Properties

Label 129.2.j.a.113.8
Level $129$
Weight $2$
Character 129.113
Analytic conductor $1.030$
Analytic rank $0$
Dimension $72$
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] = [129,2,Mod(2,129)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(129, base_ring=CyclotomicField(14))
 
chi = DirichletCharacter(H, H._module([7, 9]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("129.2");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 129 = 3 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 129.j (of order \(14\), degree \(6\), 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: \(1.03007018607\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(12\) over \(\Q(\zeta_{14})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label 113.8
Character \(\chi\) \(=\) 129.113
Dual form 129.2.j.a.8.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.178779 + 0.783281i) q^{2} +(-1.60231 - 0.657721i) q^{3} +(1.22037 - 0.587699i) q^{4} +(-2.53156 - 3.17448i) q^{5} +(0.228721 - 1.37265i) q^{6} -3.17594i q^{7} +(1.68036 + 2.10711i) q^{8} +(2.13481 + 2.10775i) q^{9} +O(q^{10})\) \(q+(0.178779 + 0.783281i) q^{2} +(-1.60231 - 0.657721i) q^{3} +(1.22037 - 0.587699i) q^{4} +(-2.53156 - 3.17448i) q^{5} +(0.228721 - 1.37265i) q^{6} -3.17594i q^{7} +(1.68036 + 2.10711i) q^{8} +(2.13481 + 2.10775i) q^{9} +(2.03392 - 2.55046i) q^{10} +(-0.516214 + 1.07193i) q^{11} +(-2.34196 + 0.139015i) q^{12} +(0.593805 + 0.744608i) q^{13} +(2.48766 - 0.567791i) q^{14} +(1.96843 + 6.75157i) q^{15} +(0.338999 - 0.425091i) q^{16} +(0.109436 + 0.0872725i) q^{17} +(-1.26930 + 2.04897i) q^{18} +(-0.157259 - 0.326551i) q^{19} +(-4.95509 - 2.38624i) q^{20} +(-2.08888 + 5.08885i) q^{21} +(-0.931910 - 0.212702i) q^{22} +(3.80396 - 7.89901i) q^{23} +(-1.30658 - 4.48146i) q^{24} +(-2.55591 + 11.1982i) q^{25} +(-0.477077 + 0.598236i) q^{26} +(-2.03432 - 4.78138i) q^{27} +(-1.86650 - 3.87583i) q^{28} +(1.25733 + 5.50874i) q^{29} +(-4.93646 + 2.74887i) q^{30} +(1.51188 + 6.62398i) q^{31} +(5.24997 + 2.52825i) q^{32} +(1.53217 - 1.37804i) q^{33} +(-0.0487940 + 0.101322i) q^{34} +(-10.0820 + 8.04010i) q^{35} +(3.84398 + 1.31761i) q^{36} -1.16757i q^{37} +(0.227667 - 0.181558i) q^{38} +(-0.461717 - 1.58365i) q^{39} +(2.43503 - 10.6686i) q^{40} +(6.60740 - 1.50809i) q^{41} +(-4.35945 - 0.726404i) q^{42} +(-5.93308 - 2.79260i) q^{43} +1.61153i q^{44} +(1.28660 - 12.1128i) q^{45} +(6.86721 + 1.56740i) q^{46} +(0.952840 + 1.97859i) q^{47} +(-0.822774 + 0.458162i) q^{48} -3.08661 q^{49} -9.22825 q^{50} +(-0.117950 - 0.211816i) q^{51} +(1.16227 + 0.559718i) q^{52} +(6.04937 + 4.82421i) q^{53} +(3.38147 - 2.44825i) q^{54} +(4.70965 - 1.07495i) q^{55} +(6.69206 - 5.33674i) q^{56} +(0.0371981 + 0.626669i) q^{57} +(-4.09011 + 1.96969i) q^{58} +(-5.49104 - 4.37895i) q^{59} +(6.37011 + 7.08257i) q^{60} +(5.92730 + 1.35287i) q^{61} +(-4.91814 + 2.36845i) q^{62} +(6.69408 - 6.78003i) q^{63} +(-0.799773 + 3.50404i) q^{64} +(0.860488 - 3.77004i) q^{65} +(1.35331 + 0.953752i) q^{66} +(4.43756 - 2.13702i) q^{67} +(0.184843 + 0.0421891i) q^{68} +(-11.2905 + 10.1547i) q^{69} +(-8.10010 - 6.45962i) q^{70} +(8.40760 - 4.04888i) q^{71} +(-0.854002 + 8.04006i) q^{72} +(-5.34444 + 4.26205i) q^{73} +(0.914532 - 0.208736i) q^{74} +(11.4606 - 16.2619i) q^{75} +(-0.383828 - 0.306092i) q^{76} +(3.40438 + 1.63947i) q^{77} +(1.15790 - 0.644777i) q^{78} -6.11283 q^{79} -2.20764 q^{80} +(0.114804 + 8.99927i) q^{81} +(2.36252 + 4.90583i) q^{82} +(-12.3961 - 2.82932i) q^{83} +(0.441504 + 7.43792i) q^{84} -0.568339i q^{85} +(1.12668 - 5.14652i) q^{86} +(1.60857 - 9.65369i) q^{87} +(-3.12610 + 0.713512i) q^{88} +(-0.425398 + 1.86379i) q^{89} +(9.71774 - 1.15774i) q^{90} +(2.36483 - 1.88589i) q^{91} -11.8753i q^{92} +(1.93422 - 11.6081i) q^{93} +(-1.37945 + 1.10007i) q^{94} +(-0.638520 + 1.32590i) q^{95} +(-6.74920 - 7.50406i) q^{96} +(2.31217 + 1.11348i) q^{97} +(-0.551821 - 2.41768i) q^{98} +(-3.36137 + 1.20031i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q - 7 q^{3} - 18 q^{4} - 14 q^{6} - 9 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 72 q - 7 q^{3} - 18 q^{4} - 14 q^{6} - 9 q^{9} - 10 q^{10} + 7 q^{12} - 12 q^{13} + q^{15} - 10 q^{16} - 7 q^{18} - 56 q^{19} + 18 q^{21} - 56 q^{22} + 2 q^{24} - 14 q^{25} - 7 q^{27} + 42 q^{28} - 42 q^{30} + 54 q^{31} + 14 q^{33} + 28 q^{34} + 6 q^{36} - 7 q^{39} + 86 q^{40} - 4 q^{43} - 21 q^{45} - 42 q^{46} + 35 q^{48} + 24 q^{49} - 28 q^{51} + 76 q^{52} - 47 q^{54} - 56 q^{55} - 19 q^{57} - 42 q^{58} - 81 q^{60} - 14 q^{61} + 7 q^{63} - 42 q^{64} + 55 q^{66} - 34 q^{67} + 63 q^{69} + 154 q^{70} - 14 q^{72} - 42 q^{73} + 7 q^{75} - 70 q^{76} + 82 q^{78} - 84 q^{79} - 5 q^{81} - 14 q^{82} + 144 q^{84} + 78 q^{87} + 56 q^{88} + 148 q^{90} + 56 q^{91} - 70 q^{94} - 64 q^{96} + 18 q^{97} + 26 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/129\mathbb{Z}\right)^\times\).

\(n\) \(44\) \(46\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{14}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.178779 + 0.783281i 0.126416 + 0.553863i 0.997977 + 0.0635767i \(0.0202508\pi\)
−0.871561 + 0.490287i \(0.836892\pi\)
\(3\) −1.60231 0.657721i −0.925095 0.379735i
\(4\) 1.22037 0.587699i 0.610185 0.293850i
\(5\) −2.53156 3.17448i −1.13215 1.41967i −0.893785 0.448495i \(-0.851960\pi\)
−0.238364 0.971176i \(-0.576611\pi\)
\(6\) 0.228721 1.37265i 0.0933748 0.560381i
\(7\) 3.17594i 1.20039i −0.799852 0.600197i \(-0.795089\pi\)
0.799852 0.600197i \(-0.204911\pi\)
\(8\) 1.68036 + 2.10711i 0.594098 + 0.744976i
\(9\) 2.13481 + 2.10775i 0.711602 + 0.702582i
\(10\) 2.03392 2.55046i 0.643182 0.806525i
\(11\) −0.516214 + 1.07193i −0.155644 + 0.323199i −0.964180 0.265248i \(-0.914546\pi\)
0.808536 + 0.588447i \(0.200260\pi\)
\(12\) −2.34196 + 0.139015i −0.676064 + 0.0401302i
\(13\) 0.593805 + 0.744608i 0.164692 + 0.206517i 0.857329 0.514770i \(-0.172123\pi\)
−0.692637 + 0.721287i \(0.743551\pi\)
\(14\) 2.48766 0.567791i 0.664854 0.151749i
\(15\) 1.96843 + 6.75157i 0.508247 + 1.74325i
\(16\) 0.338999 0.425091i 0.0847498 0.106273i
\(17\) 0.109436 + 0.0872725i 0.0265422 + 0.0211667i 0.636671 0.771136i \(-0.280311\pi\)
−0.610129 + 0.792302i \(0.708882\pi\)
\(18\) −1.26930 + 2.04897i −0.299177 + 0.482948i
\(19\) −0.157259 0.326551i −0.0360776 0.0749159i 0.882151 0.470967i \(-0.156095\pi\)
−0.918229 + 0.396051i \(0.870380\pi\)
\(20\) −4.95509 2.38624i −1.10799 0.533580i
\(21\) −2.08888 + 5.08885i −0.455832 + 1.11048i
\(22\) −0.931910 0.212702i −0.198684 0.0453483i
\(23\) 3.80396 7.89901i 0.793181 1.64706i 0.0311525 0.999515i \(-0.490082\pi\)
0.762029 0.647543i \(-0.224203\pi\)
\(24\) −1.30658 4.48146i −0.266704 0.914774i
\(25\) −2.55591 + 11.1982i −0.511181 + 2.23963i
\(26\) −0.477077 + 0.598236i −0.0935626 + 0.117324i
\(27\) −2.03432 4.78138i −0.391505 0.920176i
\(28\) −1.86650 3.87583i −0.352735 0.732462i
\(29\) 1.25733 + 5.50874i 0.233481 + 1.02295i 0.946728 + 0.322034i \(0.104367\pi\)
−0.713247 + 0.700913i \(0.752776\pi\)
\(30\) −4.93646 + 2.74887i −0.901271 + 0.501873i
\(31\) 1.51188 + 6.62398i 0.271542 + 1.18970i 0.908194 + 0.418550i \(0.137462\pi\)
−0.636652 + 0.771151i \(0.719681\pi\)
\(32\) 5.24997 + 2.52825i 0.928071 + 0.446936i
\(33\) 1.53217 1.37804i 0.266716 0.239886i
\(34\) −0.0487940 + 0.101322i −0.00836810 + 0.0173765i
\(35\) −10.0820 + 8.04010i −1.70416 + 1.35903i
\(36\) 3.84398 + 1.31761i 0.640663 + 0.219601i
\(37\) 1.16757i 0.191947i −0.995384 0.0959733i \(-0.969404\pi\)
0.995384 0.0959733i \(-0.0305963\pi\)
\(38\) 0.227667 0.181558i 0.0369324 0.0294526i
\(39\) −0.461717 1.58365i −0.0739338 0.253587i
\(40\) 2.43503 10.6686i 0.385012 1.68685i
\(41\) 6.60740 1.50809i 1.03190 0.235525i 0.327145 0.944974i \(-0.393913\pi\)
0.704757 + 0.709449i \(0.251056\pi\)
\(42\) −4.35945 0.726404i −0.672677 0.112087i
\(43\) −5.93308 2.79260i −0.904786 0.425867i
\(44\) 1.61153i 0.242947i
\(45\) 1.28660 12.1128i 0.191795 1.80567i
\(46\) 6.86721 + 1.56740i 1.01252 + 0.231100i
