Properties

Label 462.2.w.b.29.3
Level $462$
Weight $2$
Character 462.29
Analytic conductor $3.689$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [462,2,Mod(29,462)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(462, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 0, 7]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("462.29");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 462.w (of order \(10\), 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: \(3.68908857338\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(12\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 29.3
Character \(\chi\) \(=\) 462.29
Dual form 462.2.w.b.239.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.809017 + 0.587785i) q^{2} +(-1.35082 + 1.08410i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.96876 + 2.70976i) q^{5} +(-1.73006 + 0.0830614i) q^{6} +(0.951057 - 0.309017i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.649451 - 2.92886i) q^{9} +O(q^{10})\) \(q+(0.809017 + 0.587785i) q^{2} +(-1.35082 + 1.08410i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.96876 + 2.70976i) q^{5} +(-1.73006 + 0.0830614i) q^{6} +(0.951057 - 0.309017i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.649451 - 2.92886i) q^{9} +3.34945i q^{10} +(3.09211 + 1.19953i) q^{11} +(-1.44847 - 0.949704i) q^{12} +(-1.74405 + 2.40048i) q^{13} +(0.951057 + 0.309017i) q^{14} +(-5.59711 - 1.52608i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(1.58988 - 1.15511i) q^{17} +(2.24696 - 1.98776i) q^{18} +(-5.05108 - 1.64119i) q^{19} +(-1.96876 + 2.70976i) q^{20} +(-0.949704 + 1.44847i) q^{21} +(1.79650 + 2.78794i) q^{22} -3.29064i q^{23} +(-0.613613 - 1.61972i) q^{24} +(-1.92173 + 5.91447i) q^{25} +(-2.82194 + 0.916903i) q^{26} +(2.29788 + 4.66044i) q^{27} +(0.587785 + 0.809017i) q^{28} +(0.984118 + 3.02880i) q^{29} +(-3.63114 - 4.52452i) q^{30} +(-5.28711 - 3.84131i) q^{31} -1.00000 q^{32} +(-5.47730 + 1.73180i) q^{33} +1.96520 q^{34} +(2.70976 + 1.96876i) q^{35} +(2.98620 - 0.287402i) q^{36} +(-0.250519 - 0.771018i) q^{37} +(-3.12174 - 4.29670i) q^{38} +(-0.246457 - 5.13336i) q^{39} +(-3.18552 + 1.03504i) q^{40} +(-2.61320 + 8.04261i) q^{41} +(-1.61972 + 0.613613i) q^{42} -6.94527i q^{43} +(-0.185308 + 3.31144i) q^{44} +(9.21513 - 4.00636i) q^{45} +(1.93419 - 2.66218i) q^{46} +(4.03556 + 1.31123i) q^{47} +(0.455621 - 1.67105i) q^{48} +(0.809017 - 0.587785i) q^{49} +(-5.03115 + 3.65534i) q^{50} +(-0.895385 + 3.28394i) q^{51} +(-2.82194 - 0.916903i) q^{52} +(7.18083 - 9.88356i) q^{53} +(-0.880313 + 5.12104i) q^{54} +(2.83717 + 10.7405i) q^{55} +1.00000i q^{56} +(8.60233 - 3.25891i) q^{57} +(-0.984118 + 3.02880i) q^{58} +(6.46724 - 2.10133i) q^{59} +(-0.278210 - 5.79475i) q^{60} +(9.05317 + 12.4606i) q^{61} +(-2.01950 - 6.21537i) q^{62} +(-0.287402 - 2.98620i) q^{63} +(-0.809017 - 0.587785i) q^{64} -9.93837 q^{65} +(-5.44916 - 1.81842i) q^{66} -0.291541 q^{67} +(1.58988 + 1.15511i) q^{68} +(3.56738 + 4.44507i) q^{69} +(1.03504 + 3.18552i) q^{70} +(-5.37987 - 7.40476i) q^{71} +(2.58482 + 1.52273i) q^{72} +(12.3912 - 4.02614i) q^{73} +(0.250519 - 0.771018i) q^{74} +(-3.81596 - 10.0727i) q^{75} -5.31102i q^{76} +(3.31144 + 0.185308i) q^{77} +(2.81793 - 4.29784i) q^{78} +(0.656580 - 0.903705i) q^{79} +(-3.18552 - 1.03504i) q^{80} +(-8.15643 - 3.80430i) q^{81} +(-6.84145 + 4.97060i) q^{82} +(0.505739 - 0.367441i) q^{83} +(-1.67105 - 0.455621i) q^{84} +(6.26017 + 2.03405i) q^{85} +(4.08233 - 5.61884i) q^{86} +(-4.61290 - 3.02450i) q^{87} +(-2.09634 + 2.57009i) q^{88} -8.89950i q^{89} +(9.81008 + 2.17531i) q^{90} +(-0.916903 + 2.82194i) q^{91} +(3.12958 - 1.01686i) q^{92} +(11.3063 - 0.542826i) q^{93} +(2.49411 + 3.43285i) q^{94} +(-5.49710 - 16.9183i) q^{95} +(1.35082 - 1.08410i) q^{96} +(-7.11192 - 5.16711i) q^{97} +1.00000 q^{98} +(5.52143 - 8.27731i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q + 12 q^{2} - 4 q^{3} - 12 q^{4} + 4 q^{6} + 12 q^{8} + 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 48 q + 12 q^{2} - 4 q^{3} - 12 q^{4} + 4 q^{6} + 12 q^{8} + 10 q^{9} + 8 q^{11} + 6 q^{12} - 24 q^{15} - 12 q^{16} + 24 q^{17} + 10 q^{18} + 30 q^{19} - 8 q^{22} - 6 q^{24} + 18 q^{25} + 20 q^{26} + 38 q^{27} - 8 q^{29} - 36 q^{30} - 32 q^{31} - 48 q^{32} + 24 q^{33} - 4 q^{34} - 6 q^{35} - 20 q^{37} - 20 q^{38} - 34 q^{39} - 22 q^{44} + 12 q^{45} + 20 q^{46} - 20 q^{47} - 4 q^{48} + 12 q^{49} - 28 q^{50} + 2 q^{51} + 20 q^{52} - 20 q^{53} - 18 q^{54} + 16 q^{55} + 12 q^{57} + 8 q^{58} - 30 q^{59} - 4 q^{60} - 20 q^{61} - 8 q^{62} - 4 q^{63} - 12 q^{64} + 46 q^{66} + 36 q^{67} + 24 q^{68} + 30 q^{69} - 4 q^{70} - 10 q^{72} - 20 q^{73} + 20 q^{74} + 40 q^{75} + 16 q^{77} - 16 q^{78} - 20 q^{79} - 54 q^{81} - 10 q^{82} + 46 q^{83} - 10 q^{84} + 10 q^{85} + 30 q^{86} - 8 q^{87} - 8 q^{88} - 62 q^{90} - 36 q^{91} - 10 q^{92} + 44 q^{93} - 50 q^{95} + 4 q^{96} - 2 q^{97} + 48 q^{98} - 26 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(211\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{7}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.809017 + 0.587785i 0.572061 + 0.415627i
\(3\) −1.35082 + 1.08410i −0.779899 + 0.625906i
\(4\) 0.309017 + 0.951057i 0.154508 + 0.475528i
\(5\) 1.96876 + 2.70976i 0.880456 + 1.21184i 0.976294 + 0.216447i \(0.0694468\pi\)
−0.0958385 + 0.995397i \(0.530553\pi\)
\(6\) −1.73006 + 0.0830614i −0.706293 + 0.0339097i
\(7\) 0.951057 0.309017i 0.359466 0.116797i
\(8\) −0.309017 + 0.951057i −0.109254 + 0.336249i
\(9\) 0.649451 2.92886i 0.216484 0.976286i
\(10\) 3.34945i 1.05919i
\(11\) 3.09211 + 1.19953i 0.932305 + 0.361672i
\(12\) −1.44847 0.949704i −0.418137 0.274156i
\(13\) −1.74405 + 2.40048i −0.483714 + 0.665775i −0.979213 0.202834i \(-0.934985\pi\)
0.495500 + 0.868608i \(0.334985\pi\)
\(14\) 0.951057 + 0.309017i 0.254181 + 0.0825883i
\(15\) −5.59711 1.52608i −1.44517 0.394033i
\(16\) −0.809017 + 0.587785i −0.202254 + 0.146946i
\(17\) 1.58988 1.15511i 0.385602 0.280156i −0.378049 0.925786i \(-0.623405\pi\)
0.763651 + 0.645629i \(0.223405\pi\)
\(18\) 2.24696 1.98776i 0.529613 0.468519i
\(19\) −5.05108 1.64119i −1.15880 0.376516i −0.334346 0.942450i \(-0.608515\pi\)
−0.824450 + 0.565935i \(0.808515\pi\)
\(20\) −1.96876 + 2.70976i −0.440228 + 0.605922i
\(21\) −0.949704 + 1.44847i −0.207243 + 0.316082i
\(22\) 1.79650 + 2.78794i 0.383015 + 0.594390i
\(23\) 3.29064i 0.686145i −0.939309 0.343073i \(-0.888532\pi\)
0.939309 0.343073i \(-0.111468\pi\)
\(24\) −0.613613 1.61972i −0.125253 0.330623i
\(25\) −1.92173 + 5.91447i −0.384345 + 1.18289i
\(26\) −2.82194 + 0.916903i −0.553428 + 0.179820i
\(27\) 2.29788 + 4.66044i 0.442228 + 0.896903i
\(28\) 0.587785 + 0.809017i 0.111081 + 0.152890i
\(29\) 0.984118 + 3.02880i 0.182746 + 0.562435i 0.999902 0.0139816i \(-0.00445061\pi\)
−0.817156 + 0.576416i \(0.804451\pi\)
\(30\) −3.63114 4.52452i −0.662953 0.826061i
\(31\) −5.28711 3.84131i −0.949593 0.689920i 0.00111724 0.999999i \(-0.499644\pi\)
−0.950711 + 0.310079i \(0.899644\pi\)
\(32\) −1.00000 −0.176777
\(33\) −5.47730 + 1.73180i −0.953476 + 0.301468i
\(34\) 1.96520 0.337029
\(35\) 2.70976 + 1.96876i 0.458034 + 0.332781i
\(36\) 2.98620 0.287402i 0.497700 0.0479004i
\(37\) −0.250519 0.771018i −0.0411851 0.126755i 0.928350 0.371707i \(-0.121228\pi\)
−0.969535 + 0.244953i \(0.921228\pi\)
\(38\) −3.12174 4.29670i −0.506413 0.697017i
\(39\) −0.246457 5.13336i −0.0394647 0.821996i
\(40\) −3.18552 + 1.03504i −0.503675 + 0.163654i
\(41\) −2.61320 + 8.04261i −0.408113 + 1.25604i 0.510154 + 0.860083i \(0.329588\pi\)
−0.918267 + 0.395961i \(0.870412\pi\)
\(42\) −1.61972 + 0.613613i −0.249928 + 0.0946826i
\(43\) 6.94527i 1.05914i −0.848265 0.529572i \(-0.822353\pi\)
0.848265 0.529572i \(-0.177647\pi\)
\(44\) −0.185308 + 3.31144i −0.0279362 + 0.499219i
\(45\) 9.21513 4.00636i 1.37371 0.597233i
\(46\) 1.93419 2.66218i 0.285181 0.392517i
