Properties

Label 49.2.g.a.32.2
Level $49$
Weight $2$
Character 49.32
Analytic conductor $0.391$
Analytic rank $0$
Dimension $48$
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] = [49,2,Mod(2,49)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(49, base_ring=CyclotomicField(42))
 
chi = DirichletCharacter(H, H._module([26]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("49.2");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 49 = 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 49.g (of order \(21\), degree \(12\), 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: \(0.391266969904\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(4\) over \(\Q(\zeta_{21})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label 32.2
Character \(\chi\) \(=\) 49.32
Dual form 49.2.g.a.23.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.118164 - 1.57679i) q^{2} +(-3.07373 - 0.948121i) q^{3} +(-0.494650 + 0.0745565i) q^{4} +(0.291074 - 0.270077i) q^{5} +(-1.13178 + 4.95867i) q^{6} +(2.43713 - 1.02976i) q^{7} +(-0.527696 - 2.31199i) q^{8} +(6.07018 + 4.13858i) q^{9} +O(q^{10})\) \(q+(-0.118164 - 1.57679i) q^{2} +(-3.07373 - 0.948121i) q^{3} +(-0.494650 + 0.0745565i) q^{4} +(0.291074 - 0.270077i) q^{5} +(-1.13178 + 4.95867i) q^{6} +(2.43713 - 1.02976i) q^{7} +(-0.527696 - 2.31199i) q^{8} +(6.07018 + 4.13858i) q^{9} +(-0.460250 - 0.427049i) q^{10} +(-1.83363 + 1.25015i) q^{11} +(1.59111 + 0.239821i) q^{12} +(1.92814 + 0.928542i) q^{13} +(-1.91170 - 3.72117i) q^{14} +(-1.15075 + 0.554171i) q^{15} +(-4.53920 + 1.40016i) q^{16} +(0.243684 + 0.620897i) q^{17} +(5.80840 - 10.0604i) q^{18} +(0.781344 + 1.35333i) q^{19} +(-0.123844 + 0.155295i) q^{20} +(-8.46742 + 0.854511i) q^{21} +(2.18790 + 2.74354i) q^{22} +(-0.231397 + 0.589589i) q^{23} +(-0.570047 + 7.60675i) q^{24} +(-0.361868 + 4.82879i) q^{25} +(1.23628 - 3.14999i) q^{26} +(-8.71761 - 10.9315i) q^{27} +(-1.12875 + 0.691074i) q^{28} +(3.83058 - 4.80339i) q^{29} +(1.00979 + 1.74901i) q^{30} +(1.69627 - 2.93803i) q^{31} +(1.01136 + 2.57689i) q^{32} +(6.82140 - 2.10412i) q^{33} +(0.950231 - 0.457607i) q^{34} +(0.431270 - 0.957948i) q^{35} +(-3.31117 - 1.59458i) q^{36} +(-4.20292 - 0.633488i) q^{37} +(2.04159 - 1.39193i) q^{38} +(-5.04621 - 4.68220i) q^{39} +(-0.778013 - 0.530440i) q^{40} +(1.37484 + 6.02357i) q^{41} +(2.34793 + 13.2504i) q^{42} +(-1.37677 + 6.03200i) q^{43} +(0.813801 - 0.755097i) q^{44} +(2.88460 - 0.434784i) q^{45} +(0.957002 + 0.295196i) q^{46} +(0.409784 + 5.46818i) q^{47} +15.2798 q^{48} +(4.87919 - 5.01931i) q^{49} +7.65677 q^{50} +(-0.160334 - 2.13951i) q^{51} +(-1.02298 - 0.315548i) q^{52} +(-9.05069 + 1.36417i) q^{53} +(-16.2067 + 15.0376i) q^{54} +(-0.196086 + 0.859108i) q^{55} +(-3.66685 - 5.09121i) q^{56} +(-1.11852 - 4.90058i) q^{57} +(-8.02659 - 5.47244i) q^{58} +(6.10584 + 5.66539i) q^{59} +(0.527901 - 0.359917i) q^{60} +(-9.38126 - 1.41400i) q^{61} +(-4.83310 - 2.32750i) q^{62} +(19.0556 + 3.83543i) q^{63} +(-4.61591 + 2.22291i) q^{64} +(0.812008 - 0.250471i) q^{65} +(-4.12381 - 10.5073i) q^{66} +(0.892421 - 1.54572i) q^{67} +(-0.166830 - 0.288959i) q^{68} +(1.27025 - 1.59285i) q^{69} +(-1.56145 - 0.566828i) q^{70} +(-1.30754 - 1.63960i) q^{71} +(6.36514 - 16.2181i) q^{72} +(1.08006 - 14.4124i) q^{73} +(-0.502244 + 6.70198i) q^{74} +(5.69057 - 14.4993i) q^{75} +(-0.487392 - 0.611170i) q^{76} +(-3.18145 + 4.93498i) q^{77} +(-6.78657 + 8.51010i) q^{78} +(0.821284 + 1.42251i) q^{79} +(-0.943091 + 1.63348i) q^{80} +(8.37897 + 21.3493i) q^{81} +(9.33547 - 2.87961i) q^{82} +(-5.20544 + 2.50681i) q^{83} +(4.12470 - 1.05399i) q^{84} +(0.238620 + 0.114913i) q^{85} +(9.67390 + 1.45811i) q^{86} +(-16.3284 + 11.1325i) q^{87} +(3.85794 + 3.57964i) q^{88} +(-10.5898 - 7.21999i) q^{89} +(-1.02642 - 4.49705i) q^{90} +(5.65530 + 0.277460i) q^{91} +(0.0705027 - 0.308892i) q^{92} +(-7.99948 + 7.42244i) q^{93} +(8.57377 - 1.29229i) q^{94} +(0.592931 + 0.182895i) q^{95} +(-0.665431 - 8.87956i) q^{96} -9.59518 q^{97} +(-8.49096 - 7.10037i) q^{98} -16.3043 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q - 13 q^{2} - 14 q^{3} - 9 q^{4} - 14 q^{5} - 14 q^{7} - 20 q^{8} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 13 q^{2} - 14 q^{3} - 9 q^{4} - 14 q^{5} - 14 q^{7} - 20 q^{8} + 6 q^{9} - 14 q^{10} - 3 q^{11} + 21 q^{12} - 14 q^{13} + 21 q^{14} - 12 q^{15} - 3 q^{16} - 7 q^{17} + 2 q^{18} + 21 q^{19} + 14 q^{20} - 14 q^{21} - 20 q^{22} + 15 q^{23} + 28 q^{24} - 4 q^{25} + 7 q^{27} + 28 q^{28} + 12 q^{29} + 11 q^{30} + 35 q^{31} + 45 q^{32} - 14 q^{33} + 70 q^{34} - 12 q^{36} + 15 q^{37} - 28 q^{38} - 7 q^{39} - 42 q^{40} - 42 q^{41} + 28 q^{42} - 30 q^{43} - 50 q^{44} + 7 q^{45} - 78 q^{46} + 21 q^{47} - 84 q^{48} - 70 q^{49} + 40 q^{50} - 52 q^{51} - 70 q^{52} + 11 q^{53} - 77 q^{54} - 7 q^{55} - 28 q^{56} - 12 q^{57} + 16 q^{58} - 28 q^{59} + 56 q^{60} + 7 q^{61} - 28 q^{62} + 35 q^{63} - 32 q^{64} + 14 q^{65} + 154 q^{66} + 11 q^{67} + 77 q^{68} + 70 q^{69} + 70 q^{70} + 19 q^{71} + 170 q^{72} + 7 q^{73} + 34 q^{74} + 112 q^{75} + 119 q^{76} + 7 q^{77} + 28 q^{78} + 15 q^{79} + 70 q^{80} + 64 q^{81} - 14 q^{82} - 84 q^{84} - 26 q^{85} - 33 q^{86} - 112 q^{87} - 77 q^{88} - 14 q^{89} - 182 q^{90} + 84 q^{91} - 38 q^{92} - 80 q^{93} + 14 q^{94} - 61 q^{95} - 70 q^{96} - 161 q^{98} - 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/49\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{2}{21}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.118164 1.57679i −0.0835548 1.11496i −0.868597 0.495519i \(-0.834978\pi\)
0.785042 0.619442i \(-0.212641\pi\)
\(3\) −3.07373 0.948121i −1.77462 0.547398i −0.777905 0.628382i \(-0.783717\pi\)
−0.996715 + 0.0809843i \(0.974194\pi\)
\(4\) −0.494650 + 0.0745565i −0.247325 + 0.0372783i
\(5\) 0.291074 0.270077i 0.130172 0.120782i −0.612400 0.790548i \(-0.709796\pi\)
0.742572 + 0.669766i \(0.233605\pi\)
\(6\) −1.13178 + 4.95867i −0.462049 + 2.02437i
\(7\) 2.43713 1.02976i 0.921148 0.389212i
\(8\) −0.527696 2.31199i −0.186569 0.817411i
\(9\) 6.07018 + 4.13858i 2.02339 + 1.37953i
\(10\) −0.460250 0.427049i −0.145544 0.135045i
\(11\) −1.83363 + 1.25015i −0.552862 + 0.376935i −0.807288 0.590157i \(-0.799066\pi\)
0.254427 + 0.967092i \(0.418113\pi\)
\(12\) 1.59111 + 0.239821i 0.459314 + 0.0692305i
\(13\) 1.92814 + 0.928542i 0.534769 + 0.257531i 0.681721 0.731612i \(-0.261232\pi\)
−0.146952 + 0.989144i \(0.546946\pi\)
\(14\) −1.91170 3.72117i −0.510923 0.994523i
\(15\) −1.15075 + 0.554171i −0.297122 + 0.143086i
\(16\) −4.53920 + 1.40016i −1.13480 + 0.350039i
\(17\) 0.243684 + 0.620897i 0.0591021 + 0.150590i 0.957375 0.288849i \(-0.0932726\pi\)
−0.898273 + 0.439439i \(0.855177\pi\)
\(18\) 5.80840 10.0604i 1.36905 2.37127i
\(19\) 0.781344 + 1.35333i 0.179253 + 0.310475i 0.941625 0.336664i \(-0.109299\pi\)
−0.762372 + 0.647139i \(0.775965\pi\)
\(20\) −0.123844 + 0.155295i −0.0276923 + 0.0347250i
\(21\) −8.46742 + 0.854511i −1.84774 + 0.186470i
\(22\) 2.18790 + 2.74354i 0.466462 + 0.584924i
\(23\) −0.231397 + 0.589589i −0.0482495 + 0.122938i −0.952967 0.303075i \(-0.901987\pi\)
0.904717 + 0.426013i \(0.140082\pi\)
\(24\) −0.570047 + 7.60675i −0.116360 + 1.55272i
\(25\) −0.361868 + 4.82879i −0.0723736 + 0.965759i
\(26\) 1.23628 3.14999i 0.242455 0.617765i
\(27\) −8.71761 10.9315i −1.67771 2.10378i
\(28\) −1.12875 + 0.691074i −0.213314 + 0.130601i
\(29\) 3.83058 4.80339i 0.711320 0.891967i −0.286492 0.958083i \(-0.592489\pi\)
0.997812 + 0.0661153i \(0.0210605\pi\)
\(30\) 1.00979 + 1.74901i 0.184362 + 0.319324i
\(31\) 1.69627 2.93803i 0.304659 0.527685i −0.672526 0.740073i \(-0.734791\pi\)
0.977185 + 0.212388i \(0.0681241\pi\)
\(32\) 1.01136 + 2.57689i 0.178784 + 0.455535i
\(33\) 6.82140 2.10412i 1.18745 0.366281i
\(34\) 0.950231 0.457607i 0.162963 0.0784789i
\(35\) 0.431270 0.957948i 0.0728979 0.161923i
\(36\) −3.31117 1.59458i −0.551862 0.265763i
\(37\) −4.20292 0.633488i −0.690955 0.104145i −0.205828 0.978588i \(-0.565989\pi\)
−0.485127 + 0.874444i \(0.661227\pi\)
\(38\) 2.04159 1.39193i 0.331190 0.225801i
\(39\) −5.04621 4.68220i −0.808040 0.749752i
\(40\) −0.778013 0.530440i −0.123015 0.0838700i
\(41\) 1.37484 + 6.02357i 0.214714 + 0.940724i 0.961315 + 0.275452i \(0.0888274\pi\)
−0.746601 + 0.665272i \(0.768315\pi\)
