Properties

Label 729.2.e.j.568.2
Level $729$
Weight $2$
Character 729.568
Analytic conductor $5.821$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [729,2,Mod(82,729)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(729, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("729.82");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 729 = 3^{6} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 729.e (of order \(9\), degree \(6\), not 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: \(5.82109430735\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(2\) over \(\Q(\zeta_{9})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} + 18x^{10} + 105x^{8} + 266x^{6} + 306x^{4} + 132x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 568.2
Root \(1.22778i\) of defining polynomial
Character \(\chi\) \(=\) 729.568
Dual form 729.2.e.j.163.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.48321 + 0.539846i) q^{2} +(0.376403 + 0.315840i) q^{4} +(0.291470 - 1.65301i) q^{5} +(2.12905 - 1.78649i) q^{7} +(-1.19062 - 2.06222i) q^{8} +O(q^{10})\) \(q+(1.48321 + 0.539846i) q^{2} +(0.376403 + 0.315840i) q^{4} +(0.291470 - 1.65301i) q^{5} +(2.12905 - 1.78649i) q^{7} +(-1.19062 - 2.06222i) q^{8} +(1.32468 - 2.29442i) q^{10} +(-0.720852 - 4.08816i) q^{11} +(-6.46137 + 2.35175i) q^{13} +(4.12227 - 1.50038i) q^{14} +(-0.823316 - 4.66925i) q^{16} +(-0.488276 + 0.845718i) q^{17} +(-1.34264 - 2.32553i) q^{19} +(0.631796 - 0.530140i) q^{20} +(1.13780 - 6.45276i) q^{22} +(1.23576 + 1.03693i) q^{23} +(2.05098 + 0.746497i) q^{25} -10.8532 q^{26} +1.36563 q^{28} +(7.73168 + 2.81410i) q^{29} +(0.799803 + 0.671115i) q^{31} +(0.472527 - 2.67984i) q^{32} +(-1.18078 + 0.990788i) q^{34} +(-2.33252 - 4.04005i) q^{35} +(0.654172 - 1.13306i) q^{37} +(-0.736003 - 4.17408i) q^{38} +(-3.75589 + 1.36703i) q^{40} +(4.55579 - 1.65817i) q^{41} +(1.70874 + 9.69073i) q^{43} +(1.01987 - 1.76647i) q^{44} +(1.27312 + 2.20510i) q^{46} +(9.57379 - 8.03337i) q^{47} +(0.125792 - 0.713402i) q^{49} +(2.63906 + 2.21443i) q^{50} +(-3.17486 - 1.15555i) q^{52} +7.34280 q^{53} -6.96786 q^{55} +(-6.21903 - 2.26354i) q^{56} +(9.94855 + 8.34783i) q^{58} +(1.57184 - 8.91436i) q^{59} +(-0.984935 + 0.826459i) q^{61} +(0.823982 + 1.42718i) q^{62} +(-2.59373 + 4.49247i) q^{64} +(2.00416 + 11.3662i) q^{65} +(4.36609 - 1.58913i) q^{67} +(-0.450900 + 0.164114i) q^{68} +(-1.27863 - 7.25146i) q^{70} +(-2.81187 + 4.87030i) q^{71} +(2.28072 + 3.95033i) q^{73} +(1.58196 - 1.32742i) q^{74} +(0.229119 - 1.29940i) q^{76} +(-8.83817 - 7.41611i) q^{77} +(-4.37596 - 1.59272i) q^{79} -7.95828 q^{80} +7.65237 q^{82} +(-5.41676 - 1.97154i) q^{83} +(1.25566 + 1.05362i) q^{85} +(-2.69708 + 15.2959i) q^{86} +(-7.57240 + 6.35400i) q^{88} +(-2.27221 - 3.93558i) q^{89} +(-9.55523 + 16.5502i) q^{91} +(0.137642 + 0.780605i) q^{92} +(18.5368 - 6.74683i) q^{94} +(-4.23546 + 1.54158i) q^{95} +(1.48911 + 8.44516i) q^{97} +(0.571704 - 0.990221i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 6 q^{2} + 6 q^{4} + 6 q^{5} - 3 q^{7} + 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 6 q^{2} + 6 q^{4} + 6 q^{5} - 3 q^{7} + 6 q^{8} - 6 q^{10} + 12 q^{11} - 3 q^{13} + 15 q^{14} - 36 q^{16} - 9 q^{17} - 12 q^{19} + 42 q^{20} + 6 q^{22} + 6 q^{23} + 6 q^{25} - 48 q^{26} + 6 q^{28} + 12 q^{29} + 6 q^{31} + 54 q^{32} - 9 q^{34} + 30 q^{35} - 3 q^{37} + 42 q^{38} - 57 q^{40} + 24 q^{41} + 6 q^{43} - 33 q^{44} + 3 q^{46} + 21 q^{47} + 33 q^{49} + 21 q^{50} + 45 q^{52} + 18 q^{53} + 30 q^{55} + 3 q^{56} + 33 q^{58} + 15 q^{59} + 33 q^{61} - 30 q^{62} - 6 q^{64} - 6 q^{65} + 42 q^{67} - 18 q^{68} + 24 q^{70} - 12 q^{73} - 3 q^{74} - 87 q^{76} - 57 q^{77} - 48 q^{79} + 42 q^{80} - 42 q^{82} + 12 q^{83} - 36 q^{85} - 30 q^{86} + 30 q^{88} - 9 q^{89} - 18 q^{91} - 48 q^{92} + 33 q^{94} + 30 q^{95} - 3 q^{97} + 18 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/729\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{9}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.48321 + 0.539846i 1.04879 + 0.381729i 0.808206 0.588899i \(-0.200439\pi\)
0.240585 + 0.970628i \(0.422661\pi\)
\(3\) 0 0
\(4\) 0.376403 + 0.315840i 0.188202 + 0.157920i
\(5\) 0.291470 1.65301i 0.130349 0.739247i −0.847637 0.530577i \(-0.821975\pi\)
0.977986 0.208670i \(-0.0669136\pi\)
\(6\) 0 0
\(7\) 2.12905 1.78649i 0.804707 0.675229i −0.144632 0.989486i \(-0.546200\pi\)
0.949338 + 0.314257i \(0.101755\pi\)
\(8\) −1.19062 2.06222i −0.420948 0.729104i
\(9\) 0 0
\(10\) 1.32468 2.29442i 0.418901 0.725558i
\(11\) −0.720852 4.08816i −0.217345 1.23263i −0.876790 0.480873i \(-0.840320\pi\)
0.659445 0.751753i \(-0.270791\pi\)
\(12\) 0 0
\(13\) −6.46137 + 2.35175i −1.79206 + 0.652257i −0.792987 + 0.609239i \(0.791475\pi\)
−0.999074 + 0.0430184i \(0.986303\pi\)
\(14\) 4.12227 1.50038i 1.10172 0.400995i
\(15\) 0 0
\(16\) −0.823316 4.66925i −0.205829 1.16731i
\(17\) −0.488276 + 0.845718i −0.118424 + 0.205117i −0.919143 0.393923i \(-0.871118\pi\)
0.800719 + 0.599040i \(0.204451\pi\)
\(18\) 0 0
\(19\) −1.34264 2.32553i −0.308024 0.533513i 0.669906 0.742446i \(-0.266334\pi\)
−0.977930 + 0.208933i \(0.933001\pi\)
\(20\) 0.631796 0.530140i 0.141274 0.118543i
\(21\) 0 0
\(22\) 1.13780 6.45276i 0.242579 1.37573i
\(23\) 1.23576 + 1.03693i 0.257674 + 0.216214i 0.762468 0.647026i \(-0.223987\pi\)
−0.504795 + 0.863239i \(0.668432\pi\)
\(24\) 0 0
\(25\) 2.05098 + 0.746497i 0.410197 + 0.149299i
\(26\) −10.8532 −2.12848
\(27\) 0 0
\(28\) 1.36563 0.258079
\(29\) 7.73168 + 2.81410i 1.43574 + 0.522565i 0.938570 0.345090i \(-0.112152\pi\)
0.497166 + 0.867655i \(0.334374\pi\)
\(30\) 0 0
\(31\) 0.799803 + 0.671115i 0.143649 + 0.120536i 0.711780 0.702402i \(-0.247889\pi\)
−0.568132 + 0.822938i \(0.692334\pi\)
\(32\) 0.472527 2.67984i 0.0835318 0.473733i
\(33\) 0 0
\(34\) −1.18078 + 0.990788i −0.202501 + 0.169919i
\(35\) −2.33252 4.04005i −0.394268 0.682893i
\(36\) 0 0
\(37\) 0.654172 1.13306i 0.107545 0.186274i −0.807230 0.590237i \(-0.799034\pi\)
0.914775 + 0.403963i \(0.132368\pi\)
\(38\) −0.736003 4.17408i −0.119395 0.677125i
\(39\) 0 0
\(40\) −3.75589 + 1.36703i −0.593859 + 0.216147i
\(41\) 4.55579 1.65817i 0.711495 0.258963i 0.0391841 0.999232i \(-0.487524\pi\)
0.672311 + 0.740269i \(0.265302\pi\)
\(42\) 0 0
\(43\) 1.70874 + 9.69073i 0.260580 + 1.47782i 0.781332 + 0.624115i \(0.214540\pi\)
−0.520752 + 0.853708i \(0.674348\pi\)
\(44\) 1.01987 1.76647i 0.153751 0.266305i
\(45\) 0 0
\(46\) 1.27312 + 2.20510i 0.187711 + 0.325125i
