Properties

Label 546.2.bg.a.467.16
Level $546$
Weight $2$
Character 546.467
Analytic conductor $4.360$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [546,2,Mod(311,546)]
 
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, 1, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("546.311");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.bg (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: \(36\)
Relative dimension: \(18\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 467.16
Character \(\chi\) \(=\) 546.467
Dual form 546.2.bg.a.311.16

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(1.57792 - 0.714250i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.19770 + 1.26884i) q^{5} +(-0.170404 + 1.72365i) q^{6} +(2.61925 - 0.373536i) q^{7} +1.00000 q^{8} +(1.97969 - 2.25407i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(1.57792 - 0.714250i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.19770 + 1.26884i) q^{5} +(-0.170404 + 1.72365i) q^{6} +(2.61925 - 0.373536i) q^{7} +1.00000 q^{8} +(1.97969 - 2.25407i) q^{9} +(-2.19770 + 1.26884i) q^{10} +(1.32440 + 2.29393i) q^{11} +(-1.40752 - 1.00940i) q^{12} +(-3.59958 + 0.207354i) q^{13} +(-0.986133 + 2.45511i) q^{14} +(4.37407 + 0.432430i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.84623 - 3.19777i) q^{17} +(0.962231 + 2.84150i) q^{18} +(0.241819 - 0.418842i) q^{19} -2.53768i q^{20} +(3.86618 - 2.46021i) q^{21} -2.64880 q^{22} +(-4.09436 - 2.36388i) q^{23} +(1.57792 - 0.714250i) q^{24} +(0.719909 + 1.24692i) q^{25} +(1.62022 - 3.22101i) q^{26} +(1.51384 - 4.97074i) q^{27} +(-1.63312 - 2.08157i) q^{28} +6.93400i q^{29} +(-2.56153 + 3.57184i) q^{30} +(2.71148 + 4.69643i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(3.72824 + 2.67369i) q^{33} +3.69246 q^{34} +(6.23027 + 2.50249i) q^{35} +(-2.94193 - 0.587433i) q^{36} +(-5.90071 - 3.40678i) q^{37} +(0.241819 + 0.418842i) q^{38} +(-5.53177 + 2.89819i) q^{39} +(2.19770 + 1.26884i) q^{40} +3.03693i q^{41} +(0.197515 + 4.57832i) q^{42} +5.11062 q^{43} +(1.32440 - 2.29393i) q^{44} +(7.21081 - 2.44183i) q^{45} +(4.09436 - 2.36388i) q^{46} +(-6.66192 - 3.84626i) q^{47} +(-0.170404 + 1.72365i) q^{48} +(6.72094 - 1.95677i) q^{49} -1.43982 q^{50} +(-5.19722 - 3.72716i) q^{51} +(1.97937 + 3.01365i) q^{52} +(8.13530 - 4.69692i) q^{53} +(3.54787 + 3.79640i) q^{54} +6.72180i q^{55} +(2.61925 - 0.373536i) q^{56} +(0.0824136 - 0.833620i) q^{57} +(-6.00502 - 3.46700i) q^{58} +(-4.98510 + 2.87815i) q^{59} +(-1.81254 - 4.00427i) q^{60} +(4.25236 + 2.45510i) q^{61} -5.42297 q^{62} +(4.34334 - 6.64345i) q^{63} +1.00000 q^{64} +(-8.17389 - 4.11159i) q^{65} +(-4.17960 + 1.89190i) q^{66} +(1.38217 - 0.797996i) q^{67} +(-1.84623 + 3.19777i) q^{68} +(-8.14900 - 0.805629i) q^{69} +(-5.28236 + 4.14433i) q^{70} -12.9028 q^{71} +(1.97969 - 2.25407i) q^{72} +(6.57447 + 11.3873i) q^{73} +(5.90071 - 3.40678i) q^{74} +(2.02658 + 1.45335i) q^{75} -0.483637 q^{76} +(4.32580 + 5.51365i) q^{77} +(0.255978 - 6.23975i) q^{78} +(-3.75864 + 6.51016i) q^{79} +(-2.19770 + 1.26884i) q^{80} +(-1.16162 - 8.92472i) q^{81} +(-2.63006 - 1.51847i) q^{82} +3.10022i q^{83} +(-4.06370 - 2.11811i) q^{84} -9.37029i q^{85} +(-2.55531 + 4.42592i) q^{86} +(4.95261 + 10.9413i) q^{87} +(1.32440 + 2.29393i) q^{88} +(-2.37997 - 1.37408i) q^{89} +(-1.49072 + 7.46566i) q^{90} +(-9.35076 + 1.88769i) q^{91} +4.72776i q^{92} +(7.63294 + 5.47393i) q^{93} +(6.66192 - 3.84626i) q^{94} +(1.06289 - 0.613658i) q^{95} +(-1.40752 - 1.00940i) q^{96} -5.91584 q^{97} +(-1.66586 + 6.79889i) q^{98} +(7.79256 + 1.55599i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q - 18 q^{2} - 18 q^{4} + 36 q^{8} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 36 q - 18 q^{2} - 18 q^{4} + 36 q^{8} + 4 q^{9} - 14 q^{15} - 18 q^{16} + 4 q^{18} + 23 q^{21} + 14 q^{25} - 6 q^{26} + 7 q^{30} - 18 q^{32} + 24 q^{33} - 8 q^{36} - 10 q^{39} - 16 q^{42} - 16 q^{43} - 9 q^{45} + 72 q^{47} + 12 q^{49} - 28 q^{50} - 3 q^{51} + 6 q^{52} + 9 q^{54} - 8 q^{57} + 24 q^{59} + 7 q^{60} - 36 q^{61} - 39 q^{63} + 36 q^{64} + 18 q^{65} - 24 q^{66} - 72 q^{71} + 4 q^{72} + 54 q^{75} + 20 q^{78} + 20 q^{79} - 20 q^{81} - 24 q^{82} - 7 q^{84} + 8 q^{86} - 24 q^{87} - 72 q^{89} - 2 q^{91} - 14 q^{93} - 72 q^{94} - 12 q^{98} + 72 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) 1.57792 0.714250i 0.911015 0.412372i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 2.19770 + 1.26884i 0.982839 + 0.567442i 0.903126 0.429375i \(-0.141266\pi\)
0.0797131 + 0.996818i \(0.474600\pi\)
\(6\) −0.170404 + 1.72365i −0.0695671 + 0.703676i
\(7\) 2.61925 0.373536i 0.989983 0.141183i
\(8\) 1.00000 0.353553
\(9\) 1.97969 2.25407i 0.659898 0.751355i
\(10\) −2.19770 + 1.26884i −0.694972 + 0.401242i
\(11\) 1.32440 + 2.29393i 0.399321 + 0.691645i 0.993642 0.112583i \(-0.0359125\pi\)
−0.594321 + 0.804228i \(0.702579\pi\)
\(12\) −1.40752 1.00940i −0.406316 0.291388i
\(13\) −3.59958 + 0.207354i −0.998345 + 0.0575096i
\(14\) −0.986133 + 2.45511i −0.263555 + 0.656154i
\(15\) 4.37407 + 0.432430i 1.12938 + 0.111653i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −1.84623 3.19777i −0.447777 0.775572i 0.550464 0.834859i \(-0.314451\pi\)
−0.998241 + 0.0592866i \(0.981117\pi\)
\(18\) 0.962231 + 2.84150i 0.226800 + 0.669748i
\(19\) 0.241819 0.418842i 0.0554770 0.0960890i −0.836953 0.547274i \(-0.815665\pi\)
0.892430 + 0.451185i \(0.148999\pi\)
\(20\) 2.53768i 0.567442i
\(21\) 3.86618 2.46021i 0.843670 0.536862i
\(22\) −2.64880 −0.564725
\(23\) −4.09436 2.36388i −0.853734 0.492903i 0.00817520 0.999967i \(-0.497398\pi\)
−0.861909 + 0.507063i \(0.830731\pi\)
\(24\) 1.57792 0.714250i 0.322093 0.145796i
\(25\) 0.719909 + 1.24692i 0.143982 + 0.249384i
\(26\) 1.62022 3.22101i 0.317751 0.631692i
\(27\) 1.51384 4.97074i 0.291339 0.956620i
\(28\) −1.63312 2.08157i −0.308630 0.393380i
\(29\) 6.93400i 1.28761i 0.765189 + 0.643805i \(0.222645\pi\)
−0.765189 + 0.643805i \(0.777355\pi\)
\(30\) −2.56153 + 3.57184i −0.467669 + 0.652125i
\(31\) 2.71148 + 4.69643i 0.486997 + 0.843503i 0.999888 0.0149503i \(-0.00475901\pi\)
−0.512891 + 0.858453i \(0.671426\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 3.72824 + 2.67369i 0.649003 + 0.465430i
\(34\) 3.69246 0.633252
\(35\) 6.23027 + 2.50249i 1.05311 + 0.422998i
\(36\) −2.94193 0.587433i −0.490321 0.0979054i
\(37\) −5.90071 3.40678i −0.970071 0.560071i −0.0708132 0.997490i \(-0.522559\pi\)
−0.899258 + 0.437419i \(0.855893\pi\)
\(38\) 0.241819 + 0.418842i 0.0392282 + 0.0679452i
\(39\) −5.53177 + 2.89819i −0.885792 + 0.464082i
\(40\) 2.19770 + 1.26884i 0.347486 + 0.200621i
\(41\) 3.03693i 0.474289i 0.971474 + 0.237145i \(0.0762115\pi\)
−0.971474 + 0.237145i \(0.923788\pi\)
\(42\) 0.197515 + 4.57832i 0.0304772 + 0.706450i
\(43\) 5.11062 0.779362 0.389681 0.920950i \(-0.372585\pi\)
0.389681 + 0.920950i \(0.372585\pi\)
\(44\) 1.32440 2.29393i 0.199661 0.345822i
\(45\) 7.21081 2.44183i 1.07492 0.364007i
\(46\) 4.09436 2.36388i 0.603681 0.348535i
\(47\) −6.66192 3.84626i −0.971741 0.561035i −0.0719745 0.997406i \(-0.522930\pi\)
−0.899767 + 0.436371i \(0.856263\pi\)
\(48\) −0.170404 + 1.72365i −0.0245957 + 0.248787i
\(49\) 6.72094 1.95677i 0.960134 0.279539i
\(50\) −1.43982 −0.203621
\(51\) −5.19722 3.72716i −0.727756 0.521907i
\(52\) 1.97937 + 3.01365i 0.274489 + 0.417919i
\(53\) 8.13530 4.69692i 1.11747 0.645171i 0.176716 0.984262i \(-0.443453\pi\)
0.940754 + 0.339091i \(0.110119\pi\)
\(54\) 3.54787 + 3.79640i 0.482804 + 0.516624i
\(55\) 6.72180i 0.906367i
\(56\) 2.61925 0.373536i 0.350012 0.0499159i
\(57\) 0.0824136 0.833620i 0.0109160 0.110416i
\(58\) −6.00502 3.46700i −0.788497 0.455239i
