | \(-0.273370\pi\) | ||||
0.653332 | + | 0.757071i | \(0.273370\pi\) | |||||||
\(150\) | 9.11684 | + | 4.10891i | 0.744387 | + | 0.335491i | ||||
\(151\) | −5.31662 | − | 9.20866i | −0.432661 | − | 0.749390i | 0.564441 | − | 0.825474i | \(-0.309092\pi\) |
−0.997101 | + | 0.0760832i | \(0.975759\pi\) | |||||||
\(152\) | 3.73831 | − | 2.15831i | 0.303217 | − | 0.175062i | ||||
\(153\) | 4.60433 | − | 2.65831i | 0.372238 | − | 0.214912i | ||||
\(154\) | 10.0000 | 0.805823 | ||||||||
\(155\) | −1.08854 | + | 5.06447i | −0.0874336 | + | 0.406788i | ||||
\(156\) | 8.00000 | 0.640513 | ||||||||
\(157\) | 2.59808 | + | 1.50000i | 0.207349 | + | 0.119713i | 0.600079 | − | 0.799941i | \(-0.295136\pi\) |
−0.392730 | + | 0.919654i | \(0.628469\pi\) | |||||||
\(158\) | 10.9499i | 0.871125i | ||||||||
\(159\) | −17.2665 | −1.36932 | ||||||||
\(160\) | 0.686141 | + | 2.12819i | 0.0542442 | + | 0.168249i | ||||
\(161\) | 6.94987 | + | 12.0375i | 0.547727 | + | 0.948691i | ||||
\(162\) | − | 11.0000i | − | 0.864242i | ||||||
\(163\) | 19.2399 | + | 11.1082i | 1.50699 | + | 0.870060i | 0.999967 | + | 0.00812707i | \(0.00258695\pi\) |
0.507022 | + | 0.861933i | \(0.330746\pi\) | |||||||
\(164\) | 3.81662 | − | 6.61059i | 0.298028 | − | 0.516200i | ||||
\(165\) | 5.92362 | + | 18.3732i | 0.461153 | + | 1.43035i | ||||
\(166\) | 3.31662 | + | 5.74456i | 0.257420 | + | 0.445865i | ||||
\(167\) | −8.02502 | + | 4.63325i | −0.620995 | + | 0.358532i | −0.777256 | − | 0.629184i | \(-0.783389\pi\) |
0.156261 | + | 0.987716i | \(0.450056\pi\) | |||||||
\(168\) | 4.01251 | + | 2.31662i | 0.309572 | + | 0.178731i | ||||
\(169\) | 1.50000 | − | 2.59808i | 0.115385 | − | 0.199852i | ||||
\(170\) | 11.3148 | − | 3.64795i | 0.867806 | − | 0.279785i | ||||
\(171\) | 4.31662 | 0.330101 | ||||||||
\(172\) | −7.75082 | + | 4.47494i | −0.590994 | + | 0.341211i | ||||
\(173\) | 10.6231 | + | 6.13325i | 0.807659 | + | 0.466302i | 0.846142 | − | 0.532957i | \(-0.178919\pi\) |
−0.0384830 | + | 0.999259i | \(0.512253\pi\) | |||||||
\(174\) | 6.63325 | 0.502865 | ||||||||
\(175\) | 11.5251 | − | 1.15831i | 0.871213 | − | 0.0875602i | ||||
\(176\) | −2.15831 | + | 3.73831i | −0.162689 | + | 0.281785i | ||||
\(177\) | − | 25.2665i | − | 1.89915i | ||||||
\(178\) | −10.0747 | + | 5.81662i | −0.755130 | + | 0.435974i | ||||
\(179\) | 5.26650 | 0.393637 | 0.196818 | − | 0.980440i | \(-0.436939\pi\) | ||||
0.196818 | + | 0.980440i | \(0.436939\pi\) | |||||||
\(180\) | −0.469882 | + | 2.18614i | −0.0350229 | + | 0.162945i | ||||
\(181\) | −6.65831 | − | 11.5325i | −0.494908 | − | 0.857207i | 0.505074 | − | 0.863076i | \(-0.331465\pi\) |
−0.999983 | + | 0.00586926i | \(0.998132\pi\) | |||||||
\(182\) | 8.02502 | − | 4.63325i | 0.594854 | − | 0.343439i | ||||
\(183\) | −20.6978 | − | 11.9499i | −1.53002 | − | 0.883360i | ||||
\(184\) | −6.00000 | −0.442326 | ||||||||
\(185\) | −10.8030 | − | 8.26411i | −0.794251 | − | 0.607589i | ||||
\(186\) | −4.63325 | −0.339726 | ||||||||
\(187\) | 19.8752 | + | 11.4749i | 1.45342 | + | 0.839131i | ||||
\(188\) | 3.73831 | − | 2.15831i | 0.272644 | − | 0.157411i | ||||
\(189\) | −4.63325 | − | 8.02502i | −0.337019 | − | 0.583735i | ||||
\(190\) | 9.43675 | + | 2.02830i | 0.684614 | + | 0.147149i | ||||
\(191\) | 6.63325 | 0.479965 | 0.239983 | − | 0.970777i | \(-0.422858\pi\) | ||||
0.239983 | + | 0.970777i | \(0.422858\pi\) | |||||||
\(192\) | −1.73205 | + | 1.00000i | −0.125000 | + | 0.0721688i | ||||
\(193\) | − | 1.31662i | − | 0.0947727i | −0.998877 | − | 0.0473864i | \(-0.984911\pi\) | ||
0.998877 | − | 0.0473864i | \(-0.0150892\pi\) | |||||||
\(194\) | −4.97494 | + | 8.61684i | −0.357180 | + | 0.618653i | ||||
\(195\) | 13.2665 | + | 12.0000i | 0.950034 | + | 0.859338i | ||||
\(196\) | −1.63325 | −0.116661 | ||||||||
\(197\) | −3.78172 | − | 2.18338i | −0.269436 | − | 0.155559i | 0.359195 | − | 0.933262i | \(-0.383051\pi\) |
−0.628631 | + | 0.777703i | \(0.716385\pi\) | |||||||
\(198\) | −3.73831 | + | 2.15831i | −0.265670 | + | 0.153385i | ||||
\(199\) | 16.9499 | 1.20154 | 0.600772 | − | 0.799420i | \(-0.294860\pi\) | ||||
0.600772 | + | 0.799420i | \(0.294860\pi\) | |||||||
\(200\) | −2.05446 | + | 4.55842i | −0.145272 | + | 0.322329i | ||||
\(201\) | −1.68338 | + | 2.91569i | −0.118736 | + | 0.205657i | ||||
\(202\) | 13.2646 | + | 7.65831i | 0.933293 | + | 0.538837i | ||||
\(203\) | 6.65400 | − | 3.84169i | 0.467019 | − | 0.269634i | ||||
\(204\) | 5.31662 | + | 9.20866i | 0.372238 | + | 0.644735i | ||||
\(205\) | 16.2450 | − | 5.23748i | 1.13460 | − | 0.365802i | ||||
\(206\) | 4.84169 | − | 8.38605i | 0.337336 | − | 0.584284i | ||||
\(207\) | −5.19615 | − | 3.00000i | −0.361158 | − | 0.208514i | ||||
\(208\) | 4.00000i | 0.277350i | ||||||||
\(209\) | 9.31662 | + | 16.1369i | 0.644444 | + | 1.11621i | ||||
\(210\) | 3.17906 | + | 9.86046i | 0.219376 | + | 0.680436i | ||||
\(211\) | −14.3166 | −0.985597 | −0.492799 | − | 0.870143i | \(-0.664026\pi\) | ||||
−0.492799 | + | 0.870143i | \(0.664026\pi\) | |||||||
\(212\) | − | 8.63325i | − | 0.592934i | ||||||
\(213\) | 13.3080 | + | 7.68338i | 0.911849 | + | 0.526456i | ||||
\(214\) | 0.316625 | 0.0216440 | ||||||||
\(215\) | −19.5657 | − | 4.20538i | −1.33437 | − | 0.286805i | ||||
\(216\) | 4.00000 | 0.272166 | ||||||||
\(217\) | −4.64774 | + | 2.68338i | −0.315509 | + | 0.182159i | ||||
\(218\) | −3.42069 | + | 1.97494i | −0.231678 | + | 0.133760i | ||||
\(219\) | 2.63325 | + | 4.56092i | 0.177939 | + | 0.308199i | ||||
\(220\) | −9.18662 | + | 2.96181i | −0.619362 | + | 0.199685i | ||||
\(221\) | 21.2665 | 1.43054 | ||||||||
\(222\) | 5.19615 | − | 11.0000i | 0.348743 | − | 0.738272i | ||||
\(223\) | − | 13.3668i | − | 0.895104i | −0.894258 | − | 0.447552i | \(-0.852296\pi\) | ||
0.894258 | − | 0.447552i | \(-0.147704\pi\) | |||||||
\(224\) | −1.15831 | + | 2.00626i | −0.0773930 | + | 0.134049i | ||||
\(225\) | −4.05842 | + | 2.92048i | −0.270561 | + | 0.194699i | ||||
\(226\) | −2.68338 | − | 4.64774i | −0.178495 | − | 0.309163i | ||||
\(227\) | 6.01877 | − | 3.47494i | 0.399480 | − | 0.230640i | −0.286780 | − | 0.957997i | \(-0.592585\pi\) |
0.686259 | + | 0.727357i | \(0.259251\pi\) | |||||||
\(228\) | 8.63325i | 0.571751i | ||||||||
\(229\) | −1.97494 | − | 3.42069i | −0.130508 | − | 0.226046i | 0.793365 | − | 0.608746i | \(-0.208327\pi\) |
−0.923872 | + | 0.382701i | \(0.874994\pi\) | |||||||
\(230\) | −9.94987 | − | 9.00000i | −0.656075 | − | 0.593442i | ||||
\(231\) | −10.0000 | + | 17.3205i | −0.657952 | + | 1.13961i | ||||
\(232\) | 3.31662i | 0.217747i | ||||||||
\(233\) | − | 27.9499i | − | 1.83106i | −0.402253 | − | 0.915529i | \(-0.631773\pi\) | ||
0.402253 | − | 0.915529i | \(-0.368227\pi\) | |||||||
\(234\) | −2.00000 | + | 3.46410i | −0.130744 | + | 0.226455i | ||||
\(235\) | 9.43675 | + | 2.02830i | 0.615586 | + | 0.132312i | ||||
\(236\) | 12.6332 | 0.822355 | ||||||||
\(237\) | −18.9657 | − | 10.9499i | −1.23196 | − | 0.711271i | ||||
\(238\) | 10.6665 | + | 6.15831i | 0.691407 | + | 0.399184i | ||||
\(239\) | −4.15831 | + | 7.20241i | −0.268979 | + | 0.465885i | −0.968598 | − | 0.248631i | \(-0.920020\pi\) |
0.699620 | + | 0.714516i | \(0.253353\pi\) | |||||||
\(240\) | −4.37228 | − | 0.939764i | −0.282230 | − | 0.0606615i | ||||
\(241\) | −14.6332 | − | 25.3455i | −0.942610 | − | 1.63265i | −0.760466 | − | 0.649377i | \(-0.775030\pi\) |
−0.182144 | − | 0.983272i | \(-0.558304\pi\) | |||||||
\(242\) | −6.61059 | − | 3.81662i | −0.424945 | − | 0.245342i | ||||
\(243\) | 8.66025 | + | 5.00000i | 0.555556 | + | 0.320750i | ||||
\(244\) | 5.97494 | − | 10.3489i | 0.382506 | − | 0.662520i | ||||
\(245\) | −2.70844 | − | 2.44987i | −0.173036 | − | 0.156517i | ||||
\(246\) | 7.63325 | + | 13.2212i | 0.486678 | + | 0.842951i | ||||
\(247\) | 14.9532 | + | 8.63325i | 0.951451 | + | 0.549321i | ||||
\(248\) | − | 2.31662i | − | 0.147106i | ||||||
\(249\) | −13.2665 | −0.840730 | ||||||||
\(250\) | −10.2446 | + | 4.47760i | −0.647923 | + | 0.283189i | ||||
\(251\) | 2.31662 | 0.146224 | 0.0731120 | − | 0.997324i | \(-0.476707\pi\) | ||||
0.0731120 | + | 0.997324i | \(0.476707\pi\) | |||||||
\(252\) | −2.00626 | + | 1.15831i | −0.126382 | + | 0.0729668i | ||||
