Properties

Label 546.2.z.b.131.2
Level $546$
Weight $2$
Character 546.131
Analytic conductor $4.360$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

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 131.2
Character \(\chi\) \(=\) 546.131
Dual form 546.2.z.b.521.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(-1.44180 - 0.959803i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.50901 - 2.61368i) q^{5} +(0.768732 + 1.55211i) q^{6} +(0.237102 - 2.63511i) q^{7} -1.00000i q^{8} +(1.15756 + 2.76768i) q^{9} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(-1.44180 - 0.959803i) 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} +(1.15756 + 2.76768i) q^{9} +(-2.61368 + 1.50901i) q^{10} +(4.75486 - 2.74522i) q^{11} +(0.110315 - 1.72853i) 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} +(0.381366 - 2.97566i) q^{18} +(5.49095 + 3.17020i) q^{19} +3.01802 q^{20} +(-2.87103 + 3.57172i) q^{21} -5.49044 q^{22} +(-3.22876 - 1.86412i) q^{23} +(-0.959803 + 1.44180i) 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} +(5.21675 + 0.332932i) q^{30} +(4.87257 - 2.81318i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-9.49041 - 0.605677i) 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} +(-0.959803 + 1.44180i) q^{39} +(-2.61368 - 1.50901i) q^{40} -4.26441 q^{41} +(4.27225 - 1.65768i) q^{42} -10.2841 q^{43} +(4.75486 + 2.74522i) q^{44} +(8.98060 + 1.15097i) 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} +(0.132068 - 2.06938i) q^{51} +(0.866025 - 0.500000i) q^{52} +(-6.53582 + 3.77346i) q^{53} +(-3.40590 + 3.92426i) 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} +(-4.35137 - 2.89670i) q^{60} +(8.26163 + 4.76985i) q^{61} -5.62636 q^{62} +(7.56759 - 2.39407i) q^{63} -1.00000 q^{64} +(-2.61368 - 1.50901i) q^{65} +(7.91610 + 5.26974i) 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} +(2.76768 - 1.15756i) q^{72} +(-0.501169 + 0.289350i) q^{73} +(8.25912 - 4.76840i) q^{74} +(-0.453221 + 7.10156i) 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} +(-6.32012 + 6.40750i) q^{81} +(3.69309 + 2.13220i) q^{82} -11.4985 q^{83} +(-4.52871 - 0.700530i) q^{84} +3.61313 q^{85} +(8.90626 + 5.14203i) q^{86} +(-2.04002 + 3.06448i) 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} +(-9.72535 - 0.620671i) q^{93} +(-6.75123 + 3.89783i) q^{94} +(16.5718 - 9.56773i) q^{95} +(-1.72853 - 0.110315i) 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 \( 32 q + 16 q^{4} + 2 q^{7} + 2 q^{9} + 6 q^{10} + 24 q^{11} - 4 q^{14} - 12 q^{15} - 16 q^{16} - 4 q^{17} - 24 q^{18} + 4 q^{21} - 12 q^{22} - 6 q^{24} - 18 q^{25} - 16 q^{26} + 6 q^{27} - 2 q^{28} - 8 q^{30} - 6 q^{31} + 14 q^{33} - 48 q^{35} + 4 q^{36} - 16 q^{38} - 6 q^{39} + 6 q^{40} - 16 q^{41} + 14 q^{42} + 32 q^{43} + 24 q^{44} + 20 q^{45} + 16 q^{46} - 20 q^{47} - 26 q^{49} - 46 q^{51} + 60 q^{53} + 6 q^{54} - 8 q^{56} - 8 q^{57} - 10 q^{58} - 8 q^{59} - 6 q^{60} + 36 q^{61} - 36 q^{62} + 84 q^{63} - 32 q^{64} + 6 q^{65} + 36 q^{66} + 4 q^{68} + 36 q^{69} - 18 q^{70} - 24 q^{72} - 48 q^{73} + 84 q^{74} - 2 q^{75} - 52 q^{77} + 18 q^{79} - 74 q^{81} - 24 q^{83} + 8 q^{84} - 32 q^{85} + 24 q^{86} + 14 q^{87} - 6 q^{88} + 20 q^{89} + 6 q^{90} - 8 q^{91} - 40 q^{93} + 72 q^{95} - 6 q^{96} - 32 q^{98}+O(q^{100}) \) 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
\(3\) −1.44180 0.959803i −0.832422 0.554142i
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 1.50901 2.61368i 0.674849 1.16887i −0.301664 0.953414i \(-0.597542\pi\)
0.976513 0.215459i \(-0.0691247\pi\)
\(6\) 0.768732 + 1.55211i 0.313833 + 0.633647i
\(7\) 0.237102 2.63511i 0.0896160 0.995976i
\(8\) 1.00000i 0.353553i
\(9\) 1.15756 + 2.76768i 0.385853 + 0.922560i
\(10\) −2.61368 + 1.50901i −0.826518 + 0.477190i
\(11\) 4.75486 2.74522i 1.43364 0.827715i 0.436248 0.899827i \(-0.356307\pi\)
0.997397 + 0.0721117i \(0.0229738\pi\)
\(12\) 0.110315 1.72853i 0.0318452 0.498985i
\(13\) 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 0.929440 0.368973i \(-0.120290\pi\)
−0.784260 + 0.620432i \(0.786957\pi\)
\(18\) 0.381366 2.97566i 0.0898889 0.701370i
\(19\) 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
\(21\) −2.87103 + 3.57172i −0.626511 + 0.779413i
\(22\) −5.49044 −1.17057
\(23\) −3.22876 1.86412i −0.673242 0.388697i 0.124062 0.992274i \(-0.460408\pi\)
−0.797304 + 0.603578i \(0.793741\pi\)
\(24\) −0.959803 + 1.44180i −0.195919 + 0.294306i
\(25\) −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 \(-0.936768\pi\)
0.980334 0.197344i \(-0.0632315\pi\)
\(30\) 5.21675 + 0.332932i 0.952443 + 0.0607848i
\(31\) 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
\(33\) −9.49041 0.605677i −1.65207 0.105435i
\(34\) 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
\(39\) −0.959803 + 1.44180i −0.153691 + 0.230872i
\(40\) −2.61368 1.50901i −0.413259 0.238595i
\(41\) −4.26441 −0.665989 −0.332994 0.942929i \(-0.608059\pi\)
−0.332994 + 0.942929i \(0.608059\pi\)
\(42\) 4.27225 1.65768i 0.659222 0.255786i
\(43\) −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
