Properties

Label 729.2.e.u.163.1
Level $729$
Weight $2$
Character 729.163
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 163.1
Root \(1.22778i\) of defining polynomial
Character \(\chi\) \(=\) 729.163
Dual form 729.2.e.u.568.1

$q$-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 \(\left(\mathbb{Z}/729\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{8}{9}\right)\)

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 \(-0.799561\pi\)
−0.240585 + 0.970628i \(0.577339\pi\)
\(3\) 0 0
\(4\) 0.376403 0.315840i 0.188202 0.157920i
\(5\) −0.291470 1.65301i −0.130349 0.739247i −0.977986 0.208670i \(-0.933086\pi\)
0.847637 0.530577i \(-0.178025\pi\)
\(6\) 0 0
\(7\) 2.12905 + 1.78649i 0.804707 + 0.675229i 0.949338 0.314257i \(-0.101755\pi\)
−0.144632 + 0.989486i \(0.546200\pi\)
\(8\) 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 −0.659445 0.751753i \(-0.729209\pi\)
0.876790 0.480873i \(-0.159680\pi\)
\(12\) 0 0
\(13\) −6.46137 2.35175i −1.79206 0.652257i −0.999074 0.0430184i \(-0.986303\pi\)
−0.792987 0.609239i \(-0.791475\pi\)
\(14\) −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 \(-0.128882\pi\)
−0.800719 + 0.599040i \(0.795549\pi\)
\(18\) 0 0
\(19\) −1.34264 + 2.32553i −0.308024 + 0.533513i −0.977930 0.208933i \(-0.933001\pi\)
0.669906 + 0.742446i \(0.266334\pi\)
\(20\) −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 \(-0.776013\pi\)
0.504795 + 0.863239i \(0.331568\pi\)
\(24\) 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 \(-0.887848\pi\)
−0.497166 + 0.867655i \(0.665626\pi\)
\(30\) 0 0
\(31\) 0.799803 0.671115i 0.143649 0.120536i −0.568132 0.822938i \(-0.692334\pi\)
0.711780 + 0.702402i \(0.247889\pi\)
\(32\) −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 0.914775 0.403963i \(-0.132368\pi\)
−0.807230 + 0.590237i \(0.799034\pi\)
\(38\) 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 \(-0.512476\pi\)
−0.672311 + 0.740269i \(0.734698\pi\)
\(42\) 0 0
\(43\) 1.70874 9.69073i 0.260580 1.47782i −0.520752 0.853708i \(-0.674348\pi\)
0.781332 0.624115i \(-0.214540\pi\)
\(44\) −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 −0.962636 0.270800i \(-0.912712\pi\)
−0.433846 0.900987i \(-0.642844\pi\)
\(48\) 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 \(-0.668251\pi\)
−0.504305 + 0.863525i \(0.668251\pi\)
\(54\) 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 −0.898011 0.439973i \(-0.854988\pi\)
0.693375 0.720577i \(-0.256123\pi\)
\(60\) 0 0
\(61\) −0.984935 0.826459i −0.126108 0.105817i 0.577552 0.816354i \(-0.304008\pi\)
−0.703660 + 0.710536i \(0.748452\pi\)
\(62\) −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 0.594657 0.803979i \(-0.297288\pi\)
−0.0612541 + 0.998122i \(0.519510\pi\)
\(68\) 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 \(-0.0583670\pi\)
−0.649528 + 0.760337i \(0.725034\pi\)
\(72\) 0 0
\(73\) 2.28072 3.95033i 0.266938 0.462351i −0.701131 0.713032i \(-0.747321\pi\)
0.968070 + 0.250681i \(0.0806547\pi\)
\(74\) −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 −0.576243 0.817278i \(-0.695482\pi\)
0.0839088 + 0.996473i \(0.473260\pi\)
\(80\) 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 \(-0.508650\pi\)
0.621737 + 0.783226i \(0.286427\pi\)
\(84\) 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 \(-0.755906\pi\)
0.960958 + 0.276695i \(0.0892393\pi\)
\(90\) 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 −0.810985 0.585067i \(-0.801068\pi\)
0.962181 0.272410i \(-0.0878205\pi\)
\(98\) −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 \(-0.150824\pi\)
−0.294845 + 0.955545i \(0.595268\pi\)
\(102\) 0 0
\(103\) −0.376148 2.13324i −0.0370629 0.210194i 0.960652 0.277754i \(-0.0895899\pi\)
−0.997715 + 0.0675594i \(0.978479\pi\)
\(104\) −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 \(-0.708155\pi\)
−0.608317 + 0.793695i \(0.708155\pi\)
\(108\) 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 \(-0.0623060\pi\)
−0.988269 + 0.152726i \(0.951195\pi\)
\(114\) 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 −0.854004 0.520267i \(-0.825833\pi\)
0.877566 + 0.479456i \(0.159166\pi\)
\(128\) 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 \(-0.556029\pi\)
0.939183 + 0.343417i \(0.111584\pi\)
