Properties

Label 108.2.l.a.23.2
Level $108$
Weight $2$
Character 108.23
Analytic conductor $0.862$
Analytic rank $0$
Dimension $96$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [108,2,Mod(11,108)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(108, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([9, 13]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("108.11");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 108.l (of order \(18\), degree \(6\), 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: \(0.862384341830\)
Analytic rank: \(0\)
Dimension: \(96\)
Relative dimension: \(16\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 23.2
Character \(\chi\) \(=\) 108.23
Dual form 108.2.l.a.47.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.33631 - 0.462897i) q^{2} +(-0.808457 + 1.53180i) q^{3} +(1.57145 + 1.23715i) q^{4} +(-3.39370 - 0.598401i) q^{5} +(1.78941 - 1.67272i) q^{6} +(-1.88319 - 2.24430i) q^{7} +(-1.52728 - 2.38064i) q^{8} +(-1.69280 - 2.47678i) q^{9} +O(q^{10})\) \(q+(-1.33631 - 0.462897i) q^{2} +(-0.808457 + 1.53180i) q^{3} +(1.57145 + 1.23715i) q^{4} +(-3.39370 - 0.598401i) q^{5} +(1.78941 - 1.67272i) q^{6} +(-1.88319 - 2.24430i) q^{7} +(-1.52728 - 2.38064i) q^{8} +(-1.69280 - 2.47678i) q^{9} +(4.25804 + 2.37058i) q^{10} +(0.453915 + 2.57428i) q^{11} +(-3.16551 + 1.40696i) q^{12} +(-5.09721 + 1.85523i) q^{13} +(1.47765 + 3.87081i) q^{14} +(3.66029 - 4.71467i) q^{15} +(0.938928 + 3.88824i) q^{16} +(1.15583 + 0.667320i) q^{17} +(1.11561 + 4.09334i) q^{18} +(-0.0790760 + 0.0456546i) q^{19} +(-4.59273 - 5.13887i) q^{20} +(4.96030 - 1.07025i) q^{21} +(0.585055 - 3.65015i) q^{22} +(-0.650322 - 0.545685i) q^{23} +(4.88138 - 0.414836i) q^{24} +(6.46065 + 2.35148i) q^{25} +(7.67024 - 0.119685i) q^{26} +(5.16247 - 0.590647i) q^{27} +(-0.182815 - 5.85661i) q^{28} +(-0.171418 + 0.470966i) q^{29} +(-7.07369 + 4.60593i) q^{30} +(-4.28324 + 5.10457i) q^{31} +(0.545155 - 5.63052i) q^{32} +(-4.31024 - 1.38589i) q^{33} +(-1.23565 - 1.42678i) q^{34} +(5.04800 + 8.74340i) q^{35} +(0.403996 - 5.98638i) q^{36} +(2.75869 - 4.77819i) q^{37} +(0.126804 - 0.0244046i) q^{38} +(1.27904 - 9.30777i) q^{39} +(3.75855 + 8.99308i) q^{40} +(-0.976880 - 2.68396i) q^{41} +(-7.12391 - 0.865923i) q^{42} +(-5.59737 + 0.986968i) q^{43} +(-2.47146 + 4.60692i) q^{44} +(4.26273 + 9.41842i) q^{45} +(0.616436 + 1.03024i) q^{46} +(-5.06200 + 4.24752i) q^{47} +(-6.71507 - 1.70523i) q^{48} +(-0.274941 + 1.55927i) q^{49} +(-7.54494 - 6.13293i) q^{50} +(-1.95664 + 1.23100i) q^{51} +(-10.3052 - 3.39060i) q^{52} +7.37249i q^{53} +(-7.17208 - 1.60041i) q^{54} -9.00795i q^{55} +(-2.46671 + 7.91087i) q^{56} +(-0.00600393 - 0.158038i) q^{57} +(0.447076 - 0.550009i) q^{58} +(0.528787 - 2.99890i) q^{59} +(11.5847 - 2.88057i) q^{60} +(-1.85759 + 1.55871i) q^{61} +(8.08663 - 4.83859i) q^{62} +(-2.37078 + 8.46341i) q^{63} +(-3.33485 + 7.27178i) q^{64} +(18.4086 - 3.24593i) q^{65} +(5.11830 + 3.84717i) q^{66} +(-1.64904 - 4.53069i) q^{67} +(0.990762 + 2.47860i) q^{68} +(1.36164 - 0.554998i) q^{69} +(-2.69841 - 14.0206i) q^{70} +(5.91940 - 10.2527i) q^{71} +(-3.31094 + 7.81266i) q^{72} +(-5.83049 - 10.0987i) q^{73} +(-5.89828 + 5.10816i) q^{74} +(-8.82515 + 7.99532i) q^{75} +(-0.180746 - 0.0260848i) q^{76} +(4.92266 - 5.86659i) q^{77} +(-6.01773 + 11.8460i) q^{78} +(0.576990 - 1.58527i) q^{79} +(-0.859714 - 13.7574i) q^{80} +(-3.26889 + 8.38537i) q^{81} +(0.0630204 + 4.03879i) q^{82} +(-2.02940 - 0.738640i) q^{83} +(9.11892 + 4.45478i) q^{84} +(-3.52322 - 2.95633i) q^{85} +(7.93669 + 1.27211i) q^{86} +(-0.582840 - 0.643333i) q^{87} +(5.43517 - 5.01224i) q^{88} +(-12.5801 + 7.26310i) q^{89} +(-1.33658 - 14.5591i) q^{90} +(13.7628 + 7.94593i) q^{91} +(-0.346857 - 1.66206i) q^{92} +(-4.35634 - 10.6879i) q^{93} +(8.73057 - 3.33283i) q^{94} +(0.295680 - 0.107619i) q^{95} +(8.18408 + 5.38710i) q^{96} +(1.14607 + 6.49971i) q^{97} +(1.08919 - 1.95639i) q^{98} +(5.60754 - 5.48198i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 96 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 9 q^{8} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 96 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 9 q^{8} - 12 q^{9} - 3 q^{10} - 15 q^{12} - 12 q^{13} - 21 q^{14} - 6 q^{16} - 18 q^{17} - 27 q^{18} - 27 q^{20} - 12 q^{21} - 6 q^{22} - 12 q^{24} - 12 q^{25} - 12 q^{28} - 24 q^{29} + 9 q^{30} + 24 q^{32} - 42 q^{33} - 12 q^{34} + 24 q^{36} - 6 q^{37} + 18 q^{38} - 21 q^{40} - 42 q^{41} + 54 q^{42} + 63 q^{44} - 24 q^{45} - 3 q^{46} + 69 q^{48} - 12 q^{49} + 87 q^{50} - 33 q^{52} + 78 q^{54} + 99 q^{56} - 24 q^{57} - 33 q^{58} + 102 q^{60} - 12 q^{61} + 90 q^{62} - 3 q^{64} + 12 q^{65} + 87 q^{66} + 51 q^{68} + 12 q^{69} - 21 q^{70} + 12 q^{72} - 6 q^{73} + 21 q^{74} - 18 q^{76} + 12 q^{77} - 24 q^{78} + 12 q^{81} - 12 q^{82} - 12 q^{84} - 42 q^{85} - 30 q^{86} + 18 q^{88} - 78 q^{90} - 123 q^{92} + 60 q^{93} + 21 q^{94} - 138 q^{96} - 30 q^{97} - 180 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{11}{18}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.33631 0.462897i −0.944914 0.327318i
\(3\) −0.808457 + 1.53180i −0.466763 + 0.884383i
\(4\) 1.57145 + 1.23715i 0.785726 + 0.618574i
\(5\) −3.39370 0.598401i −1.51771 0.267613i −0.648177 0.761490i \(-0.724468\pi\)
−0.869532 + 0.493877i \(0.835579\pi\)
\(6\) 1.78941 1.67272i 0.730525 0.682886i
\(7\) −1.88319 2.24430i −0.711781 0.848267i 0.282024 0.959407i \(-0.408994\pi\)
−0.993805 + 0.111140i \(0.964550\pi\)
\(8\) −1.52728 2.38064i −0.539974 0.841682i
\(9\) −1.69280 2.47678i −0.564265 0.825594i
\(10\) 4.25804 + 2.37058i 1.34651 + 0.749644i
\(11\) 0.453915 + 2.57428i 0.136861 + 0.776174i 0.973546 + 0.228491i \(0.0733791\pi\)
−0.836686 + 0.547684i \(0.815510\pi\)
\(12\) −3.16551 + 1.40696i −0.913804 + 0.406155i
\(13\) −5.09721 + 1.85523i −1.41371 + 0.514549i −0.932217 0.361899i \(-0.882128\pi\)
−0.481496 + 0.876449i \(0.659906\pi\)
\(14\) 1.47765 + 3.87081i 0.394919 + 1.03452i
\(15\) 3.66029 4.71467i 0.945082 1.21732i
\(16\) 0.938928 + 3.88824i 0.234732 + 0.972060i
\(17\) 1.15583 + 0.667320i 0.280330 + 0.161849i 0.633573 0.773683i \(-0.281588\pi\)
−0.353243 + 0.935532i \(0.614921\pi\)
\(18\) 1.11561 + 4.09334i 0.262951 + 0.964809i
\(19\) −0.0790760 + 0.0456546i −0.0181413 + 0.0104739i −0.509043 0.860741i \(-0.670001\pi\)
0.490902 + 0.871215i \(0.336667\pi\)
\(20\) −4.59273 5.13887i −1.02697 1.14909i
\(21\) 4.96030 1.07025i 1.08243 0.233547i
\(22\) 0.585055 3.65015i 0.124734 0.778215i
\(23\) −0.650322 0.545685i −0.135602 0.113783i 0.572464 0.819930i \(-0.305988\pi\)
−0.708066 + 0.706147i \(0.750432\pi\)
\(24\) 4.88138 0.414836i 0.996408 0.0846781i
\(25\) 6.46065 + 2.35148i 1.29213 + 0.470297i
\(26\) 7.67024 0.119685i 1.50426 0.0234721i
\(27\) 5.16247 0.590647i 0.993519 0.113670i
\(28\) −0.182815 5.85661i −0.0345487 1.10679i
\(29\) −0.171418 + 0.470966i −0.0318315 + 0.0874562i −0.954590 0.297922i \(-0.903707\pi\)
0.922759 + 0.385378i \(0.125929\pi\)
\(30\) −7.07369 + 4.60593i −1.29147 + 0.840924i
\(31\) −4.28324 + 5.10457i −0.769293 + 0.916807i −0.998397 0.0565946i \(-0.981976\pi\)
0.229105 + 0.973402i \(0.426420\pi\)
\(32\) 0.545155 5.63052i 0.0963706 0.995346i
\(33\) −4.31024 1.38589i −0.750317 0.241252i
\(34\) −1.23565 1.42678i −0.211912 0.244690i
\(35\) 5.04800 + 8.74340i 0.853268 + 1.47790i
\(36\) 0.403996 5.98638i 0.0673327 0.997731i
\(37\) 2.75869 4.77819i 0.453526 0.785530i −0.545076 0.838387i \(-0.683499\pi\)
0.998602 + 0.0528563i \(0.0168325\pi\)
\(38\) 0.126804 0.0244046i 0.0205702 0.00395896i
\(39\) 1.27904 9.30777i 0.204810 1.49044i
\(40\) 3.75855 + 8.99308i 0.594278 + 1.42193i
\(41\) −0.976880 2.68396i −0.152563 0.419163i 0.839741 0.542987i \(-0.182707\pi\)
−0.992304 + 0.123823i \(0.960484\pi\)
\(42\) −7.12391 0.865923i −1.09924 0.133615i
\(43\) −5.59737 + 0.986968i −0.853591 + 0.150511i −0.583289 0.812264i \(-0.698235\pi\)
−0.270302 + 0.962776i \(0.587124\pi\)
\(44\) −2.47146 + 4.60692i −0.372587 + 0.694519i
\(45\) 4.26273 + 9.41842i 0.635451 + 1.40402i
\(46\) 0.616436 + 1.03024i 0.0908886 + 0.151900i
\(47\) −5.06200 + 4.24752i −0.738369 + 0.619565i −0.932399 0.361430i \(-0.882288\pi\)
0.194030 + 0.980996i \(0.437844\pi\)
\(48\) −6.71507 1.70523i −0.969237 0.246128i
