Properties

Label 572.2.s.a.43.6
Level $572$
Weight $2$
Character 572.43
Analytic conductor $4.567$
Analytic rank $0$
Dimension $160$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [572,2,Mod(43,572)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(572, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("572.43");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 572.s (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.56744299562\)
Analytic rank: \(0\)
Dimension: \(160\)
Relative dimension: \(80\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 43.6
Character \(\chi\) \(=\) 572.43
Dual form 572.2.s.a.439.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.37518 + 0.329974i) q^{2} +(-0.622539 - 0.359423i) q^{3} +(1.78223 - 0.907548i) q^{4} -2.91525i q^{5} +(0.974703 + 0.288849i) q^{6} +(4.00752 - 2.31374i) q^{7} +(-2.15142 + 1.83613i) q^{8} +(-1.24163 - 2.15057i) q^{9} +O(q^{10})\) \(q+(-1.37518 + 0.329974i) q^{2} +(-0.622539 - 0.359423i) q^{3} +(1.78223 - 0.907548i) q^{4} -2.91525i q^{5} +(0.974703 + 0.288849i) q^{6} +(4.00752 - 2.31374i) q^{7} +(-2.15142 + 1.83613i) q^{8} +(-1.24163 - 2.15057i) q^{9} +(0.961958 + 4.00899i) q^{10} +(3.25587 + 0.631899i) q^{11} +(-1.43570 - 0.0755922i) q^{12} +(2.91119 - 2.12719i) q^{13} +(-4.74758 + 4.50419i) q^{14} +(-1.04781 + 1.81486i) q^{15} +(2.35272 - 3.23492i) q^{16} +(-3.76678 + 2.17475i) q^{17} +(2.41710 + 2.54771i) q^{18} +(-1.85637 + 1.07178i) q^{19} +(-2.64573 - 5.19566i) q^{20} -3.32645 q^{21} +(-4.68592 + 0.205380i) q^{22} +(1.45298 + 0.838881i) q^{23} +(1.99929 - 0.369792i) q^{24} -3.49869 q^{25} +(-3.30149 + 3.88589i) q^{26} +3.94162i q^{27} +(5.04250 - 7.76064i) q^{28} +(-1.43446 - 0.828186i) q^{29} +(0.842068 - 2.84150i) q^{30} +2.84877 q^{31} +(-2.16796 + 5.22493i) q^{32} +(-1.79979 - 1.56362i) q^{33} +(4.46239 - 4.23362i) q^{34} +(-6.74514 - 11.6829i) q^{35} +(-4.16462 - 2.70597i) q^{36} +(-3.68360 - 2.12673i) q^{37} +(2.19919 - 2.08644i) q^{38} +(-2.57689 + 0.277909i) q^{39} +(5.35279 + 6.27194i) q^{40} +(-4.60908 + 7.98316i) q^{41} +(4.57446 - 1.09764i) q^{42} +(0.0570117 + 0.0987471i) q^{43} +(6.37620 - 1.82867i) q^{44} +(-6.26944 + 3.61966i) q^{45} +(-2.27492 - 0.674164i) q^{46} +10.1873 q^{47} +(-2.62736 + 1.16825i) q^{48} +(7.20680 - 12.4825i) q^{49} +(4.81133 - 1.15448i) q^{50} +3.12662 q^{51} +(3.25790 - 6.43320i) q^{52} +1.88818 q^{53} +(-1.30063 - 5.42043i) q^{54} +(1.84214 - 9.49169i) q^{55} +(-4.37353 + 12.3362i) q^{56} +1.54089 q^{57} +(2.24592 + 0.665569i) q^{58} +(-6.71441 - 11.6297i) q^{59} +(-0.220370 + 4.18544i) q^{60} +(10.1518 - 5.86113i) q^{61} +(-3.91757 + 0.940021i) q^{62} +(-9.95171 - 5.74562i) q^{63} +(1.25724 - 7.90059i) q^{64} +(-6.20130 - 8.48687i) q^{65} +(2.99098 + 1.55637i) q^{66} +(-3.39711 + 5.88396i) q^{67} +(-4.73960 + 7.29445i) q^{68} +(-0.603026 - 1.04447i) q^{69} +(13.1308 + 13.8404i) q^{70} +(-1.78354 - 3.08919i) q^{71} +(6.62000 + 2.34698i) q^{72} -10.6906 q^{73} +(5.76737 + 1.70914i) q^{74} +(2.17807 + 1.25751i) q^{75} +(-2.33580 + 3.59491i) q^{76} +(14.5100 - 5.00090i) q^{77} +(3.45199 - 1.23248i) q^{78} -1.97986 q^{79} +(-9.43062 - 6.85876i) q^{80} +(-2.30818 + 3.99789i) q^{81} +(3.70407 - 12.4991i) q^{82} +12.7567i q^{83} +(-5.92851 + 3.01891i) q^{84} +(6.33995 + 10.9811i) q^{85} +(-0.110985 - 0.116983i) q^{86} +(0.595338 + 1.03116i) q^{87} +(-8.16501 + 4.61873i) q^{88} +(10.8016 + 6.23631i) q^{89} +(7.42721 - 7.04644i) q^{90} +(6.74489 - 15.2605i) q^{91} +(3.35088 + 0.176430i) q^{92} +(-1.77347 - 1.02391i) q^{93} +(-14.0094 + 3.36155i) q^{94} +(3.12450 + 5.41180i) q^{95} +(3.22760 - 2.47351i) q^{96} +(-6.47679 + 3.73938i) q^{97} +(-5.79172 + 19.5438i) q^{98} +(-2.68365 - 7.78656i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 160 q - 2 q^{4} + 68 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 160 q - 2 q^{4} + 68 q^{9} - 36 q^{12} - 8 q^{14} - 6 q^{16} + 30 q^{20} - 20 q^{22} - 144 q^{25} - 40 q^{26} - 6 q^{33} + 46 q^{36} - 12 q^{37} - 56 q^{38} - 2 q^{42} + 48 q^{45} - 40 q^{48} + 44 q^{49} - 32 q^{53} + 30 q^{56} + 78 q^{58} + 64 q^{64} - 4 q^{66} - 44 q^{69} - 44 q^{77} + 16 q^{78} + 24 q^{80} - 40 q^{81} - 6 q^{82} - 10 q^{88} + 24 q^{89} - 24 q^{92} - 96 q^{93}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/572\mathbb{Z}\right)^\times\).

\(n\) \(287\) \(353\) \(365\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.37518 + 0.329974i −0.972398 + 0.233327i
\(3\) −0.622539 0.359423i −0.359423 0.207513i 0.309405 0.950930i \(-0.399870\pi\)
−0.668828 + 0.743418i \(0.733204\pi\)
\(4\) 1.78223 0.907548i 0.891117 0.453774i
\(5\) 2.91525i 1.30374i −0.758331 0.651870i \(-0.773985\pi\)
0.758331 0.651870i \(-0.226015\pi\)
\(6\) 0.974703 + 0.288849i 0.397921 + 0.117922i
\(7\) 4.00752 2.31374i 1.51470 0.874512i 0.514848 0.857282i \(-0.327848\pi\)
0.999852 0.0172305i \(-0.00548490\pi\)
\(8\) −2.15142 + 1.83613i −0.760643 + 0.649171i
\(9\) −1.24163 2.15057i −0.413877 0.716856i
\(10\) 0.961958 + 4.00899i 0.304198 + 1.26775i
\(11\) 3.25587 + 0.631899i 0.981682 + 0.190525i
\(12\) −1.43570 0.0755922i −0.414452 0.0218216i
\(13\) 2.91119 2.12719i 0.807420 0.589977i
\(14\) −4.74758 + 4.50419i −1.26884 + 1.20379i
\(15\) −1.04781 + 1.81486i −0.270543 + 0.468594i
\(16\) 2.35272 3.23492i 0.588179 0.808731i
\(17\) −3.76678 + 2.17475i −0.913579 + 0.527455i −0.881581 0.472033i \(-0.843520\pi\)
−0.0319979 + 0.999488i \(0.510187\pi\)
\(18\) 2.41710 + 2.54771i 0.569715 + 0.600501i
\(19\) −1.85637 + 1.07178i −0.425881 + 0.245883i −0.697591 0.716497i \(-0.745744\pi\)
0.271709 + 0.962379i \(0.412411\pi\)
\(20\) −2.64573 5.19566i −0.591603 1.16178i
\(21\) −3.32645 −0.725890
\(22\) −4.68592 + 0.205380i −0.999041 + 0.0437872i
\(23\) 1.45298 + 0.838881i 0.302968 + 0.174919i 0.643775 0.765214i \(-0.277367\pi\)
−0.340807 + 0.940133i \(0.610700\pi\)
\(24\) 1.99929 0.369792i 0.408104 0.0754836i
\(25\) −3.49869 −0.699738
\(26\) −3.30149 + 3.88589i −0.647476 + 0.762086i
\(27\) 3.94162i 0.758565i
\(28\) 5.04250 7.76064i 0.952944 1.46662i
\(29\) −1.43446 0.828186i −0.266373 0.153790i 0.360865 0.932618i \(-0.382481\pi\)
−0.627238 + 0.778828i \(0.715815\pi\)
\(30\) 0.842068 2.84150i 0.153740 0.518785i
\(31\) 2.84877 0.511654 0.255827 0.966723i \(-0.417652\pi\)
0.255827 + 0.966723i \(0.417652\pi\)
\(32\) −2.16796 + 5.22493i −0.383245 + 0.923647i
\(33\) −1.79979 1.56362i −0.313303 0.272191i
\(34\) 4.46239 4.23362i 0.765293 0.726059i
\(35\) −6.74514 11.6829i −1.14014 1.97477i
\(36\) −4.16462 2.70597i −0.694103 0.450996i
\(37\) −3.68360 2.12673i −0.605580 0.349632i 0.165654 0.986184i \(-0.447027\pi\)
−0.771233 + 0.636552i \(0.780360\pi\)
\(38\) 2.19919 2.08644i 0.356755 0.338466i
\(39\) −2.57689 + 0.277909i −0.412633 + 0.0445011i
\(40\) 5.35279 + 6.27194i 0.846350 + 0.991681i
\(41\) −4.60908 + 7.98316i −0.719817 + 1.24676i 0.241255 + 0.970462i \(0.422441\pi\)
−0.961072 + 0.276298i \(0.910892\pi\)
\(42\) 4.57446 1.09764i 0.705854 0.169370i
\(43\) 0.0570117 + 0.0987471i 0.00869420 + 0.0150588i 0.870340 0.492452i \(-0.163899\pi\)
−0.861646 + 0.507510i \(0.830566\pi\)
\(44\) 6.37620 1.82867i 0.961249 0.275682i
\(45\) −6.26944 + 3.61966i −0.934593 + 0.539588i
\(46\) −2.27492 0.674164i −0.335419 0.0994000i
\(47\) 10.1873 1.48597 0.742986 0.669307i \(-0.233409\pi\)
0.742986 + 0.669307i \(0.233409\pi\)
\(48\) −2.62736 + 1.16825i −0.379227 + 0.168622i
\(49\) 7.20680 12.4825i 1.02954 1.78322i
\(50\) 4.81133 1.15448i 0.680425 0.163268i
\(51\) 3.12662 0.437815
\(52\) 3.25790 6.43320i 0.451790 0.892124i
\(53\) 1.88818 0.259361 0.129680 0.991556i \(-0.458605\pi\)
0.129680 + 0.991556i \(0.458605\pi\)
\(54\) −1.30063 5.42043i −0.176994 0.737627i
\(55\) 1.84214 9.49169i 0.248395 1.27986i
\(56\) −4.37353 + 12.3362i −0.584438 + 1.64849i
\(57\) 1.54089 0.204095
