Properties

Label 462.2.n.f.65.12
Level $462$
Weight $2$
Character 462.65
Analytic conductor $3.689$
Analytic rank $0$
Dimension $24$
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] = [462,2,Mod(65,462)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(462, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 2, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("462.65");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 462.n (of order \(6\), 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: \(3.68908857338\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 65.12
Character \(\chi\) \(=\) 462.65
Dual form 462.2.n.f.263.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(1.72543 - 0.151338i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.246102 - 0.142087i) q^{5} +(0.731651 - 1.56993i) q^{6} +(2.09441 + 1.61662i) q^{7} -1.00000 q^{8} +(2.95419 - 0.522246i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(1.72543 - 0.151338i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.246102 - 0.142087i) q^{5} +(0.731651 - 1.56993i) q^{6} +(2.09441 + 1.61662i) q^{7} -1.00000 q^{8} +(2.95419 - 0.522246i) q^{9} +(-0.246102 + 0.142087i) q^{10} +(3.25335 - 0.644763i) q^{11} +(-0.993776 - 1.41859i) q^{12} +6.02702i q^{13} +(2.44724 - 1.00550i) q^{14} +(-0.446134 - 0.207916i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.12688 - 5.41591i) q^{17} +(1.02482 - 2.81953i) q^{18} +(-4.70688 - 2.71752i) q^{19} +0.284174i q^{20} +(3.85840 + 2.47240i) q^{21} +(1.06829 - 3.13986i) q^{22} +(1.55587 + 0.898282i) q^{23} +(-1.72543 + 0.151338i) q^{24} +(-2.45962 - 4.26019i) q^{25} +(5.21955 + 3.01351i) q^{26} +(5.01821 - 1.34818i) q^{27} +(0.352833 - 2.62212i) q^{28} -0.434446 q^{29} +(-0.403128 + 0.282406i) q^{30} +(-3.64386 - 6.31135i) q^{31} +(0.500000 + 0.866025i) q^{32} +(5.51584 - 1.60485i) q^{33} -6.25376 q^{34} +(-0.285737 - 0.695442i) q^{35} +(-1.92937 - 2.29728i) q^{36} +(-5.57207 + 9.65112i) q^{37} +(-4.70688 + 2.71752i) q^{38} +(0.912118 + 10.3992i) q^{39} +(0.246102 + 0.142087i) q^{40} +0.326715 q^{41} +(4.07036 - 2.10527i) q^{42} +2.29940i q^{43} +(-2.18506 - 2.49510i) q^{44} +(-0.801238 - 0.291227i) q^{45} +(1.55587 - 0.898282i) q^{46} +(3.52794 + 2.03685i) q^{47} +(-0.731651 + 1.56993i) q^{48} +(1.77307 + 6.77172i) q^{49} -4.91924 q^{50} +(-6.21483 - 8.87154i) q^{51} +(5.21955 - 3.01351i) q^{52} +(1.66437 - 0.960923i) q^{53} +(1.34155 - 5.01999i) q^{54} +(-0.892269 - 0.303581i) q^{55} +(-2.09441 - 1.61662i) q^{56} +(-8.53264 - 3.97655i) q^{57} +(-0.217223 + 0.376241i) q^{58} +(-8.38305 + 4.83996i) q^{59} +(0.0430064 + 0.490322i) q^{60} +(3.37831 + 1.95047i) q^{61} -7.28772 q^{62} +(7.03155 + 3.68202i) q^{63} +1.00000 q^{64} +(0.856362 - 1.48326i) q^{65} +(1.36808 - 5.57928i) q^{66} +(4.34158 + 7.51984i) q^{67} +(-3.12688 + 5.41591i) q^{68} +(2.82048 + 1.31446i) q^{69} +(-0.745139 - 0.100266i) q^{70} -3.88436i q^{71} +(-2.95419 + 0.522246i) q^{72} +(-3.80459 + 2.19658i) q^{73} +(5.57207 + 9.65112i) q^{74} +(-4.88863 - 6.97841i) q^{75} +5.43503i q^{76} +(7.85617 + 3.90904i) q^{77} +(9.46201 + 4.40967i) q^{78} +(-4.63260 - 2.67463i) q^{79} +(0.246102 - 0.142087i) q^{80} +(8.45452 - 3.08563i) q^{81} +(0.163357 - 0.282943i) q^{82} -1.61235 q^{83} +(0.211960 - 4.57767i) q^{84} +1.77716i q^{85} +(1.99134 + 1.14970i) q^{86} +(-0.749605 + 0.0657483i) q^{87} +(-3.25335 + 0.644763i) q^{88} +(-14.8319 - 8.56318i) q^{89} +(-0.652829 + 0.548279i) q^{90} +(-9.74341 + 12.6230i) q^{91} -1.79656i q^{92} +(-7.24236 - 10.3383i) q^{93} +(3.52794 - 2.03685i) q^{94} +(0.772248 + 1.33757i) q^{95} +(0.993776 + 1.41859i) q^{96} +6.98710 q^{97} +(6.75102 + 1.85034i) q^{98} +(9.27430 - 3.60380i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 12 q^{2} - 12 q^{4} - 24 q^{8} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 12 q^{2} - 12 q^{4} - 24 q^{8} - 8 q^{9} + 4 q^{11} + 4 q^{15} - 12 q^{16} - 4 q^{17} + 8 q^{18} + 8 q^{22} + 20 q^{25} - 12 q^{27} - 40 q^{29} + 2 q^{30} - 28 q^{31} + 12 q^{32} + 24 q^{33} - 8 q^{34} + 32 q^{35} + 16 q^{36} - 16 q^{37} + 8 q^{41} + 6 q^{42} + 4 q^{44} - 28 q^{45} - 8 q^{49} + 40 q^{50} + 34 q^{51} - 6 q^{54} + 8 q^{55} - 40 q^{57} - 20 q^{58} - 2 q^{60} - 56 q^{62} + 14 q^{63} + 24 q^{64} + 44 q^{65} - 24 q^{66} - 4 q^{68} - 20 q^{69} + 64 q^{70} + 8 q^{72} + 16 q^{74} - 26 q^{75} + 24 q^{81} + 4 q^{82} - 144 q^{83} + 6 q^{84} - 8 q^{87} - 4 q^{88} - 56 q^{90} - 32 q^{91} - 22 q^{93} + 44 q^{95} + 64 q^{97} + 8 q^{98} + 28 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(155\) \(199\) \(211\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(-1\)

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
\(3\) 1.72543 0.151338i 0.996175 0.0873751i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −0.246102 0.142087i −0.110060 0.0635433i 0.443959 0.896047i \(-0.353573\pi\)
−0.554020 + 0.832504i \(0.686907\pi\)
\(6\) 0.731651 1.56993i 0.298695 0.640922i
\(7\) 2.09441 + 1.61662i 0.791611 + 0.611026i
\(8\) −1.00000 −0.353553
\(9\) 2.95419 0.522246i 0.984731 0.174082i
\(10\) −0.246102 + 0.142087i −0.0778243 + 0.0449319i
\(11\) 3.25335 0.644763i 0.980922 0.194403i
\(12\) −0.993776 1.41859i −0.286878 0.409513i
\(13\) 6.02702i 1.67159i 0.549039 + 0.835797i \(0.314994\pi\)
−0.549039 + 0.835797i \(0.685006\pi\)
\(14\) 2.44724 1.00550i 0.654052 0.268731i
\(15\) −0.446134 0.207916i −0.115191 0.0536837i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −3.12688 5.41591i −0.758380 1.31355i −0.943677 0.330869i \(-0.892658\pi\)
0.185297 0.982683i \(-0.440675\pi\)
\(18\) 1.02482 2.81953i 0.241552 0.664569i
\(19\) −4.70688 2.71752i −1.07983 0.623441i −0.148981 0.988840i \(-0.547599\pi\)
−0.930851 + 0.365399i \(0.880933\pi\)
\(20\) 0.284174i 0.0635433i
\(21\) 3.85840 + 2.47240i 0.841972 + 0.539522i
\(22\) 1.06829 3.13986i 0.227761 0.669421i
\(23\) 1.55587 + 0.898282i 0.324421 + 0.187305i 0.653362 0.757046i \(-0.273358\pi\)
−0.328940 + 0.944351i \(0.606691\pi\)
\(24\) −1.72543 + 0.151338i −0.352201 + 0.0308918i
\(25\) −2.45962 4.26019i −0.491924 0.852038i
\(26\) 5.21955 + 3.01351i 1.02364 + 0.590998i
\(27\) 5.01821 1.34818i 0.965755 0.259457i
\(28\) 0.352833 2.62212i 0.0666791 0.495534i
\(29\) −0.434446 −0.0806746 −0.0403373 0.999186i \(-0.512843\pi\)
−0.0403373 + 0.999186i \(0.512843\pi\)
\(30\) −0.403128 + 0.282406i −0.0736008 + 0.0515600i
\(31\) −3.64386 6.31135i −0.654456 1.13355i −0.982030 0.188726i \(-0.939564\pi\)
0.327573 0.944826i \(-0.393769\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 5.51584 1.60485i 0.960184 0.279368i
\(34\) −6.25376 −1.07251
\(35\) −0.285737 0.695442i −0.0482983 0.117551i
\(36\) −1.92937 2.29728i −0.321562 0.382881i
\(37\) −5.57207 + 9.65112i −0.916043 + 1.58663i −0.110677 + 0.993856i \(0.535302\pi\)
−0.805367 + 0.592777i \(0.798032\pi\)
\(38\) −4.70688 + 2.71752i −0.763556 + 0.440839i
\(39\) 0.912118 + 10.3992i 0.146056 + 1.66520i
\(40\) 0.246102 + 0.142087i 0.0389122 + 0.0224659i
\(41\) 0.326715 0.0510243 0.0255121 0.999675i \(-0.491878\pi\)
0.0255121 + 0.999675i \(0.491878\pi\)
\(42\) 4.07036 2.10527i 0.628070 0.324851i
\(43\) 2.29940i 0.350655i 0.984510 + 0.175327i \(0.0560984\pi\)
−0.984510 + 0.175327i \(0.943902\pi\)
\(44\) −2.18506 2.49510i −0.329410 0.376151i
\(45\) −0.801238 0.291227i −0.119441 0.0434136i
\(46\) 1.55587 0.898282i 0.229401 0.132444i
\(47\) 3.52794 + 2.03685i 0.514602 + 0.297106i 0.734723 0.678367i \(-0.237312\pi\)
−0.220121 + 0.975473i \(0.570645\pi\)
\(48\) −0.731651 + 1.56993i −0.105605 + 0.226600i
\(49\) 1.77307 + 6.77172i 0.253296 + 0.967389i
\(50\) −4.91924 −0.695686
\(51\) −6.21483 8.87154i −0.870251 1.24226i
\(52\) 5.21955 3.01351i 0.723821 0.417899i
\(53\) 1.66437 0.960923i 0.228618 0.131993i −0.381316 0.924445i \(-0.624529\pi\)
