Properties

Label 324.2.l.a.179.2
Level $324$
Weight $2$
Character 324.179
Analytic conductor $2.587$
Analytic rank $0$
Dimension $96$
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] = [324,2,Mod(35,324)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(324, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([9, 13]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("324.35");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 324 = 2^{2} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 324.l (of order \(18\), 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: \(2.58715302549\)
Analytic rank: \(0\)
Dimension: \(96\)
Relative dimension: \(16\) over \(\Q(\zeta_{18})\)
Twist minimal: no (minimal twist has level 108)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 179.2
Character \(\chi\) \(=\) 324.179
Dual form 324.2.l.a.143.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.32122 - 0.504364i) q^{2} +(1.49123 + 1.33275i) q^{4} +(3.39370 + 0.598401i) q^{5} +(1.88319 + 2.24430i) q^{7} +(-1.29805 - 2.51298i) q^{8} +O(q^{10})\) \(q+(-1.32122 - 0.504364i) q^{2} +(1.49123 + 1.33275i) q^{4} +(3.39370 + 0.598401i) q^{5} +(1.88319 + 2.24430i) q^{7} +(-1.29805 - 2.51298i) q^{8} +(-4.18200 - 2.50228i) q^{10} +(0.453915 + 2.57428i) q^{11} +(-5.09721 + 1.85523i) q^{13} +(-1.35616 - 3.91503i) q^{14} +(0.447553 + 3.97488i) q^{16} +(-1.15583 - 0.667320i) q^{17} +(0.0790760 - 0.0456546i) q^{19} +(4.26328 + 5.41531i) q^{20} +(0.698654 - 3.63012i) q^{22} +(-0.650322 - 0.545685i) q^{23} +(6.46065 + 2.35148i) q^{25} +(7.67024 + 0.119685i) q^{26} +(-0.182815 + 5.85661i) q^{28} +(0.171418 - 0.470966i) q^{29} +(4.28324 - 5.10457i) q^{31} +(1.41348 - 5.47742i) q^{32} +(1.19053 + 1.46464i) q^{34} +(5.04800 + 8.74340i) q^{35} +(2.75869 - 4.77819i) q^{37} +(-0.127503 + 0.0204365i) q^{38} +(-2.90143 - 9.30505i) q^{40} +(0.976880 + 2.68396i) q^{41} +(5.59737 - 0.986968i) q^{43} +(-2.75398 + 4.44381i) q^{44} +(0.583993 + 1.04897i) q^{46} +(-5.06200 + 4.24752i) q^{47} +(-0.274941 + 1.55927i) q^{49} +(-7.34992 - 6.36534i) q^{50} +(-10.0737 - 4.02673i) q^{52} -7.37249i q^{53} +9.00795i q^{55} +(3.19540 - 7.64565i) q^{56} +(-0.464019 + 0.535792i) q^{58} +(0.528787 - 2.99890i) q^{59} +(-1.85759 + 1.55871i) q^{61} +(-8.23365 + 4.58393i) q^{62} +(-4.63012 + 6.52395i) q^{64} +(-18.4086 + 3.24593i) q^{65} +(1.64904 + 4.53069i) q^{67} +(-0.834244 - 2.53557i) q^{68} +(-2.25965 - 14.0980i) q^{70} +(5.91940 - 10.2527i) q^{71} +(-5.83049 - 10.0987i) q^{73} +(-6.05478 + 4.92165i) q^{74} +(0.178767 + 0.0373070i) q^{76} +(-4.92266 + 5.86659i) q^{77} +(-0.576990 + 1.58527i) q^{79} +(-0.859714 + 13.7574i) q^{80} +(0.0630204 - 4.03879i) q^{82} +(-2.02940 - 0.738640i) q^{83} +(-3.52322 - 2.95633i) q^{85} +(-7.89314 - 1.51912i) q^{86} +(5.87990 - 4.48223i) q^{88} +(12.5801 - 7.26310i) q^{89} +(-13.7628 - 7.94593i) q^{91} +(-0.242520 - 1.68046i) q^{92} +(8.83031 - 3.05881i) q^{94} +(0.295680 - 0.107619i) q^{95} +(1.14607 + 6.49971i) q^{97} +(1.14969 - 1.92146i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8} - 3 q^{10} - 12 q^{13} + 21 q^{14} - 6 q^{16} + 18 q^{17} + 27 q^{20} - 6 q^{22} - 12 q^{25} - 12 q^{28} + 24 q^{29} - 24 q^{32} - 12 q^{34} - 6 q^{37} - 18 q^{38} - 21 q^{40} + 42 q^{41} - 63 q^{44} - 3 q^{46} - 12 q^{49} - 87 q^{50} - 33 q^{52} - 99 q^{56} - 33 q^{58} - 12 q^{61} - 90 q^{62} - 3 q^{64} - 12 q^{65} - 51 q^{68} - 21 q^{70} - 6 q^{73} - 21 q^{74} - 18 q^{76} - 12 q^{77} - 12 q^{82} - 42 q^{85} + 30 q^{86} + 18 q^{88} + 123 q^{92} + 21 q^{94} - 30 q^{97} + 180 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).

\(n\) \(163\) \(245\)
\(\chi(n)\) \(-1\) \(e\left(\frac{11}{18}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.32122 0.504364i −0.934242 0.356639i
\(3\) 0 0
\(4\) 1.49123 + 1.33275i 0.745617 + 0.666375i
\(5\) 3.39370 + 0.598401i 1.51771 + 0.267613i 0.869532 0.493877i \(-0.164421\pi\)
0.648177 + 0.761490i \(0.275532\pi\)
\(6\) 0 0
\(7\) 1.88319 + 2.24430i 0.711781 + 0.848267i 0.993805 0.111140i \(-0.0354503\pi\)
−0.282024 + 0.959407i \(0.591006\pi\)
\(8\) −1.29805 2.51298i −0.458931 0.888472i
\(9\) 0 0
\(10\) −4.18200 2.50228i −1.32247 0.791290i
\(11\) 0.453915 + 2.57428i 0.136861 + 0.776174i 0.973546 + 0.228491i \(0.0733791\pi\)
−0.836686 + 0.547684i \(0.815510\pi\)
\(12\) 0 0
\(13\) −5.09721 + 1.85523i −1.41371 + 0.514549i −0.932217 0.361899i \(-0.882128\pi\)
−0.481496 + 0.876449i \(0.659906\pi\)
\(14\) −1.35616 3.91503i −0.362450 1.04634i
\(15\) 0 0
\(16\) 0.447553 + 3.97488i 0.111888 + 0.993721i
\(17\) −1.15583 0.667320i −0.280330 0.161849i 0.353243 0.935532i \(-0.385079\pi\)
−0.633573 + 0.773683i \(0.718412\pi\)
\(18\) 0 0
\(19\) 0.0790760 0.0456546i 0.0181413 0.0104739i −0.490902 0.871215i \(-0.663333\pi\)
0.509043 + 0.860741i \(0.329999\pi\)
\(20\) 4.26328 + 5.41531i 0.953298 + 1.21090i
\(21\) 0 0
\(22\) 0.698654 3.63012i 0.148954 0.773945i
\(23\) −0.650322 0.545685i −0.135602 0.113783i 0.572464 0.819930i \(-0.305988\pi\)
−0.708066 + 0.706147i \(0.750432\pi\)
\(24\) 0 0
\(25\) 6.46065 + 2.35148i 1.29213 + 0.470297i
\(26\) 7.67024 + 0.119685i 1.50426 + 0.0234721i
\(27\) 0 0
\(28\) −0.182815 + 5.85661i −0.0345487 + 1.10679i
\(29\) 0.171418 0.470966i 0.0318315 0.0874562i −0.922759 0.385378i \(-0.874071\pi\)
0.954590 + 0.297922i \(0.0962934\pi\)
\(30\) 0 0
\(31\) 4.28324 5.10457i 0.769293 0.916807i −0.229105 0.973402i \(-0.573580\pi\)
0.998397 + 0.0565946i \(0.0180243\pi\)
\(32\) 1.41348 5.47742i 0.249869 0.968280i
\(33\) 0 0
\(34\) 1.19053 + 1.46464i 0.204175 + 0.251183i
\(35\) 5.04800 + 8.74340i 0.853268 + 1.47790i
\(36\) 0 0
\(37\) 2.75869 4.77819i 0.453526 0.785530i −0.545076 0.838387i \(-0.683499\pi\)
0.998602 + 0.0528563i \(0.0168325\pi\)
\(38\) −0.127503 + 0.0204365i −0.0206838 + 0.00331524i
\(39\) 0 0
\(40\) −2.90143 9.30505i −0.458756 1.47126i
\(41\) 0.976880 + 2.68396i 0.152563 + 0.419163i 0.992304 0.123823i \(-0.0395156\pi\)
−0.839741 + 0.542987i \(0.817293\pi\)
\(42\) 0 0
\(43\) 5.59737 0.986968i 0.853591 0.150511i 0.270302 0.962776i \(-0.412876\pi\)
0.583289 + 0.812264i \(0.301765\pi\)
\(44\) −2.75398 + 4.44381i −0.415178 + 0.669929i
\(45\) 0 0
\(46\) 0.583993 + 1.04897i 0.0861051 + 0.154662i
\(47\) −5.06200 + 4.24752i −0.738369 + 0.619565i −0.932399 0.361430i \(-0.882288\pi\)
0.194030 + 0.980996i \(0.437844\pi\)
\(48\) 0 0
\(49\) −0.274941 + 1.55927i −0.0392772 + 0.222752i
\(50\) −7.34992 6.36534i −1.03944 0.900196i
\(51\) 0 0
\(52\) −10.0737 4.02673i −1.39697 0.558407i
\(53\) 7.37249i 1.01269i −0.862331 0.506345i \(-0.830996\pi\)
0.862331 0.506345i \(-0.169004\pi\)
\(54\) 0 0
