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 | 19.2 | ||
Root | \(1.40376 - 0.171630i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.19 |
Dual form | 252.2.bf.f.199.2 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.553244 | + | 1.30151i | −0.391203 | + | 0.920305i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.38784 | − | 1.44010i | −0.693921 | − | 0.720051i | ||||
\(5\) | −0.834598 | − | 0.481855i | −0.373244 | − | 0.215492i | 0.301631 | − | 0.953425i | \(-0.402469\pi\) |
−0.674875 | + | 0.737932i | \(0.735802\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.20103 | − | 2.35744i | 0.453948 | − | 0.891028i | ||||
\(8\) | 2.64212 | − | 1.00956i | 0.934130 | − | 0.356933i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.08887 | − | 0.819652i | 0.344332 | − | 0.259197i | ||||
\(11\) | 4.74861 | − | 2.74161i | 1.43176 | − | 0.826626i | 0.434504 | − | 0.900670i | \(-0.356924\pi\) |
0.997255 | + | 0.0740437i | \(0.0235904\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.75117i | 1.04039i | 0.854048 | + | 0.520193i | \(0.174140\pi\) | ||||
−0.854048 | + | 0.520193i | \(0.825860\pi\) | |||||||
\(14\) | 2.40376 | + | 2.86739i | 0.642432 | + | 0.766343i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.147789 | + | 3.99727i | −0.0369471 | + | 0.999317i | ||||
\(17\) | 0.594545 | − | 0.343260i | 0.144198 | − | 0.0832529i | −0.426165 | − | 0.904645i | \(-0.640136\pi\) |
0.570363 | + | 0.821393i | \(0.306802\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.44109 | − | 4.22809i | 0.560024 | − | 0.969989i | −0.437470 | − | 0.899233i | \(-0.644125\pi\) |
0.997494 | − | 0.0707563i | \(-0.0225413\pi\) | |||||||
\(20\) | 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 | \(-0.374630\pi\) |
−0.607838 | + | 0.794061i | \(0.707963\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.03563 | − | 3.52582i | −0.407126 | − | 0.705163i | ||||
\(26\) | −4.88217 | − | 2.07531i | −0.957473 | − | 0.407002i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −5.06180 | + | 1.54214i | −0.956590 | + | 0.291438i | ||||
\(29\) | 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 | \(-0.0239208\pi\) |
−0.563609 | + | 0.826042i | \(0.690587\pi\) | |||||||
\(32\) | −5.12071 | − | 2.40381i | −0.905222 | − | 0.424938i | ||||
\(33\) | 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 | −0.731571 | − | 0.681765i | \(-0.761213\pi\) |
0.956212 | + | 0.292677i | \(0.0945459\pi\) | |||||||
\(38\) | 4.15237 | + | 5.51625i | 0.673603 | + | 0.894855i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.69157 | − | 0.430544i | −0.425574 | − | 0.0680749i | ||||
\(41\) | 9.42976i | 1.47268i | 0.676611 | + | 0.736340i | \(0.263448\pi\) | ||||
−0.676611 | + | 0.736340i | \(0.736552\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 5.97437i | − | 0.911083i | −0.890215 | − | 0.455541i | \(-0.849446\pi\) | ||
0.890215 | − | 0.455541i | \(-0.150554\pi\) | |||||||
\(44\) | −10.5385 | − | 3.03356i | −1.58874 | − | 0.457326i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.40207 | − | 1.05541i | 0.206723 | − | 0.155611i | ||||
\(47\) | −1.80752 | + | 3.13072i | −0.263654 | + | 0.456662i | −0.967210 | − | 0.253978i | \(-0.918261\pi\) |
0.703556 | + | 0.710640i | \(0.251594\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.11504 | − | 5.66272i | −0.587863 | − | 0.808960i | ||||
\(50\) | 5.71508 | − | 0.698752i | 0.808234 | − | 0.0988184i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.40207 | − | 5.20603i | 0.749132 | − | 0.721946i | ||||
\(53\) | −2.04757 | − | 3.54650i | −0.281256 | − | 0.487150i | 0.690438 | − | 0.723391i | \(-0.257418\pi\) |
−0.971694 | + | 0.236242i | \(0.924084\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.28424 | −0.712526 | ||||||||
\(56\) | 0.793298 | − | 7.44115i | 0.106009 | − | 0.994365i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.37210 | + | 3.22788i | −0.180166 | + | 0.423841i | ||||
\(59\) | −6.34315 | − | 10.9867i | −0.825808 | − | 1.43034i | −0.901300 | − | 0.433195i | \(-0.857386\pi\) |
0.0754923 | − | 0.997146i | \(-0.475947\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.01711 | + | 5.20603i | 1.15452 | + | 0.666564i | 0.949985 | − | 0.312295i | \(-0.101098\pi\) |
0.204537 | + | 0.978859i | \(0.434431\pi\) | |||||||
\(62\) | −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 | \(-0.862267\pi\) |
−0.0907716 | + | 0.995872i | \(0.528933\pi\) | |||||||
\(68\) | −1.31946 | − | 0.379814i | −0.160009 | − | 0.0460592i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.624505 | − | 3.55138i | −0.0746427 | − | 0.424472i | ||||
\(71\) | 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 | −0.798026 | − | 0.602623i | \(-0.794122\pi\) |
0.122874 | + | 0.992422i | \(0.460789\pi\) | |||||||
\(74\) | 2.32435 | + | 3.08781i | 0.270200 | + | 0.358950i | ||||
\(75\) | 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 | \(-0.358687\pi\) |
−0.567322 | + | 0.823496i | \(0.692020\pi\) | |||||||
\(80\) | 2.04945 | − | 3.26490i | 0.229135 | − | 0.365027i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −12.2729 | − | 5.21696i | −1.35531 | − | 0.576117i | ||||
\(83\) | 0.543780 | 0.0596876 | 0.0298438 | − | 0.999555i | \(-0.490499\pi\) | ||||
0.0298438 | + | 0.999555i | \(0.490499\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.661608 | −0.0717614 | ||||||||
\(86\) | 7.77568 | + | 3.30528i | 0.838474 | + | 0.356418i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 9.77857 | − | 12.0377i | 1.04240 | − | 1.28322i | ||||
\(89\) | −0.480107 | − | 0.277190i | −0.0508912 | − | 0.0293821i | 0.474339 | − | 0.880343i | \(-0.342687\pi\) |
−0.525230 | + | 0.850960i | \(0.676021\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.84315 | + | 4.50528i | 0.927014 | + | 0.472281i | ||||
\(92\) | 0.597935 | + | 2.40870i | 0.0623390 | + | 0.251124i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.07465 | − | 4.08455i | −0.317126 | − | 0.421289i | ||||
\(95\) | −4.07465 | + | 2.35250i | −0.418050 | + | 0.241362i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.8747i | 1.10416i | 0.833790 | + | 0.552081i | \(0.186166\pi\) | ||||
−0.833790 | + | 0.552081i | \(0.813834\pi\) | |||||||
\(98\) | 9.64670 | − | 2.22289i | 0.974464 | − | 0.224546i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.25240 | + | 7.82479i | −0.225240 | + | 0.782479i | ||||
\(101\) | −12.4972 | + | 7.21527i | −1.24352 | + | 0.717946i | −0.969809 | − | 0.243866i | \(-0.921584\pi\) |
−0.273710 | + | 0.961812i | \(0.588251\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.51235 | + | 13.0118i | −0.740214 | + | 1.28209i | 0.212184 | + | 0.977230i | \(0.431942\pi\) |
−0.952398 | + | 0.304858i | \(0.901391\pi\) | |||||||
\(104\) | 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 | \(-0.134180\pi\) |
0.101883 | + | 0.994796i | \(0.467513\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.03563 | + | 5.25787i | 0.290761 | + | 0.503612i | 0.973990 | − | 0.226592i | \(-0.0727583\pi\) |
−0.683229 | + | 0.730204i | \(0.739425\pi\) | |||||||
