Properties

Label 729.2.g.b.28.5
Level $729$
Weight $2$
Character 729.28
Analytic conductor $5.821$
Analytic rank $0$
Dimension $144$
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(28,729)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(729, base_ring=CyclotomicField(54))
 
chi = DirichletCharacter(H, H._module([44]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("729.28");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 729 = 3^{6} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 729.g (of order \(27\), degree \(18\), 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: \(144\)
Relative dimension: \(8\) over \(\Q(\zeta_{27})\)
Twist minimal: no (minimal twist has level 81)
Sato-Tate group: $\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label 28.5
Character \(\chi\) \(=\) 729.28
Dual form 729.2.g.b.703.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.474230 + 0.311906i) q^{2} +(-0.664551 + 1.54060i) q^{4} +(1.99266 - 2.11209i) q^{5} +(-3.10865 - 0.363349i) q^{7} +(-0.362501 - 2.05585i) q^{8} +O(q^{10})\) \(q+(-0.474230 + 0.311906i) q^{2} +(-0.664551 + 1.54060i) q^{4} +(1.99266 - 2.11209i) q^{5} +(-3.10865 - 0.363349i) q^{7} +(-0.362501 - 2.05585i) q^{8} +(-0.286203 + 1.62314i) q^{10} +(-0.984350 + 3.28796i) q^{11} +(0.231870 - 3.98106i) q^{13} +(1.58755 - 0.797296i) q^{14} +(-1.48964 - 1.57893i) q^{16} +(-0.878443 + 0.319727i) q^{17} +(-4.55845 - 1.65914i) q^{19} +(1.92967 + 4.47349i) q^{20} +(-0.558725 - 1.86627i) q^{22} +(-6.11065 + 0.714233i) q^{23} +(-0.199532 - 3.42583i) q^{25} +(1.13175 + 1.96026i) q^{26} +(2.62564 - 4.54773i) q^{28} +(-1.60828 - 0.807706i) q^{29} +(0.403603 + 0.542133i) q^{31} +(5.26149 + 1.24700i) q^{32} +(0.316859 - 0.425615i) q^{34} +(-6.96191 + 5.84174i) q^{35} +(-8.73079 - 7.32600i) q^{37} +(2.67925 - 0.634993i) q^{38} +(-5.06448 - 3.33096i) q^{40} +(5.55820 + 3.65568i) q^{41} +(-2.17613 + 0.515752i) q^{43} +(-4.41129 - 3.70151i) q^{44} +(2.67508 - 2.24466i) q^{46} +(1.89278 - 2.54245i) q^{47} +(2.72039 + 0.644744i) q^{49} +(1.16316 + 1.56239i) q^{50} +(5.97913 + 3.00283i) q^{52} +(4.18963 - 7.25666i) q^{53} +(4.98301 + 8.63082i) q^{55} +(0.379900 + 6.52263i) q^{56} +(1.01462 - 0.118592i) q^{58} +(-1.44287 - 4.81952i) q^{59} +(-0.226018 - 0.523969i) q^{61} +(-0.360495 - 0.131209i) q^{62} +(1.19553 - 0.435136i) q^{64} +(-7.94633 - 8.42262i) q^{65} +(-12.2150 + 6.13461i) q^{67} +(0.0911978 - 1.56581i) q^{68} +(1.47947 - 4.94179i) q^{70} +(2.31784 - 13.1452i) q^{71} +(-1.17142 - 6.64347i) q^{73} +(6.42542 + 0.751024i) q^{74} +(5.58539 - 5.92017i) q^{76} +(4.25468 - 9.86346i) q^{77} +(-0.622719 + 0.409569i) q^{79} -6.30319 q^{80} -3.77609 q^{82} +(-3.04071 + 1.99991i) q^{83} +(-1.07514 + 2.49246i) q^{85} +(0.871119 - 0.923332i) q^{86} +(7.11637 + 0.831784i) q^{88} +(2.27781 + 12.9181i) q^{89} +(-2.16732 + 12.2915i) q^{91} +(2.96049 - 9.88873i) q^{92} +(-0.104609 + 1.79607i) q^{94} +(-12.5877 + 6.32177i) q^{95} +(-8.58165 - 9.09602i) q^{97} +(-1.49119 + 0.542748i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} + 63 q^{20} + 9 q^{22} - 36 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28} + 45 q^{29} + 9 q^{31} - 63 q^{32} + 9 q^{34} - 9 q^{35} - 18 q^{37} + 9 q^{38} + 9 q^{40} + 27 q^{41} + 9 q^{43} - 54 q^{44} - 18 q^{46} - 63 q^{47} + 9 q^{49} + 225 q^{50} + 27 q^{52} - 45 q^{53} - 9 q^{55} - 99 q^{56} + 9 q^{58} + 117 q^{59} + 9 q^{61} - 81 q^{62} - 18 q^{64} - 81 q^{65} + 36 q^{67} + 18 q^{68} + 63 q^{70} + 90 q^{71} - 18 q^{73} - 81 q^{74} + 90 q^{76} - 81 q^{77} + 63 q^{79} + 288 q^{80} - 36 q^{82} - 45 q^{83} + 63 q^{85} - 81 q^{86} + 90 q^{88} + 81 q^{89} - 18 q^{91} + 63 q^{92} + 63 q^{94} - 153 q^{95} + 36 q^{97} - 81 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{22}{27}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.474230 + 0.311906i −0.335331 + 0.220551i −0.705996 0.708216i \(-0.749500\pi\)
0.370665 + 0.928767i \(0.379130\pi\)
\(3\) 0 0
\(4\) −0.664551 + 1.54060i −0.332275 + 0.770301i
\(5\) 1.99266 2.11209i 0.891144 0.944557i −0.107623 0.994192i \(-0.534324\pi\)
0.998767 + 0.0496342i \(0.0158056\pi\)
\(6\) 0 0
\(7\) −3.10865 0.363349i −1.17496 0.137333i −0.493872 0.869535i \(-0.664419\pi\)
−0.681088 + 0.732201i \(0.738493\pi\)
\(8\) −0.362501 2.05585i −0.128164 0.726852i
\(9\) 0 0
\(10\) −0.286203 + 1.62314i −0.0905055 + 0.513282i
\(11\) −0.984350 + 3.28796i −0.296793 + 0.991357i 0.671388 + 0.741106i \(0.265698\pi\)
−0.968181 + 0.250251i \(0.919487\pi\)
\(12\) 0 0
\(13\) 0.231870 3.98106i 0.0643092 1.10415i −0.799611 0.600518i \(-0.794961\pi\)
0.863920 0.503628i \(-0.168002\pi\)
\(14\) 1.58755 0.797296i 0.424290 0.213086i
\(15\) 0 0
\(16\) −1.48964 1.57893i −0.372410 0.394732i
\(17\) −0.878443 + 0.319727i −0.213054 + 0.0775452i −0.446342 0.894862i \(-0.647274\pi\)
0.233289 + 0.972408i \(0.425051\pi\)
\(18\) 0 0
\(19\) −4.55845 1.65914i −1.04578 0.380633i −0.238711 0.971091i \(-0.576725\pi\)
−0.807068 + 0.590458i \(0.798947\pi\)
\(20\) 1.92967 + 4.47349i 0.431488 + 1.00030i
\(21\) 0 0
\(22\) −0.558725 1.86627i −0.119121 0.397891i
\(23\) −6.11065 + 0.714233i −1.27416 + 0.148928i −0.726145 0.687542i \(-0.758690\pi\)
−0.548014 + 0.836469i \(0.684616\pi\)
\(24\) 0 0
