Properties

Label 567.2.w.a.37.19
Level $567$
Weight $2$
Character 567.37
Analytic conductor $4.528$
Analytic rank $0$
Dimension $132$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [567,2,Mod(37,567)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(567, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([14, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("567.37");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 567 = 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 567.w (of order \(9\), degree \(6\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.52751779461\)
Analytic rank: \(0\)
Dimension: \(132\)
Relative dimension: \(22\) over \(\Q(\zeta_{9})\)
Twist minimal: no (minimal twist has level 189)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 37.19
Character \(\chi\) \(=\) 567.37
Dual form 567.2.w.a.46.19

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.345866 + 1.96151i) q^{2} +(-1.84850 + 0.672798i) q^{4} +(-0.424474 + 2.40731i) q^{5} +(2.63001 + 0.288173i) q^{7} +(0.0327363 + 0.0567010i) q^{8} +O(q^{10})\) \(q+(0.345866 + 1.96151i) q^{2} +(-1.84850 + 0.672798i) q^{4} +(-0.424474 + 2.40731i) q^{5} +(2.63001 + 0.288173i) q^{7} +(0.0327363 + 0.0567010i) q^{8} -4.86876 q^{10} +(-0.315676 - 1.79029i) q^{11} +(3.42377 + 2.87288i) q^{13} +(0.344379 + 5.25845i) q^{14} +(-3.11371 + 2.61271i) q^{16} -1.57135 q^{17} -3.38132 q^{19} +(-0.834994 - 4.73549i) q^{20} +(3.40248 - 1.23840i) q^{22} +(-0.757936 - 0.635984i) q^{23} +(-0.916503 - 0.333580i) q^{25} +(-4.45101 + 7.70937i) q^{26} +(-5.05545 + 1.23678i) q^{28} +(0.421937 - 0.354047i) q^{29} +(4.15707 - 1.51305i) q^{31} +(-6.10147 - 5.11974i) q^{32} +(-0.543477 - 3.08221i) q^{34} +(-1.81009 + 6.20893i) q^{35} +(-5.35942 - 9.28278i) q^{37} +(-1.16948 - 6.63247i) q^{38} +(-0.150393 + 0.0547385i) q^{40} +(4.76040 + 3.99445i) q^{41} +(-7.65301 - 2.78547i) q^{43} +(1.78803 + 3.09695i) q^{44} +(0.985341 - 1.70666i) q^{46} +(-9.10892 - 3.31537i) q^{47} +(6.83391 + 1.51580i) q^{49} +(0.337331 - 1.91310i) q^{50} +(-8.26169 - 3.00701i) q^{52} +(3.29952 + 5.71493i) q^{53} +4.44377 q^{55} +(0.0697572 + 0.158558i) q^{56} +(0.840399 + 0.705179i) q^{58} +(-0.320720 - 0.269116i) q^{59} +(13.2522 + 4.82341i) q^{61} +(4.40565 + 7.63081i) q^{62} +(3.86745 - 6.69862i) q^{64} +(-8.36922 + 7.02261i) q^{65} +(-2.62814 + 14.9049i) q^{67} +(2.90464 - 1.05720i) q^{68} +(-12.8049 - 1.40305i) q^{70} +(6.86573 - 11.8918i) q^{71} +(0.764596 - 1.32432i) q^{73} +(16.3546 - 13.7231i) q^{74} +(6.25035 - 2.27494i) q^{76} +(-0.314318 - 4.79944i) q^{77} +(-1.51289 - 8.58003i) q^{79} +(-4.96793 - 8.60470i) q^{80} +(-6.18867 + 10.7191i) q^{82} +(9.94030 - 8.34090i) q^{83} +(0.666997 - 3.78273i) q^{85} +(2.81679 - 15.9748i) q^{86} +(0.0911770 - 0.0765066i) q^{88} +8.50607 q^{89} +(8.17666 + 8.54235i) q^{91} +(1.82893 + 0.665676i) q^{92} +(3.35266 - 19.0139i) q^{94} +(1.43528 - 8.13988i) q^{95} +(13.9735 + 5.08592i) q^{97} +(-0.609626 + 13.9290i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 132 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 6 q^{7} + 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 132 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 6 q^{7} + 6 q^{8} - 6 q^{10} - 3 q^{11} - 12 q^{13} - 15 q^{14} - 9 q^{16} + 54 q^{17} - 6 q^{19} + 18 q^{20} - 12 q^{22} - 3 q^{25} - 30 q^{26} - 12 q^{28} + 30 q^{29} - 3 q^{31} - 51 q^{32} - 18 q^{34} + 12 q^{35} + 3 q^{37} + 57 q^{38} - 66 q^{40} - 12 q^{43} - 3 q^{44} + 3 q^{46} + 21 q^{47} + 12 q^{49} + 39 q^{50} + 9 q^{52} - 9 q^{53} - 24 q^{55} - 57 q^{56} - 3 q^{58} + 18 q^{59} + 33 q^{61} - 75 q^{62} - 30 q^{64} - 81 q^{65} - 3 q^{67} - 6 q^{68} - 42 q^{70} + 18 q^{71} + 21 q^{73} + 93 q^{74} - 24 q^{76} - 87 q^{77} + 15 q^{79} - 102 q^{80} - 6 q^{82} + 42 q^{83} - 63 q^{85} - 159 q^{86} + 57 q^{88} + 150 q^{89} + 6 q^{91} + 66 q^{92} + 33 q^{94} + 147 q^{95} - 12 q^{97} - 99 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/567\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(407\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{9}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.345866 + 1.96151i 0.244564 + 1.38699i 0.821502 + 0.570206i \(0.193137\pi\)
−0.576937 + 0.816788i \(0.695752\pi\)
\(3\) 0 0
\(4\) −1.84850 + 0.672798i −0.924248 + 0.336399i
\(5\) −0.424474 + 2.40731i −0.189830 + 1.07658i 0.729760 + 0.683703i \(0.239632\pi\)
−0.919590 + 0.392879i \(0.871479\pi\)
\(6\) 0 0
\(7\) 2.63001 + 0.288173i 0.994051 + 0.108919i
\(8\) 0.0327363 + 0.0567010i 0.0115740 + 0.0200468i
\(9\) 0 0
\(10\) −4.86876 −1.53964
\(11\) −0.315676 1.79029i −0.0951799 0.539792i −0.994692 0.102896i \(-0.967189\pi\)
0.899512 0.436896i \(-0.143922\pi\)
\(12\) 0 0
\(13\) 3.42377 + 2.87288i 0.949582 + 0.796794i 0.979227 0.202766i \(-0.0649932\pi\)
−0.0296447 + 0.999560i \(0.509438\pi\)
\(14\) 0.344379 + 5.25845i 0.0920390 + 1.40538i
\(15\) 0 0
\(16\) −3.11371 + 2.61271i −0.778428 + 0.653179i
\(17\) −1.57135 −0.381109 −0.190554 0.981677i \(-0.561029\pi\)
−0.190554 + 0.981677i \(0.561029\pi\)
\(18\) 0 0
\(19\) −3.38132 −0.775727 −0.387864 0.921717i \(-0.626787\pi\)
−0.387864 + 0.921717i \(0.626787\pi\)
