Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [930,2,Mod(481,930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(930, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("930.481");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 930.n (of order \(5\), degree \(4\), 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: | \(7.42608738798\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.13140625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 481.2 | ||
Root | \(-0.386111 + 0.280526i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 930.481 |
Dual form | 930.2.n.a.901.2 |
$q$-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 \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).
\(n\) | \(187\) | \(311\) | \(871\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.809017 | + | 0.587785i | −0.572061 | + | 0.415627i | ||||
\(3\) | 0.809017 | + | 0.587785i | 0.467086 | + | 0.339358i | ||||
\(4\) | 0.309017 | − | 0.951057i | 0.154508 | − | 0.475528i | ||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −0.0268854 | + | 0.0827449i | −0.0101617 | + | 0.0312746i | −0.956009 | − | 0.293338i | \(-0.905234\pi\) |
0.945847 | + | 0.324613i | \(0.105234\pi\) | |||||||
\(8\) | 0.309017 | + | 0.951057i | 0.109254 | + | 0.336249i | ||||
\(9\) | 0.309017 | + | 0.951057i | 0.103006 | + | 0.317019i | ||||
\(10\) | −0.809017 | + | 0.587785i | −0.255834 | + | 0.185874i | ||||
\(11\) | 1.49878 | − | 4.61276i | 0.451898 | − | 1.39080i | −0.422840 | − | 0.906204i | \(-0.638967\pi\) |
0.874738 | − | 0.484596i | \(-0.161033\pi\) | |||||||
\(12\) | 0.809017 | − | 0.587785i | 0.233543 | − | 0.169679i | ||||
\(13\) | 0.724576 | + | 0.526435i | 0.200961 | + | 0.146007i | 0.683715 | − | 0.729749i | \(-0.260363\pi\) |
−0.482753 | + | 0.875756i | \(0.660363\pi\) | |||||||
\(14\) | −0.0268854 | − | 0.0827449i | −0.00718544 | − | 0.0221145i | ||||
\(15\) | 0.809017 | + | 0.587785i | 0.208887 | + | 0.151765i | ||||
\(16\) | −0.809017 | − | 0.587785i | −0.202254 | − | 0.146946i | ||||
\(17\) | 0.634650 | + | 1.95325i | 0.153925 | + | 0.473733i | 0.998050 | − | 0.0624129i | \(-0.0198796\pi\) |
−0.844125 | + | 0.536146i | \(0.819880\pi\) | |||||||
\(18\) | −0.809017 | − | 0.587785i | −0.190687 | − | 0.138542i | ||||
\(19\) | 3.67653 | − | 2.67116i | 0.843455 | − | 0.612806i | −0.0798789 | − | 0.996805i | \(-0.525453\pi\) |
0.923334 | + | 0.383999i | \(0.125453\pi\) | |||||||
\(20\) | 0.309017 | − | 0.951057i | 0.0690983 | − | 0.212663i | ||||
\(21\) | −0.0703870 | + | 0.0511391i | −0.0153597 | + | 0.0111595i | ||||
\(22\) | 1.49878 | + | 4.61276i | 0.319540 | + | 0.983444i | ||||
\(23\) | −0.583218 | − | 1.79496i | −0.121609 | − | 0.374275i | 0.871659 | − | 0.490113i | \(-0.163045\pi\) |
−0.993268 | + | 0.115838i | \(0.963045\pi\) | |||||||
\(24\) | −0.309017 | + | 0.951057i | −0.0630778 | + | 0.194134i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −0.895625 | −0.175647 | ||||||||
\(27\) | −0.309017 | + | 0.951057i | −0.0594703 | + | 0.183031i | ||||
\(28\) | 0.0703870 | + | 0.0511391i | 0.0133019 | + | 0.00966439i | ||||
\(29\) | 5.84892 | − | 4.24949i | 1.08612 | − | 0.789111i | 0.107378 | − | 0.994218i | \(-0.465754\pi\) |
0.978739 | + | 0.205108i | \(0.0657544\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | −3.10078 | + | 4.62441i | −0.556916 | + | 0.830569i | ||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 3.92385 | − | 2.85084i | 0.683055 | − | 0.496268i | ||||
\(34\) | −1.66154 | − | 1.20718i | −0.284951 | − | 0.207029i | ||||
\(35\) | −0.0268854 | + | 0.0827449i | −0.00454447 | + | 0.0139864i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 2.92641 | 0.481099 | 0.240550 | − | 0.970637i | \(-0.422672\pi\) | ||||
0.240550 | + | 0.970637i | \(0.422672\pi\) | |||||||
\(38\) | −1.40431 | + | 4.32202i | −0.227809 | + | 0.701125i | ||||
\(39\) | 0.276763 | + | 0.851790i | 0.0443176 | + | 0.136396i | ||||
\(40\) | 0.309017 | + | 0.951057i | 0.0488599 | + | 0.150375i | ||||
\(41\) | 3.41620 | − | 2.48201i | 0.533521 | − | 0.387625i | −0.288152 | − | 0.957585i | \(-0.593041\pi\) |
0.821673 | + | 0.569959i | \(0.193041\pi\) | |||||||
\(42\) | 0.0268854 | − | 0.0827449i | 0.00414851 | − | 0.0127678i | ||||
\(43\) | −4.99073 | + | 3.62598i | −0.761079 | + | 0.552956i | −0.899241 | − | 0.437453i | \(-0.855881\pi\) |
0.138162 | + | 0.990410i | \(0.455881\pi\) | |||||||
\(44\) | −3.92385 | − | 2.85084i | −0.591543 | − | 0.429781i | ||||
\(45\) | 0.309017 | + | 0.951057i | 0.0460655 | + | 0.141775i | ||||
\(46\) | 1.52689 | + | 1.10935i | 0.225127 | + | 0.163564i | ||||
\(47\) | 2.86401 | + | 2.08083i | 0.417759 | + | 0.303520i | 0.776735 | − | 0.629827i | \(-0.216874\pi\) |
−0.358977 | + | 0.933347i | \(0.616874\pi\) | |||||||
\(48\) | −0.309017 | − | 0.951057i | −0.0446028 | − | 0.137273i | ||||
\(49\) | 5.65700 | + | 4.11005i | 0.808142 | + | 0.587150i | ||||
\(50\) | −0.809017 | + | 0.587785i | −0.114412 | + | 0.0831254i | ||||
\(51\) | −0.634650 | + | 1.95325i | −0.0888688 | + | 0.273510i | ||||
\(52\) | 0.724576 | − | 0.526435i | 0.100481 | − | 0.0730034i | ||||
\(53\) | −2.11191 | − | 6.49979i | −0.290093 | − | 0.892815i | −0.984826 | − | 0.173547i | \(-0.944477\pi\) |
0.694732 | − | 0.719268i | \(-0.255523\pi\) | |||||||
\(54\) | −0.309017 | − | 0.951057i | −0.0420519 | − | 0.129422i | ||||
\(55\) | 1.49878 | − | 4.61276i | 0.202095 | − | 0.621985i | ||||
\(56\) | −0.0870031 | −0.0116263 | ||||||||
\(57\) | 4.54445 | 0.601927 | ||||||||
\(58\) | −2.23409 | + | 6.87582i | −0.293350 | + | 0.902839i | ||||
\(59\) | −1.75165 | − | 1.27265i | −0.228045 | − | 0.165685i | 0.467895 | − | 0.883784i | \(-0.345012\pi\) |
−0.695941 | + | 0.718099i | \(0.745012\pi\) | |||||||
\(60\) | 0.809017 | − | 0.587785i | 0.104444 | − | 0.0758827i | ||||
\(61\) | −4.85410 | −0.621504 | −0.310752 | − | 0.950491i | \(-0.600581\pi\) | ||||
−0.310752 | + | 0.950491i | \(0.600581\pi\) | |||||||
\(62\) | −0.209578 | − | 5.56382i | −0.0266164 | − | 0.706606i | ||||
\(63\) | −0.0870031 | −0.0109614 | ||||||||
\(64\) | −0.809017 | + | 0.587785i | −0.101127 | + | 0.0734732i | ||||
\(65\) | 0.724576 | + | 0.526435i | 0.0898726 | + | 0.0652963i | ||||
\(66\) | −1.49878 | + | 4.61276i | −0.184487 | + | 0.567792i | ||||
\(67\) | 14.6191 | 1.78601 | 0.893006 | − | 0.450045i | \(-0.148592\pi\) | ||||
0.893006 | + | 0.450045i | \(0.148592\pi\) | |||||||
\(68\) | 2.05377 | 0.249056 | ||||||||
\(69\) | 0.583218 | − | 1.79496i | 0.0702112 | − | 0.216088i | ||||
\(70\) | −0.0268854 | − | 0.0827449i | −0.00321342 | − | 0.00988990i | ||||
\(71\) | −4.42590 | − | 13.6215i | −0.525258 | − | 1.61658i | −0.763806 | − | 0.645446i | \(-0.776671\pi\) |
0.238548 | − | 0.971131i | \(-0.423329\pi\) | |||||||
\(72\) | −0.809017 | + | 0.587785i | −0.0953436 | + | 0.0692712i | ||||
\(73\) | −2.92973 | + | 9.01678i | −0.342899 | + | 1.05533i | 0.619800 | + | 0.784760i | \(0.287214\pi\) |
−0.962699 | + | 0.270575i | \(0.912786\pi\) | |||||||
\(74\) | −2.36752 | + | 1.72010i | −0.275218 | + | 0.199958i | ||||
\(75\) | 0.809017 | + | 0.587785i | 0.0934172 | + | 0.0678716i | ||||
\(76\) | −1.40431 | − | 4.32202i | −0.161086 | − | 0.495770i | ||||
\(77\) | 0.341387 | + | 0.248032i | 0.0389047 | + | 0.0282659i | ||||
\(78\) | −0.724576 | − | 0.526435i | −0.0820421 | − | 0.0596070i | ||||
\(79\) | 3.51524 | + | 10.8188i | 0.395496 | + | 1.21721i | 0.928575 | + | 0.371145i | \(0.121035\pi\) |
−0.533079 | + | 0.846065i | \(0.678965\pi\) | |||||||
\(80\) | −0.809017 | − | 0.587785i | −0.0904508 | − | 0.0657164i | ||||
\(81\) | −0.809017 | + | 0.587785i | −0.0898908 | + | 0.0653095i | ||||
\(82\) | −1.30487 | + | 4.01598i | −0.144099 | + | 0.443491i | ||||
\(83\) | 2.42168 | − | 1.75946i | 0.265814 | − | 0.193125i | −0.446892 | − | 0.894588i | \(-0.647469\pi\) |
0.712706 | + | 0.701463i | \(0.247469\pi\) | |||||||
\(84\) | 0.0268854 | + | 0.0827449i | 0.00293344 | + | 0.00902821i | ||||
\(85\) | 0.634650 | + | 1.95325i | 0.0688375 | + | 0.211860i | ||||
\(86\) | 1.90629 | − | 5.86696i | 0.205560 | − | 0.632650i | ||||
\(87\) | 7.22967 | 0.775102 | ||||||||
\(88\) | 4.85015 | 0.517027 | ||||||||
\(89\) | −2.03384 | + | 6.25951i | −0.215586 | + | 0.663506i | 0.783525 | + | 0.621360i | \(0.213420\pi\) |
−0.999111 | + | 0.0421463i | \(0.986580\pi\) | |||||||
\(90\) | −0.809017 | − | 0.587785i | −0.0852779 | − | 0.0619580i | ||||
\(91\) | −0.0630404 | + | 0.0458015i | −0.00660843 | + | 0.00480130i | ||||
\(92\) | −1.88733 | −0.196768 | ||||||||
\(93\) | −5.22674 | + | 1.91863i | −0.541988 | + | 0.198953i | ||||
\(94\) | −3.54011 | −0.365135 | ||||||||
\(95\) | 3.67653 | − | 2.67116i | 0.377204 | − | 0.274055i | ||||
\(96\) | 0.809017 | + | 0.587785i | 0.0825700 | + | 0.0599906i | ||||
\(97\) | −3.84920 | + | 11.8466i | −0.390827 | + | 1.20284i | 0.541337 | + | 0.840806i | \(0.317918\pi\) |
−0.932164 | + | 0.362036i | \(0.882082\pi\) | |||||||
\(98\) | −6.99243 | −0.706342 | ||||||||
\(99\) | 4.85015 | 0.487458 | ||||||||
\(100\) | 0.309017 | − | 0.951057i | 0.0309017 | − | 0.0951057i | ||||
\(101\) | 0.576339 | + | 1.77379i | 0.0573478 | + | 0.176499i | 0.975627 | − | 0.219435i | \(-0.0704212\pi\) |
−0.918279 | + | 0.395933i | \(0.870421\pi\) | |||||||
\(102\) | −0.634650 | − | 1.95325i | −0.0628397 | − | 0.193401i | ||||
\(103\) | 3.97253 | − | 2.88621i | 0.391425 | − | 0.284387i | −0.374614 | − | 0.927181i | \(-0.622225\pi\) |
0.766039 | + | 0.642794i | \(0.222225\pi\) | |||||||
\(104\) | −0.276763 | + | 0.851790i | −0.0271389 | + | 0.0835249i | ||||
\(105\) | −0.0703870 | + | 0.0511391i | −0.00686907 | + | 0.00499067i | ||||
\(106\) | 5.52905 | + | 4.01709i | 0.537029 | + | 0.390174i | ||||
\(107\) | −2.13706 | − | 6.57720i | −0.206598 | − | 0.635842i | −0.999644 | − | 0.0266806i | \(-0.991506\pi\) |
0.793047 | − | 0.609161i | \(-0.208494\pi\) | |||||||
\(108\) | 0.809017 | + | 0.587785i | 0.0778477 | + | 0.0565597i | ||||
\(109\) | 1.00887 | + | 0.732990i | 0.0966326 | + | 0.0702077i | 0.635052 | − | 0.772469i | \(-0.280978\pi\) |
−0.538420 | + | 0.842677i | \(0.680978\pi\) | |||||||
\(110\) | 1.49878 | + | 4.61276i | 0.142903 | + | 0.439810i | ||||
