Properties

Label 675.2.u.b.49.2
Level $675$
Weight $2$
Character 675.49
Analytic conductor $5.390$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [675,2,Mod(49,675)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(675, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([14, 9]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("675.49");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 675 = 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 675.u (of order \(18\), degree \(6\), not 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: \(5.38990213644\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(4\) over \(\Q(\zeta_{18})\)
Twist minimal: no (minimal twist has level 27)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 49.2
Character \(\chi\) \(=\) 675.49
Dual form 675.2.u.b.124.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.267057 - 0.318266i) q^{2} +(-1.72466 - 0.159815i) q^{3} +(0.317323 - 1.79963i) q^{4} +(0.409719 + 0.591580i) q^{6} +(1.29958 - 0.229151i) q^{7} +(-1.37711 + 0.795075i) q^{8} +(2.94892 + 0.551252i) q^{9} +O(q^{10})\) \(q+(-0.267057 - 0.318266i) q^{2} +(-1.72466 - 0.159815i) q^{3} +(0.317323 - 1.79963i) q^{4} +(0.409719 + 0.591580i) q^{6} +(1.29958 - 0.229151i) q^{7} +(-1.37711 + 0.795075i) q^{8} +(2.94892 + 0.551252i) q^{9} +(4.90067 + 1.78370i) q^{11} +(-0.834881 + 3.05303i) q^{12} +(-0.0116078 + 0.0138336i) q^{13} +(-0.419993 - 0.352416i) q^{14} +(-2.81355 - 1.02405i) q^{16} +(2.71308 + 1.56640i) q^{17} +(-0.612083 - 1.08575i) q^{18} +(0.208676 + 0.361438i) q^{19} +(-2.27796 + 0.187516i) q^{21} +(-0.741067 - 2.03606i) q^{22} +(1.01867 + 0.179619i) q^{23} +(2.50212 - 1.15115i) q^{24} +0.00750270 q^{26} +(-4.99779 - 1.42200i) q^{27} -2.41147i q^{28} +(5.98068 - 5.01839i) q^{29} +(0.647649 - 3.67300i) q^{31} +(1.51319 + 4.15744i) q^{32} +(-8.16694 - 3.85948i) q^{33} +(-0.226015 - 1.28180i) q^{34} +(1.92781 - 5.13202i) q^{36} +(-3.83195 - 2.21238i) q^{37} +(0.0593049 - 0.162939i) q^{38} +(0.0222303 - 0.0220032i) q^{39} +(-2.81517 - 2.36221i) q^{41} +(0.668024 + 0.674919i) q^{42} +(2.84146 - 7.80685i) q^{43} +(4.76508 - 8.25337i) q^{44} +(-0.214876 - 0.372177i) q^{46} +(6.99008 - 1.23254i) q^{47} +(4.68877 + 2.21579i) q^{48} +(-4.94145 + 1.79854i) q^{49} +(-4.42881 - 3.13510i) q^{51} +(0.0212119 + 0.0252794i) q^{52} +1.30057i q^{53} +(0.882118 + 1.97038i) q^{54} +(-1.60747 + 1.34883i) q^{56} +(-0.302133 - 0.656707i) q^{57} +(-3.19436 - 0.563252i) q^{58} +(-3.47856 + 1.26609i) q^{59} +(1.20064 + 6.80919i) q^{61} +(-1.34195 + 0.774775i) q^{62} +(3.95868 + 0.0406486i) q^{63} +(-2.07506 + 3.59410i) q^{64} +(0.952697 + 3.62996i) q^{66} +(7.08789 - 8.44702i) q^{67} +(3.67985 - 4.38548i) q^{68} +(-1.72816 - 0.472581i) q^{69} +(3.04214 - 5.26914i) q^{71} +(-4.49927 + 1.58548i) q^{72} +(0.473692 - 0.273486i) q^{73} +(0.319224 + 1.81041i) q^{74} +(0.716670 - 0.260847i) q^{76} +(6.77756 + 1.19507i) q^{77} +(-0.0129396 - 0.00119904i) q^{78} +(-0.374706 + 0.314416i) q^{79} +(8.39224 + 3.25120i) q^{81} +1.52681i q^{82} +(-2.96561 - 3.53428i) q^{83} +(-0.385389 + 4.15898i) q^{84} +(-3.24348 + 1.18053i) q^{86} +(-11.1167 + 7.69922i) q^{87} +(-8.16694 + 1.44005i) q^{88} +(-1.68653 - 2.92116i) q^{89} +(-0.0119153 + 0.0206379i) q^{91} +(0.646495 - 1.77623i) q^{92} +(-1.70398 + 6.23118i) q^{93} +(-2.25902 - 1.89554i) q^{94} +(-1.94531 - 7.41201i) q^{96} +(3.40014 - 9.34182i) q^{97} +(1.89206 + 1.09238i) q^{98} +(13.4684 + 7.96149i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 12 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 12 q^{4} + 6 q^{11} - 30 q^{14} + 6 q^{19} - 24 q^{21} + 36 q^{24} - 60 q^{26} + 12 q^{29} + 6 q^{31} - 18 q^{34} + 36 q^{36} - 66 q^{39} + 30 q^{41} - 6 q^{44} - 6 q^{46} - 24 q^{49} - 36 q^{51} + 108 q^{54} - 66 q^{56} + 24 q^{59} + 24 q^{61} - 24 q^{64} - 18 q^{66} - 18 q^{69} + 54 q^{71} - 66 q^{74} - 96 q^{76} + 84 q^{79} + 72 q^{81} - 12 q^{84} + 102 q^{86} - 18 q^{89} + 12 q^{91} + 30 q^{94} + 54 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/675\mathbb{Z}\right)^\times\).

\(n\) \(326\) \(352\)
\(\chi(n)\) \(e\left(\frac{7}{9}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.267057 0.318266i −0.188837 0.225048i 0.663316 0.748339i \(-0.269148\pi\)
−0.852154 + 0.523291i \(0.824704\pi\)
\(3\) −1.72466 0.159815i −0.995734 0.0922690i
\(4\) 0.317323 1.79963i 0.158661 0.899813i
\(5\) 0 0
\(6\) 0.409719 + 0.591580i 0.167267 + 0.241512i
\(7\) 1.29958 0.229151i 0.491195 0.0866110i 0.0774361 0.996997i \(-0.475327\pi\)
0.413759 + 0.910386i \(0.364216\pi\)
\(8\) −1.37711 + 0.795075i −0.486882 + 0.281102i
\(9\) 2.94892 + 0.551252i 0.982973 + 0.183751i
\(10\) 0 0
\(11\) 4.90067 + 1.78370i 1.47761 + 0.537805i 0.950155 0.311778i \(-0.100925\pi\)
0.527454 + 0.849584i \(0.323147\pi\)
\(12\) −0.834881 + 3.05303i −0.241009 + 0.881335i
\(13\) −0.0116078 + 0.0138336i −0.00321942 + 0.00383676i −0.767652 0.640867i \(-0.778575\pi\)
0.764432 + 0.644704i \(0.223019\pi\)
\(14\) −0.419993 0.352416i −0.112248 0.0941870i
\(15\) 0 0
\(16\) −2.81355 1.02405i −0.703389 0.256012i
\(17\) 2.71308 + 1.56640i 0.658019 + 0.379907i 0.791522 0.611141i \(-0.209289\pi\)
−0.133503 + 0.991048i \(0.542623\pi\)
\(18\) −0.612083 1.08575i −0.144269 0.255915i
\(19\) 0.208676 + 0.361438i 0.0478736 + 0.0829195i 0.888969 0.457967i \(-0.151422\pi\)
−0.841096 + 0.540886i \(0.818089\pi\)
\(20\) 0 0
\(21\) −2.27796 + 0.187516i −0.497092 + 0.0409194i
\(22\) −0.741067 2.03606i −0.157996 0.434090i
\(23\) 1.01867 + 0.179619i 0.212408 + 0.0374532i 0.278839 0.960338i \(-0.410050\pi\)
−0.0664316 + 0.997791i \(0.521161\pi\)
\(24\) 2.50212 1.15115i 0.510742 0.234978i
\(25\) 0 0
\(26\) 0.00750270 0.00147140
\(27\) −4.99779 1.42200i −0.961825 0.273665i
\(28\) 2.41147i 0.455726i
\(29\) 5.98068 5.01839i 1.11058 0.931891i 0.112493 0.993652i \(-0.464116\pi\)
0.998091 + 0.0617615i \(0.0196718\pi\)
\(30\) 0 0
\(31\) 0.647649 3.67300i 0.116321 0.659691i −0.869766 0.493464i \(-0.835730\pi\)
0.986088 0.166227i \(-0.0531584\pi\)
\(32\) 1.51319 + 4.15744i 0.267496 + 0.734939i
\(33\) −8.16694 3.85948i −1.42168 0.671849i
\(34\) −0.226015 1.28180i −0.0387613 0.219826i
\(35\) 0 0
\(36\) 1.92781 5.13202i 0.321301 0.855337i
\(37\) −3.83195 2.21238i −0.629969 0.363713i 0.150771 0.988569i \(-0.451824\pi\)
−0.780740 + 0.624856i \(0.785158\pi\)
\(38\) 0.0593049 0.162939i 0.00962052 0.0264322i
\(39\) 0.0222303 0.0220032i 0.00355970 0.00352334i
\(40\) 0 0
\(41\) −2.81517 2.36221i −0.439655 0.368915i 0.395925 0.918283i \(-0.370424\pi\)
−0.835580 + 0.549368i \(0.814868\pi\)
\(42\) 0.668024 + 0.674919i 0.103078 + 0.104142i
\(43\) 2.84146 7.80685i 0.433319 1.19053i −0.510445 0.859911i \(-0.670519\pi\)
0.943763 0.330622i \(-0.107259\pi\)
\(44\) 4.76508 8.25337i 0.718363 1.24424i
\(45\) 0 0
\(46\) −0.214876 0.372177i −0.0316818 0.0548745i
\(47\) 6.99008 1.23254i 1.01961 0.179784i 0.361234 0.932475i \(-0.382356\pi\)
0.658374 + 0.752691i \(0.271245\pi\)
\(48\) 4.68877 + 2.21579i 0.676766 + 0.319821i
\(49\) −4.94145 + 1.79854i −0.705921 + 0.256934i
\(50\) 0 0
\(51\) −4.42881 3.13510i −0.620158 0.439001i
\(52\) 0.0212119 + 0.0252794i 0.00294157 + 0.00350562i
\(53\) 1.30057i 0.178648i 0.996003 + 0.0893238i \(0.0284706\pi\)
−0.996003 + 0.0893238i \(0.971529\pi\)
\(54\) 0.882118 + 1.97038i 0.120041 + 0.268135i
