Properties

Label 462.2.n.e.263.4
Level $462$
Weight $2$
Character 462.263
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 263.4
Character \(\chi\) \(=\) 462.263
Dual form 462.2.n.e.65.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.993776 - 1.41859i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.246102 - 0.142087i) q^{5} +(-0.731651 + 1.56993i) q^{6} +(2.09441 - 1.61662i) q^{7} +1.00000 q^{8} +(-1.02482 + 2.81953i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.993776 - 1.41859i) 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} +(-1.02482 + 2.81953i) q^{9} +(-0.246102 - 0.142087i) q^{10} +(-3.25335 - 0.644763i) q^{11} +(1.72543 - 0.151338i) 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} +(2.95419 - 0.522246i) q^{18} +(-4.70688 + 2.71752i) q^{19} +0.284174i q^{20} +(-4.37470 - 1.36455i) q^{21} +(1.06829 + 3.13986i) q^{22} +(-1.55587 + 0.898282i) q^{23} +(-0.993776 - 1.41859i) 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} +(0.0430064 + 0.490322i) q^{30} +(-3.64386 + 6.31135i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(2.31844 + 5.25593i) 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} +(-8.54989 + 5.98951i) q^{39} +(0.246102 - 0.142087i) q^{40} -0.326715 q^{41} +(1.00561 + 4.47088i) q^{42} -2.29940i q^{43} +(2.18506 - 2.49510i) q^{44} +(0.148409 + 0.839506i) 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} +(-10.7904 + 0.946432i) q^{51} +(5.21955 + 3.01351i) q^{52} +(-1.66437 - 0.960923i) q^{53} +(-3.67666 - 3.67181i) 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} +(0.403128 - 0.282406i) q^{60} +(3.37831 - 1.95047i) q^{61} +7.28772 q^{62} +(2.41173 + 7.56198i) q^{63} +1.00000 q^{64} +(-0.856362 - 1.48326i) q^{65} +(3.39255 - 4.63580i) 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} +(-1.02482 + 2.81953i) q^{72} +(-3.80459 - 2.19658i) q^{73} +(-5.57207 + 9.65112i) q^{74} +(8.48780 - 0.744470i) 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} +(-6.89949 - 5.77901i) q^{81} +(0.163357 + 0.282943i) q^{82} +1.61235 q^{83} +(3.36909 - 3.10633i) q^{84} -1.77716i q^{85} +(-1.99134 + 1.14970i) q^{86} +(-0.431742 - 0.616303i) 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} +(12.5744 - 1.10291i) q^{93} +(3.52794 + 2.03685i) q^{94} +(-0.772248 + 1.33757i) q^{95} +(1.72543 - 0.151338i) q^{96} +6.98710 q^{97} +(-6.75102 + 1.85034i) q^{98} +(5.15202 - 8.51215i) 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 \( 24 q - 12 q^{2} - 12 q^{4} + 24 q^{8} - 8 q^{9} - 4 q^{11} + 4 q^{15} - 12 q^{16} + 4 q^{17} - 8 q^{18} + 8 q^{22} + 20 q^{25} - 12 q^{27} + 40 q^{29} - 2 q^{30} - 28 q^{31} - 12 q^{32} + 32 q^{33} - 8 q^{34} - 32 q^{35} + 16 q^{36} - 16 q^{37} - 8 q^{41} + 6 q^{42} - 4 q^{44} - 28 q^{45} - 8 q^{49} - 40 q^{50} - 34 q^{51} + 6 q^{54} + 8 q^{55} + 40 q^{57} - 20 q^{58} - 2 q^{60} + 56 q^{62} - 14 q^{63} + 24 q^{64} - 44 q^{65} + 32 q^{66} + 4 q^{68} - 20 q^{69} + 64 q^{70} - 8 q^{72} - 16 q^{74} - 26 q^{75} + 24 q^{81} + 4 q^{82} + 144 q^{83} - 6 q^{84} + 8 q^{87} - 4 q^{88} + 56 q^{90} - 32 q^{91} - 22 q^{93} - 44 q^{95} + 64 q^{97} - 8 q^{98} - 52 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(155\) \(199\) \(211\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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
\(3\) −0.993776 1.41859i −0.573757 0.819026i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 0.246102 0.142087i 0.110060 0.0635433i −0.443959 0.896047i \(-0.646427\pi\)
0.554020 + 0.832504i \(0.313093\pi\)
\(6\) −0.731651 + 1.56993i −0.298695 + 0.640922i
\(7\) 2.09441 1.61662i 0.791611 0.611026i
\(8\) 1.00000 0.353553
\(9\) −1.02482 + 2.81953i −0.341606 + 0.939843i
\(10\) −0.246102 0.142087i −0.0778243 0.0449319i
\(11\) −3.25335 0.644763i −0.980922 0.194403i
\(12\) 1.72543 0.151338i 0.498088 0.0436876i
\(13\) 6.02702i 1.67159i −0.549039 0.835797i \(-0.685006\pi\)
0.549039 0.835797i \(-0.314994\pi\)
\(14\) −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 −0.185297 0.982683i \(-0.559325\pi\)
0.943677 0.330869i \(-0.107342\pi\)
\(18\) 2.95419 0.522246i 0.696310 0.123095i
\(19\) −4.70688 + 2.71752i −1.07983 + 0.623441i −0.930851 0.365399i \(-0.880933\pi\)
−0.148981 + 0.988840i \(0.547599\pi\)
\(20\) 0.284174i 0.0635433i
\(21\) −4.37470 1.36455i −0.954638 0.297770i
\(22\) 1.06829 + 3.13986i 0.227761 + 0.669421i
\(23\) −1.55587 + 0.898282i −0.324421 + 0.187305i −0.653362 0.757046i \(-0.726642\pi\)
0.328940 + 0.944351i \(0.393309\pi\)
\(24\) −0.993776 1.41859i −0.202854 0.289569i
\(25\) −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 \(-0.487157\pi\)
0.0403373 + 0.999186i \(0.487157\pi\)
\(30\) 0.0430064 + 0.490322i 0.00785186 + 0.0895201i
\(31\) −3.64386 + 6.31135i −0.654456 + 1.13355i 0.327573 + 0.944826i \(0.393769\pi\)
−0.982030 + 0.188726i \(0.939564\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 2.31844 + 5.25593i 0.403589 + 0.914940i
\(34\) −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 −0.805367 0.592777i \(-0.798032\pi\)
−0.110677 0.993856i \(-0.535302\pi\)
\(38\) 4.70688 + 2.71752i 0.763556 + 0.440839i
\(39\) −8.54989 + 5.98951i −1.36908 + 0.959089i
\(40\) 0.246102 0.142087i 0.0389122 0.0224659i
\(41\) −0.326715 −0.0510243 −0.0255121 0.999675i \(-0.508122\pi\)
−0.0255121 + 0.999675i \(0.508122\pi\)
\(42\) 1.00561 + 4.47088i 0.155170 + 0.689871i
\(43\) 2.29940i 0.350655i −0.984510 0.175327i \(-0.943902\pi\)
0.984510 0.175327i \(-0.0560984\pi\)
\(44\) 2.18506 2.49510i 0.329410 0.376151i
\(45\) 0.148409 + 0.839506i 0.0221235 + 0.125146i
\(46\) 1.55587 + 0.898282i 0.229401 + 0.132444i
\(47\) −3.52794 + 2.03685i −0.514602 + 0.297106i −0.734723 0.678367i \(-0.762688\pi\)
0.220121 + 0.975473i \(0.429355\pi\)
\(48\) −0.731651 + 1.56993i −0.105605 + 0.226600i
\(49\) 1.77307 6.77172i 0.253296 0.967389i
\(50\) 4.91924 0.695686
\(51\) −10.7904 + 0.946432i −1.51096 + 0.132527i
\(52\) 5.21955 + 3.01351i 0.723821 + 0.417899i
\(53\) −1.66437 0.960923i −0.228618 0.131993i 0.381316 0.924445i \(-0.375471\pi\)
−0.609935 + 0.792452i \(0.708804\pi\)
\(54\) −3.67666 3.67181i −0.500330 0.499670i