\(110\) | 2.92347 | − | 6.87747i | 0.278742 | − | 0.655741i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 9.24582 | + | 5.14925i | 0.873648 | + | 0.486559i | ||||
\(113\) | 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 | ||||
\(116\) | −3.44200 | − | 3.57161i | −0.319581 | − | 0.331615i | ||||
\(117\) | 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 | ||||
\(122\) | −11.7643 | + | 8.85562i | −1.06509 | + | 0.801751i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.67107 | − | 9.27924i | 0.239869 | − | 0.833301i | ||||
\(125\) | 8.74207i | 0.781915i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.6431i | 1.03316i | 0.856240 | + | 0.516578i | \(0.172794\pi\) | ||||
−0.856240 | + | 0.516578i | \(0.827206\pi\) | |||||||
\(128\) | 3.64500 | + | 10.7105i | 0.322176 | + | 0.946680i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 3.07465 | + | 4.08455i | 0.269665 | + | 0.358239i | ||||
\(131\) | 4.63078 | − | 8.02074i | 0.404593 | − | 0.700776i | −0.589681 | − | 0.807636i | \(-0.700747\pi\) |
0.994274 | + | 0.106861i | \(0.0340798\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.03563 | − | 10.8328i | −0.610067 | − | 0.939321i | ||||
\(134\) | −1.61993 | − | 13.2494i | −0.139940 | − | 1.14457i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.22432 | − | 1.50716i | 0.104984 | − | 0.129238i | ||||
\(137\) | 3.61504 | + | 6.26144i | 0.308854 | + | 0.534951i | 0.978112 | − | 0.208080i | \(-0.0667213\pi\) |
−0.669258 | + | 0.743030i | \(0.733388\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.30812 | 0.450229 | 0.225115 | − | 0.974332i | \(-0.427724\pi\) | ||||
0.225115 | + | 0.974332i | \(0.427724\pi\) | |||||||
\(140\) | 4.96766 | + | 1.15198i | 0.419844 | + | 0.0973604i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −13.1664 | − | 5.59677i | −1.10490 | − | 0.469671i | ||||
\(143\) | 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 | −0.754617 | − | 0.656165i | \(-0.772178\pi\) |
0.945564 | + | 0.325435i | \(0.105511\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.5709 | − | 6.10309i | 0.860244 | − | 0.496662i | −0.00384988 | − | 0.999993i | \(-0.501225\pi\) |
0.864094 | + | 0.503330i | \(0.167892\pi\) | |||||||
\(152\) | 2.18114 | − | 13.6355i | 0.176914 | − | 1.10599i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 19.2758 | + | 7.02594i | 1.55329 | + | 0.566167i | ||||
\(155\) | − | 4.65281i | − | 0.373723i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18.9944 | + | 10.9664i | −1.51592 | + | 0.875217i | −0.516095 | + | 0.856531i | \(0.672615\pi\) |
−0.999825 | + | 0.0186856i | \(0.994052\pi\) | |||||||
\(158\) | 1.59812 | − | 1.20298i | 0.127139 | − | 0.0957042i | ||||
\(159\) | 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 | \(-0.383637\pi\) |
−0.630061 | + | 0.776546i | \(0.716970\pi\) | |||||||
\(164\) | 13.5798 | − | 13.0870i | 1.06041 | − | 1.02192i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.300843 | + | 0.707734i | −0.0233499 | + | 0.0549308i | ||||
\(167\) | −14.7178 | −1.13890 | −0.569448 | − | 0.822027i | \(-0.692843\pi\) | ||||
−0.569448 | + | 0.822027i | \(0.692843\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.07126 | −0.0824047 | ||||||||
\(170\) | 0.366030 | − | 0.861087i | 0.0280733 | − | 0.0660424i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −8.60370 | + | 8.29148i | −0.656026 | + | 0.632219i | ||||
\(173\) | 10.0918 | + | 5.82648i | 0.767262 | + | 0.442979i | 0.831897 | − | 0.554930i | \(-0.187255\pi\) |
−0.0646349 | + | 0.997909i | \(0.520588\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10.7568 | + | 0.564256i | −0.813134 | + | 0.0426538i | ||||
\(176\) | 10.2572 | + | 19.3866i | 0.773163 | + | 1.46132i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.626381 | − | 0.471509i | 0.0469492 | − | 0.0353411i | ||||
\(179\) | 2.24663 | − | 1.29709i | 0.167921 | − | 0.0969494i | −0.413684 | − | 0.910421i | \(-0.635758\pi\) |
0.581605 | + | 0.813471i | \(0.302425\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 9.53343i | − | 0.708615i | −0.935129 | − | 0.354307i | \(-0.884717\pi\) | ||
0.935129 | − | 0.354307i | \(-0.115283\pi\) | |||||||
\(182\) | −10.7561 | + | 9.01691i | −0.797293 | + | 0.668378i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.46574 | − | 0.554380i | −0.255498 | − | 0.0408694i | ||||
\(185\) | −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 | \(-0.430810\pi\) |
−0.737817 | + | 0.675001i | \(0.764143\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.18630 | + | 10.7150i | 0.445300 | + | 0.771282i | 0.998073 | − | 0.0620498i | \(-0.0197638\pi\) |
−0.552773 | + | 0.833332i | \(0.686430\pi\) | |||||||
\(194\) | −14.1536 | − | 6.01639i | −1.01617 | − | 0.431951i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.44387 | + | 13.7850i | −0.174562 | + | 0.984646i | ||||
\(197\) | −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 | −0.974495 | − | 0.224410i | \(-0.927955\pi\) |
0.292903 | − | 0.956142i | \(-0.405379\pi\) | |||||||
\(200\) | −8.93790 | − | 7.26054i | −0.632005 | − | 0.513397i | ||||
\(201\) | 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 | ||||
\(206\) | −12.7787 | − | 16.9761i | −0.890338 | − | 1.18278i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −14.9944 | − | 0.554380i | −1.03968 | − | 0.0384393i | ||||
\(209\) | − | 26.7700i | − | 1.85172i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 9.24637i | − | 0.636546i | −0.947999 | − | 0.318273i | \(-0.896897\pi\) | ||
0.947999 | − | 0.318273i | \(-0.103103\pi\) | |||||||
\(212\) | −2.26562 | + | 7.87070i | −0.155603 | + | 0.540562i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −13.6892 | + | 10.3046i | −0.935773 | + | 0.704405i | ||||
\(215\) | −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 | ||||||||
\(220\) | 7.33369 | + | 7.60984i | 0.494437 | + | 0.513055i | ||||
\(221\) | 1.28763 | + | 2.23024i | 0.0866152 | + | 0.150022i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.94585 | 0.130303 | 0.0651517 | − | 0.997875i | \(-0.479247\pi\) | ||||
0.0651517 | + | 0.997875i | \(0.479247\pi\) | |||||||
\(224\) | −11.8170 | + | 9.18471i | −0.789556 | + | 0.613679i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.08260 | + | 9.60432i | −0.271571 | + | 0.638870i | ||||
\(227\) | −4.32265 | − | 7.48706i | −0.286905 | − | 0.496933i | 0.686165 | − | 0.727446i | \(-0.259293\pi\) |
−0.973069 | + | 0.230513i | \(0.925960\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.5396 | + | 8.39446i | 0.960805 | + | 0.554721i | 0.896421 | − | 0.443204i | \(-0.146158\pi\) |
0.0643846 | + | 0.997925i | \(0.479492\pi\) | |||||||
\(230\) | −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 | −0.882657 | − | 0.470018i | \(-0.844248\pi\) |
0.848376 | + | 0.529395i | \(0.177581\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.01711 | − | 1.74193i | 0.196814 | − | 0.113631i | ||||
\(236\) | −7.01862 | + | 24.3825i | −0.456873 | + | 1.58717i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.41340 | + | 0.879676i | 0.156438 | + | 0.0570210i | ||||
