Properties

Label 52.2.l.b.15.1
Level $52$
Weight $2$
Character 52.15
Analytic conductor $0.415$
Analytic rank $0$
Dimension $16$
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] = [52,2,Mod(7,52)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(52, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([6, 11]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("52.7");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 52 = 2^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 52.l (of order \(12\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.415222090511\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{12})\)
Coefficient field: 16.0.102930383934669717504.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 4 x^{15} + 5 x^{14} - 2 x^{13} + 5 x^{12} - 8 x^{11} - 12 x^{10} + 32 x^{9} - 36 x^{8} + 64 x^{7} - 48 x^{6} - 64 x^{5} + 80 x^{4} - 64 x^{3} + 320 x^{2} - 512 x + 256 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 15.1
Root \(1.31256 - 0.526485i\) of defining polynomial
Character \(\chi\) \(=\) 52.15
Dual form 52.2.l.b.7.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.11223 + 0.873468i) q^{2} +(-2.16981 + 1.25274i) q^{3} +(0.474107 - 1.94299i) q^{4} +(-2.19962 + 2.19962i) q^{5} +(1.31910 - 3.28859i) q^{6} +(0.152604 + 0.569525i) q^{7} +(1.16983 + 2.57517i) q^{8} +(1.63871 - 2.83834i) q^{9} +O(q^{10})\) \(q+(-1.11223 + 0.873468i) q^{2} +(-2.16981 + 1.25274i) q^{3} +(0.474107 - 1.94299i) q^{4} +(-2.19962 + 2.19962i) q^{5} +(1.31910 - 3.28859i) q^{6} +(0.152604 + 0.569525i) q^{7} +(1.16983 + 2.57517i) q^{8} +(1.63871 - 2.83834i) q^{9} +(0.525184 - 4.36778i) q^{10} +(2.85302 + 0.764465i) q^{11} +(1.40534 + 4.80986i) q^{12} +(2.37076 + 2.71652i) q^{13} +(-0.667192 - 0.500148i) q^{14} +(2.01721 - 7.52831i) q^{15} +(-3.55045 - 1.84237i) q^{16} +(-2.30986 - 1.33360i) q^{17} +(0.656570 + 4.58824i) q^{18} +(-3.11932 + 0.835818i) q^{19} +(3.23099 + 5.31671i) q^{20} +(-1.04459 - 1.04459i) q^{21} +(-3.84095 + 1.64176i) q^{22} +(1.03076 + 1.78533i) q^{23} +(-5.76432 - 4.12214i) q^{24} -4.67667i q^{25} +(-5.00963 - 0.950604i) q^{26} +0.695088i q^{27} +(1.17893 - 0.0264924i) q^{28} +(-0.621816 - 1.07702i) q^{29} +(4.33215 + 10.1352i) q^{30} +(6.34495 + 6.34495i) q^{31} +(5.55816 - 1.05206i) q^{32} +(-7.14819 + 1.91535i) q^{33} +(3.73394 - 0.534321i) q^{34} +(-1.58841 - 0.917069i) q^{35} +(-4.73794 - 4.52968i) q^{36} +(-0.133975 + 0.500000i) q^{37} +(2.73933 - 3.65425i) q^{38} +(-8.54720 - 2.92438i) q^{39} +(-8.23758 - 3.09122i) q^{40} +(5.59808 + 1.50000i) q^{41} +(2.07423 + 0.249407i) q^{42} +(3.60759 - 6.24853i) q^{43} +(2.83799 - 5.18097i) q^{44} +(2.63871 + 9.84781i) q^{45} +(-2.70587 - 1.08536i) q^{46} +(-3.16813 + 3.16813i) q^{47} +(10.0118 - 0.450187i) q^{48} +(5.76111 - 3.32618i) q^{49} +(4.08492 + 5.20153i) q^{50} +6.68260 q^{51} +(6.40217 - 3.31846i) q^{52} +3.67667 q^{53} +(-0.607137 - 0.773097i) q^{54} +(-7.95711 + 4.59404i) q^{55} +(-1.28810 + 1.05923i) q^{56} +(5.72126 - 5.72126i) q^{57} +(1.63234 + 0.654753i) q^{58} +(-1.82424 - 6.80816i) q^{59} +(-13.6711 - 7.48864i) q^{60} +(-3.97705 + 6.88845i) q^{61} +(-12.5991 - 1.51493i) q^{62} +(1.86658 + 0.500148i) q^{63} +(-5.26301 + 6.02501i) q^{64} +(-11.1901 - 0.760530i) q^{65} +(6.27743 - 8.37403i) q^{66} +(-1.92408 + 7.18077i) q^{67} +(-3.68629 + 3.85577i) q^{68} +(-4.47310 - 2.58254i) q^{69} +(2.56771 - 0.367435i) q^{70} +(-1.98027 + 0.530611i) q^{71} +(9.22621 + 0.899605i) q^{72} +(0.0440105 + 0.0440105i) q^{73} +(-0.287724 - 0.673137i) q^{74} +(5.85865 + 10.1475i) q^{75} +(0.145100 + 6.45708i) q^{76} +1.74153i q^{77} +(12.0608 - 4.21313i) q^{78} +2.73286i q^{79} +(11.8622 - 3.75711i) q^{80} +(4.04538 + 7.00680i) q^{81} +(-7.53655 + 3.22140i) q^{82} +(-10.1844 - 10.1844i) q^{83} +(-2.52487 + 1.53438i) q^{84} +(8.01422 - 2.14740i) q^{85} +(1.44543 + 10.1009i) q^{86} +(2.69844 + 1.55795i) q^{87} +(1.36892 + 8.24131i) q^{88} +(2.14761 - 8.01501i) q^{89} +(-11.5366 - 8.64819i) q^{90} +(-1.18534 + 1.76476i) q^{91} +(3.95757 - 1.15632i) q^{92} +(-21.7159 - 5.81876i) q^{93} +(0.756425 - 6.29094i) q^{94} +(5.02283 - 8.69980i) q^{95} +(-10.7422 + 9.24570i) q^{96} +(-1.22731 - 4.58039i) q^{97} +(-3.50236 + 8.73161i) q^{98} +(6.84510 - 6.84510i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 2 q^{2} - 6 q^{4} - 12 q^{5} - 14 q^{6} + 10 q^{8} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 2 q^{2} - 6 q^{4} - 12 q^{5} - 14 q^{6} + 10 q^{8} + 4 q^{9} - 12 q^{13} + 8 q^{14} - 2 q^{16} + 12 q^{17} - 6 q^{18} + 2 q^{20} - 28 q^{21} + 10 q^{24} + 16 q^{26} + 12 q^{28} - 8 q^{29} + 42 q^{30} + 28 q^{32} - 20 q^{33} + 14 q^{34} - 6 q^{36} - 16 q^{37} - 40 q^{40} + 48 q^{41} - 28 q^{42} - 8 q^{44} + 20 q^{45} - 46 q^{46} - 10 q^{48} + 60 q^{49} + 10 q^{50} - 32 q^{52} - 32 q^{53} - 16 q^{54} - 60 q^{56} + 12 q^{57} - 48 q^{58} - 24 q^{60} + 4 q^{61} - 18 q^{62} - 8 q^{65} + 56 q^{66} + 16 q^{68} - 12 q^{69} + 28 q^{70} + 56 q^{72} + 20 q^{73} + 4 q^{74} + 22 q^{76} + 68 q^{78} + 44 q^{80} + 48 q^{81} + 84 q^{84} + 20 q^{85} + 16 q^{86} + 36 q^{88} - 52 q^{89} - 12 q^{92} - 92 q^{93} - 38 q^{94} - 72 q^{96} - 28 q^{97} - 2 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/52\mathbb{Z}\right)^\times\).

\(n\) \(27\) \(41\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{12}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.11223 + 0.873468i −0.786465 + 0.617635i
\(3\) −2.16981 + 1.25274i −1.25274 + 0.723270i −0.971653 0.236413i \(-0.924028\pi\)
−0.281087 + 0.959682i \(0.590695\pi\)
\(4\) 0.474107 1.94299i 0.237053 0.971497i
\(5\) −2.19962 + 2.19962i −0.983701 + 0.983701i −0.999869 0.0161686i \(-0.994853\pi\)
0.0161686 + 0.999869i \(0.494853\pi\)
\(6\) 1.31910 3.28859i 0.538519 1.34256i
\(7\) 0.152604 + 0.569525i 0.0576788 + 0.215260i 0.988750 0.149577i \(-0.0477912\pi\)
−0.931071 + 0.364837i \(0.881125\pi\)
\(8\) 1.16983 + 2.57517i 0.413596 + 0.910460i
\(9\) 1.63871 2.83834i 0.546238 0.946112i
\(10\) 0.525184 4.36778i 0.166078 1.38121i
\(11\) 2.85302 + 0.764465i 0.860219 + 0.230495i 0.661854 0.749633i \(-0.269770\pi\)
0.198365 + 0.980128i \(0.436437\pi\)
\(12\) 1.40534 + 4.80986i 0.405688 + 1.38849i
\(13\) 2.37076 + 2.71652i 0.657532 + 0.753427i
\(14\) −0.667192 0.500148i −0.178315 0.133670i
\(15\) 2.01721 7.52831i 0.520840 1.94380i
\(16\) −3.55045 1.84237i −0.887611 0.460593i
\(17\) −2.30986 1.33360i −0.560222 0.323445i 0.193012 0.981196i \(-0.438174\pi\)
−0.753235 + 0.657752i \(0.771508\pi\)
\(18\) 0.656570 + 4.58824i 0.154755 + 1.08146i
\(19\) −3.11932 + 0.835818i −0.715620 + 0.191750i −0.598217 0.801334i \(-0.704124\pi\)
−0.117404 + 0.993084i \(0.537457\pi\)
\(20\) 3.23099 + 5.31671i 0.722472 + 1.18885i
\(21\) −1.04459 1.04459i −0.227948 0.227948i
\(22\) −3.84095 + 1.64176i −0.818894 + 0.350025i
\(23\) 1.03076 + 1.78533i 0.214928 + 0.372266i 0.953250 0.302182i \(-0.0977150\pi\)
−0.738322 + 0.674448i \(0.764382\pi\)
\(24\) −5.76432 4.12214i −1.17664 0.841428i
\(25\) 4.67667i 0.935334i
\(26\) −5.00963 0.950604i −0.982468 0.186429i
\(27\) 0.695088i 0.133770i
\(28\) 1.17893 0.0264924i 0.222798 0.00500659i
\(29\) −0.621816 1.07702i −0.115468 0.199997i 0.802499 0.596654i \(-0.203504\pi\)
−0.917967 + 0.396657i \(0.870170\pi\)
\(30\) 4.33215 + 10.1352i 0.790938 + 1.85042i
\(31\) 6.34495 + 6.34495i 1.13959 + 1.13959i 0.988524 + 0.151062i \(0.0482694\pi\)
0.151062 + 0.988524i \(0.451731\pi\)
\(32\) 5.55816 1.05206i 0.982554 0.185980i
\(33\) −7.14819 + 1.91535i −1.24434 + 0.333420i
\(34\) 3.73394 0.534321i 0.640366 0.0916354i
\(35\) −1.58841 0.917069i −0.268490 0.155013i
\(36\) −4.73794 4.52968i −0.789657 0.754947i
\(37\) −0.133975 + 0.500000i −0.0220253 + 0.0821995i −0.976064 0.217485i \(-0.930215\pi\)
0.954038 + 0.299684i \(0.0968814\pi\)
\(38\) 2.73933 3.65425i 0.444379 0.592797i
\(39\) −8.54720 2.92438i −1.36865 0.468275i
\(40\) −8.23758 3.09122i −1.30248 0.488765i
\(41\) 5.59808 + 1.50000i 0.874273 + 0.234261i 0.667934 0.744220i \(-0.267179\pi\)
0.206338 + 0.978481i \(0.433845\pi\)
\(42\) 2.07423 + 0.249407i 0.320061 + 0.0384843i
\(43\) 3.60759 6.24853i 0.550152 0.952892i −0.448111 0.893978i \(-0.647903\pi\)
0.998263 0.0589139i \(-0.0187638\pi\)
\(44\) 2.83799 5.18097i 0.427843 0.781060i
\(45\) 2.63871 + 9.84781i 0.393356 + 1.46803i
