Properties

Label 392.2.z.a.109.44
Level $392$
Weight $2$
Character 392.109
Analytic conductor $3.130$
Analytic rank $0$
Dimension $648$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [392,2,Mod(37,392)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(392, base_ring=CyclotomicField(42))
 
chi = DirichletCharacter(H, H._module([0, 21, 32]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("392.37");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 392 = 2^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 392.z (of order \(42\), degree \(12\), 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: \(3.13013575923\)
Analytic rank: \(0\)
Dimension: \(648\)
Relative dimension: \(54\) over \(\Q(\zeta_{42})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label 109.44
Character \(\chi\) \(=\) 392.109
Dual form 392.2.z.a.205.44

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.21309 + 0.726927i) q^{2} +(0.0230268 + 0.152773i) q^{3} +(0.943154 + 1.76365i) q^{4} +(0.525668 + 0.206310i) q^{5} +(-0.0831214 + 0.202066i) q^{6} +(-2.63610 - 0.225735i) q^{7} +(-0.137919 + 2.82506i) q^{8} +(2.84391 - 0.877230i) q^{9} +O(q^{10})\) \(q+(1.21309 + 0.726927i) q^{2} +(0.0230268 + 0.152773i) q^{3} +(0.943154 + 1.76365i) q^{4} +(0.525668 + 0.206310i) q^{5} +(-0.0831214 + 0.202066i) q^{6} +(-2.63610 - 0.225735i) q^{7} +(-0.137919 + 2.82506i) q^{8} +(2.84391 - 0.877230i) q^{9} +(0.487708 + 0.632394i) q^{10} +(-1.80388 + 5.84803i) q^{11} +(-0.247720 + 0.184700i) q^{12} +(6.52741 - 1.48984i) q^{13} +(-3.03373 - 2.19009i) q^{14} +(-0.0194141 + 0.0850586i) q^{15} +(-2.22092 + 3.32679i) q^{16} +(-4.09945 + 2.79496i) q^{17} +(4.08759 + 1.00316i) q^{18} +(3.64219 - 2.10282i) q^{19} +(0.131928 + 1.12168i) q^{20} +(-0.0262149 - 0.407924i) q^{21} +(-6.43935 + 5.78287i) q^{22} +(-1.89465 - 1.29175i) q^{23} +(-0.434769 + 0.0439819i) q^{24} +(-3.43150 - 3.18396i) q^{25} +(9.00131 + 2.93765i) q^{26} +(0.400607 + 0.831868i) q^{27} +(-2.08813 - 4.86207i) q^{28} +(2.65570 - 5.51461i) q^{29} +(-0.0853823 + 0.0890707i) q^{30} +(3.34270 - 5.78972i) q^{31} +(-5.11250 + 2.42123i) q^{32} +(-0.934959 - 0.140922i) q^{33} +(-7.00472 + 0.410521i) q^{34} +(-1.33914 - 0.662515i) q^{35} +(4.22937 + 4.18830i) q^{36} +(-5.30623 + 0.397647i) q^{37} +(5.94688 + 0.0967071i) q^{38} +(0.377912 + 0.962905i) q^{39} +(-0.655337 + 1.45659i) q^{40} +(-4.66691 - 5.85212i) q^{41} +(0.264730 - 0.513903i) q^{42} +(1.84701 + 1.47294i) q^{43} +(-12.0152 + 2.33418i) q^{44} +(1.67593 + 0.125594i) q^{45} +(-1.35936 - 2.94428i) q^{46} +(2.94701 - 2.73443i) q^{47} +(-0.559384 - 0.262692i) q^{48} +(6.89809 + 1.19012i) q^{49} +(-1.84819 - 6.35687i) q^{50} +(-0.521392 - 0.561927i) q^{51} +(8.78390 + 10.1069i) q^{52} +(2.92702 + 0.219350i) q^{53} +(-0.118738 + 1.30034i) q^{54} +(-2.15475 + 2.70197i) q^{55} +(1.00128 - 7.41603i) q^{56} +(0.405122 + 0.508007i) q^{57} +(7.23031 - 4.75920i) q^{58} +(-0.729205 + 0.286192i) q^{59} +(-0.168324 + 0.0459837i) q^{60} +(1.54097 - 0.115480i) q^{61} +(8.26369 - 4.59353i) q^{62} +(-7.69486 + 1.67050i) q^{63} +(-7.96196 - 0.779261i) q^{64} +(3.73862 + 0.563506i) q^{65} +(-1.03174 - 0.850598i) q^{66} +(0.598085 + 0.345304i) q^{67} +(-8.79574 - 4.59392i) q^{68} +(0.153717 - 0.319197i) q^{69} +(-1.14290 - 1.77715i) q^{70} +(-2.58966 + 1.24711i) q^{71} +(2.08600 + 8.15521i) q^{72} +(5.90067 + 5.47502i) q^{73} +(-6.72597 - 3.37486i) q^{74} +(0.407407 - 0.597557i) q^{75} +(7.14378 + 4.44026i) q^{76} +(6.07531 - 15.0088i) q^{77} +(-0.241522 + 1.44280i) q^{78} +(-5.41460 - 9.37836i) q^{79} +(-1.85382 + 1.29059i) q^{80} +(7.25912 - 4.94918i) q^{81} +(-1.40730 - 10.4916i) q^{82} +(-10.4710 - 2.38994i) q^{83} +(0.694710 - 0.430969i) q^{84} +(-2.73158 + 0.623465i) q^{85} +(1.16986 + 3.12945i) q^{86} +(0.903637 + 0.278735i) q^{87} +(-16.2723 - 5.90263i) q^{88} +(9.73745 - 3.00360i) q^{89} +(1.94175 + 1.37064i) q^{90} +(-17.5432 + 2.45390i) q^{91} +(0.491250 - 4.55982i) q^{92} +(0.961485 + 0.377355i) q^{93} +(5.56271 - 1.17483i) q^{94} +(2.34841 - 0.353966i) q^{95} +(-0.487623 - 0.725299i) q^{96} -8.51056 q^{97} +(7.50284 + 6.45813i) q^{98} +18.2137i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 648 q - 13 q^{2} - 13 q^{4} - 6 q^{6} - 24 q^{7} - 16 q^{8} - 76 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 648 q - 13 q^{2} - 13 q^{4} - 6 q^{6} - 24 q^{7} - 16 q^{8} - 76 q^{9} - 6 q^{10} - 47 q^{12} - 33 q^{14} - 8 q^{15} - 17 q^{16} - 26 q^{17} - 8 q^{18} - 22 q^{20} - 18 q^{22} - 26 q^{23} - 74 q^{24} - 72 q^{25} - 12 q^{26} + 2 q^{28} - 11 q^{30} + 60 q^{31} - 13 q^{32} - 14 q^{33} - 18 q^{34} + 8 q^{36} - 46 q^{38} - 32 q^{39} + 32 q^{40} - 20 q^{41} - 36 q^{42} + 38 q^{44} - 22 q^{46} - 58 q^{47} + 28 q^{48} - 16 q^{49} - 132 q^{50} + 18 q^{52} - 37 q^{54} - 32 q^{55} + 96 q^{56} - 66 q^{57} + 100 q^{60} + 28 q^{62} - 72 q^{63} - 28 q^{64} - 36 q^{65} - 4 q^{66} - 11 q^{68} - 36 q^{70} + 60 q^{71} - 130 q^{72} - 18 q^{73} - 12 q^{74} + 11 q^{76} - 132 q^{78} - 12 q^{79} - 64 q^{80} - 58 q^{81} + 152 q^{82} - 224 q^{84} + 55 q^{86} - 8 q^{87} - 169 q^{88} - 18 q^{89} + 144 q^{90} - 54 q^{92} + 154 q^{94} - 64 q^{95} - 142 q^{96} - 96 q^{97} + 151 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/392\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(295\) \(297\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{20}{21}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.21309 + 0.726927i 0.857781 + 0.514015i
\(3\) 0.0230268 + 0.152773i 0.0132945 + 0.0882036i 0.994494 0.104792i \(-0.0334177\pi\)
−0.981200 + 0.192996i \(0.938180\pi\)
\(4\) 0.943154 + 1.76365i 0.471577 + 0.881825i
\(5\) 0.525668 + 0.206310i 0.235086 + 0.0922644i 0.479960 0.877291i \(-0.340651\pi\)
−0.244874 + 0.969555i \(0.578747\pi\)
\(6\) −0.0831214 + 0.202066i −0.0339342 + 0.0824929i
\(7\) −2.63610 0.225735i −0.996354 0.0853197i
\(8\) −0.137919 + 2.82506i −0.0487618 + 0.998810i
\(9\) 2.84391 0.877230i 0.947970 0.292410i
\(10\) 0.487708 + 0.632394i 0.154227 + 0.199980i
\(11\) −1.80388 + 5.84803i −0.543890 + 1.76325i 0.0966457 + 0.995319i \(0.469189\pi\)
−0.640535 + 0.767929i \(0.721288\pi\)
\(12\) −0.247720 + 0.184700i −0.0715107 + 0.0533182i
\(13\) 6.52741 1.48984i 1.81038 0.413207i 0.822541 0.568706i \(-0.192556\pi\)
0.987836 + 0.155500i \(0.0496988\pi\)
\(14\) −3.03373 2.19009i −0.810798 0.585327i
\(15\) −0.0194141 + 0.0850586i −0.00501269 + 0.0219620i
\(16\) −2.22092 + 3.32679i −0.555231 + 0.831696i
\(17\) −4.09945 + 2.79496i −0.994263 + 0.677877i −0.947076 0.321009i \(-0.895978\pi\)
−0.0471870 + 0.998886i \(0.515026\pi\)
\(18\) 4.08759 + 1.00316i 0.963454 + 0.236447i
\(19\) 3.64219 2.10282i 0.835575 0.482419i −0.0201826 0.999796i \(-0.506425\pi\)
0.855758 + 0.517377i \(0.173091\pi\)
\(20\) 0.131928 + 1.12168i 0.0295000 + 0.250814i
\(21\) −0.0262149 0.407924i −0.00572057 0.0890162i
\(22\) −6.43935 + 5.78287i −1.37287 + 1.23291i
\(23\) −1.89465 1.29175i −0.395062 0.269349i 0.349454 0.936954i \(-0.386367\pi\)
−0.744516 + 0.667605i \(0.767320\pi\)
\(24\) −0.434769 + 0.0439819i −0.0887469 + 0.00897777i
\(25\) −3.43150 3.18396i −0.686299 0.636793i
\(26\) 9.00131 + 2.93765i 1.76530 + 0.576120i
\(27\) 0.400607 + 0.831868i 0.0770968 + 0.160093i
\(28\) −2.08813 4.86207i −0.394620 0.918844i
\(29\) 2.65570 5.51461i 0.493151 1.02404i −0.494762 0.869028i \(-0.664745\pi\)
0.987913 0.155010i \(-0.0495409\pi\)
\(30\) −0.0853823 + 0.0890707i −0.0155886 + 0.0162620i
\(31\) 3.34270 5.78972i 0.600366 1.03986i −0.392399 0.919795i \(-0.628355\pi\)
0.992765 0.120070i \(-0.0383119\pi\)
\(32\) −5.11250 + 2.42123i −0.903771 + 0.428016i
\(33\) −0.934959 0.140922i −0.162755 0.0245314i
\(34\) −7.00472 + 0.410521i −1.20130 + 0.0704038i
\(35\) −1.33914 0.662515i −0.226357 0.111985i
\(36\) 4.22937 + 4.18830i 0.704895 + 0.698050i
\(37\) −5.30623 + 0.397647i −0.872339 + 0.0653728i −0.503372 0.864070i \(-0.667907\pi\)
−0.368967 + 0.929443i \(0.620288\pi\)
\(38\) 5.94688 + 0.0967071i 0.964711 + 0.0156880i
\(39\) 0.377912 + 0.962905i 0.0605144 + 0.154188i
\(40\) −0.655337 + 1.45659i −0.103618 + 0.230307i
\(41\) −4.66691 5.85212i −0.728849 0.913948i 0.269953 0.962873i \(-0.412992\pi\)
−0.998802 + 0.0489255i \(0.984420\pi\)
\(42\) 0.264730 0.513903i 0.0408487 0.0792969i
\(43\) 1.84701 + 1.47294i 0.281667 + 0.224622i 0.754124 0.656732i \(-0.228062\pi\)
