Properties

Label 731.2.e.a.681.3
Level $731$
Weight $2$
Character 731.681
Analytic conductor $5.837$
Analytic rank $0$
Dimension $58$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [731,2,Mod(307,731)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(731, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("731.307");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 731 = 17 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 731.e (of order \(3\), 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: \(5.83706438776\)
Analytic rank: \(0\)
Dimension: \(58\)
Relative dimension: \(29\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 681.3
Character \(\chi\) \(=\) 731.681
Dual form 731.2.e.a.307.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.32507 q^{2} +(1.39344 + 2.41351i) q^{3} +3.40595 q^{4} +(1.48534 + 2.57269i) q^{5} +(-3.23985 - 5.61158i) q^{6} +(1.79579 - 3.11040i) q^{7} -3.26893 q^{8} +(-2.38336 + 4.12809i) q^{9} +O(q^{10})\) \(q-2.32507 q^{2} +(1.39344 + 2.41351i) q^{3} +3.40595 q^{4} +(1.48534 + 2.57269i) q^{5} +(-3.23985 - 5.61158i) q^{6} +(1.79579 - 3.11040i) q^{7} -3.26893 q^{8} +(-2.38336 + 4.12809i) q^{9} +(-3.45353 - 5.98168i) q^{10} +0.503913 q^{11} +(4.74599 + 8.22030i) q^{12} +(1.43942 - 2.49315i) q^{13} +(-4.17534 + 7.23190i) q^{14} +(-4.13948 + 7.16978i) q^{15} +0.788599 q^{16} +(0.500000 - 0.866025i) q^{17} +(5.54147 - 9.59811i) q^{18} +(2.51253 + 4.35183i) q^{19} +(5.05901 + 8.76246i) q^{20} +10.0093 q^{21} -1.17163 q^{22} +(3.29078 + 5.69981i) q^{23} +(-4.55507 - 7.88961i) q^{24} +(-1.91249 + 3.31253i) q^{25} +(-3.34676 + 5.79676i) q^{26} -4.92362 q^{27} +(6.11638 - 10.5939i) q^{28} +(-2.23638 + 3.87352i) q^{29} +(9.62457 - 16.6702i) q^{30} +(-3.21859 - 5.57477i) q^{31} +4.70432 q^{32} +(0.702173 + 1.21620i) q^{33} +(-1.16254 + 2.01357i) q^{34} +10.6695 q^{35} +(-8.11759 + 14.0601i) q^{36} +(3.83987 + 6.65085i) q^{37} +(-5.84181 - 10.1183i) q^{38} +8.02301 q^{39} +(-4.85549 - 8.40995i) q^{40} +4.22141 q^{41} -23.2724 q^{42} +(-3.41951 - 5.59526i) q^{43} +1.71630 q^{44} -14.1604 q^{45} +(-7.65130 - 13.2524i) q^{46} -9.51331 q^{47} +(1.09887 + 1.90329i) q^{48} +(-2.94974 - 5.10909i) q^{49} +(4.44667 - 7.70186i) q^{50} +2.78688 q^{51} +(4.90260 - 8.49156i) q^{52} +(-2.74262 - 4.75036i) q^{53} +11.4478 q^{54} +(0.748484 + 1.29641i) q^{55} +(-5.87032 + 10.1677i) q^{56} +(-7.00213 + 12.1280i) q^{57} +(5.19973 - 9.00620i) q^{58} -2.40870 q^{59} +(-14.0989 + 24.4199i) q^{60} +(-2.28404 + 3.95607i) q^{61} +(7.48346 + 12.9617i) q^{62} +(8.56002 + 14.8264i) q^{63} -12.5151 q^{64} +8.55215 q^{65} +(-1.63260 - 2.82775i) q^{66} +(0.943401 + 1.63402i) q^{67} +(1.70298 - 2.94964i) q^{68} +(-9.17103 + 15.8847i) q^{69} -24.8073 q^{70} +(6.37565 - 11.0430i) q^{71} +(7.79103 - 13.4945i) q^{72} +(1.74386 - 3.02046i) q^{73} +(-8.92797 - 15.4637i) q^{74} -10.6598 q^{75} +(8.55755 + 14.8221i) q^{76} +(0.904923 - 1.56737i) q^{77} -18.6541 q^{78} +(2.32739 - 4.03115i) q^{79} +(1.17134 + 2.02882i) q^{80} +(0.289298 + 0.501079i) q^{81} -9.81508 q^{82} +(5.65525 + 9.79519i) q^{83} +34.0913 q^{84} +2.97069 q^{85} +(7.95060 + 13.0094i) q^{86} -12.4650 q^{87} -1.64726 q^{88} +(4.14612 + 7.18130i) q^{89} +32.9239 q^{90} +(-5.16981 - 8.95437i) q^{91} +(11.2082 + 19.4133i) q^{92} +(8.96984 - 15.5362i) q^{93} +22.1191 q^{94} +(-7.46394 + 12.9279i) q^{95} +(6.55519 + 11.3539i) q^{96} -10.2402 q^{97} +(6.85835 + 11.8790i) q^{98} +(-1.20100 + 2.08020i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 58 q - 6 q^{2} + 3 q^{3} + 54 q^{4} - q^{5} + 12 q^{6} + 7 q^{7} - 12 q^{8} - 22 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 58 q - 6 q^{2} + 3 q^{3} + 54 q^{4} - q^{5} + 12 q^{6} + 7 q^{7} - 12 q^{8} - 22 q^{9} + 4 q^{10} + 16 q^{11} + 12 q^{12} + 2 q^{13} - 11 q^{14} + 7 q^{15} + 30 q^{16} + 29 q^{17} + 8 q^{18} + 8 q^{19} - 33 q^{20} - 26 q^{21} - 22 q^{22} - 5 q^{23} + 12 q^{24} - 36 q^{25} - 12 q^{27} + 15 q^{28} + 2 q^{29} + 11 q^{30} + 3 q^{31} - 40 q^{32} + 17 q^{33} - 3 q^{34} + 38 q^{35} - 7 q^{36} + 2 q^{37} + q^{38} - 54 q^{39} + 5 q^{40} + 14 q^{41} - 112 q^{42} + 31 q^{43} - 24 q^{44} - 46 q^{45} - 13 q^{46} - 28 q^{47} - 28 q^{49} - 13 q^{50} + 6 q^{51} + 85 q^{52} - 10 q^{53} + 34 q^{54} + 36 q^{55} - 54 q^{56} - 23 q^{57} + 3 q^{58} + 12 q^{59} + 2 q^{60} - q^{61} - q^{62} - 14 q^{63} + 28 q^{64} + 80 q^{65} - 74 q^{66} + 11 q^{67} + 27 q^{68} - 11 q^{69} + 2 q^{70} + 16 q^{71} + 21 q^{72} + 14 q^{73} + 21 q^{74} - 54 q^{75} + 44 q^{76} + 25 q^{77} + 88 q^{78} - 4 q^{79} - 112 q^{80} + 11 q^{81} - 176 q^{82} - 3 q^{83} + 100 q^{84} - 2 q^{85} + 44 q^{86} + 8 q^{87} - 106 q^{88} + 82 q^{89} + 54 q^{90} - 15 q^{91} + 42 q^{92} + 88 q^{94} + 29 q^{95} + 20 q^{96} + 20 q^{97} + 44 q^{98} - 54 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/731\mathbb{Z}\right)^\times\).

\(n\) \(173\) \(562\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.32507 −1.64407 −0.822036 0.569435i \(-0.807162\pi\)
−0.822036 + 0.569435i \(0.807162\pi\)
\(3\) 1.39344 + 2.41351i 0.804504 + 1.39344i 0.916626 + 0.399747i \(0.130902\pi\)
−0.112122 + 0.993694i \(0.535765\pi\)
\(4\) 3.40595 1.70298
\(5\) 1.48534 + 2.57269i 0.664266 + 1.15054i 0.979484 + 0.201523i \(0.0645890\pi\)
−0.315218 + 0.949019i \(0.602078\pi\)
\(6\) −3.23985 5.61158i −1.32266 2.29092i
\(7\) 1.79579 3.11040i 0.678746 1.17562i −0.296613 0.954998i \(-0.595857\pi\)
0.975359 0.220624i \(-0.0708094\pi\)
\(8\) −3.26893 −1.15574
\(9\) −2.38336 + 4.12809i −0.794452 + 1.37603i
\(10\) −3.45353 5.98168i −1.09210 1.89157i
\(11\) 0.503913 0.151935 0.0759677 0.997110i \(-0.475795\pi\)
0.0759677 + 0.997110i \(0.475795\pi\)
\(12\) 4.74599 + 8.22030i 1.37005 + 2.37300i
\(13\) 1.43942 2.49315i 0.399224 0.691477i −0.594406 0.804165i \(-0.702613\pi\)
0.993630 + 0.112688i \(0.0359462\pi\)
\(14\) −4.17534 + 7.23190i −1.11591 + 1.93281i
\(15\) −4.13948 + 7.16978i −1.06881 + 1.85123i
\(16\) 0.788599 0.197150
\(17\) 0.500000 0.866025i 0.121268 0.210042i
\(18\) 5.54147 9.59811i 1.30614 2.26230i
\(19\) 2.51253 + 4.35183i 0.576414 + 0.998378i 0.995886 + 0.0906103i \(0.0288818\pi\)
−0.419472 + 0.907768i \(0.637785\pi\)
\(20\) 5.05901 + 8.76246i 1.13123 + 1.95934i
\(21\) 10.0093 2.18421
\(22\) −1.17163 −0.249793
\(23\) 3.29078 + 5.69981i 0.686176 + 1.18849i 0.973066 + 0.230528i \(0.0740453\pi\)
−0.286890 + 0.957964i \(0.592621\pi\)
\(24\) −4.55507 7.88961i −0.929799 1.61046i
\(25\) −1.91249 + 3.31253i −0.382498 + 0.662506i
\(26\) −3.34676 + 5.79676i −0.656354 + 1.13684i
\(27\) −4.92362 −0.947550
\(28\) 6.11638 10.5939i 1.15589 2.00205i
\(29\) −2.23638 + 3.87352i −0.415285 + 0.719294i −0.995458 0.0951986i \(-0.969651\pi\)
0.580174 + 0.814493i \(0.302985\pi\)
\(30\) 9.62457 16.6702i 1.75720 3.04356i
\(31\) −3.21859 5.57477i −0.578077 1.00126i −0.995700 0.0926378i \(-0.970470\pi\)
0.417623 0.908620i \(-0.362863\pi\)
\(32\) 4.70432 0.831614
\(33\) 0.702173 + 1.21620i 0.122233 + 0.211713i
\(34\) −1.16254 + 2.01357i −0.199373 + 0.345324i
\(35\) 10.6695 1.80347
\(36\) −8.11759 + 14.0601i −1.35293 + 2.34335i
\(37\) 3.83987 + 6.65085i 0.631271 + 1.09339i 0.987292 + 0.158915i \(0.0507997\pi\)
−0.356021 + 0.934478i \(0.615867\pi\)
