Properties

Label 429.2.bg.a.334.7
Level $429$
Weight $2$
Character 429.334
Analytic conductor $3.426$
Analytic rank $0$
Dimension $112$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [429,2,Mod(16,429)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(429, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([0, 12, 10]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("429.16");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 429 = 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 429.bg (of order \(15\), degree \(8\), 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: \(3.42558224671\)
Analytic rank: \(0\)
Dimension: \(112\)
Relative dimension: \(14\) over \(\Q(\zeta_{15})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label 334.7
Character \(\chi\) \(=\) 429.334
Dual form 429.2.bg.a.289.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.426907 + 0.190071i) q^{2} +(-0.669131 - 0.743145i) q^{3} +(-1.19214 + 1.32400i) q^{4} +(0.757885 - 0.550636i) q^{5} +(0.426907 + 0.190071i) q^{6} +(0.718277 - 0.797728i) q^{7} +(0.546090 - 1.68069i) q^{8} +(-0.104528 + 0.994522i) q^{9} +O(q^{10})\) \(q+(-0.426907 + 0.190071i) q^{2} +(-0.669131 - 0.743145i) q^{3} +(-1.19214 + 1.32400i) q^{4} +(0.757885 - 0.550636i) q^{5} +(0.426907 + 0.190071i) q^{6} +(0.718277 - 0.797728i) q^{7} +(0.546090 - 1.68069i) q^{8} +(-0.104528 + 0.994522i) q^{9} +(-0.218887 + 0.379123i) q^{10} +(-2.58952 + 2.07229i) q^{11} +1.78162 q^{12} +(3.60513 - 0.0550045i) q^{13} +(-0.155013 + 0.477080i) q^{14} +(-0.916326 - 0.194771i) q^{15} +(-0.286139 - 2.72243i) q^{16} +(2.20862 + 0.983339i) q^{17} +(-0.144406 - 0.444437i) q^{18} +(5.15717 - 1.09619i) q^{19} +(-0.174460 + 1.65988i) q^{20} -1.07345 q^{21} +(0.711601 - 1.37687i) q^{22} +(3.45980 - 5.99255i) q^{23} +(-1.61440 + 0.718778i) q^{24} +(-1.27390 + 3.92065i) q^{25} +(-1.52860 + 0.708714i) q^{26} +(0.809017 - 0.587785i) q^{27} +(0.199909 + 1.90200i) q^{28} +(3.51009 + 0.746093i) q^{29} +(0.428207 - 0.0910181i) q^{30} +(3.07661 + 2.23529i) q^{31} +(2.40679 + 4.16869i) q^{32} +(3.27274 + 0.537754i) q^{33} -1.12978 q^{34} +(0.105114 - 1.00009i) q^{35} +(-1.19214 - 1.32400i) q^{36} +(9.93371 + 2.11147i) q^{37} +(-1.99328 + 1.44820i) q^{38} +(-2.45318 - 2.64233i) q^{39} +(-0.511575 - 1.57447i) q^{40} +(-1.35402 - 1.50379i) q^{41} +(0.458263 - 0.204032i) q^{42} +(2.06088 + 3.56955i) q^{43} +(0.343343 - 5.89899i) q^{44} +(0.468399 + 0.811290i) q^{45} +(-0.338002 + 3.21587i) q^{46} +(3.07221 - 9.45529i) q^{47} +(-1.83170 + 2.03430i) q^{48} +(0.611252 + 5.81567i) q^{49} +(-0.201367 - 1.91588i) q^{50} +(-0.747089 - 2.29930i) q^{51} +(-4.22499 + 4.83878i) q^{52} +(-8.05930 - 5.85542i) q^{53} +(-0.233654 + 0.404701i) q^{54} +(-0.821480 + 2.99644i) q^{55} +(-0.948490 - 1.64283i) q^{56} +(-4.26545 - 3.09903i) q^{57} +(-1.64030 + 0.348655i) q^{58} +(-0.420199 + 0.466679i) q^{59} +(1.35026 - 0.981025i) q^{60} +(-5.26644 - 2.34477i) q^{61} +(-1.73829 - 0.369485i) q^{62} +(0.718277 + 0.797728i) q^{63} +(2.60942 + 1.89586i) q^{64} +(2.70199 - 2.02680i) q^{65} +(-1.49937 + 0.392483i) q^{66} +(4.40574 - 7.63097i) q^{67} +(-3.93492 + 1.75194i) q^{68} +(-6.76839 + 1.43867i) q^{69} +(0.145215 + 0.446927i) q^{70} +(-5.55464 - 2.47309i) q^{71} +(1.61440 + 0.718778i) q^{72} +(1.37223 + 4.22329i) q^{73} +(-4.64210 + 0.986710i) q^{74} +(3.76601 - 1.67674i) q^{75} +(-4.69670 + 8.13492i) q^{76} +(-0.206868 + 3.55421i) q^{77} +(1.54951 + 0.661751i) q^{78} +(-9.22352 - 6.70128i) q^{79} +(-1.71593 - 1.90573i) q^{80} +(-0.978148 - 0.207912i) q^{81} +(0.863870 + 0.384620i) q^{82} +(-13.3400 + 9.69209i) q^{83} +(1.27970 - 1.42125i) q^{84} +(2.21534 - 0.470885i) q^{85} +(-1.55828 - 1.13215i) q^{86} +(-1.79425 - 3.10774i) q^{87} +(2.06877 + 5.48384i) q^{88} +(-5.13874 + 8.90055i) q^{89} +(-0.354166 - 0.257317i) q^{90} +(2.54561 - 2.91542i) q^{91} +(3.80960 + 11.7247i) q^{92} +(-0.397511 - 3.78207i) q^{93} +(0.485631 + 4.62047i) q^{94} +(3.30494 - 3.67051i) q^{95} +(1.48748 - 4.57800i) q^{96} +(-0.966686 + 9.19740i) q^{97} +(-1.36634 - 2.36657i) q^{98} +(-1.79026 - 2.79195i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 112 q - 14 q^{3} + 20 q^{4} + 6 q^{5} + 24 q^{8} + 14 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 112 q - 14 q^{3} + 20 q^{4} + 6 q^{5} + 24 q^{8} + 14 q^{9} + 3 q^{11} - 120 q^{12} + q^{13} + 6 q^{14} - 2 q^{15} - 16 q^{16} - 20 q^{17} - 40 q^{20} + 15 q^{22} + 4 q^{23} - 18 q^{24} - 26 q^{25} + 49 q^{26} + 28 q^{27} - 6 q^{28} - 10 q^{29} - 10 q^{30} - 4 q^{31} - 34 q^{32} - 8 q^{33} + 96 q^{34} - 12 q^{35} + 20 q^{36} + 20 q^{37} - 62 q^{38} - 4 q^{39} - 20 q^{40} - 50 q^{41} + 8 q^{42} + 44 q^{43} - 12 q^{44} + 2 q^{45} + 42 q^{46} + 18 q^{47} - 34 q^{48} + 48 q^{49} - 37 q^{50} + 10 q^{51} - 19 q^{52} - 46 q^{53} + 48 q^{55} - 12 q^{56} - 40 q^{58} - 18 q^{59} - 80 q^{60} + 2 q^{61} - 49 q^{62} + 68 q^{64} + 24 q^{65} - 20 q^{66} - 52 q^{67} - 56 q^{68} + 11 q^{69} + 220 q^{70} - 54 q^{71} + 18 q^{72} - 50 q^{73} - 64 q^{74} - 28 q^{75} + 28 q^{76} + 84 q^{77} + 2 q^{78} - 68 q^{79} + 34 q^{80} + 14 q^{81} + 51 q^{82} - 72 q^{83} - 9 q^{84} + 14 q^{85} - 10 q^{86} - 60 q^{87} - 22 q^{88} + 120 q^{89} + 20 q^{90} - 43 q^{91} + 122 q^{92} - 2 q^{93} + 30 q^{94} - 16 q^{95} - 68 q^{96} + 51 q^{97} - 24 q^{98} + 14 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).

\(n\) \(67\) \(79\) \(287\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{5}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.426907 + 0.190071i −0.301869 + 0.134401i −0.552081 0.833790i \(-0.686166\pi\)
0.250212 + 0.968191i \(0.419500\pi\)
\(3\) −0.669131 0.743145i −0.386323 0.429055i
\(4\) −1.19214 + 1.32400i −0.596069 + 0.662002i
\(5\) 0.757885 0.550636i 0.338936 0.246252i −0.405277 0.914194i \(-0.632825\pi\)
0.744213 + 0.667942i \(0.232825\pi\)
\(6\) 0.426907 + 0.190071i 0.174284 + 0.0775963i
\(7\) 0.718277 0.797728i 0.271483 0.301513i −0.591951 0.805974i \(-0.701642\pi\)
0.863434 + 0.504461i \(0.168309\pi\)
\(8\) 0.546090 1.68069i 0.193072 0.594214i
\(9\) −0.104528 + 0.994522i −0.0348428 + 0.331507i
\(10\) −0.218887 + 0.379123i −0.0692180 + 0.119889i
\(11\) −2.58952 + 2.07229i −0.780769 + 0.624819i
\(12\) 1.78162 0.514310
\(13\) 3.60513 0.0550045i 0.999884 0.0152555i
\(14\) −0.155013 + 0.477080i −0.0414289 + 0.127505i
\(15\) −0.916326 0.194771i −0.236594 0.0502897i
\(16\) −0.286139 2.72243i −0.0715347 0.680608i
\(17\) 2.20862 + 0.983339i 0.535668 + 0.238495i 0.656697 0.754154i \(-0.271953\pi\)
−0.121029 + 0.992649i \(0.538620\pi\)
\(18\) −0.144406 0.444437i −0.0340369 0.104755i
\(19\) 5.15717 1.09619i 1.18314 0.251483i 0.425989 0.904728i \(-0.359926\pi\)
0.757147 + 0.653245i \(0.226593\pi\)
\(20\) −0.174460 + 1.65988i −0.0390104 + 0.371160i
\(21\) −1.07345 −0.234246
\(22\) 0.711601 1.37687i 0.151714 0.293550i
\(23\) 3.45980 5.99255i 0.721418 1.24953i −0.239014 0.971016i \(-0.576824\pi\)
0.960432 0.278516i \(-0.0898426\pi\)
\(24\) −1.61440 + 0.718778i −0.329539 + 0.146720i
\(25\) −1.27390 + 3.92065i −0.254779 + 0.784129i
\(26\) −1.52860 + 0.708714i −0.299784 + 0.138990i
\(27\) 0.809017 0.587785i 0.155695 0.113119i
\(28\) 0.199909 + 1.90200i 0.0377792 + 0.359445i
\(29\) 3.51009 + 0.746093i 0.651808 + 0.138546i 0.521936 0.852985i \(-0.325210\pi\)
0.129872 + 0.991531i \(0.458543\pi\)
\(30\) 0.428207 0.0910181i 0.0781795 0.0166176i
\(31\) 3.07661 + 2.23529i 0.552576 + 0.401470i 0.828734 0.559642i \(-0.189062\pi\)
−0.276159 + 0.961112i \(0.589062\pi\)
\(32\) 2.40679 + 4.16869i 0.425465 + 0.736927i
\(33\) 3.27274 + 0.537754i 0.569711 + 0.0936110i
\(34\) −1.12978 −0.193756
\(35\) 0.105114 1.00009i 0.0177675 0.169047i
\(36\) −1.19214 1.32400i −0.198690 0.220667i
\(37\) 9.93371 + 2.11147i 1.63309 + 0.347124i 0.931016 0.364978i \(-0.118924\pi\)
0.702075 + 0.712103i \(0.252257\pi\)
\(38\) −1.99328 + 1.44820i −0.323353 + 0.234929i
\(39\) −2.45318 2.64233i −0.392823 0.423111i
\(40\) −0.511575 1.57447i −0.0808872 0.248945i
\(41\) −1.35402 1.50379i −0.211463 0.234853i 0.628077 0.778151i \(-0.283842\pi\)
−0.839540 + 0.543298i \(0.817175\pi\)
\(42\) 0.458263 0.204032i 0.0707115 0.0314828i
