Properties

Label 546.2.bi.f.257.15
Level $546$
Weight $2$
Character 546.257
Analytic conductor $4.360$
Analytic rank $0$
Dimension $34$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [546,2,Mod(17,546)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(546, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("546.17");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.bi (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: \(4.35983195036\)
Analytic rank: \(0\)
Dimension: \(34\)
Relative dimension: \(17\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 257.15
Character \(\chi\) \(=\) 546.257
Dual form 546.2.bi.f.17.15

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} +(1.67564 + 0.438430i) q^{3} +1.00000 q^{4} +(1.57344 + 0.908426i) q^{5} +(1.67564 + 0.438430i) q^{6} +(-2.47008 + 0.947995i) q^{7} +1.00000 q^{8} +(2.61556 + 1.46930i) q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +(1.67564 + 0.438430i) q^{3} +1.00000 q^{4} +(1.57344 + 0.908426i) q^{5} +(1.67564 + 0.438430i) q^{6} +(-2.47008 + 0.947995i) q^{7} +1.00000 q^{8} +(2.61556 + 1.46930i) q^{9} +(1.57344 + 0.908426i) q^{10} +(-1.02563 + 1.77645i) q^{11} +(1.67564 + 0.438430i) q^{12} +(-3.57560 + 0.463745i) q^{13} +(-2.47008 + 0.947995i) q^{14} +(2.23824 + 2.21204i) q^{15} +1.00000 q^{16} +5.68717 q^{17} +(2.61556 + 1.46930i) q^{18} +(-0.796762 - 1.38003i) q^{19} +(1.57344 + 0.908426i) q^{20} +(-4.55461 + 0.505542i) q^{21} +(-1.02563 + 1.77645i) q^{22} -8.73960i q^{23} +(1.67564 + 0.438430i) q^{24} +(-0.849523 - 1.47142i) q^{25} +(-3.57560 + 0.463745i) q^{26} +(3.73855 + 3.60877i) q^{27} +(-2.47008 + 0.947995i) q^{28} +(0.724381 - 0.418222i) q^{29} +(2.23824 + 2.21204i) q^{30} +(-3.97501 - 6.88493i) q^{31} +1.00000 q^{32} +(-2.49744 + 2.52703i) q^{33} +5.68717 q^{34} +(-4.74771 - 0.752275i) q^{35} +(2.61556 + 1.46930i) q^{36} +4.21819i q^{37} +(-0.796762 - 1.38003i) q^{38} +(-6.19475 - 0.790580i) q^{39} +(1.57344 + 0.908426i) q^{40} +(0.397180 - 0.229312i) q^{41} +(-4.55461 + 0.505542i) q^{42} +(0.836012 - 1.44802i) q^{43} +(-1.02563 + 1.77645i) q^{44} +(2.78067 + 4.68791i) q^{45} -8.73960i q^{46} +(-1.94760 - 1.12445i) q^{47} +(1.67564 + 0.438430i) q^{48} +(5.20261 - 4.68325i) q^{49} +(-0.849523 - 1.47142i) q^{50} +(9.52967 + 2.49343i) q^{51} +(-3.57560 + 0.463745i) q^{52} +(0.497067 - 0.286982i) q^{53} +(3.73855 + 3.60877i) q^{54} +(-3.22755 + 1.86343i) q^{55} +(-2.47008 + 0.947995i) q^{56} +(-0.730041 - 2.66176i) q^{57} +(0.724381 - 0.418222i) q^{58} +2.19150i q^{59} +(2.23824 + 2.21204i) q^{60} +(-5.97394 + 3.44906i) q^{61} +(-3.97501 - 6.88493i) q^{62} +(-7.85354 - 1.14977i) q^{63} +1.00000 q^{64} +(-6.04728 - 2.51850i) q^{65} +(-2.49744 + 2.52703i) q^{66} +(-4.46448 - 2.57757i) q^{67} +5.68717 q^{68} +(3.83170 - 14.6444i) q^{69} +(-4.74771 - 0.752275i) q^{70} +(4.24250 - 7.34823i) q^{71} +(2.61556 + 1.46930i) q^{72} +(5.11752 + 8.86381i) q^{73} +4.21819i q^{74} +(-0.778384 - 2.83803i) q^{75} +(-0.796762 - 1.38003i) q^{76} +(0.849335 - 5.36027i) q^{77} +(-6.19475 - 0.790580i) q^{78} +(-3.68537 + 6.38325i) q^{79} +(1.57344 + 0.908426i) q^{80} +(4.68229 + 7.68610i) q^{81} +(0.397180 - 0.229312i) q^{82} +15.0678i q^{83} +(-4.55461 + 0.505542i) q^{84} +(8.94843 + 5.16638i) q^{85} +(0.836012 - 1.44802i) q^{86} +(1.39717 - 0.383200i) q^{87} +(-1.02563 + 1.77645i) q^{88} -3.86314i q^{89} +(2.78067 + 4.68791i) q^{90} +(8.39241 - 4.53514i) q^{91} -8.73960i q^{92} +(-3.64215 - 13.2794i) q^{93} +(-1.94760 - 1.12445i) q^{94} -2.89520i q^{95} +(1.67564 + 0.438430i) q^{96} +(-1.72410 + 2.98622i) q^{97} +(5.20261 - 4.68325i) q^{98} +(-5.29275 + 3.13944i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 34 q + 34 q^{2} + 6 q^{3} + 34 q^{4} + 9 q^{5} + 6 q^{6} + 4 q^{7} + 34 q^{8} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 34 q + 34 q^{2} + 6 q^{3} + 34 q^{4} + 9 q^{5} + 6 q^{6} + 4 q^{7} + 34 q^{8} + 4 q^{9} + 9 q^{10} + 9 q^{11} + 6 q^{12} + 8 q^{13} + 4 q^{14} - 17 q^{15} + 34 q^{16} + 12 q^{17} + 4 q^{18} - 5 q^{19} + 9 q^{20} - 7 q^{21} + 9 q^{22} + 6 q^{24} + 16 q^{25} + 8 q^{26} - 18 q^{27} + 4 q^{28} + 27 q^{29} - 17 q^{30} - q^{31} + 34 q^{32} + 12 q^{34} - 3 q^{35} + 4 q^{36} - 5 q^{38} - 10 q^{39} + 9 q^{40} - 3 q^{41} - 7 q^{42} - 3 q^{43} + 9 q^{44} + 9 q^{45} - 27 q^{47} + 6 q^{48} - 2 q^{49} + 16 q^{50} - 36 q^{51} + 8 q^{52} - 21 q^{53} - 18 q^{54} - 57 q^{55} + 4 q^{56} - 17 q^{57} + 27 q^{58} - 17 q^{60} - 51 q^{61} - q^{62} - 24 q^{63} + 34 q^{64} - 21 q^{65} - 21 q^{67} + 12 q^{68} + 30 q^{69} - 3 q^{70} - 15 q^{71} + 4 q^{72} - 19 q^{73} - 54 q^{75} - 5 q^{76} + 9 q^{77} - 10 q^{78} - 9 q^{79} + 9 q^{80} + 28 q^{81} - 3 q^{82} - 7 q^{84} - 42 q^{85} - 3 q^{86} - 81 q^{87} + 9 q^{88} + 9 q^{90} - 72 q^{91} - 17 q^{93} - 27 q^{94} + 6 q^{96} + 19 q^{97} - 2 q^{98} - 27 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 1.67564 + 0.438430i 0.967433 + 0.253128i
\(4\) 1.00000 0.500000
\(5\) 1.57344 + 0.908426i 0.703664 + 0.406261i 0.808711 0.588207i \(-0.200166\pi\)
−0.105047 + 0.994467i \(0.533499\pi\)
\(6\) 1.67564 + 0.438430i 0.684078 + 0.178988i
\(7\) −2.47008 + 0.947995i −0.933603 + 0.358308i
\(8\) 1.00000 0.353553
\(9\) 2.61556 + 1.46930i 0.871853 + 0.489768i
\(10\) 1.57344 + 0.908426i 0.497566 + 0.287270i
\(11\) −1.02563 + 1.77645i −0.309240 + 0.535620i −0.978196 0.207682i \(-0.933408\pi\)
0.668956 + 0.743302i \(0.266741\pi\)
\(12\) 1.67564 + 0.438430i 0.483716 + 0.126564i
\(13\) −3.57560 + 0.463745i −0.991694 + 0.128620i
\(14\) −2.47008 + 0.947995i −0.660157 + 0.253362i
\(15\) 2.23824 + 2.21204i 0.577912 + 0.571147i
\(16\) 1.00000 0.250000
\(17\) 5.68717 1.37934 0.689671 0.724123i \(-0.257755\pi\)
0.689671 + 0.724123i \(0.257755\pi\)
\(18\) 2.61556 + 1.46930i 0.616493 + 0.346318i
\(19\) −0.796762 1.38003i −0.182790 0.316601i 0.760040 0.649876i \(-0.225179\pi\)
−0.942829 + 0.333276i \(0.891846\pi\)
\(20\) 1.57344 + 0.908426i 0.351832 + 0.203130i
\(21\) −4.55461 + 0.505542i −0.993896 + 0.110318i
\(22\) −1.02563 + 1.77645i −0.218666 + 0.378740i
\(23\) 8.73960i 1.82233i −0.412039 0.911166i \(-0.635183\pi\)
0.412039 0.911166i \(-0.364817\pi\)
\(24\) 1.67564 + 0.438430i 0.342039 + 0.0894942i
\(25\) −0.849523 1.47142i −0.169905 0.294283i
\(26\) −3.57560 + 0.463745i −0.701234 + 0.0909480i
\(27\) 3.73855 + 3.60877i 0.719485 + 0.694508i
\(28\) −2.47008 + 0.947995i −0.466802 + 0.179154i
\(29\) 0.724381 0.418222i 0.134514 0.0776618i −0.431233 0.902241i \(-0.641921\pi\)
0.565747 + 0.824579i \(0.308588\pi\)
\(30\) 2.23824 + 2.21204i 0.408645 + 0.403862i
\(31\) −3.97501 6.88493i −0.713934 1.23657i −0.963369 0.268178i \(-0.913579\pi\)
0.249436 0.968391i \(-0.419755\pi\)
\(32\) 1.00000 0.176777
\(33\) −2.49744 + 2.52703i −0.434749 + 0.439899i
\(34\) 5.68717 0.975342
\(35\) −4.74771 0.752275i −0.802510 0.127158i
\(36\) 2.61556 + 1.46930i 0.435926 + 0.244884i
\(37\) 4.21819i 0.693466i 0.937964 + 0.346733i \(0.112709\pi\)
−0.937964 + 0.346733i \(0.887291\pi\)
\(38\) −0.796762 1.38003i −0.129252 0.223871i
\(39\) −6.19475 0.790580i −0.991955 0.126594i
\(40\) 1.57344 + 0.908426i 0.248783 + 0.143635i
\(41\) 0.397180 0.229312i 0.0620290 0.0358125i −0.468665 0.883376i \(-0.655265\pi\)
0.530694 + 0.847564i \(0.321931\pi\)
\(42\) −4.55461 + 0.505542i −0.702791 + 0.0780069i
\(43\) 0.836012 1.44802i 0.127491 0.220820i −0.795213 0.606330i \(-0.792641\pi\)
0.922704 + 0.385510i \(0.125974\pi\)
\(44\) −1.02563 + 1.77645i −0.154620 + 0.267810i
\(45\) 2.78067 + 4.68791i 0.414518 + 0.698832i
\(46\) 8.73960i 1.28858i
\(47\) −1.94760 1.12445i −0.284086 0.164017i 0.351186 0.936306i \(-0.385779\pi\)
−0.635272 + 0.772289i \(0.719112\pi\)
\(48\) 1.67564 + 0.438430i 0.241858 + 0.0632819i
\(49\) 5.20261 4.68325i 0.743230 0.669036i
\(50\) −0.849523 1.47142i −0.120141 0.208090i