\(38\) −5.84181 10.1183i −0.947667 1.64141i
\(39\) 8.02301 1.28471
\(40\) −4.85549 8.40995i −0.767720 1.32973i
\(41\) 4.22141 0.659274 0.329637 0.944108i \(-0.393074\pi\)
0.329637 + 0.944108i \(0.393074\pi\)
\(42\) −23.2724 −3.59100
\(43\) −3.41951 5.59526i −0.521470 0.853270i
\(44\) 1.71630 0.258742
\(45\) −14.1604 −2.11091
\(46\) −7.65130 13.2524i −1.12812 1.95397i
\(47\) −9.51331 −1.38766 −0.693829 0.720140i \(-0.744078\pi\)
−0.693829 + 0.720140i \(0.744078\pi\)
\(48\) 1.09887 + 1.90329i 0.158608 + 0.274716i
\(49\) −2.94974 5.10909i −0.421391 0.729871i
\(50\) 4.44667 7.70186i 0.628854 1.08921i
\(51\) 2.78688 0.390242
\(52\) 4.90260 8.49156i 0.679869 1.17757i
\(53\) −2.74262 4.75036i −0.376728 0.652512i 0.613856 0.789418i \(-0.289618\pi\)
−0.990584 + 0.136906i \(0.956284\pi\)
\(54\) 11.4478 1.55784
\(55\) 0.748484 + 1.29641i 0.100926 + 0.174808i
\(56\) −5.87032 + 10.1677i −0.784455 + 1.35872i
\(57\) −7.00213 + 12.1280i −0.927454 + 1.60640i
\(58\) 5.19973 9.00620i 0.682758 1.18257i
\(59\) −2.40870 −0.313585 −0.156793 0.987632i \(-0.550115\pi\)
−0.156793 + 0.987632i \(0.550115\pi\)
\(60\) −14.0989 + 24.4199i −1.82015 + 3.15260i
\(61\) −2.28404 + 3.95607i −0.292441 + 0.506522i −0.974386 0.224881i \(-0.927801\pi\)
0.681946 + 0.731403i \(0.261134\pi\)
\(62\) 7.48346 + 12.9617i 0.950400 + 1.64614i
\(63\) 8.56002 + 14.8264i 1.07846 + 1.86795i
\(64\) −12.5151 −1.56438
\(65\) 8.55215 1.06076
\(66\) −1.63260 2.82775i −0.200959 0.348072i
\(67\) 0.943401 + 1.63402i 0.115255 + 0.199627i 0.917882 0.396854i \(-0.129898\pi\)
−0.802627 + 0.596482i \(0.796565\pi\)
\(68\) 1.70298 2.94964i 0.206516 0.357696i
\(69\) −9.17103 + 15.8847i −1.10406 + 1.91229i
\(70\) −24.8073 −2.96504
\(71\) 6.37565 11.0430i 0.756651 1.31056i −0.187899 0.982188i \(-0.560168\pi\)
0.944549 0.328369i \(-0.106499\pi\)
\(72\) 7.79103 13.4945i 0.918182 1.59034i
\(73\) 1.74386 3.02046i 0.204104 0.353518i −0.745743 0.666234i \(-0.767905\pi\)
0.949847 + 0.312716i \(0.101239\pi\)
\(74\) −8.92797 15.4637i −1.03786 1.79762i
\(75\) −10.6598 −1.23088
\(76\) 8.55755 + 14.8221i 0.981619 + 1.70021i
\(77\) 0.904923 1.56737i 0.103126 0.178619i
\(78\) −18.6541 −2.11216
\(79\) 2.32739 4.03115i 0.261852 0.453540i −0.704882 0.709324i \(-0.749000\pi\)
0.966734 + 0.255784i \(0.0823336\pi\)
\(80\) 1.17134 + 2.02882i 0.130960 + 0.226829i
\(81\) 0.289298 + 0.501079i 0.0321442 + 0.0556755i
\(82\) −9.81508 −1.08389
\(83\) 5.65525 + 9.79519i 0.620745 + 1.07516i 0.989347 + 0.145574i \(0.0465030\pi\)
−0.368602 + 0.929587i \(0.620164\pi\)
\(84\) 34.0913 3.71966
\(85\) 2.97069 0.322216
\(86\) 7.95060 + 13.0094i 0.857335 + 1.40284i
\(87\) −12.4650 −1.33639
\(88\) −1.64726 −0.175598
\(89\) 4.14612 + 7.18130i 0.439488 + 0.761216i 0.997650 0.0685162i \(-0.0218265\pi\)
−0.558162 + 0.829732i \(0.688493\pi\)
\(90\) 32.9239 3.47049
\(91\) −5.16981 8.95437i −0.541943 0.938673i
\(92\) 11.2082 + 19.4133i 1.16854 + 2.02397i
\(93\) 8.96984 15.5362i 0.930129 1.61103i
\(94\) 22.1191 2.28141
\(95\) −7.46394 + 12.9279i −0.765784 + 1.32638i
\(96\) 6.55519 + 11.3539i 0.669037 + 1.15881i
\(97\) −10.2402 −1.03973 −0.519867 0.854247i \(-0.674018\pi\)
−0.519867 + 0.854247i \(0.674018\pi\)
\(98\) 6.85835 + 11.8790i 0.692798 + 1.19996i
\(99\) −1.20100 + 2.08020i −0.120705 + 0.209068i
\(100\) −6.51384 + 11.2823i −0.651384 + 1.12823i
\(101\) 6.61995 11.4661i 0.658709 1.14092i −0.322241 0.946658i \(-0.604436\pi\)
0.980950 0.194260i \(-0.0622307\pi\)
\(102\) −6.47970 −0.641585
\(103\) −7.17269 + 12.4235i −0.706746 + 1.22412i 0.259311 + 0.965794i \(0.416504\pi\)
−0.966058 + 0.258327i \(0.916829\pi\)
\(104\) −4.70538 + 8.14996i −0.461400 + 0.799169i
\(105\) 14.8673 + 25.7509i 1.45090 + 2.51303i
\(106\) 6.37679 + 11.0449i 0.619368 + 1.07278i
\(107\) −12.0291 −1.16290 −0.581451 0.813582i \(-0.697515\pi\)
−0.581451 + 0.813582i \(0.697515\pi\)
\(108\) −16.7696 −1.61365
\(109\) −6.41856 11.1173i −0.614786 1.06484i −0.990422 0.138074i \(-0.955909\pi\)
0.375635 0.926767i \(-0.377424\pi\)
\(110\) −1.74028 3.01425i −0.165929 0.287397i
\(111\) −10.7013 + 18.5351i −1.01572 + 1.75928i
\(112\) 1.41616 2.45286i 0.133814 0.231773i
\(113\) −4.82605 −0.453997 −0.226998 0.973895i \(-0.572891\pi\)
−0.226998 + 0.973895i \(0.572891\pi\)
\(114\) 16.2804 28.1985i 1.52480 2.64103i
\(115\) −9.77589 + 16.9323i −0.911606 + 1.57895i
\(116\) −7.61699 + 13.1930i −0.707220 + 1.22494i
\(117\) 6.86132 + 11.8841i 0.634329 + 1.09869i
\(118\) 5.60039 0.515557
\(119\) −1.79579 3.11040i −0.164620 0.285130i
\(120\) 13.5317 23.4375i 1.23527 2.13955i
\(121\) −10.7461 −0.976916
\(122\) 5.31054 9.19813i 0.480794 0.832759i
\(123\) 5.88229 + 10.1884i 0.530388 + 0.918660i
\(124\) −10.9624 18.9874i −0.984450 1.70512i
\(125\) 3.49062 0.312210
\(126\) −19.9027 34.4724i −1.77307 3.07105i
\(127\) 16.4456 1.45931 0.729654 0.683817i \(-0.239681\pi\)
0.729654 + 0.683817i \(0.239681\pi\)
\(128\) 19.6898 1.74035
\(129\) 8.73934 16.0497i 0.769456 1.41310i
\(130\) −19.8843 −1.74397
\(131\) −11.6217 −1.01539 −0.507697 0.861536i \(-0.669503\pi\)
−0.507697 + 0.861536i \(0.669503\pi\)
\(132\) 2.39157 + 4.14231i 0.208159 + 0.360542i
\(133\) 18.0479 1.56495
\(134\) −2.19347 3.79921i −0.189487 0.328202i
\(135\) −7.31326 12.6669i −0.629425 1.09020i
\(136\) −1.63447 + 2.83098i −0.140154 + 0.242755i
\(137\) −5.12027 −0.437455 −0.218727 0.975786i \(-0.570191\pi\)
−0.218727 + 0.975786i \(0.570191\pi\)
\(138\) 21.3233 36.9330i 1.81516 3.14395i
\(139\) −11.0870 19.2033i −0.940390 1.62880i −0.764729 0.644352i \(-0.777127\pi\)
−0.175661 0.984451i \(-0.556206\pi\)
\(140\) 36.3397 3.07126
\(141\) −13.2562 22.9605i −1.11638 1.93362i
\(142\) −14.8238 + 25.6756i −1.24399 + 2.15465i
\(143\) 0.725344 1.25633i 0.0606563 0.105060i
\(144\) −1.87951 + 3.25541i −0.156626 + 0.271284i
\(145\) −13.2871 −1.10344
\(146\) −4.05460 + 7.02278i −0.335561 + 0.581209i
\(147\) 8.22057 14.2384i 0.678021 1.17437i
\(148\) 13.0784 + 22.6525i 1.07504 + 1.86202i
\(149\) −8.58539 14.8703i −0.703343 1.21823i −0.967286 0.253687i \(-0.918357\pi\)
0.263943 0.964538i \(-0.414977\pi\)
\(150\) 24.7847 2.02366
\(151\) −1.84274 −0.149960 −0.0749799 0.997185i \(-0.523889\pi\)
−0.0749799 + 0.997185i \(0.523889\pi\)
\(152\) −8.21330 14.2258i −0.666186 1.15387i
\(153\) 2.38336 + 4.12809i 0.192683 + 0.333737i
\(154\) −2.10401 + 3.64425i −0.169546 + 0.293662i
\(155\) 9.56144 16.5609i 0.767993 1.33020i
\(156\) 27.3260 2.18783
\(157\) 3.20156 5.54526i 0.255512 0.442560i −0.709522 0.704683i \(-0.751089\pi\)
0.965035 + 0.262123i \(0.0844226\pi\)
\(158\) −5.41134 + 9.37271i −0.430503 + 0.745653i
\(159\) 7.64336 13.2387i 0.606158 1.04990i
\(160\) 6.98753 + 12.1028i 0.552413 + 0.956807i
\(161\) 23.6383 1.86296
\(162\) −0.672638 1.16504i −0.0528475 0.0915345i
\(163\) 10.5226 18.2258i 0.824197 1.42755i −0.0783343 0.996927i \(-0.524960\pi\)
0.902531 0.430624i \(-0.141707\pi\)
\(164\) 14.3779 1.12273
\(165\) −2.08594 + 3.61295i −0.162390 + 0.281268i
\(166\) −13.1489 22.7745i −1.02055 1.76764i
\(167\) 4.65036 + 8.05466i 0.359856 + 0.623289i 0.987936 0.154860i \(-0.0494926\pi\)
−0.628081 + 0.778148i \(0.716159\pi\)
\(168\) −32.7198 −2.52439
\(169\) 2.35612 + 4.08092i 0.181240 + 0.313917i
\(170\) −6.90705 −0.529747
\(171\) −23.9530 −1.83173
