Properties

Label 171.2.x.a.14.2
Level $171$
Weight $2$
Character 171.14
Analytic conductor $1.365$
Analytic rank $0$
Dimension $108$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

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 14.2
Character \(\chi\) \(=\) 171.14
Dual form 171.2.x.a.110.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.86688 - 1.56649i) q^{2} +(-1.40345 + 1.01505i) q^{3} +(0.684023 + 3.87929i) q^{4} +(0.0603078 + 0.165694i) q^{5} +(4.21014 + 0.303523i) q^{6} +(0.340059 - 0.588999i) q^{7} +(2.36286 - 4.09260i) q^{8} +(0.939343 - 2.84915i) q^{9} +O(q^{10})\) \(q+(-1.86688 - 1.56649i) q^{2} +(-1.40345 + 1.01505i) q^{3} +(0.684023 + 3.87929i) q^{4} +(0.0603078 + 0.165694i) q^{5} +(4.21014 + 0.303523i) q^{6} +(0.340059 - 0.588999i) q^{7} +(2.36286 - 4.09260i) q^{8} +(0.939343 - 2.84915i) q^{9} +(0.146972 - 0.403802i) q^{10} -5.07127i q^{11} +(-4.89766 - 4.75006i) q^{12} +(-0.848831 + 2.33215i) q^{13} +(-1.55751 + 0.566888i) q^{14} +(-0.252827 - 0.171328i) q^{15} +(-3.41905 + 1.24443i) q^{16} +(-1.07653 - 2.95775i) q^{17} +(-6.21681 + 3.84753i) q^{18} +(-0.122437 - 4.35718i) q^{19} +(-0.601523 + 0.347290i) q^{20} +(0.120609 + 1.17181i) q^{21} +(-7.94412 + 9.46744i) q^{22} +(-0.413419 + 0.0728969i) q^{23} +(0.838036 + 8.14218i) q^{24} +(3.80640 - 3.19395i) q^{25} +(5.23796 - 3.02414i) q^{26} +(1.57371 + 4.95212i) q^{27} +(2.51750 + 0.916297i) q^{28} +(0.0433231 + 0.245698i) q^{29} +(0.203612 + 0.715901i) q^{30} -9.69968i q^{31} +(-0.549104 - 0.199857i) q^{32} +(5.14760 + 7.11728i) q^{33} +(-2.62355 + 7.20814i) q^{34} +(0.118102 + 0.0208246i) q^{35} +(11.6952 + 1.69510i) q^{36} -5.05202i q^{37} +(-6.59692 + 8.32611i) q^{38} +(-1.17595 - 4.13466i) q^{39} +(0.820619 + 0.144697i) q^{40} +(8.91555 + 7.48103i) q^{41} +(1.61047 - 2.37655i) q^{42} +(0.329703 - 1.86984i) q^{43} +(19.6729 - 3.46887i) q^{44} +(0.528737 - 0.0161819i) q^{45} +(0.885995 + 0.511529i) q^{46} +(0.352276 - 0.0621158i) q^{47} +(3.53531 - 5.21702i) q^{48} +(3.26872 + 5.66159i) q^{49} -12.1094 q^{50} +(4.51313 + 3.05832i) q^{51} +(-9.62768 - 1.69762i) q^{52} +(-4.97407 + 4.17374i) q^{53} +(4.81954 - 11.7102i) q^{54} +(0.840281 - 0.305837i) q^{55} +(-1.60702 - 2.78345i) q^{56} +(4.59459 + 5.99080i) q^{57} +(0.304005 - 0.526553i) q^{58} +(-0.574271 + 3.25685i) q^{59} +(0.491691 - 1.09798i) q^{60} +(-7.26652 - 2.64480i) q^{61} +(-15.1945 + 18.1081i) q^{62} +(-1.35871 - 1.52215i) q^{63} +(4.35051 + 7.53531i) q^{64} -0.437614 q^{65} +(1.53925 - 21.3508i) q^{66} +(-4.89332 - 5.83164i) q^{67} +(10.7376 - 6.19936i) q^{68} +(0.506219 - 0.521949i) q^{69} +(-0.187860 - 0.223883i) q^{70} +(-10.2100 - 8.56721i) q^{71} +(-9.44087 - 10.5765i) q^{72} +(-2.55026 + 14.4632i) q^{73} +(-7.91396 + 9.43149i) q^{74} +(-2.10007 + 8.34625i) q^{75} +(16.8190 - 3.45538i) q^{76} +(-2.98698 - 1.72453i) q^{77} +(-4.28156 + 9.56101i) q^{78} +(2.04479 + 5.61802i) q^{79} +(-0.412391 - 0.491469i) q^{80} +(-7.23527 - 5.35265i) q^{81} +(-4.92522 - 27.9323i) q^{82} +(-0.844295 - 0.487454i) q^{83} +(-4.46328 + 1.26942i) q^{84} +(0.425160 - 0.356751i) q^{85} +(-3.54460 + 2.97428i) q^{86} +(-0.310198 - 0.300849i) q^{87} +(-20.7547 - 11.9827i) q^{88} +(-1.48229 - 8.40648i) q^{89} +(-1.01243 - 0.798054i) q^{90} +(1.08498 + 1.29303i) q^{91} +(-0.565576 - 1.55391i) q^{92} +(9.84567 + 13.6130i) q^{93} +(-0.754960 - 0.435876i) q^{94} +(0.714576 - 0.283059i) q^{95} +(0.973505 - 0.276878i) q^{96} +(8.73912 - 10.4149i) q^{97} +(2.76656 - 15.6899i) q^{98} +(-14.4488 - 4.76367i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.86688 1.56649i −1.32008 1.10768i −0.986288 0.165032i \(-0.947227\pi\)
−0.333792 0.942647i \(-0.608328\pi\)
\(3\) −1.40345 + 1.01505i −0.810282 + 0.586040i
\(4\) 0.684023 + 3.87929i 0.342011 + 1.93964i
\(5\) 0.0603078 + 0.165694i 0.0269705 + 0.0741007i 0.952447 0.304704i \(-0.0985575\pi\)
−0.925477 + 0.378805i \(0.876335\pi\)
\(6\) 4.21014 + 0.303523i 1.71878 + 0.123913i
\(7\) 0.340059 0.588999i 0.128530 0.222621i −0.794577 0.607163i \(-0.792307\pi\)
0.923107 + 0.384542i \(0.125641\pi\)
\(8\) 2.36286 4.09260i 0.835398 1.44695i
\(9\) 0.939343 2.84915i 0.313114 0.949715i
\(10\) 0.146972 0.403802i 0.0464766 0.127694i
\(11\) 5.07127i 1.52905i −0.644596 0.764523i \(-0.722974\pi\)
0.644596 0.764523i \(-0.277026\pi\)
\(12\) −4.89766 4.75006i −1.41383 1.37123i
\(13\) −0.848831 + 2.33215i −0.235423 + 0.646821i 0.764574 + 0.644536i \(0.222949\pi\)
−0.999997 + 0.00228466i \(0.999273\pi\)
\(14\) −1.55751 + 0.566888i −0.416263 + 0.151507i
\(15\) −0.252827 0.171328i −0.0652797 0.0442367i
\(16\) −3.41905 + 1.24443i −0.854764 + 0.311109i
\(17\) −1.07653 2.95775i −0.261098 0.717361i −0.999094 0.0425558i \(-0.986450\pi\)
0.737996 0.674805i \(-0.235772\pi\)
\(18\) −6.21681 + 3.84753i −1.46532 + 0.906871i
\(19\) −0.122437 4.35718i −0.0280891 0.999605i
\(20\) −0.601523 + 0.347290i −0.134505 + 0.0776563i
\(21\) 0.120609 + 1.17181i 0.0263190 + 0.255710i
\(22\) −7.94412 + 9.46744i −1.69369 + 2.01846i
\(23\) −0.413419 + 0.0728969i −0.0862038 + 0.0152001i −0.216584 0.976264i \(-0.569491\pi\)
0.130380 + 0.991464i \(0.458380\pi\)
\(24\) 0.838036 + 8.14218i 0.171063 + 1.66202i
\(25\) 3.80640 3.19395i 0.761281 0.638791i
\(26\) 5.23796 3.02414i 1.02725 0.593082i
\(27\) 1.57371 + 4.95212i 0.302860 + 0.953035i
\(28\) 2.51750 + 0.916297i 0.475764 + 0.173164i
\(29\) 0.0433231 + 0.245698i 0.00804490 + 0.0456249i 0.988566 0.150789i \(-0.0481814\pi\)
−0.980521 + 0.196414i \(0.937070\pi\)
\(30\) 0.203612 + 0.715901i 0.0371743 + 0.130705i
\(31\) 9.69968i 1.74211i −0.491181 0.871057i \(-0.663435\pi\)
0.491181 0.871057i \(-0.336565\pi\)
\(32\) −0.549104 0.199857i −0.0970687 0.0353301i
\(33\) 5.14760 + 7.11728i 0.896083 + 1.23896i
\(34\) −2.62355 + 7.20814i −0.449935 + 1.23619i
\(35\) 0.118102 + 0.0208246i 0.0199629 + 0.00352000i
\(36\) 11.6952 + 1.69510i 1.94920 + 0.282516i
\(37\) 5.05202i 0.830547i −0.909697 0.415273i \(-0.863686\pi\)
0.909697 0.415273i \(-0.136314\pi\)
\(38\) −6.59692 + 8.32611i −1.07016 + 1.35067i
\(39\) −1.17595 4.13466i −0.188303 0.662075i
\(40\) 0.820619 + 0.144697i 0.129751 + 0.0228786i
\(41\) 8.91555 + 7.48103i 1.39237 + 1.16834i 0.964368 + 0.264565i \(0.0852285\pi\)
0.428007 + 0.903776i \(0.359216\pi\)
\(42\) 1.61047 2.37655i 0.248501 0.366710i
\(43\) 0.329703 1.86984i 0.0502792 0.285147i −0.949293 0.314393i \(-0.898199\pi\)
0.999572 + 0.0292450i \(0.00931031\pi\)
\(44\) 19.6729 3.46887i 2.96580 0.522951i
\(45\) 0.528737 0.0161819i 0.0788194 0.00241226i
\(46\) 0.885995 + 0.511529i 0.130633 + 0.0754209i
\(47\) 0.352276 0.0621158i 0.0513848 0.00906052i −0.147897 0.989003i \(-0.547250\pi\)
0.199281 + 0.979942i \(0.436139\pi\)
\(48\) 3.53531 5.21702i 0.510278 0.753011i
\(49\) 3.26872 + 5.66159i 0.466960 + 0.808798i
\(50\) −12.1094 −1.71253
\(51\) 4.51313 + 3.05832i 0.631965 + 0.428251i
\(52\) −9.62768 1.69762i −1.33512 0.235417i
\(53\) −4.97407 + 4.17374i −0.683241 + 0.573308i −0.916951 0.398999i \(-0.869358\pi\)
0.233710 + 0.972306i \(0.424913\pi\)
\(54\) 4.81954 11.7102i 0.655857 1.59355i
\(55\) 0.840281 0.305837i 0.113303 0.0412391i
