Properties

Label 729.2.e.r.325.1
Level $729$
Weight $2$
Character 729.325
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 325.1
Root \(0.342020 - 0.939693i\) of defining polynomial
Character \(\chi\) \(=\) 729.325
Dual form 729.2.e.r.406.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.524005 + 0.439693i) q^{2} +(-0.266044 + 1.50881i) q^{4} +(0.984808 - 0.358441i) q^{5} +(-0.0209445 - 0.118782i) q^{7} +(-1.20805 - 2.09240i) q^{8} +O(q^{10})\) \(q+(-0.524005 + 0.439693i) q^{2} +(-0.266044 + 1.50881i) q^{4} +(0.984808 - 0.358441i) q^{5} +(-0.0209445 - 0.118782i) q^{7} +(-1.20805 - 2.09240i) q^{8} +(-0.358441 + 0.620838i) q^{10} +(-5.10602 - 1.85844i) q^{11} +(-3.50387 - 2.94010i) q^{13} +(0.0632028 + 0.0530334i) q^{14} +(-1.32635 - 0.482753i) q^{16} +(2.38917 - 4.13816i) q^{17} +(0.294263 + 0.509678i) q^{19} +(0.278817 + 1.58125i) q^{20} +(3.49273 - 1.27125i) q^{22} +(1.35375 - 7.67752i) q^{23} +(-2.98886 + 2.50795i) q^{25} +3.12879 q^{26} +0.184793 q^{28} +(-3.88365 + 3.25877i) q^{29} +(-1.52094 + 8.62571i) q^{31} +(5.44804 - 1.98293i) q^{32} +(0.567581 + 3.21891i) q^{34} +(-0.0632028 - 0.109470i) q^{35} +(1.09240 - 1.89209i) q^{37} +(-0.378297 - 0.137689i) q^{38} +(-1.93969 - 1.62760i) q^{40} +(-5.79006 - 4.85844i) q^{41} +(1.22668 + 0.446476i) q^{43} +(4.16247 - 7.20961i) q^{44} +(2.66637 + 4.61830i) q^{46} +(-0.419550 - 2.37939i) q^{47} +(6.56418 - 2.38917i) q^{49} +(0.463450 - 2.62836i) q^{50} +(5.36824 - 4.50449i) q^{52} +3.04628 q^{53} -5.69459 q^{55} +(-0.223238 + 0.187319i) q^{56} +(0.602196 - 3.41523i) q^{58} +(-0.0412527 + 0.0150147i) q^{59} +(-1.77332 - 10.0570i) q^{61} +(-2.99568 - 5.18866i) q^{62} +(-0.571452 + 0.989783i) q^{64} +(-4.50449 - 1.63950i) q^{65} +(-1.42468 - 1.19545i) q^{67} +(5.60808 + 4.70574i) q^{68} +(0.0812519 + 0.0295733i) q^{70} +(-3.25519 + 5.63816i) q^{71} +(-6.11721 - 10.5953i) q^{73} +(0.259515 + 1.47178i) q^{74} +(-0.847296 + 0.308391i) q^{76} +(-0.113807 + 0.645430i) q^{77} +(0.538019 - 0.451451i) q^{79} -1.47924 q^{80} +5.17024 q^{82} +(-5.19118 + 4.35591i) q^{83} +(0.869585 - 4.93166i) q^{85} +(-0.839100 + 0.305407i) q^{86} +(2.27972 + 12.9289i) q^{88} +(3.42782 + 5.93717i) q^{89} +(-0.275845 + 0.477777i) q^{91} +(11.2238 + 4.08512i) q^{92} +(1.26604 + 1.06234i) q^{94} +(0.472482 + 0.396459i) q^{95} +(8.48293 + 3.08753i) q^{97} +(-2.38917 + 4.13816i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 6 q^{4} + 6 q^{7}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/729\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{7}{9}\right)\)

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 \(-0.799975\pi\)
0.438443 + 0.898759i \(0.355530\pi\)
\(3\) 0 0
\(4\) −0.266044 + 1.50881i −0.133022 + 0.754407i
\(5\) 0.984808 0.358441i 0.440419 0.160300i −0.112287 0.993676i \(-0.535817\pi\)
0.552706 + 0.833376i \(0.313595\pi\)
\(6\) 0 0
\(7\) −0.0209445 0.118782i −0.00791629 0.0448955i 0.980594 0.196051i \(-0.0628118\pi\)
−0.988510 + 0.151155i \(0.951701\pi\)
\(8\) −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 \(-0.694451\pi\)
−0.965931 + 0.258799i \(0.916673\pi\)
\(12\) 0 0
\(13\) −3.50387 2.94010i −0.971799 0.815436i 0.0110331 0.999939i \(-0.496488\pi\)
−0.982832 + 0.184503i \(0.940932\pi\)
\(14\) 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 −0.416084 0.909326i \(-0.636598\pi\)
0.995542 0.0943239i \(-0.0300689\pi\)
\(18\) 0 0
\(19\) 0.294263 + 0.509678i 0.0675085 + 0.116928i 0.897804 0.440395i \(-0.145162\pi\)
−0.830295 + 0.557323i \(0.811828\pi\)
\(20\) 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 −0.432575 0.901598i \(-0.642395\pi\)
0.714852 0.699275i \(-0.246494\pi\)
\(24\) 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 \(-0.878226\pi\)
0.206534 + 0.978439i \(0.433781\pi\)
\(30\) 0 0
\(31\) −1.52094 + 8.62571i −0.273170 + 1.54922i 0.471547 + 0.881841i \(0.343696\pi\)