\(59\) −4.98510 + 2.87815i −0.649005 + 0.374703i −0.788075 0.615579i \(-0.788922\pi\)
0.139070 + 0.990283i \(0.455589\pi\)
\(60\) −1.81254 4.00427i −0.233998 0.516949i
\(61\) 4.25236 + 2.45510i 0.544459 + 0.314343i 0.746884 0.664954i \(-0.231549\pi\)
−0.202425 + 0.979298i \(0.564882\pi\)
\(62\) −5.42297 −0.688717
\(63\) 4.34334 6.64345i 0.547209 0.836996i
\(64\) 1.00000 0.125000
\(65\) −8.17389 4.11159i −1.01385 0.509981i
\(66\) −4.17960 + 1.89190i −0.514474 + 0.232877i
\(67\) 1.38217 0.797996i 0.168859 0.0974908i −0.413189 0.910645i \(-0.635585\pi\)
0.582048 + 0.813155i \(0.302252\pi\)
\(68\) −1.84623 + 3.19777i −0.223888 + 0.387786i
\(69\) −8.14900 0.805629i −0.981024 0.0969863i
\(70\) −5.28236 + 4.14433i −0.631362 + 0.495342i
\(71\) −12.9028 −1.53128 −0.765638 0.643272i \(-0.777577\pi\)
−0.765638 + 0.643272i \(0.777577\pi\)
\(72\) 1.97969 2.25407i 0.233309 0.265644i
\(73\) 6.57447 + 11.3873i 0.769484 + 1.33279i 0.937843 + 0.347060i \(0.112820\pi\)
−0.168359 + 0.985726i \(0.553847\pi\)
\(74\) 5.90071 3.40678i 0.685944 0.396030i
\(75\) 2.02658 + 1.45335i 0.234009 + 0.167818i
\(76\) −0.483637 −0.0554770
\(77\) 4.32580 + 5.51365i 0.492970 + 0.628339i
\(78\) 0.255978 6.23975i 0.0289838 0.706513i
\(79\) −3.75864 + 6.51016i −0.422880 + 0.732450i −0.996220 0.0868676i \(-0.972314\pi\)
0.573339 + 0.819318i \(0.305648\pi\)
\(80\) −2.19770 + 1.26884i −0.245710 + 0.141861i
\(81\) −1.16162 8.92472i −0.129069 0.991636i
\(82\) −2.63006 1.51847i −0.290442 0.167687i
\(83\) 3.10022i 0.340293i 0.985419 + 0.170146i \(0.0544241\pi\)
−0.985419 + 0.170146i \(0.945576\pi\)
\(84\) −4.06370 2.11811i −0.443386 0.231104i
\(85\) 9.37029i 1.01635i
\(86\) −2.55531 + 4.42592i −0.275546 + 0.477260i
\(87\) 4.95261 + 10.9413i 0.530975 + 1.17303i
\(88\) 1.32440 + 2.29393i 0.141181 + 0.244533i
\(89\) −2.37997 1.37408i −0.252276 0.145652i 0.368530 0.929616i \(-0.379861\pi\)
−0.620806 + 0.783964i \(0.713195\pi\)
\(90\) −1.49072 + 7.46566i −0.157135 + 0.786950i
\(91\) −9.35076 + 1.88769i −0.980226 + 0.197883i
\(92\) 4.72776i 0.492903i
\(93\) 7.63294 + 5.47393i 0.791499 + 0.567620i
\(94\) 6.66192 3.84626i 0.687125 0.396712i
\(95\) 1.06289 0.613658i 0.109050 0.0629600i
\(96\) −1.40752 1.00940i −0.143655 0.103021i
\(97\) −5.91584 −0.600663 −0.300331 0.953835i \(-0.597097\pi\)
−0.300331 + 0.953835i \(0.597097\pi\)
\(98\) −1.66586 + 6.79889i −0.168277 + 0.686792i
\(99\) 7.79256 + 1.55599i 0.783182 + 0.156383i
\(100\) 0.719909 1.24692i 0.0719909 0.124692i
\(101\) −6.93191 12.0064i −0.689751 1.19468i −0.971918 0.235318i \(-0.924387\pi\)
0.282167 0.959365i \(-0.408947\pi\)
\(102\) 5.82643 2.63734i 0.576902 0.261136i
\(103\) −7.90784 4.56559i −0.779183 0.449861i 0.0569579 0.998377i \(-0.481860\pi\)
−0.836141 + 0.548515i \(0.815193\pi\)
\(104\) −3.59958 + 0.207354i −0.352968 + 0.0203327i
\(105\) 11.6183 0.501230i 1.13383 0.0489150i
\(106\) 9.39383i 0.912410i
\(107\) −6.73065 3.88594i −0.650677 0.375668i 0.138039 0.990427i \(-0.455920\pi\)
−0.788716 + 0.614758i \(0.789254\pi\)
\(108\) −5.06171 + 1.17435i −0.487063 + 0.113001i
\(109\) 11.8250 6.82718i 1.13263 0.653925i 0.188037 0.982162i \(-0.439788\pi\)
0.944596 + 0.328237i \(0.106454\pi\)
\(110\) −5.82125 3.36090i −0.555034 0.320449i
\(111\) −11.7442 1.16106i −1.11471 0.110203i
\(112\) −0.986133 + 2.45511i −0.0931808 + 0.231986i
\(113\) 20.5235i 1.93068i 0.260987 + 0.965342i \(0.415952\pi\)
−0.260987 + 0.965342i \(0.584048\pi\)
\(114\) 0.680730 + 0.488182i 0.0637562 + 0.0457225i
\(115\) −5.99877 10.3902i −0.559389 0.968889i
\(116\) 6.00502 3.46700i 0.557552 0.321903i
\(117\) −6.65869 + 8.52420i −0.615596 + 0.788062i
\(118\) 5.75630i 0.529910i
\(119\) −6.03022 7.68611i −0.552790 0.704585i
\(120\) 4.37407 + 0.432430i 0.399296 + 0.0394753i
\(121\) 1.99194 3.45014i 0.181085 0.313649i
\(122\) −4.25236 + 2.45510i −0.384990 + 0.222274i
\(123\) 2.16913 + 4.79205i 0.195584 + 0.432085i
\(124\) 2.71148 4.69643i 0.243498 0.421752i
\(125\) 9.03460i 0.808079i
\(126\) 3.58173 + 7.08317i 0.319086 + 0.631019i
\(127\) −10.7047 −0.949889 −0.474945 0.880016i \(-0.657532\pi\)
−0.474945 + 0.880016i \(0.657532\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 8.06417 3.65026i 0.710010 0.321387i
\(130\) 7.64769 5.02300i 0.670747 0.440546i
\(131\) 3.16842 5.48787i 0.276826 0.479478i −0.693768 0.720199i \(-0.744051\pi\)
0.970594 + 0.240721i \(0.0773839\pi\)
\(132\) 0.451365 4.56559i 0.0392863 0.397384i
\(133\) 0.476931 1.18738i 0.0413551 0.102959i
\(134\) 1.59599i 0.137873i
\(135\) 9.63404 9.00335i 0.829166 0.774885i
\(136\) −1.84623 3.19777i −0.158313 0.274206i
\(137\) −8.84134 15.3136i −0.755367 1.30833i −0.945192 0.326515i \(-0.894126\pi\)
0.189825 0.981818i \(-0.439208\pi\)
\(138\) 4.77219 6.65443i 0.406236 0.566462i
\(139\) 16.0938i 1.36506i −0.730858 0.682530i \(-0.760880\pi\)
0.730858 0.682530i \(-0.239120\pi\)
\(140\) −0.947916 6.64682i −0.0801135 0.561759i
\(141\) −13.2592 1.31084i −1.11663 0.110392i
\(142\) 6.45138 11.1741i 0.541388 0.937711i
\(143\) −5.24294 7.98256i −0.438437 0.667535i
\(144\) 0.962231 + 2.84150i 0.0801859 + 0.236792i
\(145\) −8.79813 + 15.2388i −0.730645 + 1.26551i
\(146\) −13.1489 −1.08821
\(147\) 9.20752 7.88807i 0.759423 0.650597i
\(148\) 6.81356i 0.560071i
\(149\) −1.28692 + 2.22901i −0.105429 + 0.182608i −0.913913 0.405910i \(-0.866955\pi\)
0.808485 + 0.588517i \(0.200288\pi\)
\(150\) −2.27193 + 1.02839i −0.185502 + 0.0839677i
\(151\) −3.68114 + 2.12531i −0.299567 + 0.172955i −0.642248 0.766497i \(-0.721998\pi\)
0.342681 + 0.939452i \(0.388665\pi\)
\(152\) 0.241819 0.418842i 0.0196141 0.0339726i
\(153\) −10.8629 2.16907i −0.878217 0.175359i
\(154\) −6.93786 + 0.989422i −0.559069 + 0.0797299i
\(155\) 13.7618i 1.10537i
\(156\) 5.27579 + 3.34156i 0.422401 + 0.267539i
\(157\) −0.823957 + 0.475712i −0.0657589 + 0.0379659i −0.532519 0.846418i \(-0.678755\pi\)
0.466760 + 0.884384i \(0.345421\pi\)
\(158\) −3.75864 6.51016i −0.299022 0.517921i
\(159\) 9.48212 13.2220i 0.751981 1.04857i
\(160\) 2.53768i 0.200621i
\(161\) −11.6072 4.66220i −0.914772 0.367433i
\(162\) 8.30985 + 3.45636i 0.652883 + 0.271558i
\(163\) 4.74897 + 2.74182i 0.371968 + 0.214756i 0.674318 0.738441i \(-0.264438\pi\)
−0.302350 + 0.953197i \(0.597771\pi\)
\(164\) 2.63006 1.51847i 0.205373 0.118572i
\(165\) 4.80104 + 10.6065i 0.373761 + 0.825714i
\(166\) −2.68487 1.55011i −0.208386 0.120312i
\(167\) 6.15740i 0.476474i −0.971207 0.238237i \(-0.923431\pi\)
0.971207 0.238237i \(-0.0765694\pi\)
\(168\) 3.86618 2.46021i 0.298282 0.189809i
\(169\) 12.9140 1.49278i 0.993385 0.114829i
\(170\) 8.11491 + 4.68514i 0.622385 + 0.359334i
\(171\) −0.465371 1.37425i −0.0355878 0.105092i
\(172\) −2.55531 4.42592i −0.194840 0.337473i
\(173\) 3.45361 5.98183i 0.262573 0.454790i −0.704352 0.709851i \(-0.748762\pi\)
0.966925 + 0.255061i \(0.0820955\pi\)
\(174\) −11.9518 1.18158i −0.906061 0.0895753i
\(175\) 2.35139 + 2.99708i 0.177749 + 0.226558i
\(176\) −2.64880 −0.199661
\(177\) −5.81040 + 8.10211i −0.436736 + 0.608992i
\(178\) 2.37997 1.37408i 0.178386 0.102991i
\(179\) 1.49413 0.862637i 0.111677 0.0644765i −0.443121 0.896462i \(-0.646129\pi\)
0.554798 + 0.831985i \(0.312796\pi\)
\(180\) −5.72010 5.02383i −0.426351 0.374454i
\(181\) 22.0637i 1.63998i 0.572376 + 0.819991i \(0.306022\pi\)
−0.572376 + 0.819991i \(0.693978\pi\)
\(182\) 3.04059 9.04184i 0.225384 0.670225i
\(183\) 8.46346 + 0.836717i 0.625637 + 0.0618519i
\(184\) −4.09436 2.36388i −0.301840 0.174268i
\(185\) −8.64531 14.9741i −0.635616 1.10092i
\(186\) −8.55703 + 3.87335i −0.627432 + 0.284008i
\(187\) 4.89029 8.47023i 0.357614 0.619405i
\(188\) 7.69252i 0.561035i
\(189\) 2.10838 13.5851i 0.153362 0.988170i