\(45\) 8.98060 + 1.15097i 1.33875 + 0.171576i
\(46\) 1.86412 + 3.22876i 0.274850 + 0.476054i
\(47\) 3.89783 6.75123i 0.568556 0.984768i −0.428153 0.903706i \(-0.640835\pi\)
0.996709 0.0810620i \(-0.0258312\pi\)
\(48\) 1.55211 0.768732i 0.224028 0.110957i
\(49\) −6.88757 1.24958i −0.983938 0.178511i
\(50\) 4.10843i 0.581020i
\(51\) 0.132068 2.06938i 0.0184932 0.289771i
\(52\) 0.866025 0.500000i 0.120096 0.0693375i
\(53\) −6.53582 + 3.77346i −0.897764 + 0.518324i −0.876474 0.481449i \(-0.840111\pi\)
−0.0212900 + 0.999773i \(0.506777\pi\)
\(54\) −3.40590 + 3.92426i −0.463484 + 0.534025i
\(55\) 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 0.700010 0.714133i \(-0.253179\pi\)
−0.968462 + 0.249160i \(0.919846\pi\)
\(60\) −4.35137 2.89670i −0.561759 0.373963i
\(61\) 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
\(63\) 7.56759 2.39407i 0.953427 0.301624i
\(64\) −1.00000 −0.125000
\(65\) −2.61368 1.50901i −0.324187 0.187170i
\(66\) 7.91610 + 5.26974i 0.974405 + 0.648660i
\(67\) 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 \(-0.957237\pi\)
0.990989 0.133941i \(-0.0427632\pi\)
\(72\) 2.76768 1.15756i 0.326174 0.136419i
\(73\) −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
\(75\) −0.453221 + 7.10156i −0.0523335 + 0.820018i
\(76\) 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
\(81\) −6.32012 + 6.40750i −0.702236 + 0.711945i
\(82\) 3.69309 + 2.13220i 0.407833 + 0.235463i
\(83\) −11.4985 −1.26212 −0.631061 0.775733i \(-0.717380\pi\)
−0.631061 + 0.775733i \(0.717380\pi\)
\(84\) −4.52871 0.700530i −0.494123 0.0764341i
\(85\) 3.61313 0.391899
\(86\) 8.90626 + 5.14203i 0.960387 + 0.554480i
\(87\) −2.04002 + 3.06448i −0.218713 + 0.328547i
\(88\) −2.74522 4.75486i −0.292641 0.506870i
\(89\) −2.75175 + 4.76616i −0.291685 + 0.505212i −0.974208 0.225651i \(-0.927549\pi\)
0.682524 + 0.730863i \(0.260882\pi\)
\(90\) −7.20194 5.48707i −0.759151 0.578388i
\(91\) −2.63511 0.237102i −0.276234 0.0248550i
\(92\) 3.72825i 0.388697i
\(93\) −9.72535 0.620671i −1.00847 0.0643606i
\(94\) −6.75123 + 3.89783i −0.696336 + 0.402030i
\(95\) 16.5718 9.56773i 1.70023 0.981628i
\(96\) −1.72853 0.110315i −0.176418 0.0112590i
\(97\) 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 \(0.105392\pi\)
−0.191314 + 0.981529i \(0.561275\pi\)
\(102\) −1.14906 + 1.72610i −0.113774 + 0.170910i
\(103\) 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
\(105\) 5.00291 + 12.8937i 0.488234 + 1.25830i
\(106\) 7.54692 0.733021
\(107\) 9.22412 + 5.32555i 0.891730 + 0.514840i 0.874508 0.485011i \(-0.161185\pi\)
0.0172218 + 0.999852i \(0.494518\pi\)
\(108\) 4.91173 1.69556i 0.472631 0.163156i
\(109\) 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 \(0.230255\pi\)
−0.749581 + 0.661912i \(0.769745\pi\)
\(114\) −0.699441 + 10.9596i −0.0655087 + 1.02646i
\(115\) −9.74444 + 5.62596i −0.908674 + 0.524623i
\(116\) 1.84070 1.06273i 0.170905 0.0986719i
\(117\) 2.76768 1.15756i 0.255872 0.107016i
\(118\) 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
\(123\) 6.14841 + 4.09299i 0.554384 + 0.369053i
\(124\) 4.87257 + 2.81318i 0.437570 + 0.252631i
\(125\) 2.69077 0.240670
\(126\) −7.75076 1.71047i −0.690493 0.152381i
\(127\) −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
\(129\) 14.8275 + 9.87067i 1.30549 + 0.869064i
\(130\) 1.50901 + 2.61368i 0.132349 + 0.229235i
\(131\) 7.37542 12.7746i 0.644393 1.11612i −0.340048 0.940408i \(-0.610443\pi\)
0.984441 0.175714i \(-0.0562233\pi\)
\(132\) −4.22067 8.52178i −0.367363 0.741725i
\(133\) 9.65573 13.7176i 0.837258 1.18946i
\(134\) 9.94757i 0.859339i
\(135\) −11.8435 10.2791i −1.01933 0.884681i
\(136\) 1.03680 0.598594i 0.0889045 0.0513290i
\(137\) −3.58345 + 2.06890i −0.306154 + 0.176758i −0.645204 0.764010i \(-0.723228\pi\)
0.339050 + 0.940768i \(0.389894\pi\)
\(138\) 0.411281 6.44440i 0.0350106 0.548584i
\(139\) 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
\(144\) −2.97566 0.381366i −0.247972 0.0317805i
\(145\) −5.55526 3.20733i −0.461340 0.266355i
\(146\) 0.578700 0.0478935
\(147\) 8.73113 + 8.41234i 0.720131 + 0.693838i
\(148\) −9.53681 −0.783921
\(149\) −15.6769 9.05107i −1.28430 0.741492i −0.306671 0.951816i \(-0.599215\pi\)
−0.977632 + 0.210323i \(0.932548\pi\)
\(150\) 3.94328 5.92352i 0.321968 0.483654i
\(151\) 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
\(156\) −1.72853 0.110315i −0.138393 0.00883226i
\(157\) 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
\(159\) 13.0451 + 0.832537i 1.03454 + 0.0660245i
\(160\) 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
\(165\) −15.9042 + 23.8909i −1.23814 + 1.85991i
\(166\) 9.95798 + 5.74924i 0.772889 + 0.446228i
\(167\) 8.02801 0.621226 0.310613 0.950536i \(-0.399466\pi\)
0.310613 + 0.950536i \(0.399466\pi\)
\(168\) 3.57172 + 2.87103i 0.275564 + 0.221505i
\(169\) −1.00000 −0.0769231
\(170\) −3.12907 1.80657i −0.239988 0.138557i
\(171\) −2.41802 + 18.8669i −0.184910 + 1.44279i
\(172\) −5.14203 8.90626i −0.392076 0.679096i
