Properties

Label 288.2.bf.a.83.18
Level $288$
Weight $2$
Character 288.83
Analytic conductor $2.300$
Analytic rank $0$
Dimension $368$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [288,2,Mod(11,288)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(288, base_ring=CyclotomicField(24))
 
chi = DirichletCharacter(H, H._module([12, 15, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("288.11");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 288 = 2^{5} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 288.bf (of order \(24\), degree \(8\), 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: \(2.29969157821\)
Analytic rank: \(0\)
Dimension: \(368\)
Relative dimension: \(46\) over \(\Q(\zeta_{24})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label 83.18
Character \(\chi\) \(=\) 288.83
Dual form 288.2.bf.a.59.18

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.447661 + 1.34149i) q^{2} +(-0.897422 + 1.48143i) q^{3} +(-1.59920 - 1.20107i) q^{4} +(1.68794 - 2.19977i) q^{5} +(-1.58558 - 1.86706i) q^{6} +(3.57293 - 0.957363i) q^{7} +(2.32712 - 1.60764i) q^{8} +(-1.38927 - 2.65894i) q^{9} +O(q^{10})\) \(q+(-0.447661 + 1.34149i) q^{2} +(-0.897422 + 1.48143i) q^{3} +(-1.59920 - 1.20107i) q^{4} +(1.68794 - 2.19977i) q^{5} +(-1.58558 - 1.86706i) q^{6} +(3.57293 - 0.957363i) q^{7} +(2.32712 - 1.60764i) q^{8} +(-1.38927 - 2.65894i) q^{9} +(2.19534 + 3.24911i) q^{10} +(2.76923 + 0.364576i) q^{11} +(3.21445 - 1.29124i) q^{12} +(-0.0949795 - 0.721441i) q^{13} +(-0.315165 + 5.22163i) q^{14} +(1.74400 + 4.47468i) q^{15} +(1.11488 + 3.84149i) q^{16} -4.88192 q^{17} +(4.18886 - 0.673388i) q^{18} +(3.20076 - 7.72731i) q^{19} +(-5.34142 + 1.49054i) q^{20} +(-1.78816 + 6.15220i) q^{21} +(-1.72875 + 3.55169i) q^{22} +(-2.38745 + 8.91007i) q^{23} +(0.293201 + 4.89020i) q^{24} +(-0.695734 - 2.59651i) q^{25} +(1.01033 + 0.195546i) q^{26} +(5.18578 + 0.328089i) q^{27} +(-6.86368 - 2.76031i) q^{28} +(-0.969012 + 0.743549i) q^{29} +(-6.78347 + 0.336426i) q^{30} +(2.36525 - 1.36558i) q^{31} +(-5.65241 - 0.224081i) q^{32} +(-3.02526 + 3.77524i) q^{33} +(2.18545 - 6.54906i) q^{34} +(3.92491 - 9.47558i) q^{35} +(-0.971844 + 5.92077i) q^{36} +(4.41073 - 1.82698i) q^{37} +(8.93326 + 7.75300i) q^{38} +(1.15400 + 0.506732i) q^{39} +(0.391598 - 7.83272i) q^{40} +(0.884682 + 0.237050i) q^{41} +(-7.45264 - 5.15290i) q^{42} +(-1.36547 + 10.3718i) q^{43} +(-3.99067 - 3.90906i) q^{44} +(-8.19403 - 1.43206i) q^{45} +(-10.8840 - 7.19143i) q^{46} +(-1.50468 - 0.868729i) q^{47} +(-6.69141 - 1.79582i) q^{48} +(5.78709 - 3.34118i) q^{49} +(3.79466 + 0.229036i) q^{50} +(4.38115 - 7.23222i) q^{51} +(-0.714607 + 1.26780i) q^{52} +(4.81164 - 1.99305i) q^{53} +(-2.76160 + 6.80981i) q^{54} +(5.47627 - 5.47627i) q^{55} +(6.77553 - 7.97189i) q^{56} +(8.57503 + 11.6764i) q^{57} +(-0.563676 - 1.63278i) q^{58} +(3.40167 + 2.61019i) q^{59} +(2.58538 - 9.25057i) q^{60} +(-3.79052 - 4.93990i) q^{61} +(0.773080 + 3.78427i) q^{62} +(-7.50931 - 8.17015i) q^{63} +(2.83097 - 7.48235i) q^{64} +(-1.74732 - 1.00882i) q^{65} +(-3.71016 - 5.74839i) q^{66} +(-0.814488 - 6.18665i) q^{67} +(7.80717 + 5.86351i) q^{68} +(-11.0571 - 11.5329i) q^{69} +(10.9544 + 9.50708i) q^{70} +(-6.73879 + 6.73879i) q^{71} +(-7.50761 - 3.95422i) q^{72} +(0.311054 + 0.311054i) q^{73} +(0.476374 + 6.73483i) q^{74} +(4.47092 + 1.29949i) q^{75} +(-14.3997 + 8.51319i) q^{76} +(10.2433 - 1.34855i) q^{77} +(-1.19638 + 1.32124i) q^{78} +(-1.58640 + 2.74773i) q^{79} +(10.3322 + 4.03173i) q^{80} +(-5.13988 + 7.38794i) q^{81} +(-0.714038 + 1.08068i) q^{82} +(-6.50289 + 4.98984i) q^{83} +(10.2488 - 7.69090i) q^{84} +(-8.24039 + 10.7391i) q^{85} +(-13.3024 - 6.47479i) q^{86} +(-0.231902 - 2.10280i) q^{87} +(7.03044 - 3.60352i) q^{88} +(-1.28293 - 1.28293i) q^{89} +(5.58925 - 10.3511i) q^{90} +(-1.03004 - 2.48673i) q^{91} +(14.5196 - 11.3815i) q^{92} +(-0.0996213 + 4.72944i) q^{93} +(1.83898 - 1.62962i) q^{94} +(-11.5956 - 20.0841i) q^{95} +(5.40456 - 8.17256i) q^{96} +(-2.19738 + 3.80597i) q^{97} +(1.89151 + 9.25905i) q^{98} +(-2.87781 - 7.86970i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} - 8 q^{12} - 4 q^{13} - 12 q^{14} - 16 q^{15} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 12 q^{20} - 8 q^{21} - 4 q^{22} - 12 q^{23} + 32 q^{24} - 4 q^{25} + 16 q^{27} - 16 q^{28} - 12 q^{29} - 56 q^{30} - 12 q^{32} - 16 q^{33} - 12 q^{34} - 60 q^{36} - 16 q^{37} - 12 q^{38} + 16 q^{39} - 4 q^{40} - 12 q^{41} - 8 q^{42} - 4 q^{43} - 8 q^{45} - 16 q^{46} - 24 q^{47} - 60 q^{48} - 168 q^{50} - 32 q^{51} - 4 q^{52} - 52 q^{54} - 16 q^{55} - 12 q^{56} - 8 q^{57} + 32 q^{58} - 12 q^{59} - 20 q^{60} - 4 q^{61} - 16 q^{64} - 24 q^{65} - 80 q^{66} - 4 q^{67} - 60 q^{68} - 8 q^{69} - 4 q^{70} + 52 q^{72} - 16 q^{73} - 12 q^{74} - 28 q^{75} - 28 q^{76} - 12 q^{77} + 80 q^{78} - 8 q^{79} - 16 q^{82} - 132 q^{83} - 104 q^{84} - 24 q^{85} - 12 q^{86} - 64 q^{87} - 4 q^{88} + 124 q^{90} - 16 q^{91} + 216 q^{92} - 20 q^{93} - 20 q^{94} + 92 q^{96} - 8 q^{97} - 72 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/288\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.447661 + 1.34149i −0.316544 + 0.948578i
\(3\) −0.897422 + 1.48143i −0.518127 + 0.855304i
\(4\) −1.59920 1.20107i −0.799600 0.600533i
\(5\) 1.68794 2.19977i 0.754870 0.983765i −0.245029 0.969516i \(-0.578797\pi\)
0.999898 0.0142494i \(-0.00453588\pi\)
\(6\) −1.58558 1.86706i −0.647312 0.762225i
\(7\) 3.57293 0.957363i 1.35044 0.361849i 0.490143 0.871642i \(-0.336945\pi\)
0.860297 + 0.509793i \(0.170278\pi\)
\(8\) 2.32712 1.60764i 0.822761 0.568388i
\(9\) −1.38927 2.65894i −0.463089 0.886312i
\(10\) 2.19534 + 3.24911i 0.694228 + 1.02746i
\(11\) 2.76923 + 0.364576i 0.834954 + 0.109924i 0.535867 0.844302i \(-0.319985\pi\)
0.299087 + 0.954226i \(0.403318\pi\)
\(12\) 3.21445 1.29124i 0.927932 0.372748i
\(13\) −0.0949795 0.721441i −0.0263426 0.200092i 0.973213 0.229906i \(-0.0738418\pi\)
−0.999555 + 0.0298141i \(0.990508\pi\)
\(14\) −0.315165 + 5.22163i −0.0842313 + 1.39554i
\(15\) 1.74400 + 4.47468i 0.450300 + 1.15536i
\(16\) 1.11488 + 3.84149i 0.278720 + 0.960372i
\(17\) −4.88192 −1.18404 −0.592020 0.805923i \(-0.701669\pi\)
−0.592020 + 0.805923i \(0.701669\pi\)
\(18\) 4.18886 0.673388i 0.987324 0.158719i
\(19\) 3.20076 7.72731i 0.734304 1.77277i 0.106616 0.994300i \(-0.465998\pi\)
0.627688 0.778465i \(-0.284002\pi\)
\(20\) −5.34142 + 1.49054i −1.19438 + 0.333294i
\(21\) −1.78816 + 6.15220i −0.390208 + 1.34252i
\(22\) −1.72875 + 3.55169i −0.368571 + 0.757223i
\(23\) −2.38745 + 8.91007i −0.497817 + 1.85788i 0.0158258 + 0.999875i \(0.494962\pi\)
−0.513643 + 0.858004i \(0.671704\pi\)
\(24\) 0.293201 + 4.89020i 0.0598494 + 0.998207i
\(25\) −0.695734 2.59651i −0.139147 0.519303i
\(26\) 1.01033 + 0.195546i 0.198141 + 0.0383498i
\(27\) 5.18578 + 0.328089i 0.998005 + 0.0631408i
\(28\) −6.86368 2.76031i −1.29711 0.521649i
\(29\) −0.969012 + 0.743549i −0.179941 + 0.138074i −0.694805 0.719198i \(-0.744509\pi\)
0.514864 + 0.857272i \(0.327843\pi\)
\(30\) −6.78347 + 0.336426i −1.23849 + 0.0614227i
\(31\) 2.36525 1.36558i 0.424811 0.245265i −0.272323 0.962206i \(-0.587792\pi\)
0.697133 + 0.716941i \(0.254458\pi\)
\(32\) −5.65241 0.224081i −0.999215 0.0396124i
\(33\) −3.02526 + 3.77524i −0.526631 + 0.657185i
\(34\) 2.18545 6.54906i 0.374801 1.12315i
\(35\) 3.92491 9.47558i 0.663431 1.60166i
\(36\) −0.971844 + 5.92077i −0.161974 + 0.986795i
\(37\) 4.41073 1.82698i 0.725119 0.300354i 0.0105747 0.999944i \(-0.496634\pi\)
0.714545 + 0.699590i \(0.246634\pi\)
\(38\) 8.93326 + 7.75300i 1.44917 + 1.25770i
\(39\) 1.15400 + 0.506732i 0.184788 + 0.0811420i
\(40\) 0.391598 7.83272i 0.0619171 1.23846i
\(41\) 0.884682 + 0.237050i 0.138164 + 0.0370210i 0.327238 0.944942i \(-0.393882\pi\)
−0.189074 + 0.981963i \(0.560549\pi\)
\(42\) −7.45264 5.15290i −1.14997 0.795110i
\(43\) −1.36547 + 10.3718i −0.208232 + 1.58168i 0.493827 + 0.869560i \(0.335598\pi\)
−0.702059 + 0.712119i \(0.747736\pi\)
\(44\) −3.99067 3.90906i −0.601616 0.589313i
\(45\) −8.19403 1.43206i −1.22149 0.213479i
\(46\) −10.8840 7.19143i −1.60476 1.06032i
\(47\) −1.50468 0.868729i −0.219481 0.126717i 0.386229 0.922403i \(-0.373777\pi\)
