Properties

Label 570.2.v.b.83.2
Level $570$
Weight $2$
Character 570.83
Analytic conductor $4.551$
Analytic rank $0$
Dimension $8$
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] = [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 83.2
Root \(-0.965926 - 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 570.83
Dual form 570.2.v.b.467.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.258819 - 0.965926i) q^{2} +(-0.724745 + 1.57313i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(1.67303 + 1.48356i) q^{5} +(1.33195 + 1.10721i) q^{6} +(2.12132 - 2.12132i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.94949 - 2.28024i) q^{9} +O(q^{10})\) \(q+(0.258819 - 0.965926i) q^{2} +(-0.724745 + 1.57313i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(1.67303 + 1.48356i) 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} +(1.86603 - 1.23205i) q^{10} +0.171573i q^{11} +(1.41421 - 1.00000i) q^{12} +(2.73205 - 0.732051i) q^{13} +(-1.50000 - 2.59808i) q^{14} +(-3.54636 + 1.55670i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-0.580438 + 2.16622i) q^{17} +(-2.70711 + 1.29289i) q^{18} +(4.33013 - 0.500000i) q^{19} +(-0.707107 - 2.12132i) q^{20} +(1.79970 + 4.87453i) q^{21} +(0.165727 + 0.0444063i) q^{22} +(0.776457 + 2.89778i) q^{23} +(-0.599900 - 1.62484i) q^{24} +(0.598076 + 4.96410i) q^{25} -2.82843i q^{26} +(5.00000 - 1.41421i) q^{27} +(-2.89778 + 0.776457i) q^{28} +(-1.58579 + 2.74666i) q^{29} +(0.585786 + 3.82843i) q^{30} +6.24264 q^{31} +(0.965926 - 0.258819i) q^{32} +(-0.269907 - 0.124347i) q^{33} +(1.94218 + 1.12132i) q^{34} +(6.69615 - 0.401924i) q^{35} +(0.548188 + 2.94949i) q^{36} +(-2.12132 + 2.12132i) q^{37} +(0.637756 - 4.31199i) q^{38} +(-0.828427 + 4.82843i) q^{39} +(-2.23205 + 0.133975i) q^{40} +(-2.59808 + 1.50000i) q^{41} +(5.17423 - 0.476756i) q^{42} +(1.09808 - 4.09808i) q^{43} +(0.0857864 - 0.148586i) q^{44} +(0.121320 - 6.70711i) q^{45} +3.00000 q^{46} +(6.26430 - 1.67851i) q^{47} +(-1.72474 + 0.158919i) q^{48} -2.00000i q^{49} +(4.94975 + 0.707107i) q^{50} +(-2.98709 - 2.48307i) q^{51} +(-2.73205 - 0.732051i) q^{52} +(-2.45497 - 9.16208i) q^{53} +(-0.0719302 - 5.19565i) q^{54} +(-0.254539 + 0.287047i) q^{55} +3.00000i q^{56} +(-2.35167 + 7.17423i) q^{57} +(2.24264 + 2.24264i) q^{58} +(2.82843 + 4.89898i) q^{59} +(3.84959 + 0.425044i) q^{60} +(-1.12132 + 1.94218i) q^{61} +(1.61571 - 6.02993i) q^{62} +(-8.97261 - 0.701625i) q^{63} -1.00000i q^{64} +(5.65685 + 2.82843i) q^{65} +(-0.189967 + 0.228527i) q^{66} +(-1.46410 - 5.46410i) q^{67} +(1.58579 - 1.58579i) q^{68} +(-5.12132 - 0.878680i) q^{69} +(1.34486 - 6.57201i) q^{70} +(-9.16756 + 5.29289i) q^{71} +(2.99087 + 0.233875i) q^{72} +(4.20390 - 15.6892i) q^{73} +(1.50000 + 2.59808i) q^{74} +(-8.24264 - 2.65685i) q^{75} +(-4.00000 - 1.73205i) q^{76} +(0.363961 + 0.363961i) q^{77} +(4.44949 + 2.04989i) q^{78} +(-5.61642 + 3.24264i) q^{79} +(-0.448288 + 2.19067i) q^{80} +(-1.39898 + 8.89060i) q^{81} +(0.776457 + 2.89778i) q^{82} +(3.00000 - 3.00000i) q^{83} +(0.878680 - 5.12132i) q^{84} +(-4.18482 + 2.76305i) q^{85} +(-3.67423 - 2.12132i) q^{86} +(-3.17157 - 4.48528i) q^{87} +(-0.121320 - 0.121320i) q^{88} +(-5.91421 + 10.2437i) q^{89} +(-6.44717 - 1.85311i) q^{90} +(4.24264 - 7.34847i) q^{91} +(0.776457 - 2.89778i) q^{92} +(-4.52432 + 9.82050i) q^{93} -6.48528i q^{94} +(7.98623 + 5.58750i) q^{95} +(-0.292893 + 1.70711i) q^{96} +(-13.9917 - 3.74907i) q^{97} +(-1.93185 - 0.517638i) q^{98} +(0.391227 - 0.334480i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{3} - 4 q^{6} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 4 q^{3} - 4 q^{6} + 4 q^{9} + 8 q^{10} + 8 q^{13} - 12 q^{14} - 4 q^{15} + 4 q^{16} + 12 q^{17} - 16 q^{18} + 12 q^{21} - 8 q^{22} - 4 q^{24} - 16 q^{25} + 40 q^{27} - 24 q^{29} + 16 q^{30} + 16 q^{31} + 16 q^{33} + 12 q^{35} + 16 q^{39} - 4 q^{40} + 12 q^{42} - 12 q^{43} + 12 q^{44} - 16 q^{45} + 24 q^{46} + 24 q^{47} - 4 q^{48} - 20 q^{51} - 8 q^{52} + 24 q^{53} - 4 q^{54} - 8 q^{55} - 16 q^{58} + 12 q^{60} + 8 q^{61} - 12 q^{62} - 24 q^{63} - 4 q^{66} + 16 q^{67} + 24 q^{68} - 24 q^{69} + 8 q^{72} - 12 q^{73} + 12 q^{74} - 32 q^{75} - 32 q^{76} - 48 q^{77} + 16 q^{78} + 28 q^{81} + 24 q^{83} + 24 q^{84} + 16 q^{85} - 48 q^{87} + 16 q^{88} - 36 q^{89} - 8 q^{90} + 8 q^{93} - 8 q^{96} - 24 q^{97} - 32 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.258819 0.965926i 0.183013 0.683013i
\(3\) −0.724745 + 1.57313i −0.418432 + 0.908248i
\(4\) −0.866025 0.500000i −0.433013 0.250000i
\(5\) 1.67303 + 1.48356i 0.748203 + 0.663470i
\(6\) 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
\(10\) 1.86603 1.23205i 0.590089 0.389609i
\(11\) 0.171573i 0.0517312i 0.999665 + 0.0258656i \(0.00823419\pi\)
−0.999665 + 0.0258656i \(0.991766\pi\)
\(12\) 1.41421 1.00000i 0.408248 0.288675i
\(13\) 2.73205 0.732051i 0.757735 0.203034i 0.140788 0.990040i \(-0.455036\pi\)
0.616946 + 0.787005i \(0.288370\pi\)
\(14\) −1.50000 2.59808i −0.400892 0.694365i
\(15\) −3.54636 + 1.55670i −0.915667 + 0.401937i
\(16\) 0.500000 + 0.866025i 0.125000 + 0.216506i
\(17\) −0.580438 + 2.16622i −0.140777 + 0.525387i 0.859130 + 0.511757i \(0.171005\pi\)
−0.999907 + 0.0136295i \(0.995661\pi\)
\(18\) −2.70711 + 1.29289i −0.638071 + 0.304738i
\(19\) 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
\(22\) 0.165727 + 0.0444063i 0.0353330 + 0.00946746i
\(23\) 0.776457 + 2.89778i 0.161903 + 0.604228i 0.998415 + 0.0562805i \(0.0179241\pi\)
−0.836512 + 0.547948i \(0.815409\pi\)
\(24\) −0.599900 1.62484i −0.122454 0.331670i
\(25\) 0.598076 + 4.96410i 0.119615 + 0.992820i
\(26\) 2.82843i 0.554700i
\(27\) 5.00000 1.41421i 0.962250 0.272166i
\(28\) −2.89778 + 0.776457i −0.547628 + 0.146737i
\(29\) −1.58579 + 2.74666i −0.294473 + 0.510042i −0.974862 0.222809i \(-0.928477\pi\)
0.680389 + 0.732851i \(0.261811\pi\)
\(30\) 0.585786 + 3.82843i 0.106949 + 0.698972i
\(31\) 6.24264 1.12121 0.560606 0.828083i \(-0.310568\pi\)
0.560606 + 0.828083i \(0.310568\pi\)
\(32\) 0.965926 0.258819i 0.170753 0.0457532i
\(33\) −0.269907 0.124347i −0.0469847 0.0216460i
\(34\) 1.94218 + 1.12132i 0.333082 + 0.192305i
\(35\) 6.69615 0.401924i 1.13186 0.0679375i
\(36\) 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 \(0.329313\pi\)
\(38\) 0.637756 4.31199i 0.103458 0.699497i
\(39\) −0.828427 + 4.82843i −0.132655 + 0.773167i
\(40\) −2.23205 + 0.133975i −0.352918 + 0.0211832i
\(41\) −2.59808 + 1.50000i −0.405751 + 0.234261i −0.688963 0.724797i \(-0.741934\pi\)
0.283211 + 0.959058i \(0.408600\pi\)
\(42\) 5.17423 0.476756i 0.798402 0.0735650i
\(43\) 1.09808 4.09808i 0.167455 0.624951i −0.830259 0.557377i \(-0.811808\pi\)
0.997714 0.0675734i \(-0.0215257\pi\)
\(44\) 0.0857864 0.148586i 0.0129328 0.0224003i
\(45\) 0.121320 6.70711i 0.0180854 0.999836i
\(46\) 3.00000 0.442326
\(47\) 6.26430 1.67851i 0.913742 0.244836i 0.228834 0.973466i \(-0.426509\pi\)
0.684909 + 0.728629i \(0.259842\pi\)
\(48\) −1.72474 + 0.158919i −0.248945 + 0.0229379i
\(49\) 2.00000i 0.285714i
\(50\) 4.94975 + 0.707107i 0.700000 + 0.100000i
\(51\) −2.98709 2.48307i −0.418276 0.347699i
\(52\) −2.73205 0.732051i −0.378867 0.101517i
\(53\) −2.45497 9.16208i −0.337216 1.25851i −0.901446 0.432891i \(-0.857494\pi\)
0.564230 0.825618i \(-0.309173\pi\)
\(54\) −0.0719302 5.19565i −0.00978846 0.707039i
