Properties

Label 546.2.z.a.131.12
Level $546$
Weight $2$
Character 546.131
Analytic conductor $4.360$
Analytic rank $0$
Dimension $32$
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(131,546)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(546, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 5, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("546.131");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.z (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.35983195036\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 131.12
Character \(\chi\) \(=\) 546.131
Dual form 546.2.z.a.521.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.866025 + 0.500000i) q^{2} +(0.110315 + 1.72853i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.50901 + 2.61368i) q^{5} +(-0.768732 + 1.55211i) q^{6} +(0.237102 - 2.63511i) q^{7} +1.00000i q^{8} +(-2.97566 + 0.381366i) q^{9} +O(q^{10})\) \(q+(0.866025 + 0.500000i) q^{2} +(0.110315 + 1.72853i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.50901 + 2.61368i) q^{5} +(-0.768732 + 1.55211i) q^{6} +(0.237102 - 2.63511i) q^{7} +1.00000i q^{8} +(-2.97566 + 0.381366i) q^{9} +(-2.61368 + 1.50901i) q^{10} +(-4.75486 + 2.74522i) q^{11} +(-1.44180 + 0.959803i) q^{12} -1.00000i q^{13} +(1.52289 - 2.16352i) q^{14} +(-4.68430 - 2.32005i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.598594 - 1.03680i) q^{17} +(-2.76768 - 1.15756i) q^{18} +(5.49095 + 3.17020i) q^{19} -3.01802 q^{20} +(4.58103 + 0.119147i) q^{21} -5.49044 q^{22} +(3.22876 + 1.86412i) q^{23} +(-1.72853 + 0.110315i) q^{24} +(-2.05422 - 3.55800i) q^{25} +(0.500000 - 0.866025i) q^{26} +(-0.987464 - 5.10146i) q^{27} +(2.40062 - 1.11222i) q^{28} +2.12546i q^{29} +(-2.89670 - 4.35137i) q^{30} +(4.87257 - 2.81318i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-5.26974 - 7.91610i) q^{33} -1.19719i q^{34} +(6.52953 + 4.59611i) q^{35} +(-1.81810 - 2.38632i) q^{36} +(-4.76840 + 8.25912i) q^{37} +(3.17020 + 5.49095i) q^{38} +(1.72853 - 0.110315i) q^{39} +(-2.61368 - 1.50901i) q^{40} +4.26441 q^{41} +(3.90771 + 2.39370i) q^{42} -10.2841 q^{43} +(-4.75486 - 2.74522i) q^{44} +(3.49353 - 8.35291i) q^{45} +(1.86412 + 3.22876i) q^{46} +(-3.89783 + 6.75123i) q^{47} +(-1.55211 - 0.768732i) q^{48} +(-6.88757 - 1.24958i) q^{49} -4.10843i q^{50} +(1.72610 - 1.14906i) q^{51} +(0.866025 - 0.500000i) q^{52} +(6.53582 - 3.77346i) q^{53} +(1.69556 - 4.91173i) q^{54} -16.5702i q^{55} +(2.63511 + 0.237102i) q^{56} +(-4.87407 + 9.84102i) q^{57} +(-1.06273 + 1.84070i) q^{58} +(2.06202 + 3.57153i) q^{59} +(-0.332932 - 5.21675i) q^{60} +(8.26163 + 4.76985i) q^{61} +5.62636 q^{62} +(0.299406 + 7.93160i) q^{63} -1.00000 q^{64} +(2.61368 + 1.50901i) q^{65} +(-0.605677 - 9.49041i) q^{66} +(4.97378 + 8.61485i) q^{67} +(0.598594 - 1.03680i) q^{68} +(-2.86602 + 5.78666i) q^{69} +(3.35669 + 7.24511i) q^{70} +2.25721i q^{71} +(-0.381366 - 2.97566i) q^{72} +(-0.501169 + 0.289350i) q^{73} +(-8.25912 + 4.76840i) q^{74} +(5.92352 - 3.94328i) q^{75} +6.34040i q^{76} +(6.10656 + 13.1805i) q^{77} +(1.55211 + 0.768732i) q^{78} +(0.649232 - 1.12450i) q^{79} +(-1.50901 - 2.61368i) q^{80} +(8.70912 - 2.26963i) q^{81} +(3.69309 + 2.13220i) q^{82} +11.4985 q^{83} +(2.18733 + 4.02686i) q^{84} +3.61313 q^{85} +(-8.90626 - 5.14203i) q^{86} +(-3.67393 + 0.234470i) q^{87} +(-2.74522 - 4.75486i) q^{88} +(2.75175 - 4.76616i) q^{89} +(7.20194 - 5.48707i) q^{90} +(-2.63511 - 0.237102i) q^{91} +3.72825i q^{92} +(5.40019 + 8.11207i) q^{93} +(-6.75123 + 3.89783i) q^{94} +(-16.5718 + 9.56773i) q^{95} +(-0.959803 - 1.44180i) q^{96} -9.59143i q^{97} +(-5.34002 - 4.52595i) q^{98} +(13.1019 - 9.98219i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 16 q^{4} + 2 q^{7} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 16 q^{4} + 2 q^{7} + 2 q^{9} + 6 q^{10} - 24 q^{11} + 4 q^{14} - 12 q^{15} - 16 q^{16} + 4 q^{17} + 24 q^{18} - 12 q^{21} - 12 q^{22} - 6 q^{24} - 18 q^{25} + 16 q^{26} - 6 q^{27} - 2 q^{28} + 10 q^{30} - 6 q^{31} - 14 q^{33} + 48 q^{35} + 4 q^{36} + 16 q^{38} + 6 q^{39} + 6 q^{40} + 16 q^{41} - 18 q^{42} + 32 q^{43} - 24 q^{44} - 20 q^{45} + 16 q^{46} + 20 q^{47} - 26 q^{49} + 44 q^{51} - 60 q^{53} - 6 q^{54} + 8 q^{56} - 8 q^{57} - 10 q^{58} + 8 q^{59} - 6 q^{60} + 36 q^{61} + 36 q^{62} - 28 q^{63} - 32 q^{64} - 6 q^{65} + 12 q^{66} - 4 q^{68} - 36 q^{69} - 18 q^{70} + 24 q^{72} - 48 q^{73} - 84 q^{74} + 14 q^{75} + 52 q^{77} + 18 q^{79} + 70 q^{81} + 24 q^{83} - 24 q^{84} - 32 q^{85} - 24 q^{86} - 26 q^{87} - 6 q^{88} - 20 q^{89} - 6 q^{90} - 8 q^{91} + 92 q^{93} - 72 q^{95} - 6 q^{96} + 32 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 + 0.500000i 0.612372 + 0.353553i
\(3\) 0.110315 + 1.72853i 0.0636903 + 0.997970i
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) −1.50901 + 2.61368i −0.674849 + 1.16887i 0.301664 + 0.953414i \(0.402458\pi\)
−0.976513 + 0.215459i \(0.930875\pi\)
\(6\) −0.768732 + 1.55211i −0.313833 + 0.633647i
\(7\) 0.237102 2.63511i 0.0896160 0.995976i
\(8\) 1.00000i 0.353553i
\(9\) −2.97566 + 0.381366i −0.991887 + 0.127122i
\(10\) −2.61368 + 1.50901i −0.826518 + 0.477190i
\(11\) −4.75486 + 2.74522i −1.43364 + 0.827715i −0.997397 0.0721117i \(-0.977026\pi\)
−0.436248 + 0.899827i \(0.643693\pi\)
\(12\) −1.44180 + 0.959803i −0.416211 + 0.277071i
\(13\) 1.00000i 0.277350i
\(14\) 1.52289 2.16352i 0.407009 0.578224i
\(15\) −4.68430 2.32005i −1.20948 0.599033i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −0.598594 1.03680i −0.145180 0.251460i 0.784260 0.620432i \(-0.213043\pi\)
−0.929440 + 0.368973i \(0.879710\pi\)
\(18\) −2.76768 1.15756i −0.652349 0.272839i
\(19\) 5.49095 + 3.17020i 1.25971 + 0.727294i 0.973018 0.230728i \(-0.0741109\pi\)
0.286692 + 0.958023i \(0.407444\pi\)
\(20\) −3.01802 −0.674849
\(21\) 4.58103 + 0.119147i 0.999662 + 0.0260000i
\(22\) −5.49044 −1.17057
\(23\) 3.22876 + 1.86412i 0.673242 + 0.388697i 0.797304 0.603578i \(-0.206259\pi\)
−0.124062 + 0.992274i \(0.539592\pi\)
\(24\) −1.72853 + 0.110315i −0.352836 + 0.0225179i
\(25\) −2.05422 3.55800i −0.410843 0.711601i
\(26\) 0.500000 0.866025i 0.0980581 0.169842i
\(27\) −0.987464 5.10146i −0.190038 0.981777i
\(28\) 2.40062 1.11222i 0.453674 0.210189i
\(29\) 2.12546i 0.394687i 0.980334 + 0.197344i \(0.0632315\pi\)
−0.980334 + 0.197344i \(0.936768\pi\)
\(30\) −2.89670 4.35137i −0.528863 0.794448i
\(31\) 4.87257 2.81318i 0.875139 0.505262i 0.00608662 0.999981i \(-0.498063\pi\)
0.869053 + 0.494720i \(0.164729\pi\)
\(32\) −0.866025 + 0.500000i −0.153093 + 0.0883883i
\(33\) −5.26974 7.91610i −0.917344 1.37802i
\(34\) 1.19719i 0.205316i
\(35\) 6.52953 + 4.59611i 1.10369 + 0.776884i
\(36\) −1.81810 2.38632i −0.303017 0.397719i
\(37\) −4.76840 + 8.25912i −0.783921 + 1.35779i 0.145721 + 0.989326i \(0.453450\pi\)
−0.929642 + 0.368465i \(0.879884\pi\)
\(38\) 3.17020 + 5.49095i 0.514275 + 0.890750i
\(39\) 1.72853 0.110315i 0.276787 0.0176645i
\(40\) −2.61368 1.50901i −0.413259 0.238595i
\(41\) 4.26441 0.665989 0.332994 0.942929i \(-0.391941\pi\)
0.332994 + 0.942929i \(0.391941\pi\)
\(42\) 3.90771 + 2.39370i 0.602973 + 0.369356i
\(43\) −10.2841 −1.56831 −0.784153 0.620568i \(-0.786902\pi\)
−0.784153 + 0.620568i \(0.786902\pi\)
\(44\) −4.75486 2.74522i −0.716822 0.413857i
\(45\) 3.49353 8.35291i 0.520785 1.24518i
\(46\) 1.86412 + 3.22876i 0.274850 + 0.476054i
\(47\) −3.89783 + 6.75123i −0.568556 + 0.984768i 0.428153 + 0.903706i \(0.359165\pi\)
−0.996709 + 0.0810620i \(0.974169\pi\)
\(48\) −1.55211 0.768732i −0.224028 0.110957i
\(49\) −6.88757 1.24958i −0.983938 0.178511i
\(50\) 4.10843i 0.581020i
\(51\) 1.72610 1.14906i 0.241703 0.160901i
