Properties

Label 81.2.g.a.7.7
Level $81$
Weight $2$
Character 81.7
Analytic conductor $0.647$
Analytic rank $0$
Dimension $144$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [81,2,Mod(4,81)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(81, base_ring=CyclotomicField(54))
 
chi = DirichletCharacter(H, H._module([2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("81.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 81 = 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 81.g (of order \(27\), degree \(18\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.646788256372\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(8\) over \(\Q(\zeta_{27})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label 7.7
Character \(\chi\) \(=\) 81.7
Dual form 81.2.g.a.58.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.925932 + 1.24374i) q^{2} +(1.03494 - 1.38884i) q^{3} +(-0.115939 + 0.387262i) q^{4} +(-2.65494 + 1.74618i) q^{5} +(2.68565 + 0.00122935i) q^{6} +(-0.200969 + 0.213014i) q^{7} +(2.32510 - 0.846267i) q^{8} +(-0.857778 - 2.87476i) q^{9} +O(q^{10})\) \(q+(0.925932 + 1.24374i) q^{2} +(1.03494 - 1.38884i) q^{3} +(-0.115939 + 0.387262i) q^{4} +(-2.65494 + 1.74618i) q^{5} +(2.68565 + 0.00122935i) q^{6} +(-0.200969 + 0.213014i) q^{7} +(2.32510 - 0.846267i) q^{8} +(-0.857778 - 2.87476i) q^{9} +(-4.63010 - 1.68522i) q^{10} +(-5.19744 + 2.61025i) q^{11} +(0.417857 + 0.561816i) q^{12} +(0.0996078 + 0.230917i) q^{13} +(-0.451018 - 0.0527165i) q^{14} +(-0.322542 + 5.49450i) q^{15} +(3.88090 + 2.55251i) q^{16} +(3.14189 - 2.63636i) q^{17} +(2.78121 - 3.72868i) q^{18} +(-3.55906 - 2.98641i) q^{19} +(-0.368420 - 1.23061i) q^{20} +(0.0878524 + 0.499573i) q^{21} +(-8.05895 - 4.04736i) q^{22} +(3.14672 + 3.33533i) q^{23} +(1.23102 - 4.10504i) q^{24} +(2.01916 - 4.68094i) q^{25} +(-0.194971 + 0.337700i) q^{26} +(-4.88034 - 1.78389i) q^{27} +(-0.0591924 - 0.102524i) q^{28} +(5.08083 - 0.593863i) q^{29} +(-7.13240 + 4.68638i) q^{30} +(5.76404 - 1.36610i) q^{31} +(0.131049 + 2.25003i) q^{32} +(-1.75383 + 9.91990i) q^{33} +(6.18813 + 1.46661i) q^{34} +(0.161598 - 0.916469i) q^{35} +(1.21273 + 0.00111025i) q^{36} +(0.850864 + 4.82549i) q^{37} +(0.418873 - 7.19176i) q^{38} +(0.423796 + 0.100646i) q^{39} +(-4.69526 + 6.30683i) q^{40} +(-1.08777 + 1.46113i) q^{41} +(-0.539994 + 0.571836i) q^{42} +(-0.127010 + 2.18068i) q^{43} +(-0.408268 - 2.31540i) q^{44} +(7.29720 + 6.13447i) q^{45} +(-1.23464 + 7.00200i) q^{46} +(-7.45323 - 1.76645i) q^{47} +(7.56156 - 2.74826i) q^{48} +(0.402027 + 6.90254i) q^{49} +(7.69149 - 1.82292i) q^{50} +(-0.409810 - 7.09209i) q^{51} +(-0.100974 + 0.0118021i) q^{52} +(-3.52502 - 6.10552i) q^{53} +(-2.30016 - 7.72165i) q^{54} +(9.24092 - 16.0057i) q^{55} +(-0.287005 + 0.665353i) q^{56} +(-7.83109 + 1.85222i) q^{57} +(5.44311 + 5.76936i) q^{58} +(-8.21945 - 4.12796i) q^{59} +(-2.09042 - 0.761934i) q^{60} +(0.893301 + 2.98383i) q^{61} +(7.03618 + 5.90406i) q^{62} +(0.784751 + 0.395017i) q^{63} +(4.43955 - 3.72523i) q^{64} +(-0.667676 - 0.439137i) q^{65} +(-13.9617 + 7.00384i) q^{66} +(6.79169 + 0.793835i) q^{67} +(0.656696 + 1.52239i) q^{68} +(7.88894 - 0.918424i) q^{69} +(1.28948 - 0.647601i) q^{70} +(4.71278 + 1.71531i) q^{71} +(-4.42723 - 5.95818i) q^{72} +(-1.71510 + 0.624247i) q^{73} +(-5.21382 + 5.52633i) q^{74} +(-4.41138 - 7.64882i) q^{75} +(1.56916 - 1.03205i) q^{76} +(0.488501 - 1.63171i) q^{77} +(0.267228 + 0.620285i) q^{78} +(-6.45435 - 8.66969i) q^{79} -14.7607 q^{80} +(-7.52843 + 4.93180i) q^{81} -2.82447 q^{82} +(-6.02991 - 8.09957i) q^{83} +(-0.203651 - 0.0238979i) q^{84} +(-3.73797 + 12.4857i) q^{85} +(-2.82981 + 1.86120i) q^{86} +(4.43359 - 7.67109i) q^{87} +(-9.87559 + 10.4675i) q^{88} +(9.79723 - 3.56590i) q^{89} +(-0.872991 + 14.7559i) q^{90} +(-0.0692067 - 0.0251892i) q^{91} +(-1.65647 + 0.831912i) q^{92} +(4.06816 - 9.41919i) q^{93} +(-4.70418 - 10.9055i) q^{94} +(14.6639 + 1.71396i) q^{95} +(3.26057 + 2.14665i) q^{96} +(-5.45395 - 3.58712i) q^{97} +(-8.21273 + 6.89130i) q^{98} +(11.9621 + 12.7023i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} - 18 q^{10} - 18 q^{11} - 18 q^{12} - 18 q^{13} - 18 q^{14} - 18 q^{15} - 18 q^{16} - 18 q^{17} - 9 q^{18} - 18 q^{19} + 18 q^{20} + 9 q^{21} - 18 q^{22} + 9 q^{23} + 36 q^{24} - 18 q^{25} + 45 q^{26} + 9 q^{27} - 9 q^{28} + 9 q^{29} + 36 q^{30} - 18 q^{31} + 36 q^{32} + 9 q^{33} - 18 q^{34} + 9 q^{35} + 18 q^{36} - 18 q^{37} - 9 q^{38} - 18 q^{39} - 18 q^{40} + 27 q^{42} - 18 q^{43} + 54 q^{44} + 36 q^{45} - 18 q^{46} + 36 q^{47} + 81 q^{48} - 18 q^{49} + 99 q^{50} + 45 q^{51} + 45 q^{53} + 108 q^{54} - 9 q^{55} + 126 q^{56} + 36 q^{57} - 18 q^{58} + 45 q^{59} + 99 q^{60} - 18 q^{61} + 81 q^{62} + 36 q^{63} - 18 q^{64} - 18 q^{66} + 9 q^{67} - 99 q^{68} - 72 q^{69} + 36 q^{70} - 90 q^{71} - 234 q^{72} - 18 q^{73} - 162 q^{74} - 108 q^{75} + 63 q^{76} - 162 q^{77} - 135 q^{78} + 36 q^{79} - 288 q^{80} - 90 q^{81} - 36 q^{82} - 90 q^{83} - 243 q^{84} + 36 q^{85} - 162 q^{86} - 162 q^{87} + 63 q^{88} - 81 q^{89} - 99 q^{90} - 18 q^{91} - 144 q^{92} + 36 q^{94} + 18 q^{95} - 27 q^{96} + 9 q^{97} + 81 q^{98} + 54 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{8}{27}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.925932 + 1.24374i 0.654733 + 0.879459i 0.998216 0.0597000i \(-0.0190144\pi\)
−0.343484 + 0.939159i \(0.611607\pi\)
\(3\) 1.03494 1.38884i 0.597526 0.801850i
\(4\) −0.115939 + 0.387262i −0.0579693 + 0.193631i
\(5\) −2.65494 + 1.74618i −1.18733 + 0.780916i −0.980318 0.197423i \(-0.936743\pi\)
−0.207007 + 0.978339i \(0.566372\pi\)
\(6\) 2.68565 + 0.00122935i 1.09641 + 0.000501881i
\(7\) −0.200969 + 0.213014i −0.0759591 + 0.0805119i −0.764238 0.644934i \(-0.776885\pi\)
0.688279 + 0.725446i \(0.258366\pi\)
\(8\) 2.32510 0.846267i 0.822047 0.299200i
\(9\) −0.857778 2.87476i −0.285926 0.958252i
\(10\) −4.63010 1.68522i −1.46416 0.532912i
\(11\) −5.19744 + 2.61025i −1.56709 + 0.787020i −0.999345 0.0361867i \(-0.988479\pi\)
−0.567741 + 0.823207i \(0.692183\pi\)
\(12\) 0.417857 + 0.561816i 0.120625 + 0.162182i
\(13\) 0.0996078 + 0.230917i 0.0276262 + 0.0640448i 0.931471 0.363816i \(-0.118526\pi\)
−0.903844 + 0.427861i \(0.859267\pi\)
\(14\) −0.451018 0.0527165i −0.120540 0.0140891i
\(15\) −0.322542 + 5.49450i −0.0832800 + 1.41867i
\(16\) 3.88090 + 2.55251i 0.970226 + 0.638128i
\(17\) 3.14189 2.63636i 0.762021 0.639411i −0.176631 0.984277i \(-0.556520\pi\)
0.938652 + 0.344866i \(0.112076\pi\)
\(18\) 2.78121 3.72868i 0.655538 0.878859i
\(19\) −3.55906 2.98641i −0.816505 0.685129i 0.135646 0.990757i \(-0.456689\pi\)
−0.952151 + 0.305629i \(0.901133\pi\)
\(20\) −0.368420 1.23061i −0.0823812 0.275172i
\(21\) 0.0878524 + 0.499573i 0.0191710 + 0.109016i
\(22\) −8.05895 4.04736i −1.71817 0.862900i
\(23\) 3.14672 + 3.33533i 0.656137 + 0.695464i 0.966938 0.255011i \(-0.0820789\pi\)
−0.310802 + 0.950475i \(0.600597\pi\)
\(24\) 1.23102 4.10504i 0.251280 0.837938i
\(25\) 2.01916 4.68094i 0.403832 0.936188i
\(26\) −0.194971 + 0.337700i −0.0382370 + 0.0662284i
\(27\) −4.88034 1.78389i −0.939222 0.343310i
\(28\) −0.0591924 0.102524i −0.0111863 0.0193753i
\(29\) 5.08083 0.593863i 0.943486 0.110278i 0.369580 0.929199i \(-0.379502\pi\)
0.573906 + 0.818921i \(0.305428\pi\)
\(30\) −7.13240 + 4.68638i −1.30219 + 0.855611i
\(31\) 5.76404 1.36610i 1.03525 0.245359i 0.322348 0.946621i \(-0.395528\pi\)
0.712904 + 0.701262i \(0.247380\pi\)
\(32\) 0.131049 + 2.25003i 0.0231665 + 0.397753i
\(33\) −1.75383 + 9.91990i −0.305302 + 1.72683i
\(34\) 6.18813 + 1.46661i 1.06126 + 0.251522i
\(35\) 0.161598 0.916469i 0.0273151 0.154912i
\(36\) 1.21273 + 0.00111025i 0.202122 + 0.000185042i
\(37\) 0.850864 + 4.82549i 0.139881 + 0.793306i 0.971336 + 0.237713i \(0.0763977\pi\)
−0.831454 + 0.555593i \(0.812491\pi\)
\(38\) 0.418873 7.19176i 0.0679501 1.16666i
\(39\) 0.423796 + 0.100646i 0.0678617 + 0.0161163i
\(40\) −4.69526 + 6.30683i −0.742387 + 0.997198i
\(41\) −1.08777 + 1.46113i −0.169881 + 0.228190i −0.878908 0.476992i \(-0.841727\pi\)
0.709027 + 0.705182i \(0.249135\pi\)
\(42\) −0.539994 + 0.571836i −0.0833229 + 0.0882362i
\(43\) −0.127010 + 2.18068i −0.0193689 + 0.332551i 0.974679 + 0.223608i \(0.0717836\pi\)
−0.994048 + 0.108943i \(0.965253\pi\)
\(44\) −0.408268 2.31540i −0.0615486 0.349060i
