Properties

Label 91.2.w.a.24.2
Level $91$
Weight $2$
Character 91.24
Analytic conductor $0.727$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [91,2,Mod(19,91)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(91, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([10, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("91.19");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 91 = 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 91.w (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: \(0.726638658394\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(7\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 24.2
Character \(\chi\) \(=\) 91.24
Dual form 91.2.w.a.19.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.56673 + 0.419805i) q^{2} -0.513926i q^{3} +(0.546366 - 0.315445i) q^{4} +(1.47457 + 0.395109i) q^{5} +(0.215749 + 0.805186i) q^{6} +(1.27657 + 2.31741i) q^{7} +(1.57027 - 1.57027i) q^{8} +2.73588 q^{9} +O(q^{10})\) \(q+(-1.56673 + 0.419805i) q^{2} -0.513926i q^{3} +(0.546366 - 0.315445i) q^{4} +(1.47457 + 0.395109i) q^{5} +(0.215749 + 0.805186i) q^{6} +(1.27657 + 2.31741i) q^{7} +(1.57027 - 1.57027i) q^{8} +2.73588 q^{9} -2.47612 q^{10} +(-2.03695 + 2.03695i) q^{11} +(-0.162115 - 0.280792i) q^{12} +(2.94467 + 2.08061i) q^{13} +(-2.97290 - 3.09485i) q^{14} +(0.203057 - 0.757819i) q^{15} +(-2.43188 + 4.21214i) q^{16} +(-3.10787 - 5.38299i) q^{17} +(-4.28639 + 1.14854i) q^{18} +(1.63531 - 1.63531i) q^{19} +(0.930289 - 0.249270i) q^{20} +(1.19098 - 0.656063i) q^{21} +(2.33623 - 4.04647i) q^{22} +(-4.86913 - 2.81119i) q^{23} +(-0.807004 - 0.807004i) q^{24} +(-2.31189 - 1.33477i) q^{25} +(-5.48696 - 2.02357i) q^{26} -2.94782i q^{27} +(1.42849 + 0.863465i) q^{28} +(0.379237 + 0.656858i) q^{29} +1.27255i q^{30} +(2.24084 + 8.36292i) q^{31} +(0.892311 - 3.33015i) q^{32} +(1.04684 + 1.04684i) q^{33} +(7.12901 + 7.12901i) q^{34} +(0.966761 + 3.92156i) q^{35} +(1.49479 - 0.863019i) q^{36} +(-1.56036 - 5.82334i) q^{37} +(-1.87558 + 3.24860i) q^{38} +(1.06928 - 1.51334i) q^{39} +(2.93590 - 1.69504i) q^{40} +(1.94919 + 0.522283i) q^{41} +(-1.59052 + 1.52785i) q^{42} +(-2.24252 - 1.29472i) q^{43} +(-0.470375 + 1.75546i) q^{44} +(4.03424 + 1.08097i) q^{45} +(8.80878 + 2.36030i) q^{46} +(-0.571791 + 2.13395i) q^{47} +(2.16473 + 1.24981i) q^{48} +(-3.74074 + 5.91666i) q^{49} +(4.18246 + 1.12069i) q^{50} +(-2.76646 + 1.59722i) q^{51} +(2.26518 + 0.207895i) q^{52} +(2.47328 - 4.28385i) q^{53} +(1.23751 + 4.61845i) q^{54} +(-3.80843 + 2.19880i) q^{55} +(5.64352 + 1.63439i) q^{56} +(-0.840427 - 0.840427i) q^{57} +(-0.869915 - 0.869915i) q^{58} +(0.228132 - 0.851400i) q^{59} +(-0.128107 - 0.478100i) q^{60} -5.17593i q^{61} +(-7.02159 - 12.1617i) q^{62} +(3.49254 + 6.34014i) q^{63} -4.13546i q^{64} +(3.52004 + 4.23146i) q^{65} +(-2.07959 - 1.20065i) q^{66} +(-11.1026 - 11.1026i) q^{67} +(-3.39607 - 1.96072i) q^{68} +(-1.44475 + 2.50237i) q^{69} +(-3.16095 - 5.73818i) q^{70} +(-10.3040 + 2.76095i) q^{71} +(4.29607 - 4.29607i) q^{72} +(6.72052 - 1.80076i) q^{73} +(4.88933 + 8.46857i) q^{74} +(-0.685973 + 1.18814i) q^{75} +(0.377628 - 1.40933i) q^{76} +(-7.32073 - 2.12012i) q^{77} +(-1.03997 + 2.81989i) q^{78} +(-4.24764 - 7.35713i) q^{79} +(-5.25022 + 5.25022i) q^{80} +6.69268 q^{81} -3.27311 q^{82} +(1.51432 - 1.51432i) q^{83} +(0.443758 - 0.734138i) q^{84} +(-2.45590 - 9.16553i) q^{85} +(4.05696 + 1.08706i) q^{86} +(0.337576 - 0.194900i) q^{87} +6.39711i q^{88} +(-8.08103 + 2.16531i) q^{89} -6.77438 q^{90} +(-1.06254 + 9.48003i) q^{91} -3.54710 q^{92} +(4.29792 - 1.15162i) q^{93} -3.58337i q^{94} +(3.05750 - 1.76525i) q^{95} +(-1.71145 - 0.458582i) q^{96} +(0.933928 + 3.48547i) q^{97} +(3.37689 - 10.8402i) q^{98} +(-5.57284 + 5.57284i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q - 2 q^{2} - 6 q^{4} - 6 q^{5} + 12 q^{6} + 2 q^{7} - 4 q^{8} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 28 q - 2 q^{2} - 6 q^{4} - 6 q^{5} + 12 q^{6} + 2 q^{7} - 4 q^{8} - 12 q^{9} - 12 q^{10} + 2 q^{11} + 8 q^{12} - 20 q^{14} + 10 q^{15} - 2 q^{16} - 6 q^{17} - 4 q^{18} - 8 q^{19} - 36 q^{20} - 2 q^{21} - 8 q^{22} - 6 q^{23} + 12 q^{24} + 24 q^{26} - 18 q^{28} - 8 q^{29} - 38 q^{31} - 20 q^{32} + 18 q^{33} + 12 q^{34} - 2 q^{35} + 54 q^{36} - 16 q^{37} + 28 q^{39} + 48 q^{40} + 18 q^{41} - 4 q^{42} + 48 q^{43} - 6 q^{44} + 12 q^{45} + 18 q^{46} - 42 q^{47} + 12 q^{48} + 8 q^{49} + 10 q^{50} + 12 q^{51} - 28 q^{52} + 12 q^{53} - 30 q^{54} - 6 q^{55} - 24 q^{56} + 12 q^{57} + 62 q^{58} - 6 q^{59} + 16 q^{60} - 36 q^{62} - 38 q^{63} - 2 q^{65} + 66 q^{66} - 4 q^{67} + 30 q^{68} + 42 q^{69} + 68 q^{70} - 42 q^{71} - 38 q^{72} + 14 q^{73} - 6 q^{74} - 20 q^{75} + 52 q^{76} - 62 q^{78} + 4 q^{79} + 12 q^{80} + 12 q^{81} - 108 q^{82} - 66 q^{83} - 56 q^{84} - 54 q^{85} - 30 q^{86} + 42 q^{87} - 30 q^{89} - 72 q^{90} - 42 q^{91} - 156 q^{92} + 14 q^{93} - 6 q^{95} + 18 q^{96} + 62 q^{97} + 112 q^{98} - 36 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/91\mathbb{Z}\right)^\times\).

\(n\) \(15\) \(66\)
\(\chi(n)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.56673 + 0.419805i −1.10785 + 0.296847i −0.765956 0.642893i \(-0.777734\pi\)
−0.341891 + 0.939739i \(0.611068\pi\)
\(3\) 0.513926i 0.296716i −0.988934 0.148358i \(-0.952601\pi\)
0.988934 0.148358i \(-0.0473987\pi\)
\(4\) 0.546366 0.315445i 0.273183 0.157722i
\(5\) 1.47457 + 0.395109i 0.659447 + 0.176698i 0.572996 0.819558i \(-0.305781\pi\)
0.0864504 + 0.996256i \(0.472448\pi\)
\(6\) 0.215749 + 0.805186i 0.0880791 + 0.328716i
\(7\) 1.27657 + 2.31741i 0.482498 + 0.875897i
\(8\) 1.57027 1.57027i 0.555175 0.555175i
\(9\) 2.73588 0.911960
\(10\) −2.47612 −0.783019
\(11\) −2.03695 + 2.03695i −0.614162 + 0.614162i −0.944028 0.329866i \(-0.892996\pi\)
0.329866 + 0.944028i \(0.392996\pi\)
\(12\) −0.162115 0.280792i −0.0467987 0.0810577i
\(13\) 2.94467 + 2.08061i 0.816704 + 0.577057i
\(14\) −2.97290 3.09485i −0.794542 0.827132i
\(15\) 0.203057 0.757819i 0.0524291 0.195668i
\(16\) −2.43188 + 4.21214i −0.607970 + 1.05303i
\(17\) −3.10787 5.38299i −0.753769 1.30557i −0.945984 0.324213i \(-0.894900\pi\)
0.192215 0.981353i \(-0.438433\pi\)
\(18\) −4.28639 + 1.14854i −1.01031 + 0.270712i
\(19\) 1.63531 1.63531i 0.375165 0.375165i −0.494189 0.869354i \(-0.664535\pi\)
0.869354 + 0.494189i \(0.164535\pi\)
\(20\) 0.930289 0.249270i 0.208019 0.0557385i
\(21\) 1.19098 0.656063i 0.259892 0.143165i
\(22\) 2.33623 4.04647i 0.498086 0.862710i
\(23\) −4.86913 2.81119i −1.01528 0.586174i −0.102549 0.994728i \(-0.532700\pi\)
−0.912734 + 0.408554i \(0.866033\pi\)
\(24\) −0.807004 0.807004i −0.164729 0.164729i
\(25\) −2.31189 1.33477i −0.462378 0.266954i
\(26\) −5.48696 2.02357i −1.07608 0.396855i
\(27\) 2.94782i 0.567308i
\(28\) 1.42849 + 0.863465i 0.269959 + 0.163180i
\(29\) 0.379237 + 0.656858i 0.0704225 + 0.121975i 0.899087 0.437771i \(-0.144232\pi\)
−0.828664 + 0.559746i \(0.810899\pi\)
\(30\) 1.27255i 0.232334i
\(31\) 2.24084 + 8.36292i 0.402466 + 1.50202i 0.808682 + 0.588247i \(0.200182\pi\)
−0.406215 + 0.913777i \(0.633152\pi\)
\(32\) 0.892311 3.33015i 0.157740 0.588693i
\(33\) 1.04684 + 1.04684i 0.182231 + 0.182231i
\(34\) 7.12901 + 7.12901i 1.22261 + 1.22261i
\(35\) 0.966761 + 3.92156i 0.163412 + 0.662864i
\(36\) 1.49479 0.863019i 0.249132 0.143837i
\(37\) −1.56036 5.82334i −0.256521 0.957351i −0.967238 0.253872i \(-0.918296\pi\)
0.710716 0.703479i \(-0.248371\pi\)
\(38\) −1.87558 + 3.24860i −0.304259 + 0.526992i
\(39\) 1.06928 1.51334i 0.171222 0.242329i
\(40\) 2.93590 1.69504i 0.464207 0.268010i
\(41\) 1.94919 + 0.522283i 0.304412 + 0.0815669i 0.407792 0.913075i \(-0.366299\pi\)
−0.103380 + 0.994642i \(0.532966\pi\)
\(42\) −1.59052 + 1.52785i −0.245423 + 0.235753i
\(43\) −2.24252 1.29472i −0.341981 0.197443i 0.319167 0.947699i \(-0.396597\pi\)
−0.661148 + 0.750256i \(0.729930\pi\)
\(44\) −0.470375 + 1.75546i −0.0709116 + 0.264646i
\(45\) 4.03424 + 1.08097i 0.601389 + 0.161142i
