Properties

Label 150.2.l.a.137.2
Level $150$
Weight $2$
Character 150.137
Analytic conductor $1.198$
Analytic rank $0$
Dimension $80$
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] = [150,2,Mod(17,150)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(150, base_ring=CyclotomicField(20))
 
chi = DirichletCharacter(H, H._module([10, 13]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("150.17");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 150.l (of order \(20\), degree \(8\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.19775603032\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(10\) over \(\Q(\zeta_{20})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label 137.2
Character \(\chi\) \(=\) 150.137
Dual form 150.2.l.a.23.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.987688 + 0.156434i) q^{2} +(-1.36724 + 1.06332i) q^{3} +(0.951057 - 0.309017i) q^{4} +(-1.48885 - 1.66833i) q^{5} +(1.18407 - 1.26411i) q^{6} +(-1.08662 - 1.08662i) q^{7} +(-0.891007 + 0.453990i) q^{8} +(0.738706 - 2.90763i) q^{9} +O(q^{10})\) \(q+(-0.987688 + 0.156434i) q^{2} +(-1.36724 + 1.06332i) q^{3} +(0.951057 - 0.309017i) q^{4} +(-1.48885 - 1.66833i) q^{5} +(1.18407 - 1.26411i) q^{6} +(-1.08662 - 1.08662i) q^{7} +(-0.891007 + 0.453990i) q^{8} +(0.738706 - 2.90763i) q^{9} +(1.73150 + 1.41488i) q^{10} +(1.61222 - 2.21903i) q^{11} +(-0.971742 + 1.43378i) q^{12} +(0.355240 - 2.24289i) q^{13} +(1.24323 + 0.903260i) q^{14} +(3.80959 + 0.697893i) q^{15} +(0.809017 - 0.587785i) q^{16} +(-2.77486 - 5.44598i) q^{17} +(-0.274758 + 2.98739i) q^{18} +(-4.05302 - 1.31690i) q^{19} +(-1.93152 - 1.12660i) q^{20} +(2.64110 + 0.330251i) q^{21} +(-1.24524 + 2.44391i) q^{22} +(0.805034 + 5.08279i) q^{23} +(0.735486 - 1.56814i) q^{24} +(-0.566658 + 4.96779i) q^{25} +2.27085i q^{26} +(2.08175 + 4.76092i) q^{27} +(-1.36922 - 0.697655i) q^{28} +(-2.37081 - 7.29662i) q^{29} +(-3.87186 - 0.0933498i) q^{30} +(-1.85692 + 5.71500i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(0.155241 + 4.74825i) q^{33} +(3.59264 + 4.94484i) q^{34} +(-0.195030 + 3.43066i) q^{35} +(-0.195956 - 2.99359i) q^{36} +(-3.29028 - 0.521129i) q^{37} +(4.20913 + 0.666660i) q^{38} +(1.89921 + 3.44431i) q^{39} +(2.08398 + 0.810571i) q^{40} +(5.36418 + 7.38316i) q^{41} +(-2.66025 + 0.0869750i) q^{42} +(6.65663 - 6.65663i) q^{43} +(0.847593 - 2.60862i) q^{44} +(-5.95071 + 3.09662i) q^{45} +(-1.59025 - 4.89427i) q^{46} +(-2.15191 - 1.09645i) q^{47} +(-0.481119 + 1.66389i) q^{48} -4.63850i q^{49} +(-0.217452 - 4.99527i) q^{50} +(9.58472 + 4.49541i) q^{51} +(-0.355240 - 2.24289i) q^{52} +(-0.199432 + 0.391408i) q^{53} +(-2.80089 - 4.37664i) q^{54} +(-6.10242 + 0.614083i) q^{55} +(1.46150 + 0.474872i) q^{56} +(6.94175 - 2.50912i) q^{57} +(3.48307 + 6.83591i) q^{58} +(-5.86967 + 4.26457i) q^{59} +(3.83879 - 0.513492i) q^{60} +(-8.14808 - 5.91993i) q^{61} +(0.940031 - 5.93512i) q^{62} +(-3.96219 + 2.35680i) q^{63} +(0.587785 - 0.809017i) q^{64} +(-4.27079 + 2.74667i) q^{65} +(-0.896119 - 4.66550i) q^{66} +(5.28646 - 2.69358i) q^{67} +(-4.32195 - 4.32195i) q^{68} +(-6.50530 - 6.09340i) q^{69} +(-0.344046 - 3.41894i) q^{70} +(5.89152 - 1.91427i) q^{71} +(0.661845 + 2.92608i) q^{72} +(10.2696 - 1.62655i) q^{73} +3.33129 q^{74} +(-4.50758 - 7.39471i) q^{75} -4.26159 q^{76} +(-4.16312 + 0.659373i) q^{77} +(-2.41464 - 3.10481i) q^{78} +(6.06800 - 1.97161i) q^{79} +(-2.18512 - 0.474585i) q^{80} +(-7.90863 - 4.29577i) q^{81} +(-6.45312 - 6.45312i) q^{82} +(6.92579 - 3.52887i) q^{83} +(2.61389 - 0.502059i) q^{84} +(-4.95434 + 12.7376i) q^{85} +(-5.53335 + 7.61600i) q^{86} +(11.0001 + 7.45532i) q^{87} +(-0.429079 + 2.70910i) q^{88} +(8.12567 + 5.90364i) q^{89} +(5.39303 - 3.98939i) q^{90} +(-2.82319 + 2.05117i) q^{91} +(2.33630 + 4.58525i) q^{92} +(-3.53801 - 9.78829i) q^{93} +(2.29694 + 0.746320i) q^{94} +(3.83730 + 8.72245i) q^{95} +(0.214907 - 1.71867i) q^{96} +(5.51066 - 10.8153i) q^{97} +(0.725621 + 4.58139i) q^{98} +(-5.26115 - 6.32694i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q + 4 q^{3} + 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 80 q + 4 q^{3} + 4 q^{7} - 4 q^{10} - 4 q^{12} - 8 q^{15} + 20 q^{16} - 8 q^{18} - 40 q^{19} - 36 q^{22} - 104 q^{25} + 4 q^{27} - 16 q^{28} + 12 q^{30} + 4 q^{33} - 40 q^{34} - 24 q^{37} - 40 q^{39} - 8 q^{40} - 4 q^{42} - 24 q^{43} - 72 q^{45} - 4 q^{48} - 12 q^{55} - 64 q^{57} + 20 q^{58} + 24 q^{60} + 64 q^{63} + 96 q^{67} + 140 q^{69} + 76 q^{70} + 8 q^{72} + 100 q^{73} + 132 q^{75} + 100 q^{78} + 80 q^{79} - 40 q^{81} + 96 q^{82} + 60 q^{84} + 32 q^{85} + 80 q^{87} + 4 q^{88} + 52 q^{90} + 12 q^{93} - 32 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/150\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(-1\) \(e\left(\frac{9}{20}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.987688 + 0.156434i −0.698401 + 0.110616i
\(3\) −1.36724 + 1.06332i −0.789378 + 0.613907i
\(4\) 0.951057 0.309017i 0.475528 0.154508i
\(5\) −1.48885 1.66833i −0.665833 0.746100i
\(6\) 1.18407 1.26411i 0.483395 0.516071i
\(7\) −1.08662 1.08662i −0.410705 0.410705i 0.471279 0.881984i \(-0.343792\pi\)
−0.881984 + 0.471279i \(0.843792\pi\)
\(8\) −0.891007 + 0.453990i −0.315018 + 0.160510i
\(9\) 0.738706 2.90763i 0.246235 0.969210i
\(10\) 1.73150 + 1.41488i 0.547549 + 0.447426i
\(11\) 1.61222 2.21903i 0.486102 0.669062i −0.493561 0.869711i \(-0.664305\pi\)
0.979663 + 0.200649i \(0.0643052\pi\)
\(12\) −0.971742 + 1.43378i −0.280518 + 0.413896i
\(13\) 0.355240 2.24289i 0.0985257 0.622067i −0.888173 0.459509i \(-0.848025\pi\)
0.986699 0.162558i \(-0.0519745\pi\)
\(14\) 1.24323 + 0.903260i 0.332267 + 0.241406i
\(15\) 3.80959 + 0.697893i 0.983631 + 0.180195i
\(16\) 0.809017 0.587785i 0.202254 0.146946i
\(17\) −2.77486 5.44598i −0.673003 1.32084i −0.934612 0.355669i \(-0.884253\pi\)
0.261608 0.965174i \(-0.415747\pi\)
\(18\) −0.274758 + 2.98739i −0.0647610 + 0.704135i
\(19\) −4.05302 1.31690i −0.929826 0.302119i −0.195334 0.980737i \(-0.562579\pi\)
−0.734491 + 0.678618i \(0.762579\pi\)
\(20\) −1.93152 1.12660i −0.431901 0.251915i
\(21\) 2.64110 + 0.330251i 0.576336 + 0.0720666i
\(22\) −1.24524 + 2.44391i −0.265485 + 0.521044i
\(23\) 0.805034 + 5.08279i 0.167861 + 1.05983i 0.917427 + 0.397904i \(0.130262\pi\)
−0.749566 + 0.661930i \(0.769738\pi\)
\(24\) 0.735486 1.56814i 0.150130 0.320095i
\(25\) −0.566658 + 4.96779i −0.113332 + 0.993557i
\(26\) 2.27085i 0.445351i
\(27\) 2.08175 + 4.76092i 0.400633 + 0.916239i
\(28\) −1.36922 0.697655i −0.258759 0.131844i
\(29\) −2.37081 7.29662i −0.440249 1.35495i −0.887611 0.460595i \(-0.847636\pi\)
0.447361 0.894353i \(-0.352364\pi\)
\(30\) −3.87186 0.0933498i −0.706901 0.0170433i
\(31\) −1.85692 + 5.71500i −0.333512 + 1.02644i 0.633938 + 0.773383i \(0.281437\pi\)
−0.967450 + 0.253061i \(0.918563\pi\)
\(32\) −0.707107 + 0.707107i −0.125000 + 0.125000i
\(33\) 0.155241 + 4.74825i 0.0270239 + 0.826564i
\(34\) 3.59264 + 4.94484i 0.616133 + 0.848034i
\(35\) −0.195030 + 3.43066i −0.0329660 + 0.579888i
\(36\) −0.195956 2.99359i −0.0326594 0.498932i
\(37\) −3.29028 0.521129i −0.540919 0.0856731i −0.120004 0.992773i \(-0.538291\pi\)
−0.420915 + 0.907100i \(0.638291\pi\)
\(38\) 4.20913 + 0.666660i 0.682810 + 0.108147i
\(39\) 1.89921 + 3.44431i 0.304118 + 0.551532i
\(40\) 2.08398 + 0.810571i 0.329506 + 0.128162i
\(41\) 5.36418 + 7.38316i 0.837744 + 1.15306i 0.986432 + 0.164172i \(0.0524952\pi\)
−0.148687 + 0.988884i \(0.547505\pi\)
\(42\) −2.66025 + 0.0869750i −0.410486 + 0.0134205i
\(43\) 6.65663 6.65663i 1.01513 1.01513i 0.0152431 0.999884i \(-0.495148\pi\)
0.999884 0.0152431i \(-0.00485222\pi\)
\(44\) 0.847593 2.60862i 0.127779 0.393265i
\(45\) −5.95071 + 3.09662i −0.887080 + 0.461616i
\(46\) −1.59025 4.89427i −0.234469 0.721621i
\(47\) −2.15191 1.09645i −0.313888 0.159934i 0.289948 0.957042i \(-0.406362\pi\)
−0.603836 + 0.797108i \(0.706362\pi\)
\(48\) −0.481119 + 1.66389i −0.0694436 + 0.240162i
\(49\) 4.63850i 0.662643i
\(50\) −0.217452 4.99527i −0.0307523 0.706438i
\(51\) 9.58472 + 4.49541i 1.34213 + 0.629483i
\(52\) −0.355240 2.24289i −0.0492629 0.311033i