\(58\) 2.24592 + 0.665569i 0.294904 + 0.0873935i
\(59\) −6.71441 11.6297i −0.874142 1.51406i −0.857674 0.514194i \(-0.828091\pi\)
−0.0164679 0.999864i \(-0.505242\pi\)
\(60\) −0.220370 + 4.18544i −0.0284497 + 0.540337i
\(61\) 10.1518 5.86113i 1.29980 0.750440i 0.319431 0.947609i \(-0.396508\pi\)
0.980370 + 0.197169i \(0.0631748\pi\)
\(62\) −3.91757 + 0.940021i −0.497532 + 0.119383i
\(63\) −9.95171 5.74562i −1.25380 0.723880i
\(64\) 1.25724 7.90059i 0.157155 0.987574i
\(65\) −6.20130 8.48687i −0.769177 1.05267i
\(66\) 2.99098 + 1.55637i 0.368165 + 0.191576i
\(67\) −3.39711 + 5.88396i −0.415023 + 0.718841i −0.995431 0.0954852i \(-0.969560\pi\)
0.580408 + 0.814326i \(0.302893\pi\)
\(68\) −4.73960 + 7.29445i −0.574760 + 0.884582i
\(69\) −0.603026 1.04447i −0.0725958 0.125740i
\(70\) 13.1308 + 13.8404i 1.56944 + 1.65424i
\(71\) −1.78354 3.08919i −0.211668 0.366619i 0.740569 0.671980i \(-0.234556\pi\)
−0.952237 + 0.305361i \(0.901223\pi\)
\(72\) 6.62000 + 2.34698i 0.780174 + 0.276594i
\(73\) −10.6906 −1.25124 −0.625620 0.780128i \(-0.715154\pi\)
−0.625620 + 0.780128i \(0.715154\pi\)
\(74\) 5.76737 + 1.70914i 0.670443 + 0.198683i
\(75\) 2.17807 + 1.25751i 0.251502 + 0.145205i
\(76\) −2.33580 + 3.59491i −0.267935 + 0.412364i
\(77\) 14.5100 5.00090i 1.65357 0.569905i
\(78\) 3.45199 1.23248i 0.390860 0.139551i
\(79\) −1.97986 −0.222752 −0.111376 0.993778i \(-0.535526\pi\)
−0.111376 + 0.993778i \(0.535526\pi\)
\(80\) −9.43062 6.85876i −1.05438 0.766832i
\(81\) −2.30818 + 3.99789i −0.256465 + 0.444210i
\(82\) 3.70407 12.4991i 0.409046 1.38030i
\(83\) 12.7567i 1.40023i 0.714028 + 0.700117i \(0.246869\pi\)
−0.714028 + 0.700117i \(0.753131\pi\)
\(84\) −5.92851 + 3.01891i −0.646853 + 0.329390i
\(85\) 6.33995 + 10.9811i 0.687664 + 1.19107i
\(86\) −0.110985 0.116983i −0.0119678 0.0126146i
\(87\) 0.595338 + 1.03116i 0.0638269 + 0.110551i
\(88\) −8.16501 + 4.61873i −0.870393 + 0.492358i
\(89\) 10.8016 + 6.23631i 1.14497 + 0.661048i 0.947656 0.319293i \(-0.103445\pi\)
0.197313 + 0.980341i \(0.436779\pi\)
\(90\) 7.42721 7.04644i 0.782897 0.742760i
\(91\) 6.74489 15.2605i 0.707057 1.59974i
\(92\) 3.35088 + 0.176430i 0.349354 + 0.0183941i
\(93\) −1.77347 1.02391i −0.183900 0.106175i
\(94\) −14.0094 + 3.36155i −1.44496 + 0.346718i
\(95\) 3.12450 + 5.41180i 0.320567 + 0.555239i
\(96\) 3.22760 2.47351i 0.329416 0.252451i
\(97\) −6.47679 + 3.73938i −0.657619 + 0.379676i −0.791369 0.611339i \(-0.790631\pi\)
0.133750 + 0.991015i \(0.457298\pi\)
\(98\) −5.79172 + 19.5438i −0.585052 + 1.97422i
\(99\) −2.68365 7.78656i −0.269717 0.782578i
\(100\) −6.23549 + 3.17523i −0.623549 + 0.317523i
\(101\) −14.3556 8.28821i −1.42844 0.824708i −0.431438 0.902142i \(-0.641994\pi\)
−0.996997 + 0.0774348i \(0.975327\pi\)
\(102\) −4.29967 + 1.03171i −0.425730 + 0.102154i
\(103\) 11.8678i 1.16937i 0.811261 + 0.584685i \(0.198782\pi\)
−0.811261 + 0.584685i \(0.801218\pi\)
\(104\) −2.35741 + 9.92183i −0.231163 + 0.972915i
\(105\) 9.69743i 0.946372i
\(106\) −2.59658 + 0.623050i −0.252202 + 0.0605159i
\(107\) 5.70299 9.87786i 0.551329 0.954929i −0.446850 0.894609i \(-0.647454\pi\)
0.998179 0.0603204i \(-0.0192123\pi\)
\(108\) 3.57721 + 7.02489i 0.344217 + 0.675970i
\(109\) 1.31148 0.125617 0.0628084 0.998026i \(-0.479994\pi\)
0.0628084 + 0.998026i \(0.479994\pi\)
\(110\) 0.598735 + 13.6606i 0.0570871 + 1.30249i
\(111\) 1.52879 + 2.64794i 0.145106 + 0.251331i
\(112\) 1.94377 18.4076i 0.183669 1.73935i
\(113\) 1.62523 + 2.81498i 0.152889 + 0.264811i 0.932288 0.361716i \(-0.117809\pi\)
−0.779399 + 0.626527i \(0.784476\pi\)
\(114\) −2.11899 + 0.508453i −0.198462 + 0.0476210i
\(115\) 2.44555 4.23581i 0.228049 0.394992i
\(116\) −3.30816 0.174180i −0.307155 0.0161722i
\(117\) −8.18930 3.61953i −0.757101 0.334626i
\(118\) 13.0710 + 13.7773i 1.20328 + 1.26831i
\(119\) −10.0636 + 17.4307i −0.922531 + 1.59787i
\(120\) −1.07804 5.82844i −0.0984109 0.532061i
\(121\) 10.2014 + 4.11476i 0.927401 + 0.374069i
\(122\) −12.0265 + 11.4099i −1.08883 + 1.03301i
\(123\) 5.73866 3.31322i 0.517437 0.298743i
\(124\) 5.07717 2.58539i 0.455944 0.232175i
\(125\) 4.37669i 0.391463i
\(126\) 15.5813 + 4.61745i 1.38809 + 0.411355i
\(127\) −5.62820 + 9.74833i −0.499422 + 0.865024i −1.00000 0.000667308i \(-0.999788\pi\)
0.500578 + 0.865692i \(0.333121\pi\)
\(128\) 0.878061 + 11.2796i 0.0776103 + 0.996984i
\(129\) 0.0819652i 0.00721663i
\(130\) 11.3283 + 9.62469i 0.993562 + 0.844141i
\(131\) 9.95784 0.870020 0.435010 0.900426i \(-0.356745\pi\)
0.435010 + 0.900426i \(0.356745\pi\)
\(132\) −4.62670 1.15334i −0.402702 0.100385i
\(133\) −4.95964 + 8.59034i −0.430055 + 0.744877i
\(134\) 2.73007 9.21246i 0.235842 0.795835i
\(135\) 11.4908 0.988972
\(136\) 4.11081 11.5951i 0.352499 0.994273i
\(137\) −16.8462 + 9.72613i −1.43926 + 0.830959i −0.997798 0.0663190i \(-0.978874\pi\)
−0.441465 + 0.897278i \(0.645541\pi\)
\(138\) 1.17392 + 1.23735i 0.0999305 + 0.105330i
\(139\) −1.01506 1.75813i −0.0860962 0.149123i 0.819762 0.572705i \(-0.194106\pi\)
−0.905858 + 0.423582i \(0.860773\pi\)
\(140\) −22.6242 14.7002i −1.91210 1.24239i
\(141\) −6.34200 3.66155i −0.534093 0.308358i
\(142\) 3.47204 + 3.65966i 0.291367 + 0.307112i
\(143\) 10.8226 5.08628i 0.905035 0.425336i
\(144\) −9.87812 1.04309i −0.823177 0.0869243i
\(145\) −2.41437 + 4.18181i −0.200503 + 0.347281i
\(146\) 14.7015 3.52762i 1.21670 0.291948i
\(147\) −8.97302 + 5.18058i −0.740083 + 0.427287i
\(148\) −8.49514 0.447283i −0.698296 0.0367665i
\(149\) −5.01492 8.68609i −0.410838 0.711592i 0.584144 0.811650i \(-0.301430\pi\)
−0.994982 + 0.100058i \(0.968097\pi\)
\(150\) −3.41018 1.01059i −0.278440 0.0825146i
\(151\) 13.6452i 1.11043i 0.831707 + 0.555215i \(0.187364\pi\)
−0.831707 + 0.555215i \(0.812636\pi\)
\(152\) 2.02592 5.71440i 0.164324 0.463499i
\(153\) 9.35390 + 5.40048i 0.756218 + 0.436603i
\(154\) −18.3037 + 11.6651i −1.47495 + 0.939998i
\(155\) 8.30488i 0.667064i
\(156\) −4.34041 + 2.83395i −0.347511 + 0.226898i
\(157\) 19.6742 1.57017 0.785085 0.619388i \(-0.212619\pi\)
0.785085 + 0.619388i \(0.212619\pi\)
\(158\) 2.72267 0.653304i 0.216604 0.0519741i
\(159\) −1.17546 0.678654i −0.0932202 0.0538207i
\(160\) 15.2320 + 6.32016i 1.20420 + 0.499652i
\(161\) 7.76381 0.611874
\(162\) 1.85496 6.25945i 0.145740 0.491789i
\(163\) 7.13145 + 12.3520i 0.558578 + 0.967486i 0.997615 + 0.0690168i \(0.0219862\pi\)
−0.439037 + 0.898469i \(0.644680\pi\)
\(164\) −0.969360 + 18.4108i −0.0756943 + 1.43764i
\(165\) −4.55834 + 5.24683i −0.354866 + 0.408465i
\(166\) −4.20940 17.5428i −0.326713 1.36159i
\(167\) 11.4360 + 6.60257i 0.884943 + 0.510922i 0.872285 0.488998i \(-0.162637\pi\)
0.0126578 + 0.999920i \(0.495971\pi\)
\(168\) 7.15659 6.10779i 0.552143 0.471227i
\(169\) 3.95011 12.3853i 0.303855 0.952718i
\(170\) −12.3421 13.0090i −0.946592 0.997743i
\(171\) 4.60986 + 2.66150i 0.352525 + 0.203530i
\(172\) 0.191226 + 0.124250i 0.0145808 + 0.00947394i
\(173\) 0.304514 0.175811i 0.0231517 0.0133667i −0.488379 0.872631i \(-0.662412\pi\)
0.511531 + 0.859265i \(0.329078\pi\)
\(174\) −1.15895 1.22158i −0.0878599 0.0926075i
\(175\) −14.0211 + 8.09507i −1.05989 + 0.611930i
\(176\) 9.70428 9.04582i 0.731488 0.681854i
\(177\) 9.65325i 0.725583i
\(178\) −16.9120 5.01179i −1.26761 0.375650i
\(179\) −9.12304 5.26719i −0.681888 0.393688i 0.118678 0.992933i \(-0.462134\pi\)
−0.800566 + 0.599245i \(0.795468\pi\)
\(180\) −7.88860 + 12.1409i −0.587981 + 0.904930i
\(181\) 7.71981 0.573809 0.286905 0.957959i \(-0.407374\pi\)
0.286905 + 0.957959i \(0.407374\pi\)
\(182\) −4.23986 + 23.2116i −0.314279 + 1.72056i
\(183\) −8.42649 −0.622904
\(184\) −4.66628 + 0.863083i −0.344003 + 0.0636273i
\(185\) −6.19994 + 10.7386i −0.455829 + 0.789519i
\(186\) 2.77670 + 0.822864i 0.203598 + 0.0603353i
\(187\) −13.6384 + 4.70049i −0.997337 + 0.343734i