\(46\) 8.80878 + 2.36030i 1.29878 + 0.348008i
\(47\) −0.571791 + 2.13395i −0.0834043 + 0.311269i −0.995007 0.0998029i \(-0.968179\pi\)
0.911603 + 0.411072i \(0.134845\pi\)
\(48\) 2.16473 + 1.24981i 0.312452 + 0.180394i
\(49\) −3.74074 + 5.91666i −0.534391 + 0.845237i
\(50\) 4.18246 + 1.12069i 0.591488 + 0.158489i
\(51\) −2.76646 + 1.59722i −0.387382 + 0.223655i
\(52\) 2.26518 + 0.207895i 0.314125 + 0.0288298i
\(53\) 2.47328 4.28385i 0.339732 0.588433i −0.644650 0.764477i \(-0.722997\pi\)
0.984382 + 0.176045i \(0.0563304\pi\)
\(54\) 1.23751 + 4.61845i 0.168404 + 0.628491i
\(55\) −3.80843 + 2.19880i −0.513529 + 0.296486i
\(56\) 5.64352 + 1.63439i 0.754147 + 0.218405i
\(57\) −0.840427 0.840427i −0.111317 0.111317i
\(58\) −0.869915 0.869915i −0.114225 0.114225i
\(59\) 0.228132 0.851400i 0.0297003 0.110843i −0.949484 0.313814i \(-0.898393\pi\)
0.979185 + 0.202971i \(0.0650598\pi\)
\(60\) −0.128107 0.478100i −0.0165385 0.0617225i
\(61\) 5.17593i 0.662710i −0.943506 0.331355i \(-0.892494\pi\)
0.943506 0.331355i \(-0.107506\pi\)
\(62\) −7.02159 12.1617i −0.891742 1.54454i
\(63\) 3.49254 + 6.34014i 0.440019 + 0.798783i
\(64\) 4.13546i 0.516933i
\(65\) 3.52004 + 4.23146i 0.436608 + 0.524849i
\(66\) −2.07959 1.20065i −0.255980 0.147790i
\(67\) −11.1026 11.1026i −1.35640 1.35640i −0.878315 0.478082i \(-0.841332\pi\)
−0.478082 0.878315i \(-0.658668\pi\)
\(68\) −3.39607 1.96072i −0.411834 0.237773i
\(69\) −1.44475 + 2.50237i −0.173927 + 0.301250i
\(70\) −3.16095 5.73818i −0.377805 0.685844i
\(71\) −10.3040 + 2.76095i −1.22286 + 0.327665i −0.811796 0.583941i \(-0.801510\pi\)
−0.411066 + 0.911606i \(0.634843\pi\)
\(72\) 4.29607 4.29607i 0.506297 0.506297i
\(73\) 6.72052 1.80076i 0.786578 0.210763i 0.156895 0.987615i \(-0.449852\pi\)
0.629683 + 0.776852i \(0.283185\pi\)
\(74\) 4.88933 + 8.46857i 0.568373 + 0.984452i
\(75\) −0.685973 + 1.18814i −0.0792094 + 0.137195i
\(76\) 0.377628 1.40933i 0.0433169 0.161661i
\(77\) −7.32073 2.12012i −0.834275 0.241611i
\(78\) −1.03997 + 2.81989i −0.117753 + 0.319290i
\(79\) −4.24764 7.35713i −0.477897 0.827742i 0.521782 0.853079i \(-0.325267\pi\)
−0.999679 + 0.0253371i \(0.991934\pi\)
\(80\) −5.25022 + 5.25022i −0.586993 + 0.586993i
\(81\) 6.69268 0.743631
\(82\) −3.27311 −0.361455
\(83\) 1.51432 1.51432i 0.166218 0.166218i −0.619096 0.785315i \(-0.712501\pi\)
0.785315 + 0.619096i \(0.212501\pi\)
\(84\) 0.443758 0.734138i 0.0484179 0.0801010i
\(85\) −2.45590 9.16553i −0.266379 0.994141i
\(86\) 4.05696 + 1.08706i 0.437473 + 0.117221i
\(87\) 0.337576 0.194900i 0.0361920 0.0208955i
\(88\) 6.39711i 0.681935i
\(89\) −8.08103 + 2.16531i −0.856588 + 0.229522i −0.660279 0.751020i \(-0.729562\pi\)
−0.196308 + 0.980542i \(0.562895\pi\)
\(90\) −6.77438 −0.714082
\(91\) −1.06254 + 9.48003i −0.111384 + 0.993777i
\(92\) −3.54710 −0.369811
\(93\) 4.29792 1.15162i 0.445674 0.119418i
\(94\) 3.58337i 0.369597i
\(95\) 3.05750 1.76525i 0.313692 0.181110i
\(96\) −1.71145 0.458582i −0.174674 0.0468038i
\(97\) 0.933928 + 3.48547i 0.0948260 + 0.353896i 0.996993 0.0774914i \(-0.0246910\pi\)
−0.902167 + 0.431387i \(0.858024\pi\)
\(98\) 3.37689 10.8402i 0.341118 1.09503i
\(99\) −5.57284 + 5.57284i −0.560091 + 0.560091i
\(100\) −1.68418 −0.168418
\(101\) 19.6895 1.95918 0.979589 0.201012i \(-0.0644231\pi\)
0.979589 + 0.201012i \(0.0644231\pi\)
\(102\) 3.66379 3.66379i 0.362769 0.362769i
\(103\) 4.70130 + 8.14290i 0.463233 + 0.802344i 0.999120 0.0419464i \(-0.0133559\pi\)
−0.535887 + 0.844290i \(0.680023\pi\)
\(104\) 7.89105 1.35681i 0.773781 0.133046i
\(105\) 2.01539 0.496844i 0.196682 0.0484870i
\(106\) −2.07659 + 7.74995i −0.201697 + 0.752742i
\(107\) −0.0359206 + 0.0622163i −0.00347258 + 0.00601468i −0.867756 0.496990i \(-0.834439\pi\)
0.864284 + 0.503004i \(0.167772\pi\)
\(108\) −0.929874 1.61059i −0.0894772 0.154979i
\(109\) −7.07523 + 1.89580i −0.677684 + 0.181585i −0.581214 0.813751i \(-0.697422\pi\)
−0.0964705 + 0.995336i \(0.530755\pi\)
\(110\) 5.04373 5.04373i 0.480901 0.480901i
\(111\) −2.99277 + 0.801910i −0.284061 + 0.0761139i
\(112\) −12.8657 0.258560i −1.21569 0.0244316i
\(113\) −8.15754 + 14.1293i −0.767396 + 1.32917i 0.171574 + 0.985171i \(0.445115\pi\)
−0.938970 + 0.343998i \(0.888219\pi\)
\(114\) 1.66954 + 0.963910i 0.156367 + 0.0902784i
\(115\) −6.06913 6.06913i −0.565949 0.565949i
\(116\) 0.414405 + 0.239257i 0.0384765 + 0.0222144i
\(117\) 8.05626 + 5.69230i 0.744801 + 0.526253i
\(118\) 1.42969i 0.131613i
\(119\) 8.50715 14.0740i 0.779849 1.29016i
\(120\) −0.871127 1.50884i −0.0795227 0.137737i
\(121\) 2.70171i 0.245610i
\(122\) 2.17288 + 8.10931i 0.196724 + 0.734182i
\(123\) 0.268415 1.00174i 0.0242022 0.0903238i
\(124\) 3.86236 + 3.86236i 0.346850 + 0.346850i
\(125\) −8.27895 8.27895i −0.740492 0.740492i
\(126\) −8.13351 8.46713i −0.724590 0.754312i
\(127\) 14.9037 8.60464i 1.32249 0.763538i 0.338362 0.941016i \(-0.390127\pi\)
0.984125 + 0.177478i \(0.0567937\pi\)
\(128\) 3.52071 + 13.1395i 0.311190 + 1.16138i
\(129\) −0.665390 + 1.15249i −0.0585843 + 0.101471i
\(130\) −7.29136 5.15184i −0.639495 0.451847i
\(131\) 4.73734 2.73511i 0.413904 0.238967i −0.278562 0.960418i \(-0.589858\pi\)
0.692466 + 0.721451i \(0.256524\pi\)
\(132\) 0.902178 + 0.241738i 0.0785245 + 0.0210406i
\(133\) 5.87725 + 1.70208i 0.509622 + 0.147589i
\(134\) 22.0557 + 12.7339i 1.90532 + 1.10004i
\(135\) 1.16471 4.34676i 0.100242 0.374110i
\(136\) −13.3330 3.57255i −1.14329 0.306344i
\(137\) 1.69468 + 0.454089i 0.144787 + 0.0387955i 0.330484 0.943811i \(-0.392788\pi\)
−0.185698 + 0.982607i \(0.559455\pi\)
\(138\) 1.21302 4.52706i 0.103259 0.385369i
\(139\) −7.13953 4.12201i −0.605567 0.349624i 0.165662 0.986183i \(-0.447024\pi\)
−0.771228 + 0.636559i \(0.780357\pi\)
\(140\) 1.76524 + 1.83765i 0.149190 + 0.155310i
\(141\) 1.09669 + 0.293858i 0.0923583 + 0.0247473i
\(142\) 14.9846 8.65135i 1.25748 0.726005i
\(143\) −10.2362 + 1.76004i −0.855995 + 0.147182i
\(144\) −6.65333 + 11.5239i −0.554444 + 0.960325i
\(145\) 0.299680 + 1.11842i 0.0248871 + 0.0928798i
\(146\) −9.77330 + 5.64262i −0.808844 + 0.466986i
\(147\) 3.04073 + 1.92246i 0.250795 + 0.158562i
\(148\) −2.68947 2.68947i −0.221073 0.221073i
\(149\) 3.14690 + 3.14690i 0.257804 + 0.257804i 0.824160 0.566356i \(-0.191647\pi\)
−0.566356 + 0.824160i \(0.691647\pi\)
\(150\) 0.575950 2.14947i 0.0470261 0.175504i
\(151\) 2.32966 + 8.69443i 0.189585 + 0.707542i 0.993602 + 0.112936i \(0.0360255\pi\)
−0.804017 + 0.594606i \(0.797308\pi\)
\(152\) 5.13575i 0.416564i
\(153\) −8.50276 14.7272i −0.687407 1.19062i
\(154\) 12.3597 + 0.248390i 0.995971 + 0.0200159i
\(155\) 13.2171i 1.06162i
\(156\) 0.106843 1.16414i 0.00855425 0.0932056i
\(157\) −4.21105 2.43125i −0.336078 0.194035i 0.322458 0.946584i \(-0.395491\pi\)
−0.658537 + 0.752549i \(0.728824\pi\)
\(158\) 9.74348 + 9.74348i 0.775150 + 0.775150i
\(159\) −2.20159 1.27109i −0.174597 0.100804i
\(160\) 2.63155 4.55797i 0.208042 0.360339i
\(161\) 0.298889 14.8724i 0.0235557 1.17211i
\(162\) −10.4856 + 2.80962i −0.823830 + 0.220744i
\(163\) −4.51748 + 4.51748i −0.353836 + 0.353836i −0.861535 0.507699i \(-0.830496\pi\)
0.507699 + 0.861535i \(0.330496\pi\)
\(164\) 1.22972 0.329503i 0.0960252 0.0257299i
\(165\) 1.13002 + 1.95725i 0.0879719 + 0.152372i
\(166\) −1.73682 + 3.00826i −0.134803 + 0.233486i
\(167\) −2.62064 + 9.78037i −0.202791 + 0.756828i 0.787320 + 0.616544i \(0.211468\pi\)
−0.990111 + 0.140283i \(0.955199\pi\)
\(168\) 0.839958 2.90035i 0.0648042 0.223767i
\(169\) 4.34213 + 12.2534i 0.334010 + 0.942569i
\(170\) 7.69547 + 13.3289i 0.590215 + 1.02228i
\(171\) 4.47400 4.47400i 0.342136 0.342136i
\(172\) −1.63365 −0.124565
\(173\) −17.6476 −1.34172 −0.670861 0.741583i \(-0.734075\pi\)
−0.670861 + 0.741583i \(0.734075\pi\)
\(174\) −0.447072 + 0.447072i −0.0338925 + 0.0338925i
\(175\) 0.141914 7.06151i 0.0107277 0.533800i
\(176\) −3.62629 13.5335i −0.273342 1.02013i
\(177\) −0.437557 0.117243i −0.0328888 0.00881253i
\(178\) 11.7518 6.78491i 0.880836 0.508551i
\(179\) 20.2232i 1.51155i 0.654831 + 0.755775i \(0.272740\pi\)
