Properties

Label 819.2.ew.a.470.66
Level $819$
Weight $2$
Character 819.470
Analytic conductor $6.540$
Analytic rank $0$
Dimension $336$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [819,2,Mod(176,819)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(819, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([10, 0, 11]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("819.176");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.ew (of order \(12\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.53974792554\)
Analytic rank: \(0\)
Dimension: \(336\)
Relative dimension: \(84\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 470.66
Character \(\chi\) \(=\) 819.470
Dual form 819.2.ew.a.176.66

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.24887 + 1.24887i) q^{2} +(-0.599129 - 1.62513i) q^{3} +1.11938i q^{4} +(-0.587158 + 2.19131i) q^{5} +(1.28135 - 2.77782i) q^{6} +(-0.258819 + 0.965926i) q^{7} +(1.09979 - 1.09979i) q^{8} +(-2.28209 + 1.94732i) q^{9} +O(q^{10})\) \(q+(1.24887 + 1.24887i) q^{2} +(-0.599129 - 1.62513i) q^{3} +1.11938i q^{4} +(-0.587158 + 2.19131i) q^{5} +(1.28135 - 2.77782i) q^{6} +(-0.258819 + 0.965926i) q^{7} +(1.09979 - 1.09979i) q^{8} +(-2.28209 + 1.94732i) q^{9} +(-3.46995 + 2.00338i) q^{10} +(-2.29766 + 2.29766i) q^{11} +(1.81913 - 0.670650i) q^{12} +(-2.31332 + 2.76560i) q^{13} +(-1.52955 + 0.883088i) q^{14} +(3.91294 - 0.358666i) q^{15} +4.98575 q^{16} +(-0.515980 + 0.893703i) q^{17} +(-5.28201 - 0.418079i) q^{18} +(1.09206 + 4.07562i) q^{19} +(-2.45289 - 0.657251i) q^{20} +(1.72482 - 0.158100i) q^{21} -5.73897 q^{22} +(-0.536080 + 0.928518i) q^{23} +(-2.44622 - 1.12838i) q^{24} +(-0.126936 - 0.0732865i) q^{25} +(-6.34294 + 0.564832i) q^{26} +(4.53192 + 2.54199i) q^{27} +(-1.08123 - 0.289716i) q^{28} -1.61779i q^{29} +(5.33470 + 4.43884i) q^{30} +(0.634016 + 0.169884i) q^{31} +(4.02700 + 4.02700i) q^{32} +(5.11058 + 2.35740i) q^{33} +(-1.76052 + 0.471729i) q^{34} +(-1.96467 - 1.13430i) q^{35} +(-2.17979 - 2.55451i) q^{36} +(-2.27102 + 8.47557i) q^{37} +(-3.72609 + 6.45378i) q^{38} +(5.88043 + 2.10250i) q^{39} +(1.76422 + 3.05573i) q^{40} +(-5.51787 + 1.47851i) q^{41} +(2.35153 + 1.95664i) q^{42} +(8.91134 - 5.14496i) q^{43} +(-2.57194 - 2.57194i) q^{44} +(-2.92723 - 6.14414i) q^{45} +(-1.82910 + 0.490106i) q^{46} +(-0.876570 - 3.27140i) q^{47} +(-2.98711 - 8.10249i) q^{48} +(-0.866025 - 0.500000i) q^{49} +(-0.0670014 - 0.250053i) q^{50} +(1.76152 + 0.303090i) q^{51} +(-3.09574 - 2.58948i) q^{52} -4.95146i q^{53} +(2.48517 + 8.83442i) q^{54} +(-3.68578 - 6.38396i) q^{55} +(0.777669 + 1.34696i) q^{56} +(5.96912 - 4.21656i) q^{57} +(2.02041 - 2.02041i) q^{58} +(-7.44066 + 7.44066i) q^{59} +(0.401482 + 4.38005i) q^{60} +(-1.16522 - 2.01822i) q^{61} +(0.579643 + 1.00397i) q^{62} +(-1.29032 - 2.70833i) q^{63} +0.0869266i q^{64} +(-4.70198 - 6.69304i) q^{65} +(3.43838 + 9.32657i) q^{66} +(3.01634 + 11.2571i) q^{67} +(-1.00039 - 0.577575i) q^{68} +(1.83014 + 0.314897i) q^{69} +(-1.03702 - 3.87023i) q^{70} +(6.76346 - 1.81226i) q^{71} +(-0.368171 + 4.65147i) q^{72} +(-5.26512 - 5.26512i) q^{73} +(-13.4211 + 7.74870i) q^{74} +(-0.0430490 + 0.250195i) q^{75} +(-4.56215 + 1.22242i) q^{76} +(-1.62469 - 2.81404i) q^{77} +(4.71816 + 9.96968i) q^{78} +(3.20406 - 5.54959i) q^{79} +(-2.92742 + 10.9253i) q^{80} +(1.41586 - 8.88793i) q^{81} +(-8.73759 - 5.04465i) q^{82} +(-14.5449 + 3.89728i) q^{83} +(0.176973 + 1.93072i) q^{84} +(-1.65541 - 1.65541i) q^{85} +(17.5546 + 4.70373i) q^{86} +(-2.62911 + 0.969262i) q^{87} +5.05388i q^{88} +(-7.37301 - 1.97559i) q^{89} +(4.01751 - 11.3290i) q^{90} +(-2.07263 - 2.95029i) q^{91} +(-1.03936 - 0.600075i) q^{92} +(-0.103774 - 1.13214i) q^{93} +(2.99085 - 5.18030i) q^{94} -9.57214 q^{95} +(4.13170 - 8.95708i) q^{96} +(13.6438 + 3.65583i) q^{97} +(-0.457120 - 1.70599i) q^{98} +(0.769174 - 9.71774i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 336 q + 24 q^{6} - 36 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 336 q + 24 q^{6} - 36 q^{8} + 16 q^{15} - 336 q^{16} + 20 q^{18} + 8 q^{21} + 8 q^{24} + 96 q^{26} + 24 q^{27} - 96 q^{30} - 72 q^{32} - 36 q^{33} - 12 q^{36} - 72 q^{38} - 16 q^{39} - 48 q^{41} - 28 q^{45} + 60 q^{47} - 48 q^{48} + 132 q^{50} - 36 q^{52} - 108 q^{54} + 68 q^{57} - 72 q^{58} - 44 q^{60} - 36 q^{62} - 8 q^{63} - 72 q^{65} - 20 q^{66} - 72 q^{69} + 48 q^{71} - 104 q^{72} + 12 q^{74} + 104 q^{78} - 12 q^{79} + 96 q^{80} - 68 q^{81} - 120 q^{83} - 12 q^{84} + 36 q^{85} + 48 q^{86} - 24 q^{87} - 60 q^{89} - 72 q^{92} - 172 q^{93} - 48 q^{94} - 152 q^{96} + 48 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.24887 + 1.24887i 0.883088 + 0.883088i 0.993847 0.110760i \(-0.0353284\pi\)
−0.110760 + 0.993847i \(0.535328\pi\)
\(3\) −0.599129 1.62513i −0.345907 0.938269i
\(4\) 1.11938i 0.559688i
\(5\) −0.587158 + 2.19131i −0.262585 + 0.979981i 0.701127 + 0.713037i \(0.252681\pi\)
−0.963712 + 0.266945i \(0.913986\pi\)
\(6\) 1.28135 2.77782i 0.523107 1.13404i
\(7\) −0.258819 + 0.965926i −0.0978244 + 0.365086i
\(8\) 1.09979 1.09979i 0.388834 0.388834i
\(9\) −2.28209 + 1.94732i −0.760696 + 0.649108i
\(10\) −3.46995 + 2.00338i −1.09730 + 0.633524i
\(11\) −2.29766 + 2.29766i −0.692770 + 0.692770i −0.962840 0.270071i \(-0.912953\pi\)
0.270071 + 0.962840i \(0.412953\pi\)
\(12\) 1.81913 0.670650i 0.525137 0.193600i
\(13\) −2.31332 + 2.76560i −0.641601 + 0.767039i
\(14\) −1.52955 + 0.883088i −0.408790 + 0.236015i
\(15\) 3.91294 0.358666i 1.01032 0.0926073i
\(16\) 4.98575 1.24644
\(17\) −0.515980 + 0.893703i −0.125144 + 0.216755i −0.921789 0.387692i \(-0.873272\pi\)
0.796646 + 0.604447i \(0.206606\pi\)
\(18\) −5.28201 0.418079i −1.24498 0.0985422i
\(19\) 1.09206 + 4.07562i 0.250535 + 0.935011i 0.970520 + 0.241021i \(0.0774822\pi\)
−0.719984 + 0.693990i \(0.755851\pi\)
\(20\) −2.45289 0.657251i −0.548483 0.146966i
\(21\) 1.72482 0.158100i 0.376387 0.0345002i
\(22\) −5.73897 −1.22355
\(23\) −0.536080 + 0.928518i −0.111780 + 0.193609i −0.916488 0.400062i \(-0.868989\pi\)
0.804708 + 0.593671i \(0.202322\pi\)
\(24\) −2.44622 1.12838i −0.499332 0.230330i
\(25\) −0.126936 0.0732865i −0.0253872 0.0146573i
\(26\) −6.34294 + 0.564832i −1.24395 + 0.110773i
\(27\) 4.53192 + 2.54199i 0.872168 + 0.489206i
\(28\) −1.08123 0.289716i −0.204334 0.0547511i
\(29\) 1.61779i 0.300415i −0.988654 0.150208i \(-0.952006\pi\)
0.988654 0.150208i \(-0.0479942\pi\)
\(30\) 5.33470 + 4.43884i 0.973978 + 0.810417i
\(31\) 0.634016 + 0.169884i 0.113873 + 0.0305121i 0.315305 0.948990i \(-0.397893\pi\)
−0.201433 + 0.979502i \(0.564560\pi\)
\(32\) 4.02700 + 4.02700i 0.711879 + 0.711879i
\(33\) 5.11058 + 2.35740i 0.889638 + 0.410370i
\(34\) −1.76052 + 0.471729i −0.301926 + 0.0809009i
\(35\) −1.96467 1.13430i −0.332090 0.191732i
\(36\) −2.17979 2.55451i −0.363298 0.425752i
\(37\) −2.27102 + 8.47557i −0.373354 + 1.39337i 0.482382 + 0.875961i \(0.339772\pi\)
−0.855736 + 0.517413i \(0.826895\pi\)
\(38\) −3.72609 + 6.45378i −0.604452 + 1.04694i
\(39\) 5.88043 + 2.10250i 0.941623 + 0.336670i
\(40\) 1.76422 + 3.05573i 0.278948 + 0.483153i
\(41\) −5.51787 + 1.47851i −0.861746 + 0.230904i −0.662515 0.749049i \(-0.730511\pi\)
−0.199231 + 0.979953i \(0.563844\pi\)
\(42\) 2.35153 + 1.95664i 0.362849 + 0.301916i
\(43\) 8.91134 5.14496i 1.35897 0.784600i 0.369482 0.929238i \(-0.379535\pi\)
0.989485 + 0.144638i \(0.0462019\pi\)
\(44\) −2.57194 2.57194i −0.387735 0.387735i
\(45\) −2.92723 6.14414i −0.436366 0.915914i
\(46\) −1.82910 + 0.490106i −0.269686 + 0.0722621i
\(47\) −0.876570 3.27140i −0.127861 0.477183i 0.872065 0.489391i \(-0.162781\pi\)
−0.999925 + 0.0122074i \(0.996114\pi\)
\(48\) −2.98711 8.10249i −0.431152 1.16949i
\(49\) −0.866025 0.500000i −0.123718 0.0714286i
\(50\) −0.0670014 0.250053i −0.00947544 0.0353628i
\(51\) 1.76152 + 0.303090i 0.246662 + 0.0424411i
\(52\) −3.09574 2.58948i −0.429302 0.359096i
