Properties

Label 81.2.g.a.43.5
Level $81$
Weight $2$
Character 81.43
Analytic conductor $0.647$
Analytic rank $0$
Dimension $144$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [81,2,Mod(4,81)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(81, base_ring=CyclotomicField(54))
 
chi = DirichletCharacter(H, H._module([2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("81.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 81 = 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 81.g (of order \(27\), degree \(18\), 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: \(0.646788256372\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(8\) over \(\Q(\zeta_{27})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label 43.5
Character \(\chi\) \(=\) 81.43
Dual form 81.2.g.a.49.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.0876154 + 0.292656i) q^{2} +(0.419241 + 1.68055i) q^{3} +(1.59300 - 1.04774i) q^{4} +(-1.04144 - 2.41432i) q^{5} +(-0.455090 + 0.269935i) q^{6} +(-0.211661 + 3.63407i) q^{7} +(0.914234 + 0.767134i) q^{8} +(-2.64847 + 1.40911i) q^{9} +O(q^{10})\) \(q+(0.0876154 + 0.292656i) q^{2} +(0.419241 + 1.68055i) q^{3} +(1.59300 - 1.04774i) q^{4} +(-1.04144 - 2.41432i) q^{5} +(-0.455090 + 0.269935i) q^{6} +(-0.211661 + 3.63407i) q^{7} +(0.914234 + 0.767134i) q^{8} +(-2.64847 + 1.40911i) q^{9} +(0.615319 - 0.516314i) q^{10} +(-1.49756 - 2.01157i) q^{11} +(2.42862 + 2.23787i) q^{12} +(-2.52512 - 2.67647i) q^{13} +(-1.08208 + 0.256457i) q^{14} +(3.62077 - 2.76237i) q^{15} +(1.36599 - 3.16671i) q^{16} +(-0.339876 - 1.92753i) q^{17} +(-0.644430 - 0.651632i) q^{18} +(0.311537 - 1.76682i) q^{19} +(-4.18859 - 2.75488i) q^{20} +(-6.19596 + 1.16785i) q^{21} +(0.457489 - 0.614514i) q^{22} +(0.494053 + 8.48256i) q^{23} +(-0.905920 + 1.85803i) q^{24} +(-1.31316 + 1.39186i) q^{25} +(0.562046 - 0.973492i) q^{26} +(-3.47842 - 3.86013i) q^{27} +(3.47037 + 6.01086i) q^{28} +(-1.99862 - 0.473681i) q^{29} +(1.12566 + 0.817613i) q^{30} +(1.16881 + 0.586998i) q^{31} +(3.41720 + 0.399413i) q^{32} +(2.75270 - 3.36005i) q^{33} +(0.534324 - 0.268348i) q^{34} +(8.99425 - 3.27364i) q^{35} +(-2.74266 + 5.01962i) q^{36} +(4.98391 + 1.81400i) q^{37} +(0.544364 - 0.0636270i) q^{38} +(3.43931 - 5.36568i) q^{39} +(0.899991 - 3.00618i) q^{40} +(-1.81134 + 6.05029i) q^{41} +(-0.884638 - 1.71096i) q^{42} +(-10.0257 + 1.17184i) q^{43} +(-4.49321 - 1.63540i) q^{44} +(6.16026 + 4.92678i) q^{45} +(-2.43918 + 0.887789i) q^{46} +(8.24768 - 4.14214i) q^{47} +(5.89449 + 0.967989i) q^{48} +(-6.20900 - 0.725728i) q^{49} +(-0.522390 - 0.262354i) q^{50} +(3.09681 - 1.37928i) q^{51} +(-6.82677 - 1.61797i) q^{52} +(6.60535 + 11.4408i) q^{53} +(0.824926 - 1.35619i) q^{54} +(-3.29697 + 5.71052i) q^{55} +(-2.98133 + 3.16002i) q^{56} +(3.09983 - 0.217168i) q^{57} +(-0.0364842 - 0.626409i) q^{58} +(-0.558312 + 0.749943i) q^{59} +(2.87367 - 8.19407i) q^{60} +(1.64977 + 1.08507i) q^{61} +(-0.0693827 + 0.393489i) q^{62} +(-4.56022 - 9.92300i) q^{63} +(-1.01524 - 5.75769i) q^{64} +(-3.83212 + 8.88384i) q^{65} +(1.22452 + 0.511202i) q^{66} +(5.81052 - 1.37712i) q^{67} +(-2.56097 - 2.71446i) q^{68} +(-14.0482 + 4.38651i) q^{69} +(1.74608 + 2.34540i) q^{70} +(4.97716 - 4.17634i) q^{71} +(-3.50230 - 0.743480i) q^{72} +(-5.04878 - 4.23643i) q^{73} +(-0.0942089 + 1.61750i) q^{74} +(-2.88962 - 1.62329i) q^{75} +(-1.35488 - 3.14095i) q^{76} +(7.62717 - 5.01647i) q^{77} +(1.87163 + 0.536417i) q^{78} +(3.33457 + 11.1382i) q^{79} -9.06806 q^{80} +(5.02883 - 7.46397i) q^{81} -1.92935 q^{82} +(-4.89203 - 16.3405i) q^{83} +(-8.64660 + 8.35211i) q^{84} +(-4.29972 + 2.82797i) q^{85} +(-1.22135 - 2.83140i) q^{86} +(-0.0418588 - 3.55736i) q^{87} +(0.174024 - 2.98788i) q^{88} +(-3.64757 - 3.06067i) q^{89} +(-0.902116 + 2.23450i) q^{90} +(10.2610 - 8.60997i) q^{91} +(9.67450 + 12.9951i) q^{92} +(-0.496465 + 2.21033i) q^{93} +(1.93484 + 2.05081i) q^{94} +(-4.59011 + 1.08788i) q^{95} +(0.761396 + 5.91021i) q^{96} +(3.59792 - 8.34092i) q^{97} +(-0.331615 - 1.88068i) q^{98} +(6.80077 + 3.21737i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} - 18 q^{10} - 18 q^{11} - 18 q^{12} - 18 q^{13} - 18 q^{14} - 18 q^{15} - 18 q^{16} - 18 q^{17} - 9 q^{18} - 18 q^{19} + 18 q^{20} + 9 q^{21} - 18 q^{22} + 9 q^{23} + 36 q^{24} - 18 q^{25} + 45 q^{26} + 9 q^{27} - 9 q^{28} + 9 q^{29} + 36 q^{30} - 18 q^{31} + 36 q^{32} + 9 q^{33} - 18 q^{34} + 9 q^{35} + 18 q^{36} - 18 q^{37} - 9 q^{38} - 18 q^{39} - 18 q^{40} + 27 q^{42} - 18 q^{43} + 54 q^{44} + 36 q^{45} - 18 q^{46} + 36 q^{47} + 81 q^{48} - 18 q^{49} + 99 q^{50} + 45 q^{51} + 45 q^{53} + 108 q^{54} - 9 q^{55} + 126 q^{56} + 36 q^{57} - 18 q^{58} + 45 q^{59} + 99 q^{60} - 18 q^{61} + 81 q^{62} + 36 q^{63} - 18 q^{64} - 18 q^{66} + 9 q^{67} - 99 q^{68} - 72 q^{69} + 36 q^{70} - 90 q^{71} - 234 q^{72} - 18 q^{73} - 162 q^{74} - 108 q^{75} + 63 q^{76} - 162 q^{77} - 135 q^{78} + 36 q^{79} - 288 q^{80} - 90 q^{81} - 36 q^{82} - 90 q^{83} - 243 q^{84} + 36 q^{85} - 162 q^{86} - 162 q^{87} + 63 q^{88} - 81 q^{89} - 99 q^{90} - 18 q^{91} - 144 q^{92} + 36 q^{94} + 18 q^{95} - 27 q^{96} + 9 q^{97} + 81 q^{98} + 54 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/81\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{11}{27}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0876154 + 0.292656i 0.0619534 + 0.206939i 0.983362 0.181656i \(-0.0581458\pi\)
−0.921409 + 0.388595i \(0.872961\pi\)
\(3\) 0.419241 + 1.68055i 0.242049 + 0.970264i
\(4\) 1.59300 1.04774i 0.796502 0.523868i
\(5\) −1.04144 2.41432i −0.465745 1.07972i −0.975619 0.219469i \(-0.929567\pi\)
0.509874 0.860249i \(-0.329692\pi\)
\(6\) −0.455090 + 0.269935i −0.185790 + 0.110200i
\(7\) −0.211661 + 3.63407i −0.0800002 + 1.37355i 0.684541 + 0.728975i \(0.260003\pi\)
−0.764541 + 0.644575i \(0.777034\pi\)
\(8\) 0.914234 + 0.767134i 0.323231 + 0.271223i
\(9\) −2.64847 + 1.40911i −0.882825 + 0.469702i
\(10\) 0.615319 0.516314i 0.194581 0.163273i
\(11\) −1.49756 2.01157i −0.451531 0.606512i 0.516823 0.856092i \(-0.327115\pi\)
−0.968354 + 0.249581i \(0.919707\pi\)
\(12\) 2.42862 + 2.23787i 0.701083 + 0.646016i
\(13\) −2.52512 2.67647i −0.700343 0.742320i 0.275378 0.961336i \(-0.411197\pi\)
−0.975721 + 0.219016i \(0.929715\pi\)
\(14\) −1.08208 + 0.256457i −0.289197 + 0.0685410i
\(15\) 3.62077 2.76237i 0.934879 0.713240i
\(16\) 1.36599 3.16671i 0.341497 0.791678i
\(17\) −0.339876 1.92753i −0.0824319 0.467495i −0.997881 0.0650615i \(-0.979276\pi\)
0.915449 0.402433i \(-0.131835\pi\)
\(18\) −0.644430 0.651632i −0.151894 0.153591i
\(19\) 0.311537 1.76682i 0.0714716 0.405335i −0.927992 0.372599i \(-0.878467\pi\)
0.999464 0.0327364i \(-0.0104222\pi\)
\(20\) −4.18859 2.75488i −0.936597 0.616009i
\(21\) −6.19596 + 1.16785i −1.35207 + 0.254845i
\(22\) 0.457489 0.614514i 0.0975369 0.131015i
\(23\) 0.494053 + 8.48256i 0.103017 + 1.76874i 0.514664 + 0.857392i \(0.327917\pi\)
−0.411647 + 0.911343i \(0.635046\pi\)
\(24\) −0.905920 + 1.85803i −0.184920 + 0.379268i
\(25\) −1.31316 + 1.39186i −0.262631 + 0.278373i
\(26\) 0.562046 0.973492i 0.110226 0.190917i
\(27\) −3.47842 3.86013i −0.669422 0.742882i
\(28\) 3.47037 + 6.01086i 0.655838 + 1.13595i
\(29\) −1.99862 0.473681i −0.371134 0.0879604i 0.0408163 0.999167i \(-0.487004\pi\)
−0.411950 + 0.911206i \(0.635152\pi\)
\(30\) 1.12566 + 0.817613i 0.205516 + 0.149275i
\(31\) 1.16881 + 0.586998i 0.209924 + 0.105428i 0.550655 0.834733i \(-0.314378\pi\)
−0.340731 + 0.940161i \(0.610674\pi\)
\(32\) 3.41720 + 0.399413i 0.604080 + 0.0706069i
\(33\) 2.75270 3.36005i 0.479184 0.584910i
\(34\) 0.534324 0.268348i 0.0916359 0.0460213i
\(35\) 8.99425 3.27364i 1.52031 0.553346i
\(36\) −2.74266 + 5.01962i −0.457110 + 0.836603i
\(37\) 4.98391 + 1.81400i 0.819351 + 0.298219i 0.717481 0.696579i \(-0.245295\pi\)
0.101870 + 0.994798i \(0.467517\pi\)
\(38\) 0.544364 0.0636270i 0.0883075 0.0103217i
\(39\) 3.43931 5.36568i 0.550730 0.859196i
\(40\) 0.899991 3.00618i 0.142301 0.475319i
\(41\) −1.81134 + 6.05029i −0.282883 + 0.944896i 0.691947 + 0.721948i \(0.256753\pi\)
−0.974830 + 0.222948i \(0.928432\pi\)
\(42\) −0.884638 1.71096i −0.136503 0.264007i
\(43\) −10.0257 + 1.17184i −1.52890 + 0.178703i −0.838572 0.544790i \(-0.816609\pi\)
−0.690331 + 0.723494i \(0.742535\pi\)
\(44\) −4.49321 1.63540i −0.677378 0.246545i