\(111\) | 2.36752 | + | 1.72010i | 0.224715 | + | 0.163265i | ||||
\(112\) | 0.0703870 | − | 0.0511391i | 0.00665095 | − | 0.00483220i | ||||
\(113\) | −5.48216 | + | 16.8724i | −0.515718 | + | 1.58722i | 0.266253 | + | 0.963903i | \(0.414214\pi\) |
−0.781971 | + | 0.623315i | \(0.785786\pi\) | |||||||
\(114\) | −3.67653 | + | 2.67116i | −0.344339 | + | 0.250177i | ||||
\(115\) | −0.583218 | − | 1.79496i | −0.0543854 | − | 0.167381i | ||||
\(116\) | −2.23409 | − | 6.87582i | −0.207430 | − | 0.638404i | ||||
\(117\) | −0.276763 | + | 0.851790i | −0.0255868 | + | 0.0787480i | ||||
\(118\) | 2.16516 | 0.199319 | ||||||||
\(119\) | −0.178684 | −0.0163800 | ||||||||
\(120\) | −0.309017 | + | 0.951057i | −0.0282093 | + | 0.0868192i | ||||
\(121\) | −10.1321 | − | 7.36137i | −0.921096 | − | 0.669215i | ||||
\(122\) | 3.92705 | − | 2.85317i | 0.355538 | − | 0.258314i | ||||
\(123\) | 4.22265 | 0.380744 | ||||||||
\(124\) | 3.43988 | + | 4.37804i | 0.308911 | + | 0.393159i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0.0703870 | − | 0.0511391i | 0.00627057 | − | 0.00455584i | ||||
\(127\) | 12.7832 | + | 9.28756i | 1.13433 | + | 0.824138i | 0.986319 | − | 0.164848i | \(-0.0527134\pi\) |
0.148009 | + | 0.988986i | \(0.452713\pi\) | |||||||
\(128\) | 0.309017 | − | 0.951057i | 0.0273135 | − | 0.0840623i | ||||
\(129\) | −6.16888 | −0.543140 | ||||||||
\(130\) | −0.895625 | −0.0785515 | ||||||||
\(131\) | −1.39796 | + | 4.30249i | −0.122141 | + | 0.375910i | −0.993369 | − | 0.114967i | \(-0.963324\pi\) |
0.871229 | + | 0.490878i | \(0.163324\pi\) | |||||||
\(132\) | −1.49878 | − | 4.61276i | −0.130452 | − | 0.401489i | ||||
\(133\) | 0.122179 | + | 0.376030i | 0.0105943 | + | 0.0326059i | ||||
\(134\) | −11.8271 | + | 8.59291i | −1.02171 | + | 0.742314i | ||||
\(135\) | −0.309017 | + | 0.951057i | −0.0265959 | + | 0.0818539i | ||||
\(136\) | −1.66154 | + | 1.20718i | −0.142475 | + | 0.103515i | ||||
\(137\) | 8.64492 | + | 6.28090i | 0.738585 | + | 0.536614i | 0.892268 | − | 0.451507i | \(-0.149113\pi\) |
−0.153682 | + | 0.988120i | \(0.549113\pi\) | |||||||
\(138\) | 0.583218 | + | 1.79496i | 0.0496468 | + | 0.152797i | ||||
\(139\) | −11.0169 | − | 8.00424i | −0.934440 | − | 0.678911i | 0.0126358 | − | 0.999920i | \(-0.495978\pi\) |
−0.947076 | + | 0.321010i | \(0.895978\pi\) | |||||||
\(140\) | 0.0703870 | + | 0.0511391i | 0.00594879 | + | 0.00432205i | ||||
\(141\) | 1.09395 | + | 3.36685i | 0.0921276 | + | 0.283540i | ||||
\(142\) | 11.5872 | + | 8.41856i | 0.972373 | + | 0.706470i | ||||
\(143\) | 3.51430 | − | 2.55329i | 0.293880 | − | 0.213517i | ||||
\(144\) | 0.309017 | − | 0.951057i | 0.0257514 | − | 0.0792547i | ||||
\(145\) | 5.84892 | − | 4.24949i | 0.485727 | − | 0.352901i | ||||
\(146\) | −2.92973 | − | 9.01678i | −0.242466 | − | 0.746234i | ||||
\(147\) | 2.16078 | + | 6.65020i | 0.178218 | + | 0.548499i | ||||
\(148\) | 0.904311 | − | 2.78318i | 0.0743339 | − | 0.228776i | ||||
\(149\) | −9.98720 | −0.818183 | −0.409091 | − | 0.912493i | \(-0.634154\pi\) | ||||
−0.409091 | + | 0.912493i | \(0.634154\pi\) | |||||||
\(150\) | −1.00000 | −0.0816497 | ||||||||
\(151\) | 3.47265 | − | 10.6877i | 0.282600 | − | 0.869754i | −0.704508 | − | 0.709696i | \(-0.748832\pi\) |
0.987108 | − | 0.160057i | \(-0.0511679\pi\) | |||||||
\(152\) | 3.67653 | + | 2.67116i | 0.298206 | + | 0.216660i | ||||
\(153\) | −1.66154 | + | 1.20718i | −0.134327 | + | 0.0975944i | ||||
\(154\) | −0.421978 | −0.0340039 | ||||||||
\(155\) | −3.10078 | + | 4.62441i | −0.249061 | + | 0.371442i | ||||
\(156\) | 0.895625 | 0.0717074 | ||||||||
\(157\) | −0.109743 | + | 0.0797330i | −0.00875845 | + | 0.00636339i | −0.592156 | − | 0.805823i | \(-0.701723\pi\) |
0.583397 | + | 0.812187i | \(0.301723\pi\) | |||||||
\(158\) | −9.20302 | − | 6.68639i | −0.732153 | − | 0.531941i | ||||
\(159\) | 2.11191 | − | 6.49979i | 0.167485 | − | 0.515467i | ||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 0.164204 | 0.0129411 | ||||||||
\(162\) | 0.309017 | − | 0.951057i | 0.0242787 | − | 0.0747221i | ||||
\(163\) | −4.50094 | − | 13.8525i | −0.352541 | − | 1.08501i | −0.957421 | − | 0.288694i | \(-0.906779\pi\) |
0.604880 | − | 0.796316i | \(-0.293221\pi\) | |||||||
\(164\) | −1.30487 | − | 4.01598i | −0.101893 | − | 0.313595i | ||||
\(165\) | 3.92385 | − | 2.85084i | 0.305471 | − | 0.221938i | ||||
\(166\) | −0.925001 | + | 2.84686i | −0.0717940 | + | 0.220959i | ||||
\(167\) | −10.0053 | + | 7.26930i | −0.774236 | + | 0.562515i | −0.903244 | − | 0.429128i | \(-0.858821\pi\) |
0.129008 | + | 0.991644i | \(0.458821\pi\) | |||||||
\(168\) | −0.0703870 | − | 0.0511391i | −0.00543047 | − | 0.00394547i | ||||
\(169\) | −3.76934 | − | 11.6009i | −0.289950 | − | 0.892373i | ||||
\(170\) | −1.66154 | − | 1.20718i | −0.127434 | − | 0.0925862i | ||||
\(171\) | 3.67653 | + | 2.67116i | 0.281152 | + | 0.204269i | ||||
\(172\) | 1.90629 | + | 5.86696i | 0.145353 | + | 0.447351i | ||||
\(173\) | −14.4624 | − | 10.5076i | −1.09956 | − | 0.798875i | −0.118570 | − | 0.992946i | \(-0.537831\pi\) |
−0.980988 | + | 0.194071i | \(0.937831\pi\) | |||||||
\(174\) | −5.84892 | + | 4.24949i | −0.443406 | + | 0.322153i | ||||
\(175\) | −0.0268854 | + | 0.0827449i | −0.00203235 | + | 0.00625492i | ||||
\(176\) | −3.92385 | + | 2.85084i | −0.295771 | + | 0.214890i | ||||
\(177\) | −0.669071 | − | 2.05919i | −0.0502904 | − | 0.154778i | ||||
\(178\) | −2.03384 | − | 6.25951i | −0.152443 | − | 0.469170i | ||||
\(179\) | 7.65653 | − | 23.5644i | 0.572276 | − | 1.76128i | −0.0729978 | − | 0.997332i | \(-0.523257\pi\) |
0.645274 | − | 0.763952i | \(-0.276743\pi\) | |||||||
\(180\) | 1.00000 | 0.0745356 | ||||||||
\(181\) | −10.0153 | −0.744432 | −0.372216 | − | 0.928146i | \(-0.621402\pi\) | ||||
−0.372216 | + | 0.928146i | \(0.621402\pi\) | |||||||
\(182\) | 0.0240793 | − | 0.0741084i | 0.00178487 | − | 0.00549328i | ||||
\(183\) | −3.92705 | − | 2.85317i | −0.290296 | − | 0.210912i | ||||
\(184\) | 1.52689 | − | 1.10935i | 0.112563 | − | 0.0817822i | ||||
\(185\) | 2.92641 | 0.215154 | ||||||||
\(186\) | 3.10078 | − | 4.62441i | 0.227360 | − | 0.339078i | ||||
\(187\) | 9.96109 | 0.728427 | ||||||||
\(188\) | 2.86401 | − | 2.08083i | 0.208879 | − | 0.151760i | ||||
\(189\) | −0.0703870 | − | 0.0511391i | −0.00511990 | − | 0.00371983i | ||||
\(190\) | −1.40431 | + | 4.32202i | −0.101879 | + | 0.313553i | ||||
\(191\) | −12.5405 | −0.907398 | −0.453699 | − | 0.891155i | \(-0.649896\pi\) | ||||
−0.453699 | + | 0.891155i | \(0.649896\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −0.505485 | + | 1.55572i | −0.0363856 | + | 0.111983i | −0.967600 | − | 0.252489i | \(-0.918751\pi\) |
0.931214 | + | 0.364473i | \(0.118751\pi\) | |||||||
\(194\) | −3.84920 | − | 11.8466i | −0.276357 | − | 0.850538i | ||||
\(195\) | 0.276763 | + | 0.851790i | 0.0198194 | + | 0.0609980i | ||||
\(196\) | 5.65700 | − | 4.11005i | 0.404071 | − | 0.293575i | ||||
\(197\) | 3.82236 | − | 11.7640i | 0.272332 | − | 0.838151i | −0.717581 | − | 0.696475i | \(-0.754751\pi\) |
0.989913 | − | 0.141676i | \(-0.0452492\pi\) | |||||||
\(198\) | −3.92385 | + | 2.85084i | −0.278856 | + | 0.202601i | ||||
\(199\) | −5.53350 | − | 4.02033i | −0.392260 | − | 0.284993i | 0.374121 | − | 0.927380i | \(-0.377944\pi\) |
−0.766381 | + | 0.642387i | \(0.777944\pi\) | |||||||
\(200\) | 0.309017 | + | 0.951057i | 0.0218508 | + | 0.0672499i | ||||
\(201\) | 11.8271 | + | 8.59291i | 0.834221 | + | 0.606097i | ||||
\(202\) | −1.50887 | − | 1.09626i | −0.106164 | − | 0.0771327i | ||||
\(203\) | 0.194373 | + | 0.598218i | 0.0136423 | + | 0.0419867i | ||||
\(204\) | 1.66154 | + | 1.20718i | 0.116331 | + | 0.0845192i | ||||
\(205\) | 3.41620 | − | 2.48201i | 0.238598 | − | 0.173351i | ||||
\(206\) | −1.51737 | + | 4.66999i | −0.105720 | + | 0.325374i | ||||
\(207\) | 1.52689 | − | 1.10935i | 0.106126 | − | 0.0771050i | ||||
\(208\) | −0.276763 | − | 0.851790i | −0.0191901 | − | 0.0590610i | ||||
\(209\) | −6.81111 | − | 20.9624i | −0.471134 | − | 1.45000i | ||||
\(210\) | 0.0268854 | − | 0.0827449i | 0.00185527 | − | 0.00570994i | ||||
\(211\) | −20.0023 | −1.37701 | −0.688506 | − | 0.725230i | \(-0.741733\pi\) | ||||
−0.688506 | + | 0.725230i | \(0.741733\pi\) | |||||||
\(212\) | −6.83428 | −0.469381 | ||||||||
\(213\) | 4.42590 | − | 13.6215i | 0.303258 | − | 0.933331i | ||||
\(214\) | 5.59490 | + | 4.06493i | 0.382459 | + | 0.277873i | ||||
\(215\) | −4.99073 | + | 3.62598i | −0.340365 | + | 0.247290i | ||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −0.299280 | − | 0.380903i | −0.0203165 | − | 0.0258574i | ||||
\(218\) | −1.24704 | −0.0844600 | ||||||||
\(219\) | −7.67013 | + | 5.57268i | −0.518299 | + | 0.376567i | ||||
\(220\) | −3.92385 | − | 2.85084i | −0.264546 | − | 0.192204i | ||||
\(221\) | −0.568409 | + | 1.74938i | −0.0382353 | + | 0.117676i | ||||
\(222\) | −2.92641 | −0.196408 | ||||||||
\(223\) | −25.4270 | −1.70272 | −0.851358 | − | 0.524586i | \(-0.824220\pi\) | ||||
−0.851358 | + | 0.524586i | \(0.824220\pi\) | |||||||
\(224\) | −0.0268854 | + | 0.0827449i | −0.00179636 | + | 0.00552862i | ||||
\(225\) | 0.309017 | + | 0.951057i | 0.0206011 | + | 0.0634038i | ||||
\(226\) | −5.48216 | − | 16.8724i | −0.364668 | − | 1.12233i | ||||
\(227\) | 4.10813 | − | 2.98473i | 0.272666 | − | 0.198103i | −0.443046 | − | 0.896499i | \(-0.646102\pi\) |
0.715712 | + | 0.698395i | \(0.246102\pi\) | |||||||
\(228\) | 1.40431 | − | 4.32202i | 0.0930028 | − | 0.286233i | ||||
\(229\) | −16.0261 | + | 11.6436i | −1.05903 | + | 0.769433i | −0.973909 | − | 0.226937i | \(-0.927129\pi\) |
−0.0851247 | + | 0.996370i | \(0.527129\pi\) | |||||||
\(230\) | 1.52689 | + | 1.10935i | 0.100680 | + | 0.0731482i | ||||
\(231\) | 0.130398 | + | 0.401325i | 0.00857958 | + | 0.0264052i | ||||
\(232\) | 5.84892 | + | 4.24949i | 0.384001 | + | 0.278993i | ||||
\(233\) | 6.31789 | + | 4.59022i | 0.413899 | + | 0.300715i | 0.775178 | − | 0.631742i | \(-0.217660\pi\) |
−0.361280 | + | 0.932458i | \(0.617660\pi\) | |||||||
\(234\) | −0.276763 | − | 0.851790i | −0.0180926 | − | 0.0556833i | ||||