\(20\) −0.834994 4.73549i −0.186710 1.05889i
\(21\) 0 0
\(22\) 3.40248 1.23840i 0.725411 0.264028i
\(23\) −0.757936 0.635984i −0.158041 0.132612i 0.560338 0.828264i \(-0.310671\pi\)
−0.718379 + 0.695652i \(0.755116\pi\)
\(24\) 0 0
\(25\) −0.916503 0.333580i −0.183301 0.0667159i
\(26\) −4.45101 + 7.70937i −0.872915 + 1.51193i
\(27\) 0 0
\(28\) −5.05545 + 1.23678i −0.955390 + 0.233729i
\(29\) 0.421937 0.354047i 0.0783517 0.0657449i −0.602771 0.797914i \(-0.705937\pi\)
0.681122 + 0.732170i \(0.261492\pi\)
\(30\) 0 0
\(31\) 4.15707 1.51305i 0.746632 0.271752i 0.0594442 0.998232i \(-0.481067\pi\)
0.687188 + 0.726480i \(0.258845\pi\)
\(32\) −6.10147 5.11974i −1.07860 0.905051i
\(33\) 0 0
\(34\) −0.543477 3.08221i −0.0932056 0.528595i
\(35\) −1.81009 + 6.20893i −0.305962 + 1.04950i
\(36\) 0 0
\(37\) −5.35942 9.28278i −0.881083 1.52608i −0.850139 0.526559i \(-0.823482\pi\)
−0.0309438 0.999521i \(-0.509851\pi\)
\(38\) −1.16948 6.63247i −0.189715 1.07593i
\(39\) 0 0
\(40\) −0.150393 + 0.0547385i −0.0237792 + 0.00865491i
\(41\) 4.76040 + 3.99445i 0.743449 + 0.623828i 0.933762 0.357896i \(-0.116506\pi\)
−0.190312 + 0.981724i \(0.560950\pi\)
\(42\) 0 0
\(43\) −7.65301 2.78547i −1.16707 0.424780i −0.315454 0.948941i \(-0.602157\pi\)
−0.851619 + 0.524161i \(0.824379\pi\)
\(44\) 1.78803 + 3.09695i 0.269555 + 0.466883i
\(45\) 0 0
\(46\) 0.985341 1.70666i 0.145281 0.251633i
\(47\) −9.10892 3.31537i −1.32867 0.483597i −0.422445 0.906388i \(-0.638828\pi\)
−0.906227 + 0.422791i \(0.861050\pi\)
\(48\) 0 0
\(49\) 6.83391 + 1.51580i 0.976273 + 0.216543i
\(50\) 0.337331 1.91310i 0.0477058 0.270553i
\(51\) 0 0
\(52\) −8.26169 3.00701i −1.14569 0.416997i
\(53\) 3.29952 + 5.71493i 0.453223 + 0.785006i 0.998584 0.0531954i \(-0.0169406\pi\)
−0.545361 + 0.838202i \(0.683607\pi\)
\(54\) 0 0
\(55\) 4.44377 0.599198
\(56\) 0.0697572 + 0.158558i 0.00932170 + 0.0211882i
\(57\) 0 0
\(58\) 0.840399 + 0.705179i 0.110350 + 0.0925945i
\(59\) −0.320720 0.269116i −0.0417541 0.0350359i 0.621672 0.783278i \(-0.286454\pi\)
−0.663426 + 0.748242i \(0.730898\pi\)
\(60\) 0 0
\(61\) 13.2522 + 4.82341i 1.69677 + 0.617574i 0.995451 0.0952720i \(-0.0303721\pi\)
0.701320 + 0.712846i \(0.252594\pi\)
\(62\) 4.40565 + 7.63081i 0.559518 + 0.969113i
\(63\) 0 0
\(64\) 3.86745 6.69862i 0.483431 0.837328i
\(65\) −8.36922 + 7.02261i −1.03807 + 0.871048i
\(66\) 0 0
\(67\) −2.62814 + 14.9049i −0.321078 + 1.82092i 0.214835 + 0.976650i \(0.431079\pi\)
−0.535913 + 0.844273i \(0.680033\pi\)
\(68\) 2.90464 1.05720i 0.352239 0.128204i
\(69\) 0 0
\(70\) −12.8049 1.40305i −1.53048 0.167696i
\(71\) 6.86573 11.8918i 0.814812 1.41130i −0.0946510 0.995511i \(-0.530174\pi\)
0.909463 0.415785i \(-0.136493\pi\)
\(72\) 0 0
\(73\) 0.764596 1.32432i 0.0894892 0.155000i −0.817806 0.575494i \(-0.804810\pi\)
0.907295 + 0.420494i \(0.138143\pi\)
\(74\) 16.3546 13.7231i 1.90118 1.59528i
\(75\) 0 0
\(76\) 6.25035 2.27494i 0.716965 0.260954i
\(77\) −0.314318 4.79944i −0.0358199 0.546947i
\(78\) 0 0
\(79\) −1.51289 8.58003i −0.170213 0.965329i −0.943525 0.331302i \(-0.892512\pi\)
0.773311 0.634027i \(-0.218599\pi\)
\(80\) −4.96793 8.60470i −0.555431 0.962035i
\(81\) 0 0
\(82\) −6.18867 + 10.7191i −0.683425 + 1.18373i
\(83\) 9.94030 8.34090i 1.09109 0.915533i 0.0942960 0.995544i \(-0.469940\pi\)
0.996794 + 0.0800110i \(0.0254956\pi\)
\(84\) 0 0
\(85\) 0.666997 3.78273i 0.0723460 0.410295i
\(86\) 2.81679 15.9748i 0.303742 1.72261i
\(87\) 0 0
\(88\) 0.0911770 0.0765066i 0.00971950 0.00815563i
\(89\) 8.50607 0.901642 0.450821 0.892614i \(-0.351131\pi\)
0.450821 + 0.892614i \(0.351131\pi\)
\(90\) 0 0
\(91\) 8.17666 + 8.54235i 0.857147 + 0.895482i
\(92\) 1.82893 + 0.665676i 0.190679 + 0.0694015i
\(93\) 0 0
\(94\) 3.35266 19.0139i 0.345800 1.96113i
\(95\) 1.43528 8.13988i 0.147257 0.835134i
\(96\) 0 0
\(97\) 13.9735 + 5.08592i 1.41879 + 0.516397i 0.933696 0.358066i \(-0.116564\pi\)
0.485093 + 0.874463i \(0.338786\pi\)
\(98\) −0.609626 + 13.9290i −0.0615816 + 1.40704i
\(99\) 0 0
\(100\) 1.91858 0.191858
\(101\) −6.20929 + 5.21021i −0.617848 + 0.518436i −0.897126 0.441774i \(-0.854349\pi\)
0.279279 + 0.960210i \(0.409905\pi\)
\(102\) 0 0
\(103\) −1.58169 + 8.97019i −0.155848 + 0.883859i 0.802158 + 0.597112i \(0.203685\pi\)
−0.958006 + 0.286747i \(0.907426\pi\)
\(104\) −0.0508137 + 0.288179i −0.00498269 + 0.0282583i
\(105\) 0 0
\(106\) −10.0687 + 8.44862i −0.977956 + 0.820603i
\(107\) 5.11175 8.85382i 0.494172 0.855931i −0.505806 0.862648i \(-0.668805\pi\)
0.999977 + 0.00671665i \(0.00213799\pi\)
\(108\) 0 0
\(109\) −2.81440 4.87468i −0.269570 0.466909i 0.699181 0.714945i \(-0.253548\pi\)
−0.968751 + 0.248036i \(0.920215\pi\)
\(110\) 1.53695 + 8.71649i 0.146543 + 0.831084i
\(111\) 0 0
\(112\) −8.94201 + 5.97418i −0.844941 + 0.564507i
\(113\) 7.10998 2.58782i 0.668851 0.243442i 0.0147979 0.999891i \(-0.495289\pi\)
0.654053 + 0.756449i \(0.273067\pi\)
\(114\) 0 0
\(115\) 1.85273 1.55463i 0.172768 0.144970i
\(116\) −0.541747 + 0.938333i −0.0502999 + 0.0871220i
\(117\) 0 0
\(118\) 0.416946 0.722172i 0.0383830 0.0664813i
\(119\) −4.13267 0.452822i −0.378841 0.0415101i
\(120\) 0 0
\(121\) 7.23114 2.63192i 0.657377 0.239265i