\(56\) −1.60702 2.78345i −0.214748 0.371954i
\(57\) 4.59459 + 5.99080i 0.608569 + 0.793501i
\(58\) 0.304005 0.526553i 0.0399178 0.0691397i
\(59\) −0.574271 + 3.25685i −0.0747637 + 0.424006i 0.924336 + 0.381580i \(0.124620\pi\)
−0.999100 + 0.0424263i \(0.986491\pi\)
\(60\) 0.491691 1.09798i 0.0634771 0.141749i
\(61\) −7.26652 2.64480i −0.930382 0.338632i −0.168021 0.985783i \(-0.553738\pi\)
−0.762361 + 0.647152i \(0.775960\pi\)
\(62\) −15.1945 + 18.1081i −1.92970 + 2.29973i
\(63\) −1.35871 1.52215i −0.171182 0.191773i
\(64\) 4.35051 + 7.53531i 0.543814 + 0.941914i
\(65\) −0.437614 −0.0542794
\(66\) 1.53925 21.3508i 0.189468 2.62810i
\(67\) −4.89332 5.83164i −0.597815 0.712448i 0.379273 0.925285i \(-0.376174\pi\)
−0.977088 + 0.212837i \(0.931730\pi\)
\(68\) 10.7376 6.19936i 1.30213 0.751782i
\(69\) 0.506219 0.521949i 0.0609416 0.0628352i
\(70\) −0.187860 0.223883i −0.0224536 0.0267591i
\(71\) −10.2100 8.56721i −1.21170 1.01674i −0.999217 0.0395775i \(-0.987399\pi\)
−0.212488 0.977164i \(-0.568157\pi\)
\(72\) −9.44087 10.5765i −1.11262 1.24645i
\(73\) −2.55026 + 14.4632i −0.298485 + 1.69279i 0.354204 + 0.935168i \(0.384752\pi\)
−0.652689 + 0.757626i \(0.726359\pi\)
\(74\) −7.91396 + 9.43149i −0.919979 + 1.09639i
\(75\) −2.10007 + 8.34625i −0.242496 + 0.963742i
\(76\) 16.8190 3.45538i 1.92927 0.396359i
\(77\) −2.98698 1.72453i −0.340398 0.196529i
\(78\) −4.28156 + 9.56101i −0.484791 + 1.08257i
\(79\) 2.04479 + 5.61802i 0.230057 + 0.632077i 0.999982 0.00605797i \(-0.00192832\pi\)
−0.769924 + 0.638135i \(0.779706\pi\)
\(80\) −0.412391 0.491469i −0.0461067 0.0549479i
\(81\) −7.23527 5.35265i −0.803919 0.594739i
\(82\) −4.92522 27.9323i −0.543900 3.08461i
\(83\) −0.844295 0.487454i −0.0926734 0.0535050i 0.452947 0.891537i \(-0.350373\pi\)
−0.545621 + 0.838032i \(0.683706\pi\)
\(84\) −4.46328 + 1.26942i −0.486984 + 0.138505i
\(85\) 0.425160 0.356751i 0.0461150 0.0386951i
\(86\) −3.54460 + 2.97428i −0.382224 + 0.320724i
\(87\) −0.310198 0.300849i −0.0332567 0.0322544i
\(88\) −20.7547 11.9827i −2.21246 1.27736i
\(89\) −1.48229 8.40648i −0.157122 0.891085i −0.956820 0.290682i \(-0.906118\pi\)
0.799698 0.600403i \(-0.204993\pi\)
\(90\) −1.01243 0.798054i −0.106720 0.0841223i
\(91\) 1.08498 + 1.29303i 0.113737 + 0.135546i
\(92\) −0.565576 1.55391i −0.0589654 0.162006i
\(93\) 9.84567 + 13.6130i 1.02095 + 1.41160i
\(94\) −0.754960 0.435876i −0.0778682 0.0449572i
\(95\) 0.714576 0.283059i 0.0733139 0.0290412i
\(96\) 0.973505 0.276878i 0.0993579 0.0282588i
\(97\) 8.73912 10.4149i 0.887323 1.05747i −0.110652 0.993859i \(-0.535294\pi\)
0.997975 0.0636112i \(-0.0202617\pi\)
\(98\) 2.76656 15.6899i 0.279464 1.58492i
\(99\) −14.4488 4.76367i −1.45216 0.478766i
\(100\) 14.9939 + 12.5814i 1.49939 + 1.25814i
\(101\) 10.1706 + 12.1208i 1.01201 + 1.20607i 0.978419 + 0.206633i \(0.0662505\pi\)
0.0335929 + 0.999436i \(0.489305\pi\)
\(102\) −3.63461 12.7793i −0.359880 1.26534i
\(103\) 4.22161 2.43735i 0.415968 0.240159i −0.277383 0.960759i \(-0.589467\pi\)
0.693351 + 0.720600i \(0.256134\pi\)
\(104\) 7.53886 + 8.98446i 0.739246 + 0.880999i
\(105\) −0.186888 + 0.0906533i −0.0182384 + 0.00884686i
\(106\) 15.8241 1.53697
\(107\) 4.81520 + 8.34017i 0.465503 + 0.806274i 0.999224 0.0393861i \(-0.0125402\pi\)
−0.533721 + 0.845660i \(0.679207\pi\)
\(108\) −18.1342 + 9.49222i −1.74497 + 0.913389i
\(109\) −3.66067 + 4.36262i −0.350629 + 0.417863i −0.912316 0.409486i \(-0.865708\pi\)
0.561687 + 0.827350i \(0.310152\pi\)
\(110\) −2.04779 0.745336i −0.195249 0.0710650i
\(111\) 5.12806 + 7.09026i 0.486734 + 0.672977i
\(112\) −0.429709 + 2.43700i −0.0406037 + 0.230275i
\(113\) 7.66584 13.2776i 0.721142 1.24905i −0.239401 0.970921i \(-0.576951\pi\)
0.960542 0.278134i \(-0.0897158\pi\)
\(114\) 0.807025 18.3815i 0.0755848 1.72158i
\(115\) −0.0370110 0.0641049i −0.00345129 0.00597781i
\(116\) −0.923498 + 0.336126i −0.0857446 + 0.0312085i
\(117\) 5.84728 + 4.60913i 0.540581 + 0.426114i
\(118\) 6.17394 5.18055i 0.568357 0.476908i
\(119\) −2.10820 0.371733i −0.193258 0.0340767i
\(120\) −1.29857 + 0.629894i −0.118543 + 0.0575012i
\(121\) −14.7178 −1.33798
\(122\) 9.42263 + 16.3205i 0.853085 + 1.47759i
\(123\) −20.1062 1.44952i −1.81291 0.130699i
\(124\) 37.6278 6.63480i 3.37908 0.595823i
\(125\) 1.52230 + 0.878900i 0.136159 + 0.0786112i
\(126\) 0.152109 + 4.97008i 0.0135509 + 0.442770i
\(127\) −15.7611 + 2.77910i −1.39857 + 0.246606i −0.821556 0.570128i \(-0.806893\pi\)
−0.577014 + 0.816734i \(0.695782\pi\)
\(128\) 3.47922 19.7316i 0.307522 1.74404i
\(129\) 1.43526 + 2.95889i 0.126367 + 0.260516i
\(130\) 0.816971 + 0.685520i 0.0716531 + 0.0601241i
\(131\) 3.52417 + 0.621407i 0.307908 + 0.0542925i 0.325467 0.945553i \(-0.394478\pi\)
−0.0175590 + 0.999846i \(0.505590\pi\)
\(132\) −24.0889 + 24.8374i −2.09667 + 2.16182i
\(133\) −2.60801 1.40958i −0.226143 0.122226i
\(134\) 18.5523i 1.60267i
\(135\) −0.725630 + 0.559405i −0.0624523 + 0.0481460i
\(136\) −14.6486 2.58294i −1.25611 0.221485i
\(137\) 3.43710 9.44335i 0.293651 0.806800i −0.701874 0.712301i \(-0.747653\pi\)
0.995525 0.0944987i \(-0.0301248\pi\)
\(138\) −1.76268 + 0.181424i −0.150049 + 0.0154438i
\(139\) −7.18300 2.61440i −0.609254 0.221750i 0.0189230 0.999821i \(-0.493976\pi\)
−0.628177 + 0.778071i \(0.716198\pi\)
\(140\) 0.472396i 0.0399247i
\(141\) −0.431351 + 0.444755i −0.0363263 + 0.0374551i
\(142\) 5.64032 + 31.9878i 0.473325 + 2.68436i
\(143\) 11.8269 + 4.30466i 0.989019 + 0.359974i
\(144\) 0.333910 + 10.9103i 0.0278258 + 0.909195i
\(145\) −0.0380980 + 0.0219959i −0.00316387 + 0.00182666i
\(146\) 27.4176 23.0061i 2.26910 1.90400i
\(147\) −10.3343 4.62784i −0.852358 0.381698i
\(148\) 19.5982 3.45570i 1.61096 0.284056i
\(149\) −4.59930 + 5.48124i −0.376790 + 0.449040i −0.920798 0.390039i \(-0.872461\pi\)
0.544009 + 0.839080i \(0.316906\pi\)
\(150\) 16.9949 12.2917i 1.38763 1.00361i
\(151\) 15.1021 8.71921i 1.22899 0.709560i 0.262174 0.965021i \(-0.415561\pi\)
0.966819 + 0.255461i \(0.0822273\pi\)
\(152\) −18.1215 9.79432i −1.46985 0.794424i
\(153\) −9.43831 + 0.288859i −0.763042 + 0.0233528i
\(154\) 2.87484 + 7.89857i 0.231662 + 0.636485i
\(155\) 1.60718 0.584966i 0.129092 0.0469856i
\(156\) 15.2351 7.39006i 1.21979 0.591678i
\(157\) 7.70027 2.80267i 0.614548 0.223677i −0.0159440 0.999873i \(-0.505075\pi\)
0.630492 + 0.776196i \(0.282853\pi\)
\(158\) 4.98323 13.6913i 0.396444 1.08922i
\(159\) 2.74430 10.9066i 0.217637 0.864948i
\(160\) 0.103036i 0.00814573i
\(161\) −0.0976506 + 0.268293i −0.00769595 + 0.0211444i
\(162\) 5.12245 + 21.3267i 0.402458 + 1.67559i
\(163\) 0.902969 1.56399i 0.0707260 0.122501i −0.828494 0.559998i \(-0.810802\pi\)
0.899220 + 0.437497i \(0.144135\pi\)
\(164\) −22.9226 + 39.7031i −1.78996 + 3.10029i
\(165\) −0.868852 + 1.28216i −0.0676400 + 0.0998157i
\(166\) 0.812600 + 2.23260i 0.0630700 + 0.173283i
\(167\) 2.52373 + 14.3128i 0.195292 + 1.10756i 0.912002 + 0.410185i \(0.134536\pi\)
−0.716710 + 0.697371i \(0.754353\pi\)
\(168\) 5.08072 + 2.27522i 0.391986 + 0.175537i
\(169\) 5.24019 + 4.39704i 0.403092 + 0.338234i
\(170\) −1.35257 −0.103737
