Properties

Label 143.2.h.c.27.7
Level $143$
Weight $2$
Character 143.27
Analytic conductor $1.142$
Analytic rank $0$
Dimension $28$
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] = [143,2,Mod(14,143)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(143, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([8, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("143.14");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 143 = 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 143.h (of order \(5\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.14186074890\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(7\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 27.7
Character \(\chi\) \(=\) 143.27
Dual form 143.2.h.c.53.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.762214 + 2.34585i) q^{2} +(-2.07347 - 1.50647i) q^{3} +(-3.30403 + 2.40052i) q^{4} +(-0.598707 + 1.84263i) q^{5} +(1.95352 - 6.01232i) q^{6} +(-2.84556 + 2.06742i) q^{7} +(-4.15864 - 3.02143i) q^{8} +(1.10280 + 3.39406i) q^{9} +O(q^{10})\) \(q+(0.762214 + 2.34585i) q^{2} +(-2.07347 - 1.50647i) q^{3} +(-3.30403 + 2.40052i) q^{4} +(-0.598707 + 1.84263i) q^{5} +(1.95352 - 6.01232i) q^{6} +(-2.84556 + 2.06742i) q^{7} +(-4.15864 - 3.02143i) q^{8} +(1.10280 + 3.39406i) q^{9} -4.77889 q^{10} +(1.29945 - 3.05146i) q^{11} +10.4671 q^{12} +(0.309017 + 0.951057i) q^{13} +(-7.01879 - 5.09945i) q^{14} +(4.01727 - 2.91871i) q^{15} +(1.39400 - 4.29030i) q^{16} +(-1.82552 + 5.61838i) q^{17} +(-7.12141 + 5.17401i) q^{18} +(4.86716 + 3.53620i) q^{19} +(-2.44512 - 7.52532i) q^{20} +9.01468 q^{21} +(8.14875 + 0.722457i) q^{22} +1.92952 q^{23} +(4.07115 + 12.5297i) q^{24} +(1.00824 + 0.732532i) q^{25} +(-1.99550 + 1.44982i) q^{26} +(0.450430 - 1.38628i) q^{27} +(4.43893 - 13.6616i) q^{28} +(0.398361 - 0.289426i) q^{29} +(9.90890 + 7.19924i) q^{30} +(-2.16776 - 6.67168i) q^{31} +0.846233 q^{32} +(-7.29130 + 4.36954i) q^{33} -14.5713 q^{34} +(-2.10583 - 6.48109i) q^{35} +(-11.7912 - 8.56680i) q^{36} +(0.182935 - 0.132910i) q^{37} +(-4.58559 + 14.1130i) q^{38} +(0.791996 - 2.43751i) q^{39} +(8.05719 - 5.85389i) q^{40} +(-1.73413 - 1.25992i) q^{41} +(6.87112 + 21.1471i) q^{42} +6.19789 q^{43} +(3.03166 + 13.2015i) q^{44} -6.91426 q^{45} +(1.47071 + 4.52637i) q^{46} +(-8.84554 - 6.42666i) q^{47} +(-9.35362 + 6.79580i) q^{48} +(1.65986 - 5.10852i) q^{49} +(-0.949915 + 2.92354i) q^{50} +(12.2491 - 8.89947i) q^{51} +(-3.30403 - 2.40052i) q^{52} +(2.22144 + 6.83688i) q^{53} +3.59534 q^{54} +(4.84473 + 4.22135i) q^{55} +18.0802 q^{56} +(-4.76476 - 14.6644i) q^{57} +(0.982589 + 0.713893i) q^{58} +(-6.81817 + 4.95369i) q^{59} +(-6.26674 + 19.2870i) q^{60} +(-2.38315 + 7.33458i) q^{61} +(13.9985 - 10.1705i) q^{62} +(-10.1550 - 7.37805i) q^{63} +(-2.14300 - 6.59547i) q^{64} -1.93746 q^{65} +(-15.8078 - 13.7738i) q^{66} +7.34591 q^{67} +(-7.45545 - 22.9455i) q^{68} +(-4.00081 - 2.90676i) q^{69} +(13.5986 - 9.87997i) q^{70} +(1.11647 - 3.43613i) q^{71} +(5.66878 - 17.4467i) q^{72} +(11.5395 - 8.38392i) q^{73} +(0.451223 + 0.327833i) q^{74} +(-0.987031 - 3.03777i) q^{75} -24.5700 q^{76} +(2.61098 + 11.3696i) q^{77} +6.32172 q^{78} +(2.63171 + 8.09956i) q^{79} +(7.07085 + 5.13727i) q^{80} +(5.63915 - 4.09708i) q^{81} +(1.63381 - 5.02836i) q^{82} +(-1.93692 + 5.96121i) q^{83} +(-29.7848 + 21.6399i) q^{84} +(-9.25966 - 6.72753i) q^{85} +(4.72412 + 14.5394i) q^{86} -1.26200 q^{87} +(-14.6237 + 8.76373i) q^{88} +9.78785 q^{89} +(-5.27015 - 16.2198i) q^{90} +(-2.84556 - 2.06742i) q^{91} +(-6.37519 + 4.63185i) q^{92} +(-5.55587 + 17.0992i) q^{93} +(8.33382 - 25.6488i) q^{94} +(-9.42993 + 6.85124i) q^{95} +(-1.75464 - 1.27482i) q^{96} +(1.63493 + 5.03180i) q^{97} +13.2490 q^{98} +(11.7899 + 1.04528i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q - 3 q^{2} - 7 q^{3} - 5 q^{4} - 7 q^{5} - 4 q^{6} - 7 q^{7} + q^{8} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 28 q - 3 q^{2} - 7 q^{3} - 5 q^{4} - 7 q^{5} - 4 q^{6} - 7 q^{7} + q^{8} - 6 q^{9} - 24 q^{10} - 5 q^{11} + 38 q^{12} - 7 q^{13} - 7 q^{14} + 8 q^{15} - 19 q^{16} + 7 q^{17} + 5 q^{18} + 5 q^{19} + 9 q^{20} - 33 q^{22} + 50 q^{23} - 7 q^{24} - 34 q^{25} + 2 q^{26} - 19 q^{27} + 30 q^{28} + 8 q^{29} - 6 q^{30} + 17 q^{31} + 24 q^{32} - 26 q^{33} + 26 q^{34} - 4 q^{35} - 27 q^{36} + 17 q^{37} - 51 q^{38} - 2 q^{39} + 39 q^{40} - 23 q^{41} + 80 q^{42} - 32 q^{43} + q^{44} + 78 q^{45} - 31 q^{46} - 29 q^{47} + 52 q^{48} - 52 q^{49} + 6 q^{50} + 7 q^{51} - 5 q^{52} - 16 q^{53} - 42 q^{54} - 5 q^{55} + 34 q^{56} - 7 q^{57} - 13 q^{58} - 11 q^{59} - 74 q^{60} + 37 q^{61} + 23 q^{62} - 38 q^{63} + 67 q^{64} + 18 q^{65} - 65 q^{66} + 58 q^{67} - 68 q^{68} - 28 q^{69} + 44 q^{70} - 47 q^{71} + 10 q^{72} + 44 q^{73} - 46 q^{74} + 17 q^{75} + 6 q^{76} + 21 q^{77} + 26 q^{78} + 51 q^{79} + 23 q^{80} - 14 q^{81} - 47 q^{82} - 13 q^{83} - 107 q^{84} - q^{85} + 38 q^{86} - 12 q^{87} + 9 q^{88} + 38 q^{89} - 74 q^{90} - 7 q^{91} - 41 q^{92} - 51 q^{93} - 5 q^{94} + 47 q^{95} - 71 q^{96} - 20 q^{97} + 162 q^{98} + 60 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/143\mathbb{Z}\right)^\times\).

\(n\) \(67\) \(79\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{5}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.762214 + 2.34585i 0.538967 + 1.65877i 0.734918 + 0.678156i \(0.237221\pi\)
−0.195951 + 0.980614i \(0.562779\pi\)
\(3\) −2.07347 1.50647i −1.19712 0.869758i −0.203121 0.979154i \(-0.565109\pi\)
−0.993998 + 0.109395i \(0.965109\pi\)
\(4\) −3.30403 + 2.40052i −1.65202 + 1.20026i
\(5\) −0.598707 + 1.84263i −0.267750 + 0.824050i 0.723297 + 0.690537i \(0.242626\pi\)
−0.991047 + 0.133513i \(0.957374\pi\)
\(6\) 1.95352 6.01232i 0.797521 2.45452i
\(7\) −2.84556 + 2.06742i −1.07552 + 0.781411i −0.976896 0.213714i \(-0.931444\pi\)
−0.0986233 + 0.995125i \(0.531444\pi\)
\(8\) −4.15864 3.02143i −1.47030 1.06824i
\(9\) 1.10280 + 3.39406i 0.367599 + 1.13135i
\(10\) −4.77889 −1.51122
\(11\) 1.29945 3.05146i 0.391800 0.920051i
\(12\) 10.4671 3.02160
\(13\) 0.309017 + 0.951057i 0.0857059 + 0.263776i
\(14\) −7.01879 5.09945i −1.87585 1.36288i
\(15\) 4.01727 2.91871i 1.03725 0.753609i
\(16\) 1.39400 4.29030i 0.348501 1.07258i
\(17\) −1.82552 + 5.61838i −0.442754 + 1.36266i 0.442174 + 0.896930i \(0.354208\pi\)
−0.884928 + 0.465728i \(0.845792\pi\)
\(18\) −7.12141 + 5.17401i −1.67853 + 1.21952i
\(19\) 4.86716 + 3.53620i 1.11660 + 0.811260i 0.983691 0.179867i \(-0.0575668\pi\)
0.132913 + 0.991128i \(0.457567\pi\)
\(20\) −2.44512 7.52532i −0.546746 1.68271i
\(21\) 9.01468 1.96716
\(22\) 8.14875 + 0.722457i 1.73732 + 0.154028i
\(23\) 1.92952 0.402333 0.201166 0.979557i \(-0.435527\pi\)
0.201166 + 0.979557i \(0.435527\pi\)
\(24\) 4.07115 + 12.5297i 0.831019 + 2.55761i
\(25\) 1.00824 + 0.732532i 0.201649 + 0.146506i
\(26\) −1.99550 + 1.44982i −0.391350 + 0.284333i
\(27\) 0.450430 1.38628i 0.0866852 0.266790i
\(28\) 4.43893 13.6616i 0.838879 2.58180i
\(29\) 0.398361 0.289426i 0.0739738 0.0537451i −0.550184 0.835044i \(-0.685442\pi\)
0.624158 + 0.781299i \(0.285442\pi\)
\(30\) 9.90890 + 7.19924i 1.80911 + 1.31439i
\(31\) −2.16776 6.67168i −0.389341 1.19827i −0.933282 0.359145i \(-0.883068\pi\)
0.543940 0.839124i \(-0.316932\pi\)
\(32\) 0.846233 0.149594
\(33\) −7.29130 + 4.36954i −1.26925 + 0.760640i
\(34\) −14.5713 −2.49897
\(35\) −2.10583 6.48109i −0.355951 1.09550i
\(36\) −11.7912 8.56680i −1.96520 1.42780i
\(37\) 0.182935 0.132910i 0.0300743 0.0218503i −0.572647 0.819802i \(-0.694083\pi\)
0.602721 + 0.797952i \(0.294083\pi\)
\(38\) −4.58559 + 14.1130i −0.743881 + 2.28943i
\(39\) 0.791996 2.43751i 0.126821 0.390314i
\(40\) 8.05719 5.85389i 1.27395 0.925581i