\(173\) −4.44940 + 7.70658i −0.338281 + 0.585921i −0.984110 0.177562i \(-0.943179\pi\)
0.645828 + 0.763483i \(0.276512\pi\)
\(174\) 3.29895 1.63391i 0.250093 0.123866i
\(175\) −9.86278 + 4.56946i −0.745556 + 0.345419i
\(176\) 5.49044i 0.413857i
\(177\) −0.454943 + 7.12855i −0.0341956 + 0.535815i
\(178\) 4.76616 2.75175i 0.357239 0.206252i
\(179\) −15.8867 + 9.17219i −1.18743 + 0.685562i −0.957721 0.287698i \(-0.907110\pi\)
−0.229707 + 0.973260i \(0.573777\pi\)
\(180\) 3.49353 + 8.35291i 0.260392 + 0.622589i
\(181\) 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
\(186\) 8.11207 + 5.40019i 0.594806 + 0.395961i
\(187\) 5.69246 + 3.28654i 0.416274 + 0.240336i
\(188\) 7.79565 0.568556
\(189\) −13.2088 3.81164i −0.960796 0.277256i
\(190\) −19.1355 −1.38823
\(191\) 0.471000 + 0.271932i 0.0340803 + 0.0196763i 0.516943 0.856020i \(-0.327070\pi\)
−0.482863 + 0.875696i \(0.660403\pi\)
\(192\) 1.44180 + 0.959803i 0.104053 + 0.0692678i
\(193\) 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 \(-0.959659\pi\)
0.991980 0.126396i \(-0.0403410\pi\)
\(198\) −6.35550 15.1958i −0.451666 1.07992i
\(199\) −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
\(201\) 1.09737 17.1947i 0.0774022 1.21282i
\(202\) 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
\(207\) 1.42183 11.0940i 0.0988238 0.771086i
\(208\) 0.866025 + 0.500000i 0.0600481 + 0.0346688i
\(209\) 34.8116 2.40797
\(210\) 2.11421 13.6677i 0.145894 0.943164i
\(211\) −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
\(213\) −2.16648 + 3.25444i −0.148444 + 0.222990i
\(214\) −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
\(219\) 1.00030 + 0.0638392i 0.0675942 + 0.00431385i
\(220\) 14.3503 8.28512i 0.967494 0.558583i
\(221\) 1.03680 0.598594i 0.0697424 0.0402658i
\(222\) −16.4847 1.05205i −1.10638 0.0706091i
\(223\) 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 0.787583 0.616208i \(-0.211332\pi\)
−0.927444 + 0.373963i \(0.877999\pi\)
\(228\) 6.08554 9.14158i 0.403025 0.605416i
\(229\) 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
\(231\) −3.84622 + 24.8646i −0.253063 + 1.63597i
\(232\) −2.12546 −0.139543
\(233\) 14.8550 + 8.57656i 0.973186 + 0.561869i 0.900206 0.435464i \(-0.143416\pi\)
0.0729798 + 0.997333i \(0.476749\pi\)
\(234\) −2.97566 0.381366i −0.194525 0.0249307i
\(235\) −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 \(-0.831247\pi\)
0.862730 0.505664i \(-0.168753\pi\)
\(240\) 0.332932 5.21675i 0.0214907 0.336740i
\(241\) 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
\(243\) 15.2623 3.17225i 0.979075 0.203500i
\(244\) 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
\(249\) 16.5785 + 11.0363i 1.05062 + 0.699395i
\(250\) −2.33028 1.34539i −0.147380 0.0850897i
\(251\) −25.7693 −1.62654 −0.813272 0.581884i \(-0.802316\pi\)
−0.813272 + 0.581884i \(0.802316\pi\)
\(252\) 5.85712 + 5.35669i 0.368964 + 0.337440i
\(253\) −20.4697 −1.28692
\(254\) 5.16871 + 2.98416i 0.324314 + 0.187243i
\(255\) −5.20941 3.46790i −0.326226 0.217168i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −2.76476 + 4.78871i −0.172461 + 0.298711i −0.939280 0.343153i \(-0.888505\pi\)
0.766819 + 0.641864i \(0.221839\pi\)
\(258\) −7.90569 15.9620i −0.492187 0.993752i
\(259\) 20.6330 + 14.5235i 1.28208 + 0.902446i
\(260\) 3.01802i 0.187170i
\(261\) 5.88259 2.46034i 0.364123 0.152291i
\(262\) −12.7746 + 7.37542i −0.789217 + 0.455655i
\(263\) 20.3542 11.7515i 1.25510 0.724630i 0.282980 0.959126i \(-0.408677\pi\)
0.972117 + 0.234495i \(0.0753438\pi\)
\(264\) −0.605677 + 9.49041i −0.0372769 + 0.584095i
\(265\) 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 0.772606 0.634886i \(-0.218953\pi\)
−0.936130 + 0.351654i \(0.885620\pi\)
\(270\) 5.11724 + 14.8237i 0.311425 + 0.902140i
\(271\) −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
\(273\) 3.57172 + 2.87103i 0.216170 + 0.173763i
\(274\) 4.13781 0.249974
\(275\) −19.5350 11.2785i −1.17801 0.680122i
\(276\) −3.57838 + 5.37538i −0.215393 + 0.323560i
\(277\) −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 \(0.172445\pi\)
−0.856807 + 0.515637i \(0.827555\pi\)
\(282\) 13.4751 + 0.859977i 0.802428 + 0.0512109i
\(283\) −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
\(285\) −33.0763 2.11093i −1.95927 0.125040i
\(286\) 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
\(291\) −9.20588 + 13.8289i −0.539658 + 0.810664i
\(292\) −0.501169 0.289350i −0.0293287 0.0169329i
\(293\) 6.07556 0.354938 0.177469 0.984126i \(-0.443209\pi\)
0.177469 + 0.984126i \(0.443209\pi\)
\(294\) −3.35521 11.6509i −0.195680 0.679492i
\(295\) −12.4464 −0.724659
\(296\) 8.25912 + 4.76840i 0.480051 + 0.277158i
\(297\) −9.30938 26.9675i −0.540185 1.56482i
\(298\) 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
\(303\) 1.67267 26.2092i 0.0960924 1.50568i
\(304\) −5.49095 + 3.17020i −0.314928 + 0.181824i
\(305\) 24.9337 14.3955i 1.42770 0.824284i
\(306\) 3.31344 1.38581i 0.189416 0.0792217i
\(307\) 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 0.839603 0.543200i \(-0.182787\pi\)
−0.890227 + 0.455518i \(0.849454\pi\)