\(42\) 2.34793 + 13.2504i 0.362294 + 2.04458i
\(43\) −1.37677 + 6.03200i −0.209955 + 0.919872i 0.754641 + 0.656138i \(0.227811\pi\)
−0.964596 + 0.263734i \(0.915046\pi\)
\(44\) 0.813801 0.755097i 0.122685 0.113835i
\(45\) 2.88460 0.434784i 0.430011 0.0648138i
\(46\) 0.957002 + 0.295196i 0.141102 + 0.0435243i
\(47\) 0.409784 + 5.46818i 0.0597731 + 0.797616i 0.943871 + 0.330314i \(0.107155\pi\)
−0.884098 + 0.467302i \(0.845226\pi\)
\(48\) 15.2798 2.20545
\(49\) 4.87919 5.01931i 0.697028 0.717044i
\(50\) 7.65677 1.08283
\(51\) −0.160334 2.13951i −0.0224513 0.299592i
\(52\) −1.02298 0.315548i −0.141862 0.0437587i
\(53\) −9.05069 + 1.36417i −1.24321 + 0.187383i −0.737515 0.675331i \(-0.764001\pi\)
−0.505692 + 0.862714i \(0.668763\pi\)
\(54\) −16.2067 + 15.0376i −2.20545 + 2.04636i
\(55\) −0.196086 + 0.859108i −0.0264402 + 0.115842i
\(56\) −3.66685 5.09121i −0.490004 0.680342i
\(57\) −1.11852 4.90058i −0.148152 0.649097i
\(58\) −8.02659 5.47244i −1.05394 0.718566i
\(59\) 6.10584 + 5.66539i 0.794912 + 0.737571i 0.968974 0.247164i \(-0.0794987\pi\)
−0.174061 + 0.984735i \(0.555689\pi\)
\(60\) 0.527901 0.359917i 0.0681517 0.0464650i
\(61\) −9.38126 1.41400i −1.20115 0.181044i −0.482170 0.876077i \(-0.660151\pi\)
−0.718977 + 0.695033i \(0.755390\pi\)
\(62\) −4.83310 2.32750i −0.613804 0.295592i
\(63\) 19.0556 + 3.83543i 2.40077 + 0.483218i
\(64\) −4.61591 + 2.22291i −0.576989 + 0.277863i
\(65\) 0.812008 0.250471i 0.100717 0.0310671i
\(66\) −4.12381 10.5073i −0.507606 1.29336i
\(67\) 0.892421 1.54572i 0.109027 0.188840i −0.806350 0.591439i \(-0.798560\pi\)
0.915376 + 0.402600i \(0.131893\pi\)
\(68\) −0.166830 0.288959i −0.0202311 0.0350414i
\(69\) 1.27025 1.59285i 0.152920 0.191756i
\(70\) −1.56145 0.566828i −0.186628 0.0677489i
\(71\) −1.30754 1.63960i −0.155176 0.194585i 0.698166 0.715936i \(-0.254000\pi\)
−0.853342 + 0.521351i \(0.825428\pi\)
\(72\) 6.36514 16.2181i 0.750138 1.91132i
\(73\) 1.08006 14.4124i 0.126412 1.68684i −0.468822 0.883292i \(-0.655322\pi\)
0.595234 0.803552i \(-0.297059\pi\)
\(74\) −0.502244 + 6.70198i −0.0583847 + 0.779090i
\(75\) 5.69057 14.4993i 0.657090 1.67424i
\(76\) −0.487392 0.611170i −0.0559076 0.0701060i
\(77\) −3.18145 + 4.93498i −0.362560 + 0.562393i
\(78\) −6.78657 + 8.51010i −0.768428 + 0.963579i
\(79\) 0.821284 + 1.42251i 0.0924017 + 0.160044i 0.908521 0.417839i \(-0.137212\pi\)
−0.816120 + 0.577883i \(0.803879\pi\)
\(80\) −0.943091 + 1.63348i −0.105441 + 0.182629i
\(81\) 8.37897 + 21.3493i 0.930996 + 2.37214i
\(82\) 9.33547 2.87961i 1.03093 0.318000i
\(83\) −5.20544 + 2.50681i −0.571371 + 0.275158i −0.697179 0.716897i \(-0.745562\pi\)
0.125808 + 0.992055i \(0.459848\pi\)
\(84\) 4.12470 1.05399i 0.450042 0.114999i
\(85\) 0.238620 + 0.114913i 0.0258820 + 0.0124641i
\(86\) 9.67390 + 1.45811i 1.04316 + 0.157232i
\(87\) −16.3284 + 11.1325i −1.75058 + 1.19353i
\(88\) 3.85794 + 3.57964i 0.411257 + 0.381591i
\(89\) −10.5898 7.21999i −1.12251 0.765318i −0.147855 0.989009i \(-0.547237\pi\)
−0.974660 + 0.223691i \(0.928189\pi\)
\(90\) −1.02642 4.49705i −0.108194 0.474030i
\(91\) 5.65530 + 0.277460i 0.592836 + 0.0290857i
\(92\) 0.0705027 0.308892i 0.00735041 0.0322043i
\(93\) −7.99948 + 7.42244i −0.829508 + 0.769671i
\(94\) 8.57377 1.29229i 0.884317 0.133289i
\(95\) 0.592931 + 0.182895i 0.0608335 + 0.0187646i
\(96\) −0.665431 8.87956i −0.0679153 0.906267i
\(97\) −9.59518 −0.974243 −0.487121 0.873334i \(-0.661953\pi\)
−0.487121 + 0.873334i \(0.661953\pi\)
\(98\) −8.49096 7.10037i −0.857716 0.717246i
\(99\) −16.3043 −1.63865
\(100\) −0.181020 2.41554i −0.0181020 0.241554i
\(101\) 11.8441 + 3.65343i 1.17853 + 0.363530i 0.821306 0.570488i \(-0.193246\pi\)
0.357228 + 0.934017i \(0.383722\pi\)
\(102\) −3.35462 + 0.505628i −0.332157 + 0.0500646i
\(103\) 0.999008 0.926944i 0.0984352 0.0913345i −0.629420 0.777065i \(-0.716708\pi\)
0.727856 + 0.685730i \(0.240517\pi\)
\(104\) 1.12931 4.94782i 0.110738 0.485174i
\(105\) −2.23386 + 2.53558i −0.218002 + 0.247447i
\(106\) 3.22048 + 14.1099i 0.312801 + 1.37047i
\(107\) 5.93297 + 4.04503i 0.573562 + 0.391048i 0.815080 0.579348i \(-0.196693\pi\)
−0.241518 + 0.970396i \(0.577645\pi\)
\(108\) 5.12719 + 4.75734i 0.493364 + 0.457775i
\(109\) 15.8905 10.8340i 1.52203 1.03770i 0.541650 0.840604i \(-0.317800\pi\)
0.980383 0.197101i \(-0.0631526\pi\)
\(110\) 1.37781 + 0.207671i 0.131369 + 0.0198006i
\(111\) 12.3180 + 5.93204i 1.16917 + 0.563045i
\(112\) −9.62079 + 8.08664i −0.909079 + 0.764116i
\(113\) −3.02699 + 1.45772i −0.284755 + 0.137131i −0.570809 0.821083i \(-0.693370\pi\)
0.286054 + 0.958213i \(0.407656\pi\)
\(114\) −7.59502 + 2.34275i −0.711339 + 0.219419i
\(115\) 0.0918809 + 0.234109i 0.00856794 + 0.0218307i
\(116\) −1.53667 + 2.66159i −0.142676 + 0.247123i
\(117\) 7.86130 + 13.6162i 0.726778 + 1.25882i
\(118\) 8.21165 10.2971i 0.755944 0.947923i
\(119\) 1.23326 + 1.26227i 0.113053 + 0.115712i
\(120\) 1.88848 + 2.36808i 0.172394 + 0.216175i
\(121\) −2.21941 + 5.65497i −0.201765 + 0.514088i
\(122\) −1.12105 + 14.9594i −0.101495 + 1.35436i
\(123\) 1.48518 19.8184i 0.133914 1.78696i
\(124\) −0.620012 + 1.57976i −0.0556787 + 0.141867i
\(125\) 2.43666 + 3.05548i 0.217942 + 0.273290i
\(126\) 3.79599 30.4999i 0.338174 2.71714i
\(127\) 2.74253 3.43902i 0.243360 0.305164i −0.645118 0.764083i \(-0.723192\pi\)
0.888478 + 0.458919i \(0.151763\pi\)
\(128\) 6.81875 + 11.8104i 0.602698 + 1.04390i
\(129\) 9.95088 17.2354i 0.876126 1.51749i
\(130\) −0.490892 1.25077i −0.0430541 0.109700i
\(131\) −8.59848 + 2.65228i −0.751253 + 0.231731i −0.646654 0.762784i \(-0.723832\pi\)
−0.104599 + 0.994514i \(0.533356\pi\)
\(132\) −3.21733 + 1.54938i −0.280033 + 0.134857i
\(133\) 3.29784 + 2.49364i 0.285959 + 0.216226i
\(134\) −2.54273 1.22451i −0.219658 0.105782i
\(135\) −5.48983 0.827458i −0.472489 0.0712162i
\(136\) 1.30691 0.891039i 0.112067 0.0764060i
\(137\) 9.84840 + 9.13798i 0.841406 + 0.780711i 0.977711 0.209956i \(-0.0673322\pi\)
−0.136305 + 0.990667i \(0.543523\pi\)
\(138\) −2.66169 1.81471i −0.226578 0.154478i
\(139\) 0.369690 + 1.61972i 0.0313567 + 0.137383i 0.988183 0.153277i \(-0.0489826\pi\)
−0.956827 + 0.290659i \(0.906125\pi\)
\(140\) −0.141907 + 0.506003i −0.0119933 + 0.0427651i
\(141\) 3.92493 17.1963i 0.330539 1.44819i
\(142\) −2.43080 + 2.25546i −0.203988 + 0.189274i
\(143\) −4.69632 + 0.707856i −0.392726 + 0.0591939i
\(144\) −33.3484 10.2866i −2.77903 0.857219i
\(145\) −0.182305 2.43269i −0.0151396 0.202024i
\(146\) −22.8530 −1.89133
\(147\) −19.7562 + 10.8020i −1.62947 + 0.890930i
\(148\) 2.12620 0.174773
\(149\) −0.677911 9.04609i −0.0555366 0.741085i −0.953573 0.301163i \(-0.902625\pi\)
0.898036 0.439922i \(-0.144994\pi\)
\(150\) −23.5349 7.25954i −1.92161 0.592739i
\(151\) −9.05271 + 1.36448i −0.736699 + 0.111039i −0.506665 0.862143i \(-0.669122\pi\)
−0.230034 + 0.973183i \(0.573884\pi\)
\(152\) 2.71657 2.52060i 0.220343 0.204448i
\(153\) −1.09042 + 4.77746i −0.0881556 + 0.386235i
\(154\) 8.15737 + 4.43335i 0.657340 + 0.357249i
\(155\) −0.299753 1.31331i −0.0240768 0.105487i
\(156\) 2.84520 + 1.93982i 0.227798 + 0.155310i
\(157\) −4.93123 4.57551i −0.393555 0.365166i 0.458431 0.888730i \(-0.348412\pi\)
−0.851986 + 0.523564i \(0.824602\pi\)
\(158\) 2.14595 1.46308i 0.170723 0.116397i
\(159\) 29.1128 + 4.38805i 2.30879 + 0.347995i
\(160\) 0.990338 + 0.476922i 0.0782931 + 0.0377040i
\(161\) 0.0431911 + 1.67519i 0.00340394 + 0.132023i
\(162\) 32.6733 15.7346i 2.56705 1.23623i
\(163\) 2.71032 0.836022i 0.212288 0.0654823i −0.186787 0.982400i \(-0.559807\pi\)
0.399075 + 0.916918i \(0.369331\pi\)
\(164\) −1.12916 2.87706i −0.0881728 0.224661i
\(165\) 1.41725 2.45476i 0.110333 0.191102i
\(166\) 4.56781 + 7.91168i 0.354531 + 0.614065i
\(167\) 3.84685 4.82380i 0.297678 0.373277i −0.610389 0.792102i \(-0.708987\pi\)
0.908067 + 0.418826i \(0.137558\pi\)
\(168\) 6.44384 + 19.1256i 0.497153 + 1.47558i
\(169\) −5.24984 6.58309i −0.403834 0.506392i
\(170\) 0.152998 0.389833i 0.0117344 0.0298988i
\(171\) −0.857954 + 11.4486i −0.0656094 + 0.875496i
\(172\) 0.231292 3.08638i 0.0176359 0.235334i
\(173\) −6.01320 + 15.3214i −0.457175 + 1.16486i 0.497567 + 0.867426i \(0.334227\pi\)
−0.954741 + 0.297437i \(0.903868\pi\)
\(174\) 19.4831 + 24.4310i 1.47701 + 1.85211i
\(175\) 4.09058 + 12.1410i 0.309218 + 0.917776i
