Properties

Label 72.2.l.b.59.7
Level $72$
Weight $2$
Character 72.59
Analytic conductor $0.575$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [72,2,Mod(11,72)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(72, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("72.11");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 72 = 2^{3} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 72.l (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.574922894553\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 3 x^{15} + 7 x^{14} - 12 x^{13} + 16 x^{12} - 12 x^{11} - 8 x^{10} + 36 x^{9} - 68 x^{8} + 72 x^{7} - 32 x^{6} - 96 x^{5} + 256 x^{4} - 384 x^{3} + 448 x^{2} - 384 x + 256 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 59.7
Root \(0.867527 - 1.11687i\) of defining polynomial
Character \(\chi\) \(=\) 72.59
Dual form 72.2.l.b.11.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.533474 + 1.30973i) q^{2} +(0.925606 - 1.46399i) q^{3} +(-1.43081 + 1.39742i) q^{4} +(-0.895377 + 1.55084i) q^{5} +(2.41122 + 0.431300i) q^{6} +(2.08793 - 1.20546i) q^{7} +(-2.59355 - 1.12850i) q^{8} +(-1.28651 - 2.71015i) q^{9} +O(q^{10})\) \(q+(0.533474 + 1.30973i) q^{2} +(0.925606 - 1.46399i) q^{3} +(-1.43081 + 1.39742i) q^{4} +(-0.895377 + 1.55084i) q^{5} +(2.41122 + 0.431300i) q^{6} +(2.08793 - 1.20546i) q^{7} +(-2.59355 - 1.12850i) q^{8} +(-1.28651 - 2.71015i) q^{9} +(-2.50885 - 0.345375i) q^{10} +(-1.36975 + 0.790826i) q^{11} +(0.721434 + 3.38815i) q^{12} +(-5.35491 - 3.09166i) q^{13} +(2.69269 + 2.09155i) q^{14} +(1.44164 + 2.74629i) q^{15} +(0.0944399 - 3.99888i) q^{16} +3.69943i q^{17} +(2.86326 - 3.13078i) q^{18} +3.12941 q^{19} +(-0.886056 - 3.47017i) q^{20} +(0.167814 - 4.17248i) q^{21} +(-1.76650 - 1.37212i) q^{22} +(1.36036 - 2.35622i) q^{23} +(-4.05271 + 2.75238i) q^{24} +(0.896599 + 1.55296i) q^{25} +(1.19255 - 8.66283i) q^{26} +(-5.15842 - 0.625100i) q^{27} +(-1.30289 + 4.64250i) q^{28} +(2.55291 + 4.42177i) q^{29} +(-2.82783 + 3.35324i) q^{30} +(5.95312 + 3.43703i) q^{31} +(5.28786 - 2.00961i) q^{32} +(-0.110092 + 2.73729i) q^{33} +(-4.84528 + 1.97355i) q^{34} +4.31738i q^{35} +(5.62796 + 2.07992i) q^{36} +5.24328i q^{37} +(1.66946 + 4.09870i) q^{38} +(-9.48268 + 4.97786i) q^{39} +(4.07232 - 3.01175i) q^{40} +(-5.32220 - 3.07278i) q^{41} +(5.55436 - 2.00612i) q^{42} +(-0.452455 - 0.783675i) q^{43} +(0.854739 - 3.04564i) q^{44} +(5.35491 + 0.431438i) q^{45} +(3.81174 + 0.524733i) q^{46} +(-4.88993 - 8.46960i) q^{47} +(-5.76690 - 3.83965i) q^{48} +(-0.593711 + 1.02834i) q^{49} +(-1.55565 + 2.00277i) q^{50} +(5.41592 + 3.42422i) q^{51} +(11.9822 - 3.05948i) q^{52} +7.05913 q^{53} +(-1.93317 - 7.08963i) q^{54} -2.83235i q^{55} +(-6.77550 + 0.770215i) q^{56} +(2.89660 - 4.58141i) q^{57} +(-4.42944 + 5.70254i) q^{58} +(-6.10118 - 3.52252i) q^{59} +(-5.90042 - 1.91484i) q^{60} +(3.05109 - 1.76155i) q^{61} +(-1.32577 + 9.63057i) q^{62} +(-5.95312 - 4.10775i) q^{63} +(5.45299 + 5.85362i) q^{64} +(9.58933 - 5.53640i) q^{65} +(-3.64385 + 1.31608i) q^{66} +(1.03786 - 1.79762i) q^{67} +(-5.16966 - 5.29319i) q^{68} +(-2.19031 - 4.17248i) q^{69} +(-5.65463 + 2.30321i) q^{70} -3.31507 q^{71} +(0.278229 + 8.48072i) q^{72} +0.631029 q^{73} +(-6.86730 + 2.79715i) q^{74} +(3.10340 + 0.124816i) q^{75} +(-4.47759 + 4.37310i) q^{76} +(-1.90662 + 3.30237i) q^{77} +(-11.5784 - 9.76424i) q^{78} +(-7.82515 + 4.51785i) q^{79} +(6.11707 + 3.72697i) q^{80} +(-5.68980 + 6.97325i) q^{81} +(1.18526 - 8.60992i) q^{82} +(13.5542 - 7.82551i) q^{83} +(5.59059 + 6.20453i) q^{84} +(-5.73722 - 3.31239i) q^{85} +(0.785033 - 1.01067i) q^{86} +(8.83640 + 0.355393i) q^{87} +(4.44496 - 0.505287i) q^{88} -1.16402i q^{89} +(2.29164 + 7.24368i) q^{90} -14.9075 q^{91} +(1.34620 + 5.27230i) q^{92} +(10.5420 - 5.53394i) q^{93} +(8.48428 - 10.9228i) q^{94} +(-2.80200 + 4.85321i) q^{95} +(1.95243 - 9.60146i) q^{96} +(-6.72981 - 11.6564i) q^{97} +(-1.66358 - 0.229013i) q^{98} +(3.90545 + 2.69482i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 3 q^{2} - 6 q^{3} - 5 q^{4} - 3 q^{6} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 3 q^{2} - 6 q^{3} - 5 q^{4} - 3 q^{6} - 6 q^{9} + 12 q^{11} - 6 q^{12} - 18 q^{14} + 7 q^{16} - 4 q^{19} + 18 q^{20} - q^{22} + 21 q^{24} - 14 q^{25} - 36 q^{27} - 12 q^{28} + 12 q^{30} + 27 q^{32} + 12 q^{33} - 13 q^{34} + 27 q^{36} - 15 q^{38} - 12 q^{40} - 36 q^{41} + 42 q^{42} + 8 q^{43} + 12 q^{46} - 27 q^{48} + 10 q^{49} + 51 q^{50} + 18 q^{51} - 18 q^{52} + 39 q^{54} - 66 q^{56} + 18 q^{57} + 12 q^{58} + 12 q^{59} - 72 q^{60} + 34 q^{64} - 6 q^{65} - 24 q^{66} - 16 q^{67} - 9 q^{68} + 18 q^{70} - 21 q^{72} - 4 q^{73} - 60 q^{74} + 78 q^{75} - 7 q^{76} - 72 q^{78} - 6 q^{81} - 22 q^{82} + 54 q^{83} + 12 q^{84} - 51 q^{86} - 13 q^{88} - 66 q^{90} - 36 q^{91} + 84 q^{92} + 24 q^{94} + 42 q^{96} + 8 q^{97} - 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/72\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(55\) \(65\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.533474 + 1.30973i 0.377223 + 0.926122i
\(3\) 0.925606 1.46399i 0.534399 0.845232i
\(4\) −1.43081 + 1.39742i −0.715405 + 0.698710i
\(5\) −0.895377 + 1.55084i −0.400425 + 0.693556i −0.993777 0.111387i \(-0.964471\pi\)
0.593352 + 0.804943i \(0.297804\pi\)
\(6\) 2.41122 + 0.431300i 0.984376 + 0.176078i
\(7\) 2.08793 1.20546i 0.789162 0.455623i −0.0505056 0.998724i \(-0.516083\pi\)
0.839667 + 0.543101i \(0.182750\pi\)
\(8\) −2.59355 1.12850i −0.916958 0.398984i
\(9\) −1.28651 2.71015i −0.428836 0.903382i
\(10\) −2.50885 0.345375i −0.793368 0.109217i
\(11\) −1.36975 + 0.790826i −0.412995 + 0.238443i −0.692076 0.721825i \(-0.743304\pi\)
0.279081 + 0.960268i \(0.409970\pi\)
\(12\) 0.721434 + 3.38815i 0.208260 + 0.978073i
\(13\) −5.35491 3.09166i −1.48519 0.857472i −0.485327 0.874332i \(-0.661300\pi\)
−0.999858 + 0.0168604i \(0.994633\pi\)
\(14\) 2.69269 + 2.09155i 0.719652 + 0.558989i
\(15\) 1.44164 + 2.74629i 0.372230 + 0.709088i
\(16\) 0.0944399 3.99888i 0.0236100 0.999721i
\(17\) 3.69943i 0.897244i 0.893722 + 0.448622i \(0.148085\pi\)
−0.893722 + 0.448622i \(0.851915\pi\)
\(18\) 2.86326 3.13078i 0.674876 0.737931i
\(19\) 3.12941 0.717936 0.358968 0.933350i \(-0.383129\pi\)
0.358968 + 0.933350i \(0.383129\pi\)
\(20\) −0.886056 3.47017i −0.198128 0.775955i
\(21\) 0.167814 4.17248i 0.0366200 0.910509i
\(22\) −1.76650 1.37212i −0.376619 0.292538i
\(23\) 1.36036 2.35622i 0.283655 0.491305i −0.688627 0.725116i \(-0.741786\pi\)
0.972282 + 0.233811i \(0.0751196\pi\)
\(24\) −4.05271 + 2.75238i −0.827255 + 0.561826i
\(25\) 0.896599 + 1.55296i 0.179320 + 0.310591i
\(26\) 1.19255 8.66283i 0.233878 1.69892i
\(27\) −5.15842 0.625100i −0.992738 0.120301i
\(28\) −1.30289 + 4.64250i −0.246223 + 0.877350i
\(29\) 2.55291 + 4.42177i 0.474064 + 0.821102i 0.999559 0.0296942i \(-0.00945336\pi\)
−0.525495 + 0.850796i \(0.676120\pi\)
\(30\) −2.82783 + 3.35324i −0.516288 + 0.612215i
\(31\) 5.95312 + 3.43703i 1.06921 + 0.617310i 0.927966 0.372665i \(-0.121556\pi\)
0.141246 + 0.989975i \(0.454889\pi\)
\(32\) 5.28786 2.00961i 0.934770 0.355252i
\(33\) −0.110092 + 2.73729i −0.0191645 + 0.476501i
\(34\) −4.84528 + 1.97355i −0.830958 + 0.338461i
\(35\) 4.31738i 0.729771i
\(36\) 5.62796 + 2.07992i 0.937993 + 0.346653i
\(37\) 5.24328i 0.861990i 0.902354 + 0.430995i \(0.141837\pi\)
−0.902354 + 0.430995i \(0.858163\pi\)
\(38\) 1.66946 + 4.09870i 0.270822 + 0.664896i
\(39\) −9.48268 + 4.97786i −1.51844 + 0.797095i
\(40\) 4.07232 3.01175i 0.643890 0.476199i
\(41\) −5.32220 3.07278i −0.831189 0.479887i 0.0230708 0.999734i \(-0.492656\pi\)
−0.854260 + 0.519847i \(0.825989\pi\)
\(42\) 5.55436 2.00612i 0.857057 0.309551i
\(43\) −0.452455 0.783675i −0.0689987 0.119509i 0.829462 0.558563i \(-0.188647\pi\)
−0.898461 + 0.439054i \(0.855314\pi\)
\(44\) 0.854739 3.04564i 0.128857 0.459147i
\(45\) 5.35491 + 0.431438i 0.798263 + 0.0643150i
\(46\) 3.81174 + 0.524733i 0.562010 + 0.0773677i
\(47\) −4.88993 8.46960i −0.713269 1.23542i −0.963623 0.267264i \(-0.913880\pi\)
0.250354 0.968154i \(-0.419453\pi\)