0.609935 + 0.792452i \(0.291196\pi\)
\(54\) 1.34155 5.01999i 0.182561 0.683133i
\(55\) −0.892269 0.303581i −0.120313 0.0409349i
\(56\) −2.09441 1.61662i −0.279877 0.216030i
\(57\) −8.53264 3.97655i −1.13018 0.526706i
\(58\) −0.217223 + 0.376241i −0.0285228 + 0.0494029i
\(59\) −8.38305 + 4.83996i −1.09138 + 0.630109i −0.933944 0.357420i \(-0.883656\pi\)
−0.157437 + 0.987529i \(0.550323\pi\)
\(60\) 0.0430064 + 0.490322i 0.00555210 + 0.0633003i
\(61\) 3.37831 + 1.95047i 0.432548 + 0.249732i 0.700432 0.713719i \(-0.252991\pi\)
−0.267883 + 0.963451i \(0.586324\pi\)
\(62\) −7.28772 −0.925541
\(63\) 7.03155 + 3.68202i 0.885892 + 0.463891i
\(64\) 1.00000 0.125000
\(65\) 0.856362 1.48326i 0.106219 0.183976i
\(66\) 1.36808 5.57928i 0.168399 0.686762i
\(67\) 4.34158 + 7.51984i 0.530409 + 0.918695i 0.999371 + 0.0354765i \(0.0112949\pi\)
−0.468962 + 0.883218i \(0.655372\pi\)
\(68\) −3.12688 + 5.41591i −0.379190 + 0.656776i
\(69\) 2.82048 + 1.31446i 0.339546 + 0.158242i
\(70\) −0.745139 0.100266i −0.0890611 0.0119841i
\(71\) 3.88436i 0.460989i −0.973074 0.230495i \(-0.925966\pi\)
0.973074 0.230495i \(-0.0740344\pi\)
\(72\) −2.95419 + 0.522246i −0.348155 + 0.0615473i
\(73\) −3.80459 + 2.19658i −0.445294 + 0.257091i −0.705841 0.708371i \(-0.749431\pi\)
0.260547 + 0.965461i \(0.416097\pi\)
\(74\) 5.57207 + 9.65112i 0.647740 + 1.12192i
\(75\) −4.88863 6.97841i −0.564490 0.805798i
\(76\) 5.43503i 0.623441i
\(77\) 7.85617 + 3.90904i 0.895294 + 0.445476i
\(78\) 9.46201 + 4.40967i 1.07136 + 0.499297i
\(79\) −4.63260 2.67463i −0.521208 0.300920i 0.216221 0.976345i \(-0.430627\pi\)
−0.737429 + 0.675425i \(0.763960\pi\)
\(80\) 0.246102 0.142087i 0.0275151 0.0158858i
\(81\) 8.45452 3.08563i 0.939391 0.342848i
\(82\) 0.163357 0.282943i 0.0180398 0.0312459i
\(83\) −1.61235 −0.176978 −0.0884892 0.996077i \(-0.528204\pi\)
−0.0884892 + 0.996077i \(0.528204\pi\)
\(84\) 0.211960 4.57767i 0.0231267 0.499465i
\(85\) 1.77716i 0.192760i
\(86\) 1.99134 + 1.14970i 0.214731 + 0.123975i
\(87\) −0.749605 + 0.0657483i −0.0803661 + 0.00704896i
\(88\) −3.25335 + 0.644763i −0.346808 + 0.0687320i
\(89\) −14.8319 8.56318i −1.57217 0.907695i −0.995902 0.0904364i \(-0.971174\pi\)
−0.576271 0.817258i \(-0.695493\pi\)
\(90\) −0.652829 + 0.548279i −0.0688142 + 0.0577936i
\(91\) −9.74341 + 12.6230i −1.02139 + 1.32325i
\(92\) 1.79656i 0.187305i
\(93\) −7.24236 10.3383i −0.750998 1.07203i
\(94\) 3.52794 2.03685i 0.363879 0.210086i
\(95\) 0.772248 + 1.33757i 0.0792310 + 0.137232i
\(96\) 0.993776 + 1.41859i 0.101427 + 0.144785i
\(97\) 6.98710 0.709432 0.354716 0.934974i \(-0.384578\pi\)
0.354716 + 0.934974i \(0.384578\pi\)
\(98\) 6.75102 + 1.85034i 0.681956 + 0.186912i
\(99\) 9.27430 3.60380i 0.932102 0.362196i
\(100\) −2.45962 + 4.26019i −0.245962 + 0.426019i
\(101\) −5.50494 9.53484i −0.547762 0.948752i −0.998427 0.0560587i \(-0.982147\pi\)
0.450665 0.892693i \(-0.351187\pi\)
\(102\) −10.7904 + 0.946432i −1.06841 + 0.0937108i
\(103\) −3.87592 + 6.71328i −0.381905 + 0.661480i −0.991335 0.131361i \(-0.958065\pi\)
0.609429 + 0.792840i \(0.291399\pi\)
\(104\) 6.02702i 0.590998i
\(105\) −0.598264 1.15669i −0.0583846 0.112882i
\(106\) 1.92185i 0.186666i
\(107\) 7.32460 12.6866i 0.708096 1.22646i −0.257466 0.966287i \(-0.582888\pi\)
0.965563 0.260171i \(-0.0837790\pi\)
\(108\) −3.67666 3.67181i −0.353787 0.353320i
\(109\) 13.7850 7.95877i 1.32036 0.762312i 0.336577 0.941656i \(-0.390731\pi\)
0.983786 + 0.179344i \(0.0573975\pi\)
\(110\) −0.709044 + 0.620937i −0.0676046 + 0.0592040i
\(111\) −8.15362 + 17.4956i −0.773908 + 1.66060i
\(112\) −2.44724 + 1.00550i −0.231242 + 0.0950106i
\(113\) 12.2685i 1.15412i 0.816702 + 0.577060i \(0.195800\pi\)
−0.816702 + 0.577060i \(0.804200\pi\)
\(114\) −7.71011 + 5.40121i −0.722118 + 0.505869i
\(115\) −0.255269 0.442138i −0.0238039 0.0412296i
\(116\) 0.217223 + 0.376241i 0.0201687 + 0.0349331i
\(117\) 3.14758 + 17.8050i 0.290994 + 1.64607i
\(118\) 9.67991i 0.891108i
\(119\) 2.20653 16.3981i 0.202272 1.50321i
\(120\) 0.446134 + 0.207916i 0.0407263 + 0.0189801i
\(121\) 10.1686 4.19528i 0.924415 0.381389i
\(122\) 3.37831 1.95047i 0.305858 0.176587i
\(123\) 0.563722 0.0494444i 0.0508291 0.00445825i
\(124\) −3.64386 + 6.31135i −0.327228 + 0.566776i
\(125\) 2.81879i 0.252121i
\(126\) 6.70450 4.24849i 0.597284 0.378486i
\(127\) 5.55609i 0.493023i 0.969140 + 0.246511i \(0.0792843\pi\)
−0.969140 + 0.246511i \(0.920716\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 0.347987 + 3.96744i 0.0306385 + 0.349314i
\(130\) −0.856362 1.48326i −0.0751079 0.130091i
\(131\) −9.44368 + 16.3569i −0.825099 + 1.42911i 0.0767455 + 0.997051i \(0.475547\pi\)
−0.901844 + 0.432062i \(0.857786\pi\)
\(132\) −4.14776 3.97443i −0.361016 0.345930i
\(133\) −5.46491 13.3008i −0.473868 1.15333i
\(134\) 8.68317 0.750111
\(135\) −1.42655 0.381233i −0.122778 0.0328113i
\(136\) 3.12688 + 5.41591i 0.268128 + 0.464411i
\(137\) −14.6388 + 8.45173i −1.25068 + 0.722080i −0.971244 0.238084i \(-0.923481\pi\)
−0.279435 + 0.960165i \(0.590147\pi\)
\(138\) 2.54860 1.78538i 0.216951 0.151982i
\(139\) 12.1306i 1.02890i 0.857519 + 0.514452i \(0.172005\pi\)
−0.857519 + 0.514452i \(0.827995\pi\)
\(140\) −0.459402 + 0.595176i −0.0388266 + 0.0503016i
\(141\) 6.39545 + 2.98053i 0.538594 + 0.251006i
\(142\) −3.36396 1.94218i −0.282297 0.162984i
\(143\) 3.88600 + 19.6080i 0.324964 + 1.63970i
\(144\) −1.02482 + 2.81953i −0.0854016 + 0.234961i
\(145\) 0.106918 + 0.0617292i 0.00887907 + 0.00512633i
\(146\) 4.39317i 0.363581i
\(147\) 4.08412 + 11.4158i 0.336853 + 0.941557i
\(148\) 11.1441 0.916043
\(149\) 5.93990 10.2882i 0.486616 0.842843i −0.513266 0.858230i \(-0.671564\pi\)
0.999882 + 0.0153863i \(0.00489782\pi\)
\(150\) −8.48780 + 0.744470i −0.693026 + 0.0607857i
\(151\) −1.49875 + 0.865305i −0.121967 + 0.0704175i −0.559742 0.828667i \(-0.689100\pi\)
0.437775 + 0.899084i \(0.355766\pi\)
\(152\) 4.70688 + 2.71752i 0.381778 + 0.220420i
\(153\) −12.0658 14.3667i −0.975466 1.16148i
\(154\) 7.31341 4.84912i 0.589332 0.390754i
\(155\) 2.07098i 0.166345i
\(156\) 8.54989 5.98951i 0.684539 0.479544i
\(157\) −5.57046 9.64832i −0.444571 0.770020i 0.553451 0.832882i \(-0.313311\pi\)
−0.998022 + 0.0628618i \(0.979977\pi\)
\(158\) −4.63260 + 2.67463i −0.368550 + 0.212782i
\(159\) 2.72632 1.90988i 0.216211 0.151464i
\(160\) 0.284174i 0.0224659i
\(161\) 1.80644 + 4.39662i 0.142367 + 0.346502i
\(162\) 1.55503 8.86464i 0.122174 0.696472i
\(163\) 0.415887 0.720337i 0.0325748 0.0564211i −0.849278 0.527945i \(-0.822963\pi\)
0.881853 + 0.471524i \(0.156296\pi\)
\(164\) −0.163357 0.282943i −0.0127561 0.0220942i
\(165\) −1.58549 0.388773i −0.123430 0.0302659i
\(166\) −0.806175 + 1.39634i −0.0625713 + 0.108377i
\(167\) −19.1395 −1.48106 −0.740529 0.672025i \(-0.765425\pi\)
−0.740529 + 0.672025i \(0.765425\pi\)
\(168\) −3.85840 2.47240i −0.297682 0.190750i
\(169\) −23.3249 −1.79423
\(170\) 1.53906 + 0.888578i 0.118041 + 0.0681509i
\(171\) −15.3242 5.56992i −1.17187 0.425943i
\(172\) 1.99134 1.14970i 0.151838 0.0876637i
\(173\) 8.80633 15.2530i 0.669533 1.15967i −0.308502 0.951224i \(-0.599828\pi\)
0.978035 0.208442i \(-0.0668391\pi\)
\(174\) −0.317863 + 0.682051i −0.0240971 + 0.0517062i
\(175\) 1.73567 12.8988i 0.131204 0.975061i
\(176\) −1.06829 + 3.13986i −0.0805256 + 0.236676i
\(177\) −13.7319 + 9.61966i −1.03215 + 0.723058i
\(178\) −14.8319 + 8.56318i −1.11169 + 0.641837i
\(179\) 7.84070 4.52683i 0.586041 0.338351i −0.177489 0.984123i \(-0.556798\pi\)
0.763531 + 0.645772i \(0.223464\pi\)
\(180\) 0.148409 + 0.839506i 0.0110617 + 0.0625731i
\(181\) 21.1949 1.57540 0.787701 0.616057i \(-0.211271\pi\)
0.787701 + 0.616057i \(0.211271\pi\)
\(182\) 6.06015 + 14.7495i 0.449208 + 1.09331i
\(183\) 6.12421 + 2.85412i 0.452715 + 0.210983i
