Properties

Label 729.2.g.c.703.4
Level $729$
Weight $2$
Character 729.703
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 703.4
Character \(\chi\) \(=\) 729.703
Dual form 729.2.g.c.28.4

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

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{5}{27}\right)\)

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 \(-0.250500\pi\)
−0.370665 + 0.928767i \(0.620870\pi\)
\(3\) 0 0
\(4\) −0.664551 1.54060i −0.332275 0.770301i
\(5\) −1.99266 2.11209i −0.891144 0.944557i 0.107623 0.994192i \(-0.465676\pi\)
−0.998767 + 0.0496342i \(0.984194\pi\)
\(6\) 0 0
\(7\) −3.10865 + 0.363349i −1.17496 + 0.137333i −0.681088 0.732201i \(-0.738493\pi\)
−0.493872 + 0.869535i \(0.664419\pi\)
\(8\) 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 0.968181 + 0.250251i \(0.0805132\pi\)
−0.671388 + 0.741106i \(0.734302\pi\)
\(12\) 0 0
\(13\) 0.231870 + 3.98106i 0.0643092 + 1.10415i 0.863920 + 0.503628i \(0.168002\pi\)
−0.799611 + 0.600518i \(0.794961\pi\)
\(14\) −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 \(-0.352726\pi\)
−0.233289 + 0.972408i \(0.574949\pi\)
\(18\) 0 0
\(19\) −4.55845 + 1.65914i −1.04578 + 0.380633i −0.807068 0.590458i \(-0.798947\pi\)
−0.238711 + 0.971091i \(0.576725\pi\)
\(20\) −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 \(-0.241310\pi\)
0.548014 + 0.836469i \(0.315384\pi\)
\(24\) 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 \(-0.594708\pi\)
0.591814 + 0.806075i \(0.298412\pi\)
\(30\) 0 0
\(31\) 0.403603 0.542133i 0.0724892 0.0973699i −0.764400 0.644743i \(-0.776965\pi\)
0.836889 + 0.547373i \(0.184372\pi\)
\(32\) −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 −0.492858 + 0.870110i \(0.664048\pi\)
−0.942475 + 0.334277i \(0.891508\pi\)
\(38\) −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 \(-0.859061\pi\)
0.0355222 + 0.999369i \(0.488691\pi\)
\(42\) 0 0
\(43\) −2.17613 0.515752i −0.331857 0.0786515i 0.0613098 0.998119i \(-0.480472\pi\)
−0.393166 + 0.919467i \(0.628620\pi\)
\(44\) 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 \(-0.277959\pi\)
−0.918442 + 0.395556i \(0.870552\pi\)
\(48\) 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 −0.995988 0.0894851i \(-0.971478\pi\)
0.420498 0.907294i \(-0.361855\pi\)
\(54\) 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 −0.811241 0.584712i \(-0.801207\pi\)
0.999086 0.0427359i \(-0.0136074\pi\)
\(60\) 0 0
\(61\) −0.226018 + 0.523969i −0.0289387 + 0.0670874i −0.932073 0.362272i \(-0.882001\pi\)
0.903134 + 0.429359i \(0.141261\pi\)
\(62\) 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 −0.499173 0.866502i \(-0.666363\pi\)
−0.993127 + 0.117041i \(0.962659\pi\)
\(68\) −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 −0.738715 0.674017i \(-0.764567\pi\)
0.463638 0.886025i \(-0.346544\pi\)
\(72\) 0 0
\(73\) −1.17142 + 6.64347i −0.137105 + 0.777560i 0.836266 + 0.548324i \(0.184734\pi\)
−0.973371 + 0.229236i \(0.926377\pi\)
\(74\) −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 0.513995 0.857793i \(-0.328165\pi\)
−0.584056 + 0.811713i \(0.698535\pi\)
\(80\) 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 \(-0.250805\pi\)
−0.371555 + 0.928411i \(0.621175\pi\)
\(84\) 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 0.587154 + 0.809475i \(0.300248\pi\)
−0.828601 + 0.559839i \(0.810863\pi\)
\(90\) 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 −0.997656 0.0684283i \(-0.978202\pi\)
0.126321 + 0.991989i \(0.459683\pi\)
\(98\) 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 \(-0.966592\pi\)
0.758667 + 0.651478i \(0.225851\pi\)
\(102\) 0 0