\(48\) −5.76690 3.83965i −0.832380 0.554206i
\(49\) −0.593711 + 1.02834i −0.0848159 + 0.146905i
\(50\) −1.55565 + 2.00277i −0.220002 + 0.283234i
\(51\) 5.41592 + 3.42422i 0.758380 + 0.479486i
\(52\) 11.9822 3.05948i 1.66163 0.424273i
\(53\) 7.05913 0.969646 0.484823 0.874612i \(-0.338884\pi\)
0.484823 + 0.874612i \(0.338884\pi\)
\(54\) −1.93317 7.08963i −0.263071 0.964777i
\(55\) 2.83235i 0.381914i
\(56\) −6.77550 + 0.770215i −0.905414 + 0.102924i
\(57\) 2.89660 4.58141i 0.383664 0.606822i
\(58\) −4.42944 + 5.70254i −0.581613 + 0.748780i
\(59\) −6.10118 3.52252i −0.794306 0.458593i 0.0471702 0.998887i \(-0.484980\pi\)
−0.841476 + 0.540294i \(0.818313\pi\)
\(60\) −5.90042 1.91484i −0.761742 0.247205i
\(61\) 3.05109 1.76155i 0.390652 0.225543i −0.291790 0.956482i \(-0.594251\pi\)
0.682443 + 0.730939i \(0.260918\pi\)
\(62\) −1.32577 + 9.63057i −0.168373 + 1.22308i
\(63\) −5.95312 4.10775i −0.750022 0.517527i
\(64\) 5.45299 + 5.85362i 0.681624 + 0.731703i
\(65\) 9.58933 5.53640i 1.18941 0.686706i
\(66\) −3.64385 + 1.31608i −0.448527 + 0.161998i
\(67\) 1.03786 1.79762i 0.126794 0.219614i −0.795639 0.605772i \(-0.792865\pi\)
0.922433 + 0.386158i \(0.126198\pi\)
\(68\) −5.16966 5.29319i −0.626913 0.641893i
\(69\) −2.19031 4.17248i −0.263682 0.502307i
\(70\) −5.65463 + 2.30321i −0.675857 + 0.275286i
\(71\) −3.31507 −0.393426 −0.196713 0.980461i \(-0.563027\pi\)
−0.196713 + 0.980461i \(0.563027\pi\)
\(72\) 0.278229 + 8.48072i 0.0327896 + 0.999462i
\(73\) 0.631029 0.0738563 0.0369282 0.999318i \(-0.488243\pi\)
0.0369282 + 0.999318i \(0.488243\pi\)
\(74\) −6.86730 + 2.79715i −0.798308 + 0.325162i
\(75\) 3.10340 + 0.124816i 0.358350 + 0.0144125i
\(76\) −4.47759 + 4.37310i −0.513615 + 0.501628i
\(77\) −1.90662 + 3.30237i −0.217280 + 0.376340i
\(78\) −11.5784 9.76424i −1.31100 1.10558i
\(79\) −7.82515 + 4.51785i −0.880398 + 0.508298i −0.870790 0.491656i \(-0.836392\pi\)
−0.00960849 + 0.999954i \(0.503059\pi\)
\(80\) 6.11707 + 3.72697i 0.683909 + 0.416688i
\(81\) −5.68980 + 6.97325i −0.632200 + 0.774806i
\(82\) 1.18526 8.60992i 0.130891 0.950807i
\(83\) 13.5542 7.82551i 1.48776 0.858961i 0.487861 0.872921i \(-0.337777\pi\)
0.999903 + 0.0139604i \(0.00444387\pi\)
\(84\) 5.59059 + 6.20453i 0.609983 + 0.676970i
\(85\) −5.73722 3.31239i −0.622289 0.359279i
\(86\) 0.785033 1.01067i 0.0846523 0.108983i
\(87\) 8.83640 + 0.355393i 0.947361 + 0.0381021i
\(88\) 4.44496 0.505287i 0.473834 0.0538638i
\(89\) 1.16402i 0.123386i −0.998095 0.0616929i \(-0.980350\pi\)
0.998095 0.0616929i \(-0.0196499\pi\)
\(90\) 2.29164 + 7.24368i 0.241560 + 0.763550i
\(91\) −14.9075 −1.56274
\(92\) 1.34620 + 5.27230i 0.140351 + 0.549675i
\(93\) 10.5420 5.53394i 1.09316 0.573843i
\(94\) 8.48428 10.9228i 0.875087 1.12660i
\(95\) −2.80200 + 4.85321i −0.287479 + 0.497929i
\(96\) 1.95243 9.60146i 0.199270 0.979945i
\(97\) −6.72981 11.6564i −0.683309 1.18353i −0.973965 0.226698i \(-0.927207\pi\)
0.290656 0.956827i \(-0.406126\pi\)
\(98\) −1.66358 0.229013i −0.168047 0.0231338i
\(99\) 3.90545 + 2.69482i 0.392512 + 0.270840i
\(100\) −3.45299 0.969060i −0.345299 0.0969060i
\(101\) −3.28047 5.68195i −0.326419 0.565375i 0.655379 0.755300i \(-0.272509\pi\)
−0.981799 + 0.189925i \(0.939175\pi\)
\(102\) −1.59557 + 8.92014i −0.157985 + 0.883226i
\(103\) 5.12167 + 2.95700i 0.504653 + 0.291361i 0.730633 0.682771i \(-0.239225\pi\)
−0.225980 + 0.974132i \(0.572558\pi\)
\(104\) 10.3993 + 14.0614i 1.01974 + 1.37883i
\(105\) 6.32058 + 3.99619i 0.616826 + 0.389989i
\(106\) 3.76586 + 9.24559i 0.365773 + 0.898011i
\(107\) 1.01487i 0.0981111i −0.998796 0.0490555i \(-0.984379\pi\)
0.998796 0.0490555i \(-0.0156211\pi\)
\(108\) 8.25424 6.31407i 0.794265 0.607572i
\(109\) 4.46314i 0.427491i 0.976889 + 0.213746i \(0.0685664\pi\)
−0.976889 + 0.213746i \(0.931434\pi\)
\(110\) 3.70963 1.51098i 0.353699 0.144067i
\(111\) 7.67608 + 4.85321i 0.728582 + 0.460646i
\(112\) −4.62333 8.46322i −0.436864 0.799699i
\(113\) 7.35628 + 4.24715i 0.692021 + 0.399538i 0.804369 0.594131i \(-0.202504\pi\)
−0.112348 + 0.993669i \(0.535837\pi\)
\(114\) 7.54569 + 1.34971i 0.706719 + 0.126412i
\(115\) 2.43607 + 4.21940i 0.227165 + 0.393462i
\(116\) −9.83180 2.75923i −0.912860 0.256188i
\(117\) −1.48972 + 18.4900i −0.137725 + 1.70941i
\(118\) 1.35874 9.87010i 0.125082 0.908616i
\(119\) 4.45953 + 7.72414i 0.408805 + 0.708071i
\(120\) −0.639790 8.74951i −0.0584046 0.798717i
\(121\) −4.24919 + 7.35981i −0.386290 + 0.669074i
\(122\) 3.93484 + 3.05638i 0.356244 + 0.276712i
\(123\) −9.42476 + 4.94745i −0.849802 + 0.446097i
\(124\) −13.3208 + 3.40125i −1.19624 + 0.305442i
\(125\) −12.1650 −1.08807
\(126\) 2.20423 9.98838i 0.196368 0.889836i
\(127\) 15.9098i 1.41176i −0.708329 0.705882i \(-0.750551\pi\)
0.708329 0.705882i \(-0.249449\pi\)
\(128\) −4.75766 + 10.2647i −0.420522 + 0.907282i
\(129\) −1.56608 0.0629866i −0.137886 0.00554566i
\(130\) 12.3669 + 9.60596i 1.08465 + 0.842498i
\(131\) 1.38769 + 0.801182i 0.121243 + 0.0699996i 0.559395 0.828901i \(-0.311034\pi\)
−0.438152 + 0.898901i \(0.644367\pi\)
\(132\) −3.66762 4.07038i −0.319225 0.354281i
\(133\) 6.53397 3.77239i 0.566567 0.327108i
\(134\) 2.90807 + 0.400333i 0.251219 + 0.0345835i
\(135\) 5.58816 7.44017i 0.480952 0.640348i
\(136\) 4.17480 9.59466i 0.357986 0.822735i
\(137\) −10.6153 + 6.12877i −0.906930 + 0.523616i −0.879442 0.476006i \(-0.842084\pi\)
−0.0274877 + 0.999622i \(0.508751\pi\)
\(138\) 4.29637 5.09463i 0.365731 0.433684i
\(139\) −0.618940 + 1.07204i −0.0524978 + 0.0909289i −0.891080 0.453846i \(-0.850052\pi\)
0.838582 + 0.544775i \(0.183385\pi\)
\(140\) −6.03319 6.17736i −0.509898 0.522082i
\(141\) −16.9255 0.680731i −1.42539 0.0573279i
\(142\) −1.76850 4.34186i −0.148409 0.364361i
\(143\) 9.77985 0.817832
\(144\) −10.9591 + 4.88865i −0.913255 + 0.407387i
\(145\) −9.14327 −0.759307
\(146\) 0.336637 + 0.826480i 0.0278603 + 0.0684000i
\(147\) 0.955929 + 1.82102i 0.0788437 + 0.150195i
\(148\) −7.32706 7.50214i −0.602280 0.616672i
\(149\) 2.96982 5.14387i 0.243297 0.421402i −0.718355 0.695677i \(-0.755104\pi\)
0.961651 + 0.274275i \(0.0884378\pi\)
\(150\) 1.49211 + 4.13122i 0.121830 + 0.337313i
\(151\) −11.9663 + 6.90874i −0.973803 + 0.562226i −0.900394 0.435076i \(-0.856721\pi\)
−0.0734098 + 0.997302i \(0.523388\pi\)
\(152\) −8.11627 3.53153i −0.658317 0.286445i
\(153\) 10.0260 4.75935i 0.810555 0.384770i
\(154\) −5.34236 0.735444i −0.430500 0.0592637i
\(155\) −10.6606 + 6.15488i −0.856278 + 0.494372i
\(156\) 6.61178 20.3737i 0.529366 1.63120i
\(157\) 4.98995 + 2.88095i 0.398241 + 0.229925i 0.685725 0.727861i \(-0.259485\pi\)
−0.287483 + 0.957786i \(0.592819\pi\)
\(158\) −10.0917 7.83871i −0.802853 0.623615i
\(159\) 6.53397 10.3345i 0.518178 0.819576i
\(160\) −1.61805 + 9.99998i −0.127918 + 0.790568i
\(161\) 6.55947i 0.516959i
\(162\) −12.1685 3.73208i −0.956045 0.293220i
\(163\) 11.2888 0.884209 0.442104 0.896964i \(-0.354232\pi\)
0.442104 + 0.896964i \(0.354232\pi\)
\(164\) 11.9090 3.04079i 0.929939 0.237446i
\(165\) −4.14652 2.62164i −0.322806 0.204094i
\(166\) 17.4801 + 13.5777i 1.35672 + 1.05383i
\(167\) 0.378448 0.655492i 0.0292852 0.0507235i −0.851011 0.525147i \(-0.824010\pi\)
0.880297 + 0.474424i \(0.157344\pi\)
\(168\) −5.14386 + 10.6321i −0.396857 + 0.820288i
\(169\) 12.6167 + 21.8528i 0.970517 + 1.68098i
\(170\) 1.27769 9.28132i 0.0979943 0.711844i
\(171\) −4.02601 8.48116i −0.307876 0.648570i
\(172\) 1.74250 + 0.489021i 0.132864 + 0.0372875i
\(173\) −4.62735 8.01480i −0.351811 0.609354i 0.634756 0.772713i \(-0.281101\pi\)
−0.986567 + 0.163359i \(0.947767\pi\)
\(174\) 4.24852 + 11.7629i 0.322079 + 0.891745i
\(175\) 3.74406 + 2.16164i 0.283025 + 0.163404i
\(176\) 3.03306 + 5.55216i 0.228626 + 0.418510i
\(177\) −10.8042 + 5.67158i −0.812094 + 0.426302i
\(178\) 1.52456 0.620974i 0.114270 0.0465439i
\(179\) 1.56530i 0.116996i 0.998288 + 0.0584980i \(0.0186311\pi\)
−0.998288 + 0.0584980i \(0.981369\pi\)
\(180\) −8.26477 + 6.86575i −0.616019 + 0.511743i
\(181\) 3.68300i 0.273755i 0.990588 + 0.136878i \(0.0437067\pi\)
−0.990588 + 0.136878i \(0.956293\pi\)