\(45\) 7.29720 + 6.13447i 1.08780 + 0.914473i
\(46\) −1.23464 + 7.00200i −0.182038 + 1.03239i
\(47\) −7.45323 1.76645i −1.08717 0.257663i −0.352308 0.935884i \(-0.614603\pi\)
−0.734858 + 0.678221i \(0.762751\pi\)
\(48\) 7.56156 2.74826i 1.09142 0.396678i
\(49\) 0.402027 + 6.90254i 0.0574324 + 0.986077i
\(50\) 7.69149 1.82292i 1.08774 0.257799i
\(51\) −0.409810 7.09209i −0.0573849 0.993091i
\(52\) −0.100974 + 0.0118021i −0.0140025 + 0.00163666i
\(53\) −3.52502 6.10552i −0.484199 0.838657i 0.515636 0.856808i \(-0.327556\pi\)
−0.999835 + 0.0181502i \(0.994222\pi\)
\(54\) −2.30016 7.72165i −0.313012 1.05078i
\(55\) 9.24092 16.0057i 1.24604 2.15821i
\(56\) −0.287005 + 0.665353i −0.0383527 + 0.0889115i
\(57\) −7.83109 + 1.85222i −1.03725 + 0.245332i
\(58\) 5.44311 + 5.76936i 0.714716 + 0.757554i
\(59\) −8.21945 4.12796i −1.07008 0.537415i −0.175573 0.984466i \(-0.556178\pi\)
−0.894508 + 0.447051i \(0.852474\pi\)
\(60\) −2.09042 0.761934i −0.269872 0.0983652i
\(61\) 0.893301 + 2.98383i 0.114375 + 0.382041i 0.995940 0.0900236i \(-0.0286943\pi\)
−0.881564 + 0.472064i \(0.843509\pi\)
\(62\) 7.03618 + 5.90406i 0.893596 + 0.749816i
\(63\) 0.784751 + 0.395017i 0.0988693 + 0.0497674i
\(64\) 4.43955 3.72523i 0.554944 0.465653i
\(65\) −0.667676 0.439137i −0.0828150 0.0544683i
\(66\) −13.9617 + 7.00384i −1.71857 + 0.862113i
\(67\) 6.79169 + 0.793835i 0.829738 + 0.0969824i 0.520349 0.853953i \(-0.325802\pi\)
0.309388 + 0.950936i \(0.399876\pi\)
\(68\) 0.656696 + 1.52239i 0.0796361 + 0.184617i
\(69\) 7.88894 0.918424i 0.949716 0.110565i
\(70\) 1.28948 0.647601i 0.154122 0.0774032i
\(71\) 4.71278 + 1.71531i 0.559304 + 0.203570i 0.606175 0.795331i \(-0.292703\pi\)
−0.0468717 + 0.998901i \(0.514925\pi\)
\(72\) −4.42723 5.95818i −0.521754 0.702178i
\(73\) −1.71510 + 0.624247i −0.200738 + 0.0730626i −0.440432 0.897786i \(-0.645175\pi\)
0.239695 + 0.970848i \(0.422953\pi\)
\(74\) −5.21382 + 5.52633i −0.606095 + 0.642423i
\(75\) −4.41138 7.64882i −0.509382 0.883209i
\(76\) 1.56916 1.03205i 0.179994 0.118384i
\(77\) 0.488501 1.63171i 0.0556699 0.185950i
\(78\) 0.267228 + 0.620285i 0.0302576 + 0.0702335i
\(79\) −6.45435 8.66969i −0.726171 0.975417i −0.999907 0.0136119i \(-0.995667\pi\)
0.273737 0.961805i \(-0.411740\pi\)
\(80\) −14.7607 −1.65030
\(81\) −7.52843 + 4.93180i −0.836493 + 0.547978i
\(82\) −2.82447 −0.311911
\(83\) −6.02991 8.09957i −0.661868 0.889043i 0.336750 0.941594i \(-0.390672\pi\)
−0.998618 + 0.0525508i \(0.983265\pi\)
\(84\) −0.203651 0.0238979i −0.0222202 0.00260747i
\(85\) −3.73797 + 12.4857i −0.405440 + 1.35426i
\(86\) −2.82981 + 1.86120i −0.305147 + 0.200698i
\(87\) 4.43359 7.67109i 0.475331 0.822427i
\(88\) −9.87559 + 10.4675i −1.05274 + 1.11584i
\(89\) 9.79723 3.56590i 1.03850 0.377985i 0.234192 0.972190i \(-0.424756\pi\)
0.804313 + 0.594206i \(0.202533\pi\)
\(90\) −0.872991 + 14.7559i −0.0920213 + 1.55541i
\(91\) −0.0692067 0.0251892i −0.00725483 0.00264054i
\(92\) −1.65647 + 0.831912i −0.172699 + 0.0867329i
\(93\) 4.06816 9.41919i 0.421848 0.976725i
\(94\) −4.70418 10.9055i −0.485199 1.12482i
\(95\) 14.6639 + 1.71396i 1.50449 + 0.175849i
\(96\) 3.26057 + 2.14665i 0.332781 + 0.219092i
\(97\) −5.45395 3.58712i −0.553765 0.364217i 0.241574 0.970382i \(-0.422336\pi\)
−0.795338 + 0.606166i \(0.792707\pi\)
\(98\) −8.21273 + 6.89130i −0.829611 + 0.696126i
\(99\) 11.9621 + 12.7023i 1.20223 + 1.27663i
\(100\) 1.57865 + 1.32465i 0.157865 + 0.132465i
\(101\) −0.0889104 0.296981i −0.00884692 0.0295508i 0.953452 0.301545i \(-0.0975022\pi\)
−0.962299 + 0.271994i \(0.912317\pi\)
\(102\) 8.44128 7.07649i 0.835811 0.700677i
\(103\) −8.62814 4.33322i −0.850156 0.426964i −0.0303046 0.999541i \(-0.509648\pi\)
−0.819851 + 0.572576i \(0.805944\pi\)
\(104\) 0.427015 + 0.452610i 0.0418723 + 0.0443820i
\(105\) −1.10559 1.17293i −0.107894 0.114466i
\(106\) 4.32976 10.0375i 0.420544 0.974929i
\(107\) −5.31399 + 9.20410i −0.513723 + 0.889794i 0.486150 + 0.873875i \(0.338401\pi\)
−0.999873 + 0.0159189i \(0.994933\pi\)
\(108\) 1.25665 1.68315i 0.120922 0.161961i
\(109\) 8.57766 + 14.8569i 0.821590 + 1.42304i 0.904497 + 0.426479i \(0.140246\pi\)
−0.0829070 + 0.996557i \(0.526420\pi\)
\(110\) 28.4635 3.32690i 2.71389 0.317208i
\(111\) 7.58245 + 3.81240i 0.719695 + 0.361857i
\(112\) −1.32366 + 0.313714i −0.125074 + 0.0296432i
\(113\) −0.615864 10.5740i −0.0579356 0.994717i −0.894562 0.446943i \(-0.852513\pi\)
0.836627 0.547773i \(-0.184524\pi\)
\(114\) −9.55473 8.02483i −0.894883 0.751594i
\(115\) −14.1785 3.36036i −1.32215 0.313355i
\(116\) −0.359083 + 2.03646i −0.0333401 + 0.189081i
\(117\) 0.578388 0.484424i 0.0534720 0.0447850i
\(118\) −2.47653 14.0451i −0.227983 1.29296i
\(119\) −0.0698393 + 1.19909i −0.00640216 + 0.109921i
\(120\) 3.89987 + 13.0482i 0.356008 + 1.19113i
\(121\) 13.6312 18.3099i 1.23920 1.66453i
\(122\) −2.88398 + 3.87386i −0.261104 + 0.350723i
\(123\) 0.903500 + 3.02293i 0.0814658 + 0.272569i
\(124\) −0.139235 + 2.39058i −0.0125037 + 0.214680i
\(125\) 0.0540020 + 0.306261i 0.00483008 + 0.0273928i
\(126\) 0.235327 + 1.34179i 0.0209646 + 0.119536i
\(127\) −2.51136 + 14.2427i −0.222848 + 1.26383i 0.643910 + 0.765101i \(0.277311\pi\)
−0.866757 + 0.498730i \(0.833800\pi\)
\(128\) 13.1301 + 3.11190i 1.16055 + 0.275056i
\(129\) 2.89718 + 2.43329i 0.255083 + 0.214239i
\(130\) −0.0720487 1.23703i −0.00631909 0.108495i
\(131\) −3.72370 + 0.882534i −0.325342 + 0.0771074i −0.390041 0.920797i \(-0.627539\pi\)
0.0646996 + 0.997905i \(0.479391\pi\)
\(132\) −3.63827 1.82929i −0.316670 0.159219i
\(133\) 1.35141 0.157957i 0.117182 0.0136966i
\(134\) 5.30132 + 9.18216i 0.457964 + 0.793217i
\(135\) 16.0720 3.78584i 1.38326 0.325833i
\(136\) 5.07415 8.78868i 0.435104 0.753623i
\(137\) −5.65021 + 13.0987i −0.482730 + 1.11909i 0.486666 + 0.873588i \(0.338213\pi\)
−0.969395 + 0.245505i \(0.921046\pi\)
\(138\) 8.44690 + 8.96141i 0.719048 + 0.762846i
\(139\) −4.04427 4.28668i −0.343031 0.363591i 0.532773 0.846258i \(-0.321150\pi\)
−0.875804 + 0.482667i \(0.839668\pi\)
\(140\) 0.336178 + 0.168835i 0.0284123 + 0.0142692i
\(141\) −10.1670 + 8.52320i −0.856216 + 0.717783i
\(142\) 2.23031 + 7.44974i 0.187163 + 0.625168i
\(143\) −1.12046 0.940175i −0.0936973 0.0786213i
\(144\) 4.00889 13.3461i 0.334074 1.11218i
\(145\) −12.4523 + 10.4487i −1.03411 + 0.867719i
\(146\) −2.36447 1.55514i −0.195685 0.128704i
\(147\) 10.0026 + 6.58539i 0.825003 + 0.543154i
\(148\) −1.96738 0.229954i −0.161717 0.0189021i
\(149\) 5.58042 + 12.9369i 0.457166 + 1.05983i 0.978457 + 0.206451i \(0.0661913\pi\)
−0.521291 + 0.853379i \(0.674549\pi\)
\(150\) 5.42852 12.5689i 0.443237 1.02625i
\(151\) 1.41535 0.710815i 0.115180 0.0578453i −0.390276 0.920698i \(-0.627621\pi\)
0.505456 + 0.862852i \(0.331324\pi\)
\(152\) −10.8025 3.93178i −0.876196 0.318909i
\(153\) −10.2739 6.77076i −0.830599 0.547383i
\(154\) 2.48174 0.903281i 0.199985 0.0727884i
\(155\) −12.9177 + 13.6920i −1.03758 + 1.09977i
\(156\) −0.0881110 + 0.152451i −0.00705452 + 0.0122059i
\(157\) −4.28135 + 2.81589i −0.341689 + 0.224732i −0.708742 0.705468i \(-0.750737\pi\)
0.367053 + 0.930200i \(0.380367\pi\)
\(158\) 4.80658 16.0551i 0.382391 1.27727i
\(159\) −12.1278 1.42317i −0.961799 0.112864i
\(160\) −4.27689 5.74486i −0.338118 0.454171i
\(161\) −1.34287 −0.105833
\(162\) −13.1047 4.79692i −1.02960 0.376881i
\(163\) −17.6764 −1.38452 −0.692262 0.721646i \(-0.743386\pi\)
−0.692262 + 0.721646i \(0.743386\pi\)
\(164\) −0.439726 0.590654i −0.0343368 0.0461223i
\(165\) −12.6656 29.3992i −0.986019 2.28873i
\(166\) 4.49050 14.9993i 0.348530 1.16417i
\(167\) −1.15161 + 0.757426i −0.0891143 + 0.0586114i −0.593284 0.804993i \(-0.702169\pi\)
0.504170 + 0.863605i \(0.331799\pi\)
\(168\) 0.627037 + 1.08721i 0.0483770 + 0.0838800i
\(169\) 8.87774 9.40986i 0.682903 0.723835i
\(170\) −18.9901 + 6.91183i −1.45647 + 0.530113i
\(171\) −5.53230 + 12.7931i −0.423066 + 0.978313i
\(172\) −0.829771 0.302012i −0.0632695 0.0230282i
\(173\) 11.6171 5.83431i 0.883230 0.443575i 0.0514468 0.998676i \(-0.483617\pi\)
0.831783 + 0.555101i \(0.187320\pi\)
\(174\) 13.6461 1.58866i 1.03451 0.120436i
\(175\) 0.591320 + 1.37083i 0.0446996 + 0.103625i
\(176\) −26.8335 3.13638i −2.02265 0.236414i
\(177\) −14.2398 + 7.14333i −1.07033 + 0.536925i
\(178\) 13.5066 + 8.88345i 1.01237 + 0.665843i
