Properties

Label 162.2.e.a.19.1
Level $162$
Weight $2$
Character 162.19
Analytic conductor $1.294$
Analytic rank $0$
Dimension $6$
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] = [162,2,Mod(19,162)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(162, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([16]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("162.19");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 162 = 2 \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 162.e (of order \(9\), degree \(6\), not 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: \(1.29357651274\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\Q(\zeta_{18})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{3} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 54)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 19.1
Root \(-0.173648 + 0.984808i\) of defining polynomial
Character \(\chi\) \(=\) 162.19
Dual form 162.2.e.a.145.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.939693 + 0.342020i) q^{2} +(0.766044 - 0.642788i) q^{4} +(-0.439693 - 2.49362i) q^{5} +(-1.79813 - 1.50881i) q^{7} +(-0.500000 + 0.866025i) q^{8} +O(q^{10})\) \(q+(-0.939693 + 0.342020i) q^{2} +(0.766044 - 0.642788i) q^{4} +(-0.439693 - 2.49362i) q^{5} +(-1.79813 - 1.50881i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(1.26604 + 2.19285i) q^{10} +(0.745100 - 4.22567i) q^{11} +(-0.713011 - 0.259515i) q^{13} +(2.20574 + 0.802823i) q^{14} +(0.173648 - 0.984808i) q^{16} +(2.46064 + 4.26195i) q^{17} +(3.62449 - 6.27779i) q^{19} +(-1.93969 - 1.62760i) q^{20} +(0.745100 + 4.22567i) q^{22} +(0.233956 - 0.196312i) q^{23} +(-1.32635 + 0.482753i) q^{25} +0.758770 q^{26} -2.34730 q^{28} +(-2.91875 + 1.06234i) q^{29} +(-6.58512 + 5.52557i) q^{31} +(0.173648 + 0.984808i) q^{32} +(-3.76991 - 3.16333i) q^{34} +(-2.97178 + 5.14728i) q^{35} +(3.78699 + 6.55926i) q^{37} +(-1.25877 + 7.13884i) q^{38} +(2.37939 + 0.866025i) q^{40} +(4.60607 + 1.67647i) q^{41} +(-0.283119 + 1.60565i) q^{43} +(-2.14543 - 3.71599i) q^{44} +(-0.152704 + 0.264490i) q^{46} +(1.39053 + 1.16679i) q^{47} +(-0.258770 - 1.46756i) q^{49} +(1.08125 - 0.907278i) q^{50} +(-0.713011 + 0.259515i) q^{52} -0.573978 q^{53} -10.8648 q^{55} +(2.20574 - 0.802823i) q^{56} +(2.37939 - 1.99654i) q^{58} +(-0.950837 - 5.39246i) q^{59} +(8.46451 + 7.10257i) q^{61} +(4.29813 - 7.44459i) q^{62} +(-0.500000 - 0.866025i) q^{64} +(-0.333626 + 1.89209i) q^{65} +(-0.0393628 - 0.0143269i) q^{67} +(4.62449 + 1.68317i) q^{68} +(1.03209 - 5.85327i) q^{70} +(-2.10220 - 3.64111i) q^{71} +(5.54576 - 9.60554i) q^{73} +(-5.80200 - 4.86846i) q^{74} +(-1.25877 - 7.13884i) q^{76} +(-7.71554 + 6.47410i) q^{77} +(6.92989 - 2.52227i) q^{79} -2.53209 q^{80} -4.90167 q^{82} +(6.41147 - 2.33359i) q^{83} +(9.54576 - 8.00984i) q^{85} +(-0.283119 - 1.60565i) q^{86} +(3.28699 + 2.75811i) q^{88} +(3.96064 - 6.86002i) q^{89} +(0.890530 + 1.54244i) q^{91} +(0.0530334 - 0.300767i) q^{92} +(-1.70574 - 0.620838i) q^{94} +(-17.2481 - 6.27779i) q^{95} +(-0.570108 + 3.23324i) q^{97} +(0.745100 + 1.29055i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 3 q^{5} + 3 q^{7} - 3 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 3 q^{5} + 3 q^{7} - 3 q^{8} + 3 q^{10} + 3 q^{11} - 12 q^{13} + 3 q^{14} + 6 q^{17} + 9 q^{19} - 6 q^{20} + 3 q^{22} + 6 q^{23} - 9 q^{25} - 18 q^{26} - 12 q^{28} - 15 q^{29} - 18 q^{31} + 6 q^{34} - 3 q^{35} + 15 q^{37} + 15 q^{38} + 3 q^{40} + 3 q^{41} - 18 q^{43} + 3 q^{44} - 3 q^{46} - 9 q^{47} + 21 q^{49} + 9 q^{50} - 12 q^{52} + 12 q^{53} - 18 q^{55} + 3 q^{56} + 3 q^{58} + 6 q^{59} + 18 q^{61} + 12 q^{62} - 3 q^{64} - 21 q^{65} - 9 q^{67} + 15 q^{68} - 3 q^{70} - 12 q^{71} + 3 q^{73} + 3 q^{74} + 15 q^{76} - 39 q^{77} + 33 q^{79} - 6 q^{80} - 6 q^{82} + 18 q^{83} + 27 q^{85} - 18 q^{86} + 12 q^{88} + 15 q^{89} - 12 q^{91} - 12 q^{92} - 21 q^{95} - 12 q^{97} + 3 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).

\(n\) \(83\)
\(\chi(n)\) \(e\left(\frac{8}{9}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.939693 + 0.342020i −0.664463 + 0.241845i
\(3\) 0 0
\(4\) 0.766044 0.642788i 0.383022 0.321394i
\(5\) −0.439693 2.49362i −0.196637 1.11518i −0.910069 0.414457i \(-0.863972\pi\)
0.713432 0.700724i \(-0.247140\pi\)
\(6\) 0 0
\(7\) −1.79813 1.50881i −0.679631 0.570278i 0.236268 0.971688i \(-0.424076\pi\)
−0.915898 + 0.401410i \(0.868520\pi\)
\(8\) −0.500000 + 0.866025i −0.176777 + 0.306186i
\(9\) 0 0
\(10\) 1.26604 + 2.19285i 0.400358 + 0.693441i
\(11\) 0.745100 4.22567i 0.224656 1.27409i −0.638685 0.769468i \(-0.720521\pi\)
0.863342 0.504620i \(-0.168367\pi\)
\(12\) 0 0
\(13\) −0.713011 0.259515i −0.197754 0.0719765i 0.241245 0.970464i \(-0.422444\pi\)
−0.438998 + 0.898488i \(0.644667\pi\)
\(14\) 2.20574 + 0.802823i 0.589508 + 0.214563i
\(15\) 0 0
\(16\) 0.173648 0.984808i 0.0434120 0.246202i
\(17\) 2.46064 + 4.26195i 0.596792 + 1.03367i 0.993291 + 0.115639i \(0.0368917\pi\)
−0.396499 + 0.918035i \(0.629775\pi\)
\(18\) 0 0
\(19\) 3.62449 6.27779i 0.831514 1.44022i −0.0653235 0.997864i \(-0.520808\pi\)
0.896837 0.442360i \(-0.145859\pi\)
\(20\) −1.93969 1.62760i −0.433728 0.363941i
\(21\) 0 0
\(22\) 0.745100 + 4.22567i 0.158856 + 0.900916i
\(23\) 0.233956 0.196312i 0.0487831 0.0409339i −0.618070 0.786123i \(-0.712085\pi\)
0.666853 + 0.745189i \(0.267641\pi\)
\(24\) 0 0
\(25\) −1.32635 + 0.482753i −0.265270 + 0.0965505i
\(26\) 0.758770 0.148807
\(27\) 0 0
\(28\) −2.34730 −0.443597
\(29\) −2.91875 + 1.06234i −0.541998 + 0.197271i −0.598488 0.801132i \(-0.704231\pi\)
0.0564897 + 0.998403i \(0.482009\pi\)
\(30\) 0 0
\(31\) −6.58512 + 5.52557i −1.18272 + 0.992422i −0.182766 + 0.983156i \(0.558505\pi\)
−0.999957 + 0.00926586i \(0.997051\pi\)
\(32\) 0.173648 + 0.984808i 0.0306970 + 0.174091i
\(33\) 0 0
\(34\) −3.76991 3.16333i −0.646535 0.542507i
\(35\) −2.97178 + 5.14728i −0.502323 + 0.870049i
\(36\) 0 0
\(37\) 3.78699 + 6.55926i 0.622577 + 1.07834i 0.989004 + 0.147888i \(0.0472477\pi\)
−0.366427 + 0.930447i \(0.619419\pi\)
\(38\) −1.25877 + 7.13884i −0.204200 + 1.15807i
\(39\) 0 0
\(40\) 2.37939 + 0.866025i 0.376214 + 0.136931i
\(41\) 4.60607 + 1.67647i 0.719347 + 0.261821i 0.675648 0.737224i \(-0.263864\pi\)
0.0436983 + 0.999045i \(0.486086\pi\)
\(42\) 0 0
\(43\) −0.283119 + 1.60565i −0.0431752 + 0.244859i −0.998756 0.0498718i \(-0.984119\pi\)
0.955580 + 0.294730i \(0.0952298\pi\)
\(44\) −2.14543 3.71599i −0.323436 0.560207i
\(45\) 0 0
\(46\) −0.152704 + 0.264490i −0.0225149 + 0.0389970i