\(41\) −1.73413 1.25992i −0.270826 0.196767i 0.444080 0.895987i \(-0.353531\pi\)
−0.714906 + 0.699220i \(0.753531\pi\)
\(42\) 6.87112 + 21.1471i 1.06024 + 3.26307i
\(43\) 6.19789 0.945170 0.472585 0.881285i \(-0.343321\pi\)
0.472585 + 0.881285i \(0.343321\pi\)
\(44\) 3.03166 + 13.2015i 0.457040 + 1.99020i
\(45\) −6.91426 −1.03072
\(46\) 1.47071 + 4.52637i 0.216844 + 0.667377i
\(47\) −8.84554 6.42666i −1.29025 0.937425i −0.290444 0.956892i \(-0.593803\pi\)
−0.999810 + 0.0194672i \(0.993803\pi\)
\(48\) −9.35362 + 6.79580i −1.35008 + 0.980890i
\(49\) 1.65986 5.10852i 0.237123 0.729788i
\(50\) −0.949915 + 2.92354i −0.134338 + 0.413451i
\(51\) 12.2491 8.89947i 1.71521 1.24618i
\(52\) −3.30403 2.40052i −0.458187 0.332892i
\(53\) 2.22144 + 6.83688i 0.305138 + 0.939118i 0.979626 + 0.200832i \(0.0643646\pi\)
−0.674488 + 0.738286i \(0.735635\pi\)
\(54\) 3.59534 0.489263
\(55\) 4.84473 + 4.22135i 0.653263 + 0.569206i
\(56\) 18.0802 2.41607
\(57\) −4.76476 14.6644i −0.631108 1.94235i
\(58\) 0.982589 + 0.713893i 0.129020 + 0.0937387i
\(59\) −6.81817 + 4.95369i −0.887651 + 0.644916i −0.935264 0.353950i \(-0.884838\pi\)
0.0476138 + 0.998866i \(0.484838\pi\)
\(60\) −6.26674 + 19.2870i −0.809032 + 2.48995i
\(61\) −2.38315 + 7.33458i −0.305131 + 0.939096i 0.674497 + 0.738277i \(0.264360\pi\)
−0.979628 + 0.200819i \(0.935640\pi\)
\(62\) 13.9985 10.1705i 1.77781 1.29166i
\(63\) −10.1550 7.37805i −1.27941 0.929547i
\(64\) −2.14300 6.59547i −0.267875 0.824433i
\(65\) −1.93746 −0.240312
\(66\) −15.8078 13.7738i −1.94581 1.69544i
\(67\) 7.34591 0.897446 0.448723 0.893671i \(-0.351879\pi\)
0.448723 + 0.893671i \(0.351879\pi\)
\(68\) −7.45545 22.9455i −0.904106 2.78255i
\(69\) −4.00081 2.90676i −0.481641 0.349932i
\(70\) 13.5986 9.87997i 1.62534 1.18088i
\(71\) 1.11647 3.43613i 0.132500 0.407793i −0.862693 0.505728i \(-0.831224\pi\)
0.995193 + 0.0979351i \(0.0312238\pi\)
\(72\) 5.66878 17.4467i 0.668072 2.05611i
\(73\) 11.5395 8.38392i 1.35059 0.981264i 0.351612 0.936146i \(-0.385634\pi\)
0.998982 0.0451176i \(-0.0143663\pi\)
\(74\) 0.451223 + 0.327833i 0.0524536 + 0.0381098i
\(75\) −0.987031 3.03777i −0.113972 0.350771i
\(76\) −24.5700 −2.81837
\(77\) 2.61098 + 11.3696i 0.297549 + 1.29569i
\(78\) 6.32172 0.715794
\(79\) 2.63171 + 8.09956i 0.296090 + 0.911272i 0.982853 + 0.184390i \(0.0590310\pi\)
−0.686763 + 0.726881i \(0.740969\pi\)
\(80\) 7.07085 + 5.13727i 0.790545 + 0.574364i
\(81\) 5.63915 4.09708i 0.626572 0.455231i
\(82\) 1.63381 5.02836i 0.180424 0.555289i
\(83\) −1.93692 + 5.96121i −0.212604 + 0.654328i 0.786711 + 0.617322i \(0.211782\pi\)
−0.999315 + 0.0370065i \(0.988218\pi\)
\(84\) −29.7848 + 21.6399i −3.24978 + 2.36111i
\(85\) −9.25966 6.72753i −1.00435 0.729703i
\(86\) 4.72412 + 14.5394i 0.509415 + 1.56782i
\(87\) −1.26200 −0.135301
\(88\) −14.6237 + 8.76373i −1.55890 + 0.934217i
\(89\) 9.78785 1.03751 0.518755 0.854923i \(-0.326396\pi\)
0.518755 + 0.854923i \(0.326396\pi\)
\(90\) −5.27015 16.2198i −0.555522 1.70972i
\(91\) −2.84556 2.06742i −0.298295 0.216724i
\(92\) −6.37519 + 4.63185i −0.664660 + 0.482904i
\(93\) −5.55587 + 17.0992i −0.576117 + 1.77310i
\(94\) 8.33382 25.6488i 0.859567 2.64548i
\(95\) −9.42993 + 6.85124i −0.967490 + 0.702923i
\(96\) −1.75464 1.27482i −0.179082 0.130111i
\(97\) 1.63493 + 5.03180i 0.166002 + 0.510902i 0.999109 0.0422105i \(-0.0134400\pi\)
−0.833107 + 0.553112i \(0.813440\pi\)
\(98\) 13.2490 1.33835
\(99\) 11.7899 + 1.04528i 1.18493 + 0.105054i
\(100\) −5.08972 −0.508972
\(101\) 0.612759 + 1.88588i 0.0609718 + 0.187652i 0.976903 0.213684i \(-0.0685462\pi\)
−0.915931 + 0.401335i \(0.868546\pi\)
\(102\) 30.2133 + 21.9512i 2.99156 + 2.17350i
\(103\) −7.72597 + 5.61325i −0.761263 + 0.553090i −0.899297 0.437338i \(-0.855922\pi\)
0.138035 + 0.990427i \(0.455922\pi\)
\(104\) 1.58846 4.88877i 0.155761 0.479384i
\(105\) −5.39716 + 16.6107i −0.526708 + 1.62104i
\(106\) −14.3451 + 10.4223i −1.39332 + 1.01231i
\(107\) 0.641334 + 0.465957i 0.0620001 + 0.0450457i 0.618354 0.785900i \(-0.287800\pi\)
−0.556354 + 0.830946i \(0.687800\pi\)
\(108\) 1.83956 + 5.66158i 0.177011 + 0.544785i
\(109\) 7.84859 0.751758 0.375879 0.926669i \(-0.377341\pi\)
0.375879 + 0.926669i \(0.377341\pi\)
\(110\) −6.20994 + 14.5826i −0.592095 + 1.39040i
\(111\) −0.579534 −0.0550070
\(112\) 4.90313 + 15.0903i 0.463302 + 1.42590i
\(113\) 0.652862 + 0.474332i 0.0614161 + 0.0446214i 0.618070 0.786123i \(-0.287915\pi\)
−0.556654 + 0.830745i \(0.687915\pi\)
\(114\) 30.7689 22.3549i 2.88177 2.09373i
\(115\) −1.15522 + 3.55540i −0.107725 + 0.331542i
\(116\) −0.621424 + 1.91255i −0.0576978 + 0.177575i
\(117\) −2.88716 + 2.09765i −0.266918 + 0.193927i
\(118\) −16.8176 12.2187i −1.54818 1.12482i
\(119\) −6.42092 19.7615i −0.588604 1.81154i
\(120\) −25.5250 −2.33011
\(121\) −7.62285 7.93046i −0.692986 0.720951i
\(122\) −19.0223 −1.72220
\(123\) 1.69765 + 5.22483i 0.153072 + 0.471107i
\(124\) 23.1778 + 16.8397i 2.08143 + 1.51225i
\(125\) −9.79061 + 7.11329i −0.875699 + 0.636232i
\(126\) 9.56754 29.4459i 0.852344 2.62325i
\(127\) −3.45507 + 10.6336i −0.306588 + 0.943581i 0.672492 + 0.740104i \(0.265224\pi\)
−0.979080 + 0.203476i \(0.934776\pi\)
\(128\) 15.2078 11.0491i 1.34419 0.976614i
\(129\) −12.8512 9.33691i −1.13148 0.822069i
\(130\) −1.47676 4.54499i −0.129520 0.398622i
\(131\) −3.74429 −0.327140 −0.163570 0.986532i \(-0.552301\pi\)
−0.163570 + 0.986532i \(0.552301\pi\)
\(132\) 13.6015 31.9400i 1.18386 2.78002i
\(133\) −21.1606 −1.83486
\(134\) 5.59916 + 17.2324i 0.483694 + 1.48866i
\(135\) 2.28473 + 1.65995i 0.196638 + 0.142866i
\(136\) 24.5672 17.8491i 2.10662 1.53055i
\(137\) 1.12965 3.47671i 0.0965127 0.297035i −0.891132 0.453744i \(-0.850088\pi\)
0.987645 + 0.156708i \(0.0500882\pi\)
\(138\) 3.76936 11.6009i 0.320869 0.987533i
\(139\) 17.9224 13.0214i 1.52015 1.10446i 0.558743 0.829341i \(-0.311284\pi\)
0.961411 0.275116i \(-0.0887161\pi\)
\(140\) 22.5157 + 16.3586i 1.90293 + 1.38256i
\(141\) 8.65944 + 26.6510i 0.729256 + 2.24442i
\(142\) 8.91164 0.747849
\(143\) 3.30367 + 0.292899i 0.276266 + 0.0244934i
\(144\) 16.0989 1.34157
\(145\) 0.294804 + 0.907315i 0.0244822 + 0.0753484i
\(146\) 28.4630 + 20.6796i 2.35562 + 1.71145i
\(147\) −11.1375 + 8.09185i −0.918604 + 0.667405i
\(148\) −0.285369 + 0.878277i −0.0234572 + 0.0721939i
\(149\) 4.49249 13.8264i 0.368039 1.13271i −0.580017 0.814604i \(-0.696954\pi\)
0.948056 0.318103i \(-0.103046\pi\)
\(150\) 6.37383 4.63086i 0.520421 0.378108i
\(151\) 13.2214 + 9.60592i 1.07594 + 0.781719i 0.976971 0.213372i \(-0.0684445\pi\)
0.0989722 + 0.995090i \(0.468445\pi\)
\(152\) −9.55640 29.4116i −0.775127 2.38559i
\(153\) −21.0823 −1.70440
\(154\) −24.6814 + 14.7911i −1.98888 + 1.19190i
\(155\) 13.5913 1.09168
\(156\) 3.23452 + 9.95482i 0.258969 + 0.797023i
\(157\) 3.44483 + 2.50281i 0.274927 + 0.199746i 0.716702 0.697380i \(-0.245651\pi\)
−0.441775 + 0.897126i \(0.645651\pi\)
\(158\) −16.9945 + 12.3472i −1.35201 + 0.982291i
\(159\) 5.69344 17.5226i 0.451519 1.38963i
\(160\) −0.506646 + 1.55930i −0.0400539 + 0.123273i
\(161\) −5.49056 + 3.98913i −0.432717 + 0.314387i
\(162\) 13.9094 + 10.1058i 1.09283 + 0.793984i
\(163\) 0.784470 + 2.41435i 0.0614445 + 0.189107i 0.977067 0.212933i \(-0.0683015\pi\)
−0.915622 + 0.402039i \(0.868302\pi\)
\(164\) 8.75410 0.683580
\(165\) −3.68610 16.0513i −0.286963 1.24959i
\(166\) −15.4605 −1.19997
\(167\) −5.01302 15.4285i −0.387919 1.19389i −0.934341 0.356382i \(-0.884010\pi\)
0.546422 0.837510i \(-0.315990\pi\)
\(168\) −37.4888 27.2372i −2.89232 2.10140i
\(169\) −0.809017 + 0.587785i −0.0622321 + 0.0452143i
\(170\) 8.72397 26.8496i 0.669098 2.05927i
\(171\) −6.63459 + 20.4192i −0.507360 + 1.56149i
