Properties

Label 546.2.k.b.445.3
Level $546$
Weight $2$
Character 546.445
Analytic conductor $4.360$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [546,2,Mod(373,546)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(546, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("546.373");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.k (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.35983195036\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.447703281.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{7} - 2x^{6} + 2x^{5} + 3x^{4} + 4x^{3} - 8x^{2} - 8x + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 445.3
Root \(-1.38232 - 0.298668i\) of defining polynomial
Character \(\chi\) \(=\) 546.445
Dual form 546.2.k.b.373.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} -1.00000 q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.14553 + 1.98411i) q^{5} +(0.500000 - 0.866025i) q^{6} +(-1.12588 - 2.39424i) q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} -1.00000 q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.14553 + 1.98411i) q^{5} +(0.500000 - 0.866025i) q^{6} +(-1.12588 - 2.39424i) q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.29105 q^{10} +0.878558 q^{11} +(0.500000 + 0.866025i) q^{12} +(-0.786978 + 3.51862i) q^{13} +(2.63641 + 0.222079i) q^{14} +(-1.14553 - 1.98411i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.20391 + 5.54934i) q^{17} +(-0.500000 + 0.866025i) q^{18} +1.50820 q^{19} +(1.14553 - 1.98411i) q^{20} +(1.12588 + 2.39424i) q^{21} +(-0.439279 + 0.760853i) q^{22} +(-0.658760 + 1.14101i) q^{23} -1.00000 q^{24} +(-0.124459 + 0.215569i) q^{25} +(-2.65372 - 2.44085i) q^{26} -1.00000 q^{27} +(-1.51053 + 2.17216i) q^{28} +(-0.669294 - 1.15925i) q^{29} +2.29105 q^{30} +(-1.94748 + 3.37313i) q^{31} +(-0.500000 - 0.866025i) q^{32} -0.878558 q^{33} -6.40782 q^{34} +(3.46071 - 4.97654i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-4.69338 + 8.12917i) q^{37} +(-0.754098 + 1.30614i) q^{38} +(0.786978 - 3.51862i) q^{39} +(1.14553 + 1.98411i) q^{40} +(1.80195 + 3.12107i) q^{41} +(-2.63641 - 0.222079i) q^{42} +(-4.95801 + 8.58752i) q^{43} +(-0.439279 - 0.760853i) q^{44} +(1.14553 + 1.98411i) q^{45} +(-0.658760 - 1.14101i) q^{46} +(-0.188939 - 0.327251i) q^{47} +(0.500000 - 0.866025i) q^{48} +(-4.46478 + 5.39126i) q^{49} +(-0.124459 - 0.215569i) q^{50} +(-3.20391 - 5.54934i) q^{51} +(3.44070 - 1.07777i) q^{52} +(-1.22356 + 2.11926i) q^{53} +(0.500000 - 0.866025i) q^{54} +(1.00641 + 1.74315i) q^{55} +(-1.12588 - 2.39424i) q^{56} -1.50820 q^{57} +1.33859 q^{58} +(2.98411 + 5.16864i) q^{59} +(-1.14553 + 1.98411i) q^{60} +4.81564 q^{61} +(-1.94748 - 3.37313i) q^{62} +(-1.12588 - 2.39424i) q^{63} +1.00000 q^{64} +(-7.88282 + 2.46922i) q^{65} +(0.439279 - 0.760853i) q^{66} +9.75996 q^{67} +(3.20391 - 5.54934i) q^{68} +(0.658760 - 1.14101i) q^{69} +(2.57945 + 5.48533i) q^{70} +(1.02408 - 1.77376i) q^{71} +1.00000 q^{72} +(0.432504 - 0.749119i) q^{73} +(-4.69338 - 8.12917i) q^{74} +(0.124459 - 0.215569i) q^{75} +(-0.754098 - 1.30614i) q^{76} +(-0.989151 - 2.10348i) q^{77} +(2.65372 + 2.44085i) q^{78} +(-4.18014 - 7.24022i) q^{79} -2.29105 q^{80} +1.00000 q^{81} -3.60390 q^{82} +8.66710 q^{83} +(1.51053 - 2.17216i) q^{84} +(-7.34033 + 12.7138i) q^{85} +(-4.95801 - 8.58752i) q^{86} +(0.669294 + 1.15925i) q^{87} +0.878558 q^{88} +(6.41693 - 11.1145i) q^{89} -2.29105 q^{90} +(9.31046 - 2.07733i) q^{91} +1.31752 q^{92} +(1.94748 - 3.37313i) q^{93} +0.377877 q^{94} +(1.72768 + 2.99243i) q^{95} +(0.500000 + 0.866025i) q^{96} +(4.40338 - 7.62688i) q^{97} +(-2.43658 - 6.56225i) q^{98} +0.878558 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 4 q^{2} - 8 q^{3} - 4 q^{4} + 2 q^{5} + 4 q^{6} + 3 q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 4 q^{2} - 8 q^{3} - 4 q^{4} + 2 q^{5} + 4 q^{6} + 3 q^{7} + 8 q^{8} + 8 q^{9} - 4 q^{10} + 12 q^{11} + 4 q^{12} - 11 q^{13} - 3 q^{14} - 2 q^{15} - 4 q^{16} + 4 q^{17} - 4 q^{18} - 12 q^{19} + 2 q^{20} - 3 q^{21} - 6 q^{22} - 10 q^{23} - 8 q^{24} - 18 q^{25} + 10 q^{26} - 8 q^{27} + 2 q^{29} + 4 q^{30} + 6 q^{31} - 4 q^{32} - 12 q^{33} - 8 q^{34} + 18 q^{35} - 4 q^{36} - 28 q^{37} + 6 q^{38} + 11 q^{39} + 2 q^{40} + 3 q^{42} - 6 q^{43} - 6 q^{44} + 2 q^{45} - 10 q^{46} + q^{47} + 4 q^{48} - 7 q^{49} - 18 q^{50} - 4 q^{51} + q^{52} + 7 q^{53} + 4 q^{54} + q^{55} + 3 q^{56} + 12 q^{57} - 4 q^{58} + 2 q^{59} - 2 q^{60} - 48 q^{61} + 6 q^{62} + 3 q^{63} + 8 q^{64} + 19 q^{65} + 6 q^{66} + 30 q^{67} + 4 q^{68} + 10 q^{69} - 18 q^{70} + 6 q^{71} + 8 q^{72} + q^{73} - 28 q^{74} + 18 q^{75} + 6 q^{76} - 22 q^{77} - 10 q^{78} - 12 q^{79} - 4 q^{80} + 8 q^{81} - 32 q^{83} - 13 q^{85} - 6 q^{86} - 2 q^{87} + 12 q^{88} + 25 q^{89} - 4 q^{90} + 34 q^{91} + 20 q^{92} - 6 q^{93} - 2 q^{94} - 8 q^{95} + 4 q^{96} - q^{97} + 2 q^{98} + 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) −1.00000 −0.577350
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 1.14553 + 1.98411i 0.512295 + 0.887321i 0.999898 + 0.0142554i \(0.00453779\pi\)
−0.487604 + 0.873065i \(0.662129\pi\)
\(6\) 0.500000 0.866025i 0.204124 0.353553i
\(7\) −1.12588 2.39424i −0.425543 0.904938i
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) −2.29105 −0.724494
\(11\) 0.878558 0.264895 0.132448 0.991190i \(-0.457716\pi\)
0.132448 + 0.991190i \(0.457716\pi\)
\(12\) 0.500000 + 0.866025i 0.144338 + 0.250000i
\(13\) −0.786978 + 3.51862i −0.218268 + 0.975889i
\(14\) 2.63641 + 0.222079i 0.704611 + 0.0593532i
\(15\) −1.14553 1.98411i −0.295774 0.512295i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 3.20391 + 5.54934i 0.777062 + 1.34591i 0.933628 + 0.358244i \(0.116624\pi\)
−0.156565 + 0.987668i \(0.550042\pi\)
\(18\) −0.500000 + 0.866025i −0.117851 + 0.204124i
\(19\) 1.50820 0.346004 0.173002 0.984921i \(-0.444653\pi\)
0.173002 + 0.984921i \(0.444653\pi\)
\(20\) 1.14553 1.98411i 0.256147 0.443660i
\(21\) 1.12588 + 2.39424i 0.245687 + 0.522466i
\(22\) −0.439279 + 0.760853i −0.0936545 + 0.162214i
\(23\) −0.658760 + 1.14101i −0.137361 + 0.237916i −0.926497 0.376302i \(-0.877195\pi\)
0.789136 + 0.614219i \(0.210529\pi\)
\(24\) −1.00000 −0.204124
\(25\) −0.124459 + 0.215569i −0.0248918 + 0.0431139i
\(26\) −2.65372 2.44085i −0.520438 0.478690i
\(27\) −1.00000 −0.192450
\(28\) −1.51053 + 2.17216i −0.285464 + 0.410500i
\(29\) −0.669294 1.15925i −0.124285 0.215267i 0.797168 0.603757i \(-0.206330\pi\)
−0.921453 + 0.388490i \(0.872997\pi\)
\(30\) 2.29105 0.418287
\(31\) −1.94748 + 3.37313i −0.349777 + 0.605831i −0.986210 0.165501i \(-0.947076\pi\)
0.636433 + 0.771332i \(0.280409\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) −0.878558 −0.152937
\(34\) −6.40782 −1.09893
\(35\) 3.46071 4.97654i 0.584967 0.841188i
\(36\) −0.500000 0.866025i −0.0833333 0.144338i
\(37\) −4.69338 + 8.12917i −0.771586 + 1.33643i 0.165107 + 0.986276i \(0.447203\pi\)
−0.936693 + 0.350151i \(0.886130\pi\)
\(38\) −0.754098 + 1.30614i −0.122331 + 0.211883i
\(39\) 0.786978 3.51862i 0.126017 0.563430i
\(40\) 1.14553 + 1.98411i 0.181124 + 0.313715i
\(41\) 1.80195 + 3.12107i 0.281417 + 0.487429i 0.971734 0.236078i \(-0.0758622\pi\)
−0.690317 + 0.723507i \(0.742529\pi\)
\(42\) −2.63641 0.222079i −0.406808 0.0342676i
\(43\) −4.95801 + 8.58752i −0.756089 + 1.30959i 0.188742 + 0.982027i \(0.439559\pi\)
−0.944831 + 0.327558i \(0.893774\pi\)
\(44\) −0.439279 0.760853i −0.0662238 0.114703i
\(45\) 1.14553 + 1.98411i 0.170765 + 0.295774i
\(46\) −0.658760 1.14101i −0.0971289 0.168232i