\(132\) 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 \(-0.668936\pi\)
0.166623 + 0.986021i \(0.446714\pi\)
\(138\) 0 0
\(139\) −8.54563 + 7.17064i −0.724831 + 0.608205i −0.928717 0.370789i \(-0.879087\pi\)
0.203886 + 0.978995i \(0.434643\pi\)
\(140\) −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 \(-0.0948662\pi\)
0.543527 + 0.839391i \(0.317088\pi\)
\(150\) 0 0
\(151\) −0.215820 + 1.22398i −0.0175632 + 0.0996059i −0.992329 0.123623i \(-0.960549\pi\)
0.974766 + 0.223229i \(0.0716598\pi\)
\(152\) 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 0.950489 0.310759i \(-0.100583\pi\)
−0.999453 + 0.0330680i \(0.989472\pi\)
\(158\) 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 0.912938 + 0.408098i \(0.133808\pi\)
−0.718304 + 0.695730i \(0.755081\pi\)
\(168\) 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 −0.780845 0.624725i \(-0.785211\pi\)
0.947423 0.319984i \(-0.103678\pi\)
\(174\) 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 \(-0.170187\pi\)
−0.871502 + 0.490393i \(0.836853\pi\)
\(180\) 0 0
\(181\) −0.710251 + 1.23019i −0.0527925 + 0.0914393i −0.891214 0.453583i \(-0.850146\pi\)
0.838421 + 0.545022i \(0.183479\pi\)
\(182\) 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 \(-0.879212\pi\)
−0.473446 + 0.880823i \(0.656990\pi\)
\(192\) 0 0
\(193\) −16.0532 + 13.4702i −1.15553 + 0.969608i −0.999834 0.0181970i \(-0.994207\pi\)
−0.155699 + 0.987805i \(0.549763\pi\)
\(194\) 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 \(-0.722280\pi\)
0.984776 + 0.173826i \(0.0556129\pi\)
\(198\) 0 0
\(199\) 5.34583 + 9.25925i 0.378956 + 0.656371i 0.990911 0.134522i \(-0.0429498\pi\)
−0.611955 + 0.790893i \(0.709616\pi\)
\(200\) 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 −0.932314 0.361650i \(-0.882213\pi\)
0.752397 0.658710i \(-0.228898\pi\)
\(212\) −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 0.270683 0.962669i \(-0.412751\pi\)
−0.901040 + 0.433736i \(0.857195\pi\)
\(224\) 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 \(-0.904701\pi\)
0.998766 + 0.0496553i \(0.0158123\pi\)
\(228\) 0 0
\(229\) 17.4806 + 6.36240i 1.15515 + 0.420439i 0.847362 0.531016i \(-0.178190\pi\)
0.307786 + 0.951456i \(0.400412\pi\)
\(230\) −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 \(-0.172358\pi\)
−0.874826 + 0.484438i \(0.839024\pi\)
\(234\) 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 \(-0.947416\pi\)
−0.00933493 + 0.999956i \(0.502971\pi\)
\(240\) 0 0
\(241\) −14.3691 + 5.22993i −0.925597 + 0.336890i −0.760463 0.649382i \(-0.775028\pi\)
−0.165134 + 0.986271i \(0.552806\pi\)
\(242\) 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 \(-0.965222\pi\)
0.591451 + 0.806341i \(0.298555\pi\)
\(252\) 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 \(-0.254863\pi\)
0.0719281 + 0.997410i \(0.477085\pi\)
\(258\) 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 \(-0.372543\pi\)
−0.839219 + 0.543794i \(0.816987\pi\)
\(264\) 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 \(-0.264155\pi\)
0.674973 + 0.737842i \(0.264155\pi\)
\(270\) 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 0.0947596 0.995500i \(-0.469792\pi\)
−0.963921 + 0.266187i \(0.914236\pi\)
\(278\) 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 0.686746 + 0.726897i \(0.259038\pi\)
−0.893944 + 0.448179i \(0.852073\pi\)
\(282\) 0 0
\(283\) −15.7352 5.72714i −0.935360 0.340443i −0.171028 0.985266i \(-0.554709\pi\)
−0.764332 + 0.644823i \(0.776931\pi\)
\(284\) 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 \(-0.528505\pi\)
0.965332 + 0.261024i \(0.0840602\pi\)
\(294\) 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 0.571258 0.820770i \(-0.306455\pi\)
−0.996437 + 0.0843392i \(0.973122\pi\)
\(308\) 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 \(-0.430452\pi\)
−0.461461 + 0.887161i \(0.652674\pi\)
\(312\) 0 0
\(313\) 2.06098 11.6884i 0.116493 0.660666i −0.869507 0.493921i \(-0.835563\pi\)
0.986000 0.166745i \(-0.0533257\pi\)
\(314\) 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 \(-0.411443\pi\)
−0.899250 + 0.437435i \(0.855887\pi\)
\(318\) 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 0.455988 0.889986i \(-0.349286\pi\)
−0.797284 + 0.603605i \(0.793730\pi\)
