Properties

Label 456.2.bk.a.253.17
Level $456$
Weight $2$
Character 456.253
Analytic conductor $3.641$
Analytic rank $0$
Dimension $240$
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] = [456,2,Mod(61,456)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(456, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 9, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("456.61");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 456.bk (of order \(18\), degree \(6\), 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: \(3.64117833217\)
Analytic rank: \(0\)
Dimension: \(240\)
Relative dimension: \(40\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 253.17
Character \(\chi\) \(=\) 456.253
Dual form 456.2.bk.a.301.17

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.378045 + 1.36275i) q^{2} +(0.342020 - 0.939693i) q^{3} +(-1.71416 - 1.03036i) q^{4} +(-2.71912 + 0.479454i) q^{5} +(1.15127 + 0.821333i) q^{6} +(-1.39493 + 2.41609i) q^{7} +(2.05215 - 1.94645i) q^{8} +(-0.766044 - 0.642788i) q^{9} +O(q^{10})\) \(q+(-0.378045 + 1.36275i) q^{2} +(0.342020 - 0.939693i) q^{3} +(-1.71416 - 1.03036i) q^{4} +(-2.71912 + 0.479454i) q^{5} +(1.15127 + 0.821333i) q^{6} +(-1.39493 + 2.41609i) q^{7} +(2.05215 - 1.94645i) q^{8} +(-0.766044 - 0.642788i) q^{9} +(0.374574 - 3.88673i) q^{10} +(5.27263 - 3.04415i) q^{11} +(-1.55450 + 1.25838i) q^{12} +(-0.786737 - 2.16154i) q^{13} +(-2.76518 - 2.81433i) q^{14} +(-0.479454 + 2.71912i) q^{15} +(1.87672 + 3.53241i) q^{16} +(2.16237 - 1.81444i) q^{17} +(1.16556 - 0.800923i) q^{18} +(-0.359711 - 4.34403i) q^{19} +(5.15503 + 1.97981i) q^{20} +(1.79329 + 2.13716i) q^{21} +(2.15512 + 8.33609i) q^{22} +(1.07942 - 6.12172i) q^{23} +(-1.12719 - 2.59412i) q^{24} +(2.46527 - 0.897283i) q^{25} +(3.24306 - 0.254965i) q^{26} +(-0.866025 + 0.500000i) q^{27} +(4.88058 - 2.70430i) q^{28} +(4.49931 - 5.36207i) q^{29} +(-3.52422 - 1.68132i) q^{30} +(-2.36156 + 4.09034i) q^{31} +(-5.52327 + 1.22208i) q^{32} +(-1.05722 - 5.99581i) q^{33} +(1.65516 + 3.63271i) q^{34} +(2.63458 - 7.23844i) q^{35} +(0.650824 + 1.89114i) q^{36} -8.19803i q^{37} +(6.05581 + 1.15204i) q^{38} -2.30027 q^{39} +(-4.64681 + 6.27654i) q^{40} +(0.915065 + 0.333056i) q^{41} +(-3.59035 + 1.63586i) q^{42} +(-9.76716 + 1.72221i) q^{43} +(-12.1747 - 0.214525i) q^{44} +(2.39115 + 1.38053i) q^{45} +(7.93429 + 3.78527i) q^{46} +(-1.90860 - 1.60150i) q^{47} +(3.96126 - 0.555382i) q^{48} +(-0.391662 - 0.678379i) q^{49} +(0.290790 + 3.69875i) q^{50} +(-0.965445 - 2.65254i) q^{51} +(-0.878570 + 4.51586i) q^{52} +(2.92483 + 0.515727i) q^{53} +(-0.353978 - 1.36920i) q^{54} +(-12.8774 + 10.8054i) q^{55} +(1.84019 + 7.67335i) q^{56} +(-4.20508 - 1.14773i) q^{57} +(5.60620 + 8.15852i) q^{58} +(4.93781 + 5.88465i) q^{59} +(3.62353 - 4.16701i) q^{60} +(5.77620 + 1.01850i) q^{61} +(-4.68133 - 4.76455i) q^{62} +(2.62161 - 0.954189i) q^{63} +(0.422652 - 7.98883i) q^{64} +(3.17559 + 5.50029i) q^{65} +(8.57046 + 0.825956i) q^{66} +(-1.91047 + 2.27681i) q^{67} +(-5.57619 + 0.882236i) q^{68} +(-5.38335 - 3.10808i) q^{69} +(8.86818 + 6.32672i) q^{70} +(0.854943 + 4.84862i) q^{71} +(-2.82319 + 0.171971i) q^{72} +(6.15912 + 2.24174i) q^{73} +(11.1719 + 3.09922i) q^{74} -2.62348i q^{75} +(-3.85931 + 7.81701i) q^{76} +16.9855i q^{77} +(0.869604 - 3.13468i) q^{78} +(1.75413 + 0.638451i) q^{79} +(-6.79665 - 8.70524i) q^{80} +(0.173648 + 0.984808i) q^{81} +(-0.799808 + 1.12109i) q^{82} +(-12.2921 - 7.09683i) q^{83} +(-0.871949 - 5.51117i) q^{84} +(-5.00980 + 5.97044i) q^{85} +(1.34548 - 13.9613i) q^{86} +(-3.49984 - 6.06190i) q^{87} +(4.89493 - 16.5100i) q^{88} +(-2.58398 + 0.940492i) q^{89} +(-2.78528 + 2.73664i) q^{90} +(6.31993 + 1.11437i) q^{91} +(-8.15788 + 9.38143i) q^{92} +(3.03596 + 3.61812i) q^{93} +(2.90398 - 1.99550i) q^{94} +(3.06086 + 11.6395i) q^{95} +(-0.740687 + 5.60815i) q^{96} +(-1.53526 + 1.28824i) q^{97} +(1.07253 - 0.277279i) q^{98} +(-5.99581 - 1.05722i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 240 q + 6 q^{4} + 6 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 240 q + 6 q^{4} + 6 q^{6} - 24 q^{10} + 18 q^{14} - 6 q^{16} + 60 q^{20} - 36 q^{28} - 72 q^{31} - 90 q^{32} + 66 q^{34} - 6 q^{36} + 72 q^{38} - 114 q^{40} - 60 q^{44} + 30 q^{46} + 72 q^{47} + 24 q^{48} - 120 q^{49} + 18 q^{50} + 6 q^{52} - 6 q^{54} + 72 q^{58} - 12 q^{60} + 12 q^{62} + 30 q^{64} - 48 q^{66} - 78 q^{68} - 108 q^{70} - 36 q^{72} - 24 q^{73} - 96 q^{74} - 48 q^{76} - 96 q^{78} - 114 q^{80} - 66 q^{82} - 36 q^{84} - 24 q^{86} - 24 q^{88} + 6 q^{90} - 108 q^{94} + 120 q^{95} - 12 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/456\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(229\) \(305\) \(343\)
\(\chi(n)\) \(e\left(\frac{7}{9}\right)\) \(-1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.378045 + 1.36275i −0.267318 + 0.963608i
\(3\) 0.342020 0.939693i 0.197465 0.542532i
\(4\) −1.71416 1.03036i −0.857082 0.515180i
\(5\) −2.71912 + 0.479454i −1.21603 + 0.214418i −0.744615 0.667495i \(-0.767367\pi\)
−0.471412 + 0.881913i \(0.656256\pi\)
\(6\) 1.15127 + 0.821333i 0.470002 + 0.335308i
\(7\) −1.39493 + 2.41609i −0.527234 + 0.913196i 0.472262 + 0.881458i \(0.343438\pi\)
−0.999496 + 0.0317382i \(0.989896\pi\)
\(8\) 2.05215 1.94645i 0.725545 0.688175i
\(9\) −0.766044 0.642788i −0.255348 0.214263i
\(10\) 0.374574 3.88673i 0.118451 1.22909i
\(11\) 5.27263 3.04415i 1.58976 0.917847i 0.596411 0.802679i \(-0.296593\pi\)
0.993346 0.115167i \(-0.0367404\pi\)
\(12\) −1.55450 + 1.25838i −0.448746 + 0.363264i
\(13\) −0.786737 2.16154i −0.218202 0.599504i 0.781501 0.623905i \(-0.214455\pi\)
−0.999702 + 0.0244003i \(0.992232\pi\)
\(14\) −2.76518 2.81433i −0.739024 0.752161i
\(15\) −0.479454 + 2.71912i −0.123794 + 0.702073i
\(16\) 1.87672 + 3.53241i 0.469179 + 0.883103i
\(17\) 2.16237 1.81444i 0.524452 0.440067i −0.341729 0.939799i \(-0.611012\pi\)
0.866180 + 0.499731i \(0.166568\pi\)
\(18\) 1.16556 0.800923i 0.274724 0.188779i
\(19\) −0.359711 4.34403i −0.0825234 0.996589i
\(20\) 5.15503 + 1.97981i 1.15270 + 0.442698i
\(21\) 1.79329 + 2.13716i 0.391328 + 0.466366i
\(22\) 2.15512 + 8.33609i 0.459474 + 1.77726i
\(23\) 1.07942 6.12172i 0.225075 1.27647i −0.637465 0.770479i \(-0.720017\pi\)
0.862541 0.505987i \(-0.168872\pi\)
\(24\) −1.12719 2.59412i −0.230087 0.529522i
\(25\) 2.46527 0.897283i 0.493053 0.179457i
\(26\) 3.24306 0.254965i 0.636017 0.0500027i
\(27\) −0.866025 + 0.500000i −0.166667 + 0.0962250i
\(28\) 4.88058 2.70430i 0.922343 0.511064i
\(29\) 4.49931 5.36207i 0.835500 0.995711i −0.164456 0.986384i \(-0.552587\pi\)
0.999957 0.00932617i \(-0.00296866\pi\)
\(30\) −3.52422 1.68132i −0.643431 0.306966i
\(31\) −2.36156 + 4.09034i −0.424149 + 0.734647i −0.996341 0.0854726i \(-0.972760\pi\)
0.572192 + 0.820120i \(0.306093\pi\)
\(32\) −5.52327 + 1.22208i −0.976385 + 0.216036i
\(33\) −1.05722 5.99581i −0.184039 1.04374i
\(34\) 1.65516 + 3.63271i 0.283857 + 0.623004i
\(35\) 2.63458 7.23844i 0.445325 1.22352i
\(36\) 0.650824 + 1.89114i 0.108471 + 0.315191i
\(37\) 8.19803i 1.34775i −0.738846 0.673874i \(-0.764629\pi\)
0.738846 0.673874i \(-0.235371\pi\)
\(38\) 6.05581 + 1.15204i 0.982382 + 0.186886i
\(39\) −2.30027 −0.368337
\(40\) −4.64681 + 6.27654i −0.734725 + 0.992409i
\(41\) 0.915065 + 0.333056i 0.142909 + 0.0520147i 0.412484 0.910965i \(-0.364661\pi\)
−0.269575 + 0.962979i \(0.586883\pi\)
\(42\) −3.59035 + 1.63586i −0.554003 + 0.252418i
\(43\) −9.76716 + 1.72221i −1.48948 + 0.262635i −0.858359 0.513050i \(-0.828515\pi\)
−0.631120 + 0.775685i \(0.717404\pi\)
\(44\) −12.1747 0.214525i −1.83541 0.0323408i
\(45\) 2.39115 + 1.38053i 0.356452 + 0.205798i
\(46\) 7.93429 + 3.78527i 1.16985 + 0.558107i
\(47\) −1.90860 1.60150i −0.278398 0.233603i 0.492888 0.870093i \(-0.335941\pi\)
−0.771285 + 0.636490i \(0.780386\pi\)
\(48\) 3.96126 0.555382i 0.571758 0.0801625i
\(49\) −0.391662 0.678379i −0.0559518 0.0969113i
\(50\) 0.290790 + 3.69875i 0.0411239 + 0.523082i
\(51\) −0.965445 2.65254i −0.135189 0.371430i