\(179\) 19.1637 16.0803i 1.43237 1.20190i 0.488067 0.872806i \(-0.337702\pi\)
0.944298 0.329091i \(-0.106742\pi\)
\(180\) −3.22168 + 2.11471i −0.240129 + 0.157621i
\(181\) 3.52910 + 2.96126i 0.262316 + 0.220109i 0.764454 0.644678i \(-0.223009\pi\)
−0.502138 + 0.864787i \(0.667453\pi\)
\(182\) −0.0327518 0.109399i −0.00242773 0.00810917i
\(183\) 5.06860 + 1.84745i 0.374681 + 0.136567i
\(184\) 10.1390 + 5.09201i 0.747458 + 0.375388i
\(185\) −10.6852 11.3256i −0.785590 0.832677i
\(186\) 15.4819 3.66179i 1.13519 0.268495i
\(187\) −9.44823 + 21.9035i −0.690923 + 1.60174i
\(188\) 1.54820 2.68156i 0.112914 0.195573i
\(189\) 1.36079 0.681076i 0.0989830 0.0495410i
\(190\) 11.4460 + 19.8251i 0.830384 + 1.43827i
\(191\) −2.66989 + 0.312065i −0.193186 + 0.0225803i −0.212136 0.977240i \(-0.568042\pi\)
0.0189494 + 0.999820i \(0.493968\pi\)
\(192\) −0.579069 10.0213i −0.0417907 0.723222i
\(193\) 6.42800 1.52346i 0.462697 0.109661i 0.00734588 0.999973i \(-0.497662\pi\)
0.455352 + 0.890312i \(0.349514\pi\)
\(194\) −0.588534 10.1047i −0.0422543 0.725478i
\(195\) −1.30090 + 0.472815i −0.0931595 + 0.0338590i
\(196\) −2.71970 0.644581i −0.194264 0.0460415i
\(197\) −2.65657 + 15.0662i −0.189273 + 1.07342i 0.731068 + 0.682304i \(0.239022\pi\)
−0.920341 + 0.391116i \(0.872089\pi\)
\(198\) −4.72237 + 26.6393i −0.335604 + 1.89317i
\(199\) 2.44426 + 13.8621i 0.173269 + 0.982657i 0.940123 + 0.340835i \(0.110710\pi\)
−0.766854 + 0.641821i \(0.778179\pi\)
\(200\) 0.733424 12.5924i 0.0518609 0.890417i
\(201\) 8.13154 8.61103i 0.573555 0.607375i
\(202\) 0.287043 0.385566i 0.0201963 0.0271283i
\(203\) −0.894586 + 1.20164i −0.0627876 + 0.0843384i
\(204\) 2.79401 + 0.663544i 0.195620 + 0.0464574i
\(205\) 0.336569 5.77866i 0.0235070 0.403599i
\(206\) −2.59967 14.7434i −0.181127 1.02722i
\(207\) 6.88907 11.9070i 0.478823 0.827596i
\(208\) −0.202849 + 1.15042i −0.0140651 + 0.0797670i
\(209\) 26.2933 + 6.23162i 1.81874 + 0.431050i
\(210\) 0.435123 2.46112i 0.0300264 0.169833i
\(211\) −0.898645 15.4291i −0.0618653 1.06219i −0.876249 0.481859i \(-0.839962\pi\)
0.814384 0.580327i \(-0.197075\pi\)
\(212\) 2.77312 0.657242i 0.190459 0.0451396i
\(213\) 7.25976 4.77006i 0.497431 0.326839i
\(214\) −16.3679 + 1.91314i −1.11889 + 0.130779i
\(215\) −3.47067 6.01137i −0.236698 0.409972i
\(216\) −12.8569 0.0176557i −0.874803 0.00120132i
\(217\) −0.867392 + 1.50237i −0.0588824 + 0.101987i
\(218\) −10.5359 + 24.4249i −0.713579 + 1.65426i
\(219\) −0.908056 + 3.02807i −0.0613608 + 0.204618i
\(220\) 5.12704 + 5.43434i 0.345665 + 0.366383i
\(221\) 0.921737 + 0.462914i 0.0620028 + 0.0311390i
\(222\) 2.27919 + 12.9606i 0.152969 + 0.869861i
\(223\) −1.39226 4.65047i −0.0932325 0.311418i 0.898634 0.438699i \(-0.144560\pi\)
−0.991867 + 0.127280i \(0.959375\pi\)
\(224\) −0.505626 0.424270i −0.0337836 0.0283478i
\(225\) −15.1886 1.78938i −1.01257 0.119292i
\(226\) 12.5811 10.5568i 0.836880 0.702225i
\(227\) 16.1686 + 10.6342i 1.07315 + 0.705820i 0.957780 0.287503i \(-0.0928252\pi\)
0.115367 + 0.993323i \(0.463196\pi\)
\(228\) 0.190633 3.24743i 0.0126250 0.215066i
\(229\) 3.65865 + 0.427635i 0.241770 + 0.0282589i 0.236115 0.971725i \(-0.424126\pi\)
0.00565534 + 0.999984i \(0.498200\pi\)
\(230\) −8.94887 20.7458i −0.590071 1.36794i
\(231\) −1.76062 2.36718i −0.115840 0.155749i
\(232\) 11.3109 5.68053i 0.742594 0.372945i
\(233\) −1.43618 0.522727i −0.0940872 0.0342450i 0.294548 0.955637i \(-0.404831\pi\)
−0.388635 + 0.921392i \(0.627053\pi\)
\(234\) 1.13805 + 0.270822i 0.0743964 + 0.0177042i
\(235\) 22.8724 8.32488i 1.49203 0.543056i
\(236\) 2.55156 2.70449i 0.166092 0.176047i
\(237\) −18.7207 0.00856939i −1.21604 0.000556642i
\(238\) −1.55603 + 1.02342i −0.100863 + 0.0663383i
\(239\) −1.36488 + 4.55903i −0.0882871 + 0.294899i −0.990718 0.135936i \(-0.956596\pi\)
0.902431 + 0.430835i \(0.141781\pi\)
\(240\) −15.2765 + 20.5003i −0.986096 + 1.32329i
\(241\) 15.1105 + 20.2969i 0.973350 + 1.30744i 0.951491 + 0.307675i \(0.0995511\pi\)
0.0218591 + 0.999761i \(0.493041\pi\)
\(242\) 35.3943 2.27523
\(243\) −0.942003 + 15.5600i −0.0604295 + 0.998172i
\(244\) −1.25909 −0.0806052
\(245\) −13.1204 17.6238i −0.838235 1.12594i
\(246\) −2.92317 + 3.92275i −0.186375 + 0.250106i
\(247\) 0.335101 1.11932i 0.0213220 0.0712204i
\(248\) 12.2459 8.05424i 0.777614 0.511444i
\(249\) −17.4897 0.00800586i −1.10836 0.000507351i
\(250\) −0.330907 + 0.350741i −0.0209284 + 0.0221828i
\(251\) −2.06755 + 0.752528i −0.130503 + 0.0474991i −0.406446 0.913675i \(-0.633232\pi\)
0.275943 + 0.961174i \(0.411010\pi\)
\(252\) −0.243958 + 0.258107i −0.0153679 + 0.0162592i
\(253\) −25.0609 9.12143i −1.57557 0.573460i
\(254\) −20.0395 + 10.0642i −1.25739 + 0.631487i
\(255\) 13.4721 + 18.1135i 0.843656 + 1.13431i
\(256\) 3.69630 + 8.56900i 0.231019 + 0.535562i
\(257\) 10.1971 + 1.19186i 0.636075 + 0.0743465i 0.428018 0.903770i \(-0.359212\pi\)
0.208057 + 0.978117i \(0.433286\pi\)
\(258\) −0.343787 + 5.85641i −0.0214032 + 0.364604i
\(259\) −1.19890 0.788527i −0.0744958 0.0489967i
\(260\) 0.247471 0.207653i 0.0153475 0.0128781i
\(261\) −6.06543 14.0967i −0.375441 0.872565i
\(262\) −4.54554 3.81416i −0.280825 0.235640i
\(263\) −0.455133 1.52025i −0.0280647 0.0937426i 0.942810 0.333331i \(-0.108173\pi\)
−0.970875 + 0.239588i \(0.922987\pi\)
\(264\) 4.31706 + 24.5490i 0.265696 + 1.51088i
\(265\) 20.0201 + 10.0545i 1.22982 + 0.617641i
\(266\) 1.44777 + 1.53455i 0.0887684 + 0.0940890i
\(267\) 5.18711 17.2973i 0.317446 1.05858i
\(268\) −1.09484 + 2.53813i −0.0668782 + 0.155041i
\(269\) 2.49753 4.32585i 0.152277 0.263752i −0.779787 0.626045i \(-0.784673\pi\)
0.932064 + 0.362293i \(0.118006\pi\)
\(270\) 19.5902 + 16.4840i 1.19222 + 1.00319i
\(271\) −4.63580 8.02944i −0.281605 0.487754i 0.690175 0.723642i \(-0.257533\pi\)
−0.971780 + 0.235888i \(0.924200\pi\)
\(272\) 18.9227 2.21175i 1.14736 0.134107i
\(273\) −0.106609 + 0.0700479i −0.00645227 + 0.00423949i
\(274\) −21.5231 + 5.10106i −1.30026 + 0.308166i
\(275\) 1.72397 + 29.5994i 0.103959 + 1.78491i
\(276\) −0.558962 + 3.16157i −0.0336456 + 0.190304i
\(277\) −25.1474 5.96004i −1.51096 0.358104i −0.610139 0.792294i \(-0.708887\pi\)
−0.900821 + 0.434190i \(0.857035\pi\)
\(278\) 1.58680 8.99921i 0.0951701 0.539737i
\(279\) −8.87147 15.3984i −0.531121 0.921877i
\(280\) −0.399845 2.26764i −0.0238953 0.135517i
\(281\) 1.68385 28.9105i 0.100450 1.72466i −0.452775 0.891625i \(-0.649566\pi\)
0.553225 0.833032i \(-0.313397\pi\)
\(282\) −20.0146 4.75323i −1.19185 0.283051i
\(283\) 0.616270 0.827794i 0.0366334 0.0492072i −0.783429 0.621481i \(-0.786531\pi\)
0.820062 + 0.572274i \(0.193939\pi\)
\(284\) −1.21067 + 1.62621i −0.0718399 + 0.0964978i
\(285\) 17.5568 18.5920i 1.03997 1.10130i
\(286\) 0.131869 2.26410i 0.00779755 0.133879i
\(287\) −0.0926338 0.525353i −0.00546800 0.0310106i
\(288\) 6.35588 2.30676i 0.374524 0.135927i
\(289\) −0.0309285 + 0.175404i −0.00181932 + 0.0103179i
\(290\) −24.5255 5.81265i −1.44019 0.341331i
\(291\) −10.6265 + 3.86222i −0.622936 + 0.226407i
\(292\) −0.0429003 0.736569i −0.00251055 0.0431045i
\(293\) 6.75313 1.60052i 0.394522 0.0935035i −0.0285661 0.999592i \(-0.509094\pi\)
0.423088 + 0.906088i \(0.360946\pi\)
\(294\) 1.07122 + 18.5383i 0.0624748 + 1.08118i
\(295\) 29.0303 3.39316i 1.69021 0.197557i
\(296\) 6.06200 + 10.4997i 0.352346 + 0.610282i
\(297\) 30.0217 3.46725i 1.74203 0.201190i
\(298\) −10.9230 + 18.9193i −0.632755 + 1.09596i
\(299\) −0.456746 + 1.05886i −0.0264143 + 0.0612352i
\(300\) 3.47355 0.821567i 0.200545 0.0474332i
\(301\) −0.438992 0.465305i −0.0253031 0.0268197i
\(302\) 2.19459 + 1.10216i 0.126284 + 0.0634224i
\(303\) −0.504479 0.183877i −0.0289815 0.0105634i
\(304\) −6.18954 20.6745i −0.354994 1.18576i
\(305\) −7.58197 6.36203i −0.434143 0.364289i
\(306\) −1.09189 19.0474i −0.0624191 1.08887i
\(307\) 14.0395 11.7805i 0.801275 0.672350i −0.147233 0.989102i \(-0.547037\pi\)
0.948508 + 0.316752i \(0.102592\pi\)
\(308\) 0.575263 + 0.378356i 0.0327786 + 0.0215588i
\(309\) −14.9478 + 7.49851i −0.850351 + 0.426575i
\(310\) −28.9902 3.38847i −1.64653 0.192452i
\(311\) 5.82070 + 13.4939i 0.330062 + 0.765169i 0.999746 + 0.0225232i \(0.00716997\pi\)
−0.669685 + 0.742645i \(0.733571\pi\)
\(312\) 1.07054 0.124632i 0.0606075 0.00705588i
\(313\) 5.05726 2.53985i 0.285853 0.143561i −0.300095 0.953909i \(-0.597018\pi\)