\(47\) 9.57379 8.03337i 1.39648 1.17179i 0.433846 0.900987i \(-0.357156\pi\)
0.962636 0.270800i \(-0.0872882\pi\)
\(48\) 0 0
\(49\) 0.125792 0.713402i 0.0179703 0.101915i
\(50\) 2.63906 + 2.21443i 0.373219 + 0.313168i
\(51\) 0 0
\(52\) −3.17486 1.15555i −0.440273 0.160246i
\(53\) 7.34280 1.00861 0.504305 0.863525i \(-0.331749\pi\)
0.504305 + 0.863525i \(0.331749\pi\)
\(54\) 0 0
\(55\) −6.96786 −0.939546
\(56\) −6.21903 2.26354i −0.831052 0.302478i
\(57\) 0 0
\(58\) 9.94855 + 8.34783i 1.30631 + 1.09612i
\(59\) 1.57184 8.91436i 0.204636 1.16055i −0.693375 0.720577i \(-0.743877\pi\)
0.898011 0.439973i \(-0.145012\pi\)
\(60\) 0 0
\(61\) −0.984935 + 0.826459i −0.126108 + 0.105817i −0.703660 0.710536i \(-0.748452\pi\)
0.577552 + 0.816354i \(0.304008\pi\)
\(62\) 0.823982 + 1.42718i 0.104646 + 0.181252i
\(63\) 0 0
\(64\) −2.59373 + 4.49247i −0.324216 + 0.561558i
\(65\) 2.00416 + 11.3662i 0.248585 + 1.40980i
\(66\) 0 0
\(67\) 4.36609 1.58913i 0.533403 0.194143i −0.0612541 0.998122i \(-0.519510\pi\)
0.594657 + 0.803979i \(0.297288\pi\)
\(68\) −0.450900 + 0.164114i −0.0546797 + 0.0199018i
\(69\) 0 0
\(70\) −1.27863 7.25146i −0.152825 0.866716i
\(71\) −2.81187 + 4.87030i −0.333707 + 0.577998i −0.983236 0.182339i \(-0.941633\pi\)
0.649528 + 0.760337i \(0.274966\pi\)
\(72\) 0 0
\(73\) 2.28072 + 3.95033i 0.266938 + 0.462351i 0.968070 0.250681i \(-0.0806547\pi\)
−0.701131 + 0.713032i \(0.747321\pi\)
\(74\) 1.58196 1.32742i 0.183899 0.154309i
\(75\) 0 0
\(76\) 0.229119 1.29940i 0.0262817 0.149051i
\(77\) −8.83817 7.41611i −1.00720 0.845144i
\(78\) 0 0
\(79\) −4.37596 1.59272i −0.492334 0.179195i 0.0839088 0.996473i \(-0.473260\pi\)
−0.576243 + 0.817278i \(0.695482\pi\)
\(80\) −7.95828 −0.889763
\(81\) 0 0
\(82\) 7.65237 0.845063
\(83\) −5.41676 1.97154i −0.594566 0.216404i 0.0271703 0.999631i \(-0.491350\pi\)
−0.621737 + 0.783226i \(0.713573\pi\)
\(84\) 0 0
\(85\) 1.25566 + 1.05362i 0.136196 + 0.114282i
\(86\) −2.69708 + 15.2959i −0.290833 + 1.64940i
\(87\) 0 0
\(88\) −7.57240 + 6.35400i −0.807221 + 0.677339i
\(89\) −2.27221 3.93558i −0.240854 0.417171i 0.720104 0.693866i \(-0.244094\pi\)
−0.960958 + 0.276695i \(0.910761\pi\)
\(90\) 0 0
\(91\) −9.55523 + 16.5502i −1.00166 + 1.73493i
\(92\) 0.137642 + 0.780605i 0.0143501 + 0.0813837i
\(93\) 0 0
\(94\) 18.5368 6.74683i 1.91192 0.695883i
\(95\) −4.23546 + 1.54158i −0.434549 + 0.158163i
\(96\) 0 0
\(97\) 1.48911 + 8.44516i 0.151196 + 0.857476i 0.962181 + 0.272410i \(0.0878205\pi\)
−0.810985 + 0.585067i \(0.801068\pi\)
\(98\) 0.571704 0.990221i 0.0577508 0.100027i
\(99\) 0 0
\(100\) 0.536224 + 0.928767i 0.0536224 + 0.0928767i
\(101\) −5.97952 + 5.01741i −0.594984 + 0.499251i −0.889829 0.456294i \(-0.849176\pi\)
0.294845 + 0.955545i \(0.404732\pi\)
\(102\) 0 0
\(103\) −0.376148 + 2.13324i −0.0370629 + 0.210194i −0.997715 0.0675594i \(-0.978479\pi\)
0.960652 + 0.277754i \(0.0895899\pi\)
\(104\) 12.5429 + 10.5247i 1.22993 + 1.03203i
\(105\) 0 0
\(106\) 10.8909 + 3.96398i 1.05782 + 0.385016i
\(107\) 12.5849 1.21663 0.608317 0.793695i \(-0.291845\pi\)
0.608317 + 0.793695i \(0.291845\pi\)
\(108\) 0 0
\(109\) −12.2140 −1.16989 −0.584945 0.811073i \(-0.698884\pi\)
−0.584945 + 0.811073i \(0.698884\pi\)
\(110\) −10.3348 3.76157i −0.985387 0.358652i
\(111\) 0 0
\(112\) −10.0944 8.47025i −0.953836 0.800363i
\(113\) 0.0782863 0.443984i 0.00736456 0.0417665i −0.980904 0.194492i \(-0.937694\pi\)
0.988269 + 0.152726i \(0.0488052\pi\)
\(114\) 0 0
\(115\) 2.07423 1.74049i 0.193423 0.162301i
\(116\) 2.02142 + 3.50121i 0.187685 + 0.325079i
\(117\) 0 0
\(118\) 7.14376 12.3734i 0.657636 1.13906i
\(119\) 0.471300 + 2.67288i 0.0432040 + 0.245022i
\(120\) 0 0
\(121\) −5.85677 + 2.13169i −0.532434 + 0.193790i
\(122\) −1.90703 + 0.694103i −0.172655 + 0.0628411i
\(123\) 0 0
\(124\) 0.0890839 + 0.505220i 0.00799997 + 0.0453701i
\(125\) 6.02803 10.4409i 0.539164 0.933859i
\(126\) 0 0
\(127\) 0.265534 + 0.459919i 0.0235624 + 0.0408112i 0.877566 0.479456i \(-0.159166\pi\)
−0.854004 + 0.520267i \(0.825833\pi\)
\(128\) −10.4414 + 8.76136i −0.922896 + 0.774402i
\(129\) 0 0
\(130\) −3.16337 + 17.9404i −0.277446 + 1.57348i
\(131\) −8.74519 7.33809i −0.764071 0.641132i 0.175112 0.984548i \(-0.443971\pi\)
−0.939183 + 0.343417i \(0.888416\pi\)
\(132\) 0 0
\(133\) −7.01309 2.55256i −0.608112 0.221335i
\(134\) 7.33374 0.633539
\(135\) 0 0
\(136\) 2.32541 0.199402
\(137\) 3.97419 + 1.44649i 0.339538 + 0.123582i 0.506161 0.862439i \(-0.331064\pi\)
−0.166623 + 0.986021i \(0.553286\pi\)
\(138\) 0 0
\(139\) −8.54563 7.17064i −0.724831 0.608205i 0.203886 0.978995i \(-0.434643\pi\)
−0.928717 + 0.370789i \(0.879087\pi\)
\(140\) 0.398039 2.25739i 0.0336404 0.190784i
\(141\) 0 0
\(142\) −6.79981 + 5.70572i −0.570628 + 0.478813i
\(143\) 14.2720 + 24.7198i 1.19348 + 2.06718i
\(144\) 0 0
\(145\) 6.90528 11.9603i 0.573452 0.993248i
\(146\) 1.25023 + 7.09042i 0.103470 + 0.586807i
\(147\) 0 0
\(148\) 0.604098 0.219874i 0.0496566 0.0180735i
\(149\) −18.3030 + 6.66176i −1.49944 + 0.545753i −0.955917 0.293639i \(-0.905134\pi\)
−0.543527 + 0.839391i \(0.682912\pi\)
\(150\) 0 0
\(151\) −0.215820 1.22398i −0.0175632 0.0996059i 0.974766 0.223229i \(-0.0716598\pi\)
−0.992329 + 0.123623i \(0.960549\pi\)
\(152\) −3.19716 + 5.53765i −0.259324 + 0.449163i
\(153\) 0 0
\(154\) −9.10535 15.7709i −0.733730 1.27086i
\(155\) 1.34248 1.12647i 0.107830 0.0904803i
\(156\) 0 0
\(157\) −0.613523 + 3.47946i −0.0489645 + 0.277691i −0.999453 0.0330680i \(-0.989472\pi\)
0.950489 + 0.310759i \(0.100583\pi\)
\(158\) −5.63067 4.72469i −0.447952 0.375876i
\(159\) 0 0
\(160\) −4.29206 1.56218i −0.339317 0.123501i
\(161\) 4.48345 0.353346
\(162\) 0 0
\(163\) 15.9509 1.24937 0.624685 0.780877i \(-0.285228\pi\)
0.624685 + 0.780877i \(0.285228\pi\)
\(164\) 2.23853 + 0.814759i 0.174800 + 0.0636220i
\(165\) 0 0
\(166\) −6.96989 5.84843i −0.540968 0.453926i
\(167\) −2.51523 + 14.2646i −0.194635 + 1.10383i 0.718304 + 0.695730i \(0.244919\pi\)
−0.912938 + 0.408098i \(0.866192\pi\)
\(168\) 0 0
\(169\) 26.2600 22.0348i 2.02000 1.69498i
\(170\) 1.29362 + 2.24061i 0.0992161 + 0.171847i
\(171\) 0 0
\(172\) −2.41755 + 4.18731i −0.184336 + 0.319280i
\(173\) −2.19099 12.4257i −0.166578 0.944709i −0.947423 0.319984i \(-0.896322\pi\)
0.780845 0.624725i \(-0.214789\pi\)
\(174\) 0 0
\(175\) 5.70026 2.07473i 0.430900 0.156835i
\(176\) −18.4952 + 6.73168i −1.39412 + 0.507420i
\(177\) 0 0
\(178\) −1.24557 7.06396i −0.0933591 0.529466i
\(179\) 0.147949 0.256256i 0.0110582 0.0191534i −0.860443 0.509546i \(-0.829813\pi\)
