Properties

Label 23.2.c.a.13.1
Level $23$
Weight $2$
Character 23.13
Analytic conductor $0.184$
Analytic rank $0$
Dimension $10$
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] = [23,2,Mod(2,23)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(23, base_ring=CyclotomicField(22))
 
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("23.2");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 23.c (of order \(11\), degree \(10\), 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: \(0.183655924649\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\Q(\zeta_{22})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label 13.1
Root \(0.654861 + 0.755750i\) of defining polynomial
Character \(\chi\) \(=\) 23.13
Dual form 23.2.c.a.16.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.04408 - 1.20493i) q^{2} +(0.198939 + 0.127850i) q^{3} +(-0.0771283 + 0.536439i) q^{4} +(-1.33083 + 2.91411i) q^{5} +(-0.0536570 - 0.373193i) q^{6} +(0.874908 + 0.256896i) q^{7} +(-1.95561 + 1.25679i) q^{8} +(-1.22301 - 2.67803i) q^{9} +O(q^{10})\) \(q+(-1.04408 - 1.20493i) q^{2} +(0.198939 + 0.127850i) q^{3} +(-0.0771283 + 0.536439i) q^{4} +(-1.33083 + 2.91411i) q^{5} +(-0.0536570 - 0.373193i) q^{6} +(0.874908 + 0.256896i) q^{7} +(-1.95561 + 1.25679i) q^{8} +(-1.22301 - 2.67803i) q^{9} +(4.90079 - 1.43900i) q^{10} +(2.88000 - 3.32369i) q^{11} +(-0.0839276 + 0.0968577i) q^{12} +(-3.55742 + 1.04455i) q^{13} +(-0.603930 - 1.32242i) q^{14} +(-0.637323 + 0.409583i) q^{15} +(4.59616 + 1.34955i) q^{16} +(0.0287523 + 0.199977i) q^{17} +(-1.94991 + 4.26972i) q^{18} +(-0.498050 + 3.46401i) q^{19} +(-1.46060 - 0.938670i) q^{20} +(0.141209 + 0.162964i) q^{21} -7.01176 q^{22} +(3.35197 - 3.42992i) q^{23} -0.549727 q^{24} +(-3.44663 - 3.97763i) q^{25} +(4.97283 + 3.19584i) q^{26} +(0.200045 - 1.39134i) q^{27} +(-0.205289 + 0.449521i) q^{28} +(0.339618 + 2.36209i) q^{29} +(1.15893 + 0.340294i) q^{30} +(3.00866 - 1.93355i) q^{31} +(-1.24125 - 2.71797i) q^{32} +(0.997878 - 0.293003i) q^{33} +(0.210938 - 0.243436i) q^{34} +(-1.91298 + 2.20769i) q^{35} +(1.53093 - 0.449521i) q^{36} +(2.46427 + 5.39599i) q^{37} +(4.69389 - 3.01658i) q^{38} +(-0.841254 - 0.247014i) q^{39} +(-1.05985 - 7.37143i) q^{40} +(-1.56316 + 3.42285i) q^{41} +(0.0489268 - 0.340294i) q^{42} +(-4.40468 - 2.83071i) q^{43} +(1.56083 + 1.80129i) q^{44} +9.43169 q^{45} +(-7.63252 - 0.457786i) q^{46} -8.39946 q^{47} +(0.741813 + 0.856098i) q^{48} +(-5.18931 - 3.33496i) q^{49} +(-1.19421 + 8.30590i) q^{50} +(-0.0198471 + 0.0434591i) q^{51} +(-0.285961 - 1.98890i) q^{52} +(4.09368 + 1.20201i) q^{53} +(-1.88533 + 1.21163i) q^{54} +(5.85283 + 12.8159i) q^{55} +(-2.03384 + 0.597190i) q^{56} +(-0.541956 + 0.625450i) q^{57} +(2.49157 - 2.87543i) q^{58} +(2.96598 - 0.870890i) q^{59} +(-0.170561 - 0.373476i) q^{60} +(-1.20106 + 0.771875i) q^{61} +(-5.47107 - 1.60645i) q^{62} +(-0.382050 - 2.65722i) q^{63} +(2.00084 - 4.38124i) q^{64} +(1.69038 - 11.7568i) q^{65} +(-1.39491 - 0.896455i) q^{66} +(3.65467 + 4.21772i) q^{67} -0.109493 q^{68} +(1.10535 - 0.253794i) q^{69} +4.65742 q^{70} +(0.868900 + 1.00276i) q^{71} +(5.75746 + 3.70009i) q^{72} +(1.41481 - 9.84023i) q^{73} +(3.92891 - 8.60311i) q^{74} +(-0.177129 - 1.23196i) q^{75} +(-1.81982 - 0.534347i) q^{76} +(3.37358 - 2.16807i) q^{77} +(0.580699 + 1.27155i) q^{78} +(-12.4545 + 3.65697i) q^{79} +(-10.0495 + 11.5977i) q^{80} +(-5.56620 + 6.42374i) q^{81} +(5.75635 - 1.69022i) q^{82} +(-0.397033 - 0.869381i) q^{83} +(-0.0983113 + 0.0631808i) q^{84} +(-0.621019 - 0.182348i) q^{85} +(1.18801 + 8.26281i) q^{86} +(-0.234431 + 0.513332i) q^{87} +(-1.45495 + 10.1194i) q^{88} +(9.64833 + 6.20061i) q^{89} +(-9.84742 - 11.3645i) q^{90} -3.38075 q^{91} +(1.58141 + 2.06267i) q^{92} +0.845743 q^{93} +(8.76969 + 10.1208i) q^{94} +(-9.43169 - 6.06138i) q^{95} +(0.100559 - 0.699403i) q^{96} +(1.94216 - 4.25273i) q^{97} +(1.39964 + 9.73472i) q^{98} +(-12.4232 - 3.64779i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 7 q^{2} - 7 q^{3} - 3 q^{4} - 3 q^{5} + 6 q^{6} - 5 q^{7} + 4 q^{8} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q - 7 q^{2} - 7 q^{3} - 3 q^{4} - 3 q^{5} + 6 q^{6} - 5 q^{7} + 4 q^{8} - 2 q^{9} + q^{10} + 7 q^{11} + 12 q^{12} - 3 q^{13} + 9 q^{14} + 12 q^{15} + q^{16} - 10 q^{17} - 14 q^{18} + 2 q^{19} - 9 q^{20} - 2 q^{21} - 6 q^{22} - 12 q^{23} - 38 q^{24} - 4 q^{25} + 12 q^{26} - 4 q^{27} + 7 q^{28} + 14 q^{29} + 7 q^{30} + 10 q^{31} + 21 q^{32} + 16 q^{33} + 29 q^{34} + 7 q^{35} + 27 q^{36} - 19 q^{37} - 8 q^{38} + q^{39} + q^{40} + 7 q^{41} - 25 q^{42} - 11 q^{43} - 34 q^{44} - 6 q^{45} - 29 q^{46} - 18 q^{47} + 18 q^{48} - 18 q^{49} + 16 q^{50} + 7 q^{51} - 20 q^{52} + 29 q^{53} - 6 q^{54} - q^{55} - 2 q^{56} - 8 q^{57} - 23 q^{58} - 21 q^{59} + 25 q^{60} + 3 q^{61} + 4 q^{62} + 34 q^{63} + 24 q^{64} + 2 q^{65} + 2 q^{66} + 45 q^{67} - 30 q^{68} + 26 q^{69} + 38 q^{70} - 14 q^{71} + 19 q^{72} + 19 q^{73} + 10 q^{74} - 28 q^{75} - 16 q^{76} + 2 q^{77} - 4 q^{78} - 15 q^{79} - 52 q^{80} - 44 q^{81} + 16 q^{82} + 18 q^{83} - 17 q^{84} - 19 q^{85} - 11 q^{86} - 23 q^{87} + 27 q^{88} + 25 q^{89} - 20 q^{90} - 4 q^{91} + 52 q^{92} + 4 q^{93} + 17 q^{94} + 6 q^{95} - 51 q^{96} - 34 q^{97} + 17 q^{98} - 30 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/23\mathbb{Z}\right)^\times\).

\(n\) \(5\)
\(\chi(n)\) \(e\left(\frac{7}{11}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.04408 1.20493i −0.738275 0.852014i 0.255102 0.966914i \(-0.417891\pi\)
−0.993377 + 0.114900i \(0.963345\pi\)
\(3\) 0.198939 + 0.127850i 0.114857 + 0.0738143i 0.596808 0.802384i \(-0.296435\pi\)
−0.481951 + 0.876198i \(0.660072\pi\)
\(4\) −0.0771283 + 0.536439i −0.0385642 + 0.268220i
\(5\) −1.33083 + 2.91411i −0.595165 + 1.30323i 0.337105 + 0.941467i \(0.390552\pi\)
−0.932270 + 0.361763i \(0.882175\pi\)
\(6\) −0.0536570 0.373193i −0.0219054 0.152355i
\(7\) 0.874908 + 0.256896i 0.330684 + 0.0970976i 0.442860 0.896591i \(-0.353964\pi\)
−0.112176 + 0.993688i \(0.535782\pi\)
\(8\) −1.95561 + 1.25679i −0.691412 + 0.444343i
\(9\) −1.22301 2.67803i −0.407671 0.892676i
\(10\) 4.90079 1.43900i 1.54977 0.455052i
\(11\) 2.88000 3.32369i 0.868352 1.00213i −0.131590 0.991304i \(-0.542008\pi\)
0.999941 0.0108271i \(-0.00344646\pi\)
\(12\) −0.0839276 + 0.0968577i −0.0242278 + 0.0279604i
\(13\) −3.55742 + 1.04455i −0.986649 + 0.289706i −0.734967 0.678103i \(-0.762802\pi\)
−0.251683 + 0.967810i \(0.580984\pi\)
\(14\) −0.603930 1.32242i −0.161407 0.353432i
\(15\) −0.637323 + 0.409583i −0.164556 + 0.105754i
\(16\) 4.59616 + 1.34955i 1.14904 + 0.337388i
\(17\) 0.0287523 + 0.199977i 0.00697346 + 0.0485015i 0.993011 0.118021i \(-0.0376551\pi\)
−0.986038 + 0.166523i \(0.946746\pi\)
\(18\) −1.94991 + 4.26972i −0.459599 + 1.00638i
\(19\) −0.498050 + 3.46401i −0.114260 + 0.794699i 0.849435 + 0.527694i \(0.176943\pi\)
−0.963695 + 0.267005i \(0.913966\pi\)
\(20\) −1.46060 0.938670i −0.326600 0.209893i
\(21\) 0.141209 + 0.162964i 0.0308143 + 0.0355616i
\(22\) −7.01176 −1.49491
\(23\) 3.35197 3.42992i 0.698933 0.715187i
\(24\) −0.549727 −0.112213
\(25\) −3.44663 3.97763i −0.689326 0.795525i
\(26\) 4.97283 + 3.19584i 0.975252 + 0.626757i
\(27\) 0.200045 1.39134i 0.0384986 0.267764i
\(28\) −0.205289 + 0.449521i −0.0387960 + 0.0849515i
\(29\) 0.339618 + 2.36209i 0.0630655 + 0.438630i 0.996752 + 0.0805374i \(0.0256637\pi\)
−0.933686 + 0.358092i \(0.883427\pi\)
\(30\) 1.15893 + 0.340294i 0.211591 + 0.0621288i
\(31\) 3.00866 1.93355i 0.540371 0.347276i −0.241813 0.970323i \(-0.577742\pi\)
0.782184 + 0.623047i \(0.214106\pi\)
\(32\) −1.24125 2.71797i −0.219425 0.480473i
\(33\) 0.997878 0.293003i 0.173708 0.0510053i
\(34\) 0.210938 0.243436i 0.0361756 0.0417489i
\(35\) −1.91298 + 2.20769i −0.323352 + 0.373168i
\(36\) 1.53093 0.449521i 0.255155 0.0749202i
\(37\) 2.46427 + 5.39599i 0.405123 + 0.887096i 0.996725 + 0.0808656i \(0.0257684\pi\)
−0.591602 + 0.806230i \(0.701504\pi\)
\(38\) 4.69389 3.01658i 0.761450 0.489354i
\(39\) −0.841254 0.247014i −0.134708 0.0395539i
\(40\) −1.05985 7.37143i −0.167577 1.16553i
\(41\) −1.56316 + 3.42285i −0.244125 + 0.534559i −0.991540 0.129798i \(-0.958567\pi\)
0.747416 + 0.664357i \(0.231294\pi\)
\(42\) 0.0489268 0.340294i 0.00754957 0.0525084i
\(43\) −4.40468 2.83071i −0.671707 0.431680i 0.159834 0.987144i \(-0.448904\pi\)
−0.831540 + 0.555464i \(0.812541\pi\)