\(312\) 1.44180 + 0.959803i 0.0816257 + 0.0543381i
\(313\) 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
\(315\) 5.16224 23.3919i 0.290859 1.31799i
\(316\) 1.29846 0.0730443
\(317\) 23.6484 + 13.6534i 1.32822 + 0.766850i 0.985025 0.172412i \(-0.0551561\pi\)
0.343199 + 0.939263i \(0.388489\pi\)
\(318\) −10.8811 7.24355i −0.610183 0.406198i
\(319\) −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
\(324\) −8.70912 2.26963i −0.483840 0.126091i
\(325\) −3.55800 + 2.05422i −0.197363 + 0.113947i
\(326\) −10.9299 + 6.31039i −0.605352 + 0.349500i
\(327\) 0.344048 5.39092i 0.0190259 0.298119i
\(328\) 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
\(333\) −28.3783 3.63702i −1.55512 0.199307i
\(334\) −6.95246 4.01401i −0.380422 0.219637i
\(335\) 30.0219 1.64027
\(336\) −1.65768 4.27225i −0.0904339 0.233070i
\(337\) −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
\(339\) 13.5068 20.2896i 0.733587 1.10198i
\(340\) 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
\(345\) 19.4493 + 1.24125i 1.04712 + 0.0668269i
\(346\) 7.70658 4.44940i 0.414308 0.239201i
\(347\) 8.89289 5.13431i 0.477395 0.275624i −0.241935 0.970292i \(-0.577782\pi\)
0.719330 + 0.694668i \(0.244449\pi\)
\(348\) −3.67393 0.234470i −0.196943 0.0125689i
\(349\) 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 0.916140 0.400859i \(-0.131288\pi\)
−0.805224 + 0.592971i \(0.797955\pi\)
\(354\) 3.95827 5.94603i 0.210380 0.316028i
\(355\) −5.89962 3.40615i −0.313119 0.180780i
\(356\) −5.50349 −0.291685
\(357\) −5.42172 0.838666i −0.286948 0.0443869i
\(358\) 18.3444 0.969531
\(359\) 11.1296 + 6.42566i 0.587396 + 0.339134i 0.764067 0.645136i \(-0.223199\pi\)
−0.176671 + 0.984270i \(0.556533\pi\)
\(360\) 1.15097 8.98060i 0.0606614 0.473319i
\(361\) 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
\(366\) −1.05237 + 16.4897i −0.0550084 + 0.861931i
\(367\) 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
\(369\) −4.93630 11.8025i −0.256973 0.614415i
\(370\) 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
\(375\) −3.87955 2.58261i −0.200339 0.133366i
\(376\) −6.75123 3.89783i −0.348168 0.201015i
\(377\) −2.12546 −0.109467
\(378\) 9.53330 + 9.90536i 0.490340 + 0.509477i
\(379\) 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
\(381\) 8.60510 + 5.72840i 0.440852 + 0.293475i
\(382\) −0.271932 0.471000i −0.0139132 0.0240984i
\(383\) −5.50293 + 9.53136i −0.281187 + 0.487030i −0.971677 0.236312i \(-0.924061\pi\)
0.690491 + 0.723341i \(0.257395\pi\)
\(384\) −0.768732 1.55211i −0.0392292 0.0792059i
\(385\) −43.6643 3.92883i −2.22534 0.200232i
\(386\) 13.7110i 0.697870i
\(387\) −11.9044 28.4630i −0.605135 1.44686i
\(388\) 8.30642 4.79571i 0.421695 0.243466i
\(389\) 16.2200 9.36461i 0.822385 0.474804i −0.0288530 0.999584i \(-0.509185\pi\)
0.851238 + 0.524779i \(0.175852\pi\)
\(390\) 0.332932 5.21675i 0.0168587 0.264160i
\(391\) 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
\(396\) −2.09387 + 16.3377i −0.105221 + 0.821000i
\(397\) −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
\(399\) −27.0878 + 10.5104i −1.35608 + 0.526176i
\(400\) 4.10843 0.205422
\(401\) −17.6755 10.2050i −0.882673 0.509612i −0.0111344 0.999938i \(-0.503544\pi\)
−0.871539 + 0.490326i \(0.836878\pi\)
\(402\) −9.54770 + 14.3424i −0.476196 + 0.715333i
\(403\) −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
\(408\) −2.06938 0.132068i −0.102450 0.00653833i
\(409\) 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
\(411\) 7.15234 + 0.456462i 0.352799 + 0.0225156i
\(412\) 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
\(417\) 6.38150 9.58617i 0.312504 0.469437i
\(418\) −30.1477 17.4058i −1.47457 0.851346i
\(419\) −11.3462 −0.554298 −0.277149 0.960827i \(-0.589390\pi\)
−0.277149 + 0.960827i \(0.589390\pi\)
\(420\) −8.66483 + 10.7795i −0.422800 + 0.525986i
\(421\) 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
\(423\) 23.1972 + 2.97300i 1.12789 + 0.144552i
\(424\) 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
\(429\) −0.605677 + 9.49041i −0.0292424 + 0.458201i
\(430\) 26.8793 15.5187i 1.29623 0.748380i
\(431\) 24.3157 14.0387i 1.17125 0.676220i 0.217274 0.976111i \(-0.430284\pi\)
0.953973 + 0.299891i \(0.0969503\pi\)
\(432\) 3.92426 + 3.40590i 0.188806 + 0.163866i
\(433\) 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
\(438\) −0.834368 0.555438i −0.0398676 0.0265398i
\(439\) 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
\(441\) −4.51433 20.5090i −0.214968 0.976621i
\(442\) −1.19719 −0.0569444
\(443\) 14.3748 + 8.29928i 0.682966 + 0.394311i 0.800972 0.598702i \(-0.204317\pi\)
−0.118005 + 0.993013i \(0.537650\pi\)
\(444\) 13.7501 + 9.15345i 0.652553 + 0.434404i
\(445\) 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 \(0.127102\pi\)
−0.921332 + 0.388776i \(0.872898\pi\)
\(450\) −11.3708 + 4.75575i −0.536026 + 0.224188i
\(451\) −20.2767 + 11.7067i −0.954791 + 0.551249i
\(452\) −12.1871 + 7.03622i −0.573233 + 0.330956i
\(453\) 0.677344 10.6134i 0.0318244 0.498659i