0.585948 + 0.810348i \(0.300722\pi\)
\(314\) −7.46647 2.71757i −0.421358 0.153362i
\(315\) −2.77324 + 0.321572i −0.156254 + 0.0181185i
\(316\) 4.10575 1.49437i 0.230967 0.0840650i
\(317\) 15.7261 16.6687i 0.883267 0.936208i −0.115099 0.993354i \(-0.536719\pi\)
0.998366 + 0.0571458i \(0.0182000\pi\)
\(318\) −9.45948 16.4016i −0.530461 0.919758i
\(319\) −24.8571 + 16.3488i −1.39173 + 0.915357i
\(320\) −5.28183 + 17.6425i −0.295263 + 0.986247i
\(321\) 7.28338 + 16.9060i 0.406519 + 0.943603i
\(322\) −1.24340 1.67018i −0.0692921 0.0930755i
\(323\) −19.0554 −1.06027
\(324\) −1.03706 3.48726i −0.0576147 0.193737i
\(325\) 1.28203 0.0711144
\(326\) −16.3672 21.9849i −0.906493 1.21763i
\(327\) 29.5114 + 3.46308i 1.63198 + 0.191509i
\(328\) −1.29267 + 4.31782i −0.0713757 + 0.238412i
\(329\) 1.87415 1.23264i 0.103325 0.0679579i
\(330\) 24.8376 42.9745i 1.36726 2.36567i
\(331\) −2.11190 + 2.23849i −0.116081 + 0.123038i −0.782808 0.622264i \(-0.786213\pi\)
0.666727 + 0.745302i \(0.267695\pi\)
\(332\) 3.83576 1.39610i 0.210515 0.0766210i
\(333\) 13.1423 6.58523i 0.720191 0.360868i
\(334\) −2.00836 0.730982i −0.109892 0.0399975i
\(335\) −19.4177 + 9.75195i −1.06090 + 0.532806i
\(336\) −0.934218 + 2.16304i −0.0509658 + 0.118003i
\(337\) −1.62778 3.77363i −0.0886711 0.205563i 0.868110 0.496372i \(-0.165335\pi\)
−0.956781 + 0.290809i \(0.906076\pi\)
\(338\) 19.9236 + 2.32874i 1.08370 + 0.126667i
\(339\) −15.3230 10.0881i −0.832231 0.547913i
\(340\) −4.40186 2.89515i −0.238725 0.157012i
\(341\) −26.3924 + 22.1458i −1.42923 + 1.19926i
\(342\) −21.0339 + 4.96478i −1.13738 + 0.268465i
\(343\) −3.12151 2.61926i −0.168546 0.141427i
\(344\) 1.55013 + 5.17779i 0.0835774 + 0.279168i
\(345\) −19.3409 + 16.2139i −1.04128 + 0.872926i
\(346\) 18.0130 + 9.04647i 0.968385 + 0.486341i
\(347\) 6.14191 + 6.51005i 0.329715 + 0.349478i 0.870930 0.491407i \(-0.163517\pi\)
−0.541215 + 0.840884i \(0.682036\pi\)
\(348\) 2.45670 + 2.60634i 0.131693 + 0.139714i
\(349\) 1.96434 4.55386i 0.105149 0.243762i −0.857517 0.514456i \(-0.827994\pi\)
0.962666 + 0.270694i \(0.0872531\pi\)
\(350\) −1.15744 + 2.00475i −0.0618679 + 0.107158i
\(351\) −0.0741893 1.30464i −0.00395993 0.0696367i
\(352\) −6.55427 11.3523i −0.349344 0.605081i
\(353\) −20.1602 + 2.35639i −1.07302 + 0.125418i −0.634209 0.773161i \(-0.718674\pi\)
−0.438811 + 0.898579i \(0.644600\pi\)
\(354\) −22.0695 11.0964i −1.17298 0.589766i
\(355\) −15.5074 + 3.67532i −0.823047 + 0.195066i
\(356\) 0.245060 + 4.20752i 0.0129882 + 0.222998i
\(357\) 1.59308 + 1.33799i 0.0843145 + 0.0708141i
\(358\) 37.7441 + 8.94551i 1.99484 + 0.472785i
\(359\) −1.35166 + 7.66566i −0.0713380 + 0.404578i 0.928139 + 0.372234i \(0.121408\pi\)
−0.999477 + 0.0323438i \(0.989703\pi\)
\(360\) 22.1581 + 8.08787i 1.16783 + 0.426268i
\(361\) 0.448974 + 2.54626i 0.0236302 + 0.134014i
\(362\) −0.415346 + 7.13122i −0.0218301 + 0.374808i
\(363\) −11.3220 37.8813i −0.594253 1.98825i
\(364\) 0.0177785 0.0238807i 0.000931849 0.00125169i
\(365\) 3.46345 4.65222i 0.181285 0.243508i
\(366\) 2.39543 + 8.01464i 0.125211 + 0.418932i
\(367\) 0.0112963 0.193950i 0.000589663 0.0101241i −0.998000 0.0632061i \(-0.979867\pi\)
0.998590 + 0.0530820i \(0.0169045\pi\)
\(368\) 3.69866 + 20.9761i 0.192806 + 1.09346i
\(369\) 5.13346 + 1.87375i 0.267237 + 0.0975435i
\(370\) 4.19242 23.7764i 0.217953 1.23607i
\(371\) 2.00898 + 0.476138i 0.104301 + 0.0247198i
\(372\) 3.17604 + 2.66749i 0.164670 + 0.138303i
\(373\) −0.132942 2.28253i −0.00688350 0.118185i −0.999999 0.00104965i \(-0.999666\pi\)
0.993116 0.117135i \(-0.0373712\pi\)
\(374\) −35.9907 + 8.52994i −1.86103 + 0.441073i
\(375\) 0.481237 + 0.241962i 0.0248510 + 0.0124949i
\(376\) −18.8244 + 2.20026i −0.970794 + 0.113469i
\(377\) 0.643223 + 1.11409i 0.0331277 + 0.0573788i
\(378\) 2.10708 + 1.06184i 0.108377 + 0.0546153i
\(379\) 3.62704 6.28222i 0.186309 0.322696i −0.757708 0.652594i \(-0.773681\pi\)
0.944017 + 0.329898i \(0.107014\pi\)
\(380\) −2.36387 + 5.48006i −0.121264 + 0.281121i
\(381\) 17.1817 + 18.2283i 0.880246 + 0.933862i
\(382\) −2.86027 3.03170i −0.146344 0.155115i
\(383\) 24.1849 + 12.1461i 1.23579 + 0.620637i 0.942122 0.335271i \(-0.108828\pi\)
0.293667 + 0.955908i \(0.405124\pi\)
\(384\) 17.9109 15.0151i 0.914012 0.766234i
\(385\) 1.55232 + 5.18510i 0.0791134 + 0.264257i
\(386\) 7.84669 + 6.58415i 0.399386 + 0.335124i
\(387\) 6.37788 1.50542i 0.324206 0.0765248i
\(388\) 2.02148 1.69622i 0.102625 0.0861126i
\(389\) 19.1210 + 12.5761i 0.969474 + 0.637633i 0.932304 0.361676i \(-0.117795\pi\)
0.0371701 + 0.999309i \(0.488166\pi\)
\(390\) −1.79261 1.18019i −0.0907721 0.0597613i
\(391\) 18.6798 + 2.18335i 0.944678 + 0.110417i
\(392\) 6.77614 + 15.7089i 0.342247 + 0.793417i
\(393\) −2.62813 + 6.08502i −0.132571 + 0.306949i
\(394\) −21.1982 + 10.6462i −1.06795 + 0.536346i
\(395\) 32.2748 + 11.7471i 1.62392 + 0.591059i
\(396\) −6.30601 + 3.15977i −0.316889 + 0.158784i
\(397\) −16.8844 + 6.14542i −0.847403 + 0.308430i −0.728981 0.684534i \(-0.760006\pi\)
−0.118422 + 0.992963i \(0.537784\pi\)
\(398\) −14.9776 + 15.8754i −0.750761 + 0.795760i
\(399\) 1.17925 2.04037i 0.0590366 0.102146i
\(400\) 19.7843 13.0124i 0.989216 0.650618i
\(401\) 0.411776 1.37543i 0.0205631 0.0686856i −0.947092 0.320962i \(-0.895994\pi\)
0.967655 + 0.252276i \(0.0811791\pi\)
\(402\) 18.2392 + 2.14032i 0.909687 + 0.106749i
\(403\) 0.889599 + 1.19494i 0.0443141 + 0.0595242i
\(404\) 0.125318 0.00623480
\(405\) 11.3757 26.2397i 0.565264 1.30386i
\(406\) −2.32285 −0.115281
\(407\) −17.0181 22.8592i −0.843554 1.13309i
\(408\) −6.95465 16.1430i −0.344306 0.799198i
\(409\) −3.73740 + 12.4838i −0.184803 + 0.617284i 0.814508 + 0.580153i \(0.197007\pi\)
−0.999310 + 0.0371312i \(0.988178\pi\)
\(410\) 7.49881 4.93204i 0.370340 0.243576i
\(411\) 12.3443 + 21.4036i 0.608901 + 1.05576i
\(412\) 2.67843 2.83897i 0.131957 0.139866i
\(413\) 2.53117 0.921270i 0.124551 0.0453328i
\(414\) 21.1881 2.45687i 1.04134 0.120749i
\(415\) 30.1524 + 10.9746i 1.48012 + 0.538720i
\(416\) −0.506517 + 0.254382i −0.0248340 + 0.0124721i
\(417\) −10.1391 + 1.18039i −0.496515 + 0.0578040i
\(418\) 16.5952 + 38.4721i 0.811700 + 1.88173i
\(419\) −29.7448 3.47667i −1.45313 0.169846i −0.647408 0.762143i \(-0.724147\pi\)
−0.805720 + 0.592297i \(0.798221\pi\)
\(420\) 0.582412 0.292164i 0.0284188 0.0142562i
\(421\) −26.9903 17.7518i −1.31543 0.865171i −0.318849 0.947806i \(-0.603296\pi\)
−0.996580 + 0.0826343i \(0.973667\pi\)
\(422\) 18.3578 15.4040i 0.893643 0.749856i
\(423\) 1.31511 + 22.9414i 0.0639430 + 1.11545i
\(424\) −13.3629 11.2128i −0.648961 0.544543i
\(425\) −5.99666 20.0303i −0.290881 0.971610i
\(426\) 12.6548 + 4.61252i 0.613126 + 0.223477i
\(427\) −0.815125 0.409371i −0.0394467 0.0198109i
\(428\) −2.94830 3.12502i −0.142512 0.151053i
\(429\) −2.46537 + 0.583111i −0.119029 + 0.0281529i
\(430\) 4.26300 9.88274i 0.205580 0.476588i
\(431\) 15.3414 26.5721i 0.738970 1.27993i −0.213989 0.976836i \(-0.568646\pi\)
0.952960 0.303098i \(-0.0980208\pi\)
\(432\) −14.3867 19.3802i −0.692182 0.932432i
\(433\) −19.2517 33.3449i −0.925176 1.60245i −0.791277 0.611457i \(-0.790584\pi\)
−0.133899 0.990995i \(-0.542750\pi\)
\(434\) −2.67170 + 0.312277i −0.128246 + 0.0149898i
\(435\) 1.62420 + 28.1082i 0.0778746 + 1.34768i
\(436\) −6.74801 + 1.59931i −0.323171 + 0.0765930i
\(437\) −1.23872 21.2680i −0.0592561 1.01739i
\(438\) −4.60694 + 1.67440i −0.220128 + 0.0800060i
\(439\) 38.5142 + 9.12802i 1.83818 + 0.435657i 0.994817 0.101686i \(-0.0324237\pi\)
0.843364 + 0.537343i \(0.180572\pi\)
\(440\) 7.94092 45.0352i 0.378569 2.14697i
\(441\) 19.4983 7.07658i 0.928488 0.336980i
\(442\) 0.277720 + 1.57503i 0.0132098 + 0.0749166i
\(443\) −0.351273 + 6.03112i −0.0166895 + 0.286547i 0.979629 + 0.200816i \(0.0643595\pi\)
−0.996318 + 0.0857306i \(0.972678\pi\)
\(444\) −2.35550 + 2.49439i −0.111787 + 0.118379i
\(445\) −19.7844 + 26.5750i −0.937869 + 1.25978i
\(446\) 4.49485 6.03763i 0.212837 0.285890i
\(447\) 23.7427 + 5.63861i 1.12299 + 0.266697i
\(448\) −0.0986843 + 1.69434i −0.00466239 + 0.0800502i
\(449\) −0.417057 2.36525i −0.0196821 0.111623i 0.973384 0.229181i \(-0.0736046\pi\)
−0.993066 + 0.117558i \(0.962494\pi\)
\(450\) −11.8380 20.5475i −0.558050 0.968618i
\(451\) 1.83971 10.4335i 0.0866284 0.491294i
\(452\) 4.16631 + 0.987433i 0.195967 + 0.0464449i