\(122\) −4.87765 + 27.6625i −0.441602 + 2.50445i
\(123\) 0 0
\(124\) −6.66635 + 5.59373i −0.598656 + 0.502332i
\(125\) −4.91906 + 8.52006i −0.439974 + 0.762057i
\(126\) 0 0
\(127\) −0.00921577 0.0159622i −0.000817768 0.00141642i 0.865616 0.500708i \(-0.166927\pi\)
−0.866434 + 0.499292i \(0.833594\pi\)
\(128\) −0.492127 0.179120i −0.0434983 0.0158321i
\(129\) 0 0
\(130\) −16.6695 13.9874i −1.46201 1.22678i
\(131\) 13.4190 + 11.2599i 1.17242 + 0.983781i 0.999999 0.00124189i \(-0.000395307\pi\)
0.172425 + 0.985023i \(0.444840\pi\)
\(132\) 0 0
\(133\) −8.89290 0.974406i −0.771112 0.0844917i
\(134\) −30.1450 −2.60413
\(135\) 0 0
\(136\) −0.0514403 0.0890972i −0.00441097 0.00764002i
\(137\) −12.8777 4.68711i −1.10022 0.400446i −0.272821 0.962065i \(-0.587957\pi\)
−0.827396 + 0.561618i \(0.810179\pi\)
\(138\) 0 0
\(139\) 0.384140 2.17857i 0.0325823 0.184784i −0.964173 0.265274i \(-0.914538\pi\)
0.996755 + 0.0804905i \(0.0256487\pi\)
\(140\) −0.831402 12.6950i −0.0702663 1.07292i
\(141\) 0 0
\(142\) 25.7004 + 9.35419i 2.15673 + 0.784986i
\(143\) 4.06248 7.03643i 0.339722 0.588416i
\(144\) 0 0
\(145\) 0.673200 + 1.16602i 0.0559062 + 0.0968324i
\(146\) 2.86211 + 1.04172i 0.236870 + 0.0862135i
\(147\) 0 0
\(148\) 16.1523 + 13.5534i 1.32771 + 1.11408i
\(149\) 2.01370 0.732927i 0.164969 0.0600437i −0.258216 0.966087i \(-0.583135\pi\)
0.423184 + 0.906044i \(0.360912\pi\)
\(150\) 0 0
\(151\) 2.40128 + 13.6183i 0.195413 + 1.10824i 0.911829 + 0.410570i \(0.134670\pi\)
−0.716415 + 0.697674i \(0.754218\pi\)
\(152\) −0.110692 0.191724i −0.00897831 0.0155509i
\(153\) 0 0
\(154\) 9.30542 2.27650i 0.749852 0.183446i
\(155\) 1.87781 + 10.6496i 0.150830 + 0.855397i
\(156\) 0 0
\(157\) −0.997555 0.837048i −0.0796136 0.0668037i 0.602112 0.798411i \(-0.294326\pi\)
−0.681726 + 0.731608i \(0.738770\pi\)
\(158\) 16.3065 5.93509i 1.29728 0.472170i
\(159\) 0 0
\(160\) 14.9147 12.5149i 1.17911 0.989393i
\(161\) −1.81011 1.89106i −0.142656 0.149036i
\(162\) 0 0
\(163\) 7.88495 13.6571i 0.617597 1.06971i −0.372326 0.928102i \(-0.621440\pi\)
0.989923 0.141607i \(-0.0452270\pi\)
\(164\) −11.4870 4.18094i −0.896987 0.326476i
\(165\) 0 0
\(166\) 19.7987 + 16.6131i 1.53668 + 1.28943i
\(167\) −9.41406 + 3.42644i −0.728482 + 0.265146i −0.679522 0.733655i \(-0.737813\pi\)
−0.0489600 + 0.998801i \(0.515591\pi\)
\(168\) 0 0
\(169\) 1.21131 + 6.86967i 0.0931775 + 0.528436i
\(170\) 7.65054 0.586769
\(171\) 0 0
\(172\) 16.0206 1.22156
\(173\) 2.60037 2.18197i 0.197702 0.165892i −0.538562 0.842586i \(-0.681032\pi\)
0.736265 + 0.676694i \(0.236588\pi\)
\(174\) 0 0
\(175\) −2.31428 1.14143i −0.174943 0.0862840i
\(176\) 5.66043 + 4.74967i 0.426671 + 0.358020i
\(177\) 0 0
\(178\) 2.94197 + 16.6847i 0.220510 + 1.25057i
\(179\) −9.18650 −0.686631 −0.343316 0.939220i \(-0.611550\pi\)
−0.343316 + 0.939220i \(0.611550\pi\)
\(180\) 0 0
\(181\) −9.24118 16.0062i −0.686891 1.18973i −0.972838 0.231485i \(-0.925642\pi\)
0.285947 0.958245i \(-0.407692\pi\)
\(182\) −13.9278 + 18.9931i −1.03240 + 1.40786i
\(183\) 0 0
\(184\) 0.0112489 0.0637955i 0.000829278 0.00470307i
\(185\) 24.6215 8.96148i 1.81021 0.658861i
\(186\) 0 0
\(187\) 0.496038 + 2.81317i 0.0362739 + 0.205719i
\(188\) 19.0684 1.39070
\(189\) 0 0
\(190\) 16.4628 1.19434
\(191\) −0.774038 4.38979i −0.0560074 0.317634i 0.943914 0.330192i \(-0.107114\pi\)
−0.999921 + 0.0125584i \(0.996002\pi\)
\(192\) 0 0
\(193\) −7.18196 + 2.61402i −0.516969 + 0.188161i −0.587311 0.809362i \(-0.699813\pi\)
0.0703416 + 0.997523i \(0.477591\pi\)
\(194\) −5.14312 + 29.1681i −0.369254 + 2.09414i
\(195\) 0 0
\(196\) −13.6523 + 1.79589i −0.975163 + 0.128278i
\(197\) −8.03194 13.9117i −0.572252 0.991169i −0.996334 0.0855457i \(-0.972737\pi\)
0.424082 0.905624i \(-0.360597\pi\)
\(198\) 0 0
\(199\) −3.81611 −0.270517 −0.135259 0.990810i \(-0.543187\pi\)
−0.135259 + 0.990810i \(0.543187\pi\)
\(200\) −0.0110886 0.0628868i −0.000784086 0.00444677i
\(201\) 0 0
\(202\) −12.3674 10.3775i −0.870171 0.730160i
\(203\) 1.21173 0.809557i 0.0850465 0.0568197i
\(204\) 0 0
\(205\) −11.6365 + 9.76422i −0.812731 + 0.681963i
\(206\) −18.1421 −1.26402
\(207\) 0 0
\(208\) −18.1667 −1.25963
\(209\) 1.06740 + 6.05353i 0.0738336 + 0.418731i
\(210\) 0 0
\(211\) 1.09756 0.399481i 0.0755595 0.0275014i −0.303964 0.952684i \(-0.598310\pi\)
0.379523 + 0.925182i \(0.376088\pi\)
\(212\) −9.94413 8.34412i −0.682966 0.573076i
\(213\) 0 0
\(214\) 19.1348 + 6.96450i 1.30803 + 0.476083i
\(215\) 9.95399 17.2408i 0.678856 1.17581i
\(216\) 0 0
\(217\) 11.3692 2.78138i 0.771789 0.188812i
\(218\) 8.58830 7.20644i 0.581673 0.488082i
\(219\) 0 0
\(220\) −8.21430 + 2.98976i −0.553808 + 0.201570i
\(221\) −5.37994 4.51431i −0.361894 0.303665i
\(222\) 0 0
\(223\) 0.428021 + 2.42743i 0.0286624 + 0.162553i 0.995779 0.0917795i \(-0.0292555\pi\)
−0.967117 + 0.254332i \(0.918144\pi\)
\(224\) −14.5716 15.2233i −0.973604 1.01715i
\(225\) 0 0
\(226\) 7.53513 + 13.0512i 0.501230 + 0.868155i
\(227\) 2.61412 + 14.8254i 0.173505 + 0.983997i 0.939855 + 0.341573i \(0.110960\pi\)
−0.766350 + 0.642423i \(0.777929\pi\)
\(228\) 0 0
\(229\) −16.5114 + 6.00964i −1.09110 + 0.397128i −0.824029 0.566548i \(-0.808278\pi\)