−0.605710 + 0.795686i \(0.707111\pi\)
\(48\) −6.69141 1.79582i −0.965822 0.259205i
\(49\) 5.78709 3.34118i 0.826727 0.477311i
\(50\) 3.79466 + 0.229036i 0.536645 + 0.0323906i
\(51\) 4.38115 7.23222i 0.613483 1.01271i
\(52\) −0.714607 + 1.26780i −0.0990981 + 0.175813i
\(53\) 4.81164 1.99305i 0.660930 0.273766i −0.0268999 0.999638i \(-0.508564\pi\)
0.687830 + 0.725872i \(0.258564\pi\)
\(54\) −2.76160 + 6.80981i −0.375806 + 0.926698i
\(55\) 5.47627 5.47627i 0.738421 0.738421i
\(56\) 6.77553 7.97189i 0.905418 1.06529i
\(57\) 8.57503 + 11.6764i 1.13579 + 1.54657i
\(58\) −0.563676 1.63278i −0.0740143 0.214394i
\(59\) 3.40167 + 2.61019i 0.442859 + 0.339818i 0.805999 0.591917i \(-0.201629\pi\)
−0.363140 + 0.931735i \(0.618295\pi\)
\(60\) 2.58538 9.25057i 0.333771 1.19424i
\(61\) −3.79052 4.93990i −0.485326 0.632489i 0.484935 0.874550i \(-0.338843\pi\)
−0.970261 + 0.242061i \(0.922177\pi\)
\(62\) 0.773080 + 3.78427i 0.0981813 + 0.480603i
\(63\) −7.50931 8.17015i −0.946085 1.02934i
\(64\) 2.83097 7.48235i 0.353871 0.935294i
\(65\) −1.74732 1.00882i −0.216728 0.125128i
\(66\) −3.71016 5.74839i −0.456689 0.707578i
\(67\) −0.814488 6.18665i −0.0995055 0.755820i −0.966348 0.257238i \(-0.917188\pi\)
0.866843 0.498582i \(-0.166146\pi\)
\(68\) 7.80717 + 5.86351i 0.946758 + 0.711055i
\(69\) −11.0571 11.5329i −1.33112 1.38840i
\(70\) 10.9544 + 9.50708i 1.30930 + 1.13631i
\(71\) −6.73879 + 6.73879i −0.799747 + 0.799747i −0.983055 0.183309i \(-0.941319\pi\)
0.183309 + 0.983055i \(0.441319\pi\)
\(72\) −7.50761 3.95422i −0.884780 0.466009i
\(73\) 0.311054 + 0.311054i 0.0364061 + 0.0364061i 0.725075 0.688669i \(-0.241805\pi\)
−0.688669 + 0.725075i \(0.741805\pi\)
\(74\) 0.476374 + 6.73483i 0.0553773 + 0.782908i
\(75\) 4.47092 + 1.29949i 0.516257 + 0.150052i
\(76\) −14.3997 + 8.51319i −1.65175 + 0.976530i
\(77\) 10.2433 1.34855i 1.16733 0.153682i
\(78\) −1.19638 + 1.32124i −0.135463 + 0.149601i
\(79\) −1.58640 + 2.74773i −0.178484 + 0.309144i −0.941362 0.337399i \(-0.890453\pi\)
0.762877 + 0.646543i \(0.223786\pi\)
\(80\) 10.3322 + 4.03173i 1.15518 + 0.450761i
\(81\) −5.13988 + 7.38794i −0.571098 + 0.820882i
\(82\) −0.714038 + 1.08068i −0.0788523 + 0.119341i
\(83\) −6.50289 + 4.98984i −0.713785 + 0.547706i −0.900579 0.434693i \(-0.856857\pi\)
0.186794 + 0.982399i \(0.440190\pi\)
\(84\) 10.2488 7.69090i 1.11824 0.839146i
\(85\) −8.24039 + 10.7391i −0.893796 + 1.16482i
\(86\) −13.3024 6.47479i −1.43443 0.698195i
\(87\) −0.231902 2.10280i −0.0248625 0.225444i
\(88\) 7.03044 3.60352i 0.749447 0.384137i
\(89\) −1.28293 1.28293i −0.135991 0.135991i 0.635835 0.771825i \(-0.280656\pi\)
−0.771825 + 0.635835i \(0.780656\pi\)
\(90\) 5.58925 10.3511i 0.589158 1.09111i
\(91\) −1.03004 2.48673i −0.107977 0.260680i
\(92\) 14.5196 11.3815i 1.51377 1.18660i
\(93\) −0.0996213 + 4.72944i −0.0103302 + 0.490420i
\(94\) 1.83898 1.62962i 0.189676 0.168083i
\(95\) −11.5956 20.0841i −1.18968 2.06059i
\(96\) 5.40456 8.17256i 0.551601 0.834108i
\(97\) −2.19738 + 3.80597i −0.223110 + 0.386438i −0.955751 0.294178i \(-0.904954\pi\)
0.732641 + 0.680616i \(0.238288\pi\)
\(98\) 1.89151 + 9.25905i 0.191071 + 0.935305i
\(99\) −2.87781 7.86970i −0.289231 0.790934i
\(100\) −2.00597 + 4.98797i −0.200597 + 0.498797i
\(101\) −8.67469 1.14205i −0.863164 0.113638i −0.314072 0.949399i \(-0.601693\pi\)
−0.549093 + 0.835762i \(0.685027\pi\)
\(102\) 7.74070 + 9.11485i 0.766444 + 0.902505i
\(103\) −2.69438 + 10.0556i −0.265485 + 0.990804i 0.696468 + 0.717588i \(0.254754\pi\)
−0.961953 + 0.273216i \(0.911913\pi\)
\(104\) −1.38085 1.52619i −0.135403 0.149655i
\(105\) 10.5151 + 14.3181i 1.02617 + 1.39730i
\(106\) 0.519674 + 7.34699i 0.0504752 + 0.713602i
\(107\) −4.65937 11.2487i −0.450438 1.08745i −0.972156 0.234336i \(-0.924708\pi\)
0.521717 0.853118i \(-0.325292\pi\)
\(108\) −7.89905 6.75315i −0.760086 0.649822i
\(109\) −11.5309 4.77627i −1.10446 0.457483i −0.245435 0.969413i \(-0.578931\pi\)
−0.859027 + 0.511930i \(0.828931\pi\)
\(110\) 4.89486 + 9.79789i 0.466707 + 0.934192i
\(111\) −1.25174 + 8.17376i −0.118810 + 0.775819i
\(112\) 7.66109 + 12.6580i 0.723905 + 1.19607i
\(113\) −3.16267 5.47791i −0.297519 0.515319i 0.678048 0.735017i \(-0.262826\pi\)
−0.975568 + 0.219699i \(0.929493\pi\)
\(114\) −19.5024 + 6.27629i −1.82657 + 0.587828i
\(115\) 15.5702 + 20.2915i 1.45193 + 1.89219i
\(116\) 2.44270 0.0252360i 0.226799 0.00234310i
\(117\) −1.78631 + 1.25482i −0.165145 + 0.116008i
\(118\) −5.02434 + 3.39483i −0.462528 + 0.312519i
\(119\) −17.4428 + 4.67377i −1.59898 + 0.428444i
\(120\) 11.2522 + 7.60939i 1.02718 + 0.694639i
\(121\) −3.08947 0.827820i −0.280860 0.0752563i
\(122\) 8.32370 2.87355i 0.753592 0.260159i
\(123\) −1.14511 + 1.09786i −0.103251 + 0.0989907i
\(124\) −5.42265 0.656989i −0.486968 0.0589994i
\(125\) 5.92233 + 2.45311i 0.529709 + 0.219413i
\(126\) 14.3218 6.41623i 1.27589 0.571603i
\(127\) 8.04728i 0.714081i 0.934089 + 0.357040i \(0.116214\pi\)
−0.934089 + 0.357040i \(0.883786\pi\)
\(128\) 8.77020 + 7.14727i 0.775184 + 0.631736i
\(129\) −14.1396 11.3307i −1.24492 0.997612i
\(130\) 2.13552 1.89241i 0.187298 0.165975i
\(131\) 8.49485 1.11837i 0.742198 0.0977123i 0.250061 0.968230i \(-0.419549\pi\)
0.492137 + 0.870518i \(0.336216\pi\)
\(132\) 9.37231 2.40382i 0.815755 0.209226i
\(133\) 4.03823 30.6734i 0.350159 2.65972i
\(134\) 8.66395 + 1.67689i 0.748452 + 0.144861i
\(135\) 9.47501 10.8537i 0.815479 0.934139i
\(136\) −11.3608 + 7.84839i −0.974182 + 0.672994i
\(137\) −0.336242 1.25487i −0.0287271 0.107211i 0.950074 0.312026i \(-0.101008\pi\)
−0.978801 + 0.204815i \(0.934341\pi\)
\(138\) 20.4212 9.67016i 1.73836 0.823179i
\(139\) 14.7882 + 11.3473i 1.25431 + 0.962469i 0.999989 0.00464928i \(-0.00147992\pi\)
0.254325 + 0.967119i \(0.418147\pi\)
\(140\) −17.6575 + 10.4393i −1.49233 + 0.882278i
\(141\) 2.63730 1.44946i 0.222100 0.122067i
\(142\) −6.02334 12.0567i −0.505467 1.01178i
\(143\) 2.03246i 0.169963i
\(144\) 8.66541 8.30125i 0.722117 0.691770i
\(145\) 3.38667i 0.281247i
\(146\) −0.556523 + 0.278030i −0.0460582 + 0.0230099i
\(147\) −0.243745 + 11.5716i −0.0201038 + 0.954411i
\(148\) −9.24797 2.37587i −0.760178 0.195295i
\(149\) −2.26076 1.73474i −0.185209 0.142116i 0.511996 0.858988i \(-0.328906\pi\)
−0.697204 + 0.716872i \(0.745573\pi\)
\(150\) −3.74471 + 5.41597i −0.305754 + 0.442212i
\(151\) 0.711717 + 2.65617i 0.0579187 + 0.216156i 0.988820 0.149116i \(-0.0476428\pi\)
−0.930901 + 0.365272i \(0.880976\pi\)
\(152\) −4.97421 23.1280i −0.403462 1.87593i
\(153\) 6.78229 + 12.9807i 0.548316 + 1.04943i
\(154\) −2.77644 + 14.3450i −0.223732 + 1.15595i
\(155\) 0.988446 7.50800i 0.0793939 0.603057i
\(156\) −1.23686 2.19640i −0.0990279 0.175852i
\(157\) −9.88965 + 1.30200i −0.789280 + 0.103911i −0.514380 0.857562i \(-0.671978\pi\)
−0.274900 + 0.961473i \(0.588645\pi\)
\(158\) −2.97589 3.35820i −0.236749 0.267164i
\(159\) −1.36552 + 8.91671i −0.108293 + 0.707141i
\(160\) −10.0339 + 12.0558i −0.793246 + 0.953091i
\(161\) 34.1207i 2.68909i
\(162\) −7.60994 10.2024i −0.597893 0.801576i
\(163\) 20.2425 + 8.38472i 1.58551 + 0.656742i 0.989275 0.146065i \(-0.0466608\pi\)
0.596240 + 0.802806i \(0.296661\pi\)
\(164\) −1.13007 1.44165i −0.0882437 0.112574i
\(165\) 3.19818 + 13.0272i 0.248978 + 1.01417i
\(166\) −3.78274 10.9573i −0.293598 0.850453i
\(167\) 9.08552 + 2.43446i 0.703059 + 0.188384i 0.592600 0.805497i \(-0.298101\pi\)
0.110458 + 0.993881i \(0.464768\pi\)
\(168\) 5.72928 + 17.1916i 0.442024 + 1.32636i
\(169\) 12.0456 3.22760i 0.926583 0.248277i
\(170\) −10.7175 15.8619i −0.821994 1.21655i
\(171\) −24.9931 + 2.22468i −1.91127 + 0.170126i
\(172\) 14.6408 14.9465i 1.11635 1.13966i
\(173\) 3.33965 + 4.35232i 0.253909 + 0.330901i 0.902864 0.429926i \(-0.141460\pi\)
−0.648955 + 0.760827i \(0.724794\pi\)
\(174\) 2.92470 + 0.630246i 0.221721 + 0.0477788i
\(175\) −4.97161 8.61109i −0.375819 0.650937i
\(176\) 1.68684 + 11.0444i 0.127151 + 0.832505i
\(177\) −6.91954 + 2.69688i −0.520105 + 0.202710i
\(178\) 2.29536 1.14673i 0.172045 0.0859508i
\(179\) −18.6550 7.72714i −1.39434 0.577554i −0.446062 0.895002i \(-0.647174\pi\)
−0.948276 + 0.317448i \(0.897174\pi\)
