Properties

Label 729.2.g.c.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.c.703.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.652974 - 0.429468i) q^{2} +(-0.550227 + 1.27557i) q^{4} +(1.01614 - 1.07704i) q^{5} +(3.77556 + 0.441300i) q^{7} +(0.459961 + 2.60857i) q^{8} +O(q^{10})\) \(q+(0.652974 - 0.429468i) q^{2} +(-0.550227 + 1.27557i) q^{4} +(1.01614 - 1.07704i) q^{5} +(3.77556 + 0.441300i) q^{7} +(0.459961 + 2.60857i) q^{8} +(0.200956 - 1.13968i) q^{10} +(-1.44963 + 4.84210i) q^{11} +(0.261201 - 4.48466i) q^{13} +(2.65487 - 1.33332i) q^{14} +(-0.485993 - 0.515122i) q^{16} +(-4.30582 + 1.56719i) q^{17} +(4.19524 + 1.52694i) q^{19} +(0.814736 + 1.88877i) q^{20} +(1.13295 + 3.78433i) q^{22} +(3.43157 - 0.401093i) q^{23} +(0.163239 + 2.80270i) q^{25} +(-1.75546 - 3.04054i) q^{26} +(-2.64032 + 4.57318i) q^{28} +(0.583488 + 0.293038i) q^{29} +(0.393020 + 0.527918i) q^{31} +(-5.69339 - 1.34936i) q^{32} +(-2.13853 + 2.87254i) q^{34} +(4.31178 - 3.61801i) q^{35} +(0.766165 + 0.642889i) q^{37} +(3.39516 - 0.804667i) q^{38} +(3.27692 + 2.15526i) q^{40} +(0.570482 + 0.375212i) q^{41} +(8.16684 - 1.93558i) q^{43} +(-5.37881 - 4.51336i) q^{44} +(2.06847 - 1.73565i) q^{46} +(4.73832 - 6.36466i) q^{47} +(7.24880 + 1.71800i) q^{49} +(1.31026 + 1.75998i) q^{50} +(5.57677 + 2.80076i) q^{52} +(-2.07469 + 3.59347i) q^{53} +(3.74212 + 6.48154i) q^{55} +(0.585450 + 10.0518i) q^{56} +(0.506853 - 0.0592426i) q^{58} +(-1.51145 - 5.04858i) q^{59} +(-2.68977 - 6.23558i) q^{61} +(0.483356 + 0.175927i) q^{62} +(-2.96617 + 1.07960i) q^{64} +(-4.56474 - 4.83835i) q^{65} +(4.73732 - 2.37917i) q^{67} +(0.370118 - 6.35468i) q^{68} +(1.26166 - 4.21424i) q^{70} +(-1.06500 + 6.03991i) q^{71} +(-0.764322 - 4.33469i) q^{73} +(0.776385 + 0.0907464i) q^{74} +(-4.25606 + 4.51116i) q^{76} +(-7.60998 + 17.6419i) q^{77} +(-9.39300 + 6.17788i) q^{79} -1.04864 q^{80} +0.533651 q^{82} +(-1.35486 + 0.891108i) q^{83} +(-2.68737 + 6.23002i) q^{85} +(4.50147 - 4.77127i) q^{86} +(-13.2977 - 1.55428i) q^{88} +(-0.181087 - 1.02699i) q^{89} +(2.96526 - 16.8168i) q^{91} +(-1.37652 + 4.59790i) q^{92} +(0.360580 - 6.19091i) q^{94} +(5.90752 - 2.96687i) q^{95} +(-3.42307 - 3.62824i) q^{97} +(5.47110 - 1.99132i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.652974 0.429468i 0.461722 0.303679i −0.297253 0.954799i \(-0.596071\pi\)
0.758975 + 0.651119i \(0.225700\pi\)
\(3\) 0 0
\(4\) −0.550227 + 1.27557i −0.275114 + 0.637785i
\(5\) 1.01614 1.07704i 0.454430 0.481668i −0.459132 0.888368i \(-0.651839\pi\)
0.913561 + 0.406701i \(0.133321\pi\)
\(6\) 0 0
\(7\) 3.77556 + 0.441300i 1.42703 + 0.166796i 0.794275 0.607558i \(-0.207851\pi\)
0.632753 + 0.774354i \(0.281925\pi\)
\(8\) 0.459961 + 2.60857i 0.162621 + 0.922268i
\(9\) 0 0
\(10\) 0.200956 1.13968i 0.0635478 0.360398i
\(11\) −1.44963 + 4.84210i −0.437079 + 1.45995i 0.401849 + 0.915706i \(0.368368\pi\)
−0.838929 + 0.544241i \(0.816818\pi\)
\(12\) 0 0
\(13\) 0.261201 4.48466i 0.0724443 1.24382i −0.744705 0.667394i \(-0.767410\pi\)
0.817149 0.576426i \(-0.195553\pi\)
\(14\) 2.65487 1.33332i 0.709543 0.356346i
\(15\) 0 0
\(16\) −0.485993 0.515122i −0.121498 0.128781i
\(17\) −4.30582 + 1.56719i −1.04431 + 0.380099i −0.806514 0.591215i \(-0.798648\pi\)
−0.237800 + 0.971314i \(0.576426\pi\)
\(18\) 0 0
\(19\) 4.19524 + 1.52694i 0.962455 + 0.350305i 0.774995 0.631967i \(-0.217752\pi\)
0.187460 + 0.982272i \(0.439975\pi\)
\(20\) 0.814736 + 1.88877i 0.182181 + 0.422342i
\(21\) 0 0
\(22\) 1.13295 + 3.78433i 0.241547 + 0.806822i
\(23\) 3.43157 0.401093i 0.715532 0.0836337i 0.249466 0.968384i \(-0.419745\pi\)
0.466066 + 0.884750i \(0.345671\pi\)
\(24\) 0 0
\(25\) 0.163239 + 2.80270i 0.0326477 + 0.560540i
\(26\) −1.75546 3.04054i −0.344273 0.596299i
\(27\) 0 0
\(28\) −2.64032 + 4.57318i −0.498974 + 0.864249i
\(29\) 0.583488 + 0.293038i 0.108351 + 0.0544159i 0.502149 0.864781i \(-0.332543\pi\)
−0.393798 + 0.919197i \(0.628839\pi\)
\(30\) 0 0
\(31\) 0.393020 + 0.527918i 0.0705886 + 0.0948169i 0.836015 0.548706i \(-0.184879\pi\)
−0.765427 + 0.643523i \(0.777472\pi\)
\(32\) −5.69339 1.34936i −1.00646 0.238535i
\(33\) 0 0
\(34\) −2.13853 + 2.87254i −0.366755 + 0.492637i
\(35\) 4.31178 3.61801i 0.728824 0.611556i
\(36\) 0 0
\(37\) 0.766165 + 0.642889i 0.125957 + 0.105690i 0.703590 0.710606i \(-0.251579\pi\)
−0.577633 + 0.816296i \(0.696024\pi\)
\(38\) 3.39516 0.804667i 0.550767 0.130534i
\(39\) 0 0
\(40\) 3.27692 + 2.15526i 0.518126 + 0.340777i
\(41\) 0.570482 + 0.375212i 0.0890943 + 0.0585983i 0.593274 0.805000i \(-0.297835\pi\)
−0.504180 + 0.863598i \(0.668205\pi\)
\(42\) 0 0
\(43\) 8.16684 1.93558i 1.24543 0.295173i 0.445510 0.895277i \(-0.353022\pi\)
0.799922 + 0.600104i \(0.204874\pi\)
\(44\) −5.37881 4.51336i −0.810886 0.680414i
\(45\) 0 0
\(46\) 2.06847 1.73565i 0.304979 0.255908i
\(47\) 4.73832 6.36466i 0.691155 0.928382i −0.308585 0.951197i \(-0.599855\pi\)
0.999740 + 0.0228150i \(0.00726288\pi\)
\(48\) 0 0
\(49\) 7.24880 + 1.71800i 1.03554 + 0.245428i
\(50\) 1.31026 + 1.75998i 0.185299 + 0.248899i
\(51\) 0 0
\(52\) 5.57677 + 2.80076i 0.773359 + 0.388396i
\(53\) −2.07469 + 3.59347i −0.284981 + 0.493601i −0.972605 0.232466i \(-0.925321\pi\)
0.687624 + 0.726067i \(0.258654\pi\)
\(54\) 0 0
\(55\) 3.74212 + 6.48154i 0.504587 + 0.873971i
\(56\) 0.585450 + 10.0518i 0.0782340 + 1.34323i
\(57\) 0 0
\(58\) 0.506853 0.0592426i 0.0665530 0.00777893i
\(59\) −1.51145 5.04858i −0.196773 0.657269i −0.998244 0.0592349i \(-0.981134\pi\)
0.801471 0.598034i \(-0.204051\pi\)
\(60\) 0 0
\(61\) −2.68977 6.23558i −0.344389 0.798384i −0.999096 0.0425013i \(-0.986467\pi\)
0.654707 0.755883i \(-0.272792\pi\)
\(62\) 0.483356 + 0.175927i 0.0613862 + 0.0223428i
\(63\) 0 0
\(64\) −2.96617 + 1.07960i −0.370771 + 0.134950i
\(65\) −4.56474 4.83835i −0.566187 0.600123i
\(66\) 0 0
\(67\) 4.73732 2.37917i 0.578756 0.290662i −0.135239 0.990813i \(-0.543180\pi\)
0.713995 + 0.700151i \(0.246884\pi\)
\(68\) 0.370118 6.35468i 0.0448834 0.770618i
\(69\) 0 0
\(70\) 1.26166 4.21424i 0.150797 0.503698i
\(71\) −1.06500 + 6.03991i −0.126392 + 0.716805i 0.854079 + 0.520143i \(0.174121\pi\)
−0.980471 + 0.196662i \(0.936990\pi\)
\(72\) 0 0
\(73\) −0.764322 4.33469i −0.0894571 0.507337i −0.996306 0.0858796i \(-0.972630\pi\)
0.906848 0.421457i \(-0.138481\pi\)
\(74\) 0.776385 + 0.0907464i 0.0902530 + 0.0105491i
\(75\) 0 0
\(76\) −4.25606 + 4.51116i −0.488204 + 0.517466i