\(47\) 0.952840 + 1.97859i 0.138986 + 0.288607i 0.958831 0.283979i \(-0.0916545\pi\)
−0.819845 + 0.572586i \(0.805940\pi\)
\(48\) −0.822774 + 0.458162i −0.118757 + 0.0661300i
\(49\) −3.08661 −0.440944
\(50\) −9.22825 −1.30507
\(51\) −0.117950 0.211816i −0.0165163 0.0296602i
\(52\) 1.16227 + 0.559718i 0.161177 + 0.0776190i
\(53\) 6.04937 + 4.82421i 0.830945 + 0.662657i 0.943640 0.330973i \(-0.107377\pi\)
−0.112695 + 0.993630i \(0.535948\pi\)
\(54\) 3.38147 2.44825i 0.460159 0.333165i
\(55\) 4.70965 1.07495i 0.635048 0.144946i
\(56\) 6.69206 5.33674i 0.894264 0.713152i
\(57\) 0.0371981 + 0.626669i 0.00492701 + 0.0830043i
\(58\) −4.09011 + 1.96969i −0.537057 + 0.258633i
\(59\) −5.49104 4.37895i −0.714872 0.570091i 0.197080 0.980387i \(-0.436854\pi\)
−0.911952 + 0.410296i \(0.865425\pi\)
\(60\) 6.37011 + 7.08257i 0.822378 + 0.914356i
\(61\) 5.92730 + 1.35287i 0.758913 + 0.173217i 0.584431 0.811443i \(-0.301318\pi\)
0.174482 + 0.984660i \(0.444175\pi\)
\(62\) −4.91814 + 2.36845i −0.624605 + 0.300794i
\(63\) 6.69408 6.78003i 0.843375 0.854203i
\(64\) −0.799773 + 3.50404i −0.0999716 + 0.438004i
\(65\) 0.860488 3.77004i 0.106730 0.467616i
\(66\) 1.35331 + 0.953752i 0.166581 + 0.117399i
\(67\) 4.43756 2.13702i 0.542134 0.261078i −0.142714 0.989764i \(-0.545583\pi\)
0.684848 + 0.728686i \(0.259869\pi\)
\(68\) 0.184843 + 0.0421891i 0.0224155 + 0.00511618i
\(69\) −11.2905 + 10.1547i −1.35921 + 1.22249i
\(70\) −8.10010 6.45962i −0.968147 0.772072i
\(71\) 8.40760 4.04888i 0.997798 0.480514i 0.137607 0.990487i \(-0.456059\pi\)
0.860191 + 0.509973i \(0.170344\pi\)
\(72\) −0.854002 + 8.04006i −0.100645 + 0.947530i
\(73\) −5.34444 + 4.26205i −0.625519 + 0.498835i −0.884188 0.467131i \(-0.845288\pi\)
0.258669 + 0.965966i \(0.416716\pi\)
\(74\) 0.914532 0.208736i 0.106312 0.0242651i
\(75\) 11.4606 16.2619i 1.32336 1.87776i
\(76\) −0.383828 0.306092i −0.0440281 0.0351112i
\(77\) 3.40438 + 1.63947i 0.387966 + 0.186834i
\(78\) 1.15790 0.644777i 0.131106 0.0730066i
\(79\) −6.11283 −0.687747 −0.343873 0.939016i \(-0.611739\pi\)
−0.343873 + 0.939016i \(0.611739\pi\)
\(80\) −2.20764 −0.246822
\(81\) 0.114804 + 8.99927i 0.0127560 + 0.999919i
\(82\) 2.36252 + 4.90583i 0.260897 + 0.541759i
\(83\) −12.3961 2.82932i −1.36065 0.310559i −0.520937 0.853595i \(-0.674417\pi\)
−0.839709 + 0.543036i \(0.817275\pi\)
\(84\) 0.441504 + 7.43792i 0.0481720 + 0.811543i
\(85\) 0.568339i 0.0616450i
\(86\) 1.12668 5.14652i 0.121493 0.554964i
\(87\) 1.60857 9.65369i 0.172457 1.03498i
\(88\) −3.12610 + 0.713512i −0.333243 + 0.0760606i
\(89\) −0.425398 + 1.86379i −0.0450921 + 0.197561i −0.992457 0.122595i \(-0.960878\pi\)
0.947365 + 0.320156i \(0.103735\pi\)
\(90\) 9.71774 1.15774i 1.02434 0.122037i
\(91\) 2.36483 1.88589i 0.247902 0.197695i
\(92\) 11.8753i 1.23809i
\(93\) 1.93422 11.6081i 0.200570 1.20370i
\(94\) −1.37945 + 1.10007i −0.142279 + 0.113464i
\(95\) −0.638520 + 1.32590i −0.0655107 + 0.136034i
\(96\) −6.74920 7.50406i −0.688837 0.765879i
\(97\) 2.31217 + 1.11348i 0.234765 + 0.113057i 0.547568 0.836761i \(-0.315554\pi\)
−0.312803 + 0.949818i \(0.601268\pi\)
\(98\) −0.551821 2.41768i −0.0557423 0.244223i
\(99\) −3.36137 + 1.20031i −0.337831 + 0.120636i
\(100\) 3.46200 + 15.1680i 0.346200 + 1.51680i
\(101\) 1.71938 + 3.57032i 0.171084 + 0.355260i 0.968827 0.247738i \(-0.0796871\pi\)
−0.797743 + 0.602998i \(0.793973\pi\)
\(102\) 0.144825 0.130256i 0.0143398 0.0128973i
\(103\) 8.04400 10.0869i 0.792598 0.993887i −0.207280 0.978282i \(-0.566461\pi\)
0.999878 0.0156053i \(-0.00496754\pi\)
\(104\) −0.571162 + 2.50242i −0.0560070 + 0.245383i
\(105\) 21.4426 6.25163i 2.09258 0.610097i
\(106\) −2.69722 + 5.60082i −0.261977 + 0.544000i
\(107\) −10.9413 2.49728i −1.05773 0.241421i −0.341932 0.939725i \(-0.611081\pi\)
−0.715801 + 0.698304i \(0.753938\pi\)
\(108\) −5.29263 4.63948i −0.509284 0.446434i
\(109\) −15.3693 7.40145i −1.47211 0.708931i −0.485836 0.874050i \(-0.661485\pi\)
−0.986274 + 0.165119i \(0.947199\pi\)
\(110\) 1.68397 + 3.49680i 0.160560 + 0.333407i
\(111\) −0.767932 + 1.87080i −0.0728889 + 0.177569i
\(112\) −1.35007 1.07664i −0.127569 0.101733i
\(113\) −10.3069 + 12.9245i −0.969596 + 1.21584i 0.00682852 + 0.999977i \(0.497826\pi\)
−0.976425 + 0.215858i \(0.930745\pi\)
\(114\) −0.484208 + 0.141172i −0.0453502 + 0.0132219i
\(115\) −34.7052 + 7.92124i −3.23628 + 0.738660i
\(116\) 4.77190 + 5.98377i 0.443059 + 0.555579i
\(117\) −0.301786 + 2.84118i −0.0279001 + 0.262668i
\(118\) 2.44827 5.08389i 0.225382 0.468010i
\(119\) 0.277172 0.347563i 0.0254083 0.0318611i
\(120\) −10.9186 + 15.4928i −0.996729 + 1.41429i
\(121\) 5.97583 + 7.49346i 0.543258 + 0.681223i
\(122\) 4.88460i 0.442231i
\(123\) −11.5790 1.92938i −1.04404 0.173966i
\(124\) 5.73796 + 7.19518i 0.515284 + 0.646146i
\(125\) 23.7277 11.4267i 2.12227 1.02203i
\(126\) 6.50743 + 4.03122i 0.579728 + 0.359130i
\(127\) 2.90055 + 12.7081i 0.257382 + 1.12767i 0.924038 + 0.382300i \(0.124868\pi\)
−0.666656 + 0.745365i \(0.732275\pi\)
\(128\) 8.76642 0.774849
\(129\) 7.66989 + 8.37692i 0.675296 + 0.737547i
\(130\) 3.10684 0.272488
\(131\) 2.58570 + 11.3287i 0.225913 + 0.989791i 0.952934 + 0.303176i \(0.0980471\pi\)
−0.727021 + 0.686615i \(0.759096\pi\)
\(132\) 1.05994 2.58217i 0.0922556 0.224749i
\(133\) −1.03711 + 0.499445i −0.0899286 + 0.0433073i
\(134\) 2.46722 + 3.09380i 0.213136 + 0.267264i
\(135\) −10.0284 + 18.5623i −0.863105 + 1.59759i
\(136\) 0.377244i 0.0323484i
\(137\) −2.84902 3.57256i −0.243408 0.305224i 0.645088 0.764108i \(-0.276821\pi\)
−0.888496 + 0.458884i \(0.848249\pi\)
\(138\) −9.97251 7.02817i −0.848916 0.598277i
\(139\) −2.27559 + 2.85350i −0.193013 + 0.242031i −0.868916 0.494960i \(-0.835183\pi\)
0.675903 + 0.736991i \(0.263754\pi\)
\(140\) −7.57857 + 15.7371i −0.640506 + 1.33002i
\(141\) −0.225386 3.79702i −0.0189809 0.319767i
\(142\) 4.67451 + 5.86166i 0.392277 + 0.491899i
\(143\) −1.10470 + 0.252140i −0.0923794 + 0.0210850i
\(144\) 1.61968 0.192964i 0.134974 0.0160803i
\(145\) 14.3044 17.9371i 1.18791 1.48960i
\(146\) −4.29385 3.42423i −0.355362 0.283391i
\(147\) 4.94571 + 2.03013i 0.407916 + 0.167442i
\(148\) −0.686178 1.42486i −0.0564035 0.117123i
\(149\) −8.08783 3.89489i −0.662581 0.319082i 0.0721967 0.997390i \(-0.476999\pi\)
−0.734777 + 0.678308i \(0.762713\pi\)
\(150\) 14.7865 + 6.06961i 1.20732 + 0.495582i
\(151\) −3.48583 0.795617i −0.283672 0.0647464i 0.0783172 0.996928i \(-0.475045\pi\)
−0.361990 + 0.932182i \(0.617902\pi\)
\(152\) 0.423827 0.880086i 0.0343769 0.0713844i
\(153\) 0.0496769 + 0.416974i 0.00401614 + 0.0337103i
\(154\) −0.675530 + 2.95969i −0.0544358 + 0.238499i
\(155\) 17.2003 21.5685i 1.38156 1.73242i
\(156\) −1.49418 1.66129i −0.119630 0.133010i
\(157\) 4.15038 + 8.61836i 0.331237 + 0.687820i 0.998367 0.0571207i \(-0.0181920\pi\)
−0.667131 + 0.744941i \(0.732478\pi\)
\(158\) −1.09284 4.78806i −0.0869420 0.380918i
\(159\) −6.52000 11.7087i −0.517069 0.928559i
\(160\) −5.26474 23.0663i −0.416214 1.82355i
\(161\) −25.0868 12.0812i −1.97712 0.952130i
\(162\) −7.02843 + 1.69880i −0.552206 + 0.133470i
\(163\) 4.39342 9.12303i 0.344119 0.714571i −0.655039 0.755595i \(-0.727348\pi\)
0.999158 + 0.0410241i \(0.0130621\pi\)
\(164\) 7.17716 5.72360i 0.560442 0.446938i
\(165\) −8.25334 1.37523i −0.642521 0.107062i
\(166\) 10.2154i 0.792872i
\(167\) 2.37247 1.89198i 0.183587 0.146406i −0.527384 0.849627i \(-0.676827\pi\)
0.710971 + 0.703221i \(0.248256\pi\)
\(168\) −14.2329 + 4.14962i −1.09809 + 0.320150i
\(169\) 2.69094 11.7898i 0.206995 0.906905i
\(170\) 0.445169 0.101607i 0.0341429 0.00779290i
\(171\) 0.352570 1.02859i 0.0269617 0.0786579i
\(172\) −8.88176 + 0.0788599i −0.677228 + 0.00601301i
\(173\) 12.6343i 0.960572i 0.877112 + 0.480286i \(0.159467\pi\)
−0.877112 + 0.480286i \(0.840533\pi\)
\(174\) 7.84913 0.465913i 0.595041 0.0353208i
\(175\) 35.5647 + 8.11741i 2.68844 + 0.613619i
\(176\) 0.280672 + 0.582821i 0.0211564 + 0.0439318i
\(177\) 5.91822 + 10.6280i 0.444841 + 0.798851i
\(178\) −1.53592 −0.115122