−0.472457 + 0.881354i \(0.656633\pi\)
\(44\) −12.0152 + 2.33418i −1.81136 + 0.351891i
\(45\) 1.67593 + 0.125594i 0.249833 + 0.0187224i
\(46\) −1.35936 2.94428i −0.200427 0.434110i
\(47\) 2.94701 2.73443i 0.429866 0.398858i −0.435346 0.900263i \(-0.643374\pi\)
0.865212 + 0.501406i \(0.167184\pi\)
\(48\) −0.559384 0.262692i −0.0807401 0.0379163i
\(49\) 6.89809 + 1.19012i 0.985441 + 0.170017i
\(50\) −1.84819 6.35687i −0.261373 0.898997i
\(51\) −0.521392 0.561927i −0.0730095 0.0786855i
\(52\) 8.78390 + 10.1069i 1.21811 + 1.40158i
\(53\) 2.92702 + 0.219350i 0.402058 + 0.0301300i 0.274225 0.961666i \(-0.411579\pi\)
0.127833 + 0.991796i \(0.459198\pi\)
\(54\) −0.118738 + 1.30034i −0.0161581 + 0.176954i
\(55\) −2.15475 + 2.70197i −0.290546 + 0.364333i
\(56\) 1.00128 7.41603i 0.133802 0.991008i
\(57\) 0.405122 + 0.508007i 0.0536597 + 0.0672871i
\(58\) 7.23031 4.75920i 0.949386 0.624913i
\(59\) −0.729205 + 0.286192i −0.0949344 + 0.0372590i −0.412333 0.911033i \(-0.635286\pi\)
0.317399 + 0.948292i \(0.397191\pi\)
\(60\) −0.168324 + 0.0459837i −0.0217305 + 0.00593647i
\(61\) 1.54097 0.115480i 0.197301 0.0147857i 0.0242871 0.999705i \(-0.492268\pi\)
0.173014 + 0.984919i \(0.444649\pi\)
\(62\) 8.26369 4.59353i 1.04949 0.583379i
\(63\) −7.69486 + 1.67050i −0.969461 + 0.210463i
\(64\) −7.96196 0.779261i −0.995245 0.0974076i
\(65\) 3.73862 + 0.563506i 0.463718 + 0.0698943i
\(66\) −1.03174 0.850598i −0.126999 0.104701i
\(67\) 0.598085 + 0.345304i 0.0730677 + 0.0421856i 0.536089 0.844162i \(-0.319901\pi\)
−0.463021 + 0.886347i \(0.653235\pi\)
\(68\) −8.79574 4.59392i −1.06664 0.557095i
\(69\) 0.153717 0.319197i 0.0185053 0.0384267i
\(70\) −1.14290 1.77715i −0.136602 0.212410i
\(71\) −2.58966 + 1.24711i −0.307336 + 0.148005i −0.581194 0.813765i \(-0.697414\pi\)
0.273858 + 0.961770i \(0.411700\pi\)
\(72\) 2.08600 + 8.15521i 0.245837 + 0.961100i
\(73\) 5.90067 + 5.47502i 0.690621 + 0.640803i 0.945292 0.326225i \(-0.105777\pi\)
−0.254671 + 0.967028i \(0.581967\pi\)
\(74\) −6.72597 3.37486i −0.781878 0.392320i
\(75\) 0.407407 0.597557i 0.0470433 0.0689999i
\(76\) 7.14378 + 4.44026i 0.819447 + 0.509333i
\(77\) 6.07531 15.0088i 0.692346 1.71041i
\(78\) −0.241522 + 1.44280i −0.0273470 + 0.163365i
\(79\) −5.41460 9.37836i −0.609190 1.05515i −0.991374 0.131062i \(-0.958161\pi\)
0.382184 0.924086i \(-0.375172\pi\)
\(80\) −1.85382 + 1.29059i −0.207263 + 0.144292i
\(81\) 7.25912 4.94918i 0.806569 0.549909i
\(82\) −1.40730 10.4916i −0.155410 1.15861i
\(83\) −10.4710 2.38994i −1.14934 0.262330i −0.394917 0.918717i \(-0.629227\pi\)
−0.754424 + 0.656387i \(0.772084\pi\)
\(84\) 0.694710 0.430969i 0.0757990 0.0470225i
\(85\) −2.73158 + 0.623465i −0.296281 + 0.0676242i
\(86\) 1.16986 + 3.12945i 0.126150 + 0.337458i
\(87\) 0.903637 + 0.278735i 0.0968800 + 0.0298835i
\(88\) −16.2723 5.90263i −1.73463 0.629222i
\(89\) 9.73745 3.00360i 1.03217 0.318381i 0.268013 0.963415i \(-0.413633\pi\)
0.764154 + 0.645034i \(0.223157\pi\)
\(90\) 1.94175 + 1.37064i 0.204679 + 0.144478i
\(91\) −17.5432 + 2.45390i −1.83903 + 0.257239i
\(92\) 0.491250 4.55982i 0.0512164 0.475394i
\(93\) 0.961485 + 0.377355i 0.0997014 + 0.0391299i
\(94\) 5.56271 1.17483i 0.573750 0.121175i
\(95\) 2.34841 0.353966i 0.240942 0.0363162i
\(96\) −0.487623 0.725299i −0.0497678 0.0740255i
\(97\) −8.51056 −0.864116 −0.432058 0.901846i \(-0.642212\pi\)
−0.432058 + 0.901846i \(0.642212\pi\)
\(98\) 7.50284 + 6.45813i 0.757901 + 0.652369i
\(99\) 18.2137i 1.83054i
\(100\) 2.37897 9.05492i 0.237897 0.905492i
\(101\) −1.11690 7.41014i −0.111136 0.737336i −0.973103 0.230372i \(-0.926006\pi\)
0.861967 0.506964i \(-0.169232\pi\)
\(102\) −0.224013 1.06068i −0.0221806 0.105023i
\(103\) 5.19123 13.2270i 0.511507 1.30330i −0.408986 0.912541i \(-0.634117\pi\)
0.920493 0.390759i \(-0.127787\pi\)
\(104\) 3.30863 + 18.6458i 0.324438 + 1.82837i
\(105\) 0.0703782 0.219841i 0.00686820 0.0214543i
\(106\) 3.39128 + 2.39382i 0.329390 + 0.232509i
\(107\) 2.65746 + 8.61527i 0.256906 + 0.832870i 0.988512 + 0.151142i \(0.0482950\pi\)
−0.731606 + 0.681728i \(0.761229\pi\)
\(108\) −1.08929 + 1.49111i −0.104817 + 0.143482i
\(109\) −3.39822 + 11.0168i −0.325491 + 1.05522i 0.633966 + 0.773361i \(0.281426\pi\)
−0.959457 + 0.281855i \(0.909050\pi\)
\(110\) −4.57802 + 1.71137i −0.436497 + 0.163173i
\(111\) −0.182935 0.801492i −0.0173635 0.0760743i
\(112\) 6.60555 8.26841i 0.624166 0.781292i
\(113\) −3.01275 + 13.1997i −0.283416 + 1.24173i 0.609965 + 0.792428i \(0.291183\pi\)
−0.893381 + 0.449299i \(0.851674\pi\)
\(114\) 0.122164 + 0.910750i 0.0114417 + 0.0852995i
\(115\) −0.729457 1.06992i −0.0680222 0.0997703i
\(116\) 12.2306 0.517406i 1.13558 0.0480399i
\(117\) 17.2564 9.96300i 1.59536 0.921079i
\(118\) −1.09263 0.182904i −0.100585 0.0168377i
\(119\) 11.4375 6.44241i 1.04847 0.590575i
\(120\) −0.237618 0.0665771i −0.0216915 0.00607763i
\(121\) −21.8569 14.9017i −1.98699 1.35470i
\(122\) 1.95328 + 0.980087i 0.176841 + 0.0887329i
\(123\) 0.786582 0.847734i 0.0709237 0.0764376i
\(124\) 13.3637 + 0.434752i 1.20010 + 0.0390419i
\(125\) −2.37203 4.92556i −0.212160 0.440556i
\(126\) −10.5489 3.56715i −0.939767 0.317787i
\(127\) 8.18124 + 3.93988i 0.725968 + 0.349608i 0.760097 0.649810i \(-0.225151\pi\)
−0.0341292 + 0.999417i \(0.510866\pi\)
\(128\) −9.09207 6.73307i −0.803633 0.595125i
\(129\) −0.182495 + 0.316091i −0.0160678 + 0.0278303i
\(130\) 4.12563 + 3.40128i 0.361842 + 0.298312i
\(131\) −1.35426 + 8.98496i −0.118323 + 0.785020i 0.848430 + 0.529307i \(0.177548\pi\)
−0.966753 + 0.255712i \(0.917690\pi\)
\(132\) −0.633272 1.78185i −0.0551193 0.155090i
\(133\) −10.0759 + 4.72108i −0.873688 + 0.409369i
\(134\) 0.474517 + 0.853648i 0.0409920 + 0.0737439i
\(135\) 0.0389638 + 0.519936i 0.00335347 + 0.0447489i
\(136\) −7.33054 11.9667i −0.628589 1.02613i
\(137\) 6.69369 + 17.0552i 0.571880 + 1.45713i 0.865355 + 0.501160i \(0.167093\pi\)
−0.293474 + 0.955967i \(0.594811\pi\)
\(138\) 0.418505 0.275472i 0.0356255 0.0234497i
\(139\) 4.30096 3.42991i 0.364803 0.290921i −0.423883 0.905717i \(-0.639333\pi\)
0.788686 + 0.614796i \(0.210762\pi\)
\(140\) −0.0945744 2.98664i −0.00799300 0.252417i
\(141\) 0.485608 + 0.387259i 0.0408955 + 0.0326131i
\(142\) −4.04804 0.369638i −0.339704 0.0310193i
\(143\) −3.06203 + 40.8599i −0.256060 + 3.41688i
\(144\) −3.39775 + 11.4093i −0.283146 + 0.950778i
\(145\) 2.53373 2.35096i 0.210415 0.195237i
\(146\) 3.17808 + 10.9310i 0.263019 + 0.904659i
\(147\) −0.0229773 + 1.08125i −0.00189513 + 0.0891797i
\(148\) −5.70590 8.98329i −0.469022 0.738422i
\(149\) −5.00550 5.39464i −0.410066 0.441946i 0.493920 0.869507i \(-0.335563\pi\)
−0.903987 + 0.427561i \(0.859373\pi\)
\(150\) 0.928600 0.428732i 0.0758199 0.0350058i
\(151\) −0.366619 + 4.89220i −0.0298351 + 0.398121i 0.962216 + 0.272287i \(0.0877799\pi\)
−0.992051 + 0.125835i \(0.959839\pi\)
\(152\) 5.43826 + 10.5794i 0.441101 + 0.858105i
\(153\) −9.20665 + 11.5448i −0.744313 + 0.933339i
\(154\) 18.2802 13.7907i 1.47306 1.11128i
\(155\) 2.95162 2.35384i 0.237080 0.189065i
\(156\) −1.34180 + 1.57467i −0.107430 + 0.126075i
\(157\) −8.20797 + 3.22139i −0.655067 + 0.257095i −0.669513 0.742801i \(-0.733497\pi\)
0.0144453 + 0.999896i \(0.495402\pi\)
\(158\) 0.249013 15.3128i 0.0198104 1.21822i
\(159\) 0.0338893 + 0.452221i 0.00268760 + 0.0358635i
\(160\) −3.18700 + 0.218004i −0.251954 + 0.0172347i
\(161\) 4.70290 + 3.83288i 0.370641 + 0.302073i
\(162\) 12.4036 0.726932i 0.974521 0.0571132i
\(163\) −0.262654 + 1.74260i −0.0205727 + 0.136491i −0.996759 0.0804416i \(-0.974367\pi\)
0.976187 + 0.216932i \(0.0696051\pi\)
\(164\) 5.91948 13.7502i 0.462234 1.07371i
\(165\) −0.462404 0.266969i −0.0359981 0.0207835i
\(166\) −10.9649 10.5108i −0.851042 0.815800i
\(167\) −13.7789 6.63555i −1.06624 0.513474i −0.183347 0.983048i \(-0.558693\pi\)
−0.882893 + 0.469574i \(0.844408\pi\)
\(168\) 1.15603 0.0177983i 0.0891893 0.00137317i
\(169\) 28.6748 13.8091i 2.20575 1.06224i
\(170\) −3.76685 1.22934i −0.288904 0.0942862i
\(171\) 8.51339 9.17526i 0.651036 0.701649i
\(172\) −0.855741 + 4.64670i −0.0652496 + 0.354308i
\(173\) −8.98475 + 13.1782i −0.683098 + 1.00192i 0.315497 + 0.948926i \(0.397829\pi\)
−0.998595 + 0.0529936i \(0.983124\pi\)
\(174\) 0.893568 + 0.995007i 0.0677413 + 0.0754313i
