Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [406,2,Mod(233,406)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(406, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("406.233");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 406 = 2 \cdot 7 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 406.e (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.24192632206\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 10.0.3118758597603.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 4x^{8} - 16x^{6} - 34x^{5} + 43x^{4} + 155x^{3} + 199x^{2} + 124x + 43 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 291.5 | ||
Root | \(-1.80582 + 0.194943i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 406.291 |
Dual form | 406.2.e.a.233.5 |
$q$-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 \(\left(\mathbb{Z}/406\mathbb{Z}\right)^\times\).
\(n\) | \(59\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | 1.22122 | − | 2.11522i | 0.705074 | − | 1.22122i | −0.261591 | − | 0.965179i | \(-0.584247\pi\) |
0.966665 | − | 0.256045i | \(-0.0824194\pi\) | |||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | −2.07173 | − | 3.58835i | −0.926508 | − | 1.60476i | −0.789118 | − | 0.614241i | \(-0.789462\pi\) |
−0.137390 | − | 0.990517i | \(-0.543871\pi\) | |||||||
\(6\) | −2.44245 | −0.997125 | ||||||||
\(7\) | −0.335903 | + | 2.62434i | −0.126959 | + | 0.991908i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −1.48277 | − | 2.56824i | −0.494258 | − | 0.856080i | ||||
\(10\) | −2.07173 | + | 3.58835i | −0.655140 | + | 1.13474i | ||||
\(11\) | 2.35349 | − | 4.07636i | 0.709603 | − | 1.22907i | −0.255402 | − | 0.966835i | \(-0.582208\pi\) |
0.965005 | − | 0.262233i | \(-0.0844589\pi\) | |||||||
\(12\) | 1.22122 | + | 2.11522i | 0.352537 | + | 0.610612i | ||||
\(13\) | −1.91061 | −0.529908 | −0.264954 | − | 0.964261i | \(-0.585357\pi\) | ||||
−0.264954 | + | 0.964261i | \(0.585357\pi\) | |||||||
\(14\) | 2.44070 | − | 1.02127i | 0.652304 | − | 0.272946i | ||||
\(15\) | −10.1202 | −2.61302 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −1.38357 | + | 2.39642i | −0.335565 | + | 0.581216i | −0.983593 | − | 0.180400i | \(-0.942261\pi\) |
0.648028 | + | 0.761617i | \(0.275594\pi\) | |||||||
\(18\) | −1.48277 | + | 2.56824i | −0.349493 | + | 0.605340i | ||||
\(19\) | −2.02020 | − | 3.49909i | −0.463466 | − | 0.802747i | 0.535665 | − | 0.844431i | \(-0.320061\pi\) |
−0.999131 | + | 0.0416840i | \(0.986728\pi\) | |||||||
\(20\) | 4.14347 | 0.926508 | ||||||||
\(21\) | 5.14085 | + | 3.91542i | 1.12183 | + | 0.854414i | ||||
\(22\) | −4.70697 | −1.00353 | ||||||||
\(23\) | 1.08634 | + | 1.88160i | 0.226518 | + | 0.392341i | 0.956774 | − | 0.290833i | \(-0.0939324\pi\) |
−0.730256 | + | 0.683174i | \(0.760599\pi\) | |||||||
\(24\) | 1.22122 | − | 2.11522i | 0.249281 | − | 0.431768i | ||||
\(25\) | −6.08417 | + | 10.5381i | −1.21683 | + | 2.10762i | ||||
\(26\) | 0.955306 | + | 1.65464i | 0.187351 | + | 0.324501i | ||||
\(27\) | 0.0841506 | 0.0161948 | ||||||||
\(28\) | −2.10480 | − | 1.60307i | −0.397769 | − | 0.302952i | ||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 5.06010 | + | 8.76435i | 0.923844 | + | 1.60014i | ||||
\(31\) | 0.484522 | − | 0.839217i | 0.0870227 | − | 0.150728i | −0.819229 | − | 0.573467i | \(-0.805598\pi\) |
0.906251 | + | 0.422739i | \(0.138931\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | −5.74826 | − | 9.95629i | −1.00064 | − | 1.73317i | ||||
\(34\) | 2.76714 | 0.474561 | ||||||||
\(35\) | 10.1130 | − | 4.23160i | 1.70940 | − | 0.715271i | ||||
\(36\) | 2.96555 | 0.494258 | ||||||||
\(37\) | 0.736701 | + | 1.27600i | 0.121113 | + | 0.209774i | 0.920207 | − | 0.391432i | \(-0.128020\pi\) |
−0.799094 | + | 0.601206i | \(0.794687\pi\) | |||||||
\(38\) | −2.02020 | + | 3.49909i | −0.327720 | + | 0.567628i | ||||
\(39\) | −2.33328 | + | 4.04137i | −0.373625 | + | 0.647137i | ||||
\(40\) | −2.07173 | − | 3.58835i | −0.327570 | − | 0.567368i | ||||
\(41\) | 10.4741 | 1.63578 | 0.817891 | − | 0.575373i | \(-0.195143\pi\) | ||||
0.817891 | + | 0.575373i | \(0.195143\pi\) | |||||||
\(42\) | 0.820425 | − | 6.40982i | 0.126594 | − | 0.989056i | ||||
\(43\) | 7.84520 | 1.19638 | 0.598191 | − | 0.801353i | \(-0.295886\pi\) | ||||
0.598191 | + | 0.801353i | \(0.295886\pi\) | |||||||
\(44\) | 2.35349 | + | 4.07636i | 0.354801 | + | 0.614534i | ||||
\(45\) | −6.14382 | + | 10.6414i | −0.915867 | + | 1.58633i | ||||
\(46\) | 1.08634 | − | 1.88160i | 0.160172 | − | 0.277427i | ||||
\(47\) | −5.86469 | − | 10.1579i | −0.855453 | − | 1.48169i | −0.876224 | − | 0.481904i | \(-0.839945\pi\) |
0.0207706 | − | 0.999784i | \(-0.493388\pi\) | |||||||
\(48\) | −2.44245 | −0.352537 | ||||||||
\(49\) | −6.77434 | − | 1.76305i | −0.967763 | − | 0.251864i | ||||
\(50\) | 12.1683 | 1.72086 | ||||||||
\(51\) | 3.37930 | + | 5.85312i | 0.473197 | + | 0.819601i | ||||
\(52\) | 0.955306 | − | 1.65464i | 0.132477 | − | 0.229457i | ||||
\(53\) | 1.39041 | − | 2.40826i | 0.190988 | − | 0.330800i | −0.754590 | − | 0.656196i | \(-0.772164\pi\) |
0.945578 | + | 0.325396i | \(0.105498\pi\) | |||||||
\(54\) | −0.0420753 | − | 0.0728765i | −0.00572572 | − | 0.00991724i | ||||
\(55\) | −19.5032 | −2.62981 | ||||||||
\(56\) | −0.335903 | + | 2.62434i | −0.0448869 | + | 0.350692i | ||||
\(57\) | −9.86847 | −1.30711 | ||||||||
\(58\) | 0.500000 | + | 0.866025i | 0.0656532 | + | 0.113715i | ||||
\(59\) | −1.70836 | + | 2.95897i | −0.222410 | + | 0.385226i | −0.955539 | − | 0.294864i | \(-0.904726\pi\) |
0.733129 | + | 0.680089i | \(0.238059\pi\) | |||||||
\(60\) | 5.06010 | − | 8.76435i | 0.653256 | − | 1.13147i | ||||
\(61\) | −5.70959 | − | 9.88930i | −0.731038 | − | 1.26620i | −0.956440 | − | 0.291929i | \(-0.905703\pi\) |
0.225402 | − | 0.974266i | \(-0.427631\pi\) | |||||||
\(62\) | −0.969044 | −0.123069 | ||||||||
\(63\) | 7.23800 | − | 3.02862i | 0.911903 | − | 0.381571i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.95828 | + | 6.85594i | 0.490964 | + | 0.850375i | ||||
\(66\) | −5.74826 | + | 9.95629i | −0.707562 | + | 1.22553i | ||||
\(67\) | 1.13788 | − | 1.97086i | 0.139014 | − | 0.240779i | −0.788110 | − | 0.615535i | \(-0.788940\pi\) |
0.927124 | + | 0.374756i | \(0.122273\pi\) | |||||||
\(68\) | −1.38357 | − | 2.39642i | −0.167783 | − | 0.290608i | ||||
\(69\) | 5.30667 | 0.638848 | ||||||||
\(70\) | −8.72115 | − | 6.64228i | −1.04238 | − | 0.793904i | ||||
\(71\) | −6.24653 | −0.741327 | −0.370664 | − | 0.928767i | \(-0.620870\pi\) | ||||
−0.370664 | + | 0.928767i | \(0.620870\pi\) | |||||||
\(72\) | −1.48277 | − | 2.56824i | −0.174747 | − | 0.302670i | ||||
\(73\) | 6.76148 | − | 11.7112i | 0.791371 | − | 1.37070i | −0.133747 | − | 0.991016i | \(-0.542701\pi\) |
0.925118 | − | 0.379680i | \(-0.123966\pi\) | |||||||
\(74\) | 0.736701 | − | 1.27600i | 0.0856398 | − | 0.148332i | ||||
\(75\) | 14.8603 | + | 25.7387i | 1.71591 | + | 2.97205i | ||||
\(76\) | 4.04040 | 0.463466 | ||||||||
\(77\) | 9.90721 | + | 7.54561i | 1.12903 | + | 0.859902i | ||||
\(78\) | 4.66657 | 0.528385 | ||||||||
\(79\) | 2.23146 | + | 3.86501i | 0.251059 | + | 0.434847i | 0.963818 | − | 0.266562i | \(-0.0858877\pi\) |
−0.712758 | + | 0.701410i | \(0.752554\pi\) | |||||||
\(80\) | −2.07173 | + | 3.58835i | −0.231627 | + | 0.401190i | ||||
\(81\) | 4.55109 | − | 7.88271i | 0.505676 | − | 0.875857i | ||||
\(82\) | −5.23706 | − | 9.07085i | −0.578336 | − | 1.00171i | ||||
\(83\) | −6.06003 | −0.665175 | −0.332587 | − | 0.943072i | \(-0.607922\pi\) | ||||
−0.332587 | + | 0.943072i | \(0.607922\pi\) | |||||||
\(84\) | −5.96128 | + | 2.49440i | −0.650428 | + | 0.272161i | ||||
\(85\) | 11.4656 | 1.24362 | ||||||||
\(86\) | −3.92260 | − | 6.79415i | −0.422985 | − | 0.732632i | ||||
\(87\) | −1.22122 | + | 2.11522i | −0.130929 | + | 0.226775i | ||||
\(88\) | 2.35349 | − | 4.07636i | 0.250882 | − | 0.434541i | ||||
\(89\) | −6.63308 | − | 11.4888i | −0.703105 | − | 1.21781i | −0.967371 | − | 0.253364i | \(-0.918463\pi\) |
0.264266 | − | 0.964450i | \(-0.414870\pi\) | |||||||
\(90\) | 12.2876 | 1.29523 | ||||||||
\(91\) | 0.641780 | − | 5.01410i | 0.0672768 | − | 0.525620i | ||||
\(92\) | −2.17268 | −0.226518 | ||||||||
\(93\) | −1.18342 | − | 2.04974i | −0.122715 | − | 0.212548i | ||||
\(94\) | −5.86469 | + | 10.1579i | −0.604897 | + | 1.04771i | ||||
\(95\) | −8.37064 | + | 14.4984i | −0.858810 | + | 1.48750i | ||||
\(96\) | 1.22122 | + | 2.11522i | 0.124641 | + | 0.215884i | ||||
\(97\) | 16.8452 | 1.71037 | 0.855186 | − | 0.518322i | \(-0.173443\pi\) | ||||
0.855186 | + | 0.518322i | \(0.173443\pi\) | |||||||
\(98\) | 1.86032 | + | 6.74827i | 0.187921 | + | 0.681679i | ||||
\(99\) | −13.9587 | −1.40291 | ||||||||
\(100\) | −6.08417 | − | 10.5381i | −0.608417 | − | 1.05381i | ||||
\(101\) | 6.21303 | − | 10.7613i | 0.618219 | − | 1.07079i | −0.371591 | − | 0.928396i | \(-0.621188\pi\) |
0.989811 | − | 0.142391i | \(-0.0454790\pi\) | |||||||
\(102\) | 3.37930 | − | 5.85312i | 0.334601 | − | 0.579545i | ||||
\(103\) | 8.08592 | + | 14.0052i | 0.796729 | + | 1.37998i | 0.921736 | + | 0.387819i | \(0.126771\pi\) |
−0.125007 | + | 0.992156i | \(0.539895\pi\) | |||||||
\(104\) | −1.91061 | −0.187351 | ||||||||
\(105\) | 3.39941 | − | 26.5589i | 0.331748 | − | 2.59188i | ||||
\(106\) | −2.78082 | −0.270097 | ||||||||
\(107\) | −5.31229 | − | 9.20116i | −0.513558 | − | 0.889509i | −0.999876 | − | 0.0157273i | \(-0.994994\pi\) |
0.486318 | − | 0.873782i | \(-0.338340\pi\) | |||||||
\(108\) | −0.0420753 | + | 0.0728765i | −0.00404870 | + | 0.00701255i | ||||
\(109\) | −3.04942 | + | 5.28175i | −0.292081 | + | 0.505900i | −0.974302 | − | 0.225247i | \(-0.927681\pi\) |