\(77\) −7.60998 + 17.6419i −0.867237 + 2.01048i
\(78\) 0 0
\(79\) −9.39300 + 6.17788i −1.05680 + 0.695065i −0.954052 0.299643i \(-0.903133\pi\)
−0.102744 + 0.994708i \(0.532762\pi\)
\(80\) −1.04864 −0.117242
\(81\) 0 0
\(82\) 0.533651 0.0589319
\(83\) −1.35486 + 0.891108i −0.148716 + 0.0978119i −0.621686 0.783266i \(-0.713552\pi\)
0.472971 + 0.881078i \(0.343182\pi\)
\(84\) 0 0
\(85\) −2.68737 + 6.23002i −0.291486 + 0.675741i
\(86\) 4.50147 4.77127i 0.485406 0.514500i
\(87\) 0 0
\(88\) −13.2977 1.55428i −1.41754 0.165687i
\(89\) −0.181087 1.02699i −0.0191952 0.108861i 0.973705 0.227813i \(-0.0731576\pi\)
−0.992900 + 0.118952i \(0.962046\pi\)
\(90\) 0 0
\(91\) 2.96526 16.8168i 0.310844 1.76288i
\(92\) −1.37652 + 4.59790i −0.143512 + 0.479364i
\(93\) 0 0
\(94\) 0.360580 6.19091i 0.0371909 0.638544i
\(95\) 5.90752 2.96687i 0.606099 0.304394i
\(96\) 0 0
\(97\) −3.42307 3.62824i −0.347560 0.368392i 0.529885 0.848070i \(-0.322235\pi\)
−0.877445 + 0.479677i \(0.840754\pi\)
\(98\) 5.47110 1.99132i 0.552664 0.201153i
\(99\) 0 0
\(100\) −3.66486 1.33390i −0.366486 0.133390i
\(101\) −3.79067 8.78777i −0.377186 0.874416i −0.996040 0.0889095i \(-0.971662\pi\)
0.618854 0.785506i \(-0.287597\pi\)
\(102\) 0 0
\(103\) −0.933584 3.11839i −0.0919888 0.307264i 0.899596 0.436723i \(-0.143861\pi\)
−0.991585 + 0.129459i \(0.958676\pi\)
\(104\) 11.8187 1.38140i 1.15892 0.135458i
\(105\) 0 0
\(106\) 0.188560 + 3.23746i 0.0183146 + 0.314450i
\(107\) −8.40680 14.5610i −0.812716 1.40767i −0.910956 0.412503i \(-0.864655\pi\)
0.0982402 0.995163i \(-0.468679\pi\)
\(108\) 0 0
\(109\) −3.81772 + 6.61249i −0.365671 + 0.633361i −0.988884 0.148691i \(-0.952494\pi\)
0.623212 + 0.782053i \(0.285827\pi\)
\(110\) 5.22712 + 2.62516i 0.498386 + 0.250299i
\(111\) 0 0
\(112\) −1.60757 2.15934i −0.151901 0.204039i
\(113\) −9.74930 2.31063i −0.917137 0.217365i −0.255168 0.966897i \(-0.582131\pi\)
−0.661969 + 0.749531i \(0.730279\pi\)
\(114\) 0 0
\(115\) 3.05495 4.10351i 0.284875 0.382654i
\(116\) −0.694842 + 0.583042i −0.0645144 + 0.0541340i
\(117\) 0 0
\(118\) −3.15514 2.64747i −0.290454 0.243720i
\(119\) −16.9485 + 4.01686i −1.55366 + 0.368225i
\(120\) 0 0
\(121\) −12.1541 7.99389i −1.10492 0.726717i
\(122\) −4.43432 2.91650i −0.401465 0.264048i
\(123\) 0 0
\(124\) −0.889647 + 0.210850i −0.0798927 + 0.0189349i
\(125\) 8.85601 + 7.43107i 0.792105 + 0.664655i
\(126\) 0 0
\(127\) 2.97665 2.49770i 0.264135 0.221635i −0.501096 0.865392i \(-0.667070\pi\)
0.765230 + 0.643757i \(0.222625\pi\)
\(128\) 5.51490 7.40779i 0.487453 0.654763i
\(129\) 0 0
\(130\) −5.05857 1.19890i −0.443666 0.105151i
\(131\) −9.94222 13.3547i −0.868656 1.16681i −0.984820 0.173577i \(-0.944467\pi\)
0.116165 0.993230i \(-0.462940\pi\)
\(132\) 0 0
\(133\) 15.1656 + 7.61643i 1.31502 + 0.660428i
\(134\) 2.07157 3.58807i 0.178956 0.309962i
\(135\) 0 0
\(136\) −6.06863 10.5112i −0.520380 0.901325i
\(137\) −0.539345 9.26019i −0.0460793 0.791152i −0.939631 0.342190i \(-0.888831\pi\)
0.893551 0.448961i \(-0.148206\pi\)
\(138\) 0 0
\(139\) −15.8135 + 1.84833i −1.34128 + 0.156774i −0.756275 0.654253i \(-0.772983\pi\)
−0.585009 + 0.811027i \(0.698909\pi\)
\(140\) 2.24257 + 7.49071i 0.189532 + 0.633080i
\(141\) 0 0
\(142\) 1.89853 + 4.40128i 0.159321 + 0.369348i
\(143\) 21.3365 + 7.76585i 1.78425 + 0.649413i
\(144\) 0 0
\(145\) 0.908517 0.330673i 0.0754483 0.0274609i
\(146\) −2.36069 2.50218i −0.195372 0.207082i
\(147\) 0 0
\(148\) −1.24161 + 0.623562i −0.102060 + 0.0512565i
\(149\) −1.35720 + 23.3023i −0.111186 + 1.90900i 0.236899 + 0.971534i \(0.423869\pi\)
−0.348085 + 0.937463i \(0.613168\pi\)
\(150\) 0 0
\(151\) 0.668852 2.23412i 0.0544304 0.181810i −0.926452 0.376414i \(-0.877157\pi\)
0.980882 + 0.194604i \(0.0623422\pi\)
\(152\) −2.05349 + 11.6459i −0.166560 + 0.944608i
\(153\) 0 0
\(154\) 2.60751 + 14.7879i 0.210119 + 1.19165i
\(155\) 0.967952 + 0.113137i 0.0777478 + 0.00908741i
\(156\) 0 0
\(157\) 13.5075 14.3171i 1.07801 1.14263i 0.0888142 0.996048i \(-0.471692\pi\)
0.989199 0.146579i \(-0.0468263\pi\)
\(158\) −3.48019 + 8.06798i −0.276869 + 0.641854i
\(159\) 0 0
\(160\) −7.23857 + 4.76088i −0.572259 + 0.376381i
\(161\) 13.1331 1.03503
\(162\) 0 0
\(163\) −17.6622 −1.38341 −0.691707 0.722179i \(-0.743141\pi\)
−0.691707 + 0.722179i \(0.743141\pi\)
\(164\) −0.792504 + 0.521238i −0.0618842 + 0.0407018i
\(165\) 0 0
\(166\) −0.501989 + 1.16374i −0.0389619 + 0.0903238i
\(167\) −2.32646 + 2.46590i −0.180027 + 0.190817i −0.811102 0.584904i \(-0.801132\pi\)
0.631076 + 0.775721i \(0.282614\pi\)
\(168\) 0 0
\(169\) −7.13182 0.833590i −0.548601 0.0641223i
\(170\) 0.920811 + 5.22218i 0.0706230 + 0.400523i
\(171\) 0 0
\(172\) −2.02465 + 11.4824i −0.154378 + 0.875524i
\(173\) 5.35719 17.8943i 0.407300 1.36048i −0.470901 0.882186i \(-0.656071\pi\)
0.878201 0.478291i \(-0.158744\pi\)
\(174\) 0 0
\(175\) −0.620513 + 10.6538i −0.0469064 + 0.805351i
\(176\) 3.19878 1.60649i 0.241117 0.121094i
\(177\) 0 0
\(178\) −0.559306 0.592829i −0.0419217 0.0444344i
\(179\) −11.1678 + 4.06476i −0.834723 + 0.303814i −0.723796 0.690014i \(-0.757604\pi\)
−0.110927 + 0.993829i \(0.535382\pi\)
\(180\) 0 0
\(181\) 14.8329 + 5.39873i 1.10252 + 0.401284i 0.828244 0.560367i \(-0.189340\pi\)
0.274275 + 0.961651i \(0.411562\pi\)
\(182\) −5.28604 12.2544i −0.391828 0.908358i
\(183\) 0 0
\(184\) 2.62467 + 8.76699i 0.193493 + 0.646311i
\(185\) 1.47095 0.171929i 0.108146 0.0126405i
\(186\) 0 0
\(187\) −1.34665 23.1210i −0.0984765 1.69078i
\(188\) 5.51142 + 9.54607i 0.401962 + 0.696219i
\(189\) 0 0
\(190\) 2.58328 4.47437i 0.187411 0.324605i
\(191\) 5.15323 + 2.58805i 0.372875 + 0.187265i 0.625361 0.780336i \(-0.284952\pi\)
−0.252486 + 0.967601i \(0.581248\pi\)
\(192\) 0 0
\(193\) 0.104955 + 0.140979i 0.00755483 + 0.0101479i 0.805885 0.592073i \(-0.201690\pi\)
−0.798330 + 0.602221i \(0.794283\pi\)
\(194\) −3.79339 0.899050i −0.272349 0.0645480i
\(195\) 0 0
\(196\) −6.17991 + 8.30106i −0.441422 + 0.592933i
\(197\) 8.59155 7.20917i 0.612123 0.513632i −0.283194 0.959063i \(-0.591394\pi\)
0.895316 + 0.445431i \(0.146950\pi\)
\(198\) 0 0
\(199\) −15.6873 13.1632i −1.11204 0.933114i −0.113866 0.993496i \(-0.536324\pi\)
−0.998175 + 0.0603824i \(0.980768\pi\)
\(200\) −7.23595 + 1.71495i −0.511659 + 0.121265i
\(201\) 0 0
\(202\) −6.24927 4.11021i −0.439697 0.289193i
\(203\) 2.07367 + 1.36388i 0.145543 + 0.0957254i
\(204\) 0 0
\(205\) 0.983806 0.233166i 0.0687120 0.0162850i