\(179\) 11.9633 0.894179 0.447090 0.894489i \(-0.352460\pi\)
0.447090 + 0.894489i \(0.352460\pi\)
\(180\) −5.54855 15.5382i −0.413565 1.15815i
\(181\) 6.56258 + 3.16037i 0.487793 + 0.234909i 0.661580 0.749875i \(-0.269886\pi\)
−0.173787 + 0.984783i \(0.555600\pi\)
\(182\) 1.89996 + 1.51517i 0.140835 + 0.112312i
\(183\) −8.60757 6.06622i −0.636290 0.448428i
\(184\) 23.0361 5.25785i 1.69825 0.387614i
\(185\) −3.70641 + 2.95577i −0.272501 + 0.217312i
\(186\) 9.43818 0.560237i 0.692041 0.0410785i
\(187\) −0.150042 + 0.0722566i −0.0109722 + 0.00528392i
\(188\) 2.32563 + 1.85463i 0.169614 + 0.135263i
\(189\) −15.1854 + 6.46088i −1.10457 + 0.469960i
\(190\) −1.15271 0.263098i −0.0836261 0.0190871i
\(191\) −7.98825 + 3.84694i −0.578010 + 0.278355i −0.699961 0.714181i \(-0.746799\pi\)
0.121951 + 0.992536i \(0.461085\pi\)
\(192\) 3.58616 5.08853i 0.258809 0.367233i
\(193\) −0.202622 + 0.887747i −0.0145851 + 0.0639014i −0.981697 0.190451i \(-0.939005\pi\)
0.967112 + 0.254352i \(0.0818622\pi\)
\(194\) −0.458803 + 2.01015i −0.0329401 + 0.144320i
\(195\) −3.85840 + 5.47482i −0.276306 + 0.392060i
\(196\) −3.76681 + 1.81400i −0.269058 + 0.129571i
\(197\) −12.8758 2.93881i −0.917361 0.209382i −0.262325 0.964980i \(-0.584489\pi\)
−0.655036 + 0.755598i \(0.727346\pi\)
\(198\) −1.54112 2.41831i −0.109523 0.171862i
\(199\) −0.480775 0.383405i −0.0340812 0.0271789i 0.606301 0.795235i \(-0.292653\pi\)
−0.640382 + 0.768056i \(0.721224\pi\)
\(200\) −27.8906 + 13.4314i −1.97216 + 0.949744i
\(201\) −8.51591 + 0.505492i −0.600666 + 0.0356546i
\(202\) −2.48918 + 1.98505i −0.175138 + 0.139668i
\(203\) 17.4954 3.99322i 1.22794 0.280269i
\(204\) −0.268427 0.189175i −0.0187936 0.0132449i
\(205\) −21.5145 17.1572i −1.50264 1.19831i
\(206\) 9.33894 + 4.49739i 0.650675 + 0.313348i
\(207\) 24.7698 8.84507i 1.72162 0.614775i
\(208\) 0.517825 0.0359047
\(209\) 0.431219 0.0298280
\(210\) 8.73027 + 15.6779i 0.602446 + 1.08188i
\(211\) −0.320283 0.665076i −0.0220492 0.0457857i 0.889653 0.456636i \(-0.150946\pi\)
−0.911703 + 0.410851i \(0.865232\pi\)
\(212\) 10.2177 + 2.33211i 0.701752 + 0.160170i
\(213\) −16.1346 + 0.957728i −1.10553 + 0.0656224i
\(214\) 9.01656i 0.616359i
\(215\) 6.15491 + 25.9041i 0.419761 + 1.76664i
\(216\) 6.65649 12.3210i 0.452917 0.838337i
\(217\) 21.0374 4.80164i 1.42811 0.325957i
\(218\) 3.04972 13.3617i 0.206553 0.904968i
\(219\) 11.3667 3.31398i 0.768090 0.223938i
\(220\) 5.11577 4.07969i 0.344905 0.275052i
\(221\) 0.133310i 0.00896739i
\(222\) −1.60266 0.267046i −0.107563 0.0179230i
\(223\) −15.8052 + 12.6042i −1.05839 + 0.844040i −0.988150 0.153490i \(-0.950949\pi\)
−0.0702421 + 0.997530i \(0.522377\pi\)
\(224\) 8.02958 16.6736i 0.536499 1.11405i
\(225\) −29.0593 + 18.5187i −1.93728 + 1.23458i
\(226\) −11.9662 5.76261i −0.795979 0.383323i
\(227\) 4.25201 + 18.6293i 0.282216 + 1.23647i 0.894945 + 0.446176i \(0.147214\pi\)
−0.612729 + 0.790293i \(0.709928\pi\)
\(228\) 0.413688 + 0.742907i 0.0273972 + 0.0492002i
\(229\) −3.73076 16.3455i −0.246536 1.08014i −0.934937 0.354814i \(-0.884544\pi\)
0.688401 0.725330i \(-0.258313\pi\)
\(230\) −12.4091 25.7678i −0.818233 1.69908i
\(231\) −4.37658 4.86607i −0.287958 0.320164i
\(232\) −9.49474 + 11.9060i −0.623360 + 0.781669i
\(233\) 4.97440 21.7943i 0.325884 1.42779i −0.501014 0.865439i \(-0.667040\pi\)
0.826898 0.562352i \(-0.190103\pi\)
\(234\) −2.27940 + 0.271560i −0.149009 + 0.0177524i
\(235\) 3.86883 8.03370i 0.252374 0.524061i
\(236\) −9.27461 2.11687i −0.603725 0.137796i
\(237\) 9.79466 + 4.02053i 0.636231 + 0.261162i
\(238\) 0.321792 + 0.154967i 0.0208587 + 0.0100450i
\(239\) 3.56593 + 7.40473i 0.230661 + 0.478972i 0.983887 0.178789i \(-0.0572180\pi\)
−0.753227 + 0.657761i \(0.771504\pi\)
\(240\) 3.53733 + 1.45201i 0.228334 + 0.0937269i
\(241\) 9.03066 + 7.20171i 0.581716 + 0.463903i 0.869596 0.493763i \(-0.164379\pi\)
−0.287880 + 0.957666i \(0.592950\pi\)
\(242\) −4.80113 + 6.02043i −0.308628 + 0.387008i
\(243\) 5.73505 14.4951i 0.367904 0.929864i
\(244\) 8.02858 1.83247i 0.513977 0.117312i
\(245\) 7.81395 + 9.79839i 0.499215 + 0.625996i
\(246\) −0.558834 9.41455i −0.0356300 0.600250i
\(247\) 0.149771 0.311004i 0.00952973 0.0197887i
\(248\) −11.4169 + 14.3164i −0.724977 + 0.909092i
\(249\) 18.0015 + 12.6866i 1.14080 + 0.803982i
\(250\) 13.1923 + 16.5426i 0.834354 + 1.04625i
\(251\) 11.8664i 0.748999i 0.927227 + 0.374499i \(0.122185\pi\)
−0.927227 + 0.374499i \(0.877815\pi\)
\(252\) 4.18464 12.2083i 0.263608 0.769048i
\(253\) 6.50352 + 8.15516i 0.408873 + 0.512710i
\(254\) −9.43549 + 4.54389i −0.592035 + 0.285109i
\(255\) −0.373808 + 0.910656i −0.0234088 + 0.0570275i
\(256\) 3.16680 + 13.8746i 0.197925 + 0.867165i
\(257\) 10.5406 0.657507 0.328754 0.944416i \(-0.393371\pi\)
0.328754 + 0.944416i \(0.393371\pi\)
\(258\) −5.19027 + 7.50529i −0.323132 + 0.467259i
\(259\) −3.70812 −0.230411
\(260\) −1.16554 5.10656i −0.0722836 0.316695i
\(261\) −8.92687 + 14.4102i −0.552559 + 0.891971i
\(262\) −8.41127 + 4.05066i −0.519650 + 0.250250i
\(263\) 5.48797 + 6.88170i 0.338403 + 0.424344i 0.921693 0.387920i \(-0.126806\pi\)
−0.583290 + 0.812264i \(0.698235\pi\)
\(264\) 5.47828 + 0.912831i 0.337165 + 0.0561809i
\(265\) 31.4164i 1.92989i
\(266\) −0.576618 0.723056i −0.0353547 0.0443334i
\(267\) 1.90747 2.70658i 0.116735 0.165640i
\(268\) 4.15954 5.21590i 0.254084 0.318612i
\(269\) 1.83234 3.80490i 0.111720 0.231989i −0.837611 0.546267i \(-0.816048\pi\)
0.949331 + 0.314279i \(0.101763\pi\)
\(270\) −16.3323 4.53650i −0.993954 0.276083i
\(271\) 3.08033 + 3.86261i 0.187117 + 0.234637i 0.866537 0.499112i \(-0.166340\pi\)
−0.679421 + 0.733749i \(0.737769\pi\)
\(272\) 0.0741975 0.0169351i 0.00449889 0.00102684i
\(273\) −5.02958 + 1.46639i −0.304404 + 0.0887497i
\(274\) 2.28897 2.87028i 0.138282 0.173400i
\(275\) −10.6842 8.52039i −0.644284 0.513799i
\(276\) −7.81063 + 19.0279i −0.470145 + 1.14535i
\(277\) 11.7799 + 24.4612i 0.707784 + 1.46973i 0.875159 + 0.483836i \(0.160757\pi\)
−0.167375 + 0.985893i \(0.553529\pi\)
\(278\) −2.64192 1.27228i −0.158452 0.0763064i
\(279\) −10.7341 + 17.3276i −0.642634 + 1.03737i
\(280\) −33.8828 7.73352i −2.02488 0.462166i
\(281\) −6.64615 + 13.8009i −0.396476 + 0.823291i 0.603194 + 0.797595i \(0.293895\pi\)
−0.999670 + 0.0256961i \(0.991820\pi\)
\(282\) 2.93384 0.855368i 0.174708 0.0509364i
\(283\) −4.28936 + 18.7929i −0.254976 + 1.11712i 0.671570 + 0.740941i \(0.265620\pi\)
−0.926546 + 0.376182i \(0.877237\pi\)
\(284\) 7.88085 9.88228i 0.467643 0.586405i
\(285\) 1.89518 1.70454i 0.112261 0.100968i
\(286\) −0.394993 0.820211i −0.0233564 0.0485001i
\(287\) −4.78962 20.9847i −0.282722 1.23869i
\(288\) 5.87875 + 16.4629i 0.346409 + 0.970087i
\(289\) −3.77850 16.5547i −0.222264 0.973804i
\(290\) 16.6071 + 7.99756i 0.975203 + 0.469633i
\(291\) −2.97246 3.30491i −0.174248 0.193737i
\(292\) −4.01739 + 8.34220i −0.235100 + 0.488190i
\(293\) 5.39776 4.30457i 0.315341 0.251476i −0.453009 0.891506i \(-0.649650\pi\)
0.768350 + 0.640030i \(0.221078\pi\)
\(294\) −0.705972 + 4.23683i −0.0411731 + 0.247097i
\(295\) 28.5168i 1.66031i
\(296\) 2.46019 1.96194i 0.142996 0.114035i
\(297\) 6.17544 + 0.287567i 0.358335 + 0.0166863i
\(298\) 1.60486 7.03137i 0.0929672 0.407316i
\(299\) 8.14048 1.85801i 0.470776 0.107452i
\(300\) 4.42911 26.5809i 0.255715 1.53465i
\(301\) −8.86913 + 18.8431i −0.511208 + 1.08610i
\(302\) 2.87262i 0.165301i
\(303\) −0.406703 6.85164i −0.0233645 0.393616i
\(304\) −0.192125 0.0438512i −0.0110191 0.00251504i
\(305\) −10.7107 22.2410i −0.613292 1.27351i
\(306\) −0.317726 + 0.113457i −0.0181632 + 0.00648591i
\(307\) 3.33442 0.190305 0.0951527 0.995463i \(-0.469666\pi\)
0.0951527 + 0.995463i \(0.469666\pi\)
\(308\) 5.11812 0.291632
\(309\) −19.5233 + 10.8716i −1.11064 + 0.618463i
\(310\) 19.9692 + 9.61666i 1.13417 + 0.546190i
\(311\) −10.7871 8.60241i −0.611679 0.487798i 0.267966 0.963428i \(-0.413649\pi\)
−0.879645 + 0.475631i \(0.842220\pi\)
\(312\) 2.56108 3.63400i 0.144992 0.205735i