\(239\) | − | 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 | −0.574922 | − | 0.818208i | \(-0.694968\pi\) |
0.421128 | + | 0.907001i | \(0.361634\pi\) | |||||||
\(242\) | 16.2157 | + | 21.5419i | 1.04238 | + | 1.38476i | ||||
\(243\) | 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 | ||||
\(248\) | 10.5992 | + | 8.61011i | 0.673053 | + | 0.546742i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −11.3779 | − | 4.83650i | −0.719600 | − | 0.305887i | ||||
\(251\) | 20.7493 | 1.30968 | 0.654841 | − | 0.755767i | \(-0.272736\pi\) | ||||
0.654841 | + | 0.755767i | \(0.272736\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.80413 | −0.427772 | ||||||||
\(254\) | −15.1536 | − | 6.44147i | −0.950819 | − | 0.404173i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −15.9563 | − | 1.18150i | −0.997270 | − | 0.0738438i | ||||
\(257\) | −6.45283 | − | 3.72554i | −0.402516 | − | 0.232393i | 0.285053 | − | 0.958512i | \(-0.407989\pi\) |
−0.687569 | + | 0.726119i | \(0.741322\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.93830 | − | 6.06381i | −0.244714 | − | 0.376787i | ||||
\(260\) | −7.01711 | + | 1.74193i | −0.435182 | + | 0.108030i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 7.87711 | + | 10.4644i | 0.486649 | + | 0.646494i | ||||
\(263\) | −25.7034 | + | 14.8399i | −1.58494 | + | 0.915066i | −0.590818 | + | 0.806805i | \(0.701195\pi\) |
−0.994123 | + | 0.108260i | \(0.965472\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.94654i | 0.242434i | ||||||||
\(266\) | 17.9914 | − | 3.16375i | 1.10312 | − | 0.193982i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 18.1403 | + | 5.22178i | 1.10810 | + | 0.318971i | ||||
\(269\) | 3.73727 | − | 2.15771i | 0.227865 | − | 0.131558i | −0.381722 | − | 0.924277i | \(-0.624669\pi\) |
0.609587 | + | 0.792719i | \(0.291335\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.79142 | − | 11.7631i | 0.412550 | − | 0.714557i | −0.582618 | − | 0.812746i | \(-0.697972\pi\) |
0.995168 | + | 0.0981892i | \(0.0313050\pi\) | |||||||
\(272\) | 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 | 0.833235 | − | 0.552920i | \(-0.186486\pi\) |
−0.895460 | + | 0.445143i | \(0.853153\pi\) | |||||||
\(278\) | −2.93669 | + | 6.90856i | −0.176131 | + | 0.414348i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −4.24764 | + | 5.82811i | −0.253845 | + | 0.348296i | ||||
\(281\) | −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 | \(-0.285336\pi\) |
−0.988653 | + | 0.150216i | \(0.952003\pi\) | |||||||
\(284\) | 14.5685 | − | 14.0398i | 0.864480 | − | 0.833109i | ||||
\(285\) | 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 | ||||
\(290\) | 2.70053 | − | 2.03282i | 0.158580 | − | 0.119372i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 12.8019 | + | 3.68510i | 0.749177 | + | 0.215654i | ||||
\(293\) | 10.7090i | 0.625626i | 0.949815 | + | 0.312813i | \(0.101271\pi\) | ||||
−0.949815 | + | 0.312813i | \(0.898729\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.2259i | 0.711821i | ||||||||
\(296\) | 1.22093 | − | 7.63269i | 0.0709649 | − | 0.443641i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.96477 | + | 5.26704i | 0.229673 | + | 0.305112i | ||||
\(299\) | 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 | ||||||||
\(304\) | 16.5400 | + | 10.3825i | 0.948636 | + | 0.595480i | ||||
\(305\) | −5.01711 | − | 8.68988i | −0.287279 | − | 0.497581i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.22056 | 0.240880 | 0.120440 | − | 0.992721i | \(-0.461569\pi\) | ||||
0.120440 | + | 0.992721i | \(0.461569\pi\) | |||||||
\(308\) | −19.8085 | + | 21.2005i | −1.12870 | + | 1.20801i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 6.05567 | + | 2.57414i | 0.343939 | + | 0.146201i | ||||
\(311\) | 4.85070 | + | 8.40165i | 0.275058 | + | 0.476414i | 0.970150 | − | 0.242507i | \(-0.0779697\pi\) |
−0.695092 | + | 0.718921i | \(0.744636\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.8328 | + | 6.83168i | 0.668831 | + | 0.386149i | 0.795633 | − | 0.605778i | \(-0.207138\pi\) |
−0.126803 | + | 0.991928i | \(0.540472\pi\) | |||||||
\(314\) | −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 | −0.432992 | − | 0.901398i | \(-0.642542\pi\) |
0.997129 | − | 0.0757171i | \(-0.0241246\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.7771 | − | 6.79948i | 0.659388 | − | 0.380698i | ||||
\(320\) | −7.54610 | + | 1.57975i | −0.421840 | + | 0.0883106i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.804130 | − | 4.57286i | −0.0448124 | − | 0.254836i | ||||
\(323\) | − | 3.35171i | − | 0.186494i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 13.2259 | − | 7.63599i | 0.733642 | − | 0.423569i | ||||
\(326\) | 4.54039 | − | 3.41778i | 0.251469 | − | 0.189294i | ||||
\(327\) | 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 | \(-0.249969\pi\) |
−0.258724 | + | 0.965951i | \(0.583302\pi\) | |||||||
\(332\) | −0.754681 | − | 0.783099i | −0.0414185 | − | 0.0429781i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 8.14252 | − | 19.1553i | 0.445539 | − | 1.04813i | ||||
\(335\) | 9.09596 | 0.496965 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.4411 | −0.732185 | −0.366092 | − | 0.930578i | \(-0.619305\pi\) | ||||
−0.366092 | + | 0.930578i | \(0.619305\pi\) | |||||||
\(338\) | 0.592669 | − | 1.39425i | 0.0322369 | − | 0.0758374i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.918207 | + | 0.952783i | 0.0497968 | + | 0.0516719i | ||||
\(341\) | 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 | ||||||||
\(346\) | −13.1664 | + | 9.91103i | −0.707831 | + | 0.532820i | ||||
\(347\) | 19.5890 | − | 11.3097i | 1.05159 | − | 0.607136i | 0.128497 | − | 0.991710i | \(-0.458985\pi\) |
0.923094 | + | 0.384574i | \(0.125651\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 2.48180i | − | 0.132848i | −0.997791 | − | 0.0664239i | \(-0.978841\pi\) | ||
0.997791 | − | 0.0664239i | \(-0.0211590\pi\) | |||||||
\(350\) | 5.21673 | − | 14.3122i | 0.278846 | − | 0.765018i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −30.9066 | + | 2.62423i | −1.64733 | + | 0.139872i | ||||
\(353\) | 7.89315 | − | 4.55711i | 0.420110 | − | 0.242551i | −0.275014 | − | 0.961440i | \(-0.588683\pi\) |
0.695124 | + | 0.718889i | \(0.255349\pi\) | |||||||
\(354\) | 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 | \(-0.274808\pi\) |
−0.333238 | + | 0.942843i | \(0.608141\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.41780 | − | 4.18776i | −0.127253 | − | 0.220408i | ||||
\(362\) | 12.4078 | + | 5.27431i | 0.652141 | + | 0.277212i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −5.78484 | − | 18.9877i | −0.303208 | − | 0.995223i | ||||
\(365\) | 6.41917 | 0.335995 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.91680 | − | 3.31999i | −0.100056 | − | 0.173302i | 0.811652 | − | 0.584142i | \(-0.198569\pi\) |
−0.911707 | + | 0.410840i | \(0.865235\pi\) | |||||||
\(368\) | 2.63893 | − | 4.20398i | 0.137564 | − | 0.219147i | ||||
\(369\) | 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 | −0.275711 | − | 0.961241i | \(-0.588913\pi\) |