\(46\) −2.70587 1.08536i −0.398958 0.160027i
\(47\) −3.16813 + 3.16813i −0.462119 + 0.462119i −0.899350 0.437230i \(-0.855959\pi\)
0.437230 + 0.899350i \(0.355959\pi\)
\(48\) 10.0118 0.450187i 1.44508 0.0649789i
\(49\) 5.76111 3.32618i 0.823015 0.475168i
\(50\) 4.08492 + 5.20153i 0.577695 + 0.735607i
\(51\) 6.68260 0.935751
\(52\) 6.40217 3.31846i 0.887822 0.460187i
\(53\) 3.67667 0.505030 0.252515 0.967593i \(-0.418742\pi\)
0.252515 + 0.967593i \(0.418742\pi\)
\(54\) −0.607137 0.773097i −0.0826209 0.105205i
\(55\) −7.95711 + 4.59404i −1.07294 + 0.619460i
\(56\) −1.28810 + 1.05923i −0.172130 + 0.141545i
\(57\) 5.72126 5.72126i 0.757799 0.757799i
\(58\) 1.63234 + 0.654753i 0.214337 + 0.0859733i
\(59\) −1.82424 6.80816i −0.237496 0.886347i −0.977008 0.213203i \(-0.931610\pi\)
0.739512 0.673143i \(-0.235056\pi\)
\(60\) −13.6711 7.48864i −1.76493 0.966779i
\(61\) −3.97705 + 6.88845i −0.509209 + 0.881976i 0.490734 + 0.871309i \(0.336729\pi\)
−0.999943 + 0.0106664i \(0.996605\pi\)
\(62\) −12.5991 1.51493i −1.60009 0.192396i
\(63\) 1.86658 + 0.500148i 0.235167 + 0.0630127i
\(64\) −5.26301 + 6.02501i −0.657876 + 0.753126i
\(65\) −11.1901 0.760530i −1.38796 0.0943321i
\(66\) 6.27743 8.37403i 0.772698 1.03077i
\(67\) −1.92408 + 7.18077i −0.235064 + 0.877270i 0.743056 + 0.669229i \(0.233376\pi\)
−0.978120 + 0.208041i \(0.933291\pi\)
\(68\) −3.68629 + 3.85577i −0.447028 + 0.467581i
\(69\) −4.47310 2.58254i −0.538498 0.310902i
\(70\) 2.56771 0.367435i 0.306900 0.0439169i
\(71\) −1.98027 + 0.530611i −0.235014 + 0.0629719i −0.374404 0.927266i \(-0.622153\pi\)
0.139390 + 0.990238i \(0.455486\pi\)
\(72\) 9.22621 + 0.899605i 1.08732 + 0.106020i
\(73\) 0.0440105 + 0.0440105i 0.00515104 + 0.00515104i 0.709678 0.704527i \(-0.248841\pi\)
−0.704527 + 0.709678i \(0.748841\pi\)
\(74\) −0.287724 0.673137i −0.0334472 0.0782506i
\(75\) 5.85865 + 10.1475i 0.676499 + 1.17173i
\(76\) 0.145100 + 6.45708i 0.0166441 + 0.740678i
\(77\) 1.74153i 0.198466i
\(78\) 12.0608 4.21313i 1.36562 0.477043i
\(79\) 2.73286i 0.307471i 0.988112 + 0.153735i \(0.0491303\pi\)
−0.988112 + 0.153735i \(0.950870\pi\)
\(80\) 11.8622 3.75711i 1.32623 0.420058i
\(81\) 4.04538 + 7.00680i 0.449486 + 0.778533i
\(82\) −7.53655 + 3.22140i −0.832272 + 0.355744i
\(83\) −10.1844 10.1844i −1.11789 1.11789i −0.992051 0.125834i \(-0.959839\pi\)
−0.125834 0.992051i \(-0.540161\pi\)
\(84\) −2.52487 + 1.53438i −0.275486 + 0.167415i
\(85\) 8.01422 2.14740i 0.869264 0.232919i
\(86\) 1.44543 + 10.1009i 0.155864 + 1.08921i
\(87\) 2.69844 + 1.55795i 0.289304 + 0.167029i
\(88\) 1.36892 + 8.24131i 0.145927 + 0.878527i
\(89\) 2.14761 8.01501i 0.227647 0.849589i −0.753680 0.657241i \(-0.771723\pi\)
0.981327 0.192348i \(-0.0616101\pi\)
\(90\) −11.5366 8.64819i −1.21606 0.911599i
\(91\) −1.18534 + 1.76476i −0.124257 + 0.184997i
\(92\) 3.95757 1.15632i 0.412605 0.120555i
\(93\) −21.7159 5.81876i −2.25183 0.603377i
\(94\) 0.756425 6.29094i 0.0780193 0.648861i
\(95\) 5.02283 8.69980i 0.515332 0.892581i
\(96\) −10.7422 + 9.24570i −1.09637 + 0.943635i
\(97\) −1.22731 4.58039i −0.124615 0.465068i 0.875211 0.483741i \(-0.160722\pi\)
−0.999826 + 0.0186732i \(0.994056\pi\)
\(98\) −3.50236 + 8.73161i −0.353792 + 0.882026i
\(99\) 6.84510 6.84510i 0.687958 0.687958i
\(100\) −9.08674 2.21724i −0.908674 0.221724i
\(101\) 7.77554 4.48921i 0.773695 0.446693i −0.0604964 0.998168i \(-0.519268\pi\)
0.834191 + 0.551476i \(0.185935\pi\)
\(102\) −7.43258 + 5.83703i −0.735935 + 0.577953i
\(103\) 9.60170 0.946084 0.473042 0.881040i \(-0.343156\pi\)
0.473042 + 0.881040i \(0.343156\pi\)
\(104\) −4.22212 + 9.28298i −0.414013 + 0.910271i
\(105\) 4.59540 0.448465
\(106\) −4.08930 + 3.21145i −0.397188 + 0.311924i
\(107\) 16.3364 9.43183i 1.57930 0.911809i 0.584343 0.811507i \(-0.301352\pi\)
0.994957 0.100302i \(-0.0319810\pi\)
\(108\) 1.35055 + 0.329546i 0.129957 + 0.0317106i
\(109\) −2.95252 + 2.95252i −0.282800 + 0.282800i −0.834225 0.551425i \(-0.814084\pi\)
0.551425 + 0.834225i \(0.314084\pi\)
\(110\) 4.83738 12.0599i 0.461226 1.14987i
\(111\) −0.335671 1.25274i −0.0318604 0.118905i
\(112\) 0.507466 2.30322i 0.0479510 0.217634i
\(113\) −2.82144 + 4.88687i −0.265419 + 0.459718i −0.967673 0.252207i \(-0.918843\pi\)
0.702255 + 0.711926i \(0.252177\pi\)
\(114\) −1.36601 + 11.3607i −0.127939 + 1.06403i
\(115\) −6.19432 1.65976i −0.577623 0.154774i
\(116\) −2.38744 + 0.697563i −0.221669 + 0.0647671i
\(117\) 11.5954 2.27743i 1.07199 0.210548i
\(118\) 7.97568 + 5.97882i 0.734221 + 0.550395i
\(119\) 0.407024 1.51903i 0.0373118 0.139250i
\(120\) 21.7465 3.61218i 1.98517 0.329745i
\(121\) −1.97094 1.13792i −0.179177 0.103448i
\(122\) −1.59345 11.1354i −0.144264 1.00815i
\(123\) −14.0259 + 3.75822i −1.26467 + 0.338867i
\(124\) 15.3364 9.32001i 1.37725 0.836962i
\(125\) −0.711203 0.711203i −0.0636119 0.0636119i
\(126\) −2.51292 + 1.07412i −0.223869 + 0.0956899i
\(127\) −6.04172 10.4646i −0.536116 0.928580i −0.999108 0.0422176i \(-0.986558\pi\)
0.462993 0.886362i \(-0.346776\pi\)
\(128\) 0.591017 11.2983i 0.0522390 0.998635i
\(129\) 18.0775i 1.59163i
\(130\) 13.1103 8.92831i 1.14985 0.783065i
\(131\) 19.1689i 1.67479i 0.546597 + 0.837396i \(0.315923\pi\)
−0.546597 + 0.837396i \(0.684077\pi\)
\(132\) 0.332510 + 14.7970i 0.0289412 + 1.28791i
\(133\) −0.952039 1.64898i −0.0825523 0.142985i
\(134\) −4.13215 9.66728i −0.356964 0.835126i
\(135\) −1.52893 1.52893i −0.131589 0.131589i
\(136\) 0.732105 7.50835i 0.0627775 0.643836i
\(137\) −7.01027 + 1.87840i −0.598927 + 0.160482i −0.545530 0.838091i \(-0.683672\pi\)
−0.0533974 + 0.998573i \(0.517005\pi\)
\(138\) 7.23088 1.03473i 0.615533 0.0880819i
\(139\) 9.61885 + 5.55344i 0.815860 + 0.471037i 0.848987 0.528414i \(-0.177213\pi\)
−0.0331268 + 0.999451i \(0.510547\pi\)
\(140\) −2.53494 + 2.65148i −0.214241 + 0.224091i
\(141\) 2.90539 10.8431i 0.244678 0.913152i
\(142\) 1.73904 2.31986i 0.145937 0.194678i
\(143\) 4.68716 + 9.56266i 0.391960 + 0.799670i
\(144\) −11.0474 + 7.05823i −0.920620 + 0.588186i
\(145\) 3.73679 + 1.00127i 0.310324 + 0.0831509i
\(146\) −0.0873915 0.0105080i −0.00723257 0.000869647i
\(147\) −8.33367 + 14.4343i −0.687349 + 1.19052i
\(148\) 0.907978 + 0.497365i 0.0746354 + 0.0408832i
\(149\) 1.34497 + 5.01948i 0.110184 + 0.411212i 0.998882 0.0472817i \(-0.0150558\pi\)
−0.888698 + 0.458494i \(0.848389\pi\)
\(150\) −15.3797 6.16898i −1.25574 0.503695i
\(151\) 3.67697 3.67697i 0.299227 0.299227i −0.541484 0.840711i \(-0.682137\pi\)
0.840711 + 0.541484i \(0.182137\pi\)
\(152\) −5.80144 7.05501i −0.470559 0.572237i
\(153\) −7.57039 + 4.37076i −0.612029 + 0.353355i
\(154\) −1.52117 1.93698i −0.122579 0.156086i
\(155\) −27.9130 −2.24202
\(156\) −9.73433 + 15.2207i −0.779370 + 1.21863i
\(157\) −10.7605 −0.858780 −0.429390 0.903119i \(-0.641271\pi\)
−0.429390 + 0.903119i \(0.641271\pi\)
\(158\) −2.38706 3.03956i −0.189905 0.241815i
\(159\) −7.97767 + 4.60591i −0.632671 + 0.365272i
\(160\) −9.91172 + 14.5400i −0.783590 + 1.14949i
\(161\) −0.859490 + 0.859490i −0.0677373 + 0.0677373i
\(162\) −10.6196 4.25966i −0.834355 0.334670i
\(163\) −3.67817 13.7271i −0.288097 1.07519i −0.946547 0.322567i \(-0.895454\pi\)
0.658450 0.752625i \(-0.271213\pi\)
\(164\) 5.56858 10.1659i 0.434833 0.793821i
\(165\) 11.5103 19.9364i 0.896073 1.55204i
\(166\) 20.2232 + 2.43164i 1.56962 + 0.188732i
\(167\) 9.00303 + 2.41236i 0.696676 + 0.186674i 0.589741 0.807592i \(-0.299230\pi\)
0.106935 + 0.994266i \(0.465896\pi\)
\(168\) 1.46800 3.91198i 0.113259 0.301816i
\(169\) −1.75895 + 12.8805i −0.135304 + 0.990804i
\(170\) −7.03796 + 9.38857i −0.539787 + 0.720070i
\(171\) −2.73933 + 10.2233i −0.209482 + 0.781798i
\(172\) −10.4305 9.97200i −0.795316 0.760358i
\(173\) 19.8249 + 11.4459i 1.50726 + 0.870215i 0.999964 + 0.00844060i \(0.00268676\pi\)
0.507292 + 0.861774i \(0.330647\pi\)
\(174\) −4.36210 + 0.624210i −0.330690 + 0.0473213i
\(175\) 2.66348 0.713678i 0.201340 0.0539490i
\(176\) −8.72107 7.97053i −0.657376 0.600801i
\(177\) 12.4871 + 12.4871i 0.938588 + 0.938588i
\(178\) 4.61221 + 10.7904i 0.345700 + 0.808774i
\(179\) 6.60927 + 11.4476i 0.494000 + 0.855633i 0.999976 0.00691464i \(-0.00220102\pi\)
−0.505976 + 0.862547i \(0.668868\pi\)
\(180\) 20.3853 0.458087i 1.51943 0.0341438i