\(55\) 9.00795i 1.21463i
\(56\) 3.19540 7.64565i 0.427004 1.02169i
\(57\) 0 0
\(58\) −0.464019 + 0.535792i −0.0609286 + 0.0703529i
\(59\) 0.528787 2.99890i 0.0688422 0.390423i −0.930845 0.365414i \(-0.880927\pi\)
0.999687 0.0250093i \(-0.00796152\pi\)
\(60\) 0 0
\(61\) −1.85759 + 1.55871i −0.237841 + 0.199572i −0.753915 0.656972i \(-0.771837\pi\)
0.516075 + 0.856544i \(0.327393\pi\)
\(62\) −8.23365 + 4.58393i −1.04568 + 0.582160i
\(63\) 0 0
\(64\) −4.63012 + 6.52395i −0.578765 + 0.815494i
\(65\) −18.4086 + 3.24593i −2.28330 + 0.402608i
\(66\) 0 0
\(67\) 1.64904 + 4.53069i 0.201462 + 0.553512i 0.998744 0.0500945i \(-0.0159522\pi\)
−0.797283 + 0.603606i \(0.793730\pi\)
\(68\) −0.834244 2.53557i −0.101167 0.307482i
\(69\) 0 0
\(70\) −2.25965 14.0980i −0.270080 1.68503i
\(71\) 5.91940 10.2527i 0.702504 1.21677i −0.265081 0.964226i \(-0.585399\pi\)
0.967585 0.252546i \(-0.0812678\pi\)
\(72\) 0 0
\(73\) −5.83049 10.0987i −0.682408 1.18197i −0.974244 0.225497i \(-0.927600\pi\)
0.291836 0.956468i \(-0.405734\pi\)
\(74\) −6.05478 + 4.92165i −0.703854 + 0.572130i
\(75\) 0 0
\(76\) 0.178767 + 0.0373070i 0.0205060 + 0.00427941i
\(77\) −4.92266 + 5.86659i −0.560989 + 0.668560i
\(78\) 0 0
\(79\) −0.576990 + 1.58527i −0.0649165 + 0.178357i −0.967910 0.251298i \(-0.919143\pi\)
0.902993 + 0.429655i \(0.141365\pi\)
\(80\) −0.859714 + 13.7574i −0.0961190 + 1.53812i
\(81\) 0 0
\(82\) 0.0630204 4.03879i 0.00695944 0.446010i
\(83\) −2.02940 0.738640i −0.222755 0.0810763i 0.228232 0.973607i \(-0.426706\pi\)
−0.450987 + 0.892531i \(0.648928\pi\)
\(84\) 0 0
\(85\) −3.52322 2.95633i −0.382147 0.320659i
\(86\) −7.89314 1.51912i −0.851139 0.163810i
\(87\) 0 0
\(88\) 5.87990 4.48223i 0.626800 0.477807i
\(89\) 12.5801 7.26310i 1.33348 0.769887i 0.347652 0.937624i \(-0.386979\pi\)
0.985832 + 0.167737i \(0.0536458\pi\)
\(90\) 0 0
\(91\) −13.7628 7.94593i −1.44273 0.832960i
\(92\) −0.242520 1.68046i −0.0252844 0.175200i
\(93\) 0 0
\(94\) 8.83031 3.05881i 0.910777 0.315492i
\(95\) 0.295680 0.107619i 0.0303361 0.0110414i
\(96\) 0 0
\(97\) 1.14607 + 6.49971i 0.116366 + 0.659946i 0.986065 + 0.166362i \(0.0532021\pi\)
−0.869698 + 0.493583i \(0.835687\pi\)
\(98\) 1.14969 1.92146i 0.116137 0.194097i
\(99\) 0 0
\(100\) 6.50039 + 12.1170i 0.650039 + 1.21170i
\(101\) 5.29995 + 6.31623i 0.527365 + 0.628489i 0.962306 0.271970i \(-0.0876752\pi\)
−0.434941 + 0.900459i \(0.643231\pi\)
\(102\) 0 0
\(103\) −15.8523 2.79519i −1.56197 0.275418i −0.675203 0.737632i \(-0.735944\pi\)
−0.886769 + 0.462214i \(0.847055\pi\)
\(104\) 11.2786 + 10.4010i 1.10596 + 1.01990i
\(105\) 0 0
\(106\) −3.71842 + 9.74067i −0.361165 + 0.946097i
\(107\) −9.71808 −0.939482 −0.469741 0.882804i \(-0.655653\pi\)
−0.469741 + 0.882804i \(0.655653\pi\)
\(108\) 0 0
\(109\) −4.69860 −0.450044 −0.225022 0.974354i \(-0.572245\pi\)
−0.225022 + 0.974354i \(0.572245\pi\)
\(110\) 4.54329 11.9015i 0.433186 1.13476i
\(111\) 0 0
\(112\) −8.07802 + 8.48992i −0.763301 + 0.802222i
\(113\) −0.555886 0.0980178i −0.0522934 0.00922074i 0.147440 0.989071i \(-0.452897\pi\)
−0.199734 + 0.979850i \(0.564008\pi\)
\(114\) 0 0
\(115\) −1.88046 2.24104i −0.175354 0.208978i
\(116\) 0.883304 0.473863i 0.0820127 0.0439971i
\(117\) 0 0
\(118\) −2.21118 + 3.69550i −0.203556 + 0.340198i
\(119\) −0.678988 3.85073i −0.0622427 0.352996i
\(120\) 0 0
\(121\) 3.91574 1.42521i 0.355977 0.129565i
\(122\) 3.24044 1.12249i 0.293376 0.101625i
\(123\) 0 0
\(124\) 13.1904 1.90361i 1.18453 0.170949i
\(125\) 5.59652 + 3.23116i 0.500568 + 0.289003i
\(126\) 0 0
\(127\) 9.63141 5.56070i 0.854649 0.493432i −0.00756758 0.999971i \(-0.502409\pi\)
0.862217 + 0.506539i \(0.169076\pi\)
\(128\) 9.40785 6.28430i 0.831544 0.555458i
\(129\) 0 0
\(130\) 25.9589 + 4.99605i 2.27674 + 0.438183i
\(131\) −2.37648 1.99411i −0.207634 0.174226i 0.533040 0.846090i \(-0.321049\pi\)
−0.740675 + 0.671864i \(0.765494\pi\)
\(132\) 0 0
\(133\) 0.251378 + 0.0914942i 0.0217973 + 0.00793355i
\(134\) 0.106382 6.81774i 0.00919004 0.588963i
\(135\) 0 0
\(136\) −0.176631 + 3.77080i −0.0151459 + 0.323343i
\(137\) 5.90609 16.2268i 0.504591 1.38635i −0.382156 0.924098i \(-0.624818\pi\)
0.886747 0.462255i \(-0.152959\pi\)
\(138\) 0 0
\(139\) 7.19280 8.57205i 0.610085 0.727071i −0.369246 0.929332i \(-0.620384\pi\)
0.979332 + 0.202260i \(0.0648286\pi\)
\(140\) −4.12502 + 19.7662i −0.348628 + 1.67055i
\(141\) 0 0
\(142\) −12.9919 + 10.5605i −1.09026 + 0.886219i
\(143\) −7.08959 12.2795i −0.592862 1.02687i
\(144\) 0 0
\(145\) 0.863567 1.49574i 0.0717153 0.124215i
\(146\) 2.60992 + 16.2833i 0.215999 + 1.34762i
\(147\) 0 0
\(148\) 10.4820 3.44875i 0.861615 0.283486i
\(149\) 6.24250 + 17.1511i 0.511406 + 1.40508i 0.879773 + 0.475395i \(0.157695\pi\)
−0.368367 + 0.929680i \(0.620083\pi\)
\(150\) 0 0
\(151\) −18.9571 + 3.34265i −1.54271 + 0.272021i −0.879311 0.476248i \(-0.841996\pi\)
−0.663396 + 0.748269i \(0.730885\pi\)
\(152\) −0.217374 0.139454i −0.0176313 0.0113112i
\(153\) 0 0
\(154\) 9.46280 5.26823i 0.762534 0.424526i
\(155\) 17.5906 14.7603i 1.41291 1.18557i
\(156\) 0 0
\(157\) −2.92425 + 16.5843i −0.233381 + 1.32357i 0.612617 + 0.790380i \(0.290117\pi\)
−0.845997 + 0.533187i \(0.820994\pi\)
\(158\) 1.56188 1.80347i 0.124257 0.143476i
\(159\) 0 0
\(160\) 8.07460 17.7429i 0.638353 1.40270i
\(161\) 2.48715i 0.196015i
\(162\) 0 0
\(163\) 8.02606i 0.628650i −0.949315 0.314325i \(-0.898222\pi\)
0.949315 0.314325i \(-0.101778\pi\)
\(164\) −2.12029 + 5.30434i −0.165567 + 0.414199i
\(165\) 0 0
\(166\) 2.30873 + 1.99946i 0.179192 + 0.155188i
\(167\) −0.226727 + 1.28583i −0.0175447 + 0.0995008i −0.992323 0.123676i \(-0.960532\pi\)
0.974778 + 0.223177i \(0.0716427\pi\)
\(168\) 0 0
\(169\) 12.5811 10.5568i 0.967779 0.812063i
\(170\) 3.16387 + 5.68295i 0.242658 + 0.435862i
\(171\) 0 0
\(172\) 9.66237 + 5.98810i 0.736749 + 0.456588i
\(173\) −11.2769 + 1.98842i −0.857366 + 0.151177i −0.585016 0.811022i \(-0.698912\pi\)
−0.272350 + 0.962198i \(0.587801\pi\)
\(174\) 0 0
\(175\) 6.88921 + 18.9280i 0.520776 + 1.43082i
\(176\) −10.0293 + 2.95638i −0.755988 + 0.222846i
\(177\) 0 0
\(178\) −20.2842 + 3.25120i −1.52037 + 0.243688i
\(179\) −10.7064 + 18.5441i −0.800237 + 1.38605i 0.119222 + 0.992868i \(0.461960\pi\)
−0.919460 + 0.393184i \(0.871373\pi\)
\(180\) 0 0
\(181\) 7.31416 + 12.6685i 0.543657 + 0.941641i 0.998690 + 0.0511670i \(0.0162941\pi\)
−0.455033 + 0.890474i \(0.650373\pi\)
\(182\) 14.1760 + 17.4397i 1.05079 + 1.29272i
\(183\) 0 0
\(184\) −0.527143 + 2.34257i −0.0388615 + 0.172697i
\(185\) 12.2214 14.5650i 0.898539 1.07084i
\(186\) 0 0
\(187\) 1.19322 3.27834i 0.0872568 0.239736i