\(47\) −0.188939 0.327251i −0.0275595 0.0477345i 0.851917 0.523677i \(-0.175440\pi\)
−0.879476 + 0.475943i \(0.842107\pi\)
\(48\) 0.500000 0.866025i 0.0721688 0.125000i
\(49\) −4.46478 + 5.39126i −0.637826 + 0.770180i
\(50\) −0.124459 0.215569i −0.0176012 0.0304861i
\(51\) −3.20391 5.54934i −0.448637 0.777062i
\(52\) 3.44070 1.07777i 0.477139 0.149459i
\(53\) −1.22356 + 2.11926i −0.168068 + 0.291103i −0.937741 0.347336i \(-0.887086\pi\)
0.769672 + 0.638439i \(0.220420\pi\)
\(54\) 0.500000 0.866025i 0.0680414 0.117851i
\(55\) 1.00641 + 1.74315i 0.135704 + 0.235047i
\(56\) −1.12588 2.39424i −0.150452 0.319944i
\(57\) −1.50820 −0.199766
\(58\) 1.33859 0.175765
\(59\) 2.98411 + 5.16864i 0.388498 + 0.672899i 0.992248 0.124275i \(-0.0396605\pi\)
−0.603749 + 0.797174i \(0.706327\pi\)
\(60\) −1.14553 + 1.98411i −0.147887 + 0.256147i
\(61\) 4.81564 0.616580 0.308290 0.951292i \(-0.400243\pi\)
0.308290 + 0.951292i \(0.400243\pi\)
\(62\) −1.94748 3.37313i −0.247330 0.428388i
\(63\) −1.12588 2.39424i −0.141848 0.301646i
\(64\) 1.00000 0.125000
\(65\) −7.88282 + 2.46922i −0.977744 + 0.306269i
\(66\) 0.439279 0.760853i 0.0540715 0.0936545i
\(67\) 9.75996 1.19237 0.596184 0.802848i \(-0.296683\pi\)
0.596184 + 0.802848i \(0.296683\pi\)
\(68\) 3.20391 5.54934i 0.388531 0.672956i
\(69\) 0.658760 1.14101i 0.0793054 0.137361i
\(70\) 2.57945 + 5.48533i 0.308303 + 0.655622i
\(71\) 1.02408 1.77376i 0.121536 0.210507i −0.798837 0.601547i \(-0.794551\pi\)
0.920374 + 0.391040i \(0.127885\pi\)
\(72\) 1.00000 0.117851
\(73\) 0.432504 0.749119i 0.0506207 0.0876777i −0.839605 0.543198i \(-0.817213\pi\)
0.890225 + 0.455520i \(0.150547\pi\)
\(74\) −4.69338 8.12917i −0.545594 0.944997i
\(75\) 0.124459 0.215569i 0.0143713 0.0248918i
\(76\) −0.754098 1.30614i −0.0865010 0.149824i
\(77\) −0.989151 2.10348i −0.112724 0.239714i
\(78\) 2.65372 + 2.44085i 0.300475 + 0.276372i
\(79\) −4.18014 7.24022i −0.470303 0.814588i 0.529120 0.848547i \(-0.322522\pi\)
−0.999423 + 0.0339584i \(0.989189\pi\)
\(80\) −2.29105 −0.256147
\(81\) 1.00000 0.111111
\(82\) −3.60390 −0.397984
\(83\) 8.66710 0.951338 0.475669 0.879624i \(-0.342206\pi\)
0.475669 + 0.879624i \(0.342206\pi\)
\(84\) 1.51053 2.17216i 0.164813 0.237002i
\(85\) −7.34033 + 12.7138i −0.796170 + 1.37901i
\(86\) −4.95801 8.58752i −0.534636 0.926016i
\(87\) 0.669294 + 1.15925i 0.0717558 + 0.124285i
\(88\) 0.878558 0.0936545
\(89\) 6.41693 11.1145i 0.680194 1.17813i −0.294728 0.955581i \(-0.595229\pi\)
0.974922 0.222549i \(-0.0714376\pi\)
\(90\) −2.29105 −0.241498
\(91\) 9.31046 2.07733i 0.976002 0.217763i
\(92\) 1.31752 0.137361
\(93\) 1.94748 3.37313i 0.201944 0.349777i
\(94\) 0.377877 0.0389751
\(95\) 1.72768 + 2.99243i 0.177256 + 0.307017i
\(96\) 0.500000 + 0.866025i 0.0510310 + 0.0883883i
\(97\) 4.40338 7.62688i 0.447096 0.774393i −0.551100 0.834439i \(-0.685792\pi\)
0.998196 + 0.0600467i \(0.0191250\pi\)
\(98\) −2.43658 6.56225i −0.246132 0.662887i
\(99\) 0.878558 0.0882984
\(100\) 0.248918 0.0248918
\(101\) −10.0539 −1.00040 −0.500198 0.865911i \(-0.666739\pi\)
−0.500198 + 0.865911i \(0.666739\pi\)
\(102\) 6.40782 0.634469
\(103\) −6.17983 10.7038i −0.608916 1.05467i −0.991419 0.130720i \(-0.958271\pi\)
0.382503 0.923954i \(-0.375062\pi\)
\(104\) −0.786978 + 3.51862i −0.0771695 + 0.345029i
\(105\) −3.46071 + 4.97654i −0.337731 + 0.485660i
\(106\) −1.22356 2.11926i −0.118842 0.205841i
\(107\) 3.40406 5.89601i 0.329083 0.569989i −0.653247 0.757145i \(-0.726594\pi\)
0.982330 + 0.187156i \(0.0599270\pi\)
\(108\) 0.500000 + 0.866025i 0.0481125 + 0.0833333i
\(109\) −0.460710 + 0.797973i −0.0441280 + 0.0764320i −0.887246 0.461297i \(-0.847384\pi\)
0.843118 + 0.537729i \(0.180718\pi\)
\(110\) −2.01282 −0.191915
\(111\) 4.69338 8.12917i 0.445476 0.771586i
\(112\) 2.63641 + 0.222079i 0.249118 + 0.0209845i
\(113\) 5.68802 9.85195i 0.535084 0.926793i −0.464075 0.885796i \(-0.653613\pi\)
0.999159 0.0409973i \(-0.0130535\pi\)
\(114\) 0.754098 1.30614i 0.0706278 0.122331i
\(115\) −3.01851 −0.281477
\(116\) −0.669294 + 1.15925i −0.0621424 + 0.107634i
\(117\) −0.786978 + 3.51862i −0.0727561 + 0.325296i
\(118\) −5.96823 −0.549420
\(119\) 9.67923 13.9188i 0.887293 1.27594i
\(120\) −1.14553 1.98411i −0.104572 0.181124i
\(121\) −10.2281 −0.929831
\(122\) −2.40782 + 4.17047i −0.217994 + 0.377576i
\(123\) −1.80195 3.12107i −0.162476 0.281417i
\(124\) 3.89495 0.349777
\(125\) 10.8850 0.973582
\(126\) 2.63641 + 0.222079i 0.234870 + 0.0197844i
\(127\) 4.26019 + 7.37887i 0.378031 + 0.654769i 0.990776 0.135512i \(-0.0432679\pi\)
−0.612745 + 0.790281i \(0.709935\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 4.95801 8.58752i 0.436528 0.756089i
\(130\) 1.80301 8.06133i 0.158134 0.707026i
\(131\) 2.51964 + 4.36415i 0.220142 + 0.381298i 0.954851 0.297085i \(-0.0960145\pi\)
−0.734709 + 0.678383i \(0.762681\pi\)
\(132\) 0.439279 + 0.760853i 0.0382343 + 0.0662238i
\(133\) −1.69805 3.61099i −0.147240 0.313112i
\(134\) −4.87998 + 8.45237i −0.421566 + 0.730174i
\(135\) −1.14553 1.98411i −0.0985912 0.170765i
\(136\) 3.20391 + 5.54934i 0.274733 + 0.475852i
\(137\) 9.47262 + 16.4071i 0.809300 + 1.40175i 0.913349 + 0.407177i \(0.133487\pi\)
−0.104049 + 0.994572i \(0.533180\pi\)
\(138\) 0.658760 + 1.14101i 0.0560774 + 0.0971289i
\(139\) 0.565160 0.978885i 0.0479362 0.0830280i −0.841062 0.540939i \(-0.818069\pi\)
0.888998 + 0.457911i \(0.151402\pi\)
\(140\) −6.04016 0.508795i −0.510487 0.0430010i
\(141\) 0.188939 + 0.327251i 0.0159115 + 0.0275595i
\(142\) 1.02408 + 1.77376i 0.0859392 + 0.148851i
\(143\) −0.691405 + 3.09131i −0.0578182 + 0.258508i
\(144\) −0.500000 + 0.866025i −0.0416667 + 0.0721688i
\(145\) 1.53339 2.65590i 0.127341 0.220561i
\(146\) 0.432504 + 0.749119i 0.0357943 + 0.0619975i
\(147\) 4.46478 5.39126i 0.368249 0.444664i
\(148\) 9.38675 0.771586
\(149\) 1.60500 0.131487 0.0657433 0.997837i \(-0.479058\pi\)
0.0657433 + 0.997837i \(0.479058\pi\)
\(150\) 0.124459 + 0.215569i 0.0101620 + 0.0176012i
\(151\) 10.2417 17.7391i 0.833457 1.44359i −0.0618242 0.998087i \(-0.519692\pi\)
0.895281 0.445502i \(-0.146975\pi\)
\(152\) 1.50820 0.122331
\(153\) 3.20391 + 5.54934i 0.259021 + 0.448637i
\(154\) 2.31624 + 0.195109i 0.186648 + 0.0157224i
\(155\) −8.92354 −0.716756
\(156\) −3.44070 + 1.07777i −0.275477 + 0.0862903i
\(157\) −5.16462 + 8.94539i −0.412182 + 0.713919i −0.995128 0.0985911i \(-0.968566\pi\)
0.582946 + 0.812511i \(0.301900\pi\)
\(158\) 8.36029 0.665109
\(159\) 1.22356 2.11926i 0.0970343 0.168068i
\(160\) 1.14553 1.98411i 0.0905618 0.156858i
\(161\) 3.47353 + 0.292594i 0.273753 + 0.0230596i
\(162\) −0.500000 + 0.866025i −0.0392837 + 0.0680414i
\(163\) −6.89780 −0.540277 −0.270139 0.962821i \(-0.587069\pi\)
−0.270139 + 0.962821i \(0.587069\pi\)
\(164\) 1.80195 3.12107i 0.140709 0.243715i
\(165\) −1.00641 1.74315i −0.0783489 0.135704i
\(166\) −4.33355 + 7.50593i −0.336349 + 0.582573i
\(167\) 9.73115 + 16.8549i 0.753019 + 1.30427i 0.946353 + 0.323135i \(0.104737\pi\)
−0.193334 + 0.981133i \(0.561930\pi\)
\(168\) 1.12588 + 2.39424i 0.0868636 + 0.184720i
\(169\) −11.7613 5.53815i −0.904718 0.426011i
\(170\) −7.34033 12.7138i −0.562977 0.975105i
\(171\) 1.50820 0.115335
\(172\) 9.91602 0.756089
\(173\) 22.0138 1.67368 0.836840 0.547447i \(-0.184400\pi\)
0.836840 + 0.547447i \(0.184400\pi\)
\(174\) −1.33859 −0.101478
\(175\) 0.656251 + 0.0552795i 0.0496079 + 0.00417874i
\(176\) −0.439279 + 0.760853i −0.0331119 + 0.0573515i
\(177\) −2.98411 5.16864i −0.224300 0.388498i
\(178\) 6.41693 + 11.1145i 0.480969 + 0.833064i