\(181\) 26.1208i 1.94154i −0.240009 0.970771i \(-0.577151\pi\)
0.240009 0.970771i \(-0.422849\pi\)
\(182\) −0.223095 2.99817i −0.0165369 0.222239i
\(183\) 19.9288i 1.47318i
\(184\) −3.39171 + 4.74290i −0.250040 + 0.349651i
\(185\) −0.805117 1.39450i −0.0591934 0.102526i
\(186\) 29.2355 12.4964i 2.14365 0.916277i
\(187\) −5.57059 5.57059i −0.407362 0.407362i
\(188\) 4.65362 + 7.65768i 0.339400 + 0.558494i
\(189\) −0.395870 + 0.106073i −0.0287953 + 0.00771568i
\(190\) 2.01246 + 14.0635i 0.145999 + 1.02027i
\(191\) −12.2440 7.06905i −0.885942 0.511499i −0.0133290 0.999911i \(-0.504243\pi\)
−0.872613 + 0.488412i \(0.837576\pi\)
\(192\) 3.87195 19.6663i 0.279434 1.41929i
\(193\) −6.00426 + 22.4082i −0.432196 + 1.61298i 0.315493 + 0.948928i \(0.397830\pi\)
−0.747689 + 0.664049i \(0.768837\pi\)
\(194\) 5.36588 + 4.02243i 0.385247 + 0.288793i
\(195\) 25.2331 12.3681i 1.80698 0.885696i
\(196\) −3.73136 12.7708i −0.266526 0.912197i
\(197\) 5.99473 + 1.60628i 0.427107 + 0.114443i 0.465968 0.884802i \(-0.345706\pi\)
−0.0388607 + 0.999245i \(0.512373\pi\)
\(198\) −1.63434 + 13.5923i −0.116148 + 0.965962i
\(199\) −1.50716 + 2.61048i −0.106840 + 0.185052i −0.914488 0.404612i \(-0.867407\pi\)
0.807649 + 0.589664i \(0.200740\pi\)
\(200\) 12.0432 5.47090i 0.851585 0.386851i
\(201\) −4.82075 17.9913i −0.340029 1.26901i
\(202\) −4.72700 + 11.7847i −0.332590 + 0.829169i
\(203\) 0.518497 0.518497i 0.0363913 0.0363913i
\(204\) 3.16826 12.9842i 0.221823 0.909079i
\(205\) −15.6131 + 9.01422i −1.09046 + 0.629580i
\(206\) −10.6793 + 8.38678i −0.744062 + 0.584335i
\(207\) 6.75647 0.469607
\(208\) −3.41243 14.0127i −0.236609 0.971605i
\(209\) −9.53844 −0.659788
\(210\) −5.11113 + 4.01393i −0.352702 + 0.276988i
\(211\) 15.7735 9.10682i 1.08589 0.626940i 0.153412 0.988162i \(-0.450974\pi\)
0.932480 + 0.361223i \(0.117641\pi\)
\(212\) 1.74313 7.14375i 0.119719 0.490634i
\(213\) 3.63208 3.63208i 0.248866 0.248866i
\(214\) −9.93142 + 24.7597i −0.678898 + 1.69254i
\(215\) 5.80907 + 21.6797i 0.396175 + 1.47855i
\(216\) −1.78997 + 0.813133i −0.121792 + 0.0553267i
\(217\) −2.64534 + 4.58187i −0.179578 + 0.311038i
\(218\) 0.704946 5.86281i 0.0477450 0.397080i
\(219\) −0.150628 0.0403607i −0.0101785 0.00272732i
\(220\) 5.15367 + 17.6387i 0.347460 + 1.18920i
\(221\) −1.85339 9.43641i −0.124672 0.634762i
\(222\) 1.46757 + 1.10014i 0.0984969 + 0.0738363i
\(223\) −0.919045 + 3.42992i −0.0615438 + 0.229685i −0.989846 0.142141i \(-0.954601\pi\)
0.928303 + 0.371826i \(0.121268\pi\)
\(224\) 1.44737 + 3.00496i 0.0967066 + 0.200778i
\(225\) −13.2740 7.66372i −0.884931 0.510915i
\(226\) −1.13044 7.89976i −0.0751960 0.525484i
\(227\) 16.8419 4.51279i 1.11784 0.299524i 0.347831 0.937557i \(-0.386918\pi\)
0.770009 + 0.638033i \(0.220252\pi\)
\(228\) −8.40388 13.8289i −0.556560 0.915838i
\(229\) −14.2869 14.2869i −0.944105 0.944105i 0.0544132 0.998519i \(-0.482671\pi\)
−0.998519 + 0.0544132i \(0.982671\pi\)
\(230\) 8.33925 3.56451i 0.549874 0.235037i
\(231\) −2.18168 3.77878i −0.143544 0.248626i
\(232\) 2.04609 2.86121i 0.134332 0.187847i
\(233\) 13.3205i 0.872655i −0.899788 0.436328i \(-0.856279\pi\)
0.899788 0.436328i \(-0.143721\pi\)
\(234\) −10.9075 + 12.6612i −0.713044 + 0.827690i
\(235\) 13.9374i 0.909174i
\(236\) −14.0931 + 0.316692i −0.917382 + 0.0206149i
\(237\) −3.42356 5.92978i −0.222384 0.385181i
\(238\) 0.874123 + 2.04503i 0.0566610 + 0.132560i
\(239\) 10.2493 + 10.2493i 0.662972 + 0.662972i 0.956079 0.293108i \(-0.0946894\pi\)
−0.293108 + 0.956079i \(0.594689\pi\)
\(240\) −21.0319 + 23.0124i −1.35761 + 1.48545i
\(241\) 13.3784 3.58474i 0.861781 0.230914i 0.199251 0.979949i \(-0.436149\pi\)
0.662531 + 0.749035i \(0.269482\pi\)
\(242\) 3.18608 0.455923i 0.204809 0.0293079i
\(243\) −19.3613 11.1782i −1.24203 0.717084i
\(244\) 11.4987 + 10.9932i 0.736127 + 0.703770i
\(245\) −5.35593 + 19.9886i −0.342178 + 1.27702i
\(246\) 12.3173 16.4311i 0.785322 1.04761i
\(247\) −9.66568 6.49216i −0.615013 0.413086i
\(248\) −8.91683 + 23.7618i −0.566219 + 1.50888i
\(249\) 34.8567 + 9.33982i 2.20895 + 0.591887i
\(250\) 1.41223 + 0.169807i 0.0893175 + 0.0107396i
\(251\) −1.25814 + 2.17916i −0.0794129 + 0.137547i −0.902997 0.429647i \(-0.858638\pi\)
0.823584 + 0.567195i \(0.191971\pi\)
\(252\) 1.85674 3.38962i 0.116964 0.213526i
\(253\) 1.57596 + 5.88156i 0.0990797 + 0.369770i
\(254\) 15.8602 + 6.36174i 0.995160 + 0.399171i
\(255\) −14.6992 + 14.6992i −0.920498 + 0.920498i
\(256\) 9.21132 + 13.0825i 0.575708 + 0.817656i
\(257\) 5.55423 3.20673i 0.346463 0.200031i −0.316663 0.948538i \(-0.602563\pi\)
0.663126 + 0.748507i \(0.269229\pi\)
\(258\) −15.7901 20.1063i −0.983049 1.25176i
\(259\) −0.305208 −0.0189647
\(260\) −6.78301 + 21.3817i −0.420664 + 1.32604i
\(261\) −4.07591 −0.252293
\(262\) −16.7434 21.3202i −1.03441 1.31716i
\(263\) −4.59709 + 2.65413i −0.283469 + 0.163661i −0.634993 0.772518i \(-0.718997\pi\)
0.351524 + 0.936179i \(0.385664\pi\)
\(264\) −13.2945 16.1672i −0.818220 0.995021i
\(265\) −8.08728 + 8.08728i −0.496798 + 0.496798i
\(266\) 2.49922 + 1.00247i 0.153237 + 0.0614652i
\(267\) 5.38080 + 20.0814i 0.329300 + 1.22896i
\(268\) 13.0400 + 7.14293i 0.796543 + 0.436324i
\(269\) 5.00048 8.66109i 0.304885 0.528076i −0.672351 0.740233i \(-0.734715\pi\)
0.977236 + 0.212157i \(0.0680487\pi\)
\(270\) 3.03599 + 0.365049i 0.184765 + 0.0222162i
\(271\) −24.6484 6.60453i −1.49729 0.401196i −0.585096 0.810964i \(-0.698943\pi\)
−0.912190 + 0.409768i \(0.865610\pi\)
\(272\) 5.74404 + 8.99048i 0.348283 + 0.545128i
\(273\) 0.361171 5.31411i 0.0218591 0.321625i
\(274\) 6.15630 8.21245i 0.371916 0.496132i
\(275\) 3.57515 13.3427i 0.215590 0.804592i
\(276\) −7.13859 + 7.46680i −0.429693 + 0.449448i
\(277\) 0.462736 + 0.267161i 0.0278031 + 0.0160521i 0.513837 0.857888i \(-0.328224\pi\)
−0.486034 + 0.873940i \(0.661557\pi\)
\(278\) −15.5491 + 2.22505i −0.932574 + 0.133450i
\(279\) 28.4066 7.61154i 1.70066 0.455691i
\(280\) 0.503444 5.16324i 0.0300865 0.308563i
\(281\) −0.275535 0.275535i −0.0164370 0.0164370i 0.698840 0.715278i \(-0.253700\pi\)
−0.715278 + 0.698840i \(0.753700\pi\)
\(282\) 6.23962 + 14.5978i 0.371564 + 0.869283i
\(283\) −8.03188 13.9116i −0.477446 0.826960i 0.522220 0.852811i \(-0.325104\pi\)
−0.999666 + 0.0258504i \(0.991771\pi\)
\(284\) 0.0921153 + 4.09921i 0.00546604 + 0.243243i
\(285\) 25.1692i 1.49090i
\(286\) −13.5659 6.54178i −0.802167 0.386824i
\(287\) 3.41715i 0.201708i
\(288\) 6.12214 17.5000i 0.360750 1.03119i
\(289\) −4.94304 8.56160i −0.290767 0.503624i
\(290\) −5.03074 + 2.15033i −0.295415 + 0.126271i
\(291\) 8.40107 + 8.40107i 0.492479 + 0.492479i
\(292\) 0.106378 0.0646464i 0.00622529 0.00378314i
\(293\) 1.97920 0.530326i 0.115626 0.0309820i −0.200542 0.979685i \(-0.564270\pi\)
0.316168 + 0.948703i \(0.397604\pi\)
\(294\) −3.33898 23.3335i −0.194734 1.36084i
\(295\) 18.9880 + 10.9627i 1.10552 + 0.638275i
\(296\) −1.44431 + 0.239906i −0.0839490 + 0.0139443i
\(297\) −0.531371 + 1.98310i −0.0308333 + 0.115071i
\(298\) −5.88027 4.40803i −0.340635 0.255350i
\(299\) −2.40619 + 7.03266i −0.139153 + 0.406709i
\(300\) 22.4941 6.57233i 1.29870 0.379454i
\(301\) 4.10923 + 1.10106i 0.236852 + 0.0634643i
\(302\) −0.877916 + 7.30135i −0.0505184 + 0.420145i
\(303\) −11.2476 + 19.4814i −0.646159 + 1.11918i
\(304\) 12.6149 + 2.77942i 0.723511 + 0.159410i
\(305\) −6.40398 23.9000i −0.366691 1.36851i
\(306\) 4.60228 11.4738i 0.263095 0.655912i
\(307\) −11.4337 + 11.4337i −0.652558 + 0.652558i −0.953608 0.301050i \(-0.902663\pi\)
0.301050 + 0.953608i \(0.402663\pi\)
\(308\) 3.38378 + 0.825671i 0.192809 + 0.0470470i
\(309\) −20.8339 + 12.0284i −1.18520 + 0.684274i
\(310\) 31.0456 24.3811i 1.76327 1.38475i
\(311\) −24.0242 −1.36229 −0.681143 0.732151i \(-0.738517\pi\)
−0.681143 + 0.732151i \(0.738517\pi\)
\(312\) −2.46797 25.4315i −0.139722 1.43978i
\(313\) 28.9008 1.63357 0.816786 0.576941i \(-0.195754\pi\)
0.816786 + 0.576941i \(0.195754\pi\)
\(314\) 11.9681 9.39894i 0.675400 0.530413i
\(315\) −5.20590 + 3.00563i −0.293319 + 0.169348i
\(316\) 5.30993 + 1.29567i 0.298707 + 0.0728870i
\(317\) 0.0141017 0.0141017i 0.000792031 0.000792031i −0.706711 0.707503i \(-0.749822\pi\)
0.707503 + 0.706711i \(0.249822\pi\)
\(318\) 4.84988 12.0911i 0.271968 0.678034i
\(319\) −0.950714 3.54811i −0.0532297 0.198656i