\(313\) −24.7910 + 5.65838i −1.40127 + 0.319830i −0.855369 0.518020i \(-0.826669\pi\)
−0.545900 + 0.837850i \(0.683812\pi\)
\(314\) −6.00860 + 4.79170i −0.339085 + 0.270411i
\(315\) −38.4696 4.08617i −2.16751 0.230230i
\(316\) −7.45991 + 3.59251i −0.419653 + 0.202094i
\(317\) −12.6297 10.0719i −0.709355 0.565692i 0.200964 0.979599i \(-0.435593\pi\)
−0.910319 + 0.413907i \(0.864164\pi\)
\(318\) 8.00556 7.20025i 0.448929 0.403770i
\(319\) −6.55403 1.49591i −0.366955 0.0837551i
\(320\) 13.1482 6.33182i 0.735005 0.353960i
\(321\) 15.8888 + 11.1977i 0.886828 + 0.624996i
\(322\) 4.97796 21.8099i 0.277411 1.21542i
\(323\) 0.0112891 0.0494609i 0.000628143 0.00275208i
\(324\) 5.42897 + 10.9150i 0.301609 + 0.606387i
\(325\) −9.85594 + 4.74637i −0.546709 + 0.263281i
\(326\) 7.93135 + 1.81028i 0.439277 + 0.100262i
\(327\) 19.7583 + 21.9681i 1.09264 + 1.21484i
\(328\) 14.2806 + 11.3884i 0.788512 + 0.628817i
\(329\) 6.28389 3.02616i 0.346442 0.166838i
\(330\) −0.398328 6.71054i −0.0219272 0.369403i
\(331\) 12.0012 9.57060i 0.659643 0.526048i −0.235473 0.971881i \(-0.575664\pi\)
0.895116 + 0.445833i \(0.147092\pi\)
\(332\) −16.7906 + 3.83235i −0.921504 + 0.210327i
\(333\) 2.46093 2.49253i 0.134858 0.136590i
\(334\) 1.90610 + 1.52006i 0.104297 + 0.0831741i
\(335\) −18.0179 8.67695i −0.984422 0.474073i
\(336\) 1.45510 + 2.61308i 0.0793821 + 0.142555i
\(337\) −24.5061 −1.33493 −0.667467 0.744639i \(-0.732621\pi\)
−0.667467 + 0.744639i \(0.732621\pi\)
\(338\) 9.71578 0.528469
\(339\) 25.0157 13.9300i 1.35866 0.756574i
\(340\) −0.334012 0.693584i −0.0181144 0.0376149i
\(341\) −7.88089 1.79876i −0.426774 0.0974084i
\(342\) 0.868703 + 0.0922722i 0.0469741 + 0.00498951i
\(343\) 12.4287i 0.671087i
\(344\) −4.08541 17.1942i −0.220271 0.927051i
\(345\) 60.8186 + 10.1340i 3.27436 + 0.545599i
\(346\) −9.89624 + 2.25875i −0.532025 + 0.121431i
\(347\) −1.12947 + 4.94853i −0.0606331 + 0.265651i −0.996154 0.0876206i \(-0.972074\pi\)
0.935521 + 0.353272i \(0.114931\pi\)
\(348\) −3.71042 12.7264i −0.198899 0.682209i
\(349\) 1.24279 0.991090i 0.0665249 0.0530518i −0.589663 0.807650i \(-0.700739\pi\)
0.656188 + 0.754598i \(0.272168\pi\)
\(350\) 29.3084i 1.56660i
\(351\) 2.35226 4.35397i 0.125554 0.232398i
\(352\) −5.42021 + 4.32247i −0.288898 + 0.230389i
\(353\) −8.89967 + 18.4804i −0.473682 + 0.983611i 0.518058 + 0.855345i \(0.326655\pi\)
−0.991740 + 0.128265i \(0.959059\pi\)
\(354\) −7.26667 + 6.53570i −0.386219 + 0.347368i
\(355\) −34.1375 16.4397i −1.81183 0.872531i
\(356\) 0.576205 + 2.52452i 0.0305388 + 0.133799i
\(357\) −0.672716 + 0.374603i −0.0356039 + 0.0198261i
\(358\) 2.13879 + 9.37063i 0.113038 + 0.495253i
\(359\) 8.37325 + 17.3872i 0.441923 + 0.917663i 0.996344 + 0.0854266i \(0.0272253\pi\)
−0.554421 + 0.832236i \(0.687060\pi\)
\(360\) 27.6850 17.6429i 1.45913 0.929863i
\(361\) 11.7644 14.7521i 0.619179 0.776426i
\(362\) −1.30221 + 5.70535i −0.0684426 + 0.299867i
\(363\) −4.64655 15.9373i −0.243880 0.836491i
\(364\) 1.77763 3.69129i 0.0931733 0.193476i
\(365\) 27.0596 + 6.17617i 1.41636 + 0.323275i
\(366\) 3.21271 7.82666i 0.167931 0.409106i
\(367\) 13.8076 + 6.64938i 0.720750 + 0.347095i 0.758039 0.652210i \(-0.226158\pi\)
−0.0372887 + 0.999305i \(0.511872\pi\)
\(368\) −2.06826 4.29479i −0.107816 0.223881i
\(369\) 17.2842 + 10.7072i 0.899779 + 0.557396i
\(370\) −2.97782 2.37474i −0.154810 0.123457i
\(371\) 15.3214 19.2125i 0.795449 0.997461i
\(372\) −4.46159 15.3029i −0.231323 0.793418i
\(373\) 20.4553 4.66878i 1.05913 0.241740i 0.342736 0.939432i \(-0.388646\pi\)
0.716398 + 0.697691i \(0.245789\pi\)
\(374\) −0.0834216 0.104607i −0.00431363 0.00540912i
\(375\) −45.5347 + 2.70287i −2.35140 + 0.139576i
\(376\) −2.56799 + 5.33249i −0.132434 + 0.275002i
\(377\) −3.35524 + 4.20734i −0.172804 + 0.216689i
\(378\) −7.77551 10.7393i −0.399929 0.552372i
\(379\) 4.84820 + 6.07946i 0.249036 + 0.312281i 0.890599 0.454789i \(-0.150285\pi\)
−0.641564 + 0.767070i \(0.721714\pi\)
\(380\) 1.99335i 0.102256i
\(381\) 3.71082 22.2702i 0.190111 1.14093i
\(382\) −4.44137 5.56930i −0.227240 0.284950i
\(383\) −23.5908 + 11.3607i −1.20543 + 0.580506i −0.925220 0.379431i \(-0.876120\pi\)
−0.280214 + 0.959938i \(0.590405\pi\)
\(384\) −14.0465 5.76585i −0.716809 0.294237i
\(385\) −3.41397 14.9576i −0.173992 0.762308i
\(386\) −0.731580 −0.0372364
\(387\) −6.77988 18.4671i −0.344641 0.938735i
\(388\) 3.47610 0.176472
\(389\) 1.95759 + 8.57675i 0.0992536 + 0.434858i 1.00000 0.000512711i \(0.000163201\pi\)
−0.900746 + 0.434346i \(0.856980\pi\)
\(390\) −4.97813 2.04343i −0.252077 0.103473i
\(391\) 1.10566 0.532457i 0.0559155 0.0269275i
\(392\) −5.18663 6.50383i −0.261964 0.328493i
\(393\) 3.30801 19.8527i 0.166867 1.00144i
\(394\) 10.6107i 0.534562i
\(395\) 15.4750 + 19.4051i 0.778632 + 0.976374i
\(396\) −3.39670 + 3.44030i −0.170690 + 0.172882i
\(397\) 3.26814 4.09811i 0.164023 0.205678i −0.693027 0.720912i \(-0.743723\pi\)
0.857050 + 0.515233i \(0.172295\pi\)
\(398\) 0.214362 0.445127i 0.0107450 0.0223122i
\(399\) 1.99026 0.118139i 0.0996379 0.00591436i
\(400\) 3.89379 + 4.88266i 0.194690 + 0.244133i
\(401\) 12.4548 2.84272i 0.621962 0.141959i 0.100084 0.994979i \(-0.468089\pi\)
0.521878 + 0.853020i \(0.325232\pi\)
\(402\) −1.91841 6.57998i −0.0956814 0.328180i
\(403\) −4.03450 + 5.05911i −0.200973 + 0.252012i
\(404\) 4.19655 + 3.34664i 0.208786 + 0.166501i
\(405\) 28.2774 23.1467i 1.40511 1.15017i
\(406\) 6.25563 + 12.9899i 0.310462 + 0.644680i
\(407\) 1.25155 + 0.602713i 0.0620369 + 0.0298754i
\(408\) 0.248121 0.604462i 0.0122838 0.0299253i
\(409\) −29.5751 6.75032i −1.46239 0.333782i −0.584014 0.811744i \(-0.698519\pi\)
−0.878381 + 0.477962i \(0.841376\pi\)
\(410\) 9.59259 19.9192i 0.473744 0.983740i
\(411\) 2.21528 + 7.59822i 0.109271 + 0.374792i
\(412\) 3.88862 17.0371i 0.191578 0.839360i
\(413\) −13.9073 + 17.4392i −0.684334 + 0.858128i
\(414\) 11.3565 + 17.8204i 0.558142 + 0.875827i
\(415\) 22.3998 + 46.5137i 1.09956 + 2.28327i
\(416\) 1.23490 + 5.41045i 0.0605460 + 0.265269i
\(417\) 5.52301 3.07549i 0.270463 0.150608i
\(418\) 0.0770927 + 0.337765i 0.00377073 + 0.0165206i
\(419\) −5.42569 2.61287i −0.265062 0.127647i 0.296633 0.954992i \(-0.404136\pi\)
−0.561695 + 0.827344i \(0.689851\pi\)
\(420\) 22.4938 20.2311i 1.09759 0.987177i
\(421\) 10.3277 21.4457i 0.503340 1.04520i −0.482248 0.876035i \(-0.660180\pi\)
0.985588 0.169162i \(-0.0541062\pi\)
\(422\) 0.463681 0.369773i 0.0225716 0.0180003i
\(423\) −2.13624 + 6.23226i −0.103868 + 0.303023i
\(424\) 20.8531i 1.01272i
\(425\) −1.25700 + 1.00242i −0.0609734 + 0.0486247i
\(426\) −3.63470 12.4667i −0.176102 0.604015i
\(427\) 4.29663 18.8248i 0.207928 0.910994i
\(428\) −14.8201 + 3.38258i −0.716355 + 0.163503i
\(429\) 1.93591 + 0.322575i 0.0934664 + 0.0155741i
\(430\) −19.1898 + 9.45212i −0.925415 + 0.455822i
\(431\) 27.4545i 1.32244i −0.750194 0.661218i \(-0.770040\pi\)
0.750194 0.661218i \(-0.229960\pi\)
\(432\) −2.72215 0.756110i −0.130970 0.0363784i
\(433\) 30.6353 + 6.99230i 1.47224 + 0.336028i 0.882018 0.471215i \(-0.156185\pi\)
0.590218 + 0.807244i \(0.299042\pi\)
\(434\) 7.52207 + 15.6197i 0.361071 + 0.749772i
\(435\) −34.7177 + 19.3326i −1.66458 + 0.926926i
\(436\) −23.1060 −1.10658
\(437\) −3.17764 −0.152007
\(438\) 4.62790 + 8.31084i 0.221130 + 0.397107i
\(439\) 5.50138 + 2.64933i 0.262567 + 0.126445i 0.560536 0.828130i \(-0.310595\pi\)
−0.297969 + 0.954575i \(0.596309\pi\)
\(440\) 10.1789 + 8.11744i 0.485262 + 0.386984i
\(441\) −6.58932 6.50580i −0.313777 0.309800i
\(442\) −0.104419 + 0.0238330i −0.00496671 + 0.00113362i
\(443\) 3.54107 2.82391i 0.168241 0.134168i −0.535750 0.844377i \(-0.679971\pi\)
0.703991 + 0.710209i \(0.251400\pi\)
\(444\) 0.162309 + 2.73439i 0.00770285 + 0.129768i
\(445\) 6.99349 3.36789i 0.331523 0.159653i
\(446\) −12.6983 10.1265i −0.601280 0.479505i
\(447\) 10.3975 + 11.5604i 0.491784 + 0.546786i
\(448\) 11.1286 + 2.54003i 0.525778 + 0.120005i
\(449\) −15.2686 + 7.35295i −0.720568 + 0.347007i −0.757967 0.652293i \(-0.773807\pi\)
