Properties

Label 342.2.j.f.65.3
Level $342$
Weight $2$
Character 342.65
Analytic conductor $2.731$
Analytic rank $0$
Dimension $18$
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] = [342,2,Mod(65,342)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(342, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("342.65");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 342.j (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: \(2.73088374913\)
Analytic rank: \(0\)
Dimension: \(18\)
Relative dimension: \(9\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{18} - 5 x^{17} + 13 x^{16} - 30 x^{15} + 54 x^{14} - 69 x^{13} + 66 x^{12} + 36 x^{11} - 243 x^{10} + 432 x^{9} - 729 x^{8} + 324 x^{7} + 1782 x^{6} - 5589 x^{5} + 13122 x^{4} + \cdots + 19683 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 65.3
Root \(0.565455 + 1.63715i\) of defining polynomial
Character \(\chi\) \(=\) 342.65
Dual form 342.2.j.f.221.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-1.13509 - 1.30827i) q^{3} +(-0.500000 + 0.866025i) q^{4} +2.55258i q^{5} +(-0.565455 + 1.63715i) q^{6} +(0.762878 - 1.32134i) q^{7} +1.00000 q^{8} +(-0.423160 + 2.97001i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-1.13509 - 1.30827i) q^{3} +(-0.500000 + 0.866025i) q^{4} +2.55258i q^{5} +(-0.565455 + 1.63715i) q^{6} +(0.762878 - 1.32134i) q^{7} +1.00000 q^{8} +(-0.423160 + 2.97001i) q^{9} +(2.21060 - 1.27629i) q^{10} +(1.01188 + 0.584208i) q^{11} +(1.70054 - 0.328876i) q^{12} +(1.91472 + 1.10547i) q^{13} -1.52576 q^{14} +(3.33948 - 2.89740i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(6.71222 + 3.87530i) q^{17} +(2.78368 - 1.11854i) q^{18} +(-1.14556 - 4.20567i) q^{19} +(-2.21060 - 1.27629i) q^{20} +(-2.59461 + 0.501785i) q^{21} -1.16842i q^{22} +(-0.116908 - 0.0674966i) q^{23} +(-1.13509 - 1.30827i) q^{24} -1.51567 q^{25} -2.21093i q^{26} +(4.36590 - 2.81760i) q^{27} +(0.762878 + 1.32134i) q^{28} +4.13926 q^{29} +(-4.17896 - 1.44337i) q^{30} +(0.334751 - 0.193269i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.384265 - 1.98694i) q^{33} -7.75061i q^{34} +(3.37284 + 1.94731i) q^{35} +(-2.36052 - 1.85147i) q^{36} -8.30368i q^{37} +(-3.06944 + 3.09492i) q^{38} +(-0.727123 - 3.75978i) q^{39} +2.55258i q^{40} -6.75990 q^{41} +(1.73186 + 1.99611i) q^{42} +(0.944197 + 1.63540i) q^{43} +(-1.01188 + 0.584208i) q^{44} +(-7.58118 - 1.08015i) q^{45} +0.134993i q^{46} +9.81867i q^{47} +(-0.565455 + 1.63715i) q^{48} +(2.33603 + 4.04613i) q^{49} +(0.757836 + 1.31261i) q^{50} +(-2.54899 - 13.1802i) q^{51} +(-1.91472 + 1.10547i) q^{52} +(4.43603 + 7.68344i) q^{53} +(-4.62307 - 2.37218i) q^{54} +(-1.49124 + 2.58290i) q^{55} +(0.762878 - 1.32134i) q^{56} +(-4.20186 + 6.27251i) q^{57} +(-2.06963 - 3.58471i) q^{58} +7.77614 q^{59} +(0.839484 + 4.34077i) q^{60} +0.918405 q^{61} +(-0.334751 - 0.193269i) q^{62} +(3.60158 + 2.82489i) q^{63} +1.00000 q^{64} +(-2.82179 + 4.88749i) q^{65} +(-1.52861 + 1.32625i) q^{66} +(6.16782 + 3.56099i) q^{67} +(-6.71222 + 3.87530i) q^{68} +(0.0443961 + 0.229562i) q^{69} -3.89462i q^{70} +(-4.47829 + 7.75662i) q^{71} +(-0.423160 + 2.97001i) q^{72} +(-5.36599 + 9.29417i) q^{73} +(-7.19119 + 4.15184i) q^{74} +(1.72042 + 1.98291i) q^{75} +(4.21500 + 1.11075i) q^{76} +(1.54388 - 0.891360i) q^{77} +(-2.89250 + 2.50960i) q^{78} +(8.72967 - 5.04008i) q^{79} +(2.21060 - 1.27629i) q^{80} +(-8.64187 - 2.51358i) q^{81} +(3.37995 + 5.85424i) q^{82} +(-13.4929 - 7.79012i) q^{83} +(0.862747 - 2.49789i) q^{84} +(-9.89203 + 17.1335i) q^{85} +(0.944197 - 1.63540i) q^{86} +(-4.69842 - 5.41529i) q^{87} +(1.01188 + 0.584208i) q^{88} +(-3.33058 - 5.76874i) q^{89} +(2.85515 + 7.10557i) q^{90} +(2.92140 - 1.68667i) q^{91} +(0.116908 - 0.0674966i) q^{92} +(-0.632820 - 0.218570i) q^{93} +(8.50321 - 4.90933i) q^{94} +(10.7353 - 2.92414i) q^{95} +(1.70054 - 0.328876i) q^{96} +(-0.462464 + 0.267004i) q^{97} +(2.33603 - 4.04613i) q^{98} +(-2.16329 + 2.75807i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18 q - 9 q^{2} + 4 q^{3} - 9 q^{4} - 5 q^{6} + 18 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 18 q - 9 q^{2} + 4 q^{3} - 9 q^{4} - 5 q^{6} + 18 q^{8} - 4 q^{9} - 3 q^{10} + 15 q^{11} + q^{12} + 3 q^{13} - 10 q^{15} - 9 q^{16} + 15 q^{17} + 5 q^{18} + 6 q^{19} + 3 q^{20} - 13 q^{21} + 4 q^{24} - 36 q^{25} - 20 q^{27} + 36 q^{29} + 17 q^{30} - 9 q^{31} - 9 q^{32} - 4 q^{33} + 3 q^{35} - q^{36} + 6 q^{38} + 18 q^{39} + 14 q^{42} - 6 q^{43} - 15 q^{44} - 17 q^{45} - 5 q^{48} + 3 q^{49} + 18 q^{50} - 13 q^{51} - 3 q^{52} + 15 q^{53} + 10 q^{54} - 9 q^{55} - 29 q^{57} - 18 q^{58} - 7 q^{60} + 18 q^{61} + 9 q^{62} + 49 q^{63} + 18 q^{64} + 9 q^{65} + 5 q^{66} - 6 q^{67} - 15 q^{68} + 8 q^{69} + 6 q^{71} - 4 q^{72} + 24 q^{73} - 30 q^{74} + 9 q^{75} - 12 q^{76} + 3 q^{77} - 21 q^{78} - 6 q^{79} - 3 q^{80} - 52 q^{81} + 3 q^{83} - q^{84} - 3 q^{85} - 6 q^{86} - 60 q^{87} + 15 q^{88} - 24 q^{89} + 4 q^{90} - 81 q^{91} + 6 q^{93} - 18 q^{94} - 21 q^{95} + q^{96} - 15 q^{97} + 3 q^{98} + 28 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/342\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(325\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) −1.13509 1.30827i −0.655342 0.755332i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 2.55258i 1.14155i 0.821107 + 0.570775i \(0.193357\pi\)
−0.821107 + 0.570775i \(0.806643\pi\)
\(6\) −0.565455 + 1.63715i −0.230846 + 0.668364i
\(7\) 0.762878 1.32134i 0.288341 0.499421i −0.685073 0.728474i \(-0.740230\pi\)
0.973414 + 0.229053i \(0.0735631\pi\)
\(8\) 1.00000 0.353553
\(9\) −0.423160 + 2.97001i −0.141053 + 0.990002i
\(10\) 2.21060 1.27629i 0.699053 0.403599i
\(11\) 1.01188 + 0.584208i 0.305093 + 0.176145i 0.644729 0.764412i \(-0.276970\pi\)
−0.339636 + 0.940557i \(0.610304\pi\)
\(12\) 1.70054 0.328876i 0.490904 0.0949384i
\(13\) 1.91472 + 1.10547i 0.531048 + 0.306601i 0.741443 0.671016i \(-0.234142\pi\)
−0.210395 + 0.977616i \(0.567475\pi\)
\(14\) −1.52576 −0.407776
\(15\) 3.33948 2.89740i 0.862249 0.748105i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 6.71222 + 3.87530i 1.62795 + 0.939899i 0.984703 + 0.174244i \(0.0557481\pi\)
0.643251 + 0.765655i \(0.277585\pi\)
\(18\) 2.78368 1.11854i 0.656120 0.263641i
\(19\) −1.14556 4.20567i −0.262810 0.964848i
\(20\) −2.21060 1.27629i −0.494305 0.285387i
\(21\) −2.59461 + 0.501785i −0.566191 + 0.109498i
\(22\) 1.16842i 0.249107i
\(23\) −0.116908 0.0674966i −0.0243769 0.0140740i 0.487762 0.872977i \(-0.337813\pi\)
−0.512139 + 0.858903i \(0.671147\pi\)
\(24\) −1.13509 1.30827i −0.231698 0.267050i
\(25\) −1.51567 −0.303134
\(26\) 2.21093i 0.433599i
\(27\) 4.36590 2.81760i 0.840219 0.542248i
\(28\) 0.762878 + 1.32134i 0.144170 + 0.249710i
\(29\) 4.13926 0.768641 0.384321 0.923200i \(-0.374436\pi\)
0.384321 + 0.923200i \(0.374436\pi\)
\(30\) −4.17896 1.44337i −0.762970 0.263522i
\(31\) 0.334751 0.193269i 0.0601231 0.0347121i −0.469637 0.882860i \(-0.655615\pi\)
0.529760 + 0.848147i \(0.322282\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) −0.384265 1.98694i −0.0668919 0.345882i
\(34\) 7.75061i 1.32922i
\(35\) 3.37284 + 1.94731i 0.570114 + 0.329155i
\(36\) −2.36052 1.85147i −0.393420 0.308578i
\(37\) 8.30368i 1.36512i −0.730832 0.682558i \(-0.760867\pi\)
0.730832 0.682558i \(-0.239133\pi\)
\(38\) −3.06944 + 3.09492i −0.497929 + 0.502063i
\(39\) −0.727123 3.75978i −0.116433 0.602047i
\(40\) 2.55258i 0.403599i
\(41\) −6.75990 −1.05572 −0.527859 0.849332i \(-0.677005\pi\)
−0.527859 + 0.849332i \(0.677005\pi\)
\(42\) 1.73186 + 1.99611i 0.267232 + 0.308006i
\(43\) 0.944197 + 1.63540i 0.143989 + 0.249396i 0.928995 0.370092i \(-0.120674\pi\)
−0.785006 + 0.619488i \(0.787340\pi\)
\(44\) −1.01188 + 0.584208i −0.152546 + 0.0880727i