\(45\) 6.16026 + 4.92678i 0.918317 + 0.734440i
\(46\) −2.43918 + 0.887789i −0.359638 + 0.130897i
\(47\) 8.24768 4.14214i 1.20305 0.604193i 0.269623 0.962966i \(-0.413101\pi\)
0.933425 + 0.358773i \(0.116805\pi\)
\(48\) 5.89449 + 0.967989i 0.850796 + 0.139717i
\(49\) −6.20900 0.725728i −0.887000 0.103675i
\(50\) −0.522390 0.262354i −0.0738770 0.0371024i
\(51\) 3.09681 1.37928i 0.433641 0.193137i
\(52\) −6.82677 1.61797i −0.946703 0.224373i
\(53\) 6.60535 + 11.4408i 0.907314 + 1.57151i 0.817781 + 0.575530i \(0.195204\pi\)
0.0895334 + 0.995984i \(0.471462\pi\)
\(54\) 0.824926 1.35619i 0.112258 0.184554i
\(55\) −3.29697 + 5.71052i −0.444563 + 0.770006i
\(56\) −2.98133 + 3.16002i −0.398396 + 0.422276i
\(57\) 3.09983 0.217168i 0.410582 0.0287646i
\(58\) −0.0364842 0.626409i −0.00479060 0.0822515i
\(59\) −0.558312 + 0.749943i −0.0726860 + 0.0976343i −0.836979 0.547235i \(-0.815681\pi\)
0.764293 + 0.644869i \(0.223088\pi\)
\(60\) 2.87367 8.19407i 0.370990 1.05785i
\(61\) 1.64977 + 1.08507i 0.211232 + 0.138929i 0.650717 0.759321i \(-0.274469\pi\)
−0.439485 + 0.898250i \(0.644839\pi\)
\(62\) −0.0693827 + 0.393489i −0.00881161 + 0.0499731i
\(63\) −4.56022 9.92300i −0.574533 1.25018i
\(64\) −1.01524 5.75769i −0.126904 0.719711i
\(65\) −3.83212 + 8.88384i −0.475316 + 1.10191i
\(66\) 1.22452 + 0.511202i 0.150728 + 0.0629246i
\(67\) 5.81052 1.37712i 0.709868 0.168242i 0.140208 0.990122i \(-0.455223\pi\)
0.569660 + 0.821880i \(0.307075\pi\)
\(68\) −2.56097 2.71446i −0.310563 0.329177i
\(69\) −14.0482 + 4.38651i −1.69121 + 0.528074i
\(70\) 1.74608 + 2.34540i 0.208697 + 0.280329i
\(71\) 4.97716 4.17634i 0.590681 0.495640i −0.297754 0.954643i \(-0.596238\pi\)
0.888435 + 0.459003i \(0.151793\pi\)
\(72\) −3.50230 0.743480i −0.412750 0.0876199i
\(73\) −5.04878 4.23643i −0.590915 0.495837i 0.297596 0.954692i \(-0.403815\pi\)
−0.888511 + 0.458855i \(0.848260\pi\)
\(74\) −0.0942089 + 1.61750i −0.0109516 + 0.188031i
\(75\) −2.88962 1.62329i −0.333665 0.187442i
\(76\) −1.35488 3.14095i −0.155415 0.360292i
\(77\) 7.62717 5.01647i 0.869196 0.571680i
\(78\) 1.87163 + 0.536417i 0.211921 + 0.0607372i
\(79\) 3.33457 + 11.1382i 0.375168 + 1.25315i 0.912255 + 0.409622i \(0.134339\pi\)
−0.537087 + 0.843527i \(0.680475\pi\)
\(80\) −9.06806 −1.01384
\(81\) 5.02883 7.46397i 0.558759 0.829330i
\(82\) −1.92935 −0.213061
\(83\) −4.89203 16.3405i −0.536970 1.79361i −0.605366 0.795947i \(-0.706973\pi\)
0.0683955 0.997658i \(-0.478212\pi\)
\(84\) −8.64660 + 8.35211i −0.943422 + 0.911290i
\(85\) −4.29972 + 2.82797i −0.466370 + 0.306737i
\(86\) −1.22135 2.83140i −0.131701 0.305318i
\(87\) −0.0418588 3.55736i −0.00448773 0.381389i
\(88\) 0.174024 2.98788i 0.0185510 0.318509i
\(89\) −3.64757 3.06067i −0.386641 0.324430i 0.428662 0.903465i \(-0.358985\pi\)
−0.815303 + 0.579035i \(0.803430\pi\)
\(90\) −0.902116 + 2.23450i −0.0950913 + 0.235537i
\(91\) 10.2610 8.60997i 1.07564 0.902570i
\(92\) 9.67450 + 12.9951i 1.00864 + 1.35483i
\(93\) −0.496465 + 2.21033i −0.0514810 + 0.229201i
\(94\) 1.93484 + 2.05081i 0.199564 + 0.211525i
\(95\) −4.59011 + 1.08788i −0.470935 + 0.111614i
\(96\) 0.761396 + 5.91021i 0.0777096 + 0.603208i
\(97\) 3.59792 8.34092i 0.365314 0.846892i −0.632091 0.774894i \(-0.717803\pi\)
0.997405 0.0719981i \(-0.0229376\pi\)
\(98\) −0.331615 1.88068i −0.0334982 0.189978i
\(99\) 6.80077 + 3.21737i 0.683503 + 0.323358i
\(100\) −0.633558 + 3.59309i −0.0633558 + 0.359309i
\(101\) −0.123664 0.0813354i −0.0123051 0.00809317i 0.543342 0.839512i \(-0.317159\pi\)
−0.555647 + 0.831419i \(0.687529\pi\)
\(102\) 0.674981 + 0.785455i 0.0668331 + 0.0777716i
\(103\) −8.14782 + 10.9444i −0.802829 + 1.07839i 0.192448 + 0.981307i \(0.438357\pi\)
−0.995277 + 0.0970787i \(0.969050\pi\)
\(104\) −0.255341 4.38403i −0.0250382 0.429890i
\(105\) 9.27226 + 13.7428i 0.904880 + 1.34116i
\(106\) −2.76948 + 2.93548i −0.268996 + 0.285119i
\(107\) −0.424082 + 0.734532i −0.0409976 + 0.0710098i −0.885796 0.464075i \(-0.846387\pi\)
0.844799 + 0.535085i \(0.179720\pi\)
\(108\) −9.58553 2.50474i −0.922368 0.241019i
\(109\) −2.42376 4.19808i −0.232154 0.402103i 0.726288 0.687391i \(-0.241244\pi\)
−0.958442 + 0.285288i \(0.907911\pi\)
\(110\) −1.96008 0.464548i −0.186886 0.0442929i
\(111\) −0.959046 + 9.13620i −0.0910286 + 0.867170i
\(112\) 11.2189 + 5.63436i 1.06009 + 0.532397i
\(113\) −9.08877 1.06233i −0.855000 0.0999352i −0.322711 0.946498i \(-0.604594\pi\)
−0.532289 + 0.846563i \(0.678668\pi\)
\(114\) 0.335148 + 0.888154i 0.0313895 + 0.0831833i
\(115\) 19.9651 10.0269i 1.86176 0.935009i
\(116\) −3.68010 + 1.33945i −0.341689 + 0.124365i
\(117\) 10.4592 + 3.53040i 0.966950 + 0.326386i
\(118\) −0.268392 0.0976866i −0.0247075 0.00899278i
\(119\) 7.07672 0.827150i 0.648722 0.0758247i
\(120\) 5.42934 + 0.252164i 0.495628 + 0.0230193i
\(121\) 1.35110 4.51299i 0.122827 0.410272i
\(122\) −0.173007 + 0.577884i −0.0156633 + 0.0523192i
\(123\) −10.9272 0.507510i −0.985270 0.0457606i
\(124\) 2.47694 0.289512i 0.222435 0.0259990i
\(125\) −7.62598 2.77563i −0.682089 0.248260i
\(126\) 2.50448 2.20398i 0.223116 0.196346i
\(127\) −0.721881 + 0.262743i −0.0640566 + 0.0233147i −0.373850 0.927489i \(-0.621962\pi\)
0.309793 + 0.950804i \(0.399740\pi\)
\(128\) 7.74508 3.88973i 0.684575 0.343806i
\(129\) −6.17250 16.3574i −0.543458 1.44019i
\(130\) −2.93566 0.343129i −0.257474 0.0300944i
\(131\) 7.23834 + 3.63523i 0.632417 + 0.317612i 0.735972 0.677012i \(-0.236726\pi\)
−0.103555 + 0.994624i \(0.533022\pi\)
\(132\) 0.864621 8.23668i 0.0752556 0.716911i
\(133\) 6.35479 + 1.50611i 0.551031 + 0.130597i
\(134\) 0.912112 + 1.57982i 0.0787945 + 0.136476i
\(135\) −5.69705 + 12.4181i −0.490324 + 1.06878i
\(136\) 1.16795 2.02294i 0.100151 0.173466i
\(137\) −6.33321 + 6.71281i −0.541082 + 0.573514i −0.939004 0.343905i \(-0.888250\pi\)
0.397922 + 0.917419i \(0.369732\pi\)
\(138\) −2.51458 3.72696i −0.214055 0.317260i
\(139\) 0.581362 + 9.98160i 0.0493105 + 0.846628i 0.928770 + 0.370655i \(0.120867\pi\)
−0.879460 + 0.475973i \(0.842096\pi\)
\(140\) 10.8980 14.6385i 0.921047 1.23718i
\(141\) 10.4188 + 12.1241i 0.877423 + 1.02103i
\(142\) 1.65830 + 1.09068i 0.139162 + 0.0915282i
\(143\) −1.60240 + 9.08765i −0.133999 + 0.759947i
\(144\) 0.844458 + 10.3118i 0.0703715 + 0.859315i
\(145\) 0.937816 + 5.31862i 0.0778814 + 0.441687i
\(146\) 0.797465 1.84873i 0.0659986 0.153002i
\(147\) −1.38345 10.7388i −0.114105 0.885719i
\(148\) 9.83999 2.33212i 0.808842 0.191699i
\(149\) 1.12805 + 1.19566i 0.0924131 + 0.0979522i 0.771929 0.635708i \(-0.219292\pi\)
−0.679516 + 0.733660i \(0.737810\pi\)
\(150\) 0.221891 0.987889i 0.0181173 0.0806608i
\(151\) −8.90781 11.9653i −0.724908 0.973720i −0.999925 0.0122805i \(-0.996091\pi\)
0.275017 0.961439i \(-0.411317\pi\)
\(152\) 1.64020 1.37629i 0.133038 0.111632i
\(153\) 3.61625 + 4.62609i 0.292356 + 0.373997i
\(154\) 2.13635 + 1.79261i 0.172152 + 0.144453i
\(155\) 0.199961 3.43320i 0.0160613 0.275762i
\(156\) −0.142979 12.1510i −0.0114475 0.972861i
\(157\) −0.107424 0.249037i −0.00857337 0.0198753i 0.913876 0.405994i \(-0.133075\pi\)
−0.922449 + 0.386119i \(0.873815\pi\)
\(158\) −2.96751 + 1.95176i −0.236082 + 0.155274i
\(159\) −16.4576 + 15.8970i −1.30517 + 1.26072i
\(160\) −2.59448 8.66618i −0.205112 0.685121i
\(161\) −30.9308 −2.43769
\(162\) 2.62498 + 0.817758i 0.206238 + 0.0642492i
\(163\) −1.95301 −0.152972 −0.0764858 0.997071i \(-0.524370\pi\)
−0.0764858 + 0.997071i \(0.524370\pi\)
\(164\) 3.45363 + 11.5359i 0.269683 + 0.900805i
\(165\) −10.9790 3.14663i −0.854715 0.244965i
\(166\) 4.35353 2.86336i 0.337900 0.222240i
\(167\) −3.03463 7.03507i −0.234827 0.544390i 0.759531 0.650472i \(-0.225429\pi\)
−0.994357 + 0.106082i \(0.966169\pi\)
\(168\) −6.56046 3.68545i −0.506150 0.284338i
\(169\) −0.0313845 + 0.538851i −0.00241419 + 0.0414501i
\(170\) −1.20434 1.01056i −0.0923689 0.0775067i
\(171\) 1.66453 + 5.11836i 0.127290 + 0.391410i
\(172\) −14.7432 + 12.3710i −1.12416 + 0.943281i
\(173\) −3.61748 4.85912i −0.275032 0.369432i 0.643049 0.765825i \(-0.277669\pi\)
−0.918081 + 0.396393i \(0.870262\pi\)
\(174\) 1.03741 0.323929i 0.0786461 0.0245570i
\(175\) −4.78019 5.06670i −0.361348 0.383007i
\(176\) −8.41572 + 1.99456i −0.634358 + 0.150346i
\(177\) −1.49438 0.623863i −0.112325 0.0468924i
\(178\) 0.576140 1.33564i 0.0431835 0.100111i
