Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,2,Mod(181,825)]
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, 4, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.181");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.p (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: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 466.1 | ||
Root | \(0.809017 - 0.587785i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.466 |
Dual form | 825.2.p.a.586.1 |
$q$-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 \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).
\(n\) | \(376\) | \(551\) | \(727\) |
\(\chi(n)\) | \(e\left(\frac{1}{5}\right)\) | \(1\) | \(e\left(\frac{1}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.690983 | − | 2.12663i | −0.488599 | − | 1.50375i | −0.826700 | − | 0.562643i | \(-0.809785\pi\) |
0.338101 | − | 0.941110i | \(-0.390215\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −2.42705 | + | 1.76336i | −1.21353 | + | 0.881678i | ||||
\(5\) | −1.80902 | − | 1.31433i | −0.809017 | − | 0.587785i | ||||
\(6\) | −0.690983 | − | 2.12663i | −0.282093 | − | 0.868192i | ||||
\(7\) | 0.809017 | + | 2.48990i | 0.305780 | + | 0.941093i | 0.979385 | + | 0.202002i | \(0.0647447\pi\) |
−0.673605 | + | 0.739091i | \(0.735255\pi\) | |||||||
\(8\) | 1.80902 | + | 1.31433i | 0.639584 | + | 0.464685i | ||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.54508 | + | 4.75528i | −0.488599 | + | 1.50375i | ||||
\(11\) | 0.809017 | − | 3.21644i | 0.243928 | − | 0.969793i | ||||
\(12\) | −2.42705 | + | 1.76336i | −0.700629 | + | 0.509037i | ||||
\(13\) | −6.00000 | −1.66410 | −0.832050 | − | 0.554700i | \(-0.812833\pi\) | ||||
−0.832050 | + | 0.554700i | \(0.812833\pi\) | |||||||
\(14\) | 4.73607 | − | 3.44095i | 1.26577 | − | 0.919634i | ||||
\(15\) | −1.80902 | − | 1.31433i | −0.467086 | − | 0.339358i | ||||
\(16\) | −0.309017 | + | 0.951057i | −0.0772542 | + | 0.237764i | ||||
\(17\) | 1.92705 | + | 5.93085i | 0.467379 | + | 1.43844i | 0.855966 | + | 0.517031i | \(0.172963\pi\) |
−0.388588 | + | 0.921412i | \(0.627037\pi\) | |||||||
\(18\) | −0.690983 | − | 2.12663i | −0.162866 | − | 0.501251i | ||||
\(19\) | −5.35410 | − | 3.88998i | −1.22832 | − | 0.892423i | −0.231552 | − | 0.972822i | \(-0.574381\pi\) |
−0.996763 | + | 0.0803992i | \(0.974381\pi\) | |||||||
\(20\) | 6.70820 | 1.50000 | ||||||||
\(21\) | 0.809017 | + | 2.48990i | 0.176542 | + | 0.543340i | ||||
\(22\) | −7.39919 | + | 0.502029i | −1.57751 | + | 0.107033i | ||||
\(23\) | −4.42705 | − | 3.21644i | −0.923104 | − | 0.670674i | 0.0211907 | − | 0.999775i | \(-0.493254\pi\) |
−0.944295 | + | 0.329101i | \(0.893254\pi\) | |||||||
\(24\) | 1.80902 | + | 1.31433i | 0.369264 | + | 0.268286i | ||||
\(25\) | 1.54508 | + | 4.75528i | 0.309017 | + | 0.951057i | ||||
\(26\) | 4.14590 | + | 12.7598i | 0.813077 | + | 2.50240i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −6.35410 | − | 4.61653i | −1.20081 | − | 0.872441i | ||||
\(29\) | −5.73607 | + | 4.16750i | −1.06516 | + | 0.773885i | −0.975036 | − | 0.222046i | \(-0.928727\pi\) |
−0.0901248 | + | 0.995930i | \(0.528727\pi\) | |||||||
\(30\) | −1.54508 | + | 4.75528i | −0.282093 | + | 0.868192i | ||||
\(31\) | −6.04508 | + | 4.39201i | −1.08573 | + | 0.788829i | −0.978673 | − | 0.205424i | \(-0.934143\pi\) |
−0.107056 | + | 0.994253i | \(0.534143\pi\) | |||||||
\(32\) | 6.70820 | 1.18585 | ||||||||
\(33\) | 0.809017 | − | 3.21644i | 0.140832 | − | 0.559910i | ||||
\(34\) | 11.2812 | − | 8.19624i | 1.93470 | − | 1.40564i | ||||
\(35\) | 1.80902 | − | 5.56758i | 0.305780 | − | 0.941093i | ||||
\(36\) | −2.42705 | + | 1.76336i | −0.404508 | + | 0.293893i | ||||
\(37\) | −0.927051 | − | 0.673542i | −0.152406 | − | 0.110730i | 0.508969 | − | 0.860785i | \(-0.330027\pi\) |
−0.661375 | + | 0.750055i | \(0.730027\pi\) | |||||||
\(38\) | −4.57295 | + | 14.0741i | −0.741830 | + | 2.28312i | ||||
\(39\) | −6.00000 | −0.960769 | ||||||||
\(40\) | −1.54508 | − | 4.75528i | −0.244299 | − | 0.751876i | ||||
\(41\) | 0.545085 | + | 1.67760i | 0.0851280 | + | 0.261997i | 0.984555 | − | 0.175073i | \(-0.0560162\pi\) |
−0.899427 | + | 0.437070i | \(0.856016\pi\) | |||||||
\(42\) | 4.73607 | − | 3.44095i | 0.730791 | − | 0.530951i | ||||
\(43\) | 7.94427 | 1.21149 | 0.605745 | − | 0.795659i | \(-0.292875\pi\) | ||||
0.605745 | + | 0.795659i | \(0.292875\pi\) | |||||||
\(44\) | 3.70820 | + | 9.23305i | 0.559033 | + | 1.39193i | ||||
\(45\) | −1.80902 | − | 1.31433i | −0.269672 | − | 0.195928i | ||||
\(46\) | −3.78115 | + | 11.6372i | −0.557501 | + | 1.71581i | ||||
\(47\) | 8.09017 | 1.18007 | 0.590036 | − | 0.807377i | \(-0.299113\pi\) | ||||
0.590036 | + | 0.807377i | \(0.299113\pi\) | |||||||
\(48\) | −0.309017 | + | 0.951057i | −0.0446028 | + | 0.137273i | ||||
\(49\) | 0.118034 | − | 0.0857567i | 0.0168620 | − | 0.0122510i | ||||
\(50\) | 9.04508 | − | 6.57164i | 1.27917 | − | 0.929370i | ||||
\(51\) | 1.92705 | + | 5.93085i | 0.269841 | + | 0.830486i | ||||
\(52\) | 14.5623 | − | 10.5801i | 2.01943 | − | 1.46720i | ||||
\(53\) | −0.309017 | + | 0.951057i | −0.0424467 | + | 0.130638i | −0.970034 | − | 0.242968i | \(-0.921879\pi\) |
0.927587 | + | 0.373606i | \(0.121879\pi\) | |||||||
\(54\) | −0.690983 | − | 2.12663i | −0.0940309 | − | 0.289397i | ||||
\(55\) | −5.69098 | + | 4.75528i | −0.767372 | + | 0.641202i | ||||
\(56\) | −1.80902 | + | 5.56758i | −0.241740 | + | 0.743999i | ||||
\(57\) | −5.35410 | − | 3.88998i | −0.709168 | − | 0.515241i | ||||
\(58\) | 12.8262 | + | 9.31881i | 1.68417 | + | 1.22362i | ||||
\(59\) | −9.47214 | − | 6.88191i | −1.23317 | − | 0.895948i | −0.236044 | − | 0.971742i | \(-0.575851\pi\) |
−0.997123 | + | 0.0757942i | \(0.975851\pi\) | |||||||
\(60\) | 6.70820 | 0.866025 | ||||||||
\(61\) | −5.32624 | −0.681955 | −0.340977 | − | 0.940071i | \(-0.610758\pi\) | ||||
−0.340977 | + | 0.940071i | \(0.610758\pi\) | |||||||
\(62\) | 13.5172 | + | 9.82084i | 1.71669 | + | 1.24725i | ||||
\(63\) | 0.809017 | + | 2.48990i | 0.101927 | + | 0.313698i | ||||
\(64\) | −4.01722 | − | 12.3637i | −0.502153 | − | 1.54547i | ||||
\(65\) | 10.8541 | + | 7.88597i | 1.34629 | + | 0.978134i | ||||
\(66\) | −7.39919 | + | 0.502029i | −0.910777 | + | 0.0617954i | ||||
\(67\) | −1.80902 | + | 5.56758i | −0.221007 | + | 0.680188i | 0.777666 | + | 0.628678i | \(0.216404\pi\) |
−0.998672 | + | 0.0515105i | \(0.983596\pi\) | |||||||
\(68\) | −15.1353 | − | 10.9964i | −1.83542 | − | 1.33351i | ||||
\(69\) | −4.42705 | − | 3.21644i | −0.532954 | − | 0.387214i | ||||
\(70\) | −13.0902 | −1.56457 | ||||||||
\(71\) | −6.04508 | − | 4.39201i | −0.717420 | − | 0.521236i | 0.168139 | − | 0.985763i | \(-0.446224\pi\) |
−0.885559 | + | 0.464527i | \(0.846224\pi\) | |||||||
\(72\) | 1.80902 | + | 1.31433i | 0.213195 | + | 0.154895i | ||||
\(73\) | −1.00000 | + | 3.07768i | −0.117041 | + | 0.360216i | −0.992367 | − | 0.123317i | \(-0.960647\pi\) |
0.875326 | + | 0.483533i | \(0.160647\pi\) | |||||||
\(74\) | −0.791796 | + | 2.43690i | −0.0920444 | + | 0.283284i | ||||
\(75\) | 1.54508 | + | 4.75528i | 0.178411 | + | 0.549093i | ||||
\(76\) | 19.8541 | 2.27742 | ||||||||
\(77\) | 8.66312 | − | 0.587785i | 0.987254 | − | 0.0669843i | ||||
\(78\) | 4.14590 | + | 12.7598i | 0.469431 | + | 1.44476i | ||||
\(79\) | −4.00000 | + | 12.3107i | −0.450035 | + | 1.38507i | 0.426831 | + | 0.904331i | \(0.359630\pi\) |
−0.876866 | + | 0.480734i | \(0.840370\pi\) | |||||||
\(80\) | 1.80902 | − | 1.31433i | 0.202254 | − | 0.146946i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 3.19098 | − | 2.31838i | 0.352385 | − | 0.256023i | ||||
\(83\) | −2.64590 | − | 8.14324i | −0.290425 | − | 0.893836i | −0.984720 | − | 0.174146i | \(-0.944284\pi\) |
0.694295 | − | 0.719691i | \(-0.255716\pi\) | |||||||
\(84\) | −6.35410 | − | 4.61653i | −0.693289 | − | 0.503704i | ||||
\(85\) | 4.30902 | − | 13.2618i | 0.467379 | − | 1.43844i | ||||
\(86\) | −5.48936 | − | 16.8945i | −0.591933 | − | 1.82178i | ||||
\(87\) | −5.73607 | + | 4.16750i | −0.614971 | + | 0.446803i | ||||
\(88\) | 5.69098 | − | 4.75528i | 0.606661 | − | 0.506915i | ||||
\(89\) | −2.88197 | − | 2.09387i | −0.305488 | − | 0.221950i | 0.424470 | − | 0.905442i | \(-0.360460\pi\) |
−0.729958 | + | 0.683492i | \(0.760460\pi\) | |||||||
\(90\) | −1.54508 | + | 4.75528i | −0.162866 | + | 0.501251i | ||||
\(91\) | −4.85410 | − | 14.9394i | −0.508848 | − | 1.56607i | ||||
\(92\) | 16.4164 | 1.71153 | ||||||||
\(93\) | −6.04508 | + | 4.39201i | −0.626846 | + | 0.455430i | ||||
\(94\) | −5.59017 | − | 17.2048i | −0.576582 | − | 1.77454i | ||||
\(95\) | 4.57295 | + | 14.0741i | 0.469175 | + | 1.44397i | ||||
\(96\) | 6.70820 | 0.684653 | ||||||||
\(97\) | 0.781153 | − | 2.40414i | 0.0793141 | − | 0.244104i | −0.903535 | − | 0.428514i | \(-0.859037\pi\) |
0.982849 | + | 0.184410i | \(0.0590374\pi\) | |||||||
\(98\) | −0.263932 | − | 0.191758i | −0.0266612 | − | 0.0193705i | ||||
\(99\) | 0.809017 | − | 3.21644i | 0.0813093 | − | 0.323264i | ||||
\(100\) | −12.1353 | − | 8.81678i | −1.21353 | − | 0.881678i | ||||
\(101\) | 2.66312 | + | 1.93487i | 0.264990 | + | 0.192527i | 0.712344 | − | 0.701830i | \(-0.247634\pi\) |
−0.447354 | + | 0.894357i | \(0.647634\pi\) | |||||||
\(102\) | 11.2812 | − | 8.19624i | 1.11700 | − | 0.811548i | ||||
\(103\) | 7.04508 | − | 5.11855i | 0.694173 | − | 0.504346i | −0.183856 | − | 0.982953i | \(-0.558858\pi\) |
0.878029 | + | 0.478607i | \(0.158858\pi\) | |||||||
\(104\) | −10.8541 | − | 7.88597i | −1.06433 | − | 0.773283i | ||||
\(105\) | 1.80902 | − | 5.56758i | 0.176542 | − | 0.543340i | ||||
\(106\) | 2.23607 | 0.217186 | ||||||||
\(107\) | 3.83688 | − | 11.8087i | 0.370925 | − | 1.14159i | −0.575261 | − | 0.817970i | \(-0.695100\pi\) |
0.946187 | − | 0.323621i | \(-0.104900\pi\) | |||||||
\(108\) | −2.42705 | + | 1.76336i | −0.233543 | + | 0.169679i | ||||
\(109\) | −3.47214 | + | 2.52265i | −0.332570 | + | 0.241626i | −0.741520 | − | 0.670930i | \(-0.765895\pi\) |
0.408950 | + | 0.912557i | \(0.365895\pi\) | |||||||