\(172\) −20.4780 + 14.8782i −1.56143 + 1.13445i
\(173\) 1.32237 + 0.960756i 0.100538 + 0.0730449i 0.636918 0.770931i \(-0.280209\pi\)
−0.536381 + 0.843976i \(0.680209\pi\)
\(174\) −0.961916 2.96047i −0.0729227 0.224433i
\(175\) −4.38346 −0.331359
\(176\) −11.2803 9.82879i −0.850281 0.740873i
\(177\) 21.5999 1.62355
\(178\) 7.46044 + 22.9609i 0.559184 + 1.72099i
\(179\) 4.56832 + 3.31908i 0.341452 + 0.248080i 0.745274 0.666758i \(-0.232319\pi\)
−0.403822 + 0.914838i \(0.632319\pi\)
\(180\) 22.8449 16.5978i 1.70276 1.23713i
\(181\) −0.142085 + 0.437292i −0.0105611 + 0.0325036i −0.956198 0.292720i \(-0.905440\pi\)
0.945637 + 0.325224i \(0.105440\pi\)
\(182\) 2.68094 8.25108i 0.198724 0.611611i
\(183\) 15.9907 11.6179i 1.18207 0.858821i
\(184\) −8.02418 5.82991i −0.591550 0.429787i
\(185\) 0.135380 + 0.416656i 0.00995331 + 0.0306331i
\(186\) −44.3470 −3.25168
\(187\) 14.7721 + 12.8713i 1.08024 + 0.941245i
\(188\) 44.6532 3.25667
\(189\) 1.58430 + 4.87597i 0.115241 + 0.354674i
\(190\) −23.2596 16.8991i −1.68743 1.22599i
\(191\) 6.17030 4.48298i 0.446467 0.324377i −0.341732 0.939797i \(-0.611014\pi\)
0.788199 + 0.615420i \(0.211014\pi\)
\(192\) −5.49240 + 16.9039i −0.396380 + 1.21993i
\(193\) 3.22018 9.91071i 0.231794 0.713389i −0.765737 0.643154i \(-0.777625\pi\)
0.997531 0.0702342i \(-0.0223747\pi\)
\(194\) −10.5577 + 7.67062i −0.757999 + 0.550718i
\(195\) 4.01727 + 2.91871i 0.287682 + 0.209013i
\(196\) 6.77887 + 20.8632i 0.484205 + 1.49023i
\(197\) −5.76023 −0.410400 −0.205200 0.978720i \(-0.565784\pi\)
−0.205200 + 0.978720i \(0.565784\pi\)
\(198\) 6.53436 + 28.4541i 0.464376 + 2.02214i
\(199\) −16.6746 −1.18203 −0.591015 0.806661i \(-0.701273\pi\)
−0.591015 + 0.806661i \(0.701273\pi\)
\(200\) −1.97963 6.09267i −0.139981 0.430817i
\(201\) −15.2315 11.0664i −1.07435 0.780561i
\(202\) −3.95694 + 2.87489i −0.278409 + 0.202276i
\(203\) −0.535194 + 1.64716i −0.0375633 + 0.115608i
\(204\) −19.1080 + 58.8082i −1.33782 + 4.11740i
\(205\) 3.35981 2.44105i 0.234660 0.170490i
\(206\) −19.0567 13.8455i −1.32774 0.964663i
\(207\) 2.12787 + 6.54891i 0.147897 + 0.455181i
\(208\) 4.51109 0.312788
\(209\) 17.1152 10.2568i 1.18389 0.709481i
\(210\) −43.0802 −2.97281
\(211\) 0.885970 + 2.72674i 0.0609927 + 0.187716i 0.976910 0.213650i \(-0.0685353\pi\)
−0.915917 + 0.401367i \(0.868535\pi\)
\(212\) −23.7518 17.2567i −1.63128 1.18519i
\(213\) −7.49137 + 5.44280i −0.513300 + 0.372934i
\(214\) −0.604232 + 1.85964i −0.0413045 + 0.127122i
\(215\) −3.71072 + 11.4204i −0.253069 + 0.778867i
\(216\) −6.06172 + 4.40410i −0.412448 + 0.299661i
\(217\) 19.9616 + 14.5030i 1.35508 + 0.984526i
\(218\) 5.98231 + 18.4116i 0.405173 + 1.24699i
\(219\) −36.5569 −2.47028
\(220\) −26.1406 2.31759i −1.76240 0.156252i
\(221\) −5.90752 −0.397383
\(222\) −0.441729 1.35950i −0.0296469 0.0912439i
\(223\) 10.5485 + 7.66391i 0.706377 + 0.513213i 0.882003 0.471244i \(-0.156195\pi\)
−0.175626 + 0.984457i \(0.556195\pi\)
\(224\) −2.40800 + 1.74952i −0.160892 + 0.116895i
\(225\) −1.37437 + 4.22987i −0.0916246 + 0.281992i
\(226\) −0.615093 + 1.89306i −0.0409154 + 0.125925i
\(227\) −9.80337 + 7.12256i −0.650672 + 0.472741i −0.863500 0.504349i \(-0.831733\pi\)
0.212828 + 0.977090i \(0.431733\pi\)
\(228\) 50.9452 + 37.0138i 3.37393 + 2.45130i
\(229\) −2.47017 7.60241i −0.163234 0.502382i 0.835668 0.549235i \(-0.185081\pi\)
−0.998902 + 0.0468532i \(0.985081\pi\)
\(230\) −9.22096 −0.608012
\(231\) 11.7141 27.5080i 0.770734 1.80989i
\(232\) −2.53112 −0.166176
\(233\) −1.52277 4.68660i −0.0997599 0.307029i 0.888705 0.458479i \(-0.151606\pi\)
−0.988465 + 0.151450i \(0.951606\pi\)
\(234\) −7.12141 5.17401i −0.465541 0.338235i
\(235\) 17.1379 12.4514i 1.11795 0.812239i
\(236\) 10.6360 32.7343i 0.692346 2.13082i
\(237\) 6.74494 20.7588i 0.438131 1.34843i
\(238\) 41.4636 30.1251i 2.68769 1.95272i
\(239\) −15.2172 11.0559i −0.984317 0.715148i −0.0256481 0.999671i \(-0.508165\pi\)
−0.958669 + 0.284523i \(0.908165\pi\)
\(240\) −6.92208 21.3040i −0.446819 1.37517i
\(241\) 14.7032 0.947118 0.473559 0.880762i \(-0.342969\pi\)
0.473559 + 0.880762i \(0.342969\pi\)
\(242\) 12.7935 23.9268i 0.822395 1.53807i
\(243\) −22.2376 −1.42654
\(244\) −9.73279 29.9545i −0.623078 1.91764i
\(245\) 8.41935 + 6.11701i 0.537892 + 0.390802i
\(246\) −10.9627 + 7.96488i −0.698957 + 0.507822i
\(247\) −1.85909 + 5.72169i −0.118291 + 0.364063i
\(248\) −11.1431 + 34.2949i −0.707586 + 2.17773i
\(249\) 12.9965 9.44251i 0.823620 0.598395i
\(250\) −24.1493 17.5455i −1.52734 1.10967i
\(251\) 6.96454 + 21.4346i 0.439598 + 1.35294i 0.888301 + 0.459262i \(0.151886\pi\)
−0.448703 + 0.893681i \(0.648114\pi\)
\(252\) 51.2636 3.22931
\(253\) 2.50732 5.88786i 0.157634 0.370166i
\(254\) −27.5784 −1.73042
\(255\) 9.06484 + 27.8987i 0.567662 + 1.74708i
\(256\) 26.2904 + 19.1011i 1.64315 + 1.19382i
\(257\) −19.6569 + 14.2816i −1.22616 + 0.890860i −0.996597 0.0824327i \(-0.973731\pi\)
−0.229567 + 0.973293i \(0.573731\pi\)
\(258\) 12.1077 37.2637i 0.753793 2.31994i
\(259\) −0.245771 + 0.756405i −0.0152715 + 0.0470007i
\(260\) 6.40142 4.65090i 0.396999 0.288437i
\(261\) 1.42164 + 1.03288i 0.0879974 + 0.0639339i
\(262\) −2.85395 8.78356i −0.176318 0.542650i
\(263\) −5.32245 −0.328197 −0.164098 0.986444i \(-0.552471\pi\)
−0.164098 + 0.986444i \(0.552471\pi\)
\(264\) 43.5242 + 3.85880i 2.67873 + 0.237492i
\(265\) −13.9279 −0.855581
\(266\) −16.1289 49.6397i −0.988927 3.04361i
\(267\) −20.2948 14.7451i −1.24202 0.902383i
\(268\) −24.2711 + 17.6340i −1.48259 + 1.07717i
\(269\) −2.36933 + 7.29206i −0.144461 + 0.444605i −0.996941 0.0781544i \(-0.975097\pi\)
0.852480 + 0.522759i \(0.175097\pi\)
\(270\) −2.15255 + 6.62488i −0.131000 + 0.403177i
\(271\) −0.761939 + 0.553581i −0.0462845 + 0.0336277i −0.610687 0.791872i \(-0.709107\pi\)
0.564402 + 0.825500i \(0.309107\pi\)
\(272\) 21.5598 + 15.6641i 1.30725 + 0.949775i
\(273\) 2.78569 + 8.57347i 0.168598 + 0.518890i
\(274\) 9.01689 0.544731
\(275\) 3.54546 2.12473i 0.213799 0.128126i
\(276\) 20.1965 1.21569
\(277\) −2.38624 7.34409i −0.143375 0.441264i 0.853423 0.521219i \(-0.174522\pi\)
−0.996798 + 0.0799549i \(0.974522\pi\)
\(278\) 44.2069 + 32.1182i 2.65135 + 1.92632i
\(279\) 20.2535 14.7150i 1.21254 0.880965i
\(280\) −10.8248 + 33.3152i −0.646903 + 1.99096i
\(281\) 7.28468 22.4199i 0.434567 1.33746i −0.458962 0.888456i \(-0.651779\pi\)
0.893529 0.449005i \(-0.148221\pi\)
\(282\) −55.9190 + 40.6276i −3.32993 + 2.41934i
\(283\) −1.83874 1.33592i −0.109302 0.0794124i 0.531792 0.846875i \(-0.321519\pi\)
−0.641094 + 0.767463i \(0.721519\pi\)
\(284\) 4.55965 + 14.0332i 0.270566 + 0.832715i
\(285\) 29.8739 1.76957
\(286\) 1.83100 + 7.97317i 0.108270 + 0.471464i
\(287\) 7.53937 0.445035
\(288\) 0.933223 + 2.87217i 0.0549907 + 0.169244i
\(289\) −14.4804 10.5206i −0.851788 0.618860i
\(290\) −1.90372 + 1.38314i −0.111791 + 0.0812206i
\(291\) 4.19025 12.8963i 0.245637 0.755992i
\(292\) −18.0010 + 55.4014i −1.05343 + 3.24212i
\(293\) 3.19555 2.32170i 0.186686 0.135635i −0.490517 0.871432i \(-0.663192\pi\)
0.677203 + 0.735797i \(0.263192\pi\)
\(294\) −27.4715 19.9592i −1.60217 1.16404i
\(295\) −5.04574 15.5292i −0.293774 0.904145i
\(296\) −1.16234 −0.0675595
\(297\) −3.64487 3.17587i −0.211497 0.184283i
\(298\) 35.8591 2.07726
\(299\) 0.596254 + 1.83508i 0.0344823 + 0.106126i
\(300\) 10.5534 + 7.66749i 0.609301 + 0.442683i
\(301\) −17.6365 + 12.8136i −1.01655 + 0.738566i
\(302\) −12.4565 + 38.3373i −0.716793 + 2.20606i
\(303\) 1.57047 4.83341i 0.0902212 0.277672i
\(304\) 21.9562 15.9521i 1.25928 0.914917i
\(305\) −12.0881 8.78253i −0.692164 0.502886i
\(306\) −16.0692 49.4560i −0.918618 2.82721i
\(307\) 32.9418 1.88009 0.940044 0.341054i \(-0.110784\pi\)