\(182\) −7.95279 19.5249i −0.589500 1.44728i
\(183\) 0.245227 6.09726i 0.0181277 0.450722i
\(184\) −6.18715 + 4.57580i −0.456122 + 0.337332i
\(185\) −8.13148 4.69471i −0.597838 0.345162i
\(186\) 12.8719 + 10.8550i 0.943812 + 0.795929i
\(187\) −2.92561 5.06730i −0.213941 0.370558i
\(188\) 18.8321 + 5.28512i 1.37348 + 0.385457i
\(189\) −11.5239 + 4.91312i −0.838242 + 0.357377i
\(190\) −7.85121 1.08082i −0.569587 0.0784108i
\(191\) 11.8678 + 20.5556i 0.858722 + 1.48735i 0.873148 + 0.487455i \(0.162075\pi\)
−0.0144258 + 0.999896i \(0.504592\pi\)
\(192\) 13.6169 2.56496i 0.982718 0.185110i
\(193\) 12.8012 22.1723i 0.921451 1.59600i 0.124279 0.992247i \(-0.460338\pi\)
0.797172 0.603752i \(-0.206328\pi\)
\(194\) 11.6766 15.0326i 0.838330 1.07928i
\(195\) 0.770728 19.1632i 0.0551929 1.37230i
\(196\) −0.587531 2.30102i −0.0419665 0.164359i
\(197\) −5.76656 −0.410850 −0.205425 0.978673i \(-0.565858\pi\)
−0.205425 + 0.978673i \(0.565858\pi\)
\(198\) −1.44605 + 6.55272i −0.102766 + 0.465681i
\(199\) 1.24163i 0.0880169i 0.999031 + 0.0440085i \(0.0140129\pi\)
−0.999031 + 0.0440085i \(0.985987\pi\)
\(200\) −0.572870 5.03947i −0.0405080 0.356345i
\(201\) −1.67104 3.18329i −0.117866 0.224532i
\(202\) 5.69180 7.32772i 0.400473 0.515577i
\(203\) 10.6606 + 6.15488i 0.748226 + 0.431988i
\(204\) −12.5342 + 2.66890i −0.877571 + 0.186860i
\(205\) 9.53076 5.50259i 0.665657 0.384317i
\(206\) −1.14060 + 8.28550i −0.0794696 + 0.577278i
\(207\) −8.13581 0.655492i −0.565478 0.0455598i
\(208\) −12.8689 + 21.1217i −0.892298 + 1.46453i
\(209\) −4.28651 + 2.47482i −0.296504 + 0.171187i
\(210\) −1.86209 + 10.4102i −0.128496 + 0.718369i
\(211\) 1.62194 2.80928i 0.111659 0.193399i −0.804780 0.593573i \(-0.797717\pi\)
0.916439 + 0.400174i \(0.131050\pi\)
\(212\) −10.1003 + 9.86456i −0.693690 + 0.677501i
\(213\) −3.06844 + 4.85321i −0.210246 + 0.332536i
\(214\) 1.32921 0.541406i 0.0908629 0.0370098i
\(215\) 1.62047 0.110515
\(216\) 12.6732 + 7.44248i 0.862301 + 0.506397i
\(217\) 16.5729 1.12504
\(218\) −5.84553 + 2.38097i −0.395909 + 0.161260i
\(219\) 0.584084 0.923817i 0.0394687 0.0624258i
\(220\) 3.95798 + 4.05256i 0.266847 + 0.273223i
\(221\) 11.4374 19.8101i 0.769362 1.33257i
\(222\) −2.26143 + 12.6427i −0.151777 + 0.848522i
\(223\) −12.1221 + 6.99871i −0.811758 + 0.468669i −0.847566 0.530690i \(-0.821933\pi\)
0.0358081 + 0.999359i \(0.488599\pi\)
\(224\) 8.61815 10.5702i 0.575824 0.706254i
\(225\) 3.05526 4.42780i 0.203684 0.295187i
\(226\) −1.63826 + 11.9005i −0.108975 + 0.791611i
\(227\) −8.75366 + 5.05393i −0.581001 + 0.335441i −0.761531 0.648128i \(-0.775552\pi\)
0.180530 + 0.983569i \(0.442219\pi\)
\(228\) 2.25766 + 10.6029i 0.149517 + 0.702194i
\(229\) 9.93043 + 5.73334i 0.656221 + 0.378869i 0.790836 0.612029i \(-0.209646\pi\)
−0.134615 + 0.990898i \(0.542980\pi\)
\(230\) −4.22672 + 5.44155i −0.278702 + 0.358805i
\(231\) 3.06984 + 5.84796i 0.201981 + 0.384768i
\(232\) −1.63115 14.3490i −0.107090 0.942060i
\(233\) 6.74860i 0.442115i 0.975261 + 0.221058i \(0.0709509\pi\)
−0.975261 + 0.221058i \(0.929049\pi\)
\(234\) −25.0118 + 7.91282i −1.63507 + 0.517277i
\(235\) 17.5133 1.14244
\(236\) 13.6521 3.48585i 0.888674 0.226909i
\(237\) −0.628934 + 15.6377i −0.0408537 + 1.01578i
\(238\) −7.73753 + 9.96144i −0.501550 + 0.645704i
\(239\) 0.0677896 0.117415i 0.00438494 0.00759495i −0.863825 0.503793i \(-0.831938\pi\)
0.868210 + 0.496198i \(0.165271\pi\)
\(240\) 11.1182 5.50559i 0.717678 0.355384i
\(241\) −9.71742 16.8311i −0.625954 1.08418i −0.988355 0.152163i \(-0.951376\pi\)
0.362401 0.932022i \(-0.381957\pi\)
\(242\) −11.9062 1.63904i −0.765362 0.105362i
\(243\) 4.94223 + 14.7843i 0.317044 + 0.948411i
\(244\) −1.90391 + 6.78410i −0.121886 + 0.434307i
\(245\) −1.06319 1.84150i −0.0679248 0.117649i
\(246\) −11.5077 9.70461i −0.733705 0.618743i
\(247\) −16.7577 9.67507i −1.06627 0.615610i
\(248\) −11.5610 15.6322i −0.734126 0.992645i
\(249\) 1.08940 27.0864i 0.0690376 1.71653i
\(250\) −6.48969 15.9329i −0.410444 1.00768i
\(251\) 18.7837i 1.18561i −0.805344 0.592807i \(-0.798020\pi\)
0.805344 0.592807i \(-0.201980\pi\)
\(252\) 14.2580 2.44159i 0.898171 0.153806i
\(253\) 4.30324i 0.270542i
\(254\) 20.8376 8.48745i 1.30747 0.532550i
\(255\) −10.1597 + 5.33325i −0.636225 + 0.333981i
\(256\) −15.9822 0.755308i −0.998885 0.0472068i
\(257\) 18.6937 + 10.7928i 1.16608 + 0.673238i 0.952754 0.303742i \(-0.0982362\pi\)
0.213329 + 0.976981i \(0.431570\pi\)
\(258\) −0.752969 2.08476i −0.0468778 0.129791i
\(259\) 6.32058 + 10.9476i 0.392742 + 0.680249i
\(260\) −5.98385 + 21.3219i −0.371102 + 1.32233i
\(261\) 8.69931 12.6074i 0.538474 0.780379i
\(262\) −0.309041 + 2.24491i −0.0190926 + 0.138691i
\(263\) −8.56995 14.8436i −0.528446 0.915295i −0.999450 0.0331642i \(-0.989442\pi\)
0.471004 0.882131i \(-0.343892\pi\)
\(264\) 3.37455 6.97505i 0.207689 0.429285i
\(265\) −6.32058 + 10.9476i −0.388270 + 0.672504i
\(266\) 8.42654 + 6.54530i 0.516664 + 0.401318i
\(267\) −1.70411 1.07742i −0.104290 0.0659372i
\(268\) 1.02705 + 4.02237i 0.0627371 + 0.245705i
\(269\) 20.1271 1.22717 0.613585 0.789629i \(-0.289727\pi\)
0.613585 + 0.789629i \(0.289727\pi\)
\(270\) 12.7258 + 3.34987i 0.774467 + 0.203866i
\(271\) 6.20336i 0.376827i −0.982090 0.188414i \(-0.939665\pi\)
0.982090 0.188414i \(-0.0603345\pi\)
\(272\) 14.7936 + 0.349374i 0.896994 + 0.0211839i
\(273\) −13.7985 + 21.8244i −0.835124 + 1.32087i
\(274\) −13.6901 10.6337i −0.827047 0.642408i
\(275\) −2.45623 1.41811i −0.148116 0.0855151i
\(276\) 8.96462 + 2.90925i 0.539606 + 0.175116i
\(277\) 10.6060 6.12340i 0.637256 0.367920i −0.146301 0.989240i \(-0.546737\pi\)
0.783557 + 0.621320i \(0.213403\pi\)
\(278\) −1.73427 0.238744i −0.104015 0.0143189i
\(279\) 1.65614 20.5556i 0.0991504 1.23063i
\(280\) 4.87215 11.1973i 0.291167 0.669169i
\(281\) −15.1623 + 8.75399i −0.904510 + 0.522219i −0.878661 0.477447i \(-0.841562\pi\)
−0.0258492 + 0.999666i \(0.508229\pi\)
\(282\) −8.13775 22.5311i −0.484596 1.34171i
\(283\) −3.79698 + 6.57656i −0.225707 + 0.390936i −0.956531 0.291630i \(-0.905802\pi\)
0.730824 + 0.682565i \(0.239136\pi\)
\(284\) 4.74323 4.63254i 0.281459 0.274890i
\(285\) 4.51148 + 8.59425i 0.267237 + 0.509079i
\(286\) 5.21730 + 12.8090i 0.308505 + 0.757413i
\(287\) −14.8165 −0.874590
\(288\) −12.2492 11.7455i −0.721792 0.692110i
\(289\) 3.31420 0.194953
\(290\) −4.87770 11.9753i −0.286428 0.703212i
\(291\) −23.2939 0.936863i −1.36551 0.0549199i
\(292\) −0.902883 + 0.881812i −0.0528372 + 0.0516041i
\(293\) −12.6164 + 21.8523i −0.737061 + 1.27663i 0.216753 + 0.976227i \(0.430454\pi\)
−0.953813 + 0.300400i \(0.902880\pi\)
\(294\) −1.87509 + 2.22348i −0.109357 + 0.129676i
\(295\) 10.9257 6.30797i 0.636120 0.367264i
\(296\) 5.91702 13.5987i 0.343920 0.790408i
\(297\) 7.56008 3.22318i 0.438681 0.187028i
\(298\) 8.32143 + 1.14555i 0.482047 + 0.0663599i
\(299\) −14.5692 + 8.41155i −0.842561 + 0.486453i
\(300\) −4.61480 + 4.15816i −0.266436 + 0.240072i
\(301\) −1.88938 1.09084i −0.108902 0.0628748i
\(302\) −15.4323 11.9870i −0.888031 0.689777i
\(303\) −11.3547 0.456678i −0.652311 0.0262354i
\(304\) 0.295541 12.5141i 0.0169504 0.717735i
\(305\) 6.30900i 0.361253i
\(306\) 11.5821 + 10.5924i 0.662105 + 0.605529i
\(307\) −29.5997 −1.68934 −0.844671 0.535286i \(-0.820204\pi\)
−0.844671 + 0.535286i \(0.820204\pi\)
\(308\) −1.88678 7.38942i −0.107509 0.421051i
\(309\) 9.06964 4.76103i 0.515954 0.270846i
\(310\) −13.7484 10.6791i −0.780857 0.606529i
\(311\) −10.3607 + 17.9453i −0.587502 + 1.01758i 0.407057 + 0.913403i \(0.366555\pi\)
−0.994558 + 0.104180i \(0.966778\pi\)
\(312\) 30.2113 2.20914i 1.71038 0.125068i
\(313\) 1.73680 + 3.00823i 0.0981700 + 0.170035i 0.910927 0.412567i \(-0.135368\pi\)
−0.812757 + 0.582603i \(0.802034\pi\)
\(314\) −1.11127 + 8.07242i −0.0627126 + 0.455553i
\(315\) 11.7007 5.55434i 0.659262 0.312952i
\(316\) 4.88298 17.3992i 0.274689 0.978782i
\(317\) 7.64385 + 13.2395i 0.429321 + 0.743606i 0.996813 0.0797728i \(-0.0254195\pi\)
−0.567492 + 0.823379i \(0.692086\pi\)
\(318\) 17.0211 + 3.04460i 0.954497 + 0.170733i