\(53\) −0.199432 + 0.391408i −0.0273941 + 0.0537640i −0.904298 0.426902i \(-0.859605\pi\)
0.876904 + 0.480666i \(0.159605\pi\)
\(54\) −2.80089 4.37664i −0.381153 0.595586i
\(55\) −6.10242 + 0.614083i −0.822850 + 0.0828029i
\(56\) 1.46150 + 0.474872i 0.195302 + 0.0634574i
\(57\) 6.94175 2.50912i 0.919457 0.332341i
\(58\) 3.48307 + 6.83591i 0.457349 + 0.897599i
\(59\) −5.86967 + 4.26457i −0.764166 + 0.555199i −0.900185 0.435507i \(-0.856569\pi\)
0.136019 + 0.990706i \(0.456569\pi\)
\(60\) 3.83879 0.513492i 0.495586 0.0662915i
\(61\) −8.14808 5.91993i −1.04326 0.757969i −0.0723370 0.997380i \(-0.523046\pi\)
−0.970918 + 0.239411i \(0.923046\pi\)
\(62\) 0.940031 5.93512i 0.119384 0.753761i
\(63\) −3.96219 + 2.35680i −0.499189 + 0.296929i
\(64\) 0.587785 0.809017i 0.0734732 0.101127i
\(65\) −4.27079 + 2.74667i −0.529726 + 0.340683i
\(66\) −0.896119 4.66550i −0.110305 0.574284i
\(67\) 5.28646 2.69358i 0.645843 0.329074i −0.100204 0.994967i \(-0.531949\pi\)
0.746047 + 0.665893i \(0.231949\pi\)
\(68\) −4.32195 4.32195i −0.524114 0.524114i
\(69\) −6.50530 6.09340i −0.783146 0.733559i
\(70\) −0.344046 3.41894i −0.0411213 0.408641i
\(71\) 5.89152 1.91427i 0.699195 0.227182i 0.0622154 0.998063i \(-0.480183\pi\)
0.636980 + 0.770880i \(0.280183\pi\)
\(72\) 0.661845 + 2.92608i 0.0779992 + 0.344842i
\(73\) 10.2696 1.62655i 1.20197 0.190373i 0.476841 0.878989i \(-0.341782\pi\)
0.725126 + 0.688616i \(0.241782\pi\)
\(74\) 3.33129 0.387255
\(75\) −4.50758 7.39471i −0.520491 0.853867i
\(76\) −4.26159 −0.488838
\(77\) −4.16312 + 0.659373i −0.474431 + 0.0751425i
\(78\) −2.41464 3.10481i −0.273404 0.351550i
\(79\) 6.06800 1.97161i 0.682703 0.221824i 0.0529246 0.998599i \(-0.483146\pi\)
0.629778 + 0.776775i \(0.283146\pi\)
\(80\) −2.18512 0.474585i −0.244304 0.0530602i
\(81\) −7.90863 4.29577i −0.878736 0.477307i
\(82\) −6.45312 6.45312i −0.712628 0.712628i
\(83\) 6.92579 3.52887i 0.760204 0.387343i −0.0305056 0.999535i \(-0.509712\pi\)
0.790710 + 0.612191i \(0.209712\pi\)
\(84\) 2.61389 0.502059i 0.285199 0.0547791i
\(85\) −4.95434 + 12.7376i −0.537374 + 1.38159i
\(86\) −5.53335 + 7.61600i −0.596677 + 0.821255i
\(87\) 11.0001 + 7.45532i 1.17934 + 0.799294i
\(88\) −0.429079 + 2.70910i −0.0457400 + 0.288791i
\(89\) 8.12567 + 5.90364i 0.861319 + 0.625785i 0.928243 0.371973i \(-0.121319\pi\)
−0.0669245 + 0.997758i \(0.521319\pi\)
\(90\) 5.39303 3.98939i 0.568475 0.420518i
\(91\) −2.82319 + 2.05117i −0.295951 + 0.215021i
\(92\) 2.33630 + 4.58525i 0.243576 + 0.478045i
\(93\) −3.53801 9.78829i −0.366875 1.01500i
\(94\) 2.29694 + 0.746320i 0.236911 + 0.0769770i
\(95\) 3.83730 + 8.72245i 0.393698 + 0.894904i
\(96\) 0.214907 1.71867i 0.0219338 0.175411i
\(97\) 5.51066 10.8153i 0.559523 1.09813i −0.421967 0.906611i \(-0.638660\pi\)
0.981490 0.191514i \(-0.0613398\pi\)
\(98\) 0.725621 + 4.58139i 0.0732988 + 0.462791i
\(99\) −5.26115 6.32694i −0.528766 0.635881i
\(100\) 0.996207 + 4.89975i 0.0996207 + 0.489975i
\(101\) 3.53757i 0.352002i −0.984390 0.176001i \(-0.943684\pi\)
0.984390 0.176001i \(-0.0563161\pi\)
\(102\) −10.1700 2.94068i −1.00698 0.291171i
\(103\) −14.6853 7.48254i −1.44699 0.737277i −0.458516 0.888686i \(-0.651619\pi\)
−0.988471 + 0.151409i \(0.951619\pi\)
\(104\) 0.701732 + 2.15971i 0.0688105 + 0.211777i
\(105\) −3.38124 4.89793i −0.329975 0.477989i
\(106\) 0.135747 0.417787i 0.0131849 0.0405791i
\(107\) −1.32720 + 1.32720i −0.128305 + 0.128305i −0.768343 0.640038i \(-0.778919\pi\)
0.640038 + 0.768343i \(0.278919\pi\)
\(108\) 3.45106 + 3.88461i 0.332079 + 0.373796i
\(109\) 10.6696 + 14.6855i 1.02196 + 1.40661i 0.910818 + 0.412809i \(0.135452\pi\)
0.111147 + 0.993804i \(0.464548\pi\)
\(110\) 5.93122 1.56115i 0.565520 0.148850i
\(111\) 5.05274 2.78611i 0.479585 0.264446i
\(112\) −1.51780 0.240395i −0.143418 0.0227152i
\(113\) 6.54968 + 1.03737i 0.616142 + 0.0975873i 0.456701 0.889620i \(-0.349031\pi\)
0.159441 + 0.987207i \(0.449031\pi\)
\(114\) −6.46377 + 3.56416i −0.605388 + 0.333814i
\(115\) 7.28120 8.91056i 0.678975 0.830914i
\(116\) −4.50956 6.20687i −0.418702 0.576294i
\(117\) −6.25909 2.68974i −0.578653 0.248667i
\(118\) 5.13028 5.13028i 0.472281 0.472281i
\(119\) −2.90249 + 8.93296i −0.266071 + 0.818883i
\(120\) −3.71120 + 1.10769i −0.338785 + 0.101118i
\(121\) 1.07435 + 3.30652i 0.0976685 + 0.300593i
\(122\) 8.97385 + 4.57240i 0.812454 + 0.413966i
\(123\) −15.1848 4.39074i −1.36917 0.395900i
\(124\) 6.00911i 0.539634i
\(125\) 9.13158 6.45091i 0.816753 0.576987i
\(126\) 3.54473 2.94761i 0.315789 0.262594i
\(127\) 1.37095 + 8.65582i 0.121652 + 0.768080i 0.970794 + 0.239915i \(0.0771197\pi\)
−0.849142 + 0.528165i \(0.822880\pi\)
\(128\) −0.453990 + 0.891007i −0.0401275 + 0.0787546i
\(129\) −2.02311 + 16.1794i −0.178125 + 1.42451i
\(130\) 3.78853 3.38096i 0.332276 0.296529i
\(131\) −11.0161 3.57935i −0.962481 0.312729i −0.214704 0.976679i \(-0.568879\pi\)
−0.747777 + 0.663950i \(0.768879\pi\)
\(132\) 1.61493 + 4.46788i 0.140562 + 0.388879i
\(133\) 2.97312 + 5.83508i 0.257802 + 0.505966i
\(134\) −4.80000 + 3.48741i −0.414657 + 0.301266i
\(135\) 4.84338 10.5613i 0.416852 0.908975i
\(136\) 4.94484 + 3.59264i 0.424017 + 0.308066i
\(137\) −1.14803 + 7.24839i −0.0980830 + 0.619272i 0.888857 + 0.458184i \(0.151500\pi\)
−0.986940 + 0.161087i \(0.948500\pi\)
\(138\) 7.37843 + 5.00072i 0.628093 + 0.425690i
\(139\) −5.12432 + 7.05302i −0.434639 + 0.598230i −0.969010 0.247020i \(-0.920549\pi\)
0.534371 + 0.845250i \(0.320549\pi\)
\(140\) 0.874649 + 3.32302i 0.0739214 + 0.280847i
\(141\) 4.10806 0.789048i 0.345961 0.0664499i
\(142\) −5.51953 + 2.81234i −0.463189 + 0.236007i
\(143\) −4.40432 4.40432i −0.368308 0.368308i
\(144\) −1.11144 2.78652i −0.0926197 0.232210i
\(145\) −8.64339 + 14.8189i −0.717794 + 1.23064i
\(146\) −9.88873 + 3.21304i −0.818397 + 0.265913i
\(147\) 4.93221 + 6.34196i 0.406801 + 0.523076i
\(148\) −3.29028 + 0.521129i −0.270459 + 0.0428366i
\(149\) −0.907025 −0.0743064 −0.0371532 0.999310i \(-0.511829\pi\)
−0.0371532 + 0.999310i \(0.511829\pi\)
\(150\) 5.60887 + 6.59853i 0.457963 + 0.538767i
\(151\) −7.07775 −0.575979 −0.287989 0.957634i \(-0.592987\pi\)
−0.287989 + 0.957634i \(0.592987\pi\)
\(152\) 4.20913 0.666660i 0.341405 0.0540733i
\(153\) −17.8847 + 4.04530i −1.44589 + 0.327043i
\(154\) 4.00871 1.30251i 0.323031 0.104959i
\(155\) 12.2992 5.41082i 0.987894 0.434608i
\(156\) 2.87061 + 2.68885i 0.229833 + 0.215280i
\(157\) −3.09020 3.09020i −0.246625 0.246625i 0.572959 0.819584i \(-0.305795\pi\)
−0.819584 + 0.572959i \(0.805795\pi\)
\(158\) −5.68486 + 2.89658i −0.452263 + 0.230440i
\(159\) −0.143519 0.747210i −0.0113818 0.0592576i
\(160\) 2.23246 + 0.126913i 0.176492 + 0.0100334i
\(161\) 4.64830 6.39784i 0.366338 0.504221i
\(162\) 8.48327 + 3.00570i 0.666508 + 0.236150i
\(163\) −1.19195 + 7.52570i −0.0933610 + 0.589458i 0.896009 + 0.444036i \(0.146454\pi\)
−0.989370 + 0.145422i \(0.953546\pi\)
\(164\) 7.38316 + 5.36418i 0.576528 + 0.418872i
\(165\) 7.69052 7.32842i 0.598706 0.570516i
\(166\) −6.28849 + 4.56885i −0.488081 + 0.354612i
\(167\) 7.13033 + 13.9941i 0.551761 + 1.08289i 0.983502 + 0.180895i \(0.0578995\pi\)
−0.431741 + 0.901998i \(0.642101\pi\)
\(168\) −2.50317 + 0.904781i −0.193124 + 0.0698053i
\(169\) 7.45935 + 2.42369i 0.573797 + 0.186438i
\(170\) 2.90074 13.3558i 0.222477 1.02435i
\(171\) −6.82306 + 10.8119i −0.521772 + 0.826804i
\(172\) 4.27382 8.38785i 0.325876 0.639567i
\(173\) −2.95227 18.6399i −0.224457 1.41717i −0.800297 0.599603i \(-0.795325\pi\)
0.575840 0.817562i \(-0.304675\pi\)
\(174\) −12.0309 5.64273i −0.912064 0.427774i
\(175\) 6.01385 4.78237i 0.454605 0.361513i
\(176\) 2.74287i 0.206751i
\(177\) 3.49067 12.0720i 0.262375 0.907389i
\(178\) −8.94916 4.55982i −0.670768 0.341773i
\(179\) −8.00048 24.6229i −0.597984 1.84040i −0.539275 0.842130i \(-0.681302\pi\)
−0.0587089 0.998275i \(-0.518698\pi\)
\(180\) −4.70256 + 4.78393i −0.350508 + 0.356573i
\(181\) −2.63278 + 8.10287i −0.195693 + 0.602282i 0.804275 + 0.594258i \(0.202554\pi\)
−0.999968 + 0.00802385i \(0.997446\pi\)
\(182\) 2.46756 2.46756i 0.182908 0.182908i
\(183\) 17.4352 0.570031i 1.28885 0.0421379i
\(184\) −3.02483 4.16332i −0.222993 0.306924i