\(188\) −13.2095 0.412337i −0.963403 0.0300728i
\(189\) 0 0
\(190\) −0.444937 0.00694269i −0.0322791 0.000503676i
\(191\) 1.80607 + 0.657357i 0.130683 + 0.0475647i 0.406534 0.913636i \(-0.366737\pi\)
−0.275851 + 0.961200i \(0.588960\pi\)
\(192\) 0 0
\(193\) −4.79657 4.02480i −0.345264 0.289711i 0.453621 0.891195i \(-0.350132\pi\)
−0.798885 + 0.601484i \(0.794577\pi\)
\(194\) 1.76401 9.16557i 0.126648 0.658050i
\(195\) 0 0
\(196\) −2.48811 + 1.95880i −0.177722 + 0.139914i
\(197\) −13.1022 + 7.56456i −0.933494 + 0.538953i −0.887915 0.460008i \(-0.847847\pi\)
−0.0455788 + 0.998961i \(0.514513\pi\)
\(198\) 0 0
\(199\) 22.4427 + 12.9573i 1.59092 + 0.918517i 0.993150 + 0.116849i \(0.0372792\pi\)
0.597769 + 0.801669i \(0.296054\pi\)
\(200\) −2.47703 19.2878i −0.175152 1.36385i
\(201\) 0 0
\(202\) −3.81670 11.0182i −0.268542 0.775240i
\(203\) 1.37980 0.502208i 0.0968433 0.0352481i
\(204\) 0 0
\(205\) 1.70916 + 9.69310i 0.119373 + 0.676996i
\(206\) 19.5345 + 11.6884i 1.36104 + 0.814368i
\(207\) 0 0
\(208\) −9.65561 19.4305i −0.669496 1.34726i
\(209\) 0.153421 + 0.182841i 0.0106124 + 0.0126473i
\(210\) 0 0
\(211\) −17.1836 3.02993i −1.18297 0.208589i −0.452645 0.891691i \(-0.649519\pi\)
−0.730323 + 0.683102i \(0.760631\pi\)
\(212\) 9.82569 10.9941i 0.674831 0.755078i
\(213\) 0 0
\(214\) 12.8397 + 4.90145i 0.877704 + 0.335056i
\(215\) 19.5864 1.33578
\(216\) 0 0
\(217\) 19.5224 1.32526
\(218\) 6.20788 + 2.36981i 0.420450 + 0.160504i
\(219\) 0 0
\(220\) −12.0054 + 13.4330i −0.809401 + 0.905650i
\(221\) 7.12956 + 1.25713i 0.479586 + 0.0845639i
\(222\) 0 0
\(223\) −11.3619 13.5406i −0.760850 0.906746i 0.237051 0.971497i \(-0.423819\pi\)
−0.997901 + 0.0647513i \(0.979375\pi\)
\(224\) 14.9548 7.14277i 0.999212 0.477247i
\(225\) 0 0
\(226\) 0.685010 + 0.409872i 0.0455662 + 0.0272643i
\(227\) −1.62005 9.18776i −0.107527 0.609813i −0.990181 0.139791i \(-0.955357\pi\)
0.882654 0.470022i \(-0.155754\pi\)
\(228\) 0 0
\(229\) −15.8029 + 5.75180i −1.04429 + 0.380090i −0.806504 0.591228i \(-0.798643\pi\)
−0.237784 + 0.971318i \(0.576421\pi\)
\(230\) 1.35419 + 3.90934i 0.0892929 + 0.257775i
\(231\) 0 0
\(232\) −1.40604 + 0.180570i −0.0923109 + 0.0118550i
\(233\) −15.2659 8.81379i −1.00010 0.577410i −0.0918250 0.995775i \(-0.529270\pi\)
−0.908279 + 0.418365i \(0.862603\pi\)
\(234\) 0 0
\(235\) −19.7206 + 11.3857i −1.28643 + 0.742722i
\(236\) 4.78533 3.76732i 0.311498 0.245231i
\(237\) 0 0
\(238\) −1.04508 + 5.43011i −0.0677425 + 0.351982i
\(239\) 7.05862 + 5.92289i 0.456584 + 0.383120i 0.841872 0.539677i \(-0.181453\pi\)
−0.385288 + 0.922796i \(0.625898\pi\)
\(240\) 0 0
\(241\) −5.85117 2.12965i −0.376907 0.137183i 0.146618 0.989193i \(-0.453161\pi\)
−0.523525 + 0.852010i \(0.675383\pi\)
\(242\) −5.89238 0.0919433i −0.378776 0.00591034i
\(243\) 0 0
\(244\) −4.84747 0.151315i −0.310328 0.00968692i
\(245\) −1.86613 + 5.12716i −0.119223 + 0.327562i
\(246\) 0 0
\(247\) −0.318368 + 0.379416i −0.0202572 + 0.0241416i
\(248\) −18.3875 4.13770i −1.16761 0.262744i
\(249\) 0 0
\(250\) −5.76455 7.09175i −0.364582 0.448522i
\(251\) −14.1765 24.5545i −0.894814 1.54986i −0.834034 0.551713i \(-0.813974\pi\)
−0.0607805 0.998151i \(-0.519359\pi\)
\(252\) 0 0
\(253\) 1.10955 1.92181i 0.0697571 0.120823i
\(254\) −15.5298 + 2.48915i −0.974427 + 0.156183i
\(255\) 0 0
\(256\) −15.5994 + 3.55794i −0.974962 + 0.222371i
\(257\) −5.64266 15.5031i −0.351979 0.967056i −0.981734 0.190261i \(-0.939067\pi\)
0.629754 0.776795i \(-0.283156\pi\)
\(258\) 0 0
\(259\) 15.9189 2.80693i 0.989151 0.174414i
\(260\) −31.7775 19.6936i −1.97076 1.22135i
\(261\) 0 0
\(262\) 2.13410 + 3.83326i 0.131845 + 0.236820i
\(263\) −18.5512 + 15.5663i −1.14391 + 0.959859i −0.999560 0.0296674i \(-0.990555\pi\)
−0.144355 + 0.989526i \(0.546111\pi\)
\(264\) 0 0
\(265\) 4.41171 25.0200i 0.271009 1.53697i
\(266\) −0.285979 0.247670i −0.0175345 0.0151856i
\(267\) 0 0
\(268\) −3.57918 + 8.95406i −0.218633 + 0.546956i
\(269\) 12.1956i 0.743578i 0.928317 + 0.371789i \(0.121255\pi\)
−0.928317 + 0.371789i \(0.878745\pi\)
\(270\) 0 0
\(271\) 25.0009i 1.51870i −0.650683 0.759349i \(-0.725517\pi\)
0.650683 0.759349i \(-0.274483\pi\)
\(272\) 2.13522 4.89296i 0.129467 0.296679i
\(273\) 0 0
\(274\) −15.9875 + 18.4604i −0.965838 + 1.11523i
\(275\) −3.12079 + 17.6989i −0.188191 + 1.06728i
\(276\) 0 0
\(277\) −6.69358 + 5.61658i −0.402178 + 0.337468i −0.821335 0.570446i \(-0.806770\pi\)
0.419157 + 0.907914i \(0.362326\pi\)
\(278\) −13.8267 + 7.69775i −0.829270 + 0.461680i
\(279\) 0 0
\(280\) 15.4194 24.0349i 0.921485 1.43636i
\(281\) 21.5554 3.80080i 1.28589 0.226737i 0.511409 0.859338i \(-0.329124\pi\)
0.774478 + 0.632601i \(0.218013\pi\)
\(282\) 0 0
\(283\) 10.2956 + 28.2869i 0.612010 + 1.68148i 0.725737 + 0.687972i \(0.241499\pi\)
−0.113727 + 0.993512i \(0.536279\pi\)
\(284\) 22.4915 7.40009i 1.33462 0.439114i
\(285\) 0 0
\(286\) 3.17354 + 19.7997i 0.187655 + 1.17078i
\(287\) −4.18396 + 7.24682i −0.246971 + 0.427766i
\(288\) 0 0
\(289\) −7.60937 13.1798i −0.447610 0.775283i
\(290\) −1.89536 + 1.54065i −0.111299 + 0.0904700i
\(291\) 0 0
\(292\) 4.76444 22.8301i 0.278818 1.33603i
\(293\) −8.50981 + 10.1416i −0.497148 + 0.592478i −0.955021 0.296540i \(-0.904167\pi\)
0.457872 + 0.889018i \(0.348612\pi\)
\(294\) 0 0
\(295\) 3.58909 9.86094i 0.208965 0.574126i
\(296\) −15.5884 0.730189i −0.906059 0.0424413i
\(297\) 0 0
\(298\) 0.402716 25.8089i 0.0233287 1.49507i
\(299\) 4.32720 + 1.57497i 0.250249 + 0.0910831i
\(300\) 0 0
\(301\) 12.7560 + 10.7036i 0.735243 + 0.616942i
\(302\) 26.7324 + 5.14492i 1.53827 + 0.296057i
\(303\) 0 0
\(304\) 0.216862 + 0.293885i 0.0124379 + 0.0168555i
\(305\) −7.23685 + 4.17820i −0.414381 + 0.239243i
\(306\) 0 0
\(307\) 11.4064 + 6.58546i 0.650995 + 0.375852i 0.788837 0.614602i \(-0.210683\pi\)
−0.137842 + 0.990454i \(0.544017\pi\)
\(308\) −15.1595 + 2.18779i −0.863794 + 0.124661i
\(309\) 0 0
\(310\) −30.6856 + 10.6295i −1.74282 + 0.603713i
\(311\) −5.80348 + 2.11230i −0.329085 + 0.119777i −0.501279 0.865286i \(-0.667137\pi\)
0.172193 + 0.985063i \(0.444915\pi\)
\(312\) 0 0
\(313\) −3.72249 21.1113i −0.210407 1.19328i −0.888701 0.458488i \(-0.848391\pi\)
0.678293 0.734791i \(-0.262720\pi\)
\(314\) 12.2281 20.4365i 0.690070 1.15330i
\(315\) 0 0
\(316\) −2.97319 + 1.59502i −0.167255 + 0.0897269i
\(317\) 9.45061 + 11.2628i 0.530799 + 0.632582i 0.963099 0.269148i \(-0.0867422\pi\)
−0.432300 + 0.901730i \(0.642298\pi\)
\(318\) 0 0
\(319\) 1.29021 + 0.227498i 0.0722378 + 0.0127375i
\(320\) −19.6172 + 19.3697i −1.09663 + 1.08280i
\(321\) 0 0
\(322\) −1.25443 + 3.28607i −0.0699067 + 0.183125i
\(323\) −0.121865 −0.00678074
