Properties

Label 165.2.w.a.13.2
Level $165$
Weight $2$
Character 165.13
Analytic conductor $1.318$
Analytic rank $0$
Dimension $96$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [165,2,Mod(7,165)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(165, base_ring=CyclotomicField(20))
 
chi = DirichletCharacter(H, H._module([0, 5, 14]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("165.7");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 165 = 3 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 165.w (of order \(20\), 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: \(1.31753163335\)
Analytic rank: \(0\)
Dimension: \(96\)
Relative dimension: \(12\) over \(\Q(\zeta_{20})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label 13.2
Character \(\chi\) \(=\) 165.13
Dual form 165.2.w.a.127.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.93567 + 0.986271i) q^{2} +(-0.987688 - 0.156434i) q^{3} +(1.59850 - 2.20015i) q^{4} +(1.61795 + 1.54345i) q^{5} +(2.06612 - 0.671323i) q^{6} +(-0.626599 - 3.95619i) q^{7} +(-0.244529 + 1.54390i) q^{8} +(0.951057 + 0.309017i) q^{9} +O(q^{10})\) \(q+(-1.93567 + 0.986271i) q^{2} +(-0.987688 - 0.156434i) q^{3} +(1.59850 - 2.20015i) q^{4} +(1.61795 + 1.54345i) q^{5} +(2.06612 - 0.671323i) q^{6} +(-0.626599 - 3.95619i) q^{7} +(-0.244529 + 1.54390i) q^{8} +(0.951057 + 0.309017i) q^{9} +(-4.65407 - 1.39188i) q^{10} +(2.42559 + 2.26197i) q^{11} +(-1.92300 + 1.92300i) q^{12} +(2.31230 + 4.53814i) q^{13} +(5.11476 + 7.03987i) q^{14} +(-1.35658 - 1.77755i) q^{15} +(0.631388 + 1.94321i) q^{16} +(-0.566297 + 1.11142i) q^{17} +(-2.14570 + 0.339846i) q^{18} +(4.58879 - 3.33395i) q^{19} +(5.98211 - 1.09251i) q^{20} +4.00551i q^{21} +(-6.92604 - 1.98614i) q^{22} +(2.70988 + 2.70988i) q^{23} +(0.483038 - 1.48664i) q^{24} +(0.235502 + 4.99445i) q^{25} +(-8.95168 - 6.50377i) q^{26} +(-0.891007 - 0.453990i) q^{27} +(-9.70582 - 4.94536i) q^{28} +(-3.13702 - 2.27918i) q^{29} +(4.37903 + 2.10280i) q^{30} +(0.236665 - 0.728379i) q^{31} +(-5.34931 - 5.34931i) q^{32} +(-2.04187 - 2.61357i) q^{33} -2.70986i q^{34} +(5.09239 - 7.36803i) q^{35} +(2.20015 - 1.59850i) q^{36} +(8.46850 - 1.34128i) q^{37} +(-5.59418 + 10.9792i) q^{38} +(-1.57391 - 4.84399i) q^{39} +(-2.77857 + 2.12052i) q^{40} +(-2.45935 - 3.38501i) q^{41} +(-3.95051 - 7.75332i) q^{42} +(5.05226 - 5.05226i) q^{43} +(8.85398 - 1.72088i) q^{44} +(1.06181 + 1.96788i) q^{45} +(-7.91810 - 2.57275i) q^{46} +(-0.654608 + 4.13303i) q^{47} +(-0.319629 - 2.01806i) q^{48} +(-8.60143 + 2.79477i) q^{49} +(-5.38173 - 9.43532i) q^{50} +(0.733190 - 1.00915i) q^{51} +(13.6808 + 2.16682i) q^{52} +(2.96933 - 1.51295i) q^{53} +2.17245 q^{54} +(0.433218 + 7.40353i) q^{55} +6.26118 q^{56} +(-5.05384 + 2.57506i) q^{57} +(8.32012 + 1.31778i) q^{58} +(0.431206 - 0.593505i) q^{59} +(-6.07937 + 0.143250i) q^{60} +(-4.43475 + 1.44094i) q^{61} +(0.260275 + 1.64331i) q^{62} +(0.626599 - 3.95619i) q^{63} +(11.7439 + 3.81583i) q^{64} +(-3.26324 + 10.9114i) q^{65} +(6.53007 + 3.04516i) q^{66} +(-9.74376 + 9.74376i) q^{67} +(1.54006 + 3.02254i) q^{68} +(-2.25260 - 3.10044i) q^{69} +(-2.59029 + 19.2845i) q^{70} +(-3.59115 - 11.0524i) q^{71} +(-0.709652 + 1.39277i) q^{72} +(-2.28427 + 0.361793i) q^{73} +(-15.0693 + 10.9485i) q^{74} +(0.548701 - 4.96980i) q^{75} -15.4253i q^{76} +(7.42893 - 11.0134i) q^{77} +(7.82405 + 7.82405i) q^{78} +(-3.35829 + 10.3357i) q^{79} +(-1.97771 + 4.11853i) q^{80} +(0.809017 + 0.587785i) q^{81} +(8.09902 + 4.12666i) q^{82} +(0.0435972 + 0.0222139i) q^{83} +(8.81270 + 6.40280i) q^{84} +(-2.63166 + 0.924166i) q^{85} +(-4.79659 + 14.7624i) q^{86} +(2.74186 + 2.74186i) q^{87} +(-4.08538 + 3.19174i) q^{88} -4.99151i q^{89} +(-3.99617 - 2.76194i) q^{90} +(16.5049 - 11.9915i) q^{91} +(10.2939 - 1.63039i) q^{92} +(-0.347695 + 0.682389i) q^{93} +(-2.80919 - 8.64578i) q^{94} +(12.5702 + 1.68843i) q^{95} +(4.44663 + 6.12026i) q^{96} +(-2.62070 - 5.14342i) q^{97} +(13.8931 - 13.8931i) q^{98} +(1.60788 + 2.90081i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 96 q - 8 q^{5} - 20 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 96 q - 8 q^{5} - 20 q^{7} + 8 q^{11} - 16 q^{12} - 12 q^{15} + 8 q^{16} - 20 q^{17} - 60 q^{20} - 32 q^{22} + 32 q^{23} - 32 q^{25} - 60 q^{28} - 40 q^{30} + 16 q^{31} - 16 q^{33} + 24 q^{36} + 8 q^{37} + 56 q^{38} - 120 q^{41} + 12 q^{42} - 200 q^{46} + 60 q^{47} + 48 q^{48} + 80 q^{50} + 40 q^{51} + 40 q^{52} + 36 q^{53} + 80 q^{55} - 80 q^{56} + 40 q^{57} + 44 q^{58} + 48 q^{60} + 40 q^{61} + 80 q^{62} + 20 q^{63} + 56 q^{66} - 48 q^{67} + 80 q^{68} - 92 q^{70} + 32 q^{71} - 60 q^{73} - 24 q^{77} - 96 q^{78} - 80 q^{80} + 24 q^{81} + 32 q^{82} - 200 q^{83} - 80 q^{85} - 80 q^{86} - 144 q^{88} + 56 q^{91} + 20 q^{92} - 72 q^{93} + 60 q^{95} + 32 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/165\mathbb{Z}\right)^\times\).

\(n\) \(46\) \(56\) \(67\)
\(\chi(n)\) \(e\left(\frac{1}{10}\right)\) \(1\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.93567 + 0.986271i −1.36872 + 0.697399i −0.975078 0.221864i \(-0.928786\pi\)
−0.393645 + 0.919263i \(0.628786\pi\)
\(3\) −0.987688 0.156434i −0.570242 0.0903175i
\(4\) 1.59850 2.20015i 0.799250 1.10007i
\(5\) 1.61795 + 1.54345i 0.723568 + 0.690253i
\(6\) 2.06612 0.671323i 0.843490 0.274067i
\(7\) −0.626599 3.95619i −0.236832 1.49530i −0.763821 0.645428i \(-0.776679\pi\)
0.526989 0.849872i \(-0.323321\pi\)
\(8\) −0.244529 + 1.54390i −0.0864542 + 0.545850i
\(9\) 0.951057 + 0.309017i 0.317019 + 0.103006i
\(10\) −4.65407 1.39188i −1.47175 0.440150i
\(11\) 2.42559 + 2.26197i 0.731342 + 0.682011i
\(12\) −1.92300 + 1.92300i −0.555122 + 0.555122i
\(13\) 2.31230 + 4.53814i 0.641316 + 1.25865i 0.951404 + 0.307946i \(0.0996417\pi\)
−0.310087 + 0.950708i \(0.600358\pi\)
\(14\) 5.11476 + 7.03987i 1.36698 + 1.88148i
\(15\) −1.35658 1.77755i −0.350267 0.458962i
\(16\) 0.631388 + 1.94321i 0.157847 + 0.485803i
\(17\) −0.566297 + 1.11142i −0.137347 + 0.269559i −0.949427 0.313987i \(-0.898335\pi\)
0.812080 + 0.583546i \(0.198335\pi\)
\(18\) −2.14570 + 0.339846i −0.505747 + 0.0801024i
\(19\) 4.58879 3.33395i 1.05274 0.764860i 0.0800083 0.996794i \(-0.474505\pi\)
0.972732 + 0.231934i \(0.0745053\pi\)
\(20\) 5.98211 1.09251i 1.33764 0.244292i
\(21\) 4.00551i 0.874073i
\(22\) −6.92604 1.98614i −1.47664 0.423446i
\(23\) 2.70988 + 2.70988i 0.565049 + 0.565049i 0.930737 0.365688i \(-0.119166\pi\)
−0.365688 + 0.930737i \(0.619166\pi\)
\(24\) 0.483038 1.48664i 0.0985997 0.303459i
\(25\) 0.235502 + 4.99445i 0.0471005 + 0.998890i
\(26\) −8.95168 6.50377i −1.75557 1.27549i
\(27\) −0.891007 0.453990i −0.171474 0.0873705i
\(28\) −9.70582 4.94536i −1.83423 0.934586i
\(29\) −3.13702 2.27918i −0.582531 0.423233i 0.257105 0.966383i \(-0.417231\pi\)
−0.839636 + 0.543150i \(0.817231\pi\)
\(30\) 4.37903 + 2.10280i 0.799498 + 0.383916i
\(31\) 0.236665 0.728379i 0.0425063 0.130821i −0.927551 0.373696i \(-0.878090\pi\)
0.970058 + 0.242875i \(0.0780904\pi\)
\(32\) −5.34931 5.34931i −0.945633 0.945633i
\(33\) −2.04187 2.61357i −0.355445 0.454964i
\(34\) 2.70986i 0.464737i
\(35\) 5.09239 7.36803i 0.860772 1.24542i
\(36\) 2.20015 1.59850i 0.366691 0.266417i
\(37\) 8.46850 1.34128i 1.39221 0.220505i 0.585129 0.810941i \(-0.301044\pi\)
0.807085 + 0.590436i \(0.201044\pi\)
\(38\) −5.59418 + 10.9792i −0.907496 + 1.78106i
\(39\) −1.57391 4.84399i −0.252027 0.775660i
\(40\) −2.77857 + 2.12052i −0.439331 + 0.335284i
\(41\) −2.45935 3.38501i −0.384086 0.528650i 0.572575 0.819852i \(-0.305945\pi\)
−0.956661 + 0.291203i \(0.905945\pi\)
\(42\) −3.95051 7.75332i −0.609577 1.19636i
\(43\) 5.05226 5.05226i 0.770463 0.770463i −0.207725 0.978187i \(-0.566606\pi\)
0.978187 + 0.207725i \(0.0666058\pi\)
\(44\) 8.85398 1.72088i 1.33479 0.259433i
\(45\) 1.06181 + 1.96788i 0.158285 + 0.293355i
\(46\) −7.91810 2.57275i −1.16746 0.379331i
\(47\) −0.654608 + 4.13303i −0.0954843 + 0.602864i 0.892825 + 0.450403i \(0.148720\pi\)
−0.988309 + 0.152461i \(0.951280\pi\)
\(48\) −0.319629 2.01806i −0.0461345 0.291282i