\(172\) −11.6467 19.0572i −0.888051 1.45310i
\(173\) 11.0411 0.839443 0.419721 0.907653i \(-0.362128\pi\)
0.419721 + 0.907653i \(0.362128\pi\)
\(174\) 28.9821 2.19713
\(175\) 6.86887 + 11.8972i 0.519237 + 0.899346i
\(176\) 0.397385 0.0299540
\(177\) −3.35638 5.81341i −0.252281 0.436963i
\(178\) −9.64003 16.6970i −0.722551 1.25149i
\(179\) 0.475587 0.823741i 0.0355470 0.0615693i −0.847705 0.530469i \(-0.822016\pi\)
0.883252 + 0.468899i \(0.155349\pi\)
\(180\) −48.2296 −3.59483
\(181\) 11.2289 19.4491i 0.834640 1.44564i −0.0596826 0.998217i \(-0.519009\pi\)
0.894323 0.447422i \(-0.147658\pi\)
\(182\) 12.0202 + 20.8195i 0.890994 + 1.54325i
\(183\) −12.7307 −0.941079
\(184\) −10.7574 18.6323i −0.793043 1.37359i
\(185\) −11.4071 + 19.7576i −0.838663 + 1.45261i
\(186\) −20.8555 + 36.1228i −1.52920 + 2.64865i
\(187\) 0.251956 0.436401i 0.0184249 0.0319128i
\(188\) −32.4019 −2.36315
\(189\) −8.84179 + 15.3144i −0.643146 + 1.11396i
\(190\) 17.3542 30.0583i 1.25900 2.18066i
\(191\) −9.97449 17.2763i −0.721729 1.25007i −0.960306 0.278947i \(-0.910014\pi\)
0.238578 0.971123i \(-0.423319\pi\)
\(192\) −17.4390 30.2053i −1.25855 2.17988i
\(193\) −15.0663 −1.08449 −0.542247 0.840219i \(-0.682426\pi\)
−0.542247 + 0.840219i \(0.682426\pi\)
\(194\) 23.8092 1.70940
\(195\) 11.9169 + 20.6407i 0.853388 + 1.47811i
\(196\) −10.0467 17.4013i −0.717619 1.24295i
\(197\) −10.8742 + 18.8346i −0.774752 + 1.34191i 0.160181 + 0.987088i \(0.448792\pi\)
−0.934934 + 0.354823i \(0.884541\pi\)
\(198\) 2.79242 4.83661i 0.198448 0.343723i
\(199\) 17.8288 1.26385 0.631927 0.775028i \(-0.282264\pi\)
0.631927 + 0.775028i \(0.282264\pi\)
\(200\) 6.25180 10.8284i 0.442069 0.765686i
\(201\) −2.62915 + 4.55382i −0.185446 + 0.321201i
\(202\) −15.3918 + 26.6595i −1.08297 + 1.87575i
\(203\) 8.03213 + 13.9121i 0.563745 + 0.976436i
\(204\) 9.49198 0.664572
\(205\) 6.27025 + 10.8604i 0.437933 + 0.758523i
\(206\) 16.6770 28.8854i 1.16194 2.01254i
\(207\) −31.3724 −2.18054
\(208\) 1.13513 1.96610i 0.0787069 0.136324i
\(209\) 1.26610 + 2.19294i 0.0875777 + 0.151689i
\(210\) −34.5675 59.8726i −2.38538 4.13160i
\(211\) −13.6092 −0.936896 −0.468448 0.883491i \(-0.655187\pi\)
−0.468448 + 0.883491i \(0.655187\pi\)
\(212\) −9.34123 16.1795i −0.641559 1.11121i
\(213\) 35.5364 2.43491
\(214\) 27.9686 1.91189
\(215\) 9.31573 17.1082i 0.635328 1.16677i
\(216\) 16.0950 1.09512
\(217\) −23.1197 −1.56947
\(218\) 14.9236 + 25.8484i 1.01075 + 1.75068i
\(219\) 9.71988 0.656809
\(220\) 2.54930 + 4.41551i 0.171874 + 0.297694i
\(221\) −1.43942 2.49315i −0.0968261 0.167708i
\(222\) 24.8812 43.0955i 1.66992 2.89238i
\(223\) 5.89939 0.395052 0.197526 0.980298i \(-0.436709\pi\)
0.197526 + 0.980298i \(0.436709\pi\)
\(224\) 8.44798 14.6323i 0.564454 0.977664i
\(225\) −9.11629 15.7899i −0.607752 1.05266i
\(226\) 11.2209 0.746403
\(227\) −8.20693 14.2148i −0.544713 0.943471i −0.998625 0.0524241i \(-0.983305\pi\)
0.453912 0.891047i \(-0.350028\pi\)
\(228\) −23.8489 + 41.3075i −1.57943 + 2.73566i
\(229\) −1.06288 + 1.84097i −0.0702373 + 0.121655i −0.899005 0.437938i \(-0.855709\pi\)
0.828768 + 0.559592i \(0.189042\pi\)
\(230\) 22.7296 39.3689i 1.49875 2.59591i
\(231\) 5.04383 0.331859
\(232\) 7.31057 12.6623i 0.479962 0.831319i
\(233\) −1.53910 + 2.66580i −0.100830 + 0.174643i −0.912027 0.410131i \(-0.865483\pi\)
0.811197 + 0.584773i \(0.198816\pi\)
\(234\) −15.9530 27.6315i −1.04288 1.80633i
\(235\) −14.1305 24.4748i −0.921774 1.59656i
\(236\) −8.20390 −0.534028
\(237\) 12.9723 0.842642
\(238\) 4.17534 + 7.23190i 0.270647 + 0.468775i
\(239\) 14.5834 + 25.2592i 0.943322 + 1.63388i 0.759077 + 0.651000i \(0.225650\pi\)
0.184244 + 0.982880i \(0.441016\pi\)
\(240\) −3.26439 + 5.65408i −0.210715 + 0.364969i
\(241\) −7.66282 + 13.2724i −0.493606 + 0.854950i −0.999973 0.00736776i \(-0.997655\pi\)
0.506367 + 0.862318i \(0.330988\pi\)
\(242\) 24.9854 1.60612
\(243\) −8.19166 + 14.1884i −0.525496 + 0.910185i
\(244\) −7.77931 + 13.4742i −0.498019 + 0.862595i
\(245\) 8.76275 15.1775i 0.559831 0.969656i
\(246\) −13.6767 23.6888i −0.871997 1.51034i
\(247\) 14.4664 0.920474
\(248\) 10.5214 + 18.2236i 0.668108 + 1.15720i
\(249\) −15.7605 + 27.2980i −0.998783 + 1.72994i
\(250\) −8.11593 −0.513297
\(251\) 8.69612 15.0621i 0.548895 0.950713i −0.449456 0.893302i \(-0.648382\pi\)
0.998351 0.0574108i \(-0.0182845\pi\)
\(252\) 29.1550 + 50.4980i 1.83659 + 3.18107i
\(253\) 1.65827 + 2.87221i 0.104254 + 0.180574i
\(254\) −38.2371 −2.39921
\(255\) 4.13948 + 7.16978i 0.259224 + 0.448989i
\(256\) −20.7500 −1.29687
\(257\) 4.79336 0.299002 0.149501 0.988762i \(-0.452233\pi\)
0.149501 + 0.988762i \(0.452233\pi\)
\(258\) −20.3196 + 37.3166i −1.26504 + 2.32323i
\(259\) 27.5824 1.71389
\(260\) 29.1282 1.80645
\(261\) −10.6602 18.4639i −0.659847 1.14289i
\(262\) 27.0213 1.66938
\(263\) 1.15106 + 1.99370i 0.0709776 + 0.122937i 0.899330 0.437271i \(-0.144055\pi\)
−0.828352 + 0.560207i \(0.810721\pi\)
\(264\) −2.29536 3.97567i −0.141269 0.244686i
\(265\) 8.14747 14.1118i 0.500495 0.866883i
\(266\) −41.9627 −2.57290
\(267\) −11.5548 + 20.0134i −0.707140 + 1.22480i
\(268\) 3.21318 + 5.56539i 0.196276 + 0.339960i
\(269\) 6.49631 0.396087 0.198044 0.980193i \(-0.436541\pi\)
0.198044 + 0.980193i \(0.436541\pi\)
\(270\) 17.0038 + 29.4515i 1.03482 + 1.79236i
\(271\) 5.26818 9.12476i 0.320019 0.554289i −0.660472 0.750850i \(-0.729644\pi\)
0.980492 + 0.196561i \(0.0629773\pi\)
\(272\) 0.394299 0.682946i 0.0239079 0.0414097i
\(273\) 14.4076 24.9548i 0.871991 1.51033i
\(274\) 11.9050 0.719207
\(275\) −0.963728 + 1.66923i −0.0581150 + 0.100658i
\(276\) −31.2361 + 54.1025i −1.88019 + 3.25659i
\(277\) 13.4475 + 23.2917i 0.807980 + 1.39946i 0.914261 + 0.405126i \(0.132772\pi\)
−0.106281 + 0.994336i \(0.533894\pi\)
\(278\) 25.7781 + 44.6490i 1.54607 + 2.67787i
\(279\) 30.6842 1.83702
\(280\) −34.8778 −2.08435
\(281\) 2.97549 + 5.15370i 0.177503 + 0.307444i 0.941025 0.338338i \(-0.109865\pi\)
−0.763522 + 0.645782i \(0.776531\pi\)
\(282\) 30.8217 + 53.3847i 1.83540 + 3.17901i
\(283\) 9.49026 16.4376i 0.564138 0.977115i −0.432992 0.901398i \(-0.642542\pi\)
0.997129 0.0757170i \(-0.0241246\pi\)
\(284\) 21.7152 37.6118i 1.28856 2.23185i
\(285\) −41.6022 −2.46430
\(286\) −1.68648 + 2.92106i −0.0997234 + 0.172726i
\(287\) 7.58078 13.1303i 0.447479 0.775057i
\(288\) −11.2121 + 19.4199i −0.660678 + 1.14433i
\(289\) −0.500000 0.866025i −0.0294118 0.0509427i
\(290\) 30.8935 1.81413
\(291\) −14.2691 24.7148i −0.836469 1.44881i
\(292\) 5.93951 10.2875i 0.347584 0.602032i
\(293\) −4.11101 −0.240168 −0.120084 0.992764i \(-0.538316\pi\)
−0.120084 + 0.992764i \(0.538316\pi\)
\(294\) −19.1134 + 33.1054i −1.11472 + 1.93075i
\(295\) −3.57774 6.19683i −0.208304 0.360793i
\(296\) −12.5523 21.7412i −0.729587 1.26368i
\(297\) −2.48107 −0.143967
\(298\) 19.9616 + 34.5746i 1.15635 + 2.00285i
\(299\) 18.9473 1.09575
\(300\) −36.3066 −2.09616
\(301\) −23.5442 + 0.588121i −1.35707 + 0.0338988i
\(302\) 4.28449 0.246545
\(303\) 36.8980 2.11974
\(304\) 1.98138 + 3.43185i 0.113640 + 0.196830i
\(305\) −13.5703 −0.777034
\(306\) −5.54147 9.59811i −0.316785 0.548687i
\(307\) 7.22796 + 12.5192i 0.412521 + 0.714508i 0.995165 0.0982201i \(-0.0313149\pi\)