\(52\) 0.866025 0.500000i 0.120096 0.0693375i
\(53\) 6.53582 3.77346i 0.897764 0.518324i 0.0212900 0.999773i \(-0.493223\pi\)
0.876474 + 0.481449i \(0.159889\pi\)
\(54\) 1.69556 4.91173i 0.230737 0.668401i
\(55\) 16.5702i 2.23433i
\(56\) 2.63511 + 0.237102i 0.352131 + 0.0316841i
\(57\) −4.87407 + 9.84102i −0.645586 + 1.30347i
\(58\) −1.06273 + 1.84070i −0.139543 + 0.241696i
\(59\) 2.06202 + 3.57153i 0.268452 + 0.464973i 0.968462 0.249160i \(-0.0801545\pi\)
−0.700010 + 0.714133i \(0.746821\pi\)
\(60\) −0.332932 5.21675i −0.0429814 0.673479i
\(61\) 8.26163 + 4.76985i 1.05779 + 0.610717i 0.924821 0.380403i \(-0.124215\pi\)
0.132972 + 0.991120i \(0.457548\pi\)
\(62\) 5.62636 0.714548
\(63\) 0.299406 + 7.93160i 0.0377216 + 0.999288i
\(64\) −1.00000 −0.125000
\(65\) 2.61368 + 1.50901i 0.324187 + 0.187170i
\(66\) −0.605677 9.49041i −0.0745537 1.16819i
\(67\) 4.97378 + 8.61485i 0.607644 + 1.05247i 0.991628 + 0.129131i \(0.0412188\pi\)
−0.383983 + 0.923340i \(0.625448\pi\)
\(68\) 0.598594 1.03680i 0.0725902 0.125730i
\(69\) −2.86602 + 5.78666i −0.345028 + 0.696632i
\(70\) 3.35669 + 7.24511i 0.401201 + 0.865956i
\(71\) 2.25721i 0.267881i 0.990989 + 0.133941i \(0.0427632\pi\)
−0.990989 + 0.133941i \(0.957237\pi\)
\(72\) −0.381366 2.97566i −0.0449444 0.350685i
\(73\) −0.501169 + 0.289350i −0.0586574 + 0.0338658i −0.529042 0.848596i \(-0.677449\pi\)
0.470385 + 0.882462i \(0.344115\pi\)
\(74\) −8.25912 + 4.76840i −0.960103 + 0.554316i
\(75\) 5.92352 3.94328i 0.683989 0.455331i
\(76\) 6.34040i 0.727294i
\(77\) 6.10656 + 13.1805i 0.695907 + 1.50205i
\(78\) 1.55211 + 0.768732i 0.175742 + 0.0870417i
\(79\) 0.649232 1.12450i 0.0730443 0.126517i −0.827190 0.561923i \(-0.810062\pi\)
0.900234 + 0.435406i \(0.143395\pi\)
\(80\) −1.50901 2.61368i −0.168712 0.292218i
\(81\) 8.70912 2.26963i 0.967680 0.252181i
\(82\) 3.69309 + 2.13220i 0.407833 + 0.235463i
\(83\) 11.4985 1.26212 0.631061 0.775733i \(-0.282620\pi\)
0.631061 + 0.775733i \(0.282620\pi\)
\(84\) 2.18733 + 4.02686i 0.238657 + 0.439366i
\(85\) 3.61313 0.391899
\(86\) −8.90626 5.14203i −0.960387 0.554480i
\(87\) −3.67393 + 0.234470i −0.393886 + 0.0251378i
\(88\) −2.74522 4.75486i −0.292641 0.506870i
\(89\) 2.75175 4.76616i 0.291685 0.505212i −0.682524 0.730863i \(-0.739118\pi\)
0.974208 + 0.225651i \(0.0724509\pi\)
\(90\) 7.20194 5.48707i 0.759151 0.578388i
\(91\) −2.63511 0.237102i −0.276234 0.0248550i
\(92\) 3.72825i 0.388697i
\(93\) 5.40019 + 8.11207i 0.559974 + 0.841182i
\(94\) −6.75123 + 3.89783i −0.696336 + 0.402030i
\(95\) −16.5718 + 9.56773i −1.70023 + 0.981628i
\(96\) −0.959803 1.44180i −0.0979594 0.147153i
\(97\) 9.59143i 0.973862i −0.873440 0.486931i \(-0.838116\pi\)
0.873440 0.486931i \(-0.161884\pi\)
\(98\) −5.34002 4.52595i −0.539423 0.457190i
\(99\) 13.1019 9.98219i 1.31679 1.00325i
\(100\) 2.05422 3.55800i 0.205422 0.355800i
\(101\) −7.58135 13.1313i −0.754372 1.30661i −0.945686 0.325082i \(-0.894608\pi\)
0.191314 0.981529i \(-0.438725\pi\)
\(102\) 2.06938 0.132068i 0.204899 0.0130767i
\(103\) 16.8619 + 9.73525i 1.66146 + 0.959242i 0.972021 + 0.234895i \(0.0754747\pi\)
0.689435 + 0.724347i \(0.257859\pi\)
\(104\) 1.00000 0.0980581
\(105\) −7.22422 + 11.7935i −0.705012 + 1.15093i
\(106\) 7.54692 0.733021
\(107\) −9.22412 5.32555i −0.891730 0.514840i −0.0172218 0.999852i \(-0.505482\pi\)
−0.874508 + 0.485011i \(0.838815\pi\)
\(108\) 3.92426 3.40590i 0.377612 0.327733i
\(109\) 1.55939 + 2.70095i 0.149363 + 0.258704i 0.930992 0.365039i \(-0.118944\pi\)
−0.781629 + 0.623743i \(0.785611\pi\)
\(110\) 8.28512 14.3503i 0.789955 1.36824i
\(111\) −14.8022 7.33124i −1.40496 0.695851i
\(112\) 2.16352 + 1.52289i 0.204433 + 0.143899i
\(113\) 14.0724i 1.32382i −0.749581 0.661912i \(-0.769745\pi\)
0.749581 0.661912i \(-0.230255\pi\)
\(114\) −9.14158 + 6.08554i −0.856187 + 0.569963i
\(115\) −9.74444 + 5.62596i −0.908674 + 0.524623i
\(116\) −1.84070 + 1.06273i −0.170905 + 0.0986719i
\(117\) 0.381366 + 2.97566i 0.0352573 + 0.275100i
\(118\) 4.12404i 0.379649i
\(119\) −2.87399 + 1.33153i −0.263459 + 0.122061i
\(120\) 2.32005 4.68430i 0.211790 0.427616i
\(121\) 9.57246 16.5800i 0.870224 1.50727i
\(122\) 4.76985 + 8.26163i 0.431842 + 0.747973i
\(123\) 0.470428 + 7.37118i 0.0424170 + 0.664637i
\(124\) 4.87257 + 2.81318i 0.437570 + 0.252631i
\(125\) −2.69077 −0.240670
\(126\) −3.70651 + 7.01867i −0.330202 + 0.625273i
\(127\) −5.96831 −0.529602 −0.264801 0.964303i \(-0.585306\pi\)
−0.264801 + 0.964303i \(0.585306\pi\)
\(128\) −0.866025 0.500000i −0.0765466 0.0441942i
\(129\) −1.13449 17.7764i −0.0998859 1.56512i
\(130\) 1.50901 + 2.61368i 0.132349 + 0.229235i
\(131\) −7.37542 + 12.7746i −0.644393 + 1.11612i 0.340048 + 0.940408i \(0.389557\pi\)
−0.984441 + 0.175714i \(0.943777\pi\)
\(132\) 4.22067 8.52178i 0.367363 0.741725i
\(133\) 9.65573 13.7176i 0.837258 1.18946i
\(134\) 9.94757i 0.859339i
\(135\) 14.8237 + 5.11724i 1.27582 + 0.440421i
\(136\) 1.03680 0.598594i 0.0889045 0.0513290i
\(137\) 3.58345 2.06890i 0.306154 0.176758i −0.339050 0.940768i \(-0.610106\pi\)
0.645204 + 0.764010i \(0.276772\pi\)
\(138\) −5.37538 + 3.57838i −0.457582 + 0.304612i
\(139\) 6.64877i 0.563941i 0.959423 + 0.281971i \(0.0909880\pi\)
−0.959423 + 0.281971i \(0.909012\pi\)
\(140\) −0.715577 + 7.95280i −0.0604773 + 0.672134i
\(141\) −12.0997 5.99276i −1.01898 0.504682i
\(142\) −1.12860 + 1.95480i −0.0947104 + 0.164043i
\(143\) 2.74522 + 4.75486i 0.229567 + 0.397621i
\(144\) 1.15756 2.76768i 0.0964632 0.230640i
\(145\) −5.55526 3.20733i −0.461340 0.266355i
\(146\) −0.578700 −0.0478935
\(147\) 1.40013 12.0432i 0.115481 0.993310i
\(148\) −9.53681 −0.783921
\(149\) 15.6769 + 9.05107i 1.28430 + 0.741492i 0.977632 0.210323i \(-0.0674517\pi\)
0.306671 + 0.951816i \(0.400785\pi\)
\(150\) 7.10156 0.453221i 0.579840 0.0370053i
\(151\) 3.07005 + 5.31748i 0.249837 + 0.432730i 0.963480 0.267779i \(-0.0862896\pi\)
−0.713643 + 0.700509i \(0.752956\pi\)
\(152\) −3.17020 + 5.49095i −0.257137 + 0.445375i
\(153\) 2.17661 + 2.85687i 0.175969 + 0.230964i
\(154\) −1.30179 + 14.4679i −0.104901 + 1.16586i
\(155\) 16.9804i 1.36390i
\(156\) 0.959803 + 1.44180i 0.0768457 + 0.115436i
\(157\) 8.56382 4.94432i 0.683467 0.394600i −0.117693 0.993050i \(-0.537550\pi\)
0.801160 + 0.598450i \(0.204217\pi\)
\(158\) 1.12450 0.649232i 0.0894607 0.0516501i
\(159\) 7.24355 + 10.8811i 0.574451 + 0.862929i
\(160\) 3.01802i 0.238595i
\(161\) 5.67771 8.06613i 0.447466 0.635700i
\(162\) 8.67714 + 2.38900i 0.681740 + 0.187698i
\(163\) 6.31039 10.9299i 0.494268 0.856097i −0.505711 0.862703i \(-0.668770\pi\)
0.999978 + 0.00660658i \(0.00210295\pi\)
\(164\) 2.13220 + 3.69309i 0.166497 + 0.288382i
\(165\) 28.6422 1.82794i 2.22979 0.142305i
\(166\) 9.95798 + 5.74924i 0.772889 + 0.446228i
\(167\) −8.02801 −0.621226 −0.310613 0.950536i \(-0.600534\pi\)
−0.310613 + 0.950536i \(0.600534\pi\)
\(168\) −0.119147 + 4.58103i −0.00919240 + 0.353434i
\(169\) −1.00000 −0.0769231
\(170\) 3.12907 + 1.80657i 0.239988 + 0.138557i
\(171\) −17.5482 7.33939i −1.34195 0.561257i
\(172\) −5.14203 8.90626i −0.392076 0.679096i
\(173\) 4.44940 7.70658i 0.338281 0.585921i −0.645828 0.763483i \(-0.723488\pi\)
0.984110 + 0.177562i \(0.0568211\pi\)
\(174\) −3.29895 1.63391i −0.250093 0.123866i
\(175\) −9.86278 + 4.56946i −0.745556 + 0.345419i
\(176\) 5.49044i 0.413857i
\(177\) −5.94603 + 3.95827i −0.446931 + 0.297522i
\(178\) 4.76616 2.75175i 0.357239 0.206252i
\(179\) 15.8867 9.17219i 1.18743 0.685562i 0.229707 0.973260i \(-0.426223\pi\)
0.957721 + 0.287698i \(0.0928900\pi\)
\(180\) 8.98060 1.15097i 0.669374 0.0857882i
\(181\) 17.9573i 1.33476i −0.744719 0.667378i \(-0.767416\pi\)