−0.654831 + 0.755775i \(0.727260\pi\)
\(180\) 2.54516 0.681974i 0.189705 0.0508313i
\(181\) 17.4649 1.29815 0.649077 0.760722i \(-0.275155\pi\)
0.649077 + 0.760722i \(0.275155\pi\)
\(182\) −2.31505 15.2987i −0.171603 1.13402i
\(183\) −2.66005 −0.196636
\(184\) −12.0602 + 3.23152i −0.889089 + 0.238231i
\(185\) 9.20342i 0.676649i
\(186\) −6.25024 + 3.60858i −0.458290 + 0.264594i
\(187\) 17.2954 + 4.63429i 1.26477 + 0.338893i
\(188\) 0.360737 + 1.34629i 0.0263094 + 0.0981882i
\(189\) 6.83129 3.76310i 0.496904 0.273725i
\(190\) −4.04922 + 4.04922i −0.293761 + 0.293761i
\(191\) 0.0415888 0.00300926 0.00150463 0.999999i \(-0.499521\pi\)
0.00150463 + 0.999999i \(0.499521\pi\)
\(192\) −2.12532 −0.153382
\(193\) 8.83196 8.83196i 0.635738 0.635738i −0.313763 0.949501i \(-0.601590\pi\)
0.949501 + 0.313763i \(0.101590\pi\)
\(194\) −2.92643 5.06873i −0.210106 0.363914i
\(195\) 2.17466 1.80904i 0.155731 0.129548i
\(196\) −0.177433 + 4.41266i −0.0126738 + 0.315190i
\(197\) 0.962573 3.59237i 0.0685805 0.255946i −0.923121 0.384510i \(-0.874370\pi\)
0.991701 + 0.128565i \(0.0410369\pi\)
\(198\) 6.39164 11.0707i 0.454234 0.786757i
\(199\) −4.38853 7.60116i −0.311095 0.538832i 0.667505 0.744606i \(-0.267362\pi\)
−0.978600 + 0.205773i \(0.934029\pi\)
\(200\) −5.72624 + 1.53434i −0.404907 + 0.108494i
\(201\) −5.70591 + 5.70591i −0.402464 + 0.402464i
\(202\) −30.8482 + 8.26575i −2.17047 + 0.581576i
\(203\) −1.03808 + 1.71737i −0.0728591 + 0.120536i
\(204\) −1.00767 + 1.74533i −0.0705508 + 0.122198i
\(205\) 2.66785 + 1.54028i 0.186331 + 0.107578i
\(206\) −10.7841 10.7841i −0.751365 0.751365i
\(207\) −13.3213 7.69108i −0.925898 0.534567i
\(208\) −15.9249 + 7.34356i −1.10419 + 0.509184i
\(209\) 6.66206i 0.460824i
\(210\) −2.94900 + 1.62449i −0.203501 + 0.112101i
\(211\) −3.33665 5.77924i −0.229704 0.397859i 0.728016 0.685560i \(-0.240443\pi\)
−0.957720 + 0.287701i \(0.907109\pi\)
\(212\) 3.12074i 0.214333i
\(213\) 1.41893 + 5.29551i 0.0972232 + 0.362842i
\(214\) 0.0301593 0.112556i 0.00206165 0.00769417i
\(215\) −2.79519 2.79519i −0.190630 0.190630i
\(216\) −4.62888 4.62888i −0.314955 0.314955i
\(217\) −16.5197 + 15.8688i −1.12143 + 1.07724i
\(218\) 10.2891 5.94043i 0.696868 0.402337i
\(219\) −0.925457 3.45385i −0.0625366 0.233390i
\(220\) −1.38720 + 2.40270i −0.0935249 + 0.161990i
\(221\) 2.04825 22.3174i 0.137780 1.50123i
\(222\) 4.35222 2.51276i 0.292102 0.168645i
\(223\) 6.10027 + 1.63456i 0.408505 + 0.109458i 0.457219 0.889354i \(-0.348846\pi\)
−0.0487142 + 0.998813i \(0.515512\pi\)
\(224\) 8.85640 2.18332i 0.591743 0.145879i
\(225\) −6.32505 3.65177i −0.421670 0.243451i
\(226\) 6.84915 25.5614i 0.455599 1.70032i
\(227\) 22.7459 + 6.09476i 1.50970 + 0.404523i 0.916336 0.400410i \(-0.131132\pi\)
0.593365 + 0.804933i \(0.297799\pi\)
\(228\) −0.724290 0.194073i −0.0479673 0.0128528i
\(229\) 4.89785 18.2790i 0.323659 1.20791i −0.591995 0.805942i \(-0.701659\pi\)
0.915653 0.401969i \(-0.131674\pi\)
\(230\) 12.0566 + 6.96086i 0.794986 + 0.458985i
\(231\) −1.08959 + 3.76232i −0.0716896 + 0.247542i
\(232\) 1.62695 + 0.435940i 0.106814 + 0.0286209i
\(233\) −6.36747 + 3.67626i −0.417147 + 0.240840i −0.693856 0.720114i \(-0.744090\pi\)
0.276709 + 0.960954i \(0.410756\pi\)
\(234\) −15.0117 5.53625i −0.981343 0.361916i
\(235\) −1.68629 + 2.92074i −0.110001 + 0.190528i
\(236\) −0.143926 0.537140i −0.00936879 0.0349648i
\(237\) −3.78102 + 2.18297i −0.245604 + 0.141799i
\(238\) −7.42012 + 25.6215i −0.480975 + 1.66079i
\(239\) −4.08646 4.08646i −0.264331 0.264331i 0.562480 0.826811i \(-0.309847\pi\)
−0.826811 + 0.562480i \(0.809847\pi\)
\(240\) 2.69823 + 2.69823i 0.174170 + 0.174170i
\(241\) −7.43847 + 27.7607i −0.479154 + 1.78823i 0.125900 + 0.992043i \(0.459818\pi\)
−0.605054 + 0.796184i \(0.706849\pi\)
\(242\) −1.13419 4.23286i −0.0729086 0.272098i
\(243\) 12.2830i 0.787955i
\(244\) −1.63272 2.82796i −0.104524 0.181041i
\(245\) −7.85370 + 7.24652i −0.501754 + 0.462963i
\(246\) 1.68214i 0.107249i
\(247\) 8.21787 1.41300i 0.522890 0.0899071i
\(248\) 16.6508 + 9.61333i 1.05732 + 0.610447i
\(249\) −0.778250 0.778250i −0.0493196 0.0493196i
\(250\) 16.4464 + 9.49536i 1.04016 + 0.600539i
\(251\) 9.72695 16.8476i 0.613960 1.06341i −0.376606 0.926373i \(-0.622909\pi\)
0.990566 0.137036i \(-0.0437576\pi\)
\(252\) 3.90817 + 2.36234i 0.246192 + 0.148813i
\(253\) 15.6444 4.19190i 0.983554 0.263543i
\(254\) −19.7378 + 19.7378i −1.23846 + 1.23846i
\(255\) −4.71041 + 1.26215i −0.294977 + 0.0790389i
\(256\) −6.89656 11.9452i −0.431035 0.746575i
\(257\) −12.6024 + 21.8280i −0.786116 + 1.36159i 0.142215 + 0.989836i \(0.454578\pi\)
−0.928330 + 0.371756i \(0.878756\pi\)
\(258\) 0.558668 2.08498i 0.0347812 0.129805i
\(259\) 11.5031 11.0499i 0.714770 0.686607i
\(260\) 3.25803 + 1.20155i 0.202054 + 0.0745170i
\(261\) 1.03755 + 1.79708i 0.0642225 + 0.111237i
\(262\) −6.27394 + 6.27394i −0.387605 + 0.387605i
\(263\) 31.2786 1.92872 0.964362 0.264587i \(-0.0852358\pi\)
0.964362 + 0.264587i \(0.0852358\pi\)
\(264\) 3.28765 0.202341
\(265\) 5.33961 5.33961i 0.328010 0.328010i
\(266\) −9.92263 0.199414i −0.608396 0.0122268i
\(267\) 1.11281 + 4.15306i 0.0681027 + 0.254163i
\(268\) −9.56834 2.56383i −0.584479 0.156611i
\(269\) 7.80980 4.50899i 0.476172 0.274918i −0.242648 0.970114i \(-0.578016\pi\)
0.718820 + 0.695196i \(0.244683\pi\)
\(270\) 7.29917i 0.444213i
\(271\) 3.29000 0.881552i 0.199853 0.0535505i −0.157504 0.987518i \(-0.550345\pi\)
0.357357 + 0.933968i \(0.383678\pi\)
\(272\) 30.2318 1.83308
\(273\) 4.87204 + 0.546067i 0.294869 + 0.0330495i
\(274\) −2.84575 −0.171918
\(275\) 7.42804 1.99034i 0.447928 0.120022i
\(276\) 1.82295i 0.109729i
\(277\) 3.48926 2.01452i 0.209649 0.121041i −0.391499 0.920178i \(-0.628043\pi\)
0.601148 + 0.799137i \(0.294710\pi\)
\(278\) 12.9162 + 3.46088i 0.774661 + 0.207570i
\(279\) 6.13066 + 22.8799i 0.367033 + 1.36979i
\(280\) 7.67599 + 4.63983i 0.458728 + 0.277283i
\(281\) −3.28511 + 3.28511i −0.195973 + 0.195973i −0.798271 0.602298i \(-0.794252\pi\)
0.602298 + 0.798271i \(0.294252\pi\)
\(282\) −1.84159 −0.109665
\(283\) 1.02966 0.0612069 0.0306035 0.999532i \(-0.490257\pi\)
0.0306035 + 0.999532i \(0.490257\pi\)
\(284\) −4.75884 + 4.75884i −0.282385 + 0.282385i
\(285\) −0.907206 1.57133i −0.0537383 0.0930774i
\(286\) 15.2985 7.05473i 0.904622 0.417155i
\(287\) 1.27793 + 5.18379i 0.0754340 + 0.305989i
\(288\) 2.44126 9.11089i 0.143852 0.536864i
\(289\) −10.8177 + 18.7368i −0.636336 + 1.10217i
\(290\) −0.939037 1.62646i −0.0551422 0.0955090i
\(291\) 1.79127 0.479970i 0.105006 0.0281364i
\(292\) 3.10383 3.10383i 0.181638 0.181638i
\(293\) −24.6989 + 6.61806i −1.44293 + 0.386631i −0.893558 0.448948i \(-0.851799\pi\)
−0.549369 + 0.835580i \(0.685132\pi\)
\(294\) −5.57107 1.73547i −0.324911 0.101215i
\(295\) 0.672792 1.16531i 0.0391715 0.0678470i
\(296\) −11.5944 6.69404i −0.673912 0.389083i
\(297\) 6.00455 + 6.00455i 0.348419 + 0.348419i
\(298\) −6.25144 3.60927i −0.362136 0.209079i
\(299\) −8.48897 18.4088i −0.490930 1.06461i
\(300\) 0.865547i 0.0499724i
\(301\) 0.137656 6.84963i 0.00793435 0.394806i
\(302\) −7.29993 12.6438i −0.420064 0.727571i
\(303\) 10.1189i 0.581318i
\(304\) 2.91127 + 10.8650i 0.166973 + 0.623151i
\(305\) 2.04506 7.63226i 0.117100 0.437022i
\(306\) 19.5041 + 19.5041i 1.11498 + 1.11498i
\(307\) 14.0195 + 14.0195i 0.800136 + 0.800136i 0.983117 0.182981i \(-0.0585745\pi\)
−0.182981 + 0.983117i \(0.558575\pi\)
\(308\) −4.66858 + 1.15092i −0.266017 + 0.0655799i
\(309\) 4.18485 2.41612i 0.238068 0.137449i
\(310\) −5.54859 20.7076i −0.315139 1.17611i
\(311\) −3.20853 + 5.55733i −0.181939 + 0.315127i −0.942541 0.334091i \(-0.891571\pi\)
0.760602 + 0.649219i \(0.224904\pi\)
\(312\) −0.697299 4.05542i −0.0394768 0.229593i
\(313\) −21.8008 + 12.5867i −1.23225 + 0.711441i −0.967499 0.252875i \(-0.918624\pi\)
−0.264753 + 0.964316i \(0.585291\pi\)
\(314\) 7.61824 + 2.04130i 0.429922 + 0.115197i
\(315\) 2.64494 + 10.7289i 0.149026 + 0.604505i
