Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,2,Mod(301,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.301");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.n (of order \(5\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.58765816676\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.13140625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 165) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 526.1 | ||
Root | \(0.418926 - 1.28932i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.526 |
Dual form | 825.2.n.k.676.1 |
$q$-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 \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).
\(n\) | \(376\) | \(551\) | \(727\) |
\(\chi(n)\) | \(e\left(\frac{3}{5}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.758911 | + | 2.33569i | −0.536631 | + | 1.65158i | 0.203468 | + | 0.979082i | \(0.434779\pi\) |
−0.740098 | + | 0.672499i | \(0.765221\pi\) | |||||||
\(3\) | 0.809017 | − | 0.587785i | 0.467086 | − | 0.339358i | ||||
\(4\) | −3.26145 | − | 2.36959i | −1.63073 | − | 1.18479i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.758911 | + | 2.33569i | 0.309824 | + | 0.953540i | ||||
\(7\) | 2.65911 | + | 1.93196i | 1.00505 | + | 0.730211i | 0.963165 | − | 0.268911i | \(-0.0866639\pi\) |
0.0418845 | + | 0.999122i | \(0.486664\pi\) | |||||||
\(8\) | 4.03606 | − | 2.93237i | 1.42696 | − | 1.03675i | ||||
\(9\) | 0.309017 | − | 0.951057i | 0.103006 | − | 0.317019i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.96813 | − | 1.47994i | 0.894924 | − | 0.446218i | ||||
\(12\) | −4.03138 | −1.16376 | ||||||||
\(13\) | 0.0967635 | − | 0.297808i | 0.0268374 | − | 0.0825970i | −0.936741 | − | 0.350024i | \(-0.886173\pi\) |
0.963578 | + | 0.267427i | \(0.0861734\pi\) | |||||||
\(14\) | −6.53048 | + | 4.74467i | −1.74534 | + | 1.26807i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.29455 | + | 3.98423i | 0.323638 | + | 0.996057i | ||||
\(17\) | −1.54508 | − | 4.75528i | −0.374738 | − | 1.15333i | −0.943655 | − | 0.330930i | \(-0.892637\pi\) |
0.568917 | − | 0.822395i | \(-0.307363\pi\) | |||||||
\(18\) | 1.98685 | + | 1.44353i | 0.468306 | + | 0.340244i | ||||
\(19\) | 6.03048 | − | 4.38140i | 1.38349 | − | 1.00516i | 0.386941 | − | 0.922104i | \(-0.373532\pi\) |
0.996545 | − | 0.0830568i | \(-0.0264683\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.28684 | 0.717248 | ||||||||
\(22\) | 1.20413 | + | 8.05576i | 0.256721 | + | 1.71749i | ||||
\(23\) | −1.07392 | −0.223928 | −0.111964 | − | 0.993712i | \(-0.535714\pi\) | ||||
−0.111964 | + | 0.993712i | \(0.535714\pi\) | |||||||
\(24\) | 1.54164 | − | 4.74467i | 0.314685 | − | 0.968501i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.622150 | + | 0.452019i | 0.122014 | + | 0.0886482i | ||||
\(27\) | −0.309017 | − | 0.951057i | −0.0594703 | − | 0.183031i | ||||
\(28\) | −4.09463 | − | 12.6020i | −0.773813 | − | 2.38155i | ||||
\(29\) | 4.07459 | + | 2.96036i | 0.756632 | + | 0.549725i | 0.897875 | − | 0.440250i | \(-0.145110\pi\) |
−0.141243 | + | 0.989975i | \(0.545110\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.06580 | − | 3.28018i | 0.191423 | − | 0.589138i | −0.808577 | − | 0.588390i | \(-0.799762\pi\) |
1.00000 | 0.000748050i | \(-0.000238112\pi\) | ||||||||
\(32\) | −0.310680 | −0.0549210 | ||||||||
\(33\) | 1.53138 | − | 2.94192i | 0.266579 | − | 0.512122i | ||||
\(34\) | 12.2794 | 2.10591 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3.26145 | + | 2.36959i | −0.543576 | + | 0.394931i | ||||
\(37\) | 2.13118 | + | 1.54839i | 0.350364 | + | 0.254554i | 0.749022 | − | 0.662546i | \(-0.230524\pi\) |
−0.398658 | + | 0.917100i | \(0.630524\pi\) | |||||||
\(38\) | 5.65698 | + | 17.4104i | 0.917683 | + | 2.82434i | ||||
\(39\) | −0.0967635 | − | 0.297808i | −0.0154946 | − | 0.0476874i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.77557 | + | 6.37583i | −1.37051 | + | 0.995737i | −0.372817 | + | 0.927905i | \(0.621608\pi\) |
−0.997697 | + | 0.0678321i | \(0.978392\pi\) | |||||||
\(42\) | −2.49442 | + | 7.67703i | −0.384897 | + | 1.18459i | ||||
\(43\) | 5.51468 | 0.840980 | 0.420490 | − | 0.907297i | \(-0.361858\pi\) | ||||
0.420490 | + | 0.907297i | \(0.361858\pi\) | |||||||
\(44\) | −13.1873 | − | 2.20648i | −1.98805 | − | 0.332640i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.815010 | − | 2.50834i | 0.120167 | − | 0.369835i | ||||
\(47\) | −9.70674 | + | 7.05236i | −1.41587 | + | 1.02869i | −0.423438 | + | 0.905925i | \(0.639177\pi\) |
−0.992435 | + | 0.122767i | \(0.960823\pi\) | |||||||
\(48\) | 3.38919 | + | 2.46239i | 0.489187 | + | 0.355415i | ||||
\(49\) | 1.17529 | + | 3.61718i | 0.167899 | + | 0.516740i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.04508 | − | 2.93893i | −0.566425 | − | 0.411532i | ||||
\(52\) | −1.02127 | + | 0.741996i | −0.141625 | + | 0.102896i | ||||
\(53\) | −1.52513 | + | 4.69387i | −0.209493 | + | 0.644753i | 0.790006 | + | 0.613099i | \(0.210077\pi\) |
−0.999499 | + | 0.0316539i | \(0.989923\pi\) | |||||||
\(54\) | 2.45589 | 0.334204 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 16.3975 | 2.19121 | ||||||||
\(57\) | 2.30344 | − | 7.08925i | 0.305098 | − | 0.938994i | ||||
\(58\) | −10.0067 | + | 7.27031i | −1.31395 | + | 0.954639i | ||||
\(59\) | 7.41391 | + | 5.38652i | 0.965208 | + | 0.701265i | 0.954354 | − | 0.298676i | \(-0.0965451\pi\) |
0.0108537 | + | 0.999941i | \(0.496545\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.83811 | + | 8.73480i | 0.363382 | + | 1.11838i | 0.950988 | + | 0.309229i | \(0.100071\pi\) |
−0.587605 | + | 0.809148i | \(0.699929\pi\) | |||||||
\(62\) | 6.85264 | + | 4.97873i | 0.870286 | + | 0.632300i | ||||
\(63\) | 2.65911 | − | 1.93196i | 0.335016 | − | 0.243404i | ||||
\(64\) | −2.35333 | + | 7.24280i | −0.294166 | + | 0.905350i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 5.70922 | + | 5.80948i | 0.702756 | + | 0.715097i | ||||
\(67\) | 15.2739 | 1.86600 | 0.933000 | − | 0.359876i | \(-0.117181\pi\) | ||||
0.933000 | + | 0.359876i | \(0.117181\pi\) | |||||||
\(68\) | −6.22882 | + | 19.1704i | −0.755356 | + | 2.32475i | ||||
\(69\) | −0.868820 | + | 0.631235i | −0.104594 | + | 0.0759917i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.949335 | + | 2.92175i | 0.112665 | + | 0.346748i | 0.991453 | − | 0.130465i | \(-0.0416470\pi\) |
−0.878788 | + | 0.477213i | \(0.841647\pi\) | |||||||
\(72\) | −1.54164 | − | 4.74467i | −0.181684 | − | 0.559164i | ||||
\(73\) | −7.00018 | − | 5.08592i | −0.819309 | − | 0.595262i | 0.0972058 | − | 0.995264i | \(-0.469009\pi\) |
−0.916514 | + | 0.400002i | \(0.869009\pi\) | |||||||
\(74\) | −5.23394 | + | 3.80268i | −0.608433 | + | 0.442052i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −30.0502 | −3.44700 | ||||||||
\(77\) | 10.7518 | + | 1.79898i | 1.22528 | + | 0.205012i | ||||
\(78\) | 0.769020 | 0.0870744 | ||||||||
\(79\) | 1.67316 | − | 5.14946i | 0.188245 | − | 0.579360i | −0.811744 | − | 0.584014i | \(-0.801481\pi\) |
0.999989 | + | 0.00465401i | \(0.00148142\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.809017 | − | 0.587785i | −0.0898908 | − | 0.0653095i | ||||
\(82\) | −8.23206 | − | 25.3357i | −0.909079 | − | 2.79786i | ||||
\(83\) | −5.02011 | − | 15.4503i | −0.551029 | − | 1.69589i | −0.706207 | − | 0.708006i | \(-0.749595\pi\) |
0.155178 | − | 0.987887i | \(-0.450405\pi\) | |||||||
\(84\) | −10.7199 | − | 7.78845i | −1.16964 | − | 0.849790i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −4.18515 | + | 12.8806i | −0.451296 | + | 1.38895i | ||||
\(87\) | 5.03647 | 0.539966 | ||||||||
\(88\) | 7.63981 | − | 14.6768i | 0.814406 | − | 1.56455i | ||||
\(89\) | 1.62118 | 0.171845 | 0.0859223 | − | 0.996302i | \(-0.472616\pi\) | ||||
0.0859223 | + | 0.996302i | \(0.472616\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.832656 | − | 0.604960i | 0.0872861 | − | 0.0634171i | ||||
\(92\) | 3.50254 | + | 2.54475i | 0.365165 | + | 0.265308i | ||||
\(93\) | −1.06580 | − | 3.28018i | −0.110518 | − | 0.340139i | ||||
\(94\) | −9.10556 | − | 28.0240i | −0.939166 | − | 2.89046i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.251345 | + | 0.182613i | −0.0256528 | + | 0.0186379i | ||||
\(97\) | −0.0692451 | + | 0.213115i | −0.00703078 | + | 0.0216385i | −0.954510 | − | 0.298178i | \(-0.903621\pi\) |
0.947480 | + | 0.319816i | \(0.103621\pi\) | |||||||
\(98\) | −9.34054 | −0.943537 | ||||||||
\(99\) | −0.490303 | − | 3.28018i | −0.0492773 | − | 0.329671i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.156154 | + | 0.480593i | −0.0155379 | + | 0.0478208i | −0.958525 | − | 0.285009i | \(-0.908003\pi\) |
0.942987 | + | 0.332830i | \(0.108003\pi\) | |||||||
\(102\) | 9.93427 | − | 7.21767i | 0.983639 | − | 0.714656i | ||||
\(103\) | −5.17930 | − | 3.76298i | −0.510332 | − | 0.370778i | 0.302618 | − | 0.953112i | \(-0.402139\pi\) |
−0.812949 | + | 0.582334i | \(0.802139\pi\) | |||||||
\(104\) | −0.482738 | − | 1.48571i | −0.0473363 | − | 0.145686i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.80598 | − | 7.12446i | −0.952441 | − | 0.691989i | ||||
\(107\) | 1.69286 | − | 1.22993i | 0.163655 | − | 0.118902i | −0.502943 | − | 0.864319i | \(-0.667750\pi\) |
0.666598 | + | 0.745417i | \(0.267750\pi\) | |||||||
\(108\) | −1.24576 | + | 3.83407i | −0.119874 | + | 0.368934i | ||||
\(109\) | −6.69278 | −0.641052 | −0.320526 | − | 0.947240i | \(-0.603860\pi\) | ||||