\(25\) −0.199532 3.42583i −0.0399063 0.685165i
\(26\) 1.13175 + 1.96026i 0.221955 + 0.384438i
\(27\) 0 0
\(28\) 2.62564 4.54773i 0.496198 0.859441i
\(29\) −1.60828 0.807706i −0.298649 0.149987i 0.293165 0.956062i \(-0.405292\pi\)
−0.591814 + 0.806075i \(0.701588\pi\)
\(30\) 0 0
\(31\) 0.403603 + 0.542133i 0.0724892 + 0.0973699i 0.836889 0.547373i \(-0.184372\pi\)
−0.764400 + 0.644743i \(0.776965\pi\)
\(32\) 5.26149 + 1.24700i 0.930109 + 0.220440i
\(33\) 0 0
\(34\) 0.316859 0.425615i 0.0543409 0.0729924i
\(35\) −6.96191 + 5.84174i −1.17678 + 0.987434i
\(36\) 0 0
\(37\) −8.73079 7.32600i −1.43533 1.20439i −0.942475 0.334277i \(-0.891508\pi\)
−0.492858 0.870110i \(-0.664048\pi\)
\(38\) 2.67925 0.634993i 0.434631 0.103009i
\(39\) 0 0
\(40\) −5.06448 3.33096i −0.800765 0.526672i
\(41\) 5.55820 + 3.65568i 0.868045 + 0.570922i 0.903567 0.428447i \(-0.140939\pi\)
−0.0355222 + 0.999369i \(0.511309\pi\)
\(42\) 0 0
\(43\) −2.17613 + 0.515752i −0.331857 + 0.0786515i −0.393166 0.919467i \(-0.628620\pi\)
0.0613098 + 0.998119i \(0.480472\pi\)
\(44\) −4.41129 3.70151i −0.665026 0.558023i
\(45\) 0 0
\(46\) 2.67508 2.24466i 0.394419 0.330957i
\(47\) 1.89278 2.54245i 0.276091 0.370854i −0.642351 0.766411i \(-0.722041\pi\)
0.918442 + 0.395556i \(0.129448\pi\)
\(48\) 0 0
\(49\) 2.72039 + 0.644744i 0.388627 + 0.0921062i
\(50\) 1.16316 + 1.56239i 0.164496 + 0.220956i
\(51\) 0 0
\(52\) 5.97913 + 3.00283i 0.829157 + 0.416418i
\(53\) 4.18963 7.25666i 0.575490 0.996779i −0.420498 0.907294i \(-0.638145\pi\)
0.995988 0.0894851i \(-0.0285221\pi\)
\(54\) 0 0
\(55\) 4.98301 + 8.63082i 0.671909 + 1.16378i
\(56\) 0.379900 + 6.52263i 0.0507663 + 0.871623i
\(57\) 0 0
\(58\) 1.01462 0.118592i 0.133226 0.0155719i
\(59\) −1.44287 4.81952i −0.187846 0.627448i −0.999086 0.0427359i \(-0.986393\pi\)
0.811241 0.584712i \(-0.198793\pi\)
\(60\) 0 0
\(61\) −0.226018 0.523969i −0.0289387 0.0670874i 0.903134 0.429359i \(-0.141261\pi\)
−0.932073 + 0.362272i \(0.882001\pi\)
\(62\) −0.360495 0.131209i −0.0457829 0.0166636i
\(63\) 0 0
\(64\) 1.19553 0.435136i 0.149441 0.0543920i
\(65\) −7.94633 8.42262i −0.985621 1.04470i
\(66\) 0 0
\(67\) −12.2150 + 6.13461i −1.49230 + 0.749461i −0.993127 0.117041i \(-0.962659\pi\)
−0.499173 + 0.866502i \(0.666363\pi\)
\(68\) 0.0911978 1.56581i 0.0110594 0.189882i
\(69\) 0 0
\(70\) 1.47947 4.94179i 0.176831 0.590657i
\(71\) 2.31784 13.1452i 0.275078 1.56004i −0.463638 0.886025i \(-0.653456\pi\)
0.738715 0.674017i \(-0.235433\pi\)
\(72\) 0 0
\(73\) −1.17142 6.64347i −0.137105 0.777560i −0.973371 0.229236i \(-0.926377\pi\)
0.836266 0.548324i \(-0.184734\pi\)
\(74\) 6.42542 + 0.751024i 0.746940 + 0.0873048i
\(75\) 0 0
\(76\) 5.58539 5.92017i 0.640688 0.679090i
\(77\) 4.25468 9.86346i 0.484866 1.12405i
\(78\) 0 0
\(79\) −0.622719 + 0.409569i −0.0700614 + 0.0460801i −0.584056 0.811713i \(-0.698535\pi\)
0.513995 + 0.857793i \(0.328165\pi\)
\(80\) −6.30319 −0.704718
\(81\) 0 0
\(82\) −3.77609 −0.417000
\(83\) −3.04071 + 1.99991i −0.333761 + 0.219518i −0.705316 0.708893i \(-0.749195\pi\)
0.371555 + 0.928411i \(0.378825\pi\)
\(84\) 0 0
\(85\) −1.07514 + 2.49246i −0.116616 + 0.270345i
\(86\) 0.871119 0.923332i 0.0939352 0.0995655i
\(87\) 0 0
\(88\) 7.11637 + 0.831784i 0.758607 + 0.0886685i
\(89\) 2.27781 + 12.9181i 0.241447 + 1.36931i 0.828601 + 0.559839i \(0.189137\pi\)
−0.587154 + 0.809475i \(0.699752\pi\)
\(90\) 0 0
\(91\) −2.16732 + 12.2915i −0.227197 + 1.28850i
\(92\) 2.96049 9.88873i 0.308652 1.03097i
\(93\) 0 0
\(94\) −0.104609 + 1.79607i −0.0107896 + 0.185251i
\(95\) −12.5877 + 6.32177i −1.29147 + 0.648600i
\(96\) 0 0
\(97\) −8.58165 9.09602i −0.871335 0.923561i 0.126321 0.991989i \(-0.459683\pi\)
−0.997656 + 0.0684283i \(0.978202\pi\)
\(98\) −1.49119 + 0.542748i −0.150633 + 0.0548258i
\(99\) 0 0
\(100\) 5.41044 + 1.96924i 0.541044 + 0.196924i
\(101\) 2.37006 + 5.49442i 0.235830 + 0.546715i 0.994497 0.104763i \(-0.0334084\pi\)
−0.758667 + 0.651478i \(0.774149\pi\)
\(102\) 0 0
\(103\) −0.507240 1.69430i −0.0499798 0.166944i 0.929356 0.369185i \(-0.120363\pi\)
−0.979336 + 0.202240i \(0.935178\pi\)
\(104\) −8.26849 + 0.966448i −0.810792 + 0.0947680i
\(105\) 0 0
\(106\) 0.276545 + 4.74809i 0.0268604 + 0.461176i
\(107\) 3.57628 + 6.19429i 0.345732 + 0.598825i 0.985486 0.169754i \(-0.0542974\pi\)
−0.639755 + 0.768579i \(0.720964\pi\)
\(108\) 0 0
\(109\) −5.68613 + 9.84867i −0.544633 + 0.943332i 0.453997 + 0.891003i \(0.349998\pi\)
−0.998630 + 0.0523287i \(0.983336\pi\)
\(110\) −5.05509 2.53876i −0.481984 0.242062i
\(111\) 0 0
\(112\) 4.05708 + 5.44960i 0.383358 + 0.514939i
\(113\) 5.66711 + 1.34313i 0.533116 + 0.126351i 0.488352 0.872647i \(-0.337598\pi\)
0.0447643 + 0.998998i \(0.485746\pi\)
\(114\) 0 0
\(115\) −10.6679 + 14.3295i −0.994788 + 1.33623i
\(116\) 2.31313 1.94095i 0.214769 0.180213i
\(117\) 0 0
\(118\) 2.18749 + 1.83552i 0.201375 + 0.168973i
\(119\) 2.84695 0.674739i 0.260979 0.0618532i
\(120\) 0 0
\(121\) −0.651365 0.428410i −0.0592150 0.0389463i
\(122\) 0.270614 + 0.177985i 0.0245002 + 0.0161140i
\(123\) 0 0
\(124\) −1.10343 + 0.261517i −0.0990906 + 0.0234849i
\(125\) 3.48865 + 2.92733i 0.312034 + 0.261828i
\(126\) 0 0
\(127\) 8.22802 6.90413i 0.730119 0.612643i −0.200045 0.979787i \(-0.564109\pi\)