−0.744716 + 0.667381i \(0.767415\pi\)
\(32\) 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 −0.762151 0.647399i \(-0.775857\pi\)
0.941740 + 0.336342i \(0.109190\pi\)
\(38\) −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 \(-0.478733\pi\)
−0.971018 + 0.239008i \(0.923178\pi\)
\(42\) 0 0
\(43\) 1.22668 + 0.446476i 0.187067 + 0.0680869i 0.433855 0.900983i \(-0.357153\pi\)
−0.246788 + 0.969069i \(0.579375\pi\)
\(44\) 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 −0.999997 0.00260352i \(-0.999171\pi\)
0.938799 0.344465i \(-0.111940\pi\)
\(48\) 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 \(-0.432908\pi\)
0.209219 + 0.977869i \(0.432908\pi\)
\(54\) 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 \(-0.612021\pi\)
0.339333 + 0.940666i \(0.389799\pi\)
\(60\) 0 0
\(61\) −1.77332 10.0570i −0.227050 1.28767i −0.858727 0.512434i \(-0.828744\pi\)
0.631677 0.775232i \(-0.282367\pi\)
\(62\) −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 0.551600 0.834109i \(-0.314017\pi\)
−0.725652 + 0.688062i \(0.758462\pi\)
\(68\) 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 \(-0.959587\pi\)
0.605631 + 0.795745i \(0.292921\pi\)
\(72\) 0 0
\(73\) −6.11721 10.5953i −0.715965 1.24009i −0.962586 0.270976i \(-0.912653\pi\)
0.246621 0.969112i \(-0.420680\pi\)
\(74\) 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 −0.612020 0.790842i \(-0.709643\pi\)
0.672552 + 0.740050i \(0.265198\pi\)
\(80\) −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 \(-0.843521\pi\)
0.311776 + 0.950156i \(0.399076\pi\)
\(84\) 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 \(-0.0483000\pi\)
−0.625161 + 0.780496i \(0.714967\pi\)
\(90\) 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 0.734643 0.678454i \(-0.237350\pi\)
0.126668 + 0.991945i \(0.459572\pi\)
\(98\) −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 −0.863665 0.504066i \(-0.831837\pi\)
0.639179 0.769058i \(-0.279274\pi\)
\(102\) 0 0
\(103\) −8.52481 + 3.10278i −0.839975 + 0.305726i −0.725946 0.687752i \(-0.758598\pi\)
−0.114029 + 0.993477i \(0.536376\pi\)
\(104\) −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 \(-0.685519\pi\)
−0.550386 + 0.834911i \(0.685519\pi\)
\(108\) 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 \(-0.794461\pi\)
−0.225003 + 0.974358i \(0.572239\pi\)
\(114\) 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 0.973713 + 0.227777i \(0.0731456\pi\)
−0.289596 + 0.957149i \(0.593521\pi\)
\(128\) 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 0.698484 + 0.715625i \(0.253858\pi\)
−0.901119 + 0.433572i \(0.857253\pi\)
\(132\) 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 0.291684 0.956515i \(-0.405784\pi\)
0.992634 0.121156i \(-0.0386600\pi\)
\(138\) 0 0
\(139\) 2.83157 16.0586i 0.240170 1.36207i −0.591276 0.806469i \(-0.701376\pi\)
0.831447 0.555605i \(-0.187513\pi\)
\(140\) 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 \(-0.427257\pi\)
−0.919864 + 0.392238i \(0.871701\pi\)
\(150\) 0 0
\(151\) 6.39053 + 2.32596i 0.520054 + 0.189284i 0.588692 0.808357i \(-0.299643\pi\)
−0.0686380 + 0.997642i \(0.521865\pi\)
\(152\) 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 −0.885932 0.463815i \(-0.846480\pi\)
−0.380529 + 0.924769i \(0.624258\pi\)
\(158\) −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 \(-0.643496\pi\)
0.244812 + 0.969571i \(0.421274\pi\)
\(168\) 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 \(-0.222916\pi\)
0.171502 + 0.985184i \(0.445138\pi\)
\(174\) 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 0.0753784 + 0.997155i \(0.475984\pi\)
−0.901251 + 0.433298i \(0.857350\pi\)
\(180\) 0 0
\(181\) 1.02956 + 1.78325i 0.0765268 + 0.132548i 0.901749 0.432260i \(-0.142284\pi\)
−0.825222 + 0.564808i \(0.808950\pi\)
\(182\) −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 \(-0.676587\pi\)