0.682220 | + | 0.731147i | \(0.261014\pi\) | |||||||
\(110\) | 9.75159 | + | 16.8903i | 0.929778 | + | 1.61042i | ||||
\(111\) | 3.59871 | 0.341574 | ||||||||
\(112\) | 2.44070 | − | 1.02127i | 0.230624 | − | 0.0965010i | ||||
\(113\) | 14.5875 | 1.37228 | 0.686139 | − | 0.727471i | \(-0.259304\pi\) | ||||
0.686139 | + | 0.727471i | \(0.259304\pi\) | |||||||
\(114\) | 4.93423 | + | 8.54635i | 0.462133 | + | 0.800439i | ||||
\(115\) | 4.50123 | − | 7.79635i | 0.419741 | − | 0.727014i | ||||
\(116\) | 0.500000 | − | 0.866025i | 0.0464238 | − | 0.0804084i | ||||
\(117\) | 2.83300 | + | 4.90691i | 0.261911 | + | 0.453644i | ||||
\(118\) | 3.41673 | 0.314535 | ||||||||
\(119\) | −5.82427 | − | 4.43593i | −0.533910 | − | 0.406641i | ||||
\(120\) | −10.1202 | −0.923844 | ||||||||
\(121\) | −5.57779 | − | 9.66102i | −0.507072 | − | 0.878274i | ||||
\(122\) | −5.70959 | + | 9.88930i | −0.516922 | + | 0.895335i | ||||
\(123\) | 12.7912 | − | 22.1551i | 1.15335 | − | 1.99766i | ||||
\(124\) | 0.484522 | + | 0.839217i | 0.0435114 | + | 0.0753639i | ||||
\(125\) | 29.7018 | 2.65661 | ||||||||
\(126\) | −6.24187 | − | 4.75398i | −0.556070 | − | 0.423518i | ||||
\(127\) | 5.46381 | 0.484835 | 0.242418 | − | 0.970172i | \(-0.422060\pi\) | ||||
0.242418 | + | 0.970172i | \(0.422060\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 9.58075 | − | 16.5943i | 0.843538 | − | 1.46105i | ||||
\(130\) | 3.95828 | − | 6.85594i | 0.347164 | − | 0.601306i | ||||
\(131\) | 6.70909 | + | 11.6205i | 0.586176 | + | 1.01529i | 0.994728 | + | 0.102551i | \(0.0327005\pi\) |
−0.408552 | + | 0.912735i | \(0.633966\pi\) | |||||||
\(132\) | 11.4965 | 1.00064 | ||||||||
\(133\) | 9.86140 | − | 4.12634i | 0.855092 | − | 0.357799i | ||||
\(134\) | −2.27575 | −0.196595 | ||||||||
\(135\) | −0.174338 | − | 0.301962i | −0.0150046 | − | 0.0259887i | ||||
\(136\) | −1.38357 | + | 2.39642i | −0.118640 | + | 0.205491i | ||||
\(137\) | −8.55161 | + | 14.8118i | −0.730613 | + | 1.26546i | 0.226008 | + | 0.974125i | \(0.427432\pi\) |
−0.956621 | + | 0.291334i | \(0.905901\pi\) | |||||||
\(138\) | −2.65333 | − | 4.59571i | −0.225867 | − | 0.391213i | ||||
\(139\) | −3.90711 | −0.331397 | −0.165699 | − | 0.986176i | \(-0.552988\pi\) | ||||
−0.165699 | + | 0.986176i | \(0.552988\pi\) | |||||||
\(140\) | −1.39180 | + | 10.8739i | −0.117629 | + | 0.919010i | ||||
\(141\) | −28.6484 | −2.41263 | ||||||||
\(142\) | 3.12327 | + | 5.40966i | 0.262099 | + | 0.453968i | ||||
\(143\) | −4.49660 | + | 7.78834i | −0.376024 | + | 0.651293i | ||||
\(144\) | −1.48277 | + | 2.56824i | −0.123564 | + | 0.214020i | ||||
\(145\) | 2.07173 | + | 3.58835i | 0.172048 | + | 0.297996i | ||||
\(146\) | −13.5230 | −1.11917 | ||||||||
\(147\) | −12.0022 | + | 12.1761i | −0.989926 | + | 1.00427i | ||||
\(148\) | −1.47340 | −0.121113 | ||||||||
\(149\) | 3.74913 | + | 6.49369i | 0.307141 | + | 0.531984i | 0.977736 | − | 0.209840i | \(-0.0672943\pi\) |
−0.670595 | + | 0.741824i | \(0.733961\pi\) | |||||||
\(150\) | 14.8603 | − | 25.7387i | 1.21333 | − | 2.10156i | ||||
\(151\) | −4.70909 | + | 8.15638i | −0.383220 | + | 0.663757i | −0.991521 | − | 0.129950i | \(-0.958518\pi\) |
0.608300 | + | 0.793707i | \(0.291852\pi\) | |||||||
\(152\) | −2.02020 | − | 3.49909i | −0.163860 | − | 0.283814i | ||||
\(153\) | 8.20609 | 0.663423 | ||||||||
\(154\) | 1.58109 | − | 12.3527i | 0.127408 | − | 0.995409i | ||||
\(155\) | −4.01520 | −0.322509 | ||||||||
\(156\) | −2.33328 | − | 4.04137i | −0.186812 | − | 0.323568i | ||||
\(157\) | −8.91431 | + | 15.4400i | −0.711439 | + | 1.23225i | 0.252878 | + | 0.967498i | \(0.418623\pi\) |
−0.964317 | + | 0.264751i | \(0.914710\pi\) | |||||||
\(158\) | 2.23146 | − | 3.86501i | 0.177526 | − | 0.307484i | ||||
\(159\) | −3.39600 | − | 5.88205i | −0.269321 | − | 0.466477i | ||||
\(160\) | 4.14347 | 0.327570 | ||||||||
\(161\) | −5.30287 | + | 2.21890i | −0.417925 | + | 0.174874i | ||||
\(162\) | −9.10217 | −0.715134 | ||||||||
\(163\) | 5.43945 | + | 9.42141i | 0.426051 | + | 0.737942i | 0.996518 | − | 0.0833788i | \(-0.0265711\pi\) |
−0.570467 | + | 0.821320i | \(0.693238\pi\) | |||||||
\(164\) | −5.23706 | + | 9.07085i | −0.408945 | + | 0.708314i | ||||
\(165\) | −23.8178 | + | 41.2536i | −1.85421 | + | 3.21159i | ||||
\(166\) | 3.03002 | + | 5.24814i | 0.235175 | + | 0.407335i | ||||
\(167\) | 16.0326 | 1.24064 | 0.620318 | − | 0.784350i | \(-0.287003\pi\) | ||||
0.620318 | + | 0.784350i | \(0.287003\pi\) | |||||||
\(168\) | 5.14085 | + | 3.91542i | 0.396625 | + | 0.302081i | ||||
\(169\) | −9.34956 | −0.719197 | ||||||||
\(170\) | −5.73279 | − | 9.92948i | −0.439685 | − | 0.761556i | ||||
\(171\) | −5.99100 | + | 10.3767i | −0.458143 | + | 0.793528i | ||||
\(172\) | −3.92260 | + | 6.79415i | −0.299096 | + | 0.518049i | ||||
\(173\) | 3.09439 | + | 5.35964i | 0.235262 | + | 0.407486i | 0.959349 | − | 0.282223i | \(-0.0910719\pi\) |
−0.724087 | + | 0.689709i | \(0.757739\pi\) | |||||||
\(174\) | 2.44245 | 0.185161 | ||||||||
\(175\) | −25.6118 | − | 19.5067i | −1.93607 | − | 1.47457i | ||||
\(176\) | −4.70697 | −0.354801 | ||||||||
\(177\) | 4.17259 | + | 7.22714i | 0.313631 | + | 0.543225i | ||||
\(178\) | −6.63308 | + | 11.4888i | −0.497170 | + | 0.861124i | ||||
\(179\) | −0.602699 | + | 1.04391i | −0.0450479 | + | 0.0780252i | −0.887670 | − | 0.460480i | \(-0.847677\pi\) |
0.842622 | + | 0.538505i | \(0.181011\pi\) | |||||||
\(180\) | −6.14382 | − | 10.6414i | −0.457934 | − | 0.793164i | ||||
\(181\) | 6.95105 | 0.516668 | 0.258334 | − | 0.966056i | \(-0.416827\pi\) | ||||
0.258334 | + | 0.966056i | \(0.416827\pi\) | |||||||
\(182\) | −4.66323 | + | 1.95125i | −0.345661 | + | 0.144636i | ||||
\(183\) | −27.8907 | −2.06174 | ||||||||
\(184\) | 1.08634 | + | 1.88160i | 0.0800862 | + | 0.138713i | ||||
\(185\) | 3.05250 | − | 5.28708i | 0.224424 | − | 0.388714i | ||||
\(186\) | −1.18342 | + | 2.04974i | −0.0867725 | + | 0.150294i | ||||
\(187\) | 6.51243 | + | 11.2799i | 0.476236 | + | 0.824865i | ||||
\(188\) | 11.7294 | 0.855453 | ||||||||
\(189\) | −0.0282664 | + | 0.220840i | −0.00205608 | + | 0.0160637i | ||||
\(190\) | 16.7413 | 1.21454 | ||||||||
\(191\) | 3.40424 | + | 5.89631i | 0.246322 | + | 0.426642i | 0.962502 | − | 0.271273i | \(-0.0874446\pi\) |
−0.716181 | + | 0.697915i | \(0.754111\pi\) | |||||||
\(192\) | 1.22122 | − | 2.11522i | 0.0881342 | − | 0.152653i | ||||
\(193\) | 1.94832 | − | 3.37459i | 0.140243 | − | 0.242908i | −0.787345 | − | 0.616513i | \(-0.788545\pi\) |
0.927588 | + | 0.373604i | \(0.121878\pi\) | |||||||
\(194\) | −8.42260 | − | 14.5884i | −0.604708 | − | 1.04738i | ||||
\(195\) | 19.3358 | 1.38466 | ||||||||
\(196\) | 4.91401 | − | 4.98523i | 0.351001 | − | 0.356088i | ||||
\(197\) | 15.5624 | 1.10877 | 0.554386 | − | 0.832260i | \(-0.312953\pi\) | ||||
0.554386 | + | 0.832260i | \(0.312953\pi\) | |||||||
\(198\) | 6.97937 | + | 12.0886i | 0.496002 | + | 0.859101i | ||||
\(199\) | −12.2868 | + | 21.2813i | −0.870986 | + | 1.50859i | −0.0100081 | + | 0.999950i | \(0.503186\pi\) |
−0.860978 | + | 0.508642i | \(0.830148\pi\) | |||||||
\(200\) | −6.08417 | + | 10.5381i | −0.430216 | + | 0.745155i | ||||
\(201\) | −2.77920 | − | 4.81372i | −0.196030 | − | 0.339533i | ||||
\(202\) | −12.4261 | −0.874294 | ||||||||
\(203\) | 0.335903 | − | 2.62434i | 0.0235758 | − | 0.184193i | ||||
\(204\) | −6.75860 | −0.473197 | ||||||||
\(205\) | −21.6996 | − | 37.5848i | −1.51556 | − | 2.62504i | ||||
\(206\) | 8.08592 | − | 14.0052i | 0.563372 | − | 0.975790i | ||||
\(207\) | 3.22160 | − | 5.57997i | 0.223917 | − | 0.387835i | ||||
\(208\) | 0.955306 | + | 1.65464i | 0.0662386 | + | 0.114729i | ||||
\(209\) | −19.0181 | −1.31551 | ||||||||
\(210\) | −24.7004 | + | 10.3355i | −1.70449 | + | 0.713215i | ||||
\(211\) | 8.65646 | 0.595935 | 0.297968 | − | 0.954576i | \(-0.403691\pi\) | ||||
0.297968 | + | 0.954576i | \(0.403691\pi\) | |||||||
\(212\) | 1.39041 | + | 2.40826i | 0.0954938 | + | 0.165400i | ||||
\(213\) | −7.62841 | + | 13.2128i | −0.522690 | + | 0.905326i | ||||
\(214\) | −5.31229 | + | 9.20116i | −0.363141 | + | 0.628978i | ||||
\(215\) | −16.2532 | − | 28.1513i | −1.10846 | − | 1.91990i | ||||
\(216\) | 0.0841506 | 0.00572572 | ||||||||
\(217\) | 2.03964 | + | 1.55345i | 0.138460 | + | 0.105455i | ||||
\(218\) | 6.09884 | 0.413065 | ||||||||
\(219\) | −16.5146 | − | 28.6040i | −1.11595 | − | 1.93288i | ||||
\(220\) | 9.75159 | − | 16.8903i | 0.657452 | − | 1.13874i | ||||
\(221\) | 2.64347 | − | 4.57862i | 0.177819 | − | 0.307991i | ||||
\(222\) | −1.79935 | − | 3.11657i | −0.120765 | − | 0.209171i | ||||
\(223\) | −10.9191 | −0.731194 | −0.365597 | − | 0.930773i | \(-0.619135\pi\) | ||||
−0.365597 | + | 0.930773i | \(0.619135\pi\) | |||||||
\(224\) | −2.10480 | − | 1.60307i | −0.140633 | − | 0.107110i | ||||
\(225\) | 36.0858 | 2.40572 | ||||||||
\(226\) | −7.29376 | − | 12.6332i | −0.485173 | − | 0.840345i | ||||
\(227\) | 5.24754 | − | 9.08901i | 0.348292 | − | 0.603259i | −0.637655 | − | 0.770322i | \(-0.720095\pi\) |
0.985946 | + | 0.167064i | \(0.0534286\pi\) | |||||||
\(228\) | 4.93423 | − | 8.54635i | 0.326778 | − | 0.565996i | ||||
\(229\) | 3.75763 | + | 6.50840i | 0.248311 | + | 0.430087i | 0.963057 | − | 0.269297i | \(-0.0867912\pi\) |
−0.714746 | + | 0.699384i | \(0.753458\pi\) | |||||||
\(230\) | −9.00245 | −0.593604 | ||||||||
\(231\) | 28.0596 | − | 11.7411i | 1.84618 | − | 0.772505i | ||||
\(232\) | −1.00000 | −0.0656532 | ||||||||
\(233\) | −2.57131 | − | 4.45364i | −0.168452 | − | 0.291767i | 0.769424 | − | 0.638739i | \(-0.220543\pi\) |
−0.937876 | + | 0.346971i | \(0.887210\pi\) | |||||||
\(234\) | 2.83300 | − | 4.90691i | 0.185199 | − | 0.320775i | ||||