\(332\) 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 0.775110 0.631827i \(-0.217695\pi\)
0.187638 + 0.982238i \(0.439917\pi\)
\(338\) −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 \(-0.879009\pi\)
0.204128 + 0.978944i \(0.434564\pi\)
\(348\) 0 0
\(349\) 15.9647 5.81068i 0.854572 0.311039i 0.122669 0.992448i \(-0.460855\pi\)
0.731903 + 0.681409i \(0.238633\pi\)
\(350\) −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 \(-0.478965\pi\)
0.691970 + 0.721926i \(0.256743\pi\)
\(354\) 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 \(-0.853935\pi\)
0.831873 + 0.554966i \(0.187269\pi\)
\(360\) 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 −0.990182 0.139784i \(-0.955359\pi\)
0.978276 + 0.207308i \(0.0664703\pi\)
\(368\) −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 −0.997011 0.0772566i \(-0.975384\pi\)
0.910461 0.413595i \(-0.135727\pi\)
\(374\) −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 0.652881 + 0.757460i \(0.273560\pi\)
−0.354441 + 0.935078i \(0.615329\pi\)
\(384\) 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 0.845468 + 0.534026i \(0.179321\pi\)
−0.977128 + 0.212653i \(0.931790\pi\)
\(390\) 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 −0.574991 0.818159i \(-0.694995\pi\)
0.996043 + 0.0888774i \(0.0283279\pi\)
\(398\) −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 \(-0.615933\pi\)
0.858353 + 0.513060i \(0.171488\pi\)
\(402\) 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 −0.0175773 0.999846i \(-0.505595\pi\)
0.981603 + 0.190932i \(0.0611509\pi\)
\(410\) −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 \(-0.288732\pi\)
−0.0344063 + 0.999408i \(0.510954\pi\)
\(420\) 0 0
\(421\) −3.06962 + 17.4087i −0.149604 + 0.848447i 0.813950 + 0.580935i \(0.197313\pi\)
−0.963554 + 0.267513i \(0.913798\pi\)
\(422\) 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 \(-0.376592\pi\)
0.378059 + 0.925782i \(0.376592\pi\)
\(432\) 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 0.984814 0.173614i \(-0.0555444\pi\)
3.49262e−5 1.00000i \(0.499989\pi\)
\(440\) −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 −0.413310 0.910591i \(-0.635627\pi\)
0.699824 0.714315i \(-0.253262\pi\)
\(444\) 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 \(-0.00383314\pi\)
−0.510392 + 0.859942i \(0.670500\pi\)
\(450\) 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 −0.178710 0.983902i \(-0.557192\pi\)
0.495540 + 0.868585i \(0.334970\pi\)
\(458\) −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 \(-0.792143\pi\)
−0.217902 + 0.975971i \(0.569921\pi\)
\(462\) 0 0
\(463\) 3.81172 3.19841i 0.177145 0.148643i −0.549904 0.835228i \(-0.685336\pi\)
0.727049 + 0.686585i \(0.240891\pi\)
\(464\) −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 \(-0.740082\pi\)
0.973520 + 0.228602i \(0.0734156\pi\)
\(468\) 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 \(-0.0523612\pi\)
0.0100353 + 0.999950i \(0.496806\pi\)
\(480\) 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 0.994047 + 0.108955i \(0.0347503\pi\)
−0.896834 + 0.442368i \(0.854139\pi\)
\(492\) 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 0.389527 0.921015i \(-0.372639\pi\)
−0.293623 + 0.955921i \(0.594861\pi\)
\(500\) −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 −0.798920 0.601437i \(-0.794595\pi\)
−0.121399 0.992604i \(-0.538738\pi\)
\(504\) 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 \(-0.603635\pi\)
0.877529 + 0.479524i \(0.159191\pi\)
\(510\) 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 \(-0.768053\pi\)
0.949701 + 0.313157i \(0.101387\pi\)
\(522\) 0 0
\(523\) 11.3736 + 19.6996i 0.497331 + 0.861402i 0.999995 0.00307938i \(-0.000980199\pi\)
−0.502664 + 0.864482i \(0.667647\pi\)
\(524\) 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 0.982816 0.184588i \(-0.0590950\pi\)
−0.0111192 + 0.999938i \(0.503539\pi\)
\(548\) −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 \(-0.223713\pi\)
−0.941284 + 0.337615i \(0.890380\pi\)
\(558\) 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 \(-0.916726\pi\)
0.0869687 + 0.996211i \(0.472282\pi\)
\(564\) 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 \(-0.458931\pi\)
0.736007 + 0.676974i \(0.236709\pi\)
\(570\) 0 0