\(171\) −12.5293 3.74404i −0.958136 0.286314i
\(172\) 7.47916 0.570280
\(173\) −14.6287 12.2749i −1.11220 0.933246i −0.114015 0.993479i \(-0.536371\pi\)
−0.998184 + 0.0602325i \(0.980816\pi\)
\(174\) 0.107822 + 1.04757i 0.00817393 + 0.0794161i
\(175\) −0.586834 3.32810i −0.0443605 0.251581i
\(176\) 6.31087 + 17.3390i 0.475700 + 1.30697i
\(177\) −2.49991 5.15374i −0.187905 0.387379i
\(178\) −10.4015 + 18.0158i −0.779622 + 1.35034i
\(179\) 3.53331 6.11987i 0.264092 0.457420i −0.703233 0.710959i \(-0.748261\pi\)
0.967325 + 0.253539i \(0.0815945\pi\)
\(180\) 0.424442 + 2.04005i 0.0316361 + 0.152057i
\(181\) −8.71420 + 23.9421i −0.647721 + 1.77960i −0.0217366 + 0.999764i \(0.506920\pi\)
−0.625985 + 0.779835i \(0.715303\pi\)
\(182\) 4.11354i 0.304916i
\(183\) 12.8828 3.66405i 0.952324 0.270854i
\(184\) −0.678514 + 1.86420i −0.0500207 + 0.137431i
\(185\) 0.837091 0.304676i 0.0615441 0.0224002i
\(186\) 2.94407 40.8370i 0.215870 2.99431i
\(187\) −14.9996 + 5.45940i −1.09688 + 0.399231i
\(188\) 0.481930 + 1.32409i 0.0351484 + 0.0965693i
\(189\) 3.45195 + 0.757098i 0.251092 + 0.0550708i
\(190\) −1.77743 0.590943i −0.128949 0.0428715i
\(191\) −7.39281 + 4.26824i −0.534925 + 0.308839i −0.743020 0.669270i \(-0.766607\pi\)
0.208095 + 0.978109i \(0.433274\pi\)
\(192\) −13.7545 6.15944i −0.992642 0.444519i
\(193\) 5.77319 6.88022i 0.415563 0.495249i −0.517136 0.855903i \(-0.673002\pi\)
0.932700 + 0.360654i \(0.117446\pi\)
\(194\) −32.6297 + 5.75350i −2.34268 + 0.413077i
\(195\) 0.614170 0.444201i 0.0439816 0.0318099i
\(196\) −19.7270 + 16.5530i −1.40907 + 1.18235i
\(197\) 7.27273 4.19891i 0.518161 0.299160i −0.218021 0.975944i \(-0.569960\pi\)
0.736182 + 0.676784i \(0.236627\pi\)
\(198\) 19.5119 + 31.5271i 1.38665 + 2.24054i
\(199\) 5.96674 + 2.17172i 0.422971 + 0.153949i 0.544731 0.838611i \(-0.316632\pi\)
−0.121760 + 0.992560i \(0.538854\pi\)
\(200\) −4.07755 23.1249i −0.288326 1.63518i
\(201\) 12.7869 + 3.21744i 0.901921 + 0.226940i
\(202\) 38.5603i 2.71309i
\(203\) 0.159448 + 0.0580344i 0.0111911 + 0.00407322i
\(204\) −8.77702 + 19.5997i −0.614514 + 1.37225i
\(205\) −0.701887 + 1.92842i −0.0490219 + 0.134687i
\(206\) −11.6993 2.06290i −0.815130 0.143729i
\(207\) −0.180648 + 1.24637i −0.0125559 + 0.0866285i
\(208\) 9.03005i 0.626121i
\(209\) −22.0965 + 0.620913i −1.52844 + 0.0429495i
\(210\) 0.490905 + 0.123521i 0.0338757 + 0.00852376i
\(211\) −13.6964 2.41505i −0.942902 0.166259i −0.318994 0.947757i \(-0.603345\pi\)
−0.623908 + 0.781498i \(0.714456\pi\)
\(212\) −19.5935 16.4409i −1.34569 1.12917i
\(213\) 23.0254 + 1.65998i 1.57767 + 0.113740i
\(214\) 4.07545 23.1130i 0.278592 1.57997i
\(215\) 0.329705 0.0581359i 0.0224857 0.00396483i
\(216\) 23.9855 + 5.26061i 1.63200 + 0.357939i
\(217\) −5.71311 3.29846i −0.387831 0.223914i
\(218\) 13.6680 2.41004i 0.925716 0.163229i
\(219\) −11.1018 22.8871i −0.750188 1.54657i
\(220\) 1.76120 + 3.05049i 0.118740 + 0.205664i
\(221\) 7.81171 0.525472
\(222\) 1.53340 21.2697i 0.102915 1.42753i
\(223\) 3.23131 + 0.569767i 0.216385 + 0.0381544i 0.280789 0.959769i \(-0.409404\pi\)
−0.0644048 + 0.997924i \(0.520515\pi\)
\(224\) −0.304443 + 0.255458i −0.0203415 + 0.0170685i
\(225\) −5.52452 13.8452i −0.368301 0.923015i
\(226\) −35.1105 + 12.7792i −2.33552 + 0.850059i
\(227\) 6.29847 + 10.9093i 0.418044 + 0.724074i 0.995743 0.0921763i \(-0.0293823\pi\)
−0.577698 + 0.816250i \(0.696049\pi\)
\(228\) −20.0972 + 21.9216i −1.33097 + 1.45179i
\(229\) −2.16119 + 3.74330i −0.142816 + 0.247364i −0.928556 0.371193i \(-0.878949\pi\)
0.785740 + 0.618557i \(0.212282\pi\)
\(230\) −0.0313251 + 0.177653i −0.00206552 + 0.0117141i
\(231\) 5.94256 0.611640i 0.390992 0.0402429i
\(232\) 1.10791 + 0.403246i 0.0727377 + 0.0264744i
\(233\) 9.49430 11.3149i 0.621992 0.741262i −0.359419 0.933176i \(-0.617025\pi\)
0.981412 + 0.191915i \(0.0614697\pi\)
\(234\) −3.69597 17.7644i −0.241613 1.16130i
\(235\) 0.0315372 + 0.0546241i 0.00205726 + 0.00356328i
\(236\) −13.0271 −0.847991
\(237\) −8.57235 5.80905i −0.556834 0.377338i
\(238\) 3.35343 + 3.99646i 0.217371 + 0.259052i
\(239\) 12.4236 7.17276i 0.803615 0.463967i −0.0411186 0.999154i \(-0.513092\pi\)
0.844734 + 0.535187i \(0.179759\pi\)
\(240\) 1.07764 + 0.271154i 0.0695611 + 0.0175029i
\(241\) 5.11028 + 6.09020i 0.329182 + 0.392304i 0.905097 0.425206i \(-0.139798\pi\)
−0.575914 + 0.817510i \(0.695354\pi\)
\(242\) 27.4763 + 23.0554i 1.76625 + 1.48206i
\(243\) 15.5876 + 0.168010i 0.999942 + 0.0107779i
\(244\) 5.28946 29.9980i 0.338623 1.92043i
\(245\) −0.740964 + 0.883046i −0.0473384 + 0.0564157i
\(246\) 35.2650 + 34.2022i 2.24842 + 2.18066i
\(247\) 10.2655 + 3.41297i 0.653178 + 0.217162i
\(248\) −39.6969 22.9190i −2.52075 1.45536i
\(249\) 1.67972 0.172885i 0.106448 0.0109562i
\(250\) −1.46515 4.02547i −0.0926643 0.254593i
\(251\) 15.0671 + 17.9562i 0.951025 + 1.13339i 0.990956 + 0.134185i \(0.0428417\pi\)
−0.0399312 + 0.999202i \(0.512714\pi\)
\(252\) 4.97546 6.31202i 0.313425 0.397620i
\(253\) 0.369680 + 2.09656i 0.0232416 + 0.131810i
\(254\) 33.7774 + 19.5014i 2.11938 + 1.22363i
\(255\) −0.234569 + 0.932241i −0.0146893 + 0.0583792i
\(256\) −24.0740 + 20.2005i −1.50462 + 1.26253i
\(257\) 4.06877 3.41410i 0.253803 0.212966i −0.507005 0.861943i \(-0.669247\pi\)
0.760808 + 0.648977i \(0.224803\pi\)
\(258\) 1.95563 7.77220i 0.121752 0.483876i
\(259\) −2.97564 1.71798i −0.184897 0.106750i
\(260\) −0.299338 1.69763i −0.0185642 0.105283i
\(261\) 0.740724 + 0.107360i 0.0458497 + 0.00664545i
\(262\) −5.60576 6.68068i −0.346325 0.412734i
\(263\) 8.50820 + 23.3761i 0.524638 + 1.44143i 0.865304 + 0.501247i \(0.167125\pi\)
−0.340666 + 0.940184i \(0.610653\pi\)
\(264\) 41.2912 4.24991i 2.54130 0.261564i
\(265\) −0.991540 0.572466i −0.0609098 0.0351663i
\(266\) 2.66073 + 6.71695i 0.163140 + 0.411843i
\(267\) 10.6133 + 10.2935i 0.649525 + 0.629950i
\(268\) 19.2754 22.9716i 1.17743 1.40321i
\(269\) 3.82949 21.7181i 0.233488 1.32418i −0.612286 0.790636i \(-0.709750\pi\)
0.845774 0.533541i \(-0.179139\pi\)
\(270\) 2.23097 + 0.0923555i 0.135772 + 0.00562057i
\(271\) 0.263153 + 0.220812i 0.0159854 + 0.0134133i 0.650745 0.759296i \(-0.274457\pi\)
−0.634760 + 0.772709i \(0.718901\pi\)
\(272\) 7.36146 + 8.77305i 0.446354 + 0.531944i
\(273\) −2.83520 0.713391i −0.171594 0.0431764i
\(274\) −21.2096 + 12.2454i −1.28132 + 0.739770i
\(275\) −16.1974 19.3033i −0.976741 1.16403i
\(276\) 2.37105 + 1.60674i 0.142721 + 0.0967145i
\(277\) −25.1866 −1.51332 −0.756659 0.653809i \(-0.773170\pi\)
−0.756659 + 0.653809i \(0.773170\pi\)
\(278\) 9.31432 + 16.1329i 0.558636 + 0.967586i
\(279\) −27.6358 9.11133i −1.65451 0.545481i
\(280\) 0.364285 0.434138i 0.0217702 0.0259447i
\(281\) 8.78018 + 3.19573i 0.523782 + 0.190641i 0.590360 0.807140i \(-0.298986\pi\)
−0.0665779 + 0.997781i \(0.521208\pi\)
\(282\) 1.50199 0.154592i 0.0894419 0.00920584i
\(283\) 1.39729 7.92443i 0.0830604 0.471059i −0.914698 0.404138i \(-0.867571\pi\)
0.997758 0.0669205i \(-0.0213174\pi\)
\(284\) 26.2508 45.4677i 1.55770 2.69801i
\(285\) −0.715552 + 1.12259i −0.0423856 + 0.0664965i
\(286\) −15.3362 26.5631i −0.906850 1.57071i
