Properties

Label 572.2.t.a.87.12
Level $572$
Weight $2$
Character 572.87
Analytic conductor $4.567$
Analytic rank $0$
Dimension $160$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [572,2,Mod(87,572)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(572, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("572.87");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 572.t (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.56744299562\)
Analytic rank: \(0\)
Dimension: \(160\)
Relative dimension: \(80\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 87.12
Character \(\chi\) \(=\) 572.87
Dual form 572.2.t.a.263.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.30161 - 0.552996i) q^{2} +(0.965312 + 0.557323i) q^{3} +(1.38839 + 1.43957i) q^{4} -1.84918 q^{5} +(-0.948265 - 1.25923i) q^{6} +(-0.798405 - 1.38288i) q^{7} +(-1.01107 - 2.64154i) q^{8} +(-0.878782 - 1.52209i) q^{9} +O(q^{10})\) \(q+(-1.30161 - 0.552996i) q^{2} +(0.965312 + 0.557323i) q^{3} +(1.38839 + 1.43957i) q^{4} -1.84918 q^{5} +(-0.948265 - 1.25923i) q^{6} +(-0.798405 - 1.38288i) q^{7} +(-1.01107 - 2.64154i) q^{8} +(-0.878782 - 1.52209i) q^{9} +(2.40691 + 1.02259i) q^{10} +(2.69326 + 1.93554i) q^{11} +(0.537924 + 2.16342i) q^{12} +(2.38431 - 2.70463i) q^{13} +(0.274488 + 2.24149i) q^{14} +(-1.78503 - 1.03059i) q^{15} +(-0.144739 + 3.99738i) q^{16} +(-4.11682 + 2.37685i) q^{17} +(0.302122 + 2.46714i) q^{18} +(-3.85049 - 6.66924i) q^{19} +(-2.56738 - 2.66202i) q^{20} -1.77988i q^{21} +(-2.43524 - 4.00869i) q^{22} +(-0.903308 - 0.521525i) q^{23} +(0.496194 - 3.11340i) q^{24} -1.58054 q^{25} +(-4.59911 + 2.20187i) q^{26} -5.30300i q^{27} +(0.882255 - 3.06934i) q^{28} +(5.42901 + 3.13444i) q^{29} +(1.75351 + 2.32854i) q^{30} -7.92719i q^{31} +(2.39893 - 5.12300i) q^{32} +(1.52112 + 3.36942i) q^{33} +(6.67289 - 0.817150i) q^{34} +(1.47639 + 2.55719i) q^{35} +(0.971073 - 3.37833i) q^{36} +(2.22649 - 3.85640i) q^{37} +(1.32378 + 10.8101i) q^{38} +(3.80896 - 1.28198i) q^{39} +(1.86965 + 4.88468i) q^{40} +(0.356602 + 0.205884i) q^{41} +(-0.984265 + 2.31671i) q^{42} +(-1.37379 - 2.37947i) q^{43} +(0.952951 + 6.56444i) q^{44} +(1.62502 + 2.81462i) q^{45} +(0.887356 + 1.17835i) q^{46} -7.30441i q^{47} +(-2.36755 + 3.77805i) q^{48} +(2.22510 - 3.85398i) q^{49} +(2.05726 + 0.874034i) q^{50} -5.29868 q^{51} +(7.20388 - 0.322697i) q^{52} +1.01441 q^{53} +(-2.93254 + 6.90245i) q^{54} +(-4.98032 - 3.57916i) q^{55} +(-2.84569 + 3.50721i) q^{56} -8.58386i q^{57} +(-5.33314 - 7.08205i) q^{58} +(3.73111 - 2.15416i) q^{59} +(-0.994716 - 4.00055i) q^{60} +(-1.81884 + 1.05011i) q^{61} +(-4.38370 + 10.3181i) q^{62} +(-1.40325 + 2.43050i) q^{63} +(-5.95547 + 5.34157i) q^{64} +(-4.40902 + 5.00135i) q^{65} +(-0.116631 - 5.22685i) q^{66} +(-8.20917 - 4.73957i) q^{67} +(-9.13739 - 2.62647i) q^{68} +(-0.581316 - 1.00687i) q^{69} +(-0.507578 - 4.14491i) q^{70} +(7.35026 - 4.24368i) q^{71} +(-3.13216 + 3.86028i) q^{72} +6.65487i q^{73} +(-5.03060 + 3.78830i) q^{74} +(-1.52572 - 0.880874i) q^{75} +(4.25487 - 14.8026i) q^{76} +(0.526303 - 5.26980i) q^{77} +(-5.66672 - 0.437696i) q^{78} +5.74567 q^{79} +(0.267648 - 7.39186i) q^{80} +(0.319140 - 0.552767i) q^{81} +(-0.350305 - 0.465181i) q^{82} -14.0580 q^{83} +(2.56226 - 2.47117i) q^{84} +(7.61272 - 4.39521i) q^{85} +(0.472303 + 3.85685i) q^{86} +(3.49379 + 6.05143i) q^{87} +(2.38973 - 9.07134i) q^{88} +(-8.42184 + 14.5870i) q^{89} +(-0.558676 - 4.56218i) q^{90} +(-5.64383 - 1.13782i) q^{91} +(-0.503372 - 2.02446i) q^{92} +(4.41801 - 7.65221i) q^{93} +(-4.03931 + 9.50751i) q^{94} +(7.12023 + 12.3326i) q^{95} +(5.17088 - 3.60832i) q^{96} +(3.26679 + 5.65825i) q^{97} +(-5.02745 + 3.78592i) q^{98} +(0.579287 - 5.80032i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 160 q - 2 q^{4} - 16 q^{5} + 68 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 160 q - 2 q^{4} - 16 q^{5} + 68 q^{9} - 4 q^{12} + 8 q^{14} - 14 q^{16} - 26 q^{20} + 112 q^{25} - 14 q^{33} + 12 q^{34} - 6 q^{36} - 4 q^{37} + 40 q^{38} + 54 q^{42} - 16 q^{44} - 48 q^{45} - 40 q^{48} - 52 q^{49} - 32 q^{53} - 18 q^{56} - 6 q^{58} - 52 q^{60} + 16 q^{64} - 84 q^{66} - 12 q^{69} - 68 q^{70} - 4 q^{77} + 28 q^{78} - 44 q^{80} - 40 q^{81} - 38 q^{82} + 120 q^{86} - 14 q^{88} - 64 q^{92} - 8 q^{93}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/572\mathbb{Z}\right)^\times\).

\(n\) \(287\) \(353\) \(365\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.30161 0.552996i −0.920379 0.391027i
\(3\) 0.965312 + 0.557323i 0.557323 + 0.321771i 0.752070 0.659083i \(-0.229055\pi\)
−0.194747 + 0.980853i \(0.562389\pi\)
\(4\) 1.38839 + 1.43957i 0.694196 + 0.719786i
\(5\) −1.84918 −0.826977 −0.413489 0.910509i \(-0.635690\pi\)
−0.413489 + 0.910509i \(0.635690\pi\)
\(6\) −0.948265 1.25923i −0.387128 0.514079i
\(7\) −0.798405 1.38288i −0.301769 0.522679i 0.674768 0.738030i \(-0.264244\pi\)
−0.976537 + 0.215351i \(0.930910\pi\)
\(8\) −1.01107 2.64154i −0.357467 0.933926i
\(9\) −0.878782 1.52209i −0.292927 0.507365i
\(10\) 2.40691 + 1.02259i 0.761133 + 0.323370i
\(11\) 2.69326 + 1.93554i 0.812050 + 0.583588i
\(12\) 0.537924 + 2.16342i 0.155285 + 0.624525i
\(13\) 2.38431 2.70463i 0.661290 0.750131i
\(14\) 0.274488 + 2.24149i 0.0733601 + 0.599062i
\(15\) −1.78503 1.03059i −0.460894 0.266097i
\(16\) −0.144739 + 3.99738i −0.0361848 + 0.999345i
\(17\) −4.11682 + 2.37685i −0.998475 + 0.576470i −0.907797 0.419411i \(-0.862237\pi\)
−0.0906781 + 0.995880i \(0.528903\pi\)
\(18\) 0.302122 + 2.46714i 0.0712107 + 0.581511i
\(19\) −3.85049 6.66924i −0.883362 1.53003i −0.847579 0.530669i \(-0.821941\pi\)
−0.0357833 0.999360i \(-0.511393\pi\)
\(20\) −2.56738 2.66202i −0.574084 0.595247i
\(21\) 1.77988i 0.388401i
\(22\) −2.43524 4.00869i −0.519195 0.854656i
\(23\) −0.903308 0.521525i −0.188353 0.108746i 0.402858 0.915262i \(-0.368017\pi\)
−0.591211 + 0.806517i \(0.701350\pi\)
\(24\) 0.496194 3.11340i 0.101285 0.635521i
\(25\) −1.58054 −0.316109
\(26\) −4.59911 + 2.20187i −0.901959 + 0.431822i
\(27\) 5.30300i 1.02056i
\(28\) 0.882255 3.06934i 0.166731 0.580050i
\(29\) 5.42901 + 3.13444i 1.00814 + 0.582051i 0.910647 0.413185i \(-0.135584\pi\)
0.0974947 + 0.995236i \(0.468917\pi\)
\(30\) 1.75351 + 2.32854i 0.320146 + 0.425132i
\(31\) 7.92719i 1.42377i −0.702298 0.711883i \(-0.747843\pi\)
0.702298 0.711883i \(-0.252157\pi\)
\(32\) 2.39893 5.12300i 0.424075 0.905627i
\(33\) 1.52112 + 3.36942i 0.264793 + 0.586541i
\(34\) 6.67289 0.817150i 1.14439 0.140140i
\(35\) 1.47639 + 2.55719i 0.249556 + 0.432243i
\(36\) 0.971073 3.37833i 0.161845 0.563056i
\(37\) 2.22649 3.85640i 0.366033 0.633988i −0.622908 0.782295i \(-0.714049\pi\)
0.988941 + 0.148307i \(0.0473823\pi\)
\(38\) 1.32378 + 10.8101i 0.214746 + 1.75363i
\(39\) 3.80896 1.28198i 0.609922 0.205281i
\(40\) 1.86965 + 4.88468i 0.295617 + 0.772335i
\(41\) 0.356602 + 0.205884i 0.0556919 + 0.0321537i 0.527587 0.849501i \(-0.323097\pi\)
−0.471896 + 0.881654i \(0.656430\pi\)
\(42\) −0.984265 + 2.31671i −0.151875 + 0.357477i
\(43\) −1.37379 2.37947i −0.209501 0.362866i 0.742056 0.670337i \(-0.233851\pi\)
−0.951557 + 0.307471i \(0.900517\pi\)
\(44\) 0.952951 + 6.56444i 0.143663 + 0.989627i
\(45\) 1.62502 + 2.81462i 0.242244 + 0.419579i
\(46\) 0.887356 + 1.17835i 0.130834 + 0.173738i
\(47\) 7.30441i 1.06546i −0.846286 0.532729i \(-0.821167\pi\)
0.846286 0.532729i \(-0.178833\pi\)
\(48\) −2.36755 + 3.77805i −0.341727 + 0.545315i
\(49\) 2.22510 3.85398i 0.317871 0.550569i
\(50\) 2.05726 + 0.874034i 0.290940 + 0.123607i
\(51\) −5.29868 −0.741964
\(52\) 7.20388 0.322697i 0.998998 0.0447500i
\(53\) 1.01441 0.139340 0.0696701 0.997570i \(-0.477805\pi\)
0.0696701 + 0.997570i \(0.477805\pi\)
\(54\) −2.93254 + 6.90245i −0.399068 + 0.939305i
\(55\) −4.98032 3.57916i −0.671547 0.482614i