−0.320526 | + | 0.947240i | \(0.603860\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.63428 | 0.250035 | ||||||||
\(112\) | −4.25499 | + | 13.0955i | −0.402059 | + | 1.23741i | ||||
\(113\) | −8.73262 | + | 6.34462i | −0.821496 | + | 0.596852i | −0.917141 | − | 0.398564i | \(-0.869509\pi\) |
0.0956448 | + | 0.995416i | \(0.469509\pi\) | |||||||
\(114\) | 14.8102 | + | 10.7602i | 1.38710 | + | 1.00779i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −6.27426 | − | 19.3102i | −0.582550 | − | 1.79290i | ||||
\(117\) | −0.253330 | − | 0.184055i | −0.0234204 | − | 0.0170159i | ||||
\(118\) | −18.2077 | + | 13.2287i | −1.67616 | + | 1.21780i | ||||
\(119\) | 5.07845 | − | 15.6299i | 0.465541 | − | 1.43279i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.61956 | − | 8.78529i | 0.601779 | − | 0.798663i | ||||
\(122\) | −22.5556 | −2.04209 | ||||||||
\(123\) | −3.35197 | + | 10.3163i | −0.302237 | + | 0.930190i | ||||
\(124\) | −11.2487 | + | 8.17267i | −1.01017 | + | 0.733928i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.49442 | + | 7.67703i | 0.222221 | + | 0.683925i | ||||
\(127\) | 5.25430 | + | 16.1711i | 0.466244 | + | 1.43495i | 0.857411 | + | 0.514632i | \(0.172071\pi\) |
−0.391167 | + | 0.920320i | \(0.627929\pi\) | |||||||
\(128\) | −15.6336 | − | 11.3585i | −1.38183 | − | 1.00396i | ||||
\(129\) | 4.46147 | − | 3.24145i | 0.392810 | − | 0.285393i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.0430508 | −0.00376136 | −0.00188068 | − | 0.999998i | \(-0.500599\pi\) | ||||
−0.00188068 | + | 0.999998i | \(0.500599\pi\) | |||||||
\(132\) | −11.9657 | + | 5.96619i | −1.04148 | + | 0.519291i | ||||
\(133\) | 24.5004 | 2.12445 | ||||||||
\(134\) | −11.5915 | + | 35.6750i | −1.00135 | + | 3.08185i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −20.1803 | − | 14.6618i | −1.73044 | − | 1.25724i | ||||
\(137\) | −2.27516 | − | 7.00222i | −0.194380 | − | 0.598240i | −0.999983 | − | 0.00578480i | \(-0.998159\pi\) |
0.805603 | − | 0.592455i | \(-0.201841\pi\) | |||||||
\(138\) | −0.815010 | − | 2.50834i | −0.0693783 | − | 0.213524i | ||||
\(139\) | −10.7109 | − | 7.78189i | −0.908483 | − | 0.660052i | 0.0321478 | − | 0.999483i | \(-0.489765\pi\) |
−0.940631 | + | 0.339432i | \(0.889765\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.70764 | + | 11.4110i | −0.312240 | + | 0.960976i | ||||
\(142\) | −7.54476 | −0.633142 | ||||||||
\(143\) | −0.153530 | − | 1.02713i | −0.0128388 | − | 0.0858933i | ||||
\(144\) | 4.18926 | 0.349105 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 17.1916 | − | 12.4905i | 1.42279 | − | 1.03372i | ||||
\(147\) | 3.07696 | + | 2.23554i | 0.253783 | + | 0.184384i | ||||
\(148\) | −3.28170 | − | 10.1000i | −0.269754 | − | 0.830217i | ||||
\(149\) | −1.81658 | − | 5.59087i | −0.148820 | − | 0.458022i | 0.848662 | − | 0.528935i | \(-0.177409\pi\) |
−0.997482 | + | 0.0709136i | \(0.977409\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.17135 | + | 4.48375i | −0.502217 | + | 0.364882i | −0.809863 | − | 0.586619i | \(-0.800459\pi\) |
0.307646 | + | 0.951501i | \(0.400459\pi\) | |||||||
\(152\) | 11.4915 | − | 35.3671i | 0.932082 | − | 2.86865i | ||||
\(153\) | −5.00000 | −0.404226 | ||||||||
\(154\) | −12.3615 | + | 23.7475i | −0.996116 | + | 1.91363i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.390091 | + | 1.20058i | −0.0312322 | + | 0.0961230i | ||||
\(157\) | −8.19795 | + | 5.95616i | −0.654267 | + | 0.475353i | −0.864722 | − | 0.502250i | \(-0.832506\pi\) |
0.210455 | + | 0.977604i | \(0.432506\pi\) | |||||||
\(158\) | 10.7578 | + | 7.81596i | 0.855841 | + | 0.621805i | ||||
\(159\) | 1.52513 | + | 4.69387i | 0.120951 | + | 0.372248i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.85567 | − | 2.07477i | −0.225059 | − | 0.163515i | ||||
\(162\) | 1.98685 | − | 1.44353i | 0.156102 | − | 0.113415i | ||||
\(163\) | 1.55407 | − | 4.78292i | 0.121724 | − | 0.374627i | −0.871566 | − | 0.490278i | \(-0.836895\pi\) |
0.993290 | + | 0.115651i | \(0.0368953\pi\) | |||||||
\(164\) | 43.7292 | 3.41468 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 39.8969 | 3.09660 | ||||||||
\(167\) | −1.78953 | + | 5.50761i | −0.138478 | + | 0.426192i | −0.996115 | − | 0.0880642i | \(-0.971932\pi\) |
0.857637 | + | 0.514256i | \(0.171932\pi\) | |||||||
\(168\) | 13.2659 | − | 9.63822i | 1.02348 | − | 0.743605i | ||||
\(169\) | 10.4379 | + | 7.58357i | 0.802915 | + | 0.583352i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.30344 | − | 7.08925i | −0.176148 | − | 0.542128i | ||||
\(172\) | −17.9859 | − | 13.0675i | −1.37141 | − | 0.996387i | ||||
\(173\) | 12.9970 | − | 9.44290i | 0.988146 | − | 0.717930i | 0.0286316 | − | 0.999590i | \(-0.490885\pi\) |
0.959514 | + | 0.281660i | \(0.0908850\pi\) | |||||||
\(174\) | −3.82223 | + | 11.7636i | −0.289762 | + | 0.891797i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 9.73881 | + | 9.90983i | 0.734090 | + | 0.746982i | ||||
\(177\) | 9.16409 | 0.688815 | ||||||||
\(178\) | −1.23033 | + | 3.78657i | −0.0922171 | + | 0.283815i | ||||
\(179\) | 6.71734 | − | 4.88043i | 0.502078 | − | 0.364781i | −0.307732 | − | 0.951473i | \(-0.599570\pi\) |
0.809810 | + | 0.586692i | \(0.199570\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.99756 | − | 6.14787i | −0.148478 | − | 0.456968i | 0.848964 | − | 0.528451i | \(-0.177227\pi\) |
−0.997442 | + | 0.0714830i | \(0.977227\pi\) | |||||||
\(182\) | 0.781086 | + | 2.40394i | 0.0578980 | + | 0.178192i | ||||
\(183\) | 7.43026 | + | 5.39840i | 0.549261 | + | 0.399061i | ||||
\(184\) | −4.33440 | + | 3.14913i | −0.319536 | + | 0.232157i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 8.47033 | 0.621074 | ||||||||
\(187\) | −11.6235 | − | 11.8277i | −0.849997 | − | 0.864924i | ||||
\(188\) | 48.3693 | 3.52769 | ||||||||
\(189\) | 1.01569 | − | 3.12597i | 0.0738806 | − | 0.227381i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.4340 | − | 9.03384i | −0.899694 | − | 0.653666i | 0.0386935 | − | 0.999251i | \(-0.487680\pi\) |
−0.938387 | + | 0.345585i | \(0.887680\pi\) | |||||||
\(192\) | 2.35333 | + | 7.24280i | 0.169837 | + | 0.522704i | ||||
\(193\) | −4.86757 | − | 14.9808i | −0.350375 | − | 1.07834i | −0.958643 | − | 0.284612i | \(-0.908135\pi\) |
0.608267 | − | 0.793732i | \(-0.291865\pi\) | |||||||
\(194\) | −0.445218 | − | 0.323470i | −0.0319648 | − | 0.0232238i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.73805 | − | 14.5822i | 0.338432 | − | 1.04159i | ||||
\(197\) | −16.3940 | −1.16802 | −0.584010 | − | 0.811746i | \(-0.698517\pi\) | ||||
−0.584010 | + | 0.811746i | \(0.698517\pi\) | |||||||
\(198\) | 8.03358 | + | 1.34417i | 0.570922 | + | 0.0955261i | ||||
\(199\) | 6.96500 | 0.493736 | 0.246868 | − | 0.969049i | \(-0.420599\pi\) | ||||
0.246868 | + | 0.969049i | \(0.420599\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.3568 | − | 8.97776i | 0.871583 | − | 0.633242i | ||||
\(202\) | −1.00401 | − | 0.729455i | −0.0706418 | − | 0.0513242i | ||||
\(203\) | 5.11549 | + | 15.7439i | 0.359037 | + | 1.10500i | ||||
\(204\) | 6.22882 | + | 19.1704i | 0.436105 | + | 1.34219i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 12.7198 | − | 9.24146i | 0.886229 | − | 0.643883i | ||||
\(207\) | −0.331860 | + | 1.02136i | −0.0230658 | + | 0.0709894i | ||||
\(208\) | 1.31180 | 0.0909569 | ||||||||
\(209\) | 11.4150 | − | 21.9293i | 0.789594 | − | 1.51688i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.16585 | + | 18.9765i | −0.424475 | + | 1.30640i | 0.479022 | + | 0.877803i | \(0.340992\pi\) |
−0.903496 | + | 0.428596i | \(0.859008\pi\) | |||||||
\(212\) | 16.0967 | − | 11.6949i | 1.10552 | − | 0.803211i | ||||
\(213\) | 2.48539 | + | 1.80574i | 0.170296 | + | 0.123727i | ||||
\(214\) | 1.58801 | + | 4.88740i | 0.108554 | + | 0.334096i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −4.03606 | − | 2.93237i | −0.274619 | − | 0.199522i | ||||
\(217\) | 9.17124 | − | 6.66330i | 0.622585 | − | 0.452334i | ||||
\(218\) | 5.07922 | − | 15.6322i | 0.344008 | − | 1.05875i | ||||
\(219\) | −8.65269 | −0.584695 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.56567 | −0.105318 | ||||||||
\(222\) | −1.99919 | + | 6.15286i | −0.134177 | + | 0.412953i | ||||
\(223\) | −16.2990 | + | 11.8419i | −1.09146 | + | 0.792992i | −0.979645 | − | 0.200737i | \(-0.935666\pi\) |
−0.111815 | + | 0.993729i | \(0.535666\pi\) | |||||||
\(224\) | −0.826133 | − | 0.600220i | −0.0551983 | − | 0.0401039i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −8.19177 | − | 25.2117i | −0.544908 | − | 1.67706i | ||||
\(227\) | 0.431964 | + | 0.313840i | 0.0286705 | + | 0.0208303i | 0.602028 | − | 0.798475i | \(-0.294359\pi\) |
−0.573358 | + | 0.819305i | \(0.694359\pi\) | |||||||
\(228\) | −24.3111 | + | 17.6631i | −1.61004 | + | 1.16977i | ||||
\(229\) | −6.85803 | + | 21.1068i | −0.453191 | + | 1.39478i | 0.420054 | + | 0.907499i | \(0.362011\pi\) |
−0.873245 | + | 0.487281i | \(0.837989\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9.75577 | − | 4.86432i | 0.641882 | − | 0.320049i | ||||
\(232\) | 25.1261 | 1.64961 | ||||||||
\(233\) | 1.41087 | − | 4.34221i | 0.0924291 | − | 0.284467i | −0.894146 | − | 0.447775i | \(-0.852216\pi\) |
0.986575 | + | 0.163308i | \(0.0522164\pi\) | |||||||
\(234\) | 0.622150 | − | 0.452019i | 0.0406712 | − | 0.0295494i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −11.4163 | − | 35.1358i | −0.743138 | − | 2.28714i | ||||