0.744719 0.667378i \(-0.232584\pi\)
\(182\) −2.16352 1.52289i −0.160371 0.112884i
\(183\) −7.33347 + 14.8067i −0.542106 + 1.09454i
\(184\) −1.86412 + 3.22876i −0.137425 + 0.238027i
\(185\) −14.3911 24.9262i −1.05806 1.83261i
\(186\) 0.620671 + 9.72535i 0.0455098 + 0.713097i
\(187\) 5.69246 + 3.28654i 0.416274 + 0.240336i
\(188\) −7.79565 −0.568556
\(189\) −13.6770 + 1.39251i −0.994857 + 0.101290i
\(190\) −19.1355 −1.38823
\(191\) −0.471000 0.271932i −0.0340803 0.0196763i 0.482863 0.875696i \(-0.339597\pi\)
−0.516943 + 0.856020i \(0.672930\pi\)
\(192\) −0.110315 1.72853i −0.00796129 0.124746i
\(193\) 6.85549 + 11.8741i 0.493469 + 0.854713i 0.999972 0.00752531i \(-0.00239540\pi\)
−0.506503 + 0.862238i \(0.669062\pi\)
\(194\) 4.79571 8.30642i 0.344312 0.596366i
\(195\) −2.32005 + 4.68430i −0.166142 + 0.335450i
\(196\) −2.36162 6.58959i −0.168687 0.470685i
\(197\) 3.54811i 0.252792i 0.991980 + 0.126396i \(0.0403410\pi\)
−0.991980 + 0.126396i \(0.959659\pi\)
\(198\) 16.3377 2.09387i 1.16107 0.148805i
\(199\) −17.9941 + 10.3889i −1.27557 + 0.736449i −0.976030 0.217636i \(-0.930166\pi\)
−0.299537 + 0.954085i \(0.596832\pi\)
\(200\) 3.55800 2.05422i 0.251589 0.145255i
\(201\) −14.3424 + 9.54770i −1.01163 + 0.673443i
\(202\) 15.1627i 1.06684i
\(203\) 5.60080 + 0.503950i 0.393099 + 0.0353703i
\(204\) 1.85817 + 0.920316i 0.130098 + 0.0644350i
\(205\) −6.43503 + 11.1458i −0.449442 + 0.778456i
\(206\) 9.73525 + 16.8619i 0.678287 + 1.17483i
\(207\) −10.3186 4.31566i −0.717192 0.299959i
\(208\) 0.866025 + 0.500000i 0.0600481 + 0.0346688i
\(209\) −34.8116 −2.40797
\(210\) −12.1531 + 6.60140i −0.838646 + 0.455540i
\(211\) −6.94500 −0.478114 −0.239057 0.971006i \(-0.576838\pi\)
−0.239057 + 0.971006i \(0.576838\pi\)
\(212\) 6.53582 + 3.77346i 0.448882 + 0.259162i
\(213\) −3.90166 + 0.249004i −0.267338 + 0.0170615i
\(214\) −5.32555 9.22412i −0.364047 0.630548i
\(215\) 15.5187 26.8793i 1.05837 1.83315i
\(216\) 5.10146 0.987464i 0.347111 0.0671884i
\(217\) −6.25773 13.5067i −0.424802 0.916898i
\(218\) 3.11878i 0.211231i
\(219\) −0.555438 0.834368i −0.0375330 0.0563813i
\(220\) 14.3503 8.28512i 0.967494 0.558583i
\(221\) −1.03680 + 0.598594i −0.0697424 + 0.0402658i
\(222\) −9.15345 13.7501i −0.614339 0.922849i
\(223\) 8.20541i 0.549475i −0.961519 0.274737i \(-0.911409\pi\)
0.961519 0.274737i \(-0.0885909\pi\)
\(224\) 1.11222 + 2.40062i 0.0743131 + 0.160398i
\(225\) 7.46955 + 9.80401i 0.497970 + 0.653601i
\(226\) 7.03622 12.1871i 0.468043 0.810673i
\(227\) 2.10721 + 3.64980i 0.139861 + 0.242246i 0.927444 0.373963i \(-0.122001\pi\)
−0.787583 + 0.616208i \(0.788668\pi\)
\(228\) −10.9596 + 0.699441i −0.725818 + 0.0463216i
\(229\) 5.64747 + 3.26057i 0.373196 + 0.215465i 0.674854 0.737952i \(-0.264207\pi\)
−0.301658 + 0.953416i \(0.597540\pi\)
\(230\) −11.2519 −0.741929
\(231\) −22.1092 + 12.0094i −1.45468 + 0.790160i
\(232\) −2.12546 −0.139543
\(233\) −14.8550 8.57656i −0.973186 0.561869i −0.0729798 0.997333i \(-0.523251\pi\)
−0.900206 + 0.435464i \(0.856584\pi\)
\(234\) −1.15756 + 2.76768i −0.0756719 + 0.180929i
\(235\) −11.7637 20.3753i −0.767380 1.32914i
\(236\) −2.06202 + 3.57153i −0.134226 + 0.232487i
\(237\) 2.01536 + 0.998171i 0.130912 + 0.0648382i
\(238\) −3.15472 0.283855i −0.204490 0.0183996i
\(239\) 15.6348i 1.01133i 0.862730 + 0.505664i \(0.168753\pi\)
−0.862730 + 0.505664i \(0.831247\pi\)
\(240\) 4.35137 2.89670i 0.280880 0.186981i
\(241\) 12.6334 7.29387i 0.813786 0.469840i −0.0344827 0.999405i \(-0.510978\pi\)
0.848269 + 0.529566i \(0.177645\pi\)
\(242\) 16.5800 9.57246i 1.06580 0.615341i
\(243\) 4.88388 + 14.8036i 0.313301 + 0.949654i
\(244\) 9.53971i 0.610717i
\(245\) 13.6594 16.1163i 0.872666 1.02963i
\(246\) −3.27819 + 6.61884i −0.209009 + 0.422002i
\(247\) 3.17020 5.49095i 0.201715 0.349381i
\(248\) 2.81318 + 4.87257i 0.178637 + 0.309408i
\(249\) 1.26845 + 19.8755i 0.0803850 + 1.25956i
\(250\) −2.33028 1.34539i −0.147380 0.0850897i
\(251\) 25.7693 1.62654 0.813272 0.581884i \(-0.197684\pi\)
0.813272 + 0.581884i \(0.197684\pi\)
\(252\) −6.71927 + 4.22510i −0.423274 + 0.266156i
\(253\) −20.4697 −1.28692
\(254\) −5.16871 2.98416i −0.324314 0.187243i
\(255\) 0.398583 + 6.24543i 0.0249602 + 0.391104i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 2.76476 4.78871i 0.172461 0.298711i −0.766819 0.641864i \(-0.778161\pi\)
0.939280 + 0.343153i \(0.111495\pi\)
\(258\) 7.90569 15.9620i 0.492187 0.993752i
\(259\) 20.6330 + 14.5235i 1.28208 + 0.902446i
\(260\) 3.01802i 0.187170i
\(261\) −0.810577 6.32464i −0.0501735 0.391485i
\(262\) −12.7746 + 7.37542i −0.789217 + 0.455655i
\(263\) −20.3542 + 11.7515i −1.25510 + 0.724630i −0.972117 0.234495i \(-0.924656\pi\)
−0.282980 + 0.959126i \(0.591323\pi\)
\(264\) 7.91610 5.26974i 0.487202 0.324330i
\(265\) 22.7767i 1.39916i
\(266\) 15.2209 7.05190i 0.933253 0.432380i
\(267\) 8.54204 + 4.23071i 0.522764 + 0.258915i
\(268\) −4.97378 + 8.61485i −0.303822 + 0.526236i
\(269\) 2.68200 + 4.64535i 0.163524 + 0.283232i 0.936130 0.351654i \(-0.114380\pi\)
−0.772606 + 0.634886i \(0.781047\pi\)
\(270\) 10.2791 + 11.8435i 0.625564 + 0.720772i
\(271\) −11.9719 6.91197i −0.727241 0.419873i 0.0901713 0.995926i \(-0.471259\pi\)
−0.817412 + 0.576054i \(0.804592\pi\)
\(272\) 1.19719 0.0725902
\(273\) 0.119147 4.58103i 0.00721111 0.277256i
\(274\) 4.13781 0.249974
\(275\) 19.5350 + 11.2785i 1.17801 + 0.680122i
\(276\) −6.44440 + 0.411281i −0.387907 + 0.0247562i
\(277\) −12.4960 21.6437i −0.750813 1.30045i −0.947429 0.319965i \(-0.896329\pi\)
0.196617 0.980480i \(-0.437005\pi\)
\(278\) −3.32438 + 5.75800i −0.199383 + 0.345342i
\(279\) −13.4263 + 10.2293i −0.803809 + 0.612412i
\(280\) −4.59611 + 6.52953i −0.274670 + 0.390214i
\(281\) 17.2873i 1.03127i −0.856807 0.515637i \(-0.827555\pi\)
0.856807 0.515637i \(-0.172445\pi\)
\(282\) −7.48229 11.2397i −0.445564 0.669317i
\(283\) −7.72002 + 4.45715i −0.458907 + 0.264950i −0.711585 0.702600i \(-0.752022\pi\)
0.252677 + 0.967551i \(0.418689\pi\)
\(284\) −1.95480 + 1.12860i −0.115996 + 0.0669704i
\(285\) −18.3663 27.5894i −1.08792 1.63426i
\(286\) 5.49044i 0.324656i
\(287\) 1.01110 11.2372i 0.0596833 0.663309i
\(288\) 2.38632 1.81810i 0.140615 0.107133i
\(289\) 7.78337 13.4812i 0.457845 0.793011i
\(290\) −3.20733 5.55526i −0.188341 0.326216i
\(291\) 16.5791 1.05808i 0.971885 0.0620256i
\(292\) −0.501169 0.289350i −0.0293287 0.0169329i
\(293\) −6.07556 −0.354938 −0.177469 0.984126i \(-0.556791\pi\)
−0.177469 + 0.984126i \(0.556791\pi\)
\(294\) 7.23417 9.72968i 0.421905 0.567447i
\(295\) −12.4464 −0.724659
\(296\) −8.25912 4.76840i −0.480051 0.277158i
\(297\) 18.6999 + 21.5459i 1.08508 + 1.25022i
\(298\) 9.05107 + 15.6769i 0.524314 + 0.908139i
\(299\) 1.86412 3.22876i 0.107805 0.186724i
\(300\) 6.37674 + 3.15828i 0.368161 + 0.182343i
\(301\) −2.43837 + 27.0996i −0.140545 + 1.56200i
\(302\) 6.14010i 0.353323i
\(303\) 21.8615 14.5532i 1.25591 0.836059i
\(304\) −5.49095 + 3.17020i −0.314928 + 0.181824i
\(305\) −24.9337 + 14.3955i −1.42770 + 0.824284i
\(306\) 0.456567 + 3.56243i 0.0261002 + 0.203650i
\(307\) 12.9033i 0.736433i −0.929740 0.368216i \(-0.879969\pi\)
0.929740 0.368216i \(-0.120031\pi\)
\(308\) −8.36133 + 11.8787i −0.476431 + 0.676850i
\(309\) −14.9676 + 30.2204i −0.851476 + 1.71918i
\(310\) −8.49022 + 14.7055i −0.482212 + 0.835216i
\(311\) 0.892751 + 1.54629i 0.0506233 + 0.0876821i 0.890227 0.455518i \(-0.150546\pi\)
−0.839603 + 0.543200i \(0.817213\pi\)
\(312\) 0.110315 + 1.72853i 0.00624535 + 0.0978590i
\(313\) 8.90124 + 5.13913i 0.503128 + 0.290481i 0.730004 0.683442i \(-0.239518\pi\)
−0.226876 + 0.973924i \(0.572851\pi\)
\(314\) 9.88865 0.558049