\(175\) 8.32705 + 9.16787i 0.629466 + 0.693025i
\(176\) −15.4489 18.9891i −1.16450 1.43136i
\(177\) −0.0605137 0.104813i −0.00454849 0.00787821i
\(178\) 13.9958 + 3.43479i 1.04903 + 0.257448i
\(179\) −7.45455 10.9338i −0.557179 0.817231i 0.439536 0.898225i \(-0.355143\pi\)
−0.996715 + 0.0809937i \(0.974191\pi\)
\(180\) 1.35916 + 3.07421i 0.101306 + 0.229138i
\(181\) 15.7198 + 3.58795i 1.16845 + 0.266690i 0.762365 0.647147i \(-0.224038\pi\)
0.406080 + 0.913837i \(0.366895\pi\)
\(182\) −23.0652 9.77585i −1.70971 0.724634i
\(183\) 0.0531259 + 0.232760i 0.00392718 + 0.0172061i
\(184\) 3.91059 5.17435i 0.288292 0.381458i
\(185\) −2.87135 0.885695i −0.211106 0.0651176i
\(186\) 0.892054 + 1.15669i 0.0654086 + 0.0848129i
\(187\) −8.95009 29.0155i −0.654496 2.12182i
\(188\) 7.60206 + 2.61851i 0.554437 + 0.190975i
\(189\) −0.868259 2.28332i −0.0631566 0.166087i
\(190\) 3.10613 + 1.27773i 0.225343 + 0.0926966i
\(191\) −4.28466 + 10.9171i −0.310027 + 0.789936i 0.687914 + 0.725792i \(0.258527\pi\)
−0.997941 + 0.0641433i \(0.979569\pi\)
\(192\) −0.0642886 1.23432i −0.00463963 0.0890791i
\(193\) −10.4895 + 1.58103i −0.755047 + 0.113805i −0.515276 0.857024i \(-0.672311\pi\)
−0.239771 + 0.970829i \(0.577072\pi\)
\(194\) −10.3240 6.18656i −0.741222 0.444169i
\(195\) 0.584136i 0.0418308i
\(196\) 4.40700 + 13.2883i 0.314786 + 0.949163i
\(197\) 4.17578i 0.297512i 0.988874 + 0.148756i \(0.0475269\pi\)
−0.988874 + 0.148756i \(0.952473\pi\)
\(198\) −13.2400 + 22.0948i −0.940927 + 1.57021i
\(199\) −13.0444 + 1.96613i −0.924696 + 0.139375i −0.594095 0.804395i \(-0.702490\pi\)
−0.330601 + 0.943771i \(0.607251\pi\)
\(200\) 9.46816 9.25506i 0.669500 0.654432i
\(201\) −0.0389812 + 0.0993225i −0.00274952 + 0.00700567i
\(202\) 4.03174 9.80103i 0.283672 0.689598i
\(203\) −8.24554 + 13.9376i −0.578723 + 0.978228i
\(204\) 0.499290 1.44954i 0.0349573 0.101488i
\(205\) −1.24590 4.03910i −0.0870173 0.282103i
\(206\) 15.9125 12.2719i 1.10868 0.855023i
\(207\) −6.52138 2.01158i −0.453267 0.139814i
\(208\) −9.54049 + 25.0241i −0.661514 + 1.73511i
\(209\) 5.72728 + 25.0928i 0.396164 + 1.73571i
\(210\) 0.245183 0.215526i 0.0169192 0.0148727i
\(211\) 7.47606 + 1.70636i 0.514673 + 0.117471i 0.471966 0.881617i \(-0.343545\pi\)
0.0427074 + 0.999088i \(0.486402\pi\)
\(212\) 2.37378 + 5.36912i 0.163032 + 0.368753i
\(213\) −0.250157 0.366913i −0.0171405 0.0251405i
\(214\) −3.03895 + 12.3828i −0.207738 + 0.846474i
\(215\) 0.667034 + 1.15534i 0.0454913 + 0.0787933i
\(216\) −2.40533 + 1.01701i −0.163662 + 0.0691986i
\(217\) −10.1186 + 14.5077i −0.686898 + 0.984850i
\(218\) −12.1307 + 10.8940i −0.821597 + 0.737837i
\(219\) −0.700562 + 1.02754i −0.0473396 + 0.0694344i
\(220\) −6.79758 1.25185i −0.458293 0.0843996i
\(221\) −22.5947 + 24.3513i −1.51989 + 1.63805i
\(222\) 0.360710 1.10526i 0.0242093 0.0741802i
\(223\) −15.0323 + 7.23919i −1.00664 + 0.484772i −0.863187 0.504885i \(-0.831535\pi\)
−0.143453 + 0.989657i \(0.545821\pi\)
\(224\) 14.0236 5.22854i 0.936994 0.349346i
\(225\) −12.5519 6.04469i −0.836795 0.402979i
\(226\) −13.2500 + 13.8224i −0.881376 + 0.919450i
\(227\) 5.31326 + 3.06761i 0.352653 + 0.203604i 0.665853 0.746083i \(-0.268068\pi\)
−0.313200 + 0.949687i \(0.601401\pi\)
\(228\) −0.513854 + 1.19362i −0.0340308 + 0.0790495i
\(229\) −1.34697 + 8.93659i −0.0890105 + 0.590546i 0.899211 + 0.437515i \(0.144141\pi\)
−0.988221 + 0.153031i \(0.951097\pi\)
\(230\) −0.107142 1.82816i −0.00706474 0.120546i
\(231\) 2.43284 + 0.582539i 0.160069 + 0.0383282i
\(232\) 15.2129 + 8.26308i 0.998773 + 0.542498i
\(233\) −0.175776 2.34556i −0.0115155 0.153663i −0.999997 0.00232356i \(-0.999260\pi\)
0.988482 0.151339i \(-0.0483587\pi\)
\(234\) 28.1759 + 0.458191i 1.84192 + 0.0299529i
\(235\) 2.11329 0.829405i 0.137856 0.0541044i
\(236\) −1.19249 1.01614i −0.0776248 0.0661451i
\(237\) 1.30808 1.04316i 0.0849689 0.0677604i
\(238\) 18.5578 + 0.499032i 1.20293 + 0.0323474i
\(239\) 0.269401 0.337818i 0.0174261 0.0218516i −0.773042 0.634355i \(-0.781266\pi\)
0.790468 + 0.612503i \(0.209837\pi\)
\(240\) −0.239854 0.253495i −0.0154825 0.0163630i
\(241\) 0.974499 13.0038i 0.0627730 0.837648i −0.873601 0.486643i \(-0.838221\pi\)
0.936374 0.351004i \(-0.114160\pi\)
\(242\) −15.6817 33.9654i −1.00806 2.18338i
\(243\) 2.80728 + 3.02552i 0.180087 + 0.194087i
\(244\) 1.65704 + 2.60882i 0.106081 + 0.167013i
\(245\) 3.38057 + 2.04875i 0.215977 + 0.130890i
\(246\) 1.57043 0.456586i 0.100127 0.0291109i
\(247\) 20.6412 19.1522i 1.31337 1.21863i
\(248\) 15.8953 + 10.2418i 1.00935 + 0.650358i
\(249\) 0.124004 1.65472i 0.00785843 0.104864i
\(250\) 0.703055 7.69942i 0.0444651 0.486954i
\(251\) 10.8104 + 8.62100i 0.682346 + 0.544153i 0.902167 0.431388i \(-0.141976\pi\)
−0.219821 + 0.975540i \(0.570547\pi\)
\(252\) −10.2036 11.9955i −0.642767 0.755646i
\(253\) 10.9719 8.74981i 0.689799 0.550096i
\(254\) 7.06054 + 10.7266i 0.443018 + 0.673045i
\(255\) −0.158148 0.402955i −0.00990362 0.0252340i
\(256\) −6.13500 14.7771i −0.383438 0.923567i
\(257\) −0.136868 1.82637i −0.00853757 0.113926i 0.991307 0.131571i \(-0.0420021\pi\)
−0.999844 + 0.0176451i \(0.994383\pi\)
\(258\) −0.451158 + 0.250785i −0.0280879 + 0.0156132i
\(259\) 14.0775 + 0.149562i 0.874736 + 0.00929333i
\(260\) 2.53226 + 7.12508i 0.157044 + 0.441879i
\(261\) 2.71498 18.0127i 0.168053 1.11496i
\(262\) −8.17425 + 9.91507i −0.505007 + 0.612555i
\(263\) 8.96816 15.5333i 0.553000 0.957824i −0.445056 0.895503i \(-0.646816\pi\)
0.998056 0.0623217i \(-0.0198505\pi\)
\(264\) 0.527063 2.62188i 0.0324385 0.161366i
\(265\) 1.49339 + 0.719178i 0.0917381 + 0.0441788i
\(266\) −15.6548 1.59735i −0.959855 0.0979397i
\(267\) 0.683092 + 1.41846i 0.0418046 + 0.0868081i
\(268\) −0.0449103 + 1.38049i −0.00274334 + 0.0843267i
\(269\) −12.0461 + 12.9826i −0.734462 + 0.791562i −0.984258 0.176736i \(-0.943446\pi\)
0.249796 + 0.968298i \(0.419636\pi\)
\(270\) −0.330689 + 0.659050i −0.0201251 + 0.0401085i
\(271\) 6.00056 + 4.09111i 0.364508 + 0.248517i 0.731699 0.681628i \(-0.238728\pi\)
−0.367190 + 0.930146i \(0.619680\pi\)
\(272\) −0.193663 19.8454i −0.0117425 1.20330i
\(273\) −0.778855 2.62363i −0.0471385 0.158789i
\(274\) −4.27790 + 25.5553i −0.258437 + 1.54385i
\(275\) 24.8099 14.3240i 1.49609 0.863770i
\(276\) 0.707930 0.0299484i 0.0426124 0.00180268i
\(277\) 9.44232 + 13.8493i 0.567334 + 0.832126i 0.997503 0.0706220i \(-0.0224984\pi\)
−0.430169 + 0.902748i \(0.641546\pi\)
\(278\) 7.71073 1.03428i 0.462459 0.0620320i
\(279\) 4.42741 19.3978i 0.265062 1.16131i
\(280\) 2.05634 3.69179i 0.122890 0.220627i
\(281\) 2.54554 + 11.1528i 0.151854 + 0.665318i 0.992346 + 0.123492i \(0.0394095\pi\)
−0.840491 + 0.541825i \(0.817733\pi\)
\(282\) 0.307574 + 0.822780i 0.0183158 + 0.0489958i
\(283\) 8.05290 26.1069i 0.478695 1.55189i −0.318351 0.947973i \(-0.603129\pi\)
0.797046 0.603919i \(-0.206395\pi\)
\(284\) −4.64192 3.39103i −0.275447 0.201221i
\(285\) 0.108153 + 0.350623i 0.00640643 + 0.0207691i
\(286\) −33.4167 + 47.3407i −1.97597 + 2.79932i
\(287\) 10.9814 + 16.4803i 0.648214 + 0.972801i
\(288\) −12.4155 + 11.3706i −0.731591 + 0.670018i
\(289\) 2.78291 7.09075i 0.163701 0.417103i
\(290\) 4.78261 1.01008i 0.280845 0.0593138i
\(291\) −0.195971 1.30018i −0.0114880 0.0762181i
\(292\) −4.09079 + 15.5705i −0.239395 + 0.911195i
\(293\) 7.45954i 0.435791i 0.975972 + 0.217896i \(0.0699192\pi\)
−0.975972 + 0.217896i \(0.930081\pi\)
\(294\) −0.813861 + 1.29494i −0.0474653 + 0.0755225i
\(295\) −0.442364 −0.0257554
\(296\) −0.391546 15.0453i −0.0227582 0.874489i
\(297\) −5.58744 + 0.842171i −0.324216 + 0.0488677i
\(298\) −2.15058 10.1828i −0.124580 0.589873i
\(299\) −14.2917 5.60906i −0.826508 0.324380i
\(300\) 1.43813 + 0.154936i 0.0830304 + 0.00894524i
\(301\) −4.53643 4.29977i −0.261475 0.247835i
\(302\) −4.00101 + 5.66815i −0.230232 + 0.326165i
\(303\) 1.10635 0.341264i 0.0635582 0.0196051i
\(304\) −1.09339 + 16.7870i −0.0627104 + 0.962799i
\(305\) 0.833864 + 0.257213i 0.0477469 + 0.0147280i
\(306\) −19.5607 + 7.31223i −1.11821 + 0.418013i
\(307\) −28.2266 + 6.44253i −1.61097 + 0.367694i −0.930850 0.365402i \(-0.880932\pi\)
−0.680125 + 0.733096i \(0.738074\pi\)
\(308\) 32.2003 3.44089i 1.83478 0.196063i
\(309\) 2.14027 + 0.488503i 0.121756 + 0.0277900i
\(310\) 5.29165 0.709796i 0.300545 0.0403137i