−0.267072 + 0.963677i \(0.586056\pi\)
\(230\) 3.69021 + 3.09646i 0.243325 + 0.204174i
\(231\) 0 0
\(232\) 0.0338875 + 0.0123340i 0.00222482 + 0.000809770i
\(233\) −0.172021 0.297949i −0.0112695 0.0195193i 0.860336 0.509728i \(-0.170254\pi\)
−0.871605 + 0.490209i \(0.836921\pi\)
\(234\) 0 0
\(235\) 11.8476 20.5207i 0.772854 1.33862i
\(236\) 0.773910 + 0.281680i 0.0503772 + 0.0183358i
\(237\) 0 0
\(238\) −0.541140 8.26287i −0.0350769 0.535602i
\(239\) 3.65552 20.7315i 0.236456 1.34101i −0.603069 0.797689i \(-0.706056\pi\)
0.839525 0.543320i \(-0.182833\pi\)
\(240\) 0 0
\(241\) −7.98011 2.90452i −0.514044 0.187097i 0.0719559 0.997408i \(-0.477076\pi\)
−0.586000 + 0.810311i \(0.699298\pi\)
\(242\) 7.66354 + 13.2736i 0.492631 + 0.853261i
\(243\) 0 0
\(244\) −27.7418 −1.77599
\(245\) −6.54981 + 15.8079i −0.418452 + 1.00993i
\(246\) 0 0
\(247\) −11.5768 9.71413i −0.736617 0.618095i
\(248\) 0.221879 + 0.186178i 0.0140893 + 0.0118223i
\(249\) 0 0
\(250\) −18.4135 6.70196i −1.16457 0.423869i
\(251\) −11.9966 20.7787i −0.757219 1.31154i −0.944264 0.329190i \(-0.893224\pi\)
0.187045 0.982351i \(-0.440109\pi\)
\(252\) 0 0
\(253\) −0.899331 + 1.55769i −0.0565405 + 0.0979310i
\(254\) 0.0281225 0.0235976i 0.00176456 0.00148064i
\(255\) 0 0
\(256\) 2.86744 16.2620i 0.179215 1.01638i
\(257\) −12.7493 + 4.64035i −0.795276 + 0.289457i −0.707528 0.706686i \(-0.750189\pi\)
−0.0877488 + 0.996143i \(0.527967\pi\)
\(258\) 0 0
\(259\) −11.4203 25.9583i −0.709621 1.61297i
\(260\) 10.7457 18.6121i 0.666419 1.15427i
\(261\) 0 0
\(262\) −17.4451 + 30.2159i −1.07776 + 1.86674i
\(263\) 17.1738 14.4106i 1.05898 0.888593i 0.0649741 0.997887i \(-0.479304\pi\)
0.994009 + 0.109294i \(0.0348591\pi\)
\(264\) 0 0
\(265\) −15.1582 + 5.51712i −0.931159 + 0.338914i
\(266\) −1.16445 17.7805i −0.0713972 1.09019i
\(267\) 0 0
\(268\) −5.16988 29.3199i −0.315801 1.79100i
\(269\) 7.34061 + 12.7143i 0.447565 + 0.775206i 0.998227 0.0595229i \(-0.0189579\pi\)
−0.550662 + 0.834728i \(0.685625\pi\)
\(270\) 0 0
\(271\) 3.02098 5.23249i 0.183511 0.317851i −0.759562 0.650434i \(-0.774587\pi\)
0.943074 + 0.332583i \(0.107920\pi\)
\(272\) 4.89274 4.10549i 0.296666 0.248932i
\(273\) 0 0
\(274\) 4.73981 26.8808i 0.286343 1.62393i
\(275\) −0.307886 + 1.74611i −0.0185662 + 0.105294i
\(276\) 0 0
\(277\) −9.07072 + 7.61123i −0.545006 + 0.457315i −0.873246 0.487280i \(-0.837989\pi\)
0.328239 + 0.944595i \(0.393545\pi\)
\(278\) 4.40613 0.264262
\(279\) 0 0
\(280\) −0.411308 + 0.100624i −0.0245804 + 0.00601341i
\(281\) 19.4068 + 7.06348i 1.15771 + 0.421372i 0.848279 0.529550i \(-0.177639\pi\)
0.309431 + 0.950922i \(0.399861\pi\)
\(282\) 0 0
\(283\) 2.28883 12.9806i 0.136057 0.771616i −0.838061 0.545576i \(-0.816311\pi\)
0.974118 0.226040i \(-0.0725779\pi\)
\(284\) −4.69050 + 26.6012i −0.278330 + 1.57849i
\(285\) 0 0
\(286\) 15.2071 + 5.53492i 0.899213 + 0.327287i
\(287\) 11.3688 + 11.8773i 0.671079 + 0.701093i
\(288\) 0 0
\(289\) −14.5309 −0.854756
\(290\) −2.05431 + 1.72377i −0.120633 + 0.101223i
\(291\) 0 0
\(292\) −0.522354 + 2.96242i −0.0305684 + 0.173362i
\(293\) 0.430537 2.44169i 0.0251522 0.142645i −0.969646 0.244515i \(-0.921371\pi\)
0.994798 + 0.101870i \(0.0324824\pi\)
\(294\) 0 0
\(295\) 0.783982 0.657839i 0.0456452 0.0383009i
\(296\) 0.350895 0.607769i 0.0203954 0.0353258i
\(297\) 0 0
\(298\) 2.13411 + 3.69639i 0.123626 + 0.214126i
\(299\) −0.767890 4.35492i −0.0444082 0.251852i
\(300\) 0 0
\(301\) −19.3248 9.53120i −1.11386 0.549369i
\(302\) −25.8819 + 9.42025i −1.48934 + 0.542074i
\(303\) 0 0
\(304\) 10.5285 8.83442i 0.603848 0.506689i
\(305\) −17.2367 + 29.8548i −0.986968 + 1.70948i
\(306\) 0 0
\(307\) −2.98599 + 5.17189i −0.170420 + 0.295176i −0.938567 0.345098i \(-0.887846\pi\)
0.768147 + 0.640274i \(0.221179\pi\)
\(308\) 3.81007 + 8.66028i 0.217099 + 0.493465i
\(309\) 0 0
\(310\) −20.2398 + 7.36669i −1.14954 + 0.418400i
\(311\) 1.92212 10.9009i 0.108994 0.618133i −0.880556 0.473942i \(-0.842831\pi\)
0.989550 0.144192i \(-0.0460582\pi\)
\(312\) 0 0
\(313\) 8.33102 6.99055i 0.470897 0.395130i −0.376225 0.926528i \(-0.622778\pi\)
0.847122 + 0.531399i \(0.178333\pi\)
\(314\) 1.29685 2.24622i 0.0731857 0.126761i
\(315\) 0 0
\(316\) 8.56919 + 14.8423i 0.482055 + 0.834943i
\(317\) −9.69561 3.52891i −0.544559 0.198203i 0.0550682 0.998483i \(-0.482462\pi\)
−0.599628 + 0.800279i \(0.704685\pi\)
\(318\) 0 0
\(319\) −0.767041 0.643624i −0.0429461 0.0360360i
\(320\) 14.4840 + 12.1535i 0.809682 + 0.679404i
\(321\) 0 0
\(322\) 3.08327 4.20459i 0.171824 0.234313i
\(323\) 5.31324 0.295636
\(324\) 0 0
\(325\) −2.17956 3.77510i −0.120900 0.209405i
\(326\) 29.5157 + 10.7428i 1.63472 + 0.594990i
\(327\) 0 0
\(328\) −0.0706512 + 0.400683i −0.00390106 + 0.0221240i
\(329\) −23.0011 11.3444i −1.26809 0.625438i
\(330\) 0 0
\(331\) −17.0243 6.19633i −0.935739 0.340581i −0.171257 0.985226i \(-0.554783\pi\)
−0.764482 + 0.644645i \(0.777005\pi\)
\(332\) −12.7629 + 22.1059i −0.700453 + 1.21322i
\(333\) 0 0
\(334\) −9.97699 17.2807i −0.545917 0.945555i
\(335\) −34.7652 12.6535i −1.89942 0.691333i
\(336\) 0 0
\(337\) 13.9703 + 11.7225i 0.761013 + 0.638566i 0.938390 0.345577i \(-0.112317\pi\)