\(55\) 0 0
\(56\) −1.60747 + 1.34883i −0.214808 + 0.180245i
\(57\) −0.302133 0.656707i −0.0400185 0.0869830i
\(58\) −3.19436 0.563252i −0.419440 0.0739586i
\(59\) −3.47856 + 1.26609i −0.452871 + 0.164831i −0.558377 0.829587i \(-0.688576\pi\)
0.105507 + 0.994419i \(0.466354\pi\)
\(60\) 0 0
\(61\) 1.20064 + 6.80919i 0.153727 + 0.871828i 0.959941 + 0.280204i \(0.0904020\pi\)
−0.806214 + 0.591624i \(0.798487\pi\)
\(62\) −1.34195 + 0.774775i −0.170428 + 0.0983965i
\(63\) 3.95868 + 0.0406486i 0.498747 + 0.00512125i
\(64\) −2.07506 + 3.59410i −0.259382 + 0.449263i
\(65\) 0 0
\(66\) 0.952697 + 3.62996i 0.117269 + 0.446817i
\(67\) 7.08789 8.44702i 0.865923 1.03197i −0.133241 0.991084i \(-0.542538\pi\)
0.999164 0.0408835i \(-0.0130172\pi\)
\(68\) 3.67985 4.38548i 0.446247 0.531817i
\(69\) −1.72816 0.472581i −0.208046 0.0568921i
\(70\) 0 0
\(71\) 3.04214 5.26914i 0.361035 0.625332i −0.627096 0.778942i \(-0.715757\pi\)
0.988132 + 0.153610i \(0.0490900\pi\)
\(72\) −4.49927 + 1.58548i −0.530245 + 0.186850i
\(73\) 0.473692 0.273486i 0.0554415 0.0320092i −0.472023 0.881586i \(-0.656476\pi\)
0.527465 + 0.849577i \(0.323143\pi\)
\(74\) 0.319224 + 1.81041i 0.0371090 + 0.210456i
\(75\) 0 0
\(76\) 0.716670 0.260847i 0.0822077 0.0299212i
\(77\) 6.77756 + 1.19507i 0.772374 + 0.136190i
\(78\) −0.0129396 0.00119904i −0.00146512 0.000135765i
\(79\) −0.374706 + 0.314416i −0.0421577 + 0.0353745i −0.663623 0.748067i \(-0.730982\pi\)
0.621465 + 0.783442i \(0.286538\pi\)
\(80\) 0 0
\(81\) 8.39224 + 3.25120i 0.932471 + 0.361244i
\(82\) 1.52681i 0.168608i
\(83\) −2.96561 3.53428i −0.325518 0.387937i 0.578321 0.815809i \(-0.303708\pi\)
−0.903839 + 0.427872i \(0.859263\pi\)
\(84\) −0.385389 + 4.15898i −0.0420493 + 0.453782i
\(85\) 0 0
\(86\) −3.24348 + 1.18053i −0.349754 + 0.127300i
\(87\) −11.1167 + 7.69922i −1.19183 + 0.825443i
\(88\) −8.16694 + 1.44005i −0.870599 + 0.153510i
\(89\) −1.68653 2.92116i −0.178772 0.309642i 0.762688 0.646766i \(-0.223879\pi\)
−0.941460 + 0.337124i \(0.890546\pi\)
\(90\) 0 0
\(91\) −0.0119153 + 0.0206379i −0.00124906 + 0.00216344i
\(92\) 0.646495 1.77623i 0.0674018 0.185185i
\(93\) −1.70398 + 6.23118i −0.176694 + 0.646144i
\(94\) −2.25902 1.89554i −0.233000 0.195510i
\(95\) 0 0
\(96\) −1.94531 7.41201i −0.198543 0.756485i
\(97\) 3.40014 9.34182i 0.345232 0.948518i −0.638618 0.769524i \(-0.720493\pi\)
0.983850 0.178994i \(-0.0572843\pi\)
\(98\) 1.89206 + 1.09238i 0.191127 + 0.110347i
\(99\) 13.4684 + 7.96149i 1.35363 + 0.800160i
\(100\) 0 0
\(101\) 2.39626 + 13.5898i 0.238436 + 1.35224i 0.835255 + 0.549863i \(0.185320\pi\)
−0.596818 + 0.802377i \(0.703569\pi\)
\(102\) 0.184950 + 2.24679i 0.0183128 + 0.222465i
\(103\) 1.56136 + 4.28981i 0.153846 + 0.422687i 0.992541 0.121914i \(-0.0389032\pi\)
−0.838695 + 0.544601i \(0.816681\pi\)
\(104\) 0.00498644 0.0282795i 0.000488961 0.00277303i
\(105\) 0 0
\(106\) 0.413928 0.347327i 0.0402042 0.0337354i
\(107\) 11.2965i 1.09207i −0.837762 0.546035i \(-0.816136\pi\)
0.837762 0.546035i \(-0.183864\pi\)
\(108\) −4.14499 + 8.54292i −0.398851 + 0.822043i
\(109\) −14.5032 −1.38915 −0.694577 0.719419i \(-0.744408\pi\)
−0.694577 + 0.719419i \(0.744408\pi\)
\(110\) 0 0
\(111\) 6.25525 + 4.42801i 0.593722 + 0.420288i
\(112\) −3.89110 0.686107i −0.367675 0.0648310i
\(113\) 4.29523 + 11.8011i 0.404062 + 1.11015i 0.960262 + 0.279102i \(0.0900367\pi\)
−0.556200 + 0.831049i \(0.687741\pi\)
\(114\) −0.128321 + 0.271536i −0.0120183 + 0.0254317i
\(115\) 0 0
\(116\) −7.13341 12.3554i −0.662321 1.14717i
\(117\) −0.0418563 + 0.0343954i −0.00386961 + 0.00317986i
\(118\) 1.33193 + 0.768989i 0.122614 + 0.0707912i
\(119\) 3.88481 + 1.41395i 0.356120 + 0.129617i
\(120\) 0 0
\(121\) 12.4085 + 10.4120i 1.12805 + 0.946544i
\(122\) 1.84649 2.20056i 0.167174 0.199230i
\(123\) 4.47770 + 4.52391i 0.403740 + 0.407907i
\(124\) −6.40452 2.33105i −0.575143 0.209335i
\(125\) 0 0
\(126\) −1.04425 1.27077i −0.0930295 0.113209i
\(127\) −7.27027 + 4.19749i −0.645132 + 0.372467i −0.786589 0.617477i \(-0.788155\pi\)
0.141456 + 0.989944i \(0.454821\pi\)
\(128\) 10.4121 1.83594i 0.920310 0.162276i
\(129\) −6.14821 + 13.0101i −0.541319 + 1.14547i
\(130\) 0 0
\(131\) −2.69761 + 15.2989i −0.235691 + 1.33667i 0.605463 + 0.795874i \(0.292988\pi\)
−0.841154 + 0.540796i \(0.818123\pi\)
\(132\) −9.53717 + 13.4727i −0.830104 + 1.17265i
\(133\) 0.354015 + 0.421899i 0.0306970 + 0.0365833i
\(134\) −4.58126 −0.395761
\(135\) 0 0
\(136\) −4.98162 −0.427170
\(137\) 7.71820 + 9.19820i 0.659411 + 0.785855i 0.987301 0.158861i \(-0.0507821\pi\)
−0.327890 + 0.944716i \(0.606338\pi\)
\(138\) 0.311110 + 0.676219i 0.0264834 + 0.0575636i
\(139\) −1.06709 + 6.05176i −0.0905093 + 0.513304i 0.905522 + 0.424299i \(0.139480\pi\)
−0.996031 + 0.0890042i \(0.971632\pi\)
\(140\) 0 0
\(141\) −12.2525 + 1.00860i −1.03185 + 0.0849392i
\(142\) −2.48941 + 0.438950i −0.208907 + 0.0368359i
\(143\) −0.0815610 + 0.0470893i −0.00682047 + 0.00393780i
\(144\) −7.73243 4.57082i −0.644369 0.380901i
\(145\) 0 0
\(146\) −0.213544 0.0777237i −0.0176730 0.00643246i
\(147\) 8.80976 2.31216i 0.726617 0.190704i
\(148\) −5.19742 + 6.19404i −0.427225 + 0.509147i
\(149\) −0.676280 0.567466i −0.0554030 0.0464886i 0.614666 0.788788i \(-0.289291\pi\)
−0.670069 + 0.742299i \(0.733735\pi\)
\(150\) 0 0
\(151\) −7.72942 2.81328i −0.629011 0.228941i 0.00778980 0.999970i \(-0.497520\pi\)
−0.636801 + 0.771028i \(0.719743\pi\)
\(152\) −0.574740 0.331826i −0.0466176 0.0269147i
\(153\) 7.13717 + 6.11477i 0.577006 + 0.494350i
\(154\) −1.42964 2.47621i −0.115204 0.199539i
\(155\) 0 0
\(156\) −0.0325434 0.0469884i −0.00260556 0.00376208i
\(157\) −4.29571 11.8024i −0.342835 0.941932i −0.984568 0.175003i \(-0.944006\pi\)
0.641733 0.766928i \(-0.278216\pi\)
\(158\) 0.200135 + 0.0352893i 0.0159219 + 0.00280746i
\(159\) 0.207851 2.24305i 0.0164836 0.177886i
\(160\) 0 0
\(161\) 1.36501 0.107578
\(162\) −1.20646 3.53922i −0.0947884 0.278067i
\(163\) 3.31466i 0.259624i −0.991539 0.129812i \(-0.958563\pi\)
0.991539 0.129812i \(-0.0414374\pi\)
\(164\) −5.14440 + 4.31667i −0.401710 + 0.337075i
\(165\) 0 0
\(166\) −0.332853 + 1.88770i −0.0258344 + 0.146514i
\(167\) 7.03295 + 19.3229i 0.544226 + 1.49525i 0.841393 + 0.540424i \(0.181736\pi\)
−0.297167 + 0.954826i \(0.596042\pi\)
\(168\) 2.98791 2.06938i 0.230522 0.159656i
\(169\) 2.25737 + 12.8022i 0.173644 + 0.984783i
\(170\) 0 0
\(171\) 0.416126 + 1.18088i 0.0318219 + 0.0903044i
\(172\) −13.1477 7.59085i −1.00251 0.578797i
\(173\) −4.79966 + 13.1870i −0.364911 + 1.00259i 0.612357 + 0.790581i \(0.290221\pi\)
−0.977269 + 0.212005i \(0.932001\pi\)
\(174\) 5.41917 + 1.48192i 0.410827 + 0.112344i
\(175\) 0 0
\(176\) −11.9617 10.0371i −0.901648 0.756572i
\(177\) 6.20169 1.62766i 0.466148 0.122342i
\(178\) −0.479305 + 1.31688i −0.0359254 + 0.0987043i
\(179\) 5.09500 8.82479i 0.380818 0.659596i −0.610361 0.792123i \(-0.708976\pi\)
0.991179 + 0.132527i \(0.0423091\pi\)
\(180\) 0 0
\(181\) −12.0274 20.8320i −0.893987 1.54843i −0.835054 0.550169i \(-0.814563\pi\)
−0.0589331 0.998262i \(-0.518770\pi\)
\(182\) 0.00975037 0.00171925i 0.000722746 0.000127440i
\(183\) −0.982498 11.9354i −0.0726283 0.882293i
\(184\) −1.54563 + 0.562565i −0.113946 + 0.0414728i
\(185\) 0 0
\(186\) 2.43823 1.12176i 0.178780 0.0822516i
\(187\) 10.5019 + 12.5157i 0.767978 + 0.915240i