\(53\) 4.95146i 0.680135i −0.940401 0.340068i \(-0.889550\pi\)
0.940401 0.340068i \(-0.110450\pi\)
\(54\) 2.48517 + 8.83442i 0.338189 + 1.20221i
\(55\) −3.68578 6.38396i −0.496990 0.860813i
\(56\) 0.777669 + 1.34696i 0.103920 + 0.179995i
\(57\) 5.96912 4.21656i 0.790630 0.558497i
\(58\) 2.02041 2.02041i 0.265293 0.265293i
\(59\) −7.44066 + 7.44066i −0.968691 + 0.968691i −0.999525 0.0308332i \(-0.990184\pi\)
0.0308332 + 0.999525i \(0.490184\pi\)
\(60\) 0.401482 + 4.38005i 0.0518311 + 0.565461i
\(61\) −1.16522 2.01822i −0.149191 0.258406i 0.781738 0.623607i \(-0.214334\pi\)
−0.930929 + 0.365201i \(0.881000\pi\)
\(62\) 0.579643 + 1.00397i 0.0736147 + 0.127504i
\(63\) −1.29032 2.70833i −0.162565 0.341218i
\(64\) 0.0869266i 0.0108658i
\(65\) −4.70198 6.69304i −0.583209 0.830170i
\(66\) 3.43838 + 9.32657i 0.423236 + 1.14802i
\(67\) 3.01634 + 11.2571i 0.368504 + 1.37528i 0.862608 + 0.505873i \(0.168830\pi\)
−0.494104 + 0.869403i \(0.664504\pi\)
\(68\) −1.00039 0.577575i −0.121315 0.0700413i
\(69\) 1.83014 + 0.314897i 0.220323 + 0.0379092i
\(70\) −1.03702 3.87023i −0.123948 0.462581i
\(71\) 6.76346 1.81226i 0.802675 0.215076i 0.165917 0.986140i \(-0.446942\pi\)
0.636758 + 0.771064i \(0.280275\pi\)
\(72\) −0.368171 + 4.65147i −0.0433893 + 0.548180i
\(73\) −5.26512 5.26512i −0.616235 0.616235i 0.328328 0.944564i \(-0.393515\pi\)
−0.944564 + 0.328328i \(0.893515\pi\)
\(74\) −13.4211 + 7.74870i −1.56018 + 0.900768i
\(75\) −0.0430490 + 0.250195i −0.00497087 + 0.0288901i
\(76\) −4.56215 + 1.22242i −0.523314 + 0.140222i
\(77\) −1.62469 2.81404i −0.185151 0.320690i
\(78\) 4.71816 + 9.96968i 0.534227 + 1.12884i
\(79\) 3.20406 5.54959i 0.360485 0.624378i −0.627556 0.778571i \(-0.715945\pi\)
0.988041 + 0.154194i \(0.0492780\pi\)
\(80\) −2.92742 + 10.9253i −0.327296 + 1.22149i
\(81\) 1.41586 8.88793i 0.157318 0.987548i
\(82\) −8.73759 5.04465i −0.964906 0.557088i
\(83\) −14.5449 + 3.89728i −1.59651 + 0.427782i −0.943985 0.329988i \(-0.892955\pi\)
−0.652521 + 0.757771i \(0.726288\pi\)
\(84\) 0.176973 + 1.93072i 0.0193094 + 0.210659i
\(85\) −1.65541 1.65541i −0.179555 0.179555i
\(86\) 17.5546 + 4.70373i 1.89296 + 0.507216i
\(87\) −2.62911 + 0.969262i −0.281870 + 0.103916i
\(88\) 5.05388i 0.538745i
\(89\) −7.37301 1.97559i −0.781538 0.209412i −0.154075 0.988059i \(-0.549240\pi\)
−0.627463 + 0.778647i \(0.715906\pi\)
\(90\) 4.01751 11.3290i 0.423483 1.19418i
\(91\) −2.07263 2.95029i −0.217271 0.309274i
\(92\) −1.03936 0.600075i −0.108361 0.0625621i
\(93\) −0.103774 1.13214i −0.0107609 0.117397i
\(94\) 2.99085 5.18030i 0.308482 0.534307i
\(95\) −9.57214 −0.982080
\(96\) 4.13170 8.95708i 0.421690 0.914178i
\(97\) 13.6438 + 3.65583i 1.38531 + 0.371194i 0.873048 0.487634i \(-0.162140\pi\)
0.512265 + 0.858827i \(0.328807\pi\)
\(98\) −0.457120 1.70599i −0.0461761 0.172331i
\(99\) 0.769174 9.71774i 0.0773049 0.976670i
\(100\) 0.0820351 0.142089i 0.00820351 0.0142089i
\(101\) 12.8100 1.27464 0.637322 0.770598i \(-0.280042\pi\)
0.637322 + 0.770598i \(0.280042\pi\)
\(102\) 1.82140 + 2.57844i 0.180345 + 0.255304i
\(103\) −7.14294 + 4.12398i −0.703815 + 0.406348i −0.808767 0.588130i \(-0.799864\pi\)
0.104952 + 0.994477i \(0.466531\pi\)
\(104\) 0.497405 + 5.58575i 0.0487745 + 0.547728i
\(105\) −0.666298 + 3.87244i −0.0650240 + 0.377911i
\(106\) 6.18375 6.18375i 0.600619 0.600619i
\(107\) 12.4272 7.17485i 1.20138 0.693619i 0.240520 0.970644i \(-0.422682\pi\)
0.960863 + 0.277025i \(0.0893486\pi\)
\(108\) −2.84544 + 5.07292i −0.273803 + 0.488142i
\(109\) 13.6878 13.6878i 1.31105 1.31105i 0.390416 0.920639i \(-0.372331\pi\)
0.920639 0.390416i \(-0.127669\pi\)
\(110\) 3.36969 12.5758i 0.321287 1.19906i
\(111\) 15.1345 1.38726i 1.43651 0.131672i
\(112\) −1.29041 + 4.81586i −0.121932 + 0.455056i
\(113\) 10.9460i 1.02971i −0.857277 0.514855i \(-0.827846\pi\)
0.857277 0.514855i \(-0.172154\pi\)
\(114\) 12.7206 + 2.18873i 1.19140 + 0.204994i
\(115\) −1.71990 1.71990i −0.160382 0.160382i
\(116\) 1.81091 0.168139
\(117\) −0.106302 10.8161i −0.00982762 0.999952i
\(118\) −18.5849 −1.71088
\(119\) −0.729706 0.729706i −0.0668920 0.0668920i
\(120\) 3.90895 4.69787i 0.356837 0.428855i
\(121\) 0.441540i 0.0401400i
\(122\) 1.06529 3.97571i 0.0964467 0.359944i
\(123\) 5.70868 + 8.08143i 0.514734 + 0.728678i
\(124\) −0.190164 + 0.709702i −0.0170772 + 0.0637331i
\(125\) −7.78561 + 7.78561i −0.696366 + 0.696366i
\(126\) 1.77092 4.99382i 0.157766 0.444885i
\(127\) 4.95500 2.86077i 0.439685 0.253853i −0.263779 0.964583i \(-0.584969\pi\)
0.703464 + 0.710731i \(0.251636\pi\)
\(128\) 7.94543 7.94543i 0.702284 0.702284i
\(129\) −13.7003 11.3996i −1.20624 1.00368i
\(130\) 2.48659 14.2310i 0.218088 1.24814i
\(131\) 15.4112 8.89768i 1.34649 0.777394i 0.358736 0.933439i \(-0.383208\pi\)
0.987750 + 0.156045i \(0.0498745\pi\)
\(132\) −2.63881 + 5.72066i −0.229679 + 0.497920i
\(133\) −4.21939 −0.365868
\(134\) −10.2917 + 17.8258i −0.889068 + 1.53991i
\(135\) −8.23123 + 8.43827i −0.708431 + 0.726250i
\(136\) 0.415416 + 1.55036i 0.0356217 + 0.132942i
\(137\) −11.3607 3.04410i −0.970614 0.260075i −0.261527 0.965196i \(-0.584226\pi\)
−0.709087 + 0.705121i \(0.750893\pi\)
\(138\) 1.89235 + 2.67888i 0.161088 + 0.228042i
\(139\) 14.4548 1.22604 0.613019 0.790068i \(-0.289955\pi\)
0.613019 + 0.790068i \(0.289955\pi\)
\(140\) 1.26971 2.19920i 0.107310 0.185867i
\(141\) −4.79128 + 3.38453i −0.403498 + 0.285029i
\(142\) 10.7100 + 6.18342i 0.898763 + 0.518901i
\(143\) −1.03917 11.6696i −0.0868995 0.975863i
\(144\) −11.3779 + 9.70887i −0.948160 + 0.809073i
\(145\) 3.54506 + 0.949896i 0.294401 + 0.0788846i
\(146\) 13.1509i 1.08838i
\(147\) −0.293704 + 1.70697i −0.0242243 + 0.140788i
\(148\) −9.48734 2.54212i −0.779854 0.208961i
\(149\) −3.21647 3.21647i −0.263503 0.263503i 0.562972 0.826476i \(-0.309658\pi\)
−0.826476 + 0.562972i \(0.809658\pi\)
\(150\) −0.366226 + 0.258700i −0.0299022 + 0.0211228i
\(151\) 0.446291 0.119583i 0.0363187 0.00973156i −0.240614 0.970621i \(-0.577349\pi\)
0.276933 + 0.960889i \(0.410682\pi\)
\(152\) 5.68336 + 3.28129i 0.460981 + 0.266148i
\(153\) −0.562818 3.04429i −0.0455012 0.246116i
\(154\) 1.48536 5.54342i 0.119693 0.446702i
\(155\) −0.744536 + 1.28957i −0.0598026 + 0.103581i
\(156\) −2.35349 + 6.58241i −0.188430 + 0.527015i
\(157\) 0.333940 + 0.578401i 0.0266513 + 0.0461615i 0.879043 0.476742i \(-0.158182\pi\)
−0.852392 + 0.522903i \(0.824849\pi\)
\(158\) 10.9322 2.92928i 0.869720 0.233041i
\(159\) −8.04676 + 2.96656i −0.638150 + 0.235264i
\(160\) −11.1889 + 6.45989i −0.884557 + 0.510699i
\(161\) −0.758131 0.758131i −0.0597491 0.0597491i
\(162\) 12.8681 9.33168i 1.01102 0.733166i
\(163\) 3.61581 0.968854i 0.283212 0.0758865i −0.114416 0.993433i \(-0.536500\pi\)
0.397629 + 0.917546i \(0.369833\pi\)
\(164\) −1.65500 6.17656i −0.129234 0.482308i
\(165\) −8.16650 + 9.81468i −0.635761 + 0.764072i
\(166\) −23.0319 13.2975i −1.78762 1.03209i
\(167\) 5.39182 + 20.1225i 0.417232 + 1.55713i 0.780323 + 0.625376i \(0.215054\pi\)
−0.363092 + 0.931753i \(0.618279\pi\)
\(168\) 1.72306 2.07082i 0.132937 0.159767i
\(169\) −2.29706 12.7954i −0.176697 0.984265i
\(170\) 4.13481i 0.317126i
\(171\) −10.4287 7.17433i −0.797505 0.548635i
\(172\) 5.75915 + 9.97513i 0.439131 + 0.760597i
\(173\) 0.810815 + 1.40437i 0.0616451 + 0.106772i 0.895201 0.445663i \(-0.147032\pi\)
−0.833556 + 0.552435i \(0.813699\pi\)
\(174\) −4.49392 2.07294i −0.340683 0.157149i
\(175\) 0.103643 0.103643i 0.00783466 0.00783466i
\(176\) −11.4555 + 11.4555i −0.863494 + 0.863494i
\(177\) 16.5499 + 7.63412i 1.24397 + 0.573815i
\(178\) −6.74070 11.6752i −0.505237 0.875096i
\(179\) 5.63634 + 9.76243i 0.421280 + 0.729678i 0.996065 0.0886263i \(-0.0282477\pi\)
−0.574785 + 0.818304i \(0.694914\pi\)
\(180\) 6.87760 3.27667i 0.512626 0.244229i
\(181\) 17.8891i 1.32968i −0.746984 0.664842i \(-0.768499\pi\)
0.746984 0.664842i \(-0.231501\pi\)
\(182\) 1.09609 6.27300i 0.0812474 0.464985i