\(235\) | −24.3002 | + | 42.0891i | −1.58517 | + | 2.74559i | ||||
\(236\) | −1.70836 | − | 2.95897i | −0.111205 | − | 0.192613i | ||||
\(237\) | 10.9005 | 0.708061 | ||||||||
\(238\) | −0.929492 | + | 7.26193i | −0.0602500 | + | 0.470721i | ||||
\(239\) | 0.749673 | 0.0484923 | 0.0242462 | − | 0.999706i | \(-0.492281\pi\) | ||||
0.0242462 | + | 0.999706i | \(0.492281\pi\) | |||||||
\(240\) | 5.06010 | + | 8.76435i | 0.326628 | + | 0.565737i | ||||
\(241\) | 4.50979 | − | 7.81119i | 0.290501 | − | 0.503163i | −0.683427 | − | 0.730019i | \(-0.739511\pi\) |
0.973928 | + | 0.226856i | \(0.0728446\pi\) | |||||||
\(242\) | −5.57779 | + | 9.66102i | −0.358554 | + | 0.621034i | ||||
\(243\) | −10.9896 | − | 19.0345i | −0.704981 | − | 1.22106i | ||||
\(244\) | 11.4192 | 0.731038 | ||||||||
\(245\) | 7.70820 | + | 27.9613i | 0.492459 | + | 1.78638i | ||||
\(246\) | −25.5825 | −1.63108 | ||||||||
\(247\) | 3.85982 | + | 6.68541i | 0.245595 | + | 0.425382i | ||||
\(248\) | 0.484522 | − | 0.839217i | 0.0307672 | − | 0.0532903i | ||||
\(249\) | −7.40065 | + | 12.8183i | −0.468997 | + | 0.812327i | ||||
\(250\) | −14.8509 | − | 25.7225i | −0.939252 | − | 1.62683i | ||||
\(251\) | −29.1169 | −1.83784 | −0.918921 | − | 0.394441i | \(-0.870938\pi\) | ||||
−0.918921 | + | 0.394441i | \(0.870938\pi\) | |||||||
\(252\) | −0.996136 | + | 7.78261i | −0.0627507 | + | 0.490258i | ||||
\(253\) | 10.2268 | 0.642951 | ||||||||
\(254\) | −2.73191 | − | 4.73180i | −0.171415 | − | 0.296900i | ||||
\(255\) | 14.0020 | − | 24.2522i | 0.876841 | − | 1.51873i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 11.6138 | + | 20.1156i | 0.724447 | + | 1.25478i | 0.959201 | + | 0.282725i | \(0.0912383\pi\) |
−0.234754 | + | 0.972055i | \(0.575428\pi\) | |||||||
\(258\) | −19.1615 | −1.19294 | ||||||||
\(259\) | −3.59613 | + | 1.50474i | −0.223453 | + | 0.0935001i | ||||
\(260\) | −7.91656 | −0.490964 | ||||||||
\(261\) | 1.48277 | + | 2.56824i | 0.0917814 | + | 0.158970i | ||||
\(262\) | 6.70909 | − | 11.6205i | 0.414489 | − | 0.717916i | ||||
\(263\) | 10.2517 | − | 17.7564i | 0.632145 | − | 1.09491i | −0.354968 | − | 0.934879i | \(-0.615508\pi\) |
0.987112 | − | 0.160028i | \(-0.0511585\pi\) | |||||||
\(264\) | −5.74826 | − | 9.95629i | −0.353781 | − | 0.612767i | ||||
\(265\) | −11.5222 | −0.707806 | ||||||||
\(266\) | −8.50422 | − | 6.47705i | −0.521427 | − | 0.397134i | ||||
\(267\) | −32.4019 | −1.98296 | ||||||||
\(268\) | 1.13788 | + | 1.97086i | 0.0695068 | + | 0.120389i | ||||
\(269\) | 5.69760 | − | 9.86853i | 0.347389 | − | 0.601695i | −0.638396 | − | 0.769708i | \(-0.720402\pi\) |
0.985785 | + | 0.168013i | \(0.0537351\pi\) | |||||||
\(270\) | −0.174338 | + | 0.301962i | −0.0106098 | + | 0.0183768i | ||||
\(271\) | −8.98753 | − | 15.5669i | −0.545954 | − | 0.945620i | −0.998546 | − | 0.0539021i | \(-0.982834\pi\) |
0.452592 | − | 0.891717i | \(-0.350499\pi\) | |||||||
\(272\) | 2.76714 | 0.167783 | ||||||||
\(273\) | −9.82217 | − | 7.48084i | −0.594465 | − | 0.452761i | ||||
\(274\) | 17.1032 | 1.03324 | ||||||||
\(275\) | 28.6380 | + | 49.6025i | 1.72694 | + | 2.99114i | ||||
\(276\) | −2.65333 | + | 4.59571i | −0.159712 | + | 0.276629i | ||||
\(277\) | 1.04016 | − | 1.80161i | 0.0624971 | − | 0.108248i | −0.833084 | − | 0.553147i | \(-0.813427\pi\) |
0.895581 | + | 0.444898i | \(0.146760\pi\) | |||||||
\(278\) | 1.95356 | + | 3.38366i | 0.117167 | + | 0.202938i | ||||
\(279\) | −2.87375 | −0.172047 | ||||||||
\(280\) | 10.1130 | − | 4.23160i | 0.604365 | − | 0.252887i | ||||
\(281\) | 7.35741 | 0.438906 | 0.219453 | − | 0.975623i | \(-0.429573\pi\) | ||||
0.219453 | + | 0.975623i | \(0.429573\pi\) | |||||||
\(282\) | 14.3242 | + | 24.8102i | 0.852994 | + | 1.47743i | ||||
\(283\) | 3.04027 | − | 5.26590i | 0.180725 | − | 0.313025i | −0.761403 | − | 0.648279i | \(-0.775489\pi\) |
0.942128 | + | 0.335254i | \(0.108822\pi\) | |||||||
\(284\) | 3.12327 | − | 5.40966i | 0.185332 | − | 0.321004i | ||||
\(285\) | 20.4448 | + | 35.4115i | 1.21105 | + | 2.09760i | ||||
\(286\) | 8.99320 | 0.531779 | ||||||||
\(287\) | −3.51829 | + | 27.4877i | −0.207678 | + | 1.62255i | ||||
\(288\) | 2.96555 | 0.174747 | ||||||||
\(289\) | 4.67146 | + | 8.09120i | 0.274792 | + | 0.475953i | ||||
\(290\) | 2.07173 | − | 3.58835i | 0.121656 | − | 0.210715i | ||||
\(291\) | 20.5718 | − | 35.6313i | 1.20594 | − | 2.08875i | ||||
\(292\) | 6.76148 | + | 11.7112i | 0.395686 | + | 0.685348i | ||||
\(293\) | 13.7159 | 0.801291 | 0.400646 | − | 0.916233i | \(-0.368786\pi\) | ||||
0.400646 | + | 0.916233i | \(0.368786\pi\) | |||||||
\(294\) | 16.5460 | + | 4.30615i | 0.964980 | + | 0.251140i | ||||
\(295\) | 14.1571 | 0.824259 | ||||||||
\(296\) | 0.736701 | + | 1.27600i | 0.0428199 | + | 0.0741662i | ||||
\(297\) | 0.198047 | − | 0.343028i | 0.0114919 | − | 0.0199045i | ||||
\(298\) | 3.74913 | − | 6.49369i | 0.217181 | − | 0.376169i | ||||
\(299\) | −2.07558 | − | 3.59501i | −0.120034 | − | 0.207905i | ||||
\(300\) | −29.7205 | −1.71591 | ||||||||
\(301\) | −2.63523 | + | 20.5885i | −0.151892 | + | 1.18670i | ||||
\(302\) | 9.41817 | 0.541955 | ||||||||
\(303\) | −15.1750 | − | 26.2839i | −0.871780 | − | 1.50997i | ||||
\(304\) | −2.02020 | + | 3.49909i | −0.115867 | + | 0.200687i | ||||
\(305\) | −23.6575 | + | 40.9760i | −1.35463 | + | 2.34628i | ||||
\(306\) | −4.10305 | − | 7.10668i | −0.234556 | − | 0.406262i | ||||
\(307\) | 7.64494 | 0.436320 | 0.218160 | − | 0.975913i | \(-0.429995\pi\) | ||||
0.218160 | + | 0.975913i | \(0.429995\pi\) | |||||||
\(308\) | −11.4883 | + | 4.80709i | −0.654606 | + | 0.273909i | ||||
\(309\) | 39.4988 | 2.24701 | ||||||||
\(310\) | 2.00760 | + | 3.47727i | 0.114024 | + | 0.197496i | ||||
\(311\) | −12.2126 | + | 21.1528i | −0.692512 | + | 1.19947i | 0.278500 | + | 0.960436i | \(0.410163\pi\) |
−0.971012 | + | 0.239030i | \(0.923171\pi\) | |||||||
\(312\) | −2.33328 | + | 4.04137i | −0.132096 | + | 0.228797i | ||||
\(313\) | 9.13225 | + | 15.8175i | 0.516185 | + | 0.894059i | 0.999823 | + | 0.0187912i | \(0.00598179\pi\) |
−0.483638 | + | 0.875268i | \(0.660685\pi\) | |||||||
\(314\) | 17.8286 | 1.00613 | ||||||||
\(315\) | −25.8630 | − | 19.6980i | −1.45721 | − | 1.10986i | ||||
\(316\) | −4.46293 | −0.251059 | ||||||||
\(317\) | 5.21086 | + | 9.02547i | 0.292671 | + | 0.506921i | 0.974440 | − | 0.224646i | \(-0.0721227\pi\) |
−0.681770 | + | 0.731567i | \(0.738789\pi\) | |||||||
\(318\) | −3.39600 | + | 5.88205i | −0.190438 | + | 0.329849i | ||||
\(319\) | −2.35349 | + | 4.07636i | −0.131770 | + | 0.228232i | ||||
\(320\) | −2.07173 | − | 3.58835i | −0.115813 | − | 0.200595i | ||||
\(321\) | −25.9500 | −1.44839 | ||||||||
\(322\) | 4.57306 | + | 3.48297i | 0.254846 | + | 0.194098i | ||||
\(323\) | 11.1804 | 0.622093 | ||||||||
\(324\) | 4.55109 | + | 7.88271i | 0.252838 | + | 0.437929i | ||||
\(325\) | 11.6245 | − | 20.1342i | 0.644810 | − | 1.11684i | ||||
\(326\) | 5.43945 | − | 9.42141i | 0.301263 | − | 0.521804i | ||||
\(327\) | 7.44804 | + | 12.9004i | 0.411878 | + | 0.713393i | ||||
\(328\) | 10.4741 | 0.578336 | ||||||||
\(329\) | 28.6279 | − | 11.9789i | 1.57831 | − | 0.660417i | ||||
\(330\) | 47.6355 | 2.62225 | ||||||||
\(331\) | −2.34176 | − | 4.05604i | −0.128715 | − | 0.222940i | 0.794464 | − | 0.607311i | \(-0.207752\pi\) |
−0.923179 | + | 0.384371i | \(0.874418\pi\) | |||||||
\(332\) | 3.03002 | − | 5.24814i | 0.166294 | − | 0.288029i | ||||
\(333\) | 2.18472 | − | 3.78405i | 0.119722 | − | 0.207365i | ||||
\(334\) | −8.01628 | − | 13.8846i | −0.438631 | − | 0.759731i | ||||
\(335\) | −9.42950 | −0.515189 | ||||||||
\(336\) | 0.820425 | − | 6.40982i | 0.0447579 | − | 0.349684i | ||||
\(337\) | −25.3719 | −1.38210 | −0.691048 | − | 0.722809i | \(-0.742851\pi\) | ||||
−0.691048 | + | 0.722809i | \(0.742851\pi\) | |||||||
\(338\) | 4.67478 | + | 8.09696i | 0.254275 | + | 0.440416i | ||||
\(339\) | 17.8146 | − | 30.8558i | 0.967557 | − | 1.67586i | ||||
\(340\) | −5.73279 | + | 9.92948i | −0.310904 | + | 0.538501i | ||||
\(341\) | −2.28063 | − | 3.95017i | −0.123503 | − | 0.213914i | ||||
\(342\) | 11.9820 | 0.647913 | ||||||||
\(343\) | 6.90236 | − | 17.1860i | 0.372692 | − | 0.927955i | ||||
\(344\) | 7.84520 | 0.422985 | ||||||||
\(345\) | −10.9940 | − | 19.0422i | −0.591897 | − | 1.02520i | ||||
\(346\) | 3.09439 | − | 5.35964i | 0.166355 | − | 0.288136i | ||||
\(347\) | 0.965287 | − | 1.67193i | 0.0518193 | − | 0.0897537i | −0.838952 | − | 0.544205i | \(-0.816831\pi\) |
0.890772 | + | 0.454451i | \(0.150165\pi\) | |||||||
\(348\) | −1.22122 | − | 2.11522i | −0.0654644 | − | 0.113388i | ||||
\(349\) | 1.95782 | 0.104800 | 0.0523998 | − | 0.998626i | \(-0.483313\pi\) | ||||
0.0523998 | + | 0.998626i | \(0.483313\pi\) | |||||||
\(350\) | −4.08738 | + | 31.9339i | −0.218480 | + | 1.70694i | ||||
\(351\) | −0.160779 | −0.00858175 | ||||||||
\(352\) | 2.35349 | + | 4.07636i | 0.125441 | + | 0.217271i | ||||
\(353\) | 8.16649 | − | 14.1448i | 0.434658 | − | 0.752850i | −0.562609 | − | 0.826723i | \(-0.690202\pi\) |
0.997268 | + | 0.0738726i | \(0.0235358\pi\) | |||||||
\(354\) | 4.17259 | − | 7.22714i | 0.221771 | − | 0.384118i | ||||
\(355\) | 12.9412 | + | 22.4147i | 0.686845 | + | 1.18965i | ||||
\(356\) | 13.2662 | 0.703105 | ||||||||
\(357\) | −16.4957 | + | 6.90236i | −0.873045 | + | 0.365312i | ||||
\(358\) | 1.20540 | 0.0637073 | ||||||||
\(359\) | 5.89004 | + | 10.2019i | 0.310865 | + | 0.538433i | 0.978550 | − | 0.206010i | \(-0.0660481\pi\) |
−0.667685 | + | 0.744444i | \(0.732715\pi\) | |||||||
\(360\) | −6.14382 | + | 10.6414i | −0.323808 | + | 0.560852i | ||||
\(361\) | 1.33757 | − | 2.31674i | 0.0703985 | − | 0.121934i | ||||
