Properties

Label 570.2.v.a.353.2
Level $570$
Weight $2$
Character 570.353
Analytic conductor $4.551$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [570,2,Mod(83,570)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(570, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([6, 9, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("570.83");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 570.v (of order \(12\), degree \(4\), 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: \(4.55147291521\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\Q(\zeta_{24})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 353.2
Root \(-0.258819 - 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 570.353
Dual form 570.2.v.a.197.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.965926 - 0.258819i) q^{2} +(1.57313 - 0.724745i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.448288 + 2.19067i) q^{5} +(1.33195 - 1.10721i) q^{6} +(2.12132 - 2.12132i) q^{7} +(0.707107 - 0.707107i) q^{8} +(1.94949 - 2.28024i) q^{9} +O(q^{10})\) \(q+(0.965926 - 0.258819i) q^{2} +(1.57313 - 0.724745i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.448288 + 2.19067i) q^{5} +(1.33195 - 1.10721i) q^{6} +(2.12132 - 2.12132i) q^{7} +(0.707107 - 0.707107i) q^{8} +(1.94949 - 2.28024i) q^{9} +(0.133975 + 2.23205i) q^{10} -0.171573i q^{11} +(1.00000 - 1.41421i) q^{12} +(-0.732051 + 2.73205i) q^{13} +(1.50000 - 2.59808i) q^{14} +(0.882461 + 3.77111i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-2.16622 + 0.580438i) q^{17} +(1.29289 - 2.70711i) q^{18} +(-4.33013 - 0.500000i) q^{19} +(0.707107 + 2.12132i) q^{20} +(1.79970 - 4.87453i) q^{21} +(-0.0444063 - 0.165727i) q^{22} +(2.89778 + 0.776457i) q^{23} +(0.599900 - 1.62484i) q^{24} +(-4.59808 - 1.96410i) q^{25} +2.82843i q^{26} +(1.41421 - 5.00000i) q^{27} +(0.776457 - 2.89778i) q^{28} +(1.58579 + 2.74666i) q^{29} +(1.82843 + 3.41421i) q^{30} +6.24264 q^{31} +(0.258819 - 0.965926i) q^{32} +(-0.124347 - 0.269907i) q^{33} +(-1.94218 + 1.12132i) q^{34} +(3.69615 + 5.59808i) q^{35} +(0.548188 - 2.94949i) q^{36} +(-2.12132 + 2.12132i) q^{37} +(-4.31199 + 0.637756i) q^{38} +(0.828427 + 4.82843i) q^{39} +(1.23205 + 1.86603i) q^{40} +(-2.59808 - 1.50000i) q^{41} +(0.476756 - 5.17423i) q^{42} +(-4.09808 + 1.09808i) q^{43} +(-0.0857864 - 0.148586i) q^{44} +(4.12132 + 5.29289i) q^{45} +3.00000 q^{46} +(1.67851 - 6.26430i) q^{47} +(0.158919 - 1.72474i) q^{48} -2.00000i q^{49} +(-4.94975 - 0.707107i) q^{50} +(-2.98709 + 2.48307i) q^{51} +(0.732051 + 2.73205i) q^{52} +(-9.16208 - 2.45497i) q^{53} +(0.0719302 - 5.19565i) q^{54} +(0.375860 + 0.0769140i) q^{55} -3.00000i q^{56} +(-7.17423 + 2.35167i) q^{57} +(2.24264 + 2.24264i) q^{58} +(-2.82843 + 4.89898i) q^{59} +(2.64979 + 2.82465i) q^{60} +(-1.12132 - 1.94218i) q^{61} +(6.02993 - 1.61571i) q^{62} +(-0.701625 - 8.97261i) q^{63} -1.00000i q^{64} +(-5.65685 - 2.82843i) q^{65} +(-0.189967 - 0.228527i) q^{66} +(5.46410 + 1.46410i) q^{67} +(-1.58579 + 1.58579i) q^{68} +(5.12132 - 0.878680i) q^{69} +(5.01910 + 4.45069i) q^{70} +(-9.16756 - 5.29289i) q^{71} +(-0.233875 - 2.99087i) q^{72} +(-15.6892 + 4.20390i) q^{73} +(-1.50000 + 2.59808i) q^{74} +(-8.65685 + 0.242641i) q^{75} +(-4.00000 + 1.73205i) q^{76} +(-0.363961 - 0.363961i) q^{77} +(2.04989 + 4.44949i) q^{78} +(5.61642 + 3.24264i) q^{79} +(1.67303 + 1.48356i) q^{80} +(-1.39898 - 8.89060i) q^{81} +(-2.89778 - 0.776457i) q^{82} +(-3.00000 + 3.00000i) q^{83} +(-0.878680 - 5.12132i) q^{84} +(-0.300457 - 5.00569i) q^{85} +(-3.67423 + 2.12132i) q^{86} +(4.48528 + 3.17157i) q^{87} +(-0.121320 - 0.121320i) q^{88} +(5.91421 + 10.2437i) q^{89} +(5.35079 + 4.04587i) q^{90} +(4.24264 + 7.34847i) q^{91} +(2.89778 - 0.776457i) q^{92} +(9.82050 - 4.52432i) q^{93} -6.48528i q^{94} +(3.03648 - 9.26174i) q^{95} +(-0.292893 - 1.70711i) q^{96} +(3.74907 + 13.9917i) q^{97} +(-0.517638 - 1.93185i) q^{98} +(-0.391227 - 0.334480i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 4 q^{6} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 4 q^{6} - 4 q^{9} + 8 q^{10} + 8 q^{12} + 8 q^{13} + 12 q^{14} + 12 q^{15} + 4 q^{16} - 12 q^{17} + 16 q^{18} + 12 q^{21} - 8 q^{22} + 4 q^{24} - 16 q^{25} + 24 q^{29} - 8 q^{30} + 16 q^{31} + 12 q^{33} - 12 q^{35} - 16 q^{39} - 4 q^{40} - 12 q^{43} - 12 q^{44} + 16 q^{45} + 24 q^{46} - 24 q^{47} - 20 q^{51} - 8 q^{52} - 24 q^{53} + 4 q^{54} - 8 q^{55} - 28 q^{57} - 16 q^{58} + 4 q^{60} + 8 q^{61} + 12 q^{62} - 24 q^{63} - 4 q^{66} + 16 q^{67} - 24 q^{68} + 24 q^{69} - 8 q^{72} - 12 q^{73} - 12 q^{74} - 24 q^{75} - 32 q^{76} + 48 q^{77} + 28 q^{81} - 24 q^{83} - 24 q^{84} + 16 q^{85} - 32 q^{87} + 16 q^{88} + 36 q^{89} + 8 q^{90} + 24 q^{93} - 8 q^{96} - 24 q^{97} + 32 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(211\) \(457\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.965926 0.258819i 0.683013 0.183013i
\(3\) 1.57313 0.724745i 0.908248 0.418432i
\(4\) 0.866025 0.500000i 0.433013 0.250000i
\(5\) −0.448288 + 2.19067i −0.200480 + 0.979698i
\(6\) 1.33195 1.10721i 0.543767 0.452015i
\(7\) 2.12132 2.12132i 0.801784 0.801784i −0.181591 0.983374i \(-0.558125\pi\)
0.983374 + 0.181591i \(0.0581245\pi\)
\(8\) 0.707107 0.707107i 0.250000 0.250000i
\(9\) 1.94949 2.28024i 0.649830 0.760080i
\(10\) 0.133975 + 2.23205i 0.0423665 + 0.705836i
\(11\) 0.171573i 0.0517312i −0.999665 0.0258656i \(-0.991766\pi\)
0.999665 0.0258656i \(-0.00823419\pi\)
\(12\) 1.00000 1.41421i 0.288675 0.408248i
\(13\) −0.732051 + 2.73205i −0.203034 + 0.757735i 0.787005 + 0.616946i \(0.211630\pi\)
−0.990040 + 0.140788i \(0.955036\pi\)
\(14\) 1.50000 2.59808i 0.400892 0.694365i
\(15\) 0.882461 + 3.77111i 0.227851 + 0.973696i
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) −2.16622 + 0.580438i −0.525387 + 0.140777i −0.511757 0.859130i \(-0.671005\pi\)
−0.0136295 + 0.999907i \(0.504339\pi\)
\(18\) 1.29289 2.70711i 0.304738 0.638071i
\(19\) −4.33013 0.500000i −0.993399 0.114708i
\(20\) 0.707107 + 2.12132i 0.158114 + 0.474342i
\(21\) 1.79970 4.87453i 0.392727 1.06371i
\(22\) −0.0444063 0.165727i −0.00946746 0.0353330i
\(23\) 2.89778 + 0.776457i 0.604228 + 0.161903i 0.547948 0.836512i \(-0.315409\pi\)
0.0562805 + 0.998415i \(0.482076\pi\)
\(24\) 0.599900 1.62484i 0.122454 0.331670i
\(25\) −4.59808 1.96410i −0.919615 0.392820i
\(26\) 2.82843i 0.554700i
\(27\) 1.41421 5.00000i 0.272166 0.962250i
\(28\) 0.776457 2.89778i 0.146737 0.547628i
\(29\) 1.58579 + 2.74666i 0.294473 + 0.510042i 0.974862 0.222809i \(-0.0715225\pi\)
−0.680389 + 0.732851i \(0.738189\pi\)
\(30\) 1.82843 + 3.41421i 0.333824 + 0.623347i
\(31\) 6.24264 1.12121 0.560606 0.828083i \(-0.310568\pi\)
0.560606 + 0.828083i \(0.310568\pi\)
\(32\) 0.258819 0.965926i 0.0457532 0.170753i
\(33\) −0.124347 0.269907i −0.0216460 0.0469847i
\(34\) −1.94218 + 1.12132i −0.333082 + 0.192305i
\(35\) 3.69615 + 5.59808i 0.624764 + 0.946248i
\(36\) 0.548188 2.94949i 0.0913647 0.491582i
\(37\) −2.12132 + 2.12132i −0.348743 + 0.348743i −0.859641 0.510898i \(-0.829313\pi\)
0.510898 + 0.859641i \(0.329313\pi\)
\(38\) −4.31199 + 0.637756i −0.699497 + 0.103458i
\(39\) 0.828427 + 4.82843i 0.132655 + 0.773167i
\(40\) 1.23205 + 1.86603i 0.194804 + 0.295045i
\(41\) −2.59808 1.50000i −0.405751 0.234261i 0.283211 0.959058i \(-0.408600\pi\)
−0.688963 + 0.724797i \(0.741934\pi\)
\(42\) 0.476756 5.17423i 0.0735650 0.798402i
\(43\) −4.09808 + 1.09808i −0.624951 + 0.167455i −0.557377 0.830259i \(-0.688192\pi\)
−0.0675734 + 0.997714i \(0.521526\pi\)
\(44\) −0.0857864 0.148586i −0.0129328 0.0224003i
\(45\) 4.12132 + 5.29289i 0.614370 + 0.789018i
\(46\) 3.00000 0.442326
\(47\) 1.67851 6.26430i 0.244836 0.913742i −0.728629 0.684909i \(-0.759842\pi\)
0.973466 0.228834i \(-0.0734912\pi\)
\(48\) 0.158919 1.72474i 0.0229379 0.248945i
\(49\) 2.00000i 0.285714i
\(50\) −4.94975 0.707107i −0.700000 0.100000i
\(51\) −2.98709 + 2.48307i −0.418276 + 0.347699i
\(52\) 0.732051 + 2.73205i 0.101517 + 0.378867i