\(453\) 0.477597 2.70136i 0.0224395 0.126921i
\(454\) 1.74475 + 29.9561i 0.0818850 + 1.40591i
\(455\) 0.227725 0.0539717i 0.0106759 0.00253023i
\(456\) −16.6406 + 10.9338i −0.779267 + 0.512021i
\(457\) 12.8119 1.49750i 0.599317 0.0700501i 0.188975 0.981982i \(-0.439483\pi\)
0.410342 + 0.911932i \(0.365409\pi\)
\(458\) 2.85579 + 4.94638i 0.133442 + 0.231129i
\(459\) −20.0365 + 7.26154i −0.935223 + 0.338940i
\(460\) 2.94517 5.10118i 0.137319 0.237844i
\(461\) −11.7178 + 27.1648i −0.545750 + 1.26519i 0.392665 + 0.919682i \(0.371553\pi\)
−0.938415 + 0.345510i \(0.887706\pi\)
\(462\) 1.31395 4.38160i 0.0611305 0.203851i
\(463\) −23.7270 25.1492i −1.10269 1.16878i −0.984426 0.175798i \(-0.943750\pi\)
−0.118261 0.992983i \(-0.537732\pi\)
\(464\) 21.2340 + 10.6641i 0.985766 + 0.495070i
\(465\) 5.64691 + 32.1111i 0.261869 + 1.48912i
\(466\) −0.679667 2.27025i −0.0314850 0.105167i
\(467\) −24.0070 20.1443i −1.11091 0.932165i −0.112801 0.993618i \(-0.535982\pi\)
−0.998110 + 0.0614529i \(0.980427\pi\)
\(468\) 0.120541 + 0.280151i 0.00557203 + 0.0129500i
\(469\) −1.53402 + 1.28719i −0.0708343 + 0.0594371i
\(470\) 31.5323 + 20.7391i 1.45448 + 0.956625i
\(471\) −0.520130 + 8.86041i −0.0239663 + 0.408266i
\(472\) −22.6044 2.64208i −1.04045 0.121611i
\(473\) −5.03201 11.6655i −0.231372 0.536380i
\(474\) −17.3235 23.2917i −0.795694 1.06982i
\(475\) −21.1655 + 10.6297i −0.971140 + 0.487725i
\(476\) −0.456267 0.166068i −0.0209130 0.00761170i
\(477\) −14.5282 + 15.3708i −0.665200 + 0.703779i
\(478\) −6.93405 + 2.52379i −0.317156 + 0.115435i
\(479\) 6.50596 6.89591i 0.297265 0.315082i −0.561475 0.827493i \(-0.689766\pi\)
0.858740 + 0.512411i \(0.171248\pi\)
\(480\) −12.4051 0.00567840i −0.566211 0.000259182i
\(481\) −1.02953 + 0.677135i −0.0469427 + 0.0308747i
\(482\) −11.2528 + 37.5870i −0.512552 + 1.71204i
\(483\) −1.38979 + 1.86503i −0.0632377 + 0.0848619i
\(484\) 5.51034 + 7.40167i 0.250470 + 0.336440i
\(485\) 20.7437 0.941922
\(486\) −20.2248 + 13.2359i −0.917417 + 0.600391i
\(487\) −16.8494 −0.763520 −0.381760 0.924261i \(-0.624682\pi\)
−0.381760 + 0.924261i \(0.624682\pi\)
\(488\) 4.60213 + 6.18173i 0.208329 + 0.279834i
\(489\) −18.2941 + 24.5498i −0.827288 + 1.11018i
\(490\) 9.77085 32.6369i 0.441402 1.47439i
\(491\) −12.9995 + 8.54993i −0.586661 + 0.385853i −0.807859 0.589376i \(-0.799374\pi\)
0.221198 + 0.975229i \(0.429003\pi\)
\(492\) −1.27542 0.000583821i −0.0575003 2.63207e-5i
\(493\) 14.3978 15.2607i 0.648443 0.687309i
\(494\) 1.70242 0.619631i 0.0765956 0.0278785i
\(495\) −53.9392 12.8360i −2.42439 0.576935i
\(496\) 25.8567 + 9.41106i 1.16100 + 0.422569i
\(497\) −1.31251 + 0.659166i −0.0588740 + 0.0295676i
\(498\) −16.1843 21.7600i −0.725235 0.975091i
\(499\) −7.23826 16.7802i −0.324029 0.751184i −0.999900 0.0141637i \(-0.995491\pi\)
0.675871 0.737020i \(-0.263768\pi\)
\(500\) −0.124864 0.0145945i −0.00558409 0.000652686i
\(501\) −0.139906 + 2.38330i −0.00625055 + 0.106478i
\(502\) −2.85036 1.87471i −0.127218 0.0836726i
\(503\) −22.0539 + 18.5054i −0.983333 + 0.825114i −0.984589 0.174885i \(-0.944045\pi\)
0.00125604 + 0.999999i \(0.499600\pi\)
\(504\) 2.15891 + 0.254344i 0.0961656 + 0.0113294i
\(505\) 0.754636 + 0.633215i 0.0335808 + 0.0281777i
\(506\) −11.8600 39.6152i −0.527242 1.76111i
\(507\) −3.88085 22.0685i −0.172355 0.980096i
\(508\) −5.22448 2.62383i −0.231799 0.116414i
\(509\) −6.35316 6.73395i −0.281599 0.298477i 0.571100 0.820881i \(-0.306517\pi\)
−0.852698 + 0.522404i \(0.825035\pi\)
\(510\) −10.0542 + 33.5277i −0.445210 + 1.48463i
\(511\) 0.211709 0.490796i 0.00936545 0.0217115i
\(512\) 6.25876 10.8405i 0.276601 0.479086i
\(513\) 12.0420 + 20.9237i 0.531667 + 0.923802i
\(514\) 7.95941 + 13.7861i 0.351074 + 0.608079i
\(515\) 30.4738 3.56188i 1.34284 0.156955i
\(516\) −1.27822 + 0.839858i −0.0562703 + 0.0369727i
\(517\) 43.3486 10.2738i 1.90647 0.451841i
\(518\) −0.129372 2.22124i −0.00568430 0.0975957i
\(519\) 3.92008 22.1725i 0.172072 0.973265i
\(520\) −1.92404 0.456006i −0.0843747 0.0199972i
\(521\) −0.982915 + 5.57439i −0.0430623 + 0.244218i −0.998739 0.0501990i \(-0.984014\pi\)
0.955677 + 0.294417i \(0.0951256\pi\)
\(522\) 11.9165 20.5964i 0.521572 0.901482i
\(523\) 2.68166 + 15.2084i 0.117261 + 0.665018i 0.985606 + 0.169058i \(0.0540726\pi\)
−0.868345 + 0.495960i \(0.834816\pi\)
\(524\) 0.0899493 1.54437i 0.00392945 0.0674661i
\(525\) 2.51586 + 0.597486i 0.109801 + 0.0260764i
\(526\) 1.46938 1.97372i 0.0640679 0.0860581i
\(527\) 14.5084 19.4882i 0.631998 0.848921i
\(528\) −32.1271 + 34.0215i −1.39815 + 1.48060i
\(529\) 0.114762 1.97038i 0.00498964 0.0856687i
\(530\) 6.03207 + 34.2096i 0.262016 + 1.48597i
\(531\) −4.81642 + 27.1698i −0.209015 + 1.17907i
\(532\) −0.0955097 + 0.541662i −0.00414087 + 0.0234840i
\(533\) −0.445750 0.105645i −0.0193076 0.00457598i
\(534\) 26.3164 9.56473i 1.13882 0.413906i
\(535\) −1.96371 33.7155i −0.0848984 1.45765i
\(536\) 16.4632 3.90184i 0.711100 0.168534i
\(537\) −2.49960 43.2577i −0.107866 1.86671i
\(538\) 7.69278 0.899157i 0.331659 0.0387654i
\(539\) −20.1069 34.8261i −0.866064 1.50007i
\(540\) −0.397258 + 6.66301i −0.0170953 + 0.286730i
\(541\) −19.5695 + 33.8953i −0.841357 + 1.45727i 0.0473898 + 0.998876i \(0.484910\pi\)
−0.888747 + 0.458397i \(0.848424\pi\)
\(542\) 5.69412 13.2005i 0.244584 0.567008i
\(543\) 7.76516 1.83662i 0.333235 0.0788170i
\(544\) 6.34364 + 6.72386i 0.271981 + 0.288283i
\(545\) −48.7161 24.4661i −2.08677 1.04801i
\(546\) −0.185834 0.0677345i −0.00795297 0.00289877i
\(547\) 6.08425 + 20.3228i 0.260144 + 0.868941i 0.983875 + 0.178859i \(0.0572405\pi\)
−0.723731 + 0.690082i \(0.757574\pi\)
\(548\) −4.41754 3.70675i −0.188708 0.158345i
\(549\) 7.81153 5.12749i 0.333388 0.218836i
\(550\) −35.2178 + 29.5512i −1.50169 + 1.26007i
\(551\) −19.8565 13.0598i −0.845915 0.556367i
\(552\) 17.5653 8.81157i 0.747630 0.375045i
\(553\) 3.14389 + 0.367468i 0.133692 + 0.0156263i
\(554\) −15.8720 36.7955i −0.674337 1.56329i
\(555\) −26.7881 + 3.11865i −1.13709 + 0.132379i
\(556\) 2.12896 1.06920i 0.0902879 0.0453443i
\(557\) 2.55364 + 0.929451i 0.108201 + 0.0393821i 0.395554 0.918443i \(-0.370553\pi\)
−0.287352 + 0.957825i \(0.592775\pi\)
\(558\) 10.9372 25.2917i 0.463010 1.07068i
\(559\) −0.516208 + 0.187884i −0.0218333 + 0.00794666i
\(560\) 2.96644 3.14425i 0.125355 0.132869i
\(561\) 20.6421 + 35.7910i 0.871510 + 1.51110i
\(562\) 37.5164 24.6749i 1.58253 1.04085i
\(563\) 5.25606 17.5564i 0.221516 0.739916i −0.772913 0.634512i \(-0.781201\pi\)
0.994429 0.105404i \(-0.0336136\pi\)
\(564\) −2.12196 4.92547i −0.0893508 0.207400i
\(565\) 20.0992 + 26.9979i 0.845579 + 1.13581i
\(566\) 1.60019 0.0672608
\(567\) 0.462434 2.59480i 0.0194204 0.108972i
\(568\) 12.4093 0.520682
\(569\) 6.69263 + 8.98976i 0.280570 + 0.376870i 0.919960 0.392012i \(-0.128221\pi\)
−0.639391 + 0.768882i \(0.720813\pi\)
\(570\) 39.3801 + 4.62114i 1.64945 + 0.193558i
\(571\) −0.125284 + 0.418478i −0.00524298 + 0.0175128i −0.960571 0.278035i \(-0.910317\pi\)
0.955328 + 0.295548i \(0.0955021\pi\)
\(572\) 0.493998 0.324908i 0.0206551 0.0135851i
\(573\) −2.32978 + 4.03103i −0.0973279 + 0.168399i
\(574\) 0.567631 0.601653i 0.0236924 0.0251125i
\(575\) 21.9662 7.99505i 0.916055 0.333417i
\(576\) −14.5173 9.56721i −0.604886 0.398634i
\(577\) 34.0165 + 12.3810i 1.41612 + 0.515427i 0.932921 0.360081i \(-0.117251\pi\)
0.483203 + 0.875508i \(0.339473\pi\)
\(578\) −0.246795 + 0.123945i −0.0102653 + 0.00515544i
\(579\) 4.53677 10.5042i 0.188542 0.436539i
\(580\) −2.60269 6.03372i −0.108071 0.250536i
\(581\) 2.93715 + 0.343303i 0.121853 + 0.0142426i
\(582\) −14.6430 9.64046i −0.606972 0.399610i
\(583\) 34.2580 + 22.5319i 1.41882 + 0.933174i
\(584\) −3.45951 + 2.90287i −0.143155 + 0.120122i
\(585\) −0.689694 + 2.29609i −0.0285154 + 0.0949315i
\(586\) 8.24358 + 6.91718i 0.340539 + 0.285746i
\(587\) 0.230578 + 0.770183i 0.00951696 + 0.0317889i 0.962616 0.270869i \(-0.0873111\pi\)
−0.953099 + 0.302658i \(0.902126\pi\)
\(588\) −3.70997 + 3.11014i −0.152996 + 0.128260i
\(589\) −24.5943 12.3517i −1.01339 0.508944i
\(590\) 31.1003 + 32.9644i 1.28038 + 1.35712i
\(591\) 18.1752 + 19.2822i 0.747626 + 0.793165i
\(592\) −9.01499 + 20.8991i −0.370514 + 0.858948i
\(593\) −18.8891 + 32.7169i −0.775683 + 1.34352i 0.158726 + 0.987323i \(0.449261\pi\)
−0.934410 + 0.356200i \(0.884072\pi\)