\(185\) 4.02931 + 6.26516i 0.296241 + 0.460624i
\(186\) 5.02568 + 9.11431i 0.368501 + 0.668293i
\(187\) −16.5585 2.62260i −1.21087 0.191784i
\(188\) −2.38541 0.377811i −0.173974 0.0275547i
\(189\) 2.91125 7.43540i 0.211762 0.540845i
\(190\) −5.15454 8.01477i −0.373950 0.581453i
\(191\) −5.15251 7.09182i −0.372822 0.513146i 0.580843 0.814016i \(-0.302723\pi\)
−0.953665 + 0.300870i \(0.902723\pi\)
\(192\) 0.0565979 + 1.73113i 0.00408460 + 0.124933i
\(193\) 16.8199 16.8199i 1.21072 1.21072i 0.239930 0.970790i \(-0.422875\pi\)
0.970790 0.239930i \(-0.0771245\pi\)
\(194\) −3.75093 + 11.5442i −0.269301 + 0.828824i
\(195\) 2.91862 8.29658i 0.209006 0.594130i
\(196\) −1.43338 4.41148i −0.102384 0.315105i
\(197\) −6.24937 3.18421i −0.445249 0.226866i 0.216966 0.976179i \(-0.430384\pi\)
−0.662216 + 0.749313i \(0.730384\pi\)
\(198\) 6.18613 + 5.42602i 0.439629 + 0.385610i
\(199\) 18.4867i 1.31048i −0.755419 0.655242i \(-0.772567\pi\)
0.755419 0.655242i \(-0.227433\pi\)
\(200\) −1.75043 4.68359i −0.123774 0.331180i
\(201\) −4.36373 + 9.30397i −0.307794 + 0.656252i
\(202\) 0.553398 + 3.49402i 0.0389370 + 0.245838i
\(203\) −5.35249 + 10.5049i −0.375671 + 0.737296i
\(204\) 10.5048 + 1.31354i 0.735481 + 0.0919665i
\(205\) 4.33110 19.9416i 0.302497 1.39278i
\(206\) 15.6750 + 5.09313i 1.09213 + 0.354855i
\(207\) 15.3735 + 1.41394i 1.06854 + 0.0982757i
\(208\) −1.03095 2.02334i −0.0714832 0.140294i
\(209\) −9.45659 + 6.87061i −0.654126 + 0.475250i
\(210\) 4.10581 + 4.30869i 0.283328 + 0.297328i
\(211\) 12.6782 + 9.21124i 0.872802 + 0.634128i 0.931337 0.364158i \(-0.118643\pi\)
−0.0585355 + 0.998285i \(0.518643\pi\)
\(212\) −0.0687197 + 0.433879i −0.00471969 + 0.0297989i
\(213\) −6.01966 + 8.88184i −0.412460 + 0.608574i
\(214\) 1.10324 1.51848i 0.0754158 0.103801i
\(215\) −21.0162 1.19475i −1.43329 0.0814811i
\(216\) −4.01626 3.29691i −0.273272 0.224327i
\(217\) 8.22782 4.19228i 0.558541 0.284591i
\(218\) −12.8356 12.8356i −0.869335 0.869335i
\(219\) −12.3115 + 13.1438i −0.831935 + 0.888173i
\(220\) −5.61398 + 2.46978i −0.378495 + 0.166512i
\(221\) −13.2005 + 4.28910i −0.887961 + 0.288516i
\(222\) −4.55469 + 3.54223i −0.305691 + 0.237739i
\(223\) −24.2212 + 3.83626i −1.62197 + 0.256895i −0.900278 0.435316i \(-0.856637\pi\)
−0.721695 + 0.692211i \(0.756637\pi\)
\(224\) 1.53672 0.102676
\(225\) 14.0259 + 5.31736i 0.935059 + 0.354491i
\(226\) −6.63132 −0.441109
\(227\) 21.5518 3.41347i 1.43044 0.226560i 0.607335 0.794446i \(-0.292239\pi\)
0.823107 + 0.567886i \(0.192239\pi\)
\(228\) 5.82663 4.53143i 0.385878 0.300102i
\(229\) 14.1502 4.59767i 0.935070 0.303823i 0.198436 0.980114i \(-0.436414\pi\)
0.736634 + 0.676291i \(0.236414\pi\)
\(230\) −5.79763 + 9.93989i −0.382285 + 0.655417i
\(231\) 4.99087 5.32824i 0.328375 0.350573i
\(232\) 5.42501 + 5.42501i 0.356169 + 0.356169i
\(233\) 8.91074 4.54025i 0.583762 0.297442i −0.137059 0.990563i \(-0.543765\pi\)
0.720821 + 0.693121i \(0.243765\pi\)
\(234\) 6.60280 + 1.67749i 0.431638 + 0.109661i
\(235\) 1.37462 + 5.22255i 0.0896704 + 0.340681i
\(236\) −4.26457 + 5.86967i −0.277600 + 0.382083i
\(237\) −6.19997 + 9.14789i −0.402731 + 0.594219i
\(238\) 1.46934 9.27703i 0.0952429 0.601340i
\(239\) −5.42628 3.94243i −0.350997 0.255014i 0.398290 0.917260i \(-0.369604\pi\)
−0.749287 + 0.662245i \(0.769604\pi\)
\(240\) 3.49223 1.67461i 0.225423 0.108096i
\(241\) 7.73169 5.61740i 0.498042 0.361849i −0.310227 0.950663i \(-0.600405\pi\)
0.808269 + 0.588814i \(0.200405\pi\)
\(242\) −1.57838 3.09774i −0.101462 0.199131i
\(243\) 15.3808 2.53604i 0.986678 0.162687i
\(244\) −9.57865 3.11229i −0.613210 0.199244i
\(245\) −7.73856 + 6.90603i −0.494398 + 0.441210i
\(246\) 15.6847 + 1.96126i 1.00002 + 0.125045i
\(247\) −4.39347 + 8.62267i −0.279550 + 0.548647i
\(248\) −0.940031 5.93512i −0.0596920 0.376881i
\(249\) −5.71693 + 12.1891i −0.362295 + 0.772455i
\(250\) −8.01001 + 7.79998i −0.506598 + 0.493314i
\(251\) 14.1774i 0.894872i −0.894316 0.447436i \(-0.852337\pi\)
0.894316 0.447436i \(-0.147663\pi\)
\(252\) −3.03998 + 3.46584i −0.191501 + 0.218327i
\(253\) 12.5767 + 6.40816i 0.790692 + 0.402878i
\(254\) −2.70814 8.33479i −0.169924 0.522971i
\(255\) −6.77038 22.6835i −0.423977 1.42049i
\(256\) 0.309017 0.951057i 0.0193136 0.0594410i
\(257\) −13.7580 + 13.7580i −0.858198 + 0.858198i −0.991126 0.132928i \(-0.957562\pi\)
0.132928 + 0.991126i \(0.457562\pi\)
\(258\) −0.532807 16.2966i −0.0331711 1.01458i
\(259\) 3.00902 + 4.14157i 0.186972 + 0.257344i
\(260\) −3.21299 + 3.93199i −0.199261 + 0.243852i
\(261\) −22.9672 + 1.50340i −1.42163 + 0.0930581i
\(262\) 11.4404 + 1.81198i 0.706791 + 0.111945i
\(263\) −11.7698 1.86416i −0.725759 0.114949i −0.217386 0.976086i \(-0.569753\pi\)
−0.508373 + 0.861137i \(0.669753\pi\)
\(264\) −2.29398 4.16024i −0.141185 0.256045i
\(265\) 0.949923 0.250028i 0.0583533 0.0153591i
\(266\) −3.84933 5.29814i −0.236017 0.324850i
\(267\) −17.3872 + 0.568462i −1.06408 + 0.0347893i
\(268\) 4.19536 4.19536i 0.256272 0.256272i
\(269\) 4.78303 14.7206i 0.291626 0.897534i −0.692707 0.721219i \(-0.743582\pi\)
0.984334 0.176315i \(-0.0564178\pi\)
\(270\) −3.13159 + 11.1890i −0.190583 + 0.680939i
\(271\) −1.58590 4.88090i −0.0963366 0.296494i 0.891263 0.453487i \(-0.149820\pi\)
−0.987600 + 0.156993i \(0.949820\pi\)
\(272\) −5.44598 2.77486i −0.330211 0.168251i
\(273\) 1.67894 5.80640i 0.101614 0.351419i
\(274\) 7.33874i 0.443350i
\(275\) 10.1101 + 9.26658i 0.609660 + 0.558796i
\(276\) −8.06987 3.78491i −0.485749 0.227825i
\(277\) −0.610374 3.85375i −0.0366738 0.231549i 0.962543 0.271131i \(-0.0873976\pi\)
−0.999216 + 0.0395814i \(0.987398\pi\)
\(278\) 3.95790 7.76781i 0.237379 0.465882i
\(279\) 15.2454 + 9.62093i 0.912718 + 0.575990i
\(280\) −1.38372 3.14529i −0.0826929 0.187967i
\(281\) 2.23510 + 0.726229i 0.133335 + 0.0433232i 0.374924 0.927055i \(-0.377669\pi\)
−0.241589 + 0.970379i \(0.577669\pi\)
\(282\) −3.93405 + 1.42198i −0.234269 + 0.0846774i
\(283\) 1.55470 + 3.05128i 0.0924175 + 0.181380i 0.932588 0.360943i \(-0.117545\pi\)
−0.840170 + 0.542322i \(0.817545\pi\)
\(284\) 5.01163 3.64116i 0.297386 0.216063i
\(285\) −14.5213 7.84543i −0.860165 0.464723i
\(286\) 5.03908 + 3.66111i 0.297967 + 0.216486i
\(287\) 2.19387 13.8516i 0.129500 0.817631i
\(288\) 1.53366 + 2.57835i 0.0903719 + 0.151931i
\(289\) −11.9665 + 16.4704i −0.703909 + 0.968848i
\(290\) 6.21879 15.9885i 0.365180 0.938880i
\(291\) 3.96568 + 20.6467i 0.232472 + 1.21033i
\(292\) 9.26435 4.72042i 0.542155 0.276242i
\(293\) 13.9865 + 13.9865i 0.817101 + 0.817101i 0.985687 0.168586i \(-0.0539201\pi\)
−0.168586 + 0.985687i \(0.553920\pi\)
\(294\) −5.86358 5.49231i −0.341971 0.320318i
\(295\) 15.8538 + 3.44326i 0.923042 + 0.200474i
\(296\) 3.16825 1.02943i 0.184151 0.0598342i
\(297\) 13.9208 + 3.05618i 0.807768 + 0.177337i
\(298\) 0.895858 0.141890i 0.0518957 0.00821947i
\(299\) 11.6861 0.675827
\(300\) −6.57206 5.63987i −0.379438 0.325618i
\(301\) −14.4665 −0.833835
\(302\) 6.99061 1.10720i 0.402264 0.0637124i
\(303\) 3.76157 + 4.83672i 0.216096 + 0.277862i
\(304\) −4.05302 + 1.31690i −0.232456 + 0.0755297i
\(305\) 2.25486 + 22.4076i 0.129113 + 1.28305i
\(306\) 17.0317 6.79328i 0.973636 0.388346i
\(307\) −0.108217 0.108217i −0.00617628 0.00617628i 0.704012 0.710188i \(-0.251390\pi\)
−0.710188 + 0.704012i \(0.751390\pi\)
\(308\) −3.75560 + 1.91357i −0.213995 + 0.109036i
\(309\) 28.0347 5.38472i 1.59484 0.306326i
\(310\) −11.3013 + 7.26822i −0.641872 + 0.412807i
\(311\) 9.64088 13.2695i 0.546684 0.752446i −0.442874 0.896584i \(-0.646041\pi\)
0.989558 + 0.144138i \(0.0460410\pi\)
\(312\) −3.25590 2.20668i −0.184329 0.124929i
\(313\) −3.64820 + 23.0338i −0.206208 + 1.30195i 0.639702 + 0.768623i \(0.279058\pi\)
−0.845911 + 0.533325i \(0.820942\pi\)
\(314\) 3.53557 + 2.56874i 0.199523 + 0.144962i
\(315\) 9.83103 + 3.10133i 0.553916 + 0.174740i
\(316\) 5.16175 3.75023i 0.290371 0.210967i
\(317\) 3.25049 + 6.37945i 0.182566 + 0.358305i 0.964093 0.265566i \(-0.0855589\pi\)
−0.781527 + 0.623872i \(0.785559\pi\)
\(318\) 0.258641 + 0.715559i 0.0145039 + 0.0401266i
\(319\) −20.0137 6.50283i −1.12055 0.364089i
\(320\) −2.22483 + 0.223884i −0.124372 + 0.0125155i