\(179\) −9.81637 −0.733710 −0.366855 0.930278i \(-0.619565\pi\)
−0.366855 + 0.930278i \(0.619565\pi\)
\(180\) 1.14553 1.98411i 0.0853825 0.147887i
\(181\) 22.9753 1.70774 0.853869 0.520487i \(-0.174250\pi\)
0.853869 + 0.520487i \(0.174250\pi\)
\(182\) −2.85621 + 9.10176i −0.211716 + 0.674667i
\(183\) −4.81564 −0.355983
\(184\) −0.658760 + 1.14101i −0.0485645 + 0.0841161i
\(185\) −21.5055 −1.58112
\(186\) 1.94748 + 3.37313i 0.142796 + 0.247330i
\(187\) 2.81482 + 4.87541i 0.205840 + 0.356525i
\(188\) −0.188939 + 0.327251i −0.0137798 + 0.0238673i
\(189\) 1.12588 + 2.39424i 0.0818958 + 0.174155i
\(190\) −3.45536 −0.250678
\(191\) −9.69073 −0.701196 −0.350598 0.936526i \(-0.614022\pi\)
−0.350598 + 0.936526i \(0.614022\pi\)
\(192\) −1.00000 −0.0721688
\(193\) −21.1067 −1.51929 −0.759647 0.650336i \(-0.774628\pi\)
−0.759647 + 0.650336i \(0.774628\pi\)
\(194\) 4.40338 + 7.62688i 0.316144 + 0.547578i
\(195\) 7.88282 2.46922i 0.564501 0.176824i
\(196\) 6.90136 + 1.17099i 0.492954 + 0.0836418i
\(197\) −6.76019 11.7090i −0.481644 0.834232i 0.518134 0.855299i \(-0.326627\pi\)
−0.999778 + 0.0210677i \(0.993293\pi\)
\(198\) −0.439279 + 0.760853i −0.0312182 + 0.0540715i
\(199\) 3.79449 + 6.57226i 0.268985 + 0.465895i 0.968600 0.248625i \(-0.0799786\pi\)
−0.699615 + 0.714520i \(0.746645\pi\)
\(200\) −0.124459 + 0.215569i −0.00880058 + 0.0152431i
\(201\) −9.75996 −0.688414
\(202\) 5.02693 8.70689i 0.353693 0.612615i
\(203\) −2.02198 + 2.90763i −0.141915 + 0.204076i
\(204\) −3.20391 + 5.54934i −0.224319 + 0.388531i
\(205\) −4.12836 + 7.15053i −0.288337 + 0.499415i
\(206\) 12.3597 0.861138
\(207\) −0.658760 + 1.14101i −0.0457870 + 0.0793054i
\(208\) −2.65372 2.44085i −0.184003 0.169243i
\(209\) 1.32504 0.0916548
\(210\) −2.57945 5.48533i −0.177999 0.378524i
\(211\) −6.06832 10.5106i −0.417760 0.723582i 0.577954 0.816070i \(-0.303851\pi\)
−0.995714 + 0.0924876i \(0.970518\pi\)
\(212\) 2.44711 0.168068
\(213\) −1.02408 + 1.77376i −0.0701690 + 0.121536i
\(214\) 3.40406 + 5.89601i 0.232697 + 0.403043i
\(215\) −22.7181 −1.54936
\(216\) −1.00000 −0.0680414
\(217\) 10.2687 + 0.864988i 0.697085 + 0.0587192i
\(218\) −0.460710 0.797973i −0.0312032 0.0540456i
\(219\) −0.432504 + 0.749119i −0.0292259 + 0.0506207i
\(220\) 1.00641 1.74315i 0.0678522 0.117523i
\(221\) −22.0474 + 6.90613i −1.48307 + 0.464557i
\(222\) 4.69338 + 8.12917i 0.314999 + 0.545594i
\(223\) −11.0968 19.2202i −0.743094 1.28708i −0.951080 0.308945i \(-0.900024\pi\)
0.207986 0.978132i \(-0.433309\pi\)
\(224\) −1.51053 + 2.17216i −0.100927 + 0.145134i
\(225\) −0.124459 + 0.215569i −0.00829727 + 0.0143713i
\(226\) 5.68802 + 9.85195i 0.378362 + 0.655342i
\(227\) 12.2142 + 21.1556i 0.810686 + 1.40415i 0.912385 + 0.409333i \(0.134239\pi\)
−0.101699 + 0.994815i \(0.532428\pi\)
\(228\) 0.754098 + 1.30614i 0.0499414 + 0.0865010i
\(229\) −14.9717 25.9317i −0.989358 1.71362i −0.620688 0.784058i \(-0.713147\pi\)
−0.368670 0.929560i \(-0.620187\pi\)
\(230\) 1.50925 2.61410i 0.0995173 0.172369i
\(231\) 0.989151 + 2.10348i 0.0650814 + 0.138399i
\(232\) −0.669294 1.15925i −0.0439413 0.0761086i
\(233\) −11.4574 19.8448i −0.750600 1.30008i −0.947532 0.319660i \(-0.896431\pi\)
0.196932 0.980417i \(-0.436902\pi\)
\(234\) −2.65372 2.44085i −0.173479 0.159563i
\(235\) 0.432868 0.749750i 0.0282372 0.0489083i
\(236\) 2.98411 5.16864i 0.194249 0.336450i
\(237\) 4.18014 + 7.24022i 0.271529 + 0.470303i
\(238\) 7.21444 + 15.3419i 0.467643 + 0.994466i
\(239\) −1.03992 −0.0672669 −0.0336334 0.999434i \(-0.510708\pi\)
−0.0336334 + 0.999434i \(0.510708\pi\)
\(240\) 2.29105 0.147887
\(241\) −3.23944 5.61088i −0.208671 0.361428i 0.742625 0.669707i \(-0.233580\pi\)
−0.951296 + 0.308279i \(0.900247\pi\)
\(242\) 5.11407 8.85783i 0.328745 0.569403i
\(243\) −1.00000 −0.0641500
\(244\) −2.40782 4.17047i −0.154145 0.266987i
\(245\) −15.8114 2.68279i −1.01015 0.171397i
\(246\) 3.60390 0.229776
\(247\) −1.18692 + 5.30677i −0.0755218 + 0.337662i
\(248\) −1.94748 + 3.37313i −0.123665 + 0.214194i
\(249\) −8.66710 −0.549255
\(250\) −5.44249 + 9.42666i −0.344213 + 0.596195i
\(251\) 5.33039 9.23251i 0.336451 0.582751i −0.647311 0.762226i \(-0.724107\pi\)
0.983763 + 0.179475i \(0.0574399\pi\)
\(252\) −1.51053 + 2.17216i −0.0951547 + 0.136833i
\(253\) −0.578759 + 1.00244i −0.0363863 + 0.0630229i
\(254\) −8.52039 −0.534617
\(255\) 7.34033 12.7138i 0.459669 0.796170i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −14.0419 + 24.3213i −0.875910 + 1.51712i −0.0201190 + 0.999798i \(0.506405\pi\)
−0.855791 + 0.517322i \(0.826929\pi\)
\(258\) 4.95801 + 8.58752i 0.308672 + 0.534636i
\(259\) 24.7474 + 2.08460i 1.53773 + 0.129531i
\(260\) 6.07982 + 5.59212i 0.377054 + 0.346808i
\(261\) −0.669294 1.15925i −0.0414282 0.0717558i
\(262\) −5.03929 −0.311328
\(263\) −24.1769 −1.49081 −0.745407 0.666610i \(-0.767745\pi\)
−0.745407 + 0.666610i \(0.767745\pi\)
\(264\) −0.878558 −0.0540715
\(265\) −5.60646 −0.344402
\(266\) 3.97623 + 0.334939i 0.243798 + 0.0205364i
\(267\) −6.41693 + 11.1145i −0.392710 + 0.680194i
\(268\) −4.87998 8.45237i −0.298092 0.516311i
\(269\) 3.96946 + 6.87530i 0.242022 + 0.419195i 0.961290 0.275538i \(-0.0888560\pi\)
−0.719268 + 0.694733i \(0.755523\pi\)
\(270\) 2.29105 0.139429
\(271\) 14.3347 24.8284i 0.870770 1.50822i 0.00956909 0.999954i \(-0.496954\pi\)
0.861201 0.508264i \(-0.169713\pi\)
\(272\) −6.40782 −0.388531
\(273\) −9.31046 + 2.07733i −0.563495 + 0.125726i
\(274\) −18.9452 −1.14452
\(275\) −0.109344 + 0.189390i −0.00659372 + 0.0114207i
\(276\) −1.31752 −0.0793054
\(277\) −6.24357 10.8142i −0.375139 0.649761i 0.615208 0.788364i \(-0.289072\pi\)
−0.990348 + 0.138604i \(0.955739\pi\)
\(278\) 0.565160 + 0.978885i 0.0338960 + 0.0587096i
\(279\) −1.94748 + 3.37313i −0.116592 + 0.201944i
\(280\) 3.46071 4.97654i 0.206817 0.297405i
\(281\) 23.4616 1.39960 0.699800 0.714339i \(-0.253272\pi\)
0.699800 + 0.714339i \(0.253272\pi\)
\(282\) −0.377877 −0.0225023
\(283\) −15.7899 −0.938612 −0.469306 0.883036i \(-0.655496\pi\)
−0.469306 + 0.883036i \(0.655496\pi\)
\(284\) −2.04817 −0.121536
\(285\) −1.72768 2.99243i −0.102339 0.177256i
\(286\) −2.33145 2.14443i −0.137861 0.126803i
\(287\) 5.44381 7.82825i 0.321338 0.462087i
\(288\) −0.500000 0.866025i −0.0294628 0.0510310i
\(289\) −12.0301 + 20.8367i −0.707652 + 1.22569i
\(290\) 1.53339 + 2.65590i 0.0900436 + 0.155960i
\(291\) −4.40338 + 7.62688i −0.258131 + 0.447096i
\(292\) −0.865008 −0.0506207
\(293\) 3.38969 5.87112i 0.198028 0.342994i −0.749861 0.661595i \(-0.769880\pi\)
0.947889 + 0.318601i \(0.103213\pi\)
\(294\) 2.43658 + 6.56225i 0.142104 + 0.382718i
\(295\) −6.83676 + 11.8416i −0.398051 + 0.689445i
\(296\) −4.69338 + 8.12917i −0.272797 + 0.472498i
\(297\) −0.878558 −0.0509791
\(298\) −0.802500 + 1.38997i −0.0464876 + 0.0805188i
\(299\) −3.49634 3.21587i −0.202198 0.185979i
\(300\) −0.248918 −0.0143713
\(301\) 26.1427 + 2.20214i 1.50684 + 0.126929i
\(302\) 10.2417 + 17.7391i 0.589343 + 1.02077i
\(303\) 10.0539 0.577579
\(304\) −0.754098 + 1.30614i −0.0432505 + 0.0749121i
\(305\) 5.51644 + 9.55476i 0.315871 + 0.547104i
\(306\) −6.40782 −0.366311
\(307\) −1.27687 −0.0728749 −0.0364374 0.999336i \(-0.511601\pi\)
−0.0364374 + 0.999336i \(0.511601\pi\)
\(308\) −1.32709 + 1.90837i −0.0756180 + 0.108739i
\(309\) 6.17983 + 10.7038i 0.351558 + 0.608916i
\(310\) 4.46177 7.72801i 0.253411 0.438921i
\(311\) −12.4336 + 21.5357i −0.705047 + 1.22118i 0.261627 + 0.965169i \(0.415741\pi\)
−0.966675 + 0.256009i \(0.917592\pi\)
\(312\) 0.786978 3.51862i 0.0445539 0.199202i
