Properties

Label 729.2.e.r.406.2
Level $729$
Weight $2$
Character 729.406
Analytic conductor $5.821$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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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: \(\Q(\zeta_{36})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - x^{6} + 1 \) 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 406.2
Root \(-0.342020 - 0.939693i\) of defining polynomial
Character \(\chi\) \(=\) 729.406
Dual form 729.2.e.r.325.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.524005 + 0.439693i) q^{2} +(-0.266044 - 1.50881i) q^{4} +(-0.984808 - 0.358441i) q^{5} +(-0.0209445 + 0.118782i) q^{7} +(1.20805 - 2.09240i) q^{8} +O(q^{10})\) \(q+(0.524005 + 0.439693i) q^{2} +(-0.266044 - 1.50881i) q^{4} +(-0.984808 - 0.358441i) q^{5} +(-0.0209445 + 0.118782i) q^{7} +(1.20805 - 2.09240i) q^{8} +(-0.358441 - 0.620838i) q^{10} +(5.10602 - 1.85844i) q^{11} +(-3.50387 + 2.94010i) q^{13} +(-0.0632028 + 0.0530334i) q^{14} +(-1.32635 + 0.482753i) q^{16} +(-2.38917 - 4.13816i) q^{17} +(0.294263 - 0.509678i) q^{19} +(-0.278817 + 1.58125i) q^{20} +(3.49273 + 1.27125i) q^{22} +(-1.35375 - 7.67752i) q^{23} +(-2.98886 - 2.50795i) q^{25} -3.12879 q^{26} +0.184793 q^{28} +(3.88365 + 3.25877i) q^{29} +(-1.52094 - 8.62571i) q^{31} +(-5.44804 - 1.98293i) q^{32} +(0.567581 - 3.21891i) q^{34} +(0.0632028 - 0.109470i) q^{35} +(1.09240 + 1.89209i) q^{37} +(0.378297 - 0.137689i) q^{38} +(-1.93969 + 1.62760i) q^{40} +(5.79006 - 4.85844i) q^{41} +(1.22668 - 0.446476i) q^{43} +(-4.16247 - 7.20961i) q^{44} +(2.66637 - 4.61830i) q^{46} +(0.419550 - 2.37939i) q^{47} +(6.56418 + 2.38917i) q^{49} +(-0.463450 - 2.62836i) q^{50} +(5.36824 + 4.50449i) q^{52} -3.04628 q^{53} -5.69459 q^{55} +(0.223238 + 0.187319i) q^{56} +(0.602196 + 3.41523i) q^{58} +(0.0412527 + 0.0150147i) q^{59} +(-1.77332 + 10.0570i) q^{61} +(2.99568 - 5.18866i) q^{62} +(-0.571452 - 0.989783i) q^{64} +(4.50449 - 1.63950i) q^{65} +(-1.42468 + 1.19545i) q^{67} +(-5.60808 + 4.70574i) q^{68} +(0.0812519 - 0.0295733i) q^{70} +(3.25519 + 5.63816i) q^{71} +(-6.11721 + 10.5953i) q^{73} +(-0.259515 + 1.47178i) q^{74} +(-0.847296 - 0.308391i) q^{76} +(0.113807 + 0.645430i) q^{77} +(0.538019 + 0.451451i) q^{79} +1.47924 q^{80} +5.17024 q^{82} +(5.19118 + 4.35591i) q^{83} +(0.869585 + 4.93166i) q^{85} +(0.839100 + 0.305407i) q^{86} +(2.27972 - 12.9289i) q^{88} +(-3.42782 + 5.93717i) q^{89} +(-0.275845 - 0.477777i) q^{91} +(-11.2238 + 4.08512i) q^{92} +(1.26604 - 1.06234i) q^{94} +(-0.472482 + 0.396459i) q^{95} +(8.48293 - 3.08753i) q^{97} +(2.38917 + 4.13816i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 6 q^{4} + 6 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 6 q^{4} + 6 q^{7} + 12 q^{10} + 6 q^{13} - 18 q^{16} + 24 q^{19} + 6 q^{22} - 48 q^{25} - 12 q^{28} - 12 q^{31} + 54 q^{34} + 6 q^{37} - 12 q^{40} - 12 q^{43} - 6 q^{46} + 42 q^{49} + 54 q^{52} - 60 q^{55} + 6 q^{58} - 48 q^{61} - 6 q^{64} - 66 q^{67} + 6 q^{70} - 12 q^{73} - 6 q^{76} + 42 q^{79} - 24 q^{82} - 18 q^{85} - 24 q^{88} + 6 q^{94} + 60 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.524005 + 0.439693i 0.370528 + 0.310910i 0.808970 0.587850i \(-0.200025\pi\)
−0.438443 + 0.898759i \(0.644470\pi\)
\(3\) 0 0
\(4\) −0.266044 1.50881i −0.133022 0.754407i
\(5\) −0.984808 0.358441i −0.440419 0.160300i 0.112287 0.993676i \(-0.464183\pi\)
−0.552706 + 0.833376i \(0.686405\pi\)
\(6\) 0 0
\(7\) −0.0209445 + 0.118782i −0.00791629 + 0.0448955i −0.988510 0.151155i \(-0.951701\pi\)
0.980594 + 0.196051i \(0.0628118\pi\)
\(8\) 1.20805 2.09240i 0.427109 0.739774i
\(9\) 0 0
\(10\) −0.358441 0.620838i −0.113349 0.196326i
\(11\) 5.10602 1.85844i 1.53952 0.560341i 0.573593 0.819140i \(-0.305549\pi\)
0.965931 + 0.258799i \(0.0833269\pi\)
\(12\) 0 0
\(13\) −3.50387 + 2.94010i −0.971799 + 0.815436i −0.982832 0.184503i \(-0.940932\pi\)
0.0110331 + 0.999939i \(0.496488\pi\)
\(14\) −0.0632028 + 0.0530334i −0.0168917 + 0.0141738i
\(15\) 0 0
\(16\) −1.32635 + 0.482753i −0.331588 + 0.120688i
\(17\) −2.38917 4.13816i −0.579458 1.00365i −0.995542 0.0943239i \(-0.969931\pi\)
0.416084 0.909326i \(-0.363402\pi\)
\(18\) 0 0
\(19\) 0.294263 0.509678i 0.0675085 0.116928i −0.830295 0.557323i \(-0.811828\pi\)
0.897804 + 0.440395i \(0.145162\pi\)
\(20\) −0.278817 + 1.58125i −0.0623455 + 0.353579i
\(21\) 0 0
\(22\) 3.49273 + 1.27125i 0.744652 + 0.271031i
\(23\) −1.35375 7.67752i −0.282277 1.60087i −0.714852 0.699275i \(-0.753506\pi\)
0.432575 0.901598i \(-0.357605\pi\)
\(24\) 0 0
\(25\) −2.98886 2.50795i −0.597771 0.501590i
\(26\) −3.12879 −0.613605
\(27\) 0 0
\(28\) 0.184793 0.0349225
\(29\) 3.88365 + 3.25877i 0.721176 + 0.605138i 0.927710 0.373301i \(-0.121774\pi\)
−0.206534 + 0.978439i \(0.566219\pi\)
\(30\) 0 0
\(31\) −1.52094 8.62571i −0.273170 1.54922i −0.744716 0.667381i \(-0.767415\pi\)
0.471547 0.881841i \(-0.343696\pi\)
\(32\) −5.44804 1.98293i −0.963087 0.350535i
\(33\) 0 0
\(34\) 0.567581 3.21891i 0.0973394 0.552039i
\(35\) 0.0632028 0.109470i 0.0106832 0.0185039i