\(362\) | −3.47553 | − | 6.01979i | −0.182670 | − | 0.316393i | ||||
\(363\) | −27.2469 | −1.43009 | ||||||||
\(364\) | 4.02145 | + | 3.06285i | 0.210781 | + | 0.160537i | ||||
\(365\) | −56.0320 | −2.93285 | ||||||||
\(366\) | 13.9454 | + | 24.1541i | 0.728936 | + | 1.26255i | ||||
\(367\) | −17.8219 | + | 30.8684i | −0.930295 | + | 1.61132i | −0.147478 | + | 0.989065i | \(0.547116\pi\) |
−0.782816 | + | 0.622253i | \(0.786218\pi\) | |||||||
\(368\) | 1.08634 | − | 1.88160i | 0.0566295 | − | 0.0980852i | ||||
\(369\) | −15.5307 | − | 26.9000i | −0.808498 | − | 1.40036i | ||||
\(370\) | −6.10500 | −0.317384 | ||||||||
\(371\) | 5.85306 | + | 4.45785i | 0.303876 | + | 0.231440i | ||||
\(372\) | 2.36684 | 0.122715 | ||||||||
\(373\) | −8.87414 | − | 15.3705i | −0.459486 | − | 0.795852i | 0.539448 | − | 0.842019i | \(-0.318633\pi\) |
−0.998934 | + | 0.0461665i | \(0.985300\pi\) | |||||||
\(374\) | 6.51243 | − | 11.2799i | 0.336750 | − | 0.583268i | ||||
\(375\) | 36.2725 | − | 62.8258i | 1.87310 | − | 3.24431i | ||||
\(376\) | −5.86469 | − | 10.1579i | −0.302448 | − | 0.523856i | ||||
\(377\) | 1.91061 | 0.0984015 | ||||||||
\(378\) | 0.205386 | − | 0.0859405i | 0.0105639 | − | 0.00442030i | ||||
\(379\) | −15.2263 | −0.782124 | −0.391062 | − | 0.920364i | \(-0.627892\pi\) | ||||
−0.391062 | + | 0.920364i | \(0.627892\pi\) | |||||||
\(380\) | −8.37064 | − | 14.4984i | −0.429405 | − | 0.743751i | ||||
\(381\) | 6.67254 | − | 11.5572i | 0.341844 | − | 0.592092i | ||||
\(382\) | 3.40424 | − | 5.89631i | 0.174176 | − | 0.301681i | ||||
\(383\) | 7.90588 | + | 13.6934i | 0.403971 | + | 0.699699i | 0.994201 | − | 0.107536i | \(-0.0342962\pi\) |
−0.590230 | + | 0.807235i | \(0.700963\pi\) | |||||||
\(384\) | −2.44245 | −0.124641 | ||||||||
\(385\) | 6.55118 | − | 51.1830i | 0.333879 | − | 2.60853i | ||||
\(386\) | −3.89664 | −0.198334 | ||||||||
\(387\) | −11.6327 | − | 20.1484i | −0.591321 | − | 1.02420i | ||||
\(388\) | −8.42260 | + | 14.5884i | −0.427593 | + | 0.740612i | ||||
\(389\) | 10.8586 | − | 18.8076i | 0.550552 | − | 0.953584i | −0.447683 | − | 0.894193i | \(-0.647751\pi\) |
0.998235 | − | 0.0593917i | \(-0.0189161\pi\) | |||||||
\(390\) | −9.66789 | − | 16.7453i | −0.489553 | − | 0.847930i | ||||
\(391\) | −6.01213 | −0.304047 | ||||||||
\(392\) | −6.77434 | − | 1.76305i | −0.342156 | − | 0.0890474i | ||||
\(393\) | 32.7732 | 1.65319 | ||||||||
\(394\) | −7.78118 | − | 13.4774i | −0.392010 | − | 0.678981i | ||||
\(395\) | 9.24600 | − | 16.0145i | 0.465217 | − | 0.805779i | ||||
\(396\) | 6.97937 | − | 12.0886i | 0.350727 | − | 0.607476i | ||||
\(397\) | −0.630167 | − | 1.09148i | −0.0316272 | − | 0.0547798i | 0.849779 | − | 0.527140i | \(-0.176736\pi\) |
−0.881406 | + | 0.472360i | \(0.843402\pi\) | |||||||
\(398\) | 24.5735 | 1.23176 | ||||||||
\(399\) | 3.31485 | − | 25.8982i | 0.165950 | − | 1.29653i | ||||
\(400\) | 12.1683 | 0.608417 | ||||||||
\(401\) | 0.955905 | + | 1.65568i | 0.0477356 | + | 0.0826806i | 0.888906 | − | 0.458090i | \(-0.151466\pi\) |
−0.841170 | + | 0.540770i | \(0.818133\pi\) | |||||||
\(402\) | −2.77920 | + | 4.81372i | −0.138614 | + | 0.240086i | ||||
\(403\) | −0.925734 | + | 1.60342i | −0.0461141 | + | 0.0798719i | ||||
\(404\) | 6.21303 | + | 10.7613i | 0.309110 | + | 0.535394i | ||||
\(405\) | −37.7146 | −1.87405 | ||||||||
\(406\) | −2.44070 | + | 1.02127i | −0.121130 | + | 0.0506848i | ||||
\(407\) | 6.93526 | 0.343768 | ||||||||
\(408\) | 3.37930 | + | 5.85312i | 0.167300 | + | 0.289773i | ||||
\(409\) | 1.50907 | − | 2.61379i | 0.0746189 | − | 0.129244i | −0.826302 | − | 0.563228i | \(-0.809559\pi\) |
0.900921 | + | 0.433984i | \(0.142893\pi\) | |||||||
\(410\) | −21.6996 | + | 37.5848i | −1.07167 | + | 1.85618i | ||||
\(411\) | 20.8869 | + | 36.1771i | 1.03027 | + | 1.78448i | ||||
\(412\) | −16.1718 | −0.796729 | ||||||||
\(413\) | −7.19151 | − | 5.47726i | −0.353871 | − | 0.269518i | ||||
\(414\) | −6.44320 | −0.316666 | ||||||||
\(415\) | 12.5548 | + | 21.7455i | 0.616290 | + | 1.06744i | ||||
\(416\) | 0.955306 | − | 1.65464i | 0.0468377 | − | 0.0811253i | ||||
\(417\) | −4.77146 | + | 8.26441i | −0.233659 | + | 0.404710i | ||||
\(418\) | 9.50903 | + | 16.4701i | 0.465102 | + | 0.805580i | ||||
\(419\) | 4.64504 | 0.226925 | 0.113463 | − | 0.993542i | \(-0.463806\pi\) | ||||
0.113463 | + | 0.993542i | \(0.463806\pi\) | |||||||
\(420\) | 21.3010 | + | 16.2234i | 1.03938 | + | 0.791621i | ||||
\(421\) | −26.6202 | −1.29739 | −0.648695 | − | 0.761048i | \(-0.724685\pi\) | ||||
−0.648695 | + | 0.761048i | \(0.724685\pi\) | |||||||
\(422\) | −4.32823 | − | 7.49671i | −0.210695 | − | 0.364934i | ||||
\(423\) | −17.3920 | + | 30.1239i | −0.845629 | + | 1.46467i | ||||
\(424\) | 1.39041 | − | 2.40826i | 0.0675243 | − | 0.116956i | ||||
\(425\) | −16.8358 | − | 29.1604i | −0.816654 | − | 1.41449i | ||||
\(426\) | 15.2568 | 0.739196 | ||||||||
\(427\) | 27.8708 | − | 11.6621i | 1.34876 | − | 0.564367i | ||||
\(428\) | 10.6246 | 0.513558 | ||||||||
\(429\) | 10.9827 | + | 19.0226i | 0.530250 | + | 0.918420i | ||||
\(430\) | −16.2532 | + | 28.1513i | −0.783798 | + | 1.35758i | ||||
\(431\) | 4.81935 | − | 8.34735i | 0.232140 | − | 0.402078i | −0.726298 | − | 0.687380i | \(-0.758761\pi\) |
0.958438 | + | 0.285302i | \(0.0920940\pi\) | |||||||
\(432\) | −0.0420753 | − | 0.0728765i | −0.00202435 | − | 0.00350627i | ||||
\(433\) | −3.16466 | −0.152084 | −0.0760420 | − | 0.997105i | \(-0.524228\pi\) | ||||
−0.0760420 | + | 0.997105i | \(0.524228\pi\) | |||||||
\(434\) | 0.325505 | − | 2.54310i | 0.0156247 | − | 0.122073i | ||||
\(435\) | 10.1202 | 0.485227 | ||||||||
\(436\) | −3.04942 | − | 5.28175i | −0.146041 | − | 0.252950i | ||||
\(437\) | 4.38926 | − | 7.60242i | 0.209967 | − | 0.363673i | ||||
\(438\) | −16.5146 | + | 28.6040i | −0.789096 | + | 1.36675i | ||||
\(439\) | −6.94499 | − | 12.0291i | −0.331467 | − | 0.574117i | 0.651333 | − | 0.758792i | \(-0.274210\pi\) |
−0.982800 | + | 0.184675i | \(0.940877\pi\) | |||||||
\(440\) | −19.5032 | −0.929778 | ||||||||
\(441\) | 5.51688 | + | 20.0123i | 0.262709 | + | 0.952968i | ||||
\(442\) | −5.28694 | −0.251474 | ||||||||
\(443\) | −10.1854 | − | 17.6416i | −0.483923 | − | 0.838179i | 0.515907 | − | 0.856645i | \(-0.327455\pi\) |
−0.999829 | + | 0.0184661i | \(0.994122\pi\) | |||||||
\(444\) | −1.79935 | + | 3.11657i | −0.0853936 | + | 0.147906i | ||||
\(445\) | −27.4840 | + | 47.6036i | −1.30286 | + | 2.25663i | ||||
\(446\) | 5.45953 | + | 9.45618i | 0.258516 | + | 0.447763i | ||||
\(447\) | 18.3141 | 0.866228 | ||||||||
\(448\) | −0.335903 | + | 2.62434i | −0.0158699 | + | 0.123988i | ||||
\(449\) | 33.1442 | 1.56417 | 0.782086 | − | 0.623170i | \(-0.214156\pi\) | ||||
0.782086 | + | 0.623170i | \(0.214156\pi\) | |||||||
\(450\) | −18.0429 | − | 31.2512i | −0.850550 | − | 1.47320i | ||||
\(451\) | 24.6507 | − | 42.6962i | 1.16076 | − | 2.01049i | ||||
\(452\) | −7.29376 | + | 12.6332i | −0.343069 | + | 0.594214i | ||||
\(453\) | 11.5017 | + | 19.9215i | 0.540397 | + | 0.935995i | ||||
\(454\) | −10.4951 | −0.492559 | ||||||||
\(455\) | −19.3219 | + | 8.08495i | −0.905826 | + | 0.379028i | ||||
\(456\) | −9.86847 | −0.462133 | ||||||||
\(457\) | 9.10435 | + | 15.7692i | 0.425883 | + | 0.737652i | 0.996502 | − | 0.0835631i | \(-0.0266300\pi\) |
−0.570619 | + | 0.821215i | \(0.693297\pi\) | |||||||
\(458\) | 3.75763 | − | 6.50840i | 0.175582 | − | 0.304117i | ||||
\(459\) | −0.116428 | + | 0.201660i | −0.00543441 | + | 0.00941267i | ||||
\(460\) | 4.50123 | + | 7.79635i | 0.209871 | + | 0.363507i | ||||
\(461\) | −3.52484 | −0.164168 | −0.0820841 | − | 0.996625i | \(-0.526158\pi\) | ||||
−0.0820841 | + | 0.996625i | \(0.526158\pi\) | |||||||
\(462\) | −24.1978 | − | 18.4298i | −1.12579 | − | 0.857430i | ||||
\(463\) | 10.7653 | 0.500304 | 0.250152 | − | 0.968207i | \(-0.419519\pi\) | ||||
0.250152 | + | 0.968207i | \(0.419519\pi\) | |||||||
\(464\) | 0.500000 | + | 0.866025i | 0.0232119 | + | 0.0402042i | ||||
\(465\) | −4.90346 | + | 8.49305i | −0.227393 | + | 0.393856i | ||||
\(466\) | −2.57131 | + | 4.45364i | −0.119114 | + | 0.206311i | ||||
\(467\) | −6.00994 | − | 10.4095i | −0.278107 | − | 0.481695i | 0.692807 | − | 0.721123i | \(-0.256374\pi\) |
−0.970914 | + | 0.239427i | \(0.923040\pi\) | |||||||
\(468\) | −5.66601 | −0.261911 | ||||||||
\(469\) | 4.78999 | + | 3.64819i | 0.221181 | + | 0.168458i | ||||
\(470\) | 48.6003 | 2.24177 | ||||||||
\(471\) | 21.7727 | + | 37.7115i | 1.00323 | + | 1.73765i | ||||
\(472\) | −1.70836 | + | 2.95897i | −0.0786338 | + | 0.136198i | ||||
\(473\) | 18.4636 | − | 31.9798i | 0.848956 | − | 1.47043i | ||||
\(474\) | −5.45023 | − | 9.44008i | −0.250337 | − | 0.433597i | ||||
\(475\) | 49.1650 | 2.25584 | ||||||||
\(476\) | 6.75376 | − | 2.82600i | 0.309558 | − | 0.129530i | ||||
\(477\) | −8.24666 | −0.377588 | ||||||||
\(478\) | −0.374837 | − | 0.649236i | −0.0171446 | − | 0.0296954i | ||||
\(479\) | −4.14601 | + | 7.18110i | −0.189436 | + | 0.328113i | −0.945062 | − | 0.326890i | \(-0.893999\pi\) |
0.755626 | + | 0.655003i | \(0.227333\pi\) | |||||||
\(480\) | 5.06010 | − | 8.76435i | 0.230961 | − | 0.400036i | ||||
\(481\) | −1.40755 | − | 2.43795i | −0.0641788 | − | 0.111161i | ||||
\(482\) | −9.01959 | −0.410831 | ||||||||
\(483\) | −1.78253 | + | 13.9265i | −0.0811077 | + | 0.633678i | ||||
\(484\) | 11.1556 | 0.507072 | ||||||||
\(485\) | −34.8988 | − | 60.4465i | −1.58467 | − | 2.74473i | ||||
\(486\) | −10.9896 | + | 19.0345i | −0.498497 | + | 0.863421i | ||||
\(487\) | −3.94673 | + | 6.83593i | −0.178843 | + | 0.309766i | −0.941485 | − | 0.337056i | \(-0.890569\pi\) |
0.762641 | + | 0.646822i | \(0.223902\pi\) | |||||||