\(103\) −0.507240 + 1.69430i −0.0499798 + 0.166944i −0.979336 0.202240i \(-0.935178\pi\)
0.929356 + 0.369185i \(0.120363\pi\)
\(104\) 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 \(-0.945703\pi\)
0.639755 + 0.768579i \(0.279036\pi\)
\(108\) 0 0
\(109\) −5.68613 9.84867i −0.544633 0.943332i −0.998630 0.0523287i \(-0.983336\pi\)
0.453997 0.891003i \(-0.349998\pi\)
\(110\) 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 \(-0.662402\pi\)
−0.0447643 + 0.998998i \(0.514254\pi\)
\(114\) 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 0.930164 0.367144i \(-0.119664\pi\)
−0.200045 + 0.979787i \(0.564109\pi\)
\(128\) 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 \(-0.897597\pi\)
0.574994 + 0.818158i \(0.305004\pi\)
\(132\) 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 −0.906575 0.422044i \(-0.861313\pi\)
0.949442 0.313944i \(-0.101650\pi\)
\(138\) 0 0
\(139\) 5.85926 + 0.684849i 0.496976 + 0.0580882i 0.360889 0.932609i \(-0.382473\pi\)
0.136087 + 0.990697i \(0.456547\pi\)
\(140\) 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 0.856516 + 0.516121i \(0.172624\pi\)
−0.790807 + 0.612066i \(0.790339\pi\)
\(150\) 0 0
\(151\) −1.80026 6.01330i −0.146503 0.489356i 0.852965 0.521969i \(-0.174802\pi\)
−0.999468 + 0.0326132i \(0.989617\pi\)
\(152\) 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 0.731906 0.681406i \(-0.238631\pi\)
−0.722809 + 0.691048i \(0.757150\pi\)
\(158\) −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 0.999576 + 0.0291056i \(0.00926592\pi\)
−0.0290638 + 0.999578i \(0.509253\pi\)
\(168\) 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 −0.873626 0.486598i \(-0.838238\pi\)
0.462514 0.886612i \(-0.346948\pi\)
\(174\) 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 \(-0.263164\pi\)
0.0458930 + 0.998946i \(0.485387\pi\)
\(180\) 0 0
\(181\) 0.770198 0.280329i 0.0572484 0.0208367i −0.313237 0.949675i \(-0.601414\pi\)
0.370486 + 0.928838i \(0.379191\pi\)
\(182\) 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 \(-0.656960\pi\)
0.423893 + 0.905712i \(0.360663\pi\)
\(192\) 0 0
\(193\) 5.58623 7.50362i 0.402106 0.540122i −0.554241 0.832356i \(-0.686991\pi\)
0.956347 + 0.292234i \(0.0943987\pi\)
\(194\) −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 \(-0.265076\pi\)
−0.611717 + 0.791077i \(0.709521\pi\)
\(198\) 0 0
\(199\) 5.88368 4.93699i 0.417083 0.349974i −0.409969 0.912099i \(-0.634461\pi\)
0.827052 + 0.562125i \(0.190016\pi\)
\(200\) 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 −0.558707 0.829365i \(-0.688702\pi\)
−0.127060 + 0.991895i \(0.540554\pi\)
\(212\) −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 −0.968700 0.248234i \(-0.920150\pi\)
0.845321 + 0.534258i \(0.179409\pi\)
\(224\) 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 \(-0.914492\pi\)
0.321024 + 0.947071i \(0.395973\pi\)
\(228\) 0 0
\(229\) −4.63378 2.32717i −0.306208 0.153784i 0.289059 0.957311i \(-0.406658\pi\)
−0.595268 + 0.803528i \(0.702954\pi\)
\(230\) −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 \(-0.00895483\pi\)
−0.948941 + 0.315452i \(0.897844\pi\)
\(234\) 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 −0.685773 0.727815i \(-0.740536\pi\)
−0.0587876 0.998271i \(-0.518723\pi\)
\(240\) 0 0
\(241\) −20.8739 13.7290i −1.34460 0.884360i −0.346055 0.938214i \(-0.612479\pi\)
−0.998549 + 0.0538543i \(0.982849\pi\)
\(242\) −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 −0.803152 0.595775i \(-0.796845\pi\)
0.958483 0.285151i \(-0.0920438\pi\)
\(252\) 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 \(-0.200258\pi\)
0.0108263 + 0.999941i \(0.496554\pi\)