\(51\) 9.52967 + 2.49343i 1.33442 + 0.349150i
\(52\) −3.57560 + 0.463745i −0.495847 + 0.0643099i
\(53\) 0.497067 0.286982i 0.0682774 0.0394200i −0.465473 0.885062i \(-0.654116\pi\)
0.533750 + 0.845642i \(0.320782\pi\)
\(54\) 3.73855 + 3.60877i 0.508753 + 0.491091i
\(55\) −3.22755 + 1.86343i −0.435202 + 0.251264i
\(56\) −2.47008 + 0.947995i −0.330079 + 0.126681i
\(57\) −0.730041 2.66176i −0.0966962 0.352559i
\(58\) 0.724381 0.418222i 0.0951159 0.0549152i
\(59\) 2.19150i 0.285308i 0.989773 + 0.142654i \(0.0455637\pi\)
−0.989773 + 0.142654i \(0.954436\pi\)
\(60\) 2.23824 + 2.21204i 0.288956 + 0.285573i
\(61\) −5.97394 + 3.44906i −0.764885 + 0.441607i −0.831047 0.556202i \(-0.812258\pi\)
0.0661618 + 0.997809i \(0.478925\pi\)
\(62\) −3.97501 6.88493i −0.504827 0.874386i
\(63\) −7.85354 1.14977i −0.989453 0.144857i
\(64\) 1.00000 0.125000
\(65\) −6.04728 2.51850i −0.750073 0.312381i
\(66\) −2.49744 + 2.52703i −0.307414 + 0.311055i
\(67\) −4.46448 2.57757i −0.545423 0.314900i 0.201851 0.979416i \(-0.435304\pi\)
−0.747274 + 0.664516i \(0.768638\pi\)
\(68\) 5.68717 0.689671
\(69\) 3.83170 14.6444i 0.461283 1.76298i
\(70\) −4.74771 0.752275i −0.567460 0.0899140i
\(71\) 4.24250 7.34823i 0.503493 0.872075i −0.496499 0.868037i \(-0.665381\pi\)
0.999992 0.00403764i \(-0.00128522\pi\)
\(72\) 2.61556 + 1.46930i 0.308246 + 0.173159i
\(73\) 5.11752 + 8.86381i 0.598961 + 1.03743i 0.992975 + 0.118326i \(0.0377528\pi\)
−0.394014 + 0.919104i \(0.628914\pi\)
\(74\) 4.21819i 0.490354i
\(75\) −0.778384 2.83803i −0.0898800 0.327707i
\(76\) −0.796762 1.38003i −0.0913948 0.158300i
\(77\) 0.849335 5.36027i 0.0967907 0.610860i
\(78\) −6.19475 0.790580i −0.701418 0.0895156i
\(79\) −3.68537 + 6.38325i −0.414637 + 0.718172i −0.995390 0.0959076i \(-0.969425\pi\)
0.580754 + 0.814079i \(0.302758\pi\)
\(80\) 1.57344 + 0.908426i 0.175916 + 0.101565i
\(81\) 4.68229 + 7.68610i 0.520254 + 0.854011i
\(82\) 0.397180 0.229312i 0.0438612 0.0253233i
\(83\) 15.0678i 1.65391i 0.562269 + 0.826954i \(0.309929\pi\)
−0.562269 + 0.826954i \(0.690071\pi\)
\(84\) −4.55461 + 0.505542i −0.496948 + 0.0551592i
\(85\) 8.94843 + 5.16638i 0.970594 + 0.560373i
\(86\) 0.836012 1.44802i 0.0901495 0.156143i
\(87\) 1.39717 0.383200i 0.149792 0.0410833i
\(88\) −1.02563 + 1.77645i −0.109333 + 0.189370i
\(89\) 3.86314i 0.409492i −0.978815 0.204746i \(-0.934363\pi\)
0.978815 0.204746i \(-0.0656368\pi\)
\(90\) 2.78067 + 4.68791i 0.293108 + 0.494149i
\(91\) 8.39241 4.53514i 0.879763 0.475412i
\(92\) 8.73960i 0.911166i
\(93\) −3.64215 13.2794i −0.377673 1.37701i
\(94\) −1.94760 1.12445i −0.200879 0.115978i
\(95\) 2.89520i 0.297041i
\(96\) 1.67564 + 0.438430i 0.171020 + 0.0447471i
\(97\) −1.72410 + 2.98622i −0.175056 + 0.303205i −0.940180 0.340677i \(-0.889344\pi\)
0.765125 + 0.643882i \(0.222677\pi\)
\(98\) 5.20261 4.68325i 0.525543 0.473080i
\(99\) −5.29275 + 3.13944i −0.531941 + 0.315526i
\(100\) −0.849523 1.47142i −0.0849523 0.147142i
\(101\) −4.84811 + 8.39717i −0.482405 + 0.835550i −0.999796 0.0201992i \(-0.993570\pi\)
0.517391 + 0.855749i \(0.326903\pi\)
\(102\) 9.52967 + 2.49343i 0.943578 + 0.246886i
\(103\) 8.08628 + 4.66861i 0.796765 + 0.460012i 0.842339 0.538949i \(-0.181178\pi\)
−0.0455739 + 0.998961i \(0.514512\pi\)
\(104\) −3.57560 + 0.463745i −0.350617 + 0.0454740i
\(105\) −7.62565 3.34208i −0.744187 0.326154i
\(106\) 0.497067 0.286982i 0.0482794 0.0278742i
\(107\) 10.7060i 1.03499i −0.855687 0.517493i \(-0.826865\pi\)
0.855687 0.517493i \(-0.173135\pi\)
\(108\) 3.73855 + 3.60877i 0.359743 + 0.347254i
\(109\) −4.30381 + 2.48481i −0.412230 + 0.238001i −0.691748 0.722139i \(-0.743159\pi\)
0.279517 + 0.960141i \(0.409826\pi\)
\(110\) −3.22755 + 1.86343i −0.307735 + 0.177671i
\(111\) −1.84938 + 7.06818i −0.175535 + 0.670882i
\(112\) −2.47008 + 0.947995i −0.233401 + 0.0895771i
\(113\) −14.4435 8.33897i −1.35873 0.784464i −0.369279 0.929319i \(-0.620395\pi\)
−0.989453 + 0.144855i \(0.953729\pi\)
\(114\) −0.730041 2.66176i −0.0683746 0.249297i
\(115\) 7.93928 13.7512i 0.740342 1.28231i
\(116\) 0.724381 0.418222i 0.0672571 0.0388309i
\(117\) −10.0336 4.04070i −0.927605 0.373563i
\(118\) 2.19150i 0.201743i
\(119\) −14.0478 + 5.39141i −1.28776 + 0.494230i
\(120\) 2.23824 + 2.21204i 0.204323 + 0.201931i
\(121\) 3.39615 + 5.88231i 0.308741 + 0.534755i
\(122\) −5.97394 + 3.44906i −0.540855 + 0.312263i
\(123\) 0.766068 0.210109i 0.0690741 0.0189449i
\(124\) −3.97501 6.88493i −0.356967 0.618285i
\(125\) 12.1712i 1.08862i
\(126\) −7.85354 1.14977i −0.699649 0.102429i
\(127\) −10.6930 18.5208i −0.948852 1.64346i −0.747849 0.663869i \(-0.768913\pi\)
−0.201003 0.979591i \(-0.564420\pi\)
\(128\) 1.00000 0.0883883
\(129\) 2.03571 2.05982i 0.179234 0.181357i
\(130\) −6.04728 2.51850i −0.530381 0.220887i
\(131\) −7.44741 + 12.8993i −0.650683 + 1.12702i 0.332274 + 0.943183i \(0.392184\pi\)
−0.982957 + 0.183834i \(0.941149\pi\)
\(132\) −2.49744 + 2.52703i −0.217375 + 0.219949i
\(133\) 3.27633 + 2.65347i 0.284094 + 0.230085i
\(134\) −4.46448 2.57757i −0.385672 0.222668i
\(135\) 2.60409 + 9.07439i 0.224125 + 0.780999i
\(136\) 5.68717 0.487671
\(137\) −11.6043 −0.991424 −0.495712 0.868487i \(-0.665093\pi\)
−0.495712 + 0.868487i \(0.665093\pi\)
\(138\) 3.83170 14.6444i 0.326176 1.24662i
\(139\) 13.6556 + 7.88408i 1.15825 + 0.668719i 0.950885 0.309544i \(-0.100176\pi\)
0.207370 + 0.978263i \(0.433510\pi\)
\(140\) −4.74771 0.752275i −0.401255 0.0635788i
\(141\) −2.77049 2.73805i −0.233317 0.230586i
\(142\) 4.24250 7.34823i 0.356023 0.616650i
\(143\) 2.84344 6.82751i 0.237780 0.570945i
\(144\) 2.61556 + 1.46930i 0.217963 + 0.122442i
\(145\) 1.51969 0.126204
\(146\) 5.11752 + 8.86381i 0.423529 + 0.733574i
\(147\) 10.7710 5.56647i 0.888377 0.459115i
\(148\) 4.21819i 0.346733i
\(149\) 2.40740 + 4.16974i 0.197222 + 0.341599i 0.947627 0.319380i \(-0.103475\pi\)
−0.750405 + 0.660979i \(0.770141\pi\)
\(150\) −0.778384 2.83803i −0.0635548 0.231724i
\(151\) −1.23569 + 0.713427i −0.100559 + 0.0580579i −0.549436 0.835536i \(-0.685157\pi\)
0.448877 + 0.893594i \(0.351824\pi\)
\(152\) −0.796762 1.38003i −0.0646259 0.111935i
\(153\) 14.8751 + 8.35619i 1.20258 + 0.675558i
\(154\) 0.849335 5.36027i 0.0684414 0.431943i
\(155\) 14.4440i 1.16017i
\(156\) −6.19475 0.790580i −0.495977 0.0632971i
\(157\) 7.14347 4.12428i 0.570111 0.329154i −0.187083 0.982344i \(-0.559903\pi\)
0.757194 + 0.653191i \(0.226570\pi\)
\(158\) −3.68537 + 6.38325i −0.293192 + 0.507824i
\(159\) 0.958729 0.262950i 0.0760321 0.0208533i
\(160\) 1.57344 + 0.908426i 0.124391 + 0.0718174i
\(161\) 8.28509 + 21.5875i 0.652957 + 1.70134i
\(162\) 4.68229 + 7.68610i 0.367875 + 0.603877i
\(163\) −20.7420 + 11.9754i −1.62464 + 0.937985i −0.638981 + 0.769223i \(0.720644\pi\)
−0.985657 + 0.168762i \(0.946023\pi\)
\(164\) 0.397180 0.229312i 0.0310145 0.0179062i
\(165\) −6.22520 + 1.70738i −0.484631 + 0.132920i
\(166\) 15.0678i 1.16949i
\(167\) 20.2949 11.7173i 1.57047 0.906711i 0.574358 0.818604i \(-0.305252\pi\)
0.996111 0.0881060i \(-0.0280814\pi\)
\(168\) −4.55461 + 0.505542i −0.351395 + 0.0390034i
\(169\) 12.5699 3.31634i 0.966914 0.255103i
\(170\) 8.94843 + 5.16638i 0.686313 + 0.396243i
\(171\) −0.0562900 4.78024i −0.00430461 0.365554i
\(172\) 0.836012 1.44802i 0.0637453 0.110410i
\(173\) 3.80295 + 6.58691i 0.289133 + 0.500794i 0.973603 0.228248i \(-0.0732996\pi\)
−0.684470 + 0.729041i \(0.739966\pi\)
\(174\) 1.39717 0.383200i 0.105919 0.0290503i
\(175\) 3.49329 + 2.82918i 0.264068 + 0.213866i
\(176\) −1.02563 + 1.77645i −0.0773101 + 0.133905i
\(177\) −0.960817 + 3.67216i −0.0722194 + 0.276017i
\(178\) 3.86314i 0.289554i
\(179\) −15.9356 9.20041i −1.19108 0.687671i −0.232530 0.972589i \(-0.574700\pi\)
−0.958552 + 0.284918i \(0.908034\pi\)
\(180\) 2.78067 + 4.68791i 0.207259 + 0.349416i
