Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,2,Mod(19,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.19");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.bf (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.01223013094\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.562828176.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + x^{6} + 2x^{5} - 6x^{4} + 4x^{3} + 4x^{2} - 16x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 84) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 199.2 | ||
Root | \(1.40376 - 0.171630i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.199 |
Dual form | 252.2.bf.g.19.2 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.850516 | − | 1.12988i | −0.601406 | − | 0.798944i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.553244 | + | 1.92196i | −0.276622 | + | 0.960979i | ||||
\(5\) | −0.834598 | + | 0.481855i | −0.373244 | + | 0.215492i | −0.674875 | − | 0.737932i | \(-0.735802\pi\) |
0.301631 | + | 0.953425i | \(0.402469\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.20103 | − | 2.35744i | −0.453948 | − | 0.891028i | ||||
\(8\) | 2.64212 | − | 1.00956i | 0.934130 | − | 0.356933i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.25428 | + | 0.533167i | 0.396637 | + | 0.168602i | ||||
\(11\) | −4.74861 | − | 2.74161i | −1.43176 | − | 0.826626i | −0.434504 | − | 0.900670i | \(-0.643076\pi\) |
−0.997255 | + | 0.0740437i | \(0.976410\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 3.75117i | − | 1.04039i | −0.854048 | − | 0.520193i | \(-0.825860\pi\) | ||
0.854048 | − | 0.520193i | \(-0.174140\pi\) | |||||||
\(14\) | −1.64212 | + | 3.36206i | −0.438875 | + | 0.898548i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.38784 | − | 2.12662i | −0.846961 | − | 0.531656i | ||||
\(17\) | 0.594545 | + | 0.343260i | 0.144198 | + | 0.0832529i | 0.570363 | − | 0.821393i | \(-0.306802\pi\) |
−0.426165 | + | 0.904645i | \(0.640136\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.44109 | − | 4.22809i | −0.560024 | − | 0.969989i | −0.997494 | − | 0.0707563i | \(-0.977459\pi\) |
0.437470 | − | 0.899233i | \(-0.355875\pi\) | |||||||
\(20\) | −0.464369 | − | 1.87065i | −0.103836 | − | 0.418289i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.941086 | + | 7.69713i | 0.200640 | + | 1.64103i | ||||
\(23\) | 1.07465 | − | 0.620450i | 0.224080 | − | 0.129373i | −0.383758 | − | 0.923434i | \(-0.625370\pi\) |
0.607838 | + | 0.794061i | \(0.292037\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.03563 | + | 3.52582i | −0.407126 | + | 0.705163i | ||||
\(26\) | −4.23836 | + | 3.19043i | −0.831210 | + | 0.625695i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 5.19536 | − | 1.00409i | 0.981831 | − | 0.189756i | ||||
\(29\) | 2.48011 | 0.460544 | 0.230272 | − | 0.973126i | \(-0.426038\pi\) | ||||
0.230272 | + | 0.973126i | \(0.426038\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.41401 | + | 4.18119i | −0.433569 | + | 0.750963i | −0.997178 | − | 0.0750787i | \(-0.976079\pi\) |
0.563609 | + | 0.826042i | \(0.309413\pi\) | |||||||
\(32\) | 0.478592 | + | 5.63657i | 0.0846040 | + | 0.996415i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.117828 | − | 0.963711i | −0.0202073 | − | 0.165275i | ||||
\(35\) | 2.13832 | + | 1.38879i | 0.361443 | + | 0.234748i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.36643 | + | 2.36673i | 0.224640 | + | 0.389089i | 0.956212 | − | 0.292677i | \(-0.0945459\pi\) |
−0.731571 | + | 0.681765i | \(0.761213\pi\) | |||||||
\(38\) | −2.70103 | + | 6.35418i | −0.438165 | + | 1.03078i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.71865 | + | 2.11569i | −0.271742 | + | 0.334521i | ||||
\(41\) | − | 9.42976i | − | 1.47268i | −0.676611 | − | 0.736340i | \(-0.736552\pi\) | ||
0.676611 | − | 0.736340i | \(-0.263448\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 5.97437i | − | 0.911083i | −0.890215 | − | 0.455541i | \(-0.849446\pi\) | ||
0.890215 | − | 0.455541i | \(-0.150554\pi\) | |||||||
\(44\) | 7.89640 | − | 7.60984i | 1.19043 | − | 1.14723i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.61504 | − | 0.686521i | −0.238125 | − | 0.101222i | ||||
\(47\) | 1.80752 | + | 3.13072i | 0.263654 | + | 0.456662i | 0.967210 | − | 0.253978i | \(-0.0817390\pi\) |
−0.703556 | + | 0.710640i | \(0.748406\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.11504 | + | 5.66272i | −0.587863 | + | 0.808960i | ||||
\(50\) | 5.71508 | − | 0.698752i | 0.808234 | − | 0.0988184i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 7.20959 | + | 2.07531i | 0.999790 | + | 0.287794i | ||||
\(53\) | −2.04757 | + | 3.54650i | −0.281256 | + | 0.487150i | −0.971694 | − | 0.236242i | \(-0.924084\pi\) |
0.690438 | + | 0.723391i | \(0.257418\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.28424 | 0.712526 | ||||||||
\(56\) | −5.55324 | − | 5.01612i | −0.742083 | − | 0.670308i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.10937 | − | 2.80222i | −0.276974 | − | 0.367949i | ||||
\(59\) | 6.34315 | − | 10.9867i | 0.825808 | − | 1.43034i | −0.0754923 | − | 0.997146i | \(-0.524053\pi\) |
0.901300 | − | 0.433195i | \(-0.142614\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.01711 | − | 5.20603i | 1.15452 | − | 0.666564i | 0.204537 | − | 0.978859i | \(-0.434431\pi\) |
0.949985 | + | 0.312295i | \(0.101098\pi\) | |||||||
\(62\) | 6.77738 | − | 0.828634i | 0.860728 | − | 0.105237i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 5.96158 | − | 5.33475i | 0.745198 | − | 0.666843i | ||||
\(65\) | 1.80752 | + | 3.13072i | 0.224195 | + | 0.388318i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.17396 | + | 4.71924i | 0.998608 | + | 0.576546i | 0.907836 | − | 0.419325i | \(-0.137733\pi\) |
0.0907716 | + | 0.995872i | \(0.471067\pi\) | |||||||
\(68\) | −0.988660 | + | 0.952783i | −0.119893 | + | 0.115542i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.249518 | − | 3.59723i | −0.0298231 | − | 0.429952i | ||||
\(71\) | 10.1163i | 1.20058i | 0.799782 | + | 0.600291i | \(0.204948\pi\) | ||||
−0.799782 | + | 0.600291i | \(0.795052\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.76850 | − | 3.33044i | −0.675152 | − | 0.389799i | 0.122874 | − | 0.992422i | \(-0.460789\pi\) |
−0.798026 | + | 0.602623i | \(0.794122\pi\) | |||||||
\(74\) | 1.51194 | − | 3.55685i | 0.175760 | − | 0.413475i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 9.47672 | − | 2.35250i | 1.08705 | − | 0.269850i | ||||
\(77\) | −0.759946 | + | 14.4873i | −0.0866039 | + | 1.65098i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.22492 | − | 0.707208i | 0.137814 | − | 0.0795671i | −0.429508 | − | 0.903063i | \(-0.641313\pi\) |
0.567322 | + | 0.823496i | \(0.307980\pi\) | |||||||
\(80\) | 3.85221 | + | 0.142425i | 0.430690 | + | 0.0159237i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −10.6545 | + | 8.02016i | −1.17659 | + | 0.885679i | ||||
\(83\) | −0.543780 | −0.0596876 | −0.0298438 | − | 0.999555i | \(-0.509501\pi\) | ||||
−0.0298438 | + | 0.999555i | \(0.509501\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.661608 | −0.0717614 | ||||||||
\(86\) | −6.75030 | + | 5.08130i | −0.727904 | + | 0.547930i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −15.3142 | − | 2.44966i | −1.63250 | − | 0.261135i | ||||
\(89\) | −0.480107 | + | 0.277190i | −0.0508912 | + | 0.0293821i | −0.525230 | − | 0.850960i | \(-0.676021\pi\) |
0.474339 | + | 0.880343i | \(0.342687\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.84315 | + | 4.50528i | −0.927014 | + | 0.472281i | ||||
\(92\) | 0.597935 | + | 2.40870i | 0.0623390 | + | 0.251124i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.00000 | − | 4.70500i | 0.206284 | − | 0.485284i | ||||
\(95\) | 4.07465 | + | 2.35250i | 0.418050 | + | 0.241362i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 10.8747i | − | 1.10416i | −0.833790 | − | 0.552081i | \(-0.813834\pi\) | ||
0.833790 | − | 0.552081i | \(-0.186166\pi\) | |||||||
\(98\) | 9.89809 | − | 0.166748i | 0.999858 | − | 0.0168441i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −5.65027 | − | 5.86303i | −0.565027 | − | 0.586303i | ||||
\(101\) | −12.4972 | − | 7.21527i | −1.24352 | − | 0.717946i | −0.273710 | − | 0.961812i | \(-0.588251\pi\) |
−0.969809 | + | 0.243866i | \(0.921584\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.51235 | + | 13.0118i | 0.740214 | + | 1.28209i | 0.952398 | + | 0.304858i | \(0.0986090\pi\) |
−0.212184 | + | 0.977230i | \(0.568058\pi\) | |||||||
\(104\) | −3.78702 | − | 9.91103i | −0.371348 | − | 0.971857i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.74861 | − | 0.702851i | 0.558354 | − | 0.0682669i | ||||
\(107\) | −10.4925 | + | 6.05782i | −1.01434 | + | 0.585632i | −0.912461 | − | 0.409165i | \(-0.865820\pi\) |
−0.101883 | + | 0.994796i | \(0.532487\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.03563 | − | 5.25787i | 0.290761 | − | 0.503612i | −0.683229 | − | 0.730204i | \(-0.739425\pi\) |
0.973990 | + | 0.226592i | \(0.0727583\pi\) | |||||||