\(43\) 2.06088 + 3.56955i 0.314281 + 0.544351i 0.979284 0.202489i \(-0.0649031\pi\)
−0.665003 + 0.746841i \(0.731570\pi\)
\(44\) 0.343343 5.89899i 0.0517609 0.889306i
\(45\) 0.468399 + 0.811290i 0.0698247 + 0.120940i
\(46\) −0.338002 + 3.21587i −0.0498356 + 0.474154i
\(47\) 3.07221 9.45529i 0.448128 1.37920i −0.430888 0.902405i \(-0.641800\pi\)
0.879017 0.476791i \(-0.158200\pi\)
\(48\) −1.83170 + 2.03430i −0.264383 + 0.293627i
\(49\) 0.611252 + 5.81567i 0.0873217 + 0.830811i
\(50\) −0.201367 1.91588i −0.0284777 0.270947i
\(51\) −0.747089 2.29930i −0.104613 0.321967i
\(52\) −4.22499 + 4.83878i −0.585901 + 0.671018i
\(53\) −8.05930 5.85542i −1.10703 0.804304i −0.124836 0.992177i \(-0.539841\pi\)
−0.982193 + 0.187873i \(0.939841\pi\)
\(54\) −0.233654 + 0.404701i −0.0317963 + 0.0550728i
\(55\) −0.821480 + 2.99644i −0.110768 + 0.404040i
\(56\) −0.948490 1.64283i −0.126747 0.219533i
\(57\) −4.26545 3.09903i −0.564972 0.410477i
\(58\) −1.64030 + 0.348655i −0.215381 + 0.0457807i
\(59\) −0.420199 + 0.466679i −0.0547053 + 0.0607564i −0.769876 0.638193i \(-0.779682\pi\)
0.715171 + 0.698949i \(0.246349\pi\)
\(60\) 1.35026 0.981025i 0.174318 0.126650i
\(61\) −5.26644 2.34477i −0.674298 0.300217i 0.0408749 0.999164i \(-0.486985\pi\)
−0.715173 + 0.698947i \(0.753652\pi\)
\(62\) −1.73829 0.369485i −0.220763 0.0469247i
\(63\) 0.718277 + 0.797728i 0.0904944 + 0.100504i
\(64\) 2.60942 + 1.89586i 0.326178 + 0.236982i
\(65\) 2.70199 2.02680i 0.335140 0.251394i
\(66\) −1.49937 + 0.392483i −0.184559 + 0.0483113i
\(67\) 4.40574 7.63097i 0.538247 0.932271i −0.460751 0.887529i \(-0.652420\pi\)
0.998999 0.0447421i \(-0.0142466\pi\)
\(68\) −3.93492 + 1.75194i −0.477179 + 0.212454i
\(69\) −6.76839 + 1.43867i −0.814818 + 0.173195i
\(70\) 0.145215 + 0.446927i 0.0173566 + 0.0534180i
\(71\) −5.55464 2.47309i −0.659215 0.293501i 0.0497328 0.998763i \(-0.484163\pi\)
−0.708947 + 0.705261i \(0.750830\pi\)
\(72\) 1.61440 + 0.718778i 0.190259 + 0.0847088i
\(73\) 1.37223 + 4.22329i 0.160607 + 0.494299i 0.998686 0.0512512i \(-0.0163209\pi\)
−0.838078 + 0.545550i \(0.816321\pi\)
\(74\) −4.64210 + 0.986710i −0.539634 + 0.114703i
\(75\) 3.76601 1.67674i 0.434861 0.193613i
\(76\) −4.69670 + 8.13492i −0.538749 + 0.933140i
\(77\) −0.206868 + 3.55421i −0.0235748 + 0.405040i
\(78\) 1.54951 + 0.661751i 0.175448 + 0.0749285i
\(79\) −9.22352 6.70128i −1.03773 0.753953i −0.0678865 0.997693i \(-0.521626\pi\)
−0.969841 + 0.243740i \(0.921626\pi\)
\(80\) −1.71593 1.90573i −0.191847 0.213067i
\(81\) −0.978148 0.207912i −0.108683 0.0231013i
\(82\) 0.863870 + 0.384620i 0.0953984 + 0.0424741i
\(83\) −13.3400 + 9.69209i −1.46426 + 1.06385i −0.482029 + 0.876155i \(0.660100\pi\)
−0.982228 + 0.187690i \(0.939900\pi\)
\(84\) 1.27970 1.42125i 0.139627 0.155071i
\(85\) 2.21534 0.470885i 0.240287 0.0510746i
\(86\) −1.55828 1.13215i −0.168033 0.122083i
\(87\) −1.79425 3.10774i −0.192364 0.333185i
\(88\) 2.06877 + 5.48384i 0.220532 + 0.584579i
\(89\) −5.13874 + 8.90055i −0.544705 + 0.943457i 0.453920 + 0.891042i \(0.350025\pi\)
−0.998625 + 0.0524146i \(0.983308\pi\)
\(90\) −0.354166 0.257317i −0.0373324 0.0271235i
\(91\) 2.54561 2.91542i 0.266852 0.305619i
\(92\) 3.80960 + 11.7247i 0.397178 + 1.22239i
\(93\) −0.397511 3.78207i −0.0412200 0.392182i
\(94\) 0.485631 + 4.62047i 0.0500891 + 0.476566i
\(95\) 3.30494 3.67051i 0.339080 0.376586i
\(96\) 1.48748 4.57800i 0.151815 0.467240i
\(97\) −0.966686 + 9.19740i −0.0981521 + 0.933855i 0.829020 + 0.559219i \(0.188899\pi\)
−0.927172 + 0.374636i \(0.877768\pi\)
\(98\) −1.36634 2.36657i −0.138021 0.239060i
\(99\) −1.79026 2.79195i −0.179928 0.280601i
\(100\) −3.67229 6.36059i −0.367229 0.636059i
\(101\) 12.0961 5.38551i 1.20360 0.535878i 0.295789 0.955253i \(-0.404417\pi\)
0.907813 + 0.419375i \(0.137751\pi\)
\(102\) 0.755970 + 0.839590i 0.0748522 + 0.0831318i
\(103\) 4.75332 + 14.6292i 0.468359 + 1.44146i 0.854709 + 0.519108i \(0.173736\pi\)
−0.386350 + 0.922352i \(0.626264\pi\)
\(104\) 1.87628 6.08915i 0.183984 0.597090i
\(105\) −0.813550 + 0.591079i −0.0793944 + 0.0576834i
\(106\) 4.55352 + 0.967881i 0.442277 + 0.0940089i
\(107\) −4.29847 4.77394i −0.415549 0.461514i 0.498636 0.866812i \(-0.333835\pi\)
−0.914185 + 0.405298i \(0.867168\pi\)
\(108\) −0.186230 + 1.77186i −0.0179200 + 0.170498i
\(109\) −15.6346 −1.49752 −0.748761 0.662840i \(-0.769351\pi\)
−0.748761 + 0.662840i \(0.769351\pi\)
\(110\) −0.218842 1.43534i −0.0208657 0.136854i
\(111\) −5.07782 8.79503i −0.481965 0.834788i
\(112\) −2.37729 1.72720i −0.224632 0.163205i
\(113\) 7.95153 1.69015i 0.748017 0.158996i 0.181896 0.983318i \(-0.441777\pi\)
0.566121 + 0.824322i \(0.308443\pi\)
\(114\) 2.40999 + 0.512259i 0.225716 + 0.0479774i
\(115\) −0.677581 6.44675i −0.0631847 0.601162i
\(116\) −5.17235 + 3.75793i −0.480240 + 0.348915i
\(117\) −0.322136 + 3.59113i −0.0297815 + 0.332000i
\(118\) 0.0906839 0.279096i 0.00834813 0.0256929i
\(119\) 2.37084 1.05556i 0.217334 0.0967634i
\(120\) −0.827746 + 1.43370i −0.0755626 + 0.130878i
\(121\) 2.41122 10.7325i 0.219202 0.975680i
\(122\) 2.69395 0.243899
\(123\) −0.211519 + 2.01247i −0.0190720 + 0.181458i
\(124\) −6.62728 + 1.40867i −0.595147 + 0.126502i
\(125\) 2.64081 + 8.12759i 0.236201 + 0.726953i
\(126\) −0.458263 0.204032i −0.0408253 0.0181766i
\(127\) −1.26700 12.0547i −0.112428 1.06968i −0.894677 0.446714i \(-0.852594\pi\)
0.782249 0.622966i \(-0.214073\pi\)
\(128\) −10.8911 2.31498i −0.962649 0.204617i
\(129\) 1.27369 3.92003i 0.112143 0.345139i
\(130\) −0.768261 + 1.37883i −0.0673810 + 0.120931i
\(131\) −7.27611 −0.635717 −0.317858 0.948138i \(-0.602964\pi\)
−0.317858 + 0.948138i \(0.602964\pi\)
\(132\) −4.61355 + 3.69204i −0.401558 + 0.321351i
\(133\) 2.82982 4.90139i 0.245376 0.425004i
\(134\) −0.430415 + 4.09512i −0.0371822 + 0.353765i
\(135\) 0.289486 0.890947i 0.0249150 0.0766805i
\(136\) 2.85879 3.17501i 0.245139 0.272255i
\(137\) 4.16119 + 1.85268i 0.355514 + 0.158285i 0.576720 0.816942i \(-0.304333\pi\)
−0.221206 + 0.975227i \(0.570999\pi\)
\(138\) 2.61603 1.90065i 0.222691 0.161794i
\(139\) 0.903982 1.00397i 0.0766748 0.0851560i −0.703587 0.710609i \(-0.748419\pi\)
0.780261 + 0.625453i \(0.215086\pi\)
\(140\) 1.19882 + 1.33142i 0.101319 + 0.112526i
\(141\) −9.08236 + 4.04373i −0.764873 + 0.340543i
\(142\) 2.84138 0.238443
\(143\) −9.22157 + 7.61332i −0.771147 + 0.636658i
\(144\) 2.73743 0.228119
\(145\) 3.07107 1.36733i 0.255039 0.113550i
\(146\) −1.38854 1.54213i −0.114916 0.127628i
\(147\) 3.91288 4.34569i 0.322729 0.358427i
\(148\) −14.6380 + 10.6351i −1.20323 + 0.874200i
\(149\) 12.3923 + 5.51743i 1.01522 + 0.452005i 0.845778 0.533535i \(-0.179137\pi\)
0.169442 + 0.985540i \(0.445803\pi\)
\(150\) −1.28904 + 1.43162i −0.105250 + 0.116891i
\(151\) 2.52659 7.77606i 0.205611 0.632807i −0.794076 0.607818i \(-0.792045\pi\)
0.999688 0.0249887i \(-0.00795499\pi\)
\(152\) 0.973920 9.26623i 0.0789954 0.751591i
\(153\) −1.20882 + 2.09373i −0.0977270 + 0.169268i
\(154\) −0.587240 1.55664i −0.0473212 0.125437i
\(155\) 3.56255 0.286151
\(156\) 6.42299 0.0979972i 0.514250 0.00784606i
\(157\) 5.32266 16.3815i 0.424795 1.30738i −0.478396 0.878144i \(-0.658782\pi\)
0.903191 0.429240i \(-0.141218\pi\)
\(158\) 5.21131 + 1.10770i 0.414590 + 0.0881237i
\(159\) 1.04130 + 9.90726i 0.0825801 + 0.785697i
\(160\) 4.11950 + 1.83412i 0.325675 + 0.145000i
\(161\) −2.29533 7.06429i −0.180897 0.556744i
\(162\) 0.457096 0.0971589i 0.0359129 0.00763352i
\(163\) −1.06091 + 10.0939i −0.0830971 + 0.790616i 0.871033 + 0.491224i \(0.163450\pi\)
−0.954130 + 0.299392i \(0.903216\pi\)
\(164\) 3.60521 0.281519
\(165\) 2.77647 1.39453i 0.216148 0.108564i
\(166\) 3.85276 6.67318i 0.299032 0.517939i
\(167\) 6.66039 2.96540i 0.515397 0.229469i −0.132520 0.991180i \(-0.542307\pi\)
0.647917 + 0.761711i \(0.275640\pi\)
\(168\) −0.586199 + 1.80414i −0.0452263 + 0.139192i
\(169\) 12.9939 0.396597i 0.999535 0.0305074i
\(170\) −0.856243 + 0.622097i −0.0656708 + 0.0477126i
\(171\) 0.551114 + 5.24350i 0.0421448 + 0.400981i
\(172\) −7.18296 1.52678i −0.547695 0.116416i
\(173\) −21.8597 + 4.64643i −1.66196 + 0.353261i −0.940658 0.339355i \(-0.889791\pi\)
−0.721306 + 0.692616i \(0.756458\pi\)
\(174\) 1.35667 + 0.985681i 0.102849 + 0.0747243i