0.940044 + 0.341054i \(0.110784\pi\)
\(308\) −35.9198 31.2979i −2.04672 1.78336i
\(309\) 24.4758 1.39238
\(310\) 10.3595 + 31.8832i 0.588379 + 1.81085i
\(311\) −17.9252 13.0234i −1.01645 0.738492i −0.0508951 0.998704i \(-0.516207\pi\)
−0.965551 + 0.260212i \(0.916207\pi\)
\(312\) −10.6584 + 7.74378i −0.603413 + 0.438405i
\(313\) 6.79495 20.9127i 0.384073 1.18206i −0.553077 0.833130i \(-0.686546\pi\)
0.937150 0.348926i \(-0.113454\pi\)
\(314\) −3.24554 + 9.98874i −0.183156 + 0.563697i
\(315\) 19.6749 14.2947i 1.10856 0.805413i
\(316\) −28.1384 20.4437i −1.58291 1.15005i
\(317\) −0.571375 1.75851i −0.0320916 0.0987678i 0.933728 0.357984i \(-0.116536\pi\)
−0.965819 + 0.259216i \(0.916536\pi\)
\(318\) 45.4451 2.54844
\(319\) −0.365522 1.59168i −0.0204653 0.0891170i
\(320\) 13.4360 0.751098
\(321\) −0.627841 1.93230i −0.0350427 0.107850i
\(322\) −13.5429 9.83949i −0.754716 0.548333i
\(323\) −28.7529 + 20.8902i −1.59985 + 1.16236i
\(324\) −8.79679 + 27.0737i −0.488711 + 1.50410i
\(325\) −0.385115 + 1.18526i −0.0213623 + 0.0657464i
\(326\) −5.06578 + 3.68051i −0.280568 + 0.203844i
\(327\) −16.2738 11.8236i −0.899945 0.653848i
\(328\) 3.40488 + 10.4791i 0.188003 + 0.578613i
\(329\) 38.4571 2.12021
\(330\) 34.8443 20.8816i 1.91812 1.14949i
\(331\) −26.6418 −1.46437 −0.732183 0.681108i \(-0.761498\pi\)
−0.732183 + 0.681108i \(0.761498\pi\)
\(332\) −7.91037 24.3456i −0.434138 1.33614i
\(333\) 0.652844 + 0.474319i 0.0357756 + 0.0259925i
\(334\) 32.3720 23.5196i 1.77132 1.28694i
\(335\) −4.39805 + 13.5358i −0.240291 + 0.739540i
\(336\) 12.5665 38.6757i 0.685559 2.10993i
\(337\) −12.3999 + 9.00906i −0.675466 + 0.490755i −0.871851 0.489772i \(-0.837080\pi\)
0.196384 + 0.980527i \(0.437080\pi\)
\(338\) −1.99550 1.44982i −0.108541 0.0788597i
\(339\) −0.639126 1.96703i −0.0347126 0.106834i
\(340\) 46.7437 2.53504
\(341\) −23.1753 2.05469i −1.25501 0.111268i
\(342\) −52.9574 −2.86361
\(343\) −1.77012 5.44787i −0.0955775 0.294157i
\(344\) −25.7748 18.7265i −1.38968 1.00966i
\(345\) 7.75139 5.63172i 0.417321 0.303201i
\(346\) −1.24587 + 3.83438i −0.0669782 + 0.206138i
\(347\) 4.09539 12.6043i 0.219852 0.676635i −0.778921 0.627122i \(-0.784233\pi\)
0.998773 0.0495135i \(-0.0157671\pi\)
\(348\) 4.16969 3.02946i 0.223519 0.162396i
\(349\) 28.0038 + 20.3459i 1.49901 + 1.08909i 0.970775 + 0.239992i \(0.0771449\pi\)
0.528232 + 0.849100i \(0.322855\pi\)
\(350\) −3.34114 10.2830i −0.178591 0.549648i
\(351\) 1.45762 0.0778021
\(352\) 1.09964 2.58225i 0.0586110 0.137634i
\(353\) −14.9660 −0.796559 −0.398279 0.917264i \(-0.630393\pi\)
−0.398279 + 0.917264i \(0.630393\pi\)
\(354\) 16.4637 + 50.6701i 0.875037 + 2.69309i
\(355\) 5.66308 + 4.11447i 0.300565 + 0.218373i
\(356\) −32.3394 + 23.4959i −1.71398 + 1.24528i
\(357\) −16.4565 + 50.6479i −0.870970 + 2.68057i
\(358\) −4.30404 + 13.2465i −0.227475 + 0.700097i
\(359\) −22.2062 + 16.1337i −1.17200 + 0.851505i −0.991247 0.132024i \(-0.957852\pi\)
−0.180750 + 0.983529i \(0.557852\pi\)
\(360\) 28.7539 + 20.8909i 1.51546 + 1.10105i
\(361\) 5.31324 + 16.3525i 0.279644 + 0.860657i
\(362\) −1.13412 −0.0596081
\(363\) 3.85880 + 27.9271i 0.202534 + 1.46580i
\(364\) 14.3647 0.752914
\(365\) 8.53971 + 26.2825i 0.446989 + 1.37569i
\(366\) 39.4423 + 28.6565i 2.06168 + 1.49790i
\(367\) 9.22041 6.69902i 0.481302 0.349686i −0.320528 0.947239i \(-0.603860\pi\)
0.801829 + 0.597553i \(0.203860\pi\)
\(368\) 2.68976 8.27823i 0.140213 0.431532i
\(369\) 2.36386 7.27520i 0.123057 0.378732i
\(370\) −0.874225 + 0.635162i −0.0454488 + 0.0330205i
\(371\) −20.4559 14.8621i −1.06202 0.771602i
\(372\) −22.6902 69.8332i −1.17643 3.62068i
\(373\) 13.8159 0.715361 0.357681 0.933844i \(-0.383568\pi\)
0.357681 + 0.933844i \(0.383568\pi\)
\(374\) −18.9348 + 44.4639i −0.979094 + 2.29917i
\(375\) 31.0165 1.60168
\(376\) 17.3677 + 53.4523i 0.895672 + 2.75659i
\(377\) 0.398361 + 0.289426i 0.0205166 + 0.0149062i
\(378\) −10.2307 + 7.43306i −0.526212 + 0.382315i
\(379\) −4.42005 + 13.6035i −0.227043 + 0.698766i 0.771035 + 0.636793i \(0.219739\pi\)
−0.998078 + 0.0619734i \(0.980261\pi\)
\(380\) 14.7102 45.2734i 0.754619 2.32248i
\(381\) 23.1832 16.8436i 1.18771 0.862922i
\(382\) 15.2195 + 11.0576i 0.778698 + 0.565758i
\(383\) −4.76327 14.6598i −0.243392 0.749083i −0.995897 0.0904965i \(-0.971155\pi\)
0.752505 0.658587i \(-0.228845\pi\)
\(384\) −48.1781 −2.45858
\(385\) −22.5132 1.99599i −1.14738 0.101725i
\(386\) 25.7036 1.30828
\(387\) 6.83502 + 21.0360i 0.347444 + 1.06932i
\(388\) −17.4808 12.7005i −0.887452 0.644772i
\(389\) 15.0230 10.9149i 0.761697 0.553405i −0.137733 0.990469i \(-0.543982\pi\)
0.899430 + 0.437064i \(0.143982\pi\)
\(390\) −3.78486 + 11.6486i −0.191654 + 0.589850i
\(391\) −3.52238 + 10.8408i −0.178135 + 0.548242i
\(392\) −22.3378 + 16.2293i −1.12823 + 0.819706i
\(393\) 7.76368 + 5.64064i 0.391626 + 0.284533i
\(394\) −4.39053 13.5127i −0.221192 0.680758i
\(395\) −16.5001 −0.830212
\(396\) −41.4633 + 24.8482i −2.08361 + 1.24867i
\(397\) 16.7962 0.842978 0.421489 0.906834i \(-0.361508\pi\)
0.421489 + 0.906834i \(0.361508\pi\)
\(398\) −12.7096 39.1161i −0.637075 1.96072i
\(399\) 43.8759 + 31.8777i 2.19654 + 1.59588i
\(400\) 4.54828 3.30452i 0.227414 0.165226i
\(401\) 6.90539 21.2526i 0.344839 1.06130i −0.616832 0.787095i \(-0.711584\pi\)
0.961670 0.274209i \(-0.0884160\pi\)
\(402\) 14.3504 44.1659i 0.715732 2.20280i
\(403\) 5.67527 4.12333i 0.282705 0.205397i
\(404\) −6.55165 4.76006i −0.325957 0.236822i
\(405\) 4.17321 + 12.8438i 0.207369 + 0.638215i
\(406\) −4.27193 −0.212012
\(407\) −0.167855 0.730929i −0.00832024 0.0362308i
\(408\) −77.8286 −3.85309
\(409\) 2.38794 + 7.34932i 0.118076 + 0.363400i 0.992576 0.121625i \(-0.0388104\pi\)
−0.874500 + 0.485025i \(0.838810\pi\)
\(410\) 8.28724 + 6.02103i 0.409278 + 0.297358i
\(411\) −7.57985 + 5.50708i −0.373886 + 0.271644i
\(412\) 12.0521 37.0927i 0.593767 1.82743i
\(413\) 9.16015 28.1920i 0.450741 1.38724i
\(414\) −13.7409 + 9.98335i −0.675328 + 0.490655i
\(415\) −9.82467 7.13804i −0.482274 0.350393i
\(416\) 0.261500 + 0.804815i 0.0128211 + 0.0394593i
\(417\) −56.7777 −2.78042
\(418\) 37.1065 + 32.3319i 1.81494 + 1.58141i
\(419\) 30.0056 1.46587 0.732934 0.680300i \(-0.238150\pi\)
0.732934 + 0.680300i \(0.238150\pi\)
\(420\) −22.0420 67.8383i −1.07554 3.31017i
\(421\) −7.85903 5.70992i −0.383026 0.278284i 0.379566 0.925165i \(-0.376073\pi\)
−0.762592 + 0.646880i \(0.776073\pi\)
\(422\) −5.72123 + 4.15672i −0.278505 + 0.202346i
\(423\) 12.0576 37.1096i 0.586263 1.80433i
\(424\) 11.4190 35.1441i 0.554556 1.70675i
\(425\) −5.95621 + 4.32744i −0.288919 + 0.209912i
\(426\) −18.4780 13.4251i −0.895264 0.650448i
\(427\) −8.38225 25.7979i −0.405646 1.24845i
\(428\) −3.23753 −0.156492
\(429\) −6.40882 5.58418i −0.309421 0.269607i
\(430\) −29.6190 −1.42836
\(431\) 1.78534 + 5.49472i 0.0859969 + 0.264671i 0.984803 0.173675i \(-0.0555643\pi\)
−0.898806 + 0.438347i \(0.855564\pi\)
\(432\) −5.31966 3.86496i −0.255942 0.185953i
\(433\) 9.89470 7.18892i 0.475509 0.345477i −0.324075 0.946031i \(-0.605053\pi\)
0.799584 + 0.600554i \(0.205053\pi\)
\(434\) −18.8068 + 57.8815i −0.902757 + 2.77840i
\(435\) 0.755570 2.32540i 0.0362268 0.111495i
\(436\) −25.9320 + 18.8407i −1.24192 + 0.902305i
\(437\) 9.39129 + 6.82317i 0.449246 + 0.326397i
\(438\) −27.8642 85.7571i −1.33140 4.09763i
\(439\) 0.393039 0.0187587 0.00937937 0.999956i \(-0.497014\pi\)
0.00937937 + 0.999956i \(0.497014\pi\)
\(440\) −7.39300 32.1931i −0.352447 1.53474i
\(441\) 19.1691 0.912815
\(442\) −4.50279 13.8582i −0.214176 0.659166i
\(443\) −6.91106 5.02118i −0.328354 0.238563i 0.411378 0.911465i \(-0.365048\pi\)
−0.739732 + 0.672902i \(0.765048\pi\)
