Properties

Label 72.2.n.b.61.4
Level $72$
Weight $2$
Character 72.61
Analytic conductor $0.575$
Analytic rank $0$
Dimension $16$
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] = [72,2,Mod(13,72)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(72, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("72.13");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 72 = 2^{3} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 72.n (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.574922894553\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - x^{15} + x^{14} + 2 x^{12} - 4 x^{11} - 8 x^{9} + 4 x^{8} - 16 x^{7} - 32 x^{5} + 32 x^{4} + 64 x^{2} - 128 x + 256 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 61.4
Root \(-1.12494 + 0.857038i\) of defining polynomial
Character \(\chi\) \(=\) 72.61
Dual form 72.2.n.b.13.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.179748 + 1.40274i) q^{2} +(0.986088 + 1.42395i) q^{3} +(-1.93538 - 0.504281i) q^{4} +(-1.19115 + 0.687709i) q^{5} +(-2.17468 + 1.12728i) q^{6} +(1.80469 - 3.12581i) q^{7} +(1.05526 - 2.62420i) q^{8} +(-1.05526 + 2.80828i) q^{9} +O(q^{10})\) \(q+(-0.179748 + 1.40274i) q^{2} +(0.986088 + 1.42395i) q^{3} +(-1.93538 - 0.504281i) q^{4} +(-1.19115 + 0.687709i) q^{5} +(-2.17468 + 1.12728i) q^{6} +(1.80469 - 3.12581i) q^{7} +(1.05526 - 2.62420i) q^{8} +(-1.05526 + 2.80828i) q^{9} +(-0.750573 - 1.79449i) q^{10} +(1.83294 + 1.05825i) q^{11} +(-1.19039 - 3.25315i) q^{12} +(-0.887751 + 0.512543i) q^{13} +(4.06032 + 3.09337i) q^{14} +(-2.15384 - 1.01799i) q^{15} +(3.49140 + 1.95195i) q^{16} +0.808822 q^{17} +(-3.74961 - 1.98504i) q^{18} -7.43122i q^{19} +(2.65212 - 0.730306i) q^{20} +(6.23057 - 0.512543i) q^{21} +(-1.81392 + 2.38093i) q^{22} +(-1.65498 - 2.86652i) q^{23} +(4.77731 - 1.08506i) q^{24} +(-1.55411 + 2.69180i) q^{25} +(-0.559395 - 1.33742i) q^{26} +(-5.03942 + 1.26658i) q^{27} +(-5.06904 + 5.13956i) q^{28} +(-7.71083 - 4.45185i) q^{29} +(1.81513 - 2.83830i) q^{30} +(3.26436 + 5.65403i) q^{31} +(-3.36566 + 4.54668i) q^{32} +(0.300550 + 3.65354i) q^{33} +(-0.145384 + 1.13457i) q^{34} +4.96439i q^{35} +(3.45849 - 4.90294i) q^{36} +4.01531i q^{37} +(10.4241 + 1.33575i) q^{38} +(-1.60524 - 0.758698i) q^{39} +(0.547718 + 3.85152i) q^{40} +(-3.45852 - 5.99034i) q^{41} +(-0.400967 + 8.83202i) q^{42} +(-0.245957 - 0.142003i) q^{43} +(-3.01378 - 2.97243i) q^{44} +(-0.674310 - 4.07078i) q^{45} +(4.31847 - 1.80627i) q^{46} +(-3.61351 + 6.25878i) q^{47} +(0.663349 + 6.89637i) q^{48} +(-3.01378 - 5.22003i) q^{49} +(-3.49656 - 2.66387i) q^{50} +(0.797570 + 1.15172i) q^{51} +(1.97660 - 0.544290i) q^{52} +3.86330i q^{53} +(-0.870856 - 7.29668i) q^{54} -2.91107 q^{55} +(-6.29834 - 8.03439i) q^{56} +(10.5817 - 7.32784i) q^{57} +(7.63082 - 10.0161i) q^{58} +(7.06904 - 4.08131i) q^{59} +(3.65514 + 3.05634i) q^{60} +(6.31237 + 3.64445i) q^{61} +(-8.51792 + 3.56275i) q^{62} +(6.87373 + 8.36660i) q^{63} +(-5.77286 - 5.53842i) q^{64} +(0.704961 - 1.22103i) q^{65} +(-5.17900 - 0.235123i) q^{66} +(-2.43973 + 1.40858i) q^{67} +(-1.56538 - 0.407874i) q^{68} +(2.44981 - 5.18325i) q^{69} +(-6.96377 - 0.892341i) q^{70} +4.69830 q^{71} +(6.25591 + 5.73267i) q^{72} +0.409922 q^{73} +(-5.63245 - 0.721745i) q^{74} +(-5.36548 + 0.441379i) q^{75} +(-3.74743 + 14.3822i) q^{76} +(6.61576 - 3.81961i) q^{77} +(1.35280 - 2.11536i) q^{78} +(-0.0456121 + 0.0790024i) q^{79} +(-5.50115 + 0.0760042i) q^{80} +(-6.77286 - 5.92692i) q^{81} +(9.02458 - 3.77467i) q^{82} +(-2.40891 - 1.39079i) q^{83} +(-12.3170 - 2.14999i) q^{84} +(-0.963426 + 0.556234i) q^{85} +(0.243405 - 0.319490i) q^{86} +(-1.26436 - 15.3697i) q^{87} +(4.71128 - 3.69328i) q^{88} +8.91934 q^{89} +(5.83147 - 0.214168i) q^{90} +3.69992i q^{91} +(1.75749 + 6.38238i) q^{92} +(-4.83210 + 10.2236i) q^{93} +(-8.12994 - 6.19383i) q^{94} +(5.11052 + 8.85168i) q^{95} +(-9.79308 - 0.309103i) q^{96} +(-2.76022 + 4.78084i) q^{97} +(7.86408 - 3.28928i) q^{98} +(-4.90608 + 4.03068i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + q^{2} - q^{4} - 7 q^{6} + 6 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + q^{2} - q^{4} - 7 q^{6} + 6 q^{7} - 2 q^{8} + 2 q^{9} - 16 q^{10} - 16 q^{12} + 16 q^{14} - 10 q^{15} - 9 q^{16} - 28 q^{17} + 4 q^{18} - 8 q^{20} + q^{22} - 10 q^{23} + 7 q^{24} + 2 q^{25} + 28 q^{26} + 4 q^{28} + 22 q^{30} - 10 q^{31} + 11 q^{32} + q^{34} + 27 q^{36} + 23 q^{38} + 2 q^{39} + 6 q^{40} - 8 q^{41} + 8 q^{42} + 18 q^{44} - 20 q^{46} + 6 q^{47} + 39 q^{48} + 18 q^{49} - 23 q^{50} - 8 q^{52} - 29 q^{54} - 4 q^{55} + 10 q^{56} + 10 q^{57} - 14 q^{58} + 6 q^{60} - 52 q^{62} + 2 q^{63} + 26 q^{64} - 14 q^{65} - 72 q^{66} - 39 q^{68} + 72 q^{71} - 77 q^{72} - 44 q^{73} - 38 q^{74} + 5 q^{76} + 10 q^{78} - 30 q^{79} - 96 q^{80} + 10 q^{81} + 38 q^{82} - 28 q^{84} + 7 q^{86} + 42 q^{87} + 31 q^{88} + 64 q^{89} + 64 q^{90} - 30 q^{92} - 12 q^{94} + 44 q^{95} - 26 q^{96} + 66 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(37\) \(55\) \(65\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.179748 + 1.40274i −0.127101 + 0.991890i
\(3\) 0.986088 + 1.42395i 0.569318 + 0.822117i
\(4\) −1.93538 0.504281i −0.967691 0.252141i
\(5\) −1.19115 + 0.687709i −0.532697 + 0.307553i −0.742114 0.670274i \(-0.766177\pi\)
0.209417 + 0.977826i \(0.432843\pi\)
\(6\) −2.17468 + 1.12728i −0.887811 + 0.460209i
\(7\) 1.80469 3.12581i 0.682107 1.18144i −0.292229 0.956348i \(-0.594397\pi\)
0.974337 0.225096i \(-0.0722696\pi\)
\(8\) 1.05526 2.62420i 0.373090 0.927795i
\(9\) −1.05526 + 2.80828i −0.351753 + 0.936093i
\(10\) −0.750573 1.79449i −0.237352 0.567467i
\(11\) 1.83294 + 1.05825i 0.552652 + 0.319074i 0.750191 0.661221i \(-0.229961\pi\)
−0.197539 + 0.980295i \(0.563295\pi\)
\(12\) −1.19039 3.25315i −0.343635 0.939103i
\(13\) −0.887751 + 0.512543i −0.246218 + 0.142154i −0.618031 0.786154i \(-0.712069\pi\)
0.371813 + 0.928307i \(0.378736\pi\)
\(14\) 4.06032 + 3.09337i 1.08517 + 0.826738i
\(15\) −2.15384 1.01799i −0.556119 0.262844i
\(16\) 3.49140 + 1.95195i 0.872850 + 0.487988i
\(17\) 0.808822 0.196168 0.0980841 0.995178i \(-0.468729\pi\)
0.0980841 + 0.995178i \(0.468729\pi\)
\(18\) −3.74961 1.98504i −0.883793 0.467879i
\(19\) 7.43122i 1.70484i −0.522858 0.852420i \(-0.675134\pi\)
0.522858 0.852420i \(-0.324866\pi\)
\(20\) 2.65212 0.730306i 0.593032 0.163301i
\(21\) 6.23057 0.512543i 1.35962 0.111846i
\(22\) −1.81392 + 2.38093i −0.386729 + 0.507615i
\(23\) −1.65498 2.86652i −0.345088 0.597710i 0.640282 0.768140i \(-0.278818\pi\)
−0.985370 + 0.170430i \(0.945484\pi\)
\(24\) 4.77731 1.08506i 0.975163 0.221487i
\(25\) −1.55411 + 2.69180i −0.310823 + 0.538361i
\(26\) −0.559395 1.33742i −0.109706 0.262289i
\(27\) −5.03942 + 1.26658i −0.969837 + 0.243753i
\(28\) −5.06904 + 5.13956i −0.957959 + 0.971286i
\(29\) −7.71083 4.45185i −1.43187 0.826688i −0.434603 0.900622i \(-0.643111\pi\)
−0.997263 + 0.0739344i \(0.976444\pi\)
\(30\) 1.81513 2.83830i 0.331395 0.518201i
\(31\) 3.26436 + 5.65403i 0.586296 + 1.01549i 0.994713 + 0.102698i \(0.0327476\pi\)
−0.408417 + 0.912796i \(0.633919\pi\)
\(32\) −3.36566 + 4.54668i −0.594971 + 0.803747i
\(33\) 0.300550 + 3.65354i 0.0523190 + 0.636000i
\(34\) −0.145384 + 1.13457i −0.0249332 + 0.194577i
\(35\) 4.96439i 0.839136i
\(36\) 3.45849 4.90294i 0.576415 0.817157i
\(37\) 4.01531i 0.660113i 0.943961 + 0.330057i \(0.107068\pi\)
−0.943961 + 0.330057i \(0.892932\pi\)
\(38\) 10.4241 + 1.33575i 1.69101 + 0.216687i
\(39\) −1.60524 0.758698i −0.257043 0.121489i
\(40\) 0.547718 + 3.85152i 0.0866018 + 0.608979i
\(41\) −3.45852 5.99034i −0.540131 0.935534i −0.998896 0.0469764i \(-0.985041\pi\)
0.458765 0.888557i \(-0.348292\pi\)
\(42\) −0.400967 + 8.83202i −0.0618705 + 1.36281i
\(43\) −0.245957 0.142003i −0.0375081 0.0216553i 0.481129 0.876650i \(-0.340227\pi\)
−0.518637 + 0.854995i \(0.673560\pi\)
\(44\) −3.01378 2.97243i −0.454345 0.448111i
\(45\) −0.674310 4.07078i −0.100520 0.606836i
\(46\) 4.31847 1.80627i 0.636724 0.266320i
\(47\) −3.61351 + 6.25878i −0.527084 + 0.912937i 0.472417 + 0.881375i \(0.343381\pi\)