\(319\) −6.99370 4.03781i −0.391572 0.226074i
\(320\) −13.9605 + 3.21551i −0.780416 + 0.179753i
\(321\) −1.48575 0.939368i −0.0829267 0.0524304i
\(322\) 8.59117 3.49931i 0.478767 0.195009i
\(323\) 11.5770i 0.644164i
\(324\) −1.60353 17.9284i −0.0890849 0.996024i
\(325\) 11.0879i 0.615047i
\(326\) 6.02229 + 14.7854i 0.333544 + 0.818885i
\(327\) 6.53397 + 4.13111i 0.361329 + 0.228451i
\(328\) 10.3358 + 13.9755i 0.570698 + 0.771667i
\(329\) −20.4196 11.7893i −1.12577 0.649963i
\(330\) 1.22159 6.82942i 0.0672464 0.375947i
\(331\) 3.09986 + 5.36912i 0.170384 + 0.295114i 0.938554 0.345132i \(-0.112166\pi\)
−0.768170 + 0.640246i \(0.778833\pi\)
\(332\) −8.45795 + 30.1377i −0.464190 + 1.65402i
\(333\) 14.2101 6.74552i 0.778706 0.369652i
\(334\) 1.06041 + 0.145979i 0.0580232 + 0.00798763i
\(335\) 1.85854 + 3.21909i 0.101543 + 0.175878i
\(336\) −16.6694 1.06512i −0.909391 0.0581068i
\(337\) −9.63097 + 16.6813i −0.524632 + 0.908690i 0.474956 + 0.880009i \(0.342464\pi\)
−0.999589 + 0.0286803i \(0.990870\pi\)
\(338\) −21.8907 + 28.1825i −1.19070 + 1.53292i
\(339\) 13.0268 6.83830i 0.707518 0.371406i
\(340\) 12.8377 3.27791i 0.696221 0.177769i
\(341\) −10.8724 −0.588772
\(342\) 8.96030 9.79748i 0.484517 0.529787i
\(343\) 19.7393i 1.06582i
\(344\) 0.289090 + 2.54309i 0.0155867 + 0.137114i
\(345\) 8.43199 + 0.339128i 0.453963 + 0.0182580i
\(346\) 8.02870 10.3363i 0.431625 0.555682i
\(347\) 22.9191 + 13.2323i 1.23036 + 0.710349i 0.967105 0.254378i \(-0.0818706\pi\)
0.263255 + 0.964726i \(0.415204\pi\)
\(348\) −13.1398 + 11.8396i −0.704370 + 0.634672i
\(349\) −14.8362 + 8.56568i −0.794164 + 0.458511i −0.841426 0.540372i \(-0.818284\pi\)
0.0472627 + 0.998882i \(0.484950\pi\)
\(350\) −0.833810 + 6.05691i −0.0445690 + 0.323755i
\(351\) 25.6903 + 19.2954i 1.37124 + 1.02991i
\(352\) −5.65380 + 6.93444i −0.301348 + 0.369607i
\(353\) 26.8134 15.4807i 1.42713 0.823955i 0.430239 0.902715i \(-0.358429\pi\)
0.996894 + 0.0787597i \(0.0250960\pi\)
\(354\) −13.1920 11.1250i −0.701148 0.591287i
\(355\) 2.96823 5.14113i 0.157538 0.272863i
\(356\) 1.62662 + 1.66549i 0.0862108 + 0.0882708i
\(357\) 15.4358 + 0.620816i 0.816949 + 0.0328570i
\(358\) −2.05013 + 0.835047i −0.108353 + 0.0441336i
\(359\) 6.43781 0.339775 0.169887 0.985463i \(-0.445660\pi\)
0.169887 + 0.985463i \(0.445660\pi\)
\(360\) −13.4013 7.16195i −0.706313 0.377468i
\(361\) −9.20680 −0.484569
\(362\) −4.82376 + 1.96479i −0.253531 + 0.103267i
\(363\) 6.84158 + 13.0330i 0.359090 + 0.684057i
\(364\) 21.3299 20.8321i 1.11799 1.09190i
\(365\) −0.565009 + 0.978624i −0.0295739 + 0.0512235i
\(366\) 8.11661 2.93155i 0.424262 0.153234i
\(367\) 23.8725 13.7828i 1.24614 0.719457i 0.275800 0.961215i \(-0.411057\pi\)
0.970337 + 0.241758i \(0.0777241\pi\)
\(368\) −9.29376 5.66245i −0.484471 0.295176i
\(369\) −1.48062 + 18.3771i −0.0770780 + 0.956674i
\(370\) 1.81089 13.1546i 0.0941439 0.683875i
\(371\) 14.7389 8.50953i 0.765208 0.441793i
\(372\) −7.35039 + 22.6496i −0.381100 + 1.17433i
\(373\) −23.2547 13.4261i −1.20408 0.695178i −0.242623 0.970121i \(-0.578008\pi\)
−0.961461 + 0.274942i \(0.911341\pi\)
\(374\) 5.07608 6.53504i 0.262478 0.337919i
\(375\) −11.2599 + 17.8093i −0.581461 + 0.919669i
\(376\) 3.12435 + 27.4846i 0.161126 + 1.41741i
\(377\) 31.5709i 1.62599i
\(378\) −12.5826 12.4723i −0.647179 0.641504i
\(379\) 4.63966 0.238323 0.119162 0.992875i \(-0.461979\pi\)
0.119162 + 0.992875i \(0.461979\pi\)
\(380\) −2.77283 10.8596i −0.142243 0.557085i
\(381\) −23.2917 14.7262i −1.19327 0.754445i
\(382\) −20.5912 + 26.5095i −1.05354 + 1.35635i
\(383\) 17.7531 30.7493i 0.907141 1.57122i 0.0891248 0.996020i \(-0.471593\pi\)
0.818017 0.575195i \(-0.195074\pi\)
\(384\) 10.6237 + 16.4662i 0.542138 + 0.840289i
\(385\) −3.41430 5.91373i −0.174009 0.301392i
\(386\) 35.8690 + 4.93782i 1.82568 + 0.251328i
\(387\) −1.54179 + 2.23442i −0.0783735 + 0.113582i
\(388\) 25.9179 + 7.27370i 1.31578 + 0.369266i
\(389\) 3.19920 + 5.54117i 0.162206 + 0.280949i 0.935659 0.352904i \(-0.114806\pi\)
−0.773454 + 0.633853i \(0.781473\pi\)
\(390\) 25.5098 9.21361i 1.29174 0.466549i
\(391\) 8.71666 + 5.03257i 0.440821 + 0.254508i
\(392\) 2.70029 1.99704i 0.136385 0.100866i
\(393\) 2.45737 1.28998i 0.123958 0.0650707i
\(394\) −3.07631 7.55266i −0.154982 0.380498i
\(395\) 16.1807i 0.814141i
\(396\) −9.35375 + 1.60177i −0.470044 + 0.0804918i
\(397\) 3.01894i 0.151516i 0.997126 + 0.0757581i \(0.0241377\pi\)
−0.997126 + 0.0757581i \(0.975862\pi\)
\(398\) −1.62621 + 0.662378i −0.0815144 + 0.0332020i
\(399\) 0.525158 13.0574i 0.0262908 0.653687i
\(400\) 6.29476 3.43874i 0.314738 0.171937i
\(401\) 25.1191 + 14.5025i 1.25439 + 0.724222i 0.971978 0.235072i \(-0.0755326\pi\)
0.282411 + 0.959294i \(0.408866\pi\)
\(402\) 3.27781 3.88683i 0.163482 0.193857i
\(403\) −21.2523 36.8100i −1.05865 1.83364i
\(404\) 12.6338 + 3.54560i 0.628555 + 0.176400i
\(405\) −5.71987 15.0676i −0.284223 0.748717i
\(406\) −2.37413 + 17.2460i −0.117826 + 0.855904i
\(407\) −4.14652 7.18198i −0.205535 0.355998i
\(408\) −10.1822 14.9927i −0.504095 0.742250i
\(409\) −0.662169 + 1.14691i −0.0327422 + 0.0567111i −0.881932 0.471376i \(-0.843757\pi\)
0.849190 + 0.528087i \(0.177091\pi\)
\(410\) 12.2913 + 9.54728i 0.607026 + 0.471507i
\(411\) −0.853191 + 21.2135i −0.0420848 + 1.04639i
\(412\) −11.4603 + 2.92621i −0.564608 + 0.144164i
\(413\) −16.9851 −0.835781
\(414\) −3.48172 11.0054i −0.171117 0.540888i
\(415\) 28.0271i 1.37580i
\(416\) −34.5291 5.58698i −1.69293 0.273924i
\(417\) 0.996550 + 1.89840i 0.0488013 + 0.0929651i
\(418\) −5.52809 4.29394i −0.270388 0.210023i
\(419\) −27.2974 15.7602i −1.33357 0.769935i −0.347722 0.937598i \(-0.613045\pi\)
−0.985844 + 0.167663i \(0.946378\pi\)
\(420\) −14.6279 + 3.11471i −0.713769 + 0.151982i
\(421\) −30.9851 + 17.8893i −1.51012 + 0.871869i −0.510192 + 0.860061i \(0.670426\pi\)
−0.999930 + 0.0118087i \(0.996241\pi\)
\(422\) 4.54468 + 0.625632i 0.221231 + 0.0304553i
\(423\) −16.6629 + 24.1486i −0.810180 + 1.17415i
\(424\) −18.3082 7.96620i −0.889125 0.386873i
\(425\) −5.74505 + 3.31691i −0.278676 + 0.160894i
\(426\) −7.99335 1.42979i −0.387279 0.0692735i
\(427\) 4.24697 7.35597i 0.205525 0.355980i
\(428\) 1.41820 + 1.45209i 0.0685511 + 0.0701892i
\(429\) 9.05229 14.3176i 0.437049 0.691259i
\(430\) 0.864479 + 2.12239i 0.0416889 + 0.102351i
\(431\) −17.1129 −0.824301 −0.412150 0.911116i \(-0.635222\pi\)
−0.412150 + 0.911116i \(0.635222\pi\)
\(432\) −2.98686 + 20.5689i −0.143705 + 0.989620i
\(433\) −19.1099 −0.918363 −0.459182 0.888342i \(-0.651857\pi\)
−0.459182 + 0.888342i \(0.651857\pi\)
\(434\) 8.84121 + 21.7061i 0.424391 + 1.04193i
\(435\) −8.46307 + 13.3856i −0.405773 + 0.641791i
\(436\) −6.23688 6.38591i −0.298692 0.305830i
\(437\) 4.25713 7.37356i 0.203646 0.352725i
\(438\) 1.52155 + 0.272163i 0.0727024 + 0.0130044i
\(439\) 29.4886 17.0253i 1.40742 0.812572i 0.412277 0.911058i \(-0.364734\pi\)
0.995138 + 0.0984868i \(0.0314002\pi\)
\(440\) −3.19630 + 7.34584i −0.152377 + 0.350199i
\(441\) 3.55076 + 0.286080i 0.169084 + 0.0136229i
\(442\) 32.0476 + 4.41175i 1.52435 + 0.209846i
\(443\) 17.1586 9.90651i 0.815229 0.470673i −0.0335394 0.999437i \(-0.510678\pi\)
0.848768 + 0.528765i \(0.177345\pi\)
\(444\) −17.7650 + 3.78268i −0.843089 + 0.179518i
\(445\) 1.80521 + 1.04224i 0.0855749 + 0.0494067i
\(446\) −15.6333 12.1431i −0.740258 0.574995i
\(447\) −4.78167 9.10896i −0.226165 0.430839i
\(448\) 18.4418 + 5.64854i 0.871292 + 0.266868i
\(449\) 8.73916i 0.412426i −0.978507 0.206213i \(-0.933886\pi\)
0.978507 0.206213i \(-0.0661140\pi\)
\(450\) 7.42915 + 1.63946i 0.350213 + 0.0772847i
\(451\) 9.72012 0.457703
\(452\) −16.4605 + 4.20294i −0.774237 + 0.197690i
\(453\) −0.961772 + 23.9133i −0.0451880 + 1.12354i
\(454\) −11.2892 8.76883i −0.529826 0.411542i
\(455\) 13.3479 23.1192i 0.625758 1.08384i
\(456\) −12.6826 + 8.61331i −0.593916 + 0.403355i
\(457\) −1.25081 2.16647i −0.0585104 0.101343i 0.835287 0.549815i \(-0.185302\pi\)
−0.893797 + 0.448472i \(0.851968\pi\)
\(458\) −2.21152 + 16.0648i −0.103338 + 0.750659i
\(459\) 2.31252 19.0832i 0.107939 0.890728i