\(316\) −4.64154 2.67979i −0.261107 0.150750i
\(317\) −6.23639 + 23.2745i −0.350271 + 1.30723i 0.536062 + 0.844178i \(0.319911\pi\)
−0.886333 + 0.463049i \(0.846755\pi\)
\(318\) 3.98291 + 1.06722i 0.223350 + 0.0598465i
\(319\) −2.11047 0.565498i −0.118163 0.0316618i
\(320\) 1.63396 6.09802i 0.0913411 0.340890i
\(321\) 0.0319746 + 0.0184606i 0.00178465 + 0.00103037i
\(322\) 5.77524 + 23.4266i 0.321842 + 1.30551i
\(323\) −13.8852 3.72052i −0.772591 0.207015i
\(324\) 3.65665 2.11117i 0.203147 0.117287i
\(325\) −4.03061 8.74059i −0.223578 0.484841i
\(326\) 5.18123 8.97415i 0.286962 0.497032i
\(327\) 0.974303 + 3.63615i 0.0538791 + 0.201079i
\(328\) 3.88088 2.24063i 0.214286 0.123718i
\(329\) −5.67516 + 1.39907i −0.312882 + 0.0771332i
\(330\) −2.59210 2.59210i −0.142691 0.142691i
\(331\) −4.17975 4.17975i −0.229740 0.229740i 0.582844 0.812584i \(-0.301940\pi\)
−0.812584 + 0.582844i \(0.801940\pi\)
\(332\) 0.349690 1.30506i 0.0191917 0.0716245i
\(333\) −4.26895 15.9320i −0.233937 0.873066i
\(334\) 16.4234i 0.898648i
\(335\) −11.9848 20.7583i −0.654799 1.13414i
\(336\) −0.132881 + 6.61202i −0.00724924 + 0.360715i
\(337\) 11.5318i 0.628179i −0.949393 0.314089i \(-0.898301\pi\)
0.949393 0.314089i \(-0.101699\pi\)
\(338\) −11.9470 17.3750i −0.649831 0.945073i
\(339\) 7.26140 + 4.19237i 0.394385 + 0.227698i
\(340\) −4.23304 4.23304i −0.229569 0.229569i
\(341\) −21.5993 12.4703i −1.16967 0.675307i
\(342\) −5.13136 + 8.88778i −0.277472 + 0.480596i
\(343\) −18.4866 1.11577i −0.998184 0.0602459i
\(344\) −5.55442 + 1.48830i −0.299474 + 0.0802439i
\(345\) −3.11909 + 3.11909i −0.167926 + 0.167926i
\(346\) 27.6491 7.40855i 1.48642 0.398286i
\(347\) −4.53652 7.85749i −0.243533 0.421812i 0.718185 0.695852i \(-0.244973\pi\)
−0.961718 + 0.274040i \(0.911640\pi\)
\(348\) 0.122960 0.212973i 0.00659136 0.0114166i
\(349\) 7.77792 29.0276i 0.416342 1.55381i −0.365789 0.930698i \(-0.619201\pi\)
0.782132 0.623113i \(-0.214132\pi\)
\(350\) 2.74212 + 11.1231i 0.146572 + 0.594554i
\(351\) 6.13326 8.68035i 0.327369 0.463323i
\(352\) 4.96574 + 8.60092i 0.264675 + 0.458431i
\(353\) −20.4906 + 20.4906i −1.09060 + 1.09060i −0.0951398 + 0.995464i \(0.530330\pi\)
−0.995464 + 0.0951398i \(0.969670\pi\)
\(354\) 0.734755 0.0390518
\(355\) −16.2848 −0.864310
\(356\) −3.73217 + 3.73217i −0.197805 + 0.197805i
\(357\) −7.23298 4.37205i −0.382810 0.231393i
\(358\) −8.48978 31.6843i −0.448699 1.67457i
\(359\) −8.52708 2.28482i −0.450042 0.120588i 0.0266770 0.999644i \(-0.491507\pi\)
−0.476719 + 0.879056i \(0.658174\pi\)
\(360\) 8.03227 4.63743i 0.423338 0.244414i
\(361\) 13.6515i 0.718502i
\(362\) −27.3628 + 7.33185i −1.43816 + 0.385353i
\(363\) 1.38848 0.0728763
\(364\) 2.40989 + 5.51474i 0.126313 + 0.289051i
\(365\) 10.6214 0.555947
\(366\) 4.16759 1.11670i 0.217843 0.0583709i
\(367\) 13.2885i 0.693656i −0.937929 0.346828i \(-0.887259\pi\)
0.937929 0.346828i \(-0.112741\pi\)
\(368\) 23.6823 13.6730i 1.23452 0.712752i
\(369\) 5.33274 + 1.42890i 0.277611 + 0.0743858i
\(370\) 3.86364 + 14.4193i 0.200861 + 0.749624i
\(371\) 13.0847 + 0.262962i 0.679326 + 0.0136523i
\(372\) 1.98497 1.98497i 0.102916 0.102916i
\(373\) −8.24992 −0.427164 −0.213582 0.976925i \(-0.568513\pi\)
−0.213582 + 0.976925i \(0.568513\pi\)
\(374\) −29.0428 −1.50177
\(375\) −4.25477 + 4.25477i −0.219715 + 0.219715i
\(376\) 2.45302 + 4.24875i 0.126505 + 0.219113i
\(377\) −0.249937 + 2.72327i −0.0128724 + 0.140256i
\(378\) −9.12305 + 8.76358i −0.469239 + 0.450750i
\(379\) 0.896568 3.34604i 0.0460536 0.171874i −0.939069 0.343730i \(-0.888310\pi\)
0.985122 + 0.171855i \(0.0549762\pi\)
\(380\) 1.11368 1.92894i 0.0571303 0.0989526i
\(381\) −4.42215 7.65939i −0.226554 0.392402i
\(382\) −0.0651586 + 0.0174592i −0.00333381 + 0.000893291i
\(383\) 24.3450 24.3450i 1.24397 1.24397i 0.285631 0.958340i \(-0.407797\pi\)
0.958340 0.285631i \(-0.0922032\pi\)
\(384\) 6.75272 1.80939i 0.344598 0.0923348i
\(385\) −9.95723 6.01876i −0.507468 0.306744i
\(386\) −10.1296 + 17.5450i −0.515584 + 0.893018i
\(387\) −6.13526 3.54220i −0.311873 0.180060i
\(388\) 1.60974 + 1.60974i 0.0817221 + 0.0817221i
\(389\) 8.07601 + 4.66269i 0.409470 + 0.236408i 0.690562 0.723273i \(-0.257363\pi\)
−0.281092 + 0.959681i \(0.590697\pi\)
\(390\) −2.64767 + 3.74722i −0.134070 + 0.189748i
\(391\) 34.9473i 1.76736i
\(392\) 3.41679 + 15.1647i 0.172574 + 0.765935i
\(393\) −1.40564 2.43465i −0.0709053 0.122812i
\(394\) 6.03238i 0.303907i
\(395\) −3.35656 12.5269i −0.168887 0.630295i
\(396\) −1.28689 + 4.80273i −0.0646686 + 0.241346i
\(397\) 13.9887 + 13.9887i 0.702073 + 0.702073i 0.964855 0.262782i \(-0.0846401\pi\)
−0.262782 + 0.964855i \(0.584640\pi\)
\(398\) 10.0667 + 10.0667i 0.504596 + 0.504596i
\(399\) 0.874746 3.02048i 0.0437921 0.151213i
\(400\) 11.2445 6.49199i 0.562223 0.324600i
\(401\) 3.11669 + 11.6317i 0.155640 + 0.580857i 0.999050 + 0.0435858i \(0.0138782\pi\)
−0.843409 + 0.537271i \(0.819455\pi\)
\(402\) 6.54427 11.3350i 0.326399 0.565339i
\(403\) −10.8014 + 29.2883i −0.538058 + 1.45895i
\(404\) 10.7577 6.21095i 0.535214 0.309006i
\(405\) 9.86881 + 2.64434i 0.490385 + 0.131398i
\(406\) 0.905438 3.12645i 0.0449361 0.155163i
\(407\) 15.0402 + 8.68346i 0.745514 + 0.430423i
\(408\) −1.83603 + 6.85216i −0.0908970 + 0.339232i
\(409\) −18.8327 5.04619i −0.931215 0.249518i −0.238842 0.971058i \(-0.576768\pi\)
−0.692373 + 0.721540i \(0.743435\pi\)
\(410\) −4.82643 1.29324i −0.238360 0.0638685i
\(411\) 0.233368 0.870943i 0.0115112 0.0429605i
\(412\) 5.13727 + 2.96600i 0.253095 + 0.146125i
\(413\) 2.26427 0.558198i 0.111417 0.0274671i
\(414\) 24.0998 + 6.45751i 1.18444 + 0.317369i
\(415\) 2.83129 1.63465i 0.138983 0.0802417i
\(416\) 9.55630 7.94963i 0.468536 0.389763i
\(417\) −2.11841 + 3.66919i −0.103739 + 0.179681i
\(418\) −2.79677 10.4377i −0.136794 0.510523i
\(419\) 3.34749 1.93268i 0.163536 0.0944174i −0.415999 0.909365i \(-0.636568\pi\)
0.579534 + 0.814948i \(0.303235\pi\)
\(420\) 0.944415 0.907204i 0.0460827 0.0442670i
\(421\) 3.65782 + 3.65782i 0.178271 + 0.178271i 0.790602 0.612331i \(-0.209768\pi\)
−0.612331 + 0.790602i \(0.709768\pi\)
\(422\) 7.65379 + 7.65379i 0.372581 + 0.372581i
\(423\) −1.56435 + 5.83824i −0.0760613 + 0.283865i
\(424\) −2.84309 10.6105i −0.138072 0.515293i
\(425\) 16.5932i 0.804886i
\(426\) −4.44616 7.70097i −0.215417 0.373113i
\(427\) 11.9947 6.60744i 0.580466 0.319757i
\(428\) 0.0453239i 0.00219081i
\(429\) 0.904531 + 5.26066i 0.0436712 + 0.253987i
\(430\) 5.55275 + 3.20588i 0.267778 + 0.154601i
\(431\) −7.11488 7.11488i −0.342712 0.342712i 0.514674 0.857386i \(-0.327913\pi\)
−0.857386 + 0.514674i \(0.827913\pi\)
\(432\) 12.4166 + 7.16874i 0.597395 + 0.344906i
\(433\) 3.80951 6.59826i 0.183073 0.317092i −0.759852 0.650096i \(-0.774729\pi\)
0.942926 + 0.333004i \(0.108062\pi\)
\(434\) 19.2201 31.7972i 0.922596 1.52631i
\(435\) 0.574786 0.154013i 0.0275589 0.00738438i
\(436\) −3.26765 + 3.26765i −0.156492 + 0.156492i
\(437\) −12.5597 + 3.36536i −0.600811 + 0.160987i
\(438\) 2.89989 + 5.02276i 0.138562 + 0.239997i
\(439\) 11.1814 19.3667i 0.533658 0.924323i −0.465569 0.885012i \(-0.654150\pi\)
0.999227 0.0393115i \(-0.0125165\pi\)
\(440\) −2.52756 + 9.43298i −0.120497 + 0.449700i
\(441\) −10.2342 + 16.1873i −0.487343 + 0.770823i
\(442\) 6.15988 + 35.8252i 0.292996 + 1.70403i
\(443\) −12.8459 22.2497i −0.610326 1.05712i −0.991185 0.132483i \(-0.957705\pi\)
0.380859 0.924633i \(-0.375628\pi\)
\(444\) −1.38219 + 1.38219i −0.0655958 + 0.0655958i
\(445\) −12.7716 −0.605430
\(446\) −10.2437 −0.485053
\(447\) 1.61727 1.61727i 0.0764945 0.0764945i
\(448\) 9.58354 5.27921i 0.452780 0.249419i
\(449\) −0.821652 3.06645i −0.0387761 0.144715i 0.943824 0.330449i \(-0.107200\pi\)
−0.982600 + 0.185735i \(0.940534\pi\)
\(450\) 11.4427 + 3.06606i 0.539414 + 0.144535i
\(451\) −5.03425 + 2.90653i −0.237054 + 0.136863i
\(452\) 10.2930i 0.484142i
\(453\) 4.46829 1.19728i 0.209939 0.0562529i
\(454\) −38.1954 −1.79260
\(455\) −5.31243 + 13.5591i −0.249051 + 0.635662i