\(258\) 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 −0.592235 0.805765i \(-0.701754\pi\)
0.992509 0.122174i \(-0.0389865\pi\)
\(264\) 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 \(-0.720739\pi\)
0.985606 + 0.169057i \(0.0540721\pi\)
\(270\) 0 0
\(271\) −1.38266 2.39483i −0.0839903 0.145476i 0.820970 0.570971i \(-0.193433\pi\)
−0.904961 + 0.425496i \(0.860100\pi\)
\(272\) −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 0.998520 0.0543783i \(-0.0173177\pi\)
−0.338473 + 0.940976i \(0.609910\pi\)
\(278\) 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 \(-0.322195\pi\)
0.0930358 + 0.995663i \(0.470343\pi\)
\(282\) 0 0
\(283\) 11.9407 7.85355i 0.709804 0.466845i −0.142566 0.989785i \(-0.545535\pi\)
0.852369 + 0.522940i \(0.175165\pi\)
\(284\) −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 0.236518 + 0.971627i \(0.423994\pi\)
−0.998643 + 0.0520843i \(0.983414\pi\)
\(294\) 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 −0.648344 0.761347i \(-0.724538\pi\)
−0.986045 + 0.166478i \(0.946760\pi\)
\(308\) −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 −0.683227 0.730206i \(-0.739424\pi\)
0.593835 0.804587i \(-0.297613\pi\)
\(312\) 0 0
\(313\) 2.32494 + 7.76583i 0.131413 + 0.438950i 0.998216 0.0596999i \(-0.0190144\pi\)
−0.866803 + 0.498650i \(0.833829\pi\)
\(314\) 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 \(-0.353437\pi\)
0.638966 + 0.769235i \(0.279363\pi\)
\(318\) 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 −0.170150 0.985418i \(-0.554425\pi\)
0.0616891 + 0.998095i \(0.480351\pi\)
\(332\) 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 0.893661 + 0.448743i \(0.148128\pi\)
−0.835522 + 0.549456i \(0.814835\pi\)
\(338\) −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 \(-0.718326\pi\)
−0.794754 + 0.606931i \(0.792400\pi\)
\(348\) 0 0
\(349\) 0.762246 13.0873i 0.0408021 0.700545i −0.914440 0.404721i \(-0.867369\pi\)
0.955242 0.295824i \(-0.0955943\pi\)
\(350\) 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 \(-0.821176\pi\)
−0.0780814 + 0.996947i \(0.524879\pi\)
\(354\) 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 \(-0.404369\pi\)
−0.889308 + 0.457309i \(0.848813\pi\)
\(360\) 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 −0.0582894 0.998300i \(-0.518565\pi\)
−0.500125 + 0.865953i \(0.666713\pi\)
\(368\) −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 −0.710121 0.704080i \(-0.751360\pi\)
−0.318596 + 0.947890i \(0.603211\pi\)
\(374\) −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 0.309753 + 0.950817i \(0.399754\pi\)
−0.978308 + 0.207155i \(0.933580\pi\)
\(380\) 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 −0.593123 0.805112i \(-0.702105\pi\)
0.937963 0.346735i \(-0.112710\pi\)
\(384\) 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 0.178825 0.983881i \(-0.442770\pi\)
0.971819 0.235730i \(-0.0757481\pi\)
\(390\) 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 −0.985048 0.172282i \(-0.944886\pi\)
0.984566 + 0.175014i \(0.0559972\pi\)
\(398\) 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 −0.925037 0.379878i \(-0.875966\pi\)
0.358486 0.933535i \(-0.383293\pi\)
\(402\) 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 0.885604 + 0.464441i \(0.153745\pi\)
−0.269916 + 0.962884i \(0.586996\pi\)
\(410\) 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 \(-0.378117\pi\)
−0.520927 + 0.853601i \(0.674414\pi\)
\(420\) 0 0
\(421\) −17.3369 + 18.3761i −0.844950 + 0.895594i −0.995668 0.0929825i \(-0.970360\pi\)
0.150718 + 0.988577i \(0.451841\pi\)