\(49\) −0.274941 + 1.55927i −0.0392772 + 0.222752i
\(50\) −7.54494 6.13293i −1.06702 0.867327i
\(51\) −1.95664 + 1.23100i −0.273984 + 0.172374i
\(52\) −10.3052 3.39060i −1.42908 0.470191i
\(53\) 7.37249i 1.01269i 0.862331 + 0.506345i \(0.169004\pi\)
−0.862331 + 0.506345i \(0.830996\pi\)
\(54\) −7.17208 1.60041i −0.975996 0.217788i
\(55\) 9.00795i 1.21463i
\(56\) −2.46671 + 7.91087i −0.329628 + 1.05713i
\(57\) −0.00600393 0.158038i −0.000795239 0.0209327i
\(58\) 0.447076 0.550009i 0.0587040 0.0722197i
\(59\) 0.528787 2.99890i 0.0688422 0.390423i −0.930845 0.365414i \(-0.880927\pi\)
0.999687 0.0250093i \(-0.00796152\pi\)
\(60\) 11.5847 2.88057i 1.49558 0.371880i
\(61\) −1.85759 + 1.55871i −0.237841 + 0.199572i −0.753915 0.656972i \(-0.771837\pi\)
0.516075 + 0.856544i \(0.327393\pi\)
\(62\) 8.08663 4.83859i 1.02700 0.614501i
\(63\) −2.37078 + 8.46341i −0.298691 + 1.06629i
\(64\) −3.33485 + 7.27178i −0.416856 + 0.908973i
\(65\) 18.4086 3.24593i 2.28330 0.402608i
\(66\) 5.11830 + 3.84717i 0.630019 + 0.473554i
\(67\) −1.64904 4.53069i −0.201462 0.553512i 0.797283 0.603606i \(-0.206270\pi\)
−0.998744 + 0.0500945i \(0.984048\pi\)
\(68\) 0.990762 + 2.47860i 0.120148 + 0.300574i
\(69\) 1.36164 0.554998i 0.163922 0.0668139i
\(70\) −2.69841 14.0206i −0.322522 1.67578i
\(71\) 5.91940 10.2527i 0.702504 1.21677i −0.265081 0.964226i \(-0.585399\pi\)
0.967585 0.252546i \(-0.0812678\pi\)
\(72\) −3.31094 + 7.81266i −0.390198 + 0.920731i
\(73\) −5.83049 10.0987i −0.682408 1.18197i −0.974244 0.225497i \(-0.927600\pi\)
0.291836 0.956468i \(-0.405734\pi\)
\(74\) −5.89828 + 5.10816i −0.685661 + 0.593812i
\(75\) −8.82515 + 7.99532i −1.01904 + 0.923220i
\(76\) −0.180746 0.0260848i −0.0207330 0.00299213i
\(77\) 4.92266 5.86659i 0.560989 0.668560i
\(78\) −6.01773 + 11.8460i −0.681373 + 1.34130i
\(79\) 0.576990 1.58527i 0.0649165 0.178357i −0.902993 0.429655i \(-0.858635\pi\)
0.967910 + 0.251298i \(0.0808575\pi\)
\(80\) −0.859714 13.7574i −0.0961190 1.53812i
\(81\) −3.26889 + 8.38537i −0.363209 + 0.931707i
\(82\) 0.0630204 + 4.03879i 0.00695944 + 0.446010i
\(83\) −2.02940 0.738640i −0.222755 0.0810763i 0.228232 0.973607i \(-0.426706\pi\)
−0.450987 + 0.892531i \(0.648928\pi\)
\(84\) 9.11892 + 4.45478i 0.994956 + 0.486056i
\(85\) −3.52322 2.95633i −0.382147 0.320659i
\(86\) 7.93669 + 1.27211i 0.855836 + 0.137175i
\(87\) −0.582840 0.643333i −0.0624870 0.0689725i
\(88\) 5.43517 5.01224i 0.579391 0.534307i
\(89\) −12.5801 + 7.26310i −1.33348 + 0.769887i −0.985832 0.167737i \(-0.946354\pi\)
−0.347652 + 0.937624i \(0.613021\pi\)
\(90\) −1.33658 14.5591i −0.140888 1.53467i
\(91\) 13.7628 + 7.94593i 1.44273 + 0.832960i
\(92\) −0.346857 1.66206i −0.0361624 0.173282i
\(93\) −4.35634 10.6879i −0.451731 1.10828i
\(94\) 8.73057 3.33283i 0.900490 0.343755i
\(95\) 0.295680 0.107619i 0.0303361 0.0110414i
\(96\) 8.18408 + 5.38710i 0.835284 + 0.549819i
\(97\) 1.14607 + 6.49971i 0.116366 + 0.659946i 0.986065 + 0.166362i \(0.0532021\pi\)
−0.869698 + 0.493583i \(0.835687\pi\)
\(98\) 1.08919 1.95639i 0.110024 0.197626i
\(99\) 5.60754 5.48198i 0.563579 0.550959i
\(100\) 7.24347 + 11.6880i 0.724347 + 1.16880i
\(101\) −5.29995 6.31623i −0.527365 0.628489i 0.434941 0.900459i \(-0.356769\pi\)
−0.962306 + 0.271970i \(0.912325\pi\)
\(102\) 3.18450 0.739276i 0.315313 0.0731992i
\(103\) 15.8523 + 2.79519i 1.56197 + 0.275418i 0.886769 0.462214i \(-0.152945\pi\)
0.675203 + 0.737632i \(0.264056\pi\)
\(104\) 12.2015 + 9.30115i 1.19646 + 0.912053i
\(105\) −17.4742 + 0.663851i −1.70531 + 0.0647852i
\(106\) 3.41270 9.85194i 0.331471 0.956905i
\(107\) −9.71808 −0.939482 −0.469741 0.882804i \(-0.655653\pi\)
−0.469741 + 0.882804i \(0.655653\pi\)
\(108\) 8.84330 + 5.45857i 0.850947 + 0.525251i
\(109\) −4.69860 −0.450044 −0.225022 0.974354i \(-0.572245\pi\)
−0.225022 + 0.974354i \(0.572245\pi\)
\(110\) −4.16975 + 12.0374i −0.397570 + 1.14772i
\(111\) 5.08893 + 8.08872i 0.483020 + 0.767747i
\(112\) 6.95821 9.42955i 0.657489 0.891009i
\(113\) 0.555886 + 0.0980178i 0.0522934 + 0.00922074i 0.199734 0.979850i \(-0.435992\pi\)
−0.147440 + 0.989071i \(0.547103\pi\)
\(114\) −0.0651322 + 0.213967i −0.00610019 + 0.0200399i
\(115\) 1.88046 + 2.24104i 0.175354 + 0.208978i
\(116\) −0.852030 + 0.528032i −0.0791090 + 0.0490266i
\(117\) 13.2236 + 9.48415i 1.22252 + 0.876810i
\(118\) −2.09480 + 3.76269i −0.192842 + 0.346383i
\(119\) −0.678988 3.85073i −0.0622427 0.352996i
\(120\) −16.8142 1.51319i −1.53492 0.138135i
\(121\) 3.91574 1.42521i 0.355977 0.129565i
\(122\) 3.20384 1.22304i 0.290062 0.110729i
\(123\) 4.90104 + 0.673481i 0.441911 + 0.0607258i
\(124\) −13.0460 + 2.72258i −1.17157 + 0.244495i
\(125\) −5.59652 3.23116i −0.500568 0.289003i
\(126\) 7.08579 10.2123i 0.631252 0.909785i
\(127\) −9.63141 + 5.56070i −0.854649 + 0.493432i −0.862217 0.506539i \(-0.830924\pi\)
0.00756758 + 0.999971i \(0.497591\pi\)
\(128\) 7.82248 8.17367i 0.691416 0.722457i
\(129\) 3.01340 9.37195i 0.265315 0.825154i
\(130\) −26.1021 4.18371i −2.28931 0.366935i
\(131\) −2.37648 1.99411i −0.207634 0.174226i 0.533040 0.846090i \(-0.321049\pi\)
−0.740675 + 0.671864i \(0.765494\pi\)
\(132\) −5.05879 7.51027i −0.440311 0.653685i
\(133\) 0.251378 + 0.0914942i 0.0217973 + 0.00793355i
\(134\) 0.106382 + 6.81774i 0.00919004 + 0.588963i
\(135\) −17.8733 1.08475i −1.53829 0.0933604i
\(136\) −0.176631 3.77080i −0.0151459 0.323343i
\(137\) −5.90609 + 16.2268i −0.504591 + 1.38635i 0.382156 + 0.924098i \(0.375182\pi\)
−0.886747 + 0.462255i \(0.847041\pi\)
\(138\) −2.07647 + 0.111353i −0.176761 + 0.00947899i
\(139\) −7.19280 + 8.57205i −0.610085 + 0.727071i −0.979332 0.202260i \(-0.935171\pi\)
0.369246 + 0.929332i \(0.379616\pi\)
\(140\) −2.88418 + 19.9850i −0.243758 + 1.68904i
\(141\) −2.41393 11.1879i −0.203290 0.942191i
\(142\) −12.6561 + 10.9607i −1.06208 + 0.919803i
\(143\) −7.08959 12.2795i −0.592862 1.02687i
\(144\) 8.04091 8.90752i 0.670075 0.742293i
\(145\) 0.863567 1.49574i 0.0717153 0.124215i
\(146\) 3.11669 + 16.1939i 0.257939 + 1.34022i
\(147\) −2.16620 1.68175i −0.178665 0.138709i
\(148\) 10.2465 4.09580i 0.842256 0.336672i
\(149\) −6.24250 17.1511i −0.511406 1.40508i −0.879773 0.475395i \(-0.842305\pi\)
0.368367 0.929680i \(-0.379917\pi\)
\(150\) 15.4941 6.59910i 1.26509 0.538814i
\(151\) 18.9571 3.34265i 1.54271 0.272021i 0.663396 0.748269i \(-0.269115\pi\)
0.879311 + 0.476248i \(0.158004\pi\)
\(152\) 0.229458 + 0.118524i 0.0186115 + 0.00961357i
\(153\) −0.303782 3.99238i −0.0245593 0.322765i
\(154\) −9.29382 + 5.56091i −0.748918 + 0.448111i
\(155\) 17.5906 14.7603i 1.41291 1.18557i
\(156\) 13.5250 13.0444i 1.08287 1.04438i
\(157\) −2.92425 + 16.5843i −0.233381 + 1.32357i 0.612617 + 0.790380i \(0.290117\pi\)
−0.845997 + 0.533187i \(0.820994\pi\)
\(158\) −1.50485 + 1.85132i −0.119720 + 0.147283i
\(159\) −11.2932 5.96034i −0.895605 0.472686i
\(160\) −5.21940 + 18.7821i −0.412630 + 1.48485i
\(161\) 2.48715i 0.196015i
\(162\) 8.24981 9.69230i 0.648166 0.761499i
\(163\) 8.02606i 0.628650i 0.949315 + 0.314325i \(0.101778\pi\)
−0.949315 + 0.314325i \(0.898222\pi\)
\(164\) 1.78533 5.42625i 0.139411 0.423719i
\(165\) 13.7983 + 7.28254i 1.07420 + 0.566945i
\(166\) 2.36999 + 1.92645i 0.183947 + 0.149522i
\(167\) −0.226727 + 1.28583i −0.0175447 + 0.0995008i −0.992323 0.123676i \(-0.960532\pi\)
0.974778 + 0.223177i \(0.0716427\pi\)
\(168\) −10.1236 10.1741i −0.781054 0.784948i
\(169\) 12.5811 10.5568i 0.967779 0.812063i
\(170\) 3.33964 + 5.58147i 0.256139 + 0.428079i
\(171\) 0.246936 + 0.118570i 0.0188837 + 0.00906729i
\(172\) −10.0170 5.37381i −0.763792 0.409749i
\(173\) 11.2769 1.98842i 0.857366 0.151177i 0.272350 0.962198i \(-0.412199\pi\)
0.585016 + 0.811022i \(0.301088\pi\)
\(174\) 0.481059 + 1.12949i 0.0364690 + 0.0856262i
\(175\) −6.88921 18.9280i −0.520776 1.43082i
\(176\) −9.58322 + 4.18199i −0.722363 + 0.315230i
\(177\) 4.16620 + 3.23447i 0.313151 + 0.243118i
\(178\) 20.1729 3.88249i 1.51203 0.291005i
\(179\) −10.7064 + 18.5441i −0.800237 + 1.38605i 0.119222 + 0.992868i \(0.461960\pi\)
−0.919460 + 0.393184i \(0.871373\pi\)
\(180\) −4.95330 + 20.0742i −0.369197 + 1.49625i
\(181\) 7.31416 + 12.6685i 0.543657 + 0.941641i 0.998690 + 0.0511670i \(0.0162941\pi\)
−0.455033 + 0.890474i \(0.650373\pi\)
\(182\) −14.7132 16.9890i −1.09061 1.25931i