\(181\) 0.190838i 0.0141849i −0.999975 0.00709245i \(-0.997742\pi\)
0.999975 0.00709245i \(-0.00225762\pi\)
\(182\) 8.39241 4.53514i 0.622087 0.336167i
\(183\) −11.5224 + 3.16023i −0.851758 + 0.233611i
\(184\) 8.73960i 0.644292i
\(185\) −3.83191 + 6.63707i −0.281728 + 0.487967i
\(186\) −3.64215 13.2794i −0.267055 0.973696i
\(187\) −5.83296 + 10.1030i −0.426548 + 0.738803i
\(188\) −1.94760 1.12445i −0.142043 0.0820086i
\(189\) −12.6556 5.36983i −0.920562 0.390597i
\(190\) 2.89520i 0.210040i
\(191\) −4.50022 + 2.59820i −0.325625 + 0.187999i −0.653897 0.756584i \(-0.726867\pi\)
0.328272 + 0.944583i \(0.393534\pi\)
\(192\) 1.67564 + 0.438430i 0.120929 + 0.0316410i
\(193\) 9.53669 + 5.50601i 0.686466 + 0.396331i 0.802287 0.596939i \(-0.203616\pi\)
−0.115821 + 0.993270i \(0.536950\pi\)
\(194\) −1.72410 + 2.98622i −0.123783 + 0.214398i
\(195\) −9.02890 6.87141i −0.646573 0.492072i
\(196\) 5.20261 4.68325i 0.371615 0.334518i
\(197\) −11.1333 19.2835i −0.793218 1.37389i −0.923964 0.382478i \(-0.875071\pi\)
0.130746 0.991416i \(-0.458263\pi\)
\(198\) −5.29275 + 3.13944i −0.376139 + 0.223110i
\(199\) 19.0946i 1.35358i 0.736177 + 0.676789i \(0.236629\pi\)
−0.736177 + 0.676789i \(0.763371\pi\)
\(200\) −0.849523 1.47142i −0.0600703 0.104045i
\(201\) −6.35079 6.27645i −0.447950 0.442706i
\(202\) −4.84811 + 8.39717i −0.341112 + 0.590823i
\(203\) −1.39281 + 1.71975i −0.0977560 + 0.120703i
\(204\) 9.52967 + 2.49343i 0.667211 + 0.174575i
\(205\) 0.833252 0.0581968
\(206\) 8.08628 + 4.66861i 0.563398 + 0.325278i
\(207\) 12.8411 22.8589i 0.892520 1.58881i
\(208\) −3.57560 + 0.463745i −0.247923 + 0.0321550i
\(209\) 3.26874 0.226104
\(210\) −7.62565 3.34208i −0.526220 0.230626i
\(211\) −7.80557 13.5196i −0.537358 0.930731i −0.999045 0.0436882i \(-0.986089\pi\)
0.461688 0.887043i \(-0.347244\pi\)
\(212\) 0.497067 0.286982i 0.0341387 0.0197100i
\(213\) 10.3306 10.4530i 0.707842 0.716226i
\(214\) 10.7060i 0.731846i
\(215\) 2.63083 1.51891i 0.179421 0.103589i
\(216\) 3.73855 + 3.60877i 0.254376 + 0.245546i
\(217\) 16.3455 + 13.2380i 1.10960 + 0.898657i
\(218\) −4.30381 + 2.48481i −0.291491 + 0.168292i
\(219\) 4.68898 + 17.0963i 0.316852 + 1.15526i
\(220\) −3.22755 + 1.86343i −0.217601 + 0.125632i
\(221\) −20.3351 + 2.63740i −1.36789 + 0.177411i
\(222\) −1.84938 + 7.06818i −0.124122 + 0.474385i
\(223\) −4.91509 8.51319i −0.329139 0.570085i 0.653202 0.757183i \(-0.273425\pi\)
−0.982341 + 0.187098i \(0.940092\pi\)
\(224\) −2.47008 + 0.947995i −0.165039 + 0.0633406i
\(225\) −0.0600175 5.09678i −0.00400117 0.339786i
\(226\) −14.4435 8.33897i −0.960768 0.554700i
\(227\) 11.3725i 0.754821i 0.926046 + 0.377410i \(0.123185\pi\)
−0.926046 + 0.377410i \(0.876815\pi\)
\(228\) −0.730041 2.66176i −0.0483481 0.176280i
\(229\) −9.48968 + 16.4366i −0.627096 + 1.08616i 0.361036 + 0.932552i \(0.382423\pi\)
−0.988132 + 0.153610i \(0.950910\pi\)
\(230\) 7.93928 13.7512i 0.523501 0.906730i
\(231\) 3.77329 8.60953i 0.248264 0.566465i
\(232\) 0.724381 0.418222i 0.0475580 0.0274576i
\(233\) 18.2307 + 10.5255i 1.19433 + 0.689550i 0.959287 0.282434i \(-0.0911419\pi\)
0.235048 + 0.971984i \(0.424475\pi\)
\(234\) −10.0336 4.04070i −0.655916 0.264149i
\(235\) −2.04295 3.53850i −0.133267 0.230826i
\(236\) 2.19150i 0.142654i
\(237\) −8.97398 + 9.08027i −0.582922 + 0.589827i
\(238\) −14.0478 + 5.39141i −0.910583 + 0.349473i
\(239\) 16.6885 1.07949 0.539746 0.841828i \(-0.318520\pi\)
0.539746 + 0.841828i \(0.318520\pi\)
\(240\) 2.23824 + 2.21204i 0.144478 + 0.142787i
\(241\) 15.2747 0.983927 0.491963 0.870616i \(-0.336279\pi\)
0.491963 + 0.870616i \(0.336279\pi\)
\(242\) 3.39615 + 5.88231i 0.218313 + 0.378129i
\(243\) 4.47603 + 14.9320i 0.287137 + 0.957889i
\(244\) −5.97394 + 3.44906i −0.382443 + 0.220803i
\(245\) 12.4404 2.64262i 0.794787 0.168831i
\(246\) 0.766068 0.210109i 0.0488427 0.0133961i
\(247\) 3.48889 + 4.56495i 0.221993 + 0.290461i
\(248\) −3.97501 6.88493i −0.252414 0.437193i
\(249\) −6.60619 + 25.2483i −0.418650 + 1.60005i
\(250\) 12.1712i 0.769773i
\(251\) 4.91975 8.52125i 0.310532 0.537857i −0.667946 0.744210i \(-0.732826\pi\)
0.978478 + 0.206353i \(0.0661596\pi\)
\(252\) −7.85354 1.14977i −0.494726 0.0724285i
\(253\) 15.5255 + 8.96363i 0.976077 + 0.563538i
\(254\) −10.6930 18.5208i −0.670940 1.16210i
\(255\) 12.7293 + 12.5803i 0.797138 + 0.787807i
\(256\) 1.00000 0.0625000
\(257\) 1.53233 0.0955843 0.0477921 0.998857i \(-0.484781\pi\)
0.0477921 + 0.998857i \(0.484781\pi\)
\(258\) 2.03571 2.05982i 0.126738 0.128239i
\(259\) −3.99882 10.4193i −0.248475 0.647422i
\(260\) −6.04728 2.51850i −0.375036 0.156191i
\(261\) 2.50916 0.0295467i 0.155313 0.00182890i
\(262\) −7.44741 + 12.8993i −0.460103 + 0.796921i
\(263\) 16.9520 + 9.78724i 1.04530 + 0.603507i 0.921331 0.388779i \(-0.127103\pi\)
0.123973 + 0.992286i \(0.460436\pi\)
\(264\) −2.49744 + 2.52703i −0.153707 + 0.155528i
\(265\) 1.04281 0.0640592
\(266\) 3.27633 + 2.65347i 0.200885 + 0.162694i
\(267\) 1.69372 6.47324i 0.103654 0.396156i
\(268\) −4.46448 2.57757i −0.272712 0.157450i
\(269\) 13.5580 0.826646 0.413323 0.910584i \(-0.364368\pi\)
0.413323 + 0.910584i \(0.364368\pi\)
\(270\) 2.60409 + 9.07439i 0.158480 + 0.552250i
\(271\) −28.0556 −1.70425 −0.852127 0.523335i \(-0.824688\pi\)
−0.852127 + 0.523335i \(0.824688\pi\)
\(272\) 5.68717 0.344836
\(273\) 16.0510 3.91980i 0.971452 0.237237i
\(274\) −11.6043 −0.701042
\(275\) 3.48520 0.210165
\(276\) 3.83170 14.6444i 0.230641 0.881492i
\(277\) 23.3285 1.40167 0.700836 0.713323i \(-0.252811\pi\)
0.700836 + 0.713323i \(0.252811\pi\)
\(278\) 13.6556 + 7.88408i 0.819010 + 0.472856i
\(279\) −0.280829 23.8484i −0.0168128 1.42777i
\(280\) −4.74771 0.752275i −0.283730 0.0449570i
\(281\) 26.6302 1.58862 0.794311 0.607512i \(-0.207832\pi\)
0.794311 + 0.607512i \(0.207832\pi\)
\(282\) −2.77049 2.73805i −0.164980 0.163049i
\(283\) −23.3128 13.4597i −1.38580 0.800093i −0.392964 0.919554i \(-0.628550\pi\)
−0.992839 + 0.119461i \(0.961884\pi\)
\(284\) 4.24250 7.34823i 0.251746 0.436037i
\(285\) 1.26934 4.85132i 0.0751893 0.287367i
\(286\) 2.84344 6.82751i 0.168136 0.403719i
\(287\) −0.763680 + 0.942943i −0.0450786 + 0.0556602i
\(288\) 2.61556 + 1.46930i 0.154123 + 0.0865796i
\(289\) 15.3439 0.902585
\(290\) 1.51969 0.0892395
\(291\) −4.19822 + 4.24795i −0.246104 + 0.249019i
\(292\) 5.11752 + 8.86381i 0.299480 + 0.518715i
\(293\) 6.97220 + 4.02540i 0.407320 + 0.235167i 0.689638 0.724154i \(-0.257770\pi\)
−0.282317 + 0.959321i \(0.591103\pi\)
\(294\) 10.7710 5.56647i 0.628177 0.324643i
\(295\) −1.99081 + 3.44819i −0.115910 + 0.200761i
\(296\) 4.21819i 0.245177i
\(297\) −10.2452 + 2.94008i −0.594486 + 0.170601i
\(298\) 2.40740 + 4.16974i 0.139457 + 0.241547i
\(299\) 4.05295 + 31.2493i 0.234388 + 1.80720i
\(300\) −0.778384 2.83803i −0.0449400 0.163853i
\(301\) −0.692308 + 4.36925i −0.0399039 + 0.251839i
\(302\) −1.23569 + 0.713427i −0.0711061 + 0.0410531i
\(303\) −11.8053 + 11.9451i −0.678195 + 0.686228i
\(304\) −0.796762 1.38003i −0.0456974 0.0791502i
\(305\) −12.5329 −0.717630
\(306\) 14.8751 + 8.35619i 0.850355 + 0.477692i
\(307\) 13.6194 0.777300 0.388650 0.921385i \(-0.372942\pi\)
0.388650 + 0.921385i \(0.372942\pi\)
\(308\) 0.849335 5.36027i 0.0483953 0.305430i
\(309\) 11.5029 + 11.3682i 0.654374 + 0.646714i
\(310\) 14.4440i 0.820366i
\(311\) 12.6742 + 21.9523i 0.718685 + 1.24480i 0.961521 + 0.274732i \(0.0885892\pi\)
−0.242835 + 0.970068i \(0.578077\pi\)
\(312\) −6.19475 0.790580i −0.350709 0.0447578i
\(313\) −7.41295 4.27987i −0.419005 0.241913i 0.275647 0.961259i \(-0.411108\pi\)
−0.694651 + 0.719347i \(0.744441\pi\)
\(314\) 7.14347 4.12428i 0.403129 0.232747i
\(315\) −11.3126 8.94345i −0.637393 0.503906i
\(316\) −3.68537 + 6.38325i −0.207318 + 0.359086i