\(235\) | 2.86401 | + | 2.08083i | 0.186827 | + | 0.135738i | ||||
\(236\) | −1.75165 | + | 1.27265i | −0.114023 | + | 0.0828423i | ||||
\(237\) | −3.51524 | + | 10.8188i | −0.228340 | + | 0.702757i | ||||
\(238\) | 0.144559 | − | 0.105028i | 0.00937035 | − | 0.00680796i | ||||
\(239\) | 1.30377 | + | 4.01258i | 0.0843336 | + | 0.259552i | 0.984327 | − | 0.176351i | \(-0.0564292\pi\) |
−0.899994 | + | 0.435903i | \(0.856429\pi\) | |||||||
\(240\) | −0.309017 | − | 0.951057i | −0.0199470 | − | 0.0613904i | ||||
\(241\) | −5.95805 | + | 18.3370i | −0.383792 | + | 1.18119i | 0.553562 | + | 0.832808i | \(0.313268\pi\) |
−0.937353 | + | 0.348381i | \(0.886732\pi\) | |||||||
\(242\) | 12.5239 | 0.805067 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −1.50000 | + | 4.61653i | −0.0960277 | + | 0.295543i | ||||
\(245\) | 5.65700 | + | 4.11005i | 0.361412 | + | 0.262581i | ||||
\(246\) | −3.41620 | + | 2.48201i | −0.217809 | + | 0.158247i | ||||
\(247\) | 4.07012 | 0.258976 | ||||||||
\(248\) | −5.35627 | − | 1.51999i | −0.340123 | − | 0.0965197i | ||||
\(249\) | 2.99336 | 0.189697 | ||||||||
\(250\) | −0.809017 | + | 0.587785i | −0.0511667 | + | 0.0371748i | ||||
\(251\) | 6.85702 | + | 4.98192i | 0.432812 | + | 0.314456i | 0.782772 | − | 0.622308i | \(-0.213805\pi\) |
−0.349961 | + | 0.936764i | \(0.613805\pi\) | |||||||
\(252\) | −0.0268854 | + | 0.0827449i | −0.00169362 | + | 0.00521244i | ||||
\(253\) | −9.15384 | −0.575497 | ||||||||
\(254\) | −15.8009 | −0.991439 | ||||||||
\(255\) | −0.634650 | + | 1.95325i | −0.0397433 | + | 0.122317i | ||||
\(256\) | 0.309017 | + | 0.951057i | 0.0193136 | + | 0.0594410i | ||||
\(257\) | −2.70050 | − | 8.31127i | −0.168452 | − | 0.518443i | 0.830822 | − | 0.556539i | \(-0.187871\pi\) |
−0.999274 | + | 0.0380956i | \(0.987871\pi\) | |||||||
\(258\) | 4.99073 | − | 3.62598i | 0.310709 | − | 0.225744i | ||||
\(259\) | −0.0786779 | + | 0.242146i | −0.00488880 | + | 0.0150462i | ||||
\(260\) | 0.724576 | − | 0.526435i | 0.0449363 | − | 0.0326481i | ||||
\(261\) | 5.84892 | + | 4.24949i | 0.362039 | + | 0.263037i | ||||
\(262\) | −1.39796 | − | 4.30249i | −0.0863665 | − | 0.265809i | ||||
\(263\) | −3.46568 | − | 2.51796i | −0.213703 | − | 0.155264i | 0.475785 | − | 0.879562i | \(-0.342164\pi\) |
−0.689487 | + | 0.724298i | \(0.742164\pi\) | |||||||
\(264\) | 3.92385 | + | 2.85084i | 0.241496 | + | 0.175457i | ||||
\(265\) | −2.11191 | − | 6.49979i | −0.129734 | − | 0.399279i | ||||
\(266\) | −0.319870 | − | 0.232399i | −0.0196125 | − | 0.0142493i | ||||
\(267\) | −5.32465 | + | 3.86859i | −0.325864 | + | 0.236754i | ||||
\(268\) | 4.51756 | − | 13.9036i | 0.275954 | − | 0.849299i | ||||
\(269\) | −7.82081 | + | 5.68215i | −0.476843 | + | 0.346447i | −0.800102 | − | 0.599864i | \(-0.795222\pi\) |
0.323259 | + | 0.946311i | \(0.395222\pi\) | |||||||
\(270\) | −0.309017 | − | 0.951057i | −0.0188062 | − | 0.0578795i | ||||
\(271\) | −7.83428 | − | 24.1114i | −0.475899 | − | 1.46467i | −0.844742 | − | 0.535174i | \(-0.820246\pi\) |
0.368843 | − | 0.929492i | \(-0.379754\pi\) | |||||||
\(272\) | 0.634650 | − | 1.95325i | 0.0384813 | − | 0.118433i | ||||
\(273\) | −0.0779222 | −0.00471606 | ||||||||
\(274\) | −10.6857 | −0.645547 | ||||||||
\(275\) | 1.49878 | − | 4.61276i | 0.0903797 | − | 0.278160i | ||||
\(276\) | −1.52689 | − | 1.10935i | −0.0919077 | − | 0.0667749i | ||||
\(277\) | −21.1613 | + | 15.3746i | −1.27146 | + | 0.923769i | −0.999260 | − | 0.0384719i | \(-0.987751\pi\) |
−0.272199 | + | 0.962241i | \(0.587751\pi\) | |||||||
\(278\) | 13.6176 | 0.816731 | ||||||||
\(279\) | −5.35627 | − | 1.51999i | −0.320671 | − | 0.0909997i | ||||
\(280\) | −0.0870031 | −0.00519943 | ||||||||
\(281\) | 1.14965 | − | 0.835268i | 0.0685823 | − | 0.0498279i | −0.552966 | − | 0.833204i | \(-0.686504\pi\) |
0.621548 | + | 0.783376i | \(0.286504\pi\) | |||||||
\(282\) | −2.86401 | − | 2.08083i | −0.170549 | − | 0.123911i | ||||
\(283\) | 4.40001 | − | 13.5419i | 0.261554 | − | 0.804980i | −0.730914 | − | 0.682470i | \(-0.760906\pi\) |
0.992467 | − | 0.122510i | \(-0.0390942\pi\) | |||||||
\(284\) | −14.3225 | −0.849885 | ||||||||
\(285\) | 4.54445 | 0.269190 | ||||||||
\(286\) | −1.34234 | + | 4.13131i | −0.0793744 | + | 0.244289i | ||||
\(287\) | 0.113528 | + | 0.349403i | 0.00670134 | + | 0.0206246i | ||||
\(288\) | 0.309017 | + | 0.951057i | 0.0182090 | + | 0.0560415i | ||||
\(289\) | 10.3409 | − | 7.51309i | 0.608287 | − | 0.441946i | ||||
\(290\) | −2.23409 | + | 6.87582i | −0.131190 | + | 0.403762i | ||||
\(291\) | −10.0773 | + | 7.32162i | −0.590744 | + | 0.429201i | ||||
\(292\) | 7.67013 | + | 5.57268i | 0.448860 | + | 0.326116i | ||||
\(293\) | 0.622296 | + | 1.91523i | 0.0363549 | + | 0.111889i | 0.967587 | − | 0.252537i | \(-0.0812651\pi\) |
−0.931232 | + | 0.364426i | \(0.881265\pi\) | |||||||
\(294\) | −5.65700 | − | 4.11005i | −0.329923 | − | 0.239703i | ||||
\(295\) | −1.75165 | − | 1.27265i | −0.101985 | − | 0.0740964i | ||||
\(296\) | 0.904311 | + | 2.78318i | 0.0525620 | + | 0.161769i | ||||
\(297\) | 3.92385 | + | 2.85084i | 0.227685 | + | 0.165423i | ||||
\(298\) | 8.07981 | − | 5.87033i | 0.468051 | − | 0.340059i | ||||
\(299\) | 0.522345 | − | 1.60761i | 0.0302080 | − | 0.0929706i | ||||
\(300\) | 0.809017 | − | 0.587785i | 0.0467086 | − | 0.0339358i | ||||
\(301\) | −0.165853 | − | 0.510443i | −0.00955961 | − | 0.0294215i | ||||
\(302\) | 3.47265 | + | 10.6877i | 0.199828 | + | 0.615009i | ||||
\(303\) | −0.576339 | + | 1.77379i | −0.0331098 | + | 0.101901i | ||||
\(304\) | −4.54445 | −0.260642 | ||||||||
\(305\) | −4.85410 | −0.277945 | ||||||||
\(306\) | 0.634650 | − | 1.95325i | 0.0362805 | − | 0.111660i | ||||
\(307\) | 18.8620 | + | 13.7040i | 1.07651 | + | 0.782131i | 0.977071 | − | 0.212913i | \(-0.0682949\pi\) |
0.0994398 | + | 0.995044i | \(0.468295\pi\) | |||||||
\(308\) | 0.341387 | − | 0.248032i | 0.0194523 | − | 0.0141330i | ||||
\(309\) | 4.91032 | 0.279338 | ||||||||
\(310\) | −0.209578 | − | 5.56382i | −0.0119032 | − | 0.316004i | ||||
\(311\) | −22.4709 | −1.27421 | −0.637103 | − | 0.770779i | \(-0.719867\pi\) | ||||
−0.637103 | + | 0.770779i | \(0.719867\pi\) | |||||||
\(312\) | −0.724576 | + | 0.526435i | −0.0410210 | + | 0.0298035i | ||||
\(313\) | −15.5379 | − | 11.2889i | −0.878254 | − | 0.638089i | 0.0545353 | − | 0.998512i | \(-0.482632\pi\) |
−0.932789 | + | 0.360423i | \(0.882632\pi\) | |||||||
\(314\) | 0.0419181 | − | 0.129011i | 0.00236558 | − | 0.00728050i | ||||
\(315\) | −0.0870031 | −0.00490207 | ||||||||
\(316\) | 11.3756 | 0.639925 | ||||||||
\(317\) | 7.21770 | − | 22.2138i | 0.405386 | − | 1.24765i | −0.515186 | − | 0.857078i | \(-0.672277\pi\) |
0.920572 | − | 0.390572i | \(-0.127723\pi\) | |||||||
\(318\) | 2.11191 | + | 6.49979i | 0.118430 | + | 0.364490i | ||||
\(319\) | −10.8357 | − | 33.3487i | −0.606680 | − | 1.86717i | ||||
\(320\) | −0.809017 | + | 0.587785i | −0.0452254 | + | 0.0328582i | ||||
\(321\) | 2.13706 | − | 6.57720i | 0.119279 | − | 0.367103i | ||||
\(322\) | −0.132844 | + | 0.0965167i | −0.00740309 | + | 0.00537866i | ||||
\(323\) | 7.55076 | + | 5.48595i | 0.420135 | + | 0.305246i | ||||
\(324\) | 0.309017 | + | 0.951057i | 0.0171676 | + | 0.0528365i | ||||
\(325\) | 0.724576 | + | 0.526435i | 0.0401922 | + | 0.0292014i | ||||
\(326\) | 11.7836 | + | 8.56130i | 0.652635 | + | 0.474167i | ||||
\(327\) | 0.385356 | + | 1.18600i | 0.0213102 | + | 0.0655861i | ||||
\(328\) | 3.41620 | + | 2.48201i | 0.188628 | + | 0.137046i | ||||
\(329\) | −0.249178 | + | 0.181038i | −0.0137376 | + | 0.00998096i | ||||
\(330\) | −1.49878 | + | 4.61276i | −0.0825050 | + | 0.253924i | ||||
\(331\) | 13.5275 | − | 9.82832i | 0.743540 | − | 0.540213i | −0.150278 | − | 0.988644i | \(-0.548017\pi\) |
0.893818 | + | 0.448430i | \(0.148017\pi\) | |||||||
\(332\) | −0.925001 | − | 2.84686i | −0.0507660 | − | 0.156242i | ||||
\(333\) | 0.904311 | + | 2.78318i | 0.0495559 | + | 0.152517i | ||||
\(334\) | 3.82170 | − | 11.7620i | 0.209114 | − | 0.643587i | ||||
\(335\) | 14.6191 | 0.798729 | ||||||||
\(336\) | 0.0870031 | 0.00474641 | ||||||||
\(337\) | −1.55435 | + | 4.78381i | −0.0846711 | + | 0.260591i | −0.984424 | − | 0.175808i | \(-0.943746\pi\) |
0.899753 | + | 0.436399i | \(0.143746\pi\) | |||||||
\(338\) | 9.86827 | + | 7.16972i | 0.536763 | + | 0.389981i | ||||
\(339\) | −14.3525 | + | 10.4277i | −0.779520 | + | 0.566354i | ||||
\(340\) | 2.05377 | 0.111381 | ||||||||
\(341\) | 16.6839 | + | 21.2341i | 0.903485 | + | 1.14989i | ||||
\(342\) | −4.54445 | −0.245735 | ||||||||
\(343\) | −0.984885 | + | 0.715561i | −0.0531788 | + | 0.0386367i | ||||
\(344\) | −4.99073 | − | 3.62598i | −0.269082 | − | 0.195500i | ||||
\(345\) | 0.583218 | − | 1.79496i | 0.0313994 | − | 0.0966375i | ||||
\(346\) | 17.8765 | 0.961048 | ||||||||
\(347\) | −2.27381 | −0.122065 | −0.0610324 | − | 0.998136i | \(-0.519439\pi\) | ||||
−0.0610324 | + | 0.998136i | \(0.519439\pi\) | |||||||
\(348\) | 2.23409 | − | 6.87582i | 0.119760 | − | 0.368583i | ||||
\(349\) | 8.64111 | + | 26.5946i | 0.462548 | + | 1.42358i | 0.862040 | + | 0.506840i | \(0.169187\pi\) |
−0.399492 | + | 0.916737i | \(0.630813\pi\) | |||||||
\(350\) | −0.0268854 | − | 0.0827449i | −0.00143709 | − | 0.00442290i | ||||
\(351\) | −0.724576 | + | 0.526435i | −0.0386750 | + | 0.0280990i | ||||
\(352\) | 1.49878 | − | 4.61276i | 0.0798851 | − | 0.245861i | ||||
\(353\) | −18.2129 | + | 13.2324i | −0.969375 | + | 0.704292i | −0.955309 | − | 0.295609i | \(-0.904477\pi\) |
−0.0140658 | + | 0.999901i | \(0.504477\pi\) | |||||||
\(354\) | 1.75165 | + | 1.27265i | 0.0930991 | + | 0.0676405i | ||||
\(355\) | −4.42590 | − | 13.6215i | −0.234902 | − | 0.722955i | ||||
\(356\) | 5.32465 | + | 3.86859i | 0.282206 | + | 0.205035i | ||||
\(357\) | −0.144559 | − | 0.105028i | −0.00765086 | − | 0.00555868i | ||||
\(358\) | 7.65653 | + | 23.5644i | 0.404660 | + | 1.24542i | ||||
\(359\) | 1.47771 | + | 1.07362i | 0.0779906 | + | 0.0566635i | 0.626097 | − | 0.779745i | \(-0.284651\pi\) |
−0.548107 | + | 0.836408i | \(0.684651\pi\) | |||||||
\(360\) | −0.809017 | + | 0.587785i | −0.0426389 | + | 0.0309790i | ||||