\(184\) −1.55587 0.898282i −0.114700 0.0662222i
\(185\) 2.74260 1.58344i 0.201640 0.116417i
\(186\) −12.5744 + 1.10291i −0.922001 + 0.0808693i
\(187\) −13.6648 15.6038i −0.999270 1.14106i
\(188\) 4.07371i 0.297106i
\(189\) 12.6897 + 5.28891i 0.923037 + 0.384712i
\(190\) 1.54450 0.112050
\(191\) 10.7800 + 6.22381i 0.780010 + 0.450339i 0.836434 0.548068i \(-0.184636\pi\)
−0.0564238 + 0.998407i \(0.517970\pi\)
\(192\) 1.72543 0.151338i 0.124522 0.0109219i
\(193\) 12.9542 7.47910i 0.932463 0.538357i 0.0448730 0.998993i \(-0.485712\pi\)
0.887590 + 0.460635i \(0.152378\pi\)
\(194\) 3.49355 6.05100i 0.250822 0.434437i
\(195\) 1.25312 2.68886i 0.0897374 0.192553i
\(196\) 4.97795 4.92138i 0.355568 0.351527i
\(197\) 8.24633 0.587527 0.293763 0.955878i \(-0.405092\pi\)
0.293763 + 0.955878i \(0.405092\pi\)
\(198\) 1.51616 9.83368i 0.107749 0.698849i
\(199\) 7.13434 + 12.3570i 0.505740 + 0.875967i 0.999978 + 0.00664051i \(0.00211376\pi\)
−0.494238 + 0.869327i \(0.664553\pi\)
\(200\) 2.45962 + 4.26019i 0.173922 + 0.301241i
\(201\) 8.62912 + 12.3179i 0.608651 + 0.868837i
\(202\) −11.0099 −0.774652
\(203\) −0.909907 0.702335i −0.0638629 0.0492943i
\(204\) −4.57557 + 9.81798i −0.320354 + 0.687396i
\(205\) −0.0804052 0.0464220i −0.00561574 0.00324225i
\(206\) 3.87592 + 6.71328i 0.270048 + 0.467737i
\(207\) 5.06547 + 1.84115i 0.352074 + 0.127969i
\(208\) −5.21955 3.01351i −0.361911 0.208949i
\(209\) −17.0653 5.80621i −1.18043 0.401624i
\(210\) −1.30086 0.0602336i −0.0897676 0.00415651i
\(211\) 16.7368i 1.15221i −0.817376 0.576105i \(-0.804572\pi\)
0.817376 0.576105i \(-0.195428\pi\)
\(212\) −1.66437 0.960923i −0.114309 0.0659964i
\(213\) −0.587853 6.70219i −0.0402790 0.459226i
\(214\) −7.32460 12.6866i −0.500700 0.867237i
\(215\) 0.326715 0.565887i 0.0222818 0.0385932i
\(216\) −5.01821 + 1.34818i −0.341446 + 0.0917320i
\(217\) 2.57134 19.1093i 0.174554 1.29722i
\(218\) 15.9175i 1.07807i
\(219\) −6.23212 + 4.36582i −0.421128 + 0.295015i
\(220\) 0.183225 + 0.924518i 0.0123530 + 0.0623310i
\(221\) 32.6418 18.8458i 2.19573 1.26770i
\(222\) 11.0748 + 15.8090i 0.743291 + 1.06103i
\(223\) 1.08771 0.0728383 0.0364192 0.999337i \(-0.488405\pi\)
0.0364192 + 0.999337i \(0.488405\pi\)
\(224\) −0.352833 + 2.62212i −0.0235746 + 0.175198i
\(225\) −9.49107 11.3009i −0.632738 0.753393i
\(226\) 10.6248 + 6.13423i 0.706751 + 0.408043i
\(227\) −4.48346 7.76558i −0.297578 0.515420i 0.678003 0.735059i \(-0.262845\pi\)
−0.975581 + 0.219639i \(0.929512\pi\)
\(228\) 0.822528 + 9.37775i 0.0544733 + 0.621057i
\(229\) 6.22490 10.7818i 0.411353 0.712485i −0.583685 0.811980i \(-0.698390\pi\)
0.995038 + 0.0994957i \(0.0317230\pi\)
\(230\) −0.510537 −0.0336638
\(231\) 14.1468 + 5.55582i 0.930793 + 0.365546i
\(232\) 0.434446 0.0285228
\(233\) 9.19303 15.9228i 0.602255 1.04314i −0.390224 0.920720i \(-0.627602\pi\)
0.992479 0.122417i \(-0.0390644\pi\)
\(234\) 16.9934 + 6.17660i 1.11089 + 0.403777i
\(235\) −0.578822 1.00255i −0.0377582 0.0653991i
\(236\) 8.38305 + 4.83996i 0.545690 + 0.315054i
\(237\) −8.39798 3.91379i −0.545508 0.254228i
\(238\) −13.0979 10.1100i −0.849011 0.655331i
\(239\) −24.8394 −1.60673 −0.803365 0.595487i \(-0.796959\pi\)
−0.803365 + 0.595487i \(0.796959\pi\)
\(240\) 0.403128 0.282406i 0.0260218 0.0182292i
\(241\) 7.62307 4.40118i 0.491045 0.283505i −0.233963 0.972246i \(-0.575169\pi\)
0.725008 + 0.688741i \(0.241836\pi\)
\(242\) 1.45106 10.9039i 0.0932777 0.700927i
\(243\) 14.1207 6.60352i 0.905842 0.423616i
\(244\) 3.90094i 0.249732i
\(245\) 0.525818 1.91847i 0.0335933 0.122566i
\(246\) 0.239041 0.512920i 0.0152407 0.0327026i
\(247\) 16.3785 28.3684i 1.04214 1.80504i
\(248\) 3.64386 + 6.31135i 0.231385 + 0.400771i
\(249\) −2.78199 + 0.244010i −0.176301 + 0.0154635i
\(250\) 2.44115 + 1.40940i 0.154392 + 0.0891381i
\(251\) 14.0216i 0.885034i 0.896760 + 0.442517i \(0.145914\pi\)
−0.896760 + 0.442517i \(0.854086\pi\)
\(252\) −0.327055 7.93051i −0.0206025 0.499575i
\(253\) 5.64097 + 1.91926i 0.354645 + 0.120663i
\(254\) 4.81171 + 2.77804i 0.301914 + 0.174310i
\(255\) 0.268952 + 3.06635i 0.0168424 + 0.192023i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 7.60623 + 4.39146i 0.474464 + 0.273932i 0.718106 0.695933i \(-0.245009\pi\)
−0.243643 + 0.969865i \(0.578342\pi\)
\(258\) 3.60990 + 1.68236i 0.224743 + 0.104739i
\(259\) −27.2724 + 11.2054i −1.69462 + 0.696271i
\(260\) −1.71272 −0.106219
\(261\) −1.28344 + 0.226888i −0.0794428 + 0.0140440i
\(262\) 9.44368 + 16.3569i 0.583433 + 1.01054i
\(263\) −3.93874 6.82210i −0.242873 0.420669i 0.718658 0.695363i \(-0.244757\pi\)
−0.961532 + 0.274695i \(0.911423\pi\)
\(264\) −5.51584 + 1.60485i −0.339476 + 0.0987715i
\(265\) −0.546139 −0.0335490
\(266\) −14.2513 1.91766i −0.873804 0.117579i
\(267\) −26.8872 12.5305i −1.64547 0.766854i
\(268\) 4.34158 7.51984i 0.265204 0.459347i
\(269\) 5.23920 3.02485i 0.319440 0.184429i −0.331703 0.943384i \(-0.607623\pi\)
0.651143 + 0.758955i \(0.274290\pi\)
\(270\) −1.04343 + 1.04481i −0.0635013 + 0.0635853i
\(271\) 0.886543 + 0.511846i 0.0538536 + 0.0310924i 0.526685 0.850060i \(-0.323435\pi\)
−0.472831 + 0.881153i \(0.656768\pi\)
\(272\) 6.25376 0.379190
\(273\) −14.9012 + 23.2546i −0.901861 + 1.40744i
\(274\) 16.9035i 1.02118i
\(275\) −10.7488 12.2740i −0.648179 0.740151i
\(276\) −0.271889 3.09984i −0.0163658 0.186588i
\(277\) −0.717044 + 0.413986i −0.0430830 + 0.0248740i −0.521387 0.853320i \(-0.674585\pi\)
0.478304 + 0.878194i \(0.341252\pi\)
\(278\) 10.5054 + 6.06530i 0.630072 + 0.363772i
\(279\) −14.0607 16.7420i −0.841794 1.00231i
\(280\) 0.285737 + 0.695442i 0.0170760 + 0.0415606i
\(281\) 21.7279 1.29618 0.648089 0.761564i \(-0.275568\pi\)
0.648089 + 0.761564i \(0.275568\pi\)
\(282\) 5.77894 4.04835i 0.344131 0.241076i
\(283\) −12.2598 + 7.07821i −0.728770 + 0.420756i −0.817972 0.575258i \(-0.804902\pi\)
0.0892018 + 0.996014i \(0.471568\pi\)
\(284\) −3.36396 + 1.94218i −0.199614 + 0.115247i
\(285\) 1.53488 + 2.19101i 0.0909187 + 0.129784i
\(286\) 18.9240 + 6.43862i 1.11900 + 0.380724i
\(287\) 0.684273 + 0.528174i 0.0403914 + 0.0311771i
\(288\) 1.92937 + 2.29728i 0.113690 + 0.135369i
\(289\) −11.0547 + 19.1474i −0.650279 + 1.12632i
\(290\) 0.106918 0.0617292i 0.00627845 0.00362486i
\(291\) 12.0557 1.05741i 0.706719 0.0619867i
\(292\) 3.80459 + 2.19658i 0.222647 + 0.128545i
\(293\) 5.75882 0.336434 0.168217 0.985750i \(-0.446199\pi\)
0.168217 + 0.985750i \(0.446199\pi\)
\(294\) 11.9284 + 2.17094i 0.695679 + 0.126612i
\(295\) 2.75078 0.160157
\(296\) 5.57207 9.65112i 0.323870 0.560960i
\(297\) 15.4567 7.62165i 0.896890 0.442253i
\(298\) −5.93990 10.2882i −0.344089 0.595980i
\(299\) −5.41396 + 9.37726i −0.313098 + 0.542301i
\(300\) −3.59917 + 7.72288i −0.207798 + 0.445881i
\(301\) −3.71726 + 4.81587i −0.214259 + 0.277582i
\(302\) 1.73061i 0.0995854i
\(303\) −10.9414 15.6186i −0.628564 0.897262i
\(304\) 4.70688 2.71752i 0.269958 0.155860i
\(305\) −0.554273 0.960029i −0.0317376 0.0549711i
\(306\) −18.4748 + 3.26600i −1.05613 + 0.186705i
\(307\) 10.5810i 0.603888i 0.953326 + 0.301944i \(0.0976355\pi\)
−0.953326 + 0.301944i \(0.902364\pi\)
\(308\) −0.542759 8.75816i −0.0309265 0.499043i
\(309\) −5.67163 + 12.1699i −0.322648 + 0.692319i
\(310\) 1.79352 + 1.03549i 0.101865 + 0.0588119i
\(311\) −5.90443 + 3.40892i −0.334809 + 0.193302i −0.657974 0.753040i \(-0.728586\pi\)
0.323165 + 0.946343i \(0.395253\pi\)
\(312\) −0.912118 10.3992i −0.0516385 0.588737i
\(313\) 13.6258 23.6005i 0.770174 1.33398i −0.167293 0.985907i \(-0.553503\pi\)
0.937467 0.348074i \(-0.113164\pi\)
\(314\) −11.1409 −0.628719
\(315\) −1.20731 1.90525i −0.0680244 0.107348i
\(316\) 5.34926i 0.300920i
\(317\) −11.6116 6.70397i −0.652173 0.376533i 0.137115 0.990555i \(-0.456217\pi\)
−0.789288 + 0.614023i \(0.789550\pi\)