\(47\) 4.03556 + 1.31123i 0.588646 + 0.191263i 0.588170 0.808737i \(-0.299848\pi\)
0.000476052 1.00000i \(0.499848\pi\)
\(48\) 0.455621 1.67105i 0.0657633 0.241195i
\(49\) 0.809017 0.587785i 0.115574 0.0839693i
\(50\) −5.03115 + 3.65534i −0.711511 + 0.516943i
\(51\) −0.895385 + 3.28394i −0.125379 + 0.459844i
\(52\) −2.82194 0.916903i −0.391332 0.127152i
\(53\) 7.18083 9.88356i 0.986363 1.35761i 0.0530322 0.998593i \(-0.483111\pi\)
0.933330 0.359019i \(-0.116889\pi\)
\(54\) −0.880313 + 5.12104i −0.119795 + 0.696885i
\(55\) 2.83717 + 10.7405i 0.382564 + 1.44824i
\(56\) 1.00000i 0.133631i
\(57\) 8.60233 3.25891i 1.13941 0.431653i
\(58\) −0.984118 + 3.02880i −0.129221 + 0.397702i
\(59\) 6.46724 2.10133i 0.841962 0.273570i 0.143887 0.989594i \(-0.454040\pi\)
0.698076 + 0.716024i \(0.254040\pi\)
\(60\) −0.278210 5.79475i −0.0359168 0.748099i
\(61\) 9.05317 + 12.4606i 1.15914 + 1.59542i 0.714361 + 0.699778i \(0.246718\pi\)
0.444779 + 0.895640i \(0.353282\pi\)
\(62\) −2.01950 6.21537i −0.256476 0.789353i
\(63\) −0.287402 2.98620i −0.0362093 0.376226i
\(64\) −0.809017 0.587785i −0.101127 0.0734732i
\(65\) −9.93837 −1.23270
\(66\) −5.44916 1.81842i −0.670745 0.223832i
\(67\) −0.291541 −0.0356175 −0.0178087 0.999841i \(-0.505669\pi\)
−0.0178087 + 0.999841i \(0.505669\pi\)
\(68\) 1.58988 + 1.15511i 0.192801 + 0.140078i
\(69\) 3.56738 + 4.44507i 0.429462 + 0.535124i
\(70\) 1.03504 + 3.18552i 0.123711 + 0.380742i
\(71\) −5.37987 7.40476i −0.638473 0.878783i 0.360060 0.932929i \(-0.382756\pi\)
−0.998533 + 0.0541460i \(0.982756\pi\)
\(72\) 2.58482 + 1.52273i 0.304624 + 0.179456i
\(73\) 12.3912 4.02614i 1.45028 0.471224i 0.525193 0.850983i \(-0.323993\pi\)
0.925086 + 0.379759i \(0.123993\pi\)
\(74\) 0.250519 0.771018i 0.0291222 0.0896290i
\(75\) −3.81596 10.0727i −0.440629 1.16310i
\(76\) 5.31102i 0.609215i
\(77\) 3.31144 + 0.185308i 0.377374 + 0.0211178i
\(78\) 2.81793 4.29784i 0.319067 0.486635i
\(79\) 0.656580 0.903705i 0.0738710 0.101675i −0.770483 0.637461i \(-0.779985\pi\)
0.844354 + 0.535786i \(0.179985\pi\)
\(80\) −3.18552 1.03504i −0.356152 0.115721i
\(81\) −8.15643 3.80430i −0.906270 0.422700i
\(82\) −6.84145 + 4.97060i −0.755512 + 0.548911i
\(83\) 0.505739 0.367441i 0.0555120 0.0403319i −0.559683 0.828707i \(-0.689077\pi\)
0.615195 + 0.788375i \(0.289077\pi\)
\(84\) −1.67105 0.455621i −0.182327 0.0497123i
\(85\) 6.26017 + 2.03405i 0.679011 + 0.220624i
\(86\) 4.08233 5.61884i 0.440209 0.605896i
\(87\) −4.61290 3.02450i −0.494555 0.324260i
\(88\) −2.09634 + 2.57009i −0.223470 + 0.273973i
\(89\) 8.89950i 0.943345i −0.881774 0.471672i \(-0.843650\pi\)
0.881774 0.471672i \(-0.156350\pi\)
\(90\) 9.81008 + 2.17531i 1.03407 + 0.229297i
\(91\) −0.916903 + 2.82194i −0.0961176 + 0.295820i
\(92\) 3.12958 1.01686i 0.326282 0.106015i
\(93\) 11.3063 0.542826i 1.17241 0.0562884i
\(94\) 2.49411 + 3.43285i 0.257248 + 0.354071i
\(95\) −5.49710 16.9183i −0.563991 1.73579i
\(96\) 1.35082 1.08410i 0.137868 0.110646i
\(97\) −7.11192 5.16711i −0.722106 0.524641i 0.164950 0.986302i \(-0.447254\pi\)
−0.887056 + 0.461661i \(0.847254\pi\)
\(98\) 1.00000 0.101015
\(99\) 5.52143 8.27731i 0.554924 0.831901i
\(100\) −6.21884 −0.621884
\(101\) 13.3152 + 9.67404i 1.32491 + 0.962603i 0.999857 + 0.0169069i \(0.00538188\pi\)
0.325052 + 0.945696i \(0.394618\pi\)
\(102\) −2.65464 + 2.13047i −0.262848 + 0.210948i
\(103\) −3.29384 10.1374i −0.324552 0.998867i −0.971643 0.236454i \(-0.924015\pi\)
0.647091 0.762413i \(-0.275985\pi\)
\(104\) −1.74405 2.40048i −0.171019 0.235387i
\(105\) −5.79475 + 0.278210i −0.565510 + 0.0271506i
\(106\) 11.6188 3.77518i 1.12852 0.366678i
\(107\) 0.120130 0.369723i 0.0116134 0.0357425i −0.945082 0.326834i \(-0.894018\pi\)
0.956695 + 0.291091i \(0.0940183\pi\)
\(108\) −3.72226 + 3.62557i −0.358175 + 0.348871i
\(109\) 0.316649i 0.0303294i 0.999885 + 0.0151647i \(0.00482726\pi\)
−0.999885 + 0.0151647i \(0.995173\pi\)
\(110\) −4.01777 + 10.3569i −0.383080 + 0.987489i
\(111\) 1.17427 + 0.769922i 0.111457 + 0.0730778i
\(112\) −0.587785 + 0.809017i −0.0555405 + 0.0764449i
\(113\) −17.7799 5.77704i −1.67259 0.543458i −0.689140 0.724628i \(-0.742012\pi\)
−0.983452 + 0.181170i \(0.942012\pi\)
\(114\) 8.87497 + 2.41981i 0.831217 + 0.226636i
\(115\) 8.91685 6.47847i 0.831501 0.604121i
\(116\) −2.57646 + 1.87190i −0.239218 + 0.173802i
\(117\) 5.89800 + 6.66709i 0.545270 + 0.616372i
\(118\) 6.46724 + 2.10133i 0.595357 + 0.193443i
\(119\) 1.15511 1.58988i 0.105889 0.145744i
\(120\) 3.18099 4.85158i 0.290383 0.442886i
\(121\) 8.12225 + 7.41816i 0.738387 + 0.674378i
\(122\) 15.4022i 1.39445i
\(123\) −5.18902 13.6971i −0.467878 1.23503i
\(124\) 2.01950 6.21537i 0.181356 0.558157i
\(125\) −3.88263 + 1.26154i −0.347273 + 0.112836i
\(126\) 1.52273 2.58482i 0.135656 0.230274i
\(127\) 8.33877 + 11.4773i 0.739946 + 1.01845i 0.998622 + 0.0524841i \(0.0167139\pi\)
−0.258676 + 0.965964i \(0.583286\pi\)
\(128\) −0.309017 0.951057i −0.0273135 0.0840623i
\(129\) 7.52938 + 9.38184i 0.662925 + 0.826025i
\(130\) −8.04031 5.84163i −0.705182 0.512345i
\(131\) −7.35577 −0.642677 −0.321339 0.946964i \(-0.604133\pi\)
−0.321339 + 0.946964i \(0.604133\pi\)
\(132\) −3.33962 4.67407i −0.290677 0.406826i
\(133\) −5.31102 −0.460523
\(134\) −0.235862 0.171364i −0.0203754 0.0148036i
\(135\) −8.10473 + 15.4020i −0.697544 + 1.32559i
\(136\) 0.607279 + 1.86901i 0.0520738 + 0.160267i
\(137\) 9.75835 + 13.4312i 0.833713 + 1.14751i 0.987221 + 0.159359i \(0.0509429\pi\)
−0.153508 + 0.988147i \(0.549057\pi\)
\(138\) 0.273325 + 5.69299i 0.0232670 + 0.484620i
\(139\) −15.3443 + 4.98567i −1.30149 + 0.422879i −0.876099 0.482131i \(-0.839863\pi\)
−0.425390 + 0.905010i \(0.639863\pi\)
\(140\) −1.03504 + 3.18552i −0.0874767 + 0.269226i
\(141\) −6.87283 + 2.60371i −0.578797 + 0.219272i
\(142\) 9.15279i 0.768085i
\(143\) −8.27226 + 5.33051i −0.691761 + 0.445759i
\(144\) 1.19612 + 2.75123i 0.0996769 + 0.229270i
\(145\) −6.26986 + 8.62972i −0.520683 + 0.716659i
\(146\) 12.3912 + 4.02614i 1.02550 + 0.333206i
\(147\) −0.455621 + 1.67105i −0.0375790 + 0.137826i
\(148\) 0.655867 0.476515i 0.0539119 0.0391693i
\(149\) −8.85496 + 6.43351i −0.725427 + 0.527053i −0.888113 0.459624i \(-0.847984\pi\)
0.162687 + 0.986678i \(0.447984\pi\)
\(150\) 2.83343 10.3920i 0.231349 0.848503i
\(151\) 13.5674 + 4.40833i 1.10410 + 0.358745i 0.803680 0.595062i \(-0.202872\pi\)
0.300422 + 0.953806i \(0.402872\pi\)
\(152\) 3.12174 4.29670i 0.253206 0.348509i
\(153\) −2.35062 5.40672i −0.190036 0.437107i
\(154\) 2.57009 + 2.09634i 0.207104 + 0.168928i
\(155\) 21.8894i 1.75820i
\(156\) 4.80596 1.82069i 0.384785 0.145772i
\(157\) 6.23366 19.1852i 0.497500 1.53115i −0.315524 0.948918i \(-0.602180\pi\)
0.813024 0.582230i \(-0.197820\pi\)
\(158\) 1.06237 0.345184i 0.0845175 0.0274614i
\(159\) 1.01474 + 21.1357i 0.0804742 + 1.67617i
\(160\) −1.96876 2.70976i −0.155644 0.214226i
\(161\) −1.01686 3.12958i −0.0801400 0.246646i
\(162\) −4.36257 7.87197i −0.342756 0.618481i
\(163\) 4.79493 + 3.48372i 0.375568 + 0.272866i 0.759516 0.650488i \(-0.225436\pi\)
−0.383948 + 0.923355i \(0.625436\pi\)
\(164\) −8.45650 −0.660341
\(165\) −15.4763 11.4327i −1.20483 0.890035i
\(166\) 0.625127 0.0485193
\(167\) 3.55491 + 2.58279i 0.275087 + 0.199862i 0.716772 0.697308i \(-0.245619\pi\)
−0.441685 + 0.897170i \(0.645619\pi\)
\(168\) −1.08410 1.35082i −0.0836402 0.104218i
\(169\) 1.29662 + 3.99059i 0.0997400 + 0.306968i
\(170\) 3.86900 + 5.32522i 0.296739 + 0.408426i
\(171\) −8.08725 + 13.7280i −0.618448 + 1.04981i
\(172\) 6.60535 2.14621i 0.503653 0.163647i
\(173\) −0.709968 + 2.18506i −0.0539779 + 0.166127i −0.974411 0.224773i \(-0.927836\pi\)
0.920433 + 0.390900i \(0.127836\pi\)
\(174\) −1.95416 5.15827i −0.148144 0.391047i
\(175\) 6.21884i 0.470100i
\(176\) −3.20663 + 0.847054i −0.241709 + 0.0638491i
\(177\) −6.45804 + 9.84967i −0.485416 + 0.740346i
\(178\) 5.23099 7.19984i 0.392080 0.539651i