0.871502 + 0.490393i \(0.163147\pi\)
\(180\) 0 0
\(181\) −0.710251 1.23019i −0.0527925 0.0914393i 0.838421 0.545022i \(-0.183479\pi\)
−0.891214 + 0.453583i \(0.850146\pi\)
\(182\) −23.1070 + 19.3891i −1.71280 + 1.43721i
\(183\) 0 0
\(184\) 0.667044 3.78299i 0.0491751 0.278886i
\(185\) −1.68228 1.41160i −0.123684 0.103783i
\(186\) 0 0
\(187\) 3.80940 + 1.38651i 0.278571 + 0.101392i
\(188\) 6.14087 0.447869
\(189\) 0 0
\(190\) −7.11431 −0.516126
\(191\) 19.3803 + 7.05385i 1.40231 + 0.510399i 0.928863 0.370424i \(-0.120788\pi\)
0.473446 + 0.880823i \(0.343010\pi\)
\(192\) 0 0
\(193\) −16.0532 13.4702i −1.15553 0.969608i −0.155699 0.987805i \(-0.549763\pi\)
−0.999834 + 0.0181970i \(0.994207\pi\)
\(194\) −2.35042 + 13.3299i −0.168750 + 0.957029i
\(195\) 0 0
\(196\) 0.272670 0.228797i 0.0194764 0.0163426i
\(197\) −4.79810 8.31056i −0.341851 0.592103i 0.642926 0.765929i \(-0.277720\pi\)
−0.984776 + 0.173826i \(0.944387\pi\)
\(198\) 0 0
\(199\) 5.34583 9.25925i 0.378956 0.656371i −0.611955 0.790893i \(-0.709616\pi\)
0.990911 + 0.134522i \(0.0429498\pi\)
\(200\) −0.902507 5.11837i −0.0638169 0.361924i
\(201\) 0 0
\(202\) −11.5775 + 4.21388i −0.814592 + 0.296487i
\(203\) 21.4885 7.82118i 1.50820 0.548939i
\(204\) 0 0
\(205\) −1.41310 8.01406i −0.0986948 0.559726i
\(206\) −1.70953 + 2.96099i −0.119108 + 0.206302i
\(207\) 0 0
\(208\) 16.3006 + 28.2335i 1.13025 + 1.95764i
\(209\) −8.53927 + 7.16530i −0.590674 + 0.495634i
\(210\) 0 0
\(211\) −2.61345 + 14.8216i −0.179917 + 1.02036i 0.752397 + 0.658710i \(0.228898\pi\)
−0.932314 + 0.361650i \(0.882213\pi\)
\(212\) 2.76385 + 2.31915i 0.189822 + 0.159280i
\(213\) 0 0
\(214\) 18.6662 + 6.79394i 1.27599 + 0.464424i
\(215\) 16.5169 1.12644
\(216\) 0 0
\(217\) 2.90176 0.196984
\(218\) −18.1160 6.59368i −1.22697 0.446580i
\(219\) 0 0
\(220\) −2.62273 2.20073i −0.176824 0.148373i
\(221\) 1.16601 6.61280i 0.0784346 0.444825i
\(222\) 0 0
\(223\) −9.41324 + 7.89864i −0.630357 + 0.528932i −0.901040 0.433736i \(-0.857195\pi\)
0.270683 + 0.962669i \(0.412751\pi\)
\(224\) −3.78146 6.54968i −0.252659 0.437619i
\(225\) 0 0
\(226\) 0.355798 0.616261i 0.0236674 0.0409931i
\(227\) −0.651625 3.69555i −0.0432499 0.245282i 0.955517 0.294938i \(-0.0952988\pi\)
−0.998766 + 0.0496553i \(0.984188\pi\)
\(228\) 0 0
\(229\) 17.4806 6.36240i 1.15515 0.420439i 0.307786 0.951456i \(-0.400412\pi\)
0.847362 + 0.531016i \(0.178190\pi\)
\(230\) 4.01613 1.46175i 0.264816 0.0963850i
\(231\) 0 0
\(232\) −3.40222 19.2949i −0.223366 1.26677i
\(233\) 0.272892 0.472663i 0.0178777 0.0309652i −0.856948 0.515403i \(-0.827642\pi\)
0.874826 + 0.484438i \(0.160976\pi\)
\(234\) 0 0
\(235\) −10.4887 18.1670i −0.684210 1.18509i
\(236\) 3.40716 2.85894i 0.221787 0.186101i
\(237\) 0 0
\(238\) −0.743903 + 4.21888i −0.0482200 + 0.273469i
\(239\) 15.3935 + 12.9167i 0.995721 + 0.835509i 0.986386 0.164448i \(-0.0525841\pi\)
0.00933493 + 0.999956i \(0.497029\pi\)
\(240\) 0 0
\(241\) −14.3691 5.22993i −0.925597 0.336890i −0.165134 0.986271i \(-0.552806\pi\)
−0.760463 + 0.649382i \(0.775028\pi\)
\(242\) −9.83763 −0.632387
\(243\) 0 0
\(244\) −0.631762 −0.0404444
\(245\) −1.14259 0.415871i −0.0729977 0.0265690i
\(246\) 0 0
\(247\) 14.1444 + 11.8685i 0.899985 + 0.755177i
\(248\) 0.431721 2.44841i 0.0274143 0.155474i
\(249\) 0 0
\(250\) 14.5773 12.2318i 0.921951 0.773609i
\(251\) 6.37816 + 11.0473i 0.402586 + 0.697299i 0.994037 0.109042i \(-0.0347782\pi\)
−0.591451 + 0.806341i \(0.701445\pi\)
\(252\) 0 0
\(253\) 3.34831 5.79945i 0.210507 0.364608i
\(254\) 0.145559 + 0.825506i 0.00913319 + 0.0517969i
\(255\) 0 0
\(256\) −10.4674 + 3.80981i −0.654210 + 0.238113i
\(257\) −12.3144 + 4.48207i −0.768151 + 0.279584i −0.696223 0.717826i \(-0.745137\pi\)
−0.0719281 + 0.997410i \(0.522915\pi\)
\(258\) 0 0
\(259\) −0.631430 3.58102i −0.0392351 0.222513i
\(260\) −2.83551 + 4.91125i −0.175851 + 0.304583i
\(261\) 0 0
\(262\) −9.00956 15.6050i −0.556613 0.964081i
\(263\) 7.28828 6.11559i 0.449415 0.377104i −0.389804 0.920898i \(-0.627457\pi\)
0.839219 + 0.543794i \(0.183013\pi\)
\(264\) 0 0
\(265\) 2.14020 12.1377i 0.131472 0.745613i
\(266\) −9.02393 7.57198i −0.553293 0.464268i
\(267\) 0 0
\(268\) 2.14532 + 0.780834i 0.131046 + 0.0476970i
\(269\) −22.1408 −1.34995 −0.674973 0.737842i \(-0.735845\pi\)
−0.674973 + 0.737842i \(0.735845\pi\)
\(270\) 0 0
\(271\) 27.9627 1.69861 0.849307 0.527899i \(-0.177020\pi\)
0.849307 + 0.527899i \(0.177020\pi\)
\(272\) 4.35088 + 1.58359i 0.263811 + 0.0960193i
\(273\) 0 0
\(274\) 5.11369 + 4.29090i 0.308930 + 0.259223i
\(275\) 1.57334 8.92286i 0.0948760 0.538069i
\(276\) 0 0
\(277\) −14.4657 + 12.1382i −0.869162 + 0.729313i −0.963921 0.266187i \(-0.914236\pi\)
0.0947596 + 0.995500i \(0.469792\pi\)
\(278\) −8.80397 15.2489i −0.528027 0.914569i
\(279\) 0 0
\(280\) −5.55431 + 9.62034i −0.331933 + 0.574925i
\(281\) 3.47327 + 19.6979i 0.207198 + 1.17508i 0.893944 + 0.448179i \(0.147927\pi\)
−0.686746 + 0.726897i \(0.740962\pi\)
\(282\) 0 0
\(283\) −15.7352 + 5.72714i −0.935360 + 0.340443i −0.764332 0.644823i \(-0.776931\pi\)
−0.171028 + 0.985266i \(0.554709\pi\)
\(284\) −2.59663 + 0.945097i −0.154082 + 0.0560812i
\(285\) 0 0
\(286\) 7.82354 + 44.3695i 0.462615 + 2.62362i
\(287\) 6.73722 11.6692i 0.397685 0.688811i
\(288\) 0 0
\(289\) 8.02317 + 13.8965i 0.471951 + 0.817444i
\(290\) 16.6987 14.0119i 0.980583 0.822807i
\(291\) 0 0
\(292\) −0.389199 + 2.20726i −0.0227762 + 0.129170i
\(293\) −14.9930 12.5806i −0.875902 0.734969i 0.0894304 0.995993i \(-0.471495\pi\)
−0.965332 + 0.261024i \(0.915940\pi\)
\(294\) 0 0
\(295\) −14.2774 5.19653i −0.831260 0.302554i
\(296\) −3.11549 −0.181084
\(297\) 0 0
\(298\) −30.7437 −1.78093
\(299\) −10.4233 3.79377i −0.602794 0.219399i
\(300\) 0 0
\(301\) 20.9504 + 17.5794i 1.20756 + 1.01326i
\(302\) 0.340652 1.93193i 0.0196023 0.111170i
\(303\) 0 0
\(304\) −9.75306 + 8.18379i −0.559377 + 0.469373i
\(305\) 1.07906 + 1.86899i 0.0617870 + 0.107018i
\(306\) 0 0
\(307\) −7.44973 + 12.9033i −0.425179 + 0.736431i −0.996437 0.0843392i \(-0.973122\pi\)
0.571258 + 0.820770i \(0.306455\pi\)
\(308\) −0.984416 5.58290i −0.0560923 0.318115i
\(309\) 0 0
\(310\) 2.59930 0.946068i 0.147630 0.0537331i
\(311\) 4.31541 1.57068i 0.244704 0.0890651i −0.216756 0.976226i \(-0.569548\pi\)
0.461461 + 0.887161i \(0.347326\pi\)
\(312\) 0 0
\(313\) 2.06098 + 11.6884i 0.116493 + 0.660666i 0.986000 + 0.166745i \(0.0533257\pi\)
−0.869507 + 0.493921i \(0.835563\pi\)
\(314\) −2.78836 + 4.82958i −0.157356 + 0.272549i
\(315\) 0 0