\(56\) −2.84569 + 3.50721i −0.380271 + 0.468670i
\(57\) 8.58386i 1.13696i
\(58\) −5.33314 7.08205i −0.700275 0.929918i
\(59\) 3.73111 2.15416i 0.485749 0.280447i −0.237060 0.971495i \(-0.576184\pi\)
0.722809 + 0.691048i \(0.242851\pi\)
\(60\) −0.994716 4.00055i −0.128417 0.516468i
\(61\) −1.81884 + 1.05011i −0.232879 + 0.134453i −0.611899 0.790936i \(-0.709594\pi\)
0.379021 + 0.925388i \(0.376261\pi\)
\(62\) −4.38370 + 10.3181i −0.556731 + 1.31040i
\(63\) −1.40325 + 2.43050i −0.176793 + 0.306214i
\(64\) −5.95547 + 5.34157i −0.744434 + 0.667696i
\(65\) −4.40902 + 5.00135i −0.546872 + 0.620341i
\(66\) −0.116631 5.22685i −0.0143563 0.643381i
\(67\) −8.20917 4.73957i −1.00291 0.579030i −0.0938020 0.995591i \(-0.529902\pi\)
−0.909108 + 0.416561i \(0.863235\pi\)
\(68\) −9.13739 2.62647i −1.10807 0.318506i
\(69\) −0.581316 1.00687i −0.0699822 0.121213i
\(70\) −0.507578 4.14491i −0.0606671 0.495411i
\(71\) 7.35026 4.24368i 0.872316 0.503632i 0.00419858 0.999991i \(-0.498664\pi\)
0.868117 + 0.496360i \(0.165330\pi\)
\(72\) −3.13216 + 3.86028i −0.369129 + 0.454939i
\(73\) 6.65487i 0.778894i 0.921049 + 0.389447i \(0.127334\pi\)
−0.921049 + 0.389447i \(0.872666\pi\)
\(74\) −5.03060 + 3.78830i −0.584796 + 0.440381i
\(75\) −1.52572 0.880874i −0.176175 0.101715i
\(76\) 4.25487 14.8026i 0.488067 1.69797i
\(77\) 0.526303 5.26980i 0.0599778 0.600550i
\(78\) −5.66672 0.437696i −0.641630 0.0495593i
\(79\) 5.74567 0.646438 0.323219 0.946324i \(-0.395235\pi\)
0.323219 + 0.946324i \(0.395235\pi\)
\(80\) 0.267648 7.39186i 0.0299240 0.826436i
\(81\) 0.319140 0.552767i 0.0354600 0.0614185i
\(82\) −0.350305 0.465181i −0.0386847 0.0513707i
\(83\) −14.0580 −1.54306 −0.771531 0.636192i \(-0.780509\pi\)
−0.771531 + 0.636192i \(0.780509\pi\)
\(84\) 2.56226 2.47117i 0.279566 0.269627i
\(85\) 7.61272 4.39521i 0.825716 0.476727i
\(86\) 0.472303 + 3.85685i 0.0509298 + 0.415895i
\(87\) 3.49379 + 6.05143i 0.374574 + 0.648781i
\(88\) 2.38973 9.07134i 0.254747 0.967008i
\(89\) −8.42184 + 14.5870i −0.892713 + 1.54622i −0.0561030 + 0.998425i \(0.517868\pi\)
−0.836610 + 0.547799i \(0.815466\pi\)
\(90\) −0.558676 4.56218i −0.0588897 0.480896i
\(91\) −5.64383 1.13782i −0.591634 0.119276i
\(92\) −0.503372 2.02446i −0.0524801 0.211064i
\(93\) 4.41801 7.65221i 0.458126 0.793498i
\(94\) −4.03931 + 9.50751i −0.416623 + 0.980625i
\(95\) 7.12023 + 12.3326i 0.730521 + 1.26530i
\(96\) 5.17088 3.60832i 0.527751 0.368272i
\(97\) 3.26679 + 5.65825i 0.331692 + 0.574508i 0.982844 0.184440i \(-0.0590471\pi\)
−0.651152 + 0.758948i \(0.725714\pi\)
\(98\) −5.02745 + 3.78592i −0.507849 + 0.382436i
\(99\) 0.579287 5.80032i 0.0582205 0.582954i
\(100\) −2.19441 2.27531i −0.219441 0.227531i
\(101\) −0.244316 0.141056i −0.0243104 0.0140356i 0.487796 0.872958i \(-0.337801\pi\)
−0.512106 + 0.858922i \(0.671134\pi\)
\(102\) 6.89683 + 2.93015i 0.682888 + 0.290128i
\(103\) 15.3800i 1.51544i 0.652582 + 0.757718i \(0.273686\pi\)
−0.652582 + 0.757718i \(0.726314\pi\)
\(104\) −9.55511 3.56369i −0.936956 0.349448i
\(105\) 3.29131i 0.321199i
\(106\) −1.32037 0.560966i −0.128246 0.0544858i
\(107\) −0.669022 + 1.15878i −0.0646768 + 0.112023i −0.896551 0.442941i \(-0.853935\pi\)
0.831874 + 0.554965i \(0.187268\pi\)
\(108\) 7.63406 7.36264i 0.734587 0.708470i
\(109\) 2.84899i 0.272884i 0.990648 + 0.136442i \(0.0435667\pi\)
−0.990648 + 0.136442i \(0.956433\pi\)
\(110\) 4.50319 + 7.41278i 0.429362 + 0.706781i
\(111\) 4.29852 2.48175i 0.407998 0.235558i
\(112\) 5.64345 2.99137i 0.533256 0.282658i
\(113\) 0.774542 + 1.34155i 0.0728628 + 0.126202i 0.900155 0.435570i \(-0.143453\pi\)
−0.827292 + 0.561772i \(0.810120\pi\)
\(114\) −4.74684 + 11.1729i −0.444582 + 1.04643i
\(115\) 1.67038 + 0.964392i 0.155763 + 0.0899301i
\(116\) 3.02534 + 12.1673i 0.280895 + 1.12970i
\(117\) −6.21200 1.25237i −0.574300 0.115782i
\(118\) −6.04769 + 0.740590i −0.556735 + 0.0681768i
\(119\) 6.57378 + 3.79537i 0.602617 + 0.347921i
\(120\) −0.917550 + 5.75724i −0.0837605 + 0.525561i
\(121\) 3.50735 + 10.4259i 0.318850 + 0.947805i
\(122\) 2.94814 0.361023i 0.266912 0.0326855i
\(123\) 0.229488 + 0.397485i 0.0206923 + 0.0358400i
\(124\) 11.4118 11.0060i 1.02481 0.988372i
\(125\) 12.1686 1.08839
\(126\) 3.17054 2.38757i 0.282454 0.212702i
\(127\) 8.86456 15.3539i 0.786603 1.36244i −0.141434 0.989948i \(-0.545171\pi\)
0.928037 0.372488i \(-0.121495\pi\)
\(128\) 10.7056 3.65930i 0.946249 0.323439i
\(129\) 3.06258i 0.269645i
\(130\) 8.50456 4.07165i 0.745899 0.357107i
\(131\) −5.47271 −0.478153 −0.239076 0.971001i \(-0.576845\pi\)
−0.239076 + 0.971001i \(0.576845\pi\)
\(132\) −2.73862 + 6.86784i −0.238366 + 0.597768i
\(133\) −6.14850 + 10.6495i −0.533142 + 0.923430i
\(134\) 8.06420 + 10.7087i 0.696641 + 0.925092i
\(135\) 9.80619i 0.843982i
\(136\) 10.4409 + 8.47158i 0.895302 + 0.726432i
\(137\) −9.15702 15.8604i −0.782337 1.35505i −0.930577 0.366096i \(-0.880694\pi\)
0.148241 0.988951i \(-0.452639\pi\)
\(138\) 0.199854 + 1.63202i 0.0170127 + 0.138927i
\(139\) 9.02218 + 15.6269i 0.765251 + 1.32545i 0.940114 + 0.340861i \(0.110718\pi\)
−0.174863 + 0.984593i \(0.555948\pi\)
\(140\) −1.63145 + 5.67575i −0.137882 + 0.479688i
\(141\) 4.07092 7.05103i 0.342833 0.593804i
\(142\) −11.9139 + 1.45896i −0.999795 + 0.122433i
\(143\) 11.6565 2.66935i 0.974768 0.223223i
\(144\) 6.21159 3.29252i 0.517632 0.274377i
\(145\) −10.0392 5.79614i −0.833710 0.481343i
\(146\) 3.68012 8.66207i 0.304569 0.716878i
\(147\) 4.29583 2.48020i 0.354314 0.204563i
\(148\) 8.64281 2.14899i 0.710435 0.176646i
\(149\) −10.4707 + 6.04526i −0.857793 + 0.495247i −0.863272 0.504738i \(-0.831589\pi\)
0.00547986 + 0.999985i \(0.498256\pi\)
\(150\) 1.49877 + 1.99027i 0.122374 + 0.162505i
\(151\) 15.7601 1.28254 0.641269 0.767316i \(-0.278408\pi\)
0.641269 + 0.767316i \(0.278408\pi\)
\(152\) −13.7240 + 16.9143i −1.11316 + 1.37193i
\(153\) 7.23557 + 4.17746i 0.584961 + 0.337727i
\(154\) −3.59922 + 6.56820i −0.290034 + 0.529281i
\(155\) 14.6588i 1.17742i
\(156\) 7.13384 + 3.70339i 0.571164 + 0.296508i
\(157\) −20.9722 −1.67377 −0.836884 0.547381i \(-0.815625\pi\)
−0.836884 + 0.547381i \(0.815625\pi\)
\(158\) −7.47863 3.17733i −0.594968 0.252775i
\(159\) 0.979224 + 0.565355i 0.0776575 + 0.0448356i
\(160\) −4.43604 + 9.47334i −0.350700 + 0.748933i
\(161\) 1.66555i 0.131264i
\(162\) −0.721075 + 0.543005i −0.0566530 + 0.0426625i
\(163\) −6.82798 + 3.94214i −0.534809 + 0.308772i −0.742972 0.669322i \(-0.766585\pi\)
0.208164 + 0.978094i \(0.433251\pi\)
\(164\) 0.198718 + 0.799203i 0.0155173 + 0.0624072i
\(165\) −2.81282 6.23066i −0.218978 0.485056i
\(166\) 18.2980 + 7.77399i 1.42020 + 0.603379i
\(167\) −4.98810 + 8.63965i −0.385991 + 0.668556i −0.991906 0.126973i \(-0.959474\pi\)
0.605915 + 0.795529i \(0.292807\pi\)
\(168\) −4.70162 + 1.79958i −0.362738 + 0.138841i
\(169\) −1.63009 12.8974i −0.125392 0.992107i
\(170\) −12.3393 + 1.51105i −0.946385 + 0.115893i
\(171\) −6.76748 + 11.7216i −0.517522 + 0.896374i
\(172\) 1.51807 5.28131i 0.115752 0.402696i
\(173\) 5.40454 3.12031i 0.410900 0.237233i −0.280277 0.959919i \(-0.590426\pi\)
0.691176 + 0.722686i \(0.257093\pi\)
\(174\) −1.20115 9.80867i −0.0910591 0.743593i
\(175\) 1.26191 + 2.18570i 0.0953918 + 0.165223i
\(176\) −8.12692 + 10.4859i −0.612590 + 0.790401i
\(177\) 4.80224 0.360959
\(178\) 19.0285 14.3294i 1.42625 1.07404i
\(179\) 16.7679 + 9.68096i 1.25329 + 0.723589i 0.971762 0.235963i \(-0.0758245\pi\)
0.281531 + 0.959552i \(0.409158\pi\)
\(180\) −1.79569 + 6.24714i −0.133843 + 0.465634i
\(181\) 2.15037 0.159836 0.0799179 0.996801i \(-0.474534\pi\)
0.0799179 + 0.996801i \(0.474534\pi\)
\(182\) 6.71687 + 4.60202i 0.497887 + 0.341124i
\(183\) −2.34100 −0.173052
\(184\) −0.464322 + 2.91342i −0.0342303 + 0.214780i
\(185\) −4.11718 + 7.13116i −0.302701 + 0.524294i
\(186\) −9.98218 + 7.51708i −0.731929 + 0.551179i