\(110\) | −4.49433 | − | 5.97054i | −0.428518 | − | 0.569268i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.944476 | + | 10.5408i | −0.0892446 | + | 0.996010i | ||||
\(113\) | 7.37939 | 0.694194 | 0.347097 | − | 0.937829i | \(-0.387167\pi\) | ||||
0.347097 | + | 0.937829i | \(0.387167\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.597935 | + | 1.03565i | −0.0557577 | + | 0.0965752i | ||||
\(116\) | −1.37210 | + | 4.76666i | −0.127397 | + | 0.442573i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −17.8085 | + | 2.17735i | −1.63941 | + | 0.200442i | ||||
\(119\) | 0.0951483 | − | 1.81387i | 0.00872223 | − | 0.166277i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.53284 | + | 16.5114i | 0.866622 | + | 1.50103i | ||||
\(122\) | −13.5514 | − | 5.76041i | −1.22688 | − | 0.521523i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −6.70053 | − | 6.95284i | −0.601725 | − | 0.624383i | ||||
\(125\) | − | 8.74207i | − | 0.781915i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.6431i | 1.03316i | 0.856240 | + | 0.516578i | \(0.172794\pi\) | ||||
−0.856240 | + | 0.516578i | \(0.827206\pi\) | |||||||
\(128\) | −11.0980 | − | 2.19857i | −0.980937 | − | 0.194328i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.00000 | − | 4.70500i | 0.175412 | − | 0.412656i | ||||
\(131\) | −4.63078 | − | 8.02074i | −0.404593 | − | 0.700776i | 0.589681 | − | 0.807636i | \(-0.299253\pi\) |
−0.994274 | + | 0.106861i | \(0.965920\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.03563 | + | 10.8328i | −0.610067 | + | 0.939321i | ||||
\(134\) | −1.61993 | − | 13.2494i | −0.139940 | − | 1.14457i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.91740 | + | 0.306707i | 0.164416 | + | 0.0262999i | ||||
\(137\) | 3.61504 | − | 6.26144i | 0.308854 | − | 0.534951i | −0.669258 | − | 0.743030i | \(-0.733388\pi\) |
0.978112 | + | 0.208080i | \(0.0667213\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.30812 | −0.450229 | −0.225115 | − | 0.974332i | \(-0.572276\pi\) | ||||
−0.225115 | + | 0.974332i | \(0.572276\pi\) | |||||||
\(140\) | −3.85221 | + | 3.34143i | −0.325571 | + | 0.282402i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 11.4302 | − | 8.60406i | 0.959197 | − | 0.722037i | ||||
\(143\) | −10.2842 | + | 17.8128i | −0.860011 | + | 1.48958i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.06989 | + | 1.19505i | −0.171895 | + | 0.0992438i | ||||
\(146\) | 1.14321 | + | 9.35029i | 0.0946127 | + | 0.773836i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.30473 | + | 1.31685i | −0.436046 | + | 0.108244i | ||||
\(149\) | 2.33080 | + | 4.03707i | 0.190947 | + | 0.330730i | 0.945564 | − | 0.325435i | \(-0.105511\pi\) |
−0.754617 | + | 0.656165i | \(0.772178\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.5709 | − | 6.10309i | −0.860244 | − | 0.496662i | 0.00384988 | − | 0.999993i | \(-0.498775\pi\) |
−0.864094 | + | 0.503330i | \(0.832108\pi\) | |||||||
\(152\) | −10.7181 | − | 8.70668i | −0.869356 | − | 0.706205i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 17.0152 | − | 11.4631i | 1.37113 | − | 0.923719i | ||||
\(155\) | − | 4.65281i | − | 0.373723i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18.9944 | − | 10.9664i | −1.51592 | − | 0.875217i | −0.999825 | − | 0.0186856i | \(-0.994052\pi\) |
−0.516095 | − | 0.856531i | \(-0.672615\pi\) | |||||||
\(158\) | −1.84087 | − | 0.782517i | −0.146452 | − | 0.0622537i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.11545 | − | 4.47366i | −0.246298 | − | 0.353674i | ||||
\(161\) | −2.75337 | − | 1.78824i | −0.216996 | − | 0.140933i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.48011 | − | 2.00924i | 0.272583 | − | 0.157376i | −0.357478 | − | 0.933922i | \(-0.616363\pi\) |
0.630061 | + | 0.776546i | \(0.283030\pi\) | |||||||
\(164\) | 18.1236 | + | 5.21696i | 1.41521 | + | 0.407376i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.462494 | + | 0.614404i | 0.0358965 | + | 0.0476870i | ||||
\(167\) | 14.7178 | 1.13890 | 0.569448 | − | 0.822027i | \(-0.307157\pi\) | ||||
0.569448 | + | 0.822027i | \(0.307157\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.07126 | −0.0824047 | ||||||||
\(170\) | 0.562708 | + | 0.747535i | 0.0431577 | + | 0.0573333i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 11.4825 | + | 3.30528i | 0.875531 | + | 0.252026i | ||||
\(173\) | 10.0918 | − | 5.82648i | 0.767262 | − | 0.442979i | −0.0646349 | − | 0.997909i | \(-0.520588\pi\) |
0.831897 | + | 0.554930i | \(0.187255\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.7568 | + | 0.564256i | 0.813134 | + | 0.0426538i | ||||
\(176\) | 10.2572 | + | 19.3866i | 0.773163 | + | 1.46132i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.721529 | + | 0.306707i | 0.0540809 | + | 0.0229887i | ||||
\(179\) | −2.24663 | − | 1.29709i | −0.167921 | − | 0.0969494i | 0.413684 | − | 0.910421i | \(-0.364242\pi\) |
−0.581605 | + | 0.813471i | \(0.697575\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.53343i | 0.708615i | 0.935129 | + | 0.354307i | \(0.115283\pi\) | ||||
−0.935129 | + | 0.354307i | \(0.884717\pi\) | |||||||
\(182\) | 12.6117 | + | 6.15986i | 0.934838 | + | 0.456599i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.21298 | − | 2.72423i | 0.163143 | − | 0.200833i | ||||
\(185\) | −2.28085 | − | 1.31685i | −0.167691 | − | 0.0968166i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.88217 | − | 3.26002i | −0.137638 | − | 0.238396i | ||||
\(188\) | −7.01711 | + | 1.74193i | −0.511775 | + | 0.127043i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.807521 | − | 6.60470i | −0.0585837 | − | 0.479155i | ||||
\(191\) | 7.21637 | − | 4.16637i | 0.522158 | − | 0.301468i | −0.215659 | − | 0.976469i | \(-0.569190\pi\) |
0.737817 | + | 0.675001i | \(0.235857\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.18630 | − | 10.7150i | 0.445300 | − | 0.771282i | −0.552773 | − | 0.833332i | \(-0.686430\pi\) |
0.998073 | + | 0.0620498i | \(0.0197638\pi\) | |||||||
\(194\) | −12.2871 | + | 9.24915i | −0.882164 | + | 0.664050i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −8.60689 | − | 11.0418i | −0.614778 | − | 0.788700i | ||||
\(197\) | −3.23686 | −0.230617 | −0.115308 | − | 0.993330i | \(-0.536786\pi\) | ||||
−0.115308 | + | 0.993330i | \(0.536786\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.61504 | − | 16.6537i | 0.681592 | − | 1.18055i | −0.292903 | − | 0.956142i | \(-0.594621\pi\) |
0.974495 | − | 0.224410i | \(-0.0720455\pi\) | |||||||
\(200\) | −1.81886 | + | 11.3707i | −0.128613 | + | 0.804031i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.47672 | + | 20.2570i | 0.174261 | + | 1.42528i | ||||
\(203\) | −2.97869 | − | 5.84670i | −0.209063 | − | 0.410358i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.54378 | + | 7.87006i | 0.317351 | + | 0.549669i | ||||
\(206\) | 8.31232 | − | 19.5547i | 0.579147 | − | 1.36244i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −7.97732 | + | 12.7084i | −0.553128 | + | 0.881167i | ||||
\(209\) | 26.7700i | 1.85172i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 9.24637i | − | 0.636546i | −0.947999 | − | 0.318273i | \(-0.896897\pi\) | ||
0.947999 | − | 0.318273i | \(-0.103103\pi\) | |||||||
\(212\) | −5.68342 | − | 5.89743i | −0.390339 | − | 0.405037i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 15.7686 | + | 6.70291i | 1.07792 | + | 0.458201i | ||||
\(215\) | 2.87878 | + | 4.98620i | 0.196331 | + | 0.340056i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.7562 | + | 0.669139i | 0.865947 | + | 0.0454241i | ||||
\(218\) | −8.52260 | + | 1.04201i | −0.577223 | + | 0.0705740i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.92347 | + | 10.1561i | −0.197100 | + | 0.684723i | ||||
\(221\) | 1.28763 | − | 2.23024i | 0.0866152 | − | 0.150022i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.94585 | −0.130303 | −0.0651517 | − | 0.997875i | \(-0.520753\pi\) | ||||
−0.0651517 | + | 0.997875i | \(0.520753\pi\) | |||||||
\(224\) | 12.7131 | − | 7.89796i | 0.849428 | − | 0.527705i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.27629 | − | 8.33780i | −0.417492 | − | 0.554622i | ||||
\(227\) | 4.32265 | − | 7.48706i | 0.286905 | − | 0.496933i | −0.686165 | − | 0.727446i | \(-0.740707\pi\) |
0.973069 | + | 0.230513i | \(0.0740404\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.5396 | − | 8.39446i | 0.960805 | − | 0.554721i | 0.0643846 | − | 0.997925i | \(-0.479492\pi\) |
0.896421 | + | 0.443204i | \(0.146158\pi\) | |||||||
\(230\) | 1.67871 | − | 0.205247i | 0.110691 | − | 0.0135336i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.55274 | − | 2.50381i | 0.430208 | − | 0.164383i | ||||
\(233\) | −0.523283 | − | 0.906353i | −0.0342814 | − | 0.0593772i | 0.848376 | − | 0.529395i | \(-0.177581\pi\) |
−0.882657 | + | 0.470018i | \(0.844248\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.01711 | − | 1.74193i | −0.196814 | − | 0.113631i | ||||
\(236\) | 17.6066 | + | 18.2696i | 1.14609 | + | 1.18925i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.13037 | + | 1.43522i | −0.138092 | + | 0.0930315i | ||||
\(239\) | − | 19.2479i | − | 1.24505i | −0.782602 | − | 0.622523i | \(-0.786108\pi\) | ||