\(444\) 1.91480 1.39118i 0.0908723 0.0660226i
\(445\) −5.86006 + 18.0354i −0.277793 + 0.854960i
\(446\) −9.93822 + 30.5867i −0.470588 + 1.44832i
\(447\) −30.1441 + 21.9010i −1.42577 + 1.03588i
\(448\) 19.7336 + 14.3373i 0.932325 + 0.677374i
\(449\) 5.73668 + 17.6557i 0.270731 + 0.833224i 0.990317 + 0.138821i \(0.0443314\pi\)
−0.719587 + 0.694403i \(0.755669\pi\)
\(450\) −10.9702 −0.517142
\(451\) −6.09803 + 3.65444i −0.287145 + 0.172081i
\(452\) −3.29572 −0.155017
\(453\) −12.9432 39.8352i −0.608127 1.87162i
\(454\) −24.1808 17.5684i −1.13486 0.824524i
\(455\) 5.51315 4.00554i 0.258460 0.187782i
\(456\) −24.4926 + 75.3805i −1.14697 + 3.53002i
\(457\) −0.868675 + 2.67351i −0.0406349 + 0.125061i −0.969316 0.245818i \(-0.920944\pi\)
0.928681 + 0.370879i \(0.120944\pi\)
\(458\) 15.9514 11.5893i 0.745358 0.541534i
\(459\) 6.96638 + 5.06137i 0.325163 + 0.236245i
\(460\) −4.71792 14.5203i −0.219974 0.677010i
\(461\) 31.3380 1.45956 0.729778 0.683684i \(-0.239623\pi\)
0.729778 + 0.683684i \(0.239623\pi\)
\(462\) 73.4584 + 6.51272i 3.41759 + 0.302999i
\(463\) −30.6432 −1.42411 −0.712055 0.702123i \(-0.752235\pi\)
−0.712055 + 0.702123i \(0.752235\pi\)
\(464\) −0.686410 2.11255i −0.0318658 0.0980727i
\(465\) −28.1812 20.4748i −1.30687 0.949498i
\(466\) 9.83341 7.14439i 0.455524 0.330957i
\(467\) 3.60391 11.0917i 0.166769 0.513263i −0.832393 0.554186i \(-0.813030\pi\)
0.999162 + 0.0409228i \(0.0130298\pi\)
\(468\) 4.50383 13.8614i 0.208190 0.640742i
\(469\) −20.9032 + 15.1871i −0.965220 + 0.701274i
\(470\) 42.2719 + 30.7123i 1.94986 + 1.41665i
\(471\) −3.37235 10.3790i −0.155390 0.478240i
\(472\) 43.3216 1.99404
\(473\) 8.05386 18.9126i 0.370317 0.869604i
\(474\) 53.8382 2.47287
\(475\) 2.31691 + 7.13070i 0.106307 + 0.327179i
\(476\) 68.6528 + 49.8792i 3.14670 + 2.28621i
\(477\) −20.7550 + 15.0794i −0.950306 + 0.690438i
\(478\) 14.3368 44.1243i 0.655752 2.01820i
\(479\) −8.62988 + 26.5600i −0.394309 + 1.21356i 0.535189 + 0.844732i \(0.320240\pi\)
−0.929498 + 0.368827i \(0.879760\pi\)
\(480\) 3.39954 2.46991i 0.155167 0.112736i
\(481\) 0.182935 + 0.132910i 0.00834111 + 0.00606017i
\(482\) 11.2070 + 34.4916i 0.510466 + 1.57105i
\(483\) 17.3940 0.791455
\(484\) 44.2233 + 7.90369i 2.01015 + 0.359259i
\(485\) −10.2506 −0.465456
\(486\) −16.9498 52.1662i −0.768859 2.36630i
\(487\) −12.9501 9.40877i −0.586823 0.426352i 0.254354 0.967111i \(-0.418137\pi\)
−0.841177 + 0.540759i \(0.818137\pi\)
\(488\) 32.0716 23.3014i 1.45181 1.05480i
\(489\) 2.01056 6.18787i 0.0909207 0.279825i
\(490\) −7.93228 + 24.4130i −0.358344 + 1.10287i
\(491\) 22.7520 16.5303i 1.02678 0.746002i 0.0591212 0.998251i \(-0.481170\pi\)
0.967662 + 0.252249i \(0.0811702\pi\)
\(492\) −18.1514 13.1878i −0.818328 0.594550i
\(493\) 0.898890 + 2.76650i 0.0404840 + 0.124597i
\(494\) −14.8393 −0.667651
\(495\) −8.98475 + 21.0986i −0.403834 + 0.948312i
\(496\) −31.6454 −1.42092
\(497\) 3.92695 + 12.0859i 0.176148 + 0.542127i
\(498\) 32.0569 + 23.2907i 1.43650 + 1.04368i
\(499\) 2.16106 1.57010i 0.0967425 0.0702875i −0.538362 0.842713i \(-0.680957\pi\)
0.635105 + 0.772426i \(0.280957\pi\)
\(500\) 15.2729 47.0051i 0.683024 2.10213i
\(501\) −12.8481 + 39.5425i −0.574012 + 1.76663i
\(502\) −44.9741 + 32.6756i −2.00729 + 1.45838i
\(503\) 18.7295 + 13.6078i 0.835107 + 0.606741i 0.921000 0.389563i \(-0.127374\pi\)
−0.0858922 + 0.996304i \(0.527374\pi\)
\(504\) 19.9388 + 61.3653i 0.888145 + 2.73343i
\(505\) −3.84184 −0.170960
\(506\) 15.7232 + 1.39400i 0.698980 + 0.0619707i
\(507\) 2.56295 0.113825
\(508\) −14.1105 43.4277i −0.626054 1.92679i
\(509\) 1.63946 + 1.19114i 0.0726677 + 0.0527962i 0.623526 0.781803i \(-0.285700\pi\)
−0.550858 + 0.834599i \(0.685700\pi\)
\(510\) −58.5370 + 42.5296i −2.59206 + 1.88324i
\(511\) −15.5032 + 47.7138i −0.685820 + 2.11074i
\(512\) −13.1517 + 40.4768i −0.581229 + 1.78884i
\(513\) 7.09448 5.15444i 0.313229 0.227574i
\(514\) −48.4853 35.2266i −2.13859 1.55378i
\(515\) −5.71755 17.5968i −0.251946 0.775409i
\(516\) 64.8740 2.85592
\(517\) −31.1051 + 18.6407i −1.36800 + 0.819817i
\(518\) −1.96175 −0.0861942
\(519\) −1.29455 3.98420i −0.0568242 0.174887i
\(520\) 8.05719 + 5.85389i 0.353331 + 0.256710i
\(521\) 11.1244 8.08238i 0.487370 0.354095i −0.316802 0.948492i \(-0.602609\pi\)
0.804172 + 0.594396i \(0.202609\pi\)
\(522\) −1.33940 + 4.12225i −0.0586239 + 0.180426i
\(523\) −2.98708 + 9.19328i −0.130616 + 0.401994i −0.994882 0.101040i \(-0.967783\pi\)
0.864267 + 0.503034i \(0.167783\pi\)
\(524\) 12.3712 8.98823i 0.540440 0.392653i
\(525\) 9.08899 + 6.60354i 0.396676 + 0.288202i
\(526\) −4.05685 12.4857i −0.176887 0.544403i
\(527\) 41.4413 1.80521
\(528\) 8.58256 + 37.3731i 0.373508 + 1.62645i
\(529\) −19.2770 −0.838128
\(530\) −10.6160 32.6727i −0.461130 1.41921i
\(531\) −24.3322 17.6784i −1.05593 0.767176i
\(532\) 69.9153 50.7964i 3.03121 2.20230i
\(533\) 0.662381 2.03860i 0.0286909 0.0883015i
\(534\) 19.1208 58.8476i 0.827436 2.54659i
\(535\) −1.24256 + 0.902771i −0.0537205 + 0.0390302i
\(536\) −30.5490 22.1951i −1.31952 0.958684i
\(537\) −4.47221 13.7640i −0.192990 0.593962i
\(538\) −18.9121 −0.815356
\(539\) −13.4315 11.7033i −0.578538 0.504095i
\(540\) −11.5336 −0.496325
\(541\) 10.7047 + 32.9458i 0.460233 + 1.41645i 0.864880 + 0.501978i \(0.167394\pi\)
−0.404647 + 0.914473i \(0.632606\pi\)
\(542\) −1.87938 1.36545i −0.0807264 0.0586511i
\(543\) 0.953374 0.692666i 0.0409132 0.0297252i
\(544\) −1.54482 + 4.75446i −0.0662335 + 0.203846i
\(545\) −4.69901 + 14.4621i −0.201283 + 0.619486i
\(546\) −17.9888 + 13.0696i −0.769851 + 0.559329i
\(547\) 16.4451 + 11.9481i 0.703144 + 0.510864i 0.880955 0.473201i \(-0.156902\pi\)
−0.177811 + 0.984065i \(0.556902\pi\)
\(548\) 4.61350 + 14.1989i 0.197079 + 0.606547i
\(549\) −27.5221 −1.17462
\(550\) 7.68670 + 6.69763i 0.327762 + 0.285588i
\(551\) 2.96236 0.126201
\(552\) 7.85536 + 24.1763i 0.334346 + 1.02901i
\(553\) −24.2338 17.6069i −1.03053 0.748722i
\(554\) 15.4093 11.1955i 0.654680 0.475653i
\(555\) 0.346972 1.06787i 0.0147281 0.0453285i
\(556\) −27.9580 + 86.0459i −1.18568 + 3.64916i
\(557\) 14.9478 10.8602i 0.633359 0.460162i −0.224203 0.974542i \(-0.571978\pi\)
0.857562 + 0.514380i \(0.171978\pi\)
\(558\) 49.9568 + 36.2957i 2.11484 + 1.53652i
\(559\) 1.91525 + 5.89455i 0.0810066 + 0.249313i
\(560\) −30.7414 −1.29906
\(561\) −11.2393 48.9420i −0.474525 2.06633i
\(562\) 58.1464 2.45276
\(563\) 4.83122 + 14.8690i 0.203612 + 0.626652i 0.999768 + 0.0215604i \(0.00686343\pi\)
−0.796156 + 0.605091i \(0.793137\pi\)
\(564\) −92.5873 67.2686i −3.89863 2.83252i
\(565\) −1.26489 + 0.918998i −0.0532144 + 0.0386625i
\(566\) 1.73237 5.33168i 0.0728169 0.224107i
\(567\) −7.57614 + 23.3169i −0.318168 + 0.979220i
\(568\) −15.0250 + 10.9163i −0.630435 + 0.458038i
\(569\) 27.0846 + 19.6781i 1.13545 + 0.824951i 0.986478 0.163891i \(-0.0524046\pi\)
0.148969 + 0.988842i \(0.452405\pi\)
\(570\) 22.7703 + 70.0797i 0.953742 + 2.93532i
\(571\) −35.1015 −1.46895 −0.734476 0.678635i \(-0.762572\pi\)
−0.734476 + 0.678635i \(0.762572\pi\)
\(572\) −11.6185 + 6.96277i −0.485795 + 0.291128i
\(573\) −19.5474 −0.816605
\(574\) 5.74661 + 17.6863i 0.239859 + 0.738210i
\(575\) 1.94543 + 1.41343i 0.0811298 + 0.0589443i
\(576\) 20.0221 14.5469i 0.834255 0.606122i
\(577\) 9.67856 29.7875i 0.402924 1.24007i −0.519693 0.854353i \(-0.673954\pi\)
0.922617 0.385719i \(-0.126046\pi\)
\(578\) 13.6427 41.9879i 0.567461 1.74646i
\(579\) −21.6071 + 15.6985i −0.897961 + 0.652407i
\(580\) −3.15207 2.29011i −0.130883 0.0950917i
\(581\) −6.81272 20.9674i −0.282639 0.869874i
\(582\) 33.4466 1.38641
\(583\) 23.7491 + 2.10557i 0.983589 + 0.0872037i
\(584\) −73.3199 −3.03400