\(456\) −2.63940 −0.123601
\(457\) 31.7143 8.49782i 1.48353 0.397511i 0.575985 0.817460i \(-0.304619\pi\)
0.907548 + 0.419949i \(0.137952\pi\)
\(458\) 30.6945i 1.43426i
\(459\) −15.8681 + 9.16144i −0.740658 + 0.427619i
\(460\) −5.23045 1.40149i −0.243871 0.0653450i
\(461\) 1.38662 + 5.17492i 0.0645811 + 0.241020i 0.990669 0.136287i \(-0.0435169\pi\)
−0.926088 + 0.377307i \(0.876850\pi\)
\(462\) 0.127654 6.35196i 0.00593902 0.295520i
\(463\) −17.0182 + 17.0182i −0.790903 + 0.790903i −0.981641 0.190738i \(-0.938912\pi\)
0.190738 + 0.981641i \(0.438912\pi\)
\(464\) −3.68903 −0.171259
\(465\) 6.79260 0.314999
\(466\) 8.43282 8.43282i 0.390643 0.390643i
\(467\) 3.73447 + 6.46829i 0.172811 + 0.299317i 0.939401 0.342819i \(-0.111382\pi\)
−0.766591 + 0.642136i \(0.778049\pi\)
\(468\) 6.19727 + 0.568775i 0.286469 + 0.0262916i
\(469\) 11.5560 39.9024i 0.533605 1.84252i
\(470\) 1.41582 5.28393i 0.0653071 0.243729i
\(471\) −1.24948 + 2.16417i −0.0575732 + 0.0997197i
\(472\) −0.978701 1.69516i −0.0450483 0.0780260i
\(473\) 7.20516 1.93062i 0.331294 0.0887698i
\(474\) 5.00743 5.00743i 0.229999 0.229999i
\(475\) −5.96340 + 1.59789i −0.273620 + 0.0733162i
\(476\) 0.208466 10.3731i 0.00955502 0.475449i
\(477\) 6.76661 11.7201i 0.309822 0.536627i
\(478\) 8.11792 + 4.68688i 0.371305 + 0.214373i
\(479\) −14.7412 14.7412i −0.673544 0.673544i 0.284987 0.958531i \(-0.408011\pi\)
−0.958531 + 0.284987i \(0.908011\pi\)
\(480\) −2.34246 1.35242i −0.106918 0.0617293i
\(481\) 7.52135 20.3943i 0.342944 0.929900i
\(482\) 46.6164i 2.12332i
\(483\) −7.64333 0.153607i −0.347784 0.00698935i
\(484\) 0.852240 + 1.47612i 0.0387382 + 0.0670965i
\(485\) 5.50856i 0.250131i
\(486\) 5.15647 + 19.2442i 0.233902 + 0.872934i
\(487\) −4.83239 + 18.0347i −0.218977 + 0.817232i 0.765752 + 0.643136i \(0.222367\pi\)
−0.984729 + 0.174096i \(0.944300\pi\)
\(488\) −8.12762 8.12762i −0.367920 0.367920i
\(489\) 2.32165 + 2.32165i 0.104989 + 0.104989i
\(490\) 9.26253 14.6504i 0.418438 0.661837i
\(491\) 26.9636 15.5675i 1.21685 0.702550i 0.252609 0.967569i \(-0.418711\pi\)
0.964243 + 0.265019i \(0.0853781\pi\)
\(492\) −0.169340 0.631987i −0.00763445 0.0284922i
\(493\) 2.35724 4.08286i 0.106165 0.183883i
\(494\) −12.2820 + 5.66370i −0.552594 + 0.254822i
\(495\) −10.4194 + 6.01565i −0.468317 + 0.270383i
\(496\) −40.6752 10.8989i −1.82637 0.489374i
\(497\) −19.5520 20.3540i −0.877029 0.913003i
\(498\) 1.54602 + 0.892597i 0.0692790 + 0.0399982i
\(499\) −4.79636 + 17.9002i −0.214714 + 0.801325i 0.771553 + 0.636166i \(0.219481\pi\)
−0.986267 + 0.165159i \(0.947186\pi\)
\(500\) −7.13489 1.91179i −0.319082 0.0854978i
\(501\) 5.02639 + 1.34682i 0.224563 + 0.0601713i
\(502\) −8.16684 + 30.4791i −0.364504 + 1.36035i
\(503\) 22.0368 + 12.7230i 0.982573 + 0.567289i 0.903046 0.429544i \(-0.141326\pi\)
0.0795268 + 0.996833i \(0.474659\pi\)
\(504\) 15.4400 + 4.47151i 0.687752 + 0.199177i
\(505\) 29.0335 + 7.77950i 1.29197 + 0.346183i
\(506\) −22.7508 + 13.1352i −1.01140 + 0.583930i
\(507\) 6.29735 2.23154i 0.279675 0.0991061i
\(508\) 5.42858 9.40257i 0.240854 0.417172i
\(509\) 6.41875 + 23.9551i 0.284506 + 1.06179i 0.949200 + 0.314674i \(0.101895\pi\)
−0.664694 + 0.747116i \(0.731438\pi\)
\(510\) 6.85009 3.95490i 0.303327 0.175126i
\(511\) 12.7523 + 13.2754i 0.564129 + 0.587268i
\(512\) −3.41779 3.41779i −0.151046 0.151046i
\(513\) −4.82059 4.82059i −0.212834 0.212834i
\(514\) 10.5811 39.4892i 0.466712 1.74179i
\(515\) 3.71506 + 13.8648i 0.163705 + 0.610955i
\(516\) 0.839576i 0.0369603i
\(517\) −3.18204 5.51145i −0.139946 0.242393i
\(518\) −13.3835 + 22.1413i −0.588039 + 0.972833i
\(519\) 9.06957i 0.398110i
\(520\) 12.1720 + 1.11712i 0.533776 + 0.0489891i
\(521\) −3.53287 2.03970i −0.154778 0.0893610i 0.420611 0.907241i \(-0.361816\pi\)
−0.575389 + 0.817880i \(0.695149\pi\)
\(522\) −2.37998 2.37998i −0.104169 0.104169i
\(523\) 25.5006 + 14.7228i 1.11506 + 0.643781i 0.940136 0.340800i \(-0.110698\pi\)
0.174926 + 0.984582i \(0.444031\pi\)
\(524\) 1.72555 2.98874i 0.0753810 0.130564i
\(525\) −3.62910 0.0729334i −0.158387 0.00318307i
\(526\) −49.0053 + 13.1309i −2.13673 + 0.572536i
\(527\) 38.0532 38.0532i 1.65763 1.65763i
\(528\) −6.95522 + 1.86365i −0.302687 + 0.0811048i
\(529\) 4.30560 + 7.45752i 0.187200 + 0.324240i
\(530\) −6.12416 + 10.6073i −0.266016 + 0.460754i
\(531\) 0.624142 2.32933i 0.0270854 0.101084i
\(532\) 3.74805 0.923987i 0.162498 0.0400599i
\(533\) 4.65304 + 5.59345i 0.201546 + 0.242279i
\(534\) −3.48695 6.03957i −0.150895 0.261358i
\(535\) −0.0775496 + 0.0775496i −0.00335276 + 0.00335276i
\(536\) −34.8682 −1.50608
\(537\) 10.3932 0.448500
\(538\) −10.3430 + 10.3430i −0.445917 + 0.445917i
\(539\) −4.43224 19.6716i −0.190910 0.847315i
\(540\) −0.734804 2.74233i −0.0316209 0.118011i
\(541\) 36.3539 + 9.74099i 1.56298 + 0.418798i 0.933604 0.358307i \(-0.116646\pi\)
0.629371 + 0.777105i \(0.283312\pi\)
\(542\) −4.78447 + 2.76232i −0.205511 + 0.118652i
\(543\) 8.97567i 0.385183i
\(544\) −20.6993 + 5.54637i −0.887477 + 0.237799i
\(545\) −11.1820 −0.478982
\(546\) −7.86243 + 1.18976i −0.336481 + 0.0509172i
\(547\) −36.7251 −1.57025 −0.785125 0.619337i \(-0.787401\pi\)
−0.785125 + 0.619337i \(0.787401\pi\)
\(548\) 1.06916 0.286480i 0.0456722 0.0122378i
\(549\) 14.1607i 0.604365i
\(550\) −10.8022 + 6.23666i −0.460608 + 0.265932i
\(551\) 1.69433 + 0.453995i 0.0721810 + 0.0193408i
\(552\) 1.66076 + 6.19805i 0.0706867 + 0.263806i
\(553\) 11.6270 19.2354i 0.494432 0.817972i
\(554\) −4.62103 + 4.62103i −0.196329 + 0.196329i
\(555\) −4.72988 −0.200772
\(556\) −5.20106 −0.220574
\(557\) −14.1477 + 14.1477i −0.599459 + 0.599459i −0.940168 0.340710i \(-0.889333\pi\)
0.340710 + 0.940168i \(0.389333\pi\)
\(558\) −19.2102 33.2731i −0.813233 1.40856i
\(559\) −3.90967 8.47832i −0.165361 0.358595i
\(560\) −18.8692 5.46462i −0.797368 0.230922i
\(561\) 2.38168 8.88857i 0.100555 0.375276i
\(562\) 3.76778 6.52599i 0.158934 0.275282i
\(563\) 7.84601 + 13.5897i 0.330670 + 0.572737i 0.982643 0.185505i \(-0.0593919\pi\)
−0.651973 + 0.758242i \(0.726059\pi\)
\(564\) 0.691893 0.185392i 0.0291340 0.00780642i
\(565\) −17.6114 + 17.6114i −0.740919 + 0.740919i
\(566\) −1.61320 + 0.432256i −0.0678079 + 0.0181691i
\(567\) 8.54367 + 15.5096i 0.358800 + 0.651344i
\(568\) −11.8447 + 20.5155i −0.496991 + 0.860813i
\(569\) 4.39537 + 2.53767i 0.184263 + 0.106385i 0.589294 0.807918i \(-0.299406\pi\)
−0.405031 + 0.914303i \(0.632739\pi\)
\(570\) 2.08100 + 2.08100i 0.0871636 + 0.0871636i
\(571\) 17.5642 + 10.1407i 0.735038 + 0.424374i 0.820262 0.571988i \(-0.193827\pi\)
−0.0852246 + 0.996362i \(0.527161\pi\)
\(572\) −5.03753 + 4.19059i −0.210630 + 0.175217i
\(573\) 0.0213736i 0.000892895i
\(574\) −4.17836 7.58513i −0.174401 0.316597i
\(575\) 7.50459 + 12.9983i 0.312963 + 0.542068i
\(576\) 11.3141i 0.471422i
\(577\) −6.77811 25.2962i −0.282176 1.05310i −0.950878 0.309566i \(-0.899816\pi\)
0.668702 0.743531i \(-0.266850\pi\)
\(578\) 9.08265 33.8969i 0.377789 1.40993i
\(579\) −4.53898 4.53898i −0.188633 0.188633i
\(580\) 0.516535 + 0.516535i 0.0214480 + 0.0214480i
\(581\) 5.44244 + 1.57616i 0.225790 + 0.0653901i
\(582\) −2.60495 + 1.50397i −0.107979 + 0.0623416i
\(583\) 3.68803 + 13.7639i 0.152743 + 0.570043i
\(584\) 7.72537 13.3807i 0.319678 0.553698i
\(585\) 9.63042 + 11.5768i 0.398169 + 0.478641i
\(586\) 35.9183 20.7375i 1.48377 0.856657i
\(587\) −1.75410 0.470009i −0.0723994 0.0193994i 0.222438 0.974947i \(-0.428599\pi\)
−0.294837 + 0.955548i \(0.595265\pi\)
\(588\) 2.26778 + 0.0911874i 0.0935218 + 0.00376050i
\(589\) 17.3404 + 10.0115i 0.714498 + 0.412516i
\(590\) −0.564883 + 2.10817i −0.0232559 + 0.0867921i
\(591\) −1.84621 0.494692i −0.0759431 0.0203489i
\(592\) 28.3233 + 7.58921i 1.16408 + 0.311915i
\(593\) 8.29320 30.9506i 0.340561 1.27099i −0.557153 0.830410i \(-0.688106\pi\)
0.897713 0.440580i \(-0.145227\pi\)
\(594\) −11.9283 6.88679i −0.489423 0.282568i
\(595\) 18.1051 17.3917i 0.742238 0.712992i
\(596\) 2.71203 + 0.726687i 0.111089 + 0.0297663i