0.930164 + 0.367144i \(0.119664\pi\)
\(128\) −6.88920 + 9.25380i −0.608925 + 0.817928i
\(129\) 0 0
\(130\) 6.39545 + 1.51575i 0.560918 + 0.132940i
\(131\) 4.27722 + 5.74530i 0.373702 + 0.501969i 0.948697 0.316188i \(-0.102403\pi\)
−0.574994 + 0.818158i \(0.694996\pi\)
\(132\) 0 0
\(133\) 13.5678 + 6.81400i 1.17648 + 0.590848i
\(134\) 3.87930 6.71914i 0.335120 0.580446i
\(135\) 0 0
\(136\) 0.975746 + 1.69004i 0.0836695 + 0.144920i
\(137\) −0.501738 8.61452i −0.0428664 0.735988i −0.949442 0.313944i \(-0.898350\pi\)
0.906575 0.422044i \(-0.138687\pi\)
\(138\) 0 0
\(139\) 5.85926 0.684849i 0.496976 0.0580882i 0.136087 0.990697i \(-0.456547\pi\)
0.360889 + 0.932609i \(0.382473\pi\)
\(140\) −4.37325 14.6077i −0.369607 1.23457i
\(141\) 0 0
\(142\) 3.00086 + 6.95677i 0.251826 + 0.583799i
\(143\) 12.8613 + 4.68113i 1.07552 + 0.391456i
\(144\) 0 0
\(145\) −4.91069 + 1.78735i −0.407811 + 0.148431i
\(146\) 2.62766 + 2.78516i 0.217467 + 0.230501i
\(147\) 0 0
\(148\) 17.0885 8.58217i 1.40467 0.705450i
\(149\) −0.802085 + 13.7713i −0.0657094 + 1.12819i 0.790807 + 0.612066i \(0.209661\pi\)
−0.856516 + 0.516121i \(0.827376\pi\)
\(150\) 0 0
\(151\) −1.80026 + 6.01330i −0.146503 + 0.489356i −0.999468 0.0326132i \(-0.989617\pi\)
0.852965 + 0.521969i \(0.174802\pi\)
\(152\) −1.75849 + 9.97291i −0.142633 + 0.808910i
\(153\) 0 0
\(154\) 1.05877 + 6.00461i 0.0853185 + 0.483865i
\(155\) 1.94928 + 0.227838i 0.156570 + 0.0183004i
\(156\) 0 0
\(157\) 0.113981 0.120812i 0.00909664 0.00964187i −0.722809 0.691048i \(-0.757150\pi\)
0.731906 + 0.681406i \(0.238631\pi\)
\(158\) 0.167565 0.388460i 0.0133308 0.0309042i
\(159\) 0 0
\(160\) 13.1181 8.62793i 1.03708 0.682098i
\(161\) 19.2554 1.51754
\(162\) 0 0
\(163\) 16.2014 1.26899 0.634495 0.772927i \(-0.281208\pi\)
0.634495 + 0.772927i \(0.281208\pi\)
\(164\) −9.32566 + 6.13358i −0.728212 + 0.478952i
\(165\) 0 0
\(166\) 0.818213 1.89683i 0.0635056 0.147223i
\(167\) −12.5418 + 13.2935i −0.970513 + 1.02868i 0.0290638 + 0.999578i \(0.490747\pi\)
−0.999576 + 0.0291056i \(0.990734\pi\)
\(168\) 0 0
\(169\) −2.88294 0.336968i −0.221765 0.0259206i
\(170\) −0.267548 1.51734i −0.0205200 0.116375i
\(171\) 0 0
\(172\) 0.651580 3.69529i 0.0496825 0.281763i
\(173\) 5.40734 18.0618i 0.411112 1.37321i −0.462514 0.886612i \(-0.653052\pi\)
0.873626 0.486598i \(-0.161762\pi\)
\(174\) 0 0
\(175\) −0.624497 + 10.7222i −0.0472076 + 0.810523i
\(176\) 6.65778 3.34366i 0.501849 0.252038i
\(177\) 0 0
\(178\) −5.10943 5.41568i −0.382968 0.405922i
\(179\) −9.67521 + 3.52149i −0.723159 + 0.263209i −0.677266 0.735738i \(-0.736836\pi\)
−0.0458930 + 0.998946i \(0.514613\pi\)
\(180\) 0 0
\(181\) 0.770198 + 0.280329i 0.0572484 + 0.0208367i 0.370486 0.928838i \(-0.379191\pi\)
−0.313237 + 0.949675i \(0.601414\pi\)
\(182\) −2.80597 6.50498i −0.207993 0.482181i
\(183\) 0 0
\(184\) 3.68347 + 12.3037i 0.271549 + 0.907037i
\(185\) −32.8707 + 3.84203i −2.41670 + 0.282472i
\(186\) 0 0
\(187\) −0.186554 3.20301i −0.0136422 0.234227i
\(188\) 2.65905 + 4.60561i 0.193931 + 0.335899i
\(189\) 0 0
\(190\) 3.99766 6.92415i 0.290021 0.502330i
\(191\) 0.683675 + 0.343354i 0.0494690 + 0.0248442i 0.473362 0.880868i \(-0.343040\pi\)
−0.423893 + 0.905712i \(0.639337\pi\)
\(192\) 0 0
\(193\) 5.58623 + 7.50362i 0.402106 + 0.540122i 0.956347 0.292234i \(-0.0943987\pi\)
−0.554241 + 0.832356i \(0.686991\pi\)
\(194\) 6.90678 + 1.63694i 0.495878 + 0.117525i
\(195\) 0 0
\(196\) −2.80113 + 3.76257i −0.200081 + 0.268755i
\(197\) −0.857832 + 0.719807i −0.0611180 + 0.0512841i −0.672835 0.739793i \(-0.734924\pi\)
0.611717 + 0.791077i \(0.290479\pi\)
\(198\) 0 0
\(199\) 5.88368 + 4.93699i 0.417083 + 0.349974i 0.827052 0.562125i \(-0.190016\pi\)
−0.409969 + 0.912099i \(0.634461\pi\)
\(200\) −6.97064 + 1.65207i −0.492899 + 0.116819i
\(201\) 0 0
\(202\) −2.83769 1.86638i −0.199660 0.131318i
\(203\) 4.70609 + 3.09524i 0.330303 + 0.217244i
\(204\) 0 0
\(205\) 18.7967 4.45491i 1.31282 0.311144i
\(206\) 0.769010 + 0.645276i 0.0535794 + 0.0449585i
\(207\) 0 0
\(208\) −6.63120 + 5.56424i −0.459791 + 0.385811i
\(209\) 9.94229 13.3548i 0.687723 0.923772i
\(210\) 0 0
\(211\) −9.96134 2.36088i −0.685767 0.162530i −0.127060 0.991895i \(-0.540554\pi\)
−0.558707 + 0.829365i \(0.688702\pi\)
\(212\) 8.39540 + 11.2770i 0.576598 + 0.774506i
\(213\) 0 0
\(214\) −3.62801 1.82206i −0.248006 0.124553i
\(215\) −3.24697 + 5.62391i −0.221441 + 0.383547i
\(216\) 0 0
\(217\) −1.05768 1.83195i −0.0717999 0.124361i
\(218\) −0.375325 6.44407i −0.0254202 0.436448i
\(219\) 0 0
\(220\) −16.6081 + 1.94121i −1.11972 + 0.130876i
\(221\) 1.06917 + 3.57126i 0.0719199 + 0.240229i
\(222\) 0 0
\(223\) −1.84243 4.27124i −0.123379 0.286024i 0.845321 0.534258i \(-0.179409\pi\)
−0.968700 + 0.248234i \(0.920150\pi\)
\(224\) −15.9031 5.78824i −1.06257 0.386743i
\(225\) 0 0
\(226\) −3.10644 + 1.13065i −0.206637 + 0.0752098i
\(227\) 9.68944 + 10.2702i 0.643111 + 0.681658i 0.964135 0.265414i \(-0.0855085\pi\)
−0.321024 + 0.947071i \(0.604027\pi\)
\(228\) 0 0
\(229\) −4.63378 + 2.32717i −0.306208 + 0.153784i −0.595268 0.803528i \(-0.702954\pi\)
0.289059 + 0.957311i \(0.406658\pi\)
\(230\) 0.589589 10.1229i 0.0388764 0.667481i
\(231\) 0 0
\(232\) −1.07752 + 3.59916i −0.0707425 + 0.236297i