\(53\) −9.16208 2.45497i −1.25851 0.337216i −0.432891 0.901446i \(-0.642506\pi\)
−0.825618 + 0.564230i \(0.809173\pi\)
\(54\) 0.0719302 5.19565i 0.00978846 0.707039i
\(55\) 0.375860 + 0.0769140i 0.0506809 + 0.0103711i
\(56\) 3.00000i 0.400892i
\(57\) −7.17423 + 2.35167i −0.950251 + 0.311486i
\(58\) 2.24264 + 2.24264i 0.294473 + 0.294473i
\(59\) −2.82843 + 4.89898i −0.368230 + 0.637793i −0.989289 0.145971i \(-0.953369\pi\)
0.621059 + 0.783764i \(0.286703\pi\)
\(60\) 2.64979 + 2.82465i 0.342086 + 0.364660i
\(61\) −1.12132 1.94218i −0.143570 0.248671i 0.785268 0.619156i \(-0.212525\pi\)
−0.928839 + 0.370484i \(0.879192\pi\)
\(62\) 6.02993 1.61571i 0.765802 0.205196i
\(63\) −0.701625 8.97261i −0.0883964 1.13044i
\(64\) 1.00000i 0.125000i
\(65\) −5.65685 2.82843i −0.701646 0.350823i
\(66\) −0.189967 0.228527i −0.0233833 0.0281297i
\(67\) 5.46410 + 1.46410i 0.667546 + 0.178868i 0.576649 0.816992i \(-0.304360\pi\)
0.0908970 + 0.995860i \(0.471027\pi\)
\(68\) −1.58579 + 1.58579i −0.192305 + 0.192305i
\(69\) 5.12132 0.878680i 0.616535 0.105781i
\(70\) 5.01910 + 4.45069i 0.599897 + 0.531959i
\(71\) −9.16756 5.29289i −1.08799 0.628151i −0.154949 0.987922i \(-0.549521\pi\)
−0.933040 + 0.359772i \(0.882855\pi\)
\(72\) −0.233875 2.99087i −0.0275624 0.352477i
\(73\) −15.6892 + 4.20390i −1.83628 + 0.492030i −0.998539 0.0540373i \(-0.982791\pi\)
−0.837741 + 0.546067i \(0.816124\pi\)
\(74\) −1.50000 + 2.59808i −0.174371 + 0.302020i
\(75\) −8.65685 + 0.242641i −0.999607 + 0.0280177i
\(76\) −4.00000 + 1.73205i −0.458831 + 0.198680i
\(77\) −0.363961 0.363961i −0.0414772 0.0414772i
\(78\) 2.04989 + 4.44949i 0.232104 + 0.503806i
\(79\) 5.61642 + 3.24264i 0.631896 + 0.364826i 0.781486 0.623923i \(-0.214462\pi\)
−0.149590 + 0.988748i \(0.547795\pi\)
\(80\) 1.67303 + 1.48356i 0.187051 + 0.165867i
\(81\) −1.39898 8.89060i −0.155442 0.987845i
\(82\) −2.89778 0.776457i −0.320006 0.0857453i
\(83\) −3.00000 + 3.00000i −0.329293 + 0.329293i −0.852318 0.523025i \(-0.824804\pi\)
0.523025 + 0.852318i \(0.324804\pi\)
\(84\) −0.878680 5.12132i −0.0958718 0.558782i
\(85\) −0.300457 5.00569i −0.0325891 0.542943i
\(86\) −3.67423 + 2.12132i −0.396203 + 0.228748i
\(87\) 4.48528 + 3.17157i 0.480873 + 0.340028i
\(88\) −0.121320 0.121320i −0.0129328 0.0129328i
\(89\) 5.91421 + 10.2437i 0.626905 + 1.08583i 0.988169 + 0.153368i \(0.0490121\pi\)
−0.361264 + 0.932464i \(0.617655\pi\)
\(90\) 5.35079 + 4.04587i 0.564023 + 0.426472i
\(91\) 4.24264 + 7.34847i 0.444750 + 0.770329i
\(92\) 2.89778 0.776457i 0.302114 0.0809513i
\(93\) 9.82050 4.52432i 1.01834 0.469150i
\(94\) 6.48528i 0.668906i
\(95\) 3.03648 9.26174i 0.311536 0.950234i
\(96\) −0.292893 1.70711i −0.0298933 0.174231i
\(97\) 3.74907 + 13.9917i 0.380660 + 1.42064i 0.844896 + 0.534931i \(0.179662\pi\)
−0.464236 + 0.885712i \(0.653671\pi\)
\(98\) −0.517638 1.93185i −0.0522893 0.195146i
\(99\) −0.391227 0.334480i −0.0393198 0.0336165i
\(100\) −4.96410 + 0.598076i −0.496410 + 0.0598076i
\(101\) −14.9941 + 8.65685i −1.49197 + 0.861389i −0.999958 0.00919913i \(-0.997072\pi\)
−0.492012 + 0.870588i \(0.663738\pi\)
\(102\) −2.24264 + 3.17157i −0.222055 + 0.314033i
\(103\) −2.12132 2.12132i −0.209020 0.209020i 0.594831 0.803851i \(-0.297219\pi\)
−0.803851 + 0.594831i \(0.797219\pi\)
\(104\) 1.41421 + 2.44949i 0.138675 + 0.240192i
\(105\) 9.87171 + 6.12775i 0.963381 + 0.598007i
\(106\) −9.48528 −0.921292
\(107\) 6.00000 + 6.00000i 0.580042 + 0.580042i 0.934915 0.354873i \(-0.115476\pi\)
−0.354873 + 0.934915i \(0.615476\pi\)
\(108\) −1.27526 5.03723i −0.122711 0.484708i
\(109\) −1.94218 1.12132i −0.186027 0.107403i 0.404094 0.914717i \(-0.367587\pi\)
−0.590122 + 0.807314i \(0.700920\pi\)
\(110\) 0.382959 0.0229864i 0.0365137 0.00219167i
\(111\) −1.79970 + 4.87453i −0.170820 + 0.462670i
\(112\) −0.776457 2.89778i −0.0733683 0.273814i
\(113\) 14.1421 14.1421i 1.33038 1.33038i 0.425352 0.905028i \(-0.360150\pi\)
0.905028 0.425352i \(-0.139850\pi\)
\(114\) −6.32112 + 4.12837i −0.592027 + 0.386657i
\(115\) −3.00000 + 6.00000i −0.279751 + 0.559503i
\(116\) 2.74666 + 1.58579i 0.255021 + 0.147237i
\(117\) 4.80260 + 6.99536i 0.444001 + 0.646721i
\(118\) −1.46410 + 5.46410i −0.134781 + 0.503011i
\(119\) −3.36396 + 5.82655i −0.308374 + 0.534119i
\(120\) 3.29057 + 2.04258i 0.300387 + 0.186461i
\(121\) 10.9706 0.997324
\(122\) −1.58579 1.58579i −0.143570 0.143570i
\(123\) −5.17423 0.476756i −0.466545 0.0429876i
\(124\) 5.40629 3.12132i 0.485499 0.280303i
\(125\) 6.36396 9.19239i 0.569210 0.822192i
\(126\) −3.00000 8.48528i −0.267261 0.755929i
\(127\) 2.56632 + 0.687644i 0.227724 + 0.0610186i 0.370877 0.928682i \(-0.379057\pi\)
−0.143152 + 0.989701i \(0.545724\pi\)
\(128\) −0.258819 0.965926i −0.0228766 0.0853766i
\(129\) −5.65099 + 4.69748i −0.497542 + 0.413590i
\(130\) −6.19615 1.26795i −0.543439 0.111207i
\(131\) 12.9904 + 7.50000i 1.13497 + 0.655278i 0.945181 0.326546i \(-0.105885\pi\)
0.189794 + 0.981824i \(0.439218\pi\)
\(132\) −0.242641 0.171573i −0.0211192 0.0149335i
\(133\) −10.2462 + 8.12493i −0.888462 + 0.704520i
\(134\) 5.65685 0.488678
\(135\) 10.3194 + 5.33951i 0.888151 + 0.459552i
\(136\) −1.12132 + 1.94218i −0.0961524 + 0.166541i
\(137\) 5.30198 19.7873i 0.452979 1.69054i −0.240984 0.970529i \(-0.577470\pi\)
0.693963 0.720011i \(-0.255863\pi\)
\(138\) 4.71940 2.17423i 0.401742 0.185083i
\(139\) −12.1244 + 7.00000i −1.02837 + 0.593732i −0.916519 0.399992i \(-0.869013\pi\)
−0.111856 + 0.993724i \(0.535679\pi\)
\(140\) 6.00000 + 3.00000i 0.507093 + 0.253546i
\(141\) −1.89949 11.0711i −0.159966 0.932352i
\(142\) −10.2251 2.73980i −0.858070 0.229919i
\(143\) 0.468746 + 0.125600i 0.0391985 + 0.0105032i
\(144\) −1.00000 2.82843i −0.0833333 0.235702i
\(145\) −6.72792 + 2.24264i −0.558724 + 0.186241i
\(146\) −14.0665 + 8.12132i −1.16416 + 0.672125i
\(147\) −1.44949 3.14626i −0.119552 0.259500i
\(148\) −0.776457 + 2.89778i −0.0638244 + 0.238196i
\(149\) 5.65685 9.79796i 0.463428 0.802680i −0.535701 0.844407i \(-0.679953\pi\)
0.999129 + 0.0417274i \(0.0132861\pi\)
\(150\) −8.29908 + 2.47493i −0.677617 + 0.202077i
\(151\) −10.7279 −0.873026 −0.436513 0.899698i \(-0.643787\pi\)
−0.436513 + 0.899698i \(0.643787\pi\)
\(152\) −3.41542 + 2.70831i −0.277027 + 0.219673i
\(153\) −2.89949 + 6.07107i −0.234410 + 0.490817i
\(154\) −0.445759 0.257359i −0.0359203 0.0207386i
\(155\) −2.79850 + 13.6756i −0.224781 + 1.09845i
\(156\) 3.13165 + 3.76733i 0.250733 + 0.301628i
\(157\) 3.06142 + 11.4254i 0.244328 + 0.911845i 0.973720 + 0.227749i \(0.0731365\pi\)
−0.729392 + 0.684096i \(0.760197\pi\)
\(158\) 6.26430 + 1.67851i 0.498361 + 0.133535i
\(159\) −16.1924 + 2.77817i −1.28414 + 0.220324i
\(160\) 2.00000 + 1.00000i 0.158114 + 0.0790569i
\(161\) 7.79423 4.50000i 0.614271 0.354650i
\(162\) −3.65237 8.22558i −0.286957 0.646263i
\(163\) −14.2426 14.2426i −1.11557 1.11557i −0.992384 0.123186i \(-0.960689\pi\)
−0.123186 0.992384i \(-0.539311\pi\)
\(164\) −3.00000 −0.234261
\(165\) 0.647020 0.151406i 0.0503704 0.0117870i
\(166\) −2.12132 + 3.67423i −0.164646 + 0.285176i
\(167\) 6.07844 22.6850i 0.470364 1.75542i −0.168101 0.985770i \(-0.553763\pi\)
0.638464 0.769651i \(-0.279570\pi\)
\(168\) −2.17423 4.71940i −0.167746 0.364109i
\(169\) 4.33013 + 2.50000i 0.333087 + 0.192308i
\(170\) −1.58579 4.75736i −0.121624 0.364873i
\(171\) −9.58166 + 8.89898i −0.732728 + 0.680522i
\(172\) −3.00000 + 3.00000i −0.228748 + 0.228748i
\(173\) −5.16876 19.2901i −0.392974 1.46660i −0.825204 0.564835i \(-0.808940\pi\)
0.432230 0.901763i \(-0.357727\pi\)
\(174\) 5.15331 + 1.90263i 0.390672 + 0.144238i
\(175\) −13.9205 + 5.58750i −1.05229 + 0.422376i
\(176\) −0.148586 0.0857864i −0.0112001 0.00646640i
\(177\) −0.898979 + 9.75663i −0.0675714 + 0.733353i
\(178\) 8.36396 + 8.36396i 0.626905 + 0.626905i
\(179\) −9.34315 −0.698340 −0.349170 0.937059i \(-0.613536\pi\)
−0.349170 + 0.937059i \(0.613536\pi\)
\(180\) 6.21561 + 2.52312i 0.463285 + 0.188062i
\(181\) −7.24264 12.5446i −0.538341 0.932434i −0.998994 0.0448537i \(-0.985718\pi\)
0.460652 0.887581i \(-0.347616\pi\)