\(190\) 1.22732i 0.0890389i
\(191\) 22.6677 + 13.0872i 1.64018 + 0.946957i 0.980769 + 0.195172i \(0.0625266\pi\)
0.659409 + 0.751785i \(0.270807\pi\)
\(192\) 1.57792 0.714250i 0.113877 0.0515466i
\(193\) 1.84511 1.06527i 0.132814 0.0766801i −0.432121 0.901816i \(-0.642235\pi\)
0.564935 + 0.825136i \(0.308901\pi\)
\(194\) 2.95792 5.12327i 0.212366 0.367829i
\(195\) −15.8345 0.649589i −1.13393 0.0465181i
\(196\) −5.05508 4.84212i −0.361077 0.345866i
\(197\) −4.36762 −0.311180 −0.155590 0.987822i \(-0.549728\pi\)
−0.155590 + 0.987822i \(0.549728\pi\)
\(198\) −5.24381 + 5.97056i −0.372661 + 0.424309i
\(199\) −23.1724 + 13.3786i −1.64265 + 0.948383i −0.662760 + 0.748832i \(0.730615\pi\)
−0.979887 + 0.199551i \(0.936052\pi\)
\(200\) 0.719909 + 1.24692i 0.0509053 + 0.0881705i
\(201\) 1.61099 2.24639i 0.113631 0.158448i
\(202\) 13.8638 0.975455
\(203\) 2.59010 + 18.1619i 0.181789 + 1.27471i
\(204\) −0.629210 + 6.36451i −0.0440535 + 0.445604i
\(205\) −3.85338 + 6.67425i −0.269132 + 0.466150i
\(206\) 7.90784 4.56559i 0.550965 0.318100i
\(207\) −13.4339 + 4.54920i −0.933723 + 0.316191i
\(208\) 1.62022 3.22101i 0.112342 0.223337i
\(209\) 1.28106 0.0886125
\(210\) −5.37507 + 10.3124i −0.370915 + 0.711620i
\(211\) −17.3315 −1.19315 −0.596575 0.802557i \(-0.703472\pi\)
−0.596575 + 0.802557i \(0.703472\pi\)
\(212\) −8.13530 4.69692i −0.558735 0.322586i
\(213\) −20.3596 + 9.21580i −1.39502 + 0.631456i
\(214\) 6.73065 3.88594i 0.460098 0.265638i
\(215\) 11.2316 + 6.48455i 0.765987 + 0.442243i
\(216\) 1.51384 4.97074i 0.103004 0.338216i
\(217\) 8.85634 + 11.2883i 0.601207 + 0.766298i
\(218\) 13.6544i 0.924790i
\(219\) 18.5074 + 13.2725i 1.25062 + 0.896874i
\(220\) 5.82125 3.36090i 0.392468 0.226592i
\(221\) 7.30873 + 11.1278i 0.491639 + 0.748537i
\(222\) 6.87759 9.59022i 0.461594 0.643654i
\(223\) −4.35497 −0.291630 −0.145815 0.989312i \(-0.546580\pi\)
−0.145815 + 0.989312i \(0.546580\pi\)
\(224\) −1.63312 2.08157i −0.109117 0.139081i
\(225\) 4.23584 + 0.845796i 0.282389 + 0.0563864i
\(226\) −17.7738 10.2617i −1.18230 0.682600i
\(227\) 17.3580 10.0217i 1.15209 0.665160i 0.202696 0.979242i \(-0.435030\pi\)
0.949396 + 0.314081i \(0.101696\pi\)
\(228\) −0.763143 + 0.345438i −0.0505404 + 0.0228772i
\(229\) −13.3120 + 23.0571i −0.879683 + 1.52365i −0.0279931 + 0.999608i \(0.508912\pi\)
−0.851689 + 0.524047i \(0.824422\pi\)
\(230\) 11.9975 0.791095
\(231\) 10.7639 + 5.61043i 0.708213 + 0.369139i
\(232\) 6.93400i 0.455239i
\(233\) 20.2573 + 11.6956i 1.32710 + 0.766203i 0.984850 0.173406i \(-0.0554772\pi\)
0.342252 + 0.939608i \(0.388810\pi\)
\(234\) −4.05283 10.0287i −0.264942 0.655596i
\(235\) −9.76058 16.9058i −0.636710 1.10281i
\(236\) 4.98510 + 2.87815i 0.324503 + 0.187352i
\(237\) −1.28097 + 12.9572i −0.0832082 + 0.841658i
\(238\) 9.67148 1.37927i 0.626909 0.0894047i
\(239\) 10.6771 0.690642 0.345321 0.938485i \(-0.387770\pi\)
0.345321 + 0.938485i \(0.387770\pi\)
\(240\) −2.56153 + 3.57184i −0.165346 + 0.230561i
\(241\) −6.08041 10.5316i −0.391673 0.678398i 0.600997 0.799251i \(-0.294770\pi\)
−0.992670 + 0.120853i \(0.961437\pi\)
\(242\) 1.99194 + 3.45014i 0.128047 + 0.221783i
\(243\) −8.20744 13.2528i −0.526507 0.850171i
\(244\) 4.91020i 0.314343i
\(245\) 17.2534 + 4.22741i 1.10228 + 0.270080i
\(246\) −5.23460 0.517505i −0.333746 0.0329949i
\(247\) −0.783598 + 1.55780i −0.0498591 + 0.0991204i
\(248\) 2.71148 + 4.69643i 0.172179 + 0.298223i
\(249\) 2.21433 + 4.89191i 0.140327 + 0.310012i
\(250\) 7.82419 + 4.51730i 0.494845 + 0.285699i
\(251\) −25.7551 −1.62565 −0.812825 0.582508i \(-0.802072\pi\)
−0.812825 + 0.582508i \(0.802072\pi\)
\(252\) −7.92506 0.439716i −0.499232 0.0276995i
\(253\) 12.5229i 0.787307i
\(254\) 5.35236 9.27055i 0.335837 0.581686i
\(255\) −6.69273 14.7856i −0.419115 0.925911i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 8.74076 15.1394i 0.545233 0.944372i −0.453359 0.891328i \(-0.649774\pi\)
0.998592 0.0530439i \(-0.0168923\pi\)
\(258\) −0.870869 + 8.80890i −0.0542179 + 0.548418i
\(259\) −16.7280 6.71907i −1.03943 0.417503i
\(260\) 0.526198 + 9.13459i 0.0326334 + 0.566503i
\(261\) 15.6297 + 13.7272i 0.967453 + 0.849692i
\(262\) 3.16842 + 5.48787i 0.195746 + 0.339042i
\(263\) −17.8986 + 10.3338i −1.10368 + 0.637208i −0.937184 0.348834i \(-0.886578\pi\)
−0.166493 + 0.986043i \(0.553244\pi\)
\(264\) 3.72824 + 2.67369i 0.229457 + 0.164554i
\(265\) 23.8385 1.46439
\(266\) 0.789836 + 1.00672i 0.0484280 + 0.0617262i
\(267\) −4.73684 0.468295i −0.289890 0.0286592i
\(268\) −1.38217 0.797996i −0.0844295 0.0487454i
\(269\) −0.237662 0.411643i −0.0144905 0.0250983i 0.858689 0.512497i \(-0.171279\pi\)
−0.873180 + 0.487398i \(0.837946\pi\)
\(270\) 2.98011 + 12.8450i 0.181364 + 0.781722i
\(271\) 0.772450 1.33792i 0.0469230 0.0812730i −0.841610 0.540086i \(-0.818392\pi\)
0.888533 + 0.458813i \(0.151725\pi\)
\(272\) 3.69246 0.223888
\(273\) −13.4065 + 9.65741i −0.811399 + 0.584493i
\(274\) 17.6827 1.06825
\(275\) −1.90689 + 3.30284i −0.114990 + 0.199169i
\(276\) 3.37680 + 7.46005i 0.203260 + 0.449043i
\(277\) 14.0171 + 24.2784i 0.842209 + 1.45875i 0.888023 + 0.459798i \(0.152078\pi\)
−0.0458149 + 0.998950i \(0.514588\pi\)
\(278\) 13.9377 + 8.04691i 0.835925 + 0.482622i
\(279\) 15.9540 + 3.18563i 0.955139 + 0.190718i
\(280\) 6.23027 + 2.50249i 0.372330 + 0.149552i
\(281\) 30.3889 1.81285 0.906426 0.422365i \(-0.138800\pi\)
0.906426 + 0.422365i \(0.138800\pi\)
\(282\) 7.76482 10.8274i 0.462388 0.644762i
\(283\) 6.07652 3.50828i 0.361212 0.208546i −0.308400 0.951257i \(-0.599794\pi\)
0.669612 + 0.742711i \(0.266460\pi\)
\(284\) 6.45138 + 11.1741i 0.382819 + 0.663062i
\(285\) 1.23885 1.72747i 0.0733832 0.102327i
\(286\) 9.53457 0.549239i 0.563791 0.0324772i
\(287\) 1.13441 + 7.95449i 0.0669618 + 0.469539i
\(288\) −2.94193 0.587433i −0.173355 0.0346148i
\(289\) 1.68286 2.91480i 0.0989918 0.171459i
\(290\) −8.79813 15.2388i −0.516644 0.894854i
\(291\) −9.33476 + 4.22539i −0.547213 + 0.247697i
\(292\) 6.57447 11.3873i 0.384742 0.666393i
\(293\) 32.4228i 1.89416i 0.321000 + 0.947079i \(0.395981\pi\)
−0.321000 + 0.947079i \(0.604019\pi\)
\(294\) 2.22751 + 11.9180i 0.129911 + 0.695071i
\(295\) −14.6076 −0.850490
\(296\) −5.90071 3.40678i −0.342972 0.198015i
\(297\) 13.4074 3.11060i 0.777979 0.180495i
\(298\) −1.28692 2.22901i −0.0745493 0.129123i
\(299\) 15.2282 + 7.66001i 0.880667 + 0.442990i
\(300\) 0.245351 2.48174i 0.0141653 0.143283i
\(301\) 13.3860 1.90900i 0.771555 0.110033i
\(302\) 4.25062i 0.244595i
\(303\) −19.5136 13.9941i −1.12103 0.803941i
\(304\) 0.241819 + 0.418842i 0.0138692 + 0.0240222i
\(305\) 6.23026 + 10.7911i 0.356743 + 0.617898i
\(306\) 7.30995 8.32305i 0.417882 0.475797i
\(307\) −30.0357 −1.71423 −0.857113 0.515128i \(-0.827744\pi\)
−0.857113 + 0.515128i \(0.827744\pi\)
\(308\) 2.61207 6.50308i 0.148836 0.370547i
\(309\) −15.7390 1.55599i −0.895358 0.0885172i
\(310\) −11.9180 6.88088i −0.676898 0.390808i
\(311\) −3.19493 5.53379i −0.181168 0.313792i 0.761111 0.648622i \(-0.224654\pi\)
−0.942279 + 0.334830i \(0.891321\pi\)
\(312\) −5.53177 + 2.89819i −0.313175 + 0.164078i
\(313\) 8.58761 + 4.95806i 0.485400 + 0.280246i 0.722664 0.691199i \(-0.242917\pi\)
−0.237264 + 0.971445i \(0.576251\pi\)
\(314\) 0.951424i 0.0536920i
\(315\) 17.9748 9.08928i 1.01277 0.512123i
\(316\) 7.51729 0.422880
\(317\) 15.9691 27.6594i 0.896916 1.55350i 0.0655007 0.997853i \(-0.479136\pi\)
0.831415 0.555652i \(-0.187531\pi\)
\(318\) 6.70955 + 14.8228i 0.376253 + 0.831219i
\(319\) −15.9061 + 9.18337i −0.890569 + 0.514170i
\(320\) 2.19770 + 1.26884i 0.122855 + 0.0709303i
\(321\) −13.3960 1.32436i −0.747692 0.0739186i
\(322\) 9.84116 7.72099i 0.548427 0.430274i