−0.582643 + 0.812728i \(0.697982\pi\)
\(308\) 3.08212 5.33839i 0.175620 0.304183i
\(309\) −39.9789 −2.27432
\(310\) −22.2310 + 38.5052i −1.26264 + 2.18695i
\(311\) 5.40542 + 9.36246i 0.306513 + 0.530896i 0.977597 0.210485i \(-0.0675044\pi\)
−0.671084 + 0.741381i \(0.734171\pi\)
\(312\) −26.2267 −1.48479
\(313\) 13.4845 + 23.3558i 0.762187 + 1.32015i 0.941721 + 0.336395i \(0.109208\pi\)
−0.179534 + 0.983752i \(0.557459\pi\)
\(314\) −7.44385 + 12.8931i −0.420081 + 0.727601i
\(315\) −25.4291 + 44.0446i −1.43277 + 2.48163i
\(316\) 7.92697 13.7299i 0.445927 0.772368i
\(317\) −19.2227 −1.07965 −0.539826 0.841777i \(-0.681510\pi\)
−0.539826 + 0.841777i \(0.681510\pi\)
\(318\) −17.7714 + 30.7809i −0.996568 + 1.72611i
\(319\) −1.12694 + 1.95192i −0.0630965 + 0.109286i
\(320\) −18.5892 32.1974i −1.03917 1.79989i
\(321\) −16.7619 29.0325i −0.935558 1.62043i
\(322\) −54.9606 −3.06283
\(323\) 5.02506 0.279602
\(324\) 0.985335 + 1.70665i 0.0547408 + 0.0948139i
\(325\) 5.50576 + 9.53626i 0.305405 + 0.528977i
\(326\) −24.4659 + 42.3762i −1.35504 + 2.34700i
\(327\) 17.8878 30.9825i 0.989196 1.71334i
\(328\) −13.7995 −0.761951
\(329\) −17.0839 + 29.5902i −0.941867 + 1.63136i
\(330\) 4.84995 8.40035i 0.266981 0.462424i
\(331\) 15.9850 27.6868i 0.878613 1.52180i 0.0257503 0.999668i \(-0.491803\pi\)
0.852863 0.522135i \(-0.174864\pi\)
\(332\) 19.2615 + 33.3619i 1.05711 + 1.83097i
\(333\) −36.6071 −2.00606
\(334\) −10.8124 18.7277i −0.591629 1.02473i
\(335\) −2.80255 + 4.85416i −0.153120 + 0.265211i
\(336\) 7.89334 0.430617
\(337\) 13.6496 23.6418i 0.743541 1.28785i −0.207333 0.978270i \(-0.566478\pi\)
0.950874 0.309580i \(-0.100188\pi\)
\(338\) −5.47815 9.48843i −0.297972 0.516102i
\(339\) −6.72482 11.6477i −0.365242 0.632618i
\(340\) 10.1180 0.548726
\(341\) −1.62189 2.80920i −0.0878303 0.152127i
\(342\) 55.6924 3.01150
\(343\) 3.95263 0.213422
\(344\) 11.1781 + 18.2905i 0.602685 + 0.986160i
\(345\) −54.4885 −2.93356
\(346\) −25.6714 −1.38011
\(347\) −2.25420 3.90439i −0.121012 0.209599i 0.799155 0.601125i \(-0.205281\pi\)
−0.920167 + 0.391526i \(0.871947\pi\)
\(348\) −42.4553 −2.27584
\(349\) 0.902306 + 1.56284i 0.0482993 + 0.0836569i 0.889164 0.457588i \(-0.151287\pi\)
−0.840865 + 0.541245i \(0.817953\pi\)
\(350\) −15.9706 27.6619i −0.853664 1.47859i
\(351\) −7.08717 + 12.2753i −0.378285 + 0.655209i
\(352\) 2.37057 0.126352
\(353\) −15.8692 + 27.4862i −0.844631 + 1.46294i 0.0413108 + 0.999146i \(0.486847\pi\)
−0.885942 + 0.463797i \(0.846487\pi\)
\(354\) 7.80381 + 13.5166i 0.414768 + 0.718399i
\(355\) 37.8801 2.01047
\(356\) 14.1215 + 24.4591i 0.748438 + 1.29633i
\(357\) 5.00466 8.66833i 0.264875 0.458776i
\(358\) −1.10577 + 1.91525i −0.0584419 + 0.101224i
\(359\) 15.5614 26.9532i 0.821301 1.42253i −0.0834133 0.996515i \(-0.526582\pi\)
0.904714 0.426019i \(-0.140085\pi\)
\(360\) 46.2894 2.43967
\(361\) −3.12562 + 5.41373i −0.164506 + 0.284933i
\(362\) −26.1081 + 45.2205i −1.37221 + 2.37674i
\(363\) −14.9740 25.9358i −0.785932 1.36127i
\(364\) −17.6081 30.4982i −0.922916 1.59854i
\(365\) 10.3609 0.542316
\(366\) 29.5997 1.54720
\(367\) 12.9247 + 22.3863i 0.674664 + 1.16855i 0.976567 + 0.215214i \(0.0690449\pi\)
−0.301903 + 0.953339i \(0.597622\pi\)
\(368\) 2.59511 + 4.49486i 0.135279 + 0.234311i
\(369\) −10.0611 + 17.4264i −0.523762 + 0.907182i
\(370\) 26.5222 45.9378i 1.37882 2.38819i
\(371\) −19.7007 −1.02281
\(372\) 30.5508 52.9156i 1.58399 2.74355i
\(373\) 11.7173 20.2950i 0.606701 1.05084i −0.385079 0.922884i \(-0.625826\pi\)
0.991780 0.127954i \(-0.0408409\pi\)
\(374\) −0.585816 + 1.01466i −0.0302918 + 0.0524670i
\(375\) 4.86397 + 8.42465i 0.251174 + 0.435047i
\(376\) 31.0984 1.60378
\(377\) 6.43819 + 11.1513i 0.331583 + 0.574319i
\(378\) 20.5578 35.6071i 1.05738 1.83143i
\(379\) 15.0200 0.771525 0.385762 0.922598i \(-0.373938\pi\)
0.385762 + 0.922598i \(0.373938\pi\)
\(380\) −25.4218 + 44.0319i −1.30411 + 2.25879i
\(381\) 22.9159 + 39.6915i 1.17402 + 2.03346i
\(382\) 23.1914 + 40.1687i 1.18657 + 2.05521i
\(383\) −13.4675 −0.688155 −0.344078 0.938941i \(-0.611808\pi\)
−0.344078 + 0.938941i \(0.611808\pi\)
\(384\) 27.4365 + 47.5215i 1.40012 + 2.42507i
\(385\) 5.37648 0.274011
\(386\) 35.0301 1.78299
\(387\) 31.2477 0.780548i 1.58841 0.0396775i
\(388\) −34.8776 −1.77064
\(389\) −33.1441 −1.68047 −0.840236 0.542221i \(-0.817583\pi\)
−0.840236 + 0.542221i \(0.817583\pi\)
\(390\) −27.7077 47.9911i −1.40303 2.43012i
\(391\) 6.58157 0.332844
\(392\) 9.64250 + 16.7013i 0.487020 + 0.843543i
\(393\) −16.1942 28.0491i −0.816888 1.41489i
\(394\) 25.2832 43.7918i 1.27375 2.20620i
\(395\) 13.8279 0.695756
\(396\) −4.09056 + 7.08506i −0.205558 + 0.356037i
\(397\) −6.22428 10.7808i −0.312388 0.541071i 0.666491 0.745513i \(-0.267795\pi\)
−0.978879 + 0.204442i \(0.934462\pi\)
\(398\) −41.4533 −2.07787
\(399\) 25.1487 + 43.5589i 1.25901 + 2.18067i
\(400\) −1.50819 + 2.61226i −0.0754093 + 0.130613i
\(401\) −7.18772 + 12.4495i −0.358938 + 0.621699i −0.987784 0.155831i \(-0.950194\pi\)
0.628846 + 0.777530i \(0.283528\pi\)
\(402\) 6.11295 10.5879i 0.304886 0.528079i
\(403\) −18.5317 −0.923129
\(404\) 22.5472 39.0529i 1.12177 1.94296i
\(405\) −0.859414 + 1.48855i −0.0427046 + 0.0739666i
\(406\) −18.6753 32.3465i −0.926838 1.60533i
\(407\) 1.93496 + 3.35145i 0.0959124 + 0.166125i
\(408\) −9.11013 −0.451019
\(409\) 12.2907 0.607738 0.303869 0.952714i \(-0.401722\pi\)
0.303869 + 0.952714i \(0.401722\pi\)
\(410\) −14.5788 25.2512i −0.719994 1.24707i
\(411\) −7.13480 12.3578i −0.351934 0.609567i
\(412\) −24.4298 + 42.3137i −1.20357 + 2.08465i
\(413\) −4.32552 + 7.49201i −0.212845 + 0.368658i
\(414\) 72.9431 3.58496
\(415\) −16.8000 + 29.0984i −0.824679 + 1.42839i
\(416\) 6.77151 11.7286i 0.332001 0.575042i
\(417\) 30.8983 53.5173i 1.51309 2.62076i
\(418\) −2.94376 5.09875i −0.143984 0.249388i
\(419\) −10.2081 −0.498696 −0.249348 0.968414i \(-0.580216\pi\)
−0.249348 + 0.968414i \(0.580216\pi\)
\(420\) 50.6372 + 87.7062i 2.47084 + 4.27963i
\(421\) −5.73239 + 9.92879i −0.279380 + 0.483900i −0.971231 0.238141i \(-0.923462\pi\)
0.691851 + 0.722040i \(0.256795\pi\)
\(422\) 31.6423 1.54032
\(423\) 22.6736 39.2718i 1.10243 1.90946i
\(424\) 8.96545 + 15.5286i 0.435401 + 0.754136i
\(425\) 1.91249 + 3.31253i 0.0927694 + 0.160681i
\(426\) −82.6246 −4.00317
\(427\) 8.20330 + 14.2085i 0.396986 + 0.687599i
\(428\) −40.9707 −1.98039
\(429\) 4.04290 0.195193
\(430\) −21.6597 + 39.7778i −1.04452 + 1.91826i
\(431\) 12.6265 0.608196 0.304098 0.952641i \(-0.401645\pi\)
0.304098 + 0.952641i \(0.401645\pi\)
\(432\) −3.88276 −0.186809
\(433\) −4.74544 8.21934i −0.228051 0.394996i 0.729179 0.684323i \(-0.239902\pi\)
−0.957230 + 0.289326i \(0.906569\pi\)
\(434\) 53.7549 2.58032
\(435\) −18.5149 32.0687i −0.887719 1.53758i
\(436\) −21.8613 37.8649i −1.04697 1.81340i
\(437\) −16.5364 + 28.6419i −0.791043 + 1.37013i
\(438\) −22.5994 −1.07984
\(439\) 7.16534 12.4107i 0.341983 0.592332i −0.642818 0.766019i \(-0.722235\pi\)
0.984801 + 0.173687i \(0.0555681\pi\)
\(440\) −2.44674 4.23788i −0.116644 0.202033i
\(441\) 28.1211 1.33910
\(442\) 3.34676 + 5.79676i 0.159189 + 0.275724i
\(443\) −0.108587 + 0.188078i −0.00515913 + 0.00893587i −0.868593 0.495525i \(-0.834976\pi\)