\(318\) −0.290849 3.31600i −0.0163100 0.185952i
\(319\) −1.41341 + 0.280115i −0.0791355 + 0.0156834i
\(320\) −0.246102 0.142087i −0.0137575 0.00794291i
\(321\) 10.7181 22.9983i 0.598226 1.28364i
\(322\) 4.71081 + 0.633886i 0.262523 + 0.0353251i
\(323\) 33.9894i 1.89122i
\(324\) −6.89949 5.77901i −0.383305 0.321056i
\(325\) 25.6762 14.8242i 1.42426 0.822298i
\(326\) −0.415887 0.720337i −0.0230338 0.0398958i
\(327\) 22.5805 15.8185i 1.24871 0.874763i
\(328\) −0.326715 −0.0180398
\(329\) 4.09611 + 9.96934i 0.225826 + 0.549627i
\(330\) −1.12943 + 1.17869i −0.0621731 + 0.0648845i
\(331\) 5.97956 10.3569i 0.328666 0.569267i −0.653581 0.756857i \(-0.726734\pi\)
0.982248 + 0.187590i \(0.0600675\pi\)
\(332\) 0.806175 + 1.39634i 0.0442446 + 0.0766339i
\(333\) −11.4207 + 31.4213i −0.625852 + 1.72187i
\(334\) −9.56974 + 16.5753i −0.523633 + 0.906959i
\(335\) 2.46753i 0.134816i
\(336\) −4.07036 + 2.10527i −0.222056 + 0.114852i
\(337\) 7.11663i 0.387668i −0.981034 0.193834i \(-0.937908\pi\)
0.981034 0.193834i \(-0.0620923\pi\)
\(338\) −11.6625 + 20.2000i −0.634355 + 1.09874i
\(339\) 1.85669 + 21.1683i 0.100841 + 1.14971i
\(340\) 1.53906 0.888578i 0.0834674 0.0481899i
\(341\) −15.9241 18.1836i −0.862337 0.984697i
\(342\) −12.4858 + 10.4862i −0.675156 + 0.567030i
\(343\) −7.23379 + 17.0491i −0.390588 + 0.920566i
\(344\) 2.29940i 0.123975i
\(345\) −0.507360 0.724245i −0.0273153 0.0389920i
\(346\) −8.80633 15.2530i −0.473431 0.820007i
\(347\) 0.501160 + 0.868034i 0.0269037 + 0.0465985i 0.879164 0.476520i \(-0.158102\pi\)
−0.852260 + 0.523118i \(0.824769\pi\)
\(348\) 0.431742 + 0.616303i 0.0231438 + 0.0330373i
\(349\) 18.5808i 0.994607i 0.867577 + 0.497304i \(0.165677\pi\)
−0.867577 + 0.497304i \(0.834323\pi\)
\(350\) −10.3029 7.95256i −0.550713 0.425082i
\(351\) 8.12550 + 30.2448i 0.433707 + 1.61435i
\(352\) 2.18506 + 2.49510i 0.116464 + 0.132989i
\(353\) 3.11174 1.79656i 0.165621 0.0956215i −0.414898 0.909868i \(-0.636183\pi\)
0.580519 + 0.814246i \(0.302850\pi\)
\(354\) 1.46494 + 16.7020i 0.0778607 + 0.887700i
\(355\) −0.551918 + 0.955950i −0.0292928 + 0.0507366i
\(356\) 17.1264i 0.907695i
\(357\) 1.32555 28.6276i 0.0701553 1.51514i
\(358\) 9.05366i 0.478501i
\(359\) −5.21329 + 9.02968i −0.275147 + 0.476569i −0.970172 0.242417i \(-0.922060\pi\)
0.695025 + 0.718985i \(0.255393\pi\)
\(360\) 0.801238 + 0.291227i 0.0422289 + 0.0153490i
\(361\) 5.26980 + 9.12756i 0.277358 + 0.480398i
\(362\) 10.5974 18.3553i 0.556989 0.964733i
\(363\) 16.9102 8.77754i 0.887555 0.460701i
\(364\) 15.8036 + 2.12653i 0.828332 + 0.111460i
\(365\) 1.24842 0.0653455
\(366\) 5.53385 3.87666i 0.289259 0.202636i
\(367\) 0.802276 + 1.38958i 0.0418785 + 0.0725356i 0.886205 0.463294i \(-0.153332\pi\)
−0.844326 + 0.535829i \(0.819999\pi\)
\(368\) −1.55587 + 0.898282i −0.0811053 + 0.0468262i
\(369\) 0.965179 0.170625i 0.0502452 0.00888241i
\(370\) 3.16688i 0.164638i
\(371\) 5.03931 + 0.678090i 0.261628 + 0.0352047i
\(372\) −5.33206 + 11.4412i −0.276455 + 0.593200i
\(373\) 0.443041 + 0.255790i 0.0229398 + 0.0132443i 0.511426 0.859327i \(-0.329117\pi\)
−0.488486 + 0.872572i \(0.662451\pi\)
\(374\) −20.3457 + 4.03219i −1.05205 + 0.208500i
\(375\) 0.426591 + 4.86362i 0.0220291 + 0.251156i
\(376\) −3.52794 2.03685i −0.181939 0.105043i
\(377\) 2.61842i 0.134855i
\(378\) 10.9252 8.34511i 0.561930 0.429226i
\(379\) 5.08365 0.261130 0.130565 0.991440i \(-0.458321\pi\)
0.130565 + 0.991440i \(0.458321\pi\)
\(380\) 0.772248 1.33757i 0.0396155 0.0686161i
\(381\) 0.840848 + 9.58662i 0.0430779 + 0.491137i
\(382\) 10.7800 6.22381i 0.551550 0.318438i
\(383\) 4.59160 + 2.65096i 0.234620 + 0.135458i 0.612702 0.790314i \(-0.290083\pi\)
−0.378082 + 0.925772i \(0.623416\pi\)
\(384\) 0.731651 1.56993i 0.0373369 0.0801153i
\(385\) −1.37800 2.07828i −0.0702292 0.105919i
\(386\) 14.9582i 0.761352i
\(387\) 1.20085 + 6.79287i 0.0610427 + 0.345301i
\(388\) −3.49355 6.05100i −0.177358 0.307193i
\(389\) −25.9986 + 15.0103i −1.31818 + 0.761053i −0.983436 0.181255i \(-0.941984\pi\)
−0.334747 + 0.942308i \(0.608651\pi\)
\(390\) −1.70206 2.42966i −0.0861873 0.123031i
\(391\) 11.2353i 0.568192i
\(392\) −1.77307 6.77172i −0.0895535 0.342024i
\(393\) −13.8190 + 29.6519i −0.697074 + 1.49574i
\(394\) 4.12317 7.14153i 0.207722 0.359785i
\(395\) 0.760061 + 1.31647i 0.0382428 + 0.0662385i
\(396\) −7.75813 6.22988i −0.389861 0.313063i
\(397\) −5.20199 + 9.01011i −0.261080 + 0.452204i −0.966529 0.256556i \(-0.917412\pi\)
0.705449 + 0.708761i \(0.250745\pi\)
\(398\) 14.2687 0.715224
\(399\) −11.4422 22.1225i −0.572828 1.10751i
\(400\) 4.91924 0.245962
\(401\) 12.6464 + 7.30138i 0.631529 + 0.364614i 0.781344 0.624100i \(-0.214534\pi\)
−0.149815 + 0.988714i \(0.547868\pi\)
\(402\) 14.9822 1.31409i 0.747242 0.0655411i
\(403\) 38.0386 21.9616i 1.89484 1.09399i
\(404\) −5.50494 + 9.53484i −0.273881 + 0.474376i
\(405\) −2.51910 0.441898i −0.125175 0.0219581i
\(406\) −1.06319 + 0.436835i −0.0527654 + 0.0216797i
\(407\) −11.9052 + 34.9911i −0.590120 + 1.73445i
\(408\) 6.21483 + 8.87154i 0.307680 + 0.439207i
\(409\) −21.6325 + 12.4895i −1.06966 + 0.617566i −0.928087 0.372362i \(-0.878548\pi\)
−0.141568 + 0.989928i \(0.545215\pi\)
\(410\) −0.0804052 + 0.0464220i −0.00397093 + 0.00229262i
\(411\) −23.9792 + 16.7983i −1.18280 + 0.828597i
\(412\) 7.75183 0.381905
\(413\) −25.3819 3.41539i −1.24896 0.168060i
\(414\) 4.12722 3.46625i 0.202842 0.170357i
\(415\) 0.396803 + 0.229094i 0.0194783 + 0.0112458i
\(416\) −5.21955 + 3.01351i −0.255910 + 0.147749i
\(417\) 1.83582 + 20.9305i 0.0899006 + 1.02497i
\(418\) −13.5610 + 11.8759i −0.663288 + 0.580867i
\(419\) 35.4041i 1.72960i −0.502113 0.864802i \(-0.667444\pi\)
0.502113 0.864802i \(-0.332556\pi\)
\(420\) −0.702592 + 1.09646i −0.0342830 + 0.0535017i
\(421\) 0.877958 0.0427891 0.0213945 0.999771i \(-0.493189\pi\)
0.0213945 + 0.999771i \(0.493189\pi\)
\(422\) −14.4945 8.36841i −0.705581 0.407368i
\(423\) 11.4859 + 4.17481i 0.558466 + 0.202986i
\(424\) −1.66437 + 0.960923i −0.0808288 + 0.0466665i
\(425\) −15.3819 + 26.6422i −0.746131 + 1.29234i
\(426\) −6.09819 2.84200i −0.295458 0.137695i
\(427\) 3.92238 + 9.54652i 0.189817 + 0.461989i
\(428\) −14.6492 −0.708096
\(429\) 9.67245 + 33.2441i 0.466990 + 1.60504i
\(430\) −0.326715 0.565887i −0.0157556 0.0272895i
\(431\) 9.95132 + 17.2362i 0.479338 + 0.830238i 0.999719 0.0236962i \(-0.00754343\pi\)
−0.520381 + 0.853934i \(0.674210\pi\)
\(432\) −1.34155 + 5.01999i −0.0645452 + 0.241524i
\(433\) 13.8697 0.666538 0.333269 0.942832i \(-0.391848\pi\)
0.333269 + 0.942832i \(0.391848\pi\)
\(434\) −15.2634 11.7815i −0.732668 0.565529i
\(435\) 0.193821 + 0.0903284i 0.00929302 + 0.00433092i
\(436\) −13.7850 7.95877i −0.660182 0.381156i
\(437\) −4.88219 8.45621i −0.233547 0.404515i
\(438\) 0.664854 + 7.58009i 0.0317679 + 0.362191i
\(439\) 9.43561 + 5.44765i 0.450337 + 0.260002i 0.707973 0.706240i \(-0.249610\pi\)
−0.257635 + 0.966242i \(0.582943\pi\)
\(440\) 0.892269 + 0.303581i 0.0425372 + 0.0144727i
\(441\) 8.77449 + 19.0790i 0.417833 + 0.908524i
\(442\) 37.6915i 1.79280i
\(443\) 12.2275 + 7.05956i 0.580947 + 0.335410i 0.761510 0.648154i \(-0.224459\pi\)
−0.180563 + 0.983563i \(0.557792\pi\)
\(444\) 19.2284 1.68653i 0.912540 0.0800394i
\(445\) 2.43343 + 4.21483i 0.115356 + 0.199802i
\(446\) 0.543854 0.941983i 0.0257522 0.0446042i
\(447\) 8.69187 18.6505i 0.411111 0.882138i
\(448\) 2.09441 + 1.61662i 0.0989514 + 0.0763782i
\(449\) 35.3836i 1.66985i −0.550361 0.834927i \(-0.685510\pi\)
0.550361 0.834927i \(-0.314490\pi\)
\(450\) −14.5324 + 2.56905i −0.685064 + 0.121106i
\(451\) 1.06292 0.210654i 0.0500508 0.00991930i
\(452\) 10.6248 6.13423i 0.499749 0.288530i
\(453\) −2.45503 + 1.71984i −0.115348 + 0.0808051i
\(454\) −8.96692 −0.420838
\(455\) 4.19144 1.72214i 0.196498 0.0807351i