\(321\) 0.403367 3.22583i 0.0225137 0.180049i
\(322\) −3.59023 + 7.04623i −0.200076 + 0.392671i
\(323\) 4.07474 + 25.7269i 0.226724 + 1.43148i
\(324\) −8.84902 1.64162i −0.491612 0.0912009i
\(325\) 10.9409 + 3.03571i 0.606893 + 0.168391i
\(326\) 7.61951i 0.422005i
\(327\) −30.2033 8.73340i −1.67025 0.482958i
\(328\) −8.13141 4.14316i −0.448982 0.228768i
\(329\) 1.14688 + 3.52974i 0.0632297 + 0.194601i
\(330\) −6.44942 + 8.44125i −0.355029 + 0.464676i
\(331\) 5.06152 15.5778i 0.278206 0.856231i −0.710147 0.704054i \(-0.751371\pi\)
0.988353 0.152177i \(-0.0486285\pi\)
\(332\) 5.49634 5.49634i 0.301651 0.301651i
\(333\) −3.94580 + 9.18196i −0.216229 + 0.503168i
\(334\) −9.23170 12.7063i −0.505136 0.695260i
\(335\) −12.3645 4.80922i −0.675546 0.262756i
\(336\) 2.33081 1.28522i 0.127156 0.0701147i
\(337\) 9.30661 + 1.47402i 0.506963 + 0.0802951i 0.404677 0.914460i \(-0.367384\pi\)
0.102287 + 0.994755i \(0.467384\pi\)
\(338\) −7.74667 1.22695i −0.421363 0.0667374i
\(339\) −10.0581 + 5.54606i −0.546278 + 0.301221i
\(340\) −0.775714 + 13.6452i −0.0420690 + 0.740014i
\(341\) 9.68798 + 13.3344i 0.524634 + 0.722096i
\(342\) 5.04771 11.7461i 0.272949 0.635157i
\(343\) −12.6467 + 12.6467i −0.682856 + 0.682856i
\(344\) −2.90906 + 8.95315i −0.156846 + 0.482722i
\(345\) −0.480392 + 19.9251i −0.0258634 + 1.07273i
\(346\) 5.83185 + 17.9486i 0.313522 + 0.964922i
\(347\) −21.2743 10.8398i −1.14207 0.581912i −0.222533 0.974925i \(-0.571433\pi\)
−0.919533 + 0.393013i \(0.871433\pi\)
\(348\) 12.7655 + 3.69121i 0.684305 + 0.197869i
\(349\) 21.3598i 1.14336i 0.820476 + 0.571681i \(0.193708\pi\)
−0.820476 + 0.571681i \(0.806292\pi\)
\(350\) −5.19169 + 5.66426i −0.277507 + 0.302768i
\(351\) 11.4178 2.97788i 0.609435 0.158947i
\(352\) 0.429079 + 2.70910i 0.0228700 + 0.144395i
\(353\) −5.39943 + 10.5970i −0.287383 + 0.564020i −0.988891 0.148641i \(-0.952510\pi\)
0.701509 + 0.712661i \(0.252510\pi\)
\(354\) −1.55921 + 12.4695i −0.0828713 + 0.662745i
\(355\) −11.9652 6.97895i −0.635048 0.370404i
\(356\) 9.55229 + 3.10373i 0.506271 + 0.164497i
\(357\) −5.53017 15.2998i −0.292687 0.809751i
\(358\) 11.7539 + 23.0682i 0.621211 + 1.21919i
\(359\) 25.6736 18.6530i 1.35500 0.984467i 0.356257 0.934388i \(-0.384053\pi\)
0.998745 0.0500792i \(-0.0159474\pi\)
\(360\) 3.89629 5.46067i 0.205352 0.287803i
\(361\) −0.678618 0.493045i −0.0357167 0.0259497i
\(362\) 1.33280 8.41497i 0.0700504 0.442281i
\(363\) −4.98479 3.37843i −0.261633 0.177322i
\(364\) −2.05117 + 2.82319i −0.107510 + 0.147975i
\(365\) −18.0035 14.7114i −0.942347 0.770032i
\(366\) −17.1314 + 3.29048i −0.895470 + 0.171996i
\(367\) −7.10027 + 3.61777i −0.370631 + 0.188846i −0.629378 0.777099i \(-0.716690\pi\)
0.258747 + 0.965945i \(0.416690\pi\)
\(368\) 3.63887 + 3.63887i 0.189689 + 0.189689i
\(369\) 25.4301 10.1431i 1.32384 0.528027i
\(370\) −4.95979 5.55770i −0.257847 0.288931i
\(371\) 0.642021 0.208605i 0.0333320 0.0108302i
\(372\) −6.38960 8.21591i −0.331285 0.425975i
\(373\) 6.60991 1.04691i 0.342248 0.0542068i 0.0170555 0.999855i \(-0.494571\pi\)
0.325193 + 0.945648i \(0.394571\pi\)
\(374\) 16.7649 0.866890
\(375\) −5.62571 + 18.5297i −0.290511 + 0.956872i
\(376\) 2.41514 0.124551
\(377\) −17.2077 + 2.72544i −0.886244 + 0.140367i
\(378\) −1.71225 + 7.79927i −0.0880687 + 0.401151i
\(379\) −2.68053 + 0.870958i −0.137690 + 0.0447381i −0.377051 0.926192i \(-0.623062\pi\)
0.239361 + 0.970931i \(0.423062\pi\)
\(380\) 6.34487 + 7.10975i 0.325485 + 0.364722i
\(381\) −11.0783 10.3769i −0.567560 0.531623i
\(382\) 6.19848 + 6.19848i 0.317142 + 0.317142i
\(383\) 4.98907 2.54206i 0.254930 0.129893i −0.321856 0.946789i \(-0.604307\pi\)
0.576786 + 0.816895i \(0.304307\pi\)
\(384\) −0.326709 1.70096i −0.0166723 0.0868017i
\(385\) 7.29830 + 5.96375i 0.371956 + 0.303941i
\(386\) −13.9816 + 19.2440i −0.711643 + 0.979493i
\(387\) −14.4377 24.2723i −0.733911 1.23383i
\(388\) 1.89884 11.9888i 0.0963992 0.608641i
\(389\) 4.72410 + 3.43226i 0.239521 + 0.174022i 0.701070 0.713092i \(-0.252706\pi\)
−0.461549 + 0.887115i \(0.652706\pi\)
\(390\) −1.58481 + 8.65101i −0.0802500 + 0.438061i
\(391\) 25.4469 18.4882i 1.28690 0.934991i
\(392\) 2.10584 + 4.13293i 0.106361 + 0.208745i
\(393\) 18.8677 6.81979i 0.951748 0.344013i
\(394\) 6.67055 + 2.16739i 0.336058 + 0.109192i
\(395\) −12.3236 7.18800i −0.620069 0.361667i
\(396\) −6.95879 4.39149i −0.349692 0.220681i
\(397\) −2.73792 + 5.37347i −0.137412 + 0.269687i −0.949450 0.313918i \(-0.898358\pi\)
0.812038 + 0.583605i \(0.198358\pi\)
\(398\) 2.89195 + 18.2591i 0.144960 + 0.915244i
\(399\) −10.2695 4.81659i −0.514120 0.241131i
\(400\) 2.46156 + 4.35210i 0.123078 + 0.217605i
\(401\) 21.8156i 1.08942i 0.838626 + 0.544708i \(0.183360\pi\)
−0.838626 + 0.544708i \(0.816640\pi\)
\(402\) 2.85454 9.87206i 0.142372 0.492374i
\(403\) 12.1585 + 6.19506i 0.605658 + 0.308598i
\(404\) −1.09317 3.36443i −0.0543872 0.167387i
\(405\) 4.60799 + 19.5900i 0.228973 + 0.973433i
\(406\) 3.64327 11.2128i 0.180812 0.556484i
\(407\) −6.46105 + 6.46105i −0.320262 + 0.320262i
\(408\) −10.5809 + 0.345936i −0.523834 + 0.0171264i
\(409\) −10.2656 14.1294i −0.507603 0.698656i 0.475910 0.879494i \(-0.342119\pi\)
−0.983513 + 0.180838i \(0.942119\pi\)
\(410\) −1.15822 + 20.3737i −0.0572004 + 1.00618i
\(411\) −6.13771 11.1310i −0.302751 0.549053i
\(412\) −16.2788 2.57831i −0.801999 0.127024i
\(413\) 11.0121 + 1.74414i 0.541870 + 0.0858237i
\(414\) −15.4055 + 1.00842i −0.757137 + 0.0495611i
\(415\) −16.1988 6.30056i −0.795166 0.309282i
\(416\) 1.33477 + 1.83716i 0.0654427 + 0.0900741i
\(417\) −0.493421 15.0920i −0.0241630 0.739058i
\(418\) 8.26536 8.26536i 0.404272 0.404272i
\(419\) −2.70937 + 8.33859i −0.132361 + 0.407367i −0.995170 0.0981637i \(-0.968703\pi\)
0.862809 + 0.505530i \(0.168703\pi\)
\(420\) −4.72929 3.61335i −0.230766 0.176313i
\(421\) −10.5794 32.5601i −0.515610 1.58688i −0.782170 0.623065i \(-0.785887\pi\)
0.266560 0.963818i \(-0.414113\pi\)
\(422\) −13.9630 7.11453i −0.679710 0.346330i
\(423\) −4.77770 + 5.44700i −0.232300 + 0.264842i
\(424\) 0.439287i 0.0213337i
\(425\) 28.6269 10.6989i 1.38861 0.518974i
\(426\) 4.55612 9.71418i 0.220745 0.470653i
\(427\) 2.42116 + 15.2866i 0.117168 + 0.739772i
\(428\) −0.852113 + 1.67237i −0.0411884 + 0.0808369i
\(429\) 10.7050 + 1.33858i 0.516841 + 0.0646271i
\(430\) 20.9443 2.10762i 1.01003 0.101638i
\(431\) 2.50367 + 0.813491i 0.120597 + 0.0391845i 0.368694 0.929551i \(-0.379805\pi\)
−0.248097 + 0.968735i \(0.579805\pi\)
\(432\) 4.48257 + 2.62804i 0.215668 + 0.126442i
\(433\) −17.1431 33.6451i −0.823843 1.61688i −0.786509 0.617579i \(-0.788114\pi\)
−0.0373338 0.999303i \(-0.511886\pi\)
\(434\) −7.47070 + 5.42778i −0.358605 + 0.260542i
\(435\) −3.93957 29.4517i −0.188888 1.41210i
\(436\) 14.6855 + 10.6696i 0.703307 + 0.510982i
\(437\) 3.43073 21.6608i 0.164114 1.03618i
\(438\) 10.1038 14.9079i 0.482778 0.712326i
\(439\) 1.73789 2.39200i 0.0829451 0.114164i −0.765528 0.643402i \(-0.777522\pi\)
0.848473 + 0.529238i \(0.177522\pi\)
\(440\) 5.15851 3.31759i 0.245922 0.158160i
\(441\) −13.4870 3.42649i −0.642240 0.163166i
\(442\) 12.3670 6.30131i 0.588239 0.299723i
\(443\) 8.33207 + 8.33207i 0.395869 + 0.395869i 0.876773 0.480904i \(-0.159692\pi\)
−0.480904 + 0.876773i \(0.659692\pi\)
\(444\) 3.94449 4.21113i 0.187197 0.199851i
\(445\) −2.24866 22.3459i −0.106597 1.05930i
\(446\) 23.3229 7.57807i 1.10437 0.358832i
\(447\) 1.24012 0.964457i 0.0586558 0.0456172i
\(448\) −1.51780 + 0.240395i −0.0717092 + 0.0113576i
\(449\) 11.1961 0.528377 0.264188 0.964471i \(-0.414896\pi\)
0.264188 + 0.964471i \(0.414896\pi\)
\(450\) −14.6850 3.05777i −0.692259 0.144144i
\(451\) 25.0317 1.17869
\(452\) 6.54968 1.03737i 0.308071 0.0487936i
\(453\) 9.67700 7.52590i 0.454665 0.353598i
\(454\) −20.7525 + 6.74288i −0.973961 + 0.316459i
\(455\) 7.62534 + 1.65614i 0.357481 + 0.0776410i
\(456\) −5.04603 + 5.38713i −0.236302 + 0.252275i
\(457\) −7.27927 7.27927i −0.340510 0.340510i 0.516049 0.856559i \(-0.327402\pi\)
−0.856559 + 0.516049i \(0.827402\pi\)
\(458\) −13.2567 + 6.75464i −0.619446 + 0.315624i
\(459\) 20.1513 24.5480i 0.940581 1.14580i