\(55\) −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 \(-0.116344\pi\)
0.157437 + 0.987529i \(0.449677\pi\)
\(60\) 0.403128 0.282406i 0.0520436 0.0364584i
\(61\) 3.37831 1.95047i 0.432548 0.249732i −0.267883 0.963451i \(-0.586324\pi\)
0.700432 + 0.713719i \(0.252991\pi\)
\(62\) 7.28772 0.925541
\(63\) 2.41173 + 7.56198i 0.303849 + 0.952720i
\(64\) 1.00000 0.125000
\(65\) −0.856362 1.48326i −0.106219 0.183976i
\(66\) 3.39255 4.63580i 0.417594 0.570627i
\(67\) 4.34158 7.51984i 0.530409 0.918695i −0.468962 0.883218i \(-0.655372\pi\)
0.999371 0.0354765i \(-0.0112949\pi\)
\(68\) 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 \(-0.0740344\pi\)
\(72\) −1.02482 + 2.81953i −0.120776 + 0.332285i
\(73\) −3.80459 2.19658i −0.445294 0.257091i 0.260547 0.965461i \(-0.416097\pi\)
−0.705841 + 0.708371i \(0.749431\pi\)
\(74\) −5.57207 + 9.65112i −0.647740 + 1.12192i
\(75\) 8.48780 0.744470i 0.980086 0.0859639i
\(76\) 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 −0.737429 0.675425i \(-0.763960\pi\)
0.216221 + 0.976345i \(0.430627\pi\)
\(80\) −0.246102 0.142087i −0.0275151 0.0158858i
\(81\) −6.89949 5.77901i −0.766610 0.642113i
\(82\) 0.163357 + 0.282943i 0.0180398 + 0.0312459i
\(83\) 1.61235 0.176978 0.0884892 0.996077i \(-0.471796\pi\)
0.0884892 + 0.996077i \(0.471796\pi\)
\(84\) 3.36909 3.10633i 0.367597 0.338928i
\(85\) 1.77716i 0.192760i
\(86\) −1.99134 + 1.14970i −0.214731 + 0.123975i
\(87\) −0.431742 0.616303i −0.0462876 0.0660746i
\(88\) −3.25335 0.644763i −0.346808 0.0687320i
\(89\) 14.8319 8.56318i 1.57217 0.907695i 0.576271 0.817258i \(-0.304507\pi\)
0.995902 0.0904364i \(-0.0288262\pi\)
\(90\) 0.652829 0.548279i 0.0688142 0.0577936i
\(91\) −9.74341 12.6230i −1.02139 1.32325i
\(92\) 1.79656i 0.187305i
\(93\) 12.5744 1.10291i 1.30391 0.114366i
\(94\) 3.52794 + 2.03685i 0.363879 + 0.210086i
\(95\) −0.772248 + 1.33757i −0.0792310 + 0.137232i
\(96\) 1.72543 0.151338i 0.176101 0.0154459i
\(97\) 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
\(99\) 5.15202 8.51215i 0.517798 0.855503i
\(100\) −2.45962 4.26019i −0.245962 0.426019i
\(101\) 5.50494 9.53484i 0.547762 0.948752i −0.450665 0.892693i \(-0.648813\pi\)
0.998427 0.0560587i \(-0.0178534\pi\)
\(102\) 6.21483 + 8.87154i 0.615360 + 0.878414i
\(103\) −3.87592 6.71328i −0.381905 0.661480i 0.609429 0.792840i \(-0.291399\pi\)
−0.991335 + 0.131361i \(0.958065\pi\)
\(104\) 6.02702i 0.590998i
\(105\) −1.27051 + 0.285769i −0.123989 + 0.0278882i
\(106\) 1.92185i 0.186666i
\(107\) −7.32460 12.6866i −0.708096 1.22646i −0.965563 0.260171i \(-0.916221\pi\)
0.257466 0.966287i \(-0.417112\pi\)
\(108\) −1.34155 + 5.01999i −0.129090 + 0.483048i
\(109\) 13.7850 + 7.95877i 1.32036 + 0.762312i 0.983786 0.179344i \(-0.0573975\pi\)
0.336577 + 0.941656i \(0.390731\pi\)
\(110\) 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 \(0.804200\pi\)
\(114\) −0.822528 9.37775i −0.0770368 0.878307i
\(115\) −0.255269 + 0.442138i −0.0238039 + 0.0412296i
\(116\) −0.217223 + 0.376241i −0.0201687 + 0.0349331i
\(117\) 16.9934 + 6.17660i 1.57104 + 0.571027i
\(118\) 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
\(123\) 0.324681 + 0.463476i 0.0292755 + 0.0417902i
\(124\) −3.64386 6.31135i −0.327228 0.566776i
\(125\) 2.81879i 0.252121i
\(126\) 5.34301 5.86961i 0.475993 0.522906i
\(127\) 5.55609i 0.493023i −0.969140 0.246511i \(-0.920716\pi\)
0.969140 0.246511i \(-0.0792843\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) −3.26191 + 2.28509i −0.287195 + 0.201191i
\(130\) −0.856362 + 1.48326i −0.0751079 + 0.130091i
\(131\) 9.44368 + 16.3569i 0.825099 + 1.42911i 0.901844 + 0.432062i \(0.142214\pi\)
−0.0767455 + 0.997051i \(0.524453\pi\)
\(132\) −5.71099 0.620136i −0.497078 0.0539759i
\(133\) −5.46491 + 13.3008i −0.473868 + 1.15333i
\(134\) −8.68317 −0.750111
\(135\) 1.04343 1.04481i 0.0898044 0.0899231i
\(136\) 3.12688 5.41591i 0.268128 0.464411i
\(137\) 14.6388 + 8.45173i 1.25068 + 0.722080i 0.971244 0.238084i \(-0.0765195\pi\)
0.279435 + 0.960165i \(0.409853\pi\)
\(138\) −0.271889 3.09984i −0.0231447 0.263876i
\(139\) 12.1306i 1.02890i −0.857519 0.514452i \(-0.827995\pi\)
0.857519 0.514452i \(-0.172005\pi\)
\(140\) 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
\(144\) 2.95419 0.522246i 0.246183 0.0435205i
\(145\) 0.106918 0.0617292i 0.00887907 0.00512633i
\(146\) 4.39317i 0.363581i
\(147\) −11.3684 + 4.21431i −0.937646 + 0.347590i
\(148\) 11.1441 0.916043
\(149\) −5.93990 10.2882i −0.486616 0.842843i 0.513266 0.858230i \(-0.328436\pi\)
−0.999882 + 0.0153863i \(0.995102\pi\)
\(150\) −4.88863 6.97841i −0.399155 0.569785i
\(151\) −1.49875 0.865305i −0.121967 0.0704175i 0.437775 0.899084i \(-0.355766\pi\)
−0.559742 + 0.828667i \(0.689100\pi\)
\(152\) −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
\(156\) −0.912118 10.3992i −0.0730279 0.832601i
\(157\) −5.57046 + 9.64832i −0.444571 + 0.770020i −0.998022 0.0628618i \(-0.979977\pi\)
0.553451 + 0.832882i \(0.313311\pi\)
\(158\) 4.63260 + 2.67463i 0.368550 + 0.212782i
\(159\) 0.290849 + 3.31600i 0.0230658 + 0.262976i
\(160\) 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 0.881853 0.471524i \(-0.156296\pi\)
−0.849278 + 0.527945i \(0.822963\pi\)
\(164\) 0.163357 0.282943i 0.0127561 0.0220942i
\(165\) 1.31737 + 0.964075i 0.102557 + 0.0750532i
\(166\) −0.806175 1.39634i −0.0625713 0.108377i
\(167\) 19.1395 1.48106 0.740529 0.672025i \(-0.234575\pi\)
0.740529 + 0.672025i \(0.234575\pi\)
\(168\) −4.37470 1.36455i −0.337515 0.105277i
\(169\) −23.3249 −1.79423
\(170\) −1.53906 + 0.888578i −0.118041 + 0.0681509i
\(171\) −2.83842 16.0561i −0.217060 1.22784i
\(172\) 1.99134 + 1.14970i 0.151838 + 0.0876637i
\(173\) −8.80633 15.2530i −0.669533 1.15967i −0.978035 0.208442i \(-0.933161\pi\)
0.308502 0.951224i \(-0.400172\pi\)
\(174\) −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
\(177\) −1.46494 16.7020i −0.110112 1.25540i
\(178\) −14.8319 8.56318i −1.11169 0.641837i
\(179\) −7.84070 4.52683i −0.586041 0.338351i 0.177489 0.984123i \(-0.443202\pi\)
−0.763531 + 0.645772i \(0.776536\pi\)