\(45\) −7.58118 1.08015i −1.13014 0.161019i
\(46\) 0.134993i 0.0199037i
\(47\) 9.81867i 1.43220i 0.697998 + 0.716100i \(0.254074\pi\)
−0.697998 + 0.716100i \(0.745926\pi\)
\(48\) −0.565455 + 1.63715i −0.0816164 + 0.236302i
\(49\) 2.33603 + 4.04613i 0.333719 + 0.578018i
\(50\) 0.757836 + 1.31261i 0.107174 + 0.185631i
\(51\) −2.54899 13.1802i −0.356930 1.84560i
\(52\) −1.91472 + 1.10547i −0.265524 + 0.153300i
\(53\) 4.43603 + 7.68344i 0.609336 + 1.05540i 0.991350 + 0.131245i \(0.0418973\pi\)
−0.382014 + 0.924157i \(0.624769\pi\)
\(54\) −4.62307 2.37218i −0.629120 0.322813i
\(55\) −1.49124 + 2.58290i −0.201079 + 0.348279i
\(56\) 0.762878 1.32134i 0.101944 0.176572i
\(57\) −4.20186 + 6.27251i −0.556550 + 0.830814i
\(58\) −2.06963 3.58471i −0.271756 0.470695i
\(59\) 7.77614 1.01237 0.506183 0.862426i \(-0.331056\pi\)
0.506183 + 0.862426i \(0.331056\pi\)
\(60\) 0.839484 + 4.34077i 0.108377 + 0.560391i
\(61\) 0.918405 0.117590 0.0587949 0.998270i \(-0.481274\pi\)
0.0587949 + 0.998270i \(0.481274\pi\)
\(62\) −0.334751 0.193269i −0.0425135 0.0245452i
\(63\) 3.60158 + 2.82489i 0.453756 + 0.355903i
\(64\) 1.00000 0.125000
\(65\) −2.82179 + 4.88749i −0.350000 + 0.606218i
\(66\) −1.52861 + 1.32625i −0.188159 + 0.163251i
\(67\) 6.16782 + 3.56099i 0.753519 + 0.435044i 0.826964 0.562255i \(-0.190066\pi\)
−0.0734452 + 0.997299i \(0.523399\pi\)
\(68\) −6.71222 + 3.87530i −0.813977 + 0.469950i
\(69\) 0.0443961 + 0.229562i 0.00534466 + 0.0276360i
\(70\) 3.89462i 0.465496i
\(71\) −4.47829 + 7.75662i −0.531475 + 0.920541i 0.467850 + 0.883808i \(0.345029\pi\)
−0.999325 + 0.0367336i \(0.988305\pi\)
\(72\) −0.423160 + 2.97001i −0.0498699 + 0.350019i
\(73\) −5.36599 + 9.29417i −0.628042 + 1.08780i 0.359902 + 0.932990i \(0.382810\pi\)
−0.987944 + 0.154810i \(0.950523\pi\)
\(74\) −7.19119 + 4.15184i −0.835959 + 0.482641i
\(75\) 1.72042 + 1.98291i 0.198657 + 0.228967i
\(76\) 4.21500 + 1.11075i 0.483494 + 0.127412i
\(77\) 1.54388 0.891360i 0.175941 0.101580i
\(78\) −2.89250 + 2.50960i −0.327511 + 0.284156i
\(79\) 8.72967 5.04008i 0.982165 0.567053i 0.0792420 0.996855i \(-0.474750\pi\)
0.902923 + 0.429802i \(0.141417\pi\)
\(80\) 2.21060 1.27629i 0.247153 0.142694i
\(81\) −8.64187 2.51358i −0.960208 0.279286i
\(82\) 3.37995 + 5.85424i 0.373253 + 0.646493i
\(83\) −13.4929 7.79012i −1.48104 0.855076i −0.481267 0.876574i \(-0.659823\pi\)
−0.999769 + 0.0214976i \(0.993157\pi\)
\(84\) 0.862747 2.49789i 0.0941334 0.272542i
\(85\) −9.89203 + 17.1335i −1.07294 + 1.85839i
\(86\) 0.944197 1.63540i 0.101815 0.176349i
\(87\) −4.69842 5.41529i −0.503723 0.580580i
\(88\) 1.01188 + 0.584208i 0.107867 + 0.0622768i
\(89\) −3.33058 5.76874i −0.353041 0.611485i 0.633739 0.773547i \(-0.281519\pi\)
−0.986781 + 0.162061i \(0.948186\pi\)
\(90\) 2.85515 + 7.10557i 0.300960 + 0.748993i
\(91\) 2.92140 1.68667i 0.306246 0.176811i
\(92\) 0.116908 0.0674966i 0.0121885 0.00703701i
\(93\) −0.632820 0.218570i −0.0656204 0.0226646i
\(94\) 8.50321 4.90933i 0.877040 0.506359i
\(95\) 10.7353 2.92414i 1.10142 0.300011i
\(96\) 1.70054 0.328876i 0.173561 0.0335658i
\(97\) −0.462464 + 0.267004i −0.0469561 + 0.0271101i −0.523294 0.852152i \(-0.675297\pi\)
0.476338 + 0.879262i \(0.341964\pi\)
\(98\) 2.33603 4.04613i 0.235975 0.408721i
\(99\) −2.16329 + 2.75807i −0.217419 + 0.277197i
\(100\) 0.757836 1.31261i 0.0757836 0.131261i
\(101\) 18.6864i 1.85937i −0.368360 0.929683i \(-0.620080\pi\)
0.368360 0.929683i \(-0.379920\pi\)
\(102\) −10.1399 + 8.79761i −1.00400 + 0.871093i
\(103\) 5.51194 3.18232i 0.543108 0.313563i −0.203230 0.979131i \(-0.565144\pi\)
0.746337 + 0.665568i \(0.231811\pi\)
\(104\) 1.91472 + 1.10547i 0.187754 + 0.108400i
\(105\) −1.28085 6.62296i −0.124998 0.646334i
\(106\) 4.43603 7.68344i 0.430866 0.746281i
\(107\) −9.68605 −0.936386 −0.468193 0.883626i \(-0.655095\pi\)
−0.468193 + 0.883626i \(0.655095\pi\)
\(108\) 0.257164 + 5.18978i 0.0247456 + 0.499387i
\(109\) −11.7103 6.76093i −1.12164 0.647580i −0.179822 0.983699i \(-0.557552\pi\)
−0.941819 + 0.336120i \(0.890885\pi\)
\(110\) 2.98248 0.284368
\(111\) −10.8635 + 9.42538i −1.03112 + 0.894618i
\(112\) −1.52576 −0.144170
\(113\) −2.63721 4.56778i −0.248088 0.429701i 0.714907 0.699219i \(-0.246469\pi\)
−0.962995 + 0.269518i \(0.913136\pi\)
\(114\) 7.53308 + 0.502660i 0.705538 + 0.0470785i
\(115\) 0.172291 0.298416i 0.0160662 0.0278274i
\(116\) −2.06963 + 3.58471i −0.192160 + 0.332832i
\(117\) −4.09347 + 5.21895i −0.378442 + 0.482492i
\(118\) −3.88807 6.73433i −0.357926 0.619946i
\(119\) 10.2412 5.91277i 0.938811 0.542023i
\(120\) 3.33948 2.89740i 0.304851 0.264495i
\(121\) −4.81740 8.34398i −0.437946 0.758544i
\(122\) −0.459203 0.795362i −0.0415743 0.0720087i
\(123\) 7.67307 + 8.84380i 0.691857 + 0.797418i
\(124\) 0.386537i 0.0347121i
\(125\) 8.89403i 0.795506i
\(126\) 0.645639 4.53151i 0.0575181 0.403699i
\(127\) −5.70970 + 3.29650i −0.506654 + 0.292517i −0.731457 0.681887i \(-0.761159\pi\)
0.224803 + 0.974404i \(0.427826\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 1.06780 3.09158i 0.0940148 0.272199i
\(130\) 5.64358 0.494975
\(131\) 0.750276i 0.0655519i −0.999463 0.0327760i \(-0.989565\pi\)
0.999463 0.0327760i \(-0.0104348\pi\)
\(132\) 1.91287 + 0.660688i 0.166494 + 0.0575055i
\(133\) −6.43106 1.69473i −0.557644 0.146952i
\(134\) 7.12198i 0.615245i
\(135\) 7.19216 + 11.1443i 0.619003 + 0.959151i
\(136\) 6.71222 + 3.87530i 0.575568 + 0.332305i
\(137\) 2.01675i 0.172303i 0.996282 + 0.0861513i \(0.0274568\pi\)
−0.996282 + 0.0861513i \(0.972543\pi\)
\(138\) 0.176608 0.153229i 0.0150339 0.0130437i
\(139\) −0.470675 + 0.815232i −0.0399221 + 0.0691471i −0.885296 0.465028i \(-0.846044\pi\)
0.845374 + 0.534175i \(0.179378\pi\)
\(140\) −3.37284 + 1.94731i −0.285057 + 0.164578i
\(141\) 12.8455 11.1450i 1.08179 0.938581i
\(142\) 8.95657 0.751619
\(143\) 1.29164 + 2.23719i 0.108013 + 0.187084i
\(144\) 2.78368 1.11854i 0.231973 0.0932113i
\(145\) 10.5658i 0.877442i
\(146\) 10.7320 0.888185
\(147\) 2.64185 7.64888i 0.217896 0.630869i
\(148\) 7.19119 + 4.15184i 0.591112 + 0.341279i
\(149\) 14.2026i 1.16352i −0.813361 0.581760i \(-0.802364\pi\)
0.813361 0.581760i \(-0.197636\pi\)
\(150\) 0.857045 2.48138i 0.0699774 0.202604i
\(151\) −1.58378 0.914396i −0.128886 0.0744125i 0.434171 0.900831i \(-0.357041\pi\)
−0.563057 + 0.826418i \(0.690375\pi\)
\(152\) −1.14556 4.20567i −0.0929175 0.341125i
\(153\) −14.3500 + 18.2955i −1.16013 + 1.47910i
\(154\) −1.54388 0.891360i −0.124409 0.0718278i
\(155\) 0.493334 + 0.854480i 0.0396256 + 0.0686335i
\(156\) 3.61963 + 1.25018i 0.289802 + 0.100095i
\(157\) 20.9348 1.67078 0.835390 0.549658i \(-0.185242\pi\)
0.835390 + 0.549658i \(0.185242\pi\)
\(158\) −8.72967 5.04008i −0.694496 0.400967i
\(159\) 5.01676 14.5249i 0.397855 1.15190i
\(160\) −2.21060 1.27629i −0.174763 0.100900i
\(161\) −0.178372 + 0.102983i −0.0140577 + 0.00811623i
\(162\) 2.14411 + 8.74087i 0.168458 + 0.686747i
\(163\) −17.9035 −1.40231 −0.701156 0.713008i \(-0.747333\pi\)
−0.701156 + 0.713008i \(0.747333\pi\)
\(164\) 3.37995 5.85424i 0.263930 0.457140i
\(165\) 5.07183 0.980867i 0.394841 0.0763604i
\(166\) 15.5802i 1.20926i
\(167\) 0.368544 0.638336i 0.0285188 0.0493959i −0.851414 0.524495i \(-0.824254\pi\)
0.879933 + 0.475099i \(0.157588\pi\)
\(168\) −2.59461 + 0.501785i −0.200179 + 0.0387136i
\(169\) −4.05589 7.02501i −0.311992 0.540385i
\(170\) 19.7841 1.51737
\(171\) 12.9756 1.62266i 0.992271 0.124088i
\(172\) −1.88839 −0.143989
\(173\) 5.01877 + 8.69276i 0.381570 + 0.660898i 0.991287 0.131721i \(-0.0420502\pi\)
−0.609717 + 0.792619i \(0.708717\pi\)
\(174\) −2.34057 + 6.77659i −0.177438 + 0.513732i
\(175\) −1.15627 + 2.00272i −0.0874060 + 0.151392i
\(176\) 1.16842i 0.0880727i