\(317\) −11.7752 + 20.3952i −0.661360 + 1.14551i 0.318898 + 0.947789i \(0.396687\pi\)
−0.980258 + 0.197721i \(0.936646\pi\)
\(318\) 0.958729 0.262950i 0.0537628 0.0147455i
\(319\) 1.71577i 0.0960646i
\(320\) 1.57344 + 0.908426i 0.0879580 + 0.0507826i
\(321\) 4.69382 17.9394i 0.261984 1.00128i
\(322\) 8.28509 + 21.5875i 0.461710 + 1.20303i
\(323\) −4.53132 7.84848i −0.252129 0.436701i
\(324\) 4.68229 + 7.68610i 0.260127 + 0.427006i
\(325\) 3.71992 + 4.86724i 0.206344 + 0.269986i
\(326\) −20.7420 + 11.9754i −1.14879 + 0.663256i
\(327\) −8.30107 + 2.27673i −0.459050 + 0.125903i
\(328\) 0.397180 0.229312i 0.0219306 0.0126616i
\(329\) 5.87669 + 0.931162i 0.323992 + 0.0513366i
\(330\) −6.22520 + 1.70738i −0.342686 + 0.0939883i
\(331\) 6.15849 3.55561i 0.338501 0.195434i −0.321108 0.947043i \(-0.604055\pi\)
0.659609 + 0.751609i \(0.270722\pi\)
\(332\) 15.0678i 0.826954i
\(333\) −6.19780 + 11.0329i −0.339638 + 0.604600i
\(334\) 20.2949 11.7173i 1.11049 0.641141i
\(335\) −4.68306 8.11130i −0.255863 0.443168i
\(336\) −4.55461 + 0.505542i −0.248474 + 0.0275796i
\(337\) 19.1187 1.04146 0.520730 0.853722i \(-0.325660\pi\)
0.520730 + 0.853722i \(0.325660\pi\)
\(338\) 12.5699 3.31634i 0.683711 0.180385i
\(339\) −20.5461 20.3056i −1.11591 1.10285i
\(340\) 8.94843 + 5.16638i 0.485297 + 0.280186i
\(341\) 16.3076 0.883108
\(342\) −0.0562900 4.78024i −0.00304382 0.258486i
\(343\) −8.41119 + 16.5001i −0.454161 + 0.890919i
\(344\) 0.836012 1.44802i 0.0450747 0.0780717i
\(345\) 19.3324 19.5613i 1.04082 1.05315i
\(346\) 3.80295 + 6.58691i 0.204448 + 0.354114i
\(347\) 23.0701i 1.23847i −0.785207 0.619233i \(-0.787444\pi\)
0.785207 0.619233i \(-0.212556\pi\)
\(348\) 1.39717 0.383200i 0.0748959 0.0205417i
\(349\) 2.11359 + 3.66085i 0.113138 + 0.195961i 0.917034 0.398809i \(-0.130576\pi\)
−0.803896 + 0.594770i \(0.797243\pi\)
\(350\) 3.49329 + 2.82918i 0.186724 + 0.151226i
\(351\) −15.0411 11.1698i −0.802837 0.596199i
\(352\) −1.02563 + 1.77645i −0.0546665 + 0.0946851i
\(353\) 27.6603 + 15.9697i 1.47221 + 0.849981i 0.999512 0.0312428i \(-0.00994650\pi\)
0.472699 + 0.881224i \(0.343280\pi\)
\(354\) −0.960817 + 3.67216i −0.0510669 + 0.195173i
\(355\) 13.3507 7.70801i 0.708579 0.409098i
\(356\) 3.86314i 0.204746i
\(357\) −25.9028 + 2.87511i −1.37092 + 0.152167i
\(358\) −15.9356 9.20041i −0.842222 0.486257i
\(359\) −12.2496 + 21.2169i −0.646509 + 1.11979i 0.337442 + 0.941346i \(0.390438\pi\)
−0.983951 + 0.178440i \(0.942895\pi\)
\(360\) 2.78067 + 4.68791i 0.146554 + 0.247074i
\(361\) 8.23034 14.2554i 0.433176 0.750283i
\(362\) 0.190838i 0.0100302i
\(363\) 3.11176 + 11.3456i 0.163325 + 0.595491i
\(364\) 8.39241 4.53514i 0.439882 0.237706i
\(365\) 18.5956i 0.973337i
\(366\) −11.5224 + 3.16023i −0.602284 + 0.165188i
\(367\) −28.7618 16.6056i −1.50135 0.866807i −0.999999 0.00156589i \(-0.999502\pi\)
−0.501355 0.865241i \(-0.667165\pi\)
\(368\) 8.73960i 0.455583i
\(369\) 1.37578 0.0162005i 0.0716200 0.000843366i
\(370\) −3.83191 + 6.63707i −0.199212 + 0.345045i
\(371\) −0.955740 + 1.18009i −0.0496195 + 0.0612670i
\(372\) −3.64215 13.2794i −0.188836 0.688507i
\(373\) 2.06003 + 3.56807i 0.106664 + 0.184748i 0.914417 0.404774i \(-0.132650\pi\)
−0.807753 + 0.589521i \(0.799316\pi\)
\(374\) −5.83296 + 10.1030i −0.301615 + 0.522413i
\(375\) 5.33621 20.3946i 0.275561 1.05317i
\(376\) −1.94760 1.12445i −0.100440 0.0579888i
\(377\) −2.39615 + 1.83132i −0.123408 + 0.0943179i
\(378\) −12.6556 5.36983i −0.650935 0.276194i
\(379\) −2.80001 + 1.61659i −0.143827 + 0.0830385i −0.570187 0.821515i \(-0.693129\pi\)
0.426360 + 0.904554i \(0.359796\pi\)
\(380\) 2.89520i 0.148520i
\(381\) −9.79758 35.7225i −0.501945 1.83012i
\(382\) −4.50022 + 2.59820i −0.230251 + 0.132936i
\(383\) −3.61672 + 2.08811i −0.184806 + 0.106698i −0.589549 0.807733i \(-0.700694\pi\)
0.404743 + 0.914430i \(0.367361\pi\)
\(384\) 1.67564 + 0.438430i 0.0855098 + 0.0223735i
\(385\) 6.20579 7.66251i 0.316276 0.390518i
\(386\) 9.53669 + 5.50601i 0.485405 + 0.280249i
\(387\) 4.31421 2.55901i 0.219304 0.130082i
\(388\) −1.72410 + 2.98622i −0.0875278 + 0.151603i
\(389\) −3.57665 + 2.06498i −0.181343 + 0.104699i −0.587924 0.808916i \(-0.700054\pi\)
0.406580 + 0.913615i \(0.366721\pi\)
\(390\) −9.02890 6.87141i −0.457196 0.347947i
\(391\) 49.7036i 2.51362i
\(392\) 5.20261 4.68325i 0.262772 0.236540i
\(393\) −18.1346 + 18.3494i −0.914772 + 0.925607i
\(394\) −11.1333 19.2835i −0.560890 0.971490i
\(395\) −11.5974 + 6.69578i −0.583530 + 0.336901i
\(396\) −5.29275 + 3.13944i −0.265971 + 0.157763i
\(397\) 2.38133 + 4.12458i 0.119515 + 0.207007i 0.919576 0.392913i \(-0.128533\pi\)
−0.800060 + 0.599920i \(0.795199\pi\)
\(398\) 19.0946i 0.957124i
\(399\) 4.32660 + 5.88270i 0.216601 + 0.294503i
\(400\) −0.849523 1.47142i −0.0424761 0.0735708i
\(401\) 15.4809 0.773080 0.386540 0.922273i \(-0.373670\pi\)
0.386540 + 0.922273i \(0.373670\pi\)
\(402\) −6.35079 6.27645i −0.316749 0.313041i
\(403\) 17.4059 + 22.7744i 0.867051 + 1.13447i
\(404\) −4.84811 + 8.39717i −0.241202 + 0.417775i
\(405\) 0.385047 + 16.3471i 0.0191331 + 0.812296i
\(406\) −1.39281 + 1.71975i −0.0691240 + 0.0853498i
\(407\) −7.49340 4.32632i −0.371434 0.214448i
\(408\) 9.52967 + 2.49343i 0.471789 + 0.123443i
\(409\) −39.7884 −1.96741 −0.983706 0.179784i \(-0.942460\pi\)
−0.983706 + 0.179784i \(0.942460\pi\)
\(410\) 0.833252 0.0411514
\(411\) −19.4447 5.08768i −0.959136 0.250957i
\(412\) 8.08628 + 4.66861i 0.398382 + 0.230006i
\(413\) −2.07753 5.41317i −0.102228 0.266365i
\(414\) 12.8411 22.8589i 0.631107 1.12345i
\(415\) −13.6880 + 23.7083i −0.671918 + 1.16380i
\(416\) −3.57560 + 0.463745i −0.175308 + 0.0227370i
\(417\) 19.4253 + 19.1979i 0.951263 + 0.940127i
\(418\) 3.26874 0.159879
\(419\) 13.1146 + 22.7152i 0.640690 + 1.10971i 0.985279 + 0.170954i \(0.0546850\pi\)
−0.344589 + 0.938754i \(0.611982\pi\)
\(420\) −7.62565 3.34208i −0.372094 0.163077i
\(421\) 14.0343i 0.683989i 0.939702 + 0.341994i \(0.111102\pi\)
−0.939702 + 0.341994i \(0.888898\pi\)
\(422\) −7.80557 13.5196i −0.379969 0.658126i
\(423\) −3.44190 5.80266i −0.167351 0.282135i
\(424\) 0.497067 0.286982i 0.0241397 0.0139371i
\(425\) −4.83138 8.36820i −0.234357 0.405917i
\(426\) 10.3306 10.4530i 0.500520 0.506448i
\(427\) 11.4864 14.1827i 0.555868 0.686350i
\(428\) 10.7060i 0.517493i
\(429\) 7.75798 10.1938i 0.374559 0.492162i
\(430\) 2.63083 1.51891i 0.126870 0.0732484i
\(431\) 8.06272 13.9650i 0.388368 0.672673i −0.603862 0.797089i \(-0.706372\pi\)
0.992230 + 0.124416i \(0.0397057\pi\)
\(432\) 3.73855 + 3.60877i 0.179871 + 0.173627i
\(433\) −13.9038 8.02734i −0.668172 0.385769i 0.127211 0.991876i \(-0.459397\pi\)
−0.795384 + 0.606106i \(0.792731\pi\)
\(434\) 16.3455 + 13.2380i 0.784608 + 0.635446i
\(435\) 2.54647 + 0.666280i 0.122094 + 0.0319457i
\(436\) −4.30381 + 2.48481i −0.206115 + 0.119001i
\(437\) −12.0609 + 6.96338i −0.576952 + 0.333103i
\(438\) 4.68898 + 17.0963i 0.224048 + 0.816891i
\(439\) 16.1774i 0.772104i 0.922477 + 0.386052i \(0.126162\pi\)
−0.922477 + 0.386052i \(0.873838\pi\)
\(440\) −3.22755 + 1.86343i −0.153867 + 0.0888353i
\(441\) 20.4889 4.60509i 0.975660 0.219290i
\(442\) −20.3351 + 2.63740i −0.967241 + 0.125448i
\(443\) −10.8594 6.26970i −0.515948 0.297883i 0.219327 0.975651i \(-0.429614\pi\)
−0.735275 + 0.677769i \(0.762947\pi\)
\(444\) −1.84938 + 7.06818i −0.0877677 + 0.335441i
\(445\) 3.50938 6.07842i 0.166360 0.288145i
\(446\) −4.91509 8.51319i −0.232736 0.403111i
\(447\) 2.20581 + 8.04248i 0.104331 + 0.380396i
\(448\) −2.47008 + 0.947995i −0.116700 + 0.0447885i
\(449\) −8.48307 + 14.6931i −0.400341 + 0.693411i −0.993767 0.111478i \(-0.964442\pi\)
0.593426 + 0.804888i \(0.297775\pi\)
\(450\) −0.0600175 5.09678i −0.00282925 0.240265i
\(451\) 0.940760i 0.0442986i
\(452\) −14.4435 8.33897i −0.679366 0.392232i