\(179\) 0.479893 + 2.72161i 0.0358689 + 0.203423i 0.997476 0.0710082i \(-0.0226217\pi\)
−0.961607 + 0.274431i \(0.911511\pi\)
\(180\) 14.9753 + 1.39405i 1.11619 + 0.103907i
\(181\) 1.53100 8.68276i 0.113799 0.645384i −0.873539 0.486754i \(-0.838181\pi\)
0.987338 0.158631i \(-0.0507080\pi\)
\(182\) 3.41878 + 2.24856i 0.253417 + 0.166675i
\(183\) −1.13186 + 3.22743i −0.0836697 + 0.238578i
\(184\) −6.05558 + 8.13405i −0.446423 + 0.599650i
\(185\) −0.810861 13.9219i −0.0596157 1.02356i
\(186\) −0.690364 + 0.0483657i −0.0506199 + 0.00354634i
\(187\) −3.36838 + 3.57028i −0.246320 + 0.261084i
\(188\) 8.79872 15.2398i 0.641713 1.11148i
\(189\) 14.7642 11.8238i 1.07394 0.860054i
\(190\) −0.720537 1.24801i −0.0522733 0.0905400i
\(191\) 1.80248 + 0.427196i 0.130423 + 0.0309108i 0.295309 0.955402i \(-0.404577\pi\)
−0.164886 + 0.986313i \(0.552726\pi\)
\(192\) 9.25043 4.12001i 0.667593 0.297336i
\(193\) 0.308962 + 0.155167i 0.0222396 + 0.0111691i 0.459884 0.887979i \(-0.347891\pi\)
−0.437645 + 0.899148i \(0.644187\pi\)
\(194\) 2.75625 + 0.322160i 0.197887 + 0.0231297i
\(195\) −16.5363 2.71558i −1.18419 0.194467i
\(196\) −10.6513 + 5.34931i −0.760810 + 0.382093i
\(197\) 21.2308 7.72738i 1.51263 0.550553i 0.553336 0.832958i \(-0.313354\pi\)
0.959295 + 0.282405i \(0.0911322\pi\)
\(198\) −0.345731 + 2.27217i −0.0245700 + 0.161476i
\(199\) −13.8558 5.04311i −0.982214 0.357497i −0.199513 0.979895i \(-0.563936\pi\)
−0.782700 + 0.622399i \(0.786158\pi\)
\(200\) −2.26828 + 0.265124i −0.160391 + 0.0187471i
\(201\) 4.75032 + 9.18750i 0.335062 + 0.648036i
\(202\) 0.0129684 0.0433173i 0.000912451 0.00304780i
\(203\) 2.14442 7.16286i 0.150509 0.502734i
\(204\) 3.48812 5.44184i 0.244218 0.381005i
\(205\) 16.4937 1.92784i 1.15197 0.134646i
\(206\) −3.91682 1.42561i −0.272898 0.0993267i
\(207\) −13.2613 21.7697i −0.921725 1.51310i
\(208\) −11.9249 + 4.34031i −0.826844 + 0.300947i
\(209\) −4.02062 + 2.01923i −0.278112 + 0.139673i
\(210\) −3.20952 + 3.91766i −0.221478 + 0.270344i
\(211\) 12.8979 + 1.50755i 0.887926 + 0.103784i 0.547813 0.836601i \(-0.315460\pi\)
0.340113 + 0.940384i \(0.389535\pi\)
\(212\) 22.5093 + 11.3046i 1.54594 + 0.776402i
\(213\) 9.10516 + 6.61347i 0.623875 + 0.453147i
\(214\) −0.252121 0.0597538i −0.0172346 0.00408468i
\(215\) 13.2703 + 22.9849i 0.905028 + 1.56755i
\(216\) −0.218854 6.19748i −0.0148912 0.421685i
\(217\) −2.38058 + 4.12329i −0.161604 + 0.279907i
\(218\) 1.01623 1.07714i 0.0688279 0.0729534i
\(219\) 5.00286 10.2608i 0.338062 0.693360i
\(220\) 0.731026 + 12.5512i 0.0492858 + 0.846204i
\(221\) −4.30076 + 5.77692i −0.289300 + 0.388598i
\(222\) −2.75779 + 0.519801i −0.185091 + 0.0348868i
\(223\) 12.3994 + 8.15524i 0.830328 + 0.546115i 0.892028 0.451979i \(-0.149282\pi\)
−0.0617002 + 0.998095i \(0.519652\pi\)
\(224\) −2.17478 + 12.3338i −0.145309 + 0.824086i
\(225\) 1.51657 5.53669i 0.101105 0.369113i
\(226\) −0.485421 2.75296i −0.0322897 0.183124i
\(227\) −2.21901 + 5.14424i −0.147281 + 0.341435i −0.975847 0.218456i \(-0.929898\pi\)
0.828566 + 0.559892i \(0.189157\pi\)
\(228\) 4.71050 3.59375i 0.311961 0.238002i
\(229\) −19.3832 + 4.59389i −1.28088 + 0.303573i −0.814059 0.580782i \(-0.802747\pi\)
−0.466816 + 0.884355i \(0.654599\pi\)
\(230\) 4.68367 + 4.96440i 0.308832 + 0.327343i
\(231\) 11.6280 + 10.7147i 0.765068 + 0.704976i
\(232\) −1.46383 1.96626i −0.0961051 0.129092i
\(233\) −4.48492 + 3.76330i −0.293817 + 0.246542i −0.777765 0.628555i \(-0.783647\pi\)
0.483948 + 0.875097i \(0.339202\pi\)
\(234\) −0.116809 + 3.37025i −0.00763607 + 0.220320i
\(235\) −18.5899 15.5988i −1.21267 1.01755i
\(236\) −0.103651 + 1.77963i −0.00674713 + 0.115844i
\(237\) −17.3203 + 10.2735i −1.12508 + 0.667335i
\(238\) 0.862099 + 1.99857i 0.0558816 + 0.129548i
\(239\) −12.4619 + 8.19630i −0.806091 + 0.530174i −0.884386 0.466756i \(-0.845423\pi\)
0.0782952 + 0.996930i \(0.475052\pi\)
\(240\) −3.80170 15.2393i −0.245399 0.983692i
\(241\) 0.0645147 + 0.215494i 0.00415575 + 0.0138812i 0.960042 0.279855i \(-0.0902864\pi\)
−0.955886 + 0.293736i \(0.905101\pi\)
\(242\) 1.43913 0.0925107
\(243\) 14.6518 + 5.32199i 0.939916 + 0.341406i
\(244\) 3.76497 0.241027
\(245\) 4.71414 + 15.7463i 0.301176 + 1.00600i
\(246\) −0.808863 3.24236i −0.0515712 0.206726i
\(247\) −5.51551 + 3.62761i −0.350943 + 0.230819i
\(248\) 0.618259 + 1.43329i 0.0392595 + 0.0910138i
\(249\) 25.4101 15.0719i 1.61030 0.955143i
\(250\) 0.144151 2.47498i 0.00911690 0.156531i
\(251\) 0.0887945 + 0.0745074i 0.00560466 + 0.00470286i 0.645586 0.763688i \(-0.276613\pi\)
−0.639981 + 0.768391i \(0.721058\pi\)
\(252\) −17.6611 11.0295i −1.11255 0.694792i
\(253\) 16.3234 13.6970i 1.02624 0.861120i
\(254\) −0.140141 0.188242i −0.00879323 0.0118114i
\(255\) −6.55516 6.04028i −0.410500 0.378257i
\(256\) −6.20730 6.57935i −0.387956 0.411209i
\(257\) 8.70398 2.06288i 0.542939 0.128679i 0.0500106 0.998749i \(-0.484074\pi\)
0.492929 + 0.870070i \(0.335926\pi\)
\(258\) 4.24627 3.23957i 0.264361 0.201687i
\(259\) −7.64709 + 17.7279i −0.475167 + 1.10156i
\(260\) 3.20334 + 18.1671i 0.198663 + 1.12667i
\(261\) 5.96076 1.56174i 0.368962 0.0966690i
\(262\) −0.429681 + 2.43684i −0.0265458 + 0.150549i
\(263\) 13.1978 + 8.68030i 0.813809 + 0.535250i 0.886839 0.462079i \(-0.152897\pi\)
−0.0730300 + 0.997330i \(0.523267\pi\)
\(264\) 5.09422 0.960184i 0.313528 0.0590952i
\(265\) 20.7427 27.8623i 1.27422 1.71157i
\(266\) 0.116005 + 1.99173i 0.00711271 + 0.122121i
\(267\) 3.61439 7.41306i 0.221197 0.453672i
\(268\) 7.81333 8.28164i 0.477275 0.505882i
\(269\) 12.1223 20.9965i 0.739111 1.28018i −0.213784 0.976881i \(-0.568579\pi\)
0.952896 0.303298i \(-0.0980877\pi\)
\(270\) −4.13338 0.579255i −0.251549 0.0352524i
\(271\) 7.20041 + 12.4715i 0.437394 + 0.757588i 0.997488 0.0708408i \(-0.0225682\pi\)
−0.560094 + 0.828429i \(0.689235\pi\)
\(272\) −6.56820 1.55669i −0.398256 0.0943883i
\(273\) 18.7713 + 13.6344i 1.13609 + 0.825190i
\(274\) −2.51943 1.26530i −0.152204 0.0764398i
\(275\) 4.76636 + 0.557108i 0.287423 + 0.0335949i
\(276\) −17.7830 + 21.7065i −1.07041 + 1.30658i
\(277\) −24.8427 + 12.4765i −1.49266 + 0.749640i −0.993169 0.116682i \(-0.962774\pi\)
−0.499486 + 0.866322i \(0.666478\pi\)
\(278\) −2.87024 + 1.04468i −0.172145 + 0.0626558i
\(279\) −3.92270 + 0.0923282i −0.234846 + 0.00552755i
\(280\) 10.7342 + 3.90692i 0.641490 + 0.233483i
\(281\) −10.1221 + 1.18311i −0.603835 + 0.0705782i −0.412517 0.910950i \(-0.635350\pi\)
−0.191318 + 0.981528i \(0.561276\pi\)
\(282\) −2.63532 + 4.11138i −0.156931 + 0.244829i
\(283\) −8.29289 + 27.7002i −0.492961 + 1.64661i 0.243332 + 0.969943i \(0.421760\pi\)
−0.736293 + 0.676663i \(0.763426\pi\)
\(284\) 3.55295 11.8677i 0.210829 0.704217i
\(285\) −3.75259 7.25781i −0.222284 0.429916i
\(286\) −2.79995 + 0.327267i −0.165564 + 0.0193517i
\(287\) −21.6038 7.86313i −1.27523 0.464146i
\(288\) −9.61317 + 3.75736i −0.566461 + 0.221405i
\(289\) 12.3749 4.50410i 0.727936 0.264947i
\(290\) −1.47436 + 0.740450i −0.0865772 + 0.0434807i
\(291\) 15.5257 + 2.54962i 0.910133 + 0.149462i
\(292\) −12.4814 1.45887i −0.730418 0.0853736i
\(293\) −26.4909 13.3042i −1.54761 0.777241i −0.549319 0.835613i \(-0.685113\pi\)
−0.998295 + 0.0583717i \(0.981409\pi\)
\(294\) 3.02155 1.34576i 0.176220 0.0784860i
\(295\) 2.39205 + 0.566927i 0.139271 + 0.0330077i
\(296\) 3.16489 + 5.48175i 0.183955 + 0.318620i
\(297\) −2.55579 + 12.7779i −0.148302 + 0.741447i
\(298\) −0.251082 + 0.434887i −0.0145448 + 0.0251923i
\(299\) 21.4558 22.7418i 1.24082 1.31519i
\(300\) −6.30396 + 0.441644i −0.363959 + 0.0254983i
\(301\) −2.13649 36.6821i −0.123145 2.11432i
\(302\) 2.72124 3.65526i 0.156590 0.210337i
\(303\) 0.0848428 0.241923i 0.00487409 0.0138981i
\(304\) −5.16944 3.40000i −0.296488 0.195003i
\(305\) 0.901581 5.11312i 0.0516244 0.292776i
\(306\) −1.03701 + 1.46363i −0.0592821 + 0.0836703i
\(307\) 1.79762 + 10.1948i 0.102595 + 0.581848i 0.992154 + 0.125026i \(0.0399013\pi\)
−0.889558 + 0.456822i \(0.848988\pi\)
\(308\) 6.89418 15.9825i 0.392833 0.910688i
\(309\) −21.8085 9.10444i −1.24064 0.517934i
\(310\) 1.02227 0.242282i 0.0580608 0.0137607i
\(311\) −5.51859 5.84936i −0.312930 0.331687i 0.551750 0.834010i \(-0.313960\pi\)
−0.864680 + 0.502323i \(0.832479\pi\)
\(312\) 7.26052 2.26708i 0.411046 0.128348i
\(313\) 2.01619 + 2.70821i 0.113962 + 0.153077i 0.855444 0.517895i \(-0.173284\pi\)