\(188\) 12.9706i 0.945981i
\(189\) −6.82089 0.702760i −0.496146 0.0511182i
\(190\) 0 0
\(191\) 8.38541 7.03619i 0.606747 0.509121i −0.286860 0.957973i \(-0.592611\pi\)
0.893606 + 0.448852i \(0.148167\pi\)
\(192\) 4.15316 5.86699i 0.299729 0.423414i
\(193\) 10.6418 + 1.87644i 0.766013 + 0.135069i 0.542984 0.839743i \(-0.317294\pi\)
0.223029 + 0.974812i \(0.428405\pi\)
\(194\) −3.88121 + 1.41265i −0.278655 + 0.101422i
\(195\) 0 0
\(196\) 1.66867 + 9.46347i 0.119190 + 0.675962i
\(197\) −19.1161 + 11.0367i −1.36196 + 0.786331i −0.989885 0.141870i \(-0.954689\pi\)
−0.372080 + 0.928201i \(0.621355\pi\)
\(198\) −1.06296 6.41270i −0.0755413 0.455731i
\(199\) 6.44338 11.1603i 0.456759 0.791130i −0.542028 0.840360i \(-0.682343\pi\)
0.998787 + 0.0492301i \(0.0156768\pi\)
\(200\) 0 0
\(201\) −13.5742 + 13.4355i −0.957448 + 0.947667i
\(202\) 3.68524 4.39190i 0.259293 0.309013i
\(203\) 6.62241 7.89228i 0.464802 0.553929i
\(204\) −7.04736 + 6.97537i −0.493414 + 0.488374i
\(205\) 0 0
\(206\) 0.948326 1.64255i 0.0660730 0.114442i
\(207\) 2.90496 + 1.09123i 0.201909 + 0.0758456i
\(208\) 0.0468255 0.0270347i 0.00324676 0.00187452i
\(209\) 0.377957 + 2.14350i 0.0261439 + 0.148269i
\(210\) 0 0
\(211\) 22.5485 8.20699i 1.55230 0.564992i 0.583347 0.812223i \(-0.301743\pi\)
0.968957 + 0.247230i \(0.0795204\pi\)
\(212\) 2.34055 + 0.412702i 0.160749 + 0.0283445i
\(213\) −6.08875 + 8.60131i −0.417194 + 0.589352i
\(214\) −3.59528 + 3.01680i −0.245768 + 0.206224i
\(215\) 0 0
\(216\) 8.01311 2.01536i 0.545223 0.137128i
\(217\) 4.92177i 0.334112i
\(218\) 3.87317 + 4.61587i 0.262324 + 0.312626i
\(219\) −0.860667 + 0.395969i −0.0581585 + 0.0267571i
\(220\) 0 0
\(221\) −0.0531618 + 0.0193493i −0.00357605 + 0.00130158i
\(222\) −0.261224 3.17336i −0.0175322 0.212982i
\(223\) 21.3331 3.76160i 1.42857 0.251895i 0.594740 0.803918i \(-0.297255\pi\)
0.833829 + 0.552023i \(0.186144\pi\)
\(224\) 2.91919 + 5.05618i 0.195047 + 0.337831i
\(225\) 0 0
\(226\) 2.60880 4.51858i 0.173535 0.300571i
\(227\) 7.40196 20.3367i 0.491285 1.34979i −0.408220 0.912884i \(-0.633850\pi\)
0.899505 0.436911i \(-0.143928\pi\)
\(228\) −1.27770 + 0.335338i −0.0846178 + 0.0222083i
\(229\) 8.27739 + 6.94555i 0.546985 + 0.458975i 0.873919 0.486072i \(-0.161571\pi\)
−0.326934 + 0.945047i \(0.606015\pi\)
\(230\) 0 0
\(231\) −11.4980 3.14424i −0.756513 0.206876i
\(232\) −4.24606 + 11.6660i −0.278768 + 0.765908i
\(233\) 6.61557 + 3.81950i 0.433400 + 0.250224i 0.700794 0.713364i \(-0.252829\pi\)
−0.267394 + 0.963587i \(0.586162\pi\)
\(234\) 0.0221249 + 0.00413588i 0.00144635 + 0.000270371i
\(235\) 0 0
\(236\) 1.17467 + 6.66187i 0.0764644 + 0.433651i
\(237\) 0.696490 0.482377i 0.0452419 0.0313338i
\(238\) −0.587451 1.61401i −0.0380788 0.104621i
\(239\) 0.561143 3.18240i 0.0362973 0.205852i −0.961266 0.275623i \(-0.911116\pi\)
0.997563 + 0.0697711i \(0.0222269\pi\)
\(240\) 0 0
\(241\) −20.3346 + 17.0628i −1.30987 + 1.09911i −0.321518 + 0.946903i \(0.604193\pi\)
−0.988349 + 0.152206i \(0.951362\pi\)
\(242\) 6.72979i 0.432608i
\(243\) −13.9542 6.94842i −0.895162 0.445741i
\(244\) 12.6350 0.808873
\(245\) 0 0
\(246\) 0.244007 2.63324i 0.0155573 0.167889i
\(247\) −0.00742226 0.00130875i −0.000472267 8.32735e-5i
\(248\) 2.02843 + 5.57306i 0.128805 + 0.353890i
\(249\) 4.54985 + 6.56938i 0.288335 + 0.416318i
\(250\) 0 0
\(251\) 2.24965 + 3.89651i 0.141997 + 0.245945i 0.928248 0.371961i \(-0.121314\pi\)
−0.786252 + 0.617906i \(0.787981\pi\)
\(252\) 1.32933 7.11124i 0.0837399 0.447966i
\(253\) 4.67179 + 2.69726i 0.293713 + 0.169575i
\(254\) 3.27749 + 1.19291i 0.205648 + 0.0748498i
\(255\) 0 0
\(256\) 2.99340 + 2.51176i 0.187088 + 0.156985i
\(257\) −8.82895 + 10.5219i −0.550735 + 0.656340i −0.967559 0.252647i \(-0.918699\pi\)
0.416824 + 0.908987i \(0.363143\pi\)
\(258\) 5.78258 1.51766i 0.360007 0.0944854i
\(259\) −5.48690 1.99707i −0.340939 0.124092i
\(260\) 0 0
\(261\) 20.4029 11.5020i 1.26291 0.711953i
\(262\) 5.58952 3.22711i 0.345322 0.199372i
\(263\) −23.8349 + 4.20273i −1.46972 + 0.259151i −0.850462 0.526036i \(-0.823678\pi\)
−0.619258 + 0.785187i \(0.712567\pi\)
\(264\) 14.3154 1.17841i 0.881049 0.0725260i
\(265\) 0 0
\(266\) 0.0397339 0.225342i 0.00243624 0.0138166i
\(267\) 2.44185 + 5.30755i 0.149439 + 0.324817i
\(268\) −12.9523 15.4360i −0.791189 0.942902i
\(269\) −12.0062 −0.732032 −0.366016 0.930609i \(-0.619278\pi\)
−0.366016 + 0.930609i \(0.619278\pi\)
\(270\) 0 0
\(271\) 3.71777 0.225839 0.112919 0.993604i \(-0.463980\pi\)
0.112919 + 0.993604i \(0.463980\pi\)
\(272\) −6.02933 7.18547i −0.365582 0.435683i
\(273\) 0.0238481 0.0336891i 0.00144335 0.00203896i
\(274\) 0.866273 4.91288i 0.0523335 0.296798i
\(275\) 0 0
\(276\) −1.39885 + 2.96008i −0.0842011 + 0.178176i
\(277\) 23.1264 4.07780i 1.38953 0.245011i 0.571695 0.820466i \(-0.306286\pi\)
0.817833 + 0.575455i \(0.195175\pi\)
\(278\) 2.21104 1.27654i 0.132609 0.0765621i
\(279\) 3.93462 10.4744i 0.235559 0.627084i
\(280\) 0 0
\(281\) 19.1432 + 6.96754i 1.14199 + 0.415649i 0.842630 0.538493i \(-0.181006\pi\)
0.299356 + 0.954142i \(0.403228\pi\)
\(282\) 3.59311 + 3.63020i 0.213967 + 0.216175i
\(283\) 7.45630 8.88607i 0.443231 0.528222i −0.497460 0.867487i \(-0.665734\pi\)
0.940691 + 0.339265i \(0.110178\pi\)
\(284\) −8.51714 7.14673i −0.505399 0.424080i
\(285\) 0 0
\(286\) 0.0367683 + 0.0133826i 0.00217416 + 0.000791328i
\(287\) −4.19984 2.42478i −0.247909 0.143130i
\(288\) 2.17046 + 13.0941i 0.127896 + 0.771578i
\(289\) −3.59280 6.22291i −0.211341 0.366053i
\(290\) 0 0
\(291\) −7.35706 + 15.5681i −0.431279 + 0.912618i
\(292\) −0.341860 0.939253i −0.0200058 0.0549656i
\(293\) −31.0945 5.48280i −1.81656 0.320308i −0.841165 0.540779i \(-0.818130\pi\)
−0.975394 + 0.220470i \(0.929241\pi\)
\(294\) −3.08858 2.18637i −0.180130 0.127511i
\(295\) 0 0
\(296\) 7.03603 0.408961
\(297\) −21.9561 15.8833i −1.27402 0.921644i
\(298\) 0.366782i 0.0212471i
\(299\) −0.0143093 + 0.0120069i −0.000827529 + 0.000694379i
\(300\) 0 0
\(301\) 1.90376 10.7968i 0.109731 0.622315i
\(302\) 1.16882 + 3.21131i 0.0672581 + 0.184790i
\(303\) −1.96088 23.8208i −0.112649 1.36847i
\(304\) −0.216991 1.23062i −0.0124453 0.0705809i
\(305\) 0 0
\(306\) 0.0400924 3.90451i 0.00229193 0.223206i
\(307\) 7.03259 + 4.06027i 0.401371 + 0.231732i 0.687075 0.726586i \(-0.258894\pi\)
−0.285704 + 0.958318i \(0.592227\pi\)
\(308\) 4.30134 11.8178i 0.245092 0.673384i
\(309\) −2.00725 7.64800i −0.114188 0.435079i
\(310\) 0 0
\(311\) −18.2691 15.3296i −1.03594 0.869259i −0.0443970 0.999014i \(-0.514137\pi\)
−0.991546 + 0.129754i \(0.958581\pi\)
\(312\) −0.0131194 + 0.0479757i −0.000742740 + 0.00271609i
\(313\) −9.20392 + 25.2876i −0.520236 + 1.42934i 0.350022 + 0.936742i \(0.386174\pi\)
−0.870258 + 0.492596i \(0.836048\pi\)
\(314\) −2.60909 + 4.51908i −0.147240 + 0.255026i
\(315\) 0 0
\(316\) 0.446928 + 0.774102i 0.0251417 + 0.0435466i
\(317\) 8.20574 1.44689i 0.460881 0.0812657i 0.0616130 0.998100i \(-0.480376\pi\)
0.399268 + 0.916834i \(0.369264\pi\)
\(318\) −0.769394 + 0.532870i −0.0431455 + 0.0298819i
\(319\) 38.2606 13.9257i 2.14218 0.779692i
\(320\) 0 0
\(321\) −1.80534 + 19.4826i −0.100764 + 1.08741i
\(322\) −0.364534 0.434435i −0.0203147 0.0242101i
\(323\) 1.30748i 0.0727501i
\(324\) 8.51398 14.0712i 0.472999 0.781734i
\(325\) 0 0
