Properties

Label 546.2.cg.b.145.10
Level $546$
Weight $2$
Character 546.145
Analytic conductor $4.360$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [546,2,Mod(145,546)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(546, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 10, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("546.145");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.cg (of order \(12\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.35983195036\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(10\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 145.10
Character \(\chi\) \(=\) 546.145
Dual form 546.2.cg.b.241.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{2} +(-0.866025 - 0.500000i) q^{3} -1.00000i q^{4} +(2.65393 - 0.711118i) q^{5} +(-0.965926 + 0.258819i) q^{6} +(1.40673 - 2.24078i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.707107 - 0.707107i) q^{2} +(-0.866025 - 0.500000i) q^{3} -1.00000i q^{4} +(2.65393 - 0.711118i) q^{5} +(-0.965926 + 0.258819i) q^{6} +(1.40673 - 2.24078i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(1.37378 - 2.37945i) q^{10} +(2.14199 - 0.573943i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-0.354780 + 3.58805i) q^{13} +(-0.589766 - 2.57918i) q^{14} +(-2.65393 - 0.711118i) q^{15} -1.00000 q^{16} -1.67627 q^{17} +(0.965926 + 0.258819i) q^{18} +(-0.0474662 + 0.177146i) q^{19} +(-0.711118 - 2.65393i) q^{20} +(-2.33866 + 1.23721i) q^{21} +(1.10877 - 1.92045i) q^{22} -0.546143i q^{23} +(0.258819 + 0.965926i) q^{24} +(2.20753 - 1.27452i) q^{25} +(2.28627 + 2.78800i) q^{26} -1.00000i q^{27} +(-2.24078 - 1.40673i) q^{28} +(-2.18139 - 3.77828i) q^{29} +(-2.37945 + 1.37378i) q^{30} +(2.02462 - 7.55600i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-2.14199 - 0.573943i) q^{33} +(-1.18530 + 1.18530i) q^{34} +(2.13990 - 6.94723i) q^{35} +(0.866025 - 0.500000i) q^{36} +(0.909963 + 0.909963i) q^{37} +(0.0916976 + 0.158825i) q^{38} +(2.10128 - 2.92996i) q^{39} +(-2.37945 - 1.37378i) q^{40} +(-1.32782 + 4.95550i) q^{41} +(-0.778839 + 2.52852i) q^{42} +(-2.86766 - 1.65565i) q^{43} +(-0.573943 - 2.14199i) q^{44} +(1.94281 + 1.94281i) q^{45} +(-0.386181 - 0.386181i) q^{46} +(2.61197 + 9.74801i) q^{47} +(0.866025 + 0.500000i) q^{48} +(-3.04223 - 6.30435i) q^{49} +(0.659739 - 2.46218i) q^{50} +(1.45169 + 0.838134i) q^{51} +(3.58805 + 0.354780i) q^{52} +(1.78093 + 3.08467i) q^{53} +(-0.707107 - 0.707107i) q^{54} +(5.27654 - 3.04641i) q^{55} +(-2.57918 + 0.589766i) q^{56} +(0.129680 - 0.129680i) q^{57} +(-4.21412 - 1.12917i) q^{58} +(-1.05173 + 1.05173i) q^{59} +(-0.711118 + 2.65393i) q^{60} +(-11.8307 + 6.83046i) q^{61} +(-3.91127 - 6.77452i) q^{62} +(2.64394 + 0.0978714i) q^{63} +1.00000i q^{64} +(1.60997 + 9.77473i) q^{65} +(-1.92045 + 1.10877i) q^{66} +(-1.82429 - 6.80833i) q^{67} +1.67627i q^{68} +(-0.273071 + 0.472973i) q^{69} +(-3.39930 - 6.42557i) q^{70} +(1.04867 + 3.91368i) q^{71} +(0.258819 - 0.965926i) q^{72} +(8.57385 + 2.29736i) q^{73} +1.28688 q^{74} -2.54903 q^{75} +(0.177146 + 0.0474662i) q^{76} +(1.72711 - 5.60711i) q^{77} +(-0.585966 - 3.55762i) q^{78} +(4.42139 - 7.65808i) q^{79} +(-2.65393 + 0.711118i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(2.56516 + 4.44298i) q^{82} +(11.3594 + 11.3594i) q^{83} +(1.23721 + 2.33866i) q^{84} +(-4.44870 + 1.19203i) q^{85} +(-3.19846 + 0.857026i) q^{86} +4.36278i q^{87} +(-1.92045 - 1.10877i) q^{88} +(-11.3766 + 11.3766i) q^{89} +2.74755 q^{90} +(7.54097 + 5.84241i) q^{91} -0.546143 q^{92} +(-5.53137 + 5.53137i) q^{93} +(8.73983 + 5.04594i) q^{94} +0.503888i q^{95} +(0.965926 - 0.258819i) q^{96} +(15.6069 - 4.18186i) q^{97} +(-6.60903 - 2.30667i) q^{98} +(1.56804 + 1.56804i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q + 4 q^{7} + 20 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 40 q + 4 q^{7} + 20 q^{9} + 8 q^{11} - 20 q^{12} + 4 q^{14} - 40 q^{16} + 16 q^{17} + 4 q^{19} + 4 q^{21} - 4 q^{22} - 24 q^{25} + 8 q^{26} - 4 q^{28} - 12 q^{29} - 8 q^{33} - 8 q^{34} - 32 q^{35} + 40 q^{37} + 8 q^{38} + 20 q^{39} + 20 q^{41} + 12 q^{42} - 24 q^{43} - 4 q^{44} + 32 q^{46} + 4 q^{47} + 32 q^{49} - 16 q^{50} + 24 q^{51} + 16 q^{52} - 4 q^{53} + 24 q^{55} + 12 q^{56} + 8 q^{57} + 12 q^{58} + 24 q^{59} + 60 q^{61} + 32 q^{62} - 4 q^{63} + 44 q^{65} - 12 q^{67} - 8 q^{69} - 24 q^{70} - 28 q^{71} + 60 q^{73} - 40 q^{74} - 72 q^{75} + 4 q^{76} - 12 q^{77} + 4 q^{78} - 20 q^{81} - 24 q^{82} + 60 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{89} - 16 q^{92} - 24 q^{93} - 48 q^{97} - 88 q^{98} + 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(e\left(\frac{1}{12}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 0.707107i 0.500000 0.500000i
\(3\) −0.866025 0.500000i −0.500000 0.288675i
\(4\) 1.00000i 0.500000i
\(5\) 2.65393 0.711118i 1.18687 0.318022i 0.389224 0.921143i \(-0.372743\pi\)
0.797650 + 0.603121i \(0.206077\pi\)
\(6\) −0.965926 + 0.258819i −0.394338 + 0.105662i
\(7\) 1.40673 2.24078i 0.531694 0.846937i
\(8\) −0.707107 0.707107i −0.250000 0.250000i
\(9\) 0.500000 + 0.866025i 0.166667 + 0.288675i
\(10\) 1.37378 2.37945i 0.434426 0.752448i
\(11\) 2.14199 0.573943i 0.645833 0.173050i 0.0789889 0.996875i \(-0.474831\pi\)
0.566844 + 0.823825i \(0.308164\pi\)
\(12\) −0.500000 + 0.866025i −0.144338 + 0.250000i
\(13\) −0.354780 + 3.58805i −0.0983982 + 0.995147i
\(14\) −0.589766 2.57918i −0.157621 0.689315i
\(15\) −2.65393 0.711118i −0.685242 0.183610i
\(16\) −1.00000 −0.250000
\(17\) −1.67627 −0.406555 −0.203277 0.979121i \(-0.565159\pi\)
−0.203277 + 0.979121i \(0.565159\pi\)
\(18\) 0.965926 + 0.258819i 0.227671 + 0.0610042i
\(19\) −0.0474662 + 0.177146i −0.0108895 + 0.0406401i −0.971157 0.238442i \(-0.923363\pi\)
0.960267 + 0.279082i \(0.0900301\pi\)
\(20\) −0.711118 2.65393i −0.159011 0.593437i
\(21\) −2.33866 + 1.23721i −0.510336 + 0.269982i
\(22\) 1.10877 1.92045i 0.236391 0.409442i
\(23\) 0.546143i 0.113879i −0.998378 0.0569393i \(-0.981866\pi\)
0.998378 0.0569393i \(-0.0181342\pi\)
\(24\) 0.258819 + 0.965926i 0.0528312 + 0.197169i
\(25\) 2.20753 1.27452i 0.441506 0.254903i
\(26\) 2.28627 + 2.78800i 0.448374 + 0.546773i
\(27\) 1.00000i 0.192450i
\(28\) −2.24078 1.40673i −0.423468 0.265847i
\(29\) −2.18139 3.77828i −0.405074 0.701609i 0.589256 0.807946i \(-0.299421\pi\)
−0.994330 + 0.106337i \(0.966088\pi\)
\(30\) −2.37945 + 1.37378i −0.434426 + 0.250816i
\(31\) 2.02462 7.55600i 0.363633 1.35710i −0.505631 0.862750i \(-0.668740\pi\)
0.869264 0.494347i \(-0.164593\pi\)
\(32\) −0.707107 + 0.707107i −0.125000 + 0.125000i
\(33\) −2.14199 0.573943i −0.372872 0.0999107i
\(34\) −1.18530 + 1.18530i −0.203277 + 0.203277i
\(35\) 2.13990 6.94723i 0.361709 1.17430i
\(36\) 0.866025 0.500000i 0.144338 0.0833333i
\(37\) 0.909963 + 0.909963i 0.149597 + 0.149597i 0.777938 0.628341i \(-0.216266\pi\)
−0.628341 + 0.777938i \(0.716266\pi\)
\(38\) 0.0916976 + 0.158825i 0.0148753 + 0.0257648i
\(39\) 2.10128 2.92996i 0.336473 0.469168i
\(40\) −2.37945 1.37378i −0.376224 0.217213i
\(41\) −1.32782 + 4.95550i −0.207371 + 0.773919i 0.781343 + 0.624102i \(0.214535\pi\)
−0.988714 + 0.149817i \(0.952132\pi\)
\(42\) −0.778839 + 2.52852i −0.120177 + 0.390159i
\(43\) −2.86766 1.65565i −0.437315 0.252484i 0.265143 0.964209i \(-0.414581\pi\)
−0.702458 + 0.711725i \(0.747914\pi\)
\(44\) −0.573943 2.14199i −0.0865252 0.322917i
\(45\) 1.94281 + 1.94281i 0.289617 + 0.289617i
\(46\) −0.386181 0.386181i −0.0569393 0.0569393i
\(47\) 2.61197 + 9.74801i 0.380995 + 1.42189i 0.844384 + 0.535738i \(0.179967\pi\)
−0.463389 + 0.886155i \(0.653367\pi\)
\(48\) 0.866025 + 0.500000i 0.125000 + 0.0721688i
\(49\) −3.04223 6.30435i −0.434604 0.900622i
\(50\) 0.659739 2.46218i 0.0933011 0.348205i
\(51\) 1.45169 + 0.838134i 0.203277 + 0.117362i
\(52\) 3.58805 + 0.354780i 0.497574 + 0.0491991i