−0.999502 + 0.0315619i \(0.989952\pi\)
\(48\) 0.663349 + 6.89637i 0.0957461 + 0.995406i
\(49\) −3.01378 5.22003i −0.430540 0.745718i
\(50\) −3.49656 2.66387i −0.494488 0.376728i
\(51\) 0.797570 + 1.15172i 0.111682 + 0.161273i
\(52\) 1.97660 0.544290i 0.274105 0.0754795i
\(53\) 3.86330i 0.530666i 0.964157 + 0.265333i \(0.0854818\pi\)
−0.964157 + 0.265333i \(0.914518\pi\)
\(54\) −0.870856 7.29668i −0.118508 0.992953i
\(55\) −2.91107 −0.392528
\(56\) −6.29834 8.03439i −0.841650 1.07364i
\(57\) 10.5817 7.32784i 1.40158 0.970597i
\(58\) 7.63082 10.0161i 1.00198 1.31518i
\(59\) 7.06904 4.08131i 0.920310 0.531341i 0.0365764 0.999331i \(-0.488355\pi\)
0.883734 + 0.467989i \(0.155021\pi\)
\(60\) 3.65514 + 3.05634i 0.471877 + 0.394572i
\(61\) 6.31237 + 3.64445i 0.808216 + 0.466624i 0.846336 0.532650i \(-0.178804\pi\)
−0.0381201 + 0.999273i \(0.512137\pi\)
\(62\) −8.51792 + 3.56275i −1.08178 + 0.452470i
\(63\) 6.87373 + 8.36660i 0.866008 + 1.05409i
\(64\) −5.77286 5.53842i −0.721607 0.692303i
\(65\) 0.704961 1.22103i 0.0874396 0.151450i
\(66\) −5.17900 0.235123i −0.637491 0.0289416i
\(67\) −2.43973 + 1.40858i −0.298061 + 0.172085i −0.641571 0.767063i \(-0.721717\pi\)
0.343511 + 0.939149i \(0.388384\pi\)
\(68\) −1.56538 0.407874i −0.189830 0.0494620i
\(69\) 2.44981 5.18325i 0.294923 0.623990i
\(70\) −6.96377 0.892341i −0.832330 0.106655i
\(71\) 4.69830 0.557586 0.278793 0.960351i \(-0.410066\pi\)
0.278793 + 0.960351i \(0.410066\pi\)
\(72\) 6.25591 + 5.73267i 0.737267 + 0.675602i
\(73\) 0.409922 0.0479777 0.0239889 0.999712i \(-0.492363\pi\)
0.0239889 + 0.999712i \(0.492363\pi\)
\(74\) −5.63245 0.721745i −0.654760 0.0839012i
\(75\) −5.36548 + 0.441379i −0.619552 + 0.0509660i
\(76\) −3.74743 + 14.3822i −0.429859 + 1.64976i
\(77\) 6.61576 3.81961i 0.753936 0.435285i
\(78\) 1.35280 2.11536i 0.153174 0.239517i
\(79\) −0.0456121 + 0.0790024i −0.00513176 + 0.00888847i −0.868580 0.495549i \(-0.834967\pi\)
0.863448 + 0.504438i \(0.168300\pi\)
\(80\) −5.50115 + 0.0760042i −0.615047 + 0.00849752i
\(81\) −6.77286 5.92692i −0.752540 0.658547i
\(82\) 9.02458 3.77467i 0.996598 0.416843i
\(83\) −2.40891 1.39079i −0.264412 0.152659i 0.361933 0.932204i \(-0.382117\pi\)
−0.626346 + 0.779545i \(0.715450\pi\)
\(84\) −12.3170 2.14999i −1.34389 0.234584i
\(85\) −0.963426 + 0.556234i −0.104498 + 0.0603321i
\(86\) 0.243405 0.319490i 0.0262470 0.0344515i
\(87\) −1.26436 15.3697i −0.135553 1.64781i
\(88\) 4.71128 3.69328i 0.502224 0.393705i
\(89\) 8.91934 0.945448 0.472724 0.881210i \(-0.343271\pi\)
0.472724 + 0.881210i \(0.343271\pi\)
\(90\) 5.83147 0.214168i 0.614691 0.0225753i
\(91\) 3.69992i 0.387857i
\(92\) 1.75749 + 6.38238i 0.183231 + 0.665409i
\(93\) −4.83210 + 10.2236i −0.501066 + 1.06014i
\(94\) −8.12994 6.19383i −0.838540 0.638845i
\(95\) 5.11052 + 8.85168i 0.524328 + 0.908163i
\(96\) −9.79308 0.309103i −0.999502 0.0315476i
\(97\) −2.76022 + 4.78084i −0.280258 + 0.485421i −0.971448 0.237252i \(-0.923753\pi\)
0.691190 + 0.722673i \(0.257087\pi\)
\(98\) 7.86408 3.28928i 0.794392 0.332267i
\(99\) −4.90608 + 4.03068i −0.493080 + 0.405099i
\(100\) 4.36523 4.42595i 0.436523 0.442595i
\(101\) 5.63193 + 3.25160i 0.560398 + 0.323546i 0.753305 0.657671i \(-0.228458\pi\)
−0.192907 + 0.981217i \(0.561792\pi\)
\(102\) −1.75893 + 0.911767i −0.174160 + 0.0902784i
\(103\) −1.50528 2.60723i −0.148320 0.256898i 0.782287 0.622918i \(-0.214053\pi\)
−0.930607 + 0.366021i \(0.880720\pi\)
\(104\) 0.408209 + 2.87050i 0.0400282 + 0.281476i
\(105\) −7.06904 + 4.89533i −0.689868 + 0.477735i
\(106\) −5.41923 0.694422i −0.526362 0.0674482i
\(107\) 0.447393i 0.0432511i 0.999766 + 0.0216256i \(0.00688417\pi\)
−0.999766 + 0.0216256i \(0.993116\pi\)
\(108\) 10.3919 + 0.0899786i 0.999963 + 0.00865820i
\(109\) 9.36497i 0.897002i 0.893782 + 0.448501i \(0.148042\pi\)
−0.893782 + 0.448501i \(0.851958\pi\)
\(110\) 0.523259 4.08348i 0.0498908 0.389345i
\(111\) −5.71760 + 3.95945i −0.542690 + 0.375815i
\(112\) 12.4023 7.39078i 1.17191 0.698363i
\(113\) 5.66349 + 9.80944i 0.532776 + 0.922795i 0.999267 + 0.0382692i \(0.0121844\pi\)
−0.466492 + 0.884526i \(0.654482\pi\)
\(114\) 8.37705 + 16.1606i 0.784583 + 1.51357i
\(115\) 3.94266 + 2.27629i 0.367655 + 0.212266i
\(116\) 12.6784 + 12.5045i 1.17716 + 1.16101i
\(117\) −0.502557 3.03392i −0.0464614 0.280486i
\(118\) 4.45439 + 10.6497i 0.410060 + 0.980381i
\(119\) 1.45967 2.52822i 0.133808 0.231762i
\(120\) −4.94427 + 4.57786i −0.451348 + 0.417900i
\(121\) −3.26022 5.64687i −0.296384 0.513351i
\(122\) −6.24686 + 8.19955i −0.565564 + 0.742353i
\(123\) 5.11952 10.8318i 0.461612 0.976667i
\(124\) −3.46655 12.5889i −0.311305 1.13051i
\(125\) 11.1522i 0.997483i
\(126\) −12.9717 + 8.13820i −1.15561 + 0.725008i
\(127\) −11.8341 −1.05011 −0.525053 0.851069i \(-0.675955\pi\)
−0.525053 + 0.851069i \(0.675955\pi\)
\(128\) 8.80665 7.10232i 0.778405 0.627762i
\(129\) −0.0403299 0.490258i −0.00355085 0.0431648i
\(130\) 1.58607 + 1.20836i 0.139108 + 0.105980i
\(131\) 2.40891 1.39079i 0.210468 0.121514i −0.391061 0.920365i \(-0.627892\pi\)
0.601529 + 0.798851i \(0.294559\pi\)
\(132\) 1.26073 7.22255i 0.109733 0.628643i
\(133\) −23.2286 13.4110i −2.01417 1.16288i
\(134\) −1.53734 3.67551i −0.132806 0.317516i
\(135\) 5.13166 4.97433i 0.441663 0.428123i
\(136\) 0.853517 2.12251i 0.0731885 0.182004i
\(137\) −8.17841 + 14.1654i −0.698729 + 1.21023i 0.270178 + 0.962810i \(0.412917\pi\)
−0.968907 + 0.247424i \(0.920416\pi\)
\(138\) 6.83042 + 4.36814i 0.581444 + 0.371841i
\(139\) 1.22979 0.710017i 0.104309 0.0602229i −0.446938 0.894565i \(-0.647486\pi\)
0.551247 + 0.834342i \(0.314152\pi\)
\(140\) 2.50345 9.60800i 0.211580 0.812024i
\(141\) −12.4754 + 1.02626i −1.05062 + 0.0864268i
\(142\) −0.844512 + 6.59052i −0.0708699 + 0.553064i
\(143\) −2.16959 −0.181430
\(144\) −9.16596 + 7.74501i −0.763830 + 0.645417i
\(145\) 12.2463 1.01700
\(146\) −0.0736827 + 0.575015i −0.00609802 + 0.0475886i
\(147\) 4.46119 9.43888i 0.367953 0.778506i
\(148\) 2.02485 7.77116i 0.166441 0.638785i
\(149\) −4.91390 + 2.83704i −0.402563 + 0.232420i −0.687589 0.726100i \(-0.741331\pi\)
0.285027 + 0.958520i \(0.407998\pi\)
\(150\) 0.345294 7.60573i 0.0281932 0.621006i
\(151\) 7.07318 12.2511i 0.575607 0.996981i −0.420368 0.907354i \(-0.638099\pi\)
0.995975 0.0896271i \(-0.0285675\pi\)
\(152\) −19.5010 7.84186i −1.58174 0.636059i
\(153\) −0.853517 + 2.27140i −0.0690027 + 0.183632i
\(154\) 4.16877 + 9.96679i 0.335929 + 0.803147i
\(155\) −7.77665 4.48985i −0.624636 0.360634i
\(156\) 2.72415 + 2.27786i 0.218106 + 0.182375i
\(157\) 18.6713 10.7799i 1.49013 0.860328i 0.490196 0.871612i \(-0.336925\pi\)
0.999936 + 0.0112838i \(0.00359181\pi\)
\(158\) −0.102622 0.0781826i −0.00816413 0.00621987i
\(159\) −5.50115 + 3.80956i −0.436269 + 0.302118i
\(160\) 0.882207 7.73036i 0.0697446 0.611139i
\(161\) −11.9469 −0.941548
\(162\) 9.53136 8.43523i 0.748855 0.662734i
\(163\) 14.9239i 1.16893i 0.811418 + 0.584466i \(0.198696\pi\)
−0.811418 + 0.584466i \(0.801304\pi\)
\(164\) 3.67275 + 13.3377i 0.286793 + 1.04150i
\(165\) −2.87057 4.14521i −0.223474 0.322704i
\(166\) 2.38391 3.12910i 0.185028 0.242865i
\(167\) −11.0234 19.0931i −0.853019 1.47747i −0.878471 0.477796i \(-0.841436\pi\)
0.0254524 0.999676i \(-0.491897\pi\)
\(168\) 5.22985 16.8911i 0.403492 1.30318i
\(169\) −5.97460 + 10.3483i −0.459585 + 0.796024i
\(170\) −0.607080 1.45142i −0.0465609 0.111319i
\(171\) 20.8689 + 7.84186i 1.59589 + 0.599682i
\(172\) 0.404411 + 0.398862i 0.0308361 + 0.0304130i
\(173\) 10.9052 + 6.29612i 0.829107 + 0.478685i 0.853547 0.521016i \(-0.174447\pi\)
−0.0244397 + 0.999701i \(0.507780\pi\)
\(174\) 21.7871 + 0.989117i 1.65167 + 0.0749847i
\(175\) 5.60937 + 9.71572i 0.424029 + 0.734439i
\(176\) 4.33388 + 7.27258i 0.326678 + 0.548192i
\(177\) 12.7823 + 6.04141i 0.960775 + 0.454100i
\(178\) −1.60324 + 12.5116i −0.120168 + 0.937780i
\(179\) 12.1116i 0.905264i −0.891697 0.452632i \(-0.850485\pi\)
0.891697 0.452632i \(-0.149515\pi\)
\(180\) −0.747773 + 8.21856i −0.0557357 + 0.612575i
\(181\) 17.6790i 1.31407i −0.753862 0.657033i \(-0.771811\pi\)
0.753862 0.657033i \(-0.228189\pi\)