0.0373987 + 0.999300i \(0.488093\pi\)
\(450\) −19.7005 19.4508i −0.928692 0.916920i
\(451\) −1.79426 + 7.86116i −0.0844883 + 0.370167i
\(452\) −4.98257 + 21.8301i −0.234360 + 1.02680i
\(453\) 5.06209 + 3.56753i 0.237838 + 0.167617i
\(454\) −13.8318 + 6.66104i −0.649158 + 0.312618i
\(455\) −11.9734 2.73286i −0.561323 0.128118i
\(456\) −1.25795 + 1.13141i −0.0589091 + 0.0529833i
\(457\) −17.1713 13.6937i −0.803240 0.640563i 0.133318 0.991073i \(-0.457437\pi\)
−0.936559 + 0.350510i \(0.886008\pi\)
\(458\) 12.1362 5.84447i 0.567086 0.273094i
\(459\) 0.194654 0.700795i 0.00908568 0.0327103i
\(460\) −37.6979 + 30.0631i −1.75768 + 1.40170i
\(461\) 23.5163 5.36745i 1.09527 0.249987i 0.363535 0.931581i \(-0.381570\pi\)
0.731731 + 0.681594i \(0.238713\pi\)
\(462\) 3.02906 4.29804i 0.140925 0.199963i
\(463\) 5.77693 + 4.60695i 0.268477 + 0.214103i 0.748469 0.663170i \(-0.230789\pi\)
−0.479992 + 0.877273i \(0.659361\pi\)
\(464\) 2.76795 + 1.33298i 0.128499 + 0.0618818i
\(465\) −41.7462 + 23.2464i −1.93593 + 1.07803i
\(466\) 17.9604 0.831998
\(467\) 18.6616 0.863557 0.431778 0.901980i \(-0.357886\pi\)
0.431778 + 0.901980i \(0.357886\pi\)
\(468\) 1.30147 + 3.64466i 0.0601605 + 0.168474i
\(469\) −6.78704 14.0934i −0.313396 0.650774i
\(470\) 6.98431 + 1.59412i 0.322162 + 0.0735314i
\(471\) −0.981736 16.5391i −0.0452360 0.762081i
\(472\) 18.9285i 0.871253i
\(473\) 6.05620 4.91826i 0.278465 0.226142i
\(474\) −1.39813 + 8.39076i −0.0642183 + 0.385400i
\(475\) 4.05871 0.926374i 0.186226 0.0425050i
\(476\) 0.133990 0.587050i 0.00614143 0.0269074i
\(477\) 2.74602 + 23.0493i 0.125732 + 1.05536i
\(478\) −5.16247 + 4.11693i −0.236126 + 0.188304i
\(479\) 29.8133i 1.36221i −0.732187 0.681103i \(-0.761500\pi\)
0.732187 0.681103i \(-0.238500\pi\)
\(480\) −6.73545 + 40.4222i −0.307430 + 1.84501i
\(481\) 0.869378 0.693306i 0.0396402 0.0316120i
\(482\) −4.02648 + 8.36106i −0.183401 + 0.380836i
\(483\) 32.2509 + 35.8579i 1.46746 + 1.63159i
\(484\) 11.6966 + 5.63280i 0.531665 + 0.256036i
\(485\) −2.31868 10.1588i −0.105286 0.461287i
\(486\) 12.3791 + 1.90073i 0.561526 + 0.0862190i
\(487\) −2.72443 11.9365i −0.123456 0.540894i −0.998394 0.0566591i \(-0.981955\pi\)
0.874938 0.484235i \(-0.160902\pi\)
\(488\) 7.10938 + 14.7628i 0.321827 + 0.668280i
\(489\) −13.0400 + 11.7283i −0.589691 + 0.530372i
\(490\) −6.27792 + 7.87226i −0.283608 + 0.355633i
\(491\) −7.20808 + 31.5806i −0.325296 + 1.42521i 0.502691 + 0.864466i \(0.332343\pi\)
−0.827987 + 0.560748i \(0.810514\pi\)
\(492\) −15.2646 + 4.45042i −0.688180 + 0.200640i
\(493\) −0.343163 + 0.712586i −0.0154553 + 0.0320933i
\(494\) 0.270379 + 0.0617123i 0.0121649 + 0.00277657i
\(495\) 12.3199 + 7.63194i 0.553738 + 0.343030i
\(496\) 3.32832 + 1.60284i 0.149446 + 0.0719694i
\(497\) −12.8590 26.7020i −0.576806 1.19775i
\(498\) −6.71890 + 16.3683i −0.301081 + 0.733482i
\(499\) −14.2706 11.3804i −0.638841 0.509459i 0.249660 0.968334i \(-0.419681\pi\)
−0.888501 + 0.458875i \(0.848253\pi\)
\(500\) 22.2411 27.8895i 0.994654 1.24726i
\(501\) −5.04583 + 1.47112i −0.225431 + 0.0657248i
\(502\) −9.29471 + 2.12146i −0.414843 + 0.0946852i
\(503\) −27.8541 34.9279i −1.24195 1.55736i −0.691108 0.722751i \(-0.742877\pi\)
−0.550844 0.834608i \(-0.685694\pi\)
\(504\) 25.5348 + 2.71226i 1.13741 + 0.120814i
\(505\) 6.98120 14.4966i 0.310660 0.645091i
\(506\) −5.22509 + 6.55205i −0.232284 + 0.291274i
\(507\) −12.0661 + 17.1210i −0.535874 + 0.760370i
\(508\) 11.0083 + 13.8040i 0.488415 + 0.612453i
\(509\) 30.1551i 1.33660i −0.743892 0.668300i \(-0.767022\pi\)
0.743892 0.668300i \(-0.232978\pi\)
\(510\) −0.780129 0.129991i −0.0345447 0.00575609i
\(511\) 13.5360 + 16.9736i 0.598798 + 0.750869i
\(512\) 5.49495 2.64623i 0.242845 0.116948i
\(513\) −1.24145 + 1.41622i −0.0548113 + 0.0625277i
\(514\) 1.88444 + 8.25629i 0.0831192 + 0.364169i
\(515\) −52.3844 −2.30833
\(516\) 14.2832 + 5.71536i 0.628784 + 0.251605i
\(517\) −2.61278 −0.114910
\(518\) −0.662933 2.90450i −0.0291276 0.127616i
\(519\) 8.30987 20.2442i 0.364763 0.888620i
\(520\) 9.38983 4.52190i 0.411771 0.198299i
\(521\) −17.3711 21.7827i −0.761043 0.954317i 0.238817 0.971065i \(-0.423240\pi\)
−0.999860 + 0.0167473i \(0.994669\pi\)
\(522\) −12.8832 4.41600i −0.563882 0.193283i
\(523\) 1.81842i 0.0795139i 0.999209 + 0.0397570i \(0.0126584\pi\)
−0.999209 + 0.0397570i \(0.987342\pi\)
\(524\) 9.81337 + 12.3056i 0.428699 + 0.537572i
\(525\) −51.6468 36.3983i −2.25405 1.58855i
\(526\) −4.40917 + 5.52893i −0.192249 + 0.241073i
\(527\) −0.412636 + 0.856848i −0.0179747 + 0.0373249i
\(528\) −0.0663904 1.11846i −0.00288927 0.0486749i
\(529\) −33.5840 42.1130i −1.46017 1.83100i
\(530\) 24.6079 5.61659i 1.06890 0.243969i
\(531\) −2.49257 20.9219i −0.108168 0.907935i
\(532\) −0.972132 + 1.21901i −0.0421473 + 0.0528510i
\(533\) 5.04644 + 4.02440i 0.218586 + 0.174316i
\(534\) 2.46103 + 1.01021i 0.106499 + 0.0437160i
\(535\) 19.7710 + 41.0549i 0.854775 + 1.77496i
\(536\) 11.9596 + 5.75946i 0.516578 + 0.248771i
\(537\) −19.1689 7.86851i −0.827201 0.339551i
\(538\) 3.30789 + 0.755004i 0.142613 + 0.0325505i
\(539\) 1.59335 3.30863i 0.0686305 0.142513i
\(540\) −1.32930 + 28.5465i −0.0572041 + 1.22845i
\(541\) 7.06940 30.9731i 0.303937 1.33164i −0.560190 0.828364i \(-0.689272\pi\)
0.864128 0.503272i \(-0.167871\pi\)
\(542\) −2.47481 + 3.10331i −0.106302 + 0.133299i
\(543\) −8.43666 9.38025i −0.362052 0.402545i
\(544\) 0.353890 + 0.734859i 0.0151729 + 0.0315068i
\(545\) 15.4125 + 67.5267i 0.660200 + 2.89253i
\(546\) −2.04778 3.67742i −0.0876367 0.157379i
\(547\) −2.62727 11.5108i −0.112334 0.492167i −0.999527 0.0307676i \(-0.990205\pi\)
0.887193 0.461399i \(-0.152652\pi\)
\(548\) −5.57645 2.68548i −0.238214 0.114718i
\(549\) 9.80214 + 15.3814i 0.418345 + 0.656460i
\(550\) 4.76375 9.89203i 0.203127 0.421797i
\(551\) 1.60116 1.27688i 0.0682116 0.0543970i
\(552\) −40.3693 6.72663i −1.71823 0.286304i
\(553\) 19.4140i 0.825567i
\(554\) −17.0540 + 13.6001i −0.724554 + 0.577813i
\(555\) 7.88290 2.29828i 0.334611 0.0975564i
\(556\) −1.10006 + 4.81969i −0.0466531 + 0.204400i
\(557\) 10.7005 2.44233i 0.453396 0.103485i 0.0102766 0.999947i \(-0.496729\pi\)
0.443120 + 0.896462i \(0.353872\pi\)
\(558\) −15.4914 5.31001i −0.655803 0.224791i
\(559\) −1.44370 6.07607i −0.0610619 0.256990i
\(560\) 7.01134i 0.296283i
\(561\) 0.287939 0.0170916i 0.0121568 0.000721610i
\(562\) −11.9981 2.73850i −0.506111 0.115517i
\(563\) −4.14050 8.59785i −0.174501 0.362356i 0.795313 0.606198i \(-0.207306\pi\)
−0.969815 + 0.243842i \(0.921592\pi\)
\(564\) −2.50656 4.50132i −0.105545 0.189540i
\(565\) 67.1213 2.82381
\(566\) −15.4870 −0.650966
\(567\) 28.5812 0.364610i 1.20030 0.0153122i
\(568\) 22.6593 + 10.9121i 0.950762 + 0.457863i
\(569\) 7.39020 + 5.89349i 0.309813 + 0.247068i 0.766036 0.642798i \(-0.222226\pi\)
−0.456223 + 0.889866i \(0.650798\pi\)
\(570\) 1.67395 + 1.17972i 0.0701140 + 0.0494131i
\(571\) 1.34224 0.306357i 0.0561709 0.0128206i −0.194343 0.980934i \(-0.562258\pi\)
0.250514 + 0.968113i \(0.419400\pi\)
\(572\) −1.19996 + 0.956933i −0.0501727 + 0.0400114i
\(573\) 15.3299 0.909959i 0.640415 0.0380141i
\(574\) 15.5806 7.50324i 0.650323 0.313179i
\(575\) 78.7318 + 62.7865i 3.28334 + 2.61838i
\(576\) −9.09298 + 5.79472i −0.378874 + 0.241447i
\(577\) −36.3279 8.29160i −1.51235 0.345184i −0.615720 0.787965i \(-0.711135\pi\)
−0.896630 + 0.442781i \(0.853992\pi\)
\(578\) 12.2914 5.91925i 0.511257 0.246208i
\(579\) 0.908554 1.28918i 0.0377582 0.0535764i
\(580\) 6.91500 30.2966i 0.287130 1.25800i
\(581\) −8.98577 + 39.3692i −0.372793 + 1.63331i
\(582\) 2.05726 2.91912i 0.0852761 0.121001i
\(583\) −8.29398 + 3.99417i −0.343502 + 0.165422i
\(584\) −17.9612 4.09953i −0.743240 0.169640i
\(585\) 9.78327 6.23462i 0.404489 0.257770i
\(586\) 4.33670 + 3.45840i 0.179147 + 0.142865i
\(587\) −1.73828 + 0.837112i −0.0717465 + 0.0345513i −0.469413 0.882979i \(-0.655534\pi\)
0.397666 + 0.917530i \(0.369820\pi\)
\(588\) 7.22871 0.429085i 0.298107 0.0176952i