\(585\) −2.13662 6.57585i −0.0883385 0.271878i
\(586\) 7.88206 + 5.72665i 0.325605 + 0.236566i
\(587\) 29.6215 21.5213i 1.22261 0.888280i 0.226298 0.974058i \(-0.427338\pi\)
0.996314 + 0.0857787i \(0.0273378\pi\)
\(588\) 17.3739 53.4714i 0.716489 2.20512i
\(589\) 13.0416 40.1378i 0.537368 1.65385i
\(590\) 32.5833 23.6732i 1.34143 0.974608i
\(591\) 11.9437 + 8.67759i 0.491297 + 0.356948i
\(592\) −0.315212 0.970122i −0.0129551 0.0398718i
\(593\) −31.4710 −1.29236 −0.646179 0.763186i \(-0.723634\pi\)
−0.646179 + 0.763186i \(0.723634\pi\)
\(594\) 4.67197 10.9710i 0.191693 0.450147i
\(595\) 40.2575 1.65040
\(596\) 18.3473 + 56.4673i 0.751536 + 2.31299i
\(597\) 34.5743 + 25.1197i 1.41503 + 1.02808i
\(598\) −3.85036 + 2.79745i −0.157453 + 0.114396i
\(599\) −14.0939 + 43.3767i −0.575863 + 1.77232i 0.0573593 + 0.998354i \(0.481732\pi\)
−0.633222 + 0.773970i \(0.718268\pi\)
\(600\) −5.07369 + 15.6152i −0.207133 + 0.637489i
\(601\) −0.886401 + 0.644008i −0.0361571 + 0.0262696i −0.605717 0.795680i \(-0.707114\pi\)
0.569560 + 0.821950i \(0.307114\pi\)
\(602\) −43.5017 31.6058i −1.77300 1.28816i
\(603\) 8.10105 + 24.9325i 0.329900 + 1.01533i
\(604\) −66.7431 −2.71574
\(605\) 19.1768 9.29808i 0.779647 0.378021i
\(606\) 12.5355 0.509221
\(607\) −0.481829 1.48292i −0.0195568 0.0601898i 0.940802 0.338957i \(-0.110074\pi\)
−0.960359 + 0.278767i \(0.910074\pi\)
\(608\) 4.11875 + 2.99245i 0.167038 + 0.121360i
\(609\) 3.59110 2.60909i 0.145519 0.105725i
\(610\) 11.3888 35.0511i 0.461119 1.41918i
\(611\) 3.37870 10.3986i 0.136687 0.420681i
\(612\) 69.6566 50.6085i 2.81570 2.04573i
\(613\) −13.8208 10.0414i −0.558215 0.405567i 0.272590 0.962130i \(-0.412120\pi\)
−0.830805 + 0.556563i \(0.812120\pi\)
\(614\) 25.1087 + 77.2767i 1.01331 + 3.11863i
\(615\) −10.6438 −0.429201
\(616\) 23.4944 55.1711i 0.946615 2.22291i
\(617\) −30.7086 −1.23628 −0.618142 0.786067i \(-0.712114\pi\)
−0.618142 + 0.786067i \(0.712114\pi\)
\(618\) 18.6558 + 57.4166i 0.750446 + 2.30963i
\(619\) −30.2921 22.0085i −1.21754 0.884598i −0.221650 0.975126i \(-0.571144\pi\)
−0.995894 + 0.0905285i \(0.971144\pi\)
\(620\) −44.9061 + 32.6262i −1.80347 + 1.31030i
\(621\) 0.869113 2.67486i 0.0348763 0.107338i
\(622\) 16.8882 51.9766i 0.677157 2.08407i
\(623\) −27.8519 + 20.2356i −1.11586 + 0.810721i
\(624\) −9.35362 6.79580i −0.374445 0.272050i
\(625\) −5.31990 16.3730i −0.212796 0.654919i
\(626\) 54.2374 2.16776
\(627\) −50.9396 4.51623i −2.03433 0.180361i
\(628\) −17.3899 −0.693931
\(629\) 0.412787 + 1.27043i 0.0164589 + 0.0506553i
\(630\) 48.5297 + 35.2589i 1.93347 + 1.40475i
\(631\) −33.6226 + 24.4282i −1.33849 + 0.972472i −0.338995 + 0.940788i \(0.610087\pi\)
−0.999498 + 0.0316841i \(0.989913\pi\)
\(632\) 13.5279 41.6347i 0.538112 1.65614i
\(633\) 2.27070 6.98850i 0.0902522 0.277768i
\(634\) 3.68970 2.68072i 0.146537 0.106465i
\(635\) −17.5253 12.7328i −0.695469 0.505288i
\(636\) 23.2520 + 71.5624i 0.922004 + 2.83764i
\(637\) 5.37141 0.212823
\(638\) 3.45524 2.07066i 0.136794 0.0819784i
\(639\) 12.8937 0.510066
\(640\) 11.2544 + 34.6376i 0.444871 + 1.36917i
\(641\) 6.25865 + 4.54718i 0.247202 + 0.179603i 0.704486 0.709718i \(-0.251178\pi\)
−0.457284 + 0.889321i \(0.651178\pi\)
\(642\) 4.05434 2.94565i 0.160012 0.116255i
\(643\) −0.788549 + 2.42690i −0.0310973 + 0.0957078i −0.965401 0.260772i \(-0.916023\pi\)
0.934303 + 0.356479i \(0.116023\pi\)
\(644\) 8.56501 26.3604i 0.337509 1.03874i
\(645\) 24.8986 18.0899i 0.980380 0.712288i
\(646\) −70.9211 51.5272i −2.79036 2.02731i
\(647\) −3.42857 10.5521i −0.134791 0.414845i 0.860766 0.509000i \(-0.169985\pi\)
−0.995557 + 0.0941558i \(0.969985\pi\)
\(648\) −35.8302 −1.40754
\(649\) 6.25612 + 27.2425i 0.245574 + 1.06936i
\(650\) −3.07399 −0.120572
\(651\) −19.5417 60.1431i −0.765898 2.35719i
\(652\) −8.38761 6.09395i −0.328484 0.238658i
\(653\) 18.2463 13.2567i 0.714033 0.518775i −0.170439 0.985368i \(-0.554519\pi\)
0.884472 + 0.466593i \(0.154519\pi\)
\(654\) 15.3324 47.1882i 0.599543 1.84520i
\(655\) 2.24173 6.89935i 0.0875918 0.269580i
\(656\) −7.82284 + 5.68363i −0.305431 + 0.221908i
\(657\) 41.1812 + 29.9199i 1.60663 + 1.16729i
\(658\) 29.3125 + 90.2147i 1.14272 + 3.51694i
\(659\) −12.2913 −0.478800 −0.239400 0.970921i \(-0.576951\pi\)
−0.239400 + 0.970921i \(0.576951\pi\)
\(660\) 50.7103 + 44.1853i 1.97390 + 1.71991i
\(661\) 25.4759 0.990899 0.495449 0.868637i \(-0.335003\pi\)
0.495449 + 0.868637i \(0.335003\pi\)
\(662\) −20.3068 62.4978i −0.789244 2.42904i
\(663\) 12.2491 + 8.89947i 0.475715 + 0.345627i
\(664\) 26.0663 18.9383i 1.01157 0.734948i
\(665\) 12.6690 38.9912i 0.491283 1.51201i
\(666\) −0.615077 + 1.89301i −0.0238337 + 0.0733527i
\(667\) 0.768646 0.558454i 0.0297621 0.0216234i
\(668\) 53.5995 + 38.9423i 2.07383 + 1.50672i
\(669\) −10.3265 31.7818i −0.399247 1.22876i
\(670\) −35.1053 −1.35624
\(671\) 19.2844 + 16.8030i 0.744466 + 0.648673i
\(672\) 7.62852 0.294276
\(673\) −4.51463 13.8946i −0.174026 0.535597i 0.825562 0.564312i \(-0.190858\pi\)
−0.999588 + 0.0287149i \(0.990858\pi\)
\(674\) −30.5854 22.2216i −1.17810 0.855942i
\(675\) 1.46964 1.06775i 0.0565663 0.0410978i
\(676\) 1.26203 3.88412i 0.0485395 0.149389i
\(677\) 7.70688 23.7193i 0.296199 0.911608i −0.686616 0.727020i \(-0.740905\pi\)
0.982816 0.184588i \(-0.0590952\pi\)
\(678\) 4.12721 2.99859i 0.158505 0.115160i
\(679\) −15.0551 10.9382i −0.577763 0.419769i
\(680\) 18.1808 + 55.9548i 0.697202 + 2.14577i
\(681\) 31.0569 1.19010
\(682\) −12.8445 55.9320i −0.491843 2.14175i
\(683\) 21.1675 0.809952 0.404976 0.914327i \(-0.367280\pi\)
0.404976 + 0.914327i \(0.367280\pi\)
\(684\) −27.0957 83.3920i −1.03603 3.18857i
\(685\) 5.72997 + 4.16306i 0.218931 + 0.159063i
\(686\) 11.4307 8.30489i 0.436426 0.317082i
\(687\) −6.33094 + 19.4846i −0.241540 + 0.743385i
\(688\) 8.63988 26.5908i 0.329393 1.01377i
\(689\) −5.81580 + 4.22543i −0.221564 + 0.160976i
\(690\) 19.1194 + 13.8911i 0.727864 + 0.528824i
\(691\) −13.2518 40.7848i −0.504122 1.55153i −0.802242 0.596998i \(-0.796360\pi\)
0.298121 0.954528i \(-0.403640\pi\)
\(692\) −6.67545 −0.253763
\(693\) −35.7098 + 21.4002i −1.35650 + 0.812927i
\(694\) 32.6895 1.24087
\(695\) 13.2633 + 40.8203i 0.503106 + 1.54840i
\(696\) 5.24821 + 3.81305i 0.198933 + 0.144533i
\(697\) 10.2444 7.44301i 0.388035 0.281924i
\(698\) −26.3837 + 81.2007i −0.998638 + 3.07349i
\(699\) −3.90278 + 12.0115i −0.147617 + 0.454318i
\(700\) 14.4831 10.5226i 0.547409 0.397716i
\(701\) 5.81876 + 4.22758i 0.219771 + 0.159673i 0.692224 0.721683i \(-0.256631\pi\)
−0.472452 + 0.881356i \(0.656631\pi\)
\(702\) 1.11102 + 3.41937i 0.0419327 + 0.129056i
\(703\) 1.36037 0.0513073
\(704\) −22.9105 2.03122i −0.863473 0.0765544i
\(705\) −54.2925 −2.04477
\(706\) −11.4073 35.1080i −0.429319 1.32131i
\(707\) −5.64254 4.09954i −0.212209 0.154179i
\(708\) −71.3666 + 51.8509i −2.68212 + 1.94867i
\(709\) 7.26263 22.3521i 0.272754 0.839450i −0.717051 0.697020i \(-0.754509\pi\)
0.989805 0.142429i \(-0.0454913\pi\)
\(710\) −5.33547 + 16.4209i −0.200237 + 0.616265i
\(711\) −24.5882 + 17.8643i −0.922128 + 0.669965i
\(712\) −40.7042 29.5733i −1.52545 1.10831i
\(713\) −4.18274 12.8731i −0.156645 0.482103i
\(714\) −131.356 −4.91588
\(715\) −2.51763 + 5.91208i −0.0941542 + 0.221099i
\(716\) −23.0614 −0.861844
\(717\) 14.8970 + 45.8483i 0.556339 + 1.71224i
\(718\) −54.7732 39.7951i −2.04412 1.48514i
\(719\) 32.4137 23.5499i 1.20883 0.878265i 0.213704 0.976898i \(-0.431447\pi\)
0.995124 + 0.0986338i \(0.0314472\pi\)
\(720\) −9.63850 + 29.6643i −0.359206 + 1.10552i
\(721\) 10.3798 31.9456i 0.386563 1.18972i
\(722\) −34.3107 + 24.9282i −1.27691 + 0.927731i
\(723\) −30.4867 22.1499i −1.13381 0.823764i
\(724\) −0.580275 1.78590i −0.0215657 0.0663725i