\(237\) | −1.67316 | − | 5.14946i | −0.108684 | − | 0.334493i | ||||
\(238\) | 32.6524 | + | 23.7233i | 2.11654 | + | 1.53776i | ||||
\(239\) | 4.74126 | − | 3.44473i | 0.306687 | − | 0.222821i | −0.423787 | − | 0.905762i | \(-0.639299\pi\) |
0.730474 | + | 0.682941i | \(0.239299\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.96074 | 0.641628 | 0.320814 | − | 0.947142i | \(-0.396044\pi\) | ||||
0.320814 | + | 0.947142i | \(0.396044\pi\) | |||||||
\(242\) | 15.4960 | + | 22.1285i | 0.996123 | + | 1.42247i | ||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 11.4415 | − | 35.2133i | 0.732466 | − | 2.25430i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −21.5518 | − | 15.6583i | −1.37409 | − | 0.998337i | ||||
\(247\) | −0.721283 | − | 2.21988i | −0.0458941 | − | 0.141248i | ||||
\(248\) | −5.31709 | − | 16.3643i | −0.337635 | − | 1.03913i | ||||
\(249\) | −13.1428 | − | 9.54882i | −0.832892 | − | 0.605132i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.21584 | + | 16.0527i | −0.329221 | + | 1.01324i | 0.640279 | + | 0.768143i | \(0.278819\pi\) |
−0.969499 | + | 0.245094i | \(0.921181\pi\) | |||||||
\(252\) | −13.2505 | −0.834704 | ||||||||
\(253\) | −3.18753 | + | 1.58934i | −0.200399 | + | 0.0999207i | ||||
\(254\) | −41.7581 | −2.62014 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 26.0723 | − | 18.9426i | 1.62952 | − | 1.18391i | ||||
\(257\) | 9.01534 | + | 6.55003i | 0.562362 | + | 0.408580i | 0.832323 | − | 0.554292i | \(-0.187011\pi\) |
−0.269961 | + | 0.962871i | \(0.587011\pi\) | |||||||
\(258\) | 4.18515 | + | 12.8806i | 0.260556 | + | 0.801909i | ||||
\(259\) | 2.67561 | + | 8.23470i | 0.166255 | + | 0.511679i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.07459 | − | 2.96036i | 0.252211 | − | 0.183242i | ||||
\(262\) | 0.0326717 | − | 0.100553i | 0.00201846 | − | 0.00621220i | ||||
\(263\) | 26.8726 | 1.65704 | 0.828519 | − | 0.559961i | \(-0.189184\pi\) | ||||
0.828519 | + | 0.559961i | \(0.189184\pi\) | |||||||
\(264\) | −2.44604 | − | 16.3643i | −0.150544 | − | 1.00715i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −18.5936 | + | 57.2252i | −1.14005 | + | 3.50870i | ||||
\(267\) | 1.31156 | − | 0.952905i | 0.0802662 | − | 0.0583168i | ||||
\(268\) | −49.8150 | − | 36.1927i | −3.04294 | − | 2.21082i | ||||
\(269\) | −3.10961 | − | 9.57038i | −0.189596 | − | 0.583516i | 0.810401 | − | 0.585875i | \(-0.199249\pi\) |
−0.999997 | + | 0.00235886i | \(0.999249\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.53037 | − | 6.19767i | −0.518183 | − | 0.376482i | 0.297736 | − | 0.954648i | \(-0.403768\pi\) |
−0.815919 | + | 0.578166i | \(0.803768\pi\) | |||||||
\(272\) | 16.9459 | − | 12.3119i | 1.02750 | − | 0.746521i | ||||
\(273\) | 0.318046 | − | 0.978846i | 0.0192490 | − | 0.0592425i | ||||
\(274\) | 18.0816 | 1.09235 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 4.32938 | 0.260598 | ||||||||
\(277\) | 5.54302 | − | 17.0597i | 0.333048 | − | 1.02502i | −0.634628 | − | 0.772818i | \(-0.718847\pi\) |
0.967676 | − | 0.252198i | \(-0.0811534\pi\) | |||||||
\(278\) | 26.3047 | − | 19.1114i | 1.57765 | − | 1.14623i | ||||
\(279\) | −2.79029 | − | 2.02726i | −0.167050 | − | 0.121369i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.29013 | + | 7.04830i | 0.136618 | + | 0.420467i | 0.995838 | − | 0.0911392i | \(-0.0290508\pi\) |
−0.859220 | + | 0.511606i | \(0.829051\pi\) | |||||||
\(282\) | −23.8387 | − | 17.3198i | −1.41957 | − | 1.03138i | ||||
\(283\) | 4.35804 | − | 3.16630i | 0.259059 | − | 0.188217i | −0.450673 | − | 0.892689i | \(-0.648816\pi\) |
0.709732 | + | 0.704472i | \(0.248816\pi\) | |||||||
\(284\) | 3.82713 | − | 11.7787i | 0.227098 | − | 0.698937i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.51558 | + | 0.420905i | 0.148749 | + | 0.0248886i | ||||
\(287\) | −35.6530 | −2.10453 | ||||||||
\(288\) | −0.0960054 | + | 0.295474i | −0.00565717 | + | 0.0174110i | ||||
\(289\) | −6.47214 | + | 4.70228i | −0.380714 | + | 0.276605i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.0692451 | + | 0.213115i | 0.00405922 | + | 0.0124930i | ||||
\(292\) | 10.7792 | + | 33.1750i | 0.630806 | + | 1.94142i | ||||
\(293\) | −1.40774 | − | 1.02278i | −0.0822409 | − | 0.0597515i | 0.545905 | − | 0.837847i | \(-0.316186\pi\) |
−0.628146 | + | 0.778096i | \(0.716186\pi\) | |||||||
\(294\) | −7.55666 | + | 5.49023i | −0.440713 | + | 0.320197i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 13.1420 | 0.763864 | ||||||||
\(297\) | −2.32471 | − | 2.36553i | −0.134893 | − | 0.137262i | ||||
\(298\) | 14.4371 | 0.836321 | ||||||||
\(299\) | −0.103916 | + | 0.319822i | −0.00600964 | + | 0.0184958i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 14.6641 | + | 10.6541i | 0.845227 | + | 0.614093i | ||||
\(302\) | −5.78913 | − | 17.8171i | −0.333127 | − | 1.02526i | ||||
\(303\) | 0.156154 | + | 0.480593i | 0.00897082 | + | 0.0276094i | ||||
\(304\) | 25.2633 | + | 18.3548i | 1.44895 | + | 1.05272i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 3.79455 | − | 11.6784i | 0.216920 | − | 0.667612i | ||||
\(307\) | −21.3566 | −1.21889 | −0.609444 | − | 0.792829i | \(-0.708607\pi\) | ||||
−0.609444 | + | 0.792829i | \(0.708607\pi\) | |||||||
\(308\) | −30.8035 | − | 31.3445i | −1.75519 | − | 1.78602i | ||||
\(309\) | −6.40197 | −0.364195 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −26.5435 | + | 19.2850i | −1.50514 | + | 1.09355i | −0.536870 | + | 0.843665i | \(0.680393\pi\) |
−0.968275 | + | 0.249886i | \(0.919607\pi\) | |||||||
\(312\) | −1.26382 | − | 0.918222i | −0.0715499 | − | 0.0519841i | ||||
\(313\) | 1.06874 | + | 3.28925i | 0.0604089 | + | 0.185919i | 0.976707 | − | 0.214578i | \(-0.0688375\pi\) |
−0.916298 | + | 0.400497i | \(0.868837\pi\) | |||||||
\(314\) | −7.69021 | − | 23.6680i | −0.433984 | − | 1.33566i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −17.6590 | + | 12.8300i | −0.993398 | + | 0.721746i | ||||
\(317\) | 0.888626 | − | 2.73491i | 0.0499102 | − | 0.153608i | −0.922995 | − | 0.384812i | \(-0.874266\pi\) |
0.972905 | + | 0.231204i | \(0.0742664\pi\) | |||||||
\(318\) | −12.1209 | −0.679704 | ||||||||
\(319\) | 16.4751 | + | 2.75659i | 0.922426 | + | 0.154340i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.646615 | − | 1.99008i | 0.0360905 | − | 0.111075i | ||||
\(322\) | 7.01321 | − | 5.09540i | 0.390831 | − | 0.283955i | ||||
\(323\) | −30.1524 | − | 21.9070i | −1.67772 | − | 1.21894i | ||||
\(324\) | 1.24576 | + | 3.83407i | 0.0692092 | + | 0.213004i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 9.99201 | + | 7.25962i | 0.553406 | + | 0.402073i | ||||
\(327\) | −5.41457 | + | 3.93392i | −0.299427 | + | 0.217546i | ||||
\(328\) | −16.7224 | + | 51.4664i | −0.923342 | + | 2.84176i | ||||
\(329\) | −39.4362 | −2.17419 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.1221 | −0.776219 | −0.388109 | − | 0.921613i | \(-0.626872\pi\) | ||||
−0.388109 | + | 0.921613i | \(0.626872\pi\) | |||||||
\(332\) | −20.2380 | + | 62.2861i | −1.11070 | + | 3.41839i | ||||
\(333\) | 2.13118 | − | 1.54839i | 0.116788 | − | 0.0848514i | ||||
\(334\) | −11.5060 | − | 8.35958i | −0.629579 | − | 0.457416i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 4.25499 | + | 13.0955i | 0.232129 | + | 0.714419i | ||||
\(337\) | 12.9030 | + | 9.37457i | 0.702870 | + | 0.510665i | 0.880866 | − | 0.473366i | \(-0.156961\pi\) |
−0.177995 | + | 0.984031i | \(0.556961\pi\) | |||||||
\(338\) | −25.6343 | + | 18.6244i | −1.39432 | + | 1.01303i | ||||
\(339\) | −3.33556 | + | 10.2658i | −0.181163 | + | 0.557562i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.69105 | − | 11.3133i | −0.0915755 | − | 0.612650i | ||||
\(342\) | 18.3064 | 0.989895 | ||||||||
\(343\) | 3.24683 | − | 9.99271i | 0.175312 | − | 0.539555i | ||||
\(344\) | 22.2575 | − | 16.1711i | 1.20005 | − | 0.871885i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 12.1921 | + | 37.5233i | 0.655449 | + | 2.01727i | ||||
\(347\) | −9.17166 | − | 28.2275i | −0.492360 | − | 1.51533i | −0.821030 | − | 0.570884i | \(-0.806600\pi\) |
0.328670 | − | 0.944445i | \(-0.393400\pi\) | |||||||
\(348\) | −16.4262 | − | 11.9343i | −0.880537 | − | 0.639748i | ||||
\(349\) | −25.6408 | + | 18.6291i | −1.37252 | + | 0.997194i | −0.374984 | + | 0.927031i | \(0.622352\pi\) |
−0.997536 | + | 0.0701620i | \(0.977648\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.313133 | −0.0167138 | ||||||||
\(352\) | −0.922138 | + | 0.459787i | −0.0491501 | + | 0.0245067i | ||||
\(353\) | −1.20189 | −0.0639703 | −0.0319852 | − | 0.999488i | \(-0.510183\pi\) | ||||
−0.0319852 | + | 0.999488i | \(0.510183\pi\) | |||||||
\(354\) | −6.95473 | + | 21.4044i | −0.369640 | + | 1.13763i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −5.28740 | − | 3.84152i | −0.280232 | − | 0.203600i | ||||
\(357\) | −5.07845 | − | 15.6299i | −0.268780 | − | 0.827220i | ||||
\(358\) | 6.30130 | + | 19.3934i | 0.333034 | + | 1.02497i | ||||
\(359\) | 9.43239 | + | 6.85304i | 0.497823 | + | 0.361689i | 0.808185 | − | 0.588929i | \(-0.200450\pi\) |
−0.310362 | + | 0.950618i | \(0.600450\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.2987 | − | 34.7737i | 0.594667 | − | 1.83020i | ||||
\(362\) | 15.8755 | 0.834396 | ||||||||
\(363\) | 0.191475 | − | 10.9983i | 0.0100498 | − | 0.577263i | ||||
\(364\) | −4.14918 | −0.217476 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −18.2479 | + | 13.2579i | −0.953832 | + | 0.693000i | ||||