\(176\) 6.57282 8.24206i 0.495445 0.621269i
\(177\) −13.3962 23.2030i −1.00692 1.74404i
\(178\) −10.1331 + 17.5510i −0.759508 + 1.31551i
\(179\) −5.90683 15.0504i −0.441497 1.12492i −0.962481 0.271350i \(-0.912530\pi\)
0.520983 0.853567i \(-0.325565\pi\)
\(180\) −1.39445 + 0.430132i −0.103937 + 0.0320602i
\(181\) −6.74759 + 3.24947i −0.501545 + 0.241531i −0.667511 0.744600i \(-0.732640\pi\)
0.165966 + 0.986131i \(0.446926\pi\)
\(182\) −0.230757 8.95001i −0.0171049 0.663419i
\(183\) 27.4949 + 13.2408i 2.03248 + 0.978790i
\(184\) 1.48523 + 0.223862i 0.109493 + 0.0165033i
\(185\) −1.39445 + 0.950719i −0.102522 + 0.0698983i
\(186\) 12.6489 + 11.7365i 0.927462 + 0.860559i
\(187\) −1.22304 0.833856i −0.0894377 0.0609776i
\(188\) −0.610388 2.67429i −0.0445171 0.195042i
\(189\) −32.5028 17.6645i −2.36423 1.28491i
\(190\) 0.218324 0.956541i 0.0158389 0.0693948i
\(191\) 16.2118 15.0424i 1.17305 1.08843i 0.178520 0.983936i \(-0.442869\pi\)
0.994526 0.104491i \(-0.0333214\pi\)
\(192\) 16.2957 2.45618i 1.17604 0.177259i
\(193\) −20.0866 6.19590i −1.44587 0.445991i −0.530180 0.847885i \(-0.677876\pi\)
−0.915686 + 0.401894i \(0.868352\pi\)
\(194\) 1.13381 + 15.1296i 0.0814026 + 1.08624i
\(195\) −2.73337 −0.195741
\(196\) −2.03927 + 2.84658i −0.145662 + 0.203327i
\(197\) 14.9189 1.06293 0.531464 0.847081i \(-0.321642\pi\)
0.531464 + 0.847081i \(0.321642\pi\)
\(198\) 1.92659 + 25.7086i 0.136917 + 1.82703i
\(199\) −10.4493 3.22319i −0.740734 0.228486i −0.0986518 0.995122i \(-0.531453\pi\)
−0.642082 + 0.766636i \(0.721929\pi\)
\(200\) 11.3551 1.71150i 0.802925 0.121021i
\(201\) −4.20859 + 3.90500i −0.296851 + 0.275438i
\(202\) 4.36115 19.1074i 0.306849 1.34439i
\(203\) 4.38927 15.6511i 0.308067 1.09849i
\(204\) 0.238824 + 1.04636i 0.0167210 + 0.0732596i
\(205\) 2.02701 + 1.38199i 0.141572 + 0.0965224i
\(206\) −1.57965 1.46570i −0.110059 0.102120i
\(207\) −3.84468 + 2.62126i −0.267224 + 0.182190i
\(208\) −10.0523 1.51514i −0.697002 0.105056i
\(209\) −3.12456 1.50471i −0.216131 0.104083i
\(210\) 4.26205 + 3.22272i 0.294109 + 0.222389i
\(211\) −15.2742 + 7.35566i −1.05152 + 0.506384i −0.878106 0.478465i \(-0.841193\pi\)
−0.173411 + 0.984850i \(0.555479\pi\)
\(212\) 4.37522 1.34958i 0.300491 0.0926892i
\(213\) 2.46448 + 6.27939i 0.168863 + 0.430257i
\(214\) 5.67711 9.83305i 0.388079 0.672173i
\(215\) 1.22836 + 2.12759i 0.0837738 + 0.145100i
\(216\) −20.6733 + 25.9236i −1.40664 + 1.76387i
\(217\) 1.10857 8.90710i 0.0752546 0.604653i
\(218\) −18.9606 23.7758i −1.28417 1.61030i
\(219\) −16.9845 + 43.2759i −1.14771 + 2.92431i
\(220\) 0.0329418 0.439578i 0.00222094 0.0296363i
\(221\) −0.106673 + 1.42345i −0.00717557 + 0.0957513i
\(222\) 7.89805 20.1239i 0.530083 1.35063i
\(223\) 13.4548 + 16.8717i 0.900998 + 1.12982i 0.990998 + 0.133874i \(0.0427417\pi\)
−0.0900007 + 0.995942i \(0.528687\pi\)
\(224\) 5.11838 + 5.23877i 0.341986 + 0.350030i
\(225\) −22.1810 + 27.8140i −1.47873 + 1.85427i
\(226\) 2.65620 + 4.60068i 0.176688 + 0.306033i
\(227\) 8.44939 14.6348i 0.560806 0.971344i −0.436621 0.899646i \(-0.643825\pi\)
0.997426 0.0716980i \(-0.0228418\pi\)
\(228\) 0.918648 + 2.34068i 0.0608390 + 0.155015i
\(229\) 19.2696 5.94389i 1.27337 0.392783i 0.416888 0.908958i \(-0.363121\pi\)
0.856483 + 0.516175i \(0.172645\pi\)
\(230\) 0.358284 0.172540i 0.0236245 0.0113770i
\(231\) 14.4579 12.1524i 0.951259 0.799570i
\(232\) −13.1268 6.32152i −0.861814 0.415028i
\(233\) 0.873594 + 0.131673i 0.0572310 + 0.00862619i 0.177595 0.984104i \(-0.443168\pi\)
−0.120364 + 0.992730i \(0.538406\pi\)
\(234\) 20.5410 14.0046i 1.34280 0.915508i
\(235\) 1.59611 + 1.48097i 0.104119 + 0.0966079i
\(236\) −3.44265 2.34716i −0.224097 0.152787i
\(237\) −1.17570 5.15108i −0.0763699 0.334599i
\(238\) 1.84461 2.09376i 0.119568 0.135718i
\(239\) −0.533986 + 2.33954i −0.0345407 + 0.151333i −0.989258 0.146183i \(-0.953301\pi\)
0.954717 + 0.297516i \(0.0961582\pi\)
\(240\) 4.44755 4.12672i 0.287088 0.266379i
\(241\) −20.6241 + 3.10858i −1.32851 + 0.200241i −0.774663 0.632374i \(-0.782081\pi\)
−0.553851 + 0.832616i \(0.686842\pi\)
\(242\) 9.17897 + 2.83134i 0.590047 + 0.182005i
\(243\) −2.37840 31.7376i −0.152575 2.03597i
\(244\) 4.74587 0.303823
\(245\) 0.0646049 2.77875i 0.00412746 0.177528i
\(246\) −31.4249 −2.00358
\(247\) 0.249917 + 3.33491i 0.0159019 + 0.212195i
\(248\) −7.68780 2.37137i −0.488176 0.150582i
\(249\) 18.3769 2.76987i 1.16459 0.175533i
\(250\) 4.52993 4.20316i 0.286498 0.265831i
\(251\) 5.88168 25.7693i 0.371248 1.62655i −0.352030 0.935989i \(-0.614508\pi\)
0.723278 0.690557i \(-0.242634\pi\)
\(252\) −9.71179 0.476479i −0.611785 0.0300154i
\(253\) −0.312778 1.37037i −0.0196642 0.0861545i
\(254\) −5.74669 3.91803i −0.360579 0.245839i
\(255\) −0.624502 0.579453i −0.0391078 0.0362868i
\(256\) 9.35075 6.37523i 0.584422 0.398452i
\(257\) −11.1370 1.67863i −0.694704 0.104710i −0.207808 0.978170i \(-0.566633\pi\)
−0.486896 + 0.873460i \(0.661871\pi\)
\(258\) −28.3525 13.6539i −1.76515 0.850052i
\(259\) −10.8954 + 2.78410i −0.677006 + 0.172996i
\(260\) −0.382986 + 0.184436i −0.0237518 + 0.0114383i
\(261\) 43.1315 13.3043i 2.66977 0.823516i
\(262\) 5.19813 + 13.2446i 0.321142 + 0.818255i
\(263\) −11.1542 + 19.3196i −0.687795 + 1.19130i 0.284755 + 0.958600i \(0.408088\pi\)
−0.972550 + 0.232695i \(0.925246\pi\)
\(264\) −8.46433 14.6606i −0.520943 0.902301i
\(265\) −2.26599 + 2.84146i −0.139198 + 0.174549i
\(266\) 3.54226 5.49466i 0.217190 0.336899i
\(267\) 25.7047 + 32.2327i 1.57310 + 1.97261i
\(268\) −0.326193 + 0.831126i −0.0199254 + 0.0507691i
\(269\) −1.48850 + 19.8626i −0.0907554 + 1.21105i 0.746934 + 0.664899i \(0.231525\pi\)
−0.837689 + 0.546148i \(0.816094\pi\)
\(270\) −0.656028 + 8.75409i −0.0399246 + 0.532757i
\(271\) −3.73698 + 9.52168i −0.227006 + 0.578401i −0.998313 0.0580620i \(-0.981508\pi\)
0.771307 + 0.636463i \(0.219603\pi\)
\(272\) −1.97548 2.47718i −0.119781 0.150201i
\(273\) −17.1198 6.21474i −1.03614 0.376133i
\(274\) 13.2450 16.6087i 0.800158 1.00337i
\(275\) −5.37319 9.30663i −0.324015 0.561211i
\(276\) −0.509574 + 0.882607i −0.0306727 + 0.0531267i
\(277\) 2.87132 + 7.31602i 0.172521 + 0.439577i 0.990815 0.135223i \(-0.0431751\pi\)
−0.818294 + 0.574800i \(0.805080\pi\)
\(278\) 2.51027 0.774317i 0.150556 0.0464404i
\(279\) 22.4559 10.8142i 1.34440 0.647429i
\(280\) −2.44234 0.491586i −0.145958 0.0293779i
\(281\) −10.3585 4.98841i −0.617939 0.297584i 0.0986041 0.995127i \(-0.468562\pi\)
−0.716543 + 0.697543i \(0.754277\pi\)
\(282\) −27.5787 4.15682i −1.64229 0.247535i
\(283\) −6.67767 + 4.55276i −0.396946 + 0.270634i −0.745299 0.666730i \(-0.767693\pi\)
0.348353 + 0.937363i \(0.386741\pi\)
\(284\) 0.769016 + 0.713542i 0.0456327 + 0.0423410i
\(285\) −1.64911 1.12434i −0.0976846 0.0666002i
\(286\) 1.67108 + 7.32148i 0.0988130 + 0.432928i
\(287\) 9.55349 + 13.2645i 0.563925 + 0.782977i
\(288\) −4.52556 + 19.8278i −0.266671 + 1.16836i
\(289\) 12.1358 11.2603i 0.713868 0.662372i
\(290\) −3.81431 + 0.574914i −0.223984 + 0.0337601i
\(291\) 29.4930 + 9.09739i 1.72891 + 0.533298i
\(292\) 0.540287 + 7.20963i 0.0316179 + 0.421912i
\(293\) 4.90918 0.286797 0.143399 0.989665i \(-0.454197\pi\)
0.143399 + 0.989665i \(0.454197\pi\)
\(294\) 19.3669 + 29.8751i 1.12950 + 1.74235i
\(295\) 3.30734 0.192561
\(296\) 0.753247 + 10.0514i 0.0437816 + 0.584225i
\(297\) 29.6510 + 9.14612i 1.72053 + 0.530712i
\(298\) −14.1837 + 2.13785i −0.821640 + 0.123842i
\(299\) −0.993623 + 0.921947i −0.0574627 + 0.0533176i
\(300\) −1.73382 + 7.59637i −0.100102 + 0.438576i
\(301\) 2.85615 + 16.1185i 0.164626 + 0.929055i
\(302\) 3.22120 + 14.1130i 0.185359 + 0.812112i
\(303\) −32.9418 22.4593i −1.89246 1.29025i
\(304\) −5.44155 5.04902i −0.312094 0.289581i
\(305\) −3.11253 + 2.12209i −0.178223 + 0.121510i
\(306\) 7.66191 + 1.15485i 0.438002 + 0.0660183i
\(307\) 5.02321 + 2.41905i 0.286690 + 0.138063i 0.571702 0.820461i \(-0.306283\pi\)
−0.285012 + 0.958524i \(0.591998\pi\)
\(308\) 1.20577 2.67829i 0.0687051 0.152610i
\(309\) −3.94954 + 1.90200i −0.224681 + 0.108201i
\(310\) −2.03539 + 0.627835i −0.115602 + 0.0356586i
\(311\) −7.39363 18.8386i −0.419254 1.06824i −0.972019 0.234904i \(-0.924522\pi\)
0.552764 0.833338i \(-0.313573\pi\)
\(312\) −8.16232 + 14.1376i −0.462101 + 0.800382i