\(253\) | − | 25.8997i | − | 1.62830i | ||||||
\(254\) | −0.683375 | − | 1.18364i | −0.0428788 | − | 0.0742682i | ||||
\(255\) | −4.99637 | + | 23.2458i | −0.312885 | + | 1.45571i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −20.1928 | − | 11.6583i | −1.25959 | − | 0.727226i | −0.286597 | − | 0.958051i | \(-0.592524\pi\) |
−0.972995 | + | 0.230826i | \(0.925857\pi\) | |||||||
\(258\) | − | 17.8997i | − | 1.11439i | ||||||
\(259\) | −1.15831 | − | 14.0438i | −0.0719740 | − | 0.872639i | ||||
\(260\) | −6.00000 | + | 6.63325i | −0.372104 | + | 0.411377i | ||||
\(261\) | −1.65831 | + | 2.87228i | −0.102647 | + | 0.177790i | ||||
\(262\) | −1.18364 | + | 0.683375i | −0.0731256 | + | 0.0422191i | ||||
\(263\) | −11.4891 | + | 6.63325i | −0.708450 | + | 0.409024i | −0.810487 | − | 0.585757i | \(-0.800797\pi\) |
0.102037 | + | 0.994781i | \(0.467464\pi\) | |||||||
\(264\) | −4.31662 | − | 7.47661i | −0.265670 | − | 0.460154i | ||||
\(265\) | 12.9499 | − | 14.3166i | 0.795504 | − | 0.879463i | ||||
\(266\) | 5.00000 | + | 8.66025i | 0.306570 | + | 0.530994i | ||||
\(267\) | − | 23.2665i | − | 1.42389i | ||||||
\(268\) | −1.45785 | − | 0.841688i | −0.0890521 | − | 0.0514143i | ||||
\(269\) | −1.26650 | −0.0772198 | −0.0386099 | − | 0.999254i | \(-0.512293\pi\) | ||||
−0.0386099 | + | 0.999254i | \(0.512293\pi\) | |||||||
\(270\) | 6.63325 | + | 6.00000i | 0.403687 | + | 0.365148i | ||||
\(271\) | −13.7916 | + | 23.8877i | −0.837778 | + | 1.45107i | 0.0539709 | + | 0.998543i | \(0.482812\pi\) |
−0.891749 | + | 0.452531i | \(0.850521\pi\) | |||||||
\(272\) | −4.60433 | + | 2.65831i | −0.279179 | + | 0.161184i | ||||
\(273\) | 18.5330i | 1.12167i | ||||||||
\(274\) | −5.65831 | + | 9.80048i | −0.341831 | + | 0.592069i | ||||
\(275\) | −19.6770 | − | 8.86832i | −1.18657 | − | 0.534780i | ||||
\(276\) | 6.00000 | − | 10.3923i | 0.361158 | − | 0.625543i | ||||
\(277\) | 4.87854 | − | 2.81662i | 0.293123 | − | 0.169235i | −0.346226 | − | 0.938151i | \(-0.612537\pi\) |
0.639349 | + | 0.768916i | \(0.279204\pi\) | |||||||
\(278\) | 17.2337 | − | 9.94987i | 1.03361 | − | 0.596754i | ||||
\(279\) | 1.15831 | − | 2.00626i | 0.0693463 | − | 0.120111i | ||||
\(280\) | −4.93023 | + | 1.58953i | −0.294637 | + | 0.0949926i | ||||
\(281\) | −8.18338 | + | 14.1740i | −0.488179 | + | 0.845551i | −0.999908 | − | 0.0135961i | \(-0.995672\pi\) |
0.511728 | + | 0.859147i | \(0.329005\pi\) | |||||||
\(282\) | 8.63325i | 0.514103i | ||||||||
\(283\) | −7.20241 | + | 4.15831i | −0.428139 | + | 0.247186i | −0.698553 | − | 0.715558i | \(-0.746173\pi\) |
0.270415 | + | 0.962744i | \(0.412839\pi\) | |||||||
\(284\) | −3.84169 | + | 6.65400i | −0.227962 | + | 0.394842i | ||||
\(285\) | −12.9499 | + | 14.3166i | −0.767084 | + | 0.848044i | ||||
\(286\) | −17.2665 | −1.02099 | ||||||||
\(287\) | 15.3143 | + | 8.84169i | 0.903972 | + | 0.521908i | ||||
\(288\) | − | 1.00000i | − | 0.0589256i | ||||||
\(289\) | 5.63325 | + | 9.75707i | 0.331368 | + | 0.573946i | ||||
\(290\) | −4.97494 | + | 5.50000i | −0.292138 | + | 0.322971i | ||||
\(291\) | −9.94987 | − | 17.2337i | −0.583272 | − | 1.01026i | ||||
\(292\) | −2.28046 | + | 1.31662i | −0.133454 | + | 0.0770496i | ||||
\(293\) | 2.04967 | − | 1.18338i | 0.119743 | − | 0.0691335i | −0.438932 | − | 0.898520i | \(-0.644643\pi\) |
0.558675 | + | 0.829387i | \(0.311310\pi\) | |||||||
\(294\) | 1.63325 | − | 2.82887i | 0.0952530 | − | 0.164983i | ||||
\(295\) | 20.9499 | + | 18.9499i | 1.21975 | + | 1.10330i | ||||
\(296\) | 5.50000 | + | 2.59808i | 0.319681 | + | 0.151010i | ||||
\(297\) | 17.2665i | 1.00190i | ||||||||
\(298\) | −13.8130 | − | 7.97494i | −0.800165 | − | 0.461976i | ||||
\(299\) | −12.0000 | − | 20.7846i | −0.693978 | − | 1.20201i | ||||
\(300\) | −5.84096 | − | 8.11684i | −0.337228 | − | 0.468626i | ||||
\(301\) | −10.3668 | − | 17.9557i | −0.597530 | − | 1.03495i | ||||
\(302\) | 10.6332i | 0.611875i | ||||||||
\(303\) | −26.5292 | + | 15.3166i | −1.52406 | + | 0.879917i | ||||
\(304\) | −4.31662 | −0.247575 | ||||||||
\(305\) | 25.4317 | − | 8.19929i | 1.45621 | − | 0.469490i | ||||
\(306\) | −5.31662 | −0.303931 | ||||||||
\(307\) | 15.6834i | 0.895098i | 0.894260 | + | 0.447549i | \(0.147703\pi\) | ||||
−0.894260 | + | 0.447549i | \(0.852297\pi\) | |||||||
\(308\) | −8.66025 | − | 5.00000i | −0.493464 | − | 0.284901i | ||||
\(309\) | 9.68338 | + | 16.7721i | 0.550868 | + | 0.954131i | ||||
\(310\) | 3.47494 | − | 3.84169i | 0.197363 | − | 0.218193i | ||||
\(311\) | −4.79156 | + | 8.29923i | −0.271705 | + | 0.470606i | −0.969298 | − | 0.245887i | \(-0.920921\pi\) |
0.697594 | + | 0.716493i | \(0.254254\pi\) | |||||||
\(312\) | −6.92820 | − | 4.00000i | −0.392232 | − | 0.226455i | ||||
\(313\) | 3.50751 | + | 2.02506i | 0.198256 | + | 0.114463i | 0.595842 | − | 0.803102i | \(-0.296818\pi\) |
−0.397586 | + | 0.917565i | \(0.630152\pi\) | |||||||
\(314\) | −1.50000 | − | 2.59808i | −0.0846499 | − | 0.146618i | ||||
\(315\) | −5.06447 | − | 1.08854i | −0.285350 | − | 0.0613323i | ||||
\(316\) | 5.47494 | − | 9.48287i | 0.307989 | − | 0.533453i | ||||
\(317\) | −7.24582 | − | 4.18338i | −0.406966 | − | 0.234962i | 0.282519 | − | 0.959262i | \(-0.408830\pi\) |
−0.689485 | + | 0.724300i | \(0.742163\pi\) | |||||||
\(318\) | 14.9532 | + | 8.63325i | 0.838535 | + | 0.484129i | ||||
\(319\) | −14.3166 | −0.801577 | ||||||||
\(320\) | 0.469882 | − | 2.18614i | 0.0262672 | − | 0.122209i | ||||
\(321\) | −0.316625 | + | 0.548410i | −0.0176723 | + | 0.0306093i | ||||
\(322\) | − | 13.8997i | − | 0.774603i | ||||||
\(323\) | 22.9499i | 1.27697i | ||||||||
\(324\) | −5.50000 | + | 9.52628i | −0.305556 | + | 0.529238i | ||||
\(325\) | −19.8997 | + | 2.00000i | −1.10384 | + | 0.110940i | ||||
\(326\) | −11.1082 | − | 19.2399i | −0.615226 | − | 1.06560i | ||||
\(327\) | − | 7.89975i | − | 0.436857i | ||||||
\(328\) | −6.61059 | + | 3.81662i | −0.365009 | + | 0.210738i | ||||
\(329\) | 5.00000 | + | 8.66025i | 0.275659 | + | 0.477455i | ||||
\(330\) | 4.05661 | − | 18.8735i | 0.223309 | − | 1.03895i | ||||
\(331\) | 16.9499 | − | 29.3580i | 0.931649 | − | 1.61366i | 0.151147 | − | 0.988511i | \(-0.451703\pi\) |
0.780502 | − | 0.625153i | \(-0.214963\pi\) | |||||||
\(332\) | − | 6.63325i | − | 0.364047i | ||||||
\(333\) | 3.46410 | + | 5.00000i | 0.189832 | + | 0.273998i | ||||
\(334\) | 9.26650 | 0.507040 | ||||||||
\(335\) | −1.15503 | − | 3.58255i | −0.0631061 | − | 0.195736i | ||||
\(336\) | −2.31662 | − | 4.01251i | −0.126382 | − | 0.218900i | ||||
\(337\) | −10.3489 | + | 5.97494i | −0.563740 | + | 0.325476i | −0.754645 | − | 0.656133i | \(-0.772191\pi\) |
0.190905 | + | 0.981608i | \(0.438858\pi\) | |||||||
\(338\) | −2.59808 | + | 1.50000i | −0.141317 | + | 0.0815892i | ||||
\(339\) | 10.7335 | 0.582964 | ||||||||
\(340\) | −11.6229 | − | 2.49819i | −0.630340 | − | 0.135483i | ||||
\(341\) | 10.0000 | 0.541530 | ||||||||
\(342\) | −3.73831 | − | 2.15831i | −0.202144 | − | 0.116708i | ||||
\(343\) | − | 20.0000i | − | 1.07990i | ||||||
\(344\) | 8.94987 | 0.482545 | ||||||||
\(345\) | 25.5383 | − | 8.23369i | 1.37494 | − | 0.443287i | ||||
\(346\) | −6.13325 | − | 10.6231i | −0.329726 | − | 0.571101i | ||||
\(347\) | 15.2665i | 0.819549i | 0.912187 | + | 0.409774i | \(0.134393\pi\) | ||||
−0.912187 | + | 0.409774i | \(0.865607\pi\) | |||||||
\(348\) | −5.74456 | − | 3.31662i | −0.307941 | − | 0.177790i | ||||
\(349\) | −14.3417 | + | 24.8405i | −0.767693 | + | 1.32968i | 0.171118 | + | 0.985251i | \(0.445262\pi\) |
−0.938811 | + | 0.344433i | \(0.888071\pi\) | |||||||
\(350\) | −10.5602 | − | 4.75940i | −0.564464 | − | 0.254401i | ||||
\(351\) | 8.00000 | + | 13.8564i | 0.427008 | + | 0.739600i | ||||
\(352\) | 3.73831 | − | 2.15831i | 0.199252 | − | 0.115038i | ||||
\(353\) | 23.5701 | + | 13.6082i | 1.25451 | + | 0.724291i | 0.972002 | − | 0.234975i | \(-0.0755007\pi\) |
0.282507 | + | 0.959265i | \(0.408834\pi\) | |||||||
\(354\) | −12.6332 | + | 21.8814i | −0.671450 | + | 1.16298i | ||||
\(355\) | −16.3517 | + | 5.27188i | −0.867859 | + | 0.279802i | ||||
\(356\) | 11.6332 | 0.616561 | ||||||||
\(357\) | −21.3330 | + | 12.3166i | −1.12906 | + | 0.651865i | ||||
\(358\) | −4.56092 | − | 2.63325i | −0.241052 | − | 0.139172i | ||||