\(367\) | 12.9330 | + | 9.39636i | 0.675096 | + | 0.490486i | 0.871727 | − | 0.489991i | \(-0.163000\pi\) |
−0.196631 | + | 0.980478i | \(0.563000\pi\) | |||||||
\(368\) | −1.39025 | − | 4.27874i | −0.0724717 | − | 0.223045i | ||||
\(369\) | 3.35197 | + | 10.3163i | 0.174497 | + | 0.537045i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −13.1239 | + | 9.53504i | −0.681357 | + | 0.495035i | ||||
\(372\) | −4.29663 | + | 13.2237i | −0.222770 | + | 0.685615i | ||||
\(373\) | −0.321975 | −0.0166712 | −0.00833561 | − | 0.999965i | \(-0.502653\pi\) | ||||
−0.00833561 | + | 0.999965i | \(0.502653\pi\) | |||||||
\(374\) | 36.4469 | − | 18.1728i | 1.88463 | − | 0.939693i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −18.4968 | + | 56.9274i | −0.953902 | + | 2.93581i | ||||
\(377\) | 1.27589 | − | 0.926988i | 0.0657117 | − | 0.0477423i | ||||
\(378\) | 6.53048 | + | 4.74467i | 0.335891 | + | 0.244039i | ||||
\(379\) | 3.52819 | + | 10.8586i | 0.181231 | + | 0.557771i | 0.999863 | − | 0.0165471i | \(-0.00526734\pi\) |
−0.818632 | + | 0.574318i | \(0.805267\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 13.7559 | + | 9.99428i | 0.704738 | + | 0.512022i | ||||
\(382\) | 30.5365 | − | 22.1861i | 1.56239 | − | 1.13514i | ||||
\(383\) | −8.76597 | + | 26.9789i | −0.447920 | + | 1.37856i | 0.431329 | + | 0.902195i | \(0.358045\pi\) |
−0.879249 | + | 0.476362i | \(0.841955\pi\) | |||||||
\(384\) | −19.3242 | −0.986136 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 38.6846 | 1.96899 | ||||||||
\(387\) | 1.70413 | − | 5.24477i | 0.0866257 | − | 0.266607i | ||||
\(388\) | 0.730833 | − | 0.530981i | 0.0371024 | − | 0.0269565i | ||||
\(389\) | −12.2810 | − | 8.92269i | −0.622673 | − | 0.452398i | 0.231181 | − | 0.972911i | \(-0.425741\pi\) |
−0.853854 | + | 0.520513i | \(0.825741\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.65930 | + | 5.10680i | 0.0839143 | + | 0.258262i | ||||
\(392\) | 15.3504 | + | 11.1528i | 0.775315 | + | 0.563299i | ||||
\(393\) | −0.0348288 | + | 0.0253046i | −0.00175688 | + | 0.00127645i | ||||
\(394\) | 12.4415 | − | 38.2911i | 0.626796 | − | 1.92908i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −6.17357 | + | 11.8600i | −0.310234 | + | 0.595987i | ||||
\(397\) | −5.22461 | −0.262216 | −0.131108 | − | 0.991368i | \(-0.541853\pi\) | ||||
−0.131108 | + | 0.991368i | \(0.541853\pi\) | |||||||
\(398\) | −5.28581 | + | 16.2681i | −0.264954 | + | 0.815444i | ||||
\(399\) | 19.8212 | − | 14.4010i | 0.992302 | − | 0.720950i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.32644 | + | 13.3154i | 0.216052 | + | 0.664941i | 0.999077 | + | 0.0429502i | \(0.0136757\pi\) |
−0.783025 | + | 0.621990i | \(0.786324\pi\) | |||||||
\(402\) | 11.5915 | + | 35.6750i | 0.578132 | + | 1.77931i | ||||
\(403\) | −0.873733 | − | 0.634804i | −0.0435238 | − | 0.0316219i | ||||
\(404\) | 1.64810 | − | 1.19741i | 0.0819959 | − | 0.0595735i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −40.6549 | −2.01767 | ||||||||
\(407\) | 8.61714 | + | 1.44181i | 0.427136 | + | 0.0714680i | ||||
\(408\) | −24.9442 | −1.23492 | ||||||||
\(409\) | 10.2937 | − | 31.6809i | 0.508993 | − | 1.56652i | −0.284960 | − | 0.958539i | \(-0.591980\pi\) |
0.793953 | − | 0.607979i | \(-0.208020\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.95645 | − | 4.32761i | −0.293810 | − | 0.213465i | ||||
\(412\) | 7.97535 | + | 24.5456i | 0.392917 | + | 1.20927i | ||||
\(413\) | 9.30787 | + | 28.6467i | 0.458011 | + | 1.40961i | ||||
\(414\) | −2.13372 | − | 1.55024i | −0.104867 | − | 0.0761902i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.0300625 | + | 0.0925229i | −0.00147394 | + | 0.00453631i | ||||
\(417\) | −13.2393 | −0.648334 | ||||||||
\(418\) | 42.5569 | + | 43.3043i | 2.08153 | + | 2.11808i | ||||
\(419\) | −5.28460 | −0.258170 | −0.129085 | − | 0.991634i | \(-0.541204\pi\) | ||||
−0.129085 | + | 0.991634i | \(0.541204\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 24.9023 | − | 18.0926i | 1.21367 | − | 0.881780i | 0.218107 | − | 0.975925i | \(-0.430012\pi\) |
0.995558 | + | 0.0941452i | \(0.0300118\pi\) | |||||||
\(422\) | −39.6439 | − | 28.8030i | −1.92984 | − | 1.40211i | ||||
\(423\) | 3.70764 | + | 11.4110i | 0.180272 | + | 0.554820i | ||||
\(424\) | 7.60864 | + | 23.4170i | 0.369508 | + | 1.13723i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −6.10384 | + | 4.43470i | −0.295732 | + | 0.214862i | ||||
\(427\) | −9.32841 | + | 28.7099i | −0.451433 | + | 1.38937i | ||||
\(428\) | −8.43562 | −0.407751 | ||||||||
\(429\) | −0.727943 | − | 0.740727i | −0.0351454 | − | 0.0357626i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.81656 | − | 11.7462i | 0.183837 | − | 0.565793i | −0.816089 | − | 0.577926i | \(-0.803862\pi\) |
0.999926 | + | 0.0121333i | \(0.00386225\pi\) | |||||||
\(432\) | 3.38919 | − | 2.46239i | 0.163062 | − | 0.118472i | ||||
\(433\) | 1.14304 | + | 0.830465i | 0.0549308 | + | 0.0399096i | 0.614912 | − | 0.788596i | \(-0.289192\pi\) |
−0.559981 | + | 0.828505i | \(0.689192\pi\) | |||||||
\(434\) | 8.60323 | + | 26.4780i | 0.412968 | + | 1.27098i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 21.8282 | + | 15.8591i | 1.04538 | + | 0.759514i | ||||
\(437\) | −6.47625 | + | 4.70527i | −0.309801 | + | 0.225084i | ||||
\(438\) | 6.56662 | − | 20.2100i | 0.313765 | − | 0.965670i | ||||
\(439\) | −7.58532 | −0.362028 | −0.181014 | − | 0.983481i | \(-0.557938\pi\) | ||||
−0.181014 | + | 0.983481i | \(0.557938\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.80333 | 0.181111 | ||||||||
\(442\) | 1.18820 | − | 3.65691i | 0.0565170 | − | 0.173941i | ||||
\(443\) | 8.95274 | − | 6.50455i | 0.425358 | − | 0.309040i | −0.354432 | − | 0.935082i | \(-0.615326\pi\) |
0.779790 | + | 0.626041i | \(0.215326\pi\) | |||||||
\(444\) | −8.59160 | − | 6.24216i | −0.407739 | − | 0.296240i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −15.2895 | − | 47.0562i | −0.723979 | − | 2.22818i | ||||
\(447\) | −4.75587 | − | 3.45534i | −0.224945 | − | 0.163432i | ||||
\(448\) | −20.2505 | + | 14.7129i | −0.956748 | + | 0.695118i | ||||
\(449\) | 1.95563 | − | 6.01882i | 0.0922920 | − | 0.284045i | −0.894247 | − | 0.447575i | \(-0.852288\pi\) |
0.986538 | + | 0.163529i | \(0.0522878\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −16.6112 | + | 31.9116i | −0.782190 | + | 1.50266i | ||||
\(452\) | 43.5152 | 2.04678 | ||||||||
\(453\) | −2.35725 | + | 7.25486i | −0.110753 | + | 0.340863i | ||||
\(454\) | −1.06085 | + | 0.770756i | −0.0497884 | + | 0.0361734i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −11.4915 | − | 35.3671i | −0.538138 | − | 1.65622i | ||||
\(457\) | 0.0585832 | + | 0.180300i | 0.00274040 | + | 0.00843410i | 0.952417 | − | 0.304797i | \(-0.0985886\pi\) |
−0.949677 | + | 0.313231i | \(0.898589\pi\) | |||||||
\(458\) | −44.0944 | − | 32.0364i | −2.06039 | − | 1.49696i | ||||
\(459\) | −4.04508 | + | 2.93893i | −0.188808 | + | 0.137177i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −26.6198 | −1.23981 | −0.619904 | − | 0.784678i | \(-0.712828\pi\) | ||||
−0.619904 | + | 0.784678i | \(0.712828\pi\) | |||||||
\(462\) | 3.95778 | + | 26.4780i | 0.184133 | + | 1.23187i | ||||
\(463\) | −20.9935 | −0.975652 | −0.487826 | − | 0.872941i | \(-0.662210\pi\) | ||||
−0.487826 | + | 0.872941i | \(0.662210\pi\) | |||||||
\(464\) | −6.51998 | + | 20.0664i | −0.302682 | + | 0.931561i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 9.07131 | + | 6.59070i | 0.420221 | + | 0.305308i | ||||
\(467\) | −2.44120 | − | 7.51324i | −0.112965 | − | 0.347671i | 0.878552 | − | 0.477647i | \(-0.158510\pi\) |
−0.991517 | + | 0.129976i | \(0.958510\pi\) | |||||||
\(468\) | 0.390091 | + | 1.20058i | 0.0180319 | + | 0.0554966i | ||||
\(469\) | 40.6149 | + | 29.5085i | 1.87542 | + | 1.36257i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.13134 | + | 9.63727i | −0.144284 | + | 0.444062i | ||||
\(472\) | 45.7182 | 2.10435 | ||||||||
\(473\) | 16.3683 | − | 8.16138i | 0.752614 | − | 0.375261i | ||||
\(474\) | 13.2973 | 0.610766 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −53.5994 | + | 38.9423i | −2.45673 | + | 1.78492i | ||||
\(477\) | 3.99285 | + | 2.90097i | 0.182820 | + | 0.132826i | ||||
\(478\) | 4.44762 | + | 13.6884i | 0.203429 | + | 0.626091i | ||||
\(479\) | 12.3523 | + | 38.0164i | 0.564389 | + | 1.73701i | 0.669758 | + | 0.742579i | \(0.266398\pi\) |
−0.105369 | + | 0.994433i | \(0.533602\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.667344 | − | 0.484854i | 0.0304282 | − | 0.0221074i | ||||
\(482\) | −7.55931 | + | 23.2652i | −0.344317 | + | 1.05970i | ||||
\(483\) | −3.52981 | −0.160612 | ||||||||
\(484\) | −42.4069 | + | 12.9672i | −1.92759 | + | 0.589419i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.758911 | − | 2.33569i | 0.0344249 | − | 0.105949i | ||||
\(487\) | −8.03804 | + | 5.83998i | −0.364238 | + | 0.264635i | −0.754818 | − | 0.655935i | \(-0.772275\pi\) |
0.390579 | + | 0.920569i | \(0.372275\pi\) | |||||||
\(488\) | 37.0684 | + | 26.9318i | 1.67801 | + | 1.21914i | ||||
\(489\) | −1.55407 | − | 4.78292i | −0.0702773 | − | 0.216291i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.02364 | − | 2.92335i | −0.181584 | − | 0.131929i | 0.493280 | − | 0.869871i | \(-0.335798\pi\) |
−0.674864 | + | 0.737942i | \(0.735798\pi\) | |||||||
\(492\) | 35.3777 | − | 25.7034i | 1.59495 | − | 1.15880i | ||||
\(493\) | 7.78177 | − | 23.9498i | 0.350473 | − | 1.07865i | ||||