\(47\) 1.39053 + 1.16679i 0.202830 + 0.170194i 0.738545 0.674205i \(-0.235513\pi\)
−0.535715 + 0.844399i \(0.679958\pi\)
\(48\) 0 0
\(49\) −0.258770 1.46756i −0.0369672 0.209651i
\(50\) 1.08125 0.907278i 0.152912 0.128308i
\(51\) 0 0
\(52\) −0.713011 + 0.259515i −0.0988768 + 0.0359882i
\(53\) −0.573978 −0.0788419 −0.0394210 0.999223i \(-0.512551\pi\)
−0.0394210 + 0.999223i \(0.512551\pi\)
\(54\) 0 0
\(55\) −10.8648 −1.46501
\(56\) 2.20574 0.802823i 0.294754 0.107282i
\(57\) 0 0
\(58\) 2.37939 1.99654i 0.312429 0.262159i
\(59\) −0.950837 5.39246i −0.123788 0.702039i −0.982020 0.188777i \(-0.939548\pi\)
0.858232 0.513263i \(-0.171563\pi\)
\(60\) 0 0
\(61\) 8.46451 + 7.10257i 1.08377 + 0.909390i 0.996228 0.0867707i \(-0.0276547\pi\)
0.0875408 + 0.996161i \(0.472099\pi\)
\(62\) 4.29813 7.44459i 0.545863 0.945463i
\(63\) 0 0
\(64\) −0.500000 0.866025i −0.0625000 0.108253i
\(65\) −0.333626 + 1.89209i −0.0413812 + 0.234684i
\(66\) 0 0
\(67\) −0.0393628 0.0143269i −0.00480894 0.00175031i 0.339615 0.940565i \(-0.389703\pi\)
−0.344423 + 0.938814i \(0.611926\pi\)
\(68\) 4.62449 + 1.68317i 0.560801 + 0.204115i
\(69\) 0 0
\(70\) 1.03209 5.85327i 0.123358 0.699599i
\(71\) −2.10220 3.64111i −0.249485 0.432120i 0.713898 0.700250i \(-0.246928\pi\)
−0.963383 + 0.268129i \(0.913595\pi\)
\(72\) 0 0
\(73\) 5.54576 9.60554i 0.649082 1.12424i −0.334260 0.942481i \(-0.608487\pi\)
0.983342 0.181762i \(-0.0581802\pi\)
\(74\) −5.80200 4.86846i −0.674469 0.565947i
\(75\) 0 0
\(76\) −1.25877 7.13884i −0.144391 0.818881i
\(77\) −7.71554 + 6.47410i −0.879267 + 0.737793i
\(78\) 0 0
\(79\) 6.92989 2.52227i 0.779674 0.283778i 0.0786372 0.996903i \(-0.474943\pi\)
0.701037 + 0.713125i \(0.252721\pi\)
\(80\) −2.53209 −0.283096
\(81\) 0 0
\(82\) −4.90167 −0.541299
\(83\) 6.41147 2.33359i 0.703751 0.256144i 0.0347393 0.999396i \(-0.488940\pi\)
0.669011 + 0.743252i \(0.266718\pi\)
\(84\) 0 0
\(85\) 9.54576 8.00984i 1.03538 0.868789i
\(86\) −0.283119 1.60565i −0.0305295 0.173141i
\(87\) 0 0
\(88\) 3.28699 + 2.75811i 0.350394 + 0.294016i
\(89\) 3.96064 6.86002i 0.419827 0.727161i −0.576095 0.817383i \(-0.695424\pi\)
0.995922 + 0.0902216i \(0.0287575\pi\)
\(90\) 0 0
\(91\) 0.890530 + 1.54244i 0.0933529 + 0.161692i
\(92\) 0.0530334 0.300767i 0.00552912 0.0313572i
\(93\) 0 0
\(94\) −1.70574 0.620838i −0.175933 0.0640345i
\(95\) −17.2481 6.27779i −1.76962 0.644088i
\(96\) 0 0
\(97\) −0.570108 + 3.23324i −0.0578857 + 0.328286i −0.999975 0.00707624i \(-0.997748\pi\)
0.942089 + 0.335362i \(0.108859\pi\)
\(98\) 0.745100 + 1.29055i 0.0752665 + 0.130365i
\(99\) 0 0
\(100\) −0.705737 + 1.22237i −0.0705737 + 0.122237i
\(101\) 9.18732 + 7.70908i 0.914172 + 0.767082i 0.972908 0.231192i \(-0.0742625\pi\)
−0.0587358 + 0.998274i \(0.518707\pi\)
\(102\) 0 0
\(103\) 0.418748 + 2.37484i 0.0412605 + 0.234000i 0.998463 0.0554184i \(-0.0176493\pi\)
−0.957203 + 0.289418i \(0.906538\pi\)
\(104\) 0.581252 0.487728i 0.0569964 0.0478257i
\(105\) 0 0
\(106\) 0.539363 0.196312i 0.0523876 0.0190675i
\(107\) 2.42602 0.234532 0.117266 0.993101i \(-0.462587\pi\)
0.117266 + 0.993101i \(0.462587\pi\)
\(108\) 0 0
\(109\) −2.32770 −0.222953 −0.111476 0.993767i \(-0.535558\pi\)
−0.111476 + 0.993767i \(0.535558\pi\)
\(110\) 10.2096 3.71599i 0.973448 0.354306i
\(111\) 0 0
\(112\) −1.79813 + 1.50881i −0.169908 + 0.142569i
\(113\) 2.96198 + 16.7982i 0.278640 + 1.58024i 0.727157 + 0.686471i \(0.240841\pi\)
−0.448518 + 0.893774i \(0.648048\pi\)
\(114\) 0 0
\(115\) −0.592396 0.497079i −0.0552412 0.0463529i
\(116\) −1.55303 + 2.68993i −0.144196 + 0.249754i
\(117\) 0 0
\(118\) 2.73783 + 4.74205i 0.252037 + 0.436541i
\(119\) 2.00593 11.3762i 0.183883 1.04285i
\(120\) 0 0
\(121\) −6.96451 2.53487i −0.633137 0.230443i
\(122\) −10.3833 3.77920i −0.940056 0.342152i
\(123\) 0 0
\(124\) −1.49273 + 8.46567i −0.134051 + 0.760240i
\(125\) −4.54323 7.86911i −0.406359 0.703835i
\(126\) 0 0
\(127\) −6.32295 + 10.9517i −0.561071 + 0.971803i 0.436332 + 0.899786i \(0.356277\pi\)
−0.997403 + 0.0720178i \(0.977056\pi\)
\(128\) 0.766044 + 0.642788i 0.0677094 + 0.0568149i
\(129\) 0 0
\(130\) −0.333626 1.89209i −0.0292609 0.165947i
\(131\) 3.97565 3.33597i 0.347354 0.291465i −0.452372 0.891829i \(-0.649422\pi\)
0.799727 + 0.600364i \(0.204978\pi\)
\(132\) 0 0
\(133\) −15.9893 + 5.81964i −1.38645 + 0.504627i
\(134\) 0.0418891 0.00361866
\(135\) 0 0
\(136\) −4.92127 −0.421996
\(137\) −16.0817 + 5.85327i −1.37395 + 0.500078i −0.920340 0.391120i \(-0.872088\pi\)
−0.453614 + 0.891198i \(0.649866\pi\)
\(138\) 0 0
\(139\) 9.34389 7.84046i 0.792539 0.665019i −0.153834 0.988097i \(-0.549162\pi\)
0.946372 + 0.323078i \(0.104718\pi\)
\(140\) 1.03209 + 5.85327i 0.0872274 + 0.494691i
\(141\) 0 0
\(142\) 3.22075 + 2.70253i 0.270279 + 0.226791i
\(143\) −1.62789 + 2.81959i −0.136131 + 0.235786i
\(144\) 0 0
\(145\) 3.93242 + 6.81115i 0.326570 + 0.565635i
\(146\) −1.92602 + 10.9230i −0.159399 + 0.903995i
\(147\) 0 0
\(148\) 7.11721 + 2.59045i 0.585031 + 0.212934i
\(149\) 7.23783 + 2.63435i 0.592946 + 0.215815i 0.621025 0.783791i \(-0.286717\pi\)
−0.0280788 + 0.999606i \(0.508939\pi\)
\(150\) 0 0
\(151\) −0.135630 + 0.769193i −0.0110374 + 0.0625961i −0.989829 0.142262i \(-0.954562\pi\)
0.978792 + 0.204858i \(0.0656734\pi\)
\(152\) 3.62449 + 6.27779i 0.293985 + 0.509196i
\(153\) 0 0
\(154\) 5.03596 8.72254i 0.405809 0.702882i
\(155\) 16.6741 + 13.9912i 1.33930 + 1.12380i
\(156\) 0 0
\(157\) −1.80793 10.2533i −0.144289 0.818302i −0.967935 0.251199i \(-0.919175\pi\)
0.823647 0.567103i \(-0.191936\pi\)
\(158\) −5.64930 + 4.74033i −0.449434 + 0.377120i
\(159\) 0 0
\(160\) 2.37939 0.866025i 0.188107 0.0684653i
\(161\) −0.716881 −0.0564982
\(162\) 0 0
\(163\) −10.5740 −0.828218 −0.414109 0.910227i \(-0.635907\pi\)
−0.414109 + 0.910227i \(0.635907\pi\)
\(164\) 4.60607 1.67647i 0.359673 0.130910i
\(165\) 0 0
\(166\) −5.22668 + 4.38571i −0.405669 + 0.340397i
\(167\) −0.260992 1.48016i −0.0201962 0.114538i 0.973043 0.230623i \(-0.0740765\pi\)
−0.993239 + 0.116085i \(0.962965\pi\)
\(168\) 0 0
\(169\) −9.51754 7.98617i −0.732119 0.614320i
\(170\) −6.23055 + 10.7916i −0.477862 + 0.827680i
\(171\) 0 0
\(172\) 0.815207 + 1.41198i 0.0621590 + 0.107663i
\(173\) 1.93629 10.9812i 0.147213 0.834888i −0.818350 0.574720i \(-0.805111\pi\)
0.965563 0.260168i \(-0.0837780\pi\)
\(174\) 0 0
\(175\) 3.11334 + 1.13316i 0.235346 + 0.0856591i
\(176\) −4.03209 1.46756i −0.303930 0.110622i
\(177\) 0 0
\(178\) −1.37551 + 7.80093i −0.103099 + 0.584705i
\(179\) 3.90420 + 6.76227i 0.291814 + 0.505436i 0.974239 0.225520i \(-0.0724080\pi\)