−0.741482 + 0.670972i \(0.765877\pi\)
\(314\) 0.0634701 0.0532577i 0.00358182 0.00300551i
\(315\) −19.2081 + 21.3440i −1.08226 + 1.20260i
\(316\) 16.9819 + 14.2495i 0.955306 + 0.801597i
\(317\) 0.646483 11.0997i 0.0363101 0.623420i −0.930242 0.366948i \(-0.880403\pi\)
0.966552 0.256472i \(-0.0825602\pi\)
\(318\) −6.09429 3.42357i −0.341751 0.191984i
\(319\) 2.04021 + 4.72973i 0.114230 + 0.264814i
\(320\) −12.8436 + 8.44738i −0.717980 + 0.472223i
\(321\) −1.41221 0.404744i −0.0788217 0.0225906i
\(322\) −2.71001 9.05207i −0.151023 0.504452i
\(323\) −3.51148 −0.195384
\(324\) 0.190689 17.1590i 0.0105938 0.953279i
\(325\) 7.04117 0.390574
\(326\) −0.171114 0.571560i −0.00947711 0.0316558i
\(327\) 6.03893 5.83325i 0.333953 0.322579i
\(328\) −6.29736 + 4.14184i −0.347714 + 0.228695i
\(329\) 13.3071 + 30.8494i 0.733645 + 1.70078i
\(330\) −0.0410516 3.48876i −0.00225982 0.192050i
\(331\) 1.23279 21.1661i 0.0677601 1.16340i −0.777444 0.628952i \(-0.783484\pi\)
0.845204 0.534444i \(-0.179479\pi\)
\(332\) −24.9136 20.9050i −1.36731 1.14731i
\(333\) −15.7559 + 2.21855i −0.863417 + 0.121576i
\(334\) 1.79297 1.50448i 0.0981071 0.0823216i
\(335\) −9.37610 12.5943i −0.512271 0.688099i
\(336\) −4.76537 + 21.2161i −0.259972 + 1.15743i
\(337\) 9.04532 + 9.58748i 0.492730 + 0.522263i 0.925248 0.379362i \(-0.123856\pi\)
−0.432518 + 0.901625i \(0.642375\pi\)
\(338\) −0.160448 + 0.0380268i −0.00872720 + 0.00206838i
\(339\) −2.02510 15.7195i −0.109988 0.853765i
\(340\) −3.88651 + 9.00994i −0.210776 + 0.488633i
\(341\) −0.569573 3.23021i −0.0308441 0.174926i
\(342\) −1.35208 + 0.935582i −0.0731120 + 0.0505905i
\(343\) −0.473286 + 2.68414i −0.0255550 + 0.144930i
\(344\) −10.0648 6.61971i −0.542657 0.356911i
\(345\) 25.2208 + 29.3486i 1.35784 + 1.58008i
\(346\) 1.10510 1.48441i 0.0594107 0.0798024i
\(347\) 0.670324 + 11.5090i 0.0359849 + 0.617836i 0.967302 + 0.253627i \(0.0816237\pi\)
−0.931317 + 0.364209i \(0.881339\pi\)
\(348\) −3.79385 5.62303i −0.203372 0.301426i
\(349\) −5.45928 + 5.78650i −0.292229 + 0.309744i −0.856809 0.515634i \(-0.827557\pi\)
0.564580 + 0.825378i \(0.309038\pi\)
\(350\) 1.06398 1.84287i 0.0568722 0.0985056i
\(351\) −1.54810 + 19.0572i −0.0826316 + 1.01720i
\(352\) −4.31401 7.47208i −0.229937 0.398263i
\(353\) −2.60195 0.616672i −0.138488 0.0328222i 0.160787 0.986989i \(-0.448597\pi\)
−0.299275 + 0.954167i \(0.596745\pi\)
\(354\) 0.0516462 0.491999i 0.00274496 0.0261495i
\(355\) −15.2664 7.66709i −0.810258 0.406927i
\(356\) −9.01736 1.05398i −0.477919 0.0558608i
\(357\) 4.35691 + 11.5460i 0.230592 + 0.611078i
\(358\) −0.754449 + 0.378898i −0.0398738 + 0.0200254i
\(359\) 18.3022 6.66145i 0.965952 0.351578i 0.189589 0.981864i \(-0.439285\pi\)
0.776363 + 0.630286i \(0.217062\pi\)
\(360\) 1.85243 + 9.22997i 0.0976314 + 0.486462i
\(361\) 14.8296 + 5.39752i 0.780504 + 0.284080i
\(362\) 2.67520 0.312686i 0.140605 0.0164344i
\(363\) 8.15072 + 0.378558i 0.427802 + 0.0198691i
\(364\) 7.32479 24.4665i 0.383923 1.28239i
\(365\) −4.97012 + 16.6014i −0.260148 + 0.868955i
\(366\) −1.04369 0.0484741i −0.0545547 0.00253378i
\(367\) 10.4769 1.22458i 0.546892 0.0639225i 0.161839 0.986817i \(-0.448257\pi\)
0.385053 + 0.922895i \(0.374183\pi\)
\(368\) 27.5367 + 10.0225i 1.43545 + 0.522461i
\(369\) −3.72822 18.5764i −0.194084 0.967048i
\(370\) 4.00329 1.45708i 0.208121 0.0757499i
\(371\) −42.9747 + 21.5827i −2.23114 + 1.12052i
\(372\) 1.52497 + 4.04123i 0.0790661 + 0.209528i
\(373\) 18.7088 + 2.18675i 0.968705 + 0.113225i 0.585706 0.810523i \(-0.300817\pi\)
0.382999 + 0.923749i \(0.374891\pi\)
\(374\) −1.33998 0.672965i −0.0692889 0.0347982i
\(375\) 1.46745 13.9795i 0.0757790 0.721897i
\(376\) 10.7179 + 2.54019i 0.552733 + 0.131000i
\(377\) 3.77896 + 6.54536i 0.194626 + 0.337103i
\(378\) 4.75387 + 3.28489i 0.244513 + 0.168957i
\(379\) 4.33052 7.50069i 0.222444 0.385285i −0.733105 0.680115i \(-0.761930\pi\)
0.955550 + 0.294830i \(0.0952632\pi\)
\(380\) −6.17226 + 6.54222i −0.316630 + 0.335609i
\(381\) −0.744194 1.10300i −0.0381262 0.0565085i
\(382\) 0.0329037 + 0.564935i 0.00168350 + 0.0289046i
\(383\) −18.0681 + 24.2697i −0.923238 + 1.24012i 0.0472278 + 0.998884i \(0.484961\pi\)
−0.970466 + 0.241239i \(0.922446\pi\)
\(384\) 9.78392 + 11.3852i 0.499284 + 0.581001i
\(385\) −20.0546 13.1901i −1.02208 0.672230i
\(386\) −0.0183406 + 0.104015i −0.000933511 + 0.00529420i
\(387\) 24.9015 17.2308i 1.26582 0.875893i
\(388\) −3.00757 17.0568i −0.152686 0.865928i
\(389\) 6.44975 14.9522i 0.327015 0.758107i −0.672817 0.739809i \(-0.734916\pi\)
0.999833 0.0182980i \(-0.00582476\pi\)
\(390\) −0.654103 5.07737i −0.0331218 0.257102i
\(391\) 16.1825 3.83531i 0.818382 0.193960i
\(392\) −5.11975 5.42662i −0.258587 0.274086i
\(393\) −3.07457 + 13.6884i −0.155091 + 0.690488i
\(394\) 4.12160 + 5.53628i 0.207643 + 0.278914i
\(395\) 23.4185 19.6505i 1.17831 0.988723i
\(396\) 14.2046 2.00012i 0.713809 0.100510i
\(397\) 22.8963 + 19.2123i 1.14913 + 0.964236i 0.999699 0.0245358i \(-0.00781077\pi\)
0.149433 + 0.988772i \(0.452255\pi\)
\(398\) 0.261911 4.49684i 0.0131284 0.225406i
\(399\) 0.133094 + 11.3110i 0.00666303 + 0.566256i
\(400\) 2.61388 + 6.05966i 0.130694 + 0.302983i
\(401\) 26.1226 17.1811i 1.30450 0.857983i 0.308846 0.951112i \(-0.400057\pi\)
0.995654 + 0.0931291i \(0.0296869\pi\)
\(402\) −2.27257 + 2.19517i −0.113346 + 0.109485i
\(403\) −1.38030 4.61053i −0.0687577 0.229667i
\(404\) −0.282216 −0.0140408
\(405\) −23.2576 4.36797i −1.15568 0.217046i
\(406\) 2.28414 0.113360
\(407\) −3.81473 12.7421i −0.189089 0.631601i
\(408\) 3.88930 + 1.11469i 0.192549 + 0.0551854i
\(409\) 22.0215 14.4838i 1.08889 0.716177i 0.127634 0.991821i \(-0.459262\pi\)
0.961260 + 0.275645i \(0.0888913\pi\)
\(410\) 2.00930 + 4.65808i 0.0992322 + 0.230046i
\(411\) −13.9363 7.82897i −0.687428 0.386175i
\(412\) −1.51265 + 25.9713i −0.0745231 + 1.27951i
\(413\) −2.60717 2.18768i −0.128291 0.107649i
\(414\) 5.20912 5.78836i 0.256014 0.284482i
\(415\) −34.3566 + 28.8286i −1.68650 + 1.41514i
\(416\) −7.55982 10.1546i −0.370651 0.497870i
\(417\) −16.5308 + 5.16170i −0.809518 + 0.252770i
\(418\) −0.943208 0.999742i −0.0461338 0.0488990i
\(419\) 15.2679 3.61856i 0.745886 0.176778i 0.159938 0.987127i \(-0.448870\pi\)
0.585948 + 0.810349i \(0.300722\pi\)
\(420\) 29.1696 + 12.1775i 1.42333 + 0.594201i
\(421\) −9.02857 + 20.9306i −0.440025 + 1.02009i 0.543514 + 0.839400i \(0.317093\pi\)
−0.983539 + 0.180693i \(0.942166\pi\)
\(422\) 0.688860 + 3.90672i 0.0335332 + 0.190176i
\(423\) −16.0070 + 22.5922i −0.778289 + 1.09847i
\(424\) −2.73779 + 15.5268i −0.132959 + 0.754046i
\(425\) 3.12917 + 2.05809i 0.151787 + 0.0998319i
\(426\) −1.13772 + 3.24412i −0.0551226 + 0.157178i
\(427\) −4.29242 + 5.76572i −0.207725 + 0.279023i
\(428\) 0.0940303 + 1.61444i 0.00454513 + 0.0780368i
\(429\) −15.9440 + 1.11701i −0.769784 + 0.0539297i
\(430\) −5.56397 + 5.89746i −0.268318 + 0.284401i
\(431\) 17.0699 29.5659i 0.822227 1.42414i −0.0817934 0.996649i \(-0.526065\pi\)
0.904020 0.427490i \(-0.140602\pi\)
\(432\) −16.9754 + 5.74227i −0.816729 + 0.276275i
\(433\) −11.6224 20.1306i −0.558539 0.967417i −0.997619 0.0689692i \(-0.978029\pi\)
0.439080 0.898448i \(-0.355304\pi\)
\(434\) −1.41528 0.335428i −0.0679356 0.0161010i
\(435\) −8.54502 + 3.80583i −0.409702 + 0.182475i
\(436\) −8.25954 4.14810i −0.395560 0.198658i
\(437\) 15.1410 + 1.76973i 0.724294 + 0.0846578i
\(438\) 3.44121 + 0.565113i 0.164427 + 0.0270022i
\(439\) 6.16848 3.09793i 0.294406 0.147856i −0.295466 0.955353i \(-0.595475\pi\)
0.589871 + 0.807497i \(0.299178\pi\)
\(440\) −7.39493 + 2.69154i −0.352540 + 0.128314i
\(441\) 17.4670 6.82708i 0.831763 0.325099i
\(442\) −2.06746 0.752494i −0.0983391 0.0357925i
\(443\) −16.0121 + 1.87155i −0.760760 + 0.0889201i −0.487622 0.873055i \(-0.662136\pi\)
−0.273138 + 0.961975i \(0.588062\pi\)
\(444\) 8.04456 + 15.5588i 0.381778 + 0.738390i
\(445\) −3.59074 + 11.9939i −0.170217 + 0.568565i
\(446\) −1.30030 + 4.34329i −0.0615708 + 0.205661i
\(447\) −1.53644 + 2.39700i −0.0726710 + 0.113374i
\(448\) 21.1387 2.47076i 0.998711 0.116733i
\(449\) 20.7990 + 7.57021i 0.981565 + 0.357261i 0.782449 0.622715i \(-0.213971\pi\)
0.199117 + 0.979976i \(0.436193\pi\)
\(450\) 1.75322 0.0412653i 0.0826476 0.00194527i
\(451\) 14.8832 5.41703i 0.700821 0.255078i
\(452\) −15.5915 + 7.83034i −0.733362 + 0.368308i
