Properties

Label 171.2.x.a.14.3
Level $171$
Weight $2$
Character 171.14
Analytic conductor $1.365$
Analytic rank $0$
Dimension $108$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [171,2,Mod(14,171)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(171, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([15, 7]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("171.14");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 171 = 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 171.x (of order \(18\), 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: \(1.36544187456\)
Analytic rank: \(0\)
Dimension: \(108\)
Relative dimension: \(18\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 14.3
Character \(\chi\) \(=\) 171.14
Dual form 171.2.x.a.110.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.80901 - 1.51794i) q^{2} +(-0.419122 - 1.68058i) q^{3} +(0.621081 + 3.52233i) q^{4} +(-1.22473 - 3.36492i) q^{5} +(-1.79282 + 3.67638i) q^{6} +(0.850912 - 1.47382i) q^{7} +(1.86164 - 3.22446i) q^{8} +(-2.64867 + 1.40873i) q^{9} +O(q^{10})\) \(q+(-1.80901 - 1.51794i) q^{2} +(-0.419122 - 1.68058i) q^{3} +(0.621081 + 3.52233i) q^{4} +(-1.22473 - 3.36492i) q^{5} +(-1.79282 + 3.67638i) q^{6} +(0.850912 - 1.47382i) q^{7} +(1.86164 - 3.22446i) q^{8} +(-2.64867 + 1.40873i) q^{9} +(-2.89220 + 7.94624i) q^{10} +0.0685816i q^{11} +(5.65923 - 2.52006i) q^{12} +(0.947862 - 2.60423i) q^{13} +(-3.77648 + 1.37453i) q^{14} +(-5.14169 + 3.46856i) q^{15} +(-1.54034 + 0.560636i) q^{16} +(2.40059 + 6.59558i) q^{17} +(6.92985 + 1.47211i) q^{18} +(-3.88520 + 1.97616i) q^{19} +(11.0917 - 6.40378i) q^{20} +(-2.83351 - 0.812310i) q^{21} +(0.104103 - 0.124065i) q^{22} +(2.95636 - 0.521285i) q^{23} +(-6.19920 - 1.77719i) q^{24} +(-5.99249 + 5.02830i) q^{25} +(-5.66776 + 3.27228i) q^{26} +(3.47760 + 3.86087i) q^{27} +(5.71977 + 2.08182i) q^{28} +(-1.00498 - 5.69952i) q^{29} +(14.5664 + 1.53011i) q^{30} -2.56914i q^{31} +(-3.35999 - 1.22294i) q^{32} +(0.115257 - 0.0287441i) q^{33} +(5.66899 - 15.5754i) q^{34} +(-6.00143 - 1.05821i) q^{35} +(-6.60706 - 8.45455i) q^{36} -7.77355i q^{37} +(10.0281 + 2.32260i) q^{38} +(-4.77388 - 0.501464i) q^{39} +(-13.1300 - 2.31518i) q^{40} +(-8.32894 - 6.98881i) q^{41} +(3.89281 + 5.77057i) q^{42} +(0.683977 - 3.87902i) q^{43} +(-0.241567 + 0.0425947i) q^{44} +(7.98418 + 7.18725i) q^{45} +(-6.13936 - 3.54456i) q^{46} +(-0.713950 + 0.125889i) q^{47} +(1.58778 + 2.35368i) q^{48} +(2.05190 + 3.55399i) q^{49} +18.4731 q^{50} +(10.0782 - 6.79873i) q^{51} +(9.76164 + 1.72124i) q^{52} +(6.47151 - 5.43024i) q^{53} +(-0.430456 - 12.2631i) q^{54} +(0.230771 - 0.0839939i) q^{55} +(-3.16818 - 5.48746i) q^{56} +(4.94947 + 5.70112i) q^{57} +(-6.83351 + 11.8360i) q^{58} +(-1.93552 + 10.9769i) q^{59} +(-15.4108 - 15.9564i) q^{60} +(-1.83166 - 0.666669i) q^{61} +(-3.89981 + 4.64761i) q^{62} +(-0.177564 + 5.10238i) q^{63} +(5.86110 + 10.1517i) q^{64} -9.92389 q^{65} +(-0.252132 - 0.122954i) q^{66} +(-5.17654 - 6.16916i) q^{67} +(-21.7408 + 12.5521i) q^{68} +(-2.11513 - 4.74990i) q^{69} +(9.25034 + 11.0241i) q^{70} +(4.92220 + 4.13021i) q^{71} +(-0.388478 + 11.1631i) q^{72} +(1.28461 - 7.28540i) q^{73} +(-11.7998 + 14.0624i) q^{74} +(10.9620 + 7.96337i) q^{75} +(-9.37372 - 12.4576i) q^{76} +(0.101077 + 0.0583569i) q^{77} +(7.87480 + 8.15361i) q^{78} +(3.66753 + 10.0764i) q^{79} +(3.77299 + 4.49647i) q^{80} +(5.03094 - 7.46255i) q^{81} +(4.45854 + 25.2857i) q^{82} +(-0.302529 - 0.174665i) q^{83} +(1.10138 - 10.4850i) q^{84} +(19.2535 - 16.1556i) q^{85} +(-7.12545 + 5.97896i) q^{86} +(-9.15727 + 4.07774i) q^{87} +(0.221138 + 0.127674i) q^{88} +(-0.881834 - 5.00113i) q^{89} +(-3.53366 - 25.1213i) q^{90} +(-3.03162 - 3.61295i) q^{91} +(3.67227 + 10.0895i) q^{92} +(-4.31764 + 1.07678i) q^{93} +(1.48263 + 0.855999i) q^{94} +(11.4080 + 10.6531i) q^{95} +(-0.646991 + 6.15927i) q^{96} +(2.44747 - 2.91678i) q^{97} +(1.68284 - 9.54387i) q^{98} +(-0.0966132 - 0.181650i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 108 q - 9 q^{2} - 3 q^{4} - 9 q^{5} + 3 q^{7} - 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 108 q - 9 q^{2} - 3 q^{4} - 9 q^{5} + 3 q^{7} - 24 q^{9} - 12 q^{10} - 9 q^{12} - 6 q^{13} - 9 q^{14} - 36 q^{15} - 9 q^{16} + 27 q^{17} + 36 q^{18} - 15 q^{19} - 18 q^{20} + 3 q^{21} + 30 q^{22} - 45 q^{23} - 21 q^{24} - 3 q^{25} - 72 q^{26} - 36 q^{28} - 9 q^{29} - 21 q^{30} - 9 q^{32} - 6 q^{33} + 33 q^{34} + 45 q^{35} + 18 q^{36} - 9 q^{38} - 18 q^{39} + 15 q^{40} - 9 q^{41} + 15 q^{42} + 9 q^{43} - 63 q^{44} + 33 q^{45} - 18 q^{46} - 9 q^{47} + 3 q^{48} - 15 q^{49} + 126 q^{50} + 39 q^{51} - 39 q^{52} - 51 q^{54} + 3 q^{55} + 63 q^{56} - 78 q^{57} - 6 q^{58} + 36 q^{59} - 75 q^{60} - 24 q^{61} + 18 q^{62} - 9 q^{63} - 18 q^{65} + 159 q^{66} - 63 q^{67} + 54 q^{68} - 9 q^{69} + 39 q^{70} + 141 q^{72} - 45 q^{73} - 117 q^{74} - 3 q^{76} - 18 q^{77} + 27 q^{78} + 3 q^{79} + 126 q^{80} - 60 q^{81} - 3 q^{82} + 27 q^{83} - 117 q^{84} - 3 q^{85} - 171 q^{86} + 15 q^{87} - 9 q^{88} + 54 q^{89} - 21 q^{90} - 9 q^{91} - 27 q^{92} + 42 q^{93} + 99 q^{95} + 207 q^{96} - 57 q^{97} - 27 q^{98} + 39 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/171\mathbb{Z}\right)^\times\).

\(n\) \(20\) \(154\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{18}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.80901 1.51794i −1.27916 1.07335i −0.993359 0.115058i \(-0.963295\pi\)
−0.285805 0.958288i \(-0.592261\pi\)
\(3\) −0.419122 1.68058i −0.241980 0.970281i
\(4\) 0.621081 + 3.52233i 0.310540 + 1.76116i
\(5\) −1.22473 3.36492i −0.547716 1.50484i −0.836786 0.547529i \(-0.815568\pi\)
0.289070 0.957308i \(-0.406654\pi\)
\(6\) −1.79282 + 3.67638i −0.731915 + 1.50088i
\(7\) 0.850912 1.47382i 0.321614 0.557052i −0.659207 0.751962i \(-0.729108\pi\)
0.980821 + 0.194909i \(0.0624412\pi\)
\(8\) 1.86164 3.22446i 0.658190 1.14002i
\(9\) −2.64867 + 1.40873i −0.882891 + 0.469578i
\(10\) −2.89220 + 7.94624i −0.914592 + 2.51282i
\(11\) 0.0685816i 0.0206781i 0.999947 + 0.0103391i \(0.00329108\pi\)
−0.999947 + 0.0103391i \(0.996709\pi\)
\(12\) 5.65923 2.52006i 1.63368 0.727478i
\(13\) 0.947862 2.60423i 0.262890 0.722283i −0.736080 0.676895i \(-0.763325\pi\)
0.998969 0.0453885i \(-0.0144526\pi\)
\(14\) −3.77648 + 1.37453i −1.00931 + 0.367358i
\(15\) −5.14169 + 3.46856i −1.32758 + 0.895579i
\(16\) −1.54034 + 0.560636i −0.385084 + 0.140159i
\(17\) 2.40059 + 6.59558i 0.582230 + 1.59966i 0.784361 + 0.620304i \(0.212991\pi\)
−0.202132 + 0.979358i \(0.564787\pi\)
\(18\) 6.92985 + 1.47211i 1.63338 + 0.346980i
\(19\) −3.88520 + 1.97616i −0.891326 + 0.453363i
\(20\) 11.0917 6.40378i 2.48018 1.43193i
\(21\) −2.83351 0.812310i −0.618322 0.177261i
\(22\) 0.104103 0.124065i 0.0221948 0.0264507i
\(23\) 2.95636 0.521285i 0.616443 0.108696i 0.143297 0.989680i \(-0.454229\pi\)
0.473146 + 0.880984i \(0.343118\pi\)
\(24\) −6.19920 1.77719i −1.26541 0.362767i
\(25\) −5.99249 + 5.02830i −1.19850 + 1.00566i
\(26\) −5.66776 + 3.27228i −1.11154 + 0.641747i
\(27\) 3.47760 + 3.86087i 0.669265 + 0.743024i
\(28\) 5.71977 + 2.08182i 1.08093 + 0.393428i
\(29\) −1.00498 5.69952i −0.186620 1.05837i −0.923856 0.382739i \(-0.874981\pi\)
0.737236 0.675635i \(-0.236130\pi\)
\(30\) 14.5664 + 1.53011i 2.65946 + 0.279358i
\(31\) 2.56914i 0.461432i −0.973021 0.230716i \(-0.925893\pi\)
0.973021 0.230716i \(-0.0741068\pi\)
\(32\) −3.35999 1.22294i −0.593967 0.216186i
\(33\) 0.115257 0.0287441i 0.0200636 0.00500370i
\(34\) 5.66899 15.5754i 0.972224 2.67116i
\(35\) −6.00143 1.05821i −1.01443 0.178871i
\(36\) −6.60706 8.45455i −1.10118 1.40909i
\(37\) 7.77355i 1.27796i −0.769221 0.638982i \(-0.779356\pi\)
0.769221 0.638982i \(-0.220644\pi\)
\(38\) 10.0281 + 2.32260i 1.62677 + 0.376775i
\(39\) −4.77388 0.501464i −0.764432 0.0802985i
\(40\) −13.1300 2.31518i −2.07604 0.366062i
\(41\) −8.32894 6.98881i −1.30076 1.09147i −0.990013 0.140977i \(-0.954976\pi\)
−0.310749 0.950492i \(-0.600580\pi\)
\(42\) 3.89281 + 5.77057i 0.600673 + 0.890419i
\(43\) 0.683977 3.87902i 0.104305 0.591546i −0.887190 0.461404i \(-0.847346\pi\)