\(206\) −1.94885 1.63528i −0.135783 0.113935i
\(207\) 0 0
\(208\) −2.43709 + 2.04496i −0.168982 + 0.141792i
\(209\) −13.4752 + 18.1003i −0.932096 + 1.25202i
\(210\) 0 0
\(211\) 1.15927 + 0.274753i 0.0798076 + 0.0189147i 0.270326 0.962769i \(-0.412869\pi\)
−0.190518 + 0.981684i \(0.561017\pi\)
\(212\) −3.44217 4.62364i −0.236409 0.317553i
\(213\) 0 0
\(214\) −11.7429 5.89751i −0.802728 0.403145i
\(215\) 6.21393 10.7628i 0.423786 0.734019i
\(216\) 0 0
\(217\) 1.25090 + 2.16663i 0.0849168 + 0.147080i
\(218\) 0.346977 + 5.95737i 0.0235003 + 0.403484i
\(219\) 0 0
\(220\) −10.3267 + 1.20702i −0.696224 + 0.0813769i
\(221\) 5.90362 + 19.7195i 0.397120 + 1.32647i
\(222\) 0 0
\(223\) −5.90154 13.6813i −0.395197 0.916169i −0.993387 0.114815i \(-0.963373\pi\)
0.598190 0.801354i \(-0.295887\pi\)
\(224\) −20.9003 7.60707i −1.39646 0.508269i
\(225\) 0 0
\(226\) −7.35838 + 2.67823i −0.489472 + 0.178153i
\(227\) 16.8807 + 17.8925i 1.12041 + 1.18757i 0.980317 + 0.197430i \(0.0632594\pi\)
0.140095 + 0.990138i \(0.455259\pi\)
\(228\) 0 0
\(229\) 1.36456 0.685307i 0.0901726 0.0452864i −0.403141 0.915138i \(-0.632082\pi\)
0.493314 + 0.869851i \(0.335785\pi\)
\(230\) 0.232477 3.99148i 0.0153291 0.263191i
\(231\) 0 0
\(232\) −0.496029 + 1.65685i −0.0325659 + 0.108778i
\(233\) 2.44148 13.8463i 0.159946 0.907101i −0.794177 0.607687i \(-0.792098\pi\)
0.954123 0.299414i \(-0.0967912\pi\)
\(234\) 0 0
\(235\) −2.04023 11.5707i −0.133090 0.754791i
\(236\) 7.27145 + 0.849911i 0.473331 + 0.0553245i
\(237\) 0 0
\(238\) −9.34179 + 9.90172i −0.605539 + 0.641833i
\(239\) −9.07711 + 21.0431i −0.587149 + 1.36116i 0.322809 + 0.946464i \(0.395373\pi\)
−0.909958 + 0.414701i \(0.863886\pi\)
\(240\) 0 0
\(241\) 5.90585 3.88434i 0.380429 0.250212i −0.344864 0.938653i \(-0.612075\pi\)
0.725293 + 0.688441i \(0.241704\pi\)
\(242\) −11.3694 −0.730855
\(243\) 0 0
\(244\) 9.43390 0.603943
\(245\) 9.21612 6.06153i 0.588796 0.387257i
\(246\) 0 0
\(247\) 7.94362 18.4154i 0.505441 1.17174i
\(248\) −1.19634 + 1.26804i −0.0759674 + 0.0805207i
\(249\) 0 0
\(250\) 8.97414 + 1.04893i 0.567575 + 0.0663400i
\(251\) 0.0115419 + 0.0654574i 0.000728518 + 0.00413163i 0.985170 0.171582i \(-0.0548878\pi\)
−0.984441 + 0.175714i \(0.943777\pi\)
\(252\) 0 0
\(253\) −3.03237 + 17.1974i −0.190644 + 1.08119i
\(254\) 0.870990 2.90931i 0.0546508 0.182546i
\(255\) 0 0
\(256\) 0.786748 13.5079i 0.0491718 0.844246i
\(257\) 17.2862 8.68143i 1.07828 0.541533i 0.181221 0.983442i \(-0.441995\pi\)
0.897060 + 0.441909i \(0.145699\pi\)
\(258\) 0 0
\(259\) 2.60900 + 2.76537i 0.162115 + 0.171832i
\(260\) 8.68330 3.16046i 0.538515 0.196003i
\(261\) 0 0
\(262\) −12.2274 4.45042i −0.755413 0.274948i
\(263\) 5.96501 + 13.8284i 0.367818 + 0.852698i 0.997142 + 0.0755547i \(0.0240727\pi\)
−0.629324 + 0.777143i \(0.716668\pi\)
\(264\) 0 0
\(265\) 1.76215 + 5.88599i 0.108248 + 0.361573i
\(266\) 13.1737 1.53979i 0.807732 0.0944104i
\(267\) 0 0
\(268\) 0.428198 + 7.35188i 0.0261564 + 0.449087i
\(269\) 5.86823 + 10.1641i 0.357792 + 0.619715i 0.987592 0.157043i \(-0.0501962\pi\)
−0.629799 + 0.776758i \(0.716863\pi\)
\(270\) 0 0
\(271\) 1.44013 2.49438i 0.0874817 0.151523i −0.818964 0.573844i \(-0.805451\pi\)
0.906446 + 0.422322i \(0.138785\pi\)
\(272\) 2.89989 + 1.45638i 0.175832 + 0.0883060i
\(273\) 0 0
\(274\) −4.32913 5.81503i −0.261532 0.351299i
\(275\) −13.8076 3.27246i −0.832628 0.197337i
\(276\) 0 0
\(277\) −1.37408 + 1.84571i −0.0825603 + 0.110898i −0.841485 0.540281i \(-0.818318\pi\)
0.758924 + 0.651179i \(0.225725\pi\)
\(278\) −9.53200 + 7.99830i −0.571692 + 0.479706i
\(279\) 0 0
\(280\) 11.4211 + 9.58343i 0.682540 + 0.572719i
\(281\) 6.17447 1.46338i 0.368338 0.0872977i −0.0422786 0.999106i \(-0.513462\pi\)
0.410616 + 0.911808i \(0.365314\pi\)
\(282\) 0 0
\(283\) 12.2665 + 8.06777i 0.729165 + 0.479579i 0.859012 0.511955i \(-0.171078\pi\)
−0.129848 + 0.991534i \(0.541449\pi\)
\(284\) −7.11834 4.68180i −0.422396 0.277814i
\(285\) 0 0
\(286\) 17.2674 4.09244i 1.02104 0.241991i
\(287\) 1.98831 + 1.66839i 0.117366 + 0.0984819i
\(288\) 0 0
\(289\) 3.06122 2.56867i 0.180072 0.151098i
\(290\) 0.451224 0.606100i 0.0264968 0.0355914i
\(291\) 0 0
\(292\) 5.94975 + 1.41012i 0.348183 + 0.0825208i
\(293\) −15.1411 20.3380i −0.884553 1.18816i −0.981229 0.192845i \(-0.938229\pi\)
0.0966764 0.995316i \(-0.469179\pi\)
\(294\) 0 0
\(295\) −6.97336 3.50215i −0.406005 0.203903i
\(296\) −1.32461 + 2.29430i −0.0769916 + 0.133353i
\(297\) 0 0
\(298\) 9.12136 + 15.7987i 0.528386 + 0.915191i
\(299\) −0.902433 15.4942i −0.0521891 0.896051i
\(300\) 0 0
\(301\) 31.6886 3.70386i 1.82650 0.213487i
\(302\) −0.522740 1.74607i −0.0300803 0.100475i
\(303\) 0 0
\(304\) −1.25230 2.90315i −0.0718241 0.166507i
\(305\) −9.44914 3.43921i −0.541056 0.196928i
\(306\) 0 0
\(307\) 11.4486 4.16694i 0.653405 0.237820i 0.00601852 0.999982i \(-0.498084\pi\)
0.647386 + 0.762162i \(0.275862\pi\)
\(308\) −18.3163 19.4141i −1.04367 1.10622i
\(309\) 0 0
\(310\) 0.680636 0.341828i 0.0386575 0.0194145i
\(311\) 1.46151 25.0931i 0.0828745 1.42290i −0.658890 0.752239i \(-0.728974\pi\)
0.741764 0.670661i \(-0.233989\pi\)
\(312\) 0 0
\(313\) −8.47873 + 28.3209i −0.479246 + 1.60079i 0.286787 + 0.957994i \(0.407413\pi\)
−0.766034 + 0.642800i \(0.777773\pi\)
\(314\) 2.67130 15.1497i 0.150750 0.854947i
\(315\) 0 0
\(316\) −2.71203 15.3807i −0.152563 0.865230i
\(317\) −4.25913 0.497821i −0.239217 0.0279604i −0.00436034 0.999990i \(-0.501388\pi\)
−0.234856 + 0.972030i \(0.575462\pi\)
\(318\) 0 0
\(319\) −2.26476 + 2.40051i −0.126802 + 0.134403i
\(320\) −1.85126 + 4.29170i −0.103489 + 0.239913i
\(321\) 0 0
\(322\) 8.57557 5.64024i 0.477898 0.314318i
\(323\) −20.4570 −1.13826
\(324\) 0 0
\(325\) 12.6118 0.699576
\(326\) −11.5330 + 7.58536i −0.638752 + 0.420114i
\(327\) 0 0
\(328\) −0.716366 + 1.66072i −0.0395547 + 0.0916981i
\(329\) 20.6985 21.9392i 1.14115 1.20954i
\(330\) 0 0
\(331\) 27.6432 + 3.23102i 1.51941 + 0.177593i 0.834487 0.551027i \(-0.185764\pi\)
0.684918 + 0.728620i \(0.259838\pi\)
\(332\) −0.391188 2.21854i −0.0214692 0.121758i
\(333\) 0 0
\(334\) −0.460091 + 2.60930i −0.0251750 + 0.142775i
\(335\) 2.25130 7.51986i 0.123002 0.410854i
\(336\) 0 0
\(337\) −1.56420 + 26.8562i −0.0852071 + 1.46295i 0.636781 + 0.771045i \(0.280266\pi\)
−0.721988 + 0.691905i \(0.756772\pi\)
\(338\) −5.01489 + 2.51857i −0.272774 + 0.136992i
\(339\) 0 0
\(340\) −6.46816 6.85585i −0.350785 0.371811i
