Properties

Label 731.2.u.b.52.8
Level $731$
Weight $2$
Character 731.52
Analytic conductor $5.837$
Analytic rank $0$
Dimension $348$
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(52,731)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(731, base_ring=CyclotomicField(42))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("731.52");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 731 = 17 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 731.u (of order \(21\), degree \(12\), 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: \(348\)
Relative dimension: \(29\) over \(\Q(\zeta_{21})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label 52.8
Character \(\chi\) \(=\) 731.52
Dual form 731.2.u.b.239.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.02252 - 1.28220i) q^{2} +(-0.661263 - 0.0996693i) q^{3} +(-0.153446 + 0.672293i) q^{4} +(-0.0486121 - 0.0331432i) q^{5} +(0.548358 + 0.949785i) q^{6} +(0.748574 - 1.29657i) q^{7} +(-1.93625 + 0.932450i) q^{8} +(-2.43938 - 0.752450i) q^{9} +O(q^{10})\) \(q+(-1.02252 - 1.28220i) q^{2} +(-0.661263 - 0.0996693i) q^{3} +(-0.153446 + 0.672293i) q^{4} +(-0.0486121 - 0.0331432i) q^{5} +(0.548358 + 0.949785i) q^{6} +(0.748574 - 1.29657i) q^{7} +(-1.93625 + 0.932450i) q^{8} +(-2.43938 - 0.752450i) q^{9} +(0.00721069 + 0.0962200i) q^{10} +(-0.569855 - 2.49670i) q^{11} +(0.168475 - 0.429268i) q^{12} +(-0.245559 + 3.27676i) q^{13} +(-2.42789 + 0.365946i) q^{14} +(0.0288420 + 0.0267615i) q^{15} +(4.41803 + 2.12761i) q^{16} +(-0.826239 + 0.563320i) q^{17} +(1.52953 + 3.89717i) q^{18} +(-0.256656 + 0.0791678i) q^{19} +(0.0297413 - 0.0275959i) q^{20} +(-0.624232 + 0.782762i) q^{21} +(-2.61857 + 3.28359i) q^{22} +(1.49745 - 1.38943i) q^{23} +(1.37331 - 0.423610i) q^{24} +(-1.82544 - 4.65115i) q^{25} +(4.45255 - 3.03570i) q^{26} +(3.34560 + 1.61115i) q^{27} +(0.756807 + 0.702215i) q^{28} +(-9.62463 + 1.45068i) q^{29} +(0.00482202 - 0.0643454i) q^{30} +(-3.66011 + 9.32581i) q^{31} +(-0.833071 - 3.64992i) q^{32} +(0.127980 + 1.70777i) q^{33} +(1.56713 + 0.483397i) q^{34} +(-0.0793621 + 0.0382188i) q^{35} +(0.880182 - 1.52452i) q^{36} +(1.96187 + 3.39806i) q^{37} +(0.363944 + 0.248133i) q^{38} +(0.488972 - 2.14232i) q^{39} +(0.125030 + 0.0188452i) q^{40} +(-1.68748 - 2.11603i) q^{41} +1.64195 q^{42} +(-6.00110 + 2.64325i) q^{43} +1.76595 q^{44} +(0.0936450 + 0.117427i) q^{45} +(-3.31270 - 0.499309i) q^{46} +(0.979699 - 4.29234i) q^{47} +(-2.70942 - 1.84725i) q^{48} +(2.37927 + 4.12102i) q^{49} +(-4.09715 + 7.09647i) q^{50} +(0.602507 - 0.290152i) q^{51} +(-2.16526 - 0.667895i) q^{52} +(0.663148 + 8.84910i) q^{53} +(-1.35512 - 5.93716i) q^{54} +(-0.0550466 + 0.140256i) q^{55} +(-0.240443 + 3.20849i) q^{56} +(0.177607 - 0.0267700i) q^{57} +(11.7014 + 10.8573i) q^{58} +(6.85139 + 3.29946i) q^{59} +(-0.0224173 + 0.0152838i) q^{60} +(3.14670 + 8.01767i) q^{61} +(15.7001 - 4.84283i) q^{62} +(-2.80166 + 2.59956i) q^{63} +(2.28664 - 2.86736i) q^{64} +(0.120539 - 0.151152i) q^{65} +(2.05884 - 1.91032i) q^{66} +(6.79803 - 2.09692i) q^{67} +(-0.251933 - 0.641914i) q^{68} +(-1.12869 + 0.769528i) q^{69} +(0.130153 + 0.0626786i) q^{70} +(2.14062 + 1.98621i) q^{71} +(5.42489 - 0.817670i) q^{72} +(0.781737 - 10.4316i) q^{73} +(2.35094 - 5.99009i) q^{74} +(0.743519 + 3.25757i) q^{75} +(-0.0138410 - 0.184696i) q^{76} +(-3.66372 - 1.13011i) q^{77} +(-3.24687 + 1.56361i) q^{78} +(-6.37877 + 11.0484i) q^{79} +(-0.144254 - 0.249855i) q^{80} +(4.27593 + 2.91528i) q^{81} +(-0.987693 + 4.32737i) q^{82} +(-11.6680 - 1.75867i) q^{83} +(-0.430459 - 0.539779i) q^{84} +0.0588354 q^{85} +(9.52542 + 4.99184i) q^{86} +6.50900 q^{87} +(3.43143 + 4.30287i) q^{88} +(-4.80204 - 0.723790i) q^{89} +(0.0548111 - 0.240143i) q^{90} +(4.06472 + 2.77128i) q^{91} +(0.704325 + 1.21993i) q^{92} +(3.34979 - 5.80201i) q^{93} +(-6.50540 + 3.13283i) q^{94} +(0.0151004 + 0.00465787i) q^{95} +(0.187094 + 2.49659i) q^{96} +(-2.56761 - 11.2494i) q^{97} +(2.85112 - 7.26453i) q^{98} +(-0.488546 + 6.51919i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 348 q + 6 q^{2} - 3 q^{3} - 54 q^{4} + q^{5} - 12 q^{6} + 49 q^{7} - 2 q^{8} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 348 q + 6 q^{2} - 3 q^{3} - 54 q^{4} + q^{5} - 12 q^{6} + 49 q^{7} - 2 q^{8} + 8 q^{9} - 4 q^{10} - 16 q^{11} - 12 q^{12} - 9 q^{13} - 3 q^{14} - 14 q^{15} - 30 q^{16} - 29 q^{17} - 204 q^{18} - 8 q^{19} + 61 q^{20} + 26 q^{21} + 85 q^{22} - 79 q^{23} - 12 q^{24} + 22 q^{25} - 14 q^{26} + 12 q^{27} - 15 q^{28} + 54 q^{29} - 46 q^{30} - 52 q^{31} + 33 q^{32} + 39 q^{33} + 3 q^{34} + 32 q^{35} - 161 q^{36} + 68 q^{37} - 29 q^{38} + 61 q^{39} + 107 q^{40} + 63 q^{41} - 56 q^{42} - 45 q^{43} - 74 q^{44} + 144 q^{45} - 22 q^{46} - 70 q^{47} + 168 q^{48} - 119 q^{49} + 97 q^{50} - 6 q^{51} + 27 q^{52} + 10 q^{53} - 34 q^{54} - 78 q^{55} - 44 q^{56} - 40 q^{57} - 38 q^{58} - 47 q^{59} - 72 q^{60} - 76 q^{61} - 41 q^{62} + 63 q^{63} - 112 q^{64} - 31 q^{65} - 598 q^{66} - 39 q^{67} - 20 q^{68} - 17 q^{69} - 72 q^{70} - 37 q^{71} + 245 q^{72} + 14 q^{73} + 77 q^{74} - 121 q^{75} + 152 q^{76} + 59 q^{77} + 220 q^{78} + 4 q^{79} - 42 q^{80} - 109 q^{81} + 148 q^{82} + 59 q^{83} + 390 q^{84} + 2 q^{85} + 12 q^{86} - 78 q^{87} + 344 q^{88} - 103 q^{89} - 75 q^{90} + 148 q^{91} + 28 q^{92} + 140 q^{93} + 24 q^{94} - 302 q^{95} + 22 q^{96} + 57 q^{97} - 72 q^{98} - 128 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(173\) \(562\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{21}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.02252 1.28220i −0.723031 0.906652i 0.275474 0.961308i \(-0.411165\pi\)
−0.998505 + 0.0546565i \(0.982594\pi\)
\(3\) −0.661263 0.0996693i −0.381780 0.0575441i −0.0446514 0.999003i \(-0.514218\pi\)
−0.337129 + 0.941459i \(0.609456\pi\)
\(4\) −0.153446 + 0.672293i −0.0767232 + 0.336146i
\(5\) −0.0486121 0.0331432i −0.0217400 0.0148221i 0.552401 0.833578i \(-0.313712\pi\)
−0.574141 + 0.818756i \(0.694664\pi\)
\(6\) 0.548358 + 0.949785i 0.223866 + 0.387748i
\(7\) 0.748574 1.29657i 0.282934 0.490057i −0.689172 0.724598i \(-0.742025\pi\)
0.972106 + 0.234541i \(0.0753588\pi\)
\(8\) −1.93625 + 0.932450i −0.684569 + 0.329671i
\(9\) −2.43938 0.752450i −0.813128 0.250817i
\(10\) 0.00721069 + 0.0962200i 0.00228022 + 0.0304274i
\(11\) −0.569855 2.49670i −0.171818 0.752782i −0.985250 0.171122i \(-0.945261\pi\)
0.813432 0.581660i \(-0.197597\pi\)
\(12\) 0.168475 0.429268i 0.0486347 0.123919i
\(13\) −0.245559 + 3.27676i −0.0681059 + 0.908810i 0.853602 + 0.520925i \(0.174413\pi\)
−0.921708 + 0.387884i \(0.873206\pi\)
\(14\) −2.42789 + 0.365946i −0.648881 + 0.0978031i
\(15\) 0.0288420 + 0.0267615i 0.00744698 + 0.00690978i
\(16\) 4.41803 + 2.12761i 1.10451 + 0.531902i
\(17\) −0.826239 + 0.563320i −0.200392 + 0.136625i
\(18\) 1.52953 + 3.89717i 0.360513 + 0.918572i
\(19\) −0.256656 + 0.0791678i −0.0588808 + 0.0181623i −0.324056 0.946038i \(-0.605047\pi\)
0.265175 + 0.964200i \(0.414570\pi\)
\(20\) 0.0297413 0.0275959i 0.00665035 0.00617062i
\(21\) −0.624232 + 0.782762i −0.136219 + 0.170813i
\(22\) −2.61857 + 3.28359i −0.558282 + 0.700063i
\(23\) 1.49745 1.38943i 0.312240 0.289716i −0.508449 0.861092i \(-0.669781\pi\)
0.820688 + 0.571376i \(0.193590\pi\)
\(24\) 1.37331 0.423610i 0.280325 0.0864689i
\(25\) −1.82544 4.65115i −0.365088 0.930229i
\(26\) 4.45255 3.03570i 0.873217 0.595349i
\(27\) 3.34560 + 1.61115i 0.643861 + 0.310067i
\(28\) 0.756807 + 0.702215i 0.143023 + 0.132706i
\(29\) −9.62463 + 1.45068i −1.78725 + 0.269384i −0.957433 0.288654i \(-0.906792\pi\)
−0.829815 + 0.558038i \(0.811554\pi\)
\(30\) 0.00482202 0.0643454i 0.000880376 0.0117478i
\(31\) −3.66011 + 9.32581i −0.657375 + 1.67496i 0.0776986 + 0.996977i \(0.475243\pi\)
−0.735074 + 0.677987i \(0.762852\pi\)
\(32\) −0.833071 3.64992i −0.147268 0.645221i
\(33\) 0.127980 + 1.70777i 0.0222784 + 0.297284i
\(34\) 1.56713 + 0.483397i 0.268761 + 0.0829019i
\(35\) −0.0793621 + 0.0382188i −0.0134146 + 0.00646015i
\(36\) 0.880182 1.52452i 0.146697 0.254087i
\(37\) 1.96187 + 3.39806i 0.322529 + 0.558637i 0.981009 0.193961i \(-0.0621336\pi\)
−0.658480 + 0.752598i \(0.728800\pi\)
\(38\) 0.363944 + 0.248133i 0.0590396 + 0.0402525i
\(39\) 0.488972 2.14232i 0.0782981 0.343046i
\(40\) 0.125030 + 0.0188452i 0.0197689 + 0.00297969i