\(316\) −1.14408 1.98161i −0.0643597 0.111474i
\(317\) 11.1209 9.33157i 0.624614 0.524113i −0.274636 0.961548i \(-0.588557\pi\)
0.899250 + 0.437435i \(0.144113\pi\)
\(318\) 0 0
\(319\) 5.93108 33.6368i 0.332077 1.88330i
\(320\) 6.67009 + 5.59687i 0.372869 + 0.312874i
\(321\) 0 0
\(322\) 6.64992 + 2.42037i 0.370586 + 0.134882i
\(323\) 2.62232 0.145910
\(324\) 0 0
\(325\) −15.0077 −0.832480
\(326\) 23.6586 + 8.61102i 1.31033 + 0.476920i
\(327\) 0 0
\(328\) −8.84373 7.42077i −0.488314 0.409744i
\(329\) 6.03161 34.2069i 0.332533 1.88589i
\(330\) 0 0
\(331\) −6.20933 + 5.21024i −0.341296 + 0.286381i −0.797284 0.603605i \(-0.793730\pi\)
0.455988 + 0.889986i \(0.349286\pi\)
\(332\) −1.41620 2.45292i −0.0777238 0.134622i
\(333\) 0 0
\(334\) −11.4313 + 19.7996i −0.625494 + 1.08339i
\(335\) −1.35426 7.68037i −0.0739909 0.419623i
\(336\) 0 0
\(337\) 17.6737 6.43270i 0.962748 0.350412i 0.187638 0.982238i \(-0.439917\pi\)
0.775110 + 0.631827i \(0.217695\pi\)
\(338\) 50.8446 18.5059i 2.76558 1.00659i
\(339\) 0 0
\(340\) 0.139858 + 0.793176i 0.00758488 + 0.0430160i
\(341\) 2.16708 3.75350i 0.117354 0.203263i
\(342\) 0 0
\(343\) 8.72082 + 15.1049i 0.470880 + 0.815588i
\(344\) 17.9499 15.0618i 0.967796 0.812077i
\(345\) 0 0
\(346\) 3.45826 19.6128i 0.185917 1.05439i
\(347\) 13.4959 + 11.3244i 0.724497 + 0.607925i 0.928625 0.371019i \(-0.120991\pi\)
−0.204128 + 0.978944i \(0.565436\pi\)
\(348\) 0 0
\(349\) 15.9647 + 5.81068i 0.854572 + 0.311039i 0.731903 0.681409i \(-0.238633\pi\)
0.122669 + 0.992448i \(0.460855\pi\)
\(350\) 9.57475 0.511792
\(351\) 0 0
\(352\) −11.2962 −0.602090
\(353\) −14.2416 5.18352i −0.758004 0.275891i −0.0660343 0.997817i \(-0.521035\pi\)
−0.691970 + 0.721926i \(0.743257\pi\)
\(354\) 0 0
\(355\) 7.23106 + 6.06758i 0.383785 + 0.322034i
\(356\) 0.387747 2.19902i 0.0205505 0.116548i
\(357\) 0 0
\(358\) 0.357779 0.300212i 0.0189092 0.0158667i
\(359\) 1.22548 + 2.12259i 0.0646783 + 0.112026i 0.896551 0.442940i \(-0.146065\pi\)
−0.831873 + 0.554966i \(0.812731\pi\)
\(360\) 0 0
\(361\) 5.89461 10.2098i 0.310243 0.537356i
\(362\) −0.389341 2.20806i −0.0204633 0.116053i
\(363\) 0 0
\(364\) −8.82382 + 3.21161i −0.462494 + 0.168334i
\(365\) 7.19468 2.61865i 0.376587 0.137066i
\(366\) 0 0
\(367\) −0.228093 1.29358i −0.0119063 0.0675242i 0.978276 0.207308i \(-0.0664703\pi\)
−0.990182 + 0.139784i \(0.955359\pi\)
\(368\) 3.82425 6.62379i 0.199353 0.345289i
\(369\) 0 0
\(370\) −1.73314 3.00189i −0.0901017 0.156061i
\(371\) 15.6332 13.1178i 0.811636 0.681043i
\(372\) 0 0
\(373\) −1.67157 + 9.47993i −0.0865505 + 0.490852i 0.910461 + 0.413595i \(0.135727\pi\)
−0.997011 + 0.0772566i \(0.975384\pi\)
\(374\) 4.90166 + 4.11298i 0.253459 + 0.212677i
\(375\) 0 0
\(376\) −27.9653 10.1785i −1.44220 0.524918i
\(377\) −56.5753 −2.91377
\(378\) 0 0
\(379\) −8.56311 −0.439857 −0.219929 0.975516i \(-0.570582\pi\)
−0.219929 + 0.975516i \(0.570582\pi\)
\(380\) −2.08113 0.757470i −0.106760 0.0388574i
\(381\) 0 0
\(382\) 24.9372 + 20.9248i 1.27590 + 1.07060i
\(383\) −5.84059 + 33.1236i −0.298440 + 1.69254i 0.354441 + 0.935078i \(0.384671\pi\)
−0.652881 + 0.757460i \(0.726440\pi\)
\(384\) 0 0
\(385\) −14.8349 + 12.4480i −0.756059 + 0.634409i
\(386\) −16.5385 28.6455i −0.841786 1.45802i
\(387\) 0 0
\(388\) −2.10681 + 3.64911i −0.106957 + 0.185255i
\(389\) 2.59673 + 14.7268i 0.131660 + 0.746678i 0.977128 + 0.212653i \(0.0682103\pi\)
−0.845468 + 0.534026i \(0.820679\pi\)
\(390\) 0 0
\(391\) −1.48034 + 0.538799i −0.0748639 + 0.0272482i
\(392\) −1.62096 + 0.589982i −0.0818709 + 0.0297986i
\(393\) 0 0
\(394\) −2.63020 14.9166i −0.132507 0.751487i
\(395\) −3.90824 + 6.76927i −0.196645 + 0.340599i
\(396\) 0 0
\(397\) 8.38938 + 14.5308i 0.421051 + 0.729282i 0.996043 0.0888774i \(-0.0283279\pi\)
−0.574991 + 0.818159i \(0.694995\pi\)
\(398\) 12.9276 10.8475i 0.648001 0.543738i
\(399\) 0 0
\(400\) 1.79698 10.1912i 0.0898489 0.509559i
\(401\) −10.0553 8.43742i −0.502139 0.421345i 0.356214 0.934404i \(-0.384067\pi\)
−0.858353 + 0.513060i \(0.828512\pi\)
\(402\) 0 0
\(403\) −6.74612 2.45539i −0.336048 0.122311i
\(404\) −3.83541 −0.190819
\(405\) 0 0
\(406\) 36.0943 1.79133
\(407\) −5.10369 1.85759i −0.252980 0.0920773i
\(408\) 0 0
\(409\) 19.4962 + 16.3593i 0.964026 + 0.808914i 0.981603 0.190932i \(-0.0611509\pi\)
−0.0175773 + 0.999846i \(0.505595\pi\)
\(410\) 2.23044 12.6494i 0.110153 0.624711i
\(411\) 0 0
\(412\) −0.815345 + 0.684156i −0.0401692 + 0.0337059i
\(413\) −12.5789 21.7872i −0.618965 1.07208i
\(414\) 0 0
\(415\) −4.83779 + 8.37929i −0.237478 + 0.411323i
\(416\) 3.24912 + 18.4267i 0.159301 + 0.903442i
\(417\) 0 0
\(418\) −16.5337 + 6.01779i −0.808692 + 0.294340i
\(419\) −11.9060 + 4.33341i −0.581644 + 0.211701i −0.616050 0.787707i \(-0.711268\pi\)
0.0344063 + 0.999408i \(0.489046\pi\)
\(420\) 0 0
\(421\) −3.06962 17.4087i −0.149604 0.848447i −0.963554 0.267513i \(-0.913798\pi\)
0.813950 0.580935i \(-0.197313\pi\)
\(422\) −11.8777 + 20.5727i −0.578196 + 1.00147i
\(423\) 0 0
\(424\) −8.74249 15.1424i −0.424573 0.735382i
\(425\) −1.63277 + 1.37006i −0.0792011 + 0.0664576i
\(426\) 0 0
\(427\) −0.620521 + 3.51915i −0.0300291 + 0.170304i
\(428\) 4.73702 + 3.97483i 0.228972 + 0.192131i
\(429\) 0 0
\(430\) 24.4981 + 8.91658i 1.18140 + 0.429996i
\(431\) −15.6974 −0.756117 −0.378059 0.925782i \(-0.623408\pi\)
−0.378059 + 0.925782i \(0.623408\pi\)
\(432\) 0 0
\(433\) −12.6258 −0.606759 −0.303380 0.952870i \(-0.598115\pi\)
−0.303380 + 0.952870i \(0.598115\pi\)
\(434\) 4.30394 + 1.56651i 0.206596 + 0.0751947i
\(435\) 0 0
\(436\) −4.59739 3.85767i −0.220175 0.184749i
\(437\) 0.752214 4.26602i 0.0359833 0.204071i
\(438\) 0 0
\(439\) 20.6349 17.3147i 0.984849 0.826386i 3.49262e−5 1.00000i \(-0.499989\pi\)
0.984814 + 0.173614i \(0.0555444\pi\)
\(440\) 8.29608 + 14.3692i 0.395500 + 0.685027i
\(441\) 0 0
\(442\) 5.29934 9.17873i 0.252064 0.436588i
\(443\) −6.03044 34.2003i −0.286515 1.62491i −0.699824 0.714315i \(-0.746738\pi\)
0.413310 0.910591i \(-0.364373\pi\)
\(444\) 0 0
\(445\) −7.16783 + 2.60888i −0.339788 + 0.123673i
\(446\) −18.2259 + 6.63369i −0.863022 + 0.314114i
\(447\) 0 0
\(448\) 2.50355 + 14.1984i 0.118282 + 0.670810i
\(449\) −10.3731 + 17.9667i −0.489535 + 0.847900i −0.999927 0.0120419i \(-0.996167\pi\)
0.510392 + 0.859942i \(0.329500\pi\)
\(450\) 0 0
\(451\) −10.0629 17.4295i −0.473844 0.820722i
\(452\) 0.169695 0.142391i 0.00798179 0.00669752i
\(453\) 0 0
\(454\) 1.02853 5.83307i 0.0482712 0.273760i
\(455\) 24.5725 + 20.6187i 1.15197 + 0.966621i
\(456\) 0 0