\(460\) 4.17131 10.7245i 0.194488 0.500031i
\(461\) 11.8441 16.3020i 0.551633 0.759258i −0.438600 0.898683i \(-0.644525\pi\)
0.990233 + 0.139425i \(0.0445253\pi\)
\(462\) −4.09590 + 6.04339i −0.190559 + 0.281164i
\(463\) −0.0186291 + 0.117620i −0.000865770 + 0.00546626i −0.988117 0.153701i \(-0.950881\pi\)
0.987252 + 0.159167i \(0.0508808\pi\)
\(464\) −6.20687 4.50956i −0.288147 0.209351i
\(465\) −11.0625 + 20.4759i −0.513013 + 0.949545i
\(466\) −8.09078 + 5.87830i −0.374798 + 0.272307i
\(467\) 7.83859 + 15.3841i 0.362727 + 0.711892i 0.998184 0.0602449i \(-0.0191882\pi\)
−0.635457 + 0.772136i \(0.719188\pi\)
\(468\) −6.78393 0.623934i −0.313587 0.0288413i
\(469\) −8.67129 2.81747i −0.400403 0.130099i
\(470\) −2.17468 4.94321i −0.100311 0.228013i
\(471\) 7.51091 + 0.939185i 0.346085 + 0.0432754i
\(472\) 3.29384 6.46453i 0.151611 0.297554i
\(473\) −4.03931 25.5032i −0.185728 1.17264i
\(474\) 4.69260 10.0052i 0.215538 0.459552i
\(475\) 8.83878 19.3883i 0.405551 0.889596i
\(476\) 9.39267i 0.430512i
\(477\) 0.990748 + 0.869011i 0.0453632 + 0.0397893i
\(478\) 5.97621 + 3.04503i 0.273345 + 0.139276i
\(479\) −6.64843 20.4618i −0.303775 0.934922i −0.980132 0.198348i \(-0.936442\pi\)
0.676357 0.736574i \(-0.263558\pi\)
\(480\) −3.18727 + 2.20030i −0.145478 + 0.100429i
\(481\) −2.33768 + 7.19463i −0.106589 + 0.328047i
\(482\) −6.75775 + 6.75775i −0.307807 + 0.307807i
\(483\) 0.447586 + 13.6900i 0.0203659 + 0.622918i
\(484\) 2.04354 + 2.81269i 0.0928882 + 0.127850i
\(485\) −26.2480 + 6.90871i −1.19186 + 0.313708i
\(486\) −14.7947 + 4.91090i −0.671101 + 0.222763i
\(487\) 2.58759 + 0.409833i 0.117255 + 0.0185713i 0.214786 0.976661i \(-0.431095\pi\)
−0.0975313 + 0.995232i \(0.531095\pi\)
\(488\) 9.94759 + 1.57554i 0.450306 + 0.0713215i
\(489\) −6.37253 11.5569i −0.288176 0.522620i
\(490\) 6.56294 8.03158i 0.296483 0.362830i
\(491\) 4.48442 + 6.17227i 0.202379 + 0.278551i 0.898128 0.439734i \(-0.144927\pi\)
−0.695749 + 0.718285i \(0.744927\pi\)
\(492\) −15.7984 + 0.516518i −0.712247 + 0.0232864i
\(493\) −33.1585 + 33.1585i −1.49338 + 1.49338i
\(494\) 2.99050 9.20380i 0.134549 0.414099i
\(495\) −2.72237 + 18.1972i −0.122361 + 0.817903i
\(496\) 1.85692 + 5.71500i 0.0833780 + 0.256611i
\(497\) −8.48196 4.32177i −0.380468 0.193858i
\(498\) 3.73974 12.9334i 0.167582 0.579559i
\(499\) 26.6590i 1.19342i −0.802456 0.596711i \(-0.796474\pi\)
0.802456 0.596711i \(-0.203526\pi\)
\(500\) 6.69121 8.95699i 0.299240 0.400569i
\(501\) −24.6290 11.5515i −1.10034 0.516081i
\(502\) 2.21784 + 14.0029i 0.0989870 + 0.624979i
\(503\) −7.87808 + 15.4616i −0.351266 + 0.689399i −0.997263 0.0739419i \(-0.976442\pi\)
0.645996 + 0.763340i \(0.276442\pi\)
\(504\) 2.46037 3.89872i 0.109594 0.173663i
\(505\) −5.90184 + 5.26691i −0.262629 + 0.234374i
\(506\) −13.4243 4.36183i −0.596785 0.193907i
\(507\) −12.7759 + 4.61790i −0.567398 + 0.205088i
\(508\) 3.97865 + 7.80853i 0.176524 + 0.346448i
\(509\) −33.7904 + 24.5502i −1.49773 + 1.08817i −0.526461 + 0.850199i \(0.676482\pi\)
−0.971273 + 0.237969i \(0.923518\pi\)
\(510\) 10.2355 + 21.3451i 0.453236 + 0.945176i
\(511\) −12.9266 9.39175i −0.571841 0.415467i
\(512\) −0.156434 + 0.987688i −0.00691349 + 0.0436501i
\(513\) −2.16769 22.0375i −0.0957056 0.972981i
\(514\) 11.4364 15.7408i 0.504436 0.694297i
\(515\) 9.38086 + 35.6403i 0.413370 + 1.57050i
\(516\) 3.07560 + 16.0127i 0.135396 + 0.704918i
\(517\) −5.90240 + 3.00742i −0.259587 + 0.132266i
\(518\) −3.61986 3.61986i −0.159048 0.159048i
\(519\) 23.8566 + 22.3461i 1.04719 + 0.980884i
\(520\) 2.55834 4.38620i 0.112190 0.192348i
\(521\) 16.9663 5.51270i 0.743309 0.241516i 0.0872091 0.996190i \(-0.472205\pi\)
0.656099 + 0.754674i \(0.272205\pi\)
\(522\) 22.4493 5.07775i 0.982577 0.222247i
\(523\) 5.49799 0.870797i 0.240410 0.0380773i −0.0350664 0.999385i \(-0.511164\pi\)
0.275477 + 0.961308i \(0.411164\pi\)
\(524\) −11.5830 −0.506006
\(525\) −3.13722 + 12.9333i −0.136919 + 0.564456i
\(526\) 11.9165 0.519586
\(527\) 36.2764 5.74562i 1.58023 0.250283i
\(528\) 2.91654 + 3.75017i 0.126926 + 0.163205i
\(529\) −3.31234 + 1.07624i −0.144015 + 0.0467932i
\(530\) −0.899114 + 0.395551i −0.0390550 + 0.0171816i
\(531\) 8.06382 + 20.2171i 0.349940 + 0.877347i
\(532\) 4.63075 + 4.63075i 0.200768 + 0.200768i
\(533\) 18.4652 9.40850i 0.799818 0.407527i
\(534\) 17.0842 3.28142i 0.739307 0.142001i
\(535\) 4.19020 + 0.238208i 0.181158 + 0.0102986i
\(536\) −3.48741 + 4.80000i −0.150633 + 0.207328i
\(537\) 37.1206 + 25.1585i 1.60187 + 1.08567i
\(538\) −2.42133 + 15.2876i −0.104391 + 0.659097i
\(539\) −10.2930 7.47827i −0.443349 0.322112i
\(540\) 1.34269 11.5411i 0.0577804 0.496650i
\(541\) −11.9935 + 8.71377i −0.515640 + 0.374634i −0.814959 0.579519i \(-0.803241\pi\)
0.299319 + 0.954153i \(0.403241\pi\)
\(542\) 2.32992 + 4.57272i 0.100079 + 0.196415i
\(543\) −5.01628 13.8781i −0.215269 0.595565i
\(544\) 5.81301 + 1.88876i 0.249231 + 0.0809800i
\(545\) 8.61478 39.6649i 0.369017 1.69906i
\(546\) −0.749951 + 5.99756i −0.0320949 + 0.256672i
\(547\) −16.7685 + 32.9101i −0.716970 + 1.40713i 0.188221 + 0.982127i \(0.439728\pi\)
−0.905191 + 0.425006i \(0.860272\pi\)
\(548\) 1.14803 + 7.24839i 0.0490415 + 0.309636i
\(549\) −23.2320 + 19.3185i −0.991518 + 0.824495i
\(550\) −11.4352 7.57093i −0.487599 0.322825i
\(551\) 32.6954i 1.39287i
\(552\) 8.56261 + 2.47591i 0.364449 + 0.105382i
\(553\) −8.73602 4.45123i −0.371493 0.189285i
\(554\) 1.20572 + 3.71082i 0.0512261 + 0.157658i
\(555\) −12.1709 4.28155i −0.516627 0.181742i
\(556\) −2.69402 + 8.29133i −0.114252 + 0.351631i
\(557\) −7.87026 + 7.87026i −0.333474 + 0.333474i −0.853904 0.520430i \(-0.825772\pi\)
0.520430 + 0.853904i \(0.325772\pi\)
\(558\) −16.5627 7.11757i −0.701157 0.301311i
\(559\) −12.5654 17.2948i −0.531461 0.731493i
\(560\) 1.85871 + 2.89010i 0.0785449 + 0.122129i
\(561\) 25.4281 14.0212i 1.07357 0.591975i
\(562\) −2.32119 0.367641i −0.0979136 0.0155080i
\(563\) −3.65971 0.579641i −0.154238 0.0244289i 0.0788377 0.996887i \(-0.474879\pi\)
−0.233076 + 0.972459i \(0.574879\pi\)
\(564\) 3.66317 2.01989i 0.154247 0.0850527i
\(565\) −8.02081 12.4715i −0.337438 0.524681i
\(566\) −2.01289 2.77050i −0.0846079 0.116453i
\(567\) 3.92582 + 13.2616i 0.164869 + 0.556934i
\(568\) −4.38033 + 4.38033i −0.183794 + 0.183794i
\(569\) −1.23085 + 3.78815i −0.0515998 + 0.158808i −0.973536 0.228534i \(-0.926607\pi\)
0.921936 + 0.387342i \(0.126607\pi\)
\(570\) 15.5698 + 5.47722i 0.652146 + 0.229415i
\(571\) 9.70723 + 29.8758i 0.406235 + 1.25026i 0.919860 + 0.392248i \(0.128302\pi\)
−0.513625 + 0.858015i \(0.671698\pi\)
\(572\) −5.54976 2.82775i −0.232047 0.118234i
\(573\) 14.5856 + 4.21748i 0.609322 + 0.176188i
\(574\) 14.0242i 0.585359i
\(575\) −25.7064 + 1.11904i −1.07203 + 0.0466671i
\(576\) −1.91812 2.30669i −0.0799217 0.0961120i
\(577\) 2.77556 + 17.5242i 0.115548 + 0.729541i 0.975636 + 0.219395i \(0.0704084\pi\)
−0.860088 + 0.510145i \(0.829592\pi\)
\(578\) 9.24259 18.1396i 0.384441 0.754508i
\(579\) −5.11196 + 40.8817i −0.212446 + 1.69899i
\(580\) −3.64107 + 16.7645i −0.151187 + 0.696109i
\(581\) −11.3603 3.69118i −0.471303 0.153136i
\(582\) −7.14671 19.7721i −0.296241 0.819582i
\(583\) 0.547016 + 1.07358i 0.0226551 + 0.0444631i
\(584\) −8.41185 + 6.11157i −0.348085 + 0.252899i
\(585\) 4.83145 + 14.4469i 0.199756 + 0.597304i
\(586\) −16.0023 11.6263i −0.661049 0.480280i
\(587\) 0.244573 1.54417i 0.0100946 0.0637349i −0.982127 0.188220i \(-0.939728\pi\)
0.992221 + 0.124486i \(0.0397280\pi\)
\(588\) 6.65058 + 4.50742i 0.274265 + 0.185883i
\(589\) 15.0522 20.7176i 0.620216 0.853654i
\(590\) −16.1972 0.920794i −0.666829 0.0379085i
\(591\) 11.9302 2.29148i 0.490745 0.0942590i
\(592\) −2.96821 + 1.51238i −0.121992 + 0.0621583i
\(593\) −10.2180 10.2180i −0.419603 0.419603i 0.465464 0.885067i \(-0.345887\pi\)
−0.885067 + 0.465464i \(0.845887\pi\)
\(594\) −14.2275 0.840853i −0.583763 0.0345006i
\(595\) 19.2245 8.45750i 0.788128 0.346724i
\(596\) −0.862632 + 0.280286i −0.0353348 + 0.0114810i
\(597\) 19.6572 + 25.2757i 0.804516 + 1.03447i
\(598\) −11.5423 + 1.82811i −0.471998 + 0.0747571i
\(599\) 22.7078 0.927816 0.463908 0.885883i \(-0.346447\pi\)