\(183\) −0.885836 4.10560i −0.0654829 0.303495i
\(184\) −0.305855 + 2.38159i −0.0225479 + 0.175573i
\(185\) −12.2214 + 14.5650i −0.898539 + 1.07084i
\(186\) 0.874041 + 16.2988i 0.0640878 + 1.19509i
\(187\) −1.19322 + 3.27834i −0.0872568 + 0.239736i
\(188\) −13.2095 + 0.412337i −0.963403 + 0.0300728i
\(189\) −11.0475 10.4739i −0.803590 0.761861i
\(190\) −0.444937 + 0.00694269i −0.0322791 + 0.000503676i
\(191\) 1.80607 + 0.657357i 0.130683 + 0.0475647i 0.406534 0.913636i \(-0.366737\pi\)
−0.275851 + 0.961200i \(0.588960\pi\)
\(192\) −8.44280 10.9872i −0.609307 0.792935i
\(193\) −4.79657 4.02480i −0.345264 0.289711i 0.453621 0.891195i \(-0.350132\pi\)
−0.798885 + 0.601484i \(0.794577\pi\)
\(194\) 1.47718 9.21615i 0.106056 0.661681i
\(195\) −9.91044 + 30.8224i −0.709701 + 2.20724i
\(196\) −2.36110 + 2.11017i −0.168650 + 0.150726i
\(197\) 13.1022 7.56456i 0.933494 0.538953i 0.0455788 0.998961i \(-0.485487\pi\)
0.887915 + 0.460008i \(0.152153\pi\)
\(198\) −10.0310 + 4.72991i −0.712873 + 0.336140i
\(199\) −22.4427 12.9573i −1.59092 0.918517i −0.993150 0.116849i \(-0.962721\pi\)
−0.597769 0.801669i \(-0.703946\pi\)
\(200\) −4.26918 18.9718i −0.301876 1.34151i
\(201\) 8.27326 + 1.13688i 0.583551 + 0.0801893i
\(202\) 4.15861 + 10.8938i 0.292599 + 0.766484i
\(203\) 1.37980 0.502208i 0.0968433 0.0352481i
\(204\) −4.59769 0.486194i −0.321903 0.0340404i
\(205\) 1.70916 + 9.69310i 0.119373 + 0.676996i
\(206\) −19.8897 11.0732i −1.38578 0.771507i
\(207\) −0.250680 + 2.53444i −0.0174234 + 0.176156i
\(208\) −11.9995 18.0773i −0.832017 1.25343i
\(209\) −0.153421 0.182841i −0.0106124 0.0126473i
\(210\) 23.6582 + 7.20164i 1.63257 + 0.496960i
\(211\) 17.1836 + 3.02993i 1.18297 + 0.208589i 0.730323 0.683102i \(-0.239369\pi\)
0.452645 + 0.891691i \(0.350481\pi\)
\(212\) −9.12087 + 11.5855i −0.626424 + 0.795697i
\(213\) 10.9195 + 17.3562i 0.748189 + 1.18923i
\(214\) 12.9864 + 4.49847i 0.887730 + 0.307509i
\(215\) 19.5864 1.33578
\(216\) −9.29064 11.3879i −0.632148 0.774847i
\(217\) 19.5224 1.32526
\(218\) 6.27879 + 2.17497i 0.425253 + 0.147307i
\(219\) 20.1829 0.766755i 1.36383 0.0518125i
\(220\) 11.1442 14.1556i 0.751340 0.954369i
\(221\) −7.12956 1.25713i −0.479586 0.0845639i
\(222\) −3.05616 13.1647i −0.205116 0.883556i
\(223\) 11.3619 + 13.5406i 0.760850 + 0.906746i 0.997901 0.0647513i \(-0.0206254\pi\)
−0.237051 + 0.971497i \(0.576181\pi\)
\(224\) −13.6632 + 9.37988i −0.912914 + 0.626720i
\(225\) −5.11245 19.9822i −0.340830 1.33215i
\(226\) −0.697465 0.388300i −0.0463947 0.0258294i
\(227\) −1.62005 9.18776i −0.107527 0.609813i −0.990181 0.139791i \(-0.955357\pi\)
0.882654 0.470022i \(-0.155754\pi\)
\(228\) 0.186082 0.255777i 0.0123236 0.0169393i
\(229\) −15.8029 + 5.75180i −1.04429 + 0.380090i −0.806504 0.591228i \(-0.798643\pi\)
−0.237784 + 0.971318i \(0.576421\pi\)
\(230\) −1.47551 3.86519i −0.0972920 0.254863i
\(231\) 5.00667 + 12.2834i 0.329414 + 0.808188i
\(232\) 1.38300 0.311213i 0.0907985 0.0204321i
\(233\) 15.2659 + 8.81379i 1.00010 + 0.577410i 0.908279 0.418365i \(-0.137397\pi\)
0.0918250 + 0.995775i \(0.470730\pi\)
\(234\) −13.2806 18.7949i −0.868179 1.22866i
\(235\) 19.7206 11.3857i 1.28643 0.742722i
\(236\) 4.54105 4.05844i 0.295597 0.264182i
\(237\) 1.96183 + 2.16545i 0.127435 + 0.140661i
\(238\) −0.875153 + 5.46007i −0.0567277 + 0.353924i
\(239\) 7.05862 + 5.92289i 0.456584 + 0.383120i 0.841872 0.539677i \(-0.181453\pi\)
−0.385288 + 0.922796i \(0.625898\pi\)
\(240\) 21.7685 + 9.80533i 1.40515 + 0.632932i
\(241\) −5.85117 2.12965i −0.376907 0.137183i 0.146618 0.989193i \(-0.453161\pi\)
−0.523525 + 0.852010i \(0.675383\pi\)
\(242\) −5.89238 + 0.0919433i −0.378776 + 0.00591034i
\(243\) −10.2019 11.7865i −0.654453 0.756102i
\(244\) −4.84747 + 0.151315i −0.310328 + 0.00968692i
\(245\) 1.86613 5.12716i 0.119223 0.327562i
\(246\) −6.23755 3.16865i −0.397692 0.202026i
\(247\) 0.318368 0.379416i 0.0202572 0.0241416i
\(248\) 18.6938 + 2.40074i 1.18706 + 0.152447i
\(249\) 2.77212 2.51146i 0.175676 0.159157i
\(250\) 5.98300 + 6.90844i 0.378398 + 0.436928i
\(251\) −14.1765 24.5545i −0.894814 1.54986i −0.834034 0.551713i \(-0.813974\pi\)
−0.0607805 0.998151i \(-0.519359\pi\)
\(252\) −14.1961 + 10.3668i −0.894268 + 0.653049i
\(253\) 1.10955 1.92181i 0.0697571 0.120823i
\(254\) 15.4446 2.97247i 0.969079 0.186509i
\(255\) 7.37687 3.00679i 0.461958 0.188292i
\(256\) −14.2368 + 7.30156i −0.889802 + 0.456347i
\(257\) 5.64266 + 15.5031i 0.351979 + 0.967056i 0.981734 + 0.190261i \(0.0609334\pi\)
−0.629754 + 0.776795i \(0.716844\pi\)
\(258\) −8.36509 + 11.1289i −0.520788 + 0.692858i
\(259\) −15.9189 + 2.80693i −0.989151 + 0.174414i
\(260\) 32.9439 + 17.6733i 2.04310 + 1.09605i
\(261\) 1.45666 0.372686i 0.0901647 0.0230687i
\(262\) 2.25266 + 3.76481i 0.139170 + 0.232591i
\(263\) −18.5512 + 15.5663i −1.14391 + 0.959859i −0.999560 0.0296674i \(-0.990555\pi\)
−0.144355 + 0.989526i \(0.546111\pi\)
\(264\) 3.28364 + 12.3777i 0.202094 + 0.761798i
\(265\) 4.41171 25.0200i 0.271009 1.53697i
\(266\) −0.293567 0.238627i −0.0179998 0.0146312i
\(267\) −0.955153 25.1420i −0.0584544 1.53866i
\(268\) 3.01375 9.15986i 0.184094 0.559528i
\(269\) 12.1956i 0.743578i −0.928317 0.371789i \(-0.878745\pi\)
0.928317 0.371789i \(-0.121255\pi\)
\(270\) 23.3822 + 9.72307i 1.42299 + 0.591727i
\(271\) 25.0009i 1.51870i 0.650683 + 0.759349i \(0.274483\pi\)
−0.650683 + 0.759349i \(0.725517\pi\)
\(272\) −1.50946 + 5.12072i −0.0915243 + 0.310489i
\(273\) −23.2981 + 14.6578i −1.41007 + 0.887130i
\(274\) 15.4037 18.9502i 0.930573 1.14482i
\(275\) −3.12079 + 17.6989i −0.188191 + 1.06728i
\(276\) 2.82636 + 0.812392i 0.170127 + 0.0489002i
\(277\) −6.69358 + 5.61658i −0.402178 + 0.337468i −0.821335 0.570446i \(-0.806770\pi\)
0.419157 + 0.907914i \(0.362326\pi\)
\(278\) 13.5798 8.12539i 0.814462 0.487329i
\(279\) 19.8935 + 1.96766i 1.19100 + 0.117801i
\(280\) 13.1051 25.3710i 0.783182 1.51621i
\(281\) −21.5554 + 3.80080i −1.28589 + 0.226737i −0.774478 0.632601i \(-0.781987\pi\)
−0.511409 + 0.859338i \(0.670876\pi\)
\(282\) −1.95308 + 16.0679i −0.116304 + 0.956830i
\(283\) −10.2956 28.2869i −0.612010 1.68148i −0.725737 0.687972i \(-0.758501\pi\)
0.113727 0.993512i \(-0.463721\pi\)
\(284\) 21.9862 8.78846i 1.30464 0.521499i
\(285\) −0.0741946 + 0.539926i −0.00439491 + 0.0319825i
\(286\) 3.78974 + 19.6910i 0.224092 + 1.16435i
\(287\) −4.18396 + 7.24682i −0.246971 + 0.427766i
\(288\) −14.8684 + 8.18110i −0.876129 + 0.482076i
\(289\) −7.60937 13.1798i −0.447610 0.775283i
\(290\) −1.84637 + 1.59903i −0.108422 + 0.0938984i
\(291\) −10.8828 3.49918i −0.637960 0.205126i
\(292\) 3.33126 23.0828i 0.194947 1.35082i
\(293\) 8.50981 10.1416i 0.497148 0.592478i −0.457872 0.889018i \(-0.651388\pi\)
0.955021 + 0.296540i \(0.0958327\pi\)
\(294\) 2.11624 + 3.25007i 0.123421 + 0.189548i
\(295\) −3.58909 + 9.86094i −0.208965 + 0.574126i
\(296\) −15.5884 + 0.730189i −0.906059 + 0.0424413i
\(297\) 3.86381 + 13.0215i 0.224201 + 0.755587i
\(298\) 0.402716 + 25.8089i 0.0233287 + 1.49507i
\(299\) 4.32720 + 1.57497i 0.250249 + 0.0910831i
\(300\) −23.7597 + 1.64625i −1.37177 + 0.0950465i
\(301\) 12.7560 + 10.7036i 0.735243 + 0.616942i
\(302\) −26.8799 4.30837i −1.54676 0.247919i
\(303\) 13.9600 3.01204i 0.801979 0.173037i
\(304\) −0.251763 0.264600i −0.0144396 0.0151759i
\(305\) 7.23685 4.17820i 0.414381 0.239243i
\(306\) −1.44211 + 5.47568i −0.0824401 + 0.313024i
\(307\) −11.4064 6.58546i −0.650995 0.375852i 0.137842 0.990454i \(-0.455983\pi\)
−0.788837 + 0.614602i \(0.789317\pi\)
\(308\) 14.9936 3.12902i 0.854338 0.178292i
\(309\) −17.0975 + 22.0227i −0.972645 + 1.25283i
\(310\) −30.3390 + 11.5817i −1.72314 + 0.657795i
\(311\) −5.80348 + 2.11230i −0.329085 + 0.119777i −0.501279 0.865286i \(-0.667137\pi\)
0.172193 + 0.985063i \(0.444915\pi\)
\(312\) −24.1118 + 11.1706i −1.36506 + 0.632412i
\(313\) −3.72249 21.1113i −0.210407 1.19328i −0.888701 0.458488i \(-0.848391\pi\)
0.678293 0.734791i \(-0.262720\pi\)
\(314\) 11.5845 20.8081i 0.653752 1.17427i
\(315\) 13.1102 27.3036i 0.738678 1.53838i
\(316\) 2.86792 1.77735i 0.161333 0.0999838i
\(317\) −9.45061 11.2628i −0.530799 0.632582i 0.432300 0.901730i \(-0.357702\pi\)
−0.963099 + 0.269148i \(0.913258\pi\)
\(318\) 12.3321 + 13.1924i 0.691552 + 0.739795i
\(319\) −1.29021 0.227498i −0.0722378 0.0127375i