\(183\) −2.58175 + 3.10280i −0.190848 + 0.229366i
\(184\) 0.431599 + 1.61075i 0.0318179 + 0.118746i
\(185\) −17.2391 9.95300i −1.26744 0.731759i
\(186\) 1.28430 1.54350i 0.0941695 0.113175i
\(187\) −0.867879 3.23897i −0.0634656 0.236857i
\(188\) 3.66193 0.981211i 0.267074 0.0715622i
\(189\) −3.62832 + 3.71958i −0.263921 + 0.270560i
\(190\) −11.9544 11.9544i −0.867263 0.867263i
\(191\) −6.53696 + 3.77411i −0.472998 + 0.273085i −0.717494 0.696565i \(-0.754711\pi\)
0.244496 + 0.969650i \(0.421377\pi\)
\(192\) 0.141267 0.0520802i 0.0101951 0.00375857i
\(193\) −3.73171 + 0.999908i −0.268614 + 0.0719749i −0.390612 0.920555i \(-0.627737\pi\)
0.121998 + 0.992530i \(0.461070\pi\)
\(194\) 12.4737 + 21.6050i 0.895557 + 1.55115i
\(195\) −8.05997 + 11.6513i −0.577186 + 0.834368i
\(196\) 0.559688 0.969407i 0.0399777 0.0692434i
\(197\) −4.31176 + 16.0917i −0.307200 + 1.14649i 0.623835 + 0.781556i \(0.285574\pi\)
−0.931035 + 0.364930i \(0.881093\pi\)
\(198\) 13.0968 11.1756i 0.930752 0.794218i
\(199\) −3.50190 2.02182i −0.248243 0.143323i 0.370717 0.928746i \(-0.379112\pi\)
−0.618959 + 0.785423i \(0.712445\pi\)
\(200\) −0.220203 + 0.0590031i −0.0155707 + 0.00417215i
\(201\) 16.4871 11.6464i 1.16291 0.821474i
\(202\) 15.9981 + 15.9981i 1.12562 + 1.12562i
\(203\) 1.56266 + 0.418714i 0.109677 + 0.0293879i
\(204\) −0.339272 + 1.97180i −0.0237538 + 0.138054i
\(205\) 12.9594i 0.905127i
\(206\) −14.0710 3.77030i −0.980371 0.262690i
\(207\) −0.584743 3.16288i −0.0406424 0.219835i
\(208\) −11.5337 + 13.7886i −0.799715 + 0.956066i
\(209\) −11.8736 6.85520i −0.821311 0.474184i
\(210\) −5.66831 + 4.00407i −0.391151 + 0.276307i
\(211\) −10.8715 + 18.8299i −0.748423 + 1.29631i 0.200156 + 0.979764i \(0.435855\pi\)
−0.948579 + 0.316542i \(0.897478\pi\)
\(212\) 5.54254 0.380663
\(213\) −6.99734 9.90571i −0.479450 0.678728i
\(214\) 24.4805 + 6.55953i 1.67345 + 0.448400i
\(215\) 6.04182 + 22.5484i 0.412049 + 1.53779i
\(216\) 7.77981 2.18850i 0.529349 0.148909i
\(217\) −0.328191 + 0.568443i −0.0222790 + 0.0385884i
\(218\) 34.1887 2.31555
\(219\) −5.40201 + 11.7110i −0.365034 + 0.791354i
\(220\) 7.14604 4.12577i 0.481786 0.278159i
\(221\) −1.27799 3.49442i −0.0859672 0.235060i
\(222\) 20.6336 + 17.1686i 1.38484 + 1.15228i
\(223\) 7.47418 7.47418i 0.500508 0.500508i −0.411088 0.911596i \(-0.634851\pi\)
0.911596 + 0.411088i \(0.134851\pi\)
\(224\) −4.93204 + 2.84752i −0.329536 + 0.190258i
\(225\) 0.432392 0.0799392i 0.0288261 0.00532928i
\(226\) 13.6701 13.6701i 0.909324 0.909324i
\(227\) 5.85035 21.8338i 0.388301 1.44916i −0.444595 0.895732i \(-0.646652\pi\)
0.832896 0.553429i \(-0.186681\pi\)
\(228\) 4.71991 + 6.68169i 0.312584 + 0.442506i
\(229\) −0.565081 + 2.10891i −0.0373416 + 0.139361i −0.982080 0.188464i \(-0.939649\pi\)
0.944738 + 0.327825i \(0.106316\pi\)
\(230\) 4.29588i 0.283262i
\(231\) −3.59979 + 4.32631i −0.236849 + 0.284650i
\(232\) −1.77922 1.77922i −0.116812 0.116812i
\(233\) 3.72319 0.243914 0.121957 0.992535i \(-0.461083\pi\)
0.121957 + 0.992535i \(0.461083\pi\)
\(234\) 13.3752 13.6407i 0.874366 0.891724i
\(235\) 7.68333 0.501205
\(236\) −8.32889 8.32889i −0.542165 0.542165i
\(237\) −10.9384 1.88209i −0.710528 0.122255i
\(238\) 1.82262i 0.118143i
\(239\) −3.65470 + 13.6395i −0.236403 + 0.882268i 0.741109 + 0.671385i \(0.234300\pi\)
−0.977511 + 0.210882i \(0.932366\pi\)
\(240\) 19.5089 1.78822i 1.25930 0.115429i
\(241\) 5.71740 21.3376i 0.368290 1.37448i −0.494616 0.869112i \(-0.664691\pi\)
0.862906 0.505365i \(-0.168642\pi\)
\(242\) −0.551428 + 0.551428i −0.0354471 + 0.0354471i
\(243\) −15.2923 + 3.02407i −0.981003 + 0.193994i
\(244\) 2.25914 1.30432i 0.144627 0.0835003i
\(245\) 1.60415 1.60415i 0.102485 0.102485i
\(246\) −2.96326 + 17.2221i −0.188931 + 1.09804i
\(247\) −13.7978 6.40804i −0.877933 0.407734i
\(248\) 0.884121 0.510448i 0.0561418 0.0324135i
\(249\) 15.0478 + 21.3023i 0.953618 + 1.34998i
\(250\) −19.4465 −1.22990
\(251\) −4.72679 + 8.18704i −0.298352 + 0.516762i −0.975759 0.218847i \(-0.929770\pi\)
0.677407 + 0.735609i \(0.263104\pi\)
\(252\) 3.03164 1.44436i 0.190975 0.0909858i
\(253\) −0.901688 3.36514i −0.0566886 0.211565i
\(254\) 9.76092 + 2.61543i 0.612455 + 0.164107i
\(255\) −1.69846 + 3.68207i −0.106361 + 0.230580i
\(256\) 20.0195 1.25122
\(257\) −8.93855 + 15.4820i −0.557571 + 0.965742i 0.440127 + 0.897935i \(0.354933\pi\)
−0.997698 + 0.0678065i \(0.978400\pi\)
\(258\) −2.87328 31.3466i −0.178883 1.95155i
\(259\) −7.59898 4.38728i −0.472178 0.272612i
\(260\) 7.49203 5.26328i 0.464636 0.326415i
\(261\) 3.15035 + 3.69193i 0.195002 + 0.228525i
\(262\) 30.3588 + 8.13461i 1.87557 + 0.502558i
\(263\) 21.7847i 1.34330i 0.740866 + 0.671652i \(0.234415\pi\)
−0.740866 + 0.671652i \(0.765585\pi\)
\(264\) 8.21321 3.02793i 0.505488 0.186356i
\(265\) 10.8502 + 2.90729i 0.666520 + 0.178593i
\(266\) −5.26949 5.26949i −0.323093 0.323093i
\(267\) 1.20679 + 13.1657i 0.0738545 + 0.805730i
\(268\) −12.6009 + 3.37641i −0.769725 + 0.206247i
\(269\) 5.76509 + 3.32847i 0.351504 + 0.202941i 0.665347 0.746534i \(-0.268283\pi\)
−0.313844 + 0.949475i \(0.601617\pi\)
\(270\) −20.8181 + 0.258561i −1.26695 + 0.0157355i
\(271\) −7.45243 + 27.8128i −0.452703 + 1.68951i 0.242052 + 0.970263i \(0.422179\pi\)
−0.694755 + 0.719246i \(0.744487\pi\)
\(272\) −2.57255 + 4.45578i −0.155984 + 0.270171i
\(273\) −3.55283 + 5.13589i −0.215027 + 0.310838i
\(274\) −10.3864 17.9898i −0.627468 1.08681i
\(275\) 0.460043 0.123268i 0.0277416 0.00743335i
\(276\) −0.352488 + 2.04862i −0.0212173 + 0.123312i
\(277\) −2.17999 + 1.25862i −0.130983 + 0.0756231i −0.564060 0.825734i \(-0.690761\pi\)
0.433077 + 0.901357i \(0.357428\pi\)
\(278\) 18.0522 + 18.0522i 1.08270 + 1.08270i
\(279\) −1.77770 + 0.846944i −0.106428 + 0.0507052i
\(280\) −3.40822 + 0.913230i −0.203680 + 0.0545759i
\(281\) 3.87349 + 14.4561i 0.231073 + 0.862376i 0.979880 + 0.199588i \(0.0639603\pi\)
−0.748807 + 0.662788i \(0.769373\pi\)
\(282\) −10.2106 1.75684i −0.608030 0.104619i
\(283\) 19.6687 + 11.3558i 1.16919 + 0.675030i 0.953488 0.301431i \(-0.0974642\pi\)
0.215697 + 0.976460i \(0.430798\pi\)
\(284\) 2.02860 + 7.57085i 0.120375 + 0.449247i
\(285\) 5.73495 + 15.5560i 0.339709 + 0.921455i
\(286\) 13.2761 15.8717i 0.785033 0.938512i
\(287\) 5.71251i 0.337199i
\(288\) −17.0318 1.34810i −1.00361 0.0794373i
\(289\) 7.96753 + 13.8002i 0.468678 + 0.811774i
\(290\) 3.24104 + 5.61364i 0.190320 + 0.329644i
\(291\) −2.23317 24.3632i −0.130911 1.42819i
\(292\) 5.89364 5.89364i 0.344899 0.344899i
\(293\) 9.67365 9.67365i 0.565141 0.565141i −0.365623 0.930763i \(-0.619144\pi\)
0.930763 + 0.365623i \(0.119144\pi\)
\(294\) −2.49859 + 1.76499i −0.145721 + 0.102936i
\(295\) −11.9359 20.6736i −0.694936 1.20366i
\(296\) 6.82369 + 11.8190i 0.396619 + 0.686965i
\(297\) −16.2534 + 4.57217i −0.943119 + 0.265304i
\(298\) 8.03393i 0.465393i
\(299\) −1.32778 3.63054i −0.0767874 0.209960i
\(300\) −0.280063 0.0481880i −0.0161694 0.00278214i
\(301\) 2.66323 + 9.93931i 0.153506 + 0.572892i
\(302\) 0.706707 + 0.408017i 0.0406664 + 0.0234788i
\(303\) −7.67485 20.8179i −0.440909 1.19596i
\(304\) 5.44473 + 20.3200i 0.312277 + 1.16543i
\(305\) 5.10670 1.36834i 0.292409 0.0783507i
\(306\) 3.09905 4.50483i 0.177161 0.257524i
\(307\) 9.40258 + 9.40258i 0.536633 + 0.536633i 0.922538 0.385905i \(-0.126111\pi\)
−0.385905 + 0.922538i \(0.626111\pi\)
\(308\) 3.14997 1.81864i 0.179486 0.103626i
\(309\) 10.9815 + 9.13740i 0.624718 + 0.519809i
\(310\) −2.54035 + 0.680684i −0.144282 + 0.0386603i
\(311\) 3.11022 + 5.38706i 0.176364 + 0.305472i 0.940633 0.339426i \(-0.110233\pi\)
−0.764268 + 0.644899i \(0.776900\pi\)
\(312\) 8.77955 4.15493i 0.497044 0.235227i
\(313\) 13.1775 22.8241i 0.744838 1.29010i −0.205433 0.978671i \(-0.565860\pi\)
0.950271 0.311425i \(-0.100806\pi\)
\(314\) −0.305301 + 1.13940i −0.0172292 + 0.0643001i
\(315\) 6.69241 1.23727i 0.377074 0.0697123i