\(187\) −15.6882 1.56680i −1.14723 0.114576i
\(188\) 10.5152 10.1414i 0.766902 0.739636i
\(189\) −7.33340 + 4.23394i −0.533427 + 0.307974i
\(190\) −2.44791 19.9897i −0.177590 1.45021i
\(191\) −10.9295 + 6.31013i −0.790828 + 0.456585i −0.840254 0.542193i \(-0.817594\pi\)
0.0494258 + 0.998778i \(0.484261\pi\)
\(192\) −8.72587 + 1.83715i −0.629735 + 0.132585i
\(193\) 23.1318 + 13.3551i 1.66506 + 0.961325i 0.970240 + 0.242144i \(0.0778505\pi\)
0.694823 + 0.719181i \(0.255483\pi\)
\(194\) −1.12311 9.17137i −0.0806345 0.658466i
\(195\) −7.04345 + 2.37061i −0.504392 + 0.169763i
\(196\) 8.63740 2.14765i 0.616957 0.153403i
\(197\) 8.22265 + 4.74735i 0.585840 + 0.338235i 0.763451 0.645866i \(-0.223504\pi\)
−0.177611 + 0.984101i \(0.556837\pi\)
\(198\) −3.96156 + 7.22943i −0.281536 + 0.513773i
\(199\) 7.82713 4.51900i 0.554851 0.320343i −0.196225 0.980559i \(-0.562868\pi\)
0.751076 + 0.660216i \(0.229535\pi\)
\(200\) 1.59804 + 4.17507i 0.112999 + 0.295222i
\(201\) −5.28294 9.15032i −0.372630 0.645414i
\(202\) 0.240002 + 0.318706i 0.0168865 + 0.0224241i
\(203\) 10.0102i 0.702579i
\(204\) −7.35665 7.62784i −0.515068 0.534056i
\(205\) −0.659420 0.380717i −0.0460559 0.0265904i
\(206\) 8.50508 20.0188i 0.592577 1.39478i
\(207\) 1.83323i 0.127418i
\(208\) 10.4663 + 9.92248i 0.725711 + 0.688000i
\(209\) 2.53822 25.4148i 0.175572 1.75798i
\(210\) 1.82008 4.28401i 0.125598 0.295625i
\(211\) 6.63709 11.4958i 0.456916 0.791402i −0.541880 0.840456i \(-0.682287\pi\)
0.998796 + 0.0490539i \(0.0156206\pi\)
\(212\) 1.40840 + 1.46032i 0.0967294 + 0.100295i
\(213\) 9.46040 0.648216
\(214\) 1.51161 1.13832i 0.103331 0.0778137i
\(215\) 2.54038 + 4.40007i 0.173252 + 0.300082i
\(216\) −14.0081 + 5.36171i −0.953130 + 0.364818i
\(217\) −10.9623 + 6.32911i −0.744172 + 0.429648i
\(218\) 1.57548 3.70828i 0.106705 0.251157i
\(219\) −3.70892 + 6.42403i −0.250625 + 0.434096i
\(220\) −1.76218 12.1388i −0.118806 0.818399i
\(221\) −3.38729 + 16.8016i −0.227854 + 1.13020i
\(222\) −6.96741 + 0.853216i −0.467622 + 0.0572641i
\(223\) 13.3373 + 7.70030i 0.893132 + 0.515650i 0.874966 0.484185i \(-0.160884\pi\)
0.0181666 + 0.999835i \(0.494217\pi\)
\(224\) −8.99980 + 0.772804i −0.601325 + 0.0516351i
\(225\) 1.38895 + 2.40574i 0.0925969 + 0.160382i
\(226\) −0.266284 2.17449i −0.0177130 0.144645i
\(227\) −14.7939 25.6238i −0.981906 1.70071i −0.654951 0.755671i \(-0.727311\pi\)
−0.326955 0.945040i \(-0.606023\pi\)
\(228\) 12.3571 11.9178i 0.818369 0.789273i
\(229\) −0.333607 −0.0220454 −0.0110227 0.999939i \(-0.503509\pi\)
−0.0110227 + 0.999939i \(0.503509\pi\)
\(230\) −1.64088 2.17898i −0.108196 0.143677i
\(231\) 3.44503 4.79368i 0.226666 0.315401i
\(232\) 2.79064 17.5101i 0.183215 1.14959i
\(233\) 7.45717i 0.488536i −0.969708 0.244268i \(-0.921452\pi\)
0.969708 0.244268i \(-0.0785476\pi\)
\(234\) 7.39306 + 5.06531i 0.483300 + 0.331130i
\(235\) 13.5071i 0.881109i
\(236\) 8.28130 + 2.38039i 0.539067 + 0.154950i
\(237\) 5.54636 + 3.20219i 0.360275 + 0.208005i
\(238\) −6.45769 8.57537i −0.418590 0.555859i
\(239\) −11.2274 −0.726239 −0.363119 0.931743i \(-0.618288\pi\)
−0.363119 + 0.931743i \(0.618288\pi\)
\(240\) 4.37802 6.98629i 0.282600 0.450963i
\(241\) −3.30264 + 1.90678i −0.212741 + 0.122826i −0.602585 0.798055i \(-0.705862\pi\)
0.389843 + 0.920881i \(0.372529\pi\)
\(242\) 1.20024 15.5100i 0.0771546 0.997019i
\(243\) −13.1615 + 7.59877i −0.844308 + 0.487462i
\(244\) −4.03697 1.16039i −0.258441 0.0742866i
\(245\) −4.11460 + 7.12670i −0.262872 + 0.455308i
\(246\) −0.0788971 0.644278i −0.00503030 0.0410777i
\(247\) −27.2186 5.48740i −1.73188 0.349155i
\(248\) −20.9400 + 8.01495i −1.32969 + 0.508950i
\(249\) −13.5703 7.83483i −0.859984 0.496512i
\(250\) −15.8388 6.72918i −1.00173 0.425591i
\(251\) 5.14014 2.96766i 0.324443 0.187317i −0.328928 0.944355i \(-0.606688\pi\)
0.653371 + 0.757038i \(0.273354\pi\)
\(252\) −5.44713 + 1.35440i −0.343137 + 0.0853194i
\(253\) −1.42341 3.15300i −0.0894893 0.198227i
\(254\) −20.0289 + 15.0827i −1.25672 + 0.946375i
\(255\) 9.79821 0.613587
\(256\) −15.9581 1.15715i −0.997381 0.0723221i
\(257\) 12.0556 20.8809i 0.752008 1.30252i −0.194840 0.980835i \(-0.562419\pi\)
0.946848 0.321681i \(-0.104248\pi\)
\(258\) −1.69359 + 3.98629i −0.105439 + 0.248176i
\(259\) −7.11057 −0.441830
\(260\) −13.3212 + 0.596723i −0.826149 + 0.0370072i
\(261\) 11.0180i 0.681994i
\(262\) 7.12335 + 3.02639i 0.440082 + 0.186971i
\(263\) 10.2032 17.6725i 0.629157 1.08973i −0.358564 0.933505i \(-0.616734\pi\)
0.987721 0.156227i \(-0.0499331\pi\)
\(264\) 7.36251 7.42482i 0.453131 0.456966i
\(265\) −1.87583 −0.115231
\(266\) 13.8921 10.4614i 0.851779 0.641432i
\(267\) −16.2594 + 9.38737i −0.995059 + 0.574498i
\(268\) −4.57459 18.3981i −0.279438 1.12384i
\(269\) −0.317380 0.549719i −0.0193510 0.0335170i 0.856188 0.516665i \(-0.172827\pi\)
−0.875539 + 0.483148i \(0.839493\pi\)
\(270\) 5.42278 12.7639i 0.330020 0.776784i
\(271\) 7.14235 12.3709i 0.433867 0.751479i −0.563336 0.826228i \(-0.690482\pi\)
0.997202 + 0.0747490i \(0.0238155\pi\)
\(272\) −8.90529 16.8005i −0.539963 1.01868i
\(273\) −4.81392 4.24379i −0.291352 0.256846i
\(274\) 3.14814 + 25.7079i 0.190186 + 1.55307i
\(275\) −4.25682 3.05921i −0.256696 0.184477i
\(276\) 0.642367 2.23478i 0.0386659 0.134518i
\(277\) 14.9690 8.64234i 0.899399 0.519268i 0.0223936 0.999749i \(-0.492871\pi\)
0.877005 + 0.480481i \(0.159538\pi\)
\(278\) −3.10179 25.3294i −0.186033 1.51915i
\(279\) −12.0659 + 6.96627i −0.722369 + 0.417060i
\(280\) 5.26218 6.48545i 0.314475 0.387580i
\(281\) 20.0079i 1.19357i 0.802400 + 0.596786i \(0.203556\pi\)
−0.802400 + 0.596786i \(0.796444\pi\)
\(282\) −9.19795 + 6.92652i −0.547730 + 0.412468i
\(283\) 6.47890 11.2218i 0.385131 0.667066i −0.606657 0.794964i \(-0.707490\pi\)
0.991787 + 0.127898i \(0.0408231\pi\)
\(284\) 16.3141 + 4.68935i 0.968065 + 0.278262i
\(285\) 15.8731i 0.940240i
\(286\) −16.6484 2.97154i −0.984442 0.175711i
\(287\) 0.657516i 0.0388120i
\(288\) −9.90583 + 0.850603i −0.583706 + 0.0501223i
\(289\) 2.79879 4.84764i 0.164635 0.285155i
\(290\) 9.86191 + 13.0960i 0.579111 + 0.769021i
\(291\) 7.28263i 0.426915i
\(292\) −9.58018 + 9.23957i −0.560637 + 0.540705i
\(293\) 8.79700 5.07895i 0.513926 0.296716i −0.220520 0.975383i \(-0.570775\pi\)
0.734446 + 0.678667i \(0.237442\pi\)
\(294\) −6.96304 + 0.852682i −0.406093 + 0.0497294i
\(295\) −6.89948 + 3.98341i −0.401703 + 0.231923i
\(296\) −12.4380 1.98228i −0.722943 0.115218i
\(297\) 10.2642 14.2824i 0.595588 0.828748i
\(298\) 16.9718 2.07833i 0.983149 0.120395i
\(299\) −3.56431 + 1.19964i −0.206129 + 0.0693769i
\(300\) −0.850212 3.41938i −0.0490870 0.197418i
\(301\) −2.19368 + 3.79957i −0.126442 + 0.219003i
\(302\) −20.5135 8.71527i −1.18042 0.501507i
\(303\) −0.157228 0.272326i −0.00903249 0.0156447i
\(304\) 27.2168 14.4266i 1.56099 0.827420i
\(305\) 3.36336 1.94184i 0.192586 0.111189i
\(306\) −7.10779 9.43867i −0.406325 0.539573i
\(307\) −8.65127 −0.493754 −0.246877 0.969047i \(-0.579404\pi\)
−0.246877 + 0.969047i \(0.579404\pi\)
\(308\) 8.31698 6.55890i 0.473904 0.373728i
\(309\) −8.57163 + 14.8465i −0.487623 + 0.844588i
\(310\) 8.10624 19.0801i 0.460404 1.08367i
\(311\) 12.7132i 0.720899i −0.932779 0.360449i \(-0.882623\pi\)
0.932779 0.360449i \(-0.117377\pi\)
\(312\) −7.23754 8.76536i −0.409745 0.496241i
\(313\) 22.1702 1.25313 0.626566 0.779368i \(-0.284460\pi\)
0.626566 + 0.779368i \(0.284460\pi\)
\(314\) 27.2977 + 11.5976i 1.54050 + 0.654488i
\(315\) 2.59485 4.49442i 0.146203 0.253232i
\(316\) 7.97724 + 8.27131i 0.448755 + 0.465297i
\(317\) −21.6737 −1.21732 −0.608658 0.793432i \(-0.708292\pi\)
−0.608658 + 0.793432i \(0.708292\pi\)
\(318\) −0.961932 1.27738i −0.0539424 0.0716319i
\(319\) 8.55492 + 18.9500i 0.478983 + 1.06099i
\(320\) 11.0127 9.87750i 0.615630 0.552169i