\(457\) 6.77305 + 2.46519i 0.316830 + 0.115317i 0.495540 0.868585i \(-0.334970\pi\)
−0.178710 + 0.983902i \(0.557192\pi\)
\(458\) 29.3621 1.37200
\(459\) 0 0
\(460\) 1.33046 0.0620332
\(461\) 21.7321 + 7.90984i 1.01217 + 0.368398i 0.794264 0.607573i \(-0.207857\pi\)
0.217902 + 0.975971i \(0.430079\pi\)
\(462\) 0 0
\(463\) 3.81172 + 3.19841i 0.177145 + 0.148643i 0.727049 0.686585i \(-0.240891\pi\)
−0.549904 + 0.835228i \(0.685336\pi\)
\(464\) 6.77414 38.4180i 0.314481 1.78351i
\(465\) 0 0
\(466\) 0.659922 0.553741i 0.0305703 0.0256515i
\(467\) −6.24068 10.8092i −0.288784 0.500189i 0.684735 0.728792i \(-0.259918\pi\)
−0.973520 + 0.228602i \(0.926584\pi\)
\(468\) 0 0
\(469\) 6.45669 11.1833i 0.298142 0.516397i
\(470\) −5.74966 32.6079i −0.265212 1.50409i
\(471\) 0 0
\(472\) −20.2548 + 7.37215i −0.932303 + 0.339331i
\(473\) 38.3855 13.9712i 1.76497 0.642395i
\(474\) 0 0
\(475\) −1.01774 5.77190i −0.0466972 0.264833i
\(476\) −0.666803 + 1.15494i −0.0305628 + 0.0529364i
\(477\) 0 0
\(478\) 15.8588 + 27.4683i 0.725365 + 1.25637i
\(479\) −21.8103 + 18.3010i −0.996536 + 0.836193i −0.986501 0.163757i \(-0.947639\pi\)
−0.0100353 + 0.999950i \(0.503194\pi\)
\(480\) 0 0
\(481\) −1.56218 + 8.85956i −0.0712293 + 0.403961i
\(482\) −18.4891 15.5142i −0.842157 0.706654i
\(483\) 0 0
\(484\) −2.87778 1.04743i −0.130808 0.0476103i
\(485\) 14.3939 0.653595
\(486\) 0 0
\(487\) 29.6841 1.34511 0.672557 0.740045i \(-0.265196\pi\)
0.672557 + 0.740045i \(0.265196\pi\)
\(488\) 2.87702 + 1.04715i 0.130237 + 0.0474023i
\(489\) 0 0
\(490\) −1.47021 1.23365i −0.0664172 0.0557307i
\(491\) −2.15410 + 12.2165i −0.0972131 + 0.551323i 0.896834 + 0.442368i \(0.145861\pi\)
−0.994047 + 0.108955i \(0.965250\pi\)
\(492\) 0 0
\(493\) −6.15512 + 5.16476i −0.277213 + 0.232609i
\(494\) 14.5720 + 25.2394i 0.655623 + 1.13557i
\(495\) 0 0
\(496\) 2.47512 4.28702i 0.111136 0.192493i
\(497\) 2.71411 + 15.3925i 0.121745 + 0.690448i
\(498\) 0 0
\(499\) 2.14233 0.779745i 0.0959040 0.0349062i −0.293623 0.955921i \(-0.594861\pi\)
0.389527 + 0.921015i \(0.372639\pi\)
\(500\) 5.56662 2.02608i 0.248947 0.0906092i
\(501\) 0 0
\(502\) 3.49634 + 19.8287i 0.156049 + 0.885000i
\(503\) 20.6406 35.7506i 0.920320 1.59404i 0.121399 0.992604i \(-0.461262\pi\)
0.798920 0.601437i \(-0.205405\pi\)
\(504\) 0 0
\(505\) 6.55097 + 11.3466i 0.291514 + 0.504917i
\(506\) 8.09708 6.79425i 0.359959 0.302041i
\(507\) 0 0
\(508\) −0.0453128 + 0.256982i −0.00201043 + 0.0114017i
\(509\) −12.5816 10.5572i −0.557671 0.467941i 0.319858 0.947466i \(-0.396365\pi\)
−0.877529 + 0.479524i \(0.840809\pi\)
\(510\) 0 0
\(511\) 11.9130 + 4.33597i 0.527000 + 0.191812i
\(512\) 9.67844 0.427731
\(513\) 0 0
\(514\) −20.6845 −0.912355
\(515\) 3.41662 + 1.24355i 0.150554 + 0.0547973i
\(516\) 0 0
\(517\) −39.7429 33.3483i −1.74789 1.46666i
\(518\) 0.996651 5.65229i 0.0437903 0.248347i
\(519\) 0 0
\(520\) 21.0533 17.6658i 0.923248 0.774697i
\(521\) −4.64836 8.05119i −0.203648 0.352729i 0.746053 0.665887i \(-0.231947\pi\)
−0.949701 + 0.313157i \(0.898613\pi\)
\(522\) 0 0
\(523\) 11.3736 19.6996i 0.497331 0.861402i −0.502664 0.864482i \(-0.667647\pi\)
0.999995 + 0.00307938i \(0.000980199\pi\)
\(524\) −0.974059 5.52416i −0.0425520 0.241324i
\(525\) 0 0
\(526\) 14.1116 5.13619i 0.615293 0.223949i
\(527\) −0.958098 + 0.348719i −0.0417354 + 0.0151905i
\(528\) 0 0
\(529\) −3.54202 20.0878i −0.154001 0.873382i
\(530\) 9.72687 16.8474i 0.422508 0.731806i
\(531\) 0 0
\(532\) −1.83355 3.17581i −0.0794946 0.137689i
\(533\) −25.5370 + 21.4281i −1.10613 + 0.928155i
\(534\) 0 0
\(535\) 3.66813 20.8030i 0.158587 0.899393i
\(536\) −8.47549 7.11178i −0.366086 0.307182i
\(537\) 0 0
\(538\) −32.8395 11.9526i −1.41581 0.515314i
\(539\) −3.00718 −0.129528
\(540\) 0 0
\(541\) 2.38959 0.102737 0.0513683 0.998680i \(-0.483642\pi\)
0.0513683 + 0.998680i \(0.483642\pi\)
\(542\) 41.4747 + 15.0956i 1.78149 + 0.648410i
\(543\) 0 0
\(544\) 2.03566 + 1.70812i 0.0872783 + 0.0732352i
\(545\) −3.56001 + 20.1898i −0.152494 + 0.864837i
\(546\) 0 0
\(547\) 22.7261 19.0694i 0.971697 0.815350i −0.0111192 0.999938i \(-0.503539\pi\)
0.982816 + 0.184588i \(0.0590950\pi\)
\(548\) 1.03904 + 1.79967i 0.0443856 + 0.0768781i
\(549\) 0 0
\(550\) 7.15057 12.3852i 0.304901 0.528105i
\(551\) −3.83662 21.7586i −0.163446 0.926946i
\(552\) 0 0
\(553\) −12.1620 + 4.42662i −0.517182 + 0.188239i
\(554\) −28.0085 + 10.1943i −1.18997 + 0.433113i
\(555\) 0 0
\(556\) −0.951832 5.39811i −0.0403667 0.228931i
\(557\) 4.20706 7.28685i 0.178259 0.308754i −0.763025 0.646369i \(-0.776287\pi\)
0.941284 + 0.337615i \(0.109620\pi\)
\(558\) 0 0
\(559\) −33.8309 58.5969i −1.43090 2.47838i
\(560\) −16.9436 + 14.2174i −0.715998 + 0.600794i
\(561\) 0 0
\(562\) −5.48222 + 31.0912i −0.231253 + 1.31150i
\(563\) 20.8567 + 17.5009i 0.879006 + 0.737573i 0.965974 0.258638i \(-0.0832736\pi\)
−0.0869687 + 0.996211i \(0.527718\pi\)
\(564\) 0 0
\(565\) −0.711090 0.258816i −0.0299158 0.0108885i
\(566\) −26.4304 −1.11095
\(567\) 0 0
\(568\) 13.3915 0.561894
\(569\) −20.6256 7.50711i −0.864670 0.314714i −0.128664 0.991688i \(-0.541069\pi\)
−0.736007 + 0.676974i \(0.763291\pi\)
\(570\) 0 0
\(571\) −34.3597 28.8313i −1.43791 1.20655i −0.940845 0.338837i \(-0.889966\pi\)
−0.497066 0.867713i \(-0.665589\pi\)
\(572\) −2.43548 + 13.8123i −0.101833 + 0.577521i
\(573\) 0 0
\(574\) 16.2923 13.6709i 0.680028 0.570611i
\(575\) 1.76046 + 3.04921i 0.0734163 + 0.127161i
\(576\) 0 0
\(577\) −6.00955 + 10.4088i −0.250181 + 0.433326i −0.963575 0.267437i \(-0.913823\pi\)
0.713395 + 0.700762i \(0.247157\pi\)
\(578\) 4.39810 + 24.9428i 0.182937 + 1.03749i
\(579\) 0 0
\(580\) 6.37671 2.32093i 0.264778 0.0963715i
\(581\) −15.0547 + 5.47946i −0.624574 + 0.227326i
\(582\) 0 0
\(583\) −5.29307 30.0185i −0.219217 1.24324i
\(584\) 5.43095 9.40669i 0.224734 0.389252i
\(585\) 0 0
\(586\) −15.4463 26.7537i −0.638079 1.10519i
\(587\) 13.0456 10.9466i 0.538451 0.451814i −0.332557 0.943083i \(-0.607911\pi\)
0.871008 + 0.491269i \(0.163467\pi\)
\(588\) 0 0
\(589\) 0.486845 2.76103i 0.0200601 0.113766i
\(590\) −18.3711 15.4151i −0.756324 0.634631i
\(591\) 0 0
\(592\) −5.82913 2.12163i −0.239576 0.0871985i
\(593\) 14.9284 0.613037 0.306519 0.951865i \(-0.400836\pi\)
0.306519 + 0.951865i \(0.400836\pi\)
\(594\) 0 0
\(595\) 4.55566 0.186764
\(596\) −8.99338 3.27332i −0.368383 0.134081i
\(597\) 0 0
\(598\) −13.4119 11.2539i −0.548454 0.460208i
\(599\) −2.35029 + 13.3292i −0.0960304 + 0.544615i 0.898396 + 0.439186i \(0.144733\pi\)
−0.994427 + 0.105430i \(0.966378\pi\)