\(323\) −1.78581 −0.0993652
\(324\) −7.14822 + 5.46836i −0.397123 + 0.303798i
\(325\) −2.84993 4.33912i −0.158086 0.240691i
\(326\) −4.74897 + 2.74182i −0.263021 + 0.151855i
\(327\) 13.7827 19.2188i 0.762184 1.06280i
\(328\) 3.03693i 0.167687i
\(329\) −18.8860 7.58585i −1.04122 0.418222i
\(330\) −11.5860 1.14542i −0.637789 0.0630533i
\(331\) 13.1995 + 7.62074i 0.725511 + 0.418874i 0.816778 0.576953i \(-0.195758\pi\)
−0.0912670 + 0.995826i \(0.529092\pi\)
\(332\) 2.68487 1.55011i 0.147351 0.0850732i
\(333\) −19.3607 + 6.55621i −1.06096 + 0.359278i
\(334\) 5.33246 + 3.07870i 0.291779 + 0.168459i
\(335\) 4.05012 0.221282
\(336\) 0.197515 + 4.57832i 0.0107753 + 0.249768i
\(337\) 23.2445 1.26621 0.633103 0.774067i \(-0.281781\pi\)
0.633103 + 0.774067i \(0.281781\pi\)
\(338\) −5.16422 + 11.9302i −0.280897 + 0.648920i
\(339\) 14.6589 + 32.3845i 0.796161 + 1.75888i
\(340\) −8.11491 + 4.68514i −0.440093 + 0.254088i
\(341\) −7.18217 + 12.4399i −0.388936 + 0.673657i
\(342\) 1.42282 + 0.284104i 0.0769375 + 0.0153626i
\(343\) 16.8729 7.63579i 0.911051 0.412294i
\(344\) 5.11062 0.275546
\(345\) −16.8868 12.1103i −0.909155 0.651997i
\(346\) 3.45361 + 5.98183i 0.185667 + 0.321585i
\(347\) 21.2374 12.2614i 1.14008 0.658226i 0.193631 0.981074i \(-0.437974\pi\)
0.946451 + 0.322848i \(0.104640\pi\)
\(348\) 6.99916 9.75974i 0.375194 0.523177i
\(349\) 1.10347 0.0590671 0.0295336 0.999564i \(-0.490598\pi\)
0.0295336 + 0.999564i \(0.490598\pi\)
\(350\) −3.77125 + 0.537825i −0.201582 + 0.0287479i
\(351\) −4.41850 + 18.2065i −0.235842 + 0.971791i
\(352\) 1.32440 2.29393i 0.0705907 0.122267i
\(353\) 5.34237 3.08442i 0.284346 0.164167i −0.351043 0.936359i \(-0.614173\pi\)
0.635389 + 0.772192i \(0.280840\pi\)
\(354\) −4.11144 9.08301i −0.218520 0.482756i
\(355\) −28.3563 16.3715i −1.50500 0.868911i
\(356\) 2.74815i 0.145652i
\(357\) −15.0050 7.82102i −0.794151 0.413933i
\(358\) 1.72527i 0.0911836i
\(359\) −6.24235 + 10.8121i −0.329459 + 0.570639i −0.982405 0.186765i \(-0.940200\pi\)
0.652946 + 0.757405i \(0.273533\pi\)
\(360\) 7.21081 2.44183i 0.380043 0.128696i
\(361\) 9.38305 + 16.2519i 0.493845 + 0.855364i
\(362\) −19.1077 11.0319i −1.00428 0.579821i
\(363\) 0.678868 6.86680i 0.0356313 0.360413i
\(364\) 6.31016 + 7.15415i 0.330742 + 0.374979i
\(365\) 33.3678i 1.74655i
\(366\) −4.95635 + 6.91121i −0.259072 + 0.361255i
\(367\) 20.5085 11.8406i 1.07053 0.618073i 0.142207 0.989837i \(-0.454580\pi\)
0.928327 + 0.371764i \(0.121247\pi\)
\(368\) 4.09436 2.36388i 0.213433 0.123226i
\(369\) 6.84545 + 6.01220i 0.356360 + 0.312983i
\(370\) 17.2906 0.898897
\(371\) 19.5539 15.3412i 1.01519 0.796477i
\(372\) 0.924094 9.34729i 0.0479121 0.484634i
\(373\) 1.11557 1.93222i 0.0577619 0.100046i −0.835699 0.549188i \(-0.814937\pi\)
0.893460 + 0.449142i \(0.148270\pi\)
\(374\) 4.89029 + 8.47023i 0.252871 + 0.437985i
\(375\) −6.45296 14.2559i −0.333230 0.736173i
\(376\) −6.66192 3.84626i −0.343562 0.198356i
\(377\) −1.43779 24.9595i −0.0740500 1.28548i
\(378\) 10.7108 + 8.61846i 0.550906 + 0.443286i
\(379\) 7.75732i 0.398467i −0.979952 0.199233i \(-0.936155\pi\)
0.979952 0.199233i \(-0.0638452\pi\)
\(380\) −1.06289 0.613658i −0.0545250 0.0314800i
\(381\) −16.8912 + 7.64584i −0.865364 + 0.391708i
\(382\) −22.6677 + 13.0872i −1.15978 + 0.669600i
\(383\) −7.94443 4.58672i −0.405941 0.234370i 0.283103 0.959090i \(-0.408636\pi\)
−0.689044 + 0.724719i \(0.741970\pi\)
\(384\) −0.170404 + 1.72365i −0.00869589 + 0.0879595i
\(385\) 2.51084 + 17.6061i 0.127964 + 0.897288i
\(386\) 2.13055i 0.108442i
\(387\) 10.1175 11.5197i 0.514299 0.585577i
\(388\) 2.95792 + 5.12327i 0.150166 + 0.260095i
\(389\) 29.7827 17.1950i 1.51004 0.871823i 0.510110 0.860109i \(-0.329605\pi\)
0.999931 0.0117132i \(-0.00372851\pi\)
\(390\) 8.47980 13.3883i 0.429392 0.677942i
\(391\) 17.4571i 0.882843i
\(392\) 6.72094 1.95677i 0.339459 0.0988318i
\(393\) 1.07982 10.9225i 0.0544699 0.550967i
\(394\) 2.18381 3.78247i 0.110019 0.190558i
\(395\) −16.5207 + 9.53823i −0.831247 + 0.479921i
\(396\) −2.54875 7.52655i −0.128080 0.378223i
\(397\) −6.32491 + 10.9551i −0.317438 + 0.549819i −0.979953 0.199230i \(-0.936156\pi\)
0.662515 + 0.749049i \(0.269489\pi\)
\(398\) 26.7572i 1.34122i
\(399\) −0.0955256 2.21424i −0.00478226 0.110851i
\(400\) −1.43982 −0.0719909
\(401\) −11.1563 + 19.3233i −0.557121 + 0.964962i 0.440614 + 0.897697i \(0.354761\pi\)
−0.997735 + 0.0672652i \(0.978573\pi\)
\(402\) 1.13994 + 2.51836i 0.0568549 + 0.125604i
\(403\) −10.7340 16.3429i −0.534700 0.814100i
\(404\) −6.93191 + 12.0064i −0.344875 + 0.597342i
\(405\) 8.77115 21.0877i 0.435842 1.04786i
\(406\) −17.0237 6.83784i −0.844872 0.339356i
\(407\) 18.0477i 0.894593i
\(408\) −5.19722 3.72716i −0.257301 0.184522i
\(409\) −15.2106 26.3456i −0.752118 1.30271i −0.946794 0.321839i \(-0.895699\pi\)
0.194677 0.980867i \(-0.437634\pi\)
\(410\) −3.85338 6.67425i −0.190305 0.329618i
\(411\) −24.8887 17.8489i −1.22767 0.880419i
\(412\) 9.13119i 0.449861i
\(413\) −11.9821 + 9.40071i −0.589602 + 0.462579i
\(414\) 2.77724 13.9087i 0.136494 0.683577i
\(415\) −3.93368 + 6.81333i −0.193097 + 0.334453i
\(416\) 1.97937 + 3.01365i 0.0970464 + 0.147757i
\(417\) −11.4950 25.3948i −0.562913 1.24359i
\(418\) −0.640528 + 1.10943i −0.0313293 + 0.0542639i
\(419\) −22.9563 −1.12149 −0.560744 0.827989i \(-0.689485\pi\)
−0.560744 + 0.827989i \(0.689485\pi\)
\(420\) −6.24323 9.81113i −0.304638 0.478734i
\(421\) 11.7102i 0.570721i −0.958420 0.285360i \(-0.907887\pi\)
0.958420 0.285360i \(-0.0921133\pi\)
\(422\) 8.66575 15.0095i 0.421842 0.730652i
\(423\) −21.8583 + 7.40199i −1.06279 + 0.359897i
\(424\) 8.13530 4.69692i 0.395085 0.228102i
\(425\) 2.65824 4.60420i 0.128944 0.223337i
\(426\) 2.19868 22.2398i 0.106526 1.07752i
\(427\) 12.0551 + 4.84211i 0.583385 + 0.234326i
\(428\) 7.77189i 0.375668i
\(429\) −13.9745 8.85111i −0.674695 0.427336i
\(430\) −11.2316 + 6.48455i −0.541635 + 0.312713i
\(431\) 9.15519 + 15.8573i 0.440990 + 0.763817i 0.997763 0.0668476i \(-0.0212941\pi\)
−0.556773 + 0.830664i \(0.687961\pi\)
\(432\) 3.54787 + 3.79640i 0.170697 + 0.182654i
\(433\) 21.1787i 1.01778i −0.860831 0.508891i \(-0.830056\pi\)
0.860831 0.508891i \(-0.169944\pi\)
\(434\) −14.2041 + 2.02568i −0.681819 + 0.0972355i
\(435\) −2.99847 + 30.3298i −0.143766 + 1.45420i
\(436\) −11.8250 6.82718i −0.566316 0.326963i
\(437\) −1.98019 + 1.14326i −0.0947251 + 0.0546896i
\(438\) −20.7481 + 9.39164i −0.991380 + 0.448750i
\(439\) −7.13298 4.11823i −0.340439 0.196552i 0.320027 0.947408i \(-0.396308\pi\)
−0.660466 + 0.750856i \(0.729641\pi\)
\(440\) 6.72180i 0.320449i
\(441\) 8.89472 19.0232i 0.423558 0.905869i
\(442\) −13.2913 + 0.765647i −0.632204 + 0.0364181i
\(443\) 7.54716 + 4.35736i 0.358577 + 0.207024i 0.668456 0.743752i \(-0.266955\pi\)
−0.309880 + 0.950776i \(0.600289\pi\)
\(444\) 4.86658 + 10.7513i 0.230958 + 0.510233i
\(445\) −3.48696 6.03960i −0.165298 0.286304i
\(446\) 2.17749 3.77151i 0.103107 0.178586i
\(447\) −0.438593 + 4.43640i −0.0207447 + 0.209834i
\(448\) 2.61925 0.373536i 0.123748 0.0176479i
\(449\) −22.6845 −1.07055 −0.535274 0.844679i \(-0.679792\pi\)
−0.535274 + 0.844679i \(0.679792\pi\)
\(450\) −2.85040 + 3.24545i −0.134369 + 0.152992i
\(451\) −6.96650 + 4.02211i −0.328040 + 0.189394i
\(452\) 17.7738 10.2617i 0.836011 0.482671i
\(453\) −4.29056 + 5.98283i −0.201588 + 0.281098i
\(454\) 20.0433i 0.940679i
\(455\) −22.9453 7.71605i −1.07569 0.361734i
\(456\) 0.0824136 0.833620i 0.00385937 0.0390378i
\(457\) 11.5835 + 6.68771i 0.541851 + 0.312838i 0.745829 0.666138i \(-0.232054\pi\)
−0.203978 + 0.978976i \(0.565387\pi\)
\(458\) −13.3120 23.0571i −0.622029 1.07739i