\(44\) 1.56083 + 1.80129i 0.235304 + 0.271555i
\(45\) 9.43169 1.40599
\(46\) −7.63252 0.457786i −1.12535 0.0674969i
\(47\) −8.39946 −1.22519 −0.612594 0.790398i \(-0.709874\pi\)
−0.612594 + 0.790398i \(0.709874\pi\)
\(48\) 0.741813 + 0.856098i 0.107072 + 0.123567i
\(49\) −5.18931 3.33496i −0.741329 0.476424i
\(50\) −1.19421 + 8.30590i −0.168887 + 1.17463i
\(51\) −0.0198471 + 0.0434591i −0.00277915 + 0.00608549i
\(52\) −0.285961 1.98890i −0.0396556 0.275811i
\(53\) 4.09368 + 1.20201i 0.562310 + 0.165109i 0.550521 0.834821i \(-0.314429\pi\)
0.0117890 + 0.999931i \(0.496247\pi\)
\(54\) −1.88533 + 1.21163i −0.256561 + 0.164882i
\(55\) 5.85283 + 12.8159i 0.789195 + 1.72810i
\(56\) −2.03384 + 0.597190i −0.271784 + 0.0798028i
\(57\) −0.541956 + 0.625450i −0.0717838 + 0.0828429i
\(58\) 2.49157 2.87543i 0.327159 0.377562i
\(59\) 2.96598 0.870890i 0.386137 0.113380i −0.0829014 0.996558i \(-0.526419\pi\)
0.469039 + 0.883178i \(0.344600\pi\)
\(60\) −0.170561 0.373476i −0.0220193 0.0482155i
\(61\) −1.20106 + 0.771875i −0.153780 + 0.0988285i −0.615268 0.788318i \(-0.710952\pi\)
0.461488 + 0.887147i \(0.347316\pi\)
\(62\) −5.47107 1.60645i −0.694826 0.204019i
\(63\) −0.382050 2.65722i −0.0481338 0.334778i
\(64\) 2.00084 4.38124i 0.250106 0.547655i
\(65\) 1.69038 11.7568i 0.209665 1.45825i
\(66\) −1.39491 0.896455i −0.171702 0.110346i
\(67\) 3.65467 + 4.21772i 0.446489 + 0.515276i 0.933723 0.357995i \(-0.116540\pi\)
−0.487234 + 0.873271i \(0.661994\pi\)
\(68\) −0.109493 −0.0132780
\(69\) 1.10535 0.253794i 0.133069 0.0305532i
\(70\) 4.65742 0.556668
\(71\) 0.868900 + 1.00276i 0.103119 + 0.119006i 0.804963 0.593325i \(-0.202185\pi\)
−0.701844 + 0.712331i \(0.747640\pi\)
\(72\) 5.75746 + 3.70009i 0.678523 + 0.436060i
\(73\) 1.41481 9.84023i 0.165591 1.15171i −0.722274 0.691607i \(-0.756903\pi\)
0.887865 0.460104i \(-0.152188\pi\)
\(74\) 3.92891 8.60311i 0.456726 1.00009i
\(75\) −0.177129 1.23196i −0.0204530 0.142254i
\(76\) −1.81982 0.534347i −0.208747 0.0612938i
\(77\) 3.37358 2.16807i 0.384455 0.247074i
\(78\) 0.580699 + 1.27155i 0.0657512 + 0.143975i
\(79\) −12.4545 + 3.65697i −1.40124 + 0.411442i −0.893110 0.449838i \(-0.851482\pi\)
−0.508131 + 0.861280i \(0.669664\pi\)
\(80\) −10.0495 + 11.5977i −1.12356 + 1.29666i
\(81\) −5.56620 + 6.42374i −0.618467 + 0.713749i
\(82\) 5.75635 1.69022i 0.635683 0.186653i
\(83\) −0.397033 0.869381i −0.0435800 0.0954269i 0.886590 0.462557i \(-0.153068\pi\)
−0.930170 + 0.367130i \(0.880341\pi\)
\(84\) −0.0983113 + 0.0631808i −0.0107266 + 0.00689360i
\(85\) −0.621019 0.182348i −0.0673590 0.0197784i
\(86\) 1.18801 + 8.26281i 0.128107 + 0.891002i
\(87\) −0.234431 + 0.513332i −0.0251336 + 0.0550350i
\(88\) −1.45495 + 10.1194i −0.155098 + 1.07873i
\(89\) 9.64833 + 6.20061i 1.02272 + 0.657263i 0.940655 0.339364i \(-0.110212\pi\)
0.0820661 + 0.996627i \(0.473848\pi\)
\(90\) −9.84742 11.3645i −1.03801 1.19793i
\(91\) −3.38075 −0.354399
\(92\) 1.58141 + 2.06267i 0.164873 + 0.215048i
\(93\) 0.845743 0.0876995
\(94\) 8.76969 + 10.1208i 0.904525 + 1.04388i
\(95\) −9.43169 6.06138i −0.967671 0.621885i
\(96\) 0.100559 0.699403i 0.0102633 0.0713825i
\(97\) 1.94216 4.25273i 0.197196 0.431800i −0.785041 0.619444i \(-0.787358\pi\)
0.982237 + 0.187644i \(0.0600853\pi\)
\(98\) 1.39964 + 9.73472i 0.141385 + 0.983355i
\(99\) −12.4232 3.64779i −1.24858 0.366616i
\(100\) 2.39959 1.54212i 0.239959 0.154212i
\(101\) −5.23396 11.4608i −0.520799 1.14039i −0.969136 0.246526i \(-0.920711\pi\)
0.448338 0.893864i \(-0.352016\pi\)
\(102\) 0.0730871 0.0214603i 0.00723670 0.00212489i
\(103\) 7.97697 9.20591i 0.785994 0.907085i −0.211533 0.977371i \(-0.567846\pi\)
0.997527 + 0.0702855i \(0.0223910\pi\)
\(104\) 5.64412 6.51366i 0.553452 0.638717i
\(105\) −0.662819 + 0.194621i −0.0646845 + 0.0189931i
\(106\) −2.82578 6.18759i −0.274464 0.600992i
\(107\) −1.86460 + 1.19831i −0.180258 + 0.115845i −0.627658 0.778489i \(-0.715986\pi\)
0.447400 + 0.894334i \(0.352350\pi\)
\(108\) 0.730941 + 0.214624i 0.0703348 + 0.0206522i
\(109\) 2.03670 + 14.1656i 0.195081 + 1.35682i 0.818310 + 0.574777i \(0.194911\pi\)
−0.623229 + 0.782039i \(0.714180\pi\)
\(110\) 9.33146 20.4331i 0.889720 1.94822i
\(111\) −0.199640 + 1.38853i −0.0189490 + 0.131793i
\(112\) 3.67452 + 2.36147i 0.347210 + 0.223138i
\(113\) 1.24690 + 1.43900i 0.117299 + 0.135370i 0.811362 0.584544i \(-0.198727\pi\)
−0.694063 + 0.719914i \(0.744181\pi\)
\(114\) 1.31947 0.123579
\(115\) 5.53426 + 14.3326i 0.516072 + 1.33653i
\(116\) −1.29331 −0.120081
\(117\) 7.14811 + 8.24935i 0.660843 + 0.762653i
\(118\) −4.14607 2.66452i −0.381677 0.245289i
\(119\) −0.0262176 + 0.182348i −0.00240337 + 0.0167158i
\(120\) 0.731593 1.60197i 0.0667850 0.146239i
\(121\) −1.18709 8.25642i −0.107918 0.750584i
\(122\) 2.18406 + 0.641297i 0.197735 + 0.0580603i
\(123\) −0.748585 + 0.481086i −0.0674976 + 0.0433781i
\(124\) 0.805178 + 1.76309i 0.0723072 + 0.158331i
\(125\) 0.808892 0.237512i 0.0723495 0.0212437i
\(126\) −2.80287 + 3.23468i −0.249699 + 0.288168i
\(127\) 7.77230 8.96972i 0.689680 0.795934i −0.297639 0.954678i \(-0.596199\pi\)
0.987320 + 0.158745i \(0.0507447\pi\)
\(128\) −13.1020 + 3.84710i −1.15807 + 0.340039i
\(129\) −0.514353 1.12628i −0.0452863 0.0991632i
\(130\) −15.9310 + 10.2383i −1.39724 + 0.897954i
\(131\) −5.74472 1.68680i −0.501919 0.147377i 0.0209658 0.999780i \(-0.493326\pi\)
−0.522884 + 0.852404i \(0.675144\pi\)
\(132\) 0.0802138 + 0.557900i 0.00698172 + 0.0485589i
\(133\) −1.32564 + 2.90274i −0.114947 + 0.251700i
\(134\) 1.26629 8.80725i 0.109391 0.760831i
\(135\) 3.78830 + 2.43459i 0.326045 + 0.209536i
\(136\) −0.307558 0.354940i −0.0263728 0.0304359i
\(137\) 4.31041 0.368263 0.184131 0.982902i \(-0.441053\pi\)
0.184131 + 0.982902i \(0.441053\pi\)
\(138\) −1.45988 1.06689i −0.124273 0.0908197i
\(139\) 21.6840 1.83922 0.919608 0.392838i \(-0.128507\pi\)
0.919608 + 0.392838i \(0.128507\pi\)
\(140\) −1.03675 1.19647i −0.0876213 0.101120i
\(141\) −1.67098 1.07387i −0.140722 0.0904363i
\(142\) 0.301061 2.09393i 0.0252645 0.175718i
\(143\) −6.77358 + 14.8321i −0.566435 + 1.24032i
\(144\) −2.00702 13.9592i −0.167252 1.16326i
\(145\) −7.33538 2.15386i −0.609170 0.178868i
\(146\) −13.3340 + 8.56921i −1.10353 + 0.709193i
\(147\) −0.605978 1.32691i −0.0499802 0.109441i
\(148\) −3.08469 + 0.905746i −0.253560 + 0.0744519i
\(149\) −8.29826 + 9.57670i −0.679820 + 0.784554i −0.985879 0.167459i \(-0.946444\pi\)
0.306059 + 0.952012i \(0.400989\pi\)
\(150\) −1.29949 + 1.49969i −0.106103 + 0.122449i
\(151\) 9.48489 2.78501i 0.771869 0.226641i 0.127997 0.991775i \(-0.459145\pi\)
0.643872 + 0.765133i \(0.277327\pi\)
\(152\) −3.37955 7.40019i −0.274118 0.600235i
\(153\) 0.500379 0.321574i 0.0404532 0.0259977i
\(154\) −6.13465 1.80129i −0.494344 0.145152i
\(155\) 1.63056 + 11.3408i 0.130970 + 0.910915i
\(156\) 0.197393 0.432230i 0.0158041 0.0346061i
\(157\) −0.0784492 + 0.545626i −0.00626093 + 0.0435457i −0.992712 0.120508i \(-0.961548\pi\)
0.986451 + 0.164053i \(0.0524569\pi\)
\(158\) 17.4099 + 11.1886i 1.38506 + 0.890121i
\(159\) 0.660713 + 0.762504i 0.0523980 + 0.0604705i
\(160\) 9.57235 0.756761
\(161\) 3.81379 2.13975i 0.300569 0.168636i
\(162\) 13.5517 1.06472
\(163\) −11.4878 13.2577i −0.899798 1.03842i −0.999059 0.0433605i \(-0.986194\pi\)
0.0992619 0.995061i \(-0.468352\pi\)
\(164\) −1.71559 1.10254i −0.133965 0.0860939i
\(165\) −0.474161 + 3.29786i −0.0369134 + 0.256738i
\(166\) −0.633010 + 1.38610i −0.0491311 + 0.107582i
\(167\) −0.295972 2.05853i −0.0229030 0.159294i 0.975160 0.221500i \(-0.0710954\pi\)
−0.998063 + 0.0622064i \(0.980186\pi\)
\(168\) −0.480961 0.141223i −0.0371069 0.0108956i
\(169\) 0.627818 0.403474i 0.0482937 0.0310365i
\(170\) 0.428676 + 0.938670i 0.0328780 + 0.0719927i
\(171\) 9.88584 2.90274i 0.755989 0.221978i
\(172\) 1.85823 2.14451i 0.141689 0.163518i
\(173\) −5.63739 + 6.50589i −0.428603 + 0.494634i −0.928438 0.371486i \(-0.878848\pi\)
0.499836 + 0.866120i \(0.333394\pi\)
\(174\) 0.863294 0.253486i 0.0654461 0.0192167i
\(175\) −1.99365 4.36548i −0.150706 0.330000i
\(176\) 17.7224 11.3895i 1.33588 0.858517i
\(177\) 0.701391 + 0.205947i 0.0527198 + 0.0154799i
\(178\) −2.60231 18.0995i −0.195052 1.35661i
\(179\) 6.85091 15.0014i 0.512061 1.12126i −0.460298 0.887765i \(-0.652257\pi\)
0.972359 0.233492i \(-0.0750154\pi\)
\(180\) −0.727451 + 5.05953i −0.0542210 + 0.377115i