\(36\) 0 0
\(37\) 1.09240 + 1.89209i 0.179589 + 0.311057i 0.941740 0.336342i \(-0.109190\pi\)
−0.762151 + 0.647399i \(0.775857\pi\)
\(38\) 0.378297 0.137689i 0.0613679 0.0223361i
\(39\) 0 0
\(40\) −1.93969 + 1.62760i −0.306692 + 0.257345i
\(41\) 5.79006 4.85844i 0.904256 0.758761i −0.0667615 0.997769i \(-0.521267\pi\)
0.971018 + 0.239008i \(0.0768222\pi\)
\(42\) 0 0
\(43\) 1.22668 0.446476i 0.187067 0.0680869i −0.246788 0.969069i \(-0.579375\pi\)
0.433855 + 0.900983i \(0.357153\pi\)
\(44\) −4.16247 7.20961i −0.627516 1.08689i
\(45\) 0 0
\(46\) 2.66637 4.61830i 0.393135 0.680931i
\(47\) 0.419550 2.37939i 0.0611976 0.347069i −0.938799 0.344465i \(-0.888060\pi\)
0.999997 0.00260352i \(-0.000828726\pi\)
\(48\) 0 0
\(49\) 6.56418 + 2.38917i 0.937740 + 0.341309i
\(50\) −0.463450 2.62836i −0.0655417 0.371706i
\(51\) 0 0
\(52\) 5.36824 + 4.50449i 0.744441 + 0.624660i
\(53\) −3.04628 −0.418439 −0.209219 0.977869i \(-0.567092\pi\)
−0.209219 + 0.977869i \(0.567092\pi\)
\(54\) 0 0
\(55\) −5.69459 −0.767859
\(56\) 0.223238 + 0.187319i 0.0298314 + 0.0250315i
\(57\) 0 0
\(58\) 0.602196 + 3.41523i 0.0790723 + 0.448441i
\(59\) 0.0412527 + 0.0150147i 0.00537064 + 0.00195475i 0.344704 0.938711i \(-0.387979\pi\)
−0.339333 + 0.940666i \(0.610201\pi\)
\(60\) 0 0
\(61\) −1.77332 + 10.0570i −0.227050 + 1.28767i 0.631677 + 0.775232i \(0.282367\pi\)
−0.858727 + 0.512434i \(0.828744\pi\)
\(62\) 2.99568 5.18866i 0.380451 0.658961i
\(63\) 0 0
\(64\) −0.571452 0.989783i −0.0714315 0.123723i
\(65\) 4.50449 1.63950i 0.558713 0.203355i
\(66\) 0 0
\(67\) −1.42468 + 1.19545i −0.174052 + 0.146047i −0.725652 0.688062i \(-0.758462\pi\)
0.551600 + 0.834109i \(0.314017\pi\)
\(68\) −5.60808 + 4.70574i −0.680079 + 0.570654i
\(69\) 0 0
\(70\) 0.0812519 0.0295733i 0.00971146 0.00353468i
\(71\) 3.25519 + 5.63816i 0.386320 + 0.669126i 0.991951 0.126619i \(-0.0404127\pi\)
−0.605631 + 0.795745i \(0.707079\pi\)
\(72\) 0 0
\(73\) −6.11721 + 10.5953i −0.715965 + 1.24009i 0.246621 + 0.969112i \(0.420680\pi\)
−0.962586 + 0.270976i \(0.912653\pi\)
\(74\) −0.259515 + 1.47178i −0.0301680 + 0.171091i
\(75\) 0 0
\(76\) −0.847296 0.308391i −0.0971916 0.0353748i
\(77\) 0.113807 + 0.645430i 0.0129695 + 0.0735535i
\(78\) 0 0
\(79\) 0.538019 + 0.451451i 0.0605318 + 0.0507922i 0.672552 0.740050i \(-0.265198\pi\)
−0.612020 + 0.790842i \(0.709643\pi\)
\(80\) 1.47924 0.165384
\(81\) 0 0
\(82\) 5.17024 0.570958
\(83\) 5.19118 + 4.35591i 0.569806 + 0.478124i 0.881581 0.472032i \(-0.156479\pi\)
−0.311776 + 0.950156i \(0.600924\pi\)
\(84\) 0 0
\(85\) 0.869585 + 4.93166i 0.0943197 + 0.534914i
\(86\) 0.839100 + 0.305407i 0.0904824 + 0.0329329i
\(87\) 0 0
\(88\) 2.27972 12.9289i 0.243018 1.37823i
\(89\) −3.42782 + 5.93717i −0.363349 + 0.629338i −0.988510 0.151157i \(-0.951700\pi\)
0.625161 + 0.780496i \(0.285033\pi\)
\(90\) 0 0
\(91\) −0.275845 0.477777i −0.0289164 0.0500846i
\(92\) −11.2238 + 4.08512i −1.17016 + 0.425903i
\(93\) 0 0
\(94\) 1.26604 1.06234i 0.130583 0.109572i
\(95\) −0.472482 + 0.396459i −0.0484756 + 0.0406759i
\(96\) 0 0
\(97\) 8.48293 3.08753i 0.861311 0.313491i 0.126668 0.991945i \(-0.459572\pi\)
0.734643 + 0.678454i \(0.237350\pi\)
\(98\) 2.38917 + 4.13816i 0.241342 + 0.418017i
\(99\) 0 0
\(100\) −2.98886 + 5.17685i −0.298886 + 0.517685i
\(101\) 2.25606 12.7947i 0.224486 1.27312i −0.639179 0.769058i \(-0.720726\pi\)
0.863665 0.504066i \(-0.168163\pi\)
\(102\) 0 0
\(103\) −8.52481 3.10278i −0.839975 0.305726i −0.114029 0.993477i \(-0.536376\pi\)
−0.725946 + 0.687752i \(0.758598\pi\)
\(104\) 1.91901 + 10.8833i 0.188175 + 1.06719i
\(105\) 0 0
\(106\) −1.59627 1.33943i −0.155043 0.130097i
\(107\) 11.3865 1.10077 0.550386 0.834911i \(-0.314481\pi\)
0.550386 + 0.834911i \(0.314481\pi\)
\(108\) 0 0
\(109\) 2.89899 0.277672 0.138836 0.990315i \(-0.455664\pi\)
0.138836 + 0.990315i \(0.455664\pi\)
\(110\) −2.98400 2.50387i −0.284513 0.238735i
\(111\) 0 0
\(112\) −0.0295627 0.167658i −0.00279341 0.0158422i
\(113\) 10.8818 + 3.96064i 1.02367 + 0.372585i 0.798667 0.601773i \(-0.205539\pi\)
0.225003 + 0.974358i \(0.427761\pi\)
\(114\) 0 0
\(115\) −1.41875 + 8.04612i −0.132299 + 0.750305i
\(116\) 3.88365 6.72668i 0.360588 0.624557i
\(117\) 0 0
\(118\) 0.0150147 + 0.0260063i 0.00138222 + 0.00239407i
\(119\) 0.541580 0.197119i 0.0496465 0.0180699i
\(120\) 0 0
\(121\) 14.1912 11.9078i 1.29011 1.08253i
\(122\) −5.35121 + 4.49020i −0.484476 + 0.406524i
\(123\) 0 0
\(124\) −12.6099 + 4.58964i −1.13241 + 0.412162i
\(125\) 4.66452 + 8.07919i 0.417208 + 0.722625i
\(126\) 0 0
\(127\) 7.70961 13.3534i 0.684117 1.18493i −0.289596 0.957149i \(-0.593521\pi\)
0.973713 0.227777i \(-0.0731456\pi\)
\(128\) −1.87776 + 10.6493i −0.165972 + 0.941274i
\(129\) 0 0
\(130\) 3.08125 + 1.12148i 0.270244 + 0.0983607i
\(131\) 2.31926 + 13.1532i 0.202635 + 1.14920i 0.901119 + 0.433572i \(0.142747\pi\)
−0.698484 + 0.715625i \(0.746142\pi\)
\(132\) 0 0
\(133\) 0.0543776 + 0.0456282i 0.00471514 + 0.00395647i
\(134\) −1.27217 −0.109899
\(135\) 0 0
\(136\) −11.5449 −0.989965