\(175\) 2.21260 + 3.83233i 0.167257 + 0.289697i
\(176\) 6.38263 + 6.45682i 0.481109 + 0.486701i
\(177\) 0.627978 0.0472017
\(178\) 0.502024 4.77644i 0.0376283 0.358009i
\(179\) −3.40171 3.77798i −0.254255 0.282379i 0.602482 0.798133i \(-0.294179\pi\)
−0.856737 + 0.515754i \(0.827512\pi\)
\(180\) −1.63255 0.347009i −0.121683 0.0258645i
\(181\) 17.1035 12.4264i 1.27130 0.923651i 0.272042 0.962285i \(-0.412301\pi\)
0.999253 + 0.0386347i \(0.0123009\pi\)
\(182\) −0.532599 + 1.72846i −0.0394789 + 0.128122i
\(183\) 1.78143 + 5.48268i 0.131687 + 0.405292i
\(184\) −8.18226 9.08732i −0.603204 0.669926i
\(185\) 8.69126 3.86960i 0.638994 0.284498i
\(186\) 0.888563 + 1.53904i 0.0651526 + 0.112848i
\(187\) −7.75702 + 2.03052i −0.567249 + 0.148486i
\(188\) 8.85635 + 15.3396i 0.645915 + 1.11876i
\(189\) 0.112206 1.06757i 0.00816178 0.0776541i
\(190\) −0.713245 + 2.19514i −0.0517442 + 0.159252i
\(191\) 11.1267 12.3574i 0.805100 0.894154i −0.191072 0.981576i \(-0.561196\pi\)
0.996171 + 0.0874224i \(0.0278630\pi\)
\(192\) −0.337148 3.20775i −0.0243316 0.231500i
\(193\) 0.781590 + 7.43633i 0.0562601 + 0.535279i 0.985962 + 0.166967i \(0.0533974\pi\)
−0.929702 + 0.368312i \(0.879936\pi\)
\(194\) −1.33548 4.11018i −0.0958817 0.295094i
\(195\) −3.31419 0.651773i −0.237334 0.0466745i
\(196\) −8.42867 6.12379i −0.602048 0.437413i
\(197\) −6.51639 + 11.2867i −0.464274 + 0.804146i −0.999168 0.0407730i \(-0.987018\pi\)
0.534895 + 0.844919i \(0.320351\pi\)
\(198\) 1.29494 + 0.851625i 0.0920277 + 0.0605224i
\(199\) 8.01621 + 13.8845i 0.568254 + 0.984245i 0.996739 + 0.0806958i \(0.0257142\pi\)
−0.428485 + 0.903549i \(0.640952\pi\)
\(200\) 5.89374 + 4.28205i 0.416750 + 0.302787i
\(201\) −8.61893 + 1.83201i −0.607933 + 0.129220i
\(202\) −4.14026 + 4.59823i −0.291308 + 0.323530i
\(203\) 3.11640 2.26420i 0.218728 0.158915i
\(204\) 3.93492 + 1.75194i 0.275500 + 0.122660i
\(205\) −1.85423 0.394130i −0.129505 0.0275272i
\(206\) −4.80982 5.34185i −0.335116 0.372184i
\(207\) 5.59807 + 4.06724i 0.389093 + 0.282693i
\(208\) −1.18131 9.79898i −0.0819094 0.679437i
\(209\) −11.0830 + 13.5258i −0.766625 + 0.935597i
\(210\) 0.234963 0.406969i 0.0162140 0.0280835i
\(211\) −0.263562 + 0.117345i −0.0181443 + 0.00807837i −0.415789 0.909461i \(-0.636494\pi\)
0.397644 + 0.917540i \(0.369828\pi\)
\(212\) 17.3604 3.69007i 1.19232 0.253435i
\(213\) 1.87892 + 5.78272i 0.128741 + 0.396225i
\(214\) 2.74244 + 1.22101i 0.187469 + 0.0834667i
\(215\) 3.52743 + 1.57051i 0.240569 + 0.107108i
\(216\) −0.546090 1.68069i −0.0371567 0.114357i
\(217\) 3.99301 0.848741i 0.271063 0.0576163i
\(218\) 6.67452 2.97169i 0.452056 0.201268i
\(219\) 2.22031 3.84570i 0.150035 0.259868i
\(220\) −2.98798 4.65981i −0.201450 0.314165i
\(221\) 8.01644 + 3.42358i 0.539244 + 0.230295i
\(222\) 3.83944 + 2.78952i 0.257686 + 0.187220i
\(223\) −9.41871 10.4605i −0.630724 0.700490i 0.340071 0.940400i \(-0.389549\pi\)
−0.970795 + 0.239910i \(0.922882\pi\)
\(224\) 5.05423 + 1.07431i 0.337700 + 0.0717803i
\(225\) −3.76601 1.67674i −0.251067 0.111782i
\(226\) −3.07332 + 2.23290i −0.204434 + 0.148530i
\(227\) −9.26176 + 10.2862i −0.614725 + 0.682721i −0.967466 0.253000i \(-0.918583\pi\)
0.352742 + 0.935721i \(0.385249\pi\)
\(228\) 9.18813 1.95300i 0.608499 0.129340i
\(229\) −8.01985 5.82676i −0.529967 0.385043i 0.290379 0.956912i \(-0.406219\pi\)
−0.820345 + 0.571869i \(0.806219\pi\)
\(230\) 1.51461 + 2.62338i 0.0998702 + 0.172980i
\(231\) 2.77972 2.22450i 0.182892 0.146361i
\(232\) 3.17078 5.49195i 0.208172 0.360564i
\(233\) 11.6925 + 8.49512i 0.766003 + 0.556534i 0.900746 0.434347i \(-0.143021\pi\)
−0.134743 + 0.990881i \(0.543021\pi\)
\(234\) −0.545049 1.59431i −0.0356310 0.104223i
\(235\) −2.87804 8.85769i −0.187743 0.577812i
\(236\) −0.116949 1.11269i −0.00761270 0.0724300i
\(237\) 1.19172 + 11.3384i 0.0774104 + 0.736511i
\(238\) −0.811495 + 0.901256i −0.0526014 + 0.0584198i
\(239\) 5.09581 15.6833i 0.329621 1.01447i −0.639691 0.768632i \(-0.720938\pi\)
0.969311 0.245836i \(-0.0790624\pi\)
\(240\) −0.268054 + 2.55036i −0.0173028 + 0.164625i
\(241\) 9.43820 + 16.3474i 0.607968 + 1.05303i 0.991575 + 0.129535i \(0.0413484\pi\)
−0.383607 + 0.923496i \(0.625318\pi\)
\(242\) 1.01057 + 5.04008i 0.0649619 + 0.323988i
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) 9.38281 4.17749i 0.600673 0.267437i
\(245\) 3.66558 + 4.07103i 0.234185 + 0.260089i
\(246\) −0.292214 0.899341i −0.0186309 0.0573399i
\(247\) 18.5320 4.23558i 1.17916 0.269503i
\(248\) 5.43694 3.95017i 0.345246 0.250836i
\(249\) 16.1288 + 3.42829i 1.02212 + 0.217259i
\(250\) −2.67220 2.96778i −0.169005 0.187699i
\(251\) 0.768320 7.31007i 0.0484959 0.461408i −0.943145 0.332381i \(-0.892148\pi\)
0.991641 0.129027i \(-0.0411853\pi\)
\(252\) −1.91248 −0.120475
\(253\) 3.45909 + 22.6875i 0.217471 + 1.42635i
\(254\) 2.83214 + 4.90541i 0.177704 + 0.307793i
\(255\) −1.83229 1.33123i −0.114742 0.0833651i
\(256\) −1.22036 + 0.259396i −0.0762726 + 0.0162122i
\(257\) 16.0969 + 3.42150i 1.00410 + 0.213427i 0.680485 0.732762i \(-0.261769\pi\)
0.323612 + 0.946190i \(0.395103\pi\)
\(258\) 0.201336 + 1.91558i 0.0125346 + 0.119259i
\(259\) 8.81954 6.40777i 0.548019 0.398159i
\(260\) −0.537651 + 5.99367i −0.0333437 + 0.371712i
\(261\) −1.10891 + 3.41288i −0.0686398 + 0.211252i
\(262\) 3.10622 1.38298i 0.191903 0.0854408i
\(263\) −9.57007 + 16.5759i −0.590116 + 1.02211i 0.404100 + 0.914715i \(0.367585\pi\)
−0.994216 + 0.107396i \(0.965749\pi\)
\(264\) 2.69101 5.20680i 0.165620 0.320457i
\(265\) −9.33222 −0.573274
\(266\) −0.276456 + 2.63030i −0.0169506 + 0.161274i
\(267\) 10.0529 2.13681i 0.615227 0.130770i
\(268\) 4.85118 + 14.9304i 0.296333 + 0.912019i
\(269\) −3.53255 1.57279i −0.215383 0.0958948i 0.296209 0.955123i \(-0.404277\pi\)
−0.511592 + 0.859228i \(0.670944\pi\)
\(270\) 0.0457597 + 0.435375i 0.00278485 + 0.0264961i
\(271\) −4.50125 0.956771i −0.273432 0.0581197i 0.0691550 0.997606i \(-0.477970\pi\)
−0.342587 + 0.939486i \(0.611303\pi\)
\(272\) 2.04510 6.29418i 0.124003 0.381640i
\(273\) −3.86992 + 0.0590445i −0.234218 + 0.00357353i
\(274\) −2.12858 −0.128592
\(275\) −4.82595 12.7925i −0.291015 0.771415i
\(276\) 6.16406 10.6765i 0.371033 0.642647i
\(277\) −1.85372 + 17.6370i −0.111379 + 1.05970i 0.785934 + 0.618310i \(0.212182\pi\)
−0.897314 + 0.441394i \(0.854484\pi\)
\(278\) −0.195090 + 0.600425i −0.0117007 + 0.0360111i
\(279\) −2.54464 + 2.82611i −0.152343 + 0.169194i
\(280\) −1.62345 0.722806i −0.0970196 0.0431959i
\(281\) −25.6196 + 18.6138i −1.52834 + 1.11040i −0.571187 + 0.820820i \(0.693517\pi\)
−0.957153 + 0.289584i \(0.906483\pi\)
\(282\) 3.10873 3.45260i 0.185122 0.205599i
\(283\) −18.1269 20.1319i −1.07753 1.19672i −0.979481 0.201536i \(-0.935407\pi\)
−0.0980488 0.995182i \(-0.531260\pi\)
\(284\) 9.89628 4.40611i 0.587236 0.261454i
\(285\) −4.93915 −0.292570
\(286\) 2.48968 5.00294i 0.147218 0.295830i
\(287\) −2.17218 −0.128220
\(288\) −4.39743 + 1.95786i −0.259121 + 0.115368i
\(289\) −7.46419 8.28982i −0.439070 0.487637i
\(290\) −1.05117 + 1.16745i −0.0617270 + 0.0685548i
\(291\) 7.48184 5.43588i 0.438593 0.318657i
\(292\) −7.22754 3.21791i −0.422960 0.188314i
\(293\) −12.5131 + 13.8972i −0.731022 + 0.811882i −0.987987 0.154539i \(-0.950611\pi\)
0.256965 + 0.966421i \(0.417277\pi\)
\(294\) −0.844445 + 2.59894i −0.0492491 + 0.151573i
\(295\) −0.0614928 + 0.585065i −0.00358025 + 0.0340638i
\(296\) 8.97343 15.5424i 0.521570 0.903386i
\(297\) −0.876903 + 3.19860i −0.0508830 + 0.185602i
\(298\) −6.33909 −0.367214
\(299\) 12.1434 21.7942i 0.702272 1.26039i
\(300\) −2.26960 + 6.98511i −0.131035 + 0.403286i
\(301\) 4.32781 + 0.919905i 0.249451 + 0.0530225i
\(302\) 0.399385 + 3.79989i 0.0229820 + 0.218659i
\(303\) −12.0961 5.38551i −0.694900 0.309389i
\(304\) −4.45997 13.7264i −0.255797 0.787262i
\(305\) −5.28247 + 1.12282i −0.302473 + 0.0642926i
\(306\) 0.118094 1.12359i 0.00675099 0.0642314i
\(307\) −21.8159 −1.24510 −0.622551 0.782579i \(-0.713904\pi\)
−0.622551 + 0.782579i \(0.713904\pi\)
\(308\) −4.45917 4.51101i −0.254085 0.257038i
\(309\) 7.69104 13.3213i 0.437528 0.757820i
\(310\) −1.52088 + 0.677138i −0.0863800 + 0.0384589i