\(52\) −0.878570 + 4.51586i −0.121836 + 0.626238i
\(53\) 2.92483 + 0.515727i 0.401756 + 0.0708405i 0.370876 0.928683i \(-0.379058\pi\)
0.0308809 + 0.999523i \(0.490169\pi\)
\(54\) −0.353978 1.36920i −0.0481702 0.186324i
\(55\) −12.8774 + 10.8054i −1.73638 + 1.45700i
\(56\) 1.84019 + 7.67335i 0.245906 + 1.02539i
\(57\) −4.20508 1.14773i −0.556977 0.152020i
\(58\) 5.60620 + 8.15852i 0.736131 + 1.07127i
\(59\) 4.93781 + 5.88465i 0.642848 + 0.766116i 0.984817 0.173595i \(-0.0555384\pi\)
−0.341969 + 0.939711i \(0.611094\pi\)
\(60\) 3.62353 4.16701i 0.467796 0.537958i
\(61\) 5.77620 + 1.01850i 0.739567 + 0.130406i 0.530725 0.847544i \(-0.321920\pi\)
0.208842 + 0.977949i \(0.433031\pi\)
\(62\) −4.68133 4.76455i −0.594530 0.605098i
\(63\) 2.62161 0.954189i 0.330292 0.120216i
\(64\) 0.422652 7.98883i 0.0528315 0.998603i
\(65\) 3.17559 + 5.50029i 0.393884 + 0.682227i
\(66\) 8.57046 + 0.825956i 1.05495 + 0.101668i
\(67\) −1.91047 + 2.27681i −0.233401 + 0.278156i −0.870014 0.493027i \(-0.835890\pi\)
0.636613 + 0.771183i \(0.280335\pi\)
\(68\) −5.57619 + 0.882236i −0.676212 + 0.106987i
\(69\) −5.38335 3.10808i −0.648079 0.374169i
\(70\) 8.86818 + 6.32672i 1.05995 + 0.756188i
\(71\) 0.854943 + 4.84862i 0.101463 + 0.575425i 0.992574 + 0.121640i \(0.0388155\pi\)
−0.891111 + 0.453785i \(0.850073\pi\)
\(72\) −2.82319 + 0.171971i −0.332717 + 0.0202670i
\(73\) 6.15912 + 2.24174i 0.720871 + 0.262376i 0.676296 0.736630i \(-0.263584\pi\)
0.0445755 + 0.999006i \(0.485806\pi\)
\(74\) 11.1719 + 3.09922i 1.29870 + 0.360277i
\(75\) 2.62348i 0.302933i
\(76\) −3.85931 + 7.81701i −0.442693 + 0.896673i
\(77\) 16.9855i 1.93568i
\(78\) 0.869604 3.13468i 0.0984632 0.354933i
\(79\) 1.75413 + 0.638451i 0.197355 + 0.0718313i 0.438807 0.898582i \(-0.355401\pi\)
−0.241452 + 0.970413i \(0.577624\pi\)
\(80\) −6.79665 8.70524i −0.759888 0.973276i
\(81\) 0.173648 + 0.984808i 0.0192942 + 0.109423i
\(82\) −0.799808 + 1.12109i −0.0883240 + 0.123804i
\(83\) −12.2921 7.09683i −1.34923 0.778979i −0.361090 0.932531i \(-0.617595\pi\)
−0.988141 + 0.153552i \(0.950929\pi\)
\(84\) −0.871949 5.51117i −0.0951375 0.601318i
\(85\) −5.00980 + 5.97044i −0.543389 + 0.647585i
\(86\) 1.34548 13.9613i 0.145087 1.50548i
\(87\) −3.49984 6.06190i −0.375222 0.649904i
\(88\) 4.89493 16.5100i 0.521802 1.75997i
\(89\) −2.58398 + 0.940492i −0.273901 + 0.0996920i −0.475319 0.879813i \(-0.657667\pi\)
0.201418 + 0.979505i \(0.435445\pi\)
\(90\) −2.78528 + 2.73664i −0.293594 + 0.288467i
\(91\) 6.31993 + 1.11437i 0.662509 + 0.116818i
\(92\) −8.15788 + 9.38143i −0.850518 + 0.978082i
\(93\) 3.03596 + 3.61812i 0.314815 + 0.375182i
\(94\) 2.90398 1.99550i 0.299523 0.205820i
\(95\) 3.06086 + 11.6395i 0.314038 + 1.19418i
\(96\) −0.740687 + 5.60815i −0.0755960 + 0.572380i
\(97\) −1.53526 + 1.28824i −0.155882 + 0.130801i −0.717393 0.696669i \(-0.754665\pi\)
0.561511 + 0.827469i \(0.310220\pi\)
\(98\) 1.07253 0.277279i 0.108341 0.0280094i
\(99\) −5.99581 1.05722i −0.602602 0.106255i
\(100\) −5.15039 1.00202i −0.515039 0.100202i
\(101\) −2.60411 7.15473i −0.259118 0.711922i −0.999222 0.0394294i \(-0.987446\pi\)
0.740104 0.672492i \(-0.234776\pi\)
\(102\) 3.97972 0.312880i 0.394051 0.0309797i
\(103\) −8.17891 14.1663i −0.805892 1.39585i −0.915687 0.401892i \(-0.868353\pi\)
0.109795 0.993954i \(-0.464981\pi\)
\(104\) −5.82184 2.90447i −0.570879 0.284807i
\(105\) −5.90083 4.95139i −0.575862 0.483206i
\(106\) −1.80852 + 3.79084i −0.175659 + 0.368199i
\(107\) −9.52393 5.49864i −0.920713 0.531574i −0.0368506 0.999321i \(-0.511733\pi\)
−0.883862 + 0.467747i \(0.845066\pi\)
\(108\) 1.99969 + 0.0352356i 0.192420 + 0.00339054i
\(109\) 2.68674 0.473744i 0.257343 0.0453765i −0.0434882 0.999054i \(-0.513847\pi\)
0.300831 + 0.953677i \(0.402736\pi\)
\(110\) −9.85681 21.6335i −0.939810 2.06268i
\(111\) −7.70363 2.80389i −0.731196 0.266134i
\(112\) −11.1525 0.393148i −1.05381 0.0371490i
\(113\) 10.8870 1.02417 0.512083 0.858936i \(-0.328874\pi\)
0.512083 + 0.858936i \(0.328874\pi\)
\(114\) 3.15377 5.29658i 0.295378 0.496070i
\(115\) 17.1632i 1.60048i
\(116\) −13.2374 + 4.55556i −1.22906 + 0.422973i
\(117\) −0.786737 + 2.16154i −0.0727339 + 0.199835i
\(118\) −9.88601 + 4.50432i −0.910081 + 0.414657i
\(119\) 1.36750 + 7.75550i 0.125359 + 0.710946i
\(120\) 4.30872 + 6.51328i 0.393331 + 0.594578i
\(121\) 13.0337 22.5751i 1.18488 2.05228i
\(122\) −3.57162 + 7.48647i −0.323360 + 0.677793i
\(123\) 0.625941 0.745968i 0.0564392 0.0672617i
\(124\) 8.26263 4.57826i 0.742006 0.411140i
\(125\) 5.68262 3.28086i 0.508269 0.293449i
\(126\) 0.309232 + 3.93332i 0.0275486 + 0.350408i
\(127\) 17.8973 6.51408i 1.58813 0.578031i 0.611176 0.791494i \(-0.290697\pi\)
0.976951 + 0.213463i \(0.0684744\pi\)
\(128\) 10.7270 + 3.59610i 0.948140 + 0.317854i
\(129\) −1.72221 + 9.76716i −0.151633 + 0.859951i
\(130\) −8.69602 + 2.24818i −0.762692 + 0.197178i
\(131\) −10.1706 12.1208i −0.888609 1.05900i −0.997886 0.0649917i \(-0.979298\pi\)
0.109277 0.994011i \(-0.465147\pi\)
\(132\) −4.36559 + 11.3671i −0.379976 + 0.989381i
\(133\) 10.9973 + 5.19053i 0.953591 + 0.450076i
\(134\) −2.38047 3.46422i −0.205642 0.299263i
\(135\) 2.11510 1.77478i 0.182039 0.152749i
\(136\) 0.905783 7.93246i 0.0776703 0.680203i
\(137\) 3.32209 18.8405i 0.283825 1.60965i −0.425625 0.904899i \(-0.639946\pi\)
0.709451 0.704755i \(-0.248943\pi\)
\(138\) 6.27067 6.16115i 0.533795 0.524472i
\(139\) 6.23589 + 17.1330i 0.528922 + 1.45320i 0.860342 + 0.509717i \(0.170250\pi\)
−0.331420 + 0.943483i \(0.607528\pi\)
\(140\) −11.9743 + 9.69331i −1.01201 + 0.819235i
\(141\) −2.15770 + 1.24575i −0.181711 + 0.104911i
\(142\) −6.93065 0.667925i −0.581608 0.0560510i
\(143\) −10.7282 9.00206i −0.897141 0.752790i
\(144\) 0.832941 3.91232i 0.0694117 0.326026i
\(145\) −9.66329 + 16.7373i −0.802492 + 1.38996i
\(146\) −5.38335 + 7.54586i −0.445529 + 0.624500i
\(147\) −0.771424 + 0.136023i −0.0636260 + 0.0112190i
\(148\) −8.44692 + 14.0528i −0.694333 + 1.15513i
\(149\) −3.41019 + 9.36942i −0.279374 + 0.767573i 0.718060 + 0.695981i \(0.245030\pi\)
−0.997434 + 0.0715918i \(0.977192\pi\)
\(150\) 3.57514 + 0.991793i 0.291909 + 0.0809796i
\(151\) −18.8754 −1.53606 −0.768031 0.640413i \(-0.778763\pi\)
−0.768031 + 0.640413i \(0.778763\pi\)
\(152\) −9.19363 8.21445i −0.745702 0.666280i
\(153\) −2.82277 −0.228208
\(154\) −23.1470 6.42129i −1.86524 0.517442i
\(155\) 4.46023 12.2544i 0.358254 0.984296i
\(156\) 3.94303 + 2.37010i 0.315695 + 0.189760i
\(157\) −16.8588 + 2.97265i −1.34548 + 0.237244i −0.799555 0.600593i \(-0.794931\pi\)
−0.545921 + 0.837837i \(0.683820\pi\)
\(158\) −1.53319 + 2.14907i −0.121974 + 0.170971i
\(159\) 1.48498 2.57205i 0.117766 0.203977i
\(160\) 14.4325 5.97114i 1.14099 0.472060i
\(161\) 13.2849 + 11.1474i 1.04700 + 0.878535i
\(162\) −1.40769 0.135663i −0.110599 0.0106587i
\(163\) 6.20425 3.58203i 0.485954 0.280566i −0.236940 0.971524i \(-0.576145\pi\)
0.722895 + 0.690958i \(0.242811\pi\)
\(164\) −1.22540 1.51376i −0.0956880 0.118205i
\(165\) 5.74943 + 15.7964i 0.447592 + 1.22975i
\(166\) 14.3182 14.0681i 1.11130 1.09190i
\(167\) −1.39309 + 7.90062i −0.107801 + 0.611368i 0.882264 + 0.470755i \(0.156019\pi\)
−0.990065 + 0.140613i \(0.955093\pi\)
\(168\) 7.83997 + 0.895222i 0.604867 + 0.0690679i
\(169\) 5.90526 4.95510i 0.454251 0.381162i
\(170\) −6.24228 9.08418i −0.478761 0.696725i
\(171\) −2.51673 + 3.55894i −0.192460 + 0.272159i
\(172\) 18.5170 + 7.11153i 1.41191 + 0.542249i
\(173\) −2.79141 3.32668i −0.212227 0.252922i 0.649420 0.760430i \(-0.275012\pi\)
−0.861648 + 0.507507i \(0.830567\pi\)
\(174\) 9.58394 2.47773i 0.726557 0.187836i
\(175\) −1.27096 + 7.20795i −0.0960753 + 0.544870i
\(176\) 20.6484 + 12.9121i 1.55643 + 0.973284i
\(177\) 7.21859 2.62735i 0.542582 0.197484i
\(178\) −0.304793 3.87686i −0.0228452 0.290583i
\(179\) −13.1976 + 7.61964i −0.986435 + 0.569519i −0.904207 0.427095i \(-0.859537\pi\)
−0.0822284 + 0.996614i \(0.526204\pi\)
\(180\) −2.67638 4.83021i −0.199486 0.360022i
\(181\) −4.91122 + 5.85297i −0.365048 + 0.435048i −0.917036 0.398805i \(-0.869425\pi\)