\(359\) | 8.63325 | 0.455645 | 0.227823 | − | 0.973703i | \(-0.426839\pi\) | ||||
0.227823 | + | 0.973703i | \(0.426839\pi\) | |||||||
\(360\) | 1.50000 | − | 1.65831i | 0.0790569 | − | 0.0874007i | ||||
\(361\) | 0.183375 | − | 0.317615i | 0.00965133 | − | 0.0167166i | ||||
\(362\) | 13.3166i | 0.699906i | ||||||||
\(363\) | 13.2212 | − | 7.63325i | 0.693932 | − | 0.400642i | ||||
\(364\) | −9.26650 | −0.485697 | ||||||||
\(365\) | −5.75665 | − | 1.23732i | −0.301317 | − | 0.0647641i | ||||
\(366\) | 11.9499 | + | 20.6978i | 0.624630 | + | 1.08189i | ||||
\(367\) | 3.46410 | − | 2.00000i | 0.180825 | − | 0.104399i | −0.406855 | − | 0.913493i | \(-0.633375\pi\) |
0.587680 | + | 0.809093i | \(0.300041\pi\) | |||||||
\(368\) | 5.19615 | + | 3.00000i | 0.270868 | + | 0.156386i | ||||
\(369\) | −7.63325 | −0.397371 | ||||||||
\(370\) | 5.22360 | + | 12.5584i | 0.271562 | + | 0.652881i | ||||
\(371\) | 20.0000 | 1.03835 | ||||||||
\(372\) | 4.01251 | + | 2.31662i | 0.208039 | + | 0.120111i | ||||
\(373\) | 14.6356 | − | 8.44987i | 0.757803 | − | 0.437518i | −0.0707032 | − | 0.997497i | \(-0.522524\pi\) |
0.828506 | + | 0.559979i | \(0.189191\pi\) | |||||||
\(374\) | −11.4749 | − | 19.8752i | −0.593355 | − | 1.02772i | ||||
\(375\) | 2.48913 | − | 22.2217i | 0.128538 | − | 1.14752i | ||||
\(376\) | −4.31662 | −0.222613 | ||||||||
\(377\) | −11.4891 | + | 6.63325i | −0.591720 | + | 0.341630i | ||||
\(378\) | 9.26650i | 0.476617i | ||||||||
\(379\) | 6.52506 | − | 11.3017i | 0.335170 | − | 0.580531i | −0.648348 | − | 0.761345i | \(-0.724540\pi\) |
0.983517 | + | 0.180813i | \(0.0578729\pi\) | |||||||
\(380\) | −7.15831 | − | 6.47494i | −0.367214 | − | 0.332157i | ||||
\(381\) | 2.73350 | 0.140041 | ||||||||
\(382\) | −5.74456 | − | 3.31662i | −0.293917 | − | 0.169693i | ||||
\(383\) | 26.2550 | − | 15.1583i | 1.34157 | − | 0.774554i | 0.354529 | − | 0.935045i | \(-0.384641\pi\) |
0.987037 | + | 0.160491i | \(0.0513079\pi\) | |||||||
\(384\) | 2.00000 | 0.102062 | ||||||||
\(385\) | −6.86141 | − | 21.2819i | −0.349690 | − | 1.08463i | ||||
\(386\) | −0.658312 | + | 1.14023i | −0.0335072 | + | 0.0580362i | ||||
\(387\) | 7.75082 | + | 4.47494i | 0.393996 | + | 0.227474i | ||||
\(388\) | 8.61684 | − | 4.97494i | 0.437454 | − | 0.252564i | ||||
\(389\) | 13.9749 | + | 24.2053i | 0.708557 | + | 1.22726i | 0.965392 | + | 0.260802i | \(0.0839870\pi\) |
−0.256835 | + | 0.966455i | \(0.582680\pi\) | |||||||
\(390\) | −5.48913 | − | 17.0256i | −0.277953 | − | 0.862122i | ||||
\(391\) | 15.9499 | − | 27.6260i | 0.806620 | − | 1.39711i | ||||
\(392\) | 1.41444 | + | 0.816625i | 0.0714398 | + | 0.0412458i | ||||
\(393\) | − | 2.73350i | − | 0.137887i | ||||||
\(394\) | 2.18338 | + | 3.78172i | 0.109997 | + | 0.190520i | ||||
\(395\) | 23.3035 | − | 7.51315i | 1.17252 | − | 0.378028i | ||||
\(396\) | 4.31662 | 0.216919 | ||||||||
\(397\) | 28.8997i | 1.45044i | 0.688519 | + | 0.725218i | \(0.258261\pi\) | ||||
−0.688519 | + | 0.725218i | \(0.741739\pi\) | |||||||
\(398\) | −14.6790 | − | 8.47494i | −0.735793 | − | 0.424810i | ||||
\(399\) | −20.0000 | −1.00125 | ||||||||
\(400\) | 4.05842 | − | 2.92048i | 0.202921 | − | 0.146024i | ||||
\(401\) | −37.2665 | −1.86100 | −0.930500 | − | 0.366292i | \(-0.880627\pi\) | ||||
−0.930500 | + | 0.366292i | \(0.880627\pi\) | |||||||
\(402\) | 2.91569 | − | 1.68338i | 0.145421 | − | 0.0839591i | ||||
\(403\) | 8.02502 | − | 4.63325i | 0.399755 | − | 0.230799i | ||||
\(404\) | −7.65831 | − | 13.2646i | −0.381015 | − | 0.659938i | ||||
\(405\) | −23.4101 | + | 7.54755i | −1.16326 | + | 0.375041i | ||||
\(406\) | −7.68338 | −0.381320 | ||||||||
\(407\) | −11.2149 | + | 23.7414i | −0.555903 | + | 1.17682i | ||||
\(408\) | − | 10.6332i | − | 0.526424i | ||||||
\(409\) | −17.0831 | + | 29.5888i | −0.844706 | + | 1.46307i | 0.0411701 | + | 0.999152i | \(0.486891\pi\) |
−0.885876 | + | 0.463922i | \(0.846442\pi\) | |||||||
\(410\) | −16.6874 | − | 3.58673i | −0.824130 | − | 0.177136i | ||||
\(411\) | −11.3166 | − | 19.6010i | −0.558208 | − | 0.966845i | ||||
\(412\) | −8.38605 | + | 4.84169i | −0.413151 | + | 0.238533i | ||||
\(413\) | 29.2665i | 1.44011i | ||||||||
\(414\) | 3.00000 | + | 5.19615i | 0.147442 | + | 0.255377i | ||||
\(415\) | 9.94987 | − | 11.0000i | 0.488420 | − | 0.539969i | ||||
\(416\) | 2.00000 | − | 3.46410i | 0.0980581 | − | 0.169842i | ||||
\(417\) | 39.7995i | 1.94899i | ||||||||
\(418\) | − | 18.6332i | − | 0.911382i | ||||||
\(419\) | −8.52506 | + | 14.7658i | −0.416477 | + | 0.721359i | −0.995582 | − | 0.0938939i | \(-0.970069\pi\) |
0.579106 | + | 0.815253i | \(0.303402\pi\) | |||||||
\(420\) | 2.17708 | − | 10.1289i | 0.106231 | − | 0.494241i | ||||
\(421\) | 21.9499 | 1.06977 | 0.534886 | − | 0.844924i | \(-0.320355\pi\) | ||||
0.534886 | + | 0.844924i | \(0.320355\pi\) | |||||||
\(422\) | 12.3986 | + | 7.15831i | 0.603552 | + | 0.348461i | ||||
\(423\) | −3.73831 | − | 2.15831i | −0.181763 | − | 0.104941i | ||||
\(424\) | −4.31662 | + | 7.47661i | −0.209634 | + | 0.363096i | ||||
\(425\) | −15.5271 | − | 21.5771i | −0.753175 | − | 1.04664i | ||||
\(426\) | −7.68338 | − | 13.3080i | −0.372261 | − | 0.644775i | ||||
\(427\) | 23.9745 | + | 13.8417i | 1.16021 | + | 0.669846i | ||||
\(428\) | −0.274205 | − | 0.158312i | −0.0132542 | − | 0.00765232i | ||||
\(429\) | 17.2665 | − | 29.9065i | 0.833634 | − | 1.44390i | ||||
\(430\) | 14.8417 | + | 13.4248i | 0.715730 | + | 0.647402i | ||||
\(431\) | 14.8417 | + | 25.7066i | 0.714899 | + | 1.23824i | 0.962999 | + | 0.269507i | \(0.0868607\pi\) |
−0.248100 | + | 0.968735i | \(0.579806\pi\) | |||||||
\(432\) | −3.46410 | − | 2.00000i | −0.166667 | − | 0.0962250i | ||||
\(433\) | − | 15.9499i | − | 0.766502i | −0.923644 | − | 0.383251i | \(-0.874804\pi\) | ||
0.923644 | − | 0.383251i | \(-0.125196\pi\) | |||||||
\(434\) | 5.36675 | 0.257612 | ||||||||
\(435\) | −4.55134 | − | 14.1168i | −0.218220 | − | 0.676851i | ||||
\(436\) | 3.94987 | 0.189165 | ||||||||
\(437\) | 22.4298 | − | 12.9499i | 1.07296 | − | 0.619477i | ||||
\(438\) | − | 5.26650i | − | 0.251643i | ||||||
\(439\) | 6.00000 | + | 10.3923i | 0.286364 | + | 0.495998i | 0.972939 | − | 0.231062i | \(-0.0742199\pi\) |
−0.686575 | + | 0.727059i | \(0.740887\pi\) | |||||||
\(440\) | 9.43675 | + | 2.02830i | 0.449879 | + | 0.0966956i | ||||
\(441\) | 0.816625 | + | 1.41444i | 0.0388869 | + | 0.0673541i | ||||
\(442\) | −18.4173 | − | 10.6332i | −0.876023 | − | 0.505772i | ||||
\(443\) | − | 25.2665i | − | 1.20045i | −0.799832 | − | 0.600224i | \(-0.795078\pi\) | ||
0.799832 | − | 0.600224i | \(-0.204922\pi\) | |||||||
\(444\) | −10.0000 | + | 6.92820i | −0.474579 | + | 0.328798i | ||||
\(445\) | 19.2916 | + | 17.4499i | 0.914508 | + | 0.827203i | ||||
\(446\) | −6.68338 | + | 11.5759i | −0.316467 | + | 0.548137i | ||||
\(447\) | 27.6260 | − | 15.9499i | 1.30666 | − | 0.754403i | ||||
\(448\) | 2.00626 | − | 1.15831i | 0.0947867 | − | 0.0547251i | ||||
\(449\) | −6.63325 | − | 11.4891i | −0.313042 | − | 0.542205i | 0.665977 | − | 0.745972i | \(-0.268015\pi\) |
−0.979019 | + | 0.203767i | \(0.934682\pi\) | |||||||
\(450\) | 4.97494 | − | 0.500000i | 0.234521 | − | 0.0235702i | ||||
\(451\) | −16.4749 | − | 28.5354i | −0.775774 | − | 1.34368i | ||||
\(452\) | 5.36675i | 0.252431i | ||||||||
\(453\) | −18.4173 | − | 10.6332i | −0.865322 | − | 0.499594i | ||||
\(454\) | −6.94987 | −0.326174 | ||||||||
\(455\) | −15.3668 | − | 13.8997i | −0.720404 | − | 0.651630i | ||||
\(456\) | 4.31662 | − | 7.47661i | 0.202144 | − | 0.350125i | ||||
\(457\) | −8.70366 | + | 5.02506i | −0.407140 | + | 0.235063i | −0.689560 | − | 0.724228i | \(-0.742196\pi\) |
0.282420 | + | 0.959291i | \(0.408863\pi\) | |||||||
\(458\) | 3.94987i | 0.184566i | ||||||||
\(459\) | −10.6332 | + | 18.4173i | −0.496318 | + | 0.859647i | ||||
\(460\) | 4.11684 | + | 12.7692i | 0.191949 | + | 0.595365i | ||||
\(461\) | 9.31662 | − | 16.1369i | 0.433918 | − | 0.751569i | −0.563288 | − | 0.826260i | \(-0.690464\pi\) |
0.997207 | + | 0.0746916i | \(0.0237973\pi\) | |||||||
\(462\) | 17.3205 | − | 10.0000i | 0.805823 | − | 0.465242i | ||||
\(463\) | −31.3643 | + | 18.1082i | −1.45762 | + | 0.841559i | −0.998894 | − | 0.0470176i | \(-0.985028\pi\) |