\(422\) −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 −0.135501 0.990777i \(-0.543264\pi\)
0.925789 0.378041i \(-0.123402\pi\)
\(432\) 0 0
\(433\) 6.46122 + 11.1912i 0.310507 + 0.537813i 0.978472 0.206379i \(-0.0661680\pi\)
−0.667966 + 0.744192i \(0.732835\pi\)
\(434\) −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 0.906460 + 0.422291i \(0.138774\pi\)
0.144574 + 0.989494i \(0.453819\pi\)
\(440\) −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 \(-0.729921\pi\)
−0.927526 + 0.373759i \(0.878069\pi\)
\(444\) 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 \(-0.858217\pi\)
0.267590 + 0.963533i \(0.413773\pi\)
\(450\) 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 −0.614661 0.788791i \(-0.710707\pi\)
0.265658 + 0.964067i \(0.414411\pi\)
\(458\) −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 0.851677 + 0.524067i \(0.175586\pi\)
−0.906759 + 0.421650i \(0.861451\pi\)
\(462\) 0 0
\(463\) 2.57184 + 0.300605i 0.119524 + 0.0139703i 0.175644 0.984454i \(-0.443799\pi\)
−0.0561208 + 0.998424i \(0.517873\pi\)
\(464\) −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 \(-0.519715\pi\)
0.594140 + 0.804361i \(0.297492\pi\)
\(468\) 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 \(-0.321488\pi\)
0.712827 + 0.701340i \(0.247414\pi\)
\(480\) 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 \(-0.237241\pi\)
−0.719784 + 0.694198i \(0.755759\pi\)
\(492\) 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 −0.997895 0.0648523i \(-0.979342\pi\)
0.983619 0.180262i \(-0.0576947\pi\)
\(500\) 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 \(-0.313181\pi\)
−0.110993 + 0.993821i \(0.535403\pi\)
\(504\) 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 \(-0.374299\pi\)
0.161480 + 0.986876i \(0.448373\pi\)
\(510\) 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 \(-0.405189\pi\)
−0.890483 + 0.455016i \(0.849634\pi\)
\(522\) 0 0
\(523\) −10.4002 + 8.72680i −0.454769 + 0.381596i −0.841202 0.540721i \(-0.818151\pi\)
0.386433 + 0.922317i \(0.373707\pi\)
\(524\) 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 −0.407595 0.913163i \(-0.633632\pi\)
0.994620 0.103594i \(-0.0330342\pi\)
\(542\) 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 −0.776220 0.630462i \(-0.782865\pi\)
0.991256 + 0.131953i \(0.0421247\pi\)
\(548\) −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 0.988578 + 0.150708i \(0.0481553\pi\)
−0.877415 + 0.479733i \(0.840734\pi\)
\(558\) 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 \(-0.0883814\pi\)
−0.859335 + 0.511413i \(0.829122\pi\)
\(564\) 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 \(-0.324687\pi\)
−0.575153 + 0.818046i \(0.695057\pi\)
\(570\) 0 0
\(571\) 3.49187 + 8.09506i 0.146130 + 0.338768i 0.975523 0.219898i \(-0.0705726\pi\)
−0.829393 + 0.558666i \(0.811313\pi\)
\(572\) 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 0.991810 + 0.127722i \(0.0407665\pi\)
−0.888313 + 0.459238i \(0.848122\pi\)
\(578\) −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 \(-0.926755\pi\)
0.834054 + 0.551683i \(0.186014\pi\)
\(588\) 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 0.0923915 + 0.995723i \(0.470549\pi\)
−0.908517 + 0.417848i \(0.862784\pi\)
\(594\) 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 \(-0.710749\pi\)
−0.195400 + 0.980724i \(0.562601\pi\)
\(600\) 0 0
\(601\) −8.17441 10.9801i −0.333441 0.447889i 0.603507 0.797358i \(-0.293770\pi\)
−0.936948 + 0.349469i \(0.886362\pi\)
\(602\) 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 −0.470910 0.882181i \(-0.656075\pi\)
0.623515 + 0.781812i \(0.285704\pi\)