\(180\) −0.801238 0.291227i −0.0597207 0.0217068i
\(181\) 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
\(186\) −7.24236 10.3383i −0.531035 0.758042i
\(187\) −13.6648 + 15.6038i −0.999270 + 1.14106i
\(188\) 4.07371i 0.297106i
\(189\) 8.33067 10.9362i 0.605967 0.795490i
\(190\) 1.54450 0.112050
\(191\) −10.7800 + 6.22381i −0.780010 + 0.450339i −0.836434 0.548068i \(-0.815364\pi\)
0.0564238 + 0.998407i \(0.482030\pi\)
\(192\) −0.993776 1.41859i −0.0717196 0.102378i
\(193\) 12.9542 + 7.47910i 0.932463 + 0.538357i 0.887590 0.460635i \(-0.152378\pi\)
0.0448730 + 0.998993i \(0.485712\pi\)
\(194\) −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 \(-0.594908\pi\)
−0.293763 + 0.955878i \(0.594908\pi\)
\(198\) −9.94775 0.205708i −0.706956 0.0146190i
\(199\) 7.13434 12.3570i 0.505740 0.875967i −0.494238 0.869327i \(-0.664553\pi\)
0.999978 0.00664051i \(-0.00211376\pi\)
\(200\) −2.45962 + 4.26019i −0.173922 + 0.301241i
\(201\) −14.9822 + 1.31409i −1.05676 + 0.0926891i
\(202\) −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
\(207\) −0.938248 5.30740i −0.0652127 0.368890i
\(208\) −5.21955 + 3.01351i −0.361911 + 0.208949i
\(209\) 17.0653 5.80621i 1.18043 0.401624i
\(210\) 0.882738 + 0.957408i 0.0609147 + 0.0660674i
\(211\) 16.7368i 1.15221i 0.817376 + 0.576105i \(0.195428\pi\)
−0.817376 + 0.576105i \(0.804572\pi\)
\(212\) 1.66437 0.960923i 0.114309 0.0659964i
\(213\) −5.51034 + 3.86019i −0.377562 + 0.264496i
\(214\) −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
\(219\) 0.664854 + 7.58009i 0.0449267 + 0.512215i
\(220\) 0.183225 0.924518i 0.0123530 0.0623310i
\(221\) −32.6418 18.8458i −2.19573 1.26770i
\(222\) 19.2284 1.68653i 1.29053 0.113193i
\(223\) 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 \(-0.737155\pi\)
0.975581 + 0.219639i \(0.0704879\pi\)
\(228\) −7.71011 + 5.40121i −0.510614 + 0.357704i
\(229\) 6.22490 + 10.7818i 0.411353 + 0.712485i 0.995038 0.0994957i \(-0.0317230\pi\)
−0.583685 + 0.811980i \(0.698390\pi\)
\(230\) 0.510537 0.0336638
\(231\) 13.3526 + 7.26001i 0.878537 + 0.477674i
\(232\) 0.434446 0.0285228
\(233\) −9.19303 15.9228i −0.602255 1.04314i −0.992479 0.122417i \(-0.960936\pi\)
0.390224 0.920720i \(-0.372398\pi\)
\(234\) −3.14758 17.8050i −0.205764 1.16395i
\(235\) −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 \(-0.203041\pi\)
0.803365 + 0.595487i \(0.203041\pi\)
\(240\) 0.0430064 + 0.490322i 0.00277605 + 0.0316501i
\(241\) 7.62307 + 4.40118i 0.491045 + 0.283505i 0.725008 0.688741i \(-0.241836\pi\)
−0.233963 + 0.972246i \(0.575169\pi\)
\(242\) −1.45106 10.9039i −0.0932777 0.700927i
\(243\) −1.34152 + 15.5306i −0.0860587 + 0.996290i
\(244\) 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
\(249\) −1.60231 2.28727i −0.101543 0.144950i
\(250\) 2.44115 1.40940i 0.154392 0.0891381i
\(251\) 14.0216i 0.885034i 0.896760 + 0.442517i \(0.145914\pi\)
−0.896760 + 0.442517i \(0.854086\pi\)
\(252\) −7.75473 1.69237i −0.488502 0.106610i
\(253\) 5.64097 1.91926i 0.354645 0.120663i
\(254\) −4.81171 + 2.77804i −0.301914 + 0.174310i
\(255\) −2.52106 + 1.76610i −0.157875 + 0.110597i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −7.60623 + 4.39146i −0.474464 + 0.273932i −0.718106 0.695933i \(-0.754991\pi\)
0.243643 + 0.969865i \(0.421658\pi\)
\(258\) 3.60990 + 1.68236i 0.224743 + 0.104739i
\(259\) −27.2724 11.2054i −1.69462 0.696271i
\(260\) 1.71272 0.106219
\(261\) −0.445229 + 1.22493i −0.0275590 + 0.0758215i
\(262\) 9.44368 16.3569i 0.583433 1.01054i
\(263\) 3.93874 6.82210i 0.242873 0.420669i −0.718658 0.695363i \(-0.755243\pi\)
0.961532 + 0.274695i \(0.0885767\pi\)
\(264\) 2.31844 + 5.25593i 0.142690 + 0.323480i
\(265\) −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 \(-0.392377\pi\)
−0.651143 + 0.758955i \(0.725710\pi\)
\(270\) −1.42655 0.381233i −0.0868171 0.0232011i
\(271\) 0.886543 0.511846i 0.0538536 0.0310924i −0.472831 0.881153i \(-0.656768\pi\)
0.526685 + 0.850060i \(0.323435\pi\)
\(272\) −6.25376 −0.379190
\(273\) −8.22418 + 26.3664i −0.497750 + 1.59577i
\(274\) 16.9035i 1.02118i
\(275\) 10.7488 12.2740i 0.648179 0.740151i
\(276\) −2.54860 + 1.78538i −0.153407 + 0.107467i
\(277\) −0.717044 0.413986i −0.0430830 0.0248740i 0.478304 0.878194i \(-0.341252\pi\)
−0.521387 + 0.853320i \(0.674585\pi\)
\(278\) −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 \(-0.724432\pi\)
−0.648089 + 0.761564i \(0.724432\pi\)
\(282\) −0.616508 7.02889i −0.0367125 0.418564i
\(283\) −12.2598 7.07821i −0.728770 0.420756i 0.0892018 0.996014i \(-0.471568\pi\)
−0.817972 + 0.575258i \(0.804902\pi\)
\(284\) 3.36396 + 1.94218i 0.199614 + 0.115247i
\(285\) 2.66492 0.233741i 0.157856 0.0138456i
\(286\) 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
\(291\) −6.94361 9.91186i −0.407042 0.581043i
\(292\) 3.80459 2.19658i 0.222647 0.128545i
\(293\) −5.75882 −0.336434 −0.168217 0.985750i \(-0.553801\pi\)
−0.168217 + 0.985750i \(0.553801\pi\)
\(294\) 9.33388 + 7.73813i 0.544363 + 0.451297i
\(295\) 2.75078 0.160157
\(296\) −5.57207 9.65112i −0.323870 0.560960i
\(297\) −17.1952 + 1.15054i −0.997769 + 0.0667611i
\(298\) −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
\(303\) −18.9967 + 1.66622i −1.09133 + 0.0957216i
\(304\) 4.70688 + 2.71752i 0.269958 + 0.155860i
\(305\) 0.554273 0.960029i 0.0317376 0.0549711i
\(306\) 6.40897 17.6327i 0.366376 1.00799i
\(307\) 10.5810i 0.603888i −0.953326 0.301944i \(-0.902364\pi\)
0.953326 0.301944i \(-0.0976355\pi\)
\(308\) 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 \(-0.271414\pi\)
−0.323165 + 0.946343i \(0.604747\pi\)
\(312\) −8.54989 + 5.98951i −0.484042 + 0.339089i
\(313\) 13.6258 + 23.6005i 0.770174 + 1.33398i 0.937467 + 0.348074i \(0.113164\pi\)
−0.167293 + 0.985907i \(0.553503\pi\)
\(314\) 11.1409 0.628719
\(315\) 1.66799 + 1.51834i 0.0939807 + 0.0855490i
\(316\) 5.34926i 0.300920i
\(317\) 11.6116 6.70397i 0.652173 0.376533i −0.137115 0.990555i \(-0.543783\pi\)
0.789288 + 0.614023i \(0.210450\pi\)
\(318\) 2.72632 1.90988i 0.152884 0.107101i
\(319\) −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