\(311\) 7.80813 24.0310i 0.442759 1.36267i −0.442164 0.896934i \(-0.645789\pi\)
0.884923 0.465737i \(-0.154211\pi\)
\(312\) −5.78060 + 2.68009i −0.327262 + 0.151730i
\(313\) 2.76214 2.00681i 0.156125 0.113432i −0.506980 0.861958i \(-0.669238\pi\)
0.663105 + 0.748526i \(0.269238\pi\)
\(314\) 0.841365 + 8.00506i 0.0474810 + 0.451752i
\(315\) 0.983629 + 0.209077i 0.0554212 + 0.0117801i
\(316\) 19.8682 4.22312i 1.11768 0.237569i
\(317\) −19.7716 14.3649i −1.11048 0.806814i −0.127745 0.991807i \(-0.540774\pi\)
−0.982740 + 0.184993i \(0.940774\pi\)
\(318\) −2.32762 4.03156i −0.130527 0.226079i
\(319\) −10.6356 + 5.34191i −0.595478 + 0.299090i
\(320\) 3.02157 0.168911
\(321\) −0.671487 + 6.38877i −0.0374788 + 0.356587i
\(322\) 2.32261 + 2.57952i 0.129434 + 0.143751i
\(323\) 12.4681 + 2.65018i 0.693746 + 0.147460i
\(324\) 1.44136 1.04721i 0.0800757 0.0581784i
\(325\) −4.37691 + 14.2045i −0.242787 + 0.787925i
\(326\) −1.46565 4.51081i −0.0811750 0.249831i
\(327\) 10.4616 + 11.6188i 0.578527 + 0.642519i
\(328\) −3.26683 + 1.45449i −0.180380 + 0.0803106i
\(329\) −5.33605 9.24231i −0.294186 0.509545i
\(330\) −0.920233 + 1.12306i −0.0506572 + 0.0618225i
\(331\) 4.08824 + 7.08105i 0.224710 + 0.389210i 0.956232 0.292608i \(-0.0945231\pi\)
−0.731522 + 0.681818i \(0.761190\pi\)
\(332\) 3.07078 29.2166i 0.168531 1.60347i
\(333\) −3.13826 + 9.65858i −0.171976 + 0.529287i
\(334\) −2.27973 + 2.53190i −0.124741 + 0.138539i
\(335\) −0.862838 8.20935i −0.0471419 0.448525i
\(336\) 0.307155 + 2.92239i 0.0167567 + 0.159429i
\(337\) 0.384423 + 1.18313i 0.0209409 + 0.0644493i 0.960981 0.276615i \(-0.0892126\pi\)
−0.940040 + 0.341064i \(0.889213\pi\)
\(338\) −5.47183 + 2.63909i −0.297628 + 0.143547i
\(339\) −6.57664 4.77821i −0.357194 0.259517i
\(340\) −2.01754 + 3.49448i −0.109416 + 0.189515i
\(341\) −12.5991 + 0.587312i −0.682280 + 0.0318047i
\(342\) −1.23191 2.13374i −0.0666143 0.115379i
\(343\) 11.1574 + 8.10635i 0.602445 + 0.437702i
\(344\) 7.12474 1.51441i 0.384140 0.0816515i
\(345\) −4.33748 + 4.81726i −0.233522 + 0.259352i
\(346\) 8.44893 6.13850i 0.454217 0.330008i
\(347\) 13.2931 + 5.91848i 0.713612 + 0.317720i 0.731236 0.682124i \(-0.238944\pi\)
−0.0176245 + 0.999845i \(0.505610\pi\)
\(348\) 6.25366 + 1.32926i 0.335231 + 0.0712556i
\(349\) −6.57606 7.30345i −0.352008 0.390945i 0.540972 0.841041i \(-0.318057\pi\)
−0.892980 + 0.450096i \(0.851390\pi\)
\(350\) −1.67299 1.21550i −0.0894251 0.0649712i
\(351\) 2.88428 2.16354i 0.153952 0.115481i
\(352\) −14.8712 5.80732i −0.792637 0.309531i
\(353\) −1.26142 + 2.18485i −0.0671388 + 0.116288i −0.897641 0.440728i \(-0.854720\pi\)
0.830502 + 0.557016i \(0.188054\pi\)
\(354\) −0.268088 + 0.119361i −0.0142487 + 0.00634395i
\(355\) −5.57155 + 1.18427i −0.295707 + 0.0628545i
\(356\) −5.65828 17.4144i −0.299888 0.922961i
\(357\) −2.37084 1.05556i −0.125478 0.0558664i
\(358\) 2.17030 + 0.966279i 0.114704 + 0.0510694i
\(359\) 5.99961 + 18.4649i 0.316647 + 0.974540i 0.975071 + 0.221893i \(0.0712235\pi\)
−0.658424 + 0.752647i \(0.728776\pi\)
\(360\) 1.61932 0.344196i 0.0853455 0.0181407i
\(361\) 8.03741 3.57848i 0.423021 0.188341i
\(362\) −4.93971 + 8.55584i −0.259626 + 0.449685i
\(363\) −9.58920 + 5.38954i −0.503303 + 0.282878i
\(364\) 0.825316 + 6.84598i 0.0432583 + 0.358827i
\(365\) 3.36548 + 2.44517i 0.176158 + 0.127986i
\(366\) −1.80261 2.00200i −0.0942238 0.104646i
\(367\) −26.6571 5.66614i −1.39149 0.295770i −0.549603 0.835426i \(-0.685221\pi\)
−0.841886 + 0.539656i \(0.818554\pi\)
\(368\) −17.3043 7.70436i −0.902048 0.401617i
\(369\) 1.63709 1.18941i 0.0852234 0.0619184i
\(370\) −2.97486 + 3.30392i −0.154656 + 0.171763i
\(371\) −10.4598 + 2.22331i −0.543048 + 0.115428i
\(372\) 5.48136 + 3.98244i 0.284195 + 0.206480i
\(373\) −12.9402 22.4131i −0.670020 1.16051i −0.977898 0.209082i \(-0.932952\pi\)
0.307879 0.951426i \(-0.400381\pi\)
\(374\) 2.92558 2.34123i 0.151278 0.121062i
\(375\) 4.27292 7.40092i 0.220653 0.382182i
\(376\) −14.2137 10.3269i −0.733017 0.532568i
\(377\) 12.6954 + 2.49669i 0.653845 + 0.128586i
\(378\) 0.155013 + 0.477080i 0.00797299 + 0.0245383i
\(379\) −0.150988 1.43655i −0.00775573 0.0737908i 0.989959 0.141352i \(-0.0451449\pi\)
−0.997715 + 0.0675611i \(0.978478\pi\)
\(380\) 0.919820 + 8.75151i 0.0471858 + 0.448943i
\(381\) −8.11059 + 9.00772i −0.415518 + 0.461479i
\(382\) −2.40127 + 7.39035i −0.122860 + 0.378123i
\(383\) −0.373163 + 3.55041i −0.0190677 + 0.181417i −0.999910 0.0133841i \(-0.995740\pi\)
0.980843 + 0.194801i \(0.0624063\pi\)
\(384\) 5.56722 + 9.64271i 0.284101 + 0.492078i
\(385\) 1.80029 + 2.80759i 0.0917514 + 0.143088i
\(386\) −1.74710 3.02607i −0.0889251 0.154023i
\(387\) −3.76542 + 1.67647i −0.191407 + 0.0852199i
\(388\) −11.0250 12.2445i −0.559708 0.621619i
\(389\) 1.85031 + 5.69466i 0.0938144 + 0.288731i 0.986943 0.161071i \(-0.0514947\pi\)
−0.893129 + 0.449802i \(0.851495\pi\)
\(390\) 1.53874 0.351686i 0.0779169 0.0178083i
\(391\) 13.5341 9.83308i 0.684448 0.497280i
\(392\) 10.1082 + 2.14855i 0.510539 + 0.108518i
\(393\) 4.86867 + 5.40720i 0.245592 + 0.272757i
\(394\) 0.636613 6.05697i 0.0320721 0.305146i
\(395\) −10.6803 −0.537386
\(396\) 5.83079 + 0.958075i 0.293008 + 0.0481451i
\(397\) −10.5275 18.2342i −0.528362 0.915151i −0.999453 0.0330658i \(-0.989473\pi\)
0.471091 0.882085i \(-0.343860\pi\)
\(398\) −6.06122 4.40374i −0.303822 0.220739i
\(399\) −5.53596 + 1.17670i −0.277144 + 0.0589089i
\(400\) 11.0382 + 2.34624i 0.551910 + 0.117312i
\(401\) 2.49433 + 23.7320i 0.124561 + 1.18512i 0.860996 + 0.508611i \(0.169841\pi\)
−0.736435 + 0.676508i \(0.763492\pi\)
\(402\) 3.33127 2.42031i 0.166149 0.120714i
\(403\) 11.2145 + 7.88928i 0.558636 + 0.392993i
\(404\) −7.28973 + 22.4355i −0.362678 + 1.11621i
\(405\) −0.855807 + 0.381030i −0.0425254 + 0.0189335i
\(406\) −0.900054 + 1.55894i −0.0446690 + 0.0773689i
\(407\) −30.0991 + 15.1178i −1.49196 + 0.749363i
\(408\) −4.27240 −0.211515
\(409\) −0.971283 + 9.24114i −0.0480268 + 0.456945i 0.943909 + 0.330205i \(0.107118\pi\)
−0.991936 + 0.126740i \(0.959549\pi\)
\(410\) 0.866499 0.184180i 0.0427933 0.00909600i
\(411\) −1.40757 4.33205i −0.0694302 0.213684i
\(412\) −25.0358 11.1466i −1.23342 0.549156i
\(413\) 0.0704628 + 0.670409i 0.00346725 + 0.0329887i
\(414\) −3.16292 0.672300i −0.155449 0.0330417i
\(415\) −4.77339 + 14.6910i −0.234316 + 0.721152i
\(416\) 8.90611 + 14.8963i 0.436658 + 0.730351i
\(417\) −1.35098 −0.0661578
\(418\) 2.16054 7.88080i 0.105675 0.385463i
\(419\) −5.83140 + 10.1003i −0.284882 + 0.493431i −0.972581 0.232566i \(-0.925288\pi\)
0.687698 + 0.725997i \(0.258621\pi\)
\(420\) 0.187274 1.78179i 0.00913803 0.0869425i
\(421\) −11.1057 + 34.1798i −0.541258 + 1.66582i 0.188466 + 0.982080i \(0.439649\pi\)
−0.729724 + 0.683742i \(0.760351\pi\)
\(422\) 0.0902124 0.100191i 0.00439147 0.00487722i
\(423\) 9.08236 + 4.04373i 0.441600 + 0.196613i
\(424\) −14.2423 + 10.3476i −0.691665 + 0.502524i
\(425\) −6.66887 + 7.40653i −0.323488 + 0.359270i
\(426\) −1.90125 2.11156i −0.0921161 0.102305i
\(427\) −5.65325 + 2.51699i −0.273580 + 0.121806i
\(428\) 11.4451 0.553219
\(429\) 11.8282 + 1.75866i 0.571073 + 0.0849088i
\(430\) −1.80440 −0.0870157
\(431\) 2.46855 1.09907i 0.118906 0.0529403i −0.346422 0.938079i \(-0.612603\pi\)
0.465327 + 0.885139i \(0.345937\pi\)
\(432\) −1.83170 2.03430i −0.0881275 0.0978755i
\(433\) 18.1835 20.1948i 0.873841 0.970499i −0.125927 0.992040i \(-0.540191\pi\)
0.999768 + 0.0215409i \(0.00685720\pi\)
\(434\) −1.54332 + 1.12129i −0.0740819 + 0.0538237i
\(435\) −3.07107 1.36733i −0.147247 0.0655584i
\(436\) 18.6386 20.7003i 0.892627 0.991363i
\(437\) 11.2738 34.6972i 0.539299 1.65979i
\(438\) −0.216911 + 2.06377i −0.0103644 + 0.0986110i
\(439\) −5.01219 + 8.68137i −0.239219 + 0.414339i −0.960490 0.278313i \(-0.910225\pi\)
0.721272 + 0.692652i \(0.243558\pi\)
\(440\) 4.58749 + 3.01698i 0.218700 + 0.143829i
\(441\) −5.84771 −0.278462
\(442\) −4.07300 + 0.0621429i −0.193733 + 0.00295584i
\(443\) −11.8370 + 36.4307i −0.562395 + 1.73087i 0.113172 + 0.993575i \(0.463899\pi\)
−0.675567 + 0.737298i \(0.736101\pi\)
\(444\) 17.6981 + 3.76185i 0.839916 + 0.178530i
\(445\) 1.00639 + 9.57517i 0.0477075 + 0.453906i