\(320\) −1.67611 24.8294i −0.0936976 1.38800i
\(321\) −23.6312 + 40.9305i −1.31897 + 2.28452i
\(322\) 0.205213 1.70669i 0.0114361 0.0951100i
\(323\) 8.31982 + 2.22929i 0.462927 + 0.124041i
\(324\) 15.5321 4.53817i 0.862894 0.252120i
\(325\) 12.7043 11.0873i 0.704706 0.615012i
\(326\) 16.0812 + 12.0549i 0.890654 + 0.667662i
\(327\) 2.70767 10.1051i 0.149734 0.558816i
\(328\) 2.68603 + 16.1707i 0.148311 + 0.892880i
\(329\) −2.28780 1.32086i −0.126130 0.0728214i
\(330\) 4.61173 + 32.2277i 0.253867 + 1.77407i
\(331\) 4.08070 1.09342i 0.224295 0.0600998i −0.144921 0.989443i \(-0.546293\pi\)
0.369216 + 0.929343i \(0.379626\pi\)
\(332\) −24.6168 + 14.9598i −1.35102 + 0.821023i
\(333\) 1.19962 + 1.19962i 0.0657389 + 0.0657389i
\(334\) −12.1205 + 5.18077i −0.663207 + 0.283479i
\(335\) −11.5627 20.0272i −0.631739 1.09420i
\(336\) 1.78423 + 5.63327i 0.0973378 + 0.307320i
\(337\) 9.58550i 0.522155i 0.965318 + 0.261078i \(0.0840778\pi\)
−0.965318 + 0.261078i \(0.915922\pi\)
\(338\) −9.29431 15.8624i −0.505544 0.862801i
\(339\) 14.1381i 0.767877i
\(340\) −0.372794 16.5897i −0.0202176 0.899701i
\(341\) 13.2518 + 22.9528i 0.717625 + 1.24296i
\(342\) −5.88299 13.7634i −0.318116 0.744240i
\(343\) 5.69196 + 5.69196i 0.307337 + 0.307337i
\(344\) 20.3113 + 1.98046i 1.09511 + 0.106779i
\(345\) 15.5197 4.15850i 0.835555 0.223886i
\(346\) −32.0474 + 4.58593i −1.72288 + 0.246541i
\(347\) 3.56473 + 2.05810i 0.191364 + 0.110484i 0.592621 0.805481i \(-0.298093\pi\)
−0.401257 + 0.915966i \(0.631426\pi\)
\(348\) 4.30643 4.50442i 0.230849 0.241463i
\(349\) 7.51958 28.0634i 0.402514 1.50220i −0.406082 0.913837i \(-0.633105\pi\)
0.808595 0.588365i \(-0.200228\pi\)
\(350\) −2.33903 + 3.12024i −0.125026 + 0.166784i
\(351\) −1.88822 + 1.64789i −0.100786 + 0.0879579i
\(352\) 16.6618 + 1.24747i 0.888079 + 0.0664904i
\(353\) −25.4328 6.81469i −1.35365 0.362709i −0.492169 0.870500i \(-0.663796\pi\)
−0.861481 + 0.507790i \(0.830463\pi\)
\(354\) −24.7956 2.98143i −1.31787 0.158461i
\(355\) 3.18869 5.52298i 0.169238 0.293129i
\(356\) −14.5549 7.97277i −0.771408 0.422556i
\(357\) 1.01979 + 3.80591i 0.0539730 + 0.201430i
\(358\) −17.3501 6.95935i −0.916982 0.367813i
\(359\) 7.69873 7.69873i 0.406324 0.406324i −0.474131 0.880454i \(-0.657238\pi\)
0.880454 + 0.474131i \(0.157238\pi\)
\(360\) −22.2730 + 18.3154i −1.17389 + 0.965305i
\(361\) −7.42294 + 4.28564i −0.390681 + 0.225560i
\(362\) 22.8157 + 29.0523i 1.19916 + 1.52695i
\(363\) 5.70210 0.299282
\(364\) 2.86694 + 3.13979i 0.150269 + 0.164570i
\(365\) −0.193613 −0.0101342
\(366\) 17.4072 + 22.1654i 0.909889 + 1.15861i
\(367\) −1.81711 + 1.04911i −0.0948522 + 0.0547630i −0.546676 0.837344i \(-0.684107\pi\)
0.451824 + 0.892107i \(0.350774\pi\)
\(368\) −0.370415 8.23775i −0.0193092 0.429422i
\(369\) 13.4311 13.4311i 0.699198 0.699198i
\(370\) 2.11353 + 0.847764i 0.109877 + 0.0440731i
\(371\) 0.561074 + 2.09396i 0.0291295 + 0.108713i
\(372\) −21.6015 + 39.4351i −1.11998 + 2.04462i
\(373\) 14.1524 24.5126i 0.732781 1.26921i −0.222909 0.974839i \(-0.571555\pi\)
0.955690 0.294375i \(-0.0951114\pi\)
\(374\) 11.0615 + 1.33004i 0.571976 + 0.0687746i
\(375\) 2.43413 + 0.652222i 0.125698 + 0.0336806i
\(376\) −11.8646 4.45231i −0.611872 0.229610i
\(377\) 1.45156 4.24253i 0.0747590 0.218501i
\(378\) 0.347647 0.463757i 0.0178810 0.0238531i
\(379\) −7.48268 + 27.9257i −0.384360 + 1.43445i 0.454814 + 0.890586i \(0.349706\pi\)
−0.839174 + 0.543863i \(0.816961\pi\)
\(380\) −14.5223 13.8840i −0.744978 0.712232i
\(381\) 26.2187 + 15.1374i 1.34323 + 0.775512i
\(382\) 19.7927 2.83230i 1.01268 0.144913i
\(383\) 14.6205 3.91754i 0.747070 0.200177i 0.134852 0.990866i \(-0.456944\pi\)
0.612218 + 0.790689i \(0.290277\pi\)
\(384\) 12.8714 + 25.2555i 0.656840 + 1.28881i
\(385\) −3.83070 3.83070i −0.195231 0.195231i
\(386\) −12.8947 30.1676i −0.656325 1.53549i
\(387\) −11.8236 20.4791i −0.601028 1.04101i
\(388\) −9.48154 + 0.213064i −0.481352 + 0.0108167i
\(389\) 30.3695i 1.53979i 0.638168 + 0.769897i \(0.279692\pi\)
−0.638168 + 0.769897i \(0.720308\pi\)
\(390\) −17.2619 + 35.7965i −0.874090 + 1.81262i
\(391\) 5.49846i 0.278069i
\(392\) 15.3050 + 10.9448i 0.773018 + 0.552795i
\(393\) −24.0136 41.5928i −1.21133 2.09808i
\(394\) −8.07056 + 3.44965i −0.406589 + 0.173791i
\(395\) −6.01125 6.01125i −0.302459 0.302459i
\(396\) −10.0547 16.5453i −0.505266 0.831432i
\(397\) −15.4588 + 4.14218i −0.775857 + 0.207890i −0.624957 0.780659i \(-0.714884\pi\)
−0.150899 + 0.988549i \(0.548217\pi\)
\(398\) −0.603862 4.21990i −0.0302689 0.211525i
\(399\) 4.13149 + 2.38531i 0.206833 + 0.119415i
\(400\) −8.61617 + 16.6043i −0.430809 + 0.830213i
\(401\) 3.56354 13.2993i 0.177955 0.664137i −0.818075 0.575112i \(-0.804958\pi\)
0.996029 0.0890245i \(-0.0283749\pi\)
\(402\) 21.0766 + 15.7996i 1.05120 + 0.788014i
\(403\) −2.19380 + 32.2786i −0.109281 + 1.60791i
\(404\) −5.03606 17.2362i −0.250554 0.857532i
\(405\) −24.3106 6.51401i −1.20800 0.323684i
\(406\) −0.123797 + 1.02958i −0.00614393 + 0.0510971i
\(407\) −0.764465 + 1.32409i −0.0378931 + 0.0656328i
\(408\) 7.81748 + 17.2088i 0.387023 + 0.851964i
\(409\) 0.151353 + 0.564858i 0.00748394 + 0.0279305i 0.969567 0.244827i \(-0.0787311\pi\)
−0.962083 + 0.272757i \(0.912064\pi\)
\(410\) 9.49169 23.6634i 0.468761 1.16865i
\(411\) 12.8578 12.8578i 0.634228 0.634228i
\(412\) 4.55223 18.6560i 0.224272 0.919117i
\(413\) 3.59903 2.07790i 0.177097 0.102247i
\(414\) −7.51475 + 5.90156i −0.369330 + 0.290046i
\(415\) 44.8037 2.19933
\(416\) 16.0350 + 12.6047i 0.786182 + 0.617995i
\(417\) −27.8281 −1.36275
\(418\) 10.6089 8.33152i 0.518900 0.407508i
\(419\) −31.9541 + 18.4487i −1.56106 + 0.901278i −0.563910 + 0.825836i \(0.690703\pi\)
−0.997150 + 0.0754420i \(0.975963\pi\)
\(420\) 2.17871 8.92882i 0.106310 0.435682i
\(421\) −22.1875 + 22.1875i −1.08135 + 1.08135i −0.0849697 + 0.996384i \(0.527079\pi\)
−0.996384 + 0.0849697i \(0.972921\pi\)
\(422\) −9.58920 + 23.9065i −0.466795 + 1.16375i
\(423\) 3.80056 + 14.1839i 0.184789 + 0.689643i
\(424\) 4.30107 + 9.46805i 0.208878 + 0.459809i
\(425\) −6.23679 + 10.8024i −0.302529 + 0.523995i
\(426\) −0.867199 + 7.21222i −0.0420159 + 0.349433i
\(427\) −4.53006 1.21383i −0.219225 0.0587411i
\(428\) −10.5808 36.2132i −0.511441 1.75043i
\(429\) −22.1498 14.8774i −1.06940 0.718285i
\(430\) −25.3976 19.0388i −1.22478 0.918132i
\(431\) 8.05023 30.0439i 0.387766 1.44716i −0.445994 0.895036i \(-0.647150\pi\)
0.833760 0.552127i \(-0.186183\pi\)
\(432\) 1.28061 2.46787i 0.0616134 0.118736i
\(433\) 9.34712 + 5.39656i 0.449194 + 0.259342i 0.707490 0.706724i \(-0.249828\pi\)
−0.258296 + 0.966066i \(0.583161\pi\)
\(434\) −1.05989 7.40671i −0.0508763 0.355534i
\(435\) −9.36245 + 2.50866i −0.448895 + 0.120281i
\(436\) 4.33692 + 7.13654i 0.207701 + 0.341778i
\(437\) −4.70747 4.70747i −0.225189 0.225189i
\(438\) 0.202787 0.0866785i 0.00968952 0.00414166i
\(439\) −6.48316 11.2292i −0.309424 0.535938i 0.668812 0.743431i \(-0.266803\pi\)
−0.978237 + 0.207493i \(0.933470\pi\)
\(440\) −21.1389 15.1167i −1.00776 0.720659i
\(441\) 21.8026i 1.03822i
\(442\) 10.3038 + 8.87658i 0.490101 + 0.422216i
\(443\) 15.6512i 0.743611i −0.928311 0.371805i \(-0.878739\pi\)
0.928311 0.371805i \(-0.121261\pi\)
\(444\) −2.59321 + 0.0582732i −0.123068 + 0.00276552i
\(445\) 12.9060 + 22.3539i 0.611805 + 1.05968i
\(446\) −1.97374 4.61762i −0.0934593 0.218650i
\(447\) −9.20642 9.20642i −0.435449 0.435449i
\(448\) −4.23455 2.07798i −0.200064 0.0981751i
\(449\) 10.8227 2.89994i 0.510755 0.136856i 0.00576812 0.999983i \(-0.498164\pi\)
0.504987 + 0.863127i \(0.331497\pi\)
\(450\) 21.4577 3.07056i 1.01153 0.144748i
\(451\) 14.8247 + 8.55907i 0.698070 + 0.403031i
\(452\) 8.15750 + 7.79893i 0.383696 + 0.366831i
\(453\) −3.37203 + 12.5846i −0.158432 + 0.591276i
\(454\) −14.7903 + 19.7302i −0.694145 + 0.925982i
\(455\) −1.27451 6.48910i −0.0597500 0.304214i
\(456\) 21.4261 + 8.04033i 1.00337 + 0.376523i
\(457\) 18.5601 + 4.97316i 0.868204 + 0.232634i 0.665311 0.746566i \(-0.268299\pi\)
0.202893 + 0.979201i \(0.434966\pi\)
\(458\) 28.3695 + 3.41115i 1.32562 + 0.159393i
\(459\) 0.926967 1.60555i 0.0432671 0.0749408i
\(460\) −6.16168 + 11.2486i −0.287290 + 0.524470i
\(461\) 6.34751 + 23.6892i 0.295633 + 1.10332i 0.940713 + 0.339202i \(0.110157\pi\)