−0.458729 | + | 0.888576i | \(0.651695\pi\) | |||||||
\(464\) | 1.65831 | − | 2.87228i | 0.0769852 | − | 0.133342i | ||||
\(465\) | 3.17906 | + | 9.86046i | 0.147425 | + | 0.457268i | ||||
\(466\) | −13.9749 | + | 24.2053i | −0.647376 | + | 1.12129i | ||||
\(467\) | − | 25.8997i | − | 1.19850i | −0.800563 | − | 0.599249i | \(-0.795466\pi\) | ||
0.800563 | − | 0.599249i | \(-0.204534\pi\) | |||||||
\(468\) | 3.46410 | − | 2.00000i | 0.160128 | − | 0.0924500i | ||||
\(469\) | 1.94987 | − | 3.37728i | 0.0900368 | − | 0.155948i | ||||
\(470\) | −7.15831 | − | 6.47494i | −0.330188 | − | 0.298667i | ||||
\(471\) | 6.00000 | 0.276465 | ||||||||
\(472\) | −10.9407 | − | 6.31662i | −0.503587 | − | 0.290746i | ||||
\(473\) | 38.6332i | 1.77636i | ||||||||
\(474\) | 10.9499 | + | 18.9657i | 0.502944 | + | 0.871125i | ||||
\(475\) | −2.15831 | − | 21.4749i | −0.0990302 | − | 0.985338i | ||||
\(476\) | −6.15831 | − | 10.6665i | −0.282266 | − | 0.488899i | ||||
\(477\) | −7.47661 | + | 4.31662i | −0.342331 | + | 0.197645i | ||||
\(478\) | 7.20241 | − | 4.15831i | 0.329430 | − | 0.190197i | ||||
\(479\) | −11.6834 | + | 20.2362i | −0.533827 | + | 0.924616i | 0.465392 | + | 0.885105i | \(0.345913\pi\) |
−0.999219 | + | 0.0395109i | \(0.987420\pi\) | |||||||
\(480\) | 3.31662 | + | 3.00000i | 0.151383 | + | 0.136931i | ||||
\(481\) | 2.00000 | + | 24.2487i | 0.0911922 | + | 1.10565i | ||||
\(482\) | 29.2665i | 1.33305i | ||||||||
\(483\) | 24.0751 | + | 13.8997i | 1.09545 | + | 0.632460i | ||||
\(484\) | 3.81662 | + | 6.61059i | 0.173483 | + | 0.300481i | ||||
\(485\) | 21.7518 | + | 4.67527i | 0.987699 | + | 0.212293i | ||||
\(486\) | −5.00000 | − | 8.66025i | −0.226805 | − | 0.392837i | ||||
\(487\) | − | 18.0000i | − | 0.815658i | −0.913058 | − | 0.407829i | \(-0.866286\pi\) | ||
0.913058 | − | 0.407829i | \(-0.133714\pi\) | |||||||
\(488\) | −10.3489 | + | 5.97494i | −0.468472 | + | 0.270473i | ||||
\(489\) | 44.4327 | 2.00932 | ||||||||
\(490\) | 1.12064 | + | 3.47587i | 0.0506253 | + | 0.157024i | ||||
\(491\) | 24.3166 | 1.09739 | 0.548697 | − | 0.836021i | \(-0.315124\pi\) | ||||
0.548697 | + | 0.836021i | \(0.315124\pi\) | |||||||
\(492\) | − | 15.2665i | − | 0.688267i | ||||||
\(493\) | −15.2708 | − | 8.81662i | −0.687764 | − | 0.397081i | ||||
\(494\) | −8.63325 | − | 14.9532i | −0.388428 | − | 0.672777i | ||||
\(495\) | 7.15831 | + | 6.47494i | 0.321742 | + | 0.291027i | ||||
\(496\) | −1.15831 | + | 2.00626i | −0.0520098 | + | 0.0900836i | ||||
\(497\) | −15.4148 | − | 8.89975i | −0.691449 | − | 0.399208i | ||||
\(498\) | 11.4891 | + | 6.63325i | 0.514840 | + | 0.297243i | ||||
\(499\) | −8.47494 | − | 14.6790i | −0.379390 | − | 0.657123i | 0.611583 | − | 0.791180i | \(-0.290533\pi\) |
−0.990974 | + | 0.134057i | \(0.957200\pi\) | |||||||
\(500\) | 11.1109 | + | 1.24456i | 0.496892 | + | 0.0556585i | ||||
\(501\) | −9.26650 | + | 16.0500i | −0.413997 | + | 0.717063i | ||||
\(502\) | −2.00626 | − | 1.15831i | −0.0895436 | − | 0.0516980i | ||||
\(503\) | −22.1556 | − | 12.7916i | −0.987871 | − | 0.570348i | −0.0832337 | − | 0.996530i | \(-0.526525\pi\) |
−0.904637 | + | 0.426182i | \(0.859858\pi\) | |||||||
\(504\) | 2.31662 | 0.103191 | ||||||||
\(505\) | 7.19700 | − | 33.4843i | 0.320263 | − | 1.49003i | ||||
\(506\) | −12.9499 | + | 22.4298i | −0.575692 | + | 0.997128i | ||||
\(507\) | − | 6.00000i | − | 0.266469i | ||||||
\(508\) | 1.36675i | 0.0606397i | ||||||||
\(509\) | −0.658312 | + | 1.14023i | −0.0291792 | + | 0.0505398i | −0.880246 | − | 0.474517i | \(-0.842623\pi\) |
0.851067 | + | 0.525057i | \(0.175956\pi\) | |||||||
\(510\) | 15.9499 | − | 17.6332i | 0.706272 | − | 0.780813i | ||||
\(511\) | −3.05013 | − | 5.28297i | −0.134930 | − | 0.233705i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −14.9532 | + | 8.63325i | −0.660201 | + | 0.381167i | ||||
\(514\) | 11.6583 | + | 20.1928i | 0.514226 | + | 0.890666i | ||||
\(515\) | −21.1692 | − | 4.55004i | −0.932827 | − | 0.200499i | ||||
\(516\) | −8.94987 | + | 15.5016i | −0.393996 | + | 0.682422i | ||||
\(517\) | − | 18.6332i | − | 0.819489i | ||||||
\(518\) | −6.01877 | + | 12.7414i | −0.264449 | + | 0.559827i | ||||
\(519\) | 24.5330 | 1.07688 | ||||||||
\(520\) | 8.51278 | − | 2.74456i | 0.373310 | − | 0.120357i | ||||
\(521\) | 14.6332 | + | 25.3455i | 0.641094 | + | 1.11041i | 0.985189 | + | 0.171473i | \(0.0548526\pi\) |
−0.344095 | + | 0.938935i | \(0.611814\pi\) | |||||||
\(522\) | 2.87228 | − | 1.65831i | 0.125716 | − | 0.0725824i | ||||
\(523\) | −0.0868201 | + | 0.0501256i | −0.00379638 | + | 0.00219184i | −0.501897 | − | 0.864927i | \(-0.667364\pi\) |
0.498101 | + | 0.867119i | \(0.334031\pi\) | |||||||
\(524\) | 1.36675 | 0.0597068 | ||||||||
\(525\) | 18.8037 | − | 13.5313i | 0.820660 | − | 0.590555i | ||||
\(526\) | 13.2665 | 0.578447 | ||||||||
\(527\) | 10.6665 | + | 6.15831i | 0.464640 | + | 0.268260i | ||||
\(528\) | 8.63325i | 0.375714i | ||||||||
\(529\) | −13.0000 | −0.565217 | ||||||||
\(530\) | −18.3732 | + | 5.92362i | −0.798082 | + | 0.257306i | ||||
\(531\) | −6.31662 | − | 10.9407i | −0.274118 | − | 0.474787i | ||||
\(532\) | − | 10.0000i | − | 0.433555i | ||||||
\(533\) | −26.4424 | − | 15.2665i | −1.14535 | − | 0.661265i | ||||
\(534\) | −11.6332 | + | 20.1494i | −0.503420 | + | 0.871949i | ||||
\(535\) | −0.217249 | − | 0.673839i | −0.00939250 | − | 0.0291326i | ||||
\(536\) | 0.841688 | + | 1.45785i | 0.0363554 | + | 0.0629693i | ||||
\(537\) | 9.12184 | − | 5.26650i | 0.393637 | − | 0.227266i | ||||
\(538\) | 1.09682 | + | 0.633250i | 0.0472873 | + | 0.0273013i | ||||
\(539\) | −3.52506 | + | 6.10559i | −0.151835 | + | 0.262986i | ||||
\(540\) | −2.74456 | − | 8.51278i | −0.118107 | − | 0.366332i | ||||
\(541\) | −2.05013 | −0.0881418 | −0.0440709 | − | 0.999028i | \(-0.514033\pi\) | ||||
−0.0440709 | + | 0.999028i | \(0.514033\pi\) | |||||||
\(542\) | 23.8877 | − | 13.7916i | 1.02606 | − | 0.592398i | ||||
\(543\) | −23.0651 | − | 13.3166i | −0.989817 | − | 0.571471i | ||||
\(544\) | 5.31662 | 0.227948 | ||||||||
\(545\) | 6.55013 | + | 5.92481i | 0.280577 | + | 0.253791i | ||||
\(546\) | 9.26650 | − | 16.0500i | 0.396570 | − | 0.686879i | ||||
\(547\) | − | 21.6834i | − | 0.927114i | −0.886067 | − | 0.463557i | \(-0.846573\pi\) | ||
0.886067 | − | 0.463557i | \(-0.153427\pi\) | |||||||
\(548\) | 9.80048 | − | 5.65831i | 0.418656 | − | 0.241711i | ||||
\(549\) | −11.9499 | −0.510008 | ||||||||
\(550\) | 12.6066 | + | 17.5187i | 0.537548 | + | 0.746999i | ||||
\(551\) | −7.15831 | − | 12.3986i | −0.304954 | − | 0.528196i | ||||
\(552\) | −10.3923 | + | 6.00000i | −0.442326 | + | 0.255377i | ||||
\(553\) | 21.9683 | + | 12.6834i | 0.934185 | + | 0.539352i | ||||
\(554\) | −5.63325 | −0.239334 | ||||||||
\(555\) | −26.9754 | − | 3.51087i | −1.14504 | − | 0.149028i | ||||
\(556\) | −19.8997 | −0.843937 | ||||||||
\(557\) | −12.3552 | − | 7.13325i | −0.523505 | − | 0.302245i | 0.214863 | − | 0.976644i | \(-0.431070\pi\) |
−0.738367 | + | 0.674399i | \(0.764403\pi\) | |||||||
\(558\) | −2.00626 | + | 1.15831i | −0.0849316 | + | 0.0490353i | ||||
\(559\) | 17.8997 | + | 31.0033i | 0.757079 | + | 1.31130i | ||||
\(560\) | 5.06447 | + | 1.08854i | 0.214013 | + | 0.0459992i | ||||
\(561\) | 45.8997 | 1.93789 | ||||||||
\(562\) | 14.1740 | − | 8.18338i | 0.597895 | − | 0.345195i | ||||
\(563\) | − | 8.53300i | − | 0.359623i | −0.983701 | − | 0.179812i | \(-0.942451\pi\) | ||
0.983701 | − | 0.179812i | \(-0.0575488\pi\) | |||||||
\(564\) | 4.31662 | − | 7.47661i | 0.181763 | − | 0.314822i | ||||
\(565\) | −8.05013 | + | 8.89975i | −0.338671 | + | 0.374415i | ||||
\(566\) | 8.31662 | 0.349574 | ||||||||
\(567\) | −22.0688 | − | 12.7414i | −0.926803 | − | 0.535090i | ||||
\(568\) | 6.65400 | − | 3.84169i | 0.279196 | − | 0.161194i | ||||
\(569\) | −34.1662 | −1.43232 | −0.716162 | − | 0.697934i | \(-0.754103\pi\) | ||||
−0.716162 | + | 0.697934i | \(0.754103\pi\) | |||||||
\(570\) | 18.3732 | − | 5.92362i | 0.769570 | − | 0.248113i | ||||
\(571\) | −8.26650 | + | 14.3180i | −0.345942 | + | 0.599190i | −0.985524 | − | 0.169533i | \(-0.945774\pi\) |
0.639582 | + | 0.768723i | \(0.279107\pi\) | |||||||
\(572\) | 14.9532 | + | 8.63325i | 0.625226 | + | 0.360974i | ||||