\(110\) | 14.0451 | + | 8.81678i | 1.33915 | + | 0.840647i | ||||
\(111\) | −0.927051 | − | 0.673542i | −0.0879918 | − | 0.0639298i | ||||
\(112\) | −2.61803 | −0.247381 | ||||||||
\(113\) | −2.30902 | − | 7.10642i | −0.217214 | − | 0.668516i | −0.998989 | − | 0.0449554i | \(-0.985685\pi\) |
0.781775 | − | 0.623561i | \(-0.214315\pi\) | |||||||
\(114\) | −4.57295 | + | 14.0741i | −0.428296 | + | 1.31816i | ||||
\(115\) | 3.78115 | + | 11.6372i | 0.352594 | + | 1.08517i | ||||
\(116\) | 6.57295 | − | 20.2295i | 0.610283 | − | 1.87826i | ||||
\(117\) | −6.00000 | −0.554700 | ||||||||
\(118\) | −8.09017 | + | 24.8990i | −0.744761 | + | 2.29214i | ||||
\(119\) | −13.2082 | + | 9.59632i | −1.21079 | + | 0.879693i | ||||
\(120\) | −1.54508 | − | 4.75528i | −0.141046 | − | 0.434096i | ||||
\(121\) | −9.69098 | − | 5.20431i | −0.880998 | − | 0.473119i | ||||
\(122\) | 3.68034 | + | 11.3269i | 0.333202 | + | 1.02549i | ||||
\(123\) | 0.545085 | + | 1.67760i | 0.0491487 | + | 0.151264i | ||||
\(124\) | 6.92705 | − | 21.3193i | 0.622068 | − | 1.91453i | ||||
\(125\) | 3.45492 | − | 10.6331i | 0.309017 | − | 0.951057i | ||||
\(126\) | 4.73607 | − | 3.44095i | 0.421922 | − | 0.306545i | ||||
\(127\) | 7.14590 | 0.634096 | 0.317048 | − | 0.948410i | \(-0.397308\pi\) | ||||
0.317048 | + | 0.948410i | \(0.397308\pi\) | |||||||
\(128\) | −12.6631 | + | 9.20029i | −1.11927 | + | 0.813199i | ||||
\(129\) | 7.94427 | 0.699454 | ||||||||
\(130\) | 9.27051 | − | 28.5317i | 0.813077 | − | 2.50240i | ||||
\(131\) | −5.35410 | + | 16.4782i | −0.467790 | + | 1.43971i | 0.387649 | + | 0.921807i | \(0.373287\pi\) |
−0.855439 | + | 0.517903i | \(0.826713\pi\) | |||||||
\(132\) | 3.70820 | + | 9.23305i | 0.322758 | + | 0.803634i | ||||
\(133\) | 5.35410 | − | 16.4782i | 0.464260 | − | 1.42884i | ||||
\(134\) | 13.0902 | 1.13082 | ||||||||
\(135\) | −1.80902 | − | 1.31433i | −0.155695 | − | 0.113119i | ||||
\(136\) | −4.30902 | + | 13.2618i | −0.369495 | + | 1.13719i | ||||
\(137\) | 6.70820 | − | 20.6457i | 0.573121 | − | 1.76388i | −0.0693711 | − | 0.997591i | \(-0.522099\pi\) |
0.642492 | − | 0.766293i | \(-0.277901\pi\) | |||||||
\(138\) | −3.78115 | + | 11.6372i | −0.321873 | + | 0.990624i | ||||
\(139\) | 1.59017 | − | 4.89404i | 0.134876 | − | 0.415107i | −0.860694 | − | 0.509122i | \(-0.829970\pi\) |
0.995571 | + | 0.0940150i | \(0.0299702\pi\) | |||||||
\(140\) | 5.42705 | + | 16.7027i | 0.458670 | + | 1.41164i | ||||
\(141\) | 8.09017 | 0.681315 | ||||||||
\(142\) | −5.16312 | + | 15.8904i | −0.433279 | + | 1.33350i | ||||
\(143\) | −4.85410 | + | 19.2986i | −0.405920 | + | 1.61383i | ||||
\(144\) | −0.309017 | + | 0.951057i | −0.0257514 | + | 0.0792547i | ||||
\(145\) | 15.8541 | 1.31661 | ||||||||
\(146\) | 7.23607 | 0.598861 | ||||||||
\(147\) | 0.118034 | − | 0.0857567i | 0.00973528 | − | 0.00707309i | ||||
\(148\) | 3.43769 | 0.282577 | ||||||||
\(149\) | 0.545085 | − | 0.396027i | 0.0446551 | − | 0.0324438i | −0.565234 | − | 0.824931i | \(-0.691214\pi\) |
0.609889 | + | 0.792487i | \(0.291214\pi\) | |||||||
\(150\) | 9.04508 | − | 6.57164i | 0.738528 | − | 0.536572i | ||||
\(151\) | 0.500000 | − | 1.53884i | 0.0406894 | − | 0.125229i | −0.928648 | − | 0.370961i | \(-0.879028\pi\) |
0.969338 | + | 0.245732i | \(0.0790283\pi\) | |||||||
\(152\) | −4.57295 | − | 14.0741i | −0.370915 | − | 1.14156i | ||||
\(153\) | 1.92705 | + | 5.93085i | 0.155793 | + | 0.479481i | ||||
\(154\) | −7.23607 | − | 18.0171i | −0.583099 | − | 1.45186i | ||||
\(155\) | 16.7082 | 1.34204 | ||||||||
\(156\) | 14.5623 | − | 10.5801i | 1.16592 | − | 0.847089i | ||||
\(157\) | −2.69098 | + | 8.28199i | −0.214764 | + | 0.660975i | 0.784406 | + | 0.620247i | \(0.212968\pi\) |
−0.999170 | + | 0.0407279i | \(0.987032\pi\) | |||||||
\(158\) | 28.9443 | 2.30268 | ||||||||
\(159\) | −0.309017 | + | 0.951057i | −0.0245066 | + | 0.0754237i | ||||
\(160\) | −12.1353 | − | 8.81678i | −0.959376 | − | 0.697028i | ||||
\(161\) | 4.42705 | − | 13.6251i | 0.348900 | − | 1.07381i | ||||
\(162\) | −0.690983 | − | 2.12663i | −0.0542888 | − | 0.167084i | ||||
\(163\) | −13.0000 | −1.01824 | −0.509119 | − | 0.860696i | \(-0.670029\pi\) | ||||
−0.509119 | + | 0.860696i | \(0.670029\pi\) | |||||||
\(164\) | −4.28115 | − | 3.11044i | −0.334302 | − | 0.242885i | ||||
\(165\) | −5.69098 | + | 4.75528i | −0.443042 | + | 0.370198i | ||||
\(166\) | −15.4894 | + | 11.2537i | −1.20221 | + | 0.873455i | ||||
\(167\) | −20.4894 | + | 14.8864i | −1.58551 | + | 1.15194i | −0.675505 | + | 0.737356i | \(0.736074\pi\) |
−0.910009 | + | 0.414588i | \(0.863926\pi\) | |||||||
\(168\) | −1.80902 | + | 5.56758i | −0.139569 | + | 0.429548i | ||||
\(169\) | 23.0000 | 1.76923 | ||||||||
\(170\) | −31.1803 | −2.39142 | ||||||||
\(171\) | −5.35410 | − | 3.88998i | −0.409438 | − | 0.297474i | ||||
\(172\) | −19.2812 | + | 14.0086i | −1.47017 | + | 1.06814i | ||||
\(173\) | −16.3992 | + | 11.9147i | −1.24681 | + | 0.905858i | −0.998032 | − | 0.0627030i | \(-0.980028\pi\) |
−0.248775 | + | 0.968561i | \(0.580028\pi\) | |||||||
\(174\) | 12.8262 | + | 9.31881i | 0.972355 | + | 0.706457i | ||||
\(175\) | −10.5902 | + | 7.69421i | −0.800542 | + | 0.581628i | ||||
\(176\) | 2.80902 | + | 1.76336i | 0.211738 | + | 0.132918i | ||||
\(177\) | −9.47214 | − | 6.88191i | −0.711969 | − | 0.517276i | ||||
\(178\) | −2.46149 | + | 7.57570i | −0.184497 | + | 0.567822i | ||||
\(179\) | 8.65248 | 0.646716 | 0.323358 | − | 0.946277i | \(-0.395188\pi\) | ||||
0.323358 | + | 0.946277i | \(0.395188\pi\) | |||||||
\(180\) | 6.70820 | 0.500000 | ||||||||
\(181\) | −3.51722 | − | 10.8249i | −0.261433 | − | 0.804608i | −0.992494 | − | 0.122296i | \(-0.960974\pi\) |
0.731061 | − | 0.682312i | \(-0.239026\pi\) | |||||||
\(182\) | −28.4164 | + | 20.6457i | −2.10636 | + | 1.53036i | ||||
\(183\) | −5.32624 | −0.393727 | ||||||||
\(184\) | −3.78115 | − | 11.6372i | −0.278750 | − | 0.857905i | ||||
\(185\) | 0.791796 | + | 2.43690i | 0.0582140 | + | 0.179164i | ||||
\(186\) | 13.5172 | + | 9.82084i | 0.991131 | + | 0.720099i | ||||
\(187\) | 20.6353 | − | 1.40008i | 1.50900 | − | 0.102384i | ||||
\(188\) | −19.6353 | + | 14.2658i | −1.43205 | + | 1.04044i | ||||
\(189\) | 0.809017 | + | 2.48990i | 0.0588473 | + | 0.181113i | ||||
\(190\) | 26.7705 | − | 19.4499i | 1.94214 | − | 1.41105i | ||||
\(191\) | −11.6353 | − | 8.45351i | −0.841897 | − | 0.611674i | 0.0810026 | − | 0.996714i | \(-0.474188\pi\) |
−0.922900 | + | 0.385040i | \(0.874188\pi\) | |||||||
\(192\) | −4.01722 | − | 12.3637i | −0.289918 | − | 0.892276i | ||||
\(193\) | 2.73607 | − | 1.98787i | 0.196946 | − | 0.143090i | −0.484942 | − | 0.874547i | \(-0.661159\pi\) |
0.681888 | + | 0.731457i | \(0.261159\pi\) | |||||||
\(194\) | −5.65248 | −0.405824 | ||||||||
\(195\) | 10.8541 | + | 7.88597i | 0.777278 | + | 0.564726i | ||||
\(196\) | −0.135255 | + | 0.416272i | −0.00966107 | + | 0.0297337i | ||||
\(197\) | −2.01722 | − | 6.20837i | −0.143721 | − | 0.442328i | 0.853123 | − | 0.521709i | \(-0.174705\pi\) |
−0.996844 | + | 0.0793815i | \(0.974705\pi\) | |||||||
\(198\) | −7.39919 | + | 0.502029i | −0.525837 | + | 0.0356776i | ||||
\(199\) | −13.7984 | −0.978141 | −0.489070 | − | 0.872244i | \(-0.662664\pi\) | ||||
−0.489070 | + | 0.872244i | \(0.662664\pi\) | |||||||
\(200\) | −3.45492 | + | 10.6331i | −0.244299 | + | 0.751876i | ||||
\(201\) | −1.80902 | + | 5.56758i | −0.127598 | + | 0.392707i | ||||
\(202\) | 2.27458 | − | 7.00042i | 0.160039 | − | 0.492548i | ||||
\(203\) | −15.0172 | − | 10.9106i | −1.05400 | − | 0.765777i | ||||
\(204\) | −15.1353 | − | 10.9964i | −1.05968 | − | 0.769902i | ||||
\(205\) | 1.21885 | − | 3.75123i | 0.0851280 | − | 0.261997i | ||||
\(206\) | −15.7533 | − | 11.4454i | −1.09758 | − | 0.797441i | ||||
\(207\) | −4.42705 | − | 3.21644i | −0.307701 | − | 0.223558i | ||||
\(208\) | 1.85410 | − | 5.70634i | 0.128559 | − | 0.395663i | ||||
\(209\) | −16.8435 | + | 14.0741i | −1.16509 | + | 0.973525i | ||||
\(210\) | −13.0902 | −0.903308 | ||||||||
\(211\) | −3.61803 | − | 11.1352i | −0.249076 | − | 0.766576i | −0.994939 | − | 0.100478i | \(-0.967963\pi\) |
0.745864 | − | 0.666099i | \(-0.232037\pi\) | |||||||
\(212\) | −0.927051 | − | 2.85317i | −0.0636701 | − | 0.195956i | ||||
\(213\) | −6.04508 | − | 4.39201i | −0.414202 | − | 0.300936i | ||||
\(214\) | −27.7639 | −1.89790 | ||||||||
\(215\) | −14.3713 | − | 10.4414i | −0.980116 | − | 0.712096i | ||||
\(216\) | 1.80902 | + | 1.31433i | 0.123088 | + | 0.0894287i | ||||
\(217\) | −15.8262 | − | 11.4984i | −1.07436 | − | 0.780565i | ||||
\(218\) | 7.76393 | + | 5.64083i | 0.525840 | + | 0.382045i | ||||
\(219\) | −1.00000 | + | 3.07768i | −0.0675737 | + | 0.207971i | ||||
\(220\) | 5.42705 | − | 21.5765i | 0.365892 | − | 1.45469i | ||||
\(221\) | −11.5623 | − | 35.5851i | −0.777765 | − | 2.39371i | ||||
\(222\) | −0.791796 | + | 2.43690i | −0.0531419 | + | 0.163554i | ||||
\(223\) | −2.92705 | + | 2.12663i | −0.196010 | + | 0.142409i | −0.681461 | − | 0.731854i | \(-0.738655\pi\) |
0.485451 | + | 0.874264i | \(0.338655\pi\) | |||||||
\(224\) | 5.42705 | + | 16.7027i | 0.362610 | + | 1.11600i | ||||
\(225\) | 1.54508 | + | 4.75528i | 0.103006 | + | 0.317019i | ||||
\(226\) | −13.5172 | + | 9.82084i | −0.899152 | + | 0.653272i | ||||
\(227\) | 2.87132 | − | 8.83702i | 0.190576 | − | 0.586534i | −0.809423 | − | 0.587226i | \(-0.800220\pi\) |
1.00000 | 0.000691691i | \(0.000220172\pi\) | ||||||||
\(228\) | 19.8541 | 1.31487 | ||||||||
\(229\) | 5.25329 | − | 16.1680i | 0.347147 | − | 1.06841i | −0.613277 | − | 0.789868i | \(-0.710149\pi\) |
0.960424 | − | 0.278541i | \(-0.0898509\pi\) | |||||||
\(230\) | 22.1353 | − | 16.0822i | 1.45956 | − | 1.06043i | ||||
\(231\) | 8.66312 | − | 0.587785i | 0.569991 | − | 0.0386734i | ||||
\(232\) | −15.8541 | −1.04087 | ||||||||
\(233\) | −19.7082 | + | 14.3188i | −1.29113 | + | 0.938059i | −0.999828 | − | 0.0185729i | \(-0.994088\pi\) |
−0.291300 | + | 0.956632i | \(0.594088\pi\) | |||||||
\(234\) | 4.14590 | + | 12.7598i | 0.271026 | + | 0.834132i | ||||