\(181\) −16.6213 10.6819i −1.23545 0.793976i −0.250720 0.968060i \(-0.580667\pi\)
−0.984731 + 0.174084i \(0.944304\pi\)
\(182\) 3.52977 + 4.07357i 0.261644 + 0.301953i
\(183\) −0.337622 −0.0249577
\(184\) −2.24444 + 10.9203i −0.165462 + 0.805055i
\(185\) −19.0040 −1.39721
\(186\) −0.883022 1.01906i −0.0647463 0.0747212i
\(187\) 0.747468 + 0.480369i 0.0546603 + 0.0351280i
\(188\) 0.647836 4.50580i 0.0472483 0.328619i
\(189\) 0.532451 1.16590i 0.0387301 0.0848071i
\(190\) 2.54388 + 17.6931i 0.184553 + 1.28359i
\(191\) 10.5692 + 3.10340i 0.764762 + 0.224554i 0.640774 0.767729i \(-0.278613\pi\)
0.123988 + 0.992284i \(0.460432\pi\)
\(192\) 0.958187 0.615790i 0.0691512 0.0444408i
\(193\) −1.64970 3.61233i −0.118748 0.260021i 0.840919 0.541161i \(-0.182015\pi\)
−0.959667 + 0.281139i \(0.909288\pi\)
\(194\) −7.15201 + 2.10002i −0.513485 + 0.150773i
\(195\) 1.83939 2.12277i 0.131722 0.152015i
\(196\) 2.18925 2.52653i 0.156375 0.180466i
\(197\) 2.23909 0.657455i 0.159528 0.0468417i −0.200993 0.979593i \(-0.564417\pi\)
0.360522 + 0.932751i \(0.382599\pi\)
\(198\) 8.57548 + 18.7777i 0.609433 + 1.33447i
\(199\) −10.1219 + 6.50498i −0.717526 + 0.461126i −0.847775 0.530356i \(-0.822058\pi\)
0.130250 + 0.991481i \(0.458422\pi\)
\(200\) 11.7393 + 3.44697i 0.830095 + 0.243738i
\(201\) 0.187820 + 1.30632i 0.0132478 + 0.0921406i
\(202\) −8.34477 + 18.2725i −0.587136 + 1.28565i
\(203\) −0.309679 + 2.15386i −0.0217352 + 0.151171i
\(204\) −0.0217824 0.0139987i −0.00152507 0.000980105i
\(205\) −7.89425 9.11045i −0.551359 0.636302i
\(206\) −19.4211 −1.35313
\(207\) −13.2849 4.78182i −0.923365 0.332360i
\(208\) −17.7601 −1.23144
\(209\) 10.0789 + 11.6317i 0.697174 + 0.804582i
\(210\) 0.926540 + 0.595451i 0.0639373 + 0.0410900i
\(211\) −1.69412 + 11.7829i −0.116628 + 0.811165i 0.844598 + 0.535402i \(0.179840\pi\)
−0.961226 + 0.275764i \(0.911069\pi\)
\(212\) −0.960545 + 2.10330i −0.0659705 + 0.144455i
\(213\) 0.0446543 + 0.310578i 0.00305966 + 0.0212804i
\(214\) 3.39067 + 0.995589i 0.231781 + 0.0680571i
\(215\) 14.1109 9.06852i 0.962355 0.618468i
\(216\) 1.35742 + 2.97233i 0.0923606 + 0.202242i
\(217\) 3.12902 0.918764i 0.212412 0.0623697i
\(218\) 14.9421 17.2441i 1.01200 1.16792i
\(219\) 1.53953 1.77672i 0.104032 0.120059i
\(220\) −7.32637 + 2.15122i −0.493944 + 0.145035i
\(221\) −0.311170 0.681367i −0.0209316 0.0458337i
\(222\) 1.88152 1.20918i 0.126279 0.0811548i
\(223\) 11.9082 + 3.49655i 0.797429 + 0.234146i 0.654971 0.755654i \(-0.272681\pi\)
0.142459 + 0.989801i \(0.454499\pi\)
\(224\) −0.387747 2.69684i −0.0259075 0.180190i
\(225\) −6.43691 + 14.0949i −0.429127 + 0.939658i
\(226\) 0.432034 3.00486i 0.0287385 0.199880i
\(227\) −23.5600 15.1411i −1.56373 1.00495i −0.981395 0.192001i \(-0.938502\pi\)
−0.582336 0.812948i \(-0.697861\pi\)
\(228\) −0.293716 0.338966i −0.0194518 0.0224486i
\(229\) 3.50285 0.231475 0.115737 0.993280i \(-0.463077\pi\)
0.115737 + 0.993280i \(0.463077\pi\)
\(230\) 11.4916 21.6328i 0.757736 1.42642i
\(231\) 0.948323 0.0623950
\(232\) −3.63282 4.19250i −0.238506 0.275251i
\(233\) 20.2298 + 13.0009i 1.32530 + 0.851718i 0.995721 0.0924099i \(-0.0294570\pi\)
0.329578 + 0.944128i \(0.393093\pi\)
\(234\) 2.47672 17.2259i 0.161908 1.12609i
\(235\) 11.1783 24.4770i 0.729189 1.59670i
\(236\) 0.238418 + 1.65824i 0.0155197 + 0.107942i
\(237\) −2.94523 0.864797i −0.191313 0.0561746i
\(238\) 0.247089 0.158795i 0.0160164 0.0102931i
\(239\) 2.49818 + 5.47024i 0.161594 + 0.353841i 0.973058 0.230562i \(-0.0740563\pi\)
−0.811464 + 0.584402i \(0.801329\pi\)
\(240\) −3.48199 + 1.02241i −0.224762 + 0.0659960i
\(241\) −5.45109 + 6.29089i −0.351136 + 0.405232i −0.903650 0.428271i \(-0.859123\pi\)
0.552515 + 0.833503i \(0.313668\pi\)
\(242\) −8.70899 + 10.0507i −0.559835 + 0.646084i
\(243\) −5.97474 + 1.75434i −0.383280 + 0.112541i
\(244\) −0.321428 0.703830i −0.0205773 0.0450581i
\(245\) 16.6245 10.6839i 1.06210 0.682572i
\(246\) 1.36126 + 0.399701i 0.0867905 + 0.0254840i
\(247\) −1.84657 12.8432i −0.117494 0.817191i
\(248\) −3.45369 + 7.56252i −0.219309 + 0.480221i
\(249\) 0.0321652 0.223714i 0.00203839 0.0141773i
\(250\) −1.13073 0.726677i −0.0715138 0.0459591i
\(251\) 19.5443 + 22.5554i 1.23363 + 1.42368i 0.870665 + 0.491877i \(0.163689\pi\)
0.362962 + 0.931804i \(0.381765\pi\)
\(252\) 1.45490 0.0916502
\(253\) −1.74634 21.0191i −0.109791 1.32146i
\(254\) −18.9228 −1.18732
\(255\) −0.100232 0.115673i −0.00627674 0.00724375i
\(256\) 10.2112 + 6.56236i 0.638202 + 0.410148i
\(257\) −2.78702 + 19.3841i −0.173849 + 1.20915i 0.696807 + 0.717258i \(0.254603\pi\)
−0.870657 + 0.491891i \(0.836306\pi\)
\(258\) −0.820060 + 1.79568i −0.0510547 + 0.111794i
\(259\) 0.769797 + 5.35406i 0.0478329 + 0.332685i
\(260\) 6.17645 + 1.81357i 0.383047 + 0.112473i
\(261\) 5.91040 3.79838i 0.365844 0.235114i
\(262\) 3.96546 + 8.68314i 0.244987 + 0.536446i
\(263\) 4.92329 1.44561i 0.303583 0.0891401i −0.126393 0.991980i \(-0.540340\pi\)
0.429976 + 0.902840i \(0.358522\pi\)
\(264\) −1.58321 + 1.82712i −0.0974400 + 0.112452i
\(265\) −8.95079 + 10.3298i −0.549842 + 0.634552i
\(266\) 4.88167 1.43339i 0.299315 0.0878867i
\(267\) 1.12668 + 2.46708i 0.0689516 + 0.150983i
\(268\) −2.54443 + 1.63520i −0.155426 + 0.0998860i
\(269\) −15.8646 4.65828i −0.967284 0.284020i −0.240318 0.970694i \(-0.577252\pi\)
−0.726965 + 0.686674i \(0.759070\pi\)
\(270\) −1.02177 7.10654i −0.0621827 0.432490i
\(271\) −9.93303 + 21.7503i −0.603388 + 1.32124i 0.323617 + 0.946188i \(0.395101\pi\)
−0.927005 + 0.375048i \(0.877626\pi\)
\(272\) −0.137729 + 0.957928i −0.00835106 + 0.0580829i
\(273\) −0.672562 0.432230i −0.0407053 0.0261597i
\(274\) −4.50040 5.19374i −0.271879 0.313765i
\(275\) −23.1467 −1.39580
\(276\) 0.0508910 + 0.612528i 0.00306328 + 0.0368699i
\(277\) −0.0941406 −0.00565636 −0.00282818 0.999996i \(-0.500900\pi\)
−0.00282818 + 0.999996i \(0.500900\pi\)
\(278\) −22.6398 26.1277i −1.35785 1.56704i
\(279\) −8.85773 5.69252i −0.530298 0.340802i
\(280\) 0.966420 6.72160i 0.0577546 0.401692i
\(281\) −4.73202 + 10.3617i −0.282289 + 0.618126i −0.996662 0.0816386i \(-0.973985\pi\)
0.714373 + 0.699765i \(0.246712\pi\)
\(282\) 0.450690 + 3.13462i 0.0268382 + 0.186664i
\(283\) 23.0419 + 6.76571i 1.36970 + 0.402179i 0.882171 0.470929i \(-0.156081\pi\)
0.487526 + 0.873108i \(0.337899\pi\)
\(284\) −0.604939 + 0.388770i −0.0358965 + 0.0230693i
\(285\) −1.10138 2.41169i −0.0652401 0.142856i
\(286\) 24.9437 7.32414i 1.47495 0.433086i
\(287\) −2.24694 + 2.59311i −0.132633 + 0.153066i
\(288\) −5.76072 + 6.64822i −0.339453 + 0.391750i
\(289\) 16.2722 4.77795i 0.957189 0.281056i
\(290\) 5.06345 + 11.0874i 0.297336 + 0.651076i
\(291\) 0.930083 0.597728i 0.0545224 0.0350395i
\(292\) 5.16956 + 1.51792i 0.302526 + 0.0888296i
\(293\) −2.81242 19.5608i −0.164303 1.14276i −0.890405 0.455168i \(-0.849579\pi\)
0.726102 0.687587i \(-0.241330\pi\)
\(294\) −0.966142 + 2.11556i −0.0563465 + 0.123382i
\(295\) −1.40934 + 9.80219i −0.0820551 + 0.570706i
\(296\) −11.6008 7.45537i −0.674282 0.433335i
\(297\) −4.04826 4.67195i −0.234904 0.271094i
\(298\) 20.2033 1.17034
\(299\) −8.34161 + 15.7029i −0.482408 + 0.908124i
\(300\) 0.674531 0.0389441
\(301\) −3.12649 3.60816i −0.180208 0.207971i
\(302\) −13.2587 8.52086i −0.762953 0.490320i
\(303\) 0.424024 2.94915i 0.0243596 0.169424i
\(304\) −6.96398 + 15.2490i −0.399412 + 0.874590i
\(305\) −0.650922 4.52726i −0.0372717 0.259230i
\(306\) −0.909909 0.267173i −0.0520160 0.0152733i
\(307\) −16.8093 + 10.8027i −0.959358 + 0.616542i −0.923820 0.382826i \(-0.874951\pi\)
−0.0355380 + 0.999368i \(0.511314\pi\)
\(308\) 0.902837 + 1.97694i 0.0514439 + 0.112647i
\(309\) 2.76390 0.811556i 0.157233 0.0461678i
\(310\) 11.9624 13.8054i 0.679421 0.784093i
\(311\) 19.1386 22.0872i 1.08525 1.25245i 0.119541 0.992829i \(-0.461858\pi\)
0.965711 0.259619i \(-0.0835969\pi\)
\(312\) 1.95561 0.574218i 0.110714 0.0325087i
\(313\) 6.74129 + 14.7614i 0.381040 + 0.834362i 0.998846 + 0.0480311i \(0.0152947\pi\)
−0.617805 + 0.786331i \(0.711978\pi\)
\(314\) 0.739348 0.475150i 0.0417238 0.0268143i
\(315\) 8.25186 + 2.42297i 0.464940 + 0.136519i
\(316\) −1.00115 6.96314i −0.0563190 0.391707i
\(317\) 4.38812 9.60864i 0.246461 0.539675i −0.745457 0.666554i \(-0.767769\pi\)
0.991918 + 0.126879i \(0.0404959\pi\)
\(318\) 0.228928 1.59223i 0.0128376 0.0892877i
\(319\) 8.82898 + 5.67404i 0.494328 + 0.317685i