\(361\) | 0.510492 | − | 1.57113i | 0.0268680 | − | 0.0826912i | ||||
\(362\) | 8.10255 | − | 5.88685i | 0.425861 | − | 0.309406i | ||||
\(363\) | −3.87010 | − | 11.9109i | −0.203128 | − | 0.625162i | ||||
\(364\) | 0.0240793 | + | 0.0741084i | 0.00126210 | + | 0.00388433i | ||||
\(365\) | −2.92973 | + | 9.01678i | −0.153349 | + | 0.471960i | ||||
\(366\) | 4.85410 | 0.253728 | ||||||||
\(367\) | −2.33192 | −0.121725 | −0.0608626 | − | 0.998146i | \(-0.519385\pi\) | ||||
−0.0608626 | + | 0.998146i | \(0.519385\pi\) | |||||||
\(368\) | −0.583218 | + | 1.79496i | −0.0304024 | + | 0.0935688i | ||||
\(369\) | 3.41620 | + | 2.48201i | 0.177840 | + | 0.129208i | ||||
\(370\) | −2.36752 | + | 1.72010i | −0.123081 | + | 0.0894238i | ||||
\(371\) | 0.594604 | 0.0308703 | ||||||||
\(372\) | 0.209578 | + | 5.56382i | 0.0108661 | + | 0.288471i | ||||
\(373\) | 6.96653 | 0.360713 | 0.180357 | − | 0.983601i | \(-0.442275\pi\) | ||||
0.180357 | + | 0.983601i | \(0.442275\pi\) | |||||||
\(374\) | −8.05869 | + | 5.85498i | −0.416705 | + | 0.302754i | ||||
\(375\) | 0.809017 | + | 0.587785i | 0.0417775 | + | 0.0303531i | ||||
\(376\) | −1.09395 | + | 3.36685i | −0.0564164 | + | 0.173632i | ||||
\(377\) | 6.47507 | 0.333483 | ||||||||
\(378\) | 0.0870031 | 0.00447496 | ||||||||
\(379\) | −1.90582 | + | 5.86552i | −0.0978955 | + | 0.301291i | −0.987997 | − | 0.154470i | \(-0.950633\pi\) |
0.890102 | + | 0.455761i | \(0.150633\pi\) | |||||||
\(380\) | −1.40431 | − | 4.32202i | −0.0720396 | − | 0.221715i | ||||
\(381\) | 4.88276 | + | 15.0276i | 0.250151 | + | 0.769887i | ||||
\(382\) | 10.1455 | − | 7.37111i | 0.519087 | − | 0.377139i | ||||
\(383\) | −0.455787 | + | 1.40277i | −0.0232896 | + | 0.0716781i | −0.962026 | − | 0.272958i | \(-0.911998\pi\) |
0.938736 | + | 0.344637i | \(0.111998\pi\) | |||||||
\(384\) | 0.809017 | − | 0.587785i | 0.0412850 | − | 0.0299953i | ||||
\(385\) | 0.341387 | + | 0.248032i | 0.0173987 | + | 0.0126409i | ||||
\(386\) | −0.505485 | − | 1.55572i | −0.0257285 | − | 0.0791842i | ||||
\(387\) | −4.99073 | − | 3.62598i | −0.253693 | − | 0.184319i | ||||
\(388\) | 10.0773 | + | 7.32162i | 0.511599 | + | 0.371699i | ||||
\(389\) | 7.56653 | + | 23.2874i | 0.383638 | + | 1.18072i | 0.937463 | + | 0.348084i | \(0.113168\pi\) |
−0.553825 | + | 0.832633i | \(0.686832\pi\) | |||||||
\(390\) | −0.724576 | − | 0.526435i | −0.0366903 | − | 0.0266571i | ||||
\(391\) | 3.13587 | − | 2.27834i | 0.158588 | − | 0.115221i | ||||
\(392\) | −2.16078 | + | 6.65020i | −0.109136 | + | 0.335886i | ||||
\(393\) | −3.65992 | + | 2.65909i | −0.184618 | + | 0.134133i | ||||
\(394\) | 3.82236 | + | 11.7640i | 0.192568 | + | 0.592662i | ||||
\(395\) | 3.51524 | + | 10.8188i | 0.176871 | + | 0.544353i | ||||
\(396\) | 1.49878 | − | 4.61276i | 0.0753164 | − | 0.231800i | ||||
\(397\) | −1.64693 | −0.0826572 | −0.0413286 | − | 0.999146i | \(-0.513159\pi\) | ||||
−0.0413286 | + | 0.999146i | \(0.513159\pi\) | |||||||
\(398\) | 6.83979 | 0.342847 | ||||||||
\(399\) | −0.122179 | + | 0.376030i | −0.00611662 | + | 0.0188250i | ||||
\(400\) | −0.809017 | − | 0.587785i | −0.0404508 | − | 0.0293893i | ||||
\(401\) | −10.2514 | + | 7.44808i | −0.511931 | + | 0.371939i | −0.813555 | − | 0.581487i | \(-0.802471\pi\) |
0.301625 | + | 0.953427i | \(0.402471\pi\) | |||||||
\(402\) | −14.6191 | −0.729136 | ||||||||
\(403\) | −4.68120 | + | 1.71838i | −0.233187 | + | 0.0855985i | ||||
\(404\) | 1.86507 | 0.0927908 | ||||||||
\(405\) | −0.809017 | + | 0.587785i | −0.0402004 | + | 0.0292073i | ||||
\(406\) | −0.508874 | − | 0.369719i | −0.0252550 | − | 0.0183488i | ||||
\(407\) | 4.38604 | − | 13.4988i | 0.217408 | − | 0.669113i | ||||
\(408\) | −2.05377 | −0.101677 | ||||||||
\(409\) | −2.64425 | −0.130750 | −0.0653750 | − | 0.997861i | \(-0.520824\pi\) | ||||
−0.0653750 | + | 0.997861i | \(0.520824\pi\) | |||||||
\(410\) | −1.30487 | + | 4.01598i | −0.0644430 | + | 0.198335i | ||||
\(411\) | 3.30207 | + | 10.1627i | 0.162879 | + | 0.501290i | ||||
\(412\) | −1.51737 | − | 4.66999i | −0.0747555 | − | 0.230074i | ||||
\(413\) | 0.152399 | − | 0.110724i | 0.00749906 | − | 0.00544839i | ||||
\(414\) | −0.583218 | + | 1.79496i | −0.0286636 | + | 0.0882175i | ||||
\(415\) | 2.42168 | − | 1.75946i | 0.118876 | − | 0.0863683i | ||||
\(416\) | 0.724576 | + | 0.526435i | 0.0355253 | + | 0.0258106i | ||||
\(417\) | −4.20808 | − | 12.9511i | −0.206070 | − | 0.634219i | ||||
\(418\) | 17.8317 | + | 12.9555i | 0.872178 | + | 0.633674i | ||||
\(419\) | −4.10773 | − | 2.98444i | −0.200676 | − | 0.145799i | 0.482909 | − | 0.875670i | \(-0.339580\pi\) |
−0.683585 | + | 0.729871i | \(0.739580\pi\) | |||||||
\(420\) | 0.0268854 | + | 0.0827449i | 0.00131188 | + | 0.00403754i | ||||
\(421\) | −14.6484 | − | 10.6427i | −0.713918 | − | 0.518692i | 0.170518 | − | 0.985355i | \(-0.445456\pi\) |
−0.884435 | + | 0.466663i | \(0.845456\pi\) | |||||||
\(422\) | 16.1822 | − | 11.7570i | 0.787736 | − | 0.572324i | ||||
\(423\) | −1.09395 | + | 3.36685i | −0.0531899 | + | 0.163702i | ||||
\(424\) | 5.52905 | − | 4.01709i | 0.268515 | − | 0.195087i | ||||
\(425\) | 0.634650 | + | 1.95325i | 0.0307851 | + | 0.0947466i | ||||
\(426\) | 4.42590 | + | 13.6215i | 0.214436 | + | 0.659965i | ||||
\(427\) | 0.130505 | − | 0.401652i | 0.00631556 | − | 0.0194373i | ||||
\(428\) | −6.91568 | −0.334282 | ||||||||
\(429\) | 4.34391 | 0.209726 | ||||||||
\(430\) | 1.90629 | − | 5.86696i | 0.0919294 | − | 0.282930i | ||||
\(431\) | 12.3825 | + | 8.99638i | 0.596442 | + | 0.433340i | 0.844614 | − | 0.535376i | \(-0.179830\pi\) |
−0.248172 | + | 0.968716i | \(0.579830\pi\) | |||||||
\(432\) | 0.809017 | − | 0.587785i | 0.0389238 | − | 0.0282798i | ||||
\(433\) | 10.1625 | 0.488378 | 0.244189 | − | 0.969728i | \(-0.421478\pi\) | ||||
0.244189 | + | 0.969728i | \(0.421478\pi\) | |||||||
\(434\) | 0.466012 | + | 0.132244i | 0.0223693 | + | 0.00634793i | ||||
\(435\) | 7.22967 | 0.346636 | ||||||||
\(436\) | 1.00887 | − | 0.732990i | 0.0483163 | − | 0.0351039i | ||||
\(437\) | −6.93885 | − | 5.04137i | −0.331930 | − | 0.241161i | ||||
\(438\) | 2.92973 | − | 9.01678i | 0.139988 | − | 0.430838i | ||||
\(439\) | 12.0628 | 0.575725 | 0.287863 | − | 0.957672i | \(-0.407055\pi\) | ||||
0.287863 | + | 0.957672i | \(0.407055\pi\) | |||||||
\(440\) | 4.85015 | 0.231222 | ||||||||
\(441\) | −2.16078 | + | 6.65020i | −0.102894 | + | 0.316676i | ||||
\(442\) | −0.568409 | − | 1.74938i | −0.0270364 | − | 0.0832096i | ||||
\(443\) | 4.73507 | + | 14.5730i | 0.224970 | + | 0.692386i | 0.998295 | + | 0.0583760i | \(0.0185922\pi\) |
−0.773325 | + | 0.634010i | \(0.781408\pi\) | |||||||
\(444\) | 2.36752 | − | 1.72010i | 0.112357 | − | 0.0816324i | ||||
\(445\) | −2.03384 | + | 6.25951i | −0.0964131 | + | 0.296729i | ||||
\(446\) | 20.5708 | − | 14.9456i | 0.974058 | − | 0.707694i | ||||
\(447\) | −8.07981 | − | 5.87033i | −0.382162 | − | 0.277657i | ||||
\(448\) | −0.0268854 | − | 0.0827449i | −0.00127022 | − | 0.00390933i | ||||
\(449\) | 27.6410 | + | 20.0824i | 1.30446 | + | 0.947746i | 0.999989 | − | 0.00477508i | \(-0.00151996\pi\) |
0.304472 | + | 0.952521i | \(0.401520\pi\) | |||||||
\(450\) | −0.809017 | − | 0.587785i | −0.0381374 | − | 0.0277085i | ||||
\(451\) | −6.32882 | − | 19.4781i | −0.298012 | − | 0.917188i | ||||
\(452\) | 14.3525 | + | 10.4277i | 0.675084 | + | 0.490477i | ||||
\(453\) | 9.09151 | − | 6.60537i | 0.427156 | − | 0.310347i | ||||
\(454\) | −1.56916 | + | 4.82939i | −0.0736445 | + | 0.226655i | ||||
\(455\) | −0.0630404 | + | 0.0458015i | −0.00295538 | + | 0.00214721i | ||||
\(456\) | 1.40431 | + | 4.32202i | 0.0657629 | + | 0.202397i | ||||
\(457\) | 2.21162 | + | 6.80666i | 0.103455 | + | 0.318402i | 0.989365 | − | 0.145456i | \(-0.0464649\pi\) |
−0.885910 | + | 0.463858i | \(0.846465\pi\) | |||||||
\(458\) | 6.12142 | − | 18.8398i | 0.286035 | − | 0.880326i | ||||
\(459\) | −2.05377 | −0.0958618 | ||||||||
\(460\) | −1.88733 | −0.0879974 | ||||||||
\(461\) | −2.90633 | + | 8.94478i | −0.135361 | + | 0.416600i | −0.995646 | − | 0.0932143i | \(-0.970286\pi\) |
0.860285 | + | 0.509814i | \(0.170286\pi\) | |||||||
\(462\) | −0.341387 | − | 0.248032i | −0.0158828 | − | 0.0115395i | ||||
\(463\) | −4.60730 | + | 3.34740i | −0.214119 | + | 0.155567i | −0.689676 | − | 0.724119i | \(-0.742247\pi\) |
0.475556 | + | 0.879685i | \(0.342247\pi\) | |||||||
\(464\) | −7.22967 | −0.335629 | ||||||||
\(465\) | −5.22674 | + | 1.91863i | −0.242384 | + | 0.0889745i | ||||
\(466\) | −7.80934 | −0.361761 | ||||||||
\(467\) | 1.27804 | − | 0.928552i | 0.0591407 | − | 0.0429682i | −0.557822 | − | 0.829961i | \(-0.688363\pi\) |
0.616963 | + | 0.786992i | \(0.288363\pi\) | |||||||
\(468\) | 0.724576 | + | 0.526435i | 0.0334935 | + | 0.0243345i | ||||
\(469\) | −0.393042 | + | 1.20966i | −0.0181490 | + | 0.0558568i | ||||
\(470\) | −3.54011 | −0.163293 | ||||||||
\(471\) | −0.135650 | −0.00625042 | ||||||||
\(472\) | 0.669071 | − | 2.05919i | 0.0307965 | − | 0.0947818i | ||||
\(473\) | 9.24578 | + | 28.4556i | 0.425121 | + | 1.30839i | ||||
\(474\) | −3.51524 | − | 10.8188i | −0.161460 | − | 0.496924i | ||||
\(475\) | 3.67653 | − | 2.67116i | 0.168691 | − | 0.122561i | ||||
\(476\) | −0.0552165 | + | 0.169939i | −0.00253085 | + | 0.00778914i | ||||
\(477\) | 5.52905 | − | 4.01709i | 0.253158 | − | 0.183930i | ||||
\(478\) | −3.41330 | − | 2.47991i | −0.156121 | − | 0.113428i | ||||
\(479\) | 9.45889 | + | 29.1115i | 0.432188 | + | 1.33014i | 0.895941 | + | 0.444173i | \(0.146502\pi\) |
−0.463754 | + | 0.885964i | \(0.653498\pi\) | |||||||
\(480\) | 0.809017 | + | 0.587785i | 0.0369264 | + | 0.0268286i | ||||
\(481\) | 2.12041 | + | 1.54057i | 0.0966823 | + | 0.0702438i | ||||
\(482\) | −5.95805 | − | 18.3370i | −0.271382 | − | 0.835227i | ||||
\(483\) | 0.132844 | + | 0.0965167i | 0.00604460 | + | 0.00439166i | ||||
\(484\) | −10.1321 | + | 7.36137i | −0.460548 | + | 0.334608i | ||||
\(485\) | −3.84920 | + | 11.8466i | −0.174783 | + | 0.537927i | ||||
\(486\) | 0.809017 | − | 0.587785i | 0.0366978 | − | 0.0266625i | ||||