−0.645081 + 0.764114i \(0.723176\pi\)
\(462\) 5.72718 + 2.29724i 0.266452 + 0.106877i
\(463\) 13.2027 13.2027i 0.613581 0.613581i −0.330296 0.943877i \(-0.607149\pi\)
0.943877 + 0.330296i \(0.107149\pi\)
\(464\) 0.223457 + 4.96951i 0.0103737 + 0.230704i
\(465\) 60.5658 34.9677i 2.80867 1.62159i
\(466\) 11.6350 + 14.8155i 0.538983 + 0.686313i
\(467\) 22.6548 1.04834 0.524171 0.851613i \(-0.324375\pi\)
0.524171 + 0.851613i \(0.324375\pi\)
\(468\) 1.07243 23.6095i 0.0495731 1.09135i
\(469\) −4.38325 −0.202400
\(470\) 12.1738 + 15.5015i 0.561538 + 0.715033i
\(471\) 23.3482 13.4801i 1.07583 0.621130i
\(472\) 15.3981 12.6621i 0.708756 0.582820i
\(473\) 15.0693 15.0693i 0.692888 0.692888i
\(474\) 8.98726 + 3.60490i 0.412798 + 0.165579i
\(475\) 3.90885 + 14.5880i 0.179350 + 0.669344i
\(476\) −2.75850 1.51103i −0.126436 0.0692579i
\(477\) 6.02501 10.4356i 0.275866 0.477814i
\(478\) −20.3520 2.44713i −0.930879 0.111929i
\(479\) −3.13701 0.840559i −0.143334 0.0384061i 0.186439 0.982467i \(-0.440305\pi\)
−0.329772 + 0.944060i \(0.606972\pi\)
\(480\) 3.29172 43.9658i 0.150246 2.00676i
\(481\) −1.67588 + 0.821438i −0.0764136 + 0.0374543i
\(482\) −11.7487 + 15.6727i −0.535140 + 0.713872i
\(483\) 0.788212 2.94165i 0.0358649 0.133850i
\(484\) −3.14542 + 3.29003i −0.142974 + 0.149547i
\(485\) 12.7747 + 7.37550i 0.580071 + 0.334904i
\(486\) 31.2980 4.47870i 1.41971 0.203158i
\(487\) −41.4268 + 11.1003i −1.87723 + 0.503002i −0.877503 + 0.479571i \(0.840792\pi\)
−0.999725 + 0.0234304i \(0.992541\pi\)
\(488\) −22.3914 2.18328i −1.01361 0.0988326i
\(489\) 25.1775 + 25.1775i 1.13856 + 1.13856i
\(490\) −11.5024 26.9101i −0.519624 1.21568i
\(491\) 0.796904 + 1.38028i 0.0359638 + 0.0622911i 0.883447 0.468531i \(-0.155217\pi\)
−0.847483 + 0.530822i \(0.821883\pi\)
\(492\) 0.652435 + 29.0340i 0.0294141 + 1.30895i
\(493\) 3.31701i 0.149390i
\(494\) 16.4211 1.22190i 0.738822 0.0549759i
\(495\) 30.1132i 1.35349i
\(496\) −10.8376 34.2172i −0.486624 1.53640i
\(497\) −0.604392 1.04684i −0.0271107 0.0469571i
\(498\) −46.9266 + 20.0582i −2.10283 + 0.898828i
\(499\) 2.89721 + 2.89721i 0.129697 + 0.129697i 0.768975 0.639278i \(-0.220767\pi\)
−0.639278 + 0.768975i \(0.720767\pi\)
\(500\) −1.71905 + 1.04468i −0.0768782 + 0.0467193i
\(501\) −22.5569 + 6.04411i −1.00777 + 0.270031i
\(502\) −0.504088 3.52267i −0.0224986 0.157224i
\(503\) −13.0990 7.56273i −0.584057 0.337205i 0.178687 0.983906i \(-0.442815\pi\)
−0.762744 + 0.646701i \(0.776148\pi\)
\(504\) 0.895607 + 5.39184i 0.0398935 + 0.240172i
\(505\) −7.22868 + 26.9778i −0.321672 + 1.20050i
\(506\) −6.89018 5.16509i −0.306306 0.229616i
\(507\) −12.3193 30.1516i −0.547118 1.33908i
\(508\) −23.1970 + 6.77770i −1.02920 + 0.300712i
\(509\) −24.1589 6.47337i −1.07083 0.286927i −0.319994 0.947420i \(-0.603681\pi\)
−0.750832 + 0.660493i \(0.770347\pi\)
\(510\) 3.50959 29.1881i 0.155407 1.29247i
\(511\) −0.0183489 + 0.0317812i −0.000811708 + 0.00140592i
\(512\) −21.6722 6.50493i −0.957787 0.287480i
\(513\) −0.580967 2.16820i −0.0256503 0.0957284i
\(514\) −3.37659 + 8.41806i −0.148935 + 0.371305i
\(515\) −21.1201 + 21.1201i −0.930663 + 0.930663i
\(516\) 35.1244 + 8.57066i 1.54627 + 0.377302i
\(517\) −11.4607 + 6.61682i −0.504040 + 0.291007i
\(518\) 0.339461 0.266589i 0.0149150 0.0117133i
\(519\) −57.3549 −2.51760
\(520\) −11.1320 29.7061i −0.488170 1.30270i
\(521\) −41.1166 −1.80135 −0.900675 0.434494i \(-0.856927\pi\)
−0.900675 + 0.434494i \(0.856927\pi\)
\(522\) 4.53335 3.56018i 0.198419 0.155825i
\(523\) 2.27834 1.31540i 0.0996249 0.0575185i −0.449360 0.893351i \(-0.648348\pi\)
0.548985 + 0.835832i \(0.315015\pi\)
\(524\) 37.2450 + 9.08809i 1.62705 + 0.397015i
\(525\) −4.88519 + 4.88519i −0.213207 + 0.213207i
\(526\) 2.79472 6.96741i 0.121856 0.303794i
\(527\) −6.19432 23.1175i −0.269829 1.00702i
\(528\) 28.9081 + 6.36928i 1.25806 + 0.277187i
\(529\) 9.37507 16.2381i 0.407612 0.706004i
\(530\) 1.93093 16.0589i 0.0838741 0.697554i
\(531\) −22.3132 5.97882i −0.968312 0.259459i
\(532\) −3.65533 + 1.06801i −0.158478 + 0.0463042i
\(533\) 9.19694 + 18.7634i 0.398364 + 0.812734i
\(534\) −23.5252 17.6352i −1.01803 0.763149i
\(535\) −15.1875 + 56.6804i −0.656611 + 2.45051i
\(536\) −20.7425 + 3.44542i −0.895941 + 0.148820i
\(537\) −28.6817 16.5594i −1.23771 0.714590i
\(538\) 2.00350 + 14.0009i 0.0863772 + 0.603621i
\(539\) 18.9793 5.08549i 0.817497 0.219048i
\(540\) −3.69558 + 2.24583i −0.159032 + 0.0966449i
\(541\) 14.2591 + 14.2591i 0.613047 + 0.613047i 0.943739 0.330692i \(-0.107282\pi\)
−0.330692 + 0.943739i \(0.607282\pi\)
\(542\) 33.1835 14.1839i 1.42536 0.609249i
\(543\) 32.7225 + 56.6771i 1.40426 + 2.43225i
\(544\) −14.2416 4.98224i −0.610603 0.213612i
\(545\) 12.9889i 0.556381i
\(546\) 4.24000 + 6.22598i 0.181455 + 0.266447i
\(547\) 40.9532i 1.75103i 0.483190 + 0.875515i \(0.339478\pi\)
−0.483190 + 0.875515i \(0.660522\pi\)
\(548\) 0.326094 + 14.5115i 0.0139300 + 0.619899i
\(549\) 13.0345 + 22.5764i 0.556298 + 0.963537i
\(550\) 7.67799 + 17.9629i 0.327391 + 0.765939i
\(551\) 2.83983 + 2.83983i 0.120981 + 0.120981i
\(552\) 1.41774 14.5401i 0.0603431 0.618869i
\(553\) −1.55643 + 0.417045i −0.0661862 + 0.0177345i
\(554\) −0.748024 + 0.107041i −0.0317805 + 0.00454774i
\(555\) 3.49390 + 2.01721i 0.148308 + 0.0856256i
\(556\) 15.3507 16.0564i 0.651013 0.680944i
\(557\) 7.78980 29.0719i 0.330064 1.23182i −0.579058 0.815287i \(-0.696579\pi\)
0.909122 0.416530i \(-0.136754\pi\)
\(558\) −24.9463 + 33.2781i −1.05606 + 1.40877i
\(559\) 25.5270 5.01370i 1.07968 0.212057i
\(560\) 3.94998 + 6.18245i 0.166917 + 0.261256i
\(561\) 19.0656 + 5.10861i 0.804950 + 0.215686i
\(562\) 0.547129 + 0.0657870i 0.0230793 + 0.00277506i
\(563\) 7.94721 13.7650i 0.334935 0.580124i −0.648537 0.761183i \(-0.724619\pi\)
0.983472 + 0.181058i \(0.0579523\pi\)
\(564\) −19.6906 10.7859i −0.829122 0.454170i
\(565\) −4.54318 16.9554i −0.191133 0.713318i
\(566\) 21.0847 + 8.45732i 0.886254 + 0.355488i
\(567\) −3.37321 + 3.37321i −0.141661 + 0.141661i
\(568\) −3.68298 4.47880i −0.154535 0.187926i
\(569\) −19.5646 + 11.2956i −0.820192 + 0.473538i −0.850483 0.526003i \(-0.823690\pi\)
0.0302909 + 0.999541i \(0.490357\pi\)
\(570\) −21.9845 27.9939i −0.920829 1.17254i
\(571\) 2.17784 0.0911398 0.0455699 0.998961i \(-0.485490\pi\)
0.0455699 + 0.998961i \(0.485490\pi\)
\(572\) 20.8024 4.57340i 0.869792 0.191223i
\(573\) 35.4227 1.47981
\(574\) −2.98477 3.80065i −0.124582 0.158636i
\(575\) 8.34938 4.82052i 0.348193 0.201030i
\(576\) 8.47643 + 24.8114i 0.353185 + 1.03381i
\(577\) 15.8624 15.8624i 0.660361 0.660361i −0.295104 0.955465i \(-0.595354\pi\)
0.955465 + 0.295104i \(0.0953543\pi\)
\(578\) 12.9761 + 5.20487i 0.539734 + 0.216494i
\(579\) −15.0435 56.1433i −0.625188 2.33323i
\(580\) 3.71710 6.78585i 0.154344 0.281767i
\(581\) 4.24610 7.35446i 0.176158 0.305115i
\(582\) −16.6820 2.00585i −0.691490 0.0831450i
\(583\) 10.4896 + 2.81069i 0.434436 + 0.116407i
\(584\) −0.0618498 + 0.164819i −0.00255936 + 0.00682027i
\(585\) −20.4960 + 30.5150i −0.847406 + 1.26164i
\(586\) −1.73810 + 2.31861i −0.0718004 + 0.0957811i
\(587\) 5.61437 20.9531i 0.231730 0.864827i −0.747866 0.663850i \(-0.768921\pi\)
0.979596 0.200978i \(-0.0644119\pi\)
\(588\) 24.0948 + 23.0357i 0.993651 + 0.949975i
\(589\) −25.0951 14.4887i −1.03403 0.596996i
\(590\) −30.6946 + 4.39235i −1.26368 + 0.180830i
\(591\) −15.0197 + 4.02451i −0.617827 + 0.165546i
\(592\) 1.39686 1.52839i 0.0574104 0.0628165i
\(593\) 0.858298 + 0.858298i 0.0352461 + 0.0352461i 0.724510 0.689264i \(-0.242066\pi\)
−0.689264 + 0.724510i \(0.742066\pi\)
\(594\) −1.14117 2.66980i −0.0468228 0.109543i
\(595\) 2.44600 + 4.23660i 0.100276 + 0.173683i
\(596\) 10.3905 0.233489i 0.425611 0.00956409i
\(597\) 7.55231i 0.309096i
\(598\) −3.46658 9.92366i −0.141759 0.405809i
\(599\) 7.16374i 0.292702i −0.989233 0.146351i \(-0.953247\pi\)
0.989233 0.146351i \(-0.0467529\pi\)
\(600\) −19.2779 + 26.9578i −0.787016 + 1.10055i
\(601\) −8.02549 13.9006i −0.327367 0.567016i 0.654622 0.755956i \(-0.272828\pi\)
−0.981988 + 0.188941i \(0.939495\pi\)
\(602\) −5.53215 + 2.36464i −0.225473 + 0.0963757i
\(603\) 17.2284 + 17.2284i 0.701595 + 0.701595i
\(604\) −5.40105 8.88760i −0.219766 0.361631i
\(605\) 6.83834 1.83233i 0.278018 0.0744947i