\(326\) −1.05494 + 0.885201i −0.0584278 + 0.0490268i
\(327\) 25.0131 + 2.31782i 1.38323 + 0.128176i
\(328\) 5.75493 + 1.01475i 0.317763 + 0.0560301i
\(329\) 8.80173 3.20357i 0.485255 0.176618i
\(330\) 0 0
\(331\) −1.11487 6.32272i −0.0612786 0.347528i −0.999996 0.00284030i \(-0.999096\pi\)
0.938717 0.344688i \(-0.112015\pi\)
\(332\) −7.30143 + 4.21548i −0.400718 + 0.231355i
\(333\) −10.0805 8.63650i −0.552410 0.473277i
\(334\) 4.27161 7.39865i 0.233732 0.404836i
\(335\) 0 0
\(336\) 6.60119 + 1.80516i 0.360124 + 0.0984794i
\(337\) −4.80477 + 5.72610i −0.261732 + 0.311921i −0.880867 0.473365i \(-0.843039\pi\)
0.619134 + 0.785285i \(0.287484\pi\)
\(338\) 3.47165 4.13735i 0.188833 0.225042i
\(339\) −5.52185 21.0393i −0.299906 1.14270i
\(340\) 0 0
\(341\) 9.72545 16.8450i 0.526663 0.912206i
\(342\) 0.264706 0.447801i 0.0143136 0.0242143i
\(343\) −14.0095 + 8.08839i −0.756442 + 0.436732i
\(344\) 2.29403 + 13.0101i 0.123686 + 0.701456i
\(345\) 0 0
\(346\) 5.47874 1.99410i 0.294539 0.107203i
\(347\) −30.9766 5.46202i −1.66291 0.293216i −0.738399 0.674364i \(-0.764418\pi\)
−0.924514 + 0.381148i \(0.875529\pi\)
\(348\) 10.3281 + 22.4490i 0.553647 + 1.20339i
\(349\) −9.07988 + 7.61893i −0.486035 + 0.407832i −0.852603 0.522560i \(-0.824977\pi\)
0.366568 + 0.930391i \(0.380533\pi\)
\(350\) 0 0
\(351\) 0.0776848 0.0526312i 0.00414651 0.00280925i
\(352\) 23.0733i 1.22981i
\(353\) 5.27541 + 6.28699i 0.280782 + 0.334623i 0.887941 0.459958i \(-0.152135\pi\)
−0.607159 + 0.794580i \(0.707691\pi\)
\(354\) −2.17423 1.53911i −0.115559 0.0818026i
\(355\) 0 0
\(356\) −5.79217 + 2.10818i −0.306984 + 0.111733i
\(357\) −6.47401 3.05944i −0.342641 0.161923i
\(358\) −4.16928 + 0.735157i −0.220353 + 0.0388542i
\(359\) 8.86365 + 15.3523i 0.467806 + 0.810263i 0.999323 0.0367840i \(-0.0117114\pi\)
−0.531517 + 0.847047i \(0.678378\pi\)
\(360\) 0 0
\(361\) 9.41291 16.3036i 0.495416 0.858086i
\(362\) −3.41812 + 9.39122i −0.179653 + 0.493591i
\(363\) −19.7365 19.9402i −1.03590 1.04659i
\(364\) 0.0333594 + 0.0279919i 0.00174851 + 0.00146717i
\(365\) 0 0
\(366\) −3.53626 + 3.50013i −0.184843 + 0.182955i
\(367\) −6.94969 + 19.0941i −0.362771 + 0.996704i 0.615275 + 0.788313i \(0.289045\pi\)
−0.978045 + 0.208392i \(0.933177\pi\)
\(368\) −2.68215 1.54854i −0.139817 0.0807232i
\(369\) −6.99953 8.51782i −0.364381 0.443420i
\(370\) 0 0
\(371\) 0.298028 + 1.69020i 0.0154728 + 0.0877509i
\(372\) 10.6731 + 5.04381i 0.553374 + 0.261510i
\(373\) −3.31125 9.09758i −0.171450 0.471055i 0.823972 0.566630i \(-0.191753\pi\)
−0.995422 + 0.0955754i \(0.969531\pi\)
\(374\) 1.17871 6.68481i 0.0609498 0.345663i
\(375\) 0 0
\(376\) −8.64615 + 7.25498i −0.445891 + 0.374147i
\(377\) 0.140987i 0.00726119i
\(378\) 1.59790 + 2.35853i 0.0821870 + 0.121310i
\(379\) 4.12905 0.212095 0.106048 0.994361i \(-0.466180\pi\)
0.106048 + 0.994361i \(0.466180\pi\)
\(380\) 0 0
\(381\) 13.2096 6.07736i 0.676748 0.311353i
\(382\) −4.47876 0.789725i −0.229153 0.0404059i
\(383\) 1.62466 + 4.46371i 0.0830162 + 0.228085i 0.974255 0.225450i \(-0.0723851\pi\)
−0.891239 + 0.453535i \(0.850163\pi\)
\(384\) −18.2508 + 1.50236i −0.931357 + 0.0766672i
\(385\) 0 0
\(386\) −2.24476 3.88803i −0.114255 0.197896i
\(387\) 12.6828 21.4554i 0.644702 1.09064i
\(388\) −15.7328 9.08336i −0.798714 0.461138i
\(389\) −20.4978 7.46059i −1.03928 0.378267i −0.234673 0.972074i \(-0.575402\pi\)
−0.804607 + 0.593807i \(0.797624\pi\)
\(390\) 0 0
\(391\) 2.48238 + 2.08297i 0.125539 + 0.105340i
\(392\) 5.37495 6.40561i 0.271476 0.323532i
\(393\) 7.09745 25.9543i 0.358019 1.30922i
\(394\) 8.61767 + 3.13658i 0.434152 + 0.158018i
\(395\) 0 0
\(396\) 18.6015 21.7117i 0.934762 1.09106i
\(397\) −30.1802 + 17.4245i −1.51470 + 0.874512i −0.514847 + 0.857282i \(0.672151\pi\)
−0.999852 + 0.0172294i \(0.994515\pi\)
\(398\) −5.27268 + 0.929715i −0.264295 + 0.0466024i
\(399\) −0.543131 0.784210i −0.0271906 0.0392596i
\(400\) 0 0
\(401\) −3.26911 + 18.5401i −0.163252 + 0.925847i 0.787597 + 0.616191i \(0.211325\pi\)
−0.950849 + 0.309656i \(0.899786\pi\)
\(402\) 7.90113 + 0.732152i 0.394072 + 0.0365164i
\(403\) 0.0432932 + 0.0515948i 0.00215659 + 0.00257012i
\(404\) 25.2170 1.25459
\(405\) 0 0
\(406\) −4.28040 −0.212433
\(407\) −14.8329 17.6772i −0.735241 0.876226i
\(408\) 8.59160 + 0.796135i 0.425348 + 0.0394145i
\(409\) 1.10439 6.26334i 0.0546088 0.309702i −0.945253 0.326339i \(-0.894185\pi\)
0.999862 + 0.0166371i \(0.00529599\pi\)
\(410\) 0 0
\(411\) −11.8413 17.0973i −0.584088 0.843346i
\(412\) 8.21551 1.44862i 0.404749 0.0713682i
\(413\) −4.23055 + 2.44251i −0.208172 + 0.120188i
\(414\) −0.428490 1.21597i −0.0210591 0.0597617i
\(415\) 0 0
\(416\) −0.0750772 0.0273259i −0.00368096 0.00133976i
\(417\) 2.80753 10.2667i 0.137485 0.502763i
\(418\) 0.581267 0.692727i 0.0284307 0.0338824i
\(419\) 18.6286 + 15.6313i 0.910069 + 0.763638i 0.972132 0.234434i \(-0.0753236\pi\)
−0.0620632 + 0.998072i \(0.519768\pi\)
\(420\) 0 0
\(421\) 7.50818 + 2.73275i 0.365926 + 0.133186i 0.518438 0.855115i \(-0.326514\pi\)
−0.152511 + 0.988302i \(0.548736\pi\)
\(422\) −8.63373 4.98469i −0.420283 0.242651i
\(423\) 21.2926 + 0.218637i 1.03528 + 0.0106305i
\(424\) −1.03405 1.79103i −0.0502181 0.0869803i
\(425\) 0 0
\(426\) 4.36354 0.359197i 0.211414 0.0174031i
\(427\) 3.12067 + 8.57397i 0.151020 + 0.414924i
\(428\) −20.3294 3.58462i −0.982659 0.173269i
\(429\) 0.148191 0.0681784i 0.00715472 0.00329169i
\(430\) 0 0
\(431\) 9.87124 0.475481 0.237740 0.971329i \(-0.423593\pi\)
0.237740 + 0.971329i \(0.423593\pi\)
\(432\) 12.6053 + 9.11887i 0.606475 + 0.438732i
\(433\) 6.10369i 0.293325i 0.989187 + 0.146662i \(0.0468531\pi\)
−0.989187 + 0.146662i \(0.953147\pi\)
\(434\) −1.56643 + 1.31439i −0.0751911 + 0.0630928i
\(435\) 0 0
\(436\) −4.60219 + 26.1003i −0.220405 + 1.24998i
\(437\) 0.147651 + 0.405669i 0.00706312 + 0.0194058i
\(438\) 0.355870 + 0.168174i 0.0170041 + 0.00803569i
\(439\) 2.62800 + 14.9041i 0.125427 + 0.711334i 0.981053 + 0.193739i \(0.0620615\pi\)
−0.855626 + 0.517595i \(0.826827\pi\)
\(440\) 0 0
\(441\) −15.5634 + 2.57976i −0.741113 + 0.122846i
\(442\) 0.0203554 + 0.0117522i 0.000968210 + 0.000558996i
\(443\) 0.247210 0.679204i 0.0117453 0.0322699i −0.933681 0.358105i \(-0.883423\pi\)
0.945427 + 0.325835i \(0.105645\pi\)
\(444\) 9.95369 9.85201i 0.472381 0.467555i
\(445\) 0 0
\(446\) −6.89432 5.78502i −0.326456 0.273929i
\(447\) 1.07566 + 1.08677i 0.0508772 + 0.0514023i
\(448\) −1.87311 + 5.14633i −0.0884962 + 0.243141i
\(449\) 0.834224 1.44492i 0.0393695 0.0681899i −0.845669 0.533707i \(-0.820798\pi\)
0.885039 + 0.465517i \(0.154132\pi\)
\(450\) 0 0
\(451\) −9.58275 16.5978i −0.451234 0.781560i
\(452\) 22.6005 3.98507i 1.06304 0.187442i
\(453\) 12.8810 + 6.08723i 0.605204 + 0.286003i
\(454\) −8.44922 + 3.07526i −0.396541 + 0.144329i
\(455\) 0 0
\(456\) 0.938202 + 0.664140i 0.0439353 + 0.0311012i
\(457\) 7.12430 + 8.49041i 0.333261 + 0.397165i 0.906488 0.422232i \(-0.138753\pi\)
−0.573227 + 0.819397i \(0.694309\pi\)
\(458\) 4.48926i 0.209769i
\(459\) −11.3320 11.6865i −0.528932 0.545481i
\(460\) 0 0
\(461\) −16.7644 + 14.0670i −0.780797 + 0.655166i −0.943449 0.331517i \(-0.892439\pi\)
0.162653 + 0.986683i \(0.447995\pi\)
\(462\) 2.06992 + 4.49911i 0.0963012 + 0.209318i
\(463\) −24.4742 4.31546i −1.13741 0.200556i −0.426938 0.904281i \(-0.640408\pi\)