\(453\) 16.3737 19.9863i 0.769302 0.939039i
\(454\) −1.69991 0.198691i −0.0797808 0.00932504i
\(455\) −31.4734 15.8065i −1.47550 0.741022i
\(456\) 3.00056 + 2.17944i 0.140514 + 0.102062i
\(457\) −25.2639 5.98766i −1.18180 0.280091i −0.407674 0.913127i \(-0.633660\pi\)
−0.774122 + 0.633037i \(0.781808\pi\)
\(458\) −3.04269 5.27010i −0.142176 0.246255i
\(459\) −6.25829 + 8.01672i −0.292112 + 0.374188i
\(460\) 21.2990 36.8910i 0.993072 1.72005i
\(461\) 1.56492 1.65872i 0.0728855 0.0772541i −0.689905 0.723900i \(-0.742348\pi\)
0.762790 + 0.646646i \(0.223829\pi\)
\(462\) −2.11693 + 4.34178i −0.0984883 + 0.201998i
\(463\) −0.321353 5.51742i −0.0149346 0.256416i −0.997509 0.0705449i \(-0.977526\pi\)
0.982574 0.185872i \(-0.0595108\pi\)
\(464\) −4.23010 + 5.68201i −0.196377 + 0.263781i
\(465\) 5.85349 1.10329i 0.271449 0.0511641i
\(466\) −1.49430 0.982815i −0.0692220 0.0455280i
\(467\) −4.62726 + 26.2425i −0.214124 + 1.21436i 0.668296 + 0.743896i \(0.267024\pi\)
−0.882420 + 0.470463i \(0.844087\pi\)
\(468\) 20.3604 5.33449i 0.941161 0.246587i
\(469\) 3.77469 + 21.4073i 0.174299 + 0.988498i
\(470\) 2.93631 6.80713i 0.135442 0.313990i
\(471\) 0.373482 0.284938i 0.0172091 0.0131292i
\(472\) −1.08573 + 0.257324i −0.0499750 + 0.0118443i
\(473\) 17.3713 + 18.4125i 0.798733 + 0.846608i
\(474\) −4.52412 4.16878i −0.207800 0.191478i
\(475\) 2.05007 + 2.75372i 0.0940637 + 0.126349i
\(476\) 10.4066 8.73219i 0.476986 0.400239i
\(477\) −33.6154 20.9930i −1.53914 0.961204i
\(478\) −3.49054 2.92891i −0.159654 0.133965i
\(479\) −1.12496 + 19.3149i −0.0514009 + 0.882520i 0.869793 + 0.493416i \(0.164252\pi\)
−0.921194 + 0.389103i \(0.872785\pi\)
\(480\) 13.4762 7.99336i 0.615102 0.364845i
\(481\) −7.72988 17.9199i −0.352452 0.817076i
\(482\) −0.0574131 + 0.0377612i −0.00261509 + 0.00171997i
\(483\) −12.9674 51.9806i −0.590039 2.36520i
\(484\) −2.57611 8.60481i −0.117096 0.391128i
\(485\) −23.8847 −1.08455
\(486\) −0.273784 + 4.75423i −0.0124191 + 0.215656i
\(487\) −23.9390 −1.08478 −0.542390 0.840127i \(-0.682480\pi\)
−0.542390 + 0.840127i \(0.682480\pi\)
\(488\) 0.675883 + 2.25761i 0.0305958 + 0.102197i
\(489\) −0.818782 3.28213i −0.0370266 0.148423i
\(490\) −4.19522 + 2.75924i −0.189521 + 0.124650i
\(491\) −10.8242 25.0934i −0.488491 1.13245i −0.967094 0.254419i \(-0.918116\pi\)
0.478603 0.878032i \(-0.341143\pi\)
\(492\) −17.9388 + 10.6403i −0.808742 + 0.479703i
\(493\) −0.233753 + 4.01339i −0.0105277 + 0.180754i
\(494\) −1.54488 1.29631i −0.0695076 0.0583238i
\(495\) 0.685206 19.7699i 0.0307977 0.888593i
\(496\) 3.45543 2.89945i 0.155153 0.130189i
\(497\) 14.1236 + 18.9713i 0.633532 + 0.850981i
\(498\) 6.63719 + 6.11587i 0.297420 + 0.274059i
\(499\) 6.54778 + 6.94024i 0.293119 + 0.310688i 0.857151 0.515065i \(-0.172232\pi\)
−0.564032 + 0.825753i \(0.690751\pi\)
\(500\) −15.0564 + 3.56842i −0.673341 + 0.159585i
\(501\) 10.5505 8.04923i 0.471362 0.359613i
\(502\) −0.0140253 + 0.0325142i −0.000625978 + 0.00145118i
\(503\) 6.80145 + 38.5730i 0.303262 + 1.71988i 0.631575 + 0.775314i \(0.282409\pi\)
−0.328314 + 0.944569i \(0.606480\pi\)
\(504\) 3.44316 12.5702i 0.153370 0.559923i
\(505\) −0.0675811 + 0.383272i −0.00300732 + 0.0170554i
\(506\) 5.43867 + 3.57707i 0.241778 + 0.159020i
\(507\) −0.918722 + 0.173165i −0.0408019 + 0.00769054i
\(508\) −0.874674 + 1.17489i −0.0388074 + 0.0521274i
\(509\) −0.0618716 1.06229i −0.00274241 0.0470853i 0.996659 0.0816713i \(-0.0260258\pi\)
−0.999402 + 0.0345860i \(0.988989\pi\)
\(510\) 1.19339 2.44763i 0.0528442 0.108383i
\(511\) 16.4641 17.4509i 0.728329 0.771984i
\(512\) 10.0486 17.4047i 0.444089 0.769185i
\(513\) −7.90380 + 4.94315i −0.348961 + 0.218245i
\(514\) 1.36632 + 2.36653i 0.0602656 + 0.104383i
\(515\) 34.9088 + 8.27354i 1.53827 + 0.364576i
\(516\) −26.9710 19.5902i −1.18733 0.862410i
\(517\) −20.6836 10.3877i −0.909664 0.456850i
\(518\) −5.85819 0.684724i −0.257394 0.0300850i
\(519\) 6.64939 8.11649i 0.291876 0.356274i
\(520\) −10.3186 + 5.18217i −0.452498 + 0.227253i
\(521\) −42.0204 + 15.2942i −1.84095 + 0.670050i −0.851654 + 0.524104i \(0.824400\pi\)
−0.989293 + 0.145946i \(0.953377\pi\)
\(522\) 0.979305 + 1.60762i 0.0428630 + 0.0703635i
\(523\) −27.5645 10.0326i −1.20531 0.438697i −0.340236 0.940340i \(-0.610507\pi\)
−0.865075 + 0.501643i \(0.832729\pi\)
\(524\) 15.3395 1.79293i 0.670108 0.0783244i
\(525\) 6.51078 10.1575i 0.284154 0.443310i
\(526\) −1.38401 + 4.62293i −0.0603458 + 0.201569i
\(527\) 0.734207 2.45242i 0.0319825 0.106829i
\(528\) −6.88016 13.3068i −0.299421 0.579104i
\(529\) −48.8652 + 5.71152i −2.12457 + 0.248327i
\(530\) 9.97144 + 3.62931i 0.433132 + 0.157647i
\(531\) 0.421925 2.77293i 0.0183100 0.120335i
\(532\) 11.7012 4.25890i 0.507313 0.184647i
\(533\) 20.7673 10.4297i 0.899531 0.451761i
\(534\) 2.48615 + 0.408274i 0.107586 + 0.0176678i
\(535\) 2.21505 + 0.258902i 0.0957650 + 0.0111933i
\(536\) 6.36861 + 3.19844i 0.275082 + 0.138151i
\(537\) −4.37260 + 1.94749i −0.188692 + 0.0840405i
\(538\) 7.20684 + 1.70805i 0.310709 + 0.0736394i
\(539\) 7.83850 + 13.5767i 0.337628 + 0.584789i
\(540\) 3.93548 + 25.7511i 0.169356 + 1.10815i
\(541\) −14.0760 + 24.3804i −0.605176 + 1.04820i 0.386848 + 0.922144i \(0.373564\pi\)
−0.992024 + 0.126052i \(0.959769\pi\)
\(542\) −3.01898 + 3.19993i −0.129676 + 0.137449i
\(543\) 15.2336 1.06724i 0.653738 0.0457997i
\(544\) −0.391541 6.72250i −0.0167872 0.288225i
\(545\) −7.61132 + 10.2238i −0.326033 + 0.437938i
\(546\) −2.34553 + 6.68810i −0.100379 + 0.286224i
\(547\) −4.24644 2.79293i −0.181565 0.119417i 0.455473 0.890250i \(-0.349470\pi\)
−0.637038 + 0.770833i \(0.719841\pi\)
\(548\) −3.05558 + 17.3291i −0.130528 + 0.740261i
\(549\) −5.89837 0.549080i −0.251736 0.0234342i
\(550\) 0.254566 + 1.44371i 0.0108547 + 0.0615602i
\(551\) −1.45955 + 3.38362i −0.0621790 + 0.144147i
\(552\) −16.2084 6.76655i −0.689875 0.288004i
\(553\) −41.1829 + 9.76053i −1.75128 + 0.415060i
\(554\) −5.82792 6.17724i −0.247605 0.262446i
\(555\) 23.0565 7.19934i 0.978695 0.305595i
\(556\) 11.3842 + 15.2916i 0.482797 + 0.648509i
\(557\) −15.3731 + 12.8995i −0.651378 + 0.546571i −0.907489 0.420076i \(-0.862003\pi\)
0.256111 + 0.966647i \(0.417559\pi\)
\(558\) −0.370709 1.13991i −0.0156934 0.0482563i
\(559\) 28.4525 + 23.8745i 1.20341 + 1.00978i
\(560\) 1.91935 32.9540i 0.0811073 1.39256i
\(561\) −7.41218 4.16392i −0.312942 0.175801i
\(562\) −1.23310 2.85864i −0.0520150 0.120584i
\(563\) 28.7647 18.9188i 1.21229 0.797333i 0.227957 0.973671i \(-0.426795\pi\)
0.984330 + 0.176338i \(0.0564251\pi\)
\(564\) 29.3000 + 8.39750i 1.23375 + 0.353599i
\(565\) 6.90059 + 23.0496i 0.290310 + 0.969703i
\(566\) −8.83320 −0.371287
\(567\) 26.0602 + 19.8550i 1.09442 + 0.833830i
\(568\) 7.75410 0.325355
\(569\) 3.91371 + 13.0727i 0.164071 + 0.548036i 1.00000 0.000802420i \(-0.000255418\pi\)
−0.835928 + 0.548838i \(0.815070\pi\)
\(570\) 1.79526 1.73411i 0.0751950 0.0726340i
\(571\) −18.3188 + 12.0485i −0.766617 + 0.504212i −0.871574 0.490265i \(-0.836900\pi\)
0.104956 + 0.994477i \(0.466530\pi\)
\(572\) 6.96883 + 16.1556i 0.291381 + 0.675498i
\(573\) 0.0377509 + 3.20825i 0.00157707 + 0.134027i
\(574\) 0.408367 7.01140i 0.0170449 0.292650i
\(575\) −12.4553 10.4513i −0.519423 0.435848i
\(576\) 10.8020 + 13.8185i 0.450084 + 0.575771i
\(577\) −4.05986 + 3.40663i −0.169014 + 0.141820i −0.723371 0.690459i \(-0.757409\pi\)
0.554357 + 0.832279i \(0.312964\pi\)
\(578\) 2.40238 + 3.22696i 0.0999260 + 0.134224i
\(579\) −0.131235 + 0.584278i −0.00545395 + 0.0242818i
\(580\) 7.06645 + 7.49000i 0.293419 + 0.311005i
\(581\) 60.4181 14.3193i 2.50656 0.594067i
\(582\) 0.614129 + 4.76707i 0.0254564 + 0.197601i
\(583\) 13.1221 30.4204i 0.543461 1.25988i
\(584\) −1.36586 7.74618i −0.0565197 0.320539i
\(585\) −2.36903 28.9285i −0.0979472 1.19605i
\(586\) 1.57255 8.91836i 0.0649614 0.368414i
\(587\) 3.69992 + 2.43348i 0.152712 + 0.100440i 0.623565 0.781771i \(-0.285683\pi\)
−0.470853 + 0.882212i \(0.656054\pi\)
\(588\) −13.4552 15.6574i −0.554884 0.645702i
\(589\) 1.40124 1.88220i 0.0577373 0.0775546i
\(590\) 0.0436662 + 0.749719i 0.00179771 + 0.0308654i
\(591\) 21.8870 + 32.4397i 0.900312 + 1.33439i
\(592\) 12.5524 13.3047i 0.515899 0.546821i
\(593\) 1.66347 2.88121i 0.0683104 0.118317i −0.829847 0.557991i \(-0.811572\pi\)
0.898158 + 0.439673i \(0.144906\pi\)