\(606\) −4.50649 31.4923i −0.183064 1.27929i
\(607\) −30.3120 17.5006i −1.23033 0.710329i −0.263229 0.964734i \(-0.584787\pi\)
−0.967098 + 0.254404i \(0.918121\pi\)
\(608\) −16.4583 + 7.92732i −0.667474 + 0.321495i
\(609\) −0.475497 + 1.77458i −0.0192681 + 0.0719096i
\(610\) 27.9986 + 20.9886i 1.13363 + 0.849803i
\(611\) −16.1172 1.09540i −0.652031 0.0443150i
\(612\) 4.90319 + 16.7814i 0.198200 + 0.678349i
\(613\) 19.8339 + 5.31448i 0.801084 + 0.214650i 0.636060 0.771640i \(-0.280563\pi\)
0.165024 + 0.986290i \(0.447230\pi\)
\(614\) 2.72993 22.7039i 0.110171 0.916256i
\(615\) 22.5849 39.1183i 0.910712 1.57740i
\(616\) −4.48473 + 2.03729i −0.180695 + 0.0820847i
\(617\) 4.87361 + 18.1886i 0.196204 + 0.732244i 0.991952 + 0.126616i \(0.0404115\pi\)
−0.795748 + 0.605628i \(0.792922\pi\)
\(618\) 12.6656 31.5761i 0.509484 1.27018i
\(619\) 28.1707 28.1707i 1.13228 1.13228i 0.142478 0.989798i \(-0.454493\pi\)
0.989798 0.142478i \(-0.0455069\pi\)
\(620\) −13.2337 + 54.2347i −0.531480 + 2.17812i
\(621\) −1.24096 + 0.716468i −0.0497980 + 0.0287509i
\(622\) 26.7204 20.9843i 1.07139 0.841395i
\(623\) 4.89248 0.196013
\(624\) 24.9586 + 26.1300i 0.999142 + 1.04604i
\(625\) 26.5121 1.06048
\(626\) −32.1443 + 25.2440i −1.28475 + 1.00895i
\(627\) 20.6966 11.9492i 0.826542 0.477204i
\(628\) −5.10162 + 20.9075i −0.203577 + 0.834302i
\(629\) 0.976260 0.976260i 0.0389260 0.0389260i
\(630\) 3.16483 7.89013i 0.126090 0.314350i
\(631\) −3.23895 12.0879i −0.128941 0.481213i 0.871009 0.491267i \(-0.163466\pi\)
−0.999949 + 0.0100543i \(0.996800\pi\)
\(632\) −7.03758 + 3.19697i −0.279940 + 0.127169i
\(633\) −22.8170 + 39.5201i −0.906893 + 1.57078i
\(634\) −0.00336694 + 0.0280017i −0.000133718 + 0.00111209i
\(635\) 36.3076 + 9.72858i 1.44082 + 0.386067i
\(636\) 5.16698 + 17.6843i 0.204884 + 0.701226i
\(637\) 22.6938 + 7.76458i 0.899163 + 0.307644i
\(638\) 4.15657 + 3.11589i 0.164560 + 0.123359i
\(639\) −1.73904 + 6.49018i −0.0687953 + 0.256748i
\(640\) 23.5519 + 26.1519i 0.930970 + 1.03375i
\(641\) −22.6933 13.1020i −0.896331 0.517497i −0.0203232 0.999793i \(-0.506470\pi\)
−0.876008 + 0.482296i \(0.839803\pi\)
\(642\) −9.46815 66.1653i −0.373678 2.61133i
\(643\) −0.362291 + 0.0970757i −0.0142874 + 0.00382829i −0.265956 0.963985i \(-0.585687\pi\)
0.251668 + 0.967814i \(0.419021\pi\)
\(644\) 1.26249 + 2.07747i 0.0497492 + 0.0818640i
\(645\) −39.7636 39.7636i −1.56569 1.56569i
\(646\) −11.2008 + 4.78762i −0.440688 + 0.188366i
\(647\) 17.6527 + 30.5754i 0.693999 + 1.20204i 0.970517 + 0.241033i \(0.0774863\pi\)
−0.276517 + 0.961009i \(0.589180\pi\)
\(648\) −13.3113 + 18.6143i −0.522918 + 0.731238i
\(649\) 20.8184i 0.817194i
\(650\) −4.44566 + 23.4284i −0.174373 + 0.918936i
\(651\) 13.2557i 0.519532i
\(652\) −28.4156 + 0.638539i −1.11284 + 0.0250071i
\(653\) −16.0606 27.8178i −0.628500 1.08859i −0.987853 0.155392i \(-0.950336\pi\)
0.359353 0.933202i \(-0.382997\pi\)
\(654\) 5.81498 + 13.6043i 0.227384 + 0.531970i
\(655\) −42.1642 42.1642i −1.64749 1.64749i
\(656\) −17.1121 15.6394i −0.668115 0.610616i
\(657\) 0.197037 0.0527959i 0.00768715 0.00205977i
\(658\) 3.69828 0.529219i 0.144174 0.0206311i
\(659\) −9.20996 5.31737i −0.358769 0.207135i 0.309772 0.950811i \(-0.399747\pi\)
−0.668541 + 0.743676i \(0.733081\pi\)
\(660\) −33.2791 31.8163i −1.29539 1.23845i
\(661\) 2.08438 7.77900i 0.0810729 0.302568i −0.913469 0.406909i \(-0.866607\pi\)
0.994542 + 0.104341i \(0.0332733\pi\)
\(662\) −3.58360 + 4.78049i −0.139281 + 0.185799i
\(663\) 15.8429 + 18.1534i 0.615286 + 0.705020i
\(664\) 14.3126 38.1406i 0.555437 1.48014i
\(665\) 5.72126 + 1.53301i 0.221861 + 0.0594474i
\(666\) −2.38209 0.286423i −0.0923039 0.0110987i
\(667\) 1.28188 2.22029i 0.0496348 0.0859699i
\(668\) 8.95559 16.3491i 0.346502 0.632566i
\(669\) −2.30265 8.59360i −0.0890255 0.332248i
\(670\) 30.3535 + 12.1752i 1.17266 + 0.470369i
\(671\) −16.6126 + 16.6126i −0.641322 + 0.641322i
\(672\) −6.90496 4.70702i −0.266365 0.181577i
\(673\) 1.15151 0.664827i 0.0443876 0.0256272i −0.477642 0.878555i \(-0.658508\pi\)
0.522030 + 0.852927i \(0.325175\pi\)
\(674\) −8.37262 10.6613i −0.322501 0.410657i
\(675\) 3.25070 0.125119
\(676\) 24.1927 + 9.52434i 0.930489 + 0.366321i
\(677\) 33.7816 1.29833 0.649167 0.760646i \(-0.275118\pi\)
0.649167 + 0.760646i \(0.275118\pi\)
\(678\) 12.3492 + 15.7248i 0.474268 + 0.603908i
\(679\) 2.42135 1.39797i 0.0929231 0.0536492i
\(680\) 14.9052 + 18.1259i 0.571587 + 0.695096i
\(681\) −30.8905 + 30.8905i −1.18373 + 1.18373i
\(682\) −34.7876 13.9537i −1.33208 0.534316i
\(683\) 11.4324 + 42.6664i 0.437449 + 1.63258i 0.735136 + 0.677920i \(0.237118\pi\)
−0.297687 + 0.954664i \(0.596215\pi\)
\(684\) 18.5651 + 10.1695i 0.709856 + 0.388839i
\(685\) 11.2882 19.5517i 0.431299 0.747032i
\(686\) −11.3025 1.35902i −0.431532 0.0518875i
\(687\) 48.8976 + 13.1021i 1.86556 + 0.499876i
\(688\) −24.3207 + 15.5385i −0.927217 + 0.592401i
\(689\) 8.71652 + 9.98775i 0.332073 + 0.380503i
\(690\) −13.6292 + 18.1812i −0.518854 + 0.692147i
\(691\) 10.7564 40.1436i 0.409195 1.52714i −0.386991 0.922083i \(-0.626486\pi\)
0.796186 0.605052i \(-0.206848\pi\)
\(692\) 31.6384 33.0930i 1.20271 1.25801i
\(693\) 4.94304 + 2.85387i 0.187771 + 0.108409i
\(694\) −5.76247 + 0.824601i −0.218740 + 0.0313014i
\(695\) −33.3733 + 8.94235i −1.26592 + 0.339203i
\(696\) −0.855267 + 8.77148i −0.0324188 + 0.332482i
\(697\) −10.9304 10.9304i −0.414017 0.414017i
\(698\) 16.1490 + 37.7811i 0.611250 + 1.43004i
\(699\) 16.6871 + 28.9030i 0.631165 + 1.09321i
\(700\) −0.123896 5.51349i −0.00468283 0.208390i
\(701\) 17.2912i 0.653080i −0.945183 0.326540i \(-0.894117\pi\)
0.945183 0.326540i \(-0.105883\pi\)
\(702\) 0.660754 3.48213i 0.0249385 0.131425i
\(703\) 1.67164i 0.0630470i
\(704\) −19.6214 + 13.1661i −0.739509 + 0.496216i
\(705\) 17.4599 + 30.2414i 0.657578 + 1.13896i
\(706\) 34.2395 14.6352i 1.28862 0.550804i
\(707\) 3.74329 + 3.74329i 0.140781 + 0.140781i
\(708\) 30.1826 18.3421i 1.13433 0.689340i
\(709\) −40.4498 + 10.8385i −1.51913 + 0.407048i −0.919454 0.393198i \(-0.871369\pi\)
−0.599672 + 0.800246i \(0.704702\pi\)
\(710\) 1.27759 + 8.92804i 0.0479471 + 0.335063i
\(711\) 7.75677 + 4.47837i 0.290902 + 0.167952i
\(712\) 23.1523 3.84570i 0.867671 0.144124i
\(713\) −4.78769 + 17.8679i −0.179301 + 0.669159i
\(714\) −4.45858 3.34229i −0.166858 0.125082i
\(715\) −31.3442 10.7243i −1.17221 0.401064i
\(716\) 25.3761 7.41438i 0.948349 0.277088i
\(717\) −35.0787 9.39931i −1.31004 0.351024i
\(718\) −1.83816 + 15.2874i −0.0685994 + 0.570519i
\(719\) −17.2567 + 29.8894i −0.643565 + 1.11469i 0.341066 + 0.940039i \(0.389212\pi\)
−0.984631 + 0.174647i \(0.944121\pi\)
\(720\) 8.77474 39.8256i 0.327015 1.48421i
\(721\) 1.46526 + 5.46841i 0.0545690 + 0.203654i
\(722\) 4.51264 11.2503i 0.167943 0.418693i
\(723\) −24.5379 + 24.5379i −0.912575 + 0.912575i
\(724\) −50.7525 12.3840i −1.88620 0.460249i
\(725\) −5.03685 + 2.90803i −0.187064 + 0.108001i
\(726\) −6.34204 + 4.98060i −0.235375 + 0.184847i
\(727\) −3.77644 −0.140060 −0.0700302 0.997545i \(-0.522310\pi\)
−0.0700302 + 0.997545i \(0.522310\pi\)
\(728\) −5.93120 0.987983i −0.219825 0.0366171i
\(729\) 31.7414 1.17561
\(730\) 0.215342 0.169115i 0.00797016 0.00625921i
\(731\) −16.6660 + 9.62214i −0.616416 + 0.355888i
\(732\) −38.7216 9.44839i −1.43119 0.349223i
\(733\) 4.25026 4.25026i 0.156987 0.156987i −0.624243 0.781230i \(-0.714593\pi\)
0.781230 + 0.624243i \(0.214593\pi\)
\(734\) 1.10468 2.75403i 0.0407744 0.101653i
\(735\) −13.4192 50.0810i −0.494973 1.84727i
\(736\) 7.60739 + 8.83871i 0.280412 + 0.325799i
\(737\) −10.9789 + 19.0160i −0.404413 + 0.700464i
\(738\) −3.20683 + 26.6702i −0.118045 + 0.981743i
\(739\) −17.4311 4.67066i −0.641215 0.171813i −0.0764613 0.997073i \(-0.524362\pi\)
−0.564754 + 0.825260i \(0.691029\pi\)
\(740\) −3.09122 + 0.903194i −0.113636 + 0.0332021i
\(741\) 29.1057 + 1.97815i 1.06922 + 0.0726692i
\(742\) −2.45305 1.83888i −0.0900542 0.0675074i
\(743\) −3.46818 + 12.9434i −0.127235 + 0.474848i −0.999909 0.0134546i \(-0.995717\pi\)
0.872674 + 0.488303i \(0.162384\pi\)
\(744\) −10.4196 62.7291i −0.381999 2.29976i
\(745\) −13.9994 8.08254i −0.512898 0.296122i
\(746\) 5.67031 + 39.6252i 0.207605 + 1.45078i
\(747\) −45.5961 + 12.2174i −1.66828 + 0.447013i
\(748\) −13.4647 + 8.18256i −0.492317 + 0.299184i