\(313\) 13.1601 + 22.7940i 0.743855 + 1.28839i 0.950728 + 0.310026i \(0.100338\pi\)
−0.206873 + 0.978368i \(0.566329\pi\)
\(314\) −5.16462 8.94539i −0.291456 0.504817i
\(315\) 3.46071 4.97654i 0.194989 0.280396i
\(316\) −4.18014 + 7.24022i −0.235151 + 0.407294i
\(317\) 9.33620 + 16.1708i 0.524373 + 0.908241i 0.999597 + 0.0283764i \(0.00903370\pi\)
−0.475224 + 0.879865i \(0.657633\pi\)
\(318\) 1.22356 + 2.11926i 0.0686136 + 0.118842i
\(319\) −0.588013 1.01847i −0.0329224 0.0570233i
\(320\) 1.14553 + 1.98411i 0.0640368 + 0.110915i
\(321\) −3.40406 + 5.89601i −0.189996 + 0.329083i
\(322\) −1.99016 + 2.86187i −0.110907 + 0.159486i
\(323\) 4.83213 + 8.36949i 0.268867 + 0.465691i
\(324\) −0.500000 0.866025i −0.0277778 0.0481125i
\(325\) −0.660560 0.607572i −0.0366413 0.0337020i
\(326\) 3.44890 5.97367i 0.191017 0.330851i
\(327\) 0.460710 0.797973i 0.0254773 0.0441280i
\(328\) 1.80195 + 3.12107i 0.0994960 + 0.172332i
\(329\) −0.570797 + 0.820811i −0.0314690 + 0.0452528i
\(330\) 2.01282 0.110802
\(331\) 36.0485 1.98140 0.990701 0.136057i \(-0.0434429\pi\)
0.990701 + 0.136057i \(0.0434429\pi\)
\(332\) −4.33355 7.50593i −0.237834 0.411941i
\(333\) −4.69338 + 8.12917i −0.257195 + 0.445476i
\(334\) −19.4623 −1.06493
\(335\) 11.1803 + 19.3648i 0.610844 + 1.05801i
\(336\) −2.63641 0.222079i −0.143828 0.0121154i
\(337\) 16.9888 0.925440 0.462720 0.886504i \(-0.346873\pi\)
0.462720 + 0.886504i \(0.346873\pi\)
\(338\) 10.6768 7.41654i 0.580744 0.403406i
\(339\) −5.68802 + 9.85195i −0.308931 + 0.535084i
\(340\) 14.6807 0.796170
\(341\) −1.71097 + 2.96349i −0.0926542 + 0.160482i
\(342\) −0.754098 + 1.30614i −0.0407770 + 0.0706278i
\(343\) 17.9348 + 4.61985i 0.968388 + 0.249449i
\(344\) −4.95801 + 8.58752i −0.267318 + 0.463008i
\(345\) 3.01851 0.162511
\(346\) −11.0069 + 19.0645i −0.591736 + 1.02492i
\(347\) −6.01805 10.4236i −0.323066 0.559566i 0.658053 0.752971i \(-0.271380\pi\)
−0.981119 + 0.193405i \(0.938047\pi\)
\(348\) 0.669294 1.15925i 0.0358779 0.0621424i
\(349\) −11.4544 19.8396i −0.613140 1.06199i −0.990708 0.136007i \(-0.956573\pi\)
0.377568 0.925982i \(-0.376760\pi\)
\(350\) −0.375999 + 0.540690i −0.0200980 + 0.0289011i
\(351\) 0.786978 3.51862i 0.0420058 0.187810i
\(352\) −0.439279 0.760853i −0.0234136 0.0405536i
\(353\) 24.3166 1.29424 0.647121 0.762387i \(-0.275973\pi\)
0.647121 + 0.762387i \(0.275973\pi\)
\(354\) 5.96823 0.317208
\(355\) 4.69246 0.249050
\(356\) −12.8339 −0.680194
\(357\) −9.67923 + 13.9188i −0.512279 + 0.736662i
\(358\) 4.90819 8.50123i 0.259406 0.449304i
\(359\) −14.4734 25.0686i −0.763875 1.32307i −0.940840 0.338853i \(-0.889961\pi\)
0.176965 0.984217i \(-0.443372\pi\)
\(360\) 1.14553 + 1.98411i 0.0603745 + 0.104572i
\(361\) −16.7253 −0.880281
\(362\) −11.4876 + 19.8972i −0.603777 + 1.04577i
\(363\) 10.2281 0.536838
\(364\) −6.45425 7.02443i −0.338295 0.368180i
\(365\) 1.98178 0.103731
\(366\) 2.40782 4.17047i 0.125859 0.217994i
\(367\) −27.0045 −1.40962 −0.704811 0.709395i \(-0.748968\pi\)
−0.704811 + 0.709395i \(0.748968\pi\)
\(368\) −0.658760 1.14101i −0.0343403 0.0594791i
\(369\) 1.80195 + 3.12107i 0.0938058 + 0.162476i
\(370\) 10.7528 18.6243i 0.559010 0.968234i
\(371\) 6.45160 + 0.543452i 0.334950 + 0.0282146i
\(372\) −3.89495 −0.201944
\(373\) 19.2350 0.995952 0.497976 0.867191i \(-0.334077\pi\)
0.497976 + 0.867191i \(0.334077\pi\)
\(374\) −5.62964 −0.291102
\(375\) −10.8850 −0.562098
\(376\) −0.188939 0.327251i −0.00974377 0.0168767i
\(377\) 4.60568 1.44268i 0.237205 0.0743020i
\(378\) −2.63641 0.222079i −0.135603 0.0114225i
\(379\) −16.1551 27.9815i −0.829834 1.43731i −0.898168 0.439652i \(-0.855102\pi\)
0.0683340 0.997662i \(-0.478232\pi\)
\(380\) 1.72768 2.99243i 0.0886280 0.153508i
\(381\) −4.26019 7.37887i −0.218256 0.378031i
\(382\) 4.84536 8.39241i 0.247910 0.429393i
\(383\) −31.4223 −1.60560 −0.802802 0.596246i \(-0.796658\pi\)
−0.802802 + 0.596246i \(0.796658\pi\)
\(384\) 0.500000 0.866025i 0.0255155 0.0441942i
\(385\) 3.04043 4.37217i 0.154955 0.222827i
\(386\) 10.5533 18.2789i 0.537151 0.930373i
\(387\) −4.95801 + 8.58752i −0.252030 + 0.436528i
\(388\) −8.80677 −0.447096
\(389\) 2.89119 5.00769i 0.146589 0.253900i −0.783375 0.621549i \(-0.786504\pi\)
0.929965 + 0.367649i \(0.119837\pi\)
\(390\) −1.80301 + 8.06133i −0.0912988 + 0.408201i
\(391\) −8.44244 −0.426952
\(392\) −4.46478 + 5.39126i −0.225506 + 0.272300i
\(393\) −2.51964 4.36415i −0.127099 0.220142i
\(394\) 13.5204 0.681147
\(395\) 9.57692 16.5877i 0.481867 0.834619i
\(396\) −0.439279 0.760853i −0.0220746 0.0382343i
\(397\) 6.98708 0.350672 0.175336 0.984509i \(-0.443899\pi\)
0.175336 + 0.984509i \(0.443899\pi\)
\(398\) −7.58899 −0.380402
\(399\) 1.69805 + 3.61099i 0.0850088 + 0.180775i
\(400\) −0.124459 0.215569i −0.00622295 0.0107785i
\(401\) 2.96749 5.13984i 0.148189 0.256671i −0.782369 0.622815i \(-0.785989\pi\)
0.930558 + 0.366144i \(0.119322\pi\)
\(402\) 4.87998 8.45237i 0.243391 0.421566i
\(403\) −10.3361 9.50700i −0.514879 0.473577i
\(404\) 5.02693 + 8.70689i 0.250099 + 0.433184i
\(405\) 1.14553 + 1.98411i 0.0569216 + 0.0985912i
\(406\) −1.50709 3.20490i −0.0747956 0.159057i
\(407\) −4.12340 + 7.14194i −0.204389 + 0.354013i
\(408\) −3.20391 5.54934i −0.158617 0.274733i
\(409\) 7.38923 + 12.7985i 0.365374 + 0.632846i 0.988836 0.149007i \(-0.0476077\pi\)
−0.623462 + 0.781854i \(0.714274\pi\)
\(410\) −4.12836 7.15053i −0.203885 0.353139i
\(411\) −9.47262 16.4071i −0.467250 0.809300i
\(412\) −6.17983 + 10.7038i −0.304458 + 0.527337i
\(413\) 9.01521 12.9640i 0.443609 0.637915i
\(414\) −0.658760 1.14101i −0.0323763 0.0560774i
\(415\) 9.92839 + 17.1965i 0.487365 + 0.844142i
\(416\) 3.44070 1.07777i 0.168694 0.0528418i
\(417\) −0.565160 + 0.978885i −0.0276760 + 0.0479362i
\(418\) −0.662519 + 1.14752i −0.0324049 + 0.0561269i
\(419\) −5.07336 8.78731i −0.247850 0.429288i 0.715079 0.699043i \(-0.246391\pi\)
−0.962929 + 0.269755i \(0.913057\pi\)
\(420\) 6.04016 + 0.508795i 0.294730 + 0.0248266i
\(421\) 7.70885 0.375706 0.187853 0.982197i \(-0.439847\pi\)
0.187853 + 0.982197i \(0.439847\pi\)
\(422\) 12.1366 0.590802
\(423\) −0.188939 0.327251i −0.00918652 0.0159115i
\(424\) −1.22356 + 2.11926i −0.0594211 + 0.102920i
\(425\) −1.59502 −0.0773700
\(426\) −1.02408 1.77376i −0.0496170 0.0859392i
\(427\) −5.42184 11.5298i −0.262381 0.557967i
\(428\) −6.80813 −0.329083
\(429\) 0.691405 3.09131i 0.0333814 0.149250i
\(430\) 11.3591 19.6745i 0.547782 0.948787i
\(431\) 35.7786 1.72339 0.861696 0.507424i \(-0.169402\pi\)
0.861696 + 0.507424i \(0.169402\pi\)
\(432\) 0.500000 0.866025i 0.0240563 0.0416667i
\(433\) −6.32535 + 10.9558i −0.303977 + 0.526504i −0.977033 0.213088i \(-0.931648\pi\)
0.673056 + 0.739592i \(0.264981\pi\)
\(434\) −5.88345 + 8.46047i −0.282415 + 0.406115i
\(435\) −1.53339 + 2.65590i −0.0735203 + 0.127341i
\(436\) 0.921420 0.0441280
\(437\) −0.993540 + 1.72086i −0.0475275 + 0.0823200i
\(438\) −0.432504 0.749119i −0.0206658 0.0357943i
\(439\) 13.6023 23.5598i 0.649200 1.12445i −0.334114 0.942533i \(-0.608437\pi\)
0.983314 0.181915i \(-0.0582296\pi\)
\(440\) 1.00641 + 1.74315i 0.0479787 + 0.0831016i
\(441\) −4.46478 + 5.39126i −0.212609 + 0.256727i
\(442\) 5.04281 22.5467i 0.239862 1.07244i
\(443\) −1.74860 3.02867i −0.0830786 0.143896i 0.821492 0.570220i \(-0.193142\pi\)
−0.904571 + 0.426323i \(0.859809\pi\)
\(444\) −9.38675 −0.445476
\(445\) 29.4030 1.39384
\(446\) 22.1935 1.05089
\(447\) −1.60500 −0.0759139
\(448\) −1.12588 2.39424i −0.0531929 0.113117i
\(449\) 8.08366 14.0013i 0.381491 0.660762i −0.609784 0.792567i \(-0.708744\pi\)