\(320\) 15.6689 22.6827i 0.875919 1.26800i
\(321\) 7.85665 14.8861i 0.438515 0.830862i
\(322\) 1.15129 3.32361i 0.0641591 0.185217i
\(323\) −0.121865 −0.00678074
\(324\) −15.5108 + 9.13311i −0.861713 + 0.507395i
\(325\) −37.2939 −2.06869
\(326\) 3.71524 10.7253i 0.205768 0.594020i
\(327\) 3.79862 7.19730i 0.210064 0.398011i
\(328\) −4.89755 + 6.42474i −0.270422 + 0.354747i
\(329\) 19.0655 + 3.36176i 1.05111 + 0.185340i
\(330\) −15.0678 16.1189i −0.829456 0.887319i
\(331\) −17.0491 20.3184i −0.937106 1.11680i −0.992971 0.118361i \(-0.962236\pi\)
0.0558649 0.998438i \(-0.482208\pi\)
\(332\) −2.27529 3.67140i −0.124873 0.201494i
\(333\) −16.5044 + 1.25583i −0.904438 + 0.0688192i
\(334\) 0.898186 1.61332i 0.0491466 0.0882770i
\(335\) 2.88516 + 16.3626i 0.157633 + 0.893983i
\(336\) 8.81874 + 18.2819i 0.481102 + 0.997361i
\(337\) 14.4992 5.27727i 0.789820 0.287471i 0.0845588 0.996418i \(-0.473052\pi\)
0.705261 + 0.708948i \(0.250830\pi\)
\(338\) −21.6990 + 8.28342i −1.18027 + 0.450559i
\(339\) −0.599553 + 0.772261i −0.0325633 + 0.0419435i
\(340\) −1.87915 9.00449i −0.101911 0.488337i
\(341\) −15.0848 8.70922i −0.816888 0.471631i
\(342\) −0.275097 0.272752i −0.0148756 0.0147488i
\(343\) −13.7433 + 7.93471i −0.742069 + 0.428434i
\(344\) 10.8983 + 11.8179i 0.587600 + 0.637180i
\(345\) −4.95309 + 1.06869i −0.266665 + 0.0575365i
\(346\) −15.9899 2.56289i −0.859620 0.137782i
\(347\) 16.4887 + 13.8357i 0.885162 + 0.742739i 0.967234 0.253888i \(-0.0817093\pi\)
−0.0820721 + 0.996626i \(0.526154\pi\)
\(348\) −0.120008 1.73203i −0.00643311 0.0928464i
\(349\) −11.8787 4.32349i −0.635851 0.231431i 0.00392469 0.999992i \(-0.498751\pi\)
−0.639776 + 0.768561i \(0.720973\pi\)
\(350\) 0.444436 + 28.4826i 0.0237561 + 1.52246i
\(351\) −25.2184 + 12.5883i −1.34606 + 0.671911i
\(352\) 14.7420 1.15240i 0.785751 0.0614231i
\(353\) 3.82687 10.5142i 0.203684 0.559617i −0.795225 0.606314i \(-0.792647\pi\)
0.998909 + 0.0466973i \(0.0148696\pi\)
\(354\) −4.07011 6.25078i −0.216324 0.332225i
\(355\) −26.2239 + 31.2524i −1.39182 + 1.65871i
\(356\) −28.7545 4.14978i −1.52399 0.219938i
\(357\) 6.44747 + 2.07308i 0.341236 + 0.109719i
\(358\) 22.8912 19.8247i 1.20983 1.04777i
\(359\) 16.1699 + 28.0070i 0.853413 + 1.47816i 0.878109 + 0.478460i \(0.158805\pi\)
−0.0246959 + 0.999695i \(0.507862\pi\)
\(360\) 15.9114 24.5325i 0.838607 1.29298i
\(361\) −9.49583 + 16.4473i −0.499781 + 0.865645i
\(362\) −3.90978 20.3147i −0.205494 1.06772i
\(363\) −0.982572 + 7.15034i −0.0515717 + 0.375296i
\(364\) 11.7972 + 29.5132i 0.618343 + 1.54691i
\(365\) 13.7439 + 37.7610i 0.719387 + 1.97650i
\(366\) −0.716719 + 5.89641i −0.0374635 + 0.308210i
\(367\) −0.656339 + 0.115730i −0.0342606 + 0.00604107i −0.190752 0.981638i \(-0.561093\pi\)
0.156492 + 0.987679i \(0.449982\pi\)
\(368\) 1.51115 3.04097i 0.0787741 0.158521i
\(369\) −4.99391 + 6.96290i −0.259973 + 0.362474i
\(370\) 23.0737 13.8060i 1.19955 0.717741i
\(371\) 16.5461 13.8838i 0.859031 0.720813i
\(372\) 6.37670 22.1849i 0.330616 1.15023i
\(373\) 3.61725 20.5144i 0.187294 1.06220i −0.735678 0.677331i \(-0.763136\pi\)
0.922972 0.384867i \(-0.125753\pi\)
\(374\) 3.11204 3.82855i 0.160920 0.197969i
\(375\) 9.47402 5.96048i 0.489236 0.307798i
\(376\) 17.8429 + 5.56363i 0.920177 + 0.286923i
\(377\) 2.71864i 0.140017i
\(378\) 9.91462 + 19.1102i 0.509953 + 0.982922i
\(379\) 19.1904i 0.985744i −0.870102 0.492872i \(-0.835947\pi\)
0.870102 0.492872i \(-0.164053\pi\)
\(380\) 0.597788 + 0.196682i 0.0306659 + 0.0100896i
\(381\) −0.731274 19.2489i −0.0374643 0.986153i
\(382\) −2.10919 1.71446i −0.107915 0.0877194i
\(383\) 1.37744 7.81186i 0.0703840 0.399168i −0.929180 0.369629i \(-0.879485\pi\)
0.999564 0.0295390i \(-0.00940393\pi\)
\(384\) 6.19625 + 18.5905i 0.316201 + 0.948692i
\(385\) −20.2166 + 16.9637i −1.03033 + 0.864552i
\(386\) 4.54664 + 7.59870i 0.231418 + 0.386763i
\(387\) 11.9197 + 12.1927i 0.605913 + 0.619791i
\(388\) −6.24010 + 11.6319i −0.316793 + 0.590518i
\(389\) −12.1585 + 2.14387i −0.616461 + 0.108699i −0.473154 0.880980i \(-0.656885\pi\)
−0.143307 + 0.989678i \(0.545774\pi\)
\(390\) 27.5110 36.6008i 1.39307 1.85335i
\(391\) −0.387517 1.06469i −0.0195976 0.0538438i
\(392\) 4.13195 1.72690i 0.208695 0.0872215i
\(393\) 4.97585 2.02814i 0.250998 0.102306i
\(394\) −21.0102 + 4.04364i −1.05848 + 0.203715i
\(395\) −2.90676 + 5.03465i −0.146255 + 0.253321i
\(396\) 15.5940 1.67731i 0.783628 0.0842880i
\(397\) 11.5959 + 20.0847i 0.581982 + 1.00802i 0.995244 + 0.0974099i \(0.0310558\pi\)
−0.413263 + 0.910612i \(0.635611\pi\)
\(398\) 23.9925 + 27.7036i 1.20263 + 1.38866i
\(399\) −0.343379 + 0.311091i −0.0171904 + 0.0155740i
\(400\) −3.07705 + 27.3284i −0.153852 + 1.36642i
\(401\) 4.36829 5.20593i 0.218142 0.259972i −0.645865 0.763452i \(-0.723503\pi\)
0.864007 + 0.503480i \(0.167947\pi\)
\(402\) −10.5294 5.34889i −0.525158 0.266778i
\(403\) 12.3624 33.9655i 0.615816 1.69194i
\(404\) −0.514503 16.4825i −0.0255975 0.820034i
\(405\) 16.1114 26.5013i 0.800583 1.31686i
\(406\) −2.07632 + 0.0323984i −0.103046 + 0.00160790i
\(407\) 13.5526 + 4.93275i 0.671778 + 0.244507i
\(408\) 5.91889 + 2.77796i 0.293029 + 0.137530i
\(409\) 13.9170 + 11.6777i 0.688149 + 0.577426i 0.918375 0.395712i \(-0.129502\pi\)
−0.230226 + 0.973137i \(0.573946\pi\)
\(410\) 2.20294 13.7442i 0.108796 0.678776i
\(411\) −20.0814 22.1656i −0.990542 1.09335i
\(412\) 21.4531 + 24.0041i 1.05692 + 1.18260i
\(413\) −7.72625 + 4.46075i −0.380184 + 0.219499i
\(414\) 1.50817 3.27076i 0.0741225 0.160749i
\(415\) 6.44516 + 3.72111i 0.316380 + 0.182662i
\(416\) 7.66717 + 29.7114i 0.375914 + 1.45672i
\(417\) −7.31556 17.9480i −0.358244 0.878919i
\(418\) 0.120382 + 0.315350i 0.00588809 + 0.0154243i
\(419\) 4.62462 1.68322i 0.225927 0.0822309i −0.226576 0.973993i \(-0.572753\pi\)
0.452504 + 0.891763i \(0.350531\pi\)
\(420\) −28.2811 20.5750i −1.37998 1.00395i
\(421\) −2.04359 11.5898i −0.0995984 0.564851i −0.993241 0.116071i \(-0.962970\pi\)
0.893642 0.448780i \(-0.148141\pi\)
\(422\) −21.5601 12.0032i −1.04953 0.584305i
\(423\) 19.0891 + 5.34728i 0.928145 + 0.259994i
\(424\) 17.5512 11.2598i 0.852362 0.546826i
\(425\) 5.89823 + 7.02924i 0.286106 + 0.340968i
\(426\) −6.55768 28.2478i −0.317721 1.36861i
\(427\) 6.99642 + 1.23366i 0.338581 + 0.0597009i
\(428\) −15.2715 12.0227i −0.738176 0.581139i
\(429\) 24.5414 0.932336i 1.18487 0.0450136i
\(430\) −26.1735 9.06649i −1.26220 0.437225i
\(431\) −4.40894 −0.212371 −0.106186 0.994346i \(-0.533864\pi\)
−0.106186 + 0.994346i \(0.533864\pi\)
\(432\) 7.14377 + 19.5184i 0.343705 + 0.939078i
\(433\) 28.5232 1.37074 0.685369 0.728196i \(-0.259641\pi\)
0.685369 + 0.728196i \(0.259641\pi\)
\(434\) −26.0880 9.03684i −1.25226 0.433782i
\(435\) 1.59301 + 2.53205i 0.0763792 + 0.121402i
\(436\) −7.38363 5.81287i −0.353612 0.278386i
\(437\) 0.0763379 + 0.0134604i 0.00365174 + 0.000643900i
\(438\) −27.3255 8.31796i −1.30566 0.397448i
\(439\) 3.10907 + 3.70524i 0.148388 + 0.176842i 0.835118 0.550071i \(-0.185399\pi\)
−0.686730 + 0.726912i \(0.740955\pi\)
\(440\) −21.4447 + 13.7576i −1.02233 + 0.655870i
\(441\) 4.32738 1.95855i 0.206066 0.0932643i
\(442\) 8.94538 + 4.98017i 0.425488 + 0.236883i
\(443\) 1.26185 + 7.15628i 0.0599521 + 0.340005i 0.999999 0.00103872i \(-0.000330635\pi\)
−0.940047 + 0.341044i \(0.889220\pi\)
\(444\) −2.00992 + 19.0068i −0.0953865 + 0.902023i
\(445\) 47.0392 17.1209i 2.22987 0.811607i
\(446\) −8.91515 23.3538i −0.422144 1.10584i
\(447\) 31.3188 + 4.30371i 1.48133 + 0.203558i
\(448\) 22.6003 6.20976i 1.06776 0.293384i
\(449\) −5.50442 3.17798i −0.259769 0.149978i 0.364460 0.931219i \(-0.381254\pi\)
−0.624229 + 0.781241i \(0.714587\pi\)
\(450\) −2.41788 + 29.0690i −0.113980 + 1.37032i
\(451\) 6.46583 3.73305i 0.304464 0.175782i
\(452\) 0.752287 + 0.841744i 0.0353846 + 0.0395923i
\(453\) −10.2057 + 31.7408i −0.479507 + 1.49131i
\(454\) −2.08810 + 13.0276i −0.0979992 + 0.611417i
\(455\) −41.9518 35.2017i −1.96673 1.65028i
\(456\) −0.367061 + 0.255661i −0.0171892 + 0.0119724i
\(457\) 0.840235 + 0.305821i 0.0393045 + 0.0143057i 0.361598 0.932334i \(-0.382231\pi\)
−0.322293 + 0.946640i \(0.604454\pi\)
\(458\) 23.7801 0.371060i 1.11117 0.0173385i
\(459\) 6.36110 + 2.76233i 0.296911 + 0.128935i
\(460\) 0.182549 + 5.84810i 0.00851140 + 0.272669i