\(233\) −0.773336 + 4.38581i −0.0506629 + 0.287324i −0.999604 0.0281287i \(-0.991045\pi\)
0.948941 + 0.315452i \(0.102156\pi\)
\(234\) 0 0
\(235\) −1.59822 9.06397i −0.104257 0.591268i
\(236\) 8.38382 + 0.979929i 0.545740 + 0.0637879i
\(237\) 0 0
\(238\) −1.13965 + 1.20796i −0.0738726 + 0.0783004i
\(239\) 11.5106 26.6846i 0.744561 1.72609i 0.0587876 0.998271i \(-0.481277\pi\)
0.685773 0.727815i \(-0.259464\pi\)
\(240\) 0 0
\(241\) −20.8739 + 13.7290i −1.34460 + 0.884360i −0.998549 0.0538543i \(-0.982849\pi\)
−0.346055 + 0.938214i \(0.612479\pi\)
\(242\) 0.442520 0.0284463
\(243\) 0 0
\(244\) 0.957429 0.0612931
\(245\) 6.78256 4.46096i 0.433322 0.285000i
\(246\) 0 0
\(247\) −7.66209 + 17.7627i −0.487527 + 1.13022i
\(248\) 0.968235 1.02627i 0.0614830 0.0651682i
\(249\) 0 0
\(250\) −2.56747 0.300094i −0.162381 0.0189796i
\(251\) −2.46091 13.9565i −0.155331 0.880926i −0.958483 0.285151i \(-0.907956\pi\)
0.803152 0.595775i \(-0.203155\pi\)
\(252\) 0 0
\(253\) 3.66665 20.7946i 0.230521 1.30735i
\(254\) −1.74853 + 5.84051i −0.109713 + 0.366466i
\(255\) 0 0
\(256\) 0.232799 3.99701i 0.0145499 0.249813i
\(257\) −13.1355 + 6.59688i −0.819367 + 0.411502i −0.808541 0.588440i \(-0.799742\pi\)
−0.0108263 + 0.999941i \(0.503446\pi\)
\(258\) 0 0
\(259\) 24.4791 + 25.9463i 1.52106 + 1.61223i
\(260\) 18.2566 6.64487i 1.13223 0.412098i
\(261\) 0 0
\(262\) −3.82038 1.39050i −0.236024 0.0859056i
\(263\) −6.49135 15.0486i −0.400274 0.927939i −0.992509 0.122174i \(-0.961014\pi\)
0.592235 0.805765i \(-0.298246\pi\)
\(264\) 0 0
\(265\) −6.97824 23.3089i −0.428670 1.43186i
\(266\) −8.55957 + 1.00047i −0.524821 + 0.0613428i
\(267\) 0 0
\(268\) −1.33349 22.8952i −0.0814561 1.39855i
\(269\) −5.68131 9.84032i −0.346396 0.599975i 0.639211 0.769032i \(-0.279261\pi\)
−0.985606 + 0.169057i \(0.945928\pi\)
\(270\) 0 0
\(271\) −1.38266 + 2.39483i −0.0839903 + 0.145476i −0.904961 0.425496i \(-0.860100\pi\)
0.820970 + 0.570971i \(0.193433\pi\)
\(272\) 1.81339 + 0.910719i 0.109953 + 0.0552204i
\(273\) 0 0
\(274\) 2.92486 + 3.92877i 0.176697 + 0.237345i
\(275\) 11.4604 + 2.71616i 0.691087 + 0.163791i
\(276\) 0 0
\(277\) 10.9854 14.7559i 0.660048 0.886598i −0.338473 0.940976i \(-0.609910\pi\)
0.998520 + 0.0543783i \(0.0173177\pi\)
\(278\) −2.56503 + 2.15231i −0.153840 + 0.129087i
\(279\) 0 0
\(280\) 14.5334 + 12.1950i 0.868538 + 0.728790i
\(281\) −10.4439 + 2.47524i −0.623028 + 0.147660i −0.529992 0.848002i \(-0.677805\pi\)
−0.0930358 + 0.995663i \(0.529657\pi\)
\(282\) 0 0
\(283\) 11.9407 + 7.85355i 0.709804 + 0.466845i 0.852369 0.522940i \(-0.175165\pi\)
−0.142566 + 0.989785i \(0.545535\pi\)
\(284\) 18.7111 + 12.3065i 1.11030 + 0.730256i
\(285\) 0 0
\(286\) −7.55929 + 1.79158i −0.446990 + 0.105939i
\(287\) −15.9502 13.3838i −0.941512 0.790022i
\(288\) 0 0
\(289\) −12.3533 + 10.3657i −0.726666 + 0.609745i
\(290\) 1.77131 2.37929i 0.104015 0.139717i
\(291\) 0 0
\(292\) 11.0134 + 2.61023i 0.644512 + 0.152752i
\(293\) 13.0455 + 17.5231i 0.762125 + 1.02371i 0.998643 + 0.0520843i \(0.0165864\pi\)
−0.236518 + 0.971627i \(0.576006\pi\)
\(294\) 0 0
\(295\) −13.0544 6.55618i −0.760058 0.381716i
\(296\) −11.8962 + 20.6048i −0.691453 + 1.19763i
\(297\) 0 0
\(298\) −3.91497 6.78092i −0.226788 0.392808i
\(299\) 1.42652 + 24.4925i 0.0824979 + 1.41643i
\(300\) 0 0
\(301\) 6.95223 0.812599i 0.400720 0.0468374i
\(302\) −1.02184 3.41320i −0.0588006 0.196408i
\(303\) 0 0
\(304\) 4.17079 + 9.66898i 0.239211 + 0.554554i
\(305\) −1.55705 0.566720i −0.0891564 0.0324503i
\(306\) 0 0
\(307\) −28.6368 + 10.4229i −1.63439 + 0.594869i −0.986045 0.166478i \(-0.946760\pi\)
−0.648344 + 0.761347i \(0.724538\pi\)
\(308\) 12.3682 + 13.1095i 0.704745 + 0.746986i
\(309\) 0 0
\(310\) −0.995470 + 0.499944i −0.0565389 + 0.0283949i
\(311\) 1.57644 27.0664i 0.0893915 1.53479i −0.593835 0.804587i \(-0.702387\pi\)
0.683227 0.730206i \(-0.260576\pi\)
\(312\) 0 0
\(313\) 2.32494 7.76583i 0.131413 0.438950i −0.866803 0.498650i \(-0.833829\pi\)
0.998216 + 0.0596999i \(0.0190144\pi\)
\(314\) −0.0163709 + 0.0928440i −0.000923863 + 0.00523949i
\(315\) 0 0
\(316\) −0.217154 1.23154i −0.0122159 0.0692797i
\(317\) −19.2878 2.25442i −1.08331 0.126621i −0.444345 0.895856i \(-0.646563\pi\)
−0.638966 + 0.769235i \(0.720637\pi\)
\(318\) 0 0
\(319\) 4.23881 4.49288i 0.237328 0.251553i
\(320\) 1.46323 3.39214i 0.0817969 0.189627i
\(321\) 0 0
\(322\) −9.13149 + 6.00587i −0.508878 + 0.334694i
\(323\) 4.53480 0.252323
\(324\) 0 0
\(325\) −13.6847 −0.759089
\(326\) −7.68317 + 5.05330i −0.425531 + 0.279876i
\(327\) 0 0
\(328\) 5.50067 12.7520i 0.303724 0.704111i
\(329\) −6.80780 + 7.21585i −0.375326 + 0.397823i
\(330\) 0 0
\(331\) −1.97328 0.230643i −0.108461 0.0126773i 0.0616891 0.998095i \(-0.480351\pi\)
−0.170150 + 0.985418i \(0.554425\pi\)
\(332\) −1.06035 6.01357i −0.0581945 0.330037i
\(333\) 0 0
\(334\) 1.80136 10.2160i 0.0985662 0.558997i
\(335\) −11.3835 + 38.0234i −0.621945 + 2.07744i
\(336\) 0 0
\(337\) 1.06728 18.3245i 0.0581385 0.998199i −0.835522 0.549456i \(-0.814835\pi\)
0.893661 0.448743i \(-0.148128\pi\)
\(338\) 1.47228 0.739406i 0.0800814 0.0402184i
\(339\) 0 0
\(340\) −3.12540 3.31273i −0.169499 0.179658i
\(341\) −2.17980 + 0.793381i −0.118043 + 0.0429640i