\(320\) 10.1046 + 11.6614i 0.564866 + 0.651890i
\(321\) −0.524145 −0.0292549
\(322\) −6.56015 2.36129i −0.365583 0.131589i
\(323\) −0.707042 −0.0393409
\(324\) −3.01663 3.48138i −0.167591 0.193410i
\(325\) 16.4159 + 10.5499i 0.910592 + 0.585202i
\(326\) −3.98037 + 27.6841i −0.220453 + 1.53328i
\(327\) −1.40589 + 3.07848i −0.0777460 + 0.170240i
\(328\) −1.24488 8.65831i −0.0687369 0.478075i
\(329\) −7.34875 2.15779i −0.405150 0.118963i
\(330\) 4.46876 2.87190i 0.245997 0.158093i
\(331\) −6.40519 14.0254i −0.352061 0.770906i −0.999958 0.00917776i \(-0.997079\pi\)
0.647897 0.761728i \(-0.275649\pi\)
\(332\) 0.496992 0.145930i 0.0272760 0.00800896i
\(333\) 11.4368 13.1988i 0.626732 0.723287i
\(334\) −2.17137 + 2.50589i −0.118812 + 0.137116i
\(335\) −17.1546 + 5.03706i −0.937259 + 0.275204i
\(336\) 0.429090 + 0.939576i 0.0234088 + 0.0512581i
\(337\) 22.3899 14.3891i 1.21966 0.783825i 0.237407 0.971410i \(-0.423702\pi\)
0.982248 + 0.187585i \(0.0600661\pi\)
\(338\) −1.14165 0.335219i −0.0620976 0.0182335i
\(339\) 0.0640805 + 0.445690i 0.00348038 + 0.0242065i
\(340\) 0.145717 0.319075i 0.00790259 0.0173043i
\(341\) 2.23841 15.5685i 0.121217 0.843080i
\(342\) −13.8192 8.88105i −0.747256 0.480232i
\(343\) −7.86334 9.07478i −0.424581 0.489992i
\(344\) 12.1714 0.656240
\(345\) −0.731452 + 3.55887i −0.0393800 + 0.191603i
\(346\) 13.7250 0.737861
\(347\) −10.3737 11.9719i −0.556890 0.642685i 0.405584 0.914058i \(-0.367068\pi\)
−0.962474 + 0.271372i \(0.912523\pi\)
\(348\) −0.257290 0.165350i −0.0137922 0.00886371i
\(349\) −0.279995 + 1.94741i −0.0149878 + 0.104242i −0.995942 0.0899963i \(-0.971314\pi\)
0.980954 + 0.194239i \(0.0622236\pi\)
\(350\) −3.17858 + 6.96011i −0.169902 + 0.372034i
\(351\) 0.741685 + 5.15854i 0.0395882 + 0.275342i
\(352\) −12.6085 3.70219i −0.672035 0.197327i
\(353\) −19.0703 + 12.2557i −1.01501 + 0.652306i −0.938685 0.344777i \(-0.887955\pi\)
−0.0763236 + 0.997083i \(0.524318\pi\)
\(354\) −0.484155 1.06015i −0.0257326 0.0563464i
\(355\) −4.07852 + 1.19756i −0.216466 + 0.0635600i
\(356\) −4.07041 + 4.69750i −0.215731 + 0.248967i
\(357\) −0.0285289 + 0.0329241i −0.00150991 + 0.00174253i
\(358\) −25.2285 + 7.40776i −1.33337 + 0.391512i
\(359\) −8.65670 18.9555i −0.456883 1.00044i −0.988187 0.153254i \(-0.951025\pi\)
0.531304 0.847182i \(-0.321702\pi\)
\(360\) −18.4447 + 11.8537i −0.972120 + 0.624744i
\(361\) 6.47905 + 1.90242i 0.341003 + 0.100127i
\(362\) 4.48303 + 31.1802i 0.235623 + 1.63879i
\(363\) 0.819426 1.79429i 0.0430087 0.0941759i
\(364\) 0.260752 1.81357i 0.0136671 0.0950568i
\(365\) 26.7926 + 17.2186i 1.40239 + 0.901262i
\(366\) 0.352504 + 0.406811i 0.0184257 + 0.0212643i
\(367\) −20.5752 −1.07402 −0.537008 0.843577i \(-0.680445\pi\)
−0.537008 + 0.843577i \(0.680445\pi\)
\(368\) 20.0350 11.2408i 1.04440 0.585966i
\(369\) 11.0782 0.576710
\(370\) 19.8417 + 22.8985i 1.03152 + 1.19044i
\(371\) 3.27280 + 2.10330i 0.169915 + 0.109198i
\(372\) −0.0652308 + 0.453690i −0.00338206 + 0.0235227i
\(373\) −9.27749 + 20.3149i −0.480370 + 1.05186i 0.501992 + 0.864872i \(0.332601\pi\)
−0.982362 + 0.186991i \(0.940126\pi\)
\(374\) −0.201604 1.40219i −0.0104247 0.0725055i
\(375\) 0.191286 + 0.0561666i 0.00987796 + 0.00290043i
\(376\) 16.4260 10.5564i 0.847109 0.544404i
\(377\) −3.67549 8.04820i −0.189297 0.414503i
\(378\) −1.96075 + 0.575729i −0.100850 + 0.0296123i
\(379\) −11.2346 + 12.9654i −0.577082 + 0.665988i −0.966975 0.254872i \(-0.917967\pi\)
0.389893 + 0.920860i \(0.372512\pi\)
\(380\) 3.97901 4.59203i 0.204119 0.235566i
\(381\) 2.69299 0.790734i 0.137966 0.0405105i
\(382\) −7.29571 15.9754i −0.373281 0.817371i
\(383\) −28.1427 + 18.0862i −1.43803 + 0.924163i −0.438347 + 0.898806i \(0.644436\pi\)
−0.999678 + 0.0253574i \(0.991928\pi\)
\(384\) −3.09835 0.909758i −0.158112 0.0464259i
\(385\) 1.82833 + 12.7163i 0.0931803 + 0.648083i
\(386\) −2.63020 + 5.75933i −0.133873 + 0.293142i
\(387\) −2.19375 + 15.2578i −0.111514 + 0.775600i
\(388\) 2.13154 + 1.36986i 0.108212 + 0.0695439i
\(389\) −9.69166 11.1848i −0.491387 0.567090i 0.454849 0.890569i \(-0.349693\pi\)
−0.946236 + 0.323478i \(0.895148\pi\)
\(390\) −4.47826 −0.226766
\(391\) 0.782280 + 0.571698i 0.0395616 + 0.0289120i
\(392\) 14.3396 0.724259
\(393\) −0.927190 1.07003i −0.0467705 0.0539761i
\(394\) −3.12997 2.01151i −0.157686 0.101338i
\(395\) 5.91801 41.1606i 0.297767 2.07102i
\(396\) 2.91500 6.38296i 0.146484 0.320756i
\(397\) −1.79497 12.4843i −0.0900869 0.626568i −0.983979 0.178285i \(-0.942945\pi\)
0.893892 0.448283i \(-0.147964\pi\)
\(398\) 18.4061 + 5.40453i 0.922617 + 0.270905i
\(399\) −0.634837 + 0.407985i −0.0317816 + 0.0204248i
\(400\) −10.4732 22.9332i −0.523662 1.14666i
\(401\) 16.2478 4.77079i 0.811378 0.238242i 0.150378 0.988629i \(-0.451951\pi\)
0.660999 + 0.750387i \(0.270133\pi\)
\(402\) 1.37792 1.59021i 0.0687246 0.0793124i
\(403\) −8.68336 + 10.0211i −0.432549 + 0.499188i
\(404\) 6.55170 1.92375i 0.325959 0.0957102i
\(405\) −11.3118 24.7694i −0.562089 1.23080i
\(406\) 2.91858 1.87566i 0.144847 0.0930874i
\(407\) 25.0317 + 7.34997i 1.24078 + 0.364325i
\(408\) −0.0158059 0.109933i −0.000782510 0.00544248i
\(409\) 12.9449 28.3453i 0.640083 1.40159i −0.259889 0.965639i \(-0.583686\pi\)
0.899972 0.435948i \(-0.143587\pi\)
\(410\) −2.73525 + 19.0240i −0.135084 + 0.939531i
\(411\) 0.857507 + 0.551086i 0.0422977 + 0.0271831i
\(412\) 4.32316 + 4.98919i 0.212987 + 0.245800i
\(413\) 2.81869 0.138698
\(414\) 8.10872 + 21.0000i 0.398522 + 1.03209i
\(415\) 3.06186 0.150301
\(416\) 7.25471 + 8.37238i 0.355691 + 0.410490i
\(417\) 4.31379 + 2.77231i 0.211247 + 0.135760i
\(418\) 3.49220 24.2888i 0.170809 1.18800i
\(419\) 13.9220 30.4850i 0.680136 1.48929i −0.182363 0.983231i \(-0.558375\pi\)
0.862499 0.506059i \(-0.168898\pi\)
\(420\) −0.0532804 0.370573i −0.00259982 0.0180821i
\(421\) −34.3342 10.0814i −1.67335 0.491339i −0.698761 0.715356i \(-0.746265\pi\)
−0.974585 + 0.224017i \(0.928083\pi\)
\(422\) 15.9663 10.2609i 0.777228 0.499494i
\(423\) 10.2727 + 22.4940i 0.499474 + 1.09369i
\(424\) −9.51630 + 2.79424i −0.462153 + 0.135700i
\(425\) 0.696334 0.803613i 0.0337772 0.0389809i
\(426\) 0.327602 0.378072i 0.0158724 0.0183177i
\(427\) −1.24911 + 0.366772i −0.0604487 + 0.0177493i
\(428\) −0.499005 1.09267i −0.0241203 0.0528161i
\(429\) −3.24381 + 2.08467i −0.156613 + 0.100649i
\(430\) −25.6598 7.53440i −1.23743 0.363341i
\(431\) 0.576458 + 4.00936i 0.0277670 + 0.193124i 0.998984 0.0450741i \(-0.0143524\pi\)
−0.971217 + 0.238198i \(0.923443\pi\)
\(432\) 2.79713 6.12485i 0.134577 0.294682i
\(433\) −1.49601 + 10.4050i −0.0718936 + 0.500031i 0.921779 + 0.387716i \(0.126736\pi\)
−0.993673 + 0.112315i \(0.964173\pi\)
\(434\) −4.37399 2.81099i −0.209958 0.134932i
\(435\) −1.18392 1.36632i −0.0567646 0.0655098i
\(436\) −7.75606 −0.371448
\(437\) 10.2118 + 13.3195i 0.488498 + 0.637159i
\(438\) −3.74822 −0.179097
\(439\) 13.7805 + 15.9035i 0.657706 + 0.759034i 0.982401 0.186785i \(-0.0598069\pi\)
−0.324694 + 0.945819i \(0.605261\pi\)
\(440\) −27.5528 17.7071i −1.31353 0.844152i
\(441\) −2.58453 + 17.9758i −0.123073 + 0.855991i
\(442\) −0.496114 + 1.08634i −0.0235977 + 0.0516719i
\(443\) 5.00633 + 34.8198i 0.237858 + 1.65434i 0.662562 + 0.749007i \(0.269469\pi\)
−0.424704 + 0.905332i \(0.639622\pi\)
\(444\) −0.729463 0.214190i −0.0346188 0.0101650i
\(445\) −30.9096 + 19.8644i −1.46525 + 0.941661i
\(446\) −8.21995 17.9992i −0.389226 0.852285i
\(447\) −2.87523 + 0.844243i −0.135994 + 0.0399313i
\(448\) 2.87608 3.31917i 0.135882 0.156816i
\(449\) 4.79080 5.52888i 0.226092 0.260924i −0.631358 0.775492i \(-0.717502\pi\)
0.857450 + 0.514568i \(0.172048\pi\)
\(450\) 23.7040 6.96011i 1.11742 0.328103i
\(451\) 6.87459 + 15.0533i 0.323712 + 0.708830i
\(452\) −0.868109 + 0.557900i −0.0408324 + 0.0262414i
\(453\) 2.24298 + 0.658597i 0.105384 + 0.0309436i
\(454\) 6.35451 + 44.1966i 0.298232 + 2.07425i
\(455\) 4.49921 9.85189i 0.210926 0.461864i
\(456\) 0.273791 1.90426i 0.0128215 0.0891752i
\(457\) 25.2155 + 16.2050i 1.17953 + 0.758039i 0.975300 0.220884i \(-0.0708943\pi\)
0.204231 + 0.978923i \(0.434531\pi\)
\(458\) −3.65725 4.22069i −0.170892 0.197220i
\(459\) 0.283988 0.0132554
\(460\) −8.11544 + 1.86334i −0.378384 + 0.0868787i
\(461\) −6.05104 −0.281825 −0.140913 0.990022i \(-0.545004\pi\)
−0.140913 + 0.990022i \(0.545004\pi\)