\(341\) −3.12596 + 1.13776i −0.169280 + 0.0616130i
\(342\) 0 0
\(343\) 1.60598 + 0.584529i 0.0867148 + 0.0315616i
\(344\) 8.80551 + 20.4135i 0.474761 + 1.10062i
\(345\) 0 0
\(346\) −4.18690 13.9852i −0.225089 0.751851i
\(347\) 30.2925 3.54069i 1.62619 0.190074i 0.746419 0.665476i \(-0.231771\pi\)
0.879769 + 0.475402i \(0.157697\pi\)
\(348\) 0 0
\(349\) 0.463724 + 7.96184i 0.0248226 + 0.426187i 0.987711 + 0.156289i \(0.0499531\pi\)
−0.962889 + 0.269898i \(0.913010\pi\)
\(350\) 4.17028 + 7.22314i 0.222911 + 0.386093i
\(351\) 0 0
\(352\) 14.7870 25.6119i 0.788151 1.36512i
\(353\) −19.5082 9.79737i −1.03831 0.521461i −0.153863 0.988092i \(-0.549171\pi\)
−0.884452 + 0.466631i \(0.845468\pi\)
\(354\) 0 0
\(355\) 5.42305 + 7.28442i 0.287826 + 0.386617i
\(356\) 1.40964 + 0.334091i 0.0747109 + 0.0177068i
\(357\) 0 0
\(358\) −5.54662 + 7.45040i −0.293148 + 0.393766i
\(359\) −13.2606 + 11.1269i −0.699866 + 0.587258i −0.921736 0.387819i \(-0.873229\pi\)
0.221869 + 0.975076i \(0.428784\pi\)
\(360\) 0 0
\(361\) 0.713665 + 0.598836i 0.0375613 + 0.0315177i
\(362\) 12.0041 2.84502i 0.630920 0.149531i
\(363\) 0 0
\(364\) 19.8195 + 13.0355i 1.03882 + 0.683244i
\(365\) −5.44529 3.58142i −0.285020 0.187460i
\(366\) 0 0
\(367\) −23.2623 + 5.51327i −1.21428 + 0.287790i −0.787358 0.616496i \(-0.788552\pi\)
−0.426926 + 0.904287i \(0.640403\pi\)
\(368\) −1.87433 1.57275i −0.0977062 0.0819853i
\(369\) 0 0
\(370\) 0.886651 0.743989i 0.0460948 0.0386781i
\(371\) −9.41892 + 12.6518i −0.489006 + 0.656849i
\(372\) 0 0
\(373\) −11.2201 2.65920i −0.580952 0.137688i −0.0703757 0.997521i \(-0.522420\pi\)
−0.510576 + 0.859832i \(0.670568\pi\)
\(374\) −10.8091 14.5191i −0.558923 0.750764i
\(375\) 0 0
\(376\) 18.7821 + 9.43272i 0.968613 + 0.486456i
\(377\) 1.46658 2.54020i 0.0755329 0.130827i
\(378\) 0 0
\(379\) −10.3656 17.9537i −0.532443 0.922218i −0.999282 0.0378763i \(-0.987941\pi\)
0.466839 0.884342i \(-0.345393\pi\)
\(380\) 0.533970 + 9.16791i 0.0273921 + 0.470304i
\(381\) 0 0
\(382\) 4.47641 0.523217i 0.229033 0.0267701i
\(383\) 4.54732 + 15.1891i 0.232357 + 0.776126i 0.992050 + 0.125845i \(0.0401640\pi\)
−0.759693 + 0.650282i \(0.774651\pi\)
\(384\) 0 0
\(385\) 11.2683 + 26.1228i 0.574285 + 1.33134i
\(386\) 0.129079 + 0.0469808i 0.00656994 + 0.00239126i
\(387\) 0 0
\(388\) 6.51155 2.37001i 0.330574 0.120319i
\(389\) 19.5641 + 20.7367i 0.991938 + 1.05139i 0.998677 + 0.0514160i \(0.0163734\pi\)
−0.00673888 + 0.999977i \(0.502145\pi\)
\(390\) 0 0
\(391\) −14.1471 + 7.10495i −0.715451 + 0.359313i
\(392\) −1.14735 + 19.6992i −0.0579498 + 0.994959i
\(393\) 0 0
\(394\) 2.51395 8.39719i 0.126651 0.423044i
\(395\) −2.89074 + 16.3942i −0.145449 + 0.824882i
\(396\) 0 0
\(397\) 5.49087 + 31.1403i 0.275579 + 1.56289i 0.737117 + 0.675765i \(0.236187\pi\)
−0.461538 + 0.887120i \(0.652702\pi\)
\(398\) −15.8965 1.85804i −0.796822 0.0931351i
\(399\) 0 0
\(400\) 1.36440 1.44618i 0.0682200 0.0723090i
\(401\) 6.75227 15.6535i 0.337192 0.781700i −0.662281 0.749255i \(-0.730412\pi\)
0.999474 0.0324445i \(-0.0103292\pi\)
\(402\) 0 0
\(403\) 2.47019 1.62467i 0.123049 0.0809305i
\(404\) 13.2952 0.661458
\(405\) 0 0
\(406\) 1.93980 0.0962705
\(407\) −4.22358 + 2.77790i −0.209355 + 0.137695i
\(408\) 0 0
\(409\) −9.44133 + 21.8875i −0.466844 + 1.08227i 0.508397 + 0.861123i \(0.330238\pi\)
−0.975241 + 0.221143i \(0.929021\pi\)
\(410\) 0.542262 0.574764i 0.0267804 0.0283856i
\(411\) 0 0
\(412\) 4.49141 + 0.524970i 0.221276 + 0.0258634i
\(413\) −3.47862 19.7282i −0.171172 0.970762i
\(414\) 0 0
\(415\) −0.416966 + 2.36473i −0.0204681 + 0.116080i
\(416\) −7.53853 + 25.1804i −0.369607 + 1.23457i
\(417\) 0 0
\(418\) −1.02544 + 17.6061i −0.0501560 + 0.861145i
\(419\) −14.0624 + 7.06241i −0.686993 + 0.345021i −0.757816 0.652468i \(-0.773734\pi\)
0.0708230 + 0.997489i \(0.477437\pi\)
\(420\) 0 0
\(421\) 16.1664 + 17.1354i 0.787901 + 0.835126i 0.989529 0.144336i \(-0.0461046\pi\)
−0.201628 + 0.979462i \(0.564623\pi\)
\(422\) 0.874971 0.318464i 0.0425929 0.0155026i
\(423\) 0 0
\(424\) −10.3281 3.75912i −0.501577 0.182559i
\(425\) −5.09524 11.8121i −0.247155 0.572970i
\(426\) 0 0
\(427\) −7.40361 24.7298i −0.358286 1.19676i
\(428\) 23.1992 2.71160i 1.12138 0.131070i
\(429\) 0 0
\(430\) −0.564759 9.69653i −0.0272351 0.467608i
\(431\) 0.705848 + 1.22256i 0.0339995 + 0.0588888i 0.882524 0.470267i \(-0.155842\pi\)
−0.848525 + 0.529155i \(0.822509\pi\)
\(432\) 0 0
\(433\) −6.50524 + 11.2674i −0.312622 + 0.541477i −0.978929 0.204200i \(-0.934541\pi\)
0.666307 + 0.745677i \(0.267874\pi\)
\(434\) 1.74730 + 0.877528i 0.0838732 + 0.0421227i
\(435\) 0 0
\(436\) −6.33408 8.50814i −0.303347 0.407466i
\(437\) 15.0087 + 3.55713i 0.717964 + 0.170161i
\(438\) 0 0
\(439\) 12.3841 16.6347i 0.591061 0.793933i −0.401477 0.915869i \(-0.631503\pi\)
0.992538 + 0.121936i \(0.0389103\pi\)
\(440\) −15.1863 + 12.7428i −0.723979 + 0.607490i
\(441\) 0 0
\(442\) 12.3238 + 10.3409i 0.586182 + 0.491865i
\(443\) 33.0519 7.83344i 1.57034 0.372178i 0.648955 0.760826i \(-0.275206\pi\)
0.921386 + 0.388649i \(0.127058\pi\)
\(444\) 0 0
\(445\) −1.29012 0.848528i −0.0611578 0.0402241i
\(446\) −9.72924 6.39902i −0.460693 0.303002i
\(447\) 0 0
\(448\) −11.6754 + 2.76711i −0.551609 + 0.130734i
\(449\) 0.919709 + 0.771727i 0.0434038 + 0.0364201i 0.664231 0.747527i \(-0.268759\pi\)
−0.620828 + 0.783947i \(0.713203\pi\)
\(450\) 0 0
\(451\) −2.64380 + 2.21841i −0.124492 + 0.104461i
\(452\) 8.31170 11.1645i 0.390949 0.525136i
\(453\) 0 0
\(454\) 18.7069 + 4.43362i 0.877959 + 0.208080i
\(455\) −15.0993 20.2819i −0.707866 0.950830i
\(456\) 0 0
\(457\) −28.6438 14.3855i −1.33990 0.672923i −0.372941 0.927855i \(-0.621651\pi\)
−0.966959 + 0.254932i \(0.917947\pi\)
\(458\) 0.596704 1.03352i 0.0278821 0.0482933i
\(459\) 0 0
\(460\) 3.55340 + 6.15466i 0.165678 + 0.286963i
\(461\) −0.0195765 0.336115i −0.000911768 0.0156545i 0.997822 0.0659703i \(-0.0210143\pi\)
−0.998733 + 0.0503158i \(0.983977\pi\)
\(462\) 0 0
\(463\) 2.93276 0.342791i 0.136297 0.0159308i −0.0476708 0.998863i \(-0.515180\pi\)
0.183968 + 0.982932i \(0.441106\pi\)
\(464\) −0.132620 0.442982i −0.00615673 0.0205649i
\(465\) 0 0
\(466\) −4.35232 10.0898i −0.201617 0.467401i
\(467\) −3.55605 1.29430i −0.164554 0.0598929i 0.258429 0.966030i \(-0.416795\pi\)
−0.422984 + 0.906137i \(0.639017\pi\)
\(468\) 0 0
\(469\) 18.9360 6.89213i 0.874382 0.318249i
\(470\) −6.30147 6.67917i −0.290665 0.308087i