\(182\) −5.19004 0.665054i −0.384711 0.0492970i
\(183\) 1.03505 + 12.5822i 0.0765129 + 0.930105i
\(184\) −9.26875 + 1.31809i −0.683301 + 0.0971711i
\(185\) −2.76137 4.78283i −0.203020 0.351640i
\(186\) −13.4726 8.61589i −0.987859 0.631748i
\(187\) 1.48252 + 0.855935i 0.108413 + 0.0625922i
\(188\) 10.1497 10.2909i 0.740243 0.750541i
\(189\) −5.13550 + 18.0380i −0.373553 + 1.31207i
\(190\) −13.3352 + 5.57768i −0.967440 + 0.404647i
\(191\) 9.72173 16.8385i 0.703440 1.21839i −0.263812 0.964574i \(-0.584980\pi\)
0.967252 0.253820i \(-0.0816870\pi\)
\(192\) 2.19388 13.6816i 0.158330 0.987386i
\(193\) 0.159120 + 0.275604i 0.0114537 + 0.0198384i 0.871695 0.490048i \(-0.163021\pi\)
−0.860242 + 0.509886i \(0.829687\pi\)
\(194\) −6.21015 4.73123i −0.445863 0.339682i
\(195\) 2.43384 0.200214i 0.174291 0.0143376i
\(196\) 3.20046 + 11.6225i 0.228604 + 0.830181i
\(197\) 24.5066i 1.74602i 0.487701 + 0.873011i \(0.337836\pi\)
−0.487701 + 0.873011i \(0.662164\pi\)
\(198\) −4.77215 7.60649i −0.339142 0.540569i
\(199\) −7.13579 −0.505843 −0.252921 0.967487i \(-0.581391\pi\)
−0.252921 + 0.967487i \(0.581391\pi\)
\(200\) 5.42384 + 6.91885i 0.383523 + 0.489237i
\(201\) −4.41154 2.08507i −0.311166 0.147069i
\(202\) −5.57349 + 7.31569i −0.392149 + 0.514730i
\(203\) −27.8313 + 16.0684i −1.95337 + 1.12778i
\(204\) −0.962811 2.63122i −0.0674102 0.184222i
\(205\) 8.23922 + 4.75692i 0.575452 + 0.332237i
\(206\) 3.92784 1.64288i 0.273666 0.114465i
\(207\) 9.79641 1.62274i 0.680898 0.112788i
\(208\) −4.09995 + 0.0566452i −0.284281 + 0.00392764i
\(209\) 7.86408 13.6210i 0.543970 0.942183i
\(210\) −5.59625 10.7960i −0.386178 0.744994i
\(211\) −7.00175 + 4.04246i −0.482020 + 0.278294i −0.721258 0.692667i \(-0.756436\pi\)
0.239238 + 0.970961i \(0.423102\pi\)
\(212\) 1.94819 7.47697i 0.133802 0.513520i
\(213\) 4.63294 + 6.69014i 0.317444 + 0.458401i
\(214\) −0.627578 0.0804181i −0.0429003 0.00549727i
\(215\) 0.390628 0.0266406
\(216\) −1.99415 + 14.5610i −0.135684 + 0.990752i
\(217\) 23.5646 1.59967
\(218\) −13.1367 1.68334i −0.889727 0.114010i
\(219\) 0.404219 + 0.583708i 0.0273146 + 0.0394433i
\(220\) 5.63403 + 1.46800i 0.379846 + 0.0989724i
\(221\) −0.718032 + 0.414556i −0.0483001 + 0.0278861i
\(222\) −4.52637 8.73203i −0.303790 0.586056i
\(223\) −2.11236 + 3.65872i −0.141454 + 0.245006i −0.928044 0.372469i \(-0.878511\pi\)
0.786590 + 0.617475i \(0.211844\pi\)
\(224\) 8.13808 + 18.7257i 0.543749 + 1.25117i
\(225\) −5.91934 7.20493i −0.394623 0.480329i
\(226\) −14.7781 + 6.18119i −0.983027 + 0.411167i
\(227\) 1.09451 + 0.631913i 0.0726449 + 0.0419415i 0.535882 0.844293i \(-0.319979\pi\)
−0.463238 + 0.886234i \(0.653312\pi\)
\(228\) −24.1749 + 8.84603i −1.60102 + 0.585842i
\(229\) −6.29196 + 3.63267i −0.415785 + 0.240053i −0.693272 0.720676i \(-0.743832\pi\)
0.277487 + 0.960729i \(0.410498\pi\)
\(230\) −3.90174 + 5.12138i −0.257273 + 0.337694i
\(231\) 11.9627 + 5.65403i 0.787085 + 0.372008i
\(232\) −19.8195 + 15.5369i −1.30121 + 1.02005i
\(233\) −5.91061 −0.387217 −0.193608 0.981079i \(-0.562019\pi\)
−0.193608 + 0.981079i \(0.562019\pi\)
\(234\) 4.34614 0.159618i 0.284116 0.0104345i
\(235\) 9.94017i 0.648425i
\(236\) −15.7394 + 4.33411i −1.02455 + 0.282126i
\(237\) −0.157473 + 0.0129541i −0.0102290 + 0.000841462i
\(238\) 3.28408 + 2.50199i 0.212875 + 0.162180i
\(239\) 5.96266 + 10.3276i 0.385692 + 0.668039i 0.991865 0.127294i \(-0.0406293\pi\)
−0.606173 + 0.795333i \(0.707296\pi\)
\(240\) −5.53284 7.75840i −0.357143 0.500803i
\(241\) 1.80170 3.12063i 0.116057 0.201017i −0.802145 0.597130i \(-0.796308\pi\)
0.918202 + 0.396113i \(0.129641\pi\)
\(242\) 8.50713 3.55824i 0.546859 0.228732i
\(243\) 1.76100 15.4887i 0.112968 0.993599i
\(244\) −10.3790 10.2366i −0.664448 0.655331i
\(245\) 7.17972 + 4.14521i 0.458695 + 0.264828i
\(246\) 14.2740 + 9.12837i 0.910075 + 0.582004i
\(247\) 3.80882 + 6.59707i 0.242350 + 0.419762i
\(248\) 18.2821 2.59986i 1.16091 0.165091i
\(249\) −0.394993 4.80161i −0.0250316 0.304289i
\(250\) 15.6437 + 2.00459i 0.989393 + 0.126781i
\(251\) 0.641516i 0.0404922i −0.999795 0.0202461i \(-0.993555\pi\)
0.999795 0.0202461i \(-0.00644497\pi\)
\(252\) −9.08416 19.6588i −0.572249 1.23839i
\(253\) 7.00554i 0.440434i
\(254\) 2.12716 16.6002i 0.133470 1.04159i
\(255\) −1.74207 0.823373i −0.109093 0.0515616i
\(256\) 8.37976 + 13.6301i 0.523735 + 0.851881i
\(257\) −1.99885 3.46212i −0.124685 0.215961i 0.796925 0.604079i \(-0.206459\pi\)
−0.921610 + 0.388118i \(0.873125\pi\)
\(258\) 0.694956 + 0.0315505i 0.0432661 + 0.00196425i
\(259\) 12.5511 + 7.24638i 0.779887 + 0.450268i
\(260\) −1.98011 + 2.00766i −0.122801 + 0.124510i
\(261\) 20.6390 16.9563i 1.27752 1.04957i
\(262\) 1.51792 + 3.62908i 0.0937774 + 0.224205i
\(263\) −5.64671 + 9.78039i −0.348191 + 0.603085i −0.985928 0.167169i \(-0.946537\pi\)
0.637737 + 0.770254i \(0.279871\pi\)
\(264\) 9.90478 + 3.06673i 0.609597 + 0.188744i
\(265\) −2.65683 4.60176i −0.163208 0.282684i
\(266\) 22.9875 30.1731i 1.40946 1.85003i
\(267\) 8.79526 + 12.7007i 0.538261 + 0.777269i
\(268\) 5.43213 1.49583i 0.331820 0.0913722i
\(269\) 24.2695i 1.47974i −0.672750 0.739870i \(-0.734887\pi\)
0.672750 0.739870i \(-0.265113\pi\)
\(270\) 6.05531 + 8.09253i 0.368515 + 0.492496i
\(271\) 12.2330 0.743102 0.371551 0.928413i \(-0.378826\pi\)
0.371551 + 0.928413i \(0.378826\pi\)
\(272\) 2.82392 + 1.57878i 0.171225 + 0.0957278i
\(273\) −5.26849 + 3.64845i −0.318864 + 0.220814i
\(274\) −18.4004 14.0184i −1.11161 0.846884i
\(275\) −5.69719 + 3.28928i −0.343554 + 0.198351i
\(276\) −7.35514 + 8.79617i −0.442727 + 0.529467i
\(277\) −10.9249 6.30750i −0.656414 0.378981i 0.134495 0.990914i \(-0.457059\pi\)
−0.790909 + 0.611933i \(0.790392\pi\)
\(278\) 0.774920 + 1.85270i 0.0464766 + 0.111117i
\(279\) −19.3228 + 3.20075i −1.15683 + 0.191624i
\(280\) 13.0276 + 5.23872i 0.778546 + 0.313073i
\(281\) 9.54364 16.5301i 0.569326 0.986101i −0.427307 0.904107i \(-0.640538\pi\)
0.996633 0.0819947i \(-0.0261291\pi\)
\(282\) 0.802853 17.6843i 0.0478092 1.05308i
\(283\) −1.01045 + 0.583382i −0.0600649 + 0.0346785i −0.529732 0.848165i \(-0.677707\pi\)
0.469667 + 0.882844i \(0.344374\pi\)
\(284\) −9.09301 2.36927i −0.539571 0.140590i
\(285\) −7.56491 + 16.0057i −0.448107 + 0.948093i
\(286\) 0.389980 3.04338i 0.0230600 0.179959i
\(287\) −24.9662 −1.47371
\(288\) −9.21670 14.2496i −0.543099 0.839669i
\(289\) −16.3458 −0.961518
\(290\) −2.20125 + 17.1784i −0.129262 + 1.00875i
\(291\) −9.52949 + 0.783921i −0.558629 + 0.0459543i
\(292\) −0.793355 0.206716i −0.0464276 0.0120971i
\(293\) 2.11446 1.22079i 0.123528 0.0713191i −0.436963 0.899480i \(-0.643946\pi\)
0.560491 + 0.828161i \(0.310612\pi\)
\(294\) 12.4384 + 7.95453i 0.725425 + 0.463918i
\(295\) −5.61351 + 9.72288i −0.326831 + 0.566088i
\(296\) 10.5370 + 4.23719i 0.612450 + 0.246282i
\(297\) −10.5773 3.01140i −0.613758 0.174739i
\(298\) −3.09638 7.40290i −0.179368 0.428839i
\(299\) 2.93843 + 1.69650i 0.169934 + 0.0981112i
\(300\) 10.6068 + 1.85148i 0.612386 + 0.106895i
\(301\) −0.887751 + 0.512543i −0.0511691 + 0.0295425i
\(302\) 15.9138 + 12.1240i 0.915735 + 0.697656i
\(303\) 0.923476 + 11.2260i 0.0530523 + 0.644914i
\(304\) 14.5054 25.9454i 0.831942 1.48807i
\(305\) −10.0253 −0.574046
\(306\) −3.03277 1.60555i −0.173372 0.0917829i
\(307\) 15.7452i 0.898626i −0.893374 0.449313i \(-0.851669\pi\)
0.893374 0.449313i \(-0.148331\pi\)
\(308\) −14.7302 + 4.05620i −0.839330 + 0.231123i
\(309\) 2.22821 4.71440i 0.126759 0.268193i
\(310\) 7.69595 10.1016i 0.437101 0.573733i
\(311\) 9.90129 + 17.1495i 0.561451 + 0.972461i 0.997370 + 0.0724757i \(0.0230900\pi\)
−0.435919 + 0.899986i \(0.643577\pi\)
\(312\) −3.68492 + 3.41184i −0.208617 + 0.193157i
\(313\) 16.2557 28.1557i 0.918828 1.59146i 0.117630 0.993057i \(-0.462470\pi\)
0.801198 0.598399i \(-0.204196\pi\)
\(314\) 11.7653 + 28.1287i 0.663953 + 1.58740i
\(315\) −13.9414 5.23872i −0.785509 0.295169i
\(316\) 0.128116 0.129899i 0.00720710 0.00730736i
\(317\) −13.9271 8.04083i −0.782225 0.451618i 0.0549932 0.998487i \(-0.482486\pi\)
−0.837218 + 0.546869i \(0.815820\pi\)