\(573\) | 11.4891 | − | 6.63325i | 0.479965 | − | 0.277108i | ||||
\(574\) | −8.84169 | − | 15.3143i | −0.369045 | − | 0.639205i | ||||
\(575\) | −12.3267 | + | 27.3505i | −0.514060 | + | 1.14060i | ||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | 15.5885 | + | 9.00000i | 0.648956 | + | 0.374675i | 0.788056 | − | 0.615603i | \(-0.211088\pi\) |
−0.139100 | + | 0.990278i | \(0.544421\pi\) | |||||||
\(578\) | − | 11.2665i | − | 0.468625i | ||||||
\(579\) | −1.31662 | − | 2.28046i | −0.0547171 | − | 0.0947727i | ||||
\(580\) | 7.05842 | − | 2.27567i | 0.293085 | − | 0.0944921i | ||||
\(581\) | 15.3668 | 0.637520 | ||||||||
\(582\) | 19.8997i | 0.824871i | ||||||||
\(583\) | −32.2737 | − | 18.6332i | −1.33664 | − | 0.771710i | ||||
\(584\) | 2.63325 | 0.108965 | ||||||||
\(585\) | 8.74456 | + | 1.87953i | 0.361543 | + | 0.0777089i | ||||
\(586\) | −2.36675 | −0.0977696 | ||||||||
\(587\) | 16.6853 | − | 9.63325i | 0.688675 | − | 0.397607i | −0.114440 | − | 0.993430i | \(-0.536507\pi\) |
0.803116 | + | 0.595823i | \(0.203174\pi\) | |||||||
\(588\) | −2.82887 | + | 1.63325i | −0.116661 | + | 0.0673541i | ||||
\(589\) | 5.00000 | + | 8.66025i | 0.206021 | + | 0.356840i | ||||
\(590\) | −8.66819 | − | 26.8860i | −0.356864 | − | 1.10688i | ||||
\(591\) | −8.73350 | −0.359248 | ||||||||
\(592\) | −3.46410 | − | 5.00000i | −0.142374 | − | 0.205499i | ||||
\(593\) | 29.8496i | 1.22578i | 0.790169 | + | 0.612889i | \(0.209993\pi\) | ||||
−0.790169 | + | 0.612889i | \(0.790007\pi\) | |||||||
\(594\) | 8.63325 | − | 14.9532i | 0.354227 | − | 0.613538i | ||||
\(595\) | 5.78736 | − | 26.9259i | 0.237259 | − | 1.10385i | ||||
\(596\) | 7.97494 | + | 13.8130i | 0.326666 | + | 0.565802i | ||||
\(597\) | 29.3580 | − | 16.9499i | 1.20154 | − | 0.693712i | ||||
\(598\) | 24.0000i | 0.981433i | ||||||||
\(599\) | 15.7916 | + | 27.3518i | 0.645226 | + | 1.11756i | 0.984249 | + | 0.176786i | \(0.0565700\pi\) |
−0.339024 | + | 0.940778i | \(0.610097\pi\) | |||||||
\(600\) | 1.00000 | + | 9.94987i | 0.0408248 | + | 0.406202i | ||||
\(601\) | −17.5000 | + | 30.3109i | −0.713840 | + | 1.23641i | 0.249565 | + | 0.968358i | \(0.419712\pi\) |
−0.963405 | + | 0.268049i | \(0.913621\pi\) | |||||||
\(602\) | 20.7335i | 0.845034i | ||||||||
\(603\) | 1.68338i | 0.0685523i | ||||||||
\(604\) | 5.31662 | − | 9.20866i | 0.216330 | − | 0.374695i | ||||
\(605\) | −3.58673 | + | 16.6874i | −0.145821 | + | 0.678438i | ||||
\(606\) | 30.6332 | 1.24439 | ||||||||
\(607\) | 36.0120 | + | 20.7916i | 1.46168 | + | 0.843903i | 0.999089 | − | 0.0426666i | \(-0.0135853\pi\) |
0.462594 | + | 0.886570i | \(0.346919\pi\) | |||||||
\(608\) | 3.73831 | + | 2.15831i | 0.151608 | + | 0.0875311i | ||||
\(609\) | 7.68338 | − | 13.3080i | 0.311346 | − | 0.539267i | ||||
\(610\) | −26.1241 | − | 5.61503i | −1.05773 | − | 0.227346i | ||||
\(611\) | −8.63325 | − | 14.9532i | −0.349264 | − | 0.604943i | ||||
\(612\) | 4.60433 | + | 2.65831i | 0.186119 | + | 0.107456i | ||||
\(613\) | 11.8067 | + | 6.81662i | 0.476870 | + | 0.275321i | 0.719111 | − | 0.694895i | \(-0.244549\pi\) |
−0.242241 | + | 0.970216i | \(0.577883\pi\) | |||||||
\(614\) | 7.84169 | − | 13.5822i | 0.316465 | − | 0.548133i | ||||
\(615\) | 22.8997 | − | 25.3166i | 0.923407 | − | 1.02086i | ||||
\(616\) | 5.00000 | + | 8.66025i | 0.201456 | + | 0.348932i | ||||
\(617\) | −31.1769 | − | 18.0000i | −1.25514 | − | 0.724653i | −0.283011 | − | 0.959117i | \(-0.591333\pi\) |
−0.972125 | + | 0.234464i | \(0.924666\pi\) | |||||||
\(618\) | − | 19.3668i | − | 0.779045i | ||||||
\(619\) | 22.9499 | 0.922433 | 0.461217 | − | 0.887288i | \(-0.347413\pi\) | ||||
0.461217 | + | 0.887288i | \(0.347413\pi\) | |||||||
\(620\) | −4.93023 | + | 1.58953i | −0.198003 | + | 0.0638371i | ||||
\(621\) | 24.0000 | 0.963087 | ||||||||
\(622\) | 8.29923 | − | 4.79156i | 0.332769 | − | 0.192124i | ||||
\(623\) | 26.9499i | 1.07972i | ||||||||
\(624\) | 4.00000 | + | 6.92820i | 0.160128 | + | 0.277350i | ||||
\(625\) | 16.5584 | + | 18.7302i | 0.662337 | + | 0.749206i | ||||
\(626\) | −2.02506 | − | 3.50751i | −0.0809378 | − | 0.140188i | ||||
\(627\) | 32.2737 | + | 18.6332i | 1.28889 | + | 0.744140i | ||||
\(628\) | 3.00000i | 0.119713i | ||||||||
\(629\) | −26.5831 | + | 18.4173i | −1.05994 | + | 0.734347i | ||||
\(630\) | 3.84169 | + | 3.47494i | 0.153056 | + | 0.138445i | ||||
\(631\) | −5.00000 | + | 8.66025i | −0.199047 | + | 0.344759i | −0.948220 | − | 0.317615i | \(-0.897118\pi\) |
0.749173 | + | 0.662375i | \(0.230451\pi\) | |||||||
\(632\) | −9.48287 | + | 5.47494i | −0.377208 | + | 0.217781i | ||||
\(633\) | −24.7971 | + | 14.3166i | −0.985597 | + | 0.569035i | ||||
\(634\) | 4.18338 | + | 7.24582i | 0.166143 | + | 0.287768i | ||||
\(635\) | −2.05013 | + | 2.26650i | −0.0813568 | + | 0.0899433i | ||||
\(636\) | −8.63325 | − | 14.9532i | −0.342331 | − | 0.592934i | ||||
\(637\) | 6.53300i | 0.258847i | ||||||||
\(638\) | 12.3986 | + | 7.15831i | 0.490864 | + | 0.283400i | ||||
\(639\) | 7.68338 | 0.303950 | ||||||||
\(640\) | −1.50000 | + | 1.65831i | −0.0592927 | + | 0.0655506i | ||||
\(641\) | 5.13325 | − | 8.89105i | 0.202751 | − | 0.351175i | −0.746663 | − | 0.665203i | \(-0.768345\pi\) |
0.949414 | + | 0.314027i | \(0.101678\pi\) | |||||||
\(642\) | 0.548410 | − | 0.316625i | 0.0216440 | − | 0.0124962i | ||||
\(643\) | 36.8496i | 1.45321i | 0.687057 | + | 0.726604i | \(0.258902\pi\) | ||||
−0.687057 | + | 0.726604i | \(0.741098\pi\) | |||||||
\(644\) | −6.94987 | + | 12.0375i | −0.273863 | + | 0.474345i | ||||
\(645\) | −38.0941 | + | 12.2817i | −1.49996 | + | 0.483593i | ||||
\(646\) | 11.4749 | − | 19.8752i | 0.451475 | − | 0.781978i | ||||
\(647\) | −26.8034 | + | 15.4749i | −1.05375 | + | 0.608383i | −0.923697 | − | 0.383125i | \(-0.874848\pi\) |
−0.130053 | + | 0.991507i | \(0.541515\pi\) | |||||||
\(648\) | 9.52628 | − | 5.50000i | 0.374228 | − | 0.216060i | ||||
\(649\) | 27.2665 | − | 47.2270i | 1.07030 | − | 1.85382i | ||||
\(650\) | 18.2337 | + | 8.21782i | 0.715184 | + | 0.322330i | ||||
\(651\) | −5.36675 | + | 9.29548i | −0.210340 | + | 0.364319i | ||||
\(652\) | 22.2164i | 0.870060i | ||||||||
\(653\) | −25.0279 | + | 14.4499i | −0.979418 | + | 0.565467i | −0.902094 | − | 0.431539i | \(-0.857971\pi\) |
−0.0773237 | + | 0.997006i | \(0.524637\pi\) | |||||||
\(654\) | −3.94987 | + | 6.84138i | −0.154452 | + | 0.267519i | ||||
\(655\) | 2.26650 | + | 2.05013i | 0.0885595 | + | 0.0801050i | ||||
\(656\) | 7.63325 | 0.298028 | ||||||||
\(657\) | 2.28046 | + | 1.31662i | 0.0889693 | + | 0.0513664i | ||||
\(658\) | − | 10.0000i | − | 0.389841i | ||||||
\(659\) | −7.68338 | − | 13.3080i | −0.299302 | − | 0.518406i | 0.676675 | − | 0.736282i | \(-0.263420\pi\) |
−0.975976 | + | 0.217876i | \(0.930087\pi\) | |||||||
\(660\) | −12.9499 | + | 14.3166i | −0.504073 | + | 0.557274i | ||||
\(661\) | −10.0251 | − | 17.3639i | −0.389930 | − | 0.675378i | 0.602510 | − | 0.798111i | \(-0.294167\pi\) |
−0.992440 | + | 0.122733i | \(0.960834\pi\) | |||||||
\(662\) | −29.3580 | + | 16.9499i | −1.14103 | + | 0.658776i | ||||
\(663\) | 36.8347 | − | 21.2665i | 1.43054 | − | 0.825922i | ||||
\(664\) | −3.31662 | + | 5.74456i | −0.128710 | + | 0.222932i | ||||
\(665\) | 15.0000 | − | 16.5831i | 0.581675 | − | 0.643066i | ||||
\(666\) | −0.500000 | − | 6.06218i | −0.0193746 | − | 0.234905i | ||||
\(667\) | 19.8997i | 0.770521i | ||||||||
\(668\) | −8.02502 | − | 4.63325i | −0.310497 | − | 0.179266i | ||||
\(669\) | −13.3668 | − | 23.1519i | −0.516788 | − | 0.895104i | ||||
\(670\) | −0.790988 | + | 3.68009i | −0.0305585 | + | 0.142174i | ||||
\(671\) | −25.7916 | − | 44.6723i | −0.995672 | − | 1.72455i | ||||
\(672\) | 4.63325i | 0.178731i | ||||||||
\(673\) | −7.01502 | + | 4.05013i | −0.270409 | + | 0.156121i | −0.629074 | − | 0.777346i | \(-0.716566\pi\) |
0.358664 | + | 0.933467i | \(0.383232\pi\) | |||||||
\(674\) | 11.9499 | 0.460292 | ||||||||
\(675\) | 8.21782 | − | 18.2337i | 0.316304 | − | 0.701815i | ||||
\(676\) | 3.00000 | 0.115385 | ||||||||
\(677\) | 8.36675i | 0.321560i | 0.986990 | + | 0.160780i | \(0.0514010\pi\) | ||||
−0.986990 | + | 0.160780i | \(0.948599\pi\) | |||||||