\(460\) −9.38184 2.63295i −0.437430 0.122762i
\(461\) −2.63419 4.56255i −0.122686 0.212499i 0.798140 0.602472i \(-0.205818\pi\)
−0.920826 + 0.389973i \(0.872484\pi\)
\(462\) −6.02160 + 7.14041i −0.280150 + 0.332202i
\(463\) 15.2227 + 8.78883i 0.707459 + 0.408451i 0.810119 0.586265i \(-0.199402\pi\)
−0.102661 + 0.994716i \(0.532736\pi\)
\(464\) 17.9232 9.79120i 0.832066 0.454545i
\(465\) −0.856827 + 21.3039i −0.0397344 + 0.987946i
\(466\) −8.83888 + 3.60020i −0.409453 + 0.166776i
\(467\) 2.29842i 0.106358i −0.998585 0.0531791i \(-0.983065\pi\)
0.998585 0.0531791i \(-0.0169354\pi\)
\(468\) −23.7068 28.5375i −1.09585 1.31915i
\(469\) 5.00439i 0.231081i
\(470\) 9.34290 + 22.9378i 0.430956 + 1.05804i
\(471\) 8.83640 4.63859i 0.407160 0.213735i
\(472\) 11.8486 + 16.0210i 0.545374 + 0.737425i
\(473\) 1.23950 + 0.715626i 0.0569923 + 0.0329045i
\(474\) −20.8167 + 7.51855i −0.956143 + 0.345338i
\(475\) 2.80582 + 4.85983i 0.128740 + 0.222984i
\(476\) −17.1746 4.81995i −0.787197 0.220922i
\(477\) −9.08162 19.1313i −0.415819 0.875961i
\(478\) 0.189947 + 0.0261485i 0.00868795 + 0.00119601i
\(479\) −18.0219 31.2149i −0.823442 1.42624i −0.903104 0.429422i \(-0.858717\pi\)
0.0796622 0.996822i \(-0.474616\pi\)
\(480\) 13.1422 + 11.6248i 0.599854 + 0.530599i
\(481\) 16.2104 28.0773i 0.739132 1.28021i
\(482\) 16.8603 21.7062i 0.767963 0.988690i
\(483\) −9.60297 6.07149i −0.436950 0.276262i
\(484\) −4.20496 16.4684i −0.191134 0.748564i
\(485\) 24.1029 1.09446
\(486\) −16.7269 + 14.3600i −0.758748 + 0.651384i
\(487\) 2.72292i 0.123387i 0.998095 + 0.0616937i \(0.0196502\pi\)
−0.998095 + 0.0616937i \(0.980350\pi\)
\(488\) −9.90106 + 1.12552i −0.448200 + 0.0509498i
\(489\) 10.4490 16.5267i 0.472520 0.747362i
\(490\) 1.84469 2.37489i 0.0833347 0.107287i
\(491\) 13.1715 + 7.60457i 0.594421 + 0.343189i 0.766844 0.641834i \(-0.221826\pi\)
−0.172422 + 0.985023i \(0.555159\pi\)
\(492\) 6.57139 20.2492i 0.296261 0.912905i
\(493\) −16.3580 + 9.44432i −0.736729 + 0.425351i
\(494\) 3.73197 27.1095i 0.167909 1.21972i
\(495\) −7.67608 + 3.64384i −0.345014 + 0.163778i
\(496\) 14.3065 23.4812i 0.642382 1.05434i
\(497\) −6.92161 + 3.99619i −0.310477 + 0.179254i
\(498\) 36.0572 13.0231i 1.61576 0.583579i
\(499\) −19.7305 + 34.1743i −0.883260 + 1.52985i −0.0355642 + 0.999367i \(0.511323\pi\)
−0.847695 + 0.530483i \(0.822010\pi\)
\(500\) 17.4057 16.9995i 0.778409 0.760242i
\(501\) −0.609336 1.16077i −0.0272231 0.0518594i
\(502\) 24.6016 10.0206i 1.09802 0.447241i
\(503\) 18.4749 0.823756 0.411878 0.911239i \(-0.364873\pi\)
0.411878 + 0.911239i \(0.364873\pi\)
\(504\) 10.8041 + 17.3717i 0.481254 + 0.773798i
\(505\) 11.7490 0.522826
\(506\) −5.63610 + 2.29566i −0.250555 + 0.102055i
\(507\) 43.6703 + 1.75638i 1.93947 + 0.0780038i
\(508\) 22.2326 + 22.7639i 0.986413 + 1.00998i
\(509\) −17.0068 + 29.4566i −0.753813 + 1.30564i 0.192149 + 0.981366i \(0.438454\pi\)
−0.945962 + 0.324277i \(0.894879\pi\)
\(510\) −12.4051 10.4614i −0.549306 0.463237i
\(511\) 1.31754 0.760683i 0.0582846 0.0336506i
\(512\) −7.53681 21.3353i −0.333083 0.942897i
\(513\) −16.1428 1.95619i −0.712722 0.0863680i
\(514\) −4.16313 + 30.2415i −0.183628 + 1.33390i
\(515\) −9.17165 + 5.29525i −0.404151 + 0.233337i
\(516\) 2.32879 2.09835i 0.102519 0.0923748i
\(517\) 13.3960 + 7.73416i 0.589153 + 0.340148i
\(518\) −10.9666 + 14.1185i −0.481843 + 0.620333i
\(519\) −16.0167 0.644177i −0.703053 0.0282762i
\(520\) −31.1182 + 3.53741i −1.36462 + 0.155126i
\(521\) 12.0788i 0.529182i 0.964361 + 0.264591i \(0.0852369\pi\)
−0.964361 + 0.264591i \(0.914763\pi\)
\(522\) 21.1532 + 4.66807i 0.925851 + 0.204316i
\(523\) 5.27483 0.230652 0.115326 0.993328i \(-0.463209\pi\)
0.115326 + 0.993328i \(0.463209\pi\)
\(524\) −3.10511 + 0.792842i −0.135647 + 0.0346354i
\(525\) 6.63013 3.48043i 0.289363 0.151899i
\(526\) 14.8693 19.1430i 0.648333 0.834676i
\(527\) −12.7151 + 22.0232i −0.553877 + 0.959344i
\(528\) 10.9357 + 0.698752i 0.475915 + 0.0304093i
\(529\) 7.79883 + 13.5080i 0.339080 + 0.587303i
\(530\) −17.7103 2.43804i −0.769286 0.105902i
\(531\) −1.69733 + 21.0668i −0.0736578 + 0.914223i
\(532\) −4.07727 + 14.5283i −0.176772 + 0.629881i
\(533\) 19.0000 + 32.9089i 0.822980 + 1.42544i
\(534\) 0.502041 2.80670i 0.0217254 0.121458i
\(535\) 1.57390 + 0.908690i 0.0680455 + 0.0392861i
\(536\) −4.72033 + 3.49099i −0.203887 + 0.150788i
\(537\) 2.29158 + 1.44885i 0.0988889 + 0.0625226i
\(538\) 10.7373 + 26.3611i 0.462917 + 1.13651i
\(539\) 1.87809i 0.0808950i
\(540\) 2.40144 + 18.4545i 0.103342 + 0.794154i
\(541\) 23.6734i 1.01780i −0.860826 0.508900i \(-0.830052\pi\)
0.860826 0.508900i \(-0.169948\pi\)
\(542\) 8.12475 3.30933i 0.348988 0.142148i
\(543\) 5.39186 + 3.40901i 0.231387 + 0.146295i
\(544\) 7.43442 + 19.5621i 0.318748 + 0.838717i
\(545\) −6.92161 3.99619i −0.296489 0.171178i
\(546\) −35.9454 6.42962i −1.53832 0.275163i
\(547\) 10.5319 + 18.2418i 0.450312 + 0.779964i 0.998405 0.0564536i \(-0.0179793\pi\)
−0.548093 + 0.836417i \(0.684646\pi\)
\(548\) 6.62409 23.6032i 0.282967 1.00828i
\(549\) −8.69931 6.00266i −0.371278 0.256187i
\(550\) 0.547007 3.97354i 0.0233245 0.169432i
\(551\) 7.98910 + 13.8375i 0.340347 + 0.589498i
\(552\) 0.972044 + 13.2933i 0.0413729 + 0.565800i
\(553\) −10.8922 + 18.8659i −0.463184 + 0.802259i
\(554\) 13.6781 + 10.6244i 0.581126 + 0.451389i
\(555\) −14.3995 + 7.55892i −0.611226 + 0.320858i
\(556\) −0.612497 2.39880i −0.0259756 0.101732i
\(557\) 9.64427 0.408641 0.204321 0.978904i \(-0.434502\pi\)
0.204321 + 0.978904i \(0.434502\pi\)
\(558\) 27.8059 8.79677i 1.17712 0.372397i
\(559\) 5.59535i 0.236658i
\(560\) 17.2647 + 0.407733i 0.729567 + 0.0172299i
\(561\) −10.1264 0.407276i −0.427537 0.0171952i
\(562\) −19.5541 15.1886i −0.824841 0.640694i
\(563\) −36.8534 21.2773i −1.55319 0.896733i −0.997880 0.0650873i \(-0.979267\pi\)
−0.555307 0.831645i \(-0.687399\pi\)
\(564\) 25.1685 22.6780i 1.05978 0.954918i
\(565\) −13.1733 + 7.60561i −0.554205 + 0.319970i
\(566\) −10.6391 1.46461i −0.447196 0.0615622i
\(567\) −3.47387 + 21.4185i −0.145889 + 0.899491i
\(568\) 8.59779 + 3.74104i 0.360755 + 0.156971i
\(569\) −8.25996 + 4.76889i −0.346275 + 0.199922i −0.663044 0.748581i \(-0.730736\pi\)
0.316768 + 0.948503i \(0.397402\pi\)
\(570\) −8.84943 + 10.4936i −0.370662 + 0.439531i
\(571\) 13.4455 23.2882i 0.562675 0.974582i −0.434587 0.900630i \(-0.643106\pi\)
0.997262 0.0739518i \(-0.0235611\pi\)
\(572\) −13.9931 + 13.6666i −0.585082 + 0.571427i
\(573\) 41.0780 + 1.65212i 1.71606 + 0.0690185i
\(574\) −7.90421 19.4057i −0.329915 0.809977i
\(575\) 4.87880 0.203460
\(576\) 8.84886 22.3091i 0.368702 0.929547i
\(577\) −8.52363 −0.354843 −0.177422 0.984135i \(-0.556776\pi\)
−0.177422 + 0.984135i \(0.556776\pi\)
\(578\) 1.76804 + 4.34072i 0.0735407 + 0.180550i
\(579\) −20.6111 39.2636i −0.856569 1.63174i
\(580\) 13.0823 12.7770i 0.543213 0.530535i
\(581\) 18.8667 32.6781i 0.782724 1.35572i
\(582\) −11.1997 31.0086i −0.464241 1.28535i
\(583\) −9.66924 + 5.58254i −0.400459 + 0.231205i
\(584\) −1.63660 0.712114i −0.0677232 0.0294675i
\(585\) −27.3412 18.8659i −1.13042 0.780008i
\(586\) −35.3513 4.86655i −1.46035 0.201035i
\(587\) −19.4568 + 11.2334i −0.803067 + 0.463651i −0.844542 0.535489i \(-0.820127\pi\)
0.0414756 + 0.999140i \(0.486794\pi\)
\(588\) −3.91248 1.26970i −0.161348 0.0523616i
\(589\) 18.6297 + 10.7559i 0.767625 + 0.443189i
\(590\) 14.0903 + 10.9447i 0.580090 + 0.450584i
\(591\) −5.33756 + 8.44216i −0.219558 + 0.347264i
\(592\) 20.9673 + 0.495174i 0.861749 + 0.0203515i
\(593\) 28.8424i 1.18442i 0.805785 + 0.592208i \(0.201743\pi\)
−0.805785 + 0.592208i \(0.798257\pi\)
\(594\) 8.25462 + 8.18223i 0.338691 + 0.335721i
\(595\) −15.9719 −0.654783
\(596\) 2.93890 + 11.5100i 0.120382 + 0.471467i
\(597\) 1.81773 + 1.14926i 0.0743947 + 0.0470361i
\(598\) −18.7892 14.5945i −0.768348 0.596813i
\(599\) −8.40225 + 14.5531i −0.343307 + 0.594625i −0.985045 0.172299i \(-0.944880\pi\)
0.641738 + 0.766924i \(0.278214\pi\)
\(600\) −7.90797 3.82589i −0.322841 0.156191i
\(601\) 14.8802 + 25.7732i 0.606974 + 1.05131i 0.991736 + 0.128294i \(0.0409502\pi\)