\(287\) 7.43813 2.70726i 0.439059 0.159804i
\(288\) −1.08522 + 1.37674i −0.0639472 + 0.0811253i
\(289\) 5.43337 4.55914i 0.319610 0.268185i
\(290\) 0.105581 + 0.0186167i 0.00619991 + 0.00109321i
\(291\) −1.69328 + 23.4874i −0.0992621 + 1.37686i
\(292\) −57.8515 −3.38550
\(293\) 12.4915 + 21.6360i 0.729764 + 1.26399i 0.956983 + 0.290144i \(0.0937032\pi\)
−0.227219 + 0.973844i \(0.572963\pi\)
\(294\) 12.0433 + 24.8282i 0.702382 + 1.44801i
\(295\) −0.574275 + 0.101260i −0.0334356 + 0.00589560i
\(296\) −20.6759 11.9372i −1.20176 0.693837i
\(297\) 25.1135 7.98071i 1.45724 0.463087i
\(298\) 17.1727 3.02800i 0.994785 0.175408i
\(299\) 0.180917 1.02603i 0.0104627 0.0593369i
\(300\) −33.8140 2.43776i −1.95225 0.140744i
\(301\) −0.989214 0.830050i −0.0570174 0.0478433i
\(302\) −41.8524 7.37970i −2.40833 0.424654i
\(303\) −26.5772 6.68732i −1.52682 0.384176i
\(304\) 5.84084 + 14.7451i 0.334995 + 0.845688i
\(305\) 1.36352i 0.0780751i
\(306\) 18.0726 + 14.2458i 1.03314 + 0.814378i
\(307\) 16.5638 + 2.92064i 0.945343 + 0.166690i 0.625011 0.780616i \(-0.285094\pi\)
0.320332 + 0.947305i \(0.396205\pi\)
\(308\) 4.64679 12.7670i 0.264776 0.727465i
\(309\) −3.45079 + 7.70584i −0.196308 + 0.438370i
\(310\) −3.91676 1.42558i −0.222457 0.0809676i
\(311\) 11.1764i 0.633753i 0.948467 + 0.316877i \(0.102634\pi\)
−0.948467 + 0.316877i \(0.897366\pi\)
\(312\) −19.7001 4.95691i −1.11530 0.280630i
\(313\) 1.68577 + 9.56048i 0.0952854 + 0.540390i 0.994660 + 0.103211i \(0.0329115\pi\)
−0.899374 + 0.437180i \(0.855977\pi\)
\(314\) −18.7658 6.83019i −1.05902 0.385450i
\(315\) 0.170271 0.316929i 0.00959366 0.0178569i
\(316\) −20.3952 + 11.7752i −1.14732 + 0.662406i
\(317\) −11.5630 + 9.70254i −0.649445 + 0.544949i −0.906903 0.421341i \(-0.861560\pi\)
0.257457 + 0.966290i \(0.417115\pi\)
\(318\) −22.2084 + 16.0623i −1.24538 + 0.900728i
\(319\) 1.24600 0.219704i 0.0697626 0.0123010i
\(320\) −0.986188 + 1.17529i −0.0551296 + 0.0657009i
\(321\) −15.2236 6.81733i −0.849697 0.380506i
\(322\) 0.602581 0.347900i 0.0335805 0.0193877i
\(323\) −12.7557 + 5.05279i −0.709744 + 0.281145i
\(324\) 15.8154 31.7290i 0.878632 1.76272i
\(325\) 4.21777 + 11.5882i 0.233960 + 0.642799i
\(326\) −4.13571 + 1.50528i −0.229056 + 0.0833695i
\(327\) 0.709289 9.83849i 0.0392238 0.544070i
\(328\) 51.6830 18.8111i 2.85372 1.03867i
\(329\) 0.0832085 0.228614i 0.00458744 0.0126039i
\(330\) 3.63053 1.03257i 0.199854 0.0568413i
\(331\) 13.2009i 0.725585i 0.931870 + 0.362793i \(0.118177\pi\)
−0.931870 + 0.362793i \(0.881823\pi\)
\(332\) 1.31346 3.60869i 0.0720853 0.198053i
\(333\) −14.3939 4.74558i −0.788783 0.260056i
\(334\) 17.7094 30.6736i 0.969016 1.67838i
\(335\) 0.671163 1.16249i 0.0366696 0.0635135i
\(336\) −1.87061 3.85639i −0.102050 0.210383i
\(337\) 7.18695 + 19.7460i 0.391498 + 1.07563i 0.966318 + 0.257352i \(0.0828499\pi\)
−0.574820 + 0.818280i \(0.694928\pi\)
\(338\) −2.89484 16.4175i −0.157459 0.892992i
\(339\) 2.71884 + 26.4157i 0.147667 + 1.43470i
\(340\) 1.67476 + 1.40529i 0.0908265 + 0.0762125i
\(341\) −49.1898 −2.66377
\(342\) 17.5255 + 26.6167i 0.947672 + 1.43926i
\(343\) 9.20705 0.497134
\(344\) −6.87345 5.76751i −0.370591 0.310963i
\(345\) 0.117013 + 0.0524000i 0.00629976 + 0.00282112i
\(346\) 8.08134 + 45.8316i 0.434456 + 2.46392i
\(347\) −3.04230 8.35865i −0.163319 0.448716i 0.830857 0.556487i \(-0.187851\pi\)
−0.994176 + 0.107771i \(0.965629\pi\)
\(348\) 0.954898 1.40913i 0.0511879 0.0755374i
\(349\) 3.92052 6.79054i 0.209861 0.363489i −0.741810 0.670610i \(-0.766032\pi\)
0.951670 + 0.307121i \(0.0993657\pi\)
\(350\) −4.11791 + 7.13242i −0.220111 + 0.381244i
\(351\) −12.8849 0.533395i −0.687743 0.0284705i
\(352\) −1.01353 + 2.78466i −0.0540214 + 0.148423i
\(353\) 0.171537i 0.00913001i −0.999990 0.00456501i \(-0.998547\pi\)
0.999990 0.00456501i \(-0.00145309\pi\)
\(354\) −3.40629 + 13.5375i −0.181042 + 0.719510i
\(355\) 0.803795 2.20841i 0.0426610 0.117210i
\(356\) 31.5972 11.5004i 1.67465 0.609522i
\(357\) 3.33608 1.61822i 0.176564 0.0856454i
\(358\) −16.1830 + 5.89012i −0.855297 + 0.311303i
\(359\) −4.87953 13.4064i −0.257532 0.707563i −0.999318 0.0369264i \(-0.988243\pi\)
0.741786 0.670636i \(-0.233979\pi\)
\(360\) 1.18311 2.20214i 0.0623552 0.116063i
\(361\) −18.9700 + 1.06696i −0.998422 + 0.0561559i
\(362\) 53.7734 31.0461i 2.82627 1.63175i
\(363\) 20.6557 14.9393i 1.08414 0.784112i
\(364\) −4.27387 + 5.09341i −0.224012 + 0.266967i
\(365\) −2.55028 + 0.449683i −0.133488 + 0.0235375i
\(366\) −29.7903 13.3405i −1.55716 0.697320i
\(367\) −3.46143 + 2.90449i −0.180685 + 0.151613i −0.728645 0.684892i \(-0.759849\pi\)
0.547959 + 0.836505i \(0.315405\pi\)
\(368\) 1.32279 0.763711i 0.0689550 0.0398112i
\(369\) 29.6893 18.3744i 1.54556 0.956535i
\(370\) −2.04002 0.742506i −0.106055 0.0386010i
\(371\) 0.766854 + 4.34904i 0.0398131 + 0.225791i
\(372\) −46.0741 + 47.5058i −2.38883 + 2.46306i
\(373\) 6.81791i 0.353018i 0.984299 + 0.176509i \(0.0564805\pi\)
−0.984299 + 0.176509i \(0.943519\pi\)
\(374\) 36.5545 + 13.3047i 1.89019 + 0.687972i
\(375\) −3.02860 + 0.311719i −0.156396 + 0.0160971i
\(376\) 0.578165 1.58850i 0.0298166 0.0819204i
\(377\) −0.609777 0.107520i −0.0314051 0.00553757i
\(378\) −5.25836 6.82086i −0.270461 0.350827i
\(379\) 2.43440i 0.125047i −0.998044 0.0625233i \(-0.980085\pi\)
0.998044 0.0625233i \(-0.0199148\pi\)
\(380\) 1.58685 + 2.57842i 0.0814038 + 0.132270i
\(381\) 19.2990 19.8986i 0.988715 1.01944i
\(382\) 20.4876 + 3.61252i 1.04824 + 0.184833i
\(383\) −6.13769 5.15013i −0.313621 0.263159i 0.472366 0.881403i \(-0.343400\pi\)
−0.785987 + 0.618243i \(0.787845\pi\)
\(384\) 15.1457 + 31.2239i 0.772900 + 1.59339i
\(385\) 0.105607 0.598928i 0.00538224 0.0305242i
\(386\) −21.5557 + 3.80084i −1.09715 + 0.193458i
\(387\) −5.01774 2.69579i −0.255066 0.137035i
\(388\) 46.3800 + 26.7775i 2.35459 + 1.35942i
\(389\) 36.2433 6.39067i 1.83761 0.324020i 0.856303 0.516474i \(-0.172756\pi\)
0.981306 + 0.192454i \(0.0616445\pi\)
\(390\) −1.84242 0.132826i −0.0932944 0.00672590i
\(391\) 0.660671 + 1.14432i 0.0334116 + 0.0578705i
\(392\) 30.8941 1.56039
\(393\) −5.57676 + 2.70510i −0.281310 + 0.136454i
\(394\) −20.1549 3.55385i −1.01539 0.179040i
\(395\) −0.807558 + 0.677621i −0.0406326 + 0.0340948i
\(396\) 8.59631 59.3095i 0.431981 2.98041i
\(397\) 16.0394 5.83787i 0.804996 0.292995i 0.0934407 0.995625i \(-0.470213\pi\)
0.711555 + 0.702630i \(0.247991\pi\)
\(398\) −7.73719 13.4012i −0.387830 0.671741i
\(399\) 5.09101 0.668987i 0.254869 0.0334912i
\(400\) −9.03964 + 15.6571i −0.451982 + 0.782856i
\(401\) 2.03940 11.5660i 0.101843 0.577579i −0.890592 0.454804i \(-0.849709\pi\)
0.992434 0.122775i \(-0.0391794\pi\)
\(402\) −18.8315 26.0372i −0.939231 1.29862i
\(403\) 22.6211 + 8.23340i 1.12684 + 0.410135i
\(404\) −40.0633 + 47.7455i −1.99322 + 2.37543i
\(405\) 0.450561 1.52165i 0.0223885 0.0756114i
\(406\) −0.206759 0.358118i −0.0102613 0.0177731i
\(407\) −25.6202 −1.26994
\(408\) 23.1804 11.2440i 1.14760 0.556663i
\(409\) 5.19289 + 6.18865i 0.256772 + 0.306009i 0.878995 0.476831i \(-0.158215\pi\)
−0.622223 + 0.782840i \(0.713770\pi\)