\(49\) −8.60143 + 2.79477i −1.22878 + 0.399253i
\(50\) −5.38173 9.43532i −0.761092 1.33436i
\(51\) 0.733190 1.00915i 0.102667 0.141309i
\(52\) 13.6808 + 2.16682i 1.89718 + 0.300484i
\(53\) 2.96933 1.51295i 0.407869 0.207820i −0.238005 0.971264i \(-0.576493\pi\)
0.645873 + 0.763444i \(0.276493\pi\)
\(54\) 2.17245 0.295633
\(55\) 0.433218 + 7.40353i 0.0584152 + 0.998292i
\(56\) 6.26118 0.836685
\(57\) −5.05384 + 2.57506i −0.669397 + 0.341075i
\(58\) 8.32012 + 1.31778i 1.09248 + 0.173033i
\(59\) 0.431206 0.593505i 0.0561383 0.0772677i −0.780025 0.625749i \(-0.784794\pi\)
0.836163 + 0.548481i \(0.184794\pi\)
\(60\) −6.07937 + 0.143250i −0.784843 + 0.0184935i
\(61\) −4.43475 + 1.44094i −0.567812 + 0.184493i −0.578833 0.815446i \(-0.696492\pi\)
0.0110211 + 0.999939i \(0.496492\pi\)
\(62\) 0.260275 + 1.64331i 0.0330550 + 0.208701i
\(63\) 0.626599 3.95619i 0.0789441 0.498433i
\(64\) 11.7439 + 3.81583i 1.46799 + 0.476978i
\(65\) −3.26324 + 10.9114i −0.404755 + 1.35339i
\(66\) 6.53007 + 3.04516i 0.803796 + 0.374833i
\(67\) −9.74376 + 9.74376i −1.19039 + 1.19039i −0.213431 + 0.976958i \(0.568464\pi\)
−0.976958 + 0.213431i \(0.931536\pi\)
\(68\) 1.54006 + 3.02254i 0.186760 + 0.366537i
\(69\) −2.25260 3.10044i −0.271181 0.373249i
\(70\) −2.59029 + 19.2845i −0.309599 + 2.30494i
\(71\) −3.59115 11.0524i −0.426192 1.31168i −0.901849 0.432052i \(-0.857790\pi\)
0.475657 0.879631i \(-0.342210\pi\)
\(72\) −0.709652 + 1.39277i −0.0836333 + 0.164140i
\(73\) −2.28427 + 0.361793i −0.267354 + 0.0423447i −0.288672 0.957428i \(-0.593214\pi\)
0.0213181 + 0.999773i \(0.493214\pi\)
\(74\) −15.0693 + 10.9485i −1.75177 + 1.27274i
\(75\) 0.548701 4.96980i 0.0633586 0.573863i
\(76\) 15.4253i 1.76941i
\(77\) 7.42893 11.0134i 0.846605 1.25510i
\(78\) 7.82405 + 7.82405i 0.885899 + 0.885899i
\(79\) −3.35829 + 10.3357i −0.377837 + 1.16286i 0.563708 + 0.825974i \(0.309374\pi\)
−0.941545 + 0.336888i \(0.890626\pi\)
\(80\) −1.97771 + 4.11853i −0.221114 + 0.460466i
\(81\) 0.809017 + 0.587785i 0.0898908 + 0.0653095i
\(82\) 8.09902 + 4.12666i 0.894387 + 0.455713i
\(83\) 0.0435972 + 0.0222139i 0.00478542 + 0.00243829i 0.456382 0.889784i \(-0.349145\pi\)
−0.451596 + 0.892222i \(0.649145\pi\)
\(84\) 8.81270 + 6.40280i 0.961544 + 0.698603i
\(85\) −2.63166 + 0.924166i −0.285444 + 0.100240i
\(86\) −4.79659 + 14.7624i −0.517230 + 1.59187i
\(87\) 2.74186 + 2.74186i 0.293958 + 0.293958i
\(88\) −4.08538 + 3.19174i −0.435503 + 0.340241i
\(89\) 4.99151i 0.529099i −0.964372 0.264550i \(-0.914777\pi\)
0.964372 0.264550i \(-0.0852233\pi\)
\(90\) −3.99617 2.76194i −0.421233 0.291134i
\(91\) 16.5049 11.9915i 1.73018 1.25705i
\(92\) 10.2939 1.63039i 1.07321 0.169980i
\(93\) −0.347695 + 0.682389i −0.0360543 + 0.0707605i
\(94\) −2.80919 8.64578i −0.289745 0.891744i
\(95\) 12.5702 + 1.68843i 1.28968 + 0.173229i
\(96\) 4.44663 + 6.12026i 0.453833 + 0.624647i
\(97\) −2.62070 5.14342i −0.266092 0.522235i 0.718840 0.695175i \(-0.244673\pi\)
−0.984932 + 0.172940i \(0.944673\pi\)
\(98\) 13.8931 13.8931i 1.40341 1.40341i
\(99\) 1.60788 + 2.90081i 0.161598 + 0.291543i
\(100\) 11.3650 + 7.46549i 1.13650 + 0.746549i
\(101\) 3.17814 + 1.03264i 0.316237 + 0.102752i 0.462835 0.886445i \(-0.346832\pi\)
−0.146598 + 0.989196i \(0.546832\pi\)
\(102\) −0.423916 + 2.67650i −0.0419739 + 0.265013i
\(103\) −2.56145 16.1724i −0.252388 1.59351i −0.709895 0.704307i \(-0.751258\pi\)
0.457508 0.889206i \(-0.348742\pi\)
\(104\) −7.57185 + 2.46024i −0.742481 + 0.241247i
\(105\) −6.18231 + 6.48069i −0.603332 + 0.632451i
\(106\) −4.25545 + 5.85713i −0.413326 + 0.568894i
\(107\) −11.7537 1.86160i −1.13627 0.179967i −0.440171 0.897914i \(-0.645082\pi\)
−0.696098 + 0.717946i \(0.745082\pi\)
\(108\) −2.42312 + 1.23464i −0.233165 + 0.118803i
\(109\) −7.37791 −0.706676 −0.353338 0.935496i \(-0.614953\pi\)
−0.353338 + 0.935496i \(0.614953\pi\)
\(110\) −8.14046 13.9035i −0.776162 1.32565i
\(111\) −8.57406 −0.813814
\(112\) 7.29209 3.71551i 0.689038 0.351082i
\(113\) −4.64778 0.736136i −0.437227 0.0692499i −0.0660588 0.997816i \(-0.521042\pi\)
−0.371168 + 0.928566i \(0.621042\pi\)
\(114\) 7.24283 9.96890i 0.678353 0.933673i
\(115\) 0.201867 + 8.56702i 0.0188242 + 0.798879i
\(116\) −10.0291 + 3.25864i −0.931175 + 0.302557i
\(117\) 0.796764 + 5.03057i 0.0736609 + 0.465076i
\(118\) −0.249315 + 1.57411i −0.0229513 + 0.144909i
\(119\) 4.75183 + 1.54396i 0.435600 + 0.141535i
\(120\) 3.07608 1.65975i 0.280807 0.151514i
\(121\) 0.766946 + 10.9732i 0.0697224 + 0.997566i
\(122\) 7.16305 7.16305i 0.648512 0.648512i
\(123\) 1.89954 + 3.72806i 0.171276 + 0.336148i
\(124\) −1.22423 1.68501i −0.109939 0.151319i
\(125\) −7.32767 + 8.44424i −0.655407 + 0.755276i
\(126\) 2.68899 + 8.27586i 0.239554 + 0.737272i
\(127\) −1.80811 + 3.54861i −0.160444 + 0.314888i −0.957208 0.289402i \(-0.906543\pi\)
0.796764 + 0.604291i \(0.206543\pi\)
\(128\) −11.5519 + 1.82964i −1.02105 + 0.161719i
\(129\) −5.78041 + 4.19971i −0.508937 + 0.369764i
\(130\) −4.44506 24.3393i −0.389858 2.13469i
\(131\) 6.08791i 0.531903i 0.963986 + 0.265952i \(0.0856862\pi\)
−0.963986 + 0.265952i \(0.914314\pi\)
\(132\) −9.01417 + 0.314628i −0.784583 + 0.0273848i
\(133\) −16.0651 16.0651i −1.39302 1.39302i
\(134\) 9.25067 28.4706i 0.799136 2.45949i
\(135\) −0.740888 2.10976i −0.0637655 0.181579i
\(136\) −1.57744 1.14608i −0.135265 0.0982756i
\(137\) 5.81380 + 2.96228i 0.496707 + 0.253085i 0.684352 0.729152i \(-0.260085\pi\)
−0.187645 + 0.982237i \(0.560085\pi\)
\(138\) 7.41815 + 3.77974i 0.631475 + 0.321752i
\(139\) −8.08385 5.87326i −0.685664 0.498164i 0.189568 0.981868i \(-0.439291\pi\)
−0.875232 + 0.483704i \(0.839291\pi\)
\(140\) −8.07056 22.9818i −0.682087 1.94232i
\(141\) 1.29310 3.97974i 0.108898 0.335155i
\(142\) 17.8520 + 17.8520i 1.49810 + 1.49810i
\(143\) −4.65648 + 16.2380i −0.389394 + 1.35789i
\(144\) 2.04321i 0.170268i
\(145\) −1.55773 8.52944i −0.129362 0.708332i
\(146\) 4.06476 2.95322i 0.336402 0.244411i
\(147\) 8.93273 1.41481i 0.736759 0.116691i
\(148\) 10.5859 20.7760i 0.870155 1.70778i
\(149\) 1.31084 + 4.03436i 0.107389 + 0.330508i 0.990284 0.139062i \(-0.0444089\pi\)
−0.882895 + 0.469570i \(0.844409\pi\)
\(150\) 3.83947 + 10.1610i 0.313491 + 0.829646i
\(151\) 1.16711 + 1.60638i 0.0949777 + 0.130726i 0.853861 0.520501i \(-0.174255\pi\)
−0.758883 + 0.651227i \(0.774255\pi\)
\(152\) 4.02518 + 7.89987i 0.326486 + 0.640764i
\(153\) −0.882028 + 0.882028i −0.0713078 + 0.0713078i
\(154\) −3.51769 + 28.6453i −0.283464 + 2.30830i
\(155\) 1.50713 0.813198i 0.121056 0.0653176i
\(156\) −13.1734 4.28029i −1.05472 0.342698i
\(157\) 0.578509 3.65256i 0.0461701 0.291506i −0.953790 0.300475i \(-0.902855\pi\)
0.999960 + 0.00896859i \(0.00285483\pi\)
\(158\) −3.69332 23.3187i −0.293825 1.85514i
\(159\) −3.16945 + 1.02982i −0.251354 + 0.0816698i
\(160\) −0.398486 16.9113i −0.0315031 1.33696i
\(161\) 9.02280 12.4188i 0.711096 0.978740i
\(162\) −2.14570 0.339846i −0.168582 0.0267008i
\(163\) 3.30833 1.68568i 0.259129 0.132033i −0.319601 0.947552i \(-0.603549\pi\)
0.578729 + 0.815520i \(0.303549\pi\)
\(164\) −11.3788 −0.888534
\(165\) 0.730283 7.38015i 0.0568525 0.574544i
\(166\) −0.106299 −0.00825037
\(167\) −7.21819 + 3.67785i −0.558560 + 0.284601i −0.710393 0.703806i \(-0.751483\pi\)
0.151832 + 0.988406i \(0.451483\pi\)
\(168\) −6.18409 0.979464i −0.477113 0.0755673i
\(169\) −7.60680 + 10.4699i −0.585139 + 0.805374i
\(170\) 4.18254 4.38441i 0.320786 0.336269i
\(171\) 5.39444 1.75276i 0.412523 0.134037i
\(172\) −3.03968 19.1918i −0.231773 1.46336i
\(173\) −3.11076 + 19.6406i −0.236507 + 1.49325i 0.528340 + 0.849033i \(0.322815\pi\)
−0.764847 + 0.644212i \(0.777185\pi\)
\(174\) −8.01154 2.60311i −0.607353 0.197341i
\(175\) 19.6114 4.06121i 1.48249 0.306999i
\(176\) −2.86401 + 6.14161i −0.215883 + 0.462942i
\(177\) −0.518742 + 0.518742i −0.0389910 + 0.0389910i
\(178\) 4.92298 + 9.66189i 0.368993 + 0.724190i
\(179\) −12.5391 17.2586i −0.937215 1.28997i −0.956978 0.290161i \(-0.906291\pi\)
0.0197634 0.999805i \(-0.493709\pi\)
\(180\) 6.02693 + 0.809536i 0.449221 + 0.0603393i