0.551987 + 0.833852i \(0.313870\pi\)
\(182\) −3.90783 + 8.19119i −0.289667 + 0.607171i
\(183\) 2.93266 5.07951i 0.216788 0.375488i
\(184\) −9.70049 14.6637i −0.715129 1.08103i
\(185\) 3.93058 + 22.2914i 0.288982 + 1.63890i
\(186\) −6.07832 + 2.76944i −0.445684 + 0.203065i
\(187\) 5.87793 16.1495i 0.429836 1.18097i
\(188\) 1.62153 + 4.71178i 0.118262 + 0.343642i
\(189\) 2.78986i 0.202933i
\(190\) −17.0188 0.229061i −1.23467 0.0166178i
\(191\) 27.3299 1.97752 0.988761 0.149508i \(-0.0477688\pi\)
0.988761 + 0.149508i \(0.0477688\pi\)
\(192\) −7.36249 3.12950i −0.531342 0.225852i
\(193\) −3.54277 1.28946i −0.255014 0.0928176i 0.211350 0.977411i \(-0.432214\pi\)
−0.466364 + 0.884593i \(0.654436\pi\)
\(194\) −1.17515 2.57919i −0.0843705 0.185175i
\(195\) 6.25470 1.10287i 0.447908 0.0789783i
\(196\) −0.0276009 + 1.56641i −0.00197149 + 0.111886i
\(197\) 17.6472 + 10.1886i 1.25731 + 0.725907i 0.972550 0.232693i \(-0.0747537\pi\)
0.284757 + 0.958600i \(0.408087\pi\)
\(198\) 3.70741 7.77110i 0.263474 0.552268i
\(199\) 0.892196 + 0.748642i 0.0632461 + 0.0530698i 0.673863 0.738857i \(-0.264634\pi\)
−0.610617 + 0.791926i \(0.709078\pi\)
\(200\) 3.31258 6.63988i 0.234235 0.469510i
\(201\) 1.48608 + 2.57397i 0.104820 + 0.181554i
\(202\) 10.7346 0.843935i 0.755281 0.0593791i
\(203\) 6.67901 + 18.3504i 0.468775 + 1.28795i
\(204\) −1.07814 + 5.54164i −0.0754847 + 0.387993i
\(205\) −2.64786 0.466888i −0.184934 0.0326089i
\(206\) 22.3971 5.79030i 1.56048 0.403430i
\(207\) −4.76185 + 3.99567i −0.330972 + 0.277718i
\(208\) 6.15898 6.83569i 0.427048 0.473970i
\(209\) −15.1205 21.8094i −1.04591 1.50859i
\(210\) 8.97827 6.16950i 0.619559 0.425736i
\(211\) −9.42729 11.2350i −0.649002 0.773450i 0.336762 0.941590i \(-0.390668\pi\)
−0.985763 + 0.168140i \(0.946224\pi\)
\(212\) −4.48226 3.89767i −0.307843 0.267693i
\(213\) 4.84862 + 0.854943i 0.332222 + 0.0585797i
\(214\) 11.0937 10.9000i 0.758352 0.745107i
\(215\) 25.7323 9.36581i 1.75493 0.638743i
\(216\) −0.803989 + 2.71175i −0.0547046 + 0.184511i
\(217\) −6.58843 11.4115i −0.447252 0.774662i
\(218\) −0.370113 + 3.84044i −0.0250672 + 0.260108i
\(219\) 4.21309 5.02096i 0.284694 0.339285i
\(220\) 33.2074 5.25390i 2.23884 0.354218i
\(221\) −5.62322 3.24656i −0.378258 0.218388i
\(222\) 6.73332 9.43811i 0.451911 0.633445i
\(223\) 2.86843 + 16.2677i 0.192084 + 1.08936i 0.916510 + 0.400011i \(0.130994\pi\)
−0.724426 + 0.689353i \(0.757895\pi\)
\(224\) 4.75191 15.0494i 0.317501 1.00553i
\(225\) −2.46527 0.897283i −0.164351 0.0598189i
\(226\) −4.11579 + 14.8363i −0.273778 + 0.986895i
\(227\) 14.8667i 0.986740i 0.869820 + 0.493370i \(0.164235\pi\)
−0.869820 + 0.493370i \(0.835765\pi\)
\(228\) 6.02563 + 6.30014i 0.399057 + 0.417237i
\(229\) 1.65268i 0.109212i −0.998508 0.0546060i \(-0.982610\pi\)
0.998508 0.0546060i \(-0.0173903\pi\)
\(230\) −23.3891 6.48846i −1.54223 0.427837i
\(231\) 15.9612 + 5.80939i 1.05017 + 0.382230i
\(232\) −1.20374 19.7615i −0.0790295 1.29740i
\(233\) 1.80216 + 10.2206i 0.118063 + 0.669571i 0.985188 + 0.171479i \(0.0548546\pi\)
−0.867124 + 0.498092i \(0.834034\pi\)
\(234\) −2.64822 1.88929i −0.173119 0.123506i
\(235\) 5.95755 + 3.43959i 0.388628 + 0.224374i
\(236\) −2.40091 15.1750i −0.156286 0.987806i
\(237\) 1.19989 1.42998i 0.0779415 0.0928871i
\(238\) −11.0858 1.06836i −0.718584 0.0692517i
\(239\) 7.86624 + 13.6247i 0.508825 + 0.881310i 0.999948 + 0.0102200i \(0.00325317\pi\)
−0.491123 + 0.871090i \(0.663413\pi\)
\(240\) −10.5048 + 3.40939i −0.678085 + 0.220075i
\(241\) 18.3057 6.66274i 1.17918 0.429185i 0.323265 0.946309i \(-0.395220\pi\)
0.855911 + 0.517124i \(0.172997\pi\)
\(242\) 25.8368 + 26.2961i 1.66085 + 1.69038i
\(243\) 0.984808 + 0.173648i 0.0631754 + 0.0111395i
\(244\) −8.85194 7.69744i −0.566687 0.492778i
\(245\) 1.39023 + 1.65681i 0.0888184 + 0.105850i
\(246\) 0.779932 + 1.13501i 0.0497267 + 0.0723656i
\(247\) −9.10681 + 4.19514i −0.579453 + 0.266931i
\(248\) 3.11537 + 12.9907i 0.197827 + 0.824908i
\(249\) −10.8730 + 9.12351i −0.689047 + 0.578179i
\(250\) 2.32270 + 8.98429i 0.146901 + 0.568217i
\(251\) 29.5760 + 5.21504i 1.86682 + 0.329171i 0.988775 0.149409i \(-0.0477372\pi\)
0.878044 + 0.478580i \(0.158848\pi\)
\(252\) −5.47703 1.06557i −0.345021 0.0671244i
\(253\) −12.9440 35.5635i −0.813785 2.23586i
\(254\) 2.11107 + 26.8521i 0.132460 + 1.68485i
\(255\) 3.89693 + 6.74968i 0.244035 + 0.422681i
\(256\) −8.95586 + 13.2587i −0.559741 + 0.828667i
\(257\) −15.2311 12.7804i −0.950089 0.797219i 0.0292239 0.999573i \(-0.490696\pi\)
−0.979312 + 0.202354i \(0.935141\pi\)
\(258\) −12.6591 6.03937i −0.788122 0.375995i
\(259\) 19.8072 + 11.4357i 1.23076 + 0.710579i
\(260\) 0.223788 12.7004i 0.0138787 0.787645i
\(261\) −6.89334 + 1.21548i −0.426687 + 0.0752364i
\(262\) 20.3626 9.27774i 1.25801 0.573180i
\(263\) −12.7334 4.63459i −0.785177 0.285781i −0.0818473 0.996645i \(-0.526082\pi\)
−0.703330 + 0.710864i \(0.748304\pi\)
\(264\) −13.8401 10.2465i −0.851802 0.630627i
\(265\) −8.20023 −0.503736
\(266\) −11.2309 + 13.0244i −0.688609 + 0.798575i
\(267\) 2.74981i 0.168286i
\(268\) 5.62079 1.93435i 0.343344 0.118159i
\(269\) −1.36842 + 3.75969i −0.0834339 + 0.229233i −0.974393 0.224850i \(-0.927811\pi\)
0.890960 + 0.454083i \(0.150033\pi\)
\(270\) 1.61897 + 3.55329i 0.0985276 + 0.216246i
\(271\) 0.148533 + 0.842375i 0.00902276 + 0.0511706i 0.988987 0.148004i \(-0.0472849\pi\)
−0.979964 + 0.199175i \(0.936174\pi\)
\(272\) 10.4675 + 4.23318i 0.634686 + 0.256674i
\(273\) 3.20871 5.55765i 0.194200 0.336364i
\(274\) 24.4190 + 11.6497i 1.47520 + 0.703786i
\(275\) 10.2670 12.2357i 0.619121 0.737839i
\(276\) 6.02550 + 10.8745i 0.362693 + 0.654570i
\(277\) −2.77849 + 1.60416i −0.166943 + 0.0963849i −0.581144 0.813801i \(-0.697395\pi\)
0.414200 + 0.910186i \(0.364061\pi\)
\(278\) −25.7054 + 2.02092i −1.54171 + 0.121207i
\(279\) 4.43828 1.61540i 0.265713 0.0967116i
\(280\) −8.68272 19.9825i −0.518892 1.19418i
\(281\) −3.11653 + 17.6747i −0.185916 + 1.05438i 0.738856 + 0.673864i \(0.235366\pi\)
−0.924772 + 0.380521i \(0.875745\pi\)
\(282\) −0.881934 3.41135i −0.0525184 0.203143i
\(283\) 8.33789 + 9.93671i 0.495636 + 0.590676i 0.954642 0.297757i \(-0.0962386\pi\)
−0.459006 + 0.888433i \(0.651794\pi\)
\(284\) 3.53031 9.19223i 0.209485 0.545459i
\(285\) 11.9844 + 1.10467i 0.709895 + 0.0654347i
\(286\) 16.3233 11.2167i 0.965217 0.663258i
\(287\) −2.08115 + 1.74629i −0.122846 + 0.103080i
\(288\) 5.01661 + 2.61412i 0.295607 + 0.154038i
\(289\) −1.56838 + 8.89474i −0.0922578 + 0.523220i
\(290\) −19.1556 19.4961i −1.12485 1.14485i
\(291\) 0.685457 + 1.88328i 0.0401822 + 0.110400i
\(292\) −8.24795 10.1888i −0.482675 0.596256i
\(293\) 10.4417 6.02855i 0.610014 0.352191i −0.162957 0.986633i \(-0.552103\pi\)
0.772971 + 0.634442i \(0.218770\pi\)
\(294\) 0.106268 1.10268i 0.00619768 0.0643096i
\(295\) −16.2479 13.6336i −0.945989 0.793779i
\(296\) −15.9571 16.8236i −0.927486 0.977852i
\(297\) −3.04415 + 5.27263i −0.176640 + 0.305949i
\(298\) −11.4790 8.18929i −0.664958 0.474393i
\(299\) −14.0816 + 2.48296i −0.814359 + 0.143593i
\(300\) −2.70313 + 4.49708i −0.156065 + 0.259639i
\(301\) 9.46349 26.0007i 0.545466 1.49866i
\(302\) 7.13576 25.7225i 0.410617 1.48016i
\(303\) −7.61390 −0.437407
\(304\) 14.6698 9.42317i 0.841372 0.540456i
\(305\) −16.1945 −0.927295
\(306\) 1.06713 3.84673i 0.0610040 0.219903i
\(307\) −10.4114 + 28.6052i −0.594212 + 1.63258i 0.168393 + 0.985720i \(0.446142\pi\)
−0.762605 + 0.646865i \(0.776080\pi\)
\(308\) 17.5012 29.1160i 0.997224 1.65904i
\(309\) −16.1093 + 2.84051i −0.916427 + 0.161591i
\(310\) 15.0135 + 10.7109i 0.852708 + 0.608337i
\(311\) −7.60513 + 13.1725i −0.431247 + 0.746942i −0.996981 0.0776457i \(-0.975260\pi\)
0.565734 + 0.824588i \(0.308593\pi\)
\(312\) −4.72050 + 4.47736i −0.267245 + 0.253480i
\(313\) 10.7624 + 9.03069i 0.608325 + 0.510445i 0.894109 0.447849i \(-0.147810\pi\)
−0.285785 + 0.958294i \(0.592254\pi\)
\(314\) 2.32239 24.0980i 0.131060 1.35993i
\(315\) −6.67098 + 3.85149i −0.375867 + 0.217007i