\(453\) −2.38337 + 0.653685i −0.111980 + 0.0307128i
\(454\) 11.3725i 0.533739i
\(455\) 17.3248 + 0.488106i 0.812199 + 0.0228828i
\(456\) −0.730041 2.66176i −0.0341873 0.124649i
\(457\) 9.47441i 0.443194i 0.975138 + 0.221597i \(0.0711270\pi\)
−0.975138 + 0.221597i \(0.928873\pi\)
\(458\) −9.48968 + 16.4366i −0.443424 + 0.768032i
\(459\) 21.2618 + 20.5237i 0.992416 + 0.957964i
\(460\) 7.93928 13.7512i 0.370171 0.641155i
\(461\) −31.5250 18.2010i −1.46827 0.847703i −0.468898 0.883253i \(-0.655349\pi\)
−0.999368 + 0.0355490i \(0.988682\pi\)
\(462\) 3.77329 8.60953i 0.175549 0.400551i
\(463\) 17.8517i 0.829638i −0.909904 0.414819i \(-0.863845\pi\)
0.909904 0.414819i \(-0.136155\pi\)
\(464\) 0.724381 0.418222i 0.0336286 0.0194155i
\(465\) 6.33270 24.2030i 0.293672 1.12239i
\(466\) 18.2307 + 10.5255i 0.844522 + 0.487585i
\(467\) 15.1928 26.3147i 0.703039 1.21770i −0.264355 0.964425i \(-0.585159\pi\)
0.967394 0.253274i \(-0.0815075\pi\)
\(468\) −10.0336 4.04070i −0.463803 0.186781i
\(469\) 13.4712 + 2.13450i 0.622040 + 0.0985622i
\(470\) −2.04295 3.53850i −0.0942343 0.163219i
\(471\) 13.7781 3.77892i 0.634862 0.174123i
\(472\) 2.19150i 0.100872i
\(473\) 1.71488 + 2.97027i 0.0788505 + 0.136573i
\(474\) −8.97398 + 9.08027i −0.412188 + 0.417071i
\(475\) −1.35373 + 2.34474i −0.0621136 + 0.107584i
\(476\) −14.0478 + 5.39141i −0.643879 + 0.247115i
\(477\) 1.72177 0.0202748i 0.0788345 0.000928322i
\(478\) 16.6885 0.763316
\(479\) −19.9492 11.5177i −0.911504 0.526257i −0.0305891 0.999532i \(-0.509738\pi\)
−0.880915 + 0.473275i \(0.843072\pi\)
\(480\) 2.23824 + 2.21204i 0.102161 + 0.100965i
\(481\) −1.95617 15.0826i −0.0891935 0.687706i
\(482\) 15.2747 0.695741
\(483\) 4.41824 + 39.8054i 0.201037 + 1.81121i
\(484\) 3.39615 + 5.88231i 0.154370 + 0.267378i
\(485\) −5.42553 + 3.13243i −0.246361 + 0.142236i
\(486\) 4.47603 + 14.9320i 0.203037 + 0.677330i
\(487\) 14.2075i 0.643804i −0.946773 0.321902i \(-0.895678\pi\)
0.946773 0.321902i \(-0.104322\pi\)
\(488\) −5.97394 + 3.44906i −0.270428 + 0.156132i
\(489\) −40.0065 + 10.9726i −1.80916 + 0.496197i
\(490\) 12.4404 2.64262i 0.562000 0.119382i
\(491\) 2.47085 1.42654i 0.111508 0.0643790i −0.443209 0.896418i \(-0.646160\pi\)
0.554717 + 0.832039i \(0.312827\pi\)
\(492\) 0.766068 0.210109i 0.0345370 0.00947245i
\(493\) 4.11968 2.37850i 0.185541 0.107122i
\(494\) 3.48889 + 4.56495i 0.156972 + 0.205387i
\(495\) −11.1798 + 0.131648i −0.502494 + 0.00591715i
\(496\) −3.97501 6.88493i −0.178483 0.309142i
\(497\) −3.51325 + 22.1726i −0.157591 + 0.994578i
\(498\) −6.60619 + 25.2483i −0.296030 + 1.13140i
\(499\) −15.9720 9.22146i −0.715007 0.412809i 0.0979055 0.995196i \(-0.468786\pi\)
−0.812912 + 0.582386i \(0.802119\pi\)
\(500\) 12.1712i 0.544312i
\(501\) 39.1443 10.7361i 1.74884 0.479652i
\(502\) 4.91975 8.52125i 0.219579 0.380322i
\(503\) 6.05432 10.4864i 0.269949 0.467565i −0.698900 0.715220i \(-0.746327\pi\)
0.968848 + 0.247655i \(0.0796599\pi\)
\(504\) −7.85354 1.14977i −0.349824 0.0512147i
\(505\) −15.2564 + 8.80830i −0.678902 + 0.391964i
\(506\) 15.5255 + 8.96363i 0.690191 + 0.398482i
\(507\) 22.5166 0.0459880i 0.999998 0.00204240i
\(508\) −10.6930 18.5208i −0.474426 0.821730i
\(509\) 36.9477i 1.63768i −0.574023 0.818839i \(-0.694618\pi\)
0.574023 0.818839i \(-0.305382\pi\)
\(510\) 12.7293 + 12.5803i 0.563662 + 0.557064i
\(511\) −21.0435 17.0430i −0.930912 0.753936i
\(512\) 1.00000 0.0441942
\(513\) 2.00148 8.03465i 0.0883674 0.354739i
\(514\) 1.53233 0.0675883
\(515\) 8.48219 + 14.6916i 0.373770 + 0.647388i
\(516\) 2.03571 2.05982i 0.0896172 0.0906787i
\(517\) 3.99504 2.30654i 0.175702 0.101441i
\(518\) −3.99882 10.4193i −0.175698 0.457797i
\(519\) 3.48449 + 12.7046i 0.152952 + 0.557672i
\(520\) −6.04728 2.51850i −0.265191 0.110443i
\(521\) −9.03063 15.6415i −0.395639 0.685267i 0.597543 0.801837i \(-0.296144\pi\)
−0.993183 + 0.116569i \(0.962810\pi\)
\(522\) 2.50916 0.0295467i 0.109823 0.00129323i
\(523\) 39.5905i 1.73117i 0.500762 + 0.865585i \(0.333053\pi\)
−0.500762 + 0.865585i \(0.666947\pi\)
\(524\) −7.44741 + 12.8993i −0.325342 + 0.563508i
\(525\) 4.61310 + 6.27225i 0.201332 + 0.273744i
\(526\) 16.9520 + 9.78724i 0.739142 + 0.426744i
\(527\) −22.6066 39.1558i −0.984759 1.70565i
\(528\) −2.49744 + 2.52703i −0.108687 + 0.109975i
\(529\) −53.3806 −2.32089
\(530\) 1.04281 0.0452967
\(531\) −3.21997 + 5.73198i −0.139735 + 0.248747i
\(532\) 3.27633 + 2.65347i 0.142047 + 0.115042i
\(533\) −1.31381 + 1.00412i −0.0569076 + 0.0434932i
\(534\) 1.69372 6.47324i 0.0732943 0.280125i
\(535\) 9.72559 16.8452i 0.420474 0.728283i
\(536\) −4.46448 2.57757i −0.192836 0.111334i
\(537\) −22.6686 22.4032i −0.978223 0.966771i
\(538\) 13.5580 0.584527
\(539\) 2.98358 + 14.0455i 0.128512 + 0.604982i
\(540\) 2.60409 + 9.07439i 0.112062 + 0.390499i
\(541\) −21.7849 12.5775i −0.936606 0.540750i −0.0477116 0.998861i \(-0.515193\pi\)
−0.888895 + 0.458111i \(0.848526\pi\)
\(542\) −28.0556 −1.20509
\(543\) 0.0836693 0.319777i 0.00359059 0.0137229i
\(544\) 5.68717 0.243836
\(545\) −9.02906 −0.386762
\(546\) 16.0510 3.91980i 0.686920 0.167752i
\(547\) 9.83208 0.420389 0.210195 0.977660i \(-0.432590\pi\)
0.210195 + 0.977660i \(0.432590\pi\)
\(548\) −11.6043 −0.495712
\(549\) −20.6929 + 0.243671i −0.883152 + 0.0103996i
\(550\) 3.48520 0.148609
\(551\) −1.15432 0.666446i −0.0491756 0.0283916i
\(552\) 3.83170 14.6444i 0.163088 0.623309i
\(553\) 3.05188 19.2609i 0.129779 0.819055i
\(554\) 23.3285 0.991131
\(555\) −9.33081 + 9.44133i −0.396071 + 0.400762i
\(556\) 13.6556 + 7.88408i 0.579127 + 0.334359i
\(557\) 2.73252 4.73287i 0.115781 0.200538i −0.802311 0.596906i \(-0.796396\pi\)
0.918092 + 0.396368i \(0.129730\pi\)
\(558\) −0.280829 23.8484i −0.0118884 1.00958i
\(559\) −2.31774 + 5.56522i −0.0980298 + 0.235384i
\(560\) −4.74771 0.752275i −0.200627 0.0317894i
\(561\) −14.2034 + 14.3716i −0.599668 + 0.606771i
\(562\) 26.6302 1.12333
\(563\) 25.5357 1.07620 0.538101 0.842880i \(-0.319142\pi\)
0.538101 + 0.842880i \(0.319142\pi\)
\(564\) −2.77049 2.73805i −0.116658 0.115293i
\(565\) −15.1507 26.2417i −0.637394 1.10400i
\(566\) −23.3128 13.4597i −0.979910 0.565752i
\(567\) −18.8520 14.5465i −0.791711 0.610896i
\(568\) 4.24250 7.34823i 0.178012 0.308325i
\(569\) 16.5159i 0.692384i −0.938164 0.346192i \(-0.887475\pi\)
0.938164 0.346192i \(-0.112525\pi\)
\(570\) 1.26934 4.85132i 0.0531669 0.203199i
\(571\) −1.84946 3.20337i −0.0773977 0.134057i 0.824729 0.565529i \(-0.191328\pi\)
−0.902126 + 0.431472i \(0.857994\pi\)
\(572\) 2.84344 6.82751i 0.118890 0.285473i
\(573\) −8.67989 + 2.38063i −0.362608 + 0.0994522i
\(574\) −0.763680 + 0.942943i −0.0318754 + 0.0393577i
\(575\) −12.8596 + 7.42449i −0.536282 + 0.309623i
\(576\) 2.61556 + 1.46930i 0.108982 + 0.0612210i
\(577\) −4.25571 7.37111i −0.177168 0.306863i 0.763742 0.645522i \(-0.223360\pi\)
−0.940909 + 0.338659i \(0.890027\pi\)
\(578\) 15.3439 0.638224
\(579\) 13.5661 + 13.4073i 0.563787 + 0.557188i
\(580\) 1.51969 0.0631019
\(581\) −14.2842 37.2188i −0.592609 1.54409i
\(582\) −4.19822 + 4.24795i −0.174022 + 0.176083i
\(583\) 1.17735i 0.0487610i
\(584\) 5.11752 + 8.86381i 0.211765 + 0.366787i
\(585\) −12.1166 15.4726i −0.500959 0.639712i
\(586\) 6.97220 + 4.02540i 0.288019 + 0.166288i
\(587\) −5.89064 + 3.40096i −0.243133 + 0.140373i −0.616616 0.787264i \(-0.711497\pi\)
0.373483 + 0.927637i \(0.378163\pi\)
\(588\) 10.7710 5.56647i 0.444188 0.229557i
\(589\) −6.33428 + 10.9713i −0.260999 + 0.452064i
\(590\) −1.99081 + 3.44819i −0.0819604 + 0.141960i
\(591\) −10.2010 37.1935i −0.419615 1.52994i
\(592\) 4.21819i 0.173366i
\(593\) −6.06317 3.50057i −0.248984 0.143751i 0.370315 0.928906i \(-0.379250\pi\)
−0.619299 + 0.785155i \(0.712583\pi\)
\(594\) −10.2452 + 2.94008i −0.420365 + 0.120633i