0.970314 | − | 0.241848i | \(-0.0777534\pi\) | |||||||
\(374\) | 3.20164 | + | 4.25325i | 0.165553 | + | 0.219930i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.61504 | + | 10.0965i | −0.0832894 | + | 0.520689i | ||||
\(377\) | 9.30330i | 0.479144i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 6.93692i | − | 0.356325i | −0.984001 | − | 0.178163i | \(-0.942985\pi\) | ||
0.984001 | − | 0.178163i | \(-0.0570153\pi\) | |||||||
\(380\) | 9.04282 | + | 2.60301i | 0.463887 | + | 0.133532i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 9.41497 | − | 7.08713i | 0.481712 | − | 0.362609i | ||||
\(383\) | −1.12881 | + | 1.95515i | −0.0576793 | + | 0.0999035i | −0.893423 | − | 0.449216i | \(-0.851703\pi\) |
0.835744 | + | 0.549119i | \(0.185037\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.34654 | + | 12.4573i | −0.323450 | + | 0.634881i | ||||
\(386\) | −17.3682 | + | 2.12351i | −0.884017 | + | 0.108084i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 15.6607 | − | 15.0924i | 0.795054 | − | 0.766202i | ||||
\(389\) | 15.3047 | + | 26.5086i | 0.775981 | + | 1.34404i | 0.934242 | + | 0.356641i | \(0.116078\pi\) |
−0.158261 | + | 0.987397i | \(0.550589\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.851904 | −0.0430827 | ||||||||
\(392\) | −16.5893 | − | 10.8072i | −0.837885 | − | 0.545847i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.79078 | − | 4.21280i | 0.0902179 | − | 0.212238i | ||||
\(395\) | 0.681544 | + | 1.18047i | 0.0342922 | + | 0.0593958i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.0368 | − | 6.94947i | −0.604112 | − | 0.348784i | 0.166546 | − | 0.986034i | \(-0.446739\pi\) |
−0.770657 | + | 0.637250i | \(0.780072\pi\) | |||||||
\(398\) | 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 | −0.965328 | − | 0.261041i | \(-0.915934\pi\) |
0.708732 | + | 0.705478i | \(0.249268\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −15.6843 | + | 9.05535i | −0.781292 | + | 0.451079i | ||||
\(404\) | 27.7349 | + | 7.98361i | 1.37986 | + | 0.397199i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 5.96158 | + | 7.11144i | 0.295868 | + | 0.352935i | ||||
\(407\) | − | 14.9849i | − | 0.742775i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.5342 | − | 6.08193i | 0.520883 | − | 0.300732i | −0.216413 | − | 0.976302i | \(-0.569436\pi\) |
0.737296 | + | 0.675570i | \(0.236102\pi\) | |||||||
\(410\) | 7.72912 | + | 10.2678i | 0.381714 | + | 0.507092i | ||||
\(411\) | 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 | ||||
\(416\) | 9.01711 | − | 19.2086i | 0.442100 | − | 0.941781i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 34.8414 | + | 14.8104i | 1.70415 | + | 0.724398i | ||||
\(419\) | −16.2245 | −0.792619 | −0.396310 | − | 0.918117i | \(-0.629709\pi\) | ||||
−0.396310 | + | 0.918117i | \(0.629709\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.58477 | −0.467133 | −0.233567 | − | 0.972341i | \(-0.575040\pi\) | ||||
−0.233567 | + | 0.972341i | \(0.575040\pi\) | |||||||
\(422\) | 12.0342 | + | 5.11550i | 0.585816 | + | 0.249019i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −8.99034 | − | 7.30313i | −0.436609 | − | 0.354672i | ||||
\(425\) | −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 | ||||||||
\(430\) | −4.89690 | − | 6.50534i | −0.236150 | − | 0.313715i | ||||
\(431\) | 0.131544 | − | 0.0759470i | 0.00633626 | − | 0.00365824i | −0.496829 | − | 0.867849i | \(-0.665502\pi\) |
0.503165 | + | 0.864190i | \(0.332169\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 9.46997i | − | 0.455098i | −0.973767 | − | 0.227549i | \(-0.926929\pi\) | ||
0.973767 | − | 0.227549i | \(-0.0730711\pi\) | |||||||
\(434\) | −6.18640 | + | 16.9725i | −0.296957 | + | 0.814705i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.35889 | − | 11.6687i | 0.160862 | − | 0.558830i | ||||
\(437\) | −5.24663 | + | 3.02915i | −0.250981 | + | 0.144904i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16.7373 | + | 28.9898i | −0.798826 | + | 1.38361i | 0.121555 | + | 0.992585i | \(0.461212\pi\) |
−0.920381 | + | 0.391023i | \(0.872121\pi\) | |||||||
\(440\) | −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 | \(-0.119921\pi\) |
0.146327 | + | 0.989236i | \(0.453255\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.267131 | + | 0.462684i | 0.0126632 | + | 0.0219333i | ||||
\(446\) | −1.07653 | + | 2.53253i | −0.0509750 | + | 0.119919i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −5.41629 | − | 20.4613i | −0.255896 | − | 0.966704i | ||||
\(449\) | −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 | ||||
\(452\) | −10.2414 | − | 10.6271i | −0.481716 | − | 0.499855i | ||||
\(453\) | 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 | −0.971153 | − | 0.238458i | \(-0.923358\pi\) |
0.692087 | + | 0.721814i | \(0.256691\pi\) | |||||||
\(458\) | −18.9694 | + | 14.2792i | −0.886382 | + | 0.667225i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.661608 | − | 2.29841i | 0.0308476 | − | 0.107164i | ||||
\(461\) | − | 30.0093i | − | 1.39767i | −0.715281 | − | 0.698837i | \(-0.753701\pi\) | ||
0.715281 | − | 0.698837i | \(-0.246299\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.2736i | 0.616875i | 0.951245 | + | 0.308437i | \(0.0998060\pi\) | ||||
−0.951245 | + | 0.308437i | \(0.900194\pi\) | |||||||
\(464\) | −0.366532 | + | 9.91365i | −0.0170158 | + | 0.460230i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.890122 | − | 1.18249i | −0.0412341 | − | 0.0547778i | ||||
\(467\) | −14.8246 | + | 25.6770i | −0.686002 | + | 1.18819i | 0.287119 | + | 0.957895i | \(0.407303\pi\) |
−0.973121 | + | 0.230295i | \(0.926031\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.30812 | + | 24.9376i | 0.0604036 | + | 1.15151i | ||||
\(470\) | 0.597935 | + | 4.89050i | 0.0275807 | + | 0.225582i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −27.8510 | − | 22.6243i | −1.28195 | − | 1.04137i | ||||
\(473\) | −16.3794 | − | 28.3699i | −0.753125 | − | 1.30445i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −19.8766 | −0.912001 | ||||||||
\(476\) | −2.48011 | + | 2.65439i | −0.113676 | + | 0.121664i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 25.0513 | + | 10.6488i | 1.14582 | + | 0.487065i | ||||
\(479\) | 5.76773 | + | 9.99001i | 0.263535 | + | 0.456455i | 0.967179 | − | 0.254097i | \(-0.0817784\pi\) |
−0.703644 | + | 0.710553i | \(0.748445\pi\) | |||||||
\(480\) | 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 | \(-0.737607\pi\) |
0.296221 | + | 0.955119i | \(0.404273\pi\) | |||||||
\(488\) | 29.0801 | + | 4.65165i | 1.31639 | + | 0.210570i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −9.12223 | − | 2.79310i | −0.412100 | − | 0.126179i | ||||
\(491\) | 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 | ||||
\(494\) | −20.6924 | + | 15.5762i | −0.930995 | + | 0.700808i | ||||
\(495\) | 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 | \(-0.587125\pi\) |
−0.968941 | + | 0.247294i | \(0.920459\pi\) | |||||||
\(500\) | 12.5895 | − | 12.1326i | 0.563019 | − | 0.542587i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −11.4794 | + | 27.0053i | −0.512351 | + | 1.20531i | ||||