0.991495 0.130141i \(-0.0415431\pi\)
\(44\) −0.241567 + 0.0425947i −0.0364175 + 0.00642139i
\(45\) 7.98418 + 7.18725i 1.19021 + 1.07141i
\(46\) −6.13936 3.54456i −0.905200 0.522617i
\(47\) −0.713950 + 0.125889i −0.104140 + 0.0183627i −0.225475 0.974249i \(-0.572394\pi\)
0.121335 + 0.992612i \(0.461282\pi\)
\(48\) 1.58778 + 2.35368i 0.229176 + 0.339724i
\(49\) 2.05190 + 3.55399i 0.293128 + 0.507713i
\(50\) 18.4731 2.61250
\(51\) 10.0782 6.79873i 1.41123 0.952013i
\(52\) 9.76164 + 1.72124i 1.35370 + 0.238693i
\(53\) 6.47151 5.43024i 0.888930 0.745901i −0.0790654 0.996869i \(-0.525194\pi\)
0.967995 + 0.250969i \(0.0807492\pi\)
\(54\) −0.430456 12.2631i −0.0585776 1.66880i
\(55\) 0.230771 0.0839939i 0.0311172 0.0113257i
\(56\) −3.16818 5.48746i −0.423366 0.733292i
\(57\) 4.94947 + 5.70112i 0.655573 + 0.755132i
\(58\) −6.83351 + 11.8360i −0.897284 + 1.55414i
\(59\) −1.93552 + 10.9769i −0.251983 + 1.42907i 0.551716 + 0.834032i \(0.313973\pi\)
−0.803699 + 0.595036i \(0.797138\pi\)
\(60\) −15.4108 15.9564i −1.98953 2.05997i
\(61\) −1.83166 0.666669i −0.234520 0.0853582i 0.222087 0.975027i \(-0.428713\pi\)
−0.456607 + 0.889669i \(0.650935\pi\)
\(62\) −3.89981 + 4.64761i −0.495276 + 0.590247i
\(63\) −0.177564 + 5.10238i −0.0223710 + 0.642840i
\(64\) 5.86110 + 10.1517i 0.732638 + 1.26897i
\(65\) −9.92389 −1.23091
\(66\) −0.252132 0.122954i −0.0310353 0.0151346i
\(67\) −5.17654 6.16916i −0.632415 0.753683i 0.350737 0.936474i \(-0.385931\pi\)
−0.983152 + 0.182791i \(0.941487\pi\)
\(68\) −21.7408 + 12.5521i −2.63646 + 1.52216i
\(69\) −2.11513 4.74990i −0.254632 0.571821i
\(70\) 9.25034 + 11.0241i 1.10563 + 1.31764i
\(71\) 4.92220 + 4.13021i 0.584157 + 0.490166i 0.886309 0.463093i \(-0.153261\pi\)
−0.302152 + 0.953260i \(0.597705\pi\)
\(72\) −0.388478 + 11.1631i −0.0457826 + 1.31558i
\(73\) 1.28461 7.28540i 0.150353 0.852692i −0.812560 0.582878i \(-0.801927\pi\)
0.962912 0.269814i \(-0.0869623\pi\)
\(74\) −11.7998 + 14.0624i −1.37170 + 1.63473i
\(75\) 10.9620 + 7.96337i 1.26579 + 0.919530i
\(76\) −9.37372 12.4576i −1.07524 1.42898i
\(77\) 0.101077 + 0.0583569i 0.0115188 + 0.00665038i
\(78\) 7.87480 + 8.15361i 0.891645 + 0.923215i
\(79\) 3.66753 + 10.0764i 0.412629 + 1.13369i 0.955787 + 0.294058i \(0.0950060\pi\)
−0.543159 + 0.839630i \(0.682772\pi\)
\(80\) 3.77299 + 4.49647i 0.421833 + 0.502721i
\(81\) 5.03094 7.46255i 0.558993 0.829172i
\(82\) 4.45854 + 25.2857i 0.492364 + 2.79233i
\(83\) −0.302529 0.174665i −0.0332069 0.0191720i 0.483305 0.875452i \(-0.339436\pi\)
−0.516512 + 0.856280i \(0.672770\pi\)
\(84\) 1.10138 10.4850i 0.120171 1.14401i
\(85\) 19.2535 16.1556i 2.08834 1.75232i
\(86\) −7.12545 + 5.97896i −0.768357 + 0.644728i
\(87\) −9.15727 + 4.07774i −0.981762 + 0.437179i
\(88\) 0.221138 + 0.127674i 0.0235734 + 0.0136101i
\(89\) −0.881834 5.00113i −0.0934743 0.530119i −0.995204 0.0978191i \(-0.968813\pi\)
0.901730 0.432300i \(-0.142298\pi\)
\(90\) −3.53366 25.1213i −0.372480 2.64802i
\(91\) −3.03162 3.61295i −0.317801 0.378740i
\(92\) 3.67227 + 10.0895i 0.382861 + 1.05190i
\(93\) −4.31764 + 1.07678i −0.447719 + 0.111657i
\(94\) 1.48263 + 0.855999i 0.152922 + 0.0882896i
\(95\) 11.4080 + 10.6531i 1.17043 + 1.09299i
\(96\) −0.646991 + 6.15927i −0.0660332 + 0.628628i
\(97\) 2.44747 2.91678i 0.248503 0.296154i −0.627345 0.778741i \(-0.715859\pi\)
0.875848 + 0.482587i \(0.160303\pi\)
\(98\) 1.68284 9.54387i 0.169993 0.964077i
\(99\) −0.0966132 0.181650i −0.00970999 0.0182565i
\(100\) −21.4331 17.9845i −2.14331 1.79845i
\(101\) −3.71031 4.42177i −0.369189 0.439983i 0.549182 0.835703i \(-0.314939\pi\)
−0.918371 + 0.395720i \(0.870495\pi\)
\(102\) −28.5517 2.99917i −2.82704 0.296962i
\(103\) −9.35292 + 5.39991i −0.921571 + 0.532069i −0.884136 0.467230i \(-0.845252\pi\)
−0.0374351 + 0.999299i \(0.511919\pi\)
\(104\) −6.63265 7.90448i −0.650384 0.775098i
\(105\) 0.736923 + 10.5294i 0.0719163 + 1.02756i
\(106\) −19.9498 −1.93770
\(107\) 5.99297 + 10.3801i 0.579362 + 1.00348i 0.995553 + 0.0942068i \(0.0300315\pi\)
−0.416191 + 0.909277i \(0.636635\pi\)
\(108\) −11.4394 + 14.6472i −1.10075 + 1.40942i
\(109\) 1.67453 1.99563i 0.160391 0.191146i −0.679864 0.733338i \(-0.737961\pi\)
0.840255 + 0.542192i \(0.182406\pi\)
\(110\) −0.544966 0.198351i −0.0519604 0.0189121i
\(111\) −13.0641 + 3.25807i −1.23998 + 0.309242i
\(112\) −0.484411 + 2.74723i −0.0457725 + 0.259589i
\(113\) 9.89206 17.1335i 0.930567 1.61179i 0.148212 0.988956i \(-0.452648\pi\)
0.782355 0.622833i \(-0.214018\pi\)
\(114\) −0.299681 17.8264i −0.0280677 1.66959i
\(115\) −5.37482 9.30947i −0.501205 0.868112i
\(116\) 19.4514 7.07973i 1.80602 0.657336i
\(117\) 1.15809 + 8.23304i 0.107065 + 0.761144i
\(118\) 20.1636 16.9193i 1.85621 1.55755i
\(119\) 11.7634 + 2.07421i 1.07835 + 0.190142i
\(120\) 1.61225 + 23.0364i 0.147178 + 2.10292i
\(121\) 10.9953 0.999572
\(122\) 2.30152 + 3.98636i 0.208370 + 0.360908i
\(123\) −8.25438 + 16.9266i −0.744273 + 1.52622i
\(124\) 9.04936 1.59565i 0.812656 0.143293i
\(125\) 8.75336 + 5.05376i 0.782924 + 0.452022i
\(126\) 8.06632 8.96073i 0.718605 0.798285i
\(127\) 1.09837 0.193673i 0.0974648 0.0171857i −0.124703 0.992194i \(-0.539798\pi\)
0.222168 + 0.975008i \(0.428687\pi\)
\(128\) 3.56512 20.2188i 0.315115 1.78710i
\(129\) −6.80567 + 0.476310i −0.599206 + 0.0419368i
\(130\) 17.9524 + 15.0639i 1.57453 + 1.32119i
\(131\) 0.0109927 + 0.00193831i 0.000960439 + 0.000169351i 0.174128 0.984723i \(-0.444289\pi\)
−0.173168 + 0.984892i \(0.555400\pi\)
\(132\) 0.172830 + 0.388119i 0.0150429 + 0.0337814i
\(133\) −0.393447 + 7.40763i −0.0341162 + 0.642323i
\(134\) 19.0178i 1.64288i
\(135\) 8.73237 16.4304i 0.751563 1.41410i
\(136\) 25.7362 + 4.53799i 2.20686 + 0.389129i
\(137\) −1.11583 + 3.06570i −0.0953314 + 0.261921i −0.978188 0.207722i \(-0.933395\pi\)
0.882857 + 0.469643i \(0.155617\pi\)
\(138\) −3.38376 + 11.8033i −0.288045 + 1.00476i
\(139\) 8.02855 + 2.92215i 0.680973 + 0.247854i 0.659265 0.751911i \(-0.270868\pi\)
0.0217075 + 0.999764i \(0.493090\pi\)
\(140\) 21.7962i 1.84212i
\(141\) 0.510798 + 1.14708i 0.0430169 + 0.0966019i
\(142\) −2.63489 14.9432i −0.221115 1.25401i
\(143\) 0.178602 + 0.0650059i 0.0149355 + 0.00543606i
\(144\) 3.29006 3.65486i 0.274171 0.304572i
\(145\) −17.9476 + 10.3620i −1.49047 + 0.860521i
\(146\) −13.3827 + 11.2294i −1.10756 + 0.929352i
\(147\) 5.11276 4.93793i 0.421693 0.407274i
\(148\) 27.3810 4.82801i 2.25070 0.396860i
\(149\) 0.600370 0.715493i 0.0491842 0.0586155i −0.740891 0.671625i \(-0.765597\pi\)
0.790076 + 0.613009i \(0.210041\pi\)
\(150\) −7.74250 31.0455i −0.632172 2.53486i
\(151\) −10.8642 + 6.27247i −0.884119 + 0.510447i −0.872014 0.489480i \(-0.837187\pi\)
−0.0121050 + 0.999927i \(0.503853\pi\)
\(152\) −0.860791 + 16.2066i −0.0698194 + 1.31453i
\(153\) −15.6498 14.0877i −1.26521 1.13893i
\(154\) −0.0942672 0.258997i −0.00759627 0.0208706i
\(155\) −8.64496 + 3.14651i −0.694380 + 0.252734i
\(156\) −1.19864 17.1266i −0.0959683 1.37122i
\(157\) −10.9534 + 3.98670i −0.874174 + 0.318173i −0.739856 0.672765i \(-0.765106\pi\)
−0.134318 + 0.990938i \(0.542884\pi\)
\(158\) 8.66085 23.7955i 0.689020 1.89307i
\(159\) −11.8383 8.59993i −0.938837 0.682019i
\(160\) 12.8038i 1.01223i
\(161\) 1.74732 4.80071i 0.137708 0.378349i
\(162\) −20.4287 + 5.86317i −1.60503 + 0.460654i
\(163\) 8.85463 15.3367i 0.693548 1.20126i −0.277120 0.960835i \(-0.589380\pi\)
0.970668 0.240425i \(-0.0772868\pi\)
\(164\) 19.4439 33.6778i 1.51831 2.62980i
\(165\) −0.237880 0.352625i −0.0185189 0.0274518i
\(166\) 0.282147 + 0.775192i 0.0218989 + 0.0601666i
\(167\) 0.198247 + 1.12432i 0.0153408 + 0.0870022i 0.991517 0.129978i \(-0.0414905\pi\)
−0.976176 + 0.216980i \(0.930379\pi\)
\(168\) −7.89423 + 7.62429i −0.609053 + 0.588227i
\(169\) 4.07501 + 3.41934i 0.313462 + 0.263026i
\(170\) −59.3530 −4.55217
\(171\) 7.50673 10.7074i 0.574054 0.818817i
\(172\) 14.0880 1.07420
\(173\) 0.683168 + 0.573246i 0.0519403 + 0.0435831i 0.668388 0.743813i \(-0.266984\pi\)
−0.616448 + 0.787396i \(0.711429\pi\)
\(174\) 22.7554 + 6.52351i 1.72508 + 0.494546i
\(175\) 2.31173 + 13.1105i 0.174751 + 0.991061i