\(179\) 12.5257 + 4.06984i 0.936214 + 0.304194i 0.737101 0.675782i \(-0.236194\pi\)
0.199113 + 0.979977i \(0.436194\pi\)
\(180\) 6.65790 + 7.52608i 0.496251 + 0.560961i
\(181\) −21.1736 + 15.3835i −1.57382 + 1.14345i −0.650450 + 0.759549i \(0.725420\pi\)
−0.923374 + 0.383901i \(0.874580\pi\)
\(182\) −2.40048 + 1.74405i −0.177936 + 0.129278i
\(183\) −25.7378 7.01755i −1.90259 0.518753i
\(184\) 3.12958 + 1.01686i 0.230716 + 0.0749641i
\(185\) 1.59607 2.19680i 0.117345 0.161512i
\(186\) 9.46608 + 6.20654i 0.694086 + 0.455085i
\(187\) 6.30167 1.66463i 0.460824 0.121730i
\(188\) 4.24323i 0.309470i
\(189\) 3.62557 + 3.72226i 0.263722 + 0.270755i
\(190\) 5.49710 16.9183i 0.398802 1.22739i
\(191\) 10.3485 3.36244i 0.748794 0.243298i 0.0903319 0.995912i \(-0.471207\pi\)
0.658462 + 0.752614i \(0.271207\pi\)
\(192\) 1.73006 0.0830614i 0.124856 0.00599444i
\(193\) −6.32425 8.70458i −0.455229 0.626569i 0.518282 0.855210i \(-0.326572\pi\)
−0.973511 + 0.228641i \(0.926572\pi\)
\(194\) −2.71651 8.36056i −0.195034 0.600253i
\(195\) 13.4250 10.7742i 0.961383 0.771556i
\(196\) 0.809017 + 0.587785i 0.0577869 + 0.0419847i
\(197\) −5.82706 −0.415161 −0.207581 0.978218i \(-0.566559\pi\)
−0.207581 + 0.978218i \(0.566559\pi\)
\(198\) 9.33221 3.45107i 0.663211 0.245257i
\(199\) −21.0983 −1.49562 −0.747811 0.663912i \(-0.768895\pi\)
−0.747811 + 0.663912i \(0.768895\pi\)
\(200\) −5.03115 3.65534i −0.355756 0.258472i
\(201\) 0.393821 0.316060i 0.0277780 0.0222932i
\(202\) 5.08594 + 15.6529i 0.357846 + 1.10134i
\(203\) 1.87190 + 2.57646i 0.131382 + 0.180832i
\(204\) −3.39990 + 0.163232i −0.238041 + 0.0114285i
\(205\) −26.9383 + 8.75280i −1.88146 + 0.611322i
\(206\) 3.29384 10.1374i 0.229493 0.706306i
\(207\) −9.63781 2.13711i −0.669874 0.148539i
\(208\) 2.96716i 0.205736i
\(209\) −13.6498 11.1337i −0.944177 0.770132i
\(210\) −4.85158 3.18099i −0.334791 0.219509i
\(211\) 10.9320 15.0466i 0.752591 1.03585i −0.245203 0.969472i \(-0.578855\pi\)
0.997794 0.0663810i \(-0.0211453\pi\)
\(212\) 11.6188 + 3.77518i 0.797984 + 0.259281i
\(213\) 15.2948 + 4.17020i 1.04798 + 0.285738i
\(214\) 0.314505 0.228502i 0.0214991 0.0156200i
\(215\) 18.8201 13.6736i 1.28352 0.932530i
\(216\) −5.14243 + 0.745261i −0.349898 + 0.0507086i
\(217\) −6.21537 2.01950i −0.421927 0.137092i
\(218\) −0.186121 + 0.256174i −0.0126057 + 0.0173503i
\(219\) −12.3736 + 18.8719i −0.836129 + 1.27525i
\(220\) −9.33806 + 6.01730i −0.629572 + 0.405686i
\(221\) 5.83106i 0.392239i
\(222\) 0.497454 + 1.31310i 0.0333869 + 0.0881293i
\(223\) −0.294783 + 0.907249i −0.0197401 + 0.0607539i −0.960441 0.278482i \(-0.910169\pi\)
0.940701 + 0.339236i \(0.110169\pi\)
\(224\) −0.951057 + 0.309017i −0.0635451 + 0.0206471i
\(225\) 16.0746 + 9.46962i 1.07164 + 0.631308i
\(226\) −10.9886 15.1245i −0.730950 1.00607i
\(227\) 0.729476 + 2.24510i 0.0484170 + 0.149012i 0.972342 0.233561i \(-0.0750379\pi\)
−0.923925 + 0.382573i \(0.875038\pi\)
\(228\) 5.75768 + 7.17425i 0.381311 + 0.475126i
\(229\) −8.10652 5.88973i −0.535694 0.389204i 0.286789 0.957994i \(-0.407412\pi\)
−0.822483 + 0.568789i \(0.807412\pi\)
\(230\) 11.0218 0.726758
\(231\) −4.67407 + 3.33962i −0.307531 + 0.219731i
\(232\) −3.18467 −0.209084
\(233\) 0.248510 + 0.180553i 0.0162804 + 0.0118284i 0.595896 0.803062i \(-0.296797\pi\)
−0.579615 + 0.814890i \(0.696797\pi\)
\(234\) 0.852769 + 8.86054i 0.0557472 + 0.579232i
\(235\) 4.39191 + 13.5169i 0.286497 + 0.881746i
\(236\) 3.99697 + 5.50136i 0.260181 + 0.358108i
\(237\) 0.0927830 + 1.93254i 0.00602690 + 0.125532i
\(238\) 1.86901 0.607279i 0.121150 0.0393641i
\(239\) 5.13577 15.8063i 0.332205 1.02242i −0.635877 0.771790i \(-0.719361\pi\)
0.968082 0.250632i \(-0.0806386\pi\)
\(240\) 5.42516 2.05527i 0.350193 0.132667i
\(241\) 21.0956i 1.35889i −0.733727 0.679445i \(-0.762221\pi\)
0.733727 0.679445i \(-0.237779\pi\)
\(242\) 2.21076 + 10.7756i 0.142113 + 0.692679i
\(243\) 15.1421 3.70344i 0.971369 0.237576i
\(244\) −9.05317 + 12.4606i −0.579570 + 0.797709i
\(245\) 3.18552 + 1.03504i 0.203515 + 0.0661262i
\(246\) 3.85296 14.1312i 0.245656 0.900975i
\(247\) 12.7490 9.26270i 0.811200 0.589371i
\(248\) 5.28711 3.84131i 0.335732 0.243924i
\(249\) −0.284821 + 1.04462i −0.0180498 + 0.0662001i
\(250\) −3.88263 1.26154i −0.245559 0.0797870i
\(251\) 1.03236 1.42092i 0.0651620 0.0896878i −0.775192 0.631725i \(-0.782347\pi\)
0.840354 + 0.542038i \(0.182347\pi\)
\(252\) 2.75123 1.19612i 0.173311 0.0753487i
\(253\) 3.94722 10.1750i 0.248160 0.639697i
\(254\) 14.1868i 0.890156i
\(255\) −10.6615 + 4.03901i −0.667650 + 0.252933i
\(256\) 0.309017 0.951057i 0.0193136 0.0594410i
\(257\) −0.329839 + 0.107171i −0.0205748 + 0.00668515i −0.319286 0.947658i \(-0.603443\pi\)
0.298712 + 0.954343i \(0.403443\pi\)
\(258\) 0.576884 + 12.0157i 0.0359153 + 0.748066i
\(259\) −0.476515 0.655867i −0.0296092 0.0407536i
\(260\) −3.07113 9.45195i −0.190463 0.586185i
\(261\) 9.51008 0.915282i 0.588659 0.0566546i
\(262\) −5.95095 4.32362i −0.367651 0.267114i
\(263\) −21.9124 −1.35118 −0.675589 0.737279i \(-0.736111\pi\)
−0.675589 + 0.737279i \(0.736111\pi\)
\(264\) 0.0455402 5.74438i 0.00280281 0.353542i
\(265\) 40.9194 2.51366
\(266\) −4.29670 3.12174i −0.263448 0.191406i
\(267\) 9.64795 + 12.0217i 0.590445 + 0.735713i
\(268\) −0.0900912 0.277272i −0.00550320 0.0169371i
\(269\) −17.4600 24.0316i −1.06456 1.46523i −0.875469 0.483275i \(-0.839447\pi\)
−0.189087 0.981960i \(-0.560553\pi\)
\(270\) −15.6099 + 7.69665i −0.949991 + 0.468403i
\(271\) −27.9268 + 9.07396i −1.69643 + 0.551204i −0.987984 0.154559i \(-0.950604\pi\)
−0.708448 + 0.705763i \(0.750604\pi\)
\(272\) −0.607279 + 1.86901i −0.0368217 + 0.113326i
\(273\) −1.82069 4.80596i −0.110193 0.290870i
\(274\) 16.6019i 1.00296i
\(275\) −13.0368 + 15.9830i −0.786147 + 0.963811i
\(276\) −3.12513 + 4.76639i −0.188111 + 0.286903i
\(277\) 6.12398 8.42893i 0.367954 0.506445i −0.584389 0.811474i \(-0.698666\pi\)
0.952343 + 0.305028i \(0.0986658\pi\)
\(278\) −15.3443 4.98567i −0.920291 0.299021i
\(279\) −14.6844 + 12.9905i −0.879131 + 0.777719i
\(280\) −2.70976 + 1.96876i −0.161939 + 0.117656i
\(281\) −6.91785 + 5.02611i −0.412684 + 0.299833i −0.774688 0.632344i \(-0.782093\pi\)
0.362003 + 0.932177i \(0.382093\pi\)
\(282\) −7.09066 1.93331i −0.422243 0.115127i
\(283\) −25.1001 8.15553i −1.49205 0.484796i −0.554361 0.832276i \(-0.687037\pi\)
−0.937687 + 0.347480i \(0.887037\pi\)
\(284\) 5.37987 7.40476i 0.319237 0.439392i
\(285\) 25.7668 + 16.8943i 1.52629 + 1.00073i
\(286\) −9.82559 0.549839i −0.580999 0.0325126i
\(287\) 8.45650i 0.499171i
\(288\) −0.649451 + 2.92886i −0.0382693 + 0.172585i
\(289\) −4.05987 + 12.4950i −0.238816 + 0.734999i
\(290\) −10.1448 + 3.29626i −0.595726 + 0.193563i
\(291\) 15.2086 0.730178i 0.891545 0.0428038i
\(292\) 7.65818 + 10.5406i 0.448161 + 0.616841i
\(293\) 5.03408 + 15.4933i 0.294094 + 0.905129i 0.983524 + 0.180777i \(0.0578611\pi\)
−0.689430 + 0.724352i \(0.742139\pi\)
\(294\) −1.35082 + 1.08410i −0.0787817 + 0.0632260i
\(295\) 18.4265 + 13.3877i 1.07284 + 0.779460i
\(296\) 0.810696 0.0471208
\(297\) 1.51496 + 17.1670i 0.0879067 + 0.996129i
\(298\) −10.9453 −0.634046
\(299\) 7.89912 + 5.73905i 0.456818 + 0.331898i
\(300\) 8.40056 6.74185i 0.485006 0.389241i
\(301\) −2.14621 6.60535i −0.123705 0.380726i
\(302\) 8.38514 + 11.5412i 0.482510 + 0.664119i
\(303\) −28.4741 + 1.36706i −1.63579 + 0.0785357i
\(304\) 5.05108 1.64119i 0.289699 0.0941289i
\(305\) −15.9418 + 49.0639i −0.912826 + 2.80939i
\(306\) 1.27630 5.75578i 0.0729612 0.329036i
\(307\) 17.8977i 1.02147i −0.859737 0.510737i \(-0.829373\pi\)
0.859737 0.510737i \(-0.170627\pi\)
\(308\) 0.847054 + 3.20663i 0.0482654 + 0.182715i
\(309\) 15.4394 + 10.1230i 0.878314 + 0.575876i
\(310\) 12.8663 17.7089i 0.730756 1.00580i
\(311\) 19.1897 + 6.23510i 1.08815 + 0.353560i 0.797530 0.603279i \(-0.206140\pi\)
0.290617 + 0.956840i \(0.406140\pi\)
\(312\) 4.95828 + 1.35190i 0.280707 + 0.0765364i