\(316\) −2.34903 2.90179i −0.132143 0.163239i
\(317\) −2.72206 7.47879i −0.152886 0.420051i 0.839478 0.543393i \(-0.182861\pi\)
−0.992364 + 0.123343i \(0.960639\pi\)
\(318\) 2.94367 + 2.99600i 0.165073 + 0.168007i
\(319\) 7.40022 41.9688i 0.414333 2.34980i
\(320\) 2.68103 + 21.9252i 0.149874 + 1.22566i
\(321\) −8.42441 + 7.06892i −0.470205 + 0.394549i
\(322\) −20.2133 + 13.8898i −1.12644 + 0.774047i
\(323\) −8.65983 8.74072i −0.481846 0.486347i
\(324\) 0.717045 1.86704i 0.0398358 0.103725i
\(325\) −3.87903 4.62285i −0.215170 0.256430i
\(326\) 2.53591 + 9.80900i 0.140451 + 0.543270i
\(327\) 0.473744 2.68674i 0.0261981 0.148577i
\(328\) 2.52613 1.09765i 0.139482 0.0606075i
\(329\) 6.53174 2.37736i 0.360107 0.131068i
\(330\) −23.7001 + 1.86327i −1.30465 + 0.102569i
\(331\) −20.3540 + 11.7514i −1.11876 + 0.645916i −0.941084 0.338173i \(-0.890191\pi\)
−0.177675 + 0.984089i \(0.556858\pi\)
\(332\) 13.7583 + 24.8304i 0.755087 + 1.36275i
\(333\) −5.26959 + 6.28006i −0.288772 + 0.344145i
\(334\) −10.2399 4.88522i −0.560303 0.267308i
\(335\) 4.10317 7.10689i 0.224180 0.388291i
\(336\) −4.18382 + 10.3455i −0.228246 + 0.564392i
\(337\) 2.84559 + 16.1382i 0.155009 + 0.879101i 0.958777 + 0.284158i \(0.0917142\pi\)
−0.803768 + 0.594943i \(0.797175\pi\)
\(338\) 4.52010 + 9.92064i 0.245861 + 0.539612i
\(339\) 3.72358 10.2305i 0.202237 0.555642i
\(340\) 14.7393 5.07243i 0.799352 0.275091i
\(341\) 28.7558i 1.55721i
\(342\) −3.89850 4.77511i −0.210807 0.258209i
\(343\) −17.3437 −0.936470
\(344\) −16.6915 + 22.5456i −0.899945 + 1.21557i
\(345\) 16.1281 + 5.87016i 0.868310 + 0.316039i
\(346\) 5.58870 2.54636i 0.300450 0.136893i
\(347\) 11.2626 1.98589i 0.604605 0.106608i 0.137038 0.990566i \(-0.456242\pi\)
0.467567 + 0.883958i \(0.345131\pi\)
\(348\) −0.246638 + 13.9972i −0.0132212 + 0.750328i
\(349\) 15.1866 + 8.76801i 0.812922 + 0.469341i 0.847970 0.530045i \(-0.177825\pi\)
−0.0350473 + 0.999386i \(0.511158\pi\)
\(350\) −9.34214 4.45692i −0.499359 0.238232i
\(351\) 1.76211 + 1.47858i 0.0940543 + 0.0789209i
\(352\) −25.4019 + 23.2573i −1.35393 + 1.23962i
\(353\) 8.16234 + 14.1376i 0.434437 + 0.752468i 0.997250 0.0741171i \(-0.0236139\pi\)
−0.562812 + 0.826585i \(0.690281\pi\)
\(354\) 0.851468 + 10.8304i 0.0452550 + 0.575628i
\(355\) −4.64938 12.7741i −0.246763 0.677977i
\(356\) 5.39841 + 1.05027i 0.286115 + 0.0556643i
\(357\) 7.75550 + 1.36750i 0.410465 + 0.0723760i
\(358\) −5.39436 20.8656i −0.285101 1.10278i
\(359\) 14.4473 12.1227i 0.762501 0.639814i −0.176276 0.984341i \(-0.556405\pi\)
0.938777 + 0.344527i \(0.111961\pi\)
\(360\) 7.59415 1.82120i 0.400247 0.0959857i
\(361\) −18.7412 + 3.12519i −0.986380 + 0.164484i
\(362\) −6.11946 8.90545i −0.321632 0.468060i
\(363\) −16.7558 19.9688i −0.879454 1.04809i
\(364\) −9.68519 8.42202i −0.507642 0.441434i
\(365\) −17.8222 3.14253i −0.932857 0.164488i
\(366\) 5.81341 + 5.91675i 0.303872 + 0.309274i
\(367\) −1.97130 + 0.717493i −0.102901 + 0.0374528i −0.392957 0.919557i \(-0.628548\pi\)
0.290057 + 0.957009i \(0.406326\pi\)
\(368\) 23.6502 7.67577i 1.23285 0.400127i
\(369\) −0.486896 0.843329i −0.0253468 0.0439019i
\(370\) −31.8635 3.07077i −1.65651 0.159642i
\(371\) −5.32598 + 6.34725i −0.276511 + 0.329533i
\(372\) −1.47617 9.33019i −0.0765361 0.483748i
\(373\) −13.6302 7.86938i −0.705744 0.407461i 0.103739 0.994605i \(-0.466919\pi\)
−0.809483 + 0.587143i \(0.800253\pi\)
\(374\) 19.7855 + 14.1154i 1.02309 + 0.729888i
\(375\) −1.13943 6.46204i −0.0588400 0.333698i
\(376\) −7.03398 + 0.428465i −0.362750 + 0.0220964i
\(377\) −15.1301 5.50691i −0.779240 0.283620i
\(378\) 3.80188 + 1.05469i 0.195547 + 0.0542475i
\(379\) 18.9283i 0.972279i 0.873881 + 0.486140i \(0.161595\pi\)
−0.873881 + 0.486140i \(0.838405\pi\)
\(380\) 6.74602 23.1057i 0.346064 1.18530i
\(381\) 19.0459i 0.975751i
\(382\) −10.3319 + 37.2437i −0.528627 + 1.90556i
\(383\) 11.3124 + 4.11738i 0.578037 + 0.210388i 0.614459 0.788948i \(-0.289374\pi\)
−0.0364230 + 0.999336i \(0.511596\pi\)
\(384\) 7.04807 8.85012i 0.359670 0.451631i
\(385\) −8.14378 46.1857i −0.415045 2.35384i
\(386\) 3.09654 4.34043i 0.157610 0.220922i
\(387\) 8.58910 + 4.95892i 0.436608 + 0.252076i
\(388\) 3.95904 0.626379i 0.200990 0.0317996i
\(389\) 21.8140 25.9969i 1.10601 1.31810i 0.162521 0.986705i \(-0.448038\pi\)
0.943493 0.331391i \(-0.107518\pi\)
\(390\) −0.861619 + 8.94051i −0.0436298 + 0.452720i
\(391\) −8.77340 15.1960i −0.443690 0.768493i
\(392\) −2.12418 0.629785i −0.107287 0.0318089i
\(393\) −14.8684 + 5.41166i −0.750012 + 0.272982i
\(394\) −20.5559 + 20.1969i −1.03559 + 1.01750i
\(395\) −5.07579 0.894999i −0.255391 0.0450323i
\(396\) 9.18848 + 7.99010i 0.461739 + 0.401517i
\(397\) −5.99579 7.14551i −0.300920 0.358623i 0.594303 0.804241i \(-0.297428\pi\)
−0.895223 + 0.445619i \(0.852984\pi\)
\(398\) −1.35750 + 0.932819i −0.0680453 + 0.0467580i
\(399\) 8.63881 8.55886i 0.432482 0.428479i
\(400\) 7.79618 + 7.02438i 0.389809 + 0.351219i
\(401\) −0.427363 + 0.358600i −0.0213415 + 0.0179077i −0.653396 0.757016i \(-0.726656\pi\)
0.632054 + 0.774924i \(0.282212\pi\)
\(402\) −4.06948 + 1.05208i −0.202967 + 0.0524729i
\(403\) 10.6994 + 1.88659i 0.532974 + 0.0939777i
\(404\) −2.90807 + 14.9475i −0.144682 + 0.743668i
\(405\) −0.944340 2.59455i −0.0469246 0.128924i
\(406\) −27.5320 + 2.16452i −1.36639 + 0.107424i
\(407\) −24.9561 43.2252i −1.23703 2.14259i
\(408\) −7.14428 3.56422i −0.353694 0.176455i
\(409\) 5.17866 + 4.34541i 0.256068 + 0.214867i 0.761780 0.647836i \(-0.224326\pi\)
−0.505712 + 0.862702i \(0.668770\pi\)
\(410\) 1.63726 3.43185i 0.0808585 0.169487i
\(411\) −16.5681 9.56558i −0.817243 0.471835i
\(412\) −0.576377 + 32.7106i −0.0283961 + 1.61153i
\(413\) −21.1057 + 3.72151i −1.03855 + 0.183124i
\(414\) −3.64489 7.99974i −0.179137 0.393166i
\(415\) 36.8262 + 13.4036i 1.80773 + 0.657959i
\(416\) 6.98695 + 10.9773i 0.342563 + 0.538208i
\(417\) 18.2325 0.892851
\(418\) 35.4370 12.3605i 1.73328 0.604572i
\(419\) 15.5692i 0.760605i −0.924862 0.380302i \(-0.875820\pi\)
0.924862 0.380302i \(-0.124180\pi\)
\(420\) 5.01329 + 14.5675i 0.244623 + 0.710820i
\(421\) 0.477062 1.31072i 0.0232506 0.0638805i −0.927524 0.373763i \(-0.878067\pi\)
0.950775 + 0.309882i \(0.100290\pi\)
\(422\) 18.8744 8.59969i 0.918793 0.418626i
\(423\) 0.432644 + 2.45365i 0.0210359 + 0.119300i
\(424\) 7.00603 4.63469i 0.340243 0.225081i
\(425\) 3.70274 6.41334i 0.179609 0.311093i
\(426\) −2.99807 + 6.28424i −0.145257 + 0.304473i
\(427\) −10.5182 + 12.5351i −0.509011 + 0.606616i
\(428\) 10.6600 + 19.2387i 0.515271 + 0.929935i
\(429\) −12.1284 + 7.00236i −0.585567 + 0.338077i
\(430\) 3.03526 + 38.6074i 0.146373 + 1.86181i
\(431\) 11.5493 4.20361i 0.556312 0.202481i −0.0485370 0.998821i \(-0.515456\pi\)
0.604849 + 0.796341i \(0.293234\pi\)
\(432\) −3.39149 2.12080i −0.163173 0.102037i
\(433\) −4.69726 + 26.6395i −0.225736 + 1.28021i 0.635537 + 0.772070i \(0.280779\pi\)
−0.861273 + 0.508142i \(0.830332\pi\)
\(434\) 18.0417 4.66431i 0.866029 0.223894i
\(435\) 12.4229 + 14.8050i 0.595632 + 0.709846i
\(436\) −5.09364 1.95623i −0.243941 0.0936865i
\(437\) −26.9812 2.48700i −1.29069 0.118969i
\(438\) 5.24957 + 7.63953i 0.250834 + 0.365031i
\(439\) 11.5932 9.72785i 0.553313 0.464285i −0.322748 0.946485i \(-0.604607\pi\)
0.876061 + 0.482200i \(0.160162\pi\)
\(440\) −5.39413 + 47.2395i −0.257155 + 2.25205i
\(441\) −0.136023 + 0.771424i −0.00647728 + 0.0367345i
\(442\) 6.55008 6.43568i 0.311555 0.306114i
\(443\) −1.62616 4.46785i −0.0772613 0.212274i 0.895049 0.445968i \(-0.147141\pi\)
−0.972310 + 0.233695i \(0.924918\pi\)
\(444\) 10.3163 + 12.7438i 0.489589 + 0.604796i
\(445\) 6.57523 3.79621i 0.311696 0.179958i
\(446\) −23.2531 2.24096i −1.10107 0.106113i
\(447\) 7.63802 + 6.40906i 0.361266 + 0.303138i
\(448\) 18.7122 + 12.1650i 0.884067 + 0.574743i
\(449\) 15.8335 27.4245i 0.747230 1.29424i −0.201916 0.979403i \(-0.564717\pi\)
0.949146 0.314837i \(-0.101950\pi\)
\(450\) 2.15475 3.02032i 0.101576 0.142379i
\(451\) 5.83867 1.02952i 0.274932 0.0484780i