\(608\) 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 0.997866 0.0652986i \(-0.0208000\pi\)
0.108971 + 0.994045i \(0.465244\pi\)
\(614\) −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 \(-0.608929\pi\)
0.998683 + 0.0513013i \(0.0163369\pi\)
\(618\) 0 0
\(619\) −29.8724 + 15.0025i −1.20067 + 0.603001i −0.932780 0.360447i \(-0.882624\pi\)
−0.267894 + 0.963448i \(0.586328\pi\)
\(620\) 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 0.538309 0.842748i \(-0.319063\pi\)
−0.129339 + 0.991600i \(0.541286\pi\)
\(632\) −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 \(-0.478143\pi\)
0.296835 + 0.954929i \(0.404069\pi\)
\(642\) 0 0
\(643\) −0.883538 0.936495i −0.0348433 0.0369318i 0.709718 0.704486i \(-0.248823\pi\)
−0.744561 + 0.667555i \(0.767341\pi\)
\(644\) 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 \(-0.668872\pi\)
−0.505989 + 0.862540i \(0.668872\pi\)
\(648\) 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 0.993896 + 0.110323i \(0.0351885\pi\)
0.0523464 + 0.998629i \(0.483330\pi\)
\(654\) 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 0.912229 + 0.409681i \(0.134360\pi\)
−0.537033 + 0.843561i \(0.680455\pi\)
\(660\) 0 0
\(661\) −2.06029 35.3739i −0.0801361 1.37588i −0.763501 0.645807i \(-0.776521\pi\)
0.683365 0.730077i \(-0.260516\pi\)
\(662\) −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 0.816091 + 0.577923i \(0.196137\pi\)
−0.877666 + 0.479273i \(0.840900\pi\)
\(674\) −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 \(-0.706917\pi\)
0.277119 + 0.960836i \(0.410620\pi\)
\(678\) 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 \(-0.0584500\pi\)
−0.00909301 + 0.999959i \(0.502894\pi\)
\(684\) 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 0.128890 0.991659i \(-0.458859\pi\)
−0.329876 + 0.944024i \(0.607007\pi\)
\(692\) −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 −0.986055 0.166418i \(-0.946780\pi\)
0.348906 0.937158i \(-0.386553\pi\)
\(702\) 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 −0.999399 0.0346578i \(-0.988966\pi\)
0.711039 + 0.703153i \(0.248225\pi\)
\(710\) −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 \(-0.0840097\pi\)
−0.996378 + 0.0850387i \(0.972899\pi\)
\(720\) 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 0.661215 0.750197i \(-0.270041\pi\)
−0.426949 + 0.904276i \(0.640412\pi\)
\(728\) −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 0.925890 + 0.377794i \(0.123317\pi\)
−0.360587 + 0.932726i \(0.617423\pi\)
\(734\) −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 −0.520627 0.853784i \(-0.674302\pi\)
0.197218 0.980360i \(-0.436809\pi\)
\(740\) −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 \(-0.260973\pi\)
−0.178949 + 0.983858i \(0.557270\pi\)
\(744\) 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 −0.258585 0.965989i \(-0.583256\pi\)
0.746864 0.664977i \(-0.231559\pi\)
\(752\) 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 0.952560 0.304352i \(-0.0984399\pi\)
−0.739856 + 0.672765i \(0.765107\pi\)
\(758\) −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 \(-0.416706\pi\)
0.664704 + 0.747107i \(0.268558\pi\)
\(762\) 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 −0.999673 0.0255660i \(-0.991861\pi\)
−0.372475 + 0.928042i \(0.621491\pi\)
\(770\) −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 \(-0.641280\pi\)
0.814821 + 0.579713i \(0.196835\pi\)
\(774\) 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 0
\(784\) −3.03440 + 5.25573i −0.108371 + 0.187705i
\(785\) 0.0280427 0.481475i 0.00100089 0.0171846i
\(786\) 0 0
\(787\) −14.1067 1.64884i −0.502850 0.0587748i −0.139113 0.990276i \(-0.544425\pi\)