\(446\) 6.00917 + 2.67545i 0.284542 + 0.126686i
\(447\) −4.19185 12.9012i −0.198268 0.610205i
\(448\) 3.38666 0.719858i 0.160005 0.0340101i
\(449\) 0.419959 3.99564i 0.0198191 0.188566i −0.980133 0.198341i \(-0.936445\pi\)
0.999952 + 0.00977470i \(0.00311143\pi\)
\(450\) 1.92644 0.0908131
\(451\) 6.62256 + 1.08817i 0.311844 + 0.0512401i
\(452\) −7.24156 + 12.5427i −0.340614 + 0.589961i
\(453\) −7.46936 + 3.32557i −0.350941 + 0.156249i
\(454\) 1.99880 6.15166i 0.0938082 0.288712i
\(455\) 0.323941 3.61125i 0.0151866 0.169298i
\(456\) −7.53783 + 5.47656i −0.352991 + 0.256463i
\(457\) −3.07715 29.2772i −0.143943 1.36953i −0.793201 0.608960i \(-0.791587\pi\)
0.649258 0.760568i \(-0.275080\pi\)
\(458\) 4.53123 + 0.963144i 0.211731 + 0.0450047i
\(459\) 2.36480 0.502654i 0.110379 0.0234619i
\(460\) 9.34329 + 6.78830i 0.435633 + 0.316506i
\(461\) −1.67419 2.89978i −0.0779746 0.135056i 0.824401 0.566006i \(-0.191512\pi\)
−0.902376 + 0.430950i \(0.858179\pi\)
\(462\) −0.763867 + 1.47800i −0.0355383 + 0.0687627i
\(463\) 0.889383 0.0413331 0.0206666 0.999786i \(-0.493421\pi\)
0.0206666 + 0.999786i \(0.493421\pi\)
\(464\) 1.02681 9.76947i 0.0476686 0.453536i
\(465\) −2.38381 2.64749i −0.110546 0.122774i
\(466\) −6.60630 1.40421i −0.306031 0.0650489i
\(467\) 9.39423 6.82531i 0.434713 0.315838i −0.348818 0.937191i \(-0.613417\pi\)
0.783531 + 0.621353i \(0.213417\pi\)
\(468\) −4.37064 4.70764i −0.202033 0.217611i
\(469\) −2.92289 8.99573i −0.134967 0.415384i
\(470\) 2.91225 + 3.23438i 0.134332 + 0.149191i
\(471\) −15.7354 + 7.00584i −0.725047 + 0.322812i
\(472\) 0.554876 + 0.961074i 0.0255402 + 0.0442370i
\(473\) −12.7338 4.97267i −0.585503 0.228644i
\(474\) −2.66387 4.61395i −0.122355 0.211926i
\(475\) −2.27192 + 21.6159i −0.104243 + 0.991804i
\(476\) −1.42879 + 4.39737i −0.0654886 + 0.201553i
\(477\) 6.66577 7.40309i 0.305205 0.338964i
\(478\) 0.805507 + 7.66388i 0.0368430 + 0.350538i
\(479\) −1.44140 13.7140i −0.0658592 0.626609i −0.976812 0.214098i \(-0.931319\pi\)
0.910953 0.412510i \(-0.135348\pi\)
\(480\) −1.39347 4.28865i −0.0636028 0.195749i
\(481\) 35.9285 + 7.06575i 1.63820 + 0.322170i
\(482\) −7.13642 5.18491i −0.325055 0.236166i
\(483\) −3.71392 + 6.43269i −0.168989 + 0.292698i
\(484\) 11.3353 + 15.9871i 0.515243 + 0.726684i
\(485\) 4.33178 + 7.50286i 0.196696 + 0.340688i
\(486\) −0.378060 0.274677i −0.0171492 0.0124596i
\(487\) −3.39883 + 0.722444i −0.154016 + 0.0327370i −0.284274 0.958743i \(-0.591753\pi\)
0.130259 + 0.991480i \(0.458419\pi\)
\(488\) −6.81678 + 7.57080i −0.308581 + 0.342714i
\(489\) 8.21113 5.96573i 0.371320 0.269780i
\(490\) −2.33865 1.04123i −0.105649 0.0470381i
\(491\) −17.7998 3.78346i −0.803293 0.170745i −0.212071 0.977254i \(-0.568021\pi\)
−0.591222 + 0.806509i \(0.701354\pi\)
\(492\) −2.41236 2.67919i −0.108757 0.120787i
\(493\) 7.01878 + 5.09945i 0.316110 + 0.229667i
\(494\) −7.10638 + 5.33060i −0.319731 + 0.239835i
\(495\) −2.89416 1.13019i −0.130083 0.0507984i
\(496\) 5.20508 9.01546i 0.233715 0.404806i
\(497\) −5.96262 + 2.65473i −0.267460 + 0.119081i
\(498\) −7.53714 + 1.60207i −0.337747 + 0.0717904i
\(499\) −0.988032 3.04085i −0.0442304 0.136127i 0.926503 0.376288i \(-0.122800\pi\)
−0.970733 + 0.240161i \(0.922800\pi\)
\(500\) −13.9092 6.19276i −0.622037 0.276949i
\(501\) −6.66039 2.96540i −0.297564 0.132484i
\(502\) 1.06143 + 3.26676i 0.0473742 + 0.145803i
\(503\) 12.6170 2.68183i 0.562565 0.119577i 0.0821528 0.996620i \(-0.473820\pi\)
0.480412 + 0.877043i \(0.340487\pi\)
\(504\) 1.73298 0.771572i 0.0771930 0.0343685i
\(505\) 6.20196 10.7421i 0.275984 0.478018i
\(506\) −5.78896 9.02800i −0.257351 0.401343i
\(507\) −8.98938 9.39101i −0.399232 0.417069i
\(508\) 17.4709 + 12.6933i 0.775145 + 0.563176i
\(509\) −4.76343 5.29032i −0.211135 0.234489i 0.628270 0.777995i \(-0.283763\pi\)
−0.839405 + 0.543506i \(0.817097\pi\)
\(510\) 1.03525 + 0.220048i 0.0458415 + 0.00974390i
\(511\) 4.35468 + 1.93883i 0.192639 + 0.0857686i
\(512\) 18.4876 13.4320i 0.817044 0.593617i
\(513\) 3.52791 3.91815i 0.155761 0.172990i
\(514\) −7.52221 + 1.59890i −0.331791 + 0.0705243i
\(515\) 11.6578 + 8.46992i 0.513706 + 0.373229i
\(516\) 3.67171 + 6.35959i 0.161638 + 0.279966i
\(517\) 11.6386 + 30.8512i 0.511864 + 1.35683i
\(518\) −2.54719 + 4.41187i −0.111917 + 0.193846i
\(519\) 18.0800 + 13.1359i 0.793623 + 0.576601i
\(520\) −1.93090 5.64802i −0.0846755 0.247682i
\(521\) −5.84463 17.9879i −0.256058 0.788065i −0.993619 0.112785i \(-0.964023\pi\)
0.737561 0.675280i \(-0.235977\pi\)
\(522\) −0.175288 1.66775i −0.00767215 0.0729956i
\(523\) −3.08056 29.3095i −0.134703 1.28162i −0.827903 0.560871i \(-0.810466\pi\)
0.693200 0.720746i \(-0.256200\pi\)
\(524\) 8.67413 9.63360i 0.378931 0.420846i
\(525\) 1.36746 4.20861i 0.0596809 0.183679i
\(526\) 0.934939 8.89535i 0.0407653 0.387856i
\(527\) 4.59701 + 7.96225i 0.200249 + 0.346841i
\(528\) 0.527540 9.06368i 0.0229582 0.394446i
\(529\) −12.4404 21.5474i −0.540887 0.936845i
\(530\) 3.98399 1.77379i 0.173054 0.0770484i
\(531\) −0.420199 0.466679i −0.0182351 0.0202521i
\(532\) 3.11592 + 9.58982i 0.135092 + 0.415771i
\(533\) −4.96414 5.34689i −0.215021 0.231600i
\(534\) −3.88551 + 2.82299i −0.168142 + 0.122163i
\(535\) −5.88645 1.25120i −0.254493 0.0540942i
\(536\) −10.4194 11.5719i −0.450049 0.499829i
\(537\) −0.531399 + 5.05592i −0.0229315 + 0.218179i
\(538\) 1.80701 0.0779058
\(539\) −13.6346 13.7931i −0.587285 0.594111i
\(540\) 0.834510 + 1.44541i 0.0359116 + 0.0622007i
\(541\) −14.5696 10.5854i −0.626395 0.455103i 0.228754 0.973484i \(-0.426535\pi\)
−0.855150 + 0.518381i \(0.826535\pi\)
\(542\) 2.10347 0.447107i 0.0903519 0.0192049i
\(543\) −20.6791 4.39549i −0.887427 0.188628i
\(544\) 1.21645 + 11.5737i 0.0521548 + 0.496220i
\(545\) −11.8492 + 8.60896i −0.507565 + 0.368767i
\(546\) 1.64088 0.760768i 0.0702230 0.0325579i
\(547\) 3.59795 11.0733i 0.153837 0.473462i −0.844204 0.536022i \(-0.819926\pi\)
0.998041 + 0.0625598i \(0.0199264\pi\)
\(548\) −7.41366 + 3.30078i −0.316696 + 0.141002i
\(549\) 2.88242 4.99249i 0.123019 0.213074i
\(550\) 4.49171 + 4.54393i 0.191527 + 0.193754i
\(551\) 18.9200 0.806019
\(552\) −1.27819 + 12.1612i −0.0544036 + 0.517616i
\(553\) −11.9708 + 2.54448i −0.509052 + 0.108202i
\(554\) −2.56092 7.88170i −0.108803 0.334861i
\(555\) −8.69126 3.86960i −0.368923 0.164255i
\(556\) 0.251593 + 2.39375i 0.0106699 + 0.101518i
\(557\) 8.54128 + 1.81550i 0.361906 + 0.0769254i 0.385276 0.922801i \(-0.374106\pi\)
−0.0233702 + 0.999727i \(0.507440\pi\)
\(558\) 0.549162 1.69015i 0.0232479 0.0715497i
\(559\) 7.62609 + 12.7553i 0.322549 + 0.539494i
\(560\) −2.75277 −0.116326
\(561\) 6.69943 + 4.40591i 0.282850 + 0.186017i
\(562\) 7.39927 12.8159i 0.312119 0.540607i
\(563\) 0.550777 5.24030i 0.0232125 0.220852i −0.976766 0.214308i \(-0.931250\pi\)
0.999979 0.00654399i \(-0.00208303\pi\)
\(564\) 5.47352 16.8458i 0.230477 0.709335i
\(565\) 5.09569 5.65933i 0.214377 0.238090i
\(566\) 11.5650 + 5.14907i 0.486113 + 0.216431i
\(567\) −0.868438 + 0.630957i −0.0364710 + 0.0264977i
\(568\) −7.18983 + 7.98511i −0.301678 + 0.335048i
\(569\) −23.4489 26.0426i −0.983027 1.09176i −0.995773 0.0918436i \(-0.970724\pi\)
0.0127462 0.999919i \(-0.495943\pi\)
\(570\) 2.10856 0.938792i 0.0883179 0.0393217i
\(571\) −16.1379 −0.675350 −0.337675 0.941263i \(-0.609640\pi\)
−0.337675 + 0.941263i \(0.609640\pi\)
\(572\) 0.913327 21.2855i 0.0381881 0.889993i
\(573\) −16.6286 −0.694669
\(574\) 0.927320 0.412869i 0.0387056 0.0172328i
\(575\) 19.0872 + 21.1985i 0.795993 + 0.884039i
\(576\) −2.15823 + 2.39696i −0.0899262 + 0.0998732i
\(577\) −5.07503 + 3.68723i −0.211276 + 0.153501i −0.688391 0.725340i \(-0.741683\pi\)
0.477115 + 0.878841i \(0.341683\pi\)
\(578\) 4.76218 + 2.12026i 0.198080 + 0.0881911i
\(579\) 5.00329 5.55671i 0.207929 0.230929i
\(580\) −1.85079 + 5.69616i −0.0768500 + 0.236520i
\(581\) −1.85018 + 17.6033i −0.0767585 + 0.730308i
\(582\) −2.16085 + 3.74270i −0.0895701 + 0.155140i
\(583\) 33.0038 1.53849i 1.36688 0.0637175i
\(584\) 7.84741 0.324728
\(585\) 1.73326 + 2.89904i 0.0716616 + 0.119861i
\(586\) 2.70047 8.31119i 0.111555 0.343332i
\(587\) 22.9873 + 4.88611i 0.948789 + 0.201671i 0.656217 0.754572i \(-0.272155\pi\)