\(494\) | 5.73234 | 0.257910 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 14.4487 | 0.648767 | ||||||||
\(497\) | −3.12031 | + | 9.60333i | −0.139965 | + | 0.430768i | ||||
\(498\) | 32.2773 | − | 23.4508i | 1.44638 | − | 1.05086i | ||||
\(499\) | −35.4153 | − | 25.7307i | −1.58541 | − | 1.15186i | −0.910149 | − | 0.414281i | \(-0.864033\pi\) |
−0.675256 | − | 0.737584i | \(-0.735967\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.78953 | + | 5.50761i | 0.0799504 | + | 0.246062i | ||||
\(502\) | −33.5357 | − | 24.3651i | −1.49677 | − | 1.08747i | ||||
\(503\) | 5.08254 | − | 3.69268i | 0.226619 | − | 0.164648i | −0.468682 | − | 0.883367i | \(-0.655271\pi\) |
0.695301 | + | 0.718718i | \(0.255271\pi\) | |||||||
\(504\) | 5.06711 | − | 15.5950i | 0.225707 | − | 0.694655i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.29314 | − | 8.65125i | −0.0574870 | − | 0.384595i | ||||
\(507\) | 12.9019 | 0.572996 | ||||||||
\(508\) | 21.1821 | − | 65.1918i | 0.939803 | − | 2.89242i | ||||
\(509\) | −20.0945 | + | 14.5995i | −0.890671 | + | 0.647111i | −0.936053 | − | 0.351859i | \(-0.885550\pi\) |
0.0453816 | + | 0.998970i | \(0.485550\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.78845 | − | 27.0481i | −0.388778 | − | 1.19654i | ||||
\(512\) | 12.5144 | + | 38.5155i | 0.553066 | + | 1.70216i | ||||
\(513\) | −6.03048 | − | 4.38140i | −0.266252 | − | 0.193443i | ||||
\(514\) | −22.1407 | + | 16.0861i | −0.976583 | + | 0.709529i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −22.2318 | −0.978699 | ||||||||
\(517\) | −18.3738 | + | 35.2977i | −0.808078 | + | 1.55239i | ||||
\(518\) | −21.2642 | −0.934296 | ||||||||
\(519\) | 4.96442 | − | 15.2789i | 0.217914 | − | 0.670670i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.62161 | + | 4.08434i | 0.246287 | + | 0.178938i | 0.704080 | − | 0.710121i | \(-0.251360\pi\) |
−0.457792 | + | 0.889059i | \(0.651360\pi\) | |||||||
\(522\) | 3.82223 | + | 11.7636i | 0.167294 | + | 0.514879i | ||||
\(523\) | 8.26650 | + | 25.4417i | 0.361469 | + | 1.11249i | 0.952163 | + | 0.305591i | \(0.0988541\pi\) |
−0.590694 | + | 0.806896i | \(0.701146\pi\) | |||||||
\(524\) | 0.140408 | + | 0.102013i | 0.00613376 | + | 0.00445644i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −20.3939 | + | 62.7661i | −0.889218 | + | 2.73673i | ||||
\(527\) | −17.2449 | −0.751202 | ||||||||
\(528\) | 13.7037 | + | 2.29290i | 0.596378 | + | 0.0997854i | ||||
\(529\) | −21.8467 | −0.949856 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.41391 | − | 5.38652i | 0.321736 | − | 0.233755i | ||||
\(532\) | −79.9069 | − | 58.0557i | −3.46440 | − | 2.51704i | ||||
\(533\) | 1.04961 | + | 3.23038i | 0.0454638 | + | 0.139923i | ||||
\(534\) | 1.23033 | + | 3.78657i | 0.0532416 | + | 0.163861i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 61.6462 | − | 44.7886i | 2.66271 | − | 1.93457i | ||||
\(537\) | 2.56580 | − | 7.89671i | 0.110722 | − | 0.340768i | ||||
\(538\) | 24.7133 | 1.06547 | ||||||||
\(539\) | 8.84162 | + | 8.99689i | 0.380836 | + | 0.387524i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.48336 | − | 13.7984i | 0.192755 | − | 0.593237i | −0.807241 | − | 0.590222i | \(-0.799040\pi\) |
0.999995 | − | 0.00301536i | \(-0.000959822\pi\) | |||||||
\(542\) | 20.9496 | − | 15.2208i | 0.899863 | − | 0.653789i | ||||
\(543\) | −5.22969 | − | 3.79959i | −0.224428 | − | 0.163056i | ||||
\(544\) | 0.480027 | + | 1.47737i | 0.0205810 | + | 0.0633418i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 2.04491 | + | 1.48571i | 0.0875141 | + | 0.0635827i | ||||
\(547\) | −21.6287 | + | 15.7142i | −0.924777 | + | 0.671890i | −0.944708 | − | 0.327912i | \(-0.893655\pi\) |
0.0199316 | + | 0.999801i | \(0.493655\pi\) | |||||||
\(548\) | −9.17203 | + | 28.2286i | −0.391810 | + | 1.20587i | ||||
\(549\) | 9.18431 | 0.391977 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 37.5422 | 1.59935 | ||||||||
\(552\) | −1.65559 | + | 5.09540i | −0.0704668 | + | 0.216875i | ||||
\(553\) | 14.3977 | − | 10.4605i | 0.612251 | − | 0.444826i | ||||
\(554\) | 35.6394 | + | 25.8935i | 1.51417 | + | 1.10011i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 16.4931 | + | 50.7606i | 0.699464 | + | 2.15273i | ||||
\(557\) | 13.9510 | + | 10.1360i | 0.591125 | + | 0.429477i | 0.842718 | − | 0.538356i | \(-0.180954\pi\) |
−0.251593 | + | 0.967833i | \(0.580954\pi\) | |||||||
\(558\) | 6.85264 | − | 4.97873i | 0.290095 | − | 0.210767i | ||||
\(559\) | 0.533620 | − | 1.64231i | 0.0225697 | − | 0.0694624i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −16.3558 | − | 2.73663i | −0.690541 | − | 0.115541i | ||||
\(562\) | −18.2006 | −0.767748 | ||||||||
\(563\) | 0.257075 | − | 0.791197i | 0.0108344 | − | 0.0333450i | −0.945493 | − | 0.325642i | \(-0.894420\pi\) |
0.956328 | + | 0.292297i | \(0.0944196\pi\) | |||||||
\(564\) | 39.1316 | − | 28.4307i | 1.64774 | − | 1.19715i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 4.08813 | + | 12.5820i | 0.171837 | + | 0.528860i | ||||
\(567\) | −1.01569 | − | 3.12597i | −0.0426550 | − | 0.131278i | ||||
\(568\) | 12.3992 | + | 9.00855i | 0.520259 | + | 0.377991i | ||||
\(569\) | −9.38141 | + | 6.81599i | −0.393289 | + | 0.285741i | −0.766802 | − | 0.641884i | \(-0.778153\pi\) |
0.373513 | + | 0.927625i | \(0.378153\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.8414 | 0.914034 | 0.457017 | − | 0.889458i | \(-0.348918\pi\) | ||||
0.457017 | + | 0.889458i | \(0.348918\pi\) | |||||||
\(572\) | −1.93315 | + | 3.71376i | −0.0808292 | + | 0.155280i | ||||
\(573\) | −15.3693 | −0.642061 | ||||||||
\(574\) | 27.0575 | − | 83.2744i | 1.12936 | − | 3.47580i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 6.16110 | + | 4.47630i | 0.256712 | + | 0.186512i | ||||
\(577\) | −3.01164 | − | 9.26888i | −0.125376 | − | 0.385868i | 0.868593 | − | 0.495526i | \(-0.165025\pi\) |
−0.993969 | + | 0.109657i | \(0.965025\pi\) | |||||||
\(578\) | −6.07129 | − | 18.6855i | −0.252532 | − | 0.777214i | ||||
\(579\) | −12.7435 | − | 9.25867i | −0.529600 | − | 0.384777i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 16.5003 | − | 50.7827i | 0.684548 | − | 2.10682i | ||||
\(582\) | −0.550320 | −0.0228115 | ||||||||
\(583\) | 2.41986 | + | 16.1891i | 0.100220 | + | 0.670485i | ||||
\(584\) | −43.1669 | −1.78626 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.45724 | − | 2.51183i | 0.142817 | − | 0.103763i | ||||
\(587\) | 18.5622 | + | 13.4862i | 0.766143 | + | 0.556635i | 0.900788 | − | 0.434258i | \(-0.142990\pi\) |
−0.134645 | + | 0.990894i | \(0.542990\pi\) | |||||||
\(588\) | −4.73805 | − | 14.5822i | −0.195394 | − | 0.601361i | ||||
\(589\) | −7.94453 | − | 24.4507i | −0.327349 | − | 1.00748i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −13.2630 | + | 9.63612i | −0.545566 | + | 0.396377i | ||||
\(592\) | −3.41022 | + | 10.4956i | −0.140159 | + | 0.431366i | ||||
\(593\) | −28.7819 | −1.18193 | −0.590965 | − | 0.806697i | \(-0.701253\pi\) | ||||
−0.590965 | + | 0.806697i | \(0.701253\pi\) | |||||||
\(594\) | 7.28939 | − | 3.63456i | 0.299087 | − | 0.149128i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −7.32333 | + | 22.5389i | −0.299975 | + | 0.923229i | ||||
\(597\) | 5.63480 | − | 4.09392i | 0.230617 | − | 0.167553i | ||||
\(598\) | −0.668140 | − | 0.485432i | −0.0273223 | − | 0.0198508i | ||||
\(599\) | −9.02179 | − | 27.7662i | −0.368620 | − | 1.13450i | −0.947683 | − | 0.319214i | \(-0.896581\pi\) |
0.579062 | − | 0.815283i | \(-0.303419\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.40494 | + | 3.92692i | 0.220472 | + | 0.160182i | 0.692539 | − | 0.721380i | \(-0.256492\pi\) |
−0.472067 | + | 0.881563i | \(0.656492\pi\) | |||||||
\(602\) | −36.0135 | + | 26.1653i | −1.46780 | + | 1.06642i | ||||
\(603\) | 4.71989 | − | 14.5263i | 0.192209 | − | 0.591557i | ||||
\(604\) | 30.7522 | 1.25129 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.24102 | −0.0504131 | ||||||||
\(607\) | 13.1674 | − | 40.5252i | 0.534450 | − | 1.64487i | −0.210384 | − | 0.977619i | \(-0.567471\pi\) |
0.744834 | − | 0.667250i | \(-0.232529\pi\) | |||||||
\(608\) | −1.87355 | + | 1.36121i | −0.0759824 | + | 0.0552044i | ||||
\(609\) | 13.3925 | + | 9.73024i | 0.542693 | + | 0.394289i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.16099 | + | 3.57315i | 0.0469685 | + | 0.144554i | ||||
\(612\) | 16.3073 | + | 11.8479i | 0.659182 | + | 0.478924i | ||||
\(613\) | −4.71783 | + | 3.42771i | −0.190552 | + | 0.138444i | −0.678971 | − | 0.734165i | \(-0.737574\pi\) |
0.488419 | + | 0.872609i | \(0.337574\pi\) | |||||||
\(614\) | 16.2078 | − | 49.8824i | 0.654093 | − | 2.01309i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 48.6699 | − | 24.2673i | 1.96097 | − | 0.977758i | ||||
\(617\) | 33.6386 | 1.35424 | 0.677119 | − | 0.735874i | \(-0.263228\pi\) | ||||
0.677119 | + | 0.735874i | \(0.263228\pi\) | |||||||
\(618\) | 4.85852 | − | 14.9530i | 0.195438 | − | 0.601498i | ||||
\(619\) | −34.4331 | + | 25.0171i | −1.38398 | + | 1.00552i | −0.387488 | + | 0.921875i | \(0.626657\pi\) |
−0.996495 | + | 0.0836477i | \(0.973343\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.331860 | + | 1.02136i | 0.0133171 | + | 0.0409857i | ||||
\(622\) | −24.8996 | − | 76.6329i | −0.998381 | − | 3.07270i | ||||
\(623\) | 4.31089 | + | 3.13205i | 0.172712 | + | 0.125483i | ||||