\(342\) 0 0
\(343\) 12.3650 + 4.50048i 0.667646 + 0.243003i
\(344\) 1.84916 + 4.28683i 0.0996999 + 0.231130i
\(345\) 0 0
\(346\) 3.06925 + 10.2520i 0.165004 + 0.551151i
\(347\) 26.6029 3.10943i 1.42812 0.166923i 0.633364 0.773854i \(-0.281674\pi\)
0.794754 + 0.606931i \(0.207600\pi\)
\(348\) 0 0
\(349\) 0.762246 + 13.0873i 0.0408021 + 0.700545i 0.955242 + 0.295824i \(0.0955943\pi\)
−0.914440 + 0.404721i \(0.867369\pi\)
\(350\) −3.04816 5.27957i −0.162931 0.282205i
\(351\) 0 0
\(352\) −9.27922 + 16.0721i −0.494584 + 0.856645i
\(353\) 17.3676 + 8.72232i 0.924383 + 0.464242i 0.846301 0.532705i \(-0.178824\pi\)
0.0780814 + 0.996947i \(0.475121\pi\)
\(354\) 0 0
\(355\) −23.1451 31.0893i −1.22842 1.65005i
\(356\) −21.4153 5.07553i −1.13501 0.269003i
\(357\) 0 0
\(358\) 3.48990 4.68775i 0.184447 0.247755i
\(359\) 11.2428 9.43384i 0.593373 0.497899i −0.295935 0.955208i \(-0.595631\pi\)
0.889308 + 0.457309i \(0.151187\pi\)
\(360\) 0 0
\(361\) 3.47185 + 2.91323i 0.182729 + 0.153328i
\(362\) −0.452687 + 0.107289i −0.0237927 + 0.00563898i
\(363\) 0 0
\(364\) −17.4960 11.5073i −0.917038 0.603146i
\(365\) −16.3659 10.7640i −0.856630 0.563414i
\(366\) 0 0
\(367\) −10.6977 + 2.53540i −0.558415 + 0.132347i −0.500125 0.865953i \(-0.666713\pi\)
−0.0582894 + 0.998300i \(0.518565\pi\)
\(368\) 10.2304 + 8.58433i 0.533297 + 0.447489i
\(369\) 0 0
\(370\) 14.3899 12.0746i 0.748096 0.627727i
\(371\) −15.6608 + 21.0361i −0.813069 + 1.09214i
\(372\) 0 0
\(373\) −19.8678 4.70876i −1.02872 0.243810i −0.318596 0.947890i \(-0.603211\pi\)
−0.710121 + 0.704080i \(0.751360\pi\)
\(374\) 1.08751 + 1.46077i 0.0562336 + 0.0755348i
\(375\) 0 0
\(376\) −5.91302 2.96963i −0.304941 0.153147i
\(377\) −3.58843 + 6.21535i −0.184814 + 0.320107i
\(378\) 0 0
\(379\) −13.0154 22.5433i −0.668556 1.15797i −0.978308 0.207155i \(-0.933580\pi\)
0.309753 0.950817i \(-0.399754\pi\)
\(380\) −1.37418 23.5938i −0.0704939 1.21033i
\(381\) 0 0
\(382\) −0.431313 + 0.0504133i −0.0220679 + 0.00257937i
\(383\) −6.74866 22.5421i −0.344840 1.15185i −0.937963 0.346735i \(-0.887290\pi\)
0.593123 0.805112i \(-0.297895\pi\)
\(384\) 0 0
\(385\) −12.3544 28.6408i −0.629640 1.45967i
\(386\) −4.98958 1.81606i −0.253963 0.0924349i
\(387\) 0 0
\(388\) 19.7163 7.17615i 1.00094 0.364314i
\(389\) −22.6942 24.0545i −1.15064 1.21961i −0.971819 0.235730i \(-0.924252\pi\)
−0.178825 0.983881i \(-0.557230\pi\)
\(390\) 0 0
\(391\) 5.13950 2.58115i 0.259916 0.130534i
\(392\) 0.339350 5.82642i 0.0171398 0.294279i
\(393\) 0 0
\(394\) 0.182298 0.608917i 0.00918403 0.0306768i
\(395\) −0.375819 + 2.13137i −0.0189095 + 0.107241i
\(396\) 0 0
\(397\) −0.00960087 0.0544493i −0.000481854 0.00273273i 0.984566 0.175014i \(-0.0559972\pi\)
−0.985048 + 0.172282i \(0.944886\pi\)
\(398\) −4.33009 0.506115i −0.217048 0.0253693i
\(399\) 0 0
\(400\) −5.11190 + 5.41830i −0.255595 + 0.270915i
\(401\) 11.3452 26.3011i 0.566551 1.31341i −0.358486 0.933535i \(-0.616707\pi\)
0.925037 0.379878i \(-0.124034\pi\)
\(402\) 0 0
\(403\) 2.25184 1.48106i 0.112172 0.0737769i
\(404\) −10.0397 −0.499496
\(405\) 0 0
\(406\) −3.19719 −0.158674
\(407\) 32.6817 21.4951i 1.61997 1.06547i
\(408\) 0 0
\(409\) 12.4515 28.8659i 0.615688 1.42732i −0.269916 0.962884i \(-0.586996\pi\)
0.885604 0.464441i \(-0.153745\pi\)
\(410\) −7.52446 + 7.97546i −0.371607 + 0.393880i
\(411\) 0 0
\(412\) 2.94733 + 0.344493i 0.145204 + 0.0169720i
\(413\) 2.73421 + 15.5065i 0.134542 + 0.763024i
\(414\) 0 0
\(415\) −1.83511 + 10.4074i −0.0900818 + 0.510879i
\(416\) 6.18434 20.6571i 0.303212 1.01280i
\(417\) 0 0
\(418\) −0.549486 + 9.43431i −0.0268762 + 0.461447i
\(419\) 3.01535 1.51436i 0.147309 0.0739816i −0.373617 0.927583i \(-0.621883\pi\)
0.520927 + 0.853601i \(0.325586\pi\)
\(420\) 0 0
\(421\) −17.3369 18.3761i −0.844950 0.895594i 0.150718 0.988577i \(-0.451841\pi\)
−0.995668 + 0.0929825i \(0.970360\pi\)
\(422\) 5.46033 1.98740i 0.265805 0.0967451i
\(423\) 0 0
\(424\) −16.4373 5.98270i −0.798267 0.290545i
\(425\) 1.27061 + 2.94560i 0.0616335 + 0.142882i
\(426\) 0 0
\(427\) 0.512228 + 1.71096i 0.0247885 + 0.0827992i
\(428\) −11.9196 + 1.39320i −0.576154 + 0.0673427i
\(429\) 0 0
\(430\) −0.214322 3.67977i −0.0103355 0.177454i
\(431\) −16.4068 28.4174i −0.790288 1.36882i −0.925789 0.378041i \(-0.876598\pi\)
0.135501 0.990777i \(-0.456736\pi\)
\(432\) 0 0
\(433\) 6.46122 11.1912i 0.310507 0.537813i −0.667966 0.744192i \(-0.732835\pi\)
0.978472 + 0.206379i \(0.0661680\pi\)
\(434\) 1.07298 + 0.538870i 0.0515046 + 0.0258666i
\(435\) 0 0
\(436\) −11.3942 15.3050i −0.545681 0.732977i
\(437\) 29.0401 + 6.88263i 1.38918 + 0.329241i
\(438\) 0 0
\(439\) 22.0216 29.5802i 1.05103 1.41178i 0.144574 0.989494i \(-0.453819\pi\)
0.906460 0.422291i \(-0.138774\pi\)
\(440\) 15.9373 13.3730i 0.759781 0.637532i
\(441\) 0 0
\(442\) −1.62093 1.36012i −0.0770997 0.0646943i
\(443\) 33.4372 7.92477i 1.58865 0.376517i 0.661125 0.750276i \(-0.270079\pi\)
0.927526 + 0.373759i \(0.121931\pi\)
\(444\) 0 0
\(445\) 31.8231 + 20.9304i 1.50856 + 0.992196i
\(446\) 2.20596 + 1.45088i 0.104455 + 0.0687014i
\(447\) 0 0
\(448\) −3.87459 + 0.918294i −0.183057 + 0.0433853i
\(449\) 13.4520 + 11.2876i 0.634838 + 0.532693i 0.902428 0.430840i \(-0.141783\pi\)