\(488\) | −5.70959 | − | 9.88930i | −0.258461 | − | 0.447668i | ||||
\(489\) | 26.5711 | 1.20159 | ||||||||
\(490\) | 20.3611 | − | 20.6561i | 0.919819 | − | 0.933149i | ||||
\(491\) | −37.7250 | −1.70250 | −0.851252 | − | 0.524757i | \(-0.824156\pi\) | ||||
−0.851252 | + | 0.524757i | \(0.824156\pi\) | |||||||
\(492\) | 12.7912 | + | 22.1551i | 0.576673 | + | 0.998828i | ||||
\(493\) | 1.38357 | − | 2.39642i | 0.0623129 | − | 0.107929i | ||||
\(494\) | 3.85982 | − | 6.68541i | 0.173662 | − | 0.300791i | ||||
\(495\) | 28.9188 | + | 50.0888i | 1.29980 | + | 2.25133i | ||||
\(496\) | −0.969044 | −0.0435114 | ||||||||
\(497\) | 2.09823 | − | 16.3930i | 0.0941184 | − | 0.735328i | ||||
\(498\) | 14.8013 | 0.663262 | ||||||||
\(499\) | 4.23971 | + | 7.34340i | 0.189796 | + | 0.328736i | 0.945182 | − | 0.326544i | \(-0.105884\pi\) |
−0.755386 | + | 0.655280i | \(0.772551\pi\) | |||||||
\(500\) | −14.8509 | + | 25.7225i | −0.664152 | + | 1.15034i | ||||
\(501\) | 19.5793 | − | 33.9124i | 0.874740 | − | 1.51509i | ||||
\(502\) | 14.5584 | + | 25.2160i | 0.649775 | + | 1.12544i | ||||
\(503\) | −25.2796 | −1.12716 | −0.563581 | − | 0.826061i | \(-0.690577\pi\) | ||||
−0.563581 | + | 0.826061i | \(0.690577\pi\) | |||||||
\(504\) | 7.23800 | − | 3.02862i | 0.322406 | − | 0.134906i | ||||
\(505\) | −51.4870 | −2.29114 | ||||||||
\(506\) | −5.11338 | − | 8.85664i | −0.227318 | − | 0.393726i | ||||
\(507\) | −11.4179 | + | 19.7764i | −0.507087 | + | 0.878300i | ||||
\(508\) | −2.73191 | + | 4.73180i | −0.121209 | + | 0.209940i | ||||
\(509\) | −2.48482 | − | 4.30383i | −0.110138 | − | 0.190764i | 0.805688 | − | 0.592340i | \(-0.201796\pi\) |
−0.915826 | + | 0.401576i | \(0.868462\pi\) | |||||||
\(510\) | −28.0041 | −1.24004 | ||||||||
\(511\) | 28.4631 | + | 21.6783i | 1.25913 | + | 0.958990i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −0.170001 | − | 0.294451i | −0.00750573 | − | 0.0130003i | ||||
\(514\) | 11.6138 | − | 20.1156i | 0.512262 | − | 0.887263i | ||||
\(515\) | 33.5037 | − | 58.0302i | 1.47635 | − | 2.55712i | ||||
\(516\) | 9.58075 | + | 16.5943i | 0.421769 | + | 0.730525i | ||||
\(517\) | −55.2099 | −2.42813 | ||||||||
\(518\) | 3.10121 | + | 2.36197i | 0.136259 | + | 0.103779i | ||||
\(519\) | 15.1158 | 0.663508 | ||||||||
\(520\) | 3.95828 | + | 6.85594i | 0.173582 | + | 0.300653i | ||||
\(521\) | −13.4814 | + | 23.3505i | −0.590631 | + | 1.02300i | 0.403517 | + | 0.914972i | \(0.367788\pi\) |
−0.994148 | + | 0.108030i | \(0.965546\pi\) | |||||||
\(522\) | 1.48277 | − | 2.56824i | 0.0648992 | − | 0.112409i | ||||
\(523\) | 5.24494 | + | 9.08451i | 0.229345 | + | 0.397238i | 0.957614 | − | 0.288054i | \(-0.0930082\pi\) |
−0.728269 | + | 0.685291i | \(0.759675\pi\) | |||||||
\(524\) | −13.4182 | −0.586176 | ||||||||
\(525\) | −72.5388 | + | 30.3527i | −3.16585 | + | 1.32470i | ||||
\(526\) | −20.5033 | −0.893988 | ||||||||
\(527\) | 1.34074 | + | 2.32223i | 0.0584036 | + | 0.101158i | ||||
\(528\) | −5.74826 | + | 9.95629i | −0.250161 | + | 0.433292i | ||||
\(529\) | 9.13972 | − | 15.8305i | 0.397379 | − | 0.688281i | ||||
\(530\) | 5.76112 | + | 9.97856i | 0.250247 | + | 0.433441i | ||||
\(531\) | 10.1325 | 0.439712 | ||||||||
\(532\) | −1.35718 | + | 10.6034i | −0.0588414 | + | 0.459716i | ||||
\(533\) | −20.0120 | −0.866815 | ||||||||
\(534\) | 16.2009 | + | 28.0609i | 0.701084 | + | 1.21431i | ||||
\(535\) | −22.0113 | + | 38.1247i | −0.951632 | + | 1.64827i | ||||
\(536\) | 1.13788 | − | 1.97086i | 0.0491487 | − | 0.0851281i | ||||
\(537\) | 1.47206 | + | 2.54968i | 0.0635241 | + | 0.110027i | ||||
\(538\) | −11.3952 | −0.491282 | ||||||||
\(539\) | −23.1301 | + | 23.4653i | −0.996285 | + | 1.01072i | ||||
\(540\) | 0.348675 | 0.0150046 | ||||||||
\(541\) | 22.2847 | + | 38.5982i | 0.958093 | + | 1.65947i | 0.727125 | + | 0.686505i | \(0.240856\pi\) |
0.230968 | + | 0.972961i | \(0.425811\pi\) | |||||||
\(542\) | −8.98753 | + | 15.5669i | −0.386048 | + | 0.668654i | ||||
\(543\) | 8.48879 | − | 14.7030i | 0.364289 | − | 0.630967i | ||||
\(544\) | −1.38357 | − | 2.39642i | −0.0593201 | − | 0.102746i | ||||
\(545\) | 25.2703 | 1.08246 | ||||||||
\(546\) | −1.56751 | + | 12.2467i | −0.0670834 | + | 0.524109i | ||||
\(547\) | 34.8005 | 1.48796 | 0.743980 | − | 0.668202i | \(-0.232936\pi\) | ||||
0.743980 | + | 0.668202i | \(0.232936\pi\) | |||||||
\(548\) | −8.55161 | − | 14.8118i | −0.365307 | − | 0.632730i | ||||
\(549\) | −16.9321 | + | 29.3272i | −0.722643 | + | 1.25165i | ||||
\(550\) | 28.6380 | − | 49.6025i | 1.22113 | − | 2.11506i | ||||
\(551\) | 2.02020 | + | 3.49909i | 0.0860635 | + | 0.149066i | ||||
\(552\) | 5.30667 | 0.225867 | ||||||||
\(553\) | −10.8927 | + | 4.55786i | −0.463203 | + | 0.193820i | ||||
\(554\) | −2.08032 | −0.0883843 | ||||||||
\(555\) | −7.45557 | − | 12.9134i | −0.316471 | − | 0.548144i | ||||
\(556\) | 1.95356 | − | 3.38366i | 0.0828493 | − | 0.143499i | ||||
\(557\) | 16.8832 | − | 29.2426i | 0.715365 | − | 1.23905i | −0.247453 | − | 0.968900i | \(-0.579594\pi\) |
0.962818 | − | 0.270149i | \(-0.0870731\pi\) | |||||||
\(558\) | 1.43687 | + | 2.48874i | 0.0608277 | + | 0.105357i | ||||
\(559\) | −14.9891 | −0.633973 | ||||||||
\(560\) | −8.72115 | − | 6.64228i | −0.368536 | − | 0.280687i | ||||
\(561\) | 31.8125 | 1.34313 | ||||||||
\(562\) | −3.67871 | − | 6.37170i | −0.155177 | − | 0.268774i | ||||
\(563\) | −20.6204 | + | 35.7156i | −0.869047 | + | 1.50523i | −0.00607459 | + | 0.999982i | \(0.501934\pi\) |
−0.862972 | + | 0.505252i | \(0.831400\pi\) | |||||||
\(564\) | 14.3242 | − | 24.8102i | 0.603158 | − | 1.04470i | ||||
\(565\) | −30.2215 | − | 52.3451i | −1.27143 | − | 2.20217i | ||||
\(566\) | −6.08053 | −0.255584 | ||||||||
\(567\) | 19.1582 | + | 14.5914i | 0.804569 | + | 0.612783i | ||||
\(568\) | −6.24653 | −0.262099 | ||||||||
\(569\) | 12.9593 | + | 22.4461i | 0.543281 | + | 0.940990i | 0.998713 | + | 0.0507193i | \(0.0161514\pi\) |
−0.455432 | + | 0.890270i | \(0.650515\pi\) | |||||||
\(570\) | 20.4448 | − | 35.4115i | 0.856340 | − | 1.48323i | ||||
\(571\) | −7.94763 | + | 13.7657i | −0.332598 | + | 0.576077i | −0.983020 | − | 0.183496i | \(-0.941259\pi\) |
0.650422 | + | 0.759573i | \(0.274592\pi\) | |||||||
\(572\) | −4.49660 | − | 7.78834i | −0.188012 | − | 0.325647i | ||||
\(573\) | 16.6293 | 0.694700 | ||||||||
\(574\) | 25.5642 | − | 10.6969i | 1.06703 | − | 0.446480i | ||||
\(575\) | −26.4380 | −1.10254 | ||||||||
\(576\) | −1.48277 | − | 2.56824i | −0.0617822 | − | 0.107010i | ||||
\(577\) | 5.13613 | − | 8.89603i | 0.213820 | − | 0.370347i | −0.739087 | − | 0.673610i | \(-0.764743\pi\) |
0.952907 | + | 0.303263i | \(0.0980761\pi\) | |||||||
\(578\) | 4.67146 | − | 8.09120i | 0.194307 | − | 0.336550i | ||||
\(579\) | −4.75867 | − | 8.24225i | −0.197763 | − | 0.342536i | ||||
\(580\) | −4.14347 | −0.172048 | ||||||||
\(581\) | 2.03558 | − | 15.9036i | 0.0844502 | − | 0.659792i | ||||
\(582\) | −41.1435 | −1.70545 | ||||||||
\(583\) | −6.54462 | − | 11.3356i | −0.271051 | − | 0.469473i | ||||
\(584\) | 6.76148 | − | 11.7112i | 0.279792 | − | 0.484614i | ||||
\(585\) | 11.7385 | − | 20.3316i | 0.485326 | − | 0.840609i | ||||
\(586\) | −6.85795 | − | 11.8783i | −0.283299 | − | 0.490689i | ||||
\(587\) | −23.9902 | −0.990183 | −0.495091 | − | 0.868841i | \(-0.664865\pi\) | ||||
−0.495091 | + | 0.868841i | \(0.664865\pi\) | |||||||
\(588\) | −4.54374 | − | 16.4823i | −0.187381 | − | 0.679719i | ||||
\(589\) | −3.91533 | −0.161328 | ||||||||
\(590\) | −7.07855 | − | 12.2604i | −0.291419 | − | 0.504753i | ||||
\(591\) | 19.0051 | − | 32.9178i | 0.781766 | − | 1.35406i | ||||
\(592\) | 0.736701 | − | 1.27600i | 0.0302782 | − | 0.0524434i | ||||
\(593\) | 7.76833 | + | 13.4551i | 0.319007 | + | 0.552536i | 0.980281 | − | 0.197608i | \(-0.0633173\pi\) |
−0.661274 | + | 0.750144i | \(0.729984\pi\) | |||||||
\(594\) | −0.396094 | −0.0162519 | ||||||||
\(595\) | −3.85132 | + | 30.0896i | −0.157889 | + | 1.23355i | ||||
\(596\) | −7.49827 | −0.307141 | ||||||||
\(597\) | 30.0098 | + | 51.9785i | 1.22822 | + | 2.12734i | ||||
\(598\) | −2.07558 | + | 3.59501i | −0.0848767 | + | 0.147011i | ||||
\(599\) | 10.4154 | − | 18.0400i | 0.425561 | − | 0.737094i | −0.570911 | − | 0.821012i | \(-0.693410\pi\) |
0.996473 | + | 0.0839180i | \(0.0267434\pi\) | |||||||
\(600\) | 14.8603 | + | 25.7387i | 0.606667 | + | 1.05078i | ||||
\(601\) | 17.7149 | 0.722606 | 0.361303 | − | 0.932448i | \(-0.382332\pi\) | ||||
0.361303 | + | 0.932448i | \(0.382332\pi\) | |||||||
\(602\) | 19.1478 | − | 8.01207i | 0.780405 | − | 0.326548i | ||||
\(603\) | −6.74884 | −0.274834 | ||||||||
\(604\) | −4.70909 | − | 8.15638i | −0.191610 | − | 0.331878i | ||||
\(605\) | −23.1114 | + | 40.0301i | −0.939612 | + | 1.62746i | ||||
\(606\) | −15.1750 | + | 26.2839i | −0.616442 | + | 1.06771i | ||||
\(607\) | 1.22259 | + | 2.11758i | 0.0496233 | + | 0.0859501i | 0.889770 | − | 0.456409i | \(-0.150865\pi\) |
−0.840147 | + | 0.542359i | \(0.817531\pi\) | |||||||
\(608\) | 4.04040 | 0.163860 | ||||||||
\(609\) | −5.14085 | − | 3.91542i | −0.208318 | − | 0.158661i | ||||
\(610\) | 47.3150 | 1.91573 | ||||||||
\(611\) | 11.2052 | + | 19.4079i | 0.453312 | + | 0.785159i | ||||
\(612\) | −4.10305 | + | 7.10668i | −0.165856 | + | 0.287271i | ||||
\(613\) | 0.903050 | − | 1.56413i | 0.0364739 | − | 0.0631746i | −0.847212 | − | 0.531255i | \(-0.821721\pi\) |
0.883686 | + | 0.468080i | \(0.155054\pi\) | |||||||
\(614\) | −3.82247 | − | 6.62071i | −0.154262 | − | 0.267190i | ||||
\(615\) | −106.000 | −4.27434 | ||||||||
\(616\) | 9.90721 | + | 7.54561i | 0.399173 | + | 0.304021i | ||||
\(617\) | −15.0917 | −0.607567 | −0.303784 | − | 0.952741i | \(-0.598250\pi\) | ||||