0.463908 + 0.885883i \(0.346447\pi\)
\(600\) 7.37341 + 4.54233i 0.301018 + 0.185440i
\(601\) 30.2561 1.23417 0.617087 0.786895i \(-0.288313\pi\)
0.617087 + 0.786895i \(0.288313\pi\)
\(602\) 14.2884 2.26306i 0.582351 0.0922354i
\(603\) −3.92681 17.3608i −0.159912 0.706987i
\(604\) −6.73134 + 2.18714i −0.273894 + 0.0889936i
\(605\) 3.91682 6.71528i 0.159241 0.273015i
\(606\) −4.47189 4.18873i −0.181658 0.170156i
\(607\) 18.2359 + 18.2359i 0.740173 + 0.740173i 0.972611 0.232438i \(-0.0746703\pi\)
−0.232438 + 0.972611i \(0.574670\pi\)
\(608\) 3.79711 1.93472i 0.153993 0.0784634i
\(609\) −3.85186 20.0541i −0.156085 0.812633i
\(610\) −5.73242 21.7790i −0.232099 0.881805i
\(611\) −3.22367 + 4.43700i −0.130416 + 0.179502i
\(612\) −15.7593 + 9.37399i −0.637032 + 0.378921i
\(613\) −0.0961939 + 0.607344i −0.00388524 + 0.0245304i −0.989555 0.144157i \(-0.953953\pi\)
0.985670 + 0.168688i \(0.0539529\pi\)
\(614\) 0.123814 + 0.0899560i 0.00499672 + 0.00363033i
\(615\) 15.2827 + 31.8704i 0.616256 + 1.28514i
\(616\) 3.41002 2.47752i 0.137393 0.0998222i
\(617\) −5.39346 10.5853i −0.217133 0.426147i 0.756588 0.653892i \(-0.226865\pi\)
−0.973721 + 0.227745i \(0.926865\pi\)
\(618\) −26.8472 + 9.70402i −1.07995 + 0.390353i
\(619\) 17.4319 + 5.66397i 0.700647 + 0.227654i 0.637613 0.770357i \(-0.279922\pi\)
0.0630348 + 0.998011i \(0.479922\pi\)
\(620\) 10.0252 8.94665i 0.402621 0.359306i
\(621\) −22.5228 + 14.4138i −0.903811 + 0.578405i
\(622\) −7.44637 + 14.6143i −0.298572 + 0.585981i
\(623\) −2.41450 15.2446i −0.0967350 0.610761i
\(624\) 3.56101 + 1.67018i 0.142555 + 0.0668607i
\(625\) −24.3578 5.63007i −0.974312 0.225203i
\(626\) 23.3209i 0.932092i
\(627\) 5.62380 19.4492i 0.224593 0.776725i
\(628\) −3.89388 1.98403i −0.155383 0.0791714i
\(629\) 6.29202 + 19.3649i 0.250879 + 0.772127i
\(630\) −10.1952 1.52523i −0.406185 0.0607666i
\(631\) −10.2915 + 31.6740i −0.409698 + 1.26092i 0.507210 + 0.861822i \(0.330677\pi\)
−0.916908 + 0.399098i \(0.869323\pi\)
\(632\) −4.51153 + 4.51153i −0.179459 + 0.179459i
\(633\) −27.1286 + 0.886951i −1.07827 + 0.0352531i
\(634\) −4.20844 5.79242i −0.167138 0.230046i
\(635\) 12.3996 15.1744i 0.492065 0.602178i
\(636\) −0.367395 0.666289i −0.0145682 0.0264201i
\(637\) −10.4037 1.64778i −0.412208 0.0652874i
\(638\) 20.7845 + 3.29194i 0.822867 + 0.130329i
\(639\) −1.21389 18.5445i −0.0480209 0.733607i
\(640\) 2.16242 0.569168i 0.0854770 0.0224983i
\(641\) −5.38356 7.40984i −0.212638 0.292671i 0.689353 0.724425i \(-0.257895\pi\)
−0.901991 + 0.431754i \(0.857895\pi\)
\(642\) 0.106231 + 3.24922i 0.00419260 + 0.128236i
\(643\) −10.3369 + 10.3369i −0.407649 + 0.407649i −0.880918 0.473269i \(-0.843074\pi\)
0.473269 + 0.880918i \(0.343074\pi\)
\(644\) 2.44376 7.52111i 0.0962975 0.296373i
\(645\) 30.0046 20.7134i 1.18143 0.815589i
\(646\) −8.04914 24.7727i −0.316689 0.974669i
\(647\) 9.67805 + 4.93122i 0.380484 + 0.193866i 0.633763 0.773527i \(-0.281509\pi\)
−0.253280 + 0.967393i \(0.581509\pi\)
\(648\) 8.99688 + 0.237114i 0.353431 + 0.00931473i
\(649\) 19.9004i 0.781157i
\(650\) −11.2811 1.28680i −0.442481 0.0504723i
\(651\) −6.79169 + 14.4807i −0.266187 + 0.567542i
\(652\) 1.19195 + 7.52570i 0.0466805 + 0.294729i
\(653\) 14.0273 27.5300i 0.548929 1.07733i −0.435276 0.900297i \(-0.643349\pi\)
0.984204 0.177036i \(-0.0566509\pi\)
\(654\) 31.1977 + 3.90104i 1.21992 + 0.152543i
\(655\) 10.4298 + 23.7076i 0.407525 + 0.926333i
\(656\) 8.67943 + 2.82012i 0.338875 + 0.110107i
\(657\) 2.85683 31.0618i 0.111455 1.21184i
\(658\) −1.68494 3.30687i −0.0656856 0.128915i
\(659\) −32.9364 + 23.9297i −1.28302 + 0.932169i −0.999640 0.0268379i \(-0.991456\pi\)
−0.283381 + 0.959007i \(0.591456\pi\)
\(660\) 5.04951 9.34624i 0.196552 0.363802i
\(661\) 0.749210 + 0.544333i 0.0291409 + 0.0211721i 0.602260 0.798300i \(-0.294267\pi\)
−0.573119 + 0.819472i \(0.694267\pi\)
\(662\) −2.56231 + 16.1778i −0.0995869 + 0.628767i
\(663\) 13.4876 19.9006i 0.523815 0.772874i
\(664\) −4.56885 + 6.28849i −0.177306 + 0.244041i
\(665\) 5.30832 13.6477i 0.205848 0.529235i
\(666\) 2.46085 9.68617i 0.0953559 0.375332i
\(667\) 35.1786 17.9244i 1.36212 0.694034i
\(668\) 11.1057 + 11.1057i 0.429694 + 0.429694i
\(669\) 29.0371 31.0000i 1.12264 1.19853i
\(670\) 12.9646 + 2.81577i 0.500867 + 0.108783i
\(671\) −26.2730 + 8.53660i −1.01426 + 0.329552i
\(672\) −2.10107 + 1.63402i −0.0810503 + 0.0630337i
\(673\) 9.13465 1.44679i 0.352115 0.0557695i 0.0221284 0.999755i \(-0.492956\pi\)
0.329987 + 0.943986i \(0.392956\pi\)
\(674\) −9.42262 −0.362946
\(675\) −24.8309 + 7.64387i −0.955740 + 0.294213i
\(676\) 7.84323 0.301663
\(677\) −23.3458 + 3.69762i −0.897253 + 0.142111i −0.587993 0.808866i \(-0.700082\pi\)
−0.309261 + 0.950977i \(0.600082\pi\)
\(678\) 9.06663 7.05121i 0.348202 0.270800i
\(679\) −17.7401 + 5.76412i −0.680804 + 0.221207i
\(680\) −1.36841 13.5985i −0.0524763 0.521480i
\(681\) −25.8369 + 27.5835i −0.990073 + 1.05700i
\(682\) −11.6547 11.6547i −0.446280 0.446280i
\(683\) −20.2551 + 10.3205i −0.775041 + 0.394903i −0.796324 0.604870i \(-0.793225\pi\)
0.0212830 + 0.999773i \(0.493225\pi\)
\(684\) −3.14806 + 12.3911i −0.120369 + 0.473787i
\(685\) 13.8020 8.87646i 0.527346 0.339152i
\(686\) 10.5126 14.4693i 0.401372 0.552442i
\(687\) −14.4579 + 21.3323i −0.551605 + 0.813877i
\(688\) 1.47266 9.29800i 0.0561446 0.354483i
\(689\) 0.807040 + 0.586349i 0.0307458 + 0.0223381i
\(690\) −2.64250 19.7550i −0.100598 0.752059i
\(691\) 13.7351 9.97910i 0.522506 0.379623i −0.295041 0.955485i \(-0.595333\pi\)
0.817547 + 0.575862i \(0.195333\pi\)
\(692\) −8.56782 16.8153i −0.325700 0.639222i
\(693\) −1.15811 + 12.5919i −0.0439928 + 0.478326i
\(694\) 22.7081 + 7.37832i 0.861989 + 0.280077i
\(695\) 19.3961 1.95182i 0.735737 0.0740368i
\(696\) −13.1858 1.64879i −0.499807 0.0624972i
\(697\) 25.3237 49.7005i 0.959202 1.88254i
\(698\) −3.34140 21.0968i −0.126474 0.798525i
\(699\) −7.35541 + 15.6826i −0.278207 + 0.593170i
\(700\) 4.24168 6.40668i 0.160321 0.242150i
\(701\) 6.88173i 0.259920i 0.991519 + 0.129960i \(0.0414848\pi\)
−0.991519 + 0.129960i \(0.958515\pi\)
\(702\) −10.8113 + 4.72734i −0.408048 + 0.178422i
\(703\) 12.6493 + 6.44513i 0.477077 + 0.243083i
\(704\) −0.847593 2.60862i −0.0319448 0.0983161i
\(705\) −7.43267 5.67883i −0.279931 0.213877i
\(706\) 3.67522 11.3112i 0.138319 0.425701i
\(707\) −3.84401 + 3.84401i −0.144569 + 0.144569i
\(708\) −0.410636 12.5599i −0.0154326 0.472028i
\(709\) 5.55483 + 7.64557i 0.208616 + 0.287135i 0.900484 0.434888i \(-0.143212\pi\)
−0.691868 + 0.722024i \(0.743212\pi\)
\(710\) 12.9097 + 5.02126i 0.484491 + 0.188444i
\(711\) −1.25025 19.0999i −0.0468882 0.716303i
\(712\) −9.92022 1.57121i −0.371776 0.0588835i
\(713\) −30.5430 4.83754i −1.14384 0.181167i
\(714\) 7.85550 + 14.2463i 0.293985 + 0.533155i
\(715\) −0.790497 + 13.9052i −0.0295629 + 0.520026i
\(716\) −15.2178 20.9455i −0.568716 0.782771i
\(717\) 11.6111 0.379617i 0.433625 0.0141770i
\(718\) −22.4396 + 22.4396i −0.837438 + 0.837438i
\(719\) −11.9133 + 36.6654i −0.444292 + 1.36739i 0.438967 + 0.898503i \(0.355344\pi\)
−0.883259 + 0.468886i \(0.844656\pi\)
\(720\) −2.99408 + 6.00296i −0.111583 + 0.223717i
\(721\) 7.82670 + 24.0881i 0.291482 + 0.897088i
\(722\) 0.747392 + 0.380815i 0.0278151 + 0.0141725i
\(723\) −4.59801 + 15.9016i −0.171002 + 0.591387i
\(724\) 8.51986i 0.316638i
\(725\) 37.5915 7.64301i 1.39611 0.283854i
\(726\) 5.45192 + 2.55705i 0.202340 + 0.0949009i
\(727\) −5.82954 36.8063i −0.216206 1.36507i −0.822018 0.569462i \(-0.807152\pi\)
0.605812 0.795608i \(-0.292848\pi\)
\(728\) 1.58427 3.10931i 0.0587170 0.115239i
\(729\) −18.3327 + 19.8221i −0.678987 + 0.734150i
\(730\) 20.0832 + 11.7139i 0.743314 + 0.433552i
\(731\) −54.7231 17.7806i −2.02401 0.657640i
\(732\) 16.4057 5.92990i 0.606372 0.219175i
\(733\) −11.2367 22.0534i −0.415039 0.814559i −0.999994 0.00349370i \(-0.998888\pi\)
0.584955 0.811066i \(-0.301112\pi\)
\(734\) 6.44691 4.68395i 0.237960 0.172888i
\(735\) 3.23718 17.6708i 0.119405 0.651796i
\(736\) −4.16332 3.02483i −0.153462 0.111497i
\(737\) 2.54578 16.0734i 0.0937750 0.592072i
\(738\) −23.5302 + 13.9963i −0.866160 + 0.515212i