0.782602 | − | 0.622523i | \(-0.213892\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.38754 | − | 1.37844i | −0.153795 | − | 0.0887934i | 0.421128 | − | 0.907001i | \(-0.361634\pi\) |
−0.574922 | + | 0.818208i | \(0.694968\pi\) | |||||||
\(242\) | 10.5480 | − | 24.8141i | 0.678050 | − | 1.59511i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 5.01711 | + | 20.2107i | 0.321187 | + | 1.29386i | ||||
\(245\) | 0.705792 | − | 6.70895i | 0.0450914 | − | 0.428619i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −15.8603 | + | 9.15692i | −1.00916 | + | 0.582641i | ||||
\(248\) | −2.15695 | + | 13.4843i | −0.136966 | + | 0.856252i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −9.87747 | + | 7.43528i | −0.624706 | + | 0.470248i | ||||
\(251\) | −20.7493 | −1.30968 | −0.654841 | − | 0.755767i | \(-0.727264\pi\) | ||||
−0.654841 | + | 0.755767i | \(0.727264\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.80413 | −0.427772 | ||||||||
\(254\) | 13.1553 | − | 9.90263i | 0.825434 | − | 0.621346i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 6.95495 | + | 14.4093i | 0.434684 | + | 0.900583i | ||||
\(257\) | −6.45283 | + | 3.72554i | −0.402516 | + | 0.232393i | −0.687569 | − | 0.726119i | \(-0.741322\pi\) |
0.285053 | + | 0.958512i | \(0.407989\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.93830 | − | 6.06381i | 0.244714 | − | 0.376787i | ||||
\(260\) | −7.01711 | + | 1.74193i | −0.435182 | + | 0.108030i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −5.12390 | + | 12.0540i | −0.316556 | + | 0.744698i | ||||
\(263\) | 25.7034 | + | 14.8399i | 1.58494 | + | 0.915066i | 0.994123 | + | 0.108260i | \(0.0345280\pi\) |
0.590818 | + | 0.806805i | \(0.298805\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 3.94654i | − | 0.242434i | ||||||
\(266\) | 18.2236 | − | 1.26406i | 1.11736 | − | 0.0775045i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −13.5924 | + | 13.0991i | −0.830286 | + | 0.800155i | ||||
\(269\) | 3.73727 | + | 2.15771i | 0.227865 | + | 0.131558i | 0.609587 | − | 0.792719i | \(-0.291335\pi\) |
−0.381722 | + | 0.924277i | \(0.624669\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.79142 | − | 11.7631i | −0.412550 | − | 0.714557i | 0.582618 | − | 0.812746i | \(-0.302028\pi\) |
−0.995168 | + | 0.0981892i | \(0.968695\pi\) | |||||||
\(272\) | −1.28424 | − | 2.42728i | −0.0778683 | − | 0.147176i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −10.1493 | + | 1.24090i | −0.613142 | + | 0.0749656i | ||||
\(275\) | 19.3328 | − | 11.1618i | 1.16581 | − | 0.673082i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.03563 | + | 1.79376i | −0.0622250 | + | 0.107777i | −0.895460 | − | 0.445143i | \(-0.853153\pi\) |
0.833235 | + | 0.552920i | \(0.186486\pi\) | |||||||
\(278\) | 4.51465 | + | 5.99753i | 0.270770 | + | 0.359708i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 7.05177 | + | 1.51059i | 0.421424 | + | 0.0902747i | ||||
\(281\) | −23.7122 | −1.41455 | −0.707276 | − | 0.706938i | \(-0.750076\pi\) | ||||
−0.707276 | + | 0.706938i | \(0.750076\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.12739 | − | 10.6129i | 0.364235 | − | 0.630874i | −0.624418 | − | 0.781091i | \(-0.714664\pi\) |
0.988653 | + | 0.150216i | \(0.0479970\pi\) | |||||||
\(284\) | −19.4431 | − | 5.59677i | −1.15373 | − | 0.332107i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 28.8732 | − | 3.53017i | 1.70731 | − | 0.208743i | ||||
\(287\) | −22.2301 | + | 11.3254i | −1.31220 | + | 0.668520i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.26434 | − | 14.3143i | −0.486138 | − | 0.842016i | ||||
\(290\) | 3.11074 | + | 1.32231i | 0.182669 | + | 0.0776488i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 9.59236 | − | 9.24426i | 0.561351 | − | 0.540980i | ||||
\(293\) | − | 10.7090i | − | 0.625626i | −0.949815 | − | 0.312813i | \(-0.898729\pi\) | ||
0.949815 | − | 0.312813i | \(-0.101271\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.2259i | 0.711821i | ||||||||
\(296\) | 5.99964 | + | 4.87370i | 0.348722 | + | 0.283278i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.57901 | − | 6.06712i | 0.149398 | − | 0.351459i | ||||
\(299\) | −2.32741 | − | 4.03120i | −0.134598 | − | 0.233130i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −14.0842 | + | 7.17541i | −0.811801 | + | 0.413584i | ||||
\(302\) | 2.09495 | + | 17.1345i | 0.120551 | + | 0.985982i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.721529 | + | 19.5154i | −0.0413825 | + | 1.11928i | ||||
\(305\) | −5.01711 | + | 8.68988i | −0.287279 | + | 0.497581i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.22056 | −0.240880 | −0.120440 | − | 0.992721i | \(-0.538431\pi\) | ||||
−0.120440 | + | 0.992721i | \(0.538431\pi\) | |||||||
\(308\) | −27.4236 | − | 9.47561i | −1.56260 | − | 0.539923i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −5.25711 | + | 3.95729i | −0.298584 | + | 0.224759i | ||||
\(311\) | −4.85070 | + | 8.40165i | −0.275058 | + | 0.476414i | −0.970150 | − | 0.242507i | \(-0.922030\pi\) |
0.695092 | + | 0.718921i | \(0.255364\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.8328 | − | 6.83168i | 0.668831 | − | 0.386149i | −0.126803 | − | 0.991928i | \(-0.540472\pi\) |
0.795633 | + | 0.605778i | \(0.207138\pi\) | |||||||
\(314\) | 3.76434 | + | 30.7885i | 0.212434 | + | 1.73750i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.681544 | + | 2.74550i | 0.0383398 | + | 0.154447i | ||||
\(317\) | 10.0442 | + | 17.3970i | 0.564138 | + | 0.977115i | 0.997129 | + | 0.0757171i | \(0.0241246\pi\) |
−0.432992 | + | 0.901398i | \(0.642542\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −11.7771 | − | 6.79948i | −0.659388 | − | 0.380698i | ||||
\(320\) | −2.40495 | + | 7.32499i | −0.134441 | + | 0.409479i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.321286 | + | 4.63190i | 0.0179046 | + | 0.258125i | ||||
\(323\) | − | 3.35171i | − | 0.186494i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 13.2259 | + | 7.63599i | 0.733642 | + | 0.423569i | ||||
\(326\) | −5.23008 | − | 2.22320i | −0.289667 | − | 0.123132i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −9.51989 | − | 24.9145i | −0.525648 | − | 1.37568i | ||||
\(329\) | 5.20959 | − | 8.02121i | 0.287214 | − | 0.442224i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.15886 | + | 4.71052i | −0.448452 | + | 0.258914i | −0.707176 | − | 0.707037i | \(-0.750031\pi\) |
0.258724 | + | 0.965951i | \(0.416698\pi\) | |||||||
\(332\) | 0.300843 | − | 1.04512i | 0.0165109 | − | 0.0573585i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −12.5177 | − | 16.6293i | −0.684939 | − | 0.909914i | ||||
\(335\) | −9.09596 | −0.496965 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.4411 | −0.732185 | −0.366092 | − | 0.930578i | \(-0.619305\pi\) | ||||
−0.366092 | + | 0.930578i | \(0.619305\pi\) | |||||||
\(338\) | 0.911125 | + | 1.21039i | 0.0495587 | + | 0.0658367i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.366030 | − | 1.27158i | 0.0198508 | − | 0.0689612i | ||||
\(341\) | 22.9264 | − | 13.2365i | 1.24153 | − | 0.716799i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.2918 | + | 2.89985i | 0.987666 | + | 0.156577i | ||||
\(344\) | −6.03148 | − | 15.7850i | −0.325195 | − | 0.851070i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −15.1664 | − | 6.44693i | −0.815351 | − | 0.346589i | ||||
\(347\) | −19.5890 | − | 11.3097i | −1.05159 | − | 0.607136i | −0.128497 | − | 0.991710i | \(-0.541015\pi\) |
−0.923094 | + | 0.384574i | \(0.874349\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.48180i | 0.132848i | 0.997791 | + | 0.0664239i | \(0.0211590\pi\) | ||||
−0.997791 | + | 0.0664239i | \(0.978841\pi\) | |||||||
\(350\) | −8.51126 | − | 12.6337i | −0.454946 | − | 0.675301i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 13.1806 | − | 28.0780i | 0.702530 | − | 1.49656i | ||||
\(353\) | 7.89315 | + | 4.55711i | 0.420110 | + | 0.242551i | 0.695124 | − | 0.718889i | \(-0.255349\pi\) |
−0.275014 | + | 0.961440i | \(0.588683\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.87458 | − | 8.44303i | −0.258716 | − | 0.448109i | ||||
\(356\) | −0.267131 | − | 1.07610i | −0.0141579 | − | 0.0570331i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.445241 | + | 3.64162i | 0.0235317 | + | 0.192466i | ||||
\(359\) | −6.00000 | + | 3.46410i | −0.316668 | + | 0.182828i | −0.649906 | − | 0.760014i | \(-0.725192\pi\) |
0.333238 | + | 0.942843i | \(0.391859\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.41780 | + | 4.18776i | −0.127253 | + | 0.220408i | ||||
\(362\) | 10.7716 | − | 8.10834i | 0.566143 | − | 0.426165i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.76653 | − | 19.4887i | −0.197420 | − | 1.02148i | ||||
\(365\) | 6.41917 | 0.335995 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.91680 | − | 3.31999i | 0.100056 | − | 0.173302i | −0.811652 | − | 0.584142i | \(-0.801431\pi\) |
0.911707 | + | 0.410840i | \(0.134765\pi\) | |||||||
\(368\) | −4.96021 | − | 0.183391i | −0.258569 | − | 0.00955992i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0.452022 | + | 3.69708i | 0.0234995 | + | 0.192202i | ||||