−0.363737 + 0.931502i \(0.618499\pi\)
\(788\) 0.538863 1.79993i 0.0191962 0.0641197i
\(789\) 0 0
\(790\) −0.486563 + 1.12798i −0.0173112 + 0.0401318i
\(791\) 17.1290 6.23446i 0.609039 0.221672i
\(792\) 0 0
\(793\) −2.13836 0.778298i −0.0759353 0.0276382i
\(794\) −0.0215361 + 0.0228269i −0.000764286 + 0.000810096i
\(795\) 0 0
\(796\) −11.5159 5.78353i −0.408172 0.204992i
\(797\) 2.40151 + 41.2323i 0.0850658 + 1.46052i 0.723222 + 0.690616i \(0.242661\pi\)
−0.638156 + 0.769907i \(0.720302\pi\)
\(798\) 0 0
\(799\) −0.849812 2.83857i −0.0300642 0.100421i
\(800\) −3.22216 18.2738i −0.113921 0.646075i
\(801\) 0 0
\(802\) 2.82324 16.0114i 0.0996920 0.565381i
\(803\) −22.9966 + 2.68791i −0.811531 + 0.0948544i
\(804\) 0 0
\(805\) 38.3695 + 40.6693i 1.35235 + 1.43340i
\(806\) 0.605940 + 1.40473i 0.0213433 + 0.0494794i
\(807\) 0 0
\(808\) 10.4365 + 6.86422i 0.367156 + 0.241482i
\(809\) 23.8379 0.838097 0.419048 0.907964i \(-0.362364\pi\)
0.419048 + 0.907964i \(0.362364\pi\)
\(810\) 0 0
\(811\) −3.33188 −0.116998 −0.0584991 0.998287i \(-0.518631\pi\)
−0.0584991 + 0.998287i \(0.518631\pi\)
\(812\) 7.89598 + 5.19326i 0.277094 + 0.182248i
\(813\) 0 0
\(814\) −8.79420 20.3873i −0.308237 0.714573i
\(815\) −32.2838 34.2188i −1.13085 1.19863i
\(816\) 0 0
\(817\) 10.7755 1.25947i 0.376986 0.0440634i
\(818\) −3.09855 + 17.5727i −0.108338 + 0.614417i
\(819\) 0 0
\(820\) −5.62815 31.9188i −0.196543 1.11465i
\(821\) −2.57453 8.59953i −0.0898518 0.300126i 0.901237 0.433326i \(-0.142660\pi\)
−0.991089 + 0.133200i \(0.957475\pi\)
\(822\) 0 0
\(823\) 0.0754800 + 1.29594i 0.00263107 + 0.0451737i 0.999368 0.0355431i \(-0.0113161\pi\)
−0.996737 + 0.0807168i \(0.974279\pi\)
\(824\) 3.29934 + 1.65699i 0.114938 + 0.0577241i
\(825\) 0 0
\(826\) −6.13321 + 6.50082i −0.213402 + 0.226192i
\(827\) 29.6308 + 10.7847i 1.03036 + 0.375022i 0.801219 0.598371i \(-0.204185\pi\)
0.229144 + 0.973392i \(0.426407\pi\)
\(828\) 0 0
\(829\) −25.1437 + 9.15156i −0.873277 + 0.317847i −0.739493 0.673164i \(-0.764935\pi\)
−0.133783 + 0.991011i \(0.542713\pi\)
\(830\) 2.37587 5.50788i 0.0824676 0.191181i
\(831\) 0 0
\(832\) −1.45509 + 4.86035i −0.0504463 + 0.168502i
\(833\) 2.59585 + 0.303411i 0.0899407 + 0.0105126i
\(834\) 0 0
\(835\) 3.08567 52.9789i 0.106784 1.83341i
\(836\) −13.9673 + 24.1921i −0.483069 + 0.836700i
\(837\) 0 0
\(838\) −0.957629 1.65866i −0.0330807 0.0572975i
\(839\) 3.46674 1.74106i 0.119685 0.0601082i −0.387949 0.921681i \(-0.626816\pi\)
0.507634 + 0.861573i \(0.330520\pi\)
\(840\) 0 0
\(841\) −15.3834 + 20.6635i −0.530463 + 0.712536i
\(842\) −13.9533 + 3.30699i −0.480862 + 0.113966i
\(843\) 0 0
\(844\) 10.2570 + 13.7775i 0.353060 + 0.474242i
\(845\) 6.45643 + 5.41758i 0.222108 + 0.186371i
\(846\) 0 0
\(847\) 1.86921 1.56845i 0.0642267 0.0538926i
\(848\) 17.6988 + 4.19469i 0.607779 + 0.144046i
\(849\) 0 0
\(850\) −1.52131 + 1.00058i −0.0521804 + 0.0343196i
\(851\) −58.5833 + 38.5308i −2.00821 + 1.32082i
\(852\) 0 0
\(853\) −3.34652 0.793140i −0.114583 0.0271566i 0.172924 0.984935i \(-0.444678\pi\)
−0.287507 + 0.957778i \(0.592827\pi\)
\(854\) 0.776573 0.651622i 0.0265738 0.0222980i
\(855\) 0 0
\(856\) 11.4381 + 9.59772i 0.390947 + 0.328043i
\(857\) 8.75386 + 11.7585i 0.299026 + 0.401662i 0.926088 0.377308i \(-0.123150\pi\)
−0.627062 + 0.778969i \(0.715743\pi\)
\(858\) 0 0
\(859\) 9.27804 2.19894i 0.316563 0.0750268i −0.0692629 0.997598i \(-0.522065\pi\)
0.385826 + 0.922572i \(0.373917\pi\)
\(860\) 6.50643 8.73966i 0.221868 0.298020i
\(861\) 0 0
\(862\) 16.6441 8.35900i 0.566902 0.284709i
\(863\) −8.00876 13.8716i −0.272621 0.472194i 0.696911 0.717158i \(-0.254557\pi\)