\(456\) 8.53264 + 3.97655i 0.399577 + 0.186219i
\(457\) −2.96219 1.71022i −0.138565 0.0800007i 0.429115 0.903250i \(-0.358826\pi\)
−0.567680 + 0.823249i \(0.692159\pi\)
\(458\) −6.22490 10.7818i −0.290871 0.503803i
\(459\) −22.9929 22.9626i −1.07322 1.07180i
\(460\) −0.255269 + 0.442138i −0.0119020 + 0.0206148i
\(461\) 13.0512 0.607855 0.303927 0.952695i \(-0.401702\pi\)
0.303927 + 0.952695i \(0.401702\pi\)
\(462\) 11.8849 9.47361i 0.552935 0.440752i
\(463\) −18.0986 −0.841115 −0.420558 0.907266i \(-0.638166\pi\)
−0.420558 + 0.907266i \(0.638166\pi\)
\(464\) 0.217223 0.376241i 0.0100843 0.0174666i
\(465\) 0.313419 + 3.57333i 0.0145344 + 0.165709i
\(466\) −9.19303 15.9228i −0.425859 0.737609i
\(467\) −5.31873 3.07077i −0.246122 0.142098i 0.371865 0.928287i \(-0.378718\pi\)
−0.617987 + 0.786188i \(0.712052\pi\)
\(468\) 13.8458 11.6284i 0.640021 0.537522i
\(469\) −3.06370 + 22.7683i −0.141469 + 1.05134i
\(470\) −1.15764 −0.0533981
\(471\) −11.0716 15.8044i −0.510151 0.728230i
\(472\) 8.38305 4.83996i 0.385861 0.222777i
\(473\) 1.48257 + 7.48074i 0.0681685 + 0.343965i
\(474\) −7.58843 + 5.31597i −0.348548 + 0.244171i
\(475\) 26.7363i 1.22674i
\(476\) −15.3044 + 6.28814i −0.701478 + 0.288216i
\(477\) 4.41502 3.70796i 0.202150 0.169776i
\(478\) −12.4197 + 21.5116i −0.568065 + 0.983917i
\(479\) −3.63249 6.29166i −0.165973 0.287473i 0.771028 0.636802i \(-0.219743\pi\)
−0.937000 + 0.349329i \(0.886410\pi\)
\(480\) −0.0430064 0.490322i −0.00196297 0.0223800i
\(481\) −58.1674 33.5830i −2.65221 1.53125i
\(482\) 8.80236i 0.400937i
\(483\) 3.78226 + 7.31266i 0.172099 + 0.332738i
\(484\) −8.71750 6.70859i −0.396250 0.304936i
\(485\) −1.71954 0.992777i −0.0780803 0.0450797i
\(486\) 1.34152 15.5306i 0.0608527 0.704483i
\(487\) 20.5335 + 35.5650i 0.930461 + 1.61161i 0.782535 + 0.622607i \(0.213926\pi\)
0.147926 + 0.988998i \(0.452740\pi\)
\(488\) −3.37831 1.95047i −0.152929 0.0882936i
\(489\) 0.608567 1.30583i 0.0275204 0.0590516i
\(490\) −1.39853 1.41460i −0.0631792 0.0639053i
\(491\) 35.9140 1.62078 0.810389 0.585892i \(-0.199256\pi\)
0.810389 + 0.585892i \(0.199256\pi\)
\(492\) −0.324681 0.463476i −0.0146378 0.0208951i
\(493\) 1.35846 + 2.35292i 0.0611820 + 0.105970i
\(494\) −16.3785 28.3684i −0.736905 1.27636i
\(495\) −2.79448 0.430855i −0.125602 0.0193655i
\(496\) 7.28772 0.327228
\(497\) 6.27955 8.13543i 0.281676 0.364924i
\(498\) −1.17968 + 2.53128i −0.0528626 + 0.113429i
\(499\) 6.45040 11.1724i 0.288760 0.500146i −0.684754 0.728774i \(-0.740091\pi\)
0.973514 + 0.228628i \(0.0734239\pi\)
\(500\) 2.44115 1.40940i 0.109171 0.0630301i
\(501\) −33.0238 + 2.89653i −1.47539 + 0.129408i
\(502\) 12.1430 + 7.01079i 0.541971 + 0.312907i
\(503\) 2.65238 0.118264 0.0591319 0.998250i \(-0.481167\pi\)
0.0591319 + 0.998250i \(0.481167\pi\)
\(504\) −7.03155 3.68202i −0.313210 0.164010i
\(505\) 3.12872i 0.139226i
\(506\) 4.48261 3.92559i 0.199276 0.174514i
\(507\) −40.2455 + 3.52995i −1.78736 + 0.156771i
\(508\) 4.81171 2.77804i 0.213485 0.123256i
\(509\) −10.6064 6.12359i −0.470119 0.271423i 0.246171 0.969226i \(-0.420828\pi\)
−0.716289 + 0.697803i \(0.754161\pi\)
\(510\) 2.79002 + 1.30026i 0.123544 + 0.0575764i
\(511\) −11.5194 1.55005i −0.509589 0.0685703i
\(512\) −1.00000 −0.0441942
\(513\) −27.2838 7.29135i −1.20461 0.321921i
\(514\) 7.60623 4.39146i 0.335497 0.193699i
\(515\) 1.90774 1.10144i 0.0840652 0.0485351i
\(516\) 3.26191 2.28509i 0.143598 0.100595i
\(517\) 12.7909 + 4.35192i 0.562543 + 0.191397i
\(518\) −3.93202 + 29.2213i −0.172763 + 1.28391i
\(519\) 12.8863 27.6507i 0.565647 1.21373i
\(520\) −0.856362 + 1.48326i −0.0375539 + 0.0650453i
\(521\) −1.51792 + 0.876371i −0.0665012 + 0.0383945i −0.532882 0.846190i \(-0.678891\pi\)
0.466381 + 0.884584i \(0.345558\pi\)
\(522\) −0.445229 + 1.22493i −0.0194871 + 0.0536139i
\(523\) 10.9425 + 6.31768i 0.478484 + 0.276253i 0.719784 0.694198i \(-0.244241\pi\)
−0.241301 + 0.970450i \(0.577574\pi\)
\(524\) 18.8874 0.825099
\(525\) 1.04268 22.5187i 0.0455064 0.982796i
\(526\) −7.87749 −0.343475
\(527\) −22.7878 + 39.4696i −0.992653 + 1.71932i
\(528\) −1.36808 + 5.57928i −0.0595380 + 0.242807i
\(529\) −9.88618 17.1234i −0.429834 0.744494i
\(530\) −0.273069 + 0.472970i −0.0118614 + 0.0205445i
\(531\) −22.2375 + 18.6762i −0.965026 + 0.810477i
\(532\) −8.78639 + 11.3832i −0.380938 + 0.493523i
\(533\) 1.96912i 0.0852919i
\(534\) −24.2953 + 17.0198i −1.05136 + 0.736517i
\(535\) −3.60520 + 2.08146i −0.155866 + 0.0899895i
\(536\) −4.34158 7.51984i −0.187528 0.324808i
\(537\) 12.8435 8.99731i 0.554236 0.388262i
\(538\) 6.04971i 0.260822i
\(539\) 10.1346 + 20.8876i 0.436527 + 0.899691i
\(540\) 0.383118 + 1.42605i 0.0164868 + 0.0613672i
\(541\) 28.9602 + 16.7202i 1.24510 + 0.718856i 0.970127 0.242597i \(-0.0779992\pi\)
0.274969 + 0.961453i \(0.411333\pi\)
\(542\) 0.886543 0.511846i 0.0380803 0.0219857i
\(543\) 36.5702 3.20759i 1.56938 0.137651i
\(544\) 3.12688 5.41591i 0.134064 0.232205i
\(545\) −4.52336 −0.193759
\(546\) 12.6885 + 24.5321i 0.543018 + 1.04988i
\(547\) 18.9288i 0.809336i −0.914464 0.404668i \(-0.867387\pi\)
0.914464 0.404668i \(-0.132613\pi\)
\(548\) 14.6388 + 8.45173i 0.625340 + 0.361040i
\(549\) 10.9988 + 3.99775i 0.469418 + 0.170620i
\(550\) −16.0040 + 3.17175i −0.682414 + 0.135244i
\(551\) 2.04489 + 1.18061i 0.0871150 + 0.0502959i
\(552\) −2.82048 1.31446i −0.120048 0.0559470i
\(553\) −5.37867 13.0909i −0.228724 0.556683i
\(554\) 0.827971i 0.0351771i
\(555\) 4.49252 3.14717i 0.190697 0.133590i
\(556\) 10.5054 6.06530i 0.445528 0.257226i
\(557\) 8.23820 + 14.2690i 0.349064 + 0.604596i 0.986083 0.166251i \(-0.0531663\pi\)
−0.637020 + 0.770848i \(0.719833\pi\)
\(558\) −21.5293 + 3.80598i −0.911409 + 0.161120i
\(559\) −13.8585 −0.586153
\(560\) 0.745139 + 0.100266i 0.0314879 + 0.00423701i
\(561\) −25.9391 24.8551i −1.09515 1.04938i
\(562\) 10.8640 18.8169i 0.458268 0.793744i
\(563\) 14.0143 + 24.2734i 0.590631 + 1.02300i 0.994148 + 0.108031i \(0.0344546\pi\)
−0.403516 + 0.914972i \(0.632212\pi\)
\(564\) −0.616508 7.02889i −0.0259597 0.295970i
\(565\) 1.74319 3.01930i 0.0733366 0.127023i
\(566\) 14.1564i 0.595038i
\(567\) 22.6955 + 7.20520i 0.953121 + 0.302590i
\(568\) 3.88436i 0.162984i
\(569\) −13.8711 + 24.0254i −0.581506 + 1.00720i 0.413795 + 0.910370i \(0.364203\pi\)
−0.995301 + 0.0968278i \(0.969130\pi\)
\(570\) 2.66492 0.233741i 0.111621 0.00979035i
\(571\) −1.71070 + 0.987670i −0.0715904 + 0.0413327i −0.535368 0.844619i \(-0.679827\pi\)
0.463778 + 0.885952i \(0.346494\pi\)
\(572\) 15.0380 13.1694i 0.628771 0.550639i
\(573\) 19.5419 + 9.10731i 0.816375 + 0.380463i
\(574\) 0.799549 0.328511i 0.0333725 0.0137118i
\(575\) 8.83774i 0.368559i
\(576\) 2.95419 0.522246i 0.123091 0.0217602i
\(577\) 9.70603 + 16.8113i 0.404067 + 0.699865i 0.994212 0.107432i \(-0.0342628\pi\)
−0.590145 + 0.807297i \(0.700929\pi\)
\(578\) 11.0547 + 19.1474i 0.459817 + 0.796426i
\(579\) 21.2196 14.8651i 0.881857 0.617773i
\(580\) 0.123458i 0.00512633i
\(581\) −3.37691 2.60656i −0.140098 0.108138i
\(582\) 5.11211 10.9693i 0.211904 0.454691i
\(583\) 4.79520 4.19934i 0.198597 0.173919i
\(584\) 3.80459 2.19658i 0.157435 0.0908953i
\(585\) 1.75523 4.82907i 0.0725699 0.199658i
\(586\) 2.87941 4.98728i 0.118947 0.206023i
\(587\) 13.5713i 0.560148i −0.959978 0.280074i \(-0.909641\pi\)
0.959978 0.280074i \(-0.0903590\pi\)
\(588\) 7.84429 9.24484i 0.323493 0.381251i
\(589\) 39.6090i 1.63206i
\(590\) 1.37539 2.38225i 0.0566239 0.0980756i
\(591\) 14.2284 1.24799i 0.585280 0.0513352i
\(592\) −5.57207 9.65112i −0.229011 0.396658i
\(593\) 18.6257 32.2607i 0.764867 1.32479i −0.175450 0.984488i \(-0.556138\pi\)
0.940317 0.340300i \(-0.110529\pi\)
\(594\) 1.12782 17.1967i 0.0462749 0.705591i
\(595\) −2.87299 + 3.72209i −0.117781 + 0.152591i