\(461\) −4.48102 + 12.3115i −0.208702 + 0.573404i −0.999239 0.0390104i \(-0.987579\pi\)
0.790537 + 0.612415i \(0.209802\pi\)
\(462\) −1.00452 18.7320i −0.0467345 0.871491i
\(463\) 0.866856 1.03308i 0.0402862 0.0480112i −0.745525 0.666478i \(-0.767801\pi\)
0.785811 + 0.618466i \(0.212246\pi\)
\(464\) −1.99218 0.224310i −0.0924846 0.0104133i
\(465\) 8.38848 + 38.8782i 0.389006 + 1.80294i
\(466\) −16.3201 18.8445i −0.756016 0.872955i
\(467\) 9.81172 + 16.9944i 0.454032 + 0.786407i 0.998632 0.0522890i \(-0.0166517\pi\)
−0.544600 + 0.838696i \(0.683318\pi\)
\(468\) 9.04689 + 31.2634i 0.418193 + 1.44515i
\(469\) −7.06278 + 12.2331i −0.326129 + 0.564872i
\(470\) −31.6233 + 6.08623i −1.45867 + 0.280737i
\(471\) −23.0396 17.8870i −1.06161 0.824190i
\(472\) −7.94689 + 3.32130i −0.365785 + 0.152875i
\(473\) −5.08146 13.9612i −0.233646 0.641937i
\(474\) −1.61924 3.80184i −0.0743741 0.174624i
\(475\) −0.618239 + 0.109012i −0.0283667 + 0.00500182i
\(476\) 3.69693 6.89125i 0.169448 0.315860i
\(477\) 18.2600 12.4801i 0.836070 0.571426i
\(478\) −6.69083 11.1822i −0.306031 0.511464i
\(479\) −14.6017 + 12.2523i −0.667170 + 0.559822i −0.912226 0.409687i \(-0.865638\pi\)
0.245056 + 0.969509i \(0.421194\pi\)
\(480\) −24.5507 23.1796i −1.12058 1.05800i
\(481\) −5.19697 + 29.4735i −0.236962 + 1.34388i
\(482\) 6.83317 + 5.55437i 0.311242 + 0.252994i
\(483\) −3.80981 2.01075i −0.173352 0.0914925i
\(484\) 7.91661 + 2.60470i 0.359846 + 0.118395i
\(485\) 22.7439i 1.03275i
\(486\) 8.17701 + 20.4728i 0.370917 + 0.928666i
\(487\) 12.7440i 0.577486i −0.957407 0.288743i \(-0.906763\pi\)
0.957407 0.288743i \(-0.0932373\pi\)
\(488\) 6.54777 + 2.04168i 0.296404 + 0.0924224i
\(489\) −12.2943 6.48872i −0.555967 0.293430i
\(490\) −4.86708 + 5.98765i −0.219872 + 0.270494i
\(491\) 4.29474 24.3567i 0.193819 1.09920i −0.720272 0.693692i \(-0.755983\pi\)
0.914091 0.405510i \(-0.132906\pi\)
\(492\) 6.86855 + 7.12165i 0.309658 + 0.321069i
\(493\) −0.512415 + 0.429967i −0.0230780 + 0.0193648i
\(494\) −0.601068 + 0.359646i −0.0270433 + 0.0161812i
\(495\) −22.3107 + 15.2486i −1.00279 + 0.685375i
\(496\) −23.8694 11.8614i −1.07177 0.532595i
\(497\) −34.1576 + 6.02290i −1.53218 + 0.270164i
\(498\) −4.86697 + 2.07289i −0.218094 + 0.0928883i
\(499\) 13.5128 + 37.1262i 0.604917 + 1.66199i 0.741167 + 0.671320i \(0.234273\pi\)
−0.136251 + 0.990674i \(0.543505\pi\)
\(500\) −4.79726 12.0013i −0.214540 0.536716i
\(501\) −1.78634 1.38684i −0.0798076 0.0619595i
\(502\) 7.57806 + 39.3747i 0.338225 + 1.75738i
\(503\) 18.2058 31.5334i 0.811757 1.40600i −0.0998757 0.995000i \(-0.531845\pi\)
0.911633 0.411005i \(-0.134822\pi\)
\(504\) 23.7691 7.28200i 1.05876 0.324366i
\(505\) 14.2068 + 24.6069i 0.632194 + 1.09499i
\(506\) −2.37231 + 2.05452i −0.105462 + 0.0913345i
\(507\) 5.99959 + 27.8064i 0.266451 + 1.23493i
\(508\) −22.0147 3.17711i −0.976745 0.140961i
\(509\) −2.32891 + 2.77549i −0.103227 + 0.123021i −0.815184 0.579201i \(-0.803364\pi\)
0.711957 + 0.702223i \(0.247809\pi\)
\(510\) −11.2496 + 0.603272i −0.498142 + 0.0267133i
\(511\) −11.6846 + 32.1032i −0.516897 + 1.42016i
\(512\) 22.4047 3.16697i 0.990157 0.139961i
\(513\) −0.381262 + 0.282397i −0.0168331 + 0.0124681i
\(514\) −0.364019 23.3289i −0.0160562 1.02899i
\(515\) −52.1252 18.9720i −2.29691 0.836008i
\(516\) 16.3299 10.9996i 0.718884 0.484228i
\(517\) −13.2320 11.1030i −0.581944 0.488309i
\(518\) 22.5719 + 3.61787i 0.991751 + 0.158960i
\(519\) −6.07102 + 18.8814i −0.266488 + 0.828803i
\(520\) −35.8424 38.8667i −1.57179 1.70442i
\(521\) 18.0443 10.4179i 0.790534 0.456415i −0.0496162 0.998768i \(-0.515800\pi\)
0.840151 + 0.542353i \(0.182466\pi\)
\(522\) −2.11906 0.176257i −0.0927487 0.00771458i
\(523\) 19.0780 + 11.0147i 0.834223 + 0.481639i 0.855296 0.518139i \(-0.173375\pi\)
−0.0210733 + 0.999778i \(0.506708\pi\)
\(524\) −1.26753 6.07371i −0.0553722 0.265331i
\(525\) 34.5634 + 4.74957i 1.50847 + 0.207288i
\(526\) 31.9957 12.2141i 1.39508 0.532561i
\(527\) −8.35708 + 3.04173i −0.364040 + 0.132500i
\(528\) 1.34166 18.0605i 0.0583883 0.785982i
\(529\) −3.86876 21.9408i −0.168207 0.953949i
\(530\) −17.4771 + 31.3924i −0.759157 + 1.36360i
\(531\) −8.32274 + 3.76683i −0.361176 + 0.163467i
\(532\) 0.281837 + 0.454771i 0.0122192 + 0.0197168i
\(533\) 9.95873 + 11.8684i 0.431361 + 0.514075i
\(534\) −10.3618 + 34.0396i −0.448397 + 1.47304i
\(535\) 32.9802 + 5.81531i 1.42586 + 0.251418i
\(536\) −8.26738 + 10.8454i −0.357096 + 0.468449i
\(537\) −19.7501 31.3922i −0.852279 1.35467i
\(538\) −5.64530 + 16.2971i −0.243386 + 0.702617i
\(539\) −4.13879 −0.178270
\(540\) −26.7451 23.8166i −1.15093 1.02490i
\(541\) −13.2610 −0.570135 −0.285067 0.958507i \(-0.592016\pi\)
−0.285067 + 0.958507i \(0.592016\pi\)
\(542\) 11.5729 33.4090i 0.497097 1.43504i
\(543\) −25.3187 + 0.961867i −1.08653 + 0.0412777i
\(544\) 4.38747 6.14415i 0.188111 0.263428i
\(545\) 15.9456 + 2.81165i 0.683036 + 0.120438i
\(546\) 37.9186 8.80273i 1.62277 0.376722i
\(547\) −9.19354 10.9564i −0.393087 0.468463i 0.532812 0.846234i \(-0.321135\pi\)
−0.925899 + 0.377770i \(0.876691\pi\)
\(548\) −29.3561 + 18.1930i −1.25403 + 0.777167i
\(549\) 7.00510 + 1.96228i 0.298971 + 0.0837482i
\(550\) 12.3631 22.2066i 0.527165 0.946893i
\(551\) −0.00794673 0.0450681i −0.000338542 0.00191997i
\(552\) −3.40084 2.39392i −0.144749 0.101892i
\(553\) −4.64441 + 1.69043i −0.197500 + 0.0718842i
\(554\) 11.5446 4.40706i 0.490483 0.187238i
\(555\) −12.4300 30.4959i −0.527625 1.29448i
\(556\) −21.9080 + 4.57201i −0.929108 + 0.193896i
\(557\) 6.40425 + 3.69750i 0.271357 + 0.156668i 0.629504 0.776997i \(-0.283258\pi\)
−0.358147 + 0.933665i \(0.616591\pi\)
\(558\) −25.6731 11.8381i −1.08683 0.501145i
\(559\) 26.6999 15.4152i 1.12929 0.651994i
\(560\) −29.2567 + 27.8373i −1.23632 + 1.17634i
\(561\) −4.05708 4.47816i −0.171290 0.189068i
\(562\) 30.5641 + 4.89888i 1.28927 + 0.206647i
\(563\) 16.2270 + 13.6161i 0.683887 + 0.573850i 0.917139 0.398567i \(-0.130492\pi\)
−0.233252 + 0.972416i \(0.574937\pi\)
\(564\) 10.0477 20.5676i 0.423085 0.866054i
\(565\) −1.82786 0.665286i −0.0768985 0.0279888i
\(566\) 0.664189 + 42.5660i 0.0279180 + 1.78918i
\(567\) 24.9753 8.45491i 1.04886 0.355073i
\(568\) −33.4485 + 1.56679i −1.40347 + 0.0657409i
\(569\) −1.52428 + 4.18793i −0.0639012 + 0.175567i −0.967534 0.252741i \(-0.918668\pi\)
0.903633 + 0.428308i \(0.140890\pi\)
\(570\) 0.349077 0.687165i 0.0146212 0.0287822i
\(571\) −1.38240 + 1.64748i −0.0578516 + 0.0689449i −0.794194 0.607664i \(-0.792107\pi\)
0.736343 + 0.676609i \(0.236551\pi\)
\(572\) 4.05064 28.0676i 0.169366 1.17356i
\(573\) −2.46707 + 2.23509i −0.103063 + 0.0933723i
\(574\) 8.94560 7.74727i 0.373382 0.323365i
\(575\) −2.91833 5.05470i −0.121703 0.210796i
\(576\) 23.6558 4.04995i 0.985659 0.168748i
\(577\) −16.0706 + 27.8351i −0.669028 + 1.15879i 0.309148 + 0.951014i \(0.399956\pi\)
−0.978176 + 0.207777i \(0.933377\pi\)
\(578\) 4.06759 + 21.1347i 0.169189 + 0.879087i
\(579\) 10.0430 4.09349i 0.417372 0.170119i
\(580\) 3.20751 1.28213i 0.133185 0.0532374i
\(581\) 2.16402 + 5.94559i 0.0897785 + 0.246664i
\(582\) 12.9230 + 9.71360i 0.535676 + 0.402642i
\(583\) −18.9789 + 3.34648i −0.786024 + 0.138597i
\(584\) −15.1366 + 29.3038i −0.626356 + 1.21260i
\(585\) −39.2014 40.0993i −1.62078 1.65790i
\(586\) −16.0663 + 9.61316i −0.663691 + 0.397116i
\(587\) −27.6154 + 23.1721i −1.13981 + 0.956414i −0.999433 0.0336838i \(-0.989276\pi\)
−0.140378 + 0.990098i \(0.544832\pi\)
\(588\) −1.32350 5.32270i −0.0545804 0.219505i
\(589\) 0.105655 0.599198i 0.00435343 0.0246895i
\(590\) 9.36073 11.5159i 0.385375 0.474102i
\(591\) 0.994798 + 26.1855i 0.0409205 + 1.07713i
\(592\) 21.1690 + 6.24008i 0.870040 + 0.256466i
\(593\) 4.09387i 0.168115i −0.996461 0.0840576i \(-0.973212\pi\)
0.996461 0.0840576i \(-0.0267880\pi\)
\(594\) 0.864377 19.1894i 0.0354658 0.787350i
\(595\) 13.4745i 0.552402i
\(596\) 11.4087 34.6751i 0.467318 1.42035i
\(597\) 37.9918 23.9022i 1.55490 0.978251i
\(598\) −5.05344 4.10770i −0.206651 0.167977i
\(599\) 1.46823 8.32677i 0.0599904 0.340223i −0.940009 0.341149i \(-0.889184\pi\)
1.00000 0.000926605i \(0.000294948\pi\)
\(600\) 32.5124 + 8.79839i 1.32731 + 0.359193i
\(601\) 22.3724 18.7727i 0.912590 0.765754i −0.0600202 0.998197i \(-0.519116\pi\)
0.972610 + 0.232443i \(0.0746721\pi\)