\(53\) 1.78093 + 3.08467i 0.244630 + 0.423712i 0.962028 0.272952i \(-0.0880002\pi\)
−0.717397 + 0.696664i \(0.754667\pi\)
\(54\) −0.707107 0.707107i −0.0962250 0.0962250i
\(55\) 5.27654 3.04641i 0.711488 0.410778i
\(56\) −2.57918 + 0.589766i −0.344658 + 0.0788107i
\(57\) 0.129680 0.129680i 0.0171765 0.0171765i
\(58\) −4.21412 1.12917i −0.553342 0.148267i
\(59\) −1.05173 + 1.05173i −0.136923 + 0.136923i −0.772246 0.635323i \(-0.780867\pi\)
0.635323 + 0.772246i \(0.280867\pi\)
\(60\) −0.711118 + 2.65393i −0.0918050 + 0.342621i
\(61\) −11.8307 + 6.83046i −1.51477 + 0.874551i −0.514917 + 0.857240i \(0.672177\pi\)
−0.999850 + 0.0173106i \(0.994490\pi\)
\(62\) −3.91127 6.77452i −0.496732 0.860365i
\(63\) 2.64394 + 0.0978714i 0.333105 + 0.0123306i
\(64\) 1.00000i 0.125000i
\(65\) 1.60997 + 9.77473i 0.199692 + 1.21241i
\(66\) −1.92045 + 1.10877i −0.236391 + 0.136481i
\(67\) −1.82429 6.80833i −0.222872 0.831770i −0.983246 0.182284i \(-0.941651\pi\)
0.760374 0.649486i \(-0.225016\pi\)
\(68\) 1.67627i 0.203277i
\(69\) −0.273071 + 0.472973i −0.0328739 + 0.0569393i
\(70\) −3.39930 6.42557i −0.406294 0.768003i
\(71\) 1.04867 + 3.91368i 0.124454 + 0.464469i 0.999820 0.0189927i \(-0.00604594\pi\)
−0.875366 + 0.483462i \(0.839379\pi\)
\(72\) 0.258819 0.965926i 0.0305021 0.113835i
\(73\) 8.57385 + 2.29736i 1.00349 + 0.268885i 0.722908 0.690944i \(-0.242805\pi\)
0.280585 + 0.959829i \(0.409471\pi\)
\(74\) 1.28688 0.149597
\(75\) −2.54903 −0.294337
\(76\) 0.177146 + 0.0474662i 0.0203201 + 0.00544475i
\(77\) 1.72711 5.60711i 0.196823 0.638990i
\(78\) −0.585966 3.55762i −0.0663475 0.402821i
\(79\) 4.42139 7.65808i 0.497445 0.861601i −0.502550 0.864548i \(-0.667605\pi\)
0.999996 + 0.00294723i \(0.000938134\pi\)
\(80\) −2.65393 + 0.711118i −0.296718 + 0.0795055i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 2.56516 + 4.44298i 0.283274 + 0.490645i
\(83\) 11.3594 + 11.3594i 1.24686 + 1.24686i 0.957100 + 0.289759i \(0.0935751\pi\)
0.289759 + 0.957100i \(0.406425\pi\)
\(84\) 1.23721 + 2.33866i 0.134991 + 0.255168i
\(85\) −4.44870 + 1.19203i −0.482529 + 0.129293i
\(86\) −3.19846 + 0.857026i −0.344899 + 0.0924154i
\(87\) 4.36278i 0.467739i
\(88\) −1.92045 1.10877i −0.204721 0.118196i
\(89\) −11.3766 + 11.3766i −1.20592 + 1.20592i −0.233579 + 0.972338i \(0.575044\pi\)
−0.972338 + 0.233579i \(0.924956\pi\)
\(90\) 2.74755 0.289617
\(91\) 7.54097 + 5.84241i 0.790509 + 0.612451i
\(92\) −0.546143 −0.0569393
\(93\) −5.53137 + 5.53137i −0.573577 + 0.573577i
\(94\) 8.73983 + 5.04594i 0.901444 + 0.520449i
\(95\) 0.503888i 0.0516978i
\(96\) 0.965926 0.258819i 0.0985844 0.0264156i
\(97\) 15.6069 4.18186i 1.58464 0.424603i 0.644282 0.764788i \(-0.277156\pi\)
0.940358 + 0.340185i \(0.110490\pi\)
\(98\) −6.60903 2.30667i −0.667613 0.233009i
\(99\) 1.56804 + 1.56804i 0.157594 + 0.157594i
\(100\) −1.27452 2.20753i −0.127452 0.220753i
\(101\) −7.93535 + 13.7444i −0.789597 + 1.36762i 0.136618 + 0.990624i \(0.456377\pi\)
−0.926214 + 0.376997i \(0.876957\pi\)
\(102\) 1.61915 0.433850i 0.160320 0.0429576i
\(103\) −4.73336 + 8.19841i −0.466391 + 0.807814i −0.999263 0.0383824i \(-0.987779\pi\)
0.532872 + 0.846196i \(0.321113\pi\)
\(104\) 2.78800 2.28627i 0.273386 0.224187i
\(105\) −5.32682 + 4.94653i −0.519845 + 0.482732i
\(106\) 3.44050 + 0.921879i 0.334171 + 0.0895408i
\(107\) 3.20890 0.310216 0.155108 0.987897i \(-0.450427\pi\)
0.155108 + 0.987897i \(0.450427\pi\)
\(108\) −1.00000 −0.0962250
\(109\) 9.09049 + 2.43579i 0.870711 + 0.233306i 0.666395 0.745599i \(-0.267836\pi\)
0.204316 + 0.978905i \(0.434503\pi\)
\(110\) 1.57694 5.88521i 0.150355 0.561133i
\(111\) −0.333069 1.24303i −0.0316135 0.117983i
\(112\) −1.40673 + 2.24078i −0.132923 + 0.211734i
\(113\) 1.81014 3.13525i 0.170283 0.294940i −0.768235 0.640167i \(-0.778865\pi\)
0.938519 + 0.345228i \(0.112198\pi\)
\(114\) 0.183395i 0.0171765i
\(115\) −0.388372 1.44942i −0.0362159 0.135160i
\(116\) −3.77828 + 2.18139i −0.350805 + 0.202537i
\(117\) −3.28474 + 1.48678i −0.303674 + 0.137453i
\(118\) 1.48737i 0.136923i
\(119\) −2.35806 + 3.75616i −0.216163 + 0.344326i
\(120\) 1.37378 + 2.37945i 0.125408 + 0.217213i
\(121\) −5.26759 + 3.04124i −0.478872 + 0.276477i
\(122\) −3.53571 + 13.1954i −0.320108 + 1.19466i
\(123\) 3.62768 3.62768i 0.327097 0.327097i
\(124\) −7.55600 2.02462i −0.678548 0.181817i
\(125\) −4.76177 + 4.76177i −0.425905 + 0.425905i
\(126\) 1.93875 1.80034i 0.172718 0.160387i
\(127\) 11.5855 6.68890i 1.02805 0.593544i 0.111623 0.993751i \(-0.464395\pi\)
0.916425 + 0.400207i \(0.131062\pi\)
\(128\) 0.707107 + 0.707107i 0.0625000 + 0.0625000i
\(129\) 1.65565 + 2.86766i 0.145772 + 0.252484i
\(130\) 8.05020 + 5.77336i 0.706049 + 0.506357i
\(131\) 16.7924 + 9.69509i 1.46716 + 0.847064i 0.999324 0.0367535i \(-0.0117016\pi\)
0.467833 + 0.883817i \(0.345035\pi\)
\(132\) −0.573943 + 2.14199i −0.0499554 + 0.186436i
\(133\) 0.330174 + 0.355558i 0.0286297 + 0.0308308i
\(134\) −6.10419 3.52425i −0.527321 0.304449i
\(135\) −0.711118 2.65393i −0.0612033 0.228414i
\(136\) 1.18530 + 1.18530i 0.101639 + 0.101639i
\(137\) −9.80752 9.80752i −0.837913 0.837913i 0.150671 0.988584i \(-0.451857\pi\)
−0.988584 + 0.150671i \(0.951857\pi\)
\(138\) 0.141352 + 0.527533i 0.0120327 + 0.0449066i
\(139\) −13.7082 7.91444i −1.16272 0.671294i −0.210762 0.977537i \(-0.567595\pi\)
−0.951953 + 0.306243i \(0.900928\pi\)
\(140\) −6.94723 2.13990i −0.587149 0.180854i
\(141\) 2.61197 9.74801i 0.219968 0.820930i
\(142\) 3.50891 + 2.02587i 0.294461 + 0.170007i
\(143\) 1.29941 + 7.88918i 0.108662 + 0.659727i
\(144\) −0.500000 0.866025i −0.0416667 0.0721688i
\(145\) −8.47606 8.47606i −0.703899 0.703899i
\(146\) 7.68711 4.43815i 0.636189 0.367304i
\(147\) −0.517532 + 6.98084i −0.0426853 + 0.575770i
\(148\) 0.909963 0.909963i 0.0747985 0.0747985i
\(149\) 13.8974 + 3.72381i 1.13852 + 0.305066i 0.778357 0.627822i \(-0.216054\pi\)
0.360165 + 0.932888i \(0.382720\pi\)
\(150\) −1.80244 + 1.80244i −0.147169 + 0.147169i
\(151\) −0.602340 + 2.24796i −0.0490177 + 0.182937i −0.986094 0.166188i \(-0.946854\pi\)
0.937076 + 0.349124i \(0.113521\pi\)
\(152\) 0.158825 0.0916976i 0.0128824 0.00743766i
\(153\) −0.838134 1.45169i −0.0677591 0.117362i
\(154\) −2.74357 5.18608i −0.221083 0.417906i
\(155\) 21.4928i 1.72635i
\(156\) −2.92996 2.10128i −0.234584 0.168237i
\(157\) 4.62239 2.66874i 0.368907 0.212988i −0.304074 0.952648i \(-0.598347\pi\)
0.672981 + 0.739660i \(0.265014\pi\)
\(158\) −2.28868 8.54147i −0.182078 0.679523i
\(159\) 3.56187i 0.282474i
\(160\) −1.37378 + 2.37945i −0.108606 + 0.188112i
\(161\) −1.22379 0.768275i −0.0964480 0.0605486i
\(162\) 0.258819 + 0.965926i 0.0203347 + 0.0758903i
\(163\) 1.44909 5.40806i 0.113501 0.423592i −0.885669 0.464317i \(-0.846300\pi\)
0.999170 + 0.0407246i \(0.0129666\pi\)
\(164\) 4.95550 + 1.32782i 0.386960 + 0.103686i
\(165\) −6.09282 −0.474326
\(166\) 16.0646 1.24686
\(167\) −6.88324 1.84436i −0.532641 0.142721i −0.0175335 0.999846i \(-0.505581\pi\)
−0.515108 + 0.857126i \(0.672248\pi\)
\(168\) 2.52852 + 0.778839i 0.195080 + 0.0600887i
\(169\) −12.7483 2.54594i −0.980636 0.195841i
\(170\) −2.30282 + 3.98859i −0.176618 + 0.305911i
\(171\) −0.177146 + 0.0474662i −0.0135467 + 0.00362983i
\(172\) −1.65565 + 2.86766i −0.126242 + 0.218657i
\(173\) 1.42127 + 2.46170i 0.108057 + 0.187160i 0.914983 0.403492i \(-0.132204\pi\)
−0.806926 + 0.590652i \(0.798871\pi\)
\(174\) 3.08495 + 3.08495i 0.233870 + 0.233870i
\(175\) 0.249478 6.73949i 0.0188587 0.509458i
\(176\) −2.14199 + 0.573943i −0.161458 + 0.0432626i
\(177\) 1.43669 0.384959i 0.107988 0.0289353i
\(178\) 16.0889i 1.20592i
\(179\) −22.1165 12.7690i −1.65307 0.954399i −0.975801 0.218661i \(-0.929831\pi\)
−0.677266 0.735738i \(-0.736835\pi\)
\(180\) 1.94281 1.94281i 0.144809 0.144809i
\(181\) 16.1216 1.19831 0.599155 0.800633i \(-0.295503\pi\)
0.599155 + 0.800633i \(0.295503\pi\)
\(182\) 9.46348 1.20107i 0.701480 0.0890292i