\(462\) −0.990123 1.14266i −0.0460647 0.0531615i
\(463\) −18.8505 12.1145i −0.876059 0.563009i 0.0235414 0.999723i \(-0.492506\pi\)
−0.899600 + 0.436714i \(0.856142\pi\)
\(464\) −1.62684 + 11.3149i −0.0755240 + 0.525281i
\(465\) −1.12554 + 2.46459i −0.0521957 + 0.114293i
\(466\) −5.45631 37.9495i −0.252759 1.75798i
\(467\) 13.4020 + 3.93518i 0.620171 + 0.182099i 0.576700 0.816956i \(-0.304340\pi\)
0.0434710 + 0.999055i \(0.486158\pi\)
\(468\) −4.97660 + 3.19827i −0.230043 + 0.147840i
\(469\) 2.11399 + 4.62899i 0.0976149 + 0.213747i
\(470\) −41.1640 + 12.0868i −1.89875 + 0.557524i
\(471\) −0.0853649 + 0.0985164i −0.00393341 + 0.00453939i
\(472\) −4.70576 + 5.43074i −0.216600 + 0.249970i
\(473\) −22.0939 + 6.48735i −1.01588 + 0.298289i
\(474\) 2.03303 + 4.45171i 0.0933801 + 0.204474i
\(475\) 15.4951 9.95812i 0.710965 0.456910i
\(476\) −0.0957963 0.0281283i −0.00439082 0.00128926i
\(477\) −1.78760 12.4331i −0.0818488 0.569271i
\(478\) 3.98297 8.72149i 0.182177 0.398912i
\(479\) 3.48599 24.2456i 0.159279 1.10781i −0.740687 0.671850i \(-0.765500\pi\)
0.899966 0.435960i \(-0.143591\pi\)
\(480\) 1.90431 + 1.22383i 0.0869195 + 0.0558598i
\(481\) −14.4028 16.6217i −0.656712 0.757886i
\(482\) 13.2715 0.604498
\(483\) 1.03228 + 0.0619144i 0.0469703 + 0.00281720i
\(484\) 4.52063 0.205483
\(485\) 9.80826 + 11.3193i 0.445370 + 0.513985i
\(486\) 8.35195 + 5.36747i 0.378852 + 0.243474i
\(487\) −1.98438 + 13.8017i −0.0899210 + 0.625414i 0.894167 + 0.447733i \(0.147769\pi\)
−0.984088 + 0.177681i \(0.943140\pi\)
\(488\) 1.37872 3.01897i 0.0624116 0.136662i
\(489\) −0.590381 4.10619i −0.0266979 0.185688i
\(490\) −30.2307 8.87654i −1.36569 0.401001i
\(491\) 7.32754 4.70913i 0.330687 0.212520i −0.364752 0.931105i \(-0.618846\pi\)
0.695439 + 0.718585i \(0.255210\pi\)
\(492\) −0.200336 0.438676i −0.00903186 0.0197770i
\(493\) −0.462599 + 0.135831i −0.0208344 + 0.00611754i
\(494\) −13.5472 + 15.6342i −0.609515 + 0.703418i
\(495\) 27.1633 31.3481i 1.22090 1.40899i
\(496\) 16.4377 4.82655i 0.738075 0.216718i
\(497\) 0.502601 + 1.10054i 0.0225447 + 0.0493661i
\(498\) −0.303143 + 0.194818i −0.0135842 + 0.00873001i
\(499\) −20.5680 6.03930i −0.920748 0.270356i −0.213190 0.977011i \(-0.568385\pi\)
−0.707559 + 0.706655i \(0.750203\pi\)
\(500\) 0.0650224 + 0.452240i 0.00290789 + 0.0202248i
\(501\) 0.204303 0.447362i 0.00912759 0.0199866i
\(502\) 6.77183 47.0991i 0.302241 2.10214i
\(503\) 10.5239 + 6.76330i 0.469238 + 0.301561i 0.753808 0.657094i \(-0.228215\pi\)
−0.284571 + 0.958655i \(0.591851\pi\)
\(504\) 4.08671 + 4.71631i 0.182036 + 0.210081i
\(505\) 40.3635 1.79615
\(506\) −23.5032 + 24.0497i −1.04484 + 1.06914i
\(507\) 0.176482 0.00783783
\(508\) 4.21224 + 4.86119i 0.186888 + 0.215680i
\(509\) 10.9462 + 7.03471i 0.485182 + 0.311808i 0.760265 0.649613i \(-0.225069\pi\)
−0.275083 + 0.961421i \(0.588705\pi\)
\(510\) −0.0347288 + 0.241544i −0.00153782 + 0.0106958i
\(511\) 3.76575 8.24583i 0.166587 0.364774i
\(512\) 1.13252 + 7.87688i 0.0500510 + 0.348112i
\(513\) 4.71999 + 1.38591i 0.208393 + 0.0611896i
\(514\) 26.2664 16.8804i 1.15856 0.744562i
\(515\) 16.2111 + 35.4973i 0.714345 + 1.56420i
\(516\) 0.643850 0.189052i 0.0283439 0.00832253i
\(517\) −24.1904 + 27.9172i −1.06389 + 1.22780i
\(518\) 5.64754 6.51761i 0.248139 0.286367i
\(519\) −1.95327 + 0.573533i −0.0857392 + 0.0251753i
\(520\) 11.4702 + 25.1162i 0.503000 + 1.10142i
\(521\) −18.4731 + 11.8720i −0.809322 + 0.520120i −0.878646 0.477474i \(-0.841552\pi\)
0.0693233 + 0.997594i \(0.477916\pi\)
\(522\) −10.7477 3.15581i −0.470414 0.138126i
\(523\) −5.16848 35.9476i −0.226002 1.57188i −0.714705 0.699426i \(-0.753439\pi\)
0.488703 0.872450i \(-0.337470\pi\)
\(524\) 1.34795 2.95159i 0.0588854 0.128941i
\(525\) 0.161514 1.12335i 0.00704903 0.0490271i
\(526\) −6.88216 4.42290i −0.300077 0.192847i
\(527\) 0.473171 + 0.546068i 0.0206116 + 0.0237871i
\(528\) 4.98183 0.216806
\(529\) −0.528643 22.9939i −0.0229845 0.999736i
\(530\) 21.7920 0.946582
\(531\) −5.95970 6.87786i −0.258629 0.298474i
\(532\) −1.45490 0.935008i −0.0630780 0.0405378i
\(533\) 1.98548 13.8093i 0.0860005 0.598147i
\(534\) 1.79632 3.93339i 0.0777344 0.170215i
\(535\) −1.01053 7.02840i −0.0436891 0.303864i
\(536\) −12.4479 3.65503i −0.537668 0.157873i
\(537\) 3.28084 2.10847i 0.141579 0.0909871i
\(538\) 10.9510 + 23.9794i 0.472132 + 1.03382i
\(539\) −26.0296 + 7.64298i −1.12117 + 0.329206i
\(540\) −1.59820 + 1.84442i −0.0687754 + 0.0793710i
\(541\) −22.6175 + 26.1020i −0.972403 + 1.12221i 0.0200766 + 0.999798i \(0.493609\pi\)
−0.992479 + 0.122414i \(0.960936\pi\)
\(542\) 36.5784 10.7404i 1.57118 0.461340i
\(543\) −1.94094 4.25007i −0.0832937 0.182388i
\(544\) 0.507841 0.326370i 0.0217735 0.0139930i
\(545\) −43.9906 12.9168i −1.88435 0.553295i
\(546\) 0.181401 + 1.26167i 0.00776325 + 0.0539946i
\(547\) 7.34060 16.0737i 0.313862 0.687261i −0.685298 0.728263i \(-0.740328\pi\)
0.999159 + 0.0410023i \(0.0130551\pi\)
\(548\) −0.332454 + 2.31227i −0.0142017 + 0.0987753i
\(549\) 3.53602 + 2.27246i 0.150914 + 0.0969862i
\(550\) 24.1670 + 27.8902i 1.03048 + 1.18924i
\(551\) −8.35147 −0.355784
\(552\) −1.84267 + 1.88552i −0.0784291 + 0.0802529i
\(553\) −11.8360 −0.503318
\(554\) 0.0982901 + 0.113433i 0.00417595 + 0.00481930i
\(555\) −3.78064 2.42967i −0.160479 0.103134i
\(556\) −1.67245 + 11.6322i −0.0709278 + 0.493314i
\(557\) 6.89058 15.0883i 0.291963 0.639311i −0.705635 0.708576i \(-0.749338\pi\)
0.997598 + 0.0692649i \(0.0220654\pi\)
\(558\) 2.38907 + 16.6164i 0.101138 + 0.703427i
\(559\) 18.6261 + 5.46911i 0.787800 + 0.231319i
\(560\) −11.7718 + 7.56525i −0.497447 + 0.319690i
\(561\) 0.0872852 + 0.191128i 0.00368518 + 0.00806942i
\(562\) 17.4257 5.11665i 0.735059 0.215833i
\(563\) 4.25075 4.90563i 0.179148 0.206748i −0.659072 0.752079i \(-0.729051\pi\)
0.838220 + 0.545332i \(0.183596\pi\)
\(564\) 0.704947 0.813552i 0.0296836 0.0342567i
\(565\) −5.85283 + 1.71855i −0.246230 + 0.0722997i
\(566\) −15.9053 34.8278i −0.668550 1.46392i
\(567\) −6.52015 + 4.19025i −0.273821 + 0.175974i
\(568\) −2.95949 0.868986i −0.124178 0.0364618i
\(569\) −2.81349 19.5683i −0.117948 0.820344i −0.959810 0.280651i \(-0.909450\pi\)
0.841862 0.539693i \(-0.181460\pi\)
\(570\) −1.75599 + 3.84508i −0.0735502 + 0.161052i
\(571\) −3.22286 + 22.4155i −0.134872 + 0.938059i 0.804205 + 0.594352i \(0.202592\pi\)
−0.939077 + 0.343706i \(0.888318\pi\)
\(572\) −7.43407 4.77758i −0.310834 0.199761i
\(573\) 1.70586 + 1.96866i 0.0712632 + 0.0822421i
\(574\) 5.47049 0.228334
\(575\) −25.1959 1.51121i −1.05074 0.0630218i
\(576\) −14.1801 −0.590839
\(577\) 14.1842 + 16.3695i 0.590498 + 0.681471i 0.969828 0.243791i \(-0.0783910\pi\)
−0.379330 + 0.925261i \(0.623846\pi\)
\(578\) −22.7466 14.6183i −0.946132 0.608042i
\(579\) 0.133649 0.929547i 0.00555425 0.0386306i
\(580\) 1.72118 3.76886i 0.0714682 0.156493i
\(581\) −0.124027 0.862625i −0.00514549 0.0357877i
\(582\) −1.69130 0.496611i −0.0701067 0.0205852i
\(583\) 15.7849 10.1443i 0.653744 0.420136i
\(584\) 9.60031 + 21.0217i 0.397264 + 0.869886i
\(585\) −33.5524 + 9.85189i −1.38722 + 0.407325i
\(586\) −20.6330 + 23.8118i −0.852343 + 0.983656i
\(587\) 1.09947 1.26886i 0.0453800 0.0523713i −0.732606 0.680653i \(-0.761696\pi\)
0.777986 + 0.628282i \(0.216242\pi\)
\(588\) 0.758543 0.222728i 0.0312818 0.00918516i
\(589\) 5.19937 + 11.3850i 0.214236 + 0.469112i
\(590\) 13.2824 8.53610i 0.546829 0.351425i
\(591\) 0.529497 + 0.155474i 0.0217806 + 0.00639536i
\(592\) 4.04398 + 28.1265i 0.166207 + 1.15599i
\(593\) −1.18397 + 2.59252i −0.0486196 + 0.106462i −0.932383 0.361472i \(-0.882274\pi\)
0.883763 + 0.467934i \(0.155002\pi\)
\(594\) −1.40267 + 9.75575i −0.0575521 + 0.400283i
\(595\) −0.496490 0.319075i −0.0203541 0.0130808i
\(596\) −4.49729 5.19014i −0.184216 0.212597i
\(597\) −2.84531 −0.116451
\(598\) 27.6302 6.34403i 1.12988 0.259427i
\(599\) −5.04403 −0.206093 −0.103047 0.994677i \(-0.532859\pi\)
−0.103047 + 0.994677i \(0.532859\pi\)
\(600\) 1.89471 + 2.18661i 0.0773511 + 0.0892679i
\(601\) −2.38049 1.52985i −0.0971022 0.0624038i 0.491189 0.871053i \(-0.336563\pi\)
−0.588291 + 0.808649i \(0.700199\pi\)
\(602\) −1.08328 + 7.53440i −0.0441513 + 0.307079i
\(603\) 6.82545 14.9456i 0.277954 0.608634i
\(604\) 0.762438 + 5.30287i 0.0310231 + 0.215771i
\(605\) 25.6400 + 7.52857i 1.04241 + 0.306080i
\(606\) −3.99624 + 2.56823i −0.162336 + 0.104327i