\(176\) −0.0384493 0.105639i −0.00289823 0.00796281i
\(177\) 19.2587 1.34786i 1.44757 0.101312i
\(178\) −5.99617 + 10.3857i −0.449432 + 0.778439i
\(179\) 7.40214 12.8209i 0.553262 0.958278i −0.444774 0.895643i \(-0.646716\pi\)
0.998036 0.0626353i \(-0.0199505\pi\)
\(180\) −20.3570 + 32.5868i −1.51732 + 2.42887i
\(181\) 2.14356 5.88939i 0.159330 0.437755i −0.834181 0.551490i \(-0.814059\pi\)
0.993511 + 0.113735i \(0.0362816\pi\)
\(182\) 11.1377i 0.825580i
\(183\) −0.352699 + 3.35765i −0.0260723 + 0.248205i
\(184\) 3.82281 10.5031i 0.281822 0.774298i
\(185\) −26.1574 + 9.52051i −1.92313 + 0.699962i
\(186\) 9.44515 + 4.60601i 0.692552 + 0.337729i
\(187\) −0.452335 + 0.164637i −0.0330780 + 0.0120394i
\(188\) −0.886841 2.43658i −0.0646795 0.177706i
\(189\) 8.64936 1.84011i 0.629148 0.133848i
\(190\) −4.46632 36.5882i −0.324021 2.65439i
\(191\) 16.6733 9.62632i 1.20644 0.696536i 0.244457 0.969660i \(-0.421390\pi\)
0.961979 + 0.273124i \(0.0880570\pi\)
\(192\) 14.6042 14.1048i 1.05397 1.01793i
\(193\) −8.89893 + 10.6053i −0.640559 + 0.763388i −0.984458 0.175618i \(-0.943808\pi\)
0.343900 + 0.939006i \(0.388252\pi\)
\(194\) −8.85498 + 1.56137i −0.635751 + 0.112100i
\(195\) 4.15932 + 16.6779i 0.297855 + 1.19433i
\(196\) −11.2439 + 9.43477i −0.803137 + 0.673912i
\(197\) 10.1316 5.84947i 0.721845 0.416757i −0.0935863 0.995611i \(-0.529833\pi\)
0.815431 + 0.578854i \(0.196500\pi\)
\(198\) −0.100960 + 0.475260i −0.00717491 + 0.0337753i
\(199\) −5.06800 1.84460i −0.359261 0.130760i 0.156083 0.987744i \(-0.450113\pi\)
−0.515343 + 0.856984i \(0.672336\pi\)
\(200\) 5.05766 + 28.6834i 0.357630 + 2.02822i
\(201\) −8.19814 + 11.2852i −0.578252 + 0.795997i
\(202\) 13.6311i 0.959078i
\(203\) −9.25523 3.36863i −0.649590 0.236431i
\(204\) 30.2067 + 31.2762i 2.11490 + 2.18977i
\(205\) −13.3161 + 36.5856i −0.930035 + 2.55525i
\(206\) 25.1163 + 4.42868i 1.74993 + 0.308561i
\(207\) −7.09607 + 5.54543i −0.493211 + 0.385434i
\(208\) 4.54279i 0.314986i
\(209\) −0.135528 0.266453i −0.00937470 0.0184309i
\(210\) 14.6499 20.1664i 1.01094 1.39161i
\(211\) −1.39187 0.245425i −0.0958204 0.0168957i 0.125532 0.992090i \(-0.459936\pi\)
−0.221353 + 0.975194i \(0.571047\pi\)
\(212\) 23.1464 + 19.4221i 1.58970 + 1.33392i
\(213\) 4.87814 10.0032i 0.334245 0.685408i
\(214\) 4.91506 27.8747i 0.335987 1.90548i
\(215\) −13.8903 + 2.44923i −0.947310 + 0.167036i
\(216\) 18.9232 4.02583i 1.28756 0.273923i
\(217\) −3.78646 2.18611i −0.257042 0.148403i
\(218\) −6.05848 + 1.06827i −0.410332 + 0.0723526i
\(219\) −12.7821 + 0.894584i −0.863733 + 0.0604504i
\(220\) 0.439182 + 0.760685i 0.0296096 + 0.0512854i
\(221\) 19.4518 1.30847
\(222\) 28.5786 + 13.9366i 1.91807 + 0.935361i
\(223\) 7.70442 + 1.35850i 0.515926 + 0.0909716i 0.425548 0.904936i \(-0.360081\pi\)
0.0903779 + 0.995908i \(0.471193\pi\)
\(224\) −4.66144 + 3.91141i −0.311456 + 0.261342i
\(225\) 8.78862 21.7601i 0.585908 1.45068i
\(226\) −43.9025 + 15.9792i −2.92035 + 1.06292i
\(227\) 13.4006 + 23.2105i 0.889428 + 1.54053i 0.840553 + 0.541730i \(0.182231\pi\)
0.0488758 + 0.998805i \(0.484436\pi\)
\(228\) −17.0072 + 20.9745i −1.12633 + 1.38907i
\(229\) 4.04261 7.00201i 0.267143 0.462706i −0.700980 0.713181i \(-0.747254\pi\)
0.968123 + 0.250476i \(0.0805870\pi\)
\(230\) −4.40810 + 24.9996i −0.290662 + 1.64842i
\(231\) 0.0557095 0.194326i 0.00366542 0.0127857i
\(232\) −20.2488 7.36995i −1.32940 0.483861i
\(233\) 5.38901 6.42237i 0.353046 0.420743i −0.560069 0.828446i \(-0.689225\pi\)
0.913115 + 0.407702i \(0.133670\pi\)
\(234\) 10.4023 16.6516i 0.680017 1.08855i
\(235\) 1.29800 + 2.24820i 0.0846722 + 0.146657i
\(236\) −39.8662 −2.59507
\(237\) 15.3971 10.3868i 1.00015 0.674696i
\(238\) −18.1316 21.6084i −1.17530 1.40066i
\(239\) −17.2827 + 9.97818i −1.11793 + 0.645435i −0.940871 0.338766i \(-0.889991\pi\)
−0.177056 + 0.984201i \(0.556657\pi\)
\(240\) 5.97532 8.22537i 0.385706 0.530945i
\(241\) 4.31692 + 5.14471i 0.278078 + 0.331400i 0.886948 0.461870i \(-0.152821\pi\)
−0.608870 + 0.793270i \(0.708377\pi\)
\(242\) −19.8906 16.6902i −1.27862 1.07289i
\(243\) −14.6500 5.32716i −0.939796 0.341737i
\(244\) 1.21062 6.86575i 0.0775018 0.439534i
\(245\) 9.44587 11.2572i 0.603475 0.719193i
\(246\) 40.6258 18.0907i 2.59021 1.15342i
\(247\) 1.46375 + 11.9911i 0.0931363 + 0.762974i
\(248\) −8.28409 4.78282i −0.526040 0.303710i
\(249\) −0.166742 + 0.581629i −0.0105668 + 0.0368593i
\(250\) −8.16363 22.4294i −0.516313 1.41856i
\(251\) 15.1000 + 17.9955i 0.953103 + 1.13586i 0.990631 + 0.136568i \(0.0436073\pi\)
−0.0375279 + 0.999296i \(0.511948\pi\)
\(252\) −18.0825 + 2.54355i −1.13909 + 0.160229i
\(253\) 0.0357506 + 0.202752i 0.00224762 + 0.0127469i
\(254\) −2.28095 1.31691i −0.143120 0.0826302i
\(255\) −35.2203 25.5858i −2.20558 1.60225i
\(256\) −19.1808 + 16.0946i −1.19880 + 1.00591i
\(257\) 6.19757 5.20038i 0.386594 0.324391i −0.428691 0.903451i \(-0.641025\pi\)
0.815285 + 0.579061i \(0.196581\pi\)
\(258\) 13.0345 + 9.46894i 0.811495 + 0.589511i
\(259\) −11.4568 6.61461i −0.711893 0.411012i
\(260\) −6.16354 34.9552i −0.382247 2.16783i
\(261\) 10.6910 + 13.6804i 0.661754 + 0.846797i
\(262\) −0.0169437 0.0201927i −0.00104679 0.00124751i
\(263\) −6.23810 17.1390i −0.384658 1.05684i −0.969372 0.245599i \(-0.921015\pi\)
0.584714 0.811240i \(-0.301207\pi\)
\(264\) 0.121882 0.425151i 0.00750134 0.0261662i
\(265\) −26.1982 15.1255i −1.60934 0.929153i
\(266\) 11.9561 12.8033i 0.733075 0.785018i
\(267\) −8.03519 + 3.57808i −0.491745 + 0.218975i
\(268\) 18.5147 22.0650i 1.13097 1.34783i
\(269\) −1.90392 + 10.7977i −0.116084 + 0.658347i 0.870123 + 0.492834i \(0.164039\pi\)
−0.986208 + 0.165513i \(0.947072\pi\)
\(270\) −40.7373 + 16.4675i −2.47919 + 1.00218i
\(271\) 7.63501 + 6.40653i 0.463794 + 0.389169i 0.844525 0.535517i \(-0.179883\pi\)
−0.380731 + 0.924686i \(0.624328\pi\)
\(272\) −7.39544 8.81354i −0.448414 0.534399i
\(273\) −4.80121 + 6.60914i −0.290583 + 0.400003i
\(274\) 6.67210 3.85214i 0.403076 0.232716i
\(275\) −0.344848 0.410974i −0.0207951 0.0247827i
\(276\) 15.4170 10.4003i 0.927996 0.626022i
\(277\) −5.65714 −0.339905 −0.169952 0.985452i \(-0.554361\pi\)
−0.169952 + 0.985452i \(0.554361\pi\)
\(278\) −10.0881 17.4731i −0.605043 1.04796i
\(279\) 3.61924 + 6.80482i 0.216678 + 0.407394i
\(280\) −14.5847 + 17.3813i −0.871601 + 1.03873i
\(281\) 8.00493 + 2.91356i 0.477534 + 0.173808i 0.569562 0.821948i \(-0.307113\pi\)
−0.0920282 + 0.995756i \(0.529335\pi\)
\(282\) 0.817167 2.85045i 0.0486616 0.169742i
\(283\) 2.85192 16.1740i 0.169529 0.961446i −0.774742 0.632277i \(-0.782120\pi\)
0.944271 0.329169i \(-0.106769\pi\)
\(284\) −11.4909 + 19.9028i −0.681858 + 1.18101i
\(285\) 13.1220 23.6369i 0.777283 1.40013i
\(286\) −0.224418 0.388704i −0.0132701 0.0229845i
\(287\) −17.3875 + 6.32852i −1.02635 + 0.373560i
\(288\) 10.6223 1.49417i 0.625925 0.0880448i
\(289\) −24.7160 + 20.7392i −1.45388 + 1.21995i
\(290\) 48.1963 + 8.49832i 2.83019 + 0.499038i
\(291\) −5.92765 2.89067i −0.347485 0.169454i
\(292\) 26.4594 1.54842
\(293\) 11.7033 + 20.2707i 0.683714 + 1.18423i 0.973839 + 0.227238i \(0.0729696\pi\)
−0.290125 + 0.956989i \(0.593697\pi\)
\(294\) −16.7445 + 1.17190i −0.976560 + 0.0683468i
\(295\) 39.3068 6.93085i 2.28853 0.403530i
\(296\) −25.0655 14.4716i −1.45690 0.841143i
\(297\) −0.264784 + 0.238499i −0.0153643 + 0.0138391i
\(298\) −2.17215 + 0.383009i −0.125829 + 0.0221871i
\(299\) 1.44467 8.19314i 0.0835475 0.473821i
\(300\) −21.2413 + 43.5577i −1.22636 + 2.51480i
\(301\) −5.13499 4.30877i −0.295976 0.248353i
\(302\) 29.1748 + 5.14430i 1.67882 + 0.296021i
\(303\) −5.87605 + 8.08872i −0.337571 + 0.464685i
\(304\) 4.87660 5.22214i 0.279692 0.299510i
\(305\) 6.97986i 0.399666i
\(306\) 6.92632 + 49.2403i 0.395951 + 2.81488i
\(307\) 0.718463 + 0.126684i 0.0410048 + 0.00723026i 0.194113 0.980979i \(-0.437817\pi\)
−0.153108 + 0.988209i \(0.548928\pi\)
\(308\) −0.142775 + 0.392271i −0.00813535 + 0.0223517i
\(309\) 12.9950 + 13.4551i 0.739259 + 0.765433i
\(310\) 20.4150 + 7.43046i 1.15950 + 0.422022i
\(311\) 4.00327i 0.227005i −0.993538 0.113502i \(-0.963793\pi\)