\(188\) 18.1562 9.24547i 1.32418 0.674295i
\(189\) 9.11989 + 15.7961i 0.663374 + 1.14900i
\(190\) −6.08251 6.41118i −0.441271 0.465116i
\(191\) −11.8545 + 6.84419i −0.857760 + 0.495228i −0.863262 0.504757i \(-0.831582\pi\)
0.00550138 + 0.999985i \(0.498249\pi\)
\(192\) −3.62234 + 4.46654i −0.261420 + 0.322345i
\(193\) −2.33029 + 4.03619i −0.167738 + 0.290531i −0.937624 0.347650i \(-0.886980\pi\)
0.769886 + 0.638181i \(0.220313\pi\)
\(194\) 7.67285 7.27949i 0.550878 0.522637i
\(195\) 0.810176 + 7.51229i 0.0580179 + 0.537966i
\(196\) 1.51570 28.7873i 0.108264 2.05624i
\(197\) −1.71268 + 2.96646i −0.122024 + 0.211351i −0.920566 0.390588i \(-0.872272\pi\)
0.798542 + 0.601939i \(0.205605\pi\)
\(198\) 6.25986 + 9.82237i 0.444869 + 0.698046i
\(199\) 8.49991 4.90743i 0.602543 0.347878i −0.167498 0.985872i \(-0.553569\pi\)
0.770041 + 0.637994i \(0.220236\pi\)
\(200\) 7.52717 6.42406i 0.532251 0.454250i
\(201\) 4.22966 2.44200i 0.298337 0.172245i
\(202\) 22.4764 + 6.66079i 1.58144 + 0.468652i
\(203\) −7.66483 −0.537966
\(204\) 5.57237 2.83756i 0.390144 0.198669i
\(205\) 23.2729 + 13.4366i 1.62545 + 0.938454i
\(206\) −3.91607 16.3204i −0.272846 1.13709i
\(207\) 4.16632i 0.289579i
\(208\) −0.0320920 14.4222i −0.00222518 0.999998i
\(209\) −6.72137 + 2.31653i −0.464927 + 0.160238i
\(210\) −3.19990 13.3357i −0.220814 0.920251i
\(211\) 0.247474 0.428638i 0.0170368 0.0295087i −0.857381 0.514682i \(-0.827910\pi\)
0.874418 + 0.485173i \(0.161243\pi\)
\(212\) 3.36517 1.71361i 0.231121 0.117691i
\(213\) 2.56418i 0.175695i
\(214\) −4.58319 + 15.4657i −0.313300 + 1.05721i
\(215\) 0.287873 0.166203i 0.0196327 0.0113350i
\(216\) −7.23733 8.48009i −0.492438 0.576997i
\(217\) 11.4165 6.59132i 0.775002 0.447448i
\(218\) −1.80352 + 0.432754i −0.122150 + 0.0293098i
\(219\) 6.65531 + 3.84245i 0.449724 + 0.259648i
\(220\) −5.33102 18.5882i −0.359418 1.25322i
\(221\) −6.33972 + 14.3438i −0.426456 + 0.964868i
\(222\) −2.97611 3.13693i −0.199743 0.210537i
\(223\) −0.239198 + 0.414303i −0.0160179 + 0.0277438i −0.873923 0.486064i \(-0.838432\pi\)
0.857905 + 0.513808i \(0.171766\pi\)
\(224\) 3.40100 + 25.9551i 0.227239 + 1.73420i
\(225\) 4.34408 + 7.52417i 0.289606 + 0.501611i
\(226\) −3.16386 3.33482i −0.210457 0.221829i
\(227\) −0.516268 + 0.298067i −0.0342659 + 0.0197834i −0.517035 0.855964i \(-0.672964\pi\)
0.482769 + 0.875748i \(0.339631\pi\)
\(228\) 2.74622 1.39843i 0.181873 0.0926131i
\(229\) 13.4146i 0.886465i −0.896407 0.443232i \(-0.853832\pi\)
0.896407 0.443232i \(-0.146168\pi\)
\(230\) −1.96536 + 6.63197i −0.129592 + 0.437299i
\(231\) −10.8305 2.10198i −0.712594 0.138300i
\(232\) 4.60679 0.852079i 0.302450 0.0559417i
\(233\) 10.9175i 0.715230i −0.933869 0.357615i \(-0.883590\pi\)
0.933869 0.357615i \(-0.116410\pi\)
\(234\) 12.4561 + 2.27525i 0.814281 + 0.148738i
\(235\) 29.6986i 1.93732i
\(236\) −22.5212 14.6332i −1.46600 0.952540i
\(237\) 1.23254 + 0.711608i 0.0800622 + 0.0462239i
\(238\) 8.08760 27.2911i 0.524241 1.76902i
\(239\) 7.43927i 0.481207i −0.970624 0.240603i \(-0.922655\pi\)
0.970624 0.240603i \(-0.0773453\pi\)
\(240\) 3.40573 + 7.65942i 0.219839 + 0.494414i
\(241\) 4.14314 + 7.17614i 0.266883 + 0.462255i 0.968055 0.250737i \(-0.0806728\pi\)
−0.701172 + 0.712992i \(0.747339\pi\)
\(242\) −15.3865 2.29233i −0.989083 0.147357i
\(243\) 13.1145 7.57166i 0.841295 0.485722i
\(244\) 12.7736 19.6591i 0.817744 1.25855i
\(245\) −36.3898 21.0096i −2.32486 1.34226i
\(246\) −6.79841 + 6.44987i −0.433451 + 0.411229i
\(247\) −3.12439 + 7.06902i −0.198800 + 0.449791i
\(248\) −6.12891 + 5.23072i −0.389186 + 0.332151i
\(249\) 4.58506 7.94156i 0.290567 0.503276i
\(250\) 1.44420 + 6.01873i 0.0913389 + 0.380658i
\(251\) 23.6229 13.6387i 1.49107 0.860868i 0.491119 0.871092i \(-0.336588\pi\)
0.999948 + 0.0102246i \(0.00325465\pi\)
\(252\) −22.9507 1.20839i −1.44576 0.0761216i
\(253\) 4.20064 + 3.64943i 0.264092 + 0.229438i
\(254\) 4.52308 15.2629i 0.283803 0.957677i
\(255\) 9.11489i 0.570797i
\(256\) −4.92946 15.2217i −0.308091 0.951357i
\(257\) 15.6381 27.0859i 0.975476 1.68957i 0.297119 0.954841i \(-0.403974\pi\)
0.678357 0.734733i \(-0.262692\pi\)
\(258\) 0.0270464 + 0.112717i 0.00168384 + 0.00701744i
\(259\) −19.6828 −1.22303
\(260\) −18.7544 9.49760i −1.16310 0.589016i
\(261\) 4.11320i 0.254601i
\(262\) −13.6938 + 3.28583i −0.846006 + 0.202999i
\(263\) −3.78965 + 6.56386i −0.233680 + 0.404745i −0.958888 0.283784i \(-0.908410\pi\)
0.725208 + 0.688529i \(0.241743\pi\)
\(264\) 6.74311 + 0.0593538i 0.415010 + 0.00365297i
\(265\) 5.50451i 0.338139i
\(266\) 3.98579 13.4498i 0.244385 0.824661i
\(267\) −4.48295 7.76469i −0.274352 0.475192i
\(268\) −0.714464 + 13.5696i −0.0436429 + 0.828898i
\(269\) −3.68272 6.37865i −0.224539 0.388913i 0.731642 0.681689i \(-0.238754\pi\)
−0.956181 + 0.292776i \(0.905421\pi\)
\(270\) −15.8019 + 3.79167i −0.961674 + 0.230754i
\(271\) −8.87025 5.12124i −0.538829 0.311093i 0.205775 0.978599i \(-0.434028\pi\)
−0.744604 + 0.667506i \(0.767362\pi\)
\(272\) −1.82701 + 17.3018i −0.110779 + 1.04908i
\(273\) −9.68393 + 7.07599i −0.586098 + 0.428258i
\(274\) 19.9571 18.9340i 1.20565 1.14384i
\(275\) −11.3913 2.21082i −0.686921 0.133317i
\(276\) −2.02264 1.31422i −0.121749 0.0791066i
\(277\) 15.1305 8.73557i 0.909101 0.524870i 0.0289590 0.999581i \(-0.490781\pi\)
0.880142 + 0.474711i \(0.157447\pi\)
\(278\) 1.97603 + 2.08280i 0.118514 + 0.124918i
\(279\) −3.53712 6.12647i −0.211762 0.366782i
\(280\) 35.9630 + 12.7499i 2.14920 + 0.761955i
\(281\) 28.2604 1.68588 0.842938 0.538010i \(-0.180824\pi\)
0.842938 + 0.538010i \(0.180824\pi\)
\(282\) 9.92960 + 2.94260i 0.591299 + 0.175229i
\(283\) 8.03079 13.9097i 0.477381 0.826848i −0.522283 0.852772i \(-0.674920\pi\)
0.999664 + 0.0259244i \(0.00825293\pi\)
\(284\) −5.98227 3.88700i −0.354983 0.230651i
\(285\) 4.49207i 0.266087i
\(286\) −13.2047 + 10.5657i −0.780812 + 0.624766i
\(287\) 42.6569i 2.51795i
\(288\) 13.9284 1.82509i 0.820738 0.107544i
\(289\) 0.959097 1.66121i 0.0564175 0.0977180i
\(290\) 1.94030 6.54742i 0.113938 0.384478i
\(291\) 5.37607 0.315151
\(292\) −19.0531 + 9.70222i −1.11500 + 0.567780i
\(293\) −6.14458 10.6427i −0.358970 0.621755i 0.628819 0.777552i \(-0.283539\pi\)
−0.987789 + 0.155797i \(0.950205\pi\)
\(294\) 10.6301 10.0851i 0.619957 0.588174i
\(295\) −33.9035 + 19.5742i −1.97394 + 1.13965i
\(296\) 11.8299 2.18808i 0.687600 0.127180i
\(297\) −2.49070 + 12.8334i −0.144525 + 0.744670i
\(298\) 9.76259 + 10.2901i 0.565532 + 0.596091i
\(299\) 6.01438 0.648631i 0.347821 0.0375113i
\(300\) 5.02308 + 0.264474i 0.290008 + 0.0152694i
\(301\) 0.456950 + 0.263820i 0.0263382 + 0.0152064i
\(302\) −4.50256 18.7646i −0.259093 1.07978i
\(303\) 5.95795 + 10.3195i 0.342275 + 0.592838i
\(304\) −0.900399 + 8.52682i −0.0516414 + 0.489047i
\(305\) −17.0867 29.5950i −0.978379 1.69460i
\(306\) −14.6453 4.34007i −0.837216 0.248106i
\(307\) 23.8635i 1.36196i 0.732300 + 0.680982i \(0.238447\pi\)
−0.732300 + 0.680982i \(0.761553\pi\)
\(308\) 21.3217 22.0813i 1.21492 1.25820i
\(309\) 4.26556 7.38817i 0.242659 0.420298i
\(310\) 2.74040 + 11.4207i 0.155644 + 0.648652i
\(311\) 10.0151i 0.567906i 0.958838 + 0.283953i \(0.0916459\pi\)
−0.958838 + 0.283953i \(0.908354\pi\)
\(312\) 5.03371 5.32942i 0.284978 0.301719i
\(313\) 13.1590 0.743793 0.371896 0.928274i \(-0.378708\pi\)
0.371896 + 0.928274i \(0.378708\pi\)
\(314\) −27.0555 + 6.49197i −1.52683 + 0.366363i
\(315\) −16.7499 + 29.0117i −0.943752 + 1.63463i
\(316\) −3.52858 + 1.79682i −0.198498 + 0.101079i
\(317\) 6.20472i 0.348492i 0.984702 + 0.174246i \(0.0557488\pi\)
−0.984702 + 0.174246i \(0.944251\pi\)
\(318\) 1.84041 + 0.545398i 0.103205 + 0.0305844i
\(319\) −4.14709 3.60290i −0.232192 0.201724i
\(320\) −23.0322 3.66518i −1.28754 0.204890i
\(321\) −7.10066 + 4.09957i −0.396320 + 0.228816i