\(607\) −6.35531 13.9162i −0.257954 0.564840i 0.735702 0.677306i \(-0.236853\pi\)
−0.993656 + 0.112465i \(0.964125\pi\)
\(608\) 10.0333 2.94603i 0.406903 0.119477i
\(609\) −0.336979 + 0.388894i −0.0136551 + 0.0157588i
\(610\) −4.77542 + 5.51113i −0.193351 + 0.223139i
\(611\) 29.8804 8.77367i 1.20883 0.354945i
\(612\) 0.133912 + 0.293225i 0.00541305 + 0.0118529i
\(613\) 28.8965 18.5706i 1.16712 0.750061i 0.194143 0.980973i \(-0.437807\pi\)
0.972975 + 0.230912i \(0.0741710\pi\)
\(614\) 30.5667 + 8.97520i 1.23357 + 0.362210i
\(615\) −0.405700 2.82170i −0.0163594 0.113782i
\(616\) −3.87258 + 8.47977i −0.156031 + 0.341660i
\(617\) −2.59599 + 18.0555i −0.104511 + 0.726887i 0.868427 + 0.495818i \(0.165132\pi\)
−0.972937 + 0.231070i \(0.925778\pi\)
\(618\) −3.86360 2.48298i −0.155417 0.0998803i
\(619\) −13.9051 16.0474i −0.558894 0.644998i 0.404038 0.914742i \(-0.367606\pi\)
−0.962932 + 0.269745i \(0.913061\pi\)
\(620\) −6.20941 −0.249376
\(621\) −4.10164 5.34987i −0.164593 0.214683i
\(622\) −46.5957 −1.86832
\(623\) 6.84849 + 7.90358i 0.274379 + 0.316650i
\(624\) −3.53318 2.27063i −0.141440 0.0908981i
\(625\) 3.36076 23.3746i 0.134431 0.934985i
\(626\) 10.7480 23.5348i 0.429576 0.940640i
\(627\) 0.517974 + 3.60259i 0.0206859 + 0.143874i
\(628\) −0.286645 0.0841664i −0.0114384 0.00335861i
\(629\) −1.00822 + 0.647944i −0.0402004 + 0.0258352i
\(630\) −5.69608 12.4727i −0.226937 0.496924i
\(631\) −10.2333 + 3.00476i −0.407380 + 0.119618i −0.479001 0.877814i \(-0.659001\pi\)
0.0716208 + 0.997432i \(0.477183\pi\)
\(632\) 19.7601 22.8043i 0.786013 0.907108i
\(633\) −1.84347 + 2.12747i −0.0732712 + 0.0845594i
\(634\) −16.1593 + 4.74479i −0.641767 + 0.188440i
\(635\) 15.7951 + 34.5865i 0.626811 + 1.37252i
\(636\) −0.459997 + 0.295622i −0.0182401 + 0.0117222i
\(637\) 21.9441 + 6.44336i 0.869455 + 0.255295i
\(638\) −2.38132 16.5624i −0.0942773 0.655713i
\(639\) 1.62275 3.55333i 0.0641951 0.140568i
\(640\) 6.22568 43.3006i 0.246092 1.71161i
\(641\) −32.9713 21.1894i −1.30229 0.836930i −0.308829 0.951118i \(-0.599937\pi\)
−0.993459 + 0.114188i \(0.963574\pi\)
\(642\) 0.547248 + 0.631558i 0.0215982 + 0.0249256i
\(643\) 12.9985 0.512612 0.256306 0.966596i \(-0.417495\pi\)
0.256306 + 0.966596i \(0.417495\pi\)
\(644\) 0.853696 + 2.21090i 0.0336403 + 0.0871218i
\(645\) 3.96661 0.156185
\(646\) 0.738207 + 0.851936i 0.0290444 + 0.0335190i
\(647\) 35.5544 + 22.8494i 1.39779 + 0.898303i 0.999818 0.0190951i \(-0.00607851\pi\)
0.397970 + 0.917399i \(0.369715\pi\)
\(648\) 2.81200 19.5579i 0.110466 0.768306i
\(649\) 5.64744 12.3662i 0.221681 0.485414i
\(650\) −4.42765 30.7950i −0.173667 1.20788i
\(651\) 0.739948 + 0.217268i 0.0290008 + 0.00851541i
\(652\) 7.99798 5.13999i 0.313225 0.201298i
\(653\) −3.73815 8.18542i −0.146285 0.320320i 0.822279 0.569085i \(-0.192703\pi\)
−0.968564 + 0.248765i \(0.919975\pi\)
\(654\) 5.17721 1.52017i 0.202445 0.0594432i
\(655\) 12.5608 14.4959i 0.490790 0.566402i
\(656\) −11.8039 + 13.6224i −0.460863 + 0.531864i
\(657\) −28.0827 + 8.24583i −1.09561 + 0.321701i
\(658\) 5.07269 + 11.1076i 0.197754 + 0.433021i
\(659\) −5.80306 + 3.72940i −0.226055 + 0.145277i −0.648766 0.760988i \(-0.724715\pi\)
0.422711 + 0.906264i \(0.361078\pi\)
\(660\) −1.73253 0.508717i −0.0674387 0.0198018i
\(661\) 4.46340 + 31.0436i 0.173606 + 1.20746i 0.871187 + 0.490951i \(0.163351\pi\)
−0.697581 + 0.716506i \(0.745740\pi\)
\(662\) −10.2121 + 22.3614i −0.396905 + 0.869101i
\(663\) 0.0252091 0.175333i 0.000979042 0.00680939i
\(664\) 1.86907 + 1.20118i 0.0725341 + 0.0466148i
\(665\) −6.69472 7.72612i −0.259610 0.299606i
\(666\) −27.8445 −1.07895
\(667\) 9.24017 + 6.75280i 0.357781 + 0.261469i
\(668\) 1.12710 0.0436090
\(669\) 1.92196 + 2.21806i 0.0743072 + 0.0857551i
\(670\) 23.9801 + 15.4111i 0.926432 + 0.595382i
\(671\) −0.893576 + 6.21496i −0.0344961 + 0.239926i
\(672\) 0.267654 0.586080i 0.0103250 0.0226085i
\(673\) 6.00691 + 41.7790i 0.231549 + 1.61046i 0.691405 + 0.722467i \(0.256992\pi\)
−0.459856 + 0.887994i \(0.652099\pi\)
\(674\) −40.7147 11.9549i −1.56827 0.460486i
\(675\) −6.22372 + 3.99974i −0.239551 + 0.153950i
\(676\) 0.168017 + 0.367906i 0.00646219 + 0.0141502i
\(677\) 15.9891 4.69482i 0.614510 0.180436i 0.0403582 0.999185i \(-0.487150\pi\)
0.574152 + 0.818749i \(0.305332\pi\)
\(678\) 0.470120 0.542547i 0.0180549 0.0208364i
\(679\) 2.79172 3.22182i 0.107136 0.123642i
\(680\) 1.44364 0.423892i 0.0553612 0.0162555i
\(681\) −2.75120 6.02429i −0.105426 0.230851i
\(682\) −21.0960 + 13.5576i −0.807808 + 0.519147i
\(683\) 5.80453 + 1.70436i 0.222104 + 0.0652156i 0.390891 0.920437i \(-0.372167\pi\)
−0.168787 + 0.985653i \(0.553985\pi\)
\(684\) 0.794668 + 5.52703i 0.0303849 + 0.211331i
\(685\) −5.73642 + 12.5610i −0.219177 + 0.479931i
\(686\) −2.72453 + 18.9496i −0.104023 + 0.723497i
\(687\) 0.696852 + 0.447840i 0.0265866 + 0.0170861i
\(688\) −16.4244 18.9548i −0.626174 0.722643i
\(689\) −15.8185 −0.602636
\(690\) 5.05188 2.83439i 0.192322 0.107903i
\(691\) 9.53369 0.362679 0.181339 0.983421i \(-0.441957\pi\)
0.181339 + 0.983421i \(0.441957\pi\)
\(692\) −3.05521 3.52590i −0.116142 0.134035i
\(693\) −9.93207 6.38296i −0.377288 0.242468i
\(694\) −3.59434 + 24.9992i −0.136439 + 0.948957i
\(695\) −28.8578 + 63.1897i −1.09464 + 2.39692i
\(696\) −0.186697 1.29851i −0.00707674 0.0492198i
\(697\) −0.729435 0.214181i −0.0276293 0.00811270i
\(698\) 2.63882 1.69587i 0.0998810 0.0641896i
\(699\) 2.36232 + 5.17277i 0.0893513 + 0.195652i
\(700\) 2.49558 0.732769i 0.0943242 0.0276961i
\(701\) 7.90708 9.12525i 0.298646 0.344656i −0.586517 0.809937i \(-0.699501\pi\)
0.885163 + 0.465281i \(0.154047\pi\)
\(702\) 5.44130 6.27959i 0.205369 0.237008i
\(703\) −19.9191 + 5.84878i −0.751263 + 0.220591i
\(704\) −8.79947 19.2681i −0.331642 0.726196i
\(705\) 5.35317 3.44027i 0.201612 0.129568i
\(706\) 34.6781 + 10.1824i 1.30513 + 0.383220i
\(707\) −1.63500 11.3717i −0.0614907 0.427677i
\(708\) −0.164575 + 0.360369i −0.00618511 + 0.0135435i
\(709\) 0.165819 1.15329i 0.00622745 0.0433129i −0.986471 0.163937i \(-0.947581\pi\)
0.992698 + 0.120624i \(0.0384896\pi\)
\(710\) 5.70128 + 3.66399i 0.213965 + 0.137507i
\(711\) 25.0255 + 28.8810i 0.938530 + 1.08312i
\(712\) −26.6612 −0.999172
\(713\) 3.45302 16.8006i 0.129317 0.629189i
\(714\) 0.0694576 0.00259939
\(715\) −34.2078 39.4779i −1.27930 1.47639i
\(716\) 7.51894 + 4.83213i 0.280996 + 0.180585i
\(717\) −0.202387 + 1.40763i −0.00755829 + 0.0525691i
\(718\) −13.8018 + 30.2218i −0.515080 + 1.12787i
\(719\) −0.838352 5.83087i −0.0312653 0.217455i 0.968199 0.250181i \(-0.0804901\pi\)
−0.999464 + 0.0327263i \(0.989581\pi\)
\(720\) 43.3496 + 12.7286i 1.61554 + 0.474366i
\(721\) 9.34408 6.00507i 0.347992 0.223641i
\(722\) −4.47235 9.79308i −0.166444 0.364461i
\(723\) −1.88872 + 0.554580i −0.0702424 + 0.0206250i
\(724\) 7.01214 8.09244i 0.260604 0.300753i
\(725\) 8.22499 9.49214i 0.305468 0.352529i
\(726\) −3.01754 + 0.886030i −0.111991 + 0.0328837i
\(727\) −20.4681 44.8189i −0.759119 1.66224i −0.749249 0.662288i \(-0.769586\pi\)
−0.00986997 0.999951i \(-0.503142\pi\)
\(728\) 6.61142 4.24890i 0.245036 0.157475i
\(729\) 23.0537 + 6.76917i 0.853840 + 0.250710i
\(730\) −7.22641 50.2608i −0.267462 1.86024i
\(731\) 0.439432 0.962223i 0.0162530 0.0355891i
\(732\) 0.0260402 0.181114i 0.000962474 0.00669415i
\(733\) 21.9068 + 14.0786i 0.809144 + 0.520005i 0.878588 0.477580i \(-0.158486\pi\)
−0.0694437 + 0.997586i \(0.522122\pi\)
\(734\) 21.4821 + 24.7917i 0.792919 + 0.915077i
\(735\) 4.67321 0.172374
\(736\) −13.4830 4.85314i −0.496991 0.178889i
\(737\) 24.5439 0.904084
\(738\) −11.5666 13.3485i −0.425771 0.491366i
\(739\) −13.3458 8.57682i −0.490933 0.315504i 0.271647 0.962397i \(-0.412432\pi\)
−0.762581 + 0.646893i \(0.776068\pi\)
\(740\) 1.46575 10.1945i 0.0538820 0.374758i
\(741\) 1.27465 2.79109i 0.0468253 0.102533i
\(742\) −0.882727 6.13950i −0.0324059 0.225388i
\(743\) −37.2079 10.9252i −1.36503 0.400808i −0.484494 0.874795i \(-0.660996\pi\)
−0.880532 + 0.473987i \(0.842814\pi\)
\(744\) −1.65394 + 1.06292i −0.0606364 + 0.0389687i
\(745\) −16.8640 36.9270i −0.617849 1.35290i
\(746\) 34.1644 10.0316i 1.25085 0.367282i
\(747\) −1.84265 + 2.12653i −0.0674190 + 0.0778057i
\(748\) −0.315340 + 0.363921i −0.0115300 + 0.0133063i
\(749\) −1.93920 + 0.569399i −0.0708567 + 0.0208054i
\(750\) −0.132041 0.289129i −0.00482144 0.0105575i