\(313\) 5.43352 3.94769i 0.307121 0.223136i −0.423539 0.905878i \(-0.639212\pi\)
0.730660 + 0.682741i \(0.239212\pi\)
\(314\) 16.3199 11.8571i 0.920987 0.669136i
\(315\) 7.52608 6.65790i 0.424046 0.375130i
\(316\) 1.06237 + 0.345184i 0.0597629 + 0.0194181i
\(317\) 10.4071 14.3242i 0.584522 0.804525i −0.409660 0.912238i \(-0.634353\pi\)
0.994182 + 0.107713i \(0.0343527\pi\)
\(318\) −11.6023 + 17.6956i −0.650625 + 0.992319i
\(319\) −0.590145 + 10.5459i −0.0330418 + 0.590455i
\(320\) 3.34945i 0.187240i
\(321\) 0.238542 + 0.629664i 0.0133141 + 0.0351444i
\(322\) 1.01686 3.12958i 0.0566676 0.174405i
\(323\) −9.92636 + 3.22527i −0.552317 + 0.179459i
\(324\) 1.09763 8.93282i 0.0609796 0.496268i
\(325\) −10.8460 14.9282i −0.601627 0.828069i
\(326\) 1.83150 + 5.63678i 0.101437 + 0.312192i
\(327\) −0.343279 0.427737i −0.0189834 0.0236539i
\(328\) −6.84145 4.97060i −0.377756 0.274456i
\(329\) 4.24323 0.233937
\(330\) −5.80058 18.3460i −0.319312 1.00991i
\(331\) −20.9688 −1.15255 −0.576275 0.817256i \(-0.695494\pi\)
−0.576275 + 0.817256i \(0.695494\pi\)
\(332\) 0.505739 + 0.367441i 0.0277560 + 0.0201659i
\(333\) −2.42090 + 0.232996i −0.132665 + 0.0127681i
\(334\) 1.35785 + 4.17904i 0.0742984 + 0.228667i
\(335\) −0.573975 0.790009i −0.0313596 0.0431628i
\(336\) −0.0830614 1.73006i −0.00453137 0.0943824i
\(337\) −15.4283 + 5.01296i −0.840433 + 0.273073i −0.697434 0.716649i \(-0.745675\pi\)
−0.143000 + 0.989723i \(0.545675\pi\)
\(338\) −1.29662 + 3.99059i −0.0705268 + 0.217059i
\(339\) 30.2804 11.4714i 1.64461 0.623043i
\(340\) 6.58234i 0.356977i
\(341\) −11.7405 18.2198i −0.635786 0.986658i
\(342\) −14.6118 + 6.35263i −0.790118 + 0.343511i
\(343\) 0.587785 0.809017i 0.0317374 0.0436828i
\(344\) 6.60535 + 2.14621i 0.356136 + 0.115716i
\(345\) −5.02178 + 18.4180i −0.270364 + 0.991594i
\(346\) −1.85872 + 1.35044i −0.0999254 + 0.0726001i
\(347\) −11.7989 + 8.57242i −0.633400 + 0.460192i −0.857576 0.514357i \(-0.828031\pi\)
0.224177 + 0.974549i \(0.428031\pi\)
\(348\) 1.45100 5.32175i 0.0777820 0.285276i
\(349\) 4.61564 + 1.49971i 0.247070 + 0.0802778i 0.429934 0.902860i \(-0.358537\pi\)
−0.182864 + 0.983138i \(0.558537\pi\)
\(350\) −3.65534 + 5.03115i −0.195386 + 0.268926i
\(351\) −15.1950 2.61203i −0.811047 0.139420i
\(352\) −3.09211 1.19953i −0.164810 0.0639352i
\(353\) 26.4448i 1.40751i −0.710441 0.703757i \(-0.751504\pi\)
0.710441 0.703757i \(-0.248496\pi\)
\(354\) −11.0142 + 4.17260i −0.585396 + 0.221771i
\(355\) 9.47348 29.1564i 0.502800 1.54746i
\(356\) 8.46392 2.75010i 0.448587 0.145755i
\(357\) 0.163232 + 3.39990i 0.00863916 + 0.179942i
\(358\) 7.74130 + 10.6550i 0.409141 + 0.563134i
\(359\) 3.58878 + 11.0451i 0.189409 + 0.582940i 0.999996 0.00267727i \(-0.000852202\pi\)
−0.810588 + 0.585617i \(0.800852\pi\)
\(360\) 0.962640 + 10.0021i 0.0507356 + 0.527159i
\(361\) 7.44853 + 5.41167i 0.392028 + 0.284825i
\(362\) −26.1721 −1.37557
\(363\) −19.0138 1.21528i −0.997964 0.0637858i
\(364\) −2.96716 −0.155522
\(365\) 35.3052 + 25.6507i 1.84796 + 1.34262i
\(366\) −16.6975 20.8056i −0.872792 1.08753i
\(367\) −5.23853 16.1225i −0.273449 0.841590i −0.989626 0.143671i \(-0.954109\pi\)
0.716176 0.697919i \(-0.245891\pi\)
\(368\) 1.93419 + 2.66218i 0.100827 + 0.138776i
\(369\) 21.8585 + 12.8770i 1.13791 + 0.670349i
\(370\) 2.58249 0.839102i 0.134257 0.0436228i
\(371\) 3.77518 11.6188i 0.195998 0.603219i
\(372\) 4.01011 + 10.5852i 0.207914 + 0.548818i
\(373\) 17.5384i 0.908102i −0.890976 0.454051i \(-0.849978\pi\)
0.890976 0.454051i \(-0.150022\pi\)
\(374\) 6.07660 + 2.35731i 0.314213 + 0.121894i
\(375\) 3.87711 5.91329i 0.200213 0.305361i
\(376\) −2.49411 + 3.43285i −0.128624 + 0.177036i
\(377\) −8.98695 2.92004i −0.462852 0.150390i
\(378\) 0.745261 + 5.14243i 0.0383321 + 0.264498i
\(379\) −12.9746 + 9.42659i −0.666460 + 0.484211i −0.868838 0.495096i \(-0.835133\pi\)
0.202378 + 0.979307i \(0.435133\pi\)
\(380\) 14.3916 10.4561i 0.738274 0.536387i
\(381\) −23.7068 6.46379i −1.21454 0.331150i
\(382\) 10.3485 + 3.36244i 0.529477 + 0.172038i
\(383\) −3.59741 + 4.95141i −0.183819 + 0.253005i −0.890975 0.454053i \(-0.849978\pi\)
0.707156 + 0.707058i \(0.249978\pi\)
\(384\) 1.44847 + 0.949704i 0.0739169 + 0.0484644i
\(385\) 6.01730 + 9.33806i 0.306670 + 0.475912i
\(386\) 10.7595i 0.547642i
\(387\) −20.3417 4.51062i −1.03403 0.229288i
\(388\) 2.71651 8.36056i 0.137910 0.424443i
\(389\) 16.9391 5.50385i 0.858847 0.279056i 0.153700 0.988118i \(-0.450881\pi\)
0.705147 + 0.709061i \(0.250881\pi\)
\(390\) 17.1940 0.825495i 0.870650 0.0418006i
\(391\) −3.80106 5.23171i −0.192228 0.264579i
\(392\) 0.309017 + 0.951057i 0.0156077 + 0.0480356i
\(393\) 9.93636 7.97440i 0.501223 0.402255i
\(394\) −4.71419 3.42506i −0.237498 0.172552i
\(395\) 3.74147 0.188254
\(396\) 9.57840 + 2.69336i 0.481333 + 0.135347i
\(397\) 28.9597 1.45344 0.726722 0.686932i \(-0.241043\pi\)
0.726722 + 0.686932i \(0.241043\pi\)
\(398\) −17.0689 12.4013i −0.855588 0.621621i
\(399\) 7.17425 5.75768i 0.359162 0.288244i
\(400\) −1.92173 5.91447i −0.0960863 0.295723i
\(401\) −6.32086 8.69991i −0.315648 0.434453i 0.621484 0.783427i \(-0.286530\pi\)
−0.937132 + 0.348974i \(0.886530\pi\)
\(402\) 0.504384 0.0242158i 0.0251564 0.00120778i
\(403\) 18.4420 5.99218i 0.918662 0.298492i
\(404\) −5.08594 + 15.6529i −0.253035 + 0.778762i
\(405\) −5.74928 29.5918i −0.285684 1.47043i
\(406\) 3.18467i 0.158053i
\(407\) 0.150228 2.68458i 0.00744655 0.133069i
\(408\) −2.84653 1.86636i −0.140924 0.0923984i
\(409\) 8.35912 11.5053i 0.413332 0.568902i −0.550695 0.834706i \(-0.685637\pi\)
0.964027 + 0.265804i \(0.0856374\pi\)
\(410\) −26.9383 8.75280i −1.33039 0.432270i
\(411\) −27.7426 7.56418i −1.36844 0.373113i
\(412\) 8.62338 6.26525i 0.424843 0.308667i
\(413\) 5.50136 3.99697i 0.270704 0.196678i
\(414\) −6.54099 7.39392i −0.321472 0.363391i
\(415\) 1.99136 + 0.647031i 0.0977518 + 0.0317615i
\(416\) 1.74405 2.40048i 0.0855093 0.117693i
\(417\) 15.3225 23.3696i 0.750347 1.14441i
\(418\) −4.49872 17.0305i −0.220039 0.832988i
\(419\) 30.4311i 1.48666i 0.668926 + 0.743329i \(0.266754\pi\)
−0.668926 + 0.743329i \(0.733246\pi\)
\(420\) −2.05527 5.42516i −0.100287 0.264721i
\(421\) 11.1666 34.3673i 0.544228 1.67496i −0.178591 0.983923i \(-0.557154\pi\)
0.722819 0.691038i \(-0.242846\pi\)
\(422\) 17.6884 5.74730i 0.861057 0.279774i
\(423\) 6.46131 10.9680i 0.314160 0.533282i
\(424\) 7.18083 + 9.88356i 0.348732 + 0.479988i
\(425\) 3.77657 + 11.6231i 0.183191 + 0.563803i
\(426\) 9.92254 + 12.3638i 0.480749 + 0.599028i
\(427\) 12.4606 + 9.05317i 0.603011 + 0.438113i
\(428\) 0.388750 0.0187909
\(429\) 5.39556 16.1685i 0.260500 0.780624i
\(430\) 23.2629 1.12184
\(431\) 21.4925 + 15.6152i 1.03526 + 0.752157i 0.969354 0.245669i \(-0.0790077\pi\)
0.0659013 + 0.997826i \(0.479008\pi\)
\(432\) −4.59837 2.41972i −0.221239 0.116419i
\(433\) −0.366960 1.12939i −0.0176350 0.0542748i 0.941852 0.336029i \(-0.109084\pi\)
−0.959487 + 0.281754i \(0.909084\pi\)
\(434\) −3.84131 5.28711i −0.184389 0.253790i
\(435\) −0.886009 18.4544i −0.0424809 0.884820i
\(436\) −0.301151 + 0.0978498i −0.0144225 + 0.00468616i
\(437\) −5.40058 + 16.6213i −0.258345 + 0.795103i
\(438\) −21.1031 + 7.99469i −1.00834 + 0.382001i
\(439\) 25.9468i 1.23837i 0.785244 + 0.619187i \(0.212538\pi\)
−0.785244 + 0.619187i \(0.787462\pi\)
\(440\) −11.0915 0.620680i −0.528768 0.0295898i
\(441\) −1.19612 2.75123i −0.0569582 0.131011i
\(442\) −3.42741 + 4.71742i −0.163025 + 0.224385i
\(443\) 35.0160 + 11.3774i 1.66366 + 0.540556i 0.981635 0.190771i \(-0.0610987\pi\)
0.682027 + 0.731327i \(0.261099\pi\)
\(444\) −0.369370 + 1.35471i −0.0175295 + 0.0642919i
\(445\) 24.1155 17.5210i 1.14319 0.830574i
\(446\) −0.771752 + 0.560711i −0.0365435 + 0.0265504i
\(447\) 4.98693 18.2902i 0.235874 0.865097i
\(448\) −0.951057 0.309017i −0.0449332 0.0145997i
\(449\) −3.72139 + 5.12205i −0.175623 + 0.241725i −0.887750 0.460327i \(-0.847732\pi\)