\(589\) 1.92531 1.53538i 0.0793311 0.0632644i
\(590\) −22.3367 + 5.09820i −0.919586 + 0.209889i
\(591\) 18.6981 + 13.1776i 0.769137 + 0.542052i
\(592\) −0.496322 0.395804i −0.0203987 0.0162674i
\(593\) −27.3627 13.1772i −1.12365 0.541122i −0.222633 0.974902i \(-0.571465\pi\)
−0.901019 + 0.433780i \(0.857180\pi\)
\(594\) 0.878791 + 4.88851i 0.0360573 + 0.200578i
\(595\) −1.80501 −0.0739983
\(596\) −12.1592 −0.498059
\(597\) 0.518178 + 0.930551i 0.0212076 + 0.0380849i
\(598\) 2.91069 + 6.04411i 0.119027 + 0.247162i
\(599\) 19.4920 + 4.44892i 0.796421 + 0.181778i 0.601323 0.799006i \(-0.294640\pi\)
0.195098 + 0.980784i \(0.437497\pi\)
\(600\) 53.5236 3.17708i 2.18509 0.129704i
\(601\) 28.5727i 1.16551i 0.812649 + 0.582753i \(0.198025\pi\)
−0.812649 + 0.582753i \(0.801975\pi\)
\(602\) −16.3451 3.57828i −0.666175 0.145840i
\(603\) 13.9776 + 4.79113i 0.569213 + 0.195110i
\(604\) −4.72158 + 1.07767i −0.192118 + 0.0438498i
\(605\) 8.65963 37.9403i 0.352064 1.54249i
\(606\) 5.29405 1.54349i 0.215056 0.0627000i
\(607\) 3.95722 3.15578i 0.160619 0.128089i −0.539882 0.841740i \(-0.681531\pi\)
0.700501 + 0.713651i \(0.252960\pi\)
\(608\) 2.11197i 0.0856517i
\(609\) −30.6596 5.10873i −1.24239 0.207016i
\(610\) 15.5061 12.3657i 0.627823 0.500672i
\(611\) −0.907474 + 1.88439i −0.0367125 + 0.0762342i
\(612\) 0.305679 + 0.479667i 0.0123564 + 0.0193894i
\(613\) 20.8682 + 10.0496i 0.842857 + 0.405898i 0.804921 0.593382i \(-0.202208\pi\)
0.0379356 + 0.999280i \(0.487922\pi\)
\(614\) 0.596124 + 2.61179i 0.0240576 + 0.105403i
\(615\) 23.1882 + 41.6417i 0.935040 + 1.67916i
\(616\) 2.26607 + 9.92831i 0.0913027 + 0.400023i
\(617\) 16.7533 + 34.7886i 0.674462 + 1.40054i 0.904126 + 0.427265i \(0.140523\pi\)
−0.229664 + 0.973270i \(0.573763\pi\)
\(618\) −12.0059 13.3486i −0.482947 0.536961i
\(619\) 9.15819 11.4840i 0.368099 0.461581i −0.562942 0.826496i \(-0.690331\pi\)
0.931041 + 0.364915i \(0.118902\pi\)
\(620\) 8.31493 36.4301i 0.333936 1.46307i
\(621\) −45.5066 2.11907i −1.82612 0.0850354i
\(622\) 4.80960 9.98724i 0.192848 0.400452i
\(623\) 5.91929 + 1.35104i 0.237151 + 0.0541282i
\(624\) −0.829718 0.340584i −0.0332153 0.0136343i
\(625\) −44.5986 21.4776i −1.78395 0.859103i
\(626\) −8.86420 18.4067i −0.354285 0.735680i
\(627\) −0.690947 0.283621i −0.0275938 0.0113267i
\(628\) 10.1300 + 8.07841i 0.404231 + 0.322364i
\(629\) 0.101896 0.127774i 0.00406287 0.00509468i
\(630\) −3.67692 30.8630i −0.146492 1.22961i
\(631\) −30.5277 + 6.96775i −1.21529 + 0.277382i −0.781657 0.623709i \(-0.785625\pi\)
−0.433632 + 0.901090i \(0.642768\pi\)
\(632\) −10.2718 12.8804i −0.408589 0.512355i
\(633\) 0.0757602 + 1.27632i 0.00301120 + 0.0507290i
\(634\) 5.63117 11.6932i 0.223642 0.464398i
\(635\) 32.9988 41.3792i 1.30952 1.64208i
\(636\) −14.8380 10.4571i −0.588365 0.414653i
\(637\) −1.83284 2.29831i −0.0726199 0.0910625i
\(638\) 5.40109i 0.213831i
\(639\) 26.4826 + 9.07750i 1.04764 + 0.359100i
\(640\) −22.1927 27.8288i −0.877245 1.10003i
\(641\) −10.9180 + 5.25781i −0.431233 + 0.207671i −0.636892 0.770953i \(-0.719780\pi\)
0.205659 + 0.978624i \(0.434066\pi\)
\(642\) −5.93038 + 14.4473i −0.234053 + 0.570191i
\(643\) 0.771533 + 3.38031i 0.0304263 + 0.133306i 0.987860 0.155347i \(-0.0496496\pi\)
−0.957434 + 0.288653i \(0.906792\pi\)
\(644\) −37.7153 −1.48619
\(645\) 7.17556 45.5546i 0.282537 1.79371i
\(646\) 0.0407600 0.00160368
\(647\) −5.72391 25.0781i −0.225030 0.985921i −0.953630 0.300982i \(-0.902686\pi\)
0.728600 0.684940i \(-0.240171\pi\)
\(648\) −18.7695 + 15.3640i −0.737337 + 0.603553i
\(649\) 7.52848 3.62552i 0.295519 0.142314i
\(650\) −5.47978 6.87142i −0.214935 0.269519i
\(651\) −36.8666 6.14298i −1.44492 0.240763i
\(652\) 13.7155i 0.537140i
\(653\) −11.3899 14.2825i −0.445723 0.558919i 0.507319 0.861759i \(-0.330637\pi\)
−0.953042 + 0.302840i \(0.902065\pi\)
\(654\) −13.6749 + 19.4037i −0.534729 + 0.758746i
\(655\) 29.4168 36.8875i 1.14941 1.44131i
\(656\) 1.59882 3.31999i 0.0624235 0.129624i
\(657\) −20.3927 2.16607i −0.795593 0.0845066i
\(658\) 3.49376 + 4.38104i 0.136201 + 0.170791i
\(659\) −24.0957 + 5.49969i −0.938636 + 0.214237i −0.664359 0.747413i \(-0.731295\pi\)
−0.274276 + 0.961651i \(0.588438\pi\)
\(660\) −10.8803 + 3.17219i −0.423517 + 0.123477i
\(661\) −3.99505 + 5.00964i −0.155389 + 0.194852i −0.853432 0.521204i \(-0.825483\pi\)
0.698043 + 0.716056i \(0.254055\pi\)
\(662\) 9.64202 + 7.68926i 0.374748 + 0.298851i
\(663\) 0.0876806 0.213604i 0.00340523 0.00829569i
\(664\) −14.8682 30.8742i −0.576999 1.19815i
\(665\) 4.21098 + 2.02790i 0.163295 + 0.0786386i
\(666\) 2.39231 + 1.48199i 0.0927002 + 0.0574260i
\(667\) 48.2965 + 11.0234i 1.87005 + 0.426826i
\(668\) 1.78337 3.70321i 0.0690008 0.143282i
\(669\) 33.6149 9.80048i 1.29963 0.378908i
\(670\) 3.57528 15.6643i 0.138125 0.605165i
\(671\) −4.50993 + 5.65527i −0.174104 + 0.218319i
\(672\) −23.8324 + 21.4351i −0.919357 + 0.826876i
\(673\) 4.46606 + 9.27387i 0.172154 + 0.357481i 0.969138 0.246519i \(-0.0792868\pi\)
−0.796984 + 0.604000i \(0.793573\pi\)
\(674\) −4.38118 19.1952i −0.168757 0.739371i
\(675\) 58.7421 10.5599i 2.26099 0.406450i
\(676\) −3.64490 15.9693i −0.140188 0.614205i
\(677\) −8.58042 4.13211i −0.329772 0.158810i 0.261670 0.965157i \(-0.415727\pi\)
−0.591442 + 0.806348i \(0.701441\pi\)
\(678\) 15.3834 + 17.1039i 0.590795 + 0.656872i
\(679\) 3.53635 7.34332i 0.135713 0.281811i
\(680\) 1.19755 0.955016i 0.0459240 0.0366232i
\(681\) 5.43981 32.6466i 0.208454 1.25102i
\(682\) 6.49453i 0.248688i
\(683\) −22.4946 + 17.9389i −0.860732 + 0.686411i −0.950894 0.309516i \(-0.899833\pi\)
0.0901619 + 0.995927i \(0.471262\pi\)
\(684\) −0.174233 1.46246i −0.00666196 0.0559186i
\(685\) −4.12854 + 18.0883i −0.157744 + 0.691120i
\(686\) 9.73516 2.22199i 0.371690 0.0848359i
\(687\) −4.77295 + 28.6445i −0.182100 + 1.09285i
\(688\) −3.19842 + 1.57541i −0.121938 + 0.0600620i
\(689\) 7.36905i 0.280738i
\(690\) 2.93527 + 49.4498i 0.111744 + 1.88252i
\(691\) 7.50848 + 1.71376i 0.285636 + 0.0651945i 0.362938 0.931813i \(-0.381774\pi\)
−0.0773025 + 0.997008i \(0.524631\pi\)
\(692\) 7.42520 + 15.4186i 0.282264 + 0.586127i
\(693\) 3.81213 + 10.6755i 0.144811 + 0.405530i
\(694\) −4.07802 −0.154799
\(695\) 14.8192 0.562124
\(696\) 23.0444 12.8323i 0.873495 0.486407i
\(697\) 0.854703 + 0.411603i 0.0323742 + 0.0155906i
\(698\) 0.998486 + 0.796266i 0.0377933 + 0.0301391i
\(699\) −22.3051 + 31.6495i −0.843656 + 1.19709i
\(700\) 48.1727 10.9951i 1.82076 0.415576i
\(701\) 13.3189 10.6215i 0.503047 0.401167i −0.338820 0.940851i \(-0.610028\pi\)
0.841867 + 0.539684i \(0.181456\pi\)
\(702\) 3.83092 + 1.06408i 0.144589 + 0.0401612i
\(703\) −0.381270 + 0.183610i −0.0143799 + 0.00692498i
\(704\) −3.34322 2.66613i −0.126002 0.100484i
\(705\) −11.4830 + 10.3279i −0.432475 + 0.388971i
\(706\) −16.0664 3.66705i −0.604667 0.138011i
\(707\) 11.3391 5.46064i 0.426452 0.205368i
\(708\) 13.4685 + 9.49198i 0.506177 + 0.356731i
\(709\) −4.69104 + 20.5528i −0.176176 + 0.771877i 0.807198 + 0.590281i \(0.200983\pi\)
−0.983373 + 0.181595i \(0.941874\pi\)
\(710\) 6.77388 29.6783i 0.254219 1.11381i
\(711\) −13.0497 12.8843i −0.489402 0.483199i
\(712\) −4.64203 + 2.23549i −0.173968 + 0.0837784i
\(713\) 58.0740 + 13.2550i 2.17489 + 0.496404i
\(714\) −0.413686 0.459955i −0.0154818 0.0172134i
\(715\) 3.59702 + 2.86853i 0.134521 + 0.107277i
\(716\) 14.5997 7.03083i 0.545615 0.262754i
\(717\) −0.843488 14.2101i −0.0315007 0.530685i
\(718\) −12.1221 + 9.66707i −0.452394 + 0.360772i
\(719\) −24.7293 + 5.64430i −0.922247 + 0.210497i −0.657180 0.753733i \(-0.728251\pi\)
−0.265066 + 0.964230i \(0.585394\pi\)
\(720\) −4.71289 4.65315i −0.175639 0.173413i
\(721\) −32.0353 25.5473i −1.19306 0.951430i
\(722\) 13.6583 + 6.57747i 0.508308 + 0.244788i
\(723\) −9.73323 17.4790i −0.361983 0.650053i
\(724\) 9.86613 0.366672
\(725\) −64.9014 −2.41038
\(726\) 11.6527 6.48880i 0.432471 0.240822i
\(727\) 16.5937 + 34.4571i 0.615426 + 1.27794i 0.942897 + 0.333083i \(0.108089\pi\)