0.292572 + 0.956243i \(0.405489\pi\)
\(588\) 1.08902 + 10.3613i 0.0449105 + 0.427294i
\(589\) 18.3169 + 8.15521i 0.754735 + 0.336030i
\(590\) −0.0849524 0.261457i −0.00349744 0.0107640i
\(591\) 12.7480 2.70967i 0.524382 0.111461i
\(592\) 2.90592 27.6480i 0.119433 1.13633i
\(593\) 9.11249 0.374205 0.187103 0.982340i \(-0.440090\pi\)
0.187103 + 0.982340i \(0.440090\pi\)
\(594\) −0.233606 1.53218i −0.00958498 0.0628661i
\(595\) 1.21559 2.10546i 0.0498343 0.0863155i
\(596\) −22.0785 + 9.82998i −0.904370 + 0.402652i
\(597\) 4.95429 15.2477i 0.202766 0.624048i
\(598\) −1.04165 + 11.6122i −0.0425964 + 0.474859i
\(599\) 33.9571 24.6713i 1.38745 1.00804i 0.391309 0.920260i \(-0.372023\pi\)
0.996140 0.0877808i \(-0.0279775\pi\)
\(600\) −0.761496 7.24515i −0.0310879 0.295782i
\(601\) 2.40371 + 0.510924i 0.0980492 + 0.0208410i 0.256675 0.966498i \(-0.417373\pi\)
−0.158626 + 0.987339i \(0.550706\pi\)
\(602\) −2.02242 + 0.429879i −0.0824278 + 0.0175206i
\(603\) 7.12864 + 5.17926i 0.290301 + 0.210916i
\(604\) 7.28348 + 12.6154i 0.296361 + 0.513312i
\(605\) −4.08226 9.46168i −0.165967 0.384672i
\(606\) 6.18753 0.251351
\(607\) −4.38454 + 41.7161i −0.177963 + 1.69320i 0.432879 + 0.901452i \(0.357498\pi\)
−0.610842 + 0.791753i \(0.709169\pi\)
\(608\) 16.9819 + 18.8603i 0.688708 + 0.764888i
\(609\) −3.76790 0.800892i −0.152683 0.0324538i
\(610\) 2.04171 1.48339i 0.0826663 0.0600606i
\(611\) 10.5556 34.2566i 0.427036 1.38587i
\(612\) −1.33103 4.09649i −0.0538038 0.165591i
\(613\) 31.1350 + 34.5789i 1.25753 + 1.39663i 0.882972 + 0.469426i \(0.155539\pi\)
0.374559 + 0.927203i \(0.377794\pi\)
\(614\) 9.31339 4.14659i 0.375858 0.167343i
\(615\) 0.947829 + 1.64169i 0.0382202 + 0.0661993i
\(616\) 5.86056 + 2.28860i 0.236129 + 0.0922103i
\(617\) 16.6736 + 28.8795i 0.671252 + 1.16264i 0.977549 + 0.210707i \(0.0675767\pi\)
−0.306297 + 0.951936i \(0.599090\pi\)
\(618\) −0.751368 + 7.14879i −0.0302245 + 0.287567i
\(619\) 1.32065 4.06456i 0.0530816 0.163368i −0.921001 0.389559i \(-0.872627\pi\)
0.974083 + 0.226191i \(0.0726273\pi\)
\(620\) −4.24705 + 4.71682i −0.170566 + 0.189432i
\(621\) −0.723295 6.88169i −0.0290248 0.276153i
\(622\) 1.23425 + 11.7431i 0.0494889 + 0.470855i
\(623\) 3.40918 + 10.4924i 0.136586 + 0.420368i
\(624\) −6.49161 + 7.43469i −0.259872 + 0.297626i
\(625\) −10.1987 7.40981i −0.407949 0.296393i
\(626\) −0.797739 + 1.38172i −0.0318841 + 0.0552248i
\(627\) 17.4676 0.814256i 0.697587 0.0325183i
\(628\) 15.3438 + 26.5762i 0.612284 + 1.06051i
\(629\) 19.8635 + 14.4316i 0.792008 + 0.575427i
\(630\) −0.459658 + 0.0977033i −0.0183132 + 0.00389259i
\(631\) 1.19035 1.32201i 0.0473869 0.0526285i −0.718985 0.695025i \(-0.755393\pi\)
0.766372 + 0.642397i \(0.222060\pi\)
\(632\) −16.2997 + 11.8424i −0.648365 + 0.471065i
\(633\) 0.263562 + 0.117345i 0.0104756 + 0.00466405i
\(634\) 11.1710 + 2.37447i 0.443657 + 0.0943023i
\(635\) −7.59797 8.43841i −0.301516 0.334868i
\(636\) −14.3586 10.4322i −0.569357 0.413662i
\(637\) 2.52353 + 20.9326i 0.0999860 + 0.829382i
\(638\) 3.52506 4.30202i 0.139558 0.170319i
\(639\) 3.04016 5.26570i 0.120267 0.208308i
\(640\) −9.52893 + 4.24255i −0.376664 + 0.167702i
\(641\) 8.72036 1.85357i 0.344433 0.0732116i −0.0324471 0.999473i \(-0.510330\pi\)
0.376881 + 0.926262i \(0.376997\pi\)
\(642\) −0.927661 2.85505i −0.0366118 0.112680i
\(643\) −6.04002 2.68919i −0.238195 0.106051i 0.284168 0.958775i \(-0.408283\pi\)
−0.522363 + 0.852723i \(0.674949\pi\)
\(644\) 12.0895 + 5.38259i 0.476393 + 0.212104i
\(645\) −1.19319 3.67227i −0.0469820 0.144596i
\(646\) −5.82646 + 1.23845i −0.229239 + 0.0487263i
\(647\) −6.20033 + 2.76056i −0.243760 + 0.108529i −0.524981 0.851114i \(-0.675927\pi\)
0.281220 + 0.959643i \(0.409261\pi\)
\(648\) −0.883592 + 1.53043i −0.0347108 + 0.0601208i
\(649\) 0.121020 2.07925i 0.00475045 0.0816176i
\(650\) −0.831339 6.89594i −0.0326078 0.270481i
\(651\) −3.30258 2.39947i −0.129438 0.0940425i
\(652\) −12.0996 13.4380i −0.473858 0.526272i
\(653\) −28.4059 6.03786i −1.11161 0.236280i −0.384719 0.923034i \(-0.625702\pi\)
−0.726890 + 0.686754i \(0.759035\pi\)
\(654\) −6.67452 2.97169i −0.260994 0.116202i
\(655\) −5.51445 + 4.00648i −0.215467 + 0.156546i
\(656\) −3.70653 + 4.11652i −0.144716 + 0.160723i
\(657\) −4.34359 + 0.923258i −0.169460 + 0.0360197i
\(658\) 4.03470 + 2.93138i 0.157289 + 0.114277i
\(659\) −23.8671 41.3390i −0.929731 1.61034i −0.783771 0.621050i \(-0.786706\pi\)
−0.145960 0.989291i \(-0.546627\pi\)
\(660\) −1.46357 + 5.33853i −0.0569693 + 0.207802i
\(661\) 13.5521 23.4730i 0.527117 0.912994i −0.472383 0.881393i \(-0.656606\pi\)
0.999501 0.0316005i \(-0.0100604\pi\)
\(662\) −3.09121 2.24589i −0.120143 0.0872891i
\(663\) −2.81983 8.24820i −0.109513 0.320334i
\(664\) 9.00457 + 27.7132i 0.349445 + 1.07548i
\(665\) −0.554202 5.27288i −0.0214910 0.204474i
\(666\) −0.496072 4.71981i −0.0192224 0.182889i
\(667\) 16.6152 18.4531i 0.643343 0.714505i
\(668\) −4.01391 + 12.3536i −0.155303 + 0.477973i
\(669\) −1.47135 + 13.9989i −0.0568856 + 0.541230i
\(670\) 1.92872 + 3.34063i 0.0745128 + 0.129060i
\(671\) 18.4966 4.84177i 0.714053 0.186914i
\(672\) −2.58357 4.47487i −0.0996634 0.172622i
\(673\) 28.2318 12.5696i 1.08826 0.484523i 0.217411 0.976080i \(-0.430239\pi\)
0.870845 + 0.491557i \(0.163572\pi\)
\(674\) −0.388993 0.432020i −0.0149834 0.0166408i
\(675\) 1.27390 + 3.92065i 0.0490322 + 0.150906i
\(676\) −14.9655 + 17.6768i −0.575596 + 0.679878i
\(677\) 4.50395 3.27231i 0.173101 0.125765i −0.497862 0.867257i \(-0.665881\pi\)
0.670962 + 0.741491i \(0.265881\pi\)
\(678\) 3.71582 + 0.789821i 0.142705 + 0.0303329i
\(679\) 6.64268 + 7.37744i 0.254922 + 0.283120i
\(680\) 0.418362 3.98045i 0.0160434 0.152643i
\(681\) 13.8415 0.530407
\(682\) 5.26702 2.64546i 0.201685 0.101300i
\(683\) 5.57532 + 9.65673i 0.213334 + 0.369505i 0.952756 0.303737i \(-0.0982346\pi\)
−0.739422 + 0.673242i \(0.764901\pi\)
\(684\) −7.59942 5.52130i −0.290571 0.211112i
\(685\) 4.17385 0.887179i 0.159475 0.0338974i
\(686\) −6.30398 1.33995i −0.240687 0.0511596i
\(687\) 1.03620 + 9.85877i 0.0395335 + 0.376136i
\(688\) 9.12816 6.63199i 0.348008 0.252842i
\(689\) −29.3769 20.6663i −1.11917 0.787322i
\(690\) 0.936078 2.88095i 0.0356359 0.109676i
\(691\) −32.3138 + 14.3870i −1.22927 + 0.547308i −0.915549 0.402205i \(-0.868244\pi\)
−0.313725 + 0.949514i \(0.601577\pi\)
\(692\) 19.9079 34.4816i 0.756786 1.31079i
\(693\) −3.51312 0.577251i −0.133452 0.0219280i
\(694\) −6.79986 −0.258119
\(695\) 0.132291 1.25866i 0.00501807 0.0477437i
\(696\) −6.20298 + 1.31848i −0.235123 + 0.0499770i
\(697\) −1.51177 4.65276i −0.0572625 0.176236i
\(698\) 4.19555 + 1.86798i 0.158804 + 0.0707040i
\(699\) −1.51072 14.3736i −0.0571408 0.543659i
\(700\) −7.71175 1.63918i −0.291477 0.0619553i
\(701\) −13.2487 + 40.7754i −0.500397 + 1.54006i 0.307976 + 0.951394i \(0.400348\pi\)
−0.808373 + 0.588670i \(0.799652\pi\)
\(702\) −0.820094 + 1.47185i −0.0309524 + 0.0555515i
\(703\) 53.5444 2.01947
\(704\) −10.6859 + 0.498127i −0.402740 + 0.0187739i
\(705\) −4.65676 + 8.06575i −0.175384 + 0.303774i
\(706\) 0.123233 1.17249i 0.00463795 0.0441272i
\(707\) 4.39215 13.5176i 0.165184 0.508383i
\(708\) −0.748637 + 0.831445i −0.0281355 + 0.0312476i
\(709\) −12.9021 5.74438i −0.484548 0.215735i 0.149898 0.988701i \(-0.452105\pi\)
−0.634447 + 0.772967i \(0.718772\pi\)
\(710\) 2.15344 1.56457i 0.0808171 0.0587171i
\(711\) 7.62869 8.47252i 0.286098 0.317744i
\(712\) 12.1529 + 13.4971i 0.455448 + 0.505827i
\(713\) 24.0395 10.7031i 0.900287 0.400834i
\(714\) 1.21276 0.0453864
\(715\) −2.79673 + 10.8477i −0.104592 + 0.405683i
\(716\) 9.05736 0.338489
\(717\) −15.0647 + 6.70725i −0.562602 + 0.250487i
\(718\) −6.07093 6.74245i −0.226565 0.251626i
\(719\) −4.53328 + 5.03472i −0.169063 + 0.187763i −0.821722 0.569888i \(-0.806987\pi\)
0.652659 + 0.757651i \(0.273653\pi\)
\(720\) 2.07465 1.50732i 0.0773178 0.0561747i
\(721\) 15.0843 + 6.71598i 0.561770 + 0.250116i
\(722\) −2.75106 + 3.05536i −0.102384 + 0.113709i
\(723\) 5.83313 17.9525i 0.216936 0.667662i
\(724\) −3.93712 + 37.4592i −0.146322 + 1.39216i
\(725\) −7.39666 + 12.8114i −0.274705 + 0.475803i