\(181\) −2.65677 8.17671i −0.197477 0.607770i −0.999939 0.0110673i \(-0.996477\pi\)
0.802462 0.596703i \(-0.203523\pi\)
\(182\) −20.1211 + 39.4898i −1.49147 + 2.92718i
\(183\) 4.60557 0.729450i 0.340453 0.0539225i
\(184\) −4.84643 + 3.52113i −0.357283 + 0.259582i
\(185\) 15.7718 + 10.9006i 1.15956 + 0.801430i
\(186\) 1.66380i 0.121996i
\(187\) −3.88761 + 1.41490i −0.284290 + 0.103468i
\(188\) 8.04688 + 8.04688i 0.586879 + 0.586879i
\(189\) −1.23777 + 3.80946i −0.0900345 + 0.277098i
\(190\) −25.9970 + 9.12940i −1.88602 + 0.662316i
\(191\) 0.708879 + 0.515031i 0.0512927 + 0.0372663i 0.613136 0.789977i \(-0.289908\pi\)
−0.561844 + 0.827244i \(0.689908\pi\)
\(192\) −11.0024 5.60600i −0.794030 0.404578i
\(193\) 21.4951 + 10.9523i 1.54725 + 0.788363i 0.998854 0.0478565i \(-0.0152390\pi\)
0.548395 + 0.836219i \(0.315239\pi\)
\(194\) 10.1456 + 7.37122i 0.728413 + 0.529223i
\(195\) 4.92998 10.2666i 0.353043 0.735205i
\(196\) −7.60047 + 23.3918i −0.542891 + 1.67085i
\(197\) 1.54634 + 1.54634i 0.110173 + 0.110173i 0.760044 0.649872i \(-0.225177\pi\)
−0.649872 + 0.760044i \(0.725177\pi\)
\(198\) −5.97331 4.02920i −0.424505 0.286343i
\(199\) 2.84042i 0.201352i −0.994919 0.100676i \(-0.967899\pi\)
0.994919 0.100676i \(-0.0321006\pi\)
\(200\) −7.76851 0.857699i −0.549317 0.0606485i
\(201\) 11.1481 8.09954i 0.786323 0.571297i
\(202\) −7.17028 + 1.13566i −0.504499 + 0.0799048i
\(203\) −7.05122 + 13.8388i −0.494899 + 0.971293i
\(204\) −1.04827 3.22625i −0.0733937 0.225883i
\(205\) 1.24550 9.27266i 0.0869897 0.647631i
\(206\) 20.9085 + 28.7780i 1.45676 + 2.00506i
\(207\) 1.73985 + 3.41465i 0.120928 + 0.237335i
\(208\) −7.35862 + 7.35862i −0.510228 + 0.510228i
\(209\) 18.6718 + 2.29293i 1.29156 + 0.158606i
\(210\) 5.57517 18.6419i 0.384723 1.28641i
\(211\) −18.1842 5.90839i −1.25185 0.406750i −0.393266 0.919425i \(-0.628655\pi\)
−0.858583 + 0.512674i \(0.828655\pi\)
\(212\) 1.41776 8.95141i 0.0973724 0.614785i
\(213\) 1.81796 + 11.4781i 0.124564 + 0.786469i
\(214\) 24.5872 7.98887i 1.68075 0.546108i
\(215\) 15.9722 0.376358i 1.08930 0.0256674i
\(216\) 0.918792 1.26461i 0.0625159 0.0860458i
\(217\) −3.02990 0.479889i −0.205683 0.0325770i
\(218\) 14.2812 7.27662i 0.967243 0.492835i
\(219\) 2.31275 0.156281
\(220\) 16.9814 + 10.8814i 1.14488 + 0.733624i
\(221\) −6.35323 −0.427365
\(222\) 16.5965 8.45635i 1.11389 0.567553i
\(223\) −9.64672 1.52789i −0.645992 0.102315i −0.175163 0.984539i \(-0.556045\pi\)
−0.470829 + 0.882224i \(0.656045\pi\)
\(224\) −17.8110 + 24.5148i −1.19005 + 1.63796i
\(225\) −1.31939 + 4.82278i −0.0879596 + 0.321519i
\(226\) 9.72258 3.15906i 0.646736 0.210137i
\(227\) −3.63355 22.9413i −0.241167 1.52267i −0.749788 0.661679i \(-0.769844\pi\)
0.508621 0.860991i \(-0.330156\pi\)
\(228\) −2.41305 + 15.2354i −0.159808 + 1.00899i
\(229\) −0.687116 0.223257i −0.0454059 0.0147533i 0.286226 0.958162i \(-0.407599\pi\)
−0.331632 + 0.943409i \(0.607599\pi\)
\(230\) −8.84015 16.3838i −0.582902 1.08031i
\(231\) −9.06035 + 9.71570i −0.596127 + 0.639246i
\(232\) 4.28592 4.28592i 0.281384 0.281384i
\(233\) −6.82897 13.4026i −0.447380 0.878034i −0.999033 0.0439598i \(-0.986003\pi\)
0.551653 0.834074i \(-0.313997\pi\)
\(234\) −6.50377 8.95168i −0.425165 0.585189i
\(235\) −7.43826 + 5.67667i −0.485219 + 0.370305i
\(236\) −0.616514 1.89743i −0.0401316 0.123512i
\(237\) 4.93381 9.68315i 0.320485 0.628988i
\(238\) −10.7207 + 1.69800i −0.694922 + 0.110065i
\(239\) 3.25568 2.36539i 0.210593 0.153004i −0.477489 0.878638i \(-0.658453\pi\)
0.688082 + 0.725633i \(0.258453\pi\)
\(240\) 2.59764 3.75844i 0.167677 0.242607i
\(241\) 25.0056i 1.61075i 0.592766 + 0.805375i \(0.298036\pi\)
−0.592766 + 0.805375i \(0.701964\pi\)
\(242\) −12.3071 20.4841i −0.791132 1.31677i
\(243\) −0.707107 0.707107i −0.0453609 0.0453609i
\(244\) −3.91868 + 12.0605i −0.250868 + 0.772091i
\(245\) −18.2303 8.75411i −1.16469 0.559280i
\(246\) −7.35376 5.34282i −0.468858 0.340646i
\(247\) 25.7406 + 13.1155i 1.63783 + 0.834518i
\(248\) 1.06667 + 0.543497i 0.0677337 + 0.0345121i
\(249\) −0.0395854 0.0287605i −0.00250863 0.00182262i
\(250\) 5.85561 23.5723i 0.370342 1.49084i
\(251\) 1.74476 5.36983i 0.110128 0.338941i −0.880771 0.473542i \(-0.842975\pi\)
0.990900 + 0.134601i \(0.0429753\pi\)
\(252\) −7.70258 7.70258i −0.485217 0.485217i
\(253\) 0.443372 + 12.7027i 0.0278745 + 0.798614i
\(254\) 8.65220i 0.542887i
\(255\) 2.74384 0.501105i 0.171826 0.0313804i
\(256\) 0.576106 0.418566i 0.0360066 0.0261604i
\(257\) −7.68343 + 1.21694i −0.479279 + 0.0759104i −0.391400 0.920221i \(-0.628009\pi\)
−0.0878795 + 0.996131i \(0.528009\pi\)
\(258\) 7.04688 13.8303i 0.438720 0.861036i
\(259\) −10.6127 32.6626i −0.659442 2.02955i
\(260\) 18.7904 + 24.6215i 1.16533 + 1.52696i
\(261\) −2.27918 3.13702i −0.141078 0.194177i
\(262\) −6.00433 11.7842i −0.370949 0.728028i
\(263\) 22.4683 22.4683i 1.38546 1.38546i 0.550853 0.834602i \(-0.314303\pi\)
0.834602 0.550853i \(-0.185697\pi\)
\(264\) 4.53439 2.51335i 0.279072 0.154686i
\(265\) 7.13938 + 2.13515i 0.438569 + 0.131161i
\(266\) 46.9411 + 15.2521i 2.87814 + 0.935166i
\(267\) −0.780844 + 4.93006i −0.0477869 + 0.301715i
\(268\) 5.86230 + 37.0131i 0.358097 + 2.26093i
\(269\) 25.7878 8.37895i 1.57231 0.510873i 0.612247 0.790667i \(-0.290266\pi\)
0.960060 + 0.279793i \(0.0902660\pi\)
\(270\) 3.51490 + 3.35307i 0.213910 + 0.204062i
\(271\) −12.8302 + 17.6592i −0.779378 + 1.07272i 0.215972 + 0.976399i \(0.430708\pi\)
−0.995350 + 0.0963220i \(0.969292\pi\)
\(272\) −2.51728 0.398698i −0.152632 0.0241746i
\(273\) −18.1776 + 9.26193i −1.10016 + 0.560557i
\(274\) −14.1752 −0.856355
\(275\) −10.7261 + 12.6472i −0.646807 + 0.762653i
\(276\) −10.4222 −0.627342
\(277\) −3.43369 + 1.74955i −0.206310 + 0.105120i −0.554093 0.832455i \(-0.686935\pi\)
0.347782 + 0.937575i \(0.386935\pi\)
\(278\) 21.4403 + 3.39580i 1.28590 + 0.203667i
\(279\) 0.450163 0.619597i 0.0269506 0.0370943i
\(280\) 10.1303 + 9.66384i 0.605398 + 0.577525i
\(281\) 26.3633 8.56595i 1.57270 0.511002i 0.612538 0.790441i \(-0.290149\pi\)
0.960163 + 0.279439i \(0.0901486\pi\)
\(282\) 1.42210 + 8.97879i 0.0846849 + 0.534679i
\(283\) 3.73361 23.5731i 0.221940 1.40127i −0.585188 0.810898i \(-0.698979\pi\)
0.807128 0.590376i \(-0.201021\pi\)
\(284\) −30.0574 9.76625i −1.78358 0.579520i
\(285\) −12.1513 3.63405i −0.719782 0.215263i
\(286\) −7.00170 36.0239i −0.414019 2.13014i
\(287\) −11.8507 + 11.8507i −0.699526 + 0.699526i
\(288\) −3.43447 6.74052i −0.202378 0.397189i
\(289\) 9.07779 + 12.4945i 0.533987 + 0.734971i
\(290\) 11.4276 + 14.9738i 0.671050 + 0.879292i
\(291\) 1.78383 + 5.49007i 0.104570 + 0.321833i
\(292\) −2.85541 + 5.60406i −0.167100 + 0.327953i
\(293\) −12.8223 + 2.03085i −0.749087 + 0.118644i −0.519294 0.854596i \(-0.673805\pi\)
−0.229793 + 0.973239i \(0.573805\pi\)
\(294\) −15.8954 + 11.5487i −0.927038 + 0.673533i
\(295\) 1.61372 0.294712i 0.0939542 0.0171588i
\(296\) 13.4025i 0.779004i
\(297\) −1.13430 3.11663i −0.0658187 0.180845i
\(298\) −6.51633 6.51633i −0.377481 0.377481i
\(299\) −6.03177 + 18.5639i −0.348826 + 1.07358i
\(300\) −10.0572 9.15145i −0.580652 0.528359i
\(301\) −23.1535 16.8220i −1.33454 0.969602i
\(302\) −3.84346 1.95834i −0.221166 0.112690i
\(303\) −2.97747 1.51710i −0.171051 0.0871549i
\(304\) 9.37588 + 6.81197i 0.537743 + 0.390693i
\(305\) −9.39922 4.51348i −0.538198 0.258441i
\(306\) 0.837393 2.57723i 0.0478706 0.147330i
\(307\) 0.378913 + 0.378913i 0.0216257 + 0.0216257i 0.717837 0.696211i \(-0.245132\pi\)
−0.696211 + 0.717837i \(0.745132\pi\)
\(308\) −12.3560 33.9497i −0.704050 1.93446i
\(309\) 16.3740i 0.931483i
\(310\) −2.11527 + 3.06052i −0.120139 + 0.173826i
\(311\) −16.4773 + 11.9714i −0.934340 + 0.678838i −0.947052 0.321082i \(-0.895954\pi\)
0.0127116 + 0.999919i \(0.495954\pi\)
\(312\) 7.86350 1.24546i 0.445183 0.0705101i
\(313\) −2.33232 + 4.57744i −0.131831 + 0.258732i −0.947480 0.319814i \(-0.896380\pi\)
0.815650 + 0.578546i \(0.196380\pi\)
\(314\) 2.48262 + 7.64071i 0.140102 + 0.431190i
\(315\) 7.12000 5.43378i 0.401167 0.306159i
\(316\) 17.3719 + 23.9104i 0.977248 + 1.34507i