\(324\) 8.45452 3.08563i 0.469695 0.171424i
\(325\) 25.6762 + 14.8242i 1.42426 + 0.822298i
\(326\) 0.415887 0.720337i 0.0230338 0.0398958i
\(327\) −2.40893 27.4646i −0.133214 1.51879i
\(328\) −0.326715 −0.0180398
\(329\) −4.09611 + 9.96934i −0.225826 + 0.549627i
\(330\) 0.176227 1.62292i 0.00970096 0.0893386i
\(331\) 5.97956 + 10.3569i 0.328666 + 0.569267i 0.982248 0.187590i \(-0.0600675\pi\)
−0.653581 + 0.756857i \(0.726734\pi\)
\(332\) −0.806175 + 1.39634i −0.0442446 + 0.0766339i
\(333\) 32.9220 5.81998i 1.80411 0.318933i
\(334\) −9.56974 16.5753i −0.523633 0.906959i
\(335\) 2.46753i 0.134816i
\(336\) 1.00561 + 4.47088i 0.0548607 + 0.243906i
\(337\) 7.11663i 0.387668i 0.981034 + 0.193834i \(0.0620923\pi\)
−0.981034 + 0.193834i \(0.937908\pi\)
\(338\) 11.6625 + 20.2000i 0.634355 + 1.09874i
\(339\) 17.4040 12.1921i 0.945254 0.662184i
\(340\) 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
\(345\) 0.880894 0.0772638i 0.0474258 0.00415974i
\(346\) −8.80633 + 15.2530i −0.473431 + 0.820007i
\(347\) −0.501160 + 0.868034i −0.0269037 + 0.0465985i −0.879164 0.476520i \(-0.841898\pi\)
0.852260 + 0.523118i \(0.175231\pi\)
\(348\) 0.749605 0.0657483i 0.0401830 0.00352448i
\(349\) 18.5808i 0.994607i −0.867577 0.497304i \(-0.834323\pi\)
0.867577 0.497304i \(-0.165677\pi\)
\(350\) 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 \(-0.363817\pi\)
−0.580519 + 0.814246i \(0.697150\pi\)
\(354\) −13.7319 + 9.61966i −0.729841 + 0.511279i
\(355\) −0.551918 0.955950i −0.0292928 0.0507366i
\(356\) 17.1264i 0.907695i
\(357\) −21.0695 + 19.4262i −1.11511 + 1.02814i
\(358\) 9.05366i 0.478501i
\(359\) 5.21329 + 9.02968i 0.275147 + 0.476569i 0.970172 0.242417i \(-0.0779402\pi\)
−0.695025 + 0.718985i \(0.744607\pi\)
\(360\) 0.148409 + 0.839506i 0.00782183 + 0.0442458i
\(361\) 5.26980 9.12756i 0.277358 0.480398i
\(362\) −10.5974 18.3553i −0.556989 0.964733i
\(363\) −4.15387 18.5942i −0.218022 0.975944i
\(364\) 15.8036 2.12653i 0.828332 0.111460i
\(365\) −1.24842 −0.0653455
\(366\) 0.590361 + 6.73078i 0.0308587 + 0.351824i
\(367\) 0.802276 1.38958i 0.0418785 0.0725356i −0.844326 0.535829i \(-0.819999\pi\)
0.886205 + 0.463294i \(0.153332\pi\)
\(368\) 1.55587 + 0.898282i 0.0811053 + 0.0468262i
\(369\) 0.334823 0.921182i 0.0174302 0.0479548i
\(370\) 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 −0.488486 0.872572i \(-0.662451\pi\)
0.511426 + 0.859327i \(0.329117\pi\)
\(374\) 20.3457 + 4.03219i 1.05205 + 0.208500i
\(375\) 3.99872 2.80125i 0.206493 0.144656i
\(376\) −3.52794 + 2.03685i −0.181939 + 0.105043i
\(377\) 2.61842i 0.134855i
\(378\) −13.6363 1.74648i −0.701378 0.0898293i
\(379\) 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
\(381\) −7.88183 + 5.52151i −0.403799 + 0.282875i
\(382\) 10.7800 + 6.22381i 0.551550 + 0.318438i
\(383\) −4.59160 + 2.65096i −0.234620 + 0.135458i −0.612702 0.790314i \(-0.709917\pi\)
0.378082 + 0.925772i \(0.376584\pi\)
\(384\) −0.731651 + 1.56993i −0.0373369 + 0.0801153i
\(385\) −1.37800 + 2.07828i −0.0702292 + 0.105919i
\(386\) 14.9582i 0.761352i
\(387\) 6.48322 + 2.35647i 0.329561 + 0.119786i
\(388\) −3.49355 + 6.05100i −0.177358 + 0.307193i
\(389\) 25.9986 + 15.0103i 1.31818 + 0.761053i 0.983436 0.181255i \(-0.0580159\pi\)
0.334747 + 0.942308i \(0.391349\pi\)
\(390\) 2.95518 0.259200i 0.149641 0.0131251i
\(391\) 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
\(396\) 4.79573 + 8.71786i 0.240994 + 0.438089i
\(397\) −5.20199 9.01011i −0.261080 0.452204i 0.705449 0.708761i \(-0.250745\pi\)
−0.966529 + 0.256556i \(0.917412\pi\)
\(398\) −14.2687 −0.715224
\(399\) 24.2994 5.46554i 1.21649 0.273619i
\(400\) 4.91924 0.245962
\(401\) −12.6464 + 7.30138i −0.631529 + 0.364614i −0.781344 0.624100i \(-0.785466\pi\)
0.149815 + 0.988714i \(0.452132\pi\)
\(402\) 8.62912 + 12.3179i 0.430381 + 0.614360i
\(403\) 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
\(408\) −10.7904 + 0.946432i −0.534204 + 0.0468554i
\(409\) −21.6325 12.4895i −1.06966 0.617566i −0.141568 0.989928i \(-0.545215\pi\)
−0.928087 + 0.372362i \(0.878548\pi\)
\(410\) 0.0804052 + 0.0464220i 0.00397093 + 0.00229262i
\(411\) −2.55814 29.1657i −0.126184 1.43864i
\(412\) 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
\(417\) −17.2084 + 12.0551i −0.842699 + 0.590341i
\(418\) −13.5610 11.8759i −0.663288 0.580867i
\(419\) 35.4041i 1.72960i −0.502113 0.864802i \(-0.667444\pi\)
0.502113 0.864802i \(-0.332556\pi\)
\(420\) 0.387770 1.24318i 0.0189213 0.0606608i
\(421\) 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
\(423\) −2.12748 12.0345i −0.103442 0.585139i
\(424\) −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
\(429\) 31.6776 13.9733i 1.52941 0.674637i
\(430\) −0.326715 + 0.565887i −0.0157556 + 0.0272895i
\(431\) −9.95132 + 17.2362i −0.479338 + 0.830238i −0.999719 0.0236962i \(-0.992457\pi\)
0.520381 + 0.853934i \(0.325790\pi\)
\(432\) −3.67666 3.67181i −0.176893 0.176660i
\(433\) 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
\(438\) 6.23212 4.36582i 0.297782 0.208607i
\(439\) 9.43561 5.44765i 0.450337 0.260002i −0.257635 0.966242i \(-0.582943\pi\)
0.707973 + 0.706240i \(0.249610\pi\)
\(440\) −0.892269 + 0.303581i −0.0425372 + 0.0144727i
\(441\) 17.2760 + 11.9390i 0.822667 + 0.568524i
\(442\) 37.6915i 1.79280i
\(443\) −12.2275 + 7.05956i −0.580947 + 0.335410i −0.761510 0.648154i \(-0.775541\pi\)
0.180563 + 0.983563i \(0.442208\pi\)
\(444\) −11.0748 15.8090i −0.525586 0.750263i
\(445\) 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 \(-0.314490\pi\)
\(450\) −5.04133 + 13.8700i −0.237651 + 0.653836i
\(451\) 1.06292 + 0.210654i 0.0500508 + 0.00991930i
\(452\) −10.6248 6.13423i −0.499749 0.288530i
\(453\) 0.261907 + 2.98604i 0.0123055 + 0.140296i
\(454\) −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 −0.567680 0.823249i \(-0.692159\pi\)
0.429115 + 0.903250i \(0.358826\pi\)
\(458\) 6.22490 10.7818i 0.290871 0.503803i
\(459\) 8.38971 31.3938i 0.391598 1.46534i
\(460\) −0.255269 0.442138i −0.0119020 0.0206148i
\(461\) −13.0512 −0.607855 −0.303927 0.952695i \(-0.598298\pi\)