−0.177377 + 0.984143i \(0.556761\pi\)
\(338\) −13.0559 + 4.75197i −0.710150 + 0.258473i
\(339\) 0 0
\(340\) 1.31207 + 7.44111i 0.0711569 + 0.403551i
\(341\) −4.02108 6.96472i −0.217754 0.377161i
\(342\) 0 0
\(343\) 17.5364 + 5.95592i 0.946879 + 0.321589i
\(344\) −0.0925927 0.525119i −0.00499226 0.0283125i
\(345\) 0 0
\(346\) 5.17932 + 4.34597i 0.278442 + 0.233641i
\(347\) −18.5716 + 6.75950i −0.996974 + 0.362869i −0.788417 0.615141i \(-0.789099\pi\)
−0.208557 + 0.978010i \(0.566877\pi\)
\(348\) 0 0
\(349\) −13.0462 + 10.9471i −0.698349 + 0.585984i −0.921303 0.388845i \(-0.872874\pi\)
0.222954 + 0.974829i \(0.428430\pi\)
\(350\) 1.43849 4.93426i 0.0768905 0.263747i
\(351\) 0 0
\(352\) −7.23972 + 12.5396i −0.385879 + 0.668361i
\(353\) −16.6077 6.04472i −0.883940 0.321728i −0.140141 0.990132i \(-0.544756\pi\)
−0.743799 + 0.668404i \(0.766978\pi\)
\(354\) 0 0
\(355\) 25.7129 + 21.5757i 1.36470 + 1.14512i
\(356\) −15.7234 + 5.72287i −0.833341 + 0.303311i
\(357\) 0 0
\(358\) −3.17730 18.0194i −0.167926 0.952354i
\(359\) 16.8842 0.891111 0.445556 0.895254i \(-0.353006\pi\)
0.445556 + 0.895254i \(0.353006\pi\)
\(360\) 0 0
\(361\) −7.56669 −0.398247
\(362\) 28.2000 23.6626i 1.48216 1.24368i
\(363\) 0 0
\(364\) −20.8618 10.2893i −1.09346 0.539304i
\(365\) 2.86350 + 2.40276i 0.149882 + 0.125766i
\(366\) 0 0
\(367\) −1.92763 10.9321i −0.100622 0.570653i −0.992879 0.119127i \(-0.961991\pi\)
0.892257 0.451527i \(-0.149121\pi\)
\(368\) 4.02164 0.209642
\(369\) 0 0
\(370\) 26.0937 + 45.1957i 1.35655 + 2.34961i
\(371\) 7.03087 + 15.9812i 0.365025 + 0.829701i
\(372\) 0 0
\(373\) −3.72846 + 21.1451i −0.193052 + 1.09485i 0.722113 + 0.691775i \(0.243171\pi\)
−0.915165 + 0.403079i \(0.867940\pi\)
\(374\) −5.34649 + 1.94596i −0.276460 + 0.100623i
\(375\) 0 0
\(376\) −0.110208 0.625018i −0.00568352 0.0322328i
\(377\) 2.46175 0.126787
\(378\) 0 0
\(379\) 0.397147 0.0204001 0.0102000 0.999948i \(-0.496753\pi\)
0.0102000 + 0.999948i \(0.496753\pi\)
\(380\) 2.82338 + 16.0122i 0.144836 + 0.821408i
\(381\) 0 0
\(382\) 8.34288 3.03656i 0.426859 0.155364i
\(383\) 2.42502 13.7530i 0.123913 0.702743i −0.858035 0.513591i \(-0.828315\pi\)
0.981948 0.189152i \(-0.0605740\pi\)
\(384\) 0 0
\(385\) 11.6872 + 1.28058i 0.595633 + 0.0652643i
\(386\) −7.61142 13.1834i −0.387411 0.671015i
\(387\) 0 0
\(388\) −29.2517 −1.48503
\(389\) 3.83076 + 21.7253i 0.194227 + 1.10152i 0.913515 + 0.406805i \(0.133357\pi\)
−0.719288 + 0.694712i \(0.755532\pi\)
\(390\) 0 0
\(391\) 1.19098 + 0.999354i 0.0602306 + 0.0505395i
\(392\) 0.137770 + 0.437111i 0.00695844 + 0.0220775i
\(393\) 0 0
\(394\) 24.5100 20.5663i 1.23479 1.03611i
\(395\) 21.2970 1.07157
\(396\) 0 0
\(397\) −8.44125 −0.423654 −0.211827 0.977307i \(-0.567941\pi\)
−0.211827 + 0.977307i \(0.567941\pi\)
\(398\) −1.31987 7.48533i −0.0661589 0.375206i
\(399\) 0 0
\(400\) 3.72527 1.35589i 0.186264 0.0677945i
\(401\) 10.0271 + 8.41375i 0.500730 + 0.420163i 0.857853 0.513895i \(-0.171798\pi\)
−0.357123 + 0.934057i \(0.616242\pi\)
\(402\) 0 0
\(403\) 18.5797 + 6.76244i 0.925519 + 0.336861i
\(404\) 7.97243 13.8087i 0.396643 0.687006i
\(405\) 0 0
\(406\) 2.00705 + 2.09681i 0.0996080 + 0.104063i
\(407\) −14.9270 + 12.5252i −0.739904 + 0.620853i
\(408\) 0 0
\(409\) 3.16244 1.15103i 0.156373 0.0569150i −0.262648 0.964892i \(-0.584596\pi\)
0.419021 + 0.907977i \(0.362374\pi\)
\(410\) −23.1773 19.4480i −1.14464 0.960470i
\(411\) 0 0
\(412\) −3.11138 17.6455i −0.153287 0.869332i
\(413\) −0.765944 0.800200i −0.0376897 0.0393753i
\(414\) 0 0
\(415\) 15.8597 + 27.4699i 0.778524 + 1.34844i
\(416\) −6.18161 35.0576i −0.303078 1.71884i
\(417\) 0 0
\(418\) −11.5049 + 4.18742i −0.562721 + 0.204814i
\(419\) −15.7960 13.2544i −0.771686 0.647521i 0.169454 0.985538i \(-0.445799\pi\)
−0.941140 + 0.338017i \(0.890244\pi\)
\(420\) 0 0
\(421\) 0.936453 + 0.340841i 0.0456399 + 0.0166116i 0.364739 0.931110i \(-0.381158\pi\)
−0.319099 + 0.947721i \(0.603380\pi\)
\(422\) 1.16319 + 2.01471i 0.0566234 + 0.0980747i
\(423\) 0 0
\(424\) −0.216028 + 0.374172i −0.0104913 + 0.0181714i
\(425\) 1.44015 + 0.524171i 0.0698574 + 0.0254260i
\(426\) 0 0
\(427\) 33.4635 + 16.5046i 1.61941 + 0.798711i
\(428\) −3.49223 + 19.8054i −0.168803 + 0.957331i
\(429\) 0 0
\(430\) 37.2607 + 13.5618i 1.79687 + 0.654007i
\(431\) 17.8597 + 30.9340i 0.860274 + 1.49004i 0.871665 + 0.490102i \(0.163041\pi\)
−0.0113913 + 0.999935i \(0.503626\pi\)
\(432\) 0 0
\(433\) 13.4491 0.646321 0.323160 0.946344i \(-0.395255\pi\)
0.323160 + 0.946344i \(0.395255\pi\)
\(434\) 9.38791 + 21.3387i 0.450634 + 1.02429i
\(435\) 0 0
\(436\) 8.48207 + 7.11730i 0.406217 + 0.340857i
\(437\) 2.56282 + 2.15046i 0.122596 + 0.102871i
\(438\) 0 0
\(439\) −12.7002 4.62248i −0.606146 0.220619i 0.0206703 0.999786i \(-0.493420\pi\)
−0.626816 + 0.779167i \(0.715642\pi\)
\(440\) 0.145473 + 0.251966i 0.00693515 + 0.0120120i
\(441\) 0 0
\(442\) 6.99410 12.1141i 0.332675 0.576211i
\(443\) −19.1371 + 16.0580i −0.909232 + 0.762936i −0.971973 0.235094i \(-0.924460\pi\)
0.0627407 + 0.998030i \(0.480016\pi\)
\(444\) 0 0
\(445\) −3.61061 + 20.4768i −0.171159 + 0.970692i