\(317\) 12.1823 + 23.9090i 0.684224 + 1.34287i 0.927835 + 0.372992i \(0.121668\pi\)
−0.243610 + 0.969873i \(0.578332\pi\)
\(318\) 5.11932 5.11932i 0.287077 0.287077i
\(319\) −2.45367 12.6242i −0.137379 0.706820i
\(320\) 13.1115 + 24.3000i 0.732953 + 1.35841i
\(321\) 11.3177 + 3.67736i 0.631695 + 0.205250i
\(322\) −5.21680 + 32.9376i −0.290721 + 1.83554i
\(323\) 1.10680 + 6.98808i 0.0615842 + 0.388827i
\(324\) 2.58643 0.840381i 0.143690 0.0466878i
\(325\) −22.1210 + 12.6174i −1.22705 + 0.699888i
\(326\) −4.74129 + 6.52582i −0.262596 + 0.361432i
\(327\) 7.28708 + 1.15416i 0.402976 + 0.0638252i
\(328\) 5.82749 2.96926i 0.321769 0.163950i
\(329\) 16.7612 0.924077
\(330\) 5.86525 + 15.0058i 0.322871 + 0.826040i
\(331\) 33.1897 1.82427 0.912135 0.409890i \(-0.134433\pi\)
0.912135 + 0.409890i \(0.134433\pi\)
\(332\) 0.118564 0.0604114i 0.00650704 0.00331550i
\(333\) 8.46850 + 1.34128i 0.464071 + 0.0735016i
\(334\) 10.3446 14.2382i 0.566034 0.779079i
\(335\) −30.8039 + 0.725842i −1.68300 + 0.0396570i
\(336\) −7.78355 + 2.52903i −0.424627 + 0.137970i
\(337\) −4.61561 29.1418i −0.251428 1.58745i −0.713528 0.700626i \(-0.752904\pi\)
0.462100 0.886828i \(-0.347096\pi\)
\(338\) 4.39810 27.7685i 0.239225 1.51041i
\(339\) 4.47540 + 1.45415i 0.243071 + 0.0789784i
\(340\) −2.17342 + 7.26733i −0.117870 + 0.394126i
\(341\) 2.22163 1.23142i 0.120308 0.0666850i
\(342\) −8.71314 + 8.71314i −0.471153 + 0.471153i
\(343\) 3.71707 + 7.29516i 0.200703 + 0.393902i
\(344\) 6.56475 + 9.03561i 0.353948 + 0.487167i
\(345\) 1.14080 8.49312i 0.0614183 0.457254i
\(346\) −13.3495 41.0856i −0.717675 2.20878i
\(347\) −5.64195 + 11.0730i −0.302876 + 0.594428i −0.991412 0.130774i \(-0.958254\pi\)
0.688536 + 0.725202i \(0.258254\pi\)
\(348\) 10.4154 1.64963i 0.558321 0.0884294i
\(349\) −9.84617 + 7.15366i −0.527053 + 0.382927i −0.819254 0.573430i \(-0.805612\pi\)
0.292201 + 0.956357i \(0.405612\pi\)
\(350\) −33.9557 + 27.2033i −1.81501 + 1.45408i
\(351\) 5.09328i 0.271859i
\(352\) −0.875216 25.0752i −0.0466492 1.33651i
\(353\) −21.2693 21.2693i −1.13205 1.13205i −0.989836 0.142216i \(-0.954577\pi\)
−0.142216 0.989836i \(-0.545423\pi\)
\(354\) 0.492491 1.51573i 0.0261756 0.0805602i
\(355\) 11.2486 23.4250i 0.597015 1.24327i
\(356\) −10.9821 7.97893i −0.582048 0.422882i
\(357\) −4.45180 2.26831i −0.235614 0.120051i
\(358\) 41.2931 + 21.0399i 2.18241 + 1.11199i
\(359\) 17.1501 + 12.4603i 0.905149 + 0.657629i 0.939783 0.341771i \(-0.111027\pi\)
−0.0346345 + 0.999400i \(0.511027\pi\)
\(360\) −3.29786 + 1.15811i −0.173812 + 0.0610379i
\(361\) 4.07043 12.5275i 0.214233 0.659341i
\(362\) 13.2071 + 13.2071i 0.694149 + 0.694149i
\(363\) 0.959088 10.9581i 0.0503391 0.575152i
\(364\) 55.4815i 2.90802i
\(365\) −4.25424 2.94031i −0.222677 0.153903i
\(366\) −8.19540 + 5.95431i −0.428381 + 0.311237i
\(367\) 13.6498 2.16192i 0.712514 0.112851i 0.210353 0.977625i \(-0.432539\pi\)
0.502161 + 0.864774i \(0.332539\pi\)
\(368\) −3.55489 + 6.97686i −0.185311 + 0.363694i
\(369\) −1.29296 3.97932i −0.0673087 0.207155i
\(370\) −41.2799 5.54471i −2.14604 0.288256i
\(371\) −7.84610 10.7992i −0.407349 0.560668i
\(372\) 0.945567 + 1.85578i 0.0490253 + 0.0962176i
\(373\) −12.0946 + 12.0946i −0.626236 + 0.626236i −0.947119 0.320883i \(-0.896020\pi\)
0.320883 + 0.947119i \(0.396020\pi\)
\(374\) 6.12964 6.57300i 0.316956 0.339882i
\(375\) 8.55843 7.19398i 0.441955 0.371495i
\(376\) −6.22091 2.02129i −0.320819 0.104240i
\(377\) 3.08951 19.5064i 0.159118 1.00463i
\(378\) −1.36125 8.59462i −0.0700154 0.442060i
\(379\) 0.349194 0.113460i 0.0179369 0.00582804i −0.300035 0.953928i \(-0.596998\pi\)
0.317972 + 0.948100i \(0.396998\pi\)
\(380\) 23.8083 24.9573i 1.22134 1.28028i
\(381\) 2.34097 3.22207i 0.119932 0.165072i
\(382\) −1.88011 0.297780i −0.0961949 0.0152358i
\(383\) −28.0388 + 14.2865i −1.43272 + 0.730005i −0.986322 0.164831i \(-0.947292\pi\)
−0.446394 + 0.894836i \(0.647292\pi\)
\(384\) 11.6959 0.596852
\(385\) 29.0183 6.35294i 1.47891 0.323776i
\(386\) −52.4092 −2.66756
\(387\) 6.36622 3.24375i 0.323613 0.164889i
\(388\) −15.5055 2.45583i −0.787171 0.124676i
\(389\) 20.5153 28.2368i 1.04016 1.43166i 0.143130 0.989704i \(-0.454283\pi\)
0.897035 0.441960i \(-0.145717\pi\)
\(390\) 0.582837 + 24.7350i 0.0295131 + 1.25250i
\(391\) −4.54642 + 1.47722i −0.229922 + 0.0747062i
\(392\) −2.21154 13.9631i −0.111700 0.705245i
\(393\) 0.952359 6.01296i 0.0480402 0.303314i
\(394\) −4.51832 1.46809i −0.227630 0.0739614i
\(395\) −21.3863 + 11.5393i −1.07606 + 0.580607i
\(396\) 8.95241 + 1.09937i 0.449876 + 0.0552456i
\(397\) 8.10434 8.10434i 0.406745 0.406745i −0.473857 0.880602i \(-0.657139\pi\)
0.880602 + 0.473857i \(0.157139\pi\)
\(398\) 2.80143 + 5.49811i 0.140423 + 0.275595i
\(399\) 13.3542 + 18.3804i 0.668544 + 0.920172i
\(400\) −9.55659 + 3.61107i −0.477829 + 0.180553i
\(401\) −7.45244 22.9363i −0.372157 1.14538i −0.945377 0.325980i \(-0.894306\pi\)
0.573220 0.819402i \(-0.305694\pi\)
\(402\) −13.5906 + 26.6730i −0.677836 + 1.33033i
\(403\) 3.85273 0.610212i 0.191918 0.0303968i
\(404\) 7.35221 5.34170i 0.365786 0.265759i
\(405\) 0.401727 + 2.19969i 0.0199620 + 0.109303i
\(406\) 33.7417i 1.67457i
\(407\) 23.5750 + 15.9021i 1.16857 + 0.788240i
\(408\) 1.37874 + 1.37874i 0.0682576 + 0.0682576i
\(409\) −4.96063 + 15.2673i −0.245288 + 0.754918i 0.750301 + 0.661096i \(0.229908\pi\)
−0.995589 + 0.0938217i \(0.970092\pi\)
\(410\) 6.73448 + 19.1772i 0.332592 + 0.947093i
\(411\) −5.27882 3.83529i −0.260385 0.189181i
\(412\) −39.6761 20.2160i −1.95470 0.995970i
\(413\) −2.61821 1.33405i −0.128834 0.0656441i
\(414\) −6.73554 4.89366i −0.331034 0.240510i
\(415\) 0.0362519 + 0.103231i 0.00177953 + 0.00506742i
\(416\) 11.9067 36.6451i 0.583775 1.79667i
\(417\) 7.06555 + 7.06555i 0.346001 + 0.346001i
\(418\) −38.4038 + 13.9771i −1.87839 + 0.683643i
\(419\) 1.01897i 0.0497800i 0.999690 + 0.0248900i \(0.00792355\pi\)
−0.999690 + 0.0248900i \(0.992076\pi\)
\(420\) 4.37605 + 23.9614i 0.213529 + 1.16920i
\(421\) 2.48285 1.80389i 0.121007 0.0879164i −0.525636 0.850710i \(-0.676173\pi\)
0.646642 + 0.762793i \(0.276173\pi\)
\(422\) 41.0257 6.49784i 1.99710 0.316310i
\(423\) −1.89975 + 3.72846i −0.0923688 + 0.181284i
\(424\) 1.60975 + 4.95430i 0.0781764 + 0.240602i
\(425\) −5.68430 2.56660i −0.275729 0.124498i
\(426\) −14.8395 20.4248i −0.718977 0.989587i
\(427\) 8.47944 + 16.6418i 0.410349 + 0.805355i
\(428\) −22.8840 + 22.8840i −1.10614 + 1.10614i
\(429\) 7.13934 15.3097i 0.344690 0.739158i
\(430\) −30.5457 + 16.4814i −1.47304 + 0.794806i
\(431\) 3.18922 + 1.03624i 0.153620 + 0.0499140i 0.384817 0.922993i \(-0.374264\pi\)
−0.231198 + 0.972907i \(0.574264\pi\)
\(432\) 0.319629 2.01806i 0.0153782 0.0970939i
\(433\) 0.201389 + 1.27152i 0.00967815 + 0.0611054i 0.992055 0.125807i \(-0.0401520\pi\)
−0.982377 + 0.186912i \(0.940152\pi\)
\(434\) 6.33818 2.05940i 0.304242 0.0988543i
\(435\) 0.204249 + 8.66811i 0.00979301 + 0.415604i
\(436\) −11.7936 + 16.2325i −0.564811 + 0.777395i
\(437\) 21.4697 + 3.40046i 1.02703 + 0.162666i
\(438\) −4.47671 + 2.28100i −0.213905 + 0.108990i
\(439\) −29.7921 −1.42190 −0.710950 0.703243i \(-0.751735\pi\)
−0.710950 + 0.703243i \(0.751735\pi\)
\(440\) −11.5362 1.14154i −0.549969 0.0544206i
\(441\) −9.04408 −0.430670
\(442\) 12.2977 6.26601i 0.584944 0.298044i
\(443\) −3.32439 0.526532i −0.157947 0.0250163i 0.0769603 0.997034i \(-0.475479\pi\)
−0.234907 + 0.972018i \(0.575479\pi\)
\(444\) −13.7056 + 18.8642i −0.650441 + 0.895255i
\(445\) 7.70416 8.07600i 0.365212 0.382839i
\(446\) 20.1797 6.55680i 0.955539 0.310473i
\(447\) −0.663592 4.18975i −0.0313868 0.198169i
\(448\) 7.73742 48.8521i 0.365559 2.30805i
\(449\) −39.2062 12.7389i −1.85026 0.601185i −0.996792 0.0800330i \(-0.974497\pi\)
−0.853464 0.521152i \(-0.825503\pi\)
\(450\) −2.20266 10.6366i −0.103834 0.501413i
\(451\) 1.69143 13.7736i 0.0796462 0.648575i
\(452\) −9.04909 + 9.04909i −0.425633 + 0.425633i
\(453\) −0.901443 1.76918i −0.0423535 0.0831234i
\(454\) 29.6597 + 40.8231i 1.39200 + 1.91592i
\(455\) 45.2123 + 6.07291i 2.11959 + 0.284702i