\(624\) | 1.06127 | − | 0.771056i | 0.0424847 | − | 0.0308669i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −8.49374 | −0.339478 | ||||||||
\(627\) | −3.65476 | − | 24.4507i | −0.145957 | − | 0.976468i | ||||
\(628\) | 40.8509 | 1.63013 | ||||||||
\(629\) | 4.07019 | − | 12.5268i | 0.162289 | − | 0.499475i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.20016 | + | 5.23122i | 0.286634 | + | 0.208252i | 0.721806 | − | 0.692096i | \(-0.243312\pi\) |
−0.435172 | + | 0.900347i | \(0.643312\pi\) | |||||||
\(632\) | −8.34713 | − | 25.6898i | −0.332031 | − | 1.02189i | ||||
\(633\) | 6.16585 | + | 18.9765i | 0.245071 | + | 0.754250i | ||||
\(634\) | 5.71351 | + | 4.15111i | 0.226912 | + | 0.164862i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 6.14839 | − | 18.9228i | 0.243799 | − | 0.750337i | ||||
\(637\) | 1.19095 | 0.0471871 | ||||||||
\(638\) | −18.9416 | + | 36.3886i | −0.749906 | + | 1.44064i | ||||
\(639\) | 3.07211 | 0.121531 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.99007 | − | 3.62549i | 0.197096 | − | 0.143198i | −0.484860 | − | 0.874592i | \(-0.661130\pi\) |
0.681956 | + | 0.731393i | \(0.261130\pi\) | |||||||
\(642\) | 4.15747 | + | 3.02058i | 0.164082 | + | 0.119213i | ||||
\(643\) | −1.34526 | − | 4.14029i | −0.0530519 | − | 0.163277i | 0.921020 | − | 0.389515i | \(-0.127357\pi\) |
−0.974072 | + | 0.226238i | \(0.927357\pi\) | |||||||
\(644\) | 4.39731 | + | 13.5335i | 0.173278 | + | 0.533296i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 74.0508 | − | 53.8011i | 2.91349 | − | 2.11677i | ||||
\(647\) | −4.16967 | + | 12.8329i | −0.163927 | + | 0.504514i | −0.998956 | − | 0.0456916i | \(-0.985451\pi\) |
0.835029 | + | 0.550206i | \(0.185451\pi\) | |||||||
\(648\) | −4.98884 | −0.195980 | ||||||||
\(649\) | 29.9771 | + | 5.01575i | 1.17671 | + | 0.196885i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.50310 | − | 10.7814i | 0.137297 | − | 0.422558i | ||||
\(652\) | −16.4021 | + | 11.9168i | −0.642354 | + | 0.466697i | ||||
\(653\) | 22.2060 | + | 16.1336i | 0.868988 | + | 0.631357i | 0.930315 | − | 0.366761i | \(-0.119533\pi\) |
−0.0613270 | + | 0.998118i | \(0.519533\pi\) | |||||||
\(654\) | −5.07922 | − | 15.6322i | −0.198613 | − | 0.611269i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −36.7632 | − | 26.7100i | −1.43536 | − | 1.04285i | ||||
\(657\) | −7.00018 | + | 5.08592i | −0.273103 | + | 0.198421i | ||||
\(658\) | 29.9285 | − | 92.1105i | 1.16674 | − | 3.59084i | ||||
\(659\) | −18.7768 | −0.731441 | −0.365721 | − | 0.930725i | \(-0.619177\pi\) | ||||
−0.365721 | + | 0.930725i | \(0.619177\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.6525 | −0.842184 | −0.421092 | − | 0.907018i | \(-0.638353\pi\) | ||||
−0.421092 | + | 0.907018i | \(0.638353\pi\) | |||||||
\(662\) | 10.7174 | − | 32.9847i | 0.416543 | − | 1.28199i | ||||
\(663\) | −1.26665 | + | 0.920276i | −0.0491927 | + | 0.0357406i | ||||
\(664\) | −65.5674 | − | 47.6375i | −2.54451 | − | 1.84869i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.99919 | + | 6.15286i | 0.0774669 | + | 0.238419i | ||||
\(667\) | −4.37578 | − | 3.17919i | −0.169431 | − | 0.123099i | ||||
\(668\) | 18.8872 | − | 13.7224i | 0.730769 | − | 0.530935i | ||||
\(669\) | −6.22565 | + | 19.1606i | −0.240698 | + | 0.740791i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 21.3508 | + | 21.7258i | 0.824240 | + | 0.838714i | ||||
\(672\) | −1.02116 | −0.0393919 | ||||||||
\(673\) | −7.20076 | + | 22.1617i | −0.277569 | + | 0.854269i | 0.710959 | + | 0.703233i | \(0.248261\pi\) |
−0.988528 | + | 0.151036i | \(0.951739\pi\) | |||||||
\(674\) | −31.6883 | + | 23.0229i | −1.22059 | + | 0.886808i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −16.0728 | − | 49.4670i | −0.618184 | − | 1.90258i | ||||
\(677\) | −10.2843 | − | 31.6519i | −0.395259 | − | 1.21648i | −0.928760 | − | 0.370683i | \(-0.879124\pi\) |
0.533501 | − | 0.845800i | \(-0.320876\pi\) | |||||||
\(678\) | −21.4463 | − | 15.5817i | −0.823641 | − | 0.598410i | ||||
\(679\) | −0.595859 | + | 0.432917i | −0.0228670 | + | 0.0166138i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.533937 | 0.0204605 | ||||||||
\(682\) | 27.7077 | + | 4.63603i | 1.06098 | + | 0.177523i | ||||
\(683\) | −16.9244 | −0.647593 | −0.323796 | − | 0.946127i | \(-0.604959\pi\) | ||||
−0.323796 | + | 0.946127i | \(0.604959\pi\) | |||||||
\(684\) | −9.28603 | + | 28.5795i | −0.355060 | + | 1.09276i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 20.8758 | + | 15.1671i | 0.797041 | + | 0.579084i | ||||
\(687\) | 6.85803 | + | 21.1068i | 0.261650 | + | 0.805276i | ||||
\(688\) | 7.13905 | + | 21.9717i | 0.272174 | + | 0.837664i | ||||
\(689\) | 1.25029 | + | 0.908392i | 0.0476324 | + | 0.0346070i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.9668 | + | 46.0630i | −0.569363 | + | 1.75232i | 0.0852532 | + | 0.996359i | \(0.472830\pi\) |
−0.654617 | + | 0.755961i | \(0.727170\pi\) | |||||||
\(692\) | −64.7650 | −2.46200 | ||||||||
\(693\) | 5.03340 | − | 9.66962i | 0.191203 | − | 0.367318i | ||||
\(694\) | 72.8910 | 2.76690 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 20.3275 | − | 14.7688i | 0.770511 | − | 0.559809i | ||||
\(697\) | 43.8779 | + | 31.8791i | 1.66199 | + | 1.20751i | ||||
\(698\) | −24.0527 | − | 74.0267i | −0.910409 | − | 2.80195i | ||||
\(699\) | −1.41087 | − | 4.34221i | −0.0533640 | − | 0.164237i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 36.7424 | − | 26.6949i | 1.38774 | − | 1.00825i | 0.391634 | − | 0.920121i | \(-0.371910\pi\) |
0.996109 | − | 0.0881330i | \(-0.0280900\pi\) | |||||||
\(702\) | 0.237640 | − | 0.731382i | 0.00896916 | − | 0.0276042i | ||||
\(703\) | 19.6361 | 0.740591 | ||||||||
\(704\) | 3.73392 | + | 24.9803i | 0.140727 | + | 0.941482i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.912130 | − | 2.80725i | 0.0343285 | − | 0.105652i | ||||
\(707\) | −1.34372 | + | 0.976267i | −0.0505357 | + | 0.0367163i | ||||
\(708\) | −29.8883 | − | 21.7151i | −1.12327 | − | 0.816103i | ||||
\(709\) | −0.545405 | − | 1.67858i | −0.0204831 | − | 0.0630406i | 0.940292 | − | 0.340368i | \(-0.110551\pi\) |
−0.960776 | + | 0.277327i | \(0.910551\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.38039 | − | 3.18254i | −0.164278 | − | 0.119355i | ||||
\(712\) | 6.54317 | − | 4.75389i | 0.245216 | − | 0.178160i | ||||
\(713\) | −1.14458 | + | 3.52266i | −0.0428649 | + | 0.131925i | ||||
\(714\) | 40.3606 | 1.51046 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −33.4729 | −1.25094 | ||||||||
\(717\) | 1.81100 | − | 5.57369i | 0.0676331 | − | 0.208153i | ||||
\(718\) | −23.1649 | + | 16.8303i | −0.864506 | + | 0.628100i | ||||
\(719\) | 2.66974 | + | 1.93968i | 0.0995645 | + | 0.0723379i | 0.636454 | − | 0.771315i | \(-0.280401\pi\) |
−0.536889 | + | 0.843653i | \(0.680401\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.50241 | − | 20.0124i | −0.242163 | − | 0.745300i | ||||
\(722\) | 72.6459 | + | 52.7803i | 2.70360 | + | 1.96428i | ||||
\(723\) | 8.05841 | − | 5.85477i | 0.299695 | − | 0.217741i | ||||
\(724\) | −8.05294 | + | 24.7844i | −0.299285 | + | 0.921105i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 25.5434 | + | 8.79398i | 0.948003 | + | 0.326375i | ||||
\(727\) | −11.7838 | −0.437037 | −0.218519 | − | 0.975833i | \(-0.570122\pi\) | ||||
−0.218519 | + | 0.975833i | \(0.570122\pi\) | |||||||
\(728\) | 1.58668 | − | 4.88331i | 0.0588064 | − | 0.180987i | ||||
\(729\) | −0.809017 | + | 0.587785i | −0.0299636 | + | 0.0217698i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.52064 | − | 26.2238i | −0.315147 | − | 0.969924i | ||||
\(732\) | −11.4415 | − | 35.2133i | −0.422890 | − | 1.30152i | ||||
\(733\) | 4.63654 | + | 3.36865i | 0.171255 | + | 0.124424i | 0.670111 | − | 0.742261i | \(-0.266246\pi\) |
−0.498856 | + | 0.866685i | \(0.666246\pi\) | |||||||
\(734\) | −31.7619 | + | 23.0764i | −1.17235 | + | 0.851765i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.333646 | 0.0122983 | ||||||||
\(737\) | 45.3348 | − | 22.6044i | 1.66993 | − | 0.832643i | ||||
\(738\) | −26.6395 | −0.980614 | ||||||||
\(739\) | −6.50638 | + | 20.0246i | −0.239341 | + | 0.736616i | 0.757175 | + | 0.653212i | \(0.226579\pi\) |
−0.996516 | + | 0.0834038i | \(0.973421\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.88834 | − | 1.37196i | −0.0693700 | − | 0.0504003i | ||||
\(742\) | −12.3110 | − | 37.8895i | −0.451952 | − | 1.39097i | ||||
\(743\) | −4.05686 | − | 12.4857i | −0.148832 | − | 0.458058i | 0.848652 | − | 0.528952i | \(-0.177415\pi\) |
−0.997484 | + | 0.0708942i | \(0.977415\pi\) | |||||||
\(744\) | −13.9203 | − | 10.1137i | −0.510343 | − | 0.370786i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0.244350 | − | 0.752032i | 0.00894629 | − | 0.0275339i | ||||
\(747\) | −16.2454 | −0.594389 | ||||||||
\(748\) | 9.88299 | + | 66.1183i | 0.361358 | + | 2.41753i | ||||
\(749\) | 6.87768 | 0.251305 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.7311 | + | 15.0621i | −0.756490 | + | 0.549622i | −0.897832 | − | 0.440339i | \(-0.854858\pi\) |
0.141342 | + | 0.989961i | \(0.454858\pi\) | |||||||
\(752\) | −40.6641 | − | 29.5442i | −1.48287 | − | 1.07737i | ||||
\(753\) | 5.21584 | + | 16.0527i | 0.190076 | + | 0.584993i | ||||
\(754\) | 1.19687 | + | 3.68358i | 0.0435874 | + | 0.134148i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −10.7199 | + | 7.78845i | −0.389878 | + | 0.283263i | ||||