\(235\) | −14.6353 | − | 10.6331i | −0.954699 | − | 0.693629i | ||||
\(236\) | 35.1246 | 2.28642 | ||||||||
\(237\) | −4.00000 | + | 12.3107i | −0.259828 | + | 0.799668i | ||||
\(238\) | 29.5344 | + | 21.4580i | 1.91443 | + | 1.39092i | ||||
\(239\) | 10.5902 | − | 7.69421i | 0.685021 | − | 0.497697i | −0.189999 | − | 0.981784i | \(-0.560848\pi\) |
0.875020 | + | 0.484087i | \(0.160848\pi\) | |||||||
\(240\) | 1.80902 | − | 1.31433i | 0.116772 | − | 0.0848395i | ||||
\(241\) | −14.4443 | + | 10.4944i | −0.930437 | + | 0.676002i | −0.946100 | − | 0.323875i | \(-0.895014\pi\) |
0.0156625 | + | 0.999877i | \(0.495014\pi\) | |||||||
\(242\) | −4.37132 | + | 24.2052i | −0.280999 | + | 1.55597i | ||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 12.9271 | − | 9.39205i | 0.827570 | − | 0.601265i | ||||
\(245\) | −0.326238 | −0.0208426 | ||||||||
\(246\) | 3.19098 | − | 2.31838i | 0.203450 | − | 0.147815i | ||||
\(247\) | 32.1246 | + | 23.3399i | 2.04404 | + | 1.48508i | ||||
\(248\) | −16.7082 | −1.06097 | ||||||||
\(249\) | −2.64590 | − | 8.14324i | −0.167677 | − | 0.516057i | ||||
\(250\) | −25.0000 | −1.58114 | ||||||||
\(251\) | 0.0278640 | + | 0.0202444i | 0.00175876 | + | 0.00127782i | 0.588664 | − | 0.808378i | \(-0.299654\pi\) |
−0.586906 | + | 0.809655i | \(0.699654\pi\) | |||||||
\(252\) | −6.35410 | − | 4.61653i | −0.400271 | − | 0.290814i | ||||
\(253\) | −13.9271 | + | 11.6372i | −0.875586 | + | 0.731624i | ||||
\(254\) | −4.93769 | − | 15.1967i | −0.309818 | − | 0.953523i | ||||
\(255\) | 4.30902 | − | 13.2618i | 0.269841 | − | 0.830486i | ||||
\(256\) | 7.28115 | + | 5.29007i | 0.455072 | + | 0.330629i | ||||
\(257\) | 5.01722 | + | 15.4414i | 0.312966 | + | 0.963209i | 0.976584 | + | 0.215138i | \(0.0690200\pi\) |
−0.663618 | + | 0.748072i | \(0.730980\pi\) | |||||||
\(258\) | −5.48936 | − | 16.8945i | −0.341752 | − | 1.05181i | ||||
\(259\) | 0.927051 | − | 2.85317i | 0.0576041 | − | 0.177287i | ||||
\(260\) | −40.2492 | −2.49615 | ||||||||
\(261\) | −5.73607 | + | 4.16750i | −0.355054 | + | 0.257962i | ||||
\(262\) | 38.7426 | 2.39353 | ||||||||
\(263\) | 18.7082 | − | 13.5923i | 1.15360 | − | 0.838137i | 0.164642 | − | 0.986353i | \(-0.447353\pi\) |
0.988955 | + | 0.148216i | \(0.0473530\pi\) | |||||||
\(264\) | 5.69098 | − | 4.75528i | 0.350256 | − | 0.292667i | ||||
\(265\) | 1.80902 | − | 1.31433i | 0.111127 | − | 0.0807385i | ||||
\(266\) | −38.7426 | −2.37546 | ||||||||
\(267\) | −2.88197 | − | 2.09387i | −0.176373 | − | 0.128143i | ||||
\(268\) | −5.42705 | − | 16.7027i | −0.331510 | − | 1.02028i | ||||
\(269\) | −5.45492 | − | 16.7885i | −0.332592 | − | 1.02361i | −0.967896 | − | 0.251351i | \(-0.919125\pi\) |
0.635304 | − | 0.772262i | \(-0.280875\pi\) | |||||||
\(270\) | −1.54508 | + | 4.75528i | −0.0940309 | + | 0.289397i | ||||
\(271\) | −3.07295 | + | 2.23263i | −0.186668 | + | 0.135623i | −0.677195 | − | 0.735804i | \(-0.736805\pi\) |
0.490526 | + | 0.871426i | \(0.336805\pi\) | |||||||
\(272\) | −6.23607 | −0.378117 | ||||||||
\(273\) | −4.85410 | − | 14.9394i | −0.293784 | − | 0.904173i | ||||
\(274\) | −48.5410 | −2.93247 | ||||||||
\(275\) | 16.5451 | − | 1.12257i | 0.997706 | − | 0.0676935i | ||||
\(276\) | 16.4164 | 0.988152 | ||||||||
\(277\) | 6.37132 | + | 19.6089i | 0.382816 | + | 1.17819i | 0.938052 | + | 0.346493i | \(0.112628\pi\) |
−0.555237 | + | 0.831692i | \(0.687372\pi\) | |||||||
\(278\) | −11.5066 | −0.690119 | ||||||||
\(279\) | −6.04508 | + | 4.39201i | −0.361910 | + | 0.262943i | ||||
\(280\) | 10.5902 | − | 7.69421i | 0.632884 | − | 0.459817i | ||||
\(281\) | 4.39919 | + | 13.5393i | 0.262433 | + | 0.807687i | 0.992274 | + | 0.124069i | \(0.0395945\pi\) |
−0.729840 | + | 0.683618i | \(0.760405\pi\) | |||||||
\(282\) | −5.59017 | − | 17.2048i | −0.332890 | − | 1.02453i | ||||
\(283\) | 15.2812 | + | 11.1024i | 0.908370 | + | 0.659970i | 0.940602 | − | 0.339511i | \(-0.110262\pi\) |
−0.0322319 | + | 0.999480i | \(0.510262\pi\) | |||||||
\(284\) | 22.4164 | 1.33017 | ||||||||
\(285\) | 4.57295 | + | 14.0741i | 0.270878 | + | 0.833677i | ||||
\(286\) | 44.3951 | − | 3.01217i | 2.62514 | − | 0.178113i | ||||
\(287\) | −3.73607 | + | 2.71441i | −0.220533 | + | 0.160227i | ||||
\(288\) | 6.70820 | 0.395285 | ||||||||
\(289\) | −17.7082 | + | 12.8658i | −1.04166 | + | 0.756810i | ||||
\(290\) | −10.9549 | − | 33.7158i | −0.643295 | − | 1.97986i | ||||
\(291\) | 0.781153 | − | 2.40414i | 0.0457920 | − | 0.140933i | ||||
\(292\) | −3.00000 | − | 9.23305i | −0.175562 | − | 0.540323i | ||||
\(293\) | −9.03444 | − | 27.8052i | −0.527798 | − | 1.62439i | −0.758716 | − | 0.651421i | \(-0.774173\pi\) |
0.230918 | − | 0.972973i | \(-0.425827\pi\) | |||||||
\(294\) | −0.263932 | − | 0.191758i | −0.0153928 | − | 0.0111835i | ||||
\(295\) | 8.09017 | + | 24.8990i | 0.471028 | + | 1.44967i | ||||
\(296\) | −0.791796 | − | 2.43690i | −0.0460222 | − | 0.141642i | ||||
\(297\) | 0.809017 | − | 3.21644i | 0.0469439 | − | 0.186637i | ||||
\(298\) | −1.21885 | − | 0.885544i | −0.0706059 | − | 0.0512982i | ||||
\(299\) | 26.5623 | + | 19.2986i | 1.53614 | + | 1.11607i | ||||
\(300\) | −12.1353 | − | 8.81678i | −0.700629 | − | 0.509037i | ||||
\(301\) | 6.42705 | + | 19.7804i | 0.370449 | + | 1.14012i | ||||
\(302\) | −3.61803 | −0.208194 | ||||||||
\(303\) | 2.66312 | + | 1.93487i | 0.152992 | + | 0.111155i | ||||
\(304\) | 5.35410 | − | 3.88998i | 0.307079 | − | 0.223106i | ||||
\(305\) | 9.63525 | + | 7.00042i | 0.551713 | + | 0.400843i | ||||
\(306\) | 11.2812 | − | 8.19624i | 0.644901 | − | 0.468548i | ||||
\(307\) | 1.58359 | 0.0903804 | 0.0451902 | − | 0.998978i | \(-0.485611\pi\) | ||||
0.0451902 | + | 0.998978i | \(0.485611\pi\) | |||||||
\(308\) | −19.9894 | + | 16.7027i | −1.13900 | + | 0.951727i | ||||
\(309\) | 7.04508 | − | 5.11855i | 0.400781 | − | 0.291184i | ||||
\(310\) | −11.5451 | − | 35.5321i | −0.655717 | − | 2.01809i | ||||
\(311\) | 22.3713 | − | 16.2537i | 1.26856 | − | 0.921664i | 0.269417 | − | 0.963024i | \(-0.413169\pi\) |
0.999144 | + | 0.0413598i | \(0.0131690\pi\) | |||||||
\(312\) | −10.8541 | − | 7.88597i | −0.614493 | − | 0.446455i | ||||
\(313\) | −8.16312 | + | 25.1235i | −0.461407 | + | 1.42006i | 0.402039 | + | 0.915622i | \(0.368302\pi\) |
−0.863446 | + | 0.504442i | \(0.831698\pi\) | |||||||
\(314\) | 19.4721 | 1.09888 | ||||||||
\(315\) | 1.80902 | − | 5.56758i | 0.101927 | − | 0.313698i | ||||
\(316\) | −12.0000 | − | 36.9322i | −0.675053 | − | 2.07760i | ||||
\(317\) | 8.09017 | − | 5.87785i | 0.454389 | − | 0.330133i | −0.336937 | − | 0.941527i | \(-0.609391\pi\) |
0.791326 | + | 0.611394i | \(0.209391\pi\) | |||||||
\(318\) | 2.23607 | 0.125392 | ||||||||
\(319\) | 8.76393 | + | 21.8213i | 0.490686 | + | 1.22176i | ||||
\(320\) | −8.98278 | + | 27.6462i | −0.502153 | + | 1.54547i | ||||
\(321\) | 3.83688 | − | 11.8087i | 0.214154 | − | 0.659098i | ||||
\(322\) | −32.0344 | −1.78521 | ||||||||
\(323\) | 12.7533 | − | 39.2506i | 0.709612 | − | 2.18396i | ||||
\(324\) | −2.42705 | + | 1.76336i | −0.134836 | + | 0.0979642i | ||||
\(325\) | −9.27051 | − | 28.5317i | −0.514235 | − | 1.58265i | ||||
\(326\) | 8.98278 | + | 27.6462i | 0.497510 | + | 1.53118i | ||||
\(327\) | −3.47214 | + | 2.52265i | −0.192010 | + | 0.139503i | ||||
\(328\) | −1.21885 | + | 3.75123i | −0.0672996 | + | 0.207127i | ||||
\(329\) | 6.54508 | + | 20.1437i | 0.360842 | + | 1.11056i | ||||
\(330\) | 14.0451 | + | 8.81678i | 0.773156 | + | 0.485348i | ||||
\(331\) | 2.18034 | − | 6.71040i | 0.119842 | − | 0.368837i | −0.873084 | − | 0.487570i | \(-0.837883\pi\) |
0.992926 | + | 0.118733i | \(0.0378834\pi\) | |||||||
\(332\) | 20.7812 | + | 15.0984i | 1.14051 | + | 0.828632i | ||||
\(333\) | −0.927051 | − | 0.673542i | −0.0508021 | − | 0.0369099i | ||||
\(334\) | 45.8156 | + | 33.2870i | 2.50692 | + | 1.82138i | ||||
\(335\) | 10.5902 | − | 7.69421i | 0.578603 | − | 0.420380i | ||||
\(336\) | −2.61803 | −0.142825 | ||||||||
\(337\) | −9.80902 | − | 7.12667i | −0.534331 | − | 0.388214i | 0.287644 | − | 0.957737i | \(-0.407128\pi\) |
−0.821975 | + | 0.569523i | \(0.807128\pi\) | |||||||
\(338\) | −15.8926 | − | 48.9124i | −0.864444 | − | 2.66048i | ||||
\(339\) | −2.30902 | − | 7.10642i | −0.125409 | − | 0.385968i | ||||
\(340\) | 12.9271 | + | 39.7854i | 0.701068 | + | 2.15766i | ||||
\(341\) | 9.23607 | + | 22.9969i | 0.500161 | + | 1.24535i | ||||
\(342\) | −4.57295 | + | 14.0741i | −0.247277 | + | 0.761040i | ||||
\(343\) | 15.1353 | + | 10.9964i | 0.817227 | + | 0.593750i | ||||
\(344\) | 14.3713 | + | 10.4414i | 0.774850 | + | 0.562961i | ||||
\(345\) | 3.78115 | + | 11.6372i | 0.203570 | + | 0.626525i | ||||
\(346\) | 36.6697 | + | 26.6421i | 1.97138 | + | 1.43229i | ||||
\(347\) | −14.5172 | − | 10.5474i | −0.779325 | − | 0.566213i | 0.125451 | − | 0.992100i | \(-0.459962\pi\) |
−0.904776 | + | 0.425887i | \(0.859962\pi\) | |||||||
\(348\) | 6.57295 | − | 20.2295i | 0.352347 | − | 1.08441i | ||||
\(349\) | −0.100813 | + | 0.310271i | −0.00539640 | + | 0.0166084i | −0.953718 | − | 0.300701i | \(-0.902779\pi\) |
0.948322 | + | 0.317309i | \(0.102779\pi\) | |||||||
\(350\) | 23.6803 | + | 17.2048i | 1.26577 | + | 0.919634i | ||||
\(351\) | −6.00000 | −0.320256 | ||||||||
\(352\) | 5.42705 | − | 21.5765i | 0.289263 | − | 1.15003i | ||||
\(353\) | 4.50000 | + | 13.8496i | 0.239511 | + | 0.737139i | 0.996491 | + | 0.0837006i | \(0.0266739\pi\) |
−0.756980 | + | 0.653438i | \(0.773326\pi\) | |||||||
\(354\) | −8.09017 | + | 24.8990i | −0.429988 | + | 1.32337i | ||||
\(355\) | 5.16312 | + | 15.8904i | 0.274030 | + | 0.843377i | ||||
\(356\) | 10.6869 | 0.566406 | ||||||||
\(357\) | −13.2082 | + | 9.59632i | −0.699052 | + | 0.507891i | ||||
\(358\) | −5.97871 | − | 18.4006i | −0.315985 | − | 0.972501i | ||||
\(359\) | 8.56231 | + | 6.22088i | 0.451901 | + | 0.328325i | 0.790346 | − | 0.612661i | \(-0.209901\pi\) |
−0.338445 | + | 0.940986i | \(0.609901\pi\) | |||||||
\(360\) | −1.54508 | − | 4.75528i | −0.0814331 | − | 0.250625i | ||||