−0.303927 + 0.952695i \(0.598298\pi\)
\(462\) −0.388954 15.1937i −0.0180958 0.706875i
\(463\) −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
\(465\) 2.93788 2.05809i 0.136241 0.0954417i
\(466\) −9.19303 + 15.9228i −0.425859 + 0.737609i
\(467\) 5.31873 3.07077i 0.246122 0.142098i −0.371865 0.928287i \(-0.621282\pi\)
0.617987 + 0.786188i \(0.287948\pi\)
\(468\) −13.8458 + 11.6284i −0.640021 + 0.537522i
\(469\) −3.06370 22.7683i −0.141469 1.05134i
\(470\) 1.15764 0.0533981
\(471\) 19.2228 1.68605i 0.885742 0.0776889i
\(472\) 8.38305 + 4.83996i 0.385861 + 0.222777i
\(473\) −1.48257 + 7.48074i −0.0681685 + 0.343965i
\(474\) −0.809548 9.22976i −0.0371838 0.423937i
\(475\) 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 \(-0.780257\pi\)
0.937000 + 0.349329i \(0.113590\pi\)
\(480\) 0.403128 0.282406i 0.0184002 0.0128900i
\(481\) −58.1674 + 33.5830i −2.65221 + 1.53125i
\(482\) 8.80236i 0.400937i
\(483\) 8.03222 1.80665i 0.365479 0.0822054i
\(484\) −8.71750 + 6.70859i −0.396250 + 0.304936i
\(485\) 1.71954 0.992777i 0.0780803 0.0450797i
\(486\) 14.1207 6.60352i 0.640527 0.299542i
\(487\) 20.5335 35.5650i 0.930461 1.61161i 0.147926 0.988998i \(-0.452740\pi\)
0.782535 0.622607i \(-0.213926\pi\)
\(488\) 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 \(-0.800744\pi\)
−0.810389 + 0.585892i \(0.800744\pi\)
\(492\) −0.563722 + 0.0494444i −0.0254146 + 0.00222913i
\(493\) 1.35846 2.35292i 0.0611820 0.105970i
\(494\) 16.3785 28.3684i 0.736905 1.27636i
\(495\) 0.0584568 2.82689i 0.00262744 0.127059i
\(496\) 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 0.973514 0.228628i \(-0.0734239\pi\)
−0.684754 + 0.728774i \(0.740091\pi\)
\(500\) −2.44115 1.40940i −0.109171 0.0630301i
\(501\) −19.0204 27.1512i −0.849767 1.21302i
\(502\) 12.1430 7.01079i 0.541971 0.312907i
\(503\) −2.65238 −0.118264 −0.0591319 0.998250i \(-0.518833\pi\)
−0.0591319 + 0.998250i \(0.518833\pi\)
\(504\) 2.41173 + 7.56198i 0.107427 + 0.336837i
\(505\) 3.12872i 0.139226i
\(506\) −4.48261 3.92559i −0.199276 0.174514i
\(507\) 23.1798 + 33.0886i 1.02945 + 1.46952i
\(508\) 4.81171 + 2.77804i 0.213485 + 0.123256i
\(509\) 10.6064 6.12359i 0.470119 0.271423i −0.246171 0.969226i \(-0.579172\pi\)
0.716289 + 0.697803i \(0.245839\pi\)
\(510\) 2.79002 + 1.30026i 0.123544 + 0.0575764i
\(511\) −11.5194 + 1.55005i −0.509589 + 0.0685703i
\(512\) 1.00000 0.0441942
\(513\) −19.9564 + 19.9828i −0.881096 + 0.882261i
\(514\) 7.60623 + 4.39146i 0.335497 + 0.193699i
\(515\) −1.90774 1.10144i −0.0840652 0.0485351i
\(516\) −0.347987 3.96744i −0.0153193 0.174657i
\(517\) 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 \(-0.321109\pi\)
−0.466381 + 0.884584i \(0.654442\pi\)
\(522\) 1.28344 0.226888i 0.0561746 0.00993060i
\(523\) 10.9425 6.31768i 0.478484 0.276253i −0.241301 0.970450i \(-0.577574\pi\)
0.719784 + 0.694198i \(0.244241\pi\)
\(524\) −18.8874 −0.825099
\(525\) 16.5734 15.2808i 0.723321 0.666908i
\(526\) −7.87749 −0.343475
\(527\) 22.7878 + 39.4696i 0.992653 + 1.71932i
\(528\) 3.39255 4.63580i 0.147642 0.201747i
\(529\) −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
\(534\) 2.59187 + 29.5503i 0.112161 + 1.27876i
\(535\) −3.60520 2.08146i −0.155866 0.0899895i
\(536\) 4.34158 7.51984i 0.187528 0.324808i
\(537\) 1.37016 + 15.6214i 0.0591269 + 0.674114i
\(538\) 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 0.274969 0.961453i \(-0.411333\pi\)
0.970127 + 0.242597i \(0.0779992\pi\)
\(542\) −0.886543 0.511846i −0.0380803 0.0219857i
\(543\) −21.0630 30.0669i −0.903898 1.29030i
\(544\) 3.12688 + 5.41591i 0.134064 + 0.232205i
\(545\) 4.52336 0.193759
\(546\) 26.9461 6.06085i 1.15318 0.259380i
\(547\) 18.9288i 0.809336i 0.914464 + 0.404668i \(0.132613\pi\)
−0.914464 + 0.404668i \(0.867387\pi\)
\(548\) −14.6388 + 8.45173i −0.625340 + 0.361040i
\(549\) 2.03725 + 11.5241i 0.0869476 + 0.491838i
\(550\) −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
\(555\) 0.479270 + 5.46422i 0.0203439 + 0.231943i
\(556\) 10.5054 + 6.06530i 0.445528 + 0.257226i
\(557\) −8.23820 + 14.2690i −0.349064 + 0.604596i −0.986083 0.166251i \(-0.946834\pi\)
0.637020 + 0.770848i \(0.280167\pi\)
\(558\) −7.46859 + 20.5479i −0.316171 + 0.869863i
\(559\) −13.8585 −0.586153
\(560\) −0.745139 + 0.100266i −0.0314879 + 0.00423701i
\(561\) 35.7152 + 3.87818i 1.50790 + 0.163737i
\(562\) 10.8640 + 18.8169i 0.458268 + 0.793744i
\(563\) −14.0143 + 24.2734i −0.590631 + 1.02300i 0.403516 + 0.914972i \(0.367788\pi\)
−0.994148 + 0.108031i \(0.965545\pi\)
\(564\) −5.77894 + 4.04835i −0.243337 + 0.170466i
\(565\) 1.74319 + 3.01930i 0.0733366 + 0.127023i
\(566\) 14.1564i 0.595038i
\(567\) −23.7928 0.949727i −0.999204 0.0398848i
\(568\) 3.88436i 0.162984i
\(569\) 13.8711 + 24.0254i 0.581506 + 1.00720i 0.995301 + 0.0968278i \(0.0308696\pi\)
−0.413795 + 0.910370i \(0.635797\pi\)
\(570\) −1.53488 2.19101i −0.0642892 0.0917715i
\(571\) −1.71070 0.987670i −0.0715904 0.0413327i 0.463778 0.885952i \(-0.346494\pi\)
−0.535368 + 0.844619i \(0.679827\pi\)
\(572\) −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
\(576\) −1.02482 + 2.81953i −0.0427008 + 0.117480i
\(577\) 9.70603 16.8113i 0.404067 0.699865i −0.590145 0.807297i \(-0.700929\pi\)
0.994212 + 0.107432i \(0.0342628\pi\)
\(578\) −11.0547 + 19.1474i −0.459817 + 0.796426i
\(579\) −2.26375 25.8093i −0.0940781 1.07260i
\(580\) 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
\(585\) 5.05972 0.894463i 0.209194 0.0369815i
\(586\) 2.87941 + 4.98728i 0.118947 + 0.206023i
\(587\) 13.5713i 0.560148i −0.959978 0.280074i \(-0.909641\pi\)
0.959978 0.280074i \(-0.0903590\pi\)
\(588\) 2.03448 11.9524i 0.0839006 0.492910i
\(589\) 39.6090i 1.63206i
\(590\) −1.37539 2.38225i −0.0566239 0.0980756i
\(591\) 8.19501 + 11.6982i 0.337098 + 0.481200i
\(592\) −5.57207 + 9.65112i −0.229011 + 0.396658i
\(593\) −18.6257 32.2607i −0.764867 1.32479i −0.940317 0.340300i \(-0.889471\pi\)
0.175450 0.984488i \(-0.443862\pi\)
\(594\) 9.59402 + 14.3162i 0.393647 + 0.587403i
\(595\) −2.87299 3.72209i −0.117781 0.152591i
\(596\) 11.8798 0.486616