−0.327472 + 0.944861i \(0.606197\pi\)
\(728\) 7.94755 + 1.81398i 0.294556 + 0.0672305i
\(729\) −18.7231 + 19.4537i −0.693448 + 0.720507i
\(730\) 22.2994i 0.825338i
\(731\) −0.405576 0.823406i −0.0150008 0.0304548i
\(732\) −14.0695 2.34437i −0.520025 0.0866505i
\(733\) −23.0974 + 5.27183i −0.853122 + 0.194720i −0.626653 0.779299i \(-0.715576\pi\)
−0.226470 + 0.974018i \(0.572718\pi\)
\(734\) −2.73983 + 12.0040i −0.101129 + 0.443075i
\(735\) −6.07579 20.8395i −0.224109 0.768675i
\(736\) 39.9414 31.8522i 1.47226 1.17409i
\(737\) 5.85990i 0.215852i
\(738\) −5.29672 + 15.4526i −0.194975 + 0.568818i
\(739\) −7.57250 + 6.03887i −0.278559 + 0.222143i −0.752796 0.658254i \(-0.771295\pi\)
0.474237 + 0.880397i \(0.342724\pi\)
\(740\) −2.78610 + 5.78539i −0.102419 + 0.212675i
\(741\) −0.444534 + 0.399817i −0.0163304 + 0.0146876i
\(742\) 17.7879 + 8.56620i 0.653014 + 0.314475i
\(743\) −0.309106 1.35428i −0.0113400 0.0496838i 0.968941 0.247291i \(-0.0795402\pi\)
−0.980281 + 0.197607i \(0.936683\pi\)
\(744\) 27.7097 15.4302i 1.01589 0.565697i
\(745\) 8.11059 + 35.5348i 0.297149 + 1.30190i
\(746\) 7.31394 + 15.1876i 0.267782 + 0.556056i
\(747\) −20.4997 32.1679i −0.750046 1.17696i
\(748\) −0.140642 + 0.176360i −0.00514238 + 0.00644834i
\(749\) −7.93121 + 34.7489i −0.289800 + 1.26970i
\(750\) −10.2578 35.1833i −0.374560 1.28471i
\(751\) −20.6660 + 42.9134i −0.754113 + 1.56593i 0.0687122 + 0.997637i \(0.478111\pi\)
−0.822825 + 0.568295i \(0.807603\pi\)
\(752\) 1.16409 + 0.265697i 0.0424501 + 0.00968897i
\(753\) 7.80476 19.0136i 0.284421 0.692895i
\(754\) −3.89537 1.87591i −0.141861 0.0683167i
\(755\) 6.29892 + 13.0798i 0.229241 + 0.476024i
\(756\) −14.7347 + 16.8091i −0.535897 + 0.611341i
\(757\) 0.649695 + 0.518114i 0.0236136 + 0.0188312i 0.635225 0.772327i \(-0.280907\pi\)
−0.611612 + 0.791158i \(0.709479\pi\)
\(758\) −3.89517 + 4.88438i −0.141479 + 0.177409i
\(759\) −5.05685 17.3446i −0.183552 0.629569i
\(760\) −3.86676 + 0.882563i −0.140262 + 0.0320139i
\(761\) 0.449391 + 0.563518i 0.0162904 + 0.0204275i 0.789910 0.613223i \(-0.210127\pi\)
−0.773620 + 0.633650i \(0.781556\pi\)
\(762\) 18.1072 1.07482i 0.655955 0.0389365i
\(763\) −23.5066 + 48.8119i −0.850996 + 1.76711i
\(764\) −7.48778 + 9.38938i −0.270898 + 0.339696i
\(765\) 1.19791 1.21329i 0.0433107 0.0438667i
\(766\) −13.1162 16.4472i −0.473907 0.594260i
\(767\) 6.68891i 0.241523i
\(768\) 4.05144 24.3144i 0.146194 0.877369i
\(769\) −11.6847 14.6521i −0.421360 0.528369i 0.525164 0.851001i \(-0.324004\pi\)
−0.946524 + 0.322632i \(0.895432\pi\)
\(770\) 11.1056 5.34819i 0.400219 0.192735i
\(771\) −16.8894 6.93280i −0.608257 0.249679i
\(772\) 0.274454 + 1.20246i 0.00987781 + 0.0432775i
\(773\) 47.7797 1.71851 0.859257 0.511543i \(-0.170926\pi\)
0.859257 + 0.511543i \(0.170926\pi\)
\(774\) 13.2528 8.61208i 0.476363 0.309555i
\(775\) −78.0406 −2.80330
\(776\) 1.53906 + 6.74305i 0.0552489 + 0.242061i
\(777\) 5.94157 + 2.43891i 0.213153 + 0.0874953i
\(778\) −6.36803 + 3.06668i −0.228305 + 0.109946i
\(779\) −1.53154 1.92049i −0.0548731 0.0688087i
\(780\) −1.49113 + 8.94890i −0.0533911 + 0.320422i
\(781\) 11.1024i 0.397276i
\(782\) 0.614731 + 0.770849i 0.0219827 + 0.0275655i
\(783\) 23.7815 17.2183i 0.849883 0.615332i
\(784\) −1.04636 + 1.31209i −0.0373699 + 0.0468604i
\(785\) 16.8519 34.9932i 0.601469 1.24896i
\(786\) 16.1417 0.958146i 0.575755 0.0341760i
\(787\) −13.5786 17.0270i −0.484025 0.606948i 0.478518 0.878078i \(-0.341174\pi\)
−0.962543 + 0.271130i \(0.912603\pi\)
\(788\) −17.4404 + 3.98065i −0.621287 + 0.141805i
\(789\) −4.26721 14.6362i −0.151917 0.521062i
\(790\) −12.4330 + 15.5905i −0.442347 + 0.554685i
\(791\) 41.0475 + 32.7343i 1.45948 + 1.16390i
\(792\) −8.17752 5.06582i −0.290576 0.180006i
\(793\) 2.51230 + 5.21685i 0.0892145 + 0.185256i
\(794\) 3.79425 + 1.82721i 0.134653 + 0.0648454i
\(795\) −20.6632 + 50.3389i −0.732849 + 1.78534i
\(796\) −0.812051 0.185345i −0.0287824 0.00656939i
\(797\) −15.7815 + 32.7707i −0.559011 + 1.16080i 0.409611 + 0.912260i \(0.365664\pi\)
−0.968622 + 0.248538i \(0.920050\pi\)
\(798\) 0.448353 + 1.53782i 0.0158715 + 0.0544381i
\(799\) −0.0684014 + 0.299686i −0.00241987 + 0.0106021i
\(800\) −41.7302 + 52.3280i −1.47538 + 1.85007i
\(801\) −4.83654 + 3.08220i −0.170891 + 0.108904i
\(802\) 4.45330 + 9.24738i 0.157252 + 0.326536i
\(803\) −1.80974 7.92898i −0.0638643 0.279808i
\(804\) −10.0955 + 5.62168i −0.356040 + 0.198261i
\(805\) 25.1574 + 110.222i 0.886682 + 3.88481i
\(806\) −4.68399 2.25569i −0.164986 0.0794532i
\(807\) −5.43854 + 4.89146i −0.191446 + 0.172188i
\(808\) −4.63388 + 9.62235i −0.163019 + 0.338513i
\(809\) 27.9607 22.2979i 0.983045 0.783952i 0.00665747 0.999978i \(-0.497881\pi\)
0.976388 + 0.216025i \(0.0693094\pi\)
\(810\) 23.1857 + 18.0110i 0.814664 + 0.632842i
\(811\) 24.4260i 0.857714i −0.903372 0.428857i \(-0.858916\pi\)
0.903372 0.428857i \(-0.141084\pi\)
\(812\) 19.0041 15.1553i 0.666913 0.531846i
\(813\) −2.39513 8.21510i −0.0840008 0.288116i
\(814\) −0.248344 + 1.08807i −0.00870445 + 0.0381367i
\(815\) −40.0831 + 9.14871i −1.40405 + 0.320465i
\(816\) −0.130026 0.0216659i −0.00455183 0.000758459i
\(817\) 0.0211016 + 2.37661i 0.000738252 + 0.0831472i
\(818\) 24.3724i 0.852162i
\(819\) 9.02344 + 0.958455i 0.315304 + 0.0334911i
\(820\) −36.3389 8.29411i −1.26901 0.289643i
\(821\) 7.17012 + 14.8889i 0.250239 + 0.519626i 0.987814 0.155639i \(-0.0497436\pi\)
−0.737575 + 0.675265i \(0.764029\pi\)
\(822\) −5.55550 + 3.09358i −0.193770 + 0.107901i
\(823\) −12.1955 −0.425108 −0.212554 0.977149i \(-0.568178\pi\)
−0.212554 + 0.977149i \(0.568178\pi\)
\(824\) 34.7710 1.21130
\(825\) 11.5154 + 20.6796i 0.400916 + 0.719970i
\(826\) −16.1461 7.77557i −0.561796 0.270547i
\(827\) −8.23190 6.56472i −0.286251 0.228278i 0.469828 0.882758i \(-0.344316\pi\)
−0.756079 + 0.654480i \(0.772887\pi\)
\(828\) 25.0301 25.3515i 0.869858 0.881025i
\(829\) −31.9166 + 7.28476i −1.10851 + 0.253010i −0.737318 0.675546i \(-0.763908\pi\)
−0.371192 + 0.928556i \(0.621051\pi\)
\(830\) −32.4287 + 25.8610i −1.12562 + 0.897650i
\(831\) −2.78642 46.9423i −0.0966600 1.62841i
\(832\) −3.08404 + 1.48520i −0.106920 + 0.0514899i
\(833\) −0.337787 0.269376i −0.0117036 0.00933333i
\(834\) 3.39637 + 3.77624i 0.117607 + 0.130760i
\(835\) −12.0121 2.74168i −0.415696 0.0948799i
\(836\) 0.526246 0.253427i 0.0182006 0.00876495i
\(837\) 28.5961 20.7041i 0.988425 0.715640i
\(838\) 1.07662 4.71696i 0.0371911 0.162945i
\(839\) 1.83250 8.02870i 0.0632649 0.277182i −0.933394 0.358852i \(-0.883168\pi\)
0.996659 + 0.0816703i \(0.0260254\pi\)
\(840\) 49.2043 + 34.6769i 1.69771 + 1.19647i
\(841\) −2.63723 + 1.27002i −0.0909389 + 0.0437939i
\(842\) 18.6443 + 4.25545i 0.642526 + 0.146652i
\(843\) 19.7263 17.7420i 0.679410 0.611066i
\(844\) −0.781729 0.623408i −0.0269082 0.0214586i
\(845\) −44.2386 + 21.3042i −1.52186 + 0.732887i
\(846\) −5.26352 0.559083i −0.180964 0.0192217i
\(847\) 23.7988 18.9789i 0.817736 0.652123i
\(848\) 4.10146 0.936132i 0.140845 0.0321469i
\(849\) 19.2334 27.2909i 0.660088 0.936621i
\(850\) −1.00990 0.805372i −0.0346394 0.0276240i
\(851\) −9.22262 4.44138i −0.316147 0.152248i
\(852\) −19.1274 + 10.6511i −0.655293 + 0.364900i
\(853\) 34.0661 1.16640 0.583200 0.812329i \(-0.301800\pi\)
0.583200 + 0.812329i \(0.301800\pi\)
\(854\) 15.5132 0.530852
\(855\) −4.15778 + 1.48470i −0.142193 + 0.0507757i
\(856\) −13.1233 27.2508i −0.448545 0.931414i
\(857\) 3.08886 + 0.705013i 0.105514 + 0.0240828i 0.274952 0.961458i \(-0.411338\pi\)
−0.169438 + 0.985541i \(0.554195\pi\)
\(858\) 0.0934320 + 1.57403i 0.00318971 + 0.0537364i
\(859\) 4.31378i 0.147184i 0.997288 + 0.0735922i \(0.0234463\pi\)
−0.997288 + 0.0735922i \(0.976554\pi\)
\(860\) 22.7351 + 27.9953i 0.775260 + 0.954633i
\(861\) −6.12760 + 36.7743i −0.208828 + 1.25326i
\(862\) 21.5046 4.90828i 0.732448 0.167177i
\(863\) −5.14925 + 22.5603i −0.175282 + 0.767963i 0.808485 + 0.588516i \(0.200288\pi\)
−0.983768 + 0.179446i \(0.942569\pi\)
\(864\) 1.40841 30.2453i 0.0479151 1.02897i