\(55\) −0.254539 + 0.287047i −0.0343221 + 0.0387054i
\(56\) 3.00000i 0.400892i
\(57\) −2.35167 + 7.17423i −0.311486 + 0.950251i
\(58\) 2.24264 + 2.24264i 0.294473 + 0.294473i
\(59\) 2.82843 + 4.89898i 0.368230 + 0.637793i 0.989289 0.145971i \(-0.0466306\pi\)
−0.621059 + 0.783764i \(0.713297\pi\)
\(60\) 3.84959 + 0.425044i 0.496980 + 0.0548729i
\(61\) −1.12132 + 1.94218i −0.143570 + 0.248671i −0.928839 0.370484i \(-0.879192\pi\)
0.785268 + 0.619156i \(0.212525\pi\)
\(62\) 1.61571 6.02993i 0.205196 0.765802i
\(63\) −8.97261 0.701625i −1.13044 0.0883964i
\(64\) 1.00000i 0.125000i
\(65\) 5.65685 + 2.82843i 0.701646 + 0.350823i
\(66\) −0.189967 + 0.228527i −0.0233833 + 0.0281297i
\(67\) −1.46410 5.46410i −0.178868 0.667546i −0.995860 0.0908970i \(-0.971027\pi\)
0.816992 0.576649i \(-0.195640\pi\)
\(68\) 1.58579 1.58579i 0.192305 0.192305i
\(69\) −5.12132 0.878680i −0.616535 0.105781i
\(70\) 1.34486 6.57201i 0.160742 0.785506i
\(71\) −9.16756 + 5.29289i −1.08799 + 0.628151i −0.933040 0.359772i \(-0.882855\pi\)
−0.154949 + 0.987922i \(0.549521\pi\)
\(72\) 2.99087 + 0.233875i 0.352477 + 0.0275624i
\(73\) 4.20390 15.6892i 0.492030 1.83628i −0.0540373 0.998539i \(-0.517209\pi\)
0.546067 0.837741i \(-0.316124\pi\)
\(74\) 1.50000 + 2.59808i 0.174371 + 0.302020i
\(75\) −8.24264 2.65685i −0.951778 0.306787i
\(76\) −4.00000 1.73205i −0.458831 0.198680i
\(77\) 0.363961 + 0.363961i 0.0414772 + 0.0414772i
\(78\) 4.44949 + 2.04989i 0.503806 + 0.232104i
\(79\) −5.61642 + 3.24264i −0.631896 + 0.364826i −0.781486 0.623923i \(-0.785538\pi\)
0.149590 + 0.988748i \(0.452205\pi\)
\(80\) −0.448288 + 2.19067i −0.0501201 + 0.244924i
\(81\) −1.39898 + 8.89060i −0.155442 + 0.987845i
\(82\) 0.776457 + 2.89778i 0.0857453 + 0.320006i
\(83\) 3.00000 3.00000i 0.329293 0.329293i −0.523025 0.852318i \(-0.675196\pi\)
0.852318 + 0.523025i \(0.175196\pi\)
\(84\) 0.878680 5.12132i 0.0958718 0.558782i
\(85\) −4.18482 + 2.76305i −0.453908 + 0.299695i
\(86\) −3.67423 2.12132i −0.396203 0.228748i
\(87\) −3.17157 4.48528i −0.340028 0.480873i
\(88\) −0.121320 0.121320i −0.0129328 0.0129328i
\(89\) −5.91421 + 10.2437i −0.626905 + 1.08583i 0.361264 + 0.932464i \(0.382345\pi\)
−0.988169 + 0.153368i \(0.950988\pi\)
\(90\) −6.44717 1.85311i −0.679591 0.195335i
\(91\) 4.24264 7.34847i 0.444750 0.770329i
\(92\) 0.776457 2.89778i 0.0809513 0.302114i
\(93\) −4.52432 + 9.82050i −0.469150 + 1.01834i
\(94\) 6.48528i 0.668906i
\(95\) 7.98623 + 5.58750i 0.819369 + 0.573266i
\(96\) −0.292893 + 1.70711i −0.0298933 + 0.174231i
\(97\) −13.9917 3.74907i −1.42064 0.380660i −0.534931 0.844896i \(-0.679662\pi\)
−0.885712 + 0.464236i \(0.846329\pi\)
\(98\) −1.93185 0.517638i −0.195146 0.0522893i
\(99\) 0.391227 0.334480i 0.0393198 0.0336165i
\(100\) 1.96410 4.59808i 0.196410 0.459808i
\(101\) −14.9941 8.65685i −1.49197 0.861389i −0.492012 0.870588i \(-0.663738\pi\)
−0.999958 + 0.00919913i \(0.997072\pi\)
\(102\) −3.17157 + 2.24264i −0.314033 + 0.222055i
\(103\) −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
\(105\) −4.22072 + 10.8252i −0.411900 + 1.05643i
\(106\) −9.48528 −0.921292
\(107\) −6.00000 6.00000i −0.580042 0.580042i 0.354873 0.934915i \(-0.384524\pi\)
−0.934915 + 0.354873i \(0.884524\pi\)
\(108\) −5.03723 1.27526i −0.484708 0.122711i
\(109\) 1.94218 1.12132i 0.186027 0.107403i −0.404094 0.914717i \(-0.632413\pi\)
0.590122 + 0.807314i \(0.299080\pi\)
\(110\) 0.211386 + 0.320159i 0.0201549 + 0.0305260i
\(111\) −1.79970 4.87453i −0.170820 0.462670i
\(112\) 2.89778 + 0.776457i 0.273814 + 0.0733683i
\(113\) −14.1421 + 14.1421i −1.33038 + 1.33038i −0.425352 + 0.905028i \(0.639850\pi\)
−0.905028 + 0.425352i \(0.860150\pi\)
\(114\) 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
\(117\) −6.99536 4.80260i −0.646721 0.444001i
\(118\) 5.46410 1.46410i 0.503011 0.134781i
\(119\) 3.36396 + 5.82655i 0.308374 + 0.534119i
\(120\) 1.40691 3.60841i 0.128433 0.329401i
\(121\) 10.9706 0.997324
\(122\) 1.58579 + 1.58579i 0.143570 + 0.143570i
\(123\) −0.476756 5.17423i −0.0429876 0.466545i
\(124\) −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
\(127\) −0.687644 2.56632i −0.0610186 0.227724i 0.928682 0.370877i \(-0.120943\pi\)
−0.989701 + 0.143152i \(0.954276\pi\)
\(128\) −0.965926 0.258819i −0.0853766 0.0228766i
\(129\) 5.65099 + 4.69748i 0.497542 + 0.413590i
\(130\) 4.19615 4.73205i 0.368027 0.415028i
\(131\) 12.9904 7.50000i 1.13497 0.655278i 0.189794 0.981824i \(-0.439218\pi\)
0.945181 + 0.326546i \(0.105885\pi\)
\(132\) 0.171573 + 0.242641i 0.0149335 + 0.0211192i
\(133\) 8.12493 10.2462i 0.704520 0.888462i
\(134\) −5.65685 −0.488678
\(135\) 10.4632 + 5.05179i 0.900532 + 0.434789i
\(136\) −1.12132 1.94218i −0.0961524 0.166541i
\(137\) 19.7873 5.30198i 1.69054 0.452979i 0.720011 0.693963i \(-0.244137\pi\)
0.970529 + 0.240984i \(0.0774701\pi\)
\(138\) −2.17423 + 4.71940i −0.185083 + 0.401742i
\(139\) 12.1244 + 7.00000i 1.02837 + 0.593732i 0.916519 0.399992i \(-0.130987\pi\)
0.111856 + 0.993724i \(0.464321\pi\)
\(140\) −6.00000 3.00000i −0.507093 0.253546i
\(141\) −1.89949 + 11.0711i −0.159966 + 0.932352i
\(142\) 2.73980 + 10.2251i 0.229919 + 0.858070i
\(143\) 0.125600 + 0.468746i 0.0105032 + 0.0391985i
\(144\) 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
\(147\) 3.14626 + 1.44949i 0.259500 + 0.119552i
\(148\) 2.89778 0.776457i 0.238196 0.0638244i
\(149\) −5.65685 9.79796i −0.463428 0.802680i 0.535701 0.844407i \(-0.320047\pi\)
−0.999129 + 0.0417274i \(0.986714\pi\)
\(150\) −4.69968 + 7.27414i −0.383727 + 0.593931i
\(151\) −10.7279 −0.873026 −0.436513 0.899698i \(-0.643787\pi\)
−0.436513 + 0.899698i \(0.643787\pi\)
\(152\) −2.70831 + 3.41542i −0.219673 + 0.277027i
\(153\) 6.07107 2.89949i 0.490817 0.234410i
\(154\) 0.445759 0.257359i 0.0359203 0.0207386i
\(155\) 10.4441 + 9.26136i 0.838894 + 0.743890i
\(156\) 3.13165 3.76733i 0.250733 0.301628i
\(157\) −11.4254 3.06142i −0.911845 0.244328i −0.227749 0.973720i \(-0.573136\pi\)
−0.684096 + 0.729392i \(0.739803\pi\)
\(158\) 1.67851 + 6.26430i 0.133535 + 0.498361i
\(159\) 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
\(162\) 8.22558 + 3.65237i 0.646263 + 0.286957i
\(163\) −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
\(165\) −0.267087 0.608460i −0.0207927 0.0473685i
\(166\) −2.12132 3.67423i −0.164646 0.285176i
\(167\) 22.6850 6.07844i 1.75542 0.470364i 0.769651 0.638464i \(-0.220430\pi\)
0.985770 + 0.168101i \(0.0537634\pi\)
\(168\) −4.71940 2.17423i −0.364109 0.167746i
\(169\) −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
\(173\) −19.2901 5.16876i −1.46660 0.392974i −0.564835 0.825204i \(-0.691060\pi\)
−0.901763 + 0.432230i \(0.857727\pi\)
\(174\) −5.15331 + 1.90263i −0.390672 + 0.144238i
\(175\) 11.7992 + 9.26174i 0.891933 + 0.700122i
\(176\) −0.148586 + 0.0857864i −0.0112001 + 0.00646640i
\(177\) −9.75663 + 0.898979i −0.733353 + 0.0675714i
\(178\) 8.36396 + 8.36396i 0.626905 + 0.626905i
\(179\) 9.34315 0.698340 0.349170 0.937059i \(-0.386464\pi\)
0.349170 + 0.937059i \(0.386464\pi\)
\(180\) −3.45862 + 5.74786i −0.257790 + 0.428421i
\(181\) −7.24264 + 12.5446i −0.538341 + 0.932434i 0.460652 + 0.887581i \(0.347616\pi\)
−0.998994 + 0.0448537i \(0.985718\pi\)
\(182\) −6.00000 6.00000i −0.444750 0.444750i
\(183\) −2.24264 3.17157i −0.165781 0.234449i
\(184\) −2.59808 1.50000i −0.191533 0.110581i