\(361\) | 7.66312 | + | 23.5847i | 0.403322 | + | 1.24130i | ||||
\(362\) | −20.5902 | + | 14.9596i | −1.08220 | + | 0.786261i | ||||
\(363\) | −9.69098 | − | 5.20431i | −0.508645 | − | 0.273155i | ||||
\(364\) | 38.1246 | + | 27.6992i | 1.99827 | + | 1.45183i | ||||
\(365\) | 5.85410 | − | 4.25325i | 0.306418 | − | 0.222625i | ||||
\(366\) | 3.68034 | + | 11.3269i | 0.192374 | + | 0.592068i | ||||
\(367\) | −10.7426 | −0.560762 | −0.280381 | − | 0.959889i | \(-0.590461\pi\) | ||||
−0.280381 | + | 0.959889i | \(0.590461\pi\) | |||||||
\(368\) | 4.42705 | − | 3.21644i | 0.230776 | − | 0.167669i | ||||
\(369\) | 0.545085 | + | 1.67760i | 0.0283760 | + | 0.0873323i | ||||
\(370\) | 4.63525 | − | 3.36771i | 0.240975 | − | 0.175079i | ||||
\(371\) | −2.61803 | −0.135922 | ||||||||
\(372\) | 6.92705 | − | 21.3193i | 0.359151 | − | 1.10535i | ||||
\(373\) | 3.20820 | + | 2.33090i | 0.166115 | + | 0.120689i | 0.667737 | − | 0.744398i | \(-0.267263\pi\) |
−0.501622 | + | 0.865087i | \(0.667263\pi\) | |||||||
\(374\) | −17.2361 | − | 42.9161i | −0.891256 | − | 2.21914i | ||||
\(375\) | 3.45492 | − | 10.6331i | 0.178411 | − | 0.549093i | ||||
\(376\) | 14.6353 | + | 10.6331i | 0.754756 | + | 0.548362i | ||||
\(377\) | 34.4164 | − | 25.0050i | 1.77254 | − | 1.28782i | ||||
\(378\) | 4.73607 | − | 3.44095i | 0.243597 | − | 0.176984i | ||||
\(379\) | −21.7254 | − | 15.7844i | −1.11596 | − | 0.810792i | −0.132368 | − | 0.991201i | \(-0.542258\pi\) |
−0.983592 | + | 0.180408i | \(0.942258\pi\) | |||||||
\(380\) | −35.9164 | − | 26.0948i | −1.84247 | − | 1.33863i | ||||
\(381\) | 7.14590 | 0.366095 | ||||||||
\(382\) | −9.93769 | + | 30.5851i | −0.508457 | + | 1.56487i | ||||
\(383\) | 16.2361 | − | 11.7962i | 0.829624 | − | 0.602757i | −0.0898287 | − | 0.995957i | \(-0.528632\pi\) |
0.919453 | + | 0.393200i | \(0.128632\pi\) | |||||||
\(384\) | −12.6631 | + | 9.20029i | −0.646212 | + | 0.469501i | ||||
\(385\) | −16.4443 | − | 10.3229i | −0.838078 | − | 0.526102i | ||||
\(386\) | −6.11803 | − | 4.44501i | −0.311400 | − | 0.226245i | ||||
\(387\) | 7.94427 | 0.403830 | ||||||||
\(388\) | 2.34346 | + | 7.21242i | 0.118971 | + | 0.366155i | ||||
\(389\) | 1.48278 | − | 4.56352i | 0.0751799 | − | 0.231380i | −0.906404 | − | 0.422412i | \(-0.861184\pi\) |
0.981584 | + | 0.191032i | \(0.0611835\pi\) | |||||||
\(390\) | 9.27051 | − | 28.5317i | 0.469431 | − | 1.44476i | ||||
\(391\) | 10.5451 | − | 32.4544i | 0.533288 | − | 1.64129i | ||||
\(392\) | 0.326238 | 0.0164775 | ||||||||
\(393\) | −5.35410 | + | 16.4782i | −0.270079 | + | 0.831217i | ||||
\(394\) | −11.8090 | + | 8.57975i | −0.594930 | + | 0.432242i | ||||
\(395\) | 23.4164 | − | 17.0130i | 1.17821 | − | 0.856018i | ||||
\(396\) | 3.70820 | + | 9.23305i | 0.186344 | + | 0.463978i | ||||
\(397\) | 6.60739 | + | 20.3355i | 0.331615 | + | 1.02061i | 0.968365 | + | 0.249537i | \(0.0802784\pi\) |
−0.636750 | + | 0.771070i | \(0.719722\pi\) | |||||||
\(398\) | 9.53444 | + | 29.3440i | 0.477918 | + | 1.47088i | ||||
\(399\) | 5.35410 | − | 16.4782i | 0.268040 | − | 0.824943i | ||||
\(400\) | −5.00000 | −0.250000 | ||||||||
\(401\) | 13.2812 | − | 9.64932i | 0.663229 | − | 0.481864i | −0.204523 | − | 0.978862i | \(-0.565564\pi\) |
0.867752 | + | 0.496998i | \(0.165564\pi\) | |||||||
\(402\) | 13.0902 | 0.652878 | ||||||||
\(403\) | 36.2705 | − | 26.3521i | 1.80676 | − | 1.31269i | ||||
\(404\) | −9.87539 | −0.491319 | ||||||||
\(405\) | −1.80902 | − | 1.31433i | −0.0898908 | − | 0.0653095i | ||||
\(406\) | −12.8262 | + | 39.4751i | −0.636555 | + | 1.95912i | ||||
\(407\) | −2.91641 | + | 2.43690i | −0.144561 | + | 0.120793i | ||||
\(408\) | −4.30902 | + | 13.2618i | −0.213328 | + | 0.656556i | ||||
\(409\) | −1.94427 | −0.0961381 | −0.0480690 | − | 0.998844i | \(-0.515307\pi\) | ||||
−0.0480690 | + | 0.998844i | \(0.515307\pi\) | |||||||
\(410\) | −8.81966 | −0.435572 | ||||||||
\(411\) | 6.70820 | − | 20.6457i | 0.330891 | − | 1.01838i | ||||
\(412\) | −8.07295 | + | 24.8460i | −0.397726 | + | 1.22407i | ||||
\(413\) | 9.47214 | − | 29.1522i | 0.466093 | − | 1.43449i | ||||
\(414\) | −3.78115 | + | 11.6372i | −0.185834 | + | 0.571937i | ||||
\(415\) | −5.91641 | + | 18.2088i | −0.290425 | + | 0.893836i | ||||
\(416\) | −40.2492 | −1.97338 | ||||||||
\(417\) | 1.59017 | − | 4.89404i | 0.0778710 | − | 0.239662i | ||||
\(418\) | 41.5689 | + | 26.0948i | 2.03320 | + | 1.27634i | ||||
\(419\) | −7.05573 | + | 21.7153i | −0.344695 | + | 1.06086i | 0.617052 | + | 0.786922i | \(0.288327\pi\) |
−0.961747 | + | 0.273939i | \(0.911673\pi\) | |||||||
\(420\) | 5.42705 | + | 16.7027i | 0.264813 | + | 0.815011i | ||||
\(421\) | 25.9787 | 1.26613 | 0.633063 | − | 0.774101i | \(-0.281798\pi\) | ||||
0.633063 | + | 0.774101i | \(0.281798\pi\) | |||||||
\(422\) | −21.1803 | + | 15.3884i | −1.03104 | + | 0.749096i | ||||
\(423\) | 8.09017 | 0.393358 | ||||||||
\(424\) | −1.80902 | + | 1.31433i | −0.0878536 | + | 0.0638294i | ||||
\(425\) | −25.2254 | + | 18.3273i | −1.22361 | + | 0.889007i | ||||
\(426\) | −5.16312 | + | 15.8904i | −0.250154 | + | 0.769895i | ||||
\(427\) | −4.30902 | − | 13.2618i | −0.208528 | − | 0.641783i | ||||
\(428\) | 11.5106 | + | 35.4261i | 0.556388 | + | 1.71239i | ||||
\(429\) | −4.85410 | + | 19.2986i | −0.234358 | + | 0.931747i | ||||
\(430\) | −12.2746 | + | 37.7773i | −0.591933 | + | 1.82178i | ||||
\(431\) | −4.04508 | + | 2.93893i | −0.194845 | + | 0.141563i | −0.680930 | − | 0.732348i | \(-0.738424\pi\) |
0.486085 | + | 0.873911i | \(0.338424\pi\) | |||||||
\(432\) | −0.309017 | + | 0.951057i | −0.0148676 | + | 0.0457577i | ||||
\(433\) | 24.9443 | 1.19875 | 0.599373 | − | 0.800470i | \(-0.295417\pi\) | ||||
0.599373 | + | 0.800470i | \(0.295417\pi\) | |||||||
\(434\) | −13.5172 | + | 41.6017i | −0.648847 | + | 1.99695i | ||||
\(435\) | 15.8541 | 0.760146 | ||||||||
\(436\) | 3.97871 | − | 12.2452i | 0.190546 | − | 0.586440i | ||||
\(437\) | 11.1910 | + | 34.4423i | 0.535337 | + | 1.64760i | ||||
\(438\) | 7.23607 | 0.345753 | ||||||||
\(439\) | 3.88197 | + | 2.82041i | 0.185276 | + | 0.134611i | 0.676557 | − | 0.736390i | \(-0.263471\pi\) |
−0.491281 | + | 0.871001i | \(0.663471\pi\) | |||||||
\(440\) | −16.5451 | + | 1.12257i | −0.788756 | + | 0.0535164i | ||||
\(441\) | 0.118034 | − | 0.0857567i | 0.00562067 | − | 0.00408365i | ||||
\(442\) | −67.6869 | + | 49.1774i | −3.21954 | + | 2.33913i | ||||
\(443\) | −11.8713 | + | 36.5362i | −0.564024 | + | 1.73589i | 0.106811 | + | 0.994279i | \(0.465936\pi\) |
−0.670835 | + | 0.741607i | \(0.734064\pi\) | |||||||
\(444\) | 3.43769 | 0.163146 | ||||||||
\(445\) | 2.46149 | + | 7.57570i | 0.116686 | + | 0.359122i | ||||
\(446\) | 6.54508 | + | 4.75528i | 0.309919 | + | 0.225169i | ||||
\(447\) | 0.545085 | − | 0.396027i | 0.0257816 | − | 0.0187315i | ||||
\(448\) | 27.5344 | − | 20.0049i | 1.30088 | − | 0.945145i | ||||
\(449\) | −9.78115 | − | 7.10642i | −0.461601 | − | 0.335373i | 0.332558 | − | 0.943083i | \(-0.392088\pi\) |
−0.794159 | + | 0.607710i | \(0.792088\pi\) | |||||||
\(450\) | 9.04508 | − | 6.57164i | 0.426389 | − | 0.309790i | ||||
\(451\) | 5.83688 | − | 0.396027i | 0.274848 | − | 0.0186482i | ||||
\(452\) | 18.1353 | + | 13.1760i | 0.853011 | + | 0.619749i | ||||
\(453\) | 0.500000 | − | 1.53884i | 0.0234920 | − | 0.0723011i | ||||
\(454\) | −20.7771 | −0.975117 | ||||||||
\(455\) | −10.8541 | + | 33.4055i | −0.508848 | + | 1.56607i | ||||
\(456\) | −4.57295 | − | 14.0741i | −0.214148 | − | 0.659080i | ||||
\(457\) | −7.94427 | + | 5.77185i | −0.371617 | + | 0.269996i | −0.757881 | − | 0.652392i | \(-0.773765\pi\) |
0.386264 | + | 0.922388i | \(0.373765\pi\) | |||||||
\(458\) | −38.0132 | −1.77624 | ||||||||
\(459\) | 1.92705 | + | 5.93085i | 0.0899470 | + | 0.276829i | ||||
\(460\) | −29.6976 | − | 21.5765i | −1.38466 | − | 1.00601i | ||||
\(461\) | −25.8713 | − | 18.7966i | −1.20495 | − | 0.875446i | −0.210185 | − | 0.977662i | \(-0.567407\pi\) |
−0.994762 | + | 0.102216i | \(0.967407\pi\) | |||||||
\(462\) | −7.23607 | − | 18.0171i | −0.336652 | − | 0.838230i | ||||
\(463\) | 27.6074 | − | 20.0579i | 1.28302 | − | 0.932172i | 0.283384 | − | 0.959006i | \(-0.408543\pi\) |
0.999640 | + | 0.0268347i | \(0.00854278\pi\) | |||||||
\(464\) | −2.19098 | − | 6.74315i | −0.101714 | − | 0.313043i | ||||
\(465\) | 16.7082 | 0.774824 | ||||||||
\(466\) | 44.0689 | + | 32.0179i | 2.04145 | + | 1.48320i | ||||
\(467\) | −4.80902 | − | 14.8006i | −0.222535 | − | 0.684892i | −0.998532 | − | 0.0541559i | \(-0.982753\pi\) |
0.775998 | − | 0.630736i | \(-0.217247\pi\) | |||||||
\(468\) | 14.5623 | − | 10.5801i | 0.673143 | − | 0.489067i | ||||
\(469\) | −15.3262 | −0.707700 | ||||||||
\(470\) | −12.5000 | + | 38.4710i | −0.576582 | + | 1.77454i | ||||
\(471\) | −2.69098 | + | 8.28199i | −0.123994 | + | 0.381614i | ||||
\(472\) | −8.09017 | − | 24.8990i | −0.372380 | − | 1.14607i | ||||
\(473\) | 6.42705 | − | 25.5523i | 0.295516 | − | 1.17490i | ||||
\(474\) | 28.9443 | 1.32945 | ||||||||
\(475\) | 10.2254 | − | 31.4706i | 0.469175 | − | 1.44397i | ||||
\(476\) | 15.1353 | − | 46.5815i | 0.693723 | − | 2.13506i | ||||
\(477\) | −0.309017 | + | 0.951057i | −0.0141489 | + | 0.0435459i | ||||
\(478\) | −23.6803 | − | 17.2048i | −1.08311 | − | 0.786928i | ||||
\(479\) | −11.4271 | − | 8.30224i | −0.522115 | − | 0.379339i | 0.295285 | − | 0.955409i | \(-0.404585\pi\) |
−0.817400 | + | 0.576070i | \(0.804585\pi\) | |||||||
\(480\) | −12.1353 | − | 8.81678i | −0.553896 | − | 0.402429i | ||||
\(481\) | 5.56231 | + | 4.04125i | 0.253619 | + | 0.184265i | ||||
\(482\) | 32.2984 | + | 23.4661i | 1.47115 | + | 1.06885i | ||||
\(483\) | 4.42705 | − | 13.6251i | 0.201438 | − | 0.619962i | ||||
\(484\) | 32.6976 | − | 4.45752i | 1.48625 | − | 0.202615i | ||||
\(485\) | −4.57295 | + | 3.32244i | −0.207647 | + | 0.150864i | ||||
\(486\) | −0.690983 | − | 2.12663i | −0.0313436 | − | 0.0964658i | ||||
\(487\) | 4.66312 | + | 14.3516i | 0.211306 | + | 0.650333i | 0.999395 | + | 0.0347722i | \(0.0110706\pi\) |