\(594\) 32.1104 + 34.1288i 1.31751 + 1.40032i
\(595\) −1.90842 3.30548i −0.0782375 0.135511i
\(596\) −5.65695 + 0.661202i −0.231718 + 0.0270839i
\(597\) 21.7819 + 10.9518i 0.891476 + 0.448227i
\(598\) −1.73986 + 0.412354i −0.0711481 + 0.0168624i
\(599\) 1.70339 + 29.2461i 0.0695986 + 1.19496i 0.834571 + 0.550900i \(0.185715\pi\)
−0.764973 + 0.644063i \(0.777248\pi\)
\(600\) −16.7298 14.0511i −0.682993 0.573632i
\(601\) 3.87462 + 0.918301i 0.158049 + 0.0374583i 0.308879 0.951101i \(-0.400046\pi\)
−0.150830 + 0.988560i \(0.548194\pi\)
\(602\) 0.172242 0.976833i 0.00702006 0.0398128i
\(603\) −3.54369 20.2054i −0.144310 0.822827i
\(604\) 0.111178 + 0.630523i 0.00452377 + 0.0256556i
\(605\) −4.21765 + 72.4142i −0.171472 + 2.94406i
\(606\) −0.238417 0.797699i −0.00968505 0.0324043i
\(607\) −20.1594 + 27.0788i −0.818245 + 1.09909i 0.175171 + 0.984538i \(0.443952\pi\)
−0.993417 + 0.114556i \(0.963455\pi\)
\(608\) 6.25309 8.39936i 0.253596 0.340639i
\(609\) 0.743040 + 2.48607i 0.0301095 + 0.100741i
\(610\) 0.892337 15.3208i 0.0361297 0.620322i
\(611\) −0.334497 1.89703i −0.0135323 0.0767456i
\(612\) 3.81321 3.19372i 0.154140 0.129098i
\(613\) 7.41615 42.0591i 0.299536 1.69875i −0.348637 0.937258i \(-0.613355\pi\)
0.648173 0.761493i \(-0.275533\pi\)
\(614\) 27.6515 + 6.55353i 1.11592 + 0.264479i
\(615\) −7.67733 6.44804i −0.309580 0.260010i
\(616\) −0.245046 4.20729i −0.00987320 0.169516i
\(617\) −7.31208 + 1.73299i −0.294373 + 0.0697677i −0.375149 0.926965i \(-0.622408\pi\)
0.0807756 + 0.996732i \(0.474260\pi\)
\(618\) −23.1669 11.6481i −0.931908 0.468556i
\(619\) −20.8479 + 2.43677i −0.837946 + 0.0979419i −0.524232 0.851576i \(-0.675647\pi\)
−0.313714 + 0.949517i \(0.601573\pi\)
\(620\) −3.80472 6.58997i −0.152801 0.264660i
\(621\) −9.40720 21.8910i −0.377498 0.878454i
\(622\) −11.3934 + 19.7339i −0.456832 + 0.791256i
\(623\) −1.20935 + 2.80359i −0.0484516 + 0.112323i
\(624\) 1.38781 + 1.47234i 0.0555569 + 0.0589409i
\(625\) 16.8137 + 17.8215i 0.672547 + 0.712858i
\(626\) 7.84160 + 3.93820i 0.313413 + 0.157402i
\(627\) 35.8668 30.0679i 1.43238 1.20080i
\(628\) −0.594113 1.98447i −0.0237077 0.0791892i
\(629\) 15.3951 + 12.9180i 0.613841 + 0.515074i
\(630\) −2.96778 3.15144i −0.118239 0.125556i
\(631\) −23.1956 + 19.4634i −0.923403 + 0.774827i −0.974621 0.223860i \(-0.928134\pi\)
0.0512179 + 0.998688i \(0.483690\pi\)
\(632\) −22.3439 14.6958i −0.888791 0.584567i
\(633\) −22.3587 14.7202i −0.888679 0.585077i
\(634\) 35.2929 + 4.12515i 1.40166 + 0.163831i
\(635\) −18.2028 42.1987i −0.722354 1.67461i
\(636\) 1.95722 4.53165i 0.0776089 0.179691i
\(637\) −1.55387 + 0.780382i −0.0615665 + 0.0309198i
\(638\) −43.3497 15.7780i −1.71623 0.624657i
\(639\) 0.888580 15.0194i 0.0351517 0.594160i
\(640\) −40.2937 + 14.6657i −1.59275 + 0.579712i
\(641\) 11.3237 12.0024i 0.447258 0.474066i −0.464039 0.885815i \(-0.653600\pi\)
0.911297 + 0.411749i \(0.135082\pi\)
\(642\) −14.2828 + 24.7125i −0.563699 + 0.975324i
\(643\) 15.0954 9.92841i 0.595305 0.391538i −0.215801 0.976437i \(-0.569236\pi\)
0.811106 + 0.584899i \(0.198866\pi\)
\(644\) 0.155690 0.520041i 0.00613505 0.0204925i
\(645\) −11.9408 1.40122i −0.470169 0.0551730i
\(646\) −17.6440 23.7000i −0.694195 0.932466i
\(647\) −4.14445 −0.162935 −0.0814676 0.996676i \(-0.525961\pi\)
−0.0814676 + 0.996676i \(0.525961\pi\)
\(648\) −13.3307 + 17.8380i −0.523681 + 0.700743i
\(649\) 53.4951 2.09987
\(650\) 1.18707 + 1.59452i 0.0465609 + 0.0625421i
\(651\) 1.18885 + 2.75954i 0.0465948 + 0.108155i
\(652\) 2.04938 6.84541i 0.0802599 0.268087i
\(653\) −16.8784 + 11.1011i −0.660503 + 0.434419i −0.835009 0.550237i \(-0.814538\pi\)
0.174506 + 0.984656i \(0.444167\pi\)
\(654\) 23.0183 + 39.9111i 0.900088 + 1.56065i
\(655\) 8.34515 8.84534i 0.326072 0.345616i
\(656\) −7.95109 + 2.89396i −0.310438 + 0.112990i
\(657\) 3.26574 + 4.39504i 0.127408 + 0.171467i
\(658\) 3.26842 + 1.18961i 0.127416 + 0.0463758i
\(659\) 6.85612 3.44327i 0.267076 0.134131i −0.310222 0.950664i \(-0.600403\pi\)
0.577298 + 0.816533i \(0.304107\pi\)
\(660\) 12.8537 1.49641i 0.500328 0.0582478i
\(661\) −2.07836 4.81819i −0.0808389 0.187406i 0.873003 0.487715i \(-0.162169\pi\)
−0.953842 + 0.300309i \(0.902910\pi\)
\(662\) −4.73958 0.553978i −0.184209 0.0215310i
\(663\) 1.59686 0.801060i 0.0620170 0.0311106i
\(664\) −20.8745 13.7294i −0.810089 0.532804i
\(665\) −3.31209 + 2.77917i −0.128437 + 0.107772i
\(666\) 20.3592 + 10.2481i 0.788901 + 0.397106i
\(667\) 17.9687 + 15.0775i 0.695750 + 0.583803i
\(668\) −0.159806 0.533790i −0.00618309 0.0206530i
\(669\) −7.89969 2.87935i −0.305420 0.111322i
\(670\) −30.1084 15.1210i −1.16319 0.584176i
\(671\) −12.4314 13.1765i −0.479910 0.508675i
\(672\) −1.11254 + 0.263139i −0.0429172 + 0.0101508i
\(673\) 1.31913 3.05808i 0.0508486 0.117880i −0.890898 0.454203i \(-0.849924\pi\)
0.941747 + 0.336323i \(0.109183\pi\)
\(674\) 3.18620 5.51867i 0.122728 0.212571i
\(675\) −18.2045 + 19.2426i −0.700691 + 0.740649i
\(676\) 2.61481 + 4.52898i 0.100570 + 0.174192i
\(677\) 23.6194 2.76071i 0.907767 0.106103i 0.350621 0.936517i \(-0.385970\pi\)
0.557146 + 0.830415i \(0.311896\pi\)
\(678\) −1.64100 28.3988i −0.0630222 1.09065i
\(679\) 1.86018 0.440871i 0.0713872 0.0169191i
\(680\) 1.87508 + 32.1938i 0.0719059 + 1.23458i
\(681\) 31.5029 11.4498i 1.20719 0.438757i
\(682\) −51.9812 12.3198i −1.99046 0.471748i
\(683\) −3.07677 + 17.4492i −0.117729 + 0.667676i 0.867633 + 0.497205i \(0.165640\pi\)
−0.985363 + 0.170472i \(0.945471\pi\)
\(684\) −4.31288 3.62567i −0.164907 0.138631i
\(685\) −7.87167 44.6424i −0.300761 1.70570i
\(686\) 0.367376 6.30761i 0.0140265 0.240826i
\(687\) 4.38042 4.63872i 0.167123 0.176978i
\(688\) −6.05914 + 8.13883i −0.231002 + 0.310290i
\(689\) 1.05875 1.42214i 0.0403351 0.0541794i
\(690\) −38.0743 9.04218i −1.44946 0.344230i
\(691\) −1.65085 + 28.3440i −0.0628014 + 1.07826i 0.808813 + 0.588066i \(0.200110\pi\)
−0.871615 + 0.490192i \(0.836927\pi\)
\(692\) 0.912541 + 5.17528i 0.0346896 + 0.196734i
\(693\) −5.10979 0.00467799i −0.194105 0.000177702i
\(694\) −2.40983 + 13.6668i −0.0914758 + 0.518785i
\(695\) 18.2226 + 4.31884i 0.691224 + 0.163823i
\(696\) 3.81675 21.5881i 0.144673 0.818293i
\(697\) 0.434407 + 7.45847i 0.0164543 + 0.282510i
\(698\) 7.48267 1.77343i 0.283223 0.0671252i
\(699\) −2.21235 + 1.45364i −0.0836788 + 0.0549816i
\(700\) −0.599429 + 0.0700632i −0.0226563 + 0.00264814i
\(701\) 19.6318 + 34.0032i 0.741482 + 1.28428i 0.951820 + 0.306656i \(0.0992102\pi\)
−0.210338 + 0.977629i \(0.567456\pi\)
\(702\) 1.55395 1.30028i 0.0586499 0.0490760i
\(703\) 11.3826 19.7152i 0.429303 0.743574i
\(704\) −13.3505 + 30.9500i −0.503167 + 1.16647i
\(705\) 12.1097 40.3820i 0.456079 1.52088i
\(706\) −21.5977 22.8923i −0.812841 0.861561i
\(707\) 0.0811296 + 0.0407448i 0.00305119 + 0.00153237i
\(708\) −1.11540 6.34272i −0.0419193 0.238374i
\(709\) −14.3580 47.9591i −0.539226 1.80114i −0.596289 0.802770i \(-0.703359\pi\)
0.0570631 0.998371i \(-0.481826\pi\)
\(710\) −18.9299 15.8841i −0.710428 0.596120i
\(711\) −19.3868 + 25.9913i −0.727063 + 0.974751i
\(712\) 19.7618 16.5821i 0.740606 0.621442i
\(713\) 22.6942 + 14.9262i 0.849905 + 0.558991i
\(714\) −0.189038 + 3.22027i −0.00707458 + 0.120515i
\(715\) 4.61646 + 0.539587i 0.172646 + 0.0201794i
\(716\) 4.00547 + 9.28572i 0.149691 + 0.347024i
\(717\) 4.91921 + 6.61396i 0.183711 + 0.247003i
\(718\) −10.7857 + 5.41676i −0.402517 + 0.202152i
\(719\) 17.5102 + 6.37320i 0.653021 + 0.237680i 0.647220 0.762303i \(-0.275931\pi\)
0.00580045 + 0.999983i \(0.498154\pi\)
\(720\) 12.6614 + 42.4335i 0.471863 + 1.58140i
\(721\) 2.65702 0.967078i 0.0989528 0.0360159i
\(722\) −2.75117 + 2.91607i −0.102388 + 0.108525i
\(723\) 43.8277 + 0.0200621i 1.62997 + 0.000746116i
\(724\) −1.55594 + 1.02336i −0.0578262 + 0.0380329i
\(725\) 7.47917 24.9822i 0.277769 0.927814i
\(726\) 36.6312 49.1572i 1.35951 1.82440i
\(727\) −25.0282 33.6187i −0.928245 1.24685i −0.968844 0.247673i \(-0.920334\pi\)
0.0405990 0.999176i \(-0.487073\pi\)
\(728\) −0.182229 −0.00675386
\(729\) 20.6355 + 17.4120i 0.764276 + 0.644889i
\(730\) 8.99309 0.332849
\(731\) 5.35002 + 7.18632i 0.197878 + 0.265796i
\(732\) −1.30309 + 1.74869i −0.0481637 + 0.0646333i
\(733\) −4.09420 + 13.6756i −0.151223 + 0.505119i −0.999710 0.0240976i \(-0.992329\pi\)