\(180\) 11.3839 + 12.1317i 0.848505 + 0.904246i
\(181\) −2.04940 4.94769i −0.152331 0.367759i 0.829231 0.558907i \(-0.188779\pi\)
−0.981561 + 0.191148i \(0.938779\pi\)
\(182\) 3.79703 0.268575i 0.281454 0.0199081i
\(183\) 10.7198 1.18221i 0.792431 0.0873914i
\(184\) 8.76835 + 24.5730i 0.646411 + 1.81154i
\(185\) 3.42611 12.7864i 0.251892 0.940076i
\(186\) −6.29991 2.25083i −0.461932 0.165039i
\(187\) −13.5192 1.77983i −0.988619 0.130154i
\(188\) 1.36289 + 3.19649i 0.0993988 + 0.233128i
\(189\) 18.8425 3.79244i 1.37059 0.275859i
\(190\) 32.1336 6.56450i 2.33122 0.476239i
\(191\) −11.1492 + 19.3109i −0.806726 + 1.39729i 0.108393 + 0.994108i \(0.465429\pi\)
−0.915120 + 0.403183i \(0.867904\pi\)
\(192\) 8.54401 + 10.9087i 0.616611 + 0.787268i
\(193\) 2.37607 + 4.11548i 0.171034 + 0.296239i 0.938781 0.344513i \(-0.111956\pi\)
−0.767748 + 0.640752i \(0.778623\pi\)
\(194\) −4.12200 4.65155i −0.295942 0.333962i
\(195\) 3.06257 1.68320i 0.219315 0.120536i
\(196\) −13.2677 1.60747i −0.947692 0.114819i
\(197\) 4.97689 + 12.0153i 0.354589 + 0.856053i 0.996041 + 0.0888903i \(0.0283321\pi\)
−0.641453 + 0.767163i \(0.721668\pi\)
\(198\) 11.8454 0.337607i 0.841817 0.0239927i
\(199\) −6.53127 6.53127i −0.462989 0.462989i 0.436645 0.899634i \(-0.356167\pi\)
−0.899634 + 0.436645i \(0.856167\pi\)
\(200\) −5.79332 4.92391i −0.409650 0.348173i
\(201\) 9.89602 + 4.34543i 0.698012 + 0.306503i
\(202\) 5.41536 11.1258i 0.381024 0.782807i
\(203\) −2.75036 + 3.58434i −0.193038 + 0.251572i
\(204\) −15.6927 + 6.30372i −1.09871 + 0.441349i
\(205\) 2.01474 1.54597i 0.140716 0.107975i
\(206\) −12.2833 8.11597i −0.855817 0.565466i
\(207\) 27.0081 6.03039i 1.87719 0.419141i
\(208\) 2.66552 1.16918i 0.184820 0.0810682i
\(209\) 11.6808 20.2318i 0.807979 1.39946i
\(210\) −23.9148 + 7.69627i −1.65028 + 0.531093i
\(211\) −16.0305 + 2.11046i −1.10359 + 0.145290i −0.660236 0.751058i \(-0.729544\pi\)
−0.443351 + 0.896348i \(0.646211\pi\)
\(212\) −10.0886 2.59182i −0.692885 0.178007i
\(213\) −3.93550 16.0306i −0.269656 1.09840i
\(214\) 17.1759 1.21490i 1.17412 0.0830488i
\(215\) 20.5106 + 20.5106i 1.39881 + 1.39881i
\(216\) 12.5954 7.57339i 0.857008 0.515304i
\(217\) 7.14350 7.14350i 0.484932 0.484932i
\(218\) 11.5693 13.3305i 0.783569 0.902855i
\(219\) −0.739951 + 0.181658i −0.0500013 + 0.0122753i
\(220\) −15.3350 + 2.18029i −1.03389 + 0.146995i
\(221\) 0.463682 + 3.52202i 0.0311907 + 0.236917i
\(222\) −10.4047 5.33827i −0.698316 0.358281i
\(223\) −11.5336 6.65891i −0.772345 0.445913i 0.0613657 0.998115i \(-0.480454\pi\)
−0.833710 + 0.552202i \(0.813788\pi\)
\(224\) −20.4102 + 4.61079i −1.36371 + 0.308071i
\(225\) −5.93741 + 5.45716i −0.395827 + 0.363811i
\(226\) 8.76438 1.79046i 0.582998 0.119099i
\(227\) −11.2416 14.6504i −0.746134 0.972381i −0.999987 0.00513803i \(-0.998365\pi\)
0.253853 0.967243i \(-0.418302\pi\)
\(228\) 0.310884 28.9720i 0.0205888 1.91872i
\(229\) −1.83921 1.41128i −0.121539 0.0932600i 0.546204 0.837652i \(-0.316073\pi\)
−0.667742 + 0.744393i \(0.732739\pi\)
\(230\) −34.1910 + 11.8036i −2.25449 + 0.778307i
\(231\) −7.19477 + 16.3849i −0.473381 + 1.07805i
\(232\) −1.05964 + 3.28815i −0.0695691 + 0.215878i
\(233\) 14.0808 14.0808i 0.922462 0.922462i −0.0747408 0.997203i \(-0.523813\pi\)
0.997203 + 0.0747408i \(0.0238130\pi\)
\(234\) −0.883665 2.95806i −0.0577670 0.193374i
\(235\) −4.45081 + 1.84359i −0.290339 + 0.120262i
\(236\) −2.30493 8.25984i −0.150038 0.537670i
\(237\) −2.64690 4.81602i −0.171934 0.312834i
\(238\) 1.53861 25.4916i 0.0997332 1.65237i
\(239\) −0.761068 + 0.439403i −0.0492294 + 0.0284226i −0.524413 0.851464i \(-0.675715\pi\)
0.475183 + 0.879887i \(0.342382\pi\)
\(240\) −15.2451 + 11.6883i −0.984066 + 0.754477i
\(241\) −2.03782 1.17654i −0.131268 0.0757873i 0.432928 0.901428i \(-0.357480\pi\)
−0.564196 + 0.825641i \(0.690814\pi\)
\(242\) 2.49355 3.77391i 0.160291 0.242596i
\(243\) −6.33207 14.2445i −0.406202 0.913783i
\(244\) 0.128650 + 12.4525i 0.00823597 + 0.797193i
\(245\) 2.41845 18.3700i 0.154509 1.17361i
\(246\) −0.960151 2.02762i −0.0612170 0.129276i
\(247\) −5.87880 1.57522i −0.374059 0.100229i
\(248\) 3.30885 6.98033i 0.210112 0.443251i
\(249\) −1.55626 14.1116i −0.0986240 0.894284i
\(250\) −5.94202 + 6.84659i −0.375806 + 0.433016i
\(251\) 5.35869 2.21964i 0.338237 0.140103i −0.207099 0.978320i \(-0.566402\pi\)
0.545336 + 0.838218i \(0.316402\pi\)
\(252\) 2.19600 + 22.0849i 0.138335 + 1.39122i
\(253\) −9.85979 + 23.8036i −0.619880 + 1.49652i
\(254\) −10.7954 3.60245i −0.677361 0.226038i
\(255\) −8.51409 21.8451i −0.533173 1.36799i
\(256\) −13.5141 + 8.56560i −0.844630 + 0.535350i
\(257\) −0.643725 + 0.371655i −0.0401544 + 0.0231832i −0.519943 0.854201i \(-0.674047\pi\)
0.479788 + 0.877384i \(0.340713\pi\)
\(258\) 21.5298 13.8959i 1.34039 0.865120i
\(259\) 14.0101 10.7504i 0.870547 0.667994i
\(260\) 1.58266 + 3.71194i 0.0981524 + 0.230205i
\(261\) 3.32327 + 1.54355i 0.205705 + 0.0955436i
\(262\) −2.30253 + 11.8964i −0.142251 + 0.734963i
\(263\) −3.15312 11.7676i −0.194430 0.725621i −0.992414 0.122943i \(-0.960767\pi\)
0.797984 0.602678i \(-0.205900\pi\)
\(264\) −0.970908 + 13.6490i −0.0597553 + 0.840036i
\(265\) 3.73752 13.9486i 0.229594 0.856858i
\(266\) 39.3403 + 19.1485i 2.41211 + 1.17407i
\(267\) 3.05191 0.749242i 0.186774 0.0458529i
\(268\) −6.12805 + 10.8719i −0.374330 + 0.664110i
\(269\) −1.99968 + 4.82765i −0.121922 + 0.294347i −0.973043 0.230623i \(-0.925924\pi\)
0.851121 + 0.524970i \(0.175924\pi\)
\(270\) 10.3186 + 17.5694i 0.627969 + 1.06924i
\(271\) −21.4273 −1.30162 −0.650808 0.759243i \(-0.725570\pi\)
−0.650808 + 0.759243i \(0.725570\pi\)
\(272\) −5.44276 18.7539i −0.330016 1.13712i
\(273\) 4.60828 + 0.705718i 0.278906 + 0.0427120i
\(274\) 1.83393 + 0.110691i 0.110791 + 0.00668710i
\(275\) −0.980020 7.44399i −0.0590975 0.448890i
\(276\) 3.83069 + 31.7238i 0.230580 + 1.90955i
\(277\) −16.1147 2.12153i −0.968236 0.127471i −0.370210 0.928948i \(-0.620714\pi\)
−0.598025 + 0.801477i \(0.704048\pi\)
\(278\) −21.8424 + 14.7584i −1.31002 + 0.885151i
\(279\) −6.91693 4.39189i −0.414106 0.262936i
\(280\) −6.09961 28.3607i −0.364521 1.69487i
\(281\) 8.24786 2.21001i 0.492026 0.131838i −0.00427085 0.999991i \(-0.501359\pi\)
0.496297 + 0.868153i \(0.334693\pi\)
\(282\) 0.763830 + 4.18678i 0.0454854 + 0.249319i
\(283\) 1.56707 2.04225i 0.0931529 0.121399i −0.744451 0.667677i \(-0.767289\pi\)
0.837604 + 0.546277i \(0.183956\pi\)
\(284\) 18.8704 2.68294i 1.11975 0.159203i
\(285\) 40.1594 + 0.845919i 2.37884 + 0.0501079i
\(286\) 2.72653 + 0.909853i 0.161223 + 0.0538008i
\(287\) 3.38785 0.199978
\(288\) 7.25689 + 15.3407i 0.427616 + 0.903960i
\(289\) 6.83317 0.401951
\(290\) −4.54318 1.51608i −0.266785 0.0890271i
\(291\) −3.66630 6.67082i −0.214922 0.391051i
\(292\) −0.123841 0.871034i −0.00724725 0.0509734i
\(293\) 4.70192 6.12766i 0.274689 0.357982i −0.635554 0.772057i \(-0.719228\pi\)
0.910243 + 0.414075i \(0.135895\pi\)
\(294\) −15.4141 5.50714i −0.898969 0.321183i
\(295\) 11.4836 3.07702i 0.668602 0.179151i
\(296\) 7.32715 11.3425i 0.425882 0.659269i
\(297\) 14.2410 + 2.79917i 0.826348 + 0.162424i
\(298\) 3.33919 2.25621i 0.193434 0.130699i
\(299\) 6.65485 + 0.876127i 0.384860 + 0.0506677i
\(300\) −5.58912 7.44801i −0.322688 0.430011i
\(301\) 5.05082 + 38.3648i 0.291125 + 2.21131i
\(302\) −3.88183 0.234298i −0.223374 0.0134823i
\(303\) 9.47672 11.8261i 0.544424 0.679389i
\(304\) 33.2528 + 3.68065i 1.90718 + 0.211100i
\(305\) −17.2648 −0.988579
\(306\) −20.4497 + 3.28743i −1.16903 + 0.187930i
\(307\) 3.04950 7.36214i 0.174044 0.420179i −0.812653 0.582747i \(-0.801978\pi\)
0.986697 + 0.162568i \(0.0519777\pi\)
\(308\) −18.0008 10.1463i −1.02569 0.578137i
\(309\) −12.4786 13.0156i −0.709883 0.740433i
\(310\) 9.62943 + 4.68703i 0.546915 + 0.266205i
\(311\) 0.260434 0.971952i 0.0147678 0.0551144i −0.958149 0.286271i \(-0.907584\pi\)
0.972917 + 0.231157i \(0.0742509\pi\)
\(312\) 3.50014 0.675995i 0.198156 0.0382707i
\(313\) 3.97305 + 14.8276i 0.224570 + 0.838107i 0.982576 + 0.185859i \(0.0595069\pi\)
−0.758006 + 0.652247i \(0.773826\pi\)
\(314\) 2.68059 13.8497i 0.151274 0.781586i
\(315\) −30.6477 + 2.72801i −1.72680 + 0.153706i