\(739\) −2.95524 + 4.06754i −0.108710 + 0.149627i −0.859906 0.510453i \(-0.829478\pi\)
0.751195 + 0.660080i \(0.229478\pi\)
\(740\) 5.76815 + 4.71340i 0.212041 + 0.173268i
\(741\) −3.16171 16.4609i −0.116148 0.604708i
\(742\) −0.601483 + 0.306471i −0.0220811 + 0.0112509i
\(743\) 3.70154 + 3.70154i 0.135796 + 0.135796i 0.771738 0.635941i \(-0.219388\pi\)
−0.635941 + 0.771738i \(0.719388\pi\)
\(744\) 7.59618 + 7.11520i 0.278489 + 0.260856i
\(745\) 1.35042 + 1.51322i 0.0494757 + 0.0554400i
\(746\) −6.36476 + 2.06804i −0.233030 + 0.0757162i
\(747\) −5.14452 22.7444i −0.188228 0.832175i
\(748\) −16.5585 + 2.62260i −0.605437 + 0.0958918i
\(749\) 2.88433 0.105391
\(750\) 2.65776 19.1817i 0.0970477 0.700415i
\(751\) −21.2996 −0.777232 −0.388616 0.921400i \(-0.627047\pi\)
−0.388616 + 0.921400i \(0.627047\pi\)
\(752\) −2.38541 + 0.377811i −0.0869869 + 0.0137774i
\(753\) 15.0751 + 19.3840i 0.549368 + 0.706392i
\(754\) 16.5695 5.38377i 0.603427 0.196065i
\(755\) 10.5377 + 11.8080i 0.383506 + 0.429738i
\(756\) 0.471096 7.97111i 0.0171336 0.289906i
\(757\) 21.7093 + 21.7093i 0.789039 + 0.789039i 0.981337 0.192298i \(-0.0615939\pi\)
−0.192298 + 0.981337i \(0.561594\pi\)
\(758\) 2.51128 1.27956i 0.0912139 0.0464758i
\(759\) −24.0094 + 4.61156i −0.871484 + 0.167389i
\(760\) −7.37896 6.02966i −0.267663 0.218719i
\(761\) −2.06195 + 2.83804i −0.0747458 + 0.102879i −0.844753 0.535157i \(-0.820253\pi\)
0.770007 + 0.638035i \(0.220253\pi\)
\(762\) 12.5652 + 8.51607i 0.455190 + 0.308505i
\(763\) 4.36372 27.5514i 0.157977 0.997429i
\(764\) −7.09182 5.15251i −0.256573 0.186411i
\(765\) 33.3765 + 23.8148i 1.20673 + 0.861024i
\(766\) −4.52998 + 3.29122i −0.163675 + 0.118917i
\(767\) 7.47983 + 14.6800i 0.270081 + 0.530064i
\(768\) 0.588775 + 1.62891i 0.0212456 + 0.0587782i
\(769\) −47.9017 15.5642i −1.72738 0.561259i −0.734312 0.678812i \(-0.762495\pi\)
−0.993067 + 0.117552i \(0.962495\pi\)
\(770\) −8.14139 4.74862i −0.293395 0.171128i
\(771\) 4.18137 33.4396i 0.150588 1.20430i
\(772\) 10.7990 21.1943i 0.388665 0.762798i
\(773\) 0.721941 + 4.55815i 0.0259664 + 0.163945i 0.997264 0.0739221i \(-0.0235516\pi\)
−0.971298 + 0.237867i \(0.923552\pi\)
\(774\) 18.0570 + 21.7149i 0.649046 + 0.780527i
\(775\) −27.3387 12.4632i −0.982034 0.447692i
\(776\) 12.1383i 0.435739i
\(777\) −8.51787 2.46297i −0.305577 0.0883587i
\(778\) −5.20286 2.65099i −0.186532 0.0950426i
\(779\) −12.0182 36.9882i −0.430596 1.32524i
\(780\) 0.211984 8.79242i 0.00759023 0.314819i
\(781\) 5.25060 16.1597i 0.187881 0.578238i
\(782\) −22.2414 + 22.2414i −0.795350 + 0.795350i
\(783\) 29.8031 26.4770i 1.06508 0.946210i
\(784\) −2.72644 3.75263i −0.0973730 0.134022i
\(785\) −0.554636 + 9.75631i −0.0197958 + 0.348218i
\(786\) −17.5685 + 9.68738i −0.626649 + 0.345537i
\(787\) 47.7782 + 7.56732i 1.70311 + 0.269746i 0.930807 0.365510i \(-0.119105\pi\)
0.772302 + 0.635256i \(0.219105\pi\)
\(788\) −6.92748 1.09721i −0.246781 0.0390863i
\(789\) 18.0744 9.96632i 0.643466 0.354811i
\(790\) 13.2964 + 5.17166i 0.473063 + 0.183999i
\(791\) −5.98980 8.24426i −0.212973 0.293132i
\(792\) 7.56009 + 3.24883i 0.268636 + 0.115442i
\(793\) −16.1723 + 16.1723i −0.574295 + 0.574295i
\(794\) 1.86361 5.73562i 0.0661372 0.203549i
\(795\) −1.03292 + 1.35192i −0.0366337 + 0.0479477i
\(796\) −5.71269 17.5819i −0.202481 0.623172i
\(797\) 18.4066 + 9.37861i 0.651994 + 0.332207i 0.748509 0.663124i \(-0.230770\pi\)
−0.0965158 + 0.995331i \(0.530770\pi\)
\(798\) 10.8966 + 3.15079i 0.385735 + 0.111537i
\(799\) 14.7617i 0.522233i
\(800\) −3.11207 3.91344i −0.110028 0.138361i
\(801\) 23.1681 19.2654i 0.818604 0.680709i
\(802\) −3.41270 21.5470i −0.120507 0.760850i
\(803\) 12.9475 25.4109i 0.456907 0.896731i
\(804\) −1.27507 + 10.1971i −0.0449682 + 0.359623i
\(805\) −17.5943 + 1.77051i −0.620119 + 0.0624022i
\(806\) −12.9779 4.21678i −0.457128 0.148530i
\(807\) 9.11318 + 25.2126i 0.320799 + 0.887525i
\(808\) 1.60602 + 3.15200i 0.0564997 + 0.110887i
\(809\) −25.4154 + 18.4653i −0.893557 + 0.649207i −0.936803 0.349857i \(-0.886230\pi\)
0.0432462 + 0.999064i \(0.486230\pi\)
\(810\) −7.61580 18.6279i −0.267592 0.654519i
\(811\) 17.6536 + 12.8261i 0.619903 + 0.450386i 0.852887 0.522095i \(-0.174849\pi\)
−0.232985 + 0.972480i \(0.574849\pi\)
\(812\) −1.84434 + 11.6447i −0.0647237 + 0.408650i
\(813\) 7.35827 + 4.98706i 0.258066 + 0.174904i
\(814\) 5.37077 7.39223i 0.188245 0.259098i
\(815\) 14.3300 9.21605i 0.501958 0.322824i
\(816\) 10.3965 1.99690i 0.363952 0.0699054i
\(817\) −35.7456 + 18.2133i −1.25058 + 0.637202i
\(818\) 12.3496 + 12.3496i 0.431793 + 0.431793i
\(819\) 3.87853 + 9.72401i 0.135527 + 0.339784i
\(820\) −2.04318 20.3040i −0.0713510 0.709047i
\(821\) 3.02763 0.983735i 0.105665 0.0343326i −0.255707 0.966754i \(-0.582308\pi\)
0.361372 + 0.932422i \(0.382308\pi\)
\(822\) 7.80342 + 10.0338i 0.272176 + 0.349970i
\(823\) 53.4535 8.46621i 1.86327 0.295113i 0.879687 0.475554i \(-0.157752\pi\)
0.983586 + 0.180440i \(0.0577522\pi\)
\(824\) 16.4817 0.574168
\(825\) −23.6763 1.91943i −0.824301 0.0668260i
\(826\) −11.1494 −0.387936
\(827\) 7.32504 1.16017i 0.254716 0.0403431i −0.0277703 0.999614i \(-0.508841\pi\)
0.282487 + 0.959271i \(0.408841\pi\)
\(828\) 15.0580 3.40595i 0.523303 0.118365i
\(829\) −14.2896 + 4.64297i −0.496298 + 0.161257i −0.546462 0.837484i \(-0.684026\pi\)
0.0501637 + 0.998741i \(0.484026\pi\)
\(830\) 16.9850 + 3.68895i 0.589557 + 0.128045i
\(831\) 4.93229 + 4.61999i 0.171099 + 0.160266i
\(832\) −1.60574 1.60574i −0.0556688 0.0556688i
\(833\) −25.2612 + 12.8712i −0.875248 + 0.445961i
\(834\) 2.84825 + 14.8290i 0.0986269 + 0.513486i
\(835\) 12.7307 32.7308i 0.440565 1.13270i
\(836\) −6.87061 + 9.45659i −0.237625 + 0.327063i
\(837\) −31.0743 + 3.05657i −1.07408 + 0.105650i
\(838\) 1.37157 8.65976i 0.0473802 0.299147i
\(839\) 25.0182 + 18.1768i 0.863723 + 0.627531i 0.928895 0.370343i \(-0.120760\pi\)
−0.0651724 + 0.997874i \(0.520760\pi\)
\(840\) 5.23632 + 2.82904i 0.180670 + 0.0976111i
\(841\) −24.1584 + 17.5521i −0.833047 + 0.605244i
\(842\) 15.5427 + 30.5043i 0.535637 + 1.05125i
\(843\) −3.82814 + 1.38370i −0.131848 + 0.0476570i
\(844\) 14.9041 + 4.84263i 0.513020 + 0.166690i
\(845\) −7.06233 16.0532i −0.242952 0.552246i
\(846\) 3.86678 6.12733i 0.132943 0.210662i
\(847\) 2.42552 4.76036i 0.0833419 0.163568i
\(848\) 0.0687197 + 0.433879i 0.00235984 + 0.0148995i
\(849\) −5.37014 2.51869i −0.184303 0.0864412i
\(850\) −26.6007 + 15.0454i −0.912397 + 0.516054i
\(851\) 17.1433i 0.587666i
\(852\) −2.98040 + 10.3073i −0.102107 + 0.353123i
\(853\) 32.5101 + 16.5647i 1.11312 + 0.567165i 0.911088 0.412212i \(-0.135244\pi\)
0.202037 + 0.979378i \(0.435244\pi\)
\(854\) −4.78271 14.7197i −0.163661 0.503697i
\(855\) 28.1963 4.71412i 0.964292 0.161219i
\(856\) 0.580006 1.78508i 0.0198242 0.0610126i
\(857\) 25.3854 25.3854i 0.867150 0.867150i −0.125006 0.992156i \(-0.539895\pi\)
0.992156 + 0.125006i \(0.0398949\pi\)
\(858\) −10.7826 + 0.352528i −0.368111 + 0.0120351i
\(859\) 21.9978 + 30.2774i 0.750556 + 1.03305i 0.997941 + 0.0641342i \(0.0204286\pi\)
−0.247386 + 0.968917i \(0.579571\pi\)
\(860\) −20.3568 + 5.35809i −0.694160 + 0.182709i
\(861\) 11.7291 + 21.2712i 0.399726 + 0.724921i
\(862\) −2.60010 0.411816i −0.0885598 0.0140265i
\(863\) −29.4253 4.66051i −1.00165 0.158646i −0.365993 0.930618i \(-0.619270\pi\)
−0.635656 + 0.771972i \(0.719270\pi\)
\(864\) −4.83849 1.89446i −0.164609 0.0644508i
\(865\) −26.7020 + 32.6774i −0.907897 + 1.11106i
\(866\) 22.1953 + 30.5491i 0.754225 + 1.03810i
\(867\) −1.15225 35.2432i −0.0391325 1.19692i
\(868\) 6.52963 6.52963i 0.221630 0.221630i
\(869\) 5.40787 16.6437i 0.183449 0.564599i
\(870\) 8.49832 + 28.4728i 0.288120 + 0.965318i
\(871\) −4.16347 12.8138i −0.141074 0.434180i
\(872\) −16.1738 8.24095i −0.547713 0.279074i
\(873\) −27.3761 24.0123i −0.926540 0.812692i
\(874\) 21.9308i 0.741820i
\(875\) −16.9323 2.91288i −0.572416 0.0984732i
\(876\) −7.64730 + 16.3049i −0.258378 + 0.550892i
\(877\) −0.595727 3.76127i −0.0201163 0.127009i 0.975587 0.219615i \(-0.0704802\pi\)
−0.995703 + 0.0926062i \(0.970480\pi\)
\(878\) −1.34230 + 2.63442i −0.0453006 + 0.0889074i