\(487\) | 0.166148 | + | 0.511351i | 0.00752889 | + | 0.0231715i | 0.954750 | − | 0.297408i | \(-0.0961223\pi\) |
−0.947222 | + | 0.320580i | \(0.896122\pi\) | |||||||
\(488\) | −1.50000 | − | 4.61653i | −0.0679018 | − | 0.208980i | ||||
\(489\) | 4.50094 | − | 13.8525i | 0.203540 | − | 0.626431i | ||||
\(490\) | −6.99243 | −0.315886 | ||||||||
\(491\) | 26.6973 | 1.20483 | 0.602416 | − | 0.798182i | \(-0.294205\pi\) | ||||
0.602416 | + | 0.798182i | \(0.294205\pi\) | |||||||
\(492\) | 1.30487 | − | 4.01598i | 0.0588282 | − | 0.181054i | ||||
\(493\) | 12.0123 | + | 8.72748i | 0.541009 | + | 0.393066i | ||||
\(494\) | −3.29280 | + | 2.39236i | −0.148150 | + | 0.107637i | ||||
\(495\) | 4.85015 | 0.217998 | ||||||||
\(496\) | 5.22674 | − | 1.91863i | 0.234688 | − | 0.0861492i | ||||
\(497\) | 1.24610 | 0.0558954 | ||||||||
\(498\) | −2.42168 | + | 1.75946i | −0.108518 | + | 0.0788431i | ||||
\(499\) | −14.0300 | − | 10.1934i | −0.628067 | − | 0.456318i | 0.227663 | − | 0.973740i | \(-0.426892\pi\) |
−0.855730 | + | 0.517422i | \(0.826892\pi\) | |||||||
\(500\) | 0.309017 | − | 0.951057i | 0.0138197 | − | 0.0425325i | ||||
\(501\) | −12.3673 | −0.552529 | ||||||||
\(502\) | −8.47575 | −0.378291 | ||||||||
\(503\) | −1.57781 | + | 4.85599i | −0.0703509 | + | 0.216518i | −0.980050 | − | 0.198750i | \(-0.936312\pi\) |
0.909699 | + | 0.415267i | \(0.136312\pi\) | |||||||
\(504\) | −0.0268854 | − | 0.0827449i | −0.00119757 | − | 0.00368575i | ||||
\(505\) | 0.576339 | + | 1.77379i | 0.0256467 | + | 0.0789325i | ||||
\(506\) | 7.40562 | − | 5.38049i | 0.329220 | − | 0.239192i | ||||
\(507\) | 3.76934 | − | 11.6009i | 0.167402 | − | 0.515212i | ||||
\(508\) | 12.7832 | − | 9.28756i | 0.567164 | − | 0.412069i | ||||
\(509\) | 8.56667 | + | 6.22405i | 0.379711 | + | 0.275876i | 0.761226 | − | 0.648486i | \(-0.224598\pi\) |
−0.381515 | + | 0.924363i | \(0.624598\pi\) | |||||||
\(510\) | −0.634650 | − | 1.95325i | −0.0281028 | − | 0.0864915i | ||||
\(511\) | −0.667325 | − | 0.484840i | −0.0295207 | − | 0.0214481i | ||||
\(512\) | −0.809017 | − | 0.587785i | −0.0357538 | − | 0.0259767i | ||||
\(513\) | 1.40431 | + | 4.32202i | 0.0620018 | + | 0.190822i | ||||
\(514\) | 7.06999 | + | 5.13665i | 0.311844 | + | 0.226568i | ||||
\(515\) | 3.97253 | − | 2.88621i | 0.175051 | − | 0.127182i | ||||
\(516\) | −1.90629 | + | 5.86696i | −0.0839197 | + | 0.258278i | ||||
\(517\) | 13.8909 | − | 10.0923i | 0.610920 | − | 0.443859i | ||||
\(518\) | −0.0786779 | − | 0.242146i | −0.00345691 | − | 0.0106393i | ||||
\(519\) | −5.52415 | − | 17.0016i | −0.242483 | − | 0.746287i | ||||
\(520\) | −0.276763 | + | 0.851790i | −0.0121369 | + | 0.0373535i | ||||
\(521\) | 29.7526 | 1.30349 | 0.651744 | − | 0.758439i | \(-0.274038\pi\) | ||||
0.651744 | + | 0.758439i | \(0.274038\pi\) | |||||||
\(522\) | −7.22967 | −0.316434 | ||||||||
\(523\) | −1.88063 | + | 5.78797i | −0.0822341 | + | 0.253090i | −0.983717 | − | 0.179724i | \(-0.942480\pi\) |
0.901483 | + | 0.432815i | \(0.142480\pi\) | |||||||
\(524\) | 3.65992 | + | 2.65909i | 0.159884 | + | 0.116163i | ||||
\(525\) | −0.0703870 | + | 0.0511391i | −0.00307194 | + | 0.00223190i | ||||
\(526\) | 4.28381 | 0.186783 | ||||||||
\(527\) | −11.0005 | − | 3.12172i | −0.479191 | − | 0.135984i | ||||
\(528\) | −4.85015 | −0.211075 | ||||||||
\(529\) | 15.7256 | − | 11.4254i | 0.683724 | − | 0.496754i | ||||
\(530\) | 5.52905 | + | 4.01709i | 0.240167 | + | 0.174491i | ||||
\(531\) | 0.669071 | − | 2.05919i | 0.0290352 | − | 0.0893611i | ||||
\(532\) | 0.395381 | 0.0171419 | ||||||||
\(533\) | 3.78191 | 0.163813 | ||||||||
\(534\) | 2.03384 | − | 6.25951i | 0.0880127 | − | 0.270875i | ||||
\(535\) | −2.13706 | − | 6.57720i | −0.0923932 | − | 0.284357i | ||||
\(536\) | 4.51756 | + | 13.9036i | 0.195129 | + | 0.600545i | ||||
\(537\) | 20.0451 | − | 14.5636i | 0.865008 | − | 0.628465i | ||||
\(538\) | 2.98729 | − | 9.19392i | 0.128791 | − | 0.396378i | ||||
\(539\) | 27.4372 | − | 19.9343i | 1.18181 | − | 0.858632i | ||||
\(540\) | 0.809017 | + | 0.587785i | 0.0348145 | + | 0.0252942i | ||||
\(541\) | 6.25284 | + | 19.2443i | 0.268831 | + | 0.827375i | 0.990786 | + | 0.135436i | \(0.0432435\pi\) |
−0.721956 | + | 0.691939i | \(0.756757\pi\) | |||||||
\(542\) | 20.5104 | + | 14.9017i | 0.880998 | + | 0.640083i | ||||
\(543\) | −8.10255 | − | 5.88685i | −0.347714 | − | 0.252629i | ||||
\(544\) | 0.634650 | + | 1.95325i | 0.0272104 | + | 0.0837450i | ||||
\(545\) | 1.00887 | + | 0.732990i | 0.0432154 | + | 0.0313978i | ||||
\(546\) | 0.0630404 | − | 0.0458015i | 0.00269788 | − | 0.00196012i | ||||
\(547\) | −14.0099 | + | 43.1180i | −0.599019 | + | 1.84359i | −0.0654118 | + | 0.997858i | \(0.520836\pi\) |
−0.533607 | + | 0.845732i | \(0.679164\pi\) | |||||||
\(548\) | 8.64492 | − | 6.28090i | 0.369293 | − | 0.268307i | ||||
\(549\) | −1.50000 | − | 4.61653i | −0.0640184 | − | 0.197028i | ||||
\(550\) | 1.49878 | + | 4.61276i | 0.0639081 | + | 0.196689i | ||||
\(551\) | 10.1527 | − | 31.2468i | 0.432520 | − | 1.33116i | ||||
\(552\) | 1.88733 | 0.0803303 | ||||||||
\(553\) | −0.989709 | −0.0420867 | ||||||||
\(554\) | 8.08290 | − | 24.8766i | 0.343409 | − | 1.05691i | ||||
\(555\) | 2.36752 | + | 1.72010i | 0.100495 | + | 0.0730143i | ||||
\(556\) | −11.0169 | + | 8.00424i | −0.467220 | + | 0.339455i | ||||
\(557\) | −17.8577 | −0.756657 | −0.378328 | − | 0.925672i | \(-0.623501\pi\) | ||||
−0.378328 | + | 0.925672i | \(0.623501\pi\) | |||||||
\(558\) | 5.22674 | − | 1.91863i | 0.221266 | − | 0.0812223i | ||||
\(559\) | −5.52501 | −0.233683 | ||||||||
\(560\) | 0.0703870 | − | 0.0511391i | 0.00297439 | − | 0.00216102i | ||||
\(561\) | 8.05869 | + | 5.85498i | 0.340238 | + | 0.247197i | ||||
\(562\) | −0.439127 | + | 1.35149i | −0.0185234 | + | 0.0570093i | ||||
\(563\) | −10.2283 | −0.431070 | −0.215535 | − | 0.976496i | \(-0.569150\pi\) | ||||
−0.215535 | + | 0.976496i | \(0.569150\pi\) | |||||||
\(564\) | 3.54011 | 0.149066 | ||||||||
\(565\) | −5.48216 | + | 16.8724i | −0.230636 | + | 0.709825i | ||||
\(566\) | 4.40001 | + | 13.5419i | 0.184946 | + | 0.569207i | ||||
\(567\) | −0.0268854 | − | 0.0827449i | −0.00112908 | − | 0.00347496i | ||||
\(568\) | 11.5872 | − | 8.41856i | 0.486186 | − | 0.353235i | ||||
\(569\) | 11.6928 | − | 35.9866i | 0.490186 | − | 1.50864i | −0.334140 | − | 0.942523i | \(-0.608446\pi\) |
0.824326 | − | 0.566115i | \(-0.191554\pi\) | |||||||
\(570\) | −3.67653 | + | 2.67116i | −0.153993 | + | 0.111883i | ||||
\(571\) | 15.4777 | + | 11.2452i | 0.647721 | + | 0.470597i | 0.862494 | − | 0.506067i | \(-0.168901\pi\) |
−0.214773 | + | 0.976664i | \(0.568901\pi\) | |||||||
\(572\) | −1.34234 | − | 4.13131i | −0.0561262 | − | 0.172739i | ||||
\(573\) | −10.1455 | − | 7.37111i | −0.423833 | − | 0.307933i | ||||
\(574\) | −0.297220 | − | 0.215943i | −0.0124057 | − | 0.00901328i | ||||
\(575\) | −0.583218 | − | 1.79496i | −0.0243219 | − | 0.0748551i | ||||
\(576\) | −0.809017 | − | 0.587785i | −0.0337090 | − | 0.0244911i | ||||
\(577\) | 8.83965 | − | 6.42238i | 0.368000 | − | 0.267367i | −0.388381 | − | 0.921499i | \(-0.626966\pi\) |
0.756381 | + | 0.654131i | \(0.226966\pi\) | |||||||
\(578\) | −3.94986 | + | 12.1564i | −0.164293 | + | 0.505641i | ||||
\(579\) | −1.32338 | + | 0.961489i | −0.0549976 | + | 0.0399581i | ||||
\(580\) | −2.23409 | − | 6.87582i | −0.0927655 | − | 0.285503i | ||||
\(581\) | 0.0804779 | + | 0.247686i | 0.00333879 | + | 0.0102757i | ||||
\(582\) | 3.84920 | − | 11.8466i | 0.159555 | − | 0.491058i | ||||
\(583\) | −33.1473 | −1.37282 | ||||||||
\(584\) | −9.48080 | −0.392318 | ||||||||
\(585\) | −0.276763 | + | 0.851790i | −0.0114428 | + | 0.0352172i | ||||
\(586\) | −1.62919 | − | 1.18368i | −0.0673013 | − | 0.0488973i | ||||
\(587\) | −33.2869 | + | 24.1843i | −1.37390 | + | 0.998195i | −0.376476 | + | 0.926427i | \(0.622864\pi\) |
−0.997421 | + | 0.0717681i | \(0.977136\pi\) | |||||||
\(588\) | 6.99243 | 0.288363 | ||||||||
\(589\) | 0.952414 | + | 25.2845i | 0.0392435 | + | 1.04183i | ||||
\(590\) | 2.16516 | 0.0891382 | ||||||||
\(591\) | 10.0071 | − | 7.27056i | 0.411636 | − | 0.299071i | ||||
\(592\) | −2.36752 | − | 1.72010i | −0.0973043 | − | 0.0706957i | ||||
\(593\) | −2.91559 | + | 8.97327i | −0.119729 | + | 0.368488i | −0.992904 | − | 0.118919i | \(-0.962057\pi\) |
0.873175 | + | 0.487407i | \(0.162057\pi\) | |||||||
\(594\) | −4.85015 | −0.199004 | ||||||||
\(595\) | −0.178684 | −0.00732535 | ||||||||
\(596\) | −3.08621 | + | 9.49839i | −0.126416 | + | 0.389069i | ||||
\(597\) | −2.11361 | − | 6.50502i | −0.0865043 | − | 0.266233i | ||||
\(598\) | 0.522345 | + | 1.60761i | 0.0213603 | + | 0.0657402i | ||||
\(599\) | −10.1945 | + | 7.40677i | −0.416538 | + | 0.302632i | −0.776243 | − | 0.630433i | \(-0.782877\pi\) |
0.359705 | + | 0.933066i | \(0.382877\pi\) | |||||||
\(600\) | −0.309017 | + | 0.951057i | −0.0126156 | + | 0.0388267i | ||||
\(601\) | −35.6759 | + | 25.9200i | −1.45525 | + | 1.05730i | −0.470681 | + | 0.882304i | \(0.655992\pi\) |
−0.984569 | + | 0.174997i | \(0.944008\pi\) | |||||||
\(602\) | 0.434209 | + | 0.315471i | 0.0176970 | + | 0.0128577i | ||||
\(603\) | 4.51756 | + | 13.9036i | 0.183969 | + | 0.566199i | ||||
\(604\) | −9.09151 | − | 6.60537i | −0.369928 | − | 0.268769i | ||||
\(605\) | −10.1321 | − | 7.36137i | −0.411927 | − | 0.299282i | ||||
\(606\) | −0.576339 | − | 1.77379i | −0.0234122 | − | 0.0720552i | ||||
\(607\) | 25.5729 | + | 18.5798i | 1.03797 | + | 0.754129i | 0.969888 | − | 0.243550i | \(-0.0783121\pi\) |
0.0680818 | + | 0.997680i | \(0.478312\pi\) | |||||||
\(608\) | 3.67653 | − | 2.67116i | 0.149103 | − | 0.108330i | ||||
\(609\) | −0.194373 | + | 0.598218i | −0.00787638 | + | 0.0242410i | ||||
\(610\) | 3.92705 | − | 2.85317i | 0.159002 | − | 0.115521i | ||||
\(611\) | 0.979773 | + | 3.01543i | 0.0396374 | + | 0.121991i | ||||
\(612\) | 0.634650 | + | 1.95325i | 0.0256542 | + | 0.0789555i | ||||
\(613\) | 6.12408 | − | 18.8480i | 0.247349 | − | 0.761263i | −0.747892 | − | 0.663820i | \(-0.768934\pi\) |
0.995241 | − | 0.0974422i | \(-0.0310661\pi\) | |||||||
\(614\) | −23.3147 | −0.940905 | ||||||||