\(311\) 6.46163 4.40546i 0.366405 0.249811i −0.366095 0.930577i \(-0.619306\pi\)
0.732500 + 0.680767i \(0.238353\pi\)
\(312\) −2.77239 + 0.934823i −0.156956 + 0.0529239i
\(313\) −3.87343 6.70897i −0.218939 0.379213i 0.735545 0.677476i \(-0.236926\pi\)
−0.954484 + 0.298263i \(0.903593\pi\)
\(314\) −12.2987 2.05877i −0.694055 0.116183i
\(315\) −4.38958 0.709395i −0.247325 0.0399699i
\(316\) 11.4333 18.3947i 0.643176 1.03478i
\(317\) 6.09957 8.94642i 0.342586 0.502481i −0.615821 0.787886i \(-0.711176\pi\)
0.958407 + 0.285405i \(0.0921280\pi\)
\(318\) −0.287621 + 0.573218i −0.0161290 + 0.0321445i
\(319\) 27.4591 + 25.4783i 1.53741 + 1.42651i
\(320\) −4.02458 2.05226i −0.224981 0.114725i
\(321\) −1.25499 + 0.604371i −0.0700466 + 0.0337327i
\(322\) 2.91880 + 8.06828i 0.162658 + 0.449628i
\(323\) −9.05368 + 18.8002i −0.503760 + 1.04607i
\(324\) 15.5751 + 8.13471i 0.865283 + 0.451928i
\(325\) −27.1424 15.6706i −1.50559 0.869251i
\(326\) −1.58536 + 1.92299i −0.0878051 + 0.106504i
\(327\) −1.76132 0.265476i −0.0974010 0.0146808i
\(328\) 17.1763 12.3772i 0.948401 0.683416i
\(329\) −8.38589 + 6.54300i −0.462329 + 0.360727i
\(330\) −0.366869 0.659991i −0.0201955 0.0363313i
\(331\) 17.2550 1.29308i 0.948420 0.0710742i 0.408470 0.912772i \(-0.366062\pi\)
0.539950 + 0.841697i \(0.318443\pi\)
\(332\) −5.66074 20.7212i −0.310674 1.13723i
\(333\) −14.7416 + 5.78566i −0.807835 + 0.317052i
\(334\) −11.8914 18.0657i −0.650667 0.988513i
\(335\) 0.243154 + 0.304906i 0.0132849 + 0.0166588i
\(336\) 1.41530 + 0.818755i 0.0772107 + 0.0446668i
\(337\) 15.1848 19.0412i 0.827170 1.03724i −0.171474 0.985189i \(-0.554853\pi\)
0.998644 0.0520498i \(-0.0165755\pi\)
\(338\) 44.8232 + 4.09293i 2.43806 + 0.222626i
\(339\) −2.08594 0.156319i −0.113293 0.00849011i
\(340\) −3.67587 4.22952i −0.199352 0.229378i
\(341\) 27.8287 + 29.9922i 1.50701 + 1.62417i
\(342\) 16.9972 4.94175i 0.919104 0.267219i
\(343\) −17.9154 4.69442i −0.967342 0.253475i
\(344\) −4.41590 + 5.01478i −0.238089 + 0.270379i
\(345\) 0.146657 0.136078i 0.00789577 0.00732620i
\(346\) −20.4789 + 9.45503i −1.10095 + 0.508306i
\(347\) 6.67742 + 0.500404i 0.358463 + 0.0268631i 0.252745 0.967533i \(-0.418667\pi\)
0.105718 + 0.994396i \(0.466286\pi\)
\(348\) 0.360677 + 1.85659i 0.0193343 + 0.0995236i
\(349\) −3.69402 2.94588i −0.197736 0.157689i 0.519616 0.854400i \(-0.326075\pi\)
−0.717353 + 0.696710i \(0.754646\pi\)
\(350\) 3.43705 + 17.1746i 0.183718 + 0.918019i
\(351\) 3.85427 + 4.83310i 0.205726 + 0.257972i
\(352\) −4.93708 34.2657i −0.263147 1.82637i
\(353\) −2.90304 7.39682i −0.154513 0.393693i 0.832566 0.553926i \(-0.186871\pi\)
−0.987079 + 0.160233i \(0.948776\pi\)
\(354\) 0.00278298 0.171136i 0.000147914 0.00909577i
\(355\) −1.61859 + 0.121297i −0.0859060 + 0.00643776i
\(356\) 14.4812 + 14.3406i 0.767503 + 0.760050i
\(357\) 1.24760 + 1.59899i 0.0660298 + 0.0846277i
\(358\) −1.09492 18.6826i −0.0578682 0.987404i
\(359\) −32.5692 4.90902i −1.71894 0.259088i −0.785768 0.618522i \(-0.787732\pi\)
−0.933171 + 0.359434i \(0.882970\pi\)
\(360\) −0.585954 + 4.71729i −0.0308825 + 0.248623i
\(361\) −0.656315 + 1.13677i −0.0345429 + 0.0598301i
\(362\) 16.4613 + 15.7797i 0.865188 + 0.829360i
\(363\) 1.77329 3.68228i 0.0930737 0.193269i
\(364\) −20.8738 28.6257i −1.09408 1.50039i
\(365\) 1.97225 + 4.09541i 0.103232 + 0.214364i
\(366\) −0.104753 + 0.320976i −0.00547554 + 0.0167777i
\(367\) −25.4935 23.6546i −1.33075 1.23476i −0.950820 0.309743i \(-0.899757\pi\)
−0.379932 0.925014i \(-0.624053\pi\)
\(368\) 8.50525 3.43422i 0.443367 0.179021i
\(369\) −18.4059 12.5489i −0.958174 0.653272i
\(370\) −2.83936 3.16169i −0.147611 0.164368i
\(371\) −7.66642 1.23896i −0.398021 0.0643236i
\(372\) 0.241306 + 2.05163i 0.0125111 + 0.106372i
\(373\) −23.5536 + 13.5987i −1.21956 + 0.704113i −0.964824 0.262898i \(-0.915322\pi\)
−0.254735 + 0.967011i \(0.581988\pi\)
\(374\) 10.2349 41.7043i 0.529235 2.15648i
\(375\) 0.697873 0.475802i 0.0360380 0.0245703i
\(376\) 7.31848 + 8.70263i 0.377422 + 0.448804i
\(377\) 9.11894 39.9527i 0.469649 2.05767i
\(378\) 0.606536 3.40103i 0.0311969 0.174930i
\(379\) 23.6101 5.38885i 1.21277 0.276807i 0.432143 0.901805i \(-0.357758\pi\)
0.780626 + 0.624999i \(0.214901\pi\)
\(380\) 2.83919 + 3.80793i 0.145647 + 0.195343i
\(381\) −0.413519 + 1.34060i −0.0211852 + 0.0686808i
\(382\) −13.1336 + 10.1288i −0.671974 + 0.518233i
\(383\) 0.403219 0.124377i 0.0206035 0.00635534i −0.284436 0.958695i \(-0.591806\pi\)
0.305040 + 0.952340i \(0.401330\pi\)
\(384\) 0.819271 1.54406i 0.0418082 0.0787952i
\(385\) 6.29006 6.63626i 0.320571 0.338215i
\(386\) −13.8739 5.70714i −0.706163 0.290486i
\(387\) 6.54485 + 2.56867i 0.332694 + 0.130573i
\(388\) −8.02676 15.0096i −0.407497 0.761999i
\(389\) −2.23524 14.8299i −0.113331 0.751904i −0.971240 0.238102i \(-0.923475\pi\)
0.857909 0.513802i \(-0.171763\pi\)
\(390\) −0.424624 + 0.708606i −0.0215017 + 0.0358817i
\(391\) 11.3774 0.575381
\(392\) −4.31354 + 19.3234i −0.217867 + 0.975978i
\(393\) −1.40384 −0.0708146
\(394\) −3.03549 + 5.06557i −0.152926 + 0.255200i
\(395\) −0.911436 6.04699i −0.0458593 0.304257i
\(396\) −32.1226 + 17.1783i −1.61422 + 0.863242i
\(397\) 1.02388 + 0.401842i 0.0513869 + 0.0201679i 0.390895 0.920435i \(-0.372165\pi\)
−0.339508 + 0.940603i \(0.610261\pi\)
\(398\) −17.2533 7.09727i −0.864828 0.355754i
\(399\) −0.953269 1.43061i −0.0477231 0.0716200i
\(400\) 18.2135 4.34452i 0.910673 0.217226i
\(401\) 23.4532 7.23436i 1.17120 0.361267i 0.352678 0.935745i \(-0.385271\pi\)
0.818520 + 0.574478i \(0.194795\pi\)
\(402\) −0.119488 + 0.0921502i −0.00595951 + 0.00459603i
\(403\) 13.1934 42.7719i 0.657210 2.13062i
\(404\) 12.0155 8.95871i 0.597793 0.445713i
\(405\) 4.83695 1.10400i 0.240350 0.0548583i
\(406\) −20.1342 + 10.9136i −0.999242 + 0.541633i
\(407\) 7.24634 31.7483i 0.359188 1.57370i
\(408\) 1.65939 1.39546i 0.0821519 0.0690858i
\(409\) −28.8048 + 19.6388i −1.42430 + 0.971075i −0.426525 + 0.904476i \(0.640262\pi\)
−0.997780 + 0.0665990i \(0.978785\pi\)
\(410\) 1.42475 5.80545i 0.0703635 0.286711i
\(411\) −2.45145 + 1.41534i −0.120921 + 0.0698137i
\(412\) 28.2240 3.31962i 1.39050 0.163546i
\(413\) 1.98686 0.589825i 0.0977672 0.0290234i
\(414\) −6.44872 7.18078i −0.316937 0.352916i
\(415\) −5.01120 3.41658i −0.245990 0.167713i
\(416\) −29.7641 + 23.4211i −1.45931 + 1.14832i
\(417\) 0.623035 + 0.578092i 0.0305101 + 0.0283093i
\(418\) −11.2930 + 34.6031i −0.552358 + 1.69249i
\(419\) −16.4937 34.2495i −0.805770 1.67320i −0.737319 0.675545i \(-0.763908\pi\)
−0.0684517 0.997654i \(-0.521806\pi\)
\(420\) 0.454100 0.0832212i 0.0221578 0.00406078i
\(421\) −4.83847 + 10.0472i −0.235813 + 0.489670i −0.984971 0.172721i \(-0.944744\pi\)
0.749158 + 0.662391i \(0.230458\pi\)
\(422\) 7.82870 + 7.50452i 0.381095 + 0.365314i
\(423\) 5.98232 10.3617i 0.290870 0.503802i
\(424\) −1.02337 + 8.23877i −0.0496993 + 0.400110i
\(425\) 22.9663 + 3.46161i 1.11403 + 0.167913i
\(426\) −0.0367429 0.626943i −0.00178020 0.0303755i
\(427\) −4.08823 0.0434340i −0.197843 0.00210192i
\(428\) −12.6879 + 12.8124i −0.613294 + 0.619308i
\(429\) −6.31281 + 0.473080i −0.304785 + 0.0228405i
\(430\) −0.0306764 + 1.88641i −0.00147935 + 0.0909707i
\(431\) 3.28662 + 8.37416i 0.158311 + 0.403369i 0.987918 0.154978i \(-0.0495308\pi\)
−0.829607 + 0.558348i \(0.811436\pi\)
\(432\) −3.65716 0.514783i −0.175955 0.0247675i
\(433\) −15.6760 19.6570i −0.753338 0.944656i 0.246361 0.969178i \(-0.420765\pi\)
−0.999699 + 0.0245219i \(0.992194\pi\)
\(434\) −22.8209 + 10.2436i −1.09544 + 0.491710i
\(435\) 0.417507 + 0.332951i 0.0200179 + 0.0159638i
\(436\) −22.6348 + 4.39723i −1.08401 + 0.210589i
\(437\) −9.61699 0.720694i −0.460043 0.0344755i
\(438\) −1.59679 + 0.737231i −0.0762974 + 0.0352263i
\(439\) 13.3960 12.4296i 0.639355 0.593235i −0.292412 0.956293i \(-0.594458\pi\)
0.931767 + 0.363058i \(0.118267\pi\)
\(440\) −7.33604 6.45994i −0.349732 0.307966i
\(441\) 20.6615 2.66661i 0.983883 0.126982i
\(442\) −45.1110 + 13.1155i −2.14571 + 0.623842i
\(443\) 20.2089 + 21.7800i 0.960154 + 1.03480i 0.999367 + 0.0355690i \(0.0113244\pi\)
−0.0392133 + 0.999231i \(0.512485\pi\)
\(444\) 1.24102 1.07856i 0.0588960 0.0511864i
\(445\) 5.73834 + 0.430029i 0.272023 + 0.0203853i
\(446\) −23.4979 2.14565i −1.11266 0.101600i
\(447\) 0.708895 0.888926i 0.0335296 0.0420448i