\(324\) 0 0
\(325\) −37.2939 −2.06869
\(326\) −4.04806 + 10.6042i −0.224201 + 0.587311i
\(327\) 0 0
\(328\) 5.47668 5.93879i 0.302399 0.327915i
\(329\) −19.0655 3.36176i −1.05111 0.185340i
\(330\) 0 0
\(331\) 17.0491 + 20.3184i 0.937106 + 1.11680i 0.992971 + 0.118361i \(0.0377639\pi\)
−0.0558649 + 0.998438i \(0.517792\pi\)
\(332\) −2.04188 3.80616i −0.112063 0.208890i
\(333\) 0 0
\(334\) 0.948085 1.58451i 0.0518769 0.0867007i
\(335\) 2.88516 + 16.3626i 0.157633 + 0.893983i
\(336\) 0 0
\(337\) 14.4992 5.27727i 0.789820 0.287471i 0.0845588 0.996418i \(-0.473052\pi\)
0.705261 + 0.708948i \(0.250830\pi\)
\(338\) −21.9469 + 7.60238i −1.19375 + 0.413515i
\(339\) 0 0
\(340\) −1.31389 9.10416i −0.0712557 0.493742i
\(341\) 15.0848 + 8.70922i 0.816888 + 0.471631i
\(342\) 0 0
\(343\) 13.7433 7.93471i 0.742069 0.428434i
\(344\) −9.74591 12.7849i −0.525464 0.689318i
\(345\) 0 0
\(346\) 15.9021 + 3.06052i 0.854903 + 0.164535i
\(347\) 16.4887 + 13.8357i 0.885162 + 0.742739i 0.967234 0.253888i \(-0.0817093\pi\)
−0.0820721 + 0.996626i \(0.526154\pi\)
\(348\) 0 0
\(349\) −11.8787 4.32349i −0.635851 0.231431i 0.00392469 0.999992i \(-0.498751\pi\)
−0.639776 + 0.768561i \(0.720973\pi\)
\(350\) 0.444436 28.4826i 0.0237561 1.52246i
\(351\) 0 0
\(352\) 14.7420 + 1.15240i 0.785751 + 0.0614231i
\(353\) −3.82687 + 10.5142i −0.203684 + 0.559617i −0.998909 0.0466973i \(-0.985130\pi\)
0.795225 + 0.606314i \(0.207353\pi\)
\(354\) 0 0
\(355\) 26.2239 31.2524i 1.39182 1.65871i
\(356\) 28.4397 + 5.93510i 1.50730 + 0.314560i
\(357\) 0 0
\(358\) 23.4985 19.1009i 1.24194 1.00951i
\(359\) 16.1699 + 28.0070i 0.853413 + 1.47816i 0.878109 + 0.478460i \(0.158805\pi\)
−0.0246959 + 0.999695i \(0.507862\pi\)
\(360\) 0 0
\(361\) −9.49583 + 16.4473i −0.499781 + 0.865645i
\(362\) −3.27406 20.4268i −0.172081 1.07361i
\(363\) 0 0
\(364\) −9.93353 30.1916i −0.520659 1.58247i
\(365\) −13.7439 37.7610i −0.719387 1.97650i
\(366\) 0 0
\(367\) 0.656339 0.115730i 0.0342606 0.00604107i −0.156492 0.987679i \(-0.550018\pi\)
0.190752 + 0.981638i \(0.438907\pi\)
\(368\) 1.87798 2.82918i 0.0978965 0.147481i
\(369\) 0 0
\(370\) −23.4932 + 13.0794i −1.22136 + 0.679966i
\(371\) 16.5461 13.8838i 0.859031 0.720813i
\(372\) 0 0
\(373\) 3.61725 20.5144i 0.187294 1.06220i −0.735678 0.677331i \(-0.763136\pi\)
0.922972 0.384867i \(-0.125753\pi\)
\(374\) −3.22998 + 3.72959i −0.167018 + 0.192852i
\(375\) 0 0
\(376\) 17.2447 + 7.20720i 0.889326 + 0.371683i
\(377\) 2.71864i 0.140017i
\(378\) 0 0
\(379\) 19.1904i 0.985744i 0.870102 + 0.492872i \(0.164053\pi\)
−0.870102 + 0.492872i \(0.835947\pi\)
\(380\) 0.584357 + 0.233583i 0.0299769 + 0.0119826i
\(381\) 0 0
\(382\) −2.05467 1.77943i −0.105126 0.0910436i
\(383\) 1.37744 7.81186i 0.0703840 0.399168i −0.929180 0.369629i \(-0.879485\pi\)
0.999564 0.0295390i \(-0.00940393\pi\)
\(384\) 0 0
\(385\) −20.2166 + 16.9637i −1.03033 + 0.864552i
\(386\) 4.30735 + 7.73685i 0.219238 + 0.393795i
\(387\) 0 0
\(388\) −6.95343 + 11.2200i −0.353007 + 0.569610i
\(389\) 12.1585 2.14387i 0.616461 0.108699i 0.143307 0.989678i \(-0.454226\pi\)
0.473154 + 0.880980i \(0.343115\pi\)
\(390\) 0 0
\(391\) 0.387517 + 1.06469i 0.0195976 + 0.0538438i
\(392\) 4.27529 1.33309i 0.215935 0.0673311i
\(393\) 0 0
\(394\) 21.1262 3.38615i 1.06432 0.170592i
\(395\) −2.90676 + 5.03465i −0.146255 + 0.253321i
\(396\) 0 0
\(397\) 11.5959 + 20.0847i 0.581982 + 1.00802i 0.995244 + 0.0974099i \(0.0310558\pi\)
−0.413263 + 0.910612i \(0.635611\pi\)
\(398\) −23.1165 28.4387i −1.15872 1.42550i
\(399\) 0 0
\(400\) −6.45539 + 26.7327i −0.322770 + 1.33664i
\(401\) −4.36829 + 5.20593i −0.218142 + 0.259972i −0.864007 0.503480i \(-0.832053\pi\)
0.645865 + 0.763452i \(0.276497\pi\)
\(402\) 0 0
\(403\) −12.3624 + 33.9655i −0.615816 + 1.69194i
\(404\) −0.514503 + 16.4825i −0.0255975 + 0.820034i
\(405\) 0 0
\(406\) −2.07632 0.0323984i −0.103046 0.00160790i
\(407\) 13.5526 + 4.93275i 0.671778 + 0.244507i
\(408\) 0 0
\(409\) 13.9170 + 11.6777i 0.688149 + 0.577426i 0.918375 0.395712i \(-0.129502\pi\)
−0.230226 + 0.973137i \(0.573946\pi\)
\(410\) 2.63069 13.6687i 0.129920 0.675051i
\(411\) 0 0
\(412\) −19.9142 25.2954i −0.981101 1.24622i
\(413\) 7.72625 4.46075i 0.380184 0.219499i
\(414\) 0 0
\(415\) −6.44516 3.72111i −0.316380 0.182662i
\(416\) 2.95711 + 30.5419i 0.144984 + 1.49744i
\(417\) 0 0
\(418\) −0.110485 0.318952i −0.00540399 0.0156005i
\(419\) 4.62462 1.68322i 0.225927 0.0822309i −0.226576 0.973993i \(-0.572753\pi\)
0.452504 + 0.891763i \(0.350531\pi\)
\(420\) 0 0
\(421\) −2.04359 11.5898i −0.0995984 0.564851i −0.993241 0.116071i \(-0.962970\pi\)
0.893642 0.448780i \(-0.148141\pi\)
\(422\) 21.1751 + 12.6700i 1.03079 + 0.616766i
\(423\) 0 0
\(424\) −18.5269 + 9.56988i −0.899747 + 0.464754i
\(425\) −5.89823 7.02924i −0.286106 0.340968i
\(426\) 0 0
\(427\) −6.99642 1.23366i −0.338581 0.0597009i
\(428\) −14.4919 12.9518i −0.700494 0.626048i
\(429\) 0 0
\(430\) −25.8779 9.87868i −1.24794 0.476392i
\(431\) −4.40894 −0.212371 −0.106186 0.994346i \(-0.533864\pi\)
−0.106186 + 0.994346i \(0.533864\pi\)
\(432\) 0 0
\(433\) 28.5232 1.37074 0.685369 0.728196i \(-0.259641\pi\)
0.685369 + 0.728196i \(0.259641\pi\)
\(434\) −25.7933 9.84639i −1.23812 0.472642i
\(435\) 0 0
\(436\) −7.00671 6.26206i −0.335561 0.299898i
\(437\) −0.0763379 0.0134604i −0.00365174 0.000643900i
\(438\) 0 0
\(439\) −3.10907 3.70524i −0.148388 0.176842i 0.686730 0.726912i \(-0.259045\pi\)
−0.835118 + 0.550071i \(0.814601\pi\)
\(440\) 22.6368 11.6928i 1.07917 0.557432i
\(441\) 0 0
\(442\) −8.78565 5.25684i −0.417891 0.250042i
\(443\) 1.26185 + 7.15628i 0.0599521 + 0.340005i 0.999999 0.00103872i \(-0.000330635\pi\)
−0.940047 + 0.341044i \(0.889220\pi\)
\(444\) 0 0
\(445\) 47.0392 17.1209i 2.22987 0.811607i
\(446\) 8.18217 + 23.6206i 0.387437 + 1.11847i
\(447\) 0 0
\(448\) −23.3612 + 1.89447i −1.10371 + 0.0895054i
\(449\) 5.50442 + 3.17798i 0.259769 + 0.149978i 0.624229 0.781241i \(-0.285413\pi\)
−0.364460 + 0.931219i \(0.618746\pi\)
\(450\) 0 0
\(451\) −6.46583 + 3.73305i −0.304464 + 0.175782i
\(452\) −0.698323 0.887025i −0.0328463 0.0417222i
\(453\) 0 0
\(454\) −2.49354 + 12.9561i −0.117028 + 0.608062i
\(455\) −41.9518 35.2017i −1.96673 1.65028i
\(456\) 0 0
\(457\) 0.840235 + 0.305821i 0.0393045 + 0.0143057i 0.361598 0.932334i \(-0.382231\pi\)
−0.322293 + 0.946640i \(0.604454\pi\)
\(458\) 23.7801 + 0.371060i 1.11117 + 0.0173385i
\(459\) 0 0
\(460\) 0.182549 5.84810i 0.00851140 0.272669i
\(461\) 4.48102 12.3115i 0.208702 0.573404i −0.790537 0.612415i \(-0.790198\pi\)
0.999239 + 0.0390104i \(0.0124206\pi\)
\(462\) 0 0