\(456\) −2.73982 8.43228i −0.128304 0.394878i
\(457\) −3.12685 + 6.13680i −0.146268 + 0.287067i −0.952504 0.304528i \(-0.901501\pi\)
0.806235 + 0.591595i \(0.201501\pi\)
\(458\) 1.55022 0.245530i 0.0724369 0.0114729i
\(459\) 1.00915 0.733190i 0.0471030 0.0342224i
\(460\) 19.1714 + 13.2502i 0.893870 + 0.617796i
\(461\) 0.943983i 0.0439657i 0.999758 + 0.0219828i \(0.00699792\pi\)
−0.999758 + 0.0219828i \(0.993002\pi\)
\(462\) 7.95549 27.7423i 0.370123 1.29069i
\(463\) 16.3776 + 16.3776i 0.761130 + 0.761130i 0.976527 0.215397i \(-0.0691045\pi\)
−0.215397 + 0.976527i \(0.569105\pi\)
\(464\) 2.44825 7.53495i 0.113657 0.349801i
\(465\) −1.61579 + 0.567419i −0.0749304 + 0.0263134i
\(466\) 26.4372 + 19.2077i 1.22468 + 0.889782i
\(467\) −18.3152 9.33204i −0.847525 0.431835i −0.0244042 0.999702i \(-0.507769\pi\)
−0.823120 + 0.567867i \(0.807769\pi\)
\(468\) 12.3416 + 6.28837i 0.570491 + 0.290680i
\(469\) 44.6536 + 32.4427i 2.06191 + 1.49807i
\(470\) 8.79925 18.3243i 0.405879 0.845235i
\(471\) −1.14277 + 3.51710i −0.0526562 + 0.162059i
\(472\) 0.810868 + 0.810868i 0.0373232 + 0.0373232i
\(473\) 23.6828 0.826616i 1.08894 0.0380078i
\(474\) 23.6094i 1.08442i
\(475\) 17.7319 + 22.1333i 0.813596 + 1.01555i
\(476\) 10.9928 7.98670i 0.503852 0.366070i
\(477\) 3.29153 0.521327i 0.150709 0.0238699i
\(478\) −3.96900 + 7.78959i −0.181538 + 0.356288i
\(479\) 3.19706 + 9.83953i 0.146077 + 0.449580i 0.997148 0.0754715i \(-0.0240462\pi\)
−0.851071 + 0.525051i \(0.824046\pi\)
\(480\) −2.25193 + 16.7654i −0.102786 + 0.765234i
\(481\) 25.6686 + 35.3298i 1.17039 + 1.61090i
\(482\) −24.6623 48.4024i −1.12333 2.20467i
\(483\) −10.8544 + 10.8544i −0.493894 + 0.493894i
\(484\) 25.3687 + 15.8533i 1.15312 + 0.720605i
\(485\) 3.69847 12.3667i 0.167939 0.561544i
\(486\) 2.06612 + 0.671323i 0.0937211 + 0.0304518i
\(487\) −1.53390 + 9.68467i −0.0695077 + 0.438854i 0.928252 + 0.371952i \(0.121311\pi\)
−0.997760 + 0.0669020i \(0.978689\pi\)
\(488\) −1.14024 7.19916i −0.0516160 0.325891i
\(489\) −3.53130 + 1.14739i −0.159691 + 0.0518867i
\(490\) 43.9216 1.03494i 1.98418 0.0467537i
\(491\) −6.32001 + 8.69875i −0.285218 + 0.392569i −0.927454 0.373938i \(-0.878007\pi\)
0.642235 + 0.766507i \(0.278007\pi\)
\(492\) 11.2387 + 1.78004i 0.506680 + 0.0802502i
\(493\) 4.30962 2.19586i 0.194095 0.0988965i
\(494\) −62.7606 −2.82373
\(495\) −1.87580 + 7.17505i −0.0843111 + 0.322495i
\(496\) 1.56482 0.0702626
\(497\) −41.4753 + 21.1327i −1.86042 + 0.947933i
\(498\) 0.104990 + 0.0166288i 0.00470471 + 0.000745152i
\(499\) −0.911997 + 1.25526i −0.0408266 + 0.0561930i −0.828942 0.559334i \(-0.811057\pi\)
0.788116 + 0.615527i \(0.211057\pi\)
\(500\) 6.86528 + 29.6201i 0.307025 + 1.32465i
\(501\) 7.70467 2.50340i 0.344219 0.111844i
\(502\) 1.91883 + 12.1150i 0.0856415 + 0.540719i
\(503\) −4.24279 + 26.7879i −0.189177 + 1.19441i 0.692096 + 0.721805i \(0.256687\pi\)
−0.881273 + 0.472608i \(0.843313\pi\)
\(504\) 5.95473 + 1.93481i 0.265245 + 0.0861833i
\(505\) 3.54823 + 6.57607i 0.157894 + 0.292631i
\(506\) −13.3866 24.1510i −0.595105 1.07364i
\(507\) 9.15100 9.15100i 0.406410 0.406410i
\(508\) 4.91720 + 9.65055i 0.218166 + 0.428174i
\(509\) 10.6136 + 14.6084i 0.470442 + 0.647507i 0.976633 0.214914i \(-0.0689471\pi\)
−0.506191 + 0.862421i \(0.668947\pi\)
\(510\) −4.81692 + 3.67614i −0.213297 + 0.162782i
\(511\) 2.86265 + 8.81032i 0.126636 + 0.389746i
\(512\) 9.91729 19.4638i 0.438287 0.860186i
\(513\) −5.60222 + 0.887304i −0.247344 + 0.0391755i
\(514\) 13.6723 9.93353i 0.603060 0.438149i
\(515\) 20.8170 30.1195i 0.917308 1.32723i
\(516\) 19.4310i 0.855402i
\(517\) −10.9366 + 8.54432i −0.480992 + 0.375779i
\(518\) 52.7568 + 52.7568i 2.31800 + 2.31800i
\(519\) 6.14493 18.9121i 0.269732 0.830151i
\(520\) −16.0481 7.70626i −0.703757 0.337942i
\(521\) −10.1987 7.40977i −0.446812 0.324628i 0.341524 0.939873i \(-0.389057\pi\)
−0.788336 + 0.615245i \(0.789057\pi\)
\(522\) 7.50569 + 3.82434i 0.328515 + 0.167387i
\(523\) −14.5332 7.40503i −0.635492 0.323800i 0.106395 0.994324i \(-0.466069\pi\)
−0.741888 + 0.670524i \(0.766069\pi\)
\(524\) 13.3943 + 9.73153i 0.585133 + 0.425124i
\(525\) −20.0053 + 0.943306i −0.873103 + 0.0411692i
\(526\) −21.3313 + 65.6510i −0.930088 + 2.86252i
\(527\) 0.675513 + 0.675513i 0.0294258 + 0.0294258i
\(528\) 3.78951 5.61797i 0.164917 0.244491i
\(529\) 8.31309i 0.361438i
\(530\) −15.9253 + 2.90843i −0.691751 + 0.126334i
\(531\) 0.593505 0.431206i 0.0257559 0.0187128i
\(532\) −61.0255 + 9.66549i −2.64579 + 0.419052i
\(533\) 9.67489 18.9880i 0.419066 0.822464i
\(534\) −3.35092 10.3131i −0.145008 0.446290i
\(535\) −16.1435 21.1532i −0.697945 0.914533i
\(536\) −12.6607 17.4260i −0.546860 0.752689i
\(537\) 9.68487 + 19.0076i 0.417933 + 0.820239i
\(538\) −41.6525 + 41.6525i −1.79577 + 1.79577i
\(539\) −27.1852 12.6772i −1.17095 0.546047i
\(540\) −5.82609 1.74239i −0.250715 0.0749805i
\(541\) 15.3752 + 4.99571i 0.661033 + 0.214783i 0.620272 0.784386i \(-0.287022\pi\)
0.0407602 + 0.999169i \(0.487022\pi\)
\(542\) 7.41815 46.8364i 0.318637 2.01179i
\(543\) 1.34495 + 8.49165i 0.0577172 + 0.364412i
\(544\) 8.97463 2.91603i 0.384784 0.125024i
\(545\) −11.9371 11.3875i −0.511328 0.487786i
\(546\) 26.0509 35.8560i 1.11488 1.53449i
\(547\) −19.5699 3.09956i −0.836747 0.132528i −0.276666 0.960966i \(-0.589230\pi\)
−0.560080 + 0.828438i \(0.689230\pi\)
\(548\) 15.8108 8.05601i 0.675405 0.344136i
\(549\) −4.66298 −0.199011
\(550\) 8.28858 35.0595i 0.353426 1.49494i
\(551\) −21.9938 −0.936967
\(552\) 5.33759 2.71964i 0.227183 0.115755i
\(553\) 42.9945 + 6.80966i 1.82831 + 0.289576i
\(554\) 4.92094 6.77310i 0.209071 0.287761i
\(555\) −13.8724 13.2337i −0.588850 0.561738i
\(556\) −25.8441 + 8.39725i −1.09603 + 0.356123i
\(557\) 0.699877 + 4.41885i 0.0296547 + 0.187233i 0.998069 0.0621139i \(-0.0197842\pi\)
−0.968414 + 0.249346i \(0.919784\pi\)
\(558\) −0.260275 + 1.64331i −0.0110183 + 0.0695671i
\(559\) 34.6102 + 11.2455i 1.46386 + 0.475636i
\(560\) 17.5329 + 5.24351i 0.740901 + 0.221579i
\(561\) 4.06108 0.789323i 0.171459 0.0333252i
\(562\) −42.5821 + 42.5821i −1.79622 + 1.79622i
\(563\) −6.99197 13.7225i −0.294676 0.578335i 0.695440 0.718584i \(-0.255210\pi\)
−0.990116 + 0.140249i \(0.955210\pi\)
\(564\) −6.68900 9.20662i −0.281658 0.387669i
\(565\) −6.38367 8.36466i −0.268563 0.351904i
\(566\) 16.0224 + 49.3119i 0.673473 + 2.07274i
\(567\) 1.81846 3.56893i 0.0763682 0.149881i
\(568\) 17.9420 2.84173i 0.752829 0.119236i
\(569\) −1.28307 + 0.932205i −0.0537891 + 0.0390801i −0.614355 0.789030i \(-0.710584\pi\)
0.560566 + 0.828110i \(0.310584\pi\)
\(570\) 27.1050 4.95018i 1.13531 0.207340i
\(571\) 13.0509i 0.546163i −0.961991 0.273081i \(-0.911957\pi\)
0.961991 0.273081i \(-0.0880428\pi\)
\(572\) 28.2826 + 36.2014i 1.18256 + 1.51366i
\(573\) −0.619583 0.619583i −0.0258834 0.0258834i
\(574\) 11.2510 34.6270i 0.469608 1.44530i
\(575\) −12.8962 + 14.1726i −0.537808 + 0.591036i
\(576\) 9.98997 + 7.25814i 0.416249 + 0.302422i
\(577\) −16.0989 8.20279i −0.670205 0.341486i 0.0855567 0.996333i \(-0.472733\pi\)
−0.755762 + 0.654847i \(0.772733\pi\)
\(578\) −29.8945 15.2320i −1.24345 0.633568i
\(579\) −19.5171 14.1800i −0.811104 0.589301i
\(580\) −21.2560 10.2071i −0.882609 0.423826i
\(581\) 0.0605644 0.186398i 0.00251264 0.00773310i
\(582\) −8.86759 8.86759i −0.367574 0.367574i
\(583\) 10.6246 + 3.04676i 0.440027 + 0.126184i
\(584\) 3.61516i 0.149596i
\(585\) −6.47533 + 9.36896i −0.267722 + 0.387359i
\(586\) 22.8167 16.5773i 0.942550 0.684803i
\(587\) −11.6948 + 1.85227i −0.482695 + 0.0764514i −0.393040 0.919522i \(-0.628577\pi\)
−0.0896552 + 0.995973i \(0.528577\pi\)
\(588\) 11.1662 21.9149i 0.460486 0.903754i
\(589\) −1.34238 4.13141i −0.0553116 0.170232i
\(590\) −2.83295 + 2.16202i −0.116631 + 0.0890091i
\(591\) −1.28541 1.76921i −0.0528745 0.0727755i
\(592\) 7.95330 + 15.6092i 0.326879 + 0.641535i
\(593\) 8.80231 8.80231i 0.361467 0.361467i −0.502886 0.864353i \(-0.667728\pi\)
0.864353 + 0.502886i \(0.167728\pi\)
\(594\) 5.26946 + 4.91402i 0.216209 + 0.201625i