\(600\) 0 0
\(601\) −34.7150 + 29.1294i −1.41606 + 1.18821i −0.462642 + 0.886545i \(0.653099\pi\)
−0.953413 + 0.301667i \(0.902457\pi\)
\(602\) 21.5837 + 37.3841i 0.879686 + 1.52366i
\(603\) 0 0
\(604\) 0.305346 0.528874i 0.0124243 0.0215196i
\(605\) 1.81663 + 10.3026i 0.0738564 + 0.418861i
\(606\) 0 0
\(607\) −22.9631 + 8.35787i −0.932042 + 0.339236i −0.763019 0.646376i \(-0.776284\pi\)
−0.169024 + 0.985612i \(0.554061\pi\)
\(608\) −6.86647 + 2.49919i −0.278472 + 0.101356i
\(609\) 0 0
\(610\) 0.591515 + 3.35465i 0.0239497 + 0.135826i
\(611\) −42.9674 + 74.4217i −1.73827 + 3.01078i
\(612\) 0 0
\(613\) 12.5998 + 21.8235i 0.508901 + 0.881443i 0.999947 + 0.0103088i \(0.00328145\pi\)
−0.491046 + 0.871134i \(0.663385\pi\)
\(614\) −18.0154 + 15.1167i −0.727041 + 0.610059i
\(615\) 0 0
\(616\) −4.77071 + 27.0560i −0.192217 + 1.09012i
\(617\) −3.09624 2.59805i −0.124650 0.104594i 0.578332 0.815802i \(-0.303704\pi\)
−0.702982 + 0.711208i \(0.748148\pi\)
\(618\) 0 0
\(619\) 42.0700 + 15.3122i 1.69094 + 0.615451i 0.994743 0.102403i \(-0.0326530\pi\)
0.696194 + 0.717853i \(0.254875\pi\)
\(620\) 0.861097 0.0345825
\(621\) 0 0
\(622\) 7.24860 0.290642
\(623\) −11.8685 4.31979i −0.475502 0.173069i
\(624\) 0 0
\(625\) −7.14194 5.99280i −0.285678 0.239712i
\(626\) −3.25305 + 18.4490i −0.130018 + 0.737369i
\(627\) 0 0
\(628\) −1.32989 + 1.11591i −0.0530682 + 0.0445295i
\(629\) 0.638833 + 1.10649i 0.0254719 + 0.0441187i
\(630\) 0 0
\(631\) −15.7058 + 27.2033i −0.625238 + 1.08294i 0.363256 + 0.931689i \(0.381665\pi\)
−0.988495 + 0.151255i \(0.951668\pi\)
\(632\) 1.92558 + 10.9205i 0.0765955 + 0.434395i
\(633\) 0 0
\(634\) 21.5323 7.83713i 0.855159 0.311252i
\(635\) 0.837645 0.304878i 0.0332409 0.0120987i
\(636\) 0 0
\(637\) 0.864952 + 4.90539i 0.0342707 + 0.194359i
\(638\) 26.9558 46.6888i 1.06719 1.84843i
\(639\) 0 0
\(640\) 11.4392 + 19.8133i 0.452176 + 0.783191i
\(641\) −37.2609 + 31.2656i −1.47172 + 1.23492i −0.557192 + 0.830384i \(0.688121\pi\)
−0.914524 + 0.404533i \(0.867434\pi\)
\(642\) 0 0
\(643\) −4.86777 + 27.6065i −0.191966 + 1.08869i 0.724708 + 0.689057i \(0.241975\pi\)
−0.916674 + 0.399637i \(0.869136\pi\)
\(644\) 1.68759 + 1.41605i 0.0665003 + 0.0558003i
\(645\) 0 0
\(646\) 3.88947 + 1.41565i 0.153029 + 0.0556980i
\(647\) 37.5519 1.47632 0.738159 0.674627i \(-0.235696\pi\)
0.738159 + 0.674627i \(0.235696\pi\)
\(648\) 0 0
\(649\) −37.5763 −1.47500
\(650\) −22.2597 8.10187i −0.873097 0.317781i
\(651\) 0 0
\(652\) 6.00397 + 5.03793i 0.235134 + 0.197300i
\(653\) 0.887728 5.03455i 0.0347395 0.197017i −0.962499 0.271286i \(-0.912551\pi\)
0.997238 + 0.0742686i \(0.0236622\pi\)
\(654\) 0 0
\(655\) −14.6789 + 12.3170i −0.573551 + 0.481266i
\(656\) −11.4933 19.9069i −0.448737 0.777236i
\(657\) 0 0
\(658\) 27.4126 47.4801i 1.06866 1.85097i
\(659\) −6.07871 34.4741i −0.236793 1.34292i −0.838805 0.544433i \(-0.816745\pi\)
0.602012 0.798487i \(-0.294366\pi\)
\(660\) 0 0
\(661\) −1.25304 + 0.456071i −0.0487378 + 0.0177391i −0.366274 0.930507i \(-0.619367\pi\)
0.317536 + 0.948246i \(0.397144\pi\)
\(662\) −12.0225 + 4.37583i −0.467268 + 0.170071i
\(663\) 0 0
\(664\) 2.38357 + 13.5179i 0.0925004 + 0.524596i
\(665\) −6.26350 + 10.8487i −0.242888 + 0.420694i
\(666\) 0 0
\(667\) 6.63648 + 11.4947i 0.256966 + 0.445077i
\(668\) −5.45207 + 4.57483i −0.210947 + 0.177006i
\(669\) 0 0
\(670\) 2.13756 12.1227i 0.0825813 0.468342i
\(671\) 4.08869 + 3.43081i 0.157842 + 0.132445i
\(672\) 0 0
\(673\) 3.36366 + 1.22427i 0.129659 + 0.0471922i 0.406035 0.913858i \(-0.366911\pi\)
−0.276375 + 0.961050i \(0.589133\pi\)
\(674\) 29.6866 1.14348
\(675\) 0 0
\(676\) 16.8438 0.647839
\(677\) −34.7112 12.6338i −1.33406 0.485558i −0.426123 0.904665i \(-0.640121\pi\)
−0.907937 + 0.419107i \(0.862343\pi\)
\(678\) 0 0
\(679\) 18.2576 + 15.3199i 0.700661 + 0.587925i
\(680\) 0.677786 3.84391i 0.0259919 0.147407i
\(681\) 0 0
\(682\) 5.24056 4.39735i 0.200671 0.168383i
\(683\) 19.0083 + 32.9233i 0.727332 + 1.25978i 0.958007 + 0.286745i \(0.0925733\pi\)
−0.230675 + 0.973031i \(0.574093\pi\)
\(684\) 0 0
\(685\) 3.54941 6.14775i 0.135616 0.234894i
\(686\) 4.78053 + 27.1117i 0.182521 + 1.03513i
\(687\) 0 0
\(688\) 43.8417 15.9571i 1.67145 0.608357i
\(689\) −47.4445 + 17.2684i −1.80749 + 0.657873i
\(690\) 0 0
\(691\) 0.0955871 + 0.542101i 0.00363630 + 0.0206225i 0.986572 0.163327i \(-0.0522227\pi\)
−0.982936 + 0.183950i \(0.941112\pi\)
\(692\) 3.09984 5.36908i 0.117838 0.204102i
\(693\) 0 0
\(694\) 13.9039 + 24.0822i 0.527784 + 0.914148i
\(695\) −14.3439 + 12.0360i −0.544095 + 0.456550i
\(696\) 0 0
\(697\) −0.822135 + 4.66256i −0.0311406 + 0.176607i
\(698\) 20.5422 + 17.2370i 0.777535 + 0.652429i
\(699\) 0 0
\(700\) 2.80088 + 1.01944i 0.105863 + 0.0385311i
\(701\) −19.0242 −0.718534 −0.359267 0.933235i \(-0.616973\pi\)
−0.359267 + 0.933235i \(0.616973\pi\)
\(702\) 0 0
\(703\) −3.51328 −0.132506
\(704\) 20.2356 + 7.36515i 0.762658 + 0.277585i
\(705\) 0 0
\(706\) −18.3251 15.3765i −0.689673 0.578704i
\(707\) −3.76717 + 21.3647i −0.141679 + 0.803501i
\(708\) 0 0
\(709\) 9.31264 7.81423i 0.349743 0.293470i −0.450944 0.892552i \(-0.648912\pi\)
0.800687 + 0.599083i \(0.204468\pi\)
\(710\) 7.44966 + 12.9032i 0.279581 + 0.484248i
\(711\) 0 0
\(712\) −5.41068 + 9.37158i −0.202774 + 0.351215i
\(713\) 0.292469 + 1.65867i 0.0109530 + 0.0621178i
\(714\) 0 0
\(715\) 45.0219 16.3866i 1.68372 0.612825i
\(716\) 0.136624 0.0497272i 0.00510589 0.00185839i
\(717\) 0 0
\(718\) 0.671776 + 3.80983i 0.0250704 + 0.142182i
\(719\) 4.88834 8.46685i 0.182304 0.315760i −0.760361 0.649501i \(-0.774978\pi\)
0.942665 + 0.333741i \(0.108311\pi\)
\(720\) 0 0
\(721\) 3.01017 + 5.21376i 0.112104 + 0.194171i
\(722\) 14.2547 11.9611i 0.530504 0.445146i
\(723\) 0 0
\(724\) 0.121203 0.687374i 0.00450446 0.0255460i
\(725\) 13.7568 + 11.5434i 0.510916 + 0.428709i
\(726\) 0 0
\(727\) −4.07350 1.48263i −0.151078 0.0549878i 0.265374 0.964145i \(-0.414504\pi\)
−0.416452 + 0.909158i \(0.636727\pi\)
\(728\) 45.5067 1.68659
\(729\) 0 0
\(730\) 12.0849 0.447283
\(731\) −9.02996 3.28664i −0.333985 0.121561i
\(732\) 0 0
\(733\) 22.3636 + 18.7653i 0.826020 + 0.693113i 0.954374 0.298615i \(-0.0965248\pi\)
−0.128354 + 0.991728i \(0.540969\pi\)
\(734\) 0.360022 2.04179i 0.0132887 0.0753638i
\(735\) 0 0
\(736\) 3.36272 2.82166i 0.123952 0.104008i
\(737\) −9.64391 16.7037i −0.355238 0.615290i
\(738\) 0 0
\(739\) −20.7777 + 35.9880i −0.764319 + 1.32384i 0.176287 + 0.984339i \(0.443591\pi\)
−0.940606 + 0.339501i \(0.889742\pi\)