\(183\) 13.6609 1.00984
\(184\) −0.386181 + 0.386181i −0.0284697 + 0.0284697i
\(185\) 3.06207 + 1.76789i 0.225128 + 0.129978i
\(186\) 7.82254i 0.573577i
\(187\) −3.59054 + 0.962083i −0.262567 + 0.0703545i
\(188\) 9.74801 2.61197i 0.710947 0.190498i
\(189\) −2.24078 1.40673i −0.162993 0.102325i
\(190\) 0.356302 + 0.356302i 0.0258489 + 0.0258489i
\(191\) −0.816556 1.41432i −0.0590839 0.102336i 0.834971 0.550295i \(-0.185485\pi\)
−0.894054 + 0.447958i \(0.852151\pi\)
\(192\) 0.500000 0.866025i 0.0360844 0.0625000i
\(193\) −9.13997 + 2.44905i −0.657910 + 0.176286i −0.572303 0.820043i \(-0.693950\pi\)
−0.0856072 + 0.996329i \(0.527283\pi\)
\(194\) 8.07872 13.9928i 0.580019 1.00462i
\(195\) 3.49309 9.27015i 0.250146 0.663849i
\(196\) −6.30435 + 3.04223i −0.450311 + 0.217302i
\(197\) 10.9689 + 2.93910i 0.781500 + 0.209402i 0.627446 0.778660i \(-0.284100\pi\)
0.154054 + 0.988062i \(0.450767\pi\)
\(198\) 2.21755 0.157594
\(199\) −18.1047 −1.28340 −0.641702 0.766954i \(-0.721772\pi\)
−0.641702 + 0.766954i \(0.721772\pi\)
\(200\) −2.46218 0.659739i −0.174102 0.0466506i
\(201\) −1.82429 + 6.80833i −0.128675 + 0.480223i
\(202\) 4.10764 + 15.3299i 0.289012 + 1.07861i
\(203\) −11.5349 0.426992i −0.809594 0.0299689i
\(204\) 0.838134 1.45169i 0.0586811 0.101639i
\(205\) 14.0958i 0.984493i
\(206\) 2.45017 + 9.14414i 0.170711 + 0.637102i
\(207\) 0.472973 0.273071i 0.0328739 0.0189798i
\(208\) 0.354780 3.58805i 0.0245996 0.248787i
\(209\) 0.406688i 0.0281312i
\(210\) −0.268907 + 7.26436i −0.0185563 + 0.501288i
\(211\) 0.00906917 + 0.0157083i 0.000624347 + 0.00108140i 0.866337 0.499459i \(-0.166468\pi\)
−0.865713 + 0.500541i \(0.833135\pi\)
\(212\) 3.08467 1.78093i 0.211856 0.122315i
\(213\) 1.04867 3.91368i 0.0718536 0.268161i
\(214\) 2.26904 2.26904i 0.155108 0.155108i
\(215\) −8.78794 2.35472i −0.599332 0.160591i
\(216\) −0.707107 + 0.707107i −0.0481125 + 0.0481125i
\(217\) −14.0833 15.1660i −0.956034 1.02953i
\(218\) 8.15031 4.70559i 0.552009 0.318702i
\(219\) −6.27650 6.27650i −0.424126 0.424126i
\(220\) −3.04641 5.27654i −0.205389 0.355744i
\(221\) 0.594706 6.01454i 0.0400043 0.404582i
\(222\) −1.11447 0.643441i −0.0747985 0.0431849i
\(223\) 3.72027 13.8843i 0.249128 0.929758i −0.722136 0.691752i \(-0.756839\pi\)
0.971264 0.238007i \(-0.0764940\pi\)
\(224\) 0.589766 + 2.57918i 0.0394054 + 0.172329i
\(225\) 2.20753 + 1.27452i 0.147169 + 0.0849678i
\(226\) −0.936996 3.49692i −0.0623281 0.232612i
\(227\) −2.92840 2.92840i −0.194365 0.194365i 0.603214 0.797579i \(-0.293886\pi\)
−0.797579 + 0.603214i \(0.793886\pi\)
\(228\) −0.129680 0.129680i −0.00858827 0.00858827i
\(229\) −2.25923 8.43158i −0.149294 0.557174i −0.999527 0.0307665i \(-0.990205\pi\)
0.850232 0.526408i \(-0.176461\pi\)
\(230\) −1.29952 0.750277i −0.0856877 0.0494718i
\(231\) −4.29928 + 3.99234i −0.282872 + 0.262677i
\(232\) −1.12917 + 4.21412i −0.0741337 + 0.276671i
\(233\) 5.73199 + 3.30937i 0.375515 + 0.216804i 0.675865 0.737025i \(-0.263770\pi\)
−0.300350 + 0.953829i \(0.597103\pi\)
\(234\) −1.27135 + 3.37397i −0.0831106 + 0.220563i
\(235\) 13.8640 + 24.0131i 0.904386 + 1.56644i
\(236\) 1.05173 + 1.05173i 0.0684617 + 0.0684617i
\(237\) −7.65808 + 4.42139i −0.497445 + 0.287200i
\(238\) 0.988606 + 4.32340i 0.0640818 + 0.280244i
\(239\) −4.05600 + 4.05600i −0.262361 + 0.262361i −0.826013 0.563652i \(-0.809396\pi\)
0.563652 + 0.826013i \(0.309396\pi\)
\(240\) 2.65393 + 0.711118i 0.171310 + 0.0459025i
\(241\) 6.36407 6.36407i 0.409946 0.409946i −0.471774 0.881720i \(-0.656386\pi\)
0.881720 + 0.471774i \(0.156386\pi\)
\(242\) −1.57426 + 5.87523i −0.101197 + 0.377674i
\(243\) 0.866025 0.500000i 0.0555556 0.0320750i
\(244\) 6.83046 + 11.8307i 0.437275 + 0.757383i
\(245\) −12.5570 14.5679i −0.802237 0.930711i
\(246\) 5.13031i 0.327097i
\(247\) −0.618770 0.233159i −0.0393714 0.0148356i
\(248\) −6.77452 + 3.91127i −0.430183 + 0.248366i
\(249\) −4.15784 15.5173i −0.263492 0.983366i
\(250\) 6.73415i 0.425905i
\(251\) −7.77241 + 13.4622i −0.490590 + 0.849727i −0.999941 0.0108317i \(-0.996552\pi\)
0.509351 + 0.860559i \(0.329885\pi\)
\(252\) 0.0978714 2.64394i 0.00616532 0.166553i
\(253\) −0.313455 1.16983i −0.0197067 0.0735466i
\(254\) 3.46243 12.9220i 0.217252 0.810796i
\(255\) 4.44870 + 1.19203i 0.278588 + 0.0746475i
\(256\) 1.00000 0.0625000
\(257\) 7.17059 0.447289 0.223645 0.974671i \(-0.428204\pi\)
0.223645 + 0.974671i \(0.428204\pi\)
\(258\) 3.19846 + 0.857026i 0.199128 + 0.0533561i
\(259\) 3.31910 0.758958i 0.206239 0.0471594i
\(260\) 9.77473 1.60997i 0.606203 0.0998461i
\(261\) 2.18139 3.77828i 0.135025 0.233870i
\(262\) 18.7295 5.01855i 1.15711 0.310047i
\(263\) −3.61004 + 6.25278i −0.222605 + 0.385563i −0.955598 0.294673i \(-0.904789\pi\)
0.732993 + 0.680236i \(0.238123\pi\)
\(264\) 1.10877 + 1.92045i 0.0682403 + 0.118196i
\(265\) 6.92004 + 6.92004i 0.425094 + 0.425094i
\(266\) 0.484886 + 0.0179492i 0.0297303 + 0.00110053i
\(267\) 15.5407 4.16412i 0.951077 0.254840i
\(268\) −6.80833 + 1.82429i −0.415885 + 0.111436i
\(269\) 2.01410i 0.122802i −0.998113 0.0614010i \(-0.980443\pi\)
0.998113 0.0614010i \(-0.0195568\pi\)
\(270\) −2.37945 1.37378i −0.144809 0.0836053i
\(271\) −16.1973 + 16.1973i −0.983917 + 0.983917i −0.999873 0.0159559i \(-0.994921\pi\)
0.0159559 + 0.999873i \(0.494921\pi\)
\(272\) 1.67627 0.101639
\(273\) −3.60947 8.83016i −0.218455 0.534426i
\(274\) −13.8699 −0.837913
\(275\) 3.99699 3.99699i 0.241028 0.241028i
\(276\) 0.472973 + 0.273071i 0.0284697 + 0.0164370i
\(277\) 25.5542i 1.53540i 0.640808 + 0.767702i \(0.278600\pi\)
−0.640808 + 0.767702i \(0.721400\pi\)
\(278\) −15.2895 + 4.09682i −0.917005 + 0.245711i
\(279\) 7.55600 2.02462i 0.452366 0.121211i
\(280\) −6.42557 + 3.39930i −0.384001 + 0.203147i
\(281\) −10.1284 10.1284i −0.604210 0.604210i 0.337217 0.941427i \(-0.390514\pi\)
−0.941427 + 0.337217i \(0.890514\pi\)
\(282\) −5.04594 8.73983i −0.300481 0.520449i
\(283\) 15.2040 26.3342i 0.903786 1.56540i 0.0812472 0.996694i \(-0.474110\pi\)
0.822539 0.568709i \(-0.192557\pi\)
\(284\) 3.91368 1.04867i 0.232234 0.0622270i
\(285\) 0.251944 0.436380i 0.0149239 0.0258489i
\(286\) 6.49731 + 4.65968i 0.384194 + 0.275532i
\(287\) 9.23632 + 9.94641i 0.545203 + 0.587118i
\(288\) −0.965926 0.258819i −0.0569177 0.0152511i
\(289\) −14.1901 −0.834713
\(290\) −11.9870 −0.703899
\(291\) −15.6069 4.18186i −0.914892 0.245145i
\(292\) 2.29736 8.57385i 0.134443 0.501747i
\(293\) −1.88727 7.04340i −0.110256 0.411480i 0.888633 0.458620i \(-0.151656\pi\)
−0.998888 + 0.0471399i \(0.984989\pi\)
\(294\) 4.57025 + 5.30215i 0.266542 + 0.309228i
\(295\) −2.04331 + 3.53912i −0.118966 + 0.206055i
\(296\) 1.28688i 0.0747985i
\(297\) −0.573943 2.14199i −0.0333036 0.124291i
\(298\) 12.4601 7.19384i 0.721794 0.416728i
\(299\) 1.95959 + 0.193760i 0.113326 + 0.0112055i
\(300\) 2.54903i 0.147169i
\(301\) −7.74397 + 4.09677i −0.446355 + 0.236134i
\(302\) 1.16363 + 2.01547i 0.0669594 + 0.115977i
\(303\) 13.7444 7.93535i 0.789597 0.455874i
\(304\) 0.0474662 0.177146i 0.00272237 0.0101600i
\(305\) −26.5406 + 26.5406i −1.51971 + 1.51971i
\(306\) −1.61915 0.433850i −0.0925607 0.0248016i
\(307\) 1.04129 1.04129i 0.0594295 0.0594295i −0.676767 0.736197i \(-0.736620\pi\)
0.736197 + 0.676767i \(0.236620\pi\)
\(308\) −5.60711 1.72711i −0.319495 0.0984113i
\(309\) 8.19841 4.73336i 0.466391 0.269271i
\(310\) −15.1977 15.1977i −0.863173 0.863173i
\(311\) −10.3053 17.8493i −0.584360 1.01214i −0.994955 0.100324i \(-0.968012\pi\)
0.410594 0.911818i \(-0.365321\pi\)
\(312\) −3.55762 + 0.585966i −0.201410 + 0.0331738i
\(313\) −8.86536 5.11842i −0.501100 0.289310i 0.228068 0.973645i \(-0.426759\pi\)
−0.729168 + 0.684335i \(0.760093\pi\)
\(314\) 1.38144 5.15561i 0.0779592 0.290948i
\(315\) 7.08643 1.62041i 0.399275 0.0912998i
\(316\) −7.65808 4.42139i −0.430800 0.248723i