\(725\) 0.613659 0.0227907
\(726\) −62.5718 + 30.3387i −2.32226 + 1.12597i
\(727\) −4.31909 −0.160186 −0.0800931 0.996787i \(-0.525522\pi\)
−0.0800931 + 0.996787i \(0.525522\pi\)
\(728\) 5.58709 + 17.1953i 0.207071 + 0.637300i
\(729\) 29.1916 + 21.2089i 1.08117 + 0.785516i
\(730\) −55.1459 + 40.0658i −2.04104 + 1.48290i
\(731\) −11.3144 + 34.8221i −0.418478 + 1.28794i
\(732\) −24.9447 + 76.7718i −0.921982 + 2.83757i
\(733\) 20.8882 15.1761i 0.771522 0.560544i −0.130900 0.991396i \(-0.541787\pi\)
0.902423 + 0.430852i \(0.141787\pi\)
\(734\) 22.7429 + 16.5237i 0.839455 + 0.609899i
\(735\) −8.24221 25.3669i −0.304019 0.935673i
\(736\) 1.63282 0.0601867
\(737\) 9.54566 22.4158i 0.351619 0.825695i
\(738\) 18.8683 0.694553
\(739\) 12.5985 + 38.7742i 0.463443 + 1.42633i 0.860930 + 0.508723i \(0.169882\pi\)
−0.397487 + 0.917608i \(0.630118\pi\)
\(740\) −1.44749 1.05166i −0.0532107 0.0386598i
\(741\) 12.4743 9.06312i 0.458255 0.332942i
\(742\) 19.2725 59.3147i 0.707517 2.17751i
\(743\) 1.51598 4.66571i 0.0556159 0.171168i −0.919390 0.393347i \(-0.871317\pi\)
0.975006 + 0.222179i \(0.0713170\pi\)
\(744\) 74.7689 54.3228i 2.74116 1.99157i
\(745\) 22.7874 + 16.5560i 0.834865 + 0.606565i
\(746\) 10.5307 + 32.4101i 0.385556 + 1.18662i
\(747\) −22.3687 −0.818430
\(748\) −79.7053 7.06657i −2.91432 0.258379i
\(749\) −2.78828 −0.101882
\(750\) 23.6412 + 72.7602i 0.863255 + 2.65683i
\(751\) 32.4580 + 23.5821i 1.18441 + 0.860523i 0.992662 0.120922i \(-0.0385851\pi\)
0.191746 + 0.981445i \(0.438585\pi\)
\(752\) −39.9030 + 28.9913i −1.45511 + 1.05720i
\(753\) 17.8498 54.9360i 0.650482 2.00198i
\(754\) −0.375315 + 1.15510i −0.0136682 + 0.0420663i
\(755\) −25.6159 + 18.6111i −0.932259 + 0.677326i
\(756\) −16.9394 12.3072i −0.616080 0.447609i
\(757\) −0.827339 2.54629i −0.0300702 0.0925464i 0.934895 0.354924i \(-0.115493\pi\)
−0.964965 + 0.262378i \(0.915493\pi\)
\(758\) −35.2809 −1.28146
\(759\) −14.0687 + 8.43112i −0.510662 + 0.306030i
\(760\) 59.9162 2.17339
\(761\) 6.94557 + 21.3763i 0.251777 + 0.774889i 0.994448 + 0.105232i \(0.0335586\pi\)
−0.742671 + 0.669656i \(0.766441\pi\)
\(762\) 57.1831 + 41.5460i 2.07153 + 1.50505i
\(763\) −22.3336 + 16.2263i −0.808531 + 0.587432i
\(764\) −9.62537 + 29.6238i −0.348234 + 1.07175i
\(765\) 12.6221 38.8469i 0.456354 1.40451i
\(766\) 30.7592 22.3479i 1.11138 0.807462i
\(767\) −6.81817 4.95369i −0.246190 0.178867i
\(768\) −25.7373 79.2111i −0.928713 2.85829i
\(769\) −16.3437 −0.589369 −0.294684 0.955595i \(-0.595215\pi\)
−0.294684 + 0.955595i \(0.595215\pi\)
\(770\) −12.4776 54.3342i −0.449662 1.95807i
\(771\) 62.2727 2.24270
\(772\) 13.1513 + 40.4754i 0.473324 + 1.45674i
\(773\) −5.50419 3.99903i −0.197972 0.143835i 0.484383 0.874856i \(-0.339044\pi\)
−0.682355 + 0.731021i \(0.739044\pi\)
\(774\) −44.1377 + 32.0679i −1.58650 + 1.15266i
\(775\) 2.70159 8.31463i 0.0970439 0.298670i
\(776\) 8.40414 25.8653i 0.301691 0.928509i
\(777\) 1.64910 1.19814i 0.0591611 0.0429830i
\(778\) 37.0554 + 26.9223i 1.32850 + 0.965213i
\(779\) −3.98498 12.2645i −0.142777 0.439421i
\(780\) −20.2796 −0.726126
\(781\) −9.03442 7.87194i −0.323277 0.281680i
\(782\) −28.1157 −1.00542
\(783\) −0.221792 0.682606i −0.00792621 0.0243944i
\(784\) −19.6032 14.2426i −0.700116 0.508664i
\(785\) −6.67420 + 4.84909i −0.238213 + 0.173072i
\(786\) −7.31454 + 22.5118i −0.260901 + 0.802971i
\(787\) −4.36453 + 13.4326i −0.155579 + 0.478822i −0.998219 0.0596550i \(-0.981000\pi\)
0.842641 + 0.538477i \(0.181000\pi\)
\(788\) 19.0320 13.8275i 0.677986 0.492586i
\(789\) 11.0360 + 8.01809i 0.392891 + 0.285452i
\(790\) −12.5766 38.7069i −0.447457 1.37713i
\(791\) −2.83840 −0.100922
\(792\) −45.8717 39.9692i −1.62998 1.42024i
\(793\) −7.71203 −0.273862
\(794\) 12.8023 + 39.4015i 0.454337 + 1.39831i
\(795\) 28.8790 + 20.9818i 1.02423 + 0.744149i
\(796\) 55.0933 40.0276i 1.95273 1.41874i
\(797\) −9.50826 + 29.2634i −0.336800 + 1.03656i 0.629029 + 0.777382i \(0.283453\pi\)
−0.965829 + 0.259181i \(0.916547\pi\)
\(798\) −41.3377 + 127.224i −1.46334 + 4.50369i
\(799\) 52.2552 37.9656i 1.84865 1.34313i
\(800\) 0.853209 + 0.619892i 0.0301655 + 0.0219165i
\(801\) 10.7940 + 33.2206i 0.381388 + 1.17379i
\(802\) 55.1189 1.94632
\(803\) −10.5882 46.1068i −0.373650 1.62707i
\(804\) 76.8905 2.71172
\(805\) −4.06325 12.5054i −0.143211 0.440757i
\(806\) 13.9985 + 10.1705i 0.493076 + 0.358241i
\(807\) 15.8980 11.5506i 0.559636 0.406599i
\(808\) 3.14980 9.69409i 0.110810 0.341037i
\(809\) −11.9760 + 36.8583i −0.421053 + 1.29587i 0.485670 + 0.874142i \(0.338576\pi\)
−0.906723 + 0.421727i \(0.861424\pi\)
\(810\) −26.9489 + 19.5795i −0.946886 + 0.687953i
\(811\) −17.4912 12.7081i −0.614199 0.446242i 0.236691 0.971585i \(-0.423937\pi\)
−0.850890 + 0.525343i \(0.823937\pi\)
\(812\) −2.18574 6.72700i −0.0767043 0.236072i
\(813\) 2.41381 0.0846560
\(814\) 1.58671 0.950887i 0.0556142 0.0333286i
\(815\) −4.91843 −0.172285
\(816\) −21.1062 64.9581i −0.738864 2.27399i
\(817\) 30.1662 + 21.9170i 1.05538 + 0.766779i
\(818\) −15.4203 + 11.2035i −0.539159 + 0.391722i
\(819\) 3.87887 11.9379i 0.135539 0.417145i
\(820\) −5.24114 + 16.1306i −0.183029 + 0.563304i
\(821\) −14.4366 + 10.4888i −0.503840 + 0.366061i −0.810482 0.585764i \(-0.800795\pi\)
0.306642 + 0.951825i \(0.400795\pi\)
\(822\) −18.6963 13.5836i −0.652108 0.473784i
\(823\) 2.52135 + 7.75991i 0.0878886 + 0.270493i 0.985335 0.170630i \(-0.0545802\pi\)
−0.897447 + 0.441123i \(0.854580\pi\)
\(824\) 49.0896 1.71012
\(825\) −10.5522 0.935547i −0.367382 0.0325716i
\(826\) 73.1164 2.54405
\(827\) −5.33090 16.4068i −0.185374 0.570521i 0.814581 0.580050i \(-0.196967\pi\)
−0.999955 + 0.00952853i \(0.996967\pi\)
\(828\) −22.7513 16.5298i −0.790663 0.574450i
\(829\) −35.9473 + 26.1172i −1.24850 + 0.907088i −0.998134 0.0610630i \(-0.980551\pi\)
−0.250366 + 0.968151i \(0.580551\pi\)
\(830\) 9.25631 28.4880i 0.321291 0.988832i
\(831\) −6.11582 + 18.8226i −0.212155 + 0.652947i
\(832\) 5.61044 4.07622i 0.194507 0.141318i
\(833\) 25.6715 + 18.6514i 0.889465 + 0.646234i
\(834\) −43.2768 133.192i −1.49855 4.61207i
\(835\) 31.4303 1.08769
\(836\) −31.9275 + 74.9744i −1.10424 + 2.59304i
\(837\) −10.2252 −0.353436
\(838\) 22.8707 + 70.3887i 0.790054 + 2.43154i
\(839\) 41.3511 + 30.0433i 1.42760 + 1.03721i 0.990458 + 0.137817i \(0.0440087\pi\)
0.437140 + 0.899393i \(0.355991\pi\)
\(840\) 72.6330 52.7710i 2.50608 1.82077i
\(841\) −8.88657 + 27.3500i −0.306433 + 0.943105i
\(842\) 7.40438 22.7883i 0.255172 0.785338i
\(843\) −48.8794 + 35.5130i −1.68350 + 1.22313i
\(844\) −9.47285 6.88243i −0.326069 0.236903i
\(845\) −0.598707 1.84263i −0.0205962 0.0633885i
\(846\) 96.2443 3.30895
\(847\) 38.0868 + 6.80696i 1.30868 + 0.233890i
\(848\) 32.4290 1.11362
\(849\) 1.80006 + 5.54000i 0.0617778 + 0.190132i
\(850\) −14.6915 10.6740i −0.503913 0.366114i
\(851\) 0.352976 0.256452i 0.0120999 0.00879107i
\(852\) 11.6862 35.9663i 0.400362 1.23219i
\(853\) −5.76673 + 17.7482i −0.197449 + 0.607686i 0.802490 + 0.596665i \(0.203508\pi\)
−0.999939 + 0.0110206i \(0.996492\pi\)
\(854\) 54.1291 39.3271i 1.85226 1.34575i
\(855\) −33.6528 24.4502i −1.15090 0.836180i
\(856\) −1.25922 3.87549i −0.0430394 0.132462i
\(857\) 26.3249 0.899241 0.449621 0.893220i \(-0.351559\pi\)
0.449621 + 0.893220i \(0.351559\pi\)
\(858\) 8.21478 19.2905i 0.280448 0.658567i
\(859\) 52.8360 1.80274 0.901371 0.433048i \(-0.142562\pi\)
0.901371 + 0.433048i \(0.142562\pi\)
\(860\) −15.1546 46.6411i −0.516768 1.59045i
\(861\) −15.6327 11.3578i −0.532760 0.387073i
\(862\) −11.5290 + 8.37631i −0.392679 + 0.285298i
\(863\) 13.4412 41.3678i 0.457544 1.40818i −0.410578 0.911826i \(-0.634673\pi\)
0.868122 0.496351i \(-0.165327\pi\)