\(726\) 3.06930 4.12347i 0.113913 0.153036i
\(727\) −27.0608 −1.00363 −0.501815 0.864975i \(-0.667334\pi\)
−0.501815 + 0.864975i \(0.667334\pi\)
\(728\) −3.50980 5.87046i −0.130082 0.217574i
\(729\) 0.309017 0.951057i 0.0114451 0.0352243i
\(730\) −1.90151 0.404178i −0.0703779 0.0149593i
\(731\) 1.04162 + 9.91032i 0.0385256 + 0.366546i
\(732\) −9.38281 4.17749i −0.346798 0.154405i
\(733\) 7.38622 + 22.7324i 0.272816 + 0.839642i 0.989789 + 0.142541i \(0.0455271\pi\)
−0.716973 + 0.697101i \(0.754473\pi\)
\(734\) 12.4571 2.64783i 0.459799 0.0977333i
\(735\) 0.572619 5.44811i 0.0211214 0.200956i
\(736\) 33.3081 1.22775
\(737\) 4.40484 + 28.8905i 0.162254 + 1.06420i
\(738\) −0.472812 + 0.818934i −0.0174044 + 0.0301454i
\(739\) −36.1724 + 16.1050i −1.33062 + 0.592432i −0.944043 0.329823i \(-0.893011\pi\)
−0.386581 + 0.922255i \(0.626344\pi\)
\(740\) −5.23782 + 16.1204i −0.192546 + 0.592596i
\(741\) −15.5480 10.9378i −0.571169 0.401810i
\(742\) 4.04280 2.93726i 0.148416 0.107830i
\(743\) 3.24580 + 30.8817i 0.119077 + 1.13294i 0.876965 + 0.480555i \(0.159565\pi\)
−0.757888 + 0.652385i \(0.773769\pi\)
\(744\) −6.57357 1.39725i −0.240999 0.0512258i
\(745\) 12.4301 2.64209i 0.455402 0.0967987i
\(746\) 9.78437 + 7.10876i 0.358231 + 0.260270i
\(747\) −8.24459 14.2800i −0.301654 0.522479i
\(748\) 6.55902 12.6910i 0.239822 0.464028i
\(749\) −6.89580 −0.251967
\(750\) −0.417439 + 3.97167i −0.0152427 + 0.145025i
\(751\) 24.4314 + 27.1338i 0.891514 + 0.990127i 0.999992 0.00397213i \(-0.00126437\pi\)
−0.108478 + 0.994099i \(0.534598\pi\)
\(752\) −26.6205 5.65835i −0.970748 0.206339i
\(753\) −5.94655 + 4.32042i −0.216704 + 0.157445i
\(754\) −5.89430 + 1.34717i −0.214658 + 0.0490611i
\(755\) −2.36691 7.28459i −0.0861406 0.265113i
\(756\) 1.27970 + 1.42125i 0.0465422 + 0.0516904i
\(757\) 37.3589 16.6333i 1.35783 0.604547i 0.406767 0.913532i \(-0.366656\pi\)
0.951067 + 0.308985i \(0.0999894\pi\)
\(758\) 0.337506 + 0.584577i 0.0122588 + 0.0212328i
\(759\) 14.5455 17.7515i 0.527969 0.644339i
\(760\) −4.36420 7.55901i −0.158306 0.274194i
\(761\) 3.46514 32.9686i 0.125611 1.19511i −0.732179 0.681112i \(-0.761497\pi\)
0.857791 0.513999i \(-0.171837\pi\)
\(762\) 1.75036 5.38705i 0.0634088 0.195152i
\(763\) −11.2300 + 12.4721i −0.406552 + 0.451522i
\(764\) 3.09675 + 29.4636i 0.112036 + 1.06595i
\(765\) 0.236739 + 2.25242i 0.00855933 + 0.0814365i
\(766\) −0.515525 1.58662i −0.0186267 0.0573270i
\(767\) −1.48920 + 1.70555i −0.0537720 + 0.0615839i
\(768\) 1.00935 + 0.733336i 0.0364218 + 0.0264620i
\(769\) 10.1408 17.5643i 0.365686 0.633386i −0.623200 0.782062i \(-0.714168\pi\)
0.988886 + 0.148676i \(0.0475012\pi\)
\(770\) −1.30220 0.856397i −0.0469281 0.0308624i
\(771\) −8.22825 14.2518i −0.296333 0.513264i
\(772\) −10.7775 7.83031i −0.387891 0.281819i
\(773\) −36.7099 + 7.80293i −1.32036 + 0.280652i −0.813596 0.581431i \(-0.802493\pi\)
−0.506767 + 0.862083i \(0.669160\pi\)
\(774\) 1.28884 1.43140i 0.0463262 0.0514505i
\(775\) −12.6831 + 9.21478i −0.455589 + 0.331005i
\(776\) 14.9301 + 6.64731i 0.535959 + 0.238625i
\(777\) −10.6633 2.26656i −0.382545 0.0813124i
\(778\) −1.87230 2.07940i −0.0671253 0.0745502i
\(779\) −8.63136 6.27105i −0.309251 0.224684i
\(780\) 4.81392 3.61099i 0.172366 0.129294i
\(781\) 19.5088 5.10673i 0.698080 0.182733i
\(782\) −3.90881 + 6.77026i −0.139779 + 0.242104i
\(783\) 3.27827 1.45958i 0.117156 0.0521611i
\(784\) 15.6579 3.32818i 0.559209 0.118864i
\(785\) −4.98626 15.3461i −0.177967 0.547726i
\(786\) −3.10622 1.38298i −0.110795 0.0493293i
\(787\) −16.9842 7.56187i −0.605423 0.269552i 0.0810466 0.996710i \(-0.474174\pi\)
−0.686469 + 0.727159i \(0.740840\pi\)
\(788\) −7.17522 22.0831i −0.255607 0.786677i
\(789\) 18.7219 3.97946i 0.666517 0.141673i
\(790\) 4.55951 2.03003i 0.162220 0.0722251i
\(791\) 4.36312 7.55715i 0.155135 0.268701i
\(792\) −5.67004 + 1.48422i −0.201476 + 0.0527396i
\(793\) −19.1152 8.16352i −0.678800 0.289895i
\(794\) 7.96010 + 5.78335i 0.282493 + 0.205243i
\(795\) 6.24447 + 6.93519i 0.221469 + 0.245966i
\(796\) −27.9395 5.93873i −0.990291 0.210493i
\(797\) 3.90073 + 1.73672i 0.138171 + 0.0615177i 0.474657 0.880171i \(-0.342572\pi\)
−0.336486 + 0.941688i \(0.609239\pi\)
\(798\) 2.13968 1.55457i 0.0757439 0.0550312i
\(799\) 16.0831 17.8621i 0.568979 0.631915i
\(800\) −19.4100 + 4.12572i −0.686246 + 0.145866i
\(801\) −8.31465 6.04095i −0.293784 0.213446i
\(802\) −5.57562 9.65726i −0.196882 0.341010i
\(803\) −12.3053 8.09263i −0.434245 0.285583i
\(804\) 7.84937 13.5955i 0.276826 0.479477i
\(805\) −5.62944 4.09003i −0.198412 0.144155i
\(806\) −6.28710 1.23643i −0.221453 0.0435514i
\(807\) 1.19492 + 3.67760i 0.0420633 + 0.129458i
\(808\) −2.44585 23.2707i −0.0860447 0.818661i
\(809\) 3.12246 + 29.7082i 0.109780 + 1.04449i 0.901256 + 0.433286i \(0.142646\pi\)
−0.791477 + 0.611200i \(0.790687\pi\)
\(810\) 0.292927 0.325329i 0.0102924 0.0114309i
\(811\) −10.6181 + 32.6791i −0.372851 + 1.14752i 0.572066 + 0.820208i \(0.306142\pi\)
−0.944917 + 0.327310i \(0.893858\pi\)
\(812\) −0.717374 + 6.82536i −0.0251749 + 0.239523i
\(813\) 2.30091 + 3.98529i 0.0806963 + 0.139770i
\(814\) 9.97607 12.1749i 0.349661 0.426730i
\(815\) 4.75402 + 8.23420i 0.166526 + 0.288431i
\(816\) −6.04592 + 2.69182i −0.211650 + 0.0942325i
\(817\) 14.5412 + 16.1497i 0.508733 + 0.565005i
\(818\) −1.34183 4.12972i −0.0469159 0.144392i
\(819\) 2.63336 + 2.83640i 0.0920171 + 0.0991120i
\(820\) 2.73233 1.98516i 0.0954172 0.0693246i
\(821\) 3.42699 + 0.728429i 0.119603 + 0.0254224i 0.267324 0.963607i \(-0.413861\pi\)
−0.147721 + 0.989029i \(0.547194\pi\)
\(822\) 1.42430 + 1.58184i 0.0496781 + 0.0551732i
\(823\) −0.522237 + 4.96875i −0.0182040 + 0.173200i −0.999846 0.0175315i \(-0.994419\pi\)
0.981642 + 0.190731i \(0.0610859\pi\)
\(824\) 27.1829 0.946963
\(825\) −6.27747 + 12.1462i −0.218553 + 0.422877i
\(826\) −0.157507 0.272810i −0.00548036 0.00949226i
\(827\) −39.2481 28.5154i −1.36479 0.991578i −0.998124 0.0612247i \(-0.980499\pi\)
−0.366665 0.930353i \(-0.619501\pi\)
\(828\) −12.0587 + 2.56316i −0.419069 + 0.0890759i
\(829\) −39.4834 8.39246i −1.37132 0.291482i −0.537379 0.843341i \(-0.680585\pi\)
−0.833938 + 0.551859i \(0.813919\pi\)
\(830\) −0.754540 7.17897i −0.0261905 0.249186i
\(831\) 14.3472 10.4239i 0.497699 0.361600i
\(832\) 9.51159 + 6.69128i 0.329755 + 0.231978i
\(833\) −4.36876 + 13.4457i −0.151369 + 0.465865i
\(834\) 0.576743 0.256783i 0.0199710 0.00889166i
\(835\) 3.41496 5.91488i 0.118179 0.204693i
\(836\) −4.69574 30.7985i −0.162405 1.06519i
\(837\) 3.80290 0.131447
\(838\) 0.569693 5.42026i 0.0196797 0.187240i
\(839\) −20.1273 + 4.27818i −0.694870 + 0.147699i −0.541789 0.840515i \(-0.682253\pi\)
−0.153081 + 0.988214i \(0.548919\pi\)
\(840\) 0.549150 + 1.69011i 0.0189475 + 0.0583143i
\(841\) −14.7287 6.55765i −0.507887 0.226126i
\(842\) −1.75550 16.7025i −0.0604986 0.575606i
\(843\) 30.9756 + 6.58407i 1.06686 + 0.226767i
\(844\) 0.158836 0.488848i 0.00546738 0.0168269i
\(845\) 9.62954 7.45550i 0.331266 0.256477i
\(846\) −4.64593 −0.159730
\(847\) −6.82967 9.63239i −0.234670 0.330973i
\(848\) −13.6349 + 23.6163i −0.468224 + 0.810988i
\(849\) −2.83169 + 26.9418i −0.0971835 + 0.924639i
\(850\) 1.43922 4.42946i 0.0493648 0.151929i
\(851\) 47.0217 52.2229i 1.61188 1.79018i
\(852\) −9.89628 4.40611i −0.339041 0.150951i
\(853\) −35.4270 + 25.7392i −1.21300 + 0.881293i −0.995499 0.0947681i \(-0.969789\pi\)
−0.217496 + 0.976061i \(0.569789\pi\)
\(854\) 1.93501 2.14904i 0.0662145 0.0735387i
\(855\) 3.30494 + 3.67051i 0.113027 + 0.125529i
\(856\) −10.3709 + 4.61741i −0.354469 + 0.157820i
\(857\) 10.8476 0.370548 0.185274 0.982687i \(-0.440683\pi\)
0.185274 + 0.982687i \(0.440683\pi\)
\(858\) −5.38383 + 1.49742i −0.183801 + 0.0511212i
\(859\) −41.2734 −1.40823 −0.704115 0.710086i \(-0.748656\pi\)
−0.704115 + 0.710086i \(0.748656\pi\)
\(860\) −6.28455 + 2.79806i −0.214302 + 0.0954132i
\(861\) 1.45347 + 1.61424i 0.0495342 + 0.0550133i
\(862\) −0.844940 + 0.938401i −0.0287788 + 0.0319621i
\(863\) 19.4469 14.1290i 0.661979 0.480956i −0.205351 0.978688i \(-0.565834\pi\)
0.867331 + 0.497732i \(0.165834\pi\)
\(864\) 4.39743 + 1.95786i 0.149604 + 0.0666079i