\(317\) 0.0964049 + 0.359788i 0.00541464 + 0.0202077i 0.968580 0.248701i \(-0.0800037\pi\)
−0.963166 + 0.268909i \(0.913337\pi\)
\(318\) −2.51862 2.51862i −0.141237 0.141237i
\(319\) −6.84103 6.84103i −0.383024 0.383024i
\(320\) 0.711118 + 2.65393i 0.0397527 + 0.148359i
\(321\) −2.77899 1.60445i −0.155108 0.0895517i
\(322\) −1.40860 + 0.322096i −0.0784983 + 0.0179497i
\(323\) 0.0795661 0.296945i 0.00442718 0.0165224i
\(324\) 0.866025 + 0.500000i 0.0481125 + 0.0277778i
\(325\) 3.78985 + 8.37290i 0.210223 + 0.464445i
\(326\) −2.79942 4.84873i −0.155045 0.268547i
\(327\) −6.65470 6.65470i −0.368006 0.368006i
\(328\) 4.44298 2.56516i 0.245323 0.141637i
\(329\) 25.5175 + 7.85995i 1.40683 + 0.433333i
\(330\) −4.30828 + 4.30828i −0.237163 + 0.237163i
\(331\) 12.8651 + 3.44719i 0.707129 + 0.189475i 0.594422 0.804154i \(-0.297381\pi\)
0.112707 + 0.993628i \(0.464048\pi\)
\(332\) 11.3594 11.3594i 0.623429 0.623429i
\(333\) −0.333069 + 1.24303i −0.0182521 + 0.0681177i
\(334\) −6.17134 + 3.56303i −0.337681 + 0.194960i
\(335\) −9.68306 16.7716i −0.529042 0.916328i
\(336\) 2.33866 1.23721i 0.127584 0.0674954i
\(337\) 22.8350i 1.24390i −0.783057 0.621950i \(-0.786341\pi\)
0.783057 0.621950i \(-0.213659\pi\)
\(338\) −10.8146 + 7.21413i −0.588239 + 0.392397i
\(339\) −3.13525 + 1.81014i −0.170283 + 0.0983132i
\(340\) 1.19203 + 4.44870i 0.0646467 + 0.241265i
\(341\) 17.3469i 0.939385i
\(342\) −0.0916976 + 0.158825i −0.00495844 + 0.00858827i
\(343\) −18.4063 2.05155i −0.993846 0.110773i
\(344\) 0.857026 + 3.19846i 0.0462077 + 0.172450i
\(345\) −0.388372 + 1.44942i −0.0209093 + 0.0780344i
\(346\) 2.74567 + 0.735701i 0.147608 + 0.0395515i
\(347\) 14.8824 0.798927 0.399463 0.916749i \(-0.369196\pi\)
0.399463 + 0.916749i \(0.369196\pi\)
\(348\) 4.36278 0.233870
\(349\) −9.60502 2.57366i −0.514145 0.137765i −0.00758807 0.999971i \(-0.502415\pi\)
−0.506557 + 0.862206i \(0.669082\pi\)
\(350\) −4.58913 4.94195i −0.245300 0.264158i
\(351\) 3.58805 + 0.354780i 0.191516 + 0.0189367i
\(352\) −1.10877 + 1.92045i −0.0590978 + 0.102360i
\(353\) 20.9560 5.61514i 1.11538 0.298864i 0.346365 0.938100i \(-0.387416\pi\)
0.769011 + 0.639236i \(0.220749\pi\)
\(354\) 0.743684 1.28810i 0.0395264 0.0684617i
\(355\) 5.56619 + 9.64092i 0.295422 + 0.511687i
\(356\) 11.3766 + 11.3766i 0.602958 + 0.602958i
\(357\) 3.92021 2.07390i 0.207480 0.109762i
\(358\) −24.6678 + 6.60971i −1.30373 + 0.349334i
\(359\) −25.3972 + 6.80517i −1.34042 + 0.359163i −0.856588 0.516000i \(-0.827420\pi\)
−0.483827 + 0.875164i \(0.660754\pi\)
\(360\) 2.74755i 0.144809i
\(361\) 16.4254 + 9.48318i 0.864492 + 0.499115i
\(362\) 11.3997 11.3997i 0.599155 0.599155i
\(363\) 6.08249 0.319248
\(364\) 5.84241 7.54097i 0.306225 0.395254i
\(365\) 24.3881 1.27653
\(366\) 9.65973 9.65973i 0.504922 0.504922i
\(367\) −7.79817 4.50227i −0.407061 0.235017i 0.282465 0.959278i \(-0.408848\pi\)
−0.689526 + 0.724261i \(0.742181\pi\)
\(368\) 0.546143i 0.0284697i
\(369\) −4.95550 + 1.32782i −0.257973 + 0.0691237i
\(370\) 3.41529 0.915125i 0.177553 0.0475751i
\(371\) 9.41736 + 0.348605i 0.488925 + 0.0180987i
\(372\) 5.53137 + 5.53137i 0.286788 + 0.286788i
\(373\) 13.3657 + 23.1501i 0.692049 + 1.19866i 0.971165 + 0.238407i \(0.0766253\pi\)
−0.279116 + 0.960257i \(0.590041\pi\)
\(374\) −1.85860 + 3.21919i −0.0961060 + 0.166461i
\(375\) 6.50469 1.74293i 0.335901 0.0900044i
\(376\) 5.04594 8.73983i 0.260225 0.450722i
\(377\) 14.3306 6.48649i 0.738063 0.334071i
\(378\) −2.57918 + 0.589766i −0.132659 + 0.0303343i
\(379\) −10.5843 2.83605i −0.543678 0.145678i −0.0234808 0.999724i \(-0.507475\pi\)
−0.520197 + 0.854046i \(0.674142\pi\)
\(380\) 0.503888 0.0258489
\(381\) −13.3778 −0.685365
\(382\) −1.57746 0.422680i −0.0807101 0.0216262i
\(383\) 6.03951 22.5398i 0.308604 1.15173i −0.621193 0.783657i \(-0.713352\pi\)
0.929798 0.368070i \(-0.119981\pi\)
\(384\) −0.258819 0.965926i −0.0132078 0.0492922i
\(385\) 0.596313 16.1091i 0.0303909 0.820994i
\(386\) −4.73120 + 8.19468i −0.240812 + 0.417098i
\(387\) 3.31129i 0.168322i
\(388\) −4.18186 15.6069i −0.212302 0.792320i
\(389\) 24.3558 14.0618i 1.23489 0.712962i 0.266842 0.963740i \(-0.414020\pi\)
0.968044 + 0.250779i \(0.0806866\pi\)
\(390\) −4.08500 9.02498i −0.206852 0.456998i
\(391\) 0.915482i 0.0462979i
\(392\) −2.30667 + 6.60903i −0.116505 + 0.333806i
\(393\) −9.69509 16.7924i −0.489052 0.847064i
\(394\) 9.83442 5.67791i 0.495451 0.286049i
\(395\) 6.28827 23.4681i 0.316397 1.18081i
\(396\) 1.56804 1.56804i 0.0787971 0.0787971i
\(397\) −21.1092 5.65620i −1.05944 0.283877i −0.313294 0.949656i \(-0.601432\pi\)
−0.746148 + 0.665780i \(0.768099\pi\)
\(398\) −12.8019 + 12.8019i −0.641702 + 0.641702i
\(399\) −0.108160 0.473010i −0.00541478 0.0236801i
\(400\) −2.20753 + 1.27452i −0.110376 + 0.0637259i
\(401\) 14.5359 + 14.5359i 0.725888 + 0.725888i 0.969798 0.243910i \(-0.0784301\pi\)
−0.243910 + 0.969798i \(0.578430\pi\)
\(402\) 3.52425 + 6.10419i 0.175774 + 0.304449i
\(403\) 26.3930 + 9.94517i 1.31473 + 0.495404i
\(404\) 13.7444 + 7.93535i 0.683811 + 0.394798i
\(405\) −0.711118 + 2.65393i −0.0353358 + 0.131875i
\(406\) −8.45836 + 7.85450i −0.419781 + 0.389812i
\(407\) 2.47139 + 1.42686i 0.122502 + 0.0707268i
\(408\) −0.433850 1.61915i −0.0214788 0.0801599i
\(409\) −27.9592 27.9592i −1.38249 1.38249i −0.840173 0.542319i \(-0.817547\pi\)
−0.542319 0.840173i \(-0.682453\pi\)
\(410\) 9.96723 + 9.96723i 0.492246 + 0.492246i
\(411\) 3.58980 + 13.3973i 0.177072 + 0.660841i
\(412\) 8.19841 + 4.73336i 0.403907 + 0.233196i
\(413\) 0.877199 + 3.83619i 0.0431641 + 0.188767i
\(414\) 0.141352 0.527533i 0.00694708 0.0259269i
\(415\) 38.2250 + 22.0692i 1.87639 + 1.08334i
\(416\) −2.28627 2.78800i −0.112094 0.136693i
\(417\) 7.91444 + 13.7082i 0.387572 + 0.671294i
\(418\) 0.287572 + 0.287572i 0.0140656 + 0.0140656i
\(419\) 19.3975 11.1991i 0.947629 0.547114i 0.0552851 0.998471i \(-0.482393\pi\)
0.892343 + 0.451357i \(0.149060\pi\)
\(420\) 4.94653 + 5.32682i 0.241366 + 0.259922i
\(421\) −5.11816 + 5.11816i −0.249444 + 0.249444i −0.820742 0.571299i \(-0.806440\pi\)
0.571299 + 0.820742i \(0.306440\pi\)
\(422\) 0.0175203 + 0.00469455i 0.000852874 + 0.000228527i
\(423\) −7.13604 + 7.13604i −0.346966 + 0.346966i
\(424\) 0.921879 3.44050i 0.0447704 0.167085i
\(425\) −3.70041 + 2.13643i −0.179496 + 0.103632i
\(426\) −2.02587 3.50891i −0.0981538 0.170007i
\(427\) −1.33701 + 36.1187i −0.0647026 + 1.74790i
\(428\) 3.20890i 0.155108i
\(429\) 2.81927 7.48194i 0.136116 0.361231i
\(430\) −7.87905 + 4.54897i −0.379962 + 0.219371i
\(431\) −9.76457 36.4419i −0.470343 1.75534i −0.638539 0.769589i \(-0.720461\pi\)
0.168196 0.985754i \(-0.446206\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) −18.4530 + 31.9616i −0.886795 + 1.53597i −0.0431533 + 0.999068i \(0.513740\pi\)
−0.843642 + 0.536906i \(0.819593\pi\)
\(434\) −20.6823 0.765603i −0.992784 0.0367501i
\(435\) 3.10245 + 11.5785i 0.148751 + 0.555148i
\(436\) 2.43579 9.09049i 0.116653 0.435356i
\(437\) 0.0967471 + 0.0259233i 0.00462804 + 0.00124008i
\(438\) −8.87631 −0.424126
\(439\) 10.1657 0.485185 0.242592 0.970128i \(-0.422002\pi\)
0.242592 + 0.970128i \(0.422002\pi\)
\(440\) −5.88521 1.57694i −0.280567 0.0751776i
\(441\) 3.93862 5.78682i 0.187553 0.275563i
\(442\) −3.83240 4.67344i −0.182289 0.222293i
\(443\) −1.02220 + 1.77050i −0.0485662 + 0.0841192i −0.889287 0.457350i \(-0.848799\pi\)
0.840720 + 0.541470i \(0.182132\pi\)
\(444\) −1.24303 + 0.333069i −0.0589917 + 0.0158068i
\(445\) −22.1026 + 38.2828i −1.04776 + 1.81478i
\(446\) −7.18702 12.4483i −0.340315 0.589443i
\(447\) −10.1736 10.1736i −0.481196 0.481196i
\(448\) 2.24078 + 1.40673i 0.105867 + 0.0664617i
\(449\) −19.3298 + 5.17939i −0.912228 + 0.244431i −0.684260 0.729238i \(-0.739875\pi\)
−0.227968 + 0.973669i \(0.573208\pi\)
\(450\) 2.46218 0.659739i 0.116068 0.0311004i
\(451\) 11.3767i 0.535708i
\(452\) −3.13525 1.81014i −0.147470 0.0851417i