0.848487 + 0.529216i \(0.177514\pi\)
\(734\) 0.251684 0.165535i 0.00928982 0.00611001i
\(735\) −38.0557 0.0174199i −1.40371 0.000642544i
\(736\) −7.09222 + 7.51731i −0.261423 + 0.277092i
\(737\) −37.3715 + 13.6021i −1.37660 + 0.501041i
\(738\) 2.42277 + 8.11966i 0.0891834 + 0.298889i
\(739\) −17.4197 6.34025i −0.640794 0.233230i 0.00112859 0.999999i \(-0.499641\pi\)
−0.641923 + 0.766769i \(0.721863\pi\)
\(740\) 5.62481 2.82489i 0.206772 0.103845i
\(741\) −1.20775 1.62383i −0.0443676 0.0596531i
\(742\) 1.26799 + 2.93953i 0.0465493 + 0.107913i
\(743\) 29.2856 + 3.42299i 1.07438 + 0.125577i 0.634840 0.772644i \(-0.281066\pi\)
0.439544 + 0.898221i \(0.355140\pi\)
\(744\) 1.48772 25.3433i 0.0545424 0.929130i
\(745\) −37.4058 24.6022i −1.37044 0.901355i
\(746\) 2.71579 2.27882i 0.0994320 0.0834334i
\(747\) −18.1120 + 24.2821i −0.662682 + 0.888437i
\(748\) −7.38696 6.19840i −0.270094 0.226636i
\(749\) −0.892660 2.98169i −0.0326171 0.108949i
\(750\) 0.144654 + 0.822576i 0.00528202 + 0.0300362i
\(751\) −14.9121 7.48913i −0.544150 0.273282i 0.155418 0.987849i \(-0.450328\pi\)
−0.699568 + 0.714567i \(0.746624\pi\)
\(752\) −24.4164 25.8799i −0.890374 0.943742i
\(753\) −1.09466 + 3.65033i −0.0398916 + 0.133026i
\(754\) −0.790066 + 1.83158i −0.0287725 + 0.0667022i
\(755\) −2.51646 + 4.35863i −0.0915833 + 0.158627i
\(756\) 0.105987 + 0.605946i 0.00385470 + 0.0220380i
\(757\) −16.3993 28.4044i −0.596042 1.03237i −0.993399 0.114710i \(-0.963406\pi\)
0.397357 0.917664i \(-0.369927\pi\)
\(758\) 11.1719 1.30580i 0.405780 0.0474289i
\(759\) −38.6049 + 25.3656i −1.40127 + 0.920712i
\(760\) 35.5455 8.42444i 1.28937 0.305587i
\(761\) −1.96922 33.8102i −0.0713841 1.22562i −0.823781 0.566908i \(-0.808140\pi\)
0.752397 0.658710i \(-0.228897\pi\)
\(762\) −6.76216 + 38.2478i −0.244967 + 1.38557i
\(763\) −4.88858 1.15862i −0.176979 0.0419447i
\(764\) 0.188692 1.07013i 0.00682665 0.0387159i
\(765\) 39.0997 + 0.0357956i 1.41365 + 0.00129419i
\(766\) 7.28693 + 41.3262i 0.263287 + 1.49318i
\(767\) 0.134495 2.30919i 0.00485633 0.0833799i
\(768\) 15.7265 + 3.73485i 0.567480 + 0.134770i
\(769\) −0.882827 + 1.18584i −0.0318355 + 0.0427626i −0.817756 0.575565i \(-0.804782\pi\)
0.785920 + 0.618328i \(0.212190\pi\)
\(770\) −5.01159 + 6.73173i −0.180605 + 0.242595i
\(771\) 12.2087 12.9286i 0.439686 0.465613i
\(772\) −0.155274 + 2.66595i −0.00558843 + 0.0959496i
\(773\) 0.387181 + 2.19581i 0.0139259 + 0.0789779i 0.990979 0.134020i \(-0.0427885\pi\)
−0.977053 + 0.212997i \(0.931677\pi\)
\(774\) 7.77784 + 6.53852i 0.279569 + 0.235022i
\(775\) 5.24388 29.7395i 0.188366 1.06827i
\(776\) −15.7166 3.72491i −0.564194 0.133716i
\(777\) −2.33593 + 0.848999i −0.0838011 + 0.0304577i
\(778\) 2.06334 + 35.4262i 0.0739744 + 1.27009i
\(779\) 8.23497 1.95172i 0.295049 0.0699278i
\(780\) −0.0322786 0.558607i −0.00115576 0.0200014i
\(781\) −28.9718 + 3.38631i −1.03669 + 0.121172i
\(782\) 14.5807 + 25.2545i 0.521404 + 0.903099i
\(783\) −25.8556 6.16539i −0.924002 0.220333i
\(784\) −16.0586 + 27.8143i −0.573521 + 0.993367i
\(785\) 6.44968 14.9520i 0.230199 0.533661i
\(786\) −10.0017 + 2.36560i −0.356748 + 0.0843783i
\(787\) −2.13435 2.26228i −0.0760813 0.0806415i 0.688215 0.725507i \(-0.258395\pi\)
−0.764296 + 0.644866i \(0.776913\pi\)
\(788\) −5.52656 2.77554i −0.196876 0.0988746i
\(789\) −2.58243 0.941266i −0.0919369 0.0335100i
\(790\) 15.2739 + 51.0185i 0.543422 + 1.81516i
\(791\) 2.37618 + 1.99385i 0.0844872 + 0.0708932i
\(792\) 38.5626 + 19.4111i 1.37026 + 0.689743i
\(793\) −0.600037 + 0.503491i −0.0213080 + 0.0178795i
\(794\) −23.2771 15.3096i −0.826074 0.543317i
\(795\) 34.6838 17.3990i 1.23011 0.617078i
\(796\) −5.65164 0.660582i −0.200317 0.0234137i
\(797\) 7.82400 + 18.1381i 0.277140 + 0.642483i 0.998759 0.0498075i \(-0.0158608\pi\)
−0.721619 + 0.692291i \(0.756602\pi\)
\(798\) 3.62961 0.422556i 0.128487 0.0149583i
\(799\) −28.0742 + 14.0994i −0.993195 + 0.498802i
\(800\) 10.7969 + 3.92974i 0.381727 + 0.138937i
\(801\) −18.6549 25.1059i −0.659140 0.887073i
\(802\) 2.09195 0.761409i 0.0738694 0.0268863i
\(803\) 7.28471 7.72134i 0.257072 0.272480i
\(804\) 2.39197 + 4.14739i 0.0843582 + 0.146267i
\(805\) 3.56523 2.34489i 0.125658 0.0826465i
\(806\) −0.662488 + 2.21286i −0.0233351 + 0.0779448i
\(807\) −3.42313 7.94569i −0.120500 0.279702i
\(808\) −0.458051 0.615269i −0.0161142 0.0216451i
\(809\) −19.4534 −0.683945 −0.341973 0.939710i \(-0.611095\pi\)
−0.341973 + 0.939710i \(0.611095\pi\)
\(810\) 43.1685 10.1477i 1.51679 0.356553i
\(811\) 27.6759 0.971832 0.485916 0.874005i \(-0.338486\pi\)
0.485916 + 0.874005i \(0.338486\pi\)
\(812\) −0.361632 0.485756i −0.0126908 0.0170467i
\(813\) −15.9494 1.87162i −0.559372 0.0656407i
\(814\) 12.6734 42.3322i 0.444203 1.48374i
\(815\) 46.9298 30.8662i 1.64388 1.08120i
\(816\) 16.5122 28.5698i 0.578043 1.00014i
\(817\) 6.96445 7.38188i 0.243655 0.258259i
\(818\) −18.9872 + 6.91078i −0.663872 + 0.241630i
\(819\) −0.0130487 + 0.220559i −0.000455959 + 0.00770696i
\(820\) 2.19884 + 0.800311i 0.0767867 + 0.0279481i
\(821\) 9.32845 4.68492i 0.325565 0.163505i −0.278508 0.960434i \(-0.589840\pi\)
0.604073 + 0.796929i \(0.293544\pi\)
\(822\) −15.1906 + 35.1715i −0.529833 + 1.22675i
\(823\) 4.54256 + 10.5308i 0.158344 + 0.367082i 0.978857 0.204545i \(-0.0655715\pi\)
−0.820513 + 0.571627i \(0.806312\pi\)
\(824\) −23.7283 2.77344i −0.826616 0.0966175i
\(825\) 42.8932 + 28.2394i 1.49335 + 0.983171i
\(826\) 3.48951 + 2.29509i 0.121416 + 0.0798564i
\(827\) 8.85255 7.42817i 0.307833 0.258303i −0.475763 0.879574i \(-0.657828\pi\)
0.783596 + 0.621271i \(0.213383\pi\)
\(828\) 3.81243 + 4.04836i 0.132491 + 0.140690i
\(829\) 22.8861 + 19.2037i 0.794866 + 0.666972i 0.946945 0.321396i \(-0.104152\pi\)
−0.152078 + 0.988368i \(0.548597\pi\)
\(830\) 14.2695 + 47.6635i 0.495302 + 1.65442i
\(831\) −34.3037 + 28.7575i −1.18998 + 0.997587i
\(832\) 1.30243 + 0.654106i 0.0451537 + 0.0226770i
\(833\) 19.4607 + 20.6271i 0.674274 + 0.714688i
\(834\) −10.8562 11.5175i −0.375921 0.398819i
\(835\) 1.73485 4.02184i 0.0600371 0.139182i
\(836\) −5.46168 + 9.45990i −0.188896 + 0.327178i
\(837\) −30.5674 3.61538i −1.05657 0.124966i
\(838\) −23.2176 40.2140i −0.802038 1.38917i
\(839\) −38.7382 + 4.52784i −1.33739 + 0.156318i −0.754536 0.656258i \(-0.772138\pi\)
−0.582854 + 0.812577i \(0.698064\pi\)
\(840\) −3.56321 1.79156i −0.122942 0.0618145i
\(841\) −2.75618 + 0.653228i −0.0950408 + 0.0225251i
\(842\) −2.91252 50.0060i −0.100372 1.72332i
\(843\) −38.4095 32.2594i −1.32289 1.11107i
\(844\) 6.07931 + 1.44082i 0.209258 + 0.0495952i
\(845\) −7.13856 + 40.4848i −0.245574 + 1.39272i
\(846\) −27.3155 + 22.8779i −0.939127 + 0.786557i
\(847\) 1.16082 + 6.58336i 0.0398864 + 0.226207i
\(848\) 1.90413 32.6926i 0.0653880 1.12267i
\(849\) −0.511872 1.71262i −0.0175674 0.0587771i
\(850\) 19.3600 26.0050i 0.664042 0.891963i
\(851\) −13.4172 + 18.0224i −0.459935 + 0.617799i
\(852\) 1.00558 + 3.36447i 0.0344505 + 0.115265i
\(853\) −1.46247 + 25.1096i −0.0500740 + 0.859737i 0.875980 + 0.482347i \(0.160215\pi\)
−0.926054 + 0.377390i \(0.876822\pi\)
\(854\) −0.245598 1.39286i −0.00840419 0.0476625i
\(855\) −7.65115 43.6253i −0.261664 1.49196i
\(856\) −4.56643 + 25.8975i −0.156077 + 0.885158i
\(857\) −53.7907 12.7486i −1.83746 0.435485i −0.842756 0.538296i \(-0.819068\pi\)
−0.994701 + 0.102811i \(0.967216\pi\)
\(858\) −3.00800 2.52636i −0.102691 0.0862485i
\(859\) 1.51409 + 25.9959i 0.0516600 + 0.886968i 0.920224 + 0.391391i \(0.128006\pi\)
−0.868564 + 0.495576i \(0.834957\pi\)
\(860\) 2.73036 0.647108i 0.0931046 0.0220662i
\(861\) −0.825504 0.415057i −0.0281331 0.0141451i
\(862\) 47.2540 5.52320i 1.60948 0.188121i
\(863\) −10.0819 17.4623i −0.343191 0.594425i 0.641832 0.766845i \(-0.278175\pi\)
−0.985023 + 0.172420i \(0.944841\pi\)
\(864\) 3.37425 11.2147i 0.114794 0.381532i
\(865\) −20.6549 + 35.7753i −0.702287 + 1.21640i
\(866\) 23.6467 54.8192i 0.803547 1.86283i
\(867\) 0.211600 + 0.224489i 0.00718631 + 0.00762403i
\(868\) −0.481246 0.510091i −0.0163345 0.0173136i
\(869\) 56.1761 + 28.2127i 1.90565 + 0.957051i
\(870\) −33.4554 + 28.0463i −1.13424 + 0.950860i
\(871\) 0.493196 + 1.64739i 0.0167113 + 0.0558197i
\(872\) 32.5168 + 27.2849i 1.10116 + 0.923982i
\(873\) −5.63381 + 18.7557i −0.190676 + 0.634785i
\(874\) 25.3050 21.2334i 0.855954 0.718230i