\(471\) 0 0
\(472\) 12.4744 6.26486i 0.574179 0.288363i
\(473\) −2.46664 + 42.3505i −0.113416 + 1.94728i
\(474\) 0 0
\(475\) −3.59474 + 12.0073i −0.164938 + 0.550931i
\(476\) 4.20172 23.8292i 0.192586 1.09221i
\(477\) 0 0
\(478\) 3.11022 + 17.6389i 0.142258 + 0.806785i
\(479\) 3.14535 + 0.367638i 0.143715 + 0.0167978i 0.187646 0.982237i \(-0.439914\pi\)
−0.0439314 + 0.999035i \(0.513988\pi\)
\(480\) 0 0
\(481\) 3.08326 3.26806i 0.140584 0.149011i
\(482\) 2.18817 5.07274i 0.0996683 0.231057i
\(483\) 0 0
\(484\) 16.8843 11.1050i 0.767468 0.504771i
\(485\) −7.38607 −0.335384
\(486\) 0 0
\(487\) 1.22501 0.0555106 0.0277553 0.999615i \(-0.491164\pi\)
0.0277553 + 0.999615i \(0.491164\pi\)
\(488\) 15.0287 9.88456i 0.680319 0.447453i
\(489\) 0 0
\(490\) 3.41465 7.91605i 0.154258 0.357610i
\(491\) 27.8255 29.4933i 1.25575 1.33101i 0.334323 0.942459i \(-0.391493\pi\)
0.921425 0.388556i \(-0.127026\pi\)
\(492\) 0 0
\(493\) −2.97164 0.347335i −0.133836 0.0156432i
\(494\) −2.72183 15.4363i −0.122461 0.694512i
\(495\) 0 0
\(496\) 0.0809373 0.459018i 0.00363419 0.0206105i
\(497\) −6.68638 + 22.3341i −0.299925 + 1.00182i
\(498\) 0 0
\(499\) 2.39276 41.0820i 0.107114 1.83908i −0.335109 0.942179i \(-0.608773\pi\)
0.442224 0.896905i \(-0.354190\pi\)
\(500\) −14.3517 + 7.20768i −0.641826 + 0.322337i
\(501\) 0 0
\(502\) 0.0356484 + 0.0377851i 0.00159106 + 0.00168643i
\(503\) 9.54144 3.47280i 0.425432 0.154845i −0.120426 0.992722i \(-0.538426\pi\)
0.545858 + 0.837878i \(0.316204\pi\)
\(504\) 0 0
\(505\) −13.3166 4.84686i −0.592582 0.215682i
\(506\) 5.40568 + 12.5318i 0.240312 + 0.557105i
\(507\) 0 0
\(508\) 1.54816 + 5.17123i 0.0686887 + 0.229436i
\(509\) −24.0833 + 2.81493i −1.06747 + 0.124770i −0.631642 0.775260i \(-0.717619\pi\)
−0.435829 + 0.900029i \(0.643545\pi\)
\(510\) 0 0
\(511\) −0.972849 16.7032i −0.0430363 0.738904i
\(512\) 3.94773 + 6.83768i 0.174467 + 0.302186i
\(513\) 0 0
\(514\) 7.55901 13.0926i 0.333414 0.577490i
\(515\) −4.30728 2.16320i −0.189802 0.0953219i
\(516\) 0 0
\(517\) 23.9495 + 32.1698i 1.05330 + 1.41483i
\(518\) 2.89124 + 0.685237i 0.127034 + 0.0301076i
\(519\) 0 0
\(520\) 10.5215 14.1329i 0.461400 0.619768i
\(521\) −4.86477 + 4.08202i −0.213129 + 0.178837i −0.743102 0.669178i \(-0.766646\pi\)
0.529973 + 0.848014i \(0.322202\pi\)
\(522\) 0 0
\(523\) 21.5335 + 18.0688i 0.941595 + 0.790092i 0.977862 0.209250i \(-0.0671024\pi\)
−0.0362674 + 0.999342i \(0.511547\pi\)
\(524\) 22.5054 5.33387i 0.983151 0.233011i
\(525\) 0 0
\(526\) 9.83386 + 6.46783i 0.428777 + 0.282011i
\(527\) −2.51962 1.65718i −0.109756 0.0721879i
\(528\) 0 0
\(529\) −10.7652 + 2.55141i −0.468054 + 0.110931i
\(530\) 3.67848 + 3.08661i 0.159783 + 0.134074i
\(531\) 0 0
\(532\) −18.0598 + 15.1540i −0.782991 + 0.657008i
\(533\) 1.83171 2.46041i 0.0793400 0.106572i
\(534\) 0 0
\(535\) −24.2253 5.74149i −1.04735 0.248226i
\(536\) 8.38522 + 11.2633i 0.362186 + 0.486501i
\(537\) 0 0
\(538\) 8.19694 + 4.11666i 0.353395 + 0.177482i
\(539\) −18.8268 + 32.6089i −0.810926 + 1.40457i
\(540\) 0 0
\(541\) −1.34390 2.32771i −0.0577788 0.100076i 0.835689 0.549203i \(-0.185068\pi\)
−0.893468 + 0.449127i \(0.851735\pi\)
\(542\) −0.130888 2.24725i −0.00562211 0.0965279i
\(543\) 0 0
\(544\) 26.6294 3.11253i 1.14173 0.133449i
\(545\) 3.24260 + 10.8310i 0.138898 + 0.463950i
\(546\) 0 0
\(547\) 12.9944 + 30.1244i 0.555600 + 1.28802i 0.932299 + 0.361689i \(0.117800\pi\)
−0.376699 + 0.926336i \(0.622941\pi\)
\(548\) 12.1088 + 4.40724i 0.517262 + 0.188268i
\(549\) 0 0
\(550\) −10.4214 + 3.79308i −0.444370 + 0.161737i
\(551\) 2.00042 + 2.12032i 0.0852207 + 0.0903287i
\(552\) 0 0
\(553\) −38.1901 + 19.1798i −1.62401 + 0.815608i
\(554\) −0.104565 + 1.79532i −0.00444256 + 0.0762758i
\(555\) 0 0
\(556\) 6.34334 21.1882i 0.269018 0.898581i
\(557\) 1.71906 9.74928i 0.0728390 0.413090i −0.926485 0.376331i \(-0.877185\pi\)
0.999324 0.0367591i \(-0.0117034\pi\)
\(558\) 0 0
\(559\) −6.54721 37.1311i −0.276917 1.57048i
\(560\) −3.95921 0.462766i −0.167307 0.0195554i
\(561\) 0 0
\(562\) 3.40329 3.60728i 0.143559 0.152164i
\(563\) −2.78662 + 6.46011i −0.117442 + 0.272261i −0.966790 0.255572i \(-0.917736\pi\)
0.849348 + 0.527833i \(0.176995\pi\)
\(564\) 0 0
\(565\) −12.3953 + 8.15249i −0.521472 + 0.342978i
\(566\) 11.4745 0.482310
\(567\) 0 0
\(568\) −16.2454 −0.681640
\(569\) −3.29025 + 2.16403i −0.137935 + 0.0907209i −0.616601 0.787276i \(-0.711491\pi\)
0.478666 + 0.877997i \(0.341120\pi\)
\(570\) 0 0
\(571\) 10.1268 23.4765i 0.423791 0.982459i −0.563871 0.825863i \(-0.690689\pi\)
0.987663 0.156596i \(-0.0500521\pi\)
\(572\) −21.6458 + 22.9432i −0.905057 + 0.959304i
\(573\) 0 0
\(574\) 2.01483 + 0.235500i 0.0840975 + 0.00982958i
\(575\) 1.68431 + 9.55219i 0.0702405 + 0.398354i
\(576\) 0 0
\(577\) 0.816045 4.62802i 0.0339724 0.192667i −0.963099 0.269149i \(-0.913258\pi\)
0.997071 + 0.0764818i \(0.0243687\pi\)
\(578\) 0.895737 2.99197i 0.0372577 0.124450i
\(579\) 0 0
\(580\) −0.0780940 + 1.34082i −0.00324268 + 0.0556746i
\(581\) −5.50862 + 2.76653i −0.228536 + 0.114775i
\(582\) 0 0
\(583\) −14.3924 15.2551i −0.596073 0.631800i
\(584\) 10.9558 3.98757i 0.453353 0.165007i
\(585\) 0 0
\(586\) −18.6213 6.77759i −0.769238 0.279980i
\(587\) 11.0004 + 25.5017i 0.454034 + 1.05257i 0.979443 + 0.201719i \(0.0646528\pi\)
−0.525410 + 0.850849i \(0.676088\pi\)
\(588\) 0 0
\(589\) 0.842715 + 2.81486i 0.0347235 + 0.115984i
\(590\) −6.05748 + 0.708018i −0.249383 + 0.0291487i
\(591\) 0 0
\(592\) −0.0411844 0.707108i −0.00169267 0.0290620i
\(593\) 7.16631 + 12.4124i 0.294285 + 0.509717i 0.974818 0.223000i \(-0.0715851\pi\)
−0.680533 + 0.732717i \(0.738252\pi\)
\(594\) 0 0
\(595\) −12.8956 + 22.3359i −0.528669 + 0.915682i
\(596\) −28.9769 14.5528i −1.18694 0.596104i
\(597\) 0 0
\(598\) −7.24351 9.72973i −0.296209 0.397878i
\(599\) 26.7617 + 6.34265i 1.09346 + 0.259154i 0.737499 0.675349i \(-0.236007\pi\)
0.355957 + 0.934502i \(0.384155\pi\)
\(600\) 0 0
\(601\) 11.1968 15.0400i 0.456729 0.613493i −0.512789 0.858515i \(-0.671388\pi\)
0.969518 + 0.245022i \(0.0787951\pi\)
\(602\) 19.1011 16.0277i 0.778503 0.653242i
\(603\) 0 0
\(604\) 2.48176 + 2.08244i 0.100981 + 0.0847333i
\(605\) −20.9600 + 4.96761i −0.852144 + 0.201962i
\(606\) 0 0
\(607\) −22.0641 14.5118i −0.895556 0.589016i 0.0161458 0.999870i \(-0.494860\pi\)
−0.911701 + 0.410853i \(0.865231\pi\)
\(608\) −21.8248 14.3544i −0.885111 0.582146i