\(454\) 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
\(459\) 5.88026 2.02991i 0.274467 0.0947479i
\(460\) −9.74444 5.62596i −0.454337 0.262312i
\(461\) 25.6242 1.19344 0.596720 0.802450i \(-0.296470\pi\)
0.596720 + 0.802450i \(0.296470\pi\)
\(462\) 15.7632 19.6103i 0.733372 0.912354i
\(463\) 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
\(465\) −16.2979 + 24.4824i −0.755796 + 1.13534i
\(466\) −8.57656 14.8550i −0.397301 0.688146i
\(467\) −3.72197 + 6.44665i −0.172232 + 0.298315i −0.939200 0.343371i \(-0.888431\pi\)
0.766968 + 0.641686i \(0.221765\pi\)
\(468\) 2.38632 + 1.81810i 0.110307 + 0.0840419i
\(469\) 23.8803 11.0639i 1.10269 0.510881i
\(470\) 23.5274i 1.08524i
\(471\) −17.0929 1.09087i −0.787598 0.0502644i
\(472\) −3.57153 + 2.06202i −0.164393 + 0.0949122i
\(473\) −48.8993 + 28.2320i −2.24839 + 1.29811i
\(474\) 2.24444 + 0.143240i 0.103091 + 0.00657923i
\(475\) 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 \(-0.929766\pi\)
0.298340 0.954460i \(-0.403567\pi\)
\(480\) −2.89670 + 4.35137i −0.132216 + 0.198612i
\(481\) 8.25912 + 4.76840i 0.376583 + 0.217420i
\(482\) −14.5877 −0.664454
\(483\) 15.9280 6.18024i 0.724749 0.281211i
\(484\) 19.1449 0.870224
\(485\) −25.0689 14.4736i −1.13832 0.657210i
\(486\) −14.8036 4.88388i −0.671507 0.221537i
\(487\) 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 \(0.0158694\pi\)
−0.998757 + 0.0498344i \(0.984131\pi\)
\(492\) −0.470428 + 7.37118i −0.0212085 + 0.332318i
\(493\) 2.20366 1.27229i 0.0992480 0.0573009i
\(494\) −5.49095 + 3.17020i −0.247050 + 0.142634i
\(495\) 45.8612 19.1810i 2.06131 0.862122i
\(496\) 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
\(501\) −11.5748 7.70531i −0.517122 0.344248i
\(502\) 22.3169 + 12.8846i 0.996050 + 0.575070i
\(503\) −5.85678 −0.261141 −0.130570 0.991439i \(-0.541681\pi\)
−0.130570 + 0.991439i \(0.541681\pi\)
\(504\) −2.39407 7.56759i −0.106640 0.337087i
\(505\) 45.7613 2.03635
\(506\) 17.7273 + 10.2349i 0.788074 + 0.454995i
\(507\) 1.44180 + 0.959803i 0.0640325 + 0.0426263i
\(508\) −2.98416 5.16871i −0.132401 0.229324i
\(509\) −10.6895 + 18.5147i −0.473802 + 0.820649i −0.999550 0.0299913i \(-0.990452\pi\)
0.525748 + 0.850640i \(0.323785\pi\)
\(510\) 2.77753 + 5.60799i 0.122991 + 0.248326i
\(511\) 0.643640 + 1.38924i 0.0284729 + 0.0614563i
\(512\) 1.00000i 0.0441942i
\(513\) 21.5948 24.8814i 0.953433 1.09854i
\(514\) 4.78871 2.76476i 0.211221 0.121948i
\(515\) 50.8896 29.3811i 2.24246 1.29469i
\(516\) −1.13449 + 17.7764i −0.0499430 + 0.782561i
\(517\) 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 0.805261 0.592920i \(-0.202025\pi\)
−0.916115 + 0.400916i \(0.868692\pi\)
\(522\) −6.32464 0.810577i −0.276822 0.0354780i
\(523\) −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
\(525\) 18.6059 + 2.87808i 0.812028 + 0.125610i
\(526\) −23.5031 −1.02478
\(527\) 5.83338 + 3.36790i 0.254106 + 0.146708i
\(528\) 5.26974 7.91610i 0.229336 0.344504i
\(529\) −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
\(534\) −9.51298 0.607117i −0.411667 0.0262725i
\(535\) 27.8386 16.0726i 1.20357 0.694879i
\(536\) 8.61485 4.97378i 0.372105 0.214835i
\(537\) 31.7089 + 2.02366i 1.36834 + 0.0873273i
\(538\) 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
\(543\) −17.2355 + 25.8908i −0.739645 + 1.11108i
\(544\) 1.03680 + 0.598594i 0.0444522 + 0.0256645i
\(545\) 9.41254 0.403189
\(546\) −1.65768 4.27225i −0.0709422 0.182835i
\(547\) 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
\(549\) −3.63812 + 28.3869i −0.155271 + 1.21152i
\(550\) 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
\(555\) 3.17511 49.7511i 0.134776 2.11182i
\(556\) −5.75800 + 3.32438i −0.244194 + 0.140985i
\(557\) 11.6975 6.75356i 0.495639 0.286157i −0.231272 0.972889i \(-0.574289\pi\)
0.726911 + 0.686732i \(0.240955\pi\)
\(558\) −6.51284 15.5720i −0.275710 0.659214i
\(559\) 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 \(0.0618835\pi\)
−0.323273 + 0.946306i \(0.604783\pi\)
\(564\) −11.2397 7.48229i −0.473279 0.315061i
\(565\) 36.7809 + 21.2354i 1.54738 + 0.893382i
\(566\) 8.91431 0.374696
\(567\) 15.3859 + 18.1734i 0.646149 + 0.763212i
\(568\) −2.25721 −0.0947104
\(569\) −27.3771 15.8062i −1.14771 0.662629i −0.199380 0.979922i \(-0.563893\pi\)
−0.948328 + 0.317293i \(0.897226\pi\)
\(570\) 27.5894 + 18.3663i 1.15559 + 0.769278i
\(571\) −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
\(576\) −1.15756 2.76768i −0.0482316 0.115320i
\(577\) 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
\(579\) 1.51252 23.6999i 0.0628584 0.984934i
\(580\) 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
\(585\) 1.15097 8.98060i 0.0475867 0.371302i
\(586\) −5.26159 3.03778i −0.217354 0.125489i
\(587\) −35.5637 −1.46787 −0.733935 0.679219i \(-0.762319\pi\)
−0.733935 + 0.679219i \(0.762319\pi\)
\(588\) −2.91974 + 11.7675i −0.120408 + 0.485285i
\(589\) 35.6734 1.46990
\(590\) 10.7789 + 6.22322i 0.443761 + 0.256206i
\(591\) −3.40548 + 5.11565i −0.140083 + 0.210430i
\(592\) −4.76840 8.25912i −0.195980 0.339448i