\(503\) | −22.7110 | −1.01263 | −0.506317 | − | 0.862348i | \(-0.668993\pi\) | ||||
−0.506317 | + | 0.862348i | \(0.668993\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.9069 | 0.618847 | ||||||||
\(506\) | 3.76434 | − | 8.85562i | 0.167346 | − | 0.393681i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 16.7672 | − | 16.1588i | 0.743925 | − | 0.716929i | ||||
\(509\) | 1.98947 | + | 1.14862i | 0.0881819 | + | 0.0509118i | 0.543443 | − | 0.839446i | \(-0.317121\pi\) |
−0.455261 | + | 0.890358i | \(0.650454\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.923166 | + | 17.5989i | 0.0408384 | + | 0.778528i | ||||
\(512\) | 10.3655 | − | 20.1136i | 0.458093 | − | 0.888904i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 8.41881 | − | 6.33727i | 0.371338 | − | 0.279525i | ||||
\(515\) | 12.5396 | − | 7.23973i | 0.552560 | − | 0.319021i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 19.8221i | 0.871773i | ||||||||
\(518\) | 10.0709 | − | 1.77096i | 0.442491 | − | 0.0778114i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.61504 | − | 10.0965i | 0.0708242 | − | 0.442762i | ||||
\(521\) | 32.5712 | − | 18.8050i | 1.42697 | − | 0.823862i | 0.430090 | − | 0.902786i | \(-0.358482\pi\) |
0.996881 | + | 0.0789240i | \(0.0251485\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17.8444 | + | 30.9073i | −0.780279 | + | 1.35148i | 0.151500 | + | 0.988457i | \(0.451590\pi\) |
−0.931779 | + | 0.363026i | \(0.881744\pi\) | |||||||
\(524\) | −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 | ||||
\(530\) | −5.13645 | − | 2.18340i | −0.223113 | − | 0.0948408i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −5.83597 | + | 25.1662i | −0.253021 | + | 1.09109i | ||||
\(533\) | −35.3726 | −1.53216 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.83799 | − | 10.1117i | −0.252398 | − | 0.437167i | ||||
\(536\) | −16.8322 | + | 20.7209i | −0.727041 | + | 0.895005i | ||||
\(537\) | 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 | 0.126507 | + | 0.991966i | \(0.459623\pi\) |
−0.922321 | + | 0.386425i | \(0.873710\pi\) | |||||||
\(542\) | 11.5524 | + | 15.3469i | 0.496219 | + | 0.659208i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3.86963 | + | 0.328564i | −0.165909 | + | 0.0140871i | ||||
\(545\) | − | 5.85094i | − | 0.250627i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 2.09106i | − | 0.0894073i | −0.999000 | − | 0.0447036i | \(-0.985766\pi\) | ||
0.999000 | − | 0.0447036i | \(-0.0142344\pi\) | |||||||
\(548\) | 4.00000 | − | 13.8959i | 0.170872 | − | 0.593604i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 25.2229 | − | 18.9866i | 1.07551 | − | 0.809591i | ||||
\(551\) | 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 | ||||||||
\(556\) | −7.36684 | − | 7.64424i | −0.312424 | − | 0.324188i | ||||
\(557\) | −8.39887 | − | 14.5473i | −0.355872 | − | 0.616388i | 0.631395 | − | 0.775461i | \(-0.282483\pi\) |
−0.987267 | + | 0.159073i | \(0.949149\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 22.4109 | 0.947878 | ||||||||
\(560\) | −5.23535 | − | 8.75271i | −0.221234 | − | 0.369869i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 13.1186 | − | 30.8616i | 0.553376 | − | 1.30182i | ||||
\(563\) | −8.69784 | − | 15.0651i | −0.366570 | − | 0.634918i | 0.622456 | − | 0.782654i | \(-0.286135\pi\) |
−0.989027 | + | 0.147736i | \(0.952801\pi\) | |||||||
\(564\) | 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 | 0.242882 | + | 0.970056i | \(0.421907\pi\) |
−0.961534 | + | 0.274686i | \(0.911426\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.14176 | − | 2.96860i | 0.215176 | − | 0.124232i | −0.388539 | − | 0.921432i | \(-0.627020\pi\) |
0.603715 | + | 0.797201i | \(0.293687\pi\) | |||||||
\(572\) | 11.3794 | − | 39.5317i | 0.475796 | − | 1.65290i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −27.0388 | + | 22.6669i | −1.12858 | + | 0.946097i | ||||
\(575\) | 5.05203i | 0.210684i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 33.7930 | − | 19.5104i | 1.40682 | − | 0.812229i | 0.411742 | − | 0.911300i | \(-0.364920\pi\) |
0.995080 | + | 0.0990712i | \(0.0315871\pi\) | |||||||
\(578\) | −14.0579 | − | 18.6754i | −0.584732 | − | 0.776794i | ||||
\(579\) | 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 | ||||
\(584\) | −11.8788 | + | 14.6231i | −0.491547 | + | 0.605107i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −13.9378 | − | 5.92469i | −0.575767 | − | 0.244747i | ||||
\(587\) | 7.71931 | 0.318610 | 0.159305 | − | 0.987229i | \(-0.449075\pi\) | ||||
0.159305 | + | 0.987229i | \(0.449075\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 23.5712 | 0.971235 | ||||||||
\(590\) | −15.9121 | − | 6.76392i | −0.655092 | − | 0.278466i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 9.25853 | + | 5.81178i | 0.380523 | + | 0.238863i | ||||
\(593\) | −0.336377 | − | 0.194207i | −0.0138133 | − | 0.00797513i | 0.493077 | − | 0.869985i | \(-0.335872\pi\) |
−0.506891 | + | 0.862010i | \(0.669205\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.794612 | + | 1.55970i | −0.0325759 | + | 0.0639415i | ||||
\(596\) | −9.04858 | + | 2.24622i | −0.370644 | + | 0.0920088i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 3.95901 | + | 5.25938i | 0.161896 | + | 0.215072i | ||||
\(599\) | −18.0000 | + | 10.3923i | −0.735460 | + | 0.424618i | −0.820416 | − | 0.571767i | \(-0.806258\pi\) |
0.0849563 | + | 0.996385i | \(0.472925\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 26.4110i | − | 1.07733i | −0.842521 | − | 0.538664i | \(-0.818929\pi\) | ||
0.842521 | − | 0.538664i | \(-0.181071\pi\) | |||||||
\(602\) | 17.1309 | − | 14.3610i | 0.698202 | − | 0.585309i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −23.4598 | − | 6.75299i | −0.954564 | − | 0.274775i | ||||
\(605\) | −15.9122 | + | 9.18691i | −0.646922 | + | 0.373501i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20.3531 | − | 35.2526i | 0.826106 | − | 1.43086i | −0.0749655 | − | 0.997186i | \(-0.523885\pi\) |
0.901071 | − | 0.433671i | \(-0.142782\pi\) | |||||||
\(608\) | −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 | 0.636129 | − | 0.771583i | \(-0.280535\pi\) |
−0.986275 | + | 0.165113i | \(0.947201\pi\) | |||||||
\(614\) | −2.33500 | + | 5.49310i | −0.0942330 | + | 0.221683i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −16.6337 | − | 37.5100i | −0.670189 | − | 1.51132i | ||||
\(617\) | 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 | 0.999379 | + | 0.0352227i | \(0.0112141\pi\) |
−0.469186 | + | 0.883099i | \(0.655453\pi\) | |||||||
\(620\) | −6.70053 | + | 6.45737i | −0.269100 | + | 0.259334i | ||||
\(621\) | 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 | ||||
\(626\) | −15.4379 | + | 11.6209i | −0.617023 | + | 0.464465i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 42.1541 | + | 12.1342i | 1.68213 | + | 0.484209i | ||||
\(629\) | − | 1.87617i | − | 0.0748079i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 41.0696i | − | 1.63495i | −0.575961 | − | 0.817477i | \(-0.695372\pi\) | ||