\(446\) −4.61337 + 1.67913i −0.218450 + 0.0795092i
\(447\) 0 0
\(448\) 12.1018 16.5029i 0.571756 0.779691i
\(449\) 7.15453 12.3920i 0.337643 0.584815i −0.646346 0.763045i \(-0.723704\pi\)
0.983989 + 0.178230i \(0.0570370\pi\)
\(450\) 0 0
\(451\) 5.64847 9.78343i 0.265976 0.460684i
\(452\) −11.4017 + 9.56716i −0.536291 + 0.450001i
\(453\) 0 0
\(454\) −28.1760 + 10.2552i −1.32236 + 0.481301i
\(455\) −24.0349 + 16.0578i −1.12677 + 0.752799i
\(456\) 0 0
\(457\) −0.752561 4.26799i −0.0352033 0.199648i 0.962134 0.272578i \(-0.0878762\pi\)
−0.997337 + 0.0729298i \(0.976765\pi\)
\(458\) −17.4987 30.3086i −0.817659 1.41623i
\(459\) 0 0
\(460\) −2.37882 + 4.12024i −0.110913 + 0.192107i
\(461\) 0.788559 0.661680i 0.0367269 0.0308175i −0.624239 0.781233i \(-0.714591\pi\)
0.660966 + 0.750416i \(0.270147\pi\)
\(462\) 0 0
\(463\) 3.25304 18.4489i 0.151182 0.857394i −0.811012 0.585029i \(-0.801083\pi\)
0.962194 0.272365i \(-0.0878058\pi\)
\(464\) −0.388766 + 2.20480i −0.0180480 + 0.102355i
\(465\) 0 0
\(466\) 0.524932 0.440470i 0.0243170 0.0204044i
\(467\) 16.6529 0.770603 0.385302 0.922791i \(-0.374097\pi\)
0.385302 + 0.922791i \(0.374097\pi\)
\(468\) 0 0
\(469\) −11.2072 + 38.4427i −0.517501 + 1.77512i
\(470\) 44.3492 + 16.1418i 2.04567 + 0.744565i
\(471\) 0 0
\(472\) 0.00475995 0.0269950i 0.000219094 0.00124255i
\(473\) −2.57092 + 14.5804i −0.118211 + 0.670407i
\(474\) 0 0
\(475\) 3.09899 + 1.12794i 0.142191 + 0.0517534i
\(476\) 7.94388 1.94341i 0.364107 0.0890761i
\(477\) 0 0
\(478\) 41.9293 1.91780
\(479\) 29.4273 24.6924i 1.34457 1.12823i 0.364141 0.931344i \(-0.381363\pi\)
0.980427 0.196882i \(-0.0630817\pi\)
\(480\) 0 0
\(481\) 8.31894 47.1791i 0.379311 2.15118i
\(482\) 2.93719 16.6576i 0.133785 0.758733i
\(483\) 0 0
\(484\) −11.5960 + 9.73019i −0.527090 + 0.442281i
\(485\) −18.1748 + 31.4796i −0.825273 + 1.42941i
\(486\) 0 0
\(487\) 0.426198 + 0.738196i 0.0193129 + 0.0334509i 0.875520 0.483181i \(-0.160519\pi\)
−0.856207 + 0.516632i \(0.827185\pi\)
\(488\) 0.160337 + 0.909315i 0.00725810 + 0.0411627i
\(489\) 0 0
\(490\) −33.2727 7.38006i −1.50311 0.333397i
\(491\) −21.7016 + 7.89874i −0.979380 + 0.356465i −0.781599 0.623781i \(-0.785596\pi\)
−0.197781 + 0.980246i \(0.563373\pi\)
\(492\) 0 0
\(493\) −0.663011 + 0.556332i −0.0298605 + 0.0250559i
\(494\) 15.0503 26.0678i 0.677144 1.17285i
\(495\) 0 0
\(496\) −8.99076 + 15.5724i −0.403697 + 0.699223i
\(497\) 21.4838 29.2970i 0.963682 1.31415i
\(498\) 0 0
\(499\) −1.55555 + 0.566174i −0.0696360 + 0.0253454i −0.376603 0.926375i \(-0.622908\pi\)
0.306967 + 0.951720i \(0.400686\pi\)
\(500\) 3.36058 19.0588i 0.150290 0.852336i
\(501\) 0 0
\(502\) 36.6084 30.7181i 1.63391 1.37101i
\(503\) −12.7337 + 22.0554i −0.567768 + 0.983403i 0.429018 + 0.903296i \(0.358860\pi\)
−0.996786 + 0.0801073i \(0.974474\pi\)
\(504\) 0 0
\(505\) −9.90692 17.1593i −0.440852 0.763578i
\(506\) −3.36646 1.22529i −0.149657 0.0544709i
\(507\) 0 0
\(508\) 0.0277746 + 0.0233057i 0.00123230 + 0.00103402i
\(509\) 12.0549 + 10.1152i 0.534322 + 0.448350i 0.869591 0.493773i \(-0.164383\pi\)
−0.335269 + 0.942123i \(0.608827\pi\)
\(510\) 0 0
\(511\) 2.39253 3.26264i 0.105839 0.144331i
\(512\) 31.8424 1.40725
\(513\) 0 0
\(514\) −13.5116 23.4028i −0.595971 1.03225i
\(515\) −20.9226 7.61522i −0.921962 0.335567i
\(516\) 0 0
\(517\) −3.06001 + 17.3542i −0.134579 + 0.763235i
\(518\) 46.9674 31.3790i 2.06363 1.37871i
\(519\) 0 0
\(520\) −0.672167 0.244649i −0.0294765 0.0107286i
\(521\) −20.9438 + 36.2756i −0.917563 + 1.58926i −0.114457 + 0.993428i \(0.536513\pi\)
−0.803106 + 0.595837i \(0.796821\pi\)
\(522\) 0 0
\(523\) −6.48784 11.2373i −0.283693 0.491371i 0.688598 0.725143i \(-0.258226\pi\)
−0.972291 + 0.233772i \(0.924893\pi\)
\(524\) −32.3806 11.7856i −1.41455 0.514855i
\(525\) 0 0
\(526\) 34.2062 + 28.7024i 1.49146 + 1.25149i
\(527\) −6.53222 + 2.37753i −0.284548 + 0.103567i
\(528\) 0 0
\(529\) −3.82392 21.6865i −0.166257 0.942892i
\(530\) −16.0646 27.8247i −0.697800 1.20863i
\(531\) 0 0
\(532\) 17.0941 4.18194i 0.741122 0.181310i
\(533\) 4.82292 + 27.3521i 0.208904 + 1.18475i
\(534\) 0 0
\(535\) 19.1441 + 16.0638i 0.827671 + 0.694498i
\(536\) −0.931159 + 0.338914i −0.0402199 + 0.0146389i
\(537\) 0 0
\(538\) −22.4003 + 18.7961i −0.965747 + 0.810358i
\(539\) 0.556412 12.7132i 0.0239664 0.547595i
\(540\) 0 0
\(541\) −19.8950 + 34.4591i −0.855352 + 1.48151i 0.0209658 + 0.999780i \(0.493326\pi\)
−0.876318 + 0.481733i \(0.840007\pi\)
\(542\) 11.3084 + 4.11593i 0.485738 + 0.176794i
\(543\) 0 0
\(544\) 9.58756 + 8.04492i 0.411063 + 0.344923i
\(545\) 12.9295 4.70595i 0.553839 0.201581i
\(546\) 0 0
\(547\) −2.42536 13.7549i −0.103701 0.588117i −0.991731 0.128332i \(-0.959038\pi\)
0.888030 0.459785i \(-0.152073\pi\)
\(548\) 26.9579 1.15158
\(549\) 0 0
\(550\) −3.53149 −0.150583
\(551\) −1.42670 + 1.19715i −0.0607796 + 0.0510001i
\(552\) 0 0
\(553\) −1.50638 23.0015i −0.0640579 0.978125i
\(554\) −18.0667 15.1598i −0.767582 0.644078i
\(555\) 0 0
\(556\) 0.755653 + 4.28552i 0.0320468 + 0.181747i
\(557\) 18.7944 0.796344 0.398172 0.917311i \(-0.369645\pi\)
0.398172 + 0.917311i \(0.369645\pi\)
\(558\) 0 0
\(559\) −18.1998 31.5230i −0.769770 1.33328i