0.712126 + 0.702051i \(0.247732\pi\)
\(450\) 7.43849 + 17.1095i 0.350654 + 0.806549i
\(451\) −17.7277 + 21.7340i −0.834763 + 1.02341i
\(452\) 18.6949i 0.879334i
\(453\) −23.1063 + 8.75359i −1.08563 + 0.411280i
\(454\) −0.729476 + 2.24510i −0.0342360 + 0.105368i
\(455\) −9.45195 + 3.07113i −0.443114 + 0.143977i
\(456\) 0.441141 + 9.18836i 0.0206583 + 0.430285i
\(457\) −2.52221 3.47152i −0.117984 0.162391i 0.745940 0.666013i \(-0.232000\pi\)
−0.863924 + 0.503622i \(0.832000\pi\)
\(458\) −3.09641 9.52978i −0.144686 0.445298i
\(459\) 9.03670 + 4.75522i 0.421797 + 0.221955i
\(460\) 8.91685 + 6.47847i 0.415750 + 0.302060i
\(461\) −0.793091 −0.0369380 −0.0184690 0.999829i \(-0.505879\pi\)
−0.0184690 + 0.999829i \(0.505879\pi\)
\(462\) −5.74438 0.0455402i −0.267253 0.00211872i
\(463\) −27.5831 −1.28189 −0.640947 0.767585i \(-0.721458\pi\)
−0.640947 + 0.767585i \(0.721458\pi\)
\(464\) −2.57646 1.87190i −0.119609 0.0869010i
\(465\) 23.7304 + 29.5688i 1.10047 + 1.37122i
\(466\) 0.0949223 + 0.292141i 0.00439719 + 0.0135332i
\(467\) −1.32163 1.81906i −0.0611575 0.0841761i 0.777343 0.629077i \(-0.216567\pi\)
−0.838500 + 0.544901i \(0.816567\pi\)
\(468\) −4.51819 + 7.66958i −0.208854 + 0.354526i
\(469\) −0.277272 + 0.0900912i −0.0128032 + 0.00416003i
\(470\) −4.39191 + 13.5169i −0.202584 + 0.623488i
\(471\) 12.3781 + 32.6738i 0.570355 + 1.50553i
\(472\) 6.80005i 0.312998i
\(473\) 8.33107 21.4755i 0.383063 0.987446i
\(474\) −1.06086 + 1.61800i −0.0487268 + 0.0743171i
\(475\) 19.4136 26.7205i 0.890756 1.22602i
\(476\) 1.86901 + 0.607279i 0.0856661 + 0.0278346i
\(477\) −24.2840 27.4505i −1.11189 1.25687i
\(478\) 13.4456 9.76881i 0.614988 0.446815i
\(479\) 12.0673 8.76742i 0.551370 0.400594i −0.276921 0.960893i \(-0.589314\pi\)
0.828290 + 0.560299i \(0.189314\pi\)
\(480\) 5.59711 + 1.52608i 0.255472 + 0.0696558i
\(481\) 2.28774 + 0.743330i 0.104312 + 0.0338929i
\(482\) 12.3997 17.0667i 0.564791 0.777368i
\(483\) 4.76639 + 3.12513i 0.216878 + 0.142198i
\(484\) −4.54517 + 10.0171i −0.206599 + 0.455321i
\(485\) 29.4444i 1.33700i
\(486\) 14.4271 + 5.90418i 0.654426 + 0.267819i
\(487\) −7.48024 + 23.0218i −0.338962 + 1.04322i 0.625776 + 0.780003i \(0.284783\pi\)
−0.964737 + 0.263214i \(0.915217\pi\)
\(488\) −14.6483 + 4.75953i −0.663099 + 0.215454i
\(489\) −10.2538 + 0.492294i −0.463694 + 0.0222623i
\(490\) 1.96876 + 2.70976i 0.0889395 + 0.122415i
\(491\) 2.61492 + 8.04788i 0.118010 + 0.363196i 0.992563 0.121733i \(-0.0388453\pi\)
−0.874553 + 0.484929i \(0.838845\pi\)
\(492\) 11.4232 9.16769i 0.514999 0.413312i
\(493\) 5.06324 + 3.67866i 0.228037 + 0.165679i
\(494\) 15.7586 0.709015
\(495\) 33.2999 1.33425i 1.49672 0.0599702i
\(496\) 6.53523 0.293441
\(497\) −7.40476 5.37987i −0.332149 0.241320i
\(498\) −0.844437 + 0.677701i −0.0378401 + 0.0303685i
\(499\) −1.67031 5.14067i −0.0747731 0.230128i 0.906684 0.421811i \(-0.138605\pi\)
−0.981457 + 0.191683i \(0.938605\pi\)
\(500\) −2.39960 3.30276i −0.107313 0.147704i
\(501\) −7.60206 + 0.364981i −0.339635 + 0.0163061i
\(502\) 1.67039 0.542744i 0.0745534 0.0242239i
\(503\) 8.06902 24.8339i 0.359780 1.10729i −0.593406 0.804903i \(-0.702217\pi\)
0.953186 0.302385i \(-0.0977829\pi\)
\(504\) 2.92886 + 0.649451i 0.130462 + 0.0289289i
\(505\) 55.1268i 2.45311i
\(506\) 9.17409 5.91163i 0.407838 0.262804i
\(507\) −6.07770 3.98491i −0.269920 0.176976i
\(508\) −8.33877 + 11.4773i −0.369973 + 0.509224i
\(509\) −16.7967 5.45758i −0.744501 0.241903i −0.0878877 0.996130i \(-0.528012\pi\)
−0.656613 + 0.754227i \(0.728012\pi\)
\(510\) −10.9994 2.99905i −0.487062 0.132800i
\(511\) 10.5406 7.65818i 0.466288 0.338778i
\(512\) 0.809017 0.587785i 0.0357538 0.0259767i
\(513\) −3.95809 27.3115i −0.174754 1.20583i
\(514\) −0.329839 0.107171i −0.0145486 0.00472711i
\(515\) 20.9852 28.8836i 0.924717 1.27276i
\(516\) −6.59596 + 10.0600i −0.290371 + 0.442867i
\(517\) 10.9055 + 8.89524i 0.479624 + 0.391212i
\(518\) 0.810696i 0.0356200i
\(519\) −1.40978 3.72130i −0.0618825 0.163347i
\(520\) 3.07113 9.45195i 0.134678 0.414495i
\(521\) −24.2568 + 7.88151i −1.06271 + 0.345295i −0.787644 0.616130i \(-0.788699\pi\)
−0.275065 + 0.961426i \(0.588699\pi\)
\(522\) 8.23180 + 4.84940i 0.360296 + 0.212253i
\(523\) −15.9861 22.0030i −0.699023 0.962123i −0.999964 0.00847986i \(-0.997301\pi\)
0.300941 0.953643i \(-0.402699\pi\)
\(524\) −2.27306 6.99576i −0.0992991 0.305611i
\(525\) −6.74185 8.40056i −0.294238 0.366630i
\(526\) −17.7275 12.8798i −0.772957 0.561586i
\(527\) −12.8430 −0.559451
\(528\) 3.41331 4.62053i 0.148545 0.201083i
\(529\) 12.1717 0.529204
\(530\) 33.1045 + 24.0518i 1.43797 + 1.04475i
\(531\) −1.95435 20.3063i −0.0848116 0.881220i
\(532\) −1.64119 5.05108i −0.0711548 0.218992i
\(533\) −14.7486 20.2997i −0.638832 0.879277i
\(534\) 0.739205 + 15.3966i 0.0319885 + 0.666278i
\(535\) 1.23837 0.402371i 0.0535394 0.0173960i
\(536\) 0.0900912 0.277272i 0.00389135 0.0119763i
\(537\) −21.3321 + 8.08147i −0.920549 + 0.348741i
\(538\) 29.7047i 1.28066i
\(539\) 3.20663 0.847054i 0.138119 0.0364852i
\(540\) −17.1527 2.94857i −0.738134 0.126886i
\(541\) −6.00348 + 8.26308i −0.258110 + 0.355258i −0.918331 0.395814i \(-0.870463\pi\)
0.660221 + 0.751071i \(0.270463\pi\)
\(542\) −27.9268 9.07396i −1.19956 0.389760i
\(543\) 11.9245 43.7348i 0.511731 1.87684i
\(544\) −1.58988 + 1.15511i −0.0681654 + 0.0495251i
\(545\) −0.858043 + 0.623405i −0.0367545 + 0.0267037i
\(546\) 1.35190 4.95828i 0.0578561 0.212195i
\(547\) −28.4799 9.25370i −1.21771 0.395659i −0.371466 0.928447i \(-0.621145\pi\)
−0.846249 + 0.532787i \(0.821145\pi\)
\(548\) −9.75835 + 13.4312i −0.416856 + 0.573753i
\(549\) 42.3750 18.4229i 1.80852 0.786270i
\(550\) −19.9415 + 5.26769i −0.850310 + 0.224615i
\(551\) 16.9139i 0.720554i
\(552\) −5.32990 + 2.01918i −0.226855 + 0.0859420i
\(553\) 0.345184 1.06237i 0.0146787 0.0451765i
\(554\) 9.90880 3.21957i 0.420985 0.136786i
\(555\) 0.225544 + 4.69778i 0.00957382 + 0.199410i
\(556\) −9.48331 13.0527i −0.402182 0.553556i
\(557\) −3.84988 11.8487i −0.163124 0.502046i 0.835769 0.549082i \(-0.185022\pi\)
−0.998893 + 0.0470361i \(0.985022\pi\)
\(558\) −19.5155 + 1.87824i −0.826158 + 0.0795122i
\(559\) 16.6720 + 12.1129i 0.705151 + 0.512322i
\(560\) −3.34945 −0.141540
\(561\) −6.70782 + 9.08026i −0.283204 + 0.383369i
\(562\) −8.55093 −0.360699
\(563\) 6.90825 + 5.01914i 0.291148 + 0.211531i 0.723765 0.690046i \(-0.242410\pi\)
−0.432617 + 0.901578i \(0.642410\pi\)
\(564\) −4.60009 5.73186i −0.193699 0.241355i
\(565\) −19.3499 59.5529i −0.814057 2.50541i
\(566\) −15.5127 21.3515i −0.652049 0.897469i
\(567\) −8.93282 1.09763i −0.375143 0.0460962i
\(568\) 8.70482 2.82837i 0.365246 0.118676i
\(569\) −4.53295 + 13.9510i −0.190031 + 0.584856i −0.999999 0.00161883i \(-0.999485\pi\)
0.809967 + 0.586475i \(0.199485\pi\)
\(570\) 10.9156 + 28.8131i 0.457203 + 1.20685i
\(571\) 43.0612i 1.80206i 0.433762 + 0.901028i \(0.357186\pi\)
−0.433762 + 0.901028i \(0.642814\pi\)
\(572\) −7.62588 6.22017i −0.318854 0.260078i
\(573\) −10.3338 + 15.7609i −0.431702 + 0.658422i
\(574\) −4.97060 + 6.84145i −0.207469 + 0.285557i
\(575\) 19.4624 + 6.32371i 0.811637 + 0.263717i
\(576\) −2.24696 + 1.98776i −0.0936232 + 0.0828233i
\(577\) −17.7269 + 12.8794i −0.737982 + 0.536176i −0.892079 0.451880i \(-0.850753\pi\)
0.154096 + 0.988056i \(0.450753\pi\)
\(578\) −10.6289 + 7.72232i −0.442103 + 0.321206i
\(579\) 17.9796 + 4.90223i 0.747206 + 0.203730i
\(580\) −10.1448 3.29626i −0.421242 0.136870i
\(581\) 0.367441 0.505739i 0.0152440 0.0209816i
\(582\) 12.7332 + 8.34868i 0.527809 + 0.346064i
\(583\) 34.0595 21.9474i 1.41060 0.908969i
\(584\) 13.0289i 0.539138i
\(585\) −6.45449 + 29.1081i −0.266860 + 1.20347i
\(586\) −5.03408 + 15.4933i −0.207956 + 0.640023i
\(587\) −13.0033 + 4.22501i −0.536702 + 0.174385i −0.564812 0.825220i \(-0.691051\pi\)
0.0281098 + 0.999605i \(0.491051\pi\)
\(588\) −1.73006 + 0.0830614i −0.0713464 + 0.00342540i