\(313\) 6.09673 + 10.5598i 0.344607 + 0.596877i 0.985282 0.170935i \(-0.0546787\pi\)
−0.640675 + 0.767812i \(0.721345\pi\)
\(314\) −6.63194 + 8.31619i −0.374262 + 0.469310i
\(315\) 6.58243 4.03007i 0.370878 0.227069i
\(316\) −0.512306 0.642411i −0.0288194 0.0361384i
\(317\) 3.17739 8.09587i 0.178460 0.454709i −0.813452 0.581631i \(-0.802415\pi\)
0.991913 + 0.126922i \(0.0405098\pi\)
\(318\) 3.47895 46.4233i 0.195090 2.60329i
\(319\) −1.01891 + 13.5965i −0.0570482 + 0.761256i
\(320\) −0.743215 + 1.89368i −0.0415470 + 0.105860i
\(321\) −14.4012 18.0585i −0.803796 1.00793i
\(322\) 2.63632 0.266051i 0.146916 0.0148264i
\(323\) −0.649876 + 0.814918i −0.0361600 + 0.0453433i
\(324\) −5.73639 9.93571i −0.318688 0.551984i
\(325\) −5.18147 + 8.97457i −0.287416 + 0.497820i
\(326\) −1.63850 4.17482i −0.0907479 0.231222i
\(327\) −59.1150 + 18.2346i −3.26907 + 1.00837i
\(328\) 13.2009 6.35723i 0.728899 0.351019i
\(329\) 6.62960 + 12.9047i 0.365502 + 0.711458i
\(330\) −4.03811 1.94465i −0.222291 0.107050i
\(331\) 31.1121 + 4.68939i 1.71007 + 0.257752i 0.929901 0.367811i \(-0.119893\pi\)
0.780173 + 0.625563i \(0.215131\pi\)
\(332\) 2.38797 1.62809i 0.131057 0.0893531i
\(333\) −22.8907 21.2395i −1.25440 1.16392i
\(334\) −8.06069 5.49568i −0.441061 0.300710i
\(335\) −0.157703 0.690940i −0.00861621 0.0377501i
\(336\) 37.2388 15.7345i 2.03154 0.858388i
\(337\) 6.27847 27.5078i 0.342010 1.49844i −0.452814 0.891605i \(-0.649580\pi\)
0.794824 0.606840i \(-0.207563\pi\)
\(338\) −9.75983 + 9.05580i −0.530865 + 0.492570i
\(339\) 10.6862 1.61069i 0.580397 0.0874808i
\(340\) −0.126601 0.0390512i −0.00686590 0.00211785i
\(341\) 0.562636 + 7.50786i 0.0304685 + 0.406573i
\(342\) 18.1534 0.981626
\(343\) 6.72254 17.2571i 0.362983 0.931796i
\(344\) 14.6724 0.791085
\(345\) −0.0604539 0.806701i −0.00325473 0.0434313i
\(346\) 24.8692 + 7.67113i 1.33698 + 0.412402i
\(347\) −7.05711 + 1.06369i −0.378846 + 0.0571018i −0.335705 0.941967i \(-0.608974\pi\)
−0.0431407 + 0.999069i \(0.513736\pi\)
\(348\) 7.24683 6.72408i 0.388471 0.360448i
\(349\) −6.57045 + 28.7870i −0.351708 + 1.54093i 0.421528 + 0.906815i \(0.361494\pi\)
−0.773236 + 0.634118i \(0.781363\pi\)
\(350\) 18.6605 7.88462i 0.997447 0.421451i
\(351\) −6.65836 29.1722i −0.355397 1.55710i
\(352\) −5.07596 3.46073i −0.270550 0.184458i
\(353\) 11.9275 + 11.0671i 0.634838 + 0.589044i 0.930519 0.366243i \(-0.119356\pi\)
−0.295681 + 0.955287i \(0.595547\pi\)
\(354\) −35.0033 + 23.8648i −1.86040 + 1.26840i
\(355\) −0.823407 0.124109i −0.0437019 0.00658700i
\(356\) 5.77654 + 2.78183i 0.306156 + 0.147437i
\(357\) −2.59394 5.04916i −0.137286 0.267230i
\(358\) −23.0333 + 11.0923i −1.21735 + 0.586244i
\(359\) −25.0707 + 7.73328i −1.32318 + 0.408147i −0.874275 0.485432i \(-0.838662\pi\)
−0.448906 + 0.893579i \(0.648186\pi\)
\(360\) −2.52741 6.43974i −0.133206 0.339404i
\(361\) 8.27900 14.3397i 0.435737 0.754719i
\(362\) 5.92107 + 10.2556i 0.311204 + 0.539022i
\(363\) 12.1835 15.2776i 0.639467 0.801866i
\(364\) −2.81808 + 0.284394i −0.147708 + 0.0149063i
\(365\) −3.57808 4.48677i −0.187285 0.234848i
\(366\) 17.6291 44.9183i 0.921489 2.34792i
\(367\) 1.57231 20.9810i 0.0820740 1.09520i −0.792359 0.610055i \(-0.791147\pi\)
0.874433 0.485146i \(-0.161234\pi\)
\(368\) 0.224838 3.00025i 0.0117205 0.156399i
\(369\) −16.5835 + 42.2541i −0.863302 + 2.19966i
\(370\) 1.66386 + 2.08642i 0.0865000 + 0.108468i
\(371\) −20.6529 + 12.6447i −1.07225 + 0.656479i
\(372\) 3.40356 4.26792i 0.176466 0.221282i
\(373\) 2.07271 + 3.59004i 0.107321 + 0.185885i 0.914684 0.404170i \(-0.132439\pi\)
−0.807363 + 0.590055i \(0.799106\pi\)
\(374\) −1.17030 + 2.02702i −0.0605147 + 0.104814i
\(375\) −4.59269 11.7020i −0.237165 0.604288i
\(376\) 12.4261 3.83295i 0.640829 0.197670i
\(377\) 11.8460 5.70475i 0.610102 0.293810i
\(378\) −24.0126 + 53.3375i −1.23508 + 2.74338i
\(379\) 17.7420 + 8.54409i 0.911344 + 0.438880i 0.829973 0.557804i \(-0.188356\pi\)
0.0813713 + 0.996684i \(0.474070\pi\)
\(380\) −0.306930 0.0462622i −0.0157452 0.00237320i
\(381\) −11.6904 + 7.97038i −0.598917 + 0.408335i
\(382\) −25.6343 23.7852i −1.31157 1.21696i
\(383\) −3.72147 2.53725i −0.190158 0.129648i 0.464499 0.885574i \(-0.346235\pi\)
−0.654657 + 0.755926i \(0.727187\pi\)
\(384\) −9.76131 42.7671i −0.498130 2.18245i
\(385\) 0.406788 + 2.29568i 0.0207318 + 0.116999i
\(386\) −7.39613 + 32.4046i −0.376453 + 1.64935i
\(387\) −33.3211 + 30.9175i −1.69381 + 1.57162i
\(388\) 4.74626 0.715383i 0.240955 0.0363181i
\(389\) 24.0346 + 7.41368i 1.21860 + 0.375889i 0.836363 0.548175i \(-0.184677\pi\)
0.382238 + 0.924064i \(0.375154\pi\)
\(390\) 0.322987 + 4.30996i 0.0163551 + 0.218243i
\(391\) −0.422461 −0.0213648
\(392\) −14.1793 8.63197i −0.716164 0.435980i
\(393\) 28.9441 1.46004
\(394\) −1.76288 23.5240i −0.0888127 1.18512i
\(395\) 0.623240 + 0.192244i 0.0313586 + 0.00967285i
\(396\) 8.06495 1.21560i 0.405279 0.0610860i
\(397\) 17.3530 16.1013i 0.870924 0.808100i −0.111693 0.993743i \(-0.535627\pi\)
0.982617 + 0.185643i \(0.0594369\pi\)
\(398\) −3.84757 + 16.8573i −0.192861 + 0.844980i
\(399\) −7.77240 10.7915i −0.389107 0.540252i
\(400\) −5.11848 22.4255i −0.255924 1.12128i
\(401\) −11.0137 7.50901i −0.549997 0.374982i 0.256204 0.966623i \(-0.417528\pi\)
−0.806202 + 0.591641i \(0.798480\pi\)
\(402\) 6.65468 + 6.17464i 0.331905 + 0.307963i
\(403\) 5.99873 4.08986i 0.298818 0.203731i
\(404\) −6.13109 0.924112i −0.305033 0.0459763i
\(405\) 8.20484 + 3.95124i 0.407702 + 0.196339i
\(406\) −25.1971 5.07158i −1.25051 0.251698i
\(407\) 8.49857 4.09269i 0.421258 0.202867i
\(408\) −4.86192 + 1.49970i −0.240701 + 0.0742464i
\(409\) 12.0442 + 30.6881i 0.595547 + 1.51743i 0.837104 + 0.547043i \(0.184247\pi\)
−0.241557 + 0.970387i \(0.577658\pi\)
\(410\) 1.93959 3.35947i 0.0957896 0.165913i
\(411\) −21.6074 37.4252i −1.06582 1.84605i
\(412\) −0.425050 + 0.532996i −0.0209407 + 0.0262588i
\(413\) 20.7147 + 7.51974i 1.01930 + 0.370022i
\(414\) 4.58748 + 5.75252i 0.225462 + 0.282721i
\(415\) −0.838135 + 2.13553i −0.0411424 + 0.104829i
\(416\) −0.442720 + 5.90769i −0.0217061 + 0.289648i
\(417\) 0.399360 5.32908i 0.0195567 0.260966i
\(418\) −2.00340 + 5.10459i −0.0979897 + 0.249674i
\(419\) −24.5840 30.8274i −1.20101 1.50602i −0.810834 0.585276i \(-0.800986\pi\)
−0.390175 0.920741i \(-0.627585\pi\)
\(420\) 0.915935 1.42077i 0.0446930 0.0693267i
\(421\) −2.04607 + 2.56569i −0.0997194 + 0.125044i −0.829187 0.558971i \(-0.811196\pi\)
0.729468 + 0.684015i \(0.239768\pi\)
\(422\) 13.4032 + 23.2150i 0.652458 + 1.13009i
\(423\) −20.1430 + 34.8888i −0.979388 + 1.69635i
\(424\) 7.92996 + 20.2052i 0.385113 + 0.981252i
\(425\) −3.08636 + 0.952017i −0.149711 + 0.0461796i
\(426\) 9.61008 4.62797i 0.465610 0.224226i
\(427\) −24.3194 + 6.21435i −1.17690 + 0.300733i
\(428\) −3.23633 1.55853i −0.156434 0.0753346i
\(429\) 15.1064 + 2.27692i 0.729342 + 0.109931i
\(430\) 3.20962 2.18828i 0.154782 0.105528i
\(431\) −5.09321 4.72581i −0.245331 0.227634i 0.547917 0.836533i \(-0.315421\pi\)
−0.793248 + 0.608899i \(0.791612\pi\)
\(432\) 54.8769 + 37.4144i 2.64026 + 1.80010i
\(433\) −2.49996 10.9530i −0.120140 0.526370i −0.998802 0.0489252i \(-0.984420\pi\)
0.878662 0.477444i \(-0.158437\pi\)
\(434\) −14.1756 0.695485i −0.680452 0.0333843i
\(435\) −1.74613 + 7.65029i −0.0837205 + 0.366803i
\(436\) −7.05250 + 6.54376i −0.337753 + 0.313389i
\(437\) −0.978707 + 0.147516i −0.0468179 + 0.00705666i
\(438\) 70.2440 + 21.6674i 3.35639 + 1.03531i
\(439\) −2.24897 30.0104i −0.107337 1.43232i −0.747594 0.664156i \(-0.768791\pi\)
0.640257 0.768161i \(-0.278828\pi\)
\(440\) 2.08972 0.0996236
\(441\) 50.3904 10.2752i 2.39954 0.489295i
\(442\) 2.25708 0.107359
\(443\) −0.990368 13.2155i −0.0470538 0.627889i −0.970023 0.243015i \(-0.921864\pi\)
0.922969 0.384875i \(-0.125755\pi\)
\(444\) −6.53538 2.01590i −0.310156 0.0956703i
\(445\) −5.03236 + 0.758506i −0.238557 + 0.0359566i
\(446\) 25.0134 23.2090i 1.18442 1.09898i
\(447\) −6.49307 + 28.4480i −0.307112 + 1.34554i
\(448\) −8.96052 + 10.1708i −0.423345 + 0.480525i
\(449\) 8.14714 + 35.6949i 0.384487 + 1.68455i 0.683221 + 0.730212i \(0.260579\pi\)
−0.298734 + 0.954336i \(0.596564\pi\)
\(450\) 46.4780 + 31.6881i 2.19099 + 1.49379i
\(451\) −10.0513 9.32627i −0.473299 0.439157i
\(452\) 1.38862 0.946743i 0.0653151 0.0445311i