−0.682425 + 0.730956i \(0.739075\pi\)
\(180\) 0 0
\(181\) −5.23783 + 9.07218i −0.389325 + 0.674330i −0.992359 0.123385i \(-0.960625\pi\)
0.603034 + 0.797715i \(0.293958\pi\)
\(182\) −1.36437 1.14484i −0.101134 0.0848614i
\(183\) 0 0
\(184\) 0.0530334 + 0.300767i 0.00390968 + 0.0221729i
\(185\) 14.6912 12.3274i 1.08012 0.906326i
\(186\) 0 0
\(187\) 19.8430 7.22227i 1.45107 0.528144i
\(188\) 1.81521 0.132388
\(189\) 0 0
\(190\) 18.3550 1.33161
\(191\) −11.4918 + 4.18269i −0.831521 + 0.302649i −0.722483 0.691389i \(-0.756999\pi\)
−0.109038 + 0.994038i \(0.534777\pi\)
\(192\) 0 0
\(193\) −12.5385 + 10.5210i −0.902540 + 0.757321i −0.970685 0.240354i \(-0.922736\pi\)
0.0681452 + 0.997675i \(0.478292\pi\)
\(194\) −0.570108 3.23324i −0.0409313 0.232133i
\(195\) 0 0
\(196\) −1.14156 0.957882i −0.0815399 0.0684201i
\(197\) 9.49794 16.4509i 0.676700 1.17208i −0.299269 0.954169i \(-0.596743\pi\)
0.975969 0.217910i \(-0.0699240\pi\)
\(198\) 0 0
\(199\) −11.5214 19.9557i −0.816731 1.41462i −0.908078 0.418801i \(-0.862451\pi\)
0.0913469 0.995819i \(-0.470883\pi\)
\(200\) 0.245100 1.39003i 0.0173312 0.0982900i
\(201\) 0 0
\(202\) −11.2699 4.10191i −0.792948 0.288610i
\(203\) 6.85117 + 2.49362i 0.480858 + 0.175018i
\(204\) 0 0
\(205\) 2.15523 12.2229i 0.150528 0.853685i
\(206\) −1.20574 2.08840i −0.0840077 0.145506i
\(207\) 0 0
\(208\) −0.379385 + 0.657115i −0.0263056 + 0.0455627i
\(209\) −23.8273 19.9935i −1.64817 1.38298i
\(210\) 0 0
\(211\) 3.03849 + 17.2321i 0.209178 + 1.18631i 0.890728 + 0.454536i \(0.150195\pi\)
−0.681550 + 0.731771i \(0.738694\pi\)
\(212\) −0.439693 + 0.368946i −0.0301982 + 0.0253393i
\(213\) 0 0
\(214\) −2.27972 + 0.829748i −0.155838 + 0.0567204i
\(215\) 4.12836 0.281552
\(216\) 0 0
\(217\) 20.1780 1.36977
\(218\) 2.18732 0.796119i 0.148144 0.0539200i
\(219\) 0 0
\(220\) −8.32295 + 6.98378i −0.561133 + 0.470847i
\(221\) −0.648423 3.67739i −0.0436176 0.247368i
\(222\) 0 0
\(223\) −3.23190 2.71188i −0.216424 0.181601i 0.528130 0.849163i \(-0.322893\pi\)
−0.744554 + 0.667562i \(0.767338\pi\)
\(224\) 1.17365 2.03282i 0.0784177 0.135823i
\(225\) 0 0
\(226\) −8.52869 14.7721i −0.567320 0.982627i
\(227\) −2.77244 + 15.7233i −0.184013 + 1.04359i 0.743203 + 0.669066i \(0.233306\pi\)
−0.927216 + 0.374526i \(0.877806\pi\)
\(228\) 0 0
\(229\) 16.7713 + 6.10424i 1.10828 + 0.403379i 0.830361 0.557226i \(-0.188134\pi\)
0.277915 + 0.960606i \(0.410357\pi\)
\(230\) 0.726682 + 0.264490i 0.0479160 + 0.0174400i
\(231\) 0 0
\(232\) 0.539363 3.05888i 0.0354109 0.200825i
\(233\) −0.368241 0.637812i −0.0241243 0.0417844i 0.853711 0.520747i \(-0.174346\pi\)
−0.877835 + 0.478962i \(0.841013\pi\)
\(234\) 0 0
\(235\) 2.29813 3.98048i 0.149914 0.259658i
\(236\) −4.19459 3.51968i −0.273045 0.229112i
\(237\) 0 0
\(238\) 2.00593 + 11.3762i 0.130025 + 0.737409i
\(239\) 2.20187 1.84759i 0.142427 0.119510i −0.568791 0.822482i \(-0.692589\pi\)
0.711218 + 0.702972i \(0.248144\pi\)
\(240\) 0 0
\(241\) −2.05051 + 0.746324i −0.132085 + 0.0480749i −0.407217 0.913332i \(-0.633501\pi\)
0.275132 + 0.961406i \(0.411278\pi\)
\(242\) 7.41147 0.476428
\(243\) 0 0
\(244\) 11.0496 0.707380
\(245\) −3.54576 + 1.29055i −0.226530 + 0.0824503i
\(246\) 0 0
\(247\) −4.21348 + 3.53553i −0.268097 + 0.224960i
\(248\) −1.49273 8.46567i −0.0947882 0.537571i
\(249\) 0 0
\(250\) 6.96064 + 5.84067i 0.440229 + 0.369396i
\(251\) −13.0189 + 22.5494i −0.821745 + 1.42330i 0.0826372 + 0.996580i \(0.473666\pi\)
−0.904382 + 0.426724i \(0.859668\pi\)
\(252\) 0 0
\(253\) −0.655230 1.13489i −0.0411939 0.0713500i
\(254\) 2.19594 12.4538i 0.137785 0.781419i
\(255\) 0 0
\(256\) −0.939693 0.342020i −0.0587308 0.0213763i
\(257\) 9.38965 + 3.41755i 0.585710 + 0.213181i 0.617842 0.786302i \(-0.288007\pi\)
−0.0321313 + 0.999484i \(0.510229\pi\)
\(258\) 0 0
\(259\) 3.08718 17.5083i 0.191828 1.08791i
\(260\) 0.960637 + 1.66387i 0.0595762 + 0.103189i
\(261\) 0 0
\(262\) −2.59492 + 4.49454i −0.160315 + 0.277673i
\(263\) −11.6612 9.78487i −0.719058 0.603361i 0.208067 0.978115i \(-0.433283\pi\)
−0.927125 + 0.374753i \(0.877727\pi\)
\(264\) 0 0
\(265\) 0.252374 + 1.43128i 0.0155032 + 0.0879230i
\(266\) 13.0346 10.9373i 0.799204 0.670611i
\(267\) 0 0
\(268\) −0.0393628 + 0.0143269i −0.00240447 + 0.000875155i
\(269\) −30.5476 −1.86252 −0.931259 0.364358i \(-0.881289\pi\)
−0.931259 + 0.364358i \(0.881289\pi\)
\(270\) 0 0
\(271\) 25.8307 1.56910 0.784551 0.620064i \(-0.212893\pi\)
0.784551 + 0.620064i \(0.212893\pi\)
\(272\) 4.62449 1.68317i 0.280401 0.102057i
\(273\) 0 0
\(274\) 13.1099 11.0005i 0.792000 0.664567i
\(275\) 1.05169 + 5.96443i 0.0634192 + 0.359668i
\(276\) 0 0
\(277\) −17.1860 14.4207i −1.03261 0.866459i −0.0414465 0.999141i \(-0.513197\pi\)
−0.991159 + 0.132682i \(0.957641\pi\)
\(278\) −6.09879 + 10.5634i −0.365781 + 0.633552i
\(279\) 0 0
\(280\) −2.97178 5.14728i −0.177598 0.307609i
\(281\) −1.01485 + 5.75552i −0.0605410 + 0.343345i 0.939459 + 0.342662i \(0.111329\pi\)
−1.00000 0.000683195i \(0.999783\pi\)
\(282\) 0 0
\(283\) 6.96451 + 2.53487i 0.413997 + 0.150683i 0.540617 0.841269i \(-0.318191\pi\)
−0.126620 + 0.991951i \(0.540413\pi\)
\(284\) −3.95084 1.43799i −0.234439 0.0853288i
\(285\) 0 0
\(286\) 0.565360 3.20631i 0.0334304 0.189593i
\(287\) −5.75284 9.96421i −0.339579 0.588169i
\(288\) 0 0
\(289\) −3.60947 + 6.25179i −0.212322 + 0.367752i
\(290\) −6.02481 5.05542i −0.353789 0.296864i
\(291\) 0 0
\(292\) −1.92602 10.9230i −0.112712 0.639221i
\(293\) 6.79994 5.70583i 0.397257 0.333338i −0.422175 0.906514i \(-0.638733\pi\)
0.819432 + 0.573176i \(0.194289\pi\)
\(294\) 0 0
\(295\) −13.0287 + 4.74205i −0.758559 + 0.276093i
\(296\) −7.57398 −0.440229
\(297\) 0 0
\(298\) −7.70233 −0.446184
\(299\) −0.217759 + 0.0792577i −0.0125933 + 0.00458359i
\(300\) 0 0
\(301\) 2.93170 2.45999i 0.168981 0.141792i
\(302\) −0.135630 0.769193i −0.00780460 0.0442621i
\(303\) 0 0
\(304\) −5.55303 4.65955i −0.318488 0.267243i
\(305\) 13.9893 24.2302i 0.801026 1.38742i
\(306\) 0 0
\(307\) 8.04963 + 13.9424i 0.459417 + 0.795733i 0.998930 0.0462440i \(-0.0147252\pi\)
−0.539514 + 0.841977i \(0.681392\pi\)
\(308\) −1.74897 + 9.91890i −0.0996568 + 0.565182i
\(309\) 0 0
\(310\) −20.4538 7.44459i −1.16170 0.422824i
\(311\) 12.7699 + 4.64787i 0.724115 + 0.263556i 0.677672 0.735364i \(-0.262989\pi\)
0.0464436 + 0.998921i \(0.485211\pi\)
\(312\) 0 0
\(313\) −3.73442 + 21.1790i −0.211082 + 1.19711i 0.676495 + 0.736447i \(0.263498\pi\)
−0.887577 + 0.460659i \(0.847613\pi\)
\(314\) 5.20574 + 9.01660i 0.293777 + 0.508836i
\(315\) 0 0
\(316\) 3.68732 6.38662i 0.207428 0.359276i