\(589\) 20.4013 + 28.0799i 0.840620 + 1.15701i
\(590\) 7.03831 + 21.6617i 0.289763 + 0.891798i
\(591\) 7.87134 6.31712i 0.323783 0.259852i
\(592\) 0.655867 + 0.476515i 0.0269560 + 0.0195847i
\(593\) −25.6012 −1.05132 −0.525659 0.850696i \(-0.676181\pi\)
−0.525659 + 0.850696i \(0.676181\pi\)
\(594\) −8.86487 + 14.7788i −0.363730 + 0.606383i
\(595\) 6.58234 0.269849
\(596\) −8.85496 6.43351i −0.362713 0.263527i
\(597\) 28.5002 22.8727i 1.16643 0.936119i
\(598\) 3.01720 + 9.28598i 0.123382 + 0.379732i
\(599\) −12.9678 17.8486i −0.529848 0.729273i 0.457259 0.889333i \(-0.348831\pi\)
−0.987107 + 0.160060i \(0.948831\pi\)
\(600\) 10.7590 0.516546i 0.439232 0.0210879i
\(601\) −12.9783 + 4.21689i −0.529394 + 0.172011i −0.561505 0.827474i \(-0.689777\pi\)
0.0321101 + 0.999484i \(0.489777\pi\)
\(602\) 2.14621 6.60535i 0.0874729 0.269214i
\(603\) −0.189342 + 0.853884i −0.00771060 + 0.0347728i
\(604\) 14.2656i 0.580461i
\(605\) −4.11070 + 36.6140i −0.167124 + 1.48857i
\(606\) −23.8396 15.6307i −0.968416 0.634953i
\(607\) 1.91867 2.64082i 0.0778764 0.107188i −0.768302 0.640088i \(-0.778898\pi\)
0.846178 + 0.532900i \(0.178898\pi\)
\(608\) 5.05108 + 1.64119i 0.204848 + 0.0665592i
\(609\) −5.32175 1.45100i −0.215648 0.0587977i
\(610\) −41.7363 + 30.3232i −1.68985 + 1.22775i
\(611\) −10.1858 + 7.40043i −0.412074 + 0.299389i
\(612\) 4.41571 3.90634i 0.178495 0.157904i
\(613\) −31.9471 10.3802i −1.29033 0.419254i −0.418124 0.908390i \(-0.637312\pi\)
−0.872208 + 0.489136i \(0.837312\pi\)
\(614\) 10.5200 14.4795i 0.424552 0.584345i
\(615\) 26.9000 41.0274i 1.08471 1.65438i
\(616\) −1.19953 + 3.09211i −0.0483305 + 0.124585i
\(617\) 43.6916i 1.75896i 0.475940 + 0.879478i \(0.342108\pi\)
−0.475940 + 0.879478i \(0.657892\pi\)
\(618\) 6.54056 + 17.2647i 0.263100 + 0.694488i
\(619\) −1.99688 + 6.14575i −0.0802612 + 0.247019i −0.983133 0.182891i \(-0.941455\pi\)
0.902872 + 0.429909i \(0.141455\pi\)
\(620\) 20.8181 6.76421i 0.836075 0.271657i
\(621\) 15.3358 7.56150i 0.615406 0.303433i
\(622\) 11.8599 + 16.3237i 0.475538 + 0.654521i
\(623\) −2.75010 8.46392i −0.110180 0.339100i
\(624\) 3.21670 + 4.00811i 0.128771 + 0.160453i
\(625\) 14.0933 + 10.2394i 0.563731 + 0.409574i
\(626\) 6.71621 0.268434
\(627\) 30.5085 + 0.241865i 1.21839 + 0.00965915i
\(628\) 20.1725 0.804972
\(629\) −1.28891 0.936447i −0.0513921 0.0373386i
\(630\) 10.0021 0.962640i 0.398495 0.0383525i
\(631\) 13.4126 + 41.2797i 0.533946 + 1.64332i 0.745915 + 0.666041i \(0.232012\pi\)
−0.211969 + 0.977276i \(0.567988\pi\)
\(632\) 0.656580 + 0.903705i 0.0261173 + 0.0359474i
\(633\) 1.54483 + 32.1768i 0.0614015 + 1.27891i
\(634\) 16.8391 5.47134i 0.668765 0.217295i
\(635\) −14.6838 + 45.1922i −0.582710 + 1.79340i
\(636\) −19.7877 + 7.49636i −0.784632 + 0.297250i
\(637\) 2.96716i 0.117563i
\(638\) −6.67614 + 8.18491i −0.264311 + 0.324044i
\(639\) −25.1815 + 10.9479i −0.996163 + 0.433091i
\(640\) 1.96876 2.70976i 0.0778220 0.107113i
\(641\) −15.2776 4.96400i −0.603429 0.196066i −0.00866002 0.999963i \(-0.502757\pi\)
−0.594769 + 0.803896i \(0.702757\pi\)
\(642\) −0.177123 + 0.649621i −0.00699048 + 0.0256385i
\(643\) −5.78826 + 4.20542i −0.228267 + 0.165846i −0.696040 0.718003i \(-0.745056\pi\)
0.467773 + 0.883849i \(0.345056\pi\)
\(644\) 2.66218 1.93419i 0.104905 0.0762177i
\(645\) −10.5991 + 38.8734i −0.417337 + 1.53064i
\(646\) −9.92636 3.22527i −0.390547 0.126897i
\(647\) −0.103256 + 0.142120i −0.00405941 + 0.00558730i −0.811042 0.584988i \(-0.801099\pi\)
0.806982 + 0.590575i \(0.201099\pi\)
\(648\) 6.13858 6.58163i 0.241146 0.258551i
\(649\) 22.5180 + 1.26010i 0.883909 + 0.0494634i
\(650\) 18.4523i 0.723759i
\(651\) 10.5852 4.01011i 0.414867 0.157168i
\(652\) −1.83150 + 5.63678i −0.0717271 + 0.220753i
\(653\) 12.1656 3.95285i 0.476077 0.154687i −0.0611426 0.998129i \(-0.519474\pi\)
0.537220 + 0.843442i \(0.319474\pi\)
\(654\) −0.0263013 0.547820i −0.00102846 0.0214215i
\(655\) −14.4817 19.9324i −0.565849 0.778824i
\(656\) −2.61320 8.04261i −0.102028 0.314011i
\(657\) −3.74453 38.9068i −0.146088 1.51790i
\(658\) 3.43285 + 2.49411i 0.133826 + 0.0972306i
\(659\) −9.68624 −0.377322 −0.188661 0.982042i \(-0.560415\pi\)
−0.188661 + 0.982042i \(0.560415\pi\)
\(660\) 6.09072 18.2517i 0.237081 0.710447i
\(661\) 7.90856 0.307607 0.153804 0.988101i \(-0.450848\pi\)
0.153804 + 0.988101i \(0.450848\pi\)
\(662\) −16.9641 12.3252i −0.659330 0.479031i
\(663\) −6.32145 7.87673i −0.245505 0.305907i
\(664\) 0.193175 + 0.594531i 0.00749664 + 0.0230723i
\(665\) −10.4561 14.3916i −0.405471 0.558082i
\(666\) −2.09550 1.23447i −0.0811991 0.0478349i
\(667\) 9.96670 3.23838i 0.385912 0.125390i
\(668\) −1.35785 + 4.17904i −0.0525369 + 0.161692i
\(669\) −0.585349 1.54511i −0.0226309 0.0597374i
\(670\) 0.976504i 0.0377257i
\(671\) 13.0465 + 49.3891i 0.503653 + 1.90665i
\(672\) 0.949704 1.44847i 0.0366356 0.0558759i
\(673\) −17.6357 + 24.2735i −0.679808 + 0.935675i −0.999932 0.0117004i \(-0.996276\pi\)
0.320124 + 0.947376i \(0.396276\pi\)
\(674\) −15.4283 5.01296i −0.594276 0.193092i
\(675\) −31.9799 + 4.63466i −1.23091 + 0.178388i
\(676\) −3.39460 + 2.46632i −0.130561 + 0.0948584i
\(677\) 6.31637 4.58911i 0.242758 0.176374i −0.459753 0.888047i \(-0.652062\pi\)
0.702511 + 0.711673i \(0.252062\pi\)
\(678\) 31.2401 + 8.51779i 1.19977 + 0.327124i
\(679\) −8.36056 2.71651i −0.320849 0.104250i
\(680\) −3.86900 + 5.32522i −0.148369 + 0.204213i
\(681\) −3.41930 2.24190i −0.131028 0.0859100i
\(682\) 1.21103 21.6410i 0.0463727 0.828679i
\(683\) 47.5654i 1.82004i 0.414567 + 0.910019i \(0.363933\pi\)
−0.414567 + 0.910019i \(0.636067\pi\)
\(684\) −15.5552 3.44925i −0.594768 0.131885i
\(685\) −17.1836 + 52.8857i −0.656552 + 2.02066i
\(686\) 0.951057 0.309017i 0.0363115 0.0117983i
\(687\) 17.3355 0.832293i 0.661392 0.0317540i
\(688\) 4.08233 + 5.61884i 0.155637 + 0.214216i
\(689\) 11.2016 + 34.4749i 0.426746 + 1.31339i
\(690\) −14.8886 + 11.9488i −0.566798 + 0.454882i
\(691\) 13.4565 + 9.77672i 0.511909 + 0.371924i 0.813547 0.581499i \(-0.197533\pi\)
−0.301638 + 0.953423i \(0.597533\pi\)
\(692\) −2.29751 −0.0873380
\(693\) 2.69336 9.57840i 0.102312 0.363853i
\(694\) −14.5843 −0.553612
\(695\) −43.7193 31.7639i −1.65837 1.20487i
\(696\) 4.30193 3.45251i 0.163064 0.130867i
\(697\) 5.13546 + 15.8053i 0.194519 + 0.598669i
\(698\) 2.85262 + 3.92630i 0.107973 + 0.148613i
\(699\) −0.531431 + 0.0255144i −0.0201006 + 0.000965043i
\(700\) −5.91447 + 1.92173i −0.223546 + 0.0726344i
\(701\) 4.83599 14.8836i 0.182653 0.562147i −0.817247 0.576287i \(-0.804501\pi\)
0.999900 + 0.0141399i \(0.00450101\pi\)
\(702\) −10.7577 11.0445i −0.406022 0.416850i
\(703\) 4.30562i 0.162390i
\(704\) −1.79650 2.78794i −0.0677082 0.105074i
\(705\) −20.5864 13.4977i −0.775328 0.508352i
\(706\) 15.5439 21.3943i 0.585001 0.805185i
\(707\) 15.6529 + 5.08594i 0.588689 + 0.191277i
\(708\) −11.3632 3.09825i −0.427056 0.116439i
\(709\) −18.0240 + 13.0952i −0.676907 + 0.491802i −0.872330 0.488917i \(-0.837392\pi\)
0.195423 + 0.980719i \(0.437392\pi\)
\(710\) 24.8019 18.0196i 0.930799 0.676265i
\(711\) −2.22041 2.50994i −0.0832718 0.0941302i
\(712\) 8.46392 + 2.75010i 0.317199 + 0.103064i
\(713\) −12.6404 + 17.3980i −0.473385 + 0.651559i
\(714\) −1.86636 + 2.84653i −0.0698466 + 0.106529i
\(715\) −30.7305 11.9214i −1.14926 0.445834i
\(716\) 13.1703i 0.492197i
\(717\) 10.1981 + 26.9192i 0.380854 + 1.00532i
\(718\) −3.58878 + 11.0451i −0.133932 + 0.412201i
\(719\) 23.5096 7.63874i 0.876761 0.284877i 0.164149 0.986436i \(-0.447512\pi\)
0.712612 + 0.701559i \(0.247512\pi\)
\(720\) −5.10032 + 8.65773i −0.190078 + 0.322655i
\(721\) −6.26525 8.62338i −0.233330 0.321151i
\(722\) 2.84508 + 8.75627i 0.105883 + 0.325875i
\(723\) 22.8698 + 28.4965i 0.850537 + 1.05980i
\(724\) −21.1736 15.3835i −0.786912 0.571725i
\(725\) −19.8050 −0.735538
\(726\) −14.6681 12.1592i −0.544385 0.451270i