\(322\) −10.6766 + 2.56186i −0.594985 + 0.142767i
\(323\) 4.66170 8.07431i 0.259384 0.449267i
\(324\) −0.485447 + 9.21996i −0.0269693 + 0.512220i
\(325\) −10.1854 + 7.44239i −0.564983 + 0.412830i
\(326\) −13.8829 14.6331i −0.768901 0.810450i
\(327\) −0.816446 0.471375i −0.0451496 0.0260671i
\(328\) −4.74205 25.6380i −0.261836 1.41562i
\(329\) 40.8258 23.5708i 2.25080 1.29950i
\(330\) 4.53721 8.71947i 0.249765 0.479991i
\(331\) 1.34839 + 2.33547i 0.0741140 + 0.128369i 0.900701 0.434440i \(-0.143054\pi\)
−0.826587 + 0.562809i \(0.809720\pi\)
\(332\) 11.5773 + 22.7355i 0.635389 + 1.24777i
\(333\) 10.5624i 0.578818i
\(334\) −17.9052 5.30613i −0.979729 0.290338i
\(335\) 17.1532 + 9.90343i 0.937181 + 0.541082i
\(336\) −7.82618 + 10.7608i −0.426953 + 0.587050i
\(337\) 2.31841i 0.126292i 0.998004 + 0.0631459i \(0.0201134\pi\)
−0.998004 + 0.0631459i \(0.979887\pi\)
\(338\) −1.34526 + 18.3355i −0.0731726 + 0.997319i
\(339\) 2.33658i 0.126906i
\(340\) 21.2652 + 13.8171i 1.15327 + 0.749338i
\(341\) 9.27523 + 1.80013i 0.502282 + 0.0974828i
\(342\) −7.21761 2.13891i −0.390284 0.115659i
\(343\) 34.3063i 1.85237i
\(344\) −0.303969 0.107766i −0.0163889 0.00581034i
\(345\) −3.04490 + 1.75797i −0.163932 + 0.0946460i
\(346\) −0.360747 + 0.342253i −0.0193939 + 0.0183996i
\(347\) 17.6013 + 30.4863i 0.944885 + 1.63659i 0.755981 + 0.654593i \(0.227160\pi\)
0.188904 + 0.981996i \(0.439507\pi\)
\(348\) 1.99685 + 1.29746i 0.107043 + 0.0695513i
\(349\) 10.8640 18.8169i 0.581535 1.00725i −0.413763 0.910385i \(-0.635786\pi\)
0.995298 0.0968630i \(-0.0308809\pi\)
\(350\) 16.6103 15.7588i 0.887859 0.842341i
\(351\) 8.38458 + 11.4748i 0.447536 + 0.612481i
\(352\) −10.3602 + 15.6418i −0.552203 + 0.833710i
\(353\) 11.9167 + 6.88010i 0.634261 + 0.366191i 0.782400 0.622776i \(-0.213995\pi\)
−0.148139 + 0.988967i \(0.547328\pi\)
\(354\) −3.18533 13.2750i −0.169298 0.705556i
\(355\) −9.00576 + 5.19948i −0.477976 + 0.275959i
\(356\) 24.9108 + 1.31159i 1.32027 + 0.0695143i
\(357\) 12.5300 7.23420i 0.663158 0.382874i
\(358\) 14.2838 + 4.23296i 0.754925 + 0.223719i
\(359\) 2.71910i 0.143509i −0.997422 0.0717543i \(-0.977140\pi\)
0.997422 0.0717543i \(-0.0228598\pi\)
\(360\) 6.84204 19.2990i 0.360607 1.01714i
\(361\) −7.20258 + 12.4752i −0.379083 + 0.656592i
\(362\) −10.6161 + 2.54734i −0.557971 + 0.133885i
\(363\) −4.87183 6.22822i −0.255705 0.326897i
\(364\) −1.82866 33.3191i −0.0958480 1.74640i
\(365\) 31.1658i 1.63129i
\(366\) 11.5879 2.78053i 0.605711 0.145340i
\(367\) −8.69018 5.01728i −0.453624 0.261900i 0.255736 0.966747i \(-0.417682\pi\)
−0.709359 + 0.704847i \(0.751016\pi\)
\(368\) 6.13217 2.72665i 0.319662 0.142136i
\(369\) 22.8911 1.19166
\(370\) 4.98256 16.8133i 0.259031 0.874084i
\(371\) 7.56690 4.36875i 0.392854 0.226814i
\(372\) −4.08999 0.215345i −0.212056 0.0111651i
\(373\) −27.1292 + 15.6631i −1.40470 + 0.811003i −0.994870 0.101160i \(-0.967745\pi\)
−0.409828 + 0.912163i \(0.634411\pi\)
\(374\) 17.2042 10.9643i 0.889607 0.566952i
\(375\) −1.57308 + 2.72466i −0.0812336 + 0.140701i
\(376\) −21.9172 + 18.7052i −1.13029 + 0.964650i
\(377\) −5.93770 + 0.640361i −0.305807 + 0.0329803i
\(378\) −17.7538 18.7131i −0.913156 0.962500i
\(379\) 3.62868 6.28505i 0.186393 0.322841i −0.757652 0.652658i \(-0.773654\pi\)
0.944045 + 0.329817i \(0.106987\pi\)
\(380\) 10.4801 + 6.80945i 0.537616 + 0.349318i
\(381\) 7.00755 4.04581i 0.359007 0.207273i
\(382\) 14.0436 13.3237i 0.718534 0.681698i
\(383\) 13.4795 + 23.3472i 0.688769 + 1.19298i 0.972236 + 0.234002i \(0.0751821\pi\)
−0.283467 + 0.958982i \(0.591485\pi\)
\(384\) 3.50751 7.33757i 0.178992 0.374444i
\(385\) −14.5789 42.3003i −0.743009 2.15583i
\(386\) 1.87273 6.31942i 0.0953196 0.321650i
\(387\) 0.141575 0.245215i 0.00719665 0.0124650i
\(388\) −8.14950 + 12.5424i −0.413728 + 0.636746i
\(389\) −13.6413 −0.691640 −0.345820 0.938301i \(-0.612399\pi\)
−0.345820 + 0.938301i \(0.612399\pi\)
\(390\) −3.59300 10.0634i −0.181939 0.509580i
\(391\) −7.29743 −0.369047
\(392\) 7.41472 + 40.0879i 0.374500 + 2.02474i
\(393\) −6.19914 3.57908i −0.312705 0.180540i
\(394\) 1.37639 4.64455i 0.0693417 0.233989i
\(395\) 5.77180i 0.290411i
\(396\) −11.8496 11.4419i −0.595463 0.574978i
\(397\) −32.3041 + 18.6508i −1.62130 + 0.936056i −0.634724 + 0.772739i \(0.718886\pi\)
−0.986574 + 0.163317i \(0.947781\pi\)
\(398\) −10.0696 + 9.55334i −0.504742 + 0.478866i
\(399\) 6.17513 3.56521i 0.309143 0.178484i
\(400\) −8.23143 + 11.3180i −0.411571 + 0.565900i
\(401\) 1.81369 + 1.04713i 0.0905713 + 0.0522914i 0.544602 0.838695i \(-0.316681\pi\)
−0.454030 + 0.890986i \(0.650014\pi\)
\(402\) −5.01075 + 4.75386i −0.249913 + 0.237101i
\(403\) 8.29332 6.05988i 0.413120 0.301864i
\(404\) −33.1070 1.74314i −1.64713 0.0867244i
\(405\) 11.6549 + 6.72893i 0.579134 + 0.334363i
\(406\) 10.5405 2.52920i 0.523117 0.125522i
\(407\) −10.6494 9.25201i −0.527873 0.458605i
\(408\) −6.72669 + 5.74089i −0.333021 + 0.284217i
\(409\) −8.56078 14.8277i −0.423303 0.733183i 0.572957 0.819585i \(-0.305796\pi\)
−0.996260 + 0.0864027i \(0.972463\pi\)
\(410\) −36.4382 10.7983i −1.79955 0.533290i
\(411\) 13.9832 0.689739
\(412\) 10.7706 + 21.1512i 0.530629 + 1.04204i
\(413\) −53.8162 31.0708i −2.64812 1.52890i
\(414\) 1.37478 + 5.72943i 0.0675667 + 0.281586i
\(415\) 37.1891 1.82554
\(416\) 4.80308 + 19.8225i 0.235490 + 0.971877i
\(417\) 1.45934i 0.0714643i
\(418\) 8.47869 5.40353i 0.414706 0.264295i
\(419\) 2.58686 + 1.49353i 0.126376 + 0.0729635i 0.561856 0.827235i \(-0.310088\pi\)
−0.435479 + 0.900199i \(0.643421\pi\)
\(420\) 8.80088 + 17.2831i 0.429439 + 0.843328i
\(421\) 13.3103i 0.648706i 0.945936 + 0.324353i \(0.105147\pi\)
−0.945936 + 0.324353i \(0.894853\pi\)
\(422\) −0.198882 + 0.671114i −0.00968142 + 0.0326693i
\(423\) −12.6489 21.9085i −0.615009 1.06523i
\(424\) −4.06226 + 3.46694i −0.197281 + 0.168369i
\(425\) 13.1788 7.60879i 0.639266 0.369081i
\(426\) −0.846115 3.52621i −0.0409944 0.170846i
\(427\) 27.1223 46.9771i 1.31254 2.27338i
\(428\) 1.19943 22.7804i 0.0579765 1.10113i
\(429\) −8.56565 0.723499i −0.413553 0.0349309i
\(430\) −0.341034 + 0.323550i −0.0164461 + 0.0156030i
\(431\) −3.61441 2.08678i −0.174100 0.100517i 0.410418 0.911898i \(-0.365383\pi\)
−0.584518 + 0.811381i \(0.698716\pi\)
\(432\) 12.7508 + 9.27351i 0.613475 + 0.446172i
\(433\) 16.8758 + 29.2298i 0.811001 + 1.40469i 0.912164 + 0.409825i \(0.134410\pi\)
−0.101163 + 0.994870i \(0.532256\pi\)
\(434\) −13.5248 + 12.8314i −0.649209 + 0.615927i
\(435\) 3.00608 1.73556i 0.144130 0.0832137i
\(436\) 2.33736 1.19023i 0.111939 0.0570016i
\(437\) −3.59638 −0.172038
\(438\) −10.4202 3.08797i −0.497894 0.147549i
\(439\) −0.487942 + 0.845140i −0.0232882 + 0.0403364i −0.877435 0.479696i \(-0.840747\pi\)
0.854146 + 0.520033i \(0.174080\pi\)
\(440\) 13.4648 + 23.8031i 0.641907 + 1.13477i
\(441\) −35.7927 −1.70442
\(442\) 3.98516 21.8172i 0.189555 1.03774i
\(443\) 29.3870i 1.39622i 0.715992 + 0.698108i \(0.245975\pi\)
−0.715992 + 0.698108i \(0.754025\pi\)
\(444\) 5.12779 + 3.33180i 0.243354 + 0.158120i
\(445\) 18.1804 31.4894i 0.861835 1.49274i
\(446\) 0.192230 0.648669i 0.00910237 0.0307154i
\(447\) 7.20990i 0.341017i
\(448\) −13.2415 34.5707i −0.625602 1.63331i
\(449\) 13.5661 7.83238i 0.640223 0.369633i −0.144477 0.989508i \(-0.546150\pi\)
0.784700 + 0.619875i \(0.212817\pi\)
\(450\) −8.45667 8.91365i −0.398651 0.420193i
\(451\) −20.0511 + 23.0797i −0.944170 + 1.08678i
\(452\) 5.45127 + 3.54198i 0.256406 + 0.166601i
\(453\) 4.90439 8.49466i 0.230428 0.399114i
\(454\) 0.611606 0.580251i 0.0287041 0.0272325i
\(455\) −44.4882 19.6631i −2.08564 0.921818i
\(456\) −3.31510 + 2.82927i −0.155244 + 0.132493i
\(457\) −18.6482 + 32.2996i −0.872326 + 1.51091i −0.0127419 + 0.999919i \(0.504056\pi\)