\(757\) | −9.64039 | + | 29.6701i | −0.350386 | + | 1.07838i | 0.608251 | + | 0.793745i | \(0.291871\pi\) |
−0.958637 | + | 0.284632i | \(0.908129\pi\) | |||||||
\(758\) | −28.0400 | −1.01846 | ||||||||
\(759\) | −1.64458 | + | 3.15939i | −0.0596945 | + | 0.114678i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.51539 | − | 10.8193i | 0.127433 | − | 0.392198i | −0.866904 | − | 0.498476i | \(-0.833893\pi\) |
0.994336 | + | 0.106278i | \(0.0338932\pi\) | |||||||
\(762\) | −33.7830 | + | 24.5448i | −1.22383 | + | 0.889165i | ||||
\(763\) | −17.7968 | − | 12.9302i | −0.644289 | − | 0.468103i | ||||
\(764\) | 19.1465 | + | 58.9269i | 0.692697 | + | 2.13190i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −56.3617 | − | 40.9491i | −2.03643 | − | 1.47955i | ||||
\(767\) | 2.32154 | − | 1.68670i | 0.0838260 | − | 0.0609032i | ||||
\(768\) | 9.95872 | − | 30.6498i | 0.359354 | − | 1.10598i | ||||
\(769\) | 10.3938 | 0.374811 | 0.187405 | − | 0.982283i | \(-0.439992\pi\) | ||||
0.187405 | + | 0.982283i | \(0.439992\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.1436 | 0.401326 | ||||||||
\(772\) | −19.6230 | + | 60.3935i | −0.706248 | + | 2.17361i | ||||
\(773\) | 11.3544 | − | 8.24944i | 0.408389 | − | 0.296712i | −0.364560 | − | 0.931180i | \(-0.618781\pi\) |
0.772949 | + | 0.634468i | \(0.218781\pi\) | |||||||
\(774\) | 10.9569 | + | 7.96062i | 0.393836 | + | 0.286139i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0.345453 | + | 1.06319i | 0.0124010 | + | 0.0381665i | ||||
\(777\) | 7.00485 | + | 5.08932i | 0.251298 | + | 0.182578i | ||||
\(778\) | 30.1608 | − | 21.9131i | 1.08132 | − | 0.785623i | ||||
\(779\) | −24.9858 | + | 76.8985i | −0.895211 | + | 2.75518i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.14176 | + | 7.26717i | 0.255552 | + | 0.260040i | ||||
\(782\) | −13.1871 | −0.471571 | ||||||||
\(783\) | 1.55635 | − | 4.78997i | 0.0556196 | − | 0.171179i | ||||
\(784\) | −12.8902 | + | 9.36527i | −0.460364 | + | 0.334474i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −0.0326717 | − | 0.100553i | −0.00116536 | − | 0.00358661i | ||||
\(787\) | 4.26988 | + | 13.1414i | 0.152205 | + | 0.468439i | 0.997867 | − | 0.0652802i | \(-0.0207941\pi\) |
−0.845662 | + | 0.533719i | \(0.820794\pi\) | |||||||
\(788\) | 53.4681 | + | 38.8469i | 1.90472 | + | 1.38386i | ||||
\(789\) | 21.7404 | − | 15.7953i | 0.773980 | − | 0.562329i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −35.4785 | −1.26147 | ||||||||
\(792\) | −11.5976 | − | 11.8013i | −0.412102 | − | 0.419339i | ||||
\(793\) | 2.87591 | 0.102127 | ||||||||
\(794\) | 3.96502 | − | 12.2031i | 0.140713 | − | 0.433070i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −22.7160 | − | 16.5042i | −0.805149 | − | 0.584975i | ||||
\(797\) | 1.66435 | + | 5.12233i | 0.0589541 | + | 0.181442i | 0.976197 | − | 0.216887i | \(-0.0695902\pi\) |
−0.917243 | + | 0.398329i | \(0.869590\pi\) | |||||||
\(798\) | 18.5936 | + | 57.2252i | 0.658206 | + | 2.02575i | ||||
\(799\) | 48.5337 | + | 35.2618i | 1.71700 | + | 1.24747i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.500972 | − | 1.54183i | 0.0177010 | − | 0.0544780i | ||||
\(802\) | −34.3840 | −1.21414 | ||||||||
\(803\) | −28.3043 | − | 4.73585i | −0.998836 | − | 0.167124i | ||||
\(804\) | −61.5748 | −2.17157 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.14579 | − | 1.55901i | 0.0755822 | − | 0.0549137i | ||||
\(807\) | −8.14105 | − | 5.91482i | −0.286579 | − | 0.208212i | ||||
\(808\) | 0.779028 | + | 2.39760i | 0.0274061 | + | 0.0843473i | ||||
\(809\) | 7.34680 | + | 22.6111i | 0.258300 | + | 0.794965i | 0.993162 | + | 0.116748i | \(0.0372470\pi\) |
−0.734862 | + | 0.678217i | \(0.762753\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.65601 | + | 5.56242i | −0.268839 | + | 0.195323i | −0.714035 | − | 0.700110i | \(-0.753134\pi\) |
0.445196 | + | 0.895433i | \(0.353134\pi\) | |||||||
\(812\) | 20.6225 | − | 63.4695i | 0.723707 | − | 2.22734i | ||||
\(813\) | −10.5441 | −0.369798 | ||||||||
\(814\) | −9.90726 | + | 19.0327i | −0.347249 | + | 0.667097i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 6.47277 | − | 19.9211i | 0.226592 | − | 0.697379i | ||||
\(817\) | 33.2561 | − | 24.1620i | 1.16348 | − | 0.845321i | ||||
\(818\) | 66.1846 | + | 48.0859i | 2.31409 | + | 1.68128i | ||||
\(819\) | −0.318046 | − | 0.978846i | −0.0111134 | − | 0.0342037i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.42906 | + | 6.12407i | 0.294176 | + | 0.213731i | 0.725077 | − | 0.688668i | \(-0.241804\pi\) |
−0.430901 | + | 0.902399i | \(0.641804\pi\) | |||||||
\(822\) | 14.6284 | − | 10.6281i | 0.510223 | − | 0.370698i | ||||
\(823\) | −7.52581 | + | 23.1620i | −0.262333 | + | 0.807378i | 0.729963 | + | 0.683487i | \(0.239537\pi\) |
−0.992296 | + | 0.123891i | \(0.960463\pi\) | |||||||
\(824\) | −31.9384 | −1.11263 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −73.9736 | −2.57387 | ||||||||
\(827\) | 6.79857 | − | 20.9239i | 0.236410 | − | 0.727594i | −0.760522 | − | 0.649312i | \(-0.775057\pi\) |
0.996931 | − | 0.0782813i | \(-0.0249432\pi\) | |||||||
\(828\) | 3.50254 | − | 2.54475i | 0.121722 | − | 0.0884361i | ||||
\(829\) | −2.45366 | − | 1.78269i | −0.0852191 | − | 0.0619153i | 0.544360 | − | 0.838852i | \(-0.316773\pi\) |
−0.629579 | + | 0.776936i | \(0.716773\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.54302 | − | 17.0597i | −0.192285 | − | 0.591793i | ||||
\(832\) | 1.92924 | + | 1.40168i | 0.0668845 | + | 0.0485945i | ||||
\(833\) | 15.3848 | − | 11.1777i | 0.533051 | − | 0.387284i | ||||
\(834\) | 10.0475 | − | 30.9230i | 0.347916 | − | 1.07077i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −89.1929 | + | 44.4725i | −3.08480 | + | 1.53811i | ||||
\(837\) | −3.44899 | −0.119214 | ||||||||
\(838\) | 4.01054 | − | 12.3432i | 0.138542 | − | 0.426388i | ||||
\(839\) | 39.2683 | − | 28.5301i | 1.35569 | − | 0.984968i | 0.356987 | − | 0.934109i | \(-0.383804\pi\) |
0.998706 | − | 0.0508591i | \(-0.0161960\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.12296 | − | 3.45613i | −0.0387229 | − | 0.119177i | ||||
\(842\) | 23.3600 | + | 71.8947i | 0.805039 | + | 2.47766i | ||||
\(843\) | 5.99565 | + | 4.35609i | 0.206501 | + | 0.150032i | ||||
\(844\) | 65.0762 | − | 47.2806i | 2.24001 | − | 1.62747i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −29.4662 | −1.01307 | ||||||||
\(847\) | 34.5750 | − | 10.5723i | 1.18801 | − | 0.363270i | ||||
\(848\) | −20.6758 | −0.710011 | ||||||||
\(849\) | 1.66462 | − | 5.12319i | 0.0571298 | − | 0.175827i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.28872 | − | 1.66285i | −0.0784563 | − | 0.0570018i | ||||
\(852\) | −3.82713 | − | 11.7787i | −0.131115 | − | 0.403531i | ||||
\(853\) | 3.63504 | + | 11.1875i | 0.124461 | + | 0.383053i | 0.993803 | − | 0.111160i | \(-0.0354565\pi\) |
−0.869341 | + | 0.494213i | \(0.835456\pi\) | |||||||
\(854\) | −59.9779 | − | 43.5765i | −2.05240 | − | 1.49116i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.22586 | − | 9.92817i | 0.110258 | − | 0.339338i | ||||
\(857\) | −1.61311 | −0.0551026 | −0.0275513 | − | 0.999620i | \(-0.508771\pi\) | ||||
−0.0275513 | + | 0.999620i | \(0.508771\pi\) | |||||||
\(858\) | 2.28255 | − | 1.13810i | 0.0779250 | − | 0.0388542i | ||||
\(859\) | 47.3263 | 1.61475 | 0.807376 | − | 0.590038i | \(-0.200887\pi\) | ||||
0.807376 | + | 0.590038i | \(0.200887\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −28.8439 | + | 20.9563i | −0.982998 | + | 0.714190i | ||||
\(862\) | 24.5389 | + | 17.8286i | 0.835799 | + | 0.607244i | ||||
\(863\) | 3.08162 | + | 9.48425i | 0.104900 | + | 0.322848i | 0.989707 | − | 0.143109i | \(-0.0457101\pi\) |
−0.884807 | + | 0.465957i | \(0.845710\pi\) | |||||||
\(864\) | 0.0960054 | + | 0.295474i | 0.00326617 | + | 0.0100522i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −2.80717 | + | 2.03953i | −0.0953915 | + | 0.0693060i | ||||
\(867\) | −2.47214 | + | 7.60845i | −0.0839581 | + | 0.258397i | ||||
\(868\) | −45.7009 | −1.55119 | ||||||||
\(869\) | −2.65473 | − | 17.7604i | −0.0900555 | − | 0.602482i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.47795 | − | 4.54867i | 0.0500786 | − | 0.154126i | ||||
\(872\) | −27.0124 | + | 19.6257i | −0.914756 | + | 0.664609i | ||||
\(873\) | 0.181286 | + | 0.131712i | 0.00613560 | + | 0.00445778i | ||||
\(874\) | −6.07515 | − | 18.6974i | −0.205495 | − | 0.632448i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 28.2204 | + | 20.5033i | 0.953478 | + | 0.692742i | ||||
\(877\) | 21.0391 | − | 15.2858i | 0.710439 | − | 0.516164i | −0.172876 | − | 0.984944i | \(-0.555306\pi\) |
0.883315 | + | 0.468779i | \(0.155306\pi\) | |||||||
\(878\) | 5.75658 | − | 17.7169i | 0.194275 | − | 0.597918i | ||||
\(879\) | −1.74006 | −0.0586907 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 10.4081 | 0.350657 | 0.175329 | − | 0.984510i | \(-0.443901\pi\) | ||||
0.175329 | + | 0.984510i | \(0.443901\pi\) | |||||||
\(882\) | −2.88639 | + | 8.88338i | −0.0971897 | + | 0.299119i | ||||
\(883\) | −43.4671 | + | 31.5807i | −1.46279 | + | 1.06278i | −0.480159 | + | 0.877181i | \(0.659421\pi\) |
−0.982626 | + | 0.185595i | \(0.940579\pi\) | |||||||
\(884\) | 5.10635 | + | 3.70998i | 0.171745 | + | 0.124780i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 8.39826 | + | 25.8472i | 0.282145 | + | 0.868353i | ||||
\(887\) | −32.8660 | − | 23.8786i | −1.10353 | − | 0.801763i | −0.121900 | − | 0.992542i | \(-0.538899\pi\) |