\(137\) −15.0326 12.6138i −1.28432 1.07767i −0.992634 0.121156i \(-0.961340\pi\)
−0.291684 0.956515i \(-0.594216\pi\)
\(138\) 0 0
\(139\) 2.83157 + 16.0586i 0.240170 + 1.36207i 0.831447 + 0.555605i \(0.187513\pi\)
−0.591276 + 0.806469i \(0.701376\pi\)
\(140\) −0.181985 0.0662372i −0.0153805 0.00559806i
\(141\) 0 0
\(142\) −0.773318 + 4.38571i −0.0648954 + 0.368040i
\(143\) −12.4269 + 21.5239i −1.03919 + 1.79992i
\(144\) 0 0
\(145\) −2.65657 4.60132i −0.220616 0.382119i
\(146\) −7.86414 + 2.86231i −0.650840 + 0.236887i
\(147\) 0 0
\(148\) 2.56418 2.15160i 0.210774 0.176860i
\(149\) 8.46302 7.10132i 0.693318 0.581763i −0.226546 0.974000i \(-0.572743\pi\)
0.919864 + 0.392238i \(0.128299\pi\)
\(150\) 0 0
\(151\) 6.39053 2.32596i 0.520054 0.189284i −0.0686380 0.997642i \(-0.521865\pi\)
0.588692 + 0.808357i \(0.299643\pi\)
\(152\) −0.710966 1.23143i −0.0576670 0.0998821i
\(153\) 0 0
\(154\) −0.224155 + 0.388249i −0.0180630 + 0.0312860i
\(155\) −1.59397 + 9.03983i −0.128030 + 0.726097i
\(156\) 0 0
\(157\) −15.8687 5.77574i −1.26646 0.460954i −0.380529 0.924769i \(-0.624258\pi\)
−0.885932 + 0.463815i \(0.846480\pi\)
\(158\) 0.0834248 + 0.473126i 0.00663692 + 0.0376399i
\(159\) 0 0
\(160\) 4.65451 + 3.90560i 0.367972 + 0.308765i
\(161\) 0.940307 0.0741066
\(162\) 0 0
\(163\) 8.41147 0.658838 0.329419 0.944184i \(-0.393147\pi\)
0.329419 + 0.944184i \(0.393147\pi\)
\(164\) −8.87089 7.44356i −0.692700 0.581245i
\(165\) 0 0
\(166\) 0.804940 + 4.56504i 0.0624755 + 0.354316i
\(167\) 2.46669 + 0.897804i 0.190879 + 0.0694741i 0.435691 0.900096i \(-0.356504\pi\)
−0.244812 + 0.969571i \(0.578726\pi\)
\(168\) 0 0
\(169\) 1.37551 7.80093i 0.105809 0.600072i
\(170\) −1.71275 + 2.96657i −0.131362 + 0.227525i
\(171\) 0 0
\(172\) −1.00000 1.73205i −0.0762493 0.132068i
\(173\) −12.3130 + 4.48158i −0.936143 + 0.340728i −0.764642 0.644455i \(-0.777084\pi\)
−0.171502 + 0.985184i \(0.554862\pi\)
\(174\) 0 0
\(175\) 0.360500 0.302496i 0.0272512 0.0228665i
\(176\) −5.87522 + 4.92989i −0.442861 + 0.371605i
\(177\) 0 0
\(178\) −4.40673 + 1.60392i −0.330298 + 0.120219i
\(179\) 11.0494 + 19.1382i 0.825872 + 1.43045i 0.901251 + 0.433298i \(0.142650\pi\)
−0.0753784 + 0.997155i \(0.524016\pi\)
\(180\) 0 0
\(181\) 1.02956 1.78325i 0.0765268 0.132548i −0.825222 0.564808i \(-0.808950\pi\)
0.901749 + 0.432260i \(0.142284\pi\)
\(182\) 0.0655309 0.371644i 0.00485748 0.0275481i
\(183\) 0 0
\(184\) −17.6998 6.44220i −1.30485 0.474926i
\(185\) −0.397600 2.25490i −0.0292321 0.165784i
\(186\) 0 0
\(187\) −19.8897 16.6894i −1.45448 1.22045i
\(188\) −3.70167 −0.269972
\(189\) 0 0
\(190\) −0.421903 −0.0306081
\(191\) −3.02525 2.53849i −0.218899 0.183678i 0.526743 0.850024i \(-0.323413\pi\)
−0.745643 + 0.666346i \(0.767857\pi\)
\(192\) 0 0
\(193\) −1.46673 8.31823i −0.105577 0.598760i −0.990988 0.133950i \(-0.957234\pi\)
0.885411 0.464810i \(-0.153877\pi\)
\(194\) 5.80266 + 2.11200i 0.416607 + 0.151633i
\(195\) 0 0
\(196\) 1.85844 10.5397i 0.132746 0.752839i
\(197\) 1.14749 1.98751i 0.0817553 0.141604i −0.822249 0.569128i \(-0.807281\pi\)
0.904004 + 0.427524i \(0.140614\pi\)
\(198\) 0 0
\(199\) 11.7515 + 20.3542i 0.833042 + 1.44287i 0.895615 + 0.444830i \(0.146736\pi\)
−0.0625736 + 0.998040i \(0.519931\pi\)
\(200\) −8.85829 + 3.22416i −0.626376 + 0.227982i
\(201\) 0 0
\(202\) 6.80793 5.71253i 0.479005 0.401933i
\(203\) −0.468426 + 0.393056i −0.0328770 + 0.0275871i
\(204\) 0 0
\(205\) −7.44356 + 2.70924i −0.519881 + 0.189221i
\(206\) −3.10278 5.37417i −0.216181 0.374436i
\(207\) 0 0
\(208\) 3.22803 5.59110i 0.223823 0.387673i
\(209\) 0.555307 3.14930i 0.0384114 0.217842i
\(210\) 0 0
\(211\) 1.56670 + 0.570234i 0.107856 + 0.0392565i 0.395385 0.918516i \(-0.370611\pi\)
−0.287528 + 0.957772i \(0.592834\pi\)
\(212\) 0.810446 + 4.59627i 0.0556616 + 0.315673i
\(213\) 0 0
\(214\) 5.96657 + 5.00654i 0.407866 + 0.342240i
\(215\) −1.36808 −0.0933023
\(216\) 0 0
\(217\) 1.05644 0.0717156
\(218\) 1.51908 + 1.27466i 0.102885 + 0.0863310i
\(219\) 0 0
\(220\) 1.51501 + 8.59208i 0.102142 + 0.579278i
\(221\) 20.5379 + 7.47519i 1.38153 + 0.502835i
\(222\) 0 0
\(223\) −1.70187 + 9.65177i −0.113965 + 0.646330i 0.873292 + 0.487198i \(0.161981\pi\)
−0.987257 + 0.159133i \(0.949130\pi\)
\(224\) 0.349643 0.605600i 0.0233615 0.0404634i
\(225\) 0 0
\(226\) 3.96064 + 6.86002i 0.263458 + 0.456322i
\(227\) 14.5472 5.29473i 0.965528 0.351424i 0.189331 0.981913i \(-0.439368\pi\)
0.776198 + 0.630490i \(0.217146\pi\)
\(228\) 0 0
\(229\) −8.62108 + 7.23395i −0.569697 + 0.478033i −0.881545 0.472099i \(-0.843496\pi\)
0.311848 + 0.950132i \(0.399052\pi\)
\(230\) −4.28125 + 3.59240i −0.282297 + 0.236876i
\(231\) 0 0
\(232\) 11.5103 4.18939i 0.755686 0.275047i
\(233\) 2.61738 + 4.53343i 0.171470 + 0.296995i 0.938934 0.344097i \(-0.111815\pi\)
−0.767464 + 0.641092i \(0.778482\pi\)
\(234\) 0 0
\(235\) −1.26604 + 2.19285i −0.0825876 + 0.143046i
\(236\) 0.0116794 0.0662372i 0.000760264 0.00431167i
\(237\) 0 0
\(238\) 0.370462 + 0.134837i 0.0240135 + 0.00874020i
\(239\) 1.79028 + 10.1532i 0.115803 + 0.656754i 0.986349 + 0.164667i \(0.0526548\pi\)