−0.267590 + 0.963533i \(0.586227\pi\)
\(450\) 0 0
\(451\) −17.4910 + 14.6767i −0.823617 + 0.691097i
\(452\) −5.83531 + 7.83818i −0.274470 + 0.368677i
\(453\) 0 0
\(454\) −7.79836 1.84824i −0.365995 0.0867424i
\(455\) 21.6420 + 29.0703i 1.01459 + 1.36284i
\(456\) 0 0
\(457\) −7.46084 3.74697i −0.349003 0.175276i 0.265658 0.964067i \(-0.414411\pi\)
−0.614661 + 0.788791i \(0.710707\pi\)
\(458\) 1.47162 2.54891i 0.0687641 0.119103i
\(459\) 0 0
\(460\) −14.9867 25.9577i −0.698758 1.21028i
\(461\) 1.18266 + 20.3054i 0.0550818 + 0.945718i 0.906759 + 0.421650i \(0.138549\pi\)
−0.851677 + 0.524067i \(0.824414\pi\)
\(462\) 0 0
\(463\) 2.57184 0.300605i 0.119524 0.0139703i −0.0561208 0.998424i \(-0.517873\pi\)
0.175644 + 0.984454i \(0.443799\pi\)
\(464\) 1.12044 + 3.74254i 0.0520153 + 0.173743i
\(465\) 0 0
\(466\) −1.00122 2.32109i −0.0463806 0.107522i
\(467\) −11.5019 4.18635i −0.532244 0.193721i 0.0618958 0.998083i \(-0.480285\pi\)
−0.594140 + 0.804361i \(0.702508\pi\)
\(468\) 0 0
\(469\) 40.2012 14.6320i 1.85632 0.675645i
\(470\) 3.58503 + 3.79991i 0.165365 + 0.175277i
\(471\) 0 0
\(472\) −9.38515 + 4.71340i −0.431987 + 0.216952i
\(473\) 0.446302 7.66271i 0.0205210 0.352332i
\(474\) 0 0
\(475\) −4.77437 + 15.9475i −0.219063 + 0.731721i
\(476\) −0.852437 + 4.83441i −0.0390714 + 0.221585i
\(477\) 0 0
\(478\) 2.86441 + 16.2449i 0.131015 + 0.743024i
\(479\) −27.2416 3.18408i −1.24470 0.145485i −0.531873 0.846824i \(-0.678512\pi\)
−0.712827 + 0.701340i \(0.752586\pi\)
\(480\) 0 0
\(481\) −31.1896 + 33.0591i −1.42212 + 1.50736i
\(482\) 5.61687 13.0214i 0.255841 0.593107i
\(483\) 0 0
\(484\) 1.09287 0.718795i 0.0496761 0.0326725i
\(485\) −36.3120 −1.64884
\(486\) 0 0
\(487\) −6.02417 −0.272981 −0.136491 0.990641i \(-0.543582\pi\)
−0.136491 + 0.990641i \(0.543582\pi\)
\(488\) −0.995268 + 0.654598i −0.0450537 + 0.0296323i
\(489\) 0 0
\(490\) −1.82509 + 4.23104i −0.0824493 + 0.191139i
\(491\) −0.334399 + 0.354442i −0.0150912 + 0.0159958i −0.734875 0.678202i \(-0.762759\pi\)
0.719784 + 0.694198i \(0.244241\pi\)
\(492\) 0 0
\(493\) 1.67102 + 0.195315i 0.0752591 + 0.00879652i
\(494\) −1.90671 10.8135i −0.0857867 0.486521i
\(495\) 0 0
\(496\) 0.254765 1.44484i 0.0114393 0.0648754i
\(497\) −11.9817 + 40.0215i −0.537451 + 1.79521i
\(498\) 0 0
\(499\) −0.318908 + 5.47545i −0.0142763 + 0.245115i 0.983619 + 0.180262i \(0.0576947\pi\)
−0.997895 + 0.0648523i \(0.979342\pi\)
\(500\) −6.82823 + 3.42927i −0.305368 + 0.153361i
\(501\) 0 0
\(502\) 5.52014 + 5.85101i 0.246376 + 0.261143i
\(503\) −9.93090 + 3.61455i −0.442797 + 0.161165i −0.553790 0.832656i \(-0.686819\pi\)
0.110993 + 0.993821i \(0.464597\pi\)
\(504\) 0 0
\(505\) 16.3275 + 5.94271i 0.726562 + 0.264447i
\(506\) 4.74713 + 11.0051i 0.211036 + 0.489236i
\(507\) 0 0
\(508\) 5.16858 + 17.2643i 0.229319 + 0.765977i
\(509\) −12.3227 + 1.44032i −0.546196 + 0.0638412i −0.384716 0.923035i \(-0.625701\pi\)
−0.161480 + 0.986876i \(0.551627\pi\)
\(510\) 0 0
\(511\) 1.22765 + 21.0779i 0.0543079 + 0.932431i
\(512\) −10.4003 18.0139i −0.459634 0.796110i
\(513\) 0 0
\(514\) 4.17162 7.22546i 0.184002 0.318701i
\(515\) −4.58927 2.30482i −0.202228 0.101562i
\(516\) 0 0
\(517\) 6.49630 + 8.72605i 0.285707 + 0.383771i
\(518\) −19.7015 4.66935i −0.865635 0.205159i
\(519\) 0 0
\(520\) −14.4351 + 19.3896i −0.633019 + 0.850292i
\(521\) 13.6270 11.4344i 0.597011 0.500952i −0.293472 0.955968i \(-0.594811\pi\)
0.890483 + 0.455016i \(0.150366\pi\)
\(522\) 0 0
\(523\) −10.4002 8.72680i −0.454769 0.381596i 0.386433 0.922317i \(-0.373707\pi\)
−0.841202 + 0.540721i \(0.818151\pi\)
\(524\) −11.6937 + 2.77145i −0.510840 + 0.121071i
\(525\) 0 0
\(526\) 7.77215 + 5.11182i 0.338882 + 0.222886i
\(527\) −0.527877 0.347190i −0.0229947 0.0151238i
\(528\) 0 0
\(529\) 14.4499 3.42469i 0.628256 0.148899i
\(530\) 10.5795 + 8.87724i 0.459543 + 0.385603i
\(531\) 0 0
\(532\) −19.5141 + 16.3743i −0.846045 + 0.709916i
\(533\) 15.8423 21.2799i 0.686205 0.921733i
\(534\) 0 0
\(535\) 20.2092 + 4.78968i 0.873722 + 0.207076i
\(536\) 17.0398 + 22.8884i 0.736006 + 0.988627i
\(537\) 0 0
\(538\) 5.76350 + 2.89454i 0.248482 + 0.124792i
\(539\) −4.79771 + 8.30987i −0.206652 + 0.357931i
\(540\) 0 0
\(541\) 13.6538 + 23.6492i 0.587025 + 1.01676i 0.994620 + 0.103594i \(0.0330342\pi\)
−0.407595 + 0.913163i \(0.633632\pi\)
\(542\) −0.0912649 1.56696i −0.00392016 0.0673066i
\(543\) 0 0
\(544\) −5.02062 + 0.586826i −0.215257 + 0.0251600i
\(545\) 9.47081 + 31.6347i 0.405685 + 1.35508i
\(546\) 0 0
\(547\) 5.02926 + 11.6591i 0.215036 + 0.498509i 0.991256 0.131953i \(-0.0421247\pi\)
−0.776220 + 0.630462i \(0.782865\pi\)
\(548\) 13.6050 + 4.95181i 0.581176 + 0.211531i
\(549\) 0 0
\(550\) −6.28204 + 2.28648i −0.267867 + 0.0974957i
\(551\) 5.99114 + 6.35024i 0.255231 + 0.270529i
\(552\) 0 0
\(553\) 2.08464 1.04694i 0.0886477 0.0445206i
\(554\) −0.607135 + 10.4241i −0.0257947 + 0.442878i
\(555\) 0 0
\(556\) −2.83870 + 9.48191i −0.120388 + 0.402122i
\(557\) −2.62356 + 14.8789i −0.111164 + 0.630441i 0.877415 + 0.479733i \(0.159266\pi\)
−0.988578 + 0.150708i \(0.951845\pi\)
\(558\) 0 0
\(559\) 1.54866 + 8.78288i 0.0655013 + 0.371476i
\(560\) 19.5944 + 2.29026i 0.828016 + 0.0967812i
\(561\) 0 0