\(182\) 6.00000 + 6.00000i 0.444750 + 0.444750i
\(183\) −3.17157 2.24264i −0.234449 0.165781i
\(184\) 2.59808 1.50000i 0.191533 0.110581i
\(185\) −3.69615 5.59808i −0.271747 0.411579i
\(186\) 8.31489 6.91189i 0.609678 0.506804i
\(187\) 0.0995874 + 0.371665i 0.00728255 + 0.0271789i
\(188\) −1.67851 6.26430i −0.122418 0.456871i
\(189\) −7.60660 13.6066i −0.553299 0.989735i
\(190\) 0.535898 9.73205i 0.0388782 0.706037i
\(191\) 10.5858i 0.765961i 0.923757 + 0.382980i \(0.125102\pi\)
−0.923757 + 0.382980i \(0.874898\pi\)
\(192\) −0.724745 1.57313i −0.0523040 0.113531i
\(193\) 11.5911 3.10583i 0.834346 0.223562i 0.183737 0.982975i \(-0.441180\pi\)
0.650609 + 0.759413i \(0.274514\pi\)
\(194\) 7.24264 + 12.5446i 0.519991 + 0.900651i
\(195\) −10.9489 0.349714i −0.784065 0.0250435i
\(196\) −1.00000 1.73205i −0.0714286 0.123718i
\(197\) 6.02082 + 6.02082i 0.428965 + 0.428965i 0.888276 0.459310i \(-0.151903\pi\)
−0.459310 + 0.888276i \(0.651903\pi\)
\(198\) −0.464466 0.221825i −0.0330082 0.0157644i
\(199\) 12.3345 7.12132i 0.874369 0.504817i 0.00557117 0.999984i \(-0.498227\pi\)
0.868798 + 0.495167i \(0.164893\pi\)
\(200\) −4.64016 + 1.86250i −0.328109 + 0.131699i
\(201\) 9.65685 1.65685i 0.681142 0.116865i
\(202\) −12.2426 + 12.2426i −0.861389 + 0.861389i
\(203\) 9.19051 + 2.46259i 0.645048 + 0.172840i
\(204\) −1.34536 + 3.64394i −0.0941941 + 0.255127i
\(205\) 4.45069 5.01910i 0.310850 0.350549i
\(206\) −2.59808 1.50000i −0.181017 0.104510i
\(207\) 7.41970 5.09393i 0.515704 0.354053i
\(208\) 2.00000 + 2.00000i 0.138675 + 0.138675i
\(209\) −0.0857864 + 0.742932i −0.00593397 + 0.0513897i
\(210\) 11.1213 + 3.36396i 0.767444 + 0.232135i
\(211\) −1.74264 + 3.01834i −0.119968 + 0.207791i −0.919755 0.392493i \(-0.871613\pi\)
0.799787 + 0.600284i \(0.204946\pi\)
\(212\) −9.16208 + 2.45497i −0.629254 + 0.168608i
\(213\) −18.2578 1.68228i −1.25100 0.115268i
\(214\) 7.34847 + 4.24264i 0.502331 + 0.290021i
\(215\) −0.568406 9.46979i −0.0387650 0.645834i
\(216\) −2.53553 4.53553i −0.172521 0.308604i
\(217\) 13.2426 13.2426i 0.898969 0.898969i
\(218\) −2.16622 0.580438i −0.146715 0.0393122i
\(219\) −21.6344 + 17.9840i −1.46192 + 1.21524i
\(220\) 0.363961 0.121320i 0.0245382 0.00817942i
\(221\) 6.34315i 0.426686i
\(222\) −0.476756 + 5.17423i −0.0319978 + 0.347272i
\(223\) 16.8895 4.52552i 1.13100 0.303051i 0.355675 0.934610i \(-0.384251\pi\)
0.775328 + 0.631558i \(0.217584\pi\)
\(224\) −1.50000 2.59808i −0.100223 0.173591i
\(225\) −13.4425 + 6.65572i −0.896168 + 0.443714i
\(226\) 10.0000 17.3205i 0.665190 1.15214i
\(227\) 16.2426 + 16.2426i 1.07806 + 1.07806i 0.996683 + 0.0813787i \(0.0259323\pi\)
0.0813787 + 0.996683i \(0.474068\pi\)
\(228\) −5.03723 + 5.62372i −0.333599 + 0.372440i
\(229\) 15.7574i 1.04128i 0.853778 + 0.520638i \(0.174306\pi\)
−0.853778 + 0.520638i \(0.825694\pi\)
\(230\) −1.34486 + 6.57201i −0.0886777 + 0.433346i
\(231\) −0.836338 0.308780i −0.0550270 0.0203162i
\(232\) 3.06350 + 0.820863i 0.201129 + 0.0538923i
\(233\) 2.71379 + 10.1280i 0.177786 + 0.663508i 0.996060 + 0.0886791i \(0.0282646\pi\)
−0.818274 + 0.574828i \(0.805069\pi\)
\(234\) 6.44949 + 5.51399i 0.421616 + 0.360461i
\(235\) 12.9706 + 6.48528i 0.846106 + 0.423053i
\(236\) 5.65685i 0.368230i
\(237\) 11.1855 + 1.03063i 0.726573 + 0.0669467i
\(238\) −1.74131 + 6.49867i −0.112873 + 0.421246i
\(239\) −0.686292 −0.0443925 −0.0221963 0.999754i \(-0.507066\pi\)
−0.0221963 + 0.999754i \(0.507066\pi\)
\(240\) 3.70711 + 1.12132i 0.239293 + 0.0723809i
\(241\) 0.242641 + 0.420266i 0.0156299 + 0.0270717i 0.873735 0.486403i \(-0.161691\pi\)
−0.858105 + 0.513475i \(0.828358\pi\)
\(242\) 10.5967 2.83939i 0.681185 0.182523i
\(243\) −8.64420 12.9722i −0.554526 0.832167i
\(244\) −1.94218 1.12132i −0.124336 0.0717852i
\(245\) 4.38134 + 0.896575i 0.279914 + 0.0572801i
\(246\) −5.12132 + 0.878680i −0.326523 + 0.0560226i
\(247\) 4.53590 11.4641i 0.288612 0.729443i
\(248\) 4.41421 4.41421i 0.280303 0.280303i
\(249\) −2.54516 + 6.89363i −0.161293 + 0.436866i
\(250\) 3.76795 10.5263i 0.238306 0.665740i
\(251\) −14.9941 + 8.65685i −0.946420 + 0.546416i −0.891967 0.452101i \(-0.850675\pi\)
−0.0544529 + 0.998516i \(0.517341\pi\)
\(252\) −5.09393 7.41970i −0.320887 0.467397i
\(253\) 0.133219 0.497180i 0.00837541 0.0312574i
\(254\) 2.65685 0.166706
\(255\) −4.10051 7.65685i −0.256784 0.479491i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 2.13335 7.96178i 0.133075 0.496642i −0.866924 0.498441i \(-0.833906\pi\)
0.999998 + 0.00179903i \(0.000572648\pi\)
\(258\) −4.24264 + 6.00000i −0.264135 + 0.373544i
\(259\) 9.00000i 0.559233i
\(260\) −6.31319 + 0.378937i −0.391528 + 0.0235007i
\(261\) 9.35452 + 1.73862i 0.579030 + 0.107618i
\(262\) 14.4889 + 3.88229i 0.895126 + 0.239848i
\(263\) −0.384419 1.43467i −0.0237043 0.0884656i 0.953060 0.302780i \(-0.0979149\pi\)
−0.976765 + 0.214315i \(0.931248\pi\)
\(264\) −0.278779 0.102927i −0.0171577 0.00633470i
\(265\) 9.48528 18.9706i 0.582676 1.16535i
\(266\) −7.79423 + 10.5000i −0.477895 + 0.643796i
\(267\) 16.7279 + 11.8284i 1.02373 + 0.723888i
\(268\) 5.46410 1.46410i 0.333773 0.0894342i
\(269\) 5.46447 9.46473i 0.333174 0.577075i −0.649958 0.759970i \(-0.725214\pi\)
0.983132 + 0.182895i \(0.0585469\pi\)
\(270\) 11.3497 + 2.48672i 0.690722 + 0.151337i
\(271\) 1.00000 1.73205i 0.0607457 0.105215i −0.834053 0.551684i \(-0.813985\pi\)
0.894799 + 0.446469i \(0.147319\pi\)
\(272\) −0.580438 + 2.16622i −0.0351942 + 0.131347i
\(273\) 12.0000 + 8.48528i 0.726273 + 0.513553i
\(274\) 20.4853i 1.23756i
\(275\) −0.336987 + 0.788905i −0.0203211 + 0.0475728i
\(276\) 3.99585 3.32162i 0.240522 0.199938i
\(277\) 20.4853 20.4853i 1.23084 1.23084i 0.267200 0.963641i \(-0.413901\pi\)
0.963641 0.267200i \(-0.0860985\pi\)
\(278\) −9.89949 + 9.89949i −0.593732 + 0.593732i
\(279\) 12.1700 14.2347i 0.728597 0.852210i
\(280\) 6.57201 + 1.34486i 0.392753 + 0.0803709i
\(281\) 5.34474 3.08579i 0.318840 0.184083i −0.332035 0.943267i \(-0.607735\pi\)
0.650876 + 0.759184i \(0.274402\pi\)
\(282\) −4.70017 10.2022i −0.279891 0.607532i
\(283\) 11.2597 3.01702i 0.669317 0.179343i 0.0918699 0.995771i \(-0.470716\pi\)
0.577447 + 0.816428i \(0.304049\pi\)
\(284\) −10.5858 −0.628151
\(285\) −1.93562 16.7706i −0.114656 0.993405i
\(286\) 0.485281 0.0286953
\(287\) −8.69333 + 2.32937i −0.513151 + 0.137498i
\(288\) −1.69798 2.47323i −0.100054 0.145737i
\(289\) −10.3668 + 5.98528i −0.609812 + 0.352075i
\(290\) −5.91824 + 3.90754i −0.347531 + 0.229459i
\(291\) 16.0382 + 19.2937i 0.940176 + 1.13102i
\(292\) −11.4853 + 11.4853i −0.672125 + 0.672125i
\(293\) 18.3640 18.3640i 1.07283 1.07283i 0.0757037 0.997130i \(-0.475880\pi\)
0.997130 0.0757037i \(-0.0241203\pi\)
\(294\) −2.21441 2.66390i −0.129147 0.155362i
\(295\) −9.46410 8.39230i −0.551021 0.488619i
\(296\) 3.00000i 0.174371i
\(297\) −0.857864 0.242641i −0.0497783 0.0140794i
\(298\) 2.92820 10.9282i 0.169626 0.633054i
\(299\) −4.24264 + 7.34847i −0.245358 + 0.424973i
\(300\) −7.37574 + 4.53856i −0.425838 + 0.262034i
\(301\) −6.36396 + 11.0227i −0.366813 + 0.635338i
\(302\) −10.3624 + 2.77659i −0.596288 + 0.159775i
\(303\) −17.3137 + 24.4853i −0.994647 + 1.40664i
\(304\) −2.59808 + 3.50000i −0.149010 + 0.200739i
\(305\) 4.75736 1.58579i 0.272406 0.0908019i
\(306\) −1.22939 + 6.61465i −0.0702795 + 0.378134i
\(307\) −5.21317 19.4558i −0.297531 1.11040i −0.939186 0.343408i \(-0.888419\pi\)
0.641655 0.766993i \(-0.278248\pi\)
\(308\) −0.497180 0.133219i −0.0283295 0.00759086i
\(309\) −4.87453 1.79970i −0.277303 0.102381i
\(310\) 0.836355 + 13.9339i 0.0475018 + 0.791392i
\(311\) 8.48528i 0.481156i 0.970630 + 0.240578i \(0.0773370\pi\)
−0.970630 + 0.240578i \(0.922663\pi\)
\(312\) 4.00000 + 2.82843i 0.226455 + 0.160128i
\(313\) 5.57919 20.8218i 0.315355 1.17692i −0.608304 0.793704i \(-0.708150\pi\)
0.923659 0.383216i \(-0.125183\pi\)
\(314\) 5.91421 + 10.2437i 0.333758 + 0.578086i
\(315\) 19.9706 + 2.48528i 1.12521 + 0.140030i
\(316\) 6.48528 0.364826
\(317\) 7.36491 27.4862i 0.413655 1.54378i −0.373860 0.927485i \(-0.621966\pi\)