\(740\) −0.187377 1.06267i −0.00688810 0.0390644i
\(741\) 0 0
\(742\) 30.2690 11.0170i 1.11121 0.404447i
\(743\) 20.0881 7.31149i 0.736963 0.268232i 0.0538536 0.998549i \(-0.482850\pi\)
0.683109 + 0.730316i \(0.260627\pi\)
\(744\) 0 0
\(745\) 5.67716 + 32.1968i 0.207995 + 1.17960i
\(746\) −7.59699 + 13.1584i −0.278146 + 0.481763i
\(747\) 0 0
\(748\) 0.995957 + 1.72505i 0.0364158 + 0.0630740i
\(749\) 26.7940 22.4829i 0.979033 0.821506i
\(750\) 0 0
\(751\) −6.94030 + 39.3604i −0.253255 + 1.43628i 0.547256 + 0.836965i \(0.315672\pi\)
−0.800512 + 0.599317i \(0.795439\pi\)
\(752\) −45.3921 38.0885i −1.65528 1.38894i
\(753\) 0 0
\(754\) −83.9132 30.5419i −3.05594 1.11227i
\(755\) −2.08615 −0.0759228
\(756\) 0 0
\(757\) 6.68348 0.242915 0.121458 0.992597i \(-0.461243\pi\)
0.121458 + 0.992597i \(0.461243\pi\)
\(758\) −12.7009 4.62276i −0.461319 0.167906i
\(759\) 0 0
\(760\) 8.22190 + 6.89899i 0.298240 + 0.250253i
\(761\) −7.29757 + 41.3866i −0.264537 + 1.50026i 0.505815 + 0.862642i \(0.331192\pi\)
−0.770351 + 0.637620i \(0.779919\pi\)
\(762\) 0 0
\(763\) −26.0043 + 21.8202i −0.941417 + 0.789943i
\(764\) 5.06692 + 8.77617i 0.183315 + 0.317511i
\(765\) 0 0
\(766\) −26.5445 + 45.9764i −0.959092 + 1.66120i
\(767\) 10.8081 + 61.2955i 0.390256 + 2.21325i
\(768\) 0 0
\(769\) −2.26770 + 0.825374i −0.0817752 + 0.0297637i −0.382584 0.923921i \(-0.624966\pi\)
0.300809 + 0.953685i \(0.402743\pi\)
\(770\) −28.7234 + 10.4545i −1.03512 + 0.376753i
\(771\) 0 0
\(772\) −1.78804 10.1405i −0.0643529 0.364964i
\(773\) 0.698900 1.21053i 0.0251377 0.0435398i −0.853183 0.521612i \(-0.825331\pi\)
0.878321 + 0.478072i \(0.158664\pi\)
\(774\) 0 0
\(775\) 1.13940 + 1.97350i 0.0409284 + 0.0708901i
\(776\) 15.6428 13.1259i 0.561544 0.471191i
\(777\) 0 0
\(778\) −4.09869 + 23.2448i −0.146945 + 0.833368i
\(779\) −9.97293 8.36828i −0.357317 0.299825i
\(780\) 0 0
\(781\) 21.9375 + 7.98459i 0.784984 + 0.285711i
\(782\) −2.48653 −0.0889181
\(783\) 0 0
\(784\) −3.43462 −0.122665
\(785\) 5.57275 + 2.02832i 0.198900 + 0.0723937i
\(786\) 0 0
\(787\) −30.3748 25.4875i −1.08275 0.908532i −0.0866001 0.996243i \(-0.527600\pi\)
−0.996146 + 0.0877113i \(0.972045\pi\)
\(788\) 0.818784 4.64356i 0.0291680 0.165420i
\(789\) 0 0
\(790\) −9.45112 + 7.93043i −0.336256 + 0.282152i
\(791\) −0.626496 1.08512i −0.0222756 0.0385825i
\(792\) 0 0
\(793\) 4.42041 7.65637i 0.156973 0.271886i
\(794\) 4.59884 + 26.0813i 0.163207 + 0.925592i
\(795\) 0 0
\(796\) 4.93663 1.79679i 0.174974 0.0636854i
\(797\) −3.09522 + 1.12657i −0.109638 + 0.0399051i −0.396257 0.918140i \(-0.629691\pi\)
0.286618 + 0.958045i \(0.407469\pi\)
\(798\) 0 0
\(799\) 2.11931 + 12.0192i 0.0749760 + 0.425210i
\(800\) 2.96964 5.14356i 0.104993 0.181852i
\(801\) 0 0
\(802\) −10.3593 17.9428i −0.365800 0.633583i
\(803\) 14.5055 12.1715i 0.511887 0.429525i
\(804\) 0 0
\(805\) 1.30679 7.41118i 0.0460583 0.261210i
\(806\) −8.68041 7.28373i −0.305754 0.256558i
\(807\) 0 0
\(808\) 17.4663 + 6.35723i 0.614463 + 0.223646i
\(809\) 6.54436 0.230087 0.115044 0.993360i \(-0.463299\pi\)
0.115044 + 0.993360i \(0.463299\pi\)
\(810\) 0 0
\(811\) −44.7516 −1.57144 −0.785721 0.618581i \(-0.787708\pi\)
−0.785721 + 0.618581i \(0.787708\pi\)
\(812\) 10.5586 + 3.84301i 0.370534 + 0.134863i
\(813\) 0 0
\(814\) −6.56705 5.51041i −0.230175 0.193140i
\(815\) 4.64920 26.3669i 0.162854 0.923593i
\(816\) 0 0
\(817\) 20.2418 16.9849i 0.708173 0.594227i
\(818\) 20.0856 + 34.7893i 0.702276 + 1.21638i
\(819\) 0 0
\(820\) 1.99927 3.46283i 0.0698174 0.120927i
\(821\) 8.62753 + 48.9291i 0.301103 + 1.70764i 0.641304 + 0.767287i \(0.278394\pi\)
−0.340202 + 0.940353i \(0.610495\pi\)
\(822\) 0 0
\(823\) −9.98011 + 3.63246i −0.347885 + 0.126620i −0.510052 0.860144i \(-0.670374\pi\)
0.162167 + 0.986763i \(0.448152\pi\)
\(824\) 4.84705 1.76418i 0.168855 0.0614582i
\(825\) 0 0
\(826\) −6.89540 39.1058i −0.239922 1.36066i
\(827\) −8.20039 + 14.2035i −0.285156 + 0.493904i −0.972647 0.232289i \(-0.925379\pi\)
0.687491 + 0.726193i \(0.258712\pi\)
\(828\) 0 0
\(829\) 1.47823 + 2.56036i 0.0513409 + 0.0889251i 0.890554 0.454878i \(-0.150317\pi\)
−0.839213 + 0.543803i \(0.816984\pi\)
\(830\) −11.6990 + 9.81663i −0.406078 + 0.340740i
\(831\) 0 0
\(832\) 6.19389 35.1273i 0.214734 1.21782i
\(833\) 0.541916 + 0.454722i 0.0187763 + 0.0157552i
\(834\) 0 0
\(835\) 22.8464 + 8.31539i 0.790631 + 0.287766i
\(836\) −5.47730 −0.189436
\(837\) 0 0
\(838\) −19.9985 −0.690835
\(839\) −30.4897 11.0973i −1.05262 0.383122i −0.242969 0.970034i \(-0.578121\pi\)
−0.809651 + 0.586911i \(0.800344\pi\)
\(840\) 0 0
\(841\) 29.6444 + 24.8746i 1.02222 + 0.857744i
\(842\) 4.84510 27.4779i 0.166973 0.946952i
\(843\) 0 0
\(844\) −5.66496 + 4.75347i −0.194996 + 0.163621i
\(845\) −28.7696 49.8304i −0.989705 1.71422i
\(846\) 0 0
\(847\) −8.66114 + 15.0015i −0.297600 + 0.515459i
\(848\) −6.04544 34.2854i −0.207601 1.17736i
\(849\) 0 0
\(850\) −3.16137 + 1.15065i −0.108434 + 0.0394668i
\(851\) 1.98330 0.721862i 0.0679866 0.0247451i
\(852\) 0 0
\(853\) 4.91999 + 27.9027i 0.168457 + 0.955369i 0.945428 + 0.325832i \(0.105644\pi\)
−0.776971 + 0.629537i \(0.783245\pi\)
\(854\) −2.82017 + 4.88467i −0.0965041 + 0.167150i
\(855\) 0 0
\(856\) −14.9839 25.9529i −0.512140 0.887052i
\(857\) −10.7273 + 9.00125i −0.366437 + 0.307477i −0.807350 0.590073i \(-0.799099\pi\)
0.440913 + 0.897550i \(0.354655\pi\)
\(858\) 0 0
\(859\) −0.375040 + 2.12696i −0.0127962 + 0.0725709i −0.990537 0.137245i \(-0.956175\pi\)
0.977741 + 0.209816i \(0.0672864\pi\)
\(860\) 6.21702 + 5.21670i 0.211999 + 0.177888i
\(861\) 0 0
\(862\) −23.2826 8.47418i −0.793009 0.288632i
\(863\) 14.9487 0.508859 0.254430 0.967091i \(-0.418112\pi\)
0.254430 + 0.967091i \(0.418112\pi\)
\(864\) 0 0
\(865\) −21.1784 −0.720087
\(866\) −18.7268 6.81601i −0.636364 0.231618i
\(867\) 0 0
\(868\) 1.09223 + 0.916493i 0.0370728 + 0.0311078i
\(869\) −3.35687 + 19.0377i −0.113874 + 0.645811i
\(870\) 0 0
\(871\) −24.4737 + 20.5359i −0.829260 + 0.695832i
\(872\) 14.5423 + 25.1879i 0.492463 + 0.852971i
\(873\) 0 0
\(874\) 3.41869 5.92134i 0.115639 0.200292i
\(875\) −5.81847 32.9982i −0.196700 1.11554i
\(876\) 0 0
\(877\) 1.77327 0.645419i 0.0598792 0.0217943i −0.311907 0.950113i \(-0.600968\pi\)
0.371786 + 0.928318i \(0.378745\pi\)
\(878\) 39.9532 14.5418i 1.34836 0.490762i
\(879\) 0 0
\(880\) 5.73675 + 32.5347i 0.193386 + 1.09674i
\(881\) 23.4129 40.5523i 0.788800 1.36624i −0.137902 0.990446i \(-0.544036\pi\)
0.926702 0.375796i \(-0.122631\pi\)
\(882\) 0 0