\(463\) −0.866856 + 1.03308i −0.0402862 + 0.0480112i −0.785811 0.618466i \(-0.787754\pi\)
0.745525 + 0.666478i \(0.232199\pi\)
\(464\) 1.94875 + 0.470583i 0.0904686 + 0.0218463i
\(465\) 0 0
\(466\) 15.7243 + 19.3445i 0.728412 + 0.896118i
\(467\) 9.81172 + 16.9944i 0.454032 + 0.786407i 0.998632 0.0522890i \(-0.0166517\pi\)
−0.544600 + 0.838696i \(0.683318\pi\)
\(468\) 0 0
\(469\) −7.06278 + 12.2331i −0.326129 + 0.564872i
\(470\) 31.7978 5.09662i 1.46672 0.235090i
\(471\) 0 0
\(472\) −8.22256 + 2.56390i −0.378474 + 0.118013i
\(473\) 5.08146 + 13.9612i 0.233646 + 0.641937i
\(474\) 0 0
\(475\) 0.618239 0.109012i 0.0283667 0.00500182i
\(476\) 4.11953 6.64726i 0.188819 0.304677i
\(477\) 0 0
\(478\) −6.33869 11.3855i −0.289925 0.520763i
\(479\) −14.6017 + 12.2523i −0.667170 + 0.559822i −0.912226 0.409687i \(-0.865638\pi\)
0.245056 + 0.969509i \(0.421194\pi\)
\(480\) 0 0
\(481\) −5.19697 + 29.4735i −0.236962 + 1.34388i
\(482\) 6.65655 + 5.76486i 0.303198 + 0.262582i
\(483\) 0 0
\(484\) 7.73874 + 3.09338i 0.351761 + 0.140608i
\(485\) 22.7439i 1.03275i
\(486\) 0 0
\(487\) 12.7440i 0.577486i 0.957407 + 0.288743i \(0.0932373\pi\)
−0.957407 + 0.288743i \(0.906763\pi\)
\(488\) 6.32825 + 2.64481i 0.286466 + 0.119725i
\(489\) 0 0
\(490\) 5.05152 5.83288i 0.228204 0.263503i
\(491\) 4.29474 24.3567i 0.193819 1.09920i −0.720272 0.693692i \(-0.755983\pi\)
0.914091 0.405510i \(-0.132906\pi\)
\(492\) 0 0
\(493\) −0.512415 + 0.429967i −0.0230780 + 0.0193648i
\(494\) 0.611997 0.340718i 0.0275350 0.0153296i
\(495\) 0 0
\(496\) 22.2070 + 14.7408i 0.997125 + 0.661882i
\(497\) 34.1576 6.02290i 1.53218 0.270164i
\(498\) 0 0
\(499\) −13.5128 37.1262i −0.604917 1.66199i −0.741167 0.671320i \(-0.765727\pi\)
0.136251 0.990674i \(-0.456495\pi\)
\(500\) 4.03940 + 12.2772i 0.180647 + 0.549052i
\(501\) 0 0
\(502\) 6.34588 + 39.5919i 0.283231 + 1.76707i
\(503\) 18.2058 31.5334i 0.811757 1.40600i −0.0998757 0.995000i \(-0.531845\pi\)
0.911633 0.411005i \(-0.134822\pi\)
\(504\) 0 0
\(505\) 14.2068 + 24.6069i 0.632194 + 1.09499i
\(506\) −2.43525 + 1.97950i −0.108260 + 0.0879997i
\(507\) 0 0
\(508\) 21.7737 + 4.54397i 0.966051 + 0.201606i
\(509\) 2.32891 2.77549i 0.103227 0.123021i −0.711957 0.702223i \(-0.752191\pi\)
0.815184 + 0.579201i \(0.196636\pi\)
\(510\) 0 0
\(511\) 11.6846 32.1032i 0.516897 1.42016i
\(512\) 22.4047 + 3.16697i 0.990157 + 0.139961i
\(513\) 0 0
\(514\) −0.364019 + 23.3289i −0.0160562 + 1.02899i
\(515\) −52.1252 18.9720i −2.29691 0.836008i
\(516\) 0 0
\(517\) −13.2320 11.1030i −0.581944 0.488309i
\(518\) −22.4480 4.32035i −0.986309 0.189825i
\(519\) 0 0
\(520\) 32.0523 + 42.0470i 1.40558 + 1.84388i
\(521\) −18.0443 + 10.4179i −0.790534 + 0.456415i −0.840151 0.542353i \(-0.817534\pi\)
0.0496162 + 0.998768i \(0.484200\pi\)
\(522\) 0 0
\(523\) −19.0780 11.0147i −0.834223 0.481639i 0.0210733 0.999778i \(-0.493292\pi\)
−0.855296 + 0.518139i \(0.826625\pi\)
\(524\) −0.886245 6.14094i −0.0387158 0.268268i
\(525\) 0 0
\(526\) 32.3612 11.2099i 1.41102 0.488775i
\(527\) −8.35708 + 3.04173i −0.364040 + 0.132500i
\(528\) 0 0
\(529\) −3.86876 21.9408i −0.168207 0.953949i
\(530\) −18.4480 + 30.8318i −0.801331 + 1.33925i
\(531\) 0 0
\(532\) 0.252925 + 0.471464i 0.0109657 + 0.0204405i
\(533\) −9.95873 11.8684i −0.431361 0.514075i
\(534\) 0 0
\(535\) −32.9802 5.81531i −1.42586 0.251418i
\(536\) 9.24499 10.0251i 0.399323 0.433017i
\(537\) 0 0
\(538\) 6.15102 16.1130i 0.265189 0.694682i
\(539\) −4.13879 −0.178270
\(540\) 0 0
\(541\) −13.2610 −0.570135 −0.285067 0.958507i \(-0.592016\pi\)
−0.285067 + 0.958507i \(0.592016\pi\)
\(542\) −12.6096 + 33.0317i −0.541628 + 1.41883i
\(543\) 0 0
\(544\) −5.28893 + 5.38773i −0.226761 + 0.230997i
\(545\) −15.9456 2.81165i −0.683036 0.120438i
\(546\) 0 0
\(547\) 9.19354 + 10.9564i 0.393087 + 0.468463i 0.925899 0.377770i \(-0.123309\pi\)
−0.532812 + 0.846234i \(0.678865\pi\)
\(548\) 30.4337 16.3267i 1.30006 0.697440i
\(549\) 0 0
\(550\) 13.0499 21.8101i 0.556451 0.929985i
\(551\) −0.00794673 0.0450681i −0.000338542 0.00191997i
\(552\) 0 0
\(553\) −4.64441 + 1.69043i −0.197500 + 0.0718842i
\(554\) 11.6765 4.04472i 0.496086 0.171844i
\(555\) 0 0
\(556\) 22.1505 3.19671i 0.939392 0.135571i
\(557\) −6.40425 3.69750i −0.271357 0.156668i 0.358147 0.933665i \(-0.383409\pi\)
−0.629504 + 0.776997i \(0.716742\pi\)
\(558\) 0 0
\(559\) −26.6999 + 15.4152i −1.12929 + 0.651994i
\(560\) −32.4947 + 23.9784i −1.37315 + 1.01327i
\(561\) 0 0
\(562\) −30.3964 5.85009i −1.28219 0.246771i
\(563\) 16.2270 + 13.6161i 0.683887 + 0.573850i 0.917139 0.398567i \(-0.130492\pi\)
−0.233252 + 0.972416i \(0.574937\pi\)
\(564\) 0 0
\(565\) −1.82786 0.665286i −0.0768985 0.0279888i
\(566\) 0.664189 42.5660i 0.0279180 1.78918i
\(567\) 0 0
\(568\) −33.4485 1.56679i −1.40347 0.0657409i
\(569\) 1.52428 4.18793i 0.0639012 0.175567i −0.903633 0.428308i \(-0.859110\pi\)
0.967534 + 0.252741i \(0.0813320\pi\)
\(570\) 0 0
\(571\) 1.38240 1.64748i 0.0578516 0.0689449i −0.736343 0.676609i \(-0.763449\pi\)
0.794194 + 0.607664i \(0.207893\pi\)
\(572\) 5.79332 27.7603i 0.242231 1.16072i
\(573\) 0 0
\(574\) 9.18296 7.46439i 0.383289 0.311558i
\(575\) −2.91833 5.05470i −0.121703 0.210796i
\(576\) 0 0
\(577\) −16.0706 + 27.8351i −0.669028 + 1.15879i 0.309148 + 0.951014i \(0.399956\pi\)
−0.978176 + 0.207777i \(0.933377\pi\)
\(578\) 3.40621 + 21.2513i 0.141679 + 0.883937i
\(579\) 0 0
\(580\) 3.28123 1.07958i 0.136246 0.0448271i
\(581\) −2.16402 5.94559i −0.0897785 0.246664i
\(582\) 0 0
\(583\) 18.9789 3.34648i 0.786024 0.138597i
\(584\) −17.8096 + 27.7606i −0.736965 + 1.14874i
\(585\) 0 0
\(586\) 16.3584 9.10721i 0.675758 0.376215i
\(587\) −27.6154 + 23.1721i −1.13981 + 0.956414i −0.999433 0.0336838i \(-0.989276\pi\)
−0.140378 + 0.990098i \(0.544832\pi\)
\(588\) 0 0
\(589\) 0.105655 0.599198i 0.00435343 0.0246895i
\(590\) −9.71547 + 11.2182i −0.399980 + 0.461848i
\(591\) 0 0
\(592\) 20.2274 + 8.82698i 0.831342 + 0.362787i
\(593\) 4.09387i 0.168115i 0.996461 + 0.0840576i \(0.0267880\pi\)
−0.996461 + 0.0840576i \(0.973212\pi\)
\(594\) 0 0
\(595\) 13.4745i 0.552402i
\(596\) −13.5491 + 33.8960i −0.554995 + 1.38844i
\(597\) 0 0
\(598\) −4.92282 4.26337i −0.201309 0.174342i
\(599\) 1.46823 8.32677i 0.0599904 0.340223i −0.940009 0.341149i \(-0.889184\pi\)
1.00000 0.000926605i \(0.000294948\pi\)
\(600\) 0 0
\(601\) 22.3724 18.7727i 0.912590 0.765754i −0.0600202 0.998197i \(-0.519116\pi\)
0.972610 + 0.232443i \(0.0746721\pi\)
\(602\) −11.4550 20.5754i −0.466869 0.838590i
\(603\) 0 0
\(604\) −32.7244 20.2804i −1.33154 0.825198i
\(605\) 14.1417 2.49356i 0.574942 0.101378i
\(606\) 0 0