\(371\) | 10.8199 | + | 0.567567i | 0.561740 | + | 0.0294666i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.4150 | + | 23.2355i | 0.694603 | + | 1.20309i | 0.970314 | + | 0.241848i | \(0.0777534\pi\) |
−0.275711 | + | 0.961241i | \(0.588913\pi\) | |||||||
\(374\) | −2.08260 | + | 4.89932i | −0.107689 | + | 0.253338i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.93633 | + | 6.44693i | 0.409285 | + | 0.332475i | ||||
\(377\) | − | 9.30330i | − | 0.479144i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 6.93692i | − | 0.356325i | −0.984001 | − | 0.178163i | \(-0.942985\pi\) | ||
0.984001 | − | 0.178163i | \(-0.0570153\pi\) | |||||||
\(380\) | −6.77568 | + | 6.52980i | −0.347585 | + | 0.334972i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −10.8451 | − | 4.61004i | −0.554885 | − | 0.235870i | ||||
\(383\) | 1.12881 | + | 1.95515i | 0.0576793 | + | 0.0999035i | 0.893423 | − | 0.449216i | \(-0.148297\pi\) |
−0.835744 | + | 0.549119i | \(0.814963\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.34654 | − | 12.4573i | −0.323450 | − | 0.634881i | ||||
\(386\) | −17.3682 | + | 2.12351i | −0.884017 | + | 0.108084i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 20.9008 | + | 6.01639i | 1.06108 | + | 0.305436i | ||||
\(389\) | 15.3047 | − | 26.5086i | 0.775981 | − | 1.34404i | −0.158261 | − | 0.987397i | \(-0.550589\pi\) |
0.934242 | − | 0.356641i | \(-0.116078\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.851904 | 0.0430827 | ||||||||
\(392\) | −5.15558 | + | 19.1160i | −0.260396 | + | 0.965502i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.75300 | + | 3.65726i | 0.138694 | + | 0.184250i | ||||
\(395\) | −0.681544 | + | 1.18047i | −0.0342922 | + | 0.0593958i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.0368 | + | 6.94947i | −0.604112 | + | 0.348784i | −0.770657 | − | 0.637250i | \(-0.780072\pi\) |
0.166546 | + | 0.986034i | \(0.446739\pi\) | |||||||
\(398\) | −26.9944 | + | 3.30046i | −1.35311 | + | 0.165437i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 14.3945 | − | 7.61589i | 0.719724 | − | 0.380794i | ||||
\(401\) | −5.13832 | − | 8.89984i | −0.256596 | − | 0.444437i | 0.708732 | − | 0.705478i | \(-0.249268\pi\) |
−0.965328 | + | 0.261041i | \(0.915934\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 15.6843 | + | 9.05535i | 0.781292 | + | 0.451079i | ||||
\(404\) | 20.7815 | − | 20.0273i | 1.03392 | − | 0.996396i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.07263 | + | 8.33827i | −0.202121 | + | 0.413821i | ||||
\(407\) | − | 14.9849i | − | 0.742775i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.5342 | + | 6.08193i | 0.520883 | + | 0.300732i | 0.737296 | − | 0.675570i | \(-0.236102\pi\) |
−0.216413 | + | 0.976302i | \(0.569436\pi\) | |||||||
\(410\) | 5.02764 | − | 11.8275i | 0.248297 | − | 0.584120i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −29.1642 | + | 7.23973i | −1.43682 | + | 0.356676i | ||||
\(413\) | −33.5187 | − | 1.75826i | −1.64935 | − | 0.0865182i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.453838 | − | 0.262023i | 0.0222780 | − | 0.0128622i | ||||
\(416\) | 21.1437 | − | 1.79528i | 1.03666 | − | 0.0880209i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 30.2468 | − | 22.7683i | 1.47942 | − | 1.11364i | ||||
\(419\) | 16.2245 | 0.792619 | 0.396310 | − | 0.918117i | \(-0.370291\pi\) | ||||
0.396310 | + | 0.918117i | \(0.370291\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.58477 | −0.467133 | −0.233567 | − | 0.972341i | \(-0.575040\pi\) | ||||
−0.233567 | + | 0.972341i | \(0.575040\pi\) | |||||||
\(422\) | −10.4473 | + | 7.86419i | −0.508565 | + | 0.382823i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.82953 | + | 11.4374i | −0.0888499 | + | 0.555451i | ||||
\(425\) | −2.42055 | + | 1.39750i | −0.117414 | + | 0.0677889i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −23.1027 | − | 15.0047i | −1.11802 | − | 0.726127i | ||||
\(428\) | −5.83799 | − | 23.5175i | −0.282190 | − | 1.13676i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.18534 | − | 7.49351i | 0.153611 | − | 0.361369i | ||||
\(431\) | −0.131544 | − | 0.0759470i | −0.00633626 | − | 0.00365824i | 0.496829 | − | 0.867849i | \(-0.334498\pi\) |
−0.503165 | + | 0.864190i | \(0.667831\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.46997i | 0.455098i | 0.973767 | + | 0.227549i | \(0.0730711\pi\) | ||||
−0.973767 | + | 0.227549i | \(0.926929\pi\) | |||||||
\(434\) | −10.0933 | − | 14.9820i | −0.484494 | − | 0.719161i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.42595 | + | 8.74324i | 0.403530 | + | 0.418725i | ||||
\(437\) | −5.24663 | − | 3.02915i | −0.250981 | − | 0.144904i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.7373 | + | 28.9898i | 0.798826 | + | 1.38361i | 0.920381 | + | 0.391023i | \(0.127879\pi\) |
−0.121555 | + | 0.992585i | \(0.538788\pi\) | |||||||
\(440\) | 13.9616 | − | 5.33475i | 0.665592 | − | 0.254324i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.61504 | + | 0.441992i | −0.171950 | + | 0.0210234i | ||||
\(443\) | −22.6513 | + | 13.0777i | −1.07619 | + | 0.621341i | −0.929867 | − | 0.367895i | \(-0.880079\pi\) |
−0.146327 | + | 0.989236i | \(0.546745\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.267131 | − | 0.462684i | 0.0126632 | − | 0.0219333i | ||||
\(446\) | 1.65497 | + | 2.19857i | 0.0783652 | + | 0.104105i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −19.7364 | − | 7.64686i | −0.932457 | − | 0.361280i | ||||
\(449\) | −10.2918 | −0.485701 | −0.242851 | − | 0.970064i | \(-0.578082\pi\) | ||||
−0.242851 | + | 0.970064i | \(0.578082\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −25.8527 | + | 44.7782i | −1.21736 | + | 2.10852i | ||||
\(452\) | −4.08260 | + | 14.1829i | −0.192029 | + | 0.667106i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −12.1359 | + | 1.48380i | −0.569568 | + | 0.0696380i | ||||
\(455\) | 5.20959 | − | 8.02121i | 0.244229 | − | 0.376040i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.96574 | − | 10.3330i | −0.279065 | − | 0.483356i | 0.692087 | − | 0.721814i | \(-0.256691\pi\) |
−0.971153 | + | 0.238458i | \(0.923358\pi\) | |||||||
\(458\) | −21.8509 | − | 9.28837i | −1.02103 | − | 0.434017i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.65968 | − | 1.72217i | −0.0773829 | − | 0.0802968i | ||||
\(461\) | 30.0093i | 1.39767i | 0.715281 | + | 0.698837i | \(0.246299\pi\) | ||||
−0.715281 | + | 0.698837i | \(0.753701\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.2736i | 0.616875i | 0.951245 | + | 0.308437i | \(0.0998060\pi\) | ||||
−0.951245 | + | 0.308437i | \(0.900194\pi\) | |||||||
\(464\) | −8.40221 | − | 5.27425i | −0.390063 | − | 0.244851i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.579007 | + | 1.36211i | −0.0268220 | + | 0.0630987i | ||||
\(467\) | 14.8246 | + | 25.6770i | 0.686002 | + | 1.18819i | 0.973121 | + | 0.230295i | \(0.0739692\pi\) |
−0.287119 | + | 0.957895i | \(0.592697\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.30812 | − | 24.9376i | 0.0604036 | − | 1.15151i | ||||
\(470\) | 0.597935 | + | 4.89050i | 0.0275807 | + | 0.225582i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 5.66768 | − | 35.4318i | 0.260876 | − | 1.63088i | ||||
\(473\) | −16.3794 | + | 28.3699i | −0.753125 | + | 1.30445i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 19.8766 | 0.912001 | ||||||||
\(476\) | 3.43354 | + | 1.18638i | 0.157376 | + | 0.0543778i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −21.7478 | + | 16.3707i | −0.994721 | + | 0.748777i | ||||
\(479\) | −5.76773 | + | 9.99001i | −0.263535 | + | 0.456455i | −0.967179 | − | 0.254097i | \(-0.918222\pi\) |
0.703644 | + | 0.710553i | \(0.251555\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.87802 | − | 5.12573i | 0.404803 | − | 0.233713i | ||||
\(482\) | 0.473165 | + | 3.87001i | 0.0215521 | + | 0.176274i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −37.0081 | + | 9.18691i | −1.68219 | + | 0.417587i | ||||
\(485\) | 5.24005 | + | 9.07604i | 0.237939 | + | 0.412122i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.44822 | + | 4.87758i | 0.382825 | + | 0.221024i | 0.679047 | − | 0.734095i | \(-0.262393\pi\) |
−0.296221 | + | 0.955119i | \(0.595727\pi\) | |||||||
\(488\) | 18.5685 | − | 22.8582i | 0.840555 | − | 1.03474i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −8.18058 | + | 4.90862i | −0.369561 | + | 0.221749i | ||||
\(491\) | 40.4736i | 1.82655i | 0.407346 | + | 0.913274i | \(0.366454\pi\) | ||||
−0.407346 | + | 0.913274i | \(0.633546\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.47453 | + | 0.851323i | 0.0664097 | + | 0.0383416i | ||||
\(494\) | 23.8356 | + | 10.1320i | 1.07241 | + | 0.455861i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 17.0701 | − | 9.03151i | 0.766470 | − | 0.405527i | ||||
\(497\) | 23.8485 | − | 12.1500i | 1.06975 | − | 0.545001i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 27.6827 | − | 15.9826i | 1.23925 | − | 0.715480i | 0.270307 | − | 0.962774i | \(-0.412875\pi\) |