\(453\) 1.64562 1.64562i 0.0773181 0.0773181i
\(454\) −4.14138 −0.194365
\(455\) 24.1679 + 10.1428i 1.13301 + 0.475502i
\(456\) −0.183395 −0.00858827
\(457\) −23.3378 + 23.3378i −1.09170 + 1.09170i −0.0963505 + 0.995347i \(0.530717\pi\)
−0.995347 + 0.0963505i \(0.969283\pi\)
\(458\) −7.55955 4.36451i −0.353234 0.203940i
\(459\) 1.67627i 0.0782415i
\(460\) −1.44942 + 0.388372i −0.0675798 + 0.0181079i
\(461\) 13.7371 3.68085i 0.639801 0.171434i 0.0756877 0.997132i \(-0.475885\pi\)
0.564113 + 0.825697i \(0.309218\pi\)
\(462\) −0.217034 + 5.86306i −0.0100974 + 0.272774i
\(463\) −15.3894 15.3894i −0.715207 0.715207i 0.252412 0.967620i \(-0.418776\pi\)
−0.967620 + 0.252412i \(0.918776\pi\)
\(464\) 2.18139 + 3.77828i 0.101269 + 0.175402i
\(465\) −10.7464 + 18.6133i −0.498353 + 0.863173i
\(466\) 6.39321 1.71305i 0.296160 0.0793557i
\(467\) −20.4707 + 35.4563i −0.947272 + 1.64072i −0.196136 + 0.980577i \(0.562840\pi\)
−0.751136 + 0.660147i \(0.770494\pi\)
\(468\) 1.48678 + 3.28474i 0.0687264 + 0.151837i
\(469\) −17.8223 5.48965i −0.822957 0.253488i
\(470\) 26.7831 + 7.17652i 1.23541 + 0.331028i
\(471\) −5.33748 −0.245938
\(472\) 1.48737 0.0684617
\(473\) −7.09274 1.90049i −0.326125 0.0873848i
\(474\) −2.28868 + 8.54147i −0.105123 + 0.392323i
\(475\) 0.120993 + 0.451552i 0.00555154 + 0.0207186i
\(476\) 3.75616 + 2.35806i 0.172163 + 0.108081i
\(477\) −1.78093 + 3.08467i −0.0815433 + 0.141237i
\(478\) 5.73605i 0.262361i
\(479\) 3.00600 + 11.2186i 0.137348 + 0.512589i 0.999977 + 0.00675234i \(0.00214935\pi\)
−0.862629 + 0.505836i \(0.831184\pi\)
\(480\) 2.37945 1.37378i 0.108606 0.0627040i
\(481\) −3.58783 + 2.94216i −0.163591 + 0.134151i
\(482\) 9.00015i 0.409946i
\(483\) 0.675694 + 1.27724i 0.0307451 + 0.0581164i
\(484\) 3.04124 + 5.26759i 0.138238 + 0.239436i
\(485\) 38.4458 22.1967i 1.74573 1.00790i
\(486\) 0.258819 0.965926i 0.0117403 0.0438153i
\(487\) 7.41455 7.41455i 0.335986 0.335986i −0.518869 0.854854i \(-0.673647\pi\)
0.854854 + 0.518869i \(0.173647\pi\)
\(488\) 13.1954 + 3.53571i 0.597329 + 0.160054i
\(489\) −3.95898 + 3.95898i −0.179031 + 0.179031i
\(490\) −19.1802 1.42195i −0.866474 0.0642370i
\(491\) −3.98650 + 2.30160i −0.179908 + 0.103870i −0.587249 0.809406i \(-0.699789\pi\)
0.407341 + 0.913276i \(0.366456\pi\)
\(492\) −3.62768 3.62768i −0.163548 0.163548i
\(493\) 3.65660 + 6.33341i 0.164685 + 0.285243i
\(494\) −0.602405 + 0.272668i −0.0271035 + 0.0122679i
\(495\) 5.27654 + 3.04641i 0.237163 + 0.136926i
\(496\) −2.02462 + 7.55600i −0.0909083 + 0.339274i
\(497\) 10.2449 + 3.15566i 0.459547 + 0.141550i
\(498\) −13.9124 8.03232i −0.623429 0.359937i
\(499\) 3.26150 + 12.1721i 0.146005 + 0.544897i 0.999709 + 0.0241385i \(0.00768426\pi\)
−0.853704 + 0.520759i \(0.825649\pi\)
\(500\) 4.76177 + 4.76177i 0.212953 + 0.212953i
\(501\) 5.03888 + 5.03888i 0.225121 + 0.225121i
\(502\) 4.02329 + 15.0151i 0.179568 + 0.670159i
\(503\) −25.3394 14.6297i −1.12983 0.652306i −0.185936 0.982562i \(-0.559532\pi\)
−0.943891 + 0.330256i \(0.892865\pi\)
\(504\) −1.80034 1.93875i −0.0801936 0.0863590i
\(505\) −11.2859 + 42.1197i −0.502218 + 1.87430i
\(506\) −1.04884 0.605549i −0.0466267 0.0269199i
\(507\) 9.76735 + 8.57898i 0.433783 + 0.381006i
\(508\) −6.68890 11.5855i −0.296772 0.514024i
\(509\) −17.3157 17.3157i −0.767504 0.767504i 0.210163 0.977666i \(-0.432601\pi\)
−0.977666 + 0.210163i \(0.932601\pi\)
\(510\) 3.98859 2.30282i 0.176618 0.101970i
\(511\) 17.2090 15.9804i 0.761280 0.706931i
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) 0.177146 + 0.0474662i 0.00782120 + 0.00209568i
\(514\) 5.07038 5.07038i 0.223645 0.223645i
\(515\) −6.73195 + 25.1240i −0.296645 + 1.10710i
\(516\) 2.86766 1.65565i 0.126242 0.0728858i
\(517\) 11.1896 + 19.3810i 0.492118 + 0.852374i
\(518\) 1.81029 2.88362i 0.0795397 0.126699i
\(519\) 2.84253i 0.124773i
\(520\) 5.77336 8.05020i 0.253179 0.353025i
\(521\) 7.83904 4.52587i 0.343434 0.198282i −0.318355 0.947971i \(-0.603131\pi\)
0.661790 + 0.749690i \(0.269797\pi\)
\(522\) −1.12917 4.21412i −0.0494225 0.184447i
\(523\) 6.35492i 0.277881i 0.990301 + 0.138941i \(0.0443697\pi\)
−0.990301 + 0.138941i \(0.955630\pi\)
\(524\) 9.69509 16.7924i 0.423532 0.733579i
\(525\) −3.58580 + 5.71183i −0.156497 + 0.249285i
\(526\) 1.86870 + 6.97407i 0.0814790 + 0.304084i
\(527\) −3.39381 + 12.6659i −0.147837 + 0.551734i
\(528\) 2.14199 + 0.573943i 0.0932180 + 0.0249777i
\(529\) 22.7017 0.987032
\(530\) 9.78641 0.425094
\(531\) −1.43669 0.384959i −0.0623469 0.0167058i
\(532\) 0.355558 0.330174i 0.0154154 0.0143149i
\(533\) −17.3095 6.52241i −0.749759 0.282517i
\(534\) 8.04447 13.9334i 0.348118 0.602958i
\(535\) 8.51620 2.28191i 0.368188 0.0986556i
\(536\) −3.52425 + 6.10419i −0.152225 + 0.263661i
\(537\) 12.7690 + 22.1165i 0.551022 + 0.954399i
\(538\) −1.42419 1.42419i −0.0614010 0.0614010i
\(539\) −10.1347 11.7578i −0.436534 0.506443i
\(540\) −2.65393 + 0.711118i −0.114207 + 0.0306017i
\(541\) 1.59127 0.426380i 0.0684142 0.0183315i −0.224450 0.974486i \(-0.572058\pi\)
0.292864 + 0.956154i \(0.405392\pi\)
\(542\) 22.9065i 0.983917i
\(543\) −13.9617 8.06081i −0.599155 0.345923i
\(544\) 1.18530 1.18530i 0.0508194 0.0508194i
\(545\) 25.8577 1.10762
\(546\) −8.79615 3.69158i −0.376440 0.157985i
\(547\) 30.4255 1.30090 0.650451 0.759548i \(-0.274580\pi\)
0.650451 + 0.759548i \(0.274580\pi\)
\(548\) −9.80752 + 9.80752i −0.418956 + 0.418956i
\(549\) −11.8307 6.83046i −0.504922 0.291517i
\(550\) 5.65260i 0.241028i
\(551\) 0.772850 0.207085i 0.0329245 0.00882210i
\(552\) 0.527533 0.141352i 0.0224533 0.00601635i
\(553\) −10.9404 20.6802i −0.465233 0.879413i
\(554\) 18.0695 + 18.0695i 0.767702 + 0.767702i
\(555\) −1.76789 3.06207i −0.0750426 0.129978i
\(556\) −7.91444 + 13.7082i −0.335647 + 0.581358i
\(557\) −32.4300 + 8.68959i −1.37410 + 0.368190i −0.868976 0.494855i \(-0.835221\pi\)
−0.505127 + 0.863045i \(0.668555\pi\)
\(558\) 3.91127 6.77452i 0.165577 0.286788i
\(559\) 6.95794 9.70194i 0.294289 0.410348i
\(560\) −2.13990 + 6.94723i −0.0904272 + 0.293574i
\(561\) 3.59054 + 0.962083i 0.151593 + 0.0406192i
\(562\) −14.3237 −0.604210
\(563\) 16.0093 0.674710 0.337355 0.941378i \(-0.390468\pi\)
0.337355 + 0.941378i \(0.390468\pi\)
\(564\) −9.74801 2.61197i −0.410465 0.109984i
\(565\) 2.57444 9.60796i 0.108308 0.404210i
\(566\) −7.87019 29.3719i −0.330809 1.23459i
\(567\) 1.23721 + 2.33866i 0.0519580 + 0.0982143i
\(568\) 2.02587 3.50891i 0.0850037 0.147231i
\(569\) 4.60867i 0.193205i −0.995323 0.0966027i \(-0.969202\pi\)
0.995323 0.0966027i \(-0.0307976\pi\)
\(570\) −0.130416 0.486718i −0.00546251 0.0203864i
\(571\) −22.7993 + 13.1632i −0.954120 + 0.550861i −0.894358 0.447352i \(-0.852367\pi\)
−0.0597613 + 0.998213i \(0.519034\pi\)
\(572\) 7.88918 1.29941i 0.329863 0.0543309i
\(573\) 1.63311i 0.0682242i
\(574\) 13.5642 + 0.502111i 0.566160 + 0.0209577i
\(575\) −0.696068 1.20563i −0.0290281 0.0502781i
\(576\) −0.866025 + 0.500000i −0.0360844 + 0.0208333i
\(577\) 10.6250 39.6530i 0.442324 1.65078i −0.280582 0.959830i \(-0.590528\pi\)
0.722907 0.690946i \(-0.242806\pi\)
\(578\) −10.0339 + 10.0339i −0.417357 + 0.417357i
\(579\) 9.13997 + 2.44905i 0.379844 + 0.101779i
\(580\) −8.47606 + 8.47606i −0.351949 + 0.351949i
\(581\) 41.4336 9.47438i 1.71896 0.393063i
\(582\) −13.9928 + 8.07872i −0.580019 + 0.334874i
\(583\) 5.58516 + 5.58516i 0.231314 + 0.231314i
\(584\) −4.43815 7.68711i −0.183652 0.318095i
\(585\) −7.66018 + 6.28164i −0.316710 + 0.259714i
\(586\) −6.31494 3.64593i −0.260868 0.150612i
\(587\) −6.32248 + 23.5958i −0.260957 + 0.973904i 0.703722 + 0.710475i \(0.251520\pi\)
−0.964679 + 0.263429i \(0.915147\pi\)
\(588\) 6.98084 + 0.517532i 0.287885 + 0.0213427i
\(589\) 1.24242 + 0.717309i 0.0511928 + 0.0295562i
\(590\) 1.05770 + 3.94737i 0.0435446 + 0.162511i
\(591\) −8.02977 8.02977i −0.330301 0.330301i
\(592\) −0.909963 0.909963i −0.0373992 0.0373992i