0.863434 + 0.504461i \(0.168309\pi\)
\(444\) −36.4480 + 63.1298i −1.72974 + 2.99601i
\(445\) −12.3168 + 21.3334i −0.583874 + 1.01130i
\(446\) −13.7165 −0.649495
\(447\) 23.9265 41.4419i 1.13168 1.96013i
\(448\) −22.4745 + 38.9269i −1.06182 + 1.83912i
\(449\) −20.0777 34.7756i −0.947526 1.64116i −0.750613 0.660742i \(-0.770242\pi\)
−0.196913 0.980421i \(-0.563092\pi\)
\(450\) 21.1960 + 36.7126i 0.999189 + 1.73065i
\(451\) 2.12722 0.100167
\(452\) −16.4373 −0.773145
\(453\) −2.56774 4.44746i −0.120643 0.208960i
\(454\) 19.0817 + 33.0504i 0.895548 + 1.55113i
\(455\) 15.3579 26.6006i 0.719989 1.24706i
\(456\) 22.8895 39.6458i 1.07190 1.85658i
\(457\) 20.9761 0.981222 0.490611 0.871379i \(-0.336774\pi\)
0.490611 + 0.871379i \(0.336774\pi\)
\(458\) 2.47128 4.28038i 0.115475 0.200009i
\(459\) −2.46181 + 4.26398i −0.114907 + 0.199025i
\(460\) −33.2962 + 57.6707i −1.55244 + 2.68891i
\(461\) 3.26361 + 5.65274i 0.152002 + 0.263274i 0.931963 0.362553i \(-0.118095\pi\)
−0.779962 + 0.625827i \(0.784761\pi\)
\(462\) −11.7272 −0.545601
\(463\) 6.92572 + 11.9957i 0.321865 + 0.557487i 0.980873 0.194649i \(-0.0623568\pi\)
−0.659008 + 0.752136i \(0.729023\pi\)
\(464\) −1.76360 + 3.05465i −0.0818732 + 0.141809i
\(465\) 53.2932 2.47141
\(466\) 3.57852 6.19818i 0.165772 0.287125i
\(467\) 1.81086 + 3.13651i 0.0837968 + 0.145140i 0.904878 0.425671i \(-0.139962\pi\)
−0.821081 + 0.570812i \(0.806629\pi\)
\(468\) 23.3693 + 40.4768i 1.08025 + 1.87104i
\(469\) 6.77661 0.312915
\(470\) 32.8545 + 56.9056i 1.51546 + 2.62486i
\(471\) 17.8447 0.822242
\(472\) 7.87387 0.362424
\(473\) −1.72313 2.81952i −0.0792298 0.129642i
\(474\) −30.1615 −1.38536
\(475\) −19.2208 −0.881909
\(476\) −6.11638 10.5939i −0.280344 0.485570i
\(477\) 26.1466 1.19717
\(478\) −33.9074 58.7294i −1.55089 2.68622i
\(479\) −8.02385 13.8977i −0.366619 0.635003i 0.622416 0.782687i \(-0.286151\pi\)
−0.989035 + 0.147684i \(0.952818\pi\)
\(480\) −19.4734 + 33.7290i −0.888836 + 1.53951i
\(481\) 22.1088 1.00807
\(482\) 17.8166 30.8593i 0.811524 1.40560i
\(483\) 32.9385 + 57.0512i 1.49875 + 2.59592i
\(484\) −36.6006 −1.66366
\(485\) −15.2102 26.3448i −0.690659 1.19626i
\(486\) 19.0462 32.9890i 0.863953 1.49641i
\(487\) 0.348282 0.603242i 0.0157822 0.0273355i −0.858026 0.513605i \(-0.828310\pi\)
0.873809 + 0.486270i \(0.161643\pi\)
\(488\) 7.46636 12.9321i 0.337986 0.585409i
\(489\) 58.6507 2.65228
\(490\) −20.3740 + 35.2888i −0.920403 + 1.59419i
\(491\) 17.9222 31.0422i 0.808819 1.40092i −0.104863 0.994487i \(-0.533441\pi\)
0.913682 0.406429i \(-0.133226\pi\)
\(492\) 20.0348 + 34.7013i 0.903238 + 1.56445i
\(493\) 2.23638 + 3.87352i 0.100721 + 0.174454i
\(494\) −33.6353 −1.51333
\(495\) −7.13561 −0.320722
\(496\) −2.53818 4.39625i −0.113968 0.197398i
\(497\) −22.8987 39.6617i −1.02715 1.77907i
\(498\) 36.6443 63.4698i 1.64207 2.84415i
\(499\) 0.985814 1.70748i 0.0441311 0.0764373i −0.843116 0.537732i \(-0.819281\pi\)
0.887247 + 0.461294i \(0.152615\pi\)
\(500\) 11.8889 0.531687
\(501\) −12.9600 + 22.4474i −0.579011 + 1.00288i
\(502\) −20.2191 + 35.0205i −0.902423 + 1.56304i
\(503\) −5.79508 + 10.0374i −0.258390 + 0.447544i −0.965811 0.259248i \(-0.916525\pi\)
0.707421 + 0.706792i \(0.249859\pi\)
\(504\) −27.9821 48.4665i −1.24642 2.15887i
\(505\) 39.3316 1.75023
\(506\) −3.85559 6.67808i −0.171402 0.296877i
\(507\) −6.56623 + 11.3730i −0.291617 + 0.505095i
\(508\) 56.0128 2.48516
\(509\) −20.1338 + 34.8727i −0.892414 + 1.54571i −0.0554402 + 0.998462i \(0.517656\pi\)
−0.836973 + 0.547244i \(0.815677\pi\)
\(510\) −9.62457 16.6702i −0.426183 0.738171i
\(511\) −6.26323 10.8482i −0.277069 0.479897i
\(512\) 8.86557 0.391807
\(513\) −12.3707 21.4267i −0.546181 0.946014i
\(514\) −11.1449 −0.491581
\(515\) −42.6156 −1.87787
\(516\) 29.7658 54.6644i 1.31036 2.40647i
\(517\) −4.79388 −0.210835
\(518\) −64.1311 −2.81776
\(519\) 15.3852 + 26.6479i 0.675335 + 1.16971i
\(520\) −27.9564 −1.22597
\(521\) −20.6123 35.7015i −0.903041 1.56411i −0.823526 0.567279i \(-0.807996\pi\)
−0.0795149 0.996834i \(-0.525337\pi\)
\(522\) 24.7856 + 42.9300i 1.08484 + 1.87899i
\(523\) 15.2683 26.4454i 0.667635 1.15638i −0.310929 0.950433i \(-0.600640\pi\)
0.978564 0.205944i \(-0.0660265\pi\)
\(524\) −39.5830 −1.72919
\(525\) −19.1427 + 33.1562i −0.835457 + 1.44705i
\(526\) −2.67630 4.63550i −0.116692 0.202117i
\(527\) −6.43719 −0.280408
\(528\) 0.553733 + 0.959093i 0.0240981 + 0.0417392i
\(529\) −10.1585 + 17.5951i −0.441675 + 0.765003i
\(530\) −18.9434 + 32.8110i −0.822850 + 1.42522i
\(531\) 5.74078 9.94332i 0.249129 0.431503i
\(532\) 61.4703 2.66508
\(533\) 6.07640 10.5246i 0.263198 0.455873i
\(534\) 26.8656 46.5326i 1.16259 2.01366i
\(535\) −17.8674 30.9473i −0.772476 1.33797i
\(536\) −3.08392 5.34150i −0.133205 0.230718i
\(537\) 2.65081 0.114391
\(538\) −15.1044 −0.651196
\(539\) −1.48641 2.57454i −0.0640242 0.110893i
\(540\) −24.9086 43.1430i −1.07190 1.85658i
\(541\) −19.0950 + 33.0735i −0.820957 + 1.42194i 0.0840131 + 0.996465i \(0.473226\pi\)
−0.904970 + 0.425475i \(0.860107\pi\)
\(542\) −12.2489 + 21.2157i −0.526135 + 0.911292i
\(543\) 62.5874 2.68588
\(544\) 2.35216 4.07406i 0.100848 0.174674i
\(545\) 19.0675 33.0259i 0.816763 1.41468i
\(546\) −33.4988 + 58.0216i −1.43362 + 2.48310i
\(547\) −19.3109 33.4474i −0.825674 1.43011i −0.901403 0.432981i \(-0.857462\pi\)
0.0757291 0.997128i \(-0.475872\pi\)
\(548\) −17.4394 −0.744974
\(549\) −10.8873 18.8574i −0.464660 0.804815i
\(550\) 2.24074 3.88107i 0.0955453 0.165489i
\(551\) −22.4759 −0.957504
\(552\) 29.9795 51.9260i 1.27601 2.21012i
\(553\) −8.35901 14.4782i −0.355461 0.615677i
\(554\) −31.2663 54.1548i −1.32838 2.30082i
\(555\) −63.5802 −2.69883
\(556\) −37.7619 65.4055i −1.60146 2.77381i
\(557\) 23.3874 0.990956 0.495478 0.868621i \(-0.334993\pi\)
0.495478 + 0.868621i \(0.334993\pi\)
\(558\) −71.3430 −3.02019
\(559\) −18.8720 + 0.471411i −0.798199 + 0.0199386i
\(560\) 8.41393 0.355553
\(561\) 1.40435 0.0592915
\(562\) −6.91822 11.9827i −0.291827 0.505460i
\(563\) 1.78677 0.0753032 0.0376516 0.999291i \(-0.488012\pi\)
0.0376516 + 0.999291i \(0.488012\pi\)
\(564\) −45.1501 78.2022i −1.90116 3.29291i
\(565\) −7.16834 12.4159i −0.301574 0.522342i
\(566\) −22.0655 + 38.2186i −0.927483 + 1.60645i
\(567\) 2.07808 0.0872710
\(568\) −20.8416 + 36.0987i −0.874494 + 1.51467i
\(569\) 15.8375 + 27.4314i 0.663944 + 1.14998i 0.979571 + 0.201101i \(0.0644518\pi\)
−0.315627 + 0.948883i \(0.602215\pi\)
\(570\) 96.7281 4.05150
\(571\) 1.82524 + 3.16141i 0.0763838 + 0.132301i 0.901687 0.432389i \(-0.142329\pi\)
−0.825303 + 0.564690i \(0.808996\pi\)
\(572\) 2.47049 4.27901i 0.103296 0.178914i
\(573\) 27.7977 48.1471i 1.16127 2.01137i
\(574\) −17.6258 + 30.5289i −0.735689 + 1.27425i
\(575\) −25.1744 −1.04984
\(576\) 29.8279 51.6634i 1.24283 2.15264i
\(577\) −8.86014 + 15.3462i −0.368852 + 0.638871i −0.989386 0.145308i \(-0.953583\pi\)
0.620534 + 0.784180i \(0.286916\pi\)
\(578\) 1.16254 + 2.01357i 0.0483551 + 0.0837535i
\(579\) −20.9939 36.3626i −0.872479 1.51118i
\(580\) −45.2554 −1.87913
\(581\) 40.6226 1.68531
\(582\) 33.1767 + 57.4636i 1.37522 + 2.38194i
\(583\) −1.38204 2.39377i −0.0572384 0.0991397i
\(584\) −5.70057 + 9.87368i −0.235891 + 0.408576i