−0.859584 + 0.510994i \(0.829277\pi\)
\(458\) 4.42649 + 18.4475i 0.206836 + 0.861997i
\(459\) −8.57205 14.8472i −0.400109 0.693009i
\(460\) 0.514337 9.76866i 0.0239811 0.455466i
\(461\) 13.4457 + 23.2887i 0.626231 + 1.08466i 0.988301 + 0.152513i \(0.0487366\pi\)
−0.362071 + 0.932151i \(0.617930\pi\)
\(462\) 15.5875 0.683186i 0.725194 0.0317847i
\(463\) 33.8004 1.57084 0.785419 0.618965i \(-0.212448\pi\)
0.785419 + 0.618965i \(0.212448\pi\)
\(464\) −6.05399 + 2.69188i −0.281050 + 0.124968i
\(465\) −2.98496 + 5.17011i −0.138424 + 0.239758i
\(466\) 3.60250 + 15.0135i 0.166883 + 0.695489i
\(467\) 34.7515i 1.60811i −0.594556 0.804054i \(-0.702672\pi\)
0.594556 0.804054i \(-0.297328\pi\)
\(468\) −17.8801 + 0.981321i −0.826510 + 0.0453616i
\(469\) 31.4401i 1.45177i
\(470\) 9.79977 + 40.8409i 0.452030 + 1.88385i
\(471\) −12.2479 7.07135i −0.564355 0.325831i
\(472\) 35.7992 + 12.6919i 1.64779 + 0.584190i
\(473\) 0.123224 + 0.357534i 0.00566587 + 0.0164394i
\(474\) −1.92978 0.571882i −0.0886376 0.0262674i
\(475\) 6.49488 3.74982i 0.298006 0.172054i
\(476\) −2.11654 + 40.1988i −0.0970113 + 1.84251i
\(477\) −2.34442 4.06065i −0.107343 0.185924i
\(478\) 2.45477 + 10.2303i 0.112279 + 0.467924i
\(479\) 2.77395 + 1.60154i 0.126745 + 0.0731761i 0.562032 0.827116i \(-0.310020\pi\)
−0.435287 + 0.900292i \(0.643353\pi\)
\(480\) −7.21090 9.40927i −0.329131 0.429473i
\(481\) −15.2476 + 1.64441i −0.695232 + 0.0749784i
\(482\) −8.06550 8.50134i −0.367374 0.387225i
\(483\) −4.83327 2.79049i −0.219922 0.126972i
\(484\) 21.9156 1.92479i 0.996165 0.0874904i
\(485\) 10.9012 + 18.8815i 0.494999 + 0.857364i
\(486\) −15.5363 + 14.7398i −0.704742 + 0.668612i
\(487\) 2.70361 + 4.68278i 0.122512 + 0.212197i 0.920758 0.390135i \(-0.127572\pi\)
−0.798246 + 0.602332i \(0.794238\pi\)
\(488\) −11.0789 + 31.2497i −0.501520 + 1.41461i
\(489\) 10.2528i 0.463649i
\(490\) 56.9751 + 16.8843i 2.57387 + 0.762756i
\(491\) 4.98854 8.64040i 0.225130 0.389936i −0.731229 0.682132i \(-0.761053\pi\)
0.956358 + 0.292196i \(0.0943861\pi\)
\(492\) 7.22073 11.1130i 0.325536 0.501014i
\(493\) 7.20440 0.324470
\(494\) 1.96400 10.7521i 0.0883645 0.483761i
\(495\) −22.6998 + 7.82351i −1.02028 + 0.351641i
\(496\) 6.70234 9.21555i 0.300944 0.413791i
\(497\) −14.2952 8.25331i −0.641225 0.370212i
\(498\) −3.68477 + 12.4340i −0.165119 + 0.557182i
\(499\) 24.6688 1.10433 0.552164 0.833735i \(-0.313802\pi\)
0.552164 + 0.833735i \(0.313802\pi\)
\(500\) −3.97205 7.80028i −0.177636 0.348839i
\(501\) −4.74623 8.22071i −0.212046 0.367274i
\(502\) −27.9853 + 26.5506i −1.24905 + 1.18501i
\(503\) −18.4125 31.8914i −0.820974 1.42197i −0.904958 0.425502i \(-0.860098\pi\)
0.0839837 0.996467i \(-0.473236\pi\)
\(504\) 31.9601 5.91139i 1.42361 0.263314i
\(505\) −24.1622 + 41.8502i −1.07520 + 1.86231i
\(506\) −6.98085 3.63251i −0.310337 0.161485i
\(507\) −6.91067 + 6.29059i −0.306914 + 0.279375i
\(508\) −1.18370 + 22.4817i −0.0525181 + 0.997462i
\(509\) −14.5672 8.41037i −0.645679 0.372783i 0.141119 0.989993i \(-0.454930\pi\)
−0.786799 + 0.617209i \(0.788263\pi\)
\(510\) 3.00768 + 12.5346i 0.133182 + 0.555042i
\(511\) −42.8428 + 24.7353i −1.89525 + 1.09422i
\(512\) 11.8017 + 19.3060i 0.521565 + 0.853212i
\(513\) −4.22454 7.31712i −0.186518 0.323059i
\(514\) −12.5675 + 42.4081i −0.554328 + 1.87054i
\(515\) 34.5976 1.52455
\(516\) −0.0743873 0.146081i −0.00327472 0.00643086i
\(517\) 33.1686 + 6.43735i 1.45875 + 0.283114i
\(518\) 27.0673 6.49481i 1.18927 0.285366i
\(519\) −0.252762 −0.0110950
\(520\) 28.9246 + 6.87243i 1.26843 + 0.301376i
\(521\) 30.3431 1.32936 0.664678 0.747130i \(-0.268569\pi\)
0.664678 + 0.747130i \(0.268569\pi\)
\(522\) −1.35725 5.65639i −0.0594053 0.247573i
\(523\) 4.33296 7.50491i 0.189467 0.328167i −0.755606 0.655027i \(-0.772657\pi\)
0.945073 + 0.326860i \(0.105991\pi\)
\(524\) 17.7472 9.03721i 0.775290 0.394792i
\(525\) 11.6382 0.507933
\(526\) 3.04554 10.2770i 0.132792 0.448097i
\(527\) −10.7307 + 6.19537i −0.467436 + 0.269875i
\(528\) −9.29257 + 2.14343i −0.404407 + 0.0932809i
\(529\) −10.0926 17.4808i −0.438807 0.760036i
\(530\) 1.81635 + 7.56968i 0.0788970 + 0.328806i
\(531\) −16.6736 + 28.8796i −0.723574 + 1.25327i
\(532\) −1.04309 + 19.8111i −0.0452236 + 0.858920i
\(533\) 3.56378 + 33.0449i 0.154365 + 1.43133i
\(534\) 8.72701 + 9.19859i 0.377655 + 0.398062i
\(535\) −28.7965 16.6256i −1.24498 0.718789i
\(536\) −3.49512 18.8964i −0.150966 0.816202i
\(537\) 3.78630 + 6.55806i 0.163391 + 0.283001i
\(538\) 7.16919 + 7.55659i 0.309086 + 0.325788i
\(539\) 31.3521 36.0876i 1.35043 1.55440i
\(540\) 20.4793 10.4285i 0.881289 0.448769i
\(541\) 14.1741 0.609391 0.304696 0.952450i \(-0.401445\pi\)
0.304696 + 0.952450i \(0.401445\pi\)
\(542\) 13.8881 + 4.11567i 0.596543 + 0.176783i
\(543\) −4.80588 2.77468i −0.206240 0.119073i
\(544\) −3.19670 24.3960i −0.137057 1.04597i
\(545\) 3.82329i 0.163772i
\(546\) 10.9822 12.9262i 0.469997 0.553190i
\(547\) −5.06935 −0.216750 −0.108375 0.994110i \(-0.534565\pi\)
−0.108375 + 0.994110i \(0.534565\pi\)
\(548\) −21.1969 + 32.6229i −0.905485 + 1.39358i
\(549\) −25.2095 14.5547i −1.07591 0.621180i
\(550\) 16.3946 0.718562i 0.699067 0.0306396i
\(551\) 3.55053 0.151258
\(552\) 3.21515 + 1.13987i 0.136846 + 0.0485159i
\(553\) −7.93434 + 4.58089i −0.337402 + 0.194799i
\(554\) −17.9246 + 17.0056i −0.761542 + 0.722500i
\(555\) 7.71941 4.45680i 0.327671 0.189181i
\(556\) −3.40466 2.21219i −0.144390 0.0938178i
\(557\) −10.3577 + 17.9401i −0.438871 + 0.760147i −0.997603 0.0692018i \(-0.977955\pi\)
0.558732 + 0.829348i \(0.311288\pi\)
\(558\) 6.88575 + 7.25783i 0.291497 + 0.307249i
\(559\) 0.376026 + 0.166197i 0.0159042 + 0.00702940i
\(560\) −53.6628 5.66658i −2.26767 0.239457i
\(561\) 10.1799 + 1.97571i 0.429795 + 0.0834146i
\(562\) −38.8632 + 9.32522i −1.63934 + 0.393361i
\(563\) −11.1767 19.3586i −0.471042 0.815868i 0.528410 0.848990i \(-0.322789\pi\)
−0.999451 + 0.0331213i \(0.989455\pi\)
\(564\) −14.6260 0.770082i −0.615864 0.0324263i
\(565\) 8.20639 4.73796i 0.345245 0.199327i
\(566\) −6.45391 + 21.7783i −0.271278 + 0.915411i
\(567\) 21.3622i 0.897126i
\(568\) 9.50931 + 3.37133i 0.399002 + 0.141458i
\(569\) −22.4492 12.9610i −0.941118 0.543355i −0.0508073 0.998708i \(-0.516179\pi\)
−0.890311 + 0.455354i \(0.849513\pi\)
\(570\) 1.48227 + 6.17740i 0.0620854 + 0.258743i
\(571\) −44.2001 −1.84972 −0.924858 0.380312i \(-0.875816\pi\)
−0.924858 + 0.380312i \(0.875816\pi\)
\(572\) 14.6724 18.8870i 0.613486 0.789706i
\(573\) 9.83983 0.411065
\(574\) −14.0757 58.6608i −0.587507 2.44845i
\(575\) −5.08354 2.93499i −0.211998 0.122397i
\(576\) −18.5518 + 7.10583i −0.772991 + 0.296076i
\(577\) 22.2432i 0.925998i −0.886359 0.462999i \(-0.846773\pi\)
0.886359 0.462999i \(-0.153227\pi\)
\(578\) −0.770775 + 2.60093i −0.0320600 + 0.108184i
\(579\) 2.90140 1.67512i 0.120578 0.0696157i
\(580\) −0.507779 + 9.64412i −0.0210844 + 0.400450i
\(581\) 29.5158 + 51.1229i 1.22452 + 2.12093i
\(582\) −7.39306 + 1.77397i −0.306452 + 0.0735333i
\(583\) 6.14766 + 1.19314i 0.254610 + 0.0494147i
\(584\) 23.0000 19.6293i 0.951747 0.812268i
\(585\) −10.5518 + 23.8739i −0.436265 + 0.987063i
\(586\) 11.9617 + 12.6081i 0.494134 + 0.520836i
\(587\) 3.79207 6.56806i 0.156516 0.271093i −0.777094 0.629384i \(-0.783307\pi\)
0.933610 + 0.358291i \(0.116641\pi\)
\(588\) −11.2904 + 17.3764i −0.465609 + 0.716593i
\(589\) −5.28838 + 3.05325i −0.217904 + 0.125807i
\(590\) 40.1644 38.1053i 1.65354 1.56877i
\(591\) 2.13242 1.23116i 0.0877162 0.0506430i
\(592\) −15.5463 + 6.91258i −0.638947 + 0.284105i
\(593\) 0.273229 0.0112202 0.00561009 0.999984i \(-0.498214\pi\)
0.00561009 + 0.999984i \(0.498214\pi\)
\(594\) −0.809531 18.4701i −0.0332154 0.757837i
\(595\) 50.8149 + 29.3380i 2.08321 + 1.20274i
\(596\) −16.8208 10.9294i −0.689007 0.447684i