−0.788089 | + | 0.615561i | \(0.788929\pi\) | |||||||
\(488\) | −9.63525 | − | 7.00042i | −0.436167 | − | 0.316894i | ||||
\(489\) | −13.0000 | −0.587880 | ||||||||
\(490\) | 0.225425 | + | 0.693786i | 0.0101837 | + | 0.0313421i | ||||
\(491\) | 20.6631 | + | 15.0126i | 0.932514 | + | 0.677511i | 0.946607 | − | 0.322390i | \(-0.104486\pi\) |
−0.0140934 | + | 0.999901i | \(0.504486\pi\) | |||||||
\(492\) | −4.28115 | − | 3.11044i | −0.193009 | − | 0.140229i | ||||
\(493\) | −35.7705 | − | 25.9888i | −1.61102 | − | 1.17048i | ||||
\(494\) | 27.4377 | − | 84.4445i | 1.23448 | − | 3.79934i | ||||
\(495\) | −5.69098 | + | 4.75528i | −0.255791 | + | 0.213734i | ||||
\(496\) | −2.30902 | − | 7.10642i | −0.103678 | − | 0.319088i | ||||
\(497\) | 6.04508 | − | 18.6049i | 0.271159 | − | 0.834542i | ||||
\(498\) | −15.4894 | + | 11.2537i | −0.694095 | + | 0.504289i | ||||
\(499\) | −2.83688 | − | 8.73102i | −0.126996 | − | 0.390854i | 0.867263 | − | 0.497850i | \(-0.165877\pi\) |
−0.994259 | + | 0.106996i | \(0.965877\pi\) | |||||||
\(500\) | 10.3647 | + | 31.8994i | 0.463525 | + | 1.42658i | ||||
\(501\) | −20.4894 | + | 14.8864i | −0.915397 | + | 0.665075i | ||||
\(502\) | 0.0237987 | − | 0.0732450i | 0.00106219 | − | 0.00326908i | ||||
\(503\) | 6.00000 | 0.267527 | 0.133763 | − | 0.991013i | \(-0.457294\pi\) | ||||
0.133763 | + | 0.991013i | \(0.457294\pi\) | |||||||
\(504\) | −1.80902 | + | 5.56758i | −0.0805800 | + | 0.248000i | ||||
\(505\) | −2.27458 | − | 7.00042i | −0.101217 | − | 0.311515i | ||||
\(506\) | 34.3713 | + | 21.5765i | 1.52799 | + | 0.959194i | ||||
\(507\) | 23.0000 | 1.02147 | ||||||||
\(508\) | −17.3435 | + | 12.6008i | −0.769492 | + | 0.559068i | ||||
\(509\) | 2.90983 | + | 8.95554i | 0.128976 | + | 0.396947i | 0.994604 | − | 0.103740i | \(-0.0330809\pi\) |
−0.865629 | + | 0.500687i | \(0.833081\pi\) | |||||||
\(510\) | −31.1803 | −1.38069 | ||||||||
\(511\) | −8.47214 | −0.374785 | ||||||||
\(512\) | −3.45492 | + | 10.6331i | −0.152687 | + | 0.469923i | ||||
\(513\) | −5.35410 | − | 3.88998i | −0.236389 | − | 0.171747i | ||||
\(514\) | 29.3713 | − | 21.3395i | 1.29551 | − | 0.941246i | ||||
\(515\) | −19.4721 | −0.858045 | ||||||||
\(516\) | −19.2812 | + | 14.0086i | −0.848805 | + | 0.616693i | ||||
\(517\) | 6.54508 | − | 26.0216i | 0.287853 | − | 1.14443i | ||||
\(518\) | −6.70820 | −0.294742 | ||||||||
\(519\) | −16.3992 | + | 11.9147i | −0.719844 | + | 0.522998i | ||||
\(520\) | 9.27051 | + | 28.5317i | 0.406539 | + | 1.25120i | ||||
\(521\) | 5.23607 | − | 3.80423i | 0.229396 | − | 0.166666i | −0.467150 | − | 0.884178i | \(-0.654719\pi\) |
0.696546 | + | 0.717512i | \(0.254719\pi\) | |||||||
\(522\) | 12.8262 | + | 9.31881i | 0.561389 | + | 0.407873i | ||||
\(523\) | 31.7984 | 1.39045 | 0.695223 | − | 0.718794i | \(-0.255306\pi\) | ||||
0.695223 | + | 0.718794i | \(0.255306\pi\) | |||||||
\(524\) | −16.0623 | − | 49.4347i | −0.701685 | − | 2.15956i | ||||
\(525\) | −10.5902 | + | 7.69421i | −0.462193 | + | 0.335803i | ||||
\(526\) | −41.8328 | − | 30.3933i | −1.82400 | − | 1.32521i | ||||
\(527\) | −37.6976 | − | 27.3889i | −1.64213 | − | 1.19308i | ||||
\(528\) | 2.80902 | + | 1.76336i | 0.122247 | + | 0.0767402i | ||||
\(529\) | 2.14590 | + | 6.60440i | 0.0932999 | + | 0.287148i | ||||
\(530\) | −4.04508 | − | 2.93893i | −0.175707 | − | 0.127659i | ||||
\(531\) | −9.47214 | − | 6.88191i | −0.411056 | − | 0.298649i | ||||
\(532\) | 16.0623 | + | 49.4347i | 0.696389 | + | 2.14327i | ||||
\(533\) | −3.27051 | − | 10.0656i | −0.141662 | − | 0.435989i | ||||
\(534\) | −2.46149 | + | 7.57570i | −0.106519 | + | 0.327832i | ||||
\(535\) | −22.4615 | + | 16.3192i | −0.971095 | + | 0.705542i | ||||
\(536\) | −10.5902 | + | 7.69421i | −0.457426 | + | 0.332339i | ||||
\(537\) | 8.65248 | 0.373382 | ||||||||
\(538\) | −31.9336 | + | 23.2011i | −1.37676 | + | 1.00027i | ||||
\(539\) | −0.180340 | − | 0.449028i | −0.00776779 | − | 0.0193410i | ||||
\(540\) | 6.70820 | 0.288675 | ||||||||
\(541\) | −2.00000 | −0.0859867 | −0.0429934 | − | 0.999075i | \(-0.513689\pi\) | ||||
−0.0429934 | + | 0.999075i | \(0.513689\pi\) | |||||||
\(542\) | 6.87132 | + | 4.99231i | 0.295149 | + | 0.214438i | ||||
\(543\) | −3.51722 | − | 10.8249i | −0.150938 | − | 0.464541i | ||||
\(544\) | 12.9271 | + | 39.7854i | 0.554243 | + | 1.70578i | ||||
\(545\) | 9.59675 | 0.411080 | ||||||||
\(546\) | −28.4164 | + | 20.6457i | −1.21611 | + | 0.883556i | ||||
\(547\) | 39.7639 | 1.70018 | 0.850091 | − | 0.526635i | \(-0.176547\pi\) | ||||
0.850091 | + | 0.526635i | \(0.176547\pi\) | |||||||
\(548\) | 20.1246 | + | 61.9372i | 0.859681 | + | 2.64583i | ||||
\(549\) | −5.32624 | −0.227318 | ||||||||
\(550\) | −13.8197 | − | 34.4095i | −0.589272 | − | 1.46723i | ||||
\(551\) | 46.9230 | 1.99899 | ||||||||
\(552\) | −3.78115 | − | 11.6372i | −0.160937 | − | 0.495312i | ||||
\(553\) | −33.8885 | −1.44109 | ||||||||
\(554\) | 37.2984 | − | 27.0989i | 1.58466 | − | 1.15132i | ||||
\(555\) | 0.791796 | + | 2.43690i | 0.0336099 | + | 0.103441i | ||||
\(556\) | 4.77051 | + | 14.6821i | 0.202315 | + | 0.622661i | ||||
\(557\) | 13.2254 | + | 40.7037i | 0.560379 | + | 1.72467i | 0.681297 | + | 0.732007i | \(0.261416\pi\) |
−0.120917 | + | 0.992663i | \(0.538584\pi\) | |||||||
\(558\) | 13.5172 | + | 9.82084i | 0.572230 | + | 0.415749i | ||||
\(559\) | −47.6656 | −2.01604 | ||||||||
\(560\) | 4.73607 | + | 3.44095i | 0.200135 | + | 0.145407i | ||||
\(561\) | 20.6353 | − | 1.40008i | 0.871221 | − | 0.0591116i | ||||
\(562\) | 25.7533 | − | 18.7109i | 1.08634 | − | 0.789270i | ||||
\(563\) | −22.4377 | −0.945636 | −0.472818 | − | 0.881160i | \(-0.656763\pi\) | ||||
−0.472818 | + | 0.881160i | \(0.656763\pi\) | |||||||
\(564\) | −19.6353 | + | 14.2658i | −0.826793 | + | 0.600701i | ||||
\(565\) | −5.16312 | + | 15.8904i | −0.217214 | + | 0.668516i | ||||
\(566\) | 13.0517 | − | 40.1689i | 0.548602 | − | 1.68842i | ||||
\(567\) | 0.809017 | + | 2.48990i | 0.0339755 | + | 0.104566i | ||||
\(568\) | −5.16312 | − | 15.8904i | −0.216640 | − | 0.666748i | ||||
\(569\) | −7.07295 | − | 5.13880i | −0.296513 | − | 0.215430i | 0.429575 | − | 0.903031i | \(-0.358664\pi\) |
−0.726088 | + | 0.687602i | \(0.758664\pi\) | |||||||
\(570\) | 26.7705 | − | 19.4499i | 1.12129 | − | 0.814667i | ||||
\(571\) | 6.13525 | + | 18.8824i | 0.256752 | + | 0.790203i | 0.993479 | + | 0.114012i | \(0.0363703\pi\) |
−0.736727 | + | 0.676190i | \(0.763630\pi\) | |||||||
\(572\) | −22.2492 | − | 55.3983i | −0.930287 | − | 2.31632i | ||||
\(573\) | −11.6353 | − | 8.45351i | −0.486070 | − | 0.353150i | ||||
\(574\) | 8.35410 | + | 6.06961i | 0.348693 | + | 0.253341i | ||||
\(575\) | 8.45492 | − | 26.0216i | 0.352594 | − | 1.08517i | ||||
\(576\) | −4.01722 | − | 12.3637i | −0.167384 | − | 0.515156i | ||||
\(577\) | −8.76393 | −0.364847 | −0.182424 | − | 0.983220i | \(-0.558394\pi\) | ||||
−0.182424 | + | 0.983220i | \(0.558394\pi\) | |||||||
\(578\) | 39.5967 | + | 28.7687i | 1.64701 | + | 1.19662i | ||||
\(579\) | 2.73607 | − | 1.98787i | 0.113707 | − | 0.0826130i | ||||
\(580\) | −38.4787 | + | 27.9564i | −1.59774 | + | 1.16083i | ||||
\(581\) | 18.1353 | − | 13.1760i | 0.752377 | − | 0.546634i | ||||
\(582\) | −5.65248 | −0.234303 | ||||||||
\(583\) | 2.80902 | + | 1.76336i | 0.116338 | + | 0.0730307i | ||||
\(584\) | −5.85410 | + | 4.25325i | −0.242244 | + | 0.176001i | ||||
\(585\) | 10.8541 | + | 7.88597i | 0.448762 | + | 0.326045i | ||||
\(586\) | −52.8885 | + | 38.4258i | −2.18481 | + | 1.58735i | ||||
\(587\) | −0.500000 | − | 0.363271i | −0.0206372 | − | 0.0149938i | 0.577419 | − | 0.816448i | \(-0.304060\pi\) |
−0.598056 | + | 0.801454i | \(0.704060\pi\) | |||||||
\(588\) | −0.135255 | + | 0.416272i | −0.00557782 | + | 0.0171668i | ||||
\(589\) | 49.4508 | 2.03759 | ||||||||
\(590\) | 47.3607 | − | 34.4095i | 1.94981 | − | 1.41662i | ||||
\(591\) | −2.01722 | − | 6.20837i | −0.0829774 | − | 0.255378i | ||||
\(592\) | 0.927051 | − | 0.673542i | 0.0381016 | − | 0.0276824i | ||||
\(593\) | −20.7082 | −0.850384 | −0.425192 | − | 0.905103i | \(-0.639793\pi\) | ||||
−0.425192 | + | 0.905103i | \(0.639793\pi\) | |||||||
\(594\) | −7.39919 | + | 0.502029i | −0.303592 | + | 0.0205985i | ||||
\(595\) | 36.5066 | 1.49662 | ||||||||
\(596\) | −0.624612 | + | 1.92236i | −0.0255851 | + | 0.0787428i | ||||
\(597\) | −13.7984 | −0.564730 | ||||||||
\(598\) | 22.6869 | − | 69.8232i | 0.927737 | − | 2.85528i | ||||
\(599\) | 2.32624 | − | 1.69011i | 0.0950475 | − | 0.0690561i | −0.539246 | − | 0.842148i | \(-0.681291\pi\) |
0.634294 | + | 0.773092i | \(0.281291\pi\) | |||||||
\(600\) | −3.45492 | + | 10.6331i | −0.141046 | + | 0.434096i | ||||
\(601\) | −1.35410 | − | 4.16750i | −0.0552350 | − | 0.169996i | 0.919633 | − | 0.392778i | \(-0.128486\pi\) |
−0.974868 | + | 0.222783i | \(0.928486\pi\) | |||||||
\(602\) | 37.6246 | − | 27.3359i | 1.53346 | − | 1.11413i | ||||
\(603\) | −1.80902 | + | 5.56758i | −0.0736689 | + | 0.226729i | ||||
\(604\) | 1.50000 | + | 4.61653i | 0.0610341 | + | 0.187844i | ||||
\(605\) | 10.6910 | + | 22.1518i | 0.434650 | + | 0.900599i | ||||
\(606\) | 2.27458 | − | 7.00042i | 0.0923983 | − | 0.284373i | ||||
\(607\) | 0.954915 | + | 0.693786i | 0.0387588 | + | 0.0281599i | 0.606996 | − | 0.794705i | \(-0.292374\pi\) |
−0.568237 | + | 0.822865i | \(0.692374\pi\) | |||||||
\(608\) | −35.9164 | − | 26.0948i | −1.45660 | − | 1.05828i | ||||
\(609\) | −15.0172 | − | 10.9106i | −0.608529 | − | 0.442122i | ||||
\(610\) | 8.22949 | − | 25.3278i | 0.333202 | − | 1.02549i | ||||
\(611\) | −48.5410 | −1.96376 | ||||||||
\(612\) | −15.1353 | − | 10.9964i | −0.611806 | − | 0.444503i | ||||
\(613\) | 4.38854 | + | 13.5065i | 0.177252 | + | 0.545524i | 0.999729 | − | 0.0232732i | \(-0.00740877\pi\) |
−0.822478 | + | 0.568798i | \(0.807409\pi\) | |||||||
\(614\) | −1.09424 | − | 3.36771i | −0.0441597 | − | 0.135910i | ||||
\(615\) | 1.21885 | − | 3.75123i | 0.0491487 | − | 0.151264i | ||||
\(616\) | 16.4443 | + | 10.3229i | 0.662559 | + | 0.415920i | ||||