\(317\) 16.1578 + 13.5580i 0.907510 + 0.761491i 0.971644 0.236450i \(-0.0759840\pi\)
−0.0641337 + 0.997941i \(0.520428\pi\)
\(318\) 0 0
\(319\) 2.31433 + 13.1252i 0.129578 + 0.734871i
\(320\) −1.93969 + 1.62760i −0.108432 + 0.0909853i
\(321\) 0 0
\(322\) 0.673648 0.245188i 0.0375409 0.0136638i
\(323\) 35.6742 1.98496
\(324\) 0 0
\(325\) 1.07098 0.0594076
\(326\) 9.93629 3.61651i 0.550320 0.200300i
\(327\) 0 0
\(328\) −3.75490 + 3.15074i −0.207330 + 0.173970i
\(329\) −0.739885 4.19610i −0.0407912 0.231338i
\(330\) 0 0
\(331\) 12.5929 + 10.5667i 0.692166 + 0.580797i 0.919533 0.393013i \(-0.128567\pi\)
−0.227367 + 0.973809i \(0.573012\pi\)
\(332\) 3.41147 5.90885i 0.187229 0.324290i
\(333\) 0 0
\(334\) 0.751497 + 1.30163i 0.0411201 + 0.0712220i
\(335\) −0.0184183 + 0.104455i −0.00100630 + 0.00570701i
\(336\) 0 0
\(337\) −9.91534 3.60889i −0.540123 0.196589i 0.0575296 0.998344i \(-0.481678\pi\)
−0.597653 + 0.801755i \(0.703900\pi\)
\(338\) 11.6750 + 4.24935i 0.635036 + 0.231134i
\(339\) 0 0
\(340\) 2.16385 12.2718i 0.117351 0.665531i
\(341\) 18.4427 + 31.9437i 0.998727 + 1.72985i
\(342\) 0 0
\(343\) −9.96451 + 17.2590i −0.538033 + 0.931900i
\(344\) −1.24897 1.04801i −0.0673400 0.0565049i
\(345\) 0 0
\(346\) 1.93629 + 10.9812i 0.104096 + 0.590355i
\(347\) −21.7251 + 18.2295i −1.16626 + 0.978612i −0.999972 0.00746500i \(-0.997624\pi\)
−0.166292 + 0.986077i \(0.553179\pi\)
\(348\) 0 0
\(349\) −14.7554 + 5.37051i −0.789837 + 0.287477i −0.705268 0.708941i \(-0.749173\pi\)
−0.0845685 + 0.996418i \(0.526951\pi\)
\(350\) −3.31315 −0.177095
\(351\) 0 0
\(352\) 4.29086 0.228704
\(353\) −1.93969 + 0.705990i −0.103239 + 0.0375761i −0.393123 0.919486i \(-0.628605\pi\)
0.289884 + 0.957062i \(0.406383\pi\)
\(354\) 0 0
\(355\) −8.15523 + 6.84305i −0.432835 + 0.363191i
\(356\) −1.37551 7.80093i −0.0729021 0.413449i
\(357\) 0 0
\(358\) −5.98158 5.01914i −0.316136 0.265270i
\(359\) −17.4820 + 30.2798i −0.922667 + 1.59811i −0.127397 + 0.991852i \(0.540662\pi\)
−0.795271 + 0.606255i \(0.792671\pi\)
\(360\) 0 0
\(361\) −16.7738 29.0530i −0.882831 1.52911i
\(362\) 1.81908 10.3165i 0.0956086 0.542223i
\(363\) 0 0
\(364\) 1.67365 + 0.609158i 0.0877230 + 0.0319286i
\(365\) −26.3910 9.60554i −1.38137 0.502777i
\(366\) 0 0
\(367\) −0.0773815 + 0.438852i −0.00403928 + 0.0229079i −0.986761 0.162182i \(-0.948147\pi\)
0.982722 + 0.185090i \(0.0592578\pi\)
\(368\) −0.152704 0.264490i −0.00796023 0.0137875i
\(369\) 0 0
\(370\) −9.58899 + 16.6086i −0.498508 + 0.863441i
\(371\) 1.03209 + 0.866025i 0.0535834 + 0.0449618i
\(372\) 0 0
\(373\) −3.83110 21.7272i −0.198367 1.12499i −0.907542 0.419962i \(-0.862044\pi\)
0.709175 0.705032i \(-0.249068\pi\)
\(374\) −16.1762 + 13.5734i −0.836450 + 0.701865i
\(375\) 0 0
\(376\) −1.70574 + 0.620838i −0.0879667 + 0.0320173i
\(377\) 2.35679 0.121381
\(378\) 0 0
\(379\) 13.1138 0.673611 0.336806 0.941574i \(-0.390654\pi\)
0.336806 + 0.941574i \(0.390654\pi\)
\(380\) −17.2481 + 6.27779i −0.884808 + 0.322044i
\(381\) 0 0
\(382\) 9.36824 7.86089i 0.479321 0.402198i
\(383\) −2.79767 15.8664i −0.142954 0.810733i −0.968987 0.247111i \(-0.920519\pi\)
0.826033 0.563622i \(-0.190592\pi\)
\(384\) 0 0
\(385\) 19.5364 + 16.3930i 0.995668 + 0.835465i
\(386\) 8.18392 14.1750i 0.416550 0.721486i
\(387\) 0 0
\(388\) 1.64156 + 2.84326i 0.0833375 + 0.144345i
\(389\) −0.0984882 + 0.558554i −0.00499355 + 0.0283198i −0.987203 0.159470i \(-0.949021\pi\)
0.982209 + 0.187790i \(0.0601325\pi\)
\(390\) 0 0
\(391\) 1.41235 + 0.514054i 0.0714257 + 0.0259968i
\(392\) 1.40033 + 0.509678i 0.0707273 + 0.0257426i
\(393\) 0 0
\(394\) −3.29860 + 18.7073i −0.166181 + 0.942460i
\(395\) −9.33662 16.1715i −0.469776 0.813676i
\(396\) 0 0
\(397\) −18.0107 + 31.1955i −0.903933 + 1.56566i −0.0815894 + 0.996666i \(0.526000\pi\)
−0.822343 + 0.568992i \(0.807334\pi\)
\(398\) 17.6518 + 14.8116i 0.884806 + 0.742440i
\(399\) 0 0
\(400\) 0.245100 + 1.39003i 0.0122550 + 0.0695015i
\(401\) −27.5724 + 23.1360i −1.37690 + 1.15536i −0.406556 + 0.913626i \(0.633270\pi\)
−0.970344 + 0.241730i \(0.922285\pi\)
\(402\) 0 0
\(403\) 6.12923 2.23086i 0.305319 0.111127i
\(404\) 11.9932 0.596684
\(405\) 0 0
\(406\) −7.29086 −0.361839
\(407\) 30.5390 11.1153i 1.51376 0.550963i
\(408\) 0 0
\(409\) 9.71032 8.14793i 0.480145 0.402889i −0.370334 0.928899i \(-0.620757\pi\)
0.850479 + 0.526009i \(0.176312\pi\)
\(410\) 2.15523 + 12.2229i 0.106439 + 0.603647i
\(411\) 0 0
\(412\) 1.84730 + 1.55007i 0.0910098 + 0.0763663i
\(413\) −6.42649 + 11.1310i −0.316227 + 0.547721i
\(414\) 0 0
\(415\) −8.63816 14.9617i −0.424030 0.734442i
\(416\) 0.131759 0.747243i 0.00646002 0.0366366i
\(417\) 0 0
\(418\) 29.2285 + 10.6383i 1.42961 + 0.520336i
\(419\) 13.3991 + 4.87689i 0.654591 + 0.238252i 0.647899 0.761726i \(-0.275648\pi\)
0.00669178 + 0.999978i \(0.497870\pi\)
\(420\) 0 0
\(421\) 0.546637 3.10013i 0.0266414 0.151091i −0.968585 0.248682i \(-0.920003\pi\)
0.995227 + 0.0975909i \(0.0311137\pi\)
\(422\) −8.74897 15.1537i −0.425893 0.737669i
\(423\) 0 0
\(424\) 0.286989 0.497079i 0.0139374 0.0241403i
\(425\) −5.32114 4.46496i −0.258113 0.216583i
\(426\) 0 0
\(427\) −4.50387 25.5427i −0.217958 1.23610i
\(428\) 1.85844 1.55942i 0.0898311 0.0753773i
\(429\) 0 0
\(430\) −3.87939 + 1.41198i −0.187081 + 0.0680918i
\(431\) −15.4911 −0.746182 −0.373091 0.927795i \(-0.621702\pi\)
−0.373091 + 0.927795i \(0.621702\pi\)
\(432\) 0 0
\(433\) −2.22844 −0.107092 −0.0535459 0.998565i \(-0.517052\pi\)
−0.0535459 + 0.998565i \(0.517052\pi\)
\(434\) −18.9611 + 6.90128i −0.910162 + 0.331272i
\(435\) 0 0
\(436\) −1.78312 + 1.49621i −0.0853959 + 0.0716557i
\(437\) −0.384438 2.18025i −0.0183901 0.104296i
\(438\) 0 0
\(439\) 13.1570 + 11.0401i 0.627951 + 0.526914i 0.900292 0.435287i \(-0.143353\pi\)
−0.272340 + 0.962201i \(0.587798\pi\)
\(440\) 5.43242 9.40923i 0.258980 0.448567i
\(441\) 0 0
\(442\) 1.86706 + 3.23384i 0.0888069 + 0.153818i
\(443\) 4.10173 23.2621i 0.194879 1.10521i −0.717712 0.696340i \(-0.754810\pi\)
0.912591 0.408874i \(-0.134078\pi\)
\(444\) 0 0
\(445\) −18.8478 6.86002i −0.893470 0.325196i
\(446\) 3.96451 + 1.44296i 0.187725 + 0.0683263i
\(447\) 0 0
\(448\) −0.407604 + 2.31164i −0.0192575 + 0.109215i
\(449\) −10.1295 17.5449i −0.478042 0.827994i 0.521641 0.853165i \(-0.325320\pi\)
−0.999683 + 0.0251715i \(0.991987\pi\)
\(450\) 0 0
\(451\) 10.5162 18.2146i 0.495188 0.857691i
\(452\) 13.0667 + 10.9643i 0.614606 + 0.515716i
\(453\) 0 0
\(454\) −2.77244 15.7233i −0.130117 0.737931i
\(455\) 3.45471 2.89884i 0.161959 0.135900i
\(456\) 0 0