0.991276 + 0.131805i \(0.0420773\pi\)
\(450\) −0.124459 0.215569i −0.00586706 0.0101620i
\(451\) 1.58312 + 2.74204i 0.0745460 + 0.129118i
\(452\) −11.3760 −0.535084
\(453\) −10.2417 + 17.7391i −0.481196 + 0.833457i
\(454\) −24.4284 −1.14648
\(455\) 14.7870 + 16.0933i 0.693226 + 0.754467i
\(456\) −1.50820 −0.0706278
\(457\) −13.1305 + 22.7426i −0.614217 + 1.06386i 0.376304 + 0.926496i \(0.377195\pi\)
−0.990521 + 0.137359i \(0.956139\pi\)
\(458\) 29.9434 1.39916
\(459\) −3.20391 5.54934i −0.149546 0.259021i
\(460\) 1.50925 + 2.61410i 0.0703693 + 0.121883i
\(461\) −4.94386 + 8.56302i −0.230259 + 0.398819i −0.957884 0.287155i \(-0.907291\pi\)
0.727626 + 0.685974i \(0.240624\pi\)
\(462\) −2.31624 0.195109i −0.107761 0.00907731i
\(463\) −14.2082 −0.660310 −0.330155 0.943927i \(-0.607101\pi\)
−0.330155 + 0.943927i \(0.607101\pi\)
\(464\) 1.33859 0.0621424
\(465\) 8.92354 0.413819
\(466\) 22.9148 1.06151
\(467\) −1.47500 2.55478i −0.0682550 0.118221i 0.829878 0.557944i \(-0.188410\pi\)
−0.898133 + 0.439723i \(0.855076\pi\)
\(468\) 3.44070 1.07777i 0.159046 0.0498197i
\(469\) −10.9886 23.3677i −0.507404 1.07902i
\(470\) 0.432868 + 0.749750i 0.0199667 + 0.0345834i
\(471\) 5.16462 8.94539i 0.237973 0.412182i
\(472\) 2.98411 + 5.16864i 0.137355 + 0.237906i
\(473\) −4.35590 + 7.54463i −0.200284 + 0.346903i
\(474\) −8.36029 −0.384001
\(475\) −0.187709 + 0.325121i −0.00861267 + 0.0149176i
\(476\) −16.8937 1.42304i −0.774320 0.0652251i
\(477\) −1.22356 + 2.11926i −0.0560228 + 0.0970343i
\(478\) 0.519960 0.900598i 0.0237824 0.0411924i
\(479\) 19.8096 0.905124 0.452562 0.891733i \(-0.350510\pi\)
0.452562 + 0.891733i \(0.350510\pi\)
\(480\) −1.14553 + 1.98411i −0.0522859 + 0.0905618i
\(481\) −24.9098 22.9117i −1.13579 1.04468i
\(482\) 6.47888 0.295105
\(483\) −3.47353 0.292594i −0.158051 0.0133135i
\(484\) 5.11407 + 8.85783i 0.232458 + 0.402628i
\(485\) 20.1768 0.916179
\(486\) 0.500000 0.866025i 0.0226805 0.0392837i
\(487\) 6.29728 + 10.9072i 0.285357 + 0.494253i 0.972696 0.232084i \(-0.0745546\pi\)
−0.687339 + 0.726337i \(0.741221\pi\)
\(488\) 4.81564 0.217994
\(489\) 6.89780 0.311929
\(490\) 10.2291 12.3517i 0.462101 0.557991i
\(491\) 5.81280 + 10.0681i 0.262328 + 0.454365i 0.966860 0.255307i \(-0.0821765\pi\)
−0.704532 + 0.709672i \(0.748843\pi\)
\(492\) −1.80195 + 3.12107i −0.0812382 + 0.140709i
\(493\) 4.28872 7.42827i 0.193154 0.334553i
\(494\) −4.00234 3.68128i −0.180074 0.165629i
\(495\) 1.00641 + 1.74315i 0.0452348 + 0.0783489i
\(496\) −1.94748 3.37313i −0.0874442 0.151458i
\(497\) −5.39982 0.454855i −0.242215 0.0204030i
\(498\) 4.33355 7.50593i 0.194191 0.336349i
\(499\) 6.22713 + 10.7857i 0.278765 + 0.482834i 0.971078 0.238763i \(-0.0767418\pi\)
−0.692313 + 0.721597i \(0.743408\pi\)
\(500\) −5.44249 9.42666i −0.243395 0.421573i
\(501\) −9.73115 16.8549i −0.434756 0.753019i
\(502\) 5.33039 + 9.23251i 0.237907 + 0.412067i
\(503\) −15.7073 + 27.2058i −0.700354 + 1.21305i 0.267988 + 0.963422i \(0.413641\pi\)
−0.968342 + 0.249627i \(0.919692\pi\)
\(504\) −1.12588 2.39424i −0.0501507 0.106648i
\(505\) −11.5170 19.9479i −0.512498 0.887672i
\(506\) −0.578759 1.00244i −0.0257290 0.0445639i
\(507\) 11.7613 + 5.53815i 0.522339 + 0.245958i
\(508\) 4.26019 7.37887i 0.189016 0.327384i
\(509\) −3.59886 + 6.23341i −0.159517 + 0.276291i −0.934695 0.355452i \(-0.884327\pi\)
0.775178 + 0.631743i \(0.217660\pi\)
\(510\) 7.34033 + 12.7138i 0.325035 + 0.562977i
\(511\) −2.28052 0.192100i −0.100884 0.00849801i
\(512\) 1.00000 0.0441942
\(513\) −1.50820 −0.0665885
\(514\) −14.0419 24.3213i −0.619362 1.07277i
\(515\) 14.1583 24.5229i 0.623889 1.08061i
\(516\) −9.91602 −0.436528
\(517\) −0.165994 0.287509i −0.00730039 0.0126446i
\(518\) −14.1790 + 20.3896i −0.622990 + 0.895866i
\(519\) −22.0138 −0.966300
\(520\) −7.88282 + 2.46922i −0.345685 + 0.108282i
\(521\) 11.2983 19.5692i 0.494987 0.857342i −0.504996 0.863121i \(-0.668506\pi\)
0.999983 + 0.00577905i \(0.00183954\pi\)
\(522\) 1.33859 0.0585884
\(523\) 3.03635 5.25912i 0.132770 0.229965i −0.791973 0.610556i \(-0.790946\pi\)
0.924744 + 0.380591i \(0.124279\pi\)
\(524\) 2.51964 4.36415i 0.110071 0.190649i
\(525\) −0.656251 0.0552795i −0.0286412 0.00241260i
\(526\) 12.0885 20.9378i 0.527082 0.912933i
\(527\) −24.9582 −1.08719
\(528\) 0.439279 0.760853i 0.0191172 0.0331119i
\(529\) 10.6321 + 18.4153i 0.462264 + 0.800665i
\(530\) 2.80323 4.85534i 0.121764 0.210902i
\(531\) 2.98411 + 5.16864i 0.129499 + 0.224300i
\(532\) −2.27818 + 3.27605i −0.0987717 + 0.142035i
\(533\) −12.3999 + 3.88416i −0.537101 + 0.168242i
\(534\) −6.41693 11.1145i −0.277688 0.480969i
\(535\) 15.5978 0.674350
\(536\) 9.75996 0.421566
\(537\) 9.81637 0.423608
\(538\) −7.93891 −0.342271
\(539\) −3.92257 + 4.73653i −0.168957 + 0.204017i
\(540\) −1.14553 + 1.98411i −0.0492956 + 0.0853825i
\(541\) 3.16494 + 5.48183i 0.136071 + 0.235682i 0.926006 0.377508i \(-0.123219\pi\)
−0.789935 + 0.613191i \(0.789886\pi\)
\(542\) 14.3347 + 24.8284i 0.615728 + 1.06647i
\(543\) −22.9753 −0.985963
\(544\) 3.20391 5.54934i 0.137367 0.237926i
\(545\) −2.11102 −0.0904262
\(546\) 2.85621 9.10176i 0.122235 0.389519i
\(547\) 17.3685 0.742625 0.371312 0.928508i \(-0.378908\pi\)
0.371312 + 0.928508i \(0.378908\pi\)
\(548\) 9.47262 16.4071i 0.404650 0.700875i
\(549\) 4.81564 0.205527
\(550\) −0.109344 0.189390i −0.00466246 0.00807562i
\(551\) −1.00943 1.74838i −0.0430030 0.0744834i
\(552\) 0.658760 1.14101i 0.0280387 0.0485645i
\(553\) −12.6285 + 18.1599i −0.537018 + 0.772237i
\(554\) 12.4871 0.530527
\(555\) 21.5055 0.912859
\(556\) −1.13032 −0.0479362
\(557\) 39.8232 1.68736 0.843681 0.536845i \(-0.180384\pi\)
0.843681 + 0.536845i \(0.180384\pi\)
\(558\) −1.94748 3.37313i −0.0824432 0.142796i
\(559\) −26.3144 24.2035i −1.11298 1.02370i
\(560\) 2.57945 + 5.48533i 0.109002 + 0.231798i
\(561\) −2.81482 4.87541i −0.118842 0.205840i
\(562\) −11.7308 + 20.3183i −0.494833 + 0.857077i
\(563\) 2.29585 + 3.97654i 0.0967587 + 0.167591i 0.910341 0.413858i \(-0.135819\pi\)
−0.813583 + 0.581449i \(0.802486\pi\)
\(564\) 0.188939 0.327251i 0.00795576 0.0137798i
\(565\) 26.0631 1.09648
\(566\) 7.89495 13.6745i 0.331850 0.574780i
\(567\) −1.12588 2.39424i −0.0472826 0.100549i
\(568\) 1.02408 1.77376i 0.0429696 0.0744255i
\(569\) 8.74146 15.1407i 0.366461 0.634729i −0.622548 0.782581i \(-0.713903\pi\)
0.989010 + 0.147852i \(0.0472359\pi\)
\(570\) 3.45536 0.144729
\(571\) 8.05500 13.9517i 0.337091 0.583859i −0.646793 0.762666i \(-0.723890\pi\)
0.983884 + 0.178806i \(0.0572235\pi\)
\(572\) 3.02285 0.946879i 0.126392 0.0395910i
\(573\) 9.69073 0.404836
\(574\) 4.05756 + 8.62861i 0.169359 + 0.360151i
\(575\) −0.163977 0.284017i −0.00683833 0.0118443i
\(576\) 1.00000 0.0416667
\(577\) 3.99841 6.92544i 0.166456 0.288310i −0.770716 0.637179i \(-0.780101\pi\)
0.937171 + 0.348870i \(0.113434\pi\)
\(578\) −12.0301 20.8367i −0.500386 0.866693i
\(579\) 21.1067 0.877164
\(580\) −3.06677 −0.127341
\(581\) −9.75812 20.7511i −0.404835 0.860902i
\(582\) −4.40338 7.62688i −0.182526 0.316144i
\(583\) −1.07496 + 1.86189i −0.0445205 + 0.0771117i
\(584\) 0.432504 0.749119i 0.0178971 0.0309987i
\(585\) −7.88282 + 2.46922i −0.325915 + 0.102090i
\(586\) 3.38969 + 5.87112i 0.140027 + 0.242534i
\(587\) 10.4049 + 18.0219i 0.429458 + 0.743842i 0.996825 0.0796223i \(-0.0253714\pi\)
−0.567367 + 0.823465i \(0.692038\pi\)
\(588\) −6.90136 1.17099i −0.284607 0.0482906i
\(589\) −2.93718 + 5.08734i −0.121024 + 0.209620i
\(590\) −6.83676 11.8416i −0.281465 0.487511i