\(318\) −4.35502 8.40146i −0.244217 0.471131i
\(319\) −9.42233 16.3200i −0.527549 0.913742i
\(320\) 10.6851 + 2.62703i 0.597318 + 0.146855i
\(321\) −0.637065 + 0.441169i −0.0355575 + 0.0246237i
\(322\) 2.14743 16.7585i 0.119672 0.933912i
\(323\) 6.01054i 0.334435i
\(324\) 10.1192 + 14.8863i 0.562179 + 0.827016i
\(325\) 3.18620i 0.176739i
\(326\) −20.9344 2.68255i −1.15945 0.148573i
\(327\) −13.3352 + 9.23469i −0.737441 + 0.510680i
\(328\) −19.3695 + 2.75450i −1.06950 + 0.152092i
\(329\) 13.0425 + 22.5903i 0.719056 + 1.24544i
\(330\) 6.33065 3.28158i 0.348491 0.180645i
\(331\) −17.7569 10.2520i −0.976010 0.563499i −0.0749465 0.997188i \(-0.523879\pi\)
−0.901063 + 0.433688i \(0.857212\pi\)
\(332\) 3.96082 + 3.90647i 0.217378 + 0.214395i
\(333\) −11.2761 4.23719i −0.617927 0.232197i
\(334\) 28.7642 12.0311i 1.57391 0.658312i
\(335\) 1.93739 3.35565i 0.105851 0.183339i
\(336\) 22.7539 + 10.3723i 1.24133 + 0.565855i
\(337\) 6.21760 + 10.7692i 0.338694 + 0.586635i 0.984187 0.177131i \(-0.0566815\pi\)
−0.645493 + 0.763766i \(0.723348\pi\)
\(338\) −13.4421 10.2409i −0.731154 0.557033i
\(339\) −8.38345 + 17.7375i −0.455326 + 0.963368i
\(340\) 2.14509 0.590687i 0.116334 0.0320345i
\(341\) 13.8180i 0.748287i
\(342\) −14.7513 + 27.8642i −0.797658 + 1.50672i
\(343\) 3.50988 0.189515
\(344\) −0.632194 + 0.495590i −0.0340856 + 0.0267204i
\(345\) 0.646483 + 7.85877i 0.0348055 + 0.423102i
\(346\) −10.7920 + 14.1655i −0.580183 + 0.761541i
\(347\) 24.1550 13.9459i 1.29671 0.748654i 0.316873 0.948468i \(-0.397367\pi\)
0.979834 + 0.199814i \(0.0640339\pi\)
\(348\) −5.30367 + 30.3839i −0.284306 + 1.62875i
\(349\) 26.0103 + 15.0171i 1.39230 + 0.803846i 0.993570 0.113222i \(-0.0361171\pi\)
0.398732 + 0.917068i \(0.369450\pi\)
\(350\) −14.6369 + 6.12213i −0.782377 + 0.327242i
\(351\) 3.82458 3.70733i 0.204141 0.197882i
\(352\) −10.9806 + 4.77209i −0.585267 + 0.254353i
\(353\) −9.48011 + 16.4200i −0.504575 + 0.873950i 0.495411 + 0.868659i \(0.335018\pi\)
−0.999986 + 0.00529122i \(0.998316\pi\)
\(354\) −10.7721 + 16.8443i −0.572533 + 0.895266i
\(355\) −5.59637 + 3.23107i −0.297024 + 0.171487i
\(356\) −17.2623 4.49786i −0.914901 0.238386i
\(357\) 5.03942 0.414556i 0.266715 0.0219406i
\(358\) 16.9895 + 2.17704i 0.897922 + 0.115060i
\(359\) 28.6420 1.51167 0.755833 0.654765i \(-0.227232\pi\)
0.755833 + 0.654765i \(0.227232\pi\)
\(360\) −11.3941 2.52621i −0.600523 0.133143i
\(361\) −36.2231 −1.90648
\(362\) 24.7990 + 3.17776i 1.30341 + 0.167019i
\(363\) 4.82598 10.2107i 0.253298 0.535923i
\(364\) 1.86580 7.16075i 0.0977945 0.375325i
\(365\) −0.488277 + 0.281907i −0.0255576 + 0.0147557i
\(366\) −17.8357 0.809727i −0.932287 0.0423251i
\(367\) 5.77148 9.99650i 0.301269 0.521813i −0.675155 0.737676i \(-0.735923\pi\)
0.976424 + 0.215863i \(0.0692565\pi\)
\(368\) −0.182905 13.2386i −0.00953461 0.690110i
\(369\) 20.4722 3.39114i 1.06574 0.176536i
\(370\) 7.20543 3.01378i 0.374593 0.156679i
\(371\) 12.0759 + 6.97205i 0.626952 + 0.361971i
\(372\) 14.5076 17.3499i 0.752182 0.899551i
\(373\) −19.4301 + 11.2180i −1.00605 + 0.580846i −0.910034 0.414533i \(-0.863945\pi\)
−0.0960206 + 0.995379i \(0.530611\pi\)
\(374\) −1.46714 + 1.92575i −0.0758639 + 0.0995780i
\(375\) 15.8802 10.9971i 0.820048 0.567885i
\(376\) 12.6111 + 16.0872i 0.650368 + 0.829634i
\(377\) 9.12706 0.470068
\(378\) −24.3797 10.4461i −1.25395 0.537289i
\(379\) 22.6668i 1.16431i 0.813077 + 0.582157i \(0.197791\pi\)
−0.813077 + 0.582157i \(0.802209\pi\)
\(380\) −5.42706 19.7085i −0.278403 1.01103i
\(381\) −11.6695 16.8511i −0.597845 0.863310i
\(382\) 21.8727 + 16.6638i 1.11910 + 0.852594i
\(383\) −1.94277 3.36498i −0.0992709 0.171942i 0.812112 0.583501i \(-0.198318\pi\)
−0.911383 + 0.411559i \(0.864984\pi\)
\(384\) 18.7975 + 5.53670i 0.959254 + 0.282544i
\(385\) −5.25356 + 9.09944i −0.267746 + 0.463750i
\(386\) −0.415204 + 0.173666i −0.0211333 + 0.00883935i
\(387\) 0.658334 0.540866i 0.0334650 0.0274937i
\(388\) 7.75297 7.86082i 0.393597 0.399073i
\(389\) 11.9463 + 6.89722i 0.605703 + 0.349703i 0.771282 0.636494i \(-0.219616\pi\)
−0.165579 + 0.986197i \(0.552949\pi\)
\(390\) −0.156629 + 3.45004i −0.00793121 + 0.174699i
\(391\) −1.33859 2.31850i −0.0676953 0.117252i
\(392\) −16.8787 + 2.40029i −0.852504 + 0.121233i
\(393\) 4.35581 + 2.05873i 0.219721 + 0.103849i
\(394\) −34.3765 4.40501i −1.73186 0.221921i
\(395\) 0.125471i 0.00631315i
\(396\) 11.5277 5.32686i 0.579291 0.267685i
\(397\) 23.7680i 1.19288i 0.802657 + 0.596441i \(0.203419\pi\)
−0.802657 + 0.596441i \(0.796581\pi\)
\(398\) 1.28265 10.0097i 0.0642932 0.501740i
\(399\) −3.80882 46.3008i −0.190680 2.31794i
\(400\) −10.6803 + 6.36461i −0.534015 + 0.318230i
\(401\) −4.47782 7.75581i −0.223612 0.387307i 0.732290 0.680992i \(-0.238451\pi\)
−0.955902 + 0.293686i \(0.905118\pi\)
\(402\) 3.71778 5.81347i 0.185426 0.289950i
\(403\) −5.79587 3.34625i −0.288713 0.166688i
\(404\) −9.26022 9.13316i −0.460713 0.454392i
\(405\) 12.1435 + 2.40208i 0.603414 + 0.119360i
\(406\) −17.5372 41.9284i −0.870357 2.08087i
\(407\) −4.24920 + 7.35983i −0.210625 + 0.364813i
\(408\) 3.86399 0.877620i 0.191296 0.0434487i
\(409\) 10.4170 + 18.0429i 0.515090 + 0.892162i 0.999847 + 0.0175128i \(0.00557480\pi\)
−0.484757 + 0.874649i \(0.661092\pi\)
\(410\) −8.15372 + 10.7025i −0.402683 + 0.528557i
\(411\) −28.2355 + 2.32273i −1.39275 + 0.114572i
\(412\) 1.59852 + 5.80506i 0.0787534 + 0.285995i
\(413\) 29.4619i 1.44973i
\(414\) 0.515400 + 14.0335i 0.0253305 + 0.689711i
\(415\) 3.82582 0.187802
\(416\) 0.657501 5.76137i 0.0322366 0.282474i
\(417\) 2.22371 + 1.05101i 0.108895 + 0.0514683i
\(418\) 17.6932 + 13.4796i 0.865403 + 0.659311i
\(419\) 8.74372 5.04819i 0.427159 0.246620i −0.270977 0.962586i \(-0.587347\pi\)
0.698135 + 0.715966i \(0.254013\pi\)
\(420\) 16.1499 5.90955i 0.788035 0.288356i
\(421\) 20.2218 + 11.6751i 0.985551 + 0.569008i 0.903941 0.427656i \(-0.140661\pi\)
0.0816096 + 0.996664i \(0.473994\pi\)
\(422\) −4.41199 10.5483i −0.214772 0.513482i
\(423\) −13.7632 16.7524i −0.669190 0.814528i
\(424\) 10.1381 + 4.07679i 0.492349 + 0.197986i
\(425\) −1.25700 + 2.17719i −0.0609735 + 0.105609i
\(426\) −10.2173 + 5.29629i −0.495031 + 0.256606i
\(427\) 22.7837 13.1542i 1.10258 0.636575i
\(428\) 0.225612 0.865876i 0.0109054 0.0418537i
\(429\) −2.13941 3.08939i −0.103292 0.149157i
\(430\) −0.0702147 + 0.547951i −0.00338605 + 0.0264245i
\(431\) −6.40348 −0.308445 −0.154222 0.988036i \(-0.549287\pi\)
−0.154222 + 0.988036i \(0.549287\pi\)
\(432\) −20.0669 5.41459i −0.965471 0.260510i
\(433\) −9.82857 −0.472331 −0.236166 0.971713i \(-0.575891\pi\)
−0.236166 + 0.971713i \(0.575891\pi\)
\(434\) −4.23569 + 33.0550i −0.203319 + 1.58669i
\(435\) 12.0759 + 17.4381i 0.578997 + 0.836094i
\(436\) 4.72258 18.1248i 0.226171 0.868020i
\(437\) −21.3017 + 12.2986i −1.01900 + 0.588320i
\(438\) −0.891450 + 0.462096i −0.0425951 + 0.0220798i
\(439\) −12.3831 + 21.4482i −0.591015 + 1.02367i 0.403081 + 0.915164i \(0.367939\pi\)
−0.994096 + 0.108504i \(0.965394\pi\)
\(440\) −3.07193 + 7.63923i −0.146449 + 0.364186i
\(441\) 17.8396 2.95506i 0.849505 0.140717i
\(442\) −0.452451 1.08173i −0.0215209 0.0514527i
\(443\) 23.5518 + 13.5976i 1.11898 + 0.646044i 0.941140 0.338016i \(-0.109756\pi\)
0.177840 + 0.984059i \(0.443089\pi\)
\(444\) 13.0624 4.77977i 0.619915 0.226838i
\(445\) −10.6242 + 6.13391i −0.503637 + 0.290775i
\(446\) −4.75255 3.62075i −0.225040 0.171448i
\(447\) −8.88535 4.19957i −0.420262 0.198633i
\(448\) −27.7302 + 8.04973i −1.31013 + 0.380314i
\(449\) 32.6861 1.54255 0.771276 0.636501i \(-0.219619\pi\)
0.771276 + 0.636501i \(0.219619\pi\)
\(450\) 11.1707 7.00825i 0.526590 0.330372i
\(451\) 14.6399i 0.689367i
\(452\) −6.01428 21.8410i −0.282888 1.02731i
\(453\) 24.4197 2.00883i 1.14734 0.0943831i
\(454\) −1.08315 + 1.42173i −0.0508346 + 0.0667249i
\(455\) −2.54447 4.40714i −0.119286 0.206610i
\(456\) −8.06332 35.5012i −0.377599 1.66250i
\(457\) −10.3779 + 17.9750i −0.485456 + 0.840834i −0.999860 0.0167133i \(-0.994680\pi\)
0.514404 + 0.857548i \(0.328013\pi\)
\(458\) −3.96473 9.47898i −0.185260 0.442924i