\(596\) −11.8798 −0.486616
\(597\) 14.1799 + 20.2415i 0.580343 + 0.828428i
\(598\) 5.41396 + 9.37726i 0.221393 + 0.383465i
\(599\) −24.6430 + 14.2276i −1.00688 + 0.581325i −0.910278 0.413998i \(-0.864132\pi\)
−0.0966066 + 0.995323i \(0.530799\pi\)
\(600\) 4.88863 + 6.97841i 0.199577 + 0.284892i
\(601\) 4.98600i 0.203383i 0.994816 + 0.101692i \(0.0324255\pi\)
−0.994816 + 0.101692i \(0.967575\pi\)
\(602\) 2.31204 + 5.62717i 0.0942317 + 0.229347i
\(603\) 16.7531 + 19.9477i 0.682238 + 0.812333i
\(604\) 1.49875 + 0.865305i 0.0609834 + 0.0352088i
\(605\) −3.09860 0.412354i −0.125976 0.0167646i
\(606\) −18.9967 + 1.66622i −0.771690 + 0.0676854i
\(607\) 5.30947 + 3.06542i 0.215505 + 0.124422i 0.603867 0.797085i \(-0.293626\pi\)
−0.388362 + 0.921507i \(0.626959\pi\)
\(608\) 5.43503i 0.220420i
\(609\) −1.67627 1.07412i −0.0679258 0.0435257i
\(610\) −1.10855 −0.0448837
\(611\) −12.2762 + 21.2629i −0.496640 + 0.860206i
\(612\) −6.40897 + 17.6327i −0.259067 + 0.712758i
\(613\) −18.9061 + 10.9154i −0.763609 + 0.440870i −0.830590 0.556884i \(-0.811997\pi\)
0.0669808 + 0.997754i \(0.478663\pi\)
\(614\) 9.16339 + 5.29048i 0.369804 + 0.213507i
\(615\) −0.145759 0.0679293i −0.00587756 0.00273917i
\(616\) −7.85617 3.90904i −0.316534 0.157500i
\(617\) 8.66345i 0.348777i 0.984677 + 0.174389i \(0.0557949\pi\)
−0.984677 + 0.174389i \(0.944205\pi\)
\(618\) 7.70359 + 10.9967i 0.309884 + 0.442352i
\(619\) −15.3069 26.5123i −0.615236 1.06562i −0.990343 0.138639i \(-0.955727\pi\)
0.375107 0.926982i \(-0.377606\pi\)
\(620\) 1.79352 1.03549i 0.0720296 0.0415863i
\(621\) 9.01872 + 2.41017i 0.361909 + 0.0967170i
\(622\) 6.81785i 0.273371i
\(623\) −17.2205 41.9123i −0.689925 1.67918i
\(624\) −9.46201 4.40967i −0.378784 0.176528i
\(625\) −11.8976 + 20.6072i −0.475904 + 0.824290i
\(626\) −13.6258 23.6005i −0.544596 0.943267i
\(627\) −30.3236 7.43556i −1.21101 0.296948i
\(628\) −5.57046 + 9.64832i −0.222286 + 0.385010i
\(629\) 69.6928 2.77883
\(630\) −2.25365 + 0.0929406i −0.0897875 + 0.00370284i
\(631\) −12.7107 −0.506006 −0.253003 0.967465i \(-0.581418\pi\)
−0.253003 + 0.967465i \(0.581418\pi\)
\(632\) 4.63260 + 2.67463i 0.184275 + 0.106391i
\(633\) −2.53292 28.8781i −0.100674 1.14780i
\(634\) −11.6116 + 6.70397i −0.461156 + 0.266249i
\(635\) 0.789448 1.36736i 0.0313283 0.0542622i
\(636\) −3.01717 1.40612i −0.119638 0.0557563i
\(637\) −40.8133 + 10.6863i −1.61708 + 0.423407i
\(638\) −0.464116 + 1.36410i −0.0183745 + 0.0540053i
\(639\) −2.02859 11.4752i −0.0802499 0.453951i
\(640\) −0.246102 + 0.142087i −0.00972804 + 0.00561649i
\(641\) −6.94573 + 4.01012i −0.274340 + 0.158390i −0.630858 0.775898i \(-0.717297\pi\)
0.356518 + 0.934288i \(0.383964\pi\)
\(642\) −14.5580 20.7813i −0.574560 0.820172i
\(643\) −46.2342 −1.82330 −0.911649 0.410969i \(-0.865190\pi\)
−0.911649 + 0.410969i \(0.865190\pi\)
\(644\) 2.90436 3.76273i 0.114448 0.148272i
\(645\) 0.478082 1.02584i 0.0188245 0.0403924i
\(646\) 29.4357 + 16.9947i 1.15813 + 0.668647i
\(647\) 28.0821 16.2132i 1.10402 0.637407i 0.166747 0.986000i \(-0.446674\pi\)
0.937274 + 0.348593i \(0.113340\pi\)
\(648\) −8.45452 + 3.08563i −0.332125 + 0.121215i
\(649\) −24.1524 + 21.1512i −0.948063 + 0.830255i
\(650\) 29.6484i 1.16291i
\(651\) 1.54470 33.3608i 0.0605417 1.30751i
\(652\) −0.831773 −0.0325748
\(653\) 27.2177 + 15.7141i 1.06511 + 0.614942i 0.926842 0.375453i \(-0.122513\pi\)
0.138269 + 0.990395i \(0.455846\pi\)
\(654\) −2.40893 27.4646i −0.0941967 1.07395i
\(655\) 4.64822 2.68365i 0.181621 0.104859i
\(656\) −0.163357 + 0.282943i −0.00637804 + 0.0110471i
\(657\) −10.0923 + 8.47606i −0.393740 + 0.330683i
\(658\) 10.6818 + 1.43734i 0.416418 + 0.0560332i
\(659\) −20.9664 −0.816737 −0.408368 0.912817i \(-0.633902\pi\)
−0.408368 + 0.912817i \(0.633902\pi\)
\(660\) 0.456056 + 1.56746i 0.0177520 + 0.0610133i
\(661\) −0.654442 1.13353i −0.0254548 0.0440891i 0.853017 0.521883i \(-0.174770\pi\)
−0.878472 + 0.477793i \(0.841437\pi\)
\(662\) −5.97956 10.3569i −0.232402 0.402533i
\(663\) 53.4690 37.4569i 2.07656 1.45471i
\(664\) 1.61235 0.0625713
\(665\) −0.544949 + 4.04985i −0.0211322 + 0.157047i
\(666\) 21.5012 + 25.6013i 0.833156 + 0.992029i
\(667\) −0.675942 0.390255i −0.0261726 0.0151107i
\(668\) 9.56974 + 16.5753i 0.370264 + 0.641317i
\(669\) 1.87676 0.164612i 0.0725597 0.00636426i
\(670\) −2.13695 1.23377i −0.0825574 0.0476645i
\(671\) 12.2484 + 4.16735i 0.472845 + 0.160879i
\(672\) −0.211960 + 4.57767i −0.00817653 + 0.176587i
\(673\) 38.4311i 1.48141i −0.671829 0.740706i \(-0.734491\pi\)
0.671829 0.740706i \(-0.265509\pi\)
\(674\) −6.16319 3.55832i −0.237397 0.137061i
\(675\) −18.0864 18.0625i −0.696146 0.695227i
\(676\) 11.6625 + 20.2000i 0.448557 + 0.776923i
\(677\) 4.01555 6.95514i 0.154330 0.267308i −0.778485 0.627664i \(-0.784011\pi\)
0.932815 + 0.360356i \(0.117345\pi\)
\(678\) 19.2607 + 8.97623i 0.739701 + 0.344730i
\(679\) 14.6338 + 11.2955i 0.561594 + 0.433481i
\(680\) 1.77716i 0.0681509i
\(681\) −8.91111 12.7204i −0.341475 0.487448i
\(682\) −23.7095 + 4.69885i −0.907883 + 0.179928i
\(683\) 22.5996 13.0479i 0.864751 0.499264i −0.000849280 1.00000i \(-0.500270\pi\)
0.865600 + 0.500735i \(0.166937\pi\)
\(684\) 2.83842 + 16.0561i 0.108530 + 0.613922i
\(685\) 4.80353 0.183533
\(686\) 11.1481 + 14.7892i 0.425635 + 0.564654i
\(687\) 9.10891 19.5454i 0.347526 0.745702i
\(688\) −1.99134 1.14970i −0.0759190 0.0438319i
\(689\) 5.79150 + 10.0312i 0.220638 + 0.382157i
\(690\) −0.880894 + 0.0772638i −0.0335351 + 0.00294138i
\(691\) 6.88382 11.9231i 0.261873 0.453577i −0.704867 0.709340i \(-0.748993\pi\)
0.966740 + 0.255762i \(0.0823265\pi\)
\(692\) −17.6127 −0.669533
\(693\) 25.2501 + 7.44520i 0.959173 + 0.282820i
\(694\) 1.00232 0.0380475
\(695\) 1.72360 2.98537i 0.0653799 0.113241i
\(696\) 0.749605 0.0657483i 0.0284137 0.00249218i
\(697\) −1.02160 1.76946i −0.0386958 0.0670230i
\(698\) 16.0914 + 9.29040i 0.609070 + 0.351647i
\(699\) 13.4522 28.8649i 0.508808 1.09177i
\(700\) −12.0386 + 4.94629i −0.455015 + 0.186952i
\(701\) 16.6844 0.630162 0.315081 0.949065i \(-0.397968\pi\)
0.315081 + 0.949065i \(0.397968\pi\)
\(702\) 30.2555 + 8.08553i 1.14192 + 0.305169i
\(703\) 52.4541 30.2844i 1.97835 1.14220i
\(704\) 3.25335 0.644763i 0.122615 0.0243004i
\(705\) −1.15044 1.64223i −0.0433280 0.0618498i
\(706\) 3.59313i 0.135229i
\(707\) 3.88464 28.8692i 0.146097 1.08574i
\(708\) 15.1968 + 7.08231i 0.571131 + 0.266170i
\(709\) −9.07757 + 15.7228i −0.340915 + 0.590483i −0.984603 0.174806i \(-0.944070\pi\)
0.643688 + 0.765288i \(0.277404\pi\)
\(710\) 0.551918 + 0.955950i 0.0207131 + 0.0358762i
\(711\) −15.0824 5.48203i −0.565634 0.205592i
\(712\) 14.8319 + 8.56318i 0.555847 + 0.320919i
\(713\) 13.0929i 0.490331i
\(714\) −24.1295 15.4618i −0.903024 0.578643i
\(715\) 1.82969 5.37772i 0.0684266 0.201115i
\(716\) −7.84070 4.52683i −0.293021 0.169176i
\(717\) −42.8586 + 3.75916i −1.60059 + 0.140388i
\(718\) 5.21329 + 9.02968i 0.194558 + 0.336985i
\(719\) −13.2458 7.64744i −0.493983 0.285201i 0.232242 0.972658i \(-0.425394\pi\)
−0.726225 + 0.687457i \(0.758727\pi\)
\(720\) 0.652829 0.548279i 0.0243295 0.0204331i
\(721\) −18.9706 + 7.79445i −0.706501 + 0.290280i
\(722\) 10.5396 0.392243
\(723\) 12.4870 8.74757i 0.464396 0.325326i
\(724\) −10.5974 18.3553i −0.393851 0.682169i
\(725\) 1.06857 + 1.85082i 0.0396858 + 0.0687379i
\(726\) 0.853527 19.0334i 0.0316774 0.706397i
\(727\) 9.71636 0.360360 0.180180 0.983634i \(-0.442332\pi\)
0.180180 + 0.983634i \(0.442332\pi\)
\(728\) 9.74341 12.6230i 0.361115 0.467840i
\(729\) 23.3648 13.5309i 0.865364 0.501144i
\(730\) 0.624212 1.08117i 0.0231031 0.0400158i
\(731\) 12.4533 7.18994i 0.460603 0.265929i
\(732\) −0.590361 6.73078i −0.0218204 0.248777i
\(733\) 20.6665 + 11.9318i 0.763336 + 0.440712i 0.830492 0.557030i \(-0.188059\pi\)