\(602\) −12.0913 20.2080i −0.492806 0.823616i
\(603\) −8.43004 + 11.7538i −0.343298 + 0.478653i
\(604\) 33.9255 + 18.1999i 1.38041 + 0.740544i
\(605\) −14.1417 + 2.49356i −0.574942 + 0.101378i
\(606\) −20.0491 2.43700i −0.814439 0.0989965i
\(607\) −13.2715 36.4633i −0.538675 1.48000i −0.848495 0.529203i \(-0.822491\pi\)
0.309820 0.950795i \(-0.399731\pi\)
\(608\) 0.213951 + 0.470128i 0.00867684 + 0.0190662i
\(609\) −0.346232 + 2.51959i −0.0140300 + 0.102099i
\(610\) −11.6048 + 2.23345i −0.469863 + 0.0904299i
\(611\) 17.9220 31.0417i 0.725045 1.25581i
\(612\) 4.46178 6.64966i 0.180357 0.268797i
\(613\) −0.677216 1.17297i −0.0273525 0.0473759i 0.852025 0.523501i \(-0.175374\pi\)
−0.879378 + 0.476125i \(0.842041\pi\)
\(614\) 12.1940 + 14.0802i 0.492111 + 0.568230i
\(615\) −16.2296 5.21838i −0.654442 0.210425i
\(616\) −21.4845 2.75913i −0.865634 0.111169i
\(617\) −14.2746 + 17.0118i −0.574675 + 0.684871i −0.972583 0.232554i \(-0.925292\pi\)
0.397909 + 0.917425i \(0.369736\pi\)
\(618\) 33.0419 21.5147i 1.32914 0.865450i
\(619\) 0.757138 2.08022i 0.0304320 0.0836111i −0.923546 0.383487i \(-0.874723\pi\)
0.953978 + 0.299876i \(0.0969453\pi\)
\(620\) 45.9034 1.43288i 1.84353 0.0575459i
\(621\) −3.67958 2.43297i −0.147656 0.0976319i
\(622\) 8.73303 0.136268i 0.350163 0.00546386i
\(623\) 39.9913 + 14.5556i 1.60222 + 0.583160i
\(624\) 37.3918 3.76612i 1.49687 0.150766i
\(625\) −9.27445 7.78219i −0.370978 0.311287i
\(626\) −4.79794 + 29.9343i −0.191764 + 1.19642i
\(627\) 0.404109 0.0871916i 0.0161386 0.00348210i
\(628\) −25.1125 + 22.4436i −1.00210 + 0.895599i
\(629\) 6.37717 3.68186i 0.254274 0.146805i
\(630\) −30.1581 + 30.4174i −1.20153 + 1.21186i
\(631\) 10.3534 + 5.97752i 0.412161 + 0.237961i 0.691718 0.722168i \(-0.256854\pi\)
−0.279557 + 0.960129i \(0.590187\pi\)
\(632\) −4.65517 + 1.04754i −0.185173 + 0.0416689i
\(633\) −18.5334 + 23.8722i −0.736638 + 0.948835i
\(634\) 7.41544 + 19.4253i 0.294505 + 0.771475i
\(635\) 36.0136 13.1079i 1.42916 0.520171i
\(636\) −10.3728 23.3377i −0.411310 0.925400i
\(637\) −1.49137 8.45799i −0.0590903 0.335118i
\(638\) 1.61881 + 0.901242i 0.0640893 + 0.0356805i
\(639\) −35.4140 + 2.69467i −1.40096 + 0.106600i
\(640\) −31.4383 + 23.0580i −1.24271 + 0.911447i
\(641\) 8.66598 + 10.3277i 0.342286 + 0.407920i 0.909536 0.415625i \(-0.136437\pi\)
−0.567250 + 0.823545i \(0.691993\pi\)
\(642\) −17.3897 + 16.2557i −0.686315 + 0.641559i
\(643\) −27.1966 4.79550i −1.07253 0.189116i −0.390620 0.920552i \(-0.627739\pi\)
−0.681910 + 0.731436i \(0.738850\pi\)
\(644\) −3.07697 + 3.90844i −0.121250 + 0.154014i
\(645\) −15.8348 + 30.0024i −0.623493 + 1.18134i
\(646\) 0.162849 + 0.0564109i 0.00640722 + 0.00221946i
\(647\) 15.2634 0.600064 0.300032 0.953929i \(-0.403003\pi\)
0.300032 + 0.953929i \(0.403003\pi\)
\(648\) 24.9550 5.02476i 0.980325 0.197391i
\(649\) 7.96003 0.312458
\(650\) 49.8362 + 17.2632i 1.95474 + 0.677119i
\(651\) −15.7830 + 29.9043i −0.618584 + 1.17204i
\(652\) −9.92943 + 12.6126i −0.388866 + 0.493947i
\(653\) −30.1302 5.31277i −1.17909 0.207905i −0.450448 0.892803i \(-0.648736\pi\)
−0.728639 + 0.684898i \(0.759847\pi\)
\(654\) −8.40774 + 7.85946i −0.328769 + 0.307329i
\(655\) 6.87180 + 8.18949i 0.268503 + 0.319990i
\(656\) 9.51864 6.31838i 0.371641 0.246691i
\(657\) −15.1425 + 31.5359i −0.590764 + 1.23033i
\(658\) −23.9212 13.3177i −0.932547 0.519178i
\(659\) −7.25464 41.1431i −0.282601 1.60271i −0.713732 0.700418i \(-0.752997\pi\)
0.431132 0.902289i \(-0.358114\pi\)
\(660\) 12.6739 + 28.5148i 0.493330 + 1.10994i
\(661\) −30.7435 + 11.1897i −1.19578 + 0.435230i −0.861751 0.507331i \(-0.830632\pi\)
−0.334033 + 0.942561i \(0.608410\pi\)
\(662\) 13.3776 + 35.0437i 0.519937 + 1.36201i
\(663\) 7.68961 9.90469i 0.298640 0.384666i
\(664\) 1.34102 + 5.95936i 0.0520416 + 0.231268i
\(665\) −0.798352 0.460929i −0.0309588 0.0178741i
\(666\) 22.6364 + 5.96167i 0.877142 + 0.231010i
\(667\) 0.368476 0.212740i 0.0142674 0.00823731i
\(668\) −1.94706 + 1.74013i −0.0753339 + 0.0673277i
\(669\) −29.9271 + 6.45714i −1.15705 + 0.249647i
\(670\) 3.71871 23.2010i 0.143666 0.896334i
\(671\) −4.85574 4.07445i −0.187454 0.157292i
\(672\) −3.32192 28.5125i −0.128146 1.09989i
\(673\) −26.6470 9.69872i −1.02717 0.373858i −0.227166 0.973856i \(-0.572946\pi\)
−0.800002 + 0.599998i \(0.795168\pi\)
\(674\) −21.8182 + 0.340446i −0.840407 + 0.0131135i
\(675\) 34.7418 + 8.32351i 1.33721 + 0.320372i
\(676\) 32.8310 1.02482i 1.26273 0.0394163i
\(677\) 13.7737 37.8429i 0.529366 1.45442i −0.330453 0.943822i \(-0.607201\pi\)
0.859819 0.510599i \(-0.170576\pi\)
\(678\) 1.15867 0.754450i 0.0444983 0.0289745i
\(679\) 12.4290 14.8124i 0.476983 0.568446i
\(680\) −1.65702 + 12.9026i −0.0635437 + 0.494794i
\(681\) 15.3835 + 4.94632i 0.589498 + 0.189543i
\(682\) 16.1265 + 18.6209i 0.617516 + 0.713032i
\(683\) 2.35647 + 4.08153i 0.0901678 + 0.156175i 0.907582 0.419876i \(-0.137926\pi\)
−0.817414 + 0.576051i \(0.804593\pi\)
\(684\) 0.241359 + 0.491824i 0.00922861 + 0.0188054i
\(685\) 29.7536 51.5348i 1.13683 1.96904i
\(686\) 22.0383 4.24150i 0.841426 0.161941i
\(687\) 3.96541 28.8570i 0.151290 1.10096i
\(688\) −9.09310 20.8372i −0.346671 0.794412i
\(689\) −13.6777 37.5792i −0.521079 1.43165i
\(690\) 7.11356 + 0.864666i 0.270809 + 0.0329173i
\(691\) 47.8656 8.44000i 1.82089 0.321073i 0.844251 0.535947i \(-0.180045\pi\)
0.976642 + 0.214875i \(0.0689344\pi\)
\(692\) 20.1811 + 10.8265i 0.767169 + 0.411561i
\(693\) −22.8633 2.26140i −0.868505 0.0859033i
\(694\) −15.6296 26.1214i −0.593291 0.991553i
\(695\) 29.5397 24.7868i 1.12051 0.940216i
\(696\) −0.641382 + 2.37008i −0.0243115 + 0.0898375i
\(697\) 0.661948 3.75409i 0.0250731 0.142196i
\(698\) 13.8723 + 11.2761i 0.525074 + 0.426808i
\(699\) −25.8428 + 16.2587i −0.977463 + 0.614961i
\(700\) 12.5906 38.2674i 0.475881 1.44637i
\(701\) 5.10945i 0.192981i 0.995334 + 0.0964906i \(0.0307618\pi\)
−0.995334 + 0.0964906i \(0.969238\pi\)
\(702\) 39.5267 5.14828i 1.49184 0.194309i
\(703\) 0.503788i 0.0190007i
\(704\) −20.2333 5.28406i −0.762572 0.199151i
\(705\) 1.49731 + 39.4128i 0.0563919 + 1.48437i
\(706\) −9.98090 + 12.2789i −0.375636 + 0.462121i
\(707\) −4.19471 + 23.7894i −0.157758 + 0.894692i
\(708\) 2.54546 + 10.2370i 0.0956644 + 0.384731i
\(709\) −7.00392 + 5.87699i −0.263038 + 0.220715i −0.764762 0.644313i \(-0.777144\pi\)
0.501725 + 0.865027i \(0.332699\pi\)
\(710\) 49.5099 29.6240i 1.85807 1.11177i
\(711\) −4.90309 + 1.25446i −0.183880 + 0.0470458i
\(712\) 36.5040 + 18.8558i 1.36805 + 0.706650i
\(713\) 5.57097 0.982312i 0.208634 0.0367879i
\(714\) −7.65620 5.75479i −0.286526 0.215368i
\(715\) 16.7119 + 45.9155i 0.624988 + 1.71714i
\(716\) −39.7665 + 15.8957i −1.48614 + 0.594051i
\(717\) −14.7792 + 6.02397i −0.551941 + 0.224969i
\(718\) −8.64360 44.9111i −0.322576 1.67607i
\(719\) −11.2528 + 19.4904i −0.419658 + 0.726869i −0.995905 0.0904064i \(-0.971183\pi\)
0.576247 + 0.817276i \(0.304517\pi\)
\(720\) −32.6187 + 25.4177i −1.21563 + 0.947264i
\(721\) −23.5797 40.8412i −0.878153 1.52101i
\(722\) 20.3028 17.5831i 0.755591 0.654374i
\(723\) 7.99261 7.24107i 0.297248 0.269298i
\(724\) −4.17895 + 28.9566i −0.155309 + 1.07616i
\(725\) −2.21494 + 2.63966i −0.0822608 + 0.0980346i
\(726\) 4.62289 9.10025i 0.171572 0.337742i
\(727\) 5.99428 16.4691i 0.222316 0.610807i −0.777522 0.628856i \(-0.783523\pi\)
0.999837 + 0.0180494i \(0.00574560\pi\)
\(728\) −2.10318 44.8997i −0.0779491 1.66409i
\(729\) 26.3023 6.09840i 0.974158 0.225867i
\(730\) −0.886643 56.8224i −0.0328161 2.10309i
\(731\) −7.12825 2.59447i −0.263648 0.0959599i
\(732\) 3.68719 7.54767i 0.136282 0.278970i
\(733\) −17.2190 14.4484i −0.635998 0.533666i 0.266788 0.963755i \(-0.414038\pi\)
−0.902786 + 0.430089i \(0.858482\pi\)
\(734\) 0.930645 + 0.149166i 0.0343507 + 0.00550581i
\(735\) 6.34507 + 7.00362i 0.234041 + 0.258332i
\(736\) −3.42702 + 3.36417i −0.126322 + 0.124005i
\(737\) 10.9147 6.30162i 0.402049 0.232123i
\(738\) 9.89652 6.99294i 0.364296 0.257414i
\(739\) 7.76664 + 4.48407i 0.285700 + 0.164949i 0.636001 0.771688i \(-0.280587\pi\)
−0.350301 + 0.936637i \(0.613921\pi\)
\(740\) −37.2244 + 7.76839i −1.36840 + 0.285572i
\(741\) 0.323801 + 0.794415i 0.0118951 + 0.0291836i
\(742\) −28.5375 + 10.8940i −1.04765 + 0.399930i