\(678\) | −9.29548 | − | 5.36675i | −0.356991 | − | 0.206109i | ||||
\(679\) | 11.5251 | + | 19.9620i | 0.442291 | + | 0.766071i | ||||
\(680\) | 8.81662 | + | 7.97494i | 0.338102 | + | 0.305825i | ||||
\(681\) | 6.94987 | − | 12.0375i | 0.266320 | − | 0.461279i | ||||
\(682\) | −8.66025 | − | 5.00000i | −0.331618 | − | 0.191460i | ||||
\(683\) | 34.1932 | + | 19.7414i | 1.30837 | + | 0.755385i | 0.981823 | − | 0.189798i | \(-0.0607832\pi\) |
0.326542 | + | 0.945183i | \(0.394117\pi\) | |||||||
\(684\) | 2.15831 | + | 3.73831i | 0.0825251 | + | 0.142938i | ||||
\(685\) | 24.7397 | + | 5.31748i | 0.945257 | + | 0.203170i | ||||
\(686\) | −10.0000 | + | 17.3205i | −0.381802 | + | 0.661300i | ||||
\(687\) | −6.84138 | − | 3.94987i | −0.261015 | − | 0.150697i | ||||
\(688\) | −7.75082 | − | 4.47494i | −0.295497 | − | 0.170605i | ||||
\(689\) | −34.5330 | −1.31560 | ||||||||
\(690\) | −26.2337 | − | 5.63858i | −0.998699 | − | 0.214657i | ||||
\(691\) | 13.8417 | − | 23.9745i | 0.526563 | − | 0.912033i | −0.472958 | − | 0.881085i | \(-0.656814\pi\) |
0.999521 | − | 0.0309484i | \(-0.00985276\pi\) | |||||||
\(692\) | 12.2665i | 0.466302i | ||||||||
\(693\) | 10.0000i | 0.379869i | ||||||||
\(694\) | 7.63325 | − | 13.2212i | 0.289754 | − | 0.501869i | ||||
\(695\) | −33.0000 | − | 29.8496i | −1.25176 | − | 1.13226i | ||||
\(696\) | 3.31662 | + | 5.74456i | 0.125716 | + | 0.217747i | ||||
\(697\) | − | 40.5831i | − | 1.53720i | ||||||
\(698\) | 24.8405 | − | 14.3417i | 0.940228 | − | 0.542841i | ||||
\(699\) | −27.9499 | − | 48.4106i | −1.05716 | − | 1.83106i | ||||
\(700\) | 6.76566 | + | 9.40184i | 0.255718 | + | 0.355356i | ||||
\(701\) | −18.2665 | + | 31.6385i | −0.689916 | + | 1.19497i | 0.281948 | + | 0.959430i | \(0.409019\pi\) |
−0.971865 | + | 0.235540i | \(0.924314\pi\) | |||||||
\(702\) | − | 16.0000i | − | 0.603881i | ||||||
\(703\) | −26.1681 | + | 2.15831i | −0.986950 | + | 0.0814023i | ||||
\(704\) | −4.31662 | −0.162689 | ||||||||
\(705\) | 18.3732 | − | 5.92362i | 0.691976 | − | 0.223097i | ||||
\(706\) | −13.6082 | − | 23.5701i | −0.512151 | − | 0.887071i | ||||
\(707\) | 30.7291 | − | 17.7414i | 1.15569 | − | 0.667235i | ||||
\(708\) | 21.8814 | − | 12.6332i | 0.822355 | − | 0.474787i | ||||
\(709\) | 34.5330 | 1.29691 | 0.648457 | − | 0.761251i | \(-0.275415\pi\) | ||||
0.648457 | + | 0.761251i | \(0.275415\pi\) | |||||||
\(710\) | 16.7969 | + | 3.61028i | 0.630378 | + | 0.135491i | ||||
\(711\) | −10.9499 | −0.410652 | ||||||||
\(712\) | −10.0747 | − | 5.81662i | −0.377565 | − | 0.217987i | ||||
\(713\) | − | 13.8997i | − | 0.520550i | ||||||
\(714\) | 24.6332 | 0.921876 | ||||||||
\(715\) | 11.8472 | + | 36.7465i | 0.443062 | + | 1.37424i | ||||
\(716\) | 2.63325 | + | 4.56092i | 0.0984092 | + | 0.170450i | ||||
\(717\) | 16.6332i | 0.621180i | ||||||||
\(718\) | −7.47661 | − | 4.31662i | −0.279025 | − | 0.161095i | ||||
\(719\) | −22.5831 | + | 39.1151i | −0.842208 | + | 1.45875i | 0.0458152 | + | 0.998950i | \(0.485411\pi\) |
−0.888024 | + | 0.459798i | \(0.847922\pi\) | |||||||
\(720\) | −2.12819 | + | 0.686141i | −0.0793131 | + | 0.0255710i | ||||
\(721\) | −11.2164 | − | 19.4273i | −0.417720 | − | 0.723512i | ||||
\(722\) | −0.317615 | + | 0.183375i | −0.0118204 | + | 0.00682452i | ||||
\(723\) | −50.6911 | − | 29.2665i | −1.88522 | − | 1.08843i | ||||
\(724\) | 6.65831 | − | 11.5325i | 0.247454 | − | 0.428603i | ||||
\(725\) | 15.1186 | + | 6.81386i | 0.561490 | + | 0.253060i | ||||
\(726\) | −15.2665 | −0.566593 | ||||||||
\(727\) | 2.91569 | − | 1.68338i | 0.108137 | − | 0.0624329i | −0.444956 | − | 0.895552i | \(-0.646781\pi\) |
0.553093 | + | 0.833119i | \(0.313447\pi\) | |||||||
\(728\) | 8.02502 | + | 4.63325i | 0.297427 | + | 0.171720i | ||||
\(729\) | −13.0000 | −0.481481 | ||||||||
\(730\) | 4.36675 | + | 3.94987i | 0.161621 | + | 0.146191i | ||||
\(731\) | −23.7916 | + | 41.2082i | −0.879963 | + | 1.52414i | ||||
\(732\) | − | 23.8997i | − | 0.883360i | ||||||
\(733\) | 31.1769 | − | 18.0000i | 1.15155 | − | 0.664845i | 0.202282 | − | 0.979327i | \(-0.435164\pi\) |
0.949263 | + | 0.314482i | \(0.101831\pi\) | |||||||
\(734\) | −4.00000 | −0.147643 | ||||||||
\(735\) | −7.14103 | − | 1.53487i | −0.263401 | − | 0.0566145i | ||||
\(736\) | −3.00000 | − | 5.19615i | −0.110581 | − | 0.191533i | ||||
\(737\) | −6.29297 | + | 3.63325i | −0.231805 | + | 0.133832i | ||||
\(738\) | 6.61059 | + | 3.81662i | 0.243339 | + | 0.140492i | ||||
\(739\) | −27.8997 | −1.02631 | −0.513154 | − | 0.858296i | \(-0.671523\pi\) | ||||
−0.513154 | + | 0.858296i | \(0.671523\pi\) | |||||||
\(740\) | 1.75544 | − | 13.4877i | 0.0645312 | − | 0.495818i | ||||
\(741\) | 34.5330 | 1.26860 | ||||||||
\(742\) | −17.3205 | − | 10.0000i | −0.635856 | − | 0.367112i | ||||
\(743\) | 37.6573 | − | 21.7414i | 1.38151 | − | 0.797616i | 0.389173 | − | 0.921165i | \(-0.372761\pi\) |
0.992338 | + | 0.123549i | \(0.0394276\pi\) | |||||||
\(744\) | −2.31662 | − | 4.01251i | −0.0849316 | − | 0.147106i | ||||
\(745\) | −7.49456 | + | 34.8687i | −0.274579 | + | 1.27749i | ||||
\(746\) | −16.8997 | −0.618744 | ||||||||
\(747\) | −5.74456 | + | 3.31662i | −0.210183 | + | 0.121349i | ||||
\(748\) | 22.9499i | 0.839131i | ||||||||
\(749\) | 0.366750 | − | 0.635230i | 0.0134008 | − | 0.0232108i | ||||
\(750\) | −13.2665 | + | 18.0000i | −0.484424 | + | 0.657267i | ||||
\(751\) | 22.2164 | 0.810687 | 0.405343 | − | 0.914164i | \(-0.367152\pi\) | ||||
0.405343 | + | 0.914164i | \(0.367152\pi\) | |||||||
\(752\) | 3.73831 | + | 2.15831i | 0.136322 | + | 0.0787056i | ||||
\(753\) | 4.01251 | − | 2.31662i | 0.146224 | − | 0.0844225i | ||||
\(754\) | 13.2665 | 0.483137 | ||||||||
\(755\) | 22.6296 | − | 7.29590i | 0.823576 | − | 0.265525i | ||||
\(756\) | 4.63325 | − | 8.02502i | 0.168510 | − | 0.291867i | ||||
\(757\) | −44.0805 | − | 25.4499i | −1.60213 | − | 0.924991i | −0.991060 | − | 0.133416i | \(-0.957405\pi\) |
−0.611072 | − | 0.791575i | \(-0.709261\pi\) | |||||||
\(758\) | −11.3017 | + | 6.52506i | −0.410498 | + | 0.237001i | ||||
\(759\) | −25.8997 | − | 44.8597i | −0.940101 | − | 1.62830i | ||||
\(760\) | 2.96181 | + | 9.18662i | 0.107436 | + | 0.333234i | ||||
\(761\) | −3.13325 | + | 5.42695i | −0.113580 | + | 0.196727i | −0.917211 | − | 0.398401i | \(-0.869565\pi\) |
0.803631 | + | 0.595128i | \(0.202899\pi\) | |||||||
\(762\) | −2.36728 | − | 1.36675i | −0.0857575 | − | 0.0495121i | ||||
\(763\) | 9.15038i | 0.331266i | ||||||||
\(764\) | 3.31662 | + | 5.74456i | 0.119991 | + | 0.207831i | ||||
\(765\) | 3.64795 | + | 11.3148i | 0.131892 | + | 0.409088i | ||||
\(766\) | −30.3166 | −1.09538 | ||||||||
\(767\) | − | 50.5330i | − | 1.82464i | ||||||
\(768\) | −1.73205 | − | 1.00000i | −0.0625000 | − | 0.0360844i | ||||
\(769\) | 29.2665 | 1.05538 | 0.527688 | − | 0.849438i | \(-0.323059\pi\) | ||||
0.527688 | + | 0.849438i | \(0.323059\pi\) | |||||||
\(770\) | −4.69882 | + | 21.8614i | −0.169334 | + | 0.787830i | ||||
\(771\) | −46.6332 | −1.67946 | ||||||||
\(772\) | 1.14023 | − | 0.658312i | 0.0410378 | − | 0.0236932i | ||||
\(773\) | −26.1247 | + | 15.0831i | −0.939641 | + | 0.542502i | −0.889848 | − | 0.456257i | \(-0.849190\pi\) |
−0.0497936 | + | 0.998760i | \(0.515856\pi\) | |||||||
\(774\) | −4.47494 | − | 7.75082i | −0.160848 | − | 0.278597i | ||||
\(775\) | −10.5602 | − | 4.75940i | −0.379332 | − | 0.170963i | ||||
\(776\) | −9.94987 | −0.357180 | ||||||||
\(777\) | −16.0500 | − | 23.1662i | −0.575792 | − | 0.831085i | ||||
\(778\) | − | 27.9499i | − | 1.00205i | ||||||
\(779\) | 16.4749 | − | 28.5354i | 0.590276 | − | 1.02239i | ||||
\(780\) | −3.75906 | + | 17.4891i | −0.134596 | + | 0.626211i | ||||
\(781\) | 16.5831 | + | 28.7228i | 0.593391 | + | 1.02778i | ||||
\(782\) | −27.6260 | + | 15.9499i | −0.987903 | + | 0.570366i | ||||
\(783\) | − | 13.2665i | − | 0.474106i | ||||||
\(784\) | −0.816625 | − | 1.41444i | −0.0291652 | − | 0.0505156i | ||||
\(785\) | −4.50000 | + | 4.97494i | −0.160612 | + | 0.177563i | ||||
\(786\) | −1.36675 | + | 2.36728i | −0.0487504 | + | 0.0844381i | ||||
\(787\) | − | 24.0000i | − | 0.855508i | −0.903895 | − | 0.427754i | \(-0.859305\pi\) | ||
0.903895 | − | 0.427754i | \(-0.140695\pi\) | |||||||
\(788\) | − | 4.36675i | − | 0.155559i | ||||||
