Properties

Label 729.2.g.c.703.5
Level $729$
Weight $2$
Character 729.703
Analytic conductor $5.821$
Analytic rank $0$
Dimension $144$
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 703.5
Character \(\chi\) \(=\) 729.703
Dual form 729.2.g.c.28.5

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.652974 + 0.429468i 0.461722 + 0.303679i 0.758975 0.651119i \(-0.225700\pi\)
−0.297253 + 0.954799i \(0.596071\pi\)
\(3\) 0 0
\(4\) −0.550227 1.27557i −0.275114 0.637785i
\(5\) 1.01614 + 1.07704i 0.454430 + 0.481668i 0.913561 0.406701i \(-0.133321\pi\)
−0.459132 + 0.888368i \(0.651839\pi\)
\(6\) 0 0
\(7\) 3.77556 0.441300i 1.42703 0.166796i 0.632753 0.774354i \(-0.281925\pi\)
0.794275 + 0.607558i \(0.207851\pi\)
\(8\) 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 −0.838929 0.544241i \(-0.816818\pi\)
0.401849 0.915706i \(-0.368368\pi\)
\(12\) 0 0
\(13\) 0.261201 + 4.48466i 0.0724443 + 1.24382i 0.817149 + 0.576426i \(0.195553\pi\)
−0.744705 + 0.667394i \(0.767410\pi\)
\(14\) 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 −0.237800 0.971314i \(-0.576426\pi\)
−0.806514 + 0.591215i \(0.798648\pi\)
\(18\) 0 0
\(19\) 4.19524 1.52694i 0.962455 0.350305i 0.187460 0.982272i \(-0.439975\pi\)
0.774995 + 0.631967i \(0.217752\pi\)
\(20\) 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 0.466066 0.884750i \(-0.345671\pi\)
0.249466 + 0.968384i \(0.419745\pi\)
\(24\) 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 −0.393798 0.919197i \(-0.628839\pi\)
0.502149 + 0.864781i \(0.332543\pi\)
\(30\) 0 0
\(31\) 0.393020 0.527918i 0.0705886 0.0948169i −0.765427 0.643523i \(-0.777472\pi\)
0.836015 + 0.548706i \(0.184879\pi\)
\(32\) −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 −0.577633 0.816296i \(-0.696024\pi\)
0.703590 + 0.710606i \(0.251579\pi\)
\(38\) 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 −0.504180 0.863598i \(-0.668205\pi\)
0.593274 + 0.805000i \(0.297835\pi\)
\(42\) 0 0
\(43\) 8.16684 + 1.93558i 1.24543 + 0.295173i 0.799922 0.600104i \(-0.204874\pi\)
0.445510 + 0.895277i \(0.353022\pi\)
\(44\) −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 0.999740 0.0228150i \(-0.00726288\pi\)
−0.308585 + 0.951197i \(0.599855\pi\)
\(48\) 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 0.687624 0.726067i \(-0.258654\pi\)
−0.972605 + 0.232466i \(0.925321\pi\)
\(54\) 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 0.801471 + 0.598034i \(0.204051\pi\)
−0.998244 + 0.0592349i \(0.981134\pi\)
\(60\) 0 0
\(61\) −2.68977 + 6.23558i −0.344389 + 0.798384i 0.654707 + 0.755883i \(0.272792\pi\)
−0.999096 + 0.0425013i \(0.986467\pi\)
\(62\) 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 0.713995 0.700151i \(-0.246884\pi\)
−0.135239 + 0.990813i \(0.543180\pi\)
\(68\) 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 −0.980471 0.196662i \(-0.936990\pi\)
0.854079 0.520143i \(-0.174121\pi\)
\(72\) 0 0
\(73\) −0.764322 + 4.33469i −0.0894571 + 0.507337i 0.906848 + 0.421457i \(0.138481\pi\)
−0.996306 + 0.0858796i \(0.972630\pi\)
\(74\) 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 −0.102744 0.994708i \(-0.532762\pi\)
−0.954052 + 0.299643i \(0.903133\pi\)
\(80\) −1.04864 −0.117242
\(81\) 0 0
\(82\) 0.533651 0.0589319
\(83\) −1.35486 0.891108i −0.148716 0.0978119i 0.472971 0.881078i \(-0.343182\pi\)
−0.621686 + 0.783266i \(0.713552\pi\)
\(84\) 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 −0.992900 0.118952i \(-0.962046\pi\)
0.973705 + 0.227813i \(0.0731576\pi\)
\(90\) 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 −0.877445 0.479677i \(-0.840754\pi\)
0.529885 + 0.848070i \(0.322235\pi\)
\(98\) 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 0.618854 + 0.785506i \(0.287597\pi\)