\(595\) 5.30518 + 9.83229i 0.217491 + 0.403084i
\(596\) 10.9716 + 3.56488i 0.449413 + 0.146023i
\(597\) −0.444340 + 2.80545i −0.0181856 + 0.114820i
\(598\) −6.63353 41.8824i −0.271265 1.71270i
\(599\) 7.01059 2.27788i 0.286445 0.0930716i −0.162270 0.986746i \(-0.551882\pi\)
0.448715 + 0.893675i \(0.351882\pi\)
\(600\) 7.53869 + 2.06240i 0.307766 + 0.0841972i
\(601\) 3.77835 5.20046i 0.154122 0.212131i −0.724973 0.688777i \(-0.758148\pi\)
0.879095 + 0.476646i \(0.158148\pi\)
\(602\) 61.4084 + 9.72613i 2.50282 + 0.396407i
\(603\) −12.2778 + 6.25588i −0.499993 + 0.254759i
\(604\) 5.39990 0.219719
\(605\) −15.6958 + 18.9378i −0.638125 + 0.769933i
\(606\) 7.25965 0.294903
\(607\) −25.6589 + 13.0738i −1.04146 + 0.530651i −0.889119 0.457677i \(-0.848682\pi\)
−0.152342 + 0.988328i \(0.548682\pi\)
\(608\) −42.3811 6.71251i −1.71878 0.272228i
\(609\) 9.12927 12.5654i 0.369937 0.509174i
\(610\) 22.6453 0.533597i 0.916879 0.0216047i
\(611\) −20.2699 + 6.58610i −0.820033 + 0.266445i
\(612\) 0.530669 + 3.35051i 0.0214510 + 0.135437i
\(613\) 5.31950 33.5860i 0.214853 1.35653i −0.610549 0.791979i \(-0.709051\pi\)
0.825401 0.564547i \(-0.190949\pi\)
\(614\) −1.10716 0.359738i −0.0446814 0.0145179i
\(615\) −2.68073 + 8.96366i −0.108098 + 0.361450i
\(616\) 15.1870 + 14.1626i 0.611903 + 0.570628i
\(617\) 31.1826 31.1826i 1.25536 1.25536i 0.302082 0.953282i \(-0.402318\pi\)
0.953282 0.302082i \(-0.0976817\pi\)
\(618\) −16.1492 31.6945i −0.649615 1.27494i
\(619\) −21.3297 29.3578i −0.857311 1.17999i −0.982204 0.187818i \(-0.939859\pi\)
0.124892 0.992170i \(-0.460141\pi\)
\(620\) 0.619994 4.61581i 0.0248996 0.185375i
\(621\) −1.18426 3.64478i −0.0475228 0.146260i
\(622\) 20.0874 39.4237i 0.805431 1.58075i
\(623\) −19.7474 + 3.12768i −0.791162 + 0.125308i
\(624\) 8.41916 6.11688i 0.337036 0.244871i
\(625\) −24.8891 + 2.35241i −0.995563 + 0.0940964i
\(626\) 11.1607i 0.446071i
\(627\) −18.0832 5.18562i −0.722175 0.207094i
\(628\) −7.11143 7.11143i −0.283777 0.283777i
\(629\) −3.30496 + 10.1716i −0.131778 + 0.405569i
\(630\) −8.42276 + 17.5402i −0.335571 + 0.698819i
\(631\) 38.7679 + 28.1666i 1.54333 + 1.12129i 0.948206 + 0.317657i \(0.102896\pi\)
0.595122 + 0.803636i \(0.297104\pi\)
\(632\) −15.1361 7.71225i −0.602083 0.306777i
\(633\) 17.0360 + 8.68028i 0.677121 + 0.345010i
\(634\) −47.1616 34.2649i −1.87303 1.36083i
\(635\) −8.40253 + 2.95073i −0.333444 + 0.117096i
\(636\) −2.80062 + 8.61942i −0.111052 + 0.341782i
\(637\) −32.5721 32.5721i −1.29056 1.29056i
\(638\) 17.2004 + 22.0163i 0.680970 + 0.871632i
\(639\) 11.6212i 0.459728i
\(640\) −21.5143 14.8695i −0.850426 0.587769i
\(641\) −19.0504 + 13.8409i −0.752446 + 0.546684i −0.896584 0.442874i \(-0.853959\pi\)
0.144138 + 0.989558i \(0.453959\pi\)
\(642\) −25.5342 + 4.04422i −1.00776 + 0.159613i
\(643\) −11.0921 + 21.7694i −0.437428 + 0.858501i 0.562078 + 0.827084i \(0.310002\pi\)
−0.999506 + 0.0314167i \(0.989998\pi\)
\(644\) −12.9003 39.7030i −0.508342 1.56452i
\(645\) −15.8345 2.12688i −0.623481 0.0837459i
\(646\) −9.03454 12.4350i −0.355459 0.489247i
\(647\) 0.720564 + 1.41419i 0.0283283 + 0.0555974i 0.904737 0.425971i \(-0.140067\pi\)
−0.876409 + 0.481568i \(0.840067\pi\)
\(648\) −1.10531 + 1.10531i −0.0434206 + 0.0434206i
\(649\) 2.38842 0.464220i 0.0937537 0.0182222i
\(650\) 30.3746 46.2404i 1.19139 1.81370i
\(651\) 2.91753 + 0.947962i 0.114347 + 0.0371536i
\(652\) 1.57963 9.97338i 0.0618630 0.390588i
\(653\) 3.46756 + 21.8933i 0.135696 + 0.856750i 0.957805 + 0.287420i \(0.0927975\pi\)
−0.822109 + 0.569330i \(0.807203\pi\)
\(654\) −15.2437 + 4.95297i −0.596074 + 0.193676i
\(655\) −9.39641 + 9.84992i −0.367148 + 0.384868i
\(656\) 5.02499 6.91630i 0.196193 0.270036i
\(657\) −2.28427 0.361793i −0.0891180 0.0141149i
\(658\) −32.4441 + 16.5311i −1.26480 + 0.644450i
\(659\) 13.1372 0.511752 0.255876 0.966710i \(-0.417636\pi\)
0.255876 + 0.966710i \(0.417636\pi\)
\(660\) −15.0701 13.4039i −0.586601 0.521746i
\(661\) 30.1682 1.17341 0.586703 0.809802i \(-0.300426\pi\)
0.586703 + 0.809802i \(0.300426\pi\)
\(662\) −64.2441 + 32.7340i −2.49692 + 1.27224i
\(663\) 6.27501 + 0.993865i 0.243701 + 0.0385985i
\(664\) −0.0449568 + 0.0618777i −0.00174466 + 0.00240132i
\(665\) −1.19674 50.7881i −0.0464074 1.96948i
\(666\) −17.7151 + 5.75597i −0.686444 + 0.223039i
\(667\) −2.32465 14.6773i −0.0900109 0.568306i
\(668\) −3.44647 + 21.7601i −0.133348 + 0.841924i
\(669\) 9.28894 + 3.01816i 0.359131 + 0.116689i
\(670\) 58.9102 31.7860i 2.27590 1.22800i
\(671\) −14.0163 6.53618i −0.541091 0.252326i
\(672\) 21.4267 21.4267i 0.826552 0.826552i
\(673\) −20.4137 40.0641i −0.786889 1.54436i −0.838004 0.545664i \(-0.816277\pi\)
0.0511145 0.998693i \(-0.483723\pi\)
\(674\) 37.6760 + 51.8565i 1.45122 + 1.99744i
\(675\) 2.05760 4.55700i 0.0791970 0.175399i
\(676\) 10.8758 + 33.4722i 0.418299 + 1.28739i
\(677\) 15.4947 30.4100i 0.595508 1.16875i −0.374852 0.927085i \(-0.622306\pi\)
0.970360 0.241666i \(-0.0776937\pi\)
\(678\) −10.0971 + 1.59922i −0.387775 + 0.0614176i
\(679\) −18.7062 + 13.5909i −0.717879 + 0.521570i
\(680\) −0.783299 4.28901i −0.0300381 0.164476i
\(681\) 23.2273i 0.890072i
\(682\) −3.08581 + 4.57474i −0.118162 + 0.175176i
\(683\) 11.7243 + 11.7243i 0.448619 + 0.448619i 0.894895 0.446276i \(-0.147250\pi\)
−0.446276 + 0.894895i \(0.647250\pi\)
\(684\) 4.76669 14.6704i 0.182259 0.560935i
\(685\) 4.83428 + 13.7661i 0.184708 + 0.525978i
\(686\) −14.3900 10.4550i −0.549413 0.399172i
\(687\) 0.643731 + 0.327997i 0.0245599 + 0.0125139i
\(688\) 13.0076 + 6.62768i 0.495908 + 0.252678i
\(689\) 13.7320 + 9.97685i 0.523146 + 0.380088i
\(690\) 6.16832 + 17.5650i 0.234824 + 0.668687i
\(691\) −1.81718 + 5.59270i −0.0691287 + 0.212756i −0.979653 0.200700i \(-0.935678\pi\)
0.910524 + 0.413456i \(0.135678\pi\)
\(692\) 38.2396 + 38.2396i 1.45365 + 1.45365i
\(693\) 10.4687 8.17874i 0.397672 0.310684i
\(694\) 26.9980i 1.02483i
\(695\) −4.01413 21.9797i −0.152265 0.833737i
\(696\) −4.90362 + 3.56269i −0.185871 + 0.135043i
\(697\) 5.15489 0.816455i 0.195256 0.0309254i
\(698\) 12.0034 23.5581i 0.454337 0.891687i
\(699\) 4.64826 + 14.3059i 0.175813 + 0.541098i
\(700\) 22.4136 49.6399i 0.847155 1.87621i
\(701\) 15.7245 + 21.6429i 0.593905 + 0.817440i 0.995133 0.0985379i \(-0.0314166\pi\)
−0.401228 + 0.915978i \(0.631417\pi\)
\(702\) 5.02335 + 9.85888i 0.189594 + 0.372099i
\(703\) 34.3884 34.3884i 1.29698 1.29698i
\(704\) 19.8546 + 35.8200i 0.748297 + 1.35002i
\(705\) 8.23471 4.44318i 0.310137 0.167340i
\(706\) 62.1476 + 20.1930i 2.33896 + 0.759973i
\(707\) 2.09390 13.2204i 0.0787493 0.497203i
\(708\) 0.312099 + 1.97052i 0.0117294 + 0.0740566i
\(709\) −9.52249 + 3.09405i −0.357625 + 0.116199i −0.482318 0.875996i \(-0.660205\pi\)
0.124694 + 0.992195i \(0.460205\pi\)
\(710\) 1.32985 + 56.4372i 0.0499083 + 2.11805i
\(711\) −6.38784 + 8.79211i −0.239563 + 0.329730i
\(712\) 7.70638 + 1.22057i 0.288809 + 0.0457428i
\(713\) 2.61516 1.33249i 0.0979383 0.0499021i
\(714\) 10.8544 0.406214
\(715\) −32.5966 + 19.0852i −1.21904 + 0.713746i
\(716\) −58.0151 −2.16813
\(717\) −3.58563 + 1.82697i −0.133908 + 0.0682294i
\(718\) −45.4861 7.20429i −1.69753 0.268862i
\(719\) −15.3603 + 21.1417i −0.572843 + 0.788451i −0.992888 0.119053i \(-0.962014\pi\)
0.420045 + 0.907503i \(0.362014\pi\)
\(720\) −3.15361 + 3.30581i −0.117528 + 0.123200i
\(721\) −62.3761 + 20.2672i −2.32301 + 0.754790i
\(722\) 4.47651 + 28.2636i 0.166598 + 1.05186i
\(723\) 3.91173 24.6977i 0.145479 0.918517i
\(724\) −22.2368 7.22518i −0.826425 0.268522i
\(725\) 10.6445 16.2045i 0.395326 0.601819i
\(726\) 8.95119 + 22.1572i 0.332210 + 0.822329i
\(727\) −19.2017 + 19.2017i −0.712150 + 0.712150i −0.966985 0.254835i \(-0.917979\pi\)
0.254835 + 0.966985i \(0.417979\pi\)
\(728\) 14.4777 + 28.4141i 0.536580 + 1.05310i
\(729\) 0.587785 + 0.809017i 0.0217698 + 0.0299636i
\(730\) 11.1347 + 1.49562i 0.412115 + 0.0553552i
\(731\) 2.75411 + 8.47627i 0.101864 + 0.313506i
\(732\) 5.75710 11.2990i 0.212789 0.417621i
\(733\) 2.67135 0.423100i 0.0986686 0.0156276i −0.106905 0.994269i \(-0.534094\pi\)