\(321\) −1.29163 + 0.745723i −0.0720917 + 0.0416222i
\(322\) 0.921044 2.16791i 0.0513278 0.120813i
\(323\) 31.7035 + 18.3040i 1.76403 + 1.01846i
\(324\) 1.23884 0.308031i 0.0688244 0.0171129i
\(325\) −3.76851 + 4.27479i −0.209040 + 0.237123i
\(326\) 11.0674 1.35529i 0.612965 0.0750626i
\(327\) −1.58781 + 2.75017i −0.0878060 + 0.152084i
\(328\) 0.183302 1.15014i 0.0101212 0.0635060i
\(329\) −10.1011 + 5.83188i −0.556892 + 0.321522i
\(330\) 0.215671 + 9.66538i 0.0118723 + 0.532062i
\(331\) −8.69601 + 5.02064i −0.477976 + 0.275960i −0.719573 0.694417i \(-0.755662\pi\)
0.241597 + 0.970377i \(0.422329\pi\)
\(332\) −19.5180 20.2375i −1.07119 1.11067i
\(333\) −7.82641 −0.428884
\(334\) 11.2703 8.48707i 0.616681 0.464392i
\(335\) 15.1802 + 8.76430i 0.829384 + 0.478845i
\(336\) 7.11485 + 0.257618i 0.388147 + 0.0140542i
\(337\) 6.95326i 0.378768i −0.981903 0.189384i \(-0.939351\pi\)
0.981903 0.189384i \(-0.0606492\pi\)
\(338\) −5.01046 + 17.6888i −0.272533 + 0.962146i
\(339\) 1.72668i 0.0937804i
\(340\) 16.8967 + 4.85680i 0.916350 + 0.263397i
\(341\) 15.3434 21.3500i 0.830893 1.15617i
\(342\) 15.2906 11.5146i 0.826823 0.622639i
\(343\) −18.2838 −0.987232
\(344\) −4.89648 + 6.03474i −0.264000 + 0.325371i
\(345\) 1.07496 + 1.86188i 0.0578737 + 0.100240i
\(346\) −8.76014 + 1.07275i −0.470948 + 0.0576714i
\(347\) 8.89416 + 15.4051i 0.477463 + 0.826991i 0.999666 0.0258304i \(-0.00822300\pi\)
−0.522203 + 0.852821i \(0.674890\pi\)
\(348\) −3.86072 + 13.4313i −0.206956 + 0.719994i
\(349\) −23.5778 13.6126i −1.26209 0.728668i −0.288611 0.957446i \(-0.593194\pi\)
−0.973479 + 0.228779i \(0.926527\pi\)
\(350\) −0.433841 3.54277i −0.0231898 0.189369i
\(351\) −14.3427 12.6440i −0.765555 0.674888i
\(352\) 16.3767 9.15437i 0.872883 0.487930i
\(353\) −13.8504 + 23.9896i −0.737183 + 1.27684i 0.216576 + 0.976266i \(0.430511\pi\)
−0.953759 + 0.300573i \(0.902822\pi\)
\(354\) −6.25066 2.65562i −0.332219 0.141145i
\(355\) −13.5919 + 7.84731i −0.721385 + 0.416492i
\(356\) −32.6919 + 8.12869i −1.73267 + 0.430820i
\(357\) 4.23050 + 7.32743i 0.223902 + 0.387809i
\(358\) −16.4718 21.8735i −0.870562 1.15605i
\(359\) 15.5731 0.821919 0.410960 0.911654i \(-0.365194\pi\)
0.410960 + 0.911654i \(0.365194\pi\)
\(360\) 5.79193 7.13835i 0.305261 0.376224i
\(361\) −20.1525 + 34.9052i −1.06066 + 1.83711i
\(362\) −2.79895 1.18915i −0.147109 0.0625001i
\(363\) −2.42488 + 12.0189i −0.127273 + 0.630830i
\(364\) −6.19786 9.70444i −0.324856 0.508651i
\(365\) 12.3060i 0.644128i
\(366\) 3.04708 + 1.29456i 0.159273 + 0.0676679i
\(367\) −16.6715 9.62529i −0.870244 0.502436i −0.00281498 0.999996i \(-0.500896\pi\)
−0.867429 + 0.497560i \(0.834229\pi\)
\(368\) 2.21548 3.53538i 0.115490 0.184294i
\(369\) 0.723710i 0.0376748i
\(370\) 9.30248 7.00523i 0.483613 0.364185i
\(371\) −0.809912 1.40281i −0.0420485 0.0728302i
\(372\) 17.1498 4.26422i 0.889178 0.221090i
\(373\) −7.97094 + 4.60202i −0.412719 + 0.238284i −0.691958 0.721938i \(-0.743251\pi\)
0.279238 + 0.960222i \(0.409918\pi\)
\(374\) 19.5535 + 10.7149i 1.01109 + 0.554052i
\(375\) 11.7465 + 6.78184i 0.606586 + 0.350213i
\(376\) −19.2949 + 7.38527i −0.995058 + 0.380866i
\(377\) 21.4220 7.20999i 1.10329 0.371334i
\(378\) 11.8866 1.45561i 0.611381 0.0748686i
\(379\) 27.9886 + 16.1592i 1.43768 + 0.830043i 0.997688 0.0679598i \(-0.0216489\pi\)
0.439989 + 0.898003i \(0.354982\pi\)
\(380\) −7.86801 + 27.3726i −0.403621 + 1.40418i
\(381\) 17.1141 9.88085i 0.876784 0.506211i
\(382\) 17.7154 2.16940i 0.906399 0.110996i
\(383\) 11.7580 6.78846i 0.600803 0.346874i −0.168554 0.985692i \(-0.553910\pi\)
0.769358 + 0.638818i \(0.220576\pi\)
\(384\) 12.3736 + 2.43411i 0.631440 + 0.124215i
\(385\) −0.973228 + 9.74480i −0.0496003 + 0.496641i
\(386\) −22.7233 30.1750i −1.15659 1.53587i
\(387\) −2.41452 + 4.18208i −0.122737 + 0.212587i
\(388\) −3.60987 + 12.5586i −0.183264 + 0.637568i
\(389\) 1.16488 0.0590616 0.0295308 0.999564i \(-0.490599\pi\)
0.0295308 + 0.999564i \(0.490599\pi\)
\(390\) 10.4788 + 0.809377i 0.530614 + 0.0409844i
\(391\) 4.95834 0.250754
\(392\) −12.4302 1.98104i −0.627819 0.100058i
\(393\) −5.28287 3.05007i −0.266486 0.153856i
\(394\) −8.07745 10.7263i −0.406936 0.540383i
\(395\) −10.6248 −0.534590
\(396\) 9.15426 7.21919i 0.460019 0.362778i
\(397\) 9.86918 + 17.0939i 0.495320 + 0.857920i 0.999985 0.00539549i \(-0.00171745\pi\)
−0.504665 + 0.863315i \(0.668384\pi\)
\(398\) −12.6869 + 1.55361i −0.635936 + 0.0778756i
\(399\) −11.8704 + 6.85340i −0.594265 + 0.343099i
\(400\) 0.228766 6.31804i 0.0114383 0.315902i
\(401\) −8.36169 + 14.4829i −0.417563 + 0.723240i −0.995694 0.0927037i \(-0.970449\pi\)
0.578131 + 0.815944i \(0.303782\pi\)
\(402\) 1.81625 + 14.8316i 0.0905865 + 0.739734i
\(403\) −21.4402 18.9009i −1.06801 0.941522i
\(404\) −0.136146 0.547552i −0.00677352 0.0272417i
\(405\) −0.590147 + 1.02216i −0.0293246 + 0.0507917i
\(406\) −5.53560 + 13.0294i −0.274727 + 0.646639i
\(407\) 13.4608 6.07683i 0.667225 0.301217i
\(408\) 5.35734 + 13.9967i 0.265228 + 0.692939i
\(409\) 20.9450 12.0926i 1.03566 0.597940i 0.117061 0.993125i \(-0.462653\pi\)
0.918602 + 0.395185i \(0.129319\pi\)
\(410\) 0.647775 + 0.860202i 0.0319913 + 0.0424824i
\(411\) 20.4137i 1.00693i
\(412\) −22.1406 + 21.3535i −1.09079 + 1.05201i
\(413\) −5.95787 3.43978i −0.293168 0.169260i
\(414\) 1.01377 2.38615i 0.0498239 0.117273i
\(415\) 25.9957 1.27608
\(416\) −8.13604 18.7031i −0.398902 0.916993i
\(417\) 20.1131i 0.984941i
\(418\) −17.3581 + 31.6766i −0.849010 + 1.54935i
\(419\) −3.71065 2.14235i −0.181277 0.104660i 0.406615 0.913599i \(-0.366709\pi\)
−0.587893 + 0.808939i \(0.700042\pi\)
\(420\) −4.73808 + 4.56963i −0.231195 + 0.222975i
\(421\) 30.5974 1.49122 0.745612 0.666380i \(-0.232157\pi\)
0.745612 + 0.666380i \(0.232157\pi\)
\(422\) −14.9960 + 11.2928i −0.729996 + 0.549723i
\(423\) −11.1180 + 6.41898i −0.540576 + 0.312102i
\(424\) −1.02564 2.67961i −0.0498096 0.130133i
\(425\) 6.50681 3.75671i 0.315627 0.182227i
\(426\) −12.3138 5.23156i −0.596604 0.253470i
\(427\) 2.90435 + 1.67683i 0.140551 + 0.0811473i
\(428\) −2.59701 + 0.645734i −0.125531 + 0.0312127i
\(429\) 12.7399 + 3.91969i 0.615087 + 0.189244i
\(430\) −0.873372 7.13200i −0.0421178 0.343936i
\(431\) 9.42002 16.3159i 0.453746 0.785911i −0.544869 0.838521i \(-0.683421\pi\)
0.998615 + 0.0526098i \(0.0167539\pi\)
\(432\) 21.1981 + 0.767551i 1.01989 + 0.0369288i
\(433\) −16.6396 28.8207i −0.799649 1.38503i −0.919845 0.392283i \(-0.871685\pi\)
0.120196 0.992750i \(-0.461648\pi\)
\(434\) 17.7687 2.17592i 0.852925 0.104448i
\(435\) −6.46064 11.1902i −0.309764 0.536527i
\(436\) −4.10133 + 3.95551i −0.196418 + 0.189435i
\(437\) 8.03251i 0.384247i
\(438\) 8.38003 6.31059i 0.400414 0.301531i
\(439\) 1.98162 3.43226i 0.0945773 0.163813i −0.814855 0.579665i \(-0.803183\pi\)
0.909432 + 0.415852i \(0.136517\pi\)
\(440\) −4.41904 + 16.7745i −0.210670 + 0.799693i
\(441\) −7.82150 −0.372453
\(442\) 13.7002 19.9961i 0.651651 0.951116i
\(443\) 13.6717i 0.649563i −0.945789 0.324782i \(-0.894709\pi\)
0.945789 0.324782i \(-0.105291\pi\)
\(444\) 9.54069 + 2.74239i 0.452781 + 0.130148i
\(445\) 15.5735 26.9740i 0.738253 1.27869i
\(446\) −13.1018 17.3983i −0.620387 0.823833i
\(447\) −13.4766 −0.637424
\(448\) 12.1416 + 3.97096i 0.573637 + 0.187610i
\(449\) 7.99249 + 13.8434i 0.377189 + 0.653310i 0.990652 0.136413i \(-0.0435574\pi\)
−0.613463 + 0.789723i \(0.710224\pi\)
\(450\) −0.477516 3.89942i −0.0225103 0.183821i
\(451\) 0.561926 + 1.24472i 0.0264601 + 0.0586116i
\(452\) −0.855885 + 2.97760i −0.0402575 + 0.140054i
\(453\) 15.2134 + 8.78347i 0.714788 + 0.412683i
\(454\) 5.08608 + 41.5332i 0.238702 + 1.94925i
\(455\) 10.4364 + 2.10404i 0.489268 + 0.0986387i
\(456\) −22.6746 + 8.67889i −1.06184 + 0.406426i
\(457\) 14.8323 + 8.56342i 0.693825 + 0.400580i 0.805043 0.593216i \(-0.202142\pi\)