0.787515 0.616296i \(-0.211367\pi\)
\(318\) −14.9216 + 6.87441i −0.836762 + 0.385498i
\(319\) 0.471253 0.272078i 0.0263851 0.0152334i
\(320\) 2.19067 + 0.448288i 0.122462 + 0.0250600i
\(321\) 13.7873 + 5.09032i 0.769530 + 0.284114i
\(322\) 6.36396 6.36396i 0.354650 0.354650i
\(323\) 9.67025 1.43026i 0.538067 0.0795817i
\(324\) −5.65685 7.00000i −0.314270 0.388889i
\(325\) 8.73205 11.1244i 0.484367 0.617068i
\(326\) −17.4436 10.0711i −0.966112 0.557785i
\(327\) −3.86798 0.356397i −0.213900 0.0197088i
\(328\) −2.89778 + 0.776457i −0.160003 + 0.0428727i
\(329\) −9.72792 16.8493i −0.536318 0.928930i
\(330\) 0.585786 0.313708i 0.0322465 0.0172691i
\(331\) −12.5147 −0.687871 −0.343936 0.938993i \(-0.611760\pi\)
−0.343936 + 0.938993i \(0.611760\pi\)
\(332\) −1.09808 + 4.09808i −0.0602648 + 0.224911i
\(333\) 0.701625 + 8.97261i 0.0384488 + 0.491696i
\(334\) 23.4853i 1.28506i
\(335\) −5.65685 + 11.3137i −0.309067 + 0.618134i
\(336\) −3.32162 3.99585i −0.181209 0.217992i
\(337\) 0.643238 + 2.40060i 0.0350394 + 0.130769i 0.981230 0.192841i \(-0.0617701\pi\)
−0.946191 + 0.323610i \(0.895103\pi\)
\(338\) 4.82963 + 1.29410i 0.262697 + 0.0703895i
\(339\) 11.9980 32.4969i 0.651642 1.76499i
\(340\) −2.76305 4.18482i −0.149847 0.226954i
\(341\) 1.07107i 0.0580016i
\(342\) −6.95195 + 11.0757i −0.375918 + 0.598904i
\(343\) 10.6066 + 10.6066i 0.572703 + 0.572703i
\(344\) −2.12132 + 3.67423i −0.114374 + 0.198101i
\(345\) −0.370927 + 11.6130i −0.0199701 + 0.625224i
\(346\) −9.98528 17.2950i −0.536812 0.929786i
\(347\) −10.5967 + 2.83939i −0.568863 + 0.152426i −0.531775 0.846886i \(-0.678475\pi\)
−0.0370881 + 0.999312i \(0.511808\pi\)
\(348\) 5.47015 + 0.504022i 0.293231 + 0.0270184i
\(349\) 22.2426i 1.19062i 0.803496 + 0.595311i \(0.202971\pi\)
−0.803496 + 0.595311i \(0.797029\pi\)
\(350\) −12.0000 + 9.00000i −0.641427 + 0.481070i
\(351\) 12.6250 + 7.52396i 0.673871 + 0.401599i
\(352\) −0.165727 0.0444063i −0.00883326 0.00236687i
\(353\) −3.51472 + 3.51472i −0.187070 + 0.187070i −0.794428 0.607358i \(-0.792229\pi\)
0.607358 + 0.794428i \(0.292229\pi\)
\(354\) 1.65685 + 9.65685i 0.0880608 + 0.513256i
\(355\) 15.7047 17.7104i 0.833518 0.939969i
\(356\) 10.2437 + 5.91421i 0.542916 + 0.313453i
\(357\) −1.06919 + 11.6039i −0.0565876 + 0.614146i
\(358\) −9.02479 + 2.41818i −0.476975 + 0.127805i
\(359\) −4.60660 + 7.97887i −0.243127 + 0.421109i −0.961603 0.274443i \(-0.911507\pi\)
0.718476 + 0.695551i \(0.244840\pi\)
\(360\) 6.65685 + 0.828427i 0.350847 + 0.0436619i
\(361\) 18.5000 + 4.33013i 0.973684 + 0.227901i
\(362\) −10.2426 10.2426i −0.538341 0.538341i
\(363\) 17.2581 7.95086i 0.905818 0.417312i
\(364\) 7.34847 + 4.24264i 0.385164 + 0.222375i
\(365\) −2.17610 36.2544i −0.113902 1.89764i
\(366\) −3.64394 1.34536i −0.190472 0.0703232i
\(367\) −5.79555 1.55291i −0.302526 0.0810615i 0.104363 0.994539i \(-0.466720\pi\)
−0.406889 + 0.913478i \(0.633386\pi\)
\(368\) 2.12132 2.12132i 0.110581 0.110581i
\(369\) −8.48528 + 3.00000i −0.441726 + 0.156174i
\(370\) −5.01910 4.45069i −0.260930 0.231380i
\(371\) −24.6435 + 14.2279i −1.27943 + 0.738677i
\(372\) 6.24264 8.82843i 0.323666 0.457733i
\(373\) 12.3640 + 12.3640i 0.640182 + 0.640182i 0.950600 0.310418i \(-0.100469\pi\)
−0.310418 + 0.950600i \(0.600469\pi\)
\(374\) 0.192388 + 0.333226i 0.00994815 + 0.0172307i
\(375\) 3.34922 19.0731i 0.172953 0.984930i
\(376\) −3.24264 5.61642i −0.167226 0.289645i
\(377\) −8.66490 + 2.32175i −0.446265 + 0.119576i
\(378\) −10.8691 11.1742i −0.559044 0.574741i
\(379\) 22.4853i 1.15499i −0.816394 0.577496i \(-0.804030\pi\)
0.816394 0.577496i \(-0.195970\pi\)
\(380\) −2.00120 9.53914i −0.102659 0.489348i
\(381\) 4.53553 0.778175i 0.232362 0.0398671i
\(382\) 2.73980 + 10.2251i 0.140181 + 0.523161i
\(383\) 7.89017 + 29.4465i 0.403169 + 1.50465i 0.807408 + 0.589994i \(0.200870\pi\)
−0.404239 + 0.914653i \(0.632464\pi\)
\(384\) −1.10721 1.33195i −0.0565019 0.0679709i
\(385\) 0.960478 0.634159i 0.0489505 0.0323198i
\(386\) 10.3923 6.00000i 0.528954 0.305392i
\(387\) −5.48528 + 11.4853i −0.278833 + 0.583830i
\(388\) 10.2426 + 10.2426i 0.519991 + 0.519991i
\(389\) −2.46447 4.26858i −0.124953 0.216426i 0.796761 0.604294i \(-0.206545\pi\)
−0.921715 + 0.387868i \(0.873211\pi\)
\(390\) −10.6663 + 2.49598i −0.540109 + 0.126389i
\(391\) −6.72792 −0.340246
\(392\) −1.41421 1.41421i −0.0714286 0.0714286i
\(393\) 25.8712 + 2.38378i 1.30503 + 0.120246i
\(394\) 7.37396 + 4.25736i 0.371495 + 0.214483i
\(395\) −9.62133 + 10.8501i −0.484102 + 0.545927i
\(396\) −0.506052 0.0940542i −0.0254301 0.00472640i
\(397\) −2.06293 7.69897i −0.103536 0.386400i 0.894639 0.446789i \(-0.147433\pi\)
−0.998175 + 0.0603888i \(0.980766\pi\)
\(398\) 10.0711 10.0711i 0.504817 0.504817i
\(399\) −10.2302 + 20.2075i −0.512151 + 1.01164i
\(400\) −4.00000 + 3.00000i −0.200000 + 0.150000i
\(401\) −29.9882 17.3137i −1.49754 0.864605i −0.497544 0.867439i \(-0.665765\pi\)
−0.999996 + 0.00283317i \(0.999098\pi\)
\(402\) 8.89898 4.09978i 0.443841 0.204478i
\(403\) −4.56993 + 17.0552i −0.227644 + 0.849581i
\(404\) −8.65685 + 14.9941i −0.430695 + 0.745985i
\(405\) 20.1035 + 0.920846i 0.998953 + 0.0457572i
\(406\) 9.51472 0.472208
\(407\) 0.363961 + 0.363961i 0.0180409 + 0.0180409i
\(408\) −0.356397 + 3.86798i −0.0176443 + 0.191494i
\(409\) −21.1794 + 12.2279i −1.04725 + 0.604632i −0.921879 0.387478i \(-0.873346\pi\)
−0.125374 + 0.992110i \(0.540013\pi\)
\(410\) 3.00000 6.00000i 0.148159 0.296319i
\(411\) −6.00000 34.9706i −0.295958 1.72497i
\(412\) −2.89778 0.776457i −0.142763 0.0382533i
\(413\) 4.39230 + 16.3923i 0.216131 + 0.806613i
\(414\) 5.84847 6.84072i 0.287437 0.336203i
\(415\) −5.22715 7.91688i −0.256591 0.388624i
\(416\) 2.44949 + 1.41421i 0.120096 + 0.0693375i
\(417\) −14.0000 + 19.7990i −0.685583 + 0.969561i
\(418\) 0.109422 + 0.739821i 0.00535199 + 0.0361858i
\(419\) 29.8284 1.45721 0.728607 0.684932i \(-0.240168\pi\)
0.728607 + 0.684932i \(0.240168\pi\)
\(420\) 11.6130 + 0.370927i 0.566658 + 0.0180994i
\(421\) 10.4853 18.1610i 0.511021 0.885115i −0.488897 0.872341i \(-0.662601\pi\)
0.999918 0.0127735i \(-0.00406603\pi\)
\(422\) −0.902057 + 3.36652i −0.0439115 + 0.163880i
\(423\) −11.0119 16.0396i −0.535415 0.779872i
\(424\) −8.21449 + 4.74264i −0.398931 + 0.230323i
\(425\) 11.1005 + 1.58579i 0.538454 + 0.0769219i
\(426\) −18.0711 + 3.10051i −0.875546 + 0.150220i
\(427\) −6.49867 1.74131i −0.314493 0.0842681i
\(428\) 8.19615 + 2.19615i 0.396176 + 0.106155i
\(429\) 0.828427 0.142136i 0.0399968 0.00686237i
\(430\) −3.00000 9.00000i −0.144673 0.434019i
\(431\) 9.79796 5.65685i 0.471951 0.272481i −0.245105 0.969497i \(-0.578822\pi\)
0.717056 + 0.697015i \(0.245489\pi\)
\(432\) −3.62302 3.72474i −0.174313 0.179207i
\(433\) 2.46259 9.19051i 0.118345 0.441668i −0.881171 0.472798i \(-0.843244\pi\)
0.999515 + 0.0311302i \(0.00991067\pi\)
\(434\) 9.36396 16.2189i 0.449485 0.778530i
\(435\) −8.95857 + 8.40400i −0.429530 + 0.402941i
\(436\) −2.24264 −0.107403
\(437\) −12.1595 4.81105i −0.581669 0.230144i
\(438\) −16.2426 + 22.9706i −0.776103 + 1.09758i
\(439\) 25.5095 + 14.7279i 1.21750 + 0.702925i 0.964383 0.264510i \(-0.0852101\pi\)
0.253119 + 0.967435i \(0.418543\pi\)
\(440\) 0.320159 0.211386i 0.0152630 0.0100775i
\(441\) −4.56048 3.89898i −0.217166 0.185666i
\(442\) −1.64173 6.12701i −0.0780890 0.291432i
\(443\) 33.0759 + 8.86265i 1.57148 + 0.421077i 0.936276 0.351266i \(-0.114249\pi\)
0.635205 + 0.772343i \(0.280915\pi\)
\(444\) 0.878680 + 5.12132i 0.0417003 + 0.243047i
\(445\) −25.0919 + 8.36396i −1.18947 + 0.396490i
\(446\) 15.1427 8.74264i 0.717028 0.413976i
\(447\) 1.79796 19.5133i 0.0850405 0.922946i
\(448\) −2.12132 2.12132i −0.100223 0.100223i
\(449\) 17.8284 0.841375 0.420688 0.907205i \(-0.361789\pi\)
0.420688 + 0.907205i \(0.361789\pi\)
\(450\) −11.2619 + 9.90811i −0.530889 + 0.467073i
\(451\) −0.257359 + 0.445759i −0.0121186 + 0.0209900i
\(452\) 5.17638 19.3185i 0.243476 0.908667i
\(453\) −16.8764 + 7.77501i −0.792924 + 0.365302i