\(743\) −44.6168 + 16.2392i −1.63683 + 0.595758i −0.986481 0.163875i \(-0.947601\pi\)
−0.650352 + 0.759633i \(0.725378\pi\)
\(744\) −18.7906 + 26.6942i −0.688896 + 0.978657i
\(745\) 10.9219 + 61.9413i 0.400148 + 2.26935i
\(746\) −14.3298 + 25.7393i −0.524653 + 0.942381i
\(747\) 1.60590 + 6.27674i 0.0587570 + 0.229654i
\(748\) −5.93088 + 3.67557i −0.216854 + 0.134392i
\(749\) 18.3010 + 21.8103i 0.668705 + 0.796932i
\(750\) −15.4193 + 3.57956i −0.563034 + 0.130707i
\(751\) −13.7230 2.41974i −0.500761 0.0882976i −0.0824383 0.996596i \(-0.526271\pi\)
−0.418323 + 0.908299i \(0.637382\pi\)
\(752\) −21.2683 15.6942i −0.775573 0.572307i
\(753\) 49.0735 1.86432i 1.78834 0.0679397i
\(754\) −1.25845 + 3.63294i −0.0458300 + 0.132304i
\(755\) −66.3349 −2.41418
\(756\) −4.40297 30.1266i −0.160134 1.09569i
\(757\) 12.8098 0.465582 0.232791 0.972527i \(-0.425214\pi\)
0.232791 + 0.972527i \(0.425214\pi\)
\(758\) −8.88317 + 25.6443i −0.322651 + 0.931444i
\(759\) 2.04679 + 3.25331i 0.0742936 + 0.118088i
\(760\) −0.707786 0.539543i −0.0256741 0.0195713i
\(761\) 30.5200 + 5.38149i 1.10635 + 0.195079i 0.696839 0.717227i \(-0.254589\pi\)
0.409508 + 0.912306i \(0.365700\pi\)
\(762\) −7.93306 + 26.0611i −0.287384 + 0.944092i
\(763\) 8.84838 + 10.5451i 0.320333 + 0.381758i
\(764\) 2.02491 + 3.26739i 0.0732587 + 0.118210i
\(765\) −1.35810 + 13.7307i −0.0491021 + 0.496435i
\(766\) −5.45678 + 9.80146i −0.197161 + 0.354141i
\(767\) 2.86832 + 16.2671i 0.103569 + 0.587369i
\(768\) 0.325364 27.7109i 0.0117405 0.999931i
\(769\) −16.0889 + 5.85587i −0.580179 + 0.211168i −0.615404 0.788211i \(-0.711007\pi\)
0.0352254 + 0.999379i \(0.488785\pi\)
\(770\) 34.8681 13.3106i 1.25656 0.479681i
\(771\) −28.3094 3.89017i −1.01954 0.140101i
\(772\) −2.55831 12.2588i −0.0920755 0.441205i
\(773\) 37.1476 + 21.4472i 1.33610 + 0.771401i 0.986227 0.165395i \(-0.0528899\pi\)
0.349877 + 0.936795i \(0.386223\pi\)
\(774\) −10.2845 21.8109i −0.369667 0.783976i
\(775\) −39.6758 + 22.9068i −1.42520 + 0.822838i
\(776\) 13.7231 12.6552i 0.492629 0.454297i
\(777\) 8.57008 26.6537i 0.307450 0.956198i
\(778\) 17.2399 + 2.76326i 0.618082 + 0.0990676i
\(779\) 0.199783 + 0.167638i 0.00715795 + 0.00600624i
\(780\) −53.7057 + 36.1752i −1.92297 + 1.29528i
\(781\) 29.0802 + 10.5843i 1.04057 + 0.378737i
\(782\) 0.0249994 + 1.60214i 0.000893978 + 0.0572924i
\(783\) −0.606764 + 2.53260i −0.0216840 + 0.0905077i
\(784\) −6.32095 + 0.395004i −0.225748 + 0.0141073i
\(785\) 19.8481 54.5321i 0.708408 1.94633i
\(786\) −7.58810 + 0.406919i −0.270659 + 0.0145143i
\(787\) −3.83079 + 4.56536i −0.136553 + 0.162737i −0.829987 0.557783i \(-0.811652\pi\)
0.693434 + 0.720520i \(0.256097\pi\)
\(788\) 29.9480 + 4.32202i 1.06685 + 0.153966i
\(789\) −8.84655 41.0013i −0.314945 1.45968i
\(790\) 6.21485 5.38233i 0.221115 0.191495i
\(791\) −0.826860 1.43216i −0.0293998 0.0509219i
\(792\) −21.6149 4.97701i −0.768051 0.176850i
\(793\) 6.57679 11.3913i 0.233549 0.404518i
\(794\) −6.19859 32.2071i −0.219980 1.14299i
\(795\) 34.7589 + 26.9854i 1.23277 + 0.957075i
\(796\) −19.2375 48.1267i −0.681856 1.70580i
\(797\) 14.1501 + 38.8770i 0.501221 + 1.37709i 0.890084 + 0.455797i \(0.150646\pi\)
−0.388863 + 0.921296i \(0.627132\pi\)
\(798\) 0.602864 0.256765i 0.0213412 0.00908939i
\(799\) −8.68528 + 1.53145i −0.307263 + 0.0541788i
\(800\) 16.7621 35.0949i 0.592631 1.24079i
\(801\) 39.2846 + 18.8631i 1.38805 + 0.666495i
\(802\) −8.24720 + 4.93467i −0.291219 + 0.174249i
\(803\) 23.3504 19.5933i 0.824016 0.691432i
\(804\) 11.5946 + 12.0218i 0.408908 + 0.423976i
\(805\) 1.48831 8.44064i 0.0524561 0.297494i
\(806\) −32.2426 + 39.6659i −1.13570 + 1.39717i
\(807\) 18.6811 + 9.85960i 0.657607 + 0.347074i
\(808\) −6.94216 + 22.2639i −0.244224 + 0.783241i
\(809\) 45.8780i 1.61298i 0.591245 + 0.806492i \(0.298637\pi\)
−0.591245 + 0.806492i \(0.701363\pi\)
\(810\) −33.7972 + 27.9561i −1.18751 + 0.982276i
\(811\) 25.4302i 0.892974i −0.894790 0.446487i \(-0.852675\pi\)
0.894790 0.446487i \(-0.147325\pi\)
\(812\) 2.78960 + 0.917827i 0.0978959 + 0.0322094i
\(813\) −38.2963 20.2122i −1.34311 0.708872i
\(814\) −15.8272 12.8652i −0.554742 0.450923i
\(815\) 4.80280 27.2380i 0.168235 0.954107i
\(816\) −6.62356 6.45206i −0.231871 0.225867i
\(817\) 0.397558 0.333591i 0.0139088 0.0116709i
\(818\) −13.1918 22.0472i −0.461241 0.770861i
\(819\) −3.61721 47.5382i −0.126395 1.66112i
\(820\) −9.30595 + 17.3467i −0.324978 + 0.605774i
\(821\) −7.72253 + 1.36169i −0.269518 + 0.0475233i −0.306774 0.951782i \(-0.599250\pi\)
0.0372556 + 0.999306i \(0.488138\pi\)
\(822\) 16.5746 + 38.9158i 0.578105 + 1.35734i
\(823\) −2.99728 8.23497i −0.104479 0.287053i 0.876428 0.481534i \(-0.159920\pi\)
−0.980906 + 0.194481i \(0.937698\pi\)
\(824\) −17.5565 42.0075i −0.611610 1.46340i
\(825\) −24.5881 19.0892i −0.856046 0.664601i
\(826\) 12.3895 2.38449i 0.431087 0.0829672i
\(827\) −9.57006 + 16.5758i −0.332784 + 0.576398i −0.983057 0.183303i \(-0.941321\pi\)
0.650273 + 0.759701i \(0.274655\pi\)
\(828\) −3.52941 + 3.67262i −0.122655 + 0.127632i
\(829\) −0.0258029 0.0446919i −0.000896172 0.00155222i 0.865577 0.500776i \(-0.166952\pi\)
−0.866473 + 0.499224i \(0.833619\pi\)
\(830\) −6.89024 7.95601i −0.239164 0.276157i
\(831\) −3.19198 14.7940i −0.110729 0.513197i
\(832\) 3.50758 43.2527i 0.121604 1.49952i
\(833\) −1.35831 + 1.61878i −0.0470628 + 0.0560873i
\(834\) 1.46777 + 27.3705i 0.0508246 + 0.947763i
\(835\) 1.53889 4.22806i 0.0532554 0.146318i
\(836\) −0.0148937 0.477130i −0.000515109 0.0165019i
\(837\) −19.0971 + 28.8821i −0.660093 + 0.998310i
\(838\) −6.95909 + 0.108588i −0.240398 + 0.00375111i
\(839\) −10.1094 3.67952i −0.349015 0.127031i 0.161563 0.986862i \(-0.448346\pi\)
−0.510578 + 0.859831i \(0.670569\pi\)
\(840\) 28.2683 + 40.5858i 0.975350 + 1.40034i
\(841\) 22.0229 + 18.4794i 0.759409 + 0.637220i
\(842\) −2.63400 + 16.4335i −0.0907736 + 0.566336i
\(843\) 11.6046 36.0912i 0.399682 1.24305i
\(844\) 23.2547 + 26.0201i 0.800461 + 0.895647i
\(845\) −49.0137 + 28.2981i −1.68612 + 0.973484i
\(846\) −23.0338 15.9819i −0.791917 0.549470i
\(847\) −10.5727 6.10416i −0.363283 0.209741i
\(848\) −28.6660 + 6.92224i −0.984395 + 0.237711i
\(849\) 51.6534 + 7.09800i 1.77274 + 0.243603i
\(850\) −4.62806 12.1235i −0.158741 0.415833i
\(851\) −4.40143 + 1.60199i −0.150879 + 0.0549155i
\(852\) −4.31274 + 40.7834i −0.147752 + 1.39722i
\(853\) 6.86844 + 38.9529i 0.235171 + 1.33372i 0.842254 + 0.539082i \(0.181229\pi\)
−0.607083 + 0.794639i \(0.707660\pi\)
\(854\) −8.77834 4.88717i −0.300389 0.167236i
\(855\) −0.767074 0.550158i −0.0262334 0.0188150i
\(856\) 14.8422 + 23.1352i 0.507296 + 0.790745i
\(857\) −6.59420 7.85866i −0.225253 0.268447i 0.641567 0.767067i \(-0.278285\pi\)
−0.866820 + 0.498620i \(0.833840\pi\)
\(858\) −33.2265 10.1142i −1.13433 0.345294i
\(859\) −3.49071 0.615507i −0.119102 0.0210008i 0.113780 0.993506i \(-0.463704\pi\)
−0.232881 + 0.972505i \(0.574815\pi\)
\(860\) 30.7791 + 24.2313i 1.04956 + 0.826280i
\(861\) −7.71811 12.2677i −0.263032 0.418082i
\(862\) 5.89172 + 2.04089i 0.200673 + 0.0695129i
\(863\) 6.36151 0.216548 0.108274 0.994121i \(-0.465468\pi\)
0.108274 + 0.994121i \(0.465468\pi\)
\(864\) −0.511307 29.3894i −0.0173950 0.999849i
\(865\) −39.4602 −1.34169
\(866\) −38.1159 13.2033i −1.29523 0.448667i
\(867\) 26.3406 1.00069i 0.894574 0.0339852i
\(868\) 30.6785 + 24.1521i 1.04130 + 0.819775i
\(869\) 4.34283 + 0.765757i 0.147320 + 0.0259765i
\(870\) −0.956683 4.12101i −0.0324346 0.139715i
\(871\) 16.8110 + 20.0345i 0.569618 + 0.678844i
\(872\) 7.17607 + 11.1857i 0.243012 + 0.378794i
\(873\) 14.1583 13.8413i 0.479185 0.468456i
\(874\) −0.0957804 0.0533239i −0.00323982 0.00180371i
\(875\) 3.28765 + 18.6452i 0.111143 + 0.630323i
\(876\) 32.6650 + 23.7643i 1.10365 + 0.802921i
\(877\) 15.3450 5.58514i 0.518165 0.188597i −0.0696811 0.997569i \(-0.522198\pi\)
0.587846 + 0.808973i \(0.299976\pi\)
\(878\) −2.43954 6.39054i −0.0823303 0.215670i
\(879\) 8.65504 + 21.2343i 0.291927 + 0.716216i
\(880\) 35.0251 8.45782i 1.18070 0.285113i
\(881\) −43.1593 24.9180i −1.45407 0.839509i −0.455364 0.890306i \(-0.650491\pi\)
−0.998709 + 0.0507963i \(0.983824\pi\)
\(882\) −6.68933 + 0.614103i −0.225241 + 0.0206779i
\(883\) −38.2077 + 22.0592i −1.28579 + 0.742352i −0.977901 0.209070i \(-0.932956\pi\)