−0.0671561 + 0.997742i \(0.521393\pi\)
\(734\) 1.60455 0.0592251
\(735\) 0.616924 3.38975i 0.0227556 0.125033i
\(736\) 1.79656i 0.0662222i
\(737\) 18.9732 + 21.6654i 0.698887 + 0.798054i
\(738\) 0.334823 0.921182i 0.0123250 0.0339092i
\(739\) 13.0082 7.51031i 0.478516 0.276271i −0.241282 0.970455i \(-0.577568\pi\)
0.719798 + 0.694184i \(0.244235\pi\)
\(740\) −2.74260 1.58344i −0.100820 0.0582084i
\(741\) 23.9667 51.4264i 0.880439 1.88919i
\(742\) 3.10690 4.02512i 0.114058 0.147767i
\(743\) 29.1581 1.06971 0.534853 0.844945i \(-0.320367\pi\)
0.534853 + 0.844945i \(0.320367\pi\)
\(744\) 7.24236 + 10.3383i 0.265518 + 0.379021i
\(745\) −2.92365 + 1.68797i −0.107114 + 0.0618423i
\(746\) 0.443041 0.255790i 0.0162209 0.00936513i
\(747\) −4.76319 + 0.842043i −0.174276 + 0.0308087i
\(748\) −6.68085 + 19.6360i −0.244276 + 0.717962i
\(749\) 35.8501 14.7297i 1.30993 0.538213i
\(750\) 4.42532 + 2.06237i 0.161590 + 0.0753072i
\(751\) 10.3432 17.9150i 0.377430 0.653728i −0.613257 0.789883i \(-0.710141\pi\)
0.990688 + 0.136155i \(0.0434745\pi\)
\(752\) −3.52794 + 2.03685i −0.128651 + 0.0742765i
\(753\) 2.12200 + 24.1932i 0.0773300 + 0.881649i
\(754\) −2.26761 1.30921i −0.0825816 0.0476785i
\(755\) 0.491795 0.0178982
\(756\) −1.76450 13.6340i −0.0641742 0.495865i
\(757\) −19.7101 −0.716375 −0.358188 0.933650i \(-0.616605\pi\)
−0.358188 + 0.933650i \(0.616605\pi\)
\(758\) 2.54183 4.40257i 0.0923233 0.159909i
\(759\) 10.0235 + 2.45784i 0.363831 + 0.0892141i
\(760\) −0.772248 1.33757i −0.0280124 0.0485189i
\(761\) −20.8209 + 36.0628i −0.754757 + 1.30728i 0.190738 + 0.981641i \(0.438912\pi\)
−0.945495 + 0.325636i \(0.894422\pi\)
\(762\) 8.72268 + 4.06511i 0.315989 + 0.147264i
\(763\) 41.7377 + 5.61623i 1.51101 + 0.203321i
\(764\) 12.4476i 0.450339i
\(765\) 0.928113 + 5.25007i 0.0335560 + 0.189817i
\(766\) 4.59160 2.65096i 0.165901 0.0957832i
\(767\) −29.1705 50.5248i −1.05329 1.82434i
\(768\) −0.993776 1.41859i −0.0358598 0.0511891i
\(769\) 5.30858i 0.191432i −0.995409 0.0957161i \(-0.969486\pi\)
0.995409 0.0957161i \(-0.0305141\pi\)
\(770\) −2.48884 + 0.154238i −0.0896917 + 0.00555835i
\(771\) 13.7886 + 6.42603i 0.496584 + 0.231428i
\(772\) −12.9542 7.47910i −0.466231 0.269179i
\(773\) 27.8900 16.1023i 1.00314 0.579160i 0.0939608 0.995576i \(-0.470047\pi\)
0.909174 + 0.416415i \(0.136714\pi\)
\(774\) 6.48322 + 2.35647i 0.233035 + 0.0847014i
\(775\) −17.9250 + 31.0471i −0.643886 + 1.11524i
\(776\) −6.98710 −0.250822
\(777\) −45.3607 + 23.4615i −1.62731 + 0.841676i
\(778\) 30.0206i 1.07629i
\(779\) −1.53781 0.887853i −0.0550976 0.0318106i
\(780\) −2.95518 + 0.259200i −0.105812 + 0.00928086i
\(781\) −2.50450 12.6372i −0.0896179 0.452194i
\(782\) −9.73003 5.61764i −0.347945 0.200886i
\(783\) −2.18014 + 0.585711i −0.0779119 + 0.0209316i
\(784\) −6.75102 1.85034i −0.241108 0.0660835i
\(785\) 3.16596i 0.112998i
\(786\) 18.7698 + 26.7935i 0.669497 + 0.955693i
\(787\) 25.9819 15.0006i 0.926153 0.534715i 0.0405602 0.999177i \(-0.487086\pi\)
0.885593 + 0.464462i \(0.153752\pi\)
\(788\) −4.12317 7.14153i −0.146882 0.254407i
\(789\) −7.82846 11.1750i −0.278700 0.397839i
\(790\) 1.52012 0.0540835
\(791\) −19.8335 + 25.6951i −0.705197 + 0.913614i
\(792\) −9.27430 + 3.60380i −0.329548 + 0.128056i
\(793\) −11.7555 + 20.3611i −0.417450 + 0.723045i
\(794\) 5.20199 + 9.01011i 0.184612 + 0.319757i
\(795\) −0.942323 + 0.0826517i −0.0334207 + 0.00293135i
\(796\) 7.13434 12.3570i 0.252870 0.437984i
\(797\) 35.9024i 1.27173i 0.771802 + 0.635864i \(0.219356\pi\)
−0.771802 + 0.635864i \(0.780644\pi\)
\(798\) −24.8798 1.15201i −0.880735 0.0407807i
\(799\) 25.4760i 0.901276i
\(800\) 2.45962 4.26019i 0.0869608 0.150621i
\(801\) −48.2883 17.5514i −1.70618 0.620148i
\(802\) 12.6464 7.30138i 0.446559 0.257821i
\(803\) −10.9614 + 9.59931i −0.386819 + 0.338752i
\(804\) 6.35304 13.6320i 0.224055 0.480763i
\(805\) 0.180134 1.33869i 0.00634889 0.0471826i
\(806\) 43.9232i 1.54713i
\(807\) 8.58208 6.01206i 0.302104 0.211634i
\(808\) 5.50494 + 9.53484i 0.193663 + 0.335434i
\(809\) −22.7425 39.3912i −0.799585 1.38492i −0.919887 0.392184i \(-0.871720\pi\)
0.120302 0.992737i \(-0.461614\pi\)
\(810\) −1.64225 + 1.96066i −0.0577027 + 0.0688905i
\(811\) 15.4966i 0.544160i 0.962275 + 0.272080i \(0.0877115\pi\)
−0.962275 + 0.272080i \(0.912288\pi\)
\(812\) −0.153287 + 1.13917i −0.00537931 + 0.0399770i
\(813\) 1.60713 + 0.748985i 0.0563644 + 0.0262680i
\(814\) 24.3506 + 27.8058i 0.853488 + 0.974592i
\(815\) −0.204701 + 0.118184i −0.00717037 + 0.00413982i
\(816\) 10.7904 0.946432i 0.377740 0.0331318i
\(817\) 6.24865 10.8230i 0.218613 0.378648i
\(818\) 24.9790i 0.873370i
\(819\) −22.1916 + 42.3793i −0.775437 + 1.48085i
\(820\) 0.0928439i 0.00324225i
\(821\) −19.5209 + 33.8113i −0.681285 + 1.18002i 0.293303 + 0.956019i \(0.405245\pi\)
−0.974589 + 0.224001i \(0.928088\pi\)
\(822\) 2.55814 + 29.1657i 0.0892253 + 1.01727i
\(823\) −20.0995 34.8133i −0.700624 1.21352i −0.968248 0.249992i \(-0.919572\pi\)
0.267624 0.963523i \(-0.413761\pi\)
\(824\) 3.87592 6.71328i 0.135024 0.233868i
\(825\) −20.4038 19.5512i −0.710370 0.680686i
\(826\) −15.6488 + 20.2737i −0.544490 + 0.705411i
\(827\) −3.20205 −0.111346 −0.0556732 0.998449i \(-0.517730\pi\)
−0.0556732 + 0.998449i \(0.517730\pi\)
\(828\) −0.938248 5.30740i −0.0326064 0.184445i
\(829\) −6.56231 11.3662i −0.227918 0.394766i 0.729273 0.684223i \(-0.239859\pi\)
−0.957191 + 0.289457i \(0.906525\pi\)
\(830\) 0.396803 0.229094i 0.0137732 0.00795197i
\(831\) −1.17456 + 0.822818i −0.0407449 + 0.0285432i
\(832\) 6.02702i 0.208949i
\(833\) 31.1309 30.7771i 1.07862 1.06636i
\(834\) 19.0442 + 8.87536i 0.659447 + 0.307328i
\(835\) 4.71027 + 2.71947i 0.163006 + 0.0941113i
\(836\) 3.50431 + 17.6821i 0.121199 + 0.611547i
\(837\) −26.7945 26.7591i −0.926152 0.924929i
\(838\) −30.6609 17.7021i −1.05916 0.611507i
\(839\) 22.7217i 0.784439i 0.919872 + 0.392220i \(0.128293\pi\)
−0.919872 + 0.392220i \(0.871707\pi\)
\(840\) 0.598264 + 1.15669i 0.0206421 + 0.0399096i
\(841\) −28.8113 −0.993492
\(842\) 0.438979 0.760334i 0.0151282 0.0262028i
\(843\) 37.4899 3.28826i 1.29122 0.113254i
\(844\) −14.4945 + 8.36841i −0.498921 + 0.288052i
\(845\) 5.74032 + 3.31417i 0.197473 + 0.114011i
\(846\) 9.35847 7.85971i 0.321751 0.270223i
\(847\) 28.0793 + 7.65210i 0.964815 + 0.262929i
\(848\) 1.92185i 0.0659964i
\(849\) −20.0822 + 14.0683i −0.689220 + 0.482823i
\(850\) 15.3819 + 26.6422i 0.527594 + 0.913820i
\(851\) −17.3388 + 10.0106i −0.594368 + 0.343159i
\(852\) −5.51034 + 3.86019i −0.188781 + 0.132248i
\(853\) 21.8003i 0.746428i −0.927745 0.373214i \(-0.878256\pi\)
0.927745 0.373214i \(-0.121744\pi\)
\(854\) 10.2287 + 1.37638i 0.350020 + 0.0470987i
\(855\) 2.97991 + 3.54815i 0.101911 + 0.121344i
\(856\) −7.32460 + 12.6866i −0.250350 + 0.433619i
\(857\) 14.0547 + 24.3434i 0.480098 + 0.831554i 0.999739 0.0228304i \(-0.00726778\pi\)
−0.519641 + 0.854384i \(0.673934\pi\)
\(858\) 33.6264 + 8.24544i 1.14799 + 0.281495i
\(859\) −12.9428 + 22.4176i −0.441603 + 0.764879i −0.997809 0.0661656i \(-0.978923\pi\)
0.556205 + 0.831045i \(0.312257\pi\)
\(860\) −0.653430 −0.0222818
\(861\) 1.26060 + 0.807769i 0.0429610 + 0.0275287i
\(862\) 19.9026 0.677886
\(863\) −11.3331 6.54315i −0.385782 0.222731i 0.294549 0.955636i \(-0.404831\pi\)
−0.680331 + 0.732905i \(0.738164\pi\)
\(864\) 3.67666 + 3.67181i 0.125083 + 0.124917i
\(865\) −4.33451 + 2.50253i −0.147378 + 0.0850887i
\(866\) 6.93487 12.0116i 0.235657 0.408169i
\(867\) −16.1764 + 34.7104i −0.549380 + 1.17883i
\(868\) −17.8348 + 7.32778i −0.605352 + 0.248721i
\(869\) −16.7960 5.71458i −0.569764 0.193854i
\(870\) 0.175137 0.122690i 0.00593771 0.00415958i
\(871\) −45.3222 + 26.1668i −1.53569 + 0.886628i
\(872\) −13.7850 + 7.95877i −0.466819 + 0.269518i