0.745643 + 0.666346i \(0.232143\pi\)
\(192\) 0 0
\(193\) −1.46673 + 8.31823i −0.105577 + 0.598760i 0.885411 + 0.464810i \(0.153877\pi\)
−0.990988 + 0.133950i \(0.957234\pi\)
\(194\) −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 \(-0.192719\pi\)
−0.904004 + 0.427524i \(0.859386\pi\)
\(198\) 0 0
\(199\) 11.7515 20.3542i 0.833042 1.44287i −0.0625736 0.998040i \(-0.519931\pi\)
0.895615 0.444830i \(-0.146736\pi\)
\(200\) 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 −0.287528 0.957772i \(-0.592834\pi\)
0.395385 + 0.918516i \(0.370611\pi\)
\(212\) −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 −0.987257 0.159133i \(-0.949130\pi\)
0.873292 0.487198i \(-0.161981\pi\)
\(224\) −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 \(-0.560632\pi\)
−0.776198 + 0.630490i \(0.782854\pi\)
\(228\) 0 0
\(229\) −8.62108 7.23395i −0.569697 0.478033i 0.311848 0.950132i \(-0.399052\pi\)
−0.881545 + 0.472099i \(0.843496\pi\)
\(230\) 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 \(-0.888185\pi\)
0.767464 + 0.641092i \(0.221518\pi\)
\(234\) 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 0.870546 + 0.492087i \(0.163766\pi\)
−0.986349 + 0.164667i \(0.947345\pi\)
\(240\) 0 0
\(241\) 8.23055 6.90625i 0.530176 0.444871i −0.337986 0.941151i \(-0.609746\pi\)
0.868162 + 0.496280i \(0.165301\pi\)
\(242\) −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 \(-0.324470\pi\)
−0.999612 + 0.0278401i \(0.991137\pi\)
\(252\) 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 \(-0.310822\pi\)
−0.718708 + 0.695312i \(0.755266\pi\)
\(258\) 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 0.994857 + 0.101292i \(0.0322975\pi\)
−0.900216 + 0.435444i \(0.856591\pi\)
\(264\) 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 \(-0.420651\pi\)
0.246709 + 0.969090i \(0.420651\pi\)
\(270\) 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 0.954762 0.297370i \(-0.0961093\pi\)
−0.998890 + 0.0471120i \(0.984998\pi\)
\(278\) 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 \(-0.458778\pi\)
−0.538478 + 0.842640i \(0.681001\pi\)
\(282\) 0 0
\(283\) 12.2724 + 10.2978i 0.729521 + 0.612141i 0.930001 0.367557i \(-0.119806\pi\)
−0.200480 + 0.979698i \(0.564250\pi\)
\(284\) −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 −0.746289 0.665622i \(-0.768166\pi\)
0.928938 0.370235i \(-0.120723\pi\)
\(294\) 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 −0.606296 0.795239i \(-0.707345\pi\)
0.991845 + 0.127448i \(0.0406787\pi\)
\(308\) −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 \(-0.123613\pi\)
−0.212182 + 0.977230i \(0.568057\pi\)
\(312\) 0 0
\(313\) 18.3849 + 6.69156i 1.03918 + 0.378229i 0.804568 0.593861i \(-0.202397\pi\)
0.234608 + 0.972090i \(0.424619\pi\)
\(314\) 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 −0.836711 0.547645i \(-0.815524\pi\)
0.598945 0.800790i \(-0.295587\pi\)
\(318\) 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 0.748304 + 0.663356i \(0.230869\pi\)
−0.476294 + 0.879286i \(0.658020\pi\)
\(332\) −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 0.201564 0.979475i \(-0.435397\pi\)
−0.929594 + 0.368586i \(0.879842\pi\)
\(338\) −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 −0.608203 0.793781i \(-0.708109\pi\)
0.843013 0.537893i \(-0.180779\pi\)
\(348\) 0 0
\(349\) −9.07919 + 7.61835i −0.485998 + 0.407801i −0.852589 0.522581i \(-0.824969\pi\)
0.366591 + 0.930382i \(0.380525\pi\)
\(350\) −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 \(-0.793963\pi\)
0.455338 + 0.890319i \(0.349518\pi\)
\(354\) 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 \(-0.188862\pi\)
−0.898758 + 0.438446i \(0.855529\pi\)
\(360\) 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 0.106441 0.994319i \(-0.466054\pi\)
−0.557597 + 0.830112i \(0.688277\pi\)
\(368\) −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 0.405389 0.914144i \(-0.367136\pi\)