\(41\) −1.68748 2.11603i −0.263540 0.330468i 0.632402 0.774641i \(-0.282069\pi\)
−0.895941 + 0.444172i \(0.853498\pi\)
\(42\) 1.64195 0.253358
\(43\) −6.00110 + 2.64325i −0.915160 + 0.403091i
\(44\) 1.76595 0.266227
\(45\) 0.0936450 + 0.117427i 0.0139598 + 0.0175050i
\(46\) −3.31270 0.499309i −0.488430 0.0736190i
\(47\) 0.979699 4.29234i 0.142904 0.626102i −0.851848 0.523788i \(-0.824518\pi\)
0.994752 0.102314i \(-0.0326246\pi\)
\(48\) −2.70942 1.84725i −0.391071 0.266628i
\(49\) 2.37927 + 4.12102i 0.339896 + 0.588718i
\(50\) −4.09715 + 7.09647i −0.579424 + 1.00359i
\(51\) 0.602507 0.290152i 0.0843678 0.0406294i
\(52\) −2.16526 0.667895i −0.300268 0.0926204i
\(53\) 0.663148 + 8.84910i 0.0910904 + 1.21552i 0.836143 + 0.548511i \(0.184805\pi\)
−0.745053 + 0.667006i \(0.767576\pi\)
\(54\) −1.35512 5.93716i −0.184408 0.807945i
\(55\) −0.0550466 + 0.140256i −0.00742248 + 0.0189122i
\(56\) −0.240443 + 3.20849i −0.0321306 + 0.428753i
\(57\) 0.177607 0.0267700i 0.0235247 0.00354577i
\(58\) 11.7014 + 10.8573i 1.53647 + 1.42564i
\(59\) 6.85139 + 3.29946i 0.891976 + 0.429553i 0.822984 0.568064i \(-0.192308\pi\)
0.0689915 + 0.997617i \(0.478022\pi\)
\(60\) −0.0224173 + 0.0152838i −0.00289405 + 0.00197313i
\(61\) 3.14670 + 8.01767i 0.402894 + 1.02656i 0.978024 + 0.208495i \(0.0668564\pi\)
−0.575130 + 0.818062i \(0.695048\pi\)
\(62\) 15.7001 4.84283i 1.99391 0.615040i
\(63\) −2.80166 + 2.59956i −0.352976 + 0.327514i
\(64\) 2.28664 2.86736i 0.285830 0.358420i
\(65\) 0.120539 0.151152i 0.0149511 0.0187480i
\(66\) 2.05884 1.91032i 0.253426 0.235145i
\(67\) 6.79803 2.09692i 0.830512 0.256179i 0.149787 0.988718i \(-0.452141\pi\)
0.680725 + 0.732539i \(0.261665\pi\)
\(68\) −0.251933 0.641914i −0.0305513 0.0778435i
\(69\) −1.12869 + 0.769528i −0.135878 + 0.0926403i
\(70\) 0.130153 + 0.0626786i 0.0155563 + 0.00749153i
\(71\) 2.14062 + 1.98621i 0.254045 + 0.235719i 0.796906 0.604103i \(-0.206468\pi\)
−0.542861 + 0.839823i \(0.682659\pi\)
\(72\) 5.42489 0.817670i 0.639329 0.0963633i
\(73\) 0.781737 10.4316i 0.0914954 1.22092i −0.742766 0.669551i \(-0.766486\pi\)
0.834261 0.551370i \(-0.185895\pi\)
\(74\) 2.35094 5.99009i 0.273291 0.696334i
\(75\) 0.743519 + 3.25757i 0.0858542 + 0.376152i
\(76\) −0.0138410 0.184696i −0.00158768 0.0211861i
\(77\) −3.66372 1.13011i −0.417519 0.128788i
\(78\) −3.24687 + 1.56361i −0.367636 + 0.177044i
\(79\) −6.37877 + 11.0484i −0.717668 + 1.24304i 0.244253 + 0.969711i \(0.421457\pi\)
−0.961921 + 0.273326i \(0.911876\pi\)
\(80\) −0.144254 0.249855i −0.0161281 0.0279346i
\(81\) 4.27593 + 2.91528i 0.475103 + 0.323920i
\(82\) −0.987693 + 4.32737i −0.109072 + 0.477878i
\(83\) −11.6680 1.75867i −1.28073 0.193039i −0.526798 0.849991i \(-0.676607\pi\)
−0.753933 + 0.656952i \(0.771846\pi\)
\(84\) −0.430459 0.539779i −0.0469670 0.0588947i
\(85\) 0.0588354 0.00638160
\(86\) 9.52542 + 4.99184i 1.02715 + 0.538284i
\(87\) 6.50900 0.697838
\(88\) 3.43143 + 4.30287i 0.365791 + 0.458688i
\(89\) −4.80204 0.723790i −0.509015 0.0767216i −0.110486 0.993878i \(-0.535241\pi\)
−0.398528 + 0.917156i \(0.630479\pi\)
\(90\) 0.0548111 0.240143i 0.00577760 0.0253133i
\(91\) 4.06472 + 2.77128i 0.426099 + 0.290509i
\(92\) 0.704325 + 1.21993i 0.0734310 + 0.127186i
\(93\) 3.34979 5.80201i 0.347357 0.601640i
\(94\) −6.50540 + 3.13283i −0.670981 + 0.323127i
\(95\) 0.0151004 + 0.00465787i 0.00154927 + 0.000477887i
\(96\) 0.187094 + 2.49659i 0.0190952 + 0.254807i
\(97\) −2.56761 11.2494i −0.260701 1.14220i −0.920494 0.390757i \(-0.872213\pi\)
0.659793 0.751447i \(-0.270644\pi\)
\(98\) 2.85112 7.26453i 0.288006 0.733829i
\(99\) −0.488546 + 6.51919i −0.0491007 + 0.655203i
\(100\) 3.40704 0.513529i 0.340704 0.0513529i
\(101\) −11.1845 10.3777i −1.11290 1.03262i −0.999235 0.0391051i \(-0.987549\pi\)
−0.113669 0.993519i \(-0.536260\pi\)
\(102\) −0.988108 0.475848i −0.0978372 0.0471159i
\(103\) 0.377360 0.257280i 0.0371824 0.0253505i −0.544586 0.838705i \(-0.683313\pi\)
0.581769 + 0.813354i \(0.302361\pi\)
\(104\) −2.57995 6.57361i −0.252985 0.644595i
\(105\) 0.0562885 0.0173627i 0.00549319 0.00169443i
\(106\) 10.6682 9.89867i 1.03619 0.961444i
\(107\) −2.44319 + 3.06366i −0.236192 + 0.296176i −0.885775 0.464115i \(-0.846372\pi\)
0.649583 + 0.760291i \(0.274944\pi\)
\(108\) −1.59654 + 2.00200i −0.153627 + 0.192642i
\(109\) −8.89843 + 8.25654i −0.852315 + 0.790833i −0.979584 0.201035i \(-0.935569\pi\)
0.127269 + 0.991868i \(0.459379\pi\)
\(110\) 0.236123 0.0728343i 0.0225134 0.00694448i
\(111\) −0.958629 2.44255i −0.0909890 0.231836i
\(112\) 6.06581 4.13560i 0.573165 0.390778i
\(113\) −4.99692 2.40639i −0.470071 0.226374i 0.183825 0.982959i \(-0.441152\pi\)
−0.653895 + 0.756585i \(0.726866\pi\)
\(114\) −0.215932 0.200355i −0.0202238 0.0187650i
\(115\) −0.118844 + 0.0179129i −0.0110823 + 0.00167038i
\(116\) 0.501584 6.69317i 0.0465709 0.621445i
\(117\) 3.06461 7.80850i 0.283324 0.721897i
\(118\) −2.77512 12.1586i −0.255471 1.11929i
\(119\) 0.111882 + 1.49296i 0.0102562 + 0.136860i
\(120\) −0.0807992 0.0249232i −0.00737592 0.00227517i
\(121\) 4.00190 1.92721i 0.363809 0.175201i
\(122\) 7.06268 12.2329i 0.639425 1.10752i
\(123\) 0.904963 + 1.56744i 0.0815978 + 0.141331i
\(124\) −5.70804 3.89168i −0.512597 0.349483i
\(125\) −0.130876 + 0.573404i −0.0117059 + 0.0512868i
\(126\) 6.19791 + 0.934185i 0.552154 + 0.0832238i
\(127\) 4.87506 + 6.11314i 0.432592 + 0.542453i 0.949574 0.313543i \(-0.101516\pi\)
−0.516982 + 0.855996i \(0.672945\pi\)
\(128\) −13.5022 −1.19344
\(129\) 4.23176 1.14975i 0.372585 0.101230i
\(130\) −0.317060 −0.0278080
\(131\) 2.31987 + 2.90902i 0.202688 + 0.254163i 0.872778 0.488117i \(-0.162316\pi\)
−0.670090 + 0.742280i \(0.733745\pi\)
\(132\) −1.16776 0.176011i −0.101640 0.0153198i
\(133\) −0.0894793 + 0.392035i −0.00775884 + 0.0339937i
\(134\) −9.63979 6.57230i −0.832751 0.567760i
\(135\) −0.109238 0.189205i −0.00940169 0.0162842i
\(136\) 1.07454 1.86116i 0.0921410 0.159593i
\(137\) −16.4486 + 7.92121i −1.40530 + 0.676755i −0.974228 0.225564i \(-0.927577\pi\)
−0.431068 + 0.902319i \(0.641863\pi\)
\(138\) 2.14080 + 0.660348i 0.182237 + 0.0562126i
\(139\) −0.322315 4.30099i −0.0273384 0.364805i −0.994049 0.108933i \(-0.965257\pi\)
0.966711 0.255872i \(-0.0823625\pi\)
\(140\) −0.0135164 0.0592191i −0.00114234 0.00500493i
\(141\) −1.07565 + 2.74072i −0.0905863 + 0.230810i
\(142\) 0.357885 4.77564i 0.0300330 0.400763i
\(143\) 8.32101 1.25419i 0.695838 0.104881i
\(144\) −9.17635 8.51440i −0.764695 0.709534i
\(145\) 0.515954 + 0.248470i 0.0428476 + 0.0206343i
\(146\) −14.1747 + 9.66413i −1.17310 + 0.799809i
\(147\) −1.16259 2.96222i −0.0958884 0.244320i
\(148\) −2.58553 + 0.797531i −0.212529 + 0.0655566i
\(149\) 5.97624 5.54514i 0.489593 0.454276i −0.396330 0.918108i \(-0.629716\pi\)
0.885923 + 0.463832i \(0.153526\pi\)
\(150\) 3.41659 4.28427i 0.278964 0.349809i
\(151\) −12.0679 + 15.1326i −0.982069 + 1.23148i −0.00923803 + 0.999957i \(0.502941\pi\)
−0.972831 + 0.231518i \(0.925631\pi\)
\(152\) 0.423130 0.392607i 0.0343204 0.0318447i
\(153\) 2.43938 0.752450i 0.197213 0.0608320i
\(154\) 2.29720 + 5.85317i 0.185114 + 0.471662i
\(155\) 0.487012 0.332039i 0.0391178 0.0266700i
\(156\) 1.36524 + 0.657464i 0.109307 + 0.0526393i
\(157\) −13.4796 12.5072i −1.07579 0.998185i −0.999999 0.00106125i \(-0.999662\pi\)
−0.0757883 0.997124i \(-0.524147\pi\)
\(158\) 20.6886 3.11831i 1.64590 0.248079i
\(159\) 0.443468 5.91767i 0.0351693 0.469302i
\(160\) −0.0804727 + 0.205041i −0.00636192 + 0.0162099i
\(161\) −0.680539 2.98163i −0.0536340 0.234986i
\(162\) −0.634253 8.46352i −0.0498316 0.664957i
\(163\) −16.8617 5.20115i −1.32071 0.407386i −0.447307 0.894380i \(-0.647617\pi\)
−0.873405 + 0.486995i \(0.838093\pi\)
\(164\) 1.68153 0.809782i 0.131305 0.0632333i
\(165\) 0.0503795 0.0872599i 0.00392204 0.00679317i
\(166\) 9.67581 + 16.7590i 0.750988 + 1.30075i
\(167\) −19.3820 13.2144i −1.49983 1.02256i −0.986388 0.164436i \(-0.947419\pi\)
−0.513437 0.858127i \(-0.671628\pi\)
\(168\) 0.478784 2.09769i 0.0369390 0.161840i
\(169\) 2.17794 + 0.328272i 0.167534 + 0.0252517i
\(170\) −0.0601604 0.0754387i −0.00461409 0.00578589i
\(171\) 0.685652 0.0524331
\(172\) −0.856188 4.44010i −0.0652837 0.338554i
\(173\) 4.32790 0.329044 0.164522 0.986373i \(-0.447392\pi\)