\(459\) −18.6902 + 4.33623i −0.872383 + 0.202398i
\(460\) −5.99877 + 10.3902i −0.279694 + 0.484445i
\(461\) 0.777510i 0.0362123i −0.999836 0.0181061i \(-0.994236\pi\)
0.999836 0.0181061i \(-0.00576367\pi\)
\(462\) −10.2407 + 6.51660i −0.476442 + 0.303180i
\(463\) 3.19686i 0.148571i −0.997237 0.0742854i \(-0.976332\pi\)
0.997237 0.0742854i \(-0.0236676\pi\)
\(464\) −6.00502 3.46700i −0.278776 0.160951i
\(465\) 9.82933 + 21.7150i 0.455824 + 1.00701i
\(466\) −20.2573 + 11.6956i −0.938403 + 0.541787i
\(467\) 0.719079 1.24548i 0.0332750 0.0576340i −0.848908 0.528540i \(-0.822740\pi\)
0.882183 + 0.470906i \(0.156073\pi\)
\(468\) 10.7115 + 1.50449i 0.495140 + 0.0695452i
\(469\) 3.32217 2.60644i 0.153404 0.120354i
\(470\) 19.5212 0.900444
\(471\) −0.960365 + 1.33915i −0.0442513 + 0.0617047i
\(472\) −4.98510 + 2.87815i −0.229458 + 0.132478i
\(473\) 6.76849 + 11.7234i 0.311216 + 0.539041i
\(474\) −10.5807 7.58793i −0.485989 0.348525i
\(475\) 0.696350 0.0319507
\(476\) −3.64126 + 9.06538i −0.166897 + 0.415511i
\(477\) 5.51824 27.6360i 0.252663 1.26536i
\(478\) −5.33853 + 9.24661i −0.244179 + 0.422930i
\(479\) 9.04541 5.22237i 0.413295 0.238616i −0.278909 0.960317i \(-0.589973\pi\)
0.692205 + 0.721701i \(0.256640\pi\)
\(480\) −1.81254 4.00427i −0.0827306 0.182769i
\(481\) 21.9465 + 11.0394i 1.00068 + 0.503355i
\(482\) 12.1608 0.553910
\(483\) −21.6452 + 0.933804i −0.984891 + 0.0424896i
\(484\) −3.98387 −0.181085
\(485\) −13.0012 7.50626i −0.590355 0.340842i
\(486\) 15.5810 0.481423i 0.706769 0.0218378i
\(487\) −2.08097 + 1.20145i −0.0942979 + 0.0544429i −0.546407 0.837520i \(-0.684005\pi\)
0.452109 + 0.891962i \(0.350672\pi\)
\(488\) 4.25236 + 2.45510i 0.192495 + 0.111137i
\(489\) 9.45187 + 0.934434i 0.427428 + 0.0422565i
\(490\) −12.2878 + 12.8282i −0.555104 + 0.579518i
\(491\) 12.3575i 0.557686i 0.960337 + 0.278843i \(0.0899509\pi\)
−0.960337 + 0.278843i \(0.910049\pi\)
\(492\) 3.06547 4.27455i 0.138202 0.192711i
\(493\) 22.1733 12.8018i 0.998635 0.576562i
\(494\) −0.957295 1.45752i −0.0430707 0.0655767i
\(495\) 15.1514 + 13.3071i 0.681004 + 0.598110i
\(496\) −5.42297 −0.243498
\(497\) −33.7956 + 4.81965i −1.51594 + 0.216191i
\(498\) −5.34368 0.528289i −0.239456 0.0236732i
\(499\) 14.9074 + 8.60680i 0.667348 + 0.385293i 0.795071 0.606516i \(-0.207434\pi\)
−0.127723 + 0.991810i \(0.540767\pi\)
\(500\) −7.82419 + 4.51730i −0.349909 + 0.202020i
\(501\) −4.39792 9.71591i −0.196485 0.434075i
\(502\) 12.8776 22.3046i 0.574754 0.995503i
\(503\) 31.1852 1.39048 0.695240 0.718778i \(-0.255298\pi\)
0.695240 + 0.718778i \(0.255298\pi\)
\(504\) 4.34334 6.64345i 0.193468 0.295923i
\(505\) 35.1819i 1.56558i
\(506\) 10.8451 + 6.26144i 0.482125 + 0.278355i
\(507\) 19.3111 11.5793i 0.857637 0.514256i
\(508\) 5.35236 + 9.27055i 0.237472 + 0.411314i
\(509\) 4.87130 + 2.81245i 0.215917 + 0.124660i 0.604058 0.796940i \(-0.293549\pi\)
−0.388141 + 0.921600i \(0.626883\pi\)
\(510\) 16.1511 + 1.59673i 0.715182 + 0.0707045i
\(511\) 21.4738 + 27.3704i 0.949944 + 1.21080i
\(512\) 1.00000 0.0441942
\(513\) −1.71588 1.83608i −0.0757580 0.0810649i
\(514\) 8.74076 + 15.1394i 0.385538 + 0.667772i
\(515\) −11.5860 20.0676i −0.510541 0.884283i
\(516\) −7.19330 5.15865i −0.316667 0.227097i
\(517\) 20.3759i 0.896133i
\(518\) 14.1829 11.1273i 0.623160 0.488907i
\(519\) 1.17702 11.9056i 0.0516654 0.522599i
\(520\) −8.17389 4.11159i −0.358449 0.180305i
\(521\) −1.86664 3.23312i −0.0817791 0.141646i 0.822235 0.569148i \(-0.192727\pi\)
−0.904014 + 0.427502i \(0.859394\pi\)
\(522\) −19.7029 + 6.67211i −0.862374 + 0.292030i
\(523\) 20.8918 + 12.0619i 0.913533 + 0.527428i 0.881566 0.472061i \(-0.156490\pi\)
0.0319666 + 0.999489i \(0.489823\pi\)
\(524\) −6.33685 −0.276826
\(525\) 5.85099 + 3.04969i 0.255358 + 0.133099i
\(526\) 20.6676i 0.901149i
\(527\) 10.0120 17.3414i 0.436132 0.755402i
\(528\) −4.17960 + 1.89190i −0.181894 + 0.0823345i
\(529\) −0.324129 0.561408i −0.0140926 0.0244090i
\(530\) −11.9193 + 20.6448i −0.517740 + 0.896752i
\(531\) −3.38144 + 16.9346i −0.146742 + 0.734899i
\(532\) −1.26677 + 0.180656i −0.0549213 + 0.00783244i
\(533\) −0.629720 10.9317i −0.0272762 0.473504i
\(534\) 2.77398 3.86808i 0.120042 0.167388i
\(535\) −9.86128 17.0802i −0.426340 0.738443i
\(536\) 1.38217 0.797996i 0.0597007 0.0344682i
\(537\) 1.74149 2.42836i 0.0751508 0.104791i
\(538\) 0.475324 0.0204927
\(539\) 13.3899 + 12.8258i 0.576743 + 0.552446i
\(540\) −12.6142 3.84165i −0.542827 0.165318i
\(541\) 29.5203 + 17.0435i 1.26917 + 0.732759i 0.974832 0.222941i \(-0.0715658\pi\)
0.294343 + 0.955700i \(0.404899\pi\)
\(542\) 0.772450 + 1.33792i 0.0331796 + 0.0574687i
\(543\) 15.7590 + 34.8149i 0.676283 + 1.49405i
\(544\) −1.84623 + 3.19777i −0.0791565 + 0.137103i
\(545\) 34.6504 1.48426
\(546\) −1.66030 16.4391i −0.0710545 0.703528i
\(547\) 16.3522 0.699170 0.349585 0.936905i \(-0.386323\pi\)
0.349585 + 0.936905i \(0.386323\pi\)
\(548\) −8.84134 + 15.3136i −0.377683 + 0.654167i
\(549\) 13.9523 4.72475i 0.595471 0.201647i
\(550\) −1.90689 3.30284i −0.0813102 0.140833i
\(551\) 2.90425 + 1.67677i 0.123725 + 0.0714328i
\(552\) −8.14900 0.805629i −0.346844 0.0342898i
\(553\) −7.41304 + 18.4557i −0.315235 + 0.784817i
\(554\) −28.0343 −1.19106
\(555\) −24.3369 17.4531i −1.03304 0.740844i
\(556\) −13.9377 + 8.04691i −0.591088 + 0.341265i
\(557\) −9.83768 17.0394i −0.416836 0.721981i 0.578784 0.815481i \(-0.303528\pi\)
−0.995619 + 0.0935006i \(0.970194\pi\)
\(558\) −10.7358 + 12.2237i −0.454483 + 0.517471i
\(559\) −18.3961 + 1.05971i −0.778072 + 0.0448208i
\(560\) −5.28236 + 4.14433i −0.223220 + 0.175130i
\(561\) 1.66665 16.8583i 0.0703660 0.711757i
\(562\) −15.1945 + 26.3176i −0.640940 + 1.11014i
\(563\) −7.14030 12.3674i −0.300928 0.521222i 0.675419 0.737435i \(-0.263963\pi\)
−0.976346 + 0.216212i \(0.930630\pi\)
\(564\) 5.49439 + 12.1382i 0.231355 + 0.511112i
\(565\) −26.0410 + 45.1043i −1.09555 + 1.89755i
\(566\) 7.01656i 0.294928i
\(567\) −6.37629 22.9422i −0.267779 0.963480i
\(568\) −12.9028 −0.541388
\(569\) 14.4405 + 8.33720i 0.605376 + 0.349514i 0.771153 0.636649i \(-0.219680\pi\)
−0.165778 + 0.986163i \(0.553013\pi\)
\(570\) 0.876611 + 1.93661i 0.0367172 + 0.0811158i
\(571\) −0.208287 0.360764i −0.00871655 0.0150975i 0.861634 0.507530i \(-0.169441\pi\)
−0.870351 + 0.492432i \(0.836108\pi\)
\(572\) −4.29163 + 8.53180i −0.179442 + 0.356732i
\(573\) 45.1155 + 4.46022i 1.88473 + 0.186328i
\(574\) −7.45599 2.99482i −0.311207 0.125001i
\(575\) 6.80712i 0.283877i
\(576\) 1.97969 2.25407i 0.0824873 0.0939194i
\(577\) 1.18972 + 2.06066i 0.0495287 + 0.0857863i 0.889727 0.456493i \(-0.150895\pi\)
−0.840198 + 0.542279i \(0.817561\pi\)
\(578\) 1.68286 + 2.91480i 0.0699978 + 0.121240i
\(579\) 2.15057 2.99879i 0.0893747 0.124625i
\(580\) 17.5963 0.730645
\(581\) 1.15804 + 8.12024i 0.0480437 + 0.336884i
\(582\) 1.00808 10.1968i 0.0417864 0.422672i
\(583\) 21.5488 + 12.4412i 0.892458 + 0.515261i
\(584\) 6.57447 + 11.3873i 0.272054 + 0.471211i
\(585\) −25.4496 + 10.2848i −1.05221 + 0.425223i
\(586\) −28.0789 16.2114i −1.15993 0.669686i
\(587\) 28.1076i 1.16013i −0.814572 0.580063i \(-0.803028\pi\)
0.814572 0.580063i \(-0.196972\pi\)
\(588\) −11.4350 4.02991i −0.471573 0.166191i
\(589\) 2.62275 0.108068
\(590\) 7.30382 12.6506i 0.300694 0.520817i
\(591\) −6.89177 + 3.11957i −0.283489 + 0.128322i
\(592\) 5.90071 3.40678i 0.242518 0.140018i
\(593\) −16.2280 9.36924i −0.666404 0.384749i 0.128309 0.991734i \(-0.459045\pi\)
−0.794713 + 0.606986i \(0.792379\pi\)
\(594\) −4.00986 + 13.1665i −0.164527 + 0.540228i
\(595\) −3.50014 24.5431i −0.143492 1.00617i
\(596\) 2.57384 0.105429
\(597\) −27.0086 + 37.6613i −1.10539 + 1.54137i