0.968941 | + | 0.247294i | \(0.0795413\pi\) | |||||||
\(500\) | 16.8019 | + | 4.83650i | 0.751404 | + | 0.216295i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 17.6476 | + | 23.4441i | 0.787650 | + | 1.04636i | ||||
\(503\) | 22.7110 | 1.01263 | 0.506317 | − | 0.862348i | \(-0.331007\pi\) | ||||
0.506317 | + | 0.862348i | \(0.331007\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.9069 | 0.618847 | ||||||||
\(506\) | 5.78702 | + | 7.68783i | 0.257265 | + | 0.341766i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −22.3775 | − | 6.44147i | −0.992841 | − | 0.285794i | ||||
\(509\) | 1.98947 | − | 1.14862i | 0.0881819 | − | 0.0509118i | −0.455261 | − | 0.890358i | \(-0.650454\pi\) |
0.543443 | + | 0.839446i | \(0.317121\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.923166 | + | 17.5989i | −0.0408384 | + | 0.778528i | ||||
\(512\) | 10.3655 | − | 20.1136i | 0.458093 | − | 0.888904i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 9.69764 | + | 4.12227i | 0.427745 | + | 0.181825i | ||||
\(515\) | −12.5396 | − | 7.23973i | −0.552560 | − | 0.319021i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 19.8221i | − | 0.871773i | ||||||
\(518\) | −10.2009 | + | 0.707576i | −0.448204 | + | 0.0310891i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 7.93633 | + | 6.44693i | 0.348031 | + | 0.282717i | ||||
\(521\) | 32.5712 | + | 18.8050i | 1.42697 | + | 0.823862i | 0.996881 | − | 0.0789240i | \(-0.0251485\pi\) |
0.430090 | + | 0.902786i | \(0.358482\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.8444 | + | 30.9073i | 0.780279 | + | 1.35148i | 0.931779 | + | 0.363026i | \(0.118256\pi\) |
−0.151500 | + | 0.988457i | \(0.548410\pi\) | |||||||
\(524\) | 17.9775 | − | 4.46273i | 0.785350 | − | 0.194955i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.09394 | − | 41.6632i | −0.222106 | − | 1.81660i | ||||
\(527\) | −2.87047 | + | 1.65727i | −0.125040 | + | 0.0721917i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.7301 | + | 18.5850i | −0.466525 | + | 0.808046i | ||||
\(530\) | −4.45910 | + | 3.35660i | −0.193691 | + | 0.145801i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −16.9277 | − | 19.5154i | −0.733910 | − | 0.846098i | ||||
\(533\) | −35.3726 | −1.53216 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.83799 | − | 10.1117i | 0.252398 | − | 0.437167i | ||||
\(536\) | 26.3609 | + | 4.21669i | 1.13862 | + | 0.182133i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −0.740657 | − | 6.05782i | −0.0319320 | − | 0.261171i | ||||
\(539\) | 35.0657 | − | 15.6082i | 1.51039 | − | 0.672293i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.5102 | − | 32.0605i | −0.795814 | − | 1.37839i | −0.922321 | − | 0.386425i | \(-0.873710\pi\) |
0.126507 | − | 0.991966i | \(-0.459623\pi\) | |||||||
\(542\) | −7.51463 | + | 17.6782i | −0.322781 | + | 0.759342i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.65027 | + | 3.51548i | −0.0707547 | + | 0.150725i | ||||
\(545\) | 5.85094i | 0.250627i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 2.09106i | − | 0.0894073i | −0.999000 | − | 0.0447036i | \(-0.985766\pi\) | ||
0.999000 | − | 0.0447036i | \(-0.0142344\pi\) | |||||||
\(548\) | 10.0342 | + | 10.4121i | 0.428640 | + | 0.444781i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −29.0543 | − | 12.3504i | −1.23888 | − | 0.526623i | ||||
\(551\) | −6.05415 | − | 10.4861i | −0.257916 | − | 0.446723i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.13837 | − | 2.03829i | −0.133457 | − | 0.0866771i | ||||
\(554\) | 2.90755 | − | 0.355491i | 0.123530 | − | 0.0151034i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.93669 | − | 10.2020i | 0.124543 | − | 0.432661i | ||||
\(557\) | −8.39887 | + | 14.5473i | −0.355872 | + | 0.616388i | −0.987267 | − | 0.159073i | \(-0.949149\pi\) |
0.631395 | + | 0.775461i | \(0.282483\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −22.4109 | −0.947878 | ||||||||
\(560\) | −4.29087 | − | 9.25241i | −0.181322 | − | 0.390986i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 20.1676 | + | 26.7919i | 0.850720 | + | 1.13015i | ||||
\(563\) | 8.69784 | − | 15.0651i | 0.366570 | − | 0.634918i | −0.622456 | − | 0.782654i | \(-0.713865\pi\) |
0.989027 | + | 0.147736i | \(0.0471986\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.15882 | + | 3.55580i | −0.259104 | + | 0.149594i | ||||
\(566\) | −17.2028 | + | 2.10329i | −0.723086 | + | 0.0884079i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 10.2130 | + | 26.7284i | 0.428527 | + | 1.12150i | ||||
\(569\) | −17.1425 | − | 29.6917i | −0.718652 | − | 1.24474i | −0.961534 | − | 0.274686i | \(-0.911426\pi\) |
0.242882 | − | 0.970056i | \(-0.421907\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.14176 | − | 2.96860i | −0.215176 | − | 0.124232i | 0.388539 | − | 0.921432i | \(-0.372980\pi\) |
−0.603715 | + | 0.797201i | \(0.706313\pi\) | |||||||
\(572\) | −28.5458 | − | 29.6207i | −1.19356 | − | 1.23850i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 31.7034 | + | 15.4848i | 1.32327 | + | 0.646322i | ||||
\(575\) | 5.05203i | 0.210684i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 33.7930 | + | 19.5104i | 1.40682 | + | 0.812229i | 0.995080 | − | 0.0990712i | \(-0.0315871\pi\) |
0.411742 | + | 0.911300i | \(0.364920\pi\) | |||||||
\(578\) | −9.14440 | + | 21.5122i | −0.380357 | + | 0.894790i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.15169 | − | 4.63940i | −0.0478211 | − | 0.192641i | ||||
\(581\) | 0.653097 | + | 1.28193i | 0.0270950 | + | 0.0531833i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 19.4462 | − | 11.2273i | 0.805381 | − | 0.464987i | ||||
\(584\) | −18.6033 | − | 2.97579i | −0.769812 | − | 0.123139i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −12.0999 | + | 9.10818i | −0.499840 | + | 0.376255i | ||||
\(587\) | −7.71931 | −0.318610 | −0.159305 | − | 0.987229i | \(-0.550925\pi\) | ||||
−0.159305 | + | 0.987229i | \(0.550925\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 23.5712 | 0.971235 | ||||||||
\(590\) | 13.8138 | − | 10.3984i | 0.568705 | − | 0.428093i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.403887 | − | 10.9240i | 0.0165996 | − | 0.448974i | ||||
\(593\) | −0.336377 | + | 0.194207i | −0.0138133 | + | 0.00797513i | −0.506891 | − | 0.862010i | \(-0.669205\pi\) |
0.493077 | + | 0.869985i | \(0.335872\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.794612 | + | 1.55970i | 0.0325759 | + | 0.0639415i | ||||
\(596\) | −9.04858 | + | 2.24622i | −0.370644 | + | 0.0920088i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2.57526 | + | 6.05829i | −0.105310 | + | 0.247742i | ||||
\(599\) | 18.0000 | + | 10.3923i | 0.735460 | + | 0.424618i | 0.820416 | − | 0.571767i | \(-0.193742\pi\) |
−0.0849563 | + | 0.996385i | \(0.527075\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 26.4110i | 1.07733i | 0.842521 | + | 0.538664i | \(0.181071\pi\) | ||||
−0.842521 | + | 0.538664i | \(0.818929\pi\) | |||||||
\(602\) | 20.0862 | + | 9.81062i | 0.818652 | + | 0.399851i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 17.5781 | − | 16.9402i | 0.715244 | − | 0.689289i | ||||
\(605\) | −15.9122 | − | 9.18691i | −0.646922 | − | 0.373501i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −20.3531 | − | 35.2526i | −0.826106 | − | 1.43086i | −0.901071 | − | 0.433671i | \(-0.857218\pi\) |
0.0749655 | − | 0.997186i | \(-0.476115\pi\) | |||||||
\(608\) | 22.6636 | − | 15.7829i | 0.919131 | − | 0.640081i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 14.0856 | − | 1.72217i | 0.570310 | − | 0.0697288i | ||||
\(611\) | 11.7438 | − | 6.78031i | 0.475105 | − | 0.274302i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.66920 | + | 15.0155i | −0.350146 | + | 0.606470i | −0.986275 | − | 0.165113i | \(-0.947201\pi\) |
0.636129 | + | 0.771583i | \(0.280535\pi\) | |||||||
\(614\) | 3.58966 | + | 4.76872i | 0.144867 | + | 0.192450i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 12.6179 | + | 39.0444i | 0.508391 | + | 1.57314i | ||||
\(617\) | 46.4753 | 1.87103 | 0.935513 | − | 0.353291i | \(-0.114938\pi\) | ||||
0.935513 | + | 0.353291i | \(0.114938\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13.1911 | + | 22.8476i | −0.530194 | + | 0.918322i | 0.469186 | + | 0.883099i | \(0.344547\pi\) |
−0.999379 | + | 0.0352227i | \(0.988786\pi\) | |||||||
\(620\) | 8.94251 | + | 2.57414i | 0.359140 | + | 0.103380i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 13.6184 | − | 1.66505i | 0.546049 | − | 0.0667625i | ||||
\(623\) | 1.23008 | + | 0.798909i | 0.0492822 | + | 0.0320076i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.96574 | − | 10.3330i | −0.238630 | − | 0.413318i | ||||
\(626\) | −17.7830 | − | 7.55917i | −0.710750 | − | 0.302125i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 31.5856 | − | 30.4394i | 1.26040 | − | 1.21466i | ||||
\(629\) | 1.87617i | 0.0748079i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 41.0696i | − | 1.63495i | −0.575961 | − | 0.817477i | \(-0.695372\pi\) | ||
0.575961 | − | 0.817477i | \(-0.304628\pi\) | |||||||