\(459\) −4.07600 + 1.02444i −0.190251 + 0.0478165i
\(460\) −6.48265 6.39371i −0.302255 0.298108i
\(461\) −32.4695 18.7463i −1.51226 0.873101i −0.999897 0.0143300i \(-0.995438\pi\)
−0.512359 0.858771i \(-0.671228\pi\)
\(462\) −10.0814 + 15.7642i −0.469030 + 0.733419i
\(463\) −7.97597 13.8148i −0.370675 0.642028i 0.618995 0.785395i \(-0.287540\pi\)
−0.989670 + 0.143367i \(0.954207\pi\)
\(464\) −18.2318 30.5944i −0.846390 1.42031i
\(465\) −1.27515 15.5009i −0.0591336 0.718839i
\(466\) 1.06242 8.29107i 0.0492157 0.384077i
\(467\) 27.0476i 1.25161i 0.779979 + 0.625806i \(0.215230\pi\)
−0.779979 + 0.625806i \(0.784770\pi\)
\(468\) −0.557309 + 6.12522i −0.0257616 + 0.283138i
\(469\) 10.1682i 0.469523i
\(470\) 13.9435 + 1.78673i 0.643166 + 0.0824156i
\(471\) 33.7616 + 15.9571i 1.55565 + 0.735263i
\(472\) −3.25051 22.8574i −0.149617 1.05210i
\(473\) −0.300550 0.520568i −0.0138193 0.0239357i
\(474\) 0.0101341 0.223223i 0.000465476 0.0102530i
\(475\) 20.0034 + 11.5490i 0.917818 + 0.529903i
\(476\) −4.09995 + 4.15699i −0.187921 + 0.190535i
\(477\) −10.8492 4.07679i −0.496752 0.186663i
\(478\) −15.5588 + 6.50771i −0.711643 + 0.297656i
\(479\) 13.6550 23.6511i 0.623912 1.08065i −0.364838 0.931071i \(-0.618876\pi\)
0.988750 0.149577i \(-0.0477910\pi\)
\(480\) 11.8776 6.36660i 0.542134 0.290594i
\(481\) −2.05802 3.56460i −0.0938377 0.162532i
\(482\) 4.05359 + 3.08825i 0.184636 + 0.140666i
\(483\) −11.7807 17.0118i −0.536041 0.774063i
\(484\) 3.46216 + 12.5729i 0.157371 + 0.571496i
\(485\) 7.59291i 0.344776i
\(486\) 21.4101 + 5.25429i 0.971182 + 0.238339i
\(487\) 19.1126 0.866073 0.433036 0.901376i \(-0.357442\pi\)
0.433036 + 0.901376i \(0.357442\pi\)
\(488\) 16.2249 12.7191i 0.734469 0.575766i
\(489\) −21.2509 + 14.7163i −0.960999 + 0.665494i
\(490\) −7.10521 + 9.32621i −0.320981 + 0.421315i
\(491\) 11.1131 6.41614i 0.501526 0.289556i −0.227817 0.973704i \(-0.573159\pi\)
0.729344 + 0.684147i \(0.239826\pi\)
\(492\) −15.3705 + 18.3819i −0.692955 + 0.828721i
\(493\) −6.23669 3.60076i −0.280886 0.162170i
\(494\) −9.93863 + 4.15699i −0.447160 + 0.187032i
\(495\) 3.07193 8.17509i 0.138073 0.367443i
\(496\) 0.360770 + 26.1124i 0.0161990 + 1.17248i
\(497\) 8.47896 14.6860i 0.380334 0.658757i
\(498\) 6.80642 + 0.309006i 0.305003 + 0.0138469i
\(499\) 15.3846 8.88232i 0.688711 0.397627i −0.114418 0.993433i \(-0.536500\pi\)
0.803129 + 0.595805i \(0.203167\pi\)
\(500\) −5.62385 + 21.5838i −0.251506 + 0.965255i
\(501\) 16.3176 34.5243i 0.729015 1.54243i
\(502\) 0.899883 + 0.115311i 0.0401638 + 0.00514660i
\(503\) −24.0108 −1.07059 −0.535294 0.844666i \(-0.679799\pi\)
−0.535294 + 0.844666i \(0.679799\pi\)
\(504\) 29.2092 9.20911i 1.30108 0.410207i
\(505\) −8.94461 −0.398030
\(506\) 9.82698 + 1.25923i 0.436862 + 0.0559797i
\(507\) −20.6269 + 1.69683i −0.916075 + 0.0753587i
\(508\) 22.9035 + 5.96771i 1.01618 + 0.264775i
\(509\) 6.91916 3.99478i 0.306686 0.177065i −0.338756 0.940874i \(-0.610006\pi\)
0.645443 + 0.763809i \(0.276673\pi\)
\(510\) 1.46812 2.29568i 0.0650092 0.101654i
\(511\) 0.739780 1.28134i 0.0327259 0.0566830i
\(512\) −20.6258 + 9.30466i −0.911540 + 0.411212i
\(513\) 9.41221 + 37.4491i 0.415559 + 1.65342i
\(514\) 5.21575 2.18157i 0.230057 0.0962250i
\(515\) 3.58602 + 2.07039i 0.158019 + 0.0912324i
\(516\) −0.169174 + 0.969174i −0.00744748 + 0.0426655i
\(517\) −13.2467 + 7.64798i −0.582589 + 0.336358i
\(518\) −12.4208 + 16.3034i −0.545741 + 0.716332i
\(519\) 1.78814 + 21.7370i 0.0784907 + 0.954147i
\(520\) −2.46031 3.13846i −0.107892 0.137631i
\(521\) −36.9809 −1.62016 −0.810082 0.586317i \(-0.800577\pi\)
−0.810082 + 0.586317i \(0.800577\pi\)
\(522\) 20.0755 + 31.9990i 0.878683 + 1.40056i
\(523\) 18.4217i 0.805526i −0.915304 0.402763i \(-0.868050\pi\)
0.915304 0.402763i \(-0.131950\pi\)
\(524\) −5.36351 + 1.47693i −0.234306 + 0.0645201i
\(525\) −8.30334 + 17.5680i −0.362388 + 0.766731i
\(526\) −12.7044 9.67890i −0.553938 0.422020i
\(527\) 2.64028 + 4.57311i 0.115013 + 0.199208i
\(528\) −6.08220 + 13.3426i −0.264694 + 0.580663i
\(529\) 6.02206 10.4305i 0.261828 0.453500i
\(530\) 6.93265 2.89969i 0.301135 0.125955i
\(531\) 4.00179 + 24.1587i 0.173663 + 1.04840i
\(532\) 38.1932 + 37.6692i 1.65589 + 1.63317i
\(533\) 6.14061 + 3.54529i 0.265980 + 0.153563i
\(534\) −19.3967 + 10.0546i −0.839379 + 0.435104i
\(535\) −0.307676 0.532911i −0.0133020 0.0230397i
\(536\) 1.12185 + 7.88876i 0.0484564 + 0.340743i
\(537\) 17.2463 11.9431i 0.744233 0.515384i
\(538\) 34.0439 + 4.36241i 1.46774 + 0.188077i
\(539\) 12.7573i 0.549497i
\(540\) −12.4402 + 7.03943i −0.535340 + 0.302929i
\(541\) 13.5032i 0.580549i 0.956943 + 0.290275i \(0.0937467\pi\)
−0.956943 + 0.290275i \(0.906253\pi\)
\(542\) −2.19886 + 17.1598i −0.0944491 + 0.737075i
\(543\) 25.1739 17.4330i 1.08032 0.748122i
\(544\) −2.72222 + 3.67746i −0.116714 + 0.157670i
\(545\) −6.44038 11.1551i −0.275875 0.477830i
\(546\) −4.17083 8.04615i −0.178495 0.344343i
\(547\) −32.2252 18.6052i −1.37785 0.795501i −0.385948 0.922520i \(-0.626126\pi\)
−0.991900 + 0.127019i \(0.959459\pi\)
\(548\) 22.9717 23.2913i 0.981303 0.994954i
\(549\) −16.8958 + 13.8811i −0.721095 + 0.592429i
\(550\) −3.58995 8.58294i −0.153076 0.365978i
\(551\) −33.0827 + 57.3009i −1.40937 + 2.44110i
\(552\) −11.0167 11.8985i −0.468902 0.506432i
\(553\) 0.164631 + 0.285149i 0.00700082 + 0.0121258i
\(554\) 10.8115 14.1911i 0.459338 0.602922i
\(555\) 4.08755 8.64833i 0.173507 0.367101i
\(556\) −2.73815 + 0.753996i −0.116124 + 0.0319765i
\(557\) 16.9602i 0.718628i 0.933217 + 0.359314i \(0.116989\pi\)
−0.933217 + 0.359314i \(0.883011\pi\)
\(558\) −1.01659 27.6803i −0.0430359 1.17180i
\(559\) 0.291131 0.0123135
\(560\) −9.69027 + 17.3327i −0.409489 + 0.732440i
\(561\) 0.243091 + 2.95506i 0.0102633 + 0.124763i
\(562\) 21.4720 + 16.3585i 0.905742 + 0.690043i
\(563\) −25.0083 + 14.4385i −1.05397 + 0.608512i −0.923759 0.382974i \(-0.874900\pi\)
−0.130214 + 0.991486i \(0.541566\pi\)
\(564\) 24.6622 + 4.30492i 1.03847 + 0.181270i
\(565\) −13.4921 7.78966i −0.567616 0.327713i
\(566\) −0.636710 1.52226i −0.0267629 0.0639854i
\(567\) −30.7493 + 10.4744i −1.29135 + 0.439884i
\(568\) 4.95793 12.3293i 0.208030 0.517326i
\(569\) 2.20060 3.81154i 0.0922538 0.159788i −0.816205 0.577762i \(-0.803926\pi\)
0.908459 + 0.417974i \(0.137260\pi\)
\(570\) −21.0921 13.4886i −0.883449 0.564976i
\(571\) −28.6730 + 16.5544i −1.19993 + 0.692779i −0.960539 0.278144i \(-0.910281\pi\)
−0.239390 + 0.970924i \(0.576947\pi\)
\(572\) 4.19899 + 1.09408i 0.175568 + 0.0457460i
\(573\) 33.5637 2.76104i 1.40214 0.115344i
\(574\) 4.48763 35.0212i 0.187310 1.46176i
\(575\) 10.2881 0.429045
\(576\) 21.6453 10.3673i 0.901887 0.431972i
\(577\) 11.4122 0.475097 0.237548 0.971376i \(-0.423656\pi\)
0.237548 + 0.971376i \(0.423656\pi\)
\(578\) 2.93813 22.9290i 0.122210 0.953720i
\(579\) −0.235540 + 0.498349i −0.00978870 + 0.0207107i
\(580\) −23.7013 6.17559i −0.984142 0.256427i
\(581\) −8.69466 + 5.01986i −0.360715 + 0.208259i
\(582\) 0.613268 13.5083i 0.0254208 0.559939i
\(583\) −4.08834 + 7.08121i −0.169322 + 0.293274i
\(584\) 0.432574 1.07572i 0.0179000 0.0445135i
\(585\) 2.68507 + 3.26823i 0.111014 + 0.135125i
\(586\) 1.33238 + 3.18548i 0.0550401 + 0.131591i
\(587\) −22.5512 13.0200i −0.930788 0.537391i −0.0437275 0.999043i \(-0.513923\pi\)
−0.887061 + 0.461653i \(0.847257\pi\)
\(588\) −13.3940 + 16.0181i −0.552357 + 0.660577i
\(589\) 42.0164 24.2582i 1.73125 0.999540i
\(590\) −12.6297 9.62199i −0.519956 0.396131i
\(591\) −34.8961 + 24.1657i −1.43543 + 0.994042i
\(592\) −7.83770 + 14.0191i −0.322128 + 0.576180i
\(593\) 5.75114 0.236171 0.118086 0.993003i \(-0.462324\pi\)
0.118086 + 0.993003i \(0.462324\pi\)
\(594\) 6.12548 14.2960i 0.251331 0.586571i
\(595\) 4.01531i 0.164612i
\(596\) 10.9409 3.01277i 0.448158 0.123408i
\(597\) −7.03652 10.1610i −0.287986 0.415862i
\(598\) −2.90793 + 3.81692i −0.118914 + 0.156085i
\(599\) −8.10409 14.0367i −0.331124 0.573524i 0.651608 0.758556i \(-0.274095\pi\)
−0.982733 + 0.185032i \(0.940761\pi\)
\(600\) −4.50371 + 14.5459i −0.183863 + 0.593833i