\(751\) −2.52221 + 1.62092i −0.0920366 + 0.0591483i −0.585850 0.810420i \(-0.699239\pi\)
0.493813 + 0.869568i \(0.335603\pi\)
\(752\) −38.6053 11.3355i −1.40779 0.413364i
\(753\) 1.00442 + 6.98588i 0.0366030 + 0.254579i
\(754\) −5.86002 + 12.8317i −0.213409 + 0.467301i
\(755\) −4.50693 + 31.3464i −0.164024 + 1.14081i
\(756\) 0.584370 + 0.375552i 0.0212533 + 0.0136587i
\(757\) 7.33893 + 8.46957i 0.266738 + 0.307832i 0.873279 0.487220i \(-0.161989\pi\)
−0.606541 + 0.795052i \(0.707444\pi\)
\(758\) 27.3522 0.993477
\(759\) 2.33988 4.40477i 0.0849321 0.159883i
\(760\) 26.0626 0.945389
\(761\) −11.2261 12.9556i −0.406945 0.469639i 0.514871 0.857268i \(-0.327840\pi\)
−0.921816 + 0.387629i \(0.873294\pi\)
\(762\) −3.76447 2.41928i −0.136372 0.0876412i
\(763\) −1.85716 + 12.9168i −0.0672336 + 0.467620i
\(764\) −2.47997 + 5.43039i −0.0897223 + 0.196464i
\(765\) 0.271183 + 1.88612i 0.00980465 + 0.0681928i
\(766\) 51.1758 + 15.0266i 1.84906 + 0.542932i
\(767\) −9.64152 + 6.19623i −0.348135 + 0.223733i
\(768\) 1.19241 + 2.61102i 0.0430274 + 0.0942169i
\(769\) 49.5763 14.5569i 1.78777 0.524935i 0.791491 0.611180i \(-0.209305\pi\)
0.996274 + 0.0862449i \(0.0274868\pi\)
\(770\) 13.4133 15.4798i 0.483383 0.557854i
\(771\) −3.03271 + 3.49993i −0.109220 + 0.126047i
\(772\) 2.06504 0.606349i 0.0743222 0.0218230i
\(773\) 13.3195 + 29.1657i 0.479070 + 1.04902i 0.982718 + 0.185108i \(0.0592636\pi\)
−0.503648 + 0.863909i \(0.668009\pi\)
\(774\) 20.6751 13.2871i 0.743151 0.477594i
\(775\) −18.0607 5.30309i −0.648759 0.190493i
\(776\) 1.54671 + 10.7576i 0.0555235 + 0.386174i
\(777\) −0.531375 + 1.16355i −0.0190630 + 0.0417421i
\(778\) −3.35802 + 23.3555i −0.120391 + 0.837337i
\(779\) −11.0782 7.11956i −0.396919 0.255085i
\(780\) 0.996869 + 1.15045i 0.0356936 + 0.0411927i
\(781\) 5.83531 0.208804
\(782\) −0.127906 1.53949i −0.00457392 0.0550521i
\(783\) 3.35442 0.119877
\(784\) −19.3502 22.3313i −0.691077 0.797546i
\(785\) −1.48561 0.954745i −0.0530238 0.0340763i
\(786\) −0.321258 + 2.23440i −0.0114589 + 0.0796983i
\(787\) −13.4447 + 29.4397i −0.479251 + 1.04941i 0.503418 + 0.864043i \(0.332076\pi\)
−0.982669 + 0.185370i \(0.940652\pi\)
\(788\) 0.179988 + 1.25184i 0.00641180 + 0.0445950i
\(789\) 1.16426 + 0.341856i 0.0414486 + 0.0121704i
\(790\) −55.7745 + 35.8441i −1.98437 + 1.27528i
\(791\) 0.721251 + 1.57932i 0.0256447 + 0.0561541i
\(792\) 28.8795 8.47977i 1.02619 0.301316i
\(793\) 3.46641 4.00045i 0.123096 0.142060i
\(794\) −13.1686 + 15.1974i −0.467336 + 0.539335i
\(795\) −3.10132 + 0.910629i −0.109992 + 0.0322967i
\(796\) −2.70884 5.93153i −0.0960122 0.210237i
\(797\) −32.4918 + 20.8812i −1.15092 + 0.739650i −0.969822 0.243815i \(-0.921601\pi\)
−0.181097 + 0.983465i \(0.557965\pi\)
\(798\) 1.15441 + 0.338966i 0.0408658 + 0.0119993i
\(799\) −0.241504 1.67970i −0.00854380 0.0594234i
\(800\) −6.53291 + 14.3051i −0.230973 + 0.505761i
\(801\) 4.80535 33.4219i 0.169789 1.18091i
\(802\) −22.7125 14.5964i −0.802005 0.515417i
\(803\) −28.6312 33.0422i −1.01037 1.16603i
\(804\) −0.715246 −0.0252248
\(805\) 1.15997 + 13.9615i 0.0408835 + 0.492077i
\(806\) 21.1409 0.744656
\(807\) −2.56053 2.95501i −0.0901348 0.104021i
\(808\) 24.6394 + 15.8348i 0.866811 + 0.557065i
\(809\) −0.392324 + 2.72867i −0.0137934 + 0.0959350i −0.995555 0.0941801i \(-0.969977\pi\)
0.981762 + 0.190115i \(0.0608861\pi\)
\(810\) −18.0350 + 39.4912i −0.633686 + 1.38758i
\(811\) −4.45246 30.9676i −0.156347 1.08742i −0.905293 0.424787i \(-0.860349\pi\)
0.748946 0.662631i \(-0.230560\pi\)
\(812\) −1.13153 0.332247i −0.0397090 0.0116596i
\(813\) −4.75684 + 3.05704i −0.166830 + 0.107215i
\(814\) −17.2789 37.8354i −0.605624 1.32613i
\(815\) 53.9227 15.8331i 1.88883 0.554611i
\(816\) −0.149871 + 0.172960i −0.00524653 + 0.00605482i
\(817\) 11.9994 13.8480i 0.419805 0.484481i
\(818\) −47.6696 + 13.9971i −1.66673 + 0.489396i
\(819\) 4.13471 + 9.05375i 0.144478 + 0.316364i
\(820\) 5.49608 3.53211i 0.191931 0.123347i
\(821\) 26.1872 + 7.68927i 0.913941 + 0.268357i 0.704699 0.709506i \(-0.251082\pi\)
0.209242 + 0.977864i \(0.432900\pi\)
\(822\) −0.231284 1.60861i −0.00806694 0.0561068i
\(823\) −1.65368 + 3.62105i −0.0576436 + 0.126222i −0.936262 0.351303i \(-0.885739\pi\)
0.878618 + 0.477525i \(0.158466\pi\)
\(824\) −4.02990 + 28.0285i −0.140388 + 0.976420i
\(825\) −4.60477 2.95931i −0.160318 0.103030i
\(826\) −2.94293 3.39632i −0.102398 0.118173i
\(827\) −14.1240 −0.491139 −0.245569 0.969379i \(-0.578975\pi\)
−0.245569 + 0.969379i \(0.578975\pi\)
\(828\) 3.58980 6.75773i 0.124754 0.234847i
\(829\) −27.0753 −0.940363 −0.470181 0.882570i \(-0.655812\pi\)
−0.470181 + 0.882570i \(0.655812\pi\)
\(830\) −3.19682 3.68932i −0.110963 0.128058i
\(831\) −0.0187282 0.0120359i −0.000649674 0.000417520i
\(832\) −2.54141 + 17.6759i −0.0881074 + 0.612800i
\(833\) 0.517711 1.13363i 0.0179376 0.0392779i
\(834\) −1.16350 8.09232i −0.0402887 0.280214i
\(835\) 6.39268 + 1.87706i 0.221228 + 0.0649583i
\(836\) −7.01707 + 4.50960i −0.242691 + 0.155968i
\(837\) −2.08836 4.57287i −0.0721843 0.158061i
\(838\) −51.2680 + 15.0536i −1.77102 + 0.520020i
\(839\) 19.6366 22.6619i 0.677932 0.782375i −0.307663 0.951495i \(-0.599547\pi\)
0.985595 + 0.169120i \(0.0540925\pi\)
\(840\) 1.05162 1.21363i 0.0362842 0.0418742i
\(841\) 22.3611 6.56583i 0.771074 0.226408i
\(842\) 23.7002 + 51.8961i 0.816761 + 1.78846i
\(843\) −2.26613 + 1.45635i −0.0780495 + 0.0501594i
\(844\) −6.19012 1.81758i −0.213073 0.0625638i
\(845\) 0.340250 + 2.36649i 0.0117049 + 0.0814097i
\(846\) 16.3782 35.8633i 0.563095 1.23301i
\(847\) 1.08244 7.52857i 0.0371933 0.258685i
\(848\) 17.1930 + 11.0493i 0.590410 + 0.379434i
\(849\) 3.71892 + 4.29187i 0.127633 + 0.147297i
\(850\) −1.69532 −0.0581491
\(851\) 26.7679 + 9.63496i 0.917593 + 0.330282i
\(852\) −0.170050 −0.00582582
\(853\) −11.2526 12.9862i −0.385281 0.444638i 0.529669 0.848204i \(-0.322316\pi\)
−0.914951 + 0.403566i \(0.867771\pi\)
\(854\) 1.74610 + 1.12215i 0.0597504 + 0.0383992i
\(855\) −4.69745 + 32.6715i −0.160649 + 1.11734i
\(856\) 2.14041 4.68684i 0.0731576 0.160193i
\(857\) −6.02726 41.9205i −0.205887 1.43198i −0.786395 0.617723i \(-0.788055\pi\)
0.580508 0.814255i \(-0.302854\pi\)
\(858\) 5.89867 + 1.73201i 0.201377 + 0.0591297i
\(859\) −23.8513 + 15.3283i −0.813795 + 0.522994i −0.880091 0.474806i \(-0.842518\pi\)
0.0662954 + 0.997800i \(0.478882\pi\)
\(860\) 3.77636 + 8.26908i 0.128773 + 0.281973i
\(861\) −0.778532 + 0.228598i −0.0265323 + 0.00779059i
\(862\) 4.22913 4.88067i 0.144045 0.166236i
\(863\) −7.26115 + 8.37981i −0.247172 + 0.285252i −0.865755 0.500467i \(-0.833162\pi\)
0.618583 + 0.785719i \(0.287707\pi\)
\(864\) −4.02992 + 1.18329i −0.137101 + 0.0402564i
\(865\) −11.4565 25.0862i −0.389532 0.852957i
\(866\) 14.0992 9.06101i 0.479111 0.307906i
\(867\) 3.84804 + 1.12989i 0.130686 + 0.0383729i
\(868\) 0.251525 + 1.74939i 0.00853731 + 0.0593783i
\(869\) −23.7143 + 51.9270i −0.804452 + 1.76150i
\(870\) −0.410211 + 2.85308i −0.0139075 + 0.0967285i
\(871\) −17.4068 11.1867i −0.589807 0.379046i
\(872\) −21.7862 25.1426i −0.737774 0.851436i
\(873\) −13.7642 −0.465849
\(874\) 5.38715 26.2111i 0.182223 0.886605i
\(875\) 0.768722 0.0259876
\(876\) 0.834360 + 0.962902i 0.0281904 + 0.0325335i
\(877\) 1.08197 + 0.695339i 0.0365355 + 0.0234799i 0.558781 0.829315i \(-0.311269\pi\)
−0.522246 + 0.852795i \(0.674906\pi\)
\(878\) 4.77474 33.2090i 0.161140 1.12075i
\(879\) 1.94135 4.25097i 0.0654803 0.143382i
\(880\) 9.60477 + 66.8026i 0.323777 + 2.25192i
\(881\) 6.36967 + 1.87030i 0.214600 + 0.0630121i 0.387265 0.921968i \(-0.373420\pi\)
−0.172666 + 0.984981i \(0.555238\pi\)
\(882\) 24.3581 15.6540i 0.820178 0.527097i
\(883\) 5.84470 + 12.7981i 0.196690 + 0.430691i 0.982119 0.188261i \(-0.0602850\pi\)
−0.785429 + 0.618951i \(0.787558\pi\)
\(884\) 0.389512 0.114371i 0.0131007 0.00384672i
\(885\) −1.53358 + 1.76985i −0.0515509 + 0.0594929i
\(886\) 36.7284 42.3869i 1.23392 1.42401i
\(887\) 3.71462 1.09071i 0.124725 0.0366224i −0.218775 0.975775i \(-0.570206\pi\)
0.343499 + 0.939153i \(0.388388\pi\)
\(888\) −1.35467 2.96632i −0.0454599 0.0995433i
\(889\) 9.10434 5.85100i 0.305350 0.196236i
\(890\) 56.2072 + 16.5039i 1.88407 + 0.553212i
\(891\) 5.31990 + 37.0007i 0.178223 + 1.23957i
\(892\) −2.79414 + 6.11832i −0.0935548 + 0.204857i
\(893\) 4.18335 29.0958i 0.139990 0.973654i
\(894\) 4.01921 + 2.58299i 0.134423 + 0.0863882i