−0.996040 + 0.0889095i \(0.971662\pi\)
\(102\) 0 0
\(103\) −0.933584 + 3.11839i −0.0919888 + 0.307264i −0.991585 0.129459i \(-0.958676\pi\)
0.899596 + 0.436723i \(0.143861\pi\)
\(104\) 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 0.0982402 + 0.995163i \(0.468679\pi\)
−0.910956 + 0.412503i \(0.864655\pi\)
\(108\) 0 0
\(109\) −3.81772 6.61249i −0.365671 0.633361i 0.623212 0.782053i \(-0.285827\pi\)
−0.988884 + 0.148691i \(0.952494\pi\)
\(110\) 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 −0.661969 0.749531i \(-0.730279\pi\)
−0.255168 + 0.966897i \(0.582131\pi\)
\(114\) 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 0.765230 0.643757i \(-0.222625\pi\)
−0.501096 + 0.865392i \(0.667070\pi\)
\(128\) 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 0.116165 + 0.993230i \(0.462940\pi\)
−0.984820 + 0.173577i \(0.944467\pi\)
\(132\) 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 0.893551 + 0.448961i \(0.148206\pi\)
−0.939631 + 0.342190i \(0.888831\pi\)
\(138\) 0 0
\(139\) −15.8135 1.84833i −1.34128 0.156774i −0.585009 0.811027i \(-0.698909\pi\)
−0.756275 + 0.654253i \(0.772983\pi\)
\(140\) 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 −0.348085 0.937463i \(-0.613168\pi\)
0.236899 0.971534i \(-0.423869\pi\)
\(150\) 0 0
\(151\) 0.668852 + 2.23412i 0.0544304 + 0.181810i 0.980882 0.194604i \(-0.0623422\pi\)
−0.926452 + 0.376414i \(0.877157\pi\)
\(152\) −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 0.989199 + 0.146579i \(0.0468263\pi\)
0.0888142 + 0.996048i \(0.471692\pi\)
\(158\) −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 0.631076 0.775721i \(-0.282614\pi\)
−0.811102 + 0.584904i \(0.801132\pi\)
\(168\) 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 0.878201 + 0.478291i \(0.158744\pi\)
−0.470901 + 0.882186i \(0.656071\pi\)
\(174\) 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 −0.110927 0.993829i \(-0.535382\pi\)
−0.723796 + 0.690014i \(0.757604\pi\)
\(180\) 0 0
\(181\) 14.8329 5.39873i 1.10252 0.401284i 0.274275 0.961651i \(-0.411562\pi\)
0.828244 + 0.560367i \(0.189340\pi\)
\(182\) −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 −0.252486 0.967601i \(-0.581248\pi\)
0.625361 + 0.780336i \(0.284952\pi\)
\(192\) 0 0
\(193\) 0.104955 0.140979i 0.00755483 0.0101479i −0.798330 0.602221i \(-0.794283\pi\)
0.805885 + 0.592073i \(0.201690\pi\)
\(194\) −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 0.895316 0.445431i \(-0.146950\pi\)
−0.283194 + 0.959063i \(0.591394\pi\)
\(198\) 0 0
\(199\) −15.6873 + 13.1632i −1.11204 + 0.933114i −0.998175 0.0603824i \(-0.980768\pi\)
−0.113866 + 0.993496i \(0.536324\pi\)
\(200\) −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 −0.190518 0.981684i \(-0.561017\pi\)
0.270326 + 0.962769i \(0.412869\pi\)
\(212\) −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 0.598190 + 0.801354i \(0.295887\pi\)
−0.993387 + 0.114815i \(0.963373\pi\)
\(224\) −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 0.140095 0.990138i \(-0.455259\pi\)
0.980317 0.197430i \(-0.0632594\pi\)
\(228\) 0 0
\(229\) 1.36456 + 0.685307i 0.0901726 + 0.0452864i 0.493314 0.869851i \(-0.335785\pi\)
−0.403141 + 0.915138i \(0.632082\pi\)
\(230\) 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 0.954123 + 0.299414i \(0.0967912\pi\)
−0.794177 + 0.607687i \(0.792098\pi\)
\(234\) 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 −0.909958 0.414701i \(-0.863886\pi\)
0.322809 0.946464i \(-0.395373\pi\)
\(240\) 0 0
\(241\) 5.90585 + 3.88434i 0.380429 + 0.250212i 0.725293 0.688441i \(-0.241704\pi\)
−0.344864 + 0.938653i \(0.612075\pi\)
\(242\) −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 −0.984441 0.175714i \(-0.943777\pi\)
0.985170 + 0.171582i \(0.0548878\pi\)