\(632\) | 2.52242 | − | 3.10515i | 0.100336 | − | 0.123516i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 11.1138 | − | 26.1452i | 0.441384 | − | 1.03836i | ||||
\(635\) | −5.61028 | − | 9.71729i | −0.222637 | − | 0.385619i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 21.2418 | + | 15.4362i | 0.841632 | + | 0.611605i | ||||
\(638\) | 2.33399 | + | 19.0897i | 0.0924037 | + | 0.755768i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 10.3218 | − | 3.51273i | 0.408004 | − | 0.138853i | ||||
\(641\) | 22.7239 | − | 39.3590i | 0.897540 | − | 1.55459i | 0.0669115 | − | 0.997759i | \(-0.478685\pi\) |
0.830629 | − | 0.556827i | \(-0.187981\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 30.5534 | 1.20491 | 0.602454 | − | 0.798154i | \(-0.294190\pi\) | ||||
0.602454 | + | 0.798154i | \(0.294190\pi\) | |||||||
\(644\) | 4.96021 | − | 4.30252i | 0.195460 | − | 0.169543i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.78702 | + | 2.85069i | −0.148998 | + | 0.112159i | ||||
\(647\) | 18.0896 | − | 31.3321i | 0.711175 | − | 1.23179i | −0.253242 | − | 0.967403i | \(-0.581497\pi\) |
0.964417 | − | 0.264388i | \(-0.0851698\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −60.2423 | + | 34.7809i | −2.36472 | + | 1.36527i | ||||
\(650\) | −2.62113 | − | 21.4382i | −0.102809 | − | 0.840876i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.93633 | + | 7.80022i | 0.0758324 | + | 0.305480i | ||||
\(653\) | −4.11545 | − | 7.12816i | −0.161050 | − | 0.278946i | 0.774196 | − | 0.632946i | \(-0.218155\pi\) |
−0.935245 | + | 0.354000i | \(0.884821\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.72968 | + | 4.46273i | 0.302024 | + | 0.174373i | ||||
\(656\) | −20.0535 | + | 31.9465i | −0.782959 | + | 1.24730i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −13.4938 | + | 0.935982i | −0.526044 | + | 0.0364884i | ||||
\(659\) | 22.8837i | 0.891422i | 0.895177 | + | 0.445711i | \(0.147049\pi\) | ||||
−0.895177 | + | 0.445711i | \(0.852951\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.7212 | − | 10.2313i | −0.689275 | − | 0.397953i | 0.114065 | − | 0.993473i | \(-0.463613\pi\) |
−0.803340 | + | 0.595520i | \(0.796946\pi\) | |||||||
\(662\) | 12.2616 | + | 5.21214i | 0.476559 | + | 0.202575i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.43673 | + | 0.548978i | −0.0557560 | + | 0.0213045i | ||||
\(665\) | 0.652090 | − | 12.4312i | 0.0252870 | − | 0.482060i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.66525 | − | 1.53878i | 0.103199 | − | 0.0595819i | ||||
\(668\) | −8.14252 | + | 28.2869i | −0.315044 | + | 1.09445i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 7.73626 | + | 10.2773i | 0.298878 | + | 0.397047i | ||||
\(671\) | −57.0916 | −2.20400 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.23008 | 0.163058 | 0.0815289 | − | 0.996671i | \(-0.474020\pi\) | ||||
0.0815289 | + | 0.996671i | \(0.474020\pi\) | |||||||
\(674\) | 11.4319 | + | 15.1868i | 0.440340 | + | 0.584975i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.592669 | − | 2.05892i | 0.0227950 | − | 0.0791892i | ||||
\(677\) | −20.7962 | + | 12.0067i | −0.799262 | + | 0.461454i | −0.843213 | − | 0.537580i | \(-0.819339\pi\) |
0.0439511 | + | 0.999034i | \(0.486005\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −25.6365 | + | 13.0609i | −0.983840 | + | 0.501232i | ||||
\(680\) | −1.74805 | + | 0.667932i | −0.0670345 | + | 0.0256140i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −34.4549 | − | 14.6461i | −1.31935 | − | 0.560827i | ||||
\(683\) | −7.09951 | − | 4.09890i | −0.271655 | − | 0.156840i | 0.357984 | − | 0.933728i | \(-0.383464\pi\) |
−0.629640 | + | 0.776887i | \(0.716797\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.96771i | 0.266222i | ||||||||
\(686\) | −12.2810 | − | 23.1339i | −0.468892 | − | 0.883256i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −12.7052 | + | 20.2402i | −0.484382 | + | 0.771651i | ||||
\(689\) | 13.3035 | + | 7.68079i | 0.506824 | + | 0.292615i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17.9925 | − | 31.1638i | −0.684465 | − | 1.18553i | −0.973605 | − | 0.228242i | \(-0.926702\pi\) |
0.289139 | − | 0.957287i | \(-0.406631\pi\) | |||||||
\(692\) | 5.61504 | + | 22.6194i | 0.213452 | + | 0.859860i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.88217 | + | 31.7522i | 0.147365 | + | 1.20530i | ||||
\(695\) | 4.43015 | − | 2.55775i | 0.168045 | − | 0.0970209i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.23686 | − | 5.60641i | 0.122605 | − | 0.212358i | ||||
\(698\) | 2.80413 | − | 2.11081i | 0.106138 | − | 0.0798954i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −7.03559 | + | 20.3619i | −0.265920 | + | 0.769606i | ||||
\(701\) | 12.9471 | 0.489003 | 0.244502 | − | 0.969649i | \(-0.421376\pi\) | ||||
0.244502 | + | 0.969649i | \(0.421376\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.67117 | − | 11.5548i | 0.251608 | − | 0.435798i | ||||
\(704\) | −42.9350 | + | 8.98829i | −1.61817 | + | 0.338759i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.56428 | − | 12.7942i | −0.0588723 | − | 0.481516i | ||||
\(707\) | −2.00000 | + | 38.1272i | −0.0752177 | + | 1.43392i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.65603 | − | 11.5286i | −0.249973 | − | 0.432965i | 0.713545 | − | 0.700609i | \(-0.247088\pi\) |
−0.963518 | + | 0.267644i | \(0.913755\pi\) | |||||||
\(710\) | −5.39367 | + | 12.6886i | −0.202421 | + | 0.476195i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −0.988660 | + | 1.21706i | −0.0370516 | + | 0.0456114i | ||||
\(713\) | 5.99109i | 0.224368i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 19.8221i | − | 0.741303i | ||||||
\(716\) | 3.73590 | − | 3.60033i | 0.139617 | − | 0.134550i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 9.01711 | + | 3.83299i | 0.336515 | + | 0.143046i | ||||
\(719\) | −23.7520 | − | 41.1397i | −0.885800 | − | 1.53425i | −0.844794 | − | 0.535091i | \(-0.820277\pi\) |
−0.0410056 | − | 0.999159i | \(-0.513056\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 21.6519 | − | 33.3375i | 0.806358 | − | 1.24155i | ||||
\(722\) | 6.78803 | − | 0.829936i | 0.252624 | − | 0.0308870i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −18.3229 | − | 5.27431i | −0.680964 | − | 0.196018i | ||||
\(725\) | −5.04858 | + | 8.74440i | −0.187500 | + | 0.324759i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −24.3567 | −0.903340 | −0.451670 | − | 0.892185i | \(-0.649172\pi\) | ||||
−0.451670 | + | 0.892185i | \(0.649172\pi\) | |||||||
\(728\) | −18.8163 | + | 20.8312i | −0.697379 | + | 0.772054i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −5.45961 | − | 7.25287i | −0.202069 | − | 0.268441i | ||||
\(731\) | 2.05076 | − | 3.55203i | 0.0758503 | − | 0.131377i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.35812 | − | 1.93881i | 0.124035 | − | 0.0716117i | −0.436699 | − | 0.899608i | \(-0.643852\pi\) |
0.560734 | + | 0.827996i | \(0.310519\pi\) | |||||||
\(734\) | −5.38144 | + | 0.657960i | −0.198633 | + | 0.0242857i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.01153 | + | 5.76041i | 0.147867 | + | 0.212331i | ||||
\(737\) | −25.8766 | − | 44.8196i | −0.953177 | − | 1.65095i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.46497 | + | 4.30990i | 0.274603 | + | 0.158542i | 0.630978 | − | 0.775801i | \(-0.282654\pi\) |
−0.356374 | + | 0.934343i | \(0.615987\pi\) | |||||||
\(740\) | 3.79279 | − | 3.65515i | 0.139426 | − | 0.134366i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −8.56119 | − | 12.7078i | −0.314291 | − | 0.466520i | ||||
\(743\) | − | 6.12929i | − | 0.224862i | −0.993660 | − | 0.112431i | \(-0.964136\pi\) | ||
0.993660 | − | 0.112431i | \(-0.0358637\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.89057 | − | 2.24622i | −0.142539 | − | 0.0822952i | ||||
\(746\) | 14.8436 | − | 34.9195i | 0.543461 | − | 1.27849i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 7.30692 | − | 1.81387i | 0.267167 | − | 0.0663216i | ||||
\(749\) | 26.8827 | + | 17.4597i | 0.982273 | + | 0.637963i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −30.7146 | + | 17.7331i | −1.12079 | + | 0.647090i | −0.941603 | − | 0.336725i | \(-0.890681\pi\) |
−0.179190 | + | 0.983815i | \(0.557348\pi\) | |||||||
\(752\) | 0.534262 | − | 14.4503i | 0.0194825 | − | 0.526948i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −10.5116 | + | 7.91261i | −0.382809 | + | 0.288160i | ||||
\(755\) | 11.7632 | 0.428108 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29.4204 | 1.06930 | 0.534651 | − | 0.845073i | \(-0.320443\pi\) | ||||
0.534651 | + | 0.845073i | \(0.320443\pi\) | |||||||
\(758\) | −7.83786 | + | 5.89996i | −0.284684 | + | 0.214296i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 13.1407 | + | 2.10199i | 0.476663 | + | 0.0762471i | ||||
\(761\) | −43.5568 | + | 25.1475i | −1.57893 | + | 0.911597i | −0.583923 | + | 0.811809i | \(0.698483\pi\) |
−0.995009 | + | 0.0997877i | \(0.968184\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −16.0410 | − | 0.841446i | −0.580723 | − | 0.0304624i | ||||