−0.870546 + 0.492087i \(0.836234\pi\)
\(240\) 0 0
\(241\) 8.23055 + 6.90625i 0.530176 + 0.444871i 0.868162 0.496280i \(-0.165301\pi\)
−0.337986 + 0.941151i \(0.609746\pi\)
\(242\) 12.6720 0.814590
\(243\) 0 0
\(244\) 15.6459 1.00163
\(245\) −5.60808 4.70574i −0.358287 0.300639i
\(246\) 0 0
\(247\) 0.467444 + 2.65101i 0.0297428 + 0.168680i
\(248\) −19.8858 7.23783i −1.26275 0.459602i
\(249\) 0 0
\(250\) −1.10813 + 6.28450i −0.0700841 + 0.397466i
\(251\) 7.53644 13.0535i 0.475696 0.823930i −0.523916 0.851770i \(-0.675530\pi\)
0.999612 + 0.0278401i \(0.00886291\pi\)
\(252\) 0 0
\(253\) −21.1805 36.6857i −1.33161 2.30641i
\(254\) 9.91128 3.60741i 0.621889 0.226349i
\(255\) 0 0
\(256\) −7.41740 + 6.22394i −0.463588 + 0.388996i
\(257\) 2.54514 2.13563i 0.158762 0.133217i −0.559946 0.828529i \(-0.689178\pi\)
0.718708 + 0.695312i \(0.244734\pi\)
\(258\) 0 0
\(259\) −0.247626 + 0.0901285i −0.0153867 + 0.00560032i
\(260\) −3.67209 6.36025i −0.227734 0.394446i
\(261\) 0 0
\(262\) −4.56805 + 7.91209i −0.282215 + 0.488811i
\(263\) −1.53482 + 8.70439i −0.0946410 + 0.536736i 0.900216 + 0.435444i \(0.143409\pi\)
−0.994857 + 0.101292i \(0.967702\pi\)
\(264\) 0 0
\(265\) 3.00000 + 1.09191i 0.184289 + 0.0670755i
\(266\) 0.00843175 + 0.0478189i 0.000516984 + 0.00293196i
\(267\) 0 0
\(268\) 2.18273 + 1.83153i 0.133332 + 0.111879i
\(269\) −8.09267 −0.493419 −0.246709 0.969090i \(-0.579349\pi\)
−0.246709 + 0.969090i \(0.579349\pi\)
\(270\) 0 0
\(271\) −19.0000 −1.15417 −0.577084 0.816685i \(-0.695809\pi\)
−0.577084 + 0.816685i \(0.695809\pi\)
\(272\) 5.16658 + 4.33527i 0.313270 + 0.262865i
\(273\) 0 0
\(274\) −2.33094 13.2194i −0.140817 0.798613i
\(275\) −19.9220 7.25103i −1.20134 0.437254i
\(276\) 0 0
\(277\) −0.734422 + 4.16512i −0.0441272 + 0.250258i −0.998890 0.0471120i \(-0.984998\pi\)
0.954762 + 0.297370i \(0.0961093\pi\)
\(278\) −5.57710 + 9.65982i −0.334492 + 0.579357i
\(279\) 0 0
\(280\) −0.152704 0.264490i −0.00912579 0.0158063i
\(281\) 6.86175 2.49747i 0.409338 0.148987i −0.129140 0.991626i \(-0.541222\pi\)
0.538478 + 0.842640i \(0.318999\pi\)
\(282\) 0 0
\(283\) 12.2724 10.2978i 0.729521 0.612141i −0.200480 0.979698i \(-0.564250\pi\)
0.930001 + 0.367557i \(0.119806\pi\)
\(284\) 7.64090 6.41147i 0.453404 0.380451i
\(285\) 0 0
\(286\) −15.9757 + 5.81466i −0.944660 + 0.343828i
\(287\) 0.455827 + 0.789515i 0.0269066 + 0.0466036i
\(288\) 0 0
\(289\) −2.91622 + 5.05104i −0.171542 + 0.297120i
\(290\) 0.631108 3.57919i 0.0370600 0.210177i
\(291\) 0 0
\(292\) 17.6138 + 6.41090i 1.03077 + 0.375170i
\(293\) −3.12646 17.7310i −0.182650 1.03586i −0.928938 0.370235i \(-0.879277\pi\)
0.746289 0.665622i \(-0.231834\pi\)
\(294\) 0 0
\(295\) −0.0352441 0.0295733i −0.00205199 0.00172182i
\(296\) 5.27866 0.306816
\(297\) 0 0
\(298\) 7.55707 0.437769
\(299\) 27.3160 + 22.9209i 1.57973 + 1.32555i
\(300\) 0 0
\(301\) 0.0273411 + 0.155059i 0.00157592 + 0.00893747i
\(302\) 4.37138 + 1.59105i 0.251545 + 0.0915548i
\(303\) 0 0
\(304\) −0.144248 + 0.818069i −0.00827317 + 0.0469195i
\(305\) 5.35121 9.26857i 0.306409 0.530717i
\(306\) 0 0
\(307\) 6.75537 + 11.7006i 0.385549 + 0.667791i 0.991845 0.127448i \(-0.0406787\pi\)
−0.606296 + 0.795239i \(0.707345\pi\)
\(308\) 0.943555 0.343426i 0.0537640 0.0195685i
\(309\) 0 0
\(310\) −4.80999 + 4.03606i −0.273189 + 0.229233i
\(311\) −12.5802 + 10.5560i −0.713357 + 0.598577i −0.925539 0.378653i \(-0.876387\pi\)
0.212182 + 0.977230i \(0.431943\pi\)
\(312\) 0 0
\(313\) 18.3849 6.69156i 1.03918 0.378229i 0.234608 0.972090i \(-0.424619\pi\)
0.804568 + 0.593861i \(0.202397\pi\)
\(314\) −5.77574 10.0039i −0.325944 0.564551i
\(315\) 0 0
\(316\) 0.538019 0.931876i 0.0302659 0.0524221i
\(317\) 4.23329 24.0082i 0.237766 1.34844i −0.598945 0.800790i \(-0.704413\pi\)
0.836711 0.547645i \(-0.184476\pi\)
\(318\) 0 0
\(319\) 25.8862 + 9.42182i 1.44935 + 0.527521i
\(320\) 0.207991 + 1.17958i 0.0116271 + 0.0659404i
\(321\) 0 0
\(322\) 0.492726 + 0.413446i 0.0274585 + 0.0230405i
\(323\) −2.81217 −0.156473
\(324\) 0 0
\(325\) 17.8462 0.989927
\(326\) 4.40766 + 3.69846i 0.244118 + 0.204839i
\(327\) 0 0
\(328\) −3.17112 17.9843i −0.175096 0.993018i
\(329\) 0.273842 + 0.0996702i 0.0150974 + 0.00549500i
\(330\) 0 0
\(331\) 4.94878 28.0659i 0.272009 1.54264i −0.476294 0.879286i \(-0.658020\pi\)
0.748304 0.663356i \(-0.230869\pi\)
\(332\) 5.19118 8.99138i 0.284903 0.493466i
\(333\) 0 0
\(334\) 0.897804 + 1.55504i 0.0491256 + 0.0850881i
\(335\) 1.83153 0.666623i 0.100067 0.0364215i
\(336\) 0 0
\(337\) −13.3648 + 11.2144i −0.728029 + 0.610889i −0.929594 0.368586i \(-0.879842\pi\)
0.201564 + 0.979475i \(0.435397\pi\)
\(338\) 4.15079 3.48293i 0.225773 0.189446i
\(339\) 0 0
\(340\) 7.20961 2.62408i 0.390996 0.142311i
\(341\) −23.7963 41.2165i −1.28864 2.23200i
\(342\) 0 0
\(343\) −0.843426 + 1.46086i −0.0455407 + 0.0788788i
\(344\) 0.547683 3.10607i 0.0295291 0.167468i
\(345\) 0 0
\(346\) −8.42262 3.06558i −0.452803 0.164807i
\(347\) −4.37403 24.8063i −0.234810 1.33167i −0.843013 0.537893i \(-0.819221\pi\)