\(597\) −7.05537 −0.288757
\(598\) −8.05682 + 2.87657i −0.329468 + 0.117632i
\(599\) 20.4793i 0.836763i 0.908271 + 0.418381i \(0.137402\pi\)
−0.908271 + 0.418381i \(0.862598\pi\)
\(600\) −6.99491 + 1.29379i −0.285566 + 0.0528187i
\(601\) −19.3555 11.1749i −0.789526 0.455833i 0.0502699 0.998736i \(-0.483992\pi\)
−0.839796 + 0.542903i \(0.817325\pi\)
\(602\) −0.715443 0.212018i −0.0291593 0.00864123i
\(603\) 16.8718 0.687073
\(604\) 12.3837 + 24.3189i 0.503884 + 0.989522i
\(605\) 11.9956 29.7397i 0.487689 1.20909i
\(606\) −11.5984 12.2251i −0.471153 0.496612i
\(607\) 3.67746 + 6.36955i 0.149263 + 0.258532i 0.930955 0.365133i \(-0.118976\pi\)
−0.781692 + 0.623665i \(0.785643\pi\)
\(608\) −1.57542 12.0230i −0.0638918 0.487597i
\(609\) 4.77166 + 2.75492i 0.193357 + 0.111635i
\(610\) 33.2628 + 35.0602i 1.34677 + 1.41955i
\(611\) 29.6573 21.6704i 1.19980 0.876689i
\(612\) 21.5720 + 1.13580i 0.871998 + 0.0459122i
\(613\) 8.83401 15.3010i 0.356802 0.618000i −0.630622 0.776090i \(-0.717200\pi\)
0.987425 + 0.158090i \(0.0505336\pi\)
\(614\) −7.87435 32.8166i −0.317783 1.32437i
\(615\) −9.65886 16.7296i −0.389483 0.674604i
\(616\) −22.0349 + 37.4014i −0.887810 + 1.50694i
\(617\) −36.4181 + 21.0260i −1.46614 + 0.846474i −0.999283 0.0378613i \(-0.987945\pi\)
−0.466853 + 0.884335i \(0.654612\pi\)
\(618\) −3.42800 + 11.5676i −0.137895 + 0.465316i
\(619\) 29.7792 1.19693 0.598463 0.801150i \(-0.295778\pi\)
0.598463 + 0.801150i \(0.295778\pi\)
\(620\) −7.53707 14.8012i −0.302696 0.594432i
\(621\) −3.30655 + 5.72711i −0.132687 + 0.229821i
\(622\) −3.30473 13.7726i −0.132508 0.552230i
\(623\) 57.7169 2.31238
\(624\) −5.16368 + 8.98989i −0.206713 + 0.359884i
\(625\) −30.2526 −1.21010
\(626\) −18.0960 + 4.34214i −0.723263 + 0.173547i
\(627\) 5.01693 + 0.973685i 0.200357 + 0.0388852i
\(628\) 35.0640 17.8552i 1.39921 0.712502i
\(629\) 18.5004 0.737660
\(630\) 13.4610 45.4234i 0.536300 1.80971i
\(631\) −3.64209 6.30829i −0.144989 0.251129i 0.784380 0.620281i \(-0.212981\pi\)
−0.929369 + 0.369152i \(0.879648\pi\)
\(632\) 4.25952 3.63529i 0.169435 0.144604i
\(633\) −0.308125 + 0.177896i −0.0122469 + 0.00707073i
\(634\) −2.04740 8.53260i −0.0813126 0.338873i
\(635\) 28.4188 + 16.4076i 1.12777 + 0.651117i
\(636\) −2.71086 0.142731i −0.107493 0.00565967i
\(637\) −5.57237 51.6694i −0.220785 2.04721i
\(638\) 6.89185 + 3.58620i 0.272851 + 0.141979i
\(639\) −4.42900 + 7.67125i −0.175209 + 0.303470i
\(640\) 32.8828 2.55977i 1.29981 0.101184i
\(641\) 4.36860 + 7.56664i 0.172549 + 0.298864i 0.939310 0.343068i \(-0.111466\pi\)
−0.766761 + 0.641933i \(0.778133\pi\)
\(642\) 8.41193 7.98068i 0.331992 0.314972i
\(643\) −13.7780 23.8643i −0.543353 0.941115i −0.998709 0.0508053i \(-0.983821\pi\)
0.455356 0.890310i \(-0.349512\pi\)
\(644\) 13.8369 7.04603i 0.545251 0.277652i
\(645\) −0.238949 −0.00940861
\(646\) −3.74636 + 12.6419i −0.147399 + 0.497387i
\(647\) 31.6360 + 18.2650i 1.24374 + 0.718073i 0.969853 0.243689i \(-0.0783577\pi\)
0.273886 + 0.961762i \(0.411691\pi\)
\(648\) −2.37477 12.8393i −0.0932899 0.504375i
\(649\) −14.5125 42.1077i −0.569664 1.65287i
\(650\) 11.5509 13.5955i 0.453064 0.533261i
\(651\) −9.47628 −0.371405
\(652\) 23.9200 + 15.5421i 0.936778 + 0.608675i
\(653\) 10.9533 18.9718i 0.428638 0.742422i −0.568115 0.822949i \(-0.692327\pi\)
0.996752 + 0.0805272i \(0.0256604\pi\)
\(654\) 1.27830 + 0.378819i 0.0499855 + 0.0148130i
\(655\) 29.0296i 1.13428i
\(656\) 14.9811 + 33.6921i 0.584912 + 1.31546i
\(657\) 13.2738 + 22.9908i 0.517859 + 0.896958i
\(658\) −48.3651 + 45.8856i −1.88547 + 1.78881i
\(659\) −7.99150 13.8417i −0.311305 0.539196i 0.667340 0.744753i \(-0.267433\pi\)
−0.978645 + 0.205557i \(0.934099\pi\)
\(660\) −3.36227 + 13.4880i −0.130876 + 0.525019i
\(661\) −10.8896 6.28709i −0.423555 0.244540i 0.273042 0.962002i \(-0.411970\pi\)
−0.696597 + 0.717462i \(0.745303\pi\)
\(662\) −2.62492 2.76676i −0.102020 0.107533i
\(663\) 9.10221 6.65093i 0.353501 0.258301i
\(664\) −23.4231 27.4451i −0.908991 1.06508i
\(665\) 25.0430 + 14.4586i 0.971126 + 0.560680i
\(666\) −3.48533 14.5252i −0.135054 0.562841i
\(667\) −1.38950 2.40668i −0.0538016 0.0931871i
\(668\) 26.3737 + 1.38862i 1.02043 + 0.0537274i
\(669\) 0.297820 0.171946i 0.0115144 0.00664783i
\(670\) −26.8566 7.95885i −1.03756 0.307477i
\(671\) 36.7565 12.6682i 1.41897 0.489050i
\(672\) 7.21161 17.3805i 0.278194 0.670466i
\(673\) −11.6529 6.72782i −0.449188 0.259339i 0.258299 0.966065i \(-0.416838\pi\)
−0.707487 + 0.706726i \(0.750171\pi\)
\(674\) −0.765016 3.18823i −0.0294673 0.122806i
\(675\) 13.7905i 0.530797i
\(676\) −4.20027 25.6585i −0.161549 0.986865i
\(677\) 45.0827i 1.73267i −0.499466 0.866334i \(-0.666470\pi\)
0.499466 0.866334i \(-0.333530\pi\)
\(678\) 0.771012 + 3.21322i 0.0296105 + 0.123403i
\(679\) −17.3039 + 29.9712i −0.664063 + 1.15019i
\(680\) −33.8027 11.9840i −1.29627 0.459567i
\(681\) 0.428529 0.0164213
\(682\) −13.3491 + 0.585081i −0.511163 + 0.0224039i
\(683\) −5.72602 9.91776i −0.219100 0.379492i 0.735433 0.677597i \(-0.236979\pi\)
−0.954533 + 0.298105i \(0.903645\pi\)
\(684\) 10.6313 + 0.559756i 0.406498 + 0.0214028i
\(685\) 28.3541 + 49.1108i 1.08336 + 1.87643i
\(686\) 11.3202 + 47.1773i 0.432207 + 1.80124i
\(687\) −4.82153 + 8.35114i −0.183953 + 0.318616i
\(688\) 0.453571 + 0.0478954i 0.0172923 + 0.00182599i
\(689\) 5.49685 4.01651i 0.209413 0.153017i
\(690\) 3.60719 3.42226i 0.137323 0.130283i
\(691\) −4.05055 + 7.01575i −0.154090 + 0.266892i −0.932727 0.360583i \(-0.882578\pi\)
0.778637 + 0.627474i \(0.215911\pi\)
\(692\) 0.383158 0.589697i 0.0145655 0.0224169i
\(693\) −28.7708 24.9955i −1.09291 0.949500i
\(694\) −34.2646 36.1161i −1.30067 1.37095i
\(695\) −5.12540 + 2.95915i −0.194418 + 0.112247i
\(696\) −3.17416 1.12533i −0.120316 0.0426556i
\(697\) 40.0944i 1.51868i
\(698\) −8.73079 + 29.4615i −0.330465 + 1.11513i
\(699\) −3.92400 + 6.79658i −0.148419 + 0.257070i
\(700\) −17.6422 + 27.1521i −0.666811 + 1.02625i
\(701\) 4.43680i 0.167576i 0.996484 + 0.0837879i \(0.0267018\pi\)
−0.996484 + 0.0837879i \(0.973298\pi\)
\(702\) −15.3167 13.0132i −0.578091 0.491153i
\(703\) 9.11751 0.343874
\(704\) 9.08579 24.9289i 0.342434 0.939542i
\(705\) −10.6744 + 18.4885i −0.402019 + 0.696318i
\(706\) −18.6578 5.52917i −0.702197 0.208093i
\(707\) −76.7071 −2.88487
\(708\) 8.76079 + 17.2044i 0.329251 + 0.646579i
\(709\) −34.5585 + 19.9524i −1.29787 + 0.749327i −0.980036 0.198818i \(-0.936290\pi\)
−0.317837 + 0.948145i \(0.602956\pi\)
\(710\) 10.6688 10.1219i 0.400394 0.379867i
\(711\) 2.45826 + 4.25783i 0.0921919 + 0.159681i
\(712\) −34.6895 + 6.41623i −1.30005 + 0.240459i
\(713\) 4.13922 + 2.38978i 0.155015 + 0.0894979i
\(714\) −14.8439 + 14.0829i −0.555519 + 0.527039i
\(715\) −14.8278 31.5507i −0.554528 1.17993i
\(716\) −21.0396 1.10777i −0.786287 0.0413993i
\(717\) −2.67385 + 4.63124i −0.0998566 + 0.172957i
\(718\) 0.897233 + 3.73925i 0.0334845 + 0.139548i
\(719\) −0.748170 + 0.431956i −0.0279020 + 0.0161093i −0.513886 0.857858i \(-0.671795\pi\)
0.485984 + 0.873968i \(0.338461\pi\)
\(720\) −3.04087 + 28.7972i −0.113327 + 1.07321i
\(721\) 27.4590 + 47.5604i 1.02263 + 1.77124i
\(722\) 5.78833 19.5324i 0.215419 0.726919i
\(723\) 5.95656i 0.221527i
\(724\) 13.7585 7.00610i 0.511331 0.260380i
\(725\) 5.01873 + 2.89757i 0.186391 + 0.107613i
\(726\) 8.75479 + 6.95734i 0.324921 + 0.258211i
\(727\) 11.2985i 0.419039i −0.977804 0.209520i \(-0.932810\pi\)
0.977804 0.209520i \(-0.0671901\pi\)
\(728\) 13.5092 + 45.2163i 0.500684 + 1.67583i
\(729\) 2.96339 0.109755
\(730\) −10.2839 42.8585i −0.380624 1.58626i
\(731\) −0.429501 0.247972i −0.0158857 0.00917159i
\(732\) −15.0180 + 7.64744i −0.555081 + 0.282658i
\(733\) −36.0138 −1.33020 −0.665100 0.746754i \(-0.731611\pi\)
−0.665100 + 0.746754i \(0.731611\pi\)