−0.303784 | + | 0.952741i | \(0.598250\pi\) | |||||||
\(618\) | −19.7494 | − | 34.2070i | −0.794438 | − | 1.37601i | ||||
\(619\) | 22.2955 | − | 38.6170i | 0.896133 | − | 1.55215i | 0.0637362 | − | 0.997967i | \(-0.479698\pi\) |
0.832396 | − | 0.554181i | \(-0.186968\pi\) | |||||||
\(620\) | 2.00760 | − | 3.47727i | 0.0806272 | − | 0.139650i | ||||
\(621\) | 0.0914163 | + | 0.158338i | 0.00366841 | + | 0.00635387i | ||||
\(622\) | 24.4252 | 0.979360 | ||||||||
\(623\) | 32.3787 | − | 13.5483i | 1.29723 | − | 0.542803i | ||||
\(624\) | 4.66657 | 0.186812 | ||||||||
\(625\) | −31.1133 | − | 53.8899i | −1.24453 | − | 2.15560i | ||||
\(626\) | 9.13225 | − | 15.8175i | 0.364998 | − | 0.632195i | ||||
\(627\) | −23.2253 | + | 40.2274i | −0.927529 | + | 1.60653i | ||||
\(628\) | −8.91431 | − | 15.4400i | −0.355720 | − | 0.616125i | ||||
\(629\) | −4.07712 | −0.162565 | ||||||||
\(630\) | −4.12746 | + | 32.2470i | −0.164442 | + | 1.28475i | ||||
\(631\) | −14.3265 | −0.570328 | −0.285164 | − | 0.958479i | \(-0.592048\pi\) | ||||
−0.285164 | + | 0.958479i | \(0.592048\pi\) | |||||||
\(632\) | 2.23146 | + | 3.86501i | 0.0887629 | + | 0.153742i | ||||
\(633\) | 10.5715 | − | 18.3103i | 0.420178 | − | 0.727770i | ||||
\(634\) | 5.21086 | − | 9.02547i | 0.206950 | − | 0.358447i | ||||
\(635\) | −11.3196 | − | 19.6061i | −0.449203 | − | 0.778043i | ||||
\(636\) | 6.79201 | 0.269321 | ||||||||
\(637\) | 12.9431 | + | 3.36850i | 0.512826 | + | 0.133465i | ||||
\(638\) | 4.70697 | 0.186351 | ||||||||
\(639\) | 9.26219 | + | 16.0426i | 0.366407 | + | 0.634635i | ||||
\(640\) | −2.07173 | + | 3.58835i | −0.0818925 | + | 0.141842i | ||||
\(641\) | 8.71772 | − | 15.0995i | 0.344329 | − | 0.596395i | −0.640903 | − | 0.767622i | \(-0.721440\pi\) |
0.985232 | + | 0.171227i | \(0.0547731\pi\) | |||||||
\(642\) | 12.9750 | + | 22.4733i | 0.512082 | + | 0.886952i | ||||
\(643\) | −6.99067 | −0.275685 | −0.137843 | − | 0.990454i | \(-0.544017\pi\) | ||||
−0.137843 | + | 0.990454i | \(0.544017\pi\) | |||||||
\(644\) | 0.729811 | − | 5.70187i | 0.0287586 | − | 0.224685i | ||||
\(645\) | −79.3950 | −3.12618 | ||||||||
\(646\) | −5.59019 | − | 9.68249i | −0.219943 | − | 0.380952i | ||||
\(647\) | 8.11703 | − | 14.0591i | 0.319113 | − | 0.552721i | −0.661190 | − | 0.750219i | \(-0.729948\pi\) |
0.980303 | + | 0.197498i | \(0.0632816\pi\) | |||||||
\(648\) | 4.55109 | − | 7.88271i | 0.178784 | − | 0.309662i | ||||
\(649\) | 8.04122 | + | 13.9278i | 0.315646 | + | 0.546714i | ||||
\(650\) | −23.2490 | −0.911899 | ||||||||
\(651\) | 5.77674 | − | 2.41718i | 0.226408 | − | 0.0947369i | ||||
\(652\) | −10.8789 | −0.426051 | ||||||||
\(653\) | −11.2601 | − | 19.5030i | −0.440641 | − | 0.763212i | 0.557097 | − | 0.830448i | \(-0.311915\pi\) |
−0.997737 | + | 0.0672359i | \(0.978582\pi\) | |||||||
\(654\) | 7.44804 | − | 12.9004i | 0.291241 | − | 0.504445i | ||||
\(655\) | 27.7989 | − | 48.1491i | 1.08619 | − | 1.88134i | ||||
\(656\) | −5.23706 | − | 9.07085i | −0.204473 | − | 0.354157i | ||||
\(657\) | −40.1030 | −1.56457 | ||||||||
\(658\) | −24.6880 | − | 18.8030i | −0.962437 | − | 0.733019i | ||||
\(659\) | −6.71682 | −0.261650 | −0.130825 | − | 0.991405i | \(-0.541763\pi\) | ||||
−0.130825 | + | 0.991405i | \(0.541763\pi\) | |||||||
\(660\) | −23.8178 | − | 41.2536i | −0.927105 | − | 1.60579i | ||||
\(661\) | 17.6804 | − | 30.6234i | 0.687689 | − | 1.19111i | −0.284895 | − | 0.958559i | \(-0.591959\pi\) |
0.972584 | − | 0.232553i | \(-0.0747079\pi\) | |||||||
\(662\) | −2.34176 | + | 4.05604i | −0.0910149 | + | 0.157643i | ||||
\(663\) | −6.45653 | − | 11.1830i | −0.250751 | − | 0.434313i | ||||
\(664\) | −6.06003 | −0.235175 | ||||||||
\(665\) | −35.2370 | − | 26.8375i | −1.36643 | − | 1.04071i | ||||
\(666\) | −4.36944 | −0.169313 | ||||||||
\(667\) | −1.08634 | − | 1.88160i | −0.0420633 | − | 0.0728559i | ||||
\(668\) | −8.01628 | + | 13.8846i | −0.310159 | + | 0.537211i | ||||
\(669\) | −13.3346 | + | 23.0962i | −0.515546 | + | 0.892951i | ||||
\(670\) | 4.71475 | + | 8.16619i | 0.182147 | + | 0.315487i | ||||
\(671\) | −53.7498 | −2.07499 | ||||||||
\(672\) | −5.96128 | + | 2.49440i | −0.229961 | + | 0.0962235i | ||||
\(673\) | −23.1388 | −0.891935 | −0.445967 | − | 0.895049i | \(-0.647140\pi\) | ||||
−0.445967 | + | 0.895049i | \(0.647140\pi\) | |||||||
\(674\) | 12.6860 | + | 21.9727i | 0.488645 | + | 0.846358i | ||||
\(675\) | −0.511986 | + | 0.886786i | −0.0197064 | + | 0.0341324i | ||||
\(676\) | 4.67478 | − | 8.09696i | 0.179799 | − | 0.311421i | ||||
\(677\) | −11.3672 | − | 19.6886i | −0.436878 | − | 0.756694i | 0.560569 | − | 0.828108i | \(-0.310582\pi\) |
−0.997447 | + | 0.0714135i | \(0.977249\pi\) | |||||||
\(678\) | −35.6292 | −1.36833 | ||||||||
\(679\) | −5.65835 | + | 44.2076i | −0.217148 | + | 1.69653i | ||||
\(680\) | 11.4656 | 0.439685 | ||||||||
\(681\) | −12.8168 | − | 22.1994i | −0.491142 | − | 0.850684i | ||||
\(682\) | −2.28063 | + | 3.95017i | −0.0873299 | + | 0.151260i | ||||
\(683\) | −10.1464 | + | 17.5741i | −0.388242 | + | 0.672454i | −0.992213 | − | 0.124552i | \(-0.960251\pi\) |
0.603972 | + | 0.797006i | \(0.293584\pi\) | |||||||
\(684\) | −5.99100 | − | 10.3767i | −0.229072 | − | 0.396764i | ||||
\(685\) | 70.8667 | 2.70768 | ||||||||
\(686\) | −18.3347 | + | 2.61536i | −0.700021 | + | 0.0998550i | ||||
\(687\) | 18.3556 | 0.700310 | ||||||||
\(688\) | −3.92260 | − | 6.79415i | −0.149548 | − | 0.259024i | ||||
\(689\) | −2.65654 | + | 4.60125i | −0.101206 | + | 0.175294i | ||||
\(690\) | −10.9940 | + | 19.0422i | −0.418535 | + | 0.724923i | ||||
\(691\) | −1.00590 | − | 1.74227i | −0.0382662 | − | 0.0662790i | 0.846258 | − | 0.532773i | \(-0.178850\pi\) |
−0.884524 | + | 0.466494i | \(0.845517\pi\) | |||||||
\(692\) | −6.18878 | −0.235262 | ||||||||
\(693\) | 4.68878 | − | 36.6325i | 0.178112 | − | 1.39155i | ||||
\(694\) | −1.93057 | −0.0732836 | ||||||||
\(695\) | 8.09450 | + | 14.0201i | 0.307042 | + | 0.531812i | ||||
\(696\) | −1.22122 | + | 2.11522i | −0.0462904 | + | 0.0801772i | ||||
\(697\) | −14.4917 | + | 25.1003i | −0.548912 | + | 0.950743i | ||||
\(698\) | −0.978909 | − | 1.69552i | −0.0370523 | − | 0.0641764i | ||||
\(699\) | −12.5606 | −0.475084 | ||||||||
\(700\) | 29.6992 | − | 12.4272i | 1.12253 | − | 0.469702i | ||||
\(701\) | −3.02432 | −0.114227 | −0.0571136 | − | 0.998368i | \(-0.518190\pi\) | ||||
−0.0571136 | + | 0.998368i | \(0.518190\pi\) | |||||||
\(702\) | 0.0803895 | + | 0.139239i | 0.00303411 | + | 0.00525523i | ||||
\(703\) | 2.97657 | − | 5.15557i | 0.112263 | − | 0.194446i | ||||
\(704\) | 2.35349 | − | 4.07636i | 0.0887003 | − | 0.153633i | ||||
\(705\) | 59.3519 | + | 102.800i | 2.23532 | + | 3.87169i | ||||
\(706\) | −16.3330 | −0.614700 | ||||||||
\(707\) | 26.1543 | + | 19.9199i | 0.983634 | + | 0.749163i | ||||
\(708\) | −8.34518 | −0.313631 | ||||||||
\(709\) | 22.7334 | + | 39.3755i | 0.853772 | + | 1.47878i | 0.877779 | + | 0.479065i | \(0.159024\pi\) |
−0.0240072 | + | 0.999712i | \(0.507642\pi\) | |||||||
\(710\) | 12.9412 | − | 22.4147i | 0.485673 | − | 0.841210i | ||||
\(711\) | 6.61751 | − | 11.4619i | 0.248176 | − | 0.429853i | ||||
\(712\) | −6.63308 | − | 11.4888i | −0.248585 | − | 0.430562i | ||||
\(713\) | 2.10543 | 0.0788489 | ||||||||
\(714\) | 14.2255 | + | 10.8345i | 0.532375 | + | 0.405472i | ||||
\(715\) | 37.2630 | 1.39356 | ||||||||
\(716\) | −0.602699 | − | 1.04391i | −0.0225239 | − | 0.0390126i | ||||
\(717\) | 0.915519 | − | 1.58572i | 0.0341907 | − | 0.0592200i | ||||
\(718\) | 5.89004 | − | 10.2019i | 0.219814 | − | 0.380730i | ||||
\(719\) | −15.0720 | − | 26.1055i | −0.562092 | − | 0.973572i | −0.997314 | − | 0.0732489i | \(-0.976663\pi\) |
0.435221 | − | 0.900323i | \(-0.356670\pi\) | |||||||
\(720\) | 12.2876 | 0.457934 | ||||||||
\(721\) | −39.4706 | + | 16.5158i | −1.46996 | + | 0.615081i | ||||
\(722\) | −2.67514 | −0.0995585 | ||||||||
\(723\) | −11.0149 | − | 19.0784i | −0.409650 | − | 0.709534i | ||||
\(724\) | −3.47553 | + | 6.01979i | −0.129167 | + | 0.223724i | ||||
\(725\) | 6.08417 | − | 10.5381i | 0.225960 | − | 0.391375i | ||||
\(726\) | 13.6235 | + | 23.5965i | 0.505614 | + | 0.875749i | ||||
\(727\) | 45.6599 | 1.69343 | 0.846717 | − | 0.532044i | \(-0.178576\pi\) | ||||
0.846717 | + | 0.532044i | \(0.178576\pi\) | |||||||
\(728\) | 0.641780 | − | 5.01410i | 0.0237860 | − | 0.185835i | ||||
\(729\) | −26.3763 | −0.976901 | ||||||||
\(730\) | 28.0160 | + | 48.5251i | 1.03692 | + | 1.79599i | ||||
\(731\) | −10.8544 | + | 18.8004i | −0.401465 | + | 0.695357i | ||||
\(732\) | 13.9454 | − | 24.1541i | 0.515436 | − | 0.892761i | ||||
\(733\) | 13.6729 | + | 23.6822i | 0.505020 | + | 0.874721i | 0.999983 | + | 0.00580686i | \(0.00184839\pi\) |
−0.494963 | + | 0.868914i | \(0.664818\pi\) | |||||||
\(734\) | 35.6438 | 1.31564 | ||||||||
\(735\) | 68.5577 | + | 17.8424i | 2.52879 | + | 0.658127i | ||||
\(736\) | −2.17268 | −0.0800862 | ||||||||
\(737\) | −5.35595 | − | 9.27677i | −0.197289 | − | 0.341714i | ||||
\(738\) | −15.5307 | + | 26.9000i | −0.571694 | + | 0.990204i | ||||
\(739\) | −24.9583 | + | 43.2291i | −0.918106 | + | 1.59021i | −0.115817 | + | 0.993271i | \(0.536949\pi\) |
−0.802289 | + | 0.596936i | \(0.796385\pi\) | |||||||
\(740\) | 3.05250 | + | 5.28708i | 0.112212 | + | 0.194357i | ||||
\(741\) | 18.8548 | 0.692649 | ||||||||
\(742\) | 0.934086 | − | 7.29783i | 0.0342914 | − | 0.267912i | ||||
\(743\) | 28.6655 | 1.05164 | 0.525818 | − | 0.850597i | \(-0.323759\pi\) | ||||
0.525818 | + | 0.850597i | \(0.323759\pi\) | |||||||
\(744\) | −1.18342 | − | 2.04974i | −0.0433863 | − | 0.0751472i | ||||
\(745\) | 15.5344 | − | 26.9064i | 0.569137 | − | 0.985774i | ||||