\(865\) −14.0087 + 15.5582i −0.476309 + 0.528995i
\(866\) −3.92420 + 12.0774i −0.133350 + 0.410408i
\(867\) −1.16602 + 11.0939i −0.0396001 + 0.376770i
\(868\) −3.63649 + 6.29858i −0.123430 + 0.213788i
\(869\) 37.7715 1.76073i 1.28131 0.0597287i
\(870\) 1.57095 0.0532603
\(871\) 15.4635 27.7530i 0.523962 0.940374i
\(872\) −8.53789 + 26.2769i −0.289129 + 0.889849i
\(873\) −9.04597 1.92278i −0.306160 0.0650763i
\(874\) 1.78207 + 16.9553i 0.0602796 + 0.573522i
\(875\) 8.38043 + 3.73121i 0.283310 + 0.126138i
\(876\) 2.44480 + 7.52431i 0.0826020 + 0.254223i
\(877\) 39.5292 8.40220i 1.33481 0.283722i 0.515408 0.856945i \(-0.327640\pi\)
0.819399 + 0.573223i \(0.194307\pi\)
\(878\) 0.489661 4.65882i 0.0165253 0.157227i
\(879\) 18.7005 0.630752
\(880\) 8.39265 + 1.37902i 0.282916 + 0.0464869i
\(881\) −17.2816 + 29.9326i −0.582233 + 1.00846i 0.412982 + 0.910739i \(0.364487\pi\)
−0.995214 + 0.0977170i \(0.968846\pi\)
\(882\) 2.49643 1.11148i 0.0840592 0.0374256i
\(883\) −8.43026 + 25.9457i −0.283701 + 0.873142i 0.703084 + 0.711107i \(0.251806\pi\)
−0.986785 + 0.162035i \(0.948194\pi\)
\(884\) −14.0895 + 6.53241i −0.473883 + 0.219709i
\(885\) 0.475935 0.345787i 0.0159984 0.0116235i
\(886\) −1.87111 17.8024i −0.0628611 0.598084i
\(887\) 23.3049 + 4.95361i 0.782502 + 0.166326i 0.581806 0.813328i \(-0.302346\pi\)
0.200696 + 0.979654i \(0.435680\pi\)
\(888\) −17.5547 + 3.73136i −0.589097 + 0.125216i
\(889\) −10.5264 7.64788i −0.353044 0.256502i
\(890\) −2.24960 3.89642i −0.0754068 0.130608i
\(891\) 2.96379 1.48862i 0.0992905 0.0498705i
\(892\) 25.0782 0.839680
\(893\) 5.47911 52.1303i 0.183352 1.74447i
\(894\) 4.24168 + 4.71086i 0.141863 + 0.157555i
\(895\) −4.65839 0.990171i −0.155713 0.0330978i
\(896\) −9.66958 + 7.02536i −0.323038 + 0.234701i
\(897\) −24.3218 + 5.55887i −0.812081 + 0.185605i
\(898\) 0.580174 + 1.78559i 0.0193606 + 0.0595859i
\(899\) 9.13145 + 10.1415i 0.304551 + 0.338238i
\(900\) 6.70961 2.98731i 0.223654 0.0995770i
\(901\) −12.0420 20.8574i −0.401178 0.694861i
\(902\) −3.03405 + 0.794210i −0.101023 + 0.0264443i
\(903\) −2.21225 3.83173i −0.0736191 0.127512i
\(904\) 1.50163 14.2870i 0.0499434 0.475180i
\(905\) 6.12007 18.8356i 0.203438 0.626118i
\(906\) 2.55663 2.83942i 0.0849383 0.0943335i
\(907\) 2.23611 + 21.2752i 0.0742488 + 0.706430i 0.966809 + 0.255501i \(0.0822405\pi\)
−0.892560 + 0.450929i \(0.851093\pi\)
\(908\) −2.57770 24.5252i −0.0855441 0.813898i
\(909\) 4.09163 + 12.5927i 0.135711 + 0.417674i
\(910\) 0.548104 + 1.60324i 0.0181695 + 0.0531470i
\(911\) −30.1551 21.9090i −0.999084 0.725877i −0.0371924 0.999308i \(-0.511841\pi\)
−0.961892 + 0.273431i \(0.911841\pi\)
\(912\) −7.21638 + 12.4991i −0.238958 + 0.413888i
\(913\) 14.4594 52.7423i 0.478536 1.74551i
\(914\) 6.87841 + 11.9138i 0.227518 + 0.394072i
\(915\) 4.36908 + 3.17432i 0.144437 + 0.104940i
\(916\) 17.2754 3.67201i 0.570796 0.121326i
\(917\) −5.22626 + 5.80435i −0.172586 + 0.191677i
\(918\) −0.914011 + 0.664068i −0.0301668 + 0.0219175i
\(919\) −12.4190 5.52930i −0.409666 0.182395i 0.191548 0.981483i \(-0.438649\pi\)
−0.601214 + 0.799088i \(0.705316\pi\)
\(920\) −11.2050 2.38170i −0.369418 0.0785223i
\(921\) 14.5977 + 16.2124i 0.481011 + 0.534217i
\(922\) 1.26589 + 0.919721i 0.0416898 + 0.0302894i
\(923\) −20.1612 8.61027i −0.663615 0.283410i
\(924\) −0.368561 + 6.33226i −0.0121248 + 0.208316i
\(925\) −20.9328 + 36.2567i −0.688268 + 1.19211i
\(926\) −0.379684 + 0.169046i −0.0124772 + 0.00555520i
\(927\) −15.0459 + 3.19811i −0.494173 + 0.105040i
\(928\) 5.33784 + 16.4282i 0.175223 + 0.539281i
\(929\) −40.8712 18.1970i −1.34094 0.597025i −0.394201 0.919024i \(-0.628979\pi\)
−0.946740 + 0.321999i \(0.895645\pi\)
\(930\) 1.52088 + 0.677138i 0.0498715 + 0.0222042i
\(931\) 9.52742 + 29.3224i 0.312248 + 0.961002i
\(932\) −25.1867 + 5.35359i −0.825017 + 0.175363i
\(933\) −23.0832 + 10.2773i −0.755708 + 0.336463i
\(934\) −2.71317 + 4.69935i −0.0887776 + 0.153767i
\(935\) −4.76085 + 5.81019i −0.155696 + 0.190014i
\(936\) 5.85967 + 2.50249i 0.191529 + 0.0817965i
\(937\) 23.0481 + 16.7455i 0.752950 + 0.547050i 0.896740 0.442558i \(-0.145929\pi\)
−0.143790 + 0.989608i \(0.545929\pi\)
\(938\) 2.95764 + 3.28479i 0.0965702 + 0.107252i
\(939\) −3.33958 0.709849i −0.108983 0.0231651i
\(940\) 15.1586 + 6.74906i 0.494420 + 0.220130i
\(941\) 24.0767 17.4928i 0.784879 0.570248i −0.121560 0.992584i \(-0.538790\pi\)
0.906439 + 0.422336i \(0.138790\pi\)
\(942\) 5.38593 5.98169i 0.175483 0.194894i
\(943\) −13.6962 + 2.91122i −0.446009 + 0.0948022i
\(944\) 1.39074 + 1.01043i 0.0452646 + 0.0328866i
\(945\) −0.502802 0.870878i −0.0163561 0.0283297i
\(946\) 6.38133 0.297468i 0.207475 0.00967152i
\(947\) −7.90282 + 13.6881i −0.256807 + 0.444803i −0.965385 0.260830i \(-0.916004\pi\)
0.708578 + 0.705633i \(0.249337\pi\)
\(948\) −16.4328 11.9392i −0.533714 0.387766i
\(949\) 5.17937 + 15.1500i 0.168129 + 0.491791i
\(950\) −3.13866 9.65980i −0.101832 0.313405i
\(951\) 2.55458 + 24.3052i 0.0828378 + 0.788149i
\(952\) −0.479388 4.56108i −0.0155371 0.147825i
\(953\) −33.2299 + 36.9055i −1.07642 + 1.19549i −0.0966609 + 0.995317i \(0.530816\pi\)
−0.979761 + 0.200170i \(0.935850\pi\)
\(954\) −1.43855 + 4.42740i −0.0465748 + 0.143343i
\(955\) 1.62830 15.4923i 0.0526907 0.501318i
\(956\) 14.6898 + 25.4435i 0.475103 + 0.822903i
\(957\) 11.0864 + 4.32933i 0.358372 + 0.139947i
\(958\) 3.22198 + 5.58064i 0.104098 + 0.180302i
\(959\) 4.46682 1.98876i 0.144241 0.0642203i
\(960\) −2.02182 2.24546i −0.0652540 0.0724720i
\(961\) −5.11051 15.7285i −0.164855 0.507372i
\(962\) −16.6811 + 3.81255i −0.537821 + 0.122922i
\(963\) 5.19710 3.77591i 0.167474 0.121677i
\(964\) −32.8957 6.99220i −1.05950 0.225204i
\(965\) 4.68706 + 5.20551i 0.150882 + 0.167571i
\(966\) 0.362827 3.45207i 0.0116738 0.111069i
\(967\) −11.9835 −0.385364 −0.192682 0.981261i \(-0.561719\pi\)
−0.192682 + 0.981261i \(0.561719\pi\)
\(968\) −16.7212 9.91341i −0.537441 0.318629i
\(969\) −6.37334 11.0390i −0.204741 0.354622i
\(970\) −3.27535 2.37968i −0.105165 0.0764069i
\(971\) 43.5883 9.26499i 1.39882 0.297328i 0.554059 0.832477i \(-0.313078\pi\)
0.844757 + 0.535150i \(0.179745\pi\)
\(972\) −1.74269 0.370420i −0.0558968 0.0118812i
\(973\) −0.151588 1.44226i −0.00485969 0.0462368i
\(974\) 1.31367 0.954437i 0.0420927 0.0305821i
\(975\) 13.4847 6.25200i 0.431857 0.200224i
\(976\) −4.87654 + 15.0084i −0.156094 + 0.480408i
\(977\) 30.1420 13.4201i 0.964329 0.429347i 0.136694 0.990613i \(-0.456352\pi\)
0.827635 + 0.561267i \(0.189686\pi\)
\(978\) −2.37148 + 4.10752i −0.0758314 + 0.131344i
\(979\) −5.13768 33.6971i −0.164201 1.07696i
\(980\) −9.75994 −0.311770
\(981\) 1.63426 15.5489i 0.0521779 0.496440i
\(982\) 8.31799 1.76804i 0.265438 0.0564205i
\(983\) 11.7319 + 36.1071i 0.374189 + 1.15164i 0.944024 + 0.329877i \(0.107007\pi\)
−0.569835 + 0.821759i \(0.692993\pi\)
\(984\) 3.26683 + 1.45449i 0.104143 + 0.0463673i
\(985\) 1.27620 + 12.1422i 0.0406630 + 0.386882i
\(986\) −3.96563 0.842921i −0.126291 0.0268441i
\(987\) −3.29786 + 10.1498i −0.104972 + 0.323071i
\(988\) −16.4848 + 29.5858i −0.524450 + 0.941250i
\(989\) 28.5209 0.906913
\(990\) 1.45035 0.0676088i 0.0460953 0.00214875i
\(991\) 12.3086 21.3191i 0.390995 0.677223i −0.601586 0.798808i \(-0.705464\pi\)
0.992581 + 0.121585i \(0.0387978\pi\)
\(992\) −1.91346 + 18.2053i −0.0607523 + 0.578019i
\(993\) 2.52667 7.77630i 0.0801816 0.246774i
\(994\) 2.04090 2.26665i 0.0647334 0.0718937i
\(995\) 13.7207 + 6.10883i 0.434974 + 0.193663i
\(996\) −23.7669 + 17.2677i −0.753083 + 0.547147i
\(997\) 17.2879 19.2002i 0.547515 0.608077i −0.404347 0.914606i \(-0.632501\pi\)
0.951861 + 0.306529i \(0.0991677\pi\)
\(998\) 0.999777 + 1.11036i 0.0316474 + 0.0351480i
\(999\) 9.27763 4.13067i 0.293531 0.130689i
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 429.2.bg.a.334.7 yes 112
11.3 even 5 inner 429.2.bg.a.256.8 112
13.3 even 3 inner 429.2.bg.a.367.8 yes 112
143.3 even 15 inner 429.2.bg.a.289.7 yes 112
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
429.2.bg.a.256.8 112 11.3 even 5 inner
429.2.bg.a.289.7 yes 112 143.3 even 15 inner
429.2.bg.a.334.7 yes 112 1.1 even 1 trivial
429.2.bg.a.367.8 yes 112 13.3 even 3 inner