\(593\) 9.55230 + 35.6497i 0.392266 + 1.46396i 0.826387 + 0.563103i \(0.190392\pi\)
−0.434121 + 0.900855i \(0.642941\pi\)
\(594\) −1.92045 1.10877i −0.0787971 0.0454935i
\(595\) −3.58704 + 11.6454i −0.147054 + 0.477416i
\(596\) 3.72381 13.8974i 0.152533 0.569261i
\(597\) 15.6791 + 9.05233i 0.641702 + 0.370487i
\(598\) 1.52265 1.24863i 0.0622657 0.0510603i
\(599\) −2.06623 3.57882i −0.0844240 0.146227i 0.820722 0.571328i \(-0.193572\pi\)
−0.905146 + 0.425102i \(0.860238\pi\)
\(600\) 1.80244 + 1.80244i 0.0735843 + 0.0735843i
\(601\) −19.4142 + 11.2088i −0.791923 + 0.457217i −0.840639 0.541596i \(-0.817820\pi\)
0.0487163 + 0.998813i \(0.484487\pi\)
\(602\) −2.57896 + 8.37267i −0.105111 + 0.341244i
\(603\) 4.98405 4.98405i 0.202966 0.202966i
\(604\) 2.24796 + 0.602340i 0.0914683 + 0.0245089i
\(605\) −11.8171 + 11.8171i −0.480434 + 0.480434i
\(606\) 4.10764 15.3299i 0.166861 0.622735i
\(607\) 15.0088 8.66532i 0.609187 0.351715i −0.163460 0.986550i \(-0.552265\pi\)
0.772647 + 0.634835i \(0.218932\pi\)
\(608\) −0.0916976 0.158825i −0.00371883 0.00644120i
\(609\) 9.77605 + 6.13725i 0.396146 + 0.248694i
\(610\) 37.5341i 1.51971i
\(611\) −35.9031 + 5.91350i −1.45248 + 0.239234i
\(612\) −1.45169 + 0.838134i −0.0586811 + 0.0338796i
\(613\) −9.95649 37.1581i −0.402139 1.50080i −0.809272 0.587434i \(-0.800138\pi\)
0.407133 0.913369i \(-0.366529\pi\)
\(614\) 1.47260i 0.0594295i
\(615\) 7.04790 12.2073i 0.284199 0.492246i
\(616\) −5.18608 + 2.74357i −0.208953 + 0.110542i
\(617\) 9.83501 + 36.7048i 0.395943 + 1.47768i 0.820169 + 0.572121i \(0.193879\pi\)
−0.424226 + 0.905556i \(0.639454\pi\)
\(618\) 2.45017 9.14414i 0.0985601 0.367831i
\(619\) −22.9453 6.14818i −0.922250 0.247116i −0.233703 0.972308i \(-0.575084\pi\)
−0.688547 + 0.725192i \(0.741751\pi\)
\(620\) −21.4928 −0.863173
\(621\) −0.546143 −0.0219160
\(622\) −19.9083 5.33442i −0.798251 0.213891i
\(623\) 9.48870 + 41.4963i 0.380157 + 1.66251i
\(624\) −2.10128 + 2.92996i −0.0841183 + 0.117292i
\(625\) −15.6238 + 27.0612i −0.624952 + 1.08245i
\(626\) −9.88803 + 2.64949i −0.395205 + 0.105895i
\(627\) 0.203344 0.352202i 0.00812077 0.0140656i
\(628\) −2.66874 4.62239i −0.106494 0.184453i
\(629\) −1.52534 1.52534i −0.0608193 0.0608193i
\(630\) 3.86506 6.15667i 0.153988 0.245287i
\(631\) −38.9228 + 10.4293i −1.54949 + 0.415185i −0.929318 0.369280i \(-0.879604\pi\)
−0.620173 + 0.784465i \(0.712937\pi\)
\(632\) −8.54147 + 2.28868i −0.339762 + 0.0910388i
\(633\) 0.0181383i 0.000720934i
\(634\) 0.322577 + 0.186240i 0.0128112 + 0.00739654i
\(635\) 25.9905 25.9905i 1.03140 1.03140i
\(636\) −3.56187 −0.141237
\(637\) 23.6997 8.67901i 0.939015 0.343875i
\(638\) −9.67467 −0.383024
\(639\) −2.86502 + 2.86502i −0.113338 + 0.113338i
\(640\) 2.37945 + 1.37378i 0.0940560 + 0.0543032i
\(641\) 43.9676i 1.73661i −0.496026 0.868307i \(-0.665208\pi\)
0.496026 0.868307i \(-0.334792\pi\)
\(642\) −3.09956 + 0.830525i −0.122330 + 0.0327782i
\(643\) 25.5889 6.85652i 1.00913 0.270395i 0.283863 0.958865i \(-0.408384\pi\)
0.725265 + 0.688470i \(0.241717\pi\)
\(644\) −0.768275 + 1.22379i −0.0302743 + 0.0482240i
\(645\) 6.43322 + 6.43322i 0.253308 + 0.253308i
\(646\) −0.153710 0.266233i −0.00604763 0.0104748i
\(647\) −15.8044 + 27.3741i −0.621337 + 1.07619i 0.367900 + 0.929865i \(0.380077\pi\)
−0.989237 + 0.146321i \(0.953257\pi\)
\(648\) 0.965926 0.258819i 0.0379452 0.0101674i
\(649\) −1.64915 + 2.85642i −0.0647350 + 0.112124i
\(650\) 8.60037 + 3.24071i 0.337334 + 0.127111i
\(651\) 4.61347 + 20.1758i 0.180816 + 0.790750i
\(652\) −5.40806 1.44909i −0.211796 0.0567506i
\(653\) −0.955783 −0.0374027 −0.0187013 0.999825i \(-0.505953\pi\)
−0.0187013 + 0.999825i \(0.505953\pi\)
\(654\) −9.41117 −0.368006
\(655\) 51.4602 + 13.7887i 2.01071 + 0.538769i
\(656\) 1.32782 4.95550i 0.0518428 0.193480i
\(657\) 2.29736 + 8.57385i 0.0896284 + 0.334498i
\(658\) 23.6014 12.4858i 0.920080 0.486747i
\(659\) −12.1342 + 21.0171i −0.472681 + 0.818708i −0.999511 0.0312626i \(-0.990047\pi\)
0.526830 + 0.849971i \(0.323381\pi\)
\(660\) 6.09282i 0.237163i
\(661\) 5.48656 + 20.4761i 0.213403 + 0.796429i 0.986723 + 0.162413i \(0.0519278\pi\)
−0.773320 + 0.634016i \(0.781406\pi\)
\(662\) 11.5345 6.65946i 0.448302 0.258827i
\(663\) −3.52230 + 4.91139i −0.136795 + 0.190743i
\(664\) 16.0646i 0.623429i
\(665\) 1.12910 + 0.708834i 0.0437848 + 0.0274874i
\(666\) 0.643441 + 1.11447i 0.0249328 + 0.0431849i
\(667\) −2.06348 + 1.19135i −0.0798983 + 0.0461293i
\(668\) −1.84436 + 6.88324i −0.0713604 + 0.266321i
\(669\) −10.1640 + 10.1640i −0.392962 + 0.392962i
\(670\) −18.7062 5.01232i −0.722685 0.193643i
\(671\) −21.4209 + 21.4209i −0.826945 + 0.826945i
\(672\) 0.778839 2.52852i 0.0300444 0.0975398i
\(673\) 35.5408 20.5195i 1.37000 0.790969i 0.379070 0.925368i \(-0.376244\pi\)
0.990927 + 0.134399i \(0.0429105\pi\)
\(674\) −16.1468 16.1468i −0.621950 0.621950i
\(675\) −1.27452 2.20753i −0.0490562 0.0849678i
\(676\) −2.54594 + 12.7483i −0.0979207 + 0.490318i
\(677\) −3.46230 1.99896i −0.133067 0.0768264i 0.431989 0.901879i \(-0.357812\pi\)
−0.565056 + 0.825053i \(0.691145\pi\)
\(678\) −0.936996 + 3.49692i −0.0359851 + 0.134298i
\(679\) 12.5840 40.8544i 0.482931 1.56785i
\(680\) 3.98859 + 2.30282i 0.152956 + 0.0883090i
\(681\) 1.07187 + 4.00027i 0.0410741 + 0.153291i
\(682\) −12.2661 12.2661i −0.469692 0.469692i
\(683\) −8.30922 8.30922i −0.317944 0.317944i 0.530033 0.847977i \(-0.322179\pi\)
−0.847977 + 0.530033i \(0.822179\pi\)
\(684\) 0.0474662 + 0.177146i 0.00181492 + 0.00677336i
\(685\) −33.0028 19.0542i −1.26097 0.728022i
\(686\) −14.4659 + 11.5645i −0.552309 + 0.441536i
\(687\) −2.25923 + 8.43158i −0.0861952 + 0.321685i
\(688\) 2.86766 + 1.65565i 0.109329 + 0.0631209i
\(689\) −11.6998 + 5.29571i −0.445727 + 0.201750i
\(690\) 0.750277 + 1.29952i 0.0285626 + 0.0494718i
\(691\) 20.4063 + 20.4063i 0.776292 + 0.776292i 0.979198 0.202906i \(-0.0650385\pi\)
−0.202906 + 0.979198i \(0.565039\pi\)
\(692\) 2.46170 1.42127i 0.0935799 0.0540284i
\(693\) 5.71946 1.30783i 0.217264 0.0496805i
\(694\) 10.5234 10.5234i 0.399463 0.399463i
\(695\) −42.0088 11.2562i −1.59348 0.426972i
\(696\) 3.08495 3.08495i 0.116935 0.116935i
\(697\) 2.22579 8.30675i 0.0843077 0.314641i
\(698\) −8.61163 + 4.97193i −0.325955 + 0.188190i
\(699\) −3.30937 5.73199i −0.125172 0.216804i
\(700\) −6.73949 0.249478i −0.254729 0.00942937i
\(701\) 8.49261i 0.320761i −0.987055 0.160381i \(-0.948728\pi\)
0.987055 0.160381i \(-0.0512722\pi\)
\(702\) 2.78800 2.28627i 0.105226 0.0862897i
\(703\) −0.204389 + 0.118004i −0.00770867 + 0.00445060i
\(704\) 0.573943 + 2.14199i 0.0216313 + 0.0807291i
\(705\) 27.7280i 1.04430i
\(706\) 10.8476 18.7886i 0.408256 0.707119i
\(707\) 19.6354 + 37.1161i 0.738465 + 1.39589i
\(708\) −0.384959 1.43669i −0.0144677 0.0539940i
\(709\) 9.84414 36.7388i 0.369704 1.37976i −0.491225 0.871032i \(-0.663451\pi\)
0.860930 0.508724i \(-0.169882\pi\)
\(710\) 10.7530 + 2.88127i 0.403555 + 0.108132i
\(711\) 8.84278 0.331630
\(712\) 16.0889 0.602958
\(713\) −4.12665 1.10573i −0.154544 0.0414100i
\(714\) 1.30554 4.23848i 0.0488587 0.158621i
\(715\) 9.05868 + 20.0133i 0.338775 + 0.748455i
\(716\) −12.7690 + 22.1165i −0.477199 + 0.826534i
\(717\) 5.54060 1.48460i 0.206917 0.0554434i
\(718\) −13.1466 + 22.7705i −0.490626 + 0.849789i
\(719\) −23.9854 41.5439i −0.894503 1.54932i −0.834419 0.551131i \(-0.814196\pi\)
−0.0600843 0.998193i \(-0.519137\pi\)
\(720\) −1.94281 1.94281i −0.0724043 0.0724043i
\(721\) 11.7123 + 22.1394i 0.436190 + 0.824513i
\(722\) 18.3201 4.90886i 0.681804 0.182689i
\(723\) −8.69348 + 2.32941i −0.323314 + 0.0866317i
\(724\) 16.1216i 0.599155i
\(725\) −9.63097 5.56044i −0.357685 0.206510i
\(726\) 4.30097 4.30097i 0.159624 0.159624i
\(727\) −29.5720 −1.09677 −0.548383 0.836227i \(-0.684756\pi\)
−0.548383 + 0.836227i \(0.684756\pi\)
\(728\) −1.20107 9.46348i −0.0445146 0.350740i