−0.111218 + 0.993796i \(0.535475\pi\)
\(458\) 0.434227 + 0.184483i 0.0202901 + 0.00862034i
\(459\) 12.6044 + 21.8315i 0.588324 + 1.01901i
\(460\) 0.930824 + 3.74358i 0.0433999 + 0.174545i
\(461\) −1.36453 + 0.787811i −0.0635524 + 0.0366920i −0.531440 0.847096i \(-0.678349\pi\)
0.467887 + 0.883788i \(0.345015\pi\)
\(462\) −7.13498 + 4.33443i −0.331949 + 0.201656i
\(463\) 11.0965i 0.515699i 0.966185 + 0.257850i \(0.0830139\pi\)
−0.966185 + 0.257850i \(0.916986\pi\)
\(464\) −13.3153 + 21.2481i −0.618149 + 0.986420i
\(465\) −8.16968 + 14.1503i −0.378860 + 0.656204i
\(466\) −4.12378 + 9.70635i −0.191031 + 0.449638i
\(467\) 34.0865i 1.57733i −0.614821 0.788667i \(-0.710772\pi\)
0.614821 0.788667i \(-0.289228\pi\)
\(468\) −6.82181 10.6814i −0.315338 0.493748i
\(469\) 15.1364i 0.698933i
\(470\) 7.46940 17.5811i 0.344538 0.810954i
\(471\) −20.2448 11.6883i −0.932829 0.538569i
\(472\) −9.46270 7.67787i −0.435556 0.353402i
\(473\) 0.905593 9.06758i 0.0416392 0.416928i
\(474\) −5.44842 7.23513i −0.250254 0.332321i
\(475\) 6.08586 + 10.5410i 0.279239 + 0.483655i
\(476\) 3.66326 + 14.7329i 0.167905 + 0.675281i
\(477\) −0.891447 1.54403i −0.0408165 0.0706963i
\(478\) 14.6137 + 6.20869i 0.668415 + 0.283979i
\(479\) −17.9715 + 31.1275i −0.821137 + 1.42225i 0.0836996 + 0.996491i \(0.473326\pi\)
−0.904836 + 0.425760i \(0.860007\pi\)
\(480\) −9.56188 + 6.67242i −0.436438 + 0.304553i
\(481\) −5.12149 15.2167i −0.233520 0.693823i
\(482\) 5.35319 0.655542i 0.243831 0.0298591i
\(483\) −0.928252 + 1.60778i −0.0422369 + 0.0731565i
\(484\) −10.1392 + 19.5243i −0.460873 + 0.887466i
\(485\) −6.04087 10.4631i −0.274302 0.475105i
\(486\) 21.3332 2.61243i 0.967694 0.118502i
\(487\) 25.3230 14.6202i 1.14749 0.662506i 0.199218 0.979955i \(-0.436160\pi\)
0.948275 + 0.317449i \(0.102826\pi\)
\(488\) 4.61288 + 3.74281i 0.208815 + 0.169429i
\(489\) −8.78817 −0.397415
\(490\) 9.29665 7.00084i 0.419980 0.316266i
\(491\) −8.31415 + 14.4005i −0.375212 + 0.649887i −0.990359 0.138526i \(-0.955764\pi\)
0.615146 + 0.788413i \(0.289097\pi\)
\(492\) −0.253589 + 0.882230i −0.0114327 + 0.0397740i
\(493\) −29.8003 −1.34214
\(494\) 32.3936 + 22.1943i 1.45746 + 0.998567i
\(495\) −1.07120 + 10.7258i −0.0481471 + 0.482090i
\(496\) 31.6880 + 1.14737i 1.42283 + 0.0515186i
\(497\) −11.7370 6.77634i −0.526475 0.303961i
\(498\) 13.3307 + 17.7022i 0.597362 + 0.793256i
\(499\) 11.5815i 0.518460i −0.965816 0.259230i \(-0.916531\pi\)
0.965816 0.259230i \(-0.0834688\pi\)
\(500\) 16.8948 + 17.5176i 0.755557 + 0.783410i
\(501\) −9.63015 + 5.55997i −0.430243 + 0.248401i
\(502\) −8.33157 + 1.02027i −0.371856 + 0.0455368i
\(503\) 6.06616 + 10.5069i 0.270476 + 0.468479i 0.968984 0.247124i \(-0.0794854\pi\)
−0.698507 + 0.715603i \(0.746152\pi\)
\(504\) 7.83904 + 1.24933i 0.349178 + 0.0556497i
\(505\) 0.451784 + 0.260838i 0.0201041 + 0.0116071i
\(506\) 0.109140 + 4.89112i 0.00485184 + 0.217437i
\(507\) 5.61447 13.3585i 0.249347 0.593272i
\(508\) 34.4105 8.55600i 1.52672 0.379611i
\(509\) −0.841686 + 1.45784i −0.0373071 + 0.0646177i −0.884076 0.467343i \(-0.845211\pi\)
0.846769 + 0.531961i \(0.178545\pi\)
\(510\) −12.7535 5.41837i −0.564733 0.239929i
\(511\) 9.20288 5.31329i 0.407111 0.235046i
\(512\) 20.1314 + 10.3309i 0.889689 + 0.456567i
\(513\) −35.3670 + 20.4191i −1.56149 + 0.901527i
\(514\) −27.2388 + 20.5122i −1.20145 + 0.904753i
\(515\) 28.4403i 1.25323i
\(516\) 4.40881 4.25206i 0.194087 0.187186i
\(517\) 14.1380 19.6727i 0.621788 0.865205i
\(518\) 9.25521 + 3.93212i 0.406651 + 0.172767i
\(519\) 6.95609 0.305338
\(520\) 17.6691 + 6.58989i 0.774841 + 0.288986i
\(521\) 24.4479 1.07108 0.535541 0.844509i \(-0.320108\pi\)
0.535541 + 0.844509i \(0.320108\pi\)
\(522\) −6.09288 + 14.3411i −0.266678 + 0.627693i
\(523\) 8.24805 14.2860i 0.360662 0.624685i −0.627408 0.778691i \(-0.715884\pi\)
0.988070 + 0.154006i \(0.0492174\pi\)
\(524\) −7.59826 7.87836i −0.331932 0.344168i
\(525\) 2.81318i 0.122777i
\(526\) −23.0534 + 17.3604i −1.00518 + 0.756949i
\(527\) 18.8417 + 32.6348i 0.820758 + 1.42159i
\(528\) −13.6890 + 5.59280i −0.595738 + 0.243395i
\(529\) −10.9560 18.9764i −0.476349 0.825060i
\(530\) 2.44160 + 1.03732i 0.106056 + 0.0450585i
\(531\) −6.55766 3.78606i −0.284578 0.164301i
\(532\) −23.8673 + 5.93448i −1.03478 + 0.257292i
\(533\) 1.40709 0.473585i 0.0609480 0.0205133i
\(534\) 26.3546 3.22734i 1.14048 0.139661i
\(535\) 1.23714 2.14279i 0.0534862 0.0926409i
\(536\) −4.21971 + 26.4769i −0.182264 + 1.14363i
\(537\) 10.7908 + 18.6903i 0.465659 + 0.806546i
\(538\) 0.109114 + 0.891032i 0.00470424 + 0.0384151i
\(539\) 13.4523 6.07303i 0.579433 0.261584i
\(540\) −14.1167 + 13.6148i −0.607487 + 0.585889i
\(541\) 23.8111i 1.02372i −0.859069 0.511861i \(-0.828956\pi\)
0.859069 0.511861i \(-0.171044\pi\)
\(542\) −16.1376 + 12.1524i −0.693171 + 0.521992i
\(543\) 2.07578 + 1.19845i 0.0890801 + 0.0514304i
\(544\) 2.30063 + 26.7923i 0.0986388 + 1.14871i
\(545\) 5.26829i 0.225669i
\(546\) 3.91906 + 8.18585i 0.167720 + 0.350322i
\(547\) −12.4799 −0.533604 −0.266802 0.963751i \(-0.585967\pi\)
−0.266802 + 0.963751i \(0.585967\pi\)
\(548\) 10.1187 35.2027i 0.432249 1.50378i
\(549\) 3.19673 + 1.84563i 0.136433 + 0.0787697i
\(550\) 3.84901 + 6.33591i 0.164122 + 0.270164i
\(551\) 48.2765i 2.05665i
\(552\) −2.07193 + 2.55359i −0.0881874 + 0.108688i
\(553\) −4.58737 7.94556i −0.195075 0.337880i
\(554\) −24.2630 + 2.97120i −1.03084 + 0.126234i
\(555\) −7.94873 + 4.58920i −0.337405 + 0.194801i
\(556\) −9.96970 + 34.6843i −0.422809 + 1.47094i
\(557\) −26.6011 15.3582i −1.12713 0.650747i −0.183916 0.982942i \(-0.558877\pi\)
−0.943211 + 0.332196i \(0.892211\pi\)
\(558\) 19.5575 2.39498i 0.827935 0.101387i
\(559\) −9.71115 1.95781i −0.410738 0.0828067i
\(560\) −10.4357 + 5.53158i −0.440990 + 0.233752i
\(561\) −14.2708 10.2558i −0.602512 0.433001i
\(562\) 11.0643 26.0426i 0.466719 1.09854i
\(563\) −9.04279 15.6626i −0.381108 0.660099i 0.610113 0.792315i \(-0.291124\pi\)
−0.991221 + 0.132216i \(0.957791\pi\)
\(564\) 15.8025 3.92921i 0.665405 0.165450i
\(565\) −1.43226 2.48076i −0.0602558 0.104366i
\(566\) −14.6386 + 11.0236i −0.615307 + 0.463357i
\(567\) −1.01921 −0.0428029
\(568\) −18.6415 15.1254i −0.782179 0.634646i
\(569\) 19.8891 + 11.4830i 0.833794 + 0.481391i 0.855150 0.518381i \(-0.173465\pi\)
−0.0213557 + 0.999772i \(0.506798\pi\)
\(570\) 8.77775 20.6606i 0.367659 0.865378i
\(571\) 22.2395 0.930695 0.465348 0.885128i \(-0.345929\pi\)
0.465348 + 0.885128i \(0.345929\pi\)
\(572\) 20.0265 + 13.0743i 0.837352 + 0.546664i
\(573\) −14.0671 −0.587663
\(574\) −0.363604 + 0.855832i −0.0151765 + 0.0357217i
\(575\) 1.42772 + 0.824294i 0.0595400 + 0.0343754i
\(576\) 13.3639 + 4.37072i 0.556830 + 0.182114i
\(577\) 1.20072 0.0499865 0.0249933 0.999688i \(-0.492044\pi\)
0.0249933 + 0.999688i \(0.492044\pi\)
\(578\) −6.32366 + 4.76204i −0.263030 + 0.198075i
\(579\) 14.8863 + 25.7838i 0.618652 + 1.07154i
\(580\) −5.59438 22.4995i −0.232294 0.934239i
\(581\) 11.2239 + 19.4404i 0.465648 + 0.806526i
\(582\) 4.02726 9.47917i 0.166935 0.392924i
\(583\) 2.73208 + 1.96344i 0.113151 + 0.0813173i
\(584\) 17.5791 6.72855i 0.727429 0.278429i
\(585\) 11.4871 + 2.31585i 0.474933 + 0.0957487i
\(586\) −14.2589 + 1.74612i −0.589031 + 0.0721317i
\(587\) −28.0250 16.1802i −1.15671 0.667829i −0.206200 0.978510i \(-0.566110\pi\)
−0.950514 + 0.310681i \(0.899443\pi\)
\(588\) 9.53472 + 2.74067i 0.393205 + 0.113023i
\(589\) −52.8683 + 30.5236i −2.17840 + 1.25770i
\(590\) 11.1833 1.36948i 0.460407 0.0563807i
\(591\) 5.29162 + 9.16535i 0.217668 + 0.377012i
\(592\) 15.0932 + 9.45831i 0.620328 + 0.388734i
\(593\) 24.5418i 1.00781i −0.863758 0.503906i \(-0.831896\pi\)
0.863758 0.503906i \(-0.168104\pi\)
\(594\) −21.2581 + 12.9141i −0.872230 + 0.529871i