\(879\) −33.9951 4.25084i −1.14663 0.143377i
\(880\) −4.57601 + 4.08371i −0.154257 + 0.137662i
\(881\) 32.9569 + 10.7083i 1.11035 + 0.360773i 0.806075 0.591813i \(-0.201588\pi\)
0.304270 + 0.952586i \(0.401588\pi\)
\(882\) 13.8570 + 1.27446i 0.466590 + 0.0429134i
\(883\) −14.6498 28.7519i −0.493006 0.967578i −0.994728 0.102549i \(-0.967300\pi\)
0.501722 0.865029i \(-0.332700\pi\)
\(884\) −11.2290 + 8.15835i −0.377673 + 0.274395i
\(885\) −25.3372 + 12.1498i −0.851702 + 0.408412i
\(886\) −9.53291 6.92606i −0.320264 0.232686i
\(887\) 6.90757 43.6127i 0.231934 1.46437i −0.546930 0.837178i \(-0.684204\pi\)
0.778864 0.627193i \(-0.215796\pi\)
\(888\) −3.23716 + 4.77634i −0.108632 + 0.160283i
\(889\) 7.91591 10.8953i 0.265491 0.365417i
\(890\) 5.71665 + 21.7191i 0.191623 + 0.728024i
\(891\) −22.2828 + 10.6237i −0.746503 + 0.355909i
\(892\) −21.8503 + 11.1333i −0.731601 + 0.372770i
\(893\) 7.27779 + 7.27779i 0.243542 + 0.243542i
\(894\) −1.07398 + 1.14658i −0.0359193 + 0.0383474i
\(895\) −29.1677 + 50.0073i −0.974969 + 1.67156i
\(896\) 1.46150 0.474872i 0.0488254 0.0158643i
\(897\) −15.9778 + 12.4261i −0.533483 + 0.414895i
\(898\) −11.0583 + 1.75146i −0.369019 + 0.0584469i
\(899\) 46.1026 1.53761
\(900\) 14.9826 + 0.722875i 0.499419 + 0.0240958i
\(901\) 2.68500 0.0894502
\(902\) −24.7235 + 3.91581i −0.823202 + 0.130382i
\(903\) 19.7792 15.3825i 0.658211 0.511898i
\(904\) −6.30676 + 2.04919i −0.209760 + 0.0681551i
\(905\) 17.4381 7.67160i 0.579662 0.255013i
\(906\) −8.38055 + 8.94706i −0.278425 + 0.297246i
\(907\) −28.9644 28.9644i −0.961746 0.961746i 0.0375488 0.999295i \(-0.488045\pi\)
−0.999295 + 0.0375488i \(0.988045\pi\)
\(908\) 19.4421 9.90627i 0.645210 0.328751i
\(909\) −10.2860 2.61323i −0.341164 0.0866752i
\(910\) −7.79053 0.442883i −0.258254 0.0146814i
\(911\) −0.920803 + 1.26738i −0.0305076 + 0.0419901i −0.823998 0.566592i \(-0.808261\pi\)
0.793491 + 0.608582i \(0.208261\pi\)
\(912\) 4.14117 6.11018i 0.137128 0.202328i
\(913\) 3.33523 21.0578i 0.110380 0.696912i
\(914\) 8.32838 + 6.05092i 0.275478 + 0.200147i
\(915\) −26.9094 28.2390i −0.889596 0.933552i
\(916\) 12.0369 8.74529i 0.397709 0.288952i
\(917\) 8.08095 + 15.8597i 0.266856 + 0.523735i
\(918\) −16.0630 + 27.3982i −0.530159 + 0.904275i
\(919\) 32.7370 + 10.6369i 1.07989 + 0.350879i 0.794333 0.607482i \(-0.207820\pi\)
0.285560 + 0.958361i \(0.407820\pi\)
\(920\) −2.44228 + 11.2450i −0.0805197 + 0.370736i
\(921\) 0.263029 + 0.0328898i 0.00866709 + 0.00108376i
\(922\) −9.14806 + 17.9541i −0.301275 + 0.591286i
\(923\) −2.20061 13.8941i −0.0724339 0.457330i
\(924\) 3.10008 6.60972i 0.101985 0.217444i
\(925\) 4.45332 16.0501i 0.146424 0.527724i
\(926\) 0.119086i 0.00391341i
\(927\) −32.6046 + 37.1721i −1.07088 + 1.22089i
\(928\) 6.83591 + 3.48307i 0.224400 + 0.114337i
\(929\) 3.37519 + 10.3878i 0.110736 + 0.340811i 0.991034 0.133611i \(-0.0426571\pi\)
−0.880298 + 0.474422i \(0.842657\pi\)
\(930\) 7.72321 21.9543i 0.253254 0.719911i
\(931\) −6.10847 + 18.7999i −0.200197 + 0.616143i
\(932\) 7.07160 7.07160i 0.231638 0.231638i
\(933\) 0.928321 + 28.3940i 0.0303919 + 0.929578i
\(934\) −10.1487 13.9685i −0.332075 0.457062i
\(935\) 20.2777 + 31.5296i 0.663151 + 1.03113i
\(936\) 6.79801 0.444988i 0.222200 0.0145449i
\(937\) 24.5644 + 3.89063i 0.802485 + 0.127101i 0.544187 0.838964i \(-0.316838\pi\)
0.258298 + 0.966065i \(0.416838\pi\)
\(938\) 9.00529 + 1.42630i 0.294033 + 0.0465703i
\(939\) −19.5043 35.3720i −0.636499 1.15432i
\(940\) 2.92120 + 4.54215i 0.0952789 + 0.148149i
\(941\) 15.4350 + 21.2444i 0.503166 + 0.692548i 0.982748 0.184949i \(-0.0592119\pi\)
−0.479583 + 0.877497i \(0.659212\pi\)
\(942\) −7.56536 + 0.247344i −0.246493 + 0.00805891i
\(943\) −33.2087 + 33.2087i −1.08142 + 1.08142i
\(944\) −2.24201 + 6.90021i −0.0729714 + 0.224583i
\(945\) −16.7391 + 6.21326i −0.544523 + 0.202117i
\(946\) 7.97915 + 24.5573i 0.259425 + 0.798427i
\(947\) 37.3987 + 19.0556i 1.21529 + 0.619223i 0.939683 0.342047i \(-0.111120\pi\)
0.275610 + 0.961270i \(0.411120\pi\)
\(948\) −3.06967 + 10.6161i −0.0996983 + 0.344793i
\(949\) 23.6115i 0.766461i
\(950\) −5.69696 + 20.5323i −0.184834 + 0.666155i
\(951\) −11.2276 5.26594i −0.364080 0.170760i
\(952\) −1.46934 9.27703i −0.0476215 0.300670i
\(953\) 9.66565 18.9699i 0.313101 0.614496i −0.679805 0.733393i \(-0.737936\pi\)
0.992907 + 0.118897i \(0.0379358\pi\)
\(954\) −1.11449 0.703325i −0.0360830 0.0227710i
\(955\) −4.16020 + 19.1547i −0.134621 + 0.619833i
\(956\) −6.37898 2.07266i −0.206311 0.0670345i
\(957\) 34.2781 12.3899i 1.10805 0.400510i
\(958\) 9.76750 + 19.1698i 0.315574 + 0.619348i
\(959\) 9.12374 6.62879i 0.294621 0.214055i
\(960\) 2.80383 2.67181i 0.0904931 0.0862323i
\(961\) −4.13355 3.00320i −0.133340 0.0968775i
\(962\) 1.18341 7.47174i 0.0381546 0.240899i
\(963\) 2.87859 + 4.83941i 0.0927613 + 0.155948i
\(964\) 5.61740 7.73169i 0.180924 0.249021i
\(965\) −53.1033 3.01887i −1.70946 0.0971808i
\(966\) −2.58367 13.4515i −0.0831281 0.432794i
\(967\) −2.98519 + 1.52103i −0.0959973 + 0.0489130i −0.501330 0.865256i \(-0.667156\pi\)
0.405333 + 0.914169i \(0.367156\pi\)
\(968\) −2.45838 2.45838i −0.0790154 0.0790154i
\(969\) −32.9270 30.8421i −1.05777 0.990792i
\(970\) 24.8441 10.9297i 0.797696 0.350933i
\(971\) 20.1061 6.53286i 0.645234 0.209649i 0.0319227 0.999490i \(-0.489837\pi\)
0.613312 + 0.789841i \(0.289837\pi\)
\(972\) 13.8443 7.16484i 0.444057 0.229812i
\(973\) 13.2322 2.09577i 0.424204 0.0671874i
\(974\) −2.61984 −0.0839451
\(975\) −18.1868 + 7.48314i −0.582444 + 0.239652i
\(976\) −10.0716 −0.322384
\(977\) −0.151463 + 0.0239894i −0.00484574 + 0.000767489i −0.158857 0.987302i \(-0.550781\pi\)
0.154011 + 0.988069i \(0.450781\pi\)
\(978\) 8.10196 + 10.4177i 0.259072 + 0.333122i
\(979\) 26.2007 8.51312i 0.837377 0.272080i
\(980\) −5.22572 + 8.95937i −0.166930 + 0.286197i
\(981\) 50.5816 20.1751i 1.61495 0.644140i
\(982\) −5.39477 5.39477i −0.172154 0.172154i
\(983\) −27.8680 + 14.1994i −0.888850 + 0.452892i −0.837909 0.545810i \(-0.816222\pi\)
−0.0509408 + 0.998702i \(0.516222\pi\)
\(984\) 15.5231 2.98157i 0.494858 0.0950491i
\(985\) 3.99205 + 15.1668i 0.127197 + 0.483256i
\(986\) 27.5632 37.9374i 0.877790 1.20817i
\(987\) −5.32131 3.60651i −0.169379 0.114797i
\(988\) −1.51389 + 9.55830i −0.0481632 + 0.304090i
\(989\) 39.1931 + 28.4754i 1.24627 + 0.905466i
\(990\) −0.157821 18.3990i −0.00501588 0.584760i
\(991\) −7.72378 + 5.61165i −0.245354 + 0.178260i −0.703665 0.710532i \(-0.748454\pi\)
0.458311 + 0.888792i \(0.348454\pi\)
\(992\) −2.72808 5.35415i −0.0866165 0.169995i
\(993\) 9.64380 + 26.6806i 0.306037 + 0.846683i
\(994\) 9.05361 + 2.94169i 0.287163 + 0.0933049i
\(995\) −30.8419 + 27.5238i −0.977753 + 0.872564i
\(996\) −1.67047 + 13.3592i −0.0529308 + 0.423302i
\(997\) −16.0041 + 31.4099i −0.506856 + 0.994761i 0.485832 + 0.874052i \(0.338517\pi\)
−0.992688 + 0.120708i \(0.961483\pi\)
\(998\) 4.17039 + 26.3308i 0.132011 + 0.833487i
\(999\) −4.36848 16.7496i −0.138213 0.529934i
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 150.2.l.a.137.2 yes 80
3.2 odd 2 inner 150.2.l.a.137.8 yes 80
5.2 odd 4 750.2.l.a.293.4 80
5.3 odd 4 750.2.l.c.293.7 80
5.4 even 2 750.2.l.b.707.9 80
15.2 even 4 750.2.l.a.293.6 80
15.8 even 4 750.2.l.c.293.5 80
15.14 odd 2 750.2.l.b.707.3 80
25.2 odd 20 750.2.l.b.593.3 80
25.11 even 5 750.2.l.c.407.5 80
25.14 even 10 750.2.l.a.407.6 80
25.23 odd 20 inner 150.2.l.a.23.8 yes 80
75.2 even 20 750.2.l.b.593.9 80
75.11 odd 10 750.2.l.c.407.7 80
75.14 odd 10 750.2.l.a.407.4 80
75.23 even 20 inner 150.2.l.a.23.2 80
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
150.2.l.a.23.2 80 75.23 even 20 inner
150.2.l.a.23.8 yes 80 25.23 odd 20 inner
150.2.l.a.137.2 yes 80 1.1 even 1 trivial
150.2.l.a.137.8 yes 80 3.2 odd 2 inner
750.2.l.a.293.4 80 5.2 odd 4
750.2.l.a.293.6 80 15.2 even 4
750.2.l.a.407.4 80 75.14 odd 10
750.2.l.a.407.6 80 25.14 even 10
750.2.l.b.593.3 80 25.2 odd 20
750.2.l.b.593.9 80 75.2 even 20
750.2.l.b.707.3 80 15.14 odd 2
750.2.l.b.707.9 80 5.4 even 2
750.2.l.c.293.5 80 15.8 even 4
750.2.l.c.293.7 80 5.3 odd 4
750.2.l.c.407.5 80 25.11 even 5
750.2.l.c.407.7 80 75.11 odd 10