\(315\) −21.1825 11.1863i −1.19350 0.630277i
\(316\) 1.29846 0.0730443
\(317\) −23.6484 13.6534i −1.32822 0.766850i −0.343199 0.939263i \(-0.611511\pi\)
−0.985025 + 0.172412i \(0.944844\pi\)
\(318\) 0.832537 + 13.0451i 0.0466864 + 0.731533i
\(319\) −5.83485 10.1063i −0.326689 0.565841i
\(320\) 1.50901 2.61368i 0.0843562 0.146109i
\(321\) 8.18784 16.5317i 0.457001 0.922710i
\(322\) 8.95010 4.14662i 0.498770 0.231082i
\(323\) 7.59066i 0.422355i
\(324\) 6.32012 + 6.40750i 0.351118 + 0.355972i
\(325\) −3.55800 + 2.05422i −0.197363 + 0.113947i
\(326\) 10.9299 6.31039i 0.605352 0.349500i
\(327\) −4.49665 + 2.99342i −0.248665 + 0.165536i
\(328\) 4.26441i 0.235463i
\(329\) 16.8660 + 11.8719i 0.929854 + 0.654520i
\(330\) 25.7189 + 12.7381i 1.41578 + 0.701208i
\(331\) −4.03642 + 6.99129i −0.221862 + 0.384276i −0.955373 0.295401i \(-0.904547\pi\)
0.733512 + 0.679677i \(0.237880\pi\)
\(332\) 5.74924 + 9.95798i 0.315531 + 0.546515i
\(333\) 11.0394 26.3948i 0.604956 1.44643i
\(334\) −6.95246 4.01401i −0.380422 0.219637i
\(335\) −30.0219 −1.64027
\(336\) −2.39370 + 3.90771i −0.130587 + 0.213183i
\(337\) −16.1292 −0.878615 −0.439307 0.898337i \(-0.644776\pi\)
−0.439307 + 0.898337i \(0.644776\pi\)
\(338\) −0.866025 0.500000i −0.0471056 0.0271964i
\(339\) 24.3247 1.55240i 1.32114 0.0843148i
\(340\) 1.80657 + 3.12907i 0.0979749 + 0.169697i
\(341\) −15.4456 + 26.7525i −0.836426 + 1.44873i
\(342\) −11.5275 15.1302i −0.623336 0.818148i
\(343\) −4.92582 + 17.8532i −0.265969 + 0.963981i
\(344\) 10.2841i 0.554480i
\(345\) −10.7996 16.2230i −0.581432 0.873416i
\(346\) 7.70658 4.44940i 0.414308 0.239201i
\(347\) −8.89289 + 5.13431i −0.477395 + 0.275624i −0.719330 0.694668i \(-0.755551\pi\)
0.241935 + 0.970292i \(0.422218\pi\)
\(348\) −2.04002 3.06448i −0.109357 0.164273i
\(349\) 26.9284i 1.44144i 0.693224 + 0.720722i \(0.256189\pi\)
−0.693224 + 0.720722i \(0.743811\pi\)
\(350\) −10.8261 0.974116i −0.578682 0.0520687i
\(351\) −5.10146 + 0.987464i −0.272296 + 0.0527069i
\(352\) 2.74522 4.75486i 0.146321 0.253435i
\(353\) −2.08391 3.60944i −0.110915 0.192111i 0.805224 0.592971i \(-0.202045\pi\)
−0.916140 + 0.400859i \(0.868712\pi\)
\(354\) −7.12855 + 0.454943i −0.378878 + 0.0241800i
\(355\) −5.89962 3.40615i −0.313119 0.180780i
\(356\) 5.50349 0.291685
\(357\) −2.61864 4.82091i −0.138593 0.255149i
\(358\) 18.3444 0.969531
\(359\) −11.1296 6.42566i −0.587396 0.339134i 0.176671 0.984270i \(-0.443467\pi\)
−0.764067 + 0.645136i \(0.776801\pi\)
\(360\) 8.35291 + 3.49353i 0.440237 + 0.184125i
\(361\) 10.6004 + 18.3604i 0.557914 + 0.966335i
\(362\) 8.97866 15.5515i 0.471908 0.817368i
\(363\) 29.7151 + 14.7173i 1.55964 + 0.772458i
\(364\) −1.11222 2.40062i −0.0582960 0.125827i
\(365\) 1.74653i 0.0914174i
\(366\) −13.7543 + 9.15623i −0.718950 + 0.478604i
\(367\) 29.9194 17.2740i 1.56178 0.901693i 0.564701 0.825295i \(-0.308991\pi\)
0.997077 0.0763982i \(-0.0243420\pi\)
\(368\) −3.22876 + 1.86412i −0.168311 + 0.0971742i
\(369\) −12.6894 + 1.62630i −0.660586 + 0.0846619i
\(370\) 28.7822i 1.49632i
\(371\) −8.39381 18.1173i −0.435785 0.940602i
\(372\) −4.32516 + 8.73274i −0.224249 + 0.452771i
\(373\) 6.44752 11.1674i 0.333840 0.578228i −0.649421 0.760429i \(-0.724989\pi\)
0.983261 + 0.182201i \(0.0583221\pi\)
\(374\) 3.28654 + 5.69246i 0.169943 + 0.294350i
\(375\) −0.296832 4.65109i −0.0153284 0.240181i
\(376\) −6.75123 3.89783i −0.348168 0.201015i
\(377\) 2.12546 0.109467
\(378\) −12.5409 5.63256i −0.645034 0.289708i
\(379\) 5.03047 0.258398 0.129199 0.991619i \(-0.458759\pi\)
0.129199 + 0.991619i \(0.458759\pi\)
\(380\) −16.5718 9.56773i −0.850115 0.490814i
\(381\) −0.658394 10.3164i −0.0337305 0.528527i
\(382\) −0.271932 0.471000i −0.0139132 0.0240984i
\(383\) 5.50293 9.53136i 0.281187 0.487030i −0.690491 0.723341i \(-0.742605\pi\)
0.971677 + 0.236312i \(0.0759387\pi\)
\(384\) 0.768732 1.55211i 0.0392292 0.0792059i
\(385\) −43.6643 3.92883i −2.22534 0.200232i
\(386\) 13.7110i 0.697870i
\(387\) 30.6019 3.92200i 1.55558 0.199366i
\(388\) 8.30642 4.79571i 0.421695 0.243466i
\(389\) −16.2200 + 9.36461i −0.822385 + 0.474804i −0.851238 0.524779i \(-0.824148\pi\)
0.0288530 + 0.999584i \(0.490815\pi\)
\(390\) −4.35137 + 2.89670i −0.220340 + 0.146680i
\(391\) 4.46341i 0.225724i
\(392\) 1.24958 6.88757i 0.0631131 0.347875i
\(393\) −22.8949 11.3394i −1.15490 0.571999i
\(394\) −1.77405 + 3.07275i −0.0893755 + 0.154803i
\(395\) 1.95939 + 3.39377i 0.0985878 + 0.170759i
\(396\) 15.1958 + 6.35550i 0.763617 + 0.319376i
\(397\) −10.2811 5.93579i −0.515993 0.297909i 0.219300 0.975657i \(-0.429623\pi\)
−0.735294 + 0.677748i \(0.762956\pi\)
\(398\) −20.7778 −1.04150
\(399\) 24.7765 + 15.1770i 1.24038 + 0.759801i
\(400\) 4.10843 0.205422
\(401\) 17.6755 + 10.2050i 0.882673 + 0.509612i 0.871539 0.490326i \(-0.163122\pi\)
0.0111344 + 0.999938i \(0.496456\pi\)
\(402\) −17.1947 + 1.09737i −0.857594 + 0.0547316i
\(403\) −2.81318 4.87257i −0.140134 0.242720i
\(404\) 7.58135 13.1313i 0.377186 0.653305i
\(405\) −7.21004 + 26.1877i −0.358270 + 1.30128i
\(406\) 4.59846 + 3.23684i 0.228218 + 0.160641i
\(407\) 52.3613i 2.59545i
\(408\) 1.14906 + 1.72610i 0.0568872 + 0.0854548i
\(409\) 3.11673 1.79944i 0.154112 0.0889767i −0.420961 0.907079i \(-0.638307\pi\)
0.575073 + 0.818102i \(0.304974\pi\)
\(410\) −11.1458 + 6.43503i −0.550452 + 0.317803i
\(411\) 3.97148 + 5.96588i 0.195899 + 0.294275i
\(412\) 19.4705i 0.959242i
\(413\) 9.90026 4.58683i 0.487160 0.225703i
\(414\) −6.77834 8.89677i −0.333137 0.437252i
\(415\) −17.3513 + 30.0533i −0.851742 + 1.47526i
\(416\) 0.500000 + 0.866025i 0.0245145 + 0.0424604i
\(417\) −11.4926 + 0.733458i −0.562796 + 0.0359176i
\(418\) −30.1477 17.4058i −1.47457 0.851346i
\(419\) 11.3462 0.554298 0.277149 0.960827i \(-0.410610\pi\)
0.277149 + 0.960827i \(0.410610\pi\)
\(420\) −13.8256 0.359588i −0.674621 0.0175461i
\(421\) 3.89654 0.189906 0.0949529 0.995482i \(-0.469730\pi\)
0.0949529 + 0.995482i \(0.469730\pi\)
\(422\) −6.01455 3.47250i −0.292784 0.169039i
\(423\) 9.02392 21.5759i 0.438758 1.04906i
\(424\) 3.77346 + 6.53582i 0.183255 + 0.317408i
\(425\) −2.45928 + 4.25960i −0.119293 + 0.206621i
\(426\) −3.50344 1.73519i −0.169742 0.0840701i
\(427\) 14.5279 20.6393i 0.703055 0.998807i
\(428\) 10.6511i 0.514840i
\(429\) −7.91610 + 5.26974i −0.382193 + 0.254425i
\(430\) 26.8793 15.5187i 1.29623 0.748380i
\(431\) −24.3157 + 14.0387i −1.17125 + 0.676220i −0.953973 0.299891i \(-0.903050\pi\)
−0.217274 + 0.976111i \(0.569716\pi\)
\(432\) 4.91173 + 1.69556i 0.236316 + 0.0815778i
\(433\) 8.12334i 0.390383i 0.980765 + 0.195191i \(0.0625328\pi\)
−0.980765 + 0.195191i \(0.937467\pi\)
\(434\) 1.33402 14.8260i 0.0640350 0.711673i
\(435\) 4.93116 9.95628i 0.236431 0.477367i
\(436\) −1.55939 + 2.70095i −0.0746813 + 0.129352i
\(437\) 11.8193 + 20.4716i 0.565394 + 0.979291i
\(438\) −0.0638392 1.00030i −0.00305036 0.0477963i
\(439\) 31.4473 + 18.1561i 1.50090 + 0.866542i 0.999999 + 0.00103502i \(0.000329456\pi\)
0.500896 + 0.865507i \(0.333004\pi\)
\(440\) 16.5702 0.789955
\(441\) 20.9716 + 1.09163i 0.998648 + 0.0519825i
\(442\) −1.19719 −0.0569444
\(443\) −14.3748 8.29928i −0.682966 0.394311i 0.118005 0.993013i \(-0.462350\pi\)
−0.800972 + 0.598702i \(0.795683\pi\)
\(444\) −1.05205 16.4847i −0.0499282 0.782329i
\(445\) 8.30482 + 14.3844i 0.393686 + 0.681884i
\(446\) 4.10270 7.10609i 0.194269 0.336483i
\(447\) −13.9157 + 28.0965i −0.658189 + 1.32892i
\(448\) −0.237102 + 2.63511i −0.0112020 + 0.124497i
\(449\) 16.4761i 0.777553i −0.921332 0.388776i \(-0.872898\pi\)
0.921332 0.388776i \(-0.127102\pi\)
\(450\) 1.56682 + 12.2253i 0.0738604 + 0.576306i