0.993538 0.113502i \(-0.0362069\pi\)
\(312\) −10.5042 + 14.4596i −0.594683 + 0.818614i
\(313\) −0.440938 2.50068i −0.0249233 0.141347i 0.969807 0.243874i \(-0.0784183\pi\)
−0.994730 + 0.102527i \(0.967307\pi\)
\(314\) 25.8663 + 9.41457i 1.45972 + 0.531295i
\(315\) 17.3866 5.65155i 0.979622 0.318429i
\(316\) −33.2147 + 19.1765i −1.86847 + 1.07876i
\(317\) 24.5334 20.5860i 1.37793 1.15622i 0.407964 0.912998i \(-0.366239\pi\)
0.969970 0.243226i \(-0.0782055\pi\)
\(318\) 8.36140 + 33.5272i 0.468884 + 1.88011i
\(319\) 0.390882 0.0689230i 0.0218852 0.00385895i
\(320\) 26.9815 32.1552i 1.50831 1.79753i
\(321\) 14.9328 14.4222i 0.833468 0.804967i
\(322\) −10.4481 + 6.03222i −0.582250 + 0.336162i
\(323\) −22.3607 20.8812i −1.24418 1.16186i
\(324\) 29.4101 + 13.0858i 1.63390 + 0.726986i
\(325\) 7.41478 + 20.3719i 0.411298 + 1.13003i
\(326\) −39.2983 + 14.3034i −2.17653 + 0.792192i
\(327\) −4.05563 1.97776i −0.224277 0.109371i
\(328\) −38.0406 + 13.8456i −2.10044 + 0.764498i
\(329\) −0.421971 + 1.15935i −0.0232640 + 0.0639173i
\(330\) −0.104937 + 0.998990i −0.00577661 + 0.0549926i
\(331\) 25.6998i 1.41259i −0.707919 0.706293i \(-0.750366\pi\)
0.707919 0.706293i \(-0.249634\pi\)
\(332\) 0.427333 1.17409i 0.0234529 0.0644364i
\(333\) 10.9509 + 20.5896i 0.600104 + 1.12830i
\(334\) 1.34801 2.33483i 0.0737600 0.127756i
\(335\) −14.4189 + 24.9742i −0.787786 + 1.36449i
\(336\) 4.81996 0.337336i 0.262950 0.0184032i
\(337\) −4.70694 12.9322i −0.256404 0.704463i −0.999382 0.0351479i \(-0.988810\pi\)
0.742979 0.669315i \(-0.233412\pi\)
\(338\) −2.18138 12.3712i −0.118652 0.672907i
\(339\) −32.9402 9.44331i −1.78907 0.512890i
\(340\) 68.8633 + 57.7832i 3.73464 + 3.13373i
\(341\) 0.176196 0.00954154
\(342\) −29.8330 + 7.97507i −1.61318 + 0.431242i
\(343\) 18.8967 1.02033
\(344\) −11.2344 9.42681i −0.605720 0.508259i
\(345\) −13.3926 + 12.9346i −0.721031 + 0.696376i
\(346\) −0.365705 2.07402i −0.0196604 0.111500i
\(347\) 0.882518 + 2.42470i 0.0473761 + 0.130165i 0.961124 0.276117i \(-0.0890476\pi\)
−0.913748 + 0.406281i \(0.866825\pi\)
\(348\) −20.0505 29.7223i −1.07482 1.59328i
\(349\) 2.91543 5.04967i 0.156059 0.270303i −0.777385 0.629025i \(-0.783454\pi\)
0.933444 + 0.358723i \(0.116788\pi\)
\(350\) 15.7190 27.2261i 0.840216 1.45530i
\(351\) 13.3509 5.39690i 0.712616 0.288065i
\(352\) 0.0838708 0.230433i 0.00447033 0.0122821i
\(353\) 15.5640i 0.828389i −0.910188 0.414195i \(-0.864063\pi\)
0.910188 0.414195i \(-0.135937\pi\)
\(354\) −36.8852 26.7953i −1.96042 1.42415i
\(355\) 7.86947 21.6212i 0.417668 1.14753i
\(356\) 17.0679 6.21222i 0.904598 0.329247i
\(357\) −1.44444 20.6386i −0.0764480 1.09231i
\(358\) −32.8519 + 11.9571i −1.73628 + 0.631953i
\(359\) 3.60821 + 9.91347i 0.190434 + 0.523213i 0.997760 0.0668923i \(-0.0213084\pi\)
−0.807326 + 0.590105i \(0.799086\pi\)
\(360\) 38.0387 12.3646i 2.00481 0.651670i
\(361\) 11.1896 15.3556i 0.588924 0.808189i
\(362\) −12.8175 + 7.40017i −0.673671 + 0.388944i
\(363\) −4.60837 18.4784i −0.241877 0.969866i
\(364\) 10.8431 12.9223i 0.568333 0.677312i
\(365\) −26.0881 + 4.60003i −1.36551 + 0.240777i
\(366\) 5.73476 5.53866i 0.299761 0.289510i
\(367\) 8.48054 7.11602i 0.442681 0.371453i −0.394031 0.919097i \(-0.628920\pi\)
0.836711 + 0.547644i \(0.184475\pi\)
\(368\) −4.26153 + 2.46039i −0.222148 + 0.128257i
\(369\) 31.9060 + 6.77782i 1.66096 + 0.352839i
\(370\) 61.7705 + 22.4826i 3.21130 + 1.16882i
\(371\) −2.49653 14.1585i −0.129613 0.735073i
\(372\) −6.47439 14.5394i −0.335682 0.753831i
\(373\) 31.3106i 1.62120i 0.585599 + 0.810601i \(0.300859\pi\)
−0.585599 + 0.810601i \(0.699141\pi\)
\(374\) 1.06819 + 0.388788i 0.0552347 + 0.0201038i
\(375\) 4.82449 16.8288i 0.249136 0.869037i
\(376\) −0.923196 + 2.53646i −0.0476102 + 0.130808i
\(377\) −15.7954 2.78516i −0.813506 0.143443i
\(378\) −18.4400 9.80043i −0.948450 0.504080i
\(379\) 27.4978i 1.41247i 0.707979 + 0.706234i \(0.249607\pi\)
−0.707979 + 0.706234i \(0.750393\pi\)
\(380\) −30.4385 + 46.7990i −1.56146 + 2.40074i
\(381\) −0.785834 1.76473i −0.0402595 0.0904097i
\(382\) −44.7743 7.89492i −2.29085 0.403939i
\(383\) −14.5449 12.2046i −0.743211 0.623628i 0.190487 0.981690i \(-0.438993\pi\)
−0.933698 + 0.358062i \(0.883438\pi\)
\(384\) −35.4734 + 2.48269i −1.81024 + 0.126694i
\(385\) 0.0725740 0.411587i 0.00369871 0.0209764i
\(386\) 32.1965 5.67711i 1.63876 0.288957i
\(387\) 3.65288 + 11.2378i 0.185686 + 0.571250i
\(388\) 11.7939 + 6.80922i 0.598745 + 0.345686i
\(389\) −27.3570 + 4.82378i −1.38706 + 0.244575i −0.816813 0.576902i \(-0.804262\pi\)
−0.570242 + 0.821477i \(0.693150\pi\)
\(390\) 17.7917 36.4840i 0.900919 1.84744i
\(391\) 10.5352 + 18.2475i 0.532788 + 0.922815i
\(392\) 15.2796 0.771736
\(393\) −0.00134981 0.0192865i −6.80890e−5 0.000972876i
\(394\) −27.2073 4.79738i −1.37068 0.241688i
\(395\) 29.4147 24.6818i 1.48001 1.24188i
\(396\) 0.579826 0.453122i 0.0291374 0.0227703i
\(397\) 15.9016 5.78772i 0.798080 0.290477i 0.0893892 0.995997i \(-0.471509\pi\)
0.708690 + 0.705520i \(0.249286\pi\)
\(398\) 6.36807 + 11.0298i 0.319203 + 0.552875i
\(399\) 12.6140 2.44349i 0.631490 0.122327i
\(400\) 6.41140 11.1049i 0.320570 0.555243i
\(401\) −0.579010 + 3.28373i −0.0289144 + 0.163982i −0.995846 0.0910545i \(-0.970976\pi\)
0.966932 + 0.255036i \(0.0820874\pi\)
\(402\) 31.9608 7.97076i 1.59406 0.397545i
\(403\) −6.69064 2.43519i −0.333284 0.121306i
\(404\) 13.2705 15.8152i 0.660233 0.786835i
\(405\) −31.2724 7.78909i −1.55394 0.387043i
\(406\) 11.6294 + 20.1428i 0.577159 + 0.999669i
\(407\) 0.533123 0.0264259
\(408\) −3.16018 45.1536i −0.156452 2.23544i
\(409\) 14.4682 + 17.2425i 0.715405 + 0.852587i 0.994176 0.107771i \(-0.0343714\pi\)
−0.278771 + 0.960358i \(0.589927\pi\)
\(410\) 79.6237 45.9708i 3.93233 2.27033i
\(411\) 5.61982 + 0.590324i 0.277205 + 0.0291186i
\(412\) −24.8292 29.5903i −1.22325 1.45781i
\(413\) 14.5310 + 12.1930i 0.715024 + 0.599977i
\(414\) 21.2545 + 0.739662i 1.04460 + 0.0363524i
\(415\) −0.217218 + 1.23190i −0.0106628 + 0.0604718i
\(416\) −6.36961 + 7.59100i −0.312296 + 0.372179i
\(417\) 1.54596 14.7173i 0.0757059 0.720711i
\(418\) −0.159287 + 0.687741i −0.00779100 + 0.0336385i
\(419\) 6.84253 + 3.95053i 0.334279 + 0.192996i 0.657739 0.753246i \(-0.271513\pi\)
−0.323460 + 0.946242i \(0.604846\pi\)
\(420\) −36.6302 + 9.13528i −1.78737 + 0.445756i
\(421\) −0.951687 2.61474i −0.0463824 0.127435i 0.914339 0.404950i \(-0.132711\pi\)
−0.960721 + 0.277516i \(0.910489\pi\)
\(422\) 2.14537 + 2.55675i 0.104435 + 0.124461i
\(423\) 1.71368 1.33920i 0.0833218 0.0651143i
\(424\) −5.46195 30.9762i −0.265256 1.50434i
\(425\) −47.5501 27.4530i −2.30652 1.33167i
\(426\) −24.0089 + 10.6912i −1.16323 + 0.517989i
\(427\) −2.54113 + 2.13226i −0.122974 + 0.103187i
\(428\) −32.8400 + 27.5561i −1.58738 + 1.33197i
\(429\) 0.0343912 0.327400i 0.00166042 0.0158070i
\(430\) 28.8455 + 16.6539i 1.39105 + 0.803124i
\(431\) 2.52762 + 14.3348i 0.121751 + 0.690485i 0.983185 + 0.182614i \(0.0584560\pi\)
−0.861434 + 0.507870i \(0.830433\pi\)
\(432\) −7.52121 3.99736i −0.361865 0.192323i
\(433\) −21.0433 25.0784i −1.01128 1.20519i −0.978610 0.205725i \(-0.934045\pi\)
−0.0326658 0.999466i \(-0.510400\pi\)
\(434\) 3.53136 + 9.70232i 0.169511 + 0.465726i
\(435\) 24.9364 + 25.8193i 1.19561 + 1.23794i
\(436\) 8.06926 + 4.65879i 0.386448 + 0.223116i
\(437\) −10.4559 + 7.86754i −0.500173 + 0.376356i
\(438\) 24.4809 + 17.7841i 1.16974 + 0.849759i
\(439\) −1.20863 + 1.44038i −0.0576845 + 0.0687458i −0.794115 0.607767i \(-0.792065\pi\)
0.736431 + 0.676513i \(0.236510\pi\)
\(440\) 0.158779 0.900479i 0.00756948 0.0429287i
\(441\) −10.4414 6.52279i −0.497211 0.310609i
\(442\) −35.1886 29.5267i −1.67375 1.40444i
\(443\) 12.5216 + 14.9226i 0.594917 + 0.708994i 0.976543 0.215322i \(-0.0690802\pi\)
−0.381626 + 0.924317i \(0.624636\pi\)
\(444\) −19.5898 43.9923i −0.929691 2.08778i
\(445\) −15.7484 + 9.09234i −0.746545 + 0.431018i
\(446\) −11.8753 14.1524i −0.562310 0.670134i
\(447\) −1.45407 0.709089i −0.0687751 0.0335387i
\(448\) 19.9491 0.942507
\(449\) −1.89892 3.28902i −0.0896154 0.155218i 0.817733 0.575597i \(-0.195230\pi\)