\(598\) −14.2478 + 9.35797i −0.582638 + 0.382676i
\(599\) 0.243067 0.140335i 0.00993147 0.00573394i −0.495026 0.868878i \(-0.664841\pi\)
0.504958 + 0.863144i \(0.331508\pi\)
\(600\) 2.02658 + 1.45335i 0.0827346 + 0.0593328i
\(601\) 7.38730i 0.301334i 0.988585 + 0.150667i \(0.0481421\pi\)
−0.988585 + 0.150667i \(0.951858\pi\)
\(602\) −5.03975 + 12.5471i −0.205405 + 0.511382i
\(603\) 0.937538 4.69529i 0.0381795 0.191207i
\(604\) 3.68114 + 2.12531i 0.149784 + 0.0864776i
\(605\) 8.75534 5.05490i 0.355955 0.205511i
\(606\) 21.8761 9.90223i 0.888655 0.402251i
\(607\) 22.6313 + 13.0662i 0.918577 + 0.530341i 0.883181 0.469033i \(-0.155397\pi\)
0.0353963 + 0.999373i \(0.488731\pi\)
\(608\) −0.483637 −0.0196141
\(609\) 17.0591 + 26.8081i 0.691269 + 1.08632i
\(610\) −12.4605 −0.504511
\(611\) 24.7777 + 12.4636i 1.00240 + 0.504222i
\(612\) 3.55300 + 10.4921i 0.143622 + 0.424119i
\(613\) 15.4716 8.93253i 0.624892 0.360781i −0.153879 0.988090i \(-0.549177\pi\)
0.778771 + 0.627308i \(0.215843\pi\)
\(614\) 15.0178 26.0117i 0.606071 1.04974i
\(615\) −1.31326 + 13.2837i −0.0529558 + 0.535652i
\(616\) 4.32580 + 5.51365i 0.174291 + 0.222151i
\(617\) −29.5144 −1.18821 −0.594103 0.804389i \(-0.702493\pi\)
−0.594103 + 0.804389i \(0.702493\pi\)
\(618\) 9.21700 12.8523i 0.370762 0.516997i
\(619\) −16.8277 29.1465i −0.676363 1.17149i −0.976069 0.217463i \(-0.930222\pi\)
0.299706 0.954032i \(-0.403112\pi\)
\(620\) 11.9180 6.88088i 0.478640 0.276343i
\(621\) −17.9485 + 16.7735i −0.720247 + 0.673097i
\(622\) 6.38987 0.256210
\(623\) −6.74700 2.71004i −0.270313 0.108576i
\(624\) 0.255978 6.23975i 0.0102473 0.249790i
\(625\) 15.0630 26.0899i 0.602520 1.04360i
\(626\) −8.58761 + 4.95806i −0.343230 + 0.198164i
\(627\) 2.02141 0.914995i 0.0807274 0.0365414i
\(628\) 0.823957 + 0.475712i 0.0328795 + 0.0189830i
\(629\) 25.1588i 1.00315i
\(630\) −1.11586 + 20.1113i −0.0444569 + 0.801252i
\(631\) 41.0344i 1.63356i 0.576953 + 0.816778i \(0.304242\pi\)
−0.576953 + 0.816778i \(0.695758\pi\)
\(632\) −3.75864 + 6.51016i −0.149511 + 0.258960i
\(633\) −27.3478 + 12.3790i −1.08698 + 0.492022i
\(634\) 15.9691 + 27.6594i 0.634215 + 1.09849i
\(635\) −23.5257 13.5826i −0.933589 0.539008i
\(636\) −16.1917 1.60075i −0.642041 0.0634737i
\(637\) −23.7868 + 8.43717i −0.942469 + 0.334293i
\(638\) 18.3667i 0.727146i
\(639\) −25.5435 + 29.0837i −1.01049 + 1.15053i
\(640\) −2.19770 + 1.26884i −0.0868715 + 0.0501553i
\(641\) 10.8867 6.28542i 0.429998 0.248259i −0.269348 0.963043i \(-0.586808\pi\)
0.699346 + 0.714784i \(0.253475\pi\)
\(642\) 7.84493 10.9391i 0.309615 0.431732i
\(643\) −44.1388 −1.74067 −0.870333 0.492464i \(-0.836096\pi\)
−0.870333 + 0.492464i \(0.836096\pi\)
\(644\) 1.76599 + 12.3832i 0.0695898 + 0.487966i
\(645\) 22.3542 + 2.20999i 0.880195 + 0.0870181i
\(646\) 0.892906 1.54656i 0.0351309 0.0608485i
\(647\) −6.42771 11.1331i −0.252699 0.437688i 0.711569 0.702616i \(-0.247985\pi\)
−0.964268 + 0.264928i \(0.914652\pi\)
\(648\) −1.16162 8.92472i −0.0456329 0.350596i
\(649\) −13.2045 7.62364i −0.518323 0.299254i
\(650\) 5.18275 0.298552i 0.203284 0.0117102i
\(651\) 22.0373 + 11.4864i 0.863709 + 0.450188i
\(652\) 5.48364i 0.214756i
\(653\) −38.8978 22.4576i −1.52219 0.878835i −0.999656 0.0262147i \(-0.991655\pi\)
−0.522531 0.852620i \(-0.675012\pi\)
\(654\) 9.75263 + 21.5456i 0.381358 + 0.842498i
\(655\) 13.9265 8.04045i 0.544152 0.314166i
\(656\) −2.63006 1.51847i −0.102687 0.0592862i
\(657\) 38.6832 + 7.72412i 1.50918 + 0.301347i
\(658\) 16.0125 12.5628i 0.624233 0.489749i
\(659\) 4.26760i 0.166242i −0.996539 0.0831210i \(-0.973511\pi\)
0.996539 0.0831210i \(-0.0264888\pi\)
\(660\) 6.78497 9.46107i 0.264105 0.368272i
\(661\) −6.63233 11.4875i −0.257968 0.446814i 0.707729 0.706484i \(-0.249720\pi\)
−0.965697 + 0.259670i \(0.916386\pi\)
\(662\) −13.1995 + 7.62074i −0.513013 + 0.296188i
\(663\) 19.4807 + 12.3386i 0.756566 + 0.479191i
\(664\) 3.10022i 0.120312i
\(665\) 2.55474 2.00435i 0.0990687 0.0777254i
\(666\) 4.00250 20.0450i 0.155094 0.776727i
\(667\) 16.3911 28.3903i 0.634668 1.09928i
\(668\) −5.33246 + 3.07870i −0.206319 + 0.119118i
\(669\) −6.87182 + 3.11054i −0.265680 + 0.120260i
\(670\) −2.02506 + 3.50751i −0.0782349 + 0.135507i
\(671\) 13.0061i 0.502096i
\(672\) −4.06370 2.11811i −0.156760 0.0817077i
\(673\) 5.86953 0.226254 0.113127 0.993581i \(-0.463913\pi\)
0.113127 + 0.993581i \(0.463913\pi\)
\(674\) −11.6222 + 20.1303i −0.447672 + 0.775390i
\(675\) 7.28795 1.69084i 0.280513 0.0650806i
\(676\) −7.74979 10.4375i −0.298069 0.401441i
\(677\) −18.4065 + 31.8810i −0.707419 + 1.22529i 0.258393 + 0.966040i \(0.416807\pi\)
−0.965811 + 0.259245i \(0.916526\pi\)
\(678\) −35.3752 3.49728i −1.35858 0.134312i
\(679\) −15.4951 + 2.20978i −0.594646 + 0.0848037i
\(680\) 9.37029i 0.359334i
\(681\) 20.2317 28.2114i 0.775279 1.08106i
\(682\) −7.18217 12.4399i −0.275019 0.476348i
\(683\) −5.49782 9.52250i −0.210368 0.364368i 0.741462 0.670995i \(-0.234133\pi\)
−0.951830 + 0.306627i \(0.900800\pi\)
\(684\) −0.957454 + 1.09015i −0.0366092 + 0.0416829i
\(685\) 44.8730i 1.71451i
\(686\) −1.82366 + 18.4303i −0.0696278 + 0.703670i
\(687\) −4.53684 + 45.8904i −0.173091 + 1.75083i
\(688\) −2.55531 + 4.42592i −0.0974202 + 0.168737i
\(689\) −28.3098 + 18.5938i −1.07852 + 0.708369i
\(690\) 18.9312 8.56925i 0.720700 0.326226i
\(691\) 17.4124 30.1592i 0.662400 1.14731i −0.317583 0.948231i \(-0.602871\pi\)
0.979983 0.199081i \(-0.0637956\pi\)
\(692\) −6.90723 −0.262573
\(693\) 20.9919 + 1.16472i 0.797416 + 0.0442440i
\(694\) 24.5228i 0.930873i
\(695\) 20.4205 35.3693i 0.774593 1.34163i
\(696\) 4.95261 + 10.9413i 0.187728 + 0.414730i
\(697\) 9.71140 5.60688i 0.367846 0.212376i
\(698\) −0.551733 + 0.955629i −0.0208834 + 0.0361711i
\(699\) 40.3181 + 3.98594i 1.52497 + 0.150762i
\(700\) 1.41985 3.53491i 0.0536654 0.133607i
\(701\) 32.7821i 1.23816i −0.785327 0.619081i \(-0.787505\pi\)
0.785327 0.619081i \(-0.212495\pi\)
\(702\) −13.5580 12.9298i −0.511716 0.488003i
\(703\) −2.85380 + 1.64764i −0.107633 + 0.0621421i
\(704\) 1.32440 + 2.29393i 0.0499151 + 0.0864556i
\(705\) −27.4764 19.7046i −1.03482 0.742119i
\(706\) 6.16884i 0.232167i
\(707\) −22.6412 28.8585i −0.851512 1.08534i
\(708\) 9.92184 + 0.980896i 0.372885 + 0.0368643i
\(709\) 30.7026 + 17.7261i 1.15306 + 0.665719i 0.949631 0.313371i \(-0.101458\pi\)
0.203428 + 0.979090i \(0.434792\pi\)
\(710\) 28.3563 16.3715i 1.06419 0.614413i
\(711\) 7.23337 + 21.3604i 0.271272 + 0.801076i
\(712\) −2.37997 1.37408i −0.0891931 0.0514956i
\(713\) 25.6385i 0.960169i
\(714\) 14.2757 9.08424i 0.534256 0.339969i
\(715\) −1.39379 24.1957i −0.0521249 0.904867i
\(716\) −1.49413 0.862637i −0.0558383 0.0322383i
\(717\) 16.8476 7.62609i 0.629185 0.284802i
\(718\) −6.24235 10.8121i −0.232962 0.403503i
\(719\) −22.2486 + 38.5357i −0.829733 + 1.43714i 0.0685151 + 0.997650i \(0.478174\pi\)
−0.898248 + 0.439489i \(0.855159\pi\)
\(720\) −1.49072 + 7.46566i −0.0555557 + 0.278229i
\(721\) −22.4180 9.00456i −0.834891 0.335348i
\(722\) −18.7661 −0.698402
\(723\) −17.1166 12.2751i −0.636573 0.456516i
\(724\) 19.1077 11.0319i 0.710133 0.409996i
\(725\) −8.64614 + 4.99185i −0.321109 + 0.185393i
\(726\) 5.60739 + 4.02132i 0.208110 + 0.149245i
\(727\) 4.60691i 0.170861i −0.996344 0.0854305i \(-0.972773\pi\)
0.996344 0.0854305i \(-0.0272265\pi\)
\(728\) −9.35076 + 1.88769i −0.346562 + 0.0699624i
\(729\) −22.4166 15.0498i −0.830243 0.557402i
\(730\) −28.8974 16.6839i −1.06954 0.617499i
\(731\) −9.43538 16.3426i −0.348980 0.604451i
\(732\) −3.50711 7.74793i −0.129626 0.286372i
\(733\) −0.675297 + 1.16965i −0.0249427 + 0.0432020i −0.878227 0.478243i \(-0.841274\pi\)
0.853285 + 0.521445i \(0.174607\pi\)