\(457\) 38.1143 13.8725i 1.78291 0.648926i 0.783282 0.621666i \(-0.213544\pi\)
0.999628 0.0272600i \(-0.00867822\pi\)
\(458\) −17.8476 −0.833964
\(459\) 0 0
\(460\) −0.773318 −0.0360562
\(461\) 12.8824 4.68880i 0.599992 0.218379i −0.0241264 0.999709i \(-0.507680\pi\)
0.624119 + 0.781330i \(0.285458\pi\)
\(462\) 0 0
\(463\) 4.14022 3.47405i 0.192412 0.161453i −0.541492 0.840706i \(-0.682140\pi\)
0.733904 + 0.679253i \(0.237696\pi\)
\(464\) 0.539363 + 3.05888i 0.0250393 + 0.142005i
\(465\) 0 0
\(466\) 0.564178 + 0.473401i 0.0261350 + 0.0219299i
\(467\) 15.7451 27.2713i 0.728596 1.26197i −0.228880 0.973455i \(-0.573506\pi\)
0.957477 0.288511i \(-0.0931603\pi\)
\(468\) 0 0
\(469\) 0.0491630 + 0.0851529i 0.00227014 + 0.00393199i
\(470\) −0.798133 + 4.52644i −0.0368151 + 0.208789i
\(471\) 0 0
\(472\) 5.14543 + 1.87278i 0.236838 + 0.0862018i
\(473\) 6.57398 + 2.39273i 0.302272 + 0.110018i
\(474\) 0 0
\(475\) −1.77672 + 10.0763i −0.0815216 + 0.462332i
\(476\) −5.77584 10.0041i −0.264735 0.458535i
\(477\) 0 0
\(478\) −1.43717 + 2.48925i −0.0657345 + 0.113855i
\(479\) 16.0667 + 13.4816i 0.734106 + 0.615988i 0.931248 0.364387i \(-0.118721\pi\)
−0.197141 + 0.980375i \(0.563166\pi\)
\(480\) 0 0
\(481\) −0.997941 5.65960i −0.0455022 0.258056i
\(482\) 1.67159 1.40263i 0.0761388 0.0638880i
\(483\) 0 0
\(484\) −6.96451 + 2.53487i −0.316569 + 0.115222i
\(485\) 8.31315 0.377481
\(486\) 0 0
\(487\) −15.4492 −0.700072 −0.350036 0.936736i \(-0.613831\pi\)
−0.350036 + 0.936736i \(0.613831\pi\)
\(488\) −10.3833 + 3.77920i −0.470028 + 0.171076i
\(489\) 0 0
\(490\) 2.89053 2.42544i 0.130581 0.109570i
\(491\) −2.75443 15.6212i −0.124306 0.704973i −0.981718 0.190343i \(-0.939040\pi\)
0.857412 0.514631i \(-0.172071\pi\)
\(492\) 0 0
\(493\) −11.7096 9.82553i −0.527374 0.442519i
\(494\) 2.75015 4.76340i 0.123735 0.214316i
\(495\) 0 0
\(496\) 4.29813 + 7.44459i 0.192992 + 0.334272i
\(497\) −1.71373 + 9.71902i −0.0768711 + 0.435958i
\(498\) 0 0
\(499\) 7.03596 + 2.56088i 0.314973 + 0.114641i 0.494669 0.869081i \(-0.335289\pi\)
−0.179696 + 0.983722i \(0.557511\pi\)
\(500\) −8.53849 3.10775i −0.381853 0.138983i
\(501\) 0 0
\(502\) 4.52141 25.6422i 0.201800 1.14447i
\(503\) −10.0667 17.4360i −0.448852 0.777435i 0.549459 0.835520i \(-0.314834\pi\)
−0.998312 + 0.0580857i \(0.981500\pi\)
\(504\) 0 0
\(505\) 15.1839 26.2993i 0.675675 1.17030i
\(506\) 1.00387 + 0.842347i 0.0446275 + 0.0374469i
\(507\) 0 0
\(508\) 2.19594 + 12.4538i 0.0974289 + 0.552547i
\(509\) 28.7900 24.1577i 1.27609 1.07077i 0.282324 0.959319i \(-0.408895\pi\)
0.993770 0.111450i \(-0.0355496\pi\)
\(510\) 0 0
\(511\) −24.4650 + 8.90452i −1.08227 + 0.393913i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −9.99226 −0.440740
\(515\) 5.73783 2.08840i 0.252839 0.0920258i
\(516\) 0 0
\(517\) 5.96657 5.00654i 0.262409 0.220188i
\(518\) 3.08718 + 17.5083i 0.135643 + 0.769270i
\(519\) 0 0
\(520\) −1.47178 1.23497i −0.0645419 0.0541571i
\(521\) 13.9645 24.1872i 0.611796 1.05966i −0.379141 0.925339i \(-0.623781\pi\)
0.990938 0.134323i \(-0.0428861\pi\)
\(522\) 0 0
\(523\) −3.64677 6.31640i −0.159462 0.276197i 0.775213 0.631700i \(-0.217643\pi\)
−0.934675 + 0.355504i \(0.884309\pi\)
\(524\) 0.901207 5.11100i 0.0393694 0.223275i
\(525\) 0 0
\(526\) 14.3045 + 5.20642i 0.623707 + 0.227011i
\(527\) −39.7533 14.4690i −1.73168 0.630280i
\(528\) 0 0
\(529\) −3.97771 + 22.5587i −0.172944 + 0.980814i
\(530\) −0.726682 1.25865i −0.0315650 0.0546722i
\(531\) 0 0
\(532\) −8.50774 + 14.7358i −0.368857 + 0.638880i
\(533\) −2.84911 2.39068i −0.123409 0.103552i
\(534\) 0 0
\(535\) −1.06670 6.04958i −0.0461176 0.261546i
\(536\) 0.0320889 0.0269258i 0.00138603 0.00116302i
\(537\) 0 0
\(538\) 28.7053 10.4479i 1.23757 0.450440i
\(539\) −6.39424 −0.275419
\(540\) 0 0
\(541\) −2.88444 −0.124012 −0.0620058 0.998076i \(-0.519750\pi\)
−0.0620058 + 0.998076i \(0.519750\pi\)
\(542\) −24.2729 + 8.83462i −1.04261 + 0.379479i
\(543\) 0 0
\(544\) −3.76991 + 3.16333i −0.161634 + 0.135627i
\(545\) 1.02347 + 5.80439i 0.0438407 + 0.248633i
\(546\) 0 0
\(547\) −8.57263 7.19329i −0.366539 0.307563i 0.440851 0.897580i \(-0.354677\pi\)
−0.807391 + 0.590017i \(0.799121\pi\)
\(548\) −8.55690 + 14.8210i −0.365533 + 0.633121i
\(549\) 0 0
\(550\) −3.02822 5.24503i −0.129124 0.223649i
\(551\) −3.90983 + 22.1737i −0.166564 + 0.944632i
\(552\) 0 0
\(553\) −16.2665 5.92053i −0.691722 0.251766i
\(554\) 21.0817 + 7.67312i 0.895676 + 0.326000i
\(555\) 0 0
\(556\) 2.11809 12.0123i 0.0898270 0.509434i
\(557\) 16.6741 + 28.8804i 0.706505 + 1.22370i 0.966146 + 0.257997i \(0.0830625\pi\)
−0.259641 + 0.965705i \(0.583604\pi\)
\(558\) 0 0
\(559\) 0.618555 1.07137i 0.0261621 0.0453141i
\(560\) 4.55303 + 3.82045i 0.192401 + 0.161443i
\(561\) 0 0
\(562\) −1.01485 5.75552i −0.0428090 0.242782i
\(563\) −14.1668 + 11.8874i −0.597061 + 0.500994i −0.890500 0.454984i \(-0.849645\pi\)
0.293438 + 0.955978i \(0.405200\pi\)
\(564\) 0 0
\(565\) 40.5861 14.7721i 1.70747 0.621468i
\(566\) −7.41147 −0.311527
\(567\) 0 0
\(568\) 4.20439 0.176412
\(569\) 27.5638 10.0324i 1.15553 0.420580i 0.308033 0.951376i \(-0.400329\pi\)
0.847500 + 0.530796i \(0.178107\pi\)
\(570\) 0 0
\(571\) 1.50387 1.26190i 0.0629350 0.0528087i −0.610778 0.791802i \(-0.709143\pi\)
0.673713 + 0.738993i \(0.264699\pi\)
\(572\) 0.565360 + 3.20631i 0.0236389 + 0.134063i
\(573\) 0 0
\(574\) 8.81386 + 7.39571i 0.367884 + 0.308691i
\(575\) −0.215537 + 0.373321i −0.00898852 + 0.0155686i
\(576\) 0 0
\(577\) 5.52956 + 9.57748i 0.230199 + 0.398716i 0.957866 0.287214i \(-0.0927291\pi\)
−0.727668 + 0.685930i \(0.759396\pi\)
\(578\) 1.25356 7.10927i 0.0521411 0.295707i
\(579\) 0 0
\(580\) 7.39053 + 2.68993i 0.306875 + 0.111693i
\(581\) −15.0496 5.47762i −0.624364 0.227250i
\(582\) 0 0
\(583\) −0.427671 + 2.42544i −0.0177123 + 0.100452i
\(584\) 5.54576 + 9.60554i 0.229485 + 0.397480i
\(585\) 0 0
\(586\) −4.43835 + 7.68745i −0.183346 + 0.317565i
\(587\) −25.3917 21.3062i −1.04803 0.879400i −0.0551433 0.998478i \(-0.517562\pi\)
−0.992885 + 0.119078i \(0.962006\pi\)
\(588\) 0 0
\(589\) 10.8207 + 61.3674i 0.445860 + 2.52860i
\(590\) 10.6211 8.91215i 0.437263 0.366907i
\(591\) 0 0
\(592\) 7.11721 2.59045i 0.292516 0.106467i
\(593\) −14.8283 −0.608926 −0.304463 0.952524i \(-0.598477\pi\)
−0.304463 + 0.952524i \(0.598477\pi\)
\(594\) 0 0
\(595\) −29.2499 −1.19913
\(596\) 7.23783 2.63435i 0.296473 0.107907i
\(597\) 0 0
\(598\) 0.177519 0.148956i 0.00725927 0.00609125i
\(599\) 8.20930 + 46.5573i 0.335423 + 1.90228i 0.423016 + 0.906122i \(0.360971\pi\)