\(316\) 6.21208 + 3.58654i 0.349457 + 0.201759i
\(317\) −0.725516 + 0.194401i −0.0407490 + 0.0109187i −0.279136 0.960252i \(-0.590048\pi\)
0.238387 + 0.971170i \(0.423381\pi\)
\(318\) −13.7543 6.34453i −0.771301 0.355784i
\(319\) 3.71712 + 3.71712i 0.208119 + 0.208119i
\(320\) −0.190483 0.0510397i −0.0106483 0.00285320i
\(321\) −19.1055 15.8971i −1.06637 0.887292i
\(322\) 1.89362i 0.105527i
\(323\) −4.20588 1.12696i −0.234021 0.0627058i
\(324\) 9.94893 + 1.58488i 0.552718 + 0.0880487i
\(325\) 0.496325 0.181518i 0.0275312 0.0100688i
\(326\) 5.72567 + 3.30572i 0.317116 + 0.183087i
\(327\) −30.4452 14.0437i −1.68362 0.776618i
\(328\) −4.44244 + 7.69454i −0.245293 + 0.424860i
\(329\) 3.38681 0.186721
\(330\) −22.4562 + 2.05838i −1.23618 + 0.113310i
\(331\) 7.61419 + 2.04022i 0.418514 + 0.112140i 0.461929 0.886917i \(-0.347157\pi\)
−0.0434157 + 0.999057i \(0.513824\pi\)
\(332\) −4.36252 16.2812i −0.239425 0.893544i
\(333\) −11.3220 23.7644i −0.620442 1.30228i
\(334\) −18.3968 + 31.8642i −1.00663 + 1.74353i
\(335\) −26.4388 −1.44451
\(336\) 8.59952 0.788247i 0.469142 0.0430024i
\(337\) −3.41546 + 1.97191i −0.186052 + 0.107417i −0.590133 0.807306i \(-0.700925\pi\)
0.404081 + 0.914723i \(0.367591\pi\)
\(338\) 13.1112 18.8486i 0.713154 1.02523i
\(339\) −17.7886 + 6.55804i −0.966144 + 0.356184i
\(340\) 1.85303 1.85303i 0.100495 0.100495i
\(341\) −1.84709 + 1.06642i −0.100025 + 0.0577497i
\(342\) −4.06433 21.9840i −0.219774 1.18876i
\(343\) 0.707107 0.707107i 0.0381802 0.0381802i
\(344\) 4.14222 15.4590i 0.223334 0.833492i
\(345\) −1.76462 + 3.82551i −0.0950039 + 0.205958i
\(346\) −0.741279 + 2.76649i −0.0398514 + 0.148727i
\(347\) 6.75475i 0.362614i 0.983427 + 0.181307i \(0.0580327\pi\)
−0.983427 + 0.181307i \(0.941967\pi\)
\(348\) −1.08497 2.94296i −0.0581604 0.157759i
\(349\) 10.2639 + 10.2639i 0.549415 + 0.549415i 0.926271 0.376857i \(-0.122995\pi\)
−0.376857 + 0.926271i \(0.622995\pi\)
\(350\) 0.258874 0.0138374
\(351\) −17.5139 + 6.65301i −0.934824 + 0.355112i
\(352\) −18.5053 −0.986337
\(353\) 8.10328 + 8.10328i 0.431294 + 0.431294i 0.889069 0.457774i \(-0.151353\pi\)
−0.457774 + 0.889069i \(0.651353\pi\)
\(354\) 11.1348 + 30.2029i 0.591806 + 1.60526i
\(355\) 15.8849i 0.843082i
\(356\) 2.21143 8.25317i 0.117206 0.437417i
\(357\) −0.748678 + 1.62305i −0.0396242 + 0.0859011i
\(358\) −5.15297 + 19.2311i −0.272343 + 1.01640i
\(359\) −4.03999 + 4.03999i −0.213222 + 0.213222i −0.805635 0.592412i \(-0.798176\pi\)
0.592412 + 0.805635i \(0.298176\pi\)
\(360\) −9.97660 3.53792i −0.525813 0.186465i
\(361\) 1.03640 0.598368i 0.0545476 0.0314931i
\(362\) 22.3412 22.3412i 1.17423 1.17423i
\(363\) 0.717560 0.264540i 0.0376621 0.0138847i
\(364\) 3.30248 2.32005i 0.173097 0.121604i
\(365\) 14.6289 8.44602i 0.765713 0.442085i
\(366\) −7.09929 + 0.650733i −0.371086 + 0.0340143i
\(367\) −21.2351 −1.10846 −0.554232 0.832362i \(-0.686988\pi\)
−0.554232 + 0.832362i \(0.686988\pi\)
\(368\) −2.67276 + 4.62936i −0.139327 + 0.241322i
\(369\) 9.71312 14.1192i 0.505645 0.735014i
\(370\) −9.09943 33.9595i −0.473057 1.76547i
\(371\) 4.78274 + 1.28153i 0.248308 + 0.0665338i
\(372\) 1.26729 0.116162i 0.0657059 0.00602272i
\(373\) −25.8805 −1.34004 −0.670020 0.742343i \(-0.733714\pi\)
−0.670020 + 0.742343i \(0.733714\pi\)
\(374\) 2.96119 5.12894i 0.153120 0.265211i
\(375\) 17.3172 + 7.98803i 0.894257 + 0.412500i
\(376\) −4.56190 2.63381i −0.235262 0.135829i
\(377\) 4.47414 + 3.74246i 0.230430 + 0.192747i
\(378\) −9.17661 + 0.113974i −0.471994 + 0.00586217i
\(379\) −21.3052 5.70872i −1.09438 0.293237i −0.333904 0.942607i \(-0.608366\pi\)
−0.760473 + 0.649370i \(0.775033\pi\)
\(380\) 10.7148i 0.549658i
\(381\) −7.61781 6.33855i −0.390272 0.324734i
\(382\) −12.8772 3.45045i −0.658857 0.176540i
\(383\) −3.72865 3.72865i −0.190525 0.190525i 0.605398 0.795923i \(-0.293014\pi\)
−0.795923 + 0.605398i \(0.793014\pi\)
\(384\) −17.6727 8.15201i −0.901856 0.416006i
\(385\) 7.12038 1.90790i 0.362888 0.0972356i
\(386\) −5.90919 3.41167i −0.300770 0.173650i
\(387\) −10.3176 + 29.0945i −0.524471 + 1.47896i
\(388\) −4.09225 + 15.2725i −0.207752 + 0.775343i
\(389\) −9.65022 + 16.7147i −0.489286 + 0.847468i −0.999924 0.0123280i \(-0.996076\pi\)
0.510638 + 0.859796i \(0.329409\pi\)
\(390\) −24.6169 + 4.48515i −1.24653 + 0.227114i
\(391\) −0.553213 0.958193i −0.0279772 0.0484579i
\(392\) −1.50234 + 0.402551i −0.0758797 + 0.0203319i
\(393\) −23.6932 19.7144i −1.19516 0.994459i
\(394\) −25.4813 + 14.7117i −1.28373 + 0.741163i
\(395\) 10.2796 + 10.2796i 0.517221 + 0.517221i
\(396\) 10.8778 + 0.860995i 0.546630 + 0.0432666i
\(397\) 9.44277 2.53018i 0.473919 0.126986i −0.0139507 0.999903i \(-0.504441\pi\)
0.487870 + 0.872916i \(0.337774\pi\)
\(398\) −1.84843 6.89843i −0.0926534 0.345787i
\(399\) 2.52796 + 6.85706i 0.126556 + 0.343282i
\(400\) −0.632871 0.365388i −0.0316436 0.0182694i
\(401\) −8.56014 31.9469i −0.427473 1.59535i −0.758463 0.651716i \(-0.774049\pi\)
0.330990 0.943634i \(-0.392617\pi\)
\(402\) 35.1352 + 6.04542i 1.75238 + 0.301518i
\(403\) −1.93652 + 1.36044i −0.0964647 + 0.0677681i
\(404\) 14.3392i 0.713402i
\(405\) 18.6448 + 8.32120i 0.926470 + 0.413484i
\(406\) 1.42865 + 2.47449i 0.0709025 + 0.122807i
\(407\) −14.2559 24.6920i −0.706640 1.22394i
\(408\) 2.27064 1.60397i 0.112413 0.0794083i
\(409\) 12.4592 12.4592i 0.616070 0.616070i −0.328451 0.944521i \(-0.606527\pi\)
0.944521 + 0.328451i \(0.106527\pi\)
\(410\) 16.1847 16.1847i 0.799306 0.799306i
\(411\) 1.85949 + 20.2865i 0.0917220 + 1.00066i
\(412\) −4.61628 7.99563i −0.227428 0.393916i
\(413\) −5.26134 9.11291i −0.258894 0.448417i
\(414\) 3.21977 4.68031i 0.158243 0.230025i
\(415\) 34.1605i 1.67688i
\(416\) −20.4528 + 1.82130i −1.00278 + 0.0892966i
\(417\) −8.66027 23.4909i −0.424095 1.15035i
\(418\) −6.26730 23.3899i −0.306543 1.14404i
\(419\) 4.02077 + 2.32140i 0.196428 + 0.113408i 0.594988 0.803734i \(-0.297157\pi\)
−0.398560 + 0.917142i \(0.630490\pi\)
\(420\) −4.33471 0.745837i −0.211512 0.0363931i
\(421\) −0.405001 1.51148i −0.0197385 0.0736652i 0.955354 0.295463i \(-0.0954740\pi\)
−0.975093 + 0.221798i \(0.928807\pi\)
\(422\) −37.0933 + 9.93913i −1.80567 + 0.483829i
\(423\) 8.37090 + 5.75867i 0.407007 + 0.279996i
\(424\) −5.44557 5.44557i −0.264460 0.264460i
\(425\) 0.130993 0.0756288i 0.00635409 0.00366853i
\(426\) 3.63218 21.1098i 0.175980 1.02277i
\(427\) 2.25103 0.603161i 0.108935 0.0291890i
\(428\) 8.03135 + 13.9107i 0.388210 + 0.672399i
\(429\) −18.3420 + 8.68039i −0.885562 + 0.419093i
\(430\) −20.6146 + 35.7056i −0.994125 + 1.72187i
\(431\) 2.75336 10.2757i 0.132625 0.494962i −0.867372 0.497661i \(-0.834192\pi\)
0.999996 + 0.00269899i \(0.000859118\pi\)
\(432\) 22.5950 + 12.6737i 1.08710 + 0.609765i
\(433\) −0.273654 0.157994i −0.0131510 0.00759272i 0.493410 0.869797i \(-0.335750\pi\)
−0.506561 + 0.862204i \(0.669084\pi\)
\(434\) −1.11978 + 0.300045i −0.0537513 + 0.0144026i
\(435\) −0.580245 6.33029i −0.0278206 0.303514i
\(436\) 15.3218 + 15.3218i 0.733781 + 0.733781i
\(437\) −4.36972 1.17086i −0.209032 0.0560099i
\(438\) −21.3720 + 7.87911i −1.02119 + 0.376478i
\(439\) 13.8621i 0.661603i 0.943700 + 0.330802i \(0.107319\pi\)
−0.943700 + 0.330802i \(0.892681\pi\)
\(440\) −11.0746 2.96743i −0.527961 0.141467i
\(441\) 2.95001 0.545388i 0.140477 0.0259708i
\(442\) 2.76804 5.96015i 0.131662 0.283495i
\(443\) −16.2619 9.38880i −0.772625 0.446075i 0.0611850 0.998126i \(-0.480512\pi\)
−0.833810 + 0.552051i \(0.813845\pi\)
\(444\) 1.55286 + 16.9412i 0.0736955 + 0.803994i
\(445\) 8.65825 14.9965i 0.410440 0.710904i
\(446\) 18.6686 0.883986
\(447\) −3.30009 + 7.15425i −0.156089 + 0.338385i
\(448\) −0.0839646 0.0224983i −0.00396696 0.00106294i
\(449\) −3.97429 14.8322i −0.187558 0.699977i −0.994068 0.108757i \(-0.965313\pi\)
0.806510 0.591220i \(-0.201354\pi\)
\(450\) 0.639837 + 0.440169i 0.0301622 + 0.0207498i
\(451\) 9.28106 16.0753i 0.437028 0.756955i