\(597\) −24.6196 + 2.15940i −1.00761 + 0.0883782i
\(598\) 5.41396 9.37726i 0.221393 0.383465i
\(599\) 24.6430 + 14.2276i 1.00688 + 0.581325i 0.910278 0.413998i \(-0.135868\pi\)
0.0966066 + 0.995323i \(0.469201\pi\)
\(600\) 8.48780 0.744470i 0.346513 0.0303928i
\(601\) 4.98600i 0.203383i −0.994816 0.101692i \(-0.967575\pi\)
0.994816 0.101692i \(-0.0324255\pi\)
\(602\) −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
\(606\) 10.9414 + 15.6186i 0.444462 + 0.634460i
\(607\) 5.30947 3.06542i 0.215505 0.124422i −0.388362 0.921507i \(-0.626959\pi\)
0.603867 + 0.797085i \(0.293626\pi\)
\(608\) 5.43503i 0.220420i
\(609\) −1.90057 0.592824i −0.0770150 0.0240225i
\(610\) −1.10855 −0.0448837
\(611\) 12.2762 + 21.2629i 0.496640 + 0.860206i
\(612\) −18.4748 + 3.26600i −0.746800 + 0.132020i
\(613\) −18.9061 10.9154i −0.763609 0.440870i 0.0669808 0.997754i \(-0.478663\pi\)
−0.830590 + 0.556884i \(0.811997\pi\)
\(614\) −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 \(0.944205\pi\)
\(618\) 13.3752 1.17315i 0.538030 0.0471909i
\(619\) −15.3069 + 26.5123i −0.615236 + 1.06562i 0.375107 + 0.926982i \(0.377606\pi\)
−0.990343 + 0.138639i \(0.955727\pi\)
\(620\) −1.79352 1.03549i −0.0720296 0.0415863i
\(621\) −6.59664 + 6.60536i −0.264714 + 0.265064i
\(622\) 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
\(627\) −25.1957 18.4386i −1.00622 0.736368i
\(628\) −5.57046 9.64832i −0.222286 0.385010i
\(629\) −69.6928 −2.77883
\(630\) 0.480929 2.20370i 0.0191607 0.0877973i
\(631\) −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
\(633\) 23.7427 16.6326i 0.943689 0.661088i
\(634\) −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
\(639\) 10.9521 + 3.98077i 0.433258 + 0.157477i
\(640\) −0.246102 0.142087i −0.00972804 0.00561649i
\(641\) 6.94573 + 4.01012i 0.274340 + 0.158390i 0.630858 0.775898i \(-0.282703\pi\)
−0.356518 + 0.934288i \(0.616036\pi\)
\(642\) 25.2761 2.21698i 0.997569 0.0874974i
\(643\) −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 \(-0.553326\pi\)
−0.937274 + 0.348593i \(0.886660\pi\)
\(648\) −6.89949 5.77901i −0.271038 0.227021i
\(649\) −24.1524 21.1512i −0.948063 0.830255i
\(650\) 29.6484i 1.16291i
\(651\) 24.5529 22.6380i 0.962306 0.887254i
\(652\) −0.831773 −0.0325748
\(653\) −27.2177 + 15.7141i −1.06511 + 0.614942i −0.926842 0.375453i \(-0.877487\pi\)
−0.138269 + 0.990395i \(0.544154\pi\)
\(654\) −22.5805 + 15.8185i −0.882969 + 0.618551i
\(655\) 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 \(-0.366098\pi\)
0.408368 + 0.912817i \(0.366098\pi\)
\(660\) −1.49360 + 0.658842i −0.0581383 + 0.0256454i
\(661\) −0.654442 + 1.13353i −0.0254548 + 0.0440891i −0.878472 0.477793i \(-0.841437\pi\)
0.853017 + 0.521883i \(0.174770\pi\)
\(662\) 5.97956 10.3569i 0.232402 0.402533i
\(663\) 5.70416 + 65.0339i 0.221531 + 2.52571i
\(664\) 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
\(669\) −1.08094 1.54302i −0.0417915 0.0596565i
\(670\) −2.13695 + 1.23377i −0.0825574 + 0.0476645i
\(671\) −12.2484 + 4.16735i −0.472845 + 0.160879i
\(672\) 3.36909 3.10633i 0.129965 0.119829i
\(673\) 38.4311i 1.48141i 0.671829 + 0.740706i \(0.265509\pi\)
−0.671829 + 0.740706i \(0.734491\pi\)
\(674\) 6.16319 3.55832i 0.237397 0.137061i
\(675\) −6.59940 + 24.6945i −0.254011 + 0.950493i
\(676\) 11.6625 20.2000i 0.448557 0.776923i
\(677\) −4.01555 6.95514i −0.154330 0.267308i 0.778485 0.627664i \(-0.215989\pi\)
−0.932815 + 0.360356i \(0.882655\pi\)
\(678\) −19.2607 8.97623i −0.739701 0.344730i
\(679\) 14.6338 11.2955i 0.561594 0.433481i
\(680\) 1.77716i 0.0681509i
\(681\) −15.4718 + 1.35704i −0.592879 + 0.0520018i
\(682\) −23.7095 4.69885i −0.907883 0.179928i
\(683\) −22.5996 13.0479i −0.864751 0.499264i 0.000849280 1.00000i \(-0.499730\pi\)
−0.865600 + 0.500735i \(0.833063\pi\)
\(684\) 15.3242 + 5.56992i 0.585937 + 0.212971i
\(685\) 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
\(690\) −0.507360 0.724245i −0.0193149 0.0275715i
\(691\) 6.88382 + 11.9231i 0.261873 + 0.453577i 0.966740 0.255762i \(-0.0823265\pi\)
−0.704867 + 0.709340i \(0.748993\pi\)
\(692\) 17.6127 0.669533
\(693\) −2.97050 26.1568i −0.112840 0.993613i
\(694\) 1.00232 0.0380475
\(695\) −1.72360 2.98537i −0.0653799 0.113241i
\(696\) −0.431742 0.616303i −0.0163651 0.0233609i
\(697\) −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 \(-0.602032\pi\)
−0.315081 + 0.949065i \(0.602032\pi\)
\(702\) −22.1300 + 22.1593i −0.835245 + 0.836349i
\(703\) 52.4541 + 30.2844i 1.97835 + 1.14220i
\(704\) −3.25335 0.644763i −0.122615 0.0243004i
\(705\) 1.99743 0.175196i 0.0752275 0.00659825i
\(706\) 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 0.643688 0.765288i \(-0.277404\pi\)
−0.984603 + 0.174806i \(0.944070\pi\)
\(710\) −0.551918 + 0.955950i −0.0207131 + 0.0358762i
\(711\) −2.79363 15.8028i −0.104769 0.592650i
\(712\) 14.8319 8.56318i 0.555847 0.320919i
\(713\) 13.0929i 0.490331i
\(714\) 27.3583 + 8.53358i 1.02386 + 0.319361i
\(715\) 1.82969 + 5.37772i 0.0684266 + 0.201115i
\(716\) 7.84070 4.52683i 0.293021 0.169176i
\(717\) −24.6848 35.2371i −0.921872 1.31595i
\(718\) 5.21329 9.02968i 0.194558 0.336985i
\(719\) 13.2458 7.64744i 0.493983 0.285201i −0.232242 0.972658i \(-0.574606\pi\)
0.726225 + 0.687457i \(0.241273\pi\)
\(720\) 0.652829 0.548279i 0.0243295 0.0204331i
\(721\) −18.9706 7.79445i −0.706501 0.290280i
\(722\) −10.5396 −0.392243
\(723\) −1.33213 15.1878i −0.0495426 0.564841i
\(724\) −10.5974 + 18.3553i −0.393851 + 0.682169i
\(725\) −1.06857 + 1.85082i −0.0396858 + 0.0687379i
\(726\) −14.0261 + 12.8945i −0.520559 + 0.478559i
\(727\) 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
\(732\) 5.53385 3.87666i 0.204537 0.143285i
\(733\) 20.6665 11.9318i 0.763336 0.440712i −0.0671561 0.997742i \(-0.521393\pi\)
0.830492 + 0.557030i \(0.188059\pi\)
\(734\) −1.60455 −0.0592251
\(735\) −2.19898 + 2.65245i −0.0811105 + 0.0978370i
\(736\) 1.79656i 0.0662222i
\(737\) −18.9732 + 21.6654i −0.698887 + 0.798054i
\(738\) −0.965179 + 0.170625i −0.0355287 + 0.00628081i
\(739\) 13.0082 + 7.51031i 0.478516 + 0.276271i 0.719798 0.694184i \(-0.244235\pi\)