\(789\) | −13.2665 | + | 22.9783i | −0.472300 | + | 0.818047i | ||||
\(790\) | −23.9380 | − | 5.14515i | −0.851675 | − | 0.183056i | ||||
\(791\) | −12.4327 | −0.442058 | ||||||||
\(792\) | −3.73831 | − | 2.15831i | −0.132835 | − | 0.0766923i | ||||
\(793\) | −41.3956 | − | 23.8997i | −1.47000 | − | 0.848705i | ||||
\(794\) | 14.4499 | − | 25.0279i | 0.512807 | − | 0.888208i | ||||
\(795\) | 8.11322 | − | 37.7470i | 0.287746 | − | 1.33875i | ||||
\(796\) | 8.47494 | + | 14.6790i | 0.300386 | + | 0.520284i | ||||
\(797\) | 33.9190 | + | 19.5831i | 1.20147 | + | 0.693670i | 0.960882 | − | 0.276957i | \(-0.0893260\pi\) |
0.240589 | + | 0.970627i | \(0.422659\pi\) | |||||||
\(798\) | 17.3205 | + | 10.0000i | 0.613139 | + | 0.353996i | ||||
\(799\) | 11.4749 | − | 19.8752i | 0.405954 | − | 0.703133i | ||||
\(800\) | −4.97494 | + | 0.500000i | −0.175891 | + | 0.0176777i | ||||
\(801\) | −5.81662 | − | 10.0747i | −0.205520 | − | 0.355972i | ||||
\(802\) | 32.2737 | + | 18.6332i | 1.13963 | + | 0.657963i | ||||
\(803\) | 11.3668i | 0.401124i | ||||||||
\(804\) | −3.36675 | −0.118736 | ||||||||
\(805\) | −29.5814 | + | 9.53718i | −1.04261 | + | 0.336142i | ||||
\(806\) | −9.26650 | −0.326399 | ||||||||
\(807\) | −2.19364 | + | 1.26650i | −0.0772198 | + | 0.0445829i | ||||
\(808\) | 15.3166i | 0.538837i | ||||||||
\(809\) | −18.9499 | − | 32.8221i | −0.666242 | − | 1.15397i | −0.978947 | − | 0.204115i | \(-0.934568\pi\) |
0.312705 | − | 0.949850i | \(-0.398765\pi\) | |||||||
\(810\) | 24.0475 | + | 5.16870i | 0.844945 | + | 0.181610i | ||||
\(811\) | 6.94987 | + | 12.0375i | 0.244043 | + | 0.422695i | 0.961862 | − | 0.273535i | \(-0.0881928\pi\) |
−0.717819 | + | 0.696230i | \(0.754859\pi\) | |||||||
\(812\) | 6.65400 | + | 3.84169i | 0.233510 | + | 0.134817i | ||||
\(813\) | 55.1662i | 1.93476i | ||||||||
\(814\) | 21.5831 | − | 14.9532i | 0.756488 | − | 0.524110i | ||||
\(815\) | −33.3246 | + | 36.8417i | −1.16731 | + | 1.29051i | ||||
\(816\) | −5.31662 | + | 9.20866i | −0.186119 | + | 0.322368i | ||||
\(817\) | −33.4574 | + | 19.3166i | −1.17053 | + | 0.675803i | ||||
\(818\) | 29.5888 | − | 17.0831i | 1.03455 | − | 0.597297i | ||||
\(819\) | 4.63325 | + | 8.02502i | 0.161899 | + | 0.280417i | ||||
\(820\) | 12.6583 | + | 11.4499i | 0.442047 | + | 0.399847i | ||||
\(821\) | −21.2665 | − | 36.8347i | −0.742206 | − | 1.28554i | −0.951489 | − | 0.307683i | \(-0.900446\pi\) |
0.209283 | − | 0.977855i | \(-0.432887\pi\) | |||||||
\(822\) | 22.6332i | 0.789425i | ||||||||
\(823\) | 12.1244 | + | 7.00000i | 0.422628 | + | 0.244005i | 0.696201 | − | 0.717847i | \(-0.254872\pi\) |
−0.273573 | + | 0.961851i | \(0.588205\pi\) | |||||||
\(824\) | 9.68338 | 0.337336 | ||||||||
\(825\) | −42.9499 | + | 4.31662i | −1.49532 | + | 0.150286i | ||||
\(826\) | 14.6332 | − | 25.3455i | 0.509156 | − | 0.881884i | ||||
\(827\) | −22.9783 | + | 13.2665i | −0.799032 | + | 0.461321i | −0.843133 | − | 0.537706i | \(-0.819291\pi\) |
0.0441005 | + | 0.999027i | \(0.485958\pi\) | |||||||
\(828\) | − | 6.00000i | − | 0.208514i | ||||||
\(829\) | −8.05013 | + | 13.9432i | −0.279592 | + | 0.484268i | −0.971283 | − | 0.237925i | \(-0.923533\pi\) |
0.691691 | + | 0.722194i | \(0.256866\pi\) | |||||||
\(830\) | −14.1168 | + | 4.55134i | −0.490003 | + | 0.157979i | ||||
\(831\) | 5.63325 | − | 9.75707i | 0.195415 | − | 0.338469i | ||||
\(832\) | −3.46410 | + | 2.00000i | −0.120096 | + | 0.0693375i | ||||
\(833\) | −7.52002 | + | 4.34169i | −0.260553 | + | 0.150431i | ||||
\(834\) | 19.8997 | − | 34.4674i | 0.689072 | − | 1.19351i | ||||
\(835\) | −6.35812 | − | 19.7209i | −0.220032 | − | 0.682470i | ||||
\(836\) | −9.31662 | + | 16.1369i | −0.322222 | + | 0.558105i | ||||
\(837\) | 9.26650i | 0.320297i | ||||||||
\(838\) | 14.7658 | − | 8.52506i | 0.510078 | − | 0.294493i | ||||
\(839\) | 9.94987 | − | 17.2337i | 0.343508 | − | 0.594973i | −0.641574 | − | 0.767061i | \(-0.721718\pi\) |
0.985082 | + | 0.172088i | \(0.0550515\pi\) | |||||||
\(840\) | −6.94987 | + | 7.68338i | −0.239793 | + | 0.265102i | ||||
\(841\) | −18.0000 | −0.620690 | ||||||||
\(842\) | −19.0091 | − | 10.9749i | −0.655099 | − | 0.378221i | ||||
\(843\) | 32.7335i | 1.12740i | ||||||||
\(844\) | −7.15831 | − | 12.3986i | −0.246399 | − | 0.426776i | ||||
\(845\) | 4.97494 | + | 4.50000i | 0.171143 | + | 0.154805i | ||||
\(846\) | 2.15831 | + | 3.73831i | 0.0742043 | + | 0.128526i | ||||
\(847\) | −15.3143 | + | 8.84169i | −0.526204 | + | 0.303804i | ||||
\(848\) | 7.47661 | − | 4.31662i | 0.256748 | − | 0.148234i | ||||
\(849\) | −8.31662 | + | 14.4048i | −0.285426 | + | 0.494372i | ||||
\(850\) | 2.65831 | + | 26.4499i | 0.0911794 | + | 0.907223i | ||||
\(851\) | 33.0000 | + | 15.5885i | 1.13123 | + | 0.534365i | ||||
\(852\) | 15.3668i | 0.526456i | ||||||||
\(853\) | 8.80423 | + | 5.08312i | 0.301451 | + | 0.174043i | 0.643095 | − | 0.765787i | \(-0.277650\pi\) |
−0.341644 | + | 0.939830i | \(0.610984\pi\) | |||||||
\(854\) | −13.8417 | − | 23.9745i | −0.473653 | − | 0.820391i | ||||
\(855\) | −2.02830 | + | 9.43675i | −0.0693665 | + | 0.322730i | ||||
\(856\) | 0.158312 | + | 0.274205i | 0.00541101 | + | 0.00937214i | ||||
\(857\) | 6.58312i | 0.224875i | 0.993659 | + | 0.112438i | \(0.0358658\pi\) | ||||
−0.993659 | + | 0.112438i | \(0.964134\pi\) | |||||||
\(858\) | −29.9065 | + | 17.2665i | −1.02099 | + | 0.589469i | ||||
\(859\) | 5.05013 | 0.172308 | 0.0861540 | − | 0.996282i | \(-0.472542\pi\) | ||||
0.0861540 | + | 0.996282i | \(0.472542\pi\) | |||||||
\(860\) | −6.14087 | − | 19.0471i | −0.209402 | − | 0.649500i | ||||
\(861\) | 35.3668 | 1.20530 | ||||||||
\(862\) | − | 29.6834i | − | 1.01102i | ||||||
\(863\) | 17.8689 | + | 10.3166i | 0.608265 | + | 0.351182i | 0.772286 | − | 0.635275i | \(-0.219113\pi\) |
−0.164021 | + | 0.986457i | \(0.552447\pi\) | |||||||
\(864\) | 2.00000 | + | 3.46410i | 0.0680414 | + | 0.117851i | ||||
\(865\) | −18.3997 | + | 20.3417i | −0.625610 | + | 0.691638i | ||||
\(866\) | −7.97494 | + | 13.8130i | −0.270999 | + | 0.469385i | ||||
\(867\) | 19.5141 | + | 11.2665i | 0.662735 | + | 0.382630i | ||||
\(868\) | −4.64774 | − | 2.68338i | −0.157755 | − | 0.0910797i | ||||
\(869\) | −23.6332 | − | 40.9340i | −0.801703 | − | 1.38859i | ||||
\(870\) | −3.11684 | + | 14.5012i | −0.105671 | + | 0.491637i | ||||
\(871\) | −3.36675 | + | 5.83138i | −0.114078 | + | 0.197589i | ||||
\(872\) | −3.42069 | − | 1.97494i | −0.115839 | − | 0.0668798i | ||||
\(873\) | −8.61684 | − | 4.97494i | −0.291636 | − | 0.168376i | ||||
\(874\) | −25.8997 | −0.876072 | ||||||||
\(875\) | −2.88318 | + | 25.7397i | −0.0974694 | + | 0.870160i | ||||
\(876\) | −2.63325 | + | 4.56092i | −0.0889693 | + | 0.154099i | ||||
\(877\) | 15.0000i | 0.506514i | 0.967399 | + | 0.253257i | \(0.0815018\pi\) | ||||
−0.967399 | + | 0.253257i | \(0.918498\pi\) | |||||||
\(878\) | − | 12.0000i | − | 0.404980i | ||||||
\(879\) | 2.36675 | − | 4.09933i | 0.0798285 | − | 0.138267i | ||||
\(880\) | −7.15831 | − | 6.47494i | −0.241307 | − | 0.218270i | ||||
\(881\) | 12.1834 | + | 21.1022i | 0.410468 | + | 0.710952i | 0.994941 | − | 0.100461i | \(-0.0320319\pi\) |
−0.584473 | + | 0.811413i | \(0.698699\pi\) | |||||||
\(882\) | − | 1.63325i | − | 0.0549944i | ||||||
\(883\) | −6.84138 | + | 3.94987i | −0.230231 | + | 0.132924i | −0.610679 | − | 0.791879i | \(-0.709103\pi\) |
0.380448 | + | 0.924802i | \(0.375770\pi\) | |||||||
\(884\) | 10.6332 | + | 18.4173i | 0.357635 | + | 0.619442i | ||||
\(885\) | 55.2361 | + | 11.8723i | 1.85674 | + | 0.399082i | ||||
\(886\) | −12.6332 | + | 21.8814i | −0.424422 | + | 0.735121i | ||||
\(887\) | 4.73350i | 0.158935i | 0.996837 | + | 0.0794677i | \(0.0253221\pi\) | ||||
−0.996837 | + | 0.0794677i | \(0.974678\pi\) | |||||||
\(888\) | 12.1244 | − | 1.00000i | 0.406867 | − | 0.0335578i | ||||
\(889\) | −3.16625 | −0.106193 | ||||||||
\(890\) | −7.98205 | − | 24.7578i | −0.267559 | − | 0.829884i | ||||
\(891\) | 23.7414 | + | 41.1214i | 0.795368 | + | 1.37762i | ||||
\(892\) | 11.5759 | − | 6.68338i | 0.387591 | − | 0.223776i | ||||
\(893\) | 16.1369 | − | 9.31662i | 0.540000 | − | 0.311769i | ||||
\(894\) | −31.8997 | −1.06689 | ||||||||