\(607\) 13.2715 + 36.4633i 0.538675 + 1.48000i 0.848495 + 0.529203i \(0.177509\pi\)
−0.309820 + 0.950795i \(0.600269\pi\)
\(608\) −0.138297 0.497664i −0.00560869 0.0201829i
\(609\) 0 0
\(610\) 11.6688 1.87030i 0.472455 0.0757262i
\(611\) 17.9220 31.0417i 0.725045 1.25581i
\(612\) 0 0
\(613\) −0.677216 1.17297i −0.0273525 0.0473759i 0.852025 0.523501i \(-0.175374\pi\)
−0.879378 + 0.476125i \(0.842041\pi\)
\(614\) −11.7488 14.4538i −0.474143 0.583307i
\(615\) 0 0
\(616\) 21.1325 + 4.75539i 0.851452 + 0.191600i
\(617\) 14.2746 17.0118i 0.574675 0.684871i −0.397909 0.917425i \(-0.630264\pi\)
0.972583 + 0.232554i \(0.0747083\pi\)
\(618\) 0 0
\(619\) −0.757138 + 2.08022i −0.0304320 + 0.0836111i −0.953978 0.299876i \(-0.903055\pi\)
0.923546 + 0.383487i \(0.125277\pi\)
\(620\) 45.9034 + 1.43288i 1.84353 + 0.0575459i
\(621\) 0 0
\(622\) 8.73303 + 0.136268i 0.350163 + 0.00546386i
\(623\) 39.9913 + 14.5556i 1.60222 + 0.583160i
\(624\) 0 0
\(625\) −9.27445 7.78219i −0.370978 0.311287i
\(626\) −5.72956 + 29.7701i −0.228999 + 1.18985i
\(627\) 0 0
\(628\) −26.4634 + 20.8337i −1.05601 + 0.831355i
\(629\) −6.37717 + 3.68186i −0.254274 + 0.146805i
\(630\) 0 0
\(631\) −10.3534 5.97752i −0.412161 0.237961i 0.279557 0.960129i \(-0.409813\pi\)
−0.691718 + 0.722168i \(0.743146\pi\)
\(632\) 4.73271 0.607796i 0.188257 0.0241768i
\(633\) 0 0
\(634\) −6.80576 19.6472i −0.270291 0.780288i
\(635\) 36.0136 13.1079i 1.42916 0.520171i
\(636\) 0 0
\(637\) −1.49137 8.45799i −0.0590903 0.335118i
\(638\) −1.58990 0.951310i −0.0629449 0.0376627i
\(639\) 0 0
\(640\) 35.6879 15.6973i 1.41069 0.620492i
\(641\) −8.66598 10.3277i −0.342286 0.407920i 0.567250 0.823545i \(-0.308007\pi\)
−0.909536 + 0.415625i \(0.863563\pi\)
\(642\) 0 0
\(643\) 27.1966 + 4.79550i 1.07253 + 0.189116i 0.681910 0.731436i \(-0.261150\pi\)
0.390620 + 0.920552i \(0.372261\pi\)
\(644\) 3.31475 3.70892i 0.130620 0.146152i
\(645\) 0 0
\(646\) 0.161010 + 0.0614643i 0.00633485 + 0.00241828i
\(647\) 15.2634 0.600064 0.300032 0.953929i \(-0.403003\pi\)
0.300032 + 0.953929i \(0.403003\pi\)
\(648\) 0 0
\(649\) 7.96003 0.312458
\(650\) 49.2733 + 18.8097i 1.93266 + 0.737777i
\(651\) 0 0
\(652\) 10.6967 11.9687i 0.418917 0.468732i
\(653\) 30.1302 + 5.31277i 1.17909 + 0.207905i 0.728639 0.684898i \(-0.240153\pi\)
0.450448 + 0.892803i \(0.351264\pi\)
\(654\) 0 0
\(655\) −6.87180 8.18949i −0.268503 0.319990i
\(656\) −10.2312 + 5.08419i −0.399461 + 0.198504i
\(657\) 0 0
\(658\) 23.4941 + 14.0576i 0.915895 + 0.548021i
\(659\) −7.25464 41.1431i −0.282601 1.60271i −0.713732 0.700418i \(-0.752997\pi\)
0.431132 0.902289i \(-0.358114\pi\)
\(660\) 0 0
\(661\) −30.7435 + 11.1897i −1.19578 + 0.435230i −0.861751 0.507331i \(-0.830632\pi\)
−0.334033 + 0.942561i \(0.608410\pi\)
\(662\) −12.2778 35.4440i −0.477189 1.37757i
\(663\) 0 0
\(664\) 0.778076 + 6.05862i 0.0301952 + 0.235120i
\(665\) 0.798352 + 0.460929i 0.0309588 + 0.0178741i
\(666\) 0 0
\(667\) −0.368476 + 0.212740i −0.0142674 + 0.00823731i
\(668\) −2.05180 + 1.61531i −0.0793865 + 0.0624981i
\(669\) 0 0
\(670\) 4.44077 23.0737i 0.171562 0.891415i
\(671\) −4.85574 4.07445i −0.187454 0.157292i
\(672\) 0 0
\(673\) −26.6470 9.69872i −1.02717 0.373858i −0.227166 0.973856i \(-0.572946\pi\)
−0.800002 + 0.599998i \(0.795168\pi\)
\(674\) −21.8182 0.340446i −0.840407 0.0131135i
\(675\) 0 0
\(676\) 32.8310 + 1.02482i 1.26273 + 0.0394163i
\(677\) −13.7737 + 37.8429i −0.529366 + 1.45442i 0.330453 + 0.943822i \(0.392799\pi\)
−0.859819 + 0.510599i \(0.829424\pi\)
\(678\) 0 0
\(679\) −12.4290 + 14.8124i −0.476983 + 0.568446i
\(680\) −2.85588 + 12.6913i −0.109518 + 0.486687i
\(681\) 0 0
\(682\) −15.5377 19.1150i −0.594969 0.731952i
\(683\) 2.35647 + 4.08153i 0.0901678 + 0.156175i 0.907582 0.419876i \(-0.137926\pi\)
−0.817414 + 0.576051i \(0.804593\pi\)
\(684\) 0 0
\(685\) 29.7536 51.5348i 1.13683 1.96904i
\(686\) −22.1599 + 3.55184i −0.846069 + 0.135610i
\(687\) 0 0
\(688\) 6.42820 + 21.8072i 0.245073 + 0.831391i
\(689\) 13.6777 + 37.5792i 0.521079 + 1.43165i
\(690\) 0 0
\(691\) −47.8656 + 8.44000i −1.82089 + 0.321073i −0.976642 0.214875i \(-0.931066\pi\)
−0.844251 + 0.535947i \(0.819955\pi\)
\(692\) −19.4665 12.0641i −0.740006 0.458607i
\(693\) 0 0
\(694\) −14.8070 26.5963i −0.562065 1.00958i
\(695\) 29.5397 24.7868i 1.12051 0.940216i
\(696\) 0 0
\(697\) 0.661948 3.75409i 0.0250731 0.142196i
\(698\) 13.5137 + 11.7035i 0.511502 + 0.442982i
\(699\) 0 0
\(700\) −14.9528 + 37.4076i −0.565164 + 1.41387i
\(701\) 5.10945i 0.192981i −0.995334 0.0964906i \(-0.969238\pi\)
0.995334 0.0964906i \(-0.0307618\pi\)
\(702\) 0 0
\(703\) 0.503788i 0.0190007i
\(704\) −18.8962 8.95791i −0.712176 0.337614i
\(705\) 0 0
\(706\) 10.3591 11.9615i 0.389871 0.450176i
\(707\) −4.19471 + 23.7894i −0.157758 + 0.894692i
\(708\) 0 0
\(709\) −7.00392 + 5.87699i −0.263038 + 0.220715i −0.764762 0.644313i \(-0.777144\pi\)
0.501725 + 0.865027i \(0.332699\pi\)
\(710\) −50.4101 + 28.0649i −1.89186 + 1.05326i
\(711\) 0 0
\(712\) −34.5816 22.1855i −1.29600 0.831438i
\(713\) −5.57097 + 0.982312i −0.208634 + 0.0367879i
\(714\) 0 0
\(715\) −16.7119 45.9155i −0.624988 1.71714i
\(716\) −40.6805 + 13.3846i −1.52030 + 0.500205i
\(717\) 0 0
\(718\) −7.23817 45.1589i −0.270126 1.68532i
\(719\) −11.2528 + 19.4904i −0.419658 + 0.726869i −0.995905 0.0904064i \(-0.971183\pi\)
0.576247 + 0.817276i \(0.304517\pi\)
\(720\) 0 0
\(721\) −23.5797 40.8412i −0.878153 1.52101i
\(722\) 20.8415 16.9411i 0.775639 0.630481i
\(723\) 0 0
\(724\) −5.97682 + 28.6396i −0.222127 + 1.06438i
\(725\) 2.21494 2.63966i 0.0822608 0.0980346i
\(726\) 0 0
\(727\) −5.99428 + 16.4691i −0.222316 + 0.610807i −0.999837 0.0180494i \(-0.994254\pi\)
0.777522 + 0.628856i \(0.216477\pi\)
\(728\) −2.10318 + 44.8997i −0.0779491 + 1.66409i
\(729\) 0 0
\(730\) −0.886643 + 56.8224i −0.0328161 + 2.10309i
\(731\) −7.12825 2.59447i −0.263648 0.0959599i
\(732\) 0 0
\(733\) −17.2190 14.4484i −0.635998 0.533666i 0.266788 0.963755i \(-0.414038\pi\)
−0.902786 + 0.430089i \(0.858482\pi\)
\(734\) −0.925538 0.178129i −0.0341622 0.00657487i
\(735\) 0 0
\(736\) −3.90816 + 2.79077i −0.144057 + 0.102869i
\(737\) −10.9147 + 6.30162i −0.402049 + 0.232123i
\(738\) 0 0
\(739\) −7.76664 4.48407i −0.285700 0.164949i 0.350301 0.936637i \(-0.386079\pi\)
−0.636001 + 0.771688i \(0.719413\pi\)
\(740\) 37.6365 5.43160i 1.38354 0.199670i
\(741\) 0 0
\(742\) −28.8635 + 9.99830i −1.05961 + 0.367049i
\(743\) −44.6168 + 16.2392i −1.63683 + 0.595758i −0.986481 0.163875i \(-0.947601\pi\)
−0.650352 + 0.759633i \(0.725378\pi\)
\(744\) 0 0
\(745\) 10.9219 + 61.9413i 0.400148 + 2.26935i
\(746\) −15.1259 + 25.2796i −0.553800 + 0.925554i