−0.241282 + 0.970455i \(0.577568\pi\)
\(740\) 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 \(-0.679633\pi\)
−0.534853 + 0.844945i \(0.679633\pi\)
\(744\) 12.5744 1.10291i 0.461001 0.0404346i
\(745\) −2.92365 1.68797i −0.107114 0.0618423i
\(746\) −0.443041 0.255790i −0.0162209 0.00936513i
\(747\) −1.65237 + 4.54607i −0.0604569 + 0.166332i
\(748\) −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 0.990688 0.136155i \(-0.0434745\pi\)
−0.613257 + 0.789883i \(0.710141\pi\)
\(752\) 3.52794 + 2.03685i 0.128651 + 0.0742765i
\(753\) 19.8909 13.9343i 0.724866 0.507794i
\(754\) −2.26761 + 1.30921i −0.0825816 + 0.0476785i
\(755\) −0.491795 −0.0178982
\(756\) 5.30567 + 12.6827i 0.192965 + 0.461264i
\(757\) −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
\(759\) −8.32851 6.09493i −0.302306 0.221232i
\(760\) −0.772248 + 1.33757i −0.0280124 + 0.0485189i
\(761\) 20.8209 + 36.0628i 0.754757 + 1.30728i 0.945495 + 0.325636i \(0.105578\pi\)
−0.190738 + 0.981641i \(0.561088\pi\)
\(762\) 8.72268 + 4.06511i 0.315989 + 0.147264i
\(763\) 41.7377 5.61623i 1.51101 0.203321i
\(764\) 12.4476i 0.450339i
\(765\) 5.01075 + 1.82126i 0.181164 + 0.0658479i
\(766\) 4.59160 + 2.65096i 0.165901 + 0.0957832i
\(767\) 29.1705 50.5248i 1.05329 1.82434i
\(768\) 1.72543 0.151338i 0.0622610 0.00546095i
\(769\) 5.30858i 0.191432i 0.995409 + 0.0957161i \(0.0305141\pi\)
−0.995409 + 0.0957161i \(0.969486\pi\)
\(770\) 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 \(-0.529953\pi\)
−0.909174 + 0.416415i \(0.863286\pi\)
\(774\) −1.20085 6.79287i −0.0431637 0.244165i
\(775\) −17.9250 31.0471i −0.643886 1.11524i
\(776\) 6.98710 0.250822
\(777\) 11.2067 + 49.8241i 0.402038 + 1.78743i
\(778\) 30.0206i 1.07629i
\(779\) 1.53781 0.887853i 0.0550976 0.0318106i
\(780\) −1.70206 2.42966i −0.0609436 0.0869958i
\(781\) −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
\(786\) −32.5888 + 2.85838i −1.16240 + 0.101955i
\(787\) 25.9819 + 15.0006i 0.926153 + 0.534715i 0.885593 0.464462i \(-0.153752\pi\)
0.0405602 + 0.999177i \(0.487086\pi\)
\(788\) 4.12317 7.14153i 0.146882 0.254407i
\(789\) −13.5920 + 1.19216i −0.483889 + 0.0424422i
\(790\) 1.52012 0.0540835
\(791\) 19.8335 + 25.6951i 0.705197 + 0.913614i
\(792\) 5.15202 8.51215i 0.183069 0.302466i
\(793\) −11.7555 20.3611i −0.417450 0.723045i
\(794\) −5.20199 + 9.01011i −0.184612 + 0.319757i
\(795\) 0.542740 + 0.774749i 0.0192490 + 0.0274775i
\(796\) 7.13434 + 12.3570i 0.252870 + 0.437984i
\(797\) 35.9024i 1.27173i 0.771802 + 0.635864i \(0.219356\pi\)
−0.771802 + 0.635864i \(0.780644\pi\)
\(798\) −16.8830 18.3111i −0.597651 0.648206i
\(799\) 25.4760i 0.901276i
\(800\) −2.45962 4.26019i −0.0869608 0.150621i
\(801\) 8.94416 + 50.5946i 0.316027 + 1.78767i
\(802\) 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
\(807\) 0.915552 + 10.4383i 0.0322290 + 0.367447i
\(808\) 5.50494 9.53484i 0.193663 0.335434i
\(809\) 22.7425 39.3912i 0.799585 1.38492i −0.120302 0.992737i \(-0.538386\pi\)
0.919887 0.392184i \(-0.128280\pi\)
\(810\) 0.876857 + 2.40256i 0.0308096 + 0.0844172i
\(811\) 15.4966i 0.544160i −0.962275 0.272080i \(-0.912288\pi\)
0.962275 0.272080i \(-0.0877115\pi\)
\(812\) 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
\(816\) 6.21483 + 8.87154i 0.217563 + 0.310566i
\(817\) 6.24865 + 10.8230i 0.218613 + 0.378648i
\(818\) 24.9790i 0.873370i
\(819\) 45.5762 14.5355i 1.59256 0.507912i
\(820\) 0.0928439i 0.00324225i
\(821\) 19.5209 + 33.8113i 0.681285 + 1.18002i 0.974589 + 0.224001i \(0.0719120\pi\)
−0.293303 + 0.956019i \(0.594755\pi\)
\(822\) −23.9792 + 16.7983i −0.836369 + 0.585906i
\(823\) −20.0995 + 34.8133i −0.700624 + 1.21352i 0.267624 + 0.963523i \(0.413761\pi\)
−0.968248 + 0.249992i \(0.919572\pi\)
\(824\) −3.87592 6.71328i −0.135024 0.233868i
\(825\) −28.0938 3.05060i −0.978100 0.106208i
\(826\) −15.6488 20.2737i −0.544490 0.705411i
\(827\) 3.20205 0.111346 0.0556732 0.998449i \(-0.482270\pi\)
0.0556732 + 0.998449i \(0.482270\pi\)
\(828\) 5.06547 + 1.84115i 0.176037 + 0.0639845i
\(829\) −6.56231 + 11.3662i −0.227918 + 0.394766i −0.957191 0.289457i \(-0.906525\pi\)
0.729273 + 0.684223i \(0.239859\pi\)
\(830\) −0.396803 0.229094i −0.0137732 0.00795197i
\(831\) 0.125304 + 1.42860i 0.00434674 + 0.0495577i
\(832\) 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
\(837\) −9.77681 + 36.5842i −0.337936 + 1.26454i
\(838\) −30.6609 + 17.7021i −1.05916 + 0.611507i
\(839\) 22.7217i 0.784439i 0.919872 + 0.392220i \(0.128293\pi\)
−0.919872 + 0.392220i \(0.871707\pi\)
\(840\) −1.27051 + 0.285769i −0.0438367 + 0.00985998i
\(841\) −28.8113 −0.993492
\(842\) −0.438979 0.760334i −0.0151282 0.0262028i
\(843\) 21.5927 + 30.8231i 0.743691 + 1.06160i
\(844\) −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
\(849\) 2.14241 + 24.4259i 0.0735272 + 0.838293i
\(850\) 15.3819 26.6422i 0.527594 0.913820i
\(851\) 17.3388 + 10.0106i 0.594368 + 0.343159i
\(852\) −0.587853 6.70219i −0.0201395 0.229613i
\(853\) 21.8003i 0.746428i 0.927745 + 0.373214i \(0.121744\pi\)
−0.927745 + 0.373214i \(0.878256\pi\)
\(854\) −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 \(-0.992732\pi\)
0.519641 + 0.854384i \(0.326066\pi\)
\(858\) −27.9400 20.4470i −0.953857 0.698048i
\(859\) −12.9428 22.4176i −0.441603 0.764879i 0.556205 0.831045i \(-0.312257\pi\)
−0.997809 + 0.0661656i \(0.978923\pi\)
\(860\) 0.653430 0.0222818
\(861\) 1.42928 + 0.445819i 0.0487097 + 0.0151935i
\(862\) 19.9026 0.677886
\(863\) 11.3331 6.54315i 0.385782 0.222731i −0.294549 0.955636i \(-0.595169\pi\)
0.680331 + 0.732905i \(0.261836\pi\)
\(864\) −1.34155 + 5.01999i −0.0456404 + 0.170783i
\(865\) −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
\(870\) 0.0186840 + 0.213018i 0.000633446 + 0.00722200i
\(871\) −45.3222 26.1668i −1.53569 0.886628i
\(872\) 13.7850 + 7.95877i 0.466819 + 0.269518i
\(873\) −7.16051 + 19.7003i −0.242346 + 0.666755i
\(874\) −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 0.0533875 0.998574i \(-0.482998\pi\)
0.891484 + 0.453052i \(0.149665\pi\)
\(878\) −9.43561 5.44765i −0.318436 0.183849i