\(252\) 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 0.897060 0.441909i \(-0.145699\pi\)
0.181221 + 0.983442i \(0.441995\pi\)
\(258\) 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 −0.629324 0.777143i \(-0.716668\pi\)
0.997142 0.0755547i \(-0.0240727\pi\)
\(264\) 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 −0.629799 0.776758i \(-0.716863\pi\)
0.987592 + 0.157043i \(0.0501962\pi\)
\(270\) 0 0
\(271\) 1.44013 + 2.49438i 0.0874817 + 0.151523i 0.906446 0.422322i \(-0.138785\pi\)
−0.818964 + 0.573844i \(0.805451\pi\)
\(272\) 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 0.758924 0.651179i \(-0.225725\pi\)
−0.841485 + 0.540281i \(0.818318\pi\)
\(278\) −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 0.410616 0.911808i \(-0.365314\pi\)
−0.0422786 + 0.999106i \(0.513462\pi\)
\(282\) 0 0
\(283\) 12.2665 8.06777i 0.729165 0.479579i −0.129848 0.991534i \(-0.541449\pi\)
0.859012 + 0.511955i \(0.171078\pi\)
\(284\) −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 0.0966764 + 0.995316i \(0.469179\pi\)
−0.981229 + 0.192845i \(0.938229\pi\)
\(294\) 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 0.647386 0.762162i \(-0.275862\pi\)
0.00601852 + 0.999982i \(0.498084\pi\)
\(308\) −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 0.741764 + 0.670661i \(0.233989\pi\)
−0.658890 + 0.752239i \(0.728974\pi\)
\(312\) 0 0
\(313\) −8.47873 28.3209i −0.479246 1.60079i −0.766034 0.642800i \(-0.777773\pi\)
0.286787 0.957994i \(-0.407413\pi\)
\(314\) 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 −0.234856 0.972030i \(-0.575462\pi\)
−0.00436034 + 0.999990i \(0.501388\pi\)
\(318\) 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 0.684918 0.728620i \(-0.259838\pi\)
0.834487 + 0.551027i \(0.185764\pi\)
\(332\) −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 −0.721988 0.691905i \(-0.756772\pi\)
0.636781 0.771045i \(-0.280266\pi\)
\(338\) −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 0.879769 0.475402i \(-0.157697\pi\)
0.746419 + 0.665476i \(0.231771\pi\)
\(348\) 0 0
\(349\) 0.463724 7.96184i 0.0248226 0.426187i −0.962889 0.269898i \(-0.913010\pi\)
0.987711 0.156289i \(-0.0499531\pi\)
\(350\) 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 −0.884452 0.466631i \(-0.845468\pi\)
−0.153863 + 0.988092i \(0.549171\pi\)
\(354\) 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 0.221869 0.975076i \(-0.428784\pi\)
−0.921736 + 0.387819i \(0.873229\pi\)
\(360\) 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 −0.426926 0.904287i \(-0.640403\pi\)
−0.787358 + 0.616496i \(0.788552\pi\)
\(368\) −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 −0.510576 0.859832i \(-0.670568\pi\)
−0.0703757 + 0.997521i \(0.522420\pi\)
\(374\) −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 0.466839 + 0.884342i \(0.345393\pi\)
−0.999282 + 0.0378763i \(0.987941\pi\)
\(380\) 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 −0.759693 0.650282i \(-0.774651\pi\)
0.992050 0.125845i \(-0.0401640\pi\)
\(384\) 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 −0.00673888 0.999977i \(-0.502145\pi\)
0.998677 0.0514160i \(-0.0163734\pi\)
\(390\) 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 −0.461538 0.887120i \(-0.652702\pi\)
0.737117 0.675765i \(-0.236187\pi\)
\(398\) −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 0.999474 + 0.0324445i \(0.0103292\pi\)
−0.662281 + 0.749255i \(0.730412\pi\)
\(402\) 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 −0.975241 0.221143i \(-0.929021\pi\)
0.508397 0.861123i \(-0.330238\pi\)
\(410\) 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 0.0708230 0.997489i \(-0.477437\pi\)
−0.757816 + 0.652468i \(0.773734\pi\)
\(420\) 0 0