0.164522 + 0.986373i \(0.447392\pi\)
\(174\) −6.65558 8.34583i −0.504558 0.632696i
\(175\) −7.39701 1.11492i −0.559161 0.0842800i
\(176\) 2.79436 12.2429i 0.210633 0.922843i
\(177\) −4.20172 2.86468i −0.315820 0.215323i
\(178\) 3.98213 + 6.89726i 0.298474 + 0.516971i
\(179\) −0.759575 + 1.31562i −0.0567733 + 0.0983343i −0.893015 0.450026i \(-0.851415\pi\)
0.836242 + 0.548361i \(0.184748\pi\)
\(180\) −0.0933149 + 0.0449381i −0.00695528 + 0.00334949i
\(181\) 19.8250 + 6.11521i 1.47358 + 0.454540i 0.924485 0.381218i \(-0.124495\pi\)
0.549098 + 0.835758i \(0.314971\pi\)
\(182\) −0.602925 8.04548i −0.0446918 0.596370i
\(183\) −1.28168 5.61541i −0.0947446 0.415103i
\(184\) −1.60387 + 4.08658i −0.118238 + 0.301267i
\(185\) 0.0172518 0.230209i 0.00126838 0.0169253i
\(186\) −10.8646 + 1.63757i −0.796628 + 0.120072i
\(187\) 1.87728 + 1.74186i 0.137280 + 0.127377i
\(188\) 2.73538 + 1.31729i 0.199498 + 0.0960732i
\(189\) 4.59340 3.13173i 0.334121 0.227800i
\(190\) −0.00946818 0.0241245i −0.000686894 0.00175018i
\(191\) −16.9777 + 5.23692i −1.22846 + 0.378930i −0.840026 0.542546i \(-0.817461\pi\)
−0.388435 + 0.921476i \(0.626984\pi\)
\(192\) −1.79786 + 1.66817i −0.129749 + 0.120390i
\(193\) 15.8561 19.8829i 1.14135 1.43120i 0.255753 0.966742i \(-0.417677\pi\)
0.885593 0.464461i \(-0.153752\pi\)
\(194\) −11.7986 + 14.7949i −0.847087 + 1.06221i
\(195\) −0.0947734 + 0.0879368i −0.00678686 + 0.00629729i
\(196\) −3.13563 + 0.967212i −0.223973 + 0.0690866i
\(197\) −7.09014 18.0654i −0.505152 1.28711i −0.925157 0.379584i \(-0.876067\pi\)
0.420005 0.907522i \(-0.362028\pi\)
\(198\) 8.85845 6.03959i 0.629542 0.429215i
\(199\) −18.8360 9.07093i −1.33525 0.643021i −0.376271 0.926509i \(-0.622794\pi\)
−0.958976 + 0.283488i \(0.908508\pi\)
\(200\) 7.87148 + 7.30366i 0.556597 + 0.516447i
\(201\) −4.70428 + 0.709057i −0.331815 + 0.0500130i
\(202\) −1.86991 + 24.9523i −0.131567 + 1.75564i
\(203\) −5.32384 + 13.5649i −0.373660 + 0.952071i
\(204\) 0.102615 + 0.449584i 0.00718445 + 0.0314772i
\(205\) 0.0118999 + 0.158793i 0.000831125 + 0.0110906i
\(206\) −0.715742 0.220777i −0.0498681 0.0153823i
\(207\) −4.69833 + 2.26260i −0.326556 + 0.157261i
\(208\) −8.05655 + 13.9544i −0.558622 + 0.967561i
\(209\) 0.343914 + 0.595677i 0.0237891 + 0.0412038i
\(210\) −0.0798185 0.0544193i −0.00550800 0.00375529i
\(211\) 2.79064 12.2266i 0.192116 0.841715i −0.783353 0.621577i \(-0.786492\pi\)
0.975469 0.220138i \(-0.0706506\pi\)
\(212\) −6.05094 0.912033i −0.415581 0.0626387i
\(213\) −1.21755 1.52676i −0.0834251 0.104612i
\(214\) 6.42644 0.439302
\(215\) 0.379332 + 0.0704018i 0.0258702 + 0.00480136i
\(216\) −7.98024 −0.542987
\(217\) 9.35168 + 11.7266i 0.634833 + 0.796056i
\(218\) 19.6854 + 2.96709i 1.33326 + 0.200957i
\(219\) −1.55664 + 6.82008i −0.105188 + 0.460858i
\(220\) −0.0858467 0.0585293i −0.00578778 0.00394604i
\(221\) −1.64297 2.84571i −0.110518 0.191423i
\(222\) −2.15161 + 3.72671i −0.144407 + 0.250120i
\(223\) −1.85414 + 0.892906i −0.124162 + 0.0597934i −0.494934 0.868931i \(-0.664808\pi\)
0.370771 + 0.928724i \(0.379093\pi\)
\(224\) −5.35599 1.65210i −0.357862 0.110386i
\(225\) 0.953194 + 12.7195i 0.0635462 + 0.847966i
\(226\) 2.02398 + 8.86763i 0.134633 + 0.589866i
\(227\) −0.764601 + 1.94817i −0.0507483 + 0.129305i −0.954000 0.299806i \(-0.903078\pi\)
0.903252 + 0.429111i \(0.141173\pi\)
\(228\) −0.00925594 + 0.123512i −0.000612990 + 0.00817978i
\(229\) −16.1948 + 2.44098i −1.07019 + 0.161305i −0.660428 0.750890i \(-0.729625\pi\)
−0.409758 + 0.912194i \(0.634387\pi\)
\(230\) 0.144488 + 0.134066i 0.00952728 + 0.00884003i
\(231\) 2.31004 + 1.11246i 0.151990 + 0.0731943i
\(232\) 17.2830 11.7834i 1.13469 0.773616i
\(233\) −10.1313 25.8141i −0.663723 1.69114i −0.721140 0.692790i \(-0.756381\pi\)
0.0574164 0.998350i \(-0.481714\pi\)
\(234\) −13.1457 + 4.05491i −0.859360 + 0.265078i
\(235\) −0.189887 + 0.176189i −0.0123869 + 0.0114933i
\(236\) −3.26952 + 4.09985i −0.212828 + 0.266878i
\(237\) 5.31923 6.67010i 0.345521 0.433270i
\(238\) 1.79987 1.67004i 0.116668 0.108252i
\(239\) 9.69083 2.98923i 0.626848 0.193357i 0.0349749 0.999388i \(-0.488865\pi\)
0.591873 + 0.806031i \(0.298389\pi\)
\(240\) 0.0704868 + 0.179597i 0.00454990 + 0.0115930i
\(241\) 5.96952 4.06995i 0.384530 0.262168i −0.355591 0.934642i \(-0.615720\pi\)
0.740121 + 0.672473i \(0.234768\pi\)
\(242\) −6.56309 3.16062i −0.421892 0.203172i
\(243\) −10.7031 9.93107i −0.686607 0.637078i
\(244\) −5.87307 + 0.885223i −0.375985 + 0.0566706i
\(245\) 0.0209223 0.279188i 0.00133667 0.0178367i
\(246\) 1.08443 2.76308i 0.0691407 0.176168i
\(247\) −0.196390 0.860439i −0.0124960 0.0547484i
\(248\) −1.60895 21.4700i −0.102169 1.36335i
\(249\) 7.54033 + 2.32589i 0.477849 + 0.147397i
\(250\) 0.869042 0.418508i 0.0549630 0.0264688i
\(251\) 14.3686 24.8872i 0.906939 1.57086i 0.0886466 0.996063i \(-0.471746\pi\)
0.818293 0.574802i \(-0.194921\pi\)
\(252\) −1.31776 2.28243i −0.0830112 0.143780i
\(253\) −4.32231 2.94690i −0.271741 0.185270i
\(254\) 2.85341 12.5016i 0.179039 0.784421i
\(255\) −0.0389057 0.00586409i −0.00243637 0.000367223i
\(256\) 9.23302 + 11.5778i 0.577064 + 0.723615i
\(257\) 16.9142 1.05508 0.527539 0.849531i \(-0.323115\pi\)
0.527539 + 0.849531i \(0.323115\pi\)
\(258\) −5.80127 4.25031i −0.361171 0.264613i
\(259\) 5.87442 0.365019
\(260\) 0.0831218 + 0.104231i 0.00515499 + 0.00646416i
\(261\) 24.5697 + 3.70329i 1.52083 + 0.229228i
\(262\) 1.35784 5.94907i 0.0838874 0.367535i
\(263\) −22.2208 15.1499i −1.37019 0.934181i −0.999986 0.00523142i \(-0.998335\pi\)
−0.370206 0.928950i \(-0.620713\pi\)
\(264\) −1.84021 3.18734i −0.113257 0.196167i
\(265\) 0.261050 0.452152i 0.0160362 0.0277755i
\(266\) 0.594161 0.286133i 0.0364303 0.0175439i
\(267\) 3.10327 + 0.957231i 0.189917 + 0.0585816i
\(268\) 0.366607 + 4.89203i 0.0223941 + 0.298829i
\(269\) 3.10346 + 13.5971i 0.189221 + 0.829032i 0.977028 + 0.213110i \(0.0683592\pi\)
−0.787807 + 0.615922i \(0.788784\pi\)
\(270\) −0.130901 + 0.333531i −0.00796639 + 0.0202980i
\(271\) −1.89483 + 25.2847i −0.115103 + 1.53594i 0.578561 + 0.815639i \(0.303615\pi\)
−0.693663 + 0.720299i \(0.744004\pi\)
\(272\) −4.84887 + 0.730850i −0.294006 + 0.0443143i
\(273\) −2.41164 2.23767i −0.145959 0.135430i
\(274\) 26.9756 + 12.9907i 1.62965 + 0.784800i
\(275\) −10.5723 + 7.20805i −0.637532 + 0.434662i
\(276\) −0.344155 0.876892i −0.0207157 0.0527827i
\(277\) 2.98061 0.919397i 0.179088 0.0552412i −0.203914 0.978989i \(-0.565366\pi\)
0.383002 + 0.923747i \(0.374890\pi\)
\(278\) −5.18515 + 4.81112i −0.310985 + 0.288552i
\(279\) 15.9456 19.9952i 0.954639 1.19708i
\(280\) 0.118028 0.148002i 0.00705352 0.00884484i
\(281\) −16.8710 + 15.6540i −1.00644 + 0.933837i −0.997811 0.0661259i \(-0.978936\pi\)
−0.00862557 + 0.999963i \(0.502746\pi\)
\(282\) 4.61402 1.42324i 0.274761 0.0847526i
\(283\) 9.08875 + 23.1578i 0.540270 + 1.37659i 0.896856 + 0.442323i \(0.145845\pi\)
−0.356586 + 0.934263i \(0.616059\pi\)
\(284\) −1.66378 + 1.13435i −0.0987274 + 0.0673112i
\(285\) −0.00952111 0.00458513i −0.000563982 0.000271599i
\(286\) −10.1165 9.38676i −0.598202 0.555051i
\(287\) −4.00678 + 0.603925i −0.236513 + 0.0356486i
\(288\) −0.714205 + 9.53041i −0.0420850 + 0.561585i
\(289\) 0.365341 0.930874i 0.0214906 0.0547573i
\(290\) −0.208984 0.915621i −0.0122720 0.0537671i
\(291\) 0.576640 + 7.69473i 0.0338032 + 0.451073i
\(292\) 6.89310 + 2.12624i 0.403388 + 0.124429i
\(293\) 6.34845 3.05725i 0.370880 0.178607i −0.239154 0.970982i \(-0.576870\pi\)
0.610034 + 0.792375i \(0.291156\pi\)
\(294\) −2.60939 + 4.51960i −0.152183 + 0.263588i
\(295\) −0.223706 0.387471i −0.0130247 0.0225594i
\(296\) −6.96719 4.75015i −0.404960 0.276097i
\(297\) 2.11606 9.27106i 0.122786 0.537962i
\(298\) −13.2208 1.99272i −0.765860 0.115435i
\(299\) 4.18511 + 5.24797i 0.242031 + 0.303498i
\(300\) −2.30413 −0.133029
\(301\) −1.06512 + 9.75951i −0.0613925 + 0.562529i
\(302\) 31.7427 1.82659
\(303\) 6.36158 + 7.97717i 0.365463 + 0.458276i
\(304\) −1.30235 0.196298i −0.0746949 0.0112584i
\(305\) 0.112763 0.494047i 0.00645679 0.0282891i
\(306\) −3.45911 2.35838i −0.197744 0.134820i
\(307\) 10.1817 + 17.6352i 0.581099 + 1.00649i 0.995349 + 0.0963302i \(0.0307105\pi\)
−0.414250 + 0.910163i \(0.635956\pi\)
\(308\) 1.32195 2.28968i 0.0753249 0.130467i