\(749\) 7.86466 + 7.86466i 0.287368 + 0.287368i
\(750\) −3.27700 + 1.40071i −0.119659 + 0.0511467i
\(751\) 12.5103 + 21.6684i 0.456506 + 0.790691i 0.998773 0.0495148i \(-0.0157675\pi\)
−0.542268 + 0.840206i \(0.682434\pi\)
\(752\) 17.0851 5.41139i 0.623031 0.197333i
\(753\) 6.30448i 0.229748i
\(754\) 2.09125 + 5.98655i 0.0761588 + 0.218017i
\(755\) 16.1759i 0.588700i
\(756\) 0.0184145 + 0.819463i 0.000669730 + 0.0298036i
\(757\) 19.6123 + 33.9695i 0.712821 + 1.23464i 0.963794 + 0.266648i \(0.0859161\pi\)
−0.250973 + 0.967994i \(0.580751\pi\)
\(758\) −16.0698 37.5957i −0.583681 1.36554i
\(759\) −10.7876 10.7876i −0.391565 0.391565i
\(760\) 28.2793 + 2.75739i 1.02580 + 0.100021i
\(761\) 13.7578 3.68640i 0.498722 0.133632i −0.000685009 1.00000i \(-0.500218\pi\)
0.499407 + 0.866368i \(0.333551\pi\)
\(762\) −42.3833 + 6.06498i −1.53538 + 0.219711i
\(763\) −2.13210 1.23097i −0.0771872 0.0445641i
\(764\) −19.5401 + 20.4384i −0.706935 + 0.739437i
\(765\) 7.03796 26.2660i 0.254458 0.949650i
\(766\) −12.8394 + 17.1277i −0.463908 + 0.618849i
\(767\) 14.1696 21.0961i 0.511636 0.761737i
\(768\) −36.3758 16.8471i −1.31260 0.607918i
\(769\) 19.3143 + 5.17525i 0.696491 + 0.186624i 0.589658 0.807653i \(-0.299262\pi\)
0.106833 + 0.994277i \(0.465929\pi\)
\(770\) 7.60662 + 0.914622i 0.274124 + 0.0329607i
\(771\) −8.03441 + 13.9160i −0.289352 + 0.501172i
\(772\) 40.6923 + 22.2901i 1.46455 + 0.802239i
\(773\) 7.82826 + 29.2155i 0.281563 + 1.05081i 0.951314 + 0.308222i \(0.0997340\pi\)
−0.669751 + 0.742585i \(0.733599\pi\)
\(774\) 31.0384 + 12.4499i 1.11565 + 0.447503i
\(775\) 29.6732 29.6732i 1.06589 1.06589i
\(776\) 10.3595 8.51880i 0.371886 0.305807i
\(777\) 0.662242 0.382346i 0.0237578 0.0137166i
\(778\) −26.5268 33.7778i −0.951031 1.21099i
\(779\) −18.7159 −0.670567
\(780\) −12.0679 54.8916i −0.432100 1.96543i
\(781\) −6.05538 −0.216679
\(782\) 4.80273 + 6.11555i 0.171745 + 0.218692i
\(783\) 0.748622 0.432217i 0.0267536 0.0154462i
\(784\) −26.5826 + 1.19530i −0.949377 + 0.0426893i
\(785\) 23.6690 23.6690i 0.844783 0.844783i
\(786\) 63.0386 + 25.2856i 2.24851 + 0.901907i
\(787\) 2.42897 + 9.06504i 0.0865834 + 0.323134i 0.995609 0.0936059i \(-0.0298394\pi\)
−0.909026 + 0.416740i \(0.863173\pi\)
\(788\) 5.96314 10.8862i 0.212428 0.387804i
\(789\) 6.64987 11.5179i 0.236742 0.410049i
\(790\) 11.9365 + 1.43525i 0.424683 + 0.0510640i
\(791\) −3.21376 0.861124i −0.114268 0.0306181i
\(792\) 25.6349 + 9.61971i 0.910896 + 0.341822i
\(793\) −28.1413 + 5.52716i −0.999325 + 0.196275i
\(794\) 13.5757 18.1099i 0.481784 0.642695i
\(795\) 7.41660 27.6791i 0.263040 0.981677i
\(796\) 4.35758 + 4.16605i 0.154450 + 0.147662i
\(797\) −10.0960 5.82891i −0.357617 0.206471i 0.310418 0.950600i \(-0.399531\pi\)
−0.668035 + 0.744130i \(0.732864\pi\)
\(798\) −6.67865 + 0.955705i −0.236422 + 0.0338316i
\(799\) 11.5429 3.09292i 0.408359 0.109420i
\(800\) −4.92014 25.9937i −0.173953 0.919016i
\(801\) −19.2299 19.2299i −0.679457 0.679457i
\(802\) 7.65306 + 17.9045i 0.270239 + 0.632231i
\(803\) 0.0919184 + 0.159207i 0.00324373 + 0.00561831i
\(804\) −37.2425 + 0.836892i −1.31344 + 0.0295149i
\(805\) 3.78111i 0.133267i
\(806\) −25.7543 37.8174i −0.907156 1.33206i
\(807\) 25.0572i 0.882055i
\(808\) 20.6565 + 14.7717i 0.726693 + 0.519668i
\(809\) 15.5430 + 26.9212i 0.546461 + 0.946499i 0.998513 + 0.0545072i \(0.0173588\pi\)
−0.452052 + 0.891992i \(0.649308\pi\)
\(810\) 32.7287 13.9895i 1.14997 0.491540i
\(811\) −0.110267 0.110267i −0.00387201 0.00387201i 0.705168 0.709040i \(-0.250872\pi\)
−0.709040 + 0.705168i \(0.750872\pi\)
\(812\) −0.761613 1.25326i −0.0267274 0.0439807i
\(813\) 61.7561 16.5475i 2.16588 0.580346i
\(814\) −0.306292 2.14043i −0.0107355 0.0750221i
\(815\) 38.2851 + 22.1039i 1.34107 + 0.774266i
\(816\) −23.7262 12.3118i −0.830583 0.431000i
\(817\) −6.03058 + 22.5064i −0.210983 + 0.787401i
\(818\) −0.661725 0.496050i −0.0231367 0.0173440i
\(819\) 3.06655 + 6.25632i 0.107154 + 0.218614i
\(820\) 10.1123 + 34.6098i 0.353137 + 1.20863i
\(821\) −17.4699 4.68104i −0.609703 0.163370i −0.0592608 0.998243i \(-0.518874\pi\)
−0.550443 + 0.834873i \(0.685541\pi\)
\(822\) −3.06994 + 25.5317i −0.107076 + 0.890520i
\(823\) 13.0969 22.6845i 0.456530 0.790733i −0.542245 0.840221i \(-0.682425\pi\)
0.998775 + 0.0494874i \(0.0157588\pi\)
\(824\) 11.2323 + 24.7260i 0.391297 + 0.861372i
\(825\) 8.95747 + 33.4297i 0.311859 + 1.16387i
\(826\) −2.18797 + 5.45474i −0.0761291 + 0.189795i
\(827\) 11.7822 11.7822i 0.409707 0.409707i −0.471930 0.881636i \(-0.656442\pi\)
0.881636 + 0.471930i \(0.156442\pi\)
\(828\) 3.20329 13.1278i 0.111322 0.456222i
\(829\) −11.3492 + 6.55249i −0.394176 + 0.227577i −0.683968 0.729512i \(-0.739747\pi\)
0.289792 + 0.957090i \(0.406414\pi\)
\(830\) −49.8320 + 39.1346i −1.72969 + 1.35838i
\(831\) −1.33873 −0.0464401
\(832\) −28.8444 0.0131852i −1.00000 0.000457113i
\(833\) −17.7431 −0.614762
\(834\) 30.9512 24.3069i 1.07175 0.841680i
\(835\) −25.1095 + 14.4970i −0.868951 + 0.501689i
\(836\) −4.52224 + 18.5331i −0.156405 + 0.640981i
\(837\) −4.41030 + 4.41030i −0.152442 + 0.152442i
\(838\) 19.4259 48.4301i 0.671057 1.67299i
\(839\) −6.19456 23.1184i −0.213860 0.798136i −0.986565 0.163371i \(-0.947763\pi\)
0.772705 0.634766i \(-0.218903\pi\)
\(840\) 5.37582 + 11.8339i 0.185483 + 0.408309i
\(841\) 13.7267 23.7753i 0.473334 0.819839i
\(842\) 5.29751 44.0577i 0.182564 1.51833i
\(843\) 0.943032 + 0.252685i 0.0324798 + 0.00870293i
\(844\) −10.2162 34.9654i −0.351655 1.20356i
\(845\) −24.4631 32.2012i −0.841556 1.10775i
\(846\) −16.6162 12.4560i −0.571278 0.428248i
\(847\) 0.347303 1.29615i 0.0119335 0.0445364i
\(848\) −13.0538 6.77380i −0.448270 0.232613i
\(849\) 34.8553 + 20.1237i 1.19623 + 0.690644i
\(850\) −2.49885 17.4624i −0.0857097 0.598956i
\(851\) −1.03076 + 0.276191i −0.0353340 + 0.00946770i
\(852\) −5.33512 8.77911i −0.182778 0.300767i
\(853\) −12.1913 12.1913i −0.417422 0.417422i 0.466892 0.884314i \(-0.345374\pi\)
−0.884314 + 0.466892i \(0.845374\pi\)
\(854\) 6.09870 2.60681i 0.208693 0.0892032i
\(855\) −16.4620 28.5130i −0.562987 0.975123i
\(856\) 43.3993 + 31.0354i 1.48336 + 1.06077i
\(857\) 20.1694i 0.688974i 0.938791 + 0.344487i \(0.111947\pi\)
−0.938791 + 0.344487i \(0.888053\pi\)
\(858\) 37.6305 2.80010i 1.28468 0.0955937i
\(859\) 10.5286i 0.359231i 0.983737 + 0.179616i \(0.0574854\pi\)
−0.983737 + 0.179616i \(0.942515\pi\)
\(860\) 44.8777 1.00847i 1.53032 0.0343885i
\(861\) −4.28080 7.41456i −0.145889 0.252688i
\(862\) 17.2887 + 40.4473i 0.588854 + 1.37764i
\(863\) −0.357134 0.357134i −0.0121570 0.0121570i 0.701002 0.713159i \(-0.252736\pi\)
−0.713159 + 0.701002i \(0.752736\pi\)
\(864\) 0.731274 + 3.86341i 0.0248785 + 0.131436i
\(865\) −68.7838 + 18.4306i −2.33872 + 0.626658i
\(866\) −15.1099 + 2.16220i −0.513454 + 0.0734745i
\(867\) 21.4509 + 12.3847i 0.728511 + 0.420606i
\(868\) 7.64837 + 7.31218i 0.259603 + 0.248192i
\(869\) −2.08918 + 7.79691i −0.0708704 + 0.264492i
\(870\) 8.22195 10.9680i 0.278750 0.371850i
\(871\) −24.0682 + 11.7971i −0.815521 + 0.399730i
\(872\) −11.0572 4.14931i −0.374443 0.140513i
\(873\) −15.0119 4.02243i −0.508076 0.136138i
\(874\) 9.34761 + 1.12396i 0.316188 + 0.0380185i
\(875\) 0.296516 0.513580i 0.0100241 0.0173622i
\(876\) −0.149834 + 0.273534i −0.00506243 + 0.00924186i
\(877\) 8.27012 + 30.8645i 0.279262 + 1.04222i 0.952931 + 0.303187i \(0.0980508\pi\)
−0.673669 + 0.739033i \(0.735283\pi\)
\(878\) 17.0191 + 6.82656i 0.574366 + 0.230385i
\(879\) −3.63013 + 3.63013i −0.122441 + 0.122441i
\(880\) 36.7152 1.65092i 1.23767 0.0556526i
\(881\) 26.4430 15.2668i 0.890886 0.514353i 0.0166536 0.999861i \(-0.494699\pi\)
0.874232 + 0.485508i \(0.161365\pi\)
\(882\) 19.0439 + 24.2495i 0.641241 + 0.816523i
\(883\) 49.7844 1.67538 0.837689 0.546148i \(-0.183906\pi\)
0.837689 + 0.546148i \(0.183906\pi\)
\(884\) −19.2136 0.872752i −0.646223 0.0293538i
\(885\) −54.9338 −1.84658
\(886\) 13.6708 + 17.4077i 0.459280 + 0.584824i
\(887\) 21.7002 12.5286i 0.728621 0.420669i −0.0892967 0.996005i \(-0.528462\pi\)
0.817917 + 0.575336i \(0.195129\pi\)
\(888\) 2.83334 2.32990i 0.0950807 0.0781863i
\(889\) 5.03784 5.03784i 0.168964 0.168964i
\(890\) −33.8799 13.5897i −1.13566 0.455526i
\(891\) 6.18510 + 23.0831i 0.207209 + 0.773313i