\(410\) 4.33119 2.50062i 0.213902 0.123497i
\(411\) 4.76169 + 16.7421i 0.234877 + 0.825827i
\(412\) 12.3428 + 14.7096i 0.608088 + 0.724691i
\(413\) 1.72300 + 1.44577i 0.0847832 + 0.0711416i
\(414\) 2.28967 2.04383i 0.112531 0.100449i
\(415\) 0.0298508 0.169292i 0.00146532 0.00831022i
\(416\) 0.932193 1.11094i 0.0457045 0.0544685i
\(417\) 12.7347 3.62193i 0.623622 0.177367i
\(418\) 42.2240 + 33.4548i 2.06524 + 1.63633i
\(419\) 4.08004 + 2.35561i 0.199323 + 0.115079i 0.596340 0.802732i \(-0.296621\pi\)
−0.397017 + 0.917811i \(0.629954\pi\)
\(420\) −0.479506 0.662984i −0.0233975 0.0323503i
\(421\) 10.7149 + 29.4388i 0.522211 + 1.43476i 0.868054 + 0.496469i \(0.165371\pi\)
−0.345844 + 0.938292i \(0.612407\pi\)
\(422\) 21.7864 + 25.9640i 1.06054 + 1.26391i
\(423\) 0.153931 1.06203i 0.00748439 0.0516379i
\(424\) 5.32840 + 30.2188i 0.258770 + 1.46756i
\(425\) −13.5447 7.82001i −0.657012 0.379326i
\(426\) −40.3852 39.1681i −1.95667 1.89770i
\(427\) −4.02883 + 3.38059i −0.194969 + 0.163598i
\(428\) −29.0602 + 24.3844i −1.40468 + 1.17866i
\(429\) −20.9680 + 5.96359i −1.01234 + 0.287925i
\(430\) −0.706588 0.407949i −0.0340747 0.0196730i
\(431\) 6.11308 + 34.6690i 0.294457 + 1.66995i 0.669402 + 0.742900i \(0.266550\pi\)
−0.374946 + 0.927047i \(0.622339\pi\)
\(432\) −11.5432 14.9732i −0.555371 0.720397i
\(433\) −19.7644 23.5543i −0.949816 1.13195i −0.991143 0.132801i \(-0.957603\pi\)
0.0413267 0.999146i \(-0.486842\pi\)
\(434\) 5.49863 + 15.1074i 0.263943 + 0.725177i
\(435\) 0.0311417 0.0695415i 0.00149313 0.00333426i
\(436\) −19.4278 11.2167i −0.930424 0.537181i
\(437\) 0.368243 + 1.79242i 0.0176154 + 0.0857429i
\(438\) −15.1269 + 60.1182i −0.722790 + 2.87256i
\(439\) 18.0716 21.5369i 0.862510 1.02790i −0.136794 0.990600i \(-0.543680\pi\)
0.999304 0.0373002i \(-0.0118758\pi\)
\(440\) 0.733799 4.16158i 0.0349825 0.198396i
\(441\) 19.2011 3.99489i 0.914340 0.190233i
\(442\) −14.5835 12.2370i −0.693666 0.582055i
\(443\) −9.02653 10.7574i −0.428863 0.511099i 0.507731 0.861516i \(-0.330484\pi\)
−0.936594 + 0.350417i \(0.886040\pi\)
\(444\) −23.9974 + 24.7431i −1.13887 + 1.17426i
\(445\) 1.30351 0.752583i 0.0617924 0.0356758i
\(446\) −5.13992 6.12552i −0.243382 0.290052i
\(447\) 0.891158 12.3612i 0.0421503 0.584663i
\(448\) 5.91773 0.279586
\(449\) −12.7630 22.1062i −0.602325 1.04326i −0.992468 0.122503i \(-0.960908\pi\)
0.390143 0.920754i \(-0.372425\pi\)
\(450\) −11.3749 + 34.5014i −0.536217 + 1.62641i
\(451\) 37.9384 45.2132i 1.78645 2.12901i
\(452\) 56.7513 + 20.6558i 2.66936 + 0.971567i
\(453\) −12.3446 + 27.5664i −0.580001 + 1.29518i
\(454\) 5.33086 30.2328i 0.250189 1.41889i
\(455\) −0.148815 + 0.257755i −0.00697654 + 0.0120837i
\(456\) 35.3743 4.64838i 1.65655 0.217680i
\(457\) −6.57163 11.3824i −0.307408 0.532446i 0.670386 0.742012i \(-0.266128\pi\)
−0.977795 + 0.209566i \(0.932795\pi\)
\(458\) 9.89853 3.60277i 0.462528 0.168346i
\(459\) 12.9530 9.98576i 0.604594 0.466096i
\(460\) 0.223365 0.187425i 0.0104144 0.00873875i
\(461\) −3.13578 0.552922i −0.146048 0.0257522i 0.100146 0.994973i \(-0.468069\pi\)
−0.246194 + 0.969221i \(0.579180\pi\)
\(462\) −12.0522 8.16713i −0.560717 0.379969i
\(463\) 3.17519 0.147564 0.0737818 0.997274i \(-0.476493\pi\)
0.0737818 + 0.997274i \(0.476493\pi\)
\(464\) −0.453879 0.786141i −0.0210708 0.0364957i
\(465\) −1.66183 + 2.45234i −0.0770655 + 0.113725i
\(466\) −35.4494 + 6.25068i −1.64216 + 0.289557i
\(467\) 14.5792 + 8.41731i 0.674645 + 0.389507i 0.797834 0.602877i \(-0.205979\pi\)
−0.123189 + 0.992383i \(0.539312\pi\)
\(468\) −13.8805 + 25.8360i −0.641624 + 1.19427i
\(469\) −5.09885 + 0.899064i −0.235443 + 0.0415149i
\(470\) 0.0266923 0.151379i 0.00123122 0.00698261i
\(471\) −7.96209 + 11.7496i −0.366874 + 0.541391i
\(472\) 11.9721 + 10.0458i 0.551059 + 0.462393i
\(473\) −9.48246 1.67201i −0.436004 0.0768792i
\(474\) 6.90367 + 24.2733i 0.317096 + 1.11491i
\(475\) −14.3827 16.1941i −0.659922 0.743038i
\(476\) 8.43258i 0.386507i
\(477\) 7.21924 + 18.0924i 0.330546 + 0.828396i
\(478\) −34.4294 6.07083i −1.57476 0.277673i
\(479\) 3.80159 10.4448i 0.173699 0.477235i −0.822042 0.569427i \(-0.807165\pi\)
0.995741 + 0.0921921i \(0.0293874\pi\)
\(480\) 0.104587 + 0.144606i 0.00477373 + 0.00660034i
\(481\) 11.7820 + 4.28831i 0.537215 + 0.195530i
\(482\) 19.3749i 0.882501i
\(483\) −0.135283 0.475656i −0.00615560 0.0216431i
\(484\) −10.0673 57.0946i −0.457606 2.59521i
\(485\) 2.25272 + 0.819924i 0.102291 + 0.0372308i
\(486\) −28.8368 24.7315i −1.30807 1.12184i
\(487\) 28.5991 16.5117i 1.29595 0.748216i 0.316247 0.948677i \(-0.397577\pi\)
0.979702 + 0.200461i \(0.0642439\pi\)
\(488\) −27.9939 + 23.4896i −1.26722 + 1.06333i
\(489\) 0.320256 + 3.11154i 0.0144825 + 0.140709i
\(490\) 2.76657 0.487822i 0.124981 0.0220375i
\(491\) −4.21825 + 5.02711i −0.190367 + 0.226870i −0.852783 0.522266i \(-0.825087\pi\)
0.662416 + 0.749136i \(0.269531\pi\)
\(492\) −8.12997 78.9890i −0.366527 3.56110i
\(493\) 0.680075 0.392641i 0.0306290 0.0176837i
\(494\) −13.8180 22.4524i −0.621702 1.01018i
\(495\) −0.0820631 2.68137i −0.00368846 0.120519i
\(496\) 12.0706 + 33.1638i 0.541987 + 1.48910i
\(497\) −8.51809 + 3.10033i −0.382088 + 0.139069i
\(498\) −3.40665 2.30851i −0.152655 0.103447i
\(499\) −9.81287 + 3.57159i −0.439285 + 0.159887i −0.552188 0.833719i \(-0.686207\pi\)
0.112904 + 0.993606i \(0.463985\pi\)
\(500\) −2.36822 + 6.50662i −0.105910 + 0.290985i
\(501\) −18.0701 17.5256i −0.807314 0.782984i
\(502\) 57.1245i 2.54959i
\(503\) 6.21077 17.0640i 0.276925 0.760844i −0.720782 0.693161i \(-0.756217\pi\)
0.997707 0.0676826i \(-0.0215605\pi\)
\(504\) −9.44000 + 1.96404i −0.420491 + 0.0874851i
\(505\) −1.39499 + 2.41619i −0.0620761 + 0.107519i
\(506\) 2.59410 4.49312i 0.115322 0.199744i
\(507\) −11.8176 0.851967i −0.524837 0.0378372i
\(508\) −21.5619 59.2408i −0.956653 2.62838i
\(509\) 1.45182 + 8.23367i 0.0643507 + 0.364951i 0.999930 + 0.0118342i \(0.00376705\pi\)
−0.935579 + 0.353117i \(0.885122\pi\)
\(510\) 1.89826 1.37293i 0.0840565 0.0607942i
\(511\) 7.65160 + 6.42045i 0.338487 + 0.284024i
\(512\) 36.5150 1.61375
\(513\) 21.3846 7.46325i 0.944152 0.329511i
\(514\) −12.9441 −0.570938
\(515\) 0.658450 + 0.552506i 0.0290148 + 0.0243463i
\(516\) −10.4966 + 7.59172i −0.462088 + 0.334207i
\(517\) −0.315006 1.78649i −0.0138540 0.0785697i
\(518\) 2.86393 + 7.86858i 0.125834 + 0.345726i
\(519\) 32.9903 + 2.37838i 1.44812 + 0.104399i
\(520\) −1.03402 + 1.79098i −0.0453449 + 0.0785396i
\(521\) 0.915257 1.58527i 0.0400982 0.0694520i −0.845280 0.534324i \(-0.820566\pi\)
0.885378 + 0.464872i \(0.153900\pi\)
\(522\) −1.21466 1.36077i −0.0531642 0.0595592i
\(523\) 7.02772 19.3085i 0.307301 0.844302i −0.685880 0.727715i \(-0.740582\pi\)
0.993180 0.116587i \(-0.0371954\pi\)
\(524\) 14.0963i 0.615801i
\(525\) 4.20179 + 4.07516i 0.183381 + 0.177854i
\(526\) 20.7348 56.9683i 0.904078 2.48394i
\(527\) −28.6893 + 10.4420i −1.24972 + 0.454863i
\(528\) −26.4569 17.9285i −1.15139 0.780239i
\(529\) −21.4473 + 7.80619i −0.932493 + 0.339400i
\(530\) 0.954318 + 2.62197i 0.0414529 + 0.113891i