\(452\) 12.2526 0.576316
\(453\) −0.461725 0.653635i −0.0216937 0.0307105i
\(454\) 34.5740 19.9613i 1.62264 0.936832i
\(455\) 7.68195 2.80948i 0.360135 0.131710i
\(456\) 1.92745 11.2021i 0.0902612 0.524587i
\(457\) −7.54839 + 7.54839i −0.353099 + 0.353099i −0.861261 0.508162i \(-0.830325\pi\)
0.508162 + 0.861261i \(0.330325\pi\)
\(458\) −3.33948 + 1.92805i −0.156044 + 0.0900919i
\(459\) −4.61016 + 2.73858i −0.215184 + 0.127826i
\(460\) 1.92522 1.92522i 0.0897636 0.0897636i
\(461\) −7.95467 + 29.6872i −0.370486 + 1.38267i 0.489343 + 0.872091i \(0.337237\pi\)
−0.859829 + 0.510582i \(0.829430\pi\)
\(462\) −9.89869 + 0.907331i −0.460529 + 0.0422129i
\(463\) 0.858160 3.20270i 0.0398821 0.148842i −0.943114 0.332471i \(-0.892118\pi\)
0.982996 + 0.183629i \(0.0587844\pi\)
\(464\) 8.06587i 0.374449i
\(465\) 2.54180 + 0.437346i 0.117873 + 0.0202814i
\(466\) 4.64980 + 4.64980i 0.215398 + 0.215398i
\(467\) 22.1783 1.02629 0.513145 0.858302i \(-0.328480\pi\)
0.513145 + 0.858302i \(0.328480\pi\)
\(468\) 12.1073 0.118992i 0.559661 0.00550040i
\(469\) −11.6542 −0.538142
\(470\) 9.59552 + 9.59552i 0.442608 + 0.442608i
\(471\) 0.739904 0.889233i 0.0340930 0.0409737i
\(472\) 16.3663i 0.753321i
\(473\) −8.65384 + 32.2966i −0.397904 + 1.48500i
\(474\) −11.3103 16.0112i −0.519497 0.735420i
\(475\) 0.160066 0.597376i 0.00734435 0.0274095i
\(476\) 0.816815 0.816815i 0.0374386 0.0374386i
\(477\) 9.64210 + 11.2997i 0.441481 + 0.517376i
\(478\) −21.5983 + 12.4698i −0.987884 + 0.570355i
\(479\) 19.2594 19.2594i 0.879983 0.879983i −0.113549 0.993532i \(-0.536222\pi\)
0.993532 + 0.113549i \(0.0362220\pi\)
\(480\) 17.2017 + 14.3130i 0.785148 + 0.653298i
\(481\) −18.1864 25.8875i −0.829228 1.18037i
\(482\) 33.7883 19.5077i 1.53902 0.888551i
\(483\) −0.777843 + 1.68628i −0.0353931 + 0.0767284i
\(484\) −0.494249 −0.0224659
\(485\) −16.0221 + 27.7511i −0.727526 + 1.26011i
\(486\) −22.8749 15.3215i −1.03763 0.694998i
\(487\) 9.90918 + 36.9816i 0.449028 + 1.67579i 0.705077 + 0.709131i \(0.250913\pi\)
−0.256049 + 0.966664i \(0.582421\pi\)
\(488\) −3.50111 0.938120i −0.158488 0.0424667i
\(489\) −3.74085 5.29569i −0.169167 0.239480i
\(490\) 4.00676 0.181007
\(491\) 16.5522 28.6692i 0.746989 1.29382i −0.202271 0.979330i \(-0.564832\pi\)
0.949260 0.314493i \(-0.101835\pi\)
\(492\) −9.04615 + 6.39015i −0.407832 + 0.288090i
\(493\) 1.44582 + 0.834745i 0.0651165 + 0.0375950i
\(494\) −9.22890 25.2346i −0.415228 1.13536i
\(495\) 20.8429 + 7.39135i 0.936819 + 0.332216i
\(496\) 3.16105 + 0.847000i 0.141935 + 0.0380314i
\(497\) 7.00205i 0.314085i
\(498\) −7.81104 + 45.3968i −0.350021 + 2.03428i
\(499\) 15.1275 + 4.05341i 0.677201 + 0.181456i 0.580997 0.813906i \(-0.302663\pi\)
0.0962048 + 0.995362i \(0.469330\pi\)
\(500\) −8.71502 8.71502i −0.389747 0.389747i
\(501\) 29.4713 20.8184i 1.31668 0.930098i
\(502\) −16.1278 + 4.32142i −0.719817 + 0.192874i
\(503\) −15.3477 8.86102i −0.684322 0.395093i 0.117160 0.993113i \(-0.462621\pi\)
−0.801481 + 0.598020i \(0.795954\pi\)
\(504\) −4.39768 1.55951i −0.195888 0.0694662i
\(505\) −7.52151 + 28.0706i −0.334703 + 1.24913i
\(506\) 3.07655 5.32874i 0.136769 0.236891i
\(507\) −19.4180 + 11.3991i −0.862385 + 0.506254i
\(508\) 3.20228 + 5.54651i 0.142078 + 0.246087i
\(509\) −11.0562 + 2.96251i −0.490059 + 0.131311i −0.495382 0.868675i \(-0.664972\pi\)
0.00532371 + 0.999986i \(0.498305\pi\)
\(510\) −6.71960 + 2.47729i −0.297549 + 0.109696i
\(511\) 6.44842 3.72300i 0.285261 0.164696i
\(512\) 9.11104 + 9.11104i 0.402655 + 0.402655i
\(513\) −5.41106 + 21.2464i −0.238904 + 0.938050i
\(514\) −30.4982 + 8.17198i −1.34522 + 0.360450i
\(515\) −4.84286 18.0738i −0.213402 0.796426i
\(516\) 12.7604 15.3357i 0.561746 0.675119i
\(517\) 9.53063 + 5.50251i 0.419156 + 0.242000i
\(518\) −4.01102 14.9693i −0.176234 0.657715i
\(519\) 1.79650 2.15908i 0.0788577 0.0947730i
\(520\) −12.5321 2.18975i −0.549570 0.0960270i
\(521\) 40.6317i 1.78011i −0.455854 0.890055i \(-0.650666\pi\)
0.455854 0.890055i \(-0.349334\pi\)
\(522\) −0.676362 + 8.54515i −0.0296036 + 0.374011i
\(523\) −5.00835 8.67472i −0.219000 0.379319i 0.735503 0.677522i \(-0.236946\pi\)
−0.954503 + 0.298203i \(0.903613\pi\)
\(524\) 9.95984 + 17.2510i 0.435098 + 0.753611i
\(525\) −0.230528 0.106338i −0.0100611 0.00464095i
\(526\) −27.2064 + 27.2064i −1.18626 + 1.18626i
\(527\) −0.478966 + 0.478966i −0.0208641 + 0.0208641i
\(528\) 25.4801 + 11.7534i 1.10888 + 0.511501i
\(529\) 10.9252 + 18.9231i 0.475010 + 0.822742i
\(530\) 9.91965 + 17.1813i 0.430882 + 0.746309i
\(531\) 2.49087 31.4696i 0.108095 1.36567i
\(532\) 4.72308i 0.204772i
\(533\) 8.67566 18.6805i 0.375784 0.809141i
\(534\) −14.9352 + 17.9495i −0.646310 + 0.776750i
\(535\) 8.42554 + 31.4446i 0.364268 + 1.35947i
\(536\) 15.6978 + 9.06313i 0.678042 + 0.391468i
\(537\) 12.4883 15.0087i 0.538910 0.647675i
\(538\) 3.04302 + 11.3567i 0.131194 + 0.489623i
\(539\) 3.13866 0.841001i 0.135192 0.0362245i
\(540\) −9.44559 9.21384i −0.406473 0.396500i
\(541\) 23.4033 + 23.4033i 1.00619 + 1.00619i 0.999981 + 0.00620765i \(0.00197597\pi\)
0.00620765 + 0.999981i \(0.498024\pi\)
\(542\) −44.0419 + 25.4276i −1.89176 + 1.09221i
\(543\) −29.0721 + 10.7179i −1.24760 + 0.459948i
\(544\) −5.67679 + 1.52109i −0.243390 + 0.0652162i
\(545\) 21.9573 + 38.0311i 0.940545 + 1.62907i
\(546\) −10.8511 + 1.97705i −0.464385 + 0.0846100i
\(547\) 3.45895 5.99108i 0.147894 0.256160i −0.782555 0.622582i \(-0.786084\pi\)
0.930449 + 0.366422i \(0.119417\pi\)
\(548\) 3.40749 12.7169i 0.145561 0.543241i
\(549\) 6.58925 + 2.33669i 0.281223 + 0.0997276i
\(550\) 0.728482 + 0.420589i 0.0310626 + 0.0179340i
\(551\) 6.59348 1.76672i 0.280892 0.0752647i
\(552\) 2.35909 1.66645i 0.100410 0.0709289i
\(553\) 4.53122 + 4.53122i 0.192687 + 0.192687i
\(554\) −4.29439 1.15068i −0.182451 0.0488877i
\(555\) −5.84646 + 33.9789i −0.248168 + 1.44232i
\(556\) 16.1803i 0.686198i
\(557\) −27.7331 7.43107i −1.17509 0.314865i −0.382113 0.924116i \(-0.624803\pi\)
−0.792977 + 0.609251i \(0.791470\pi\)
\(558\) −3.27785 1.16240i −0.138763 0.0492082i
\(559\) −6.38592 + 36.5471i −0.270096 + 1.54578i
\(560\) −9.79535 5.65535i −0.413929 0.238982i
\(561\) −4.74377 + 3.35098i −0.200282 + 0.141478i
\(562\) −13.2163 + 22.8913i −0.557496 + 0.965611i
\(563\) 11.1755 0.470993 0.235496 0.971875i \(-0.424328\pi\)
0.235496 + 0.971875i \(0.424328\pi\)
\(564\) −3.78856 5.36324i −0.159527 0.225833i
\(565\) 23.9859 + 6.42701i 1.00910 + 0.270386i
\(566\) 10.3819 + 38.7457i 0.436383 + 1.62860i
\(567\) 8.21863 + 3.66798i 0.345150 + 0.154041i
\(568\) 5.44527 9.43149i 0.228479 0.395737i
\(569\) 12.2194 0.512262 0.256131 0.966642i \(-0.417552\pi\)
0.256131 + 0.966642i \(0.417552\pi\)
\(570\) −12.2652 + 26.5897i −0.513733 + 1.11372i
\(571\) 28.7181 16.5804i 1.20182 0.693869i 0.240857 0.970561i \(-0.422571\pi\)
0.960959 + 0.276692i \(0.0892381\pi\)
\(572\) 13.0627 1.16322i 0.546178 0.0486366i
\(573\) 10.0499 + 8.36222i 0.419841 + 0.349337i
\(574\) 7.13421 7.13421i 0.297776 0.297776i
\(575\) 0.136096 0.0785749i 0.00567558 0.00327680i
\(576\) −0.169274 0.198374i −0.00705309 0.00826559i
\(577\) 16.2028 16.2028i 0.674532 0.674532i −0.284225 0.958758i \(-0.591736\pi\)
0.958758 + 0.284225i \(0.0917364\pi\)
\(578\) −7.28423 + 27.1851i −0.302984 + 1.13075i
\(579\) 3.86075 + 5.46543i 0.160447 + 0.227136i
\(580\) −1.06329 + 3.96825i −0.0441507 + 0.164773i
\(581\) 15.0579i 0.624709i
\(582\) 27.6376 33.2155i 1.14562 1.37683i
\(583\) 11.3768 + 11.3768i 0.471177 + 0.471177i
\(584\) −11.5810 −0.479227
\(585\) 23.7639 + 6.11784i 0.982515 + 0.252942i
\(586\) 24.1623 0.998137
\(587\) −27.4608 27.4608i −1.13343 1.13343i −0.989603 0.143827i \(-0.954059\pi\)
−0.143827 0.989603i \(-0.545941\pi\)
\(588\) −1.91074 0.328764i −0.0787975 0.0135580i
\(589\) 2.76953i 0.114117i
\(590\) 10.9123 40.7252i 0.449252 1.67663i
\(591\) 28.7344 2.63384i 1.18197 0.108342i
\(592\) −11.3227 + 42.2570i −0.465362 + 1.73675i