\(177\) −8.82658 10.1733i −0.663447 0.764673i
\(178\) −3.33058 + 5.76874i −0.249638 + 0.432386i
\(179\) −9.74221 −0.728167 −0.364083 0.931366i \(-0.618618\pi\)
−0.364083 + 0.931366i \(0.618618\pi\)
\(180\) 4.72603 6.02542i 0.352257 0.449108i
\(181\) −11.9960 + 6.92591i −0.891658 + 0.514799i −0.874484 0.485054i \(-0.838800\pi\)
−0.0171734 + 0.999853i \(0.505467\pi\)
\(182\) −2.92140 1.68667i −0.216549 0.125024i
\(183\) −1.04247 1.20153i −0.0770615 0.0888193i
\(184\) −0.116908 0.0674966i −0.00861854 0.00497592i
\(185\) 21.1958 1.55835
\(186\) 0.127123 + 0.657323i 0.00932111 + 0.0481973i
\(187\) 4.52797 + 7.84268i 0.331118 + 0.573513i
\(188\) −8.50321 4.90933i −0.620161 0.358050i
\(189\) −0.392369 7.91835i −0.0285406 0.575975i
\(190\) −7.90004 7.83499i −0.573129 0.568410i
\(191\) 0.945198 + 0.545710i 0.0683921 + 0.0394862i 0.533806 0.845607i \(-0.320761\pi\)
−0.465414 + 0.885093i \(0.654095\pi\)
\(192\) −1.13509 1.30827i −0.0819178 0.0944165i
\(193\) 1.82307i 0.131227i −0.997845 0.0656136i \(-0.979100\pi\)
0.997845 0.0656136i \(-0.0209005\pi\)
\(194\) 0.462464 + 0.267004i 0.0332030 + 0.0191697i
\(195\) 9.59714 1.85604i 0.687266 0.132914i
\(196\) −4.67207 −0.333719
\(197\) 19.6968i 1.40334i −0.712504 0.701668i \(-0.752439\pi\)
0.712504 0.701668i \(-0.247561\pi\)
\(198\) 3.47021 + 0.494427i 0.246617 + 0.0351374i
\(199\) 4.29440 + 7.43811i 0.304422 + 0.527274i 0.977132 0.212632i \(-0.0682035\pi\)
−0.672711 + 0.739906i \(0.734870\pi\)
\(200\) −1.51567 −0.107174
\(201\) −2.34225 12.1112i −0.165210 0.854260i
\(202\) −16.1829 + 9.34320i −1.13862 + 0.657385i
\(203\) 3.15775 5.46939i 0.221631 0.383876i
\(204\) 12.6889 + 4.38262i 0.888401 + 0.306845i
\(205\) 17.2552i 1.20515i
\(206\) −5.51194 3.18232i −0.384035 0.221723i
\(207\) 0.249936 0.318654i 0.0173717 0.0221480i
\(208\) 2.21093i 0.153300i
\(209\) 1.29782 4.92488i 0.0897720 0.340661i
\(210\) −5.09523 + 4.42072i −0.351604 + 0.305059i
\(211\) 23.4844i 1.61673i −0.588681 0.808366i \(-0.700352\pi\)
0.588681 0.808366i \(-0.299648\pi\)
\(212\) −8.87207 −0.609336
\(213\) 15.2310 2.94561i 1.04361 0.201830i
\(214\) 4.84302 + 8.38837i 0.331062 + 0.573417i
\(215\) −4.17448 + 2.41014i −0.284697 + 0.164370i
\(216\) 4.36590 2.81760i 0.297062 0.191714i
\(217\) 0.589762i 0.0400357i
\(218\) 13.5219i 0.915816i
\(219\) 18.2502 3.52950i 1.23323 0.238501i
\(220\) −1.49124 2.58290i −0.100539 0.174139i
\(221\) 8.56803 + 14.8403i 0.576348 + 0.998264i
\(222\) 13.5944 + 4.69536i 0.912394 + 0.315132i
\(223\) 4.53089 2.61591i 0.303411 0.175174i −0.340563 0.940222i \(-0.610618\pi\)
0.643974 + 0.765047i \(0.277284\pi\)
\(224\) 0.762878 + 1.32134i 0.0509719 + 0.0882860i
\(225\) 0.641372 4.50155i 0.0427581 0.300104i
\(226\) −2.63721 + 4.56778i −0.175425 + 0.303844i
\(227\) 4.12452 7.14387i 0.273754 0.474156i −0.696066 0.717978i \(-0.745068\pi\)
0.969820 + 0.243822i \(0.0784013\pi\)
\(228\) −3.33122 6.77517i −0.220616 0.448697i
\(229\) 9.53515 + 16.5154i 0.630101 + 1.09137i 0.987531 + 0.157427i \(0.0503197\pi\)
−0.357430 + 0.933940i \(0.616347\pi\)
\(230\) −0.344581 −0.0227210
\(231\) −2.91858 1.00805i −0.192028 0.0663247i
\(232\) 4.13926 0.271756
\(233\) 7.66969 + 4.42810i 0.502458 + 0.290094i 0.729728 0.683738i \(-0.239647\pi\)
−0.227270 + 0.973832i \(0.572980\pi\)
\(234\) 6.56648 + 0.935578i 0.429264 + 0.0611606i
\(235\) −25.0629 −1.63493
\(236\) −3.88807 + 6.73433i −0.253092 + 0.438368i
\(237\) −16.5027 5.69988i −1.07197 0.370247i
\(238\) −10.2412 5.91277i −0.663840 0.383268i
\(239\) 4.98254 2.87667i 0.322293 0.186076i −0.330121 0.943939i \(-0.607090\pi\)
0.652414 + 0.757862i \(0.273756\pi\)
\(240\) −4.17896 1.44337i −0.269751 0.0931692i
\(241\) 27.1682i 1.75006i 0.484071 + 0.875029i \(0.339158\pi\)
−0.484071 + 0.875029i \(0.660842\pi\)
\(242\) −4.81740 + 8.34398i −0.309674 + 0.536372i
\(243\) 6.52082 + 14.1591i 0.418311 + 0.908304i
\(244\) −0.459203 + 0.795362i −0.0293974 + 0.0509179i
\(245\) −10.3281 + 5.96292i −0.659836 + 0.380957i
\(246\) 3.82242 11.0670i 0.243709 0.705604i
\(247\) 2.45579 9.31908i 0.156258 0.592959i
\(248\) 0.334751 0.193269i 0.0212567 0.0122726i
\(249\) 5.12397 + 26.4948i 0.324718 + 1.67904i
\(250\) 7.70246 4.44702i 0.487146 0.281254i
\(251\) −24.1315 + 13.9323i −1.52316 + 0.879399i −0.523539 + 0.852002i \(0.675389\pi\)
−0.999625 + 0.0273973i \(0.991278\pi\)
\(252\) −4.24722 + 1.70661i −0.267550 + 0.107506i
\(253\) −0.0788642 0.136597i −0.00495815 0.00858776i
\(254\) 5.70970 + 3.29650i 0.358258 + 0.206841i
\(255\) 33.6436 6.50651i 2.10684 0.407453i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 2.30383 3.99035i 0.143709 0.248911i −0.785182 0.619266i \(-0.787430\pi\)
0.928891 + 0.370354i \(0.120764\pi\)
\(258\) −3.21129 + 0.621048i −0.199926 + 0.0386648i
\(259\) −10.9720 6.33469i −0.681767 0.393619i
\(260\) −2.82179 4.88749i −0.175000 0.303109i
\(261\) −1.75157 + 12.2936i −0.108419 + 0.760957i
\(262\) −0.649758 + 0.375138i −0.0401422 + 0.0231761i
\(263\) 8.47535 4.89325i 0.522612 0.301730i −0.215390 0.976528i \(-0.569102\pi\)
0.738003 + 0.674798i \(0.235769\pi\)
\(264\) −0.384265 1.98694i −0.0236499 0.122288i
\(265\) −19.6126 + 11.3233i −1.20479 + 0.695587i
\(266\) 1.74785 + 6.41683i 0.107168 + 0.393441i
\(267\) −3.76659 + 10.9053i −0.230512 + 0.667396i
\(268\) −6.16782 + 3.56099i −0.376759 + 0.217522i
\(269\) 10.4195 18.0472i 0.635290 1.10035i −0.351164 0.936314i \(-0.614214\pi\)
0.986454 0.164040i \(-0.0524527\pi\)
\(270\) 6.05519 11.8008i 0.368507 0.718171i
\(271\) 10.4430 18.0878i 0.634366 1.09875i −0.352283 0.935893i \(-0.614595\pi\)
0.986649 0.162861i \(-0.0520721\pi\)
\(272\) 7.75061i 0.469950i
\(273\) −5.52267 1.90747i −0.334247 0.115446i
\(274\) 1.74656 1.00838i 0.105513 0.0609182i
\(275\) −1.53368 0.885468i −0.0924842 0.0533957i
\(276\) −0.221004 0.0763326i −0.0133029 0.00459468i
\(277\) 10.1903 17.6502i 0.612279 1.06050i −0.378577 0.925570i \(-0.623586\pi\)
0.990855 0.134928i \(-0.0430802\pi\)
\(278\) 0.941349 0.0564584
\(279\) 0.432356 + 1.07600i 0.0258845 + 0.0644183i
\(280\) 3.37284 + 1.94731i 0.201566 + 0.116374i
\(281\) −32.0813 −1.91381 −0.956904 0.290405i \(-0.906210\pi\)
−0.956904 + 0.290405i \(0.906210\pi\)
\(282\) −16.0746 5.55202i −0.957230 0.330618i
\(283\) −19.1782 −1.14003 −0.570013 0.821636i \(-0.693062\pi\)
−0.570013 + 0.821636i \(0.693062\pi\)
\(284\) −4.47829 7.75662i −0.265737 0.460271i
\(285\) −16.0111 10.7256i −0.948415 0.635329i
\(286\) 1.29164 2.23719i 0.0763766 0.132288i
\(287\) −5.15698 + 8.93215i −0.304407 + 0.527248i
\(288\) −2.36052 1.85147i −0.139095 0.109099i
\(289\) 21.5360 + 37.3014i 1.26682 + 2.19420i
\(290\) 9.15025 5.28290i 0.537321 0.310223i
\(291\) 0.874250 + 0.301957i 0.0512494 + 0.0177010i
\(292\) −5.36599 9.29417i −0.314021 0.543900i
\(293\) −3.09233 5.35608i −0.180656 0.312905i 0.761448 0.648226i \(-0.224489\pi\)
−0.942104 + 0.335320i \(0.891155\pi\)
\(294\) −7.94504 + 1.53653i −0.463364 + 0.0896124i
\(295\) 19.8492i 1.15567i
\(296\) 8.30368i 0.482641i
\(297\) 6.06383 0.300474i 0.351859 0.0174353i
\(298\) −12.2998 + 7.10128i −0.712507 + 0.411366i
\(299\) −0.149230 0.258475i −0.00863021 0.0149480i
\(300\) −2.57746 + 0.498469i −0.148810 + 0.0287791i
\(301\) 2.88123 0.166071
\(302\) 1.82879i 0.105235i
\(303\) −24.4469 + 21.2107i −1.40444 + 1.21852i
\(304\) −3.06944 + 3.09492i −0.176044 + 0.177506i
\(305\) 2.34430i 0.134234i
\(306\) 23.0194 + 3.27975i 1.31593 + 0.187491i
\(307\) 14.0179 + 8.09326i 0.800046 + 0.461907i 0.843487 0.537149i \(-0.180499\pi\)
−0.0434413 + 0.999056i \(0.513832\pi\)
\(308\) 1.78272i 0.101580i
\(309\) −10.4199 3.59892i −0.592766 0.204735i
\(310\) 0.493334 0.854480i 0.0280195 0.0485312i
\(311\) −24.8337 + 14.3377i −1.40819 + 0.813017i −0.995213 0.0977254i \(-0.968843\pi\)
−0.412974 + 0.910743i \(0.635510\pi\)