\(531\) 8.73981 + 4.69548i 0.379276 + 0.203767i
\(532\) 3.68423 11.0814i 0.159732 0.480440i
\(533\) −25.0147 + 14.4422i −1.08350 + 0.625562i
\(534\) −3.68908 35.8423i −0.159642 1.55105i
\(535\) −1.09152 + 1.30083i −0.0471907 + 0.0562397i
\(536\) −35.4288 + 6.24705i −1.53029 + 0.269831i
\(537\) 1.25316 + 12.1754i 0.0540778 + 0.525408i
\(538\) −41.1705 + 34.5461i −1.77499 + 1.48939i
\(539\) 28.7115 16.5766i 1.23669 0.714004i
\(540\) −2.66644 2.43228i −0.114745 0.104669i
\(541\) −18.9614 6.90139i −0.815214 0.296714i −0.0994383 0.995044i \(-0.531705\pi\)
−0.715776 + 0.698330i \(0.753927\pi\)
\(542\) −0.145374 0.824456i −0.00624434 0.0354134i
\(543\) −12.0725 42.4468i −0.518079 1.82157i
\(544\) 1.83927i 0.0788579i
\(545\) −0.943628 0.343453i −0.0404206 0.0147119i
\(546\) 4.17545 + 5.77314i 0.178693 + 0.247068i
\(547\) 10.3522 28.4423i 0.442627 1.21611i −0.495132 0.868818i \(-0.664880\pi\)
0.937758 0.347289i \(-0.112898\pi\)
\(548\) 38.9845 + 6.87402i 1.66534 + 0.293644i
\(549\) −14.3612 + 18.2190i −0.612920 + 0.777568i
\(550\) 61.4101i 2.61853i
\(551\) 1.06524 0.218849i 0.0453809 0.00932329i
\(552\) −0.940000 3.30504i −0.0400090 0.140672i
\(553\) 4.00436 + 0.706077i 0.170283 + 0.0300255i
\(554\) 47.0203 + 39.4547i 1.99770 + 1.67627i
\(555\) −0.865553 + 1.27729i −0.0367407 + 0.0542178i
\(556\) 5.22866 29.6532i 0.221744 1.25758i
\(557\) −32.1147 + 5.66269i −1.36074 + 0.239936i −0.805917 0.592029i \(-0.798327\pi\)
−0.554828 + 0.831965i \(0.687216\pi\)
\(558\) 37.3198 + 60.3011i 1.57987 + 2.55275i
\(559\) 4.08087 + 2.35609i 0.172602 + 0.0996520i
\(560\) −0.429712 + 0.0757698i −0.0181587 + 0.00320186i
\(561\) 15.5096 22.8873i 0.654816 0.966304i
\(562\) −11.3854 19.7201i −0.480265 0.831844i
\(563\) 9.73673 0.410354 0.205177 0.978725i \(-0.434223\pi\)
0.205177 + 0.978725i \(0.434223\pi\)
\(564\) −2.02039 1.36911i −0.0850736 0.0576501i
\(565\) 2.66234 + 0.469442i 0.112005 + 0.0197496i
\(566\) −15.0222 + 12.6051i −0.631428 + 0.529831i
\(567\) −5.61313 + 2.44135i −0.235729 + 0.102527i
\(568\) −59.1870 + 21.5423i −2.48343 + 0.903895i
\(569\) −0.953311 1.65118i −0.0399649 0.0692212i 0.845351 0.534211i \(-0.179391\pi\)
−0.885316 + 0.464990i \(0.846058\pi\)
\(570\) 3.09438 0.974827i 0.129609 0.0408310i
\(571\) −22.4448 + 38.8755i −0.939286 + 1.62689i −0.172478 + 0.985013i \(0.555177\pi\)
−0.766807 + 0.641877i \(0.778156\pi\)
\(572\) −8.60909 + 48.8246i −0.359964 + 2.04146i
\(573\) 6.04295 13.4943i 0.252448 0.563734i
\(574\) −18.1270 6.59768i −0.756605 0.275382i
\(575\) −1.34081 + 1.59792i −0.0559157 + 0.0666377i
\(576\) 25.5558 5.31701i 1.06483 0.221542i
\(577\) 4.60536 + 7.97671i 0.191724 + 0.332075i 0.945822 0.324687i \(-0.105259\pi\)
−0.754098 + 0.656762i \(0.771926\pi\)
\(578\) −17.2853 −0.718974
\(579\) −1.11861 + 15.5161i −0.0464878 + 0.644828i
\(580\) −0.111388 0.132747i −0.00462514 0.00551203i
\(581\) −0.574220 + 0.331526i −0.0238227 + 0.0137540i
\(582\) 39.9540 41.1955i 1.65615 1.70761i
\(583\) 21.1662 + 25.2249i 0.876614 + 1.04471i
\(584\) 53.1663 + 44.6118i 2.20004 + 1.84605i
\(585\) −0.411070 + 1.24683i −0.0169956 + 0.0515500i
\(586\) 10.5725 59.9596i 0.436746 2.47691i
\(587\) −11.3944 + 13.5794i −0.470299 + 0.560480i −0.948094 0.317991i \(-0.896992\pi\)
0.477795 + 0.878471i \(0.341436\pi\)
\(588\) 10.8838 43.2552i 0.448841 1.78381i
\(589\) −42.2633 + 1.18760i −1.74143 + 0.0489344i
\(590\) 1.23072 + 0.710558i 0.0506681 + 0.0292532i
\(591\) −5.94480 + 13.2752i −0.244536 + 0.546067i
\(592\) 6.28691 + 17.2731i 0.258390 + 0.709921i
\(593\) −14.9759 17.8476i −0.614988 0.732914i 0.365212 0.930924i \(-0.380996\pi\)
−0.980200 + 0.198010i \(0.936552\pi\)
\(594\) −59.3856 24.4412i −2.43662 1.00284i
\(595\) −0.0655469 0.371735i −0.00268716 0.0152397i
\(596\) −24.4093 14.0927i −0.999844 0.577260i
\(597\) −10.5784 + 3.00865i −0.432946 + 0.123136i
\(598\) −1.94502 + 1.63207i −0.0795378 + 0.0667401i
\(599\) −10.1981 + 8.55723i −0.416683 + 0.349639i −0.826900 0.562349i \(-0.809898\pi\)
0.410216 + 0.911988i \(0.365453\pi\)
\(600\) 29.1956 + 28.3158i 1.19191 + 1.15599i
\(601\) 3.88142 + 2.24094i 0.158327 + 0.0914099i 0.577070 0.816695i \(-0.304196\pi\)
−0.418743 + 0.908105i \(0.637529\pi\)
\(602\) 0.546472 + 3.09920i 0.0222725 + 0.126314i
\(603\) −21.2117 + 8.46389i −0.863807 + 0.344676i
\(604\) 44.1545 + 52.6213i 1.79662 + 2.14113i
\(605\) −0.887599 2.43866i −0.0360860 0.0991456i
\(606\) 39.1406 + 54.1174i 1.58998 + 2.19837i
\(607\) 11.4577 + 6.61510i 0.465053 + 0.268499i 0.714167 0.699976i \(-0.246806\pi\)
−0.249113 + 0.968474i \(0.580139\pi\)
\(608\) −0.803584 + 2.41701i −0.0325896 + 0.0980228i
\(609\) −0.282685 + 0.0803997i −0.0114550 + 0.00325796i
\(610\) −2.13595 + 2.54553i −0.0864821 + 0.103065i
\(611\) −0.154160 + 0.874286i −0.00623665 + 0.0353698i
\(612\) −7.57658 36.4163i −0.306265 1.47204i
\(613\) 10.4469 + 8.76601i 0.421948 + 0.354056i 0.828903 0.559392i \(-0.188965\pi\)
−0.406956 + 0.913448i \(0.633410\pi\)
\(614\) −26.3473 31.3995i −1.06329 1.26718i
\(615\) −0.972380 3.41889i −0.0392102 0.137863i
\(616\) −14.1156 + 8.14966i −0.568735 + 0.328359i
\(617\) 6.47210 + 7.71315i 0.260557 + 0.310520i 0.880424 0.474187i \(-0.157258\pi\)
−0.619867 + 0.784707i \(0.712814\pi\)
\(618\) 18.5133 8.98021i 0.744716 0.361237i
\(619\) −17.2670 −0.694018 −0.347009 0.937862i \(-0.612803\pi\)
−0.347009 + 0.937862i \(0.612803\pi\)
\(620\) 3.36860 + 5.83459i 0.135286 + 0.234323i
\(621\) −1.01159 1.93258i −0.0405939 0.0775518i
\(622\) 17.5077 20.8649i 0.701995 0.836605i
\(623\) −5.45548 1.98563i −0.218569 0.0795526i
\(624\) 9.16596 + 12.6732i 0.366932 + 0.507335i
\(625\) 4.26039 24.1619i 0.170415 0.966474i
\(626\) 11.8293 20.4890i 0.472795 0.818904i
\(627\) 30.3810 23.3004i 1.21330 0.930530i
\(628\) 16.1395 + 27.9544i 0.644036 + 1.11550i
\(629\) −14.9426 + 5.43867i −0.595802 + 0.216854i
\(630\) −0.814341 + 0.324938i −0.0324441 + 0.0129458i
\(631\) −18.9204 + 15.8761i −0.753208 + 0.632017i −0.936349 0.351070i \(-0.885818\pi\)
0.183141 + 0.983087i \(0.441373\pi\)
\(632\) 27.8239 + 4.90610i 1.10677 + 0.195154i
\(633\) 21.6737 10.5132i 0.861451 0.417862i
\(634\) 36.7857 1.46095
\(635\) −1.41100 2.44392i −0.0559937 0.0969840i
\(636\) 44.1869 + 3.18558i 1.75212 + 0.126316i
\(637\) −15.9782 + 2.81739i −0.633081 + 0.111629i
\(638\) −2.67029 1.54169i −0.105718 0.0610363i
\(639\) −33.9999 + 21.0423i −1.34502 + 0.832419i
\(640\) 3.47924 0.613484i 0.137529 0.0242501i
\(641\) −1.43513 + 8.13903i −0.0566842 + 0.321472i −0.999944 0.0105835i \(-0.996631\pi\)
0.943260 + 0.332056i \(0.107742\pi\)
\(642\) 17.7412 + 36.5748i 0.700190 + 1.44349i
\(643\) 17.9288 + 15.0440i 0.707041 + 0.593278i 0.923767 0.382954i \(-0.125093\pi\)
−0.216726 + 0.976232i \(0.569538\pi\)
\(644\) −1.10758 0.195296i −0.0436447 0.00769575i
\(645\) −0.403713 + 0.416258i −0.0158962 + 0.0163901i
\(646\) 31.7284 + 10.5487i 1.24834 + 0.415034i
\(647\) 38.0849i 1.49727i 0.662982 + 0.748635i \(0.269291\pi\)
−0.662982 + 0.748635i \(0.730709\pi\)
\(648\) −39.0022 + 16.9635i −1.53215 + 0.666388i
\(649\) 16.5164 + 2.91229i 0.648325 + 0.114317i
\(650\) 10.2788 28.2409i 0.403169 1.10770i