−0.710473 + 0.703724i \(0.751519\pi\)
\(464\) −21.9660 + 7.99499i −1.01975 + 0.371158i
\(465\) 0 0
\(466\) −0.551115 3.12553i −0.0255299 0.144787i
\(467\) −10.2499 + 5.91777i −0.474308 + 0.273842i −0.718041 0.696001i \(-0.754961\pi\)
0.243734 + 0.969842i \(0.421628\pi\)
\(468\) 0.0486170 + 0.0862400i 0.00224732 + 0.00398645i
\(469\) 7.27564 12.6018i 0.335958 0.581896i
\(470\) 0 0
\(471\) 5.52246 + 21.0416i 0.254462 + 0.969547i
\(472\) 3.78373 4.50927i 0.174160 0.207556i
\(473\) 27.8501 33.1905i 1.28055 1.52610i
\(474\) −0.339526 0.0928466i −0.0155950 0.00426459i
\(475\) 0 0
\(476\) 3.77733 6.54252i 0.173134 0.299876i
\(477\) −0.716944 + 3.83529i −0.0328266 + 0.175606i
\(478\) −1.16270 + 0.671288i −0.0531809 + 0.0307040i
\(479\) −0.501383 2.84349i −0.0229088 0.129922i 0.971209 0.238231i \(-0.0765676\pi\)
−0.994117 + 0.108309i \(0.965456\pi\)
\(480\) 0 0
\(481\) 0.0750857 0.0273290i 0.00342361 0.00124609i
\(482\) 10.8610 + 1.91508i 0.494704 + 0.0872297i
\(483\) −2.35417 0.218148i −0.107119 0.00992607i
\(484\) 22.6752 19.0267i 1.03069 0.864852i
\(485\) 0 0
\(486\) 1.51512 + 6.29676i 0.0687271 + 0.285627i
\(487\) 8.75903i 0.396910i 0.980110 + 0.198455i \(0.0635923\pi\)
−0.980110 + 0.198455i \(0.936408\pi\)
\(488\) −7.06724 8.42241i −0.319919 0.381265i
\(489\) −0.529731 + 5.71667i −0.0239553 + 0.258517i
\(490\) 0 0
\(491\) 21.2117 7.72044i 0.957272 0.348418i 0.184308 0.982869i \(-0.440996\pi\)
0.772964 + 0.634450i \(0.218773\pi\)
\(492\) 9.56222 6.62264i 0.431098 0.298572i
\(493\) 24.0869 4.24716i 1.08482 0.191283i
\(494\) 0.00156564 + 0.00271176i 7.04413e−5 + 0.000122008i
\(495\) 0 0
\(496\) −5.58354 + 9.67097i −0.250708 + 0.434239i
\(497\) 2.74608 7.54478i 0.123178 0.338430i
\(498\) 0.875741 3.20246i 0.0392429 0.143505i
\(499\) 19.4061 + 16.2836i 0.868734 + 0.728955i 0.963831 0.266513i \(-0.0858716\pi\)
−0.0950968 + 0.995468i \(0.530316\pi\)
\(500\) 0 0
\(501\) −9.04139 34.4494i −0.403940 1.53909i
\(502\) 0.639340 1.75657i 0.0285352 0.0783997i
\(503\) 3.24252 + 1.87207i 0.144577 + 0.0834714i 0.570543 0.821267i \(-0.306733\pi\)
−0.425967 + 0.904739i \(0.640066\pi\)
\(504\) −5.48386 + 3.09147i −0.244270 + 0.137705i
\(505\) 0 0
\(506\) −0.389187 2.20719i −0.0173015 0.0981216i
\(507\) −1.84723 22.4402i −0.0820382 0.996604i
\(508\) 5.24690 + 14.4157i 0.232793 + 0.639595i
\(509\) −4.22831 + 23.9800i −0.187417 + 1.06289i 0.735394 + 0.677640i \(0.236997\pi\)
−0.922811 + 0.385253i \(0.874114\pi\)
\(510\) 0 0
\(511\) 0.552932 0.463965i 0.0244603 0.0205246i
\(512\) 22.7690i 1.00626i
\(513\) −0.528954 2.10313i −0.0233539 0.0928554i
\(514\) 5.70660 0.251707
\(515\) 0 0
\(516\) 21.4623 + 15.1929i 0.944824 + 0.668828i
\(517\) 36.4546 + 6.42792i 1.60327 + 0.282700i
\(518\) 0.829715 + 2.27962i 0.0364556 + 0.100161i
\(519\) 10.3853 21.9760i 0.455862 0.964639i
\(520\) 0 0
\(521\) −9.81046 16.9922i −0.429804 0.744443i 0.567051 0.823682i \(-0.308084\pi\)
−0.996856 + 0.0792397i \(0.974751\pi\)
\(522\) −9.10941 3.42188i −0.398708 0.149772i
\(523\) 18.0267 + 10.4077i 0.788251 + 0.455097i 0.839346 0.543597i \(-0.182938\pi\)
−0.0510956 + 0.998694i \(0.516271\pi\)
\(524\) 26.6763 + 9.70937i 1.16536 + 0.424156i
\(525\) 0 0
\(526\) 7.70284 + 6.46345i 0.335860 + 0.281820i
\(527\) 7.51051 8.95067i 0.327163 0.389897i
\(528\) 19.0258 + 19.2222i 0.827993 + 0.836539i
\(529\) −20.6075 7.50052i −0.895978 0.326109i
\(530\) 0 0
\(531\) −10.9559 + 1.81604i −0.475447 + 0.0788095i
\(532\) 0.871598 0.503217i 0.0377886 0.0218172i
\(533\) 0.0653558 0.0115240i 0.00283087 0.000499159i
\(534\) 1.03710 2.19457i 0.0448795 0.0949685i
\(535\) 0 0
\(536\) −3.04479 + 17.2679i −0.131515 + 0.745859i
\(537\) −10.1975 + 14.4055i −0.440054 + 0.621645i
\(538\) 3.20634 + 3.82117i 0.138235 + 0.164742i
\(539\) −27.4245 −1.18126
\(540\) 0 0
\(541\) −30.6272 −1.31676 −0.658382 0.752684i \(-0.728759\pi\)
−0.658382 + 0.752684i \(0.728759\pi\)
\(542\) −0.992856 1.18324i −0.0426468 0.0508245i
\(543\) 17.4139 + 37.8503i 0.747301 + 1.62431i
\(544\) −2.40681 + 13.6497i −0.103191 + 0.585227i
\(545\) 0 0
\(546\) −0.0170909 + 0.00140688i −0.000731421 + 6.02089e-5i
\(547\) −22.3036 + 3.93273i −0.953633 + 0.168151i −0.628754 0.777604i \(-0.716435\pi\)
−0.324879 + 0.945756i \(0.605324\pi\)
\(548\) 19.0025 10.9711i 0.811745 0.468661i
\(549\) −0.212980 + 20.7416i −0.00908976 + 0.885231i
\(550\) 0 0
\(551\) 3.06186 + 1.11443i 0.130440 + 0.0474761i
\(552\) 2.75560 0.723220i 0.117286 0.0307823i
\(553\) −0.414912 + 0.494473i −0.0176439 + 0.0210271i
\(554\) −7.47387 6.27132i −0.317534 0.266443i
\(555\) 0 0
\(556\) 10.5523 + 3.84072i 0.447517 + 0.162883i
\(557\) −31.5682 18.2259i −1.33759 0.772256i −0.351138 0.936324i \(-0.614205\pi\)
−0.986449 + 0.164067i \(0.947539\pi\)
\(558\) −4.38440 + 1.54500i −0.185606 + 0.0654049i
\(559\) 0.0750139 + 0.129928i 0.00317275 + 0.00549537i
\(560\) 0 0
\(561\) −16.1121 23.2637i −0.680253 0.982196i
\(562\) −2.89478 7.95334i −0.122109 0.335491i
\(563\) −26.1134 4.60450i −1.10055 0.194056i −0.406263 0.913756i \(-0.633168\pi\)
−0.694285 + 0.719700i \(0.744279\pi\)
\(564\) −2.07290 + 22.3700i −0.0872847 + 0.941945i
\(565\) 0 0
\(566\) −4.81938 −0.202574
\(567\) 11.6514 + 2.30210i 0.489313 + 0.0966791i
\(568\) 9.67492i 0.405950i
\(569\) −17.5941 + 14.7632i −0.737581 + 0.618904i −0.932187 0.361978i \(-0.882102\pi\)
0.194606 + 0.980882i \(0.437657\pi\)
\(570\) 0 0
\(571\) −0.833165 + 4.72511i −0.0348669 + 0.197740i −0.997266 0.0739009i \(-0.976455\pi\)
0.962399 + 0.271641i \(0.0875662\pi\)
\(572\) 0.0588619 + 0.161722i 0.00246114 + 0.00676193i
\(573\) −15.5865 + 10.7949i −0.651134 + 0.450965i
\(574\) 0.349871 + 1.98422i 0.0146033 + 0.0828197i
\(575\) 0 0
\(576\) −8.10043 + 9.45484i −0.337518 + 0.393952i
\(577\) 3.73545 + 2.15666i 0.155509 + 0.0897831i 0.575735 0.817636i \(-0.304716\pi\)
−0.420226 + 0.907419i \(0.638049\pi\)
\(578\) −1.02106 + 2.80533i −0.0424704 + 0.116686i
\(579\) −18.0536 4.93693i −0.750283 0.205172i
\(580\) 0 0
\(581\) −4.66393 3.91351i −0.193493 0.162360i
\(582\) 6.91954 1.81606i 0.286824 0.0752782i
\(583\) −2.31983 + 6.37369i −0.0960777 + 0.263971i
\(584\) −0.434885 + 0.753242i −0.0179957 + 0.0311694i
\(585\) 0 0
\(586\) 6.55900 + 11.3605i 0.270950 + 0.469299i
\(587\) −41.1868 + 7.26235i −1.69996 + 0.299749i −0.937681 0.347497i \(-0.887032\pi\)
−0.762281 + 0.647246i \(0.775921\pi\)
\(588\) −1.36548 16.5880i −0.0563116 0.684076i
\(589\) 1.46271 0.532383i 0.0602699 0.0219365i
\(590\) 0 0
\(591\) 34.7326 15.9795i 1.42871 0.657309i
\(592\) 8.51582 + 10.1488i 0.349998 + 0.417111i
\(593\) 31.5370i 1.29507i 0.762035 + 0.647536i \(0.224200\pi\)
−0.762035 + 0.647536i \(0.775800\pi\)
\(594\) 0.808405 + 11.2296i 0.0331693 + 0.460757i
\(595\) 0 0
\(596\) −1.23583 + 1.03698i −0.0506214 + 0.0424764i
\(597\) −12.8962 + 18.2179i −0.527807 + 0.745611i
\(598\) 0.00764279 + 0.00134763i 0.000312537 + 5.51087e-5i
\(599\) −11.8686 + 4.31982i −0.484938 + 0.176503i −0.572907 0.819620i \(-0.694184\pi\)
0.0879695 + 0.996123i \(0.471962\pi\)
\(600\) 0 0
\(601\) 3.56725 + 20.2309i 0.145511 + 0.825235i 0.966955 + 0.254946i \(0.0820577\pi\)
−0.821444 + 0.570289i \(0.806831\pi\)
\(602\) −3.94465 + 2.27744i −0.160772 + 0.0928216i
\(603\) 25.5580 21.0023i 1.04080 0.855282i
\(604\) −7.51556 + 13.0173i −0.305804 + 0.529668i
\(605\) 0 0
\(606\) −7.05769 + 6.98559i −0.286699 + 0.283770i