\(452\) −18.6622 11.2176i −0.877794 0.527630i
\(453\) −6.45578 + 17.7371i −0.303319 + 0.833362i
\(454\) −20.2596 5.62029i −0.950830 0.263773i
\(455\) −17.7189 −0.830676
\(456\) −10.8635 + 5.82968i −0.508728 + 0.273000i
\(457\) 23.7799 1.11237 0.556187 0.831057i \(-0.312264\pi\)
0.556187 + 0.831057i \(0.312264\pi\)
\(458\) 2.25218 + 0.624786i 0.105238 + 0.0291943i
\(459\) −0.965445 + 2.65254i −0.0450631 + 0.123810i
\(460\) 17.6843 29.4206i 0.824534 1.37174i
\(461\) 12.3585 2.17913i 0.575591 0.101492i 0.121728 0.992564i \(-0.461157\pi\)
0.453863 + 0.891071i \(0.350045\pi\)
\(462\) −13.9508 + 19.5548i −0.649049 + 0.909774i
\(463\) 2.80858 4.86460i 0.130526 0.226077i −0.793354 0.608761i \(-0.791667\pi\)
0.923879 + 0.382684i \(0.125000\pi\)
\(464\) 27.3850 + 5.83032i 1.27131 + 0.270666i
\(465\) −9.98987 8.38249i −0.463269 0.388729i
\(466\) −14.6093 1.40794i −0.676765 0.0652215i
\(467\) −14.0915 + 8.13574i −0.652077 + 0.376477i −0.789252 0.614070i \(-0.789531\pi\)
0.137174 + 0.990547i \(0.456198\pi\)
\(468\) 3.57576 2.89462i 0.165290 0.133804i
\(469\) −2.83600 7.79186i −0.130954 0.359794i
\(470\) −6.93952 + 6.81832i −0.320096 + 0.314506i
\(471\) −2.97265 + 16.8588i −0.136973 + 0.776811i
\(472\) 21.5873 + 2.46499i 0.993637 + 0.113460i
\(473\) −46.2559 + 38.8133i −2.12685 + 1.78464i
\(474\) 1.49509 + 2.17575i 0.0686716 + 0.0999355i
\(475\) −4.78461 10.3864i −0.219533 0.476562i
\(476\) 5.64683 14.7032i 0.258822 0.673921i
\(477\) −1.90905 2.27511i −0.0874093 0.104170i
\(478\) −21.5409 + 5.56894i −0.985256 + 0.254718i
\(479\) −4.65632 + 26.4073i −0.212753 + 1.20658i 0.672012 + 0.740541i \(0.265430\pi\)
−0.884764 + 0.466039i \(0.845681\pi\)
\(480\) −0.674837 15.6044i −0.0308019 0.712238i
\(481\) −17.7204 + 6.44970i −0.807981 + 0.294081i
\(482\) 2.15925 + 27.4649i 0.0983511 + 1.25099i
\(483\) 15.0188 8.67110i 0.683379 0.394549i
\(484\) −45.6024 + 25.2680i −2.07284 + 1.14854i
\(485\) 3.55691 4.23896i 0.161511 0.192481i
\(486\) −0.608940 + 1.27640i −0.0276221 + 0.0578986i
\(487\) −8.46625 + 14.6640i −0.383643 + 0.664488i −0.991580 0.129497i \(-0.958664\pi\)
0.607937 + 0.793985i \(0.291997\pi\)
\(488\) 13.8361 9.15298i 0.626331 0.414336i
\(489\) −1.24402 7.05521i −0.0562567 0.319048i
\(490\) −2.78338 + 1.26818i −0.125740 + 0.0572906i
\(491\) 10.8728 29.8728i 0.490683 1.34814i −0.409374 0.912367i \(-0.634253\pi\)
0.900057 0.435773i \(-0.143525\pi\)
\(492\) −1.84158 + 0.633767i −0.0830249 + 0.0285724i
\(493\) 19.7585i 0.889878i
\(494\) −2.27414 13.9962i −0.102318 0.629721i
\(495\) 16.8102 0.755563
\(496\) −18.8808 0.665584i −0.847771 0.0298856i
\(497\) −12.9073 4.69787i −0.578971 0.210728i
\(498\) −8.32258 18.2662i −0.372944 0.818529i
\(499\) 23.3466 4.11663i 1.04514 0.184286i 0.375384 0.926870i \(-0.377511\pi\)
0.669753 + 0.742584i \(0.266400\pi\)
\(500\) −13.1214 0.231206i −0.586807 0.0103398i
\(501\) 6.94769 + 4.01125i 0.310400 + 0.179209i
\(502\) −18.2878 + 38.3331i −0.816226 + 1.71089i
\(503\) 11.6405 + 9.76752i 0.519023 + 0.435512i 0.864291 0.502992i \(-0.167767\pi\)
−0.345268 + 0.938504i \(0.612212\pi\)
\(504\) 3.52266 7.06098i 0.156912 0.314521i
\(505\) 10.5112 + 18.2060i 0.467744 + 0.810156i
\(506\) 53.3575 4.19488i 2.37203 0.186485i
\(507\) −2.63656 7.24388i −0.117094 0.321712i
\(508\) −37.3907 7.27444i −1.65895 0.322751i
\(509\) −2.36300 0.416661i −0.104738 0.0184682i 0.121033 0.992648i \(-0.461379\pi\)
−0.225772 + 0.974180i \(0.572490\pi\)
\(510\) −10.6713 + 2.75885i −0.472534 + 0.122164i
\(511\) −14.0078 + 11.7539i −0.619668 + 0.519963i
\(512\) −14.6825 17.2170i −0.648882 0.760889i
\(513\) 2.48353 + 3.58219i 0.109651 + 0.158157i
\(514\) 23.1745 15.9246i 1.02218 0.702402i
\(515\) 29.0315 + 34.5984i 1.27928 + 1.52459i
\(516\) 13.0158 14.9680i 0.572991 0.658930i
\(517\) −14.9386 2.63407i −0.656997 0.115846i
\(518\) −23.0720 + 22.6690i −1.01372 + 0.996019i
\(519\) −4.08077 + 1.48528i −0.179126 + 0.0651965i
\(520\) 17.2228 + 5.10629i 0.755272 + 0.223925i
\(521\) −13.8748 24.0318i −0.607865 1.05285i −0.991592 0.129406i \(-0.958693\pi\)
0.383727 0.923447i \(-0.374640\pi\)
\(522\) 0.949596 9.85339i 0.0415627 0.431271i
\(523\) 13.0236 15.5209i 0.569483 0.678684i −0.402042 0.915621i \(-0.631699\pi\)
0.971525 + 0.236938i \(0.0761437\pi\)
\(524\) 4.94524 + 31.2565i 0.216034 + 1.36545i
\(525\) 6.33857 + 3.65957i 0.276638 + 0.159717i
\(526\) 11.1296 15.6004i 0.485273 0.680209i
\(527\) 2.31513 + 13.1298i 0.100849 + 0.571941i
\(528\) 19.1956 14.9870i 0.835380 0.652225i
\(529\) −14.6973 5.34939i −0.639015 0.232582i
\(530\) 3.10005 11.1748i 0.134658 0.485404i
\(531\) 7.68186i 0.333364i
\(532\) −13.5031 20.2286i −0.585436 0.877023i
\(533\) 2.23998i 0.0970243i
\(534\) −3.74730 1.03955i −0.162162 0.0449859i
\(535\) 28.5330 + 10.3852i 1.23359 + 0.448990i
\(536\) 0.511126 + 8.39099i 0.0220773 + 0.362436i
\(537\) 2.64627 + 15.0078i 0.114195 + 0.647633i
\(538\) −4.60619 3.28614i −0.198587 0.141676i
\(539\) −4.13018 2.38456i −0.177899 0.102710i
\(540\) −5.45429 + 0.862949i −0.234715 + 0.0371354i
\(541\) 12.5034 14.9010i 0.537564 0.640644i −0.427076 0.904216i \(-0.640456\pi\)
0.964640 + 0.263572i \(0.0849007\pi\)
\(542\) −1.20410 0.116042i −0.0517204 0.00498443i
\(543\) 3.82025 + 6.61688i 0.163943 + 0.283957i
\(544\) −9.72595 + 12.6643i −0.416997 + 0.542976i
\(545\) −7.07842 + 2.57633i −0.303206 + 0.110358i
\(546\) 6.36064 + 6.47371i 0.272210 + 0.277049i
\(547\) 15.6913 + 2.76679i 0.670910 + 0.118299i 0.498718 0.866764i \(-0.333804\pi\)
0.172191 + 0.985064i \(0.444915\pi\)
\(548\) −25.1071 + 28.8728i −1.07252 + 1.23338i
\(549\) −3.77015 4.49309i −0.160906 0.191760i
\(550\) 12.7928 + 18.6169i 0.545486 + 0.793828i
\(551\) −24.9114 17.6163i −1.06126 0.750481i
\(552\) −17.0972 + 4.10018i −0.727704 + 0.174515i
\(553\) −3.98944 + 3.34754i −0.169648 + 0.142352i
\(554\) −1.13568 4.39283i −0.0482503 0.186634i
\(555\) 22.2914 + 3.93058i 0.946218 + 0.166844i
\(556\) 6.96378 35.7940i 0.295330 1.51800i
\(557\) 4.99404 + 13.7210i 0.211604 + 0.581378i 0.999403 0.0345549i \(-0.0110014\pi\)
−0.787798 + 0.615933i \(0.788779\pi\)
\(558\) 0.523517 + 6.65895i 0.0221622 + 0.281896i
\(559\) 11.4068 + 19.7572i 0.482458 + 0.835641i
\(560\) 30.5135 4.27810i 1.28943 0.180783i
\(561\) −13.1652 11.0469i −0.555834 0.466400i
\(562\) −22.9080 10.9289i −0.966315 0.461007i
\(563\) 3.34210 + 1.92956i 0.140853 + 0.0813213i 0.568770 0.822496i \(-0.307419\pi\)
−0.427918 + 0.903818i \(0.640753\pi\)
\(564\) 4.98222 + 0.0877893i 0.209789 + 0.00369660i
\(565\) −29.6031 + 5.21983i −1.24541 + 0.219600i
\(566\) −16.6933 + 7.60592i −0.701673 + 0.319701i
\(567\) −2.62161 0.954189i −0.110097 0.0400722i
\(568\) 11.1921 + 8.28600i 0.469609 + 0.347673i
\(569\) 5.88417 0.246677 0.123339 0.992365i \(-0.460640\pi\)
0.123339 + 0.992365i \(0.460640\pi\)
\(570\) −6.03602 + 15.9141i −0.252821 + 0.666568i
\(571\) 25.2352i 1.05606i −0.849226 0.528029i \(-0.822931\pi\)
0.849226 0.528029i \(-0.177069\pi\)
\(572\) 9.11460 + 26.4850i 0.381101 + 1.10739i
\(573\) 9.34737 25.6817i 0.390492 1.07287i
\(574\) −1.59299 3.49625i −0.0664899 0.145931i
\(575\) −2.83185 16.0602i −0.118096 0.669757i
\(576\) −5.45889 + 5.84812i −0.227454 + 0.243672i
\(577\) 5.88975 10.2013i 0.245193 0.424687i −0.716993 0.697081i \(-0.754482\pi\)
0.962186 + 0.272393i \(0.0878152\pi\)
\(578\) −11.5284 5.49992i −0.479517 0.228766i
\(579\) −2.42340 + 2.88809i −0.100713 + 0.120025i
\(580\) 33.8099 18.7338i 1.40388 0.777880i
\(581\) 34.2932 19.7992i 1.42272 0.821409i
\(582\) −2.82557 + 0.222142i −0.117123 + 0.00920807i
\(583\) 16.9915 6.18440i 0.703716 0.256132i
\(584\) 17.0029 7.38805i 0.703585 0.305720i
\(585\) 1.10287 6.25470i 0.0455981 0.258600i
\(586\) 4.26794 + 16.5085i 0.176307 + 0.681961i
\(587\) 0.0789445 + 0.0940823i 0.00325839 + 0.00388319i 0.767671 0.640844i \(-0.221415\pi\)
−0.764413 + 0.644727i \(0.776971\pi\)
\(588\) 1.46250 + 0.561679i 0.0603125 + 0.0231632i
\(589\) 18.6181 + 8.78735i 0.767144 + 0.362076i
\(590\) 24.7216 16.9877i 1.01777 0.699372i
\(591\) 15.6098 13.0982i 0.642102 0.538788i