\(875\) −0.0760906 0.0500456i −0.00257233 0.00169185i
\(876\) −1.06738 0.702727i −0.0360634 0.0237429i
\(877\) −11.0476 1.29128i −0.373052 0.0436036i −0.0724989 0.997368i \(-0.523097\pi\)
−0.300554 + 0.953765i \(0.597171\pi\)
\(878\) 24.3086 + 56.3536i 0.820375 + 1.90184i
\(879\) 4.76625 11.0355i 0.160761 0.372218i
\(880\) 76.7179 38.5292i 2.58616 1.29882i
\(881\) 7.85029 + 2.85727i 0.264483 + 0.0962639i 0.470858 0.882209i \(-0.343944\pi\)
−0.206375 + 0.978473i \(0.566167\pi\)
\(882\) 26.8555 + 17.6984i 0.904272 + 0.595935i
\(883\) 51.2586 18.6566i 1.72499 0.627845i 0.726736 0.686917i \(-0.241036\pi\)
0.998254 + 0.0590722i \(0.0188142\pi\)
\(884\) −0.286134 + 0.303284i −0.00962373 + 0.0102006i
\(885\) 25.3322 43.8304i 0.851534 1.47334i
\(886\) −7.82641 + 5.14751i −0.262933 + 0.172934i
\(887\) −10.9943 + 36.7235i −0.369152 + 1.23305i 0.548662 + 0.836044i \(0.315137\pi\)
−0.917814 + 0.397010i \(0.870048\pi\)
\(888\) 20.8563 + 2.44743i 0.699890 + 0.0821302i
\(889\) −2.52919 3.39729i −0.0848262 0.113941i
\(890\) −51.3714 −1.72197
\(891\) 26.2553 45.2838i 0.879586 1.51707i
\(892\) 1.96237 0.0657049
\(893\) 21.2512 + 28.5453i 0.711143 + 0.955231i
\(894\) 14.9712 + 34.7508i 0.500711 + 1.16224i
\(895\) −22.7995 + 76.1556i −0.762103 + 2.54560i
\(896\) −3.30163 + 2.17151i −0.110300 + 0.0725452i
\(897\) 0.997880 + 1.73021i 0.0333182 + 0.0577699i
\(898\) 2.55559 2.70877i 0.0852813 0.0903928i
\(899\) 28.4748 10.3640i 0.949687 0.345658i
\(900\) 2.45390 5.67449i 0.0817967 0.189150i
\(901\) −27.1716 9.88965i −0.905217 0.329472i
\(902\) 14.6800 7.37258i 0.488791 0.245480i
\(903\) −1.10057 + 0.128127i −0.0366246 + 0.00426381i
\(904\) −10.3804 24.0644i −0.345245 0.800369i
\(905\) −14.5405 1.69954i −0.483341 0.0564945i
\(906\) 3.80201 1.90726i 0.126313 0.0633646i
\(907\) 23.9072 + 15.7240i 0.793826 + 0.522107i 0.880453 0.474133i \(-0.157239\pi\)
−0.0866274 + 0.996241i \(0.527609\pi\)
\(908\) −5.99281 + 5.02856i −0.198878 + 0.166879i
\(909\) −0.777484 + 0.510340i −0.0257875 + 0.0169269i
\(910\) 0.277984 + 0.233257i 0.00921509 + 0.00773238i
\(911\) 1.86521 + 6.23023i 0.0617971 + 0.206417i 0.983312 0.181926i \(-0.0582330\pi\)
−0.921515 + 0.388342i \(0.873048\pi\)
\(912\) −35.1195 12.8007i −1.16292 0.423872i
\(913\) 52.4820 + 26.3574i 1.73690 + 0.872304i
\(914\) 13.7255 + 14.5482i 0.453998 + 0.481210i
\(915\) −16.6828 + 3.94583i −0.551516 + 0.130445i
\(916\) −0.589786 + 1.36728i −0.0194871 + 0.0451761i
\(917\) 0.560356 0.970565i 0.0185046 0.0320509i
\(918\) −27.5839 18.1965i −0.910405 0.600575i
\(919\) 9.92642 + 17.1931i 0.327442 + 0.567147i 0.982004 0.188862i \(-0.0604800\pi\)
−0.654561 + 0.756009i \(0.727147\pi\)
\(920\) −35.8101 + 4.18560i −1.18062 + 0.137995i
\(921\) −1.83123 31.6908i −0.0603409 1.04425i
\(922\) −44.6359 + 10.5789i −1.47000 + 0.348397i
\(923\) 0.0733353 + 1.25912i 0.00241386 + 0.0414444i
\(924\) 1.12084 0.407373i 0.0368730 0.0134016i
\(925\) 24.3059 + 5.76060i 0.799172 + 0.189407i
\(926\) 9.30948 52.7967i 0.305928 1.73501i
\(927\) −5.05590 + 28.5207i −0.166058 + 0.936744i
\(928\) 2.00205 + 11.3542i 0.0657205 + 0.372720i
\(929\) 2.80963 48.2395i 0.0921809 1.58269i −0.562511 0.826790i \(-0.690165\pi\)
0.654692 0.755896i \(-0.272798\pi\)
\(930\) −34.7093 + 36.7560i −1.13816 + 1.20528i
\(931\) 19.1829 25.7672i 0.628696 0.844485i
\(932\) 0.368941 0.495574i 0.0120851 0.0162331i
\(933\) 24.7650 + 5.88139i 0.810771 + 0.192548i
\(934\) 2.82543 48.5107i 0.0924508 1.58732i
\(935\) −13.1629 74.6507i −0.430474 2.44134i
\(936\) 0.934858 1.61580i 0.0305568 0.0528142i
\(937\) −9.55499 + 54.1890i −0.312148 + 1.77028i 0.275637 + 0.961262i \(0.411111\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(938\) −3.02133 0.716069i −0.0986500 0.0233805i
\(939\) 1.70653 9.65236i 0.0556904 0.314993i
\(940\) 0.572113 + 9.82280i 0.0186603 + 0.320385i
\(941\) −32.7092 + 7.75222i −1.06629 + 0.252715i −0.726063 0.687628i \(-0.758652\pi\)
−0.340227 + 0.940344i \(0.610504\pi\)
\(942\) −11.5017 + 7.55723i −0.374745 + 0.246228i
\(943\) −8.29626 + 0.969694i −0.270164 + 0.0315776i
\(944\) −21.3622 37.0005i −0.695282 1.20426i
\(945\) −2.42354 + 4.18441i −0.0788376 + 0.136119i
\(946\) 9.84958 17.0600i 0.320238 0.554668i
\(947\) 11.4018 26.4323i 0.370508 0.858934i −0.626337 0.779553i \(-0.715446\pi\)
0.996844 0.0793808i \(-0.0252943\pi\)
\(948\) 2.17378 7.24885i 0.0706010 0.235432i
\(949\) −0.314987 0.333867i −0.0102249 0.0108378i
\(950\) −32.8185 16.4820i −1.06477 0.534748i
\(951\) −6.87458 39.0923i −0.222924 1.26766i
\(952\) 0.852371 + 2.84712i 0.0276255 + 0.0922756i
\(953\) −31.9098 26.7755i −1.03366 0.867343i −0.0423778 0.999102i \(-0.513493\pi\)
−0.991282 + 0.131758i \(0.957938\pi\)
\(954\) −32.5694 3.83704i −1.05447 0.124229i
\(955\) 6.54348 5.49063i 0.211742 0.177673i
\(956\) −1.60730 1.05714i −0.0519837 0.0341902i
\(957\) −3.01983 + 51.4428i −0.0976173 + 1.66291i
\(958\) 14.6008 + 1.70659i 0.471731 + 0.0551374i
\(959\) −1.65469 3.83600i −0.0534326 0.123871i
\(960\) 19.0363 + 25.5947i 0.614395 + 0.826065i
\(961\) 3.65528 1.83575i 0.117912 0.0592178i
\(962\) −1.79546 0.653494i −0.0578880 0.0210695i
\(963\) 31.0178 + 7.38134i 0.999533 + 0.237860i
\(964\) −9.61210 + 3.49852i −0.309585 + 0.112680i
\(965\) −14.4057 + 15.2692i −0.463736 + 0.491532i
\(966\) −3.60647 0.00165086i −0.116036 5.31154e-5i
\(967\) −6.70932 + 4.41279i −0.215757 + 0.141906i −0.652788 0.757541i \(-0.726401\pi\)
0.437030 + 0.899447i \(0.356030\pi\)
\(968\) 16.1988 54.1079i 0.520651 1.73909i
\(969\) −19.7213 + 26.4650i −0.633540 + 0.850179i
\(970\) 19.2072 + 25.7998i 0.616707 + 0.828381i
\(971\) 47.3974 1.52105 0.760527 0.649306i \(-0.224941\pi\)
0.760527 + 0.649306i \(0.224941\pi\)
\(972\) −5.91657 2.16880i −0.189774 0.0695644i
\(973\) 1.72590 0.0553297
\(974\) −15.6014 20.9563i −0.499901 0.671484i
\(975\) 1.32683 1.78054i 0.0424927 0.0570230i
\(976\) −4.14945 + 13.8601i −0.132821 + 0.443652i
\(977\) −49.3929 + 32.4862i −1.58022 + 1.03933i −0.611473 + 0.791265i \(0.709423\pi\)
−0.968745 + 0.248060i \(0.920207\pi\)
\(978\) −47.4727 0.0217306i −1.51801 0.000694867i
\(979\) −41.6126 + 44.1068i −1.32994 + 1.40966i
\(980\) 8.34621 3.03777i 0.266610 0.0970380i
\(981\) 35.3523 37.4026i 1.12871 1.19417i
\(982\) −22.6706 8.25142i −0.723447 0.263313i
\(983\) −16.9223 + 8.49872i −0.539739 + 0.271067i −0.697715 0.716376i \(-0.745800\pi\)
0.157975 + 0.987443i \(0.449503\pi\)
\(984\) 4.65893 + 6.26402i 0.148521 + 0.199690i
\(985\) −19.2552 44.6387i −0.613523 1.42231i
\(986\) 32.3118 + 3.77671i 1.02902 + 0.120275i
\(987\) 0.227685 3.87862i 0.00724730 0.123458i
\(988\) 0.394618 + 0.259544i 0.0125545 + 0.00825720i
\(989\) −7.67297 + 6.43839i −0.243986 + 0.204729i
\(990\) −33.9794 78.9718i −1.07994 2.50989i
\(991\) 7.60140 + 6.37833i 0.241466 + 0.202614i 0.755487 0.655163i \(-0.227400\pi\)
−0.514021 + 0.857778i \(0.671845\pi\)
\(992\) 3.82914 + 12.7902i 0.121575 + 0.406090i
\(993\) 0.923207 + 5.24982i 0.0292971 + 0.166598i
\(994\) −2.03512 1.02208i −0.0645502 0.0324183i
\(995\) −30.6951 32.5349i −0.973099 1.03142i
\(996\) 2.03083 6.77216i 0.0643493 0.214584i
\(997\) −8.22081 + 19.0580i −0.260356 + 0.603573i −0.997384 0.0722897i \(-0.976969\pi\)
0.737028 + 0.675862i \(0.236229\pi\)
\(998\) 14.1681 24.5398i 0.448483 0.776795i
\(999\) 4.45565 25.0679i 0.140970 0.793113i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 81.2.g.a.7.7 144
3.2 odd 2 243.2.g.a.100.2 144
9.2 odd 6 729.2.g.b.55.2 144
9.4 even 3 729.2.g.d.298.2 144
9.5 odd 6 729.2.g.a.298.7 144
9.7 even 3 729.2.g.c.55.7 144
81.4 even 27 729.2.g.c.676.7 144
81.23 odd 54 243.2.g.a.226.2 144
81.25 even 27 6561.2.a.c.1.57 72
81.31 even 27 729.2.g.d.433.2 144
81.50 odd 54 729.2.g.a.433.7 144
81.56 odd 54 6561.2.a.d.1.16 72
81.58 even 27 inner 81.2.g.a.58.7 yes 144
81.77 odd 54 729.2.g.b.676.2 144
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
81.2.g.a.7.7 144 1.1 even 1 trivial
81.2.g.a.58.7 yes 144 81.58 even 27 inner
243.2.g.a.100.2 144 3.2 odd 2
243.2.g.a.226.2 144 81.23 odd 54
729.2.g.a.298.7 144 9.5 odd 6
729.2.g.a.433.7 144 81.50 odd 54
729.2.g.b.55.2 144 9.2 odd 6
729.2.g.b.676.2 144 81.77 odd 54
729.2.g.c.55.7 144 9.7 even 3
729.2.g.c.676.7 144 81.4 even 27
729.2.g.d.298.2 144 9.4 even 3
729.2.g.d.433.2 144 81.31 even 27
6561.2.a.c.1.57 72 81.25 even 27
6561.2.a.d.1.16 72 81.56 odd 54