\(729\) −1.00000 −0.0370370
\(730\) 17.2450 17.2450i 0.638266 0.638266i
\(731\) 4.80697 + 2.77531i 0.177792 + 0.102648i
\(732\) 13.6609i 0.504922i
\(733\) 32.8929 8.81361i 1.21493 0.325538i 0.406233 0.913770i \(-0.366842\pi\)
0.808693 + 0.588232i \(0.200176\pi\)
\(734\) −8.69773 + 2.33055i −0.321039 + 0.0860221i
\(735\) 3.59071 + 18.8947i 0.132445 + 0.696941i
\(736\) 0.386181 + 0.386181i 0.0142348 + 0.0142348i
\(737\) −7.81520 13.5363i −0.287876 0.498617i
\(738\) −2.56516 + 4.44298i −0.0944247 + 0.163548i
\(739\) 18.6177 4.98861i 0.684865 0.183509i 0.100423 0.994945i \(-0.467980\pi\)
0.584441 + 0.811436i \(0.301314\pi\)
\(740\) 1.76789 3.06207i 0.0649888 0.112564i
\(741\) 0.419291 + 0.511307i 0.0154030 + 0.0187833i
\(742\) 6.90558 6.41258i 0.253512 0.235413i
\(743\) −40.9049 10.9604i −1.50065 0.402099i −0.587335 0.809344i \(-0.699823\pi\)
−0.913319 + 0.407245i \(0.866490\pi\)
\(744\) 7.82254 0.286788
\(745\) 39.5309 1.44830
\(746\) 25.8205 + 6.91859i 0.945357 + 0.253308i
\(747\) −4.15784 + 15.5173i −0.152127 + 0.567747i
\(748\) 0.962083 + 3.59054i 0.0351772 + 0.131283i
\(749\) 4.51406 7.19046i 0.164940 0.262734i
\(750\) 3.36708 5.83195i 0.122948 0.212953i
\(751\) 1.51788i 0.0553884i −0.999616 0.0276942i \(-0.991184\pi\)
0.999616 0.0276942i \(-0.00881646\pi\)
\(752\) −2.61197 9.74801i −0.0952488 0.355473i
\(753\) 13.4622 7.77241i 0.490590 0.283242i
\(754\) 5.54661 14.7199i 0.201996 0.536067i
\(755\) 6.39427i 0.232711i
\(756\) −1.40673 + 2.24078i −0.0511623 + 0.0814965i
\(757\) 10.3621 + 17.9476i 0.376616 + 0.652318i 0.990568 0.137026i \(-0.0437542\pi\)
−0.613951 + 0.789344i \(0.710421\pi\)
\(758\) −9.48961 + 5.47883i −0.344678 + 0.199000i
\(759\) −0.313455 + 1.16983i −0.0113777 + 0.0424621i
\(760\) 0.356302 0.356302i 0.0129244 0.0129244i
\(761\) 10.1812 + 2.72805i 0.369069 + 0.0988918i 0.438587 0.898689i \(-0.355479\pi\)
−0.0695173 + 0.997581i \(0.522146\pi\)
\(762\) −9.45953 + 9.45953i −0.342683 + 0.342683i
\(763\) 18.2459 16.9433i 0.660547 0.613390i
\(764\) −1.41432 + 0.816556i −0.0511682 + 0.0295419i
\(765\) −3.25667 3.25667i −0.117745 0.117745i
\(766\) −11.6674 20.2086i −0.421562 0.730166i
\(767\) −3.40053 4.14679i −0.122786 0.149732i
\(768\) −0.866025 0.500000i −0.0312500 0.0180422i
\(769\) −1.89366 + 7.06724i −0.0682871 + 0.254851i −0.991627 0.129132i \(-0.958781\pi\)
0.923340 + 0.383983i \(0.125448\pi\)
\(770\) −10.9692 11.8125i −0.395301 0.425692i
\(771\) −6.20992 3.58530i −0.223645 0.129121i
\(772\) 2.44905 + 9.13997i 0.0881432 + 0.328955i
\(773\) −29.0097 29.0097i −1.04341 1.04341i −0.999014 0.0443932i \(-0.985865\pi\)
−0.0443932 0.999014i \(-0.514135\pi\)
\(774\) −2.34144 2.34144i −0.0841612 0.0841612i
\(775\) −5.16083 19.2605i −0.185383 0.691857i
\(776\) −13.9928 8.07872i −0.502311 0.290009i
\(777\) −3.25390 1.00227i −0.116733 0.0359563i
\(778\) 7.27893 27.1653i 0.260962 0.973924i
\(779\) −0.814822 0.470438i −0.0291940 0.0168552i
\(780\) −9.27015 3.49309i −0.331925 0.125073i
\(781\) 4.49247 + 7.78118i 0.160753 + 0.278433i
\(782\) 0.647343 + 0.647343i 0.0231490 + 0.0231490i
\(783\) −3.77828 + 2.18139i −0.135025 + 0.0779566i
\(784\) 3.04223 + 6.30435i 0.108651 + 0.225155i
\(785\) 10.3697 10.3697i 0.370111 0.370111i
\(786\) −18.7295 5.01855i −0.668058 0.179006i
\(787\) 36.8103 36.8103i 1.31214 1.31214i 0.392312 0.919832i \(-0.371675\pi\)
0.919832 0.392312i \(-0.128325\pi\)
\(788\) 2.93910 10.9689i 0.104701 0.390750i
\(789\) 6.25278 3.61004i 0.222605 0.128521i
\(790\) −12.1480 21.0409i −0.432206 0.748603i
\(791\) −4.47905 8.46658i −0.159257 0.301037i
\(792\) 2.21755i 0.0787971i
\(793\) −20.3108 44.8725i −0.721256 1.59347i
\(794\) −18.9260 + 10.9269i −0.671659 + 0.387783i
\(795\) −2.53291 9.45295i −0.0898330 0.335261i
\(796\) 18.1047i 0.641702i
\(797\) −9.81837 + 17.0059i −0.347784 + 0.602380i −0.985856 0.167597i \(-0.946399\pi\)
0.638071 + 0.769977i \(0.279733\pi\)
\(798\) −0.410949 0.257988i −0.0145474 0.00913266i
\(799\) −4.37836 16.3403i −0.154895 0.578078i
\(800\) −0.659739 + 2.46218i −0.0233253 + 0.0870511i
\(801\) −15.5407 4.16412i −0.549104 0.147132i
\(802\) 20.5569 0.725888
\(803\) 19.6836 0.694620
\(804\) 6.80833 + 1.82429i 0.240111 + 0.0643377i
\(805\) −3.79418 1.16869i −0.133727 0.0411909i
\(806\) 25.6950 11.6304i 0.905067 0.409663i
\(807\) −1.00705 + 1.74426i −0.0354499 + 0.0614010i
\(808\) 15.3299 4.10764i 0.539304 0.144506i
\(809\) 7.51268 13.0123i 0.264132 0.457490i −0.703204 0.710988i \(-0.748248\pi\)
0.967336 + 0.253498i \(0.0815813\pi\)
\(810\) 1.37378 + 2.37945i 0.0482695 + 0.0836053i
\(811\) −22.5797 22.5797i −0.792880 0.792880i 0.189081 0.981961i \(-0.439449\pi\)
−0.981961 + 0.189081i \(0.939449\pi\)
\(812\) −0.426992 + 11.5349i −0.0149845 + 0.404797i
\(813\) 22.1259 5.92863i 0.775991 0.207926i
\(814\) 2.75648 0.738597i 0.0966146 0.0258878i
\(815\) 15.3831i 0.538846i
\(816\) −1.45169 0.838134i −0.0508194 0.0293406i
\(817\) 0.429409 0.429409i 0.0150231 0.0150231i
\(818\) −39.5402 −1.38249
\(819\) −1.28918 + 9.45188i −0.0450478 + 0.330275i
\(820\) 14.0958 0.492246
\(821\) 38.8105 38.8105i 1.35450 1.35450i 0.473938 0.880558i \(-0.342832\pi\)
0.880558 0.473938i \(-0.157168\pi\)
\(822\) 12.0117 + 6.93496i 0.418956 + 0.241885i
\(823\) 49.2059i 1.71521i −0.514308 0.857606i \(-0.671951\pi\)
0.514308 0.857606i \(-0.328049\pi\)
\(824\) 9.14414 2.45017i 0.318551 0.0853555i
\(825\) −5.45999 + 1.46300i −0.190093 + 0.0509352i
\(826\) 3.33287 + 2.09232i 0.115965 + 0.0728013i
\(827\) 7.82426 + 7.82426i 0.272076 + 0.272076i 0.829936 0.557859i \(-0.188377\pi\)
−0.557859 + 0.829936i \(0.688377\pi\)
\(828\) −0.273071 0.472973i −0.00948989 0.0164370i
\(829\) −5.52185 + 9.56413i −0.191782 + 0.332176i −0.945841 0.324631i \(-0.894760\pi\)
0.754059 + 0.656807i \(0.228093\pi\)
\(830\) 42.6345 11.4239i 1.47986 0.396528i
\(831\) 12.7771 22.1306i 0.443233 0.767702i
\(832\) −3.58805 0.354780i −0.124393 0.0122998i
\(833\) 5.09959 + 10.5678i 0.176690 + 0.366152i
\(834\) 15.2895 + 4.09682i 0.529433 + 0.141861i
\(835\) −19.5792 −0.677566
\(836\) 0.406688 0.0140656
\(837\) −7.55600 2.02462i −0.261173 0.0699812i
\(838\) 5.79710 21.6351i 0.200257 0.747371i
\(839\) −0.556614 2.07731i −0.0192164 0.0717167i 0.955652 0.294499i \(-0.0951528\pi\)
−0.974868 + 0.222782i \(0.928486\pi\)
\(840\) 7.26436 + 0.268907i 0.250644 + 0.00927816i
\(841\) 4.98306 8.63092i 0.171830 0.297618i
\(842\) 7.23817i 0.249444i
\(843\) 3.70725 + 13.8356i 0.127684 + 0.476525i
\(844\) 0.0157083 0.00906917i 0.000540701 0.000312174i
\(845\) −35.6435 + 2.30878i −1.22617 + 0.0794245i
\(846\) 10.0919i 0.346966i
\(847\) −0.595301 + 16.0817i −0.0204548 + 0.552575i
\(848\) −1.78093 3.08467i −0.0611575 0.105928i
\(849\) −26.3342 + 15.2040i −0.903786 + 0.521801i
\(850\) −1.10590 + 4.12727i −0.0379320 + 0.141564i
\(851\) 0.496969 0.496969i 0.0170359 0.0170359i
\(852\) −3.91368 1.04867i −0.134081 0.0359268i
\(853\) 27.5693 27.5693i 0.943954 0.943954i −0.0545571 0.998511i \(-0.517375\pi\)
0.998511 + 0.0545571i \(0.0173747\pi\)
\(854\) 24.5943 + 26.4852i 0.841601 + 0.906304i
\(855\) −0.436380 + 0.251944i −0.0149239 + 0.00861630i
\(856\) −2.26904 2.26904i −0.0775541 0.0775541i
\(857\) 10.0100 + 17.3379i 0.341936 + 0.592251i 0.984792 0.173736i \(-0.0555839\pi\)
−0.642856 + 0.765987i \(0.722251\pi\)
\(858\) −3.29700 7.28406i −0.112558 0.248674i
\(859\) −22.5936 13.0444i −0.770884 0.445070i 0.0623061 0.998057i \(-0.480155\pi\)
−0.833190 + 0.552987i \(0.813488\pi\)
\(860\) −2.35472 + 8.78794i −0.0802953 + 0.299666i
\(861\) −3.02568 13.2320i −0.103115 0.450946i
\(862\) −32.6729 18.8637i −1.11284 0.642500i
\(863\) −9.36095 34.9355i −0.318651 1.18922i −0.920543 0.390642i \(-0.872253\pi\)
0.601892 0.798578i \(-0.294414\pi\)
\(864\) 0.707107 + 0.707107i 0.0240563 + 0.0240563i
\(865\) 5.52250 + 5.52250i 0.187771 + 0.187771i
\(866\) 9.55198 + 35.6485i 0.324590 + 1.21138i