\(593\) 11.7927 11.7927i 0.484267 0.484267i −0.422224 0.906491i \(-0.638751\pi\)
0.906491 + 0.422224i \(0.138751\pi\)
\(594\) −26.0086 14.5884i −1.06714 0.598570i
\(595\) 2.02746 1.17056i 0.0831178 0.0479881i
\(596\) 3.60043 3.60043i 0.147479 0.147479i
\(597\) −1.18763 + 6.90237i −0.0486065 + 0.282495i
\(598\) 2.87586 6.19232i 0.117603 0.253223i
\(599\) 22.7269 13.1214i 0.928594 0.536124i 0.0422277 0.999108i \(-0.486555\pi\)
0.886367 + 0.462984i \(0.153221\pi\)
\(600\) 0.227818 + 0.322507i 0.00930061 + 0.0131663i
\(601\) −7.73394 −0.315474 −0.157737 0.987481i \(-0.550420\pi\)
−0.157737 + 0.987481i \(0.550420\pi\)
\(602\) −9.08691 + 15.7390i −0.370355 + 0.641473i
\(603\) −28.8048 19.8160i −1.17302 0.806968i
\(604\) 0.133859 + 0.499568i 0.00544663 + 0.0203271i
\(605\) −0.967549 0.259254i −0.0393365 0.0105402i
\(606\) 16.4140 35.5839i 0.666775 1.44550i
\(607\) 1.04889 0.0425731 0.0212866 0.999773i \(-0.493224\pi\)
0.0212866 + 0.999773i \(0.493224\pi\)
\(608\) −12.0148 + 20.8102i −0.487264 + 0.843966i
\(609\) −0.255772 2.79039i −0.0103644 0.113072i
\(610\) 8.08650 + 4.66875i 0.327413 + 0.189032i
\(611\) 11.0752 + 5.14358i 0.448054 + 0.208087i
\(612\) 3.40770 0.630005i 0.137748 0.0254664i
\(613\) 41.5827 + 11.1421i 1.67951 + 0.450024i 0.967650 0.252297i \(-0.0811859\pi\)
0.711861 + 0.702320i \(0.247853\pi\)
\(614\) 23.4853i 0.947789i
\(615\) −21.0608 + 7.76438i −0.849252 + 0.313090i
\(616\) −4.88167 1.30804i −0.196688 0.0527025i
\(617\) −24.9980 24.9980i −1.00638 1.00638i −0.999980 0.00640270i \(-0.997962\pi\)
−0.00640270 0.999980i \(-0.502038\pi\)
\(618\) 2.30309 + 25.1260i 0.0926441 + 1.01072i
\(619\) 43.6389 11.6930i 1.75400 0.469982i 0.768524 0.639821i \(-0.220991\pi\)
0.985472 + 0.169839i \(0.0543247\pi\)
\(620\) −1.44352 0.833415i −0.0579730 0.0334707i
\(621\) −4.78975 + 2.84526i −0.192206 + 0.114176i
\(622\) −2.84349 + 10.6120i −0.114013 + 0.425504i
\(623\) 3.81655 6.61046i 0.152907 0.264843i
\(624\) 29.3184 + 10.4825i 1.17367 + 0.419638i
\(625\) −12.8557 22.2667i −0.514228 0.890668i
\(626\) 44.9616 12.0474i 1.79703 0.481511i
\(627\) −4.02679 + 23.4032i −0.160815 + 0.934634i
\(628\) −0.647448 + 0.373804i −0.0258360 + 0.0149164i
\(629\) −6.40284 6.40284i −0.255298 0.255298i
\(630\) 9.90317 + 6.81278i 0.394552 + 0.271428i
\(631\) −38.1044 + 10.2100i −1.51691 + 0.406455i −0.918724 0.394901i \(-0.870779\pi\)
−0.598187 + 0.801356i \(0.704112\pi\)
\(632\) −2.57959 9.62718i −0.102611 0.382948i
\(633\) 37.1145 + 6.38598i 1.47517 + 0.253820i
\(634\) −1.14886 0.663295i −0.0456271 0.0263428i
\(635\) 3.35945 + 12.5377i 0.133316 + 0.497542i
\(636\) −3.32070 9.00735i −0.131674 0.357164i
\(637\) 3.38620 1.23842i 0.134166 0.0490678i
\(638\) 9.28443i 0.367574i
\(639\) −11.9057 + 17.3064i −0.470984 + 0.684630i
\(640\) 12.7456 + 22.0761i 0.503816 + 0.872634i
\(641\) −9.61677 16.6567i −0.379840 0.657902i 0.611199 0.791477i \(-0.290688\pi\)
−0.991039 + 0.133575i \(0.957354\pi\)
\(642\) −4.00690 43.7140i −0.158140 1.72525i
\(643\) −15.6150 + 15.6150i −0.615795 + 0.615795i −0.944450 0.328655i \(-0.893405\pi\)
0.328655 + 0.944450i \(0.393405\pi\)
\(644\) 0.848634 0.848634i 0.0334409 0.0334409i
\(645\) 33.0242 23.3281i 1.30033 0.918544i
\(646\) −3.84518 6.66004i −0.151286 0.262036i
\(647\) −2.77352 4.80389i −0.109038 0.188860i 0.806343 0.591449i \(-0.201444\pi\)
−0.915381 + 0.402589i \(0.868111\pi\)
\(648\) −8.21771 11.3320i −0.322822 0.445163i
\(649\) 34.1922i 1.34216i
\(650\) 0.846541 + 0.393154i 0.0332041 + 0.0154208i
\(651\) 1.12042 + 0.192782i 0.0439128 + 0.00755571i
\(652\) 1.08451 + 4.04745i 0.0424727 + 0.158510i
\(653\) −6.42868 3.71160i −0.251574 0.145246i 0.368911 0.929465i \(-0.379731\pi\)
−0.620485 + 0.784219i \(0.713064\pi\)
\(654\) −20.4835 55.5611i −0.800966 2.17261i
\(655\) 10.4487 + 38.9951i 0.408264 + 1.52366i
\(656\) −27.5107 + 7.37147i −1.07411 + 0.287807i
\(657\) 22.2683 + 1.76257i 0.868771 + 0.0687646i
\(658\) 4.22970 + 4.22970i 0.164891 + 0.164891i
\(659\) −1.16684 + 0.673674i −0.0454536 + 0.0262426i −0.522555 0.852606i \(-0.675021\pi\)
0.477101 + 0.878848i \(0.341688\pi\)
\(660\) −10.9863 9.14137i −0.427642 0.355828i
\(661\) 37.3937 10.0196i 1.45445 0.389718i 0.556879 0.830594i \(-0.311999\pi\)
0.897568 + 0.440876i \(0.145332\pi\)
\(662\) 6.96119 + 12.0571i 0.270554 + 0.468614i
\(663\) −4.91320 + 4.17051i −0.190813 + 0.161969i
\(664\) −11.7101 + 20.2825i −0.454440 + 0.787113i
\(665\) 2.47745 9.24597i 0.0960714 0.358543i
\(666\) 15.5390 43.8185i 0.602124 1.69793i
\(667\) 1.50214 + 0.867262i 0.0581632 + 0.0335805i
\(668\) −22.5247 + 6.03547i −0.871506 + 0.233519i
\(669\) −16.6245 7.66851i −0.642741 0.296482i
\(670\) −33.0188 33.0188i −1.27563 1.27563i
\(671\) 7.31444 + 1.95990i 0.282371 + 0.0756611i
\(672\) 7.58251 + 6.30918i 0.292502 + 0.243382i
\(673\) 49.6914i 1.91546i 0.287661 + 0.957732i \(0.407122\pi\)
−0.287661 + 0.957732i \(0.592878\pi\)
\(674\) −6.72815 1.80280i −0.259159 0.0694414i
\(675\) −0.388970 0.654799i −0.0149715 0.0252032i
\(676\) 14.3229 2.57127i 0.550881 0.0988949i
\(677\) 37.1614 + 21.4552i 1.42823 + 0.824589i 0.996981 0.0776449i \(-0.0247400\pi\)
0.431248 + 0.902233i \(0.358073\pi\)
\(678\) −30.4059 14.0256i −1.16773 0.538648i
\(679\) −7.06253 + 12.2327i −0.271035 + 0.469446i
\(680\) −3.64122 −0.139634
\(681\) −38.9879 + 3.57369i −1.49402 + 0.136944i
\(682\) −3.63860 0.974960i −0.139329 0.0373332i
\(683\) −12.4932 46.6253i −0.478040 1.78407i −0.609543 0.792753i \(-0.708647\pi\)
0.131503 0.991316i \(-0.458020\pi\)
\(684\) 8.03077 11.6737i 0.307064 0.446353i
\(685\) 13.3411 23.1075i 0.509738 0.882892i
\(686\) 1.76618 0.0674329
\(687\) 3.76581 0.345180i 0.143675 0.0131695i
\(688\) 44.4297 25.6515i 1.69387 0.977954i
\(689\) 13.6937 + 11.4543i 0.521690 + 0.436375i
\(690\) −6.98136 + 2.57379i −0.265776 + 0.0979824i
\(691\) −14.9596 + 14.9596i −0.569088 + 0.569088i −0.931873 0.362785i \(-0.881826\pi\)
0.362785 + 0.931873i \(0.381826\pi\)
\(692\) −1.57202 + 0.907606i −0.0597592 + 0.0345020i
\(693\) 9.18754 + 3.25810i 0.349006 + 0.123765i
\(694\) −8.43583 + 8.43583i −0.320220 + 0.320220i
\(695\) −8.48724 + 31.6748i −0.321939 + 1.20149i
\(696\) −1.82548 + 3.95745i −0.0691948 + 0.150007i
\(697\) 1.52576 5.69422i 0.0577923 0.215684i
\(698\) 25.6367i 0.970362i
\(699\) −2.23067 6.05066i −0.0843717 0.228857i
\(700\) 0.116015 + 0.116015i 0.00438496 + 0.00438496i
\(701\) 10.0886 0.381042 0.190521 0.981683i \(-0.438982\pi\)
0.190521 + 0.981683i \(0.438982\pi\)
\(702\) −30.1815 13.5639i −1.13913 0.511937i
\(703\) −37.0233 −1.39636
\(704\) −0.199728 0.199728i −0.00752751 0.00752751i
\(705\) −4.60331 12.4864i −0.173371 0.470265i
\(706\) 20.2400i 0.761741i
\(707\) −3.31548 + 12.3735i −0.124691 + 0.465354i
\(708\) −8.54544 + 18.5256i −0.321157 + 0.696235i
\(709\) −0.0665553 + 0.248388i −0.00249954 + 0.00932840i −0.967164 0.254152i \(-0.918204\pi\)
0.964665 + 0.263480i \(0.0848704\pi\)
\(710\) −19.8382 + 19.8382i −0.744515 + 0.744515i
\(711\) 3.49491 + 18.9040i 0.131069 + 0.708955i
\(712\) −10.2815 + 5.93603i −0.385315 + 0.222462i
\(713\) −0.497624 + 0.497624i −0.0186362 + 0.0186362i
\(714\) −2.96200 + 1.09199i −0.110850 + 0.0408665i
\(715\) 26.1819 + 4.57479i 0.979146 + 0.171087i
\(716\) −10.9278 + 6.30918i −0.408392 + 0.235785i
\(717\) 24.3556 2.23248i 0.909578 0.0833734i
\(718\) −10.0909 −0.376588
\(719\) −15.6336 + 27.0782i −0.583034 + 1.00984i 0.412083 + 0.911146i \(0.364801\pi\)
−0.995117 + 0.0986987i \(0.968532\pi\)
\(720\) −14.5945 30.6331i −0.543903 1.14163i
\(721\) −2.13473 7.96691i −0.0795014 0.296703i
\(722\) 2.04163 + 0.547052i 0.0759814 + 0.0203592i
\(723\) −38.1018 + 3.49248i −1.41702 + 0.129887i
\(724\) 20.0246 0.744208
\(725\) −0.118562 + 0.205355i −0.00440328 + 0.00762670i
\(726\) 1.22652 + 0.565765i 0.0455204 + 0.0209975i
\(727\) −7.95247 4.59136i −0.294941 0.170284i 0.345227 0.938519i \(-0.387802\pi\)
−0.640168 + 0.768235i \(0.721135\pi\)