−0.969532 + 0.244964i \(0.921224\pi\)
\(864\) 0 0
\(865\) −27.3732 + 47.4117i −0.930716 + 1.61205i
\(866\) −0.426486 + 7.32248i −0.0144926 + 0.248828i
\(867\) 0 0
\(868\) 3.52519 + 0.412036i 0.119653 + 0.0139854i
\(869\) 0.733672 2.45064i 0.0248881 0.0831321i
\(870\) 0 0
\(871\) 21.5899 50.0510i 0.731546 1.69591i
\(872\) −22.3086 + 8.11966i −0.755464 + 0.274967i
\(873\) 0 0
\(874\) −15.9184 5.79383i −0.538448 0.195979i
\(875\) 9.78136 10.3676i 0.330670 0.350490i
\(876\) 0 0
\(877\) −29.5974 14.8644i −0.999432 0.501934i −0.127646 0.991820i \(-0.540742\pi\)
−0.871786 + 0.489886i \(0.837038\pi\)
\(878\) 1.21708 + 20.8965i 0.0410745 + 0.705222i
\(879\) 0 0
\(880\) 6.20455 + 20.7246i 0.209155 + 0.698628i
\(881\) 2.00755 + 11.3854i 0.0676360 + 0.383583i 0.999770 + 0.0214681i \(0.00683402\pi\)
−0.932134 + 0.362115i \(0.882055\pi\)
\(882\) 0 0
\(883\) −7.24692 + 41.0993i −0.243878 + 1.38310i 0.579206 + 0.815182i \(0.303363\pi\)
−0.823084 + 0.567920i \(0.807748\pi\)
\(884\) 6.21241 0.726127i 0.208946 0.0244223i
\(885\) 0 0
\(886\) −13.3851 14.1874i −0.449683 0.476636i
\(887\) 9.54630 + 22.1308i 0.320533 + 0.743080i 0.999956 + 0.00933326i \(0.00297091\pi\)
−0.679423 + 0.733747i \(0.737770\pi\)
\(888\) 0 0
\(889\) −28.0867 18.4729i −0.941997 0.619561i
\(890\) 21.6198 0.724697
\(891\) 0 0
\(892\) 7.80468 0.261320
\(893\) 12.8464 + 8.44922i 0.429889 + 0.282743i
\(894\) 0 0
\(895\) −11.8417 27.4521i −0.395824 0.917622i
\(896\) −24.7785 26.2637i −0.827791 0.877407i
\(897\) 0 0
\(898\) −9.89998 + 1.15714i −0.330367 + 0.0386143i
\(899\) 0.211221 1.19789i 0.00704460 0.0399519i
\(900\) 0 0
\(901\) −1.36020 7.71410i −0.0453149 0.256994i
\(902\) −3.71700 12.4156i −0.123762 0.413396i
\(903\) 0 0
\(904\) 0.706934 + 12.1376i 0.0235123 + 0.403690i
\(905\) −2.12682 1.06813i −0.0706980 0.0355059i
\(906\) 0 0
\(907\) −15.8463 + 16.7961i −0.526169 + 0.557707i −0.934883 0.354956i \(-0.884496\pi\)
0.408714 + 0.912663i \(0.365977\pi\)
\(908\) 22.2614 + 8.10250i 0.738771 + 0.268891i
\(909\) 0 0
\(910\) −19.3305 + 7.03572i −0.640799 + 0.233232i
\(911\) −9.06991 + 21.0264i −0.300500 + 0.696637i −0.999835 0.0181571i \(-0.994220\pi\)
0.699335 + 0.714794i \(0.253479\pi\)
\(912\) 0 0
\(913\) −3.58249 + 11.9663i −0.118563 + 0.396028i
\(914\) −4.70685 0.550152i −0.155689 0.0181974i
\(915\) 0 0
\(916\) −0.505863 + 8.68533i −0.0167142 + 0.286971i
\(917\) 11.2088 19.4143i 0.370148 0.641116i
\(918\) 0 0
\(919\) −9.84136 17.0457i −0.324636 0.562287i 0.656802 0.754063i \(-0.271909\pi\)
−0.981439 + 0.191776i \(0.938575\pi\)
\(920\) −33.3264 + 16.7371i −1.09874 + 0.551807i
\(921\) 0 0
\(922\) −6.89423 + 9.26056i −0.227049 + 0.304980i
\(923\) 51.7941 12.2754i 1.70482 0.404051i
\(924\) 0 0
\(925\) −23.3555 31.3719i −0.767926 1.03150i
\(926\) 1.12588 + 0.944728i 0.0369988 + 0.0310457i
\(927\) 0 0
\(928\) −7.45472 + 6.25525i −0.244713 + 0.205339i
\(929\) −28.1380 6.66884i −0.923179 0.218797i −0.258573 0.965992i \(-0.583252\pi\)
−0.664606 + 0.747194i \(0.731401\pi\)
\(930\) 0 0
\(931\) −11.3310 + 7.45253i −0.371359 + 0.244247i
\(932\) 6.24286 4.10599i 0.204492 0.134496i
\(933\) 0 0
\(934\) 6.76029 + 1.60222i 0.221203 + 0.0524262i
\(935\) 7.13679 5.98848i 0.233398 0.195844i
\(936\) 0 0
\(937\) 14.9990 + 12.5856i 0.489995 + 0.411155i 0.854025 0.520233i \(-0.174155\pi\)
−0.364029 + 0.931388i \(0.618599\pi\)
\(938\) 14.5008 + 19.4779i 0.473468 + 0.635977i
\(939\) 0 0
\(940\) 15.0261 3.56124i 0.490096 0.116155i
\(941\) −6.02898 + 8.09833i −0.196539 + 0.263998i −0.889457 0.457018i \(-0.848917\pi\)
0.692918 + 0.721016i \(0.256325\pi\)
\(942\) 0 0
\(943\) −36.5752 + 18.3688i −1.19105 + 0.598169i