\(591\) 6.76019 + 11.7090i 0.278077 + 0.481644i
\(592\) −4.69338 8.12917i −0.192897 0.334107i
\(593\) −12.2317 21.1859i −0.502296 0.870002i −0.999996 0.00265305i \(-0.999156\pi\)
0.497701 0.867349i \(-0.334178\pi\)
\(594\) 0.439279 0.760853i 0.0180238 0.0312182i
\(595\) 38.7043 + 3.26027i 1.58672 + 0.133658i
\(596\) −0.802500 1.38997i −0.0328717 0.0569354i
\(597\) −3.79449 6.57226i −0.155298 0.268985i
\(598\) 4.53319 1.41998i 0.185376 0.0580672i
\(599\) −22.4292 + 38.8484i −0.916431 + 1.58730i −0.111638 + 0.993749i \(0.535610\pi\)
−0.804793 + 0.593555i \(0.797724\pi\)
\(600\) 0.124459 0.215569i 0.00508102 0.00880058i
\(601\) 12.2159 + 21.1585i 0.498296 + 0.863073i 0.999998 0.00196699i \(-0.000626114\pi\)
−0.501702 + 0.865040i \(0.667293\pi\)
\(602\) −14.9785 + 21.5392i −0.610477 + 0.877872i
\(603\) 9.75996 0.397456
\(604\) −20.4834 −0.833457
\(605\) −11.7166 20.2937i −0.476347 0.825058i
\(606\) −5.02693 + 8.70689i −0.204205 + 0.353693i
\(607\) −36.1822 −1.46859 −0.734296 0.678829i \(-0.762488\pi\)
−0.734296 + 0.678829i \(0.762488\pi\)
\(608\) −0.754098 1.30614i −0.0305827 0.0529708i
\(609\) 2.02198 2.90763i 0.0819348 0.117823i
\(610\) −11.0329 −0.446709
\(611\) 1.30016 0.407263i 0.0525990 0.0164761i
\(612\) 3.20391 5.54934i 0.129510 0.224319i
\(613\) 6.21294 0.250938 0.125469 0.992098i \(-0.459956\pi\)
0.125469 + 0.992098i \(0.459956\pi\)
\(614\) 0.638435 1.10580i 0.0257652 0.0446266i
\(615\) 4.12836 7.15053i 0.166472 0.288337i
\(616\) −0.989151 2.10348i −0.0398540 0.0847516i
\(617\) 21.8788 37.8953i 0.880809 1.52561i 0.0303660 0.999539i \(-0.490333\pi\)
0.850443 0.526067i \(-0.176334\pi\)
\(618\) −12.3597 −0.497178
\(619\) 9.54369 16.5301i 0.383593 0.664403i −0.607980 0.793952i \(-0.708020\pi\)
0.991573 + 0.129550i \(0.0413532\pi\)
\(620\) 4.46177 + 7.72801i 0.179189 + 0.310364i
\(621\) 0.658760 1.14101i 0.0264351 0.0457870i
\(622\) −12.4336 21.5357i −0.498544 0.863503i
\(623\) −33.8354 2.85013i −1.35559 0.114188i
\(624\) 2.65372 + 2.44085i 0.106234 + 0.0977123i
\(625\) 13.0913 + 22.6748i 0.523653 + 0.906993i
\(626\) −26.3203 −1.05197
\(627\) −1.32504 −0.0529169
\(628\) 10.3292 0.412182
\(629\) −60.1486 −2.39828
\(630\) 2.57945 + 5.48533i 0.102768 + 0.218541i
\(631\) −11.2873 + 19.5502i −0.449340 + 0.778280i −0.998343 0.0575405i \(-0.981674\pi\)
0.549003 + 0.835820i \(0.315008\pi\)
\(632\) −4.18014 7.24022i −0.166277 0.288000i
\(633\) 6.06832 + 10.5106i 0.241194 + 0.417760i
\(634\) −18.6724 −0.741576
\(635\) −9.76032 + 16.9054i −0.387327 + 0.670869i
\(636\) −2.44711 −0.0970343
\(637\) −15.4561 19.9527i −0.612393 0.790554i
\(638\) 1.17603 0.0465593
\(639\) 1.02408 1.77376i 0.0405121 0.0701690i
\(640\) −2.29105 −0.0905618
\(641\) −10.9122 18.9004i −0.431005 0.746523i 0.565955 0.824436i \(-0.308508\pi\)
−0.996960 + 0.0779133i \(0.975174\pi\)
\(642\) −3.40406 5.89601i −0.134348 0.232697i
\(643\) 7.72503 13.3801i 0.304645 0.527661i −0.672537 0.740064i \(-0.734795\pi\)
0.977182 + 0.212402i \(0.0681287\pi\)
\(644\) −1.48337 3.15446i −0.0584530 0.124303i
\(645\) 22.7181 0.894525
\(646\) −9.66426 −0.380235
\(647\) 10.7846 0.423986 0.211993 0.977271i \(-0.432005\pi\)
0.211993 + 0.977271i \(0.432005\pi\)
\(648\) 1.00000 0.0392837
\(649\) 2.62172 + 4.54094i 0.102911 + 0.178248i
\(650\) 0.856453 0.268275i 0.0335928 0.0105226i
\(651\) −10.2687 0.864988i −0.402462 0.0339015i
\(652\) 3.44890 + 5.97367i 0.135069 + 0.233947i
\(653\) 10.1666 17.6091i 0.397850 0.689096i −0.595611 0.803273i \(-0.703090\pi\)
0.993460 + 0.114178i \(0.0364233\pi\)
\(654\) 0.460710 + 0.797973i 0.0180152 + 0.0312032i
\(655\) −5.77264 + 9.99850i −0.225556 + 0.390674i
\(656\) −3.60390 −0.140709
\(657\) 0.432504 0.749119i 0.0168736 0.0292259i
\(658\) −0.425445 0.904730i −0.0165856 0.0352700i
\(659\) 15.1395 26.2224i 0.589752 1.02148i −0.404512 0.914532i \(-0.632559\pi\)
0.994265 0.106948i \(-0.0341079\pi\)
\(660\) −1.00641 + 1.74315i −0.0391745 + 0.0678522i
\(661\) 9.88743 0.384577 0.192288 0.981338i \(-0.438409\pi\)
0.192288 + 0.981338i \(0.438409\pi\)
\(662\) −18.0242 + 31.2189i −0.700531 + 1.21336i
\(663\) 22.0474 6.90613i 0.856250 0.268212i
\(664\) 8.66710 0.336349
\(665\) 5.21943 7.50560i 0.202401 0.291055i
\(666\) −4.69338 8.12917i −0.181865 0.314999i
\(667\) 1.76362 0.0682875
\(668\) 9.73115 16.8549i 0.376510 0.652134i
\(669\) 11.0968 + 19.2202i 0.429026 + 0.743094i
\(670\) −22.3606 −0.863864
\(671\) 4.23082 0.163329
\(672\) 1.51053 2.17216i 0.0582701 0.0837930i
\(673\) −7.13518 12.3585i −0.275041 0.476385i 0.695104 0.718909i \(-0.255358\pi\)
−0.970146 + 0.242524i \(0.922025\pi\)
\(674\) −8.49441 + 14.7128i −0.327193 + 0.566714i
\(675\) 0.124459 0.215569i 0.00479043 0.00829727i
\(676\) 1.08449 + 12.9547i 0.0417111 + 0.498257i
\(677\) 16.7860 + 29.0742i 0.645139 + 1.11741i 0.984269 + 0.176674i \(0.0565338\pi\)
−0.339130 + 0.940739i \(0.610133\pi\)
\(678\) −5.68802 9.85195i −0.218447 0.378362i
\(679\) −23.2183 1.95580i −0.891036 0.0750567i
\(680\) −7.34033 + 12.7138i −0.281489 + 0.487553i
\(681\) −12.2142 21.1556i −0.468050 0.810686i
\(682\) −1.71097 2.96349i −0.0655164 0.113478i
\(683\) 8.84505 + 15.3201i 0.338446 + 0.586206i 0.984141 0.177390i \(-0.0567653\pi\)
−0.645694 + 0.763596i \(0.723432\pi\)
\(684\) −0.754098 1.30614i −0.0288337 0.0499414i
\(685\) −21.7023 + 37.5894i −0.829201 + 1.43622i
\(686\) −12.9683 + 13.2221i −0.495132 + 0.504821i
\(687\) 14.9717 + 25.9317i 0.571206 + 0.989358i
\(688\) −4.95801 8.58752i −0.189022 0.327396i
\(689\) −6.49395 5.97303i −0.247400 0.227554i
\(690\) −1.50925 + 2.61410i −0.0574563 + 0.0995173i
\(691\) −19.1359 + 33.1443i −0.727963 + 1.26087i 0.229780 + 0.973243i \(0.426199\pi\)
−0.957743 + 0.287626i \(0.907134\pi\)
\(692\) −11.0069 19.0645i −0.418420 0.724725i
\(693\) −0.989151 2.10348i −0.0375747 0.0799046i
\(694\) 12.0361 0.456884
\(695\) 2.58962 0.0982299
\(696\) 0.669294 + 1.15925i 0.0253695 + 0.0439413i
\(697\) −11.5466 + 19.9992i −0.437358 + 0.757526i
\(698\) 22.9088 0.867110
\(699\) 11.4574 + 19.8448i 0.433359 + 0.750600i
\(700\) −0.280252 0.595970i −0.0105925 0.0225255i
\(701\) −29.3574 −1.10882 −0.554408 0.832245i \(-0.687055\pi\)
−0.554408 + 0.832245i \(0.687055\pi\)
\(702\) 2.65372 + 2.44085i 0.100158 + 0.0921240i
\(703\) −7.07854 + 12.2604i −0.266972 + 0.462409i
\(704\) 0.878558 0.0331119
\(705\) −0.432868 + 0.749750i −0.0163028 + 0.0282372i
\(706\) −12.1583 + 21.0588i −0.457584 + 0.792558i
\(707\) 11.3194 + 24.0714i 0.425711 + 0.905296i
\(708\) −2.98411 + 5.16864i −0.112150 + 0.194249i
\(709\) −1.32163 −0.0496347 −0.0248174 0.999692i \(-0.507900\pi\)
−0.0248174 + 0.999692i \(0.507900\pi\)
\(710\) −2.34623 + 4.06379i −0.0880524 + 0.152511i
\(711\) −4.18014 7.24022i −0.156768 0.271529i
\(712\) 6.41693 11.1145i 0.240485 0.416532i
\(713\) −2.56584 4.44416i −0.0960915 0.166435i
\(714\) −7.21444 15.3419i −0.269994 0.574155i
\(715\) −6.92551 + 2.16935i −0.259000 + 0.0811291i
\(716\) 4.90819 + 8.50123i 0.183428 + 0.317706i
\(717\) 1.03992 0.0388365
\(718\) 28.9467 1.08028
\(719\) 24.7181 0.921830 0.460915 0.887444i \(-0.347521\pi\)
0.460915 + 0.887444i \(0.347521\pi\)
\(720\) −2.29105 −0.0853825
\(721\) −18.6697 + 26.8472i −0.695295 + 0.999841i
\(722\) 8.36267 14.4846i 0.311226 0.539060i
\(723\) 3.23944 + 5.61088i 0.120476 + 0.208671i
\(724\) −11.4876 19.8972i −0.426935 0.739473i
\(725\) 0.333199 0.0123747
\(726\) −5.11407 + 8.85783i −0.189801 + 0.328745i
\(727\) 8.76033 0.324903 0.162451 0.986717i \(-0.448060\pi\)
0.162451 + 0.986717i \(0.448060\pi\)
\(728\) 9.31046 2.07733i 0.345069 0.0769909i