\(867\) 12.2890 + 7.09506i 0.417357 + 0.240961i
\(868\) −15.1660 + 14.0833i −0.514767 + 0.478017i
\(869\) 5.07526 18.9411i 0.172166 0.642533i
\(870\) 10.3810 + 5.99348i 0.351949 + 0.203198i
\(871\) 25.0759 4.13018i 0.849664 0.139946i
\(872\) −4.70559 8.15031i −0.159351 0.276004i
\(873\) 11.4250 + 11.4250i 0.386679 + 0.386679i
\(874\) 0.0867411 0.0500800i 0.00293406 0.00169398i
\(875\) 3.97157 + 17.3686i 0.134264 + 0.587166i
\(876\) −6.27650 + 6.27650i −0.212063 + 0.212063i
\(877\) −23.6532 6.33785i −0.798711 0.214014i −0.163693 0.986511i \(-0.552341\pi\)
−0.635018 + 0.772497i \(0.719007\pi\)
\(878\) 7.18827 7.18827i 0.242592 0.242592i
\(879\) −1.88727 + 7.04340i −0.0636562 + 0.237568i
\(880\) −5.27654 + 3.04641i −0.177872 + 0.102694i
\(881\) −0.802614 1.39017i −0.0270407 0.0468359i 0.852188 0.523235i \(-0.175275\pi\)
−0.879229 + 0.476399i \(0.841942\pi\)
\(882\) −1.30688 6.87692i −0.0440048 0.231558i
\(883\) 38.8748i 1.30824i 0.756391 + 0.654120i \(0.226961\pi\)
−0.756391 + 0.654120i \(0.773039\pi\)
\(884\) −6.01454 0.594706i −0.202291 0.0200021i
\(885\) 3.53912 2.04331i 0.118966 0.0686851i
\(886\) 0.529130 + 1.97474i 0.0177765 + 0.0663427i
\(887\) 54.9310i 1.84440i −0.386710 0.922201i \(-0.626389\pi\)
0.386710 0.922201i \(-0.373611\pi\)
\(888\) −0.643441 + 1.11447i −0.0215925 + 0.0373992i
\(889\) 1.30930 35.3701i 0.0439126 1.18628i
\(890\) 11.4411 + 42.6989i 0.383508 + 1.43127i
\(891\) −0.573943 + 2.14199i −0.0192278 + 0.0717592i
\(892\) −13.8843 3.72027i −0.464879 0.124564i
\(893\) −1.85080 −0.0619348
\(894\) −14.3877 −0.481196
\(895\) −67.7760 18.1605i −2.26550 0.607039i
\(896\) 2.57918 0.589766i 0.0861644 0.0197027i
\(897\) −1.60017 1.14760i −0.0534283 0.0383171i
\(898\) −10.0058 + 17.3306i −0.333899 + 0.578329i
\(899\) −32.9652 + 8.83299i −1.09945 + 0.294597i
\(900\) 1.27452 2.20753i 0.0424839 0.0735843i
\(901\) −2.98532 5.17073i −0.0994555 0.172262i
\(902\) 8.04455 + 8.04455i 0.267854 + 0.267854i
\(903\) 8.75486 + 0.324081i 0.291344 + 0.0107847i
\(904\) −3.49692 + 0.936996i −0.116306 + 0.0311640i
\(905\) 42.7857 11.4644i 1.42224 0.381089i
\(906\) 2.32726i 0.0773181i
\(907\) 9.42391 + 5.44089i 0.312916 + 0.180662i 0.648230 0.761444i \(-0.275509\pi\)
−0.335315 + 0.942106i \(0.608843\pi\)
\(908\) −2.92840 + 2.92840i −0.0971824 + 0.0971824i
\(909\) −15.8707 −0.526398
\(910\) 24.2613 9.91721i 0.804255 0.328752i
\(911\) −42.6469 −1.41296 −0.706478 0.707735i \(-0.749717\pi\)
−0.706478 + 0.707735i \(0.749717\pi\)
\(912\) −0.129680 + 0.129680i −0.00429414 + 0.00429414i
\(913\) 30.8514 + 17.8121i 1.02103 + 0.589493i
\(914\) 33.0047i 1.09170i
\(915\) 36.2551 9.71453i 1.19856 0.321153i
\(916\) −8.43158 + 2.25923i −0.278587 + 0.0746472i
\(917\) 45.3469 23.9897i 1.49749 0.792211i
\(918\) 1.18530 + 1.18530i 0.0391208 + 0.0391208i
\(919\) 7.60332 + 13.1693i 0.250810 + 0.434416i 0.963749 0.266810i \(-0.0859696\pi\)
−0.712939 + 0.701226i \(0.752636\pi\)
\(920\) −0.750277 + 1.29952i −0.0247359 + 0.0428439i
\(921\) −1.42243 + 0.381138i −0.0468706 + 0.0125589i
\(922\) 7.11085 12.3164i 0.234183 0.405618i
\(923\) −14.4146 + 2.37418i −0.474461 + 0.0781472i
\(924\) 3.99234 + 4.29928i 0.131338 + 0.141436i
\(925\) 3.16853 + 0.849005i 0.104181 + 0.0279151i
\(926\) −21.7639 −0.715207
\(927\) −9.46671 −0.310928
\(928\) 4.21412 + 1.12917i 0.138335 + 0.0370669i
\(929\) 3.48112 12.9917i 0.114212 0.426244i −0.885015 0.465562i \(-0.845852\pi\)
0.999227 + 0.0393186i \(0.0125187\pi\)
\(930\) 5.56275 + 20.7605i 0.182410 + 0.680763i
\(931\) 1.26120 0.239675i 0.0413340 0.00785503i
\(932\) 3.30937 5.73199i 0.108402 0.187758i
\(933\) 20.6106i 0.674761i
\(934\) 10.5964 + 39.5464i 0.346726 + 1.29400i
\(935\) −8.84490 + 5.10660i −0.289259 + 0.167004i
\(936\) 3.37397 + 1.27135i 0.110282 + 0.0415553i
\(937\) 24.6205i 0.804315i −0.915570 0.402158i \(-0.868260\pi\)
0.915570 0.402158i \(-0.131740\pi\)
\(938\) −16.4840 + 8.72049i −0.538223 + 0.284734i
\(939\) 5.11842 + 8.86536i 0.167033 + 0.289310i
\(940\) 24.0131 13.8640i 0.783221 0.452193i
\(941\) 0.833574 3.11094i 0.0271737 0.101414i −0.951007 0.309169i \(-0.899949\pi\)
0.978181 + 0.207755i \(0.0666158\pi\)
\(942\) −3.77417 + 3.77417i −0.122969 + 0.122969i
\(943\) 2.70641 + 0.725181i 0.0881329 + 0.0236151i
\(944\) 1.05173 1.05173i 0.0342308 0.0342308i
\(945\) −6.94723 2.13990i −0.225994 0.0696109i
\(946\) −6.35918 + 3.67147i −0.206755 + 0.119370i
\(947\) 8.13118 + 8.13118i 0.264228 + 0.264228i 0.826769 0.562541i \(-0.190176\pi\)
−0.562541 + 0.826769i \(0.690176\pi\)
\(948\) 4.42139 + 7.65808i 0.143600 + 0.248723i
\(949\) −11.2849 + 29.9484i −0.366322 + 0.972166i
\(950\) 0.404850 + 0.233740i 0.0131351 + 0.00758354i
\(951\) 0.0964049 0.359788i 0.00312614 0.0116669i
\(952\) 4.32340 0.988606i 0.140122 0.0320409i
\(953\) 39.2103 + 22.6381i 1.27015 + 0.733319i 0.975015 0.222138i \(-0.0713037\pi\)
0.295130 + 0.955457i \(0.404637\pi\)
\(954\) 0.921879 + 3.44050i 0.0298469 + 0.111390i
\(955\) −3.17283 3.17283i −0.102670 0.102670i
\(956\) 4.05600 + 4.05600i 0.131180 + 0.131180i
\(957\) 2.50399 + 9.34502i 0.0809425 + 0.302082i
\(958\) 10.0583 + 5.80715i 0.324968 + 0.187620i
\(959\) −35.7731 + 8.18000i −1.15517 + 0.264146i
\(960\) 0.711118 2.65393i 0.0229512 0.0856552i
\(961\) −26.1472 15.0961i −0.843458 0.486971i
\(962\) −0.456560 + 4.61740i −0.0147201 + 0.148871i
\(963\) 1.60445 + 2.77899i 0.0517027 + 0.0895517i
\(964\) −6.36407 6.36407i −0.204973 0.204973i
\(965\) −22.5153 + 12.9992i −0.724793 + 0.418459i
\(966\) 1.38093 + 0.425357i 0.0444308 + 0.0136856i
\(967\) −31.2769 + 31.2769i −1.00580 + 1.00580i −0.00581309 + 0.999983i \(0.501850\pi\)
−0.999983 + 0.00581309i \(0.998150\pi\)
\(968\) 5.87523 + 1.57426i 0.188837 + 0.0505987i
\(969\) −0.217379 + 0.217379i −0.00698321 + 0.00698321i
\(970\) 11.4899 42.8807i 0.368917 1.37682i
\(971\) −15.6210 + 9.01878i −0.501301 + 0.289426i −0.729251 0.684247i \(-0.760131\pi\)
0.227950 + 0.973673i \(0.426798\pi\)
\(972\) −0.500000 0.866025i −0.0160375 0.0277778i
\(973\) −37.0183 + 19.5837i −1.18675 + 0.627824i
\(974\) 10.4858i 0.335986i
\(975\) 0.904346 9.14607i 0.0289623 0.292909i
\(976\) 11.8307 6.83046i 0.378692 0.218638i
\(977\) −2.68788 10.0313i −0.0859930 0.320930i 0.909507 0.415688i \(-0.136459\pi\)
−0.995500 + 0.0947576i \(0.969792\pi\)
\(978\) 5.59884i 0.179031i
\(979\) −17.8390 + 30.8980i −0.570136 + 0.987505i
\(980\) −14.5679 + 12.5570i −0.465355 + 0.401118i
\(981\) 2.43579 + 9.09049i 0.0777688 + 0.290237i
\(982\) −1.19140 + 4.44636i −0.0380190 + 0.141889i
\(983\) 22.0157 + 5.89909i 0.702192 + 0.188152i 0.592212 0.805782i \(-0.298255\pi\)
0.109980 + 0.993934i \(0.464921\pi\)
\(984\) −5.13031 −0.163548
\(985\) 31.2007 0.994136
\(986\) 7.06400 + 1.89279i 0.224964 + 0.0602788i
\(987\) −18.1688 19.5657i −0.578321 0.622782i
\(988\) −0.233159 + 0.618770i −0.00741778 + 0.0196857i
\(989\) −0.904219 + 1.56615i −0.0287525 + 0.0498008i
\(990\) 5.88521 1.57694i 0.187044 0.0501184i
\(991\) −7.76780 + 13.4542i −0.246752 + 0.427387i −0.962623 0.270846i \(-0.912697\pi\)
0.715871 + 0.698233i \(0.246030\pi\)
\(992\) 3.91127 + 6.77452i 0.124183 + 0.215091i
\(993\) −9.41790 9.41790i −0.298868 0.298868i
\(994\) 9.47563 5.01286i 0.300549 0.158998i
\(995\) −48.0485 + 12.8746i −1.52324 + 0.408151i
\(996\) −15.5173 + 4.15784i −0.491683 + 0.131746i
\(997\) 7.87487i 0.249400i −0.992195 0.124700i \(-0.960203\pi\)
0.992195 0.124700i \(-0.0397968\pi\)
\(998\) 10.9132 + 6.30073i 0.345451 + 0.199446i
\(999\) 0.909963 0.909963i 0.0287899 0.0287899i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 546.2.cg.b.145.10 yes 40
7.3 odd 6 546.2.by.b.535.10 yes 40
13.7 odd 12 546.2.by.b.397.10 40
91.59 even 12 inner 546.2.cg.b.241.10 yes 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
546.2.by.b.397.10 40 13.7 odd 12
546.2.by.b.535.10 yes 40 7.3 odd 6
546.2.cg.b.145.10 yes 40 1.1 even 1 trivial
546.2.cg.b.241.10 yes 40 91.59 even 12 inner