\(764\) | 4.01518 | + | 16.1746i | 0.145264 | + | 0.585175i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.24901 | − | 2.93830i | 0.0451286 | − | 0.106165i | ||||
\(767\) | −41.2128 | − | 23.7942i | −1.48811 | − | 0.859160i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.2817i | 0.731377i | 0.930737 | + | 0.365689i | \(0.119167\pi\) | ||||
−0.930737 | + | 0.365689i | \(0.880833\pi\) | |||||||
\(770\) | −8.67735 | + | 17.7659i | −0.312710 | + | 0.640239i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 17.1712 | + | 17.8178i | 0.618006 | + | 0.641277i | ||||
\(773\) | 18.8149 | + | 10.8628i | 0.676723 | + | 0.390706i | 0.798619 | − | 0.601836i | \(-0.205564\pi\) |
−0.121896 | + | 0.992543i | \(0.538897\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.82806 | − | 17.0227i | −0.353034 | − | 0.611473i | ||||
\(776\) | −10.9787 | − | 28.7324i | −0.394112 | − | 1.03143i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −42.9684 | + | 5.25351i | −1.54049 | + | 0.188347i | ||||
\(779\) | −39.8698 | + | 23.0189i | −1.42848 | + | 0.824736i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 27.7349 | − | 48.0382i | 0.992432 | − | 1.71894i | ||||
\(782\) | −0.724559 | − | 0.962547i | −0.0259102 | − | 0.0344206i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 25.9836 | − | 10.4333i | 0.927985 | − | 0.372617i | ||||
\(785\) | 21.1369 | 0.754410 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.299328 | + | 0.518452i | −0.0106699 | + | 0.0184808i | −0.871311 | − | 0.490731i | \(-0.836730\pi\) |
0.860641 | + | 0.509212i | \(0.170063\pi\) | |||||||
\(788\) | 1.79078 | − | 6.22111i | 0.0637937 | − | 0.221618i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.91345 | − | 0.233947i | 0.0680774 | − | 0.00832346i | ||||
\(791\) | −8.86288 | − | 17.3965i | −0.315128 | − | 0.618547i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −19.5287 | − | 33.8247i | −0.693484 | − | 1.20115i | ||||
\(794\) | 18.0896 | + | 7.68951i | 0.641975 | + | 0.272890i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 26.6883 | + | 27.6933i | 0.945942 | + | 0.981562i | ||||
\(797\) | − | 36.1789i | − | 1.28152i | −0.767741 | − | 0.640760i | \(-0.778619\pi\) | ||
0.767741 | − | 0.640760i | \(-0.221381\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.48180i | 0.0877998i | ||||||||
\(800\) | −20.8478 | − | 9.78655i | −0.737079 | − | 0.346007i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −5.68549 | + | 13.3751i | −0.200762 | + | 0.472292i | ||||
\(803\) | 18.2616 | + | 31.6299i | 0.644436 | + | 1.11620i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.15963 | + | 0.165741i | 0.111362 | + | 0.00584162i | ||||
\(806\) | −3.10834 | − | 25.4231i | −0.109487 | − | 0.895490i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −40.3034 | − | 6.44693i | −1.41787 | − | 0.226802i | ||||
\(809\) | −15.0603 | + | 26.0852i | −0.529491 | + | 0.917106i | 0.469917 | + | 0.882711i | \(0.344284\pi\) |
−0.999408 | + | 0.0343953i | \(0.989049\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21.5947 | −0.758292 | −0.379146 | − | 0.925337i | \(-0.623782\pi\) | ||||
−0.379146 | + | 0.925337i | \(0.623782\pi\) | |||||||
\(812\) | 12.8851 | − | 2.49026i | 0.452177 | − | 0.0873911i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −16.9311 | + | 12.7449i | −0.593435 | + | 0.446709i | ||||
\(815\) | −1.93633 | + | 3.35382i | −0.0678266 | + | 0.117479i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −25.2601 | + | 14.5839i | −0.883740 | + | 0.510228i | ||||
\(818\) | −2.08769 | − | 17.0751i | −0.0729942 | − | 0.597018i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −17.6397 | + | 4.37889i | −0.616006 | + | 0.152917i | ||||
\(821\) | 25.1264 | + | 43.5202i | 0.876918 | + | 1.51887i | 0.854705 | + | 0.519114i | \(0.173738\pi\) |
0.0222131 | + | 0.999753i | \(0.492929\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.87338 | − | 1.65894i | −0.100160 | − | 0.0578272i | 0.449084 | − | 0.893490i | \(-0.351751\pi\) |
−0.549243 | + | 0.835663i | \(0.685084\pi\) | |||||||
\(824\) | 32.9847 | + | 26.7945i | 1.14907 | + | 0.933430i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 26.5216 | + | 39.3675i | 0.922805 | + | 1.36977i | ||||
\(827\) | − | 29.3948i | − | 1.02216i | −0.859534 | − | 0.511078i | \(-0.829246\pi\) | ||
0.859534 | − | 0.511078i | \(-0.170754\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 28.2980 | + | 16.3379i | 0.982830 | + | 0.567437i | 0.903123 | − | 0.429381i | \(-0.141268\pi\) |
0.0797067 | + | 0.996818i | \(0.474602\pi\) | |||||||
\(830\) | −0.682050 | − | 0.289926i | −0.0236743 | − | 0.0100635i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −20.0115 | − | 22.3629i | −0.693775 | − | 0.775294i | ||||
\(833\) | −4.39036 | + | 1.95421i | −0.152117 | + | 0.0677094i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −12.2834 | + | 7.09184i | −0.425086 | + | 0.245423i | ||||
\(836\) | −51.4508 | − | 14.8104i | −1.77946 | − | 0.512227i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −13.7992 | − | 18.3317i | −0.476686 | − | 0.633258i | ||||
\(839\) | 8.66161 | 0.299032 | 0.149516 | − | 0.988759i | \(-0.452228\pi\) | ||||
0.149516 | + | 0.988759i | \(0.452228\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.8491 | −0.787899 | ||||||||
\(842\) | 8.15201 | + | 10.8296i | 0.280937 | + | 0.373213i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 17.7711 | + | 5.11550i | 0.611707 | + | 0.176083i | ||||
\(845\) | 0.894073 | − | 0.516193i | 0.0307570 | − | 0.0177576i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 27.4753 | − | 42.3038i | 0.944062 | − | 1.45358i | ||||
\(848\) | 14.4789 | − | 7.66057i | 0.497209 | − | 0.263065i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3.63772 | + | 1.54632i | 0.124773 | + | 0.0530384i | ||||
\(851\) | 2.93688 | + | 1.69561i | 0.100675 | + | 0.0581248i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 7.17809i | − | 0.245773i | −0.992421 | − | 0.122887i | \(-0.960785\pi\) | ||
0.992421 | − | 0.122887i | \(-0.0392151\pi\) | |||||||
\(854\) | 2.69582 | + | 38.8650i | 0.0922491 | + | 1.32993i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −21.6066 | + | 26.5982i | −0.738498 | + | 0.909109i | ||||
\(857\) | −39.5334 | − | 22.8246i | −1.35044 | − | 0.779675i | −0.362126 | − | 0.932129i | \(-0.617949\pi\) |
−0.988311 | + | 0.152454i | \(0.951282\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.77944 | + | 11.7423i | 0.231311 | + | 0.400643i | 0.958194 | − | 0.286118i | \(-0.0923651\pi\) |
−0.726883 | + | 0.686761i | \(0.759032\pi\) | |||||||
\(860\) | −11.1759 | + | 2.77431i | −0.381096 | + | 0.0946033i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0.0260696 | + | 0.213223i | 0.000887934 | + | 0.00726240i | ||||
\(863\) | 36.0550 | − | 20.8163i | 1.22733 | − | 0.708597i | 0.260856 | − | 0.965378i | \(-0.415995\pi\) |
0.966470 | + | 0.256781i | \(0.0826620\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.61504 | + | 9.72554i | −0.190917 | + | 0.330678i | ||||
\(866\) | 10.6999 | − | 8.05436i | 0.363597 | − | 0.273698i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −8.34335 | + | 24.1467i | −0.283192 | + | 0.819591i | ||||
\(869\) | −7.75555 | −0.263089 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17.7026 | − | 30.6619i | 0.599831 | − | 1.03894i | ||||
\(872\) | 2.71237 | − | 16.9566i | 0.0918525 | − | 0.574221i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.03979 | + | 8.50439i | 0.0351713 | + | 0.287665i | ||||
\(875\) | −20.6089 | + | 10.4995i | −0.696708 | + | 0.354948i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.84239 | + | 17.0475i | 0.332354 | + | 0.575654i | 0.982973 | − | 0.183751i | \(-0.0588239\pi\) |
−0.650619 | + | 0.759404i | \(0.725491\pi\) | |||||||
\(878\) | 18.5196 | − | 43.5673i | 0.625006 | − | 1.47033i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −17.9022 | − | 11.2376i | −0.603482 | − | 0.378819i | ||||
\(881\) | − | 7.24606i | − | 0.244126i | −0.992522 | − | 0.122063i | \(-0.961049\pi\) | ||
0.992522 | − | 0.122063i | \(-0.0389510\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 35.4533i | 1.19310i | 0.802577 | + | 0.596549i | \(0.203462\pi\) | ||||
−0.802577 | + | 0.596549i | \(0.796538\pi\) | |||||||
\(884\) | 3.57405 | + | 3.70863i | 0.120208 | + | 0.124735i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 34.0415 | + | 14.4703i | 1.14365 | + | 0.486141i | ||||
\(887\) | 8.98684 | + | 15.5657i | 0.301749 | + | 0.522644i | 0.976532 | − | 0.215372i | \(-0.0690964\pi\) |
−0.674784 | + | 0.738016i | \(0.735763\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 27.4479 | − | 13.9837i | 0.920572 | − | 0.468999i | ||||
\(890\) | −0.749976 | + | 0.0916955i | −0.0251392 | + | 0.00307364i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.07653 | − | 3.73983i | 0.0360448 | − | 0.125219i | ||||
\(893\) | 8.82463 | − | 15.2847i | 0.295305 | − | 0.511483i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.50005 | 0.0835674 | ||||||||
\(896\) | 8.14611 | + | 28.8035i | 0.272143 | + | 0.962257i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 8.75337 | + | 11.6285i | 0.292104 | + | 0.388048i | ||||