\(312\) −0.727123 3.75978i −0.0411652 0.212856i
\(313\) −7.21649 −0.407900 −0.203950 0.978981i \(-0.565378\pi\)
−0.203950 + 0.978981i \(0.565378\pi\)
\(314\) −10.4674 18.1301i −0.590710 1.02314i
\(315\) −7.21077 + 9.19332i −0.406281 + 0.517985i
\(316\) 10.0802i 0.567053i
\(317\) −5.39047 −0.302759 −0.151379 0.988476i \(-0.548372\pi\)
−0.151379 + 0.988476i \(0.548372\pi\)
\(318\) −15.0873 + 2.91781i −0.846055 + 0.163623i
\(319\) 4.18843 + 2.41819i 0.234507 + 0.135393i
\(320\) 2.55258i 0.142694i
\(321\) 10.9945 + 12.6720i 0.613653 + 0.707282i
\(322\) 0.178372 + 0.102983i 0.00994031 + 0.00573904i
\(323\) 8.60898 32.6688i 0.479017 1.81774i
\(324\) 6.49776 6.22729i 0.360986 0.345961i
\(325\) −2.90209 1.67552i −0.160979 0.0929413i
\(326\) 8.95176 + 15.5049i 0.495792 + 0.858738i
\(327\) 4.44702 + 22.9945i 0.245921 + 1.27160i
\(328\) −6.75990 −0.373253
\(329\) 12.9738 + 7.49045i 0.715271 + 0.412962i
\(330\) −3.38537 3.90190i −0.186358 0.214792i
\(331\) −20.6131 11.9010i −1.13300 0.654138i −0.188313 0.982109i \(-0.560302\pi\)
−0.944688 + 0.327971i \(0.893635\pi\)
\(332\) 13.4929 7.79012i 0.740518 0.427538i
\(333\) 24.6620 + 3.51378i 1.35147 + 0.192554i
\(334\) −0.737087 −0.0403316
\(335\) −9.08972 + 15.7439i −0.496624 + 0.860179i
\(336\) 1.73186 + 1.99611i 0.0944809 + 0.108897i
\(337\) 6.06350i 0.330300i 0.986268 + 0.165150i \(0.0528109\pi\)
−0.986268 + 0.165150i \(0.947189\pi\)
\(338\) −4.05589 + 7.02501i −0.220611 + 0.382110i
\(339\) −2.98245 + 8.63502i −0.161984 + 0.468990i
\(340\) −9.89203 17.1335i −0.536471 0.929194i
\(341\) 0.451637 0.0244575
\(342\) −7.89308 10.4259i −0.426809 0.563768i
\(343\) 17.8087 0.961581
\(344\) 0.944197 + 1.63540i 0.0509077 + 0.0881747i
\(345\) −0.585974 + 0.113325i −0.0315478 + 0.00610119i
\(346\) 5.01877 8.69276i 0.269811 0.467326i
\(347\) 19.5061i 1.04714i 0.851982 + 0.523572i \(0.175401\pi\)
−0.851982 + 0.523572i \(0.824599\pi\)
\(348\) 7.03898 1.36131i 0.377329 0.0729736i
\(349\) 12.3916 21.4628i 0.663306 1.14888i −0.316436 0.948614i \(-0.602486\pi\)
0.979742 0.200266i \(-0.0641805\pi\)
\(350\) 2.31255 0.123611
\(351\) 11.4743 0.568571i 0.612451 0.0303481i
\(352\) −1.01188 + 0.584208i −0.0539333 + 0.0311384i
\(353\) 10.2539 + 5.92008i 0.545759 + 0.315094i 0.747410 0.664364i \(-0.231297\pi\)
−0.201651 + 0.979457i \(0.564631\pi\)
\(354\) −4.39706 + 12.7307i −0.233701 + 0.676629i
\(355\) −19.7994 11.4312i −1.05084 0.606705i
\(356\) 6.66117 0.353041
\(357\) −19.3602 6.68681i −1.02465 0.353904i
\(358\) 4.87110 + 8.43700i 0.257446 + 0.445909i
\(359\) −13.8289 7.98410i −0.729859 0.421384i 0.0885114 0.996075i \(-0.471789\pi\)
−0.818371 + 0.574691i \(0.805122\pi\)
\(360\) −7.58118 1.08015i −0.399563 0.0569289i
\(361\) −16.3754 + 9.63573i −0.861861 + 0.507144i
\(362\) 11.9960 + 6.92591i 0.630497 + 0.364018i
\(363\) −5.44805 + 15.7736i −0.285948 + 0.827900i
\(364\) 3.37334i 0.176811i
\(365\) −23.7241 13.6971i −1.24178 0.716941i
\(366\) −0.519317 + 1.50357i −0.0271451 + 0.0785927i
\(367\) 22.6343 1.18150 0.590750 0.806854i \(-0.298832\pi\)
0.590750 + 0.806854i \(0.298832\pi\)
\(368\) 0.134993i 0.00703701i
\(369\) 2.86052 20.0769i 0.148913 1.04516i
\(370\) −10.5979 18.3561i −0.550959 0.954289i
\(371\) 13.5366 0.702786
\(372\) 0.505697 0.438753i 0.0262192 0.0227483i
\(373\) −7.71350 + 4.45339i −0.399390 + 0.230588i −0.686221 0.727393i \(-0.740732\pi\)
0.286831 + 0.957981i \(0.407398\pi\)
\(374\) 4.52797 7.84268i 0.234136 0.405535i
\(375\) 11.6358 10.0955i 0.600872 0.521329i
\(376\) 9.81867i 0.506359i
\(377\) 7.92554 + 4.57581i 0.408186 + 0.235666i
\(378\) −6.66130 + 4.29897i −0.342621 + 0.221115i
\(379\) 34.4271i 1.76840i −0.467109 0.884200i \(-0.654704\pi\)
0.467109 0.884200i \(-0.345296\pi\)
\(380\) −2.83528 + 10.7591i −0.145447 + 0.551932i
\(381\) 10.7937 + 3.72804i 0.552979 + 0.190993i
\(382\) 1.09142i 0.0558419i
\(383\) −35.4244 −1.81010 −0.905052 0.425301i \(-0.860168\pi\)
−0.905052 + 0.425301i \(0.860168\pi\)
\(384\) −0.565455 + 1.63715i −0.0288558 + 0.0835455i
\(385\) 2.27527 + 3.94088i 0.115958 + 0.200846i
\(386\) −1.57882 + 0.911533i −0.0803599 + 0.0463958i
\(387\) −5.25669 + 2.11224i −0.267212 + 0.107371i
\(388\) 0.534007i 0.0271101i
\(389\) 12.3362i 0.625471i −0.949840 0.312735i \(-0.898755\pi\)
0.949840 0.312735i \(-0.101245\pi\)
\(390\) −6.40595 7.38335i −0.324378 0.373870i
\(391\) −0.523140 0.906105i −0.0264563 0.0458237i
\(392\) 2.33603 + 4.04613i 0.117988 + 0.204360i
\(393\) −0.981567 + 0.851628i −0.0495135 + 0.0429589i
\(394\) −17.0579 + 9.84838i −0.859364 + 0.496154i
\(395\) 12.8652 + 22.2832i 0.647319 + 1.12119i
\(396\) −1.30692 3.25250i −0.0656750 0.163444i
\(397\) −10.2049 + 17.6754i −0.512168 + 0.887101i 0.487733 + 0.872993i \(0.337824\pi\)
−0.999900 + 0.0141076i \(0.995509\pi\)
\(398\) 4.29440 7.43811i 0.215259 0.372839i
\(399\) 5.08264 + 10.3373i 0.254450 + 0.517510i
\(400\) 0.757836 + 1.31261i 0.0378918 + 0.0656305i
\(401\) 0.691367 0.0345252 0.0172626 0.999851i \(-0.494505\pi\)
0.0172626 + 0.999851i \(0.494505\pi\)
\(402\) −9.31750 + 8.08406i −0.464715 + 0.403196i
\(403\) 0.854608 0.0425710
\(404\) 16.1829 + 9.34320i 0.805129 + 0.464842i
\(405\) 6.41611 22.0591i 0.318819 1.09612i
\(406\) −6.31550 −0.313433
\(407\) 4.85108 8.40231i 0.240459 0.416487i
\(408\) −2.54899 13.1802i −0.126194 0.652519i
\(409\) 28.3434 + 16.3641i 1.40149 + 0.809151i 0.994546 0.104301i \(-0.0332606\pi\)
0.406945 + 0.913452i \(0.366594\pi\)
\(410\) −14.9434 + 8.62760i −0.738004 + 0.426087i
\(411\) 2.63846 2.28918i 0.130146 0.112917i
\(412\) 6.36464i 0.313563i
\(413\) 5.93225 10.2750i 0.291907 0.505597i
\(414\) −0.400931 0.0571237i −0.0197047 0.00280748i
\(415\) 19.8849 34.4417i 0.976112 1.69068i
\(416\) −1.91472 + 1.10547i −0.0938770 + 0.0541999i
\(417\) 1.60080 0.309587i 0.0783917 0.0151606i
\(418\) −4.91398 + 1.33850i −0.240351 + 0.0654680i
\(419\) 31.5759 18.2304i 1.54258 0.890611i 0.543909 0.839144i \(-0.316944\pi\)
0.998675 0.0514673i \(-0.0163898\pi\)
\(420\) 6.37607 + 2.20223i 0.311120 + 0.107458i
\(421\) −11.3869 + 6.57421i −0.554962 + 0.320408i −0.751121 0.660165i \(-0.770487\pi\)
0.196159 + 0.980572i \(0.437153\pi\)
\(422\) −20.3381 + 11.7422i −0.990042 + 0.571601i
\(423\) −29.1615 4.15487i −1.41788 0.202017i
\(424\) 4.43603 + 7.68344i 0.215433 + 0.373141i
\(425\) −10.1735 5.87369i −0.493489 0.284916i
\(426\) −10.1665 11.7176i −0.492568 0.567722i
\(427\) 0.700631 1.21353i 0.0339059 0.0587268i
\(428\) 4.84302 8.38837i 0.234096 0.405467i
\(429\) 1.46073 4.22923i 0.0705249 0.204189i
\(430\) 4.17448 + 2.41014i 0.201312 + 0.116227i
\(431\) 0.191860 + 0.332312i 0.00924158 + 0.0160069i 0.870609 0.491975i \(-0.163725\pi\)
−0.861368 + 0.507982i \(0.830392\pi\)
\(432\) −4.62307 2.37218i −0.222427 0.114132i
\(433\) 15.6280 9.02281i 0.751032 0.433609i −0.0750344 0.997181i \(-0.523907\pi\)
0.826067 + 0.563572i \(0.190573\pi\)
\(434\) −0.510749 + 0.294881i −0.0245167 + 0.0141547i
\(435\) 13.8230 11.9931i 0.662760 0.575025i
\(436\) 11.7103 6.76093i 0.560820 0.323790i
\(437\) −0.149944 + 0.568997i −0.00717277 + 0.0272188i
\(438\) −12.1817 14.0404i −0.582065 0.670875i
\(439\) −9.32231 + 5.38224i −0.444930 + 0.256880i −0.705686 0.708524i \(-0.749361\pi\)
0.260757 + 0.965405i \(0.416028\pi\)
\(440\) −1.49124 + 2.58290i −0.0710921 + 0.123135i
\(441\) −13.0055 + 5.22587i −0.619312 + 0.248851i
\(442\) 8.56803 14.8403i 0.407540 0.705879i
\(443\) 6.32546i 0.300532i −0.988646 0.150266i \(-0.951987\pi\)
0.988646 0.150266i \(-0.0480129\pi\)
\(444\) −2.73088 14.1207i −0.129602 0.670141i
\(445\) 14.7252 8.50159i 0.698041 0.403014i
\(446\) −4.53089 2.61591i −0.214544 0.123867i
\(447\) −18.5808 + 16.1211i −0.878844 + 0.762503i
\(448\) 0.762878 1.32134i 0.0360426 0.0624276i