\(879\) 5.72297 + 8.16942i 0.193031 + 0.275548i
\(880\) 0.709044 + 0.620937i 0.0239019 + 0.0209318i
\(881\) 16.1735i 0.544899i 0.962170 + 0.272450i \(0.0878338\pi\)
−0.962170 + 0.272450i \(0.912166\pi\)
\(882\) 1.70149 20.9310i 0.0572920 0.704782i
\(883\) 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
\(885\) −2.73366 3.90224i −0.0918910 0.131172i
\(886\) 12.2275 + 7.05956i 0.410791 + 0.237171i
\(887\) −16.1800 28.0247i −0.543273 0.940976i −0.998713 0.0507096i \(-0.983852\pi\)
0.455441 0.890266i \(-0.349482\pi\)
\(888\) −8.15362 + 17.4956i −0.273618 + 0.587112i
\(889\) −8.98209 11.6367i −0.301250 0.390282i
\(890\) −4.86687 −0.163138
\(891\) 18.7204 + 23.2497i 0.627156 + 0.778894i
\(892\) −0.543854 + 0.941983i −0.0182096 + 0.0315399i
\(893\) 11.0704 19.1745i 0.370456 0.641649i
\(894\) 20.4977 1.79787i 0.685547 0.0601297i
\(895\) −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
\(900\) 14.5324 2.56905i 0.484413 0.0856352i
\(901\) −10.4085 + 6.00938i −0.346759 + 0.200201i
\(902\) −0.349027 1.02584i −0.0116213 0.0341567i
\(903\) −3.13765 + 10.0592i −0.104414 + 0.334748i
\(904\) 12.2685i 0.408043i
\(905\) 5.21610 3.01152i 0.173389 0.100106i
\(906\) 2.45503 1.71984i 0.0815630 0.0571378i
\(907\) 8.02681 13.9028i 0.266526 0.461636i −0.701436 0.712732i \(-0.747458\pi\)
0.967962 + 0.251096i \(0.0807909\pi\)
\(908\) 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 \(0.876829\pi\)
\(912\) −0.822528 9.37775i −0.0272366 0.310528i
\(913\) −5.24554 1.03958i −0.173602 0.0344052i
\(914\) 2.96219 + 1.71022i 0.0979805 + 0.0565690i
\(915\) −1.91271 + 0.167765i −0.0632324 + 0.00554615i
\(916\) −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 −0.873308 0.487169i \(-0.838030\pi\)
−0.0147535 + 0.999891i \(0.504696\pi\)
\(920\) −0.255269 + 0.442138i −0.00841596 + 0.0145769i
\(921\) −15.0101 + 10.5151i −0.494600 + 0.346485i
\(922\) 6.52560 + 11.3027i 0.214909 + 0.372234i
\(923\) −23.4111 −0.770587
\(924\) −12.9637 + 7.93370i −0.426473 + 0.260999i
\(925\) 54.8208 1.80250
\(926\) 9.04932 + 15.6739i 0.297379 + 0.515076i
\(927\) 22.9004 4.04836i 0.752148 0.132966i
\(928\) −0.217223 + 0.376241i −0.00713070 + 0.0123507i
\(929\) 9.05995 5.23076i 0.297247 0.171616i −0.343958 0.938985i \(-0.611768\pi\)
0.641206 + 0.767369i \(0.278435\pi\)
\(930\) −3.25130 1.51523i −0.106614 0.0496865i
\(931\) 10.0567 + 36.6920i 0.329593 + 1.20253i
\(932\) 18.3861 0.602255
\(933\) −1.03180 11.7637i −0.0337796 0.385126i
\(934\) −5.31873 3.07077i −0.174034 0.100479i
\(935\) −1.14585 + 5.78171i −0.0374732 + 0.189082i
\(936\) 16.9934 + 6.17660i 0.555445 + 0.201889i
\(937\) 27.1309i 0.886328i 0.896441 + 0.443164i \(0.146144\pi\)
−0.896441 + 0.443164i \(0.853856\pi\)
\(938\) −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 \(-0.937909\pi\)
0.658379 + 0.752686i \(0.271242\pi\)
\(942\) −11.0716 15.8044i −0.360732 0.514937i
\(943\) 0.508326 0.293482i 0.0165534 0.00955709i
\(944\) 9.67991i 0.315054i
\(945\) 0.496305 3.87510i 0.0161448 0.126057i
\(946\) 7.21980 2.45643i 0.234736 0.0798655i
\(947\) 31.4053 18.1318i 1.02053 0.589205i 0.106275 0.994337i \(-0.466108\pi\)
0.914258 + 0.405131i \(0.132774\pi\)
\(948\) −7.58843 + 5.31597i −0.246461 + 0.172655i
\(949\) −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 \(-0.281621\pi\)
0.633493 + 0.773749i \(0.281621\pi\)
\(954\) −5.41870 1.96954i −0.175437 0.0637663i
\(955\) −1.76865 + 3.06338i −0.0572320 + 0.0991288i
\(956\) −12.4197 + 21.5116i −0.401683 + 0.695735i
\(957\) 1.00724 + 2.28342i 0.0325594 + 0.0738125i
\(958\) −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
\(963\) 43.2766 7.65049i 1.39457 0.246533i
\(964\) −7.62307 + 4.40118i −0.245522 + 0.141752i
\(965\) 4.25074 0.136836
\(966\) −5.58071 6.05278i −0.179556 0.194745i
\(967\) 50.7537i 1.63213i −0.577961 0.816064i \(-0.696151\pi\)
0.577961 0.816064i \(-0.303849\pi\)
\(968\) 10.1686 + 4.19528i 0.326830 + 0.134841i
\(969\) 48.2171 33.7778i 1.54896 1.08510i
\(970\) −1.71954 0.992777i −0.0552111 0.0318761i
\(971\) −0.389942 + 0.225133i −0.0125138 + 0.00722486i −0.506244 0.862390i \(-0.668966\pi\)
0.493730 + 0.869615i \(0.335633\pi\)
\(972\) −12.7792 8.92711i −0.409892 0.286337i
\(973\) −19.6106 25.4064i −0.628686 0.814491i
\(974\) −41.0670 −1.31587
\(975\) −4.48693 51.1561i −0.143697 1.63831i
\(976\) −3.37831 1.95047i −0.108137 0.0624330i
\(977\) 4.01364 + 2.31728i 0.128408 + 0.0741363i 0.562828 0.826574i \(-0.309713\pi\)
−0.434420 + 0.900710i \(0.643047\pi\)
\(978\) −1.43516 + 0.125879i −0.0458915 + 0.00402517i
\(979\) −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 \(-0.155164\pi\)
0.0361291 + 0.999347i \(0.488497\pi\)
\(984\) 0.324681 + 0.463476i 0.0103505 + 0.0147751i
\(985\) −2.02944 + 1.17170i −0.0646633 + 0.0373334i
\(986\) −2.71692 −0.0865244
\(987\) 18.2131 4.09658i 0.579728 0.130395i
\(988\) −32.7570 −1.04214
\(989\) 2.06551 + 3.57756i 0.0656793 + 0.113760i
\(990\) −2.47739 + 1.36282i −0.0787366 + 0.0433133i
\(991\) 0.378039 0.654782i 0.0120088 0.0207998i −0.859959 0.510364i \(-0.829511\pi\)
0.871967 + 0.489564i \(0.162844\pi\)
\(992\) −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
\(996\) 2.78199 0.244010i 0.0881507 0.00773175i
\(997\) −27.9874 16.1585i −0.886368 0.511745i −0.0136154 0.999907i \(-0.504334\pi\)
−0.872753 + 0.488162i \(0.837667\pi\)
\(998\) 6.45040 11.1724i 0.204184 0.353657i
\(999\) −40.9733 40.9192i −1.29634 1.29462i
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.e.263.4 yes 24
3.2 odd 2 462.2.n.f.263.12 yes 24
7.2 even 3 inner 462.2.n.e.65.12 yes 24
11.10 odd 2 462.2.n.f.263.4 yes 24
21.2 odd 6 462.2.n.f.65.4 yes 24
33.32 even 2 inner 462.2.n.e.263.12 yes 24
77.65 odd 6 462.2.n.f.65.12 yes 24
231.65 even 6 inner 462.2.n.e.65.4 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
462.2.n.e.65.4 24 231.65 even 6 inner
462.2.n.e.65.12 yes 24 7.2 even 3 inner
462.2.n.e.263.4 yes 24 1.1 even 1 trivial
462.2.n.e.263.12 yes 24 33.32 even 2 inner
462.2.n.f.65.4 yes 24 21.2 odd 6
462.2.n.f.65.12 yes 24 77.65 odd 6
462.2.n.f.263.4 yes 24 11.10 odd 2
462.2.n.f.263.12 yes 24 3.2 odd 2