\(316\) 5.83718 2.48880i 0.328367 0.140006i
\(317\) −17.6519 + 13.5448i −0.991431 + 0.760751i −0.971010 0.239040i \(-0.923167\pi\)
−0.0204209 + 0.999791i \(0.506501\pi\)
\(318\) −11.3504 5.82349i −0.636499 0.326565i
\(319\) −2.95450 + 1.70578i −0.165420 + 0.0955053i
\(320\) −11.6809 18.8572i −0.652984 1.05415i
\(321\) 20.8456 + 3.19232i 1.16349 + 0.178178i
\(322\) −45.7726 15.2745i −2.55081 0.851214i
\(323\) −15.6258 + 37.7241i −0.869445 + 2.09903i
\(324\) 17.0931 5.64145i 0.949617 0.313414i
\(325\) −1.80715 + 0.748546i −0.100243 + 0.0415219i
\(326\) −20.3098 + 23.4016i −1.12486 + 1.29610i
\(327\) 17.4238 12.7959i 0.963539 0.707616i
\(328\) 2.43985 0.870610i 0.134718 0.0480714i
\(329\) −6.20781 1.66338i −0.342248 0.0917050i
\(330\) −18.9076 1.54145i −1.04083 0.0848541i
\(331\) −3.03406 + 23.0460i −0.166767 + 1.26672i 0.679386 + 0.733781i \(0.262246\pi\)
−0.846153 + 0.532940i \(0.821087\pi\)
\(332\) 16.3925 0.169355i 0.899658 0.00929455i
\(333\) −10.9855 9.18968i −0.602002 0.503591i
\(334\) −7.33303 + 11.0983i −0.401246 + 0.607274i
\(335\) −14.9840 8.65101i −0.818663 0.472655i
\(336\) −25.6272 0.0102317i −1.39808 0.000558186i
\(337\) 17.3997 10.0457i 0.947824 0.547227i 0.0554198 0.998463i \(-0.482350\pi\)
0.892404 + 0.451237i \(0.149017\pi\)
\(338\) −1.06253 + 17.6039i −0.0577940 + 0.957527i
\(339\) 10.9534 + 0.230723i 0.594907 + 0.0125312i
\(340\) 26.0764 7.27669i 1.41419 0.394634i
\(341\) 7.04777 2.91928i 0.381658 0.158088i
\(342\) 8.20404 34.5240i 0.443624 1.86684i
\(343\) −0.830815 + 0.830815i −0.0448598 + 0.0448598i
\(344\) 13.4965 + 26.3315i 0.727682 + 1.41970i
\(345\) −44.0335 + 4.85613i −2.37068 + 0.261445i
\(346\) −7.33364 + 2.53176i −0.394259 + 0.136108i
\(347\) 13.5418 + 10.3910i 0.726961 + 0.557817i 0.904591 0.426280i \(-0.140176\pi\)
−0.177630 + 0.984097i \(0.556843\pi\)
\(348\) −2.15474 + 3.64133i −0.115506 + 0.195196i
\(349\) 17.1062 + 22.2932i 0.915674 + 1.19333i 0.980714 + 0.195447i \(0.0626157\pi\)
−0.0650406 + 0.997883i \(0.520718\pi\)
\(350\) 13.7773 2.81453i 0.736428 0.150443i
\(351\) −0.255846 3.77240i −0.0136561 0.201356i
\(352\) −15.5711 2.68127i −0.829945 0.142912i
\(353\) 13.7167 + 7.91932i 0.730064 + 0.421503i 0.818446 0.574584i \(-0.194836\pi\)
−0.0883816 + 0.996087i \(0.528169\pi\)
\(354\) −0.520241 10.4898i −0.0276505 0.557527i
\(355\) 3.44909 + 26.1984i 0.183058 + 1.39047i
\(356\) 0.510779 + 3.59256i 0.0270712 + 0.190405i
\(357\) 8.72966 30.0346i 0.462022 1.58960i
\(358\) 18.7170 21.5663i 0.989224 1.13982i
\(359\) −8.47576 + 8.47576i −0.447333 + 0.447333i −0.894467 0.447134i \(-0.852445\pi\)
0.447134 + 0.894467i \(0.352445\pi\)
\(360\) −21.3707 + 9.84050i −1.12634 + 0.518640i
\(361\) −36.0314 36.0314i −1.89639 1.89639i
\(362\) 7.55471 0.534367i 0.397067 0.0280857i
\(363\) 3.99891 3.83392i 0.209888 0.201229i
\(364\) −1.33949 + 5.21391i −0.0702083 + 0.273283i
\(365\) 1.20929 0.159205i 0.0632969 0.00833320i
\(366\) −3.21291 + 14.9098i −0.167942 + 0.779346i
\(367\) −10.4730 + 18.1397i −0.546684 + 0.946885i 0.451814 + 0.892112i \(0.350777\pi\)
−0.998499 + 0.0547732i \(0.982556\pi\)
\(368\) −36.8897 + 0.762311i −1.92301 + 0.0397382i
\(369\) −0.598758 2.68164i −0.0311701 0.139601i
\(370\) 15.6191 + 10.3201i 0.812000 + 0.536515i
\(371\) 15.2836 11.7275i 0.793484 0.608862i
\(372\) 5.83969 7.44367i 0.302774 0.385936i
\(373\) 6.15693 8.02387i 0.318794 0.415460i −0.606278 0.795253i \(-0.707338\pi\)
0.925072 + 0.379793i \(0.124005\pi\)
\(374\) 8.43963 17.3391i 0.436403 0.896583i
\(375\) −8.94893 + 6.57203i −0.462121 + 0.339378i
\(376\) −4.89818 + 0.397357i −0.252604 + 0.0204921i
\(377\) 0.628463 + 0.628463i 0.0323675 + 0.0323675i
\(378\) −3.34754 + 26.9748i −0.172179 + 1.38744i
\(379\) −4.99838 12.0672i −0.256750 0.619848i 0.741970 0.670433i \(-0.233892\pi\)
−0.998720 + 0.0505846i \(0.983892\pi\)
\(380\) −5.57873 + 46.0456i −0.286183 + 2.36209i
\(381\) −11.9215 7.22181i −0.610756 0.369985i
\(382\) −20.9144 23.6013i −1.07007 1.20755i
\(383\) 5.03803 + 8.72613i 0.257431 + 0.445884i 0.965553 0.260206i \(-0.0837905\pi\)
−0.708122 + 0.706090i \(0.750457\pi\)
\(384\) −18.4588 + 6.57831i −0.941970 + 0.335698i
\(385\) 14.3236 24.8091i 0.729996 1.26439i
\(386\) −6.58456 + 1.34514i −0.335145 + 0.0684660i
\(387\) 29.4748 10.7784i 1.49829 0.547899i
\(388\) 8.08527 3.44731i 0.410467 0.175011i
\(389\) 32.7461 + 4.31111i 1.66029 + 0.218582i 0.901509 0.432760i \(-0.142460\pi\)
0.758785 + 0.651342i \(0.225793\pi\)
\(390\) 0.887002 + 4.86192i 0.0449151 + 0.246193i
\(391\) 11.6553 43.4983i 0.589436 2.19980i
\(392\) 8.09583 17.0789i 0.408901 0.862615i
\(393\) −5.96668 + 13.5882i −0.300979 + 0.685432i
\(394\) −18.3464 + 1.29769i −0.924276 + 0.0653767i
\(395\) 3.36661 + 8.12772i 0.169393 + 0.408950i
\(396\) −4.84983 + 16.0417i −0.243713 + 0.806124i
\(397\) 10.2226 + 4.23435i 0.513059 + 0.212516i 0.624165 0.781292i \(-0.285439\pi\)
−0.111106 + 0.993809i \(0.535439\pi\)
\(398\) 11.6854 5.83785i 0.585738 0.292625i
\(399\) 41.8165 + 33.5093i 2.09344 + 1.67757i
\(400\) 9.19882 5.56746i 0.459941 0.278373i
\(401\) −12.0434 20.8599i −0.601421 1.04169i −0.992606 0.121380i \(-0.961268\pi\)
0.391185 0.920312i \(-0.372065\pi\)
\(402\) −10.2594 + 11.3302i −0.511693 + 0.565097i
\(403\) −1.20983 1.57668i −0.0602660 0.0785402i
\(404\) 12.5009 + 12.2452i 0.621943 + 0.609223i
\(405\) 7.57593 + 23.7769i 0.376451 + 1.18148i
\(406\) −3.57714 5.29416i −0.177530 0.262745i
\(407\) 12.8804 3.45129i 0.638458 0.171074i
\(408\) −1.43138 23.8736i −0.0708641 1.18192i
\(409\) 5.08955 + 1.36374i 0.251662 + 0.0674326i 0.382445 0.923978i \(-0.375082\pi\)
−0.130783 + 0.991411i \(0.541749\pi\)
\(410\) 1.17198 + 3.39483i 0.0578800 + 0.167659i
\(411\) 2.16076 + 0.628032i 0.106582 + 0.0309786i
\(412\) 16.3863 12.8447i 0.807293 0.632814i
\(413\) 14.6528 + 6.06939i 0.721017 + 0.298655i
\(414\) −4.00075 + 38.9307i −0.196626 + 1.91334i
\(415\) 22.7274i 1.11564i
\(416\) 0.375202 + 4.09916i 0.0183958 + 0.200978i
\(417\) −30.0815 + 11.7242i −1.47310 + 0.574138i
\(418\) 21.9117 + 24.7267i 1.07174 + 1.20942i
\(419\) 28.0445 3.69212i 1.37006 0.180372i 0.590672 0.806912i \(-0.298863\pi\)
0.779389 + 0.626540i \(0.215529\pi\)
\(420\) 0.381220 35.5268i 0.0186017 1.73353i
\(421\) −2.23992 + 17.0139i −0.109167 + 0.829206i 0.846009 + 0.533168i \(0.178999\pi\)
−0.955176 + 0.296038i \(0.904335\pi\)
\(422\) 4.34508 22.4496i 0.211515 1.09283i
\(423\) −0.219490 + 5.20775i −0.0106720 + 0.253210i
\(424\) 7.99316 12.3735i 0.388182 0.600908i
\(425\) 3.39652 + 12.6760i 0.164755 + 0.614876i
\(426\) 23.2666 + 1.89682i 1.12727 + 0.0919012i
\(427\) −18.2725 14.0210i −0.884269 0.678524i
\(428\) −6.05919 + 23.5852i −0.292882 + 1.14003i
\(429\) 3.01095 + 1.82398i 0.145370 + 0.0880624i
\(430\) −36.6966 + 18.3330i −1.76967 + 0.884097i
\(431\) 9.65845i 0.465231i −0.972569 0.232616i \(-0.925272\pi\)
0.972569 0.232616i \(-0.0747284\pi\)
\(432\) 4.52118 + 20.2869i 0.217525 + 0.976055i
\(433\) 31.2869i 1.50355i 0.659419 + 0.751775i \(0.270802\pi\)
−0.659419 + 0.751775i \(0.729198\pi\)
\(434\) 6.38508 + 12.7808i 0.306494 + 0.613499i
\(435\) −5.01711 3.03927i −0.240552 0.145722i
\(436\) 12.7036 + 21.4876i 0.608394 + 1.02907i
\(437\) 61.2092 + 46.9675i 2.92803 + 2.24676i
\(438\) 0.0875548 1.07396i 0.00418353 0.0513158i
\(439\) −2.05756 7.67892i −0.0982020 0.366495i 0.899283 0.437366i \(-0.144089\pi\)
−0.997485 + 0.0708714i \(0.977422\pi\)
\(440\) 3.94005 21.5478i 0.187834 1.02725i
\(441\) −16.9238 10.7457i −0.805895 0.511701i
\(442\) −4.93233 0.954643i −0.234607 0.0454077i
\(443\) −1.19116 + 9.04775i −0.0565937 + 0.429872i 0.939570 + 0.342358i \(0.111226\pi\)
−0.996163 + 0.0875137i \(0.972108\pi\)
\(444\) 11.8190 11.5681i 0.560905 0.548996i
\(445\) −4.98767 + 0.656639i −0.236438 + 0.0311277i
\(446\) 14.0960 12.4913i 0.667465 0.591478i
\(447\) 4.59875 1.79236i 0.217514 0.0847757i
\(448\) 2.95151 29.4442i 0.139446 1.39111i
\(449\) 14.5975i 0.688900i −0.938805 0.344450i \(-0.888065\pi\)
0.938805 0.344450i \(-0.111935\pi\)
\(450\) −4.66279 10.4079i −0.219806 0.490635i
\(451\) 2.36347 + 0.978979i 0.111291 + 0.0460983i
\(452\) −1.52159 + 12.5589i −0.0715694 + 0.590719i