\(449\) 14.5374 0.686063 0.343032 0.939324i \(-0.388546\pi\)
0.343032 + 0.939324i \(0.388546\pi\)
\(450\) −4.21915 + 1.69533i −0.198892 + 0.0799188i
\(451\) −6.84020 3.94919i −0.322092 0.185960i
\(452\) 5.27442 0.248088
\(453\) 0.601446 + 3.10994i 0.0282584 + 0.146118i
\(454\) −8.24904 −0.387146
\(455\) 4.30537 + 7.45711i 0.201839 + 0.349595i
\(456\) −4.20186 + 6.27251i −0.196770 + 0.293737i
\(457\) −6.55232 + 11.3489i −0.306505 + 0.530881i −0.977595 0.210494i \(-0.932493\pi\)
0.671091 + 0.741375i \(0.265826\pi\)
\(458\) 9.53515 16.5154i 0.445548 0.771713i
\(459\) 40.2240 1.99317i 1.87750 0.0930334i
\(460\) 0.172291 + 0.298416i 0.00803309 + 0.0139137i
\(461\) 12.1860 7.03557i 0.567557 0.327679i −0.188616 0.982051i \(-0.560400\pi\)
0.756173 + 0.654372i \(0.227067\pi\)
\(462\) 0.586294 + 3.03159i 0.0272769 + 0.141042i
\(463\) 13.6189 + 23.5886i 0.632925 + 1.09626i 0.986951 + 0.161022i \(0.0514790\pi\)
−0.354026 + 0.935235i \(0.615188\pi\)
\(464\) −2.06963 3.58471i −0.0960802 0.166416i
\(465\) 0.557917 1.61532i 0.0258728 0.0749089i
\(466\) 8.85619i 0.410255i
\(467\) 16.8983i 0.781961i 0.920399 + 0.390981i \(0.127864\pi\)
−0.920399 + 0.390981i \(0.872136\pi\)
\(468\) −2.47301 6.15453i −0.114315 0.284493i
\(469\) 9.41058 5.43320i 0.434540 0.250882i
\(470\) 12.5315 + 21.7051i 0.578034 + 1.00118i
\(471\) −23.7628 27.3885i −1.09493 1.26199i
\(472\) 7.77614 0.357926
\(473\) 2.20643i 0.101452i
\(474\) 3.31513 + 17.1417i 0.152269 + 0.787346i
\(475\) 1.73630 + 6.37442i 0.0796668 + 0.292478i
\(476\) 11.8255i 0.542023i
\(477\) −24.6970 + 9.92372i −1.13080 + 0.454376i
\(478\) −4.98254 2.87667i −0.227896 0.131576i
\(479\) 40.7634i 1.86253i −0.364349 0.931263i \(-0.618708\pi\)
0.364349 0.931263i \(-0.381292\pi\)
\(480\) 0.839484 + 4.34077i 0.0383170 + 0.198128i
\(481\) 9.17943 15.8992i 0.418546 0.724943i
\(482\) 23.5284 13.5841i 1.07169 0.618739i
\(483\) 0.337198 + 0.116465i 0.0153431 + 0.00529934i
\(484\) 9.63480 0.437946
\(485\) −0.681548 1.18048i −0.0309475 0.0536027i
\(486\) 9.00169 12.7267i 0.408325 0.577296i
\(487\) 23.9395i 1.08480i −0.840120 0.542401i \(-0.817515\pi\)
0.840120 0.542401i \(-0.182485\pi\)
\(488\) 0.918405 0.0415743
\(489\) 20.3220 + 23.4227i 0.918995 + 1.05921i
\(490\) 10.3281 + 5.96292i 0.466575 + 0.269377i
\(491\) 29.0305i 1.31013i 0.755573 + 0.655064i \(0.227359\pi\)
−0.755573 + 0.655064i \(0.772641\pi\)
\(492\) −11.4955 + 2.22317i −0.518257 + 0.100228i
\(493\) 27.7836 + 16.0409i 1.25131 + 0.722446i
\(494\) −9.29845 + 2.53276i −0.418357 + 0.113954i
\(495\) −7.04020 5.52197i −0.316434 0.248194i
\(496\) −0.334751 0.193269i −0.0150308 0.00867802i
\(497\) 6.83277 + 11.8347i 0.306492 + 0.530859i
\(498\) 20.3832 17.6849i 0.913394 0.792480i
\(499\) 2.96806 0.132868 0.0664342 0.997791i \(-0.478838\pi\)
0.0664342 + 0.997791i \(0.478838\pi\)
\(500\) −7.70246 4.44702i −0.344464 0.198877i
\(501\) −1.25345 + 0.242411i −0.0559999 + 0.0108301i
\(502\) 24.1315 + 13.9323i 1.07704 + 0.621829i
\(503\) −33.9493 + 19.6006i −1.51372 + 0.873949i −0.513853 + 0.857878i \(0.671782\pi\)
−0.999871 + 0.0160702i \(0.994884\pi\)
\(504\) 3.60158 + 2.82489i 0.160427 + 0.125831i
\(505\) 47.6986 2.12256
\(506\) −0.0788642 + 0.136597i −0.00350594 + 0.00607247i
\(507\) −4.58685 + 13.2802i −0.203709 + 0.589795i
\(508\) 6.59299i 0.292517i
\(509\) −15.0166 + 26.0096i −0.665600 + 1.15285i 0.313522 + 0.949581i \(0.398491\pi\)
−0.979122 + 0.203272i \(0.934842\pi\)
\(510\) −22.4566 25.8830i −0.994395 1.14612i
\(511\) 8.18720 + 14.1806i 0.362180 + 0.627315i
\(512\) 1.00000 0.0441942
\(513\) −16.8513 15.1338i −0.744005 0.668174i
\(514\) −4.60766 −0.203235
\(515\) 8.12313 + 14.0697i 0.357948 + 0.619984i
\(516\) 2.14349 + 2.47054i 0.0943619 + 0.108759i
\(517\) −5.73615 + 9.93530i −0.252275 + 0.436954i
\(518\) 12.6694i 0.556661i
\(519\) 5.67578 16.4330i 0.249139 0.721327i
\(520\) −2.82179 + 4.88749i −0.123744 + 0.214330i
\(521\) 20.7192 0.907724 0.453862 0.891072i \(-0.350046\pi\)
0.453862 + 0.891072i \(0.350046\pi\)
\(522\) 11.5224 4.62991i 0.504321 0.202646i
\(523\) −1.90320 + 1.09881i −0.0832212 + 0.0480478i −0.541033 0.841001i \(-0.681967\pi\)
0.457812 + 0.889049i \(0.348633\pi\)
\(524\) 0.649758 + 0.375138i 0.0283848 + 0.0163880i
\(525\) 3.93258 0.760542i 0.171632 0.0331928i
\(526\) −8.47535 4.89325i −0.369543 0.213356i
\(527\) 2.99590 0.130503
\(528\) −1.52861 + 1.32625i −0.0665242 + 0.0577178i
\(529\) −11.4909 19.9028i −0.499604 0.865339i
\(530\) 19.6126 + 11.3233i 0.851917 + 0.491854i
\(531\) −3.29055 + 23.0952i −0.142798 + 1.00225i
\(532\) 4.68321 4.72210i 0.203043 0.204729i
\(533\) −12.9433 7.47284i −0.560638 0.323684i
\(534\) 11.3276 2.19070i 0.490193 0.0948009i
\(535\) 24.7244i 1.06893i
\(536\) 6.16782 + 3.56099i 0.266409 + 0.153811i
\(537\) 11.0582 + 12.7455i 0.477198 + 0.550008i
\(538\) −20.8391 −0.898436
\(539\) 5.45892i 0.235132i
\(540\) −13.2473 + 0.656431i −0.570075 + 0.0282483i
\(541\) −1.95051 3.37838i −0.0838589 0.145248i 0.821045 0.570863i \(-0.193391\pi\)
−0.904904 + 0.425615i \(0.860058\pi\)
\(542\) −20.8860 −0.897129
\(543\) 22.6775 + 7.83259i 0.973185 + 0.336128i
\(544\) −6.71222 + 3.87530i −0.287784 + 0.166152i
\(545\) 17.2578 29.8914i 0.739244 1.28041i
\(546\) 1.10941 + 5.73651i 0.0474785 + 0.245500i
\(547\) 45.5556i 1.94782i −0.226944 0.973908i \(-0.572874\pi\)
0.226944 0.973908i \(-0.427126\pi\)
\(548\) −1.74656 1.00838i −0.0746092 0.0430757i
\(549\) −0.388633 + 2.72767i −0.0165864 + 0.116414i
\(550\) 1.77094i 0.0755130i
\(551\) −4.74179 17.4084i −0.202007 0.741622i
\(552\) 0.0443961 + 0.229562i 0.00188962 + 0.00977079i
\(553\) 15.3799i 0.654018i
\(554\) −20.3807 −0.865893
\(555\) −24.0591 27.7299i −1.02125 1.17707i
\(556\) −0.470675 0.815232i −0.0199610 0.0345735i
\(557\) −34.7750 + 20.0774i −1.47346 + 0.850705i −0.999554 0.0298686i \(-0.990491\pi\)
−0.473910 + 0.880573i \(0.657158\pi\)
\(558\) 0.715663 0.912430i 0.0302964 0.0386262i
\(559\) 4.17511i 0.176588i
\(560\) 3.89462i 0.164578i
\(561\) 5.12073 14.8259i 0.216197 0.625952i
\(562\) 16.0406 + 27.7832i 0.676633 + 1.17196i
\(563\) 16.8303 + 29.1508i 0.709311 + 1.22856i 0.965113 + 0.261833i \(0.0843269\pi\)
−0.255803 + 0.966729i \(0.582340\pi\)
\(564\) 3.22913 + 16.6970i 0.135971 + 0.703072i
\(565\) 11.6596 6.73169i 0.490525 0.283204i
\(566\) 9.58910 + 16.6088i 0.403060 + 0.698120i
\(567\) −9.91399 + 9.50133i −0.416349 + 0.399018i
\(568\) −4.47829 + 7.75662i −0.187905 + 0.325461i
\(569\) −13.9198 + 24.1099i −0.583550 + 1.01074i 0.411505 + 0.911408i \(0.365003\pi\)
−0.995055 + 0.0993302i \(0.968330\pi\)
\(570\) −1.28308 + 19.2288i −0.0537424 + 0.805406i
\(571\) −6.57983 11.3966i −0.275357 0.476933i 0.694868 0.719137i \(-0.255463\pi\)
−0.970225 + 0.242205i \(0.922129\pi\)
\(572\) −2.58329 −0.108013
\(573\) −0.358942 1.85601i −0.0149950 0.0775357i
\(574\) 10.3140 0.430496
\(575\) 0.177193 + 0.102303i 0.00738948 + 0.00426632i
\(576\) −0.423160 + 2.97001i −0.0176317 + 0.123750i
\(577\) 39.9592 1.66352 0.831761 0.555134i \(-0.187333\pi\)
0.831761 + 0.555134i \(0.187333\pi\)
\(578\) 21.5360 37.3014i 0.895778 1.55153i
\(579\) −2.38507 + 2.06934i −0.0991201 + 0.0859987i
\(580\) −9.15025 5.28290i −0.379944 0.219361i
\(581\) −20.5868 + 11.8858i −0.854086 + 0.493107i
\(582\) −0.175622 0.908101i −0.00727978 0.0376420i
\(583\) 10.3663i 0.429327i
\(584\) −5.36599 + 9.29417i −0.222046 + 0.384596i
\(585\) −13.3218 10.4489i −0.550788 0.432010i
\(586\) −3.09233 + 5.35608i −0.127743 + 0.221258i
\(587\) −7.15130 + 4.12880i −0.295166 + 0.170414i −0.640269 0.768151i \(-0.721177\pi\)
0.345104 + 0.938565i \(0.387844\pi\)
\(588\) 5.30320 + 6.11234i 0.218700 + 0.252069i
\(589\) −1.19630 1.18645i −0.0492928 0.0488869i
\(590\) 17.1899 9.92461i 0.707698 0.408590i
\(591\) −25.7688 + 22.3575i −1.05999 + 0.919665i