\(585\) −20.3828 + 35.3041i −0.842726 + 1.45964i
\(586\) 9.55838 0.394853
\(587\) −9.08044 + 15.7278i −0.374790 + 0.649155i −0.990296 0.138977i \(-0.955618\pi\)
0.615506 + 0.788132i \(0.288952\pi\)
\(588\) 27.9989 48.4954i 1.15465 1.99992i
\(589\) 16.1736 28.0136i 0.666423 1.15428i
\(590\) 8.31850 + 14.4081i 0.342467 + 0.593170i
\(591\) −60.6101 −2.49316
\(592\) 3.02812 + 5.24485i 0.124455 + 0.215562i
\(593\) −8.63919 + 14.9635i −0.354769 + 0.614478i −0.987078 0.160238i \(-0.948774\pi\)
0.632309 + 0.774716i \(0.282107\pi\)
\(594\) 5.76867 0.236691
\(595\) 5.33474 9.24003i 0.218703 0.378804i
\(596\) −29.2414 50.6476i −1.19778 2.07461i
\(597\) 24.8434 + 43.0301i 1.01677 + 1.76110i
\(598\) −44.0539 −1.80150
\(599\) −0.129072 0.223559i −0.00527373 0.00913437i 0.863376 0.504560i \(-0.168345\pi\)
−0.868650 + 0.495426i \(0.835012\pi\)
\(600\) 34.8461 1.42258
\(601\) −16.1648 −0.659375 −0.329687 0.944090i \(-0.606943\pi\)
−0.329687 + 0.944090i \(0.606943\pi\)
\(602\) 54.7420 1.36742i 2.23112 0.0557320i
\(603\) −8.99384 −0.366257
\(604\) −6.27627 −0.255378
\(605\) −15.9616 27.6463i −0.648932 1.12398i
\(606\) −85.7905 −3.48500
\(607\) −11.6809 20.2319i −0.474112 0.821186i 0.525449 0.850825i \(-0.323897\pi\)
−0.999561 + 0.0296392i \(0.990564\pi\)
\(608\) 11.8197 + 20.4724i 0.479354 + 0.830266i
\(609\) −22.3846 + 38.7713i −0.907070 + 1.57109i
\(610\) 31.5519 1.27750
\(611\) −13.6937 + 23.7181i −0.553987 + 0.959533i
\(612\) 8.11759 + 14.0601i 0.328134 + 0.568345i
\(613\) −21.3899 −0.863931 −0.431965 0.901890i \(-0.642180\pi\)
−0.431965 + 0.901890i \(0.642180\pi\)
\(614\) −16.8055 29.1080i −0.678215 1.17470i
\(615\) −17.4744 + 30.2666i −0.704638 + 1.22047i
\(616\) −2.95813 + 5.12364i −0.119187 + 0.206437i
\(617\) −11.0481 + 19.1358i −0.444779 + 0.770380i −0.998037 0.0626300i \(-0.980051\pi\)
0.553258 + 0.833010i \(0.313385\pi\)
\(618\) 92.9537 3.73915
\(619\) −9.14363 + 15.8372i −0.367513 + 0.636552i −0.989176 0.146733i \(-0.953124\pi\)
0.621663 + 0.783285i \(0.286457\pi\)
\(620\) 32.5658 56.4056i 1.30787 2.26530i
\(621\) −16.2026 28.0637i −0.650186 1.12616i
\(622\) −12.5680 21.7684i −0.503930 0.872832i
\(623\) 29.7823 1.19320
\(624\) 6.32693 0.253280
\(625\) 14.7472 + 25.5429i 0.589889 + 1.02172i
\(626\) −31.3523 54.3038i −1.25309 2.17042i
\(627\) −3.52846 + 6.11147i −0.140913 + 0.244069i
\(628\) 10.9044 18.8869i 0.435131 0.753669i
\(629\) 7.67974 0.306211
\(630\) 59.1245 102.407i 2.35558 4.07998i
\(631\) −10.5426 + 18.2603i −0.419693 + 0.726930i −0.995908 0.0903679i \(-0.971196\pi\)
0.576215 + 0.817298i \(0.304529\pi\)
\(632\) −7.60807 + 13.1776i −0.302633 + 0.524176i
\(633\) −18.9636 32.8459i −0.753736 1.30551i
\(634\) 44.6940 1.77503
\(635\) 24.4273 + 42.3093i 0.969368 + 1.67899i
\(636\) 26.0329 45.0903i 1.03227 1.78795i
\(637\) −16.9837 −0.672918
\(638\) 2.62021 4.53834i 0.103735 0.179675i
\(639\) 30.3909 + 52.6386i 1.20225 + 2.08235i
\(640\) 29.2461 + 50.6557i 1.15605 + 2.00234i
\(641\) 34.1434 1.34858 0.674291 0.738466i \(-0.264449\pi\)
0.674291 + 0.738466i \(0.264449\pi\)
\(642\) 38.9726 + 67.5025i 1.53813 + 2.66411i
\(643\) 28.8469 1.13761 0.568804 0.822473i \(-0.307406\pi\)
0.568804 + 0.822473i \(0.307406\pi\)
\(644\) 80.5107 3.17257
\(645\) 54.2718 1.35568i 2.13695 0.0533798i
\(646\) −11.6836 −0.459686
\(647\) 18.7741 0.738084 0.369042 0.929413i \(-0.379686\pi\)
0.369042 + 0.929413i \(0.379686\pi\)
\(648\) −0.945696 1.63799i −0.0371505 0.0643465i
\(649\) −1.21377 −0.0476448
\(650\) −12.8013 22.1725i −0.502108 0.869676i
\(651\) −32.2159 55.7997i −1.26264 2.18696i
\(652\) 35.8396 62.0760i 1.40359 2.43108i
\(653\) −43.6976 −1.71002 −0.855010 0.518612i \(-0.826449\pi\)
−0.855010 + 0.518612i \(0.826449\pi\)
\(654\) −41.5903 + 72.0365i −1.62631 + 2.81685i
\(655\) −17.2622 29.8991i −0.674491 1.16825i
\(656\) 3.32900 0.129976
\(657\) 8.31249 + 14.3977i 0.324301 + 0.561706i
\(658\) 39.7213 68.7993i 1.54850 2.68208i
\(659\) 9.68199 16.7697i 0.377157 0.653255i −0.613490 0.789702i \(-0.710235\pi\)
0.990647 + 0.136447i \(0.0435684\pi\)
\(660\) −7.10459 + 12.3055i −0.276546 + 0.478992i
\(661\) −6.86779 −0.267126 −0.133563 0.991040i \(-0.542642\pi\)
−0.133563 + 0.991040i \(0.542642\pi\)
\(662\) −37.1662 + 64.3737i −1.44450 + 2.50195i
\(663\) 4.01150 6.94813i 0.155794 0.269843i
\(664\) −18.4867 32.0198i −0.717421 1.24261i
\(665\) 26.8074 + 46.4317i 1.03955 + 1.80054i
\(666\) 85.1141 3.29810
\(667\) −29.4377 −1.13983
\(668\) 15.8389 + 27.4338i 0.612826 + 1.06144i
\(669\) 8.22045 + 14.2382i 0.317821 + 0.550482i
\(670\) 6.51612 11.2863i 0.251740 0.436026i
\(671\) −1.15095 + 1.99351i −0.0444321 + 0.0769587i
\(672\) 47.0871 1.81642
\(673\) −16.0618 + 27.8199i −0.619138 + 1.07238i 0.370505 + 0.928830i \(0.379184\pi\)
−0.989643 + 0.143548i \(0.954149\pi\)
\(674\) −31.7363 + 54.9688i −1.22243 + 2.11732i
\(675\) 9.41636 16.3096i 0.362436 0.627758i
\(676\) 8.02483 + 13.8994i 0.308647 + 0.534593i
\(677\) −4.98440 −0.191566 −0.0957831 0.995402i \(-0.530536\pi\)
−0.0957831 + 0.995402i \(0.530536\pi\)
\(678\) 15.6357 + 27.0818i 0.600484 + 1.04007i
\(679\) −18.3892 + 31.8511i −0.705714 + 1.22233i
\(680\) −9.71098 −0.372399
\(681\) 22.8717 39.6150i 0.876447 1.51805i
\(682\) 3.77101 + 6.53158i 0.144399 + 0.250107i
\(683\) −24.4049 42.2705i −0.933827 1.61743i −0.776713 0.629854i \(-0.783115\pi\)
−0.157113 0.987581i \(-0.550219\pi\)
\(684\) −81.5828 −3.11940
\(685\) −7.60537 13.1729i −0.290586 0.503310i
\(686\) −9.19014 −0.350881
\(687\) −5.92426 −0.226025
\(688\) −2.69662 4.41242i −0.102808 0.168222i
\(689\) −15.7912 −0.601596
\(690\) 126.690 4.82299
\(691\) 3.93880 + 6.82220i 0.149839 + 0.259529i 0.931168 0.364591i \(-0.118791\pi\)
−0.781329 + 0.624120i \(0.785458\pi\)
\(692\) 37.6056 1.42955
\(693\) 4.31351 + 7.47121i 0.163857 + 0.283808i
\(694\) 5.24118 + 9.07799i 0.198952 + 0.344596i
\(695\) 32.9361 57.0470i 1.24934 2.16392i
\(696\) 40.7474 1.54453
\(697\) 2.11071 3.65585i 0.0799487 0.138475i
\(698\) −2.09793 3.63371i −0.0794076 0.137538i
\(699\) −8.57860 −0.324472
\(700\) 23.3950 + 40.5214i 0.884249 + 1.53156i
\(701\) −1.09638 + 1.89899i −0.0414097 + 0.0717237i −0.885987 0.463709i \(-0.846518\pi\)
0.844578 + 0.535433i \(0.179852\pi\)
\(702\) 16.4782 28.5410i 0.621928 1.07721i
\(703\) −19.2956 + 33.4209i −0.727747 + 1.26049i
\(704\) −6.30651 −0.237685
\(705\) 39.3801 68.2084i 1.48314 2.56888i
\(706\) 36.8969 63.9074i 1.38863 2.40519i
\(707\) −23.7761 41.1814i −0.894192 1.54879i
\(708\) −11.4316 19.8002i −0.429628 0.744137i
\(709\) 13.0818 0.491298 0.245649 0.969359i \(-0.420999\pi\)
0.245649 + 0.969359i \(0.420999\pi\)
\(710\) −88.0740 −3.30536
\(711\) 11.0940 + 19.2153i 0.416057 + 0.720632i
\(712\) −13.5534 23.4752i −0.507935 0.879770i
\(713\) 21.1834 36.6907i 0.793325 1.37408i
\(714\) −11.6362 + 20.1545i −0.435473 + 0.754262i
\(715\) 4.30954 0.161168
\(716\) 1.61983 2.80562i 0.0605357 0.104851i
\(717\) −40.6422 + 70.3944i −1.51781 + 2.62893i
\(718\) −36.1814 + 62.6680i −1.35028 + 2.33875i
\(719\) 6.34936 + 10.9974i 0.236791 + 0.410134i 0.959792 0.280713i \(-0.0905709\pi\)
−0.723000 + 0.690848i \(0.757238\pi\)
\(720\) −11.1669 −0.416165
\(721\) 25.7613 + 44.6199i 0.959402 + 1.66173i
\(722\) 7.26728 12.5873i 0.270460 0.468451i