−0.384762 + 0.923016i \(0.625716\pi\)
\(602\) 0.420769 3.05653i 0.0171493 0.124575i
\(603\) −6.20702 0.500092i −0.252769 0.0203653i
\(604\) 7.46710 26.6070i 0.303832 1.08263i
\(605\) −7.60926 13.1796i −0.309360 0.535828i
\(606\) −5.45932 15.1153i −0.221770 0.614017i
\(607\) −20.9599 12.1012i −0.850737 0.491173i 0.0101625 0.999948i \(-0.496765\pi\)
−0.860899 + 0.508775i \(0.830098\pi\)
\(608\) 16.5479 6.28889i 0.671105 0.255048i
\(609\) 18.8782 9.90993i 0.764981 0.401571i
\(610\) −8.26312 + 3.36569i −0.334564 + 0.136273i
\(611\) 60.4720i 2.44643i
\(612\) −7.69452 + 20.8203i −0.311032 + 0.841609i
\(613\) 38.3189i 1.54769i −0.633377 0.773843i \(-0.718332\pi\)
0.633377 0.773843i \(-0.281668\pi\)
\(614\) −15.7906 38.7677i −0.637259 1.56454i
\(615\) 0.766020 19.0461i 0.0308889 0.768014i
\(616\) 8.67163 6.41324i 0.349390 0.258397i
\(617\) −7.31357 4.22249i −0.294433 0.169991i 0.345506 0.938417i \(-0.387707\pi\)
−0.639939 + 0.768425i \(0.721041\pi\)
\(618\) 11.0741 + 9.33894i 0.445466 + 0.375667i
\(619\) 4.12431 + 7.14352i 0.165770 + 0.287122i 0.936929 0.349521i \(-0.113656\pi\)
−0.771158 + 0.636643i \(0.780322\pi\)
\(620\) 6.65231 23.7038i 0.267163 0.951966i
\(621\) −8.49018 + 11.3040i −0.340699 + 0.453613i
\(622\) −29.0307 3.99644i −1.16403 0.160243i
\(623\) −1.40318 2.43038i −0.0562173 0.0973713i
\(624\) 19.0103 + 38.3903i 0.761022 + 1.53684i
\(625\) 6.40923 11.1011i 0.256369 0.444044i
\(626\) −3.01345 + 3.87957i −0.120442 + 0.155059i
\(627\) −0.344521 + 8.56609i −0.0137589 + 0.342097i
\(628\) −11.1656 + 2.85096i −0.445555 + 0.113766i
\(629\) −19.3972 −0.773415
\(630\) 13.5168 + 12.3618i 0.538521 + 0.492505i
\(631\) 34.0954i 1.35732i −0.734454 0.678659i \(-0.762561\pi\)
0.734454 0.678659i \(-0.237439\pi\)
\(632\) 25.3933 2.88662i 1.01009 0.114824i
\(633\) −2.61147 4.97478i −0.103797 0.197730i
\(634\) −13.2625 + 17.0744i −0.526721 + 0.678110i
\(635\) 24.6735 + 14.2452i 0.979138 + 0.565305i
\(636\) 5.09270 + 23.9174i 0.201939 + 0.948385i
\(637\) 6.35854 3.67111i 0.251935 0.145455i
\(638\) 1.55751 11.3140i 0.0616624 0.447924i
\(639\) 4.26486 + 8.98432i 0.168715 + 0.355414i
\(640\) −11.6590 16.5692i −0.460864 0.654954i
\(641\) 20.9715 12.1079i 0.828324 0.478233i −0.0249544 0.999689i \(-0.507944\pi\)
0.853279 + 0.521455i \(0.174611\pi\)
\(642\) 0.437713 2.44707i 0.0172752 0.0965782i
\(643\) 11.3299 19.6240i 0.446808 0.773895i −0.551368 0.834262i \(-0.685894\pi\)
0.998176 + 0.0603676i \(0.0192273\pi\)
\(644\) 9.16633 + 9.38536i 0.361204 + 0.369835i
\(645\) 1.49992 2.37235i 0.0590592 0.0934110i
\(646\) −15.1628 + 6.17605i −0.596574 + 0.242993i
\(647\) −38.6020 −1.51760 −0.758800 0.651323i \(-0.774214\pi\)
−0.758800 + 0.651323i \(0.774214\pi\)
\(648\) 22.6261 11.6646i 0.888835 0.458227i
\(649\) 11.1428 0.437393
\(650\) 14.5222 5.91512i 0.569609 0.232010i
\(651\) 15.3400 24.2625i 0.601221 0.950921i
\(652\) −16.1522 + 15.7752i −0.632568 + 0.617805i
\(653\) −13.1416 + 22.7619i −0.514271 + 0.890743i 0.485592 + 0.874185i \(0.338604\pi\)
−0.999863 + 0.0165576i \(0.994729\pi\)
\(654\) −1.92495 + 10.7616i −0.0752716 + 0.420812i
\(655\) −2.48501 + 1.43472i −0.0970973 + 0.0560592i
\(656\) −12.7903 + 20.9927i −0.499378 + 0.819627i
\(657\) −0.811823 1.71018i −0.0316722 0.0667205i
\(658\) 4.54748 33.0335i 0.177279 1.28778i
\(659\) 33.1862 19.1601i 1.29275 0.746370i 0.313610 0.949552i \(-0.398462\pi\)
0.979141 + 0.203182i \(0.0651283\pi\)
\(660\) 9.59641 2.04335i 0.373540 0.0795374i
\(661\) 38.7145 + 22.3518i 1.50582 + 0.869385i 0.999977 + 0.00675901i \(0.00215148\pi\)
0.505842 + 0.862626i \(0.331182\pi\)
\(662\) −5.37843 + 6.92429i −0.209039 + 0.269120i
\(663\) −18.4152 35.0805i −0.715189 1.36242i
\(664\) −43.9845 + 5.00000i −1.70693 + 0.194038i
\(665\) 13.5109i 0.523928i
\(666\) 16.4155 + 15.0128i 0.636089 + 0.581736i
\(667\) 13.8915 0.537882
\(668\) 0.374509 + 1.46674i 0.0144902 + 0.0567497i
\(669\) −0.974297 + 24.2247i −0.0376685 + 0.936580i
\(670\) −3.22467 + 4.15150i −0.124580 + 0.160387i
\(671\) −2.78616 + 4.82576i −0.107558 + 0.186297i
\(672\) −7.49768 22.4007i −0.289229 0.864127i
\(673\) −12.8138 22.1942i −0.493937 0.855524i 0.506039 0.862511i \(-0.331109\pi\)
−0.999976 + 0.00698696i \(0.997776\pi\)
\(674\) −26.9860 3.71496i −1.03946 0.143095i
\(675\) −3.65428 8.57125i −0.140653 0.329908i
\(676\) −48.5897 13.6364i −1.86883 0.524476i
\(677\) −11.1613 19.3320i −0.428964 0.742988i 0.567817 0.823155i \(-0.307788\pi\)
−0.996781 + 0.0801666i \(0.974455\pi\)
\(678\) 15.9058 + 13.4136i 0.610859 + 0.515145i
\(679\) −28.1027 16.2251i −1.07848 0.622662i
\(680\) 11.1418 + 15.0653i 0.427267 + 0.577727i
\(681\) −0.703562 + 17.4932i −0.0269605 + 0.670340i
\(682\) −5.80013 14.2399i −0.222099 0.545275i
\(683\) 20.5229i 0.785288i 0.919691 + 0.392644i \(0.128440\pi\)
−0.919691 + 0.392644i \(0.871560\pi\)
\(684\) 17.6122 + 6.50891i 0.673419 + 0.248875i
\(685\) 21.9502i 0.838676i
\(686\) −25.8532 + 10.5304i −0.987081 + 0.402053i
\(687\) 17.5852 9.23119i 0.670917 0.352192i
\(688\) −3.17656 + 1.73530i −0.121105 + 0.0661579i
\(689\) −37.8010 21.8244i −1.44010 0.831444i
\(690\) 4.05408 + 11.2246i 0.154336 + 0.427313i
\(691\) −5.97960 10.3570i −0.227475 0.393998i 0.729584 0.683891i \(-0.239714\pi\)
−0.957059 + 0.289893i \(0.906380\pi\)
\(692\) 17.8209 + 5.00132i 0.677449 + 0.190122i
\(693\) 11.4028 + 0.918709i 0.433156 + 0.0348989i
\(694\) −5.10412 + 37.0770i −0.193750 + 1.40742i
\(695\) −1.10837 1.91975i −0.0420429 0.0728204i
\(696\) −22.5166 10.8936i −0.853488 0.412920i
\(697\) 11.3675 19.6891i 0.430576 0.745779i
\(698\) −19.1335 14.8619i −0.724214 0.562532i
\(699\) 9.87985 + 6.24654i 0.373690 + 0.236266i
\(700\) −8.37776 + 2.13913i −0.316650 + 0.0808516i
\(701\) 41.9171 1.58319 0.791593 0.611049i \(-0.209252\pi\)
0.791593 + 0.611049i \(0.209252\pi\)
\(702\) −11.5668 + 43.9410i −0.436561 + 1.65845i
\(703\) 16.4084i 0.618853i
\(704\) −12.0984 3.70563i −0.455977 0.139661i
\(705\) 16.2104 25.6392i 0.610520 0.965630i
\(706\) 34.5799 + 26.8599i 1.30143 + 1.01088i
\(707\) −13.6988 7.90899i −0.515195 0.297448i
\(708\) 7.53320 23.2130i 0.283115 0.872396i
\(709\) 4.41486 2.54892i 0.165803 0.0957266i −0.414802 0.909912i \(-0.636149\pi\)
0.580606 + 0.814185i \(0.302816\pi\)
\(710\) 8.31700 + 1.14494i 0.312131 + 0.0429688i
\(711\) 22.3112 + 15.3951i 0.836734 + 0.577360i
\(712\) −1.31359 + 3.01894i −0.0492289 + 0.113140i
\(713\) 16.1968 9.35122i 0.606575 0.350206i
\(714\) 7.42149 + 20.5480i 0.277742 + 0.768989i
\(715\) −8.75666 + 15.1670i −0.327480 + 0.567213i
\(716\) −2.18738 2.23965i −0.0817463 0.0836996i
\(717\) −0.109147 0.207923i −0.00407619 0.00776503i
\(718\) 3.43441 + 8.43183i 0.128171 + 0.314673i
\(719\) 35.1676 1.31153 0.655765 0.754965i \(-0.272346\pi\)
0.655765 + 0.754965i \(0.272346\pi\)
\(720\) 2.23099 21.3729i 0.0831441 0.796522i
\(721\) 14.2582 0.531003
\(722\) −4.91159 12.0585i −0.182790 0.448770i
\(723\) −33.6350 1.35277i −1.25090 0.0503101i
\(724\) −5.14670 5.26968i −0.191275 0.195846i
\(725\) −4.57787 + 7.92911i −0.170018 + 0.294480i
\(726\) −13.4200 + 15.9134i −0.498064 + 0.590604i
\(727\) −19.9209 + 11.5013i −0.738826 + 0.426561i −0.821642 0.570003i \(-0.806942\pi\)
0.0828164 + 0.996565i \(0.473609\pi\)
\(728\) 38.6634 + 16.8231i 1.43296 + 0.623506i
\(729\) 26.2185 + 6.44905i 0.971056 + 0.238854i
\(730\) −1.58316 0.217941i −0.0585952 0.00806637i
\(731\) 2.89915 1.67383i 0.107229 0.0619087i
\(732\) 8.16955 + 9.06670i 0.301955 + 0.335115i
\(733\) −7.38177 4.26187i −0.272652 0.157416i 0.357440 0.933936i \(-0.383650\pi\)
−0.630092 + 0.776520i \(0.716983\pi\)
\(734\) 30.7872 + 23.9139i 1.13638 + 0.882679i
\(735\) −3.68003 0.148008i −0.135740 0.00545935i
\(736\) 2.45833 15.1931i 0.0906152 0.560027i
\(737\) 3.28305i 0.120933i
\(738\) −24.8590 + 7.86449i −0.915073 + 0.289496i
\(739\) 32.3956 1.19169 0.595846 0.803099i \(-0.296817\pi\)
0.595846 + 0.803099i \(0.296817\pi\)
\(740\) 18.1951 4.64584i 0.668865 0.170784i
\(741\) −29.6752 + 15.5777i −1.09015 + 0.572263i
\(742\) 19.0081 + 14.7645i 0.697808 + 0.542021i