−0.981633 | + | 0.190779i | \(0.938899\pi\) | |||||||
\(888\) | 10.6321 | − | 7.72468i | 0.356790 | − | 0.259223i | ||||
\(889\) | −17.2701 | + | 53.1518i | −0.579219 | + | 1.78265i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.27115 | − | 0.547326i | −0.109588 | − | 0.0183361i | ||||
\(892\) | 81.2188 | 2.71941 | ||||||||
\(893\) | −27.6371 | + | 85.0582i | −0.924839 | + | 2.84636i | ||||
\(894\) | 11.6799 | − | 8.48594i | 0.390634 | − | 0.283812i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −19.6274 | − | 60.4071i | −0.655707 | − | 2.01806i | ||||
\(897\) | 0.103916 | + | 0.319822i | 0.00346967 | + | 0.0106785i | ||||
\(898\) | 12.5739 | + | 9.13549i | 0.419597 | + | 0.304855i | ||||
\(899\) | 14.0532 | − | 10.2103i | 0.468701 | − | 0.340531i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 24.6772 | 0.822115 | ||||||||
\(902\) | −61.9290 | − | 63.0166i | −2.06201 | − | 2.09822i | ||||
\(903\) | 18.1259 | 0.603191 | ||||||||
\(904\) | −16.6406 | + | 51.2145i | −0.553458 | + | 1.70337i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −15.1561 | − | 11.0116i | −0.503529 | − | 0.365835i | ||||
\(907\) | 5.99708 | + | 18.4571i | 0.199130 | + | 0.612859i | 0.999904 | + | 0.0138917i | \(0.00442202\pi\) |
−0.800774 | + | 0.598967i | \(0.795578\pi\) | |||||||
\(908\) | −0.665160 | − | 2.04715i | −0.0220741 | − | 0.0679371i | ||||
\(909\) | 0.408817 | + | 0.297023i | 0.0135596 | + | 0.00985163i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.31290 | − | 10.1960i | 0.109761 | − | 0.337810i | −0.881057 | − | 0.473010i | \(-0.843168\pi\) |
0.990818 | + | 0.135200i | \(0.0431676\pi\) | |||||||
\(912\) | 31.2271 | 1.03403 | ||||||||
\(913\) | −37.7658 | − | 38.4290i | −1.24987 | − | 1.27182i | ||||
\(914\) | −0.465585 | −0.0154002 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 72.3816 | − | 52.5883i | 2.39156 | − | 1.73757i | ||||
\(917\) | −0.114477 | − | 0.0831723i | −0.00378036 | − | 0.00274659i | ||||
\(918\) | −3.79455 | − | 11.6784i | −0.125239 | − | 0.385446i | ||||
\(919\) | −7.14787 | − | 21.9989i | −0.235787 | − | 0.725676i | −0.997016 | − | 0.0771939i | \(-0.975404\pi\) |
0.761230 | − | 0.648483i | \(-0.224596\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −17.2779 | + | 12.5531i | −0.569325 | + | 0.413639i | ||||
\(922\) | 20.2020 | − | 62.1755i | 0.665319 | − | 2.04764i | ||||
\(923\) | 0.961981 | 0.0316640 | ||||||||
\(924\) | −43.3444 | − | 7.25235i | −1.42593 | − | 0.238585i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 15.9322 | − | 49.0343i | 0.523565 | − | 1.61137i | ||||
\(927\) | −5.17930 | + | 3.76298i | −0.170111 | + | 0.123593i | ||||
\(928\) | −1.26589 | − | 0.919725i | −0.0415550 | − | 0.0301915i | ||||
\(929\) | 8.10467 | + | 24.9436i | 0.265906 | + | 0.818374i | 0.991483 | + | 0.130233i | \(0.0415727\pi\) |
−0.725578 | + | 0.688140i | \(0.758427\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 22.9359 | + | 16.6639i | 0.751693 | + | 0.546137i | ||||
\(932\) | −14.8907 | + | 10.8187i | −0.487762 | + | 0.354380i | ||||
\(933\) | −10.1387 | + | 31.2038i | −0.331927 | + | 1.02157i | ||||
\(934\) | 19.4012 | 0.634828 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.56217 | −0.0510612 | ||||||||
\(937\) | −7.23133 | + | 22.2557i | −0.236237 | + | 0.727063i | 0.760718 | + | 0.649083i | \(0.224847\pi\) |
−0.996955 | + | 0.0779804i | \(0.975153\pi\) | |||||||
\(938\) | −99.7456 | + | 72.4694i | −3.25681 | + | 2.36621i | ||||
\(939\) | 2.79800 | + | 2.03287i | 0.0913094 | + | 0.0663401i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.38952 | − | 10.4319i | −0.110495 | − | 0.340069i | 0.880486 | − | 0.474073i | \(-0.157217\pi\) |
−0.990981 | + | 0.134004i | \(0.957217\pi\) | |||||||
\(942\) | −20.1332 | − | 14.6276i | −0.655976 | − | 0.476595i | ||||
\(943\) | 9.42427 | − | 6.84713i | 0.306896 | − | 0.222973i | ||||
\(944\) | −11.8634 | + | 36.5118i | −0.386121 | + | 1.18836i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.64038 | + | 44.4249i | 0.215897 | + | 1.44438i | ||||
\(947\) | 13.3652 | 0.434310 | 0.217155 | − | 0.976137i | \(-0.430322\pi\) | ||||
0.217155 | + | 0.976137i | \(0.430322\pi\) | |||||||
\(948\) | −6.74515 | + | 20.7594i | −0.219072 | + | 0.674235i | ||||
\(949\) | −2.19199 | + | 1.59257i | −0.0711550 | + | 0.0516971i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.888626 | − | 2.73491i | −0.0288157 | − | 0.0886856i | ||||
\(952\) | −25.3356 | − | 77.9749i | −0.821130 | − | 2.52718i | ||||
\(953\) | −17.6562 | − | 12.8280i | −0.571939 | − | 0.415538i | 0.263870 | − | 0.964558i | \(-0.415001\pi\) |
−0.835809 | + | 0.549020i | \(0.815001\pi\) | |||||||
\(954\) | −9.80598 | + | 7.12446i | −0.317480 | + | 0.230663i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −23.6260 | −0.764120 | ||||||||
\(957\) | 14.9489 | − | 7.45366i | 0.483229 | − | 0.240943i | ||||
\(958\) | −98.1686 | −3.17168 | ||||||||
\(959\) | 7.47809 | − | 23.0152i | 0.241480 | − | 0.743199i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.4558 | + | 11.2293i | 0.498576 | + | 0.362236i | ||||
\(962\) | 0.626012 | + | 1.92667i | 0.0201834 | + | 0.0621182i | ||||
\(963\) | −0.646615 | − | 1.99008i | −0.0208369 | − | 0.0641293i | ||||
\(964\) | −32.4865 | − | 23.6028i | −1.04632 | − | 0.760196i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 2.67881 | − | 8.24453i | 0.0861893 | − | 0.265263i | ||||
\(967\) | −16.6600 | −0.535750 | −0.267875 | − | 0.963454i | \(-0.586321\pi\) | ||||
−0.267875 | + | 0.963454i | \(0.586321\pi\) | |||||||
\(968\) | 0.955240 | − | 54.8689i | 0.0307026 | − | 1.76355i | ||||
\(969\) | −37.2704 | −1.19730 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −8.98271 | + | 6.52632i | −0.288269 | + | 0.209440i | −0.722516 | − | 0.691354i | \(-0.757014\pi\) |
0.434247 | + | 0.900794i | \(0.357014\pi\) | |||||||
\(972\) | 3.26145 | + | 2.36959i | 0.104611 | + | 0.0760045i | ||||
\(973\) | −13.4471 | − | 41.3858i | −0.431093 | − | 1.32677i | ||||
\(974\) | −7.54021 | − | 23.2064i | −0.241604 | − | 0.743580i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −31.1273 | + | 22.6153i | −0.996362 | + | 0.723899i | ||||
\(977\) | −5.81397 | + | 17.8936i | −0.186005 | + | 0.572466i | −0.999964 | − | 0.00845665i | \(-0.997308\pi\) |
0.813959 | + | 0.580923i | \(0.197308\pi\) | |||||||
\(978\) | 12.3508 | 0.394935 | ||||||||
\(979\) | 4.81187 | − | 2.39924i | 0.153788 | − | 0.0766802i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.06818 | + | 6.36521i | −0.0660320 | + | 0.203226i | ||||
\(982\) | 9.88160 | − | 7.17940i | 0.315335 | − | 0.229104i | ||||
\(983\) | −1.11521 | − | 0.810250i | −0.0355698 | − | 0.0258430i | 0.569858 | − | 0.821743i | \(-0.306998\pi\) |
−0.605428 | + | 0.795900i | \(0.706998\pi\) | |||||||
\(984\) | 16.7224 | + | 51.4664i | 0.533092 | + | 1.64069i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 50.0336 | + | 36.3516i | 1.59340 | + | 1.15767i | ||||
\(987\) | −31.9045 | + | 23.1800i | −1.01553 | + | 0.737827i | ||||
\(988\) | −2.90777 | + | 8.94918i | −0.0925083 | + | 0.284711i | ||||
\(989\) | −5.92233 | −0.188319 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −46.3186 | −1.47136 | −0.735680 | − | 0.677329i | \(-0.763137\pi\) | ||||
−0.735680 | + | 0.677329i | \(0.763137\pi\) | |||||||
\(992\) | −0.331122 | + | 1.01909i | −0.0105131 | + | 0.0323561i | ||||
\(993\) | −11.4250 | + | 8.30074i | −0.362561 | + | 0.263416i | ||||
\(994\) | −20.0623 | − | 14.5761i | −0.636339 | − | 0.462327i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 20.2380 | + | 62.2861i | 0.641265 | + | 1.97361i | ||||
\(997\) | 11.7688 | + | 8.55054i | 0.372722 | + | 0.270798i | 0.758339 | − | 0.651861i | \(-0.226011\pi\) |
−0.385617 | + | 0.922659i | \(0.626011\pi\) | |||||||
\(998\) | 86.9759 | − | 63.1917i | 2.75317 | − | 2.00030i | ||||
\(999\) | 0.814038 | − | 2.50535i | 0.0257550 | − | 0.0792658i |
(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 | 825.2.n.k.526.1 | 8 | ||
5.2 | odd | 4 | 825.2.bx.h.724.1 | 16 | |||
5.3 | odd | 4 | 825.2.bx.h.724.4 | 16 | |||
5.4 | even | 2 | 165.2.m.a.31.2 | yes | 8 | ||
11.4 | even | 5 | 9075.2.a.cl.1.2 | 4 | |||
11.5 | even | 5 | inner | 825.2.n.k.676.1 | 8 | ||
11.7 | odd | 10 | 9075.2.a.dj.1.3 | 4 | |||
15.14 | odd | 2 | 495.2.n.d.361.1 | 8 | |||
55.4 | even | 10 | 1815.2.a.x.1.3 | 4 | |||
55.27 | odd | 20 | 825.2.bx.h.49.4 | 16 | |||
55.29 | odd | 10 | 1815.2.a.o.1.2 | 4 | |||
55.38 | odd | 20 | 825.2.bx.h.49.1 | 16 | |||
55.49 | even | 10 | 165.2.m.a.16.2 | ✓ | 8 | ||
165.29 | even | 10 | 5445.2.a.bv.1.3 | 4 | |||
165.59 | odd | 10 | 5445.2.a.be.1.2 | 4 | |||
165.104 | odd | 10 | 495.2.n.d.181.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.2.m.a.16.2 | ✓ | 8 | 55.49 | even | 10 | ||
165.2.m.a.31.2 | yes | 8 | 5.4 | even | 2 | ||
495.2.n.d.181.1 | 8 | 165.104 | odd | 10 | |||
495.2.n.d.361.1 | 8 | 15.14 | odd | 2 | |||
825.2.n.k.526.1 | 8 | 1.1 | even | 1 | trivial | ||
825.2.n.k.676.1 | 8 | 11.5 | even | 5 | inner | ||
825.2.bx.h.49.1 | 16 | 55.38 | odd | 20 | |||
825.2.bx.h.49.4 | 16 | 55.27 | odd | 20 | |||
825.2.bx.h.724.1 | 16 | 5.2 | odd | 4 | |||
825.2.bx.h.724.4 | 16 | 5.3 | odd | 4 | |||
1815.2.a.o.1.2 | 4 | 55.29 | odd | 10 | |||
1815.2.a.x.1.3 | 4 | 55.4 | even | 10 | |||
5445.2.a.be.1.2 | 4 | 165.59 | odd | 10 | |||
5445.2.a.bv.1.3 | 4 | 165.29 | even | 10 | |||
9075.2.a.cl.1.2 | 4 | 11.4 | even | 5 | |||
9075.2.a.dj.1.3 | 4 | 11.7 | odd | 10 |