\(607\) −8.30003 + 9.89160i −0.336888 + 0.401487i −0.907718 0.419581i \(-0.862177\pi\)
0.570830 + 0.821068i \(0.306622\pi\)
\(608\) −1.18689 + 1.41448i −0.0481348 + 0.0573648i
\(609\) −12.6827 + 12.5532i −0.513930 + 0.508680i
\(610\) 0 0
\(611\) −0.0640889 + 0.111005i −0.00259276 + 0.00449079i
\(612\) 13.2691 10.9039i 0.536371 0.440763i
\(613\) 26.9851 15.5799i 1.08992 0.629265i 0.156364 0.987699i \(-0.450023\pi\)
0.933555 + 0.358434i \(0.116689\pi\)
\(614\) −0.585856 3.32255i −0.0236432 0.134087i
\(615\) 0 0
\(616\) −10.2836 + 3.74293i −0.414339 + 0.150807i
\(617\) −7.03230 1.23998i −0.283110 0.0499199i 0.0302901 0.999541i \(-0.490357\pi\)
−0.313400 + 0.949621i \(0.601468\pi\)
\(618\) −1.89805 + 2.68129i −0.0763506 + 0.107857i
\(619\) 7.68412 6.44774i 0.308851 0.259157i −0.475166 0.879896i \(-0.657612\pi\)
0.784017 + 0.620740i \(0.213168\pi\)
\(620\) 0 0
\(621\) −4.83569 2.34625i −0.194049 0.0941520i
\(622\) 9.90827i 0.397285i
\(623\) −2.86117 3.40981i −0.114630 0.136611i
\(624\) −0.0850787 + 0.0391423i −0.00340587 + 0.00156695i
\(625\) 0 0
\(626\) 10.5061 3.82392i 0.419909 0.152835i
\(627\) −0.309286 3.75722i −0.0123517 0.150049i
\(628\) −22.6030 + 3.98552i −0.901957 + 0.159039i
\(629\) −6.93093 12.0047i −0.276354 0.478660i
\(630\) 0 0
\(631\) 3.53780 6.12765i 0.140838 0.243938i −0.786975 0.616985i \(-0.788354\pi\)
0.927812 + 0.373047i \(0.121687\pi\)
\(632\) 0.266028 0.730905i 0.0105820 0.0290738i
\(633\) −40.2002 + 10.5507i −1.59781 + 0.419353i
\(634\) −2.65189 2.22520i −0.105320 0.0883741i
\(635\) 0 0
\(636\) −3.97070 1.08582i −0.157448 0.0430557i
\(637\) 0.0324790 0.0892352i 0.00128686 0.00353563i
\(638\) −14.6498 8.45809i −0.579993 0.334859i
\(639\) 11.8756 13.8613i 0.469793 0.548344i
\(640\) 0 0
\(641\) −0.870188 4.93508i −0.0343704 0.194924i 0.962788 0.270258i \(-0.0871089\pi\)
−0.997158 + 0.0753337i \(0.975998\pi\)
\(642\) 6.68277 4.62838i 0.263748 0.182667i
\(643\) 0.560367 + 1.53960i 0.0220987 + 0.0607157i 0.950251 0.311484i \(-0.100826\pi\)
−0.928153 + 0.372199i \(0.878604\pi\)
\(644\) 0.433147 2.45650i 0.0170684 0.0967997i
\(645\) 0 0
\(646\) 0.416126 0.349171i 0.0163722 0.0137379i
\(647\) 34.4927i 1.35605i 0.735040 + 0.678024i \(0.237164\pi\)
−0.735040 + 0.678024i \(0.762836\pi\)
\(648\) −14.1420 + 2.19521i −0.555550 + 0.0862359i
\(649\) −19.3056 −0.757813
\(650\) 0 0
\(651\) −0.786571 + 8.48840i −0.0308282 + 0.332687i
\(652\) −5.96515 1.05182i −0.233613 0.0411923i
\(653\) 13.2569 + 36.4230i 0.518783 + 1.42534i 0.871862 + 0.489751i \(0.162912\pi\)
−0.353080 + 0.935593i \(0.614866\pi\)
\(654\) −5.94223 8.57980i −0.232360 0.335497i
\(655\) 0 0
\(656\) 5.50161 + 9.52907i 0.214802 + 0.372048i
\(657\) 1.54764 0.545365i 0.0603792 0.0212767i
\(658\) −3.37015 1.94575i −0.131382 0.0758534i
\(659\) 8.82552 + 3.21223i 0.343794 + 0.125131i 0.508146 0.861271i \(-0.330331\pi\)
−0.164352 + 0.986402i \(0.552553\pi\)
\(660\) 0 0
\(661\) −18.4980 15.5217i −0.719489 0.603723i 0.207755 0.978181i \(-0.433384\pi\)
−0.927244 + 0.374458i \(0.877829\pi\)
\(662\) −1.71457 + 2.04335i −0.0666387 + 0.0794169i
\(663\) 0.0947785 0.0248750i 0.00368089 0.000966065i
\(664\) 6.89399 + 2.50921i 0.267539 + 0.0973761i
\(665\) 0 0
\(666\) −0.0566265 + 5.51472i −0.00219423 + 0.213691i
\(667\) 6.99375 4.03784i 0.270799 0.156346i
\(668\) 37.0057 6.52510i 1.43179 0.252464i
\(669\) −37.3935 + 3.07815i −1.44572 + 0.119008i
\(670\) 0 0
\(671\) −6.26159 + 35.5112i −0.241726 + 1.37090i
\(672\) −4.22656 9.18674i −0.163043 0.354386i
\(673\) 17.0121 + 20.2742i 0.655768 + 0.781514i 0.986772 0.162115i \(-0.0518316\pi\)
−0.331003 + 0.943630i \(0.607387\pi\)
\(674\) 3.10557 0.119622
\(675\) 0 0
\(676\) 23.7554 0.913671
\(677\) 19.9694 + 23.7986i 0.767486 + 0.914654i 0.998296 0.0583448i \(-0.0185823\pi\)
−0.230811 + 0.972999i \(0.574138\pi\)
\(678\) −5.22143 + 7.37609i −0.200528 + 0.283277i
\(679\) 2.27807 12.9196i 0.0874245 0.495809i
\(680\) 0 0
\(681\) −16.0160 + 33.8910i −0.613734 + 1.29871i
\(682\) −7.95842 + 1.40328i −0.304744 + 0.0537345i
\(683\) −33.0268 + 19.0681i −1.26374 + 0.729619i −0.973796 0.227425i \(-0.926969\pi\)
−0.289942 + 0.957044i \(0.593636\pi\)
\(684\) 2.25719 0.374149i 0.0863060 0.0143060i
\(685\) 0 0
\(686\) 6.31558 + 2.29868i 0.241130 + 0.0877642i
\(687\) −13.1657 13.3016i −0.502303 0.507487i
\(688\) −15.9892 + 19.0552i −0.609583 + 0.726472i
\(689\) −0.0179917 0.0150968i −0.000685428 0.000575142i
\(690\) 0 0
\(691\) −30.9436 11.2626i −1.17715 0.428448i −0.321957 0.946754i \(-0.604341\pi\)
−0.855195 + 0.518306i \(0.826563\pi\)
\(692\) 22.2085 + 12.8221i 0.844242 + 0.487424i
\(693\) 19.3277 + 7.26030i 0.734198 + 0.275796i
\(694\) 6.53414 + 11.3175i 0.248033 + 0.429605i
\(695\) 0 0
\(696\) 9.18742 19.4413i 0.348248 0.736919i
\(697\) −3.93762 10.8185i −0.149148 0.409781i
\(698\) 4.84968 + 0.855130i 0.183563 + 0.0323672i
\(699\) −10.7992 7.64461i −0.408463 0.289146i
\(700\) 0 0
\(701\) −2.30710 −0.0871381 −0.0435690 0.999050i \(-0.513873\pi\)
−0.0435690 + 0.999050i \(0.513873\pi\)
\(702\) −0.0374969 0.0106689i −0.00141523 0.000402671i
\(703\) 1.84668i 0.0696490i
\(704\) −16.5800 + 13.9123i −0.624881 + 0.524338i
\(705\) 0 0
\(706\) 0.592100 3.35796i 0.0222840 0.126379i
\(707\) 6.22826 + 17.1120i 0.234238 + 0.643563i
\(708\) −0.961241 11.6772i −0.0361257 0.438857i
\(709\) 1.93654 + 10.9826i 0.0727281 + 0.412462i 0.999336 + 0.0364329i \(0.0115995\pi\)
−0.926608 + 0.376029i \(0.877289\pi\)
\(710\) 0 0
\(711\) −1.27830 + 0.720629i −0.0479400 + 0.0270257i
\(712\) 4.64508 + 2.68184i 0.174082 + 0.100506i
\(713\) 1.31948 3.62525i 0.0494151 0.135767i
\(714\) 0.755212 + 2.87750i 0.0282631 + 0.107688i
\(715\) 0 0
\(716\) −14.2646 11.9694i −0.533092 0.447317i
\(717\) −1.47637 + 5.39888i −0.0551362 + 0.201625i
\(718\) 2.51901 6.92093i 0.0940087 0.258287i
\(719\) −16.0850 + 27.8600i −0.599869 + 1.03900i 0.392971 + 0.919551i \(0.371447\pi\)
−0.992840 + 0.119453i \(0.961886\pi\)
\(720\) 0 0
\(721\) 3.01213 + 5.21717i 0.112178 + 0.194297i
\(722\) −7.70267 + 1.35819i −0.286664 + 0.0505465i
\(723\) 37.7972 26.1777i 1.40569 0.973560i
\(724\) −41.3064 + 15.0343i −1.53514 + 0.558745i
\(725\) 0 0
\(726\) −1.07552 + 11.6066i −0.0399163 + 0.430762i
\(727\) −3.44888 4.11022i −0.127912 0.152440i 0.698287 0.715818i \(-0.253946\pi\)
−0.826199 + 0.563378i \(0.809501\pi\)
\(728\) 0.0378942i 0.00140445i
\(729\) 22.9558 + 14.2138i 0.850215 + 0.526435i
\(730\) 0 0
\(731\) 19.9377 16.7297i 0.737424 0.618772i
\(732\) −21.7911 2.01926i −0.805422 0.0746338i
\(733\) 14.3746 + 2.53463i 0.530938 + 0.0936187i 0.432689 0.901543i \(-0.357565\pi\)
0.0982489 + 0.995162i \(0.468676\pi\)
\(734\) 7.93296 2.88736i 0.292811 0.106574i
\(735\) 0 0
\(736\) 0.794682 + 4.50687i 0.0292924 + 0.166125i
\(737\) 49.8023 28.7534i 1.83449 1.05915i
\(738\) −0.841659 + 4.50245i −0.0309819 + 0.165737i
\(739\) −21.6083 + 37.4266i −0.794873 + 1.37676i 0.128047 + 0.991768i \(0.459129\pi\)
−0.922920 + 0.384992i \(0.874204\pi\)
\(740\) 0 0
\(741\) 0.0125917 + 0.00344333i 0.000462569 + 0.000126494i
\(742\) 0.458343 0.546231i 0.0168263 0.0200528i
\(743\) 5.21443 6.21431i 0.191299 0.227981i −0.661866 0.749622i \(-0.730235\pi\)
0.853165 + 0.521641i \(0.174680\pi\)
\(744\) −2.60770 9.93582i −0.0956028 0.364265i
\(745\) 0 0
\(746\) −2.01116 + 3.48342i −0.0736336 + 0.127537i