\(451\) −20.2767 + 11.7067i −0.954791 + 0.551249i
\(452\) 12.1871 7.03622i 0.573233 0.330956i
\(453\) −8.85277 + 5.89328i −0.415940 + 0.276890i
\(454\) 4.21442i 0.197793i
\(455\) 4.59611 6.52953i 0.215469 0.306109i
\(456\) −9.84102 4.87407i −0.460848 0.228249i
\(457\) 6.09451 10.5560i 0.285089 0.493789i −0.687542 0.726145i \(-0.741310\pi\)
0.972631 + 0.232356i \(0.0746434\pi\)
\(458\) 3.26057 + 5.64747i 0.152356 + 0.263889i
\(459\) −4.69808 + 4.07750i −0.219288 + 0.190322i
\(460\) −9.74444 5.62596i −0.454337 0.262312i
\(461\) −25.6242 −1.19344 −0.596720 0.802450i \(-0.703530\pi\)
−0.596720 + 0.802450i \(0.703530\pi\)
\(462\) −25.1518 0.654170i −1.17017 0.0304347i
\(463\) 28.9883 1.34720 0.673601 0.739095i \(-0.264746\pi\)
0.673601 + 0.739095i \(0.264746\pi\)
\(464\) −1.84070 1.06273i −0.0854523 0.0493359i
\(465\) −29.3513 + 1.87320i −1.36113 + 0.0868674i
\(466\) −8.57656 14.8550i −0.397301 0.688146i
\(467\) 3.72197 6.44665i 0.172232 0.298315i −0.766968 0.641686i \(-0.778235\pi\)
0.939200 + 0.343371i \(0.111569\pi\)
\(468\) −2.38632 + 1.81810i −0.110307 + 0.0840419i
\(469\) 23.8803 11.0639i 1.10269 0.510881i
\(470\) 23.5274i 1.08524i
\(471\) 9.49115 + 14.2574i 0.437329 + 0.656947i
\(472\) −3.57153 + 2.06202i −0.164393 + 0.0949122i
\(473\) 48.8993 28.2320i 2.24839 1.29811i
\(474\) 1.24627 + 1.87212i 0.0572431 + 0.0859894i
\(475\) 26.0491i 1.19522i
\(476\) −2.59014 1.82318i −0.118719 0.0835655i
\(477\) −18.0093 + 13.7211i −0.824590 + 0.628245i
\(478\) −7.81738 + 13.5401i −0.357559 + 0.619310i
\(479\) 14.8260 + 25.6793i 0.677416 + 1.17332i 0.975756 + 0.218859i \(0.0702336\pi\)
−0.298340 + 0.954460i \(0.596433\pi\)
\(480\) 5.21675 0.332932i 0.238111 0.0151962i
\(481\) 8.25912 + 4.76840i 0.376583 + 0.217420i
\(482\) 14.5877 0.664454
\(483\) 14.5689 + 8.92430i 0.662909 + 0.406070i
\(484\) 19.1449 0.870224
\(485\) 25.0689 + 14.4736i 1.13832 + 0.657210i
\(486\) −3.17225 + 15.2623i −0.143896 + 0.692311i
\(487\) 15.0024 + 25.9849i 0.679823 + 1.17749i 0.975034 + 0.222056i \(0.0712769\pi\)
−0.295210 + 0.955432i \(0.595390\pi\)
\(488\) −4.76985 + 8.26163i −0.215921 + 0.373986i
\(489\) 19.5889 + 9.70199i 0.885839 + 0.438739i
\(490\) 19.8875 7.12740i 0.898426 0.321983i
\(491\) 2.20851i 0.0996688i −0.998757 0.0498344i \(-0.984131\pi\)
0.998757 0.0498344i \(-0.0158694\pi\)
\(492\) −6.14841 + 4.09299i −0.277192 + 0.184526i
\(493\) 2.20366 1.27229i 0.0992480 0.0573009i
\(494\) 5.49095 3.17020i 0.247050 0.142634i
\(495\) 6.31933 + 49.3074i 0.284033 + 2.21620i
\(496\) 5.62636i 0.252631i
\(497\) 5.94799 + 0.535188i 0.266804 + 0.0240065i
\(498\) −8.83924 + 17.8469i −0.396096 + 0.799740i
\(499\) −15.3354 + 26.5618i −0.686508 + 1.18907i 0.286452 + 0.958095i \(0.407524\pi\)
−0.972960 + 0.230973i \(0.925809\pi\)
\(500\) −1.34539 2.33028i −0.0601675 0.104213i
\(501\) −0.885609 13.8767i −0.0395661 0.619965i
\(502\) 22.3169 + 12.8846i 0.996050 + 0.575070i
\(503\) 5.85678 0.261141 0.130570 0.991439i \(-0.458319\pi\)
0.130570 + 0.991439i \(0.458319\pi\)
\(504\) −7.93160 + 0.299406i −0.353302 + 0.0133366i
\(505\) 45.7613 2.03635
\(506\) −17.7273 10.2349i −0.788074 0.454995i
\(507\) −0.110315 1.72853i −0.00489926 0.0767669i
\(508\) −2.98416 5.16871i −0.132401 0.229324i
\(509\) 10.6895 18.5147i 0.473802 0.820649i −0.525748 0.850640i \(-0.676215\pi\)
0.999550 + 0.0299913i \(0.00954794\pi\)
\(510\) −2.77753 + 5.60799i −0.122991 + 0.248326i
\(511\) 0.643640 + 1.38924i 0.0284729 + 0.0614563i
\(512\) 1.00000i 0.0441942i
\(513\) 10.7505 31.1423i 0.474648 1.37497i
\(514\) 4.78871 2.76476i 0.211221 0.121948i
\(515\) −50.8896 + 29.3811i −2.24246 + 1.29469i
\(516\) 14.8275 9.87067i 0.652746 0.434532i
\(517\) 42.8016i 1.88241i
\(518\) 10.6070 + 22.8942i 0.466045 + 1.00592i
\(519\) 13.8119 + 6.84078i 0.606276 + 0.300277i
\(520\) −1.50901 + 2.61368i −0.0661744 + 0.114617i
\(521\) 2.53028 + 4.38257i 0.110854 + 0.192004i 0.916115 0.400916i \(-0.131308\pi\)
−0.805261 + 0.592920i \(0.797975\pi\)
\(522\) 2.46034 5.88259i 0.107686 0.257474i
\(523\) −3.78175 2.18339i −0.165364 0.0954731i 0.415034 0.909806i \(-0.363770\pi\)
−0.580398 + 0.814333i \(0.697103\pi\)
\(524\) −14.7508 −0.644393
\(525\) −8.98649 16.5441i −0.392202 0.722042i
\(526\) −23.5031 −1.02478
\(527\) −5.83338 3.36790i −0.254106 0.146708i
\(528\) 9.49041 0.605677i 0.413017 0.0263587i
\(529\) −4.55009 7.88098i −0.197830 0.342651i
\(530\) −11.3884 + 19.7252i −0.494679 + 0.856809i
\(531\) −7.49794 9.84126i −0.325383 0.427075i
\(532\) 16.7076 + 1.50332i 0.724368 + 0.0651772i
\(533\) 4.26441i 0.184712i
\(534\) 5.28227 + 7.93492i 0.228586 + 0.343378i
\(535\) 27.8386 16.0726i 1.20357 0.694879i
\(536\) −8.61485 + 4.97378i −0.372105 + 0.214835i
\(537\) 17.6070 + 26.4489i 0.759797 + 1.14135i
\(538\) 5.36399i 0.231258i
\(539\) 36.1798 12.9663i 1.55837 0.558499i
\(540\) 2.98018 + 15.3963i 0.128247 + 0.662551i
\(541\) −20.5901 + 35.6631i −0.885237 + 1.53327i −0.0397943 + 0.999208i \(0.512670\pi\)
−0.845442 + 0.534067i \(0.820663\pi\)
\(542\) −6.91197 11.9719i −0.296895 0.514237i
\(543\) 31.0398 1.98096i 1.33205 0.0850111i
\(544\) 1.03680 + 0.598594i 0.0444522 + 0.0256645i
\(545\) −9.41254 −0.403189
\(546\) 2.39370 3.90771i 0.102441 0.167235i
\(547\) 24.8814 1.06385 0.531927 0.846790i \(-0.321468\pi\)
0.531927 + 0.846790i \(0.321468\pi\)
\(548\) 3.58345 + 2.06890i 0.153077 + 0.0883792i
\(549\) −26.4029 11.0428i −1.12685 0.471294i
\(550\) 11.2785 + 19.5350i 0.480919 + 0.832976i
\(551\) −6.73813 + 11.6708i −0.287054 + 0.497192i
\(552\) −5.78666 2.86602i −0.246296 0.121986i
\(553\) −2.80925 1.97742i −0.119462 0.0840883i
\(554\) 24.9920i 1.06181i
\(555\) 41.4982 27.6253i 1.76150 1.17263i
\(556\) −5.75800 + 3.32438i −0.244194 + 0.140985i
\(557\) −11.6975 + 6.75356i −0.495639 + 0.286157i −0.726911 0.686732i \(-0.759045\pi\)
0.231272 + 0.972889i \(0.425711\pi\)
\(558\) −16.7421 + 2.14570i −0.708751 + 0.0908348i
\(559\) 10.2841i 0.434970i
\(560\) −7.24511 + 3.35669i −0.306162 + 0.141846i
\(561\) −5.05294 + 10.2022i −0.213335 + 0.430736i
\(562\) 8.64365 14.9712i 0.364610 0.631524i
\(563\) −15.6101 27.0375i −0.657888 1.13950i −0.981161 0.193190i \(-0.938116\pi\)
0.323273 0.946306i \(-0.395217\pi\)
\(564\) −0.859977 13.4751i −0.0362115 0.567402i
\(565\) 36.7809 + 21.2354i 1.54738 + 0.893382i
\(566\) −8.91431 −0.374696
\(567\) −3.91578 23.4876i −0.164447 0.986386i
\(568\) −2.25721 −0.0947104
\(569\) 27.3771 + 15.8062i 1.14771 + 0.662629i 0.948328 0.317293i \(-0.102774\pi\)
0.199380 + 0.979922i \(0.436107\pi\)
\(570\) −2.11093 33.0763i −0.0884170 1.38541i
\(571\) −14.0217 24.2862i −0.586788 1.01635i −0.994650 0.103304i \(-0.967059\pi\)
0.407861 0.913044i \(-0.366275\pi\)
\(572\) −2.74522 + 4.75486i −0.114783 + 0.198811i
\(573\) 0.418085 0.844137i 0.0174658 0.0352643i
\(574\) 6.49422 9.22612i 0.271064 0.385091i
\(575\) 15.3172i 0.638773i
\(576\) 2.97566 0.381366i 0.123986 0.0158903i
\(577\) 12.0367 6.94939i 0.501094 0.289307i −0.228071 0.973645i \(-0.573242\pi\)
0.729165 + 0.684338i \(0.239908\pi\)
\(578\) 13.4812 7.78337i 0.560744 0.323746i
\(579\) −19.7684 + 13.1598i −0.821548 + 0.546904i
\(580\) 6.41467i 0.266355i
\(581\) 2.72631 30.2997i 0.113106 1.25704i
\(582\) 14.8870 + 7.37323i 0.617085 + 0.305630i
\(583\) −20.7179 + 35.8845i −0.858050 + 1.48619i
\(584\) −0.289350 0.501169i −0.0119734 0.0207385i
\(585\) −8.35291 3.49353i −0.345350 0.144440i
\(586\) −5.26159 3.03778i −0.217354 0.125489i
\(587\) 35.5637 1.46787 0.733935 0.679219i \(-0.237681\pi\)
0.733935 + 0.679219i \(0.237681\pi\)
\(588\) 11.1298 4.80907i 0.458986 0.198323i
\(589\) 35.6734 1.46990
\(590\) −10.7789 6.22322i −0.443761 0.256206i
\(591\) −6.13302 + 0.391409i −0.252279 + 0.0161004i