\(562\) 4.18075 4.43133i 0.176354 0.186924i
\(563\) −2.42888 + 5.63077i −0.102365 + 0.237309i −0.961700 0.274104i \(-0.911619\pi\)
0.859335 + 0.511413i \(0.170878\pi\)
\(564\) 0 0
\(565\) 14.1294 9.29307i 0.594429 0.390962i
\(566\) −8.11223 −0.340982
\(567\) 0 0
\(568\) −27.8646 −1.16917
\(569\) 1.23600 0.812928i 0.0518157 0.0340797i −0.523337 0.852126i \(-0.675313\pi\)
0.575153 + 0.818046i \(0.304943\pi\)
\(570\) 0 0
\(571\) 3.49187 8.09506i 0.146130 0.338768i −0.829393 0.558666i \(-0.811313\pi\)
0.975523 + 0.219898i \(0.0705726\pi\)
\(572\) −15.7588 + 16.7033i −0.658907 + 0.698400i
\(573\) 0 0
\(574\) 11.7386 + 1.37204i 0.489958 + 0.0572679i
\(575\) 3.66611 + 20.7915i 0.152887 + 0.867066i
\(576\) 0 0
\(577\) 2.48608 14.0993i 0.103497 0.586960i −0.888313 0.459238i \(-0.848122\pi\)
0.991810 0.127722i \(-0.0407665\pi\)
\(578\) 2.62520 8.76878i 0.109194 0.364733i
\(579\) 0 0
\(580\) 0.509816 8.75321i 0.0211690 0.363457i
\(581\) 10.1792 5.11218i 0.422304 0.212089i
\(582\) 0 0
\(583\) 19.7355 + 20.9184i 0.817362 + 0.866353i
\(584\) −13.2333 + 4.81654i −0.547599 + 0.199310i
\(585\) 0 0
\(586\) −11.6521 4.24102i −0.481344 0.175195i
\(587\) 3.38197 + 7.84028i 0.139589 + 0.323603i 0.973642 0.228080i \(-0.0732449\pi\)
−0.834054 + 0.551683i \(0.813986\pi\)
\(588\) 0 0
\(589\) −0.940329 3.14092i −0.0387456 0.129419i
\(590\) 8.23571 0.962617i 0.339059 0.0396303i
\(591\) 0 0
\(592\) 1.43852 + 24.6984i 0.0591227 + 1.01510i
\(593\) 19.8740 + 34.4227i 0.816125 + 1.41357i 0.908517 + 0.417848i \(0.137216\pi\)
−0.0923915 + 0.995723i \(0.529451\pi\)
\(594\) 0 0
\(595\) 4.24788 7.35754i 0.174146 0.301630i
\(596\) −20.6830 10.3874i −0.847210 0.425485i
\(597\) 0 0
\(598\) −8.31584 11.1701i −0.340060 0.456780i
\(599\) 19.8283 + 4.69940i 0.810164 + 0.192012i 0.614764 0.788711i \(-0.289251\pi\)
0.195400 + 0.980724i \(0.437399\pi\)
\(600\) 0 0
\(601\) −8.17441 + 10.9801i −0.333441 + 0.447889i −0.936948 0.349469i \(-0.886362\pi\)
0.603507 + 0.797358i \(0.293770\pi\)
\(602\) −3.04350 + 2.55380i −0.124044 + 0.104085i
\(603\) 0 0
\(604\) −8.06774 6.76964i −0.328272 0.275453i
\(605\) −2.20279 + 0.522071i −0.0895562 + 0.0212252i
\(606\) 0 0
\(607\) 3.75977 + 2.47284i 0.152604 + 0.100369i 0.623515 0.781812i \(-0.285704\pi\)
−0.470910 + 0.882181i \(0.656075\pi\)
\(608\) −21.9153 14.4139i −0.888782 0.584561i
\(609\) 0 0
\(610\) 0.915162 0.216897i 0.0370538 0.00878192i
\(611\) −9.68275 8.12479i −0.391722 0.328694i
\(612\) 0 0
\(613\) 27.4040 22.9947i 1.10684 0.928746i 0.108971 0.994045i \(-0.465244\pi\)
0.997866 + 0.0652986i \(0.0208000\pi\)
\(614\) 10.3295 13.8749i 0.416863 0.559944i
\(615\) 0 0
\(616\) −21.8201 5.17146i −0.879157 0.208364i
\(617\) −16.4713 22.1249i −0.663112 0.890713i 0.335572 0.942015i \(-0.391071\pi\)
−0.998683 + 0.0513013i \(0.983663\pi\)
\(618\) 0 0
\(619\) −29.8724 15.0025i −1.20067 0.603001i −0.267894 0.963448i \(-0.586328\pi\)
−0.932780 + 0.360447i \(0.882624\pi\)
\(620\) −1.64640 + 2.85165i −0.0661211 + 0.114525i
\(621\) 0 0
\(622\) 7.69456 + 13.3274i 0.308524 + 0.534379i
\(623\) −2.38713 40.9855i −0.0956384 1.64205i
\(624\) 0 0
\(625\) 30.1766 3.52714i 1.20707 0.141086i
\(626\) 1.31965 + 4.40795i 0.0527439 + 0.176177i
\(627\) 0 0
\(628\) 0.110378 + 0.255885i 0.00440455 + 0.0102109i
\(629\) 10.0118 + 3.64400i 0.399197 + 0.145296i
\(630\) 0 0
\(631\) 10.2732 3.73914i 0.408970 0.148853i −0.129339 0.991600i \(-0.541286\pi\)
0.538309 + 0.842748i \(0.319063\pi\)
\(632\) 1.06775 + 1.13175i 0.0424727 + 0.0450185i
\(633\) 0 0
\(634\) 9.85001 4.94686i 0.391194 0.196465i
\(635\) 1.81346 31.1359i 0.0719650 1.23559i
\(636\) 0 0
\(637\) 3.19754 10.6805i 0.126691 0.423177i
\(638\) −0.608816 + 3.45277i −0.0241032 + 0.136696i
\(639\) 0 0
\(640\) 5.81708 + 32.9903i 0.229940 + 1.30406i
\(641\) −9.25236 1.08145i −0.365446 0.0427145i −0.0686116 0.997643i \(-0.521857\pi\)
−0.296835 + 0.954929i \(0.595931\pi\)
\(642\) 0 0
\(643\) −0.883538 + 0.936495i −0.0348433 + 0.0369318i −0.744561 0.667555i \(-0.767341\pi\)
0.709718 + 0.704486i \(0.248823\pi\)
\(644\) −12.7962 + 29.6649i −0.504241 + 1.16896i
\(645\) 0 0
\(646\) −2.15054 + 1.41443i −0.0846118 + 0.0556501i
\(647\) 25.7409 1.01198 0.505989 0.862540i \(-0.331128\pi\)
0.505989 + 0.862540i \(0.331128\pi\)
\(648\) 0 0
\(649\) 17.2667 0.677776
\(650\) 6.48968 4.26833i 0.254546 0.167418i
\(651\) 0 0
\(652\) −10.7666 + 24.9599i −0.421654 + 0.977504i
\(653\) −26.7355 + 28.3380i −1.04624 + 1.10895i −0.0523464 + 0.998629i \(0.516670\pi\)
−0.993896 + 0.110323i \(0.964811\pi\)
\(654\) 0 0
\(655\) 20.6577 + 2.41453i 0.807162 + 0.0943437i
\(656\) −2.50766 14.2217i −0.0979077 0.555262i
\(657\) 0 0
\(658\) 0.977797 5.54536i 0.0381185 0.216181i
\(659\) −9.63166 + 32.1720i −0.375196 + 1.25324i 0.537033 + 0.843561i \(0.319545\pi\)
−0.912229 + 0.409681i \(0.865640\pi\)
\(660\) 0 0
\(661\) −2.06029 + 35.3739i −0.0801361 + 1.37588i 0.683365 + 0.730077i \(0.260516\pi\)
−0.763501 + 0.645807i \(0.776521\pi\)
\(662\) 1.00773 0.506100i 0.0391664 0.0196701i
\(663\) 0 0
\(664\) 5.21376 + 5.52627i 0.202333 + 0.214461i
\(665\) 41.4278 15.0785i 1.60650 0.584718i
\(666\) 0 0
\(667\) 10.4045 + 3.78693i 0.402864 + 0.146630i
\(668\) −12.1454 28.1561i −0.469918 1.08939i
\(669\) 0 0
\(670\) −6.46135 21.5824i −0.249624 0.833801i