\(734\) 13.6061 + 4.03212i 0.502211 + 0.148828i
\(735\) 15.1027 + 26.1586i 0.557071 + 0.964875i
\(736\) −7.53311 + 5.77308i −0.277674 + 0.212799i
\(737\) −14.7786 + 17.0108i −0.544377 + 0.626601i
\(738\) −31.4793 + 7.55347i −1.15877 + 0.278047i
\(739\) −7.70844 4.45047i −0.283560 0.163713i 0.351474 0.936198i \(-0.385681\pi\)
−0.635034 + 0.772484i \(0.719014\pi\)
\(740\) −1.30394 + 24.7655i −0.0479339 + 0.910396i
\(741\) 4.48582 3.27776i 0.164791 0.120412i
\(742\) −8.96426 + 8.50470i −0.329088 + 0.312217i
\(743\) 8.71927 + 5.03407i 0.319879 + 0.184682i 0.651339 0.758787i \(-0.274208\pi\)
−0.331460 + 0.943469i \(0.607541\pi\)
\(744\) 5.69552 1.05345i 0.208808 0.0386215i
\(745\) −25.3221 + 14.6197i −0.927731 + 0.535626i
\(746\) 32.1391 30.4915i 1.17670 1.11637i
\(747\) 27.4342 15.8392i 1.00377 0.579524i
\(748\) −20.0409 + 20.7549i −0.732767 + 0.758873i
\(749\) 52.7810i 1.92857i
\(750\) 1.26420 4.26597i 0.0461621 0.155771i
\(751\) −16.6146 9.59247i −0.606277 0.350034i 0.165230 0.986255i \(-0.447163\pi\)
−0.771507 + 0.636221i \(0.780497\pi\)
\(752\) 23.9678 32.9552i 0.874017 1.20175i
\(753\) −19.6083 −0.714565
\(754\) 7.95410 2.83990i 0.289671 0.103423i
\(755\) 39.7791 1.44771
\(756\) 30.5895 + 19.8756i 1.11253 + 0.722870i
\(757\) −16.5521 + 28.6691i −0.601598 + 1.04200i 0.390982 + 0.920399i \(0.372136\pi\)
−0.992579 + 0.121599i \(0.961198\pi\)
\(758\) −2.91617 + 9.84044i −0.105920 + 0.357421i
\(759\) −1.30337 3.78172i −0.0473095 0.137268i
\(760\) −16.6589 5.90607i −0.604282 0.214236i
\(761\) 1.79615 + 3.11102i 0.0651104 + 0.112774i 0.896743 0.442552i \(-0.145927\pi\)
−0.831633 + 0.555326i \(0.812593\pi\)
\(762\) −8.30162 + 7.87602i −0.300736 + 0.285318i
\(763\) 5.25577 3.03442i 0.190272 0.109853i
\(764\) −14.9160 + 22.9565i −0.539643 + 0.830535i
\(765\) 15.7438 27.2690i 0.569217 0.985912i
\(766\) −26.2407 27.6586i −0.948114 0.999347i
\(767\) −44.2856 19.5735i −1.59906 0.706758i
\(768\) −2.40225 + 11.2479i −0.0866837 + 0.405872i
\(769\) 3.83982 6.65076i 0.138467 0.239833i −0.788449 0.615100i \(-0.789116\pi\)
0.926917 + 0.375267i \(0.122449\pi\)
\(770\) 34.0066 + 53.3599i 1.22551 + 1.92296i
\(771\) −19.4706 + 11.2414i −0.701217 + 0.404848i
\(772\) −0.490097 + 9.30828i −0.0176390 + 0.335012i
\(773\) 39.0156 22.5257i 1.40329 0.810192i 0.408564 0.912730i \(-0.366030\pi\)
0.994729 + 0.102538i \(0.0326963\pi\)
\(774\) −0.113776 + 0.383930i −0.00408960 + 0.0138001i
\(775\) −9.96697 −0.358024
\(776\) 7.06833 19.9372i 0.253738 0.715705i
\(777\) 12.2533 + 7.07444i 0.439584 + 0.253794i
\(778\) 18.7592 4.50127i 0.672549 0.161378i
\(779\) 19.7596i 0.707962i
\(780\) 8.26168 + 12.6534i 0.295816 + 0.453064i
\(781\) −3.85493 11.1850i −0.137940 0.400231i
\(782\) 10.0353 2.40797i 0.358861 0.0861087i
\(783\) 3.26439 5.65410i 0.116660 0.202061i
\(784\) −23.4245 52.6813i −0.836590 1.88148i
\(785\) 57.3552i 2.04709i
\(786\) 9.70593 + 2.87631i 0.346199 + 0.102595i
\(787\) −17.4940 + 10.1002i −0.623593 + 0.360032i −0.778267 0.627934i \(-0.783901\pi\)
0.154673 + 0.987966i \(0.450567\pi\)
\(788\) −0.360204 + 6.84126i −0.0128317 + 0.243710i
\(789\) 4.71841 2.72417i 0.167980 0.0969831i
\(790\) −1.90455 7.93726i −0.0677607 0.282395i
\(791\) 13.0263 + 7.52073i 0.463162 + 0.267406i
\(792\) 20.0708 + 11.8246i 0.713185 + 0.420170i
\(793\) 17.0860 38.6576i 0.606743 1.37277i
\(794\) 38.2697 36.3077i 1.35814 1.28851i
\(795\) −1.97845 + 3.42677i −0.0701683 + 0.121535i
\(796\) 10.6951 16.4603i 0.379078 0.583418i
\(797\) −3.08464 5.34275i −0.109264 0.189250i 0.806209 0.591631i \(-0.201516\pi\)
−0.915472 + 0.402381i \(0.868183\pi\)
\(798\) −7.31548 + 6.94044i −0.258965 + 0.245689i
\(799\) −38.3734 + 22.1549i −1.35755 + 0.783784i
\(800\) 7.58503 18.2804i 0.268171 0.646311i
\(801\) 30.9728i 1.09437i
\(802\) −2.83967 0.841526i −0.100272 0.0297153i
\(803\) −34.8072 6.75538i −1.22832 0.238392i
\(804\) 5.32202 8.19083i 0.187693 0.288868i
\(805\) 22.6335i 0.797725i
\(806\) −9.40520 + 11.0700i −0.331284 + 0.389924i
\(807\) 5.29461i 0.186379i
\(808\) 46.1032 8.52733i 1.62191 0.299990i
\(809\) 15.3414 + 8.85737i 0.539375 + 0.311408i 0.744826 0.667259i \(-0.232533\pi\)
−0.205450 + 0.978668i \(0.565866\pi\)
\(810\) −18.2479 5.40768i −0.641165 0.190007i
\(811\) 46.4482i 1.63102i 0.578745 + 0.815509i \(0.303543\pi\)
−0.578745 + 0.815509i \(0.696457\pi\)
\(812\) −13.6605 + 6.95620i −0.479390 + 0.244115i
\(813\) 3.68138 + 6.37634i 0.129112 + 0.223628i
\(814\) 17.6978 + 9.20912i 0.620308 + 0.322780i
\(815\) 36.0093 20.7900i 1.26135 0.728241i
\(816\) 7.35605 10.1144i 0.257513 0.354074i
\(817\) −0.211670 0.122208i −0.00740539 0.00427551i
\(818\) 16.6654 + 17.5659i 0.582691 + 0.614177i
\(819\) −41.1934 + 4.44257i −1.43941 + 0.155236i
\(820\) 53.6721 + 2.82593i 1.87431 + 0.0986857i
\(821\) 9.64453 16.7048i 0.336596 0.583002i −0.647194 0.762325i \(-0.724058\pi\)
0.983790 + 0.179324i \(0.0573909\pi\)
\(822\) −19.2294 + 4.61409i −0.670701 + 0.160935i
\(823\) −30.6000 + 17.6669i −1.06665 + 0.615830i −0.927264 0.374408i \(-0.877846\pi\)
−0.139385 + 0.990238i \(0.544513\pi\)
\(824\) −21.7908 25.5327i −0.759120 0.889473i
\(825\) 6.29690 + 5.47061i 0.219230 + 0.190462i
\(826\) 84.2595 + 24.9700i 2.93176 + 0.868816i
\(827\) 7.30107i 0.253883i −0.991910 0.126941i \(-0.959484\pi\)
0.991910 0.126941i \(-0.0405160\pi\)
\(828\) −3.78113 7.42535i −0.131403 0.258049i
\(829\) −5.44359 + 9.42857i −0.189064 + 0.327468i −0.944938 0.327249i \(-0.893879\pi\)
0.755875 + 0.654716i \(0.227212\pi\)
\(830\) −51.1417 + 12.2714i −1.77515 + 0.425948i
\(831\) −12.5591 −0.435669
\(832\) −13.1460 25.6746i −0.455756 0.890105i
\(833\) 62.6920i 2.17215i
\(834\) −0.481545 2.00686i −0.0166745 0.0694917i
\(835\) 19.2481 33.3388i 0.666109 1.15374i
\(836\) −9.87670 + 10.2286i −0.341593 + 0.353762i
\(837\) 11.2288i 0.388123i
\(838\) −4.05022 1.20027i −0.139913 0.0414625i
\(839\) 18.6343 + 32.2755i 0.643326 + 1.11427i 0.984685 + 0.174341i \(0.0557794\pi\)
−0.341359 + 0.939933i \(0.610887\pi\)
\(840\) −17.8058 20.8633i −0.614357 0.719851i
\(841\) −13.1282 22.7387i −0.452697 0.784094i
\(842\) −4.39207 18.3041i −0.151361 0.630801i
\(843\) −17.5932 10.1575i −0.605943 0.349841i
\(844\) 0.0520477 0.988528i 0.00179155 0.0340265i
\(845\) −36.1064 11.5156i −1.24210 0.396147i
\(846\) 24.6237 + 25.9543i 0.846581 + 0.892327i
\(847\) 50.4028 7.11343i 1.73186 0.244420i
\(848\) 4.44234 6.10810i 0.152551 0.209753i
\(849\) −9.99895 + 5.77290i −0.343163 + 0.198125i
\(850\) −15.6125 + 14.8121i −0.535505 + 0.508051i
\(851\) −3.56814 6.18020i −0.122314 0.211854i
\(852\) 2.32712 + 4.56998i 0.0797258 + 0.156565i
\(853\) 25.5782 0.875780 0.437890 0.899028i \(-0.355726\pi\)
0.437890 + 0.899028i \(0.355726\pi\)
\(854\) −21.7967 + 73.5516i −0.745868 + 2.51688i
\(855\) 7.75896 13.4389i 0.265351 0.459601i
\(856\) 5.86752 + 31.7229i 0.200548 + 1.08427i
\(857\) 6.28218i 0.214595i −0.994227 0.107298i \(-0.965780\pi\)
0.994227 0.107298i \(-0.0342198\pi\)
\(858\) 12.0180 1.83150i 0.410289 0.0625265i
\(859\) 20.6695i 0.705234i 0.935768 + 0.352617i \(0.114708\pi\)
−0.935768 + 0.352617i \(0.885292\pi\)
\(860\) 0.362219 0.557471i 0.0123516 0.0190096i
\(861\) 15.3319 26.5555i 0.522508 0.905011i
\(862\) 5.65904 + 1.67703i 0.192748 + 0.0571200i
\(863\) 23.1284 0.787302 0.393651 0.919260i \(-0.371212\pi\)
0.393651 + 0.919260i \(0.371212\pi\)
\(864\) −20.5947 8.54528i −0.700646 0.290716i
\(865\) −0.512533 0.887734i −0.0174267 0.0301838i
\(866\) −32.8524 34.6276i −1.11637 1.17669i
\(867\) −1.19415 + 0.689443i −0.0405555 + 0.0234147i
\(868\) 14.3649 22.1083i 0.487578 0.750404i
\(869\) −6.44618 1.25107i −0.218672 0.0424398i
\(870\) −3.56121 + 3.37863i −0.120736 + 0.114546i
\(871\) 2.62668 + 24.3557i 0.0890016 + 0.825260i
\(872\) −2.82154 + 2.40805i −0.0955495 + 0.0815467i
\(873\) 16.0836 + 9.28585i 0.544346 + 0.314278i