\(873\) 20.6412 3.64898i 0.698600 0.123499i
\(874\) −9.76439 −0.330285
\(875\) −4.55692 + 5.90370i −0.154052 + 0.199581i
\(876\) 6.89697 + 3.21426i 0.233027 + 0.108600i
\(877\) 27.9816 + 16.1552i 0.944872 + 0.545522i 0.891484 0.453052i \(-0.149665\pi\)
0.0533875 + 0.998574i \(0.482998\pi\)
\(878\) 9.43561 5.44765i 0.318436 0.183849i
\(879\) 9.93641 0.871529i 0.335147 0.0293959i
\(880\) 0.709044 0.620937i 0.0239019 0.0209318i
\(881\) 16.1735i 0.544899i 0.962170 + 0.272450i \(0.0878338\pi\)
−0.962170 + 0.272450i \(0.912166\pi\)
\(882\) 20.9101 + 1.94057i 0.704081 + 0.0653423i
\(883\) 9.98793 0.336121 0.168060 0.985777i \(-0.446250\pi\)
0.168060 + 0.985777i \(0.446250\pi\)
\(884\) −32.6418 18.8458i −1.09786 0.633851i
\(885\) 4.74627 0.416298i 0.159544 0.0139937i
\(886\) 12.2275 7.05956i 0.410791 0.237171i
\(887\) 16.1800 28.0247i 0.543273 0.940976i −0.455441 0.890266i \(-0.650518\pi\)
0.998713 0.0507096i \(-0.0161483\pi\)
\(888\) 8.15362 17.4956i 0.273618 0.587112i
\(889\) −8.98209 + 11.6367i −0.301250 + 0.390282i
\(890\) 4.86687 0.163138
\(891\) 25.5160 15.4898i 0.854818 0.518928i
\(892\) −0.543854 0.941983i −0.0182096 0.0315399i
\(893\) −11.0704 19.1745i −0.370456 0.641649i
\(894\) −11.8059 16.8526i −0.394847 0.563636i
\(895\) −2.57282 −0.0859998
\(896\) 2.44724 1.00550i 0.0817565 0.0335913i
\(897\) −7.92226 + 16.9991i −0.264516 + 0.567584i
\(898\) −30.6431 17.6918i −1.02257 0.590382i
\(899\) 1.58306 + 2.74194i 0.0527980 + 0.0914489i
\(900\) −5.04133 + 13.8700i −0.168044 + 0.462332i
\(901\) −10.4085 6.00938i −0.346759 0.200201i
\(902\) 0.349027 1.02584i 0.0116213 0.0341567i
\(903\) −5.68503 + 8.87200i −0.189186 + 0.295242i
\(904\) 12.2685i 0.408043i
\(905\) −5.21610 3.01152i −0.173389 0.100106i
\(906\) 0.261907 + 2.98604i 0.00870129 + 0.0992046i
\(907\) 8.02681 + 13.9028i 0.266526 + 0.461636i 0.967962 0.251096i \(-0.0807909\pi\)
−0.701436 + 0.712732i \(0.747458\pi\)
\(908\) −4.48346 + 7.76558i −0.148789 + 0.257710i
\(909\) −21.2422 25.2928i −0.704559 0.838910i
\(910\) 0.604305 4.49096i 0.0200325 0.148874i
\(911\) 22.7800i 0.754734i 0.926064 + 0.377367i \(0.123171\pi\)
−0.926064 + 0.377367i \(0.876829\pi\)
\(912\) 7.71011 5.40121i 0.255307 0.178852i
\(913\) −5.24554 + 1.03958i −0.173602 + 0.0344052i
\(914\) −2.96219 + 1.71022i −0.0979805 + 0.0565690i
\(915\) −1.10165 1.57258i −0.0364193 0.0519878i
\(916\) −12.4498 −0.411353
\(917\) −46.2219 + 18.9912i −1.52638 + 0.627145i
\(918\) −31.3827 + 8.43118i −1.03578 + 0.278271i
\(919\) −26.9216 15.5432i −0.888061 0.512722i −0.0147535 0.999891i \(-0.504696\pi\)
−0.873308 + 0.487169i \(0.838030\pi\)
\(920\) 0.255269 + 0.442138i 0.00841596 + 0.0145769i
\(921\) 1.60130 + 18.2567i 0.0527648 + 0.601578i
\(922\) 6.52560 11.3027i 0.214909 0.372234i
\(923\) 23.4111 0.770587
\(924\) −2.26193 15.0294i −0.0744122 0.494432i
\(925\) 54.8208 1.80250
\(926\) −9.04932 + 15.6739i −0.297379 + 0.515076i
\(927\) −7.94422 + 21.8565i −0.260923 + 0.717862i
\(928\) −0.217223 0.376241i −0.00713070 0.0123507i
\(929\) −9.05995 5.23076i −0.297247 0.171616i 0.343958 0.938985i \(-0.388232\pi\)
−0.641206 + 0.767369i \(0.721565\pi\)
\(930\) 3.25130 + 1.51523i 0.106614 + 0.0496865i
\(931\) 10.0567 36.6920i 0.329593 1.20253i
\(932\) −18.3861 −0.602255
\(933\) −9.67176 + 6.77541i −0.316639 + 0.221817i
\(934\) −5.31873 + 3.07077i −0.174034 + 0.100479i
\(935\) 1.14585 + 5.78171i 0.0374732 + 0.189082i
\(936\) −3.14758 17.8050i −0.102882 0.581974i
\(937\) 27.1309i 0.886328i −0.896441 0.443164i \(-0.853856\pi\)
0.896441 0.443164i \(-0.146144\pi\)
\(938\) 18.1861 + 14.0374i 0.593796 + 0.458337i
\(939\) 19.9386 42.7831i 0.650672 1.39617i
\(940\) −0.578822 + 1.00255i −0.0188791 + 0.0326995i
\(941\) 9.89770 + 17.1433i 0.322656 + 0.558856i 0.981035 0.193830i \(-0.0620911\pi\)
−0.658379 + 0.752686i \(0.728758\pi\)
\(942\) −19.2228 + 1.68605i −0.626314 + 0.0549344i
\(943\) 0.508326 + 0.293482i 0.0165534 + 0.00955709i
\(944\) 9.67991i 0.315054i
\(945\) −2.37147 3.10465i −0.0771438 0.100994i
\(946\) 7.21980 + 2.45643i 0.234736 + 0.0798655i
\(947\) −31.4053 18.1318i −1.02053 0.589205i −0.106275 0.994337i \(-0.533892\pi\)
−0.914258 + 0.405131i \(0.867226\pi\)
\(948\) 0.809548 + 9.22976i 0.0262929 + 0.299769i
\(949\) −13.2388 22.9304i −0.429751 0.744351i
\(950\) 23.1543 + 13.3681i 0.751224 + 0.433719i
\(951\) −21.0496 9.80993i −0.682579 0.318109i
\(952\) −2.20653 + 16.3981i −0.0715140 + 0.531465i
\(953\) −39.1127 −1.26699 −0.633493 0.773749i \(-0.718379\pi\)
−0.633493 + 0.773749i \(0.718379\pi\)
\(954\) −1.00368 5.67750i −0.0324952 0.183816i
\(955\) −1.76865 3.06338i −0.0572320 0.0991288i
\(956\) 12.4197 + 21.5116i 0.401683 + 0.695735i
\(957\) −2.39633 + 0.697220i −0.0774625 + 0.0225379i
\(958\) −7.26498 −0.234721
\(959\) −44.3229 5.96409i −1.43126 0.192591i
\(960\) −0.446134 0.207916i −0.0143989 0.00671047i
\(961\) −11.0554 + 19.1485i −0.356626 + 0.617695i
\(962\) −58.1674 + 33.5830i −1.87539 + 1.08276i
\(963\) 15.0128 41.3039i 0.483780 1.33100i
\(964\) −7.62307 4.40118i −0.245522 0.141752i
\(965\) −4.25074 −0.136836
\(966\) 8.22408 + 0.380800i 0.264605 + 0.0122520i
\(967\) 50.7537i 1.63213i 0.577961 + 0.816064i \(0.303849\pi\)
−0.577961 + 0.816064i \(0.696151\pi\)
\(968\) −10.1686 + 4.19528i −0.326830 + 0.134841i
\(969\) 5.14389 + 58.6462i 0.165246 + 1.88399i
\(970\) −1.71954 + 0.992777i −0.0552111 + 0.0318761i
\(971\) 0.389942 + 0.225133i 0.0125138 + 0.00722486i 0.506244 0.862390i \(-0.331034\pi\)
−0.493730 + 0.869615i \(0.664367\pi\)
\(972\) −12.7792 8.92711i −0.409892 0.286337i
\(973\) −19.6106 + 25.4064i −0.628686 + 0.814491i
\(974\) 41.0670 1.31587
\(975\) 42.0590 29.4638i 1.34697 0.943598i
\(976\) −3.37831 + 1.95047i −0.108137 + 0.0624330i
\(977\) −4.01364 + 2.31728i −0.128408 + 0.0741363i −0.562828 0.826574i \(-0.690287\pi\)
0.434420 + 0.900710i \(0.356953\pi\)
\(978\) −0.826596 1.17995i −0.0264316 0.0377306i
\(979\) −53.7744 18.2960i −1.71864 0.584742i
\(980\) −1.92435 + 0.503861i −0.0614711 + 0.0160952i
\(981\) 36.5671 30.7109i 1.16750 0.980524i
\(982\) 17.9570 31.1025i 0.573031 0.992520i
\(983\) −28.8337 + 16.6472i −0.919654 + 0.530962i −0.883525 0.468385i \(-0.844836\pi\)
−0.0361291 + 0.999347i \(0.511503\pi\)
\(984\) −0.563722 + 0.0494444i −0.0179708 + 0.00157623i
\(985\) −2.02944 1.17170i −0.0646633 0.0373334i
\(986\) 2.71692 0.0865244
\(987\) 8.57627 + 16.5815i 0.272986 + 0.527794i
\(988\) −32.7570 −1.04214
\(989\) −2.06551 + 3.57756i −0.0656793 + 0.113760i
\(990\) −1.77037 + 2.20466i −0.0562661 + 0.0700688i
\(991\) 0.378039 + 0.654782i 0.0120088 + 0.0207998i 0.871967 0.489564i \(-0.162844\pi\)
−0.859959 + 0.510364i \(0.829511\pi\)
\(992\) 3.64386 6.31135i 0.115693 0.200386i
\(993\) 8.74990 18.7750i 0.277670 0.595807i
\(994\) −3.90572 9.50597i −0.123882 0.301511i
\(995\) 4.05479i 0.128545i
\(996\) 1.60231 + 2.28727i 0.0507713 + 0.0724749i
\(997\) −27.9874 + 16.1585i −0.886368 + 0.511745i −0.872753 0.488162i \(-0.837667\pi\)
−0.0136154 + 0.999907i \(0.504334\pi\)
\(998\) −6.45040 11.1724i −0.204184 0.353657i
\(999\) −14.9504 + 55.9435i −0.473010 + 1.76997i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 462.2.n.f.65.12 yes 24
3.2 odd 2 462.2.n.e.65.4 24
7.4 even 3 inner 462.2.n.f.263.4 yes 24
11.10 odd 2 462.2.n.e.65.12 yes 24
21.11 odd 6 462.2.n.e.263.12 yes 24
33.32 even 2 inner 462.2.n.f.65.4 yes 24
77.32 odd 6 462.2.n.e.263.4 yes 24
231.32 even 6 inner 462.2.n.f.263.12 yes 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
462.2.n.e.65.4 24 3.2 odd 2
462.2.n.e.65.12 yes 24 11.10 odd 2
462.2.n.e.263.4 yes 24 77.32 odd 6
462.2.n.e.263.12 yes 24 21.11 odd 6
462.2.n.f.65.4 yes 24 33.32 even 2 inner
462.2.n.f.65.12 yes 24 1.1 even 1 trivial
462.2.n.f.263.4 yes 24 7.4 even 3 inner
462.2.n.f.263.12 yes 24 231.32 even 6 inner