\(453\) −4.57363 1.32934i −0.214888 0.0624580i
\(454\) 24.6858 8.52217i 1.15856 0.399965i
\(455\) −7.20885 1.93161i −0.337956 0.0905551i
\(456\) 38.7265 + 13.3867i 1.81354 + 0.626888i
\(457\) 3.17779 0.851485i 0.148651 0.0398308i −0.183726 0.982977i \(-0.558816\pi\)
0.332377 + 0.943147i \(0.392149\pi\)
\(458\) 2.71656 1.83552i 0.126937 0.0857681i
\(459\) −25.3166 1.60171i −1.18168 0.0747612i
\(460\) −0.528452 51.1510i −0.0246392 2.38493i
\(461\) −13.5037 17.5983i −0.628929 0.819636i 0.364843 0.931069i \(-0.381123\pi\)
−0.993772 + 0.111433i \(0.964456\pi\)
\(462\) −18.7594 16.9866i −0.872768 0.790289i
\(463\) −17.8061 30.8410i −0.827517 1.43330i −0.899980 0.435931i \(-0.856419\pi\)
0.0724627 0.997371i \(-0.476914\pi\)
\(464\) −3.93667 2.89348i −0.182755 0.134327i
\(465\) 10.2355 + 8.20216i 0.474661 + 0.380366i
\(466\) 12.5858 + 25.1926i 0.583027 + 1.16703i
\(467\) −12.6498 5.23973i −0.585364 0.242466i 0.0702907 0.997527i \(-0.477607\pi\)
−0.655655 + 0.755061i \(0.727607\pi\)
\(468\) 4.36379 + 0.138776i 0.201716 + 0.00641493i
\(469\) −8.83298 21.3247i −0.407869 0.984683i
\(470\) −0.480703 6.79603i −0.0221732 0.313478i
\(471\) 6.94638 15.8193i 0.320072 0.728913i
\(472\) 12.1123 + 0.605558i 0.557515 + 0.0278731i
\(473\) −7.56259 + 28.2240i −0.347728 + 1.29774i
\(474\) 7.64556 1.39485i 0.351172 0.0640674i
\(475\) −22.2909 2.93466i −1.02278 0.134651i
\(476\) 33.5080 + 13.4756i 1.53584 + 0.617654i
\(477\) −11.9840 10.0250i −0.548711 0.459012i
\(478\) −0.248755 1.21767i −0.0113778 0.0556949i
\(479\) −1.08307 + 1.87594i −0.0494869 + 0.0857138i −0.889708 0.456530i \(-0.849092\pi\)
0.840221 + 0.542244i \(0.182425\pi\)
\(480\) −8.85513 25.6836i −0.404180 1.17229i
\(481\) −1.73699 3.00855i −0.0791999 0.137178i
\(482\) 2.49056 2.20703i 0.113442 0.100527i
\(483\) −50.5474 30.6207i −2.29999 1.39329i
\(484\) 3.94641 + 5.03450i 0.179382 + 0.228841i
\(485\) 4.66320 + 11.2580i 0.211745 + 0.511198i
\(486\) 21.9435 2.11772i 0.995375 0.0960619i
\(487\) 26.1827 + 26.1827i 1.18645 + 1.18645i 0.978042 + 0.208409i \(0.0668285\pi\)
0.208409 + 0.978042i \(0.433171\pi\)
\(488\) −16.7626 5.40193i −0.758806 0.244534i
\(489\) −30.5874 + 22.4632i −1.38321 + 1.01582i
\(490\) 23.5605 + 11.4678i 1.06435 + 0.518064i
\(491\) −1.14575 + 1.49317i −0.0517070 + 0.0673859i −0.818491 0.574519i \(-0.805189\pi\)
0.766784 + 0.641905i \(0.221856\pi\)
\(492\) 3.14986 0.380350i 0.142006 0.0171475i
\(493\) 4.73064 3.62995i 0.213057 0.163485i
\(494\) 4.74485 7.18120i 0.213481 0.323097i
\(495\) −22.1691 6.95306i −0.996425 0.312517i
\(496\) 7.88281 + 7.56361i 0.353949 + 0.339616i
\(497\) −17.6257 + 30.5287i −0.790622 + 1.36940i
\(498\) 19.6272 + 4.22948i 0.879517 + 0.189528i
\(499\) 5.84670 0.769733i 0.261734 0.0344580i 0.00148298 0.999999i \(-0.499528\pi\)
0.260251 + 0.965541i \(0.416195\pi\)
\(500\) −6.52464 11.0361i −0.291791 0.493550i
\(501\) −11.7600 + 11.2748i −0.525399 + 0.503722i
\(502\) 0.578756 + 8.18228i 0.0258312 + 0.365193i
\(503\) 26.9218 + 26.9218i 1.20039 + 1.20039i 0.974049 + 0.226337i \(0.0726750\pi\)
0.226337 + 0.974049i \(0.427325\pi\)
\(504\) −30.6098 6.94062i −1.36347 0.309160i
\(505\) −17.1546 + 17.1546i −0.763369 + 0.763369i
\(506\) −27.5185 23.8828i −1.22335 1.06172i
\(507\) −6.02851 + 20.7412i −0.267735 + 0.921149i
\(508\) 9.66532 12.8692i 0.428829 0.570979i
\(509\) −5.77777 43.8865i −0.256095 1.94524i −0.320343 0.947301i \(-0.603798\pi\)
0.0642483 0.997934i \(-0.479535\pi\)
\(510\) 33.1164 1.64240i 1.46642 0.0727269i
\(511\) 1.40916 + 0.813581i 0.0623378 + 0.0359907i
\(512\) −5.44096 21.9635i −0.240459 0.970659i
\(513\) 19.1337 39.0220i 0.844772 1.72286i
\(514\) −0.210401 1.02993i −0.00928040 0.0454281i
\(515\) 17.5719 + 22.9002i 0.774312 + 1.00910i
\(516\) 9.00318 + 35.1027i 0.396343 + 1.54531i
\(517\) −3.85009 2.95428i −0.169327 0.129929i
\(518\) 8.14972 + 23.6070i 0.358078 + 1.03723i
\(519\) −9.44474 + 1.04159i −0.414578 + 0.0457208i
\(520\) −5.68804 + 0.461433i −0.249437 + 0.0202352i
\(521\) 28.0278 28.0278i 1.22792 1.22792i 0.263169 0.964750i \(-0.415232\pi\)
0.964750 0.263169i \(-0.0847678\pi\)
\(522\) −3.55836 + 3.76714i −0.155745 + 0.164883i
\(523\) 24.6960 10.2294i 1.07988 0.447302i 0.229414 0.973329i \(-0.426319\pi\)
0.850468 + 0.526027i \(0.176319\pi\)
\(524\) −14.9282 8.41438i −0.652141 0.367584i
\(525\) 17.2184 + 0.362688i 0.751471 + 0.0158290i
\(526\) 17.1977 + 1.03801i 0.749853 + 0.0452593i
\(527\) −11.5469 + 6.66663i −0.502993 + 0.290403i
\(528\) −17.8754 7.41258i −0.777925 0.322591i
\(529\) −53.7709 31.0447i −2.33787 1.34977i
\(530\) 17.0388 + 11.2581i 0.740119 + 0.489021i
\(531\) 2.21451 12.6711i 0.0961015 0.549877i
\(532\) −43.2987 + 44.2027i −1.87724 + 1.91643i
\(533\) 0.0869908 0.660760i 0.00376799 0.0286207i
\(534\) −0.361118 + 4.42952i −0.0156271 + 0.191684i
\(535\) −32.6093 8.73763i −1.40982 0.377761i
\(536\) −11.8413 13.0877i −0.511468 0.565301i
\(537\) 28.1886 20.7015i 1.21643 0.893336i
\(538\) −5.58107 4.84370i −0.240617 0.208827i
\(539\) 17.2439 7.14266i 0.742747 0.307656i
\(540\) −28.1885 + 5.97715i −1.21304 + 0.257215i
\(541\) −12.0228 + 29.0255i −0.516899 + 1.24791i 0.422899 + 0.906177i \(0.361012\pi\)
−0.939799 + 0.341729i \(0.888988\pi\)
\(542\) 9.59215 28.7445i 0.412018 1.23468i
\(543\) 9.16882 + 1.40412i 0.393472 + 0.0602568i
\(544\) 27.5947 + 1.09395i 1.18311 + 0.0469026i
\(545\) −29.9702 + 17.3033i −1.28378 + 0.741191i
\(546\) −3.00966 + 5.86605i −0.128802 + 0.251044i
\(547\) −26.4382 + 20.2868i −1.13042 + 0.867399i −0.992403 0.123031i \(-0.960738\pi\)
−0.138014 + 0.990430i \(0.544072\pi\)
\(548\) −0.969468 + 2.41064i −0.0414136 + 0.102978i
\(549\) −7.86884 + 16.9416i −0.335834 + 0.723049i
\(550\) 10.4248 + 2.01769i 0.444514 + 0.0860348i
\(551\) 2.64406 + 9.86777i 0.112641 + 0.420381i
\(552\) −44.2720 9.06265i −1.88434 0.385732i
\(553\) −3.03753 + 11.3362i −0.129169 + 0.482065i
\(554\) 10.0599 20.6679i 0.427405 0.878097i
\(555\) 15.8675 + 16.5503i 0.673538 + 0.702523i
\(556\) −10.0203 35.9082i −0.424955 1.52285i
\(557\) −10.4144 + 25.1426i −0.441273 + 1.06533i 0.534230 + 0.845339i \(0.320602\pi\)
−0.975503 + 0.219988i \(0.929398\pi\)
\(558\) 8.98812 7.31293i 0.380498 0.309581i
\(559\) 7.61230 0.321966
\(560\) 40.7761 + 4.51338i 1.72311 + 0.190725i
\(561\) 14.7691 18.4304i 0.623552 0.778133i
\(562\) −0.727536 + 12.0538i −0.0306892 + 0.508457i
\(563\) −5.70321 43.3202i −0.240362 1.82573i −0.507016 0.861937i \(-0.669251\pi\)
0.266654 0.963792i \(-0.414082\pi\)
\(564\) −5.95847 0.849585i −0.250897 0.0357740i
\(565\) −17.3885 2.28924i −0.731541 0.0963092i
\(566\) 2.03814 + 3.01645i 0.0856696 + 0.126791i
\(567\) −11.2915 + 31.3173i −0.474198 + 1.31520i
\(568\) −4.84839 + 26.5155i −0.203434 + 1.11257i
\(569\) −15.9119 + 4.26359i −0.667062 + 0.178739i −0.576431 0.817146i \(-0.695555\pi\)
−0.0906312 + 0.995885i \(0.528888\pi\)
\(570\) −19.1126 + 53.4948i −0.800537 + 2.24065i
\(571\) 19.0658 24.8470i 0.797878 1.03981i −0.200315 0.979731i \(-0.564197\pi\)
0.998193 0.0600834i \(-0.0191367\pi\)
\(572\) −2.44112 + 3.25031i −0.102068 + 0.135902i
\(573\) −18.6023 33.8468i −0.777121 1.41397i
\(574\) −1.51661 + 4.54477i −0.0633019 + 0.189695i
\(575\) 24.7962 1.03407
\(576\) −23.8281 + 2.86762i −0.992836 + 0.119484i
\(577\) −0.592955 −0.0246850 −0.0123425 0.999924i \(-0.503929\pi\)
−0.0123425 + 0.999924i \(0.503929\pi\)
\(578\) −3.05894 + 9.16664i −0.127235 + 0.381282i
\(579\) −8.22914 0.173339i −0.341991 0.00720372i
\(580\) 4.06761 5.41596i 0.168898 0.224885i
\(581\) −18.4573 + 24.0540i −0.765736 + 0.997926i
\(582\) 10.5901 1.93205i 0.438974 0.0800859i
\(583\) 14.0512 3.76500i 0.581940 0.155930i
\(584\) 1.22392 + 0.223796i 0.0506463 + 0.00926074i
\(585\) −0.254884 + 6.04752i −0.0105382 + 0.250034i
\(586\) 6.11534 + 9.05070i 0.252622 + 0.373881i
\(587\) 0.0766157 + 0.0100866i 0.00316227 + 0.000416320i 0.132107 0.991235i \(-0.457826\pi\)
−0.128945 + 0.991652i \(0.541159\pi\)
\(588\) 14.2881 18.2126i 0.589230 0.751074i
\(589\) −2.98165 22.6479i −0.122857 0.933189i
\(590\) −1.01296 + 16.7826i −0.0417029 + 0.690930i
\(591\) −22.2662 3.40987i −0.915907 0.140263i
\(592\) 11.9358 + 14.9069i 0.490557 + 0.612670i
\(593\) −20.9136 −0.858817 −0.429408 0.903110i \(-0.641278\pi\)