\(723\) −42.7108 −1.58843
\(724\) 38.2452 66.2426i 1.42137 2.46189i
\(725\) −8.55409 14.8161i −0.317691 0.550257i
\(726\) 34.8156 + 60.3025i 1.29213 + 2.23803i
\(727\) −14.5455 −0.539464 −0.269732 0.962935i \(-0.586935\pi\)
−0.269732 + 0.962935i \(0.586935\pi\)
\(728\) 16.8998 + 29.2713i 0.626347 + 1.08486i
\(729\) −43.9226 −1.62676
\(730\) −24.0899 −0.891607
\(731\) −6.55539 + 0.163750i −0.242460 + 0.00605651i
\(732\) −43.3600 −1.60263
\(733\) 30.1939 1.11524 0.557619 0.830097i \(-0.311715\pi\)
0.557619 + 0.830097i \(0.311715\pi\)
\(734\) −30.0509 52.0496i −1.10920 1.92119i
\(735\) 48.8415 1.80154
\(736\) 15.4809 + 26.8137i 0.570634 + 0.988367i
\(737\) 0.475392 + 0.823403i 0.0175113 + 0.0303304i
\(738\) 23.3928 40.5176i 0.861102 1.49147i
\(739\) −4.33258 −0.159376 −0.0796882 0.996820i \(-0.525392\pi\)
−0.0796882 + 0.996820i \(0.525392\pi\)
\(740\) −38.8519 + 67.2934i −1.42822 + 2.47375i
\(741\) 20.1580 + 34.9148i 0.740524 + 1.28263i
\(742\) 45.8055 1.68157
\(743\) −2.05226 3.55461i −0.0752900 0.130406i 0.825922 0.563784i \(-0.190655\pi\)
−0.901212 + 0.433378i \(0.857322\pi\)
\(744\) −29.3218 + 50.7869i −1.07499 + 1.86194i
\(745\) 25.5045 44.1751i 0.934413 1.61845i
\(746\) −27.2437 + 47.1874i −0.997461 + 1.72765i
\(747\) −53.9139 −1.97261
\(748\) 0.858151 1.48636i 0.0313771 0.0543468i
\(749\) −21.6018 + 37.4155i −0.789314 + 1.36713i
\(750\) −11.3091 19.5879i −0.412949 0.715249i
\(751\) 6.04133 + 10.4639i 0.220451 + 0.381833i 0.954945 0.296782i \(-0.0959136\pi\)
−0.734494 + 0.678616i \(0.762580\pi\)
\(752\) −7.50218 −0.273576
\(753\) 48.4701 1.76635
\(754\) −14.9692 25.9275i −0.545147 0.944223i
\(755\) −2.73710 4.74079i −0.0996131 0.172535i
\(756\) −30.1147 + 52.1602i −1.09526 + 1.89705i
\(757\) −4.87313 + 8.44051i −0.177117 + 0.306775i −0.940892 0.338707i \(-0.890010\pi\)
0.763775 + 0.645483i \(0.223344\pi\)
\(758\) −34.9225 −1.26844
\(759\) −4.62140 + 8.00450i −0.167746 + 0.290545i
\(760\) 24.3991 42.2605i 0.885049 1.53295i
\(761\) −9.68749 + 16.7792i −0.351171 + 0.608246i −0.986455 0.164032i \(-0.947550\pi\)
0.635284 + 0.772279i \(0.280883\pi\)
\(762\) −53.2811 92.2856i −1.93017 3.34315i
\(763\) −46.1056 −1.66913
\(764\) −33.9726 58.8423i −1.22909 2.12884i
\(765\) −7.08020 + 12.2633i −0.255985 + 0.443380i
\(766\) 31.3128 1.13138
\(767\) −3.46713 + 6.00525i −0.125191 + 0.216837i
\(768\) −28.9139 50.0803i −1.04334 1.80712i
\(769\) −1.21136 2.09814i −0.0436828 0.0756609i 0.843357 0.537353i \(-0.180576\pi\)
−0.887040 + 0.461692i \(0.847242\pi\)
\(770\) −12.5007 −0.450494
\(771\) 6.67927 + 11.5688i 0.240548 + 0.416641i
\(772\) −51.3149 −1.84686
\(773\) 38.7186 1.39261 0.696306 0.717745i \(-0.254826\pi\)
0.696306 + 0.717745i \(0.254826\pi\)
\(774\) −72.6530 + 1.81483i −2.61146 + 0.0652327i
\(775\) 24.6221 0.884452
\(776\) 33.4745 1.20166
\(777\) 38.4345 + 66.5705i 1.37883 + 2.38820i
\(778\) 77.0623 2.76282
\(779\) 10.6064 + 18.3709i 0.380015 + 0.658205i
\(780\) 40.5884 + 70.3012i 1.45330 + 2.51719i
\(781\) 3.21277 5.56469i 0.114962 0.199120i
\(782\) −15.3026 −0.547220
\(783\) 11.0111 19.0717i 0.393503 0.681568i
\(784\) −2.32616 4.02902i −0.0830771 0.143894i
\(785\) 19.0217 0.678912
\(786\) 37.6526 + 65.2162i 1.34302 + 2.32618i
\(787\) −1.55343 + 2.69062i −0.0553738 + 0.0959102i −0.892384 0.451278i \(-0.850968\pi\)
0.837010 + 0.547188i \(0.184302\pi\)
\(788\) −37.0369 + 64.1498i −1.31938 + 2.28524i
\(789\) −3.20788 + 5.55621i −0.114204 + 0.197806i
\(790\) −32.1508 −1.14387
\(791\) −8.66658 + 15.0110i −0.308148 + 0.533728i
\(792\) 3.92600 6.80003i 0.139504 0.241629i
\(793\) 6.57539 + 11.3889i 0.233499 + 0.404432i
\(794\) 14.4719 + 25.0660i 0.513588 + 0.889560i
\(795\) 45.4121 1.61060
\(796\) 60.7242 2.15231
\(797\) −7.82501 13.5533i −0.277176 0.480083i 0.693506 0.720451i \(-0.256065\pi\)
−0.970682 + 0.240368i \(0.922732\pi\)
\(798\) −58.4725 101.277i −2.06991 3.58518i
\(799\) −4.75665 + 8.23877i −0.168278 + 0.291467i
\(800\) −8.99696 + 15.5832i −0.318091 + 0.550949i
\(801\) −39.5268 −1.39661
\(802\) 16.7120 28.9460i 0.590120 1.02212i
\(803\) 0.878755 1.52205i 0.0310106 0.0537119i
\(804\) −8.95475 + 15.5101i −0.315810 + 0.546998i
\(805\) 35.1109 + 60.8139i 1.23750 + 2.14341i
\(806\) 43.0875 1.51769
\(807\) 9.05223 + 15.6789i 0.318654 + 0.551924i
\(808\) −21.6402 + 37.4819i −0.761298 + 1.31861i
\(809\) −15.0932 −0.530648 −0.265324 0.964159i \(-0.585479\pi\)
−0.265324 + 0.964159i \(0.585479\pi\)
\(810\) 1.99820 3.46098i 0.0702095 0.121606i
\(811\) −18.9865 32.8856i −0.666706 1.15477i −0.978820 0.204724i \(-0.934370\pi\)
0.312113 0.950045i \(-0.398963\pi\)
\(812\) 27.3571 + 47.3838i 0.960044 + 1.66285i
\(813\) 29.3636 1.02983
\(814\) −4.49892 7.79235i −0.157687 0.273122i
\(815\) 62.5190 2.18994
\(816\) 2.19773 0.0769360
\(817\) 15.7580 28.9394i 0.551303 1.01246i
\(818\) −28.5768 −0.999165
\(819\) 49.2860 1.72219
\(820\) 21.3562 + 36.9900i 0.745789 + 1.29175i
\(821\) −21.5513 −0.752146 −0.376073 0.926590i \(-0.622726\pi\)
−0.376073 + 0.926590i \(0.622726\pi\)
\(822\) 16.5889 + 28.7328i 0.578605 + 1.00217i
\(823\) −0.486184 0.842095i −0.0169473 0.0293536i 0.857427 0.514605i \(-0.172061\pi\)
−0.874375 + 0.485251i \(0.838728\pi\)
\(824\) 23.4471 40.6115i 0.816817 1.41477i
\(825\) −5.37159 −0.187015
\(826\) 10.0571 17.4195i 0.349932 0.606100i
\(827\) −5.35696 9.27853i −0.186280 0.322646i 0.757727 0.652571i \(-0.226310\pi\)
−0.944007 + 0.329925i \(0.892976\pi\)
\(828\) −106.853 −3.71340
\(829\) −17.0147 29.4704i −0.590946 1.02355i −0.994105 0.108419i \(-0.965421\pi\)
0.403159 0.915130i \(-0.367912\pi\)
\(830\) 39.0611 67.6559i 1.35583 2.34837i
\(831\) −37.4765 + 64.9112i −1.30005 + 2.25175i
\(832\) −18.0145 + 31.2020i −0.624540 + 1.08173i
\(833\) −5.89947 −0.204405
\(834\) −71.8406 + 124.432i −2.48764 + 4.30871i
\(835\) −13.8148 + 23.9279i −0.478080 + 0.828058i
\(836\) 4.31226 + 7.46906i 0.149143 + 0.258323i
\(837\) 15.8471 + 27.4480i 0.547757 + 0.948743i
\(838\) 23.7344 0.819892
\(839\) −30.5573 −1.05496 −0.527478 0.849569i \(-0.676862\pi\)
−0.527478 + 0.849569i \(0.676862\pi\)
\(840\) −48.6001 84.1779i −1.67686 2.90441i
\(841\) 4.49724 + 7.78945i 0.155077 + 0.268602i
\(842\) 13.3282 23.0851i 0.459320 0.795566i
\(843\) −8.29233 + 14.3627i −0.285603 + 0.494679i
\(844\) −46.3523 −1.59551
\(845\) −6.99930 + 12.1231i −0.240783 + 0.417049i
\(846\) −52.7177 + 91.3097i −1.81247 + 3.13929i
\(847\) −19.2977 + 33.4246i −0.663077 + 1.14848i
\(848\) −2.16283 3.74613i −0.0742718 0.128643i
\(849\) 52.8965 1.81540
\(850\) −4.44667 7.70186i −0.152520 0.264172i
\(851\) −25.2724 + 43.7730i −0.866326 + 1.50052i
\(852\) 121.035 4.14660
\(853\) −2.05349 + 3.55674i −0.0703100 + 0.121781i −0.899037 0.437872i \(-0.855732\pi\)
0.828727 + 0.559653i \(0.189066\pi\)
\(854\) −19.0733 33.0359i −0.652673 1.13046i
\(855\) −35.5785 61.6237i −1.21676 2.10749i
\(856\) 39.3225 1.34401
\(857\) −16.5200 28.6135i −0.564314 0.977420i −0.997113 0.0759298i \(-0.975808\pi\)
0.432799 0.901490i \(-0.357526\pi\)
\(858\) −9.40002 −0.320911
\(859\) −12.4751 −0.425645 −0.212822 0.977091i \(-0.568266\pi\)
−0.212822 + 0.977091i \(0.568266\pi\)
\(860\) 31.7289 58.2698i 1.08195 1.98698i
\(861\) 42.2535 1.43999
\(862\) −29.3574 −0.999918