\(453\) 29.1193 + 4.38903i 1.36814 + 0.206214i
\(454\) −24.0744 11.5936i −1.12987 0.544116i
\(455\) 1.72104 1.44660i 0.0806838 0.0678178i
\(456\) −10.7398 + 5.17203i −0.502939 + 0.242203i
\(457\) −8.03564 + 2.47867i −0.375892 + 0.115947i −0.476943 0.878934i \(-0.658255\pi\)
0.101052 + 0.994881i \(0.467779\pi\)
\(458\) −11.6493 29.6818i −0.544334 1.38694i
\(459\) 4.66302 8.07658i 0.217651 0.376982i
\(460\) −0.0629032 0.108952i −0.00293288 0.00507989i
\(461\) −12.9757 + 16.2710i −0.604338 + 0.757816i −0.986047 0.166467i \(-0.946764\pi\)
0.381709 + 0.924282i \(0.375336\pi\)
\(462\) −20.8702 21.3611i −0.970971 0.993808i
\(463\) 1.03419 + 1.29683i 0.0480628 + 0.0602689i 0.805282 0.592892i \(-0.202014\pi\)
−0.757219 + 0.653161i \(0.773443\pi\)
\(464\) −10.6622 + 27.1670i −0.494982 + 1.26119i
\(465\) −0.323811 + 4.32095i −0.0150164 + 0.200379i
\(466\) 0.104394 1.39303i 0.00483594 0.0645311i
\(467\) 12.4402 31.6972i 0.575665 1.46677i −0.285467 0.958389i \(-0.592149\pi\)
0.861132 0.508382i \(-0.169756\pi\)
\(468\) −4.90377 6.14913i −0.226677 0.284244i
\(469\) 0.583227 4.68609i 0.0269309 0.216384i
\(470\) 2.14658 2.69173i 0.0990144 0.124160i
\(471\) 10.8191 + 18.7393i 0.498520 + 0.863462i
\(472\) 9.87628 17.1062i 0.454593 0.787378i
\(473\) −5.01643 12.7817i −0.230656 0.587701i
\(474\) −7.98326 + 2.46251i −0.366683 + 0.113107i
\(475\) −6.81768 + 3.28322i −0.312817 + 0.150645i
\(476\) −0.704145 0.532434i −0.0322744 0.0244041i
\(477\) −60.5850 29.1762i −2.77400 1.33589i
\(478\) 3.75207 + 0.565534i 0.171616 + 0.0258669i
\(479\) 20.7558 14.1511i 0.948358 0.646580i 0.0128625 0.999917i \(-0.495906\pi\)
0.935496 + 0.353337i \(0.114953\pi\)
\(480\) −2.59186 2.40489i −0.118301 0.109768i
\(481\) −7.51558 5.12404i −0.342681 0.233636i
\(482\) 7.33862 + 32.1526i 0.334265 + 1.46451i
\(483\) 1.45552 5.19002i 0.0662285 0.236154i
\(484\) 0.676218 2.96271i 0.0307372 0.134668i
\(485\) −2.79290 + 2.59144i −0.126819 + 0.117671i
\(486\) −49.7625 + 7.50049i −2.25727 + 0.340229i
\(487\) −22.1127 6.82086i −1.00202 0.309083i −0.250018 0.968241i \(-0.580436\pi\)
−0.752004 + 0.659158i \(0.770913\pi\)
\(488\) 1.68131 + 22.4355i 0.0761094 + 1.01561i
\(489\) −9.12344 −0.412576
\(490\) −4.38914 + 0.226480i −0.198281 + 0.0102313i
\(491\) −16.8361 −0.759804 −0.379902 0.925027i \(-0.624042\pi\)
−0.379902 + 0.925027i \(0.624042\pi\)
\(492\) 0.742943 + 9.91389i 0.0334945 + 0.446953i
\(493\) 3.91586 + 1.20788i 0.176362 + 0.0544003i
\(494\) 5.22894 0.788135i 0.235261 0.0354599i
\(495\) −4.74576 + 4.40343i −0.213306 + 0.197919i
\(496\) −3.58601 + 15.7113i −0.161017 + 0.705459i
\(497\) −4.87502 2.64947i −0.218675 0.118845i
\(498\) −6.53900 28.6492i −0.293019 1.28380i
\(499\) 7.00724 + 4.77746i 0.313687 + 0.213868i 0.709921 0.704281i \(-0.248731\pi\)
−0.396234 + 0.918150i \(0.629683\pi\)
\(500\) −1.43310 1.32973i −0.0640903 0.0594671i
\(501\) −16.3977 + 11.1798i −0.732596 + 0.499476i
\(502\) −41.3279 6.22918i −1.84455 0.278022i
\(503\) 30.2302 + 14.5581i 1.34790 + 0.649113i 0.961904 0.273388i \(-0.0881444\pi\)
0.385993 + 0.922502i \(0.373859\pi\)
\(504\) −1.18808 46.0802i −0.0529213 2.05257i
\(505\) 4.43422 2.13541i 0.197320 0.0950244i
\(506\) −2.12383 + 0.655115i −0.0944158 + 0.0291234i
\(507\) 9.89504 + 25.2122i 0.439454 + 1.11971i
\(508\) −1.10019 + 1.90559i −0.0488130 + 0.0845467i
\(509\) −11.3032 19.5777i −0.501005 0.867765i −0.999999 0.00116035i \(-0.999631\pi\)
0.498995 0.866605i \(-0.333703\pi\)
\(510\) −0.839884 + 1.05318i −0.0371907 + 0.0466356i
\(511\) −12.2091 36.2371i −0.540097 1.60303i
\(512\) 5.84834 + 7.33358i 0.258462 + 0.324102i
\(513\) 7.98250 20.3391i 0.352436 0.897992i
\(514\) −1.33085 + 17.7590i −0.0587015 + 0.783317i
\(515\) 0.0404388 0.539618i 0.00178195 0.0237784i
\(516\) −3.63719 + 9.26741i −0.160118 + 0.407975i
\(517\) −7.58745 9.51436i −0.333695 0.418441i
\(518\) 5.67739 + 16.8508i 0.249450 + 0.740381i
\(519\) 33.0095 41.3926i 1.44896 1.81693i
\(520\) −1.00758 1.74518i −0.0441853 0.0765312i
\(521\) 5.31567 9.20700i 0.232884 0.403366i −0.725772 0.687935i \(-0.758517\pi\)
0.958655 + 0.284569i \(0.0918506\pi\)
\(522\) −26.0747 66.4374i −1.14126 2.90788i
\(523\) 12.9549 3.99605i 0.566478 0.174735i 0.00172948 0.999999i \(-0.499449\pi\)
0.564748 + 0.825263i \(0.308973\pi\)
\(524\) 4.05550 1.95302i 0.177165 0.0853183i
\(525\) −1.06217 41.1966i −0.0463568 1.79797i
\(526\) 31.7810 + 15.3049i 1.38572 + 0.667326i
\(527\) 2.23756 + 0.337259i 0.0974699 + 0.0146912i
\(528\) −28.0176 + 19.1021i −1.21931 + 0.831310i
\(529\) 16.5661 + 15.3711i 0.720266 + 0.668309i
\(530\) 4.74814 + 3.23723i 0.206246 + 0.140616i
\(531\) 13.6169 + 59.6594i 0.590922 + 2.58900i
\(532\) −1.81719 0.987603i −0.0787853 0.0428180i
\(533\) −2.94226 + 12.8909i −0.127443 + 0.558366i
\(534\) 47.7869 44.3398i 2.06794 1.91877i
\(535\) 2.81940 0.424957i 0.121893 0.0183725i
\(536\) −4.04461 1.24760i −0.174701 0.0538880i
\(537\) 3.88646 + 51.8612i 0.167713 + 2.23798i
\(538\) 31.4951 1.35785
\(539\) −2.67176 + 15.3033i −0.115081 + 0.659160i
\(540\) 2.77724 0.119513
\(541\) 1.80015 + 24.0213i 0.0773944 + 1.03276i 0.891791 + 0.452448i \(0.149449\pi\)
−0.814396 + 0.580309i \(0.802932\pi\)
\(542\) 15.4553 + 4.76733i 0.663862 + 0.204774i
\(543\) 23.8212 3.59047i 1.02227 0.154082i
\(544\) −1.35353 + 1.25589i −0.0580322 + 0.0538461i
\(545\) 1.69930 7.44514i 0.0727902 0.318915i
\(546\) −7.77641 + 27.7287i −0.332800 + 1.18668i
\(547\) 3.58775 + 15.7189i 0.153401 + 0.672093i 0.991882 + 0.127163i \(0.0405870\pi\)
−0.838481 + 0.544931i \(0.816556\pi\)
\(548\) −5.55281 3.78584i −0.237204 0.161723i
\(549\) −51.0940 47.4083i −2.18064 2.02334i
\(550\) −14.0397 + 9.57211i −0.598655 + 0.408156i
\(551\) 9.49356 + 1.43092i 0.404439 + 0.0609594i
\(552\) −4.35295 2.09627i −0.185274 0.0892232i
\(553\) 3.46641 + 2.62111i 0.147407 + 0.111461i
\(554\) 11.1966 5.39198i 0.475696 0.229083i
\(555\) 5.18756 1.60015i 0.220200 0.0679226i
\(556\) −0.303628 0.773630i −0.0128767 0.0328092i
\(557\) 4.30428 7.45523i 0.182378 0.315888i −0.760312 0.649558i \(-0.774954\pi\)
0.942690 + 0.333670i \(0.108287\pi\)
\(558\) −19.7052 34.1305i −0.834189 1.44486i
\(559\) −8.25557 + 10.3522i −0.349173 + 0.437849i
\(560\) −0.616342 + 4.95216i −0.0260452 + 0.209267i
\(561\) 2.96871 + 3.72264i 0.125339 + 0.157170i
\(562\) −6.64168 + 16.9227i −0.280162 + 0.713842i
\(563\) 0.649338 8.66481i 0.0273663 0.365178i −0.966662 0.256056i \(-0.917577\pi\)
0.994028 0.109122i \(-0.0348040\pi\)
\(564\) −0.659376 + 8.79876i −0.0277647 + 0.370495i
\(565\) −0.487380 + 1.24182i −0.0205042 + 0.0522439i
\(566\) 7.96782 + 9.99133i 0.334912 + 0.419967i
\(567\) 42.4052 + 43.4026i 1.78085 + 1.82274i
\(568\) −3.10075 + 3.88822i −0.130105 + 0.163146i
\(569\) −16.8304 29.1511i −0.705566 1.22208i −0.966487 0.256716i \(-0.917359\pi\)
0.260921 0.965360i \(-0.415974\pi\)
\(570\) −1.57799 + 2.73315i −0.0660946 + 0.114479i
\(571\) 4.06138 + 10.3482i 0.169964 + 0.433060i 0.990322 0.138790i \(-0.0443212\pi\)
−0.820358 + 0.571850i \(0.806226\pi\)
\(572\) 2.27026 0.700283i 0.0949243 0.0292803i
\(573\) −64.0928 + 30.8654i −2.67751 + 1.28942i
\(574\) 19.7864 16.6313i 0.825870 0.694175i
\(575\) −2.76327 1.33072i −0.115236 0.0554948i
\(576\) −37.2191 5.60988i −1.55080 0.233745i
\(577\) 20.0464 13.6674i 0.834542 0.568981i −0.0689333 0.997621i \(-0.521960\pi\)
0.903475 + 0.428640i \(0.141007\pi\)
\(578\) −19.1892 17.8050i −0.798166 0.740590i
\(579\) 55.8664 + 38.0891i 2.32173 + 1.58293i
\(580\) 0.271550 + 1.18974i 0.0112755 + 0.0494012i
\(581\) −10.1049 + 11.4698i −0.419222 + 0.475846i
\(582\) 10.8597 47.5793i 0.450148 1.97223i
\(583\) 14.8902 13.8161i 0.616690 0.572205i
\(584\) −33.8913 + 5.10829i −1.40243 + 0.211382i
\(585\) 5.96563 + 1.84015i 0.246649 + 0.0760810i
\(586\) −0.580090 7.74076i −0.0239633 0.319768i
\(587\) 18.8678 0.778758 0.389379 0.921078i \(-0.372690\pi\)
0.389379 + 0.921078i \(0.372690\pi\)
\(588\) 8.96708 6.81615i 0.369796 0.281093i
\(589\) 5.30148 0.218444
\(590\) −0.390809 5.21499i −0.0160894 0.214698i
\(591\) −45.8567 14.1449i −1.88629 0.581844i
\(592\) 19.9648 3.00922i 0.820550 0.123678i
\(593\) 12.9227 11.9905i 0.530671 0.492391i −0.368717 0.929542i \(-0.620203\pi\)
0.899388 + 0.437151i \(0.144012\pi\)
\(594\) 10.9178 47.8342i 0.447965 1.96266i