\(592\) −4.76840 8.25912i −0.195980 0.339448i
\(593\) −7.87130 + 13.6335i −0.323236 + 0.559861i −0.981154 0.193229i \(-0.938104\pi\)
0.657918 + 0.753090i \(0.271437\pi\)
\(594\) 5.42161 + 28.0093i 0.222451 + 1.14923i
\(595\) 0.856681 9.52099i 0.0351205 0.390323i
\(596\) 18.1021i 0.741492i
\(597\) −19.9426 29.9573i −0.816195 1.22607i
\(598\) 3.22876 1.86412i 0.132034 0.0762297i
\(599\) 23.5223 13.5806i 0.961094 0.554888i 0.0645844 0.997912i \(-0.479428\pi\)
0.896510 + 0.443024i \(0.146094\pi\)
\(600\) 3.94328 + 5.92352i 0.160984 + 0.241827i
\(601\) 10.3648i 0.422787i −0.977401 0.211394i \(-0.932200\pi\)
0.977401 0.211394i \(-0.0678002\pi\)
\(602\) −15.6615 + 22.2498i −0.638315 + 0.906833i
\(603\) −18.0857 23.7380i −0.736507 0.966687i
\(604\) −3.07005 + 5.31748i −0.124918 + 0.216365i
\(605\) 28.8899 + 50.0387i 1.17454 + 2.03436i
\(606\) 26.2092 1.67267i 1.06468 0.0679476i
\(607\) −21.5899 12.4649i −0.876306 0.505935i −0.00686733 0.999976i \(-0.502186\pi\)
−0.869439 + 0.494041i \(0.835519\pi\)
\(608\) −6.34040 −0.257137
\(609\) −0.253242 + 9.73678i −0.0102619 + 0.394554i
\(610\) −28.7910 −1.16571
\(611\) 6.75123 + 3.89783i 0.273126 + 0.157689i
\(612\) −1.38581 + 3.31344i −0.0560182 + 0.133938i
\(613\) 12.7808 + 22.1370i 0.516213 + 0.894107i 0.999823 + 0.0188230i \(0.00599191\pi\)
−0.483610 + 0.875283i \(0.660675\pi\)
\(614\) 6.45167 11.1746i 0.260368 0.450971i
\(615\) −19.9758 9.89362i −0.805501 0.398949i
\(616\) −13.1805 + 6.10656i −0.531056 + 0.246040i
\(617\) 9.86761i 0.397255i 0.980075 + 0.198627i \(0.0636484\pi\)
−0.980075 + 0.198627i \(0.936352\pi\)
\(618\) −28.0725 + 18.6878i −1.12924 + 0.751735i
\(619\) −31.2933 + 18.0672i −1.25778 + 0.726181i −0.972643 0.232305i \(-0.925373\pi\)
−0.285140 + 0.958486i \(0.592040\pi\)
\(620\) −14.7055 + 8.49022i −0.590587 + 0.340976i
\(621\) 6.32147 18.3121i 0.253672 0.734841i
\(622\) 1.78550i 0.0715921i
\(623\) −11.9069 8.38121i −0.477040 0.335786i
\(624\) −0.768732 + 1.55211i −0.0307739 + 0.0621342i
\(625\) 14.3315 24.8228i 0.573259 0.992914i
\(626\) 5.13913 + 8.90124i 0.205401 + 0.355765i
\(627\) −3.84024 60.1731i −0.153364 2.40308i
\(628\) 8.56382 + 4.94432i 0.341734 + 0.197300i
\(629\) 11.4174 0.455240
\(630\) −12.7514 20.2789i −0.508028 0.807930i
\(631\) −16.0360 −0.638381 −0.319191 0.947691i \(-0.603411\pi\)
−0.319191 + 0.947691i \(0.603411\pi\)
\(632\) 1.12450 + 0.649232i 0.0447303 + 0.0258251i
\(633\) −0.766137 12.0047i −0.0304512 0.477143i
\(634\) −13.6534 23.6484i −0.542245 0.939196i
\(635\) 9.00624 15.5993i 0.357402 0.619038i
\(636\) −5.80155 + 11.7137i −0.230047 + 0.464477i
\(637\) −1.24958 + 6.88757i −0.0495100 + 0.272895i
\(638\) 11.6697i 0.462008i
\(639\) −0.860823 6.71669i −0.0340536 0.265708i
\(640\) 2.61368 1.50901i 0.103315 0.0596488i
\(641\) 24.6391 14.2254i 0.973186 0.561869i 0.0729801 0.997333i \(-0.476749\pi\)
0.900206 + 0.435464i \(0.143416\pi\)
\(642\) 15.3567 10.2230i 0.606082 0.403468i
\(643\) 32.6732i 1.28851i 0.764813 + 0.644253i \(0.222831\pi\)
−0.764813 + 0.644253i \(0.777169\pi\)
\(644\) 9.82433 + 0.883974i 0.387133 + 0.0348335i
\(645\) 48.1737 + 23.8595i 1.89684 + 0.939467i
\(646\) 3.79533 6.57370i 0.149325 0.258639i
\(647\) 20.6357 + 35.7421i 0.811273 + 1.40517i 0.911973 + 0.410249i \(0.134558\pi\)
−0.100700 + 0.994917i \(0.532108\pi\)
\(648\) 2.26963 + 8.70912i 0.0891596 + 0.342127i
\(649\) −19.6092 11.3214i −0.769730 0.444404i
\(650\) −4.10843 −0.161146
\(651\) 22.6566 12.3067i 0.887980 0.482337i
\(652\) 12.6208 0.494268
\(653\) 19.8709 + 11.4724i 0.777607 + 0.448952i 0.835581 0.549367i \(-0.185131\pi\)
−0.0579746 + 0.998318i \(0.518464\pi\)
\(654\) −5.39092 + 0.344048i −0.210802 + 0.0134534i
\(655\) −22.2591 38.5540i −0.869737 1.50643i
\(656\) −2.13220 + 3.69309i −0.0832486 + 0.144191i
\(657\) 1.38096 1.05214i 0.0538764 0.0410477i
\(658\) 8.67045 + 18.7144i 0.338009 + 0.729563i
\(659\) 22.1480i 0.862763i −0.902170 0.431381i \(-0.858026\pi\)
0.902170 0.431381i \(-0.141974\pi\)
\(660\) 15.9042 + 23.8909i 0.619069 + 0.929953i
\(661\) −3.70058 + 2.13653i −0.143936 + 0.0831015i −0.570239 0.821479i \(-0.693149\pi\)
0.426303 + 0.904581i \(0.359816\pi\)
\(662\) −6.99129 + 4.03642i −0.271724 + 0.156880i
\(663\) −1.14906 1.72610i −0.0446260 0.0670363i
\(664\) 11.4985i 0.446228i
\(665\) 21.2828 + 45.9369i 0.825310 + 1.78136i
\(666\) 22.7578 17.3389i 0.881848 0.671869i
\(667\) −3.96211 + 6.86258i −0.153414 + 0.265720i
\(668\) −4.01401 6.95246i −0.155307 0.268999i
\(669\) 14.1833 0.905179i 0.548359 0.0349962i
\(670\) −25.9998 15.0110i −1.00446 0.579924i
\(671\) −52.3772 −2.02200
\(672\) −4.02686 + 2.18733i −0.155339 + 0.0843780i
\(673\) 26.6969 1.02909 0.514545 0.857464i \(-0.327961\pi\)
0.514545 + 0.857464i \(0.327961\pi\)
\(674\) −13.9683 8.06461i −0.538039 0.310637i
\(675\) −16.1226 + 13.9929i −0.620558 + 0.538587i
\(676\) −0.500000 0.866025i −0.0192308 0.0333087i
\(677\) −4.59005 + 7.95020i −0.176410 + 0.305551i −0.940648 0.339383i \(-0.889782\pi\)
0.764238 + 0.644934i \(0.223115\pi\)
\(678\) 21.8420 + 10.8179i 0.838837 + 0.415460i
\(679\) −25.2744 2.27414i −0.969944 0.0872737i
\(680\) 3.61313i 0.138557i
\(681\) −6.07635 + 4.04502i −0.232846 + 0.155005i
\(682\) −26.7525 + 15.4456i −1.02441 + 0.591442i
\(683\) 43.4043 25.0595i 1.66082 0.958874i 0.688494 0.725242i \(-0.258272\pi\)
0.972325 0.233632i \(-0.0750611\pi\)
\(684\) −2.41802 18.8669i −0.0924552 0.721394i
\(685\) 12.4880i 0.477141i
\(686\) −13.1925 + 12.9984i −0.503691 + 0.496281i
\(687\) −5.01301 + 10.1215i −0.191258 + 0.386161i
\(688\) 5.14203 8.90626i 0.196038 0.339548i
\(689\) −3.77346 6.53582i −0.143757 0.248995i
\(690\) −1.24125 19.4493i −0.0472537 0.740423i
\(691\) −11.5331 6.65866i −0.438741 0.253307i 0.264322 0.964434i \(-0.414852\pi\)
−0.703063 + 0.711127i \(0.748185\pi\)
\(692\) 8.89879 0.338281
\(693\) −23.1976 36.8917i −0.881205 1.40140i
\(694\) −10.2686 −0.389792
\(695\) −17.3777 10.0330i −0.659176 0.380575i
\(696\) −0.234470 3.67393i −0.00888755 0.139260i
\(697\) −2.55265 4.42132i −0.0966885 0.167469i
\(698\) −13.4642 + 23.3207i −0.509627 + 0.882700i
\(699\) 13.1861 26.6236i 0.498746 1.00700i
\(700\) −8.88866 6.25668i −0.335960 0.236480i
\(701\) 10.5635i 0.398978i −0.979900 0.199489i \(-0.936072\pi\)
0.979900 0.199489i \(-0.0639283\pi\)
\(702\) −4.91173 1.69556i −0.185381 0.0639949i
\(703\) −52.3661 + 30.2336i −1.97503 + 1.14028i
\(704\) 4.75486 2.74522i 0.179206 0.103464i
\(705\) 33.9218 22.5817i 1.27757 0.850475i
\(706\) 4.16782i 0.156858i
\(707\) −36.3999 + 16.8642i −1.36896 + 0.634244i
\(708\) −6.40098 3.17028i −0.240563 0.119146i
\(709\) −15.2442 + 26.4038i −0.572510 + 0.991616i 0.423798 + 0.905757i \(0.360697\pi\)
−0.996307 + 0.0858589i \(0.972637\pi\)
\(710\) −3.40615 5.89962i −0.127830 0.221409i
\(711\) −1.50305 + 3.59374i −0.0563687 + 0.134776i
\(712\) 4.76616 + 2.75175i 0.178620 + 0.103126i
\(713\) 20.9765 0.785574
\(714\) 0.142641 5.48435i 0.00533822 0.205247i
\(715\) −16.5702 −0.619692
\(716\) 15.8867 + 9.17219i 0.593714 + 0.342781i
\(717\) −27.0252 + 1.72475i −1.00928 + 0.0644119i
\(718\) −6.42566 11.1296i −0.239804 0.415352i
\(719\) −24.3326 + 42.1454i −0.907454 + 1.57176i −0.0898651 + 0.995954i \(0.528644\pi\)
−0.817589 + 0.575802i \(0.804690\pi\)
\(720\) 5.48707 + 7.20194i 0.204491 + 0.268400i
\(721\) 29.6514 42.1247i 1.10428 1.56881i
\(722\) 21.2007i 0.789010i
\(723\) 14.0014 + 21.0326i 0.520716 + 0.782210i
\(724\) 15.5515 8.97866i 0.577967 0.333689i
\(725\) 7.56239 4.36615i 0.280860 0.162155i
\(726\) 18.3753 + 27.6031i 0.681973 + 1.02445i
\(727\) 36.3229i 1.34714i −0.739123 0.673570i \(-0.764760\pi\)
0.739123 0.673570i \(-0.235240\pi\)