\(617\) | 2.03851 | − | 6.27388i | 0.0820672 | − | 0.252577i | −0.901601 | − | 0.432569i | \(-0.857607\pi\) |
0.983668 | + | 0.179992i | \(0.0576072\pi\) | |||||||
\(618\) | −15.7533 | − | 11.4454i | −0.633690 | − | 0.460403i | ||||
\(619\) | −0.663119 | − | 0.481784i | −0.0266530 | − | 0.0193645i | 0.574379 | − | 0.818589i | \(-0.305244\pi\) |
−0.601032 | + | 0.799225i | \(0.705244\pi\) | |||||||
\(620\) | −40.5517 | + | 29.4625i | −1.62859 | + | 1.18324i | ||||
\(621\) | −4.42705 | − | 3.21644i | −0.177651 | − | 0.129071i | ||||
\(622\) | −50.0238 | − | 36.3444i | −2.00577 | − | 1.45728i | ||||
\(623\) | 2.88197 | − | 8.86978i | 0.115464 | − | 0.355360i | ||||
\(624\) | 1.85410 | − | 5.70634i | 0.0742235 | − | 0.228436i | ||||
\(625\) | −20.2254 | + | 14.6946i | −0.809017 | + | 0.587785i | ||||
\(626\) | 59.0689 | 2.36087 | ||||||||
\(627\) | −16.8435 | + | 14.0741i | −0.672663 | + | 0.562065i | ||||
\(628\) | −8.07295 | − | 24.8460i | −0.322146 | − | 0.991463i | ||||
\(629\) | 2.20820 | − | 6.79615i | 0.0880469 | − | 0.270980i | ||||
\(630\) | −13.0902 | −0.521525 | ||||||||
\(631\) | 14.2918 | 0.568947 | 0.284474 | − | 0.958684i | \(-0.408181\pi\) | ||||
0.284474 | + | 0.958684i | \(0.408181\pi\) | |||||||
\(632\) | −23.4164 | + | 17.0130i | −0.931455 | + | 0.676741i | ||||
\(633\) | −3.61803 | − | 11.1352i | −0.143804 | − | 0.442583i | ||||
\(634\) | −18.0902 | − | 13.1433i | −0.718452 | − | 0.521986i | ||||
\(635\) | −12.9271 | − | 9.39205i | −0.512994 | − | 0.372712i | ||||
\(636\) | −0.927051 | − | 2.85317i | −0.0367600 | − | 0.113136i | ||||
\(637\) | −0.708204 | + | 0.514540i | −0.0280601 | + | 0.0203868i | ||||
\(638\) | 40.3500 | − | 33.7158i | 1.59747 | − | 1.33482i | ||||
\(639\) | −6.04508 | − | 4.39201i | −0.239140 | − | 0.173745i | ||||
\(640\) | 35.0000 | 1.38350 | ||||||||
\(641\) | −0.927051 | − | 2.85317i | −0.0366163 | − | 0.112693i | 0.931078 | − | 0.364821i | \(-0.118870\pi\) |
−0.967694 | + | 0.252127i | \(0.918870\pi\) | |||||||
\(642\) | −27.7639 | −1.09575 | ||||||||
\(643\) | −6.61803 | + | 4.80828i | −0.260990 | + | 0.189620i | −0.710583 | − | 0.703613i | \(-0.751569\pi\) |
0.449594 | + | 0.893233i | \(0.351569\pi\) | |||||||
\(644\) | 13.2812 | + | 40.8752i | 0.523351 | + | 1.61071i | ||||
\(645\) | −14.3713 | − | 10.4414i | −0.565870 | − | 0.411129i | ||||
\(646\) | −92.2837 | −3.63085 | ||||||||
\(647\) | −7.81966 | + | 24.0664i | −0.307423 | + | 0.946149i | 0.671340 | + | 0.741150i | \(0.265719\pi\) |
−0.978762 | + | 0.204999i | \(0.934281\pi\) | |||||||
\(648\) | 1.80902 | + | 1.31433i | 0.0710649 | + | 0.0516317i | ||||
\(649\) | −29.7984 | + | 24.8990i | −1.16969 | + | 0.977371i | ||||
\(650\) | −54.2705 | + | 39.4298i | −2.12866 | + | 1.54657i | ||||
\(651\) | −15.8262 | − | 11.4984i | −0.620279 | − | 0.450659i | ||||
\(652\) | 31.5517 | − | 22.9236i | 1.23566 | − | 0.897758i | ||||
\(653\) | −6.50000 | + | 4.72253i | −0.254365 | + | 0.184807i | −0.707659 | − | 0.706554i | \(-0.750249\pi\) |
0.453294 | + | 0.891361i | \(0.350249\pi\) | |||||||
\(654\) | 7.76393 | + | 5.64083i | 0.303594 | + | 0.220574i | ||||
\(655\) | 31.3435 | − | 22.7724i | 1.22469 | − | 0.889790i | ||||
\(656\) | −1.76393 | −0.0688700 | ||||||||
\(657\) | −1.00000 | + | 3.07768i | −0.0390137 | + | 0.120072i | ||||
\(658\) | 38.3156 | − | 27.8379i | 1.49370 | − | 1.08523i | ||||
\(659\) | −19.5902 | + | 14.2331i | −0.763125 | + | 0.554443i | −0.899867 | − | 0.436164i | \(-0.856337\pi\) |
0.136742 | + | 0.990607i | \(0.456337\pi\) | |||||||
\(660\) | 5.42705 | − | 21.5765i | 0.211248 | − | 0.839866i | ||||
\(661\) | −12.9443 | − | 9.40456i | −0.503474 | − | 0.365795i | 0.306868 | − | 0.951752i | \(-0.400719\pi\) |
−0.810342 | + | 0.585957i | \(0.800719\pi\) | |||||||
\(662\) | −15.7771 | −0.613194 | ||||||||
\(663\) | −11.5623 | − | 35.5851i | −0.449043 | − | 1.38201i | ||||
\(664\) | 5.91641 | − | 18.2088i | 0.229601 | − | 0.706640i | ||||
\(665\) | −31.3435 | + | 22.7724i | −1.21545 | + | 0.883074i | ||||
\(666\) | −0.791796 | + | 2.43690i | −0.0306815 | + | 0.0944279i | ||||
\(667\) | 38.7984 | 1.50228 | ||||||||
\(668\) | 23.4787 | − | 72.2601i | 0.908419 | − | 2.79583i | ||||
\(669\) | −2.92705 | + | 2.12663i | −0.113166 | + | 0.0822202i | ||||
\(670\) | −23.6803 | − | 17.2048i | −0.914851 | − | 0.664678i | ||||
\(671\) | −4.30902 | + | 17.1315i | −0.166348 | + | 0.661355i | ||||
\(672\) | 5.42705 | + | 16.7027i | 0.209353 | + | 0.644322i | ||||
\(673\) | −7.75329 | − | 23.8622i | −0.298867 | − | 0.919819i | −0.981895 | − | 0.189426i | \(-0.939337\pi\) |
0.683028 | − | 0.730393i | \(-0.260663\pi\) | |||||||
\(674\) | −8.37790 | + | 25.7845i | −0.322705 | + | 0.993183i | ||||
\(675\) | 1.54508 | + | 4.75528i | 0.0594703 | + | 0.183031i | ||||
\(676\) | −55.8222 | + | 40.5572i | −2.14701 | + | 1.55989i | ||||
\(677\) | 5.00000 | 0.192166 | 0.0960828 | − | 0.995373i | \(-0.469369\pi\) | ||||
0.0960828 | + | 0.995373i | \(0.469369\pi\) | |||||||
\(678\) | −13.5172 | + | 9.82084i | −0.519126 | + | 0.377167i | ||||
\(679\) | 6.61803 | 0.253977 | ||||||||
\(680\) | 25.2254 | − | 18.3273i | 0.967351 | − | 0.702822i | ||||
\(681\) | 2.87132 | − | 8.83702i | 0.110029 | − | 0.338635i | ||||
\(682\) | 42.5238 | − | 35.5321i | 1.62832 | − | 1.36060i | ||||
\(683\) | −5.75329 | + | 17.7068i | −0.220143 | + | 0.677532i | 0.778605 | + | 0.627515i | \(0.215928\pi\) |
−0.998748 | + | 0.0500175i | \(0.984072\pi\) | |||||||
\(684\) | 19.8541 | 0.759141 | ||||||||
\(685\) | −39.2705 | + | 28.5317i | −1.50045 | + | 1.09014i | ||||
\(686\) | 12.9271 | − | 39.7854i | 0.493557 | − | 1.51901i | ||||
\(687\) | 5.25329 | − | 16.1680i | 0.200425 | − | 0.616846i | ||||
\(688\) | −2.45492 | + | 7.55545i | −0.0935928 | + | 0.288049i | ||||
\(689\) | 1.85410 | − | 5.70634i | 0.0706357 | − | 0.217394i | ||||
\(690\) | 22.1353 | − | 16.0822i | 0.842675 | − | 0.612239i | ||||
\(691\) | 12.5836 | 0.478702 | 0.239351 | − | 0.970933i | \(-0.423065\pi\) | ||||
0.239351 | + | 0.970933i | \(0.423065\pi\) | |||||||
\(692\) | 18.7918 | − | 57.8352i | 0.714357 | − | 2.19856i | ||||
\(693\) | 8.66312 | − | 0.587785i | 0.329085 | − | 0.0223281i | ||||
\(694\) | −12.3992 | + | 38.1608i | −0.470667 | + | 1.44856i | ||||
\(695\) | −9.30902 | + | 6.76340i | −0.353111 | + | 0.256550i | ||||
\(696\) | −15.8541 | −0.600948 | ||||||||
\(697\) | −8.89919 | + | 6.46564i | −0.337081 | + | 0.244903i | ||||
\(698\) | 0.729490 | 0.0276116 | ||||||||
\(699\) | −19.7082 | + | 14.3188i | −0.745433 | + | 0.541589i | ||||
\(700\) | 12.1353 | − | 37.3485i | 0.458670 | − | 1.41164i | ||||
\(701\) | −5.40983 | + | 16.6497i | −0.204326 | + | 0.628852i | 0.795414 | + | 0.606067i | \(0.207254\pi\) |
−0.999740 | + | 0.0227856i | \(0.992746\pi\) | |||||||
\(702\) | 4.14590 | + | 12.7598i | 0.156477 | + | 0.481586i | ||||
\(703\) | 2.34346 | + | 7.21242i | 0.0883852 | + | 0.272022i | ||||
\(704\) | −43.0172 | + | 2.91868i | −1.62127 | + | 0.110002i | ||||
\(705\) | −14.6353 | − | 10.6331i | −0.551196 | − | 0.400467i | ||||
\(706\) | 26.3435 | − | 19.1396i | 0.991449 | − | 0.720330i | ||||
\(707\) | −2.66312 | + | 8.19624i | −0.100157 | + | 0.308251i | ||||
\(708\) | 35.1246 | 1.32006 | ||||||||
\(709\) | −5.72542 | + | 17.6210i | −0.215023 | + | 0.661772i | 0.784129 | + | 0.620598i | \(0.213110\pi\) |
−0.999152 | + | 0.0411746i | \(0.986890\pi\) | |||||||
\(710\) | 30.2254 | − | 21.9601i | 1.13434 | − | 0.824146i | ||||
\(711\) | −4.00000 | + | 12.3107i | −0.150012 | + | 0.461689i | ||||
\(712\) | −2.46149 | − | 7.57570i | −0.0922483 | − | 0.283911i | ||||
\(713\) | 40.8885 | 1.53129 | ||||||||
\(714\) | 29.5344 | + | 21.4580i | 1.10530 | + | 0.803047i | ||||
\(715\) | 34.1459 | − | 28.5317i | 1.27698 | − | 1.06702i | ||||
\(716\) | −21.0000 | + | 15.2574i | −0.784807 | + | 0.570196i | ||||
\(717\) | 10.5902 | − | 7.69421i | 0.395497 | − | 0.287345i | ||||
\(718\) | 7.31308 | − | 22.5074i | 0.272922 | − | 0.839967i | ||||
\(719\) | −16.8541 | −0.628552 | −0.314276 | − | 0.949332i | \(-0.601762\pi\) | ||||
−0.314276 | + | 0.949332i | \(0.601762\pi\) | |||||||
\(720\) | 1.80902 | − | 1.31433i | 0.0674181 | − | 0.0489821i | ||||
\(721\) | 18.4443 | + | 13.4005i | 0.686901 | + | 0.499062i | ||||
\(722\) | 44.8607 | − | 32.5932i | 1.66954 | − | 1.21299i | ||||
\(723\) | −14.4443 | + | 10.4944i | −0.537188 | + | 0.390290i | ||||
\(724\) | 27.6246 | + | 20.0705i | 1.02666 | + | 0.745913i | ||||
\(725\) | −28.6803 | − | 20.8375i | −1.06516 | − | 0.773885i | ||||
\(726\) | −4.37132 | + | 24.2052i | −0.162235 | + | 0.898339i | ||||
\(727\) | 23.6803 | + | 17.2048i | 0.878255 | + | 0.638090i | 0.932789 | − | 0.360422i | \(-0.117367\pi\) |
−0.0545341 | + | 0.998512i | \(0.517367\pi\) | |||||||
\(728\) | 10.8541 | − | 33.4055i | 0.402280 | − | 1.23809i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −13.0902 | − | 9.51057i | −0.484489 | − | 0.352002i | ||||
\(731\) | 15.3090 | + | 47.1163i | 0.566224 | + | 1.74266i | ||||
\(732\) | 12.9271 | − | 9.39205i | 0.477798 | − | 0.347140i | ||||
\(733\) | −13.4377 | −0.496333 | −0.248166 | − | 0.968717i | \(-0.579828\pi\) | ||||
−0.248166 | + | 0.968717i | \(0.579828\pi\) | |||||||
\(734\) | 7.42299 | + | 22.8456i | 0.273987 | + | 0.843247i | ||||
\(735\) | −0.326238 | −0.0120335 | ||||||||
\(736\) | −29.6976 | − | 21.5765i | −1.09467 | − | 0.795322i | ||||
\(737\) | 16.4443 | + | 10.3229i | 0.605733 | + | 0.380248i | ||||
\(738\) | 3.19098 | − | 2.31838i | 0.117462 | − | 0.0853409i | ||||
\(739\) | 8.54508 | + | 26.2991i | 0.314336 | + | 0.967427i | 0.976027 | + | 0.217650i | \(0.0698391\pi\) |
−0.661691 | + | 0.749777i | \(0.730161\pi\) | |||||||
\(740\) | −6.21885 | − | 4.51826i | −0.228609 | − | 0.166094i | ||||
\(741\) | 32.1246 | + | 23.3399i | 1.18013 | + | 0.857413i | ||||
\(742\) | 1.80902 | + | 5.56758i | 0.0664111 | + | 0.204392i | ||||
\(743\) | −26.4894 | + | 19.2456i | −0.971800 | + | 0.706054i | −0.955861 | − | 0.293819i | \(-0.905074\pi\) |
−0.0159391 | + | 0.999873i | \(0.505074\pi\) | |||||||