0.898147 + 0.439696i \(0.144914\pi\)
\(374\) 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 \(-0.268946\pi\)
0.989246 + 0.146259i \(0.0467233\pi\)
\(384\) 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 \(-0.382783\pi\)
−0.323934 + 0.946080i \(0.605005\pi\)
\(390\) 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 0.764602 0.644502i \(-0.222935\pi\)
−0.940457 + 0.339914i \(0.889602\pi\)
\(398\) 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 −0.916019 0.401134i \(-0.868616\pi\)
0.997973 0.0636460i \(-0.0202728\pi\)
\(402\) 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 −0.951914 0.306365i \(-0.900887\pi\)
0.999290 + 0.0376849i \(0.0119983\pi\)
\(410\) 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 \(-0.274152\pi\)
−0.634019 + 0.773317i \(0.718596\pi\)
\(420\) 0 0
\(421\) 2.26857 + 0.825692i 0.110563 + 0.0402418i 0.396709 0.917944i \(-0.370152\pi\)
−0.286146 + 0.958186i \(0.592374\pi\)
\(422\) −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 \(-0.594120\pi\)
−0.291398 + 0.956602i \(0.594120\pi\)
\(432\) 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 −0.999075 0.0430028i \(-0.986308\pi\)
0.924116 0.382113i \(-0.124804\pi\)
\(440\) 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 \(-0.353449\pi\)
−0.235495 + 0.971876i \(0.575671\pi\)
\(444\) 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 −0.357326 0.933980i \(-0.616311\pi\)
0.987513 0.157537i \(-0.0503553\pi\)
\(450\) 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 −0.654497 0.756065i \(-0.727119\pi\)
0.630927 + 0.775843i \(0.282675\pi\)
\(458\) 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 \(-0.562084\pi\)
0.932481 + 0.361220i \(0.117640\pi\)
\(462\) 0 0
\(463\) −4.31062 + 24.4468i −0.200332 + 1.13614i 0.704287 + 0.709915i \(0.251267\pi\)
−0.904619 + 0.426222i \(0.859844\pi\)
\(464\) 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 −0.990005 0.141029i \(-0.954959\pi\)
0.372868 0.927884i \(-0.378375\pi\)
\(468\) 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 \(-0.0790402\pi\)
−0.994929 + 0.100584i \(0.967929\pi\)
\(480\) 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 \(-0.736784\pi\)
−0.0457323 + 0.998954i \(0.514562\pi\)
\(492\) 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 0.768563 0.639774i \(-0.220972\pi\)
−0.496595 + 0.867983i \(0.665416\pi\)
\(500\) −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 0.441583 + 0.897220i \(0.354417\pi\)
−0.997807 + 0.0661881i \(0.978916\pi\)
\(504\) 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 0.279818 + 0.960053i \(0.409726\pi\)
−0.591300 + 0.806451i \(0.701385\pi\)
\(510\) 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 −0.997850 0.0655394i \(-0.979123\pi\)
0.442166 0.896933i \(-0.354210\pi\)
\(522\) 0 0
\(523\) −6.36097 + 11.0175i −0.278146 + 0.481762i −0.970924 0.239388i \(-0.923053\pi\)
0.692778 + 0.721151i \(0.256386\pi\)
\(524\) −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 0.994935 0.100519i \(-0.0320502\pi\)
−0.969313 + 0.245831i \(0.920939\pi\)
\(548\) 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 \(-0.757769\pi\)
0.959322 + 0.282316i \(0.0911025\pi\)
\(558\) 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 −0.756810 0.653635i \(-0.773243\pi\)
0.934725 0.355372i \(-0.115646\pi\)
\(564\) 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 0.401726 0.915760i \(-0.368410\pi\)
0.971606 0.236603i \(-0.0760340\pi\)
\(570\) 0 0
\(571\) 3.13058 17.7544i 0.131011 0.742998i −0.846545 0.532318i \(-0.821321\pi\)
0.977555 0.210680i \(-0.0675678\pi\)
\(572\) −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 0.473403 + 0.880846i \(0.343025\pi\)
−0.999536 + 0.0304438i \(0.990308\pi\)
\(578\) 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 0.897858 + 0.440286i \(0.145123\pi\)