\(597\) −3.90644 + 2.25538i −0.159880 + 0.0923067i
\(598\) 21.0281 + 25.2779i 0.859901 + 1.03369i
\(599\) 1.81349 3.14105i 0.0740970 0.128340i −0.826596 0.562795i \(-0.809726\pi\)
0.900693 + 0.434456i \(0.143059\pi\)
\(600\) 0.788539 + 2.94287i 0.0321920 + 0.120142i
\(601\) −22.0032 + 12.7035i −0.897529 + 0.518189i −0.876398 0.481588i \(-0.840060\pi\)
−0.0211313 + 0.999777i \(0.506727\pi\)
\(602\) 2.65984 + 10.7893i 0.108407 + 0.439740i
\(603\) −30.3753 30.3753i −1.23698 1.23698i
\(604\) 4.01546 + 4.01546i 0.163387 + 0.163387i
\(605\) −1.06747 + 3.98385i −0.0433988 + 0.161967i
\(606\) 4.24798 + 15.8537i 0.172563 + 0.644012i
\(607\) 4.07542i 0.165416i −0.996574 0.0827081i \(-0.973643\pi\)
0.996574 0.0827081i \(-0.0263569\pi\)
\(608\) −3.98661 6.90502i −0.161679 0.280035i
\(609\) 0.882602 + 0.533498i 0.0357648 + 0.0216184i
\(610\) 12.8162i 0.518915i
\(611\) −6.12365 + 5.09411i −0.247736 + 0.206085i
\(612\) −9.29124 5.36430i −0.375576 0.216839i
\(613\) 16.4066 + 16.4066i 0.662658 + 0.662658i 0.956006 0.293348i \(-0.0947695\pi\)
−0.293348 + 0.956006i \(0.594769\pi\)
\(614\) −27.8503 16.0794i −1.12395 0.648911i
\(615\) 0.791593 1.37108i 0.0319201 0.0552872i
\(616\) −14.8247 + 8.16637i −0.597304 + 0.329032i
\(617\) 0.685439 0.183663i 0.0275948 0.00739399i −0.244995 0.969524i \(-0.578786\pi\)
0.272590 + 0.962130i \(0.412120\pi\)
\(618\) −5.54224 + 5.54224i −0.222942 + 0.222942i
\(619\) −13.2298 + 3.54491i −0.531751 + 0.142482i −0.514697 0.857372i \(-0.672095\pi\)
−0.0170541 + 0.999855i \(0.505429\pi\)
\(620\) 4.16925 + 7.22136i 0.167441 + 0.290017i
\(621\) −8.28689 + 14.3533i −0.332541 + 0.575979i
\(622\) 2.69391 10.0538i 0.108016 0.403121i
\(623\) −15.3339 15.9629i −0.614340 0.639539i
\(624\) 3.77405 + 8.18422i 0.151083 + 0.327631i
\(625\) −2.26294 3.91952i −0.0905174 0.156781i
\(626\) 28.8720 28.8720i 1.15396 1.15396i
\(627\) 3.42381 0.136734
\(628\) −3.06770 −0.122415
\(629\) −26.4976 + 26.4976i −1.05653 + 1.05653i
\(630\) −8.64797 15.6990i −0.344543 0.625462i
\(631\) −0.371814 1.38763i −0.0148017 0.0552407i 0.958130 0.286334i \(-0.0924365\pi\)
−0.972932 + 0.231093i \(0.925770\pi\)
\(632\) −18.2226 4.88274i −0.724858 0.194225i
\(633\) −2.97011 + 1.71479i −0.118051 + 0.0681568i
\(634\) 39.0830i 1.55219i
\(635\) 25.3762 6.79955i 1.00703 0.269832i
\(636\) −1.60383 −0.0635960
\(637\) −23.3255 + 9.63959i −0.924189 + 0.381935i
\(638\) 3.54394 0.140306
\(639\) −28.1905 + 7.55363i −1.11520 + 0.298817i
\(640\) 20.7661i 0.820852i
\(641\) 9.56157 5.52037i 0.377659 0.218042i −0.299140 0.954209i \(-0.596700\pi\)
0.676799 + 0.736168i \(0.263366\pi\)
\(642\) −0.0578455 0.0154997i −0.00228298 0.000611723i
\(643\) −11.5604 43.1441i −0.455899 1.70144i −0.685431 0.728138i \(-0.740386\pi\)
0.229532 0.973301i \(-0.426281\pi\)
\(644\) −4.52813 8.22008i −0.178433 0.323916i
\(645\) −1.43652 + 1.43652i −0.0565630 + 0.0565630i
\(646\) 23.3162 0.917365
\(647\) −10.4061 −0.409105 −0.204552 0.978856i \(-0.565574\pi\)
−0.204552 + 0.978856i \(0.565574\pi\)
\(648\) 10.5093 10.5093i 0.412845 0.412845i
\(649\) 1.26956 + 2.19895i 0.0498347 + 0.0863163i
\(650\) 9.98423 + 12.0021i 0.391614 + 0.470761i
\(651\) 8.15538 + 8.48990i 0.319635 + 0.332745i
\(652\) −1.04318 + 3.89321i −0.0408542 + 0.152470i
\(653\) 5.21928 9.04007i 0.204246 0.353765i −0.745646 0.666342i \(-0.767859\pi\)
0.949892 + 0.312577i \(0.101192\pi\)
\(654\) −3.05295 5.28786i −0.119380 0.206772i
\(655\) 8.06620 2.16133i 0.315172 0.0844502i
\(656\) −6.94012 + 6.94012i −0.270966 + 0.270966i
\(657\) 18.3865 4.92666i 0.717327 0.192207i
\(658\) 8.30413 4.57443i 0.323729 0.178330i
\(659\) −3.86557 + 6.69537i −0.150581 + 0.260815i −0.931441 0.363892i \(-0.881448\pi\)
0.780860 + 0.624706i \(0.214781\pi\)
\(660\) 1.23481 + 0.712918i 0.0480649 + 0.0277503i
\(661\) 31.6749 + 31.6749i 1.23201 + 1.23201i 0.963190 + 0.268821i \(0.0866339\pi\)
0.268821 + 0.963190i \(0.413366\pi\)
\(662\) 8.30322 + 4.79387i 0.322714 + 0.186319i
\(663\) −11.4695 1.05265i −0.445438 0.0408815i
\(664\) 4.75580i 0.184561i
\(665\) 7.99390 + 4.83200i 0.309990 + 0.187377i
\(666\) 13.3766 + 23.1690i 0.518334 + 0.897780i
\(667\) 4.26443i 0.165119i
\(668\) 1.65334 + 6.17033i 0.0639695 + 0.238737i
\(669\) 0.840045 3.13509i 0.0324780 0.121210i
\(670\) 27.4914 + 27.4914i 1.06208 + 1.06208i
\(671\) 10.5431 + 10.5431i 0.407012 + 0.407012i
\(672\) −1.12207 4.55154i −0.0432847 0.175579i
\(673\) −19.6804 + 11.3625i −0.758625 + 0.437992i −0.828802 0.559542i \(-0.810977\pi\)
0.0701768 + 0.997535i \(0.477644\pi\)
\(674\) 4.84112 + 18.0673i 0.186473 + 0.695927i
\(675\) −3.93466 + 6.81503i −0.151445 + 0.262311i
\(676\) 6.23767 + 5.32514i 0.239910 + 0.204813i
\(677\) −7.56955 + 4.37028i −0.290921 + 0.167964i −0.638357 0.769740i \(-0.720386\pi\)
0.347436 + 0.937704i \(0.387052\pi\)
\(678\) −13.1367 3.51996i −0.504510 0.135183i
\(679\) −6.88502 + 6.61373i −0.264223 + 0.253812i
\(680\) −18.2488 10.5359i −0.699809 0.404035i
\(681\) 3.13226 11.6897i 0.120028 0.447952i
\(682\) 39.0754 + 10.4702i 1.49627 + 0.400925i
\(683\) −2.15549 0.577561i −0.0824774 0.0220998i 0.217344 0.976095i \(-0.430261\pi\)
−0.299822 + 0.953995i \(0.596927\pi\)
\(684\) 1.03314 3.85575i 0.0395032 0.147428i
\(685\) 2.31951 + 1.33917i 0.0886240 + 0.0511671i
\(686\) 29.4320 6.01266i 1.12372 0.229564i
\(687\) −9.39407 2.51713i −0.358406 0.0960346i
\(688\) 10.9071 6.29720i 0.415828 0.240078i
\(689\) 16.1960 7.46859i 0.617019 0.284531i
\(690\) 3.57737 6.19618i 0.136188 0.235885i
\(691\) 1.19272 + 4.45128i 0.0453731 + 0.169335i 0.984895 0.173155i \(-0.0553963\pi\)
−0.939521 + 0.342490i \(0.888730\pi\)
\(692\) −9.64206 + 5.56685i −0.366536 + 0.211620i
\(693\) −20.0286 5.80040i −0.760825 0.220339i
\(694\) 10.4061 + 10.4061i 0.395012 + 0.395012i
\(695\) −8.89907 8.89907i −0.337561 0.337561i
\(696\) 0.224041 0.836132i 0.00849225 0.0316935i
\(697\) −3.24638 12.1156i −0.122965 0.458913i
\(698\) 48.7437i 1.84498i
\(699\) 1.88933 + 3.27241i 0.0714609 + 0.123774i
\(700\) −2.14998 3.90294i −0.0812616 0.147517i
\(701\) 10.7910i 0.407569i 0.979016 + 0.203784i \(0.0653242\pi\)
−0.979016 + 0.203784i \(0.934676\pi\)
\(702\) −5.96513 + 16.1746i −0.225139 + 0.610470i
\(703\) −12.0746 6.97128i −0.455403 0.262927i
\(704\) 8.42371 + 8.42371i 0.317481 + 0.317481i
\(705\) 1.50104 + 0.866628i 0.0565326 + 0.0326391i
\(706\) 23.5012 40.7053i 0.884481 1.53197i
\(707\) 25.1350 + 45.6285i 0.945300 + 1.71604i
\(708\) −0.276050 + 0.0739674i −0.0103746 + 0.00277987i
\(709\) 16.3787 16.3787i 0.615115 0.615115i −0.329160 0.944274i \(-0.606765\pi\)
0.944274 + 0.329160i \(0.106765\pi\)
\(710\) 25.5140 6.83646i 0.957524 0.256568i
\(711\) −11.6210 20.1282i −0.435823 0.754867i
\(712\) −9.28930 + 16.0895i −0.348131 + 0.602981i
\(713\) 12.5988 47.0195i 0.471830 1.76090i
\(714\) 13.1676 + 3.81340i 0.492783 + 0.142713i
\(715\) −15.7894 1.44912i −0.590490 0.0541941i
\(716\) 6.37929 + 11.0493i 0.238405 + 0.412930i
\(717\) −2.10014 + 2.10014i −0.0784312 + 0.0784312i
\(718\) 14.3188 0.534374
\(719\) 35.8985 1.33879 0.669394 0.742907i \(-0.266554\pi\)
0.669394 + 0.742907i \(0.266554\pi\)
\(720\) −14.3640 + 14.3640i −0.535314 + 0.535314i
\(721\) −12.8689 + 21.2898i −0.479261 + 0.792874i
\(722\) −5.73099 21.3883i −0.213285 0.795991i
\(723\) 14.2670 + 3.82283i 0.530595 + 0.142172i
\(724\) 9.54223 5.50921i 0.354634 0.204748i
\(725\) 2.02477i 0.0751983i
\(726\) −2.17538 + 0.582891i −0.0807358 + 0.0216331i
\(727\) −40.7770 −1.51234 −0.756168 0.654377i \(-0.772931\pi\)
−0.756168 + 0.654377i \(0.772931\pi\)
\(728\) 13.2178 + 16.5547i 0.489882 + 0.613558i
\(729\) 13.7655 0.509832
\(730\) −16.6408 + 4.45890i −0.615905 + 0.165031i
\(731\) 16.0953i 0.595305i
\(732\) −1.45336 + 0.839099i −0.0537178 + 0.0310140i
\(733\) −24.0007 6.43098i −0.886487 0.237533i −0.213283 0.976990i \(-0.568416\pi\)
−0.673204 + 0.739457i \(0.735082\pi\)
\(734\) 5.57860 + 20.8196i 0.205910 + 0.768466i
\(735\) 3.72418 + 4.03622i 0.137368 + 0.148878i
\(736\) −13.7065 + 13.7065i −0.505227 + 0.505227i