\(592\) 28.9588 15.3854i 1.19020 0.632336i
\(593\) −4.38985 + 24.8961i −0.180270 + 1.02236i 0.751614 + 0.659603i \(0.229275\pi\)
−0.931884 + 0.362756i \(0.881836\pi\)
\(594\) −6.03444 6.14170i −0.247596 0.251997i
\(595\) −7.43681 20.4325i −0.304880 0.837650i
\(596\) 15.4995 12.5470i 0.634884 0.513945i
\(597\) 1.00864 0.582340i 0.0412810 0.0238336i
\(598\) 1.93982 20.1283i 0.0793250 0.823108i
\(599\) −26.3972 22.1498i −1.07856 0.905018i −0.0827581 0.996570i \(-0.526373\pi\)
−0.995800 + 0.0915517i \(0.970817\pi\)
\(600\) −5.10648 5.38378i −0.208471 0.219792i
\(601\) 2.91203 5.04378i 0.118784 0.205740i −0.800502 0.599330i \(-0.795434\pi\)
0.919286 + 0.393590i \(0.128767\pi\)
\(602\) 31.8548 + 22.7258i 1.29830 + 0.926234i
\(603\) 2.92701 0.516111i 0.119197 0.0210176i
\(604\) 32.3556 + 19.4485i 1.31653 + 0.791348i
\(605\) −24.6165 + 67.6334i −1.00080 + 2.74969i
\(606\) 2.87840 10.3758i 0.116927 0.421489i
\(607\) −14.1474 −0.574226 −0.287113 0.957897i \(-0.592696\pi\)
−0.287113 + 0.957897i \(0.592696\pi\)
\(608\) 7.29555 + 23.5537i 0.295874 + 0.955227i
\(609\) 19.5281 0.791320
\(610\) 6.12225 22.0690i 0.247883 0.893549i
\(611\) −1.96015 + 5.38548i −0.0792994 + 0.217873i
\(612\) 4.83870 + 2.90847i 0.195593 + 0.117568i
\(613\) 38.3919 6.76952i 1.55063 0.273419i 0.668245 0.743941i \(-0.267046\pi\)
0.882388 + 0.470522i \(0.155935\pi\)
\(614\) −35.0457 25.0022i −1.41433 1.00901i
\(615\) −1.34435 + 2.32848i −0.0542095 + 0.0938936i
\(616\) 33.0615 + 34.8569i 1.33209 + 1.40442i
\(617\) −12.8417 10.7754i −0.516986 0.433803i 0.346593 0.938015i \(-0.387338\pi\)
−0.863580 + 0.504213i \(0.831783\pi\)
\(618\) 2.21915 23.0268i 0.0892672 0.926273i
\(619\) −3.40163 + 1.96393i −0.136723 + 0.0789371i −0.566801 0.823855i \(-0.691819\pi\)
0.430078 + 0.902792i \(0.358486\pi\)
\(620\) −20.2720 + 16.4104i −0.814143 + 0.659057i
\(621\) 2.12605 + 5.84127i 0.0853155 + 0.234402i
\(622\) −15.0757 15.3437i −0.604480 0.615225i
\(623\) 1.33216 7.55505i 0.0533718 0.302687i
\(624\) −4.31695 8.12549i −0.172816 0.325280i
\(625\) −23.9272 + 20.0773i −0.957088 + 0.803092i
\(626\) −16.3752 + 11.2524i −0.654485 + 0.449735i
\(627\) −25.6657 + 6.74937i −1.02499 + 0.269544i
\(628\) 31.9616 + 12.2750i 1.27541 + 0.489825i
\(629\) −14.8749 17.7272i −0.593100 0.706829i
\(630\) −2.72668 10.5469i −0.108634 0.420199i
\(631\) 1.75568 9.95693i 0.0698923 0.396379i −0.929713 0.368285i \(-0.879945\pi\)
0.999605 0.0280941i \(-0.00894382\pi\)
\(632\) 4.84245 2.10413i 0.192622 0.0836978i
\(633\) −13.7818 + 5.01616i −0.547777 + 0.199374i
\(634\) 11.2208 0.882160i 0.445634 0.0350350i
\(635\) −45.5416 + 26.2935i −1.80726 + 1.04342i
\(636\) −5.19563 + 2.87886i −0.206020 + 0.114154i
\(637\) −1.15821 + 1.38030i −0.0458900 + 0.0546895i
\(638\) 54.3952 + 25.9507i 2.15353 + 1.02740i
\(639\) 2.46171 4.26381i 0.0973837 0.168674i
\(640\) −30.8921 4.63514i −1.22112 0.183220i
\(641\) 2.09592 + 11.8865i 0.0827837 + 0.469490i 0.997813 + 0.0661021i \(0.0210563\pi\)
−0.915029 + 0.403388i \(0.867833\pi\)
\(642\) −6.44835 14.1527i −0.254496 0.558563i
\(643\) −9.49738 + 26.0938i −0.374540 + 1.02904i 0.599045 + 0.800716i \(0.295547\pi\)
−0.973585 + 0.228325i \(0.926675\pi\)
\(644\) −11.2867 32.7966i −0.444759 1.29237i
\(645\) 27.3838i 1.07824i
\(646\) 15.1852 8.49678i 0.597454 0.334301i
\(647\) −20.6184 −0.810595 −0.405297 0.914185i \(-0.632832\pi\)
−0.405297 + 0.914185i \(0.632832\pi\)
\(648\) 2.27323 + 1.68298i 0.0893010 + 0.0661136i
\(649\) 43.9490 + 15.9961i 1.72515 + 0.627903i
\(650\) 7.76623 3.53850i 0.304617 0.138791i
\(651\) −12.9767 + 2.28814i −0.508596 + 0.0896791i
\(652\) −14.3259 0.252429i −0.561045 0.00988590i
\(653\) −37.0472 21.3892i −1.44977 0.837025i −0.451302 0.892371i \(-0.649040\pi\)
−0.998467 + 0.0553465i \(0.982374\pi\)
\(654\) 3.48225 + 1.66130i 0.136167 + 0.0649620i
\(655\) 33.4664 + 28.0817i 1.30764 + 1.09724i
\(656\) 0.540827 + 3.85744i 0.0211157 + 0.150608i
\(657\) −3.27720 5.67628i −0.127856 0.221453i
\(658\) 0.770451 + 9.79986i 0.0300353 + 0.382039i
\(659\) −5.60271 15.3933i −0.218251 0.599639i 0.781454 0.623963i \(-0.214479\pi\)
−0.999704 + 0.0243249i \(0.992256\pi\)
\(660\) 6.42054 33.0017i 0.249919 1.28459i
\(661\) 13.9146 + 2.45352i 0.541216 + 0.0954309i 0.437572 0.899184i \(-0.355839\pi\)
0.103644 + 0.994614i \(0.466950\pi\)
\(662\) −8.31947 32.1800i −0.323345 1.25071i
\(663\) −4.97403 + 4.17370i −0.193175 + 0.162093i
\(664\) −39.0389 + 9.36216i −1.51500 + 0.363322i
\(665\) −32.3917 8.84094i −1.25610 0.342837i
\(666\) −6.56599 9.55527i −0.254427 0.370259i
\(667\) −27.9684 33.3314i −1.08294 1.29060i
\(668\) 10.5285 12.1076i 0.407359 0.468456i
\(669\) 16.2677 + 2.86843i 0.628945 + 0.110900i
\(670\) 8.13372 + 8.27831i 0.314233 + 0.319819i
\(671\) 33.5562 12.2135i 1.29542 0.471496i
\(672\) −12.5166 9.61255i −0.482838 0.370812i
\(673\) −18.1907 31.5072i −0.701199 1.21451i −0.968046 0.250773i \(-0.919315\pi\)
0.266847 0.963739i \(-0.414018\pi\)
\(674\) −23.0680 2.22312i −0.888546 0.0856314i
\(675\) −1.68634 + 2.00970i −0.0649073 + 0.0773535i
\(676\) −15.2281 + 2.40932i −0.585697 + 0.0926660i
\(677\) −33.2505 19.1972i −1.27792 0.737808i −0.301455 0.953480i \(-0.597472\pi\)
−0.976466 + 0.215672i \(0.930806\pi\)
\(678\) 12.5339 + 8.94188i 0.481360 + 0.343411i
\(679\) −0.970915 5.50633i −0.0372603 0.211314i
\(680\) 1.34032 + 22.0036i 0.0513988 + 0.843799i
\(681\) 13.9702 + 5.08472i 0.535338 + 0.194847i
\(682\) −39.1869 10.8710i −1.50054 0.416271i
\(683\) 29.9054i 1.14430i −0.820149 0.572150i \(-0.806110\pi\)
0.820149 0.572150i \(-0.193890\pi\)
\(684\) 7.98108 3.50746i 0.305164 0.134111i
\(685\) 52.8224i 2.01824i
\(686\) 6.55668 23.6350i 0.250335 0.902390i
\(687\) −1.55301 0.565249i −0.0592509 0.0215656i
\(688\) −24.4138 31.2695i −0.930766 1.19214i
\(689\) −1.18631 6.72789i −0.0451948 0.256312i
\(690\) −14.0967 + 19.7594i −0.536653 + 0.752228i
\(691\) −31.5252 18.2011i −1.19927 0.692401i −0.238880 0.971049i \(-0.576780\pi\)
−0.960393 + 0.278648i \(0.910114\pi\)
\(692\) 1.35727 + 8.57863i 0.0515955 + 0.326111i
\(693\) 10.9181 13.0117i 0.414744 0.494272i
\(694\) −1.55148 + 16.0988i −0.0588934 + 0.611101i
\(695\) −25.1706 43.5968i −0.954776 1.65372i
\(696\) −18.9814 5.62767i −0.719488 0.213316i
\(697\) 2.58302 0.940143i 0.0978389 0.0356104i
\(698\) −17.6898 + 17.3809i −0.669570 + 0.657876i
\(699\) 10.2206 + 1.80216i 0.386577 + 0.0681640i
\(700\) 9.60541 11.0461i 0.363050 0.417502i
\(701\) 17.2533 + 20.5616i 0.651647 + 0.776603i 0.986161 0.165788i \(-0.0530167\pi\)
−0.334514 + 0.942391i \(0.608572\pi\)
\(702\) −2.68109 + 1.84234i −0.101191 + 0.0695345i
\(703\) −35.6125 + 2.94892i −1.34315 + 0.111221i
\(704\) −22.0907 43.4087i −0.832576 1.63603i
\(705\) 5.26976 4.42186i 0.198471 0.166537i
\(706\) −22.3517 + 5.77857i −0.841217 + 0.217479i
\(707\) 20.9190 + 3.68859i 0.786741 + 0.138724i
\(708\) −15.0810 2.93403i −0.566777 0.110268i
\(709\) 4.62635 + 12.7108i 0.173746 + 0.477364i 0.995748 0.0921215i \(-0.0293648\pi\)
−0.822002 + 0.569485i \(0.807143\pi\)
\(710\) 19.1655 1.50676i 0.719269 0.0565478i
\(711\) −0.933352 1.61661i −0.0350034 0.0606277i
\(712\) −3.47210 + 6.95963i −0.130122 + 0.260823i
\(713\) 22.4908 + 18.8720i 0.842287 + 0.706763i
\(714\) −4.79549 + 10.0518i −0.179467 + 0.376180i
\(715\) 33.4874 + 19.3340i 1.25236 + 0.723050i
\(716\) 30.4738 + 0.536964i 1.13886 + 0.0200673i
\(717\) 15.4935 2.73192i 0.578614 0.102025i
\(718\) 11.0585 + 24.2710i 0.412700 + 0.905786i
\(719\) 15.0969 + 5.49481i 0.563018 + 0.204922i 0.607821 0.794074i \(-0.292044\pi\)
−0.0448030 + 0.998996i \(0.514266\pi\)
\(720\) −0.389090 + 11.0374i −0.0145005 + 0.411340i
\(721\) 45.6361 1.69958
\(722\) 2.82617 26.7210i 0.105179 0.994453i
\(723\) 19.4805i 0.724489i
\(724\) 14.4493 4.97262i 0.537004 0.184806i
\(725\) 6.28069 17.2561i 0.233259 0.640874i
\(726\) 33.5470 15.2849i 1.24504 0.567275i
\(727\) 3.05050 + 17.3002i 0.113137 + 0.641630i 0.987656 + 0.156639i \(0.0500660\pi\)
−0.874519 + 0.484991i \(0.838823\pi\)
\(728\) 15.1385 10.0146i 0.561071 0.371165i