\(747\) −6.79706 12.0571i −0.248692 0.441146i
\(748\) 25.8561 14.9280i 0.945393 0.545823i
\(749\) −2.58860 14.6807i −0.0945854 0.536420i
\(750\) 0 0
\(751\) −8.22744 + 2.99454i −0.300223 + 0.109272i −0.487740 0.872989i \(-0.662178\pi\)
0.187516 + 0.982261i \(0.439956\pi\)
\(752\) −20.9291 3.69037i −0.763207 0.134574i
\(753\) −3.25717 7.07968i −0.118698 0.257998i
\(754\) 0.0448713 0.0376515i 0.00163412 0.00137119i
\(755\) 0 0
\(756\) −3.42913 + 12.0520i −0.124716 + 0.438329i
\(757\) 32.1511i 1.16855i −0.811555 0.584276i \(-0.801378\pi\)
0.811555 0.584276i \(-0.198622\pi\)
\(758\) −1.10269 1.31414i −0.0400515 0.0477316i
\(759\) −7.62620 5.39848i −0.276813 0.195952i
\(760\) 0 0
\(761\) 23.0656 8.39520i 0.836128 0.304326i 0.111756 0.993736i \(-0.464352\pi\)
0.724371 + 0.689410i \(0.242130\pi\)
\(762\) −5.46192 2.58116i −0.197865 0.0935054i
\(763\) −18.8481 + 3.32342i −0.682346 + 0.120316i
\(764\) −10.0016 17.3233i −0.361846 0.626736i
\(765\) 0 0
\(766\) 0.986770 1.70914i 0.0356535 0.0617536i
\(767\) 0.0228638 0.0628177i 0.000825563 0.00226822i
\(768\) −4.76119 4.81033i −0.171805 0.173578i
\(769\) −24.0648 20.1928i −0.867800 0.728170i 0.0958338 0.995397i \(-0.469448\pi\)
−0.963634 + 0.267227i \(0.913893\pi\)
\(770\) 0 0
\(771\) 16.9085 16.7358i 0.608945 0.602725i
\(772\) 6.75377 18.5558i 0.243073 0.667839i
\(773\) 24.8675 + 14.3573i 0.894422 + 0.516395i 0.875386 0.483424i \(-0.160607\pi\)
0.0190355 + 0.999819i \(0.493940\pi\)
\(774\) −10.2155 + 1.69331i −0.367190 + 0.0608649i
\(775\) 0 0
\(776\) 2.74507 + 15.5681i 0.0985424 + 0.558862i
\(777\) 9.14389 + 4.32116i 0.328035 + 0.155021i
\(778\) 3.09962 + 8.51615i 0.111127 + 0.305319i
\(779\) 0.266332 1.51044i 0.00954233 0.0541173i
\(780\) 0 0
\(781\) 24.3071 20.3961i 0.869776 0.729829i
\(782\) 1.34633i 0.0481446i
\(783\) −37.0263 + 16.5763i −1.32321 + 0.592388i
\(784\) 15.7448 0.562315
\(785\) 0 0
\(786\) −10.1558 + 4.67239i −0.362245 + 0.166659i
\(787\) −38.2263 6.74033i −1.36262 0.240267i −0.555925 0.831233i \(-0.687636\pi\)
−0.806697 + 0.590966i \(0.798747\pi\)
\(788\) 13.7959 + 37.9040i 0.491459 + 1.35027i
\(789\) 41.7787 3.43913i 1.48736 0.122436i
\(790\) 0 0
\(791\) 8.28623 + 14.3522i 0.294625 + 0.510305i
\(792\) −24.8775 0.255448i −0.883983 0.00907694i
\(793\) −0.108133 0.0624304i −0.00383990 0.00221697i
\(794\) 13.6054 + 4.95197i 0.482839 + 0.175739i
\(795\) 0 0
\(796\) −18.0397 15.1371i −0.639399 0.536520i
\(797\) 2.59307 3.09030i 0.0918512 0.109464i −0.718161 0.695877i \(-0.755016\pi\)
0.810012 + 0.586413i \(0.199460\pi\)
\(798\) −0.104540 + 0.382289i −0.00370069 + 0.0135329i
\(799\) 20.8953 + 7.60526i 0.739222 + 0.269055i
\(800\) 0 0
\(801\) −3.36315 9.54397i −0.118831 0.337220i
\(802\) 6.77371 3.91080i 0.239188 0.138095i
\(803\) 2.80923 0.495343i 0.0991355 0.0174803i
\(804\) 19.8715 + 28.6918i 0.700813 + 1.01188i
\(805\) 0 0
\(806\) 0.00485912 0.0275575i 0.000171155 0.000970670i
\(807\) 20.7067 + 1.91877i 0.728909 + 0.0675438i
\(808\) −14.1049 16.8095i −0.496207 0.591357i
\(809\) 29.9454 1.05283 0.526413 0.850229i \(-0.323537\pi\)
0.526413 + 0.850229i \(0.323537\pi\)
\(810\) 0 0
\(811\) 20.2173 0.709927 0.354963 0.934880i \(-0.384493\pi\)
0.354963 + 0.934880i \(0.384493\pi\)
\(812\) −12.1017 14.4223i −0.424687 0.506122i
\(813\) −6.41190 0.594154i −0.224875 0.0208379i
\(814\) −1.66481 + 9.44162i −0.0583516 + 0.330929i
\(815\) 0 0
\(816\) 9.25021 + 13.3561i 0.323822 + 0.467557i
\(817\) 3.41463 0.602092i 0.119463 0.0210645i
\(818\) −2.28834 + 1.32117i −0.0800099 + 0.0461938i
\(819\) −0.0465138 + 0.0542910i −0.00162533 + 0.00189708i
\(820\) 0 0
\(821\) −25.2530 9.19133i −0.881334 0.320779i −0.138586 0.990350i \(-0.544256\pi\)
−0.742748 + 0.669571i \(0.766478\pi\)
\(822\) −2.27918 + 8.33461i −0.0794954 + 0.290703i
\(823\) 14.8190 17.6606i 0.516559 0.615611i −0.443204 0.896421i \(-0.646158\pi\)
0.959764 + 0.280809i \(0.0906029\pi\)
\(824\) −5.56089 4.66614i −0.193723 0.162553i
\(825\) 0 0
\(826\) 1.90716 + 0.694150i 0.0663587 + 0.0241526i
\(827\) 4.42498 + 2.55476i 0.153872 + 0.0888378i 0.574959 0.818182i \(-0.305018\pi\)
−0.421087 + 0.907020i \(0.638351\pi\)
\(828\) 2.88561 4.88158i 0.100282 0.169647i
\(829\) −15.2991 26.4988i −0.531360 0.920343i −0.999330 0.0365985i \(-0.988348\pi\)
0.467970 0.883744i \(-0.344986\pi\)
\(830\) 0 0
\(831\) −40.5368 + 3.33690i −1.40621 + 0.115756i
\(832\) −0.0256327 0.0704252i −0.000888653 0.00244155i
\(833\) −16.2238 2.86069i −0.562120 0.0991170i
\(834\) −4.01731 + 1.84825i −0.139108 + 0.0639997i
\(835\) 0 0
\(836\) 3.97744 0.137563
\(837\) −8.45984 + 17.4359i −0.292415 + 0.602674i
\(838\) 10.1033i 0.349013i
\(839\) 43.1350 36.1945i 1.48918 1.24957i 0.593539 0.804805i \(-0.297730\pi\)
0.895645 0.444769i \(-0.146714\pi\)
\(840\) 0 0
\(841\) 5.54853 31.4673i 0.191329 1.08508i
\(842\) −1.13537 3.11939i −0.0391273 0.107501i
\(843\) −31.9020 15.0760i −1.09876 0.519246i
\(844\) −7.61436 43.1832i −0.262097 1.48643i
\(845\) 0 0
\(846\) −5.61674 6.83509i −0.193108 0.234995i
\(847\) 18.5118 + 10.6878i 0.636073 + 0.367237i
\(848\) 1.33185 3.65924i 0.0457360 0.125659i
\(849\) −14.2797 + 14.1338i −0.490079 + 0.485072i
\(850\) 0 0
\(851\) −3.50612 2.94198i −0.120188 0.100850i
\(852\) 13.5470 + 13.6869i 0.464114 + 0.468904i
\(853\) 15.5773 42.7983i 0.533357 1.46539i −0.321695 0.946843i \(-0.604253\pi\)
0.855052 0.518542i \(-0.173525\pi\)
\(854\) 1.89540 3.28294i 0.0648594 0.112340i
\(855\) 0 0
\(856\) 8.98154 + 15.5565i 0.306983 + 0.531710i
\(857\) 17.2235 3.03696i 0.588343 0.103741i 0.128451 0.991716i \(-0.458999\pi\)
0.459892 + 0.887975i \(0.347888\pi\)
\(858\) −0.0612742 0.0289565i −0.00209187 0.000988559i
\(859\) 17.2396 6.27471i 0.588208 0.214090i −0.0307329 0.999528i \(-0.509784\pi\)
0.618941 + 0.785437i \(0.287562\pi\)
\(860\) 0 0
\(861\) 6.85579 + 4.85312i 0.233645 + 0.165394i
\(862\) −2.63618 3.14167i −0.0897886 0.107006i
\(863\) 4.65373i 0.158415i −0.996858 0.0792073i \(-0.974761\pi\)
0.996858 0.0792073i \(-0.0252389\pi\)
\(864\) −1.65068 22.9298i −0.0561574 0.780087i
\(865\) 0 0
\(866\) 1.94259 1.63003i 0.0660120 0.0553907i
\(867\) 5.20185 + 11.3066i 0.176664 + 0.383992i
\(868\) −8.85735 1.56179i −0.300638 0.0530106i
\(869\) −2.39713 + 0.872486i −0.0813172 + 0.0295971i
\(870\) 0 0
\(871\) 0.0345781 + 0.196102i 0.00117164 + 0.00664468i
\(872\) 19.9725 11.5311i 0.676354 0.390493i
\(873\) 15.1765 25.6739i 0.513645 0.868931i
\(874\) 0.0896791 0.155329i 0.00303344 0.00525407i
\(875\) 0 0
\(876\) 0.439487 + 1.67453i 0.0148489 + 0.0565770i
\(877\) 2.35716 2.80916i 0.0795958 0.0948585i −0.724777 0.688984i \(-0.758057\pi\)
0.804373 + 0.594125i \(0.202502\pi\)
\(878\) 4.04164 4.81664i 0.136399 0.162554i
\(879\) 52.7512 + 14.4253i 1.77925 + 0.486554i
\(880\) 0 0
\(881\) −19.1504 + 33.1694i −0.645193 + 1.11751i 0.339064 + 0.940763i \(0.389890\pi\)
−0.984257 + 0.176744i \(0.943444\pi\)
\(882\) 4.97735 + 4.26434i 0.167596 + 0.143588i
\(883\) −19.5844 + 11.3071i −0.659069 + 0.380513i −0.791922 0.610622i \(-0.790919\pi\)
0.132853 + 0.991136i \(0.457586\pi\)
\(884\) 0.0179521 + 0.101811i 0.000603794 + 0.00342429i
\(885\) 0 0
\(886\) −0.282186 + 0.102707i −0.00948023 + 0.00345052i
\(887\) −1.86774 0.329334i −0.0627127 0.0110579i 0.142204 0.989837i \(-0.454581\pi\)
−0.204916 + 0.978779i \(0.565692\pi\)
\(888\) −12.1348 1.12446i −0.407216 0.0377344i