\(737\) 45.2307 1.66610
\(738\) −8.95485 −0.329632
\(739\) −30.0193 + 30.0193i −1.10428 + 1.10428i −0.110389 + 0.993888i \(0.535210\pi\)
−0.993888 + 0.110389i \(0.964790\pi\)
\(740\) −2.90317 5.02844i −0.106723 0.184849i
\(741\) −0.726179 4.22338i −0.0266768 0.155150i
\(742\) −20.6107 + 5.08105i −0.756643 + 0.186531i
\(743\) −6.30753 + 23.5400i −0.231401 + 0.863600i 0.748337 + 0.663318i \(0.230852\pi\)
−0.979738 + 0.200282i \(0.935814\pi\)
\(744\) 4.94054 8.55727i 0.181129 0.313725i
\(745\) 3.39695 + 5.88369i 0.124455 + 0.215562i
\(746\) 12.9254 3.46336i 0.473233 0.126802i
\(747\) 4.14300 4.14300i 0.151585 0.151585i
\(748\) 10.9115 2.92373i 0.398964 0.106902i
\(749\) −0.190036 0.00381912i −0.00694375 0.000139547i
\(750\) 4.87992 8.45226i 0.178189 0.308633i
\(751\) −24.6348 14.2229i −0.898936 0.519001i −0.0220813 0.999756i \(-0.507029\pi\)
−0.876855 + 0.480755i \(0.840363\pi\)
\(752\) −7.59797 7.59797i −0.277070 0.277070i
\(753\) −8.65841 4.99894i −0.315530 0.182171i
\(754\) −0.751658 4.37156i −0.0273738 0.159203i
\(755\) 13.7410i 0.500086i
\(756\) 2.54534 4.21093i 0.0925731 0.153150i
\(757\) −26.0081 45.0474i −0.945282 1.63728i −0.755187 0.655510i \(-0.772454\pi\)
−0.190095 0.981766i \(-0.560880\pi\)
\(758\) 5.61873i 0.204082i
\(759\) −2.15433 8.04006i −0.0781972 0.291836i
\(760\) 2.02918 7.57301i 0.0736062 0.274702i
\(761\) −4.19144 4.19144i −0.151939 0.151939i 0.627044 0.778984i \(-0.284265\pi\)
−0.778984 + 0.627044i \(0.784265\pi\)
\(762\) 10.1438 + 10.1438i 0.367470 + 0.367470i
\(763\) −13.4254 13.9761i −0.486031 0.505967i
\(764\) 0.0227228 0.0131190i 0.000822080 0.000474628i
\(765\) −6.71904 25.0758i −0.242927 0.906617i
\(766\) −27.9220 + 48.3623i −1.00886 + 1.74740i
\(767\) 2.44320 2.03244i 0.0882190 0.0733871i
\(768\) −6.13895 + 3.54433i −0.221520 + 0.127895i
\(769\) −0.310861 0.0832949i −0.0112099 0.00300369i 0.253210 0.967411i \(-0.418514\pi\)
−0.264420 + 0.964408i \(0.585180\pi\)
\(770\) 18.1270 + 5.24969i 0.653253 + 0.189186i
\(771\) 11.2180 + 6.47670i 0.404005 + 0.233253i
\(772\) 2.03949 7.61148i 0.0734028 0.273943i
\(773\) 30.7110 + 8.22900i 1.10460 + 0.295977i 0.764636 0.644462i \(-0.222919\pi\)
0.339963 + 0.940439i \(0.389585\pi\)
\(774\) 11.0994 + 2.97406i 0.398958 + 0.106900i
\(775\) 5.98200 22.3251i 0.214880 0.801942i
\(776\) 6.93965 + 4.00661i 0.249119 + 0.143829i
\(777\) −5.67883 5.91176i −0.203727 0.212083i
\(778\) −14.6104 3.91484i −0.523807 0.140354i
\(779\) 4.04161 2.33343i 0.144806 0.0836037i
\(780\) 0.617508 1.67439i 0.0221103 0.0599526i
\(781\) 15.3648 26.6126i 0.549796 0.952274i
\(782\) −14.6710 54.7531i −0.524635 1.95797i
\(783\) 1.93630 1.11792i 0.0691976 0.0399513i
\(784\) −15.8248 30.1451i −0.565171 1.07661i
\(785\) −5.24887 5.24887i −0.187340 0.187340i
\(786\) 3.22434 + 3.22434i 0.115009 + 0.115009i
\(787\) −8.68944 + 32.4294i −0.309745 + 1.15598i 0.619038 + 0.785361i \(0.287523\pi\)
−0.928783 + 0.370623i \(0.879144\pi\)
\(788\) −0.607277 2.26639i −0.0216334 0.0807368i
\(789\) 16.0749i 0.572282i
\(790\) 10.5177 + 18.2172i 0.374202 + 0.648137i
\(791\) −43.1569 0.867317i −1.53448 0.0308383i
\(792\) 17.5017i 0.621897i
\(793\) 10.7691 15.2414i 0.382422 0.541238i
\(794\) −27.7891 16.0440i −0.986198 0.569382i
\(795\) −2.74417 2.74417i −0.0973256 0.0973256i
\(796\) −4.79549 2.76868i −0.169972 0.0981333i
\(797\) −6.34434 + 10.9887i −0.224728 + 0.389240i −0.956238 0.292591i \(-0.905483\pi\)
0.731510 + 0.681831i \(0.238816\pi\)
\(798\) −0.102484 + 5.09950i −0.00362789 + 0.180520i
\(799\) 13.2641 3.55410i 0.469250 0.125735i
\(800\) −6.50790 + 6.50790i −0.230089 + 0.230089i
\(801\) −22.1087 + 5.92402i −0.781174 + 0.209315i
\(802\) −9.76605 16.9153i −0.344851 0.597300i
\(803\) −10.0213 + 17.3574i −0.353644 + 0.612529i
\(804\) −1.31762 + 4.91742i −0.0464688 + 0.173424i
\(805\) 6.31697 21.8123i 0.222644 0.768783i
\(806\) 4.62759 50.4215i 0.163000 1.77602i
\(807\) −2.31729 4.01366i −0.0815724 0.141288i
\(808\) 30.9178 30.9178i 1.08769 1.08769i
\(809\) −42.8045 −1.50493 −0.752463 0.658635i \(-0.771134\pi\)
−0.752463 + 0.658635i \(0.771134\pi\)
\(810\) −16.5719 −0.582277
\(811\) −1.51360 + 1.51360i −0.0531496 + 0.0531496i −0.733182 0.680032i \(-0.761966\pi\)
0.680032 + 0.733182i \(0.261966\pi\)
\(812\) −0.0254380 + 1.26577i −0.000892699 + 0.0444199i
\(813\) −0.453053 1.69082i −0.0158893 0.0592995i
\(814\) −27.2093 7.29072i −0.953686 0.255539i
\(815\) −8.44623 + 4.87643i −0.295858 + 0.170814i
\(816\) 15.5369i 0.543902i
\(817\) −5.78447 + 1.54994i −0.202373 + 0.0542257i
\(818\) 31.6242 1.10571
\(819\) −2.90698 + 25.9362i −0.101578 + 0.906285i
\(820\) 1.94350 0.0678699
\(821\) −36.3415 + 9.73769i −1.26833 + 0.339848i −0.829390 0.558670i \(-0.811312\pi\)
−0.438938 + 0.898517i \(0.644645\pi\)
\(822\) 1.46250i 0.0510107i
\(823\) −38.5355 + 22.2485i −1.34326 + 0.775533i −0.987285 0.158962i \(-0.949185\pi\)
−0.355977 + 0.934495i \(0.615852\pi\)
\(824\) 20.1689 + 5.40424i 0.702616 + 0.188266i
\(825\) −1.02289 3.81747i −0.0356124 0.132907i
\(826\) −3.31317 + 1.82510i −0.115280 + 0.0635033i
\(827\) 12.3898 12.3898i 0.430835 0.430835i −0.458077 0.888912i \(-0.651462\pi\)
0.888912 + 0.458077i \(0.151462\pi\)
\(828\) −9.70445 −0.337253
\(829\) −42.2761 −1.46831 −0.734155 0.678982i \(-0.762421\pi\)
−0.734155 + 0.678982i \(0.762421\pi\)
\(830\) −3.74965 + 3.74965i −0.130152 + 0.130152i
\(831\) −1.03532 1.79322i −0.0359147 0.0622061i
\(832\) 8.60428 12.1776i 0.298300 0.422181i
\(833\) 43.4750 + 1.74813i 1.50632 + 0.0605690i
\(834\) 1.77864 6.63796i 0.0615891 0.229854i
\(835\) −7.72863 + 13.3864i −0.267460 + 0.463255i
\(836\) 2.10151 + 3.63993i 0.0726823 + 0.125889i
\(837\) 24.6524 6.60558i 0.852110 0.228322i
\(838\) −4.43328 + 4.43328i −0.153145 + 0.153145i
\(839\) −25.6907 + 6.88379i −0.886940 + 0.237655i −0.673399 0.739279i \(-0.735166\pi\)
−0.213541 + 0.976934i \(0.568500\pi\)
\(840\) 2.38453 3.94489i 0.0822742 0.136112i
\(841\) 14.2124 24.6165i 0.490081 0.848846i
\(842\) −7.26640 4.19526i −0.250417 0.144578i
\(843\) 1.68830 + 1.68830i 0.0581482 + 0.0581482i
\(844\) −3.64606 2.10506i −0.125503 0.0724590i
\(845\) 1.56134 + 19.7841i 0.0537117 + 0.680593i
\(846\) 9.80368i 0.337058i
\(847\) −6.26096 + 3.44892i −0.215129 + 0.118506i
\(848\) 12.0295 + 20.8356i 0.413093 + 0.715498i
\(849\) 0.529169i 0.0181610i
\(850\) −6.96589 25.9971i −0.238928 0.891691i
\(851\) −8.77294 + 32.7411i −0.300732 + 1.12235i
\(852\) 2.44569 + 2.44569i 0.0837881 + 0.0837881i
\(853\) 0.950856 + 0.950856i 0.0325567 + 0.0325567i 0.723198 0.690641i \(-0.242672\pi\)
−0.690641 + 0.723198i \(0.742672\pi\)
\(854\) −16.0187 + 15.3875i −0.548149 + 0.526551i
\(855\) 8.36494 4.82950i 0.286075 0.165165i
\(856\) 0.0412914 + 0.154102i 0.00141131 + 0.00526709i
\(857\) 21.1903 36.7026i 0.723845 1.25374i −0.235602 0.971850i \(-0.575706\pi\)
0.959447 0.281887i \(-0.0909605\pi\)
\(858\) −3.62561 7.86232i −0.123776 0.268415i
\(859\) −5.83030 + 3.36613i −0.198927 + 0.114851i −0.596155 0.802869i \(-0.703306\pi\)
0.397228 + 0.917720i \(0.369972\pi\)
\(860\) −2.40893 0.645470i −0.0821437 0.0220103i
\(861\) 2.66409 0.656763i 0.0907918 0.0223824i
\(862\) 14.1340 + 8.16026i 0.481405 + 0.277939i
\(863\) −4.77484 + 17.8200i −0.162537 + 0.606598i 0.835804 + 0.549028i \(0.185002\pi\)
−0.998341 + 0.0575702i \(0.981665\pi\)
\(864\) −9.81668 2.63037i −0.333970 0.0894871i
\(865\) −26.0226 6.97273i −0.884795 0.237080i
\(866\) −3.19850 + 11.9370i −0.108689 + 0.405634i
\(867\) 9.62934 + 5.55950i 0.327030 + 0.188811i
\(868\) −4.02008 + 13.8812i −0.136450 + 0.471159i
\(869\) 23.6383 + 6.33386i 0.801874 + 0.214861i
\(870\) −0.835881 + 0.482596i −0.0283390 + 0.0163615i
\(871\) −9.59329 55.7936i −0.325056 1.89049i
\(872\) −8.13311 + 14.0870i −0.275422 + 0.477045i
\(873\) 2.55511 + 9.53582i 0.0864775 + 0.322739i
\(874\) 18.2649 10.5452i 0.617819 0.356698i
\(875\) 8.61702 29.7543i 0.291309 1.00588i
\(876\) −1.59514 1.59514i −0.0538948 0.0538948i
\(877\) 10.6547 + 10.6547i 0.359785 + 0.359785i 0.863734 0.503948i \(-0.168120\pi\)