−0.429408 + 0.903110i \(0.641278\pi\)
\(594\) −10.1302 + 17.8511i −0.415647 + 0.732441i
\(595\) −19.1611 + 46.2590i −0.785529 + 1.89644i
\(596\) 1.53187 + 5.48952i 0.0627477 + 0.224859i
\(597\) 15.5369 3.81431i 0.635884 0.156109i
\(598\) −4.15443 + 8.53521i −0.169887 + 0.349031i
\(599\) −2.70415 + 10.0920i −0.110489 + 0.412349i −0.998910 0.0466798i \(-0.985136\pi\)
0.888421 + 0.459029i \(0.151803\pi\)
\(600\) 12.4935 4.16358i 0.510044 0.169977i
\(601\) 3.48752 + 13.0156i 0.142259 + 0.530917i 0.999862 + 0.0166053i \(0.00528588\pi\)
−0.857603 + 0.514312i \(0.828047\pi\)
\(602\) −53.7271 10.3988i −2.18975 0.423823i
\(603\) −15.3184 + 10.7606i −0.623812 + 0.438204i
\(604\) 2.05205 5.10256i 0.0834968 0.207620i
\(605\) −7.03584 + 5.39879i −0.286048 + 0.219492i
\(606\) 11.6222 + 18.0070i 0.472119 + 0.731485i
\(607\) 24.6212 14.2151i 0.999344 0.576972i 0.0912899 0.995824i \(-0.470901\pi\)
0.908054 + 0.418853i \(0.137568\pi\)
\(608\) −19.8235 + 42.9607i −0.803951 + 1.74229i
\(609\) −2.84171 7.29114i −0.115152 0.295452i
\(610\) 7.72877 23.1606i 0.312929 0.937744i
\(611\) −0.483822 + 1.16805i −0.0195734 + 0.0472543i
\(612\) 4.74447 28.9047i 0.191784 1.16841i
\(613\) −0.766976 + 0.317692i −0.0309779 + 0.0128315i −0.398119 0.917334i \(-0.630337\pi\)
0.367141 + 0.930165i \(0.380337\pi\)
\(614\) 8.51111 + 7.38661i 0.343480 + 0.298099i
\(615\) 0.482165 + 4.37209i 0.0194428 + 0.176300i
\(616\) 21.6694 19.6058i 0.873083 0.789940i
\(617\) −16.0528 4.30133i −0.646261 0.173165i −0.0792232 0.996857i \(-0.525244\pi\)
−0.567038 + 0.823692i \(0.691911\pi\)
\(618\) 23.0465 10.9134i 0.927068 0.439000i
\(619\) 1.16668 8.86181i 0.0468928 0.356186i −0.951872 0.306496i \(-0.900843\pi\)
0.998765 0.0496901i \(-0.0158234\pi\)
\(620\) −10.5983 + 10.8196i −0.425639 + 0.434525i
\(621\) −15.3041 + 45.4224i −0.614132 + 1.82274i
\(622\) 1.18728 + 0.784475i 0.0476056 + 0.0314546i
\(623\) −5.81206 3.35560i −0.232855 0.134439i
\(624\) −0.660032 + 4.99802i −0.0264224 + 0.200081i
\(625\) 27.0326 15.6073i 1.08131 0.624292i
\(626\) −21.6697 1.30793i −0.866096 0.0522754i
\(627\) 19.4893 + 35.4607i 0.778328 + 1.41617i
\(628\) 17.3793 + 9.79597i 0.693510 + 0.390902i
\(629\) −21.5328 + 8.91919i −0.858571 + 0.355632i
\(630\) 10.0602 42.3348i 0.400807 1.68666i
\(631\) 34.8527 34.8527i 1.38746 1.38746i 0.556855 0.830610i \(-0.312008\pi\)
0.830610 0.556855i \(-0.187992\pi\)
\(632\) 0.725621 + 8.94467i 0.0288637 + 0.355800i
\(633\) 11.2597 25.6421i 0.447532 1.01918i
\(634\) −10.2682 29.7434i −0.407801 1.18126i
\(635\) 17.7021 + 13.5833i 0.702488 + 0.539038i
\(636\) 12.8933 12.6195i 0.511252 0.500397i
\(637\) −2.96012 3.85770i −0.117284 0.152848i
\(638\) −0.965677 4.72704i −0.0382315 0.187145i
\(639\) 27.2800 + 8.55603i 1.07918 + 0.338471i
\(640\) 30.5259 7.22823i 1.20664 0.285721i
\(641\) −13.4004 7.73670i −0.529283 0.305581i 0.211442 0.977391i \(-0.432184\pi\)
−0.740724 + 0.671809i \(0.765517\pi\)
\(642\) −13.6142 + 26.5351i −0.537311 + 1.04726i
\(643\) 3.72779 + 28.3154i 0.147010 + 1.11665i 0.892795 + 0.450463i \(0.148741\pi\)
−0.745785 + 0.666187i \(0.767925\pi\)
\(644\) 40.9812 54.5658i 1.61489 2.15019i
\(645\) −48.7917 + 11.9783i −1.92117 + 0.471647i
\(646\) −43.6115 37.8495i −1.71587 1.48917i
\(647\) 21.2031 21.2031i 0.833579 0.833579i −0.154425 0.988004i \(-0.549353\pi\)
0.988004 + 0.154425i \(0.0493525\pi\)
\(648\) −0.0839444 + 25.4557i −0.00329765 + 0.999995i
\(649\) 8.46838 + 8.46838i 0.332413 + 0.332413i
\(650\) −0.195178 2.75937i −0.00765552 0.108231i
\(651\) 4.17185 + 16.9933i 0.163508 + 0.666021i
\(652\) −22.3012 37.7214i −0.873382 1.47728i
\(653\) −3.52971 + 0.464695i −0.138128 + 0.0181849i −0.199273 0.979944i \(-0.563858\pi\)
0.0611451 + 0.998129i \(0.480525\pi\)
\(654\) 9.36567 + 29.1021i 0.366227 + 1.13798i
\(655\) 11.8786 20.5744i 0.464137 0.803909i
\(656\) 0.0756900 + 3.66278i 0.00295520 + 0.143008i
\(657\) 0.394936 1.25921i 0.0154079 0.0491264i
\(658\) 5.01040 7.58310i 0.195326 0.295620i
\(659\) −14.4317 + 11.0738i −0.562178 + 0.431374i −0.850360 0.526201i \(-0.823616\pi\)
0.288182 + 0.957576i \(0.406949\pi\)
\(660\) 10.5321 24.6744i 0.409960 0.960450i
\(661\) −5.70627 + 7.43656i −0.221948 + 0.289249i −0.891034 0.453937i \(-0.850019\pi\)
0.669086 + 0.743185i \(0.266686\pi\)
\(662\) −29.5577 14.3869i −1.14879 0.559164i
\(663\) −5.63374 2.47382i −0.218796 0.0960754i
\(664\) −7.11111 + 22.0663i −0.275965 + 0.856337i
\(665\) −60.6580 60.6580i −2.35222 2.35222i
\(666\) 17.2457 10.6231i 0.668256 0.411637i
\(667\) −4.31161 10.4092i −0.166946 0.403044i
\(668\) −11.6056 14.8055i −0.449035 0.572842i
\(669\) 20.2152 11.1103i 0.781564 0.429549i
\(670\) 18.3130 16.2282i 0.707493 0.626949i
\(671\) −8.69585 15.0616i −0.335699 0.581448i
\(672\) 11.4860 34.3741i 0.443083 1.32601i
\(673\) 24.2246 41.9583i 0.933792 1.61737i 0.157017 0.987596i \(-0.449812\pi\)
0.776775 0.629778i \(-0.216854\pi\)
\(674\) 5.68710 + 27.8387i 0.219059 + 1.07231i
\(675\) −2.75604 13.6932i −0.106080 0.527053i
\(676\) −23.1399 9.30596i −0.889994 0.357921i
\(677\) −35.6488 4.69325i −1.37009 0.180376i −0.590690 0.806898i \(-0.701144\pi\)
−0.779404 + 0.626522i \(0.784478\pi\)
\(678\) −5.21292 + 14.5906i −0.200201 + 0.560349i
\(679\) −4.20738 + 15.7021i −0.161464 + 0.602593i
\(680\) −1.91175 + 38.2387i −0.0733124 + 1.46639i
\(681\) 31.7920 3.50611i 1.21827 0.134354i
\(682\) 0.761182 + 10.7614i 0.0291472 + 0.412074i
\(683\) −8.02777 19.3808i −0.307174 0.741584i −0.999794 0.0202816i \(-0.993544\pi\)
0.692620 0.721303i \(-0.256456\pi\)
\(684\) 42.6410 + 26.4607i 1.63042 + 1.01175i
\(685\) −3.32798 1.37850i −0.127156 0.0526696i
\(686\) −0.742609 1.48646i −0.0283529 0.0567531i
\(687\) 3.74126 1.45815i 0.142738 0.0556320i
\(688\) −41.3653 + 6.31784i −1.57704 + 0.240865i
\(689\) −1.89487 3.28202i −0.0721889 0.125035i
\(690\) 13.1976 61.2444i 0.502424 2.33154i
\(691\) 13.2416 + 17.2569i 0.503736 + 0.656482i 0.974134 0.225973i \(-0.0725561\pi\)
−0.470398 + 0.882455i \(0.655889\pi\)
\(692\) −0.113348 10.9714i −0.00430883 0.417069i
\(693\) −17.8164 25.3628i −0.676788 0.963451i
\(694\) −20.0015 + 13.5146i −0.759248 + 0.513006i
\(695\) 49.9230 13.3768i 1.89369 0.507412i
\(696\) −3.92022 4.52065i −0.148595 0.171355i
\(697\) −4.31895 1.15726i −0.163592 0.0438343i
\(698\) −37.5640 + 12.9680i −1.42182 + 0.490847i
\(699\) 8.22327 + 33.4961i 0.311033 + 1.26694i
\(700\) −2.39188 + 19.7421i −0.0904047 + 0.746181i
\(701\) −13.2863 5.50335i −0.501815 0.207858i 0.117393 0.993086i \(-0.462546\pi\)
−0.619208 + 0.785227i \(0.712546\pi\)
\(702\) 5.17517 + 1.34554i 0.195324 + 0.0507841i
\(703\) 39.9308i 1.50602i
\(704\) 10.5675 19.6883i 0.398277 0.742029i
\(705\) 1.26312 8.24804i 0.0475717 0.310639i
\(706\) −16.7641 + 14.8556i −0.630925 + 0.559098i
\(707\) −32.0874 + 4.22439i −1.20677 + 0.158874i
\(708\) 14.3049 + 3.99797i 0.537610 + 0.150253i
\(709\) 1.69722 12.8917i 0.0637406 0.484158i −0.929567 0.368654i \(-0.879819\pi\)
0.993307 0.115503i \(-0.0368481\pi\)
\(710\) −36.6890 7.10108i −1.37691 0.266499i
\(711\) 9.50998 + 0.400815i 0.356652 + 0.0150317i
\(712\) −5.04804 0.923040i −0.189183 0.0345924i
\(713\) 6.52048 + 24.3348i 0.244194 + 0.911344i
\(714\) 36.3832 + 25.1561i 1.36161 + 0.941442i
\(715\) −4.47094 3.43067i −0.167204 0.128300i
\(716\) 20.5522 + 34.7631i 0.768072 + 1.29916i
\(717\) 0.0320553 1.52180i 0.00119713 0.0568326i
\(718\) −7.57589 15.1644i −0.282730 0.565931i
\(719\) 7.95286i 0.296592i 0.988943 + 0.148296i \(0.0473788\pi\)
−0.988943 + 0.148296i \(0.952621\pi\)
\(720\) −3.63411 33.0739i −0.135435 1.23259i
\(721\) 38.5073i 1.43409i
\(722\) 64.4657 32.2060i 2.39916 1.19858i
\(723\) 3.57174 1.96304i 0.132834 0.0730061i
\(724\) −2.66510 + 10.3738i −0.0990477 + 0.385539i
\(725\) 2.60481 + 1.99874i 0.0967402 + 0.0742314i
\(726\) 3.35302 + 7.08080i 0.124442 + 0.262793i
\(727\) 0.524112 + 1.95601i 0.0194382 + 0.0725445i 0.974964 0.222364i \(-0.0713774\pi\)
−0.955525 + 0.294909i \(0.904711\pi\)
\(728\) −6.39478 4.13098i −0.237006 0.153104i
\(729\) 26.7847 + 3.40280i 0.992026 + 0.126030i
\(730\) −0.327777 + 1.69352i −0.0121316 + 0.0626799i
\(731\) 6.66611 50.6341i 0.246555 1.87277i