−0.907349 + 0.420379i \(0.861897\pi\)
\(450\) −48.9293 + 26.0237i −2.30655 + 1.22677i
\(451\) 0.479304 0.571212i 0.0225695 0.0268973i
\(452\) 66.4937 + 24.2017i 3.12760 + 1.13835i
\(453\) 15.0948 + 15.6293i 0.709216 + 0.734326i
\(454\) 10.9903 62.3293i 0.515802 2.92526i
\(455\) −8.44436 + 14.6261i −0.395878 + 0.685680i
\(456\) 27.5971 5.34591i 1.29235 0.250345i
\(457\) 6.13044 + 10.6182i 0.286770 + 0.496700i 0.973037 0.230650i \(-0.0740851\pi\)
−0.686267 + 0.727350i \(0.740752\pi\)
\(458\) −17.9418 + 6.53027i −0.838363 + 0.305139i
\(459\) −17.1163 + 32.2052i −0.798922 + 1.50321i
\(460\) 29.4528 24.7138i 1.37324 1.15229i
\(461\) −30.9667 5.46026i −1.44226 0.254310i −0.602871 0.797839i \(-0.705977\pi\)
−0.839390 + 0.543529i \(0.817088\pi\)
\(462\) −0.395755 + 0.266975i −0.0184122 + 0.0124208i
\(463\) 18.1595 0.843941 0.421971 0.906609i \(-0.361339\pi\)
0.421971 + 0.906609i \(0.361339\pi\)
\(464\) 4.74336 + 8.21574i 0.220205 + 0.381406i
\(465\) 8.91124 + 13.2097i 0.413249 + 0.612587i
\(466\) −19.4975 + 3.43794i −0.903206 + 0.159260i
\(467\) −33.3722 19.2674i −1.54428 0.891591i −0.998561 0.0536229i \(-0.982923\pi\)
−0.545719 0.837968i \(-0.683744\pi\)
\(468\) −28.2802 + 9.19255i −1.30725 + 0.424926i
\(469\) −13.4970 + 2.37989i −0.623234 + 0.109893i
\(470\) 1.06454 6.03731i 0.0491036 0.278480i
\(471\) 11.2908 + 16.7371i 0.520250 + 0.771203i
\(472\) 31.7912 + 26.6760i 1.46331 + 1.22786i
\(473\) 0.266030 + 0.0469082i 0.0122321 + 0.00215684i
\(474\) −43.6201 4.58200i −2.00354 0.210458i
\(475\) 13.3453 31.3781i 0.612323 1.43972i
\(476\) 42.7228i 1.95820i
\(477\) −9.49115 + 23.4996i −0.434570 + 1.07597i
\(478\) 46.4109 + 8.18350i 2.12279 + 0.374304i
\(479\) 6.27057 17.2282i 0.286510 0.787179i −0.710039 0.704163i \(-0.751323\pi\)
0.996548 0.0830160i \(-0.0264553\pi\)
\(480\) 21.5178 5.36638i 0.982151 0.244940i
\(481\) −20.2441 7.36826i −0.923052 0.335964i
\(482\) 15.8597i 0.722388i
\(483\) −8.80030 0.924413i −0.400428 0.0420623i
\(484\) 6.82897 + 38.7290i 0.310408 + 1.76041i
\(485\) −12.8122 4.66326i −0.581772 0.211748i
\(486\) 18.4156 + 31.8747i 0.835350 + 1.44586i
\(487\) −4.94599 + 2.85557i −0.224124 + 0.129398i −0.607859 0.794045i \(-0.707971\pi\)
0.383734 + 0.923444i \(0.374638\pi\)
\(488\) −5.55953 + 4.66500i −0.251668 + 0.211175i
\(489\) −29.4856 8.45294i −1.33339 0.382255i
\(490\) −34.1754 + 6.02604i −1.54389 + 0.272229i
\(491\) 1.35643 1.61653i 0.0612149 0.0729531i −0.734568 0.678535i \(-0.762615\pi\)
0.795783 + 0.605582i \(0.207060\pi\)
\(492\) −64.7476 18.5618i −2.91905 0.836833i
\(493\) 35.1791 20.3106i 1.58439 0.914746i
\(494\) 15.5538 23.9139i 0.699799 1.07594i
\(495\) −0.492913 + 0.547568i −0.0221548 + 0.0246113i
\(496\) 1.44035 + 3.95734i 0.0646738 + 0.177690i
\(497\) 10.2756 3.74000i 0.460922 0.167762i
\(498\) 1.18452 0.799070i 0.0530794 0.0358072i
\(499\) −5.97530 + 2.17483i −0.267491 + 0.0973587i −0.472284 0.881447i \(-0.656570\pi\)
0.204793 + 0.978805i \(0.434348\pi\)
\(500\) −12.3644 + 33.9710i −0.552954 + 1.51923i
\(501\) 1.80641 0.804395i 0.0807044 0.0359377i
\(502\) 55.4749i 2.47596i
\(503\) 0.199225 0.547365i 0.00888299 0.0244058i −0.935172 0.354194i \(-0.884755\pi\)
0.944055 + 0.329788i \(0.106977\pi\)
\(504\) 16.1218 + 10.0713i 0.718124 + 0.448614i
\(505\) −10.3348 + 17.9004i −0.459892 + 0.796556i
\(506\) 0.243092 0.421047i 0.0108067 0.0187178i
\(507\) 4.03853 8.28149i 0.179358 0.367794i
\(508\) 1.36436 + 3.74854i 0.0605336 + 0.166315i
\(509\) 2.67718 + 15.1830i 0.118664 + 0.672976i 0.984871 + 0.173291i \(0.0554400\pi\)
−0.866207 + 0.499686i \(0.833449\pi\)
\(510\) 24.8762 + 99.7473i 1.10154 + 4.41689i
\(511\) −9.64430 8.09253i −0.426639 0.357992i
\(512\) 18.0675 0.798477
\(513\) −21.1409 8.12792i −0.933393 0.358857i
\(514\) −19.1053 −0.842700
\(515\) 29.6251 + 24.8584i 1.30544 + 1.09539i
\(516\) −5.90459 23.6759i −0.259935 1.04228i
\(517\) −0.00863364 0.0489638i −0.000379707 0.00215343i
\(518\) 10.6850 + 29.3567i 0.469470 + 1.28986i
\(519\) 0.677053 1.38838i 0.0297193 0.0609430i
\(520\) −18.4747 + 31.9992i −0.810170 + 1.40326i
\(521\) −9.57944 + 16.5921i −0.419683 + 0.726912i −0.995907 0.0903794i \(-0.971192\pi\)
0.576225 + 0.817291i \(0.304525\pi\)
\(522\) 1.42598 40.9763i 0.0624136 1.79348i
\(523\) −3.22775 + 8.86817i −0.141140 + 0.387778i −0.990042 0.140771i \(-0.955042\pi\)
0.848902 + 0.528550i \(0.177264\pi\)
\(524\) 0.0399238i 0.00174408i
\(525\) 21.0643 9.37995i 0.919321 0.409374i
\(526\) −14.7312 + 40.4738i −0.642313 + 1.76474i
\(527\) 16.9450 6.16747i 0.738135 0.268659i
\(528\) −0.161419 + 0.108892i −0.00702485 + 0.00473894i
\(529\) −13.1446 + 4.78425i −0.571505 + 0.208011i
\(530\) 24.4331 + 67.1295i 1.06131 + 2.91592i
\(531\) −10.3369 31.8008i −0.448585 1.38004i
\(532\) −26.3365 + 3.21489i −1.14183 + 0.139383i
\(533\) −26.0951 + 15.0660i −1.13031 + 0.652583i
\(534\) 19.9670 + 5.72416i 0.864058 + 0.247708i
\(535\) 27.5885 32.8787i 1.19275 1.42147i
\(536\) −29.5290 + 5.20677i −1.27546 + 0.224898i
\(537\) −24.6489 7.06635i −1.06368 0.304935i
\(538\) 19.8345 16.6431i 0.855125 0.717535i
\(539\) −0.243738 + 0.140722i −0.0104986 + 0.00606135i
\(540\) 63.2966 + 20.5537i 2.72385 + 0.884489i
\(541\) 25.2382 + 9.18594i 1.08507 + 0.394934i 0.821794 0.569785i \(-0.192974\pi\)
0.263280 + 0.964720i \(0.415196\pi\)
\(542\) −4.08708 23.1790i −0.175555 0.995622i
\(543\) −10.7960 1.13405i −0.463300 0.0486666i
\(544\) 25.0968i 1.07602i
\(545\) −8.76597 3.19055i −0.375493 0.136668i
\(546\) 18.7177 4.66805i 0.801045 0.199774i
\(547\) −3.74695 + 10.2947i −0.160208 + 0.440168i −0.993660 0.112423i \(-0.964139\pi\)
0.833452 + 0.552591i \(0.186361\pi\)
\(548\) −11.4914 2.02625i −0.490889 0.0865570i
\(549\) 5.79062 0.814529i 0.247138 0.0347633i
\(550\) 1.26692i 0.0540215i
\(551\) 15.1677 + 20.1578i 0.646167 + 0.858750i
\(552\) −19.2535 2.02245i −0.819482 0.0860812i
\(553\) 17.9716 + 3.16888i 0.764231 + 0.134755i
\(554\) 10.2338 + 8.58720i 0.434794 + 0.364835i
\(555\) 26.9631 + 39.9692i 1.14452 + 1.69660i
\(556\) −5.30639 + 30.0940i −0.225041 + 1.27627i
\(557\) −17.4664 + 3.07981i −0.740077 + 0.130496i −0.530962 0.847396i \(-0.678169\pi\)
−0.209115 + 0.977891i \(0.567058\pi\)
\(558\) 3.78207 17.8038i 0.160108 0.753694i
\(559\) −9.45355 5.45801i −0.399843 0.230849i
\(560\) 9.83748 1.73461i 0.415710 0.0733008i
\(561\) 0.466268 + 0.691181i 0.0196858 + 0.0291817i
\(562\) −10.0584 17.4217i −0.424288 0.734888i
\(563\) −19.1862 −0.808602 −0.404301 0.914626i \(-0.632485\pi\)
−0.404301 + 0.914626i \(0.632485\pi\)
\(564\) −3.72316 + 2.51163i −0.156773 + 0.105759i
\(565\) −69.7681 12.3020i −2.93517 0.517549i
\(566\) −29.7104 + 24.9300i −1.24882 + 1.04788i
\(567\) −6.71759 13.7647i −0.282112 0.578062i
\(568\) 22.4811 8.18244i 0.943285 0.343327i
\(569\) 4.66952 + 8.08785i 0.195757 + 0.339060i 0.947148 0.320796i \(-0.103950\pi\)
−0.751392 + 0.659856i \(0.770617\pi\)
\(570\) −59.6173 + 22.8409i −2.49709 + 0.956701i
\(571\) −15.2479 + 26.4101i −0.638105 + 1.10523i 0.347743 + 0.937590i \(0.386948\pi\)
−0.985848 + 0.167640i \(0.946385\pi\)
\(572\) −0.118045 + 0.669469i −0.00493573 + 0.0279919i
\(573\) −23.1659 23.9861i −0.967769 1.00203i
\(574\) 41.0604 + 14.9448i 1.71383 + 0.623782i
\(575\) −15.0948 + 17.9892i −0.629495 + 0.750203i
\(576\) −29.8252 18.6319i −1.24272 0.776328i
\(577\) 9.96919 + 17.2671i 0.415023 + 0.718841i 0.995431 0.0954852i \(-0.0304403\pi\)
−0.580408 + 0.814326i \(0.697107\pi\)
\(578\) 76.1925 3.16919
\(579\) 21.5528 + 10.5104i 0.895704 + 0.436797i
\(580\) −47.6454 56.7816i −1.97837 2.35773i
\(581\) −0.514851 + 0.297249i −0.0213596 + 0.0123320i
\(582\) 6.33533 + 14.2271i 0.262608 + 0.589731i
\(583\) 0.372414 + 0.443826i 0.0154238 + 0.0183814i
\(584\) −21.1000 17.7050i −0.873124 0.732638i
\(585\) 26.2852 13.9801i 1.08676 0.578007i
\(586\) 9.59833 54.4348i 0.396503 2.24868i
\(587\) −28.1528 + 33.5512i −1.16199 + 1.38481i −0.253276 + 0.967394i \(0.581508\pi\)
−0.908716 + 0.417414i \(0.862936\pi\)
\(588\) 20.5684 + 14.9419i 0.848228 + 0.616196i
\(589\) 5.07705 + 9.98163i 0.209196 + 0.411286i
\(590\) −81.6270 47.1274i −3.36053 1.94020i