\(601\) 9.78181 16.9426i 0.399008 0.691102i −0.594596 0.804025i \(-0.702688\pi\)
0.993604 + 0.112922i \(0.0360212\pi\)
\(602\) −0.559395 1.33742i −0.0227992 0.0545090i
\(603\) −1.38114 8.33786i −0.0562442 0.339544i
\(604\) −19.8673 + 20.1437i −0.808389 + 0.819635i
\(605\) 7.76680 + 4.48416i 0.315765 + 0.182307i
\(606\) −15.9131 0.722444i −0.646427 0.0293473i
\(607\) −3.82627 6.62730i −0.155304 0.268994i 0.777866 0.628430i \(-0.216302\pi\)
−0.933170 + 0.359437i \(0.882969\pi\)
\(608\) 33.7874 + 25.0110i 1.37026 + 1.01433i
\(609\) −50.3246 23.7854i −2.03926 0.963834i
\(610\) 1.80203 14.0629i 0.0729619 0.569390i
\(611\) 7.40831i 0.299708i
\(612\) 2.79730 3.96561i 0.113074 0.160300i
\(613\) 27.6512i 1.11682i −0.829565 0.558410i \(-0.811412\pi\)
0.829565 0.558410i \(-0.188588\pi\)
\(614\) 22.0865 + 2.83017i 0.891338 + 0.114216i
\(615\) 1.35100 + 16.4230i 0.0544774 + 0.662238i
\(616\) −3.04209 21.3918i −0.122569 0.861899i
\(617\) −12.6938 21.9863i −0.511034 0.885136i −0.999918 0.0127878i \(-0.995929\pi\)
0.488885 0.872348i \(-0.337404\pi\)
\(618\) 6.21258 + 3.97302i 0.249907 + 0.159818i
\(619\) −19.8583 11.4652i −0.798171 0.460824i 0.0446605 0.999002i \(-0.485779\pi\)
−0.842831 + 0.538178i \(0.819113\pi\)
\(620\) 12.7866 + 12.6112i 0.513524 + 0.506478i
\(621\) 11.9708 + 12.3494i 0.480373 + 0.495565i
\(622\) −25.8362 + 10.8064i −1.03594 + 0.433296i
\(623\) 16.0966 27.8801i 0.644897 1.11699i
\(624\) −4.12358 5.78227i −0.165075 0.231476i
\(625\) −0.101100 0.175110i −0.00404398 0.00700439i
\(626\) 36.5734 + 27.8636i 1.46177 + 1.11365i
\(627\) 27.1503 2.23345i 1.08428 0.0891955i
\(628\) −41.5722 + 11.4476i −1.65891 + 0.456809i
\(629\) 3.24767i 0.129493i
\(630\) 9.85453 18.6146i 0.392614 0.741622i
\(631\) 23.2785 0.926701 0.463350 0.886175i \(-0.346647\pi\)
0.463350 + 0.886175i \(0.346647\pi\)
\(632\) 0.159186 + 0.203063i 0.00633207 + 0.00807742i
\(633\) −12.6606 5.98390i −0.503214 0.237839i
\(634\) 13.7826 18.0909i 0.547377 0.718480i
\(635\) 14.0961 8.13841i 0.559388 0.322963i
\(636\) 12.5679 4.59882i 0.498350 0.182355i
\(637\) 5.35098 + 3.08939i 0.212013 + 0.122406i
\(638\) 24.5864 10.2836i 0.973384 0.407133i
\(639\) −4.95793 + 13.1941i −0.196133 + 0.521952i
\(640\) −5.60568 + 14.5163i −0.221584 + 0.573808i
\(641\) −17.4170 + 30.1672i −0.687932 + 1.19153i 0.284574 + 0.958654i \(0.408148\pi\)
−0.972506 + 0.232879i \(0.925185\pi\)
\(642\) −0.504336 0.972938i −0.0199046 0.0383988i
\(643\) 34.0047 19.6326i 1.34102 0.774236i 0.354059 0.935223i \(-0.384801\pi\)
0.986956 + 0.160987i \(0.0514678\pi\)
\(644\) 23.1218 + 6.02460i 0.911127 + 0.237403i
\(645\) 0.385194 + 0.556234i 0.0151670 + 0.0219017i
\(646\) 8.43125 + 1.08038i 0.331723 + 0.0425071i
\(647\) 44.5092 1.74984 0.874918 0.484271i \(-0.160915\pi\)
0.874918 + 0.484271i \(0.160915\pi\)
\(648\) −22.7006 + 11.5189i −0.891762 + 0.452505i
\(649\) 17.2762 0.678149
\(650\) 4.46942 + 0.572714i 0.175305 + 0.0224637i
\(651\) 23.2367 + 33.5547i 0.910719 + 1.31511i
\(652\) 7.52586 28.8835i 0.294735 1.13116i
\(653\) 15.7763 9.10843i 0.617373 0.356440i −0.158473 0.987363i \(-0.550657\pi\)
0.775845 + 0.630923i \(0.217324\pi\)
\(654\) −10.5569 20.3659i −0.412808 0.796368i
\(655\) −1.91291 + 3.31326i −0.0747437 + 0.129460i
\(656\) −0.382229 27.6656i −0.0149235 1.08016i
\(657\) −0.432574 + 1.15117i −0.0168763 + 0.0449116i
\(658\) −34.0327 + 14.2347i −1.32673 + 0.554927i
\(659\) −36.2085 20.9050i −1.41048 0.814343i −0.415049 0.909799i \(-0.636236\pi\)
−0.995434 + 0.0954566i \(0.969569\pi\)
\(660\) 3.46530 + 9.47014i 0.134886 + 0.368625i
\(661\) 9.78973 5.65210i 0.380776 0.219841i −0.297380 0.954759i \(-0.596113\pi\)
0.678156 + 0.734918i \(0.262779\pi\)
\(662\) 17.5727 23.0657i 0.682981 0.896472i
\(663\) −1.29835 0.613652i −0.0504237 0.0238323i
\(664\) −6.19173 + 4.85383i −0.240286 + 0.188365i
\(665\) 36.8915 1.43059
\(666\) 7.97056 15.0559i 0.308853 0.583403i
\(667\) 29.4710i 1.14112i
\(668\) 11.7062 + 42.5114i 0.452927 + 1.64482i
\(669\) −7.29280 + 0.599925i −0.281956 + 0.0231945i
\(670\) 4.35888 + 3.32083i 0.168398 + 0.128295i
\(671\) 7.71346 + 13.3601i 0.297775 + 0.515761i
\(672\) −18.6396 + 30.0535i −0.719039 + 1.15934i
\(673\) 17.6390 30.5517i 0.679934 1.17768i −0.295066 0.955477i \(-0.595342\pi\)
0.975000 0.222203i \(-0.0713249\pi\)
\(674\) −16.2240 + 6.78595i −0.624926 + 0.261385i
\(675\) 4.42246 15.5335i 0.170220 0.597886i
\(676\) 16.7816 17.0150i 0.645446 0.654425i
\(677\) −17.5026 10.1051i −0.672679 0.388372i 0.124412 0.992231i \(-0.460296\pi\)
−0.797091 + 0.603859i \(0.793629\pi\)
\(678\) −23.3742 14.9481i −0.897683 0.574079i
\(679\) 9.96266 + 17.2558i 0.382332 + 0.662218i
\(680\) 0.443006 + 3.11519i 0.0169885 + 0.119462i
\(681\) 0.179468 + 2.18164i 0.00687721 + 0.0836007i
\(682\) −19.3831 2.48376i −0.742218 0.0951081i
\(683\) 43.6659i 1.67083i 0.549621 + 0.835414i \(0.314772\pi\)
−0.549621 + 0.835414i \(0.685228\pi\)
\(684\) −36.4349 25.7008i −1.39312 0.982695i
\(685\) 22.4975i 0.859584i
\(686\) −0.630894 + 4.92346i −0.0240876 + 0.187978i
\(687\) −11.3772 5.37730i −0.434066 0.205157i
\(688\) −0.581551 0.975888i −0.0221714 0.0372054i
\(689\) −1.98011 3.42965i −0.0754362 0.130659i
\(690\) −11.1400 0.505749i −0.424094 0.0192535i
\(691\) −7.91193 4.56796i −0.300984 0.173773i 0.341901 0.939736i \(-0.388929\pi\)
−0.642885 + 0.765963i \(0.722263\pi\)
\(692\) −17.9307 17.6847i −0.681623 0.672271i
\(693\) 3.74519 + 22.6096i 0.142268 + 0.858867i
\(694\) 15.2207 + 36.3900i 0.577769 + 1.38134i
\(695\) −0.976570 + 1.69147i −0.0370434 + 0.0641611i
\(696\) −41.6675 12.9011i −1.57940 0.489016i
\(697\) −2.79733 4.84512i −0.105956 0.183522i
\(698\) −25.7404 + 33.7866i −0.974290 + 1.27884i
\(699\) −5.82839 8.41641i −0.220450 0.318338i
\(700\) −5.95682 21.6323i −0.225147 0.817625i
\(701\) 44.8665i 1.69458i 0.531127 + 0.847292i \(0.321769\pi\)
−0.531127 + 0.847292i \(0.678231\pi\)
\(702\) 4.51297 + 6.03129i 0.170331 + 0.227636i
\(703\) 29.8387 1.12539
\(704\) −4.72027 16.2607i −0.177902 0.612849i
\(705\) 14.1543 9.80188i 0.533081 0.369160i
\(706\) −21.3291 16.2496i −0.802730 0.611563i
\(707\) 20.3277 11.7362i 0.764504 0.441386i
\(708\) −21.6920 18.1383i −0.815235 0.681679i
\(709\) −23.1529 13.3673i −0.869525 0.502021i −0.00233491 0.999997i \(-0.500743\pi\)
−0.867190 + 0.497977i \(0.834077\pi\)
\(710\) −3.52642 8.43105i −0.132344 0.316412i
\(711\) −0.173728 0.211459i −0.00651532 0.00793035i
\(712\) 9.41221 23.4061i 0.352738 0.877182i
\(713\) 10.8049 18.7147i 0.404647 0.700870i
\(714\) −0.324311 + 7.14354i −0.0121370 + 0.267340i
\(715\) 2.58430 1.49205i 0.0966474 0.0557994i
\(716\) −6.10766 + 23.4406i −0.228254 + 0.876016i
\(717\) −8.82630 + 18.6745i −0.329624 + 0.697411i
\(718\) −5.14834 + 40.1774i −0.192135 + 1.49941i
\(719\) −37.4738 −1.39754 −0.698768 0.715348i \(-0.746268\pi\)
−0.698768 + 0.715348i \(0.746268\pi\)
\(720\) 5.59169 15.5290i 0.208390 0.578730i
\(721\) −10.8662 −0.404680
\(722\) 6.51103 50.8117i 0.242316 1.89102i
\(723\) 6.22025 0.511694i 0.231333 0.0190301i
\(724\) −8.91517 + 34.2155i −0.331330 + 1.27161i
\(725\) 23.9670 13.8374i 0.890112 0.513907i
\(726\) 13.4555 + 8.60497i 0.499382 + 0.319360i
\(727\) −9.18140 + 15.9027i −0.340519 + 0.589797i −0.984529 0.175220i \(-0.943936\pi\)
0.644010 + 0.765017i \(0.277270\pi\)
\(728\) 9.70933 + 3.90437i 0.359852 + 0.144706i
\(729\) 23.7916 12.7656i 0.881169 0.472801i
\(730\) −0.307676 0.735600i −0.0113876 0.0272258i
\(731\) −0.198936 0.114856i −0.00735790 0.00424808i
\(732\) 4.34177 24.8734i 0.160477 0.919346i
\(733\) −35.6508 + 20.5830i −1.31679 + 0.760249i −0.983211 0.182472i \(-0.941590\pi\)
−0.333580 + 0.942722i \(0.608257\pi\)
\(734\) 12.9851 + 9.89277i 0.479289 + 0.365149i
\(735\) 1.17727 + 14.3111i 0.0434242 + 0.527873i
\(736\) 18.6033 + 2.12305i 0.685725 + 0.0782565i
\(737\) −5.96251 −0.219632
\(738\) 1.07706 + 29.3268i 0.0396472 + 1.07953i
\(739\) 45.1004i 1.65905i 0.558473 + 0.829523i \(0.311387\pi\)
−0.558473 + 0.829523i \(0.688613\pi\)
\(740\) 2.93241 + 10.6491i 0.107797 + 0.391469i
\(741\) −5.63806 + 11.9289i −0.207119 + 0.438218i
\(742\) −11.9506 + 15.6862i −0.438721 + 0.575860i