\(595\) −12.1561 7.01831i −0.498350 0.287723i
\(596\) −23.2400 6.68014i −0.951948 0.273629i
\(597\) 10.0742 0.412308
\(598\) 5.30274 + 0.409582i 0.216845 + 0.0167490i
\(599\) 17.7432i 0.724968i −0.931990 0.362484i \(-0.881929\pi\)
0.931990 0.362484i \(-0.118071\pi\)
\(600\) −0.784256 + 4.92087i −0.0320171 + 0.200894i
\(601\) 29.7495 + 17.1759i 1.21351 + 0.700618i 0.963521 0.267632i \(-0.0862412\pi\)
0.249984 + 0.968250i \(0.419574\pi\)
\(602\) 4.95647 3.73247i 0.202011 0.152124i
\(603\) 16.6602i 0.678455i
\(604\) 21.8812 + 22.6878i 0.890333 + 0.923154i
\(605\) −6.48571 19.2793i −0.263682 0.783813i
\(606\) 0.0540542 + 0.441410i 0.00219580 + 0.0179310i
\(607\) 15.1878 + 26.3060i 0.616453 + 1.06773i 0.990128 + 0.140168i \(0.0447644\pi\)
−0.373675 + 0.927560i \(0.621902\pi\)
\(608\) −43.4036 + 3.72702i −1.76025 + 0.151151i
\(609\) 5.57892 9.66298i 0.226069 0.391564i
\(610\) −5.45162 + 0.667596i −0.220730 + 0.0270302i
\(611\) −19.7558 17.4160i −0.799232 0.704576i
\(612\) 4.03205 + 16.2161i 0.162986 + 0.655496i
\(613\) 7.05850 + 4.07523i 0.285090 + 0.164597i 0.635726 0.771915i \(-0.280701\pi\)
−0.350635 + 0.936512i \(0.614034\pi\)
\(614\) 11.2606 + 4.78411i 0.454441 + 0.193071i
\(615\) −0.424364 0.735021i −0.0171120 0.0296389i
\(616\) −14.4525 + 3.93789i −0.582309 + 0.158662i
\(617\) −11.6815 20.2330i −0.470281 0.814551i 0.529141 0.848534i \(-0.322514\pi\)
−0.999422 + 0.0339829i \(0.989181\pi\)
\(618\) 19.3670 14.5843i 0.779055 0.586667i
\(619\) 22.5055i 0.904572i −0.891873 0.452286i \(-0.850609\pi\)
0.891873 0.452286i \(-0.149391\pi\)
\(620\) −21.1024 + 20.3521i −0.847492 + 0.817361i
\(621\) −2.76565 + 4.79024i −0.110982 + 0.192226i
\(622\) −7.03034 + 16.5476i −0.281891 + 0.663500i
\(623\) 26.8961 1.07757
\(624\) 4.57327 + 15.4114i 0.183077 + 0.616951i
\(625\) −14.5992 −0.583966
\(626\) −28.8570 12.2600i −1.15336 0.490009i
\(627\) 16.6144 23.1186i 0.663517 0.923269i
\(628\) −29.1177 30.1911i −1.16192 1.20475i
\(629\) 21.1681i 0.844028i
\(630\) −5.86289 + 4.41505i −0.233583 + 0.175900i
\(631\) 31.7809 18.3487i 1.26518 0.730452i 0.291108 0.956690i \(-0.405976\pi\)
0.974072 + 0.226239i \(0.0726429\pi\)
\(632\) −5.80927 15.1774i −0.231081 0.603725i
\(633\) 12.8137 7.39801i 0.509300 0.294044i
\(634\) 28.2108 + 11.9855i 1.12039 + 0.476004i
\(635\) −16.3921 + 28.3920i −0.650503 + 1.12670i
\(636\) 0.545676 + 2.19460i 0.0216375 + 0.0870215i
\(637\) −5.11828 15.2072i −0.202794 0.602531i
\(638\) −0.655944 29.3963i −0.0259691 1.16381i
\(639\) −12.9186 7.45853i −0.511050 0.295055i
\(640\) −19.7965 + 6.76669i −0.782526 + 0.267477i
\(641\) 9.88074 + 17.1139i 0.390266 + 0.675960i 0.992484 0.122371i \(-0.0390498\pi\)
−0.602219 + 0.798331i \(0.705716\pi\)
\(642\) 2.09358 0.256376i 0.0826271 0.0101184i
\(643\) −30.9171 + 17.8500i −1.21925 + 0.703934i −0.964758 0.263140i \(-0.915242\pi\)
−0.254493 + 0.967075i \(0.581908\pi\)
\(644\) −2.39769 + 2.31244i −0.0944820 + 0.0911229i
\(645\) 5.66325i 0.222990i
\(646\) −31.1436 41.3567i −1.22533 1.62716i
\(647\) 8.98413 + 5.18699i 0.353203 + 0.203922i 0.666095 0.745867i \(-0.267965\pi\)
−0.312892 + 0.949789i \(0.601298\pi\)
\(648\) −1.78283 0.284135i −0.0700361 0.0111619i
\(649\) 14.2183 + 1.42000i 0.558118 + 0.0557401i
\(650\) 7.26909 3.48015i 0.285117 0.136503i
\(651\) −14.1094 −0.552992
\(652\) −15.1549 4.35615i −0.593512 0.170600i
\(653\) 6.79736 11.7734i 0.266001 0.460728i −0.701824 0.712350i \(-0.747631\pi\)
0.967825 + 0.251623i \(0.0809641\pi\)
\(654\) 3.58754 2.70160i 0.140284 0.105641i
\(655\) 10.1200 0.395421
\(656\) −0.874612 + 1.39567i −0.0341479 + 0.0544919i
\(657\) 10.1293 5.84818i 0.395184 0.228159i
\(658\) 16.3727 2.00498i 0.638276 0.0781621i
\(659\) −5.86583 10.1599i −0.228500 0.395774i 0.728864 0.684659i \(-0.240049\pi\)
−0.957364 + 0.288885i \(0.906716\pi\)
\(660\) 5.06419 12.6998i 0.197123 0.494341i
\(661\) 2.80252 4.85412i 0.109006 0.188803i −0.806362 0.591422i \(-0.798567\pi\)
0.915368 + 0.402619i \(0.131900\pi\)
\(662\) 14.0952 1.72608i 0.547827 0.0670859i
\(663\) −12.6337 + 14.3310i −0.490653 + 0.556570i
\(664\) 14.2136 + 37.1347i 0.551594 + 1.44110i
\(665\) 11.3697 19.6928i 0.440897 0.763655i
\(666\) 10.1869 + 4.32797i 0.394736 + 0.167705i
\(667\) −3.26938 5.66273i −0.126591 0.219262i
\(668\) −19.3628 + 4.81447i −0.749171 + 0.186278i
\(669\) 8.58311 + 14.8664i 0.331842 + 0.574768i
\(670\) −14.9121 19.8023i −0.576106 0.765030i
\(671\) −6.93116 0.692225i −0.267574 0.0267231i
\(672\) −9.11832 4.26980i −0.351747 0.164711i
\(673\) −8.00086 4.61930i −0.308410 0.178061i 0.337805 0.941216i \(-0.390316\pi\)
−0.646215 + 0.763155i \(0.723649\pi\)
\(674\) −3.84513 + 9.05046i −0.148109 + 0.348611i
\(675\) 8.38163i 0.322609i
\(676\) 16.3035 20.2533i 0.627059 0.778972i
\(677\) 2.58506i 0.0993518i −0.998765 0.0496759i \(-0.984181\pi\)
0.998765 0.0496759i \(-0.0158188\pi\)
\(678\) 0.954847 2.24747i 0.0366707 0.0863135i
\(679\) 5.21644 9.03515i 0.200189 0.346737i
\(680\) −19.3071 15.6655i −0.740394 0.600743i
\(681\) 32.9799i 1.26379i
\(682\) −31.7777 + 19.3046i −1.21683 + 0.739212i
\(683\) 6.48346 3.74323i 0.248083 0.143231i −0.370803 0.928711i \(-0.620918\pi\)
0.618886 + 0.785481i \(0.287584\pi\)
\(684\) −26.2700 + 6.53191i −1.00446 + 0.249754i
\(685\) 16.9329 + 29.3287i 0.646975 + 1.12059i
\(686\) 23.7984 + 10.1109i 0.908628 + 0.386034i
\(687\) −0.322035 0.185927i −0.0122864 0.00709355i
\(688\) 9.71050 5.14716i 0.370209 0.196234i
\(689\) 2.41868 2.74361i 0.0921443 0.104523i
\(690\) −0.369566 3.01789i −0.0140691 0.114889i
\(691\) 2.43325 + 1.40484i 0.0925650 + 0.0534425i 0.545568 0.838067i \(-0.316314\pi\)
−0.453003 + 0.891509i \(0.649647\pi\)
\(692\) 11.9955 + 3.44801i 0.456002 + 0.131074i
\(693\) −8.48365 + 3.82992i −0.322267 + 0.145487i
\(694\) −3.05777 24.9699i −0.116072 0.947846i
\(695\) −16.6836 28.8968i −0.632845 1.09612i
\(696\) 12.4526 15.3474i 0.472015 0.581742i
\(697\) −1.95742 −0.0741426
\(698\) 23.1614 + 30.7568i 0.876672 + 1.16416i
\(699\) 4.15606 7.19850i 0.157196 0.272272i
\(700\) −1.39444 + 4.85122i −0.0527050 + 0.183359i
\(701\) 25.3239i 0.956470i 0.878232 + 0.478235i \(0.158723\pi\)
−0.878232 + 0.478235i \(0.841277\pi\)
\(702\) 11.6765 + 24.3891i 0.440702 + 0.920506i
\(703\) −34.2923 −1.29336
\(704\) −26.3785 + 2.85918i −0.994177 + 0.107759i
\(705\) −7.52785 + 13.0386i −0.283515 + 0.491063i
\(706\) 31.2940 23.5660i 1.17777 0.886917i
\(707\) 0.450480i 0.0169420i
\(708\) 6.66739 + 6.91318i 0.250576 + 0.259813i
\(709\) −3.28577 5.69112i −0.123400 0.213734i 0.797707 0.603046i \(-0.206046\pi\)
−0.921106 + 0.389311i \(0.872713\pi\)
\(710\) 22.0310 2.69787i 0.826807 0.101249i
\(711\) −5.04919 8.74545i −0.189359 0.327980i
\(712\) 47.0474 + 7.49809i 1.76317 + 0.281003i
\(713\) −4.13423 + 7.16070i −0.154828 + 0.268170i
\(714\) −1.45443 11.8769i −0.0544306 0.444483i
\(715\) −21.5550 + 4.93611i −0.806110 + 0.184600i
\(716\) 9.34398 + 37.5796i 0.349201 + 1.40442i
\(717\) −10.8379 6.25728i −0.404750 0.233682i
\(718\) −20.2702 8.61189i −0.756478 0.321393i
\(719\) 20.9673 12.1055i 0.781949 0.451458i −0.0551719 0.998477i \(-0.517571\pi\)
0.837120 + 0.547019i \(0.184237\pi\)
\(720\) −11.4863 + 6.08845i −0.428070 + 0.226903i
\(721\) 21.2687 12.2795i 0.792087 0.457311i
\(722\) 45.5332 34.2888i 1.69457 1.27610i
\(723\) −4.25077 −0.158088
\(724\) 2.98555 + 3.09561i 0.110957 + 0.115048i
\(725\) −8.58079 4.95412i −0.318682 0.183991i
\(726\) 9.80268 14.3030i 0.363812 0.530836i
\(727\) 19.5880i 0.726479i 0.931696 + 0.363239i \(0.118329\pi\)
−0.931696 + 0.363239i \(0.881671\pi\)
\(728\) 2.70070 + 16.0588i 0.100095 + 0.595179i
\(729\) −18.8547 −0.698323
\(730\) −6.80519 + 16.0177i −0.251871 + 0.592842i
\(731\) 11.3113 + 6.53057i 0.418363 + 0.241542i
\(732\) −3.25023 3.37004i −0.120132 0.124560i
\(733\) 3.72835i 0.137710i 0.997627 + 0.0688548i \(0.0219345\pi\)