\(448\) 20.8126 + 3.85150i 0.983305 + 0.181966i
\(449\) 0.0908312 + 0.113899i 0.00428659 + 0.00537521i 0.783970 0.620799i \(-0.213191\pi\)
−0.779684 + 0.626174i \(0.784620\pi\)
\(450\) −10.8325 16.4571i −0.510650 0.775794i
\(451\) 42.6419 16.7357i 2.00793 0.788054i
\(452\) −26.1212 + 7.13594i −1.22864 + 0.335646i
\(453\) −0.755838 + 0.0566422i −0.0355124 + 0.00266128i
\(454\) 4.21550 + 7.58362i 0.197843 + 0.355917i
\(455\) −9.72818 2.32940i −0.456064 0.109204i
\(456\) −1.49102 + 1.07443i −0.0698236 + 0.0503148i
\(457\) −8.22110 1.23913i −0.384567 0.0579641i −0.0460862 0.998937i \(-0.514675\pi\)
−0.338481 + 0.940973i \(0.609913\pi\)
\(458\) −8.13024 + 9.86169i −0.379901 + 0.460807i
\(459\) −3.96731 2.29052i −0.185178 0.106913i
\(460\) 1.19897 2.29560i 0.0559022 0.107033i
\(461\) 12.6215 26.2089i 0.587844 1.22067i −0.368827 0.929498i \(-0.620241\pi\)
0.956671 0.291172i \(-0.0940452\pi\)
\(462\) 2.52778 + 2.47517i 0.117603 + 0.115155i
\(463\) −8.60546 + 4.14417i −0.399930 + 0.192596i −0.623027 0.782200i \(-0.714097\pi\)
0.223098 + 0.974796i \(0.428383\pi\)
\(464\) 12.4478 + 21.0825i 0.577876 + 0.978729i
\(465\) 0.427570 + 0.396727i 0.0198281 + 0.0183978i
\(466\) 1.49182 2.97315i 0.0691074 0.137728i
\(467\) 13.5986 19.9455i 0.629267 0.922966i −0.370716 0.928746i \(-0.620888\pi\)
0.999983 + 0.00578075i \(0.00184008\pi\)
\(468\) 33.8467 + 21.0376i 1.56456 + 0.972465i
\(469\) −1.49867 1.04527i −0.0692020 0.0482659i
\(470\) 3.16652 + 0.530069i 0.146061 + 0.0244502i
\(471\) −0.681145 1.17978i −0.0313855 0.0543613i
\(472\) −0.707939 2.09952i −0.0325855 0.0966383i
\(473\) −11.9456 + 8.14438i −0.549260 + 0.374479i
\(474\) 2.34511 0.314562i 0.107715 0.0144483i
\(475\) −19.1934 4.38078i −0.880656 0.201004i
\(476\) 22.1495 + 14.0956i 1.01522 + 0.646069i
\(477\) 8.51661 1.94386i 0.389949 0.0890032i
\(478\) 0.572376 0.213968i 0.0261799 0.00978665i
\(479\) 31.5205 + 9.72279i 1.44021 + 0.444246i 0.913862 0.406025i \(-0.133085\pi\)
0.526346 + 0.850270i \(0.323561\pi\)
\(480\) −0.106692 0.481868i −0.00486978 0.0219942i
\(481\) −34.0435 + 10.5010i −1.55225 + 0.478806i
\(482\) 10.6350 15.0663i 0.484409 0.686252i
\(483\) −0.477268 + 0.806736i −0.0217164 + 0.0367078i
\(484\) 5.66710 52.6025i 0.257596 2.39102i
\(485\) −4.47373 1.75581i −0.203141 0.0797272i
\(486\) 1.20613 + 5.71090i 0.0547112 + 0.259052i
\(487\) 2.55149 0.384576i 0.115619 0.0174268i −0.0909777 0.995853i \(-0.528999\pi\)
0.206597 + 0.978426i \(0.433761\pi\)
\(488\) 0.113708 + 4.36927i 0.00514733 + 0.197787i
\(489\) −0.272270 −0.0123125
\(490\) 2.61163 + 4.94274i 0.117981 + 0.223290i
\(491\) 13.2843i 0.599513i 0.954016 + 0.299756i \(0.0969054\pi\)
−0.954016 + 0.299756i \(0.903095\pi\)
\(492\) 2.23697 + 0.587712i 0.100851 + 0.0264961i
\(493\) 4.52621 + 30.0295i 0.203850 + 1.35246i
\(494\) 38.9618 8.22864i 1.75297 0.370224i
\(495\) −3.75766 + 9.57435i −0.168894 + 0.430335i
\(496\) 11.8373 + 23.9790i 0.531510 + 1.07669i
\(497\) 7.10813 2.70295i 0.318843 0.121244i
\(498\) 1.35329 1.91717i 0.0606423 0.0859106i
\(499\) −0.372458 1.20748i −0.0166735 0.0540541i 0.946854 0.321664i \(-0.104242\pi\)
−0.963527 + 0.267610i \(0.913766\pi\)
\(500\) 6.44978 8.82898i 0.288443 0.394844i
\(501\) 0.696450 2.25784i 0.0311151 0.100873i
\(502\) 6.84709 + 18.3164i 0.305601 + 0.817500i
\(503\) 2.88688 + 12.6482i 0.128720 + 0.563957i 0.997619 + 0.0689684i \(0.0219708\pi\)
−0.868899 + 0.494989i \(0.835172\pi\)
\(504\) −3.65800 21.9689i −0.162940 0.978571i
\(505\) 0.941664 4.12570i 0.0419035 0.183591i
\(506\) 19.6704 2.63849i 0.874454 0.117295i
\(507\) 2.76994 + 4.06276i 0.123017 + 0.180433i
\(508\) 0.767600 + 18.1448i 0.0340568 + 0.805043i
\(509\) −0.482305 + 0.278459i −0.0213778 + 0.0123425i −0.510651 0.859788i \(-0.670595\pi\)
0.489273 + 0.872131i \(0.337262\pi\)
\(510\) 0.101072 0.603781i 0.00447553 0.0267359i
\(511\) −14.3189 15.7647i −0.633430 0.697390i
\(512\) 3.29957 22.3856i 0.145822 0.989311i
\(513\) 3.20835 + 2.18742i 0.141652 + 0.0965768i
\(514\) 1.16161 2.31504i 0.0512363 0.102112i
\(515\) 5.45773 5.88203i 0.240496 0.259193i
\(516\) −0.729596 0.0237354i −0.0321187 0.00104489i
\(517\) 10.6750 + 22.1668i 0.469485 + 0.974895i
\(518\) 16.9685 + 10.4148i 0.745555 + 0.457599i
\(519\) −2.22016 1.06917i −0.0974544 0.0469316i
\(520\) −2.10757 + 10.4841i −0.0924229 + 0.459758i
\(521\) −4.23263 + 7.33112i −0.185435 + 0.321182i −0.943723 0.330737i \(-0.892703\pi\)
0.758288 + 0.651919i \(0.226036\pi\)
\(522\) 16.3874 19.8774i 0.717259 0.870009i
\(523\) −0.783208 + 5.19624i −0.0342473 + 0.227216i −0.999407 0.0344474i \(-0.989033\pi\)
0.965159 + 0.261663i \(0.0842710\pi\)
\(524\) −17.1236 + 6.08575i −0.748048 + 0.265857i
\(525\) −1.20886 + 1.48326i −0.0527589 + 0.0647346i
\(526\) 22.1707 12.3240i 0.966689 0.537353i
\(527\) 2.47881 + 33.0774i 0.107979 + 1.44087i
\(528\) 2.54529 2.79743i 0.110770 0.121743i
\(529\) −6.48176 16.5153i −0.281816 0.718055i
\(530\) 1.28882 + 1.95801i 0.0559827 + 0.0850505i
\(531\) −1.82274 + 1.45358i −0.0791001 + 0.0630802i
\(532\) −17.8294 13.3176i −0.773003 0.577391i
\(533\) −39.1815 31.2462i −1.69714 1.35342i
\(534\) −0.202465 + 2.21727i −0.00876150 + 0.0959505i
\(535\) −0.380471 + 5.07703i −0.0164492 + 0.219499i
\(536\) −1.05799 + 1.64200i −0.0456984 + 0.0709237i
\(537\) 1.49874 1.39062i 0.0646753 0.0600099i
\(538\) −24.0503 + 6.99236i −1.03688 + 0.301462i
\(539\) −19.4032 + 38.1934i −0.835754 + 1.64511i
\(540\) −0.880235 + 0.559098i −0.0378793 + 0.0240597i
\(541\) 12.4460 + 13.4136i 0.535095 + 0.576696i 0.941507 0.336995i \(-0.109410\pi\)
−0.406411 + 0.913690i \(0.633220\pi\)
\(542\) 4.30525 + 9.32484i 0.184926 + 0.400536i
\(543\) −0.186164 + 2.48418i −0.00798906 + 0.106607i
\(544\) 14.1912 24.2149i 0.608444 1.03821i
\(545\) −4.05920 + 5.09008i −0.173877 + 0.218035i
\(546\) 0.962367 3.74885i 0.0411855 0.160436i
\(547\) −23.2370 + 18.5309i −0.993544 + 0.792325i −0.978223 0.207558i \(-0.933448\pi\)
−0.0153209 + 0.999883i \(0.504877\pi\)
\(548\) −23.7663 + 27.8910i −1.01525 + 1.19145i
\(549\) 4.28108 1.68020i 0.182712 0.0717092i
\(550\) 40.5091 + 0.658751i 1.72731 + 0.0280892i
\(551\) −1.92368 25.6697i −0.0819514 1.09357i
\(552\) 0.880550 + 0.478283i 0.0374787 + 0.0203571i
\(553\) 12.1564 + 25.9446i 0.516944 + 1.10328i
\(554\) 1.38688 + 23.6643i 0.0589229 + 1.00540i
\(555\) 0.0691922 0.459060i 0.00293705 0.0194860i
\(556\) 10.1056 + 4.35047i 0.428574 + 0.184501i
\(557\) 30.6514 + 17.6966i 1.29874 + 0.749829i 0.980187 0.198076i \(-0.0634692\pi\)
0.318555 + 0.947904i \(0.396802\pi\)
\(558\) 19.4716 20.3127i 0.824298 0.859907i
\(559\) 14.2507 + 6.86276i 0.602739 + 0.290264i
\(560\) 5.17818 2.98365i 0.218818 0.126082i
\(561\) 4.22669 2.03547i 0.178451 0.0859375i
\(562\) −5.01928 + 15.3797i −0.211726 + 0.648753i
\(563\) −30.2736 + 32.6272i −1.27588 + 1.37507i −0.383661 + 0.923474i \(0.625337\pi\)
−0.892221 + 0.451599i \(0.850854\pi\)
\(564\) −0.224987 + 1.22169i −0.00947366 + 0.0514423i
\(565\) −4.30694 + 6.31712i −0.181194 + 0.265763i
\(566\) 28.7466 25.8160i 1.20831 1.08513i
\(567\) −20.2530 + 11.4079i −0.850546 + 0.479088i
\(568\) −3.16601 7.48795i −0.132843 0.314187i
\(569\) −3.35924 5.81838i −0.140827 0.243919i 0.786981 0.616977i \(-0.211643\pi\)
−0.927808 + 0.373057i \(0.878309\pi\)
\(570\) −0.123679 + 0.503956i −0.00518034 + 0.0211084i
\(571\) 8.24621 + 12.0950i 0.345093 + 0.506159i 0.959071 0.283164i \(-0.0913841\pi\)
−0.613978 + 0.789323i \(0.710432\pi\)
\(572\) −74.9506 + 33.1369i −3.13384 + 1.38552i
\(573\) −1.76650 0.403193i −0.0737968 0.0168436i
\(574\) 1.34145 + 27.9747i 0.0559912 + 1.16764i
\(575\) 2.38860 + 10.4651i 0.0996115 + 0.436426i
\(576\) −23.3267 + 4.76832i −0.971945 + 0.198680i
\(577\) 1.85481 + 0.572132i 0.0772166 + 0.0238182i 0.333123 0.942883i \(-0.391898\pi\)
−0.255906 + 0.966702i \(0.582374\pi\)
\(578\) 8.53037 6.57871i 0.354817 0.273638i
\(579\) −0.483078 1.56610i −0.0200760 0.0650849i
\(580\) 6.53597 + 2.25130i 0.271391 + 0.0934802i
\(581\) 27.0631 + 8.66379i 1.12277 + 0.359434i
\(582\) 0.707409 1.71969i 0.0293230 0.0712835i
\(583\) −6.56276 + 16.7216i −0.271802 + 0.692539i
\(584\) −16.2811 + 15.9147i −0.673717 + 0.658553i
\(585\) 11.1266 1.67707i 0.460029 0.0693382i
\(586\) −5.42254 + 9.04906i −0.224003 + 0.373813i
\(587\) 4.96279i 0.204836i 0.994741 + 0.102418i \(0.0326579\pi\)