\(309\) −0.275177 + 0.132518i −0.0156543 + 0.00753870i
\(310\) −0.923721 0.284930i −0.0524638 0.0161829i
\(311\) −0.00474105 0.0632649i −0.000268840 0.00358742i 0.997068 0.0765237i \(-0.0243821\pi\)
−0.997337 + 0.0729363i \(0.976763\pi\)
\(312\) 1.05084 + 4.60402i 0.0594920 + 0.260651i
\(313\) −0.818670 + 2.08594i −0.0462740 + 0.117904i −0.952142 0.305656i \(-0.901124\pi\)
0.905868 + 0.423560i \(0.139220\pi\)
\(314\) −2.25361 + 30.0724i −0.127179 + 1.69708i
\(315\) 0.222352 0.0335142i 0.0125281 0.00188831i
\(316\) −6.44893 5.98374i −0.362781 0.336611i
\(317\) −20.2629 9.75809i −1.13808 0.548069i −0.232646 0.972562i \(-0.574738\pi\)
−0.905432 + 0.424492i \(0.860453\pi\)
\(318\) −8.04109 + 5.48233i −0.450922 + 0.307434i
\(319\) 9.10654 + 23.2031i 0.509869 + 1.29912i
\(320\) −0.206192 + 0.0636018i −0.0115265 + 0.00355545i
\(321\) 1.92094 1.78238i 0.107217 0.0994825i
\(322\) −3.12719 + 3.92137i −0.174271 + 0.218529i
\(323\) 0.167462 0.209991i 0.00931784 0.0116842i
\(324\) −2.61604 + 2.42733i −0.145336 + 0.134852i
\(325\) 15.6889 4.83940i 0.870266 0.268442i
\(326\) 10.5725 + 26.9384i 0.585558 + 1.49198i
\(327\) 6.70713 4.57284i 0.370905 0.252879i
\(328\) 5.24048 + 2.52368i 0.289357 + 0.139347i
\(329\) −4.83194 4.48338i −0.266393 0.247177i
\(330\) −0.163399 + 0.0246284i −0.00899480 + 0.00135575i
\(331\) −0.647856 + 8.64504i −0.0356094 + 0.475174i 0.950683 + 0.310165i \(0.100384\pi\)
−0.986292 + 0.165009i \(0.947235\pi\)
\(332\) 2.97276 7.57446i 0.163151 0.415702i
\(333\) −2.22888 9.76538i −0.122142 0.535139i
\(334\) 2.87496 + 38.3636i 0.157311 + 2.09916i
\(335\) −0.399965 0.123373i −0.0218524 0.00674058i
\(336\) −4.42329 + 2.13014i −0.241310 + 0.116209i
\(337\) 8.32477 14.4189i 0.453479 0.785449i −0.545120 0.838358i \(-0.683516\pi\)
0.998599 + 0.0529087i \(0.0168492\pi\)
\(338\) −1.80608 3.12822i −0.0982378 0.170153i
\(339\) 3.06443 + 2.08930i 0.166437 + 0.113475i
\(340\) −0.00902809 + 0.0395546i −0.000489617 + 0.00214515i
\(341\) 25.3694 + 3.82383i 1.37383 + 0.207072i
\(342\) −0.701092 0.879142i −0.0379107 0.0475386i
\(343\) 17.6043 0.950542
\(344\) 9.15496 10.7137i 0.493602 0.577645i
\(345\) 0.0803726 0.00432712
\(346\) −4.42536 5.54923i −0.237909 0.298328i
\(347\) 0.0842371 + 0.0126967i 0.00452209 + 0.000681595i 0.151303 0.988487i \(-0.451653\pi\)
−0.146781 + 0.989169i \(0.546891\pi\)
\(348\) −0.998782 + 4.37595i −0.0535404 + 0.234576i
\(349\) −14.8698 10.1381i −0.795963 0.542678i 0.0956828 0.995412i \(-0.469497\pi\)
−0.891646 + 0.452733i \(0.850449\pi\)
\(350\) 6.13404 + 10.6245i 0.327878 + 0.567901i
\(351\) −6.10091 + 10.5671i −0.325642 + 0.564029i
\(352\) −8.63802 + 4.15985i −0.460408 + 0.221721i
\(353\) 13.5261 + 4.17224i 0.719920 + 0.222066i 0.633003 0.774149i \(-0.281822\pi\)
0.0869176 + 0.996216i \(0.472298\pi\)
\(354\) 0.623246 + 8.31663i 0.0331251 + 0.442024i
\(355\) −0.0382309 0.167501i −0.00202909 0.00889002i
\(356\) 1.22345 3.11731i 0.0648430 0.165217i
\(357\) 0.0748191 0.998391i 0.00395985 0.0528405i
\(358\) 2.46357 0.371324i 0.130204 0.0196251i
\(359\) 18.6871 + 17.3391i 0.986269 + 0.915124i 0.996396 0.0848252i \(-0.0270332\pi\)
−0.0101272 + 0.999949i \(0.503224\pi\)
\(360\) −0.290815 0.140049i −0.0153273 0.00738124i
\(361\) −15.6389 + 10.6624i −0.823102 + 0.561181i
\(362\) −12.4306 31.6726i −0.653336 1.66467i
\(363\) −2.83839 + 0.875528i −0.148977 + 0.0459533i
\(364\) −2.48683 + 2.30744i −0.130345 + 0.120943i
\(365\) −0.383737 + 0.481190i −0.0200857 + 0.0251867i
\(366\) −5.88953 + 7.38524i −0.307851 + 0.386033i
\(367\) 1.52492 1.41492i 0.0796002 0.0738582i −0.639369 0.768900i \(-0.720805\pi\)
0.718970 + 0.695042i \(0.244614\pi\)
\(368\) 9.57193 2.95255i 0.498971 0.153912i
\(369\) 2.52420 + 6.43155i 0.131405 + 0.334813i
\(370\) −0.312814 + 0.213273i −0.0162625 + 0.0110876i
\(371\) 11.9699 + 5.76439i 0.621445 + 0.299272i
\(372\) 3.38663 + 3.14234i 0.175589 + 0.162923i
\(373\) −11.3199 + 1.70620i −0.586121 + 0.0883435i −0.435407 0.900234i \(-0.643395\pi\)
−0.150714 + 0.988577i \(0.548157\pi\)
\(374\) 0.313857 4.18812i 0.0162291 0.216563i
\(375\) 0.143694 0.366127i 0.00742033 0.0189067i
\(376\) 2.10545 + 9.22458i 0.108580 + 0.475721i
\(377\) −2.39011 31.8938i −0.123097 1.64262i
\(378\) −8.71234 2.68740i −0.448114 0.138225i
\(379\) −5.73548 + 2.76206i −0.294612 + 0.141878i −0.575351 0.817906i \(-0.695135\pi\)
0.280739 + 0.959784i \(0.409420\pi\)
\(380\) −0.00544856 + 0.00943719i −0.000279505 + 0.000484117i
\(381\) −2.61441 4.52828i −0.133940 0.231991i
\(382\) 24.0748 + 16.4139i 1.23177 + 0.839809i
\(383\) −4.74633 + 20.7950i −0.242526 + 1.06258i 0.696183 + 0.717864i \(0.254880\pi\)
−0.938709 + 0.344711i \(0.887977\pi\)
\(384\) 8.92853 + 1.34576i 0.455632 + 0.0686755i
\(385\) 0.140646 + 0.176364i 0.00716796 + 0.00898834i
\(386\) −41.7070 −2.12283
\(387\) 16.6279 1.93236i 0.845244 0.0982275i
\(388\) 7.95689 0.403950
\(389\) 18.9154 + 23.7191i 0.959047 + 1.20261i 0.979218 + 0.202810i \(0.0650075\pi\)
−0.0201710 + 0.999797i \(0.506421\pi\)
\(390\) 0.209660 + 0.0316012i 0.0106166 + 0.00160019i
\(391\) −0.454557 + 1.99154i −0.0229879 + 0.100717i
\(392\) −8.44952 5.76079i −0.426765 0.290964i
\(393\) −1.24410 2.15485i −0.0627567 0.108698i
\(394\) −15.9136 + 27.5632i −0.801717 + 1.38861i
\(395\) 0.676263 0.325671i 0.0340265 0.0163863i
\(396\) −4.30784 1.32879i −0.216477 0.0667743i
\(397\) −0.462717 6.17452i −0.0232231 0.309890i −0.996704 0.0811227i \(-0.974149\pi\)
0.973481 0.228768i \(-0.0734696\pi\)
\(398\) 7.62942 + 33.4267i 0.382428 + 1.67553i
\(399\) 0.0982432 0.250319i 0.00491831 0.0125316i
\(400\) 1.83098 24.4327i 0.0915490 1.22164i
\(401\) 8.63651 1.30175i 0.431287 0.0650060i 0.0701885 0.997534i \(-0.477640\pi\)
0.361098 + 0.932528i \(0.382402\pi\)
\(402\) 5.71938 + 5.30681i 0.285257 + 0.264679i
\(403\) −29.6597 14.2833i −1.47745 0.711504i
\(404\) 8.69311 5.92686i 0.432498 0.294872i
\(405\) −0.111240 0.283435i −0.00552757 0.0140840i
\(406\) 22.8367 7.04418i 1.13337 0.349597i
\(407\) 7.36594 6.83459i 0.365116 0.338778i
\(408\) −0.896053 + 1.12361i −0.0443612 + 0.0556272i
\(409\) 20.4970 25.7024i 1.01351 1.27090i 0.0512738 0.998685i \(-0.483672\pi\)
0.962236 0.272217i \(-0.0877567\pi\)
\(410\) 0.191436 0.177627i 0.00945437 0.00877238i
\(411\) 11.6663 3.59859i 0.575458 0.177505i
\(412\) 0.115063 + 0.293175i 0.00566874 + 0.0144437i
\(413\) 9.40675 6.41341i 0.462876 0.315583i
\(414\) 7.70523 + 3.71064i 0.378692 + 0.182368i
\(415\) 0.508919 + 0.472207i 0.0249818 + 0.0231798i
\(416\) 12.1645 1.83350i 0.596413 0.0898948i
\(417\) −0.215542 + 2.87621i −0.0105551 + 0.140849i
\(418\) 0.412118 1.05006i 0.0201573 0.0513600i
\(419\) 2.87135 + 12.5802i 0.140275 + 0.614583i 0.995370 + 0.0961131i \(0.0306410\pi\)
−0.855096 + 0.518470i \(0.826502\pi\)
\(420\) 0.00303555 + 0.0405066i 0.000148120 + 0.00197652i
\(421\) −31.8881 9.83617i −1.55413 0.479385i −0.605519 0.795831i \(-0.707034\pi\)
−0.948611 + 0.316446i \(0.897511\pi\)
\(422\) −18.5304 + 8.92379i −0.902048 + 0.434403i
\(423\) −5.61963 + 9.73349i −0.273236 + 0.473259i
\(424\) −9.53537 16.5157i −0.463078 0.802075i
\(425\) 4.12833 + 2.81465i 0.200254 + 0.136531i
\(426\) −0.712641 + 3.12228i −0.0345276 + 0.151275i
\(427\) 12.7510 + 1.92190i 0.617064 + 0.0930074i
\(428\) −1.68478 2.11265i −0.0814370 0.102119i
\(429\) −5.62738 −0.271692
\(430\) −0.297605 0.558366i −0.0143518 0.0269268i
\(431\) 12.7707 0.615142 0.307571 0.951525i \(-0.400484\pi\)
0.307571 + 0.951525i \(0.400484\pi\)
\(432\) 11.3530 + 14.2363i 0.546223 + 0.684942i
\(433\) −20.7725 3.13095i −0.998261 0.150464i −0.370469 0.928845i \(-0.620803\pi\)
−0.627792 + 0.778381i \(0.716041\pi\)
\(434\) 5.47361 23.9814i 0.262742 1.15115i
\(435\) −0.316416 0.215729i −0.0151710 0.0103434i
\(436\) −4.18538 7.24929i −0.200443 0.347178i
\(437\) −0.274331 + 0.475155i −0.0131230 + 0.0227297i
\(438\) 10.3364 4.97775i 0.493892 0.237846i
\(439\) −31.0667 9.58280i −1.48273 0.457362i −0.555394 0.831588i \(-0.687432\pi\)
−0.927338 + 0.374226i \(0.877909\pi\)
\(440\) −0.0241980 0.322900i −0.00115360 0.0153937i
\(441\) −2.70310 11.8430i −0.128719 0.563954i
\(442\) −1.96880 + 5.01642i −0.0936463 + 0.238607i
\(443\) −2.31253 + 30.8585i −0.109871 + 1.46613i 0.621104 + 0.783728i \(0.286685\pi\)
−0.730975 + 0.682404i \(0.760935\pi\)