−0.997627 + 0.0688548i \(0.978065\pi\)
\(734\) 16.3771 + 21.7477i 0.604489 + 0.802721i
\(735\) −7.94375 + 4.58633i −0.293010 + 0.169169i
\(736\) −4.83875 + 3.37655i −0.178359 + 0.124461i
\(737\) −12.9358 28.6541i −0.476498 1.05549i
\(738\) −0.400208 + 0.941990i −0.0147319 + 0.0346751i
\(739\) −3.60477 + 6.24364i −0.132604 + 0.229676i −0.924679 0.380746i \(-0.875667\pi\)
0.792076 + 0.610423i \(0.209000\pi\)
\(740\) −15.9821 + 3.97387i −0.587513 + 0.146082i
\(741\) −23.2162 20.4666i −0.852869 0.751860i
\(742\) 0.278444 + 2.27379i 0.0102220 + 0.0834735i
\(743\) 7.79797 13.5065i 0.286080 0.495505i −0.686791 0.726855i \(-0.740981\pi\)
0.972870 + 0.231350i \(0.0743144\pi\)
\(744\) −24.6805 3.93342i −0.904833 0.144206i
\(745\) 19.3622 11.1788i 0.709375 0.409558i
\(746\) 12.9200 1.58216i 0.473034 0.0579269i
\(747\) 12.3539 + 21.3975i 0.452005 + 0.782895i
\(748\) −19.5258 24.7596i −0.713933 0.905300i
\(749\) 2.13660 0.0780697
\(750\) −11.5391 15.3231i −0.421347 0.559520i
\(751\) −31.5072 18.1907i −1.14971 0.663787i −0.200896 0.979613i \(-0.564385\pi\)
−0.948817 + 0.315825i \(0.897719\pi\)
\(752\) 29.1985 + 1.05723i 1.06476 + 0.0385533i
\(753\) 6.61578 0.241093
\(754\) −31.8702 2.46164i −1.16064 0.0896478i
\(755\) −29.1432 −1.06063
\(756\) −16.2767 4.67860i −0.591978 0.170159i
\(757\) −23.9236 + 41.4369i −0.869518 + 1.50605i −0.00702882 + 0.999975i \(0.502237\pi\)
−0.862490 + 0.506075i \(0.831096\pi\)
\(758\) −27.4943 36.5106i −0.998639 1.32613i
\(759\) 0.383200 3.83693i 0.0139093 0.139272i
\(760\) 25.3780 31.2775i 0.920558 1.13455i
\(761\) −32.2328 + 18.6096i −1.16844 + 0.674599i −0.953312 0.301987i \(-0.902350\pi\)
−0.215127 + 0.976586i \(0.569017\pi\)
\(762\) −27.7401 + 3.39700i −1.00492 + 0.123060i
\(763\) 3.93981 2.27465i 0.142631 0.0823478i
\(764\) −24.2583 6.97283i −0.877633 0.252268i
\(765\) −13.3798 7.72486i −0.483749 0.279293i
\(766\) −19.0583 + 2.33384i −0.688604 + 0.0843252i
\(767\) 3.06993 15.2275i 0.110849 0.549832i
\(768\) −14.7596 10.0108i −0.532593 0.361235i
\(769\) 16.9714 + 9.79843i 0.612004 + 0.353341i 0.773749 0.633492i \(-0.218379\pi\)
−0.161745 + 0.986833i \(0.551712\pi\)
\(770\) 6.65560 12.1458i 0.239851 0.437703i
\(771\) 23.2748 13.4377i 0.838223 0.483948i
\(772\) 12.8903 + 51.8421i 0.463931 + 1.86584i
\(773\) −0.901057 1.56068i −0.0324088 0.0561337i 0.849366 0.527804i \(-0.176985\pi\)
−0.881775 + 0.471671i \(0.843651\pi\)
\(774\) 5.45544 4.10822i 0.196092 0.147667i
\(775\) 12.5293i 0.450065i
\(776\) 11.6435 14.3502i 0.417978 0.515144i
\(777\) −6.86392 3.96289i −0.246242 0.142168i
\(778\) −1.51622 0.644172i −0.0543590 0.0230947i
\(779\) 3.17102i 0.113614i
\(780\) −13.1917 6.84822i −0.472340 0.245205i
\(781\) 28.0100 + 2.79740i 1.00228 + 0.100099i
\(782\) −6.45384 2.74194i −0.230789 0.0980516i
\(783\) 16.6219 28.7900i 0.594020 1.02887i
\(784\) 15.0838 + 9.45239i 0.538706 + 0.337585i
\(785\) 38.7814 1.38417
\(786\) 5.18958 + 6.89141i 0.185106 + 0.245809i
\(787\) −10.8465 18.7867i −0.386637 0.669675i 0.605358 0.795954i \(-0.293030\pi\)
−0.991995 + 0.126278i \(0.959697\pi\)
\(788\) 4.58210 + 18.4283i 0.163231 + 0.656481i
\(789\) 19.6986 11.3730i 0.701288 0.404889i
\(790\) 13.8293 + 5.87545i 0.492025 + 0.209039i
\(791\) 1.23680 2.14219i 0.0439754 0.0761676i
\(792\) −15.9075 + 4.33432i −0.565248 + 0.154013i
\(793\) −1.49653 + 7.42310i −0.0531434 + 0.263602i
\(794\) −3.39298 27.7073i −0.120413 0.983295i
\(795\) −1.81076 1.04544i −0.0642210 0.0370780i
\(796\) 17.3725 + 4.99359i 0.615754 + 0.176993i
\(797\) 7.45756 + 12.9169i 0.264160 + 0.457539i 0.967343 0.253470i \(-0.0815719\pi\)
−0.703183 + 0.711009i \(0.748239\pi\)
\(798\) 19.2406 2.35617i 0.681110 0.0834076i
\(799\) 17.3615 + 30.0709i 0.614204 + 1.06383i
\(800\) −3.79161 + 8.09713i −0.134054 + 0.286277i
\(801\) 29.6038 1.04600
\(802\) 18.8927 14.2271i 0.667123 0.502377i
\(803\) −12.8808 + 17.9233i −0.454553 + 0.632501i
\(804\) 5.83777 20.3094i 0.205882 0.716258i
\(805\) 3.07990i 0.108552i
\(806\) 17.4546 + 36.4580i 0.614814 + 1.28418i
\(807\) 0.707534i 0.0249064i
\(808\) −0.125584 + 0.787989i −0.00441805 + 0.0277214i
\(809\) 37.7008 + 21.7666i 1.32549 + 0.765272i 0.984599 0.174831i \(-0.0559378\pi\)
0.340891 + 0.940103i \(0.389271\pi\)
\(810\) 1.33339 1.00411i 0.0468507 0.0352809i
\(811\) −53.5329 −1.87979 −0.939897 0.341457i \(-0.889079\pi\)
−0.939897 + 0.341457i \(0.889079\pi\)
\(812\) 14.4104 13.8981i 0.505707 0.487727i
\(813\) 13.7892 7.96119i 0.483608 0.279211i
\(814\) −20.8812 + 0.465938i −0.731884 + 0.0163311i
\(815\) 12.6261 7.28971i 0.442274 0.255347i
\(816\) 0.766926 21.1809i 0.0268478 0.741478i
\(817\) −10.5795 + 18.3243i −0.370131 + 0.641085i
\(818\) −33.9494 + 4.15738i −1.18701 + 0.145359i
\(819\) 3.22782 + 9.59034i 0.112789 + 0.335114i
\(820\) −0.367464 1.47787i −0.0128324 0.0516094i
\(821\) 41.3781 + 23.8897i 1.44411 + 0.833755i 0.998120 0.0612857i \(-0.0195201\pi\)
0.445985 + 0.895040i \(0.352853\pi\)
\(822\) −11.2887 + 26.5707i −0.393738 + 0.926759i
\(823\) −26.7640 + 15.4522i −0.932933 + 0.538629i −0.887738 0.460349i \(-0.847724\pi\)
−0.0451951 + 0.998978i \(0.514391\pi\)
\(824\) 40.6269 15.5503i 1.41531 0.541719i
\(825\) −2.40419 5.32552i −0.0837033 0.185411i
\(826\) 5.85266 + 7.77193i 0.203640 + 0.270420i
\(827\) 32.7794 1.13985 0.569926 0.821696i \(-0.306972\pi\)
0.569926 + 0.821696i \(0.306972\pi\)
\(828\) −2.63906 + 2.54524i −0.0917138 + 0.0884531i
\(829\) 23.1261 40.0556i 0.803203 1.39119i −0.114294 0.993447i \(-0.536461\pi\)
0.917498 0.397742i \(-0.130206\pi\)
\(830\) −33.8363 14.3755i −1.17447 0.498981i
\(831\) 19.2663 0.668341
\(832\) 0.247259 + 28.8434i 0.00857218 + 0.999963i
\(833\) 21.1549i 0.732973i
\(834\) 11.1224 26.1794i 0.385139 0.906519i
\(835\) 9.22388 15.9762i 0.319206 0.552880i
\(836\) 40.1105 31.6318i 1.38725 1.09401i
\(837\) −42.0379 −1.45304
\(838\) 3.64512 + 4.84048i 0.125919 + 0.167212i
\(839\) 26.2019 15.1277i 0.904589 0.522265i 0.0259029 0.999664i \(-0.491754\pi\)
0.878686 + 0.477400i \(0.158421\pi\)
\(840\) 8.69413 3.32775i 0.299976 0.114818i
\(841\) 5.14943 + 8.91907i 0.177567 + 0.307554i
\(842\) −39.8259 16.9202i −1.37249 0.583109i
\(843\) −11.1509 + 19.3139i −0.384057 + 0.665205i
\(844\) 25.7639 6.40606i 0.886830 0.220506i
\(845\) 3.01433 + 23.8496i 0.103696 + 0.820450i
\(846\) 18.0210 2.20682i 0.619575 0.0758720i
\(847\) 11.6174 13.1743i 0.399179 0.452674i
\(848\) −0.146825 + 4.05499i −0.00504199 + 0.139249i
\(849\) 12.5083 7.22168i 0.429284 0.247847i
\(850\) −10.5468 + 1.29154i −0.361752 + 0.0442995i
\(851\) −4.02242 + 2.32234i −0.137887 + 0.0796089i
\(852\) 13.1347 + 13.6189i 0.449988 + 0.466577i
\(853\) 34.2981i 1.17435i −0.809462 0.587173i \(-0.800241\pi\)
0.809462 0.587173i \(-0.199759\pi\)
\(854\) −2.85306 3.78867i −0.0976296 0.129646i
\(855\) 12.5143 21.6753i 0.427979 0.741281i
\(856\) 3.73739 + 0.595641i 0.127741 + 0.0203586i
\(857\) 27.3039i 0.932683i 0.884605 + 0.466342i \(0.154428\pi\)
−0.884605 + 0.466342i \(0.845572\pi\)
\(858\) −14.4148 12.1470i −0.492114 0.414692i
\(859\) 0.0474933i 0.00162045i 1.00000 0.000810225i \(0.000257903\pi\)
−1.00000 0.000810225i \(0.999742\pi\)
\(860\) −2.80718 + 9.76608i −0.0957239 + 0.333020i
\(861\) 0.366449 0.634708i 0.0124886 0.0216308i
\(862\) −21.2839 + 16.0278i −0.724931 + 0.545909i
\(863\) 37.8425i 1.28817i 0.764953 + 0.644087i \(0.222762\pi\)
−0.764953 + 0.644087i \(0.777238\pi\)
\(864\) −27.1673 12.7215i −0.924250 0.432795i
\(865\) −9.99395 + 5.77001i −0.339805 + 0.196186i
\(866\) 5.72063 + 46.7150i 0.194395 + 1.58744i
\(867\) 5.40341 3.11966i 0.183509 0.105949i
\(868\) −24.3312 6.99380i −0.825856 0.237385i
\(869\) 15.4746 + 11.1210i 0.524940 + 0.377254i
\(870\) 2.22114 + 18.1380i 0.0753038 + 0.614934i
\(871\) −32.3920 + 10.9022i −1.09756 + 0.369407i
\(872\) 7.52573 2.88053i 0.254853 0.0975470i