\(593\) 7.87130 13.6335i 0.323236 0.559861i −0.657918 0.753090i \(-0.728563\pi\)
0.981154 + 0.193229i \(0.0618960\pi\)
\(594\) −5.42161 + 28.0093i −0.222451 + 1.14923i
\(595\) 0.856681 9.52099i 0.0351205 0.390323i
\(596\) 18.1021i 0.741492i
\(597\) 35.9151 + 2.29210i 1.46991 + 0.0938094i
\(598\) 3.22876 1.86412i 0.132034 0.0762297i
\(599\) −23.5223 + 13.5806i −0.961094 + 0.554888i −0.896510 0.443024i \(-0.853906\pi\)
−0.0645844 + 0.997912i \(0.520572\pi\)
\(600\) 7.10156 + 0.453221i 0.289920 + 0.0185027i
\(601\) 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
\(606\) −14.5532 + 21.8615i −0.591183 + 0.888064i
\(607\) −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
\(609\) 7.59153 + 6.10226i 0.307624 + 0.247276i
\(610\) −28.7910 −1.16571
\(611\) −6.75123 3.89783i −0.273126 0.157689i
\(612\) −3.56243 0.456567i −0.144003 0.0184556i
\(613\) 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 \(-0.936352\pi\)
0.980075 0.198627i \(-0.0636484\pi\)
\(618\) −2.14789 + 33.6554i −0.0864006 + 1.35382i
\(619\) −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
\(621\) −12.6980 + 14.6306i −0.509555 + 0.587107i
\(622\) 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
\(627\) −50.1913 33.4123i −2.00445 1.33436i
\(628\) 8.56382 + 4.94432i 0.341734 + 0.197300i
\(629\) −11.4174 −0.455240
\(630\) −16.1666 + 17.6769i −0.644093 + 0.704264i
\(631\) −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
\(633\) 10.0133 + 6.66583i 0.397992 + 0.264943i
\(634\) −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
\(639\) 6.24724 2.61285i 0.247137 0.103363i
\(640\) 2.61368 1.50901i 0.103315 0.0596488i
\(641\) −24.6391 + 14.2254i −0.973186 + 0.561869i −0.900206 0.435464i \(-0.856584\pi\)
−0.0729801 + 0.997333i \(0.523251\pi\)
\(642\) −1.17498 + 18.4108i −0.0463726 + 0.726616i
\(643\) 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 \(-0.865442\pi\)
0.100700 0.994917i \(-0.467892\pi\)
\(648\) 6.40750 + 6.32012i 0.251710 + 0.248278i
\(649\) −19.6092 11.3214i −0.769730 0.444404i
\(650\) 4.10843 0.161146
\(651\) −3.94143 + 25.4802i −0.154477 + 0.998647i
\(652\) 12.6208 0.494268
\(653\) −19.8709 11.4724i −0.777607 0.448952i 0.0579746 0.998318i \(-0.481536\pi\)
−0.835581 + 0.549367i \(0.814869\pi\)
\(654\) −2.99342 + 4.49665i −0.117052 + 0.175833i
\(655\) −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 \(0.141974\pi\)
−0.902170 + 0.431381i \(0.858026\pi\)
\(660\) −28.6422 1.82794i −1.11490 0.0711527i
\(661\) −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
\(663\) −2.06938 0.132068i −0.0803681 0.00512908i
\(664\) 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
\(669\) −7.87557 + 11.8305i −0.304487 + 0.457395i
\(670\) −25.9998 15.0110i −1.00446 0.579924i
\(671\) 52.3772 2.02200
\(672\) −0.700530 + 4.52871i −0.0270235 + 0.174699i
\(673\) 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
\(675\) −20.1795 + 6.96610i −0.776709 + 0.268125i
\(676\) −0.500000 0.866025i −0.0192308 0.0333087i
\(677\) 4.59005 7.95020i 0.176410 0.305551i −0.764238 0.644934i \(-0.776885\pi\)
0.940648 + 0.339383i \(0.110218\pi\)
\(678\) −21.8420 + 10.8179i −0.838837 + 0.415460i
\(679\) −25.2744 2.27414i −0.969944 0.0872737i
\(680\) 3.61313i 0.138557i
\(681\) −0.464914 + 7.28478i −0.0178155 + 0.279153i
\(682\) −26.7525 + 15.4456i −1.02441 + 0.591442i
\(683\) −43.4043 + 25.0595i −1.66082 + 0.958874i −0.688494 + 0.725242i \(0.741728\pi\)
−0.972325 + 0.233632i \(0.924939\pi\)
\(684\) −17.5482 + 7.33939i −0.670973 + 0.280628i
\(685\) 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
\(690\) −16.2230 10.7996i −0.617598 0.411134i
\(691\) −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
\(693\) 29.4106 32.1581i 1.11722 1.22159i
\(694\) −10.2686 −0.389792
\(695\) 17.3777 + 10.0330i 0.659176 + 0.380575i
\(696\) 3.06448 + 2.04002i 0.116159 + 0.0773267i
\(697\) −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 \(0.0639283\pi\)
−0.979900 + 0.199489i \(0.936072\pi\)
\(702\) 3.92426 + 3.40590i 0.148112 + 0.128547i
\(703\) −52.3661 + 30.2336i −1.97503 + 1.14028i
\(704\) −4.75486 + 2.74522i −0.179206 + 0.103464i
\(705\) −2.59542 + 40.6679i −0.0977493 + 1.53164i
\(706\) 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
\(711\) 3.86379 + 0.495191i 0.144903 + 0.0185711i
\(712\) 4.76616 + 2.75175i 0.178620 + 0.103126i
\(713\) −20.9765 −0.785574
\(714\) 4.27602 + 3.43717i 0.160026 + 0.128633i
\(715\) −16.5702 −0.619692
\(716\) −15.8867 9.17219i −0.593714 0.342781i
\(717\) −15.0063 + 22.5422i −0.560420 + 0.841852i
\(718\) −6.42566 11.1296i −0.239804 0.415352i
\(719\) 24.3326 42.1454i 0.907454 1.57176i 0.0898651 0.995954i \(-0.471356\pi\)
0.817589 0.575802i \(-0.195310\pi\)
\(720\) −5.48707 + 7.20194i −0.204491 + 0.268400i
\(721\) 29.6514 42.1247i 1.10428 1.56881i
\(722\) 21.2007i 0.789010i
\(723\) −25.2154 1.60925i −0.937772 0.0598485i
\(724\) 15.5515 8.97866i 0.577967 0.333689i
\(725\) −7.56239 + 4.36615i −0.280860 + 0.162155i
\(726\) 33.0927 + 2.11197i 1.22818 + 0.0783826i
\(727\) 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