−0.0875932 + 0.996156i \(0.527918\pi\)
\(600\) 0 0
\(601\) 28.1996 + 23.6623i 1.15029 + 0.965206i 0.999726 0.0233949i \(-0.00744749\pi\)
0.150561 + 0.988601i \(0.451892\pi\)
\(602\) −1.91353 + 3.31434i −0.0779898 + 0.135082i
\(603\) 0 0
\(604\) 0.390530 + 0.676417i 0.0158904 + 0.0275230i
\(605\) −3.25877 + 18.4814i −0.132488 + 0.751376i
\(606\) 0 0
\(607\) −38.8764 14.1499i −1.57795 0.574326i −0.603190 0.797597i \(-0.706104\pi\)
−0.974756 + 0.223272i \(0.928326\pi\)
\(608\) 6.81180 + 2.47929i 0.276255 + 0.100549i
\(609\) 0 0
\(610\) −4.85844 + 27.5536i −0.196713 + 1.11561i
\(611\) −0.688663 1.19280i −0.0278603 0.0482555i
\(612\) 0 0
\(613\) 20.6755 35.8109i 0.835074 1.44639i −0.0588963 0.998264i \(-0.518758\pi\)
0.893970 0.448126i \(-0.147909\pi\)
\(614\) −12.3327 10.3484i −0.497709 0.417628i
\(615\) 0 0
\(616\) −1.74897 9.91890i −0.0704680 0.399644i
\(617\) −18.7867 + 15.7639i −0.756326 + 0.634633i −0.937168 0.348880i \(-0.886562\pi\)
0.180842 + 0.983512i \(0.442118\pi\)
\(618\) 0 0
\(619\) −37.2768 + 13.5676i −1.49828 + 0.545329i −0.955615 0.294619i \(-0.904807\pi\)
−0.542666 + 0.839949i \(0.682585\pi\)
\(620\) 21.7665 0.874164
\(621\) 0 0
\(622\) −13.5895 −0.544888
\(623\) −17.4722 + 6.35938i −0.700011 + 0.254783i
\(624\) 0 0
\(625\) −23.0312 + 19.3255i −0.921248 + 0.773019i
\(626\) −3.73442 21.1790i −0.149258 0.846482i
\(627\) 0 0
\(628\) −7.97565 6.69237i −0.318263 0.267054i
\(629\) −18.6368 + 32.2799i −0.743098 + 1.28708i
\(630\) 0 0
\(631\) 16.6596 + 28.8552i 0.663207 + 1.14871i 0.979768 + 0.200136i \(0.0641384\pi\)
−0.316561 + 0.948572i \(0.602528\pi\)
\(632\) −1.28059 + 7.26260i −0.0509392 + 0.288891i
\(633\) 0 0
\(634\) −19.8204 7.21404i −0.787170 0.286506i
\(635\) 30.0895 + 10.9517i 1.19406 + 0.434604i
\(636\) 0 0
\(637\) −0.196347 + 1.11354i −0.00777957 + 0.0441201i
\(638\) −6.66385 11.5421i −0.263824 0.456957i
\(639\) 0 0
\(640\) 1.26604 2.19285i 0.0500448 0.0866801i
\(641\) −5.55690 4.66280i −0.219485 0.184169i 0.526415 0.850228i \(-0.323536\pi\)
−0.745900 + 0.666058i \(0.767980\pi\)
\(642\) 0 0
\(643\) −1.34120 7.60635i −0.0528919 0.299965i 0.946874 0.321605i \(-0.104222\pi\)
−0.999766 + 0.0216400i \(0.993111\pi\)
\(644\) −0.549163 + 0.460802i −0.0216401 + 0.0181582i
\(645\) 0 0
\(646\) −33.5228 + 12.2013i −1.31894 + 0.480053i
\(647\) 40.9469 1.60979 0.804894 0.593419i \(-0.202222\pi\)
0.804894 + 0.593419i \(0.202222\pi\)
\(648\) 0 0
\(649\) −23.4953 −0.922269
\(650\) −1.00640 + 0.366298i −0.0394741 + 0.0143674i
\(651\) 0 0
\(652\) −8.10014 + 6.79682i −0.317226 + 0.266184i
\(653\) −3.45171 19.5756i −0.135076 0.766054i −0.974807 0.223051i \(-0.928398\pi\)
0.839731 0.543003i \(-0.182713\pi\)
\(654\) 0 0
\(655\) −10.0667 8.44697i −0.393339 0.330050i
\(656\) 2.45084 4.24497i 0.0956891 0.165738i
\(657\) 0 0
\(658\) 2.13041 + 3.68999i 0.0830522 + 0.143851i
\(659\) −2.98499 + 16.9287i −0.116279 + 0.659448i 0.869831 + 0.493350i \(0.164228\pi\)
−0.986109 + 0.166098i \(0.946883\pi\)
\(660\) 0 0
\(661\) 32.3276 + 11.7663i 1.25740 + 0.457655i 0.882895 0.469571i \(-0.155591\pi\)
0.374503 + 0.927226i \(0.377813\pi\)
\(662\) −15.4474 5.62241i −0.600382 0.218521i
\(663\) 0 0
\(664\) −1.18479 + 6.71929i −0.0459789 + 0.260759i
\(665\) 21.5424 + 37.3125i 0.835377 + 1.44691i
\(666\) 0 0
\(667\) −0.474308 + 0.821525i −0.0183653 + 0.0318096i
\(668\) −1.15136 0.966105i −0.0445474 0.0373797i
\(669\) 0 0
\(670\) −0.0184183 0.104455i −0.000711562 0.00403547i
\(671\) 36.3200 30.4761i 1.40212 1.17652i
\(672\) 0 0
\(673\) −22.4513 + 8.17161i −0.865434 + 0.314992i −0.736317 0.676637i \(-0.763437\pi\)
−0.129117 + 0.991629i \(0.541214\pi\)
\(674\) 10.5517 0.406436
\(675\) 0 0
\(676\) −12.4243 −0.477856
\(677\) 32.6238 11.8741i 1.25383 0.456358i 0.372138 0.928177i \(-0.378625\pi\)
0.881695 + 0.471819i \(0.156403\pi\)
\(678\) 0 0
\(679\) 5.90348 4.95361i 0.226555 0.190102i
\(680\) 2.16385 + 12.2718i 0.0829798 + 0.470602i
\(681\) 0 0
\(682\) −28.2558 23.7095i −1.08197 0.907882i
\(683\) −19.5030 + 33.7802i −0.746261 + 1.29256i 0.203342 + 0.979108i \(0.434820\pi\)
−0.949603 + 0.313455i \(0.898514\pi\)
\(684\) 0 0
\(685\) 21.6668 + 37.5281i 0.827847 + 1.43387i
\(686\) 3.46064 19.6262i 0.132128 0.749334i
\(687\) 0 0
\(688\) 1.53209 + 0.557635i 0.0584103 + 0.0212596i
\(689\) 0.409253 + 0.148956i 0.0155913 + 0.00567476i
\(690\) 0 0
\(691\) 4.39780 24.9412i 0.167300 0.948807i −0.779361 0.626576i \(-0.784456\pi\)
0.946661 0.322232i \(-0.104433\pi\)
\(692\) −5.57532 9.65674i −0.211942 0.367094i
\(693\) 0 0
\(694\) 14.1800 24.5606i 0.538267 0.932306i
\(695\) −23.6596 19.8527i −0.897459 0.753057i
\(696\) 0 0
\(697\) 4.18883 + 23.7560i 0.158663 + 0.899823i
\(698\) 12.0287 10.0933i 0.455292 0.382036i
\(699\) 0 0
\(700\) 3.11334 1.13316i 0.117673 0.0428295i
\(701\) −42.3054 −1.59785 −0.798927 0.601429i \(-0.794598\pi\)
−0.798927 + 0.601429i \(0.794598\pi\)
\(702\) 0 0
\(703\) 54.9035 2.07073
\(704\) −4.03209 + 1.46756i −0.151965 + 0.0553108i
\(705\) 0 0
\(706\) 1.58125 1.32683i 0.0595112 0.0499358i
\(707\) −4.88847 27.7239i −0.183850 1.04266i
\(708\) 0 0
\(709\) −36.7098 30.8032i −1.37867 1.15684i −0.969703 0.244288i \(-0.921446\pi\)
−0.408964 0.912551i \(-0.634110\pi\)
\(710\) 5.32295 9.21962i 0.199767 0.346006i
\(711\) 0 0
\(712\) 3.96064 + 6.86002i 0.148431 + 0.257090i
\(713\) −0.455889 + 2.58548i −0.0170732 + 0.0968269i
\(714\) 0 0
\(715\) 7.74675 + 2.81959i 0.289712 + 0.105447i
\(716\) 7.33750 + 2.67063i 0.274215 + 0.0998061i
\(717\) 0 0
\(718\) 6.07145 34.4329i 0.226585 1.28502i
\(719\) 6.15451 + 10.6599i 0.229525 + 0.397548i 0.957667 0.287877i \(-0.0929495\pi\)
−0.728143 + 0.685426i \(0.759616\pi\)
\(720\) 0 0
\(721\) 2.83022 4.90209i 0.105403 0.182563i
\(722\) 25.6989 + 21.5640i 0.956415 + 0.802528i
\(723\) 0 0
\(724\) 1.81908 + 10.3165i 0.0676055 + 0.383410i
\(725\) 3.35844 2.81807i 0.124729 0.104660i
\(726\) 0 0
\(727\) 16.3542 5.95243i 0.606542 0.220763i −0.0204474 0.999791i \(-0.506509\pi\)
0.626990 + 0.779028i \(0.284287\pi\)
\(728\) −1.78106 −0.0660104
\(729\) 0 0
\(730\) 28.0847 1.03946
\(731\) −7.53983 + 2.74427i −0.278871 + 0.101501i
\(732\) 0 0
\(733\) 11.0266 9.25244i 0.407278 0.341747i −0.416021 0.909355i \(-0.636576\pi\)
0.823299 + 0.567608i \(0.192131\pi\)
\(734\) −0.0773815 0.438852i −0.00285620 0.0161983i
\(735\) 0 0
\(736\) 0.233956 + 0.196312i 0.00862372 + 0.00723616i
\(737\) −0.0898700 + 0.155659i −0.00331041 + 0.00573379i
\(738\) 0 0
\(739\) 6.82383 + 11.8192i 0.251018 + 0.434777i 0.963806 0.266603i \(-0.0859012\pi\)
−0.712788 + 0.701380i \(0.752568\pi\)