\(560\) −10.5861 24.0621i −0.447342 1.01681i
\(561\) 0 0
\(562\) −7.14292 + 40.5095i −0.301306 + 1.70879i
\(563\) 1.70630 0.621043i 0.0719121 0.0261739i −0.305814 0.952091i \(-0.598928\pi\)
0.377726 + 0.925918i \(0.376706\pi\)
\(564\) 0 0
\(565\) 3.21169 + 18.2144i 0.135117 + 0.766286i
\(566\) 26.2531 1.10350
\(567\) 0 0
\(568\) 0.899035 0.0377227
\(569\) −8.12904 46.1021i −0.340787 1.93270i −0.360166 0.932888i \(-0.617280\pi\)
0.0193792 0.999812i \(-0.493831\pi\)
\(570\) 0 0
\(571\) 16.5782 6.03395i 0.693774 0.252513i 0.0290237 0.999579i \(-0.490760\pi\)
0.664750 + 0.747066i \(0.268538\pi\)
\(572\) −2.77539 + 15.7400i −0.116045 + 0.658124i
\(573\) 0 0
\(574\) −19.3652 + 26.4079i −0.808289 + 1.10225i
\(575\) 0.482499 + 0.835713i 0.0201216 + 0.0348516i
\(576\) 0 0
\(577\) −13.5445 −0.563865 −0.281932 0.959434i \(-0.590975\pi\)
−0.281932 + 0.959434i \(0.590975\pi\)
\(578\) −5.02573 28.5024i −0.209043 1.18554i
\(579\) 0 0
\(580\) −2.02890 1.70245i −0.0842455 0.0706904i
\(581\) 28.5467 19.0721i 1.18432 0.791246i
\(582\) 0 0
\(583\) 9.18979 7.71115i 0.380602 0.319363i
\(584\) 0.100120 0.00414301
\(585\) 0 0
\(586\) 4.93831 0.204000
\(587\) 6.71115 + 38.0608i 0.276999 + 1.57094i 0.732541 + 0.680723i \(0.238334\pi\)
−0.455542 + 0.890214i \(0.650555\pi\)
\(588\) 0 0
\(589\) −14.0564 + 5.11610i −0.579183 + 0.210805i
\(590\) 1.56151 + 1.31026i 0.0642863 + 0.0539426i
\(591\) 0 0
\(592\) 40.9409 + 14.9013i 1.68266 + 0.612439i
\(593\) −12.6557 + 21.9203i −0.519708 + 0.900161i 0.480030 + 0.877252i \(0.340626\pi\)
−0.999738 + 0.0229084i \(0.992707\pi\)
\(594\) 0 0
\(595\) 2.84429 9.75641i 0.116605 0.399974i
\(596\) −3.22920 + 2.70962i −0.132273 + 0.110991i
\(597\) 0 0
\(598\) 8.27662 3.01244i 0.338456 0.123188i
\(599\) 8.11678 + 6.81078i 0.331642 + 0.278281i 0.793369 0.608741i \(-0.208325\pi\)
−0.461726 + 0.887022i \(0.652770\pi\)
\(600\) 0 0
\(601\) −2.95616 16.7652i −0.120584 0.683867i −0.983833 0.179088i \(-0.942685\pi\)
0.863249 0.504779i \(-0.168426\pi\)
\(602\) 12.0117 41.2022i 0.489561 1.67928i
\(603\) 0 0
\(604\) −13.6011 23.5579i −0.553422 0.958556i
\(605\) 3.26642 + 18.5248i 0.132799 + 0.753140i
\(606\) 0 0
\(607\) −17.1024 + 6.22477i −0.694165 + 0.252656i −0.664918 0.746917i \(-0.731533\pi\)
−0.0292477 + 0.999572i \(0.509311\pi\)
\(608\) 20.6310 + 17.3115i 0.836698 + 0.702073i
\(609\) 0 0
\(610\) −64.5219 23.4840i −2.61241 0.950841i
\(611\) −21.6621 37.5199i −0.876356 1.51789i
\(612\) 0 0
\(613\) −11.1206 + 19.2615i −0.449157 + 0.777963i −0.998331 0.0577451i \(-0.981609\pi\)
0.549174 + 0.835708i \(0.314942\pi\)
\(614\) −11.1775 4.06826i −0.451085 0.164182i
\(615\) 0 0
\(616\) 0.261844 0.174938i 0.0105500 0.00704847i
\(617\) −1.46351 + 8.29999i −0.0589188 + 0.334145i −0.999992 0.00405846i \(-0.998708\pi\)
0.941073 + 0.338204i \(0.109819\pi\)
\(618\) 0 0
\(619\) 18.1590 + 6.60932i 0.729870 + 0.265651i 0.680110 0.733110i \(-0.261932\pi\)
0.0497601 + 0.998761i \(0.484154\pi\)
\(620\) −10.6362 18.4224i −0.427159 0.739860i
\(621\) 0 0
\(622\) 22.0470 0.884003
\(623\) 22.3711 + 2.45122i 0.896278 + 0.0982062i
\(624\) 0 0
\(625\) −22.1581 18.5929i −0.886324 0.743714i
\(626\) 16.5934 + 13.9235i 0.663207 + 0.556497i
\(627\) 0 0
\(628\) 2.40714 + 0.876127i 0.0960554 + 0.0349613i
\(629\) 8.42152 + 14.5865i 0.335788 + 0.581602i
\(630\) 0 0
\(631\) 1.77916 3.08159i 0.0708272 0.122676i −0.828437 0.560082i \(-0.810769\pi\)
0.899264 + 0.437406i \(0.144103\pi\)
\(632\) 0.436970 0.366661i 0.0173817 0.0145850i
\(633\) 0 0
\(634\) 3.56860 20.2385i 0.141727 0.803774i
\(635\) 0.0423378 0.0154097i 0.00168012 0.000611515i
\(636\) 0 0
\(637\) 19.0430 + 24.8228i 0.754512 + 0.983514i
\(638\) 0.997178 1.72716i 0.0394787 0.0683791i
\(639\) 0 0
\(640\) 0.640092 1.10867i 0.0253018 0.0438241i
\(641\) 14.0792 11.8138i 0.556094 0.466618i −0.320904 0.947112i \(-0.603987\pi\)
0.876998 + 0.480493i \(0.159542\pi\)
\(642\) 0 0
\(643\) −18.6011 + 6.77026i −0.733558 + 0.266993i −0.681670 0.731660i \(-0.738746\pi\)
−0.0518877 + 0.998653i \(0.516524\pi\)
\(644\) 4.61827 + 2.27778i 0.181986 + 0.0897573i
\(645\) 0 0
\(646\) 1.83767 + 10.4219i 0.0723022 + 0.410046i
\(647\) −13.2466 22.9438i −0.520777 0.902012i −0.999708 0.0241597i \(-0.992309\pi\)
0.478931 0.877852i \(-0.341024\pi\)
\(648\) 0 0
\(649\) −0.380551 + 0.659134i −0.0149379 + 0.0258733i
\(650\) 6.65105 5.58090i 0.260876 0.218901i
\(651\) 0 0
\(652\) −5.38681 + 30.5501i −0.210964 + 1.19644i
\(653\) −3.57842 + 20.2942i −0.140034 + 0.794174i 0.831187 + 0.555994i \(0.187662\pi\)
−0.971221 + 0.238180i \(0.923449\pi\)
\(654\) 0 0
\(655\) −32.8021 + 27.5242i −1.28168 + 1.07546i
\(656\) −25.2589 −0.986193
\(657\) 0 0
\(658\) 14.2968 49.0405i 0.557348 1.91180i
\(659\) 16.3391 + 5.94693i 0.636479 + 0.231660i 0.640049 0.768334i \(-0.278914\pi\)
−0.00356967 + 0.999994i \(0.501136\pi\)
\(660\) 0 0
\(661\) 8.39889 47.6324i 0.326679 1.85269i −0.170926 0.985284i \(-0.554676\pi\)
0.497605 0.867404i \(-0.334213\pi\)
\(662\) 6.26601 35.5363i 0.243535 1.38116i
\(663\) 0 0
\(664\) 0.798347 + 0.290575i 0.0309819 + 0.0112765i
\(665\) 6.12050 20.9944i 0.237343 0.814127i
\(666\) 0 0
\(667\) −0.544969 −0.0211013