0.608203 0.793781i \(-0.291891\pi\)
\(348\) 0 0
\(349\) −9.07919 7.61835i −0.485998 0.407801i 0.366591 0.930382i \(-0.380525\pi\)
−0.852589 + 0.522581i \(0.824969\pi\)
\(350\) 0.321909 0.0172068
\(351\) 0 0
\(352\) −31.5030 −1.67912
\(353\) 6.43285 + 5.39780i 0.342386 + 0.287296i 0.797724 0.603023i \(-0.206037\pi\)
−0.455338 + 0.890319i \(0.650482\pi\)
\(354\) 0 0
\(355\) −1.18479 6.71929i −0.0628823 0.356623i
\(356\) 9.87003 + 3.59240i 0.523110 + 0.190397i
\(357\) 0 0
\(358\) −2.62495 + 14.8868i −0.138733 + 0.786794i
\(359\) 1.32012 2.28652i 0.0696735 0.120678i −0.829084 0.559124i \(-0.811138\pi\)
0.898758 + 0.438446i \(0.144471\pi\)
\(360\) 0 0
\(361\) 9.32682 + 16.1545i 0.490885 + 0.850238i
\(362\) 1.32358 0.481744i 0.0695658 0.0253199i
\(363\) 0 0
\(364\) −0.647489 + 0.543308i −0.0339376 + 0.0284771i
\(365\) 9.82207 8.24170i 0.514111 0.431390i
\(366\) 0 0
\(367\) −8.64290 + 3.14576i −0.451156 + 0.164207i −0.557597 0.830112i \(-0.688277\pi\)
0.106441 + 0.994319i \(0.466054\pi\)
\(368\) 5.50190 + 9.52956i 0.286806 + 0.496763i
\(369\) 0 0
\(370\) 0.783119 1.35640i 0.0407124 0.0705159i
\(371\) 0.0638029 0.361844i 0.00331248 0.0187860i
\(372\) 0 0
\(373\) 25.1755 + 9.16312i 1.30354 + 0.474448i 0.898147 0.439696i \(-0.144914\pi\)
0.405389 + 0.914144i \(0.367136\pi\)
\(374\) −3.08408 17.4907i −0.159474 0.904421i
\(375\) 0 0
\(376\) −4.47178 3.75227i −0.230615 0.193509i
\(377\) −23.1889 −1.19429
\(378\) 0 0
\(379\) −27.1242 −1.39328 −0.696639 0.717422i \(-0.745322\pi\)
−0.696639 + 0.717422i \(0.745322\pi\)
\(380\) 0.723884 + 0.607411i 0.0371345 + 0.0311595i
\(381\) 0 0
\(382\) −0.469093 2.66036i −0.0240009 0.136116i
\(383\) −32.3506 11.7747i −1.65304 0.601657i −0.663793 0.747916i \(-0.731054\pi\)
−0.989246 + 0.146259i \(0.953277\pi\)
\(384\) 0 0
\(385\) 0.119271 0.676417i 0.00607859 0.0344734i
\(386\) 2.88889 5.00371i 0.147041 0.254682i
\(387\) 0 0
\(388\) −6.91534 11.9777i −0.351073 0.608077i
\(389\) −0.710966 + 0.258770i −0.0360474 + 0.0131202i −0.359981 0.932960i \(-0.617217\pi\)
0.323934 + 0.946080i \(0.394995\pi\)
\(390\) 0 0
\(391\) −28.5364 + 23.9449i −1.44315 + 1.21095i
\(392\) 12.9289 10.8486i 0.653008 0.547939i
\(393\) 0 0
\(394\) 1.47519 0.536923i 0.0743188 0.0270498i
\(395\) −0.368026 0.637441i −0.0185174 0.0320731i
\(396\) 0 0
\(397\) −3.50387 + 6.06888i −0.175854 + 0.304588i −0.940457 0.339914i \(-0.889602\pi\)
0.764602 + 0.644502i \(0.222935\pi\)
\(398\) −2.79174 + 15.8327i −0.139937 + 0.793624i
\(399\) 0 0
\(400\) 5.17499 + 1.88354i 0.258750 + 0.0941772i
\(401\) −1.64111 9.30722i −0.0819533 0.464780i −0.997973 0.0636460i \(-0.979727\pi\)
0.916019 0.401134i \(-0.131384\pi\)
\(402\) 0 0
\(403\) 30.6896 + 25.7516i 1.52876 + 1.28278i
\(404\) −19.9051 −0.990314
\(405\) 0 0
\(406\) −0.418281 −0.0207590
\(407\) 9.09413 + 7.63088i 0.450779 + 0.378249i
\(408\) 0 0
\(409\) 0.958111 + 5.43372i 0.0473755 + 0.268680i 0.999290 0.0376849i \(-0.0119983\pi\)
−0.951914 + 0.306365i \(0.900887\pi\)
\(410\) −5.09170 1.85323i −0.251461 0.0915243i
\(411\) 0 0
\(412\) −2.41353 + 13.6878i −0.118906 + 0.674351i
\(413\) −0.00264750 + 0.00458561i −0.000130275 + 0.000225643i
\(414\) 0 0
\(415\) −3.55097 6.15047i −0.174310 0.301915i
\(416\) 24.9192 9.06986i 1.22177 0.444686i
\(417\) 0 0
\(418\) 1.67571 1.40609i 0.0819615 0.0687739i
\(419\) −0.357267 + 0.299782i −0.0174536 + 0.0146453i −0.651473 0.758672i \(-0.725848\pi\)
0.634019 + 0.773317i \(0.281404\pi\)
\(420\) 0 0
\(421\) 2.26857 0.825692i 0.110563 0.0402418i −0.286146 0.958186i \(-0.592374\pi\)
0.396709 + 0.917944i \(0.370152\pi\)
\(422\) 0.570234 + 0.987674i 0.0277585 + 0.0480792i
\(423\) 0 0
\(424\) −3.68004 + 6.37402i −0.178719 + 0.309550i
\(425\) −3.23741 + 18.3603i −0.157037 + 0.890603i
\(426\) 0 0
\(427\) −1.15745 0.421278i −0.0560130 0.0203871i
\(428\) −3.02931 17.1800i −0.146427 0.830429i
\(429\) 0 0
\(430\) −0.716881 0.601535i −0.0345711 0.0290086i
\(431\) 12.0992 0.582796 0.291398 0.956602i \(-0.405880\pi\)
0.291398 + 0.956602i \(0.405880\pi\)
\(432\) 0 0
\(433\) 33.3509 1.60274 0.801371 0.598167i \(-0.204104\pi\)
0.801371 + 0.598167i \(0.204104\pi\)
\(434\) 0.553579 + 0.464508i 0.0265726 + 0.0222971i
\(435\) 0 0
\(436\) −0.771259 4.37403i −0.0369366 0.209478i
\(437\) −4.31142 1.56923i −0.206243 0.0750665i
\(438\) 0 0
\(439\) −1.57057 + 8.90717i −0.0749594 + 0.425116i 0.924116 + 0.382113i \(0.124804\pi\)
−0.999075 + 0.0430028i \(0.986308\pi\)
\(440\) −6.87933 + 11.9153i −0.327959 + 0.568042i
\(441\) 0 0
\(442\) 7.47519 + 12.9474i 0.355558 + 0.615845i
\(443\) −4.39506 + 1.59967i −0.208815 + 0.0760026i −0.444310 0.895873i \(-0.646551\pi\)
0.235495 + 0.971876i \(0.424329\pi\)
\(444\) 0 0
\(445\) 5.50387 4.61830i 0.260908 0.218928i
\(446\) −5.13560 + 4.30928i −0.243178 + 0.204050i
\(447\) 0 0
\(448\) 0.129538 0.0471478i 0.00612008 0.00222753i
\(449\) −13.3534 23.1288i −0.630187 1.09152i −0.987513 0.157537i \(-0.949645\pi\)
0.357326 0.933980i \(-0.383689\pi\)
\(450\) 0 0
\(451\) 20.5351 35.5678i 0.966959 1.67482i
\(452\) 3.08083 17.4722i 0.144910 0.821825i
\(453\) 0 0