0.205573 + 0.978642i \(0.434094\pi\)
\(734\) −24.2892 + 17.6471i −0.896531 + 0.651368i
\(735\) 16.6364 + 11.4982i 0.613641 + 0.424116i
\(736\) 28.9920i 1.06866i
\(737\) −45.6745 + 1.59421i −1.68244 + 0.0587233i
\(738\) 6.42742 + 6.42742i 0.236597 + 0.236597i
\(739\) −2.74727 + 8.45522i −0.101060 + 0.311030i −0.988786 0.149343i \(-0.952284\pi\)
0.887726 + 0.460373i \(0.152284\pi\)
\(740\) 49.1942 17.2756i 1.80841 0.635064i
\(741\) −23.3720 16.9807i −0.858590 0.623802i
\(742\) 25.8384 + 13.1653i 0.948557 + 0.483314i
\(743\) 39.4677 + 20.1098i 1.44793 + 0.737758i 0.988608 0.150512i \(-0.0480921\pi\)
0.459323 + 0.888269i \(0.348092\pi\)
\(744\) −0.968518 0.703670i −0.0355076 0.0257978i
\(745\) −4.10598 + 8.55061i −0.150431 + 0.313270i
\(746\) 11.4826 35.3397i 0.420407 1.29388i
\(747\) 0.0345989 + 0.0345989i 0.00126591 + 0.00126591i
\(748\) −3.10136 + 10.8150i −0.113397 + 0.395436i
\(749\) 47.6662i 1.74169i
\(750\) −9.47104 + 22.3661i −0.345834 + 0.816693i
\(751\) −36.3237 + 26.3907i −1.32547 + 0.963011i −0.325624 + 0.945499i \(0.605574\pi\)
−0.999847 + 0.0175112i \(0.994426\pi\)
\(752\) −8.44467 + 1.33750i −0.307945 + 0.0487737i
\(753\) −2.56331 + 5.03078i −0.0934122 + 0.183332i
\(754\) 13.2583 + 40.8050i 0.482840 + 1.48603i
\(755\) −0.591063 + 4.40042i −0.0215110 + 0.160148i
\(756\) 6.40280 + 8.81270i 0.232868 + 0.320515i
\(757\) −18.0839 35.4916i −0.657270 1.28997i −0.943363 0.331764i \(-0.892356\pi\)
0.286092 0.958202i \(-0.407644\pi\)
\(758\) −0.564020 + 0.564020i −0.0204861 + 0.0204861i
\(759\) 1.54923 12.6157i 0.0562336 0.457921i
\(760\) −5.68055 + 18.9942i −0.206055 + 0.688994i
\(761\) −21.3924 6.95080i −0.775472 0.251966i −0.105566 0.994412i \(-0.533666\pi\)
−0.669906 + 0.742446i \(0.733666\pi\)
\(762\) −1.35350 + 8.54568i −0.0490322 + 0.309577i
\(763\) 4.62299 + 29.1884i 0.167364 + 1.05669i
\(764\) 2.26629 0.736361i 0.0819913 0.0266406i
\(765\) −2.78844 + 0.0657050i −0.100816 + 0.00237557i
\(766\) 40.1834 55.3077i 1.45189 1.99835i
\(767\) 3.69049 + 0.584516i 0.133256 + 0.0211056i
\(768\) −0.634492 + 0.323290i −0.0228952 + 0.0116657i
\(769\) 30.3985 1.09620 0.548098 0.836414i \(-0.315352\pi\)
0.548098 + 0.836414i \(0.315352\pi\)
\(770\) −49.9041 + 40.9171i −1.79842 + 1.47455i
\(771\) 7.77921 0.280161
\(772\) 58.4565 29.7851i 2.10390 1.07199i
\(773\) 16.7233 + 2.64872i 0.601497 + 0.0952677i 0.449754 0.893152i \(-0.351512\pi\)
0.151743 + 0.988420i \(0.451512\pi\)
\(774\) −9.12366 + 12.5576i −0.327943 + 0.451375i
\(775\) 3.69359 + 1.01048i 0.132678 + 0.0362974i
\(776\) 8.58176 2.78838i 0.308067 0.100097i
\(777\) 5.37250 + 33.9206i 0.192737 + 1.21690i
\(778\) −11.8615 + 74.8906i −0.425256 + 2.68496i
\(779\) −22.5709 7.33373i −0.808686 0.262758i
\(780\) −14.7074 27.2578i −0.526610 0.975986i
\(781\) 16.2897 34.9317i 0.582890 1.24996i
\(782\) 7.34340 7.34340i 0.262600 0.262600i
\(783\) 1.76038 + 3.45494i 0.0629109 + 0.123470i
\(784\) −10.8617 14.9498i −0.387917 0.533922i
\(785\) 6.57356 5.01675i 0.234620 0.179056i
\(786\) 4.08696 + 12.5784i 0.145777 + 0.448655i
\(787\) −5.35395 + 10.5077i −0.190848 + 0.374560i −0.966526 0.256569i \(-0.917408\pi\)
0.775678 + 0.631129i \(0.217408\pi\)
\(788\) 5.87402 0.930353i 0.209253 0.0331425i
\(789\) −25.7065 + 18.6769i −0.915176 + 0.664914i
\(790\) 30.0158 43.4289i 1.06791 1.54513i
\(791\) 18.8488i 0.670185i
\(792\) −4.87173 + 1.77307i −0.173110 + 0.0630034i
\(793\) −16.7937 16.7937i −0.596361 0.596361i
\(794\) −7.69422 + 23.6804i −0.273058 + 0.840385i
\(795\) −6.71747 3.22571i −0.238244 0.114404i
\(796\) −6.24935 4.54042i −0.221502 0.160931i
\(797\) 32.7726 + 16.6985i 1.16086 + 0.591490i 0.924877 0.380267i \(-0.124168\pi\)
0.235987 + 0.971756i \(0.424168\pi\)
\(798\) −43.9772 22.4075i −1.55678 0.793218i
\(799\) −4.22283 3.06807i −0.149393 0.108540i
\(800\) 25.4571 27.9766i 0.900044 0.989123i
\(801\) 1.54246 4.74721i 0.0545002 0.167734i
\(802\) 37.0468 + 37.0468i 1.30817 + 1.30817i
\(803\) −6.35907 4.28941i −0.224407 0.151370i
\(804\) 37.4745i 1.32162i
\(805\) 33.7663 6.16671i 1.19010 0.217348i
\(806\) −6.85576 + 4.98100i −0.241484 + 0.175448i
\(807\) −26.7810 + 4.24170i −0.942736 + 0.149315i
\(808\) −2.37144 + 4.65421i −0.0834269 + 0.163735i
\(809\) −4.62822 14.2442i −0.162719 0.500799i 0.836142 0.548514i \(-0.184806\pi\)
−0.998861 + 0.0477147i \(0.984806\pi\)
\(810\) −2.94709 3.86164i −0.103550 0.135684i
\(811\) −4.13735 5.69458i −0.145282 0.199964i 0.730174 0.683261i \(-0.239439\pi\)
−0.875456 + 0.483298i \(0.839439\pi\)
\(812\) 19.1760 + 37.6350i 0.672946 + 1.32073i
\(813\) 15.4347 15.4347i 0.541320 0.541320i
\(814\) −61.3172 7.52987i −2.14917 0.263922i
\(815\) 7.95447 + 2.37892i 0.278633 + 0.0833299i
\(816\) 2.42392 + 0.787579i 0.0848541 + 0.0275708i
\(817\) 6.33977 40.0277i 0.221801 1.40039i
\(818\) −5.45553 34.4448i −0.190748 1.20434i
\(819\) 19.4026 6.30430i 0.677983 0.220290i
\(820\) −18.4103 17.5626i −0.642915 0.613314i
\(821\) 1.28819 1.77304i 0.0449580 0.0618794i −0.785946 0.618295i \(-0.787824\pi\)
0.830904 + 0.556416i \(0.187824\pi\)
\(822\) 14.0007 + 2.21749i 0.488329 + 0.0773438i
\(823\) 25.6846 13.0870i 0.895309 0.456183i 0.0551219 0.998480i \(-0.482445\pi\)
0.840187 + 0.542297i \(0.182445\pi\)
\(824\) 25.5949 0.891640
\(825\) 12.5725 10.8135i 0.437718 0.376479i
\(826\) 6.38371 0.222118
\(827\) 40.3331 20.5507i 1.40252 0.714619i 0.421192 0.906971i \(-0.361612\pi\)
0.981326 + 0.192353i \(0.0616118\pi\)
\(828\) 10.2939 + 1.63039i 0.357737 + 0.0566600i
\(829\) −3.77021 + 5.18925i −0.130945 + 0.180230i −0.869455 0.494012i \(-0.835530\pi\)
0.738510 + 0.674242i \(0.235530\pi\)
\(830\) −0.171985 0.164067i −0.00596970 0.00569484i
\(831\) 3.66511 1.19087i 0.127141 0.0413107i
\(832\) 9.83866 + 62.1189i 0.341094 + 2.15358i
\(833\) 1.76479 11.1425i 0.0611465 0.386064i
\(834\) −20.6451 6.70799i −0.714881 0.232279i
\(835\) −17.3552 5.19037i −0.600603 0.179620i
\(836\) 34.8917 37.4155i 1.20675 1.29404i
\(837\) −0.541547 + 0.541547i −0.0187186 + 0.0187186i
\(838\) −1.00498 1.97239i −0.0347165 0.0681349i
\(839\) −23.1815 31.9066i −0.800314 1.10154i −0.992746 0.120227i \(-0.961638\pi\)
0.192433 0.981310i \(-0.438362\pi\)
\(840\) −8.49377 11.1296i −0.293063 0.384007i
\(841\) −4.31524 13.2810i −0.148802 0.457964i
\(842\) −3.02683 + 5.94049i −0.104312 + 0.204723i
\(843\) −27.3787 + 4.33636i −0.942973 + 0.149352i
\(844\) −42.0667 + 30.5633i −1.44800 + 1.05203i
\(845\) −28.4672 + 5.19894i −0.979300 + 0.178849i
\(846\) 9.09071i 0.312545i
\(847\) 42.9316 9.91000i 1.47515 0.340512i
\(848\) 4.81478 + 4.81478i 0.165340 + 0.165340i
\(849\) −7.37528 + 22.6988i −0.253119 + 0.779020i
\(850\) 13.5343 0.638179i 0.464222 0.0218893i
\(851\) 26.5833 + 19.3139i 0.911265 + 0.662073i
\(852\) 28.1596 + 14.3480i 0.964732 + 0.491555i
\(853\) −38.8312 19.7855i −1.32955 0.677442i −0.362493 0.931986i \(-0.618074\pi\)
−0.967061 + 0.254545i \(0.918074\pi\)
\(854\) −32.8267 23.8500i −1.12331 0.816131i
\(855\) 11.4332 + 5.49020i 0.391008 + 0.187761i
\(856\) 5.74823 17.6912i 0.196471 0.604674i
\(857\) −10.6030 10.6030i −0.362190 0.362190i 0.502428 0.864619i \(-0.332440\pi\)
−0.864619 + 0.502428i \(0.832440\pi\)
\(858\) 1.28012 + 36.6757i 0.0437025 + 1.25209i
\(859\) 45.6295i 1.55686i −0.627733 0.778429i \(-0.716017\pi\)
0.627733 0.778429i \(-0.283983\pi\)
\(860\) 24.7036 35.7428i 0.842384 1.21882i
\(861\) 13.5587 9.85095i 0.462078 0.335720i
\(862\) −7.19529 + 1.13962i −0.245072 + 0.0388157i
\(863\) −1.22146 + 2.39724i −0.0415788 + 0.0816030i −0.910861 0.412713i \(-0.864581\pi\)
0.869282 + 0.494316i \(0.164581\pi\)
\(864\) 2.33773 + 7.19480i 0.0795313 + 0.244772i
\(865\) −35.3474 + 26.9761i −1.20185 + 0.917215i
\(866\) −1.64389 2.26262i −0.0558615 0.0768868i
\(867\) −7.01145 13.7608i −0.238121 0.467340i
\(868\) −5.89913 + 5.89913i −0.200229 + 0.200229i
\(869\) −31.5250 + 17.4739i −1.06941 + 0.592761i
\(870\) −8.94446 16.5771i −0.303246 0.562017i
\(871\) −66.7490 21.6881i −2.26170 0.734872i
\(872\) 1.80412 11.3907i 0.0610951 0.385739i
\(873\) −0.903033 5.70153i −0.0305630 0.192967i
\(874\) −44.9119 + 14.5928i −1.51917 + 0.493607i