\(728\) −5.52415 0.965242i −0.204739 0.0357742i
\(729\) 14.0766 + 23.0402i 0.521355 + 0.853340i
\(730\) 28.8177 + 7.72168i 1.06659 + 0.285792i
\(731\) 10.6188i 0.392750i
\(732\) −3.47320 2.88994i −0.128373 0.106815i
\(733\) −20.7831 5.56883i −0.767643 0.205689i −0.146313 0.989238i \(-0.546741\pi\)
−0.621330 + 0.783549i \(0.713407\pi\)
\(734\) −26.5200 26.5200i −0.978871 0.978871i
\(735\) −3.56804 1.64585i −0.131609 0.0607083i
\(736\) −5.89793 + 1.58035i −0.217401 + 0.0582523i
\(737\) −32.7955 18.9345i −1.20804 0.697461i
\(738\) 29.7635 5.50258i 1.09561 0.202553i
\(739\) 12.0060 44.8069i 0.441647 1.64825i −0.282994 0.959122i \(-0.591328\pi\)
0.724641 0.689127i \(-0.242006\pi\)
\(740\) 11.1411 19.2970i 0.409556 0.709373i
\(741\) −2.14722 + 26.2625i −0.0788800 + 0.964776i
\(742\) 4.37257 + 7.57352i 0.160522 + 0.278033i
\(743\) −36.3545 + 9.74116i −1.33372 + 0.357369i −0.854100 0.520109i \(-0.825891\pi\)
−0.479618 + 0.877478i \(0.659225\pi\)
\(744\) −1.35925 1.13099i −0.0498324 0.0414640i
\(745\) 8.93684 5.15968i 0.327420 0.189036i
\(746\) −32.3215 32.3215i −1.18337 1.18337i
\(747\) 25.6034 37.2175i 0.936779 1.36172i
\(748\) 3.62562 0.971483i 0.132566 0.0355209i
\(749\) 3.71397 + 13.8607i 0.135706 + 0.506460i
\(750\) 11.6510 + 31.6031i 0.425433 + 1.15398i
\(751\) 31.0725 + 17.9397i 1.13385 + 0.654629i 0.944900 0.327358i \(-0.106158\pi\)
0.188950 + 0.981987i \(0.439492\pi\)
\(752\) −4.37036 16.3104i −0.159371 0.594779i
\(753\) 16.1370 + 2.77655i 0.588064 + 0.101183i
\(754\) 0.913776 + 10.2615i 0.0332778 + 0.373702i
\(755\) 1.04818i 0.0381470i
\(756\) −4.16361 4.06145i −0.151429 0.147714i
\(757\) −9.76547 16.9143i −0.354932 0.614761i 0.632174 0.774826i \(-0.282163\pi\)
−0.987106 + 0.160066i \(0.948829\pi\)
\(758\) −19.4781 33.7370i −0.707476 1.22538i
\(759\) −4.92857 + 3.48151i −0.178896 + 0.126371i
\(760\) −10.5273 + 10.5273i −0.381867 + 0.381867i
\(761\) 15.3563 15.3563i 0.556665 0.556665i −0.371692 0.928356i \(-0.621222\pi\)
0.928356 + 0.371692i \(0.121222\pi\)
\(762\) −1.59764 17.4297i −0.0578764 0.631413i
\(763\) 9.67874 + 16.7641i 0.350394 + 0.606900i
\(764\) −4.22465 7.31731i −0.152842 0.264731i
\(765\) 7.00143 + 0.554174i 0.253137 + 0.0200362i
\(766\) 9.31323i 0.336501i
\(767\) −3.36521 37.7905i −0.121511 1.36454i
\(768\) −11.9943 32.5343i −0.432807 1.17398i
\(769\) −0.208170 0.776902i −0.00750681 0.0280158i 0.962071 0.272800i \(-0.0879496\pi\)
−0.969578 + 0.244784i \(0.921283\pi\)
\(770\) 11.2752 + 6.50973i 0.406330 + 0.234594i
\(771\) 30.5156 + 5.25057i 1.09899 + 0.189095i
\(772\) −1.11927 4.17718i −0.0402835 0.150340i
\(773\) 16.8688 4.51999i 0.606730 0.162573i 0.0576420 0.998337i \(-0.481642\pi\)
0.549088 + 0.835764i \(0.314975\pi\)
\(774\) −49.2207 + 23.4501i −1.76920 + 0.842896i
\(775\) −0.0680292 0.0680292i −0.00244368 0.00244368i
\(776\) 19.0259 10.9846i 0.682990 0.394325i
\(777\) −2.57712 + 14.9779i −0.0924535 + 0.537328i
\(778\) −32.9264 + 8.82262i −1.18047 + 0.316306i
\(779\) −12.0517 20.8741i −0.431796 0.747892i
\(780\) −13.0422 9.02213i −0.466986 0.323044i
\(781\) −11.3761 + 19.7041i −0.407071 + 0.705067i
\(782\) 0.505769 1.88756i 0.0180863 0.0674989i
\(783\) 4.11239 7.33167i 0.146965 0.262013i
\(784\) −4.31779 2.49287i −0.154207 0.0890312i
\(785\) −1.46353 + 0.392152i −0.0522356 + 0.0139965i
\(786\) −4.96904 54.2106i −0.177240 1.93363i
\(787\) −31.3406 31.3406i −1.11717 1.11717i −0.992154 0.125018i \(-0.960101\pi\)
−0.125018 0.992154i \(-0.539899\pi\)
\(788\) −18.0126 4.82647i −0.641674 0.171936i
\(789\) 35.4030 13.0519i 1.26038 0.464659i
\(790\) 25.6758i 0.913502i
\(791\) 10.5730 + 2.83302i 0.375932 + 0.100731i
\(792\) −9.84154 11.5334i −0.349704 0.409822i
\(793\) 8.27710 + 1.44627i 0.293929 + 0.0513585i
\(794\) 14.9527 + 8.63295i 0.530652 + 0.306372i
\(795\) −1.77592 19.3748i −0.0629855 0.687152i
\(796\) 2.26318 3.91994i 0.0802162 0.138938i
\(797\) −36.0844 −1.27817 −0.639087 0.769135i \(-0.720687\pi\)
−0.639087 + 0.769135i \(0.720687\pi\)
\(798\) −5.40650 + 11.7207i −0.191388 + 0.414909i
\(799\) 3.37596 + 0.904585i 0.119433 + 0.0320019i
\(800\) −0.216046 0.806295i −0.00763839 0.0285068i
\(801\) 20.6730 9.84917i 0.730444 0.348003i
\(802\) 29.2071 50.5882i 1.03134 1.78633i
\(803\) 24.1949 0.853818
\(804\) 13.0367 + 18.4552i 0.459769 + 0.650866i
\(805\) 2.10644 1.21615i 0.0742423 0.0428638i
\(806\) −4.11748 0.719452i −0.145032 0.0253416i
\(807\) 1.95517 11.3632i 0.0688252 0.400003i
\(808\) 14.0883 14.0883i 0.495625 0.495625i
\(809\) −20.7610 + 11.9864i −0.729918 + 0.421418i −0.818392 0.574660i \(-0.805134\pi\)
0.0884745 + 0.996078i \(0.471801\pi\)
\(810\) 12.8929 + 33.6772i 0.453011 + 1.18330i
\(811\) −3.86178 + 3.86178i −0.135606 + 0.135606i −0.771651 0.636046i \(-0.780569\pi\)
0.636046 + 0.771651i \(0.280569\pi\)
\(812\) −0.468698 + 1.74920i −0.0164481 + 0.0613850i
\(813\) 49.6644 4.55232i 1.74181 0.159657i
\(814\) 13.0333 48.6410i 0.456818 1.70487i
\(815\) 8.49222i 0.297470i
\(816\) 8.78251 + 1.51113i 0.307449 + 0.0529002i
\(817\) 30.7006 + 30.7006i 1.07408 + 1.07408i
\(818\) 31.1201 1.08809
\(819\) 10.4751 + 2.69674i 0.366029 + 0.0942318i
\(820\) 14.5065 0.506588
\(821\) −10.3342 10.3342i −0.360665 0.360665i 0.503393 0.864058i \(-0.332085\pi\)
−0.864058 + 0.503393i \(0.832085\pi\)
\(822\) −23.0130 + 27.6576i −0.802671 + 0.964668i
\(823\) 21.1641i 0.737733i 0.929482 + 0.368866i \(0.120254\pi\)
−0.929482 + 0.368866i \(0.879746\pi\)
\(824\) −3.32022 + 12.3912i −0.115665 + 0.431669i
\(825\) −0.475952 0.673775i −0.0165705 0.0234578i
\(826\) 4.81013 17.9516i 0.167366 0.624617i
\(827\) 36.9932 36.9932i 1.28638 1.28638i 0.349408 0.936971i \(-0.386383\pi\)
0.936971 0.349408i \(-0.113617\pi\)
\(828\) 3.54045 0.654547i 0.123039 0.0227471i
\(829\) 28.2421 16.3056i 0.980888 0.566316i 0.0783497 0.996926i \(-0.475035\pi\)
0.902538 + 0.430610i \(0.141702\pi\)
\(830\) 42.6622 42.6622i 1.48083 1.48083i
\(831\) 3.35151 + 2.78869i 0.116263 + 0.0967387i
\(832\) −0.240404 0.201089i −0.00833451 0.00697152i
\(833\) 0.893703 0.515980i 0.0309650 0.0178776i
\(834\) 18.5215 40.1527i 0.641349 1.39038i
\(835\) −47.2605 −1.63552
\(836\) 7.67354 13.2910i 0.265395 0.459678i
\(837\) 2.44147 + 2.38156i 0.0843894 + 0.0823189i
\(838\) 2.12231 + 7.92057i 0.0733140 + 0.273612i
\(839\) 12.8944 + 3.45503i 0.445163 + 0.119281i 0.474435 0.880290i \(-0.342652\pi\)
−0.0292723 + 0.999571i \(0.509319\pi\)
\(840\) 3.52608 + 4.99165i 0.121661 + 0.172228i
\(841\) 26.3828 0.909751
\(842\) 1.38186 2.39345i 0.0476220 0.0824836i
\(843\) 21.1722 14.9560i 0.729210 0.515111i
\(844\) −21.0778 12.1693i −0.725526 0.418883i
\(845\) 29.3875 + 2.47940i 1.01096 + 0.0852941i
\(846\) 3.26234 + 17.6461i 0.112162 + 0.606684i
\(847\) −0.426495 0.114279i −0.0146545 0.00392667i
\(848\) 24.6867i 0.847746i
\(849\) 6.67045 38.7678i 0.228929 1.33051i
\(850\) 0.258044 + 0.0691428i 0.00885085 + 0.00237158i
\(851\) −6.65226 6.65226i −0.228037 0.228037i
\(852\) 11.0882 7.83265i 0.379876 0.268342i
\(853\) 13.7320 3.67949i 0.470176 0.125983i −0.0159485 0.999873i \(-0.505077\pi\)
0.486125 + 0.873890i \(0.338410\pi\)
\(854\) 3.56453 + 2.05798i 0.121976 + 0.0704226i
\(855\) 21.8445 18.6401i 0.747065 0.637476i
\(856\) 5.77648 21.5581i 0.197436 0.736842i
\(857\) −2.77589 + 4.80798i −0.0948226 + 0.164238i −0.909535 0.415628i \(-0.863562\pi\)
0.814712 + 0.579866i \(0.196895\pi\)
\(858\) −33.7476 12.0662i −1.15213 0.411933i
\(859\) 4.14474 + 7.17889i 0.141417 + 0.244941i 0.928030 0.372505i \(-0.121501\pi\)
−0.786614 + 0.617445i \(0.788168\pi\)
\(860\) −25.2401 + 6.76306i −0.860680 + 0.230618i
\(861\) −9.28357 + 3.42253i −0.316383 + 0.116640i
\(862\) 16.2716 9.39443i 0.554214 0.319975i
\(863\) 3.35062 + 3.35062i 0.114056 + 0.114056i 0.761832 0.647775i \(-0.224300\pi\)
−0.647775 + 0.761832i \(0.724300\pi\)
\(864\) 8.01343 + 28.4866i 0.272623 + 0.969134i
\(865\) −3.55348 + 0.952153i −0.120822 + 0.0323742i