\(609\) 0 0
\(610\) −7.64707 + 1.81239i −0.309621 + 0.0733815i
\(611\) −27.3057 22.9122i −1.10467 0.926928i
\(612\) 0 0
\(613\) −26.7821 + 22.4728i −1.08172 + 0.907670i −0.996062 0.0886553i \(-0.971743\pi\)
−0.0856560 + 0.996325i \(0.527299\pi\)
\(614\) 5.68606 7.63770i 0.229471 0.308232i
\(615\) 0 0
\(616\) −49.5204 11.7365i −1.99523 0.472879i
\(617\) −4.27053 5.73631i −0.171925 0.230935i 0.707806 0.706407i \(-0.249685\pi\)
−0.879731 + 0.475471i \(0.842278\pi\)
\(618\) 0 0
\(619\) −16.8196 8.44712i −0.676037 0.339518i 0.0774361 0.996997i \(-0.475327\pi\)
−0.753473 + 0.657479i \(0.771623\pi\)
\(620\) −0.676908 + 1.17244i −0.0271853 + 0.0470863i
\(621\) 0 0
\(622\) −9.82235 17.0128i −0.393841 0.682152i
\(623\) −0.230492 3.95739i −0.00923446 0.158550i
\(624\) 0 0
\(625\) 3.06015 0.357680i 0.122406 0.0143072i
\(626\) 6.62654 + 22.1342i 0.264850 + 0.884660i
\(627\) 0 0
\(628\) 10.8303 + 25.1074i 0.432174 + 1.00189i
\(629\) −4.30649 1.56744i −0.171711 0.0624978i
\(630\) 0 0
\(631\) −22.0642 + 8.03070i −0.878361 + 0.319697i −0.741548 0.670900i \(-0.765908\pi\)
−0.136813 + 0.990597i \(0.543686\pi\)
\(632\) −20.4358 21.6607i −0.812893 0.861616i
\(633\) 0 0
\(634\) −2.99490 + 1.50410i −0.118943 + 0.0597353i
\(635\) 0.334549 5.74398i 0.0132762 0.227943i
\(636\) 0 0
\(637\) 9.59802 32.0596i 0.380287 1.27025i
\(638\) −0.447890 + 2.54011i −0.0177321 + 0.100564i
\(639\) 0 0
\(640\) −2.37461 13.4671i −0.0938648 0.532334i
\(641\) 4.32954 + 0.506050i 0.171006 + 0.0199878i 0.201165 0.979557i \(-0.435527\pi\)
−0.0301588 + 0.999545i \(0.509601\pi\)
\(642\) 0 0
\(643\) −13.0468 + 13.8288i −0.514516 + 0.545355i −0.931587 0.363519i \(-0.881575\pi\)
0.417071 + 0.908874i \(0.363057\pi\)
\(644\) −7.22619 + 16.7522i −0.284752 + 0.660129i
\(645\) 0 0
\(646\) −13.3579 + 8.78560i −0.525558 + 0.345665i
\(647\) −20.6268 −0.810924 −0.405462 0.914112i \(-0.632889\pi\)
−0.405462 + 0.914112i \(0.632889\pi\)
\(648\) 0 0
\(649\) 26.6367 1.04558
\(650\) 8.23516 5.41635i 0.323010 0.212447i
\(651\) 0 0
\(652\) 9.71824 22.5294i 0.380596 0.882320i
\(653\) −4.11111 + 4.35752i −0.160880 + 0.170523i −0.802799 0.596249i \(-0.796657\pi\)
0.641919 + 0.766772i \(0.278138\pi\)
\(654\) 0 0
\(655\) −24.4862 2.86203i −0.956756 0.111829i
\(656\) −0.0839701 0.476218i −0.00327848 0.0185932i
\(657\) 0 0
\(658\) 4.09344 23.2150i 0.159579 0.905016i
\(659\) 11.1391 37.2073i 0.433919 1.44939i −0.409587 0.912271i \(-0.634327\pi\)
0.843506 0.537120i \(-0.180488\pi\)
\(660\) 0 0
\(661\) −1.80224 + 30.9432i −0.0700989 + 1.20355i 0.761496 + 0.648169i \(0.224465\pi\)
−0.831595 + 0.555382i \(0.812572\pi\)
\(662\) 19.4379 9.76207i 0.755474 0.379414i
\(663\) 0 0
\(664\) −2.94770 3.12438i −0.114393 0.121249i
\(665\) 23.6135 8.59460i 0.915691 0.333284i
\(666\) 0 0
\(667\) 2.11981 + 0.771549i 0.0820795 + 0.0298745i
\(668\) −1.86535 4.32436i −0.0721725 0.167315i
\(669\) 0 0
\(670\) −1.75950 5.87713i −0.0679753 0.227053i
\(671\) 34.0924 3.98483i 1.31612 0.153833i
\(672\) 0 0
\(673\) 2.24379 + 38.5243i 0.0864916 + 1.48500i 0.710562 + 0.703635i \(0.248441\pi\)
−0.624070 + 0.781368i \(0.714522\pi\)
\(674\) 10.5125 + 18.2082i 0.404926 + 0.701352i
\(675\) 0 0
\(676\) 4.98742 8.63847i 0.191824 0.332249i
\(677\) 3.56442 + 1.79012i 0.136992 + 0.0688000i 0.515975 0.856604i \(-0.327430\pi\)
−0.378983 + 0.925404i \(0.623726\pi\)
\(678\) 0 0
\(679\) −11.3229 15.2093i −0.434532 0.583677i
\(680\) −17.4875 4.14462i −0.670615 0.158939i
\(681\) 0 0
\(682\) −1.55254 + 2.08543i −0.0594499 + 0.0798551i
\(683\) 32.2624 27.0713i 1.23449 1.03586i 0.236551 0.971619i \(-0.423983\pi\)
0.997935 0.0642370i \(-0.0204614\pi\)
\(684\) 0 0
\(685\) −10.5217 8.82872i −0.402012 0.337328i
\(686\) 1.29970 0.308034i 0.0496227 0.0117608i
\(687\) 0 0
\(688\) −4.96609 3.26625i −0.189330 0.124524i
\(689\) 15.5736 + 10.2429i 0.593306 + 0.390224i
\(690\) 0 0
\(691\) −8.32013 + 1.97191i −0.316513 + 0.0750149i −0.385802 0.922582i \(-0.626075\pi\)
0.0692889 + 0.997597i \(0.477927\pi\)
\(692\) 19.8777 + 16.6794i 0.755638 + 0.634056i
\(693\) 0 0
\(694\) 18.2596 15.3216i 0.693125 0.581601i
\(695\) −14.0779 + 18.9100i −0.534007 + 0.717296i
\(696\) 0 0
\(697\) −3.04442 0.721541i −0.115316 0.0273303i
\(698\) 3.72215 + 4.99972i 0.140885 + 0.189242i
\(699\) 0 0
\(700\) −13.2482 6.65352i −0.500737 0.251479i
\(701\) −0.440975 + 0.763791i −0.0166554 + 0.0288480i −0.874233 0.485507i \(-0.838635\pi\)
0.857578 + 0.514355i \(0.171968\pi\)
\(702\) 0 0
\(703\) 2.23259 + 3.86697i 0.0842039 + 0.145845i
\(704\) −0.927670 15.9275i −0.0349629 0.600290i
\(705\) 0 0
\(706\) −16.9460 + 1.98070i −0.637770 + 0.0745446i
\(707\) −10.4339 34.8516i −0.392406 1.31073i
\(708\) 0 0
\(709\) −15.9358 36.9432i −0.598480 1.38743i −0.900803 0.434227i \(-0.857022\pi\)
0.302324 0.953205i \(-0.402238\pi\)
\(710\) 6.66953 + 2.42751i 0.250303 + 0.0911028i
\(711\) 0 0
\(712\) 2.59569 0.944754i 0.0972777 0.0354062i
\(713\) 1.56042 + 1.65395i 0.0584382 + 0.0619409i
\(714\) 0 0
\(715\) 30.0449 15.0891i 1.12362 0.564301i
\(716\) 0.959961 16.4819i 0.0358754 0.615957i
\(717\) 0 0
\(718\) −3.88015 + 12.9606i −0.144806 + 0.483685i
\(719\) −2.39151 + 13.5629i −0.0891883 + 0.505812i 0.907186 + 0.420730i \(0.138226\pi\)
−0.996374 + 0.0850815i \(0.972885\pi\)
\(720\) 0 0
\(721\) −2.14866 12.1857i −0.0800203 0.453817i
\(722\) 0.723185 + 0.0845282i 0.0269142 + 0.00314581i
\(723\) 0 0
\(724\) −15.0479 + 15.9499i −0.559251 + 0.592772i
\(725\) −0.726051 + 1.68318i −0.0269649 + 0.0625116i
\(726\) 0 0
\(727\) 10.4310 6.86056i 0.386864 0.254444i −0.341147 0.940010i \(-0.610815\pi\)
0.728011 + 0.685566i \(0.240445\pi\)
\(728\) 45.2317 1.67640
\(729\) 0 0
\(730\) −5.09374 −0.188528
\(731\) −32.1315 + 21.1332i −1.18843 + 0.781641i
\(732\) 0 0
\(733\) −10.6438 + 24.6752i −0.393139 + 0.911398i 0.600587 + 0.799559i \(0.294933\pi\)
−0.993726 + 0.111839i \(0.964326\pi\)
\(734\) −12.8219 + 13.5904i −0.473266 + 0.501632i
\(735\) 0 0
\(736\) −20.0785 2.34684i −0.740103 0.0865056i
\(737\) 4.65283 + 26.3875i 0.171389 + 0.971996i
\(738\) 0 0
\(739\) −4.23374 + 24.0107i −0.155740 + 0.883248i 0.802365 + 0.596833i \(0.203575\pi\)
−0.958106 + 0.286415i \(0.907536\pi\)
\(740\) −0.590047 + 1.97089i −0.0216906 + 0.0724515i
\(741\) 0 0
\(742\) −0.716768 + 12.3064i −0.0263134 + 0.451783i
\(743\) −32.2333 + 16.1882i −1.18253 + 0.593887i −0.927782 0.373122i \(-0.878287\pi\)
−0.254743 + 0.967009i \(0.581991\pi\)
\(744\) 0 0