\(734\) 23.6812i 0.874088i
\(735\) 30.2440 5.65271i 1.11557 0.208503i
\(736\) 4.72776i 0.174268i
\(737\) 3.66109 + 2.11373i 0.134858 + 0.0778603i
\(738\) −8.62944 + 2.92223i −0.317654 + 0.107569i
\(739\) 21.6402 12.4940i 0.796049 0.459599i −0.0460384 0.998940i \(-0.514660\pi\)
0.842088 + 0.539340i \(0.181326\pi\)
\(740\) −8.64531 + 14.9741i −0.317808 + 0.550460i
\(741\) −0.123800 + 3.01777i −0.00454792 + 0.110861i
\(742\) 3.50894 + 24.6048i 0.128817 + 0.903271i
\(743\) 45.1839 1.65764 0.828818 0.559519i \(-0.189014\pi\)
0.828818 + 0.559519i \(0.189014\pi\)
\(744\) 7.63294 + 5.47393i 0.279837 + 0.200684i
\(745\) −5.65652 + 3.26579i −0.207239 + 0.119649i
\(746\) 1.11557 + 1.93222i 0.0408438 + 0.0707435i
\(747\) 6.98809 + 6.13748i 0.255681 + 0.224559i
\(748\) −9.78058 −0.357614
\(749\) −19.0808 7.66412i −0.697198 0.280041i
\(750\) 15.5725 + 1.53953i 0.568626 + 0.0562157i
\(751\) −13.1428 + 22.7639i −0.479586 + 0.830667i −0.999726 0.0234139i \(-0.992546\pi\)
0.520140 + 0.854081i \(0.325880\pi\)
\(752\) 6.66192 3.84626i 0.242935 0.140259i
\(753\) −40.6397 + 18.3956i −1.48099 + 0.670373i
\(754\) 22.3345 + 11.2346i 0.813373 + 0.409139i
\(755\) −10.7867 −0.392568
\(756\) −12.8192 + 4.96664i −0.466231 + 0.180635i
\(757\) −15.5743 −0.566056 −0.283028 0.959112i \(-0.591339\pi\)
−0.283028 + 0.959112i \(0.591339\pi\)
\(758\) 6.71804 + 3.87866i 0.244010 + 0.140879i
\(759\) −8.94447 19.7602i −0.324664 0.717249i
\(760\) 1.06289 0.613658i 0.0385550 0.0222597i
\(761\) 12.9920 + 7.50093i 0.470959 + 0.271909i 0.716641 0.697442i \(-0.245679\pi\)
−0.245682 + 0.969351i \(0.579012\pi\)
\(762\) 1.82412 18.4512i 0.0660810 0.668415i
\(763\) 28.4225 22.2992i 1.02896 0.807284i
\(764\) 26.1744i 0.946957i
\(765\) −21.1212 18.5503i −0.763640 0.670688i
\(766\) 7.94443 4.58672i 0.287044 0.165725i
\(767\) 17.3475 11.3938i 0.626382 0.411407i
\(768\) −1.40752 1.00940i −0.0507895 0.0364235i
\(769\) 34.6475 1.24942 0.624710 0.780857i \(-0.285217\pi\)
0.624710 + 0.780857i \(0.285217\pi\)
\(770\) −16.5027 6.62859i −0.594717 0.238878i
\(771\) 2.97892 30.1320i 0.107283 1.08518i
\(772\) −1.84511 1.06527i −0.0664069 0.0383400i
\(773\) 0.0831890 0.0480292i 0.00299210 0.00172749i −0.498503 0.866888i \(-0.666117\pi\)
0.501495 + 0.865160i \(0.332783\pi\)
\(774\) 4.91759 + 14.5218i 0.176759 + 0.521976i
\(775\) −3.90404 + 6.76200i −0.140237 + 0.242898i
\(776\) −5.91584 −0.212366
\(777\) −31.1946 + 1.34578i −1.11910 + 0.0482796i
\(778\) 34.3901i 1.23294i
\(779\) 1.27200 + 0.734387i 0.0455740 + 0.0263121i
\(780\) 7.35468 + 14.0379i 0.263340 + 0.502636i
\(781\) −17.0884 29.5980i −0.611471 1.05910i
\(782\) −15.1183 8.72854i −0.540629 0.312132i
\(783\) 34.4671 + 10.4970i 1.23175 + 0.375131i
\(784\) −1.66586 + 6.79889i −0.0594949 + 0.242818i
\(785\) −2.41441 −0.0861740
\(786\) 8.91925 + 6.39640i 0.318139 + 0.228152i
\(787\) 22.1104 + 38.2963i 0.788150 + 1.36512i 0.927099 + 0.374817i \(0.122294\pi\)
−0.138949 + 0.990300i \(0.544372\pi\)
\(788\) 2.18381 + 3.78247i 0.0777949 + 0.134745i
\(789\) −20.8618 + 29.0900i −0.742700 + 1.03563i
\(790\) 19.0765i 0.678710i
\(791\) 7.66626 + 53.7561i 0.272581 + 1.91135i
\(792\) 7.79256 + 1.55599i 0.276897 + 0.0552897i
\(793\) −15.8158 7.95559i −0.561635 0.282511i
\(794\) −6.32491 10.9551i −0.224462 0.388780i
\(795\) 37.6154 17.0267i 1.33408 0.603874i
\(796\) 23.1724 + 13.3786i 0.821324 + 0.474191i
\(797\) 50.7960 1.79929 0.899644 0.436624i \(-0.143826\pi\)
0.899644 + 0.436624i \(0.143826\pi\)
\(798\) 1.96535 + 1.02439i 0.0695728 + 0.0362632i
\(799\) 28.4044i 1.00487i
\(800\) 0.719909 1.24692i 0.0254526 0.0440853i
\(801\) −7.80886 + 2.64436i −0.275913 + 0.0934337i
\(802\) −11.1563 19.3233i −0.393944 0.682331i
\(803\) −17.4144 + 30.1627i −0.614543 + 1.06442i
\(804\) −2.75093 0.271963i −0.0970178 0.00959141i
\(805\) −19.5934 24.9737i −0.690577 0.880208i
\(806\) 19.5204 1.12447i 0.687578 0.0396079i
\(807\) −0.669029 0.479791i −0.0235509 0.0168895i
\(808\) −6.93191 12.0064i −0.243864 0.422384i
\(809\) 17.7051 10.2220i 0.622477 0.359387i −0.155356 0.987859i \(-0.549652\pi\)
0.777833 + 0.628471i \(0.216319\pi\)
\(810\) 13.8769 + 18.1399i 0.487586 + 0.637371i
\(811\) −41.1944 −1.44653 −0.723266 0.690570i \(-0.757360\pi\)
−0.723266 + 0.690570i \(0.757360\pi\)
\(812\) 14.4336 11.3240i 0.506520 0.397395i
\(813\) 0.263257 2.66286i 0.00923282 0.0933907i
\(814\) 15.6298 + 9.02386i 0.547824 + 0.316286i
\(815\) 6.95786 + 12.0514i 0.243723 + 0.422141i
\(816\) 5.82643 2.63734i 0.203966 0.0923254i
\(817\) 1.23584 2.14054i 0.0432366 0.0748881i
\(818\) 30.4213 1.06366
\(819\) −14.2567 + 24.8143i −0.498168 + 0.867080i
\(820\) 7.70676 0.269132
\(821\) −17.3162 + 29.9925i −0.604338 + 1.04674i 0.387818 + 0.921736i \(0.373229\pi\)
−0.992156 + 0.125008i \(0.960104\pi\)
\(822\) 27.9019 12.6299i 0.973192 0.440517i
\(823\) 5.62828 + 9.74847i 0.196190 + 0.339810i 0.947290 0.320378i \(-0.103810\pi\)
−0.751100 + 0.660188i \(0.770477\pi\)
\(824\) −7.90784 4.56559i −0.275483 0.159050i
\(825\) −0.649884 + 6.57363i −0.0226261 + 0.228864i
\(826\) −2.15019 15.0772i −0.0748146 0.524602i
\(827\) 35.0834 1.21997 0.609985 0.792413i \(-0.291176\pi\)
0.609985 + 0.792413i \(0.291176\pi\)
\(828\) 10.6567 + 9.35952i 0.370345 + 0.325266i
\(829\) 39.8985 23.0354i 1.38573 0.800054i 0.392903 0.919580i \(-0.371471\pi\)
0.992831 + 0.119526i \(0.0381376\pi\)
\(830\) −3.93368 6.81333i −0.136540 0.236494i
\(831\) 39.4589 + 28.2978i 1.36881 + 0.981638i
\(832\) −3.59958 + 0.207354i −0.124793 + 0.00718871i
\(833\) −18.6657 17.8793i −0.646728 0.619483i
\(834\) 27.7401 + 2.74245i 0.960560 + 0.0949632i
\(835\) 7.81275 13.5321i 0.270371 0.468297i
\(836\) −0.640528 1.10943i −0.0221531 0.0383704i
\(837\) 27.4495 6.36844i 0.948793 0.220125i
\(838\) 11.4781 19.8807i 0.396506 0.686768i
\(839\) 53.0141i 1.83025i 0.403171 + 0.915125i \(0.367908\pi\)
−0.403171 + 0.915125i \(0.632092\pi\)
\(840\) 11.6183 0.501230i 0.400870 0.0172941i
\(841\) −19.0803 −0.657941
\(842\) 10.1413 + 5.85510i 0.349494 + 0.201780i
\(843\) 47.9514 21.7053i 1.65154 0.747570i
\(844\) 8.66575 + 15.0095i 0.298288 + 0.516649i
\(845\) 30.2751 + 13.1051i 1.04150 + 0.450831i
\(846\) 4.51884 22.6308i 0.155361 0.778064i
\(847\) 3.92863 9.78083i 0.134989 0.336073i
\(848\) 9.39383i 0.322586i
\(849\) 7.08251 9.87596i 0.243071 0.338942i
\(850\) 2.65824 + 4.60420i 0.0911768 + 0.157923i
\(851\) 16.1064 + 27.8972i 0.552122 + 0.956303i
\(852\) 18.1609 + 13.0240i 0.622183 + 0.446196i
\(853\) 22.2010 0.760147 0.380074 0.924956i \(-0.375899\pi\)
0.380074 + 0.924956i \(0.375899\pi\)
\(854\) −10.2209 + 8.01893i −0.349753 + 0.274402i
\(855\) 0.720966 3.61067i 0.0246565 0.123482i
\(856\) −6.73065 3.88594i −0.230049 0.132819i
\(857\) 18.4059 + 31.8799i 0.628732 + 1.08900i 0.987806 + 0.155687i \(0.0497592\pi\)
−0.359074 + 0.933309i \(0.616907\pi\)
\(858\) 14.6525 7.67672i 0.500229 0.262079i
\(859\) −6.38470 3.68621i −0.217843 0.125772i 0.387108 0.922034i \(-0.373474\pi\)
−0.604951 + 0.796263i \(0.706807\pi\)
\(860\) 12.9691i 0.442243i
\(861\) 7.47150 + 11.7413i 0.254628 + 0.400144i
\(862\) −18.3104 −0.623654
\(863\) −17.7758 + 30.7886i −0.605096 + 1.04806i 0.386940 + 0.922105i \(0.373532\pi\)
−0.992036 + 0.125952i \(0.959801\pi\)
\(864\) −5.06171 + 1.17435i −0.172203 + 0.0399520i
\(865\) 15.1800 8.76417i 0.516135 0.297991i
\(866\) 18.3413 + 10.5893i 0.623261 + 0.359840i
\(867\) 0.573532 5.80132i 0.0194782 0.197023i
\(868\) 5.34777 13.3140i 0.181515 0.451905i
\(869\) −19.9118 −0.675460
\(870\) −24.7671 17.7616i −0.839684 0.602176i
\(871\) −4.80977 + 3.15905i −0.162973 + 0.107040i
\(872\) 11.8250 6.82718i 0.400446 0.231198i
\(873\) −11.7116 + 13.3347i −0.396376 + 0.451311i