\(444\) 1.78920 0.269679i 0.0849119 0.0127984i
\(445\) 0.209448 + 0.194340i 0.00992880 + 0.00921258i
\(446\) 3.04078 + 1.46436i 0.143985 + 0.0693395i
\(447\) −4.50455 + 3.07115i −0.213058 + 0.145260i
\(448\) −2.00601 5.11122i −0.0947749 0.241482i
\(449\) 1.70993 0.527444i 0.0806966 0.0248916i −0.254144 0.967166i \(-0.581794\pi\)
0.334841 + 0.942275i \(0.391318\pi\)
\(450\) 15.3343 14.2281i 0.722864 0.670720i
\(451\) −4.32147 + 5.41895i −0.203490 + 0.255168i
\(452\) 2.38456 2.99014i 0.112160 0.140644i
\(453\) 9.48829 8.80384i 0.445799 0.413641i
\(454\) 3.27976 1.01167i 0.153927 0.0474802i
\(455\) −0.105746 0.269436i −0.00495743 0.0126313i
\(456\) −0.318931 + 0.217444i −0.0149353 + 0.0101827i
\(457\) 22.9030 + 11.0295i 1.07136 + 0.515939i 0.884544 0.466456i \(-0.154470\pi\)
0.186814 + 0.982395i \(0.440184\pi\)
\(458\) 19.6894 + 18.2691i 0.920024 + 0.853658i
\(459\) −3.67186 + 0.553444i −0.171388 + 0.0258325i
\(460\) 0.00619352 0.0826468i 0.000288774 0.00385343i
\(461\) 11.1091 28.3055i 0.517402 1.31832i −0.398593 0.917128i \(-0.630501\pi\)
0.915995 0.401191i \(-0.131404\pi\)
\(462\) −0.935671 4.09944i −0.0435314 0.190723i
\(463\) −0.611135 8.15503i −0.0284018 0.378996i −0.993234 0.116130i \(-0.962951\pi\)
0.964832 0.262867i \(-0.0846679\pi\)
\(464\) −45.6084 14.0683i −2.11731 0.653105i
\(465\) −0.355137 + 0.171025i −0.0164691 + 0.00793110i
\(466\) −22.7394 + 39.3858i −1.05338 + 1.82451i
\(467\) 15.6510 + 27.1084i 0.724243 + 1.25442i 0.959285 + 0.282440i \(0.0911438\pi\)
−0.235042 + 0.971985i \(0.575523\pi\)
\(468\) 4.77935 + 3.25850i 0.220925 + 0.150624i
\(469\) 2.37004 10.3838i 0.109438 0.479480i
\(470\) 0.420073 + 0.0633158i 0.0193765 + 0.00292054i
\(471\) 7.66696 + 9.61406i 0.353275 + 0.442993i
\(472\) −16.3426 −0.752230
\(473\) 10.0191 + 13.4767i 0.460681 + 0.619658i
\(474\) −13.9914 −0.642647
\(475\) 0.836731 + 1.04923i 0.0383918 + 0.0481418i
\(476\) −1.02088 0.153872i −0.0467917 0.00705272i
\(477\) 5.04083 22.0853i 0.230804 1.01122i
\(478\) −13.7419 9.36904i −0.628538 0.428530i
\(479\) 1.09700 + 1.90006i 0.0501232 + 0.0868160i 0.889998 0.455964i \(-0.150705\pi\)
−0.839875 + 0.542780i \(0.817372\pi\)
\(480\) 0.0736499 0.127565i 0.00336164 0.00582253i
\(481\) −11.6164 + 5.59415i −0.529661 + 0.255071i
\(482\) −11.3224 3.49251i −0.515723 0.159079i
\(483\) 0.152837 + 2.03947i 0.00695434 + 0.0927992i
\(484\) 0.681574 + 2.98617i 0.0309807 + 0.135735i
\(485\) −0.248025 + 0.631956i −0.0112622 + 0.0286957i
\(486\) −1.78943 + 23.8783i −0.0811702 + 1.08314i
\(487\) 39.7953 5.99818i 1.80330 0.271804i 0.840459 0.541875i \(-0.182286\pi\)
0.962840 + 0.270072i \(0.0870474\pi\)
\(488\) −13.5689 12.5901i −0.614234 0.569926i
\(489\) 10.6316 + 5.11992i 0.480779 + 0.231531i
\(490\) −0.379368 + 0.258649i −0.0171381 + 0.0116846i
\(491\) 5.79660 + 14.7695i 0.261597 + 0.666538i 0.999969 0.00785518i \(-0.00250041\pi\)
−0.738372 + 0.674394i \(0.764405\pi\)
\(492\) −1.19264 + 0.367882i −0.0537685 + 0.0165854i
\(493\) 7.13504 6.62035i 0.321346 0.298166i
\(494\) −0.902443 + 1.13163i −0.0406028 + 0.0509143i
\(495\) 0.239816 0.300719i 0.0107789 0.0135163i
\(496\) −36.0121 + 33.4144i −1.61699 + 1.50035i
\(497\) 4.17767 1.28864i 0.187394 0.0578034i
\(498\) −4.72789 12.0465i −0.211862 0.539815i
\(499\) 2.02657 1.38169i 0.0907215 0.0618529i −0.517110 0.855919i \(-0.672992\pi\)
0.607831 + 0.794066i \(0.292040\pi\)
\(500\) −0.365413 0.175974i −0.0163418 0.00786978i
\(501\) 11.4995 + 10.6700i 0.513761 + 0.476701i
\(502\) −46.6025 + 7.02420i −2.07997 + 0.313505i
\(503\) −0.871139 + 11.6245i −0.0388422 + 0.518312i 0.943519 + 0.331319i \(0.107493\pi\)
−0.982361 + 0.186994i \(0.940126\pi\)
\(504\) 3.00076 7.64582i 0.133665 0.340572i
\(505\) 0.199753 + 0.875175i 0.00888889 + 0.0389448i
\(506\) 0.641133 + 8.55533i 0.0285018 + 0.380331i
\(507\) −1.40747 0.434148i −0.0625081 0.0192812i
\(508\) −4.85788 + 2.33943i −0.215534 + 0.103795i
\(509\) −10.9039 + 18.8861i −0.483308 + 0.837113i −0.999816 0.0191687i \(-0.993898\pi\)
0.516509 + 0.856282i \(0.327231\pi\)
\(510\) 0.0322629 + 0.0558810i 0.00142862 + 0.00247445i
\(511\) −12.9400 8.82236i −0.572433 0.390278i
\(512\) −0.604907 + 2.65027i −0.0267333 + 0.117126i
\(513\) −0.986218 0.148648i −0.0435426 0.00656299i
\(514\) −17.2951 21.6873i −0.762853 0.956588i
\(515\) −0.0268713 −0.00118409
\(516\) 0.123624 + 3.02141i 0.00544224 + 0.133010i
\(517\) −11.2750 −0.495872
\(518\) −6.00671 7.53217i −0.263920 0.330945i
\(519\) −2.86188 0.431359i −0.125623 0.0189345i
\(520\) −0.0924533 + 0.405065i −0.00405435 + 0.0177633i
\(521\) −29.0546 19.8091i −1.27290 0.867851i −0.277232 0.960803i \(-0.589417\pi\)
−0.995671 + 0.0929523i \(0.970370\pi\)
\(522\) −20.3747 35.2900i −0.891775 1.54460i
\(523\) −9.86269 + 17.0827i −0.431266 + 0.746974i −0.996983 0.0776256i \(-0.975266\pi\)
0.565717 + 0.824599i \(0.308599\pi\)
\(524\) −2.31169 + 1.11325i −0.100987 + 0.0486326i
\(525\) 4.78024 + 1.47451i 0.208627 + 0.0643529i
\(526\) 3.29603 + 43.9825i 0.143714 + 1.91773i
\(527\) −2.22929 9.76716i −0.0971094 0.425464i
\(528\) −3.06805 + 7.81726i −0.133520 + 0.340203i
\(529\) −1.40695 + 18.7745i −0.0611719 + 0.816282i
\(530\) −0.846678 + 0.127616i −0.0367773 + 0.00554329i
\(531\) −14.2305 13.2040i −0.617551 0.573004i
\(532\) −0.249832 0.120313i −0.0108316 0.00521621i
\(533\) 7.34810 5.00985i 0.318281 0.217001i
\(534\) −1.94579 4.95780i −0.0842026 0.214545i
\(535\) 0.220308 0.0679561i 0.00952475 0.00293800i
\(536\) −11.2074 + 10.3990i −0.484088 + 0.449168i
\(537\) 0.633406 0.794266i 0.0273335 0.0342751i
\(538\) 14.2609 17.8826i 0.614830 0.770973i
\(539\) 8.93310 8.28871i 0.384776 0.357020i
\(540\) 0.143964 0.0444069i 0.00619520 0.00191097i
\(541\) 4.25880 + 10.8512i 0.183100 + 0.466531i 0.992723 0.120419i \(-0.0384237\pi\)
−0.809623 + 0.586950i \(0.800328\pi\)
\(542\) 34.3576 23.4246i 1.47578 1.00617i
\(543\) −12.5001 6.01971i −0.536429 0.258331i
\(544\) 2.74439 + 2.54642i 0.117665 + 0.109177i
\(545\) 0.706219 0.106445i 0.0302511 0.00455962i
\(546\) −0.403195 + 5.38027i −0.0172552 + 0.230254i
\(547\) 16.2312 41.3564i 0.693996 1.76827i 0.0557464 0.998445i \(-0.482246\pi\)
0.638250 0.769829i \(-0.279659\pi\)
\(548\) −2.80140 12.2737i −0.119670 0.524308i
\(549\) −1.64312 21.9259i −0.0701266 0.935775i
\(550\) 20.0525 + 6.18538i 0.855042 + 0.263745i
\(551\) 2.35537 1.13429i 0.100342 0.0483222i
\(552\) 1.46788 2.54245i 0.0624772 0.108214i
\(553\) 9.54997 + 16.5410i 0.406106 + 0.703396i
\(554\) −4.22659 2.88164i −0.179570 0.122429i
\(555\) −0.0343528 + 0.150509i −0.00145819 + 0.00638877i
\(556\) 2.94098 + 0.443282i 0.124725 + 0.0187993i
\(557\) 19.1411 + 24.0022i 0.811034 + 1.01700i 0.999391 + 0.0349039i \(0.0111125\pi\)
−0.188357 + 0.982101i \(0.560316\pi\)
\(558\) −41.9425 −1.77557
\(559\) −7.18766 20.3133i −0.304006 0.859159i
\(560\) −0.431939 −0.0182527
\(561\) −1.06776 1.33893i −0.0450810 0.0565297i
\(562\) 37.3224 + 5.62544i 1.57435 + 0.237295i
\(563\) 1.89315 8.29443i 0.0797867 0.349569i −0.919239 0.393700i \(-0.871195\pi\)
0.999026 + 0.0441314i \(0.0140520\pi\)
\(564\) −1.67751 1.14371i −0.0706359 0.0481588i
\(565\) 0.163155 + 0.282593i 0.00686400 + 0.0118888i
\(566\) 20.3994 35.3328i 0.857452 1.48515i
\(567\) 6.98070 3.36173i 0.293162 0.141179i
\(568\) −5.99682 1.84978i −0.251621 0.0776149i
\(569\) −0.947167 12.6391i −0.0397073 0.529857i −0.981222 0.192884i \(-0.938216\pi\)
0.941514 0.336973i \(-0.109403\pi\)
\(570\) 0.00385648 + 0.0168963i 0.000161530 + 0.000707710i
\(571\) 5.30458 13.5158i 0.221990 0.565621i −0.775878 0.630882i \(-0.782693\pi\)
0.997868 + 0.0652618i \(0.0207882\pi\)
\(572\) −0.433646 + 5.78660i −0.0181317 + 0.241950i
\(573\) 11.7487 1.77083i 0.490808 0.0739773i
\(574\) 4.87136 + 4.51996i 0.203327 + 0.188660i
\(575\) −9.19594 4.42853i −0.383497 0.184683i
\(576\) −7.73555 + 5.27401i −0.322314 + 0.219750i
\(577\) −14.1037 35.9356i −0.587143 1.49602i −0.847656 0.530546i \(-0.821987\pi\)
0.260512 0.965470i \(-0.416108\pi\)
\(578\) −1.56713 + 0.483397i −0.0651842 + 0.0201067i
\(579\) −12.4668 + 11.5675i −0.518101 + 0.480727i
\(580\) −0.246216 + 0.308745i −0.0102236 + 0.0128199i
\(581\) −11.0146 + 13.8119i −0.456963 + 0.573013i
\(582\) 9.27655 8.60738i 0.384525 0.356787i
\(583\) 21.7156 6.69838i 0.899369 0.277419i
\(584\) 8.21326 + 20.9271i 0.339867 + 0.865968i