\(899\) | −5.98700 | + | 10.3698i | −0.199678 | + | 0.345852i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.43475 | + | 1.40570i | −0.0811132 | + | 0.0468307i | ||||
\(902\) | 72.5820 | − | 8.87421i | 2.41672 | − | 0.295479i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 19.4972 | − | 7.44992i | 0.648468 | − | 0.247781i | ||||
\(905\) | −4.59374 | − | 7.95658i | −0.152701 | − | 0.264486i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.60870 | + | 4.39289i | 0.252643 | + | 0.145863i | 0.620974 | − | 0.783831i | \(-0.286737\pi\) |
−0.368331 | + | 0.929695i | \(0.620071\pi\) | |||||||
\(908\) | 11.9983 | + | 12.4501i | 0.398178 | + | 0.413172i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −13.4938 | + | 0.935982i | −0.447316 | + | 0.0310275i | ||||
\(911\) | − | 21.5478i | − | 0.713911i | −0.934121 | − | 0.356955i | \(-0.883815\pi\) | ||
0.934121 | − | 0.356955i | \(-0.116185\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.58220 | + | 1.49083i | 0.0854582 | + | 0.0493393i | ||||
\(914\) | −6.60102 | + | 15.5289i | −0.218342 | + | 0.513650i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8.08983 | + | 32.5887i | 0.267295 | + | 1.07676i | ||||
\(917\) | −13.3467 | + | 20.5500i | −0.440747 | + | 0.678619i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 27.5939 | − | 15.9314i | 0.910240 | − | 0.525527i | 0.0297316 | − | 0.999558i | \(-0.490535\pi\) |
0.880508 | + | 0.474031i | \(0.157201\pi\) | |||||||
\(920\) | −0.534262 | + | 3.33997i | −0.0176141 | + | 0.110116i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 33.9069 | − | 25.5234i | 1.11666 | − | 0.840570i | ||||
\(923\) | 37.9479 | 1.24907 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11.1262 | −0.365828 | ||||||||
\(926\) | 14.9975 | − | 11.2894i | 0.492848 | − | 0.370992i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.18696 | + | 13.9793i | 0.0389639 | + | 0.458893i | ||||
\(929\) | −44.1750 | + | 25.5044i | −1.44933 | + | 0.836773i | −0.998442 | − | 0.0558058i | \(-0.982227\pi\) |
−0.450892 | + | 0.892579i | \(0.648894\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 33.9876 | + | 3.57555i | 1.11390 | + | 0.117184i | ||||
\(932\) | 2.03148 | − | 0.504294i | 0.0665432 | − | 0.0165187i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 16.4033 | − | 38.5887i | 0.536731 | − | 1.26266i | ||||
\(935\) | 3.14171 | + | 1.81387i | 0.102745 | + | 0.0593199i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.65742i | 0.0868141i | 0.999057 | + | 0.0434071i | \(0.0138212\pi\) | ||||
−0.999057 | + | 0.0434071i | \(0.986179\pi\) | |||||||
\(938\) | −29.2890 | + | 19.7318i | −0.956318 | + | 0.644266i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 5.01711 | − | 4.83504i | 0.163640 | − | 0.157702i | ||||
\(941\) | −26.2920 | − | 15.1797i | −0.857096 | − | 0.494844i | 0.00594304 | − | 0.999982i | \(-0.498108\pi\) |
−0.863039 | + | 0.505138i | \(0.831442\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.85070 | − | 10.1337i | −0.190525 | − | 0.329999i | ||||
\(944\) | −44.8541 | + | 23.7316i | −1.45988 | + | 0.772397i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 45.9855 | − | 5.62240i | 1.49512 | − | 0.182800i | ||||
\(947\) | 37.6505 | − | 21.7375i | 1.22348 | − | 0.706374i | 0.257818 | − | 0.966193i | \(-0.416996\pi\) |
0.965657 | + | 0.259819i | \(0.0836630\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.4931 | + | 21.6386i | −0.405542 | + | 0.702419i | ||||
\(950\) | −16.9054 | − | 22.4581i | −0.548483 | − | 0.728637i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.57981 | − | 4.88852i | −0.0512021 | − | 0.158438i | ||||
\(953\) | 53.8683 | 1.74497 | 0.872483 | − | 0.488645i | \(-0.162509\pi\) | ||||
0.872483 | + | 0.488645i | \(0.162509\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.01518 | + | 6.95449i | −0.129928 | + | 0.225042i | ||||
\(956\) | 36.9937 | + | 10.6488i | 1.19646 | + | 0.344407i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 16.1930 | − | 1.97984i | 0.523173 | − | 0.0639656i | ||||
\(959\) | −19.1027 | − | 1.00205i | −0.616860 | − | 0.0323580i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.84512 | + | 6.65995i | 0.124036 | + | 0.214837i | ||||
\(962\) | −13.3423 | − | 5.67155i | −0.430174 | − | 0.182858i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 3.97020 | − | 3.82613i | 0.127872 | − | 0.123231i | ||||
\(965\) | 11.9236i | 0.383835i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 44.9529i | 1.44559i | 0.691064 | + | 0.722794i | \(0.257142\pi\) | ||||
−0.691064 | + | 0.722794i | \(0.742858\pi\) | |||||||
\(968\) | 41.8561 | + | 34.0010i | 1.34531 | + | 1.09283i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 5.79806 | − | 13.6399i | 0.186164 | − | 0.437952i | ||||
\(971\) | 0.641758 | + | 1.11156i | 0.0205950 | + | 0.0356716i | 0.876139 | − | 0.482058i | \(-0.160111\pi\) |
−0.855544 | + | 0.517730i | \(0.826777\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.37523 | + | 12.5136i | 0.204381 | + | 0.401167i | ||||
\(974\) | −1.67428 | − | 13.6939i | −0.0536474 | − | 0.438781i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −41.6198 | − | 1.53878i | −1.33222 | − | 0.0492553i | ||||
\(977\) | 9.67678 | − | 16.7607i | 0.309588 | − | 0.536222i | −0.668684 | − | 0.743546i | \(-0.733142\pi\) |
0.978272 | + | 0.207325i | \(0.0664756\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.03979 | 0.0971520 | ||||||||
\(980\) | 12.5038 | + | 5.06819i | 0.399421 | + | 0.161897i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 45.7302 | − | 34.4234i | 1.45931 | − | 1.09850i | ||||
\(983\) | −4.21637 | + | 7.30296i | −0.134481 | + | 0.232928i | −0.925399 | − | 0.378994i | \(-0.876270\pi\) |
0.790918 | + | 0.611922i | \(0.209603\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.70148 | − | 1.55970i | 0.0860763 | − | 0.0496962i | ||||
\(986\) | −0.292225 | − | 2.39011i | −0.00930635 | − | 0.0761165i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −8.82463 | − | 35.5488i | −0.280749 | − | 1.13096i | ||||
\(989\) | −3.70680 | − | 6.42036i | −0.117869 | − | 0.204156i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21.1967 | − | 12.2379i | −0.673334 | − | 0.388750i | 0.124005 | − | 0.992282i | \(-0.460426\pi\) |
−0.797339 | + | 0.603532i | \(0.793760\pi\) | |||||||
\(992\) | −24.7229 | − | 11.6057i | −0.784952 | − | 0.368480i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −34.0115 | − | 16.6121i | −1.07878 | − | 0.526905i | ||||
\(995\) | 18.5322i | 0.587511i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −29.0273 | − | 16.7589i | −0.919304 | − | 0.530761i | −0.0358914 | − | 0.999356i | \(-0.511427\pi\) |
−0.883413 | + | 0.468595i | \(0.844760\pi\) | |||||||
\(998\) | −41.6030 | − | 17.6846i | −1.31692 | − | 0.559795i | ||||
\(999\) | 0 | 0 |
(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 | 252.2.bf.g.199.2 | 8 | ||
3.2 | odd | 2 | 84.2.o.a.31.3 | yes | 8 | ||
4.3 | odd | 2 | 252.2.bf.f.199.2 | 8 | |||
7.3 | odd | 6 | 1764.2.b.j.1567.7 | 8 | |||
7.4 | even | 3 | 1764.2.b.i.1567.7 | 8 | |||
7.5 | odd | 6 | 252.2.bf.f.19.2 | 8 | |||
12.11 | even | 2 | 84.2.o.b.31.3 | yes | 8 | ||
21.2 | odd | 6 | 588.2.o.b.19.3 | 8 | |||
21.5 | even | 6 | 84.2.o.b.19.3 | yes | 8 | ||
21.11 | odd | 6 | 588.2.b.b.391.2 | 8 | |||
21.17 | even | 6 | 588.2.b.a.391.2 | 8 | |||
21.20 | even | 2 | 588.2.o.d.31.3 | 8 | |||
24.5 | odd | 2 | 1344.2.bl.j.703.2 | 8 | |||
24.11 | even | 2 | 1344.2.bl.i.703.2 | 8 | |||
28.3 | even | 6 | 1764.2.b.i.1567.8 | 8 | |||
28.11 | odd | 6 | 1764.2.b.j.1567.8 | 8 | |||
28.19 | even | 6 | inner | 252.2.bf.g.19.2 | 8 | ||
84.11 | even | 6 | 588.2.b.a.391.1 | 8 | |||
84.23 | even | 6 | 588.2.o.d.19.3 | 8 | |||
84.47 | odd | 6 | 84.2.o.a.19.3 | ✓ | 8 | ||
84.59 | odd | 6 | 588.2.b.b.391.1 | 8 | |||
84.83 | odd | 2 | 588.2.o.b.31.3 | 8 | |||
168.5 | even | 6 | 1344.2.bl.i.1279.2 | 8 | |||
168.131 | odd | 6 | 1344.2.bl.j.1279.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.2.o.a.19.3 | ✓ | 8 | 84.47 | odd | 6 | ||
84.2.o.a.31.3 | yes | 8 | 3.2 | odd | 2 | ||
84.2.o.b.19.3 | yes | 8 | 21.5 | even | 6 | ||
84.2.o.b.31.3 | yes | 8 | 12.11 | even | 2 | ||
252.2.bf.f.19.2 | 8 | 7.5 | odd | 6 | |||
252.2.bf.f.199.2 | 8 | 4.3 | odd | 2 | |||
252.2.bf.g.19.2 | 8 | 28.19 | even | 6 | inner | ||
252.2.bf.g.199.2 | 8 | 1.1 | even | 1 | trivial | ||
588.2.b.a.391.1 | 8 | 84.11 | even | 6 | |||
588.2.b.a.391.2 | 8 | 21.17 | even | 6 | |||
588.2.b.b.391.1 | 8 | 84.59 | odd | 6 | |||
588.2.b.b.391.2 | 8 | 21.11 | odd | 6 | |||
588.2.o.b.19.3 | 8 | 21.2 | odd | 6 | |||
588.2.o.b.31.3 | 8 | 84.83 | odd | 2 | |||
588.2.o.d.19.3 | 8 | 84.23 | even | 6 | |||
588.2.o.d.31.3 | 8 | 21.20 | even | 2 | |||
1344.2.bl.i.703.2 | 8 | 24.11 | even | 2 | |||
1344.2.bl.i.1279.2 | 8 | 168.5 | even | 6 | |||
1344.2.bl.j.703.2 | 8 | 24.5 | odd | 2 | |||
1344.2.bl.j.1279.2 | 8 | 168.131 | odd | 6 | |||
1764.2.b.i.1567.7 | 8 | 7.4 | even | 3 | |||
1764.2.b.i.1567.8 | 8 | 28.3 | even | 6 | |||
1764.2.b.j.1567.7 | 8 | 7.3 | odd | 6 | |||
1764.2.b.j.1567.8 | 8 | 28.11 | odd | 6 |