\(454\) 19.8931 + 11.4853i 0.933629 + 0.539031i
\(455\) −18.0000 + 6.00000i −0.843853 + 0.281284i
\(456\) −3.41007 + 6.73583i −0.159691 + 0.315434i
\(457\) −24.9706 + 24.9706i −1.16807 + 1.16807i −0.185413 + 0.982661i \(0.559362\pi\)
−0.982661 + 0.185413i \(0.940638\pi\)
\(458\) 4.07830 + 15.2204i 0.190567 + 0.711204i
\(459\) −0.161314 + 11.6520i −0.00752947 + 0.543868i
\(460\) 0.401924 + 6.69615i 0.0187398 + 0.312210i
\(461\) 21.7482 + 12.5563i 1.01292 + 0.584807i 0.912044 0.410092i \(-0.134503\pi\)
0.100872 + 0.994899i \(0.467837\pi\)
\(462\) −0.887758 0.0817984i −0.0413023 0.00380560i
\(463\) −29.3345 29.3345i −1.36329 1.36329i −0.869687 0.493604i \(-0.835679\pi\)
−0.493604 0.869687i \(-0.664321\pi\)
\(464\) 3.17157 0.147237
\(465\) 5.50889 + 23.5417i 0.255469 + 1.09172i
\(466\) 5.24264 + 9.08052i 0.242861 + 0.420647i
\(467\) −1.75736 1.75736i −0.0813209 0.0813209i 0.665276 0.746597i \(-0.268314\pi\)
−0.746597 + 0.665276i \(0.768314\pi\)
\(468\) 7.65685 + 3.65685i 0.353938 + 0.169038i
\(469\) 14.6969 8.48528i 0.678642 0.391814i
\(470\) 14.2071 + 2.90727i 0.655325 + 0.134102i
\(471\) 13.0965 + 15.7549i 0.603455 + 0.725947i
\(472\) 1.46410 + 5.46410i 0.0673907 + 0.251506i
\(473\) 0.188400 + 0.703119i 0.00866265 + 0.0323294i
\(474\) 11.0711 1.89949i 0.508511 0.0872467i
\(475\) 18.9282 + 10.8038i 0.868486 + 0.495715i
\(476\) 6.72792i 0.308374i
\(477\) −23.4593 + 16.1058i −1.07413 + 0.737433i
\(478\) −0.662907 + 0.177625i −0.0303206 + 0.00812439i
\(479\) 15.1924 + 26.3140i 0.694158 + 1.20232i 0.970464 + 0.241247i \(0.0775564\pi\)
−0.276306 + 0.961070i \(0.589110\pi\)
\(480\) 3.87101 + 0.123642i 0.176687 + 0.00564348i
\(481\) −4.24264 7.34847i −0.193448 0.335061i
\(482\) 0.343146 + 0.343146i 0.0156299 + 0.0156299i
\(483\) 9.00000 12.7279i 0.409514 0.579141i
\(484\) 9.50079 5.48528i 0.431854 0.249331i
\(485\) −32.3319 + 1.94066i −1.46812 + 0.0881208i
\(486\) −11.7071 10.2929i −0.531045 0.466895i
\(487\) 24.6066 24.6066i 1.11503 1.11503i 0.122572 0.992460i \(-0.460886\pi\)
0.992460 0.122572i \(-0.0391142\pi\)
\(488\) −2.16622 0.580438i −0.0980604 0.0262752i
\(489\) −32.7278 12.0833i −1.48000 0.546425i
\(490\) 4.46410 0.267949i 0.201668 0.0121047i
\(491\) 5.93908 + 3.42893i 0.268027 + 0.154746i 0.627991 0.778221i \(-0.283878\pi\)
−0.359964 + 0.932966i \(0.617211\pi\)
\(492\) −4.71940 + 2.17423i −0.212767 + 0.0980221i
\(493\) −5.02944 5.02944i −0.226514 0.226514i
\(494\) 1.41421 12.2474i 0.0636285 0.551039i
\(495\) 0.908117 0.707107i 0.0408168 0.0317821i
\(496\) 3.12132 5.40629i 0.140151 0.242749i
\(497\) −30.6753 + 8.21941i −1.37597 + 0.368691i
\(498\) −0.674235 + 7.31747i −0.0302132 + 0.327904i
\(499\) 32.8835 + 18.9853i 1.47207 + 0.849898i 0.999507 0.0314008i \(-0.00999684\pi\)
0.472560 + 0.881299i \(0.343330\pi\)
\(500\) 0.915158 11.1428i 0.0409271 0.498322i
\(501\) −6.87868 40.0919i −0.307317 1.79117i
\(502\) −12.2426 + 12.2426i −0.546416 + 0.546416i
\(503\) −17.3582 4.65112i −0.773965 0.207383i −0.149843 0.988710i \(-0.547877\pi\)
−0.624123 + 0.781326i \(0.714543\pi\)
\(504\) −6.84072 5.84847i −0.304710 0.260512i
\(505\) −12.2426 36.7279i −0.544790 1.63437i
\(506\) 0.514719i 0.0228820i
\(507\) 8.62372 + 0.794593i 0.382993 + 0.0352891i
\(508\) 2.56632 0.687644i 0.113862 0.0305093i
\(509\) −6.36396 11.0227i −0.282078 0.488573i 0.689819 0.723982i \(-0.257690\pi\)
−0.971896 + 0.235409i \(0.924357\pi\)
\(510\) −5.94252 6.33466i −0.263139 0.280504i
\(511\) −24.3640 + 42.1996i −1.07780 + 1.86680i
\(512\) −0.707107 0.707107i −0.0312500 0.0312500i
\(513\) −8.62372 + 20.9435i −0.380747 + 0.924679i
\(514\) 8.24264i 0.363567i
\(515\) 5.59808 3.69615i 0.246681 0.162872i
\(516\) −2.54516 + 6.89363i −0.112045 + 0.303475i
\(517\) −1.07478 0.287988i −0.0472690 0.0126657i
\(518\) 2.32937 + 8.69333i 0.102347 + 0.381963i
\(519\) −22.1115 26.5998i −0.970589 1.16760i
\(520\) −6.00000 + 2.00000i −0.263117 + 0.0877058i
\(521\) 35.3137i 1.54712i 0.633722 + 0.773561i \(0.281526\pi\)
−0.633722 + 0.773561i \(0.718474\pi\)
\(522\) 9.48576 0.741752i 0.415181 0.0324656i
\(523\) −6.12284 + 22.8508i −0.267733 + 0.999194i 0.692823 + 0.721108i \(0.256367\pi\)
−0.960556 + 0.278086i \(0.910300\pi\)
\(524\) 15.0000 0.655278
\(525\) −17.8492 + 18.8787i −0.779005 + 0.823933i
\(526\) −0.742641 1.28629i −0.0323807 0.0560850i
\(527\) −13.5230 + 3.62347i −0.589069 + 0.157841i
\(528\) −0.295919 0.0272661i −0.0128782 0.00118661i
\(529\) −12.1244 7.00000i −0.527146 0.304348i
\(530\) 4.25214 20.7791i 0.184701 0.902588i
\(531\) 5.65685 + 16.0000i 0.245487 + 0.694341i
\(532\) −4.81105 + 12.1595i −0.208585 + 0.527182i
\(533\) 6.00000 6.00000i 0.259889 0.259889i
\(534\) 19.2194 + 7.09588i 0.831703 + 0.307069i
\(535\) −15.8338 + 10.4543i −0.684553 + 0.451979i
\(536\) 4.89898 2.82843i 0.211604 0.122169i
\(537\) −14.6980 + 6.77140i −0.634266 + 0.292207i
\(538\) 2.82862 10.5565i 0.121950 0.455125i
\(539\) −0.343146 −0.0147803
\(540\) 11.6066 0.535534i 0.499469 0.0230457i
\(541\) −0.636039 1.10165i −0.0273455 0.0473637i 0.852029 0.523495i \(-0.175372\pi\)
−0.879374 + 0.476131i \(0.842039\pi\)
\(542\) 0.517638 1.93185i 0.0222345 0.0829801i
\(543\) −20.4853 14.4853i −0.879108 0.621623i
\(544\) 2.24264i 0.0961524i
\(545\) 3.32710 3.75201i 0.142517 0.160718i
\(546\) 13.7873 + 5.09032i 0.590040 + 0.217846i
\(547\) −18.7929 5.03554i −0.803526 0.215304i −0.166395 0.986059i \(-0.553213\pi\)
−0.637132 + 0.770755i \(0.719879\pi\)
\(548\) −5.30198 19.7873i −0.226489 0.845270i
\(549\) −6.61465 1.22939i −0.282306 0.0524690i
\(550\) −0.121320 + 0.849242i −0.00517312 + 0.0362118i
\(551\) −5.49333 12.6863i −0.234024 0.540454i
\(552\) 3.00000 4.24264i 0.127688 0.180579i
\(553\) 18.7929 5.03554i 0.799155 0.214133i
\(554\) 14.4853 25.0892i 0.615421 1.06594i
\(555\) −9.87171 6.12775i −0.419031 0.260108i
\(556\) −7.00000 + 12.1244i −0.296866 + 0.514187i
\(557\) −3.61585 + 13.4945i −0.153208 + 0.571781i 0.846044 + 0.533114i \(0.178978\pi\)
−0.999252 + 0.0386680i \(0.987689\pi\)
\(558\) 8.07107 16.8995i 0.341676 0.715413i
\(559\) 12.0000i 0.507546i
\(560\) 6.69615 0.401924i 0.282964 0.0169844i
\(561\) 0.426027 + 0.512503i 0.0179869 + 0.0216379i
\(562\) 4.36396 4.36396i 0.184083 0.184083i
\(563\) −27.1716 + 27.1716i −1.14515 + 1.14515i −0.157650 + 0.987495i \(0.550392\pi\)
−0.987495 + 0.157650i \(0.949608\pi\)
\(564\) −7.18054 8.63808i −0.302355 0.363729i
\(565\) 24.6410 + 37.3205i 1.03666 + 1.57009i
\(566\) 10.0951 5.82843i 0.424330 0.244987i
\(567\) −21.8275 15.8921i −0.916669 0.667407i
\(568\) −10.2251 + 2.73980i −0.429035 + 0.114960i
\(569\) 10.7990 0.452717 0.226359 0.974044i \(-0.427318\pi\)
0.226359 + 0.974044i \(0.427318\pi\)
\(570\) −6.21021 15.6982i −0.260117 0.657525i
\(571\) −10.4853 −0.438795 −0.219398 0.975636i \(-0.570409\pi\)
−0.219398 + 0.975636i \(0.570409\pi\)
\(572\) 0.468746 0.125600i 0.0195992 0.00525160i
\(573\) 7.67199 + 16.6528i 0.320502 + 0.695682i
\(574\) −7.79423 + 4.50000i −0.325325 + 0.187826i
\(575\) −11.7992 9.26174i −0.492059 0.386241i
\(576\) −2.28024 1.94949i −0.0950100 0.0812287i
\(577\) −2.48528 + 2.48528i −0.103464 + 0.103464i −0.756944 0.653480i \(-0.773308\pi\)
0.653480 + 0.756944i \(0.273308\pi\)
\(578\) −8.46447 + 8.46447i −0.352075 + 0.352075i
\(579\) 15.9834 13.2865i 0.664248 0.552167i
\(580\) −4.70523 + 5.30614i −0.195374 + 0.220326i
\(581\) 12.7279i 0.528043i
\(582\) 20.4853 + 14.4853i 0.849142 + 0.600434i
\(583\) −0.421207 + 1.57196i −0.0174446 + 0.0651041i
\(584\) −8.12132 + 14.0665i −0.336063 + 0.582078i
\(585\) −17.4775 + 7.38499i −0.722604 + 0.305332i
\(586\) 12.9853 22.4912i 0.536417 0.929102i
\(587\) −39.5745 + 10.6040i −1.63342 + 0.437672i −0.954903 0.296917i \(-0.904042\pi\)
−0.678512 + 0.734589i \(0.737375\pi\)
\(588\) −2.82843 2.00000i −0.116642 0.0824786i
\(589\) −27.0314 3.12132i −1.11381 0.128612i
\(590\) −11.3137 5.65685i −0.465778 0.232889i
\(591\) 13.8351 + 5.10798i 0.569100 + 0.210114i
\(592\) 0.776457 + 2.89778i 0.0319122 + 0.119098i
\(593\) −37.1739 9.96072i −1.52655 0.409038i −0.604658 0.796485i \(-0.706690\pi\)