\(895\) 34.5983 + 39.9286i 1.15650 + 1.33467i
\(896\) −12.4514 −0.415971
\(897\) −3.66709 + 2.05744i −0.122441 + 0.0686961i
\(898\) −11.6639 −0.389229
\(899\) 5.58902 + 6.45007i 0.186404 + 0.215122i
\(900\) −7.06457 4.54012i −0.235486 0.151337i
\(901\) −0.122672 + 0.853201i −0.00408679 + 0.0284243i
\(902\) 10.9605 24.0002i 0.364945 0.799119i
\(903\) −0.160676 1.11752i −0.00534695 0.0371889i
\(904\) −4.24698 1.24703i −0.141252 0.0414754i
\(905\) 53.2482 34.2205i 1.77003 1.13753i
\(906\) −1.54828 3.39026i −0.0514381 0.112634i
\(907\) −2.54461 + 0.747165i −0.0844924 + 0.0248092i −0.323706 0.946158i \(-0.604929\pi\)
0.239213 + 0.970967i \(0.423111\pi\)
\(908\) 9.93941 11.4707i 0.329851 0.380668i
\(909\) −24.2911 + 28.0334i −0.805684 + 0.929808i
\(910\) −16.5684 + 4.86491i −0.549236 + 0.161270i
\(911\) −8.98681 19.6784i −0.297746 0.651973i 0.700340 0.713809i \(-0.253032\pi\)
−0.998086 + 0.0618359i \(0.980304\pi\)
\(912\) −3.33499 + 2.14327i −0.110433 + 0.0709707i
\(913\) −4.03301 1.18420i −0.133473 0.0391913i
\(914\) −6.80103 47.3022i −0.224958 1.56462i
\(915\) 0.449317 0.983868i 0.0148540 0.0325257i
\(916\) −0.270169 + 1.87906i −0.00892663 + 0.0620861i
\(917\) −4.59277 2.95159i −0.151667 0.0974702i
\(918\) −0.296505 0.342185i −0.00978614 0.0112938i
\(919\) −33.8729 −1.11736 −0.558681 0.829382i \(-0.688692\pi\)
−0.558681 + 0.829382i \(0.688692\pi\)
\(920\) −28.8360 21.0736i −0.950694 0.694776i
\(921\) −4.72515 −0.155699
\(922\) 6.31776 + 7.29108i 0.208064 + 0.240119i
\(923\) −4.13848 2.65964i −0.136220 0.0875430i
\(924\) −0.0731425 + 0.508717i −0.00240621 + 0.0167356i
\(925\) 12.9698 28.3999i 0.426445 0.933784i
\(926\) 5.08430 + 35.3621i 0.167080 + 1.16207i
\(927\) −34.4096 10.1036i −1.13016 0.331845i
\(928\) 5.99854 3.85503i 0.196912 0.126547i
\(929\) 0.0255013 + 0.0558401i 0.000836671 + 0.00183205i 0.910050 0.414499i \(-0.136043\pi\)
−0.909213 + 0.416331i \(0.863316\pi\)
\(930\) 4.14481 1.21703i 0.135914 0.0399079i
\(931\) 14.1369 16.3148i 0.463318 0.534697i
\(932\) −8.53449 + 9.84933i −0.279557 + 0.322626i
\(933\) 6.63126 1.94711i 0.217098 0.0637457i
\(934\) −9.25112 20.2571i −0.302706 0.662833i
\(935\) −2.39460 + 1.53892i −0.0783118 + 0.0503280i
\(936\) −24.3466 7.14881i −0.795794 0.233666i
\(937\) −0.290080 2.01755i −0.00947651 0.0659106i 0.984534 0.175191i \(-0.0560544\pi\)
−0.994011 + 0.109281i \(0.965145\pi\)
\(938\) 3.37044 7.38023i 0.110049 0.240973i
\(939\) −0.546140 + 3.79848i −0.0178226 + 0.123959i
\(940\) 12.2682 + 7.88432i 0.400146 + 0.257158i
\(941\) 10.5943 + 12.2265i 0.345365 + 0.398572i 0.901683 0.432397i \(-0.142332\pi\)
−0.556319 + 0.830969i \(0.687787\pi\)
\(942\) 0.207833 0.00677156
\(943\) 6.50041 + 16.8348i 0.211682 + 0.548216i
\(944\) 14.8074 0.481940
\(945\) 2.68898 + 3.10324i 0.0874724 + 0.100948i
\(946\) 30.8845 + 19.8483i 1.00414 + 0.645324i
\(947\) 5.90698 41.0840i 0.191951 1.33505i −0.634885 0.772607i \(-0.718952\pi\)
0.826836 0.562443i \(-0.190138\pi\)
\(948\) 0.691072 1.51324i 0.0224450 0.0491476i
\(949\) 5.24555 + 36.4836i 0.170278 + 1.18431i
\(950\) −28.1770 8.27350i −0.914181 0.268428i
\(951\) 2.10143 1.35051i 0.0681436 0.0437933i
\(952\) −0.177902 0.389551i −0.00576583 0.0126254i
\(953\) −39.4302 + 11.5777i −1.27727 + 0.375040i −0.848895 0.528562i \(-0.822731\pi\)
−0.428373 + 0.903602i \(0.640913\pi\)
\(954\) −13.1146 + 15.1350i −0.424600 + 0.490014i
\(955\) −23.1095 + 26.6698i −0.747806 + 0.863014i
\(956\) −3.12713 + 0.918209i −0.101139 + 0.0296970i
\(957\) 1.03100 + 2.25757i 0.0333274 + 0.0729769i
\(958\) −32.8539 + 21.1139i −1.06146 + 0.682160i
\(959\) 3.77121 + 1.10733i 0.121779 + 0.0357575i
\(960\) 0.519295 + 3.61178i 0.0167602 + 0.116570i
\(961\) −7.56444 + 16.5638i −0.244014 + 0.534316i
\(962\) −4.99037 + 34.7088i −0.160896 + 1.11906i
\(963\) 5.48953 + 3.52791i 0.176898 + 0.113685i
\(964\) −2.95425 3.40938i −0.0951499 0.109809i
\(965\) 12.7222 0.409542
\(966\) −1.00318 1.30847i −0.0322767 0.0420993i
\(967\) −12.7482 −0.409954 −0.204977 0.978767i \(-0.565712\pi\)
−0.204977 + 0.978767i \(0.565712\pi\)
\(968\) 12.6981 + 14.6544i 0.408132 + 0.471010i
\(969\) −0.140658 0.0903954i −0.00451859 0.00290392i
\(970\) 3.39842 23.6365i 0.109117 0.758923i
\(971\) −3.43753 + 7.52715i −0.110316 + 0.241558i −0.956736 0.290958i \(-0.906026\pi\)
0.846420 + 0.532516i \(0.178753\pi\)
\(972\) −0.480276 3.34039i −0.0154049 0.107143i
\(973\) 18.9715 + 5.57054i 0.608199 + 0.178583i
\(974\) 18.7019 12.0190i 0.599249 0.385114i
\(975\) 1.91696 + 4.19756i 0.0613919 + 0.134429i
\(976\) −6.56195 + 1.92676i −0.210043 + 0.0616742i
\(977\) −37.7993 + 43.6227i −1.20931 + 1.39561i −0.314440 + 0.949277i \(0.601817\pi\)
−0.894865 + 0.446336i \(0.852729\pi\)
\(978\) −4.33127 + 4.99855i −0.138499 + 0.159836i
\(979\) 48.3961 14.2104i 1.54675 0.454166i
\(980\) 4.44906 + 9.74209i 0.142120 + 0.311200i
\(981\) 35.4449 22.7791i 1.13167 0.727279i
\(982\) −13.3247 3.91248i −0.425208 0.124852i
\(983\) 1.24228 + 8.64025i 0.0396226 + 0.275581i 0.999995 0.00313852i \(-0.000999024\pi\)
−0.960372 + 0.278720i \(0.910090\pi\)
\(984\) 0.859312 1.88163i 0.0273939 0.0599842i
\(985\) −1.06395 + 7.39991i −0.0339001 + 0.235781i
\(986\) 0.646657 + 0.415581i 0.0205938 + 0.0132348i
\(987\) −1.18608 1.36881i −0.0377533 0.0435696i
\(988\) 7.03200 0.223718
\(989\) −24.4734 + 5.61921i −0.778210 + 0.178681i
\(990\) −66.1328 −2.10184
\(991\) 37.1510 + 42.8746i 1.18014 + 1.36196i 0.917830 + 0.396973i \(0.129939\pi\)
0.262311 + 0.964983i \(0.415515\pi\)
\(992\) −8.98983 5.77741i −0.285427 0.183433i
\(993\) 0.518910 3.60910i 0.0164671 0.114531i
\(994\) 0.801323 1.75465i 0.0254164 0.0556542i
\(995\) −5.48564 38.1535i −0.173907 1.20955i
\(996\) 0.117528 + 0.0345094i 0.00372402 + 0.00109347i
\(997\) 4.36734 2.80672i 0.138315 0.0888896i −0.469653 0.882851i \(-0.655621\pi\)
0.607968 + 0.793961i \(0.291985\pi\)
\(998\) 14.1976 + 31.0885i 0.449418 + 0.984088i
\(999\) 8.00063 2.34920i 0.253129 0.0743253i
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 23.2.c.a.13.1 10
3.2 odd 2 207.2.i.c.82.1 10
4.3 odd 2 368.2.m.c.289.1 10
5.2 odd 4 575.2.p.b.174.2 20
5.3 odd 4 575.2.p.b.174.1 20
5.4 even 2 575.2.k.b.151.1 10
23.2 even 11 529.2.c.d.466.1 10
23.3 even 11 529.2.c.g.255.1 10
23.4 even 11 529.2.a.i.1.4 5
23.5 odd 22 529.2.c.c.118.1 10
23.6 even 11 529.2.c.b.399.1 10
23.7 odd 22 529.2.c.a.177.1 10
23.8 even 11 529.2.c.d.487.1 10
23.9 even 11 529.2.c.i.501.1 10
23.10 odd 22 529.2.c.f.334.1 10
23.11 odd 22 529.2.c.h.170.1 10
23.12 even 11 529.2.c.i.170.1 10
23.13 even 11 529.2.c.g.334.1 10
23.14 odd 22 529.2.c.h.501.1 10
23.15 odd 22 529.2.c.e.487.1 10
23.16 even 11 inner 23.2.c.a.16.1 yes 10
23.17 odd 22 529.2.c.c.399.1 10
23.18 even 11 529.2.c.b.118.1 10
23.19 odd 22 529.2.a.j.1.4 5
23.20 odd 22 529.2.c.f.255.1 10
23.21 odd 22 529.2.c.e.466.1 10
23.22 odd 2 529.2.c.a.266.1 10
69.50 odd 22 4761.2.a.bo.1.2 5
69.62 odd 22 207.2.i.c.154.1 10
69.65 even 22 4761.2.a.bn.1.2 5
92.19 even 22 8464.2.a.bt.1.4 5
92.27 odd 22 8464.2.a.bs.1.4 5
92.39 odd 22 368.2.m.c.177.1 10
115.39 even 22 575.2.k.b.476.1 10
115.62 odd 44 575.2.p.b.499.1 20
115.108 odd 44 575.2.p.b.499.2 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
23.2.c.a.13.1 10 1.1 even 1 trivial
23.2.c.a.16.1 yes 10 23.16 even 11 inner
207.2.i.c.82.1 10 3.2 odd 2
207.2.i.c.154.1 10 69.62 odd 22
368.2.m.c.177.1 10 92.39 odd 22
368.2.m.c.289.1 10 4.3 odd 2
529.2.a.i.1.4 5 23.4 even 11
529.2.a.j.1.4 5 23.19 odd 22
529.2.c.a.177.1 10 23.7 odd 22
529.2.c.a.266.1 10 23.22 odd 2
529.2.c.b.118.1 10 23.18 even 11
529.2.c.b.399.1 10 23.6 even 11
529.2.c.c.118.1 10 23.5 odd 22
529.2.c.c.399.1 10 23.17 odd 22
529.2.c.d.466.1 10 23.2 even 11
529.2.c.d.487.1 10 23.8 even 11
529.2.c.e.466.1 10 23.21 odd 22
529.2.c.e.487.1 10 23.15 odd 22
529.2.c.f.255.1 10 23.20 odd 22
529.2.c.f.334.1 10 23.10 odd 22
529.2.c.g.255.1 10 23.3 even 11
529.2.c.g.334.1 10 23.13 even 11
529.2.c.h.170.1 10 23.11 odd 22
529.2.c.h.501.1 10 23.14 odd 22
529.2.c.i.170.1 10 23.12 even 11
529.2.c.i.501.1 10 23.9 even 11
575.2.k.b.151.1 10 5.4 even 2
575.2.k.b.476.1 10 115.39 even 22
575.2.p.b.174.1 20 5.3 odd 4
575.2.p.b.174.2 20 5.2 odd 4
575.2.p.b.499.1 20 115.62 odd 44
575.2.p.b.499.2 20 115.108 odd 44
4761.2.a.bn.1.2 5 69.65 even 22
4761.2.a.bo.1.2 5 69.50 odd 22
8464.2.a.bs.1.4 5 92.27 odd 22
8464.2.a.bt.1.4 5 92.19 even 22