\(185\) −6.69615 + 0.401924i −0.492311 + 0.0295500i
\(186\) 8.31489 + 6.91189i 0.609678 + 0.506804i
\(187\) −0.371665 0.0995874i −0.0271789 0.00728255i
\(188\) −6.26430 1.67851i −0.456871 0.122418i
\(189\) 7.60660 13.6066i 0.553299 0.989735i
\(190\) 7.46410 6.26795i 0.541503 0.454725i
\(191\) 10.5858i 0.765961i −0.923757 0.382980i \(-0.874898\pi\)
0.923757 0.382980i \(-0.125102\pi\)
\(192\) 1.57313 + 0.724745i 0.113531 + 0.0523040i
\(193\) −3.10583 + 11.5911i −0.223562 + 0.834346i 0.759413 + 0.650609i \(0.225486\pi\)
−0.982975 + 0.183737i \(0.941180\pi\)
\(194\) −7.24264 + 12.5446i −0.519991 + 0.900651i
\(195\) −8.54927 + 6.84909i −0.612226 + 0.490474i
\(196\) −1.00000 + 1.73205i −0.0714286 + 0.123718i
\(197\) −6.02082 6.02082i −0.428965 0.428965i 0.459310 0.888276i \(-0.348097\pi\)
−0.888276 + 0.459310i \(0.848097\pi\)
\(198\) −0.221825 0.464466i −0.0157644 0.0330082i
\(199\) −12.3345 7.12132i −0.874369 0.504817i −0.00557117 0.999984i \(-0.501773\pi\)
−0.868798 + 0.495167i \(0.835107\pi\)
\(200\) −3.93305 3.08725i −0.278109 0.218301i
\(201\) 9.65685 + 1.65685i 0.681142 + 0.116865i
\(202\) −12.2426 + 12.2426i −0.861389 + 0.861389i
\(203\) 2.46259 + 9.19051i 0.172840 + 0.645048i
\(204\) 1.34536 + 3.64394i 0.0941941 + 0.255127i
\(205\) −6.57201 1.34486i −0.459009 0.0939293i
\(206\) −2.59808 + 1.50000i −0.181017 + 0.104510i
\(207\) 5.09393 7.41970i 0.354053 0.515704i
\(208\) 2.00000 + 2.00000i 0.138675 + 0.138675i
\(209\) 0.0857864 + 0.742932i 0.00593397 + 0.0513897i
\(210\) 9.36396 + 6.87868i 0.646175 + 0.474674i
\(211\) −1.74264 3.01834i −0.119968 0.207791i 0.799787 0.600284i \(-0.204946\pi\)
−0.919755 + 0.392493i \(0.871613\pi\)
\(212\) −2.45497 + 9.16208i −0.168608 + 0.629254i
\(213\) −1.68228 18.2578i −0.115268 1.25100i
\(214\) −7.34847 + 4.24264i −0.502331 + 0.290021i
\(215\) 7.91688 5.22715i 0.539926 0.356489i
\(216\) −2.53553 + 4.53553i −0.172521 + 0.308604i
\(217\) 13.2426 13.2426i 0.898969 0.898969i
\(218\) −0.580438 2.16622i −0.0393122 0.146715i
\(219\) 21.6344 + 17.9840i 1.46192 + 1.21524i
\(220\) 0.363961 0.121320i 0.0245382 0.00817942i
\(221\) 6.34315i 0.426686i
\(222\) −5.17423 + 0.476756i −0.347272 + 0.0319978i
\(223\) −4.52552 + 16.8895i −0.303051 + 1.13100i 0.631558 + 0.775328i \(0.282416\pi\)
−0.934610 + 0.355675i \(0.884251\pi\)
\(224\) 1.50000 2.59808i 0.100223 0.173591i
\(225\) 10.1534 11.0412i 0.676893 0.736081i
\(226\) 10.0000 + 17.3205i 0.665190 + 1.15214i
\(227\) −16.2426 16.2426i −1.07806 1.07806i −0.996683 0.0813787i \(-0.974068\pi\)
−0.0813787 0.996683i \(-0.525932\pi\)
\(228\) 5.62372 5.03723i 0.372440 0.333599i
\(229\) 15.7574i 1.04128i 0.853778 + 0.520638i \(0.174306\pi\)
−0.853778 + 0.520638i \(0.825694\pi\)
\(230\) 5.01910 + 4.45069i 0.330950 + 0.293470i
\(231\) −0.836338 + 0.308780i −0.0550270 + 0.0203162i
\(232\) −0.820863 3.06350i −0.0538923 0.201129i
\(233\) 10.1280 + 2.71379i 0.663508 + 0.177786i 0.574828 0.818274i \(-0.305069\pi\)
0.0886791 + 0.996060i \(0.471735\pi\)
\(234\) −6.44949 + 5.51399i −0.421616 + 0.360461i
\(235\) 12.9706 + 6.48528i 0.846106 + 0.423053i
\(236\) 5.65685i 0.368230i
\(237\) −1.03063 11.1855i −0.0669467 0.726573i
\(238\) 6.49867 1.74131i 0.421246 0.112873i
\(239\) 0.686292 0.0443925 0.0221963 0.999754i \(-0.492934\pi\)
0.0221963 + 0.999754i \(0.492934\pi\)
\(240\) −3.12132 2.29289i −0.201480 0.148006i
\(241\) 0.242641 0.420266i 0.0156299 0.0270717i −0.858105 0.513475i \(-0.828358\pi\)
0.873735 + 0.486403i \(0.161691\pi\)
\(242\) 2.83939 10.5967i 0.182523 0.681185i
\(243\) −12.9722 8.64420i −0.832167 0.554526i
\(244\) 1.94218 1.12132i 0.124336 0.0717852i
\(245\) 2.96713 3.34607i 0.189563 0.213772i
\(246\) −5.12132 0.878680i −0.326523 0.0560226i
\(247\) 11.4641 4.53590i 0.729443 0.288612i
\(248\) −4.41421 + 4.41421i −0.280303 + 0.280303i
\(249\) 2.54516 + 6.89363i 0.161293 + 0.436866i
\(250\) 7.23205 + 8.52628i 0.457395 + 0.539249i
\(251\) −14.9941 8.65685i −0.946420 0.546416i −0.0544529 0.998516i \(-0.517341\pi\)
−0.891967 + 0.452101i \(0.850675\pi\)
\(252\) 7.41970 + 5.09393i 0.467397 + 0.320887i
\(253\) −0.497180 + 0.133219i −0.0312574 + 0.00837541i
\(254\) −2.65685 −0.166706
\(255\) −1.31371 8.58579i −0.0822676 0.537663i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 7.96178 2.13335i 0.496642 0.133075i −0.00179903 0.999998i \(-0.500573\pi\)
0.498441 + 0.866924i \(0.333906\pi\)
\(258\) 6.00000 4.24264i 0.373544 0.264135i
\(259\) 9.00000i 0.559233i
\(260\) −3.48477 5.27792i −0.216116 0.327323i
\(261\) 9.35452 1.73862i 0.579030 0.107618i
\(262\) −3.88229 14.4889i −0.239848 0.895126i
\(263\) −1.43467 0.384419i −0.0884656 0.0237043i 0.214315 0.976765i \(-0.431248\pi\)
−0.302780 + 0.953060i \(0.597915\pi\)
\(264\) 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
\(267\) −11.8284 16.7279i −0.723888 1.02373i
\(268\) −1.46410 + 5.46410i −0.0894342 + 0.333773i
\(269\) −5.46447 9.46473i −0.333174 0.577075i 0.649958 0.759970i \(-0.274786\pi\)
−0.983132 + 0.182895i \(0.941453\pi\)
\(270\) 7.58774 8.79921i 0.461775 0.535503i
\(271\) 1.00000 + 1.73205i 0.0607457 + 0.105215i 0.894799 0.446469i \(-0.147319\pi\)
−0.834053 + 0.551684i \(0.813985\pi\)
\(272\) −2.16622 + 0.580438i −0.131347 + 0.0351942i
\(273\) 8.48528 + 12.0000i 0.513553 + 0.726273i
\(274\) 20.4853i 1.23756i
\(275\) −0.851705 + 0.102614i −0.0513598 + 0.00618784i
\(276\) 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
\(280\) −4.45069 + 5.01910i −0.265980 + 0.299948i
\(281\) 5.34474 + 3.08579i 0.318840 + 0.184083i 0.650876 0.759184i \(-0.274402\pi\)
−0.332035 + 0.943267i \(0.607735\pi\)
\(282\) 10.2022 + 4.70017i 0.607532 + 0.279891i
\(283\) −3.01702 + 11.2597i −0.179343 + 0.669317i 0.816428 + 0.577447i \(0.195951\pi\)
−0.995771 + 0.0918699i \(0.970716\pi\)
\(284\) 10.5858 0.628151
\(285\) −14.5779 + 8.51387i −0.863518 + 0.504318i
\(286\) 0.485281 0.0286953
\(287\) −2.32937 + 8.69333i −0.137498 + 0.513151i
\(288\) −2.47323 1.69798i −0.145737 0.100054i
\(289\) 10.3668 + 5.98528i 0.609812 + 0.352075i
\(290\) 0.424910 + 7.07911i 0.0249516 + 0.415700i
\(291\) 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 \(0.524120\pi\)
−0.997130 + 0.0757037i \(0.975880\pi\)
\(294\) 2.21441 2.66390i 0.129147 0.155362i
\(295\) −2.53590 + 12.3923i −0.147646 + 0.721508i
\(296\) 3.00000i 0.174371i
\(297\) 0.242641 + 0.857864i 0.0140794 + 0.0497783i
\(298\) −10.9282 + 2.92820i −0.633054 + 0.169626i
\(299\) 4.24264 + 7.34847i 0.245358 + 0.424973i
\(300\) 5.80991 + 6.42222i 0.335435 + 0.370787i
\(301\) −6.36396 11.0227i −0.366813 0.635338i
\(302\) −2.77659 + 10.3624i −0.159775 + 0.596288i
\(303\) 24.4853 17.3137i 1.40664 0.994647i
\(304\) 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
\(307\) 19.4558 + 5.21317i 1.11040 + 0.297531i 0.766993 0.641655i \(-0.221752\pi\)
0.343408 + 0.939186i \(0.388419\pi\)
\(308\) −0.133219 0.497180i −0.00759086 0.0283295i
\(309\) 4.87453 1.79970i 0.277303 0.102381i
\(310\) 11.6489 7.69125i 0.661615 0.436834i
\(311\) 8.48528i 0.481156i −0.970630 0.240578i \(-0.922663\pi\)
0.970630 0.240578i \(-0.0773370\pi\)
\(312\) −2.82843 4.00000i −0.160128 0.226455i
\(313\) −20.8218 + 5.57919i −1.17692 + 0.315355i −0.793704 0.608304i \(-0.791850\pi\)
−0.383216 + 0.923659i \(0.625183\pi\)
\(314\) −5.91421 + 10.2437i −0.333758 + 0.578086i
\(315\) −13.9706 14.4853i −0.787152 0.816153i
\(316\) 6.48528 0.364826