\(743\) −21.7217 37.6231i −0.796893 1.38026i −0.921630 0.388070i \(-0.873142\pi\)
0.124737 0.992190i \(-0.460191\pi\)
\(744\) 21.7298 + 23.4690i 0.796653 + 0.860416i
\(745\) 3.90212 6.75867i 0.142963 0.247618i
\(746\) −12.2434 29.2719i −0.448264 1.07172i
\(747\) 6.44774 5.29726i 0.235911 0.193817i
\(748\) −2.43761 2.40417i −0.0891280 0.0879051i
\(749\) 1.39846 + 0.807404i 0.0510988 + 0.0295019i
\(750\) 12.5716 + 24.2525i 0.459051 + 0.885576i
\(751\) −15.3394 26.5686i −0.559742 0.969501i −0.997518 0.0704172i \(-0.977567\pi\)
0.437776 0.899084i \(-0.355766\pi\)
\(752\) −24.8331 + 14.7985i −0.905568 + 0.539646i
\(753\) 0.913486 0.632592i 0.0332893 0.0230529i
\(754\) −1.64057 + 12.8029i −0.0597461 + 0.466255i
\(755\) 19.4571i 0.708118i
\(756\) 19.0354 32.3207i 0.692311 1.17549i
\(757\) 2.84137i 0.103271i −0.998666 0.0516357i \(-0.983557\pi\)
0.998666 0.0516357i \(-0.0164435\pi\)
\(758\) −31.7957 4.07431i −1.15487 0.147986i
\(759\) 9.97553 6.90808i 0.362089 0.250747i
\(760\) 28.6215 4.07021i 1.03821 0.147642i
\(761\) 6.52480 + 11.3013i 0.236524 + 0.409672i 0.959714 0.280977i \(-0.0906585\pi\)
−0.723191 + 0.690649i \(0.757325\pi\)
\(762\) 25.7354 13.3403i 0.932295 0.483268i
\(763\) 29.2731 + 16.9008i 1.05976 + 0.611851i
\(764\) −27.3066 + 27.6865i −0.987919 + 1.00166i
\(765\) −0.545397 3.29254i −0.0197189 0.119042i
\(766\) 5.06941 2.12036i 0.183165 0.0766117i
\(767\) −4.18370 + 7.24637i −0.151065 + 0.261651i
\(768\) −11.1454 + 25.3728i −0.402174 + 0.915563i
\(769\) 13.7846 + 23.8756i 0.497084 + 0.860975i 0.999994 0.00336360i \(-0.00107067\pi\)
−0.502910 + 0.864339i \(0.667737\pi\)
\(770\) −11.8199 9.00501i −0.425958 0.324518i
\(771\) 2.95883 6.26022i 0.106560 0.225456i
\(772\) −0.168976 0.613641i −0.00608159 0.0220854i
\(773\) 15.7109i 0.565082i 0.959255 + 0.282541i \(0.0911774\pi\)
−0.959255 + 0.282541i \(0.908823\pi\)
\(774\) 0.640362 + 1.02069i 0.0230173 + 0.0366881i
\(775\) −20.2927 −0.728936
\(776\) 9.63314 + 12.2884i 0.345810 + 0.441128i
\(777\) 2.05802 + 25.0177i 0.0738311 + 0.897504i
\(778\) −11.8224 + 15.5179i −0.423852 + 0.556343i
\(779\) −44.5155 + 25.7011i −1.59494 + 0.920836i
\(780\) −4.81136 0.839848i −0.172274 0.0300714i
\(781\) 8.61171 + 4.97197i 0.308151 + 0.177911i
\(782\) 3.49287 1.46095i 0.124905 0.0522434i
\(783\) 44.4968 + 12.6684i 1.59018 + 0.452732i
\(784\) −0.333077 24.1080i −0.0118956 0.860999i
\(785\) −14.8268 + 25.6808i −0.529193 + 0.916589i
\(786\) −3.67082 + 5.74003i −0.130934 + 0.204740i
\(787\) −12.2138 + 7.05164i −0.435375 + 0.251364i −0.701634 0.712538i \(-0.747546\pi\)
0.266259 + 0.963902i \(0.414212\pi\)
\(788\) 12.3582 47.4296i 0.440243 1.68961i
\(789\) −19.4949 + 1.60370i −0.694038 + 0.0570934i
\(790\) 0.176004 + 0.0225532i 0.00626195 + 0.000802408i
\(791\) 40.8832 1.45364
\(792\) 5.40013 + 17.1280i 0.191885 + 0.608616i
\(793\) −7.47175 −0.265329
\(794\) −33.3404 4.27226i −1.18321 0.151617i
\(795\) 3.93280 8.32093i 0.139482 0.295113i
\(796\) 13.8105 + 3.59845i 0.489499 + 0.127544i
\(797\) 22.7555 13.1379i 0.806040 0.465367i −0.0395390 0.999218i \(-0.512589\pi\)
0.845579 + 0.533851i \(0.179256\pi\)
\(798\) 65.6327 + 2.97967i 2.32337 + 0.105479i
\(799\) −2.92269 + 5.06224i −0.103397 + 0.179089i
\(800\) −7.00815 16.1258i −0.247775 0.570132i
\(801\) −9.41221 + 25.0480i −0.332564 + 0.885027i
\(802\) 11.6843 4.88714i 0.412587 0.172571i
\(803\) 0.751362 + 0.433799i 0.0265150 + 0.0153084i
\(804\) 7.48655 + 6.26006i 0.264030 + 0.220775i
\(805\) 14.2305 8.21599i 0.501560 0.289576i
\(806\) 5.73572 7.52864i 0.202032 0.265185i
\(807\) 34.5586 23.9319i 1.21652 0.842443i
\(808\) 14.4760 11.3480i 0.509264 0.399223i
\(809\) −37.5390 −1.31980 −0.659901 0.751353i \(-0.729402\pi\)
−0.659901 + 0.751353i \(0.729402\pi\)
\(810\) −5.55227 + 16.6024i −0.195087 + 0.583349i
\(811\) 37.7228i 1.32463i −0.749227 0.662314i \(-0.769575\pi\)
0.749227 0.662314i \(-0.230425\pi\)
\(812\) 61.9671 17.0637i 2.17462 0.598817i
\(813\) 12.0628 + 17.4192i 0.423061 + 0.610917i
\(814\) −9.56017 7.28345i −0.335084 0.255285i
\(815\) −10.2633 17.7766i −0.359508 0.622686i
\(816\) 0.536531 + 5.57794i 0.0187823 + 0.195267i
\(817\) −1.05526 + 1.82776i −0.0369188 + 0.0639453i
\(818\) −27.1820 + 11.3693i −0.950395 + 0.397518i
\(819\) −10.3904 3.90437i −0.363070 0.136430i
\(820\) −13.5472 13.3613i −0.473089 0.466598i
\(821\) 1.06427 + 0.614456i 0.0371432 + 0.0214446i 0.518457 0.855104i \(-0.326507\pi\)
−0.481313 + 0.876549i \(0.659840\pi\)
\(822\) 1.81709 40.0247i 0.0633782 1.39602i
\(823\) −17.4937 30.2999i −0.609791 1.05619i −0.991275 0.131813i \(-0.957920\pi\)
0.381484 0.924376i \(-0.375413\pi\)
\(824\) −8.43034 + 1.19886i −0.293685 + 0.0417644i
\(825\) −10.3017 4.86899i −0.358659 0.169517i
\(826\) 41.3276 + 5.29573i 1.43797 + 0.184262i
\(827\) 48.7311i 1.69455i −0.531157 0.847273i \(-0.678243\pi\)
0.531157 0.847273i \(-0.321757\pi\)
\(828\) −19.7781 1.79953i −0.687337 0.0625380i
\(829\) 28.9573i 1.00573i −0.864366 0.502863i \(-0.832280\pi\)
0.864366 0.502863i \(-0.167720\pi\)
\(830\) −0.687685 + 5.36665i −0.0238699 + 0.186279i
\(831\) −1.79137 21.7763i −0.0621420 0.755410i
\(832\) 7.96354 + 1.95790i 0.276086 + 0.0678780i
\(833\) −2.43761 4.22207i −0.0844583 0.146286i
\(834\) −1.87401 + 2.93037i −0.0648916 + 0.101470i
\(835\) 26.2610 + 15.1618i 0.908801 + 0.524696i
\(836\) −22.0888 + 22.3961i −0.763957 + 0.774585i
\(837\) −23.6117 24.3585i −0.816141 0.841953i
\(838\) 5.50965 + 13.1726i 0.190328 + 0.455040i
\(839\) 7.66037 13.2681i 0.264465 0.458067i −0.702958 0.711231i \(-0.748138\pi\)
0.967423 + 0.253164i \(0.0814712\pi\)
\(840\) 5.38666 + 23.7164i 0.185858 + 0.818294i
\(841\) 25.1380 + 43.5402i 0.866826 + 1.50139i
\(842\) −20.0120 + 26.2675i −0.689658 + 0.905236i
\(843\) 32.9488 2.71046i 1.13482 0.0933532i
\(844\) 15.5896 4.29285i 0.536616 0.147766i
\(845\) 16.4351i 0.565386i
\(846\) 25.9732 16.2951i 0.892977 0.560235i
\(847\) −23.5347 −0.808662
\(848\) −7.54099 + 13.4883i −0.258959 + 0.463192i
\(849\) −1.82710 0.863559i −0.0627058 0.0296373i
\(850\) −2.82810 2.15460i −0.0970029 0.0739021i
\(851\) 11.5100 6.64528i 0.394556 0.227797i
\(852\) −5.59280 15.2843i −0.191606 0.523631i
\(853\) 5.67204 + 3.27476i 0.194207 + 0.112126i 0.593951 0.804502i \(-0.297567\pi\)
−0.399743 + 0.916627i \(0.630901\pi\)
\(854\) 14.3566 + 34.3241i 0.491273 + 1.17455i
\(855\) −30.2509 + 5.01095i −1.03456 + 0.171371i
\(856\) 1.17405 + 0.472116i 0.0401282 + 0.0161366i
\(857\) −6.71094 + 11.6237i −0.229241 + 0.397058i −0.957583 0.288156i \(-0.906958\pi\)
0.728342 + 0.685214i \(0.240291\pi\)
\(858\) 4.71817 2.44573i 0.161076 0.0834959i
\(859\) −2.57865 + 1.48878i −0.0879824 + 0.0507967i −0.543346 0.839509i \(-0.682843\pi\)
0.455363 + 0.890306i \(0.349509\pi\)
\(860\) −0.756014 0.196986i −0.0257799 0.00671718i
\(861\) −24.6189 35.5506i −0.839009 1.21156i
\(862\) 1.15101 8.98245i 0.0392037 0.305943i
\(863\) −24.3897 −0.830236 −0.415118 0.909768i \(-0.636260\pi\)
−0.415118 + 0.909768i \(0.636260\pi\)
\(864\) 11.2023 27.1755i 0.381109 0.924530i
\(865\) −17.3196 −0.588884
\(866\) 1.76667 13.7870i 0.0600338 0.468500i
\(867\) −16.1184 23.2756i −0.547410 0.790480i
\(868\) −45.6064 11.8832i −1.54798 0.403341i
\(869\) −0.167208 + 0.0965378i −0.00567216 + 0.00327482i
\(870\) −26.6318 + 13.8050i −0.902904 + 0.468033i
\(871\) 1.44392 2.50094i 0.0489252 0.0847410i
\(872\) 24.5756 + 9.88247i 0.832234 + 0.334663i
\(873\) −10.5132 12.7965i −0.355817 0.433096i
\(874\) −13.4228 32.0915i −0.454032 1.08551i
\(875\) −34.8596 20.1262i −1.17847 0.680390i
\(876\) −0.487965 1.33354i −0.0164868 0.0450560i
\(877\) 4.38552 2.53198i 0.148088 0.0854988i −0.424125 0.905604i \(-0.639418\pi\)
0.572213 + 0.820105i \(0.306085\pi\)
\(878\) −27.8605 21.2257i −0.940248 0.716332i
\(879\) 3.82338 + 1.80708i 0.128960 + 0.0609514i
\(880\) −10.1637 5.68227i −0.342618 0.191549i
\(881\) 28.2318 0.951154 0.475577 0.879674i \(-0.342239\pi\)
0.475577 + 0.879674i \(0.342239\pi\)
\(882\) 0.938560 + 25.5556i 0.0316030 + 0.860501i
\(883\) 28.0994i 0.945619i 0.881165 + 0.472809i \(0.156760\pi\)
−0.881165 + 0.472809i \(0.843240\pi\)