\(747\) 0 0
\(748\) 6.14858 3.29851i 0.224814 0.120605i
\(749\) −18.3010 21.8103i −0.668705 0.796932i
\(750\) 0 0
\(751\) 13.7230 + 2.41974i 0.500761 + 0.0882976i 0.418323 0.908299i \(-0.362618\pi\)
0.0824383 + 0.996596i \(0.473729\pi\)
\(752\) −19.1489 18.2199i −0.698289 0.664411i
\(753\) 0 0
\(754\) 1.37118 3.59191i 0.0499355 0.130810i
\(755\) −66.3349 −2.41418
\(756\) 0 0
\(757\) 12.8098 0.465582 0.232791 0.972527i \(-0.425214\pi\)
0.232791 + 0.972527i \(0.425214\pi\)
\(758\) 9.67895 25.3547i 0.351555 0.920924i
\(759\) 0 0
\(760\) −0.654252 0.603343i −0.0237322 0.0218855i
\(761\) −30.5200 5.38149i −1.10635 0.195079i −0.409508 0.912306i \(-0.634300\pi\)
−0.696839 + 0.717227i \(0.745411\pi\)
\(762\) 0 0
\(763\) −8.84838 10.5451i −0.320333 0.381758i
\(764\) 1.81718 + 3.38732i 0.0657434 + 0.122549i
\(765\) 0 0
\(766\) −5.75993 + 9.62644i −0.208115 + 0.347817i
\(767\) 2.86832 + 16.2671i 0.103569 + 0.587369i
\(768\) 0 0
\(769\) −16.0889 + 5.85587i −0.580179 + 0.211168i −0.615404 0.788211i \(-0.711007\pi\)
0.0352254 + 0.999379i \(0.488785\pi\)
\(770\) 35.2664 12.2163i 1.27091 0.440243i
\(771\) 0 0
\(772\) −1.78875 12.3945i −0.0643785 0.446089i
\(773\) −37.1476 21.4472i −1.33610 0.771401i −0.349877 0.936795i \(-0.613777\pi\)
−0.986227 + 0.165395i \(0.947110\pi\)
\(774\) 0 0
\(775\) 39.6758 22.9068i 1.42520 0.822838i
\(776\) 14.8460 11.3170i 0.532939 0.406257i
\(777\) 0 0
\(778\) −17.1453 3.29980i −0.614690 0.118303i
\(779\) 0.199783 + 0.167638i 0.00715795 + 0.00600624i
\(780\) 0 0
\(781\) 29.0802 + 10.5843i 1.04057 + 0.378737i
\(782\) 0.0249994 1.60214i 0.000893978 0.0572924i
\(783\) 0 0
\(784\) −6.32095 0.395004i −0.225748 0.0141073i
\(785\) −19.8481 + 54.5321i −0.708408 + 1.94633i
\(786\) 0 0
\(787\) 3.83079 4.56536i 0.136553 0.162737i −0.693434 0.720520i \(-0.743903\pi\)
0.829987 + 0.557783i \(0.188348\pi\)
\(788\) −29.6201 6.18145i −1.05517 0.220205i
\(789\) 0 0
\(790\) 6.37976 5.18580i 0.226982 0.184503i
\(791\) −0.826860 1.43216i −0.0293998 0.0509219i
\(792\) 0 0
\(793\) 6.57679 11.3913i 0.233549 0.404518i
\(794\) −5.19071 32.3848i −0.184211 1.14929i
\(795\) 0 0
\(796\) 16.1984 + 49.2328i 0.574138 + 1.74501i
\(797\) −14.1501 38.8770i −0.501221 1.37709i −0.890084 0.455797i \(-0.849354\pi\)
0.388863 0.921296i \(-0.372868\pi\)
\(798\) 0 0
\(799\) 8.68528 1.53145i 0.307263 0.0541788i
\(800\) 22.0120 32.0639i 0.778243 1.13363i
\(801\) 0 0
\(802\) 8.39715 4.67495i 0.296514 0.165078i
\(803\) 23.3504 19.5933i 0.824016 0.691432i
\(804\) 0 0
\(805\) 1.48831 8.44064i 0.0524561 0.297494i
\(806\) 33.4644 38.6406i 1.17873 1.36106i
\(807\) 0 0
\(808\) 8.99295 21.5175i 0.316371 0.756982i
\(809\) 45.8780i 1.61298i −0.591245 0.806492i \(-0.701363\pi\)
0.591245 0.806492i \(-0.298637\pi\)
\(810\) 0 0
\(811\) 25.4302i 0.892974i 0.894790 + 0.446487i \(0.147325\pi\)
−0.894790 + 0.446487i \(0.852675\pi\)
\(812\) 2.72693 + 1.09003i 0.0956964 + 0.0382524i
\(813\) 0 0
\(814\) −15.4181 13.3527i −0.540403 0.468012i
\(815\) 4.80280 27.2380i 0.168235 0.954107i
\(816\) 0 0
\(817\) 0.397558 0.333591i 0.0139088 0.0116709i
\(818\) −12.4975 22.4480i −0.436965 0.784877i
\(819\) 0 0
\(820\) −10.3697 + 16.7326i −0.362127 + 0.584326i
\(821\) 7.72253 1.36169i 0.269518 0.0475233i −0.0372556 0.999306i \(-0.511862\pi\)
0.306774 + 0.951782i \(0.400750\pi\)
\(822\) 0 0
\(823\) 2.99728 + 8.23497i 0.104479 + 0.287053i 0.980906 0.194481i \(-0.0623021\pi\)
−0.876428 + 0.481534i \(0.840080\pi\)
\(824\) 13.5528 + 43.4647i 0.472136 + 1.51417i
\(825\) 0 0
\(826\) −12.4579 + 1.99678i −0.433466 + 0.0694769i
\(827\) −9.57006 + 16.5758i −0.332784 + 0.576398i −0.983057 0.183303i \(-0.941321\pi\)
0.650273 + 0.759701i \(0.274655\pi\)
\(828\) 0 0
\(829\) −0.0258029 0.0446919i −0.000896172 0.00155222i 0.865577 0.500776i \(-0.166952\pi\)
−0.866473 + 0.499224i \(0.833619\pi\)
\(830\) 6.63866 + 8.16711i 0.230431 + 0.283485i
\(831\) 0 0
\(832\) 11.4973 41.8440i 0.398596 1.45068i
\(833\) 1.35831 1.61878i 0.0470628 0.0560873i
\(834\) 0 0
\(835\) −1.53889 + 4.22806i −0.0532554 + 0.146318i
\(836\) −0.0148937 + 0.477130i −0.000515109 + 0.0165019i
\(837\) 0 0
\(838\) −6.95909 0.108588i −0.240398 0.00375111i
\(839\) −10.1094 3.67952i −0.349015 0.127031i 0.161563 0.986862i \(-0.448346\pi\)
−0.510578 + 0.859831i \(0.670569\pi\)
\(840\) 0 0
\(841\) 22.0229 + 18.4794i 0.759409 + 0.637220i
\(842\) −3.14544 + 16.3433i −0.108399 + 0.563228i
\(843\) 0 0
\(844\) −21.5866 27.4198i −0.743042 0.943828i
\(845\) 49.0137 28.2981i 1.68612 0.973484i
\(846\) 0 0
\(847\) 10.5727 + 6.10416i 0.363283 + 0.209741i
\(848\) 29.3048 3.29958i 1.00633 0.113308i
\(849\) 0 0
\(850\) 4.24755 + 12.2620i 0.145690 + 0.420584i
\(851\) −4.40143 + 1.60199i −0.150879 + 0.0549155i
\(852\) 0 0
\(853\) 6.86844 + 38.9529i 0.235171 + 1.33372i 0.842254 + 0.539082i \(0.181229\pi\)
−0.607083 + 0.794639i \(0.707660\pi\)
\(854\) 8.62159 + 5.15868i 0.295025 + 0.176526i
\(855\) 0 0
\(856\) 12.6146 + 24.4213i 0.431157 + 0.834704i
\(857\) 6.59420 + 7.85866i 0.225253 + 0.268447i 0.866820 0.498620i \(-0.166160\pi\)
−0.641567 + 0.767067i \(0.721715\pi\)
\(858\) 0 0
\(859\) 3.49071 + 0.615507i 0.119102 + 0.0210008i 0.232881 0.972505i \(-0.425185\pi\)
−0.113780 + 0.993506i \(0.536296\pi\)
\(860\) 29.2079 + 26.1038i 0.995981 + 0.890132i
\(861\) 0 0
\(862\) 5.82517 + 2.22371i 0.198406 + 0.0757400i
\(863\) 6.36151 0.216548 0.108274 0.994121i \(-0.465468\pi\)
0.108274 + 0.994121i \(0.465468\pi\)
\(864\) 0 0
\(865\) −39.4602 −1.34169
\(866\) −37.6854 14.3861i −1.28060 0.488860i
\(867\) 0 0
\(868\) 29.1124 + 26.0184i 0.988139 + 0.883124i
\(869\) −4.34283 0.765757i −0.147320 0.0259765i
\(870\) 0 0
\(871\) −16.8110 20.0345i −0.569618 0.678844i
\(872\) 6.09903 + 11.8075i 0.206539 + 0.399852i
\(873\) 0 0
\(874\) 0.0940700 + 0.0562863i 0.00318197 + 0.00190391i
\(875\) 3.28765 + 18.6452i 0.111143 + 0.630323i
\(876\) 0 0
\(877\) 15.3450 5.58514i 0.518165 0.188597i −0.0696811 0.997569i \(-0.522198\pi\)
0.587846 + 0.808973i \(0.299976\pi\)
\(878\) 2.23896 + 6.46354i 0.0755614 + 0.218134i
\(879\) 0 0
\(880\) −35.8056 + 4.03153i −1.20701 + 0.135903i
\(881\) 43.1593 + 24.9180i 1.45407 + 0.839509i 0.998709 0.0507963i \(-0.0161759\pi\)
0.455364 + 0.890306i \(0.349509\pi\)
\(882\) 0 0
\(883\) 38.2077 22.0592i 1.28579 0.742352i 0.307890 0.951422i \(-0.400377\pi\)
0.977901 + 0.209070i \(0.0670437\pi\)
\(884\) 8.95639 + 11.3766i 0.301236 + 0.382636i
\(885\) 0 0
\(886\) 1.94220 10.0914i 0.0652495 0.339028i
\(887\) −1.84120 1.54495i −0.0618215 0.0518744i 0.611353 0.791358i \(-0.290625\pi\)
−0.673175 + 0.739483i \(0.735070\pi\)
\(888\) 0 0
\(889\) 30.6177 + 11.1439i 1.02688 + 0.373756i