\(729\) 1.00000 0.0370370
\(730\) −0.990889 + 1.71627i −0.0366744 + 0.0635220i
\(731\) −63.5401 −2.35011
\(732\) 2.40782 + 4.17047i 0.0889956 + 0.154145i
\(733\) −6.38026 11.0509i −0.235660 0.408176i 0.723804 0.690006i \(-0.242392\pi\)
−0.959464 + 0.281830i \(0.909059\pi\)
\(734\) 13.5022 23.3866i 0.498377 0.863214i
\(735\) 15.8114 + 2.68279i 0.583211 + 0.0989561i
\(736\) 1.31752 0.0485645
\(737\) 8.57469 0.315853
\(738\) −3.60390 −0.132661
\(739\) 21.6648 0.796953 0.398476 0.917179i \(-0.369539\pi\)
0.398476 + 0.917179i \(0.369539\pi\)
\(740\) 10.7528 + 18.6243i 0.395280 + 0.684645i
\(741\) 1.18692 5.30677i 0.0436025 0.194949i
\(742\) −3.69644 + 5.31552i −0.135701 + 0.195139i
\(743\) 6.46703 + 11.2012i 0.237252 + 0.410933i 0.959925 0.280258i \(-0.0904199\pi\)
−0.722673 + 0.691191i \(0.757087\pi\)
\(744\) 1.94748 3.37313i 0.0713979 0.123665i
\(745\) 1.83857 + 3.18449i 0.0673599 + 0.116671i
\(746\) −9.61751 + 16.6580i −0.352122 + 0.609893i
\(747\) 8.66710 0.317113
\(748\) 2.81482 4.87541i 0.102920 0.178263i
\(749\) −17.9490 1.51194i −0.655844 0.0552452i
\(750\) 5.44249 9.42666i 0.198732 0.344213i
\(751\) −4.30364 + 7.45412i −0.157042 + 0.272005i −0.933801 0.357794i \(-0.883529\pi\)
0.776759 + 0.629798i \(0.216862\pi\)
\(752\) 0.377877 0.0137798
\(753\) −5.33039 + 9.23251i −0.194250 + 0.336451i
\(754\) −1.05344 + 4.70998i −0.0383640 + 0.171527i
\(755\) 46.9285 1.70790
\(756\) 1.51053 2.17216i 0.0549376 0.0790008i
\(757\) 7.93369 + 13.7416i 0.288355 + 0.499445i 0.973417 0.229039i \(-0.0735584\pi\)
−0.685062 + 0.728484i \(0.740225\pi\)
\(758\) 32.3103 1.17356
\(759\) 0.578759 1.00244i 0.0210076 0.0363863i
\(760\) 1.72768 + 2.99243i 0.0626695 + 0.108547i
\(761\) 26.0348 0.943761 0.471880 0.881663i \(-0.343575\pi\)
0.471880 + 0.881663i \(0.343575\pi\)
\(762\) 8.52039 0.308661
\(763\) 2.42925 + 0.204628i 0.0879446 + 0.00740804i
\(764\) 4.84536 + 8.39241i 0.175299 + 0.303627i
\(765\) −7.34033 + 12.7138i −0.265390 + 0.459669i
\(766\) 15.7111 27.2125i 0.567667 0.983228i
\(767\) −20.5349 + 6.43235i −0.741472 + 0.232259i
\(768\) 0.500000 + 0.866025i 0.0180422 + 0.0312500i
\(769\) 18.9239 + 32.7772i 0.682415 + 1.18198i 0.974242 + 0.225506i \(0.0724036\pi\)
−0.291827 + 0.956471i \(0.594263\pi\)
\(770\) 2.26620 + 4.81918i 0.0816681 + 0.173671i
\(771\) 14.0419 24.3213i 0.505707 0.875910i
\(772\) 10.5533 + 18.2789i 0.379823 + 0.657873i
\(773\) −21.3629 37.0016i −0.768370 1.33086i −0.938446 0.345425i \(-0.887735\pi\)
0.170076 0.985431i \(-0.445599\pi\)
\(774\) −4.95801 8.58752i −0.178212 0.308672i
\(775\) −0.484762 0.839632i −0.0174132 0.0301605i
\(776\) 4.40338 7.62688i 0.158072 0.273789i
\(777\) −24.7474 2.08460i −0.887807 0.0747847i
\(778\) 2.89119 + 5.00769i 0.103654 + 0.179534i
\(779\) 2.71770 + 4.70719i 0.0973715 + 0.168652i
\(780\) −6.07982 5.59212i −0.217692 0.200230i
\(781\) 0.899716 1.55835i 0.0321944 0.0557623i
\(782\) 4.22122 7.31137i 0.150950 0.261454i
\(783\) 0.669294 + 1.15925i 0.0239186 + 0.0414282i
\(784\) −2.43658 6.56225i −0.0870206 0.234366i
\(785\) −23.6648 −0.844634
\(786\) 5.03929 0.179746
\(787\) −3.51846 6.09415i −0.125419 0.217233i 0.796477 0.604668i \(-0.206694\pi\)
−0.921897 + 0.387435i \(0.873361\pi\)
\(788\) −6.76019 + 11.7090i −0.240822 + 0.417116i
\(789\) 24.1769 0.860722
\(790\) 9.57692 + 16.5877i 0.340732 + 0.590165i
\(791\) −29.9920 2.52638i −1.06639 0.0898279i
\(792\) 0.878558 0.0312182
\(793\) −3.78980 + 16.9444i −0.134580 + 0.601713i
\(794\) −3.49354 + 6.05099i −0.123981 + 0.214742i
\(795\) 5.60646 0.198841
\(796\) 3.79449 6.57226i 0.134492 0.232947i
\(797\) 6.48013 11.2239i 0.229538 0.397572i −0.728133 0.685436i \(-0.759612\pi\)
0.957671 + 0.287864i \(0.0929451\pi\)
\(798\) −3.97623 0.334939i −0.140757 0.0118567i
\(799\) 1.21069 2.09697i 0.0428310 0.0741854i
\(800\) 0.248918 0.00880058
\(801\) 6.41693 11.1145i 0.226731 0.392710i
\(802\) 2.96749 + 5.13984i 0.104786 + 0.181494i
\(803\) 0.379979 0.658144i 0.0134092 0.0232254i
\(804\) 4.87998 + 8.45237i 0.172104 + 0.298092i
\(805\) 3.39848 + 7.22704i 0.119781 + 0.254720i
\(806\) 13.4014 4.19784i 0.472043 0.147863i
\(807\) −3.96946 6.87530i −0.139732 0.242022i
\(808\) −10.0539 −0.353693
\(809\) 24.0929 0.847060 0.423530 0.905882i \(-0.360791\pi\)
0.423530 + 0.905882i \(0.360791\pi\)
\(810\) −2.29105 −0.0804994
\(811\) −0.569121 −0.0199845 −0.00999227 0.999950i \(-0.503181\pi\)
−0.00999227 + 0.999950i \(0.503181\pi\)
\(812\) 3.52907 + 0.297272i 0.123846 + 0.0104322i
\(813\) −14.3347 + 24.8284i −0.502739 + 0.870770i
\(814\) −4.12340 7.14194i −0.144525 0.250325i
\(815\) −7.90160 13.6860i −0.276781 0.479399i
\(816\) 6.40782 0.224319
\(817\) −7.47765 + 12.9517i −0.261610 + 0.453122i
\(818\) −14.7785 −0.516717
\(819\) 9.31046 2.07733i 0.325334 0.0725877i
\(820\) 8.25672 0.288337
\(821\) −25.7343 + 44.5731i −0.898134 + 1.55561i −0.0682560 + 0.997668i \(0.521743\pi\)
−0.829878 + 0.557945i \(0.811590\pi\)
\(822\) 18.9452 0.660791
\(823\) −19.4326 33.6583i −0.677379 1.17326i −0.975767 0.218811i \(-0.929782\pi\)
0.298388 0.954445i \(-0.403551\pi\)
\(824\) −6.17983 10.7038i −0.215284 0.372884i
\(825\) 0.109344 0.189390i 0.00380688 0.00659372i
\(826\) 6.71951 + 14.2894i 0.233802 + 0.497191i
\(827\) 28.2170 0.981203 0.490601 0.871384i \(-0.336777\pi\)
0.490601 + 0.871384i \(0.336777\pi\)
\(828\) 1.31752 0.0457870
\(829\) −11.5781 −0.402124 −0.201062 0.979579i \(-0.564439\pi\)
−0.201062 + 0.979579i \(0.564439\pi\)
\(830\) −19.8568 −0.689239
\(831\) 6.24357 + 10.8142i 0.216587 + 0.375139i
\(832\) −0.786978 + 3.51862i −0.0272835 + 0.121986i
\(833\) −44.2227 7.50347i −1.53223 0.259980i
\(834\) −0.565160 0.978885i −0.0195699 0.0338960i
\(835\) −22.2946 + 38.6153i −0.771536 + 1.33634i
\(836\) −0.662519 1.14752i −0.0229137 0.0396877i
\(837\) 1.94748 3.37313i 0.0673146 0.116592i
\(838\) 10.1467 0.350512
\(839\) −15.9568 + 27.6379i −0.550889 + 0.954167i 0.447322 + 0.894373i \(0.352378\pi\)
−0.998211 + 0.0597941i \(0.980956\pi\)
\(840\) −3.46071 + 4.97654i −0.119406 + 0.171707i
\(841\) 13.6041 23.5630i 0.469107 0.812516i
\(842\) −3.85442 + 6.67606i −0.132832 + 0.230072i
\(843\) −23.4616 −0.808060
\(844\) −6.06832 + 10.5106i −0.208880 + 0.361791i
\(845\) −2.48462 29.6799i −0.0854736 1.02102i
\(846\) 0.377877 0.0129917
\(847\) 11.5157 + 24.4886i 0.395683 + 0.841439i
\(848\) −1.22356 2.11926i −0.0420171 0.0727757i
\(849\) 15.7899 0.541908
\(850\) 0.797511 1.38133i 0.0273544 0.0473792i
\(851\) −6.18362 10.7103i −0.211972 0.367146i
\(852\) 2.04817 0.0701690
\(853\) 6.06219 0.207565 0.103783 0.994600i \(-0.466905\pi\)
0.103783 + 0.994600i \(0.466905\pi\)
\(854\) 12.6960 + 1.06945i 0.434449 + 0.0365960i
\(855\) 1.72768 + 2.99243i 0.0590854 + 0.102339i
\(856\) 3.40406 5.89601i 0.116348 0.201521i
\(857\) 27.2702 47.2333i 0.931531 1.61346i 0.150825 0.988560i \(-0.451807\pi\)
0.780706 0.624899i \(-0.214860\pi\)
\(858\) 2.33145 + 2.14443i 0.0795943 + 0.0732096i
\(859\) 27.3472 + 47.3667i 0.933074 + 1.61613i 0.778033 + 0.628224i \(0.216218\pi\)
0.155042 + 0.987908i \(0.450449\pi\)
\(860\) 11.3591 + 19.6745i 0.387341 + 0.670894i
\(861\) −5.44381 + 7.82825i −0.185525 + 0.266786i
\(862\) −17.8893 + 30.9851i −0.609311 + 1.05536i
\(863\) −2.28666 3.96062i −0.0778389 0.134821i 0.824478 0.565893i \(-0.191469\pi\)
−0.902317 + 0.431073i \(0.858135\pi\)
\(864\) 0.500000 + 0.866025i 0.0170103 + 0.0294628i
\(865\) 25.2174 + 43.6778i 0.857418 + 1.48509i
\(866\) −6.32535 10.9558i −0.214944 0.372294i
\(867\) 12.0301 20.8367i 0.408563 0.707652i
\(868\) −4.38525 9.32545i −0.148845 0.316527i