\(746\) | −8.87414 | + | 15.3705i | −0.324905 | + | 0.562753i | ||||
\(747\) | 8.98565 | + | 15.5636i | 0.328768 | + | 0.569443i | ||||
\(748\) | −13.0249 | −0.476236 | ||||||||
\(749\) | 25.9314 | − | 10.8506i | 0.947512 | − | 0.396471i | ||||
\(750\) | −72.5450 | −2.64897 | ||||||||
\(751\) | 9.51580 | + | 16.4818i | 0.347236 | + | 0.601431i | 0.985757 | − | 0.168173i | \(-0.0537868\pi\) |
−0.638521 | + | 0.769604i | \(0.720453\pi\) | |||||||
\(752\) | −5.86469 | + | 10.1579i | −0.213863 | + | 0.370422i | ||||
\(753\) | −35.5582 | + | 61.5887i | −1.29581 | + | 2.24442i | ||||
\(754\) | −0.955306 | − | 1.65464i | −0.0347902 | − | 0.0602584i | ||||
\(755\) | 39.0239 | 1.42023 | ||||||||
\(756\) | −0.177120 | − | 0.134899i | −0.00644178 | − | 0.00490624i | ||||
\(757\) | −9.39694 | −0.341538 | −0.170769 | − | 0.985311i | \(-0.554625\pi\) | ||||
−0.170769 | + | 0.985311i | \(0.554625\pi\) | |||||||
\(758\) | 7.61317 | + | 13.1864i | 0.276523 | + | 0.478951i | ||||
\(759\) | 12.4892 | − | 21.6319i | 0.453328 | − | 0.785187i | ||||
\(760\) | −8.37064 | + | 14.4984i | −0.303635 | + | 0.525911i | ||||
\(761\) | 5.37464 | + | 9.30916i | 0.194831 | + | 0.337457i | 0.946845 | − | 0.321690i | \(-0.104251\pi\) |
−0.752014 | + | 0.659147i | \(0.770918\pi\) | |||||||
\(762\) | −13.3451 | −0.483441 | ||||||||
\(763\) | −12.8368 | − | 9.77687i | −0.464723 | − | 0.353946i | ||||
\(764\) | −6.80847 | −0.246322 | ||||||||
\(765\) | −17.0008 | − | 29.4463i | −0.614667 | − | 1.06463i | ||||
\(766\) | 7.90588 | − | 13.6934i | 0.285651 | − | 0.494762i | ||||
\(767\) | 3.26402 | − | 5.65345i | 0.117857 | − | 0.204134i | ||||
\(768\) | 1.22122 | + | 2.11522i | 0.0440671 | + | 0.0763265i | ||||
\(769\) | 39.3774 | 1.41998 | 0.709992 | − | 0.704209i | \(-0.248698\pi\) | ||||
0.709992 | + | 0.704209i | \(0.248698\pi\) | |||||||
\(770\) | −47.6014 | + | 19.9180i | −1.71544 | + | 0.717796i | ||||
\(771\) | 56.7321 | 2.04316 | ||||||||
\(772\) | 1.94832 | + | 3.37459i | 0.0701216 | + | 0.121454i | ||||
\(773\) | 9.52357 | − | 16.4953i | 0.342539 | − | 0.593295i | −0.642365 | − | 0.766399i | \(-0.722046\pi\) |
0.984903 | + | 0.173104i | \(0.0553798\pi\) | |||||||
\(774\) | −11.6327 | + | 20.1484i | −0.418127 | + | 0.724218i | ||||
\(775\) | 5.89583 | + | 10.2119i | 0.211784 | + | 0.366821i | ||||
\(776\) | 16.8452 | 0.604708 | ||||||||
\(777\) | −1.20882 | + | 9.44424i | −0.0433660 | + | 0.338810i | ||||
\(778\) | −21.7172 | −0.778598 | ||||||||
\(779\) | −21.1598 | − | 36.6499i | −0.758129 | − | 1.31312i | ||||
\(780\) | −9.66789 | + | 16.7453i | −0.346166 | + | 0.599577i | ||||
\(781\) | −14.7011 | + | 25.4631i | −0.526048 | + | 0.911142i | ||||
\(782\) | 3.00607 | + | 5.20666i | 0.107497 | + | 0.186190i | ||||
\(783\) | −0.0841506 | −0.00300730 | ||||||||
\(784\) | 1.86032 | + | 6.74827i | 0.0664402 | + | 0.241010i | ||||
\(785\) | 73.8723 | 2.63662 | ||||||||
\(786\) | −16.3866 | − | 28.3824i | −0.584490 | − | 1.01237i | ||||
\(787\) | −13.2223 | + | 22.9017i | −0.471325 | + | 0.816358i | −0.999462 | − | 0.0328007i | \(-0.989557\pi\) |
0.528137 | + | 0.849159i | \(0.322891\pi\) | |||||||
\(788\) | −7.78118 | + | 13.4774i | −0.277193 | + | 0.480112i | ||||
\(789\) | −25.0391 | − | 43.3691i | −0.891417 | − | 1.54398i | ||||
\(790\) | −18.4920 | −0.657916 | ||||||||
\(791\) | −4.89999 | + | 38.2826i | −0.174224 | + | 1.36117i | ||||
\(792\) | −13.9587 | −0.496002 | ||||||||
\(793\) | 10.9088 | + | 18.8946i | 0.387383 | + | 0.670968i | ||||
\(794\) | −0.630167 | + | 1.09148i | −0.0223638 | + | 0.0387352i | ||||
\(795\) | −14.0712 | + | 24.3721i | −0.499055 | + | 0.864389i | ||||
\(796\) | −12.2868 | − | 21.2813i | −0.435493 | − | 0.754296i | ||||
\(797\) | −42.8772 | −1.51879 | −0.759395 | − | 0.650630i | \(-0.774505\pi\) | ||||
−0.759395 | + | 0.650630i | \(0.774505\pi\) | |||||||
\(798\) | −24.0860 | + | 10.0784i | −0.852634 | + | 0.356771i | ||||
\(799\) | 32.4569 | 1.14824 | ||||||||
\(800\) | −6.08417 | − | 10.5381i | −0.215108 | − | 0.372578i | ||||
\(801\) | −19.6707 | + | 34.0707i | −0.695030 | + | 1.20383i | ||||
\(802\) | 0.955905 | − | 1.65568i | 0.0337542 | − | 0.0584640i | ||||
\(803\) | −31.8261 | − | 55.1244i | −1.12312 | − | 1.94530i | ||||
\(804\) | 5.55840 | 0.196030 | ||||||||
\(805\) | 18.9483 | + | 14.4316i | 0.667840 | + | 0.508646i | ||||
\(806\) | 1.85147 | 0.0652152 | ||||||||
\(807\) | −13.9161 | − | 24.1034i | −0.489869 | − | 0.848479i | ||||
\(808\) | 6.21303 | − | 10.7613i | 0.218574 | − | 0.378580i | ||||
\(809\) | 0.861958 | − | 1.49295i | 0.0303048 | − | 0.0524895i | −0.850475 | − | 0.526015i | \(-0.823686\pi\) |
0.880780 | + | 0.473526i | \(0.157019\pi\) | |||||||
\(810\) | 18.8573 | + | 32.6618i | 0.662577 | + | 1.14762i | ||||
\(811\) | 7.23311 | 0.253989 | 0.126995 | − | 0.991903i | \(-0.459467\pi\) | ||||
0.126995 | + | 0.991903i | \(0.459467\pi\) | |||||||
\(812\) | 2.10480 | + | 1.60307i | 0.0738638 | + | 0.0562568i | ||||
\(813\) | −43.9031 | −1.53975 | ||||||||
\(814\) | −3.46763 | − | 6.00611i | −0.121540 | − | 0.210514i | ||||
\(815\) | 22.5382 | − | 39.0373i | 0.789479 | − | 1.36742i | ||||
\(816\) | 3.37930 | − | 5.85312i | 0.118299 | − | 0.204900i | ||||
\(817\) | −15.8489 | − | 27.4511i | −0.554482 | − | 0.960392i | ||||
\(818\) | −3.01815 | −0.105527 | ||||||||
\(819\) | −13.8290 | + | 5.78653i | −0.483225 | + | 0.202198i | ||||
\(820\) | 43.3992 | 1.51556 | ||||||||
\(821\) | −15.3520 | − | 26.5905i | −0.535789 | − | 0.928014i | −0.999125 | − | 0.0418313i | \(-0.986681\pi\) |
0.463335 | − | 0.886183i | \(-0.346653\pi\) | |||||||
\(822\) | 20.8869 | − | 36.1771i | 0.728513 | − | 1.26182i | ||||
\(823\) | 4.79289 | − | 8.30153i | 0.167070 | − | 0.289373i | −0.770319 | − | 0.637659i | \(-0.779903\pi\) |
0.937388 | + | 0.348286i | \(0.113236\pi\) | |||||||
\(824\) | 8.08592 | + | 14.0052i | 0.281686 | + | 0.487895i | ||||
\(825\) | 139.894 | 4.87047 | ||||||||
\(826\) | −1.14769 | + | 8.96666i | −0.0399332 | + | 0.311990i | ||||
\(827\) | −6.26986 | −0.218025 | −0.109012 | − | 0.994040i | \(-0.534769\pi\) | ||||
−0.109012 | + | 0.994040i | \(0.534769\pi\) | |||||||
\(828\) | 3.22160 | + | 5.57997i | 0.111958 | + | 0.193917i | ||||
\(829\) | −5.64488 | + | 9.77723i | −0.196055 | + | 0.339577i | −0.947246 | − | 0.320508i | \(-0.896146\pi\) |
0.751191 | + | 0.660085i | \(0.229480\pi\) | |||||||
\(830\) | 12.5548 | − | 21.7455i | 0.435783 | − | 0.754798i | ||||
\(831\) | −2.54053 | − | 4.40034i | −0.0881302 | − | 0.152646i | ||||
\(832\) | −1.91061 | −0.0662386 | ||||||||
\(833\) | 13.5978 | − | 13.7948i | 0.471135 | − | 0.477963i | ||||
\(834\) | 9.54292 | 0.330444 | ||||||||
\(835\) | −33.2152 | − | 57.5304i | −1.14946 | − | 1.99092i | ||||
\(836\) | 9.50903 | − | 16.4701i | 0.328877 | − | 0.569631i | ||||
\(837\) | 0.0407728 | − | 0.0706206i | 0.00140931 | − | 0.00244100i | ||||
\(838\) | −2.32252 | − | 4.02272i | −0.0802302 | − | 0.138963i | ||||
\(839\) | −44.0101 | −1.51940 | −0.759698 | − | 0.650276i | \(-0.774653\pi\) | ||||
−0.759698 | + | 0.650276i | \(0.774653\pi\) | |||||||
\(840\) | 3.39941 | − | 26.5589i | 0.117291 | − | 0.916368i | ||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 13.3101 | + | 23.0538i | 0.458697 | + | 0.794486i | ||||
\(843\) | 8.98504 | − | 15.5625i | 0.309461 | − | 0.536003i | ||||
\(844\) | −4.32823 | + | 7.49671i | −0.148984 | + | 0.258048i | ||||
\(845\) | 19.3698 | + | 33.5495i | 0.666342 | + | 1.15414i | ||||
\(846\) | 34.7840 | 1.19590 | ||||||||
\(847\) | 27.2274 | − | 11.3929i | 0.935545 | − | 0.391463i | ||||
\(848\) | −2.78082 | −0.0954938 | ||||||||
\(849\) | −7.42569 | − | 12.8617i | −0.254849 | − | 0.441411i | ||||
\(850\) | −16.8358 | + | 29.1604i | −0.577462 | + | 1.00019i | ||||
\(851\) | −1.60062 | + | 2.77235i | −0.0548685 | + | 0.0950351i | ||||
\(852\) | −7.62841 | − | 13.2128i | −0.261345 | − | 0.452663i | ||||
\(853\) | 10.9272 | 0.374141 | 0.187070 | − | 0.982347i | \(-0.440101\pi\) | ||||
0.187070 | + | 0.982347i | \(0.440101\pi\) | |||||||
\(854\) | −24.0350 | − | 18.3058i | −0.822462 | − | 0.626410i | ||||
\(855\) | 49.6471 | 1.69789 | ||||||||
\(856\) | −5.31229 | − | 9.20116i | −0.181570 | − | 0.314489i | ||||
\(857\) | −14.6377 | + | 25.3533i | −0.500015 | + | 0.866052i | 0.499985 | + | 0.866034i | \(0.333339\pi\) |
−1.00000 | 1.75014e-5i | \(0.999994\pi\) | ||||||||
\(858\) | 10.9827 | − | 19.0226i | 0.374943 | − | 0.649421i | ||||
\(859\) | 21.6611 | + | 37.5181i | 0.739067 | + | 1.28010i | 0.952916 | + | 0.303235i | \(0.0980666\pi\) |
−0.213849 | + | 0.976867i | \(0.568600\pi\) | |||||||
\(860\) | 32.5064 | 1.10846 | ||||||||
\(861\) | 53.8459 | + | 41.0105i | 1.83506 | + | 1.39763i | ||||
\(862\) | −9.63869 | −0.328295 | ||||||||
\(863\) | 21.9190 | + | 37.9649i | 0.746133 | + | 1.29234i | 0.949664 | + | 0.313271i | \(0.101425\pi\) |
−0.203531 | + | 0.979069i | \(0.565242\pi\) | |||||||
\(864\) | −0.0420753 | + | 0.0728765i | −0.00143143 | + | 0.00247931i | ||||
\(865\) | 12.8215 | − | 22.2075i | 0.435944 | − | 0.755077i | ||||
\(866\) | 1.58233 | + | 2.74068i | 0.0537698 | + | 0.0931320i | ||||
\(867\) | 22.8196 | 0.774994 | ||||||||
\(868\) | −2.36514 | + | 0.989656i | −0.0802782 | + | 0.0335911i | ||||
\(869\) | 21.0069 | 0.712609 | ||||||||
\(870\) | −5.06010 | − | 8.76435i | −0.171553 | − | 0.297139i | ||||
\(871\) | −2.17404 | + | 3.76555i | −0.0736645 | + | 0.127591i | ||||
\(872\) | −3.04942 | + | 5.28175i | −0.103266 | + | 0.178862i | ||||
\(873\) | −24.9776 | − | 43.2625i | −0.845364 | − | 1.46421i | ||||
\(874\) | −8.77852 | −0.296938 | ||||||||
\(875\) | −9.97691 | + | 77.9476i | −0.337281 | + | 2.63511i | ||||
\(876\) | 33.0291 | 1.11595 | ||||||||