\(454\) 9.95084 + 3.62181i 0.467016 + 0.169980i
\(455\) 0.100399 + 0.569392i 0.00470679 + 0.0266935i
\(456\) 0 0
\(457\) −0.503870 0.422797i −0.0235701 0.0197776i 0.630927 0.775843i \(-0.282675\pi\)
−0.654497 + 0.756065i \(0.727119\pi\)
\(458\) −7.69820 −0.359713
\(459\) 0 0
\(460\) 12.5175 0.583633
\(461\) −15.8600 13.3081i −0.738672 0.619820i 0.193808 0.981039i \(-0.437916\pi\)
−0.932481 + 0.361220i \(0.882360\pi\)
\(462\) 0 0
\(463\) −4.31062 24.4468i −0.200332 1.13614i −0.904619 0.426222i \(-0.859844\pi\)
0.704287 0.709915i \(-0.251267\pi\)
\(464\) −6.72427 2.44743i −0.312166 0.113619i
\(465\) 0 0
\(466\) −0.621797 + 3.52638i −0.0288042 + 0.163357i
\(467\) 13.3365 23.0994i 0.617138 1.06891i −0.372868 0.927884i \(-0.621625\pi\)
0.990005 0.141029i \(-0.0450412\pi\)
\(468\) 0 0
\(469\) −0.112159 0.194265i −0.00517901 0.00897031i
\(470\) −1.62760 + 0.592396i −0.0750754 + 0.0273252i
\(471\) 0 0
\(472\) 0.0812519 0.0681784i 0.00373992 0.00313817i
\(473\) 5.43372 4.55943i 0.249843 0.209643i
\(474\) 0 0
\(475\) −2.15776 + 0.785359i −0.0990046 + 0.0360347i
\(476\) −0.441500 0.764700i −0.0202361 0.0350500i
\(477\) 0 0
\(478\) −3.52616 + 6.10749i −0.161283 + 0.279350i
\(479\) 0.560282 3.17752i 0.0255999 0.145185i −0.969329 0.245768i \(-0.920960\pi\)
0.994929 + 0.100584i \(0.0320710\pi\)
\(480\) 0 0
\(481\) −9.39053 3.41787i −0.428171 0.155842i
\(482\) 1.27622 + 7.23783i 0.0581304 + 0.329674i
\(483\) 0 0
\(484\) −21.7422 18.2438i −0.988280 0.829266i
\(485\) −9.46075 −0.429590
\(486\) 0 0
\(487\) −7.77930 −0.352514 −0.176257 0.984344i \(-0.556399\pi\)
−0.176257 + 0.984344i \(0.556399\pi\)
\(488\) 18.9010 + 15.8598i 0.855606 + 0.717939i
\(489\) 0 0
\(490\) −0.869585 4.93166i −0.0392838 0.222790i
\(491\) 16.0180 + 5.83006i 0.722880 + 0.263107i 0.677148 0.735847i \(-0.263216\pi\)
0.0457323 + 0.998954i \(0.485438\pi\)
\(492\) 0 0
\(493\) 4.20661 23.8569i 0.189456 1.07446i
\(494\) −0.920686 + 1.59467i −0.0414236 + 0.0717478i
\(495\) 0 0
\(496\) 6.18139 + 10.7065i 0.277553 + 0.480735i
\(497\) −0.737892 + 0.268571i −0.0330990 + 0.0120470i
\(498\) 0 0
\(499\) 6.07532 5.09780i 0.271969 0.228209i −0.496595 0.867983i \(-0.665416\pi\)
0.768563 + 0.639774i \(0.220972\pi\)
\(500\) 10.9490 9.18732i 0.489655 0.410869i
\(501\) 0 0
\(502\) 9.68866 3.52638i 0.432426 0.157390i
\(503\) 12.4748 + 21.6070i 0.556224 + 0.963409i 0.997807 + 0.0661881i \(0.0210837\pi\)
−0.441583 + 0.897220i \(0.645583\pi\)
\(504\) 0 0
\(505\) −6.80793 + 11.7917i −0.302949 + 0.524723i
\(506\) 5.03174 28.5364i 0.223688 1.26860i
\(507\) 0 0
\(508\) −22.1989 8.07975i −0.984918 0.358481i
\(509\) 7.02736 + 39.8542i 0.311482 + 1.76650i 0.591300 + 0.806451i \(0.298615\pi\)
−0.279818 + 0.960053i \(0.590274\pi\)
\(510\) 0 0
\(511\) −1.13041 0.948531i −0.0500066 0.0419605i
\(512\) 15.0038 0.663080
\(513\) 0 0
\(514\) 2.27269 0.100244
\(515\) 7.28314 + 6.11128i 0.320934 + 0.269295i
\(516\) 0 0
\(517\) −2.27972 12.9289i −0.100262 0.568613i
\(518\) −0.169386 0.0616516i −0.00744240 0.00270881i
\(519\) 0 0
\(520\) 2.01114 11.4058i 0.0881945 0.500176i
\(521\) 12.6837 21.9688i 0.555684 0.962473i −0.442166 0.896933i \(-0.645790\pi\)
0.997850 0.0655394i \(-0.0208768\pi\)
\(522\) 0 0
\(523\) −6.36097 11.0175i −0.278146 0.481762i 0.692778 0.721151i \(-0.256386\pi\)
−0.970924 + 0.239388i \(0.923053\pi\)
\(524\) 19.2286 6.99866i 0.840007 0.305738i
\(525\) 0 0
\(526\) −4.63151 + 3.88630i −0.201943 + 0.169451i
\(527\) −32.0607 + 26.9021i −1.39659 + 1.17188i
\(528\) 0 0
\(529\) −35.4987 + 12.9205i −1.54342 + 0.561760i
\(530\) 1.09191 + 1.89124i 0.0474296 + 0.0821504i
\(531\) 0 0
\(532\) 0.0543776 0.0941848i 0.00235757 0.00408343i
\(533\) −6.00335 + 34.0467i −0.260034 + 1.47473i
\(534\) 0 0
\(535\) −11.2135 4.08137i −0.484801 0.176453i
\(536\) 0.780272 + 4.42514i 0.0337026 + 0.191137i
\(537\) 0 0
\(538\) −4.24060 3.55829i −0.182825 0.153409i
\(539\) 37.9570 1.63492
\(540\) 0 0
\(541\) 2.09327 0.0899969 0.0449984 0.998987i \(-0.485672\pi\)
0.0449984 + 0.998987i \(0.485672\pi\)
\(542\) −9.95610 8.35416i −0.427651 0.358842i
\(543\) 0 0
\(544\) 4.81062 + 27.2824i 0.206254 + 1.16972i
\(545\) −2.85494 1.03911i −0.122292 0.0445108i
\(546\) 0 0
\(547\) 0.599260 3.39857i 0.0256225 0.145312i −0.969313 0.245831i \(-0.920939\pi\)
0.994935 + 0.100519i \(0.0320502\pi\)
\(548\) −15.0326 + 26.0371i −0.642159 + 1.11225i
\(549\) 0 0
\(550\) −7.25103 12.5592i −0.309185 0.535524i
\(551\) 2.80374 1.02048i 0.119443 0.0434738i
\(552\) 0 0
\(553\) −0.0648930 + 0.0544517i −0.00275953 + 0.00231552i
\(554\) −2.21621 + 1.85962i −0.0941578 + 0.0790078i
\(555\) 0 0
\(556\) 23.4761 8.54461i 0.995609 0.362372i
\(557\) −5.55017 9.61318i −0.235168 0.407323i 0.724153 0.689639i \(-0.242231\pi\)
−0.959322 + 0.282316i \(0.908897\pi\)
\(558\) 0 0
\(559\) −2.98545 + 5.17095i −0.126271 + 0.218708i
\(560\) −0.0309820 + 0.175708i −0.00130923 + 0.00742500i
\(561\) 0 0
\(562\) 4.69372 + 1.70837i 0.197992 + 0.0720634i
\(563\) −4.22150 23.9413i −0.177915 1.00901i −0.934725 0.355372i \(-0.884354\pi\)
0.756810 0.653635i \(-0.226757\pi\)