\(744\) | −16.7082 | −0.612552 | ||||||||
\(745\) | −1.50658 | −0.0551967 | ||||||||
\(746\) | 2.74013 | − | 8.43326i | 0.100323 | − | 0.308764i | ||||
\(747\) | −2.64590 | − | 8.14324i | −0.0968083 | − | 0.297945i | ||||
\(748\) | −47.6140 | + | 39.7854i | −1.74094 | + | 1.45470i | ||||
\(749\) | 32.5066 | 1.18776 | ||||||||
\(750\) | −25.0000 | −0.912871 | ||||||||
\(751\) | −6.78115 | + | 20.8702i | −0.247448 | + | 0.761566i | 0.747776 | + | 0.663951i | \(0.231121\pi\) |
−0.995224 | + | 0.0976154i | \(0.968879\pi\) | |||||||
\(752\) | −2.50000 | + | 7.69421i | −0.0911656 | + | 0.280579i | ||||
\(753\) | 0.0278640 | + | 0.0202444i | 0.00101542 | + | 0.000737747i | ||||
\(754\) | −76.9574 | − | 55.9128i | −2.80262 | − | 2.03623i | ||||
\(755\) | −2.92705 | + | 2.12663i | −0.106526 | + | 0.0773959i | ||||
\(756\) | −6.35410 | − | 4.61653i | −0.231096 | − | 0.167901i | ||||
\(757\) | −36.4894 | − | 26.5111i | −1.32623 | − | 0.963561i | −0.999832 | − | 0.0183282i | \(-0.994166\pi\) |
−0.326396 | − | 0.945233i | \(-0.605834\pi\) | |||||||
\(758\) | −18.5557 | + | 57.1087i | −0.673974 | + | 2.07428i | ||||
\(759\) | −13.9271 | + | 11.6372i | −0.505520 | + | 0.422403i | ||||
\(760\) | −10.2254 | + | 31.4706i | −0.370915 | + | 1.14156i | ||||
\(761\) | 9.69756 | + | 29.8460i | 0.351536 | + | 1.08192i | 0.957991 | + | 0.286799i | \(0.0925913\pi\) |
−0.606454 | + | 0.795118i | \(0.707409\pi\) | |||||||
\(762\) | −4.93769 | − | 15.1967i | −0.178874 | − | 0.550517i | ||||
\(763\) | −9.09017 | − | 6.60440i | −0.329086 | − | 0.239095i | ||||
\(764\) | 43.1459 | 1.56096 | ||||||||
\(765\) | 4.30902 | − | 13.2618i | 0.155793 | − | 0.479481i | ||||
\(766\) | −36.3050 | − | 26.3771i | −1.31175 | − | 0.953043i | ||||
\(767\) | 56.8328 | + | 41.2915i | 2.05211 | + | 1.49095i | ||||
\(768\) | 7.28115 | + | 5.29007i | 0.262736 | + | 0.190889i | ||||
\(769\) | −4.81966 | + | 14.8334i | −0.173801 | + | 0.534906i | −0.999577 | − | 0.0290936i | \(-0.990738\pi\) |
0.825775 | + | 0.563999i | \(0.190738\pi\) | |||||||
\(770\) | −10.5902 | + | 42.1038i | −0.381643 | + | 1.51731i | ||||
\(771\) | 5.01722 | + | 15.4414i | 0.180691 | + | 0.556109i | ||||
\(772\) | −3.13525 | + | 9.64932i | −0.112840 | + | 0.347287i | ||||
\(773\) | −32.4336 | + | 23.5644i | −1.16656 | + | 0.847553i | −0.990593 | − | 0.136844i | \(-0.956304\pi\) |
−0.175964 | + | 0.984397i | \(0.556304\pi\) | |||||||
\(774\) | −5.48936 | − | 16.8945i | −0.197311 | − | 0.607260i | ||||
\(775\) | −30.2254 | − | 21.9601i | −1.08573 | − | 0.788829i | ||||
\(776\) | 4.57295 | − | 3.32244i | 0.164159 | − | 0.119269i | ||||
\(777\) | 0.927051 | − | 2.85317i | 0.0332578 | − | 0.102357i | ||||
\(778\) | −10.7295 | −0.384671 | ||||||||
\(779\) | 3.60739 | − | 11.1024i | 0.129248 | − | 0.397785i | ||||
\(780\) | −40.2492 | −1.44115 | ||||||||
\(781\) | −19.0172 | + | 15.8904i | −0.680490 | + | 0.568605i | ||||
\(782\) | −76.3050 | −2.72866 | ||||||||
\(783\) | −5.73607 | + | 4.16750i | −0.204990 | + | 0.148934i | ||||
\(784\) | 0.0450850 | + | 0.138757i | 0.00161018 | + | 0.00495562i | ||||
\(785\) | 15.7533 | − | 11.4454i | 0.562259 | − | 0.408505i | ||||
\(786\) | 38.7426 | 1.38190 | ||||||||
\(787\) | −0.263932 | + | 0.812299i | −0.00940816 | + | 0.0289553i | −0.955650 | − | 0.294504i | \(-0.904846\pi\) |
0.946242 | + | 0.323459i | \(0.104846\pi\) | |||||||
\(788\) | 15.8435 | + | 11.5109i | 0.564400 | + | 0.410060i | ||||
\(789\) | 18.7082 | − | 13.5923i | 0.666030 | − | 0.483899i | ||||
\(790\) | −52.3607 | − | 38.0423i | −1.86291 | − | 1.35348i | ||||
\(791\) | 15.8262 | − | 11.4984i | 0.562716 | − | 0.408837i | ||||
\(792\) | 5.69098 | − | 4.75528i | 0.202220 | − | 0.168972i | ||||
\(793\) | 31.9574 | 1.13484 | ||||||||
\(794\) | 38.6803 | − | 28.1029i | 1.37271 | − | 0.997335i | ||||
\(795\) | 1.80902 | − | 1.31433i | 0.0641592 | − | 0.0466144i | ||||
\(796\) | 33.4894 | − | 24.3314i | 1.18700 | − | 0.862405i | ||||
\(797\) | −14.7984 | − | 10.7516i | −0.524185 | − | 0.380843i | 0.293993 | − | 0.955808i | \(-0.405016\pi\) |
−0.818178 | + | 0.574965i | \(0.805016\pi\) | |||||||
\(798\) | −38.7426 | −1.37147 | ||||||||
\(799\) | 15.5902 | + | 47.9816i | 0.551541 | + | 1.69747i | ||||
\(800\) | 10.3647 | + | 31.8994i | 0.366449 | + | 1.12781i | ||||
\(801\) | −2.88197 | − | 2.09387i | −0.101829 | − | 0.0739833i | ||||
\(802\) | −29.6976 | − | 21.5765i | −1.04866 | − | 0.761894i | ||||
\(803\) | 9.09017 | + | 5.70634i | 0.320785 | + | 0.201372i | ||||
\(804\) | −5.42705 | − | 16.7027i | −0.191397 | − | 0.589060i | ||||
\(805\) | −25.9164 | + | 18.8294i | −0.913433 | + | 0.663648i | ||||
\(806\) | −81.1033 | − | 58.9250i | −2.85674 | − | 2.07555i | ||||
\(807\) | −5.45492 | − | 16.7885i | −0.192022 | − | 0.590983i | ||||
\(808\) | 2.27458 | + | 7.00042i | 0.0800193 | + | 0.246274i | ||||
\(809\) | 7.81559 | − | 24.0539i | 0.274782 | − | 0.845691i | −0.714495 | − | 0.699640i | \(-0.753344\pi\) |
0.989277 | − | 0.146051i | \(-0.0466563\pi\) | |||||||
\(810\) | −1.54508 | + | 4.75528i | −0.0542888 | + | 0.167084i | ||||
\(811\) | −22.7533 | + | 16.5312i | −0.798976 | + | 0.580490i | −0.910614 | − | 0.413259i | \(-0.864390\pi\) |
0.111638 | + | 0.993749i | \(0.464390\pi\) | |||||||
\(812\) | 55.6869 | 1.95423 | ||||||||
\(813\) | −3.07295 | + | 2.23263i | −0.107773 | + | 0.0783017i | ||||
\(814\) | 7.19756 | + | 4.51826i | 0.252274 | + | 0.158365i | ||||
\(815\) | 23.5172 | + | 17.0863i | 0.823772 | + | 0.598506i | ||||
\(816\) | −6.23607 | −0.218306 | ||||||||
\(817\) | −42.5344 | − | 30.9031i | −1.48809 | − | 1.08116i | ||||
\(818\) | 1.34346 | + | 4.13474i | 0.0469729 | + | 0.144568i | ||||
\(819\) | −4.85410 | − | 14.9394i | −0.169616 | − | 0.522025i | ||||
\(820\) | 3.65654 | + | 11.2537i | 0.127692 | + | 0.392995i | ||||
\(821\) | −21.2812 | + | 15.4617i | −0.742717 | + | 0.539616i | −0.893561 | − | 0.448942i | \(-0.851801\pi\) |
0.150844 | + | 0.988558i | \(0.451801\pi\) | |||||||
\(822\) | −48.5410 | −1.69306 | ||||||||
\(823\) | 14.8156 | + | 45.5977i | 0.516439 | + | 1.58944i | 0.780648 | + | 0.624971i | \(0.214889\pi\) |
−0.264209 | + | 0.964465i | \(0.585111\pi\) | |||||||
\(824\) | 19.4721 | 0.678344 | ||||||||
\(825\) | 16.5451 | − | 1.12257i | 0.576026 | − | 0.0390829i | ||||
\(826\) | −68.5410 | −2.38485 | ||||||||
\(827\) | 4.92705 | + | 15.1639i | 0.171330 | + | 0.527301i | 0.999447 | − | 0.0332554i | \(-0.0105875\pi\) |
−0.828117 | + | 0.560556i | \(0.810587\pi\) | |||||||
\(828\) | 16.4164 | 0.570510 | ||||||||
\(829\) | −22.0795 | + | 16.0417i | −0.766854 | + | 0.557152i | −0.901005 | − | 0.433809i | \(-0.857169\pi\) |
0.134151 | + | 0.990961i | \(0.457169\pi\) | |||||||
\(830\) | 42.8115 | 1.48601 | ||||||||
\(831\) | 6.37132 | + | 19.6089i | 0.221019 | + | 0.680226i | ||||
\(832\) | 24.1033 | + | 74.1824i | 0.835632 | + | 2.57181i | ||||
\(833\) | 0.736068 | + | 0.534785i | 0.0255032 | + | 0.0185292i | ||||
\(834\) | −11.5066 | −0.398440 | ||||||||
\(835\) | 56.6312 | 1.95980 | ||||||||
\(836\) | 16.0623 | − | 63.8595i | 0.555526 | − | 2.20863i | ||||
\(837\) | −6.04508 | + | 4.39201i | −0.208949 | + | 0.151810i | ||||
\(838\) | 51.0557 | 1.76369 | ||||||||
\(839\) | 14.7361 | − | 10.7064i | 0.508746 | − | 0.369625i | −0.303602 | − | 0.952799i | \(-0.598189\pi\) |
0.812348 | + | 0.583174i | \(0.198189\pi\) | |||||||
\(840\) | 10.5902 | − | 7.69421i | 0.365396 | − | 0.265475i | ||||
\(841\) | 6.57295 | − | 20.2295i | 0.226653 | − | 0.697567i | ||||
\(842\) | −17.9508 | − | 55.2470i | −0.618627 | − | 1.90394i | ||||
\(843\) | 4.39919 | + | 13.5393i | 0.151516 | + | 0.466318i | ||||
\(844\) | 28.4164 | + | 20.6457i | 0.978133 | + | 0.710655i | ||||
\(845\) | −41.6074 | − | 30.2295i | −1.43134 | − | 1.03993i | ||||
\(846\) | −5.59017 | − | 17.2048i | −0.192194 | − | 0.591512i | ||||
\(847\) | 5.11803 | − | 28.3399i | 0.175858 | − | 0.973772i | ||||
\(848\) | −0.809017 | − | 0.587785i | −0.0277818 | − | 0.0201846i | ||||
\(849\) | 15.2812 | + | 11.1024i | 0.524448 | + | 0.381034i | ||||
\(850\) | 56.4058 | + | 40.9812i | 1.93470 | + | 1.40564i | ||||
\(851\) | 1.93769 | + | 5.96361i | 0.0664233 | + | 0.204430i | ||||
\(852\) | 22.4164 | 0.767973 | ||||||||
\(853\) | 18.5623 | + | 13.4863i | 0.635561 | + | 0.461762i | 0.858322 | − | 0.513111i | \(-0.171507\pi\) |
−0.222761 | + | 0.974873i | \(0.571507\pi\) | |||||||
\(854\) | −25.2254 | + | 18.3273i | −0.863196 | + | 0.627149i | ||||
\(855\) | 4.57295 | + | 14.0741i | 0.156392 | + | 0.481324i | ||||
\(856\) | 22.4615 | − | 16.3192i | 0.767718 | − | 0.557780i | ||||
\(857\) | −0.729490 | −0.0249189 | −0.0124595 | − | 0.999922i | \(-0.503966\pi\) | ||||
−0.0124595 | + | 0.999922i | \(0.503966\pi\) | |||||||
\(858\) | 44.3951 | − | 3.01217i | 1.51562 | − | 0.102834i | ||||
\(859\) | 2.28115 | − | 1.65735i | 0.0778319 | − | 0.0565482i | −0.548189 | − | 0.836355i | \(-0.684682\pi\) |
0.626021 | + | 0.779806i | \(0.284682\pi\) | |||||||
\(860\) | 53.2918 | 1.81724 | ||||||||
\(861\) | −3.73607 | + | 2.71441i | −0.127325 | + | 0.0925069i | ||||
\(862\) | 9.04508 | + | 6.57164i | 0.308077 | + | 0.223831i | ||||
\(863\) | −2.22542 | + | 6.84915i | −0.0757543 | + | 0.233148i | −0.981762 | − | 0.190113i | \(-0.939115\pi\) |
0.906008 | + | 0.423261i | \(0.139115\pi\) | |||||||
\(864\) | 6.70820 | 0.228218 | ||||||||
\(865\) | 45.3262 | 1.54114 | ||||||||
\(866\) | −17.2361 | − | 53.0472i | −0.585705 | − | 1.80262i | ||||
\(867\) | −17.7082 | + | 12.8658i | −0.601402 | + | 0.436944i | ||||
\(868\) | 58.6869 | 1.99196 | ||||||||
\(869\) | 36.3607 | + | 22.8254i | 1.23345 | + | 0.774297i | ||||
\(870\) | −10.9549 | − | 33.7158i | −0.371406 | − | 1.14307i | ||||
\(871\) | 10.8541 | − | 33.4055i | 0.367777 | − | 1.13190i | ||||
\(872\) | −9.59675 | −0.324987 | ||||||||
\(873\) | 0.781153 | − | 2.40414i | 0.0264380 | − | 0.0813679i | ||||
\(874\) | 65.5132 | − | 47.5981i | 2.21602 | − | 1.61003i | ||||
\(875\) | 29.2705 | 0.989524 | ||||||||
\(876\) | −3.00000 | − | 9.23305i | −0.101361 | − | 0.311956i | ||||