\(883\) 15.0317 + 26.0357i 0.505858 + 0.876172i 0.999977 + 0.00677750i \(0.00215736\pi\)
−0.494119 + 0.869394i \(0.664509\pi\)
\(884\) 2.52748 2.12081i 0.0850083 0.0713304i
\(885\) 0 0
\(886\) 9.51847 53.9819i 0.319779 1.81356i
\(887\) 22.9153 + 19.2283i 0.769422 + 0.645622i 0.940561 0.339625i \(-0.110300\pi\)
−0.171139 + 0.985247i \(0.554745\pi\)
\(888\) 0 0
\(889\) 1.38698 + 0.504818i 0.0465177 + 0.0169311i
\(890\) −12.0398 −0.403576
\(891\) 0 0
\(892\) −6.03788 −0.202163
\(893\) −31.5360 11.4782i −1.05531 0.384102i
\(894\) 0 0
\(895\) −0.380470 0.319252i −0.0127177 0.0106714i
\(896\) −6.57819 + 37.3068i −0.219762 + 1.24633i
\(897\) 0 0
\(898\) −25.0847 + 21.0486i −0.837088 + 0.702400i
\(899\) 4.29524 + 7.43957i 0.143254 + 0.248123i
\(900\) 0 0
\(901\) −3.58531 + 6.20994i −0.119444 + 0.206883i
\(902\) −5.51623 31.2841i −0.183670 1.04165i
\(903\) 0 0
\(904\) −1.00880 + 0.367173i −0.0335522 + 0.0122120i
\(905\) −2.24053 + 0.815486i −0.0744778 + 0.0271077i
\(906\) 0 0
\(907\) 4.64774 + 26.3586i 0.154326 + 0.875224i 0.959400 + 0.282050i \(0.0910143\pi\)
−0.805074 + 0.593174i \(0.797875\pi\)
\(908\) 0.921928 1.59683i 0.0305953 0.0529926i
\(909\) 0 0
\(910\) 25.3153 + 43.8474i 0.839194 + 1.45353i
\(911\) −0.337931 + 0.283557i −0.0111961 + 0.00939468i −0.648369 0.761327i \(-0.724548\pi\)
0.637172 + 0.770721i \(0.280104\pi\)
\(912\) 0 0
\(913\) −4.15527 + 23.5657i −0.137520 + 0.779912i
\(914\) 8.71507 + 7.31281i 0.288269 + 0.241886i
\(915\) 0 0
\(916\) 8.58925 + 3.12623i 0.283797 + 0.103294i
\(917\) −31.7284 −1.04776
\(918\) 0 0
\(919\) 49.0749 1.61883 0.809416 0.587236i \(-0.199784\pi\)
0.809416 + 0.587236i \(0.199784\pi\)
\(920\) −6.05889 2.20526i −0.199756 0.0727051i
\(921\) 0 0
\(922\) 27.9633 + 23.4640i 0.920922 + 0.772746i
\(923\) 6.71481 38.0816i 0.221021 1.25347i
\(924\) 0 0
\(925\) 2.18752 1.83555i 0.0719253 0.0603525i
\(926\) 3.92694 + 6.80167i 0.129047 + 0.223517i
\(927\) 0 0
\(928\) 11.1948 19.3899i 0.367486 0.636504i
\(929\) −5.63163 31.9385i −0.184768 1.04787i −0.926254 0.376901i \(-0.876990\pi\)
0.741486 0.670968i \(-0.234121\pi\)
\(930\) 0 0
\(931\) −1.82793 + 0.665313i −0.0599080 + 0.0218047i
\(932\) 0.252003 0.0917217i 0.00825464 0.00300444i
\(933\) 0 0
\(934\) −3.42098 19.4013i −0.111938 0.634831i
\(935\) 3.40224 5.89284i 0.111265 0.192717i
\(936\) 0 0
\(937\) −24.3079 42.1025i −0.794103 1.37543i −0.923407 0.383822i \(-0.874607\pi\)
0.129303 0.991605i \(-0.458726\pi\)
\(938\) 15.6139 13.1016i 0.509813 0.427784i
\(939\) 0 0
\(940\) 1.78988 10.1509i 0.0583794 0.331086i
\(941\) 0.544224 + 0.456658i 0.0177412 + 0.0148866i 0.651615 0.758550i \(-0.274092\pi\)
−0.633874 + 0.773436i \(0.718536\pi\)
\(942\) 0 0
\(943\) 7.34926 + 2.67491i 0.239325 + 0.0871071i
\(944\) −42.9175 −1.39685
\(945\) 0 0
\(946\) 64.4762 2.09630
\(947\) 24.5332 + 8.92937i 0.797223 + 0.290166i 0.708335 0.705876i \(-0.249446\pi\)
0.0888880 + 0.996042i \(0.471669\pi\)
\(948\) 0 0
\(949\) −24.0267 20.1608i −0.779941 0.654448i
\(950\) 1.60641 9.11040i 0.0521188 0.295580i
\(951\) 0 0
\(952\) 4.95092 4.15431i 0.160460 0.134642i
\(953\) −25.5027 44.1720i −0.826114 1.43087i −0.901065 0.433684i \(-0.857214\pi\)
0.0749515 0.997187i \(-0.476120\pi\)
\(954\) 0 0
\(955\) 17.3088 29.9798i 0.560101 0.970123i
\(956\) 1.71456 + 9.72375i 0.0554528 + 0.314488i
\(957\) 0 0
\(958\) −42.2290 + 15.3701i −1.36436 + 0.496585i
\(959\) 11.0454 4.02019i 0.356674 0.129819i
\(960\) 0 0
\(961\) −5.19380 29.4555i −0.167542 0.950178i
\(962\) −7.09985 + 12.2973i −0.228908 + 0.396481i
\(963\) 0 0
\(964\) −3.75677 6.50691i −0.120997 0.209573i
\(965\) −26.9454 + 22.6099i −0.867403 + 0.727837i
\(966\) 0 0
\(967\) 1.73732 9.85282i 0.0558684 0.316845i −0.944048 0.329809i \(-0.893016\pi\)
0.999916 + 0.0129639i \(0.00412664\pi\)
\(968\) 11.3692 + 9.53990i 0.365420 + 0.306624i
\(969\) 0 0
\(970\) 21.3493 + 7.77051i 0.685485 + 0.249496i
\(971\) −44.6269 −1.43215 −0.716073 0.698025i \(-0.754062\pi\)
−0.716073 + 0.698025i \(0.754062\pi\)
\(972\) 0 0
\(973\) −31.0044 −0.993954
\(974\) 44.0279 + 16.0248i 1.41074 + 0.513469i
\(975\) 0 0
\(976\) 4.66986 + 3.91848i 0.149479 + 0.125427i
\(977\) 6.78715 38.4918i 0.217140 1.23146i −0.660014 0.751254i \(-0.729449\pi\)
0.877154 0.480210i \(-0.159439\pi\)
\(978\) 0 0
\(979\) −14.4513 + 12.1261i −0.461867 + 0.387552i
\(980\) −0.298728 0.517412i −0.00954252 0.0165281i
\(981\) 0 0
\(982\) −9.79001 + 16.9568i −0.312412 + 0.541113i
\(983\) −1.17987 6.69136i −0.0376319 0.213421i 0.960193 0.279336i \(-0.0901145\pi\)
−0.997825 + 0.0659151i \(0.979003\pi\)
\(984\) 0 0
\(985\) −15.1359 + 5.50902i −0.482270 + 0.175532i
\(986\) −11.9175 + 4.33763i −0.379532 + 0.138138i
\(987\) 0 0
\(988\) 1.57543 + 8.93472i 0.0501212 + 0.284251i
\(989\) −7.93698 + 13.7473i −0.252381 + 0.437137i
\(990\) 0 0
\(991\) −8.60230 14.8996i −0.273261 0.473302i 0.696434 0.717621i \(-0.254769\pi\)
−0.969695 + 0.244319i \(0.921436\pi\)
\(992\) 2.17641 1.82622i 0.0691010 0.0579826i
\(993\) 0 0
\(994\) −4.28396 + 24.2956i −0.135879 + 0.770609i
\(995\) −13.7475 11.5355i −0.435824 0.365700i
\(996\) 0 0
\(997\) −6.89141 2.50827i −0.218253 0.0794376i 0.230579 0.973053i \(-0.425938\pi\)
−0.448833 + 0.893616i \(0.648160\pi\)
\(998\) 3.59848 0.113908
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (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 729.2.e.j.568.2 12
3.2 odd 2 729.2.e.u.568.1 12
9.2 odd 6 729.2.e.k.82.2 12
9.4 even 3 729.2.e.s.325.1 12
9.5 odd 6 729.2.e.l.325.2 12
9.7 even 3 729.2.e.t.82.1 12
27.2 odd 18 729.2.e.l.406.2 12
27.4 even 9 729.2.c.d.244.4 12
27.5 odd 18 729.2.c.a.487.3 12
27.7 even 9 inner 729.2.e.j.163.2 12
27.11 odd 18 729.2.e.k.649.2 12
27.13 even 9 729.2.a.b.1.3 6
27.14 odd 18 729.2.a.e.1.4 yes 6
27.16 even 9 729.2.e.t.649.1 12
27.20 odd 18 729.2.e.u.163.1 12
27.22 even 9 729.2.c.d.487.4 12
27.23 odd 18 729.2.c.a.244.3 12
27.25 even 9 729.2.e.s.406.1 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
729.2.a.b.1.3 6 27.13 even 9
729.2.a.e.1.4 yes 6 27.14 odd 18
729.2.c.a.244.3 12 27.23 odd 18
729.2.c.a.487.3 12 27.5 odd 18
729.2.c.d.244.4 12 27.4 even 9
729.2.c.d.487.4 12 27.22 even 9
729.2.e.j.163.2 12 27.7 even 9 inner
729.2.e.j.568.2 12 1.1 even 1 trivial
729.2.e.k.82.2 12 9.2 odd 6
729.2.e.k.649.2 12 27.11 odd 18
729.2.e.l.325.2 12 9.5 odd 6
729.2.e.l.406.2 12 27.2 odd 18
729.2.e.s.325.1 12 9.4 even 3
729.2.e.s.406.1 12 27.25 even 9
729.2.e.t.82.1 12 9.7 even 3
729.2.e.t.649.1 12 27.16 even 9
729.2.e.u.163.1 12 27.20 odd 18
729.2.e.u.568.1 12 3.2 odd 2