\(564\) 0 0
\(565\) −9.29679 7.80093i −0.391119 0.328188i
\(566\) 10.9587 0.460628
\(567\) 0 0
\(568\) 15.7297 0.660002
\(569\) −32.7591 27.4881i −1.37333 1.15236i −0.971606 0.236603i \(-0.923966\pi\)
−0.401726 0.915760i \(-0.631590\pi\)
\(570\) 0 0
\(571\) 3.13058 + 17.7544i 0.131011 + 0.742998i 0.977555 + 0.210680i \(0.0675678\pi\)
−0.846545 + 0.532318i \(0.821321\pi\)
\(572\) 35.7817 + 13.0235i 1.49611 + 0.544539i
\(573\) 0 0
\(574\) −0.108288 + 0.614134i −0.00451987 + 0.0256334i
\(575\) −15.2086 + 26.3421i −0.634244 + 1.09854i
\(576\) 0 0
\(577\) −12.6382 21.8899i −0.526133 0.911290i −0.999536 0.0304438i \(-0.990308\pi\)
0.473403 0.880846i \(-0.343025\pi\)
\(578\) −3.74902 + 1.36453i −0.155939 + 0.0567571i
\(579\) 0 0
\(580\) −6.23577 + 5.23243i −0.258926 + 0.217265i
\(581\) −0.626133 + 0.525388i −0.0259764 + 0.0217967i
\(582\) 0 0
\(583\) −15.5544 + 5.66133i −0.644196 + 0.234468i
\(584\) 14.7797 + 25.5993i 0.611590 + 1.05930i
\(585\) 0 0
\(586\) 6.15792 10.6658i 0.254381 0.440601i
\(587\) −4.96032 + 28.1313i −0.204734 + 1.16111i 0.693123 + 0.720819i \(0.256234\pi\)
−0.897858 + 0.440286i \(0.854877\pi\)
\(588\) 0 0
\(589\) −4.84389 1.76303i −0.199589 0.0726445i
\(590\) −0.00546492 0.0309931i −0.000224987 0.00127597i
\(591\) 0 0
\(592\) −2.36231 1.98221i −0.0970904 0.0814685i
\(593\) −20.6009 −0.845977 −0.422989 0.906135i \(-0.639019\pi\)
−0.422989 + 0.906135i \(0.639019\pi\)
\(594\) 0 0
\(595\) −0.604007 −0.0247619
\(596\) −12.9661 10.8799i −0.531112 0.445656i
\(597\) 0 0
\(598\) 4.23560 + 24.0213i 0.173207 + 0.982304i
\(599\) −13.6019 4.95067i −0.555757 0.202279i 0.0488454 0.998806i \(-0.484446\pi\)
−0.604603 + 0.796527i \(0.706668\pi\)
\(600\) 0 0
\(601\) −2.31908 + 13.1521i −0.0945972 + 0.536487i 0.900273 + 0.435326i \(0.143367\pi\)
−0.994870 + 0.101161i \(0.967744\pi\)
\(602\) −0.0538515 + 0.0932736i −0.00219483 + 0.00380155i
\(603\) 0 0
\(604\) −5.20961 9.02330i −0.211976 0.367153i
\(605\) −18.2438 + 6.64022i −0.741718 + 0.269963i
\(606\) 0 0
\(607\) 23.9106 20.0634i 0.970501 0.814347i −0.0121281 0.999926i \(-0.503861\pi\)
0.982629 + 0.185579i \(0.0594161\pi\)
\(608\) −2.61381 + 2.19325i −0.106004 + 0.0889480i
\(609\) 0 0
\(610\) 6.87939 2.50389i 0.278538 0.101380i
\(611\) 5.52557 + 9.57057i 0.223541 + 0.387184i
\(612\) 0 0
\(613\) −15.0326 + 26.0372i −0.607159 + 1.05163i 0.384547 + 0.923105i \(0.374358\pi\)
−0.991706 + 0.128525i \(0.958976\pi\)
\(614\) −1.60484 + 9.10148i −0.0647659 + 0.367306i
\(615\) 0 0
\(616\) 1.48798 + 0.541580i 0.0599524 + 0.0218209i
\(617\) 7.31991 + 41.5133i 0.294688 + 1.67126i 0.668466 + 0.743743i \(0.266951\pi\)
−0.373778 + 0.927518i \(0.621938\pi\)
\(618\) 0 0
\(619\) 8.89440 + 7.46329i 0.357496 + 0.299975i 0.803792 0.594911i \(-0.202813\pi\)
−0.446296 + 0.894886i \(0.647257\pi\)
\(620\) 14.0635 0.564803
\(621\) 0 0
\(622\) −11.2335 −0.450422
\(623\) −0.633436 0.531516i −0.0253781 0.0212947i
\(624\) 0 0
\(625\) 1.68984 + 9.58359i 0.0675938 + 0.383343i
\(626\) 12.5760 + 4.57730i 0.502639 + 0.182946i
\(627\) 0 0
\(628\) −4.49273 + 25.4795i −0.179279 + 1.01674i
\(629\) 5.21983 9.04101i 0.208128 0.360489i
\(630\) 0 0
\(631\) 14.6552 + 25.3836i 0.583415 + 1.01051i 0.995071 + 0.0991657i \(0.0316174\pi\)
−0.411655 + 0.911340i \(0.635049\pi\)
\(632\) 1.59457 0.580375i 0.0634284 0.0230861i
\(633\) 0 0
\(634\) 12.7745 10.7191i 0.507340 0.425709i
\(635\) −12.3789 + 10.3871i −0.491241 + 0.412201i
\(636\) 0 0
\(637\) −30.0244 + 10.9280i −1.18961 + 0.432983i
\(638\) 9.42182 + 16.3191i 0.373014 + 0.646078i
\(639\) 0 0
\(640\) 5.66637 9.81445i 0.223983 0.387950i
\(641\) 5.40009 30.6254i 0.213291 1.20963i −0.670558 0.741857i \(-0.733945\pi\)
0.883848 0.467774i \(-0.154944\pi\)
\(642\) 0 0
\(643\) −39.5347 14.3894i −1.55910 0.567464i −0.588566 0.808449i \(-0.700307\pi\)
−0.970529 + 0.240985i \(0.922530\pi\)
\(644\) −0.250164 1.41875i −0.00985783 0.0559065i
\(645\) 0 0
\(646\) −1.47359 1.23649i −0.0579777 0.0486491i
\(647\) −4.66717 −0.183485 −0.0917427 0.995783i \(-0.529244\pi\)
−0.0917427 + 0.995783i \(0.529244\pi\)
\(648\) 0 0
\(649\) 0.238541 0.00936356
\(650\) 9.35149 + 7.84683i 0.366796 + 0.307778i
\(651\) 0 0
\(652\) −2.23783 12.6913i −0.0876400 0.497031i
\(653\) 2.93572 + 1.06851i 0.114884 + 0.0418142i 0.398822 0.917028i \(-0.369419\pi\)
−0.283939 + 0.958842i \(0.591641\pi\)
\(654\) 0 0
\(655\) 2.43061 13.7847i 0.0949717 0.538611i
\(656\) −5.33424 + 9.23917i −0.208267 + 0.360729i
\(657\) 0 0
\(658\) 0.0996702 + 0.172634i 0.00388555 + 0.00672997i
\(659\) −35.1719 + 12.8015i −1.37010 + 0.498677i −0.919163 0.393877i \(-0.871134\pi\)
−0.450941 + 0.892554i \(0.648911\pi\)
\(660\) 0 0
\(661\) 20.3004 17.0341i 0.789594 0.662548i −0.156051 0.987749i \(-0.549876\pi\)
0.945645 + 0.325201i \(0.105432\pi\)
\(662\) 14.9336 12.5307i 0.580409 0.487021i
\(663\) 0 0
\(664\) 15.3855 5.59986i 0.597072 0.217317i
\(665\) −0.0371965 0.0644262i −0.00144242 0.00249834i
\(666\) 0 0
\(667\) 19.7618 34.2284i 0.765179 1.32533i
\(668\) 0.698367 3.96064i 0.0270206 0.153242i
\(669\) 0 0
\(670\) 1.25284 + 0.455997i 0.0484015 + 0.0176167i