\(745\) 23.7184 + 25.1401i 0.868975 + 0.921060i
\(746\) −8.46844 + 3.08226i −0.310052 + 0.112850i
\(747\) 0 0
\(748\) 30.2335 + 11.0041i 1.10544 + 0.402349i
\(749\) −25.3146 58.6859i −0.924976 2.14434i
\(750\) 0 0
\(751\) 0.670091 + 2.23826i 0.0244520 + 0.0816753i 0.969345 0.245705i \(-0.0790194\pi\)
−0.944893 + 0.327380i \(0.893834\pi\)
\(752\) −5.58137 + 0.652369i −0.203532 + 0.0237894i
\(753\) 0 0
\(754\) −0.133292 2.28853i −0.00485421 0.0833435i
\(755\) −1.72660 2.99055i −0.0628372 0.108837i
\(756\) 0 0
\(757\) 8.08646 14.0062i 0.293907 0.509063i −0.680823 0.732448i \(-0.738378\pi\)
0.974730 + 0.223386i \(0.0717109\pi\)
\(758\) −14.4790 7.27161i −0.525899 0.264117i
\(759\) 0 0
\(760\) 10.4565 + 14.0455i 0.379297 + 0.509485i
\(761\) −44.1342 10.4600i −1.59986 0.379175i −0.668630 0.743595i \(-0.733119\pi\)
−0.931234 + 0.364421i \(0.881267\pi\)
\(762\) 0 0
\(763\) −17.3321 + 23.2811i −0.627465 + 0.842832i
\(764\) −6.13669 + 5.14929i −0.222018 + 0.186295i
\(765\) 0 0
\(766\) 9.49250 + 7.96515i 0.342978 + 0.287793i
\(767\) −23.0359 + 5.45962i −0.831779 + 0.197135i
\(768\) 0 0
\(769\) −15.3444 10.0922i −0.553334 0.363934i 0.241839 0.970316i \(-0.422250\pi\)
−0.795173 + 0.606383i \(0.792620\pi\)
\(770\) 18.5768 + 12.2182i 0.669462 + 0.440312i
\(771\) 0 0
\(772\) −0.237578 + 0.0563069i −0.00855061 + 0.00202653i
\(773\) 22.5821 + 18.9486i 0.812222 + 0.681536i 0.951137 0.308769i \(-0.0999169\pi\)
−0.138915 + 0.990304i \(0.544361\pi\)
\(774\) 0 0
\(775\) −1.41544 + 1.18769i −0.0508441 + 0.0426633i
\(776\) 7.89004 10.5982i 0.283236 0.380452i
\(777\) 0 0
\(778\) 21.6806 + 5.13839i 0.777286 + 0.184220i
\(779\) 1.82038 + 2.44520i 0.0652220 + 0.0876083i
\(780\) 0 0
\(781\) −27.7020 13.9125i −0.991255 0.497827i
\(782\) −6.18635 + 10.7151i −0.221224 + 0.383170i
\(783\) 0 0
\(784\) −2.63788 4.56895i −0.0942102 0.163177i
\(785\) −1.69466 29.0962i −0.0604850 1.03849i
\(786\) 0 0
\(787\) −31.8401 + 3.72157i −1.13498 + 0.132660i −0.662766 0.748826i \(-0.730618\pi\)
−0.472210 + 0.881486i \(0.656544\pi\)
\(788\) 4.46849 + 14.9258i 0.159183 + 0.531710i
\(789\) 0 0
\(790\) 5.15320 + 11.9465i 0.183343 + 0.425036i
\(791\) −35.7894 13.0263i −1.27252 0.463161i
\(792\) 0 0
\(793\) −28.6670 + 10.4339i −1.01799 + 0.370520i
\(794\) 16.9591 + 17.9756i 0.601857 + 0.637931i
\(795\) 0 0
\(796\) 25.4221 12.7675i 0.901064 0.452531i
\(797\) −0.685319 + 11.7665i −0.0242753 + 0.416790i 0.964177 + 0.265259i \(0.0854574\pi\)
−0.988452 + 0.151531i \(0.951580\pi\)
\(798\) 0 0
\(799\) −10.4277 + 34.8309i −0.368905 + 1.23223i
\(800\) 2.85246 16.1771i 0.100850 0.571948i
\(801\) 0 0
\(802\) −2.31363 13.1212i −0.0816970 0.463327i
\(803\) 22.0970 + 2.58276i 0.779785 + 0.0911437i
\(804\) 0 0
\(805\) 13.3450 14.1449i 0.470350 0.498542i
\(806\) 0.915226 2.12173i 0.0322375 0.0747348i
\(807\) 0 0
\(808\) 21.1799 13.9303i 0.745107 0.490065i
\(809\) 21.4155 0.752929 0.376464 0.926431i \(-0.377140\pi\)
0.376464 + 0.926431i \(0.377140\pi\)
\(810\) 0 0
\(811\) 1.73790 0.0610258 0.0305129 0.999534i \(-0.490286\pi\)
0.0305129 + 0.999534i \(0.490286\pi\)
\(812\) −2.88071 + 1.89467i −0.101093 + 0.0664901i
\(813\) 0 0
\(814\) −1.56487 + 3.62779i −0.0548488 + 0.127154i
\(815\) −17.9472 + 19.0230i −0.628664 + 0.666345i
\(816\) 0 0
\(817\) 37.2174 + 4.35009i 1.30207 + 0.152190i
\(818\) 3.23502 + 18.3467i 0.113110 + 0.641477i
\(819\) 0 0
\(820\) −0.243897 + 1.38321i −0.00851725 + 0.0483037i
\(821\) 2.55794 8.54412i 0.0892728 0.298192i −0.901680 0.432404i \(-0.857665\pi\)
0.990953 + 0.134213i \(0.0428505\pi\)
\(822\) 0 0
\(823\) −0.107694 + 1.84904i −0.00375399 + 0.0644535i −0.999665 0.0258878i \(-0.991759\pi\)
0.995911 + 0.0903413i \(0.0287958\pi\)
\(824\) 7.70511 3.86965i 0.268420 0.134806i
\(825\) 0 0
\(826\) −10.7441 11.3881i −0.373834 0.396241i
\(827\) −19.7686 + 7.19517i −0.687420 + 0.250200i −0.662030 0.749477i \(-0.730305\pi\)
−0.0253900 + 0.999678i \(0.508083\pi\)
\(828\) 0 0
\(829\) −5.33030 1.94007i −0.185129 0.0673814i 0.247792 0.968813i \(-0.420295\pi\)
−0.432921 + 0.901432i \(0.642517\pi\)
\(830\) 0.743308 + 1.72318i 0.0258006 + 0.0598125i
\(831\) 0 0
\(832\) 4.06685 + 13.5842i 0.140993 + 0.470949i
\(833\) −33.9044 + 3.96286i −1.17472 + 0.137305i
\(834\) 0 0
\(835\) 0.291880 + 5.01138i 0.0101009 + 0.173426i
\(836\) −15.6738 27.1478i −0.542089 0.938925i
\(837\) 0 0
\(838\) −6.14931 + 10.6509i −0.212424 + 0.367930i
\(839\) 21.3832 + 10.7390i 0.738229 + 0.370753i 0.777840 0.628463i \(-0.216315\pi\)
−0.0396107 + 0.999215i \(0.512612\pi\)
\(840\) 0 0
\(841\) −17.0630 22.9196i −0.588380 0.790331i
\(842\) 17.9153 + 4.24600i 0.617402 + 0.146327i
\(843\) 0 0
\(844\) −0.988329 + 1.32756i −0.0340197 + 0.0456964i
\(845\) −8.14471 + 6.83422i −0.280186 + 0.235104i
\(846\) 0 0
\(847\) −42.3609 35.5450i −1.45554 1.22134i
\(848\) 2.85936 0.677682i 0.0981910 0.0232717i
\(849\) 0 0
\(850\) −8.39996 5.52474i −0.288116 0.189497i
\(851\) 2.88701 + 1.89881i 0.0989653 + 0.0650905i
\(852\) 0 0
\(853\) 6.57132 1.55743i 0.224998 0.0533254i −0.116571 0.993182i \(-0.537190\pi\)
0.341568 + 0.939857i \(0.389042\pi\)
\(854\) −15.4550 12.9683i −0.528860 0.443766i
\(855\) 0 0
\(856\) 34.1166 28.6272i 1.16608 0.978457i
\(857\) −11.2603 + 15.1252i −0.384644 + 0.516666i −0.951707 0.307008i \(-0.900672\pi\)
0.567063 + 0.823674i \(0.308080\pi\)
\(858\) 0 0
\(859\) 31.5428 + 7.47577i 1.07623 + 0.255070i 0.730255 0.683175i \(-0.239401\pi\)
0.345971 + 0.938245i \(0.387550\pi\)
\(860\) 10.3097 + 13.8483i 0.351557 + 0.472223i
\(861\) 0 0
\(862\) 0.985952 + 0.495164i 0.0335816 + 0.0168653i
\(863\) 23.6121 40.8973i 0.803765 1.39216i −0.113357 0.993554i \(-0.536160\pi\)
0.917122 0.398607i \(-0.130506\pi\)
\(864\) 0 0
\(865\) −13.8292 23.9529i −0.470208 0.814424i
\(866\) 0.591235 + 10.1511i 0.0200910 + 0.344949i
\(867\) 0 0
\(868\) −3.45196 + 0.403477i −0.117167 + 0.0136949i
\(869\) −16.2975 54.4375i −0.552855 1.84666i
\(870\) 0 0
\(871\) −9.43238 21.8667i −0.319604 0.740925i
\(872\) −19.0051 6.91730i −0.643595 0.234249i
\(873\) 0 0
\(874\) 11.3280 4.12304i 0.383174 0.139464i
\(875\) 30.1571 + 31.9646i 1.01949 + 1.08060i
\(876\) 0 0
\(877\) 5.03263 2.52748i 0.169940 0.0853470i −0.361796 0.932257i \(-0.617836\pi\)
0.531736 + 0.846910i \(0.321540\pi\)
\(878\) 0.942414 16.1806i 0.0318049 0.546070i
\(879\) 0 0
\(880\) 1.52014 5.07763i 0.0512440 0.171167i
\(881\) −0.984686 + 5.58443i −0.0331749 + 0.188144i −0.996892 0.0787820i \(-0.974897\pi\)