\(743\) −2.22350 + 3.85122i −0.0815725 + 0.141288i −0.903926 0.427690i \(-0.859328\pi\)
0.822353 + 0.568978i \(0.192661\pi\)
\(744\) −33.5862 + 2.45593i −1.23133 + 0.0900386i
\(745\) 5.31821 + 9.21141i 0.194844 + 0.337480i
\(746\) 5.17887 37.6200i 0.189612 1.37737i
\(747\) −38.6458 26.6662i −1.41398 0.975666i
\(748\) 11.2671 + 3.16205i 0.411967 + 0.115616i
\(749\) −1.22339 2.11897i −0.0447016 0.0774255i
\(750\) −29.3324 5.24674i −1.07107 0.191584i
\(751\) −32.3801 18.6946i −1.18157 0.682177i −0.225189 0.974315i \(-0.572300\pi\)
−0.956376 + 0.292138i \(0.905633\pi\)
\(752\) −34.3308 + 18.7544i −1.25191 + 0.683902i
\(753\) −27.4990 17.3863i −1.00212 0.633591i
\(754\) 41.3495 16.8423i 1.50586 0.613359i
\(755\) 24.7437i 0.900517i
\(756\) 9.62286 23.1335i 0.349980 0.841357i
\(757\) 46.7837i 1.70038i 0.526474 + 0.850191i \(0.323514\pi\)
−0.526474 + 0.850191i \(0.676486\pi\)
\(758\) 2.47514 + 6.07673i 0.0899011 + 0.220717i
\(759\) 6.29988 + 3.98310i 0.228671 + 0.144577i
\(760\) 12.7440 9.42499i 0.462272 0.341880i
\(761\) 5.83226 + 3.36726i 0.211419 + 0.122063i 0.601971 0.798518i \(-0.294382\pi\)
−0.390552 + 0.920581i \(0.627716\pi\)
\(762\) 6.86189 38.3620i 0.248580 1.38971i
\(763\) 5.38016 + 9.31870i 0.194775 + 0.337360i
\(764\) −45.7053 12.8269i −1.65356 0.464061i
\(765\) −1.59608 + 19.8101i −0.0577063 + 0.716237i
\(766\) 49.7442 + 6.84792i 1.79733 + 0.247425i
\(767\) 21.7809 + 37.7255i 0.786461 + 1.36219i
\(768\) −15.8989 + 22.6985i −0.573704 + 0.819063i
\(769\) −8.91160 + 15.4353i −0.321361 + 0.556613i −0.980769 0.195172i \(-0.937473\pi\)
0.659408 + 0.751785i \(0.270807\pi\)
\(770\) 5.92399 7.62665i 0.213486 0.274845i
\(771\) 33.1036 17.3774i 1.19220 0.625833i
\(772\) 12.6679 + 49.6131i 0.455929 + 1.78561i
\(773\) −18.9682 −0.682237 −0.341119 0.940020i \(-0.610806\pi\)
−0.341119 + 0.940020i \(0.610806\pi\)
\(774\) −3.74901 0.827326i −0.134755 0.0297376i
\(775\) 12.3266i 0.442783i
\(776\) 4.29992 + 37.8259i 0.154358 + 1.35787i
\(777\) 21.8775 + 0.879894i 0.784850 + 0.0315660i
\(778\) −5.55078 + 7.14617i −0.199005 + 0.256203i
\(779\) −16.6554 9.61597i −0.596740 0.344528i
\(780\) 25.6762 + 28.4959i 0.919356 + 1.02032i
\(781\) 4.54081 2.62164i 0.162483 0.0938096i
\(782\) −1.94122 + 14.1013i −0.0694178 + 0.504260i
\(783\) −10.4049 24.4052i −0.371842 0.872169i
\(784\) 4.05614 + 2.47130i 0.144862 + 0.0882607i
\(785\) −8.93578 + 5.15907i −0.318932 + 0.184135i
\(786\) 3.00047 + 2.53034i 0.107023 + 0.0902541i
\(787\) −1.03810 + 1.79804i −0.0370041 + 0.0640931i −0.883934 0.467611i \(-0.845115\pi\)
0.846930 + 0.531704i \(0.178448\pi\)
\(788\) 8.25085 8.05830i 0.293924 0.287065i
\(789\) −29.6632 1.19303i −1.05604 0.0424730i
\(790\) 21.1925 8.63200i 0.753994 0.307113i
\(791\) 20.4792 0.728155
\(792\) −7.08787 11.3964i −0.251857 0.404955i
\(793\) −21.7844 −0.773588
\(794\) −3.95401 + 1.61053i −0.140323 + 0.0571554i
\(795\) 10.1767 + 19.3864i 0.360931 + 0.687564i
\(796\) −1.73508 1.77654i −0.0614982 0.0629678i
\(797\) 17.7593 30.7601i 0.629068 1.08958i −0.358671 0.933464i \(-0.616770\pi\)
0.987739 0.156113i \(-0.0498965\pi\)
\(798\) 17.3819 6.27796i 0.615312 0.222237i
\(799\) 31.3327 18.0900i 1.10847 0.639977i
\(800\) 7.86192 + 6.40999i 0.277961 + 0.226628i
\(801\) −3.15466 + 1.49752i −0.111464 + 0.0529122i
\(802\) −5.59407 + 40.6361i −0.197533 + 1.43491i
\(803\) −0.864352 + 0.499034i −0.0305023 + 0.0176105i
\(804\) 6.83934 + 2.21954i 0.241205 + 0.0782772i
\(805\) 10.1727 + 5.87320i 0.358540 + 0.207003i
\(806\) 36.8738 47.4720i 1.29883 1.67213i
\(807\) 18.6297 29.4657i 0.655798 1.03724i
\(808\) 2.09601 + 18.4384i 0.0737375 + 0.648661i
\(809\) 41.7225i 1.46688i 0.679752 + 0.733442i \(0.262087\pi\)
−0.679752 + 0.733442i \(0.737913\pi\)
\(810\) 16.6832 15.5297i 0.586189 0.545659i
\(811\) −3.03064 −0.106420 −0.0532102 0.998583i \(-0.516945\pi\)
−0.0532102 + 0.998583i \(0.516945\pi\)
\(812\) −23.8542 + 6.09081i −0.837119 + 0.213746i
\(813\) −9.08162 5.74186i −0.318506 0.201376i
\(814\) 7.19443 9.26224i 0.252165 0.324641i
\(815\) −10.1078 + 17.5071i −0.354059 + 0.613248i
\(816\) 14.2045 21.3342i 0.497258 0.746848i
\(817\) −1.41592 2.45244i −0.0495366 0.0858000i
\(818\) −1.85540 0.255419i −0.0648725 0.00893052i
\(819\) 19.1787 + 40.4016i 0.670157 + 1.41175i
\(820\) −5.94730 + 21.1916i −0.207689 + 0.740044i
\(821\) −25.9259 44.9049i −0.904819 1.56719i −0.821160 0.570698i \(-0.806673\pi\)
−0.0836589 0.996494i \(-0.526661\pi\)
\(822\) −28.2393 + 10.1994i −0.984957 + 0.355745i
\(823\) 28.3812 + 16.3859i 0.989307 + 0.571177i 0.905067 0.425269i \(-0.139820\pi\)
0.0842401 + 0.996445i \(0.473154\pi\)
\(824\) −9.94633 13.4489i −0.346497 0.468514i
\(825\) −4.34959 + 2.28328i −0.151433 + 0.0794937i
\(826\) −9.06110 22.2460i −0.315276 0.774036i
\(827\) 52.8295i 1.83706i −0.395350 0.918531i \(-0.629377\pi\)
0.395350 0.918531i \(-0.370623\pi\)
\(828\) 12.5568 10.4312i 0.436379 0.362511i
\(829\) 0.0144624i 0.000502300i 1.00000 0.000251150i \(7.99435e-5\pi\)
−1.00000 0.000251150i \(0.999920\pi\)
\(830\) −36.7081 + 14.9517i −1.27416 + 0.518982i
\(831\) 0.852444 21.1950i 0.0295710 0.735245i
\(832\) −11.1029 48.2044i −0.384923 1.67119i
\(833\) −3.80427 2.19639i −0.131810 0.0761006i
\(834\) −1.95477 + 2.31796i −0.0676881 + 0.0802645i
\(835\) 0.677708 + 1.17382i 0.0234531 + 0.0406219i
\(836\) 2.67483 9.53104i 0.0925108 0.329638i
\(837\) −28.5602 21.4509i −0.987184 0.741453i
\(838\) 6.07919 44.1600i 0.210002 1.52548i
\(839\) 16.6802 + 28.8909i 0.575864 + 0.997425i 0.995947 + 0.0899399i \(0.0286675\pi\)
−0.420083 + 0.907486i \(0.637999\pi\)
\(840\) −11.8831 17.4971i −0.410004 0.603707i
\(841\) 1.46530 2.53797i 0.0505275 0.0875162i
\(842\) −39.9599 31.0388i −1.37711 1.06967i
\(843\) −1.21865 + 30.3002i −0.0419725 + 1.04359i
\(844\) 1.60505 + 6.28608i 0.0552483 + 0.216376i
\(845\) −45.1869 −1.55448
\(846\) −40.5175 8.94137i −1.39302 0.307411i
\(847\) 20.4890i 0.704010i
\(848\) 0.666663 28.2286i 0.0228933 0.969376i
\(849\) 6.11348 + 11.6460i 0.209814 + 0.399690i
\(850\) −7.40911 5.75501i −0.254130 0.197395i
\(851\) 12.3543 + 7.13276i 0.423500 + 0.244508i
\(852\) −2.39160 11.2319i −0.0819349 0.384799i
\(853\) 32.7219 18.8920i 1.12038 0.646850i 0.178880 0.983871i \(-0.442753\pi\)
0.941497 + 0.337021i \(0.109419\pi\)
\(854\) 11.9000 + 1.63819i 0.407210 + 0.0560576i
\(855\) 16.7577 + 1.35015i 0.573101 + 0.0461741i
\(856\) −1.14528 + 2.63211i −0.0391447 + 0.0899637i
\(857\) 9.00665 5.19999i 0.307661 0.177628i −0.338218 0.941068i \(-0.609824\pi\)
0.645879 + 0.763439i \(0.276491\pi\)
\(858\) 23.5814 + 4.21805i 0.805055 + 0.144002i
\(859\) −10.3547 + 17.9348i −0.353297 + 0.611929i −0.986825 0.161791i \(-0.948273\pi\)
0.633528 + 0.773720i \(0.281606\pi\)
\(860\) −2.31859 + 2.26448i −0.0790632 + 0.0772180i
\(861\) −13.7142 + 21.6911i −0.467380 + 0.739232i
\(862\) −9.12930 22.4134i −0.310945 0.763404i
\(863\) 4.67705 0.159209 0.0796043 0.996827i \(-0.474634\pi\)
0.0796043 + 0.996827i \(0.474634\pi\)
\(864\) −28.5332 + 7.06096i −0.970719 + 0.240219i
\(865\) 16.5729 0.563495
\(866\) −10.1946 25.0289i −0.346428 0.850517i
\(867\) 3.06764 4.85194i 0.104183 0.164780i
\(868\) −23.7127 + 23.1593i −0.804861 + 0.786077i
\(869\) 7.14567 12.3767i 0.242400 0.419849i
\(870\) −22.0464 3.94349i −0.747444 0.133697i
\(871\) −11.1152 + 6.41739i −0.376626 + 0.217445i
\(872\) 5.03664 11.5754i 0.170562 0.391992i
\(873\) −22.9325 + 33.2348i −0.776149 + 1.12483i
\(874\) 11.9285 + 1.64211i 0.403487 + 0.0555450i
\(875\) −25.3995 + 14.6644i −0.858660 + 0.495748i
\(876\) 0.455246 + 2.13802i 0.0153813 + 0.0722369i
\(877\) −9.04467 5.22194i −0.305417 0.176333i 0.339457 0.940622i \(-0.389757\pi\)
−0.644874 + 0.764289i \(0.723090\pi\)
\(878\) 38.0300 + 29.5397i 1.28345 + 0.996918i
\(879\) 20.3136 + 38.6969i 0.685162 + 1.30522i
\(880\) −11.3262 0.267487i −0.381807 0.00901697i
\(881\) 29.7734i 1.00309i −0.865131 0.501546i \(-0.832765\pi\)
0.865131 0.501546i \(-0.167235\pi\)
\(882\) 1.51955 + 4.80317i 0.0511659 + 0.161731i
\(883\) −52.9294 −1.78122 −0.890608 0.454772i \(-0.849721\pi\)
−0.890608 + 0.454772i \(0.849721\pi\)