\(585\) −0.407776 + 0.278017i −0.0168595 + 0.0114946i
\(586\) −10.4114 5.01388i −0.430092 0.207121i
\(587\) 1.91733 + 1.77902i 0.0791368 + 0.0734282i 0.718750 0.695269i \(-0.244715\pi\)
−0.639613 + 0.768697i \(0.720905\pi\)
\(588\) 2.16987 0.327056i 0.0894841 0.0134876i
\(589\) 0.201084 2.68328i 0.00828553 0.110563i
\(590\) −0.268070 + 0.683032i −0.0110363 + 0.0281200i
\(591\) 2.88788 + 12.6526i 0.118792 + 0.520460i
\(592\) 1.43785 + 19.1868i 0.0590954 + 0.788573i
\(593\) −8.00910 2.47048i −0.328894 0.101450i 0.125910 0.992042i \(-0.459815\pi\)
−0.454805 + 0.890591i \(0.650291\pi\)
\(594\) −14.0511 + 6.76664i −0.576522 + 0.277638i
\(595\) 0.0440427 0.0762841i 0.00180557 0.00312734i
\(596\) 2.81093 + 4.86867i 0.115140 + 0.199428i
\(597\) 11.5514 + 7.87564i 0.472769 + 0.322328i
\(598\) 2.44958 10.7323i 0.100171 0.438876i
\(599\) −16.0307 2.41624i −0.654997 0.0987249i −0.186868 0.982385i \(-0.559834\pi\)
−0.468129 + 0.883660i \(0.655072\pi\)
\(600\) −4.47716 5.61418i −0.182779 0.229198i
\(601\) −41.4229 −1.68967 −0.844837 0.535023i \(-0.820303\pi\)
−0.844837 + 0.535023i \(0.820303\pi\)
\(602\) 13.6027 8.61359i 0.554406 0.351064i
\(603\) −18.1608 −0.739567
\(604\) −8.32178 10.4352i −0.338608 0.424602i
\(605\) −0.258415 0.0389497i −0.0105061 0.00158353i
\(606\) 3.72348 16.3136i 0.151256 0.662696i
\(607\) −14.7252 10.0395i −0.597676 0.407489i 0.226345 0.974047i \(-0.427322\pi\)
−0.824022 + 0.566558i \(0.808275\pi\)
\(608\) 0.502769 + 0.870821i 0.0203900 + 0.0353165i
\(609\) 4.87247 8.43936i 0.197442 0.341980i
\(610\) −0.748769 + 0.360588i −0.0303168 + 0.0145998i
\(611\) 13.8244 + 4.26426i 0.559275 + 0.172514i
\(612\) 0.131552 + 1.75544i 0.00531768 + 0.0709595i
\(613\) 3.14569 + 13.7822i 0.127053 + 0.556656i 0.997881 + 0.0650677i \(0.0207263\pi\)
−0.870828 + 0.491588i \(0.836417\pi\)
\(614\) 12.2009 31.0873i 0.492386 1.25458i
\(615\) 0.00795784 0.106190i 0.000320891 0.00428199i
\(616\) 8.14765 1.22806i 0.328278 0.0494800i
\(617\) 17.0603 + 15.8297i 0.686823 + 0.637278i 0.944331 0.328998i \(-0.106711\pi\)
−0.257508 + 0.966276i \(0.582901\pi\)
\(618\) 0.451289 + 0.217329i 0.0181535 + 0.00874227i
\(619\) 23.3850 15.9436i 0.939921 0.640827i 0.00664143 0.999978i \(-0.497886\pi\)
0.933280 + 0.359151i \(0.116934\pi\)
\(620\) 0.148497 + 0.378365i 0.00596380 + 0.0151955i
\(621\) 7.24844 2.23585i 0.290870 0.0897215i
\(622\) −0.0762704 + 0.0707686i −0.00305816 + 0.00283756i
\(623\) −4.53312 + 5.68436i −0.181616 + 0.227739i
\(624\) 6.71832 8.42451i 0.268948 0.337250i
\(625\) −18.2882 + 16.9690i −0.731530 + 0.678760i
\(626\) 3.51169 1.08321i 0.140356 0.0432940i
\(627\) −0.168047 0.428177i −0.00671115 0.0170997i
\(628\) 10.4769 7.14304i 0.418074 0.285038i
\(629\) −3.53517 1.70245i −0.140956 0.0678810i
\(630\) −0.270332 0.250831i −0.0107703 0.00999335i
\(631\) −37.6192 + 5.67019i −1.49760 + 0.225727i −0.846141 0.532959i \(-0.821080\pi\)
−0.651457 + 0.758686i \(0.725842\pi\)
\(632\) 2.04887 27.3403i 0.0814998 1.08754i
\(633\) −3.06397 + 7.80686i −0.121782 + 0.310295i
\(634\) 8.20739 + 35.9589i 0.325957 + 1.42811i
\(635\) −0.0343784 0.458747i −0.00136426 0.0182048i
\(636\) 3.91036 + 1.20619i 0.155056 + 0.0478284i
\(637\) −14.0879 + 6.78435i −0.558181 + 0.268806i
\(638\) 20.4394 35.4020i 0.809203 1.40158i
\(639\) −3.72728 6.45583i −0.147449 0.255389i
\(640\) 0.656372 + 0.447507i 0.0259454 + 0.0176893i
\(641\) 0.0594943 0.260661i 0.00234988 0.0102955i −0.973739 0.227666i \(-0.926891\pi\)
0.976089 + 0.217370i \(0.0697478\pi\)
\(642\) −4.24957 0.640519i −0.167717 0.0252793i
\(643\) 27.9728 + 35.0768i 1.10314 + 1.38329i 0.916105 + 0.400939i \(0.131316\pi\)
0.187034 + 0.982353i \(0.440112\pi\)
\(644\) 2.10896 0.0831046
\(645\) −0.243821 0.0843618i −0.00960045 0.00332174i
\(646\) −0.440483 −0.0173306
\(647\) 0.670069 + 0.840240i 0.0263431 + 0.0330333i 0.794829 0.606834i \(-0.207561\pi\)
−0.768485 + 0.639867i \(0.778989\pi\)
\(648\) −10.9976 1.65762i −0.432027 0.0651176i
\(649\) 4.33345 18.9861i 0.170103 0.745268i
\(650\) −22.2473 15.1680i −0.872612 0.594937i
\(651\) −5.01513 8.68646i −0.196559 0.340449i
\(652\) 6.08407 10.5379i 0.238270 0.412697i
\(653\) 24.7201 11.9046i 0.967371 0.465861i 0.117628 0.993058i \(-0.462471\pi\)
0.849744 + 0.527196i \(0.176757\pi\)
\(654\) −12.7215 3.92405i −0.497449 0.153443i
\(655\) −0.0163594 0.218302i −0.000639216 0.00852975i
\(656\) −2.95324 12.9390i −0.115305 0.505182i
\(657\) −9.75618 + 24.8583i −0.380625 + 0.969816i
\(658\) −0.807838 + 10.7799i −0.0314928 + 0.420242i
\(659\) −17.5165 + 2.64018i −0.682344 + 0.102847i −0.481062 0.876686i \(-0.659749\pi\)
−0.201282 + 0.979533i \(0.564511\pi\)
\(660\) 0.0509336 + 0.0472595i 0.00198259 + 0.00183957i
\(661\) −10.1238 4.87535i −0.393769 0.189629i 0.226513 0.974008i \(-0.427268\pi\)
−0.620282 + 0.784379i \(0.712982\pi\)
\(662\) 11.7471 8.00904i 0.456564 0.311280i
\(663\) 0.802807 + 2.04552i 0.0311784 + 0.0794414i
\(664\) 24.2321 7.47461i 0.940387 0.290071i
\(665\) 0.0173430 0.0160920i 0.000672534 0.000624021i
\(666\) −10.2421 + 12.8432i −0.396873 + 0.497662i
\(667\) −12.3968 + 15.5451i −0.480005 + 0.601907i
\(668\) 11.8581 11.0027i 0.458802 0.425706i
\(669\) 1.31507 0.405645i 0.0508435 0.0156831i
\(670\) 0.250784 + 0.638986i 0.00968862 + 0.0246862i
\(671\) 18.2245 12.4253i 0.703550 0.479672i
\(672\) 3.37705 + 1.62630i 0.130273 + 0.0627360i
\(673\) −11.7371 10.8904i −0.452431 0.419794i 0.420761 0.907172i \(-0.361763\pi\)
−0.873191 + 0.487377i \(0.837954\pi\)
\(674\) −27.0002 + 4.06962i −1.04001 + 0.156756i
\(675\) 1.38653 18.5019i 0.0533675 0.712140i
\(676\) −0.554893 + 1.41384i −0.0213420 + 0.0543786i
\(677\) −2.66450 11.6739i −0.102405 0.448666i −0.999970 0.00778325i \(-0.997522\pi\)
0.897565 0.440883i \(-0.145335\pi\)
\(678\) −0.454551 6.06556i −0.0174569 0.232946i
\(679\) −16.5077 5.09194i −0.633506 0.195411i
\(680\) −0.113920 + 0.0548611i −0.00436864 + 0.00210383i
\(681\) 0.699775 1.21205i 0.0268154 0.0464457i
\(682\) −21.0378 36.4386i −0.805581 1.39531i
\(683\) −14.9639 10.2022i −0.572579 0.390378i 0.242133 0.970243i \(-0.422153\pi\)
−0.814713 + 0.579865i \(0.803105\pi\)
\(684\) −0.105211 + 0.460959i −0.00402284 + 0.0176252i
\(685\) 1.06213 + 0.160091i 0.0405820 + 0.00611676i
\(686\) −18.0007 22.5722i −0.687271 0.861811i
\(687\) 10.9523 0.417858
\(688\) −32.1368 1.09007i −1.22521 0.0415585i
\(689\) −29.1592 −1.11088
\(690\) −0.0821826 0.103054i −0.00312864 0.00392319i
\(691\) 18.3890 + 2.77170i 0.699552 + 0.105441i 0.489183 0.872181i \(-0.337295\pi\)
0.210370 + 0.977622i \(0.432533\pi\)
\(692\) −0.664101 + 2.90962i −0.0252453 + 0.110607i
\(693\) 8.08686 + 5.51353i 0.307194 + 0.209442i
\(694\) −0.0698544 0.120991i −0.00265164 0.00459277i
\(695\) −0.126880 + 0.219763i −0.00481283 + 0.00833607i
\(696\) −12.6031 + 6.06931i −0.477718 + 0.230057i
\(697\) 2.58626 + 0.797756i 0.0979616 + 0.0302172i
\(698\) 2.20566 + 29.4324i 0.0834854 + 1.11403i
\(699\) 4.12657 + 18.0797i 0.156081 + 0.683837i
\(700\) 1.88460 4.80187i 0.0712311 0.181494i
\(701\) −0.0381708 + 0.509353i −0.00144169 + 0.0192380i −0.997878 0.0651076i \(-0.979261\pi\)
0.996437 + 0.0843456i \(0.0268800\pi\)
\(702\) 19.7874 2.98247i 0.746828 0.112566i
\(703\) −0.772542 0.716814i −0.0291370 0.0270351i
\(704\) −8.46198 4.07507i −0.318923 0.153585i
\(705\) 0.143126 0.0975816i 0.00539043 0.00367513i
\(706\) −8.48104 21.6093i −0.319188 0.813278i
\(707\) −21.8279 + 6.73302i −0.820923 + 0.253221i
\(708\) 2.57064 2.38521i 0.0966107 0.0896416i
\(709\) 17.4313 21.8581i 0.654645 0.820899i −0.338104 0.941109i \(-0.609785\pi\)
0.992748 + 0.120210i \(0.0383569\pi\)
\(710\) −0.175677 + 0.220293i −0.00659306 + 0.00826743i
\(711\) 23.8736 22.1515i 0.895331 0.830745i
\(712\) 9.97285 3.07622i 0.373748 0.115286i
\(713\) 7.47672 + 19.0504i 0.280005 + 0.713442i
\(714\) −1.35664 + 0.924942i −0.0507710 + 0.0346151i
\(715\) −0.446069 0.214816i −0.0166821 0.00803365i
\(716\) −0.767930 0.712535i −0.0286989 0.0266287i
\(717\) −6.70612 + 1.01079i −0.250445 + 0.0377485i
\(718\) 3.12425 41.6902i 0.116596 1.55586i
\(719\) −11.8768 + 30.2616i −0.442930 + 1.12857i 0.518879 + 0.854848i \(0.326349\pi\)
−0.961809 + 0.273720i \(0.911746\pi\)
\(720\) 0.163887 + 0.718036i 0.00610771 + 0.0267596i
\(721\) −0.0510988 0.681866i −0.00190302 0.0253940i
\(722\) 29.6625 + 9.14967i 1.10392 + 0.340515i