\(729\) 0.500000 0.866025i 0.0185185 0.0320750i
\(730\) 11.0201 23.0991i 0.407871 0.854938i
\(731\) −17.9954 + 21.4460i −0.665582 + 0.793210i
\(732\) −10.2608 + 5.68542i −0.379249 + 0.210139i
\(733\) 9.98914 5.76723i 0.368957 0.213018i −0.304046 0.952658i \(-0.598338\pi\)
0.673003 + 0.739640i \(0.265004\pi\)
\(734\) −0.232524 2.95762i −0.00858261 0.109168i
\(735\) 2.03238 0.739725i 0.0749654 0.0272852i
\(736\) 1.51930 + 35.1310i 0.0560022 + 1.29495i
\(737\) −3.14224 + 17.8205i −0.115746 + 0.656427i
\(738\) 1.33331 0.344701i 0.0490799 0.0126886i
\(739\) 16.4847 + 19.6456i 0.606398 + 0.722677i 0.978668 0.205448i \(-0.0658650\pi\)
−0.372270 + 0.928124i \(0.621421\pi\)
\(740\) 16.2305 42.2611i 0.596646 1.55355i
\(741\) 0.827432 + 9.99243i 0.0303965 + 0.367081i
\(742\) −6.63625 9.65751i −0.243624 0.354538i
\(743\) −9.83250 + 8.25044i −0.360719 + 0.302679i −0.805077 0.593170i \(-0.797876\pi\)
0.444358 + 0.895849i \(0.353432\pi\)
\(744\) 13.2728 + 1.51558i 0.486603 + 0.0555637i
\(745\) 4.78050 27.1116i 0.175144 0.993292i
\(746\) 15.8768 15.5995i 0.581291 0.571139i
\(747\) 4.85452 + 13.3377i 0.177618 + 0.488000i
\(748\) −26.7155 + 21.6265i −0.976815 + 0.790742i
\(749\) 26.5704 15.3405i 0.970863 0.560528i
\(750\) 9.23689 + 0.890182i 0.337283 + 0.0325048i
\(751\) −10.1263 8.49701i −0.369515 0.310060i 0.439054 0.898460i \(-0.355314\pi\)
−0.808570 + 0.588400i \(0.799758\pi\)
\(752\) 2.07527 9.74753i 0.0756773 0.355456i
\(753\) 15.0161 26.0087i 0.547218 0.947809i
\(754\) 13.2244 18.5367i 0.481604 0.675066i
\(755\) 51.3246 9.04991i 1.86789 0.329360i
\(756\) −2.87456 + 4.78228i −0.104547 + 0.173930i
\(757\) −15.6186 + 42.9116i −0.567666 + 1.55965i 0.240472 + 0.970656i \(0.422698\pi\)
−0.808138 + 0.588993i \(0.799524\pi\)
\(758\) −25.7944 7.15573i −0.936896 0.259908i
\(759\) −37.8458 −1.37372
\(760\) 28.9370 + 17.9281i 1.04966 + 0.650322i
\(761\) −5.57773 −0.202192 −0.101096 0.994877i \(-0.532235\pi\)
−0.101096 + 0.994877i \(0.532235\pi\)
\(762\) 25.9548 + 7.20020i 0.940242 + 0.260836i
\(763\) −2.60320 + 7.15224i −0.0942423 + 0.258929i
\(764\) −46.8479 28.1596i −1.69490 1.01878i
\(765\) 7.67545 1.35339i 0.277507 0.0489319i
\(766\) −9.88754 + 13.8594i −0.357251 + 0.500760i
\(767\) 8.83517 15.3030i 0.319019 0.552558i
\(768\) 9.39600 + 12.9505i 0.339049 + 0.467311i
\(769\) 15.5524 + 13.0500i 0.560833 + 0.470595i 0.878590 0.477578i \(-0.158485\pi\)
−0.317757 + 0.948172i \(0.602929\pi\)
\(770\) 66.0181 + 6.36233i 2.37913 + 0.229283i
\(771\) −17.2190 + 9.94138i −0.620126 + 0.358030i
\(772\) 4.74428 + 5.86068i 0.170750 + 0.210931i
\(773\) −4.12046 11.3209i −0.148202 0.407183i 0.843272 0.537488i \(-0.180627\pi\)
−0.991474 + 0.130305i \(0.958404\pi\)
\(774\) −10.0048 + 9.83008i −0.359616 + 0.353335i
\(775\) −2.15168 + 12.2028i −0.0772905 + 0.438336i
\(776\) −0.643097 + 5.63197i −0.0230859 + 0.202176i
\(777\) 17.5205 14.7014i 0.628544 0.527411i
\(778\) 27.1806 + 39.5550i 0.974471 + 1.41812i
\(779\) 1.11765 4.09488i 0.0400439 0.146714i
\(780\) −11.8579 4.55408i −0.424582 0.163062i
\(781\) 19.2677 + 22.9624i 0.689454 + 0.821659i
\(782\) 24.0250 6.21117i 0.859133 0.222111i
\(783\) −1.21548 + 6.89334i −0.0434378 + 0.246348i
\(784\) 1.66127 2.65664i 0.0593312 0.0948800i
\(785\) 44.4157 16.1660i 1.58526 0.576989i
\(786\) −1.75380 22.3078i −0.0625561 0.795691i
\(787\) −4.49901 + 2.59751i −0.160372 + 0.0925911i −0.578038 0.816010i \(-0.696182\pi\)
0.417666 + 0.908601i \(0.362848\pi\)
\(788\) −19.7522 35.6478i −0.703643 1.26990i
\(789\) −8.71018 + 10.3804i −0.310091 + 0.369552i
\(790\) 3.13853 6.57867i 0.111664 0.234059i
\(791\) −15.1867 + 26.3041i −0.539975 + 0.935264i
\(792\) −14.3621 + 9.50097i −0.510337 + 0.337602i
\(793\) −2.34282 13.2868i −0.0831961 0.471828i
\(794\) 12.0042 5.46943i 0.426013 0.194103i
\(795\) −2.80464 + 7.70570i −0.0994705 + 0.273293i
\(796\) −0.758001 2.20258i −0.0268666 0.0780683i
\(797\) 23.0924i 0.817976i 0.912540 + 0.408988i \(0.134118\pi\)
−0.912540 + 0.408988i \(0.865882\pi\)
\(798\) 8.39771 + 15.0082i 0.297276 + 0.531283i
\(799\) −7.03293 −0.248807
\(800\) −12.5198 + 7.96870i −0.442641 + 0.281736i
\(801\) 2.58398 + 0.940492i 0.0913005 + 0.0332307i
\(802\) −0.327120 0.717956i −0.0115510 0.0253519i
\(803\) 39.2990 6.92947i 1.38683 0.244536i
\(804\) 0.104726 5.94340i 0.00369339 0.209608i
\(805\) −41.4679 23.9415i −1.46155 0.843826i
\(806\) −6.61579 + 13.8673i −0.233031 + 0.488456i
\(807\) 3.06493 + 2.57178i 0.107891 + 0.0905310i
\(808\) −19.2704 9.61381i −0.677929 0.338213i
\(809\) 1.37089 + 2.37445i 0.0481979 + 0.0834813i 0.889118 0.457678i \(-0.151319\pi\)
−0.840920 + 0.541160i \(0.817986\pi\)
\(810\) 3.89272 0.306040i 0.136776 0.0107532i
\(811\) −6.41774 17.6326i −0.225357 0.619164i 0.774554 0.632508i \(-0.217975\pi\)
−0.999911 + 0.0133442i \(0.995752\pi\)
\(812\) 7.45863 38.3375i 0.261747 1.34538i
\(813\) 0.842375 + 0.148533i 0.0295434 + 0.00520930i
\(814\) 68.3395 17.6678i 2.39530 0.619255i
\(815\) −15.1527 + 12.7146i −0.530775 + 0.445373i
\(816\) 7.55799 8.38842i 0.264583 0.293653i
\(817\) 10.9947 + 41.8094i 0.384656 + 1.46272i
\(818\) −7.87946 + 5.41445i −0.275499 + 0.189312i
\(819\) −4.12504 4.91603i −0.144141 0.171780i
\(820\) 4.05780 + 3.52857i 0.141704 + 0.123223i
\(821\) 22.9765 + 4.05138i 0.801886 + 0.141394i 0.559548 0.828798i \(-0.310975\pi\)
0.242338 + 0.970192i \(0.422086\pi\)
\(822\) 19.2990 18.9619i 0.673128 0.661372i
\(823\) 19.4943 7.09535i 0.679529 0.247328i 0.0208839 0.999782i \(-0.493352\pi\)
0.658645 + 0.752453i \(0.271130\pi\)
\(824\) −44.3584 13.1515i −1.54530 0.458155i
\(825\) −7.98627 13.8326i −0.278046 0.481590i
\(826\) 2.90743 30.1687i 0.101163 1.04970i
\(827\) −22.2099 + 26.4688i −0.772315 + 0.920409i −0.998559 0.0536612i \(-0.982911\pi\)
0.226244 + 0.974071i \(0.427355\pi\)
\(828\) 12.2796 1.94281i 0.426745 0.0675173i
\(829\) 34.8350 + 20.1120i 1.20987 + 0.698518i 0.962731 0.270462i \(-0.0871765\pi\)
0.247138 + 0.968980i \(0.420510\pi\)
\(830\) −32.1878 + 45.1177i −1.11725 + 1.56606i
\(831\) 0.557120 + 3.15959i 0.0193263 + 0.109605i
\(832\) −17.6007 + 5.37153i −0.610195 + 0.186224i
\(833\) −2.07780 0.756257i −0.0719915 0.0262028i
\(834\) −6.89272 + 24.8464i −0.238675 + 0.860359i
\(835\) 22.1506i 0.766555i
\(836\) 3.44748 + 52.9645i 0.119234 + 1.83182i
\(837\) 4.72312i 0.163255i
\(838\) 21.2169 + 5.88585i 0.732925 + 0.203323i
\(839\) 18.2914 + 6.65754i 0.631491 + 0.229844i 0.637880 0.770136i \(-0.279812\pi\)
−0.00638915 + 0.999980i \(0.502034\pi\)
\(840\) −21.7470 + 1.32469i −0.750344 + 0.0457061i
\(841\) −3.47218 19.6917i −0.119730 0.679025i
\(842\) 1.60583 + 1.14563i 0.0553404 + 0.0394809i
\(843\) 15.5429 + 8.97368i 0.535325 + 0.309070i
\(844\) 4.58383 + 28.9722i 0.157782 + 0.997263i
\(845\) −13.6814 + 16.3048i −0.470653 + 0.560903i
\(846\) −3.50726 0.338004i −0.120582 0.0116208i
\(847\) 36.3623 + 62.9814i 1.24942 + 2.16407i
\(848\) 3.66732 + 11.2996i 0.125936 + 0.388029i
\(849\) 12.1892 4.43650i 0.418332 0.152260i
\(850\) 7.33996 + 7.47044i 0.251759 + 0.256234i
\(851\) −50.1860 8.84915i −1.72036 0.303345i
\(852\) −7.43043 6.46134i −0.254562 0.221362i
\(853\) −10.9941 13.1023i −0.376431 0.448613i 0.544253 0.838921i \(-0.316813\pi\)
−0.920684 + 0.390308i \(0.872369\pi\)
\(854\) −13.1058 19.0725i −0.448472 0.652647i
\(855\) 5.13695 10.8838i 0.175680 0.372219i
\(856\) −30.2474 + 7.25382i −1.03383 + 0.247930i
\(857\) 32.1757 26.9987i 1.09910 0.922256i 0.101738 0.994811i \(-0.467560\pi\)
0.997364 + 0.0725548i \(0.0231152\pi\)
\(858\) −4.95736 19.1752i −0.169241 0.654631i
\(859\) −32.9685 5.81323i −1.12487 0.198345i −0.419892 0.907574i \(-0.637932\pi\)
−0.704978 + 0.709229i \(0.749043\pi\)
\(860\) −53.7596 10.4590i −1.83319 0.356650i
\(861\) 0.929181 + 2.55290i 0.0316664 + 0.0870028i
\(862\) 1.36230 + 17.3280i 0.0464001 + 0.590193i
\(863\) −11.7378 20.3304i −0.399558 0.692055i 0.594113 0.804381i \(-0.297503\pi\)
−0.993671 + 0.112327i \(0.964170\pi\)
\(864\) 4.17225 3.81999i 0.141943 0.129959i
\(865\) 9.18517 + 7.70727i 0.312305 + 0.262055i
\(866\) −34.5272 16.4721i −1.17328 0.559745i