\(727\) 36.8818 1.36787 0.683935 0.729543i \(-0.260267\pi\)
0.683935 + 0.729543i \(0.260267\pi\)
\(728\) −2.40048 1.74405i −0.0889679 0.0646389i
\(729\) −16.4395 + 21.4183i −0.608869 + 0.793271i
\(730\) 13.4854 + 41.5037i 0.499116 + 1.53612i
\(731\) −8.02258 11.0421i −0.296726 0.408408i
\(732\) −1.27933 26.6466i −0.0472853 0.984888i
\(733\) −24.3745 + 7.91975i −0.900292 + 0.292523i −0.722357 0.691520i \(-0.756941\pi\)
−0.177934 + 0.984042i \(0.556941\pi\)
\(734\) 5.23853 16.1225i 0.193358 0.595094i
\(735\) −5.42516 + 2.05527i −0.200110 + 0.0758098i
\(736\) 3.29064i 0.121295i
\(737\) −0.901477 0.349713i −0.0332063 0.0128818i
\(738\) 10.1150 + 23.2658i 0.372339 + 0.856426i
\(739\) −15.6277 + 21.5096i −0.574873 + 0.791244i −0.993122 0.117088i \(-0.962644\pi\)
0.418249 + 0.908332i \(0.362644\pi\)
\(740\) 2.58249 + 0.839102i 0.0949342 + 0.0308460i
\(741\) −7.17997 + 26.3335i −0.263763 + 0.967385i
\(742\) 9.88356 7.18083i 0.362837 0.263616i
\(743\) 11.0261 8.01096i 0.404510 0.293894i −0.366866 0.930274i \(-0.619569\pi\)
0.771375 + 0.636380i \(0.219569\pi\)
\(744\) −2.97759 + 10.9207i −0.109164 + 0.400372i
\(745\) −34.8666 11.3288i −1.27741 0.415057i
\(746\) 10.3088 14.1888i 0.377432 0.519490i
\(747\) −0.747729 1.71987i −0.0273580 0.0629268i
\(748\) 3.53048 + 5.47884i 0.129087 + 0.200326i
\(749\) 0.388750i 0.0142046i
\(750\) 6.61239 2.50504i 0.241450 0.0914712i
\(751\) 12.3775 38.0942i 0.451663 1.39008i −0.423346 0.905968i \(-0.639144\pi\)
0.875009 0.484107i \(-0.160856\pi\)
\(752\) −4.03556 + 1.31123i −0.147162 + 0.0478157i
\(753\) 0.145886 + 3.03860i 0.00531637 + 0.110733i
\(754\) −5.55424 7.64476i −0.202274 0.278406i
\(755\) 14.7655 + 45.4435i 0.537371 + 1.65386i
\(756\) −2.41972 + 4.59837i −0.0880042 + 0.167241i
\(757\) 20.4083 + 14.8275i 0.741751 + 0.538913i 0.893259 0.449543i \(-0.148413\pi\)
−0.151508 + 0.988456i \(0.548413\pi\)
\(758\) −16.0375 −0.582507
\(759\) 5.69873 + 18.0238i 0.206851 + 0.654223i
\(760\) 17.7890 0.645275
\(761\) −31.2556 22.7085i −1.13301 0.823183i −0.146883 0.989154i \(-0.546924\pi\)
−0.986131 + 0.165971i \(0.946924\pi\)
\(762\) −15.3799 19.1638i −0.557154 0.694232i
\(763\) 0.0978498 + 0.301151i 0.00354240 + 0.0109024i
\(764\) 6.39575 + 8.80299i 0.231390 + 0.318481i
\(765\) 10.0231 17.0141i 0.362387 0.615148i
\(766\) −5.82073 + 1.89127i −0.210311 + 0.0683343i
\(767\) −6.23499 + 19.1893i −0.225133 + 0.692887i
\(768\) 0.613613 + 1.61972i 0.0221419 + 0.0584465i
\(769\) 22.9318i 0.826942i 0.910517 + 0.413471i \(0.135684\pi\)
−0.910517 + 0.413471i \(0.864316\pi\)
\(770\) −0.620680 + 11.0915i −0.0223678 + 0.399711i
\(771\) 0.329370 0.502347i 0.0118620 0.0180916i
\(772\) 6.32425 8.70458i 0.227615 0.313285i
\(773\) 5.72599 + 1.86049i 0.205949 + 0.0669170i 0.410175 0.912007i \(-0.365468\pi\)
−0.204226 + 0.978924i \(0.565468\pi\)
\(774\) −13.8055 15.6057i −0.496229 0.560936i
\(775\) 32.8797 23.8885i 1.18107 0.858100i
\(776\) 7.11192 5.16711i 0.255303 0.185489i
\(777\) 1.35471 + 0.369370i 0.0486001 + 0.0132511i
\(778\) 16.9391 + 5.50385i 0.607296 + 0.197323i
\(779\) 26.3990 36.3350i 0.945841 1.30184i
\(780\) 14.3954 + 9.43851i 0.515439 + 0.337953i
\(781\) −7.75291 29.3496i −0.277421 1.05021i
\(782\) 6.46675i 0.231251i
\(783\) −11.8542 + 11.5463i −0.423634 + 0.412630i
\(784\) −0.309017 + 0.951057i −0.0110363 + 0.0339663i
\(785\) 64.2600 20.8793i 2.29354 0.745216i
\(786\) 12.7259 0.610981i 0.453918 0.0217930i
\(787\) 21.3866 + 29.4361i 0.762350 + 1.04929i 0.997015 + 0.0772087i \(0.0246008\pi\)
−0.234665 + 0.972076i \(0.575399\pi\)
\(788\) −1.80066 5.54187i −0.0641459 0.197421i
\(789\) 29.5998 23.7553i 1.05378 0.845710i
\(790\) 3.02692 + 2.19918i 0.107693 + 0.0782434i
\(791\) −18.6949 −0.664714
\(792\) 6.16597 + 7.80902i 0.219098 + 0.277481i
\(793\) −45.7007 −1.62288
\(794\) 23.4288 + 17.0221i 0.831459 + 0.604090i
\(795\) −55.2750 + 44.3608i −1.96040 + 1.57332i
\(796\) −6.51975 20.0657i −0.231086 0.711211i
\(797\) −31.1246 42.8393i −1.10249 1.51745i −0.832042 0.554713i \(-0.812828\pi\)
−0.270448 0.962734i \(-0.587172\pi\)
\(798\) 9.18836 0.441141i 0.325265 0.0156162i
\(799\) 7.93066 2.57683i 0.280567 0.0911616i
\(800\) 1.92173 5.91447i 0.0679433 0.209108i
\(801\) −26.0654 5.77979i −0.920975 0.204219i
\(802\) 10.7537i 0.379726i
\(803\) 43.1444 + 2.41435i 1.52253 + 0.0852007i
\(804\) 0.422289 + 0.276878i 0.0148930 + 0.00976474i
\(805\) 6.47847 8.91685i 0.228336 0.314278i
\(806\) 18.4420 + 5.99218i 0.649592 + 0.211065i
\(807\) 49.6381 + 13.5341i 1.74734 + 0.476423i
\(808\) −13.3152 + 9.67404i −0.468426 + 0.340332i
\(809\) 18.0212 13.0932i 0.633592 0.460331i −0.224051 0.974577i \(-0.571928\pi\)
0.857643 + 0.514246i \(0.171928\pi\)
\(810\) 12.7423 27.3196i 0.447720 0.959912i
\(811\) 4.56271 + 1.48251i 0.160218 + 0.0520581i 0.388028 0.921648i \(-0.373156\pi\)
−0.227810 + 0.973706i \(0.573156\pi\)
\(812\) −1.87190 + 2.57646i −0.0656910 + 0.0904159i
\(813\) 27.8871 42.5328i 0.978043 1.49169i
\(814\) 1.69949 2.08357i 0.0595671 0.0730289i
\(815\) 19.8518i 0.695377i
\(816\) −1.20587 3.18306i −0.0422139 0.111429i
\(817\) −11.3985 + 35.0811i −0.398784 + 1.22733i
\(818\) 13.5253 4.39465i 0.472902 0.153655i
\(819\) 7.66958 + 4.51819i 0.267997 + 0.157878i
\(820\) −16.6488 22.9151i −0.581402 0.800231i
\(821\) −5.49098 16.8995i −0.191636 0.589796i −0.999999 0.00111177i \(-0.999646\pi\)
0.808363 0.588684i \(-0.200354\pi\)
\(822\) −17.9981 22.4263i −0.627757 0.782205i
\(823\) −36.8421 26.7674i −1.28424 0.933052i −0.284564 0.958657i \(-0.591849\pi\)
−0.999672 + 0.0256052i \(0.991849\pi\)
\(824\) 10.6591 0.371327
\(825\) 0.283207 35.7234i 0.00986001 1.24373i
\(826\) 6.80005 0.236604
\(827\) −22.6418 16.4502i −0.787333 0.572031i 0.119838 0.992794i \(-0.461763\pi\)
−0.907171 + 0.420762i \(0.861763\pi\)
\(828\) −0.945737 9.82651i −0.0328666 0.341495i
\(829\) −3.50843 10.7978i −0.121853 0.375024i 0.871462 0.490464i \(-0.163173\pi\)
−0.993315 + 0.115439i \(0.963173\pi\)
\(830\) 1.23073 + 1.69395i 0.0427191 + 0.0587978i
\(831\) 0.865395 + 18.0250i 0.0300202 + 0.625281i
\(832\) 2.82194 0.916903i 0.0978331 0.0317879i
\(833\) 0.607279 1.86901i 0.0210410 0.0647575i
\(834\) 26.1325 9.90003i 0.904893 0.342810i
\(835\) 14.7178i 0.509332i
\(836\) 6.37073 16.4222i 0.220336 0.567975i
\(837\) 5.75305 33.4672i 0.198854 1.15679i
\(838\) −17.8870 + 24.6193i −0.617895 + 0.850460i
\(839\) −11.9547 3.88433i −0.412724 0.134102i 0.0952931 0.995449i \(-0.469621\pi\)
−0.508017 + 0.861347i \(0.669621\pi\)
\(840\) 1.52608 5.59711i 0.0526548 0.193118i
\(841\) 15.2563 11.0844i 0.526080 0.382220i
\(842\) 29.2346 21.2402i 1.00749 0.731985i
\(843\) 3.89599 14.2890i 0.134185 0.492141i
\(844\) 17.6884 + 5.74730i 0.608859 + 0.197830i
\(845\) −8.26082 + 11.3700i −0.284181 + 0.391141i
\(846\) 11.6741 5.07543i 0.401365 0.174497i
\(847\) 10.0171 + 4.54517i 0.344190 + 0.156174i
\(848\) 12.2168i 0.419525i
\(849\) 42.7473 16.1944i 1.46708 0.555790i
\(850\) −3.77657 + 11.6231i −0.129535 + 0.398669i
\(851\) −2.53714 + 0.824367i −0.0869721 + 0.0282589i
\(852\) 0.760244 + 15.8349i 0.0260455 + 0.542493i
\(853\) −9.04093 12.4438i −0.309556 0.426067i 0.625687 0.780074i \(-0.284819\pi\)
−0.935243 + 0.354007i \(0.884819\pi\)
\(854\) 4.75953 + 14.6483i 0.162868 + 0.501256i
\(855\) −53.1215 + 5.11260i −1.81672 + 0.174847i
\(856\) 0.314505 + 0.228502i 0.0107496 + 0.00781002i
\(857\) 18.5694 0.634320 0.317160 0.948372i \(-0.397271\pi\)
0.317160 + 0.948372i \(0.397271\pi\)
\(858\) 13.8687 9.90919i 0.473470 0.338294i
\(859\) −38.4864 −1.31314 −0.656570 0.754265i \(-0.727993\pi\)
−0.656570 + 0.754265i \(0.727993\pi\)
\(860\) 18.8201 + 13.6736i 0.641759 + 0.466265i
\(861\) −9.16769 11.4232i −0.312434 0.389303i
\(862\) 8.20939 + 25.2659i 0.279613 + 0.860560i
\(863\) 18.3519 + 25.2593i 0.624707 + 0.859836i 0.997685 0.0680043i \(-0.0216632\pi\)
−0.372978 + 0.927840i \(0.621663\pi\)
\(864\) −2.29788 4.66044i −0.0781756 0.158552i
\(865\) −7.31875 + 2.37801i −0.248845 + 0.0808546i