0.963717 + 0.266926i \(0.0860080\pi\)
\(882\) 0 0
\(883\) 5.95650 + 33.7810i 0.200452 + 1.13682i 0.904437 + 0.426606i \(0.140291\pi\)
−0.703985 + 0.710215i \(0.748598\pi\)
\(884\) −28.4019 3.31970i −0.955259 0.111654i
\(885\) 0 0
\(886\) 18.2178 19.3097i 0.612039 0.648723i
\(887\) 10.6481 24.6852i 0.357529 0.828846i −0.640610 0.767867i \(-0.721318\pi\)
0.998139 0.0609796i \(-0.0194225\pi\)
\(888\) 0 0
\(889\) 12.3407 8.11664i 0.413895 0.272223i
\(890\) −1.20683 −0.0404531
\(891\) 0 0
\(892\) 20.6987 0.693043
\(893\) 29.5969 19.4662i 0.990422 0.651411i
\(894\) 0 0
\(895\) −6.97012 + 16.1586i −0.232986 + 0.540121i
\(896\) 24.0909 25.5349i 0.804820 0.853059i
\(897\) 0 0
\(898\) 0.931978 + 0.108933i 0.0311005 + 0.00363513i
\(899\) 0.0746222 + 0.423204i 0.00248879 + 0.0141146i
\(900\) 0 0
\(901\) 3.30159 18.7243i 0.109992 0.623796i
\(902\) −0.773596 + 2.58399i −0.0257579 + 0.0860375i
\(903\) 0 0
\(904\) 1.54313 26.4945i 0.0513237 0.881194i
\(905\) 20.8869 10.4898i 0.694303 0.348692i
\(906\) 0 0
\(907\) −20.8882 22.1402i −0.693581 0.735153i 0.280872 0.959745i \(-0.409376\pi\)
−0.974453 + 0.224592i \(0.927895\pi\)
\(908\) −32.1114 + 11.6876i −1.06565 + 0.387866i
\(909\) 0 0
\(910\) −18.5699 6.75888i −0.615585 0.224055i
\(911\) 5.57124 + 12.9156i 0.184583 + 0.427912i 0.985233 0.171221i \(-0.0547712\pi\)
−0.800649 + 0.599133i \(0.795512\pi\)
\(912\) 0 0
\(913\) −2.35078 7.85216i −0.0777996 0.259869i
\(914\) −24.8817 + 2.90826i −0.823014 + 0.0961966i
\(915\) 0 0
\(916\) 0.123340 + 2.11766i 0.00407527 + 0.0699696i
\(917\) −31.6440 54.8090i −1.04498 1.80995i
\(918\) 0 0
\(919\) −14.5007 + 25.1160i −0.478335 + 0.828501i −0.999691 0.0248384i \(-0.992093\pi\)
0.521356 + 0.853339i \(0.325426\pi\)
\(920\) 12.1094 + 6.08159i 0.399236 + 0.200504i
\(921\) 0 0
\(922\) −0.157134 0.211067i −0.00517492 0.00695112i
\(923\) 26.8087 + 6.35379i 0.882420 + 0.209137i
\(924\) 0 0
\(925\) −1.67676 + 2.25227i −0.0551314 + 0.0740543i
\(926\) 1.76780 1.48336i 0.0580935 0.0487462i
\(927\) 0 0
\(928\) −2.92661 2.45572i −0.0960706 0.0806128i
\(929\) −43.3578 + 10.2760i −1.42252 + 0.337144i −0.868637 0.495449i \(-0.835004\pi\)
−0.553886 + 0.832593i \(0.686855\pi\)
\(930\) 0 0
\(931\) 27.7872 + 18.2759i 0.910688 + 0.598969i
\(932\) 16.3186 + 10.7329i 0.534532 + 0.351567i
\(933\) 0 0
\(934\) −2.87787 + 0.682067i −0.0941667 + 0.0223179i
\(935\) −26.2707 22.0437i −0.859143 0.720907i
\(936\) 0 0
\(937\) −15.7744 + 13.2363i −0.515326 + 0.432409i −0.862999 0.505206i \(-0.831416\pi\)
0.347673 + 0.937616i \(0.386972\pi\)
\(938\) 9.40475 12.6328i 0.307076 0.412475i
\(939\) 0 0
\(940\) 15.8819 + 3.76407i 0.518009 + 0.122770i
\(941\) 33.9079 + 45.5462i 1.10536 + 1.48476i 0.856445 + 0.516238i \(0.172668\pi\)
0.248920 + 0.968524i \(0.419925\pi\)
\(942\) 0 0
\(943\) 2.10814 + 1.05875i 0.0686506 + 0.0344776i
\(944\) −1.86608 + 3.23215i −0.0607359 + 0.105198i
\(945\) 0 0
\(946\) 16.5775 + 28.7131i 0.538982 + 0.933544i
\(947\) 0.917269 + 15.7489i 0.0298072 + 0.511770i 0.979861 + 0.199683i \(0.0639912\pi\)
−0.950053 + 0.312088i \(0.898972\pi\)
\(948\) 0 0
\(949\) −19.6392 + 2.29550i −0.637516 + 0.0745149i
\(950\) 2.80946 + 9.38425i 0.0911509 + 0.304465i
\(951\) 0 0
\(952\) −18.2739 42.3636i −0.592260 1.37301i
\(953\) 47.3933 + 17.2497i 1.53522 + 0.558774i 0.964893 0.262645i \(-0.0845947\pi\)
0.570326 + 0.821418i \(0.306817\pi\)
\(954\) 0 0
\(955\) 8.02382 2.92043i 0.259645 0.0945030i
\(956\) −21.8475 23.1570i −0.706598 0.748950i
\(957\) 0 0
\(958\) 2.21172 1.11077i 0.0714574 0.0358872i
\(959\) 2.05019 35.2004i 0.0662041 1.13668i
\(960\) 0 0
\(961\) 8.76667 29.2827i 0.282796 0.944604i
\(962\) 0.609760 3.45812i 0.0196594 0.111494i
\(963\) 0 0
\(964\) 1.70519 + 9.67059i 0.0549203 + 0.311469i
\(965\) 0.258489 + 0.0302130i 0.00832105 + 0.000972591i
\(966\) 0 0
\(967\) −15.0247 + 15.9253i −0.483162 + 0.512122i −0.922393 0.386252i \(-0.873769\pi\)
0.439231 + 0.898374i \(0.355251\pi\)
\(968\) 15.2622 35.3817i 0.490545 1.13721i
\(969\) 0 0
\(970\) −4.82291 + 3.17208i −0.154854 + 0.101849i
\(971\) −21.3313 −0.684555 −0.342277 0.939599i \(-0.611198\pi\)
−0.342277 + 0.939599i \(0.611198\pi\)
\(972\) 0 0
\(973\) −60.5205 −1.94020
\(974\) 0.799901 0.526103i 0.0256305 0.0168574i
\(975\) 0 0
\(976\) −1.90488 + 4.41600i −0.0609737 + 0.141353i
\(977\) −4.92124 + 5.21621i −0.157444 + 0.166881i −0.801294 0.598271i \(-0.795855\pi\)
0.643850 + 0.765152i \(0.277336\pi\)
\(978\) 0 0
\(979\) 5.23532 + 0.611921i 0.167321 + 0.0195571i
\(980\) 2.66095 + 15.0910i 0.0850011 + 0.482065i
\(981\) 0 0
\(982\) 5.50290 31.2085i 0.175605 0.995904i
\(983\) 11.8775 39.6737i 0.378834 1.26539i −0.529915 0.848051i \(-0.677776\pi\)
0.908749 0.417344i \(-0.137039\pi\)
\(984\) 0 0
\(985\) 0.965614 16.5789i 0.0307670 0.528249i
\(986\) −2.08957 + 1.04942i −0.0665455 + 0.0334204i
\(987\) 0 0
\(988\) 19.1193 + 20.2653i 0.608267 + 0.644725i
\(989\) 27.2487 9.91773i 0.866460 0.315365i
\(990\) 0 0
\(991\) 51.2878 + 18.6672i 1.62921 + 0.592984i 0.985105 0.171953i \(-0.0550079\pi\)
0.644105 + 0.764937i \(0.277230\pi\)
\(992\) −1.52527 3.53597i −0.0484273 0.112267i
\(993\) 0 0
\(994\) 5.22572 + 17.4551i 0.165750 + 0.553643i
\(995\) −30.1177 + 3.52026i −0.954796 + 0.111600i
\(996\) 0 0
\(997\) 1.54155 + 26.4673i 0.0488212 + 0.838228i 0.930480 + 0.366342i \(0.119390\pi\)
−0.881659 + 0.471887i \(0.843573\pi\)
\(998\) −16.0810 27.8531i −0.509035 0.881674i
\(999\) 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.28.5 144
3.2 odd 2 729.2.g.b.28.4 144
9.2 odd 6 243.2.g.a.10.5 144
9.4 even 3 729.2.g.d.514.5 144
9.5 odd 6 729.2.g.a.514.4 144
9.7 even 3 81.2.g.a.13.4 144
81.2 odd 54 243.2.g.a.73.5 144
81.25 even 27 729.2.g.d.217.5 144
81.29 odd 54 729.2.g.b.703.4 144
81.32 odd 54 6561.2.a.d.1.43 72
81.49 even 27 6561.2.a.c.1.30 72
81.52 even 27 inner 729.2.g.c.703.5 144
81.56 odd 54 729.2.g.a.217.4 144
81.79 even 27 81.2.g.a.25.4 yes 144
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
81.2.g.a.13.4 144 9.7 even 3
81.2.g.a.25.4 yes 144 81.79 even 27
243.2.g.a.10.5 144 9.2 odd 6
243.2.g.a.73.5 144 81.2 odd 54
729.2.g.a.217.4 144 81.56 odd 54
729.2.g.a.514.4 144 9.5 odd 6
729.2.g.b.28.4 144 3.2 odd 2
729.2.g.b.703.4 144 81.29 odd 54
729.2.g.c.28.5 144 1.1 even 1 trivial
729.2.g.c.703.5 144 81.52 even 27 inner
729.2.g.d.217.5 144 81.25 even 27
729.2.g.d.514.5 144 9.4 even 3
6561.2.a.c.1.30 72 81.49 even 27
6561.2.a.d.1.43 72 81.32 odd 54