\(591\) −14.0769 14.5752i −0.579044 0.599546i
\(592\) 4.35814 + 11.9739i 0.179118 + 0.492123i
\(593\) 21.7722 + 25.9471i 0.894077 + 1.06552i 0.997485 + 0.0708804i \(0.0225809\pi\)
−0.103408 + 0.994639i \(0.532975\pi\)
\(594\) 0.841025 0.0295213i 0.0345077 0.00121127i
\(595\) −7.42746 42.1232i −0.304496 1.72688i
\(596\) 2.89308 + 1.67032i 0.118505 + 0.0684190i
\(597\) −0.975882 + 9.29027i −0.0399402 + 0.380226i
\(598\) −15.0501 + 12.6285i −0.615445 + 0.516420i
\(599\) 23.5890 19.7935i 0.963820 0.808741i −0.0177500 0.999842i \(-0.505650\pi\)
0.981570 + 0.191101i \(0.0612059\pi\)
\(600\) 46.0849 20.5216i 1.88141 0.837792i
\(601\) 12.5543 + 7.24824i 0.512101 + 0.295662i 0.733697 0.679477i \(-0.237793\pi\)
−0.221596 + 0.975139i \(0.571127\pi\)
\(602\) 2.74880 + 15.5892i 0.112033 + 0.635369i
\(603\) 22.4017 + 9.04772i 0.912266 + 0.368452i
\(604\) −28.8413 34.3717i −1.17353 1.39856i
\(605\) −13.4663 36.9983i −0.547482 1.50419i
\(606\) 22.9080 5.71308i 0.930575 0.232078i
\(607\) −10.7115 6.18431i −0.434768 0.251013i 0.266608 0.963805i \(-0.414097\pi\)
−0.701376 + 0.712792i \(0.747430\pi\)
\(608\) 15.4709 1.88854i 0.627429 0.0765903i
\(609\) −1.78216 + 16.9660i −0.0722169 + 0.687496i
\(610\) 10.5950 12.6267i 0.428980 0.511238i
\(611\) −0.348883 + 1.97861i −0.0141143 + 0.0800461i
\(612\) 39.9018 63.8733i 1.61293 2.58193i
\(613\) 28.4226 + 23.8494i 1.14798 + 0.963268i 0.999670 0.0256733i \(-0.00817296\pi\)
0.148308 + 0.988941i \(0.452617\pi\)
\(614\) −1.10741 1.31976i −0.0446913 0.0532611i
\(615\) 67.0660 + 7.04483i 2.70436 + 0.284075i
\(616\) 0.376338 0.217279i 0.0151631 0.00875442i
\(617\) −19.6829 23.4572i −0.792404 0.944350i 0.207019 0.978337i \(-0.433624\pi\)
−0.999422 + 0.0339871i \(0.989179\pi\)
\(618\) −3.08406 44.0660i −0.124059 1.77259i
\(619\) 22.8389 0.917974 0.458987 0.888443i \(-0.348212\pi\)
0.458987 + 0.888443i \(0.348212\pi\)
\(620\) −16.4522 28.4961i −0.660738 1.14443i
\(621\) 12.2936 + 9.60127i 0.493327 + 0.385286i
\(622\) −6.07673 + 7.24196i −0.243654 + 0.290376i
\(623\) −8.12114 2.95585i −0.325367 0.118424i
\(624\) 7.63451 1.90398i 0.305625 0.0762204i
\(625\) −0.506966 + 2.87515i −0.0202787 + 0.115006i
\(626\) −2.99823 + 5.19308i −0.119833 + 0.207557i
\(627\) −0.390992 + 0.339442i −0.0156147 + 0.0135560i
\(628\) −20.8454 36.1053i −0.831821 1.44076i
\(629\) 51.2711 18.6611i 2.04431 0.744069i
\(630\) −40.0312 16.1680i −1.59488 0.644150i
\(631\) 19.6728 16.5075i 0.783164 0.657152i −0.160880 0.986974i \(-0.551433\pi\)
0.944043 + 0.329822i \(0.106989\pi\)
\(632\) 39.3187 + 6.93294i 1.56401 + 0.275778i
\(633\) 0.170910 + 2.44201i 0.00679305 + 0.0970612i
\(634\) −75.6295 −3.00363
\(635\) −1.99690 3.45874i −0.0792447 0.137256i
\(636\) 22.9392 47.0395i 0.909599 1.86524i
\(637\) 11.2003 1.97492i 0.443773 0.0782492i
\(638\) −0.811731 0.468653i −0.0321367 0.0185542i
\(639\) −18.8557 4.00552i −0.745919 0.158456i
\(640\) −72.4008 + 12.7662i −2.86189 + 0.504629i
\(641\) −0.122614 + 0.695380i −0.00484297 + 0.0274658i −0.987133 0.159898i \(-0.948883\pi\)
0.982291 + 0.187364i \(0.0599945\pi\)
\(642\) −48.9056 + 3.42277i −1.93015 + 0.135086i
\(643\) 34.0799 + 28.5965i 1.34398 + 1.12773i 0.980584 + 0.196100i \(0.0628276\pi\)
0.363397 + 0.931634i \(0.381617\pi\)
\(644\) 17.9949 + 3.17299i 0.709098 + 0.125033i
\(645\) 9.93785 + 22.3172i 0.391302 + 0.878737i
\(646\) 8.75444 + 71.7165i 0.344439 + 2.82165i
\(647\) 9.57031i 0.376248i −0.982145 0.188124i \(-0.939759\pi\)
0.982145 0.188124i \(-0.0602407\pi\)
\(648\) −14.6969 30.1146i −0.577347 1.18301i
\(649\) −0.752812 0.132741i −0.0295504 0.00521054i
\(650\) 17.5100 48.1083i 0.686798 1.88696i
\(651\) −2.08694 + 7.27968i −0.0817937 + 0.285313i
\(652\) 59.5202 + 21.6636i 2.33099 + 0.848411i
\(653\) 26.2999i 1.02919i 0.857432 + 0.514597i \(0.172058\pi\)
−0.857432 + 0.514597i \(0.827942\pi\)
\(654\) 4.33456 + 9.73400i 0.169495 + 0.380630i
\(655\) −0.00694086 0.0393636i −0.000271202 0.00153806i
\(656\) 16.7475 + 6.09560i 0.653881 + 0.237993i
\(657\) 6.86067 + 21.1063i 0.267660 + 0.823436i
\(658\) 2.52318 1.45676i 0.0983638 0.0567904i
\(659\) 17.1070 14.3545i 0.666394 0.559171i −0.245602 0.969371i \(-0.578986\pi\)
0.911996 + 0.410200i \(0.134541\pi\)
\(660\) 1.09432 1.05690i 0.0425963 0.0411397i
\(661\) −8.11331 + 1.43060i −0.315571 + 0.0556437i −0.329190 0.944264i \(-0.606776\pi\)
0.0136193 + 0.999907i \(0.495665\pi\)
\(662\) −39.0107 + 46.4911i −1.51619 + 1.80693i
\(663\) −8.15269 32.6903i −0.316624 1.26959i
\(664\) −1.12640 + 0.650328i −0.0437128 + 0.0252376i
\(665\) 25.4080 7.74844i 0.985278 0.300471i
\(666\) 11.4436 53.8696i 0.443429 2.08740i
\(667\) −5.94215 16.3259i −0.230081 0.632143i
\(668\) −3.83708 + 1.39658i −0.148461 + 0.0540354i
\(669\) −0.946035 13.5172i −0.0365758 0.522606i
\(670\) 63.9932 23.2916i 2.47227 0.899833i
\(671\) 0.0457212 0.125618i 0.00176505 0.00484943i
\(672\) 8.52714 + 6.19455i 0.328942 + 0.238960i
\(673\) 21.7657i 0.839008i 0.907754 + 0.419504i \(0.137796\pi\)
−0.907754 + 0.419504i \(0.862204\pi\)
\(674\) −11.1154 + 30.5394i −0.428150 + 1.17633i
\(675\) −40.2531 5.64979i −1.54934 0.217460i
\(676\) −9.51312 + 16.4772i −0.365889 + 0.633738i
\(677\) −17.5825 + 30.4538i −0.675751 + 1.17043i 0.300498 + 0.953782i \(0.402847\pi\)
−0.976249 + 0.216652i \(0.930486\pi\)
\(678\) 45.2548 + 67.0843i 1.73800 + 2.57636i
\(679\) −2.21623 6.08905i −0.0850512 0.233676i
\(680\) −16.2499 92.1580i −0.623157 3.53410i
\(681\) 33.3905 32.2487i 1.27953 1.23577i
\(682\) −0.318740 0.267455i −0.0122052 0.0102414i
\(683\) −14.9200 −0.570898 −0.285449 0.958394i \(-0.592143\pi\)
−0.285449 + 0.958394i \(0.592143\pi\)
\(684\) 42.3773 + 19.7910i 1.62034 + 0.756727i
\(685\) 11.6824 0.446363
\(686\) −34.1843 28.6841i −1.30516 1.09516i
\(687\) −13.4618 3.85922i −0.513598 0.147238i
\(688\) 1.12117 + 6.35846i 0.0427441 + 0.242414i
\(689\) −8.00749 22.0004i −0.305061 0.838149i
\(690\) 43.8612 3.06973i 1.66977 0.116863i
\(691\) 18.1022 31.3539i 0.688640 1.19276i −0.283638 0.958931i \(-0.591541\pi\)
0.972278 0.233828i \(-0.0751253\pi\)
\(692\) −1.59486 + 2.76237i −0.0606274 + 0.105010i
\(693\) −0.349929 0.0121776i −0.0132927 0.000462590i
\(694\) 2.08406 5.72592i 0.0791100 0.217353i
\(695\) 30.5943i 1.16051i
\(696\) −3.89905 + 37.1185i −0.147793 + 1.40697i
\(697\) 26.1008 71.7115i 0.988640 2.71627i
\(698\) −12.9391 + 4.70946i −0.489753 + 0.178256i
\(699\) −13.0519 6.36488i −0.493670 0.240742i
\(700\) −44.7437 + 16.2854i −1.69115 + 0.615529i
\(701\) −14.0704 38.6582i −0.531433 1.46010i −0.857366 0.514707i \(-0.827901\pi\)
0.325933 0.945393i \(-0.394322\pi\)
\(702\) −32.3440 10.5028i −1.22075 0.396401i
\(703\) 15.3618 + 30.2018i 0.579382 + 1.13908i
\(704\) −0.696221 + 0.401963i −0.0262398 + 0.0151496i
\(705\) 3.23426 3.12366i 0.121809 0.117644i
\(706\) −23.6253 + 28.1555i −0.889148 + 1.05965i
\(707\) −9.67405 + 1.70580i −0.363830 + 0.0641531i
\(708\) 16.7088 + 66.9983i 0.627956 + 2.51795i
\(709\) −21.7969 + 18.2898i −0.818600 + 0.686887i −0.952644 0.304089i \(-0.901648\pi\)
0.134044 + 0.990975i \(0.457204\pi\)
\(710\) −47.0556 + 27.1676i −1.76597 + 1.01958i
\(711\) −23.9091 21.5226i −0.896661 0.807162i
\(712\) −17.7676 6.46688i −0.665869 0.242356i
\(713\) −1.33926 7.59530i −0.0501556 0.284446i
\(714\) −28.7152 + 39.5281i −1.07464 + 1.47930i
\(715\) 0.680596i 0.0254529i
\(716\) 49.7567 + 18.1099i 1.85949 + 0.676800i
\(717\) 24.0127 + 24.8629i 0.896770 + 0.928520i
\(718\) 8.52077 23.4106i 0.317992 0.873677i
\(719\) 12.7557 + 2.24917i 0.475706 + 0.0838798i 0.406360 0.913713i \(-0.366798\pi\)
0.0693456 + 0.997593i \(0.477909\pi\)
\(720\) −16.3278 6.59455i −0.608499 0.245764i
\(721\) 18.3794i 0.684484i
\(722\) −43.5509 + 10.7933i −1.62080 + 0.401687i
\(723\) 6.83676 9.41118i 0.254262 0.350006i
\(724\) 22.0757 + 3.89253i 0.820436 + 0.144665i
\(725\) 34.6812 + 29.1010i 1.28803 + 1.08078i
\(726\) −19.7126 + 40.4229i −0.731602 + 1.50024i
\(727\) 0.223512 1.26760i 0.00828960 0.0470126i −0.980382 0.197105i \(-0.936846\pi\)
0.988672 + 0.150092i \(0.0479571\pi\)
\(728\) −17.2936 + 3.04933i −0.640943 + 0.113016i
\(729\) −2.81257 + 26.8531i −0.104169 + 0.994560i