−0.921892 + 0.387447i \(0.873357\pi\)
\(594\) −0.891433 0.0123413i −0.0365760 0.000506368i
\(595\) −11.2560 9.98130i −0.461452 0.409194i
\(596\) 11.3137i 0.463428i
\(597\) 14.2426 20.1421i 0.582912 0.824363i
\(598\) −2.19615 + 8.19615i −0.0898074 + 0.335166i
\(599\) −11.8492 20.5235i −0.484147 0.838567i 0.515687 0.856777i \(-0.327537\pi\)
−0.999834 + 0.0182098i \(0.994203\pi\)
\(600\) −5.94975 + 6.29289i −0.242897 + 0.256906i
\(601\) 23.0000 0.938190 0.469095 0.883148i \(-0.344580\pi\)
0.469095 + 0.883148i \(0.344580\pi\)
\(602\) −3.29423 + 12.2942i −0.134263 + 0.501075i
\(603\) 13.9907 9.60521i 0.569746 0.391154i
\(604\) −9.29065 + 5.36396i −0.378031 + 0.218256i
\(605\) −4.91797 + 24.0329i −0.199944 + 0.977076i
\(606\) −10.3865 + 28.1321i −0.421923 + 1.14279i
\(607\) −4.36396 + 4.36396i −0.177128 + 0.177128i −0.790102 0.612975i \(-0.789973\pi\)
0.612975 + 0.790102i \(0.289973\pi\)
\(608\) −1.60368 + 4.05317i −0.0650379 + 0.164378i
\(609\) 16.2426 2.78680i 0.658185 0.112927i
\(610\) 4.18482 2.76305i 0.169439 0.111873i
\(611\) 15.8856 + 9.17157i 0.642664 + 0.371042i
\(612\) 0.524498 + 6.70745i 0.0212016 + 0.271132i
\(613\) −10.4310 + 2.79498i −0.421305 + 0.112888i −0.463242 0.886232i \(-0.653314\pi\)
0.0419368 + 0.999120i \(0.486647\pi\)
\(614\) −10.0711 17.4436i −0.406435 0.703966i
\(615\) 3.36396 11.1213i 0.135648 0.448455i
\(616\) −0.514719 −0.0207386
\(617\) −8.32977 + 31.0871i −0.335344 + 1.25152i 0.568152 + 0.822924i \(0.307659\pi\)
−0.903496 + 0.428597i \(0.859008\pi\)
\(618\) −5.17423 0.476756i −0.208138 0.0191779i
\(619\) 24.9411i 1.00247i −0.865312 0.501234i \(-0.832879\pi\)
0.865312 0.501234i \(-0.167121\pi\)
\(620\) 4.41421 + 13.2426i 0.177279 + 0.531837i
\(621\) 7.98036 13.3908i 0.320241 0.537355i
\(622\) 2.19615 + 8.19615i 0.0880577 + 0.328636i
\(623\) 34.2761 + 9.18427i 1.37324 + 0.367960i
\(624\) 4.59575 + 1.69677i 0.183977 + 0.0679253i
\(625\) 17.2846 + 18.0622i 0.691384 + 0.722487i
\(626\) 21.5563i 0.861565i
\(627\) 0.403483 + 1.23090i 0.0161136 + 0.0491576i
\(628\) 8.36396 + 8.36396i 0.333758 + 0.333758i
\(629\) 3.36396 5.82655i 0.134130 0.232320i
\(630\) 19.9333 2.76816i 0.794162 0.110286i
\(631\) 0.121320 + 0.210133i 0.00482969 + 0.00836526i 0.868430 0.495812i \(-0.165129\pi\)
−0.863600 + 0.504177i \(0.831796\pi\)
\(632\) 6.26430 1.67851i 0.249181 0.0667677i
\(633\) −0.553876 + 6.01122i −0.0220146 + 0.238925i
\(634\) 28.4558i 1.13013i
\(635\) −2.65685 + 5.31371i −0.105434 + 0.210868i
\(636\) −12.6339 + 10.5022i −0.500968 + 0.416438i
\(637\) 5.46410 + 1.46410i 0.216496 + 0.0580098i
\(638\) 0.384776 0.384776i 0.0152334 0.0152334i
\(639\) −29.9411 + 10.5858i −1.18445 + 0.418767i
\(640\) 2.23205 0.133975i 0.0882296 0.00529581i
\(641\) −15.2913 8.82843i −0.603969 0.348702i 0.166632 0.986019i \(-0.446711\pi\)
−0.770602 + 0.637317i \(0.780044\pi\)
\(642\) 14.6349 + 1.34847i 0.577595 + 0.0532198i
\(643\) 16.0206 4.29272i 0.631792 0.169288i 0.0713094 0.997454i \(-0.477282\pi\)
0.560483 + 0.828166i \(0.310616\pi\)
\(644\) 4.50000 7.79423i 0.177325 0.307136i
\(645\) −7.75736 14.4853i −0.305446 0.570357i
\(646\) 8.97056 3.88437i 0.352942 0.152828i
\(647\) −12.7071 12.7071i −0.499568 0.499568i 0.411735 0.911303i \(-0.364923\pi\)
−0.911303 + 0.411735i \(0.864923\pi\)
\(648\) −7.27583 5.29738i −0.285822 0.208101i
\(649\) 0.840532 + 0.485281i 0.0329938 + 0.0190490i
\(650\) 5.55532 13.0053i 0.217898 0.510111i
\(651\) 11.2349 30.4300i 0.440330 1.19264i
\(652\) −19.4558 5.21317i −0.761948 0.204163i
\(653\) −14.8492 + 14.8492i −0.581096 + 0.581096i −0.935204 0.354109i \(-0.884784\pi\)
0.354109 + 0.935204i \(0.384784\pi\)
\(654\) −3.82843 + 0.656854i −0.149703 + 0.0256850i
\(655\) −22.2535 + 25.0955i −0.869515 + 0.980562i
\(656\) −2.59808 + 1.50000i −0.101438 + 0.0585652i
\(657\) −21.0000 + 43.9706i −0.819288 + 1.71546i
\(658\) −13.7574 13.7574i −0.536318 0.536318i
\(659\) 19.7132 + 34.1443i 0.767917 + 1.33007i 0.938690 + 0.344762i \(0.112040\pi\)
−0.170773 + 0.985310i \(0.554626\pi\)
\(660\) 0.484633 0.454632i 0.0188643 0.0176965i
\(661\) −2.87868 4.98602i −0.111968 0.193934i 0.804596 0.593823i \(-0.202382\pi\)
−0.916564 + 0.399889i \(0.869049\pi\)
\(662\) −12.0883 + 3.23905i −0.469825 + 0.125889i
\(663\) −4.59716 9.97861i −0.178539 0.387537i
\(664\) 4.24264i 0.164646i
\(665\) −13.2058 26.0885i −0.512098 1.01167i
\(666\) 3.00000 + 8.48528i 0.116248 + 0.328798i
\(667\) 2.46259 + 9.19051i 0.0953519 + 0.355858i
\(668\) −6.07844 22.6850i −0.235182 0.877711i
\(669\) 23.2895 19.3598i 0.900426 0.748494i
\(670\) −2.53590 + 12.3923i −0.0979703 + 0.478757i
\(671\) −0.333226 + 0.192388i −0.0128640 + 0.00742706i
\(672\) −4.24264 3.00000i −0.163663 0.115728i
\(673\) −28.9706 28.9706i −1.11673 1.11673i −0.992218 0.124515i \(-0.960262\pi\)
−0.124515 0.992218i \(-0.539738\pi\)
\(674\) 1.24264 + 2.15232i 0.0478647 + 0.0829041i
\(675\) −16.3232 + 20.2127i −0.628279 + 0.777988i
\(676\) 5.00000 0.192308
\(677\) 34.6066 + 34.6066i 1.33004 + 1.33004i 0.905329 + 0.424711i \(0.139624\pi\)
0.424711 + 0.905329i \(0.360376\pi\)
\(678\) 3.17837 34.4949i 0.122065 1.32477i
\(679\) 37.6339 + 21.7279i 1.44426 + 0.833841i
\(680\) −3.75201 3.32710i −0.143883 0.127588i
\(681\) 37.3236 + 13.7801i 1.43024 + 0.528053i
\(682\) −0.277213 1.03457i −0.0106150 0.0396158i
\(683\) −0.899495 + 0.899495i −0.0344182 + 0.0344182i −0.724106 0.689688i \(-0.757748\pi\)
0.689688 + 0.724106i \(0.257748\pi\)
\(684\) −3.84847 + 12.4976i −0.147150 + 0.477857i
\(685\) 40.9706 + 20.4853i 1.56540 + 0.782702i
\(686\) 12.9904 + 7.50000i 0.495975 + 0.286351i
\(687\) 11.4201 + 24.7884i 0.435703 + 0.945737i
\(688\) −1.09808 + 4.09808i −0.0418638 + 0.156238i
\(689\) 13.4142 23.2341i 0.511041 0.885149i
\(690\) 2.64738 + 11.3133i 0.100784 + 0.430691i
\(691\) −27.9706 −1.06405 −0.532025 0.846729i \(-0.678569\pi\)
−0.532025 + 0.846729i \(0.678569\pi\)
\(692\) −14.1213 14.1213i −0.536812 0.536812i
\(693\) −1.53946 + 0.120380i −0.0584791 + 0.00457285i
\(694\) −9.50079 + 5.48528i −0.360645 + 0.208218i
\(695\) −9.89949 29.6985i −0.375509 1.12653i
\(696\) 5.41421 0.928932i 0.205225 0.0352111i
\(697\) 6.49867 + 1.74131i 0.246155 + 0.0659570i
\(698\) 5.75682 + 21.4847i 0.217899 + 0.813209i
\(699\) 11.6094 + 13.9659i 0.439107 + 0.528238i
\(700\) −9.26174 + 11.7992i −0.350061 + 0.445966i
\(701\) 28.7635 + 16.6066i 1.08638 + 0.627223i 0.932611 0.360884i \(-0.117525\pi\)
0.153771 + 0.988107i \(0.450858\pi\)
\(702\) 14.1421 + 4.00000i 0.533761 + 0.150970i
\(703\) 10.2462 8.12493i 0.386445 0.306437i
\(704\) −0.171573 −0.00646640
\(705\) 25.1046 + 0.801856i 0.945493 + 0.0301996i
\(706\) −2.48528 + 4.30463i −0.0935348 + 0.162007i
\(707\) −13.4434 + 50.1713i −0.505589 + 1.88688i
\(708\) 4.09978 + 8.89898i 0.154079 + 0.334444i
\(709\) −37.8440 + 21.8492i −1.42126 + 0.820566i −0.996407 0.0846962i \(-0.973008\pi\)
−0.424854 + 0.905262i \(0.639675\pi\)
\(710\) 10.5858 21.1716i 0.397277 0.794555i
\(711\) 18.3431 6.48528i 0.687922 0.243217i
\(712\) 11.4254 + 3.06142i 0.428184 + 0.114732i
\(713\) 18.0898 + 4.84714i 0.677468 + 0.181527i
\(714\) 1.97056 + 11.4853i 0.0737465 + 0.429826i
\(715\) −0.485281 + 0.970563i −0.0181485 + 0.0362970i
\(716\) −8.09140 + 4.67157i −0.302390 + 0.174585i
\(717\) −1.07963 + 0.497386i −0.0403194 + 0.0185752i
\(718\) −2.38455 + 8.89927i −0.0889907 + 0.332118i
\(719\) 3.70711 6.42090i 0.138252 0.239459i −0.788583 0.614928i \(-0.789185\pi\)
0.926835 + 0.375469i \(0.122518\pi\)
\(720\) 6.64444 0.922722i 0.247624 0.0343878i
\(721\) −9.00000 −0.335178
\(722\) 18.9903 0.605571i 0.706748 0.0225370i
\(723\) 0.686292 + 0.485281i 0.0255235 + 0.0180478i
\(724\) −12.5446 7.24264i −0.466217 0.269171i
\(725\) −1.89684 15.7440i −0.0704470 0.584718i
\(726\) 14.6123 12.1467i 0.542312 0.450805i
\(727\) −3.92669 14.6546i −0.145633 0.543510i −0.999726 0.0233900i \(-0.992554\pi\)
0.854093 0.520120i \(-0.174113\pi\)
\(728\) 8.19615 + 2.19615i 0.303770 + 0.0813948i
\(729\) −23.0000 14.1421i −0.851852 0.523783i
\(730\) −11.4853 34.4558i −0.425089 1.27527i