\(863\) −22.2856 38.5998i −0.758612 1.31395i −0.943559 0.331205i \(-0.892545\pi\)
0.184947 0.982748i \(-0.440789\pi\)
\(864\) −23.1623 −0.787996
\(865\) 16.3999 + 28.4054i 0.557613 + 0.965814i
\(866\) 11.0335 + 19.1105i 0.374933 + 0.649403i
\(867\) 1.39344 2.41351i 0.0473237 0.0819671i
\(868\) −78.7446 −2.67277
\(869\) 1.17280 2.03135i 0.0397845 0.0689088i
\(870\) 43.0483 + 74.5619i 1.45948 + 2.52789i
\(871\) 5.43181 0.184050
\(872\) 20.9818 + 36.3416i 0.710535 + 1.23068i
\(873\) 24.4060 42.2724i 0.826018 1.43071i
\(874\) 38.4483 66.5943i 1.30053 2.25259i
\(875\) 6.26843 10.8572i 0.211911 0.367041i
\(876\) 33.1054 1.11853
\(877\) −3.04763 + 5.27866i −0.102911 + 0.178248i −0.912883 0.408221i \(-0.866149\pi\)
0.809972 + 0.586469i \(0.199482\pi\)
\(878\) −16.6599 + 28.8558i −0.562245 + 0.973837i
\(879\) −5.72845 9.92196i −0.193216 0.334659i
\(880\) 0.590253 + 1.02235i 0.0198974 + 0.0344634i
\(881\) −17.7513 −0.598055 −0.299028 0.954244i \(-0.596662\pi\)
−0.299028 + 0.954244i \(0.596662\pi\)
\(882\) −65.3835 −2.20158
\(883\) 16.5651 + 28.6916i 0.557460 + 0.965549i 0.997708 + 0.0676727i \(0.0215574\pi\)
−0.440248 + 0.897876i \(0.645109\pi\)
\(884\) −4.90260 8.49156i −0.164892 0.285602i
\(885\) 9.97074 17.2698i 0.335163 0.580519i
\(886\) 0.252473 0.437295i 0.00848198 0.0146912i
\(887\) 48.4779 1.62773 0.813863 0.581056i \(-0.197360\pi\)
0.813863 + 0.581056i \(0.197360\pi\)
\(888\) 34.9817 60.5901i 1.17391 2.03327i
\(889\) 29.5328 51.1523i 0.990499 1.71559i
\(890\) 28.6375 49.6016i 0.959931 1.66265i
\(891\) 0.145781 + 0.252500i 0.00488385 + 0.00845908i
\(892\) 20.0930 0.672764
\(893\) −23.9025 41.4003i −0.799866 1.38541i
\(894\) −55.6307 + 96.3553i −1.86057 + 3.22260i
\(895\) 2.82564 0.0944507
\(896\) 35.3587 61.2431i 1.18125 2.04599i
\(897\) 26.4020 + 45.7296i 0.881536 + 1.52687i
\(898\) 46.6821 + 80.8558i 1.55780 + 2.69819i
\(899\) 28.7920 0.960266
\(900\) −31.0496 53.7795i −1.03499 1.79265i
\(901\) −5.48524 −0.182740
\(902\) −4.94595 −0.164682
\(903\) −34.2270 56.0048i −1.13900 1.86372i
\(904\) 15.7760 0.524703
\(905\) 66.7153 2.21769
\(906\) 5.97018 + 10.3407i 0.198346 + 0.343545i
\(907\) 7.49684 0.248928 0.124464 0.992224i \(-0.460279\pi\)
0.124464 + 0.992224i \(0.460279\pi\)
\(908\) −27.9524 48.4150i −0.927633 1.60671i
\(909\) 31.5554 + 54.6555i 1.04663 + 1.81281i
\(910\) −35.7082 + 61.8483i −1.18371 + 2.05025i
\(911\) 36.4154 1.20649 0.603247 0.797554i \(-0.293873\pi\)
0.603247 + 0.797554i \(0.293873\pi\)
\(912\) −5.52187 + 9.56415i −0.182847 + 0.316701i
\(913\) 2.84976 + 4.93592i 0.0943131 + 0.163355i
\(914\) −48.7710 −1.61320
\(915\) −18.9094 32.7521i −0.625126 1.08275i
\(916\) −3.62013 + 6.27024i −0.119612 + 0.207175i
\(917\) −20.8702 + 36.1482i −0.689194 + 1.19372i
\(918\) 5.72388 9.91404i 0.188916 0.327212i
\(919\) 20.8956 0.689282 0.344641 0.938735i \(-0.388001\pi\)
0.344641 + 0.938735i \(0.388001\pi\)
\(920\) 31.9567 55.3507i 1.05358 1.82486i
\(921\) −20.1435 + 34.8895i −0.663750 + 1.14965i
\(922\) −7.58812 13.1430i −0.249902 0.432842i
\(923\) −18.3545 31.7910i −0.604147 1.04641i
\(924\) 17.1790 0.565148
\(925\) −29.3748 −0.965839
\(926\) −16.1028 27.8908i −0.529170 0.916550i
\(927\) −34.1901 59.2191i −1.12295 1.94501i
\(928\) −10.5206 + 18.2223i −0.345357 + 0.598175i
\(929\) −17.1962 + 29.7847i −0.564190 + 0.977206i 0.432934 + 0.901425i \(0.357478\pi\)
−0.997125 + 0.0757805i \(0.975855\pi\)
\(930\) −123.910 −4.06318
\(931\) 14.8226 25.6735i 0.485791 0.841415i
\(932\) −5.24211 + 9.07960i −0.171711 + 0.297412i
\(933\) −15.0643 + 26.0921i −0.493182 + 0.854216i
\(934\) −4.21038 7.29260i −0.137768 0.238621i
\(935\) 1.49697 0.0489561
\(936\) −22.4292 38.8485i −0.733121 1.26980i
\(937\) 24.6378 42.6739i 0.804882 1.39410i −0.111490 0.993766i \(-0.535562\pi\)
0.916371 0.400330i \(-0.131105\pi\)
\(938\) −15.7561 −0.514454
\(939\) −37.5796 + 65.0898i −1.22636 + 2.12413i
\(940\) −48.1279 83.3599i −1.56976 2.71890i
\(941\) −17.0483 29.5285i −0.555759 0.962602i −0.997844 0.0656294i \(-0.979094\pi\)
0.442085 0.896973i \(-0.354239\pi\)
\(942\) −41.4903 −1.35183
\(943\) 13.8918 + 24.0612i 0.452378 + 0.783542i
\(944\) −1.89949 −0.0618233
\(945\) −52.5324 −1.70888
\(946\) 4.00641 + 6.55559i 0.130260 + 0.213141i
\(947\) 30.3688 0.986855 0.493427 0.869787i \(-0.335744\pi\)
0.493427 + 0.869787i \(0.335744\pi\)
\(948\) 44.1830 1.43500
\(949\) −5.02031 8.69544i −0.162966 0.282266i
\(950\) 44.6896 1.44992
\(951\) −26.7856 46.3941i −0.868584 1.50443i
\(952\) 5.87032 + 10.1677i 0.190258 + 0.329537i
\(953\) −13.9581 + 24.1762i −0.452149 + 0.783145i −0.998519 0.0543989i \(-0.982676\pi\)
0.546370 + 0.837544i \(0.316009\pi\)
\(954\) −60.7926 −1.96823
\(955\) 29.6311 51.3225i 0.958839 1.66076i
\(956\) 49.6703 + 86.0315i 1.60645 + 2.78246i
\(957\) −6.28129 −0.203045
\(958\) 18.6560 + 32.3132i 0.602748 + 1.04399i
\(959\) −9.19495 + 15.9261i −0.296920 + 0.514281i
\(960\) 51.8058 89.7304i 1.67203 2.89603i
\(961\) −5.21870 + 9.03906i −0.168345 + 0.291583i
\(962\) −51.4045 −1.65735
\(963\) 28.6697 49.6574i 0.923869 1.60019i
\(964\) −26.0992 + 45.2051i −0.840598 + 1.45596i
\(965\) −22.3786 38.7608i −0.720392 1.24775i
\(966\) −76.5843 132.648i −2.46406 4.26788i
\(967\) −52.7063 −1.69492 −0.847459 0.530860i \(-0.821869\pi\)
−0.847459 + 0.530860i \(0.821869\pi\)
\(968\) 35.1282 1.12906
\(969\) 7.00213 + 12.1280i 0.224941 + 0.389609i
\(970\) 35.3648 + 61.2536i 1.13549 + 1.96673i
\(971\) −12.5472 + 21.7324i −0.402658 + 0.697425i −0.994046 0.108963i \(-0.965247\pi\)
0.591388 + 0.806388i \(0.298580\pi\)
\(972\) −27.9004 + 48.3249i −0.894906 + 1.55002i
\(973\) −79.6400 −2.55314
\(974\) −0.809780 + 1.40258i −0.0259470 + 0.0449415i
\(975\) −15.3439 + 26.5764i −0.491399 + 0.851127i
\(976\) −1.80119 + 3.11975i −0.0576546 + 0.0998607i
\(977\) −13.0026 22.5211i −0.415990 0.720515i 0.579542 0.814942i \(-0.303231\pi\)
−0.995532 + 0.0944272i \(0.969898\pi\)
\(978\) −136.367 −4.36054
\(979\) 2.08929 + 3.61875i 0.0667739 + 0.115656i
\(980\) 29.8455 51.6939i 0.953379 1.65130i
\(981\) 61.1908 1.95367
\(982\) −41.6704 + 72.1753i −1.32976 + 2.30321i
\(983\) 9.71576 + 16.8282i 0.309885 + 0.536736i 0.978337 0.207019i \(-0.0663762\pi\)
−0.668452 + 0.743755i \(0.733043\pi\)
\(984\) −19.2288 33.3053i −0.612992 1.06173i
\(985\) −64.6075 −2.05857
\(986\) −5.19973 9.00620i −0.165593 0.286816i
\(987\) −95.2217 −3.03094
\(988\) 49.2718 1.56754
\(989\) 20.6390 37.9033i 0.656283 1.20526i
\(990\) 16.5908 0.527290
\(991\) 37.5650 1.19329 0.596646 0.802504i \(-0.296500\pi\)
0.596646 + 0.802504i \(0.296500\pi\)
\(992\) −15.1413 26.2255i −0.480737 0.832661i
\(993\) 89.0964 2.82739
\(994\) 53.2411 + 92.2162i 1.68870 + 2.92492i
\(995\) 26.4820 + 45.8681i 0.839534 + 1.45412i
\(996\) −53.6796 + 92.9758i −1.70090 + 2.94605i
\(997\) −17.1424 −0.542906 −0.271453 0.962452i \(-0.587504\pi\)
−0.271453 + 0.962452i \(0.587504\pi\)
\(998\) −2.29209 + 3.97001i −0.0725548 + 0.125669i
\(999\) −18.9060 32.7462i −0.598161 1.03605i
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 731.2.e.a.681.3 yes 58
43.6 even 3 inner 731.2.e.a.307.3 58
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
731.2.e.a.307.3 58 43.6 even 3 inner
731.2.e.a.681.3 yes 58 1.1 even 1 trivial