\(866\) −0.144445 0.539074i −0.00490842 0.0183185i
\(867\) 17.6535 21.2163i 0.599543 0.720545i
\(868\) −0.636301 0.367369i −0.0215975 0.0124693i
\(869\) 5.38923 + 20.1129i 0.182817 + 0.682283i
\(870\) 7.18109 8.63040i 0.243462 0.292598i
\(871\) −38.1104 17.6994i −1.29132 0.599721i
\(872\) 30.1074i 1.01957i
\(873\) −38.2553 + 18.2259i −1.29475 + 0.616852i
\(874\) −3.99497 6.91949i −0.135132 0.234055i
\(875\) −5.50526 9.53538i −0.186112 0.322355i
\(876\) −13.1090 6.04687i −0.442911 0.204305i
\(877\) −31.6938 + 31.6938i −1.07022 + 1.07022i −0.0728827 + 0.997341i \(0.523220\pi\)
−0.997341 + 0.0728827i \(0.976780\pi\)
\(878\) −17.3121 + 17.3121i −0.584254 + 0.584254i
\(879\) −21.5167 9.92516i −0.725740 0.334767i
\(880\) −18.3764 31.8288i −0.619467 1.07295i
\(881\) 9.64233 + 16.7010i 0.324858 + 0.562671i 0.981484 0.191546i \(-0.0613500\pi\)
−0.656625 + 0.754217i \(0.728017\pi\)
\(882\) 4.36531 + 3.00307i 0.146988 + 0.101119i
\(883\) 8.54086i 0.287423i −0.989620 0.143711i \(-0.954096\pi\)
0.989620 0.143711i \(-0.0459037\pi\)
\(884\) 3.91157 1.43056i 0.131560 0.0481148i
\(885\) −26.4461 + 31.7835i −0.888977 + 1.06839i
\(886\) −8.58361 32.0345i −0.288372 1.07622i
\(887\) −36.8058 21.2498i −1.23582 0.713500i −0.267581 0.963535i \(-0.586224\pi\)
−0.968237 + 0.250035i \(0.919558\pi\)
\(888\) 15.1191 18.1705i 0.507364 0.609761i
\(889\) 1.48084 + 5.52659i 0.0496659 + 0.185356i
\(890\) 29.5419 7.91572i 0.990245 0.265335i
\(891\) 17.1683 + 23.6746i 0.575159 + 0.793128i
\(892\) 8.36642 + 8.36642i 0.280128 + 0.280128i
\(893\) 12.3757 7.14513i 0.414138 0.239103i
\(894\) −13.0562 + 4.81336i −0.436664 + 0.160983i
\(895\) −24.7019 + 6.61885i −0.825693 + 0.221244i
\(896\) 5.61827 + 9.73113i 0.187693 + 0.325094i
\(897\) −5.10459 + 4.33298i −0.170437 + 0.144674i
\(898\) 13.5602 23.4870i 0.452511 0.783771i
\(899\) 0.274836 1.02570i 0.00916630 0.0342091i
\(900\) 0.0894819 + 0.484009i 0.00298273 + 0.0161336i
\(901\) 4.42514 + 2.55485i 0.147423 + 0.0851145i
\(902\) 31.6669 8.48511i 1.05439 0.282523i
\(903\) 14.5570 10.2830i 0.484428 0.342197i
\(904\) −12.0383 12.0383i −0.400386 0.400386i
\(905\) 39.2004 + 10.5037i 1.30307 + 0.349156i
\(906\) 0.239672 1.39294i 0.00796258 0.0462775i
\(907\) 1.58959i 0.0527815i 0.999652 + 0.0263907i \(0.00840141\pi\)
−0.999652 + 0.0263907i \(0.991599\pi\)
\(908\) 24.4402 + 6.54874i 0.811077 + 0.217328i
\(909\) −29.2336 + 24.9452i −0.969617 + 0.827382i
\(910\) 13.1025 + 6.08510i 0.434343 + 0.201719i
\(911\) 38.5549 + 22.2597i 1.27738 + 0.737497i 0.976366 0.216122i \(-0.0693409\pi\)
0.301016 + 0.953619i \(0.402674\pi\)
\(912\) 29.7606 21.0227i 0.985470 0.696131i
\(913\) 24.4645 42.3737i 0.809656 1.40237i
\(914\) −18.8540 −0.623635
\(915\) −5.28329 7.47923i −0.174660 0.247256i
\(916\) −2.36066 0.632538i −0.0779985 0.0208996i
\(917\) 4.60578 + 17.1890i 0.152096 + 0.567631i
\(918\) −9.17765 2.33738i −0.302908 0.0771450i
\(919\) −20.7586 + 35.9550i −0.684763 + 1.18604i 0.288748 + 0.957405i \(0.406761\pi\)
−0.973511 + 0.228639i \(0.926572\pi\)
\(920\) −3.78306 −0.124724
\(921\) 9.64704 20.9138i 0.317881 0.689132i
\(922\) −47.0100 + 27.1413i −1.54819 + 0.893850i
\(923\) −10.6341 + 22.8974i −0.350025 + 0.753675i
\(924\) −4.84276 4.02951i −0.159315 0.132561i
\(925\) 0.909419 0.909419i 0.0299015 0.0299015i
\(926\) 5.07150 2.92803i 0.166660 0.0962211i
\(927\) 8.27010 23.3209i 0.271626 0.765959i
\(928\) 6.51482 6.51482i 0.213859 0.213859i
\(929\) 0.807683 3.01431i 0.0264992 0.0988965i −0.951410 0.307928i \(-0.900364\pi\)
0.977909 + 0.209031i \(0.0670311\pi\)
\(930\) 2.62820 + 3.72058i 0.0861819 + 0.122002i
\(931\) 1.09206 4.07562i 0.0357908 0.133573i
\(932\) 4.16765i 0.136516i
\(933\) 6.89124 8.28205i 0.225609 0.271142i
\(934\) 27.6979 + 27.6979i 0.906304 + 0.906304i
\(935\) 7.60715 0.248781
\(936\) −12.0124 11.7786i −0.392637 0.384994i
\(937\) −56.1810 −1.83535 −0.917677 0.397327i \(-0.869938\pi\)
−0.917677 + 0.397327i \(0.869938\pi\)
\(938\) −14.5547 14.5547i −0.475227 0.475227i
\(939\) −44.9872 7.74057i −1.46810 0.252604i
\(940\) 8.60053i 0.280518i
\(941\) 1.27162 4.74576i 0.0414537 0.154707i −0.942097 0.335341i \(-0.891148\pi\)
0.983550 + 0.180634i \(0.0578150\pi\)
\(942\) 2.03459 0.186494i 0.0662904 0.00607629i
\(943\) 1.58520 5.91603i 0.0516211 0.192653i
\(944\) −37.0973 + 37.0973i −1.20741 + 1.20741i
\(945\) −6.02034 10.1347i −0.195842 0.329683i
\(946\) −51.1419 + 29.5268i −1.66277 + 0.959999i
\(947\) 3.61465 3.61465i 0.117460 0.117460i −0.645933 0.763394i \(-0.723532\pi\)
0.763394 + 0.645933i \(0.223532\pi\)
\(948\) 2.10676 12.2442i 0.0684244 0.397674i
\(949\) 26.7411 2.38127i 0.868053 0.0772992i
\(950\) 0.945950 0.546145i 0.0306907 0.0177193i
\(951\) 0.750605 + 1.06258i 0.0243400 + 0.0344567i
\(952\) −1.60505 −0.0520198
\(953\) −3.63567 + 6.29716i −0.117771 + 0.203985i −0.918884 0.394528i \(-0.870908\pi\)
0.801113 + 0.598513i \(0.204241\pi\)
\(954\) −2.07010 + 26.1536i −0.0670220 + 0.846755i
\(955\) −4.43201 16.5405i −0.143416 0.535237i
\(956\) −15.2677 4.09098i −0.493794 0.132312i
\(957\) 3.81376 8.26783i 0.123281 0.267261i
\(958\) 48.1051 1.55420
\(959\) 5.88075 10.1858i 0.189899 0.328916i
\(960\) 0.0311776 + 0.340138i 0.00100625 + 0.0109779i
\(961\) −26.4737 15.2846i −0.853989 0.493051i
\(962\) 9.61767 55.0427i 0.310086 1.77465i
\(963\) −14.3882 + 40.5734i −0.463654 + 1.30746i
\(964\) 23.8848 + 6.39991i 0.769278 + 0.206127i
\(965\) 8.76441i 0.282136i
\(966\) −3.07738 + 1.13452i −0.0990131 + 0.0365027i
\(967\) −52.3672 14.0318i −1.68402 0.451231i −0.715182 0.698938i \(-0.753656\pi\)
−0.968835 + 0.247707i \(0.920323\pi\)
\(968\) 0.485601 + 0.485601i 0.0156078 + 0.0156078i
\(969\) 0.688405 + 7.51028i 0.0221148 + 0.241265i
\(970\) −54.6672 + 14.6480i −1.75526 + 0.470320i
\(971\) 28.6894 + 16.5638i 0.920686 + 0.531558i 0.883854 0.467763i \(-0.154940\pi\)
0.0368323 + 0.999321i \(0.488273\pi\)
\(972\) −3.38507 17.1178i −0.108576 0.549055i
\(973\) −3.74117 + 13.9622i −0.119936 + 0.447609i
\(974\) −33.8100 + 58.5607i −1.08334 + 1.87640i
\(975\) −0.592353 0.697840i −0.0189705 0.0223488i
\(976\) −5.80949 10.0623i −0.185957 0.322087i
\(977\) −41.0059 + 10.9875i −1.31189 + 0.351521i −0.845935 0.533286i \(-0.820957\pi\)
−0.465958 + 0.884807i \(0.654290\pi\)
\(978\) 1.94180 11.2855i 0.0620920 0.360871i
\(979\) 21.4799 12.4014i 0.686500 0.396351i
\(980\) 1.79564 + 1.79564i 0.0573597 + 0.0573597i
\(981\) −4.58219 + 57.8914i −0.146298 + 1.84833i
\(982\) 56.4758 15.1327i 1.80222 0.482902i
\(983\) 12.4105 + 46.3165i 0.395833 + 1.47727i 0.820358 + 0.571851i \(0.193774\pi\)
−0.424525 + 0.905416i \(0.639559\pi\)
\(984\) 15.1662 + 2.60952i 0.483481 + 0.0831886i
\(985\) −32.7301 18.8967i −1.04287 0.602100i
\(986\) 0.763157 + 2.84814i 0.0243039 + 0.0907033i
\(987\) −2.02913 5.50400i −0.0645881 0.175194i
\(988\) 7.17300 15.4449i 0.228203 0.491369i
\(989\) 11.0324i 0.350811i
\(990\) 16.7993 + 35.2610i 0.533917 + 1.12067i
\(991\) 12.3552 + 21.3998i 0.392474 + 0.679786i 0.992775 0.119989i \(-0.0382858\pi\)
−0.600301 + 0.799774i \(0.704952\pi\)
\(992\) 1.86906 + 3.23730i 0.0593426 + 0.102784i
\(993\) −1.24627 13.5964i −0.0395491 0.431468i
\(994\) −8.74468 + 8.74468i −0.277364 + 0.277364i
\(995\) 6.48660 6.48660i 0.205639 0.205639i
\(996\) −23.8453 + 16.8442i −0.755566 + 0.533728i
\(997\) −29.7251 51.4853i −0.941402 1.63056i −0.762800 0.646635i \(-0.776176\pi\)
−0.178602 0.983921i \(-0.557158\pi\)
\(998\) 13.8302 + 23.9546i 0.437787 + 0.758269i
\(999\) −31.8369 + 32.6377i −1.00727 + 1.03261i
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 819.2.ew.a.470.66 yes 336
9.5 odd 6 819.2.fy.a.743.66 yes 336
13.7 odd 12 819.2.fy.a.722.66 yes 336
117.59 even 12 inner 819.2.ew.a.176.66 336
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
819.2.ew.a.176.66 336 117.59 even 12 inner
819.2.ew.a.470.66 yes 336 1.1 even 1 trivial
819.2.fy.a.722.66 yes 336 13.7 odd 12
819.2.fy.a.743.66 yes 336 9.5 odd 6