\(740\) 3.33022 18.8866i 0.122421 0.694286i
\(741\) 0 0
\(742\) −1.26604 0.460802i −0.0464780 0.0169166i
\(743\) −17.2459 6.27698i −0.632690 0.230280i 0.00571190 0.999984i \(-0.498182\pi\)
−0.638402 + 0.769703i \(0.720404\pi\)
\(744\) 0 0
\(745\) 3.38666 19.2067i 0.124078 0.703679i
\(746\) 11.0312 + 19.1066i 0.403881 + 0.699543i
\(747\) 0 0
\(748\) 10.5582 18.2874i 0.386048 0.668654i
\(749\) −4.36231 3.66041i −0.159395 0.133749i
\(750\) 0 0
\(751\) −7.01460 39.7818i −0.255967 1.45166i −0.793579 0.608467i \(-0.791785\pi\)
0.537613 0.843192i \(-0.319326\pi\)
\(752\) 1.39053 1.16679i 0.0507074 0.0425486i
\(753\) 0 0
\(754\) −2.21466 + 0.806070i −0.0806532 + 0.0293553i
\(755\) 1.97771 0.0719763
\(756\) 0 0
\(757\) 3.71595 0.135058 0.0675292 0.997717i \(-0.478488\pi\)
0.0675292 + 0.997717i \(0.478488\pi\)
\(758\) −12.3229 + 4.48519i −0.447590 + 0.162909i
\(759\) 0 0
\(760\) 14.0608 11.7984i 0.510038 0.427973i
\(761\) 6.41147 + 36.3613i 0.232416 + 1.31810i 0.847988 + 0.530015i \(0.177814\pi\)
−0.615573 + 0.788080i \(0.711075\pi\)
\(762\) 0 0
\(763\) 4.18551 + 3.51206i 0.151526 + 0.127145i
\(764\) −6.11468 + 10.5909i −0.221222 + 0.383167i
\(765\) 0 0
\(766\) 8.05556 + 13.9526i 0.291059 + 0.504129i
\(767\) −0.721467 + 4.09164i −0.0260507 + 0.147741i
\(768\) 0 0
\(769\) 25.5501 + 9.29947i 0.921360 + 0.335348i 0.758779 0.651348i \(-0.225796\pi\)
0.162581 + 0.986695i \(0.448018\pi\)
\(770\) −23.9650 8.72254i −0.863638 0.314338i
\(771\) 0 0
\(772\) −2.84224 + 16.1192i −0.102295 + 0.580141i
\(773\) −0.869585 1.50617i −0.0312768 0.0541730i 0.849963 0.526842i \(-0.176624\pi\)
−0.881240 + 0.472669i \(0.843291\pi\)
\(774\) 0 0
\(775\) 6.06670 10.5078i 0.217922 0.377453i
\(776\) −2.51501 2.11035i −0.0902838 0.0757571i
\(777\) 0 0
\(778\) −0.0984882 0.558554i −0.00353097 0.0200251i
\(779\) 27.2192 22.8396i 0.975228 0.818313i
\(780\) 0 0
\(781\) −16.9525 + 6.17020i −0.606608 + 0.220787i
\(782\) −1.50299 −0.0537469
\(783\) 0 0
\(784\) −1.49020 −0.0532214
\(785\) −24.7729 + 9.01660i −0.884183 + 0.321816i
\(786\) 0 0
\(787\) −17.7271 + 14.8748i −0.631905 + 0.530231i −0.901520 0.432737i \(-0.857548\pi\)
0.269616 + 0.962968i \(0.413103\pi\)
\(788\) −3.29860 18.7073i −0.117508 0.666420i
\(789\) 0 0
\(790\) 14.3045 + 12.0029i 0.508932 + 0.427045i
\(791\) 20.0194 34.6745i 0.711806 1.23288i
\(792\) 0 0
\(793\) −4.19207 7.26087i −0.148865 0.257841i
\(794\) 6.25506 35.4742i 0.221984 1.25893i
\(795\) 0 0
\(796\) −21.6532 7.88111i −0.767476 0.279339i
\(797\) 2.32295 + 0.845484i 0.0822830 + 0.0299486i 0.382834 0.923817i \(-0.374948\pi\)
−0.300551 + 0.953766i \(0.597170\pi\)
\(798\) 0 0
\(799\) −1.55122 + 8.79742i −0.0548783 + 0.311230i
\(800\) −0.705737 1.22237i −0.0249516 0.0432174i
\(801\) 0 0
\(802\) 17.9966 31.1710i 0.635482 1.10069i
\(803\) −36.4577 30.5916i −1.28656 1.07956i
\(804\) 0 0
\(805\) 0.315207 + 1.78763i 0.0111096 + 0.0630057i
\(806\) −4.99660 + 4.19264i −0.175998 + 0.147680i
\(807\) 0 0
\(808\) −11.2699 + 4.10191i −0.396474 + 0.144305i
\(809\) −1.04870 −0.0368702 −0.0184351 0.999830i \(-0.505868\pi\)
−0.0184351 + 0.999830i \(0.505868\pi\)
\(810\) 0 0
\(811\) −21.3087 −0.748250 −0.374125 0.927378i \(-0.622057\pi\)
−0.374125 + 0.927378i \(0.622057\pi\)
\(812\) 6.85117 2.49362i 0.240429 0.0875089i
\(813\) 0 0
\(814\) −24.8956 + 20.8899i −0.872590 + 0.732190i
\(815\) 4.64930 + 26.3675i 0.162858 + 0.923613i
\(816\) 0 0
\(817\) 9.05375 + 7.59700i 0.316751 + 0.265785i
\(818\) −6.33796 + 10.9777i −0.221602 + 0.383825i
\(819\) 0 0
\(820\) −6.20574 10.7487i −0.216714 0.375359i
\(821\) 8.53209 48.3879i 0.297772 1.68875i −0.357946 0.933742i \(-0.616523\pi\)
0.655718 0.755006i \(-0.272366\pi\)
\(822\) 0 0
\(823\) −3.19207 1.16182i −0.111268 0.0404984i 0.285786 0.958293i \(-0.407745\pi\)
−0.397054 + 0.917795i \(0.629968\pi\)
\(824\) −2.26604 0.824773i −0.0789414 0.0287323i
\(825\) 0 0
\(826\) 2.23190 12.6577i 0.0776576 0.440418i
\(827\) −23.8359 41.2850i −0.828856 1.43562i −0.898937 0.438079i \(-0.855659\pi\)
0.0700811 0.997541i \(-0.477674\pi\)
\(828\) 0 0
\(829\) −1.71570 + 2.97168i −0.0595887 + 0.103211i −0.894281 0.447506i \(-0.852312\pi\)
0.834692 + 0.550717i \(0.185646\pi\)
\(830\) 13.2344 + 11.1050i 0.459374 + 0.385460i
\(831\) 0 0
\(832\) 0.131759 + 0.747243i 0.00456793 + 0.0259060i
\(833\) 5.61793 4.71400i 0.194650 0.163330i
\(834\) 0 0
\(835\) −3.57620 + 1.30163i −0.123759 + 0.0450448i
\(836\) −31.1043 −1.07577
\(837\) 0 0
\(838\) −14.2591 −0.492572
\(839\) −23.7288 + 8.63658i −0.819209 + 0.298168i −0.717422 0.696639i \(-0.754678\pi\)
−0.101787 + 0.994806i \(0.532456\pi\)
\(840\) 0 0
\(841\) −14.8248 + 12.4395i −0.511199 + 0.428947i
\(842\) 0.546637 + 3.10013i 0.0188383 + 0.106838i
\(843\) 0 0
\(844\) 13.4042 + 11.2475i 0.461392 + 0.387154i
\(845\) −15.7297 + 27.2446i −0.541117 + 0.937243i
\(846\) 0 0
\(847\) 8.69846 + 15.0662i 0.298883 + 0.517680i
\(848\) −0.0996702 + 0.565258i −0.00342269 + 0.0194110i
\(849\) 0 0
\(850\) 6.52734 + 2.37576i 0.223886 + 0.0814878i
\(851\) 2.17365 + 0.791143i 0.0745117 + 0.0271200i
\(852\) 0 0
\(853\) 6.88144 39.0266i 0.235616 1.33625i −0.605696 0.795696i \(-0.707105\pi\)
0.841312 0.540550i \(-0.181784\pi\)
\(854\) 12.9684 + 22.4619i 0.443769 + 0.768630i
\(855\) 0 0
\(856\) −1.21301 + 2.10100i −0.0414599 + 0.0718106i
\(857\) 21.3136 + 17.8842i 0.728059 + 0.610914i 0.929602 0.368566i \(-0.120151\pi\)
−0.201543 + 0.979480i \(0.564595\pi\)
\(858\) 0 0
\(859\) 1.45987 + 8.27931i 0.0498100 + 0.282486i 0.999531 0.0306097i \(-0.00974490\pi\)
−0.949721 + 0.313096i \(0.898634\pi\)
\(860\) 3.16250 2.65366i 0.107840 0.0904889i
\(861\) 0 0
\(862\) 14.5569 5.29828i 0.495810 0.180460i
\(863\) 41.9436 1.42778 0.713888 0.700260i \(-0.246933\pi\)
0.713888 + 0.700260i \(0.246933\pi\)
\(864\) 0 0
\(865\) −28.2344 −0.959999
\(866\) 2.09405 0.762170i 0.0711586 0.0258996i
\(867\) 0 0
\(868\) 15.4572 12.9702i 0.524653 0.440236i
\(869\) −5.49484 31.1628i −0.186400 1.05713i
\(870\) 0 0
\(871\) 0.0243481 + 0.0204305i 0.000825004 + 0.000692260i
\(872\) 1.16385 2.01584i 0.0394129 0.0682651i
\(873\) 0 0
\(874\) 1.10694 + 1.91728i 0.0374429 + 0.0648531i
\(875\) −3.70368 + 21.0046i −0.125207 + 0.710085i
\(876\) 0 0
\(877\) 43.7156 + 15.9112i 1.47617 + 0.537282i 0.949768 0.312953i \(-0.101318\pi\)
0.526402 + 0.850236i \(0.323541\pi\)
\(878\) −16.1395 5.87430i −0.544682 0.198248i
\(879\) 0 0
\(880\) −1.88666 + 10.6998i −0.0635993 + 0.360689i
\(881\) 5.84611 + 10.1258i 0.196961 + 0.341146i 0.947541 0.319633i \(-0.103560\pi\)
−0.750581 + 0.660779i \(0.770226\pi\)
\(882\) 0 0