\(421\) 16.1664 17.1354i 0.787901 0.835126i −0.201628 0.979462i \(-0.564623\pi\)
0.989529 + 0.144336i \(0.0461046\pi\)
\(422\) 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 −0.848525 0.529155i \(-0.822509\pi\)
0.882524 + 0.470267i \(0.155842\pi\)
\(432\) 0 0
\(433\) −6.50524 11.2674i −0.312622 0.541477i 0.666307 0.745677i \(-0.267874\pi\)
−0.978929 + 0.204200i \(0.934541\pi\)
\(434\) 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 0.992538 0.121936i \(-0.0389103\pi\)
−0.401477 + 0.915869i \(0.631503\pi\)
\(440\) −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 0.921386 0.388649i \(-0.127058\pi\)
0.648955 + 0.760826i \(0.275206\pi\)
\(444\) 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 −0.620828 0.783947i \(-0.713203\pi\)
0.664231 + 0.747527i \(0.268759\pi\)
\(450\) 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 −0.966959 0.254932i \(-0.917947\pi\)
−0.372941 + 0.927855i \(0.621651\pi\)
\(458\) 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 −0.998733 0.0503158i \(-0.983977\pi\)
0.997822 + 0.0659703i \(0.0210143\pi\)
\(462\) 0 0
\(463\) 2.93276 + 0.342791i 0.136297 + 0.0159308i 0.183968 0.982932i \(-0.441106\pi\)
−0.0476708 + 0.998863i \(0.515180\pi\)
\(464\) −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 −0.422984 0.906137i \(-0.639017\pi\)
0.258429 + 0.966030i \(0.416795\pi\)
\(468\) 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 −0.0439314 0.999035i \(-0.513988\pi\)
0.187646 + 0.982237i \(0.439914\pi\)
\(480\) 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 0.921425 + 0.388556i \(0.127026\pi\)
0.334323 + 0.942459i \(0.391493\pi\)
\(492\) 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 0.442224 + 0.896905i \(0.354190\pi\)
−0.335109 + 0.942179i \(0.608773\pi\)
\(500\) −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 0.545858 0.837878i \(-0.316204\pi\)
−0.120426 + 0.992722i \(0.538426\pi\)
\(504\) 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 −0.435829 0.900029i \(-0.643545\pi\)
−0.631642 + 0.775260i \(0.717619\pi\)
\(510\) 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 0.529973 0.848014i \(-0.322202\pi\)
−0.743102 + 0.669178i \(0.766646\pi\)
\(522\) 0 0
\(523\) 21.5335 18.0688i 0.941595 0.790092i −0.0362674 0.999342i \(-0.511547\pi\)
0.977862 + 0.209250i \(0.0671024\pi\)
\(524\) 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 −0.893468 0.449127i \(-0.851735\pi\)
0.835689 + 0.549203i \(0.185068\pi\)
\(542\) −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 −0.376699 0.926336i \(-0.622941\pi\)
0.932299 0.361689i \(-0.117800\pi\)
\(548\) 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 0.999324 + 0.0367591i \(0.0117034\pi\)
−0.926485 + 0.376331i \(0.877185\pi\)
\(558\) 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 0.849348 0.527833i \(-0.176995\pi\)
−0.966790 + 0.255572i \(0.917736\pi\)
\(564\) 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 0.478666 0.877997i \(-0.341120\pi\)
−0.616601 + 0.787276i \(0.711491\pi\)
\(570\) 0 0
\(571\) 10.1268 + 23.4765i 0.423791 + 0.982459i 0.987663 + 0.156596i \(0.0500521\pi\)
−0.563871 + 0.825863i \(0.690689\pi\)
\(572\) −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 0.997071 0.0764818i \(-0.0243687\pi\)
−0.963099 + 0.269149i \(0.913258\pi\)
\(578\) 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 −0.525410 0.850849i \(-0.676088\pi\)
0.979443 0.201719i \(-0.0646528\pi\)
\(588\) 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 −0.680533 0.732717i \(-0.738252\pi\)
0.974818 + 0.223000i \(0.0715851\pi\)
\(594\) 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 0.355957 0.934502i \(-0.384155\pi\)
0.737499 + 0.675349i \(0.236007\pi\)
\(600\) 0 0