\(728\) 0.237102 2.63511i 0.00878758 0.0976635i
\(729\) −25.0498 + 10.0750i −0.927771 + 0.373149i
\(730\) 0.873263 1.51254i 0.0323209 0.0559815i
\(731\) 6.15598 + 10.6625i 0.227687 + 0.394366i
\(732\) −16.4897 + 1.05237i −0.609477 + 0.0388968i
\(733\) 1.50247 + 0.867449i 0.0554948 + 0.0320400i 0.527491 0.849561i \(-0.323133\pi\)
−0.471996 + 0.881601i \(0.656466\pi\)
\(734\) 34.5479 1.27519
\(735\) 29.3644 + 21.8329i 1.08312 + 0.805317i
\(736\) −3.72825 −0.137425
\(737\) −47.2993 27.3083i −1.74229 1.00591i
\(738\) −11.8025 4.93630i −0.434457 0.181708i
\(739\) −6.03360 10.4505i −0.221950 0.384428i 0.733450 0.679743i \(-0.237909\pi\)
−0.955400 + 0.295315i \(0.904575\pi\)
\(740\) 14.3911 24.9262i 0.529028 0.916304i
\(741\) 9.84102 + 4.87407i 0.361519 + 0.179053i
\(742\) 1.78939 19.8869i 0.0656905 0.730072i
\(743\) 6.97172i 0.255768i −0.991789 0.127884i \(-0.959182\pi\)
0.991789 0.127884i \(-0.0408185\pi\)
\(744\) −8.11207 + 5.40019i −0.297403 + 0.197981i
\(745\) −47.3132 + 27.3163i −1.73342 + 1.00079i
\(746\) 11.1674 6.44752i 0.408869 0.236061i
\(747\) −34.2156 + 4.38513i −1.25188 + 0.160444i
\(748\) 6.57309i 0.240336i
\(749\) −16.2204 + 23.0438i −0.592682 + 0.842004i
\(750\) 2.06848 4.17638i 0.0755303 0.152500i
\(751\) −15.1364 + 26.2170i −0.552334 + 0.956671i 0.445771 + 0.895147i \(0.352930\pi\)
−0.998106 + 0.0615244i \(0.980404\pi\)
\(752\) −3.89783 6.75123i −0.142139 0.246192i
\(753\) 2.84274 + 44.5431i 0.103595 + 1.62324i
\(754\) 1.84070 + 1.06273i 0.0670343 + 0.0387023i
\(755\) −18.5309 −0.674409
\(756\) −8.04446 11.1484i −0.292574 0.405463i
\(757\) 27.9273 1.01504 0.507518 0.861641i \(-0.330563\pi\)
0.507518 + 0.861641i \(0.330563\pi\)
\(758\) 4.35651 + 2.51523i 0.158236 + 0.0913574i
\(759\) −2.25811 35.3826i −0.0819644 1.28431i
\(760\) −9.56773 16.5718i −0.347058 0.601122i
\(761\) −17.9005 + 31.0045i −0.648892 + 1.12391i 0.334496 + 0.942397i \(0.391434\pi\)
−0.983388 + 0.181516i \(0.941900\pi\)
\(762\) 4.58803 9.26349i 0.166207 0.335581i
\(763\) 7.48701 3.46876i 0.271048 0.125578i
\(764\) 0.543864i 0.0196763i
\(765\) −10.7515 + 1.37793i −0.388720 + 0.0498191i
\(766\) 9.53136 5.50293i 0.344382 0.198829i
\(767\) 3.57153 2.06202i 0.128960 0.0744553i
\(768\) 1.44180 0.959803i 0.0520264 0.0346339i
\(769\) 0.430697i 0.0155313i −0.999970 0.00776566i \(-0.997528\pi\)
0.999970 0.00776566i \(-0.00247191\pi\)
\(770\) −35.8500 25.2346i −1.29194 0.909393i
\(771\) 8.58244 + 4.25072i 0.309089 + 0.153086i
\(772\) −6.85549 + 11.8741i −0.246734 + 0.427356i
\(773\) 5.41320 + 9.37594i 0.194699 + 0.337229i 0.946802 0.321817i \(-0.104294\pi\)
−0.752103 + 0.659046i \(0.770960\pi\)
\(774\) 28.4630 + 11.9044i 1.02308 + 0.427895i
\(775\) −20.0186 11.5577i −0.719090 0.415167i
\(776\) 9.59143 0.344312
\(777\) −22.8282 + 37.2671i −0.818958 + 1.33695i
\(778\) −18.7292 −0.671475
\(779\) 23.4157 + 13.5190i 0.838953 + 0.484370i
\(780\) −5.21675 + 0.332932i −0.186789 + 0.0119209i
\(781\) −6.19654 10.7327i −0.221729 0.384047i
\(782\) 2.23171 3.86543i 0.0798057 0.138227i
\(783\) 10.8429 2.09881i 0.387495 0.0750055i
\(784\) 4.52595 5.34002i 0.161641 0.190715i
\(785\) 29.8441i 1.06518i
\(786\) −14.1579 21.2677i −0.504995 0.758594i
\(787\) 26.0383 15.0332i 0.928166 0.535877i 0.0419351 0.999120i \(-0.486648\pi\)
0.886231 + 0.463243i \(0.153314\pi\)
\(788\) −3.07275 + 1.77405i −0.109462 + 0.0631980i
\(789\) −22.5583 33.8866i −0.803097 1.20640i
\(790\) 3.91879i 0.139424i
\(791\) −37.0824 3.33660i −1.31850 0.118636i
\(792\) 9.98219 + 13.1019i 0.354702 + 0.465556i
\(793\) 4.76985 8.26163i 0.169382 0.293379i
\(794\) −5.93579 10.2811i −0.210653 0.364862i
\(795\) −39.3704 + 2.51261i −1.39632 + 0.0891132i
\(796\) −17.9941 10.3889i −0.637783 0.368224i
\(797\) 29.6965 1.05190 0.525952 0.850514i \(-0.323709\pi\)
0.525952 + 0.850514i \(0.323709\pi\)
\(798\) 13.8686 + 25.5319i 0.490941 + 0.903820i
\(799\) 9.33286 0.330173
\(800\) 3.55800 + 2.05422i 0.125794 + 0.0726275i
\(801\) −6.37061 + 15.2319i −0.225094 + 0.538193i
\(802\) 10.2050 + 17.6755i 0.360350 + 0.624144i
\(803\) 1.58866 2.75164i 0.0560625 0.0971031i
\(804\) −15.4397 7.64701i −0.544518 0.269689i
\(805\) 12.5146 + 27.0116i 0.441081 + 0.952033i
\(806\) 5.62636i 0.198180i
\(807\) −7.73379 + 5.14838i −0.272242 + 0.181231i
\(808\) 13.1313 7.58135i 0.461957 0.266711i
\(809\) −20.1548 + 11.6364i −0.708606 + 0.409114i −0.810545 0.585677i \(-0.800829\pi\)
0.101939 + 0.994791i \(0.467495\pi\)
\(810\) −19.3380 + 19.0742i −0.679466 + 0.670200i
\(811\) 4.77384i 0.167632i 0.996481 + 0.0838160i \(0.0267108\pi\)
−0.996481 + 0.0838160i \(0.973289\pi\)
\(812\) 2.36397 + 5.10241i 0.0829590 + 0.179060i
\(813\) 10.6269 21.4563i 0.372702 0.752506i
\(814\) 26.1806 45.3462i 0.917631 1.58938i
\(815\) 19.0449 + 32.9867i 0.667112 + 1.15547i
\(816\) 0.132068 + 2.06938i 0.00462329 + 0.0724428i
\(817\) −56.4693 32.6026i −1.97561 1.14062i
\(818\) 3.59889 0.125832
\(819\) 7.93160 0.299406i 0.277153 0.0104621i
\(820\) −12.8701 −0.449442
\(821\) −26.7609 15.4504i −0.933961 0.539223i −0.0458987 0.998946i \(-0.514615\pi\)
−0.888062 + 0.459724i \(0.847948\pi\)
\(822\) 0.456462 + 7.15234i 0.0159209 + 0.249467i
\(823\) 15.9072 + 27.5520i 0.554489 + 0.960403i 0.997943 + 0.0641062i \(0.0204196\pi\)
−0.443454 + 0.896297i \(0.646247\pi\)
\(824\) −9.73525 + 16.8619i −0.339143 + 0.587413i
\(825\) −17.3403 + 35.0111i −0.603713 + 1.21893i
\(826\) 10.8673 + 0.977818i 0.378121 + 0.0340226i
\(827\) 4.77010i 0.165872i −0.996555 0.0829362i \(-0.973570\pi\)
0.996555 0.0829362i \(-0.0264298\pi\)
\(828\) −1.42183 11.0940i −0.0494119 0.385543i
\(829\) −2.70219 + 1.56011i −0.0938510 + 0.0541849i −0.546191 0.837661i \(-0.683923\pi\)
0.452340 + 0.891846i \(0.350589\pi\)
\(830\) −30.0533 + 17.3513i −1.04317 + 0.602273i
\(831\) 36.0334 23.9874i 1.24999 0.832114i
\(832\) 1.00000i 0.0346688i
\(833\) 2.82730 + 7.88898i 0.0979602 + 0.273337i
\(834\) −10.3196 5.11112i −0.357340 0.176984i
\(835\) 12.1143 20.9826i 0.419234 0.726135i
\(836\) −17.4058 30.1477i −0.601992 1.04268i
\(837\) −19.1628 22.0793i −0.662364 0.763173i
\(838\) 9.82609 + 5.67310i 0.339437 + 0.195974i
\(839\) 35.9486 1.24108 0.620542 0.784173i \(-0.286913\pi\)
0.620542 + 0.784173i \(0.286913\pi\)
\(840\) −11.7935 7.22422i −0.406916 0.249259i
\(841\) 24.4824 0.844222
\(842\) 3.37450 + 1.94827i 0.116293 + 0.0671418i
\(843\) 29.8817 1.90705i 1.02918 0.0656822i
\(844\) −3.47250 6.01455i −0.119528 0.207029i
\(845\) 1.50901 2.61368i 0.0519115 0.0899133i
\(846\) 18.6029 14.1733i 0.639580 0.487288i
\(847\) −41.4204 29.1556i −1.42322 1.00180i
\(848\) 7.54692i 0.259162i
\(849\) −8.55597 12.8526i −0.293640 0.441101i
\(850\) −4.25960 + 2.45928i −0.146103 + 0.0843527i
\(851\) −30.7920 + 17.7778i −1.05554 + 0.609415i
\(852\) −2.16648 3.25444i −0.0742222 0.111495i
\(853\) 23.9134i 0.818780i 0.912359 + 0.409390i \(0.134259\pi\)
−0.912359 + 0.409390i \(0.865741\pi\)
\(854\) 22.9012 10.6102i 0.783663 0.363074i
\(855\) 45.6632 34.7902i 1.56165 1.18980i
\(856\) 5.32555 9.22412i 0.182024 0.315274i
\(857\) −25.9972 45.0284i −0.888046 1.53814i −0.842182 0.539194i \(-0.818729\pi\)
−0.0458647 0.998948i \(-0.514604\pi\)
\(858\) −9.49041 + 0.605677i −0.323997 + 0.0206775i
\(859\) −13.5281 7.81046i −0.461573 0.266490i 0.251132 0.967953i \(-0.419197\pi\)
−0.712706 + 0.701463i \(0.752530\pi\)
\(860\) 31.0375 1.05837
\(861\) 19.5354 + 0.508092i 0.665764 + 0.0173157i
\(862\) −28.0774 −0.956319
\(863\) 26.2981 + 15.1832i 0.895196 + 0.516842i 0.875639 0.482967i \(-0.160441\pi\)
0.0195575 + 0.999809i \(0.493774\pi\)
\(864\) 3.40590 + 3.92426i 0.115871 + 0.133506i
\(865\) 13.4284 + 23.2586i 0.456578 + 0.790816i