\(874\) 2.28652i 0.0773428i
\(875\) −3.37475 23.6639i −0.114087 0.799985i
\(876\) 2.24063 22.6642i 0.0757039 0.765751i
\(877\) −33.3702 19.2663i −1.12683 0.650576i −0.183695 0.982983i \(-0.558806\pi\)
−0.943136 + 0.332407i \(0.892139\pi\)
\(878\) 7.13298 4.11823i 0.240727 0.138984i
\(879\) 23.1580 + 51.1607i 0.781099 + 1.72561i
\(880\) −5.82125 3.36090i −0.196234 0.113296i
\(881\) −19.2791 −0.649530 −0.324765 0.945795i \(-0.605285\pi\)
−0.324765 + 0.945795i \(0.605285\pi\)
\(882\) 12.0273 + 17.2147i 0.404979 + 0.579648i
\(883\) 5.53806 0.186371 0.0931853 0.995649i \(-0.470295\pi\)
0.0931853 + 0.995649i \(0.470295\pi\)
\(884\) 5.98259 11.8935i 0.201216 0.400020i
\(885\) −23.0498 + 10.4335i −0.774810 + 0.350719i
\(886\) −7.54716 + 4.35736i −0.253552 + 0.146388i
\(887\) −25.0298 + 43.3529i −0.840418 + 1.45565i 0.0491228 + 0.998793i \(0.484357\pi\)
−0.889541 + 0.456855i \(0.848976\pi\)
\(888\) −11.7442 1.16106i −0.394109 0.0389625i
\(889\) −28.0383 + 3.99860i −0.940375 + 0.134109i
\(890\) 6.97393 0.233767
\(891\) 18.9342 14.4846i 0.634319 0.485251i
\(892\) 2.17749 + 3.77151i 0.0729076 + 0.126280i
\(893\) −3.22195 + 1.86020i −0.107819 + 0.0622491i
\(894\) −3.62274 2.59803i −0.121162 0.0868912i
\(895\) 4.37819 0.146347
\(896\) −0.986133 + 2.45511i −0.0329444 + 0.0820193i
\(897\) 29.5001 + 1.21020i 0.984978 + 0.0404075i
\(898\) 11.3423 19.6454i 0.378496 0.655574i
\(899\) −32.5650 + 18.8014i −1.08610 + 0.627062i
\(900\) −1.38544 4.09124i −0.0461813 0.136375i
\(901\) −30.0393 17.3432i −1.00075 0.577785i
\(902\) 8.04422i 0.267843i
\(903\) 19.7586 12.5732i 0.657524 0.418410i
\(904\) 20.5235i 0.682600i
\(905\) −27.9953 + 48.4893i −0.930596 + 1.61184i
\(906\) −3.03600 6.70715i −0.100864 0.222830i
\(907\) 2.26274 + 3.91918i 0.0751330 + 0.130134i 0.901144 0.433520i \(-0.142729\pi\)
−0.826011 + 0.563654i \(0.809395\pi\)
\(908\) −17.3580 10.0217i −0.576046 0.332580i
\(909\) −40.7863 8.14406i −1.35280 0.270121i
\(910\) 18.1549 16.0132i 0.601830 0.530832i
\(911\) 35.0796i 1.16224i −0.813818 0.581120i \(-0.802615\pi\)
0.813818 0.581120i \(-0.197385\pi\)
\(912\) 0.680730 + 0.488182i 0.0225412 + 0.0161653i
\(913\) −7.11166 + 4.10592i −0.235362 + 0.135886i
\(914\) −11.5835 + 6.68771i −0.383147 + 0.221210i
\(915\) 17.5384 + 12.5776i 0.579803 + 0.415803i
\(916\) 26.6240 0.879683
\(917\) 6.24897 15.5576i 0.206359 0.513758i
\(918\) 5.58981 18.3543i 0.184491 0.605781i
\(919\) −20.4670 + 35.4499i −0.675144 + 1.16938i 0.301283 + 0.953535i \(0.402585\pi\)
−0.976427 + 0.215848i \(0.930748\pi\)
\(920\) −5.99877 10.3902i −0.197774 0.342554i
\(921\) −47.3940 + 21.4530i −1.56169 + 0.706900i
\(922\) 0.673343 + 0.388755i 0.0221754 + 0.0128030i
\(923\) 46.4446 2.67544i 1.52874 0.0880632i
\(924\) −0.523177 12.1270i −0.0172113 0.398950i
\(925\) 9.81029i 0.322560i
\(926\) 2.76857 + 1.59843i 0.0909807 + 0.0525277i
\(927\) −25.9463 + 8.78631i −0.852187 + 0.288580i
\(928\) 6.00502 3.46700i 0.197124 0.113810i
\(929\) 15.4303 + 8.90866i 0.506250 + 0.292284i 0.731291 0.682066i \(-0.238918\pi\)
−0.225041 + 0.974349i \(0.572251\pi\)
\(930\) −23.7204 2.34506i −0.777823 0.0768974i
\(931\) 0.805671 3.28820i 0.0264048 0.107766i
\(932\) 23.3912i 0.766203i
\(933\) −8.99387 6.44992i −0.294446 0.211161i
\(934\) 0.719079 + 1.24548i 0.0235290 + 0.0407534i
\(935\) 21.4947 12.4100i 0.702953 0.405850i
\(936\) −6.65869 + 8.52420i −0.217646 + 0.278622i
\(937\) 30.8788i 1.00877i 0.863480 + 0.504383i \(0.168280\pi\)
−0.863480 + 0.504383i \(0.831720\pi\)
\(938\) 0.596161 + 4.18030i 0.0194654 + 0.136492i
\(939\) 17.0919 + 1.68974i 0.557773 + 0.0551427i
\(940\) −9.76058 + 16.9058i −0.318355 + 0.551407i
\(941\) 12.9864 7.49770i 0.423344 0.244418i −0.273163 0.961968i \(-0.588070\pi\)
0.696507 + 0.717550i \(0.254736\pi\)
\(942\) −0.679554 1.50128i −0.0221411 0.0489142i
\(943\) 7.17895 12.4343i 0.233779 0.404917i
\(944\) 5.75630i 0.187352i
\(945\) 21.8709 27.1807i 0.711460 0.884188i
\(946\) −13.5370 −0.440125
\(947\) 8.13729 14.0942i 0.264426 0.458000i −0.702987 0.711203i \(-0.748151\pi\)
0.967413 + 0.253203i \(0.0814841\pi\)
\(948\) 11.8617 5.36922i 0.385251 0.174384i
\(949\) −26.0266 39.6264i −0.844859 1.28633i
\(950\) −0.348175 + 0.603057i −0.0112963 + 0.0195657i
\(951\) 5.44240 55.0503i 0.176482 1.78513i
\(952\) −6.03022 7.68611i −0.195441 0.249108i
\(953\) 35.3790i 1.14604i 0.819542 + 0.573019i \(0.194228\pi\)
−0.819542 + 0.573019i \(0.805772\pi\)
\(954\) 21.1743 + 18.5969i 0.685544 + 0.602097i
\(955\) 33.2111 + 57.5234i 1.07469 + 1.86141i
\(956\) −5.33853 9.24661i −0.172660 0.299057i
\(957\) −18.5394 + 25.8516i −0.599292 + 0.835663i
\(958\) 10.4447i 0.337454i
\(959\) −28.8779 36.8077i −0.932515 1.18858i
\(960\) 4.37407 + 0.432430i 0.141172 + 0.0139566i
\(961\) 0.795717 1.37822i 0.0256683 0.0444588i
\(962\) −20.5337 + 13.4865i −0.662033 + 0.434823i
\(963\) −22.0838 + 7.47835i −0.711641 + 0.240987i
\(964\) −6.08041 + 10.5316i −0.195837 + 0.339199i
\(965\) 5.40665 0.174046
\(966\) 10.0139 19.2122i 0.322192 0.618142i
\(967\) 8.97650i 0.288665i −0.989529 0.144332i \(-0.953897\pi\)
0.989529 0.144332i \(-0.0461035\pi\)
\(968\) 1.99194 3.45014i 0.0640233 0.110892i
\(969\) −2.81788 + 1.27552i −0.0905233 + 0.0409755i
\(970\) 13.0012 7.50626i 0.417444 0.241011i
\(971\) 1.17336 2.03232i 0.0376550 0.0652203i −0.846584 0.532256i \(-0.821345\pi\)
0.884239 + 0.467035i \(0.154678\pi\)
\(972\) −7.37359 + 13.7343i −0.236508 + 0.440527i
\(973\) −6.01163 42.1537i −0.192724 1.35139i
\(974\) 2.40290i 0.0769939i
\(975\) −7.59619 4.81124i −0.243273 0.154083i
\(976\) −4.25236 + 2.45510i −0.136115 + 0.0785858i
\(977\) −17.3396 30.0330i −0.554742 0.960841i −0.997924 0.0644089i \(-0.979484\pi\)
0.443182 0.896432i \(-0.353850\pi\)
\(978\) −5.53518 + 7.71834i −0.176995 + 0.246805i
\(979\) 7.27929i 0.232647i
\(980\) −4.96566 17.0556i −0.158622 0.544821i
\(981\) 8.02102 40.1701i 0.256091 1.28253i
\(982\) −10.7019 6.17874i −0.341511 0.197172i
\(983\) 22.3427 12.8996i 0.712621 0.411432i −0.0994096 0.995047i \(-0.531695\pi\)
0.812031 + 0.583615i \(0.198362\pi\)
\(984\) 2.16913 + 4.79205i 0.0691493 + 0.152765i
\(985\) −9.59869 5.54180i −0.305840 0.176577i
\(986\) 25.6035i 0.815382i
\(987\) −35.2188 + 1.51939i −1.12103 + 0.0483627i
\(988\) 1.74089 0.100284i 0.0553852 0.00319046i
\(989\) −20.9247 12.0809i −0.665367 0.384150i
\(990\) −19.1000 + 6.46792i −0.607037 + 0.205564i
\(991\) 25.4169 + 44.0233i 0.807394 + 1.39845i 0.914663 + 0.404217i \(0.132456\pi\)
−0.107270 + 0.994230i \(0.534211\pi\)
\(992\) 2.71148 4.69643i 0.0860897 0.149112i
\(993\) 26.2709 + 2.59721i 0.833683 + 0.0824199i
\(994\) 12.7238 31.6776i 0.403576 1.00475i
\(995\) −67.9011 −2.15261
\(996\) 3.12935 4.36362i 0.0991573 0.138267i
\(997\) −31.3253 + 18.0857i −0.992082 + 0.572779i −0.905896 0.423500i \(-0.860801\pi\)
−0.0861859 + 0.996279i \(0.527468\pi\)
\(998\) −14.9074 + 8.60680i −0.471886 + 0.272444i
\(999\) −25.8670 + 24.1736i −0.818395 + 0.764819i
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.bg.a.467.16 yes 36
3.2 odd 2 546.2.bg.b.467.15 yes 36
7.3 odd 6 inner 546.2.bg.a.311.15 36
13.12 even 2 546.2.bg.b.467.16 yes 36
21.17 even 6 546.2.bg.b.311.16 yes 36
39.38 odd 2 inner 546.2.bg.a.467.15 yes 36
91.38 odd 6 546.2.bg.b.311.15 yes 36
273.38 even 6 inner 546.2.bg.a.311.16 yes 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
546.2.bg.a.311.15 36 7.3 odd 6 inner
546.2.bg.a.311.16 yes 36 273.38 even 6 inner
546.2.bg.a.467.15 yes 36 39.38 odd 2 inner
546.2.bg.a.467.16 yes 36 1.1 even 1 trivial
546.2.bg.b.311.15 yes 36 91.38 odd 6
546.2.bg.b.311.16 yes 36 21.17 even 6
546.2.bg.b.467.15 yes 36 3.2 odd 2
546.2.bg.b.467.16 yes 36 13.12 even 2