\(944\) 5.46032 + 9.45755i 0.177718 + 0.307817i
\(945\) 0 0
\(946\) 2.17839 3.77309i 0.0708257 0.122674i
\(947\) −1.22145 + 20.9715i −0.0396918 + 0.681483i 0.918511 + 0.395394i \(0.129392\pi\)
−0.958203 + 0.286088i \(0.907645\pi\)
\(948\) 0 0
\(949\) −26.7197 3.12308i −0.867357 0.101379i
\(950\) 2.70997 9.05193i 0.0879231 0.293683i
\(951\) 0 0
\(952\) −2.41918 + 5.60829i −0.0784061 + 0.181766i
\(953\) 6.34571 2.30965i 0.205558 0.0748169i −0.237189 0.971463i \(-0.576226\pi\)
0.442747 + 0.896647i \(0.354004\pi\)
\(954\) 0 0
\(955\) 2.08753 + 0.759798i 0.0675508 + 0.0245865i
\(956\) −33.4610 + 35.4666i −1.08221 + 1.14707i
\(957\) 0 0
\(958\) 13.9119 + 6.98682i 0.449473 + 0.225734i
\(959\) 1.57035 + 26.9619i 0.0507092 + 0.870644i
\(960\) 0 0
\(961\) 8.75989 + 29.2601i 0.282577 + 0.943873i
\(962\) −4.47973 25.4058i −0.144432 0.819117i
\(963\) 0 0
\(964\) −7.27912 + 41.2819i −0.234445 + 1.32960i
\(965\) −26.9798 + 3.15349i −0.868511 + 0.101514i
\(966\) 0 0
\(967\) −8.09307 8.57815i −0.260256 0.275855i 0.584049 0.811718i \(-0.301468\pi\)
−0.844305 + 0.535864i \(0.819986\pi\)
\(968\) 0.644624 + 1.49441i 0.0207190 + 0.0480320i
\(969\) 0 0
\(970\) 17.2202 + 11.3259i 0.552908 + 0.363653i
\(971\) 24.4687 0.785239 0.392620 0.919701i \(-0.371569\pi\)
0.392620 + 0.919701i \(0.371569\pi\)
\(972\) 0 0
\(973\) −18.4632 −0.591905
\(974\) −2.85684 1.87897i −0.0915391 0.0602062i
\(975\) 0 0
\(976\) −0.490623 1.13739i −0.0157045 0.0364071i
\(977\) −26.7064 28.3071i −0.854413 0.905625i 0.142032 0.989862i \(-0.454636\pi\)
−0.996446 + 0.0842367i \(0.973155\pi\)
\(978\) 0 0
\(979\) −44.7163 + 5.22659i −1.42914 + 0.167042i
\(980\) −2.36521 + 13.4138i −0.0755538 + 0.428487i
\(981\) 0 0
\(982\) 0.0480294 + 0.272388i 0.00153268 + 0.00869226i
\(983\) −5.36807 17.9306i −0.171215 0.571897i −0.999925 0.0122197i \(-0.996110\pi\)
0.828711 0.559677i \(-0.189075\pi\)
\(984\) 0 0
\(985\) −0.189067 3.24615i −0.00602417 0.103431i
\(986\) 0.853368 + 0.428578i 0.0271768 + 0.0136487i
\(987\) 0 0
\(988\) −22.2734 + 23.6085i −0.708613 + 0.751085i
\(989\) −12.9292 4.70584i −0.411125 0.149637i
\(990\) 0 0
\(991\) −2.15353 + 0.783819i −0.0684090 + 0.0248988i −0.375998 0.926620i \(-0.622700\pi\)
0.307589 + 0.951519i \(0.400478\pi\)
\(992\) −1.44752 + 3.35572i −0.0459587 + 0.106544i
\(993\) 0 0
\(994\) −6.80089 + 22.7165i −0.215711 + 0.720525i
\(995\) −22.1516 2.58915i −0.702252 0.0820815i
\(996\) 0 0
\(997\) −1.81875 + 31.2268i −0.0576005 + 0.988963i 0.838441 + 0.544992i \(0.183467\pi\)
−0.896042 + 0.443970i \(0.853570\pi\)
\(998\) 1.55659 2.69609i 0.0492729 0.0853432i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 729.2.g.c.703.4 144
3.2 odd 2 729.2.g.b.703.5 144
9.2 odd 6 729.2.g.a.217.5 144
9.4 even 3 81.2.g.a.25.5 yes 144
9.5 odd 6 243.2.g.a.73.4 144
9.7 even 3 729.2.g.d.217.4 144
81.13 even 27 729.2.g.d.514.4 144
81.14 odd 54 729.2.g.b.28.5 144
81.38 odd 54 6561.2.a.d.1.41 72
81.40 even 27 81.2.g.a.13.5 144
81.41 odd 54 243.2.g.a.10.4 144
81.43 even 27 6561.2.a.c.1.32 72
81.67 even 27 inner 729.2.g.c.28.4 144
81.68 odd 54 729.2.g.a.514.5 144
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
81.2.g.a.13.5 144 81.40 even 27
81.2.g.a.25.5 yes 144 9.4 even 3
243.2.g.a.10.4 144 81.41 odd 54
243.2.g.a.73.4 144 9.5 odd 6
729.2.g.a.217.5 144 9.2 odd 6
729.2.g.a.514.5 144 81.68 odd 54
729.2.g.b.28.5 144 81.14 odd 54
729.2.g.b.703.5 144 3.2 odd 2
729.2.g.c.28.4 144 81.67 even 27 inner
729.2.g.c.703.4 144 1.1 even 1 trivial
729.2.g.d.217.4 144 9.7 even 3
729.2.g.d.514.4 144 81.13 even 27
6561.2.a.c.1.32 72 81.43 even 27
6561.2.a.d.1.41 72 81.38 odd 54