\(865\) 40.1075 31.9847i 1.36370 1.08751i
\(866\) 25.2461i 0.857897i
\(867\) −4.83402 + 29.0109i −0.164172 + 0.985263i
\(868\) 22.8515 18.2234i 0.775629 0.618544i
\(869\) 3.15553 6.55252i 0.107044 0.222279i
\(870\) −21.3496 23.7374i −0.723820 0.804774i
\(871\) 4.22628 + 2.03527i 0.143202 + 0.0689625i
\(872\) −10.2303 44.8219i −0.346442 1.51786i
\(873\) 2.58910 + 7.25054i 0.0876277 + 0.245394i
\(874\) −0.568094 2.48898i −0.0192161 0.0841911i
\(875\) −36.2904 75.3578i −1.22684 2.54756i
\(876\) 11.9239 10.7245i 0.402873 0.362347i
\(877\) −26.3027 + 32.9826i −0.888181 + 1.11374i 0.104685 + 0.994505i \(0.466617\pi\)
−0.992866 + 0.119238i \(0.961955\pi\)
\(878\) −1.09164 + 4.78277i −0.0368410 + 0.161411i
\(879\) −11.4801 + 3.34705i −0.387214 + 0.112893i
\(880\) 1.13962 2.36644i 0.0384164 0.0797725i
\(881\) 30.0898 + 6.86780i 1.01375 + 0.231382i 0.696958 0.717112i \(-0.254537\pi\)
0.316794 + 0.948494i \(0.397394\pi\)
\(882\) 3.91784 6.32439i 0.131920 0.212953i
\(883\) −7.35532 3.54214i −0.247526 0.119202i 0.306008 0.952029i \(-0.401007\pi\)
−0.553534 + 0.832827i \(0.686721\pi\)
\(884\) 0.0783461 + 0.162687i 0.00263506 + 0.00547177i
\(885\) 18.7561 45.6928i 0.630479 1.53595i
\(886\) 2.84498 + 2.26880i 0.0955790 + 0.0762217i
\(887\) 13.7730 17.2707i 0.462450 0.579895i −0.494854 0.868976i \(-0.664778\pi\)
0.957304 + 0.289082i \(0.0933499\pi\)
\(888\) −5.23240 + 1.52552i −0.175588 + 0.0511930i
\(889\) 40.3603 9.21198i 1.35364 0.308960i
\(890\) 3.88829 + 4.87576i 0.130336 + 0.163436i
\(891\) −9.70584 4.52248i −0.325158 0.151509i
\(892\) −11.8807 + 24.6705i −0.397794 + 0.826029i
\(893\) 0.496269 0.622302i 0.0166070 0.0208245i
\(894\) −7.19617 + 10.2109i −0.240676 + 0.341503i
\(895\) −30.2859 37.9773i −1.01234 1.26944i
\(896\) 27.8416i 0.930124i
\(897\) −14.2656 2.37705i −0.476316 0.0793673i
\(898\) −8.48913 10.6450i −0.283286 0.355229i
\(899\) −34.5888 + 16.6571i −1.15360 + 0.555546i
\(900\) −24.5796 + 39.6778i −0.819321 + 1.32259i
\(901\) 0.240999 + 1.05589i 0.00802885 + 0.0351767i
\(902\) −6.47827 −0.215703
\(903\) 26.6046 24.3591i 0.885346 0.810621i
\(904\) −44.5528 −1.48180
\(905\) −6.58105 28.8335i −0.218762 0.958457i
\(906\) −1.88938 + 4.60283i −0.0627705 + 0.152919i
\(907\) −17.9178 + 8.62875i −0.594950 + 0.286513i −0.707027 0.707187i \(-0.749964\pi\)
0.112077 + 0.993700i \(0.464250\pi\)
\(908\) 16.1374 + 20.2357i 0.535540 + 0.671546i
\(909\) −3.85480 + 11.2460i −0.127856 + 0.373005i
\(910\) 9.86715i 0.327093i
\(911\) −32.9347 41.2988i −1.09117 1.36829i −0.924013 0.382361i \(-0.875111\pi\)
−0.167162 0.985929i \(-0.553460\pi\)
\(912\) 0.279002 + 0.196628i 0.00923867 + 0.00651099i
\(913\) 9.43186 11.8272i 0.312149 0.391423i
\(914\) 7.65612 15.8981i 0.253242 0.525863i
\(915\) 2.53352 + 42.6816i 0.0837555 + 1.41101i
\(916\) −14.1592 17.7551i −0.467833 0.586643i
\(917\) 35.9792 8.21203i 1.18814 0.271185i
\(918\) 0.583720 + 0.0271816i 0.0192656 + 0.000897128i
\(919\) −29.1593 + 36.5646i −0.961876 + 1.20615i 0.0166142 + 0.999862i \(0.494711\pi\)
−0.978490 + 0.206293i \(0.933860\pi\)
\(920\) −75.0084 59.8172i −2.47295 1.97211i
\(921\) −5.34278 2.19312i −0.176051 0.0722656i
\(922\) 8.40845 + 17.4603i 0.276918 + 0.575025i
\(923\) 8.00730 + 3.85611i 0.263563 + 0.126925i
\(924\) −8.20083 3.36629i −0.269787 0.110743i
\(925\) 13.0746 + 2.98419i 0.429890 + 0.0981195i
\(926\) −2.57574 + 5.34858i −0.0846442 + 0.175765i
\(927\) 38.4329 4.57877i 1.26230 0.150387i
\(928\) −7.32651 + 32.0995i −0.240505 + 1.05372i
\(929\) 12.1882 15.2835i 0.399881 0.501434i −0.540601 0.841279i \(-0.681803\pi\)
0.940482 + 0.339845i \(0.110375\pi\)
\(930\) −25.6718 28.5431i −0.841812 0.935964i
\(931\) 0.485396 + 1.00794i 0.0159082 + 0.0330338i
\(932\) −6.73787 29.5206i −0.220706 0.966978i
\(933\) 11.6263 + 20.8786i 0.380627 + 0.683536i
\(934\) 3.33630 + 14.6173i 0.109167 + 0.478292i
\(935\) 0.609219 + 0.293384i 0.0199236 + 0.00959469i
\(936\) −6.49380 + 4.13833i −0.212256 + 0.135265i
\(937\) −1.06523 + 2.21197i −0.0347994 + 0.0722618i −0.917644 0.397404i \(-0.869911\pi\)
0.882844 + 0.469666i \(0.155626\pi\)
\(938\) 9.82574 7.83576i 0.320822 0.255847i
\(939\) 43.4445 + 7.23905i 1.41776 + 0.236237i
\(940\) 12.0778i 0.393934i
\(941\) 36.8969 29.4243i 1.20280 0.959205i 0.203004 0.979178i \(-0.434929\pi\)
0.999801 + 0.0199729i \(0.00635798\pi\)
\(942\) 12.7792 3.72581i 0.416370 0.121394i
\(943\) 13.2218 57.9286i 0.430562 1.88642i
\(944\) −3.72291 + 0.849730i −0.121170 + 0.0276564i
\(945\) 58.9527 + 31.8495i 1.91773 + 1.03607i
\(946\) 4.93510 + 3.86443i 0.160454 + 0.125643i
\(947\) 37.4137i 1.21578i 0.794020 + 0.607891i \(0.207984\pi\)
−0.794020 + 0.607891i \(0.792016\pi\)
\(948\) 14.3160 0.849775i 0.464961 0.0275994i
\(949\) −6.34710 1.44868i −0.206036 0.0470263i
\(950\) 1.45122 + 3.01349i 0.0470839 + 0.0977707i
\(951\) 13.6123 + 24.4451i 0.441408 + 0.792686i
\(952\) 1.19810 0.0388308
\(953\) −56.2686 −1.82272 −0.911360 0.411611i \(-0.864966\pi\)
−0.911360 + 0.411611i \(0.864966\pi\)
\(954\) −17.5632 + 6.27163i −0.568628 + 0.203052i
\(955\) 32.4348 + 15.6198i 1.04957 + 0.505444i
\(956\) 8.70351 + 6.94081i 0.281491 + 0.224482i
\(957\) 9.51771 + 6.70764i 0.307664 + 0.216827i
\(958\) 23.3522 5.32999i 0.754476 0.172204i
\(959\) −11.3462 + 9.04833i −0.366389 + 0.292186i
\(960\) −25.2320 + 1.49774i −0.814361 + 0.0483392i
\(961\) −13.6613 + 6.57892i −0.440686 + 0.212223i
\(962\) 0.698480 + 0.557019i 0.0225199 + 0.0179590i
\(963\) −18.0939 28.3927i −0.583068 0.914941i
\(964\) 15.2532 + 3.48144i 0.491272 + 0.112130i
\(965\) 3.33109 1.60417i 0.107231 0.0516400i
\(966\) −22.3211 + 31.6721i −0.718168 + 1.01903i
\(967\) 13.1721 57.7109i 0.423587 1.85586i −0.0872605 0.996186i \(-0.527811\pi\)
0.510848 0.859671i \(-0.329332\pi\)
\(968\) −5.74796 + 25.1835i −0.184747 + 0.809428i
\(969\) −0.0506201 + 0.0718266i −0.00162615 + 0.00230740i
\(970\) 7.54266 3.63235i 0.242180 0.116628i
\(971\) −26.3806 6.02120i −0.846594 0.193230i −0.222845 0.974854i \(-0.571534\pi\)
−0.623749 + 0.781624i \(0.714391\pi\)
\(972\) −1.51990 21.0599i −0.0487508 0.675498i
\(973\) 9.06255 + 7.22714i 0.290532 + 0.231692i
\(974\) 8.86256 4.26798i 0.283975 0.136755i
\(975\) 18.9141 1.12271i 0.605735 0.0359556i
\(976\) 2.58444 2.06102i 0.0827259 0.0659717i
\(977\) 52.8896 12.0717i 1.69209 0.386208i 0.735471 0.677556i \(-0.236961\pi\)
0.956617 + 0.291348i \(0.0941037\pi\)
\(978\) −11.5178 8.11724i −0.368300 0.259561i
\(979\) −1.77825 1.41811i −0.0568332 0.0453230i
\(980\) 15.2944 + 7.36541i 0.488562 + 0.235279i
\(981\) −17.2101 48.1952i −0.549475 1.53876i
\(982\) −26.0252 −0.830497
\(983\) 51.0614 1.62860 0.814302 0.580441i \(-0.197120\pi\)
0.814302 + 0.580441i \(0.197120\pi\)
\(984\) −15.3915 27.6403i −0.490664 0.881141i
\(985\) 23.2666 + 48.3137i 0.741337 + 1.53940i
\(986\) −0.619506 0.141398i −0.0197291 0.00450303i
\(987\) −12.0591 + 0.715812i −0.383846 + 0.0227845i
\(988\) 0.467560i 0.0148751i
\(989\) −44.6280 + 36.2425i −1.41909 + 1.15244i
\(990\) −3.77542 + 11.0144i −0.119991 + 0.350060i
\(991\) −13.5709 + 3.09747i −0.431094 + 0.0983945i −0.432561 0.901604i \(-0.642390\pi\)
0.00146706 + 0.999999i \(0.499533\pi\)
\(992\) −8.80976 + 38.5981i −0.279710 + 1.22549i
\(993\) −25.5244 + 7.44168i −0.809992 + 0.236155i
\(994\) 18.6163 14.8460i 0.590473 0.470886i
\(995\) 2.49683i 0.0791547i
\(996\) 29.4244 + 4.90291i 0.932348 + 0.155355i
\(997\) 2.83260 2.25892i 0.0897092 0.0715407i −0.577608 0.816314i \(-0.696014\pi\)
0.667317 + 0.744773i \(0.267442\pi\)
\(998\) 6.36280 13.2125i 0.201411 0.418234i
\(999\) −5.58257 + 2.37520i −0.176625 + 0.0751480i
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 129.2.j.a.113.8 yes 72
3.2 odd 2 inner 129.2.j.a.113.5 yes 72
43.8 odd 14 inner 129.2.j.a.8.5 72
129.8 even 14 inner 129.2.j.a.8.8 yes 72
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
129.2.j.a.8.5 72 43.8 odd 14 inner
129.2.j.a.8.8 yes 72 129.8 even 14 inner
129.2.j.a.113.5 yes 72 3.2 odd 2 inner
129.2.j.a.113.8 yes 72 1.1 even 1 trivial