\(592\) −7.19119 + 4.15184i −0.295556 + 0.170639i
\(593\) −3.01185 + 1.73889i −0.123682 + 0.0714078i −0.560565 0.828111i \(-0.689416\pi\)
0.436883 + 0.899519i \(0.356083\pi\)
\(594\) −3.29213 5.10120i −0.135078 0.209305i
\(595\) 15.0928 + 26.1415i 0.618746 + 1.07170i
\(596\) 12.2998 + 7.10128i 0.503819 + 0.290880i
\(597\) 4.85658 14.0611i 0.198767 0.575484i
\(598\) −0.149230 + 0.258475i −0.00610248 + 0.0105698i
\(599\) 2.87651 4.98225i 0.117531 0.203569i −0.801258 0.598319i \(-0.795835\pi\)
0.918789 + 0.394750i \(0.129169\pi\)
\(600\) 1.72042 + 1.98291i 0.0702358 + 0.0809521i
\(601\) 3.74377 + 2.16147i 0.152712 + 0.0881681i 0.574409 0.818569i \(-0.305232\pi\)
−0.421697 + 0.906737i \(0.638565\pi\)
\(602\) −1.44061 2.49522i −0.0587151 0.101697i
\(603\) −13.1861 + 16.8116i −0.536981 + 0.684620i
\(604\) 1.58378 0.914396i 0.0644431 0.0372062i
\(605\) 21.2987 12.2968i 0.865915 0.499936i
\(606\) 30.5924 + 10.5663i 1.24273 + 0.429228i
\(607\) 24.0328 13.8753i 0.975461 0.563183i 0.0745645 0.997216i \(-0.476243\pi\)
0.900897 + 0.434033i \(0.142910\pi\)
\(608\) 4.21500 + 1.11075i 0.170941 + 0.0450468i
\(609\) −10.7398 + 2.07702i −0.435198 + 0.0841651i
\(610\) 2.03023 1.17215i 0.0822015 0.0474591i
\(611\) −10.8542 + 18.8000i −0.439114 + 0.760567i
\(612\) −8.66933 21.5752i −0.350437 0.872127i
\(613\) 23.6861 41.0255i 0.956672 1.65700i 0.226176 0.974086i \(-0.427378\pi\)
0.730496 0.682917i \(-0.239289\pi\)
\(614\) 16.1865i 0.653235i
\(615\) −22.5745 + 19.5861i −0.910292 + 0.789789i
\(616\) 1.54388 0.891360i 0.0622047 0.0359139i
\(617\) 2.44932 + 1.41412i 0.0986061 + 0.0569302i 0.548492 0.836156i \(-0.315202\pi\)
−0.449886 + 0.893086i \(0.648535\pi\)
\(618\) 2.09318 + 10.8233i 0.0842000 + 0.435378i
\(619\) −7.27971 + 12.6088i −0.292596 + 0.506792i −0.974423 0.224722i \(-0.927853\pi\)
0.681827 + 0.731514i \(0.261186\pi\)
\(620\) −0.986668 −0.0396256
\(621\) −0.700586 + 0.0347153i −0.0281135 + 0.00139308i
\(622\) 24.8337 + 14.3377i 0.995739 + 0.574890i
\(623\) −10.1633 −0.407185
\(624\) −2.89250 + 2.50960i −0.115793 + 0.100464i
\(625\) −30.2811 −1.21124
\(626\) 3.60825 + 6.24967i 0.144215 + 0.249787i
\(627\) −7.91622 + 3.89226i −0.316144 + 0.155442i
\(628\) −10.4674 + 18.1301i −0.417695 + 0.723469i
\(629\) 32.1793 55.7361i 1.28307 2.22235i
\(630\) 11.5670 + 1.64805i 0.460842 + 0.0656597i
\(631\) 6.40998 + 11.1024i 0.255177 + 0.441980i 0.964944 0.262457i \(-0.0845328\pi\)
−0.709766 + 0.704437i \(0.751199\pi\)
\(632\) 8.72967 5.04008i 0.347248 0.200484i
\(633\) −30.7240 + 26.6568i −1.22117 + 1.05951i
\(634\) 2.69523 + 4.66828i 0.107041 + 0.185401i
\(635\) −8.41458 14.5745i −0.333922 0.578370i
\(636\) 10.0706 + 11.6071i 0.399324 + 0.460251i
\(637\) 10.3296i 0.409274i
\(638\) 4.83638i 0.191474i
\(639\) −21.1422 16.5828i −0.836371 0.656007i
\(640\) 2.21060 1.27629i 0.0873817 0.0504498i
\(641\) −14.2475 24.6774i −0.562742 0.974698i −0.997256 0.0740328i \(-0.976413\pi\)
0.434514 0.900665i \(-0.356920\pi\)
\(642\) 5.47703 15.8575i 0.216161 0.625846i
\(643\) 4.59459 0.181193 0.0905964 0.995888i \(-0.471123\pi\)
0.0905964 + 0.995888i \(0.471123\pi\)
\(644\) 0.205967i 0.00811623i
\(645\) 7.89152 + 2.72565i 0.310728 + 0.107322i
\(646\) −32.5965 + 8.87882i −1.28249 + 0.349332i
\(647\) 9.46727i 0.372197i 0.982531 + 0.186098i \(0.0595843\pi\)
−0.982531 + 0.186098i \(0.940416\pi\)
\(648\) −8.64187 2.51358i −0.339485 0.0987426i
\(649\) 7.86851 + 4.54289i 0.308866 + 0.178324i
\(650\) 3.35105i 0.131439i
\(651\) −0.771570 + 0.669430i −0.0302402 + 0.0262370i
\(652\) 8.95176 15.5049i 0.350578 0.607219i
\(653\) 34.4306 19.8785i 1.34737 0.777905i 0.359495 0.933147i \(-0.382949\pi\)
0.987877 + 0.155242i \(0.0496156\pi\)
\(654\) 17.6903 15.3485i 0.691745 0.600173i
\(655\) 1.91514 0.0748308
\(656\) 3.37995 + 5.85424i 0.131965 + 0.228570i
\(657\) −25.3331 19.8700i −0.988337 0.775201i
\(658\) 14.9809i 0.584016i
\(659\) −48.5702 −1.89203 −0.946014 0.324125i \(-0.894930\pi\)
−0.946014 + 0.324125i \(0.894930\pi\)
\(660\) −1.68646 + 4.88277i −0.0656453 + 0.190061i
\(661\) −20.9317 12.0849i −0.814151 0.470050i 0.0342446 0.999413i \(-0.489097\pi\)
−0.848395 + 0.529363i \(0.822431\pi\)
\(662\) 23.8020i 0.925091i
\(663\) 9.68968 28.0543i 0.376316 1.08954i
\(664\) −13.4929 7.79012i −0.523625 0.302315i
\(665\) 4.32594 16.4158i 0.167753 0.636578i
\(666\) −9.28796 23.1148i −0.359901 0.895680i
\(667\) −0.483911 0.279386i −0.0187371 0.0108179i
\(668\) 0.368544 + 0.638336i 0.0142594 + 0.0246980i
\(669\) −8.56528 2.95836i −0.331153 0.114377i
\(670\) 18.1794 0.702333
\(671\) 0.929315 + 0.536540i 0.0358758 + 0.0207129i
\(672\) 0.862747 2.49789i 0.0332812 0.0963583i
\(673\) −0.599468 0.346103i −0.0231078 0.0133413i 0.488402 0.872619i \(-0.337580\pi\)
−0.511509 + 0.859278i \(0.670913\pi\)
\(674\) 5.25115 3.03175i 0.202267 0.116779i
\(675\) −6.61728 + 4.27056i −0.254699 + 0.164374i
\(676\) 8.11178 0.311992
\(677\) −12.3134 + 21.3274i −0.473242 + 0.819680i −0.999531 0.0306263i \(-0.990250\pi\)
0.526289 + 0.850306i \(0.323583\pi\)
\(678\) 8.96937 1.73463i 0.344467 0.0666181i
\(679\) 0.814765i 0.0312678i
\(680\) −9.89203 + 17.1335i −0.379342 + 0.657040i
\(681\) −14.0278 + 2.71291i −0.537547 + 0.103959i
\(682\) −0.225818 0.391129i −0.00864704 0.0149771i
\(683\) 8.41338 0.321929 0.160965 0.986960i \(-0.448540\pi\)
0.160965 + 0.986960i \(0.448540\pi\)
\(684\) −5.08255 + 12.0486i −0.194336 + 0.460688i
\(685\) −5.14792 −0.196692
\(686\) −8.90437 15.4228i −0.339970 0.588846i
\(687\) 10.7834 31.2210i 0.411413 1.19115i
\(688\) 0.944197 1.63540i 0.0359972 0.0623489i
\(689\) 19.6155i 0.747292i
\(690\) 0.391129 + 0.450806i 0.0148900 + 0.0171619i
\(691\) −5.59480 + 9.69047i −0.212836 + 0.368643i −0.952601 0.304223i \(-0.901603\pi\)
0.739765 + 0.672865i \(0.234937\pi\)
\(692\) −10.0375 −0.381570
\(693\) 1.99404 + 4.96252i 0.0757471 + 0.188511i
\(694\) 16.8928 9.75306i 0.641242 0.370221i
\(695\) −2.08095 1.20144i −0.0789348 0.0455730i
\(696\) −4.69842 5.41529i −0.178093 0.205266i
\(697\) −45.3740 26.1967i −1.71866 0.992270i
\(698\) −24.7832 −0.938056
\(699\) −2.91259 15.0603i −0.110164 0.569634i
\(700\) −1.15627 2.00272i −0.0437030 0.0756958i
\(701\) 31.3712 + 18.1121i 1.18487 + 0.684086i 0.957137 0.289637i \(-0.0935345\pi\)
0.227736 + 0.973723i \(0.426868\pi\)
\(702\) −6.22953 9.65271i −0.235118 0.364318i
\(703\) −34.9225 + 9.51239i −1.31713 + 0.358767i
\(704\) 1.01188 + 0.584208i 0.0381366 + 0.0220182i
\(705\) 28.4486 + 32.7892i 1.07144 + 1.23491i
\(706\) 11.8402i 0.445610i
\(707\) −24.6912 14.2554i −0.928607 0.536131i
\(708\) 13.2236 2.55739i 0.496975 0.0961125i
\(709\) −33.3507 −1.25251 −0.626255 0.779618i \(-0.715413\pi\)
−0.626255 + 0.779618i \(0.715413\pi\)
\(710\) 22.8624i 0.858010i
\(711\) 11.2750 + 28.0599i 0.422846 + 1.05233i
\(712\) −3.33058 5.76874i −0.124819 0.216193i
\(713\) −0.0521799 −0.00195415
\(714\) 3.88914 + 20.1098i 0.145547 + 0.752591i
\(715\) −5.71062 + 3.29703i −0.213565 + 0.123302i
\(716\) 4.87110 8.43700i 0.182042 0.315305i
\(717\) −9.41908 3.25325i −0.351762 0.121495i
\(718\) 15.9682i 0.595928i
\(719\) −24.1012 13.9149i −0.898825 0.518937i −0.0220061 0.999758i \(-0.507005\pi\)
−0.876819 + 0.480821i \(0.840339\pi\)
\(720\) 2.85515 + 7.10557i 0.106405 + 0.264809i
\(721\) 9.71089i 0.361652i
\(722\) 16.5325 + 9.36362i 0.615275 + 0.348478i
\(723\) 35.5434 30.8382i 1.32187 1.14689i
\(724\) 13.8518i 0.514799i
\(725\) −6.27376 −0.233002
\(726\) 16.3844 3.16866i 0.608081 0.117600i
\(727\) −20.3335 35.2187i −0.754128 1.30619i −0.945807 0.324731i \(-0.894726\pi\)
0.191678 0.981458i \(-0.438607\pi\)
\(728\) 2.92140 1.68667i 0.108274 0.0625122i
\(729\) 11.1222 24.6028i 0.411934 0.911213i
\(730\) 27.3943i 1.01391i
\(731\) 14.6362i 0.541340i