\(892\) 6.22859 + 3.41185i 0.208549 + 0.114237i
\(893\) 7.23442 12.5304i 0.242091 0.419313i
\(894\) 18.2812 + 2.19813i 0.611414 + 0.0735166i
\(895\) −39.7182 10.6425i −1.32763 0.355739i
\(896\) 6.52483 1.38756i 0.217979 0.0463551i
\(897\) −3.58913 18.2739i −0.119838 0.610146i
\(898\) −9.50433 + 12.6787i −0.317164 + 0.423093i
\(899\) 2.88823 10.7790i 0.0963278 0.359500i
\(900\) −21.1838 + 22.1578i −0.706128 + 0.738593i
\(901\) −8.49258 4.90319i −0.282929 0.163349i
\(902\) −23.9646 + 3.42930i −0.797933 + 0.114183i
\(903\) −10.2956 + 2.75869i −0.342616 + 0.0918036i
\(904\) −15.8851 1.54889i −0.528331 0.0515152i
\(905\) 57.4558 + 57.4558i 1.90990 + 1.90990i
\(906\) −7.24178 16.9423i −0.240592 0.562871i
\(907\) −25.1973 43.6429i −0.836661 1.44914i −0.892671 0.450710i \(-0.851171\pi\)
0.0560094 0.998430i \(-0.482162\pi\)
\(908\) −0.783430 34.8633i −0.0259990 1.15698i
\(909\) 29.4261i 0.976002i
\(910\) 7.08557 + 6.10412i 0.234884 + 0.202350i
\(911\) 7.50959i 0.248804i −0.992232 0.124402i \(-0.960299\pi\)
0.992232 0.124402i \(-0.0397012\pi\)
\(912\) −30.8537 + 9.77232i −1.02167 + 0.323594i
\(913\) −21.2708 36.8420i −0.703959 1.21929i
\(914\) −24.9869 + 10.6803i −0.826495 + 0.353274i
\(915\) 43.8359 + 43.8359i 1.44917 + 1.44917i
\(916\) −34.5329 + 20.9858i −1.14100 + 0.693392i
\(917\) −10.9171 + 2.92524i −0.360516 + 0.0966000i
\(918\) 0.371400 + 2.59542i 0.0122580 + 0.0856616i
\(919\) 24.3508 + 14.0590i 0.803260 + 0.463762i 0.844610 0.535382i \(-0.179832\pi\)
−0.0413499 + 0.999145i \(0.513166\pi\)
\(920\) −2.97211 17.8931i −0.0979876 0.589917i
\(921\) 10.4855 39.1325i 0.345510 1.28946i
\(922\) −27.7517 20.8035i −0.913952 0.685126i
\(923\) −6.13616 4.12148i −0.201974 0.135660i
\(924\) −8.37650 + 2.44745i −0.275567 + 0.0805151i
\(925\) 2.33834 + 0.626555i 0.0768840 + 0.0206010i
\(926\) −3.15229 + 26.2165i −0.103591 + 0.861529i
\(927\) 15.7344 27.2528i 0.516787 0.895101i
\(928\) −4.58924 5.33205i −0.150649 0.175033i
\(929\) −11.1025 41.4351i −0.364261 1.35944i −0.868420 0.495829i \(-0.834864\pi\)
0.504159 0.863611i \(-0.331802\pi\)
\(930\) −36.8199 + 91.7944i −1.20737 + 3.01006i
\(931\) −15.1906 + 15.1906i −0.497853 + 0.497853i
\(932\) −25.8817 6.31534i −0.847782 0.206866i
\(933\) 52.1278 30.0960i 1.70659 0.985300i
\(934\) −25.1974 + 19.7883i −0.824483 + 0.647492i
\(935\) 24.5064 0.801444
\(936\) 19.4294 + 27.1959i 0.635069 + 0.888927i
\(937\) −0.397858 −0.0129975 −0.00649873 0.999979i \(-0.502069\pi\)
−0.00649873 + 0.999979i \(0.502069\pi\)
\(938\) 4.87518 3.82863i 0.159180 0.125009i
\(939\) −62.7093 + 36.2052i −2.04644 + 1.18151i
\(940\) −27.0802 6.60780i −0.883259 0.215523i
\(941\) −4.33123 + 4.33123i −0.141194 + 0.141194i −0.774171 0.632977i \(-0.781833\pi\)
0.632977 + 0.774171i \(0.281833\pi\)
\(942\) −14.1941 + 35.3868i −0.462469 + 1.15297i
\(943\) 3.09228 + 11.5405i 0.100698 + 0.375811i
\(944\) −6.06630 + 27.5329i −0.197441 + 0.896120i
\(945\) 0.637444 1.10409i 0.0207360 0.0359159i
\(946\) −3.59797 + 29.9231i −0.116980 + 0.972885i
\(947\) 7.47663 + 2.00336i 0.242958 + 0.0651003i 0.378243 0.925706i \(-0.376528\pi\)
−0.135285 + 0.990807i \(0.543195\pi\)
\(948\) −13.1447 + 3.84060i −0.426919 + 0.124737i
\(949\) −0.0152168 + 0.223894i −0.000493959 + 0.00726790i
\(950\) −17.0897 12.8110i −0.554463 0.415642i
\(951\) −0.0129322 + 0.0482638i −0.000419357 + 0.00156506i
\(952\) 4.38792 0.728851i 0.142213 0.0236222i
\(953\) −12.6528 7.30512i −0.409866 0.236636i 0.280866 0.959747i \(-0.409378\pi\)
−0.690732 + 0.723111i \(0.742712\pi\)
\(954\) 2.41399 + 16.8695i 0.0781559 + 0.546169i
\(955\) 42.4813 11.3828i 1.37466 0.368340i
\(956\) 24.7736 15.0551i 0.801235 0.486915i
\(957\) 6.50773 + 6.50773i 0.210365 + 0.210365i
\(958\) 4.22327 1.80518i 0.136448 0.0583228i
\(959\) −2.13959 3.70587i −0.0690909 0.119669i
\(960\) 34.7416 + 51.7752i 1.12128 + 1.67104i
\(961\) 49.5168i 1.59731i
\(962\) 1.14646 2.37746i 0.0369635 0.0766523i
\(963\) 61.8243i 1.99226i
\(964\) −0.622320 27.6938i −0.0200436 0.891957i
\(965\) −36.0825 62.4966i −1.16154 2.01184i
\(966\) 1.69276 + 3.96026i 0.0544638 + 0.127419i
\(967\) 6.52725 + 6.52725i 0.209902 + 0.209902i 0.804226 0.594324i \(-0.202580\pi\)
−0.594324 + 0.804226i \(0.702580\pi\)
\(968\) 0.624687 6.40669i 0.0200782 0.205919i
\(969\) −20.8451 + 5.58544i −0.669642 + 0.179430i
\(970\) −20.6507 + 2.95508i −0.663054 + 0.0948821i
\(971\) −33.9607 19.6072i −1.08985 0.629226i −0.156315 0.987707i \(-0.549962\pi\)
−0.933537 + 0.358481i \(0.883295\pi\)
\(972\) −30.8986 + 32.3192i −0.991072 + 1.03664i
\(973\) −1.69495 + 6.32565i −0.0543377 + 0.202791i
\(974\) 36.3804 48.5311i 1.16570 1.55504i
\(975\) −13.6763 + 39.9724i −0.437994 + 1.28014i
\(976\) 26.8114 17.1299i 0.858212 0.548313i
\(977\) 11.3491 + 3.04098i 0.363089 + 0.0972895i 0.435751 0.900067i \(-0.356483\pi\)
−0.0726619 + 0.997357i \(0.523149\pi\)
\(978\) −49.9948 6.01139i −1.59866 0.192223i
\(979\) 12.2544 21.2252i 0.391652 0.678361i
\(980\) 36.2984 + 19.8833i 1.15951 + 0.635147i
\(981\) 3.54191 + 13.2186i 0.113084 + 0.422037i
\(982\) −2.09197 0.839115i −0.0667574 0.0267772i
\(983\) 17.0818 17.0818i 0.544823 0.544823i −0.380116 0.924939i \(-0.624116\pi\)
0.924939 + 0.380116i \(0.124116\pi\)
\(984\) −26.0859 31.7225i −0.831588 1.01128i
\(985\) −16.7194 + 9.65293i −0.532723 + 0.307568i
\(986\) −2.89730 3.68927i −0.0922688 0.117490i
\(987\) 6.61878 0.210678
\(988\) −17.1968 + 15.7024i −0.547102 + 0.499559i
\(989\) 14.8742 0.472973
\(990\) −26.3030 33.4928i −0.835963 1.06447i
\(991\) 24.9439 14.4013i 0.792368 0.457474i −0.0484275 0.998827i \(-0.515421\pi\)
0.840796 + 0.541353i \(0.182088\pi\)
\(992\) 41.9415 + 28.5910i 1.33164 + 0.907765i
\(993\) −7.48456 + 7.48456i −0.237515 + 0.237515i
\(994\) 1.58660 + 0.636406i 0.0503240 + 0.0201856i
\(995\) −2.42688 9.05724i −0.0769373 0.287134i
\(996\) 34.6730 63.2982i 1.09866 2.00568i
\(997\) −26.9659 + 46.7063i −0.854019 + 1.47920i 0.0235336 + 0.999723i \(0.492508\pi\)
−0.877552 + 0.479481i \(0.840825\pi\)
\(998\) −5.75298 0.691740i −0.182107 0.0218966i
\(999\) −0.347544 0.0931241i −0.0109958 0.00294632i
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 52.2.l.b.15.1 yes 16
3.2 odd 2 468.2.cb.f.379.4 16
4.3 odd 2 inner 52.2.l.b.15.2 yes 16
8.3 odd 2 832.2.bu.n.639.1 16
8.5 even 2 832.2.bu.n.639.4 16
12.11 even 2 468.2.cb.f.379.3 16
13.2 odd 12 676.2.f.i.99.1 16
13.3 even 3 676.2.f.h.239.5 16
13.4 even 6 676.2.l.i.19.1 16
13.5 odd 4 676.2.l.i.427.3 16
13.6 odd 12 676.2.l.k.319.3 16
13.7 odd 12 inner 52.2.l.b.7.2 yes 16
13.8 odd 4 676.2.l.m.427.2 16
13.9 even 3 676.2.l.m.19.4 16
13.10 even 6 676.2.f.i.239.4 16
13.11 odd 12 676.2.f.h.99.8 16
13.12 even 2 676.2.l.k.587.4 16
39.20 even 12 468.2.cb.f.163.3 16
52.3 odd 6 676.2.f.h.239.8 16
52.7 even 12 inner 52.2.l.b.7.1 16
52.11 even 12 676.2.f.h.99.5 16
52.15 even 12 676.2.f.i.99.4 16
52.19 even 12 676.2.l.k.319.4 16
52.23 odd 6 676.2.f.i.239.1 16
52.31 even 4 676.2.l.i.427.1 16
52.35 odd 6 676.2.l.m.19.2 16
52.43 odd 6 676.2.l.i.19.3 16
52.47 even 4 676.2.l.m.427.4 16
52.51 odd 2 676.2.l.k.587.3 16
104.59 even 12 832.2.bu.n.319.4 16
104.85 odd 12 832.2.bu.n.319.1 16
156.59 odd 12 468.2.cb.f.163.4 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
52.2.l.b.7.1 16 52.7 even 12 inner
52.2.l.b.7.2 yes 16 13.7 odd 12 inner
52.2.l.b.15.1 yes 16 1.1 even 1 trivial
52.2.l.b.15.2 yes 16 4.3 odd 2 inner
468.2.cb.f.163.3 16 39.20 even 12
468.2.cb.f.163.4 16 156.59 odd 12
468.2.cb.f.379.3 16 12.11 even 2
468.2.cb.f.379.4 16 3.2 odd 2
676.2.f.h.99.5 16 52.11 even 12
676.2.f.h.99.8 16 13.11 odd 12
676.2.f.h.239.5 16 13.3 even 3
676.2.f.h.239.8 16 52.3 odd 6
676.2.f.i.99.1 16 13.2 odd 12
676.2.f.i.99.4 16 52.15 even 12
676.2.f.i.239.1 16 52.23 odd 6
676.2.f.i.239.4 16 13.10 even 6
676.2.l.i.19.1 16 13.4 even 6
676.2.l.i.19.3 16 52.43 odd 6
676.2.l.i.427.1 16 52.31 even 4
676.2.l.i.427.3 16 13.5 odd 4
676.2.l.k.319.3 16 13.6 odd 12
676.2.l.k.319.4 16 52.19 even 12
676.2.l.k.587.3 16 52.51 odd 2
676.2.l.k.587.4 16 13.12 even 2
676.2.l.m.19.2 16 52.35 odd 6
676.2.l.m.19.4 16 13.9 even 3
676.2.l.m.427.2 16 13.8 odd 4
676.2.l.m.427.4 16 52.47 even 4
832.2.bu.n.319.1 16 104.85 odd 12
832.2.bu.n.319.4 16 104.59 even 12
832.2.bu.n.639.1 16 8.3 odd 2
832.2.bu.n.639.4 16 8.5 even 2