\(867\) 7.82190 + 4.51598i 0.265646 + 0.153371i
\(868\) −0.464294 + 26.3496i −0.0157592 + 0.894364i
\(869\) 11.1924 1.97352i 0.379676 0.0669472i
\(870\) −24.8719 + 11.3323i −0.843237 + 0.384201i
\(871\) 6.42446 + 2.33831i 0.217684 + 0.0792307i
\(872\) 4.59147 6.20180i 0.155487 0.210020i
\(873\) 2.00414 0.0678299
\(874\) 13.5893 35.8284i 0.459664 1.21191i
\(875\) 18.3063i 0.618866i
\(876\) −12.3953 + 4.26576i −0.418799 + 0.144127i
\(877\) −16.2272 + 44.5839i −0.547954 + 1.50549i 0.288514 + 0.957476i \(0.406839\pi\)
−0.836468 + 0.548016i \(0.815383\pi\)
\(878\) 8.87386 + 19.4762i 0.299478 + 0.657289i
\(879\) −2.09369 11.8739i −0.0706185 0.400497i
\(880\) −62.3363 25.2095i −2.10136 0.849811i
\(881\) 1.58829 2.75099i 0.0535107 0.0926833i −0.838029 0.545625i \(-0.816292\pi\)
0.891540 + 0.452942i \(0.149626\pi\)
\(882\) −0.999834 0.476998i −0.0336662 0.0160614i
\(883\) 16.5260 19.6949i 0.556143 0.662785i −0.412583 0.910920i \(-0.635373\pi\)
0.968725 + 0.248135i \(0.0798176\pi\)
\(884\) 6.29398 + 11.3591i 0.211690 + 0.382047i
\(885\) −18.3685 + 10.6051i −0.617451 + 0.356485i
\(886\) 6.70331 0.527004i 0.225202 0.0177051i
\(887\) −53.6611 + 19.5310i −1.80176 + 0.655788i −0.803603 + 0.595166i \(0.797086\pi\)
−0.998161 + 0.0606228i \(0.980691\pi\)
\(888\) −21.2667 + 9.24073i −0.713662 + 0.310099i
\(889\) −9.22687 + 52.3282i −0.309459 + 1.75503i
\(890\) 2.68755 + 10.3955i 0.0900867 + 0.348458i
\(891\) 3.91349 + 4.66391i 0.131107 + 0.156247i
\(892\) 11.8446 30.8410i 0.396586 1.03263i
\(893\) −6.27044 + 8.86709i −0.209832 + 0.296726i
\(894\) −11.6214 + 7.98578i −0.388679 + 0.267085i
\(895\) 32.2326 27.0463i 1.07742 0.904060i
\(896\) −23.6519 + 20.9010i −0.790154 + 0.698255i
\(897\) −2.48296 + 14.0816i −0.0829037 + 0.470170i
\(898\) 31.3868 + 31.9448i 1.04739 + 1.06601i
\(899\) 11.3073 + 31.0666i 0.377120 + 1.03613i
\(900\) 3.30134 + 4.07820i 0.110045 + 0.135940i
\(901\) 7.26032 4.19175i 0.241876 0.139647i
\(902\) −0.804310 + 8.34584i −0.0267806 + 0.277886i
\(903\) −21.1960 17.7855i −0.705358 0.591866i
\(904\) 22.3418 21.1911i 0.743078 0.704805i
\(905\) 10.5480 18.2696i 0.350626 0.607303i
\(906\) −21.7306 15.5030i −0.721952 0.515054i
\(907\) 30.4754 5.37364i 1.01192 0.178429i 0.356981 0.934111i \(-0.383806\pi\)
0.654938 + 0.755683i \(0.272695\pi\)
\(908\) 15.3181 25.4840i 0.508348 0.845717i
\(909\) −2.60411 + 7.15473i −0.0863728 + 0.237307i
\(910\) 6.69855 24.1464i 0.222055 0.800446i
\(911\) −45.2894 −1.50051 −0.750253 0.661151i \(-0.770068\pi\)
−0.750253 + 0.661151i \(0.770068\pi\)
\(912\) −3.83751 17.0080i −0.127073 0.563193i
\(913\) −86.4154 −2.85993
\(914\) −8.98985 + 32.4060i −0.297358 + 1.07189i
\(915\) −5.53885 + 15.2179i −0.183109 + 0.503087i
\(916\) −1.70285 + 2.83296i −0.0562638 + 0.0936036i
\(917\) 43.4723 7.66534i 1.43558 0.253132i
\(918\) −3.24976 2.31844i −0.107258 0.0765198i
\(919\) −24.8173 + 42.9847i −0.818646 + 1.41794i 0.0880345 + 0.996117i \(0.471941\pi\)
−0.906680 + 0.421819i \(0.861392\pi\)
\(920\) 33.4074 + 35.2215i 1.10141 + 1.16122i
\(921\) 23.3192 + 19.5671i 0.768393 + 0.644758i
\(922\) −1.70245 + 17.6653i −0.0560671 + 0.581775i
\(923\) 9.80789 5.66259i 0.322831 0.186386i
\(924\) −21.3743 26.4040i −0.703163 0.868628i
\(925\) −7.35596 20.2103i −0.241862 0.664511i
\(926\) 5.56745 + 5.66642i 0.182958 + 0.186210i
\(927\) −2.84051 + 16.1093i −0.0932945 + 0.529099i
\(928\) −18.2980 + 35.1147i −0.600661 + 1.15270i
\(929\) 31.9460 26.8058i 1.04811 0.879471i 0.0552191 0.998474i \(-0.482414\pi\)
0.992894 + 0.119003i \(0.0379698\pi\)
\(930\) 15.1998 10.4447i 0.498423 0.342496i
\(931\) −2.80601 + 1.94541i −0.0919634 + 0.0637584i
\(932\) 7.44165 19.3766i 0.243759 0.634701i
\(933\) 9.77697 + 11.6517i 0.320084 + 0.381461i
\(934\) −5.75974 22.2789i −0.188464 0.728986i
\(935\) −8.23985 + 46.7305i −0.269472 + 1.52825i
\(936\) 2.59284 + 5.96716i 0.0847495 + 0.195043i
\(937\) 46.9563 17.0907i 1.53400 0.558329i 0.569400 0.822061i \(-0.307176\pi\)
0.964596 + 0.263732i \(0.0849533\pi\)
\(938\) 11.6905 0.919087i 0.381707 0.0300093i
\(939\) 12.1670 7.02463i 0.397056 0.229240i
\(940\) −6.66820 12.0344i −0.217493 0.392520i
\(941\) 5.05759 6.02740i 0.164873 0.196487i −0.677282 0.735723i \(-0.736842\pi\)
0.842155 + 0.539236i \(0.181287\pi\)
\(942\) −21.8504 10.4243i −0.711926 0.339644i
\(943\) 3.02662 5.24226i 0.0985603 0.170711i
\(944\) −11.5201 + 28.4862i −0.374948 + 0.927146i
\(945\) 1.33761 + 7.58596i 0.0435125 + 0.246771i
\(946\) −35.4060 77.7083i −1.15115 2.52652i
\(947\) −19.2221 + 52.8122i −0.624633 + 1.71617i 0.0707190 + 0.997496i \(0.477471\pi\)
−0.695352 + 0.718669i \(0.744752\pi\)
\(948\) −3.53021 + 1.21490i −0.114656 + 0.0394580i
\(949\) 15.0769i 0.489416i
\(950\) 15.9629 2.59368i 0.517904 0.0841502i
\(951\) −7.95876 −0.258081
\(952\) 17.9020 + 13.2537i 0.580208 + 0.429554i
\(953\) −2.24194 0.815998i −0.0726234 0.0264328i 0.305453 0.952207i \(-0.401192\pi\)
−0.378076 + 0.925774i \(0.623414\pi\)
\(954\) 3.82211 1.74146i 0.123746 0.0563817i
\(955\) −74.3132 + 13.1034i −2.40472 + 0.424017i
\(956\) 0.554342 31.4601i 0.0179287 1.01749i
\(957\) −36.9067 21.3081i −1.19302 0.688793i
\(958\) −34.2262 16.3285i −1.10580 0.527551i
\(959\) 40.8863 + 34.3077i 1.32029 + 1.10785i
\(960\) 21.5199 + 4.97951i 0.694553 + 0.160713i
\(961\) 4.34606 + 7.52760i 0.140196 + 0.242826i
\(962\) −2.09021 26.5867i −0.0673910 0.857190i
\(963\) 3.76129 + 10.3341i 0.121206 + 0.333011i
\(964\) −38.2440 7.44045i −1.23176 0.239641i
\(965\) 10.2515 + 1.80761i 0.330006 + 0.0581890i
\(966\) 6.13875 + 23.7449i 0.197511 + 0.763979i
\(967\) 26.9086 22.5790i 0.865323 0.726092i −0.0977850 0.995208i \(-0.531176\pi\)
0.963108 + 0.269115i \(0.0867313\pi\)
\(968\) −17.1941 71.6970i −0.552640 2.30443i
\(969\) −11.1754 + 5.14807i −0.359007 + 0.165380i
\(970\) 4.43196 + 6.44968i 0.142302 + 0.207087i
\(971\) −10.3661 12.3538i −0.332663 0.396453i 0.573621 0.819121i \(-0.305538\pi\)
−0.906285 + 0.422668i \(0.861094\pi\)
\(972\) −1.50920 1.31237i −0.0484077 0.0420942i
\(973\) −50.0935 8.83283i −1.60592 0.283168i
\(974\) −16.7827 17.0810i −0.537752 0.547311i
\(975\) −5.67077 + 2.06399i −0.181610 + 0.0661006i
\(976\) 7.24254 + 22.3154i 0.231828 + 0.714297i
\(977\) 13.4403 + 23.2792i 0.429992 + 0.744769i 0.996872 0.0790319i \(-0.0251829\pi\)
−0.566880 + 0.823801i \(0.691850\pi\)
\(978\) 10.0848 + 0.971895i 0.322476 + 0.0310778i
\(979\) −10.7614 + 12.8249i −0.343935 + 0.409885i
\(980\) −0.675970 4.27248i −0.0215931 0.136479i
\(981\) −2.36268 1.36409i −0.0754345 0.0435521i
\(982\) 36.5987 + 26.1101i 1.16791 + 0.833208i
\(983\) 2.80181 + 15.8898i 0.0893638 + 0.506807i 0.996329 + 0.0856026i \(0.0272815\pi\)
−0.906966 + 0.421205i \(0.861607\pi\)
\(984\) −0.167464 2.74920i −0.00533855 0.0876414i
\(985\) −52.8696 19.2430i −1.68457 0.613132i
\(986\) 26.9259 + 7.46960i 0.857494 + 0.237881i
\(987\) 6.95093i 0.221251i
\(988\) 19.9331 + 2.19213i 0.634156 + 0.0697409i
\(989\) 61.6508i 1.96038i
\(990\) −6.35501 + 22.9081i −0.201976 + 0.728066i
\(991\) −35.8448 13.0464i −1.13865 0.414434i −0.297223 0.954808i \(-0.596061\pi\)
−0.841425 + 0.540374i \(0.818283\pi\)
\(992\) 8.04480 25.4781i 0.255423 0.808930i
\(993\) 4.08122 + 23.1458i 0.129514 + 0.734508i
\(994\) 11.2815 15.8134i 0.357829 0.501570i
\(995\) −2.78493 1.60788i −0.0882881 0.0509732i
\(996\) 28.0386 4.43612i 0.888436 0.140564i
\(997\) −9.49702 + 11.3181i −0.300774 + 0.358448i −0.895171 0.445724i \(-0.852946\pi\)
0.594397 + 0.804172i \(0.297391\pi\)
\(998\) −3.21612 + 33.3718i −0.101805 + 1.05637i
\(999\) 4.09902 + 7.09970i 0.129687 + 0.224625i
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 456.2.bk.a.253.17 yes 240
8.5 even 2 inner 456.2.bk.a.253.3 240
19.16 even 9 inner 456.2.bk.a.301.3 yes 240
152.149 even 18 inner 456.2.bk.a.301.17 yes 240
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
456.2.bk.a.253.3 240 8.5 even 2 inner
456.2.bk.a.253.17 yes 240 1.1 even 1 trivial
456.2.bk.a.301.3 yes 240 19.16 even 9 inner
456.2.bk.a.301.17 yes 240 152.149 even 18 inner