\(732\) 1.56179 0.302042i 0.0577253 0.0111638i
\(733\) −4.36371 7.55816i −0.161177 0.279167i 0.774114 0.633046i \(-0.218196\pi\)
−0.935291 + 0.353879i \(0.884862\pi\)
\(734\) −11.3171 19.6019i −0.417724 0.723518i
\(735\) 19.5244 + 6.74353i 0.720168 + 0.248739i
\(736\) 0.116908 0.0674966i 0.00430927 0.00248796i
\(737\) 4.16072 + 7.20658i 0.153262 + 0.265458i
\(738\) −18.8174 + 7.56119i −0.692678 + 0.278331i
\(739\) −1.87473 + 3.24713i −0.0689630 + 0.119447i −0.898445 0.439086i \(-0.855302\pi\)
0.829482 + 0.558533i \(0.188636\pi\)
\(740\) −10.5979 + 18.3561i −0.389587 + 0.674784i
\(741\) −14.9794 + 7.36511i −0.550283 + 0.270564i
\(742\) −6.76831 11.7231i −0.248472 0.430367i
\(743\) −8.47663 −0.310977 −0.155489 0.987838i \(-0.549695\pi\)
−0.155489 + 0.987838i \(0.549695\pi\)
\(744\) −0.632820 0.218570i −0.0232003 0.00801315i
\(745\) 36.2532 1.32821
\(746\) 7.71350 + 4.45339i 0.282411 + 0.163050i
\(747\) 28.8463 36.7775i 1.05543 1.34562i
\(748\) −9.05594 −0.331118
\(749\) −7.38928 + 12.7986i −0.269998 + 0.467651i
\(750\) −14.5609 5.02918i −0.531688 0.183640i
\(751\) 4.53004 + 2.61542i 0.165303 + 0.0954380i 0.580369 0.814353i \(-0.302908\pi\)
−0.415066 + 0.909791i \(0.636242\pi\)
\(752\) 8.50321 4.90933i 0.310080 0.179025i
\(753\) 45.6185 + 15.7562i 1.66243 + 0.574187i
\(754\) 9.15162i 0.333282i
\(755\) 2.33407 4.04273i 0.0849455 0.147130i
\(756\) 7.05367 + 3.61937i 0.256540 + 0.131635i
\(757\) 6.65825 11.5324i 0.241998 0.419153i −0.719285 0.694715i \(-0.755531\pi\)
0.961283 + 0.275562i \(0.0888639\pi\)
\(758\) −29.8147 + 17.2135i −1.08292 + 0.625224i
\(759\) −0.0891883 + 0.258225i −0.00323733 + 0.00937297i
\(760\) 10.7353 2.92414i 0.389411 0.106070i
\(761\) 15.2464 8.80251i 0.552681 0.319091i −0.197521 0.980299i \(-0.563289\pi\)
0.750203 + 0.661208i \(0.229956\pi\)
\(762\) −2.16828 11.2117i −0.0785485 0.406156i
\(763\) −17.8670 + 10.3155i −0.646830 + 0.373447i
\(764\) −0.945198 + 0.545710i −0.0341961 + 0.0197431i
\(765\) −46.7007 36.6296i −1.68847 1.32435i
\(766\) 17.7122 + 30.6785i 0.639968 + 1.10846i
\(767\) 14.8891 + 8.59625i 0.537616 + 0.310393i
\(768\) 1.70054 0.328876i 0.0613630 0.0118673i
\(769\) −14.0382 + 24.3149i −0.506231 + 0.876817i 0.493743 + 0.869608i \(0.335628\pi\)
−0.999974 + 0.00720967i \(0.997705\pi\)
\(770\) 2.27527 3.94088i 0.0819950 0.142019i
\(771\) −7.83551 + 1.51535i −0.282189 + 0.0545740i
\(772\) 1.57882 + 0.911533i 0.0568230 + 0.0328068i
\(773\) −1.52748 2.64567i −0.0549395 0.0951580i 0.837248 0.546824i \(-0.184163\pi\)
−0.892187 + 0.451666i \(0.850830\pi\)
\(774\) 4.45759 + 3.49631i 0.160225 + 0.125672i
\(775\) −0.507373 + 0.292932i −0.0182254 + 0.0105224i
\(776\) −0.462464 + 0.267004i −0.0166015 + 0.00958487i
\(777\) 4.16666 + 21.5448i 0.149478 + 0.772916i
\(778\) −10.6835 + 6.16811i −0.383021 + 0.221137i
\(779\) 7.74390 + 28.4299i 0.277454 + 1.01861i
\(780\) −3.19119 + 9.23939i −0.114263 + 0.330823i
\(781\) −9.06297 + 5.23251i −0.324298 + 0.187234i
\(782\) −0.523140 + 0.906105i −0.0187074 + 0.0324022i
\(783\) 18.0716 11.6628i 0.645827 0.416794i
\(784\) 2.33603 4.04613i 0.0834298 0.144505i
\(785\) 53.4378i 1.90728i
\(786\) 1.22831 + 0.424248i 0.0438125 + 0.0151324i
\(787\) −39.5679 + 22.8445i −1.41044 + 0.814320i −0.995430 0.0954955i \(-0.969556\pi\)
−0.415013 + 0.909815i \(0.636223\pi\)
\(788\) 17.0579 + 9.84838i 0.607662 + 0.350834i
\(789\) −16.0220 5.53382i −0.570397 0.197009i
\(790\) 12.8652 22.2832i 0.457724 0.792801i
\(791\) −8.04748 −0.286135
\(792\) −2.16329 + 2.75807i −0.0768691 + 0.0980038i
\(793\) 1.75849 + 1.01527i 0.0624459 + 0.0360531i
\(794\) 20.4097 0.724315
\(795\) 37.0760 + 12.8057i 1.31495 + 0.454171i
\(796\) −8.58879 −0.304422
\(797\) −3.74913 6.49368i −0.132801 0.230018i 0.791954 0.610580i \(-0.209064\pi\)
−0.924755 + 0.380562i \(0.875730\pi\)
\(798\) 6.41101 9.57032i 0.226947 0.338786i
\(799\) −38.0503 + 65.9051i −1.34612 + 2.33155i
\(800\) 0.757836 1.31261i 0.0267935 0.0464078i
\(801\) 18.5426 7.45076i 0.655169 0.263259i
\(802\) −0.345683 0.598741i −0.0122065 0.0211423i
\(803\) −10.8595 + 6.26972i −0.383222 + 0.221253i
\(804\) 11.6598 + 4.02716i 0.411208 + 0.142027i
\(805\) −0.262873 0.455310i −0.00926507 0.0160476i
\(806\) −0.427304 0.740112i −0.0150511 0.0260693i
\(807\) −35.4377 + 6.85347i −1.24747 + 0.241254i
\(808\) 18.6864i 0.657385i
\(809\) 9.70609i 0.341248i 0.985336 + 0.170624i \(0.0545784\pi\)
−0.985336 + 0.170624i \(0.945422\pi\)
\(810\) −22.3118 + 5.47303i −0.783956 + 0.192303i
\(811\) −26.3705 + 15.2250i −0.925995 + 0.534623i −0.885543 0.464558i \(-0.846213\pi\)
−0.0404523 + 0.999181i \(0.512880\pi\)
\(812\) 3.15775 + 5.46939i 0.110815 + 0.191938i
\(813\) −35.5174 + 6.86890i −1.24565 + 0.240903i
\(814\) −9.70215 −0.340060
\(815\) 45.7002i 1.60081i
\(816\) −10.1399 + 8.79761i −0.354968 + 0.307978i
\(817\) 5.79631 5.84444i 0.202787 0.204471i
\(818\) 32.7281i 1.14431i
\(819\) 3.77320 + 9.39031i 0.131846 + 0.328124i
\(820\) 14.9434 + 8.62760i 0.521847 + 0.301289i
\(821\) 17.7758i 0.620378i −0.950675 0.310189i \(-0.899608\pi\)
0.950675 0.310189i \(-0.100392\pi\)
\(822\) −3.30172 1.14038i −0.115161 0.0397754i
\(823\) −2.81911 + 4.88284i −0.0982679 + 0.170205i −0.910968 0.412478i \(-0.864664\pi\)
0.812700 + 0.582682i \(0.197997\pi\)
\(824\) 5.51194 3.18232i 0.192018 0.110861i
\(825\) 0.582419 + 3.01155i 0.0202772 + 0.104849i
\(826\) −11.8645 −0.412818
\(827\) 14.2242 + 24.6371i 0.494625 + 0.856716i 0.999981 0.00619548i \(-0.00197210\pi\)
−0.505356 + 0.862911i \(0.668639\pi\)
\(828\) 0.150995 + 0.375778i 0.00524743 + 0.0130592i
\(829\) 35.2950i 1.22584i −0.790143 0.612922i \(-0.789994\pi\)
0.790143 0.612922i \(-0.210006\pi\)
\(830\) −39.7698 −1.38043
\(831\) −34.6582 + 6.70273i −1.20228 + 0.232515i
\(832\) 1.91472 + 1.10547i 0.0663811 + 0.0383251i
\(833\) 36.2114i 1.25465i
\(834\) −1.06851 1.23154i −0.0369995 0.0426448i
\(835\) 1.62941 + 0.940738i 0.0563879 + 0.0325556i
\(836\) 3.61616 + 3.58638i 0.125068 + 0.124038i
\(837\) 0.916937 1.78699i 0.0316940 0.0617674i
\(838\) −31.5759 18.2304i −1.09077 0.629757i
\(839\) 12.2589 + 21.2330i 0.423224 + 0.733046i 0.996253 0.0864896i \(-0.0275649\pi\)
−0.573029 + 0.819535i \(0.694232\pi\)
\(840\) −1.28085 6.62296i −0.0441934 0.228514i
\(841\) −11.8665 −0.409190
\(842\) 11.3869 + 6.57421i 0.392418 + 0.226562i
\(843\) 36.4150 + 41.9711i 1.25420 + 1.44556i
\(844\) 20.3381 + 11.7422i 0.700065 + 0.404183i
\(845\) 17.9319 10.3530i 0.616876 0.356154i
\(846\) 10.9825 + 27.3320i 0.377587 + 0.939695i
\(847\) −14.7004 −0.505110
\(848\) 4.43603 7.68344i 0.152334 0.263850i
\(849\) 21.7689 + 25.0903i 0.747107 + 0.861098i
\(850\) 11.7474i 0.402932i
\(851\) −0.560470 + 0.970762i −0.0192127 + 0.0332773i
\(852\) −5.06454 + 14.6633i −0.173508 + 0.502355i
\(853\) 3.17813 + 5.50468i 0.108817 + 0.188477i 0.915291 0.402793i \(-0.131960\pi\)
−0.806474 + 0.591269i \(0.798627\pi\)
\(854\) −1.40126 −0.0479502
\(855\) 4.14197 + 33.1214i 0.141652 + 1.13273i
\(856\) −9.68605 −0.331062
\(857\) 0.502103 + 0.869669i 0.0171515 + 0.0297073i 0.874474 0.485073i \(-0.161207\pi\)
−0.857322 + 0.514780i \(0.827874\pi\)
\(858\) −4.39299 + 0.849583i −0.149974 + 0.0290043i
\(859\) −10.5678 + 18.3040i −0.360570 + 0.624525i −0.988055 0.154104i \(-0.950751\pi\)
0.627485 + 0.778629i \(0.284084\pi\)
\(860\) 4.82028i 0.164370i
\(861\) 17.5393 3.39202i 0.597738 0.115600i
\(862\) 0.191860 0.332312i 0.00653479 0.0113186i
\(863\) −19.7281 −0.671551 −0.335776 0.941942i \(-0.608998\pi\)
−0.335776 + 0.941942i \(0.608998\pi\)
\(864\) 0.257164 + 5.18978i 0.00874888 + 0.176560i
\(865\) −22.1890 + 12.8108i −0.754448 + 0.435581i
\(866\) −15.6280 9.02281i −0.531060 0.306608i
\(867\) 24.3553 70.5152i 0.827148 2.39482i
\(868\) 0.510749 + 0.294881i 0.0173359 + 0.0100089i