0.575961 | − | 0.817477i | \(-0.304628\pi\) | |||||||
\(632\) | −3.95035 | − | 0.631898i | −0.157137 | − | 0.0251356i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 17.0855 | + | 22.6974i | 0.678551 | + | 0.901428i | ||||
\(635\) | 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 | ||||||||
\(640\) | 2.11878 | − | 10.6953i | 0.0837522 | − | 0.422769i | ||||
\(641\) | 22.7239 | + | 39.3590i | 0.897540 | + | 1.55459i | 0.830629 | + | 0.556827i | \(0.187981\pi\) |
0.0669115 | + | 0.997759i | \(0.478685\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −30.5534 | −1.20491 | −0.602454 | − | 0.798154i | \(-0.705810\pi\) | ||||
−0.602454 | + | 0.798154i | \(0.705810\pi\) | |||||||
\(644\) | 6.39649 | + | 1.48333i | 0.252057 | + | 0.0584513i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.36228 | + | 1.85432i | 0.171632 | + | 0.0729571i | ||||
\(647\) | −18.0896 | − | 31.3321i | −0.711175 | − | 1.23179i | −0.964417 | − | 0.264388i | \(-0.914830\pi\) |
0.253242 | − | 0.967403i | \(-0.418503\pi\) | |||||||
\(648\) | 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 | −0.935245 | − | 0.354000i | \(-0.884821\pi\) |
0.774196 | + | 0.632946i | \(0.218155\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.72968 | + | 4.46273i | −0.302024 | + | 0.174373i | ||||
\(656\) | −37.6933 | − | 1.39361i | −1.47168 | − | 0.0544114i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −13.3218 | + | 2.34262i | −0.519339 | + | 0.0913250i | ||||
\(659\) | 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 | −0.803340 | − | 0.595520i | \(-0.796946\pi\) |
0.114065 | + | 0.993473i | \(0.463613\pi\) | |||||||
\(662\) | −10.6446 | + | 8.01275i | −0.413715 | + | 0.311424i | ||||
\(663\) | 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 | ||||
\(668\) | 20.4260 | + | 21.1951i | 0.790304 | + | 0.820063i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −5.03228 | + | 11.8385i | −0.194414 | + | 0.457359i | ||||
\(671\) | 57.0916 | 2.20400 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.23008 | 0.163058 | 0.0815289 | − | 0.996671i | \(-0.474020\pi\) | ||||
0.0815289 | + | 0.996671i | \(0.474020\pi\) | |||||||
\(674\) | 7.43622 | − | 17.4937i | 0.286433 | − | 0.673833i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.48674 | + | 1.54273i | 0.0571824 | + | 0.0593356i | ||||
\(677\) | −20.7962 | − | 12.0067i | −0.799262 | − | 0.461454i | 0.0439511 | − | 0.999034i | \(-0.486005\pi\) |
−0.843213 | + | 0.537580i | \(0.819339\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 25.6365 | + | 13.0609i | 0.983840 | + | 0.501232i | ||||
\(680\) | −1.74805 | + | 0.667932i | −0.0670345 | + | 0.0256140i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −29.9113 | + | 22.5158i | −1.14536 | + | 0.862174i | ||||
\(683\) | 7.09951 | − | 4.09890i | 0.271655 | − | 0.156840i | −0.357984 | − | 0.933728i | \(-0.616536\pi\) |
0.629640 | + | 0.776887i | \(0.283203\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 6.96771i | − | 0.266222i | ||||||
\(686\) | 6.34567 | − | 25.4113i | 0.242279 | − | 0.970207i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 23.8812 | + | 0.882944i | 0.910461 | + | 0.0336619i | ||||
\(689\) | 13.3035 | − | 7.68079i | 0.506824 | − | 0.292615i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.9925 | − | 31.1638i | 0.684465 | − | 1.18553i | −0.289139 | − | 0.957287i | \(-0.593369\pi\) |
0.973605 | − | 0.228242i | \(-0.0732976\pi\) | |||||||
\(692\) | −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 | ||||
\(698\) | 3.23008 | + | 1.37304i | 0.122260 | + | 0.0519704i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 15.7413 | + | 14.7077i | 0.594964 | + | 0.555900i | ||||
\(701\) | 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 | ||||
\(704\) | 13.6834 | − | 41.6769i | 0.515713 | − | 1.57076i | ||||
\(705\) | 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 | −0.963518 | − | 0.267644i | \(-0.913755\pi\) |
0.713545 | + | 0.700609i | \(0.247088\pi\) | |||||||
\(710\) | 8.29183 | + | 11.0154i | 0.311187 | + | 0.413399i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.54834 | − | 0.247673i | −0.0580265 | − | 0.00928192i | ||||
\(713\) | − | 5.99109i | − | 0.224368i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 19.8221i | − | 0.741303i | ||||||
\(716\) | −4.98592 | − | 1.43522i | −0.186333 | − | 0.0536367i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −7.82802 | + | 5.89255i | −0.292139 | + | 0.219908i | ||||
\(719\) | 23.7520 | − | 41.1397i | 0.885800 | − | 1.53425i | 0.0410056 | − | 0.999159i | \(-0.486944\pi\) |
0.844794 | − | 0.535091i | \(-0.179723\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 21.6519 | + | 33.3375i | 0.806358 | + | 1.24155i | ||||
\(722\) | 6.78803 | − | 0.829936i | 0.252624 | − | 0.0308870i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −13.7291 | + | 13.2309i | −0.510239 | + | 0.491723i | ||||
\(725\) | −5.04858 | − | 8.74440i | −0.187500 | − | 0.324759i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24.3567 | 0.903340 | 0.451670 | − | 0.892185i | \(-0.350828\pi\) | ||||
0.451670 | + | 0.892185i | \(0.350828\pi\) | |||||||
\(728\) | 27.9130 | + | 2.97579i | 1.03452 | + | 0.110290i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −3.55137 | + | 8.35460i | −0.131442 | + | 0.309218i | ||||
\(731\) | −2.05076 | − | 3.55203i | −0.0758503 | − | 0.131377i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.35812 | + | 1.93881i | 0.124035 | + | 0.0716117i | 0.560734 | − | 0.827996i | \(-0.310519\pi\) |
−0.436699 | + | 0.899608i | \(0.643852\pi\) | |||||||
\(734\) | 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 | \(-0.717346\pi\) |
0.356374 | + | 0.934343i | \(0.384013\pi\) | |||||||
\(740\) | 5.06185 | + | 1.45708i | 0.186077 | + | 0.0535632i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5.24733 | − | 14.3961i | 0.192636 | − | 0.528499i | ||||
\(743\) | − | 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 | ||||
\(746\) | 22.8194 | + | 30.3146i | 0.835477 | + | 1.10990i | ||||
\(747\) | 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 | \(-0.109319\pi\) |
0.179190 | + | 0.983815i | \(0.442652\pi\) | |||||||
\(752\) | −12.2472 | − | 7.68783i | −0.446609 | − | 0.280346i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −12.1083 | − | 5.14699i | −0.440959 | − | 0.187442i | ||||
\(755\) | −11.7632 | −0.428108 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29.4204 | 1.06930 | 0.534651 | − | 0.845073i | \(-0.320443\pi\) | ||||
0.534651 | + | 0.845073i | \(0.320443\pi\) | |||||||
\(758\) | 9.02845 | + | 3.83781i | 0.327928 | + | 0.139395i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −8.39073 | + | 10.3292i | −0.304364 | + | 0.374679i | ||||
\(761\) | −43.5568 | − | 25.1475i | −1.57893 | − | 0.911597i | −0.995009 | − | 0.0997877i | \(-0.968184\pi\) |
−0.583923 | − | 0.811809i | \(-0.698483\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 16.0410 | − | 0.841446i | 0.580723 | − | 0.0304624i | ||||