\(651\) 11.3662 1.16987i 0.445475 0.0458507i
\(652\) 6.68481 + 2.43307i 0.261797 + 0.0952864i
\(653\) 25.0470i 0.980164i −0.871676 0.490082i \(-0.836967\pi\)
0.871676 0.490082i \(-0.163033\pi\)
\(654\) −16.7361 + 17.2561i −0.654433 + 0.674768i
\(655\) 0.109571 + 0.621411i 0.00428131 + 0.0242805i
\(656\) −39.7924 14.4832i −1.55363 0.565476i
\(657\) 38.8123 + 20.8520i 1.51421 + 0.813514i
\(658\) −0.513462 + 0.296447i −0.0200168 + 0.0115567i
\(659\) −20.1652 + 16.9206i −0.785525 + 0.659134i −0.944634 0.328127i \(-0.893583\pi\)
0.159108 + 0.987261i \(0.449138\pi\)
\(660\) −5.56816 2.49350i −0.216740 0.0970594i
\(661\) 32.1080 5.66150i 1.24886 0.220207i 0.490148 0.871639i \(-0.336943\pi\)
0.758707 + 0.651432i \(0.225831\pi\)
\(662\) 20.6791 24.6444i 0.803716 0.957831i
\(663\) −10.9633 + 7.92928i −0.425781 + 0.307948i
\(664\) −3.98990 + 2.30357i −0.154838 + 0.0893959i
\(665\) 0.0762763 0.517141i 0.00295787 0.0200539i
\(666\) 19.4378 + 31.4074i 0.753198 + 1.21701i
\(667\) −0.0358212 0.0984180i −0.00138700 0.00381076i
\(668\) −53.7971 + 19.5805i −2.08147 + 0.757594i
\(669\) −5.11333 + 2.48031i −0.197693 + 0.0958942i
\(670\) −3.07401 + 1.11885i −0.118759 + 0.0432249i
\(671\) −13.4125 + 36.8505i −0.517783 + 1.42260i
\(672\) 0.167968 0.667549i 0.00647950 0.0257513i
\(673\) 35.9564i 1.38602i −0.720930 0.693008i \(-0.756285\pi\)
0.720930 0.693008i \(-0.243715\pi\)
\(674\) 17.5148 48.1216i 0.674646 1.85357i
\(675\) 21.8070 + 13.8234i 0.839351 + 0.532063i
\(676\) −13.4730 + 23.3359i −0.518191 + 0.897534i
\(677\) 15.4187 26.7060i 0.592590 1.02640i −0.401292 0.915950i \(-0.631439\pi\)
0.993882 0.110446i \(-0.0352280\pi\)
\(678\) 36.3043 53.5739i 1.39426 2.05749i
\(679\) −3.16254 8.68901i −0.121367 0.333453i
\(680\) −0.455445 2.58296i −0.0174655 0.0990520i
\(681\) −19.9131 8.91735i −0.763070 0.341714i
\(682\) 91.8312 + 77.0555i 3.51640 + 2.95061i
\(683\) 23.5676 0.901789 0.450895 0.892577i \(-0.351105\pi\)
0.450895 + 0.892577i \(0.351105\pi\)
\(684\) 5.95392 51.1656i 0.227654 1.95636i
\(685\) 1.77199 0.0677044
\(686\) −17.1884 14.4228i −0.656257 0.550665i
\(687\) −0.766510 7.44725i −0.0292442 0.284130i
\(688\) 1.19962 + 6.80337i 0.0457350 + 0.259376i
\(689\) −5.51162 15.1431i −0.209976 0.576905i
\(690\) −0.136364 0.281124i −0.00519129 0.0107022i
\(691\) −11.1790 + 19.3626i −0.425269 + 0.736587i −0.996445 0.0842402i \(-0.973154\pi\)
0.571177 + 0.820827i \(0.306487\pi\)
\(692\) 37.6116 65.1453i 1.42978 2.47645i
\(693\) −7.71924 + 6.89041i −0.293230 + 0.261745i
\(694\) −7.41418 + 20.3703i −0.281439 + 0.773246i
\(695\) 1.34785i 0.0511269i
\(696\) −1.96421 + 0.558648i −0.0744531 + 0.0211755i
\(697\) 12.5292 34.4236i 0.474576 1.30389i
\(698\) −17.9565 + 6.53562i −0.679662 + 0.247377i
\(699\) −1.83961 + 25.5170i −0.0695804 + 0.965143i
\(700\) 12.5092 4.55299i 0.472805 0.172087i
\(701\) −11.7795 32.3639i −0.444906 1.22237i −0.936229 0.351391i \(-0.885709\pi\)
0.491323 0.870977i \(-0.336513\pi\)
\(702\) 23.2189 + 21.1799i 0.876340 + 0.799382i
\(703\) −22.0126 + 0.618556i −0.830219 + 0.0233293i
\(704\) 38.2136 22.0627i 1.44023 0.831518i
\(705\) −0.0997072 0.0446503i −0.00375519 0.00168163i
\(706\) −0.268712 + 0.320239i −0.0101131 + 0.0120523i
\(707\) 10.5978 1.86867i 0.398570 0.0702786i
\(708\) 18.2828 13.2231i 0.687112 0.496956i
\(709\) 19.0902 16.0186i 0.716948 0.601591i −0.209591 0.977789i \(-0.567213\pi\)
0.926539 + 0.376198i \(0.122769\pi\)
\(710\) −4.96005 + 2.86368i −0.186147 + 0.107472i
\(711\) 17.9273 0.548664i 0.672328 0.0205765i
\(712\) −37.9068 13.7969i −1.42062 0.517062i
\(713\) 0.707077 + 4.01003i 0.0264803 + 0.150177i
\(714\) −8.76299 2.20493i −0.327947 0.0825175i
\(715\) 2.21926i 0.0829957i
\(716\) 26.1576 + 9.52058i 0.977555 + 0.355801i
\(717\) −10.1552 + 22.6772i −0.379252 + 0.846895i
\(718\) −11.8916 + 32.6718i −0.443790 + 1.21930i
\(719\) 3.48510 + 0.614518i 0.129972 + 0.0229177i 0.238256 0.971202i \(-0.423424\pi\)
−0.108283 + 0.994120i \(0.534535\pi\)
\(720\) −1.78764 + 0.713305i −0.0666215 + 0.0265833i
\(721\) 3.31537i 0.123471i
\(722\) 37.0861 + 27.7245i 1.38020 + 1.03180i
\(723\) −13.3539 3.36009i −0.496636 0.124963i
\(724\) −98.8388 17.4279i −3.67331 0.647704i
\(725\) 0.949652 + 0.796853i 0.0352692 + 0.0295944i
\(726\) −61.9641 4.46719i −2.29970 0.165793i
\(727\) −2.17554 + 12.3381i −0.0806863 + 0.457595i 0.917518 + 0.397694i \(0.130190\pi\)
−0.998204 + 0.0599007i \(0.980922\pi\)
\(728\) 7.85550 1.38514i 0.291144 0.0513366i
\(729\) −22.0469 + 15.5864i −0.816551 + 0.577273i
\(730\) 5.46547 + 3.15549i 0.202286 + 0.116790i
\(731\) −5.88545 + 1.03776i −0.217681 + 0.0383831i
\(732\) 23.0260 + 47.4698i 0.851066 + 1.75453i
\(733\) 19.4345 + 33.6615i 0.717829 + 1.24332i 0.961858 + 0.273549i \(0.0881975\pi\)
−0.244029 + 0.969768i \(0.578469\pi\)
\(734\) 11.0119 0.406458
\(735\) 0.143569 1.99143i 0.00529560 0.0734549i
\(736\) 0.241579 + 0.0425969i 0.00890472 + 0.00157014i
\(737\) −29.5738 + 24.8154i −1.08937 + 0.914086i
\(738\) −84.2097 12.2053i −3.09980 0.449285i
\(739\) −26.3214 + 9.58021i −0.968249 + 0.352414i −0.777261 0.629179i \(-0.783391\pi\)
−0.190988 + 0.981592i \(0.561169\pi\)
\(740\) 1.75451 + 3.03891i 0.0644972 + 0.111712i
\(741\) −17.8715 + 5.63008i −0.656524 + 0.206826i
\(742\) 5.38113 9.32040i 0.197548 0.342162i
\(743\) −3.32856 + 18.8772i −0.122113 + 0.692536i 0.860868 + 0.508828i \(0.169921\pi\)
−0.982981 + 0.183708i \(0.941190\pi\)
\(744\) 78.9766 8.12868i 2.89542 0.298012i
\(745\) −1.18558 0.431517i −0.0434364 0.0158096i
\(746\) 10.6802 12.7282i 0.391031 0.466012i
\(747\) −2.18191 + 1.94763i −0.0798319 + 0.0712602i
\(748\) −31.4386 54.4533i −1.14951 1.99101i
\(749\) 6.54980 0.239325
\(750\) 6.14232 + 4.16234i 0.224286 + 0.151987i
\(751\) 11.0746 + 13.1982i 0.404118 + 0.481609i 0.929271 0.369399i \(-0.120436\pi\)
−0.525153 + 0.851008i \(0.675992\pi\)
\(752\) −1.12715 + 0.650762i −0.0411030 + 0.0237309i
\(753\) −39.3724 9.90683i −1.43481 0.361025i
\(754\) 0.969948 + 1.15594i 0.0353234 + 0.0420968i
\(755\) 2.35550 + 1.97650i 0.0857254 + 0.0719321i
\(756\) −0.575790 + 13.9090i −0.0209413 + 0.505864i
\(757\) 1.00826 5.71811i 0.0366457 0.207828i −0.960987 0.276593i \(-0.910795\pi\)
0.997633 + 0.0687647i \(0.0219058\pi\)
\(758\) −3.81347 + 4.54471i −0.138511 + 0.165071i
\(759\) −2.64694 2.56717i −0.0960780 0.0931825i
\(760\) 0.529997 3.59330i 0.0192250 0.130343i
\(761\) −12.8353 7.41048i −0.465280 0.268630i 0.248982 0.968508i \(-0.419904\pi\)
−0.714262 + 0.699878i \(0.753237\pi\)
\(762\) −67.1999 + 6.91656i −2.43439 + 0.250561i
\(763\) 1.32474 + 3.63968i 0.0479587 + 0.131765i
\(764\) −21.6146 25.7592i −0.781988 0.931936i
\(765\) −0.617066 1.54645i −0.0223101 0.0559121i
\(766\) 3.39065 + 19.2293i 0.122509 + 0.694783i
\(767\) −7.10800 4.10380i −0.256655 0.148180i
\(768\) 13.2821 52.7867i 0.479277 1.90477i
\(769\) −28.2272 + 23.6854i −1.01790 + 0.854118i −0.989362 0.145475i \(-0.953529\pi\)
−0.0285362 + 0.999593i \(0.509085\pi\)
\(770\) −1.13537 + 0.952691i −0.0409160 + 0.0343326i
\(771\) −2.24483 + 8.92154i −0.0808455 + 0.321301i
\(772\) 30.6393 + 17.6896i 1.10273 + 0.636664i