\(317\) 27.4862 7.36491i 1.54378 0.413655i 0.616296 0.787515i \(-0.288633\pi\)
0.927485 + 0.373860i \(0.121966\pi\)
\(318\) 6.87441 14.9216i 0.385498 0.836762i
\(319\) −0.471253 0.272078i −0.0263851 0.0152334i
\(320\) 1.48356 1.67303i 0.0829337 0.0935254i
\(321\) 13.7873 5.09032i 0.769530 0.284114i
\(322\) 6.36396 6.36396i 0.354650 0.354650i
\(323\) −1.43026 + 9.67025i −0.0795817 + 0.538067i
\(324\) 5.65685 7.00000i 0.314270 0.388889i
\(325\) 5.26795 + 13.1244i 0.292213 + 0.728008i
\(326\) −17.4436 + 10.0711i −0.966112 + 0.557785i
\(327\) 0.356397 + 3.86798i 0.0197088 + 0.213900i
\(328\) 0.776457 2.89778i 0.0428727 0.160003i
\(329\) 9.72792 16.8493i 0.536318 0.928930i
\(330\) −0.656854 + 0.100505i −0.0361586 + 0.00553262i
\(331\) −12.5147 −0.687871 −0.343936 0.938993i \(-0.611760\pi\)
−0.343936 + 0.938993i \(0.611760\pi\)
\(332\) −4.09808 + 1.09808i −0.224911 + 0.0602648i
\(333\) 8.97261 + 0.701625i 0.491696 + 0.0384488i
\(334\) 23.4853i 1.28506i
\(335\) 5.65685 11.3137i 0.309067 0.618134i
\(336\) −3.32162 + 3.99585i −0.181209 + 0.217992i
\(337\) −2.40060 0.643238i −0.130769 0.0350394i 0.192841 0.981230i \(-0.438230\pi\)
−0.323610 + 0.946191i \(0.604897\pi\)
\(338\) 1.29410 + 4.82963i 0.0703895 + 0.262697i
\(339\) −11.9980 32.4969i −0.651642 1.76499i
\(340\) 5.00569 0.300457i 0.271472 0.0162946i
\(341\) 1.07107i 0.0580016i
\(342\) −11.0757 + 6.95195i −0.598904 + 0.375918i
\(343\) 10.6066 + 10.6066i 0.572703 + 0.572703i
\(344\) 2.12132 + 3.67423i 0.114374 + 0.198101i
\(345\) −7.26456 9.06787i −0.391111 0.488197i
\(346\) −9.98528 + 17.2950i −0.536812 + 0.929786i
\(347\) −2.83939 + 10.5967i −0.152426 + 0.568863i 0.846886 + 0.531775i \(0.178475\pi\)
−0.999312 + 0.0370881i \(0.988192\pi\)
\(348\) 0.504022 + 5.47015i 0.0270184 + 0.293231i
\(349\) 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
\(352\) 0.0444063 + 0.165727i 0.00236687 + 0.00883326i
\(353\) 3.51472 3.51472i 0.187070 0.187070i −0.607358 0.794428i \(-0.707771\pi\)
0.794428 + 0.607358i \(0.207771\pi\)
\(354\) −1.65685 + 9.65685i −0.0880608 + 0.513256i
\(355\) −23.1900 4.74548i −1.23080 0.251864i
\(356\) 10.2437 5.91421i 0.542916 0.313453i
\(357\) −11.6039 + 1.06919i −0.614146 + 0.0565876i
\(358\) 2.41818 9.02479i 0.127805 0.476975i
\(359\) 4.60660 + 7.97887i 0.243127 + 0.421109i 0.961603 0.274443i \(-0.0884934\pi\)
−0.718476 + 0.695551i \(0.755160\pi\)
\(360\) 4.65685 + 4.82843i 0.245438 + 0.254480i
\(361\) 18.5000 4.33013i 0.973684 0.227901i
\(362\) 10.2426 + 10.2426i 0.538341 + 0.538341i
\(363\) −7.95086 + 17.2581i −0.417312 + 0.905818i
\(364\) −7.34847 + 4.24264i −0.385164 + 0.222375i
\(365\) 30.3092 20.0118i 1.58645 1.04746i
\(366\) −3.64394 + 1.34536i −0.190472 + 0.0703232i
\(367\) 1.55291 + 5.79555i 0.0810615 + 0.302526i 0.994539 0.104363i \(-0.0332804\pi\)
−0.913478 + 0.406889i \(0.866614\pi\)
\(368\) −2.12132 + 2.12132i −0.110581 + 0.110581i
\(369\) 8.48528 + 3.00000i 0.441726 + 0.156174i
\(370\) −1.34486 + 6.57201i −0.0699161 + 0.341663i
\(371\) −24.6435 14.2279i −1.27943 0.738677i
\(372\) 8.82843 6.24264i 0.457733 0.323666i
\(373\) 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
\(375\) −9.84859 16.6735i −0.508579 0.861015i
\(376\) −3.24264 + 5.61642i −0.167226 + 0.289645i
\(377\) −2.32175 + 8.66490i −0.119576 + 0.446265i
\(378\) −11.1742 10.8691i −0.574741 0.559044i
\(379\) 22.4853i 1.15499i −0.816394 0.577496i \(-0.804030\pi\)
0.816394 0.577496i \(-0.195970\pi\)
\(380\) −4.12252 8.83203i −0.211481 0.453074i
\(381\) 4.53553 + 0.778175i 0.232362 + 0.0398671i
\(382\) −10.2251 2.73980i −0.523161 0.140181i
\(383\) 29.4465 + 7.89017i 1.50465 + 0.403169i 0.914653 0.404239i \(-0.132464\pi\)
0.589994 + 0.807408i \(0.299130\pi\)
\(384\) 1.10721 1.33195i 0.0565019 0.0679709i
\(385\) 0.0689592 + 1.14888i 0.00351449 + 0.0585523i
\(386\) 10.3923 + 6.00000i 0.528954 + 0.305392i
\(387\) −11.4853 + 5.48528i −0.583830 + 0.278833i
\(388\) 10.2426 + 10.2426i 0.519991 + 0.519991i
\(389\) 2.46447 4.26858i 0.124953 0.216426i −0.796761 0.604294i \(-0.793455\pi\)
0.921715 + 0.387868i \(0.126789\pi\)
\(390\) 4.40300 + 10.0306i 0.222955 + 0.507921i
\(391\) −6.72792 −0.340246
\(392\) 1.41421 + 1.41421i 0.0714286 + 0.0714286i
\(393\) 2.38378 + 25.8712i 0.120246 + 1.30503i
\(394\) −7.37396 + 4.25736i −0.371495 + 0.214483i
\(395\) −14.2071 2.90727i −0.714838 0.146281i
\(396\) −0.506052 + 0.0940542i −0.0254301 + 0.00472640i
\(397\) 7.69897 + 2.06293i 0.386400 + 0.103536i 0.446789 0.894639i \(-0.352567\pi\)
−0.0603888 + 0.998175i \(0.519234\pi\)
\(398\) −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 −0.999996 0.00283317i \(-0.999098\pi\)
−0.497544 + 0.867439i \(0.665765\pi\)
\(402\) 4.09978 8.89898i 0.204478 0.443841i
\(403\) 17.0552 4.56993i 0.849581 0.227644i
\(404\) 8.65685 + 14.9941i 0.430695 + 0.745985i
\(405\) −15.5303 + 12.7988i −0.771708 + 0.635977i
\(406\) 9.51472 0.472208
\(407\) −0.363961 0.363961i −0.0180409 0.0180409i
\(408\) 3.86798 0.356397i 0.191494 0.0176443i
\(409\) 21.1794 + 12.2279i 1.04725 + 0.604632i 0.921879 0.387478i \(-0.126654\pi\)
0.125374 + 0.992110i \(0.459987\pi\)
\(410\) −3.00000 + 6.00000i −0.148159 + 0.296319i
\(411\) −6.00000 + 34.9706i −0.295958 + 1.72497i
\(412\) 0.776457 + 2.89778i 0.0382533 + 0.142763i
\(413\) 16.3923 + 4.39230i 0.806613 + 0.216131i
\(414\) −5.84847 6.84072i −0.287437 0.336203i
\(415\) 9.46979 0.568406i 0.464854 0.0279020i
\(416\) 2.44949 1.41421i 0.120096 0.0693375i
\(417\) −19.7990 + 14.0000i −0.969561 + 0.685583i
\(418\) 0.739821 + 0.109422i 0.0361858 + 0.00535199i
\(419\) −29.8284 −1.45721 −0.728607 0.684932i \(-0.759832\pi\)
−0.728607 + 0.684932i \(0.759832\pi\)
\(420\) 9.06787 7.26456i 0.442467 0.354474i
\(421\) 10.4853 + 18.1610i 0.511021 + 0.885115i 0.999918 + 0.0127735i \(0.00406603\pi\)
−0.488897 + 0.872341i \(0.662601\pi\)
\(422\) −3.36652 + 0.902057i −0.163880 + 0.0439115i
\(423\) −16.0396 11.0119i −0.779872 0.535415i
\(424\) 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
\(427\) 1.74131 + 6.49867i 0.0842681 + 0.314493i
\(428\) 2.19615 + 8.19615i 0.106155 + 0.396176i
\(429\) −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 0.717056 0.697015i \(-0.245489\pi\)
−0.245105 + 0.969497i \(0.578822\pi\)
\(432\) 3.72474 + 3.62302i 0.179207 + 0.174313i
\(433\) −9.19051 + 2.46259i −0.441668 + 0.118345i −0.472798 0.881171i \(-0.656756\pi\)
0.0311302 + 0.999515i \(0.490089\pi\)
\(434\) −9.36396 16.2189i −0.449485 0.778530i
\(435\) 1.34806 12.2093i 0.0646344 0.585389i
\(436\) −2.24264 −0.107403
\(437\) 4.81105 + 12.1595i 0.230144 + 0.581669i
\(438\) 22.9706 16.2426i 1.09758 0.776103i
\(439\) −25.5095 + 14.7279i −1.21750 + 0.702925i −0.964383 0.264510i \(-0.914790\pi\)
−0.253119 + 0.967435i \(0.581457\pi\)
\(440\) −0.0229864 0.382959i −0.00109583 0.0182569i
\(441\) −4.56048 + 3.89898i −0.217166 + 0.185666i
\(442\) 6.12701 + 1.64173i 0.291432 + 0.0780890i
\(443\) 8.86265 + 33.0759i 0.421077 + 1.57148i 0.772343 + 0.635205i \(0.219085\pi\)
−0.351266 + 0.936276i \(0.614249\pi\)
\(444\) −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
\(447\) 19.5133 1.79796i 0.922946 0.0850405i
\(448\) −2.12132 2.12132i −0.100223 0.100223i
\(449\) −17.8284 −0.841375 −0.420688 0.907205i \(-0.638211\pi\)
−0.420688 + 0.907205i \(0.638211\pi\)
\(450\) −8.03711 12.6651i −0.378873 0.597039i
\(451\) −0.257359 0.445759i −0.0121186 0.0209900i