\(732\) 9.15623 13.7543i 0.338424 0.508374i
\(733\) 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
\(735\) 35.1625 10.1261i 1.29699 0.373506i
\(736\) −3.72825 −0.137425
\(737\) 47.2993 + 27.3083i 1.74229 + 1.00591i
\(738\) −1.62630 + 12.6894i −0.0598650 + 0.467105i
\(739\) −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 \(0.0408185\pi\)
−0.991789 + 0.127884i \(0.959182\pi\)
\(744\) −0.620671 + 9.72535i −0.0227549 + 0.356549i
\(745\) −47.3132 + 27.3163i −1.73342 + 1.00079i
\(746\) −11.1674 + 6.44752i −0.408869 + 0.236061i
\(747\) −13.3102 31.8241i −0.486993 1.16438i
\(748\) 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
\(753\) 37.1541 + 24.7334i 1.35397 + 0.901336i
\(754\) 1.84070 + 1.06273i 0.0670343 + 0.0387023i
\(755\) 18.5309 0.674409
\(756\) −3.30341 13.3449i −0.120144 0.485351i
\(757\) 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
\(759\) 29.5132 + 19.6469i 1.07126 + 0.713137i
\(760\) −9.56773 16.5718i −0.347058 0.601122i
\(761\) 17.9005 31.0045i 0.648892 1.12391i −0.334496 0.942397i \(-0.608566\pi\)
0.983388 0.181516i \(-0.0581005\pi\)
\(762\) −4.58803 9.26349i −0.166207 0.335581i
\(763\) 7.48701 3.46876i 0.271048 0.125578i
\(764\) 0.543864i 0.0196763i
\(765\) 4.18241 + 10.0000i 0.151215 + 0.361551i
\(766\) 9.53136 5.50293i 0.344382 0.198829i
\(767\) −3.57153 + 2.06202i −0.128960 + 0.0744553i
\(768\) −0.110315 + 1.72853i −0.00398065 + 0.0623731i
\(769\) 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 0.752103 0.659046i \(-0.229040\pi\)
−0.946802 + 0.321817i \(0.895706\pi\)
\(774\) −3.92200 + 30.6019i −0.140973 + 1.09996i
\(775\) −20.0186 11.5577i −0.719090 0.415167i
\(776\) −9.59143 −0.344312
\(777\) −15.8090 40.7436i −0.567144 1.46167i
\(778\) −18.7292 −0.671475
\(779\) −23.4157 13.5190i −0.838953 0.484370i
\(780\) −2.89670 + 4.35137i −0.103719 + 0.155804i
\(781\) −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
\(786\) 25.4973 + 1.62724i 0.909459 + 0.0580416i
\(787\) 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
\(789\) −40.6258 2.59274i −1.44632 0.0923039i
\(790\) 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
\(795\) 21.8612 32.8394i 0.775336 1.16469i
\(796\) −17.9941 10.3889i −0.637783 0.368224i
\(797\) −29.6965 −1.05190 −0.525952 0.850514i \(-0.676291\pi\)
−0.525952 + 0.850514i \(0.676291\pi\)
\(798\) 28.7139 + 4.44164i 1.01646 + 0.157232i
\(799\) 9.33286 0.330173
\(800\) −3.55800 2.05422i −0.125794 0.0726275i
\(801\) −16.3765 2.09885i −0.578636 0.0741591i
\(802\) 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
\(807\) −0.591728 + 9.27185i −0.0208298 + 0.326384i
\(808\) 13.1313 7.58135i 0.461957 0.266711i
\(809\) 20.1548 11.6364i 0.708606 0.409114i −0.101939 0.994791i \(-0.532505\pi\)
0.810545 + 0.585677i \(0.199171\pi\)
\(810\) 6.84979 26.2843i 0.240677 0.923535i
\(811\) 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
\(816\) 1.72610 + 1.14906i 0.0604257 + 0.0402253i
\(817\) −56.4693 32.6026i −1.97561 1.14062i
\(818\) −3.59889 −0.125832
\(819\) −2.39407 7.56759i −0.0836554 0.264433i
\(820\) −12.8701 −0.449442
\(821\) 26.7609 + 15.4504i 0.933961 + 0.539223i 0.888062 0.459724i \(-0.152052\pi\)
0.0458987 + 0.998946i \(0.485385\pi\)
\(822\) −5.96588 3.97148i −0.208084 0.138521i
\(823\) 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 \(0.0264298\pi\)
−0.996555 + 0.0829362i \(0.973570\pi\)
\(828\) 10.3186 4.31566i 0.358596 0.149980i
\(829\) −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
\(831\) −2.75699 + 43.1996i −0.0956390 + 1.49858i
\(832\) 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
\(837\) −9.53984 27.6351i −0.329745 0.955210i
\(838\) 9.82609 + 5.67310i 0.339437 + 0.195974i
\(839\) −35.9486 −1.24108 −0.620542 0.784173i \(-0.713087\pi\)
−0.620542 + 0.784173i \(0.713087\pi\)
\(840\) 12.8937 5.00291i 0.444875 0.172617i
\(841\) 24.4824 0.844222
\(842\) −3.37450 1.94827i −0.116293 0.0671418i
\(843\) 16.5924 24.9248i 0.571472 0.858455i
\(844\) −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
\(849\) 15.4087 + 0.983381i 0.528825 + 0.0337495i
\(850\) −4.25960 + 2.45928i −0.146103 + 0.0843527i
\(851\) 30.7920 17.7778i 1.05554 0.609415i
\(852\) −3.90166 0.249004i −0.133669 0.00853073i
\(853\) 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 \(0.181271\pi\)
0.0458647 + 0.998948i \(0.485396\pi\)
\(858\) 5.26974 7.91610i 0.179906 0.270251i
\(859\) −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
\(861\) 12.2433 15.2313i 0.417249 0.519080i
\(862\) −28.0774 −0.956319
\(863\) −26.2981 15.1832i −0.895196 0.516842i −0.0195575 0.999809i \(-0.506226\pi\)
−0.875639 + 0.482967i \(0.839559\pi\)
\(864\) −1.69556 4.91173i −0.0576842 0.167100i
\(865\) 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
\(870\) 0.707633 11.0880i 0.0239910 0.375917i
\(871\) 8.61485 4.97378i 0.291903 0.168530i
\(872\) 2.70095 1.55939i 0.0914656 0.0528077i
\(873\) 26.5460 11.1026i 0.898447 0.375767i
\(874\) 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
\(879\) −8.75972 5.83133i −0.295458 0.196686i