\(668\) 15.0966 12.6675i 0.584103 0.490121i
\(669\) 0 0
\(670\) 12.7958 72.5685i 0.494344 2.80356i
\(671\) 4.45189 25.2479i 0.171863 0.974684i
\(672\) 0 0
\(673\) −17.8256 + 14.9575i −0.687128 + 0.576569i −0.918079 0.396396i \(-0.870261\pi\)
0.230951 + 0.972965i \(0.425816\pi\)
\(674\) −18.1619 + 31.4573i −0.699570 + 1.21169i
\(675\) 0 0
\(676\) −6.86099 11.8836i −0.263884 0.457061i
\(677\) −7.24921 41.1123i −0.278610 1.58007i −0.727257 0.686365i \(-0.759205\pi\)
0.448647 0.893709i \(-0.351906\pi\)
\(678\) 0 0
\(679\) 35.2847 + 17.4028i 1.35410 + 0.667858i
\(680\) 0.236320 0.0860133i 0.00906245 0.00329846i
\(681\) 0 0
\(682\) 12.2706 10.2962i 0.469865 0.394263i
\(683\) 3.62363 6.27630i 0.138654 0.240156i −0.788333 0.615248i \(-0.789056\pi\)
0.926987 + 0.375092i \(0.122389\pi\)
\(684\) 0 0
\(685\) 16.7496 29.0111i 0.639968 1.10846i
\(686\) −5.61730 + 36.4578i −0.214469 + 1.39197i
\(687\) 0 0
\(688\) 31.1069 11.3220i 1.18594 0.431647i
\(689\) −5.12154 + 29.0457i −0.195115 + 1.10655i
\(690\) 0 0
\(691\) −13.3637 + 11.2135i −0.508380 + 0.426582i −0.860559 0.509351i \(-0.829885\pi\)
0.352179 + 0.935933i \(0.385441\pi\)
\(692\) −3.33875 + 5.78288i −0.126920 + 0.219832i
\(693\) 0 0
\(694\) −19.6821 34.0904i −0.747121 1.29405i
\(695\) 5.08143 + 1.84949i 0.192750 + 0.0701551i
\(696\) 0 0
\(697\) −7.48026 6.27668i −0.283335 0.237746i
\(698\) −25.9850 21.8040i −0.983548 0.825295i
\(699\) 0 0
\(700\) 5.04589 + 0.552885i 0.190717 + 0.0208971i
\(701\) −30.9548 −1.16915 −0.584574 0.811341i \(-0.698738\pi\)
−0.584574 + 0.811341i \(0.698738\pi\)
\(702\) 0 0
\(703\) 18.1219 + 31.3880i 0.683480 + 1.18382i
\(704\) −13.2133 4.80925i −0.497996 0.181256i
\(705\) 0 0
\(706\) 6.11270 34.6668i 0.230054 1.30470i
\(707\) −17.8319 + 11.9136i −0.670639 + 0.448056i
\(708\) 0 0
\(709\) −31.3751 11.4196i −1.17832 0.428872i −0.322710 0.946498i \(-0.604594\pi\)
−0.855607 + 0.517626i \(0.826816\pi\)
\(710\) −33.4276 + 57.8983i −1.25452 + 2.17289i
\(711\) 0 0
\(712\) 0.278458 + 0.482303i 0.0104356 + 0.0180751i
\(713\) −4.11307 1.49703i −0.154036 0.0560644i
\(714\) 0 0
\(715\) 15.2144 + 12.7664i 0.568988 + 0.477438i
\(716\) 16.9812 6.18066i 0.634618 0.230982i
\(717\) 0 0
\(718\) 5.83966 + 33.1184i 0.217934 + 1.23597i
\(719\) 19.1475 + 33.1645i 0.714082 + 1.23683i 0.963312 + 0.268383i \(0.0864892\pi\)
−0.249230 + 0.968444i \(0.580177\pi\)
\(720\) 0 0
\(721\) −6.74482 + 23.1359i −0.251190 + 0.861625i
\(722\) −2.61706 14.8421i −0.0973970 0.552366i
\(723\) 0 0
\(724\) 27.8512 + 23.3699i 1.03508 + 0.868537i
\(725\) −0.504809 + 0.183736i −0.0187481 + 0.00682377i
\(726\) 0 0
\(727\) −8.98887 + 7.54255i −0.333379 + 0.279738i −0.794075 0.607820i \(-0.792044\pi\)
0.460696 + 0.887558i \(0.347600\pi\)
\(728\) −0.216686 + 0.743270i −0.00803092 + 0.0275474i
\(729\) 0 0
\(730\) −3.72264 + 6.44780i −0.137781 + 0.238644i
\(731\) 12.0256 + 4.37695i 0.444781 + 0.161887i
\(732\) 0 0
\(733\) 17.4826 + 14.6697i 0.645736 + 0.541837i 0.905774 0.423762i \(-0.139291\pi\)
−0.260038 + 0.965598i \(0.583735\pi\)
\(734\) 20.7768 7.56212i 0.766884 0.279123i
\(735\) 0 0
\(736\) 1.36845 + 7.76088i 0.0504418 + 0.286070i
\(737\) 27.5137 1.01348
\(738\) 0 0
\(739\) −0.0904905 −0.00332875 −0.00166437 0.999999i \(-0.500530\pi\)
−0.00166437 + 0.999999i \(0.500530\pi\)
\(740\) −39.4834 + 33.1305i −1.45144 + 1.21790i
\(741\) 0 0
\(742\) −28.9154 + 19.3184i −1.06152 + 0.709202i
\(743\) 7.75878 + 6.51039i 0.284642 + 0.238843i 0.773918 0.633286i \(-0.218294\pi\)
−0.489276 + 0.872129i \(0.662739\pi\)
\(744\) 0 0
\(745\) 0.909619 + 5.15871i 0.0333259 + 0.189000i
\(746\) −42.7659 −1.56577
\(747\) 0 0
\(748\) −2.80962 4.86640i −0.102730 0.177933i
\(749\) 15.9954 21.8126i 0.584459 0.797014i
\(750\) 0 0
\(751\) 8.25832 46.8353i 0.301351 1.70904i −0.338854 0.940839i \(-0.610039\pi\)
0.640204 0.768205i \(-0.278850\pi\)
\(752\) 37.0247 13.4759i 1.35015 0.491415i
\(753\) 0 0
\(754\) 0.851436 + 4.82874i 0.0310075 + 0.175852i
\(755\) −33.8028 −1.23021
\(756\) 0 0
\(757\) 3.43113 0.124706 0.0623532 0.998054i \(-0.480139\pi\)
0.0623532 + 0.998054i \(0.480139\pi\)
\(758\) 0.137360 + 0.779007i 0.00498914 + 0.0282948i
\(759\) 0 0
\(760\) 0.508525 0.185088i 0.0184462 0.00671385i
\(761\) 5.42318 30.7564i 0.196590 1.11492i −0.713546 0.700609i \(-0.752912\pi\)
0.910136 0.414310i \(-0.135977\pi\)
\(762\) 0 0
\(763\) −5.99714 13.6315i −0.217111 0.493493i
\(764\) 4.38424 + 7.59373i 0.158616 + 0.274732i
\(765\) 0 0
\(766\) 27.8152 1.00501
\(767\) −0.324932 1.84278i −0.0117326 0.0665389i
\(768\) 0 0
\(769\) 5.81587 + 4.88009i 0.209726 + 0.175981i 0.741599 0.670843i \(-0.234068\pi\)
−0.531874 + 0.846824i \(0.678512\pi\)
\(770\) 1.53034 + 23.3674i 0.0551496 + 0.842101i
\(771\) 0 0
\(772\) 11.5171 9.66401i 0.414510 0.347815i
\(773\) 7.83386 0.281765 0.140882 0.990026i \(-0.455006\pi\)
0.140882 + 0.990026i \(0.455006\pi\)
\(774\) 0 0
\(775\) −4.31469 −0.154988
\(776\) 0.169063 + 0.958803i 0.00606900 + 0.0344190i
\(777\) 0 0
\(778\) −41.2894 + 15.0281i −1.48030 + 0.538784i
\(779\) −16.0964 13.5065i −0.576714 0.483921i
\(780\) 0 0
\(781\) −23.4571 8.53767i −0.839360 0.305502i
\(782\) −1.54832 + 2.68176i −0.0553677 + 0.0958997i
\(783\) 0 0