\(615\) | 4.22265 | 0.170274 | ||||||||
\(616\) | −0.130398 | + | 0.401325i | −0.00525390 | + | 0.0161698i | ||||
\(617\) | 4.15622 | + | 3.01967i | 0.167323 | + | 0.121567i | 0.668296 | − | 0.743896i | \(-0.267024\pi\) |
−0.500972 | + | 0.865463i | \(0.667024\pi\) | |||||||
\(618\) | −3.97253 | + | 2.88621i | −0.159799 | + | 0.116101i | ||||
\(619\) | 28.5953 | 1.14934 | 0.574671 | − | 0.818385i | \(-0.305130\pi\) | ||||
0.574671 | + | 0.818385i | \(0.305130\pi\) | |||||||
\(620\) | 3.43988 | + | 4.37804i | 0.138149 | + | 0.175826i | ||||
\(621\) | 1.88733 | 0.0757361 | ||||||||
\(622\) | 18.1793 | − | 13.2080i | 0.728924 | − | 0.529594i | ||||
\(623\) | −0.463262 | − | 0.336579i | −0.0185602 | − | 0.0134848i | ||||
\(624\) | 0.276763 | − | 0.851790i | 0.0110794 | − | 0.0340989i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 19.2059 | 0.767622 | ||||||||
\(627\) | 6.81111 | − | 20.9624i | 0.272010 | − | 0.837160i | ||||
\(628\) | 0.0419181 | + | 0.129011i | 0.00167272 | + | 0.00514809i | ||||
\(629\) | 1.85725 | + | 5.71602i | 0.0740533 | + | 0.227913i | ||||
\(630\) | 0.0703870 | − | 0.0511391i | 0.00280429 | − | 0.00203743i | ||||
\(631\) | 9.90158 | − | 30.4739i | 0.394176 | − | 1.21315i | −0.535426 | − | 0.844582i | \(-0.679849\pi\) |
0.929602 | − | 0.368566i | \(-0.120151\pi\) | |||||||
\(632\) | −9.20302 | + | 6.68639i | −0.366077 | + | 0.265970i | ||||
\(633\) | −16.1822 | − | 11.7570i | −0.643184 | − | 0.467300i | ||||
\(634\) | 7.21770 | + | 22.2138i | 0.286651 | + | 0.882222i | ||||
\(635\) | 12.7832 | + | 9.28756i | 0.507287 | + | 0.368566i | ||||
\(636\) | −5.52905 | − | 4.01709i | −0.219241 | − | 0.159288i | ||||
\(637\) | 1.93525 | + | 5.95608i | 0.0766773 | + | 0.235989i | ||||
\(638\) | 28.3681 | + | 20.6106i | 1.12310 | + | 0.815983i | ||||
\(639\) | 11.5872 | − | 8.41856i | 0.458381 | − | 0.333033i | ||||
\(640\) | 0.309017 | − | 0.951057i | 0.0122150 | − | 0.0375938i | ||||
\(641\) | −3.74247 | + | 2.71906i | −0.147819 | + | 0.107397i | −0.659237 | − | 0.751936i | \(-0.729120\pi\) |
0.511418 | + | 0.859332i | \(0.329120\pi\) | |||||||
\(642\) | 2.13706 | + | 6.57720i | 0.0843431 | + | 0.259581i | ||||
\(643\) | −11.3335 | − | 34.8809i | −0.446949 | − | 1.37557i | −0.880332 | − | 0.474358i | \(-0.842680\pi\) |
0.433383 | − | 0.901210i | \(-0.357320\pi\) | |||||||
\(644\) | 0.0507418 | − | 0.156167i | 0.00199951 | − | 0.00615385i | ||||
\(645\) | −6.16888 | −0.242899 | ||||||||
\(646\) | −9.33325 | −0.367212 | ||||||||
\(647\) | −7.39267 | + | 22.7523i | −0.290636 | + | 0.894485i | 0.694017 | + | 0.719959i | \(0.255839\pi\) |
−0.984653 | + | 0.174526i | \(0.944161\pi\) | |||||||
\(648\) | −0.809017 | − | 0.587785i | −0.0317812 | − | 0.0230904i | ||||
\(649\) | −8.49576 | + | 6.17253i | −0.333488 | + | 0.242293i | ||||
\(650\) | −0.895625 | −0.0351293 | ||||||||
\(651\) | −0.0182339 | − | 0.484070i | −0.000714643 | − | 0.0189722i | ||||
\(652\) | −14.5654 | −0.570424 | ||||||||
\(653\) | −27.1325 | + | 19.7129i | −1.06178 | + | 0.771426i | −0.974416 | − | 0.224750i | \(-0.927843\pi\) |
−0.0873609 | + | 0.996177i | \(0.527843\pi\) | |||||||
\(654\) | −1.00887 | − | 0.732990i | −0.0394501 | − | 0.0286622i | ||||
\(655\) | −1.39796 | + | 4.30249i | −0.0546230 | + | 0.168112i | ||||
\(656\) | −4.22265 | −0.164867 | ||||||||
\(657\) | −9.48080 | −0.369881 | ||||||||
\(658\) | 0.0951775 | − | 0.292926i | 0.00371040 | − | 0.0114194i | ||||
\(659\) | −1.60173 | − | 4.92963i | −0.0623947 | − | 0.192031i | 0.915000 | − | 0.403454i | \(-0.132190\pi\) |
−0.977395 | + | 0.211423i | \(0.932190\pi\) | |||||||
\(660\) | −1.49878 | − | 4.61276i | −0.0583398 | − | 0.179552i | ||||
\(661\) | −10.6985 | + | 7.77295i | −0.416125 | + | 0.302333i | −0.776077 | − | 0.630638i | \(-0.782793\pi\) |
0.359952 | + | 0.932971i | \(0.382793\pi\) | |||||||
\(662\) | −5.16705 | + | 15.9026i | −0.200823 | + | 0.618071i | ||||
\(663\) | −1.48811 | + | 1.08118i | −0.0577935 | + | 0.0419894i | ||||
\(664\) | 2.42168 | + | 1.75946i | 0.0939795 | + | 0.0682801i | ||||
\(665\) | 0.122179 | + | 0.376030i | 0.00473791 | + | 0.0145818i | ||||
\(666\) | −2.36752 | − | 1.72010i | −0.0917394 | − | 0.0666526i | ||||
\(667\) | −11.0389 | − | 8.02021i | −0.427427 | − | 0.310544i | ||||
\(668\) | 3.82170 | + | 11.7620i | 0.147866 | + | 0.455084i | ||||
\(669\) | −20.5708 | − | 14.9456i | −0.795315 | − | 0.577830i | ||||
\(670\) | −11.8271 | + | 8.59291i | −0.456922 | + | 0.331973i | ||||
\(671\) | −7.27522 | + | 22.3908i | −0.280857 | + | 0.864388i | ||||
\(672\) | −0.0703870 | + | 0.0511391i | −0.00271524 | + | 0.00197274i | ||||
\(673\) | 0.116790 | + | 0.359443i | 0.00450192 | + | 0.0138555i | 0.953282 | − | 0.302081i | \(-0.0976813\pi\) |
−0.948780 | + | 0.315937i | \(0.897681\pi\) | |||||||
\(674\) | −1.55435 | − | 4.78381i | −0.0598715 | − | 0.184266i | ||||
\(675\) | −0.309017 | + | 0.951057i | −0.0118941 | + | 0.0366062i | ||||
\(676\) | −12.1979 | −0.469148 | ||||||||
\(677\) | −49.9537 | −1.91988 | −0.959939 | − | 0.280210i | \(-0.909596\pi\) | ||||
−0.959939 | + | 0.280210i | \(0.909596\pi\) | |||||||
\(678\) | 5.48216 | − | 16.8724i | 0.210541 | − | 0.647979i | ||||
\(679\) | −0.876760 | − | 0.637003i | −0.0336470 | − | 0.0244459i | ||||
\(680\) | −1.66154 | + | 1.20718i | −0.0637170 | + | 0.0462931i | ||||
\(681\) | 5.07792 | 0.194586 | ||||||||
\(682\) | −25.9787 | − | 7.37219i | −0.994775 | − | 0.282296i | ||||
\(683\) | 15.6089 | 0.597257 | 0.298629 | − | 0.954369i | \(-0.403471\pi\) | ||||
0.298629 | + | 0.954369i | \(0.403471\pi\) | |||||||
\(684\) | 3.67653 | − | 2.67116i | 0.140576 | − | 0.102134i | ||||
\(685\) | 8.64492 | + | 6.28090i | 0.330305 | + | 0.239981i | ||||
\(686\) | 0.376193 | − | 1.15780i | 0.0143631 | − | 0.0442051i | ||||
\(687\) | −19.8093 | −0.755774 | ||||||||
\(688\) | 6.16888 | 0.235186 | ||||||||
\(689\) | 1.89148 | − | 5.82138i | 0.0720596 | − | 0.221777i | ||||
\(690\) | 0.583218 | + | 1.79496i | 0.0222027 | + | 0.0683330i | ||||
\(691\) | −12.4815 | − | 38.4142i | −0.474819 | − | 1.46134i | −0.846201 | − | 0.532864i | \(-0.821116\pi\) |
0.371382 | − | 0.928480i | \(-0.378884\pi\) | |||||||
\(692\) | −14.4624 | + | 10.5076i | −0.549779 | + | 0.399438i | ||||
\(693\) | −0.130398 | + | 0.401325i | −0.00495342 | + | 0.0152451i | ||||
\(694\) | 1.83955 | − | 1.33651i | 0.0698285 | − | 0.0507334i | ||||
\(695\) | −11.0169 | − | 8.00424i | −0.417894 | − | 0.303618i | ||||
\(696\) | 2.23409 | + | 6.87582i | 0.0846829 | + | 0.260627i | ||||
\(697\) | 7.01609 | + | 5.09749i | 0.265753 | + | 0.193081i | ||||
\(698\) | −22.6227 | − | 16.4364i | −0.856283 | − | 0.622126i | ||||
\(699\) | 2.41322 | + | 7.42713i | 0.0912764 | + | 0.280920i | ||||
\(700\) | 0.0703870 | + | 0.0511391i | 0.00266038 | + | 0.00193288i | ||||
\(701\) | 8.35493 | − | 6.07021i | 0.315561 | − | 0.229269i | −0.418718 | − | 0.908116i | \(-0.637520\pi\) |
0.734279 | + | 0.678848i | \(0.237520\pi\) | |||||||
\(702\) | 0.276763 | − | 0.851790i | 0.0104458 | − | 0.0321487i | ||||
\(703\) | 10.7591 | − | 7.81691i | 0.405785 | − | 0.294820i | ||||
\(704\) | 1.49878 | + | 4.61276i | 0.0564873 | + | 0.173850i | ||||
\(705\) | 1.09395 | + | 3.36685i | 0.0412007 | + | 0.126803i | ||||
\(706\) | 6.95671 | − | 21.4105i | 0.261819 | − | 0.805797i | ||||
\(707\) | −0.162267 | −0.00610268 | ||||||||
\(708\) | −2.16516 | −0.0813716 | ||||||||
\(709\) | −1.69498 | + | 5.21660i | −0.0636562 | + | 0.195914i | −0.977826 | − | 0.209417i | \(-0.932844\pi\) |
0.914170 | + | 0.405330i | \(0.132844\pi\) | |||||||
\(710\) | 11.5872 | + | 8.41856i | 0.434858 | + | 0.315943i | ||||
\(711\) | −9.20302 | + | 6.68639i | −0.345140 | + | 0.250759i | ||||
\(712\) | −6.58163 | −0.246657 | ||||||||
\(713\) | 10.1091 | + | 2.86874i | 0.378588 | + | 0.107435i | ||||
\(714\) | 0.178684 | 0.00668710 | ||||||||
\(715\) | 3.51430 | − | 2.55329i | 0.131427 | − | 0.0954875i | ||||
\(716\) | −20.0451 | − | 14.5636i | −0.749119 | − | 0.544267i | ||||
\(717\) | −1.30377 | + | 4.01258i | −0.0486900 | + | 0.149852i | ||||
\(718\) | −1.82655 | −0.0681663 | ||||||||
\(719\) | −7.07499 | −0.263853 | −0.131926 | − | 0.991260i | \(-0.542116\pi\) | ||||
−0.131926 | + | 0.991260i | \(0.542116\pi\) | |||||||
\(720\) | 0.309017 | − | 0.951057i | 0.0115164 | − | 0.0354438i | ||||
\(721\) | 0.132016 | + | 0.406304i | 0.00491654 | + | 0.0151315i | ||||
\(722\) | 0.510492 | + | 1.57113i | 0.0189986 | + | 0.0584715i | ||||
\(723\) | −15.5984 | + | 11.3329i | −0.580110 | + | 0.421474i | ||||
\(724\) | −3.09490 | + | 9.52512i | −0.115021 | + | 0.353998i | ||||
\(725\) | 5.84892 | − | 4.24949i | 0.217224 | − | 0.157822i | ||||
\(726\) | 10.1321 | + | 7.36137i | 0.376036 | + | 0.273206i | ||||
\(727\) | −15.6737 | − | 48.2387i | −0.581306 | − | 1.78907i | −0.613626 | − | 0.789597i | \(-0.710290\pi\) |
0.0323204 | − | 0.999478i | \(-0.489710\pi\) | |||||||
\(728\) | −0.0630404 | − | 0.0458015i | −0.00233643 | − | 0.00169752i | ||||
\(729\) | −0.809017 | − | 0.587785i | −0.0299636 | − | 0.0217698i | ||||
\(730\) | −2.92973 | − | 9.01678i | −0.108434 | − | 0.333726i | ||||
\(731\) | −10.2498 | − | 7.44693i | −0.379103 | − | 0.275435i | ||||
\(732\) | −3.92705 | + | 2.85317i | −0.145148 | + | 0.105456i | ||||
\(733\) | −13.8392 | + | 42.5928i | −0.511164 | + | 1.57320i | 0.278991 | + | 0.960294i | \(0.410000\pi\) |
−0.790155 | + | 0.612907i | \(0.790000\pi\) | |||||||
\(734\) | 1.88656 | − | 1.37067i | 0.0696343 | − | 0.0505923i | ||||
\(735\) | 2.16078 | + | 6.65020i | 0.0797016 | + | 0.245296i | ||||
\(736\) | −0.583218 | − | 1.79496i | −0.0214977 | − | 0.0661632i | ||||
\(737\) | 21.9108 | − | 67.4346i | 0.807096 | − | 2.48398i | ||||
\(738\) | −4.22265 | −0.155438 | ||||||||
\(739\) | 52.6588 | 1.93709 | 0.968543 | − | 0.248845i | \(-0.0800509\pi\) | ||||
0.968543 | + | 0.248845i | \(0.0800509\pi\) | |||||||
\(740\) | 0.904311 | − | 2.78318i | 0.0332431 | − | 0.102312i | ||||
\(741\) | 3.29280 | + | 2.39236i | 0.120964 | + | 0.0878854i | ||||
\(742\) | −0.481045 | + | 0.349499i | −0.0176597 | + | 0.0128305i | ||||
\(743\) | −25.1961 | −0.924355 | −0.462177 | − | 0.886787i | \(-0.652932\pi\) | ||||