\(452\) 19.3185 5.17638i 0.908667 0.243476i
\(453\) 7.77501 16.8764i 0.365302 0.792924i
\(454\) −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 \(0.940638\pi\)
\(458\) 15.2204 + 4.07830i 0.711204 + 0.190567i
\(459\) 0.161314 + 11.6520i 0.00752947 + 0.543868i
\(460\) 5.59808 3.69615i 0.261012 0.172334i
\(461\) 21.7482 12.5563i 1.01292 0.584807i 0.100872 0.994899i \(-0.467837\pi\)
0.912044 + 0.410092i \(0.134503\pi\)
\(462\) 0.0817984 + 0.887758i 0.00380560 + 0.0413023i
\(463\) −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
\(465\) −22.1387 + 9.71789i −1.02666 + 0.450657i
\(466\) 5.24264 9.08052i 0.242861 0.420647i
\(467\) 1.75736 + 1.75736i 0.0813209 + 0.0813209i 0.746597 0.665276i \(-0.231686\pi\)
−0.665276 + 0.746597i \(0.731686\pi\)
\(468\) 3.65685 + 7.65685i 0.169038 + 0.353938i
\(469\) −14.6969 8.48528i −0.678642 0.391814i
\(470\) 9.62133 10.8501i 0.443799 0.500477i
\(471\) 13.0965 15.7549i 0.603455 0.725947i
\(472\) −5.46410 1.46410i −0.251506 0.0673907i
\(473\) 0.703119 + 0.188400i 0.0323294 + 0.00866265i
\(474\) −11.0711 1.89949i −0.508511 0.0872467i
\(475\) 5.07180 + 21.1962i 0.232710 + 0.972546i
\(476\) 6.72792i 0.308374i
\(477\) −16.1058 + 23.4593i −0.737433 + 1.07413i
\(478\) 0.177625 0.662907i 0.00812439 0.0303206i
\(479\) −15.1924 + 26.3140i −0.694158 + 1.20232i 0.276306 + 0.961070i \(0.410890\pi\)
−0.970464 + 0.241247i \(0.922444\pi\)
\(480\) −3.02262 + 2.42152i −0.137963 + 0.110527i
\(481\) −4.24264 + 7.34847i −0.193448 + 0.335061i
\(482\) −0.343146 0.343146i −0.0156299 0.0156299i
\(483\) −12.7279 + 9.00000i −0.579141 + 0.409514i
\(484\) −9.50079 5.48528i −0.431854 0.249331i
\(485\) −17.8466 27.0299i −0.810372 1.22736i
\(486\) −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 \(-0.0391142\pi\)
\(488\) −0.580438 2.16622i −0.0262752 0.0980604i
\(489\) 32.7278 12.0833i 1.48000 0.546425i
\(490\) −2.46410 3.73205i −0.111317 0.168597i
\(491\) 5.93908 3.42893i 0.268027 0.154746i −0.359964 0.932966i \(-0.617211\pi\)
0.627991 + 0.778221i \(0.283878\pi\)
\(492\) −2.17423 + 4.71940i −0.0980221 + 0.212767i
\(493\) −5.02944 5.02944i −0.226514 0.226514i
\(494\) −1.41421 12.2474i −0.0636285 0.551039i
\(495\) 1.15076 + 0.0208153i 0.0517227 + 0.000935577i
\(496\) 3.12132 + 5.40629i 0.140151 + 0.242749i
\(497\) −8.21941 + 30.6753i −0.368691 + 1.37597i
\(498\) 7.31747 0.674235i 0.327904 0.0302132i
\(499\) −32.8835 + 18.9853i −1.47207 + 0.849898i −0.999507 0.0314008i \(-0.990003\pi\)
−0.472560 + 0.881299i \(0.656670\pi\)
\(500\) 10.1075 4.77886i 0.452023 0.213717i
\(501\) −6.87868 + 40.0919i −0.307317 + 1.79117i
\(502\) −12.2426 + 12.2426i −0.546416 + 0.546416i
\(503\) −4.65112 17.3582i −0.207383 0.773965i −0.988710 0.149843i \(-0.952123\pi\)
0.781326 0.624123i \(-0.214543\pi\)
\(504\) 6.84072 5.84847i 0.304710 0.260512i
\(505\) −12.2426 36.7279i −0.544790 1.63437i
\(506\) 0.514719i 0.0228820i
\(507\) −0.794593 8.62372i −0.0352891 0.382993i
\(508\) −0.687644 + 2.56632i −0.0305093 + 0.113862i
\(509\) 6.36396 11.0227i 0.282078 0.488573i −0.689819 0.723982i \(-0.742310\pi\)
0.971896 + 0.235409i \(0.0756431\pi\)
\(510\) −8.63325 0.953220i −0.382287 0.0422093i
\(511\) −24.3640 42.1996i −1.07780 1.86680i
\(512\) 0.707107 + 0.707107i 0.0312500 + 0.0312500i
\(513\) 20.9435 8.62372i 0.924679 0.380747i
\(514\) 8.24264i 0.363567i
\(515\) −0.401924 6.69615i −0.0177109 0.295068i
\(516\) −2.54516 6.89363i −0.112045 0.303475i
\(517\) 0.287988 + 1.07478i 0.0126657 + 0.0472690i
\(518\) 8.69333 + 2.32937i 0.381963 + 0.102347i
\(519\) 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 \(-0.718474\pi\)
0.633722 0.773561i \(-0.281526\pi\)
\(522\) 0.741752 9.48576i 0.0324656 0.415181i
\(523\) 22.8508 6.12284i 0.999194 0.267733i 0.278086 0.960556i \(-0.410300\pi\)
0.721108 + 0.692823i \(0.243633\pi\)
\(524\) −15.0000 −0.655278
\(525\) −23.1213 + 11.8492i −1.00910 + 0.517143i
\(526\) −0.742641 + 1.28629i −0.0323807 + 0.0560850i
\(527\) −3.62347 + 13.5230i −0.157841 + 0.589069i
\(528\) −0.0272661 0.295919i −0.00118661 0.0128782i
\(529\) 12.1244 7.00000i 0.527146 0.304348i
\(530\) −15.8692 14.0720i −0.689313 0.611250i
\(531\) 5.65685 16.0000i 0.245487 0.694341i
\(532\) −12.1595 + 4.81105i −0.527182 + 0.208585i
\(533\) −6.00000 + 6.00000i −0.259889 + 0.259889i
\(534\) −19.2194 + 7.09588i −0.831703 + 0.307069i
\(535\) −1.13681 18.9396i −0.0491487 0.818829i
\(536\) 4.89898 + 2.82843i 0.211604 + 0.122169i
\(537\) −6.77140 + 14.6980i −0.292207 + 0.634266i
\(538\) −10.5565 + 2.82862i −0.455125 + 0.121950i
\(539\) 0.343146 0.0147803
\(540\) −6.53553 9.60660i −0.281245 0.413402i
\(541\) −0.636039 + 1.10165i −0.0273455 + 0.0473637i −0.879374 0.476131i \(-0.842039\pi\)
0.852029 + 0.523495i \(0.175372\pi\)
\(542\) 1.93185 0.517638i 0.0829801 0.0222345i
\(543\) −14.4853 20.4853i −0.621623 0.879108i
\(544\) 2.24264i 0.0961524i
\(545\) 4.91289 + 1.00535i 0.210445 + 0.0430644i
\(546\) 13.7873 5.09032i 0.590040 0.217846i
\(547\) 5.03554 + 18.7929i 0.215304 + 0.803526i 0.986059 + 0.166395i \(0.0532126\pi\)
−0.770755 + 0.637132i \(0.780121\pi\)
\(548\) −19.7873 5.30198i −0.845270 0.226489i
\(549\) 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
\(552\) 4.24264 3.00000i 0.180579 0.127688i
\(553\) −5.03554 + 18.7929i −0.214133 + 0.799155i
\(554\) −14.4853 25.0892i −0.615421 1.06594i
\(555\) 4.22072 10.8252i 0.179160 0.459505i
\(556\) −7.00000 12.1244i −0.296866 0.514187i
\(557\) −13.4945 + 3.61585i −0.571781 + 0.153208i −0.533114 0.846044i \(-0.678978\pi\)
−0.0386680 + 0.999252i \(0.512311\pi\)
\(558\) −16.8995 + 8.07107i −0.715413 + 0.341676i
\(559\) 12.0000i 0.507546i
\(560\) 3.69615 + 5.59808i 0.156191 + 0.236562i
\(561\) 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 \(-0.449608\pi\)
0.987495 0.157650i \(-0.0503919\pi\)
\(564\) 7.18054 8.63808i 0.302355 0.363729i
\(565\) −44.6410 + 2.67949i −1.87806 + 0.112727i
\(566\) 10.0951 + 5.82843i 0.424330 + 0.244987i
\(567\) 15.8921 + 21.8275i 0.667407 + 0.916669i
\(568\) 2.73980 10.2251i 0.114960 0.429035i
\(569\) −10.7990 −0.452717 −0.226359 0.974044i \(-0.572682\pi\)
−0.226359 + 0.974044i \(0.572682\pi\)
\(570\) 4.45074 + 16.2847i 0.186421 + 0.682090i
\(571\) −10.4853 −0.438795 −0.219398 0.975636i \(-0.570409\pi\)
−0.219398 + 0.975636i \(0.570409\pi\)
\(572\) 0.125600 0.468746i 0.00525160 0.0195992i
\(573\) 16.6528 + 7.67199i 0.695682 + 0.320502i
\(574\) 7.79423 + 4.50000i 0.325325 + 0.187826i
\(575\) −13.9205 + 5.58750i −0.580524 + 0.233015i
\(576\) −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
\(580\) 6.94787 + 1.42178i 0.288495 + 0.0590361i
\(581\) 12.7279i 0.528043i
\(582\) −14.4853 20.4853i −0.600434 0.849142i
\(583\) 1.57196 0.421207i 0.0651041 0.0174446i
\(584\) 8.12132 + 14.0665i 0.336063 + 0.582078i
\(585\) −4.57849 18.4130i −0.189297 0.761283i
\(586\) 12.9853 + 22.4912i 0.536417 + 0.929102i
\(587\) −10.6040 + 39.5745i −0.437672 + 1.63342i 0.296917 + 0.954903i \(0.404042\pi\)
−0.734589 + 0.678512i \(0.762625\pi\)
\(588\) −2.00000 2.82843i −0.0824786 0.116642i
\(589\) 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
\(592\) −2.89778 0.776457i −0.119098 0.0319122i
\(593\) −9.96072 37.1739i −0.409038 1.52655i −0.796485 0.604658i \(-0.793310\pi\)
0.387447 0.921892i \(-0.373357\pi\)
\(594\) 0.891433 0.0123413i 0.0365760 0.000506368i
\(595\) −3.01604 + 14.7387i −0.123646 + 0.604226i