\(764\) | 4.01518 | + | 16.1746i | 0.145264 | + | 0.585175i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.92014 | − | 2.55082i | −0.0693774 | − | 0.0921650i | ||||
\(767\) | 41.2128 | − | 23.7942i | 1.48811 | − | 0.859160i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 20.2817i | − | 0.731377i | −0.930737 | − | 0.365689i | \(-0.880833\pi\) | ||
0.930737 | − | 0.365689i | \(-0.119167\pi\) | |||||||
\(770\) | −12.7020 | − | 15.1520i | −0.457750 | − | 0.546039i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 6.84507 | − | 23.7796i | 0.246359 | − | 0.855847i | ||||
\(773\) | 18.8149 | − | 10.8628i | 0.676723 | − | 0.390706i | −0.121896 | − | 0.992543i | \(-0.538897\pi\) |
0.798619 | + | 0.601836i | \(0.205564\pi\) | |||||||
\(774\) | 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 | ||||
\(782\) | 0.471311 | − | 1.10876i | 0.0168540 | − | 0.0396492i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 23.2436 | − | 15.6120i | 0.830128 | − | 0.557573i | ||||
\(785\) | 21.1369 | 0.754410 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.299328 | + | 0.518452i | 0.0106699 | + | 0.0184808i | 0.871311 | − | 0.490731i | \(-0.163270\pi\) |
−0.860641 | + | 0.509212i | \(0.829937\pi\) | |||||||
\(788\) | 4.49225 | + | 4.66141i | 0.160030 | + | 0.166056i | ||||
\(789\) | 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 | ||||
\(794\) | 15.7041 | − | 11.8213i | 0.557318 | − | 0.419521i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −10.6389 | + | 36.9594i | −0.377087 | + | 1.30999i | ||||
\(797\) | 36.1789i | 1.28152i | 0.767741 | + | 0.640760i | \(0.221381\pi\) | ||||
−0.767741 | + | 0.640760i | \(0.778619\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.48180i | 0.0877998i | ||||||||
\(800\) | 1.94847 | + | 22.9480i | 0.0688890 | + | 0.811333i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −8.74046 | − | 11.6113i | −0.308636 | − | 0.410011i | ||||
\(803\) | −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 | ||||||||
\(808\) | −25.7349 | + | 31.6803i | −0.905350 | + | 1.11451i | ||||
\(809\) | −15.0603 | − | 26.0852i | −0.529491 | − | 0.917106i | −0.999408 | − | 0.0343953i | \(-0.989049\pi\) |
0.469917 | − | 0.882711i | \(-0.344284\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 21.5947 | 0.758292 | 0.379146 | − | 0.925337i | \(-0.376218\pi\) | ||||
0.379146 | + | 0.925337i | \(0.376218\pi\) | |||||||
\(812\) | −12.5538 | + | 3.82468i | −0.440552 | + | 0.134220i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 19.5030 | + | 8.29032i | 0.683579 | + | 0.290575i | ||||
\(815\) | 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 | 0.0222131 | − | 0.999753i | \(-0.492929\pi\) |
0.854705 | − | 0.519114i | \(-0.173738\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.87338 | − | 1.65894i | 0.100160 | − | 0.0578272i | −0.449084 | − | 0.893490i | \(-0.648249\pi\) |
0.549243 | + | 0.835663i | \(0.314916\pi\) | |||||||
\(824\) | −6.71237 | + | 41.9628i | −0.233837 | + | 1.46184i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 16.2556 | − | 44.5976i | 0.565606 | − | 1.55175i | ||||
\(827\) | − | 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 | 0.0797067 | − | 0.996818i | \(-0.474602\pi\) |
0.903123 | + | 0.429381i | \(0.141268\pi\) | |||||||
\(830\) | 0.592108 | − | 0.445710i | 0.0205524 | − | 0.0154708i | ||||
\(831\) | 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 | ||||
\(836\) | −38.5516 | + | 37.1526i | −1.33333 | + | 1.28495i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 8.97611 | − | 21.1163i | 0.310075 | − | 0.729451i | ||||
\(839\) | −8.66161 | −0.299032 | −0.149516 | − | 0.988759i | \(-0.547772\pi\) | ||||
−0.149516 | + | 0.988759i | \(0.547772\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.8491 | −0.787899 | ||||||||
\(842\) | 5.30272 | − | 12.4747i | 0.182744 | − | 0.429905i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −13.3157 | + | 12.8325i | −0.458346 | + | 0.441713i | ||||
\(845\) | 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 | ||||||||
\(850\) | 3.15801 | − | 2.37720i | 0.108319 | − | 0.0815372i | ||||
\(851\) | −2.93688 | + | 1.69561i | −0.100675 | + | 0.0581248i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.17809i | 0.245773i | 0.992421 | + | 0.122887i | \(0.0392151\pi\) | ||||
−0.992421 | + | 0.122887i | \(0.960785\pi\) | |||||||
\(854\) | 6.74724 | + | 38.3696i | 0.230886 | + | 1.31298i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 33.8380 | + | 5.41274i | 1.15656 | + | 0.185004i | ||||
\(857\) | −39.5334 | + | 22.8246i | −1.35044 | + | 0.779675i | −0.988311 | − | 0.152454i | \(-0.951282\pi\) |
−0.362126 | + | 0.932129i | \(0.617949\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.77944 | + | 11.7423i | −0.231311 | + | 0.400643i | −0.958194 | − | 0.286118i | \(-0.907635\pi\) |
0.726883 | + | 0.686761i | \(0.240968\pi\) | |||||||
\(860\) | 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 | \(-0.584005\pi\) |
−0.966470 | + | 0.256781i | \(0.917338\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.61504 | − | 9.72554i | −0.190917 | − | 0.330678i | ||||
\(866\) | 12.3252 | + | 5.23920i | 0.418828 | + | 0.178035i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −18.6672 | − | 17.4416i | −0.633607 | − | 0.592005i | ||||
\(869\) | −7.75555 | −0.263089 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −17.7026 | − | 30.6619i | −0.599831 | − | 1.03894i | ||||
\(872\) | 13.3286 | + | 10.8273i | 0.451364 | + | 0.366657i | ||||
\(873\) | 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 | −0.650619 | − | 0.759404i | \(-0.725491\pi\) |
0.982973 | + | 0.183751i | \(0.0588239\pi\) | |||||||
\(878\) | −28.4706 | − | 37.8221i | −0.960837 | − | 1.27643i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.780950 | − | 21.1225i | 0.0263258 | − | 0.712040i | ||||
\(881\) | 7.24606i | 0.244126i | 0.992522 | + | 0.122063i | \(0.0389510\pi\) | ||||
−0.992522 | + | 0.122063i | \(0.961049\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 35.4533i | 1.19310i | 0.802577 | + | 0.596549i | \(0.203462\pi\) | ||||
−0.802577 | + | 0.596549i | \(0.796538\pi\) | |||||||
\(884\) | 1.42474 | − | 4.94953i | 0.0479193 | − | 0.166471i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −29.5524 | + | 22.2456i | −0.992833 | + | 0.747357i | ||||
\(887\) | −8.98684 | + | 15.5657i | −0.301749 | + | 0.522644i | −0.976532 | − | 0.215372i | \(-0.930904\pi\) |
0.674784 | + | 0.738016i | \(0.264237\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 27.4479 | + | 13.9837i | 0.920572 | + | 0.468999i | ||||
\(890\) | −0.749976 | + | 0.0916955i | −0.0251392 | + | 0.00307364i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2.70053 | − | 2.80222i | −0.0904203 | − | 0.0938251i | ||||
\(893\) | 8.82463 | + | 15.2847i | 0.295305 | + | 0.511483i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.50005 | −0.0835674 | ||||||||
\(896\) | 29.6270 | + | 4.27074i | 0.989770 | + | 0.142675i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 5.69389 | − | 13.3949i | 0.190008 | − | 0.446993i | ||||
\(899\) | 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 | \(-0.713263\pi\) |