\(895\) | −2.47463 | + | 11.5133i | −0.0827178 | + | 0.384847i | ||||
\(896\) | −2.31662 | −0.0773930 | ||||||||
\(897\) | −41.5692 | − | 24.0000i | −1.38796 | − | 0.801337i | ||||
\(898\) | 13.2665i | 0.442709i | ||||||||
\(899\) | −7.68338 | −0.256255 | ||||||||
\(900\) | −4.55842 | − | 2.05446i | −0.151947 | − | 0.0684819i | ||||
\(901\) | −22.9499 | − | 39.7503i | −0.764571 | − | 1.32428i | ||||
\(902\) | 32.9499i | 1.09711i | ||||||||
\(903\) | −35.9115 | − | 20.7335i | −1.19506 | − | 0.689968i | ||||
\(904\) | 2.68338 | − | 4.64774i | 0.0892477 | − | 0.154582i | ||||
\(905\) | 28.3404 | − | 9.13708i | 0.942066 | − | 0.303727i | ||||
\(906\) | 10.6332 | + | 18.4173i | 0.353266 | + | 0.611875i | ||||
\(907\) | 10.5797 | − | 6.10819i | 0.351293 | − | 0.202819i | −0.313962 | − | 0.949436i | \(-0.601656\pi\) |
0.665255 | + | 0.746617i | \(0.268323\pi\) | |||||||
\(908\) | 6.01877 | + | 3.47494i | 0.199740 | + | 0.115320i | ||||
\(909\) | −7.65831 | + | 13.2646i | −0.254010 | + | 0.439959i | ||||
\(910\) | 6.35812 | + | 19.7209i | 0.210770 | + | 0.653742i | ||||
\(911\) | −18.0000 | −0.596367 | −0.298183 | − | 0.954509i | \(-0.596381\pi\) | ||||
−0.298183 | + | 0.954509i | \(0.596381\pi\) | |||||||
\(912\) | −7.47661 | + | 4.31662i | −0.247575 | + | 0.142938i | ||||
\(913\) | −24.7971 | − | 14.3166i | −0.820665 | − | 0.473811i | ||||
\(914\) | 10.0501 | 0.332429 | ||||||||
\(915\) | 35.8496 | − | 39.6332i | 1.18515 | − | 1.31023i | ||||
\(916\) | 1.97494 | − | 3.42069i | 0.0652538 | − | 0.113023i | ||||
\(917\) | 3.16625i | 0.104559i | ||||||||
\(918\) | 18.4173 | − | 10.6332i | 0.607862 | − | 0.350950i | ||||
\(919\) | 16.1003 | 0.531098 | 0.265549 | − | 0.964097i | \(-0.414447\pi\) | ||||
0.265549 | + | 0.964097i | \(0.414447\pi\) | |||||||
\(920\) | 2.81929 | − | 13.1168i | 0.0929493 | − | 0.432450i | ||||
\(921\) | 15.6834 | + | 27.1644i | 0.516785 | + | 0.895098i | ||||
\(922\) | −16.1369 | + | 9.31662i | −0.531439 | + | 0.306827i | ||||
\(923\) | 26.6160 | + | 15.3668i | 0.876076 | + | 0.505803i | ||||
\(924\) | −20.0000 | −0.657952 | ||||||||
\(925\) | 23.1426 | − | 19.7337i | 0.760925 | − | 0.648840i | ||||
\(926\) | 36.2164 | 1.19014 | ||||||||
\(927\) | 8.38605 | + | 4.84169i | 0.275434 | + | 0.159022i | ||||
\(928\) | −2.87228 | + | 1.65831i | −0.0942873 | + | 0.0544368i | ||||
\(929\) | −11.4499 | − | 19.8318i | −0.375658 | − | 0.650659i | 0.614767 | − | 0.788709i | \(-0.289250\pi\) |
−0.990425 | + | 0.138050i | \(0.955917\pi\) | |||||||
\(930\) | 2.17708 | − | 10.1289i | 0.0713893 | − | 0.332141i | ||||
\(931\) | −7.05013 | −0.231059 | ||||||||
\(932\) | 24.2053 | − | 13.9749i | 0.792871 | − | 0.457764i | ||||
\(933\) | 19.1662i | 0.627475i | ||||||||
\(934\) | −12.9499 | + | 22.4298i | −0.423733 | + | 0.733927i | ||||
\(935\) | −34.4248 | + | 38.0581i | −1.12581 | + | 1.24463i | ||||
\(936\) | −4.00000 | −0.130744 | ||||||||
\(937\) | 5.15274 | + | 2.97494i | 0.168333 | + | 0.0971870i | 0.581799 | − | 0.813332i | \(-0.302349\pi\) |
−0.413467 | + | 0.910519i | \(0.635682\pi\) | |||||||
\(938\) | −3.37728 | + | 1.94987i | −0.110272 | + | 0.0636657i | ||||
\(939\) | 8.10025 | 0.264342 | ||||||||
\(940\) | 2.96181 | + | 9.18662i | 0.0966036 | + | 0.299634i | ||||
\(941\) | 18.2916 | − | 31.6819i | 0.596288 | − | 1.03280i | −0.397076 | − | 0.917786i | \(-0.629975\pi\) |
0.993364 | − | 0.115015i | \(-0.0366916\pi\) | |||||||
\(942\) | −5.19615 | − | 3.00000i | −0.169300 | − | 0.0977453i | ||||
\(943\) | −39.6635 | + | 22.8997i | −1.29162 | + | 0.745718i | ||||
\(944\) | 6.31662 | + | 10.9407i | 0.205589 | + | 0.356090i | ||||
\(945\) | 19.7209 | − | 6.35812i | 0.641521 | − | 0.206830i | ||||
\(946\) | 19.3166 | − | 33.4574i | 0.628038 | − | 1.08779i | ||||
\(947\) | −4.56092 | − | 2.63325i | −0.148210 | − | 0.0855691i | 0.424061 | − | 0.905634i | \(-0.360604\pi\) |
−0.572271 | + | 0.820064i | \(0.693938\pi\) | |||||||
\(948\) | − | 21.8997i | − | 0.711271i | ||||||
\(949\) | 5.26650 | + | 9.12184i | 0.170958 | + | 0.296108i | ||||
\(950\) | −8.86832 | + | 19.6770i | −0.287726 | + | 0.638406i | ||||
\(951\) | −16.7335 | −0.542621 | ||||||||
\(952\) | 12.3166i | 0.399184i | ||||||||
\(953\) | 34.0058 | + | 19.6332i | 1.10156 | + | 0.635983i | 0.936629 | − | 0.350323i | \(-0.113928\pi\) |
0.164926 | + | 0.986306i | \(0.447261\pi\) | |||||||
\(954\) | 8.63325 | 0.279512 | ||||||||
\(955\) | −3.11684 | + | 14.5012i | −0.100859 | + | 0.469248i | ||||
\(956\) | −8.31662 | −0.268979 | ||||||||
\(957\) | −24.7971 | + | 14.3166i | −0.801577 | + | 0.462791i | ||||
\(958\) | 20.2362 | − | 11.6834i | 0.653802 | − | 0.377473i | ||||
\(959\) | 13.1082 | + | 22.7040i | 0.423285 | + | 0.733152i | ||||
\(960\) | −1.37228 | − | 4.25639i | −0.0442902 | − | 0.137374i | ||||
\(961\) | −25.6332 | −0.826879 | ||||||||
\(962\) | 10.3923 | − | 22.0000i | 0.335061 | − | 0.709308i | ||||
\(963\) | 0.316625i | 0.0102031i | ||||||||
\(964\) | 14.6332 | − | 25.3455i | 0.471305 | − | 0.816325i | ||||
\(965\) | 2.87833 | + | 0.618658i | 0.0926566 | + | 0.0199153i | ||||
\(966\) | −13.8997 | − | 24.0751i | −0.447217 | − | 0.774603i | ||||
\(967\) | 25.3455 | − | 14.6332i | 0.815057 | − | 0.470574i | −0.0336517 | − | 0.999434i | \(-0.510714\pi\) |
0.848709 | + | 0.528860i | \(0.177380\pi\) | |||||||
\(968\) | − | 7.63325i | − | 0.245342i | ||||||
\(969\) | 22.9499 | + | 39.7503i | 0.737256 | + | 1.27697i | ||||
\(970\) | −16.5000 | − | 14.9248i | −0.529783 | − | 0.479207i | ||||
\(971\) | 9.94987 | − | 17.2337i | 0.319307 | − | 0.553055i | −0.661037 | − | 0.750353i | \(-0.729883\pi\) |
0.980344 | + | 0.197298i | \(0.0632167\pi\) | |||||||
\(972\) | 10.0000i | 0.320750i | ||||||||
\(973\) | − | 46.1003i | − | 1.47791i | ||||||
\(974\) | −9.00000 | + | 15.5885i | −0.288379 | + | 0.499486i | ||||
\(975\) | −32.4674 | + | 23.3639i | −1.03979 | + | 0.748242i | ||||
\(976\) | 11.9499 | 0.382506 | ||||||||
\(977\) | 51.7011 | + | 29.8496i | 1.65406 | + | 0.954974i | 0.975376 | + | 0.220547i | \(0.0707841\pi\) |
0.678687 | + | 0.734428i | \(0.262549\pi\) | |||||||
\(978\) | −38.4799 | − | 22.2164i | −1.23045 | − | 0.710401i | ||||
\(979\) | 25.1082 | − | 43.4887i | 0.802461 | − | 1.38990i | ||||
\(980\) | 0.767434 | − | 3.57051i | 0.0245148 | − | 0.114056i | ||||
\(981\) | −1.97494 | − | 3.42069i | −0.0630549 | − | 0.109214i | ||||
\(982\) | −21.0588 | − | 12.1583i | −0.672014 | − | 0.387987i | ||||
\(983\) | −20.5104 | − | 11.8417i | −0.654180 | − | 0.377691i | 0.135876 | − | 0.990726i | \(-0.456615\pi\) |
−0.790056 | + | 0.613035i | \(0.789949\pi\) | |||||||
\(984\) | −7.63325 | + | 13.2212i | −0.243339 | + | 0.421476i | ||||
\(985\) | 6.55013 | − | 7.24144i | 0.208704 | − | 0.230731i | ||||
\(986\) | 8.81662 | + | 15.2708i | 0.280779 | + | 0.486323i | ||||
\(987\) | 17.3205 | + | 10.0000i | 0.551318 | + | 0.318304i | ||||
\(988\) | 17.2665i | 0.549321i | ||||||||
\(989\) | 53.6992 | 1.70754 | ||||||||
\(990\) | −2.96181 | − | 9.18662i | −0.0941326 | − | 0.291970i | ||||
\(991\) | 39.6834 | 1.26058 | 0.630292 | − | 0.776358i | \(-0.282935\pi\) | ||||
0.630292 | + | 0.776358i | \(0.282935\pi\) | |||||||
\(992\) | 2.00626 | − | 1.15831i | 0.0636987 | − | 0.0367765i | ||||
\(993\) | − | 67.7995i | − | 2.15155i | ||||||
\(994\) | 8.89975 | + | 15.4148i | 0.282283 | + | 0.488928i | ||||
\(995\) | −7.96444 | + | 37.0548i | −0.252490 | + | 1.17472i | ||||
\(996\) | −6.63325 | − | 11.4891i | −0.210183 | − | 0.364047i | ||||
\(997\) | −41.3956 | − | 23.8997i | −1.31101 | − | 0.756913i | −0.328748 | − | 0.944418i | \(-0.606627\pi\) |
−0.982264 | + | 0.187505i | \(0.939960\pi\) | |||||||
\(998\) | 16.9499i | 0.536539i | ||||||||
\(999\) | −22.0000 | − | 10.3923i | −0.696049 | − | 0.328798i |
(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 | 370.2.n.e.269.2 | ✓ | 8 | |
5.4 | even | 2 | inner | 370.2.n.e.269.4 | yes | 8 | |
37.26 | even | 3 | inner | 370.2.n.e.359.4 | yes | 8 | |
185.174 | even | 6 | inner | 370.2.n.e.359.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
370.2.n.e.269.2 | ✓ | 8 | 1.1 | even | 1 | trivial | |
370.2.n.e.269.4 | yes | 8 | 5.4 | even | 2 | inner | |
370.2.n.e.359.2 | yes | 8 | 185.174 | even | 6 | inner | |
370.2.n.e.359.4 | yes | 8 | 37.26 | even | 3 | inner |