\(730\) 54.1762 + 31.2787i 2.00515 + 1.15768i
\(731\) 27.2264 4.80074i 1.00700 0.177562i
\(732\) −12.0458 + 0.843053i −0.445226 + 0.0311602i
\(733\) 22.0489 + 38.1898i 0.814395 + 1.41057i 0.909761 + 0.415131i \(0.136264\pi\)
−0.0953663 + 0.995442i \(0.530402\pi\)
\(734\) −26.1431 −0.964959
\(735\) −22.8775 11.1564i −0.843849 0.411510i
\(736\) −10.5708 1.86392i −0.389646 0.0687050i
\(737\) 0.423091 0.355015i 0.0155847 0.0130772i
\(738\) −47.4300 60.6926i −1.74592 2.23412i
\(739\) −38.0632 + 13.8539i −1.40018 + 0.509623i −0.928231 0.372003i \(-0.878671\pi\)
−0.471947 + 0.881627i \(0.656449\pi\)
\(740\) −49.7802 86.2218i −1.82996 3.16958i
\(741\) 19.5384 7.48567i 0.717762 0.274993i
\(742\) −16.9755 + 29.4025i −0.623191 + 1.07940i
\(743\) 7.14422 40.5169i 0.262096 1.48642i −0.515083 0.857140i \(-0.672239\pi\)
0.777179 0.629279i \(-0.216650\pi\)
\(744\) −4.56585 + 15.9266i −0.167392 + 0.583899i
\(745\) −3.14287 1.14391i −0.115146 0.0419096i
\(746\) 47.5276 56.6412i 1.74011 2.07378i
\(747\) 1.04736 + 0.0364483i 0.0383208 + 0.00133357i
\(748\) −0.860840 1.49102i −0.0314754 0.0545170i
\(749\) 20.3979 0.745324
\(750\) −34.2727 + 23.1202i −1.25146 + 0.844232i
\(751\) 21.3166 + 25.4041i 0.777854 + 0.927010i 0.998834 0.0482683i \(-0.0153703\pi\)
−0.220981 + 0.975278i \(0.570926\pi\)
\(752\) 1.02914 0.594177i 0.0375290 0.0216674i
\(753\) 23.9140 32.9190i 0.871475 1.19963i
\(754\) 24.3464 + 29.0149i 0.886644 + 1.05666i
\(755\) 34.4121 + 28.8752i 1.25239 + 1.05088i
\(756\) 11.8534 + 29.3230i 0.431105 + 1.06647i
\(757\) 5.09501 28.8952i 0.185181 1.05021i −0.740541 0.672011i \(-0.765431\pi\)
0.925722 0.378204i \(-0.123458\pi\)
\(758\) 41.7400 49.7438i 1.51607 1.80678i
\(759\) 0.325756 0.145059i 0.0118242 0.00526532i
\(760\) 55.5880 16.9522i 2.01639 0.614920i
\(761\) 26.0608 + 15.0462i 0.944704 + 0.545425i 0.891432 0.453155i \(-0.149702\pi\)
0.0532721 + 0.998580i \(0.483035\pi\)
\(762\) −1.25717 + 4.38526i −0.0455424 + 0.158861i
\(763\) −1.51632 4.16606i −0.0548945 0.150821i
\(764\) 44.2625 + 52.7500i 1.60136 + 1.90843i
\(765\) −28.2373 + 69.9140i −1.02092 + 2.52775i
\(766\) 7.78601 + 44.1566i 0.281320 + 1.59544i
\(767\) 26.7517 + 15.4451i 0.965948 + 0.557690i
\(768\) 35.0873 + 25.4892i 1.26610 + 0.919761i
\(769\) −21.5219 + 18.0590i −0.776098 + 0.651224i −0.942263 0.334874i \(-0.891306\pi\)
0.166164 + 0.986098i \(0.446862\pi\)
\(770\) −0.756052 + 0.634403i −0.0272462 + 0.0228623i
\(771\) −11.3372 8.23590i −0.408298 0.296609i
\(772\) −42.8824 24.7581i −1.54337 0.891065i
\(773\) 1.25029 + 7.09077i 0.0449700 + 0.255037i 0.999002 0.0446676i \(-0.0142229\pi\)
−0.954032 + 0.299705i \(0.903112\pi\)
\(774\) 10.4502 25.8742i 0.375625 0.930028i
\(775\) 12.9184 + 15.3956i 0.464043 + 0.553025i
\(776\) −4.84872 13.3217i −0.174059 0.478223i
\(777\) −6.31454 + 22.0264i −0.226533 + 0.790193i
\(778\) 56.8113 + 32.8000i 2.03678 + 1.17594i
\(779\) 46.1706 + 10.6936i 1.65423 + 0.383137i
\(780\) −56.1616 + 25.0088i −2.01091 + 0.895458i
\(781\) −0.283257 + 0.337572i −0.0101357 + 0.0120793i
\(782\) 8.64032 49.0017i 0.308977 1.75230i
\(783\) 18.5102 23.7007i 0.661499 0.846996i
\(784\) −5.15311 4.32397i −0.184040 0.154428i
\(785\) 26.8298 + 31.9746i 0.957598 + 1.14122i
\(786\) −0.0268339 + 0.0369384i −0.000957135 + 0.00131755i
\(787\) −4.88523 + 2.82049i −0.174140 + 0.100540i −0.584536 0.811368i \(-0.698724\pi\)
0.410397 + 0.911907i \(0.365390\pi\)
\(788\) 26.8963 + 32.0537i 0.958140 + 1.14187i
\(789\) −26.1889 + 17.6670i −0.932351 + 0.628960i
\(790\) −90.6771 −3.22614
\(791\) −16.8345 29.1583i −0.598567 1.03675i
\(792\) −0.765582 0.0266424i −0.0272038 0.000946698i
\(793\) −3.47232 + 4.13814i −0.123306 + 0.146950i
\(794\) −37.5516 13.6677i −1.33266 0.485048i
\(795\) −14.4394 + 50.3674i −0.512111 + 1.78635i
\(796\) 3.34965 18.9968i 0.118725 0.673323i
\(797\) 5.82703 10.0927i 0.206404 0.357502i −0.744175 0.667985i \(-0.767157\pi\)
0.950579 + 0.310482i \(0.100491\pi\)
\(798\) −26.5279 14.7270i −0.939078 0.521330i
\(799\) −2.54421 4.40670i −0.0900077 0.155898i
\(800\) 26.2840 9.56658i 0.929279 0.338230i
\(801\) 9.38095 + 12.0041i 0.331460 + 0.424144i
\(802\) 6.03194 5.06140i 0.212995 0.178724i
\(803\) 0.499644 + 0.0881008i 0.0176321 + 0.00310901i
\(804\) −44.8418 21.8675i −1.58145 0.771207i
\(805\) −18.2940 −0.644779
\(806\) 8.40696 + 14.5613i 0.296122 + 0.512899i
\(807\) 18.9443 1.32586i 0.666872 0.0466726i
\(808\) −21.1651 + 3.73197i −0.744585 + 0.131290i
\(809\) −35.8631 20.7056i −1.26088 0.727970i −0.287636 0.957740i \(-0.592869\pi\)
−0.973245 + 0.229770i \(0.926203\pi\)
\(810\) 44.7488 + 61.5602i 1.57231 + 2.16301i
\(811\) −33.4287 + 5.89438i −1.17384 + 0.206980i −0.726360 0.687315i \(-0.758789\pi\)
−0.447479 + 0.894294i \(0.647678\pi\)
\(812\) 6.11715 34.6921i 0.214670 1.21745i
\(813\) 7.56667 15.5163i 0.265375 0.544182i
\(814\) −0.964425 0.809248i −0.0338031 0.0283641i
\(815\) −62.4512 11.0118i −2.18757 0.385727i
\(816\) −11.7122 + 16.1225i −0.410010 + 0.564402i
\(817\) 5.00820 + 16.4224i 0.175215 + 0.574548i
\(818\) 53.1537i 1.85847i
\(819\) 13.1195 + 5.29877i 0.458431 + 0.185154i
\(820\) −137.137 24.1809i −4.78902 0.844434i
\(821\) 5.39189 14.8141i 0.188178 0.517016i −0.809346 0.587332i \(-0.800178\pi\)
0.997525 + 0.0703158i \(0.0224007\pi\)
\(822\) −9.27023 9.59845i −0.323336 0.334784i
\(823\) −24.3559 8.86482i −0.848993 0.309008i −0.119364 0.992851i \(-0.538085\pi\)
−0.729630 + 0.683842i \(0.760308\pi\)
\(824\) 40.2108i 1.40081i
\(825\) −0.546140 + 0.751793i −0.0190142 + 0.0261741i
\(826\) −7.77856 44.1144i −0.270651 1.53494i
\(827\) 7.92236 + 2.88350i 0.275487 + 0.100269i 0.476069 0.879408i \(-0.342061\pi\)
−0.200582 + 0.979677i \(0.564283\pi\)
\(828\) −23.9401 21.5505i −0.831974 0.748932i
\(829\) 23.0878 13.3297i 0.801871 0.462960i −0.0422540 0.999107i \(-0.513454\pi\)
0.844125 + 0.536146i \(0.180121\pi\)
\(830\) 2.26291 1.89880i 0.0785466 0.0659084i
\(831\) 2.37103 + 9.50726i 0.0822502 + 0.329803i
\(832\) 31.9929 5.64122i 1.10916 0.195574i
\(833\) −18.5149 + 22.0652i −0.641502 + 0.764512i
\(834\) −25.1367 + 24.2771i −0.870412 + 0.840648i
\(835\) 3.54043 2.04407i 0.122522 0.0707379i
\(836\) 0.854360 0.642864i 0.0295487 0.0222339i
\(837\) 9.91912 8.93446i 0.342855 0.308820i
\(838\) −6.38153 17.5331i −0.220446 0.605671i
\(839\) −28.8043 + 10.4839i −0.994433 + 0.361944i −0.787435 0.616397i \(-0.788592\pi\)
−0.206998 + 0.978341i \(0.566369\pi\)
\(840\) 35.3234 + 17.2257i 1.21877 + 0.594345i
\(841\) −4.22345 + 1.53721i −0.145636 + 0.0530073i
\(842\) −2.24741 + 6.17470i −0.0774507 + 0.212794i
\(843\) 1.54141 14.6740i 0.0530890 0.505400i
\(844\) 5.05506i 0.174002i
\(845\) 6.51501 17.8998i 0.224123 0.615773i
\(846\) −5.13289 0.178626i −0.176472 0.00614128i
\(847\) 9.35603 16.2051i 0.321477 0.556814i
\(848\) −6.92390 + 11.9925i −0.237768 + 0.411826i
\(849\) −28.3770 + 1.98603i −0.973896 + 0.0681604i
\(850\) 44.3465 + 121.841i 1.52107 + 4.17911i
\(851\) −4.05224 22.9814i −0.138909 0.787792i
\(852\) 38.2642 + 10.9696i 1.31091 + 0.375812i
\(853\) −23.2450 19.5049i −0.795895 0.667835i 0.151302 0.988488i \(-0.451653\pi\)
−0.947197 + 0.320653i \(0.896098\pi\)
\(854\) 7.83357 0.268059
\(855\) −45.2233 12.1458i −1.54661 0.415379i
\(856\) 44.6270 1.52532
\(857\) −25.2851 21.2167i −0.863722 0.724749i 0.0990448 0.995083i \(-0.468421\pi\)
−0.962766 + 0.270334i \(0.912866\pi\)
\(858\) −0.559188 + 0.540066i −0.0190903 + 0.0184376i
\(859\) −0.135644 0.769277i −0.00462812 0.0262474i 0.982406 0.186756i \(-0.0597975\pi\)
−0.987034 + 0.160509i \(0.948686\pi\)
\(860\) −17.2540 47.4049i −0.588356 1.61649i
\(861\) 17.9230 + 26.5685i 0.610815 + 0.905453i
\(862\) 17.1869 29.7686i 0.585389 1.01392i
\(863\) −12.6819 + 21.9656i −0.431695 + 0.747718i −0.997019 0.0771505i \(-0.975418\pi\)
0.565324 + 0.824869i \(0.308751\pi\)
\(864\) −6.96311 17.2253i −0.236890 0.586018i
\(865\) 1.09223 3.00088i 0.0371369 0.102033i
\(866\) 77.3096i 2.62709i
\(867\) 45.2129 + 32.8449i 1.53551 + 1.11547i
\(868\) 5.34850 14.6949i 0.181540 0.498777i
\(869\) −0.691058 + 0.251525i −0.0234426 + 0.00853239i