0.368331 | + | 0.929695i | \(0.379929\pi\) | |||||||
\(908\) | −4.78297 | + | 16.6159i | −0.158728 | + | 0.551419i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 13.3218 | − | 2.34262i | 0.441615 | − | 0.0776573i | ||||
\(911\) | − | 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 | ||||
\(914\) | −10.1479 | − | 13.4811i | −0.335663 | − | 0.445915i | ||||
\(915\) | 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 | \(-0.509465\pi\) |
−0.880508 | + | 0.474031i | \(0.842799\pi\) | |||||||
\(920\) | 2.62537 | + | 2.13267i | 0.0865558 | + | 0.0703120i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 39.0574 | + | 16.6025i | 1.28629 | + | 0.546774i | ||||
\(923\) | −37.9479 | −1.24907 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11.1262 | −0.365828 | ||||||||
\(926\) | −17.2756 | − | 7.34352i | −0.567713 | − | 0.241323i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −12.6999 | − | 5.96171i | −0.416895 | − | 0.195703i | ||||
\(929\) | −44.1750 | − | 25.5044i | −1.44933 | − | 0.836773i | −0.450892 | − | 0.892579i | \(-0.648894\pi\) |
−0.998442 | + | 0.0558058i | \(0.982227\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −33.9876 | + | 3.57555i | −1.11390 | + | 0.117184i | ||||
\(932\) | 2.03148 | − | 0.504294i | 0.0665432 | − | 0.0165187i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −25.2172 | − | 33.5000i | −0.825131 | − | 1.09615i | ||||
\(935\) | −3.14171 | + | 1.81387i | −0.102745 | + | 0.0593199i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 2.65742i | − | 0.0868141i | −0.999057 | − | 0.0434071i | \(-0.986179\pi\) | ||
0.999057 | − | 0.0434071i | \(-0.0138212\pi\) | |||||||
\(938\) | −33.1801 | − | 12.0940i | −1.08337 | − | 0.394884i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −6.69582 | − | 1.92742i | −0.218394 | − | 0.0628656i | ||||
\(941\) | −26.2920 | + | 15.1797i | −0.857096 | + | 0.494844i | −0.863039 | − | 0.505138i | \(-0.831442\pi\) |
0.00594304 | + | 0.999982i | \(0.498108\pi\) | |||||||
\(942\) | 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 | \(-0.583004\pi\) |
−0.965657 | + | 0.259819i | \(0.916337\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.4931 | − | 21.6386i | −0.405542 | − | 0.702419i | ||||
\(950\) | 10.9966 | − | 25.8695i | 0.356777 | − | 0.839319i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −2.08260 | − | 4.69640i | −0.0674975 | − | 0.152211i | ||||
\(953\) | 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 | ||||
\(956\) | −27.7190 | + | 26.7131i | −0.896496 | + | 0.863963i | ||||
\(957\) | 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 | ||||
\(962\) | −11.5829 | + | 8.71903i | −0.373447 | + | 0.281113i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 5.29862 | + | 1.52523i | 0.170657 | + | 0.0491244i | ||||
\(965\) | − | 11.9236i | − | 0.383835i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 44.9529i | 1.44559i | 0.691064 | + | 0.722794i | \(0.257142\pi\) | ||||
−0.691064 | + | 0.722794i | \(0.742858\pi\) | |||||||
\(968\) | 8.51771 | − | 53.2490i | 0.273770 | − | 1.71149i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 8.91350 | + | 11.8412i | 0.286195 | + | 0.380199i | ||||
\(971\) | −0.641758 | + | 1.11156i | −0.0205950 | + | 0.0356716i | −0.876139 | − | 0.482058i | \(-0.839889\pi\) |
0.855544 | + | 0.517730i | \(0.173223\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.37523 | − | 12.5136i | 0.204381 | − | 0.401167i | ||||
\(974\) | −1.67428 | − | 13.6939i | −0.0536474 | − | 0.438781i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −22.1425 | + | 35.2744i | −0.708765 | + | 1.12911i | ||||
\(977\) | 9.67678 | + | 16.7607i | 0.309588 | + | 0.536222i | 0.978272 | − | 0.207325i | \(-0.0664756\pi\) |
−0.668684 | + | 0.743546i | \(0.733142\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.03979 | −0.0971520 | ||||||||
\(980\) | 8.68205 | − | 10.3274i | 0.277338 | − | 0.329896i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −52.6767 | − | 22.3918i | −1.68098 | − | 0.714550i | ||||
\(983\) | 4.21637 | + | 7.30296i | 0.134481 | + | 0.232928i | 0.925399 | − | 0.378994i | \(-0.123730\pi\) |
−0.790918 | + | 0.611922i | \(0.790397\pi\) | |||||||
\(984\) | 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 | \(-0.539574\pi\) |
0.797339 | + | 0.603532i | \(0.206240\pi\) | |||||||
\(992\) | −2.31065 | − | 27.2135i | −0.0733633 | − | 0.864029i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −29.0073 | + | 24.3171i | −0.920057 | + | 0.771292i | ||||
\(995\) | 18.5322i | 0.587511i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −29.0273 | + | 16.7589i | −0.919304 | + | 0.530761i | −0.883413 | − | 0.468595i | \(-0.844760\pi\) |
−0.0358914 | + | 0.999356i | \(0.511427\pi\) | |||||||
\(998\) | 36.1168 | − | 27.1870i | 1.14326 | − | 0.860588i | ||||
\(999\) | 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.f.19.2 | 8 | ||
3.2 | odd | 2 | 84.2.o.b.19.3 | yes | 8 | ||
4.3 | odd | 2 | 252.2.bf.g.19.2 | 8 | |||
7.2 | even | 3 | 1764.2.b.j.1567.7 | 8 | |||
7.3 | odd | 6 | 252.2.bf.g.199.2 | 8 | |||
7.5 | odd | 6 | 1764.2.b.i.1567.7 | 8 | |||
12.11 | even | 2 | 84.2.o.a.19.3 | ✓ | 8 | ||
21.2 | odd | 6 | 588.2.b.a.391.2 | 8 | |||
21.5 | even | 6 | 588.2.b.b.391.2 | 8 | |||
21.11 | odd | 6 | 588.2.o.d.31.3 | 8 | |||
21.17 | even | 6 | 84.2.o.a.31.3 | yes | 8 | ||
21.20 | even | 2 | 588.2.o.b.19.3 | 8 | |||
24.5 | odd | 2 | 1344.2.bl.i.1279.2 | 8 | |||
24.11 | even | 2 | 1344.2.bl.j.1279.2 | 8 | |||
28.3 | even | 6 | inner | 252.2.bf.f.199.2 | 8 | ||
28.19 | even | 6 | 1764.2.b.j.1567.8 | 8 | |||
28.23 | odd | 6 | 1764.2.b.i.1567.8 | 8 | |||
84.11 | even | 6 | 588.2.o.b.31.3 | 8 | |||
84.23 | even | 6 | 588.2.b.b.391.1 | 8 | |||
84.47 | odd | 6 | 588.2.b.a.391.1 | 8 | |||
84.59 | odd | 6 | 84.2.o.b.31.3 | yes | 8 | ||
84.83 | odd | 2 | 588.2.o.d.19.3 | 8 | |||
168.59 | odd | 6 | 1344.2.bl.i.703.2 | 8 | |||
168.101 | even | 6 | 1344.2.bl.j.703.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.2.o.a.19.3 | ✓ | 8 | 12.11 | even | 2 | ||
84.2.o.a.31.3 | yes | 8 | 21.17 | even | 6 | ||
84.2.o.b.19.3 | yes | 8 | 3.2 | odd | 2 | ||
84.2.o.b.31.3 | yes | 8 | 84.59 | odd | 6 | ||
252.2.bf.f.19.2 | 8 | 1.1 | even | 1 | trivial | ||
252.2.bf.f.199.2 | 8 | 28.3 | even | 6 | inner | ||
252.2.bf.g.19.2 | 8 | 4.3 | odd | 2 | |||
252.2.bf.g.199.2 | 8 | 7.3 | odd | 6 | |||
588.2.b.a.391.1 | 8 | 84.47 | odd | 6 | |||
588.2.b.a.391.2 | 8 | 21.2 | odd | 6 | |||
588.2.b.b.391.1 | 8 | 84.23 | even | 6 | |||
588.2.b.b.391.2 | 8 | 21.5 | even | 6 | |||
588.2.o.b.19.3 | 8 | 21.20 | even | 2 | |||
588.2.o.b.31.3 | 8 | 84.11 | even | 6 | |||
588.2.o.d.19.3 | 8 | 84.83 | odd | 2 | |||
588.2.o.d.31.3 | 8 | 21.11 | odd | 6 | |||
1344.2.bl.i.703.2 | 8 | 168.59 | odd | 6 | |||
1344.2.bl.i.1279.2 | 8 | 24.5 | odd | 2 | |||
1344.2.bl.j.703.2 | 8 | 168.101 | even | 6 | |||
1344.2.bl.j.1279.2 | 8 | 24.11 | even | 2 | |||
1764.2.b.i.1567.7 | 8 | 7.5 | odd | 6 | |||
1764.2.b.i.1567.8 | 8 | 28.23 | odd | 6 | |||
1764.2.b.j.1567.7 | 8 | 7.2 | even | 3 | |||
1764.2.b.j.1567.8 | 8 | 28.19 | even | 6 |