\(723\) −4.35307 + 2.09633i −0.161892 + 0.0779632i
\(724\) −7.15330 + 12.3899i −0.265850 + 0.460466i
\(725\) 24.3165 + 42.1174i 0.903092 + 1.56420i
\(726\) 4.02491 + 2.74414i 0.149379 + 0.101845i
\(727\) 6.11025 26.7707i 0.226616 0.992872i −0.725760 0.687948i \(-0.758512\pi\)
0.952377 0.304924i \(-0.0986310\pi\)
\(728\) −10.4544 1.57575i −0.387466 0.0584012i
\(729\) −3.59223 4.50451i −0.133045 0.166834i
\(730\) 1.00936 0.0373581
\(731\) 3.46935 5.56450i 0.128319 0.205810i
\(732\) 3.97187 0.146805
\(733\) −7.60826 9.54046i −0.281018 0.352385i 0.621211 0.783644i \(-0.286641\pi\)
−0.902228 + 0.431259i \(0.858070\pi\)
\(734\) −3.37347 0.508469i −0.124517 0.0187679i
\(735\) −0.0416616 + 0.182531i −0.00153671 + 0.00673278i
\(736\) −6.31879 4.30808i −0.232914 0.158798i
\(737\) −9.10925 15.7777i −0.335544 0.581179i
\(738\) 5.66549 9.81292i 0.208550 0.361218i
\(739\) 1.09652 0.528058i 0.0403363 0.0194249i −0.413607 0.910456i \(-0.635731\pi\)
0.453943 + 0.891031i \(0.350017\pi\)
\(740\) 0.152121 + 0.0469231i 0.00559207 + 0.00172493i
\(741\) 0.0441058 + 0.588551i 0.00162027 + 0.0216209i
\(742\) −4.84834 21.2420i −0.177988 0.779817i
\(743\) −3.94900 + 10.0619i −0.144875 + 0.369135i −0.984830 0.173521i \(-0.944486\pi\)
0.839956 + 0.542655i \(0.182581\pi\)
\(744\) −1.07596 + 14.3577i −0.0394465 + 0.526378i
\(745\) −0.474301 + 0.0714894i −0.0173770 + 0.00261917i
\(746\) 13.7625 + 12.7697i 0.503880 + 0.467533i
\(747\) 27.1394 + 13.0697i 0.992980 + 0.478194i
\(748\) −1.45910 + 0.994797i −0.0533499 + 0.0363734i
\(749\) 2.14334 + 5.46114i 0.0783160 + 0.199546i
\(750\) −0.616377 + 0.190127i −0.0225069 + 0.00694246i
\(751\) 21.1760 19.6484i 0.772723 0.716982i −0.191669 0.981460i \(-0.561390\pi\)
0.964392 + 0.264478i \(0.0851996\pi\)
\(752\) 13.4608 16.8793i 0.490864 0.615523i
\(753\) −11.9819 + 15.0249i −0.436645 + 0.547536i
\(754\) −38.4503 + 35.6767i −1.40028 + 1.29927i
\(755\) 1.08819 0.335661i 0.0396032 0.0122160i
\(756\) 1.40060 + 3.56866i 0.0509392 + 0.129791i
\(757\) 41.3008 28.1584i 1.50110 1.02344i 0.515023 0.857177i \(-0.327784\pi\)
0.986082 0.166259i \(-0.0531689\pi\)
\(758\) 9.40615 + 4.52976i 0.341647 + 0.164528i
\(759\) 2.56447 + 2.37948i 0.0930843 + 0.0863696i
\(760\) −0.0335815 + 0.00506160i −0.00121813 + 0.000183603i
\(761\) −0.388288 + 5.18134i −0.0140754 + 0.187823i 0.985734 + 0.168310i \(0.0538308\pi\)
−0.999810 + 0.0195137i \(0.993788\pi\)
\(762\) −3.13288 + 7.98245i −0.113492 + 0.289174i
\(763\) 4.04403 + 17.7181i 0.146404 + 0.641437i
\(764\) −0.915579 12.2176i −0.0331245 0.442016i
\(765\) −0.143522 0.0442707i −0.00518905 0.00160061i
\(766\) 31.5166 15.1776i 1.13874 0.548388i
\(767\) −12.4940 + 21.6402i −0.451131 + 0.781381i
\(768\) −4.95150 8.57625i −0.178672 0.309469i
\(769\) −13.1019 8.93274i −0.472468 0.322123i 0.303571 0.952809i \(-0.401821\pi\)
−0.776038 + 0.630686i \(0.782774\pi\)
\(770\) 0.0823209 0.360671i 0.00296664 0.0129977i
\(771\) −11.1847 1.68582i −0.402808 0.0607135i
\(772\) 10.9341 + 13.7109i 0.393526 + 0.493466i
\(773\) 25.8123 0.928405 0.464202 0.885729i \(-0.346341\pi\)
0.464202 + 0.885729i \(0.346341\pi\)
\(774\) −19.4800 19.3444i −0.700196 0.695321i
\(775\) 50.0570 1.79810
\(776\) 15.4610 + 19.3875i 0.555019 + 0.695972i
\(777\) −3.88453 0.585499i −0.139357 0.0210047i
\(778\) 11.0713 48.5065i 0.396925 1.73904i
\(779\) 0.600622 + 0.409497i 0.0215195 + 0.0146718i
\(780\) −0.0445767 0.0772090i −0.00159610 0.00276453i
\(781\) 3.73911 6.47633i 0.133796 0.231741i
\(782\) 3.01835 1.45356i 0.107936 0.0519792i
\(783\) −34.5374 10.6534i −1.23427 0.380721i
\(784\) 1.74377 + 23.2690i 0.0622774 + 0.831034i
\(785\) 0.240742 + 1.05476i 0.00859244 + 0.0376459i
\(786\) −1.49083 + 3.79856i −0.0531760 + 0.135490i
\(787\) −1.90765 + 25.4559i −0.0680005 + 0.907404i 0.854014 + 0.520250i \(0.174161\pi\)
−0.922015 + 0.387155i \(0.873458\pi\)
\(788\) 13.2332 1.99458i 0.471413 0.0710541i
\(789\) 13.1838 + 12.2328i 0.469356 + 0.435498i
\(790\) −1.10907 0.534099i −0.0394589 0.0190024i
\(791\) −6.86061 + 4.67749i −0.243935 + 0.166312i
\(792\) −5.13287 13.0783i −0.182389 0.464719i
\(793\) −27.0447 + 8.34217i −0.960384 + 0.296239i
\(794\) −7.44383 + 6.90687i −0.264172 + 0.245116i
\(795\) −0.217688 + 0.272973i −0.00772061 + 0.00968134i
\(796\) 8.98863 11.2714i 0.318594 0.399504i
\(797\) 20.6737 19.1824i 0.732302 0.679477i −0.223097 0.974796i \(-0.571617\pi\)
0.955398 + 0.295320i \(0.0954262\pi\)
\(798\) −0.421415 + 0.129989i −0.0149179 + 0.00460157i
\(799\) 1.60850 + 4.09838i 0.0569045 + 0.144990i
\(800\) −15.4556 + 10.5375i −0.546438 + 0.372555i
\(801\) 11.1694 + 5.37890i 0.394651 + 0.190054i
\(802\) −10.5001 9.74267i −0.370772 0.344026i
\(803\) −26.4899 + 3.99271i −0.934808 + 0.140900i
\(804\) 0.245162 3.27146i 0.00864620 0.115375i
\(805\) −0.0657384 + 0.167499i −0.00231697 + 0.00590355i
\(806\) 12.0135 + 52.6346i 0.423158 + 1.85397i
\(807\) −0.696983 9.30059i −0.0245350 0.327396i
\(808\) 31.3328 + 9.66490i 1.10229 + 0.340010i
\(809\) 19.3936 9.33946i 0.681842 0.328358i −0.0607010 0.998156i \(-0.519334\pi\)
0.742543 + 0.669798i \(0.233619\pi\)
\(810\) −0.249675 + 0.432450i −0.00877270 + 0.0151948i
\(811\) −15.9074 27.5524i −0.558584 0.967497i −0.997615 0.0690245i \(-0.978011\pi\)
0.439030 0.898472i \(-0.355322\pi\)
\(812\) −8.30268 5.66067i −0.291367 0.198651i
\(813\) 3.77309 16.5310i 0.132328 0.579767i
\(814\) −16.2951 2.45609i −0.571144 0.0860861i
\(815\) 0.647301 + 0.811690i 0.0226740 + 0.0284323i
\(816\) 3.27922 0.114796
\(817\) 1.33096 1.15350i 0.0465643 0.0403558i
\(818\) −53.9141 −1.88506
\(819\) −7.83017 9.81872i −0.273608 0.343094i
\(820\) −0.108581 0.0163660i −0.00379183 0.000571526i
\(821\) −6.70569 + 29.3796i −0.234030 + 1.02535i 0.712230 + 0.701946i \(0.247685\pi\)
−0.946260 + 0.323407i \(0.895172\pi\)
\(822\) −16.5432 11.2789i −0.577009 0.393398i
\(823\) 18.5073 + 32.0556i 0.645125 + 1.11739i 0.984273 + 0.176655i \(0.0565278\pi\)
−0.339148 + 0.940733i \(0.610139\pi\)
\(824\) −0.490764 + 0.850028i −0.0170966 + 0.0296121i
\(825\) 7.70947 3.71268i 0.268409 0.129259i
\(826\) −17.8419 5.50348i −0.620798 0.191491i
\(827\) 0.862644 + 11.5112i 0.0299971 + 0.400283i 0.991911 + 0.126932i \(0.0405130\pi\)
−0.961914 + 0.273351i \(0.911868\pi\)
\(828\) −0.800185 3.50584i −0.0278084 0.121836i
\(829\) −6.98702 + 17.8026i −0.242669 + 0.618311i −0.999372 0.0354486i \(-0.988714\pi\)
0.756702 + 0.653760i \(0.226809\pi\)
\(830\) 0.0850847 1.13538i 0.00295333 0.0394095i
\(831\) −2.06260 + 0.310888i −0.0715509 + 0.0107846i
\(832\) 8.83414 + 8.19689i 0.306269 + 0.284176i
\(833\) −4.28730 2.06466i −0.148546 0.0715361i
\(834\) 3.90827 2.66461i 0.135332 0.0922680i
\(835\) 0.504232 + 1.28476i 0.0174497 + 0.0444610i
\(836\) −0.453242 + 0.139807i −0.0156757 + 0.00483531i
\(837\) −27.2706 + 25.3034i −0.942609 + 0.874613i
\(838\) 13.1943 16.5451i 0.455790 0.571543i
\(839\) 8.79264 11.0256i 0.303556 0.380647i −0.606534 0.795057i \(-0.707441\pi\)
0.910090 + 0.414410i \(0.136012\pi\)
\(840\) −0.0927988 + 0.0861047i −0.00320186 + 0.00297090i
\(841\) 62.8174 19.3766i 2.16612 0.668159i
\(842\) 19.9943 + 50.9445i 0.689048 + 1.75566i
\(843\) 12.7164 8.66986i 0.437974 0.298606i
\(844\) 7.79165 + 3.75226i 0.268200 + 0.129158i
\(845\) −0.0949944 0.0881420i −0.00326791 0.00303218i
\(846\) 18.2265 2.74720i 0.626639 0.0944506i
\(847\) 0.496955 6.63140i 0.0170756 0.227858i
\(848\) −15.8976 + 40.5065i −0.545927 + 1.39100i
\(849\) −3.70193 16.2192i −0.127050 0.556642i
\(850\) −0.612360 8.17138i −0.0210038 0.280276i
\(851\) 7.65916 + 2.36254i 0.262553 + 0.0809867i
\(852\) 1.21326 0.584274i 0.0415655 0.0200169i
\(853\) 1.42288 2.46451i 0.0487186 0.0843831i −0.840638 0.541598i \(-0.817820\pi\)
0.889356 + 0.457215i \(0.151153\pi\)
\(854\) −10.5739 18.3145i −0.361831 0.626709i
\(855\) −0.0333310 0.0227247i −0.00113989 0.000777167i
\(856\) 1.87392 8.21018i 0.0640493 0.280618i
\(857\) −32.1052 4.83907i −1.09669 0.165300i −0.424319 0.905513i \(-0.639486\pi\)
−0.672372 + 0.740213i \(0.734725\pi\)
\(858\) 5.75410 + 7.21542i 0.196442 + 0.246330i
\(859\) −10.2489 −0.349686 −0.174843 0.984596i \(-0.555942\pi\)
−0.174843 + 0.984596i \(0.555942\pi\)
\(860\) −0.105538 + 0.244219i −0.00359881 + 0.00832780i
\(861\) 2.70973 0.0923472
\(862\) −13.0583 16.3746i −0.444767 0.557720i