\(883\) 4.41400 7.64527i 0.148543 0.257284i −0.782146 0.623095i \(-0.785875\pi\)
0.930689 + 0.365811i \(0.119208\pi\)
\(884\) −2.86050 2.40024i −0.0962090 0.0807290i
\(885\) 0 0
\(886\) 4.10173 + 23.2621i 0.137800 + 0.781504i
\(887\) 3.21554 2.69816i 0.107967 0.0905952i −0.587206 0.809438i \(-0.699772\pi\)
0.695173 + 0.718842i \(0.255328\pi\)
\(888\) 0 0
\(889\) 27.8935 10.1524i 0.935519 0.340501i
\(890\) 20.0574 0.672325
\(891\) 0 0
\(892\) −4.21894 −0.141261
\(893\) 12.3648 4.50043i 0.413774 0.150601i
\(894\) 0 0
\(895\) 15.1459 12.7089i 0.506271 0.424812i
\(896\) −0.407604 2.31164i −0.0136171 0.0772263i
\(897\) 0 0
\(898\) 15.5194 + 13.0223i 0.517887 + 0.434559i
\(899\) 13.3503 23.1234i 0.445257 0.771208i
\(900\) 0 0
\(901\) −1.41235 2.44626i −0.0470522 0.0814969i
\(902\) −3.65224 + 20.7129i −0.121606 + 0.689663i
\(903\) 0 0
\(904\) −16.0287 5.83396i −0.533106 0.194035i
\(905\) 24.9256 + 9.07218i 0.828555 + 0.301569i
\(906\) 0 0
\(907\) −8.68732 + 49.2682i −0.288458 + 1.63592i 0.404209 + 0.914667i \(0.367547\pi\)
−0.692666 + 0.721258i \(0.743564\pi\)
\(908\) 7.98293 + 13.8268i 0.264923 + 0.458860i
\(909\) 0 0
\(910\) −2.25490 + 3.90560i −0.0747492 + 0.129469i
\(911\) 12.3532 + 10.3656i 0.409281 + 0.343427i 0.824068 0.566491i \(-0.191700\pi\)
−0.414787 + 0.909918i \(0.636144\pi\)
\(912\) 0 0
\(913\) −5.08378 28.8315i −0.168248 0.954185i
\(914\) −31.0710 + 26.0717i −1.02774 + 0.862375i
\(915\) 0 0
\(916\) 16.7713 6.10424i 0.554138 0.201690i
\(917\) −12.1821 −0.402289
\(918\) 0 0
\(919\) −43.4023 −1.43171 −0.715855 0.698249i \(-0.753963\pi\)
−0.715855 + 0.698249i \(0.753963\pi\)
\(920\) 0.726682 0.264490i 0.0239580 0.00871999i
\(921\) 0 0
\(922\) −10.5018 + 8.81207i −0.345859 + 0.290210i
\(923\) 0.553967 + 3.14170i 0.0182340 + 0.103410i
\(924\) 0 0
\(925\) −8.18938 6.87170i −0.269265 0.225940i
\(926\) −2.70233 + 4.68058i −0.0888042 + 0.153813i
\(927\) 0 0
\(928\) −1.55303 2.68993i −0.0509808 0.0883014i
\(929\) −3.74691 + 21.2498i −0.122932 + 0.697183i 0.859582 + 0.510997i \(0.170724\pi\)
−0.982515 + 0.186186i \(0.940387\pi\)
\(930\) 0 0
\(931\) −10.1509 3.69464i −0.332684 0.121087i
\(932\) −0.692066 0.251892i −0.0226694 0.00825098i
\(933\) 0 0
\(934\) −5.46822 + 31.0118i −0.178925 + 1.01474i
\(935\) −26.7344 46.3054i −0.874309 1.51435i
\(936\) 0 0
\(937\) 8.94625 15.4954i 0.292261 0.506211i −0.682083 0.731275i \(-0.738926\pi\)
0.974344 + 0.225064i \(0.0722590\pi\)
\(938\) −0.0753221 0.0632028i −0.00245935 0.00206364i
\(939\) 0 0
\(940\) −0.798133 4.52644i −0.0260322 0.147636i
\(941\) −23.8739 + 20.0326i −0.778268 + 0.653044i −0.942812 0.333326i \(-0.891829\pi\)
0.164544 + 0.986370i \(0.447385\pi\)
\(942\) 0 0
\(943\) 1.40673 0.512007i 0.0458093 0.0166732i
\(944\) −5.47565 −0.178217
\(945\) 0 0
\(946\) −6.99588 −0.227456
\(947\) −38.0412 + 13.8459i −1.23617 + 0.449930i −0.875707 0.482843i \(-0.839604\pi\)
−0.360465 + 0.932773i \(0.617382\pi\)
\(948\) 0 0
\(949\) −6.44697 + 5.40965i −0.209277 + 0.175605i
\(950\) −1.77672 10.0763i −0.0576445 0.326918i
\(951\) 0 0
\(952\) 8.84911 + 7.42528i 0.286801 + 0.240655i
\(953\) 23.7040 41.0565i 0.767847 1.32995i −0.170881 0.985292i \(-0.554661\pi\)
0.938728 0.344659i \(-0.112005\pi\)
\(954\) 0 0
\(955\) 15.4829 + 26.8172i 0.501016 + 0.867785i
\(956\) 0.499123 2.83067i 0.0161428 0.0915503i
\(957\) 0 0
\(958\) −19.7087 7.17339i −0.636760 0.231762i
\(959\) 37.7486 + 13.7394i 1.21896 + 0.443667i
\(960\) 0 0
\(961\) 7.44878 42.2441i 0.240283 1.36271i
\(962\) 2.87346 + 4.97697i 0.0926439 + 0.160464i
\(963\) 0 0
\(964\) −1.09105 + 1.88976i −0.0351404 + 0.0608650i
\(965\) 31.7486 + 26.6402i 1.02202 + 0.857579i
\(966\) 0 0
\(967\) 1.95817 + 11.1053i 0.0629704 + 0.357123i 0.999970 + 0.00779154i \(0.00248015\pi\)
−0.936999 + 0.349331i \(0.886409\pi\)
\(968\) 5.67752 4.76400i 0.182482 0.153121i
\(969\) 0 0
\(970\) −7.81180 + 2.84326i −0.250822 + 0.0912917i
\(971\) −7.23442 −0.232164 −0.116082 0.993240i \(-0.537033\pi\)
−0.116082 + 0.993240i \(0.537033\pi\)
\(972\) 0 0
\(973\) −28.6313 −0.917879
\(974\) 14.5175 5.28395i 0.465172 0.169309i
\(975\) 0 0
\(976\) 8.46451 7.10257i 0.270942 0.227348i
\(977\) −3.95646 22.4382i −0.126578 0.717862i −0.980358 0.197227i \(-0.936806\pi\)
0.853779 0.520635i \(-0.174305\pi\)
\(978\) 0 0
\(979\) −26.0371 21.8478i −0.832151 0.698257i
\(980\) −1.88666 + 3.26779i −0.0602671 + 0.104386i
\(981\) 0 0
\(982\) 7.93107 + 13.7370i 0.253091 + 0.438366i
\(983\) 0.254738 1.44469i 0.00812488 0.0460785i −0.980476 0.196640i \(-0.936997\pi\)
0.988601 + 0.150561i \(0.0481081\pi\)
\(984\) 0 0
\(985\) −45.1985 16.4509i −1.44014 0.524170i
\(986\) 14.3640 + 5.22805i 0.457442 + 0.166495i
\(987\) 0 0
\(988\) −0.955118 + 5.41674i −0.0303863 + 0.172330i
\(989\) 0.248970 + 0.431229i 0.00791680 + 0.0137123i
\(990\) 0 0
\(991\) 1.94475 3.36840i 0.0617769 0.107001i −0.833483 0.552545i \(-0.813657\pi\)
0.895260 + 0.445545i \(0.146990\pi\)
\(992\) −6.58512 5.52557i −0.209078 0.175437i
\(993\) 0 0
\(994\) −1.71373 9.71902i −0.0543561 0.308269i
\(995\) −44.6960 + 37.5044i −1.41696 + 1.18897i
\(996\) 0 0
\(997\) 17.9884 6.54726i 0.569700 0.207354i −0.0410778 0.999156i \(-0.513079\pi\)
0.610778 + 0.791802i \(0.290857\pi\)
\(998\) −7.48751 −0.237013
\(999\) 0 0
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 162.2.e.a.19.1 6
3.2 odd 2 54.2.e.a.7.1 6
9.2 odd 6 486.2.e.b.379.1 6
9.4 even 3 486.2.e.a.217.1 6
9.5 odd 6 486.2.e.d.217.1 6
9.7 even 3 486.2.e.c.379.1 6
12.11 even 2 432.2.u.a.385.1 6
27.2 odd 18 1458.2.a.a.1.3 3
27.4 even 9 inner 162.2.e.a.145.1 6
27.5 odd 18 486.2.e.d.271.1 6
27.7 even 9 1458.2.c.a.487.3 6
27.11 odd 18 1458.2.c.d.973.1 6
27.13 even 9 486.2.e.c.109.1 6
27.14 odd 18 486.2.e.b.109.1 6
27.16 even 9 1458.2.c.a.973.3 6
27.20 odd 18 1458.2.c.d.487.1 6
27.22 even 9 486.2.e.a.271.1 6
27.23 odd 18 54.2.e.a.31.1 yes 6
27.25 even 9 1458.2.a.d.1.1 3
108.23 even 18 432.2.u.a.193.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
54.2.e.a.7.1 6 3.2 odd 2
54.2.e.a.31.1 yes 6 27.23 odd 18
162.2.e.a.19.1 6 1.1 even 1 trivial
162.2.e.a.145.1 6 27.4 even 9 inner
432.2.u.a.193.1 6 108.23 even 18
432.2.u.a.385.1 6 12.11 even 2
486.2.e.a.217.1 6 9.4 even 3
486.2.e.a.271.1 6 27.22 even 9
486.2.e.b.109.1 6 27.14 odd 18
486.2.e.b.379.1 6 9.2 odd 6
486.2.e.c.109.1 6 27.13 even 9
486.2.e.c.379.1 6 9.7 even 3
486.2.e.d.217.1 6 9.5 odd 6
486.2.e.d.271.1 6 27.5 odd 18
1458.2.a.a.1.3 3 27.2 odd 18
1458.2.a.d.1.1 3 27.25 even 9
1458.2.c.a.487.3 6 27.7 even 9
1458.2.c.a.973.3 6 27.16 even 9
1458.2.c.d.487.1 6 27.20 odd 18
1458.2.c.d.973.1 6 27.11 odd 18