−0.307890 + 0.951422i \(0.599623\pi\)
\(884\) −9.64850 10.7958i −0.324514 0.363104i
\(885\) −12.2033 13.4699i −0.410210 0.452785i
\(886\) 1.62640 10.1471i 0.0546401 0.340899i
\(887\) −1.84120 1.54495i −0.0618215 0.0518744i 0.611353 0.791358i \(-0.290625\pi\)
−0.673175 + 0.739483i \(0.735070\pi\)
\(888\) 11.4841 24.4686i 0.385380 0.821113i
\(889\) 30.6177 + 11.1439i 1.02688 + 0.373756i
\(890\) −70.7842 + 1.10450i −2.37269 + 0.0370229i
\(891\) −23.0701 4.60878i −0.772877 0.154400i
\(892\) 1.10298 + 35.3348i 0.0369305 + 1.18310i
\(893\) 0.206364 0.566981i 0.00690571 0.0189733i
\(894\) −39.8595 20.2485i −1.33310 0.677210i
\(895\) 47.4313 56.5264i 1.58545 1.88947i
\(896\) −33.0754 2.16341i −1.10497 0.0722746i
\(897\) −5.91090 + 5.35510i −0.197359 + 0.178801i
\(898\) 5.88453 + 6.79474i 0.196369 + 0.226743i
\(899\) −1.66986 2.89227i −0.0556928 0.0964627i
\(900\) 16.6870 37.7259i 0.556232 1.25753i
\(901\) −4.91981 + 8.52136i −0.163903 + 0.283888i
\(902\) −10.3684 + 1.99550i −0.345229 + 0.0664429i
\(903\) −26.7083 + 10.8862i −0.888797 + 0.362271i
\(904\) −0.615648 1.47306i −0.0204761 0.0489933i
\(905\) −17.2412 47.3698i −0.573117 1.57463i
\(906\) 28.3307 37.6913i 0.941226 1.25221i
\(907\) −34.5531 + 6.09265i −1.14732 + 0.202303i −0.714804 0.699324i \(-0.753484\pi\)
−0.432513 + 0.901628i \(0.642373\pi\)
\(908\) 8.82079 16.4424i 0.292728 0.545660i
\(909\) −6.67219 + 23.8189i −0.221303 + 0.790023i
\(910\) 39.7659 + 66.4598i 1.31823 + 2.20312i
\(911\) −8.27443 + 6.94307i −0.274144 + 0.230034i −0.769486 0.638664i \(-0.779487\pi\)
0.495342 + 0.868698i \(0.335043\pi\)
\(912\) 0.608853 0.171731i 0.0201611 0.00568659i
\(913\) 0.980292 5.55951i 0.0324429 0.183993i
\(914\) −0.981252 0.797613i −0.0324569 0.0263827i
\(915\) 0.549465 + 14.4633i 0.0181647 + 0.478141i
\(916\) −31.9494 10.5119i −1.05564 0.347323i
\(917\) 9.08884i 0.300140i
\(918\) −7.22174 6.63587i −0.238353 0.219016i
\(919\) 20.9319i 0.690481i −0.938514 0.345241i \(-0.887797\pi\)
0.938514 0.345241i \(-0.112203\pi\)
\(920\) 2.46313 7.89938i 0.0812069 0.260435i
\(921\) 19.3091 12.1481i 0.636257 0.400295i
\(922\) 11.6870 14.3778i 0.384891 0.473506i
\(923\) −11.1513 + 63.2421i −0.367049 + 2.08164i
\(924\) −7.32863 + 25.4968i −0.241094 + 0.838782i
\(925\) 29.0588 24.3832i 0.955447 0.801715i
\(926\) −1.63660 + 0.979249i −0.0537819 + 0.0321801i
\(927\) −19.9116 43.9943i −0.653983 1.44496i
\(928\) 2.55834 + 1.22192i 0.0839816 + 0.0401115i
\(929\) 33.1245 5.84075i 1.08678 0.191629i 0.398568 0.917139i \(-0.369507\pi\)
0.688212 + 0.725510i \(0.258396\pi\)
\(930\) 6.78701 55.8364i 0.222555 1.83095i
\(931\) −0.0494464 0.135853i −0.00162054 0.00445240i
\(932\) 13.0857 + 32.7367i 0.428637 + 1.07233i
\(933\) 1.45626 10.5974i 0.0476758 0.346945i
\(934\) −5.24485 27.2516i −0.171617 0.891700i
\(935\) 6.01119 10.4117i 0.196587 0.340498i
\(936\) 2.38227 45.9654i 0.0778670 1.50243i
\(937\) −12.5767 21.7834i −0.410862 0.711634i 0.584122 0.811666i \(-0.301439\pi\)
−0.994984 + 0.100032i \(0.968106\pi\)
\(938\) 15.1007 13.0779i 0.493057 0.427008i
\(939\) 35.3476 + 11.3655i 1.15353 + 0.370898i
\(940\) 45.0759 + 6.50524i 1.47021 + 0.212177i
\(941\) 26.6235 31.7286i 0.867901 1.03432i −0.131175 0.991359i \(-0.541875\pi\)
0.999077 0.0429652i \(-0.0136805\pi\)
\(942\) 22.5082 + 34.5675i 0.733356 + 1.12627i
\(943\) −0.829308 + 2.27850i −0.0270060 + 0.0741983i
\(944\) 12.1569 0.759701i 0.395675 0.0247262i
\(945\) 31.2244 + 42.1560i 1.01573 + 1.37133i
\(946\) 0.327815 + 21.0087i 0.0106582 + 0.683052i
\(947\) 53.1276 + 19.3369i 1.72642 + 0.628364i 0.998365 0.0571597i \(-0.0182044\pi\)
0.728050 + 0.685524i \(0.240427\pi\)
\(948\) 0.403946 + 5.82998i 0.0131196 + 0.189349i
\(949\) 48.4548 + 40.6584i 1.57291 + 1.31983i
\(950\) 0.876620 + 0.140507i 0.0284413 + 0.00455864i
\(951\) 24.8927 5.37092i 0.807201 0.174164i
\(952\) −8.13018 + 7.49756i −0.263501 + 0.242997i
\(953\) −31.8569 + 18.3926i −1.03195 + 0.595795i −0.917542 0.397639i \(-0.869830\pi\)
−0.114405 + 0.993434i \(0.536496\pi\)
\(954\) −30.1781 + 8.22480i −0.977052 + 0.266288i
\(955\) −5.73591 3.31163i −0.185610 0.107162i
\(956\) 3.76480 + 18.0401i 0.121762 + 0.583459i
\(957\) 1.39156 1.79241i 0.0449827 0.0579405i
\(958\) 25.1840 9.61380i 0.813658 0.310608i
\(959\) 47.5403 17.3032i 1.53516 0.558751i
\(960\) 22.0776 + 42.3395i 0.712550 + 1.36650i
\(961\) −2.32736 13.1991i −0.0750761 0.425778i
\(962\) 20.5880 36.9801i 0.663783 1.19229i
\(963\) 16.4507 + 24.0696i 0.530117 + 0.775630i
\(964\) −6.56014 10.5854i −0.211288 0.340933i
\(965\) 13.8697 + 16.5292i 0.446480 + 0.532094i
\(966\) 4.16031 + 4.45054i 0.133856 + 0.143194i
\(967\) −44.3616 7.82215i −1.42657 0.251543i −0.593557 0.804792i \(-0.702277\pi\)
−0.833016 + 0.553249i \(0.813388\pi\)
\(968\) −9.37334 7.14526i −0.301271 0.229657i
\(969\) 0.0985224 0.186672i 0.00316500 0.00599677i
\(970\) −10.5281 + 30.3929i −0.338036 + 0.975857i
\(971\) 40.1053 1.28704 0.643520 0.765429i \(-0.277473\pi\)
0.643520 + 0.765429i \(0.277473\pi\)
\(972\) −1.45022 31.1432i −0.0465158 0.998918i
\(973\) 32.7837 1.05100
\(974\) −5.89916 + 17.0300i −0.189021 + 0.545675i
\(975\) 30.1505 57.1266i 0.965588 1.82951i
\(976\) −7.80477 5.75926i −0.249825 0.184349i
\(977\) −36.1734 6.37835i −1.15729 0.204062i −0.438134 0.898910i \(-0.644361\pi\)
−0.719157 + 0.694848i \(0.755472\pi\)
\(978\) 13.4254 + 14.3619i 0.429296 + 0.459244i
\(979\) −24.4075 29.0878i −0.780068 0.929649i
\(980\) 9.27559 5.74840i 0.296298 0.183626i
\(981\) 7.95377 + 11.6374i 0.253944 + 0.371554i
\(982\) −17.0137 + 30.5601i −0.542930 + 0.975211i
\(983\) 3.28853 + 18.6502i 0.104888 + 0.594848i 0.991265 + 0.131884i \(0.0421028\pi\)
−0.886377 + 0.462963i \(0.846786\pi\)
\(984\) −5.88193 12.6962i −0.187509 0.404739i
\(985\) −48.9916 + 17.8315i −1.56100 + 0.568158i
\(986\) 0.883777 0.337375i 0.0281452 0.0107442i
\(987\) −20.5631 + 26.4866i −0.654532 + 0.843077i
\(988\) 0.969693 0.202366i 0.0308500 0.00643812i
\(989\) 4.17867 + 2.41256i 0.132874 + 0.0767148i
\(990\) 36.8726 10.0493i 1.17189 0.319389i
\(991\) −30.3997 + 17.5513i −0.965680 + 0.557535i −0.897916 0.440166i \(-0.854920\pi\)
−0.0677633 + 0.997701i \(0.521586\pi\)
\(992\) 26.4064 + 26.8997i 0.838403 + 0.854065i
\(993\) 44.9071 9.68928i 1.42508 0.307480i
\(994\) 48.4331 + 7.76296i 1.53620 + 0.246226i
\(995\) 68.4100 + 57.4028i 2.16874 + 1.81979i
\(996\) 7.46332 0.517116i 0.236484 0.0163854i
\(997\) −22.5603 8.21129i −0.714493 0.260054i −0.0409071 0.999163i \(-0.513025\pi\)
−0.673586 + 0.739109i \(0.735247\pi\)
\(998\) −0.871737 55.8671i −0.0275944 1.76844i
\(999\) 11.4194 26.2967i 0.361295 0.831991i
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 108.2.l.a.23.2 96
3.2 odd 2 324.2.l.a.179.15 96
4.3 odd 2 inner 108.2.l.a.23.15 yes 96
9.2 odd 6 972.2.l.b.215.8 96
9.4 even 3 972.2.l.d.863.13 96
9.5 odd 6 972.2.l.a.863.4 96
9.7 even 3 972.2.l.c.215.9 96
12.11 even 2 324.2.l.a.179.2 96
27.2 odd 18 972.2.l.d.107.5 96
27.7 even 9 324.2.l.a.143.2 96
27.11 odd 18 972.2.l.c.755.7 96
27.16 even 9 972.2.l.b.755.10 96
27.20 odd 18 inner 108.2.l.a.47.15 yes 96
27.25 even 9 972.2.l.a.107.12 96
36.7 odd 6 972.2.l.c.215.7 96
36.11 even 6 972.2.l.b.215.10 96
36.23 even 6 972.2.l.a.863.12 96
36.31 odd 6 972.2.l.d.863.5 96
108.7 odd 18 324.2.l.a.143.15 96
108.11 even 18 972.2.l.c.755.9 96
108.43 odd 18 972.2.l.b.755.8 96
108.47 even 18 inner 108.2.l.a.47.2 yes 96
108.79 odd 18 972.2.l.a.107.4 96
108.83 even 18 972.2.l.d.107.13 96
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
108.2.l.a.23.2 96 1.1 even 1 trivial
108.2.l.a.23.15 yes 96 4.3 odd 2 inner
108.2.l.a.47.2 yes 96 108.47 even 18 inner
108.2.l.a.47.15 yes 96 27.20 odd 18 inner
324.2.l.a.143.2 96 27.7 even 9
324.2.l.a.143.15 96 108.7 odd 18
324.2.l.a.179.2 96 12.11 even 2
324.2.l.a.179.15 96 3.2 odd 2
972.2.l.a.107.4 96 108.79 odd 18
972.2.l.a.107.12 96 27.25 even 9
972.2.l.a.863.4 96 9.5 odd 6
972.2.l.a.863.12 96 36.23 even 6
972.2.l.b.215.8 96 9.2 odd 6
972.2.l.b.215.10 96 36.11 even 6
972.2.l.b.755.8 96 108.43 odd 18
972.2.l.b.755.10 96 27.16 even 9
972.2.l.c.215.7 96 36.7 odd 6
972.2.l.c.215.9 96 9.7 even 3
972.2.l.c.755.7 96 27.11 odd 18
972.2.l.c.755.9 96 108.11 even 18
972.2.l.d.107.5 96 27.2 odd 18
972.2.l.d.107.13 96 108.83 even 18
972.2.l.d.863.5 96 36.31 odd 6
972.2.l.d.863.13 96 9.4 even 3