\(595\) 0.699880 + 0.0343375i 0.0286923 + 0.00140770i
\(596\) 1.00977 + 4.42411i 0.0413620 + 0.181219i
\(597\) 29.0625 + 19.8145i 1.18945 + 0.810952i
\(598\) 1.57113 + 1.45780i 0.0642483 + 0.0596137i
\(599\) −25.9776 + 17.7112i −1.06142 + 0.723661i −0.962458 0.271431i \(-0.912503\pi\)
−0.0989578 + 0.995092i \(0.531551\pi\)
\(600\) −36.5252 5.50528i −1.49113 0.224752i
\(601\) −10.7945 5.19834i −0.440315 0.212045i 0.200573 0.979679i \(-0.435720\pi\)
−0.640888 + 0.767634i \(0.721434\pi\)
\(602\) 25.0780 6.40820i 1.02210 0.261179i
\(603\) 11.8142 5.68944i 0.481113 0.231692i
\(604\) 4.37619 1.34988i 0.178065 0.0549257i
\(605\) 0.881265 + 2.24543i 0.0358285 + 0.0912895i
\(606\) −31.5211 + 54.5962i −1.28046 + 2.21782i
\(607\) 16.2197 + 28.0934i 0.658338 + 1.14028i 0.981046 + 0.193777i \(0.0620737\pi\)
−0.322707 + 0.946499i \(0.604593\pi\)
\(608\) −2.69716 + 3.38214i −0.109384 + 0.137164i
\(609\) −28.3305 + 43.9456i −1.14801 + 1.78077i
\(610\) 3.71388 + 4.65706i 0.150371 + 0.188559i
\(611\) −4.28732 + 10.9239i −0.173446 + 0.441934i
\(612\) 0.183188 2.44447i 0.00740493 0.0988119i
\(613\) −1.88786 + 25.1917i −0.0762498 + 1.01748i 0.819545 + 0.573015i \(0.194226\pi\)
−0.895795 + 0.444468i \(0.853393\pi\)
\(614\) 3.22078 8.20641i 0.129980 0.331184i
\(615\) −4.92019 6.16972i −0.198401 0.248787i
\(616\) 13.0885 + 4.75130i 0.527349 + 0.191435i
\(617\) −14.9776 + 18.7813i −0.602974 + 0.756105i −0.985838 0.167699i \(-0.946366\pi\)
0.382865 + 0.923805i \(0.374938\pi\)
\(618\) 3.46575 + 6.00286i 0.139413 + 0.241470i
\(619\) −11.6230 + 20.1316i −0.467166 + 0.809156i −0.999296 0.0375069i \(-0.988058\pi\)
0.532130 + 0.846663i \(0.321392\pi\)
\(620\) 0.246189 + 0.627278i 0.00988717 + 0.0251921i
\(621\) 8.46234 2.61029i 0.339582 0.104747i
\(622\) −28.8310 + 13.8843i −1.15602 + 0.556708i
\(623\) −33.2435 6.69113i −1.33187 0.268074i
\(624\) 29.4616 + 14.1879i 1.17941 + 0.567972i
\(625\) −22.4068 3.37728i −0.896271 0.135091i
\(626\) 15.9303 10.8611i 0.636701 0.434096i
\(627\) 8.17742 + 7.58754i 0.326575 + 0.303017i
\(628\) 2.78037 + 1.89562i 0.110949 + 0.0756436i
\(629\) −0.630853 2.76395i −0.0251538 0.110206i
\(630\) −7.13240 9.90292i −0.284161 0.394542i
\(631\) −0.318104 + 1.39370i −0.0126635 + 0.0554824i −0.980865 0.194690i \(-0.937630\pi\)
0.968201 + 0.250172i \(0.0804872\pi\)
\(632\) 2.85543 2.64945i 0.113583 0.105389i
\(633\) 53.9228 8.12755i 2.14324 0.323041i
\(634\) −13.1410 4.05345i −0.521894 0.160983i
\(635\) −0.130522 1.74170i −0.00517963 0.0691173i
\(636\) −14.7278 −0.583995
\(637\) 14.0684 5.14739i 0.557410 0.203947i
\(638\) 21.5592 0.853537
\(639\) −1.15137 15.3640i −0.0455476 0.607790i
\(640\) 5.17448 + 1.59612i 0.204539 + 0.0630920i
\(641\) 23.4003 3.52703i 0.924257 0.139309i 0.330364 0.943854i \(-0.392828\pi\)
0.593893 + 0.804544i \(0.297590\pi\)
\(642\) −26.7728 + 24.8416i −1.05664 + 0.980418i
\(643\) 1.85767 8.13897i 0.0732592 0.320969i −0.924999 0.379970i \(-0.875934\pi\)
0.998258 + 0.0590007i \(0.0187914\pi\)
\(644\) −0.146261 0.825411i −0.00576348 0.0325258i
\(645\) −1.75845 7.70428i −0.0692390 0.303356i
\(646\) 1.36175 + 0.928425i 0.0535773 + 0.0365284i
\(647\) −1.33533 1.23901i −0.0524973 0.0487104i 0.653488 0.756937i \(-0.273305\pi\)
−0.705985 + 0.708227i \(0.749496\pi\)
\(648\) 44.9377 30.6380i 1.76532 1.20357i
\(649\) −18.2785 2.75503i −0.717492 0.108145i
\(650\) 14.7633 + 7.10963i 0.579064 + 0.278863i
\(651\) −11.8525 + 26.3270i −0.464534 + 1.03184i
\(652\) −1.27833 + 0.615610i −0.0500632 + 0.0241092i
\(653\) −6.66630 + 2.05628i −0.260873 + 0.0804685i −0.422433 0.906394i \(-0.638824\pi\)
0.161560 + 0.986863i \(0.448347\pi\)
\(654\) 35.7374 + 91.0575i 1.39744 + 3.56063i
\(655\) −1.78647 + 3.09426i −0.0698033 + 0.120903i
\(656\) −14.6746 25.4172i −0.572948 0.992375i
\(657\) 66.2031 83.0160i 2.58283 3.23876i
\(658\) 19.5646 11.9784i 0.762709 0.466966i
\(659\) −29.5248 37.0229i −1.15012 1.44221i −0.877171 0.480178i \(-0.840572\pi\)
−0.272950 0.962028i \(-0.587999\pi\)
\(660\) −0.518027 + 1.31991i −0.0201642 + 0.0513775i
\(661\) 0.981557 13.0980i 0.0381782 0.509452i −0.945032 0.326977i \(-0.893970\pi\)
0.983210 0.182475i \(-0.0584109\pi\)
\(662\) 3.71786 49.6114i 0.144499 1.92820i
\(663\) 1.67748 4.27415i 0.0651480 0.165994i
\(664\) 8.54259 + 10.7121i 0.331517 + 0.415709i
\(665\) 1.63339 0.164837i 0.0633401 0.00639212i
\(666\) −30.7854 + 38.6037i −1.19291 + 1.49586i
\(667\) 1.94564 + 3.36995i 0.0753356 + 0.130485i
\(668\) −1.54320 + 2.67290i −0.0597082 + 0.103418i
\(669\) −25.3599 64.6160i −0.980470 2.49820i
\(670\) −1.07083 + 0.330309i −0.0413700 + 0.0127609i
\(671\) 18.9695 9.13524i 0.732310 0.352662i
\(672\) −10.7656 20.9554i −0.415290 0.808372i
\(673\) 9.88389 + 4.75983i 0.380996 + 0.183478i 0.614572 0.788860i \(-0.289329\pi\)
−0.233576 + 0.972338i \(0.575043\pi\)
\(674\) −44.1160 6.64941i −1.69928 0.256126i
\(675\) 55.9408 38.1398i 2.15316 1.46800i
\(676\) 3.08765 + 2.86492i 0.118756 + 0.110189i
\(677\) −11.8140 8.05465i −0.454049 0.309565i 0.314614 0.949220i \(-0.398125\pi\)
−0.768663 + 0.639654i \(0.779077\pi\)
\(678\) −3.80246 16.6597i −0.146033 0.639810i
\(679\) −23.3847 + 9.88072i −0.897422 + 0.379187i
\(680\) 0.139759 0.612326i 0.00535953 0.0234816i
\(681\) −39.8467 + 36.9723i −1.52693 + 1.41678i
\(682\) 11.7719 1.77432i 0.450768 0.0679423i
\(683\) −26.8981 8.29695i −1.02923 0.317474i −0.266252 0.963903i \(-0.585785\pi\)
−0.762974 + 0.646429i \(0.776262\pi\)
\(684\) −0.429181 5.72702i −0.0164101 0.218978i
\(685\) 5.33457 0.203823
\(686\) −28.0052 8.56088i −1.06924 0.326856i
\(687\) −64.8651 −2.47476
\(688\) −2.19634 29.3081i −0.0837347 1.11736i
\(689\) −18.7177 5.77363i −0.713086 0.219958i
\(690\) −1.26486 + 0.190647i −0.0481523 + 0.00725779i
\(691\) −8.39222 + 7.78684i −0.319255 + 0.296226i −0.823478 0.567348i \(-0.807969\pi\)
0.504223 + 0.863573i \(0.331779\pi\)
\(692\) 1.83212 8.02705i 0.0696468 0.305143i
\(693\) −39.7358 + 16.7895i −1.50944 + 0.637782i
\(694\) 2.51111 + 11.0019i 0.0953206 + 0.417627i
\(695\) 0.545055 + 0.371612i 0.0206751 + 0.0140961i
\(696\) 34.3546 + 31.8764i 1.30221 + 1.20827i
\(697\) −3.40499 + 2.32148i −0.128973 + 0.0879324i
\(698\) 46.1675 + 6.95864i 1.74747 + 0.263388i
\(699\) −2.56035 1.23300i −0.0968414 0.0466363i
\(700\) −2.92860 5.70059i −0.110691 0.215462i
\(701\) 9.58967 4.61814i 0.362197 0.174425i −0.243930 0.969793i \(-0.578437\pi\)
0.606127 + 0.795368i \(0.292722\pi\)
\(702\) −45.2117 + 13.9460i −1.70641 + 0.526357i
\(703\) −2.42661 6.18289i −0.0915212 0.233192i
\(704\) 5.68493 9.84659i 0.214259 0.371107i
\(705\) −3.50187 6.06541i −0.131888 0.228437i
\(706\) 16.0412 20.1150i 0.603717 0.757037i
\(707\) 32.6278 3.29272i 1.22709 0.123835i
\(708\) 8.35638 + 10.4786i 0.314052 + 0.393809i
\(709\) 5.54993 14.1410i 0.208432 0.531076i −0.787981 0.615699i \(-0.788874\pi\)
0.996413 + 0.0846237i \(0.0269688\pi\)
\(710\) −0.0983963 + 1.31301i −0.00369275 + 0.0492763i
\(711\) −0.901810 + 12.0338i −0.0338205 + 0.451304i
\(712\) −11.1043 + 28.2934i −0.416153 + 1.06034i
\(713\) 1.33972 + 1.67995i 0.0501728 + 0.0629147i
\(714\) −7.65497 + 4.68673i −0.286480 + 0.175397i
\(715\) −1.17580 + 1.47441i −0.0439724 + 0.0551396i
\(716\) 4.04392 + 7.00427i 0.151128 + 0.261762i
\(717\) 3.85950 6.68485i 0.144136 0.249650i
\(718\) 15.1562 + 38.6175i 0.565626 + 1.44119i
\(719\) 19.1525 5.90778i 0.714270 0.220323i 0.0837394 0.996488i \(-0.473314\pi\)
0.630530 + 0.776165i \(0.282837\pi\)
\(720\) −12.4850 + 6.01247i −0.465289 + 0.224072i
\(721\) 1.48018 3.28782i 0.0551249 0.122445i
\(722\) −23.5889 11.3598i −0.877889 0.422769i
\(723\) 66.3402 + 9.99918i 2.46722 + 0.371874i
\(724\) 3.09543 2.11043i 0.115041 0.0784335i
\(725\) 21.8084 + 20.2353i 0.809945 + 0.751519i
\(726\) −25.5293 17.4056i −0.947480 0.645981i
\(727\) −11.1011 48.6369i −0.411716 1.80384i −0.576021 0.817435i \(-0.695395\pi\)
0.164305 0.986410i \(-0.447462\pi\)
\(728\) −2.34279 13.2214i −0.0868297 0.490017i
\(729\) −7.47016 + 32.7289i −0.276673 + 1.21218i
\(730\) −6.65191 + 6.17207i −0.246198 + 0.228439i
\(731\) −4.08075 + 0.615074i −0.150932 + 0.0227493i
\(732\) −14.5875 4.49966i −0.539171 0.166312i
\(733\) 0.733543 + 9.78846i 0.0270940 + 0.361545i 0.994229 + 0.107281i \(0.0342143\pi\)
−0.967135 + 0.254264i \(0.918167\pi\)
\(734\) −33.2685 −1.22796
\(735\) −2.83317 + 8.47987i −0.104503 + 0.312785i