\(671\) 9.63571 + 54.6468i 0.371982 + 2.10962i
\(672\) 0 0
\(673\) 1.31836 + 1.10624i 0.0508191 + 0.0426423i 0.667843 0.744302i \(-0.267218\pi\)
−0.617024 + 0.786944i \(0.711662\pi\)
\(674\) −11.9341 −0.459686
\(675\) 0 0
\(676\) −12.1361 −0.466773
\(677\) −21.6631 18.1775i −0.832581 0.698619i 0.123301 0.992369i \(-0.460652\pi\)
−0.955882 + 0.293751i \(0.905096\pi\)
\(678\) 0 0
\(679\) 0.189073 + 1.07229i 0.00725597 + 0.0411507i
\(680\) 11.3695 + 4.13816i 0.436000 + 0.158691i
\(681\) 0 0
\(682\) 5.65317 32.0607i 0.216471 1.22767i
\(683\) −12.3569 + 21.4029i −0.472825 + 0.818958i −0.999516 0.0310993i \(-0.990099\pi\)
0.526691 + 0.850057i \(0.323433\pi\)
\(684\) 0 0
\(685\) 10.2829 + 17.8105i 0.392888 + 0.680502i
\(686\) −1.08429 + 0.394648i −0.0413983 + 0.0150677i
\(687\) 0 0
\(688\) −1.41147 + 1.18437i −0.0538119 + 0.0451536i
\(689\) 10.6738 8.95636i 0.406638 0.341210i
\(690\) 0 0
\(691\) 41.1327 14.9711i 1.56476 0.569527i 0.592940 0.805246i \(-0.297967\pi\)
0.971821 + 0.235720i \(0.0757448\pi\)
\(692\) 10.0377 + 17.3858i 0.381576 + 0.660908i
\(693\) 0 0
\(694\) 8.61515 14.9219i 0.327027 0.566427i
\(695\) 2.96751 16.8296i 0.112564 0.638383i
\(696\) 0 0
\(697\) −33.9384 12.3526i −1.28551 0.467887i
\(698\) −1.40781 7.98411i −0.0532865 0.302203i
\(699\) 0 0
\(700\) −0.552318 0.463450i −0.0208757 0.0175168i
\(701\) 14.6504 0.553338 0.276669 0.960965i \(-0.410769\pi\)
0.276669 + 0.960965i \(0.410769\pi\)
\(702\) 0 0
\(703\) 1.28581 0.0484951
\(704\) −4.75730 3.99185i −0.179297 0.150448i
\(705\) 0 0
\(706\) 0.997474 + 5.65695i 0.0375404 + 0.212902i
\(707\) 1.47254 + 0.535959i 0.0553804 + 0.0201568i
\(708\) 0 0
\(709\) 0.881034 4.99659i 0.0330879 0.187651i −0.963784 0.266684i \(-0.914072\pi\)
0.996872 + 0.0790328i \(0.0251832\pi\)
\(710\) 2.33359 4.04189i 0.0875779 0.151689i
\(711\) 0 0
\(712\) 8.28194 + 14.3447i 0.310379 + 0.537592i
\(713\) −64.1650 + 23.3542i −2.40300 + 0.874620i
\(714\) 0 0
\(715\) 19.9531 16.7427i 0.746204 0.626140i
\(716\) 25.9363 21.7631i 0.969284 0.813326i
\(717\) 0 0
\(718\) 1.69712 0.617701i 0.0633359 0.0230524i
\(719\) −2.66858 4.62212i −0.0995213 0.172376i 0.811965 0.583706i \(-0.198398\pi\)
−0.911487 + 0.411330i \(0.865064\pi\)
\(720\) 0 0
\(721\) 0.547104 0.947611i 0.0203752 0.0352909i
\(722\) −2.21572 + 12.5660i −0.0824607 + 0.467658i
\(723\) 0 0
\(724\) −2.96451 1.07899i −0.110175 0.0401004i
\(725\) −3.43485 19.4800i −0.127567 0.723469i
\(726\) 0 0
\(727\) 28.4354 + 23.8601i 1.05461 + 0.884924i 0.993571 0.113212i \(-0.0361138\pi\)
0.0610401 + 0.998135i \(0.480558\pi\)
\(728\) −1.33293 −0.0494017
\(729\) 0 0
\(730\) 8.77063 0.324616
\(731\) −4.77833 4.00950i −0.176733 0.148297i
\(732\) 0 0
\(733\) 5.20011 + 29.4913i 0.192071 + 1.08929i 0.916529 + 0.399968i \(0.130979\pi\)
−0.724459 + 0.689318i \(0.757910\pi\)
\(734\) −5.91209 2.15183i −0.218219 0.0794254i
\(735\) 0 0
\(736\) −7.84864 + 44.5119i −0.289305 + 1.64073i
\(737\) −5.05277 + 8.75166i −0.186121 + 0.322371i
\(738\) 0 0
\(739\) 14.3050 + 24.7770i 0.526218 + 0.911436i 0.999533 + 0.0305431i \(0.00972368\pi\)
−0.473316 + 0.880893i \(0.656943\pi\)
\(740\) −3.29644 + 1.19981i −0.121180 + 0.0441058i
\(741\) 0 0
\(742\) 0.192533 0.161555i 0.00706812 0.00593086i
\(743\) −38.0292 + 31.9103i −1.39516 + 1.17068i −0.431955 + 0.901895i \(0.642176\pi\)
−0.963202 + 0.268780i \(0.913380\pi\)
\(744\) 0 0
\(745\) −10.8799 + 3.95994i −0.398607 + 0.145081i
\(746\) 9.16312 + 15.8710i 0.335486 + 0.581078i
\(747\) 0 0
\(748\) −19.8897 + 34.4499i −0.727238 + 1.25961i
\(749\) −0.238484 + 1.35251i −0.00871402 + 0.0494197i
\(750\) 0 0
\(751\) 29.7165 + 10.8159i 1.08437 + 0.394678i 0.821532 0.570162i \(-0.193120\pi\)
0.262837 + 0.964840i \(0.415342\pi\)
\(752\) 0.592184 + 3.35844i 0.0215947 + 0.122470i
\(753\) 0 0
\(754\) −12.1511 10.1960i −0.442517 0.371316i
\(755\) −7.12716 −0.259384
\(756\) 0 0
\(757\) 3.04189 0.110559 0.0552797 0.998471i \(-0.482395\pi\)
0.0552797 + 0.998471i \(0.482395\pi\)
\(758\) −14.2132 11.9263i −0.516248 0.433184i
\(759\) 0 0
\(760\) 0.258770 + 1.46756i 0.00938659 + 0.0532340i
\(761\) 35.6410 + 12.9722i 1.29198 + 0.470244i 0.894378 0.447313i \(-0.147619\pi\)
0.397606 + 0.917556i \(0.369841\pi\)
\(762\) 0 0
\(763\) −0.0607179 + 0.344348i −0.00219814 + 0.0124662i
\(764\) −3.02525 + 5.23989i −0.109450 + 0.189572i
\(765\) 0 0
\(766\) −11.7747 20.3943i −0.425436 0.736877i
\(767\) −0.188689 + 0.0686771i −0.00681316 + 0.00247979i
\(768\) 0 0
\(769\) −15.6179 + 13.1050i −0.563197 + 0.472578i −0.879380 0.476120i \(-0.842043\pi\)
0.316184 + 0.948698i \(0.397598\pi\)
\(770\) 0.359914 0.302004i 0.0129704 0.0108835i
\(771\) 0 0
\(772\) −12.1604 + 4.42604i −0.437664 + 0.159297i
\(773\) 12.2332 + 21.1885i 0.439997 + 0.762097i 0.997689 0.0679509i \(-0.0216461\pi\)
−0.557692 + 0.830048i \(0.688313\pi\)
\(774\) 0 0
\(775\) −17.0869 + 29.5954i −0.613781 + 1.06310i
\(776\) 3.78742 21.4795i 0.135960 0.771070i
\(777\) 0 0
\(778\) −0.486329 0.177009i −0.0174358 0.00634610i
\(779\) −0.772441 4.38073i −0.0276756 0.156956i
\(780\) 0