−0.994741 + 0.102418i \(0.967342\pi\)
\(588\) −1.92861 + 0.979258i −0.0795346 + 0.0403839i
\(589\) 28.1163i 1.15851i
\(590\) −0.536625 0.321566i −0.0220925 0.0132387i
\(591\) −0.637946 + 0.0961549i −0.0262416 + 0.00395528i
\(592\) 10.4618 18.5358i 0.429979 0.761818i
\(593\) −5.24114 + 13.3542i −0.215228 + 0.548391i −0.997188 0.0749366i \(-0.976125\pi\)
0.781961 + 0.623328i \(0.214220\pi\)
\(594\) −7.39024 3.04003i −0.303225 0.124734i
\(595\) 7.34146 1.02691i 0.300971 0.0420990i
\(596\) 4.79331 13.9159i 0.196342 0.570018i
\(597\) −0.600744 1.94757i −0.0245868 0.0797085i
\(598\) −13.2596 17.1933i −0.542226 0.703085i
\(599\) 23.7933 + 7.33927i 0.972168 + 0.299874i 0.739855 0.672767i \(-0.234894\pi\)
0.232314 + 0.972641i \(0.425370\pi\)
\(600\) 1.63195 + 1.23337i 0.0666239 + 0.0503519i
\(601\) 3.30801 + 14.4933i 0.134937 + 0.591196i 0.996503 + 0.0835516i \(0.0266263\pi\)
−0.861567 + 0.507644i \(0.830517\pi\)
\(602\) −2.37745 8.51364i −0.0968978 0.346990i
\(603\) 2.00381 + 0.457356i 0.0816014 + 0.0186250i
\(604\) −8.97390 + 3.96750i −0.365143 + 0.161435i
\(605\) −8.41508 12.3427i −0.342122 0.501800i
\(606\) 1.59017 + 0.390254i 0.0645963 + 0.0158530i
\(607\) −3.39956 5.88821i −0.137984 0.238995i 0.788749 0.614715i \(-0.210729\pi\)
−0.926733 + 0.375720i \(0.877396\pi\)
\(608\) −13.5293 + 19.5692i −0.548685 + 0.793637i
\(609\) −2.31916 0.938757i −0.0939771 0.0380403i
\(610\) 0.824573 + 0.918180i 0.0333860 + 0.0371760i
\(611\) 15.1625 22.2393i 0.613409 0.899706i
\(612\) −29.0442 5.34881i −1.17404 0.216213i
\(613\) −6.10109 + 6.57541i −0.246421 + 0.265578i −0.844135 0.536131i \(-0.819885\pi\)
0.597714 + 0.801709i \(0.296076\pi\)
\(614\) −38.9245 12.7033i −1.57086 0.512664i
\(615\) 0.588377 0.283347i 0.0237256 0.0114257i
\(616\) 41.5629 + 19.2331i 1.67462 + 0.774926i
\(617\) −21.0621 10.1430i −0.847928 0.408340i −0.0411197 0.999154i \(-0.513092\pi\)
−0.806808 + 0.590814i \(0.798807\pi\)
\(618\) 2.24123 + 2.14842i 0.0901554 + 0.0864221i
\(619\) 8.31967 + 4.80336i 0.334396 + 0.193064i 0.657791 0.753200i \(-0.271491\pi\)
−0.323395 + 0.946264i \(0.604824\pi\)
\(620\) 6.93519 + 2.98560i 0.278524 + 0.119905i
\(621\) 0.315557 2.09358i 0.0126629 0.0840126i
\(622\) 11.0410 0.647071i 0.442702 0.0259452i
\(623\) −26.3469 + 5.71973i −1.05557 + 0.229156i
\(624\) −4.04269 0.881305i −0.161837 0.0352804i
\(625\) 1.51839 + 20.2615i 0.0607356 + 0.810461i
\(626\) 0.178136 10.9543i 0.00711975 0.437820i
\(627\) −3.70163 + 1.45278i −0.147829 + 0.0580185i
\(628\) −13.4228 11.4377i −0.535627 0.456415i
\(629\) 20.6412 16.4608i 0.823020 0.656336i
\(630\) −4.80926 4.05146i −0.191606 0.161414i
\(631\) 6.82364 8.55657i 0.271645 0.340632i −0.627233 0.778832i \(-0.715812\pi\)
0.898877 + 0.438200i \(0.144384\pi\)
\(632\) 27.2412 14.0031i 1.08360 0.557014i
\(633\) −0.0885362 + 1.18143i −0.00351900 + 0.0469577i
\(634\) 13.9027 6.41883i 0.552147 0.254925i
\(635\) 3.48778 + 3.75893i 0.138408 + 0.149169i
\(636\) −0.765597 + 0.486283i −0.0303579 + 0.0192824i
\(637\) 46.7997 2.50863i 1.85427 0.0993956i
\(638\) 14.7893 + 50.8681i 0.585515 + 2.01389i
\(639\) −6.27075 + 5.81841i −0.248067 + 0.230173i
\(640\) −3.39031 5.41514i −0.134014 0.214052i
\(641\) 1.20591 16.0918i 0.0476306 0.635586i −0.921395 0.388627i \(-0.872950\pi\)
0.969026 0.246959i \(-0.0794314\pi\)
\(642\) −1.96174 0.179132i −0.0774238 0.00706978i
\(643\) −3.01173 2.40177i −0.118771 0.0947166i 0.562303 0.826931i \(-0.309915\pi\)
−0.681074 + 0.732215i \(0.738487\pi\)
\(644\) −2.32430 + 11.9093i −0.0915901 + 0.469291i
\(645\) −0.161145 + 0.128509i −0.00634506 + 0.00506002i
\(646\) −24.6492 + 16.2248i −0.969811 + 0.638358i
\(647\) −1.36933 3.48899i −0.0538338 0.137166i 0.901427 0.432931i \(-0.142521\pi\)
−0.955261 + 0.295765i \(0.904425\pi\)
\(648\) 12.9806 + 21.1901i 0.509925 + 0.832424i
\(649\) −0.358262 4.78067i −0.0140630 0.187658i
\(650\) −21.5346 38.7404i −0.844656 1.51952i
\(651\) −2.44939 1.21179i −0.0959993 0.0474937i
\(652\) −3.32105 + 1.18031i −0.130062 + 0.0462243i
\(653\) 1.92978 12.8032i 0.0755181 0.501030i −0.918812 0.394695i \(-0.870850\pi\)
0.994330 0.106335i \(-0.0339115\pi\)
\(654\) −1.94365 1.60239i −0.0760026 0.0626585i
\(655\) −2.56558 + 4.44371i −0.100245 + 0.173630i
\(656\) 29.8336 2.52870i 1.16481 0.0987293i
\(657\) 21.5838 + 10.3942i 0.842065 + 0.405517i
\(658\) −14.9291 + 1.84128i −0.581996 + 0.0717807i
\(659\) 1.86922 + 3.88148i 0.0728146 + 0.151201i 0.934199 0.356753i \(-0.116116\pi\)
−0.861384 + 0.507954i \(0.830402\pi\)
\(660\) 0.0347221 1.06731i 0.00135155 0.0415451i
\(661\) −30.6391 + 33.0210i −1.19172 + 1.28437i −0.242359 + 0.970187i \(0.577921\pi\)
−0.949362 + 0.314183i \(0.898269\pi\)
\(662\) 21.8718 + 10.9745i 0.850070 + 0.426536i
\(663\) −4.24052 2.89113i −0.164688 0.112282i
\(664\) 8.19587 29.2516i 0.318061 1.13518i
\(665\) −6.27056 + 0.402973i −0.243162 + 0.0156266i
\(666\) −22.0886 3.69758i −0.855915 0.143278i
\(667\) −12.1551 + 7.01777i −0.470649 + 0.271729i
\(668\) −1.29279 30.5594i −0.0500197 1.18238i
\(669\) −1.45210 2.12984i −0.0561414 0.0823444i
\(670\) 0.0733227 + 0.546633i 0.00283270 + 0.0211183i
\(671\) −2.10440 + 9.21996i −0.0812393 + 0.355933i
\(672\) 1.12170 + 2.02204i 0.0432705 + 0.0780018i
\(673\) 6.03421 + 26.4376i 0.232602 + 1.01910i 0.947472 + 0.319838i \(0.103629\pi\)
−0.714870 + 0.699257i \(0.753514\pi\)
\(674\) 32.2620 12.0603i 1.24269 0.464546i
\(675\) 1.27396 4.13007i 0.0490347 0.158966i
\(676\) 51.3991 + 37.5483i 1.97689 + 1.44416i
\(677\) 5.62486 + 18.2353i 0.216181 + 0.700841i 0.997093 + 0.0761998i \(0.0242787\pi\)
−0.780912 + 0.624642i \(0.785245\pi\)
\(678\) −2.41679 1.70595i −0.0928162 0.0655168i
\(679\) 22.4347 + 1.92113i 0.860965 + 0.0737261i
\(680\) −1.38459 7.80287i −0.0530966 0.299226i
\(681\) −0.346301 + 0.882359i −0.0132703 + 0.0338121i
\(682\) 11.9564 + 56.6125i 0.457835 + 2.16780i
\(683\) −0.653336 4.33460i −0.0249992 0.165859i 0.972848 0.231447i \(-0.0743459\pi\)
−0.997847 + 0.0655877i \(0.979108\pi\)
\(684\) 24.2114 + 6.36097i 0.925745 + 0.243218i
\(685\) 10.3464i 0.395314i
\(686\) −18.3204 18.7179i −0.699478 0.714654i
\(687\) −1.39629 −0.0532716
\(688\) −9.00225 + 2.87332i −0.343208 + 0.109544i
\(689\) 19.4327 2.92900i 0.740325 0.111586i
\(690\) 0.276827 0.0584652i 0.0105386 0.00222573i
\(691\) 27.2332 + 10.6882i 1.03600 + 0.406600i 0.821551 0.570135i \(-0.193109\pi\)
0.214449 + 0.976735i \(0.431204\pi\)
\(692\) −31.7157 3.41688i −1.20565 0.129890i
\(693\) 4.11146 48.0132i 0.156182 1.82387i
\(694\) 7.73653 + 5.46103i 0.293675 + 0.207298i
\(695\) 2.96850 0.915662i 0.112602 0.0347330i
\(696\) −0.912073 + 2.51439i −0.0345720 + 0.0953076i
\(697\) 35.4882 + 10.9467i 1.34421 + 0.414635i
\(698\) −2.33972 6.25889i −0.0885597 0.236902i
\(699\) 0.354291 0.0808647i 0.0134005 0.00305858i
\(700\) −8.31522 + 23.3327i −0.314286 + 0.881893i
\(701\) −45.5794 10.4032i −1.72151 0.392924i −0.756265 0.654265i \(-0.772978\pi\)
−0.965247 + 0.261341i \(0.915835\pi\)
\(702\) 1.16225 + 8.66474i 0.0438662 + 0.327030i
\(703\) −18.4901 + 12.6063i −0.697368 + 0.475457i
\(704\) 18.9195 45.1561i 0.713057 1.70188i
\(705\) 0.175373 + 0.303755i 0.00660493 + 0.0114401i
\(706\) 1.85532 11.0833i 0.0698258 0.417125i
\(707\) 1.27153 + 19.7860i 0.0478210 + 0.744130i
\(708\) 0.127779 0.205580i 0.00480224 0.00772615i
\(709\) 7.84984 11.5136i 0.294807 0.432403i −0.650047 0.759894i \(-0.725251\pi\)
0.944854 + 0.327491i \(0.106203\pi\)
\(710\) −2.05167 1.02946i −0.0769976 0.0386348i
\(711\) −23.6256 21.9214i −0.886029 0.822115i
\(712\) 7.14239 + 27.9231i 0.267672 + 1.04646i
\(713\) −13.8121 + 6.65157i −0.517268 + 0.249103i
\(714\) 0.351090 + 2.84663i 0.0131392 + 0.106532i
\(715\) −10.0394 + 20.8470i −0.375453 + 0.779635i
\(716\) 12.2526 23.4595i 0.457902 0.876722i
\(717\) 0.0578130 + 0.0333783i 0.00215907 + 0.00124654i
\(718\) −35.9408 29.6305i −1.34130 1.10580i
\(719\) 4.54941 + 0.685714i 0.169665 + 0.0255728i 0.233325 0.972399i \(-0.425039\pi\)
−0.0636605 + 0.997972i \(0.520277\pi\)
\(720\) −4.13994 + 5.29654i −0.154287 + 0.197390i
\(721\) −16.6704 + 33.6960i −0.620839 + 1.25491i
\(722\) −1.62252 + 0.901908i −0.0603838 + 0.0335655i
\(723\) 2.00907 0.150559i 0.0747180 0.00559934i
\(724\) 8.49832 + 31.1083i 0.315838 + 1.15613i
\(725\) −26.6713 + 10.4677i −0.990549 + 0.388762i
\(726\) 4.82790 3.17786i 0.179180 0.117942i