\(594\) −3.96344 + 0.371571i −0.162622 + 0.0152458i
\(595\) −9.36697 16.2241i −0.384008 0.665122i
\(596\) 3.04972 + 0.722796i 0.124921 + 0.0296069i
\(597\) 2.66625 25.3996i 0.109122 1.03954i
\(598\) 8.53538 + 4.28663i 0.349038 + 0.175293i
\(599\) 10.5840 + 1.23709i 0.432449 + 0.0505461i 0.329533 0.944144i \(-0.393109\pi\)
0.102916 + 0.994690i \(0.467183\pi\)
\(600\) −1.39651 3.70080i −0.0570122 0.151084i
\(601\) 5.07251 2.54751i 0.206912 0.103915i −0.342325 0.939581i \(-0.611215\pi\)
0.549237 + 0.835666i \(0.314918\pi\)
\(602\) 10.5480 3.83917i 0.429906 0.156473i
\(603\) −13.4485 + 11.8349i −0.547665 + 0.481955i
\(604\) −26.7266 9.72770i −1.08749 0.395814i
\(605\) −12.3029 + 1.43800i −0.500184 + 0.0584631i
\(606\) 0.0782337 + 0.00363354i 0.00317803 + 0.000147603i
\(607\) 0.881909 2.94578i 0.0357956 0.119566i −0.938225 0.346027i \(-0.887531\pi\)
0.974020 + 0.226461i \(0.0727157\pi\)
\(608\) 1.77027 5.91312i 0.0717940 0.239809i
\(609\) 12.9366 + 0.600835i 0.524216 + 0.0243470i
\(610\) 1.57538 0.184135i 0.0637851 0.00745541i
\(611\) −31.9127 11.6153i −1.29105 0.469904i
\(612\) 10.6076 + 3.58052i 0.428788 + 0.144734i
\(613\) −14.0676 + 5.12017i −0.568184 + 0.206802i −0.610107 0.792319i \(-0.708874\pi\)
0.0419236 + 0.999121i \(0.486651\pi\)
\(614\) −2.82607 + 1.41930i −0.114051 + 0.0572784i
\(615\) 10.1547 + 26.9103i 0.409476 + 1.08513i
\(616\) 10.8213 + 1.26483i 0.436003 + 0.0509615i
\(617\) −19.2344 9.65986i −0.774346 0.388891i 0.0173164 0.999850i \(-0.494488\pi\)
−0.791662 + 0.610959i \(0.790784\pi\)
\(618\) 0.753707 7.18007i 0.0303185 0.288825i
\(619\) 41.0179 + 9.72141i 1.64865 + 0.390737i 0.946859 0.321649i \(-0.104237\pi\)
0.701788 + 0.712386i \(0.252385\pi\)
\(620\) −3.27855 5.67862i −0.131670 0.228059i
\(621\) 31.0252 31.4130i 1.24500 1.26056i
\(622\) 1.22834 2.12754i 0.0492518 0.0853066i
\(623\) 11.8947 12.6077i 0.476553 0.505116i
\(624\) −12.2935 18.2207i −0.492134 0.729413i
\(625\) 1.79703 + 30.8538i 0.0718811 + 1.23415i
\(626\) −0.615924 + 0.827329i −0.0246173 + 0.0330667i
\(627\) −5.07902 5.91030i −0.202837 0.236035i
\(628\) −0.432052 0.284165i −0.0172407 0.0113394i
\(629\) 1.80262 10.2232i 0.0718753 0.407625i
\(630\) −7.92938 3.75131i −0.315914 0.149456i
\(631\) −0.662591 3.75774i −0.0263773 0.149593i 0.968775 0.247943i \(-0.0797547\pi\)
−0.995152 + 0.0983500i \(0.968644\pi\)
\(632\) −5.49594 + 12.7410i −0.218617 + 0.506810i
\(633\) 2.87381 + 22.3075i 0.114224 + 0.886644i
\(634\) 3.30503 0.783306i 0.131259 0.0311090i
\(635\) 1.38614 + 1.46922i 0.0550073 + 0.0583043i
\(636\) −9.56107 + 42.5672i −0.379121 + 1.68790i
\(637\) 13.7361 + 18.4508i 0.544244 + 0.731047i
\(638\) −1.20543 + 1.01148i −0.0477234 + 0.0400447i
\(639\) −7.29699 + 18.0743i −0.288664 + 0.715007i
\(640\) −17.4571 14.6482i −0.690051 0.579022i
\(641\) −2.70931 + 46.5171i −0.107011 + 1.83731i 0.337248 + 0.941416i \(0.390504\pi\)
−0.444259 + 0.895898i \(0.646533\pi\)
\(642\) −0.00528038 0.448752i −0.000208400 0.0177108i
\(643\) 2.81834 + 6.53366i 0.111145 + 0.257662i 0.964706 0.263331i \(-0.0848210\pi\)
−0.853561 + 0.520993i \(0.825562\pi\)
\(644\) −49.2729 + 32.4073i −1.94162 + 1.27703i
\(645\) −33.0637 + 31.9376i −1.30188 + 1.25754i
\(646\) −0.307659 1.02765i −0.0121047 0.0404325i
\(647\) 25.9024 1.01833 0.509164 0.860670i \(-0.329955\pi\)
0.509164 + 0.860670i \(0.329955\pi\)
\(648\) 10.3234 2.96603i 0.405541 0.116517i
\(649\) 2.34467 0.0920363
\(650\) 0.616915 + 2.06064i 0.0241974 + 0.0808249i
\(651\) −7.92742 2.27203i −0.310700 0.0890478i
\(652\) −3.11115 + 2.04624i −0.121842 + 0.0801369i
\(653\) −10.1902 23.6235i −0.398773 0.924459i −0.992774 0.119995i \(-0.961712\pi\)
0.594002 0.804464i \(-0.297547\pi\)
\(654\) 2.23624 + 1.25624i 0.0874437 + 0.0491230i
\(655\) 1.23834 21.2615i 0.0483861 0.830757i
\(656\) 16.6853 + 14.0006i 0.651450 + 0.546631i
\(657\) 19.3411 + 4.10580i 0.754570 + 0.160183i
\(658\) −7.86234 + 6.59728i −0.306506 + 0.257189i
\(659\) −15.7536 21.1608i −0.613674 0.824307i 0.381299 0.924452i \(-0.375477\pi\)
−0.994973 + 0.100145i \(0.968069\pi\)
\(660\) −20.7865 + 6.49051i −0.809112 + 0.252643i
\(661\) 19.2438 + 20.3972i 0.748498 + 0.793361i 0.983935 0.178529i \(-0.0571337\pi\)
−0.235437 + 0.971890i \(0.575652\pi\)
\(662\) 6.30240 1.49370i 0.244950 0.0580541i
\(663\) −11.5114 4.80570i −0.447067 0.186638i
\(664\) 8.06291 18.6919i 0.312901 0.725387i
\(665\) −2.98187 16.9110i −0.115632 0.655782i
\(666\) −2.02973 4.41667i −0.0786504 0.171143i
\(667\) 3.03061 17.1874i 0.117346 0.665499i
\(668\) −12.2051 8.02740i −0.472228 0.310590i
\(669\) −8.50691 + 24.2569i −0.328896 + 0.937824i
\(670\) 2.86430 3.84742i 0.110658 0.148639i
\(671\) −0.287932 4.94360i −0.0111155 0.190845i
\(672\) −21.6393 + 1.51601i −0.834753 + 0.0584813i
\(673\) 25.4683 26.9948i 0.981731 1.04057i −0.0174394 0.999848i \(-0.505551\pi\)
0.999170 0.0407261i \(-0.0129671\pi\)
\(674\) −2.01332 + 3.48718i −0.0775503 + 0.134321i
\(675\) 9.94048 + 0.227466i 0.382609 + 0.00875518i
\(676\) 0.514578 + 0.891275i 0.0197915 + 0.0342798i
\(677\) −1.54153 0.365349i −0.0592458 0.0140415i 0.200886 0.979615i \(-0.435618\pi\)
−0.260132 + 0.965573i \(0.583766\pi\)
\(678\) 4.42297 1.96992i 0.169863 0.0756545i
\(679\) 29.5500 + 14.8405i 1.13402 + 0.569528i
\(680\) −6.10039 0.713033i −0.233939 0.0273436i
\(681\) −9.57544 1.57247i −0.366932 0.0602573i
\(682\) 0.895435 0.449704i 0.0342880 0.0172201i
\(683\) −2.52567 + 0.919268i −0.0966420 + 0.0351748i −0.389889 0.920862i \(-0.627487\pi\)
0.293247 + 0.956037i \(0.405264\pi\)
\(684\) 8.01430 + 6.40957i 0.306434 + 0.245076i
\(685\) 22.8025 + 8.29944i 0.871240 + 0.317105i
\(686\) −0.826995 + 0.0966618i −0.0315748 + 0.00369057i
\(687\) −15.8465 30.6484i −0.604580 1.16931i
\(688\) −9.98409 + 33.3492i −0.380640 + 1.27143i
\(689\) 13.9417 46.5685i 0.531136 1.77412i
\(690\) −6.37931 + 9.95239i −0.242856 + 0.378881i
\(691\) −23.9826 + 2.80317i −0.912342 + 0.106638i −0.559296 0.828968i \(-0.688928\pi\)
−0.353047 + 0.935606i \(0.614854\pi\)
\(692\) −10.8537 3.95044i −0.412598 0.150173i
\(693\) −13.1316 + 24.0335i −0.498829 + 0.912957i
\(694\) −3.30945 + 1.20454i −0.125625 + 0.0457237i
\(695\) 23.4934 11.7988i 0.891154 0.447554i
\(696\) 2.69070 3.28437i 0.101991 0.124494i
\(697\) 12.2777 + 1.43506i 0.465052 + 0.0543568i
\(698\) −2.17177 1.09070i −0.0822027 0.0412837i
\(699\) −8.20465 5.95939i −0.310329 0.225405i
\(700\) −12.9234 3.06291i −0.488460 0.115767i
\(701\) −14.6288 25.3379i −0.552523 0.956998i −0.998092 0.0617504i \(-0.980332\pi\)
0.445568 0.895248i \(-0.353002\pi\)
\(702\) −5.71284 + 1.21664i −0.215617 + 0.0459192i
\(703\) 4.75767 8.24053i 0.179439 0.310798i
\(704\) −10.0616 + 10.6647i −0.379212 + 0.401941i
\(705\) 18.4208 37.7808i 0.693769 1.42291i
\(706\) −0.0474977 0.815504i −0.00178760 0.0306919i
\(707\) 0.321754 0.432190i 0.0121008 0.0162542i
\(708\) −3.03420 + 0.571901i −0.114032 + 0.0214933i
\(709\) −6.75113 4.44029i −0.253544 0.166759i 0.416374 0.909193i \(-0.363301\pi\)
−0.669918 + 0.742435i \(0.733671\pi\)
\(710\) 0.906243 5.13956i 0.0340107 0.192884i
\(711\) −24.5265 24.8005i −0.919815 0.930093i
\(712\) −0.986786 5.59634i −0.0369814 0.209732i
\(713\) −4.40179 + 10.2045i −0.164848 + 0.382161i
\(714\) −2.99726 + 2.28668i −0.112170 + 0.0855769i
\(715\) 23.6093 5.59551i 0.882938 0.209260i
\(716\) 3.61600 + 3.83274i 0.135136 + 0.143236i
\(717\) −18.9988 17.5065i −0.709522 0.653793i
\(718\) 3.55306 + 4.77259i 0.132599 + 0.178111i
\(719\) −24.5961 + 20.6385i −0.917278 + 0.769688i −0.973490 0.228731i \(-0.926542\pi\)
0.0562116 + 0.998419i \(0.482098\pi\)
\(720\) 24.0165 12.7779i 0.895043 0.476203i
\(721\) −38.0482 31.9263i −1.41699 1.18900i
\(722\) −0.280318 + 4.81287i −0.0104323 + 0.179116i
\(723\) −0.335100 + 0.198764i −0.0124625 + 0.00739210i
\(724\) −6.65834 15.4358i −0.247455 0.573666i
\(725\) 3.28380 2.15979i 0.121957 0.0802125i
\(726\) 0.603341 + 2.41852i 0.0223921 + 0.0897598i
\(727\) −4.65943 15.5636i −0.172809 0.577222i −0.999885 0.0151325i \(-0.995183\pi\)
0.827077 0.562089i \(-0.190002\pi\)
\(728\) 15.9859 0.592478
\(729\) −2.80120 + 26.8543i −0.103748 + 0.994604i
\(730\) −5.29394 −0.195938
\(731\) 5.66623 + 18.9265i 0.209573 + 0.700023i
\(732\) 1.57843 + 6.32720i 0.0583403 + 0.233860i
\(733\) 7.89518 5.19274i 0.291615 0.191798i −0.395269 0.918566i \(-0.629348\pi\)