\(864\) 0.381168 1.17312i 0.0129676 0.0399102i
\(865\) −2.56203 + 1.86142i −0.0871116 + 0.0632903i
\(866\) 24.4060 + 17.7320i 0.829351 + 0.602559i
\(867\) 14.1757 + 43.6284i 0.481433 + 1.48170i
\(868\) −100.769 −3.42031
\(869\) 28.1353 + 2.49444i 0.954424 + 0.0846180i
\(870\) 6.03097 0.204469
\(871\) 2.27001 + 6.98637i 0.0769164 + 0.236724i
\(872\) −32.6395 23.7139i −1.10531 0.803056i
\(873\) −15.2752 + 11.0981i −0.516988 + 0.375614i
\(874\) −8.84799 + 27.2313i −0.299288 + 0.921113i
\(875\) 13.1536 40.4826i 0.444672 1.36856i
\(876\) 120.785 87.7554i 4.08095 2.96498i
\(877\) −23.1416 16.8134i −0.781436 0.567747i 0.123974 0.992286i \(-0.460436\pi\)
−0.905410 + 0.424539i \(0.860436\pi\)
\(878\) 0.299580 + 0.922013i 0.0101103 + 0.0311164i
\(879\) −10.1234 −0.341455
\(880\) 24.8644 14.9008i 0.838180 0.502306i
\(881\) −35.7795 −1.20544 −0.602720 0.797952i \(-0.705917\pi\)
−0.602720 + 0.797952i \(0.705917\pi\)
\(882\) 14.6110 + 44.9679i 0.491977 + 1.51415i
\(883\) 30.1278 + 21.8891i 1.01388 + 0.736627i 0.965019 0.262178i \(-0.0844408\pi\)
0.0488612 + 0.998806i \(0.484441\pi\)
\(884\) 19.5186 14.1811i 0.656482 0.476962i
\(885\) −12.9320 + 39.8006i −0.434704 + 1.33788i
\(886\) 6.51124 20.0395i 0.218750 0.673242i
\(887\) 12.8612 9.34422i 0.431838 0.313748i −0.350546 0.936546i \(-0.614004\pi\)
0.782383 + 0.622797i \(0.214004\pi\)
\(888\) 2.41008 + 1.75102i 0.0808768 + 0.0587605i
\(889\) −12.1525 37.4016i −0.407583 1.25441i
\(890\) −46.7751 −1.56790
\(891\) −5.17428 22.5316i −0.173345 0.754837i
\(892\) −53.2498 −1.78293
\(893\) −20.3267 62.5592i −0.680208 2.09346i
\(894\) −74.3528 54.0205i −2.48673 1.80672i
\(895\) −8.85092 + 6.43057i −0.295854 + 0.214950i
\(896\) −20.4315 + 62.8818i −0.682570 + 2.10073i
\(897\) 1.52817 4.70323i 0.0510242 0.157036i
\(898\) −37.0451 + 26.9149i −1.23621 + 0.898160i
\(899\) −2.79451 2.03033i −0.0932022 0.0677153i
\(900\) −5.61293 17.2748i −0.187098 0.575827i
\(901\) −42.4675 −1.41480
\(902\) −13.2208 11.5196i −0.440204 0.383562i
\(903\) 55.8720 1.85930
\(904\) −1.28186 3.94515i −0.0426339 0.131214i
\(905\) −0.720700 0.523620i −0.0239569 0.0174057i
\(906\) 83.5821 60.7260i 2.77683 2.01748i
\(907\) 1.02403 3.15164i 0.0340024 0.104649i −0.932615 0.360873i \(-0.882479\pi\)
0.966617 + 0.256225i \(0.0824787\pi\)
\(908\) 15.2928 47.0663i 0.507509 1.56195i
\(909\) −5.72503 + 4.15948i −0.189887 + 0.137961i
\(910\) 13.5986 + 9.87997i 0.450789 + 0.327518i
\(911\) 13.2108 + 40.6587i 0.437694 + 1.34708i 0.890301 + 0.455373i \(0.150494\pi\)
−0.452607 + 0.891710i \(0.649506\pi\)
\(912\) −69.5570 −2.30326
\(913\) 15.6735 + 13.6567i 0.518717 + 0.451972i
\(914\) −6.93378 −0.229349
\(915\) 11.8338 + 36.4207i 0.391213 + 1.20403i
\(916\) 26.4113 + 19.1889i 0.872652 + 0.634019i
\(917\) 10.6546 7.74101i 0.351845 0.255631i
\(918\) −6.56337 + 20.2000i −0.216623 + 0.666698i
\(919\) 7.72921 23.7881i 0.254963 0.784696i −0.738874 0.673844i \(-0.764642\pi\)
0.993837 0.110852i \(-0.0353580\pi\)
\(920\) 15.5465 11.2952i 0.512553 0.372392i
\(921\) −68.3039 49.6257i −2.25069 1.63522i
\(922\) 23.8863 + 73.5144i 0.786653 + 2.42107i
\(923\) 3.61296 0.118922
\(924\) 27.3295 + 119.007i 0.899073 + 3.91505i
\(925\) 0.281803 0.00926564
\(926\) −23.3567 71.8845i −0.767549 2.36227i
\(927\) −27.5719 20.0322i −0.905580 0.657942i
\(928\) 0.337106 0.244922i 0.0110661 0.00803996i
\(929\) 15.9385 49.0536i 0.522924 1.60940i −0.245460 0.969407i \(-0.578939\pi\)
0.768384 0.639989i \(-0.221061\pi\)
\(930\) 26.5509 81.7152i 0.870638 2.67955i
\(931\) 26.1436 18.9944i 0.856820 0.622516i
\(932\) 16.2815 + 11.8292i 0.533320 + 0.387479i
\(933\) 17.5481 + 54.0075i 0.574499 + 1.76813i
\(934\) 28.7665 0.941268
\(935\) −32.5613 + 19.5134i −1.06487 + 0.638156i
\(936\) 18.3446 0.599610
\(937\) −9.67018 29.7617i −0.315911 0.972274i −0.975378 0.220540i \(-0.929218\pi\)
0.659467 0.751734i \(-0.270782\pi\)
\(938\) −51.5594 37.4601i −1.68347 1.22311i
\(939\) −45.5934 + 33.1256i −1.48789 + 1.08101i
\(940\) −26.7342 + 82.2795i −0.871974 + 2.68366i
\(941\) −0.407177 + 1.25316i −0.0132736 + 0.0408519i −0.957474 0.288520i \(-0.906837\pi\)
0.944200 + 0.329372i \(0.106837\pi\)
\(942\) 21.7772 15.8221i 0.709541 0.515511i
\(943\) −3.34605 2.43105i −0.108962 0.0791658i
\(944\) 11.7483 + 36.1575i 0.382374 + 1.17683i
\(945\) −9.93314 −0.323125
\(946\) 50.5051 + 4.47771i 1.64206 + 0.145583i
\(947\) 22.8334 0.741985 0.370992 0.928636i \(-0.379018\pi\)
0.370992 + 0.928636i \(0.379018\pi\)
\(948\) 27.5464 + 84.7790i 0.894664 + 2.75349i
\(949\) 11.5395 + 8.38392i 0.374587 + 0.272154i
\(950\) −14.9616 + 10.8702i −0.485419 + 0.352677i
\(951\) −1.46441 + 4.50698i −0.0474866 + 0.146149i
\(952\) −33.0058 + 101.581i −1.06973 + 3.29228i
\(953\) −6.26259 + 4.55003i −0.202865 + 0.147390i −0.684580 0.728938i \(-0.740014\pi\)
0.481715 + 0.876328i \(0.340014\pi\)
\(954\) −51.1938 37.1945i −1.65746 1.20422i
\(955\) 4.56629 + 14.0536i 0.147762 + 0.454763i
\(956\) 76.8180 2.48447
\(957\) −1.63991 + 3.85095i −0.0530108 + 0.124484i
\(958\) −68.8838 −2.22553
\(959\) 3.97333 + 12.2286i 0.128305 + 0.394883i
\(960\) −27.8593 20.2409i −0.899154 0.653274i
\(961\) −14.7326 + 10.7039i −0.475245 + 0.345286i
\(962\) −0.172352 + 0.530444i −0.00555684 + 0.0171022i
\(963\) −0.874224 + 2.69058i −0.0281715 + 0.0867029i
\(964\) −48.5799 + 35.2954i −1.56465 + 1.13679i
\(965\) 16.3338 + 11.8672i 0.525805 + 0.382020i
\(966\) 13.2580 + 40.8038i 0.426568 + 1.31284i
\(967\) −19.8903 −0.639630 −0.319815 0.947480i \(-0.603621\pi\)
−0.319815 + 0.947480i \(0.603621\pi\)
\(968\) 7.73936 + 56.0118i 0.248753 + 1.80029i
\(969\) 91.0886 2.92619
\(970\) −7.81315 24.0464i −0.250865 0.772084i
\(971\) −11.0555 8.03229i −0.354788 0.257769i 0.396087 0.918213i \(-0.370368\pi\)
−0.750875 + 0.660444i \(0.770368\pi\)
\(972\) 73.4737 53.3817i 2.35667 1.71222i
\(973\) −24.0785 + 74.1060i −0.771921 + 2.37573i
\(974\) 12.2009 37.5505i 0.390941 1.20319i
\(975\) 2.58408 1.87744i 0.0827568 0.0601263i
\(976\) 28.1454 + 20.4489i 0.900913 + 0.654552i
\(977\) 12.0458 + 37.0731i 0.385378 + 1.18607i 0.936206 + 0.351453i \(0.114312\pi\)
−0.550827 + 0.834619i \(0.685688\pi\)
\(978\) 16.0483 0.513169
\(979\) 12.7188 29.8673i 0.406496 0.954562i
\(980\) −42.5018 −1.35767
\(981\) 8.65540 + 26.6386i 0.276346 + 0.850505i
\(982\) 56.1196 + 40.7733i 1.79085 + 1.30113i
\(983\) −22.2966 + 16.1994i −0.711152 + 0.516682i −0.883545 0.468346i \(-0.844850\pi\)
0.172393 + 0.985028i \(0.444850\pi\)
\(984\) 8.72654 26.8575i 0.278192 0.856186i
\(985\) 3.44869 10.6140i 0.109885 0.338190i
\(986\) −5.80466 + 4.21733i −0.184858 + 0.134307i
\(987\) −79.7397 57.9343i −2.53814 1.84407i
\(988\) −7.59254 23.3674i −0.241551 0.743417i
\(989\) 11.9590 0.380273
\(990\) −56.3426 4.99526i −1.79068 0.158760i
\(991\) 39.9148 1.26794 0.633968 0.773359i \(-0.281425\pi\)
0.633968 + 0.773359i \(0.281425\pi\)
\(992\) −1.83443 5.64580i −0.0582432 0.179254i
\(993\) 55.2410 + 40.1349i 1.75302 + 1.27364i
\(994\) −25.3586 + 18.4241i −0.804326 + 0.584377i
\(995\) 9.98319 30.7251i 0.316489 0.974052i
\(996\) −20.2739 + 62.3967i −0.642403 + 1.97711i
\(997\) −49.2233 + 35.7628i −1.55892 + 1.13262i −0.622028 + 0.782995i \(0.713691\pi\)
−0.936890 + 0.349625i \(0.886309\pi\)
\(998\) 5.33043 + 3.87278i 0.168732 + 0.122591i
\(999\) −0.101851 0.313465i −0.00322243 0.00991761i
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 143.2.h.c.27.7 28
11.3 even 5 1573.2.a.s.1.13 14
11.8 odd 10 1573.2.a.r.1.2 14
11.9 even 5 inner 143.2.h.c.53.7 yes 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
143.2.h.c.27.7 28 1.1 even 1 trivial
143.2.h.c.53.7 yes 28 11.9 even 5 inner
1573.2.a.r.1.2 14 11.8 odd 10
1573.2.a.s.1.13 14 11.3 even 5