\(870\) −5.91809 84.5595i −0.200642 2.86683i
\(871\) −20.9725 + 7.63338i −0.710628 + 0.258647i
\(872\) −3.31744 9.11459i −0.112343 0.308659i
\(873\) −2.37358 + 11.1734i −0.0803334 + 0.378163i
\(874\) 30.8573 + 1.63894i 1.04376 + 0.0554381i
\(875\) 14.8967 8.60060i 0.503599 0.290753i
\(876\) −11.0897 44.4671i −0.374687 1.50240i
\(877\) 0.474465 0.565445i 0.0160215 0.0190937i −0.757974 0.652285i \(-0.773811\pi\)
0.773996 + 0.633191i \(0.218255\pi\)
\(878\) 4.37283 0.771048i 0.147576 0.0260216i
\(879\) 29.1613 28.1642i 0.983588 0.949954i
\(880\) −0.308375 + 0.258758i −0.0103953 + 0.00872272i
\(881\) −13.3201 + 7.69035i −0.448765 + 0.259095i −0.707308 0.706905i \(-0.750091\pi\)
0.258544 + 0.966000i \(0.416757\pi\)
\(882\) 8.98747 + 27.6493i 0.302624 + 0.930999i
\(883\) −40.2488 14.6494i −1.35448 0.492990i −0.440137 0.897931i \(-0.645070\pi\)
−0.914343 + 0.404940i \(0.867292\pi\)
\(884\) 12.0812 + 68.5157i 0.406333 + 2.30443i
\(885\) −28.1222 63.1532i −0.945316 2.12287i
\(886\) 46.0021i 1.54547i
\(887\) 23.9094 + 8.70231i 0.802799 + 0.292195i 0.710646 0.703550i \(-0.248403\pi\)
0.0921532 + 0.995745i \(0.470625\pi\)
\(888\) −13.8151 + 48.1898i −0.463603 + 1.61714i
\(889\) 0.649179 1.78360i 0.0217728 0.0598202i
\(890\) 42.2906 + 7.45698i 1.41759 + 0.249959i
\(891\) 0.511793 + 0.345030i 0.0171457 + 0.0115589i
\(892\) 27.9812i 0.936880i
\(893\) 2.52506 1.89998i 0.0844979 0.0635805i
\(894\) 1.55407 + 3.48994i 0.0519760 + 0.116721i
\(895\) −52.2069 9.20548i −1.74508 0.307705i
\(896\) −26.7653 22.4587i −0.894165 0.750294i
\(897\) −14.3747 + 1.00605i −0.479957 + 0.0335909i
\(898\) −1.55738 + 8.83232i −0.0519703 + 0.294738i
\(899\) −14.6429 + 2.58193i −0.488367 + 0.0861124i
\(900\) 82.1047 + 17.4416i 2.73682 + 0.581385i
\(901\) 51.3510 + 29.6475i 1.71075 + 0.987702i
\(902\) −1.73413 + 0.305774i −0.0577402 + 0.0101812i
\(903\) −5.08902 + 10.4356i −0.169352 + 0.347276i
\(904\) −36.8309 63.7930i −1.22498 2.12172i
\(905\) −22.4426 −0.746017
\(906\) −3.58241 51.1865i −0.119017 1.70056i
\(907\) 15.4501 + 2.72428i 0.513013 + 0.0904581i 0.424161 0.905587i \(-0.360569\pi\)
0.0888522 + 0.996045i \(0.471680\pi\)
\(908\) −73.4321 + 61.6168i −2.43693 + 2.04483i
\(909\) 16.0565 + 6.48500i 0.532560 + 0.215094i
\(910\) 37.4774 13.6407i 1.24236 0.452183i
\(911\) −0.772381 1.33780i −0.0255901 0.0443234i 0.852947 0.521998i \(-0.174813\pi\)
−0.878537 + 0.477675i \(0.841480\pi\)
\(912\) −10.8201 6.00678i −0.358289 0.198905i
\(913\) 0.0119788 0.0207479i 0.000396441 0.000686656i
\(914\) 5.02782 28.5142i 0.166305 0.943164i
\(915\) 11.7302 2.92542i 0.387788 0.0967113i
\(916\) 27.1741 + 9.89058i 0.897859 + 0.326794i
\(917\) 0.0122106 0.0145520i 0.000403229 0.000480549i
\(918\) 79.8491 32.2779i 2.63541 1.06533i
\(919\) −9.28314 16.0789i −0.306222 0.530393i 0.671310 0.741176i \(-0.265732\pi\)
−0.977533 + 0.210784i \(0.932398\pi\)
\(920\) −40.0240 −1.31955
\(921\) −0.0882209 1.26053i −0.00290698 0.0415358i
\(922\) 47.7307 + 56.8832i 1.57193 + 1.87335i
\(923\) 15.4216 8.90366i 0.507608 0.293067i
\(924\) 0.719081 + 0.0755347i 0.0236560 + 0.00248491i
\(925\) 39.0877 + 46.5829i 1.28520 + 1.53164i
\(926\) −32.8506 27.5650i −1.07954 0.905841i
\(927\) 17.1658 27.4784i 0.563799 0.902509i
\(928\) −3.59343 + 20.3793i −0.117960 + 0.668984i
\(929\) −4.09919 + 4.88523i −0.134490 + 0.160279i −0.829086 0.559121i \(-0.811139\pi\)
0.694596 + 0.719400i \(0.255583\pi\)
\(930\) 3.93107 37.4233i 0.128905 1.22716i
\(931\) −14.9953 9.75308i −0.491451 0.319644i
\(932\) 25.9687 + 14.9930i 0.850633 + 0.491113i
\(933\) −6.72780 + 1.67786i −0.220258 + 0.0549306i
\(934\) 31.1238 + 85.5120i 1.01840 + 2.79804i
\(935\) 1.10798 + 1.32044i 0.0362347 + 0.0431829i
\(936\) 28.7030 + 11.5928i 0.938188 + 0.378921i
\(937\) −4.16870 23.6419i −0.136186 0.772347i −0.974027 0.226433i \(-0.927294\pi\)
0.837841 0.545914i \(-0.183817\pi\)
\(938\) 28.0288 + 16.1824i 0.915172 + 0.528375i
\(939\) −4.01778 + 1.78912i −0.131115 + 0.0583858i
\(940\) −7.11274 + 5.96830i −0.231992 + 0.194664i
\(941\) −0.813201 + 0.682357i −0.0265096 + 0.0222442i −0.655946 0.754808i \(-0.727730\pi\)
0.629437 + 0.777052i \(0.283286\pi\)
\(942\) 4.98076 47.4162i 0.162282 1.54490i
\(943\) −28.2665 16.3197i −0.920483 0.531441i
\(944\) −3.17269 17.9932i −0.103262 0.585629i
\(945\) −16.7850 26.8508i −0.546015 0.873455i
\(946\) −0.410047 0.488675i −0.0133318 0.0158882i
\(947\) 10.1404 + 27.8606i 0.329520 + 0.905349i 0.988233 + 0.152955i \(0.0488788\pi\)
−0.658713 + 0.752394i \(0.728899\pi\)
\(948\) 46.1486 + 47.7825i 1.49884 + 1.55190i
\(949\) −17.7552 10.2510i −0.576359 0.332761i
\(950\) −71.7718 + 36.5059i −2.32858 + 1.18441i
\(951\) −44.8788 32.6022i −1.45529 1.05720i
\(952\) 28.5874 34.0692i 0.926524 1.10419i
\(953\) −6.61263 + 37.5021i −0.214204 + 1.21481i 0.668078 + 0.744091i \(0.267117\pi\)
−0.882282 + 0.470721i \(0.843994\pi\)
\(954\) 52.8405 28.1040i 1.71077 0.909899i
\(955\) −52.8120 44.3146i −1.70896 1.43399i
\(956\) −45.8804 54.6781i −1.48388 1.76842i
\(957\) −0.279658 0.628020i −0.00904005 0.0203010i
\(958\) −37.4950 + 21.6477i −1.21141 + 0.699407i
\(959\) 3.56883 + 4.25317i 0.115244 + 0.137342i
\(960\) −65.3479 31.8674i −2.10909 1.02852i
\(961\) 24.3995 0.787081
\(962\) 25.4373 + 44.0586i 0.820130 + 1.42051i
\(963\) −30.4962 19.0511i −0.982727 0.613912i
\(964\) −15.4402 + 18.4009i −0.497295 + 0.592653i
\(965\) 46.5848 + 16.9555i 1.49962 + 0.545817i
\(966\) 14.5166 + 15.0306i 0.467065 + 0.483602i
\(967\) 7.73515 43.8682i 0.248746 1.41071i −0.562884 0.826536i \(-0.690308\pi\)
0.811630 0.584172i \(-0.198580\pi\)
\(968\) 20.4693 35.4539i 0.657908 1.13953i
\(969\) −25.7205 + 46.3307i −0.826262 + 1.48836i
\(970\) 16.0989 + 27.8840i 0.516903 + 0.895303i
\(971\) −47.0073 + 17.1093i −1.50854 + 0.549063i −0.958255 0.285916i \(-0.907702\pi\)
−0.550282 + 0.834979i \(0.685480\pi\)
\(972\) 9.66517 54.9105i 0.310010 1.76126i
\(973\) 11.1383 9.34616i 0.357078 0.299624i
\(974\) 13.2819 + 2.34197i 0.425581 + 0.0750414i
\(975\) 31.1289 20.9994i 0.996923 0.672520i
\(976\) 3.19512 0.102273
\(977\) 10.2848 + 17.8137i 0.329039 + 0.569912i 0.982321 0.187202i \(-0.0599420\pi\)
−0.653283 + 0.757114i \(0.726609\pi\)
\(978\) 40.5087 + 60.0488i 1.29533 + 1.92015i
\(979\) 0.342985 0.0604776i 0.0109619 0.00193287i
\(980\) 45.5180 + 26.2798i 1.45402 + 0.839479i
\(981\) −1.62397 + 7.64473i −0.0518495 + 0.244077i
\(982\) −4.90760 + 0.865342i −0.156608 + 0.0276142i
\(983\) −2.52803 + 14.3371i −0.0806315 + 0.457284i 0.917583 + 0.397545i \(0.130138\pi\)
−0.998214 + 0.0597387i \(0.980973\pi\)
\(984\) 39.2123 + 58.1271i 1.25004 + 1.85303i
\(985\) −32.0914 26.9279i −1.02252 0.857995i
\(986\) −94.4697 16.6576i −3.00853 0.530485i
\(987\) 2.12524 + 0.223243i 0.0676472 + 0.00710589i
\(988\) −41.3274 + 12.6032i −1.31480 + 0.400963i
\(989\) 11.8243i 0.375992i
\(990\) 1.72286 0.242344i 0.0547561 0.00770219i
\(991\) 16.0707 + 2.83370i 0.510503 + 0.0900155i 0.422966 0.906146i \(-0.360989\pi\)
0.0875375 + 0.996161i \(0.472100\pi\)
\(992\) −3.14190 + 8.63229i −0.0997553 + 0.274075i
\(993\) −43.1904 + 10.7713i −1.37061 + 0.341818i
\(994\) −24.2657 8.83199i −0.769661 0.280134i
\(995\) 19.3125i 0.612249i
\(996\) −2.15225 0.226079i −0.0681966 0.00716360i
\(997\) −6.82225 38.6909i −0.216063 1.22535i −0.879052 0.476725i \(-0.841824\pi\)
0.662989 0.748629i \(-0.269287\pi\)
\(998\) 14.1106 + 5.13585i 0.446664 + 0.162573i
\(999\) 30.0127 27.0333i 0.949558 0.855297i
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 171.2.x.a.14.3 108
3.2 odd 2 513.2.bo.a.71.16 108
9.2 odd 6 171.2.bd.a.128.16 yes 108
9.7 even 3 513.2.cd.a.413.3 108
19.15 odd 18 171.2.bd.a.167.16 yes 108
57.53 even 18 513.2.cd.a.395.3 108
171.34 odd 18 513.2.bo.a.224.16 108
171.110 even 18 inner 171.2.x.a.110.3 yes 108
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
171.2.x.a.14.3 108 1.1 even 1 trivial
171.2.x.a.110.3 yes 108 171.110 even 18 inner
171.2.bd.a.128.16 yes 108 9.2 odd 6
171.2.bd.a.167.16 yes 108 19.15 odd 18
513.2.bo.a.71.16 108 3.2 odd 2
513.2.bo.a.224.16 108 171.34 odd 18
513.2.cd.a.395.3 108 57.53 even 18
513.2.cd.a.413.3 108 9.7 even 3