\(877\) | 8.26393 | − | 6.00410i | 0.279053 | − | 0.202744i | −0.439451 | − | 0.898266i | \(-0.644827\pi\) |
0.718504 | + | 0.695522i | \(0.244827\pi\) | |||||||
\(878\) | 3.31559 | − | 10.2044i | 0.111896 | − | 0.344380i | ||||
\(879\) | −9.03444 | − | 27.8052i | −0.304724 | − | 0.937845i | ||||
\(880\) | −2.76393 | − | 6.88191i | −0.0931721 | − | 0.231989i | ||||
\(881\) | 0.263932 | − | 0.812299i | 0.00889210 | − | 0.0273671i | −0.946512 | − | 0.322669i | \(-0.895420\pi\) |
0.955404 | + | 0.295301i | \(0.0954201\pi\) | |||||||
\(882\) | −0.263932 | − | 0.191758i | −0.00888705 | − | 0.00645682i | ||||
\(883\) | −12.0000 | − | 8.71851i | −0.403832 | − | 0.293401i | 0.367268 | − | 0.930115i | \(-0.380293\pi\) |
−0.771100 | + | 0.636714i | \(0.780293\pi\) | |||||||
\(884\) | 90.8115 | + | 65.9784i | 3.05432 | + | 2.21910i | ||||
\(885\) | 8.09017 | + | 24.8990i | 0.271948 | + | 0.836970i | ||||
\(886\) | 85.9017 | 2.88592 | ||||||||
\(887\) | −41.0238 | − | 29.8055i | −1.37744 | − | 1.00077i | −0.997114 | − | 0.0759213i | \(-0.975810\pi\) |
−0.380331 | − | 0.924851i | \(-0.624190\pi\) | |||||||
\(888\) | −0.791796 | − | 2.43690i | −0.0265709 | − | 0.0817769i | ||||
\(889\) | 5.78115 | + | 17.7926i | 0.193894 | + | 0.596743i | ||||
\(890\) | 14.4098 | − | 10.4694i | 0.483019 | − | 0.350934i | ||||
\(891\) | 0.809017 | − | 3.21644i | 0.0271031 | − | 0.107755i | ||||
\(892\) | 3.35410 | − | 10.3229i | 0.112304 | − | 0.345635i | ||||
\(893\) | −43.3156 | − | 31.4706i | −1.44950 | − | 1.05312i | ||||
\(894\) | −1.21885 | − | 0.885544i | −0.0407643 | − | 0.0296170i | ||||
\(895\) | −15.6525 | − | 11.3722i | −0.523205 | − | 0.380130i | ||||
\(896\) | −33.1525 | − | 24.0867i | −1.10755 | − | 0.804680i | ||||
\(897\) | 26.5623 | + | 19.2986i | 0.886890 | + | 0.644363i | ||||
\(898\) | −8.35410 | + | 25.7113i | −0.278780 | + | 0.857997i | ||||
\(899\) | 16.3713 | − | 50.3858i | 0.546014 | − | 1.68046i | ||||
\(900\) | −12.1353 | − | 8.81678i | −0.404508 | − | 0.293893i | ||||
\(901\) | −6.23607 | −0.207754 | ||||||||
\(902\) | −4.87539 | − | 12.1392i | −0.162333 | − | 0.404192i | ||||
\(903\) | 6.42705 | + | 19.7804i | 0.213879 | + | 0.658251i | ||||
\(904\) | 5.16312 | − | 15.8904i | 0.171723 | − | 0.528508i | ||||
\(905\) | −7.86475 | + | 24.2052i | −0.261433 | + | 0.804608i | ||||
\(906\) | −3.61803 | −0.120201 | ||||||||
\(907\) | 33.2533 | − | 24.1599i | 1.10416 | − | 0.802217i | 0.122424 | − | 0.992478i | \(-0.460933\pi\) |
0.981734 | + | 0.190261i | \(0.0609333\pi\) | |||||||
\(908\) | 8.61397 | + | 26.5111i | 0.285865 | + | 0.879801i | ||||
\(909\) | 2.66312 | + | 1.93487i | 0.0883301 | + | 0.0641756i | ||||
\(910\) | 78.5410 | 2.60361 | ||||||||
\(911\) | −12.0729 | − | 37.1567i | −0.399995 | − | 1.23106i | −0.925003 | − | 0.379960i | \(-0.875938\pi\) |
0.525008 | − | 0.851097i | \(-0.324062\pi\) | |||||||
\(912\) | 5.35410 | − | 3.88998i | 0.177292 | − | 0.128810i | ||||
\(913\) | −28.3328 | + | 1.92236i | −0.937679 | + | 0.0636207i | ||||
\(914\) | 17.7639 | + | 12.9063i | 0.587579 | + | 0.426901i | ||||
\(915\) | 9.63525 | + | 7.00042i | 0.318532 | + | 0.231427i | ||||
\(916\) | 15.7599 | + | 48.5039i | 0.520721 | + | 1.60261i | ||||
\(917\) | −45.3607 | −1.49794 | ||||||||
\(918\) | 11.2812 | − | 8.19624i | 0.372334 | − | 0.270516i | ||||
\(919\) | −4.21885 | − | 12.9843i | −0.139167 | − | 0.428312i | 0.857048 | − | 0.515237i | \(-0.172296\pi\) |
−0.996215 | + | 0.0869249i | \(0.972296\pi\) | |||||||
\(920\) | −8.45492 | + | 26.0216i | −0.278750 | + | 0.857905i | ||||
\(921\) | 1.58359 | 0.0521811 | ||||||||
\(922\) | −22.0967 | + | 68.0068i | −0.727718 | + | 2.23968i | ||||
\(923\) | 36.2705 | + | 26.3521i | 1.19386 | + | 0.867389i | ||||
\(924\) | −19.9894 | + | 16.7027i | −0.657602 | + | 0.549480i | ||||
\(925\) | 1.77051 | − | 5.44907i | 0.0582140 | − | 0.179164i | ||||
\(926\) | −61.7320 | − | 44.8509i | −2.02864 | − | 1.47389i | ||||
\(927\) | 7.04508 | − | 5.11855i | 0.231391 | − | 0.168115i | ||||
\(928\) | −38.4787 | + | 27.9564i | −1.26313 | + | 0.917715i | ||||
\(929\) | 22.5066 | + | 16.3520i | 0.738417 | + | 0.536491i | 0.892215 | − | 0.451611i | \(-0.149151\pi\) |
−0.153798 | + | 0.988102i | \(0.549151\pi\) | |||||||
\(930\) | −11.5451 | − | 35.5321i | −0.378578 | − | 1.16514i | ||||
\(931\) | −0.965558 | −0.0316449 | ||||||||
\(932\) | 22.5836 | − | 69.5051i | 0.739750 | − | 2.27672i | ||||
\(933\) | 22.3713 | − | 16.2537i | 0.732404 | − | 0.532123i | ||||
\(934\) | −28.1525 | + | 20.4540i | −0.921177 | + | 0.669274i | ||||
\(935\) | −39.1697 | − | 24.5887i | −1.28099 | − | 0.804137i | ||||
\(936\) | −10.8541 | − | 7.88597i | −0.354777 | − | 0.257761i | ||||
\(937\) | −37.4508 | −1.22347 | −0.611733 | − | 0.791064i | \(-0.709527\pi\) | ||||
−0.611733 | + | 0.791064i | \(0.709527\pi\) | |||||||
\(938\) | 10.5902 | + | 32.5932i | 0.345781 | + | 1.06421i | ||||
\(939\) | −8.16312 | + | 25.1235i | −0.266393 | + | 0.819874i | ||||
\(940\) | 54.2705 | 1.77011 | ||||||||
\(941\) | −0.545085 | + | 1.67760i | −0.0177693 | + | 0.0546882i | −0.959548 | − | 0.281545i | \(-0.909153\pi\) |
0.941779 | + | 0.336233i | \(0.109153\pi\) | |||||||
\(942\) | 19.4721 | 0.634436 | ||||||||
\(943\) | 2.98278 | − | 9.18005i | 0.0971327 | − | 0.298944i | ||||
\(944\) | 9.47214 | − | 6.88191i | 0.308292 | − | 0.223987i | ||||
\(945\) | 1.80902 | − | 5.56758i | 0.0588473 | − | 0.181113i | ||||
\(946\) | −58.7812 | + | 3.98825i | −1.91114 | + | 0.129669i | ||||
\(947\) | −11.9549 | − | 36.7934i | −0.388483 | − | 1.19563i | −0.933922 | − | 0.357476i | \(-0.883637\pi\) |
0.545440 | − | 0.838150i | \(-0.316363\pi\) | |||||||
\(948\) | −12.0000 | − | 36.9322i | −0.389742 | − | 1.19950i | ||||
\(949\) | 6.00000 | − | 18.4661i | 0.194768 | − | 0.599435i | ||||
\(950\) | −73.9919 | −2.40061 | ||||||||
\(951\) | 8.09017 | − | 5.87785i | 0.262342 | − | 0.190602i | ||||
\(952\) | −36.5066 | −1.18318 | ||||||||
\(953\) | 13.9721 | − | 10.1514i | 0.452602 | − | 0.328835i | −0.338020 | − | 0.941139i | \(-0.609757\pi\) |
0.790622 | + | 0.612304i | \(0.209757\pi\) | |||||||
\(954\) | 2.23607 | 0.0723954 | ||||||||
\(955\) | 9.93769 | + | 30.5851i | 0.321576 | + | 0.989710i | ||||
\(956\) | −12.1353 | + | 37.3485i | −0.392482 | + | 1.20794i | ||||
\(957\) | 8.76393 | + | 21.8213i | 0.283298 | + | 0.705382i | ||||
\(958\) | −9.75987 | + | 30.0378i | −0.315327 | + | 0.970477i | ||||
\(959\) | 56.8328 | 1.83523 | ||||||||
\(960\) | −8.98278 | + | 27.6462i | −0.289918 | + | 0.892276i | ||||
\(961\) | 7.67376 | − | 23.6174i | 0.247541 | − | 0.761852i | ||||
\(962\) | 4.75078 | − | 14.6214i | 0.153171 | − | 0.471412i | ||||
\(963\) | 3.83688 | − | 11.8087i | 0.123642 | − | 0.380530i | ||||
\(964\) | 16.5517 | − | 50.9408i | 0.533093 | − | 1.64069i | ||||
\(965\) | −7.56231 | −0.243439 | ||||||||
\(966\) | −32.0344 | −1.03069 | ||||||||
\(967\) | −9.92705 | + | 30.5523i | −0.319232 | + | 0.982496i | 0.654745 | + | 0.755850i | \(0.272776\pi\) |
−0.973977 | + | 0.226646i | \(0.927224\pi\) | |||||||
\(968\) | −10.6910 | − | 22.1518i | −0.343621 | − | 0.711986i | ||||
\(969\) | 12.7533 | − | 39.2506i | 0.409695 | − | 1.26091i | ||||
\(970\) | 10.2254 | + | 7.42921i | 0.328319 | + | 0.238537i | ||||
\(971\) | 4.12461 | 0.132365 | 0.0661825 | − | 0.997808i | \(-0.478918\pi\) | ||||
0.0661825 | + | 0.997808i | \(0.478918\pi\) | |||||||
\(972\) | −2.42705 | + | 1.76336i | −0.0778477 | + | 0.0565597i | ||||
\(973\) | 13.4721 | 0.431897 | ||||||||
\(974\) | 27.2984 | − | 19.8334i | 0.874696 | − | 0.635504i | ||||
\(975\) | −9.27051 | − | 28.5317i | −0.296894 | − | 0.913746i | ||||
\(976\) | 1.64590 | − | 5.06555i | 0.0526839 | − | 0.162144i | ||||
\(977\) | −0.416408 | − | 1.28157i | −0.0133221 | − | 0.0410011i | 0.944175 | − | 0.329446i | \(-0.106862\pi\) |
−0.957497 | + | 0.288445i | \(0.906862\pi\) | |||||||
\(978\) | 8.98278 | + | 27.6462i | 0.287238 | + | 0.884026i | ||||
\(979\) | −9.06637 | + | 7.57570i | −0.289762 | + | 0.242120i | ||||
\(980\) | 0.791796 | − | 0.575274i | 0.0252930 | − | 0.0183764i | ||||
\(981\) | −3.47214 | + | 2.52265i | −0.110857 | + | 0.0805422i | ||||
\(982\) | 17.6484 | − | 54.3162i | 0.563183 | − | 1.73330i | ||||
\(983\) | −8.94427 | −0.285278 | −0.142639 | − | 0.989775i | \(-0.545559\pi\) | ||||
−0.142639 | + | 0.989775i | \(0.545559\pi\) | |||||||
\(984\) | −1.21885 | + | 3.75123i | −0.0388554 | + | 0.119585i | ||||
\(985\) | −4.51064 | + | 13.8823i | −0.143721 | + | 0.442328i | ||||
\(986\) | −30.5517 | + | 94.0283i | −0.972963 | + | 2.99447i | ||||
\(987\) | 6.54508 | + | 20.1437i | 0.208332 | + | 0.641181i | ||||
\(988\) | −119.125 | −3.78986 | ||||||||
\(989\) | −35.1697 | − | 25.5523i | −1.11833 | − | 0.812515i | ||||
\(990\) | 14.0451 | + | 8.81678i | 0.446382 | + | 0.280216i | ||||
\(991\) | 36.9336 | − | 26.8339i | 1.17324 | − | 0.852405i | 0.181843 | − | 0.983328i | \(-0.441794\pi\) |
0.991393 | + | 0.130922i | \(0.0417938\pi\) | |||||||
\(992\) | −40.5517 | + | 29.4625i | −1.28752 | + | 0.935436i | ||||
\(993\) | 2.18034 | − | 6.71040i | 0.0691910 | − | 0.212948i | ||||
\(994\) | −43.7426 | −1.38743 | ||||||||
\(995\) | 24.9615 | + | 18.1356i | 0.791333 | + | 0.574937i | ||||
\(996\) | 20.7812 | + | 15.0984i | 0.658476 | + | 0.478411i | ||||
\(997\) | −23.1525 | + | 16.8213i | −0.733246 | + | 0.532735i | −0.890589 | − | 0.454810i | \(-0.849707\pi\) |
0.157342 | + | 0.987544i | \(0.449707\pi\) | |||||||
\(998\) | −16.6074 | + | 12.0660i | −0.525698 | + | 0.381942i | ||||
\(999\) | −0.927051 | − | 0.673542i | −0.0293306 | − | 0.0213099i |
(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.p.a.466.1 | ✓ | 4 | |
11.3 | even | 5 | 825.2.r.a.91.1 | yes | 4 | ||
25.11 | even | 5 | 825.2.r.a.136.1 | yes | 4 | ||
275.36 | even | 5 | inner | 825.2.p.a.586.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
825.2.p.a.466.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
825.2.p.a.586.1 | yes | 4 | 275.36 | even | 5 | inner | |
825.2.r.a.91.1 | yes | 4 | 11.3 | even | 5 | ||
825.2.r.a.136.1 | yes | 4 | 25.11 | even | 5 |