−0.503948 + 0.863734i \(0.668120\pi\)
\(878\) −9.38800 + 35.0365i −0.316830 + 1.18242i
\(879\) 3.40120 + 12.6934i 0.114719 + 0.428139i
\(880\) 21.3888i 0.721018i
\(881\) 22.3633 + 38.7344i 0.753439 + 1.30500i 0.946146 + 0.323739i \(0.104940\pi\)
−0.192707 + 0.981256i \(0.561727\pi\)
\(882\) 9.23877 29.6575i 0.311086 0.998620i
\(883\) 46.5076i 1.56510i −0.622585 0.782552i \(-0.713917\pi\)
0.622585 0.782552i \(-0.286083\pi\)
\(884\) −5.92080 12.8396i −0.199138 0.431842i
\(885\) −0.598884 0.345766i −0.0201313 0.0116228i
\(886\) 29.4666 + 29.4666i 0.989951 + 0.989951i
\(887\) 39.8820 + 23.0259i 1.33911 + 0.773133i 0.986675 0.162704i \(-0.0520217\pi\)
0.352431 + 0.935838i \(0.385355\pi\)
\(888\) −3.44024 + 5.95867i −0.115447 + 0.199960i
\(889\) 38.9660 + 23.5534i 1.30688 + 0.789957i
\(890\) 20.0096 5.36156i 0.670724 0.179720i
\(891\) −13.6326 + 13.6326i −0.456710 + 0.456710i
\(892\) 3.84860 1.03123i 0.128861 0.0345281i
\(893\) 2.55461 + 4.42472i 0.0854869 + 0.148068i
\(894\) −1.85490 + 3.21278i −0.0620371 + 0.107451i
\(895\) −7.99036 + 29.8204i −0.267088 + 0.996787i
\(896\) −25.9550 + 24.9324i −0.867097 + 0.832932i
\(897\) −9.46076 + 4.36271i −0.315885 + 0.145667i
\(898\) 2.57462 + 4.45937i 0.0859161 + 0.148811i
\(899\) −4.64344 + 4.64344i −0.154867 + 0.154867i
\(900\) −4.60773 −0.153591
\(901\) −30.7466 −1.02432
\(902\) 6.66715 6.66715i 0.221992 0.221992i
\(903\) −3.52020 0.0707450i −0.117145 0.00235424i
\(904\) 9.37724 + 34.9963i 0.311882 + 1.16396i
\(905\) 25.7532 + 6.90054i 0.856064 + 0.229382i
\(906\) −6.49800 + 3.75162i −0.215882 + 0.124639i
\(907\) 31.8775i 1.05847i −0.848474 0.529237i \(-0.822478\pi\)
0.848474 0.529237i \(-0.177522\pi\)
\(908\) 14.3502 3.84512i 0.476227 0.127605i
\(909\) 53.8681 1.78669
\(910\) 2.63098 23.4737i 0.0872161 0.778147i
\(911\) 34.8516 1.15469 0.577343 0.816502i \(-0.304090\pi\)
0.577343 + 0.816502i \(0.304090\pi\)
\(912\) 5.58381 1.49618i 0.184899 0.0495434i
\(913\) 6.16918i 0.204170i
\(914\) −46.1204 + 26.6276i −1.52553 + 0.880764i
\(915\) −3.92242 1.05101i −0.129671 0.0347453i
\(916\) −3.09000 11.5320i −0.102096 0.381029i
\(917\) 12.3859 + 7.48679i 0.409018 + 0.247236i
\(918\) 21.0150 21.0150i 0.693599 0.693599i
\(919\) −3.81023 −0.125688 −0.0628439 0.998023i \(-0.520017\pi\)
−0.0628439 + 0.998023i \(0.520017\pi\)
\(920\) −19.0604 −0.628402
\(921\) 7.20500 7.20500i 0.237413 0.237413i
\(922\) −4.34491 7.52561i −0.143092 0.247843i
\(923\) −36.0864 13.3085i −1.18780 0.438056i
\(924\) 0.591489 + 2.39931i 0.0194586 + 0.0789315i
\(925\) −4.16544 + 15.5456i −0.136959 + 0.511137i
\(926\) 19.5187 33.8073i 0.641423 1.11098i
\(927\) 12.8622 + 22.2780i 0.422450 + 0.731705i
\(928\) 2.52583 0.676794i 0.0829145 0.0222169i
\(929\) 26.6060 26.6060i 0.872914 0.872914i −0.119875 0.992789i \(-0.538249\pi\)
0.992789 + 0.119875i \(0.0382495\pi\)
\(930\) −10.6422 + 2.85157i −0.348971 + 0.0935065i
\(931\) 3.55830 + 15.7928i 0.116619 + 0.517588i
\(932\) −2.31931 + 4.01717i −0.0759717 + 0.131587i
\(933\) 2.85606 + 1.64895i 0.0935032 + 0.0539841i
\(934\) −8.56633 8.56633i −0.280299 0.280299i
\(935\) 23.6722 + 13.6672i 0.774164 + 0.446964i
\(936\) 21.5890 3.71206i 0.705657 0.121333i
\(937\) 38.0350i 1.24255i 0.783593 + 0.621275i \(0.213385\pi\)
−0.783593 + 0.621275i \(0.786615\pi\)
\(938\) −1.35388 + 67.3677i −0.0442057 + 2.19963i
\(939\) 6.46863 + 11.2040i 0.211096 + 0.365628i
\(940\) 2.12772i 0.0693987i
\(941\) −6.79732 25.3679i −0.221586 0.826971i −0.983744 0.179579i \(-0.942526\pi\)
0.762157 0.647392i \(-0.224140\pi\)
\(942\) 1.04908 3.91522i 0.0341808 0.127565i
\(943\) −8.02260 8.02260i −0.261252 0.261252i
\(944\) 3.03143 + 3.03143i 0.0986645 + 0.0986645i
\(945\) 11.5600 2.84984i 0.376048 0.0927052i
\(946\) −10.4781 + 6.04952i −0.340672 + 0.196687i
\(947\) −2.01713 7.52805i −0.0655480 0.244629i 0.925376 0.379050i \(-0.123749\pi\)
−0.990924 + 0.134421i \(0.957082\pi\)
\(948\) −1.37722 + 2.38541i −0.0447299 + 0.0774745i
\(949\) 23.5364 + 8.68014i 0.764023 + 0.281769i
\(950\) 8.67226 5.00693i 0.281365 0.162446i
\(951\) 11.9614 + 3.20505i 0.387875 + 0.103931i
\(952\) −8.74139 35.4585i −0.283310 1.14922i
\(953\) −7.95143 4.59076i −0.257572 0.148709i 0.365654 0.930751i \(-0.380845\pi\)
−0.623227 + 0.782041i \(0.714179\pi\)
\(954\) −5.68131 + 21.2029i −0.183939 + 0.686470i
\(955\) 0.0613256 + 0.0164321i 0.00198445 + 0.000531732i
\(956\) −3.52176 0.943653i −0.113902 0.0305199i
\(957\) −0.290624 + 1.08462i −0.00939455 + 0.0350609i
\(958\) 29.2840 + 16.9071i 0.946124 + 0.546245i
\(959\) 1.11107 + 4.50695i 0.0358785 + 0.145537i
\(960\) −3.13393 0.839735i −0.101147 0.0271023i
\(961\) −38.0702 + 21.9798i −1.22807 + 0.709027i
\(962\) −3.22233 + 35.1099i −0.103892 + 1.13199i
\(963\) −0.0982745 + 0.170216i −0.00316685 + 0.00548515i
\(964\) 4.69285 + 17.5140i 0.151147 + 0.564087i
\(965\) 16.5129 9.53373i 0.531569 0.306902i
\(966\) 12.0395 2.96805i 0.387366 0.0954954i
\(967\) 29.3315 + 29.3315i 0.943237 + 0.943237i 0.998473 0.0552359i \(-0.0175911\pi\)
−0.0552359 + 0.998473i \(0.517591\pi\)
\(968\) 4.24242 + 4.24242i 0.136356 + 0.136356i
\(969\) −1.91207 + 7.13595i −0.0614246 + 0.229240i
\(970\) −2.31252 8.63045i −0.0742506 0.277107i
\(971\) 37.5461i 1.20491i −0.798153 0.602455i \(-0.794189\pi\)
0.798153 0.602455i \(-0.205811\pi\)
\(972\) −3.87461 6.71102i −0.124278 0.215256i
\(973\) 0.438256 21.8072i 0.0140498 0.699107i
\(974\) 30.2843i 0.970371i
\(975\) −4.49202 + 2.07144i −0.143860 + 0.0663391i
\(976\) 21.8017 + 12.5872i 0.697857 + 0.402908i
\(977\) −20.3670 20.3670i −0.651599 0.651599i 0.301779 0.953378i \(-0.402420\pi\)
−0.953378 + 0.301779i \(0.902420\pi\)
\(978\) −4.61205 2.66277i −0.147477 0.0851460i
\(979\) 12.0500 20.8712i 0.385120 0.667047i
\(980\) −2.00512 + 6.43666i −0.0640512 + 0.205612i
\(981\) −19.3570 + 5.18669i −0.618021 + 0.165598i
\(982\) −35.7095 + 35.7095i −1.13954 + 1.13954i
\(983\) 19.0237 5.09738i 0.606762 0.162581i 0.0576591 0.998336i \(-0.481636\pi\)
0.549102 + 0.835755i \(0.314970\pi\)
\(984\) −1.15152 1.99449i −0.0367090 0.0635819i
\(985\) 2.83876 4.91687i 0.0904504 0.156665i
\(986\) −1.97916 + 7.38633i −0.0630293 + 0.235229i
\(987\) 0.719018 + 2.91662i 0.0228866 + 0.0928369i
\(988\) 4.04424 3.36430i 0.128665 0.107033i
\(989\) 7.27941 + 12.6083i 0.231472 + 0.400921i
\(990\) 13.7990 13.7990i 0.438562 0.438562i
\(991\) 35.2204 1.11881 0.559407 0.828893i \(-0.311029\pi\)
0.559407 + 0.828893i \(0.311029\pi\)
\(992\) 29.8493 0.947716
\(993\) −2.14808 + 2.14808i −0.0681673 + 0.0681673i
\(994\) 39.1776 + 23.6813i 1.24264 + 0.751125i
\(995\) −3.46790 12.9424i −0.109940 0.410301i
\(996\) −0.670705 0.179715i −0.0212521 0.00569448i
\(997\) −31.7101 + 18.3078i −1.00427 + 0.579814i −0.909508 0.415686i \(-0.863541\pi\)
−0.0947594 + 0.995500i \(0.530208\pi\)
\(998\) 30.0584i 0.951483i
\(999\) −17.1662 + 4.59966i −0.543113 + 0.145527i
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 91.2.w.a.24.2 yes 28
3.2 odd 2 819.2.gh.b.388.6 28
7.2 even 3 637.2.bb.a.362.6 28
7.3 odd 6 637.2.bd.b.440.6 28
7.4 even 3 637.2.bd.a.440.6 28
7.5 odd 6 91.2.ba.a.89.6 yes 28
7.6 odd 2 637.2.x.a.570.2 28
13.6 odd 12 91.2.ba.a.45.6 yes 28
21.5 even 6 819.2.et.b.271.2 28
39.32 even 12 819.2.et.b.136.2 28
91.6 even 12 637.2.bb.a.227.6 28
91.19 even 12 inner 91.2.w.a.19.2 28
91.32 odd 12 637.2.bd.b.97.6 28
91.45 even 12 637.2.bd.a.97.6 28
91.58 odd 12 637.2.x.a.19.2 28
273.110 odd 12 819.2.gh.b.19.6 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.2.w.a.19.2 28 91.19 even 12 inner
91.2.w.a.24.2 yes 28 1.1 even 1 trivial
91.2.ba.a.45.6 yes 28 13.6 odd 12
91.2.ba.a.89.6 yes 28 7.5 odd 6
637.2.x.a.19.2 28 91.58 odd 12
637.2.x.a.570.2 28 7.6 odd 2
637.2.bb.a.227.6 28 91.6 even 12
637.2.bb.a.362.6 28 7.2 even 3
637.2.bd.a.97.6 28 91.45 even 12
637.2.bd.a.440.6 28 7.4 even 3
637.2.bd.b.97.6 28 91.32 odd 12
637.2.bd.b.440.6 28 7.3 odd 6
819.2.et.b.136.2 28 39.32 even 12
819.2.et.b.271.2 28 21.5 even 6
819.2.gh.b.19.6 28 273.110 odd 12
819.2.gh.b.388.6 28 3.2 odd 2