−0.462177 | + | 0.886787i | \(0.652932\pi\) | |||||||
\(744\) | −3.43988 | − | 4.37804i | −0.126112 | − | 0.160507i | ||||
\(745\) | −9.98720 | −0.365903 | ||||||||
\(746\) | −5.63604 | + | 4.09483i | −0.206350 | + | 0.149922i | ||||
\(747\) | 2.42168 | + | 1.75946i | 0.0886047 | + | 0.0643751i | ||||
\(748\) | 3.07815 | − | 9.47356i | 0.112548 | − | 0.346388i | ||||
\(749\) | 0.601685 | 0.0219851 | ||||||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | 11.4405 | − | 35.2101i | 0.417469 | − | 1.28484i | −0.492556 | − | 0.870281i | \(-0.663937\pi\) |
0.910024 | − | 0.414555i | \(-0.136063\pi\) | |||||||
\(752\) | −1.09395 | − | 3.36685i | −0.0398924 | − | 0.122776i | ||||
\(753\) | 2.61915 | + | 8.06092i | 0.0954471 | + | 0.293756i | ||||
\(754\) | −5.23844 | + | 3.80595i | −0.190773 | + | 0.138605i | ||||
\(755\) | 3.47265 | − | 10.6877i | 0.126383 | − | 0.388966i | ||||
\(756\) | −0.0703870 | + | 0.0511391i | −0.00255995 | + | 0.00185991i | ||||
\(757\) | −4.38502 | − | 3.18590i | −0.159376 | − | 0.115794i | 0.505239 | − | 0.862980i | \(-0.331404\pi\) |
−0.664615 | + | 0.747186i | \(0.731404\pi\) | |||||||
\(758\) | −1.90582 | − | 5.86552i | −0.0692226 | − | 0.213045i | ||||
\(759\) | −7.40562 | − | 5.38049i | −0.268807 | − | 0.195300i | ||||
\(760\) | 3.67653 | + | 2.67116i | 0.133362 | + | 0.0968931i | ||||
\(761\) | 7.75680 | + | 23.8730i | 0.281184 | + | 0.865394i | 0.987517 | + | 0.157515i | \(0.0503481\pi\) |
−0.706333 | + | 0.707880i | \(0.749652\pi\) | |||||||
\(762\) | −12.7832 | − | 9.28756i | −0.463088 | − | 0.336453i | ||||
\(763\) | −0.0877752 | + | 0.0637724i | −0.00317768 | + | 0.00230872i | ||||
\(764\) | −3.87522 | + | 11.9267i | −0.140201 | + | 0.431493i | ||||
\(765\) | −1.66154 | + | 1.20718i | −0.0600729 | + | 0.0436455i | ||||
\(766\) | −0.455787 | − | 1.40277i | −0.0164683 | − | 0.0506841i | ||||
\(767\) | −0.599237 | − | 1.84426i | −0.0216372 | − | 0.0665924i | ||||
\(768\) | −0.309017 | + | 0.951057i | −0.0111507 | + | 0.0343183i | ||||
\(769\) | −18.1824 | −0.655673 | −0.327837 | − | 0.944734i | \(-0.606320\pi\) | ||||
−0.327837 | + | 0.944734i | \(0.606320\pi\) | |||||||
\(770\) | −0.421978 | −0.0152070 | ||||||||
\(771\) | 2.70050 | − | 8.31127i | 0.0972560 | − | 0.299323i | ||||
\(772\) | 1.32338 | + | 0.961489i | 0.0476293 | + | 0.0346047i | ||||
\(773\) | 5.93372 | − | 4.31110i | 0.213421 | − | 0.155060i | −0.475939 | − | 0.879478i | \(-0.657892\pi\) |
0.689360 | + | 0.724419i | \(0.257892\pi\) | |||||||
\(774\) | 6.16888 | 0.221736 | ||||||||
\(775\) | −3.10078 | + | 4.62441i | −0.111383 | + | 0.166114i | ||||
\(776\) | −12.4563 | −0.447154 | ||||||||
\(777\) | −0.205981 | + | 0.149654i | −0.00738954 | + | 0.00536881i | ||||
\(778\) | −19.8094 | − | 14.3924i | −0.710203 | − | 0.515992i | ||||
\(779\) | 5.92992 | − | 18.2504i | 0.212461 | − | 0.653889i | ||||
\(780\) | 0.895625 | 0.0320685 | ||||||||
\(781\) | −69.4663 | −2.48570 | ||||||||
\(782\) | −1.19780 | + | 3.68644i | −0.0428331 | + | 0.131827i | ||||
\(783\) | 2.23409 | + | 6.87582i | 0.0798398 | + | 0.245722i | ||||
\(784\) | −2.16078 | − | 6.65020i | −0.0771707 | − | 0.237507i | ||||
\(785\) | −0.109743 | + | 0.0797330i | −0.00391690 | + | 0.00284579i | ||||
\(786\) | 1.39796 | − | 4.30249i | 0.0498637 | − | 0.153465i | ||||
\(787\) | 3.93200 | − | 2.85676i | 0.140160 | − | 0.101833i | −0.515496 | − | 0.856892i | \(-0.672392\pi\) |
0.655656 | + | 0.755060i | \(0.272392\pi\) | |||||||
\(788\) | −10.0071 | − | 7.27056i | −0.356487 | − | 0.259003i | ||||
\(789\) | −1.32377 | − | 4.07415i | −0.0471275 | − | 0.145044i | ||||
\(790\) | −9.20302 | − | 6.68639i | −0.327429 | − | 0.237891i | ||||
\(791\) | −1.24871 | − | 0.907241i | −0.0443990 | − | 0.0322578i | ||||
\(792\) | 1.49878 | + | 4.61276i | 0.0532567 | + | 0.163907i | ||||
\(793\) | −3.51717 | − | 2.55537i | −0.124898 | − | 0.0907439i | ||||
\(794\) | 1.33240 | − | 0.968042i | 0.0472850 | − | 0.0343545i | ||||
\(795\) | 2.11191 | − | 6.49979i | 0.0749017 | − | 0.230524i | ||||
\(796\) | −5.53350 | + | 4.02033i | −0.196130 | + | 0.142497i | ||||
\(797\) | −12.3608 | − | 38.0427i | −0.437842 | − | 1.34754i | −0.890146 | − | 0.455676i | \(-0.849398\pi\) |
0.452303 | − | 0.891864i | \(-0.350602\pi\) | |||||||
\(798\) | −0.122179 | − | 0.376030i | −0.00432510 | − | 0.0133113i | ||||
\(799\) | −2.24673 | + | 6.91473i | −0.0794837 | + | 0.244626i | ||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | −6.58163 | −0.232551 | ||||||||
\(802\) | 3.91569 | − | 12.0512i | 0.138268 | − | 0.425544i | ||||
\(803\) | 37.2013 | + | 27.0283i | 1.31280 | + | 0.953808i | ||||
\(804\) | 11.8271 | − | 8.59291i | 0.417111 | − | 0.303049i | ||||
\(805\) | 0.164204 | 0.00578743 | ||||||||
\(806\) | 2.77714 | − | 4.14174i | 0.0978204 | − | 0.145886i | ||||
\(807\) | −9.66706 | −0.340297 | ||||||||
\(808\) | −1.50887 | + | 1.09626i | −0.0530820 | + | 0.0385663i | ||||
\(809\) | −8.15894 | − | 5.92782i | −0.286853 | − | 0.208411i | 0.435048 | − | 0.900407i | \(-0.356731\pi\) |
−0.721901 | + | 0.691996i | \(0.756731\pi\) | |||||||
\(810\) | 0.309017 | − | 0.951057i | 0.0108578 | − | 0.0334167i | ||||
\(811\) | −1.87311 | −0.0657737 | −0.0328868 | − | 0.999459i | \(-0.510470\pi\) | ||||
−0.0328868 | + | 0.999459i | \(0.510470\pi\) | |||||||
\(812\) | 0.629003 | 0.0220737 | ||||||||
\(813\) | 7.83428 | − | 24.1114i | 0.274760 | − | 0.845625i | ||||
\(814\) | 4.38604 | + | 13.4988i | 0.153731 | + | 0.473134i | ||||
\(815\) | −4.50094 | − | 13.8525i | −0.157661 | − | 0.485231i | ||||
\(816\) | 1.66154 | − | 1.20718i | 0.0581654 | − | 0.0422596i | ||||
\(817\) | −8.66303 | + | 26.6621i | −0.303081 | + | 0.932787i | ||||
\(818\) | 2.13925 | − | 1.55425i | 0.0747970 | − | 0.0543432i | ||||
\(819\) | −0.0630404 | − | 0.0458015i | −0.00220281 | − | 0.00160043i | ||||
\(820\) | −1.30487 | − | 4.01598i | −0.0455681 | − | 0.140244i | ||||
\(821\) | 23.8370 | + | 17.3186i | 0.831916 | + | 0.604422i | 0.920101 | − | 0.391682i | \(-0.128107\pi\) |
−0.0881851 | + | 0.996104i | \(0.528107\pi\) | |||||||
\(822\) | −8.64492 | − | 6.28090i | −0.301526 | − | 0.219072i | ||||
\(823\) | 4.31016 | + | 13.2653i | 0.150243 | + | 0.462400i | 0.997648 | − | 0.0685472i | \(-0.0218364\pi\) |
−0.847405 | + | 0.530947i | \(0.821836\pi\) | |||||||
\(824\) | 3.97253 | + | 2.88621i | 0.138390 | + | 0.100546i | ||||
\(825\) | 3.92385 | − | 2.85084i | 0.136611 | − | 0.0992536i | ||||
\(826\) | −0.0582112 | + | 0.179156i | −0.00202543 | + | 0.00623363i | ||||
\(827\) | −5.87752 | + | 4.27026i | −0.204381 | + | 0.148492i | −0.685268 | − | 0.728291i | \(-0.740315\pi\) |
0.480887 | + | 0.876783i | \(0.340315\pi\) | |||||||
\(828\) | −0.583218 | − | 1.79496i | −0.0202682 | − | 0.0623792i | ||||
\(829\) | −6.65297 | − | 20.4757i | −0.231067 | − | 0.711151i | −0.997619 | − | 0.0689688i | \(-0.978029\pi\) |
0.766552 | − | 0.642183i | \(-0.221971\pi\) | |||||||
\(830\) | −0.925001 | + | 2.84686i | −0.0321072 | + | 0.0988159i | ||||
\(831\) | −26.1568 | −0.907369 | ||||||||
\(832\) | −0.895625 | −0.0310502 | ||||||||
\(833\) | −4.43775 | + | 13.6580i | −0.153759 | + | 0.473221i | ||||
\(834\) | 11.0169 | + | 8.00424i | 0.381484 | + | 0.277164i | ||||
\(835\) | −10.0053 | + | 7.26930i | −0.346249 | + | 0.251565i | ||||
\(836\) | −22.0412 | −0.762312 | ||||||||
\(837\) | −3.43988 | − | 4.37804i | −0.118900 | − | 0.151327i | ||||
\(838\) | 5.07743 | 0.175397 | ||||||||
\(839\) | 13.0951 | − | 9.51416i | 0.452094 | − | 0.328465i | −0.338328 | − | 0.941028i | \(-0.609861\pi\) |
0.790422 | + | 0.612563i | \(0.209861\pi\) | |||||||
\(840\) | −0.0703870 | − | 0.0511391i | −0.00242858 | − | 0.00176447i | ||||
\(841\) | 7.19023 | − | 22.1292i | 0.247939 | − | 0.763077i | ||||
\(842\) | 18.1064 | 0.623987 | ||||||||
\(843\) | 1.42104 | 0.0489433 | ||||||||
\(844\) | −6.18104 | + | 19.0233i | −0.212760 | + | 0.654808i | ||||
\(845\) | −3.76934 | − | 11.6009i | −0.129669 | − | 0.399081i | ||||
\(846\) | −1.09395 | − | 3.36685i | −0.0376109 | − | 0.115755i | ||||
\(847\) | 0.881520 | − | 0.640462i | 0.0302894 | − | 0.0220065i | ||||
\(848\) | −2.11191 | + | 6.49979i | −0.0725233 | + | 0.223204i | ||||
\(849\) | 11.5194 | − | 8.36933i | 0.395344 | − | 0.287234i | ||||
\(850\) | −1.66154 | − | 1.20718i | −0.0569902 | − | 0.0414058i | ||||
\(851\) | −1.70674 | − | 5.25280i | −0.0585062 | − | 0.180064i | ||||
\(852\) | −11.5872 | − | 8.41856i | −0.396969 | − | 0.288415i | ||||
\(853\) | 39.6953 | + | 28.8403i | 1.35914 | + | 0.987473i | 0.998499 | + | 0.0547686i | \(0.0174421\pi\) |
0.360641 | + | 0.932705i | \(0.382558\pi\) | |||||||
\(854\) | 0.130505 | + | 0.401652i | 0.00446578 | + | 0.0137443i | ||||
\(855\) | 3.67653 | + | 2.67116i | 0.125735 | + | 0.0913517i | ||||
\(856\) | 5.59490 | − | 4.06493i | 0.191230 | − | 0.138937i | ||||
\(857\) | −6.91174 | + | 21.2721i | −0.236100 | + | 0.726642i | 0.760873 | + | 0.648901i | \(0.224771\pi\) |
−0.996974 | + | 0.0777417i | \(0.975229\pi\) | |||||||
\(858\) | −3.51430 | + | 2.55329i | −0.119976 | + | 0.0871678i | ||||
\(859\) | −3.23240 | − | 9.94830i | −0.110288 | − | 0.339432i | 0.880647 | − | 0.473773i | \(-0.157108\pi\) |
−0.990935 | + | 0.134341i | \(0.957108\pi\) | |||||||
\(860\) | 1.90629 | + | 5.86696i | 0.0650039 | + | 0.200062i | ||||
\(861\) | −0.113528 | + | 0.349403i | −0.00386902 | + | 0.0119076i | ||||
\(862\) | −15.3056 | −0.521309 | ||||||||
\(863\) | −30.1252 | −1.02547 | −0.512737 | − | 0.858546i | \(-0.671368\pi\) | ||||
−0.512737 | + | 0.858546i | \(0.671368\pi\) | |||||||
\(864\) | −0.309017 | + | 0.951057i | −0.0105130 | + | 0.0323556i | ||||
\(865\) | −14.4624 | − | 10.5076i | −0.491737 | − | 0.357268i | ||||
\(866\) | −8.22162 | + | 5.97336i | −0.279382 | + | 0.202983i | ||||
\(867\) | 12.7820 | 0.434100 | ||||||||
\(868\) | −0.454743 | + | 0.166927i | −0.0154350 | + | 0.00566588i | ||||
\(869\) | 55.1731 | 1.87162 | ||||||||
\(870\) | −5.84892 | + | 4.24949i | −0.198297 | + | 0.144071i | ||||
\(871\) | 10.5927 | + | 7.69603i | 0.358919 | + | 0.260770i | ||||
\(872\) | −0.385356 | + | 1.18600i | −0.0130498 | + | 0.0401631i | ||||