\(732\) −18.5630 10.9846i −0.686109 0.406003i
\(733\) 29.1017 3.83131i 1.07490 0.141513i 0.427764 0.903891i \(-0.359302\pi\)
0.647132 + 0.762378i \(0.275968\pi\)
\(734\) −19.6459 22.1698i −0.725145 0.818303i
\(735\) 25.0434 + 20.0684i 0.923740 + 0.740233i
\(736\) 15.4914 49.8284i 0.571021 1.83670i
\(737\) 17.4292i 0.642013i
\(738\) 3.86544 + 0.397235i 0.142289 + 0.0146224i
\(739\) −21.4139 8.86992i −0.787722 0.326285i −0.0476950 0.998862i \(-0.515188\pi\)
−0.740027 + 0.672577i \(0.765188\pi\)
\(740\) −20.8364 + 16.3330i −0.765960 + 0.600415i
\(741\) 7.60934 7.29539i 0.279536 0.268003i
\(742\) 8.89049 + 25.7527i 0.326380 + 0.945413i
\(743\) −37.5511 10.0618i −1.37762 0.369132i −0.507363 0.861733i \(-0.669380\pi\)
−0.870255 + 0.492601i \(0.836046\pi\)
\(744\) 7.37143 + 11.1661i 0.270250 + 0.409370i
\(745\) −7.63205 + 2.04500i −0.279617 + 0.0749231i
\(746\) 8.00773 + 11.8514i 0.293184 + 0.433912i
\(747\) 22.3019 + 10.3585i 0.815984 + 0.378999i
\(748\) 19.4822 + 19.0837i 0.712338 + 0.697770i
\(749\) −27.4167 35.7301i −1.00178 1.30555i
\(750\) −4.81024 14.9470i −0.175645 0.545786i
\(751\) 25.4455 + 44.0729i 0.928520 + 1.60824i 0.785800 + 0.618481i \(0.212251\pi\)
0.142720 + 0.989763i \(0.454415\pi\)
\(752\) 1.65967 6.74875i 0.0605220 0.246102i
\(753\) −1.52077 + 9.93048i −0.0554198 + 0.361887i
\(754\) −1.12442 + 0.561739i −0.0409488 + 0.0204573i
\(755\) 7.04428 + 2.91784i 0.256368 + 0.106191i
\(756\) −34.6879 16.5663i −1.26159 0.602509i
\(757\) 9.28367 + 22.4128i 0.337421 + 0.814606i 0.997962 + 0.0638157i \(0.0203270\pi\)
−0.660541 + 0.750790i \(0.729673\pi\)
\(758\) 18.4256 1.30329i 0.669247 0.0473377i
\(759\) −26.4150 35.9685i −0.958804 1.30557i
\(760\) −59.2724 28.0966i −2.15004 1.01917i
\(761\) 10.7086 39.9651i 0.388187 1.44873i −0.444894 0.895583i \(-0.646759\pi\)
0.833081 0.553151i \(-0.186575\pi\)
\(762\) 15.0248 12.7596i 0.544290 0.462233i
\(763\) −45.7718 6.02597i −1.65705 0.218155i
\(764\) 41.0235 17.4912i 1.48418 0.632808i
\(765\) 40.0026 + 6.99122i 1.44630 + 0.252768i
\(766\) −13.9614 + 2.85213i −0.504444 + 0.103052i
\(767\) 1.56001 2.70201i 0.0563286 0.0975641i
\(768\) −0.561491 27.7071i −0.0202610 0.999795i
\(769\) 15.0816 + 26.1221i 0.543857 + 0.941988i 0.998678 + 0.0514048i \(0.0163699\pi\)
−0.454821 + 0.890583i \(0.650297\pi\)
\(770\) 26.8691 + 30.3210i 0.968296 + 1.09269i
\(771\) 0.0271129 1.28716i 0.000976447 0.0463561i
\(772\) 1.14315 9.43530i 0.0411428 0.339584i
\(773\) 6.62853 + 16.0027i 0.238412 + 0.575576i 0.997119 0.0758553i \(-0.0241687\pi\)
−0.758707 + 0.651432i \(0.774169\pi\)
\(774\) 1.26446 + 44.3653i 0.0454501 + 1.59468i
\(775\) −5.19132 5.19132i −0.186478 0.186478i
\(776\) 1.00508 + 12.3895i 0.0360803 + 0.444759i
\(777\) 3.35288 + 30.4026i 0.120284 + 1.09069i
\(778\) −20.4425 + 41.9987i −0.732898 + 1.50573i
\(779\) 4.66341 6.07747i 0.167084 0.217748i
\(780\) −6.91930 0.986584i −0.247751 0.0353254i
\(781\) −21.1180 + 16.2044i −0.755663 + 0.579841i
\(782\) 53.1350 + 35.1080i 1.90010 + 1.25546i
\(783\) −5.26904 + 3.53796i −0.188300 + 0.126436i
\(784\) 19.2870 + 18.5060i 0.688822 + 0.660930i
\(785\) −13.8290 + 23.9526i −0.493580 + 0.854905i
\(786\) −15.5574 14.0871i −0.554913 0.502472i
\(787\) −25.6340 + 3.37478i −0.913752 + 0.120298i −0.572717 0.819753i \(-0.694111\pi\)
−0.341035 + 0.940051i \(0.610777\pi\)
\(788\) 6.47210 25.1924i 0.230559 0.897442i
\(789\) 20.2625 + 5.88938i 0.721365 + 0.209668i
\(790\) −12.4104 + 0.877821i −0.441541 + 0.0312315i
\(791\) −16.5444 16.5444i −0.588250 0.588250i
\(792\) −19.3487 13.6872i −0.687525 0.486355i
\(793\) −3.20382 + 3.20382i −0.113771 + 0.113771i
\(794\) −10.2566 + 11.8180i −0.363994 + 0.419406i
\(795\) 17.3098 + 18.0547i 0.613914 + 0.640334i
\(796\) 2.60032 + 18.2893i 0.0921658 + 0.648247i
\(797\) 2.42935 + 18.4527i 0.0860518 + 0.653629i 0.979058 + 0.203583i \(0.0652588\pi\)
−0.893006 + 0.450045i \(0.851408\pi\)
\(798\) −63.6721 + 41.0956i −2.25397 + 1.45477i
\(799\) 7.34575 + 4.24107i 0.259874 + 0.150038i
\(800\) 3.35075 + 14.8325i 0.118467 + 0.524407i
\(801\) −1.62890 + 5.19358i −0.0575545 + 0.183506i
\(802\) 33.3747 6.81804i 1.17850 0.240753i
\(803\) 0.747977 + 0.974782i 0.0263955 + 0.0343993i
\(804\) −10.6066 18.8350i −0.374065 0.664259i
\(805\) 75.0576 + 57.5937i 2.64543 + 2.02991i
\(806\) 2.65670 0.917160i 0.0935783 0.0323056i
\(807\) −5.35727 7.29482i −0.188585 0.256790i
\(808\) −22.0230 + 11.2881i −0.774768 + 0.397115i
\(809\) −4.19023 + 4.19023i −0.147321 + 0.147321i −0.776920 0.629599i \(-0.783219\pi\)
0.629599 + 0.776920i \(0.283219\pi\)
\(810\) −35.2880 0.480952i −1.23989 0.0168989i
\(811\) 34.8522 14.4363i 1.22383 0.506925i 0.325202 0.945645i \(-0.394568\pi\)
0.898624 + 0.438719i \(0.144568\pi\)
\(812\) 8.70342 2.42871i 0.305430 0.0852311i
\(813\) 19.2293 31.7430i 0.674402 1.11328i
\(814\) −1.13617 + 18.8240i −0.0398227 + 0.659779i
\(815\) 52.6125 30.3759i 1.84294 1.06402i
\(816\) 32.6670 + 8.76707i 1.14357 + 0.306909i
\(817\) 75.7752 + 43.7489i 2.65104 + 1.53058i
\(818\) −4.10784 + 6.21710i −0.143627 + 0.217376i
\(819\) −5.18105 + 6.19352i −0.181041 + 0.216419i
\(820\) −5.07879 + 0.0524700i −0.177359 + 0.00183233i
\(821\) 0.576258 4.37712i 0.0201116 0.152762i −0.978442 0.206519i \(-0.933786\pi\)
0.998554 + 0.0537570i \(0.0171196\pi\)
\(822\) −1.80979 + 2.61749i −0.0631236 + 0.0912956i
\(823\) −11.9390 3.19904i −0.416166 0.111511i 0.0446590 0.999002i \(-0.485780\pi\)
−0.460825 + 0.887491i \(0.652447\pi\)
\(824\) 9.89562 + 27.7321i 0.344730 + 0.966093i
\(825\) 11.9072 + 5.22858i 0.414557 + 0.182036i
\(826\) −14.7015 + 16.9396i −0.511531 + 0.589404i
\(827\) 2.22929 0.923401i 0.0775199 0.0321098i −0.343587 0.939121i \(-0.611642\pi\)
0.421106 + 0.907011i \(0.361642\pi\)
\(828\) −50.4343 22.7947i −1.75271 0.792172i
\(829\) 6.14466 14.8345i 0.213413 0.515225i −0.780530 0.625118i \(-0.785051\pi\)
0.993943 + 0.109893i \(0.0350509\pi\)
\(830\) −30.4886 10.1742i −1.05827 0.353150i
\(831\) 17.6046 21.9688i 0.610695 0.762090i
\(832\) −5.66696 1.33170i −0.196466 0.0461685i
\(833\) −28.2521 + 16.3114i −0.978878 + 0.565156i
\(834\) −2.26166 45.6026i −0.0783148 1.57909i
\(835\) 20.6910 15.8768i 0.716043 0.549439i
\(836\) −42.9797 + 18.3252i −1.48648 + 0.633791i
\(837\) 12.7137 6.30557i 0.439449 0.217952i
\(838\) −7.60145 + 39.2742i −0.262588 + 1.35671i
\(839\) −0.148320 0.553538i −0.00512058 0.0191103i 0.963318 0.268362i \(-0.0864822\pi\)
−0.968439 + 0.249251i \(0.919816\pi\)
\(840\) 47.4882 + 16.4153i 1.63850 + 0.566383i
\(841\) −7.11963 + 26.5708i −0.245505 + 0.916236i
\(842\) −21.8213 10.6213i −0.752010 0.366033i
\(843\) −4.12784 + 14.2019i −0.142170 + 0.489140i
\(844\) 28.1708 + 15.8787i 0.969680 + 0.546567i
\(845\) 13.2322 31.9455i 0.455203 1.09896i
\(846\) −6.88790 2.62575i −0.236811 0.0902751i
\(847\) −11.8310 −0.406517
\(848\) 13.0207 + 16.2619i 0.447132 + 0.558435i
\(849\) 1.61912 + 4.15427i 0.0555681 + 0.142574i
\(850\) −18.5252 1.11814i −0.635410 0.0383518i
\(851\) 5.74818 + 43.6618i 0.197045 + 1.49671i
\(852\) −12.9601 + 30.3629i −0.444007 + 1.04022i
\(853\) −21.6311 2.84779i −0.740636 0.0975066i −0.249239 0.968442i \(-0.580180\pi\)
−0.491397 + 0.870935i \(0.663514\pi\)
\(854\) 26.9889 18.2358i 0.923543 0.624016i
\(855\) −37.2931 + 58.7341i −1.27540 + 2.00866i
\(856\) −28.9268 18.6865i −0.988699 0.638691i
\(857\) 47.8919 12.8326i 1.63596 0.438353i 0.680323 0.732913i \(-0.261840\pi\)
0.955633 + 0.294559i \(0.0951729\pi\)
\(858\) −3.79473 + 3.22264i −0.129550 + 0.110019i
\(859\) −2.08106 + 2.71209i −0.0710048 + 0.0925352i −0.827505 0.561458i \(-0.810241\pi\)
0.756501 + 0.653993i \(0.226907\pi\)
\(860\) −8.16597 57.4352i −0.278457 1.95852i
\(861\) −3.04033 + 5.01886i −0.103614 + 0.171042i
\(862\) 12.9567 + 4.32371i 0.441308 + 0.147266i
\(863\) −19.5736 −0.666294 −0.333147 0.942875i \(-0.608111\pi\)
−0.333147 + 0.942875i \(0.608111\pi\)
\(864\) −29.2387 3.01653i −0.994720 0.102625i
\(865\) 15.2112 0.517197
\(866\) −41.9711 14.0059i −1.42624 0.475940i
\(867\) −6.13224 + 10.1229i −0.208262 + 0.343790i
\(868\) −20.0037 + 2.84407i −0.678970 + 0.0965340i
\(869\) −5.39487 + 7.03073i −0.183008 + 0.238501i
\(870\) 6.32312 5.36984i 0.214374 0.182055i