\(595\) −27.0011 4.27832i −1.10694 0.175394i
\(596\) 2.40740 + 4.16974i 0.0986111 + 0.170799i
\(597\) −8.37163 + 31.9957i −0.342628 + 1.30950i
\(598\) 4.05295 + 31.2493i 0.165737 + 1.27788i
\(599\) −36.0831 + 20.8326i −1.47432 + 0.851197i −0.999581 0.0289321i \(-0.990789\pi\)
−0.474735 + 0.880129i \(0.657456\pi\)
\(600\) −0.778384 2.83803i −0.0317774 0.115862i
\(601\) 1.93484 1.11708i 0.0789239 0.0455668i −0.460019 0.887909i \(-0.652157\pi\)
0.538943 + 0.842342i \(0.318824\pi\)
\(602\) −0.692308 + 4.36925i −0.0282164 + 0.178077i
\(603\) −7.88987 13.3015i −0.321301 0.541677i
\(604\) −1.23569 + 0.713427i −0.0502796 + 0.0290289i
\(605\) 12.3406i 0.501717i
\(606\) −11.8053 + 11.9451i −0.479556 + 0.485237i
\(607\) −0.586288 + 0.338493i −0.0237967 + 0.0137390i −0.511851 0.859074i \(-0.671040\pi\)
0.488054 + 0.872813i \(0.337707\pi\)
\(608\) −0.796762 1.38003i −0.0323129 0.0559677i
\(609\) −3.08784 + 2.27104i −0.125126 + 0.0920272i
\(610\) −12.5329 −0.507441
\(611\) 7.48529 + 3.11738i 0.302822 + 0.126116i
\(612\) 14.8751 + 8.35619i 0.601292 + 0.337779i
\(613\) 6.34919 + 3.66571i 0.256441 + 0.148057i 0.622710 0.782453i \(-0.286032\pi\)
−0.366269 + 0.930509i \(0.619365\pi\)
\(614\) 13.6194 0.549634
\(615\) 1.39623 + 0.365323i 0.0563015 + 0.0147312i
\(616\) 0.849335 5.36027i 0.0342207 0.215972i
\(617\) 22.6183 39.1761i 0.910579 1.57717i 0.0973311 0.995252i \(-0.468969\pi\)
0.813248 0.581917i \(-0.197697\pi\)
\(618\) 11.5029 + 11.3682i 0.462713 + 0.457296i
\(619\) 5.37271 + 9.30581i 0.215948 + 0.374032i 0.953565 0.301186i \(-0.0973826\pi\)
−0.737618 + 0.675219i \(0.764049\pi\)
\(620\) 14.4440i 0.580086i
\(621\) 31.5392 32.6735i 1.26562 1.31114i
\(622\) 12.6742 + 21.9523i 0.508187 + 0.880206i
\(623\) 3.66223 + 9.54227i 0.146724 + 0.382303i
\(624\) −6.19475 0.790580i −0.247989 0.0316485i
\(625\) 6.80901 11.7935i 0.272360 0.471742i
\(626\) −7.41295 4.27987i −0.296281 0.171058i
\(627\) 5.47724 + 1.43311i 0.218740 + 0.0572331i
\(628\) 7.14347 4.12428i 0.285055 0.164577i
\(629\) 23.9896i 0.956527i
\(630\) −11.3126 8.94345i −0.450705 0.356316i
\(631\) 15.7277 + 9.08038i 0.626109 + 0.361484i 0.779244 0.626721i \(-0.215603\pi\)
−0.153135 + 0.988205i \(0.548937\pi\)
\(632\) −3.68537 + 6.38325i −0.146596 + 0.253912i
\(633\) −7.15193 26.0763i −0.284264 1.03644i
\(634\) −11.7752 + 20.3952i −0.467652 + 0.809998i
\(635\) 38.8553i 1.54192i
\(636\) 0.958729 0.262950i 0.0380161 0.0104266i
\(637\) −16.4306 + 19.1581i −0.651006 + 0.759073i
\(638\) 1.71577i 0.0679279i
\(639\) 21.8933 12.9862i 0.866086 0.513726i
\(640\) 1.57344 + 0.908426i 0.0621957 + 0.0359087i
\(641\) 14.4746i 0.571714i 0.958272 + 0.285857i \(0.0922782\pi\)
−0.958272 + 0.285857i \(0.907722\pi\)
\(642\) 4.69382 17.9394i 0.185250 0.708012i
\(643\) 6.24408 10.8151i 0.246243 0.426505i −0.716238 0.697856i \(-0.754137\pi\)
0.962480 + 0.271352i \(0.0874707\pi\)
\(644\) 8.28509 + 21.5875i 0.326478 + 0.850668i
\(645\) 5.07427 1.39172i 0.199799 0.0547988i
\(646\) −4.53132 7.84848i −0.178282 0.308794i
\(647\) −16.1151 + 27.9122i −0.633550 + 1.09734i 0.353271 + 0.935521i \(0.385069\pi\)
−0.986820 + 0.161819i \(0.948264\pi\)
\(648\) 4.68229 + 7.68610i 0.183938 + 0.301939i
\(649\) −3.89308 2.24767i −0.152817 0.0882288i
\(650\) 3.71992 + 4.86724i 0.145907 + 0.190909i
\(651\) 21.5852 + 29.3486i 0.845992 + 1.15026i
\(652\) −20.7420 + 11.9754i −0.812319 + 0.468992i
\(653\) 36.7354i 1.43757i −0.695234 0.718783i \(-0.744699\pi\)
0.695234 0.718783i \(-0.255301\pi\)
\(654\) −8.30107 + 2.27673i −0.324597 + 0.0890271i
\(655\) −23.4361 + 13.5309i −0.915725 + 0.528694i
\(656\) 0.397180 0.229312i 0.0155073 0.00895312i
\(657\) 0.361545 + 30.7030i 0.0141052 + 1.19784i
\(658\) 5.87669 + 0.931162i 0.229097 + 0.0363005i
\(659\) 39.7060 + 22.9243i 1.54673 + 0.893003i 0.998389 + 0.0567462i \(0.0180726\pi\)
0.548338 + 0.836257i \(0.315261\pi\)
\(660\) −6.22520 + 1.70738i −0.242316 + 0.0664598i
\(661\) −7.51367 + 13.0141i −0.292248 + 0.506188i −0.974341 0.225077i \(-0.927737\pi\)
0.682093 + 0.731265i \(0.261070\pi\)
\(662\) 6.15849 3.55561i 0.239356 0.138193i
\(663\) −35.2306 4.49617i −1.36824 0.174617i
\(664\) 15.0678i 0.584745i
\(665\) 2.74463 + 7.15138i 0.106432 + 0.277318i
\(666\) −6.19780 + 11.0329i −0.240160 + 0.427517i
\(667\) −3.65509 6.33080i −0.141526 0.245130i
\(668\) 20.2949 11.7173i 0.785234 0.453355i
\(669\) −4.50350 16.4200i −0.174115 0.634833i
\(670\) −4.68306 8.11130i −0.180923 0.313367i
\(671\) 14.1499i 0.546250i
\(672\) −4.55461 + 0.505542i −0.175698 + 0.0195017i
\(673\) −13.8713 24.0258i −0.534700 0.926127i −0.999178 0.0405428i \(-0.987091\pi\)
0.464478 0.885585i \(-0.346242\pi\)
\(674\) 19.1187 0.736423
\(675\) 2.13401 8.56670i 0.0821383 0.329733i
\(676\) 12.5699 3.31634i 0.483457 0.127552i
\(677\) −0.275329 + 0.476883i −0.0105817 + 0.0183281i −0.871268 0.490808i \(-0.836702\pi\)
0.860686 + 0.509136i \(0.170035\pi\)
\(678\) −20.5461 20.3056i −0.789069 0.779832i
\(679\) 1.42774 9.01065i 0.0547915 0.345797i
\(680\) 8.94843 + 5.16638i 0.343157 + 0.198122i
\(681\) −4.98606 + 19.0563i −0.191066 + 0.730239i
\(682\) 16.3076 0.624452
\(683\) −36.3756 −1.39188 −0.695938 0.718102i \(-0.745011\pi\)
−0.695938 + 0.718102i \(0.745011\pi\)
\(684\) −0.0562900 4.78024i −0.00215230 0.182777i
\(685\) −18.2587 10.5417i −0.697629 0.402776i
\(686\) −8.41119 + 16.5001i −0.321141 + 0.629975i
\(687\) −23.1076 + 23.3813i −0.881610 + 0.892053i
\(688\) 0.836012 1.44802i 0.0318727 0.0552051i
\(689\) −1.64423 + 1.25665i −0.0626401 + 0.0478744i
\(690\) 19.3324 19.5613i 0.735970 0.744688i
\(691\) 32.3519 1.23073 0.615363 0.788244i \(-0.289010\pi\)
0.615363 + 0.788244i \(0.289010\pi\)
\(692\) 3.80295 + 6.58691i 0.144567 + 0.250397i
\(693\) 10.0974 12.7722i 0.383567 0.485175i
\(694\) 23.0701i 0.875728i
\(695\) 14.3242 + 24.8103i 0.543348 + 0.941107i
\(696\) 1.39717 0.383200i 0.0529594 0.0145251i
\(697\) 2.25883 1.30414i 0.0855593 0.0493977i
\(698\) 2.11359 + 3.66085i 0.0800007 + 0.138565i
\(699\) 25.9335 + 25.6299i 0.980895 + 0.969412i
\(700\) 3.49329 + 2.82918i 0.132034 + 0.106933i
\(701\) 13.2279i 0.499612i 0.968296 + 0.249806i \(0.0803669\pi\)
−0.968296 + 0.249806i \(0.919633\pi\)
\(702\) −15.0411 11.1698i −0.567691 0.421576i
\(703\) 5.82123 3.36089i 0.219552 0.126758i
\(704\) −1.02563 + 1.77645i −0.0386550 + 0.0669525i
\(705\) −1.87187 6.82495i −0.0704989 0.257042i
\(706\) 27.6603 + 15.9697i 1.04101 + 0.601028i
\(707\) 4.01476 25.3377i 0.150990 0.952922i
\(708\) −0.960817 + 3.67216i −0.0361097 + 0.138008i
\(709\) 23.6162 13.6348i 0.886926 0.512067i 0.0139902 0.999902i \(-0.495547\pi\)
0.872936 + 0.487835i \(0.162213\pi\)
\(710\) 13.3507 7.70801i 0.501041 0.289276i
\(711\) −19.0182 + 11.2808i −0.713240 + 0.423064i
\(712\) 3.86314i 0.144777i
\(713\) −60.1715 + 34.7400i −2.25344 + 1.30102i
\(714\) −25.9028 + 2.87511i −0.969389 + 0.107598i
\(715\) 10.6763 8.15963i 0.399270 0.305153i
\(716\) −15.9356 9.20041i −0.595541 0.343836i
\(717\) 27.9640 + 7.31676i 1.04434 + 0.273249i
\(718\) −12.2496 + 21.2169i −0.457151 + 0.791808i
\(719\) −7.69041 13.3202i −0.286804 0.496759i 0.686241 0.727374i \(-0.259259\pi\)
−0.973045 + 0.230615i \(0.925926\pi\)
\(720\) 2.78067 + 4.68791i 0.103629 + 0.174708i
\(721\) −24.3996 3.86611i −0.908688 0.143982i
\(722\) 8.23034 14.2554i 0.306302 0.530530i
\(723\) 25.5949 + 6.69687i 0.951883 + 0.249059i
\(724\) 0.190838i 0.00709245i
\(725\) −1.23076 0.710578i −0.0457092 0.0263902i
\(726\) 3.11176 + 11.3456i 0.115488 + 0.421075i
\(727\) 34.8309i 1.29181i −0.763420 0.645903i \(-0.776481\pi\)
0.763420 0.645903i \(-0.223519\pi\)
\(728\) 8.39241 4.53514i 0.311043 0.168084i
\(729\) 0.953579 + 26.9832i 0.0353177 + 0.999376i
\(730\) 18.5956i 0.688253i
\(731\) 4.75455 8.23511i 0.175853 0.304587i
\(732\) −11.5224 + 3.16023i −0.425879 + 0.116806i