\(869\) 11.7778 0.399535
\(870\) −17.2978 5.97449i −0.586450 0.202554i
\(871\) 7.87310 + 13.6366i 0.266770 + 0.462059i
\(872\) −11.7103 6.76093i −0.396560 0.228954i
\(873\) −0.597306 1.48651i −0.0202157 0.0503106i
\(874\) 0.567737 0.154643i 0.0192040 0.00523089i
\(875\) 11.7521 + 6.78506i 0.397293 + 0.229377i
\(876\) −6.06846 + 17.5699i −0.205034 + 0.593631i
\(877\) 8.07401i 0.272640i 0.990665 + 0.136320i \(0.0435275\pi\)
−0.990665 + 0.136320i \(0.956472\pi\)
\(878\) 9.32231 + 5.38224i 0.314613 + 0.181642i
\(879\) −3.49715 + 10.1252i −0.117956 + 0.341515i
\(880\) 2.98248 0.100539
\(881\) 3.75576i 0.126535i −0.997997 0.0632674i \(-0.979848\pi\)
0.997997 0.0632674i \(-0.0201521\pi\)
\(882\) 11.0285 + 8.65020i 0.371349 + 0.291267i
\(883\) 10.2193 + 17.7004i 0.343907 + 0.595664i 0.985155 0.171670i \(-0.0549162\pi\)
−0.641248 + 0.767334i \(0.721583\pi\)
\(884\) −17.1361 −0.576348
\(885\) 25.9682 22.5306i 0.872912 0.757357i
\(886\) −5.47801 + 3.16273i −0.184037 + 0.106254i
\(887\) 21.7923 37.7453i 0.731713 1.26736i −0.224438 0.974488i \(-0.572054\pi\)
0.956151 0.292876i \(-0.0946122\pi\)
\(888\) −10.8635 + 9.42538i −0.364555 + 0.316295i
\(889\) 10.0593i 0.337378i
\(890\) −14.7252 8.50159i −0.493589 0.284974i
\(891\) −7.27607 7.59209i −0.243758 0.254345i
\(892\) 5.23183i 0.175174i
\(893\) 41.2941 11.2479i 1.38185 0.376397i
\(894\) 23.2517 + 8.03092i 0.777654 + 0.268594i
\(895\) 24.8678i 0.831238i
\(896\) −1.52576 −0.0509719
\(897\) −0.168766 + 0.488625i −0.00563494 + 0.0163147i
\(898\) −7.26871 12.5898i −0.242560 0.420126i
\(899\) 1.38562 0.799990i 0.0462131 0.0266812i
\(900\) 3.57777 + 2.80622i 0.119259 + 0.0935407i
\(901\) 68.7639i 2.29086i
\(902\) 7.89838i 0.262987i
\(903\) −3.27044 3.76944i −0.108834 0.125439i
\(904\) −2.63721 4.56778i −0.0877123 0.151922i
\(905\) −17.6790 30.6208i −0.587668 1.01787i
\(906\) 2.39256 2.07584i 0.0794875 0.0689650i
\(907\) 41.0312 23.6894i 1.36242 0.786593i 0.372473 0.928043i \(-0.378510\pi\)
0.989945 + 0.141450i \(0.0451766\pi\)
\(908\) 4.12452 + 7.14387i 0.136877 + 0.237078i
\(909\) 55.4987 + 7.90734i 1.84078 + 0.262270i
\(910\) 4.30537 7.45711i 0.142721 0.247201i
\(911\) 14.3777 24.9029i 0.476354 0.825070i −0.523279 0.852162i \(-0.675291\pi\)
0.999633 + 0.0270919i \(0.00862468\pi\)
\(912\) 7.53308 + 0.502660i 0.249445 + 0.0166447i
\(913\) −9.10210 15.7653i −0.301236 0.521756i
\(914\) 13.1046 0.433463
\(915\) 3.06699 2.66099i 0.101392 0.0879695i
\(916\) −19.0703 −0.630101
\(917\) −0.991373 0.572369i −0.0327380 0.0189013i
\(918\) −21.8381 33.8384i −0.720766 1.11683i
\(919\) −35.0205 −1.15522 −0.577610 0.816313i \(-0.696015\pi\)
−0.577610 + 0.816313i \(0.696015\pi\)
\(920\) 0.172291 0.298416i 0.00568025 0.00983849i
\(921\) −5.32336 27.5258i −0.175411 0.907007i
\(922\) −12.1860 7.03557i −0.401323 0.231704i
\(923\) −17.1494 + 9.90118i −0.564478 + 0.325901i
\(924\) 2.33228 2.02354i 0.0767265 0.0665696i
\(925\) 12.5856i 0.413814i
\(926\) 13.6189 23.5886i 0.447545 0.775171i
\(927\) 7.11908 + 17.7171i 0.233821 + 0.581907i
\(928\) −2.06963 + 3.58471i −0.0679390 + 0.117674i
\(929\) 12.9759 7.49164i 0.425725 0.245793i −0.271798 0.962354i \(-0.587618\pi\)
0.697524 + 0.716561i \(0.254285\pi\)
\(930\) −1.67787 + 0.324492i −0.0550195 + 0.0106405i
\(931\) 14.3406 14.4597i 0.469995 0.473897i
\(932\) −7.66969 + 4.42810i −0.251229 + 0.145047i
\(933\) 46.9460 + 16.2147i 1.53694 + 0.530845i
\(934\) 14.6344 8.44916i 0.478852 0.276465i
\(935\) −20.0191 + 11.5580i −0.654694 + 0.377988i
\(936\) −4.09347 + 5.21895i −0.133799 + 0.170587i
\(937\) 3.76912 + 6.52830i 0.123132 + 0.213270i 0.921001 0.389560i \(-0.127373\pi\)
−0.797869 + 0.602830i \(0.794040\pi\)
\(938\) −9.41058 5.43320i −0.307266 0.177400i
\(939\) 8.19134 + 9.44115i 0.267314 + 0.308100i
\(940\) 12.5315 21.7051i 0.408732 0.707944i
\(941\) 23.0496 39.9231i 0.751397 1.30146i −0.195749 0.980654i \(-0.562714\pi\)
0.947146 0.320803i \(-0.103953\pi\)
\(942\) −11.8377 + 34.2734i −0.385693 + 1.11669i
\(943\) 0.790283 + 0.456270i 0.0257352 + 0.0148582i
\(944\) −3.88807 6.73433i −0.126546 0.219184i
\(945\) 20.2122 1.00155i 0.657504 0.0325805i
\(946\) 1.91083 1.10322i 0.0621263 0.0358686i
\(947\) −22.0863 + 12.7515i −0.717707 + 0.414368i −0.813908 0.580993i \(-0.802664\pi\)
0.0962010 + 0.995362i \(0.469331\pi\)
\(948\) 13.1876 11.4418i 0.428314 0.371614i
\(949\) −20.5488 + 11.8638i −0.667041 + 0.385117i
\(950\) 4.65226 4.69089i 0.150939 0.152193i
\(951\) 6.11865 + 7.05221i 0.198411 + 0.228684i
\(952\) 10.2412 5.91277i 0.331920 0.191634i
\(953\) 0.323565 0.560431i 0.0104813 0.0181542i −0.860737 0.509050i \(-0.829997\pi\)
0.871218 + 0.490895i \(0.163330\pi\)
\(954\) 20.9427 + 16.4264i 0.678045 + 0.531823i
\(955\) −1.39297 + 2.41269i −0.0450754 + 0.0780730i
\(956\) 5.75334i 0.186076i
\(957\) −1.59057 8.22447i −0.0514159 0.265859i
\(958\) −35.3021 + 20.3817i −1.14056 + 0.658502i
\(959\) 2.66482 + 1.53853i 0.0860515 + 0.0496819i
\(960\) 3.33948 2.89740i 0.107781 0.0935132i
\(961\) −15.4253 + 26.7174i −0.497590 + 0.861851i
\(962\) −18.3589 −0.591913
\(963\) 4.09875 28.7676i 0.132080 0.927024i
\(964\) −23.5284 13.5841i −0.757797 0.437514i
\(965\) 4.65352 0.149802
\(966\) −0.0677376 0.350255i −0.00217942 0.0112693i
\(967\) 42.2076 1.35730 0.678652 0.734460i \(-0.262564\pi\)
0.678652 + 0.734460i \(0.262564\pi\)
\(968\) −4.81740 8.34398i −0.154837 0.268186i
\(969\) −52.5117 + 25.8190i −1.68692 + 0.829426i
\(970\) −0.681548 + 1.18048i −0.0218832 + 0.0379028i
\(971\) 16.2173 28.0891i 0.520437 0.901423i −0.479281 0.877662i \(-0.659102\pi\)
0.999718 0.0237614i \(-0.00756421\pi\)
\(972\) −15.5225 1.43233i −0.497885 0.0459421i
\(973\) 0.718135 + 1.24385i 0.0230223 + 0.0398759i
\(974\) −20.7322 + 11.9697i −0.664303 + 0.383535i
\(975\) 1.10208 + 5.69859i 0.0352948 + 0.182501i
\(976\) −0.459203 0.795362i −0.0146987 0.0254589i
\(977\) −11.1431 19.3004i −0.356500 0.617475i 0.630874 0.775885i \(-0.282697\pi\)
−0.987373 + 0.158410i \(0.949363\pi\)
\(978\) 10.1236 29.3108i 0.323719 0.937255i
\(979\) 7.78302i 0.248747i
\(980\) 11.9258i 0.380957i
\(981\) 25.0353 31.9186i 0.799316 1.01908i
\(982\) 25.1412 14.5153i 0.802287 0.463200i
\(983\) −2.39962 4.15627i −0.0765361 0.132564i 0.825217 0.564816i \(-0.191053\pi\)
−0.901753 + 0.432251i \(0.857719\pi\)
\(984\) 7.67307 + 8.84380i 0.244608 + 0.281930i
\(985\) 50.2776 1.60198
\(986\) 32.0818i 1.02169i
\(987\) −4.92686 25.4756i −0.156824 0.810898i
\(988\) 6.84266 + 6.78632i 0.217694 + 0.215901i
\(989\) 0.254920i 0.00810600i
\(990\) −1.26207 + 8.85798i −0.0401111 + 0.281525i
\(991\) −11.2116 6.47302i −0.356148 0.205622i 0.311242 0.950331i \(-0.399255\pi\)
−0.667390 + 0.744709i \(0.732588\pi\)
\(992\) 0.386537i 0.0122726i
\(993\) 7.82792 + 40.4763i 0.248411 + 1.28448i
\(994\) 6.83277 11.8347i 0.216722 0.375374i
\(995\) −18.9864 + 10.9618i −0.601909 + 0.347512i
\(996\) −25.5072 8.80993i −0.808226 0.279153i
\(997\) −9.60690 −0.304254 −0.152127 0.988361i \(-0.548612\pi\)
−0.152127 + 0.988361i \(0.548612\pi\)
\(998\) −1.48403 2.57041i −0.0469761 0.0813650i
\(999\) −23.3965 36.2530i −0.740231 1.14700i
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 342.2.j.f.65.3 18
3.2 odd 2 1026.2.j.f.521.3 18
9.4 even 3 1026.2.n.f.179.7 18
9.5 odd 6 342.2.n.f.293.1 yes 18
19.12 odd 6 342.2.n.f.335.1 yes 18
57.50 even 6 1026.2.n.f.791.7 18
171.31 odd 6 1026.2.j.f.449.7 18
171.50 even 6 inner 342.2.j.f.221.3 yes 18
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
342.2.j.f.65.3 18 1.1 even 1 trivial
342.2.j.f.221.3 yes 18 171.50 even 6 inner
342.2.n.f.293.1 yes 18 9.5 odd 6
342.2.n.f.335.1 yes 18 19.12 odd 6
1026.2.j.f.449.7 18 171.31 odd 6
1026.2.j.f.521.3 18 3.2 odd 2
1026.2.n.f.179.7 18 9.4 even 3
1026.2.n.f.791.7 18 57.50 even 6