\(727\) −24.1259 30.2530i −0.894781 1.12202i −0.991935 0.126751i \(-0.959545\pi\)
0.0971536 0.995269i \(-0.469026\pi\)
\(728\) −4.51289 49.8992i −0.167259 1.84939i
\(729\) 16.0359 20.1084i 0.593922 0.744754i
\(730\) −0.584562 + 6.40176i −0.0216356 + 0.236940i
\(731\) −11.6886 0.875937i −0.432317 0.0323977i
\(732\) −0.360401 + 0.313224i −0.0133208 + 0.0115771i
\(733\) 10.3762 + 11.1829i 0.383254 + 0.413050i 0.894985 0.446096i \(-0.147186\pi\)
−0.511731 + 0.859146i \(0.670995\pi\)
\(734\) −13.7307 47.2270i −0.506810 1.74318i
\(735\) −0.235150 + 0.563636i −0.00867363 + 0.0207900i
\(736\) 12.8140 + 2.01670i 0.472331 + 0.0743365i
\(737\) −3.09822 + 2.87473i −0.114124 + 0.105892i
\(738\) −13.2058 28.6027i −0.486112 1.05288i
\(739\) −36.6825 2.74897i −1.34939 0.101123i −0.619665 0.784866i \(-0.712732\pi\)
−0.729723 + 0.683743i \(0.760351\pi\)
\(740\) −1.14607 5.89941i −0.0421304 0.216867i
\(741\) 3.40124 + 2.71240i 0.124948 + 0.0996425i
\(742\) −8.39939 7.07590i −0.308351 0.259764i
\(743\) 5.19664 + 6.51637i 0.190646 + 0.239063i 0.867963 0.496629i \(-0.165429\pi\)
−0.677317 + 0.735691i \(0.736857\pi\)
\(744\) −1.19866 + 2.66421i −0.0439450 + 0.0976747i
\(745\) −1.51826 3.86847i −0.0556249 0.141730i
\(746\) −38.4578 0.625393i −1.40804 0.0228973i
\(747\) −31.8751 + 2.38871i −1.16625 + 0.0873982i
\(748\) 42.7318 43.1509i 1.56243 1.57775i
\(749\) −5.06057 23.3106i −0.184909 0.851752i
\(750\) 1.19245 0.0698853i 0.0435422 0.00255185i
\(751\) 28.9433 + 4.36250i 1.05616 + 0.159190i 0.654087 0.756419i \(-0.273053\pi\)
0.402069 + 0.915609i \(0.368291\pi\)
\(752\) 2.55177 + 15.8770i 0.0930535 + 0.578976i
\(753\) −1.06813 + 1.85005i −0.0389247 + 0.0674196i
\(754\) 40.1047 41.8372i 1.46053 1.52362i
\(755\) −1.20203 + 2.49603i −0.0437462 + 0.0908400i
\(756\) 3.20808 3.68483i 0.116677 0.134016i
\(757\) −22.4704 46.6603i −0.816702 1.69590i −0.712861 0.701305i \(-0.752601\pi\)
−0.103841 0.994594i \(-0.533113\pi\)
\(758\) 32.5584 + 10.6257i 1.18257 + 0.385942i
\(759\) 1.58938 + 1.47473i 0.0576910 + 0.0535294i
\(760\) 0.676086 + 6.68323i 0.0245242 + 0.242426i
\(761\) 11.7617 + 8.01898i 0.426361 + 0.290688i 0.757427 0.652920i \(-0.226456\pi\)
−0.331066 + 0.943607i \(0.607408\pi\)
\(762\) −1.47615 + 1.32566i −0.0534753 + 0.0480236i
\(763\) 11.4449 28.2743i 0.414335 1.02360i
\(764\) −23.2951 + 2.73989i −0.842787 + 0.0991258i
\(765\) −7.22144 + 4.16930i −0.261092 + 0.150741i
\(766\) 0.579552 + 0.142231i 0.0209400 + 0.00513903i
\(767\) −4.33344 + 2.95449i −0.156471 + 0.106680i
\(768\) 2.11627 1.27753i 0.0763642 0.0460990i
\(769\) −9.60205 + 42.0693i −0.346259 + 1.51706i 0.439339 + 0.898321i \(0.355213\pi\)
−0.785598 + 0.618737i \(0.787645\pi\)
\(770\) 12.4545 3.47794i 0.448828 0.125336i
\(771\) 0.275869 0.0629652i 0.00993517 0.00226764i
\(772\) −12.6815 17.0086i −0.456419 0.612152i
\(773\) 5.06307 16.4141i 0.182106 0.590373i −0.817784 0.575526i \(-0.804797\pi\)
0.999890 0.0148476i \(-0.00472633\pi\)
\(774\) 6.07223 + 7.87364i 0.218262 + 0.283012i
\(775\) −29.9047 + 9.22438i −1.07421 + 0.331350i
\(776\) 1.17377 24.0429i 0.0421359 0.863088i
\(777\) 0.301312 + 2.15411i 0.0108095 + 0.0772783i
\(778\) 8.06870 19.6148i 0.289277 0.703223i
\(779\) −29.3037 11.5009i −1.04991 0.412061i
\(780\) −1.03021 + 0.550929i −0.0368875 + 0.0197264i
\(781\) −2.62173 17.3940i −0.0938129 0.622408i
\(782\) 13.8018 + 8.27056i 0.493551 + 0.295755i
\(783\) 5.65132 0.201962
\(784\) −19.2794 + 20.3053i −0.688550 + 0.725189i
\(785\) −4.97927 −0.177718
\(786\) −1.70298 1.02049i −0.0607434 0.0363998i
\(787\) 6.58447 + 43.6851i 0.234711 + 1.55721i 0.726916 + 0.686726i \(0.240953\pi\)
−0.492205 + 0.870479i \(0.663809\pi\)
\(788\) −7.36461 + 3.93840i −0.262353 + 0.140300i
\(789\) 2.57958 + 1.01241i 0.0918354 + 0.0360427i
\(790\) 3.29007 7.99806i 0.117055 0.284558i
\(791\) 10.9216 34.1158i 0.388326 1.21302i
\(792\) −51.4548 2.51202i −1.82837 0.0892606i
\(793\) 9.88650 3.04958i 0.351080 0.108294i
\(794\) 0.949940 + 1.23175i 0.0337121 + 0.0437133i
\(795\) −0.0754830 + 0.244710i −0.00267711 + 0.00867896i
\(796\) −15.7705 21.1515i −0.558970 0.749694i
\(797\) 14.3297 3.27067i 0.507585 0.115853i 0.0389437 0.999241i \(-0.487601\pi\)
0.468642 + 0.883388i \(0.344744\pi\)
\(798\) −0.116448 2.42841i −0.00412221 0.0859647i
\(799\) −4.43852 + 19.4464i −0.157024 + 0.687966i
\(800\) 25.2526 + 7.96958i 0.892815 + 0.281767i
\(801\) 25.0576 17.0840i 0.885365 0.603632i
\(802\) 33.7096 + 8.27289i 1.19033 + 0.292126i
\(803\) −42.6622 + 24.6310i −1.50552 + 0.869210i
\(804\) −0.211935 + 0.0249272i −0.00747438 + 0.000879113i
\(805\) 1.68141 + 2.98508i 0.0592618 + 0.105210i
\(806\) 47.0968 42.2954i 1.65891 1.48979i
\(807\) −2.26077 1.54137i −0.0795829 0.0542587i
\(808\) 21.0881 2.13331i 0.741878 0.0750495i
\(809\) 1.61225 + 1.49595i 0.0566836 + 0.0525947i 0.708006 0.706206i \(-0.249595\pi\)
−0.651322 + 0.758801i \(0.725785\pi\)
\(810\) 6.67017 + 2.17686i 0.234366 + 0.0764871i
\(811\) −13.2670 27.5493i −0.465869 0.967386i −0.993057 0.117637i \(-0.962468\pi\)
0.527188 0.849749i \(-0.323246\pi\)
\(812\) −32.3579 1.39693i −1.13554 0.0490227i
\(813\) −0.486838 + 1.01093i −0.0170741 + 0.0354548i
\(814\) 31.8691 33.2458i 1.11701 1.16527i
\(815\) −0.497583 + 0.861839i −0.0174296 + 0.0301889i
\(816\) 3.02738 0.486563i 0.105980 0.0170331i
\(817\) 9.82451 + 1.48081i 0.343716 + 0.0518069i
\(818\) −49.2186 + 2.88453i −1.72089 + 0.100855i
\(819\) −47.7387 + 22.3681i −1.66813 + 0.781605i
\(820\) 5.94849 6.00682i 0.207730 0.209767i
\(821\) −38.4944 + 2.88476i −1.34346 + 0.100679i −0.726964 0.686676i \(-0.759069\pi\)
−0.616501 + 0.787354i \(0.711450\pi\)
\(822\) −4.00267 0.0650906i −0.139609 0.00227030i
\(823\) −0.638268 1.62628i −0.0222486 0.0566886i 0.919318 0.393516i \(-0.128741\pi\)
−0.941566 + 0.336827i \(0.890646\pi\)
\(824\) 36.6513 + 16.4898i 1.27681 + 0.574450i
\(825\) 2.75962 + 3.46045i 0.0960775 + 0.120477i
\(826\) 2.83900 + 0.728798i 0.0987813 + 0.0253581i
\(827\) −11.1724 8.90972i −0.388503 0.309821i 0.409687 0.912226i \(-0.365638\pi\)
−0.798191 + 0.602405i \(0.794209\pi\)
\(828\) −2.60294 13.3987i −0.0904584 0.465636i
\(829\) 31.4628 + 2.35781i 1.09275 + 0.0818901i 0.608889 0.793256i \(-0.291616\pi\)
0.483859 + 0.875146i \(0.339235\pi\)
\(830\) −3.59541 7.78738i −0.124799 0.270304i
\(831\) −1.89838 + 1.76144i −0.0658541 + 0.0611036i
\(832\) −53.1319 + 6.77547i −1.84202 + 0.234897i
\(833\) −31.6047 + 14.4010i −1.09504 + 0.498966i
\(834\) 0.335564 + 1.15418i 0.0116196 + 0.0399658i
\(835\) −5.87413 6.33081i −0.203283 0.219087i
\(836\) −38.8533 + 33.7673i −1.34377 + 1.16787i
\(837\) 6.15539 + 0.461283i 0.212762 + 0.0159443i
\(838\) 4.88864 53.5374i 0.168875 1.84942i
\(839\) 25.4215 31.8775i 0.877646 1.10053i −0.116575 0.993182i \(-0.537191\pi\)
0.994221 0.107352i \(-0.0342371\pi\)
\(840\) 0.611357 + 0.229143i 0.0210938 + 0.00790618i
\(841\) −5.27702 6.61718i −0.181966 0.228179i
\(842\) −13.1731 + 8.67089i −0.453974 + 0.298819i
\(843\) −1.64523 + 0.645703i −0.0566646 + 0.0222392i
\(844\) 4.04165 + 14.7945i 0.139119 + 0.509248i
\(845\) 17.9224 1.34310i 0.616548 0.0462039i
\(846\) 14.7892 8.22089i 0.508465 0.282640i
\(847\) 54.2531 + 44.2164i 1.86416 + 1.51929i
\(848\) −7.23042 + 9.25042i −0.248294 + 0.317661i
\(849\) 4.17386 + 0.629108i 0.143246 + 0.0215909i
\(850\) 25.3437 + 20.8941i 0.869283 + 0.716660i
\(851\) 10.5671 + 6.10093i 0.362236 + 0.209137i
\(852\) 0.411170 0.787245i 0.0140864 0.0269706i
\(853\) 1.68044 3.48946i 0.0575371 0.119477i −0.870218 0.492667i \(-0.836022\pi\)
0.927755 + 0.373190i \(0.121736\pi\)
\(854\) −4.92780 3.02453i −0.168626 0.103497i
\(855\) 6.36816 3.06675i 0.217787 0.104880i
\(856\) −24.7052 + 6.31928i −0.844406 + 0.215988i
\(857\) −19.6015 18.1875i −0.669574 0.621274i 0.270308 0.962774i \(-0.412874\pi\)
−0.939882 + 0.341500i \(0.889065\pi\)
\(858\) −8.00187 4.01507i −0.273179 0.137072i
\(859\) 20.4450 29.9872i 0.697573 1.02315i −0.300028 0.953930i \(-0.596996\pi\)
0.997601 0.0692213i \(-0.0220515\pi\)
\(860\) −1.40849 + 2.26607i −0.0480293 + 0.0772725i
\(861\) −2.26488 + 2.05716i −0.0771868 + 0.0701077i
\(862\) −2.10046 + 12.5477i −0.0715419 + 0.427377i
\(863\) 19.5641 + 33.8861i 0.665971 + 1.15350i 0.979021 + 0.203759i \(0.0653158\pi\)
−0.313050 + 0.949737i \(0.601351\pi\)
\(864\) −4.06224 3.28297i −0.138200 0.111689i