\(733\) 9.43951 16.3497i 0.348656 0.603890i −0.637355 0.770570i \(-0.719971\pi\)
0.986011 + 0.166680i \(0.0533048\pi\)
\(734\) −28.7618 16.6056i −1.06162 0.612925i
\(735\) 22.0043 + 1.02615i 0.811639 + 0.0378500i
\(736\) 8.73960i 0.322146i
\(737\) 9.15784 5.28728i 0.337333 0.194760i
\(738\) 1.37578 0.0162005i 0.0506430 0.000596350i
\(739\) 6.89197 + 3.97908i 0.253525 + 0.146373i 0.621377 0.783511i \(-0.286573\pi\)
−0.367852 + 0.929884i \(0.619907\pi\)
\(740\) −3.83191 + 6.63707i −0.140864 + 0.243984i
\(741\) 3.84472 + 9.17886i 0.141239 + 0.337194i
\(742\) −0.955740 + 1.18009i −0.0350863 + 0.0433223i
\(743\) 9.17025 + 15.8833i 0.336424 + 0.582703i 0.983757 0.179504i \(-0.0574492\pi\)
−0.647334 + 0.762207i \(0.724116\pi\)
\(744\) −3.64215 13.2794i −0.133528 0.486848i
\(745\) 8.74779i 0.320494i
\(746\) 2.06003 + 3.56807i 0.0754230 + 0.130636i
\(747\) −22.1392 + 39.4108i −0.810032 + 1.44196i
\(748\) −5.83296 + 10.1030i −0.213274 + 0.369401i
\(749\) 10.1492 + 26.4446i 0.370844 + 0.966266i
\(750\) 5.33621 20.3946i 0.194851 0.744704i
\(751\) −13.7928 −0.503307 −0.251654 0.967817i \(-0.580974\pi\)
−0.251654 + 0.967817i \(0.580974\pi\)
\(752\) −1.94760 1.12445i −0.0710215 0.0410043i
\(753\) 11.9797 12.1216i 0.436565 0.441736i
\(754\) −2.39615 + 1.83132i −0.0872627 + 0.0666929i
\(755\) −2.59238 −0.0943465
\(756\) −12.6556 5.36983i −0.460281 0.195299i
\(757\) 21.2683 + 36.8378i 0.773010 + 1.33889i 0.935906 + 0.352249i \(0.114583\pi\)
−0.162896 + 0.986643i \(0.552084\pi\)
\(758\) −2.80001 + 1.61659i −0.101701 + 0.0587171i
\(759\) 22.0852 + 21.8267i 0.801642 + 0.792258i
\(760\) 2.89520i 0.105020i
\(761\) −27.9822 + 16.1555i −1.01435 + 0.585638i −0.912464 0.409157i \(-0.865823\pi\)
−0.101891 + 0.994796i \(0.532489\pi\)
\(762\) −9.79758 35.7225i −0.354929 1.29409i
\(763\) 8.27519 10.2177i 0.299582 0.369904i
\(764\) −4.50022 + 2.59820i −0.162812 + 0.0939997i
\(765\) 15.8142 + 26.6609i 0.571762 + 0.963928i
\(766\) −3.61672 + 2.08811i −0.130677 + 0.0754465i
\(767\) −1.01630 7.83592i −0.0366963 0.282939i
\(768\) 1.67564 + 0.438430i 0.0604646 + 0.0158205i
\(769\) 6.20736 + 10.7515i 0.223843 + 0.387707i 0.955972 0.293459i \(-0.0948064\pi\)
−0.732129 + 0.681166i \(0.761473\pi\)
\(770\) 6.20579 7.66251i 0.223641 0.276138i
\(771\) 2.56764 + 0.671821i 0.0924714 + 0.0241950i
\(772\) 9.53669 + 5.50601i 0.343233 + 0.198166i
\(773\) 12.5201i 0.450318i −0.974322 0.225159i \(-0.927710\pi\)
0.974322 0.225159i \(-0.0722901\pi\)
\(774\) 4.31421 2.55901i 0.155071 0.0919818i
\(775\) −6.75373 + 11.6978i −0.242601 + 0.420197i
\(776\) −1.72410 + 2.98622i −0.0618915 + 0.107199i
\(777\) −2.13247 19.2122i −0.0765020 0.689233i
\(778\) −3.57665 + 2.06498i −0.128229 + 0.0740331i
\(779\) −0.632915 0.365414i −0.0226765 0.0130923i
\(780\) −9.02890 6.87141i −0.323286 0.246036i
\(781\) 8.70251 + 15.0732i 0.311400 + 0.539361i
\(782\) 49.7036i 1.77740i
\(783\) 4.21740 + 1.05058i 0.150718 + 0.0375447i
\(784\) 5.20261 4.68325i 0.185808 0.167259i
\(785\) 14.9864 0.534889
\(786\) −18.1346 + 18.3494i −0.646841 + 0.654503i
\(787\) 39.3805 1.40376 0.701882 0.712294i \(-0.252344\pi\)
0.701882 + 0.712294i \(0.252344\pi\)
\(788\) −11.1333 19.2835i −0.396609 0.686947i
\(789\) 24.1145 + 23.8322i 0.858498 + 0.848448i
\(790\) −11.5974 + 6.69578i −0.412618 + 0.238225i
\(791\) 43.5820 + 6.90556i 1.54960 + 0.245533i
\(792\) −5.29275 + 3.13944i −0.188070 + 0.111555i
\(793\) 19.7610 15.1029i 0.701733 0.536318i
\(794\) 2.38133 + 4.12458i 0.0845101 + 0.146376i
\(795\) 1.74737 + 0.457198i 0.0619730 + 0.0162152i
\(796\) 19.0946i 0.676789i
\(797\) 15.1983 26.3242i 0.538350 0.932449i −0.460643 0.887585i \(-0.652381\pi\)
0.998993 0.0448640i \(-0.0142855\pi\)
\(798\) 4.32660 + 5.88270i 0.153160 + 0.208245i
\(799\) −11.0763 6.39492i −0.391852 0.226236i
\(800\) −0.849523 1.47142i −0.0300352 0.0520224i
\(801\) 5.67613 10.1043i 0.200556 0.357017i
\(802\) 15.4809 0.546650
\(803\) −20.9948 −0.740891
\(804\) −6.35079 6.27645i −0.223975 0.221353i
\(805\) −6.57458 + 41.4931i −0.231723 + 1.46244i
\(806\) 17.4059 + 22.7744i 0.613098 + 0.802193i
\(807\) 22.7184 + 5.94424i 0.799725 + 0.209247i
\(808\) −4.84811 + 8.39717i −0.170556 + 0.295412i
\(809\) 14.1316 + 8.15889i 0.496841 + 0.286851i 0.727408 0.686205i \(-0.240725\pi\)
−0.230567 + 0.973056i \(0.574058\pi\)
\(810\) 0.385047 + 16.3471i 0.0135292 + 0.574380i
\(811\) −5.92788 −0.208156 −0.104078 0.994569i \(-0.533189\pi\)
−0.104078 + 0.994569i \(0.533189\pi\)
\(812\) −1.39281 + 1.71975i −0.0488780 + 0.0603514i
\(813\) −47.0111 12.3004i −1.64875 0.431394i
\(814\) −7.49340 4.32632i −0.262644 0.151637i
\(815\) −43.5150 −1.52427
\(816\) 9.52967 + 2.49343i 0.333605 + 0.0872874i
\(817\) −2.66441 −0.0932159
\(818\) −39.7884 −1.39117
\(819\) 28.6143 + 0.469071i 0.999866 + 0.0163907i
\(820\) 0.833252 0.0290984
\(821\) −33.2585 −1.16073 −0.580364 0.814357i \(-0.697090\pi\)
−0.580364 + 0.814357i \(0.697090\pi\)
\(822\) −19.4447 5.08768i −0.678211 0.177453i
\(823\) 3.16826 0.110439 0.0552193 0.998474i \(-0.482414\pi\)
0.0552193 + 0.998474i \(0.482414\pi\)
\(824\) 8.08628 + 4.66861i 0.281699 + 0.162639i
\(825\) 5.83995 + 1.52801i 0.203321 + 0.0531987i
\(826\) −2.07753 5.41317i −0.0722864 0.188348i
\(827\) 24.0773 0.837250 0.418625 0.908159i \(-0.362512\pi\)
0.418625 + 0.908159i \(0.362512\pi\)
\(828\) 12.8411 22.8589i 0.446260 0.794403i
\(829\) 30.2946 + 17.4906i 1.05218 + 0.607474i 0.923258 0.384182i \(-0.125516\pi\)
0.128918 + 0.991655i \(0.458850\pi\)
\(830\) −13.6880 + 23.7083i −0.475118 + 0.822928i
\(831\) 39.0902 + 10.2279i 1.35602 + 0.354802i
\(832\) −3.57560 + 0.463745i −0.123962 + 0.0160775i
\(833\) 29.5882 26.6345i 1.02517 0.922829i
\(834\) 19.4253 + 19.1979i 0.672644 + 0.664770i
\(835\) 42.5772 1.47344
\(836\) 3.26874 0.113052
\(837\) 9.98530 40.0846i 0.345142 1.38553i
\(838\) 13.1146 + 22.7152i 0.453036 + 0.784682i
\(839\) 1.10165 + 0.636039i 0.0380332 + 0.0219585i 0.518896 0.854837i \(-0.326343\pi\)
−0.480863 + 0.876796i \(0.659676\pi\)
\(840\) −7.62565 3.34208i −0.263110 0.115313i
\(841\) −14.1502 + 24.5088i −0.487937 + 0.845132i
\(842\) 14.0343i 0.483653i
\(843\) 44.6226 + 11.6755i 1.53688 + 0.402124i
\(844\) −7.80557 13.5196i −0.268679 0.465365i
\(845\) 22.7906 + 6.20075i 0.784021 + 0.213312i
\(846\) −3.44190 5.80266i −0.118335 0.199500i
\(847\) −13.9652 11.3102i −0.479849 0.388625i
\(848\) 0.497067 0.286982i 0.0170694 0.00985500i
\(849\) −33.1628 32.7746i −1.13815 1.12482i
\(850\) −4.83138 8.36820i −0.165715 0.287027i
\(851\) 36.8653 1.26373
\(852\) 10.3306 10.4530i 0.353921 0.358113i
\(853\) −8.88125 −0.304088 −0.152044 0.988374i \(-0.548586\pi\)
−0.152044 + 0.988374i \(0.548586\pi\)
\(854\) 11.4864 14.1827i 0.393058 0.485323i
\(855\) 4.25393 7.57256i 0.145481 0.258976i
\(856\) 10.7060i 0.365923i
\(857\) −14.1680 24.5397i −0.483969 0.838259i 0.515861 0.856672i \(-0.327472\pi\)
−0.999830 + 0.0184131i \(0.994139\pi\)
\(858\) 7.75798 10.1938i 0.264853 0.348011i
\(859\) 15.6163 + 9.01607i 0.532821 + 0.307624i 0.742164 0.670218i \(-0.233799\pi\)
−0.209343 + 0.977842i \(0.567133\pi\)
\(860\) 2.63083 1.51891i 0.0897106 0.0517944i
\(861\) −1.69307 + 1.24522i −0.0576997 + 0.0424368i
\(862\) 8.06272 13.9650i 0.274617 0.475651i
\(863\) 20.8330 36.0838i 0.709163 1.22831i −0.256005 0.966675i \(-0.582406\pi\)
0.965168 0.261631i \(-0.0842603\pi\)
\(864\) 3.73855 + 3.60877i 0.127188 + 0.122773i
\(865\) 13.8188i 0.469854i
\(866\) −13.9038 8.02734i −0.472469 0.272780i
\(867\) 25.7110 + 6.72725i 0.873191 + 0.228469i
\(868\) 16.3455 + 13.2380i 0.554802 + 0.449328i
\(869\) −7.55968 13.0938i −0.256445 0.444175i
\(870\) 2.54647 + 0.666280i 0.0863333 + 0.0225890i
\(871\) 17.1585 + 7.14598i 0.581395 + 0.242132i
\(872\) −4.30381 + 2.48481i −0.145745 + 0.0841462i
\(873\) −8.89715 + 5.27742i −0.301123 + 0.178614i