\(571\) −34.3597 + 28.8313i −1.43791 + 1.20655i −0.497066 + 0.867713i \(0.665589\pi\)
−0.940845 + 0.338837i \(0.889966\pi\)
\(572\) 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 0.713395 0.700762i \(-0.247157\pi\)
−0.963575 + 0.267437i \(0.913823\pi\)
\(578\) −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 \(-0.392089\pi\)
−0.871008 + 0.491269i \(0.836533\pi\)
\(588\) 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 \(-0.599164\pi\)
−0.306519 + 0.951865i \(0.599164\pi\)
\(594\) 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 0.994427 + 0.105430i \(0.0336218\pi\)
−0.898396 + 0.439186i \(0.855267\pi\)
\(600\) 0 0
\(601\) −34.7150 29.1294i −1.41606 1.18821i −0.953413 0.301667i \(-0.902457\pi\)
−0.462642 0.886545i \(-0.653099\pi\)
\(602\) −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 −0.169024 0.985612i \(-0.554061\pi\)
−0.763019 + 0.646376i \(0.776284\pi\)
\(608\) 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 −0.491046 0.871134i \(-0.663385\pi\)
0.999947 0.0103088i \(-0.00328145\pi\)
\(614\) 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 \(-0.696296\pi\)
0.702982 + 0.711208i \(0.251852\pi\)
\(618\) 0 0
\(619\) 42.0700 15.3122i 1.69094 0.615451i 0.696194 0.717853i \(-0.254875\pi\)
0.994743 + 0.102403i \(0.0326530\pi\)
\(620\) −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 −0.988495 0.151255i \(-0.951668\pi\)
0.363256 0.931689i \(-0.381665\pi\)
\(632\) −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 0.914524 + 0.404533i \(0.132566\pi\)
0.557192 + 0.830384i \(0.311879\pi\)
\(642\) 0 0
\(643\) −4.86777 27.6065i −0.191966 1.08869i −0.916674 0.399637i \(-0.869136\pi\)
0.724708 0.689057i \(-0.241975\pi\)
\(644\) −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 \(-0.764304\pi\)
−0.738159 + 0.674627i \(0.764304\pi\)
\(648\) 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 \(-0.0874489\pi\)
−0.997238 + 0.0742686i \(0.976338\pi\)
\(654\) 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 −0.602012 0.798487i \(-0.705634\pi\)
0.838805 0.544433i \(-0.183255\pi\)
\(660\) 0 0
\(661\) −1.25304 0.456071i −0.0487378 0.0177391i 0.317536 0.948246i \(-0.397144\pi\)
−0.366274 + 0.930507i \(0.619367\pi\)
\(662\) 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 −0.276375 0.961050i \(-0.589133\pi\)
0.406035 + 0.913858i \(0.366911\pi\)
\(674\) −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 \(-0.359879\pi\)
0.907937 + 0.419107i \(0.137657\pi\)
\(678\) 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 0.230675 + 0.973031i \(0.425907\pi\)
−0.958007 + 0.286745i \(0.907427\pi\)
\(684\) 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 −0.982936 0.183950i \(-0.941112\pi\)
0.986572 + 0.163327i \(0.0522227\pi\)
\(692\) −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 \(-0.383027\pi\)
0.359267 + 0.933235i \(0.383027\pi\)
\(702\) 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 0.800687 0.599083i \(-0.204468\pi\)
−0.450944 + 0.892552i \(0.648912\pi\)
\(710\) −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 \(-0.225022\pi\)
−0.942665 + 0.333741i \(0.891689\pi\)
\(720\) 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 −0.416452 0.909158i \(-0.636727\pi\)
0.265374 + 0.964145i \(0.414504\pi\)
\(728\) −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 −0.128354 0.991728i \(-0.540969\pi\)
0.954374 + 0.298615i \(0.0965248\pi\)
\(734\) −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 −0.940606 0.339501i \(-0.889742\pi\)
0.176287 0.984339i \(-0.443591\pi\)
\(740\) 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 \(-0.517150\pi\)
−0.683109 + 0.730316i \(0.739373\pi\)
\(744\) 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 −0.800512 0.599317i \(-0.795439\pi\)
0.547256 0.836965i \(-0.315672\pi\)
\(752\) 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 0.770351 + 0.637620i \(0.220081\pi\)
−0.505815 + 0.862642i \(0.668808\pi\)
\(762\) 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 0.300809 0.953685i \(-0.402743\pi\)
−0.382584 + 0.923921i \(0.624966\pi\)
\(770\) 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 \(-0.174669\pi\)
−0.878321 + 0.478072i \(0.841336\pi\)
\(774\) 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