\(596\) 11.3137i 0.463428i
\(597\) 20.1421 14.2426i 0.824363 0.582912i
\(598\) 8.19615 2.19615i 0.335166 0.0898074i
\(599\) 11.8492 20.5235i 0.484147 0.838567i −0.515687 0.856777i \(-0.672463\pi\)
0.999834 + 0.0182098i \(0.00579669\pi\)
\(600\) 7.70711 3.94975i 0.314641 0.161248i
\(601\) 23.0000 0.938190 0.469095 0.883148i \(-0.344580\pi\)
0.469095 + 0.883148i \(0.344580\pi\)
\(602\) −12.2942 + 3.29423i −0.501075 + 0.134263i
\(603\) −9.60521 + 13.9907i −0.391154 + 0.569746i
\(604\) 9.29065 + 5.36396i 0.378031 + 0.218256i
\(605\) 18.3541 + 16.2755i 0.746201 + 0.661694i
\(606\) −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 \(0.289973\pi\)
\(608\) 4.05317 1.60368i 0.164378 0.0650379i
\(609\) −16.2426 2.78680i −0.658185 0.112927i
\(610\) 0.300457 + 5.00569i 0.0121651 + 0.202674i
\(611\) 15.8856 9.17157i 0.642664 0.371042i
\(612\) −6.70745 0.524498i −0.271132 0.0212016i
\(613\) 2.79498 10.4310i 0.112888 0.421305i −0.886232 0.463242i \(-0.846686\pi\)
0.999120 + 0.0419368i \(0.0133528\pi\)
\(614\) 10.0711 17.4436i 0.406435 0.703966i
\(615\) 6.87868 9.36396i 0.277375 0.377591i
\(616\) −0.514719 −0.0207386
\(617\) −31.0871 + 8.32977i −1.25152 + 0.335344i −0.822924 0.568152i \(-0.807659\pi\)
−0.428597 + 0.903496i \(0.640992\pi\)
\(618\) −0.476756 5.17423i −0.0191779 0.208138i
\(619\) 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
\(622\) −8.19615 2.19615i −0.328636 0.0880577i
\(623\) 9.18427 + 34.2761i 0.367960 + 1.37324i
\(624\) −4.59575 + 1.69677i −0.183977 + 0.0679253i
\(625\) −24.2846 + 5.93782i −0.971384 + 0.237513i
\(626\) 21.5563i 0.861565i
\(627\) −1.23090 0.403483i −0.0491576 0.0161136i
\(628\) 8.36396 + 8.36396i 0.333758 + 0.333758i
\(629\) −3.36396 5.82655i −0.134130 0.232320i
\(630\) −17.6076 + 9.74546i −0.701502 + 0.388268i
\(631\) 0.121320 0.210133i 0.00482969 0.00836526i −0.863600 0.504177i \(-0.831796\pi\)
0.868430 + 0.495812i \(0.165129\pi\)
\(632\) 1.67851 6.26430i 0.0667677 0.249181i
\(633\) 6.01122 0.553876i 0.238925 0.0220146i
\(634\) 28.4558i 1.13013i
\(635\) 2.65685 5.31371i 0.105434 0.210868i
\(636\) −12.6339 10.5022i −0.500968 0.416438i
\(637\) −1.46410 5.46410i −0.0580098 0.216496i
\(638\) −0.384776 + 0.384776i −0.0152334 + 0.0152334i
\(639\) 29.9411 + 10.5858i 1.18445 + 0.418767i
\(640\) −1.23205 1.86603i −0.0487011 0.0737611i
\(641\) −15.2913 + 8.82843i −0.603969 + 0.348702i −0.770602 0.637317i \(-0.780044\pi\)
0.166632 + 0.986019i \(0.446711\pi\)
\(642\) −1.34847 14.6349i −0.0532198 0.577595i
\(643\) −4.29272 + 16.0206i −0.169288 + 0.631792i 0.828166 + 0.560483i \(0.189384\pi\)
−0.997454 + 0.0713094i \(0.977282\pi\)
\(644\) −4.50000 7.79423i −0.177325 0.307136i
\(645\) 2.48528 + 16.2426i 0.0978579 + 0.639553i
\(646\) 8.97056 + 3.88437i 0.352942 + 0.152828i
\(647\) 12.7071 + 12.7071i 0.499568 + 0.499568i 0.911303 0.411735i \(-0.135077\pi\)
−0.411735 + 0.911303i \(0.635077\pi\)
\(648\) −5.29738 7.27583i −0.208101 0.285822i
\(649\) −0.840532 + 0.485281i −0.0329938 + 0.0190490i
\(650\) 14.0406 1.69161i 0.550718 0.0663506i
\(651\) 11.2349 + 30.4300i 0.440330 + 1.19264i
\(652\) 5.21317 + 19.4558i 0.204163 + 0.761948i
\(653\) 14.8492 14.8492i 0.581096 0.581096i −0.354109 0.935204i \(-0.615216\pi\)
0.935204 + 0.354109i \(0.115216\pi\)
\(654\) 3.82843 + 0.656854i 0.149703 + 0.0256850i
\(655\) 32.8601 + 6.72432i 1.28395 + 0.262741i
\(656\) −2.59808 1.50000i −0.101438 0.0585652i
\(657\) −43.9706 + 21.0000i −1.71546 + 0.819288i
\(658\) −13.7574 13.7574i −0.536318 0.536318i
\(659\) −19.7132 + 34.1443i −0.767917 + 1.33007i 0.170773 + 0.985310i \(0.445374\pi\)
−0.938690 + 0.344762i \(0.887960\pi\)
\(660\) −0.0729260 + 0.660485i −0.00283864 + 0.0257093i
\(661\) −2.87868 + 4.98602i −0.111968 + 0.193934i −0.916564 0.399889i \(-0.869049\pi\)
0.804596 + 0.593823i \(0.202382\pi\)
\(662\) −3.23905 + 12.0883i −0.125889 + 0.469825i
\(663\) −9.97861 4.59716i −0.387537 0.178539i
\(664\) 4.24264i 0.164646i
\(665\) 28.7942 5.08846i 1.11659 0.197322i
\(666\) 3.00000 8.48528i 0.116248 0.328798i
\(667\) −9.19051 2.46259i −0.355858 0.0953519i
\(668\) −22.6850 6.07844i −0.877711 0.235182i
\(669\) −23.2895 19.3598i −0.900426 0.748494i
\(670\) −9.46410 8.39230i −0.365630 0.324223i
\(671\) −0.333226 0.192388i −0.0128640 0.00742706i
\(672\) 3.00000 + 4.24264i 0.115728 + 0.163663i
\(673\) −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
\(675\) 10.0107 + 23.9747i 0.385311 + 0.922787i
\(676\) 5.00000 0.192308
\(677\) −34.6066 34.6066i −1.33004 1.33004i −0.905329 0.424711i \(-0.860376\pi\)
−0.424711 0.905329i \(-0.639624\pi\)
\(678\) −34.4949 + 3.17837i −1.32477 + 0.122065i
\(679\) −37.6339 + 21.7279i −1.44426 + 0.833841i
\(680\) 1.00535 4.91289i 0.0385533 0.188401i
\(681\) 37.3236 13.7801i 1.43024 0.528053i
\(682\) 1.03457 + 0.277213i 0.0396158 + 0.0106150i
\(683\) 0.899495 0.899495i 0.0344182 0.0344182i −0.689688 0.724106i \(-0.742252\pi\)
0.724106 + 0.689688i \(0.242252\pi\)
\(684\) 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
\(687\) −24.7884 11.4201i −0.945737 0.435703i
\(688\) 4.09808 1.09808i 0.156238 0.0418638i
\(689\) −13.4142 23.2341i −0.511041 0.885149i
\(690\) −10.6391 + 4.67009i −0.405023 + 0.177787i
\(691\) −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
\(693\) 0.120380 1.53946i 0.00457285 0.0584791i
\(694\) 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
\(697\) −1.74131 6.49867i −0.0659570 0.246155i
\(698\) 21.4847 + 5.75682i 0.813209 + 0.217899i
\(699\) −11.6094 + 13.9659i −0.439107 + 0.528238i
\(700\) −5.58750 13.9205i −0.211188 0.526145i
\(701\) 28.7635 16.6066i 1.08638 0.627223i 0.153771 0.988107i \(-0.450858\pi\)
0.932611 + 0.360884i \(0.117525\pi\)
\(702\) −4.00000 14.1421i −0.150970 0.533761i
\(703\) −8.12493 + 10.2462i −0.306437 + 0.386445i
\(704\) 0.171573 0.00646640
\(705\) −19.6026 + 15.7042i −0.738275 + 0.591456i
\(706\) −2.48528 4.30463i −0.0935348 0.162007i
\(707\) −50.1713 + 13.4434i −1.88688 + 0.505589i
\(708\) 8.89898 + 4.09978i 0.334444 + 0.154079i
\(709\) 37.8440 + 21.8492i 1.42126 + 0.820566i 0.996407 0.0846962i \(-0.0269920\pi\)
0.424854 + 0.905262i \(0.360325\pi\)
\(710\) −10.5858 + 21.1716i −0.397277 + 0.794555i
\(711\) 18.3431 + 6.48528i 0.687922 + 0.243217i
\(712\) −3.06142 11.4254i −0.114732 0.428184i
\(713\) 4.84714 + 18.0898i 0.181527 + 0.677468i
\(714\) −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
\(717\) −0.497386 + 1.07963i −0.0185752 + 0.0403194i
\(718\) 8.89927 2.38455i 0.332118 0.0889907i
\(719\) −3.70711 6.42090i −0.138252 0.239459i 0.788583 0.614928i \(-0.210815\pi\)
−0.926835 + 0.375469i \(0.877482\pi\)
\(720\) 5.86919 3.24849i 0.218732 0.121064i
\(721\) −9.00000 −0.335178
\(722\) 0.605571 18.9903i 0.0225370 0.706748i
\(723\) 0.485281 + 0.686292i 0.0180478 + 0.0255235i
\(724\) 12.5446 7.24264i 0.466217 0.269171i
\(725\) −14.5831 6.22929i −0.541604 0.231350i
\(726\) 14.6123 + 12.1467i 0.542312 + 0.450805i
\(727\) 14.6546 + 3.92669i 0.543510 + 0.145633i 0.520120 0.854093i \(-0.325887\pi\)
0.0233900 + 0.999726i \(0.492554\pi\)
\(728\) 2.19615 + 8.19615i 0.0813948 + 0.303770i
\(729\) 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
\(732\) 0.356397 + 3.86798i 0.0131728 + 0.142965i
\(733\) −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
\(735\) 3.11339 + 7.09273i 0.114839 + 0.261619i