\(884\) 11.3183 + 44.3274i 0.380676 + 1.49089i
\(885\) 0.878137 21.8338i 0.0295183 0.733935i
\(886\) 22.1286 + 17.1883i 0.743424 + 0.577453i
\(887\) 22.4416 38.8700i 0.753515 1.30513i −0.192594 0.981278i \(-0.561690\pi\)
0.946109 0.323848i \(-0.104977\pi\)
\(888\) −14.4315 21.2495i −0.484288 0.713085i
\(889\) −19.1787 33.2184i −0.643232 1.11411i
\(890\) −0.402022 + 2.92035i −0.0134758 + 0.0978902i
\(891\) 2.27898 14.0512i 0.0763486 0.470734i
\(892\) 7.56434 26.9535i 0.253273 0.902471i
\(893\) −15.3026 26.5048i −0.512081 0.886951i
\(894\) 9.37943 11.1221i 0.313695 0.371979i
\(895\) −2.42753 1.40153i −0.0811434 0.0468481i
\(896\) 2.44012 + 27.1672i 0.0815188 + 0.907592i
\(897\) −1.17098 + 29.1149i −0.0390979 + 0.972119i
\(898\) 11.4460 4.66211i 0.381957 0.155577i
\(899\) 35.0978i 1.17058i
\(900\) 1.81600 + 10.6048i 0.0605335 + 0.353494i
\(901\) 26.1148i 0.870009i
\(902\) 5.18543 + 12.7308i 0.172656 + 0.423889i
\(903\) −3.34579 + 1.75635i −0.111341 + 0.0584475i
\(904\) −14.2860 19.3167i −0.475145 0.642465i
\(905\) −5.71174 3.29768i −0.189865 0.109618i
\(906\) −31.8331 + 11.4974i −1.05758 + 0.381977i
\(907\) −8.19627 14.1964i −0.272153 0.471382i 0.697260 0.716818i \(-0.254402\pi\)
−0.969413 + 0.245436i \(0.921069\pi\)
\(908\) 5.46238 19.4637i 0.181275 0.645927i
\(909\) −11.1786 + 16.2004i −0.370769 + 0.537335i
\(910\) 37.4008 + 5.14869i 1.23982 + 0.170677i
\(911\) −13.4518 23.2991i −0.445677 0.771935i 0.552422 0.833564i \(-0.313704\pi\)
−0.998099 + 0.0616295i \(0.980370\pi\)
\(912\) −18.0470 12.0158i −0.597595 0.397884i
\(913\) −12.3772 + 21.4380i −0.409626 + 0.709493i
\(914\) 2.17022 2.79398i 0.0717846 0.0924168i
\(915\) 9.23629 + 5.83965i 0.305342 + 0.193053i
\(916\) −22.2204 + 5.67365i −0.734184 + 0.187463i
\(917\) 3.86319 0.127574
\(918\) 26.2276 7.15162i 0.865640 0.236038i
\(919\) 22.2518i 0.734020i 0.930217 + 0.367010i \(0.119619\pi\)
−0.930217 + 0.367010i \(0.880381\pi\)
\(920\) −1.55650 13.6923i −0.0513162 0.451423i
\(921\) −27.3976 + 43.3335i −0.902782 + 1.42789i
\(922\) 4.57046 5.88409i 0.150520 0.193782i
\(923\) 17.7519 + 10.2491i 0.584310 + 0.337352i
\(924\) −12.5644 4.07748i −0.413339 0.134139i
\(925\) −8.14257 + 4.70112i −0.267726 + 0.154572i
\(926\) −3.39012 + 24.6263i −0.111406 + 0.809271i
\(927\) 1.42483 17.6847i 0.0467976 0.580841i
\(928\) 22.3855 + 18.2513i 0.734839 + 0.599130i
\(929\) −8.55489 + 4.93917i −0.280677 + 0.162049i −0.633730 0.773555i \(-0.718477\pi\)
0.353053 + 0.935603i \(0.385144\pi\)
\(930\) −28.3596 + 10.2429i −0.929947 + 0.335877i
\(931\) −1.85796 + 3.21809i −0.0608923 + 0.105469i
\(932\) −9.43062 9.65597i −0.308910 0.316292i
\(933\) 16.6817 + 31.7782i 0.546134 + 1.04037i
\(934\) 3.01032 1.22615i 0.0985006 0.0401207i
\(935\) 10.4781 0.342670
\(936\) 24.7296 46.2737i 0.808312 1.51250i
\(937\) −2.11802 −0.0691926 −0.0345963 0.999401i \(-0.511015\pi\)
−0.0345963 + 0.999401i \(0.511015\pi\)
\(938\) 6.55442 2.66971i 0.214010 0.0871692i
\(939\) 6.01161 + 0.241782i 0.196181 + 0.00789026i
\(940\) −25.0582 + 24.4734i −0.817310 + 0.798236i
\(941\) 3.56180 6.16922i 0.116111 0.201111i −0.802112 0.597173i \(-0.796290\pi\)
0.918223 + 0.396063i \(0.129624\pi\)
\(942\) 10.7893 + 9.09877i 0.351535 + 0.296454i
\(943\) −14.4803 + 8.36018i −0.471542 + 0.272245i
\(944\) −14.6623 + 24.0653i −0.477219 + 0.783257i
\(945\) 2.69879 22.2708i 0.0877918 0.724471i
\(946\) −0.276039 + 2.00518i −0.00897480 + 0.0651942i
\(947\) 44.5581 25.7256i 1.44794 0.835970i 0.449584 0.893238i \(-0.351572\pi\)
0.998359 + 0.0572679i \(0.0182389\pi\)
\(948\) −20.9525 23.2534i −0.680505 0.755236i
\(949\) −3.37910 1.95093i −0.109690 0.0633297i
\(950\) −4.86826 + 6.26748i −0.157947 + 0.203344i
\(951\) 26.4577 + 1.06411i 0.857949 + 0.0345060i
\(952\) −2.84936 25.0655i −0.0923482 0.812378i
\(953\) 45.3652i 1.46952i −0.678326 0.734761i \(-0.737294\pi\)
0.678326 0.734761i \(-0.262706\pi\)
\(954\) 20.2121 22.1006i 0.654391 0.715532i
\(955\) −42.5046 −1.37542
\(956\) 0.0670839 + 0.262729i 0.00216965 + 0.00849727i
\(957\) −12.3847 + 6.50125i −0.400341 + 0.210156i
\(958\) 31.2690 40.2562i 1.01025 1.30062i
\(959\) −14.7760 + 25.5928i −0.477143 + 0.826436i
\(960\) −8.21446 + 23.4143i −0.265121 + 0.755693i
\(961\) 8.12641 + 14.0754i 0.262142 + 0.454044i
\(962\) 45.4216 + 6.25286i 1.46445 + 0.201600i
\(963\) −2.75044 + 1.30564i −0.0886318 + 0.0420735i
\(964\) 37.4239 + 10.5028i 1.20534 + 0.338271i
\(965\) 22.9238 + 39.7052i 0.737944 + 1.27816i
\(966\) 2.82910 15.8163i 0.0910248 0.508882i
\(967\) −2.55341 1.47421i −0.0821121 0.0474075i 0.458382 0.888755i \(-0.348429\pi\)
−0.540494 + 0.841348i \(0.681763\pi\)
\(968\) 19.3260 14.2928i 0.621161 0.459389i
\(969\) 16.9486 + 10.7158i 0.544468 + 0.344240i
\(970\) 12.8583 + 31.5684i 0.412854 + 1.01360i
\(971\) 21.8052i 0.699763i −0.936794 0.349882i \(-0.886222\pi\)
0.936794 0.349882i \(-0.113778\pi\)
\(972\) −27.7312 14.2471i −0.889479 0.456977i
\(973\) 2.98444i 0.0956768i
\(974\) −3.56631 + 1.45261i −0.114272 + 0.0465446i
\(975\) −16.2325 10.2630i −0.519858 0.328680i
\(976\) −6.75609 12.3673i −0.216257 0.395869i
\(977\) 26.7110 + 15.4216i 0.854560 + 0.493381i 0.862187 0.506590i \(-0.169094\pi\)
−0.00762657 + 0.999971i \(0.502428\pi\)
\(978\) 27.2198 + 4.86887i 0.870394 + 0.155689i
\(979\) 0.920536 + 1.59441i 0.0294204 + 0.0509577i
\(980\) 4.09457 + 1.14912i 0.130796 + 0.0367072i
\(981\) 12.0958 5.74186i 0.386188 0.183324i
\(982\) −2.93332 + 21.3080i −0.0936059 + 0.679966i
\(983\) −6.49316 11.2465i −0.207100 0.358707i 0.743700 0.668513i \(-0.233069\pi\)
−0.950800 + 0.309806i \(0.899736\pi\)
\(984\) 30.0268 2.19565i 0.957218 0.0699946i
\(985\) 5.16324 8.94300i 0.164515 0.284948i
\(986\) −21.0961 16.3864i −0.671838 0.521849i
\(987\) −36.1598 + 18.9818i −1.15098 + 0.604197i
\(988\) 37.4972 9.57435i 1.19295 0.304601i
\(989\) −2.46201 −0.0782873
\(990\) −8.86745 8.10974i −0.281826 0.257744i
\(991\) 47.5865i 1.51163i −0.654783 0.755817i \(-0.727240\pi\)
0.654783 0.755817i \(-0.272760\pi\)
\(992\) 38.3864 + 6.21111i 1.21877 + 0.197203i
\(993\) 10.7296 + 0.431535i 0.340493 + 0.0136943i
\(994\) −8.92645 6.93361i −0.283130 0.219921i
\(995\) −1.92557 1.11173i −0.0610447 0.0352442i
\(996\) 36.2924 + 40.2779i 1.14997 + 1.27625i
\(997\) −7.41748 + 4.28248i −0.234914 + 0.135628i −0.612837 0.790209i \(-0.709972\pi\)
0.377923 + 0.925837i \(0.376638\pi\)
\(998\) −55.2850 7.61067i −1.75001 0.240912i
\(999\) 3.27757 27.0470i 0.103698 0.855729i
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 72.2.l.b.59.7 yes 16
3.2 odd 2 216.2.l.b.179.2 16
4.3 odd 2 288.2.p.b.239.1 16
8.3 odd 2 inner 72.2.l.b.59.3 yes 16
8.5 even 2 288.2.p.b.239.2 16
9.2 odd 6 inner 72.2.l.b.11.3 16
9.4 even 3 648.2.f.b.323.1 16
9.5 odd 6 648.2.f.b.323.16 16
9.7 even 3 216.2.l.b.35.6 16
12.11 even 2 864.2.p.b.719.6 16
24.5 odd 2 864.2.p.b.719.3 16
24.11 even 2 216.2.l.b.179.6 16
36.7 odd 6 864.2.p.b.143.3 16
36.11 even 6 288.2.p.b.47.2 16
36.23 even 6 2592.2.f.b.1295.5 16
36.31 odd 6 2592.2.f.b.1295.11 16
72.5 odd 6 2592.2.f.b.1295.12 16
72.11 even 6 inner 72.2.l.b.11.7 yes 16
72.13 even 6 2592.2.f.b.1295.6 16
72.29 odd 6 288.2.p.b.47.1 16
72.43 odd 6 216.2.l.b.35.2 16
72.59 even 6 648.2.f.b.323.2 16
72.61 even 6 864.2.p.b.143.6 16
72.67 odd 6 648.2.f.b.323.15 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
72.2.l.b.11.3 16 9.2 odd 6 inner
72.2.l.b.11.7 yes 16 72.11 even 6 inner
72.2.l.b.59.3 yes 16 8.3 odd 2 inner
72.2.l.b.59.7 yes 16 1.1 even 1 trivial
216.2.l.b.35.2 16 72.43 odd 6
216.2.l.b.35.6 16 9.7 even 3
216.2.l.b.179.2 16 3.2 odd 2
216.2.l.b.179.6 16 24.11 even 2
288.2.p.b.47.1 16 72.29 odd 6
288.2.p.b.47.2 16 36.11 even 6
288.2.p.b.239.1 16 4.3 odd 2
288.2.p.b.239.2 16 8.5 even 2
648.2.f.b.323.1 16 9.4 even 3
648.2.f.b.323.2 16 72.59 even 6
648.2.f.b.323.15 16 72.67 odd 6
648.2.f.b.323.16 16 9.5 odd 6
864.2.p.b.143.3 16 36.7 odd 6
864.2.p.b.143.6 16 72.61 even 6
864.2.p.b.719.3 16 24.5 odd 2
864.2.p.b.719.6 16 12.11 even 2
2592.2.f.b.1295.5 16 36.23 even 6
2592.2.f.b.1295.6 16 72.13 even 6
2592.2.f.b.1295.11 16 36.31 odd 6
2592.2.f.b.1295.12 16 72.5 odd 6