\(889\) −8.48645 + 7.12097i −0.284626 + 0.238830i
\(890\) 0 0
\(891\) 35.3285 + 30.9023i 1.18355 + 1.03527i
\(892\) 39.5852i 1.32541i
\(893\) 1.90415 + 2.26928i 0.0637199 + 0.0759384i
\(894\) 0.0586171 0.632575i 0.00196045 0.0211565i
\(895\) 0 0
\(896\) 13.1107 4.77190i 0.437997 0.159418i
\(897\) 0.0265976 0.0184211i 0.000888069 0.000615062i
\(898\) −0.682653 + 0.120370i −0.0227804 + 0.00401680i
\(899\) −14.5592 25.2172i −0.485575 0.841041i
\(900\) 0 0
\(901\) −2.03722 + 3.52856i −0.0678695 + 0.117553i
\(902\) −2.72338 + 7.48241i −0.0906785 + 0.249137i
\(903\) −5.00882 + 18.3165i −0.166683 + 0.609535i
\(904\) −15.2977 12.8363i −0.508795 0.426930i
\(905\) 0 0
\(906\) −1.50261 5.72522i −0.0499208 0.190208i
\(907\) 2.23371 6.13708i 0.0741693 0.203778i −0.897068 0.441893i \(-0.854307\pi\)
0.971237 + 0.238115i \(0.0765294\pi\)
\(908\) −34.2497 19.7740i −1.13661 0.656225i
\(909\) −0.425067 + 41.3963i −0.0140986 + 1.37303i
\(910\) 0 0
\(911\) −7.47332 42.3833i −0.247602 1.40422i −0.814371 0.580344i \(-0.802918\pi\)
0.566769 0.823877i \(-0.308193\pi\)
\(912\) 0.177566 + 2.15708i 0.00587980 + 0.0714281i
\(913\) −8.22940 22.6101i −0.272353 0.748285i
\(914\) 0.799615 4.53484i 0.0264489 0.149999i
\(915\) 0 0
\(916\) 15.1260 12.6922i 0.499777 0.419363i
\(917\) 20.5003i 0.676980i
\(918\) −0.693143 + 6.72755i −0.0228771 + 0.222042i
\(919\) 16.7911 0.553887 0.276943 0.960886i \(-0.410679\pi\)
0.276943 + 0.960886i \(0.410679\pi\)
\(920\) 0 0
\(921\) −11.4800 8.12650i −0.378277 0.267777i
\(922\) 8.95409 + 1.57885i 0.294887 + 0.0519966i
\(923\) 0.0375788 + 0.103247i 0.00123692 + 0.00339841i
\(924\) −9.30703 + 19.6944i −0.306179 + 0.647897i
\(925\) 0 0
\(926\) 5.16253 + 8.94176i 0.169651 + 0.293844i
\(927\) 2.23957 + 13.5110i 0.0735570 + 0.443760i
\(928\) 29.9135 + 17.2706i 0.981960 + 0.566935i
\(929\) −10.9004 3.96744i −0.357632 0.130167i 0.156955 0.987606i \(-0.449832\pi\)
−0.514587 + 0.857438i \(0.672055\pi\)
\(930\) 0 0
\(931\) −1.68122 1.41071i −0.0550998 0.0462343i
\(932\) 8.97294 10.6935i 0.293918 0.350278i
\(933\) 29.0581 + 29.3580i 0.951318 + 0.961137i
\(934\) 4.62072 + 1.68180i 0.151195 + 0.0550303i
\(935\) 0 0
\(936\) 0.0302937 0.0806452i 0.000990182 0.00263597i
\(937\) 41.3919 23.8976i 1.35222 0.780702i 0.363656 0.931533i \(-0.381528\pi\)
0.988559 + 0.150832i \(0.0481951\pi\)
\(938\) −5.95372 + 1.04980i −0.194396 + 0.0342772i
\(939\) 19.9150 42.1416i 0.649901 1.37524i
\(940\) 0 0
\(941\) 1.95534 11.0893i 0.0637422 0.361500i −0.936207 0.351448i \(-0.885689\pi\)
0.999949 0.0100518i \(-0.00319964\pi\)
\(942\) 5.22202 7.37691i 0.170142 0.240353i
\(943\) −2.44343 2.91197i −0.0795691 0.0948268i
\(944\) 11.0837 0.360743
\(945\) 0 0
\(946\) −18.0010 −0.585261
\(947\) 4.71285 + 5.61656i 0.153147 + 0.182514i 0.837163 0.546954i \(-0.184213\pi\)
−0.684016 + 0.729467i \(0.739768\pi\)
\(948\) −0.647087 1.40649i −0.0210164 0.0456807i
\(949\) −0.00171521 + 0.00972746i −5.56782e−5 + 0.000315767i
\(950\) 0 0
\(951\) −14.3834 + 1.18401i −0.466413 + 0.0383940i
\(952\) −6.47401 + 1.14154i −0.209824 + 0.0369976i
\(953\) 21.5427 12.4377i 0.697835 0.402895i −0.108705 0.994074i \(-0.534671\pi\)
0.806541 + 0.591179i \(0.201337\pi\)
\(954\) 1.41210 0.796060i 0.0457186 0.0257734i
\(955\) 0 0
\(956\) −5.54906 2.01969i −0.179469 0.0653215i
\(957\) −68.2122 + 17.9026i −2.20499 + 0.578708i
\(958\) −0.771086 + 0.918945i −0.0249127 + 0.0296898i
\(959\) 12.1382 + 10.1852i 0.391963 + 0.328896i
\(960\) 0 0
\(961\) 16.0590 + 5.84499i 0.518031 + 0.188548i
\(962\) −0.0287500 0.0165988i −0.000926937 0.000535168i
\(963\) 6.22720 33.3124i 0.200669 1.07348i
\(964\) 24.2540 + 42.0091i 0.781167 + 1.35302i
\(965\) 0 0
\(966\) 0.559269 + 0.807511i 0.0179942 + 0.0259812i
\(967\) 11.6389 + 31.9777i 0.374283 + 1.02833i 0.973687 + 0.227888i \(0.0731819\pi\)
−0.599404 + 0.800446i \(0.704596\pi\)
\(968\) −25.3662 4.47275i −0.815301 0.143760i
\(969\) 0.208954 2.25496i 0.00671258 0.0724397i
\(970\) 0 0
\(971\) −34.2476 −1.09906 −0.549530 0.835474i \(-0.685193\pi\)
−0.549530 + 0.835474i \(0.685193\pi\)
\(972\) −16.9325 + 22.9074i −0.543111 + 0.734756i
\(973\) 8.10928i 0.259971i
\(974\) 2.78770 2.33916i 0.0893236 0.0749514i
\(975\) 0 0
\(976\) 3.59488 20.3876i 0.115069 0.652590i
\(977\) 8.00919 + 22.0051i 0.256237 + 0.704004i 0.999391 + 0.0348848i \(0.0111064\pi\)
−0.743155 + 0.669120i \(0.766671\pi\)
\(978\) 1.96089 1.35808i 0.0627022 0.0434266i
\(979\) −3.05467 17.3239i −0.0976278 0.553675i
\(980\) 0 0
\(981\) −42.7687 7.99491i −1.36550 0.255258i
\(982\) −8.12188 4.68917i −0.259180 0.149637i
\(983\) 11.3561 31.2007i 0.362205 0.995149i −0.616044 0.787712i \(-0.711266\pi\)
0.978248 0.207437i \(-0.0665122\pi\)
\(984\) −9.76314 2.66982i −0.311237 0.0851108i
\(985\) 0 0
\(986\) −7.78428 6.53178i −0.247902 0.208014i
\(987\) −15.6920 + 4.11843i −0.499482 + 0.131091i
\(988\) −0.00471050 + 0.0129420i −0.000149861 + 0.000411740i
\(989\) 4.29678 7.44223i 0.136630 0.236649i
\(990\) 0 0
\(991\) 14.0903 + 24.4051i 0.447594 + 0.775255i 0.998229 0.0594912i \(-0.0189478\pi\)
−0.550635 + 0.834746i \(0.685614\pi\)
\(992\) 16.2503 2.86537i 0.515948 0.0909755i
\(993\) 0.912305 + 11.0827i 0.0289511 + 0.351700i
\(994\) −3.13460 + 1.14090i −0.0994236 + 0.0361872i
\(995\) 0 0
\(996\) 13.2662 6.10341i 0.420355 0.193394i
\(997\) −28.8938 34.4342i −0.915075 1.09054i −0.995592 0.0937901i \(-0.970102\pi\)
0.0805175 0.996753i \(-0.474343\pi\)
\(998\) 10.5249i 0.333161i
\(999\) 16.0053 + 16.5061i 0.506385 + 0.522228i
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 675.2.u.b.49.2 24
5.2 odd 4 675.2.l.c.76.1 12
5.3 odd 4 27.2.e.a.22.2 yes 12
5.4 even 2 inner 675.2.u.b.49.3 24
15.8 even 4 81.2.e.a.37.1 12
20.3 even 4 432.2.u.c.49.1 12
27.16 even 9 inner 675.2.u.b.124.3 24
45.13 odd 12 243.2.e.d.28.2 12
45.23 even 12 243.2.e.a.28.1 12
45.38 even 12 243.2.e.b.190.2 12
45.43 odd 12 243.2.e.c.190.1 12
135.13 odd 36 729.2.c.e.487.3 12
135.23 even 36 729.2.a.d.1.3 6
135.38 even 36 81.2.e.a.46.1 12
135.43 odd 36 27.2.e.a.16.2 12
135.58 odd 36 729.2.a.a.1.4 6
135.68 even 36 729.2.c.b.487.4 12
135.83 even 36 243.2.e.b.55.2 12
135.88 odd 36 243.2.e.d.217.2 12
135.97 odd 36 675.2.l.c.151.1 12
135.103 odd 36 729.2.c.e.244.3 12
135.113 even 36 729.2.c.b.244.4 12
135.124 even 18 inner 675.2.u.b.124.2 24
135.128 even 36 243.2.e.a.217.1 12
135.133 odd 36 243.2.e.c.55.1 12
540.43 even 36 432.2.u.c.97.1 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
27.2.e.a.16.2 12 135.43 odd 36
27.2.e.a.22.2 yes 12 5.3 odd 4
81.2.e.a.37.1 12 15.8 even 4
81.2.e.a.46.1 12 135.38 even 36
243.2.e.a.28.1 12 45.23 even 12
243.2.e.a.217.1 12 135.128 even 36
243.2.e.b.55.2 12 135.83 even 36
243.2.e.b.190.2 12 45.38 even 12
243.2.e.c.55.1 12 135.133 odd 36
243.2.e.c.190.1 12 45.43 odd 12
243.2.e.d.28.2 12 45.13 odd 12
243.2.e.d.217.2 12 135.88 odd 36
432.2.u.c.49.1 12 20.3 even 4
432.2.u.c.97.1 12 540.43 even 36
675.2.l.c.76.1 12 5.2 odd 4
675.2.l.c.151.1 12 135.97 odd 36
675.2.u.b.49.2 24 1.1 even 1 trivial
675.2.u.b.49.3 24 5.4 even 2 inner
675.2.u.b.124.2 24 135.124 even 18 inner
675.2.u.b.124.3 24 27.16 even 9 inner
729.2.a.a.1.4 6 135.58 odd 36
729.2.a.d.1.3 6 135.23 even 36
729.2.c.b.244.4 12 135.113 even 36
729.2.c.b.487.4 12 135.68 even 36
729.2.c.e.244.3 12 135.103 odd 36
729.2.c.e.487.3 12 135.13 odd 36