\(863\) −6.75590 1.01829i −0.229973 0.0346629i 0.0330444 0.999454i \(-0.489480\pi\)
−0.263018 + 0.964791i \(0.584718\pi\)
\(864\) 3.09347 13.5534i 0.105242 0.461095i
\(865\) −0.210388 0.143440i −0.00715342 0.00487712i
\(866\) 17.2258 + 29.8359i 0.585355 + 1.01387i
\(867\) −0.334366 + 0.579139i −0.0113557 + 0.0196686i
\(868\) −9.31872 + 4.48766i −0.316298 + 0.152321i
\(869\) 31.2194 + 9.62990i 1.05904 + 0.326672i
\(870\) 0.0469343 + 0.626295i 0.00159122 + 0.0212334i
\(871\) 5.20177 + 22.7904i 0.176255 + 0.772225i
\(872\) 9.53080 24.2841i 0.322754 0.822363i
\(873\) −2.20125 + 29.3736i −0.0745010 + 0.994147i
\(874\) 0.889751 0.134108i 0.0300963 0.00453629i
\(875\) 0.645488 + 0.598925i 0.0218215 + 0.0202474i
\(876\) −4.34623 2.09303i −0.146846 0.0707171i
\(877\) −13.6284 + 9.29168i −0.460198 + 0.313758i −0.771134 0.636673i \(-0.780310\pi\)
0.310936 + 0.950431i \(0.399358\pi\)
\(878\) 19.4792 + 49.6323i 0.657392 + 1.67501i
\(879\) −4.50271 + 1.38890i −0.151873 + 0.0468465i
\(880\) −0.541608 + 0.502539i −0.0182576 + 0.0169406i
\(881\) 11.8439 14.8518i 0.399031 0.500369i −0.541206 0.840890i \(-0.682032\pi\)
0.940237 + 0.340521i \(0.110603\pi\)
\(882\) −12.4212 + 15.5757i −0.418243 + 0.524460i
\(883\) 9.01199 8.36191i 0.303278 0.281401i −0.513822 0.857897i \(-0.671771\pi\)
0.817100 + 0.576496i \(0.195580\pi\)
\(884\) 2.16526 0.667895i 0.0728256 0.0224637i
\(885\) 0.109310 + 0.278516i 0.00367440 + 0.00936223i
\(886\) 41.9314 28.5883i 1.40871 0.960444i
\(887\) 21.7247 + 10.4620i 0.729443 + 0.351281i 0.761465 0.648206i \(-0.224480\pi\)
−0.0320221 + 0.999487i \(0.510195\pi\)
\(888\) 4.13370 + 3.83551i 0.138718 + 0.128711i
\(889\) 11.5754 1.74472i 0.388228 0.0585159i
\(890\) 0.0350171 0.467271i 0.00117378 0.0156629i
\(891\) 4.84190 12.3370i 0.162210 0.413304i
\(892\) −0.315783 1.38354i −0.0105732 0.0463243i
\(893\) 0.0883699 + 1.17921i 0.00295719 + 0.0394609i
\(894\) 8.54381 + 2.63542i 0.285748 + 0.0881415i
\(895\) 0.0805284 0.0387805i 0.00269177 0.00129629i
\(896\) −10.1074 + 17.5066i −0.337665 + 0.584854i
\(897\) −2.24440 3.88741i −0.0749383 0.129797i
\(898\) −2.42473 1.65315i −0.0809141 0.0551663i
\(899\) 21.6984 95.0671i 0.723683 3.17066i
\(900\) −8.69748 1.31093i −0.289916 0.0436978i
\(901\) −5.53279 6.93790i −0.184324 0.231135i
\(902\) 11.3670 0.378478
\(903\) 1.67705 6.34744i 0.0558086 0.211230i
\(904\) 11.9191 0.396425
\(905\) −0.761059 0.954338i −0.0252985 0.0317233i
\(906\) −20.9902 3.16377i −0.697354 0.105109i
\(907\) −0.396490 + 1.73714i −0.0131652 + 0.0576807i −0.981084 0.193583i \(-0.937989\pi\)
0.967919 + 0.251264i \(0.0808462\pi\)
\(908\) −1.19242 0.812976i −0.0395717 0.0269795i
\(909\) 19.4747 + 33.7311i 0.645934 + 1.11879i
\(910\) −0.237343 + 0.411090i −0.00786785 + 0.0136275i
\(911\) −43.9390 + 21.1599i −1.45576 + 0.701059i −0.983585 0.180444i \(-0.942247\pi\)
−0.472179 + 0.881503i \(0.656532\pi\)
\(912\) 0.841631 + 0.259609i 0.0278692 + 0.00859650i
\(913\) 2.25821 + 30.1337i 0.0747357 + 0.997279i
\(914\) −9.27676 40.6441i −0.306848 1.34439i
\(915\) −0.123807 + 0.315456i −0.00409294 + 0.0104287i
\(916\) 0.843988 11.2622i 0.0278862 0.372115i
\(917\) 5.50834 0.830249i 0.181901 0.0274172i
\(918\) 4.46417 + 4.14215i 0.147340 + 0.136711i
\(919\) 2.44258 + 1.17628i 0.0805731 + 0.0388020i 0.473736 0.880667i \(-0.342905\pi\)
−0.393163 + 0.919469i \(0.628619\pi\)
\(920\) 0.213410 0.145500i 0.00703590 0.00479700i
\(921\) −4.97508 12.6763i −0.163934 0.417698i
\(922\) −47.6526 + 14.6989i −1.56935 + 0.484082i
\(923\) −7.03397 + 6.52657i −0.231526 + 0.214825i
\(924\) −1.10236 + 1.38232i −0.0362651 + 0.0454750i
\(925\) 12.2236 15.3279i 0.401909 0.503978i
\(926\) −9.83148 + 9.12228i −0.323082 + 0.299777i
\(927\) −1.11412 + 0.343659i −0.0365924 + 0.0112873i
\(928\) 13.3129 + 33.9206i 0.437016 + 1.11350i
\(929\) −5.24871 + 3.57851i −0.172204 + 0.117407i −0.646355 0.763037i \(-0.723708\pi\)
0.474151 + 0.880444i \(0.342755\pi\)
\(930\) 0.582423 + 0.280480i 0.0190984 + 0.00919731i
\(931\) −0.936906 0.869322i −0.0307059 0.0284909i
\(932\) 18.9093 2.85011i 0.619394 0.0933586i
\(933\) −0.00317049 + 0.0423073i −0.000103797 + 0.00138508i
\(934\) 18.7548 47.7866i 0.613677 1.56362i
\(935\) −0.0335276 0.146894i −0.00109647 0.00480395i
\(936\) 1.34718 + 17.9768i 0.0440339 + 0.587591i
\(937\) −47.5975 14.6819i −1.55494 0.479636i −0.606101 0.795388i \(-0.707267\pi\)
−0.948842 + 0.315751i \(0.897744\pi\)
\(938\) −15.7375 + 7.57879i −0.513848 + 0.247456i
\(939\) 0.749260 1.29776i 0.0244512 0.0423507i
\(940\) −0.0893134 0.154695i −0.00291308 0.00504560i
\(941\) −4.54663 3.09984i −0.148216 0.101052i 0.486942 0.873435i \(-0.338112\pi\)
−0.635158 + 0.772383i \(0.719065\pi\)
\(942\) 4.48753 19.6611i 0.146212 0.640595i
\(943\) −5.46698 0.824015i −0.178030 0.0268336i
\(944\) 23.2497 + 29.1542i 0.756713 + 0.948888i
\(945\) −0.327090 −0.0106402
\(946\) 7.03500 26.6267i 0.228728 0.865709i
\(947\) 49.9161 1.62206 0.811028 0.585007i \(-0.198908\pi\)
0.811028 + 0.585007i \(0.198908\pi\)
\(948\) 3.66804 + 4.59958i 0.119133 + 0.149387i
\(949\) 33.9897 + 5.12313i 1.10335 + 0.166304i
\(950\) 0.489745 2.14571i 0.0158894 0.0696161i
\(951\) 12.4265 + 8.47225i 0.402957 + 0.274732i
\(952\) −1.60874 2.78643i −0.0521397 0.0903086i
\(953\) −10.2470 + 17.7483i −0.331932 + 0.574923i −0.982891 0.184190i \(-0.941034\pi\)
0.650959 + 0.759113i \(0.274367\pi\)
\(954\) −33.4722 + 16.1193i −1.08370 + 0.521883i
\(955\) 0.998889 + 0.308116i 0.0323233 + 0.00997041i
\(956\) 0.522611 + 6.97376i 0.0169025 + 0.225548i
\(957\) −3.70918 16.2510i −0.119901 0.525320i
\(958\) 1.31455 3.34942i 0.0424712 0.108215i
\(959\) −2.04258 + 27.2563i −0.0659583 + 0.880152i
\(960\) 0.142686 0.0215065i 0.00460518 0.000694119i
\(961\) −50.8497 47.1816i −1.64031 1.52199i
\(962\) 19.0508 + 9.17438i 0.614222 + 0.295794i
\(963\) 8.26514 5.63507i 0.266340 0.181588i
\(964\) 1.82019 + 4.63778i 0.0586245 + 0.149373i
\(965\) −1.42978 + 0.441029i −0.0460263 + 0.0141972i
\(966\) 2.45873 2.28137i 0.0791084 0.0734018i
\(967\) −14.7409 + 18.4845i −0.474035 + 0.594422i −0.960154 0.279471i \(-0.909841\pi\)
0.486119 + 0.873893i \(0.338412\pi\)
\(968\) −5.95166 + 7.46314i −0.191294 + 0.239875i
\(969\) −0.131666 + 0.122168i −0.00422972 + 0.00392461i
\(970\) 1.06390 0.328171i 0.0341599 0.0105369i
\(971\) 10.1901 + 25.9639i 0.327015 + 0.833222i 0.995951 + 0.0899010i \(0.0286551\pi\)
−0.668935 + 0.743321i \(0.733250\pi\)
\(972\) 8.31894 5.67176i 0.266830 0.181922i
\(973\) −5.81780 2.80171i −0.186510 0.0898186i
\(974\) −48.3824 44.8923i −1.55027 1.43844i
\(975\) −10.8569 + 1.63641i −0.347698 + 0.0524070i
\(976\) −3.15625 + 42.1172i −0.101029 + 1.34814i
\(977\) 3.69581 9.41676i 0.118239 0.301269i −0.859485 0.511160i \(-0.829216\pi\)
0.977725 + 0.209892i \(0.0673111\pi\)
\(978\) −4.30629 18.8671i −0.137700 0.603303i
\(979\) 0.929377 + 12.4017i 0.0297030 + 0.396359i
\(980\) 0.184486 + 0.0569063i 0.00589318 + 0.00181781i
\(981\) 27.9193 13.4452i 0.891396 0.429273i
\(982\) 13.0103 22.5345i 0.415176 0.719105i
\(983\) 17.8776 + 30.9649i 0.570206 + 0.987627i 0.996544 + 0.0830626i \(0.0264701\pi\)
−0.426338 + 0.904564i \(0.640197\pi\)
\(984\) −3.21380 2.19113i −0.102452 0.0698507i
\(985\) −0.254078 + 1.11319i −0.00809558 + 0.0354691i
\(986\) −15.7843 2.37911i −0.502676 0.0757662i
\(987\) 2.74832 + 3.44629i 0.0874801 + 0.109697i
\(988\) 0.608603 0.0193622
\(989\) −5.31374 + 12.2962i −0.168967 + 0.390997i
\(990\) −0.630799 −0.0200481
\(991\) 6.00717 + 7.53276i 0.190824 + 0.239286i 0.868035 0.496503i \(-0.165383\pi\)
−0.677211 + 0.735789i \(0.736811\pi\)
\(992\) 37.0876 + 5.59006i 1.17753 + 0.177484i
\(993\) 1.29005 5.65207i 0.0409384 0.179363i
\(994\) −5.92404 4.03894i −0.187899 0.128107i
\(995\) 0.615017 + 1.06524i 0.0194974 + 0.0337704i
\(996\) −2.72071 + 4.71241i −0.0862091 + 0.149319i
\(997\) 20.7076 9.97224i 0.655815 0.315824i −0.0762198 0.997091i \(-0.524285\pi\)
0.732035 + 0.681267i \(0.238571\pi\)
\(998\) −3.84380 1.18566i −0.121674 0.0375313i
\(999\) 1.08883 + 14.5294i 0.0344490 + 0.459690i
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.u.b.52.8 348
43.24 even 21 inner 731.2.u.b.239.8 yes 348
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
731.2.u.b.52.8 348 1.1 even 1 trivial
731.2.u.b.239.8 yes 348 43.24 even 21 inner