0.686884 + 0.726767i \(0.258978\pi\)
\(734\) 1.27632 + 2.95885i 0.0471099 + 0.109213i
\(735\) −24.4861 + 14.5238i −0.903183 + 0.535720i
\(736\) −1.69977 + 29.1839i −0.0626543 + 1.07573i
\(737\) −11.4718 9.62596i −0.422568 0.354577i
\(738\) 5.10984 2.71866i 0.188096 0.100075i
\(739\) −0.162054 + 0.135979i −0.00596124 + 0.00500207i −0.645763 0.763538i \(-0.723461\pi\)
0.639802 + 0.768540i \(0.279016\pi\)
\(740\) −15.8782 21.3282i −0.583695 0.784039i
\(741\) −8.40869 7.74823i −0.308901 0.284638i
\(742\) −10.0816 10.6858i −0.370106 0.392289i
\(743\) −37.2760 + 8.83459i −1.36753 + 0.324110i −0.847842 0.530249i \(-0.822098\pi\)
−0.519684 + 0.854359i \(0.673950\pi\)
\(744\) −2.14951 + 1.63991i −0.0788047 + 0.0601219i
\(745\) 1.71192 3.96867i 0.0627198 0.145401i
\(746\) 0.999215 + 5.66683i 0.0365839 + 0.207477i
\(747\) 35.9820 + 36.3841i 1.31651 + 1.33122i
\(748\) −1.62514 + 9.21664i −0.0594211 + 0.336994i
\(749\) −2.57958 1.69662i −0.0942557 0.0619930i
\(750\) 4.21975 0.795358i 0.154083 0.0290424i
\(751\) 19.3084 25.9356i 0.704572 0.946405i −0.295387 0.955378i \(-0.595449\pi\)
0.999960 + 0.00897263i \(0.00285612\pi\)
\(752\) −1.85075 31.7761i −0.0674899 1.15876i
\(753\) −0.0879869 + 0.180460i −0.00320642 + 0.00657632i
\(754\) −1.58444 + 1.67941i −0.0577019 + 0.0611605i
\(755\) −19.6111 + 33.9674i −0.713721 + 1.23620i
\(756\) 11.1313 34.3044i 0.404841 1.24764i
\(757\) 16.7349 + 28.9858i 0.608242 + 1.05351i 0.991530 + 0.129877i \(0.0414581\pi\)
−0.383289 + 0.923629i \(0.625209\pi\)
\(758\) 2.57454 + 0.610177i 0.0935115 + 0.0221626i
\(759\) 29.8618 + 21.6899i 1.08391 + 0.787294i
\(760\) −5.03098 2.52666i −0.182493 0.0916514i
\(761\) 1.79342 + 0.209621i 0.0650116 + 0.00759876i 0.148537 0.988907i \(-0.452544\pi\)
−0.0835249 + 0.996506i \(0.526618\pi\)
\(762\) 0.257597 0.314432i 0.00933175 0.0113907i
\(763\) 15.7691 7.91955i 0.570881 0.286707i
\(764\) 3.31895 1.20800i 0.120075 0.0437038i
\(765\) 7.40279 13.5486i 0.267648 0.489850i
\(766\) −8.68571 3.16134i −0.313827 0.114224i
\(767\) 3.41701 0.399391i 0.123381 0.0144212i
\(768\) 8.45455 13.1900i 0.305077 0.475953i
\(769\) 9.74217 32.5411i 0.351312 1.17346i −0.581636 0.813449i \(-0.697587\pi\)
0.932947 0.360013i \(-0.117228\pi\)
\(770\) 2.10307 7.02475i 0.0757894 0.253154i
\(771\) 7.11583 + 13.7626i 0.256270 + 0.495648i
\(772\) 0.654752 0.0765296i 0.0235651 0.00275436i
\(773\) −0.0917313 0.0333874i −0.00329934 0.00120086i 0.340370 0.940292i \(-0.389448\pi\)
−0.343669 + 0.939091i \(0.611670\pi\)
\(774\) 7.22446 + 5.77789i 0.259678 + 0.207682i
\(775\) −2.35185 + 0.856003i −0.0844809 + 0.0307485i
\(776\) 9.68795 4.86547i 0.347777 0.174660i
\(777\) −32.9986 5.41901i −1.18382 0.194406i
\(778\) 4.94094 + 0.577514i 0.177141 + 0.0207049i
\(779\) 10.1254 + 5.08519i 0.362782 + 0.182196i
\(780\) −29.1876 + 12.9997i −1.04508 + 0.465465i
\(781\) −15.8546 3.75761i −0.567322 0.134458i
\(782\) 2.54026 + 4.39986i 0.0908395 + 0.157339i
\(783\) 5.12356 + 9.36259i 0.183101 + 0.334592i
\(784\) −10.7796 + 18.6708i −0.384985 + 0.666814i
\(785\) −0.489380 + 0.518713i −0.0174667 + 0.0185137i
\(786\) −4.27537 + 0.299525i −0.152497 + 0.0106837i
\(787\) −1.43264 24.5974i −0.0510680 0.876803i −0.922430 0.386163i \(-0.873800\pi\)
0.871362 0.490640i \(-0.163237\pi\)
\(788\) 25.7245 34.5540i 0.916398 1.23094i
\(789\) −9.05461 + 25.8186i −0.322353 + 0.919166i
\(790\) 7.80265 + 5.13188i 0.277606 + 0.182584i
\(791\) 5.78430 32.8044i 0.205666 1.16639i
\(792\) 3.74934 + 8.15853i 0.133227 + 0.289901i
\(793\) −1.26171 7.15552i −0.0448047 0.254100i
\(794\) −3.61651 + 8.38402i −0.128345 + 0.297538i
\(795\) 55.5201 + 23.1781i 1.96910 + 0.822042i
\(796\) −27.3562 + 6.48355i −0.969616 + 0.229803i
\(797\) −9.19976 9.75117i −0.325872 0.345404i 0.543638 0.839320i \(-0.317047\pi\)
−0.869510 + 0.493916i \(0.835565\pi\)
\(798\) −3.29855 + 1.02996i −0.116768 + 0.0364603i
\(799\) −10.7873 14.4898i −0.381627 0.512614i
\(800\) −5.04324 + 4.23178i −0.178305 + 0.149616i
\(801\) 13.9733 + 2.96630i 0.493722 + 0.104809i
\(802\) 7.31689 + 6.13960i 0.258368 + 0.216797i
\(803\) −0.961032 + 16.5003i −0.0339141 + 0.582283i
\(804\) 17.1934 + 9.65866i 0.606363 + 0.340635i
\(805\) 32.2125 + 74.6769i 1.13534 + 2.63201i
\(806\) 1.22836 0.807906i 0.0432672 0.0284573i
\(807\) 40.3678 + 11.5696i 1.42101 + 0.407268i
\(808\) −0.0506632 0.169227i −0.00178232 0.00595338i
\(809\) −25.3728 −0.892061 −0.446030 0.895018i \(-0.647163\pi\)
−0.446030 + 0.895018i \(0.647163\pi\)
\(810\) −0.759415 7.18918i −0.0266831 0.252602i
\(811\) 4.23503 0.148712 0.0743560 0.997232i \(-0.476310\pi\)
0.0743560 + 0.997232i \(0.476310\pi\)
\(812\) −4.08871 13.6573i −0.143486 0.479276i
\(813\) −17.9402 + 17.3292i −0.629190 + 0.607761i
\(814\) 3.39481 2.23280i 0.118988 0.0782597i
\(815\) 2.03394 + 4.71520i 0.0712457 + 0.165166i
\(816\) −0.137563 11.6908i −0.00481568 0.409260i
\(817\) −1.05296 + 18.0786i −0.0368384 + 0.632491i
\(818\) 6.16818 + 5.17572i 0.215665 + 0.180965i
\(819\) −15.0435 + 37.2621i −0.525664 + 1.30204i
\(820\) 24.2547 20.3521i 0.847012 0.710727i
\(821\) 22.9970 + 30.8904i 0.802601 + 1.07808i 0.995302 + 0.0968232i \(0.0308681\pi\)
−0.192700 + 0.981258i \(0.561724\pi\)
\(822\) 1.07016 4.76448i 0.0373260 0.166180i
\(823\) 7.10830 + 7.53435i 0.247780 + 0.262631i 0.839312 0.543650i \(-0.182958\pi\)
−0.591532 + 0.806281i \(0.701477\pi\)
\(824\) −15.8449 + 3.75530i −0.551982 + 0.130822i
\(825\) 1.06201 + 8.24366i 0.0369744 + 0.287007i
\(826\) 0.411808 0.954678i 0.0143286 0.0332175i
\(827\) −0.0896693 0.508540i −0.00311811 0.0176837i 0.983209 0.182483i \(-0.0584135\pi\)
−0.986327 + 0.164799i \(0.947302\pi\)
\(828\) −43.9342 20.7848i −1.52682 0.722322i
\(829\) −0.356418 + 2.02135i −0.0123789 + 0.0702043i −0.990371 0.138436i \(-0.955793\pi\)
0.977993 + 0.208640i \(0.0669037\pi\)
\(830\) −11.4470 7.52882i −0.397332 0.261329i
\(831\) −31.3824 36.5187i −1.08864 1.26682i
\(832\) −12.8467 + 17.2561i −0.445379 + 0.598248i
\(833\) 0.711425 + 12.2147i 0.0246494 + 0.423214i
\(834\) −2.95895 4.38559i −0.102460 0.151861i
\(835\) −13.8245 + 14.6532i −0.478418 + 0.507094i
\(836\) −4.28925 + 7.42920i −0.148347 + 0.256944i
\(837\) −1.79972 6.55358i −0.0622074 0.226525i
\(838\) 2.39670 + 4.15120i 0.0827925 + 0.143401i
\(839\) −5.63457 1.33542i −0.194527 0.0461037i 0.132197 0.991223i \(-0.457797\pi\)
−0.326724 + 0.945120i \(0.605945\pi\)
\(840\) −2.06556 + 19.6772i −0.0712685 + 0.678929i
\(841\) −22.1452 11.1218i −0.763629 0.383509i
\(842\) −6.91649 0.808422i −0.238358 0.0278601i
\(843\) −6.23187 16.5147i −0.214637 0.568796i
\(844\) 22.1259 11.1120i 0.761604 0.382492i
\(845\) 1.33365 0.485407i 0.0458788 0.0166985i
\(846\) −8.01420 2.70513i −0.275534 0.0930042i
\(847\) 16.1145 + 5.86521i 0.553702 + 0.201531i
\(848\) 45.2525 5.28926i 1.55398 0.181634i
\(849\) −50.0282 2.32355i −1.71696 0.0797439i
\(850\) −0.328148 + 1.09609i −0.0112554 + 0.0375956i
\(851\) −12.9250 + 43.1725i −0.443064 + 1.47994i
\(852\) 21.4337 + 0.995483i 0.734307 + 0.0341047i
\(853\) 51.3968 6.00742i 1.75979 0.205690i 0.826041 0.563610i \(-0.190588\pi\)
0.933752 + 0.357920i \(0.116514\pi\)
\(854\) −2.06345 0.751036i −0.0706100 0.0256999i
\(855\) 10.6239 9.34917i 0.363328 0.319735i
\(856\) −0.951194 + 0.346206i −0.0325112 + 0.0118331i
\(857\) 20.2333 10.1615i 0.691156 0.347112i −0.0683049 0.997664i \(-0.521759\pi\)
0.759461 + 0.650553i \(0.225463\pi\)
\(858\) −1.72384 4.56824i −0.0588509 0.155957i
\(859\) −26.7769 3.12977i −0.913615 0.106786i −0.353722 0.935351i \(-0.615084\pi\)
−0.559894 + 0.828564i \(0.689158\pi\)
\(860\) 45.2217 + 22.7112i 1.54205 + 0.774446i
\(861\) 4.15718 39.6027i 0.141676 1.34966i
\(862\) 10.1482 + 2.40517i 0.345649 + 0.0819204i
\(863\) 3.95729 + 6.85423i 0.134708 + 0.233321i 0.925486 0.378782i \(-0.123657\pi\)
−0.790778 + 0.612103i \(0.790324\pi\)
\(864\) −10.3447 14.5801i −0.351932 0.496027i
\(865\) −7.96411 + 13.7942i −0.270788 + 0.469018i
\(866\) 4.87304 5.16513i 0.165593 0.175518i
\(867\) 12.7574 + 18.9083i 0.433265 + 0.642160i
\(868\) 0.527839 + 9.06264i 0.0179160 + 0.307606i
\(869\) 17.4116 23.3879i 0.590649 0.793379i
\(870\) −1.86247 2.16730i −0.0631437 0.0734783i
\(871\) −18.3581 12.0743i −0.622040 0.409122i
\(872\) 1.00460 5.69738i 0.0340201 0.192937i
\(873\) 2.22425 + 27.1606i 0.0752794 + 0.919246i
\(874\) 0.808665 + 4.58616i 0.0273535 + 0.155129i