\(871\) −4.38594 + 1.17521i −0.148612 + 0.0398204i
\(872\) −34.5124 + 7.42267i −1.16874 + 0.251363i
\(873\) 13.1726 + 0.555182i 0.445824 + 0.0187901i
\(874\) −90.4075 + 61.0862i −3.05808 + 2.06627i
\(875\) 23.5086 + 3.09496i 0.794734 + 0.104629i
\(876\) 1.40151 + 0.598223i 0.0473527 + 0.0202121i
\(877\) −6.15843 46.7779i −0.207956 1.57958i −0.703307 0.710886i \(-0.748294\pi\)
0.495351 0.868693i \(-0.335039\pi\)
\(878\) 11.2223 + 0.677350i 0.378734 + 0.0228595i
\(879\) 4.85809 + 12.4647i 0.163859 + 0.420423i
\(880\) 27.1424 + 14.9317i 0.914972 + 0.503346i
\(881\) 33.0517 1.11354 0.556771 0.830666i \(-0.312040\pi\)
0.556771 + 0.830666i \(0.312040\pi\)
\(882\) 21.9914 17.8927i 0.740489 0.602478i
\(883\) 17.8685 43.1383i 0.601322 1.45172i −0.270899 0.962608i \(-0.587321\pi\)
0.872221 0.489112i \(-0.162679\pi\)
\(884\) 3.48866 6.18932i 0.117336 0.208169i
\(885\) −5.74726 + 19.7736i −0.193192 + 0.664681i
\(886\) −11.6042 5.64825i −0.389852 0.189757i
\(887\) −1.05516 + 3.93790i −0.0354287 + 0.132222i −0.981375 0.192101i \(-0.938470\pi\)
0.945946 + 0.324323i \(0.105136\pi\)
\(888\) 10.2275 + 21.0337i 0.343214 + 0.705844i
\(889\) 7.70417 + 28.7524i 0.258390 + 0.964323i
\(890\) 1.35191 6.98487i 0.0453161 0.234133i
\(891\) −16.9270 + 18.5850i −0.567075 + 0.622622i
\(892\) 10.4467 + 24.5015i 0.349781 + 0.820371i
\(893\) −11.5291 + 8.84656i −0.385805 + 0.296039i
\(894\) 0.345754 + 6.97156i 0.0115637 + 0.233164i
\(895\) −48.4864 + 27.9936i −1.62072 + 0.935723i
\(896\) 38.1778 + 17.1404i 1.27543 + 0.572621i
\(897\) −7.27013 + 9.07243i −0.242743 + 0.302920i
\(898\) 19.5824 + 6.53474i 0.653475 + 0.218067i
\(899\) −1.27658 + 3.08194i −0.0425763 + 0.102788i
\(900\) 16.0495 1.59587i 0.534984 0.0531958i
\(901\) −23.4901 + 9.72990i −0.782568 + 0.324150i
\(902\) −2.37132 + 2.73232i −0.0789564 + 0.0909763i
\(903\) −61.3675 26.9470i −2.04218 0.896740i
\(904\) −16.1664 7.66330i −0.537688 0.254878i
\(905\) −14.3430 3.84320i −0.476778 0.127752i
\(906\) 3.83074 5.54040i 0.127268 0.184067i
\(907\) 6.43312 48.8644i 0.213608 1.62252i −0.463129 0.886291i \(-0.653273\pi\)
0.676737 0.736225i \(-0.263393\pi\)
\(908\) 0.381541 + 36.9309i 0.0126619 + 1.22559i
\(909\) 9.01483 + 24.6521i 0.299003 + 0.817657i
\(910\) 5.81835 8.80591i 0.192876 0.291913i
\(911\) 45.9346 + 26.5203i 1.52188 + 0.878658i 0.999666 + 0.0258429i \(0.00822696\pi\)
0.522214 + 0.852815i \(0.325106\pi\)
\(912\) −35.2944 + 45.9586i −1.16872 + 1.52184i
\(913\) −19.8272 + 11.4472i −0.656183 + 0.378848i
\(914\) −0.280310 + 4.64415i −0.00927182 + 0.153615i
\(915\) 15.4938 25.5766i 0.512209 0.845535i
\(916\) 1.24623 + 4.46594i 0.0411767 + 0.147559i
\(917\) 29.2808 12.1285i 0.966937 0.400518i
\(918\) 13.4819 33.2450i 0.444970 1.09725i
\(919\) 32.9703 32.9703i 1.08759 1.08759i 0.0918145 0.995776i \(-0.470733\pi\)
0.995776 0.0918145i \(-0.0292667\pi\)
\(920\) 68.8552 + 22.1894i 2.27009 + 0.731562i
\(921\) 8.16980 + 11.1246i 0.269204 + 0.366567i
\(922\) 29.6531 10.2370i 0.976573 0.337137i
\(923\) 5.50168 + 4.22159i 0.181090 + 0.138955i
\(924\) 31.1853 17.5614i 1.02592 0.577727i
\(925\) −7.81248 10.1814i −0.256873 0.334763i
\(926\) 49.3440 10.0804i 1.62154 0.331262i
\(927\) 30.4803 6.80567i 1.00110 0.223528i
\(928\) 5.64387 3.98571i 0.185269 0.130837i
\(929\) 15.6074 + 9.01091i 0.512061 + 0.295638i 0.733680 0.679495i \(-0.237801\pi\)
−0.221620 + 0.975133i \(0.571134\pi\)
\(930\) −15.5852 + 10.0591i −0.511058 + 0.329850i
\(931\) −7.29525 55.4129i −0.239092 1.81609i
\(932\) −39.4299 + 5.60603i −1.29157 + 0.183632i
\(933\) 1.20616 + 1.25807i 0.0394879 + 0.0411872i
\(934\) 12.6919 14.6240i 0.415291 0.478512i
\(935\) −26.7348 + 26.7348i −0.874320 + 0.874320i
\(936\) −2.13966 + 5.79186i −0.0699371 + 0.189313i
\(937\) −32.2924 32.2924i −1.05495 1.05495i −0.998400 0.0565472i \(-0.981991\pi\)
−0.0565472 0.998400i \(-0.518009\pi\)
\(938\) 32.5611 2.30314i 1.06316 0.0752001i
\(939\) −25.5316 7.42085i −0.833191 0.242170i
\(940\) 9.33201 + 2.39746i 0.304377 + 0.0781964i
\(941\) 34.5452 4.54797i 1.12614 0.148260i 0.455638 0.890165i \(-0.349411\pi\)
0.670504 + 0.741906i \(0.266078\pi\)
\(942\) 18.1118 + 16.4002i 0.590114 + 0.534346i
\(943\) −4.22426 + 7.31664i −0.137561 + 0.238263i
\(944\) −6.23457 + 15.9775i −0.202918 + 0.520024i
\(945\) 23.4626 47.8506i 0.763238 1.55658i
\(946\) −34.4768 22.7799i −1.12094 0.740639i
\(947\) 28.4670 21.8435i 0.925055 0.709819i −0.0320730 0.999486i \(-0.510211\pi\)
0.957128 + 0.289666i \(0.0935442\pi\)
\(948\) −1.55144 + 10.8809i −0.0503885 + 0.353394i
\(949\) 0.194863 0.253951i 0.00632553 0.00824359i
\(950\) 13.9156 28.5894i 0.451482 0.927562i
\(951\) −4.22443 38.3055i −0.136986 1.24214i
\(952\) −33.0776 + 38.9182i −1.07205 + 1.26134i
\(953\) 32.3689 + 32.3689i 1.04853 + 1.04853i 0.998761 + 0.0497700i \(0.0158488\pi\)
0.0497700 + 0.998761i \(0.484151\pi\)
\(954\) 18.8132 11.5887i 0.609100 0.375198i
\(955\) 23.6604 + 57.1213i 0.765633 + 1.84840i
\(956\) 1.74485 + 0.211400i 0.0564326 + 0.00683717i
\(957\) 0.124440 5.90768i 0.00402257 0.190968i
\(958\) −2.03171 2.29272i −0.0656415 0.0740744i
\(959\) −2.40274 4.16167i −0.0775885 0.134387i
\(960\) 38.4184 0.381568i 1.23995 0.0123151i
\(961\) −11.7704 + 20.3869i −0.379691 + 0.657643i
\(962\) 4.81353 0.983345i 0.155194 0.0317043i
\(963\) −23.4365 + 28.0164i −0.755231 + 0.902817i
\(964\) 1.84578 + 4.32907i 0.0594487 + 0.139430i
\(965\) 13.0638 + 1.71988i 0.420537 + 0.0553648i
\(966\) 63.7055 54.1013i 2.04969 1.74068i
\(967\) −14.5763 + 54.3995i −0.468743 + 1.74937i 0.175430 + 0.984492i \(0.443868\pi\)
−0.644173 + 0.764880i \(0.722798\pi\)
\(968\) −8.52039 + 3.04032i −0.273856 + 0.0977197i
\(969\) −41.8626 57.0030i −1.34482 1.83120i
\(970\) −17.1900 + 1.21590i −0.551938 + 0.0390401i
\(971\) −13.9389 33.6514i −0.447319 1.07992i −0.973322 0.229442i \(-0.926310\pi\)
0.526003 0.850483i \(-0.323690\pi\)
\(972\) −6.98231 + 30.3850i −0.223958 + 0.974599i
\(973\) 63.7005 + 26.3856i 2.04215 + 0.845884i
\(974\) −46.8448 + 23.4029i −1.50100 + 0.749877i
\(975\) 0.512859 3.34893i 0.0164246 0.107252i
\(976\) 14.7506 20.0686i 0.472155 0.642381i
\(977\) 9.46064 + 16.3863i 0.302673 + 0.524244i 0.976740 0.214425i \(-0.0687878\pi\)
−0.674068 + 0.738669i \(0.735454\pi\)
\(978\) −16.4414 51.0887i −0.525738 1.63364i
\(979\) −3.08501 4.02047i −0.0985974 0.128495i
\(980\) −25.9311 + 26.4725i −0.828339 + 0.845633i
\(981\) 3.31974 + 37.2955i 0.105991 + 1.19075i
\(982\) −1.49017 2.20545i −0.0475532 0.0703787i
\(983\) −54.1368 + 14.5059i −1.72670 + 0.462667i −0.979418 0.201844i \(-0.935306\pi\)
−0.747278 + 0.664511i \(0.768640\pi\)
\(984\) −0.899831 + 4.39577i −0.0286856 + 0.140132i
\(985\) 34.8315 + 9.33307i 1.10982 + 0.297376i
\(986\) 2.75182 + 7.97110i 0.0876360 + 0.253852i
\(987\) 8.03521 7.70368i 0.255763 0.245211i
\(988\) 7.50943 + 9.57992i 0.238907 + 0.304778i
\(989\) −89.1532 36.9285i −2.83491 1.17426i
\(990\) 19.2517 26.6270i 0.611859 0.846262i
\(991\) 32.1444i 1.02110i 0.859848 + 0.510550i \(0.170558\pi\)
−0.859848 + 0.510550i \(0.829442\pi\)
\(992\) −13.6754 + 7.18879i −0.434193 + 0.228244i
\(993\) −31.4181 25.1767i −0.997024 0.798959i
\(994\) −33.0636 37.3112i −1.04871 1.18344i
\(995\) −25.3917 + 3.34287i −0.804969 + 0.105976i
\(996\) −14.4601 + 24.4364i −0.458187 + 0.774296i
\(997\) 6.90125 52.4202i 0.218565 1.66016i −0.432868 0.901457i \(-0.642498\pi\)
0.651433 0.758706i \(-0.274168\pi\)
\(998\) −1.58475 + 8.18788i −0.0501643 + 0.259183i
\(999\) 23.4725 8.02723i 0.742637 0.253970i
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 288.2.bf.a.83.18 yes 368
3.2 odd 2 864.2.bn.a.467.29 368
9.4 even 3 864.2.bn.a.179.14 368
9.5 odd 6 inner 288.2.bf.a.275.33 yes 368
32.27 odd 8 inner 288.2.bf.a.155.33 yes 368
96.59 even 8 864.2.bn.a.251.14 368
288.59 even 24 inner 288.2.bf.a.59.18 368
288.283 odd 24 864.2.bn.a.827.29 368
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
288.2.bf.a.59.18 368 288.59 even 24 inner
288.2.bf.a.83.18 yes 368 1.1 even 1 trivial
288.2.bf.a.155.33 yes 368 32.27 odd 8 inner
288.2.bf.a.275.33 yes 368 9.5 odd 6 inner
864.2.bn.a.179.14 368 9.4 even 3
864.2.bn.a.251.14 368 96.59 even 8
864.2.bn.a.467.29 368 3.2 odd 2
864.2.bn.a.827.29 368 288.283 odd 24