\(736\) −1.75333 −0.0646286
\(737\) 0.296007 + 3.94994i 0.0109036 + 0.145498i
\(738\) 68.5855 + 21.1558i 2.52467 + 0.778756i
\(739\) 25.0946 3.78240i 0.923120 0.139138i 0.329751 0.944068i \(-0.393035\pi\)
0.593370 + 0.804930i \(0.297797\pi\)
\(740\) 0.618882 0.574239i 0.0227506 0.0211094i
\(741\) 2.39372 10.4876i 0.0879356 0.385271i
\(742\) 22.3785 + 31.0712i 0.821540 + 1.14066i
\(743\) 2.74476 + 12.0256i 0.100696 + 0.441176i 0.999993 + 0.00383783i \(0.00122162\pi\)
−0.899297 + 0.437338i \(0.855921\pi\)
\(744\) 21.3819 + 14.5779i 0.783898 + 0.534453i
\(745\) −2.64046 2.44999i −0.0967391 0.0897607i
\(746\) 5.41583 3.69245i 0.198288 0.135190i
\(747\) −41.9726 6.32634i −1.53570 0.231469i
\(748\) 0.667148 + 0.321281i 0.0243933 + 0.0117472i
\(749\) 18.6248 + 3.74873i 0.680536 + 0.136976i
\(750\) −17.9089 + 8.62447i −0.653941 + 0.314921i
\(751\) −29.3247 + 9.04548i −1.07007 + 0.330074i −0.779257 0.626705i \(-0.784403\pi\)
−0.290817 + 0.956779i \(0.593927\pi\)
\(752\) −9.51640 24.2474i −0.347027 0.884212i
\(753\) −42.5112 + 73.6315i −1.54919 + 2.68328i
\(754\) −10.3950 18.0046i −0.378563 0.655690i
\(755\) −2.26649 + 2.84209i −0.0824861 + 0.103434i
\(756\) 17.3945 + 6.31447i 0.632633 + 0.229655i
\(757\) −7.11089 8.91678i −0.258450 0.324086i 0.635630 0.771994i \(-0.280741\pi\)
−0.894079 + 0.447908i \(0.852169\pi\)
\(758\) 11.3758 28.9850i 0.413187 1.05278i
\(759\) −0.337881 + 4.50870i −0.0122643 + 0.163656i
\(760\) 0.109964 1.46736i 0.00398880 0.0532269i
\(761\) 5.46608 13.9273i 0.198145 0.504866i −0.796920 0.604084i \(-0.793539\pi\)
0.995066 + 0.0992183i \(0.0316342\pi\)
\(762\) 13.9490 + 17.4915i 0.505320 + 0.633651i
\(763\) 27.5708 42.7671i 0.998131 1.54827i
\(764\) −6.89767 + 8.64941i −0.249549 + 0.312925i
\(765\) 0.972888 + 1.68509i 0.0351748 + 0.0609246i
\(766\) −3.56098 + 6.16780i −0.128663 + 0.222852i
\(767\) 6.51234 + 16.5932i 0.235147 + 0.599145i
\(768\) −34.7862 + 10.7301i −1.25524 + 0.387190i
\(769\) −6.62237 + 3.18917i −0.238809 + 0.115004i −0.549461 0.835519i \(-0.685167\pi\)
0.310652 + 0.950524i \(0.399453\pi\)
\(770\) 3.57174 0.912687i 0.128717 0.0328910i
\(771\) 32.6405 + 15.7188i 1.17552 + 0.566100i
\(772\) 10.3978 + 1.56722i 0.374225 + 0.0564053i
\(773\) −34.4662 + 23.4987i −1.23966 + 0.845188i −0.992315 0.123738i \(-0.960512\pi\)
−0.247348 + 0.968927i \(0.579559\pi\)
\(774\) 52.6879 + 48.8872i 1.89383 + 1.75721i
\(775\) 13.5733 + 9.25412i 0.487567 + 0.332418i
\(776\) 5.06334 + 22.1839i 0.181763 + 0.796357i
\(777\) 36.1292 + 1.77257i 1.29613 + 0.0635905i
\(778\) 8.84981 38.7736i 0.317281 1.39010i
\(779\) −7.07764 + 6.56709i −0.253583 + 0.235291i
\(780\) 1.35206 0.203791i 0.0484116 0.00729688i
\(781\) 4.44729 + 1.37181i 0.159136 + 0.0490871i
\(782\) 0.0499198 + 0.666134i 0.00178513 + 0.0238209i
\(783\) −85.9020 −3.06989
\(784\) −15.1198 + 29.6153i −0.539993 + 1.05769i
\(785\) −2.67109 −0.0953354
\(786\) −3.42016 45.6389i −0.121993 1.62788i
\(787\) 21.8351 + 6.73524i 0.778338 + 0.240085i 0.658372 0.752693i \(-0.271245\pi\)
0.119966 + 0.992778i \(0.461722\pi\)
\(788\) −7.37964 + 1.11230i −0.262889 + 0.0396241i
\(789\) 52.6022 48.8077i 1.87269 1.73760i
\(790\) 0.229484 1.00544i 0.00816469 0.0357718i
\(791\) −5.87606 + 6.66972i −0.208928 + 0.237148i
\(792\) 8.60374 + 37.6954i 0.305721 + 1.33945i
\(793\) −16.7754 11.4373i −0.595713 0.406150i
\(794\) −27.4389 25.4596i −0.973769 0.903526i
\(795\) 9.65908 6.58545i 0.342572 0.233562i
\(796\) 5.40908 + 0.815287i 0.191720 + 0.0288971i
\(797\) 44.6791 + 21.5163i 1.58261 + 0.762147i 0.998764 0.0497137i \(-0.0158309\pi\)
0.583851 + 0.811861i \(0.301545\pi\)
\(798\) −16.0976 + 13.5306i −0.569848 + 0.478979i
\(799\) −3.29532 + 1.58694i −0.116580 + 0.0561420i
\(800\) −12.8093 + 3.95113i −0.452876 + 0.139694i
\(801\) −34.4014 87.6533i −1.21551 3.09708i
\(802\) −10.5387 + 18.2536i −0.372135 + 0.644557i
\(803\) 16.0372 + 27.7773i 0.565942 + 0.980241i
\(804\) 1.79064 2.24539i 0.0631509 0.0791887i
\(805\) 0.465001 + 0.475938i 0.0163891 + 0.0167746i
\(806\) −7.15770 8.97547i −0.252119 0.316147i
\(807\) 23.4074 59.6411i 0.823980 2.09947i
\(808\) 2.19658 29.3114i 0.0772755 1.03117i
\(809\) 1.62104 21.6313i 0.0569929 0.760517i −0.893360 0.449342i \(-0.851658\pi\)
0.950353 0.311175i \(-0.100722\pi\)
\(810\) 5.26077 13.4042i 0.184845 0.470976i
\(811\) −12.7005 15.9259i −0.445974 0.559233i 0.507133 0.861868i \(-0.330705\pi\)
−0.953107 + 0.302634i \(0.902134\pi\)
\(812\) −1.00427 + 8.06905i −0.0352429 + 0.283168i
\(813\) 20.5142 25.7240i 0.719464 0.902180i
\(814\) −7.45756 12.9169i −0.261387 0.452736i
\(815\) 0.563112 0.975338i 0.0197249 0.0341646i
\(816\) 3.72344 + 9.48718i 0.130347 + 0.332118i
\(817\) −9.23900 + 2.84986i −0.323232 + 0.0997038i
\(818\) 46.9656 22.6174i 1.64211 0.790800i
\(819\) 33.1804 + 25.0891i 1.15942 + 0.876685i
\(820\) −1.10570 0.532475i −0.0386126 0.0185948i
\(821\) 23.3980 + 3.52667i 0.816594 + 0.123082i 0.544041 0.839059i \(-0.316894\pi\)
0.272554 + 0.962141i \(0.412132\pi\)
\(822\) −56.4585 + 38.4928i −1.96922 + 1.34259i
\(823\) −1.70058 1.57791i −0.0592786 0.0550025i 0.649977 0.759954i \(-0.274778\pi\)
−0.709256 + 0.704951i \(0.750969\pi\)
\(824\) −2.67026 1.82055i −0.0930228 0.0634219i
\(825\) 7.69193 + 33.7005i 0.267799 + 1.17330i
\(826\) 9.40933 33.5513i 0.327393 1.16740i
\(827\) −5.58131 + 24.4533i −0.194081 + 0.850326i 0.780297 + 0.625409i \(0.215068\pi\)
−0.974378 + 0.224916i \(0.927789\pi\)
\(828\) 1.70634 1.58325i 0.0592994 0.0550218i
\(829\) −10.6595 + 1.60666i −0.370219 + 0.0558016i −0.331517 0.943449i \(-0.607560\pi\)
−0.0387022 + 0.999251i \(0.512322\pi\)
\(830\) 3.46633 + 1.06922i 0.120318 + 0.0371132i
\(831\) −1.88922 25.2098i −0.0655362 0.874520i
\(832\) −10.9642 −0.380115
\(833\) 4.30545 + 1.80635i 0.149175 + 0.0625863i
\(834\) −8.45005 −0.292601
\(835\) −0.183079 2.44303i −0.00633572 0.0845444i
\(836\) 1.65775 + 0.511349i 0.0573346 + 0.0176854i
\(837\) −46.9046 + 7.06973i −1.62126 + 0.244366i
\(838\) −45.7035 + 42.4066i −1.57880 + 1.46491i
\(839\) −1.66884 + 7.31166i −0.0576147 + 0.252426i −0.995531 0.0944351i \(-0.969896\pi\)
0.937916 + 0.346862i \(0.112753\pi\)
\(840\) 7.04103 + 3.82664i 0.242939 + 0.132032i
\(841\) −1.94614 8.52662i −0.0671084 0.294021i
\(842\) 4.28734 + 2.92306i 0.147751 + 0.100735i
\(843\) 27.1098 + 25.1542i 0.933710 + 0.866356i
\(844\) 7.00696 4.77727i 0.241190 0.164440i
\(845\) −3.30603 0.498304i −0.113731 0.0171422i
\(846\) 57.3926 + 27.6388i 1.97320 + 0.950241i
\(847\) 0.414263 + 16.0674i 0.0142342 + 0.552081i
\(848\) 39.1728 18.8646i 1.34520 0.647814i
\(849\) 24.8419 7.66273i 0.852573 0.262984i
\(850\) 1.86583 + 4.75406i 0.0639975 + 0.163063i
\(851\) 1.34604 2.33141i 0.0461416 0.0799195i
\(852\) −1.68722 2.92236i −0.0578034 0.100118i
\(853\) −6.28444 + 7.88043i −0.215175 + 0.269821i −0.877691 0.479227i \(-0.840917\pi\)
0.662516 + 0.749048i \(0.269489\pi\)
\(854\) 12.6724 + 37.6124i 0.433641 + 1.28707i
\(855\) 2.84227 + 3.56410i 0.0972037 + 0.121890i
\(856\) 6.22126 15.8515i 0.212638 0.541794i
\(857\) −3.23114 + 43.1166i −0.110374 + 1.47284i 0.617200 + 0.786806i \(0.288267\pi\)
−0.727574 + 0.686029i \(0.759352\pi\)
\(858\) 1.80519 24.0886i 0.0616283 0.822373i
\(859\) −18.4770 + 47.0786i −0.630427 + 1.60630i 0.155396 + 0.987852i \(0.450335\pi\)
−0.785824 + 0.618451i \(0.787761\pi\)
\(860\) −0.766237 0.960830i −0.0261285 0.0327640i
\(861\) −16.7886 49.8293i −0.572153 1.69818i
\(862\) −6.84979 + 8.58936i −0.233305 + 0.292555i
\(863\) 8.61615 + 14.9236i 0.293297 + 0.508006i 0.974587 0.224008i \(-0.0719141\pi\)
−0.681290 + 0.732013i \(0.738581\pi\)
\(864\) 19.3528 33.5200i 0.658396 1.14037i
\(865\) 2.38767 + 6.08368i 0.0811831 + 0.206851i
\(866\) −16.9753 + 5.23618i −0.576843 + 0.177933i
\(867\) −47.9782 + 23.1051i −1.62943 + 0.784690i
\(868\) 0.115728 + 4.48855i 0.00392806 + 0.152351i
\(869\) −3.28428 1.58163i −0.111412 0.0536530i
\(870\) 12.2692 + 1.84929i 0.415967 + 0.0626969i
\(871\) 3.15598 2.15171i 0.106936 0.0729079i
\(872\) −33.4333 31.0216i −1.13220 1.05052i
\(873\) −58.2445 39.7104i −1.97128 1.34399i
\(874\) 0.348251 + 1.52579i 0.0117798 + 0.0516105i
\(875\) 9.08487 + 4.93742i 0.307125 + 0.166915i
\(876\) 5.17490 22.6727i 0.174844 0.766040i
\(877\) −26.5088 + 24.5965i −0.895138 + 0.830566i −0.986248 0.165274i \(-0.947149\pi\)