\(873\) 5.74159 9.94473i 0.194323 0.336578i
\(874\) 4.44194 10.4552i 0.150251 0.353653i
\(875\) −9.71547 16.8277i −0.328443 0.568879i
\(876\) −14.3973 + 3.57981i −0.486439 + 0.120951i
\(877\) −7.31343 + 4.22241i −0.246957 + 0.142581i −0.618370 0.785887i \(-0.712207\pi\)
0.371413 + 0.928468i \(0.378873\pi\)
\(878\) −4.47732 + 3.37165i −0.151102 + 0.113788i
\(879\) 11.3225 0.381898
\(880\) 15.0281 19.3902i 0.506598 0.653644i
\(881\) −20.8344 + 36.0863i −0.701930 + 1.21578i 0.265858 + 0.964012i \(0.414345\pi\)
−0.967788 + 0.251767i \(0.918988\pi\)
\(882\) 10.1806 + 4.32526i 0.342798 + 0.145639i
\(883\) 40.9787i 1.37904i 0.724266 + 0.689521i \(0.242179\pi\)
−0.724266 + 0.689521i \(0.757821\pi\)
\(884\) −28.8900 + 18.4510i −0.971678 + 0.620574i
\(885\) −8.88020 −0.298505
\(886\) −7.56041 + 17.7953i −0.253997 + 0.597845i
\(887\) 17.4268 30.1841i 0.585135 1.01348i −0.409723 0.912210i \(-0.634375\pi\)
0.994859 0.101274i \(-0.0322919\pi\)
\(888\) −10.9018 8.84549i −0.365839 0.296835i
\(889\) −28.3100 −0.949489
\(890\) −35.1872 + 26.4977i −1.17948 + 0.888205i
\(891\) 1.92943 0.871038i 0.0646384 0.0291809i
\(892\) 7.43227 + 29.8911i 0.248851 + 1.00083i
\(893\) −48.7149 + 28.1255i −1.63018 + 0.941185i
\(894\) 17.5414 + 7.45253i 0.586671 + 0.249250i
\(895\) −31.0068 17.9018i −1.03644 0.598392i
\(896\) −13.6078 11.8829i −0.454603 0.396980i
\(897\) −4.10925 0.828445i −0.137204 0.0276610i
\(898\) −2.74779 22.4386i −0.0916948 0.748784i
\(899\) 24.8473 43.0368i 0.828704 1.43536i
\(900\) −1.53482 + 5.33960i −0.0511608 + 0.177987i
\(901\) −4.17615 + 2.41110i −0.139128 + 0.0803254i
\(902\) −0.0430854 1.93089i −0.00143459 0.0642915i
\(903\) −4.23517 + 2.44518i −0.140938 + 0.0813705i
\(904\) 2.76063 3.40238i 0.0918172 0.113161i
\(905\) −3.97641 −0.132180
\(906\) −14.9447 19.8456i −0.496506 0.659327i
\(907\) 25.5599 + 14.7570i 0.848703 + 0.489999i 0.860213 0.509935i \(-0.170330\pi\)
−0.0115098 + 0.999934i \(0.503664\pi\)
\(908\) 16.3476 56.8728i 0.542514 1.88739i
\(909\) 0.495830i 0.0164456i
\(910\) −12.4207 8.50995i −0.411741 0.282102i
\(911\) 23.0961i 0.765209i 0.923912 + 0.382605i \(0.124973\pi\)
−0.923912 + 0.382605i \(0.875027\pi\)
\(912\) 34.3130 + 1.24242i 1.13622 + 0.0411406i
\(913\) −37.8618 27.2098i −1.25304 0.900512i
\(914\) −14.5704 19.3485i −0.481944 0.639990i
\(915\) 4.32893 0.143110
\(916\) −0.463177 0.480251i −0.0153038 0.0158680i
\(917\) 4.36944 + 7.56809i 0.144292 + 0.249920i
\(918\) −4.33335 35.3863i −0.143022 1.16792i
\(919\) 21.2446 + 36.7966i 0.700793 + 1.21381i 0.968188 + 0.250222i \(0.0805038\pi\)
−0.267395 + 0.963587i \(0.586163\pi\)
\(920\) 0.858614 5.38744i 0.0283077 0.177619i
\(921\) −8.35117 4.82155i −0.275181 0.158876i
\(922\) 2.21174 0.270846i 0.0728399 0.00891984i
\(923\) 6.04775 29.9980i 0.199064 0.987397i
\(924\) 11.6839 1.69614i 0.384372 0.0557988i
\(925\) −3.51907 + 6.09521i −0.115706 + 0.200409i
\(926\) 6.13633 14.4434i 0.201652 0.474639i
\(927\) 23.4098 13.5157i 0.768879 0.443913i
\(928\) 29.0815 20.2935i 0.954649 0.666168i
\(929\) 13.6195 + 23.5897i 0.446843 + 0.773954i 0.998179 0.0603291i \(-0.0192150\pi\)
−0.551336 + 0.834283i \(0.685882\pi\)
\(930\) 18.4588 13.9004i 0.605288 0.455812i
\(931\) −34.2709 −1.12318
\(932\) 10.7351 10.3535i 0.351641 0.339139i
\(933\) 7.08535 12.2722i 0.231964 0.401773i
\(934\) −18.8497 + 44.3674i −0.616780 + 1.45174i
\(935\) 29.0102 + 2.89729i 0.948735 + 0.0947516i
\(936\) 2.97259 + 17.6755i 0.0971620 + 0.577741i
\(937\) 8.35337i 0.272893i −0.990647 0.136446i \(-0.956432\pi\)
0.990647 0.136446i \(-0.0435681\pi\)
\(938\) 8.37035 19.7017i 0.273302 0.643283i
\(939\) 21.4011 + 12.3560i 0.698400 + 0.403221i
\(940\) −19.4445 + 18.7532i −0.634210 + 0.611662i
\(941\) 59.5806i 1.94227i −0.238524 0.971137i \(-0.576663\pi\)
0.238524 0.971137i \(-0.423337\pi\)
\(942\) 19.8872 + 26.4089i 0.647961 + 0.860449i
\(943\) −0.214748 0.371954i −0.00699315 0.0121125i
\(944\) 8.07094 + 15.2264i 0.262687 + 0.495578i
\(945\) 13.5608 7.82931i 0.441132 0.254687i
\(946\) −6.19306 + 11.3017i −0.201354 + 0.367450i
\(947\) 21.2899 + 12.2917i 0.691827 + 0.399427i 0.804296 0.594229i \(-0.202543\pi\)
−0.112469 + 0.993655i \(0.535876\pi\)
\(948\) 3.09073 + 12.4303i 0.100382 + 0.403717i
\(949\) 17.9990 + 15.8673i 0.584272 + 0.515075i
\(950\) −2.09230 17.0858i −0.0678830 0.554336i
\(951\) −20.9219 12.0793i −0.678439 0.391697i
\(952\) 3.37908 21.2023i 0.109517 0.687170i
\(953\) 29.7481 17.1751i 0.963637 0.556356i 0.0663462 0.997797i \(-0.478866\pi\)
0.897290 + 0.441441i \(0.145533\pi\)
\(954\) 0.306476 + 2.50270i 0.00992252 + 0.0810278i
\(955\) 20.2105 11.6685i 0.653997 0.377585i
\(956\) −15.5880 16.1626i −0.504152 0.522737i
\(957\) −2.30308 + 23.0605i −0.0744481 + 0.745439i
\(958\) 40.6052 30.5778i 1.31190 0.987923i
\(959\) −14.6220 + 25.3261i −0.472170 + 0.817822i
\(960\) 16.1357 3.39722i 0.520777 0.109645i
\(961\) −31.8404 −1.02711
\(962\) −1.74858 + 22.6384i −0.0563766 + 0.729892i
\(963\) 2.35170 0.0757824
\(964\) −7.33030 2.10703i −0.236093 0.0678629i
\(965\) −42.7748 24.6960i −1.37697 0.794994i
\(966\) 2.09732 1.57939i 0.0674801 0.0508159i
\(967\) −5.66688 −0.182235 −0.0911173 0.995840i \(-0.529044\pi\)
−0.0911173 + 0.995840i \(0.529044\pi\)
\(968\) 23.9941 19.8061i 0.771201 0.636592i
\(969\) 20.4025 + 35.3382i 0.655423 + 1.13523i
\(970\) 2.07683 + 16.9595i 0.0666829 + 0.544536i
\(971\) 8.57282 4.94952i 0.275115 0.158838i −0.356095 0.934450i \(-0.615892\pi\)
0.631210 + 0.775612i \(0.282559\pi\)
\(972\) −29.2122 8.39681i −0.936983 0.269328i
\(973\) 14.4067 24.9531i 0.461858 0.799961i
\(974\) −41.0456 + 5.02637i −1.31519 + 0.161055i
\(975\) −6.02023 + 2.02623i −0.192802 + 0.0648913i
\(976\) −3.93443 7.42260i −0.125938 0.237592i
\(977\) 20.3945 35.3243i 0.652477 1.13012i −0.330043 0.943966i \(-0.607063\pi\)
0.982520 0.186158i \(-0.0596035\pi\)
\(978\) 11.4388 + 4.85982i 0.365772 + 0.155400i
\(979\) −50.9161 + 22.9860i −1.62729 + 0.734635i
\(980\) −15.9721 + 3.97138i −0.510209 + 0.126861i
\(981\) 4.33643 2.50364i 0.138452 0.0799351i
\(982\) 18.7852 14.1462i 0.599461 0.451424i
\(983\) 32.1882i 1.02665i 0.858196 + 0.513323i \(0.171586\pi\)
−0.858196 + 0.513323i \(0.828414\pi\)
\(984\) 0.817945 1.00809i 0.0260751 0.0321367i
\(985\) −15.2051 8.77869i −0.484476 0.279712i
\(986\) 38.7885 + 16.4795i 1.23528 + 0.524813i
\(987\) −13.0010 −0.413825
\(988\) −29.8906 46.8019i −0.950946 1.48897i
\(989\) 2.86586i 0.0911292i
\(990\) 7.32563 13.3685i 0.232824 0.424879i
\(991\) −3.25161 1.87732i −0.103291 0.0596350i 0.447465 0.894302i \(-0.352327\pi\)
−0.550756 + 0.834667i \(0.685660\pi\)
\(992\) −40.6110 19.0168i −1.28940 0.603783i
\(993\) −11.1925 −0.355183
\(994\) 11.5297 + 15.3107i 0.365700 + 0.485625i
\(995\) −14.4738 + 8.35643i −0.458849 + 0.264917i
\(996\) −7.56211 30.4133i −0.239615 0.963681i
\(997\) 6.39909 3.69452i 0.202661 0.117007i −0.395235 0.918580i \(-0.629337\pi\)
0.597896 + 0.801574i \(0.296003\pi\)
\(998\) −6.40453 + 15.0747i −0.202732 + 0.477180i
\(999\) −20.4505 11.8071i −0.647025 0.373560i
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 572.2.t.a.87.12 160
4.3 odd 2 inner 572.2.t.a.87.15 yes 160
11.10 odd 2 inner 572.2.t.a.87.69 yes 160
13.3 even 3 inner 572.2.t.a.263.66 yes 160
44.43 even 2 inner 572.2.t.a.87.66 yes 160
52.3 odd 6 inner 572.2.t.a.263.69 yes 160
143.120 odd 6 inner 572.2.t.a.263.15 yes 160
572.263 even 6 inner 572.2.t.a.263.12 yes 160
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
572.2.t.a.87.12 160 1.1 even 1 trivial
572.2.t.a.87.15 yes 160 4.3 odd 2 inner
572.2.t.a.87.66 yes 160 44.43 even 2 inner
572.2.t.a.87.69 yes 160 11.10 odd 2 inner
572.2.t.a.263.12 yes 160 572.263 even 6 inner
572.2.t.a.263.15 yes 160 143.120 odd 6 inner
572.2.t.a.263.66 yes 160 13.3 even 3 inner
572.2.t.a.263.69 yes 160 52.3 odd 6 inner