\(874\) 4.94566 1.18671i 0.167289 0.0401411i
\(875\) −10.1265 17.5397i −0.342339 0.592949i
\(876\) 15.3485 + 0.808126i 0.518578 + 0.0273040i
\(877\) 11.4072 + 19.7578i 0.385193 + 0.667173i 0.991796 0.127831i \(-0.0408016\pi\)
−0.606603 + 0.795005i \(0.707468\pi\)
\(878\) 0.392133 1.32323i 0.0132338 0.0446568i
\(879\) 8.83401i 0.297964i
\(880\) −26.3708 28.2904i −0.888961 0.953670i
\(881\) 3.31125 5.73526i 0.111559 0.193226i −0.804840 0.593492i \(-0.797749\pi\)
0.916399 + 0.400266i \(0.131082\pi\)
\(882\) 49.2214 11.8107i 1.65737 0.397686i
\(883\) 8.42610i 0.283561i −0.989898 0.141780i \(-0.954717\pi\)
0.989898 0.141780i \(-0.0452827\pi\)
\(884\) 1.71881 + 31.3176i 0.0578100 + 1.05332i
\(885\) 28.1417 0.945972
\(886\) −9.69694 40.4123i −0.325775 1.35768i
\(887\) 20.7325 35.9098i 0.696131 1.20573i −0.273667 0.961824i \(-0.588237\pi\)
0.969798 0.243909i \(-0.0784300\pi\)
\(888\) −8.15103 2.88978i −0.273531 0.0969747i
\(889\) 52.0888i 1.74700i
\(890\) −14.6106 + 49.3027i −0.489750 + 1.65263i
\(891\) −10.0414 + 11.5581i −0.336400 + 0.387210i
\(892\) −0.0503070 + 0.955467i −0.00168440 + 0.0319914i
\(893\) −18.9115 + 10.9185i −0.632848 + 0.365375i
\(894\) −2.37908 9.91491i −0.0795684 0.331604i
\(895\) −15.3552 + 26.5959i −0.513267 + 0.889004i
\(896\) 29.6169 + 43.1715i 0.989431 + 1.44226i
\(897\) −3.97732 1.75791i −0.132799 0.0586948i
\(898\) −16.0713 + 15.2474i −0.536306 + 0.508812i
\(899\) −4.08645 2.35931i −0.136291 0.0786874i
\(900\) 14.5707 + 9.46737i 0.485690 + 0.315579i
\(901\) −7.11235 + 4.10631i −0.236947 + 0.136801i
\(902\) 19.9582 38.3550i 0.664534 1.27708i
\(903\) −0.189646 0.328477i −0.00631103 0.0109310i
\(904\) −8.66524 3.07208i −0.288202 0.102176i
\(905\) 22.5052i 0.748098i
\(906\) −3.94140 + 13.3000i −0.130944 + 0.441863i
\(907\) 11.2203 + 6.47804i 0.372564 + 0.215100i 0.674578 0.738204i \(-0.264326\pi\)
−0.302014 + 0.953303i \(0.597659\pi\)
\(908\) −0.649599 + 0.999763i −0.0215577 + 0.0331783i
\(909\) 41.1636i 1.36531i
\(910\) 67.6676 + 12.3602i 2.24316 + 0.409738i
\(911\) 36.2061i 1.19956i −0.800165 0.599780i \(-0.795255\pi\)
0.800165 0.599780i \(-0.204745\pi\)
\(912\) 3.62527 4.98465i 0.120045 0.165058i
\(913\) −8.06097 + 41.5343i −0.266779 + 1.37459i
\(914\) 14.9866 50.5712i 0.495711 1.67275i
\(915\) 24.5653i 0.812105i
\(916\) −12.1744 23.9080i −0.402254 0.789944i
\(917\) 39.9062 23.0399i 1.31782 0.760843i
\(918\) 16.6873 + 17.5890i 0.550763 + 0.580524i
\(919\) −2.85284 4.94127i −0.0941066 0.162997i 0.815129 0.579280i \(-0.196666\pi\)
−0.909235 + 0.416282i \(0.863333\pi\)
\(920\) 2.51610 + 13.6034i 0.0829535 + 0.448490i
\(921\) 8.57710 14.8560i 0.282625 0.489521i
\(922\) −26.1750 27.5894i −0.862027 0.908608i
\(923\) −11.7635 5.19929i −0.387201 0.171137i
\(924\) −21.2101 + 6.08296i −0.697761 + 0.200115i
\(925\) 12.8878 + 7.44076i 0.423747 + 0.244651i
\(926\) −46.4816 + 11.1533i −1.52748 + 0.366519i
\(927\) 25.5225 14.7354i 0.838269 0.483975i
\(928\) 7.43707 5.69948i 0.244134 0.187095i
\(929\) −29.7125 + 17.1545i −0.974834 + 0.562821i −0.900707 0.434428i \(-0.856951\pi\)
−0.0741278 + 0.997249i \(0.523617\pi\)
\(930\) 2.39886 8.09479i 0.0786616 0.265439i
\(931\) 30.8964i 1.01259i
\(932\) −9.90816 19.4576i −0.324553 0.637354i
\(933\) 3.59967 6.23480i 0.117848 0.204118i
\(934\) 11.4671 + 47.7895i 0.375215 + 1.56372i
\(935\) 13.7031 + 39.7593i 0.448140 + 1.30027i
\(936\) 24.2646 7.24948i 0.793113 0.236957i
\(937\) 21.3738i 0.698252i −0.937076 0.349126i \(-0.886479\pi\)
0.937076 0.349126i \(-0.113521\pi\)
\(938\) −10.3744 43.2358i −0.338737 1.41170i
\(939\) −8.19201 4.72966i −0.267336 0.154347i
\(940\) −26.9529 52.9298i −0.879106 1.72638i
\(941\) 2.75398 0.0897772 0.0448886 0.998992i \(-0.485707\pi\)
0.0448886 + 0.998992i \(0.485707\pi\)
\(942\) 19.1765 + 5.68287i 0.624803 + 0.185158i
\(943\) −13.3938 + 7.73293i −0.436163 + 0.251819i
\(944\) −53.4183 5.64077i −1.73862 0.183591i
\(945\) 46.0496 26.5868i 1.49799 0.864868i
\(946\) −0.287433 0.451012i −0.00934524 0.0146637i
\(947\) 6.51543 11.2851i 0.211723 0.366715i −0.740531 0.672022i \(-0.765426\pi\)
0.952254 + 0.305307i \(0.0987592\pi\)
\(948\) 2.84250 + 0.149662i 0.0923200 + 0.00486080i
\(949\) −31.1224 + 22.7409i −1.01028 + 0.738202i
\(950\) −7.69428 + 7.29982i −0.249635 + 0.236837i
\(951\) 2.23012 3.86268i 0.0723166 0.125256i
\(952\) −10.3540 55.9790i −0.335574 1.81429i
\(953\) −31.3723 + 18.1128i −1.01625 + 0.586730i −0.913015 0.407927i \(-0.866252\pi\)
−0.103232 + 0.994657i \(0.532919\pi\)
\(954\) 4.56390 + 4.81052i 0.147762 + 0.155746i
\(955\) 19.9525 + 34.5588i 0.645649 + 1.11830i
\(956\) −6.75149 13.2585i −0.218359 0.428811i
\(957\) 1.28676 + 3.73350i 0.0415950 + 0.120687i
\(958\) −4.34314 1.28707i −0.140320 0.0415834i
\(959\) −45.0075 + 77.9553i −1.45337 + 2.51731i
\(960\) 13.0211 + 10.5600i 0.420254 + 0.340823i
\(961\) −22.8845 −0.738210
\(962\) 20.4256 7.29268i 0.658548 0.235125i
\(963\) −28.3240 −0.912728
\(964\) 13.8967 + 9.02945i 0.447584 + 0.290819i
\(965\) 11.7665 + 6.79339i 0.378777 + 0.218687i
\(966\) 7.56741 + 2.24257i 0.243477 + 0.0721535i
\(967\) 18.6913i 0.601070i −0.953771 0.300535i \(-0.902835\pi\)
0.953771 0.300535i \(-0.0971653\pi\)
\(968\) −29.5028 + 9.87853i −0.948256 + 0.317508i
\(969\) −5.80418 + 3.35105i −0.186457 + 0.107651i
\(970\) −21.2215 22.3683i −0.681383 0.718202i
\(971\) −12.7604 + 7.36722i −0.409501 + 0.236425i −0.690575 0.723261i \(-0.742643\pi\)
0.281074 + 0.959686i \(0.409309\pi\)
\(972\) 16.5015 25.3965i 0.529284 0.814593i
\(973\) −8.13573 4.69717i −0.260820 0.150584i
\(974\) −5.26314 5.54754i −0.168642 0.177755i
\(975\) 9.01576 0.972319i 0.288735 0.0311391i
\(976\) 4.92392 46.6298i 0.157611 1.49258i
\(977\) −16.0358 9.25826i −0.513030 0.296198i 0.221048 0.975263i \(-0.429052\pi\)
−0.734078 + 0.679065i \(0.762385\pi\)
\(978\) 3.38317 + 14.0995i 0.108182 + 0.450851i
\(979\) 31.2280 + 27.1302i 0.998050 + 0.867084i
\(980\) −83.9223 4.41865i −2.68080 0.141149i
\(981\) −1.62837 2.82042i −0.0519899 0.0900491i
\(982\) −4.00902 + 13.5282i −0.127933 + 0.431702i
\(983\) −40.9928 −1.30747 −0.653734 0.756724i \(-0.726799\pi\)
−0.653734 + 0.756724i \(0.726799\pi\)
\(984\) −6.26278 + 17.6651i −0.199650 + 0.563142i
\(985\) 8.64796 + 4.99290i 0.275547 + 0.159087i
\(986\) −9.90734 + 2.37727i −0.315514 + 0.0757076i
\(987\) −33.8876 −1.07865
\(988\) 0.847079 + 15.4342i 0.0269492 + 0.491027i
\(989\) 0.191304i 0.00608311i
\(990\) 28.6347 18.2491i 0.910070 0.579993i
\(991\) 38.0381 + 21.9613i 1.20832 + 0.697623i 0.962392 0.271665i \(-0.0875744\pi\)
0.245927 + 0.969288i \(0.420908\pi\)
\(992\) −6.17603 + 14.8846i −0.196089 + 0.472588i
\(993\) 1.93856i 0.0615184i
\(994\) 22.3818 + 6.63275i 0.709907 + 0.210378i
\(995\) −14.3064 24.7794i −0.453543 0.785559i
\(996\) 0.964310 18.3149i 0.0305553 0.580329i
\(997\) 12.5472 7.24411i 0.397373 0.229423i −0.287977 0.957637i \(-0.592983\pi\)
0.685350 + 0.728214i \(0.259649\pi\)
\(998\) −33.9241 + 8.14008i −1.07385 + 0.257670i
\(999\) 8.38274 14.5193i 0.265218 0.459371i
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 572.2.s.a.43.6 160
4.3 odd 2 inner 572.2.s.a.43.47 yes 160
11.10 odd 2 inner 572.2.s.a.43.75 yes 160
13.10 even 6 inner 572.2.s.a.439.34 yes 160
44.43 even 2 inner 572.2.s.a.43.34 yes 160
52.23 odd 6 inner 572.2.s.a.439.75 yes 160
143.10 odd 6 inner 572.2.s.a.439.47 yes 160
572.439 even 6 inner 572.2.s.a.439.6 yes 160
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
572.2.s.a.43.6 160 1.1 even 1 trivial
572.2.s.a.43.34 yes 160 44.43 even 2 inner
572.2.s.a.43.47 yes 160 4.3 odd 2 inner
572.2.s.a.43.75 yes 160 11.10 odd 2 inner
572.2.s.a.439.6 yes 160 572.439 even 6 inner
572.2.s.a.439.34 yes 160 13.10 even 6 inner
572.2.s.a.439.47 yes 160 143.10 odd 6 inner
572.2.s.a.439.75 yes 160 52.23 odd 6 inner