\(875\) 37.9985 + 23.6985i 1.28459 + 0.801156i
\(876\) 3.69693 5.08838i 0.124908 0.171921i
\(877\) 24.0730 + 3.81279i 0.812887 + 0.128749i 0.549019 0.835810i \(-0.315002\pi\)
0.263868 + 0.964559i \(0.415002\pi\)
\(878\) 57.6676 29.3831i 1.94619 0.991631i
\(879\) 12.9821 0.437877
\(880\) −14.1131 + 5.51634i −0.475753 + 0.185956i
\(881\) 12.4368 0.419006 0.209503 0.977808i \(-0.432815\pi\)
0.209503 + 0.977808i \(0.432815\pi\)
\(882\) 17.5063 8.91991i 0.589468 0.300349i
\(883\) 37.1233 + 5.87975i 1.24930 + 0.197869i 0.745825 0.666141i \(-0.232055\pi\)
0.503473 + 0.864011i \(0.332055\pi\)
\(884\) −10.1556 + 13.9780i −0.341571 + 0.470133i
\(885\) −1.63995 + 0.0386427i −0.0551264 + 0.00129896i
\(886\) 6.95421 2.25956i 0.233631 0.0759114i
\(887\) 7.93686 + 50.1114i 0.266494 + 1.68258i 0.650705 + 0.759330i \(0.274473\pi\)
−0.384211 + 0.923245i \(0.625527\pi\)
\(888\) 2.09661 13.2375i 0.0703577 0.444221i
\(889\) 15.1719 + 4.92966i 0.508850 + 0.165335i
\(890\) −6.94756 + 23.2308i −0.232883 + 0.778699i
\(891\) 0.632786 + 3.25570i 0.0211991 + 0.109070i
\(892\) −18.7819 + 18.7819i −0.628864 + 0.628864i
\(893\) 10.7755 + 21.1480i 0.360587 + 0.707692i
\(894\) 5.41672 + 7.45548i 0.181162 + 0.249349i
\(895\) 6.35023 47.2769i 0.212265 1.58029i
\(896\) 14.4768 + 44.5550i 0.483635 + 1.48848i
\(897\) 8.86154 17.3918i 0.295878 0.580694i
\(898\) 88.4541 14.0098i 2.95175 0.467512i
\(899\) −2.40253 + 1.74554i −0.0801289 + 0.0582171i
\(900\) 8.50177 + 10.6121i 0.283392 + 0.353736i
\(901\) 4.15695i 0.138488i
\(902\) 10.3105 + 28.3293i 0.343302 + 0.943264i
\(903\) 20.2369 + 20.2369i 0.673441 + 0.673441i
\(904\) 2.27304 6.99569i 0.0756001 0.232673i
\(905\) 8.32186 17.3301i 0.276628 0.576072i
\(906\) 3.48978 + 2.53548i 0.115940 + 0.0842356i
\(907\) 43.0157 + 21.9176i 1.42831 + 0.727761i 0.985630 0.168918i \(-0.0540273\pi\)
0.442681 + 0.896679i \(0.354027\pi\)
\(908\) −56.2825 28.6774i −1.86780 0.951692i
\(909\) 2.70349 + 1.96420i 0.0896690 + 0.0651483i
\(910\) −93.5055 + 32.8365i −3.09968 + 1.08852i
\(911\) −9.96214 + 30.6603i −0.330060 + 1.01582i 0.639044 + 0.769170i \(0.279330\pi\)
−0.969104 + 0.246651i \(0.920670\pi\)
\(912\) −8.19482 8.19482i −0.271357 0.271357i
\(913\) 0.0555016 + 0.152497i 0.00183683 + 0.00504693i
\(914\) 14.9627i 0.494922i
\(915\) 8.57744 + 5.92827i 0.283561 + 0.195983i
\(916\) −1.58955 + 1.15488i −0.0525203 + 0.0381582i
\(917\) 24.0849 3.81468i 0.795355 0.125972i
\(918\) −1.23025 + 2.41450i −0.0406043 + 0.0796905i
\(919\) 6.16632 + 18.9780i 0.203408 + 0.626026i 0.999775 + 0.0212122i \(0.00675256\pi\)
−0.796367 + 0.604814i \(0.793247\pi\)
\(920\) −13.2760 1.78323i −0.437696 0.0587912i
\(921\) −0.314973 0.433523i −0.0103787 0.0142851i
\(922\) −0.931023 1.82724i −0.0306616 0.0601768i
\(923\) 41.8537 41.8537i 1.37763 1.37763i
\(924\) 6.89300 + 35.4646i 0.226763 + 1.16670i
\(925\) 8.69330 + 41.9796i 0.285834 + 1.38028i
\(926\) −47.8542 15.5488i −1.57259 0.510964i
\(927\) 2.56145 16.1724i 0.0841292 0.531171i
\(928\) 4.58886 + 28.9729i 0.150637 + 0.951083i
\(929\) −2.36893 + 0.769713i −0.0777222 + 0.0252535i −0.347620 0.937635i \(-0.613010\pi\)
0.269898 + 0.962889i \(0.413010\pi\)
\(930\) 2.56800 2.69194i 0.0842079 0.0882721i
\(931\) −30.1525 + 41.5013i −0.988208 + 1.36015i
\(932\) −40.4038 6.39933i −1.32347 0.209617i
\(933\) 18.1471 9.24643i 0.594111 0.302715i
\(934\) 44.6559 1.46119
\(935\) −8.47377 3.71111i −0.277122 0.121366i
\(936\) −7.96152 −0.260230
\(937\) 13.8306 7.04703i 0.451825 0.230216i −0.213243 0.976999i \(-0.568403\pi\)
0.665068 + 0.746783i \(0.268403\pi\)
\(938\) −118.432 18.7577i −3.86693 0.612462i
\(939\) 3.01968 4.15623i 0.0985434 0.135633i
\(940\) 0.599437 + 25.4394i 0.0195515 + 0.829742i
\(941\) 8.61830 2.80026i 0.280949 0.0912858i −0.165153 0.986268i \(-0.552812\pi\)
0.446102 + 0.894982i \(0.352812\pi\)
\(942\) −1.25678 7.93501i −0.0409482 0.258536i
\(943\) 2.50842 15.8375i 0.0816853 0.515741i
\(944\) 1.42556 + 0.463194i 0.0463982 + 0.0150757i
\(945\) −7.88237 + 4.25307i −0.256414 + 0.138352i
\(946\) −45.0267 + 24.9577i −1.46394 + 0.811445i
\(947\) 0.626498 0.626498i 0.0203585 0.0203585i −0.696854 0.717213i \(-0.745418\pi\)
0.717213 + 0.696854i \(0.245418\pi\)
\(948\) −13.4176 26.3336i −0.435785 0.855276i
\(949\) −6.92379 9.52979i −0.224756 0.309350i
\(950\) −56.1525 25.3542i −1.82183 0.822600i
\(951\) −8.29208 25.5204i −0.268889 0.827556i
\(952\) −3.54569 + 6.95880i −0.114916 + 0.225536i
\(953\) 39.6892 6.28614i 1.28566 0.203628i 0.524062 0.851680i \(-0.324416\pi\)
0.761596 + 0.648052i \(0.224416\pi\)
\(954\) −5.85713 + 4.25545i −0.189631 + 0.137775i
\(955\) 0.352002 + 1.92741i 0.0113905 + 0.0623696i
\(956\) 10.9441i 0.353956i
\(957\) 0.448604 + 12.8526i 0.0145013 + 0.415467i
\(958\) −15.8929 15.8929i −0.513475 0.513475i
\(959\) 8.07643 24.8567i 0.260801 0.802664i
\(960\) −9.14869 26.0519i −0.295273 0.840821i
\(961\) 24.6050 + 17.8766i 0.793710 + 0.576664i
\(962\) −84.5307 43.0705i −2.72538 1.38865i
\(963\) −10.6031 5.40257i −0.341681 0.174095i
\(964\) 55.0159 + 39.9714i 1.77194 + 1.28739i
\(965\) 17.8735 + 50.8969i 0.575369 + 1.63843i
\(966\) 10.3052 31.7160i 0.331563 1.02045i
\(967\) −12.8842 12.8842i −0.414326 0.414326i 0.468916 0.883243i \(-0.344645\pi\)
−0.883243 + 0.468916i \(0.844645\pi\)
\(968\) −17.1291 1.49919i −0.550550 0.0481858i
\(969\) 7.07519i 0.227288i
\(970\) 5.03793 + 27.5855i 0.161758 + 0.885718i
\(971\) 19.2161 13.9613i 0.616673 0.448039i −0.235085 0.971975i \(-0.575537\pi\)
0.851758 + 0.523936i \(0.175537\pi\)
\(972\) −2.68605 + 0.425428i −0.0861551 + 0.0136456i
\(973\) −18.1704 + 35.6615i −0.582517 + 1.14325i
\(974\) −6.58259 20.2591i −0.210920 0.649144i
\(975\) 23.8224 9.00158i 0.762928 0.288281i
\(976\) −5.60010 7.70788i −0.179255 0.246723i
\(977\) 22.5312 + 44.2200i 0.720838 + 1.41472i 0.902204 + 0.431309i \(0.141948\pi\)
−0.181366 + 0.983416i \(0.558052\pi\)
\(978\) 5.70378 5.70378i 0.182387 0.182387i
\(979\) 11.2907 12.1073i 0.360851 0.386952i
\(980\) −48.4014 + 26.1158i −1.54613 + 0.834238i
\(981\) −7.01681 2.27990i −0.224030 0.0727916i
\(982\) 3.65410 23.0711i 0.116607 0.736229i
\(983\) 4.66247 + 29.4377i 0.148710 + 0.938916i 0.943341 + 0.331824i \(0.107664\pi\)
−0.794632 + 0.607092i \(0.792336\pi\)
\(984\) −6.22024 + 2.02108i −0.198294 + 0.0644296i
\(985\) 0.115192 + 4.88861i 0.00367032 + 0.155764i
\(986\) −6.17626 + 8.50090i −0.196692 + 0.270724i
\(987\) −16.5549 2.62203i −0.526947 0.0834603i
\(988\) 70.0023 35.6680i 2.22707 1.13475i
\(989\) 27.3821 0.870699
\(990\) −3.44562 15.7385i −0.109509 0.500204i
\(991\) 30.9346 0.982669 0.491335 0.870971i \(-0.336509\pi\)
0.491335 + 0.870971i \(0.336509\pi\)
\(992\) −5.16232 + 2.63033i −0.163904 + 0.0835131i
\(993\) −32.7811 5.19201i −1.04028 0.164763i
\(994\) 59.4398 81.8118i 1.88531 2.59491i
\(995\) 4.38406 4.59565i 0.138984 0.145692i
\(996\) −0.126555 + 0.0411201i −0.00401004 + 0.00130294i
\(997\) 3.19720 + 20.1863i 0.101256 + 0.639307i 0.985160 + 0.171638i \(0.0549060\pi\)
−0.883904 + 0.467669i \(0.845094\pi\)
\(998\) 0.527299 3.32923i 0.0166913 0.105385i
\(999\) −8.15442 2.64953i −0.257994 0.0838275i
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 165.2.w.a.13.2 96
3.2 odd 2 495.2.bj.c.343.11 96
5.2 odd 4 inner 165.2.w.a.112.2 yes 96
5.3 odd 4 825.2.cw.b.607.11 96
5.4 even 2 825.2.cw.b.343.11 96
11.6 odd 10 inner 165.2.w.a.28.2 yes 96
15.2 even 4 495.2.bj.c.442.11 96
33.17 even 10 495.2.bj.c.28.11 96
55.17 even 20 inner 165.2.w.a.127.2 yes 96
55.28 even 20 825.2.cw.b.457.11 96
55.39 odd 10 825.2.cw.b.193.11 96
165.17 odd 20 495.2.bj.c.127.11 96
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
165.2.w.a.13.2 96 1.1 even 1 trivial
165.2.w.a.28.2 yes 96 11.6 odd 10 inner
165.2.w.a.112.2 yes 96 5.2 odd 4 inner
165.2.w.a.127.2 yes 96 55.17 even 20 inner
495.2.bj.c.28.11 96 33.17 even 10
495.2.bj.c.127.11 96 165.17 odd 20
495.2.bj.c.343.11 96 3.2 odd 2
495.2.bj.c.442.11 96 15.2 even 4
825.2.cw.b.193.11 96 55.39 odd 10
825.2.cw.b.343.11 96 5.4 even 2
825.2.cw.b.457.11 96 55.28 even 20
825.2.cw.b.607.11 96 5.3 odd 4