−0.693123 + 0.720819i \(0.743766\pi\)
\(588\) 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 \(-0.360981\pi\)
0.422989 + 0.906135i \(0.360981\pi\)
\(594\) 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 \(-0.515554\pi\)
0.604603 + 0.796527i \(0.293332\pi\)
\(600\) 0 0
\(601\) −2.31908 13.1521i −0.0945972 0.536487i −0.994870 0.101161i \(-0.967744\pi\)
0.900273 0.435326i \(-0.143367\pi\)
\(602\) 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 0.982629 0.185579i \(-0.0594161\pi\)
−0.0121281 + 0.999926i \(0.503861\pi\)
\(608\) 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 −0.991706 0.128525i \(-0.958976\pi\)
0.384547 0.923105i \(-0.374358\pi\)
\(614\) 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 0.373778 + 0.927518i \(0.378062\pi\)
−0.668466 + 0.743743i \(0.733049\pi\)
\(618\) 0 0
\(619\) 8.89440 7.46329i 0.357496 0.299975i −0.446296 0.894886i \(-0.647257\pi\)
0.803792 + 0.594911i \(0.202813\pi\)
\(620\) −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 −0.411655 0.911340i \(-0.635049\pi\)
0.995071 0.0991657i \(-0.0316174\pi\)
\(632\) −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 −0.883848 0.467774i \(-0.845056\pi\)
0.670558 0.741857i \(-0.266055\pi\)
\(642\) 0 0
\(643\) −39.5347 + 14.3894i −1.55910 + 0.567464i −0.970529 0.240985i \(-0.922530\pi\)
−0.588566 + 0.808449i \(0.700307\pi\)
\(644\) 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 \(-0.470756\pi\)
0.0917427 + 0.995783i \(0.470756\pi\)
\(648\) 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 \(-0.630581\pi\)
0.283939 + 0.958842i \(0.408359\pi\)
\(654\) 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 \(-0.128866\pi\)
0.450941 + 0.892554i \(0.351089\pi\)
\(660\) 0 0
\(661\) 20.3004 + 17.0341i 0.789594 + 0.662548i 0.945645 0.325201i \(-0.105432\pi\)
−0.156051 + 0.987749i \(0.549876\pi\)
\(662\) −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 −0.617024 0.786944i \(-0.711662\pi\)
0.667843 + 0.744302i \(0.267218\pi\)
\(674\) 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 \(-0.539348\pi\)
0.955882 + 0.293751i \(0.0949035\pi\)
\(678\) 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 \(-0.00990082\pi\)
−0.526691 + 0.850057i \(0.676567\pi\)
\(684\) 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 0.971821 0.235720i \(-0.0757448\pi\)
0.592940 + 0.805246i \(0.297967\pi\)
\(692\) −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 \(-0.589231\pi\)
−0.276669 + 0.960965i \(0.589231\pi\)
\(702\) 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 0.996872 0.0790328i \(-0.0251832\pi\)
−0.963784 + 0.266684i \(0.914072\pi\)
\(710\) −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 \(-0.801602\pi\)
0.911487 + 0.411330i \(0.134936\pi\)
\(720\) 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 0.0610401 0.998135i \(-0.480558\pi\)
0.993571 + 0.113212i \(0.0361138\pi\)
\(728\) 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 −0.724459 0.689318i \(-0.757910\pi\)
0.916529 0.399968i \(-0.130979\pi\)
\(734\) 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 −0.473316 0.880893i \(-0.656943\pi\)
0.999533 0.0305431i \(-0.00972368\pi\)
\(740\) 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 0.963202 + 0.268780i \(0.0866204\pi\)
0.431955 + 0.901895i \(0.357824\pi\)
\(744\) 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 0.262837 0.964840i \(-0.415342\pi\)
0.821532 + 0.570162i \(0.193120\pi\)
\(752\) −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 \(-0.852381\pi\)
−0.397606 + 0.917556i \(0.630159\pi\)
\(762\) 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 0.316184 0.948698i \(-0.397598\pi\)
−0.879380 + 0.476120i \(0.842043\pi\)
\(770\) −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 \(-0.978354\pi\)
0.557692 + 0.830048i \(0.311687\pi\)
\(774\) 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
\(780\)