\(869\) −3.67250 6.36095i −0.124581 0.215780i
\(870\) −1.53339 2.65590i −0.0519867 0.0900436i
\(871\) −7.68087 + 34.3416i −0.260256 + 1.16362i
\(872\) −0.460710 + 0.797973i −0.0156016 + 0.0270228i
\(873\) 4.40338 7.62688i 0.149032 0.258131i
\(874\) −0.993540 1.72086i −0.0336070 0.0582090i
\(875\) −12.2552 26.0613i −0.414301 0.881031i
\(876\) 0.865008 0.0292259
\(877\) 58.7214 1.98288 0.991440 0.130560i \(-0.0416775\pi\)
0.991440 + 0.130560i \(0.0416775\pi\)
\(878\) 13.6023 + 23.5598i 0.459054 + 0.795105i
\(879\) −3.38969 + 5.87112i −0.114331 + 0.198028i
\(880\) −2.01282 −0.0678522
\(881\) 6.95948 + 12.0542i 0.234471 + 0.406115i 0.959119 0.283004i \(-0.0913309\pi\)
−0.724648 + 0.689119i \(0.757998\pi\)
\(882\) −2.43658 6.56225i −0.0820438 0.220962i
\(883\) 40.5135 1.36339 0.681695 0.731637i \(-0.261243\pi\)
0.681695 + 0.731637i \(0.261243\pi\)
\(884\) 17.0046 + 15.6405i 0.571926 + 0.526048i
\(885\) 6.83676 11.8416i 0.229815 0.398051i
\(886\) 3.49721 0.117491
\(887\) −23.9892 + 41.5506i −0.805480 + 1.39513i 0.110487 + 0.993878i \(0.464759\pi\)
−0.915967 + 0.401255i \(0.868574\pi\)
\(888\) 4.69338 8.12917i 0.157499 0.272797i
\(889\) 12.8703 18.5077i 0.431657 0.620727i
\(890\) −14.7015 + 25.4638i −0.492796 + 0.853548i
\(891\) 0.878558 0.0294328
\(892\) −11.0968 + 19.2202i −0.371547 + 0.643538i
\(893\) −0.284957 0.493560i −0.00953572 0.0165163i
\(894\) 0.802500 1.38997i 0.0268396 0.0464876i
\(895\) −11.2449 19.4768i −0.375876 0.651036i
\(896\) 2.63641 + 0.222079i 0.0880764 + 0.00741914i
\(897\) 3.49634 + 3.21587i 0.116739 + 0.107375i
\(898\) 8.08366 + 14.0013i 0.269755 + 0.467230i
\(899\) 5.21373 0.173888
\(900\) 0.248918 0.00829727
\(901\) −15.6807 −0.522398
\(902\) −3.16623 −0.105424
\(903\) −26.1427 2.20214i −0.869976 0.0732827i
\(904\) 5.68802 9.85195i 0.189181 0.327671i
\(905\) 26.3188 + 45.5854i 0.874866 + 1.51531i
\(906\) −10.2417 17.7391i −0.340257 0.589343i
\(907\) −25.3615 −0.842114 −0.421057 0.907034i \(-0.638341\pi\)
−0.421057 + 0.907034i \(0.638341\pi\)
\(908\) 12.2142 21.1556i 0.405343 0.702074i
\(909\) −10.0539 −0.333465
\(910\) −21.3308 + 4.75927i −0.707107 + 0.157768i
\(911\) −50.6581 −1.67838 −0.839189 0.543840i \(-0.816970\pi\)
−0.839189 + 0.543840i \(0.816970\pi\)
\(912\) 0.754098 1.30614i 0.0249707 0.0432505i
\(913\) 7.61455 0.252005
\(914\) −13.1305 22.7426i −0.434317 0.752259i
\(915\) −5.51644 9.55476i −0.182368 0.315871i
\(916\) −14.9717 + 25.9317i −0.494679 + 0.856809i
\(917\) 7.61202 10.9462i 0.251371 0.361474i
\(918\) 6.40782 0.211490
\(919\) −25.1562 −0.829825 −0.414913 0.909861i \(-0.636188\pi\)
−0.414913 + 0.909861i \(0.636188\pi\)
\(920\) −3.01851 −0.0995173
\(921\) 1.27687 0.0420743
\(922\) −4.94386 8.56302i −0.162817 0.282008i
\(923\) 5.43527 + 4.99927i 0.178904 + 0.164553i
\(924\) 1.32709 1.90837i 0.0436581 0.0627807i
\(925\) −1.16827 2.02350i −0.0384124 0.0665322i
\(926\) 7.10408 12.3046i 0.233455 0.404355i
\(927\) −6.17983 10.7038i −0.202972 0.351558i
\(928\) −0.669294 + 1.15925i −0.0219706 + 0.0380543i
\(929\) 30.2210 0.991519 0.495759 0.868460i \(-0.334890\pi\)
0.495759 + 0.868460i \(0.334890\pi\)
\(930\) −4.46177 + 7.72801i −0.146307 + 0.253411i
\(931\) −6.73377 + 8.13108i −0.220691 + 0.266486i
\(932\) −11.4574 + 19.8448i −0.375300 + 0.650039i
\(933\) 12.4336 21.5357i 0.407059 0.705047i
\(934\) 2.95000 0.0965271
\(935\) −6.44890 + 11.1698i −0.210902 + 0.365292i
\(936\) −0.786978 + 3.51862i −0.0257232 + 0.115010i
\(937\) −33.2013 −1.08464 −0.542320 0.840172i \(-0.682454\pi\)
−0.542320 + 0.840172i \(0.682454\pi\)
\(938\) 25.7313 + 2.16748i 0.840157 + 0.0707709i
\(939\) −13.1601 22.7940i −0.429465 0.743855i
\(940\) −0.865737 −0.0282372
\(941\) 10.3309 17.8937i 0.336779 0.583318i −0.647046 0.762451i \(-0.723996\pi\)
0.983825 + 0.179133i \(0.0573292\pi\)
\(942\) 5.16462 + 8.94539i 0.168272 + 0.291456i
\(943\) −4.74821 −0.154623
\(944\) −5.96823 −0.194249
\(945\) −3.46071 + 4.97654i −0.112577 + 0.161887i
\(946\) −4.35590 7.54463i −0.141622 0.245297i
\(947\) −2.50723 + 4.34266i −0.0814741 + 0.141117i −0.903883 0.427779i \(-0.859296\pi\)
0.822409 + 0.568896i \(0.192629\pi\)
\(948\) 4.18014 7.24022i 0.135765 0.235151i
\(949\) 2.29549 + 2.11135i 0.0745148 + 0.0685375i
\(950\) −0.187709 0.325121i −0.00609008 0.0105483i
\(951\) −9.33620 16.1708i −0.302747 0.524373i
\(952\) 9.67923 13.9188i 0.313706 0.451112i
\(953\) 20.4600 35.4378i 0.662765 1.14794i −0.317121 0.948385i \(-0.602716\pi\)
0.979886 0.199558i \(-0.0639505\pi\)
\(954\) −1.22356 2.11926i −0.0396141 0.0686136i
\(955\) −11.1010 19.2275i −0.359219 0.622186i
\(956\) 0.519960 + 0.900598i 0.0168167 + 0.0291274i
\(957\) 0.588013 + 1.01847i 0.0190078 + 0.0329224i
\(958\) −9.90480 + 17.1556i −0.320010 + 0.554273i
\(959\) 28.6174 41.1521i 0.924104 1.32887i
\(960\) −1.14553 1.98411i −0.0369717 0.0640368i
\(961\) 7.91468 + 13.7086i 0.255312 + 0.442214i
\(962\) 32.2970 10.1167i 1.04130 0.326176i
\(963\) 3.40406 5.89601i 0.109694 0.189996i
\(964\) −3.23944 + 5.61088i −0.104335 + 0.180714i
\(965\) −24.1783 41.8780i −0.778326 1.34810i
\(966\) 1.99016 2.86187i 0.0640323 0.0920791i
\(967\) 48.1932 1.54979 0.774894 0.632091i \(-0.217803\pi\)
0.774894 + 0.632091i \(0.217803\pi\)
\(968\) −10.2281 −0.328745
\(969\) −4.83213 8.36949i −0.155230 0.268867i
\(970\) −10.0884 + 17.4736i −0.323918 + 0.561043i
\(971\) −32.1224 −1.03086 −0.515428 0.856933i \(-0.672367\pi\)
−0.515428 + 0.856933i \(0.672367\pi\)
\(972\) 0.500000 + 0.866025i 0.0160375 + 0.0277778i
\(973\) −2.97999 0.251020i −0.0955341 0.00804735i
\(974\) −12.5946 −0.403556
\(975\) 0.660560 + 0.607572i 0.0211548 + 0.0194579i
\(976\) −2.40782 + 4.17047i −0.0770725 + 0.133493i
\(977\) 19.9484 0.638205 0.319102 0.947720i \(-0.396619\pi\)
0.319102 + 0.947720i \(0.396619\pi\)
\(978\) −3.44890 + 5.97367i −0.110284 + 0.191017i
\(979\) 5.63764 9.76469i 0.180180 0.312081i
\(980\) 5.58233 + 15.0344i 0.178321 + 0.480258i
\(981\) −0.460710 + 0.797973i −0.0147093 + 0.0254773i
\(982\) −11.6256 −0.370988
\(983\) 4.74110 8.21182i 0.151218 0.261916i −0.780458 0.625208i \(-0.785014\pi\)
0.931675 + 0.363292i \(0.118347\pi\)
\(984\) −1.80195 3.12107i −0.0574441 0.0994960i
\(985\) 15.4880 26.8259i 0.493487 0.854745i
\(986\) 4.28872 + 7.42827i 0.136581 + 0.236564i
\(987\) 0.570797 0.820811i 0.0181687 0.0261267i
\(988\) 5.18925 1.62548i 0.165092 0.0517135i
\(989\) −6.53228 11.3142i −0.207714 0.359772i
\(990\) −2.01282 −0.0639716
\(991\) 25.5305 0.811002 0.405501 0.914095i \(-0.367097\pi\)
0.405501 + 0.914095i \(0.367097\pi\)
\(992\) 3.89495 0.123665
\(993\) −36.0485 −1.14396
\(994\) 3.09382 4.44895i 0.0981301 0.141112i
\(995\) −8.69338 + 15.0574i −0.275599 + 0.477351i
\(996\) 4.33355 + 7.50593i 0.137314 + 0.237834i
\(997\) −26.0704 45.1552i −0.825657 1.43008i −0.901416 0.432954i \(-0.857471\pi\)
0.0757592 0.997126i \(-0.475862\pi\)
\(998\) −12.4543 −0.394233
\(999\) 4.69338 8.12917i 0.148492 0.257195i
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 546.2.k.b.445.3 yes 8
3.2 odd 2 1638.2.p.i.991.2 8
7.2 even 3 546.2.j.d.289.3 8
13.9 even 3 546.2.j.d.529.3 yes 8
21.2 odd 6 1638.2.m.g.289.2 8
39.35 odd 6 1638.2.m.g.1621.2 8
91.9 even 3 inner 546.2.k.b.373.3 yes 8
273.191 odd 6 1638.2.p.i.919.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
546.2.j.d.289.3 8 7.2 even 3
546.2.j.d.529.3 yes 8 13.9 even 3
546.2.k.b.373.3 yes 8 91.9 even 3 inner
546.2.k.b.445.3 yes 8 1.1 even 1 trivial
1638.2.m.g.289.2 8 21.2 odd 6
1638.2.m.g.1621.2 8 39.35 odd 6
1638.2.p.i.919.2 8 273.191 odd 6
1638.2.p.i.991.2 8 3.2 odd 2