0.0911099 + 0.995841i \(0.470959\pi\)
\(878\) −47.0544 + 7.09231i −1.58801 + 0.239354i
\(879\) −15.0895 4.65450i −0.508956 0.156992i
\(880\) −0.312814 4.17421i −0.0105450 0.140713i
\(881\) 23.7204 0.799162 0.399581 0.916698i \(-0.369156\pi\)
0.399581 + 0.916698i \(0.369156\pi\)
\(882\) −22.1562 78.2410i −0.746038 2.63451i
\(883\) −44.4089 −1.49448 −0.747240 0.664554i \(-0.768621\pi\)
−0.747240 + 0.664554i \(0.768621\pi\)
\(884\) −0.0533616 0.712061i −0.00179474 0.0239492i
\(885\) −10.1659 3.13576i −0.341722 0.105407i
\(886\) −20.7211 + 3.12321i −0.696140 + 0.104926i
\(887\) −5.00558 + 4.64450i −0.168071 + 0.155947i −0.759724 0.650246i \(-0.774666\pi\)
0.591653 + 0.806193i \(0.298476\pi\)
\(888\) 7.21465 31.6094i 0.242108 1.06074i
\(889\) 3.14253 11.2055i 0.105397 0.375820i
\(890\) 1.79065 + 7.84536i 0.0600228 + 0.262977i
\(891\) −42.0538 28.6718i −1.40885 0.960540i
\(892\) −7.91330 7.34247i −0.264957 0.245844i
\(893\) −7.08006 + 4.82710i −0.236925 + 0.161533i
\(894\) 45.6239 + 6.87669i 1.52589 + 0.229991i
\(895\) −5.78408 2.78547i −0.193340 0.0931079i
\(896\) 28.7801 + 21.7618i 0.961474 + 0.727012i
\(897\) 3.92825 1.89174i 0.131160 0.0631635i
\(898\) 55.3208 17.0642i 1.84608 0.569440i
\(899\) −7.61480 19.4022i −0.253968 0.647099i
\(900\) 8.89810 15.4120i 0.296603 0.513732i
\(901\) −3.05252 5.28711i −0.101694 0.176139i
\(902\) −13.5179 + 16.9509i −0.450096 + 0.564403i
\(903\) 6.50324 52.2520i 0.216414 1.73884i
\(904\) 4.96756 + 6.22912i 0.165219 + 0.207178i
\(905\) −1.08644 + 2.76820i −0.0361145 + 0.0920182i
\(906\) 3.47972 46.4337i 0.115606 1.54266i
\(907\) 0.559176 7.46168i 0.0185671 0.247761i −0.980196 0.198032i \(-0.936545\pi\)
0.998763 0.0497293i \(-0.0158359\pi\)
\(908\) −3.08837 + 7.86905i −0.102491 + 0.261144i
\(909\) 56.7760 + 71.1948i 1.88314 + 2.36138i
\(910\) −2.48436 2.54279i −0.0823557 0.0842927i
\(911\) −18.6126 + 23.3394i −0.616662 + 0.773270i −0.987871 0.155280i \(-0.950372\pi\)
0.371208 + 0.928550i \(0.378944\pi\)
\(912\) 11.9388 + 20.6786i 0.395332 + 0.684736i
\(913\) 6.41098 11.1041i 0.212173 0.367494i
\(914\) 4.85787 + 12.3777i 0.160684 + 0.409416i
\(915\) 11.5791 3.57167i 0.382792 0.118076i
\(916\) −9.08856 + 4.37682i −0.300294 + 0.144614i
\(917\) −18.2244 + 15.3183i −0.601823 + 0.505855i
\(918\) −13.2861 6.39825i −0.438506 0.211174i
\(919\) −31.7085 4.77928i −1.04597 0.157654i −0.396492 0.918038i \(-0.629773\pi\)
−0.649474 + 0.760384i \(0.725011\pi\)
\(920\) 0.492771 0.335966i 0.0162462 0.0110765i
\(921\) −13.1465 12.1981i −0.433191 0.401942i
\(922\) 27.1892 + 18.5373i 0.895430 + 0.610494i
\(923\) −0.998674 4.37547i −0.0328717 0.144021i
\(924\) −6.24555 + 7.08912i −0.205464 + 0.233215i
\(925\) 4.57988 20.0658i 0.150586 0.659759i
\(926\) 1.92263 1.78394i 0.0631815 0.0586239i
\(927\) 9.90039 1.49224i 0.325172 0.0490117i
\(928\) 16.2519 + 5.01305i 0.533495 + 0.164561i
\(929\) −0.687857 9.17881i −0.0225678 0.301147i −0.997054 0.0767002i \(-0.975562\pi\)
0.974486 0.224447i \(-0.0720575\pi\)
\(930\) 6.85151 0.224670
\(931\) 10.6051 + 2.68134i 0.347568 + 0.0878773i
\(932\) −0.441940 −0.0144762
\(933\) 4.86471 + 64.9150i 0.159263 + 2.12522i
\(934\) −51.4499 15.8702i −1.68349 0.519288i
\(935\) −0.581201 + 0.0876019i −0.0190073 + 0.00286489i
\(936\) 27.3321 25.3604i 0.893376 0.828932i
\(937\) −4.81044 + 21.0759i −0.157150 + 0.688520i 0.833549 + 0.552446i \(0.186305\pi\)
−0.990699 + 0.136074i \(0.956552\pi\)
\(938\) −7.45791 0.365900i −0.243510 0.0119471i
\(939\) −8.72770 38.2385i −0.284818 1.24787i
\(940\) −0.899931 0.613562i −0.0293525 0.0200122i
\(941\) 41.6868 + 38.6797i 1.35895 + 1.26092i 0.934727 + 0.355365i \(0.115644\pi\)
0.424224 + 0.905557i \(0.360547\pi\)
\(942\) 28.2696 19.2739i 0.921072 0.627976i
\(943\) −3.86956 0.583243i −0.126010 0.0189930i
\(944\) −35.6480 17.1672i −1.16024 0.558744i
\(945\) −14.2315 + 3.63658i −0.462951 + 0.118298i
\(946\) −19.5613 + 9.42020i −0.635991 + 0.306277i
\(947\) 31.1926 9.62164i 1.01362 0.312661i 0.256929 0.966430i \(-0.417289\pi\)
0.756694 + 0.653769i \(0.226813\pi\)
\(948\) 0.965607 + 2.46033i 0.0313615 + 0.0799077i
\(949\) 15.4650 26.7862i 0.502016 0.869518i
\(950\) 5.98257 + 10.3621i 0.194100 + 0.336191i
\(951\) −17.4423 + 21.8720i −0.565606 + 0.709247i
\(952\) 2.26756 3.51739i 0.0734922 0.113999i
\(953\) −28.0427 35.1645i −0.908393 1.13909i −0.989808 0.142409i \(-0.954515\pi\)
0.0814149 0.996680i \(-0.474056\pi\)
\(954\) −38.8458 + 98.9776i −1.25768 + 3.20452i
\(955\) 0.656237 8.75687i 0.0212353 0.283366i
\(956\) 0.0897079 1.19707i 0.00290136 0.0387160i
\(957\) 16.0230 40.8258i 0.517949 1.31971i
\(958\) −24.7659 31.0555i −0.800151 1.00336i
\(959\) 33.4117 + 12.1290i 1.07892 + 0.391665i
\(960\) 4.07988 5.11601i 0.131678 0.165119i
\(961\) 9.74533 + 16.8794i 0.314366 + 0.544497i
\(962\) −7.19147 + 12.4560i −0.231862 + 0.401597i
\(963\) 19.2735 + 49.1082i 0.621081 + 1.58249i
\(964\) 9.96995 3.07532i 0.321110 0.0990494i
\(965\) −7.52006 + 3.62147i −0.242079 + 0.116579i
\(966\) −8.35558 1.68178i −0.268836 0.0541104i
\(967\) 21.8585 + 10.5265i 0.702922 + 0.338509i 0.750970 0.660336i \(-0.229586\pi\)
−0.0480488 + 0.998845i \(0.515300\pi\)
\(968\) 14.2454 + 2.14715i 0.457865 + 0.0690120i
\(969\) 2.77018 1.88868i 0.0889912 0.0606731i
\(970\) 4.41618 + 4.09761i 0.141795 + 0.131566i
\(971\) 22.6906 + 15.4702i 0.728178 + 0.496463i 0.869767 0.493462i \(-0.164269\pi\)
−0.141590 + 0.989925i \(0.545221\pi\)
\(972\) 3.54272 + 15.5217i 0.113633 + 0.497858i
\(973\) 2.56890 + 3.56677i 0.0823551 + 0.114345i
\(974\) −8.14216 + 35.6731i −0.260892 + 1.14304i
\(975\) 24.4354 22.6728i 0.782560 0.726110i
\(976\) 44.5632 6.71683i 1.42643 0.215000i
\(977\) 10.1209 + 3.12188i 0.323796 + 0.0998777i 0.452392 0.891819i \(-0.350571\pi\)
−0.128596 + 0.991697i \(0.541047\pi\)
\(978\) 1.07806 + 14.3858i 0.0344727 + 0.460006i
\(979\) 28.4439 0.909070
\(980\) 0.175217 + 1.37932i 0.00559710 + 0.0440609i
\(981\) 141.295 4.51121
\(982\) 1.98943 + 26.5471i 0.0634852 + 0.847152i
\(983\) 40.3107 + 12.4342i 1.28571 + 0.396589i 0.860938 0.508711i \(-0.169878\pi\)
0.424773 + 0.905300i \(0.360354\pi\)
\(984\) −46.6035 + 7.02435i −1.48567 + 0.223928i
\(985\) 4.34250 4.02925i 0.138364 0.128383i
\(986\) 1.44187 6.31723i 0.0459184 0.201182i
\(987\) −8.14243 45.9512i −0.259176 1.46264i
\(988\) −0.372261 1.63098i −0.0118432 0.0518885i
\(989\) −3.23782 2.20751i −0.102957 0.0701947i
\(990\) 7.50407 + 6.96276i 0.238495 + 0.221291i
\(991\) 40.4666 27.5897i 1.28546 0.876414i 0.288749 0.957405i \(-0.406761\pi\)
0.996715 + 0.0809906i \(0.0258084\pi\)
\(992\) 9.28651 + 1.39972i 0.294847 + 0.0444410i
\(993\) −91.1841 43.9119i −2.89364 1.39350i
\(994\) −3.60160 + 7.99997i −0.114236 + 0.253744i
\(995\) −3.91204 + 1.88394i −0.124020 + 0.0597249i
\(996\) −8.88361 + 2.74023i −0.281488 + 0.0868276i
\(997\) 13.1721 + 33.5619i 0.417164 + 1.06292i 0.972832 + 0.231512i \(0.0743671\pi\)
−0.555669 + 0.831404i \(0.687538\pi\)
\(998\) 6.70505 11.6135i 0.212245 0.367619i
\(999\) 29.7144 + 51.4669i 0.940122 + 1.62834i
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 49.2.g.a.32.2 yes 48
3.2 odd 2 441.2.bb.d.424.3 48
4.3 odd 2 784.2.bg.c.81.4 48
7.2 even 3 343.2.g.i.30.2 48
7.3 odd 6 343.2.e.c.197.6 48
7.4 even 3 343.2.e.d.197.6 48
7.5 odd 6 343.2.g.h.30.2 48
7.6 odd 2 343.2.g.g.116.2 48
49.4 even 21 343.2.e.d.148.6 48
49.11 even 21 2401.2.a.h.1.7 24
49.22 even 7 343.2.g.i.263.2 48
49.23 even 21 inner 49.2.g.a.23.2 48
49.26 odd 42 343.2.g.g.275.2 48
49.27 odd 14 343.2.g.h.263.2 48
49.38 odd 42 2401.2.a.i.1.7 24
49.45 odd 42 343.2.e.c.148.6 48
147.23 odd 42 441.2.bb.d.415.3 48
196.23 odd 42 784.2.bg.c.513.4 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
49.2.g.a.23.2 48 49.23 even 21 inner
49.2.g.a.32.2 yes 48 1.1 even 1 trivial
343.2.e.c.148.6 48 49.45 odd 42
343.2.e.c.197.6 48 7.3 odd 6
343.2.e.d.148.6 48 49.4 even 21
343.2.e.d.197.6 48 7.4 even 3
343.2.g.g.116.2 48 7.6 odd 2
343.2.g.g.275.2 48 49.26 odd 42
343.2.g.h.30.2 48 7.5 odd 6
343.2.g.h.263.2 48 49.27 odd 14
343.2.g.i.30.2 48 7.2 even 3
343.2.g.i.263.2 48 49.22 even 7
441.2.bb.d.415.3 48 147.23 odd 42
441.2.bb.d.424.3 48 3.2 odd 2
784.2.bg.c.81.4 48 4.3 odd 2
784.2.bg.c.513.4 48 196.23 odd 42
2401.2.a.h.1.7 24 49.11 even 21
2401.2.a.i.1.7 24 49.38 odd 42