\(671\) 1.94527 0.227369i 0.0750963 0.00877750i
\(672\) 0 0
\(673\) −1.59738 27.4260i −0.0615746 1.05720i −0.877666 0.479273i \(-0.840900\pi\)
0.816091 0.577923i \(-0.196137\pi\)
\(674\) 5.20938 + 9.02292i 0.200658 + 0.347550i
\(675\) 0 0
\(676\) 2.43499 4.21753i 0.0936536 0.162213i
\(677\) 8.53705 + 4.28747i 0.328106 + 0.164781i 0.605225 0.796055i \(-0.293083\pi\)
−0.277119 + 0.960836i \(0.589380\pi\)
\(678\) 0 0
\(679\) 23.3724 + 31.3945i 0.896948 + 1.20481i
\(680\) 5.51386 + 1.30681i 0.211447 + 0.0501138i
\(681\) 0 0
\(682\) 0.786265 1.05614i 0.0301076 0.0404416i
\(683\) −25.4573 + 21.3612i −0.974095 + 0.817363i −0.983188 0.182596i \(-0.941550\pi\)
0.00909301 + 0.999959i \(0.497106\pi\)
\(684\) 0 0
\(685\) −19.1945 16.1061i −0.733383 0.615381i
\(686\) −7.26757 + 1.72245i −0.277477 + 0.0657633i
\(687\) 0 0
\(688\) 4.05599 + 2.66767i 0.154633 + 0.101704i
\(689\) −27.9177 18.3618i −1.06358 0.699528i
\(690\) 0 0
\(691\) −5.28329 + 1.25216i −0.200986 + 0.0476345i −0.329876 0.944024i \(-0.607007\pi\)
0.128890 + 0.991659i \(0.458859\pi\)
\(692\) 24.2325 + 20.3335i 0.921183 + 0.772964i
\(693\) 0 0
\(694\) −11.6460 + 9.77218i −0.442077 + 0.370947i
\(695\) 10.2290 13.7400i 0.388010 0.521187i
\(696\) 0 0
\(697\) −6.05138 1.43420i −0.229212 0.0543243i
\(698\) −4.44347 5.96862i −0.168188 0.225916i
\(699\) 0 0
\(700\) −16.1036 8.08755i −0.608661 0.305681i
\(701\) 16.8694 29.2187i 0.637150 1.10358i −0.348906 0.937158i \(-0.613447\pi\)
0.986055 0.166418i \(-0.0532200\pi\)
\(702\) 0 0
\(703\) 27.6440 + 47.8808i 1.04261 + 1.80586i
\(704\) 0.253893 + 4.35917i 0.00956894 + 0.164292i
\(705\) 0 0
\(706\) −10.9568 + 1.28066i −0.412363 + 0.0481983i
\(707\) −5.37130 17.9414i −0.202009 0.674756i
\(708\) 0 0
\(709\) −7.67820 17.8001i −0.288361 0.668495i 0.711039 0.703153i \(-0.248225\pi\)
−0.999399 + 0.0346578i \(0.988966\pi\)
\(710\) 20.6730 + 7.52437i 0.775846 + 0.282385i
\(711\) 0 0
\(712\) 25.7319 9.36564i 0.964343 0.350992i
\(713\) −2.85349 3.02452i −0.106864 0.113269i
\(714\) 0 0
\(715\) 35.5152 17.8364i 1.32819 0.667044i
\(716\) 1.00446 17.2459i 0.0375383 0.644508i
\(717\) 0 0
\(718\) −2.38921 + 7.98051i −0.0891644 + 0.297830i
\(719\) 0.831346 4.71480i 0.0310040 0.175832i −0.965374 0.260871i \(-0.915990\pi\)
0.996378 + 0.0850387i \(0.0271014\pi\)
\(720\) 0 0
\(721\) 0.961210 + 5.45129i 0.0357973 + 0.203017i
\(722\) −2.55511 0.298649i −0.0950912 0.0111146i
\(723\) 0 0
\(724\) −0.943712 + 1.00028i −0.0350728 + 0.0371750i
\(725\) −2.44616 + 5.67083i −0.0908481 + 0.210610i
\(726\) 0 0
\(727\) 6.31649 4.15442i 0.234266 0.154079i −0.426949 0.904276i \(-0.640412\pi\)
0.661215 + 0.750197i \(0.270041\pi\)
\(728\) 26.0550 0.965664
\(729\) 0 0
\(730\) 11.1186 0.411516
\(731\) 1.74670 1.14883i 0.0646042 0.0424909i
\(732\) 0 0
\(733\) 15.3050 35.4810i 0.565303 1.31052i −0.360587 0.932726i \(-0.617423\pi\)
0.925890 0.377794i \(-0.123317\pi\)
\(734\) 4.28236 4.53903i 0.158065 0.167539i
\(735\) 0 0
\(736\) −33.0418 3.86203i −1.21794 0.142356i
\(737\) −8.14649 46.2010i −0.300080 1.70184i
\(738\) 0 0
\(739\) −8.79173 + 49.8604i −0.323409 + 1.83414i 0.197218 + 0.980360i \(0.436809\pi\)
−0.520627 + 0.853784i \(0.674302\pi\)
\(740\) 15.9252 53.1939i 0.585422 1.95545i
\(741\) 0 0
\(742\) 0.865535 14.8607i 0.0317748 0.545552i
\(743\) −13.7207 + 6.89082i −0.503365 + 0.252800i −0.682315 0.731059i \(-0.739027\pi\)
0.178949 + 0.983858i \(0.442730\pi\)
\(744\) 0 0
\(745\) 27.4880 + 29.1355i 1.00708 + 1.06744i
\(746\) 10.8906 3.96386i 0.398733 0.145127i
\(747\) 0 0
\(748\) 5.05853 + 1.84116i 0.184958 + 0.0673193i
\(749\) −8.86671 20.5554i −0.323983 0.751076i
\(750\) 0 0
\(751\) 13.3810 + 44.6956i 0.488279 + 1.63097i 0.746864 + 0.664977i \(0.231559\pi\)
−0.258585 + 0.965989i \(0.583256\pi\)
\(752\) −6.83391 + 0.798770i −0.249207 + 0.0291281i
\(753\) 0 0
\(754\) −0.236862 4.06676i −0.00862599 0.148103i
\(755\) 9.11335 + 15.7848i 0.331669 + 0.574467i
\(756\) 0 0
\(757\) 5.85224 10.1364i 0.212703 0.368413i −0.739856 0.672765i \(-0.765107\pi\)
0.952560 + 0.304352i \(0.0984399\pi\)
\(758\) 13.2037 + 6.63113i 0.479579 + 0.240854i
\(759\) 0 0
\(760\) 17.5596 + 23.5867i 0.636955 + 0.855580i
\(761\) −25.4732 6.03726i −0.923403 0.218851i −0.258700 0.965958i \(-0.583294\pi\)
−0.664704 + 0.747107i \(0.731442\pi\)
\(762\) 0 0
\(763\) 21.2547 28.5501i 0.769473 1.03358i
\(764\) −0.983309 + 0.825094i −0.0355749 + 0.0298509i
\(765\) 0 0
\(766\) 10.2314 + 8.58519i 0.369676 + 0.310195i
\(767\) −19.5213 + 4.62664i −0.704875 + 0.167058i
\(768\) 0 0
\(769\) −38.0508 25.0264i −1.37215 0.902476i −0.372475 0.928042i \(-0.621491\pi\)
−0.999673 + 0.0255660i \(0.991861\pi\)
\(770\) 14.7921 + 9.72890i 0.533069 + 0.350605i
\(771\) 0 0
\(772\) −15.2724 + 3.61963i −0.549667 + 0.130273i
\(773\) −10.7154 8.99131i −0.385407 0.323395i 0.429414 0.903108i \(-0.358720\pi\)
−0.814821 + 0.579713i \(0.803165\pi\)
\(774\) 0 0
\(775\) 1.77672 1.49085i 0.0638217 0.0535528i
\(776\) −15.5892 + 20.9399i −0.559618 + 0.751698i
\(777\) 0 0
\(778\) 18.2650 + 4.32889i 0.654833 + 0.155198i
\(779\) −19.2715 25.8861i −0.690472 0.927465i
\(780\) 0 0
\(781\) 40.9391 + 20.5604i 1.46492 + 0.735709i
\(782\) −1.63223 + 2.82710i −0.0583683 + 0.101097i
\(783\) 0