\(875\) 11.7010 27.1259i 0.395565 0.917022i
\(876\) −2.78102 21.5872i −0.0939618 0.729363i
\(877\) −1.01266 + 0.240004i −0.0341950 + 0.00810435i −0.247678 0.968842i \(-0.579667\pi\)
0.213483 + 0.976947i \(0.431519\pi\)
\(878\) 1.44708 + 1.53382i 0.0488366 + 0.0517638i
\(879\) 11.2523 50.0968i 0.379531 1.68972i
\(880\) 13.5800 + 18.2410i 0.457780 + 0.614906i
\(881\) 22.9183 19.2307i 0.772138 0.647900i −0.169118 0.985596i \(-0.554092\pi\)
0.941255 + 0.337695i \(0.109647\pi\)
\(882\) 3.52836 + 4.51366i 0.118806 + 0.151983i
\(883\) −4.28456 3.59517i −0.144187 0.120987i 0.567841 0.823138i \(-0.307779\pi\)
−0.712028 + 0.702151i \(0.752223\pi\)
\(884\) −0.798442 + 13.7087i −0.0268545 + 0.461074i
\(885\) 0.0500988 + 4.25763i 0.00168405 + 0.143119i
\(886\) −1.95063 4.52207i −0.0655327 0.151922i
\(887\) −9.25699 + 6.08842i −0.310819 + 0.204429i −0.695329 0.718692i \(-0.744741\pi\)
0.384509 + 0.923121i \(0.374371\pi\)
\(888\) −7.88548 + 7.61692i −0.264619 + 0.255607i
\(889\) −0.802033 2.67898i −0.0268993 0.0898500i
\(890\) −3.82469 −0.128204
\(891\) −22.5453 + 1.06188i −0.755295 + 0.0355743i
\(892\) 28.2969 0.947451
\(893\) −4.74894 15.8626i −0.158917 0.530820i
\(894\) −0.836112 0.239633i −0.0279638 0.00801453i
\(895\) 6.07107 3.99300i 0.202933 0.133471i
\(896\) 12.4962 + 28.9695i 0.417469 + 0.967802i
\(897\) 47.2138 + 26.5232i 1.57642 + 0.885583i
\(898\) −0.393155 + 6.75021i −0.0131198 + 0.225257i
\(899\) −2.05795 1.72683i −0.0686366 0.0575929i
\(900\) −3.38508 10.4089i −0.112836 0.346965i
\(901\) 19.8075 16.6204i 0.659883 0.553707i
\(902\) 2.88932 + 3.88103i 0.0962038 + 0.129224i
\(903\) 60.7503 18.9691i 2.02164 0.631252i
\(904\) −7.49432 7.94352i −0.249258 0.264198i
\(905\) −22.5574 + 5.34621i −0.749834 + 0.177714i
\(906\) 7.28370 + 3.04074i 0.241985 + 0.101022i
\(907\) 10.6048 24.5846i 0.352126 0.816319i −0.646450 0.762957i \(-0.723747\pi\)
0.998575 0.0533621i \(-0.0169938\pi\)
\(908\) 1.85491 + 10.5197i 0.0615575 + 0.349110i
\(909\) 0.442132 + 0.0411582i 0.0146646 + 0.00136513i
\(910\) 1.86832 10.5958i 0.0619342 0.351246i
\(911\) −20.4066 13.4216i −0.676100 0.444678i 0.164469 0.986382i \(-0.447409\pi\)
−0.840569 + 0.541704i \(0.817779\pi\)
\(912\) 3.54661 10.1129i 0.117440 0.334872i
\(913\) −25.5440 + 34.3116i −0.845384 + 1.13555i
\(914\) −0.461185 7.91824i −0.0152546 0.261912i
\(915\) 8.97082 0.628479i 0.296566 0.0207769i
\(916\) −26.0643 + 27.6265i −0.861188 + 0.912806i
\(917\) −14.7428 + 25.5352i −0.486849 + 0.843247i
\(918\) −2.89446 1.12914i −0.0955315 0.0372670i
\(919\) −20.5877 35.6590i −0.679127 1.17628i −0.975244 0.221131i \(-0.929025\pi\)
0.296117 0.955152i \(-0.404308\pi\)
\(920\) 25.9447 + 6.14901i 0.855372 + 0.202727i
\(921\) −16.3792 + 7.29505i −0.539713 + 0.240380i
\(922\) 0.622543 + 0.312653i 0.0205024 + 0.0102967i
\(923\) −23.7458 2.77549i −0.781603 0.0913563i
\(924\) 29.7497 + 4.88548i 0.978693 + 0.160720i
\(925\) −9.06949 + 4.55487i −0.298203 + 0.149763i
\(926\) 1.58655 0.577457i 0.0521373 0.0189764i
\(927\) 6.15743 40.4672i 0.202236 1.32912i
\(928\) −6.64048 2.41694i −0.217984 0.0793398i
\(929\) 4.41786 0.516374i 0.144945 0.0169417i −0.0433108 0.999062i \(-0.513791\pi\)
0.188256 + 0.982120i \(0.439716\pi\)
\(930\) 0.835741 + 1.61639i 0.0274050 + 0.0530036i
\(931\) −3.21656 + 10.7441i −0.105419 + 0.352123i
\(932\) −3.20156 + 10.6940i −0.104871 + 0.350292i
\(933\) 7.51651 11.7265i 0.246079 0.383910i
\(934\) −8.08544 + 0.945052i −0.264564 + 0.0309230i
\(935\) 12.1278 + 4.41414i 0.396620 + 0.144358i
\(936\) 6.85384 + 11.2512i 0.224025 + 0.367757i
\(937\) −16.9270 + 6.16093i −0.552982 + 0.201269i −0.603371 0.797461i \(-0.706176\pi\)
0.0503891 + 0.998730i \(0.483954\pi\)
\(938\) −5.93425 + 2.98029i −0.193760 + 0.0973100i
\(939\) −3.70600 + 4.52369i −0.120941 + 0.147625i
\(940\) −45.9572 5.37163i −1.49896 0.175203i
\(941\) 34.8250 + 17.4898i 1.13526 + 0.570150i 0.914262 0.405123i \(-0.132771\pi\)
0.221000 + 0.975274i \(0.429068\pi\)
\(942\) 0.116111 + 0.0843366i 0.00378311 + 0.00274784i
\(943\) −52.2168 12.3756i −1.70041 0.403005i
\(944\) 1.61221 + 2.79243i 0.0524729 + 0.0908857i
\(945\) −43.9225 23.3319i −1.42880 0.758986i
\(946\) −3.86653 + 6.69703i −0.125712 + 0.217739i
\(947\) −26.3647 + 27.9449i −0.856737 + 0.908088i −0.996626 0.0820795i \(-0.973844\pi\)
0.139889 + 0.990167i \(0.455325\pi\)
\(948\) −16.8275 + 34.5128i −0.546530 + 1.12093i
\(949\) 1.41010 + 24.2104i 0.0457737 + 0.785904i
\(950\) −0.626275 + 0.841233i −0.0203190 + 0.0272932i
\(951\) 18.9246 3.56699i 0.613671 0.115668i
\(952\) 7.10432 + 4.67258i 0.230252 + 0.151439i
\(953\) −4.09748 + 23.2380i −0.132730 + 0.752752i 0.843683 + 0.536842i \(0.180383\pi\)
−0.976413 + 0.215910i \(0.930728\pi\)
\(954\) 3.19850 11.6770i 0.103555 0.378058i
\(955\) −0.845782 4.79667i −0.0273689 0.155216i
\(956\) −11.2643 + 26.1135i −0.364312 + 0.844570i
\(957\) −7.09319 + 5.41156i −0.229290 + 0.174931i
\(958\) −5.75118 + 1.36305i −0.185812 + 0.0440383i
\(959\) −23.0543 24.4362i −0.744463 0.789085i
\(960\) −19.5808 18.0428i −0.631967 0.582329i
\(961\) −17.4904 23.4936i −0.564205 0.757859i
\(962\) 4.56710 3.83225i 0.147249 0.123557i
\(963\) 0.0881366 2.54297i 0.00284016 0.0819459i
\(964\) 0.328553 + 0.275689i 0.0105820 + 0.00887933i
\(965\) 0.0528577 0.907531i 0.00170155 0.0292145i
\(966\) 14.0763 8.34930i 0.452897 0.268634i
\(967\) −19.5806 45.3930i −0.629671 1.45974i −0.871980 0.489541i \(-0.837164\pi\)
0.242309 0.970199i \(-0.422095\pi\)
\(968\) 4.69729 3.08945i 0.150977 0.0992988i
\(969\) −1.47215 5.90120i −0.0472924 0.189574i
\(970\) −2.09267 6.98999i −0.0671914 0.224435i
\(971\) 33.2987 1.06861 0.534304 0.845292i \(-0.320574\pi\)
0.534304 + 0.845292i \(0.320574\pi\)
\(972\) 28.9165 6.87330i 0.927497 0.220461i
\(973\) −36.3969 −1.16683
\(974\) −2.09742 7.00589i −0.0672058 0.224483i
\(975\) 2.95194 + 11.8330i 0.0945379 + 0.378960i
\(976\) 5.68968 3.74216i 0.182122 0.119784i
\(977\) 1.48012 + 3.43130i 0.0473532 + 0.109777i 0.940251 0.340483i \(-0.110591\pi\)
−0.892897 + 0.450260i \(0.851331\pi\)
\(978\) 0.888795 0.527186i 0.0284205 0.0168575i
\(979\) −0.694312 + 11.9209i −0.0221903 + 0.380993i
\(980\) 24.0077 + 20.1448i 0.766896 + 0.643503i
\(981\) 12.3348 + 7.70316i 0.393820 + 0.245943i
\(982\) 6.39536 5.36635i 0.204084 0.171247i
\(983\) −11.5957 15.5758i −0.369847 0.496790i 0.577770 0.816199i \(-0.303923\pi\)
−0.947617 + 0.319409i \(0.896516\pi\)
\(984\) −9.60067 8.84659i −0.306058 0.282019i
\(985\) −40.7669 43.2104i −1.29894 1.37680i
\(986\) −1.19502 + 0.283225i −0.0380572 + 0.00901973i
\(987\) −46.2649 + 35.2965i −1.47263 + 1.12350i
\(988\) −4.98546 + 11.5576i −0.158609 + 0.367696i
\(989\) −14.8934 84.4645i −0.473582 2.68582i
\(990\) 5.84582 1.53162i 0.185792 0.0486781i
\(991\) −9.87489 + 56.0033i −0.313686 + 1.77900i 0.265808 + 0.964026i \(0.414361\pi\)
−0.579494 + 0.814976i \(0.696750\pi\)
\(992\) 3.75959 + 2.47272i 0.119367 + 0.0785091i
\(993\) 36.0875 6.80195i 1.14520 0.215853i
\(994\) −4.31462 + 5.79554i −0.136851 + 0.183823i
\(995\) 2.25428 + 38.7045i 0.0714655 + 1.22702i
\(996\) 24.6870 50.6327i 0.782238 1.60436i
\(997\) −29.5096 + 31.2784i −0.934580 + 0.990596i −0.999974 0.00726306i \(-0.997688\pi\)
0.0653941 + 0.997860i \(0.479170\pi\)
\(998\) −1.45741 + 2.52432i −0.0461337 + 0.0799058i
\(999\) −10.3339 25.5484i −0.326950 0.808316i
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 81.2.g.a.43.5 144
3.2 odd 2 243.2.g.a.46.4 144
9.2 odd 6 729.2.g.b.622.4 144
9.4 even 3 729.2.g.d.136.4 144
9.5 odd 6 729.2.g.a.136.5 144
9.7 even 3 729.2.g.c.622.5 144
81.5 odd 54 729.2.g.b.109.4 144
81.7 even 27 6561.2.a.c.1.35 72
81.22 even 27 729.2.g.d.595.4 144
81.32 odd 54 243.2.g.a.37.4 144
81.49 even 27 inner 81.2.g.a.49.5 yes 144
81.59 odd 54 729.2.g.a.595.5 144
81.74 odd 54 6561.2.a.d.1.38 72
81.76 even 27 729.2.g.c.109.5 144
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
81.2.g.a.43.5 144 1.1 even 1 trivial
81.2.g.a.49.5 yes 144 81.49 even 27 inner
243.2.g.a.37.4 144 81.32 odd 54
243.2.g.a.46.4 144 3.2 odd 2
729.2.g.a.136.5 144 9.5 odd 6
729.2.g.a.595.5 144 81.59 odd 54
729.2.g.b.109.4 144 81.5 odd 54
729.2.g.b.622.4 144 9.2 odd 6
729.2.g.c.109.5 144 81.76 even 27
729.2.g.c.622.5 144 9.7 even 3
729.2.g.d.136.4 144 9.4 even 3
729.2.g.d.595.4 144 81.22 even 27
6561.2.a.c.1.35 72 81.7 even 27
6561.2.a.d.1.38 72 81.74 odd 54