\(736\) 1.50000 + 2.59808i 0.0552907 + 0.0957664i
\(737\) 0.937492 0.251200i 0.0345329 0.00925308i
\(738\) 5.09393 7.41970i 0.187510 0.273123i
\(739\) 29.4194 16.9853i 1.08221 0.624814i 0.150718 0.988577i \(-0.451842\pi\)
0.931491 + 0.363763i \(0.118508\pi\)
\(740\) 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
\(743\) −25.0856 6.72168i −0.920303 0.246594i −0.232588 0.972575i \(-0.574719\pi\)
−0.687715 + 0.725981i \(0.741386\pi\)
\(744\) −3.74496 10.1433i −0.137297 0.371872i
\(745\) 5.07180 24.7846i 0.185816 0.908038i
\(746\) 15.1427 8.74264i 0.554414 0.320091i
\(747\) −12.6892 0.992248i −0.464273 0.0363044i
\(748\) 0.272078 + 0.272078i 0.00994815 + 0.00994815i
\(749\) −25.4558 −0.930136
\(750\) −18.6544 + 5.19759i −0.681161 + 0.189789i
\(751\) 21.6066 37.4237i 0.788436 1.36561i −0.138489 0.990364i \(-0.544224\pi\)
0.926925 0.375247i \(-0.122442\pi\)
\(752\) 4.58579 + 4.58579i 0.167226 + 0.167226i
\(753\) 24.4853 17.3137i 0.892293 0.630947i
\(754\) 7.76874 + 4.48528i 0.282921 + 0.163344i
\(755\) −17.9482 15.9156i −0.653201 0.579226i
\(756\) −13.3908 + 7.98036i −0.487019 + 0.290243i
\(757\) 44.2100 + 11.8460i 1.60684 + 0.430551i 0.947099 0.320942i \(-0.103999\pi\)
0.659741 + 0.751493i \(0.270666\pi\)
\(758\) −21.7191 5.81962i −0.788874 0.211378i
\(759\) 0.150758 0.878680i 0.00547215 0.0318941i
\(760\) −9.59808 + 1.69615i −0.348159 + 0.0615259i
\(761\) 6.51472i 0.236158i 0.993004 + 0.118079i \(0.0376737\pi\)
−0.993004 + 0.118079i \(0.962326\pi\)
\(762\) 1.92554 4.17958i 0.0697550 0.151410i
\(763\) 1.74131 6.49867i 0.0630398 0.235268i
\(764\) −5.29289 + 9.16756i −0.191490 + 0.331671i
\(765\) 14.4587 + 4.15587i 0.522755 + 0.150256i
\(766\) 15.2426 26.4010i 0.550739 0.953908i
\(767\) 11.3137 + 11.3137i 0.408514 + 0.408514i
\(768\) −1.00000 1.41421i −0.0360844 0.0510310i
\(769\) 33.7495 + 19.4853i 1.21704 + 0.702657i 0.964283 0.264873i \(-0.0853301\pi\)
0.252755 + 0.967530i \(0.418663\pi\)
\(770\) 1.12758 + 0.230742i 0.0406351 + 0.00831537i
\(771\) −2.41421 + 14.0711i −0.0869458 + 0.506757i
\(772\) 8.48528 8.48528i 0.305392 0.305392i
\(773\) 2.18853 + 8.16772i 0.0787161 + 0.293772i 0.994050 0.108923i \(-0.0347401\pi\)
−0.915334 + 0.402695i \(0.868073\pi\)
\(774\) 2.32577 + 12.5136i 0.0835979 + 0.449793i
\(775\) 3.73357 + 30.9891i 0.134114 + 1.11316i
\(776\) 12.5446 7.24264i 0.450326 0.259996i
\(777\) −14.1582 6.52270i −0.507922 0.234001i
\(778\) −3.48528 3.48528i −0.124953 0.124953i
\(779\) −10.5000 + 7.79423i −0.376202 + 0.279257i
\(780\) 10.8284 1.65685i 0.387720 0.0593249i
\(781\) −0.908117 1.57290i −0.0324950 0.0562830i
\(782\) −1.74131 + 6.49867i −0.0622693 + 0.232392i
\(783\) −4.04456 + 15.9760i −0.144541 + 0.570934i
\(784\) 1.73205 1.00000i 0.0618590 0.0357143i
\(785\) −14.5732 22.0721i −0.520141 0.787789i
\(786\) 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 \(0.228096\pi\)
\(788\) 2.20377 + 8.22459i 0.0785061 + 0.292989i
\(789\) 1.64451 1.97832i 0.0585462 0.0704301i
\(790\) −6.48528 + 12.9706i −0.230736 + 0.461472i
\(791\) 60.0000i 2.13335i
\(792\) −0.0401266 + 0.513152i −0.00142584 + 0.0182341i
\(793\) −1.64173 + 6.12701i −0.0582994 + 0.217576i
\(794\) 3.98528 6.90271i 0.141432 0.244968i
\(795\) 22.9688 + 28.6704i 0.814619 + 1.01683i
\(796\) 7.12132 + 12.3345i 0.252409 + 0.437184i
\(797\) 1.77817 + 1.77817i 0.0629862 + 0.0629862i 0.737898 0.674912i \(-0.235818\pi\)
−0.674912 + 0.737898i \(0.735818\pi\)
\(798\) 22.1667 4.65153i 0.784693 0.164662i
\(799\) 14.5442i 0.514535i
\(800\) 1.86250 + 4.64016i 0.0658494 + 0.164054i
\(801\) 34.8878 6.48420i 1.23270 0.229108i
\(802\) 8.96224 + 33.4475i 0.316468 + 1.18107i
\(803\) 2.69184 + 0.721276i 0.0949929 + 0.0254533i
\(804\) −7.53465 6.26330i −0.265727 0.220890i
\(805\) 6.36396 + 19.0919i 0.224300 + 0.672900i
\(806\) 17.6569i 0.621936i
\(807\) 18.8496 1.73681i 0.663538 0.0611386i
\(808\) 16.7238 4.48112i 0.588340 0.157645i
\(809\) 24.6863 0.867924 0.433962 0.900931i \(-0.357115\pi\)
0.433962 + 0.900931i \(0.357115\pi\)
\(810\) 8.34315 + 18.3137i 0.293148 + 0.643478i
\(811\) −10.2279 + 17.7153i −0.359151 + 0.622068i −0.987819 0.155606i \(-0.950267\pi\)
0.628668 + 0.777674i \(0.283600\pi\)
\(812\) 2.46259 9.19051i 0.0864200 0.322524i
\(813\) −3.44949 + 0.317837i −0.120979 + 0.0111470i
\(814\) −0.445759 + 0.257359i −0.0156239 + 0.00902044i
\(815\) −2.69853 44.9583i −0.0945255 1.57482i
\(816\) 0.656854 3.82843i 0.0229945 0.134022i
\(817\) 2.70577 18.2942i 0.0946630 0.640034i
\(818\) 17.2929 17.2929i 0.604632 0.604632i
\(819\) −25.0273 + 4.65153i −0.874523 + 0.162538i
\(820\) 5.01910 + 4.45069i 0.175274 + 0.155425i
\(821\) −5.79050 3.34315i −0.202090 0.116677i 0.395540 0.918449i \(-0.370557\pi\)
−0.597630 + 0.801772i \(0.703891\pi\)
\(822\) 32.2261 + 14.8466i 1.12401 + 0.517835i
\(823\) 38.0026 10.1828i 1.32469 0.354949i 0.473955 0.880549i \(-0.342826\pi\)
0.850731 + 0.525601i \(0.176159\pi\)
\(824\) 3.00000 0.104510
\(825\) 0.455844 1.41421i 0.0158705 0.0492366i
\(826\) 8.48528 14.6969i 0.295241 0.511372i
\(827\) −6.73305 + 1.80411i −0.234131 + 0.0627352i −0.373977 0.927438i \(-0.622006\pi\)
0.139846 + 0.990173i \(0.455339\pi\)
\(828\) −8.12132 + 3.87868i −0.282235 + 0.134793i
\(829\) 28.9706i 1.00619i −0.864231 0.503095i \(-0.832195\pi\)
0.864231 0.503095i \(-0.167805\pi\)
\(830\) 1.90192 9.29423i 0.0660167 0.322607i
\(831\) 17.3795 + 47.0727i 0.602887 + 1.63293i
\(832\) −0.732051 2.73205i −0.0253793 0.0947168i
\(833\) 4.33245 + 1.16088i 0.150110 + 0.0402220i
\(834\) 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
\(837\) 31.2132 8.82843i 1.07889 0.305155i
\(838\) −7.72017 + 28.8120i −0.266689 + 0.995296i
\(839\) 14.1213 + 24.4588i 0.487522 + 0.844413i 0.999897 0.0143488i \(-0.00456751\pi\)
−0.512375 + 0.858762i \(0.671234\pi\)
\(840\) −4.67009 10.6391i −0.161133 0.367084i
\(841\) 9.47056 + 16.4035i 0.326571 + 0.565638i
\(842\) 20.2560 5.42758i 0.698068 0.187047i
\(843\) −8.72792 + 6.17157i −0.300606 + 0.212560i
\(844\) 3.48528i 0.119968i
\(845\) −10.9534 2.24144i −0.376807 0.0771078i
\(846\) −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
\(850\) −4.40477 + 10.3118i −0.151083 + 0.353693i
\(851\) −7.79423 4.50000i −0.267183 0.154258i
\(852\) −7.67199 + 16.6528i −0.262838 + 0.570517i
\(853\) 5.47961 20.4502i 0.187618 0.700200i −0.806437 0.591320i \(-0.798607\pi\)
0.994055 0.108880i \(-0.0347265\pi\)
\(854\) 6.72792 0.230225
\(855\) −2.82822 29.1033i −0.0967231 0.995311i
\(856\) 8.48528 0.290021
\(857\) 2.19615 8.19615i 0.0750191 0.279975i −0.918219 0.396074i \(-0.870372\pi\)
0.993238 + 0.116099i \(0.0370390\pi\)
\(858\) −0.351705 + 0.763412i −0.0120070 + 0.0260624i
\(859\) −12.5191 7.22792i −0.427147 0.246614i 0.270983 0.962584i \(-0.412651\pi\)
−0.698131 + 0.715971i \(0.745984\pi\)
\(860\) −9.46979 + 0.568406i −0.322917 + 0.0193825i
\(861\) −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 \(0.643328\pi\)
−0.900327 + 0.435215i \(0.856672\pi\)
\(864\) 4.46360 2.66012i 0.151855 0.0904991i
\(865\) −24.6047 37.2656i −0.836587 1.26707i
\(866\) 9.51472i 0.323323i
\(867\) −16.9289 + 11.9706i −0.574937 + 0.406542i
\(868\) −18.0898 + 4.84714i −0.614007 + 0.164523i
\(869\) −0.556349 0.963625i −0.0188729 0.0326887i
\(870\) −11.4443 4.46211i −0.387999 0.151280i
\(871\) −8.00000 13.8564i −0.271070 0.469506i
\(872\) −0.580438 + 2.16622i −0.0196561 + 0.0733576i
\(873\) 18.7279 + 39.2132i 0.633844 + 1.32717i