\(884\) 1.59872 0.440234i 0.0537708 0.0148067i
\(885\) −19.3803 + 1.59427i −0.651462 + 0.0535910i
\(886\) −23.3074 + 30.5930i −0.783028 + 1.02779i
\(887\) 0.666005 + 1.15356i 0.0223623 + 0.0387326i 0.876990 0.480509i \(-0.159548\pi\)
−0.854628 + 0.519241i \(0.826215\pi\)
\(888\) 4.35685 + 19.1824i 0.146206 + 0.643718i
\(889\) −21.3568 + 36.9911i −0.716285 + 1.24064i
\(890\) −6.69462 16.0057i −0.224404 0.536511i
\(891\) −6.14209 18.0311i −0.205768 0.604063i
\(892\) 5.93325 6.01579i 0.198660 0.201424i
\(893\) 46.5104 + 26.8528i 1.55641 + 0.898594i
\(894\) 7.48804 11.7090i 0.250438 0.391608i
\(895\) 8.32926 + 14.4267i 0.278417 + 0.482232i
\(896\) −6.30725 40.3453i −0.210710 1.34784i
\(897\) 0.481818 + 5.85707i 0.0160874 + 0.195562i
\(898\) −5.87527 + 45.8502i −0.196060 + 1.53004i
\(899\) 58.1297i 1.93873i
\(900\) 7.82287 + 16.9293i 0.260762 + 0.564310i
\(901\) 3.12473i 0.104100i
\(902\) 20.5360 + 2.63150i 0.683776 + 0.0876193i
\(903\) −1.60524 0.758698i −0.0534189 0.0252479i
\(904\) 31.7184 4.51062i 1.05494 0.150021i
\(905\) 12.1580 + 21.0582i 0.404145 + 0.699999i
\(906\) −1.57153 + 34.6157i −0.0522104 + 1.15003i
\(907\) 0.778677 + 0.449569i 0.0258555 + 0.0149277i 0.512872 0.858465i \(-0.328582\pi\)
−0.487017 + 0.873393i \(0.661915\pi\)
\(908\) −1.79962 1.77493i −0.0597226 0.0589032i
\(909\) −15.0745 + 12.3848i −0.499991 + 0.410777i
\(910\) 6.63946 2.77706i 0.220096 0.0920586i
\(911\) 7.53390 13.0491i 0.249609 0.432336i −0.713808 0.700341i \(-0.753031\pi\)
0.963417 + 0.268005i \(0.0863645\pi\)
\(912\) 51.2485 4.92949i 1.69701 0.163232i
\(913\) −2.94360 5.09846i −0.0974188 0.168734i
\(914\) −23.3489 17.7885i −0.772313 0.588390i
\(915\) −9.88581 14.2755i −0.326815 0.471933i
\(916\) 14.0092 3.85768i 0.462878 0.127461i
\(917\) 10.0397i 0.331541i
\(918\) −0.704367 5.90172i −0.0232476 0.194786i
\(919\) −28.4761 −0.939339 −0.469670 0.882842i \(-0.655627\pi\)
−0.469670 + 0.882842i \(0.655627\pi\)
\(920\) 10.1340 7.94424i 0.334107 0.261914i
\(921\) 22.4204 15.5262i 0.738776 0.511604i
\(922\) 32.1326 42.1768i 1.05823 1.38902i
\(923\) −4.17092 + 2.40808i −0.137288 + 0.0792630i
\(924\) −20.3011 16.9753i −0.667857 0.558445i
\(925\) −10.8084 6.24025i −0.355379 0.205178i
\(926\) 20.8123 8.70506i 0.683934 0.286066i
\(927\) 8.91028 1.47595i 0.292652 0.0484767i
\(928\) 46.1932 20.0753i 1.51637 0.659003i
\(929\) 2.12086 3.67344i 0.0695833 0.120522i −0.829135 0.559049i \(-0.811166\pi\)
0.898718 + 0.438527i \(0.144500\pi\)
\(930\) 21.9731 + 0.997560i 0.720525 + 0.0327113i
\(931\) −38.7912 + 22.3961i −1.27133 + 0.734002i
\(932\) 11.4393 + 2.98061i 0.374706 + 0.0976332i
\(933\) −14.6565 + 31.0099i −0.479833 + 1.01522i
\(934\) −37.9408 4.86175i −1.24146 0.159081i
\(935\) −2.35454 −0.0770016
\(936\) −8.49193 1.88276i −0.277568 0.0615399i
\(937\) −15.1569 −0.495155 −0.247578 0.968868i \(-0.579634\pi\)
−0.247578 + 0.968868i \(0.579634\pi\)
\(938\) −14.2634 1.82771i −0.465715 0.0596769i
\(939\) 56.1219 4.61674i 1.83147 0.150662i
\(940\) −5.01264 + 19.2380i −0.163494 + 0.627475i
\(941\) −36.9463 + 21.3310i −1.20442 + 0.695370i −0.961534 0.274686i \(-0.911426\pi\)
−0.242882 + 0.970056i \(0.578093\pi\)
\(942\) −28.4522 + 44.4906i −0.927024 + 1.44958i
\(943\) −11.4476 + 19.8278i −0.372785 + 0.645683i
\(944\) 32.6474 0.451058i 1.06258 0.0146807i
\(945\) −6.28779 25.0177i −0.204542 0.813825i
\(946\) 0.784246 0.328023i 0.0254980 0.0106650i
\(947\) 24.7629 + 14.2969i 0.804686 + 0.464585i 0.845107 0.534597i \(-0.179537\pi\)
−0.0404213 + 0.999183i \(0.512870\pi\)
\(948\) 0.311303 + 0.0543395i 0.0101106 + 0.00176486i
\(949\) −0.363908 + 0.210103i −0.0118130 + 0.00682022i
\(950\) −19.7958 + 25.9837i −0.642261 + 0.843023i
\(951\) −2.28365 27.7605i −0.0740524 0.900195i
\(952\) −5.09423 6.49840i −0.165105 0.210614i
\(953\) −28.1424 −0.911622 −0.455811 0.890077i \(-0.650651\pi\)
−0.455811 + 0.890077i \(0.650651\pi\)
\(954\) 7.66882 14.4859i 0.248287 0.468998i
\(955\) 26.7429i 0.865380i
\(956\) −6.33199 22.9948i −0.204791 0.743704i
\(957\) 13.9475 29.5098i 0.450859 0.953917i
\(958\) 30.7220 + 23.4057i 0.992583 + 0.756204i
\(959\) 29.5189 + 51.1283i 0.953216 + 1.65102i
\(960\) 6.79574 + 17.8056i 0.219332 + 0.574672i
\(961\) −5.81204 + 10.0668i −0.187485 + 0.324734i
\(962\) 5.37014 2.24615i 0.173140 0.0724187i
\(963\) −1.25640 0.472116i −0.0404871 0.0152137i
\(964\) −5.06064 + 5.13104i −0.162992 + 0.165260i
\(965\) −0.379071 0.218857i −0.0122027 0.00704525i
\(966\) 25.9807 13.4675i 0.835916 0.433309i
\(967\) −6.99023 12.1074i −0.224791 0.389349i 0.731466 0.681878i \(-0.238836\pi\)
−0.956257 + 0.292529i \(0.905503\pi\)
\(968\) −18.2589 + 2.59656i −0.586863 + 0.0834567i
\(969\) 8.55870 5.92692i 0.274945 0.190400i
\(970\) 10.6509 + 1.36481i 0.341980 + 0.0438215i
\(971\) 17.5426i 0.562969i 0.959566 + 0.281484i \(0.0908268\pi\)
−0.959566 + 0.281484i \(0.909173\pi\)
\(972\) −11.2188 + 29.0884i −0.359845 + 0.933012i
\(973\) 5.12543i 0.164314i
\(974\) −3.43545 + 26.8100i −0.110079 + 0.859049i
\(975\) 4.53698 3.14187i 0.145300 0.100621i
\(976\) 14.9252 + 25.0457i 0.477744 + 0.801692i
\(977\) 22.7380 + 39.3834i 0.727454 + 1.25999i 0.957956 + 0.286916i \(0.0926300\pi\)
−0.230502 + 0.973072i \(0.574037\pi\)
\(978\) −16.8234 32.4548i −0.537953 1.03779i
\(979\) 16.3486 + 9.43888i 0.522504 + 0.301668i
\(980\) −11.8051 11.6432i −0.377101 0.371927i
\(981\) −26.2995 9.88247i −0.839677 0.315523i
\(982\) 7.00265 + 16.7421i 0.223463 + 0.534262i
\(983\) −5.04836 + 8.74402i −0.161018 + 0.278891i −0.935234 0.354030i \(-0.884811\pi\)
0.774216 + 0.632921i \(0.218144\pi\)
\(984\) −23.0223 24.8650i −0.733924 0.792666i
\(985\) −16.8534 29.1909i −0.536994 0.930100i
\(986\) 6.17197 8.10125i 0.196556 0.257996i
\(987\) −19.3063 + 40.8478i −0.614527 + 1.30020i
\(988\) −4.04474 14.6886i −0.128680 0.467306i
\(989\) 0.940054i 0.0298920i
\(990\) 10.9154 + 5.77859i 0.346914 + 0.183656i
\(991\) −17.6057 −0.559263 −0.279631 0.960107i \(-0.590212\pi\)
−0.279631 + 0.960107i \(0.590212\pi\)
\(992\) −36.6938 4.18758i −1.16503 0.132956i
\(993\) −2.91163 35.3943i −0.0923978 1.12320i
\(994\) 19.0766 + 14.5336i 0.605073 + 0.460978i
\(995\) 8.49978 4.90735i 0.269461 0.155573i
\(996\) −1.65690 + 9.49212i −0.0525008 + 0.300769i
\(997\) 26.1168 + 15.0786i 0.827128 + 0.477543i 0.852868 0.522126i \(-0.174861\pi\)
−0.0257404 + 0.999669i \(0.508194\pi\)
\(998\) 9.69426 + 23.1773i 0.306866 + 0.733664i
\(999\) −5.08570 20.2349i −0.160904 0.640203i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 72.2.n.b.61.4 yes 16
3.2 odd 2 216.2.n.b.181.5 16
4.3 odd 2 288.2.r.b.241.3 16
8.3 odd 2 288.2.r.b.241.6 16
8.5 even 2 inner 72.2.n.b.61.2 yes 16
9.2 odd 6 648.2.d.k.325.2 8
9.4 even 3 inner 72.2.n.b.13.2 16
9.5 odd 6 216.2.n.b.37.7 16
9.7 even 3 648.2.d.j.325.7 8
12.11 even 2 864.2.r.b.721.6 16
24.5 odd 2 216.2.n.b.181.7 16
24.11 even 2 864.2.r.b.721.3 16
36.7 odd 6 2592.2.d.j.1297.3 8
36.11 even 6 2592.2.d.k.1297.6 8
36.23 even 6 864.2.r.b.145.3 16
36.31 odd 6 288.2.r.b.49.6 16
72.5 odd 6 216.2.n.b.37.5 16
72.11 even 6 2592.2.d.k.1297.3 8
72.13 even 6 inner 72.2.n.b.13.4 yes 16
72.29 odd 6 648.2.d.k.325.1 8
72.43 odd 6 2592.2.d.j.1297.6 8
72.59 even 6 864.2.r.b.145.6 16
72.61 even 6 648.2.d.j.325.8 8
72.67 odd 6 288.2.r.b.49.3 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
72.2.n.b.13.2 16 9.4 even 3 inner
72.2.n.b.13.4 yes 16 72.13 even 6 inner
72.2.n.b.61.2 yes 16 8.5 even 2 inner
72.2.n.b.61.4 yes 16 1.1 even 1 trivial
216.2.n.b.37.5 16 72.5 odd 6
216.2.n.b.37.7 16 9.5 odd 6
216.2.n.b.181.5 16 3.2 odd 2
216.2.n.b.181.7 16 24.5 odd 2
288.2.r.b.49.3 16 72.67 odd 6
288.2.r.b.49.6 16 36.31 odd 6
288.2.r.b.241.3 16 4.3 odd 2
288.2.r.b.241.6 16 8.3 odd 2
648.2.d.j.325.7 8 9.7 even 3
648.2.d.j.325.8 8 72.61 even 6
648.2.d.k.325.1 8 72.29 odd 6
648.2.d.k.325.2 8 9.2 odd 6
864.2.r.b.145.3 16 36.23 even 6
864.2.r.b.145.6 16 72.59 even 6
864.2.r.b.721.3 16 24.11 even 2
864.2.r.b.721.6 16 12.11 even 2
2592.2.d.j.1297.3 8 36.7 odd 6
2592.2.d.j.1297.6 8 72.43 odd 6
2592.2.d.k.1297.3 8 72.11 even 6
2592.2.d.k.1297.6 8 36.11 even 6