\(866\) 0.366960 1.12939i 0.0124698 0.0383781i
\(867\) −8.06165 21.2798i −0.273788 0.722701i
\(868\) 6.53523i 0.221820i
\(869\) 3.11424 2.00676i 0.105643 0.0680748i
\(870\) 10.1304 15.4507i 0.343453 0.523828i
\(871\) 0.508464 0.699841i 0.0172286 0.0237132i
\(872\) −0.301151 0.0978498i −0.0101983 0.00331361i
\(873\) −19.7526 + 17.4740i −0.668524 + 0.591406i
\(874\) −14.1389 + 10.2725i −0.478255 + 0.347473i
\(875\) −3.30276 + 2.39960i −0.111654 + 0.0811212i
\(876\) −21.7719 5.93623i −0.735604 0.200567i
\(877\) 8.44949 + 2.74541i 0.285319 + 0.0927058i 0.448180 0.893943i \(-0.352072\pi\)
−0.162861 + 0.986649i \(0.552072\pi\)
\(878\) −15.2512 + 20.9914i −0.514701 + 0.708426i
\(879\) −23.5965 15.4713i −0.795889 0.521834i
\(880\) −8.60841 7.02158i −0.290189 0.236697i
\(881\) 16.7076i 0.562893i 0.959577 + 0.281446i \(0.0908142\pi\)
−0.959577 + 0.281446i \(0.909186\pi\)
\(882\) 0.649451 2.92886i 0.0218682 0.0986198i
\(883\) −2.68601 + 8.26670i −0.0903916 + 0.278197i −0.986025 0.166596i \(-0.946723\pi\)
0.895634 + 0.444792i \(0.146723\pi\)
\(884\) −5.54567 + 1.80190i −0.186521 + 0.0606043i
\(885\) −39.4046 + 1.89185i −1.32457 + 0.0635937i
\(886\) 21.6411 + 29.7864i 0.727047 + 1.00069i
\(887\) −4.92600 15.1607i −0.165399 0.509046i 0.833666 0.552268i \(-0.186238\pi\)
−0.999065 + 0.0432224i \(0.986238\pi\)
\(888\) −1.09511 + 0.878876i −0.0367494 + 0.0294932i
\(889\) 11.4773 + 8.33877i 0.384937 + 0.279673i
\(890\) 29.8085 0.999182
\(891\) −20.6572 21.5472i −0.692041 0.721858i
\(892\) −0.953938 −0.0319402
\(893\) −18.2319 13.2463i −0.610108 0.443269i
\(894\) 14.7852 11.8658i 0.494492 0.396853i
\(895\) 13.6318 + 41.9542i 0.455659 + 1.40237i
\(896\) −0.587785 0.809017i −0.0196365 0.0270274i
\(897\) −16.8920 + 0.811000i −0.564009 + 0.0270785i
\(898\) −6.02133 + 1.95645i −0.200934 + 0.0652876i
\(899\) 6.43144 19.7939i 0.214501 0.660165i
\(900\) −4.03883 + 18.2141i −0.134628 + 0.607137i
\(901\) 24.0083i 0.799833i
\(902\) −27.1169 + 7.16311i −0.902894 + 0.238506i
\(903\) 10.0600 + 6.59596i 0.334776 + 0.219500i
\(904\) 10.9886 15.1245i 0.365475 0.503033i
\(905\) −83.3716 27.0891i −2.77137 0.900471i
\(906\) −23.8386 6.49973i −0.791985 0.215939i
\(907\) −8.54347 + 6.20720i −0.283681 + 0.206107i −0.720522 0.693433i \(-0.756098\pi\)
0.436840 + 0.899539i \(0.356098\pi\)
\(908\) −1.90979 + 1.38755i −0.0633787 + 0.0460473i
\(909\) 36.9815 32.7154i 1.22660 1.08510i
\(910\) −9.45195 3.07113i −0.313329 0.101807i
\(911\) −25.2711 + 34.7828i −0.837271 + 1.15240i 0.149255 + 0.988799i \(0.452312\pi\)
−0.986526 + 0.163605i \(0.947688\pi\)
\(912\) −5.04390 + 7.69284i −0.167020 + 0.254735i
\(913\) 2.00455 0.529517i 0.0663411 0.0175244i
\(914\) 4.29104i 0.141935i
\(915\) −31.6556 83.5593i −1.04650 2.76238i
\(916\) 3.09641 9.52978i 0.102308 0.314873i
\(917\) −6.99576 + 2.27306i −0.231020 + 0.0750630i
\(918\) 4.51579 + 9.15869i 0.149043 + 0.302282i
\(919\) −14.3381 19.7347i −0.472969 0.650986i 0.504166 0.863607i \(-0.331800\pi\)
−0.977135 + 0.212621i \(0.931800\pi\)
\(920\) 3.40594 + 10.4824i 0.112290 + 0.345594i
\(921\) 19.4029 + 24.1766i 0.639346 + 0.796646i
\(922\) −0.641624 0.466167i −0.0211308 0.0153524i
\(923\) 27.1578 0.893910
\(924\) −4.62053 3.41331i −0.152004 0.112290i
\(925\) 5.04159 0.165766
\(926\) −22.3152 16.2129i −0.733322 0.532790i
\(927\) −31.8302 + 3.06344i −1.04544 + 0.100617i
\(928\) −0.984118 3.02880i −0.0323053 0.0994254i
\(929\) −8.39883 11.5600i −0.275557 0.379271i 0.648699 0.761045i \(-0.275313\pi\)
−0.924256 + 0.381774i \(0.875313\pi\)
\(930\) 1.81817 + 37.8700i 0.0596201 + 1.24181i
\(931\) −5.05108 + 1.64119i −0.165542 + 0.0537880i
\(932\) −0.0949223 + 0.292141i −0.00310928 + 0.00956939i
\(933\) −32.6814 + 12.3810i −1.06994 + 0.405336i
\(934\) 2.24848i 0.0735726i
\(935\) 16.9172 + 13.7988i 0.553252 + 0.451268i
\(936\) −8.16336 + 3.54909i −0.266828 + 0.116006i
\(937\) 32.1674 44.2746i 1.05086 1.44639i 0.162803 0.986659i \(-0.447947\pi\)
0.888059 0.459729i \(-0.152053\pi\)
\(938\) −0.277272 0.0900912i −0.00905326 0.00294158i
\(939\) −3.06005 + 11.2231i −0.0998608 + 0.366253i
\(940\) −11.4982 + 8.35391i −0.375029 + 0.272474i
\(941\) 1.77805 1.29183i 0.0579629 0.0421125i −0.558427 0.829554i \(-0.688595\pi\)
0.616389 + 0.787441i \(0.288595\pi\)
\(942\) −9.19104 + 33.7093i −0.299460 + 1.09831i
\(943\) 26.4653 + 8.59910i 0.861829 + 0.280025i
\(944\) −3.99697 + 5.50136i −0.130090 + 0.179054i
\(945\) −2.94857 + 17.1527i −0.0959169 + 0.557977i
\(946\) 19.3630 12.4772i 0.629545 0.405668i
\(947\) 13.1313i 0.426709i 0.976975 + 0.213354i \(0.0684389\pi\)
−0.976975 + 0.213354i \(0.931561\pi\)
\(948\) −1.80929 + 0.685431i −0.0587629 + 0.0222618i
\(949\) −11.9462 + 36.7667i −0.387791 + 1.19350i
\(950\) 31.4118 10.2063i 1.01913 0.331137i
\(951\) 1.47066 + 30.6318i 0.0476893 + 0.993304i
\(952\) 1.15511 + 1.58988i 0.0374375 + 0.0515282i
\(953\) 17.7408 + 54.6007i 0.574682 + 1.76869i 0.637260 + 0.770649i \(0.280068\pi\)
−0.0625783 + 0.998040i \(0.519932\pi\)
\(954\) −3.51112 36.4817i −0.113677 1.18114i
\(955\) 29.4852 + 21.4223i 0.954119 + 0.693208i
\(956\) 16.6197 0.537519
\(957\) −10.6356 14.8854i −0.343800 0.481176i
\(958\) 14.9160 0.481915
\(959\) 13.4312 + 9.75835i 0.433717 + 0.315114i
\(960\) 3.63114 + 4.52452i 0.117195 + 0.146028i
\(961\) 3.61835 + 11.1361i 0.116721 + 0.359231i
\(962\) 1.41390 + 1.94606i 0.0455859 + 0.0627436i
\(963\) −1.00485 0.591962i −0.0323808 0.0190757i
\(964\) 20.0631 6.51891i 0.646190 0.209960i
\(965\) 11.1364 34.2744i 0.358495 1.10333i
\(966\) 2.01918 + 5.32990i 0.0649660 + 0.171487i
\(967\) 6.11095i 0.196515i −0.995161 0.0982575i \(-0.968673\pi\)
0.995161 0.0982575i \(-0.0313269\pi\)
\(968\) −9.56500 + 5.43238i −0.307431 + 0.174603i
\(969\) 9.91225 15.1179i 0.318427 0.485658i
\(970\) 17.3070 23.8210i 0.555694 0.764848i
\(971\) −0.953745 0.309890i −0.0306071 0.00994486i 0.293673 0.955906i \(-0.405122\pi\)
−0.324281 + 0.945961i \(0.605122\pi\)
\(972\) 8.20136 + 13.2566i 0.263059 + 0.425206i
\(973\) −13.0527 + 9.48331i −0.418449 + 0.304021i
\(974\) −19.5835 + 14.2283i −0.627496 + 0.455903i
\(975\) 30.8347 + 8.40726i 0.987501 + 0.269248i
\(976\) −14.6483 4.75953i −0.468882 0.152349i
\(977\) 22.0343 30.3277i 0.704941 0.970268i −0.294950 0.955513i \(-0.595303\pi\)
0.999891 0.0147556i \(-0.00469704\pi\)
\(978\) −8.58488 5.62877i −0.274514 0.179988i
\(979\) 10.6752 27.5182i 0.341182 0.879485i
\(980\) 3.34945i 0.106994i
\(981\) 0.927419 + 0.205648i 0.0296102 + 0.00656583i
\(982\) −2.61492 + 8.04788i −0.0834453 + 0.256818i
\(983\) 2.43633 0.791611i 0.0777068 0.0252485i −0.269906 0.962887i \(-0.586992\pi\)
0.347612 + 0.937638i \(0.386992\pi\)
\(984\) 14.6302 0.702409i 0.466395 0.0223920i
\(985\) −11.4721 15.7900i −0.365531 0.503110i
\(986\) 1.93399 + 5.95220i 0.0615907 + 0.189557i
\(987\) −5.73186 + 4.60009i −0.182447 + 0.146423i
\(988\) 12.7490 + 9.26270i 0.405600 + 0.294686i
\(989\) −22.8544 −0.726727
\(990\) 27.7245 + 18.4938i 0.881141 + 0.587771i
\(991\) 4.09723 0.130153 0.0650765 0.997880i \(-0.479271\pi\)
0.0650765 + 0.997880i \(0.479271\pi\)
\(992\) 5.28711 + 3.84131i 0.167866 + 0.121962i
\(993\) 28.3252 22.7323i 0.898872 0.721388i
\(994\) −2.82837 8.70482i −0.0897103 0.276100i
\(995\) −41.5376 57.1716i −1.31683 1.81246i
\(996\) −1.08151 + 0.0519240i −0.0342688 + 0.00164527i
\(997\) 19.7978 6.43271i 0.627004 0.203726i 0.0217563 0.999763i \(-0.493074\pi\)
0.605247 + 0.796037i \(0.293074\pi\)
\(998\) 1.67031 5.14067i 0.0528726 0.162725i
\(999\) 3.01762 2.93924i 0.0954734 0.0929934i
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 462.2.w.b.29.3 yes 48
3.2 odd 2 462.2.w.a.29.8 48
11.8 odd 10 462.2.w.a.239.8 yes 48
33.8 even 10 inner 462.2.w.b.239.3 yes 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
462.2.w.a.29.8 48 3.2 odd 2
462.2.w.a.239.8 yes 48 11.8 odd 10
462.2.w.b.29.3 yes 48 1.1 even 1 trivial
462.2.w.b.239.3 yes 48 33.8 even 10 inner