\(866\) −4.06167 + 7.03502i −0.138021 + 0.239060i
\(867\) 24.1613 + 11.9666i 0.820562 + 0.406409i
\(868\) 8.56832 12.1727i 0.290828 0.413169i
\(869\) 7.12914i 0.241840i
\(870\) 9.24865 6.15681i 0.313559 0.208736i
\(871\) 8.61485 4.97378i 0.291903 0.168530i
\(872\) −2.70095 + 1.55939i −0.0914656 + 0.0528077i
\(873\) 3.65785 + 28.5408i 0.123799 + 0.965961i
\(874\) 23.6386i 0.799587i
\(875\) −0.637987 + 7.09047i −0.0215679 + 0.239702i
\(876\) 0.444865 0.898207i 0.0150306 0.0303476i
\(877\) −12.4275 + 21.5250i −0.419646 + 0.726848i −0.995904 0.0904201i \(-0.971179\pi\)
0.576258 + 0.817268i \(0.304512\pi\)
\(878\) 18.1561 + 31.4473i 0.612738 + 1.06129i
\(879\) −0.670224 10.5018i −0.0226061 0.354217i
\(880\) 14.3503 + 8.28512i 0.483747 + 0.279291i
\(881\) −5.01841 −0.169074 −0.0845372 0.996420i \(-0.526941\pi\)
−0.0845372 + 0.996420i \(0.526941\pi\)
\(882\) 17.6161 + 11.4312i 0.593166 + 0.384908i
\(883\) −55.4526 −1.86613 −0.933065 0.359709i \(-0.882876\pi\)
−0.933065 + 0.359709i \(0.882876\pi\)
\(884\) −1.03680 0.598594i −0.0348712 0.0201329i
\(885\) −1.37303 21.5141i −0.0461538 0.723188i
\(886\) −8.29928 14.3748i −0.278820 0.482930i
\(887\) −13.2901 + 23.0191i −0.446237 + 0.772904i −0.998137 0.0610053i \(-0.980569\pi\)
0.551901 + 0.833910i \(0.313903\pi\)
\(888\) 7.33124 14.8022i 0.246020 0.496729i
\(889\) −1.41510 + 15.7271i −0.0474609 + 0.527471i
\(890\) 16.6096i 0.556756i
\(891\) −35.1800 + 34.7002i −1.17857 + 1.16250i
\(892\) 7.10609 4.10270i 0.237930 0.137369i
\(893\) −42.8055 + 24.7138i −1.43243 + 0.827016i
\(894\) −26.0996 + 17.3745i −0.872901 + 0.581089i
\(895\) 55.3637i 1.85060i
\(896\) −1.52289 + 2.16352i −0.0508762 + 0.0722781i
\(897\) 5.78666 + 2.86602i 0.193211 + 0.0956937i
\(898\) 8.23803 14.2687i 0.274906 0.476152i
\(899\) 5.97929 + 10.3564i 0.199421 + 0.345407i
\(900\) −4.75575 + 11.3708i −0.158525 + 0.379028i
\(901\) −7.82461 4.51754i −0.260675 0.150501i
\(902\) −23.4135 −0.779583
\(903\) −47.1116 1.22532i −1.56778 0.0407760i
\(904\) 14.0724 0.468043
\(905\) 46.9347 + 27.0977i 1.56016 + 0.900760i
\(906\) −10.6134 + 0.677344i −0.352605 + 0.0225033i
\(907\) −15.0153 26.0073i −0.498576 0.863560i 0.501422 0.865203i \(-0.332810\pi\)
−0.999999 + 0.00164298i \(0.999477\pi\)
\(908\) −2.10721 + 3.64980i −0.0699303 + 0.121123i
\(909\) 27.5673 + 36.1830i 0.914351 + 1.20011i
\(910\) 7.24511 3.35669i 0.240173 0.111273i
\(911\) 24.4214i 0.809116i 0.914512 + 0.404558i \(0.132575\pi\)
−0.914512 + 0.404558i \(0.867425\pi\)
\(912\) −6.08554 9.14158i −0.201512 0.302708i
\(913\) −54.6737 + 31.5659i −1.80943 + 1.04468i
\(914\) 10.5560 6.09451i 0.349162 0.201589i
\(915\) −27.6337 41.5108i −0.913541 1.37230i
\(916\) 6.52114i 0.215465i
\(917\) 31.9137 + 22.4639i 1.05388 + 0.741823i
\(918\) −6.10741 + 1.18218i −0.201575 + 0.0390178i
\(919\) 3.27156 5.66651i 0.107919 0.186921i −0.807008 0.590540i \(-0.798915\pi\)
0.914927 + 0.403619i \(0.132248\pi\)
\(920\) −5.62596 9.74444i −0.185482 0.321265i
\(921\) 22.3039 1.42343i 0.734937 0.0469036i
\(922\) −22.1912 12.8121i −0.730829 0.421945i
\(923\) 2.25721 0.0742969
\(924\) −21.4551 13.1425i −0.705819 0.432355i
\(925\) 39.1813 1.28827
\(926\) 25.1046 + 14.4942i 0.824990 + 0.476308i
\(927\) −53.8881 22.5382i −1.76992 0.740252i
\(928\) −1.06273 1.84070i −0.0348858 0.0604239i
\(929\) −16.8048 + 29.1068i −0.551348 + 0.954963i 0.446829 + 0.894619i \(0.352553\pi\)
−0.998178 + 0.0603439i \(0.980780\pi\)
\(930\) −26.3556 13.0534i −0.864233 0.428038i
\(931\) −33.8579 28.6963i −1.10965 0.940485i
\(932\) 17.1531i 0.561869i
\(933\) −2.57433 + 1.71373i −0.0842798 + 0.0561050i
\(934\) 6.44665 3.72197i 0.210941 0.121787i
\(935\) −17.1799 + 9.91885i −0.561844 + 0.324381i
\(936\) −2.97566 + 0.381366i −0.0972625 + 0.0124653i
\(937\) 33.8011i 1.10424i 0.833766 + 0.552118i \(0.186180\pi\)
−0.833766 + 0.552118i \(0.813820\pi\)
\(938\) 26.2129 + 2.35859i 0.855881 + 0.0770106i
\(939\) −7.90123 + 15.9530i −0.257847 + 0.520607i
\(940\) 11.7637 20.3753i 0.383690 0.664570i
\(941\) −4.97207 8.61189i −0.162085 0.280739i 0.773531 0.633758i \(-0.218489\pi\)
−0.935616 + 0.353019i \(0.885155\pi\)
\(942\) 1.09087 + 17.0929i 0.0355423 + 0.556916i
\(943\) 13.7687 + 7.94938i 0.448372 + 0.258868i
\(944\) −4.12404 −0.134226
\(945\) 16.9992 37.8487i 0.552983 1.23122i
\(946\) 56.4640 1.83580
\(947\) −39.3441 22.7153i −1.27851 0.738149i −0.301937 0.953328i \(-0.597633\pi\)
−0.976575 + 0.215179i \(0.930967\pi\)
\(948\) 0.143240 + 2.24444i 0.00465222 + 0.0728960i
\(949\) 0.289350 + 0.501169i 0.00939270 + 0.0162686i
\(950\) 13.0246 22.5592i 0.422572 0.731917i
\(951\) 20.9916 42.3832i 0.680698 1.37437i
\(952\) −1.33153 2.87399i −0.0431552 0.0931466i
\(953\) 2.98833i 0.0968014i −0.998828 0.0484007i \(-0.984588\pi\)
0.998828 0.0484007i \(-0.0154124\pi\)
\(954\) −22.4571 + 2.87814i −0.727074 + 0.0931832i
\(955\) 1.42149 0.820695i 0.0459982 0.0265571i
\(956\) −13.5401 + 7.81738i −0.437918 + 0.252832i
\(957\) 16.8253 11.2006i 0.543886 0.362064i
\(958\) 29.6519i 0.958011i
\(959\) −4.60214 9.93330i −0.148611 0.320763i
\(960\) 4.68430 + 2.32005i 0.151185 + 0.0748791i
\(961\) 0.327955 0.568034i 0.0105792 0.0183237i
\(962\) 4.76840 + 8.25912i 0.153739 + 0.266285i
\(963\) 29.4789 + 12.3293i 0.949943 + 0.397305i
\(964\) 12.6334 + 7.29387i 0.406893 + 0.234920i
\(965\) −41.3800 −1.33207
\(966\) 8.15490 + 15.0131i 0.262380 + 0.483039i
\(967\) −2.70295 −0.0869209 −0.0434604 0.999055i \(-0.513838\pi\)
−0.0434604 + 0.999055i \(0.513838\pi\)
\(968\) 16.5800 + 9.57246i 0.532901 + 0.307671i
\(969\) 13.1207 0.837363i 0.421498 0.0269000i
\(970\) 14.4736 + 25.0689i 0.464718 + 0.804915i
\(971\) 18.6175 32.2464i 0.597464 1.03484i −0.395731 0.918367i \(-0.629509\pi\)
0.993194 0.116471i \(-0.0371581\pi\)
\(972\) −10.3784 + 11.6314i −0.332887 + 0.373077i
\(973\) 17.5202 + 1.57643i 0.561672 + 0.0505382i
\(974\) 30.0048i 0.961415i
\(975\) −3.94328 5.92352i −0.126286 0.189705i
\(976\) −8.26163 + 4.76985i −0.264448 + 0.152679i
\(977\) 21.8979 12.6427i 0.700575 0.404477i −0.106986 0.994260i \(-0.534120\pi\)
0.807562 + 0.589783i \(0.200787\pi\)
\(978\) 12.1135 + 18.1966i 0.387345 + 0.581863i
\(979\) 30.2166i 0.965726i
\(980\) 20.7868 + 3.77124i 0.664010 + 0.120468i
\(981\) −5.67027 7.44240i −0.181038 0.237618i
\(982\) 1.10426 1.91263i 0.0352382 0.0610344i
\(983\) −18.5197 32.0771i −0.590687 1.02310i −0.994140 0.108099i \(-0.965524\pi\)
0.403454 0.915000i \(-0.367810\pi\)
\(984\) −7.37118 + 0.470428i −0.234985 + 0.0149967i
\(985\) −9.27362 5.35412i −0.295482 0.170597i
\(986\) 2.54457 0.0810357
\(987\) −18.6604 + 30.4632i −0.593968 + 0.969653i
\(988\) 6.34040 0.201715
\(989\) −33.2047 19.1708i −1.05585 0.609595i
\(990\) −19.1810 + 45.8612i −0.609613 + 1.45756i
\(991\) 24.0812 + 41.7098i 0.764963 + 1.32495i 0.940266 + 0.340440i \(0.110576\pi\)
−0.175303 + 0.984515i \(0.556091\pi\)
\(992\) −2.81318 + 4.87257i −0.0893185 + 0.154704i
\(993\) −12.5300 6.20585i −0.397626 0.196937i
\(994\) 4.88351 + 3.43748i 0.154896 + 0.109030i
\(995\) 62.7077i 1.98797i
\(996\) −16.5785 + 11.0363i −0.525309 + 0.349698i
\(997\) 17.2791 9.97610i 0.547235 0.315946i −0.200771 0.979638i \(-0.564345\pi\)
0.748006 + 0.663692i \(0.231011\pi\)
\(998\) −26.5618 + 15.3354i −0.840798 + 0.485435i
\(999\) 46.8422 + 16.1702i 1.48202 + 0.511604i
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.z.a.131.12 32
3.2 odd 2 546.2.z.b.131.2 yes 32
7.3 odd 6 546.2.z.b.521.2 yes 32
21.17 even 6 inner 546.2.z.a.521.12 yes 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
546.2.z.a.131.12 32 1.1 even 1 trivial
546.2.z.a.521.12 yes 32 21.17 even 6 inner
546.2.z.b.131.2 yes 32 3.2 odd 2
546.2.z.b.521.2 yes 32 7.3 odd 6