\(877\) | −14.7536 | − | 25.5540i | −0.498194 | − | 0.862898i | 0.501804 | − | 0.864982i | \(-0.332670\pi\) |
−0.999998 | + | 0.00208396i | \(0.999337\pi\) | |||||||
\(878\) | −6.94499 | + | 12.0291i | −0.234382 | + | 0.405962i | ||||
\(879\) | 16.7502 | − | 29.0122i | 0.564969 | − | 0.978556i | ||||
\(880\) | 9.75159 | + | 16.8903i | 0.328726 | + | 0.569370i | ||||
\(881\) | −13.1060 | −0.441554 | −0.220777 | − | 0.975324i | \(-0.570859\pi\) | ||||
−0.220777 | + | 0.975324i | \(0.570859\pi\) | |||||||
\(882\) | 14.5727 | − | 14.7839i | 0.490690 | − | 0.497800i | ||||
\(883\) | −7.44435 | −0.250522 | −0.125261 | − | 0.992124i | \(-0.539977\pi\) | ||||
−0.125261 | + | 0.992124i | \(0.539977\pi\) | |||||||
\(884\) | 2.64347 | + | 4.57862i | 0.0889095 | + | 0.153996i | ||||
\(885\) | 17.2890 | − | 29.9454i | 0.581163 | − | 1.00660i | ||||
\(886\) | −10.1854 | + | 17.6416i | −0.342185 | + | 0.592682i | ||||
\(887\) | −19.3417 | − | 33.5008i | −0.649430 | − | 1.12485i | −0.983259 | − | 0.182212i | \(-0.941674\pi\) |
0.333830 | − | 0.942633i | \(-0.391659\pi\) | |||||||
\(888\) | 3.59871 | 0.120765 | ||||||||
\(889\) | −1.83531 | + | 14.3389i | −0.0615544 | + | 0.480912i | ||||
\(890\) | 54.9679 | 1.84253 | ||||||||
\(891\) | −21.4218 | − | 37.1037i | −0.717658 | − | 1.24302i | ||||
\(892\) | 5.45953 | − | 9.45618i | 0.182798 | − | 0.316616i | ||||
\(893\) | −23.6957 | + | 41.0422i | −0.792947 | + | 1.37342i | ||||
\(894\) | −9.15706 | − | 15.8605i | −0.306258 | − | 0.530454i | ||||
\(895\) | 4.99453 | 0.166949 | ||||||||
\(896\) | 2.44070 | − | 1.02127i | 0.0815380 | − | 0.0341182i | ||||
\(897\) | −10.1390 | −0.338531 | ||||||||
\(898\) | −16.5721 | − | 28.7037i | −0.553018 | − | 0.957856i | ||||
\(899\) | −0.484522 | + | 0.839217i | −0.0161597 | + | 0.0279895i | ||||
\(900\) | −18.0429 | + | 31.2512i | −0.601429 | + | 1.04171i | ||||
\(901\) | 3.84747 | + | 6.66401i | 0.128178 | + | 0.222010i | ||||
\(902\) | −49.3014 | −1.64156 | ||||||||
\(903\) | 40.3310 | + | 30.7172i | 1.34213 | + | 1.02221i | ||||
\(904\) | 14.5875 | 0.485173 | ||||||||
\(905\) | −14.4007 | − | 24.9428i | −0.478697 | − | 0.829127i | ||||
\(906\) | 11.5017 | − | 19.9215i | 0.382118 | − | 0.661848i | ||||
\(907\) | −1.21313 | + | 2.10120i | −0.0402812 | + | 0.0697691i | −0.885463 | − | 0.464710i | \(-0.846159\pi\) |
0.845182 | + | 0.534479i | \(0.179492\pi\) | |||||||
\(908\) | 5.24754 | + | 9.08901i | 0.174146 | + | 0.301629i | ||||
\(909\) | −36.8500 | −1.22224 | ||||||||
\(910\) | 16.6627 | + | 12.6908i | 0.552364 | + | 0.420696i | ||||
\(911\) | −1.86661 | −0.0618435 | −0.0309218 | − | 0.999522i | \(-0.509844\pi\) | ||||
−0.0309218 | + | 0.999522i | \(0.509844\pi\) | |||||||
\(912\) | 4.93423 | + | 8.54635i | 0.163389 | + | 0.282998i | ||||
\(913\) | −14.2622 | + | 24.7028i | −0.472010 | + | 0.817545i | ||||
\(914\) | 9.10435 | − | 15.7692i | 0.301145 | − | 0.521599i | ||||
\(915\) | 57.7822 | + | 100.082i | 1.91022 | + | 3.30860i | ||||
\(916\) | −7.51525 | −0.248311 | ||||||||
\(917\) | −32.7497 | + | 13.7036i | −1.08149 | + | 0.452532i | ||||
\(918\) | 0.232857 | 0.00768542 | ||||||||
\(919\) | −13.7029 | − | 23.7340i | −0.452015 | − | 0.782914i | 0.546496 | − | 0.837462i | \(-0.315961\pi\) |
−0.998511 | + | 0.0545482i | \(0.982628\pi\) | |||||||
\(920\) | 4.50123 | − | 7.79635i | 0.148401 | − | 0.257038i | ||||
\(921\) | 9.33618 | − | 16.1707i | 0.307638 | − | 0.532844i | ||||
\(922\) | 1.76242 | + | 3.05260i | 0.0580422 | + | 0.100532i | ||||
\(923\) | 11.9347 | 0.392836 | ||||||||
\(924\) | −3.86172 | + | 30.1708i | −0.127041 | + | 0.992547i | ||||
\(925\) | −17.9289 | −0.589497 | ||||||||
\(926\) | −5.38263 | − | 9.32299i | −0.176884 | − | 0.306372i | ||||
\(927\) | 23.9792 | − | 41.5331i | 0.787579 | − | 1.36413i | ||||
\(928\) | 0.500000 | − | 0.866025i | 0.0164133 | − | 0.0284287i | ||||
\(929\) | −21.9798 | − | 38.0701i | −0.721133 | − | 1.24904i | −0.960546 | − | 0.278121i | \(-0.910288\pi\) |
0.239413 | − | 0.970918i | \(-0.423045\pi\) | |||||||
\(930\) | 9.80692 | 0.321582 | ||||||||
\(931\) | 7.51646 | + | 27.2657i | 0.246342 | + | 0.893599i | ||||
\(932\) | 5.14262 | 0.168452 | ||||||||
\(933\) | 29.8286 | + | 51.6646i | 0.976544 | + | 1.69142i | ||||
\(934\) | −6.00994 | + | 10.4095i | −0.196651 | + | 0.340610i | ||||
\(935\) | 26.9841 | − | 46.7378i | 0.882473 | − | 1.52849i | ||||
\(936\) | 2.83300 | + | 4.90691i | 0.0925997 | + | 0.160387i | ||||
\(937\) | −29.9446 | −0.978246 | −0.489123 | − | 0.872215i | \(-0.662683\pi\) | ||||
−0.489123 | + | 0.872215i | \(0.662683\pi\) | |||||||
\(938\) | 0.764431 | − | 5.97235i | 0.0249596 | − | 0.195004i | ||||
\(939\) | 44.6101 | 1.45579 | ||||||||
\(940\) | −24.3002 | − | 42.0891i | −0.792584 | − | 1.37280i | ||||
\(941\) | −10.7861 | + | 18.6821i | −0.351618 | + | 0.609020i | −0.986533 | − | 0.163562i | \(-0.947702\pi\) |
0.634915 | + | 0.772582i | \(0.281035\pi\) | |||||||
\(942\) | 21.7727 | − | 37.7115i | 0.709394 | − | 1.22871i | ||||
\(943\) | 11.3785 | + | 19.7081i | 0.370534 | + | 0.641784i | ||||
\(944\) | 3.41673 | 0.111205 | ||||||||
\(945\) | 0.851011 | − | 0.356092i | 0.0276834 | − | 0.0115837i | ||||
\(946\) | −36.9271 | −1.20061 | ||||||||
\(947\) | −2.19606 | − | 3.80369i | −0.0713624 | − | 0.123603i | 0.828136 | − | 0.560527i | \(-0.189401\pi\) |
−0.899499 | + | 0.436924i | \(0.856068\pi\) | |||||||
\(948\) | −5.45023 | + | 9.44008i | −0.177015 | + | 0.306600i | ||||
\(949\) | −12.9186 | + | 22.3756i | −0.419354 | + | 0.726343i | ||||
\(950\) | −24.5825 | − | 42.5781i | −0.797561 | − | 1.38142i | ||||
\(951\) | 25.4545 | 0.825418 | ||||||||
\(952\) | −5.82427 | − | 4.43593i | −0.188766 | − | 0.143769i | ||||
\(953\) | 32.9052 | 1.06591 | 0.532953 | − | 0.846145i | \(-0.321082\pi\) | ||||
0.532953 | + | 0.846145i | \(0.321082\pi\) | |||||||
\(954\) | 4.12333 | + | 7.14181i | 0.133498 | + | 0.231225i | ||||
\(955\) | 14.1053 | − | 24.4312i | 0.456438 | − | 0.790574i | ||||
\(956\) | −0.374837 | + | 0.649236i | −0.0121231 | + | 0.0209978i | ||||
\(957\) | 5.74826 | + | 9.95629i | 0.185815 | + | 0.321841i | ||||
\(958\) | 8.29202 | 0.267903 | ||||||||
\(959\) | −35.9988 | − | 27.4177i | −1.16246 | − | 0.885363i | ||||
\(960\) | −10.1202 | −0.326628 | ||||||||
\(961\) | 15.0305 | + | 26.0335i | 0.484854 | + | 0.839792i | ||||
\(962\) | −1.40755 | + | 2.43795i | −0.0453812 | + | 0.0786026i | ||||
\(963\) | −15.7538 | + | 27.2865i | −0.507660 | + | 0.879294i | ||||
\(964\) | 4.50979 | + | 7.81119i | 0.145251 | + | 0.251582i | ||||
\(965\) | −16.1456 | −0.519745 | ||||||||
\(966\) | 12.9520 | − | 5.41954i | 0.416723 | − | 0.174371i | ||||
\(967\) | 4.50365 | 0.144827 | 0.0724137 | − | 0.997375i | \(-0.476930\pi\) | ||||
0.0724137 | + | 0.997375i | \(0.476930\pi\) | |||||||
\(968\) | −5.57779 | − | 9.66102i | −0.179277 | − | 0.310517i | ||||
\(969\) | 13.6537 | − | 23.6490i | 0.438621 | − | 0.759714i | ||||
\(970\) | −34.8988 | + | 60.4465i | −1.12053 | + | 1.94082i | ||||
\(971\) | −15.2094 | − | 26.3435i | −0.488094 | − | 0.845403i | 0.511813 | − | 0.859097i | \(-0.328974\pi\) |
−0.999906 | + | 0.0136941i | \(0.995641\pi\) | |||||||
\(972\) | 21.9791 | 0.704981 | ||||||||
\(973\) | 1.31241 | − | 10.2536i | 0.0420740 | − | 0.328715i | ||||
\(974\) | 7.89345 | 0.252923 | ||||||||
\(975\) | −28.3922 | − | 49.1767i | −0.909278 | − | 1.57491i | ||||
\(976\) | −5.70959 | + | 9.88930i | −0.182760 | + | 0.316549i | ||||
\(977\) | −18.7601 | + | 32.4935i | −0.600189 | + | 1.03956i | 0.392603 | + | 0.919708i | \(0.371575\pi\) |
−0.992792 | + | 0.119850i | \(0.961759\pi\) | |||||||
\(978\) | −13.2856 | − | 23.0113i | −0.424826 | − | 0.735820i | ||||
\(979\) | −62.4434 | −1.99570 | ||||||||
\(980\) | −28.0693 | − | 7.30513i | −0.896640 | − | 0.233354i | ||||
\(981\) | 18.0864 | 0.577454 | ||||||||
\(982\) | 18.8625 | + | 32.6708i | 0.601926 | + | 1.04257i | ||||
\(983\) | −21.7439 | + | 37.6615i | −0.693523 | + | 1.20122i | 0.277153 | + | 0.960826i | \(0.410609\pi\) |
−0.970676 | + | 0.240391i | \(0.922724\pi\) | |||||||
\(984\) | 12.7912 | − | 22.1551i | 0.407770 | − | 0.706278i | ||||
\(985\) | −32.2411 | − | 55.8432i | −1.02729 | − | 1.77931i | ||||
\(986\) | −2.76714 | −0.0881238 | ||||||||
\(987\) | 9.62308 | − | 75.1832i | 0.306306 | − | 2.39311i | ||||
\(988\) | −7.71964 | −0.245595 | ||||||||
\(989\) | 8.52258 | + | 14.7615i | 0.271002 | + | 0.469390i | ||||
\(990\) | 28.9188 | − | 50.0888i | 0.919100 | − | 1.59193i | ||||
\(991\) | 27.7099 | − | 47.9949i | 0.880233 | − | 1.52461i | 0.0291517 | − | 0.999575i | \(-0.490719\pi\) |
0.851081 | − | 0.525034i | \(-0.175947\pi\) | |||||||
\(992\) | 0.484522 | + | 0.839217i | 0.0153836 | + | 0.0266452i | ||||
\(993\) | −11.4392 | −0.363013 | ||||||||
\(994\) | −15.2459 | + | 6.37940i | −0.483571 | + | 0.202342i | ||||
\(995\) | 101.820 | 3.22790 | ||||||||
\(996\) | −7.40065 | − | 12.8183i | −0.234499 | − | 0.406164i | ||||
\(997\) | 11.9445 | − | 20.6884i | 0.378285 | − | 0.655209i | −0.612528 | − | 0.790449i | \(-0.709847\pi\) |
0.990813 | + | 0.135240i | \(0.0431805\pi\) | |||||||
\(998\) | 4.23971 | − | 7.34340i | 0.134206 | − | 0.232451i | ||||
\(999\) | 0.0619938 | + | 0.107376i | 0.00196140 | + | 0.00339724i |
(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 | 406.2.e.a.291.5 | yes | 10 | |
7.2 | even | 3 | inner | 406.2.e.a.233.5 | ✓ | 10 | |
7.3 | odd | 6 | 2842.2.a.x.1.5 | 5 | |||
7.4 | even | 3 | 2842.2.a.z.1.1 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
406.2.e.a.233.5 | ✓ | 10 | 7.2 | even | 3 | inner | |
406.2.e.a.291.5 | yes | 10 | 1.1 | even | 1 | trivial | |
2842.2.a.x.1.5 | 5 | 7.3 | odd | 6 | |||
2842.2.a.z.1.1 | 5 | 7.4 | even | 3 |