\(890\) −70.7842 1.10450i −2.37269 0.0370229i
\(891\) 0 0
\(892\) 1.10298 35.3348i 0.0369305 1.18310i
\(893\) −0.206364 + 0.566981i −0.00690571 + 0.0189733i
\(894\) 0 0
\(895\) −47.4313 + 56.5264i −1.58545 + 1.88947i
\(896\) 31.8207 + 9.27952i 1.06305 + 0.310007i
\(897\) 0 0
\(898\) −5.66967 6.97503i −0.189199 0.232760i
\(899\) −1.66986 2.89227i −0.0556928 0.0964627i
\(900\) 0 0
\(901\) −4.91981 + 8.52136i −0.163903 + 0.283888i
\(902\) 10.4256 1.67104i 0.347134 0.0556394i
\(903\) 0 0
\(904\) 0.475253 + 1.52416i 0.0158067 + 0.0506929i
\(905\) 17.2412 + 47.3698i 0.573117 + 1.57463i
\(906\) 0 0
\(907\) 34.5531 6.09265i 1.14732 0.202303i 0.432513 0.901628i \(-0.357627\pi\)
0.714804 + 0.699324i \(0.246516\pi\)
\(908\) 9.82912 15.8602i 0.326191 0.526340i
\(909\) 0 0
\(910\) 37.6730 + 67.6682i 1.24885 + 2.24318i
\(911\) −8.27443 + 6.94307i −0.274144 + 0.230034i −0.769486 0.638664i \(-0.779487\pi\)
0.495342 + 0.868698i \(0.335043\pi\)
\(912\) 0 0
\(913\) 0.980292 5.55951i 0.0324429 0.183993i
\(914\) −0.955888 0.827840i −0.0316180 0.0273825i
\(915\) 0 0
\(916\) −31.2316 12.4841i −1.03192 0.412486i
\(917\) 9.08884i 0.300140i
\(918\) 0 0
\(919\) 20.9319i 0.690481i 0.938514 + 0.345241i \(0.112203\pi\)
−0.938514 + 0.345241i \(0.887797\pi\)
\(920\) −3.19076 + 7.63455i −0.105196 + 0.251704i
\(921\) 0 0
\(922\) −12.1299 + 14.0061i −0.399477 + 0.461267i
\(923\) −11.1513 + 63.2421i −0.367049 + 2.08164i
\(924\) 0 0
\(925\) 29.0588 24.3832i 0.955447 0.801715i
\(926\) 1.66635 0.927710i 0.0547598 0.0304865i
\(927\) 0 0
\(928\) −2.33738 1.60463i −0.0767284 0.0526744i
\(929\) −33.1245 + 5.84075i −1.08678 + 0.191629i −0.688212 0.725510i \(-0.741604\pi\)
−0.398568 + 0.917139i \(0.630493\pi\)
\(930\) 0 0
\(931\) 0.0494464 + 0.135853i 0.00162054 + 0.00445240i
\(932\) −11.0185 33.4891i −0.360922 1.09697i
\(933\) 0 0
\(934\) −4.39205 27.4020i −0.143712 0.896621i
\(935\) 6.01119 10.4117i 0.196587 0.340498i
\(936\) 0 0
\(937\) −12.5767 21.7834i −0.410862 0.711634i 0.584122 0.811666i \(-0.301439\pi\)
−0.994984 + 0.100032i \(0.968106\pi\)
\(938\) 15.5014 12.6004i 0.506139 0.411417i
\(939\) 0 0
\(940\) −44.5824 9.30393i −1.45412 0.303461i
\(941\) −26.6235 + 31.7286i −0.867901 + 1.03432i 0.131175 + 0.991359i \(0.458125\pi\)
−0.999077 + 0.0429652i \(0.986320\pi\)
\(942\) 0 0
\(943\) 0.829308 2.27850i 0.0270060 0.0741983i
\(944\) 12.1569 + 0.759701i 0.395675 + 0.0247262i
\(945\) 0 0
\(946\) 0.327815 21.0087i 0.0106582 0.683052i
\(947\) 53.1276 + 19.3369i 1.72642 + 0.628364i 0.998365 0.0571597i \(-0.0182044\pi\)
0.728050 + 0.685524i \(0.240427\pi\)
\(948\) 0 0
\(949\) 48.4548 + 40.6584i 1.57291 + 1.31983i
\(950\) −0.871810 0.167789i −0.0282852 0.00544378i
\(951\) 0 0
\(952\) −8.79544 + 6.70473i −0.285062 + 0.217302i
\(953\) 31.8569 18.3926i 1.03195 0.595795i 0.114405 0.993434i \(-0.463504\pi\)
0.917542 + 0.397639i \(0.130170\pi\)
\(954\) 0 0
\(955\) 5.73591 + 3.31163i 0.185610 + 0.107162i
\(956\) 2.63232 + 18.2398i 0.0851354 + 0.589917i
\(957\) 0 0
\(958\) 25.4717 8.82338i 0.822953 0.285070i
\(959\) 47.5403 17.3032i 1.53516 0.558751i
\(960\) 0 0
\(961\) −2.32736 13.1991i −0.0750761 0.425778i
\(962\) 21.7317 36.3197i 0.700659 1.17100i
\(963\) 0 0
\(964\) −5.88716 10.9740i −0.189613 0.353447i
\(965\) −13.8697 16.5292i −0.446480 0.532094i
\(966\) 0 0
\(967\) 44.3616 + 7.82215i 1.42657 + 0.251543i 0.833016 0.553249i \(-0.186612\pi\)
0.593557 + 0.804792i \(0.297723\pi\)
\(968\) −8.66437 7.99018i −0.278483 0.256814i
\(969\) 0 0
\(970\) 11.4712 30.0496i 0.368318 0.964835i
\(971\) 40.1053 1.28704 0.643520 0.765429i \(-0.277473\pi\)
0.643520 + 0.765429i \(0.277473\pi\)
\(972\) 0 0
\(973\) 32.7837 1.05100
\(974\) 6.42762 16.8376i 0.205954 0.539512i
\(975\) 0 0
\(976\) −7.02705 6.68612i −0.224930 0.214017i
\(977\) 36.1734 + 6.37835i 1.15729 + 0.204062i 0.719157 0.694848i \(-0.244528\pi\)
0.438134 + 0.898910i \(0.355639\pi\)
\(978\) 0 0
\(979\) 24.4075 + 29.0878i 0.780068 + 0.929649i
\(980\) −9.61606 + 5.15870i −0.307174 + 0.164788i
\(981\) 0 0
\(982\) −17.9589 + 30.0144i −0.573093 + 0.957797i
\(983\) 3.28853 + 18.6502i 0.104888 + 0.594848i 0.991265 + 0.131884i \(0.0421028\pi\)
−0.886377 + 0.462963i \(0.846786\pi\)
\(984\) 0 0
\(985\) −48.9916 + 17.8315i −1.56100 + 0.568158i
\(986\) 0.893872 0.309637i 0.0284667 0.00986084i
\(987\) 0 0
\(988\) −0.980427 + 0.141493i −0.0311915 + 0.00450148i
\(989\) −4.17867 2.41256i −0.132874 0.0767148i
\(990\) 0 0
\(991\) 30.3997 17.5513i 0.965680 0.557535i 0.0677633 0.997701i \(-0.478414\pi\)
0.897916 + 0.440166i \(0.145080\pi\)
\(992\) −21.9056 30.6763i −0.695503 0.973972i
\(993\) 0 0
\(994\) −48.1673 9.27029i −1.52777 0.294036i
\(995\) 68.4100 + 57.4028i 2.16874 + 1.81979i
\(996\) 0 0
\(997\) −22.5603 8.21129i −0.714493 0.260054i −0.0409071 0.999163i \(-0.513025\pi\)
−0.673586 + 0.739109i \(0.735247\pi\)
\(998\) −0.871737 + 55.8671i −0.0275944 + 1.76844i
\(999\) 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 324.2.l.a.179.2 96
3.2 odd 2 108.2.l.a.23.15 yes 96
4.3 odd 2 inner 324.2.l.a.179.15 96
9.2 odd 6 972.2.l.c.215.7 96
9.4 even 3 972.2.l.a.863.12 96
9.5 odd 6 972.2.l.d.863.5 96
9.7 even 3 972.2.l.b.215.10 96
12.11 even 2 108.2.l.a.23.2 96
27.2 odd 18 972.2.l.a.107.4 96
27.7 even 9 108.2.l.a.47.2 yes 96
27.11 odd 18 972.2.l.b.755.8 96
27.16 even 9 972.2.l.c.755.9 96
27.20 odd 18 inner 324.2.l.a.143.15 96
27.25 even 9 972.2.l.d.107.13 96
36.7 odd 6 972.2.l.b.215.8 96
36.11 even 6 972.2.l.c.215.9 96
36.23 even 6 972.2.l.d.863.13 96
36.31 odd 6 972.2.l.a.863.4 96
108.7 odd 18 108.2.l.a.47.15 yes 96
108.11 even 18 972.2.l.b.755.10 96
108.43 odd 18 972.2.l.c.755.7 96
108.47 even 18 inner 324.2.l.a.143.2 96
108.79 odd 18 972.2.l.d.107.5 96
108.83 even 18 972.2.l.a.107.12 96
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
108.2.l.a.23.2 96 12.11 even 2
108.2.l.a.23.15 yes 96 3.2 odd 2
108.2.l.a.47.2 yes 96 27.7 even 9
108.2.l.a.47.15 yes 96 108.7 odd 18
324.2.l.a.143.2 96 108.47 even 18 inner
324.2.l.a.143.15 96 27.20 odd 18 inner
324.2.l.a.179.2 96 1.1 even 1 trivial
324.2.l.a.179.15 96 4.3 odd 2 inner
972.2.l.a.107.4 96 27.2 odd 18
972.2.l.a.107.12 96 108.83 even 18
972.2.l.a.863.4 96 36.31 odd 6
972.2.l.a.863.12 96 9.4 even 3
972.2.l.b.215.8 96 36.7 odd 6
972.2.l.b.215.10 96 9.7 even 3
972.2.l.b.755.8 96 27.11 odd 18
972.2.l.b.755.10 96 108.11 even 18
972.2.l.c.215.7 96 9.2 odd 6
972.2.l.c.215.9 96 36.11 even 6
972.2.l.c.755.7 96 108.43 odd 18
972.2.l.c.755.9 96 27.16 even 9
972.2.l.d.107.5 96 108.79 odd 18
972.2.l.d.107.13 96 27.25 even 9
972.2.l.d.863.5 96 9.5 odd 6
972.2.l.d.863.13 96 36.23 even 6