\(873\) | −12.4563 | −0.421581 | ||||||||
\(874\) | 8.57689 | 0.290118 | ||||||||
\(875\) | −0.0268854 | + | 0.0827449i | −0.000908894 | + | 0.00279729i | ||||
\(876\) | 2.92973 | + | 9.01678i | 0.0989864 | + | 0.304649i | ||||
\(877\) | 1.34127 | + | 4.12801i | 0.0452915 | + | 0.139393i | 0.971145 | − | 0.238490i | \(-0.0766523\pi\) |
−0.925854 | + | 0.377883i | \(0.876652\pi\) | |||||||
\(878\) | −9.75900 | + | 7.09033i | −0.329350 | + | 0.239287i | ||||
\(879\) | −0.622296 | + | 1.91523i | −0.0209895 | + | 0.0645991i | ||||
\(880\) | −3.92385 | + | 2.85084i | −0.132273 | + | 0.0961019i | ||||
\(881\) | 18.2309 | + | 13.2456i | 0.614216 | + | 0.446254i | 0.850896 | − | 0.525333i | \(-0.176059\pi\) |
−0.236680 | + | 0.971588i | \(0.576059\pi\) | |||||||
\(882\) | −2.16078 | − | 6.65020i | −0.0727572 | − | 0.223924i | ||||
\(883\) | 38.8978 | + | 28.2609i | 1.30901 | + | 0.951055i | 1.00000 | 2.63964e-6i | \(-8.40222e-7\pi\) | |
0.309014 | + | 0.951057i | \(0.400001\pi\) | |||||||
\(884\) | 1.48811 | + | 1.08118i | 0.0500507 | + | 0.0363639i | ||||
\(885\) | −0.669071 | − | 2.05919i | −0.0224906 | − | 0.0692188i | ||||
\(886\) | −12.3966 | − | 9.00663i | −0.416471 | − | 0.302584i | ||||
\(887\) | −46.6440 | + | 33.8889i | −1.56615 | + | 1.13788i | −0.635428 | + | 0.772160i | \(0.719176\pi\) |
−0.930726 | + | 0.365717i | \(0.880824\pi\) | |||||||
\(888\) | −0.904311 | + | 2.78318i | −0.0303467 | + | 0.0933975i | ||||
\(889\) | −1.11218 | + | 0.808047i | −0.0373013 | + | 0.0271010i | ||||
\(890\) | −2.03384 | − | 6.25951i | −0.0681744 | − | 0.209819i | ||||
\(891\) | 1.49878 | + | 4.61276i | 0.0502109 | + | 0.154533i | ||||
\(892\) | −7.85736 | + | 24.1825i | −0.263084 | + | 0.809689i | ||||
\(893\) | 16.0878 | 0.538359 | ||||||||
\(894\) | 9.98720 | 0.334022 | ||||||||
\(895\) | 7.65653 | − | 23.5644i | 0.255930 | − | 0.787670i | ||||
\(896\) | 0.0703870 | + | 0.0511391i | 0.00235146 | + | 0.00170844i | ||||
\(897\) | 1.36752 | − | 0.993559i | 0.0456601 | − | 0.0331740i | ||||
\(898\) | −34.1662 | −1.14014 | ||||||||
\(899\) | 1.51518 | + | 40.2245i | 0.0505339 | + | 1.34156i | ||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | 11.3554 | − | 8.25019i | 0.378303 | − | 0.274854i | ||||
\(902\) | 16.5691 | + | 12.0381i | 0.551689 | + | 0.400826i | ||||
\(903\) | 0.165853 | − | 0.510443i | 0.00551925 | − | 0.0169865i | ||||
\(904\) | −17.7406 | −0.590045 | ||||||||
\(905\) | −10.0153 | −0.332920 | ||||||||
\(906\) | −3.47265 | + | 10.6877i | −0.115371 | + | 0.355075i | ||||
\(907\) | 14.8525 | + | 45.7113i | 0.493170 | + | 1.51782i | 0.819790 | + | 0.572664i | \(0.194090\pi\) |
−0.326620 | + | 0.945156i | \(0.605910\pi\) | |||||||
\(908\) | −1.56916 | − | 4.82939i | −0.0520745 | − | 0.160269i | ||||
\(909\) | −1.50887 | + | 1.09626i | −0.0500462 | + | 0.0363607i | ||||
\(910\) | 0.0240793 | − | 0.0741084i | 0.000798220 | − | 0.00245667i | ||||
\(911\) | −8.66712 | + | 6.29703i | −0.287154 | + | 0.208630i | −0.722032 | − | 0.691860i | \(-0.756792\pi\) |
0.434878 | + | 0.900490i | \(0.356792\pi\) | |||||||
\(912\) | −3.67653 | − | 2.67116i | −0.121742 | − | 0.0884509i | ||||
\(913\) | −4.48639 | − | 13.8077i | −0.148478 | − | 0.456967i | ||||
\(914\) | −5.79009 | − | 4.20675i | −0.191519 | − | 0.139147i | ||||
\(915\) | −3.92705 | − | 2.85317i | −0.129824 | − | 0.0943229i | ||||
\(916\) | 6.12142 | + | 18.8398i | 0.202258 | + | 0.622485i | ||||
\(917\) | −0.318424 | − | 0.231349i | −0.0105153 | − | 0.00763981i | ||||
\(918\) | 1.66154 | − | 1.20718i | 0.0548388 | − | 0.0398428i | ||||
\(919\) | 5.07099 | − | 15.6069i | 0.167276 | − | 0.514824i | −0.831920 | − | 0.554895i | \(-0.812758\pi\) |
0.999197 | + | 0.0400711i | \(0.0127584\pi\) | |||||||
\(920\) | 1.52689 | − | 1.10935i | 0.0503399 | − | 0.0365741i | ||||
\(921\) | 7.20464 | + | 22.1736i | 0.237401 | + | 0.730645i | ||||
\(922\) | −2.90633 | − | 8.94478i | −0.0957150 | − | 0.294581i | ||||
\(923\) | 3.96395 | − | 12.1998i | 0.130475 | − | 0.401560i | ||||
\(924\) | 0.421978 | 0.0138820 | ||||||||
\(925\) | 2.92641 | 0.0962198 | ||||||||
\(926\) | 1.75983 | − | 5.41620i | 0.0578316 | − | 0.177987i | ||||
\(927\) | 3.97253 | + | 2.88621i | 0.130475 | + | 0.0947957i | ||||
\(928\) | 5.84892 | − | 4.24949i | 0.192000 | − | 0.139496i | ||||
\(929\) | 41.0355 | 1.34633 | 0.673165 | − | 0.739492i | \(-0.264934\pi\) | ||||
0.673165 | + | 0.739492i | \(0.264934\pi\) | |||||||
\(930\) | 3.10078 | − | 4.62441i | 0.101679 | − | 0.151640i | ||||
\(931\) | 31.7767 | 1.04144 | ||||||||
\(932\) | 6.31789 | − | 4.59022i | 0.206949 | − | 0.150358i | ||||
\(933\) | −18.1793 | − | 13.2080i | −0.595164 | − | 0.432412i | ||||
\(934\) | −0.488169 | + | 1.50243i | −0.0159734 | + | 0.0491610i | ||||
\(935\) | 9.96109 | 0.325762 | ||||||||
\(936\) | −0.895625 | −0.0292744 | ||||||||
\(937\) | 12.6357 | − | 38.8885i | 0.412789 | − | 1.27043i | −0.501425 | − | 0.865201i | \(-0.667191\pi\) |
0.914214 | − | 0.405232i | \(-0.132809\pi\) | |||||||
\(938\) | −0.393042 | − | 1.20966i | −0.0128333 | − | 0.0394967i | ||||
\(939\) | −5.93495 | − | 18.2659i | −0.193680 | − | 0.596085i | ||||
\(940\) | 2.86401 | − | 2.08083i | 0.0934137 | − | 0.0678690i | ||||
\(941\) | −15.6175 | + | 48.0658i | −0.509117 | + | 1.56690i | 0.284621 | + | 0.958640i | \(0.408132\pi\) |
−0.793738 | + | 0.608260i | \(0.791868\pi\) | |||||||
\(942\) | 0.109743 | − | 0.0797330i | 0.00357562 | − | 0.00259784i | ||||
\(943\) | −6.44751 | − | 4.68439i | −0.209960 | − | 0.152545i | ||||
\(944\) | 0.669071 | + | 2.05919i | 0.0217764 | + | 0.0670209i | ||||
\(945\) | −0.0703870 | − | 0.0511391i | −0.00228969 | − | 0.00166356i | ||||
\(946\) | −24.2058 | − | 17.5865i | −0.786997 | − | 0.571787i | ||||
\(947\) | −17.0571 | − | 52.4964i | −0.554282 | − | 1.70590i | −0.697832 | − | 0.716262i | \(-0.745852\pi\) |
0.143550 | − | 0.989643i | \(-0.454148\pi\) | |||||||
\(948\) | 9.20302 | + | 6.68639i | 0.298900 | + | 0.217164i | ||||
\(949\) | −6.86956 | + | 4.99103i | −0.222995 | + | 0.162016i | ||||
\(950\) | −1.40431 | + | 4.32202i | −0.0455619 | + | 0.140225i | ||||
\(951\) | 18.8962 | − | 13.7289i | 0.612750 | − | 0.445189i | ||||
\(952\) | −0.0552165 | − | 0.169939i | −0.00178958 | − | 0.00550776i | ||||
\(953\) | −10.0421 | − | 30.9063i | −0.325295 | − | 1.00115i | −0.971307 | − | 0.237827i | \(-0.923565\pi\) |
0.646013 | − | 0.763327i | \(-0.276435\pi\) | |||||||
\(954\) | −2.11191 | + | 6.49979i | −0.0683756 | + | 0.210439i | ||||
\(955\) | −12.5405 | −0.405801 | ||||||||
\(956\) | 4.21907 | 0.136455 | ||||||||
\(957\) | 10.8357 | − | 33.3487i | 0.350267 | − | 1.07801i | ||||
\(958\) | −24.7637 | − | 17.9919i | −0.800079 | − | 0.581291i | ||||
\(959\) | −0.752135 | + | 0.546458i | −0.0242877 | + | 0.0176460i | ||||
\(960\) | −1.00000 | −0.0322749 | ||||||||
\(961\) | −11.7703 | − | 28.6785i | −0.379688 | − | 0.925114i | ||||
\(962\) | −2.62097 | −0.0845034 | ||||||||
\(963\) | 5.59490 | − | 4.06493i | 0.180293 | − | 0.130991i | ||||
\(964\) | 15.5984 | + | 11.3329i | 0.502390 | + | 0.365007i | ||||
\(965\) | −0.505485 | + | 1.55572i | −0.0162721 | + | 0.0500805i | ||||
\(966\) | −0.164204 | −0.00528318 | ||||||||
\(967\) | −16.4658 | −0.529503 | −0.264752 | − | 0.964317i | \(-0.585290\pi\) | ||||
−0.264752 | + | 0.964317i | \(0.585290\pi\) | |||||||
\(968\) | 3.87010 | − | 11.9109i | 0.124390 | − | 0.382832i | ||||
\(969\) | 2.88413 | + | 8.87645i | 0.0926517 | + | 0.285153i | ||||
\(970\) | −3.84920 | − | 11.8466i | −0.123590 | − | 0.380372i | ||||
\(971\) | 38.2581 | − | 27.7962i | 1.22776 | − | 0.892021i | 0.231042 | − | 0.972944i | \(-0.425787\pi\) |
0.996720 | + | 0.0809223i | \(0.0257866\pi\) | |||||||
\(972\) | −0.309017 | + | 0.951057i | −0.00991172 | + | 0.0305052i | ||||
\(973\) | 0.958503 | − | 0.696394i | 0.0307282 | − | 0.0223254i | ||||
\(974\) | −0.434981 | − | 0.316032i | −0.0139377 | − | 0.0101263i | ||||
\(975\) | 0.276763 | + | 0.851790i | 0.00886352 | + | 0.0272791i | ||||
\(976\) | 3.92705 | + | 2.85317i | 0.125702 | + | 0.0913277i | ||||
\(977\) | −44.8616 | − | 32.5939i | −1.43525 | − | 1.04277i | −0.989009 | − | 0.147858i | \(-0.952762\pi\) |
−0.446241 | − | 0.894913i | \(-0.647238\pi\) | |||||||
\(978\) | 4.50094 | + | 13.8525i | 0.143924 | + | 0.442954i | ||||
\(979\) | 25.8253 | + | 18.7632i | 0.825382 | + | 0.599675i | ||||
\(980\) | 5.65700 | − | 4.11005i | 0.180706 | − | 0.131291i | ||||
\(981\) | −0.385356 | + | 1.18600i | −0.0123035 | + | 0.0378662i | ||||
\(982\) | −21.5986 | + | 15.6923i | −0.689238 | + | 0.500761i | ||||
\(983\) | −17.1152 | − | 52.6751i | −0.545889 | − | 1.68007i | −0.718866 | − | 0.695148i | \(-0.755339\pi\) |
0.172977 | − | 0.984926i | \(-0.444661\pi\) | |||||||
\(984\) | 1.30487 | + | 4.01598i | 0.0415978 | + | 0.128025i | ||||
\(985\) | 3.82236 | − | 11.7640i | 0.121791 | − | 0.374833i | ||||
\(986\) | −14.8481 | −0.472859 | ||||||||
\(987\) | −0.308001 | −0.00980377 | ||||||||
\(988\) | 1.25774 | − | 3.87091i | 0.0400139 | − | 0.123150i | ||||
\(989\) | 9.41918 | + | 6.84343i | 0.299512 | + | 0.217608i | ||||
\(990\) | −3.92385 | + | 2.85084i | −0.124708 | + | 0.0906058i | ||||
\(991\) | −24.9947 | −0.793983 | −0.396991 | − | 0.917822i | \(-0.629946\pi\) | ||||
−0.396991 | + | 0.917822i | \(0.629946\pi\) | |||||||
\(992\) | −3.10078 | + | 4.62441i | −0.0984498 | + | 0.146825i | ||||
\(993\) | 16.7209 | 0.530623 | ||||||||
\(994\) | −1.00812 | + | 0.732441i | −0.0319756 | + | 0.0232316i | ||||
\(995\) | −5.53350 | − | 4.02033i | −0.175424 | − | 0.127453i | ||||
\(996\) | 0.925001 | − | 2.84686i | 0.0293098 | − | 0.0902062i | ||||
\(997\) | 53.0729 | 1.68084 | 0.840418 | − | 0.541939i | \(-0.182309\pi\) | ||||
0.840418 | + | 0.541939i | \(0.182309\pi\) | |||||||
\(998\) | 17.3420 | 0.548951 | ||||||||
\(999\) | −0.904311 | + | 2.78318i | −0.0286111 | + | 0.0880560i |
(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 | 930.2.n.a.481.2 | ✓ | 8 | |
31.2 | even | 5 | inner | 930.2.n.a.901.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.n.a.481.2 | ✓ | 8 | 1.1 | even | 1 | trivial | |
930.2.n.a.901.2 | yes | 8 | 31.2 | even | 5 | inner |