\(880\) 14.3503 + 8.28512i 0.483747 + 0.279291i
\(881\) 5.01841 0.169074 0.0845372 0.996420i \(-0.473059\pi\)
0.0845372 + 0.996420i \(0.473059\pi\)
\(882\) −6.34500 + 20.0185i −0.213647 + 0.674058i
\(883\) −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
\(885\) 17.9452 + 11.9461i 0.603222 + 0.401564i
\(886\) −8.29928 14.3748i −0.278820 0.482930i
\(887\) 13.2901 23.0191i 0.446237 0.772904i −0.551901 0.833910i \(-0.686097\pi\)
0.998137 + 0.0610053i \(0.0194307\pi\)
\(888\) −7.33124 14.8022i −0.246020 0.496729i
\(889\) −1.41510 + 15.7271i −0.0474609 + 0.527471i
\(890\) 16.6096i 0.556756i
\(891\) −12.4613 + 47.8169i −0.417469 + 1.60193i
\(892\) 7.10609 4.10270i 0.237930 0.137369i
\(893\) 42.8055 24.7138i 1.43243 0.827016i
\(894\) 1.99694 31.2902i 0.0667875 1.04650i
\(895\) 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
\(900\) 12.2253 + 1.56682i 0.407510 + 0.0522272i
\(901\) −7.82461 4.51754i −0.260675 0.150501i
\(902\) 23.4135 0.779583
\(903\) 29.5259 36.7318i 0.982561 1.22236i
\(904\) 14.0724 0.468043
\(905\) −46.9347 27.0977i −1.56016 0.900760i
\(906\) −5.89328 + 8.85277i −0.195791 + 0.294114i
\(907\) −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 \(-0.867425\pi\)
0.914512 0.404558i \(-0.132575\pi\)
\(912\) 10.9596 + 0.699441i 0.362909 + 0.0231608i
\(913\) −54.6737 + 31.5659i −1.80943 + 1.04468i
\(914\) −10.5560 + 6.09451i −0.349162 + 0.201589i
\(915\) −49.7662 3.17608i −1.64522 0.104998i
\(916\) 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
\(921\) −12.3847 + 18.6040i −0.408088 + 0.613023i
\(922\) −22.1912 12.8121i −0.730829 0.421945i
\(923\) −2.25721 −0.0742969
\(924\) −23.4565 + 9.10140i −0.771663 + 0.299414i
\(925\) 39.1813 1.28827
\(926\) −25.1046 14.4942i −0.824990 0.476308i
\(927\) −7.42539 + 57.9376i −0.243882 + 1.90292i
\(928\) −1.06273 1.84070i −0.0348858 0.0604239i
\(929\) 16.8048 29.1068i 0.551348 0.954963i −0.446829 0.894619i \(-0.647447\pi\)
0.998178 0.0603439i \(-0.0192197\pi\)
\(930\) 26.3556 13.0534i 0.864233 0.428038i
\(931\) −33.8579 28.6963i −1.10965 0.940485i
\(932\) 17.1531i 0.561869i
\(933\) −0.196967 + 3.08630i −0.00644843 + 0.101041i
\(934\) 6.44665 3.72197i 0.210941 0.121787i
\(935\) 17.1799 9.91885i 0.561844 0.324381i
\(936\) −1.15756 2.76768i −0.0378360 0.0904645i
\(937\) 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 0.935616 0.353019i \(-0.114845\pi\)
−0.773531 + 0.633758i \(0.781511\pi\)
\(942\) 14.2574 + 9.49115i 0.464532 + 0.309238i
\(943\) 13.7687 + 7.94938i 0.448372 + 0.258868i
\(944\) 4.12404 0.134226
\(945\) −29.8945 + 28.7717i −0.972470 + 0.935943i
\(946\) 56.4640 1.83580
\(947\) 39.3441 + 22.7153i 1.27851 + 0.738149i 0.976575 0.215179i \(-0.0690334\pi\)
0.301937 + 0.953328i \(0.402367\pi\)
\(948\) −1.87212 1.24627i −0.0608037 0.0404770i
\(949\) 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 \(0.0154124\pi\)
−0.998828 + 0.0484007i \(0.984588\pi\)
\(954\) 8.73599 + 20.8875i 0.282838 + 0.676257i
\(955\) 1.42149 0.820695i 0.0459982 0.0265571i
\(956\) 13.5401 7.81738i 0.437918 0.252832i
\(957\) −1.28734 + 20.1715i −0.0416138 + 0.652051i
\(958\) 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
\(963\) −4.06197 + 31.6941i −0.130895 + 1.02133i
\(964\) 12.6334 + 7.29387i 0.406893 + 0.234920i
\(965\) 41.3800 1.33207
\(966\) −16.8842 2.61175i −0.543239 0.0840316i
\(967\) −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
\(969\) 7.28553 10.9442i 0.234045 0.351578i
\(970\) 14.4736 + 25.0689i 0.464718 + 0.804915i
\(971\) −18.6175 + 32.2464i −0.597464 + 1.03484i 0.395731 + 0.918367i \(0.370491\pi\)
−0.993194 + 0.116471i \(0.962842\pi\)
\(972\) 10.3784 + 11.6314i 0.332887 + 0.373077i
\(973\) 17.5202 + 1.57643i 0.561672 + 0.0505382i
\(974\) 30.0048i 0.961415i
\(975\) 7.10156 + 0.453221i 0.227432 + 0.0145147i
\(976\) −8.26163 + 4.76985i −0.264448 + 0.152679i
\(977\) −21.8979 + 12.6427i −0.700575 + 0.404477i −0.807562 0.589783i \(-0.799213\pi\)
0.106986 + 0.994260i \(0.465880\pi\)
\(978\) 21.8154 + 1.39226i 0.697581 + 0.0445195i
\(979\) 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 \(0.0344764\pi\)
−0.403454 + 0.915000i \(0.632190\pi\)
\(984\) 4.09299 6.14841i 0.130480 0.196004i
\(985\) −9.27362 5.35412i −0.295482 0.170597i
\(986\) −2.54457 −0.0810357
\(987\) 12.9227 + 33.3049i 0.411334 + 1.06011i
\(988\) 6.34040 0.201715
\(989\) 33.2047 + 19.1708i 1.05585 + 0.609595i
\(990\) −49.3074 6.31933i −1.56709 0.200842i
\(991\) 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
\(996\) −1.26845 + 19.8755i −0.0401925 + 0.629780i
\(997\) 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
\(999\) 37.4249 + 32.4814i 1.18407 + 1.02767i
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.b.131.2 yes 32
3.2 odd 2 546.2.z.a.131.12 32
7.3 odd 6 546.2.z.a.521.12 yes 32
21.17 even 6 inner 546.2.z.b.521.2 yes 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
546.2.z.a.131.12 32 3.2 odd 2
546.2.z.a.521.12 yes 32 7.3 odd 6
546.2.z.b.131.2 yes 32 1.1 even 1 trivial
546.2.z.b.521.2 yes 32 21.17 even 6 inner