\(874\) 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
\(877\) −27.4862 7.36491i −0.928144 0.248695i −0.237081 0.971490i \(-0.576191\pi\)
−0.691063 + 0.722794i \(0.742857\pi\)
\(878\) 7.62373 + 28.4522i 0.257289 + 0.960214i
\(879\) −15.5798 42.1981i −0.525492 1.42331i
\(880\) −0.375860 0.0769140i −0.0126702 0.00259277i
\(881\) 49.2843i 1.66043i −0.557444 0.830215i \(-0.688218\pi\)
0.557444 0.830215i \(-0.311782\pi\)
\(882\) 2.58579 + 5.41421i 0.0870680 + 0.182306i
\(883\) −3.39496 + 0.909676i −0.114249 + 0.0306130i −0.315491 0.948929i \(-0.602169\pi\)
0.201241 + 0.979542i \(0.435502\pi\)
\(884\) 3.17157 5.49333i 0.106672 0.184761i
\(885\) −17.6569 12.9706i −0.593529 0.436001i
\(886\) 34.2426 1.15040
\(887\) 18.7929 5.03554i 0.631004 0.169077i 0.0708787 0.997485i \(-0.477420\pi\)
0.560125 + 0.828408i \(0.310753\pi\)
\(888\) 4.71940 + 2.17423i 0.158373 + 0.0729625i
\(889\) −6.90271 3.98528i −0.231509 0.133662i
\(890\) 1.58471 + 26.4017i 0.0531196 + 0.884985i
\(891\) −1.52539 0.240027i −0.0511024 0.00804120i
\(892\) 12.3640 12.3640i 0.413976 0.413976i
\(893\) 26.2860 10.4003i 0.879626 0.348034i
\(894\) 3.31371 19.3137i 0.110827 0.645947i
\(895\) 15.6314 + 13.8612i 0.522500 + 0.463327i
\(896\) −2.59808 + 1.50000i −0.0867956 + 0.0501115i
\(897\) −14.6349 + 1.34847i −0.488647 + 0.0450241i
\(898\) −4.61434 + 17.2209i −0.153982 + 0.574670i
\(899\) −9.89949 + 17.1464i −0.330167 + 0.571865i
\(900\) −14.3137 + 4.48528i −0.477124 + 0.149509i
\(901\) 21.2721 0.708676
\(902\) −0.497180 + 0.133219i −0.0165543 + 0.00443571i
\(903\) 21.9524 2.02270i 0.730531 0.0673114i
\(904\) 20.0000i 0.665190i
\(905\) −30.7279 + 10.2426i −1.02143 + 0.340477i
\(906\) −14.2891 11.8780i −0.474723 0.394621i
\(907\) −30.6753 8.21941i −1.01856 0.272921i −0.289355 0.957222i \(-0.593441\pi\)
−0.729200 + 0.684301i \(0.760108\pi\)
\(908\) 5.94522 + 22.1879i 0.197299 + 0.736330i
\(909\) 9.49117 + 51.0666i 0.314802 + 1.69377i
\(910\) −1.13681 18.9396i −0.0376850 0.627841i
\(911\) 29.3137i 0.971206i −0.874179 0.485603i \(-0.838600\pi\)
0.874179 0.485603i \(-0.161400\pi\)
\(912\) −7.38891 + 1.55051i −0.244671 + 0.0513425i
\(913\) 0.514719 + 0.514719i 0.0170347 + 0.0170347i
\(914\) 17.6569 + 30.5826i 0.584037 + 1.01158i
\(915\) 0.953220 8.63325i 0.0315125 0.285406i
\(916\) 7.87868 13.6463i 0.260319 0.450886i
\(917\) 11.6469 43.4667i 0.384613 1.43540i
\(918\) 11.2967 + 2.85994i 0.372847 + 0.0943921i
\(919\) 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
\(922\) −6.49964 24.2570i −0.214054 0.798862i
\(923\) −21.1716 + 21.1716i −0.696871 + 0.696871i
\(924\) 0.878680 + 0.150758i 0.0289064 + 0.00495956i
\(925\) −11.7992 9.26174i −0.387954 0.304524i
\(926\) −35.9273 + 20.7426i −1.18064 + 0.681645i
\(927\) −0.701625 + 8.97261i −0.0230444 + 0.294699i
\(928\) −0.820863 + 3.06350i −0.0269462 + 0.100564i
\(929\) 24.2990 + 42.0871i 0.797224 + 1.38083i 0.921417 + 0.388574i \(0.127032\pi\)
−0.124193 + 0.992258i \(0.539634\pi\)
\(930\) 3.65685 + 23.8995i 0.119913 + 0.783695i
\(931\) −1.00000 8.66025i −0.0327737 0.283828i
\(932\) −7.41421 7.41421i −0.242861 0.242861i
\(933\) 13.3485 + 6.14966i 0.437009 + 0.201331i
\(934\) 2.15232 1.24264i 0.0704260 0.0406604i
\(935\) −0.474064 0.718002i −0.0155035 0.0234812i
\(936\) 8.34242 1.55051i 0.272680 0.0506800i
\(937\) −1.45333 5.42389i −0.0474781 0.177191i 0.938115 0.346323i \(-0.112570\pi\)
−0.985593 + 0.169133i \(0.945903\pi\)
\(938\) −12.0000 + 12.0000i −0.391814 + 0.391814i
\(939\) 6.31371 36.7990i 0.206040 1.20089i
\(940\) −7.99020 12.1017i −0.260611 0.394714i
\(941\) −22.3426 12.8995i −0.728347 0.420512i 0.0894699 0.995990i \(-0.471483\pi\)
−0.817817 + 0.575478i \(0.804816\pi\)
\(942\) −11.8284 16.7279i −0.385391 0.545025i
\(943\) −6.36396 6.36396i −0.207239 0.207239i
\(944\) −2.82843 + 4.89898i −0.0920575 + 0.159448i
\(945\) 32.9124 11.4794i 1.07064 0.373425i
\(946\) 0.363961 0.630399i 0.0118334 0.0204960i
\(947\) 14.2902 53.3319i 0.464370 1.73305i −0.194599 0.980883i \(-0.562341\pi\)
0.658969 0.752170i \(-0.270993\pi\)
\(948\) −4.70017 + 10.2022i −0.152655 + 0.331352i
\(949\) 45.9411i 1.49131i
\(950\) 21.7866 + 0.586988i 0.706850 + 0.0190444i
\(951\) −8.33452 + 48.5772i −0.270265 + 1.57522i
\(952\) −6.49867 1.74131i −0.210623 0.0564363i
\(953\) 4.80119 + 1.28648i 0.155526 + 0.0416731i 0.335742 0.941954i \(-0.391013\pi\)
−0.180216 + 0.983627i \(0.557680\pi\)
\(954\) 18.4915 + 21.6287i 0.598683 + 0.700255i
\(955\) 15.7047 17.7104i 0.508192 0.573094i
\(956\) −0.594346 0.343146i −0.0192225 0.0110981i
\(957\) 0.769553 0.544156i 0.0248761 0.0175901i
\(958\) 21.4853 + 21.4853i 0.694158 + 0.694158i
\(959\) 30.7279 53.2223i 0.992256 1.71864i
\(960\) 1.55670 + 3.54636i 0.0502422 + 0.114458i
\(961\) 7.97056 0.257115
\(962\) 6.00000 + 6.00000i 0.193448 + 0.193448i
\(963\) −1.98450 + 25.3784i −0.0639495 + 0.817807i
\(964\) −0.420266 + 0.242641i −0.0135359 + 0.00781493i
\(965\) −22.3923 + 14.7846i −0.720834 + 0.475933i
\(966\) 5.39910 + 14.6236i 0.173713 + 0.470507i
\(967\) 41.9751 + 11.2472i 1.34983 + 0.361686i 0.860072 0.510173i \(-0.170419\pi\)
0.489757 + 0.871859i \(0.337085\pi\)
\(968\) −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 −0.204652 0.978835i \(-0.565606\pi\)
0.745370 + 0.666651i \(0.232273\pi\)
\(972\) 6.91215 + 13.9722i 0.221707 + 0.448158i
\(973\) 40.5689 10.8704i 1.30058 0.348489i
\(974\) −17.3995 30.1368i −0.557516 0.965646i
\(975\) −24.4643 1.22463i −0.783484 0.0392195i
\(976\) −2.24264 −0.0717852
\(977\) 7.75736 + 7.75736i 0.248180 + 0.248180i 0.820223 0.572043i \(-0.193849\pi\)
−0.572043 + 0.820223i \(0.693849\pi\)
\(978\) −3.20096 34.7400i −0.102355 1.11086i
\(979\) −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
\(982\) −1.77495 6.62419i −0.0566408 0.211386i
\(983\) −15.8951 4.25909i −0.506976 0.135844i −0.00374017 0.999993i \(-0.501191\pi\)
−0.503236 + 0.864149i \(0.667857\pi\)
\(984\) 3.99585 + 3.32162i 0.127383 + 0.105889i
\(985\) −1.14076 19.0053i −0.0363475 0.605559i
\(986\) −6.15978 + 3.55635i −0.196167 + 0.113257i
\(987\) 19.4558 + 27.5147i 0.619286 + 0.875803i
\(988\) −12.1962 1.80385i −0.388011 0.0573880i
\(989\) 12.7279 0.404724
\(990\) 0.317944 1.10616i 0.0101049 0.0351560i
\(991\) −3.00000 5.19615i −0.0952981 0.165061i 0.814435 0.580255i \(-0.197047\pi\)
−0.909733 + 0.415194i \(0.863714\pi\)
\(992\) 6.02993 1.61571i 0.191450 0.0512990i
\(993\) 9.06998 19.6873i 0.287827 0.624758i
\(994\) 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
\(997\) −4.05991 15.1518i −0.128579 0.479862i 0.871363 0.490638i \(-0.163236\pi\)
−0.999942 + 0.0107763i \(0.996570\pi\)
\(998\) 9.82750 + 36.6767i 0.311084 + 1.16098i
\(999\) −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.b.83.2 yes 8
3.2 odd 2 570.2.v.a.83.1 8
5.2 odd 4 570.2.v.a.197.2 yes 8
15.2 even 4 inner 570.2.v.b.197.1 yes 8
19.11 even 3 inner 570.2.v.b.353.1 yes 8
57.11 odd 6 570.2.v.a.353.2 yes 8
95.87 odd 12 570.2.v.a.467.1 yes 8
285.182 even 12 inner 570.2.v.b.467.2 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
570.2.v.a.83.1 8 3.2 odd 2
570.2.v.a.197.2 yes 8 5.2 odd 4
570.2.v.a.353.2 yes 8 57.11 odd 6
570.2.v.a.467.1 yes 8 95.87 odd 12
570.2.v.b.83.2 yes 8 1.1 even 1 trivial
570.2.v.b.197.1 yes 8 15.2 even 4 inner
570.2.v.b.353.1 yes 8 19.11 even 3 inner
570.2.v.b.467.2 yes 8 285.182 even 12 inner