\(865\) −7.44178 + 5.07372i −0.253028 + 0.172512i
\(866\) −4.72705 35.2409i −0.160632 1.19754i
\(867\) 1.14736 + 0.261877i 0.0389663 + 0.00889380i
\(868\) −35.1300 4.16271i −1.19239 0.141292i
\(869\) 64.6122 14.7473i 2.19182 0.500268i
\(870\) 0.264441 + 0.707395i 0.00896539 + 0.0239829i
\(871\) 4.41839 + 1.36289i 0.149711 + 0.0461798i
\(872\) −30.6544 11.1196i −1.03809 0.376558i
\(873\) −24.2032 + 7.46571i −0.819156 + 0.252676i
\(874\) −11.1423 7.86512i −0.376895 0.266042i
\(875\) 5.14103 + 13.5197i 0.173799 + 0.457051i
\(876\) −2.47295 0.266422i −0.0835533 0.00900157i
\(877\) −27.9128 10.9550i −0.942548 0.369923i −0.156213 0.987723i \(-0.549929\pi\)
−0.786335 + 0.617800i \(0.788024\pi\)
\(878\) 25.2859 5.34033i 0.853358 0.180227i
\(879\) −1.13962 + 0.171770i −0.0384383 + 0.00579365i
\(880\) −4.20334 13.1692i −0.141694 0.443935i
\(881\) 43.6746 1.47143 0.735717 0.677289i \(-0.236845\pi\)
0.735717 + 0.677289i \(0.236845\pi\)
\(882\) 27.0027 + 11.7846i 0.909227 + 0.396808i
\(883\) 16.2114i 0.545559i −0.962077 0.272779i \(-0.912057\pi\)
0.962077 0.272779i \(-0.0879429\pi\)
\(884\) −64.2576 16.8822i −2.16122 0.567809i
\(885\) −0.0101862 0.0675813i −0.000342407 0.00227172i
\(886\) 8.68264 + 41.1114i 0.291699 + 1.38117i
\(887\) −18.3700 + 46.8060i −0.616805 + 1.57159i 0.190647 + 0.981659i \(0.438942\pi\)
−0.807451 + 0.589934i \(0.799154\pi\)
\(888\) 2.28950 0.406263i 0.0768305 0.0136333i
\(889\) −20.6772 12.2327i −0.693492 0.410272i
\(890\) 6.64849 + 4.69301i 0.222858 + 0.157310i
\(891\) 15.8484 + 51.3793i 0.530942 + 1.72127i
\(892\) −26.9452 19.6841i −0.902192 0.659073i
\(893\) 4.98357 16.1563i 0.166769 0.540651i
\(894\) 1.50614 0.563029i 0.0503727 0.0188305i
\(895\) −1.66287 7.28550i −0.0555835 0.243527i
\(896\) 22.4478 + 19.8015i 0.749927 + 0.661521i
\(897\) 0.527822 2.31254i 0.0176235 0.0772134i
\(898\) 0.0273899 + 0.204196i 0.000914014 + 0.00681412i
\(899\) −23.0509 33.8094i −0.768790 1.12761i
\(900\) −1.17768 27.8383i −0.0392559 0.927943i
\(901\) −12.6123 + 7.28169i −0.420175 + 0.242588i
\(902\) 63.8940 + 10.6957i 2.12744 + 0.356128i
\(903\) 0.552430 0.792054i 0.0183837 0.0263579i
\(904\) −36.8746 10.3317i −1.22643 0.343628i
\(905\) 7.52318 + 5.12922i 0.250079 + 0.170501i
\(906\) −0.958071 0.480727i −0.0318298 0.0159711i
\(907\) 27.4466 29.5804i 0.911350 0.982202i −0.0885538 0.996071i \(-0.528225\pi\)
0.999904 + 0.0138696i \(0.00441499\pi\)
\(908\) −0.398974 + 12.2639i −0.0132404 + 0.406993i
\(909\) −9.67675 20.0940i −0.320958 0.666475i
\(910\) −10.1078 9.89743i −0.335071 0.328097i
\(911\) −50.5934 24.3645i −1.67623 0.807232i −0.997332 0.0730043i \(-0.976741\pi\)
−0.678903 0.734228i \(-0.737544\pi\)
\(912\) −2.58977 + 0.219510i −0.0857560 + 0.00726870i
\(913\) 32.8648 56.9235i 1.08767 1.88389i
\(914\) −9.07214 7.47931i −0.300080 0.247394i
\(915\) −0.0200940 + 0.133315i −0.000664286 + 0.00440725i
\(916\) −17.0314 + 6.05298i −0.562734 + 0.199996i
\(917\) 5.59820 23.3796i 0.184869 0.772062i
\(918\) −3.14764 5.66255i −0.103887 0.186892i
\(919\) 0.0118754 + 0.158466i 0.000391733 + 0.00522731i 0.997396 0.0721162i \(-0.0229752\pi\)
−0.997005 + 0.0773435i \(0.975356\pi\)
\(920\) 3.12319 1.91320i 0.102968 0.0630763i
\(921\) −1.63421 4.16391i −0.0538491 0.137205i
\(922\) 34.3630 22.6187i 1.13168 0.744907i
\(923\) −15.0458 + 11.9986i −0.495237 + 0.394938i
\(924\) 1.26715 + 4.84010i 0.0416860 + 0.159228i
\(925\) 19.4744 + 15.5303i 0.640314 + 0.510634i
\(926\) −13.4517 1.22831i −0.442049 0.0403647i
\(927\) 3.16024 42.1704i 0.103796 1.38506i
\(928\) −0.225129 + 34.6235i −0.00739021 + 1.13657i
\(929\) −4.86999 + 4.51869i −0.159779 + 0.148253i −0.756011 0.654559i \(-0.772854\pi\)
0.596232 + 0.802812i \(0.296664\pi\)
\(930\) 0.230287 + 0.792076i 0.00755142 + 0.0259732i
\(931\) 27.6267 10.1708i 0.905430 0.333334i
\(932\) 3.97097 2.52223i 0.130073 0.0826185i
\(933\) 0.821827 + 0.885719i 0.0269054 + 0.0289971i
\(934\) 30.9951 14.3104i 1.01419 0.468249i
\(935\) 1.28139 17.0990i 0.0419060 0.559197i
\(936\) 25.7661 + 50.1245i 0.842191 + 1.63837i
\(937\) 30.1432 37.7984i 0.984735 1.23482i 0.0127156 0.999919i \(-0.495952\pi\)
0.972020 0.234900i \(-0.0754762\pi\)
\(938\) −1.05818 2.35742i −0.0345507 0.0769725i
\(939\) 0.935757 0.746241i 0.0305373 0.0243527i
\(940\) 3.45594 + 2.94485i 0.112720 + 0.0960503i
\(941\) −50.9319 + 19.9893i −1.66033 + 0.651633i −0.995447 0.0953124i \(-0.969615\pi\)
−0.664886 + 0.746945i \(0.731520\pi\)
\(942\) 0.0313254 1.92631i 0.00102064 0.0627627i
\(943\) 1.28268 + 17.1162i 0.0417699 + 0.557381i
\(944\) 0.667409 3.06152i 0.0217223 0.0996440i
\(945\) 0.0146550 1.37940i 0.000476726 0.0448719i
\(946\) −20.4114 + 1.19624i −0.663633 + 0.0388931i
\(947\) −8.87226 + 58.8636i −0.288310 + 1.91281i 0.106996 + 0.994259i \(0.465877\pi\)
−0.395305 + 0.918550i \(0.629361\pi\)
\(948\) 3.07349 + 1.32314i 0.0998222 + 0.0429734i
\(949\) 46.6730 + 26.9467i 1.51507 + 0.874725i
\(950\) −20.0988 19.2665i −0.652091 0.625088i
\(951\) 1.50723 + 0.725842i 0.0488751 + 0.0235370i
\(952\) 16.6228 + 33.2002i 0.538747 + 1.07602i
\(953\) −39.4668 + 19.0062i −1.27845 + 0.615671i −0.944992 0.327092i \(-0.893931\pi\)
−0.333462 + 0.942764i \(0.608217\pi\)
\(954\) 11.7444 + 3.83289i 0.380240 + 0.124094i
\(955\) −4.50461 + 4.85482i −0.145766 + 0.157098i
\(956\) 0.849880 + 0.156515i 0.0274871 + 0.00506205i
\(957\) −3.26010 + 4.78169i −0.105384 + 0.154570i
\(958\) 31.1693 + 34.7077i 1.00703 + 1.12135i
\(959\) −13.7953 46.4704i −0.445473 1.50061i
\(960\) 0.220857 0.662104i 0.00712812 0.0213693i
\(961\) −6.84726 11.8598i −0.220879 0.382574i
\(962\) −48.9311 12.0085i −1.57760 0.387169i
\(963\) 15.1151 + 22.1698i 0.487079 + 0.714413i
\(964\) 23.8532 10.5459i 0.768261 0.339660i
\(965\) −5.84015 1.33298i −0.188001 0.0429100i
\(966\) −1.16540 + 0.631701i −0.0374963 + 0.0203246i
\(967\) 4.04312 + 17.7141i 0.130018 + 0.569646i 0.997404 + 0.0720102i \(0.0229414\pi\)
−0.867386 + 0.497636i \(0.834201\pi\)
\(968\) 45.1129 59.6917i 1.44998 1.91857i
\(969\) −3.08064 0.950250i −0.0989643 0.0305264i
\(970\) −4.15067 5.38202i −0.133270 0.172806i
\(971\) 2.15414 + 6.98354i 0.0691296 + 0.224113i 0.983545 0.180665i \(-0.0578250\pi\)
−0.914415 + 0.404778i \(0.867349\pi\)
\(972\) −2.68827 + 7.80458i −0.0862264 + 0.250332i
\(973\) −12.1120 + 8.07071i −0.388294 + 0.258735i
\(974\) 3.37474 + 1.38823i 0.108134 + 0.0444817i
\(975\) 1.76905 4.50747i 0.0566549 0.144354i
\(976\) −3.03820 + 5.38295i −0.0972505 + 0.172304i
\(977\) 9.44173 1.42311i 0.302068 0.0455294i 0.00374040 0.999993i \(-0.498809\pi\)
0.298327 + 0.954464i \(0.403571\pi\)
\(978\) −0.330286 0.197920i −0.0105614 0.00632879i
\(979\) 62.3630i 1.99313i
\(980\) −0.424879 + 7.89443i −0.0135723 + 0.252178i
\(981\) 34.3117i 1.09549i
\(982\) −9.65673 + 16.1150i −0.308159 + 0.514251i
\(983\) −6.25642 + 0.943004i −0.199549 + 0.0300771i −0.248056 0.968746i \(-0.579792\pi\)
0.0485072 + 0.998823i \(0.484554\pi\)
\(984\) 2.28642 + 2.33906i 0.0728883 + 0.0745666i
\(985\) −0.861502 + 2.19507i −0.0274497 + 0.0699408i
\(986\) −16.3385 + 39.7185i −0.520325 + 1.26490i
\(987\) −1.19269 1.13047i −0.0379639 0.0359834i
\(988\) 53.2456 + 18.3403i 1.69397 + 0.583484i
\(989\) −1.59677 5.17660i −0.0507743 0.164606i
\(990\) −11.5182 + 8.88296i −0.366073 + 0.282319i
\(991\) −27.6341 8.52398i −0.877825 0.270773i −0.177090 0.984195i \(-0.556668\pi\)
−0.700735 + 0.713421i \(0.747145\pi\)
\(992\) −3.07132 + 37.6934i −0.0975144 + 1.19677i
\(993\) 0.594876 + 2.60632i 0.0188778 + 0.0827091i
\(994\) 10.5876 + 1.88819i 0.335819 + 0.0598896i
\(995\) −7.26268 1.65766i −0.230242 0.0525513i
\(996\) 3.03530 1.34195i 0.0961771 0.0425214i
\(997\) 24.5101 + 35.9497i 0.776243 + 1.13854i 0.986956 + 0.160991i \(0.0514691\pi\)
−0.210713 + 0.977548i \(0.567579\pi\)
\(998\) 0.425926 1.73552i 0.0134824 0.0549370i
\(999\) −2.45650 4.25478i −0.0777203 0.134615i
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 392.2.z.a.109.44 yes 648
8.5 even 2 inner 392.2.z.a.109.20 648
49.9 even 21 inner 392.2.z.a.205.20 yes 648
392.205 even 42 inner 392.2.z.a.205.44 yes 648
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
392.2.z.a.109.20 648 8.5 even 2 inner
392.2.z.a.109.44 yes 648 1.1 even 1 trivial
392.2.z.a.205.20 yes 648 49.9 even 21 inner
392.2.z.a.205.44 yes 648 392.205 even 42 inner