\(731\) 8.23999 4.75736i 0.304767 0.175957i
\(732\) −3.86798 0.356397i −0.142965 0.0131728i
\(733\) −8.12132 8.12132i −0.299968 0.299968i 0.541033 0.841001i \(-0.318033\pi\)
−0.841001 + 0.541033i \(0.818033\pi\)
\(734\) −6.00000 −0.221464
\(735\) 7.54222 1.76492i 0.278199 0.0651002i
\(736\) 1.50000 2.59808i 0.0552907 0.0957664i
\(737\) 0.251200 0.937492i 0.00925308 0.0345329i
\(738\) −7.41970 + 5.09393i −0.273123 + 0.187510i
\(739\) −29.4194 16.9853i −1.08221 0.624814i −0.150718 0.988577i \(-0.548158\pi\)
−0.931491 + 0.363763i \(0.881492\pi\)
\(740\) −6.00000 3.00000i −0.220564 0.110282i
\(741\) −1.17298 21.3219i −0.0430905 0.783280i
\(742\) −20.1213 + 20.1213i −0.738677 + 0.738677i
\(743\) −6.72168 25.0856i −0.246594 0.920303i −0.972575 0.232588i \(-0.925281\pi\)
0.725981 0.687715i \(-0.241386\pi\)
\(744\) 3.74496 10.1433i 0.137297 0.371872i
\(745\) 18.9282 + 16.7846i 0.693476 + 0.614941i
\(746\) 15.1427 + 8.74264i 0.554414 + 0.320091i
\(747\) 0.992248 + 12.6892i 0.0363044 + 0.464273i
\(748\) 0.272078 + 0.272078i 0.00994815 + 0.00994815i
\(749\) 25.4558 0.930136
\(750\) −1.70138 19.2900i −0.0621258 0.704372i
\(751\) 21.6066 + 37.4237i 0.788436 + 1.36561i 0.926925 + 0.375247i \(0.122442\pi\)
−0.138489 + 0.990364i \(0.544224\pi\)
\(752\) −4.58579 4.58579i −0.167226 0.167226i
\(753\) −17.3137 + 24.4853i −0.630947 + 0.892293i
\(754\) −7.76874 + 4.48528i −0.282921 + 0.163344i
\(755\) 4.80920 23.5013i 0.175025 0.855301i
\(756\) −13.3908 7.98036i −0.487019 0.290243i
\(757\) −11.8460 44.2100i −0.430551 1.60684i −0.751493 0.659741i \(-0.770666\pi\)
0.320942 0.947099i \(-0.396001\pi\)
\(758\) −5.81962 21.7191i −0.211378 0.788874i
\(759\) −0.150758 0.878680i −0.00547215 0.0318941i
\(760\) −4.40192 8.69615i −0.159675 0.315443i
\(761\) 6.51472i 0.236158i −0.993004 0.118079i \(-0.962326\pi\)
0.993004 0.118079i \(-0.0376737\pi\)
\(762\) 4.17958 1.92554i 0.151410 0.0697550i
\(763\) −6.49867 + 1.74131i −0.235268 + 0.0630398i
\(764\) 5.29289 + 9.16756i 0.191490 + 0.331671i
\(765\) −11.9999 9.07342i −0.433857 0.328050i
\(766\) 15.2426 + 26.4010i 0.550739 + 0.953908i
\(767\) −11.3137 11.3137i −0.408514 0.408514i
\(768\) −1.41421 1.00000i −0.0510310 0.0360844i
\(769\) −33.7495 + 19.4853i −1.21704 + 0.702657i −0.964283 0.264873i \(-0.914670\pi\)
−0.252755 + 0.967530i \(0.581337\pi\)
\(770\) 0.763618 0.861141i 0.0275189 0.0310334i
\(771\) −2.41421 14.0711i −0.0869458 0.506757i
\(772\) 8.48528 8.48528i 0.305392 0.305392i
\(773\) 8.16772 + 2.18853i 0.293772 + 0.0787161i 0.402695 0.915334i \(-0.368073\pi\)
−0.108923 + 0.994050i \(0.534740\pi\)
\(774\) −2.32577 + 12.5136i −0.0835979 + 0.449793i
\(775\) −28.7041 12.2612i −1.03108 0.440435i
\(776\) 12.5446 + 7.24264i 0.450326 + 0.259996i
\(777\) 6.52270 + 14.1582i 0.234001 + 0.507922i
\(778\) −3.48528 3.48528i −0.124953 0.124953i
\(779\) 10.5000 + 7.79423i 0.376202 + 0.279257i
\(780\) −9.65685 + 5.17157i −0.345771 + 0.185172i
\(781\) −0.908117 + 1.57290i −0.0324950 + 0.0562830i
\(782\) −6.49867 + 1.74131i −0.232392 + 0.0622693i
\(783\) 15.9760 4.04456i 0.570934 0.144541i
\(784\) −1.73205 1.00000i −0.0618590 0.0357143i
\(785\) −26.4017 + 1.58471i −0.942315 + 0.0565607i
\(786\) 25.6066 4.39340i 0.913357 0.156707i
\(787\) 2.72792 2.72792i 0.0972399 0.0972399i −0.656813 0.754053i \(-0.728096\pi\)
0.754053 + 0.656813i \(0.228096\pi\)
\(788\) 8.22459 + 2.20377i 0.292989 + 0.0785061i
\(789\) −1.64451 1.97832i −0.0585462 0.0704301i
\(790\) −6.48528 + 12.9706i −0.230736 + 0.461472i
\(791\) 60.0000i 2.13335i
\(792\) −0.513152 + 0.0401266i −0.0182341 + 0.00142584i
\(793\) 6.12701 1.64173i 0.217576 0.0582994i
\(794\) −3.98528 6.90271i −0.141432 0.244968i
\(795\) 1.17278 36.7176i 0.0415943 1.30224i
\(796\) 7.12132 12.3345i 0.252409 0.437184i
\(797\) −1.77817 1.77817i −0.0629862 0.0629862i 0.674912 0.737898i \(-0.264182\pi\)
−0.737898 + 0.674912i \(0.764182\pi\)
\(798\) −4.65153 + 22.1667i −0.164662 + 0.784693i
\(799\) 14.5442i 0.514535i
\(800\) −3.08725 + 3.93305i −0.109151 + 0.139054i
\(801\) 34.8878 + 6.48420i 1.23270 + 0.229108i
\(802\) −33.4475 8.96224i −1.18107 0.316468i
\(803\) 0.721276 + 2.69184i 0.0254533 + 0.0949929i
\(804\) 7.53465 6.26330i 0.265727 0.220890i
\(805\) 6.36396 + 19.0919i 0.224300 + 0.672900i
\(806\) 17.6569i 0.621936i
\(807\) 1.73681 18.8496i 0.0611386 0.663538i
\(808\) −4.48112 + 16.7238i −0.157645 + 0.588340i
\(809\) −24.6863 −0.867924 −0.433962 0.900931i \(-0.642885\pi\)
−0.433962 + 0.900931i \(0.642885\pi\)
\(810\) 19.6569 4.31371i 0.690671 0.151568i
\(811\) −10.2279 17.7153i −0.359151 0.622068i 0.628668 0.777674i \(-0.283600\pi\)
−0.987819 + 0.155606i \(0.950267\pi\)
\(812\) 9.19051 2.46259i 0.322524 0.0864200i
\(813\) 0.317837 3.44949i 0.0111470 0.120979i
\(814\) 0.445759 + 0.257359i 0.0156239 + 0.00902044i
\(815\) 37.5857 24.8161i 1.31657 0.869271i
\(816\) 0.656854 + 3.82843i 0.0229945 + 0.134022i
\(817\) 18.2942 2.70577i 0.640034 0.0946630i
\(818\) −17.2929 + 17.2929i −0.604632 + 0.604632i
\(819\) 25.0273 + 4.65153i 0.874523 + 0.162538i
\(820\) 1.34486 6.57201i 0.0469647 0.229505i
\(821\) −5.79050 + 3.34315i −0.202090 + 0.116677i −0.597630 0.801772i \(-0.703891\pi\)
0.395540 + 0.918449i \(0.370557\pi\)
\(822\) −14.8466 32.2261i −0.517835 1.12401i
\(823\) −10.1828 + 38.0026i −0.354949 + 1.32469i 0.525601 + 0.850731i \(0.323841\pi\)
−0.880549 + 0.473955i \(0.842826\pi\)
\(824\) −3.00000 −0.104510
\(825\) 0.0416306 + 1.48528i 0.00144939 + 0.0517109i
\(826\) 8.48528 + 14.6969i 0.295241 + 0.511372i
\(827\) −1.80411 + 6.73305i −0.0627352 + 0.234131i −0.990173 0.139846i \(-0.955339\pi\)
0.927438 + 0.373977i \(0.122006\pi\)
\(828\) 3.87868 8.12132i 0.134793 0.282235i
\(829\) 28.9706i 1.00619i −0.864231 0.503095i \(-0.832195\pi\)
0.864231 0.503095i \(-0.167805\pi\)
\(830\) −7.09808 6.29423i −0.246378 0.218476i
\(831\) 17.3795 47.0727i 0.602887 1.63293i
\(832\) 2.73205 + 0.732051i 0.0947168 + 0.0253793i
\(833\) 1.16088 + 4.33245i 0.0402220 + 0.150110i
\(834\) −8.39861 + 22.7478i −0.290820 + 0.787693i
\(835\) 46.9706 + 23.4853i 1.62548 + 0.812742i
\(836\) 0.297173 + 0.686292i 0.0102779 + 0.0237359i
\(837\) 8.82843 31.2132i 0.305155 1.07889i
\(838\) 28.8120 7.72017i 0.995296 0.266689i
\(839\) −14.1213 + 24.4588i −0.487522 + 0.844413i −0.999897 0.0143488i \(-0.995432\pi\)
0.512375 + 0.858762i \(0.328766\pi\)
\(840\) 11.3133 2.64738i 0.390347 0.0913434i
\(841\) 9.47056 16.4035i 0.326571 0.565638i
\(842\) 5.42758 20.2560i 0.187047 0.698068i
\(843\) 6.17157 8.72792i 0.212560 0.300606i
\(844\) 3.48528i 0.119968i
\(845\) −7.41782 + 8.36516i −0.255181 + 0.287770i
\(846\) −14.7880 12.6430i −0.508422 0.434675i
\(847\) 23.2721 23.2721i 0.799638 0.799638i
\(848\) −6.70711 + 6.70711i −0.230323 + 0.230323i
\(849\) 15.5264 12.9065i 0.532863 0.442951i
\(850\) 11.1327 1.34127i 0.381848 0.0460052i
\(851\) −7.79423 + 4.50000i −0.267183 + 0.154258i
\(852\) −16.6528 + 7.67199i −0.570517 + 0.262838i
\(853\) −20.4502 + 5.47961i −0.700200 + 0.187618i −0.591320 0.806437i \(-0.701393\pi\)
−0.108880 + 0.994055i \(0.534726\pi\)
\(854\) −6.72792 −0.230225
\(855\) −15.1994 24.9796i −0.519808 0.854283i
\(856\) 8.48528 0.290021
\(857\) 8.19615 2.19615i 0.279975 0.0750191i −0.116099 0.993238i \(-0.537039\pi\)
0.396074 + 0.918219i \(0.370372\pi\)
\(858\) 0.763412 0.351705i 0.0260624 0.0120070i
\(859\) 12.5191 7.22792i 0.427147 0.246614i −0.270983 0.962584i \(-0.587349\pi\)
0.698131 + 0.715971i \(0.254016\pi\)
\(860\) −5.22715 7.91688i −0.178244 0.269963i
\(861\) −11.9876 + 9.96486i −0.408535 + 0.339601i
\(862\) 8.00000 8.00000i 0.272481 0.272481i
\(863\) 39.2340 39.2340i 1.33554 1.33554i 0.435215 0.900327i \(-0.356672\pi\)
0.900327 0.435215i \(-0.143328\pi\)
\(864\) −4.46360 2.66012i −0.151855 0.0904991i
\(865\) 44.5753 2.67555i 1.51561 0.0909714i
\(866\) 9.51472i 0.323323i
\(867\) −11.9706 + 16.9289i −0.406542 + 0.574937i
\(868\) 4.84714 18.0898i 0.164523 0.614007i
\(869\) 0.556349 0.963625i 0.0188729 0.0326887i
\(870\) −6.47820 + 10.4363i −0.219631 + 0.353823i