\(601\) 11.1968 + 15.0400i 0.456729 + 0.613493i 0.969518 0.245022i \(-0.0787951\pi\)
−0.512789 + 0.858515i \(0.671388\pi\)
\(602\) 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 −0.911701 0.410853i \(-0.865231\pi\)
0.0161458 + 0.999870i \(0.494860\pi\)
\(608\) −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 −0.0856560 0.996325i \(-0.527299\pi\)
−0.996062 + 0.0886553i \(0.971743\pi\)
\(614\) 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 −0.879731 0.475471i \(-0.842278\pi\)
0.707806 + 0.706407i \(0.249685\pi\)
\(618\) 0 0
\(619\) −16.8196 + 8.44712i −0.676037 + 0.339518i −0.753473 0.657479i \(-0.771623\pi\)
0.0774361 + 0.996997i \(0.475327\pi\)
\(620\) −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 −0.136813 0.990597i \(-0.543686\pi\)
−0.741548 + 0.670900i \(0.765908\pi\)
\(632\) −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 −0.0301588 0.999545i \(-0.509601\pi\)
0.201165 + 0.979557i \(0.435527\pi\)
\(642\) 0 0
\(643\) −13.0468 13.8288i −0.514516 0.545355i 0.417071 0.908874i \(-0.363057\pi\)
−0.931587 + 0.363519i \(0.881575\pi\)
\(644\) −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 0.641919 0.766772i \(-0.278138\pi\)
−0.802799 + 0.596249i \(0.796657\pi\)
\(654\) 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 0.843506 + 0.537120i \(0.180488\pi\)
−0.409587 + 0.912271i \(0.634327\pi\)
\(660\) 0 0
\(661\) −1.80224 30.9432i −0.0700989 1.20355i −0.831595 0.555382i \(-0.812572\pi\)
0.761496 0.648169i \(-0.224465\pi\)
\(662\) 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 −0.624070 0.781368i \(-0.714522\pi\)
0.710562 0.703635i \(-0.248441\pi\)
\(674\) 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 −0.378983 0.925404i \(-0.623726\pi\)
0.515975 + 0.856604i \(0.327430\pi\)
\(678\) 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 0.997935 + 0.0642370i \(0.0204614\pi\)
0.236551 + 0.971619i \(0.423983\pi\)
\(684\) 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 0.0692889 0.997597i \(-0.477927\pi\)
−0.385802 + 0.922582i \(0.626075\pi\)
\(692\) 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 0.857578 0.514355i \(-0.171968\pi\)
−0.874233 + 0.485507i \(0.838635\pi\)
\(702\) 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 0.302324 + 0.953205i \(0.402238\pi\)
−0.900803 + 0.434227i \(0.857022\pi\)
\(710\) 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 −0.996374 0.0850815i \(-0.972885\pi\)
0.907186 0.420730i \(-0.138226\pi\)
\(720\) 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 0.728011 0.685566i \(-0.240445\pi\)
−0.341147 + 0.940010i \(0.610815\pi\)
\(728\) 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 −0.993726 0.111839i \(-0.964326\pi\)
0.600587 0.799559i \(-0.294933\pi\)
\(734\) −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 −0.958106 0.286415i \(-0.907536\pi\)
0.802365 0.596833i \(-0.203575\pi\)
\(740\) −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 −0.254743 0.967009i \(-0.581991\pi\)
−0.927782 + 0.373122i \(0.878287\pi\)
\(744\) 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 −0.944893 0.327380i \(-0.893834\pi\)
0.969345 + 0.245705i \(0.0790194\pi\)
\(752\) −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 0.974730 0.223386i \(-0.0717109\pi\)
−0.680823 + 0.732448i \(0.738378\pi\)
\(758\) −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 −0.931234 0.364421i \(-0.881267\pi\)
−0.668630 + 0.743595i \(0.733119\pi\)
\(762\) 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 −0.795173 0.606383i \(-0.792620\pi\)
0.241839 + 0.970316i \(0.422250\pi\)
\(770\) 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 −0.138915 0.990304i \(-0.544361\pi\)
0.951137 + 0.308769i \(0.0999169\pi\)
\(774\) 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