\(874\) −12.0609 + 6.96338i −0.407967 + 0.235540i
\(875\) 11.5382 + 30.0638i 0.390063 + 1.01634i
\(876\) 4.68898 + 17.0963i 0.158426 + 0.577629i
\(877\) −32.0440 + 18.5006i −1.08205 + 0.624722i −0.931449 0.363873i \(-0.881454\pi\)
−0.150601 + 0.988595i \(0.548121\pi\)
\(878\) 16.1774i 0.545960i
\(879\) 9.91807 + 9.80196i 0.334528 + 0.330612i
\(880\) −3.22755 + 1.86343i −0.108801 + 0.0628161i
\(881\) −12.5417 21.7228i −0.422540 0.731861i 0.573647 0.819103i \(-0.305528\pi\)
−0.996187 + 0.0872416i \(0.972195\pi\)
\(882\) 20.4889 4.60509i 0.689896 0.155061i
\(883\) 23.5431 0.792287 0.396144 0.918189i \(-0.370348\pi\)
0.396144 + 0.918189i \(0.370348\pi\)
\(884\) −20.3351 + 2.63740i −0.683943 + 0.0887054i
\(885\) −4.84768 + 4.90510i −0.162953 + 0.164883i
\(886\) −10.8594 6.26970i −0.364830 0.210635i
\(887\) 29.4455 0.988682 0.494341 0.869268i \(-0.335409\pi\)
0.494341 + 0.869268i \(0.335409\pi\)
\(888\) −1.84938 + 7.06818i −0.0620611 + 0.237193i
\(889\) 43.9703 + 35.6111i 1.47472 + 1.19436i
\(890\) 3.50938 6.07842i 0.117635 0.203749i
\(891\) −18.4563 + 0.434727i −0.618309 + 0.0145639i
\(892\) −4.91509 8.51319i −0.164569 0.285043i
\(893\) 3.58366i 0.119923i
\(894\) 2.20581 + 8.04248i 0.0737732 + 0.268981i
\(895\) −16.7158 28.9526i −0.558748 0.967779i
\(896\) −2.47008 + 0.947995i −0.0825197 + 0.0316703i
\(897\) −6.90935 + 54.1397i −0.230697 + 1.80767i
\(898\) −8.48307 + 14.6931i −0.283084 + 0.490315i
\(899\) −5.75885 3.32487i −0.192068 0.110891i
\(900\) −0.0600175 5.09678i −0.00200058 0.169893i
\(901\) 2.82691 1.63212i 0.0941780 0.0543737i
\(902\) 0.940760i 0.0313239i
\(903\) −3.07567 + 7.01778i −0.102352 + 0.233537i
\(904\) −14.4435 8.33897i −0.480384 0.277350i
\(905\) 0.173363 0.300273i 0.00576277 0.00998141i
\(906\) −2.38337 + 0.653685i −0.0791821 + 0.0217172i
\(907\) −6.92697 + 11.9979i −0.230006 + 0.398383i −0.957810 0.287403i \(-0.907208\pi\)
0.727803 + 0.685786i \(0.240541\pi\)
\(908\) 11.3725i 0.377410i
\(909\) −25.0185 + 14.8399i −0.829812 + 0.492210i
\(910\) 17.3248 + 0.488106i 0.574311 + 0.0161806i
\(911\) 27.4426i 0.909213i 0.890692 + 0.454607i \(0.150220\pi\)
−0.890692 + 0.454607i \(0.849780\pi\)
\(912\) −0.730041 2.66176i −0.0241741 0.0881398i
\(913\) −26.7672 15.4541i −0.885866 0.511455i
\(914\) 9.47441i 0.313386i
\(915\) −21.0006 5.49478i −0.694259 0.181652i
\(916\) −9.48968 + 16.4366i −0.313548 + 0.543081i
\(917\) 6.16726 38.9224i 0.203661 1.28533i
\(918\) 21.2618 + 20.5237i 0.701744 + 0.677383i
\(919\) 22.0343 + 38.1646i 0.726845 + 1.25893i 0.958210 + 0.286066i \(0.0923476\pi\)
−0.231365 + 0.972867i \(0.574319\pi\)
\(920\) 7.93928 13.7512i 0.261750 0.453365i
\(921\) 22.8212 + 5.97115i 0.751986 + 0.196756i
\(922\) −31.5250 18.2010i −1.03822 0.599417i
\(923\) −11.7618 + 28.2418i −0.387144 + 0.929590i
\(924\) 3.77329 8.60953i 0.124132 0.283233i
\(925\) 6.20671 3.58345i 0.204075 0.117823i
\(926\) 17.8517i 0.586643i
\(927\) 14.2905 + 24.0922i 0.469362 + 0.791293i
\(928\) 0.724381 0.418222i 0.0237790 0.0137288i
\(929\) 36.2869 20.9503i 1.19053 0.687356i 0.232107 0.972690i \(-0.425438\pi\)
0.958428 + 0.285335i \(0.0921047\pi\)
\(930\) 6.33270 24.2030i 0.207657 0.793649i
\(931\) −10.6083 3.44834i −0.347672 0.113015i
\(932\) 18.2307 + 10.5255i 0.597167 + 0.344775i
\(933\) 11.6128 + 42.3409i 0.380187 + 1.38618i
\(934\) 15.1928 26.3147i 0.497124 0.861044i
\(935\) −18.3556 + 10.5976i −0.600293 + 0.346579i
\(936\) −10.0336 4.04070i −0.327958 0.132074i
\(937\) 1.71598i 0.0560586i 0.999607 + 0.0280293i \(0.00892317\pi\)
−0.999607 + 0.0280293i \(0.991077\pi\)
\(938\) 13.4712 + 2.13450i 0.439849 + 0.0696940i
\(939\) −10.5450 10.4216i −0.344124 0.340096i
\(940\) −2.04295 3.53850i −0.0666337 0.115413i
\(941\) −1.26611 + 0.730989i −0.0412740 + 0.0238296i −0.520495 0.853865i \(-0.674253\pi\)
0.479221 + 0.877694i \(0.340919\pi\)
\(942\) 13.7781 3.77892i 0.448915 0.123124i
\(943\) −2.00409 3.47119i −0.0652622 0.113038i
\(944\) 2.19150i 0.0713271i
\(945\) −15.0348 19.9458i −0.489082 0.648837i
\(946\) 1.71488 + 2.97027i 0.0557557 + 0.0965717i
\(947\) −15.2680 −0.496145 −0.248072 0.968742i \(-0.579797\pi\)
−0.248072 + 0.968742i \(0.579797\pi\)
\(948\) −8.97398 + 9.08027i −0.291461 + 0.294914i
\(949\) −22.4088 29.3202i −0.727420 0.951775i
\(950\) −1.35373 + 2.34474i −0.0439209 + 0.0760733i
\(951\) −28.6729 + 29.0125i −0.929782 + 0.940795i
\(952\) −14.0478 + 5.39141i −0.455291 + 0.174737i
\(953\) 20.0074 + 11.5513i 0.648104 + 0.374183i 0.787729 0.616021i \(-0.211257\pi\)
−0.139625 + 0.990204i \(0.544590\pi\)
\(954\) 1.72177 0.0202748i 0.0557444 0.000656422i
\(955\) −9.44111 −0.305507
\(956\) 16.6885 0.539746
\(957\) −0.752245 + 2.87502i −0.0243166 + 0.0929361i
\(958\) −19.9492 11.5177i −0.644530 0.372120i
\(959\) 28.6636 11.0008i 0.925596 0.355235i
\(960\) 2.23824 + 2.21204i 0.0722390 + 0.0713933i
\(961\) −16.1015 + 27.8886i −0.519402 + 0.899631i
\(962\) −1.95617 15.0826i −0.0630693 0.486282i
\(963\) 15.7303 28.0021i 0.506903 0.902355i
\(964\) 15.2747 0.491963
\(965\) 10.0036 + 17.3268i 0.322028 + 0.557768i
\(966\) 4.41824 + 39.8054i 0.142154 + 1.28072i
\(967\) 14.3674i 0.462026i −0.972951 0.231013i \(-0.925796\pi\)
0.972951 0.231013i \(-0.0742040\pi\)
\(968\) 3.39615 + 5.88231i 0.109156 + 0.189064i
\(969\) −4.15187 15.1379i −0.133377 0.486300i
\(970\) −5.42553 + 3.13243i −0.174203 + 0.100576i
\(971\) 15.6985 + 27.1905i 0.503788 + 0.872586i 0.999990 + 0.00437930i \(0.00139398\pi\)
−0.496203 + 0.868207i \(0.665273\pi\)
\(972\) 4.47603 + 14.9320i 0.143569 + 0.478945i
\(973\) −41.2046 6.52886i −1.32096 0.209306i
\(974\) 14.2075i 0.455238i
\(975\) 4.09931 + 9.78668i 0.131283 + 0.313425i
\(976\) −5.97394 + 3.44906i −0.191221 + 0.110402i
\(977\) 21.8776 37.8931i 0.699926 1.21231i −0.268566 0.963261i \(-0.586550\pi\)
0.968492 0.249046i \(-0.0801171\pi\)
\(978\) −40.0065 + 10.9726i −1.27927 + 0.350864i
\(979\) 6.86267 + 3.96217i 0.219332 + 0.126631i
\(980\) 12.4404 2.64262i 0.397394 0.0844155i
\(981\) −14.9078 + 0.175548i −0.475970 + 0.00560481i
\(982\) 2.47085 1.42654i 0.0788479 0.0455228i
\(983\) −3.21594 + 1.85672i −0.102572 + 0.0592202i −0.550409 0.834895i \(-0.685528\pi\)
0.447836 + 0.894116i \(0.352195\pi\)
\(984\) 0.766068 0.210109i 0.0244214 0.00669804i
\(985\) 40.4553i 1.28901i
\(986\) 4.11968 2.37850i 0.131197 0.0757469i
\(987\) 9.43899 + 4.13681i 0.300446 + 0.131676i
\(988\) 3.48889 + 4.56495i 0.110996 + 0.145230i
\(989\) −12.6551 7.30641i −0.402408 0.232330i
\(990\) −11.1798 + 0.131648i −0.355317 + 0.00418406i
\(991\) 21.0267 36.4192i 0.667934 1.15690i −0.310547 0.950558i \(-0.600512\pi\)
0.978481 0.206337i \(-0.0661544\pi\)
\(992\) −3.97501 6.88493i −0.126207 0.218597i
\(993\) 11.8783 3.25786i 0.376947 0.103385i
\(994\) −3.51325 + 22.1726i −0.111434 + 0.703273i
\(995\) −17.3460 + 30.0442i −0.549905 + 0.952464i
\(996\) −6.60619 + 25.2483i −0.209325 + 0.800023i
\(997\) 45.1553i 1.43008i −0.699083 0.715041i \(-0.746408\pi\)
0.699083 0.715041i \(-0.253592\pi\)
\(998\) −15.9720 9.22146i −0.505586 0.291900i
\(999\) −15.2225 + 15.7699i −0.481618 + 0.498938i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 546.2.bi.f.257.15 yes 34
3.2 odd 2 546.2.bi.e.257.14 yes 34
7.3 odd 6 546.2.bn.e.101.10 yes 34
13.4 even 6 546.2.bn.f.173.8 yes 34
21.17 even 6 546.2.bn.f.101.8 yes 34
39.17 odd 6 546.2.bn.e.173.10 yes 34
91.17 odd 6 546.2.bi.e.17.14 34
273.17 even 6 inner 546.2.bi.f.17.15 yes 34
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
546.2.bi.e.17.14 34 91.17 odd 6
546.2.bi.e.257.14 yes 34 3.2 odd 2
546.2.bi.f.17.15 yes 34 273.17 even 6 inner
546.2.bi.f.257.15 yes 34 1.1 even 1 trivial
546.2.bn.e.101.10 yes 34 7.3 odd 6
546.2.bn.e.173.10 yes 34 39.17 odd 6
546.2.bn.f.101.8 yes 34 21.17 even 6
546.2.bn.f.173.8 yes 34 13.4 even 6