\(871\) −8.00000 + 13.8564i −0.271070 + 0.469506i
\(872\) −2.16622 + 0.580438i −0.0733576 + 0.0196561i
\(873\) 39.2132 + 18.7279i 1.32717 + 0.633844i
\(874\) −12.9904 1.50000i −0.439406 0.0507383i
\(875\) −6.00000 33.0000i −0.202837 1.11560i
\(876\) −9.74397 + 26.3918i −0.329218 + 0.891695i
\(877\) 7.36491 + 27.4862i 0.248695 + 0.928144i 0.971490 + 0.237081i \(0.0761907\pi\)
−0.722794 + 0.691063i \(0.757143\pi\)
\(878\) 28.4522 + 7.62373i 0.960214 + 0.257289i
\(879\) 15.5798 42.1981i 0.525492 1.42331i
\(880\) 0.254539 0.287047i 0.00858052 0.00967635i
\(881\) 49.2843i 1.66043i 0.557444 + 0.830215i \(0.311782\pi\)
−0.557444 + 0.830215i \(0.688218\pi\)
\(882\) −5.41421 2.58579i −0.182306 0.0870680i
\(883\) 0.909676 3.39496i 0.0306130 0.114249i −0.948929 0.315491i \(-0.897831\pi\)
0.979542 + 0.201241i \(0.0644975\pi\)
\(884\) −3.17157 5.49333i −0.106672 0.184761i
\(885\) −20.9706 6.34315i −0.704918 0.213223i
\(886\) 34.2426 1.15040
\(887\) 5.03554 18.7929i 0.169077 0.631004i −0.828408 0.560125i \(-0.810753\pi\)
0.997485 0.0708787i \(-0.0225803\pi\)
\(888\) 2.17423 + 4.71940i 0.0729625 + 0.158373i
\(889\) 6.90271 3.98528i 0.231509 0.133662i
\(890\) −22.0721 + 14.5732i −0.739860 + 0.488496i
\(891\) −1.52539 + 0.240027i −0.0511024 + 0.00804120i
\(892\) 12.3640 12.3640i 0.413976 0.413976i
\(893\) −10.4003 + 26.2860i −0.348034 + 0.879626i
\(894\) −3.31371 19.3137i −0.110827 0.645947i
\(895\) 4.18842 20.4678i 0.140003 0.684162i
\(896\) −2.59808 1.50000i −0.0867956 0.0501115i
\(897\) −1.34847 + 14.6349i −0.0450241 + 0.488647i
\(898\) 17.2209 4.61434i 0.574670 0.153982i
\(899\) 9.89949 + 17.1464i 0.330167 + 0.571865i
\(900\) −8.31371 + 12.4853i −0.277124 + 0.416176i
\(901\) 21.2721 0.708676
\(902\) −0.133219 + 0.497180i −0.00443571 + 0.0165543i
\(903\) −2.02270 + 21.9524i −0.0673114 + 0.730531i
\(904\) 20.0000i 0.665190i
\(905\) 30.7279 10.2426i 1.02143 0.340477i
\(906\) −14.2891 + 11.8780i −0.474723 + 0.394621i
\(907\) 8.21941 + 30.6753i 0.272921 + 1.01856i 0.957222 + 0.289355i \(0.0934409\pi\)
−0.684301 + 0.729200i \(0.739892\pi\)
\(908\) 22.1879 + 5.94522i 0.736330 + 0.197299i
\(909\) −9.49117 + 51.0666i −0.314802 + 1.69377i
\(910\) −15.8338 + 10.4543i −0.524884 + 0.346557i
\(911\) 29.3137i 0.971206i 0.874179 + 0.485603i \(0.161400\pi\)
−0.874179 + 0.485603i \(0.838600\pi\)
\(912\) −1.55051 + 7.38891i −0.0513425 + 0.244671i
\(913\) 0.514719 + 0.514719i 0.0170347 + 0.0170347i
\(914\) −17.6569 + 30.5826i −0.584037 + 1.01158i
\(915\) 6.33466 5.94252i 0.209418 0.196454i
\(916\) 7.87868 + 13.6463i 0.260319 + 0.450886i
\(917\) 43.4667 11.6469i 1.43540 0.384613i
\(918\) 2.85994 + 11.2967i 0.0943921 + 0.372847i
\(919\) 23.2721i 0.767675i −0.923401 0.383838i \(-0.874602\pi\)
0.923401 0.383838i \(-0.125398\pi\)
\(920\) 2.12132 + 6.36396i 0.0699379 + 0.209814i
\(921\) −22.3015 26.8283i −0.734859 0.884024i
\(922\) 24.2570 + 6.49964i 0.798862 + 0.214054i
\(923\) 21.1716 21.1716i 0.696871 0.696871i
\(924\) −0.878680 + 0.150758i −0.0289064 + 0.00495956i
\(925\) 13.9205 5.58750i 0.457703 0.183716i
\(926\) −35.9273 20.7426i −1.18064 0.681645i
\(927\) −8.97261 + 0.701625i −0.294699 + 0.0230444i
\(928\) 3.06350 0.820863i 0.100564 0.0269462i
\(929\) −24.2990 + 42.0871i −0.797224 + 1.38083i 0.124193 + 0.992258i \(0.460366\pi\)
−0.921417 + 0.388574i \(0.872968\pi\)
\(930\) 11.4142 + 21.3137i 0.374287 + 0.698904i
\(931\) −1.00000 + 8.66025i −0.0327737 + 0.283828i
\(932\) 7.41421 + 7.41421i 0.242861 + 0.242861i
\(933\) 6.14966 + 13.3485i 0.201331 + 0.437009i
\(934\) −2.15232 1.24264i −0.0704260 0.0406604i
\(935\) −0.858840 + 0.0515503i −0.0280871 + 0.00168587i
\(936\) 8.34242 + 1.55051i 0.272680 + 0.0506800i
\(937\) 5.42389 + 1.45333i 0.177191 + 0.0474781i 0.346323 0.938115i \(-0.387430\pi\)
−0.169133 + 0.985593i \(0.554097\pi\)
\(938\) 12.0000 12.0000i 0.391814 0.391814i
\(939\) −6.31371 36.7990i −0.206040 1.20089i
\(940\) 14.4755 0.868863i 0.472138 0.0283392i
\(941\) −22.3426 + 12.8995i −0.728347 + 0.420512i −0.817817 0.575478i \(-0.804816\pi\)
0.0894699 + 0.995990i \(0.471483\pi\)
\(942\) 16.7279 + 11.8284i 0.545025 + 0.385391i
\(943\) −6.36396 6.36396i −0.207239 0.207239i
\(944\) 2.82843 + 4.89898i 0.0920575 + 0.159448i
\(945\) 33.2175 10.5639i 1.08057 0.343643i
\(946\) 0.363961 + 0.630399i 0.0118334 + 0.0204960i
\(947\) 53.3319 14.2902i 1.73305 0.464370i 0.752170 0.658969i \(-0.229007\pi\)
0.980883 + 0.194599i \(0.0623407\pi\)
\(948\) 10.2022 4.70017i 0.331352 0.152655i
\(949\) 45.9411i 1.49131i
\(950\) 21.0795 + 5.53674i 0.683909 + 0.179635i
\(951\) −8.33452 48.5772i −0.270265 1.57522i
\(952\) 1.74131 + 6.49867i 0.0564363 + 0.210623i
\(953\) 1.28648 + 4.80119i 0.0416731 + 0.155526i 0.983627 0.180216i \(-0.0576797\pi\)
−0.941954 + 0.335742i \(0.891013\pi\)
\(954\) −18.4915 + 21.6287i −0.598683 + 0.700255i
\(955\) −23.1900 4.74548i −0.750410 0.153560i
\(956\) −0.594346 + 0.343146i −0.0192225 + 0.0110981i
\(957\) 0.544156 0.769553i 0.0175901 0.0248761i
\(958\) 21.4853 + 21.4853i 0.694158 + 0.694158i
\(959\) −30.7279 53.2223i −0.992256 1.71864i
\(960\) 3.77111 0.882461i 0.121712 0.0284813i
\(961\) 7.97056 0.257115
\(962\) −6.00000 6.00000i −0.193448 0.193448i
\(963\) 25.3784 1.98450i 0.817807 0.0639495i
\(964\) 0.420266 + 0.242641i 0.0135359 + 0.00781493i
\(965\) 1.60770 + 26.7846i 0.0517535 + 0.862227i
\(966\) 5.39910 14.6236i 0.173713 0.470507i
\(967\) −11.2472 41.9751i −0.361686 1.34983i −0.871859 0.489757i \(-0.837085\pi\)
0.510173 0.860072i \(-0.329581\pi\)
\(968\) 7.75736 7.75736i 0.249331 0.249331i
\(969\) 14.1760 9.25845i 0.455399 0.297424i
\(970\) −30.7279 + 10.2426i −0.986614 + 0.328871i
\(971\) 16.8493 + 9.72792i 0.540718 + 0.312184i 0.745370 0.666651i \(-0.232273\pi\)
−0.204652 + 0.978835i \(0.565606\pi\)
\(972\) −13.9722 6.91215i −0.448158 0.221707i
\(973\) −10.8704 + 40.5689i −0.348489 + 1.30058i
\(974\) 17.3995 30.1368i 0.557516 0.965646i
\(975\) 5.67435 23.8286i 0.181725 0.763126i
\(976\) −2.24264 −0.0717852
\(977\) −7.75736 7.75736i −0.248180 0.248180i 0.572043 0.820223i \(-0.306151\pi\)
−0.820223 + 0.572043i \(0.806151\pi\)
\(978\) −34.7400 3.20096i −1.11086 0.102355i
\(979\) 1.75754 1.01472i 0.0561714 0.0324305i
\(980\) 4.24264 1.41421i 0.135526 0.0451754i
\(981\) −6.34315 + 2.24264i −0.202521 + 0.0716020i
\(982\) 6.62419 + 1.77495i 0.211386 + 0.0566408i
\(983\) −4.25909 15.8951i −0.135844 0.506976i −0.999993 0.00374017i \(-0.998809\pi\)
0.864149 0.503236i \(-0.167857\pi\)
\(984\) −3.99585 + 3.32162i −0.127383 + 0.105889i
\(985\) −15.8887 + 10.4906i −0.506255 + 0.334257i
\(986\) −6.15978 3.55635i −0.196167 0.113257i
\(987\) −27.5147 19.4558i −0.875803 0.619286i
\(988\) −1.80385 12.1962i −0.0573880 0.388011i
\(989\) −12.7279 −0.404724
\(990\) 0.694161 0.918051i 0.0220619 0.0291776i
\(991\) −3.00000 + 5.19615i −0.0952981 + 0.165061i −0.909733 0.415194i \(-0.863714\pi\)
0.814435 + 0.580255i \(0.197047\pi\)
\(992\) 1.61571 6.02993i 0.0512990 0.191450i
\(993\) −19.6873 + 9.06998i −0.624758 + 0.287827i
\(994\) −27.5027 + 15.8787i −0.872332 + 0.503641i
\(995\) 10.0711 + 30.2132i 0.319274 + 0.957823i
\(996\) 1.24264 + 7.24264i 0.0393746 + 0.229492i
\(997\) 15.1518 + 4.05991i 0.479862 + 0.128579i 0.490638 0.871363i \(-0.336764\pi\)
−0.0107763 + 0.999942i \(0.503430\pi\)
\(998\) 36.6767 + 9.82750i 1.16098 + 0.311084i
\(999\) 7.60660 + 13.6066i 0.240662 + 0.430494i
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 570.2.v.a.353.2 yes 8
3.2 odd 2 570.2.v.b.353.1 yes 8
5.2 odd 4 570.2.v.b.467.2 yes 8
15.2 even 4 inner 570.2.v.a.467.1 yes 8
19.7 even 3 inner 570.2.v.a.83.1 8
57.26 odd 6 570.2.v.b.83.2 yes 8
95.7 odd 12 570.2.v.b.197.1 yes 8
285.197 even 12 inner 570.2.v.a.197.2 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
570.2.v.a.83.1 8 19.7 even 3 inner
570.2.v.a.197.2 yes 8 285.197 even 12 inner
570.2.v.a.353.2 yes 8 1.1 even 1 trivial
570.2.v.a.467.1 yes 8 15.2 even 4 inner
570.2.v.b.83.2 yes 8 57.26 odd 6
570.2.v.b.197.1 yes 8 95.7 odd 12
570.2.v.b.353.1 yes 8 3.2 odd 2
570.2.v.b.467.2 yes 8 5.2 odd 4