\(773\) −5.60834 31.8065i −0.201718 1.14400i −0.902521 0.430645i \(-0.858286\pi\)
0.700803 0.713354i \(-0.252825\pi\)
\(774\) 5.14455 + 12.8930i 0.184917 + 0.463428i
\(775\) −30.9803 36.9209i −1.11285 1.32624i
\(776\) −21.9746 60.3746i −0.788840 2.16732i
\(777\) 5.92000 0.609318i 0.212379 0.0218591i
\(778\) −77.6727 44.8444i −2.78470 1.60775i
\(779\) 31.5046 39.7626i 1.12877 1.42464i
\(780\) 2.14329 + 2.07870i 0.0767420 + 0.0744293i
\(781\) −43.4467 + 51.7777i −1.55464 + 1.85275i
\(782\) 0.559174 3.17123i 0.0199960 0.113403i
\(783\) −1.14855 + 0.601198i −0.0410457 + 0.0214851i
\(784\) −18.2214 15.2896i −0.650765 0.546056i
\(785\) 0.928772 + 1.10687i 0.0331493 + 0.0395058i
\(786\) 14.6486 + 3.68587i 0.522500 + 0.131471i
\(787\) 4.58873 2.64930i 0.163570 0.0944374i −0.415980 0.909374i \(-0.636561\pi\)
0.579551 + 0.814936i \(0.303228\pi\)
\(788\) 21.2635 + 25.3408i 0.757481 + 0.902730i
\(789\) −35.6687 24.1709i −1.26984 0.860507i
\(790\) 2.56910 0.0914045
\(791\) −5.21368 9.03035i −0.185377 0.321082i
\(792\) −53.6363 + 47.8772i −1.90588 + 1.70124i
\(793\) 12.3361 14.7016i 0.438068 0.522069i
\(794\) −39.0886 14.2271i −1.38720 0.504901i
\(795\) 1.97266 0.203037i 0.0699630 0.00720097i
\(796\) −4.34332 + 24.6322i −0.153945 + 0.873065i
\(797\) −22.0106 + 38.1235i −0.779655 + 1.35040i 0.152486 + 0.988306i \(0.451272\pi\)
−0.932141 + 0.362096i \(0.882061\pi\)
\(798\) −10.5522 6.72613i −0.373546 0.238102i
\(799\) −0.562961 0.975077i −0.0199161 0.0344957i
\(800\) −2.72845 + 0.993073i −0.0964651 + 0.0351104i
\(801\) −25.3437 3.67331i −0.895474 0.129790i
\(802\) −21.9254 + 18.3976i −0.774213 + 0.649642i
\(803\) 73.3471 + 12.9331i 2.58836 + 0.456398i
\(804\) −3.73479 + 51.8050i −0.131716 + 1.82702i
\(805\) −0.0503437 −0.00177438
\(806\) −29.3332 50.8065i −1.03322 1.78958i
\(807\) 16.6705 + 34.3674i 0.586829 + 1.20979i
\(808\) 73.6374 12.9843i 2.59055 0.456785i
\(809\) 27.7834 + 16.0408i 0.976812 + 0.563963i 0.901306 0.433182i \(-0.142609\pi\)
0.0755062 + 0.997145i \(0.475943\pi\)
\(810\) −3.22480 + 2.13493i −0.113308 + 0.0750138i
\(811\) −38.0489 + 6.70906i −1.33608 + 0.235587i −0.795626 0.605788i \(-0.792858\pi\)
−0.540453 + 0.841374i \(0.681747\pi\)
\(812\) −0.116066 + 0.658242i −0.00407311 + 0.0230998i
\(813\) −0.593457 0.0427843i −0.0208134 0.00150051i
\(814\) 47.8297 + 40.1339i 1.67643 + 1.40669i
\(815\) 0.313600 + 0.0552961i 0.0109849 + 0.00193694i
\(816\) −19.2365 4.84027i −0.673413 0.169443i
\(817\) −8.18758 1.20764i −0.286447 0.0422498i
\(818\) 19.6881i 0.688378i
\(819\) 4.70319 1.87667i 0.164343 0.0655761i
\(820\) −7.96100 1.40374i −0.278010 0.0490207i
\(821\) −6.60547 + 18.1484i −0.230532 + 0.633383i −0.999986 0.00532019i \(-0.998307\pi\)
0.769453 + 0.638703i \(0.220529\pi\)
\(822\) 17.3369 38.7146i 0.604695 1.35033i
\(823\) 17.2703 + 6.28588i 0.602005 + 0.219112i 0.625001 0.780624i \(-0.285098\pi\)
−0.0229964 + 0.999736i \(0.507321\pi\)
\(824\) 23.0365i 0.802513i
\(825\) 42.3261 + 10.6500i 1.47361 + 0.370787i
\(826\) −0.951837 5.39814i −0.0331186 0.187825i
\(827\) 35.4168 + 12.8906i 1.23156 + 0.448252i 0.874132 0.485689i \(-0.161431\pi\)
0.357429 + 0.933940i \(0.383653\pi\)
\(828\) −4.95858 + 0.151757i −0.172323 + 0.00527391i
\(829\) −11.4754 + 6.62535i −0.398559 + 0.230108i −0.685862 0.727732i \(-0.740575\pi\)
0.287303 + 0.957840i \(0.407241\pi\)
\(830\) −0.320923 + 0.269286i −0.0111394 + 0.00934706i
\(831\) 35.3482 25.5657i 1.22622 0.886865i
\(832\) −21.2663 + 3.74982i −0.737276 + 0.130002i
\(833\) 13.2267 15.7630i 0.458278 0.546154i
\(834\) −29.4479 13.1872i −1.01970 0.456634i
\(835\) −2.21935 + 1.28134i −0.0768036 + 0.0443426i
\(836\) −17.5232 85.2937i −0.606052 2.94994i
\(837\) 48.0340 15.2645i 1.66030 0.527617i
\(838\) −3.92687 10.7890i −0.135652 0.372700i
\(839\) 36.8382 13.4080i 1.27180 0.462896i 0.384085 0.923298i \(-0.374517\pi\)
0.887711 + 0.460402i \(0.152295\pi\)
\(840\) −0.0705836 + 0.979059i −0.00243537 + 0.0337808i
\(841\) 27.1926 9.89730i 0.937676 0.341286i
\(842\) 26.1125 71.7434i 0.899895 2.47244i
\(843\) −15.5664 + 4.42729i −0.536134 + 0.152484i
\(844\) 54.7844i 1.88576i
\(845\) −0.412540 + 1.13345i −0.0141918 + 0.0389917i
\(846\) −1.95104 + 1.74155i −0.0670782 + 0.0598759i
\(847\) −5.00493 + 8.66879i −0.171971 + 0.297863i
\(848\) 11.8127 20.4602i 0.405649 0.702605i
\(849\) 6.08268 + 12.5399i 0.208757 + 0.430367i
\(850\) 13.0362 + 35.8166i 0.447137 + 1.22850i
\(851\) 0.368277 + 2.08860i 0.0126244 + 0.0715963i
\(852\) 9.31037 + 90.4575i 0.318968 + 3.09902i
\(853\) 26.3930 + 22.1464i 0.903681 + 0.758278i 0.970906 0.239460i \(-0.0769703\pi\)
−0.0672256 + 0.997738i \(0.521415\pi\)
\(854\) 12.8170 0.438589
\(855\) −0.135245 2.30182i −0.00462527 0.0787206i
\(856\) 45.5106 1.55552
\(857\) 11.9299 + 10.0104i 0.407519 + 0.341949i 0.823391 0.567474i \(-0.192079\pi\)
−0.415872 + 0.909423i \(0.636524\pi\)
\(858\) 48.4865 + 21.7130i 1.65530 + 0.741268i
\(859\) −8.85977 50.2462i −0.302291 1.71438i −0.635988 0.771699i \(-0.719407\pi\)
0.333697 0.942680i \(-0.391704\pi\)
\(860\) 0.451051 + 1.23925i 0.0153807 + 0.0422582i
\(861\) −7.69104 + 11.3496i −0.262110 + 0.386793i
\(862\) 42.8964 74.2988i 1.46106 2.53063i
\(863\) −21.0067 + 36.3847i −0.715076 + 1.23855i 0.247854 + 0.968798i \(0.420275\pi\)
−0.962930 + 0.269751i \(0.913059\pi\)
\(864\) 0.125588 3.03374i 0.00427259 0.103210i
\(865\) 1.15166 3.16417i 0.0391577 0.107585i
\(866\) 74.9337i 2.54635i
\(867\) −2.99771 + 11.9137i −0.101807 + 0.404610i
\(868\) 8.88779 24.4190i 0.301671 0.828835i
\(869\) 28.4905 10.3697i 0.966476 0.351768i
\(870\) −0.167074 + 0.0810421i −0.00566434 + 0.00274758i
\(871\) 17.7538 6.46187i 0.601566 0.218952i
\(872\) 9.20478 + 25.2899i 0.311713 + 0.856425i
\(873\) −21.4645 34.6822i −0.726462 1.17381i
\(874\) 2.12035 3.92307i 0.0717218 0.132700i
\(875\) 1.03534 0.597755i 0.0350010 0.0202078i
\(876\) 81.1916 58.7222i 2.74321 1.98404i
\(877\) −6.10512 + 7.27579i −0.206155 + 0.245686i −0.859208 0.511626i \(-0.829043\pi\)
0.653053 + 0.757312i \(0.273488\pi\)
\(878\) −67.4748 + 11.8976i −2.27717 + 0.401526i
\(879\) −39.4929 17.6855i −1.33206 0.596516i
\(880\) −2.49237 + 2.09135i −0.0840179 + 0.0704994i
\(881\) 12.3480 7.12911i 0.416014 0.240186i −0.277356 0.960767i \(-0.589458\pi\)
0.693371 + 0.720581i \(0.256125\pi\)
\(882\) −42.1041 22.6205i −1.41772 0.761673i
\(883\) 48.1856 + 17.5381i 1.62157 + 0.590205i 0.983681 0.179920i \(-0.0575840\pi\)
0.637893 + 0.770125i \(0.279806\pi\)
\(884\) 5.34339 + 30.3038i 0.179718 + 1.01923i
\(885\) 0.703182 0.725032i 0.0236372 0.0243717i
\(886\) 34.2227i 1.14973i
\(887\) −42.9886 15.6466i −1.44342 0.525360i −0.502671 0.864478i \(-0.667649\pi\)
−0.940744 + 0.339118i \(0.889872\pi\)
\(888\) 41.1344 4.23377i 1.38038 0.142076i
\(889\) −3.72281 + 10.2283i −0.124859 + 0.343047i
\(890\) −3.61241 0.636965i −0.121088 0.0213511i
\(891\) −27.1448 + 36.6920i −0.909384 + 1.22923i
\(892\) 12.9249i 0.432758i
\(893\) −0.313782 1.52733i −0.0105003 0.0511100i
\(894\) −21.0274 + 21.6808i −0.703261 + 0.725114i
\(895\) 1.22711 + 0.216373i 0.0410179 + 0.00723256i
\(896\) −10.4388 8.75917i −0.348735 0.292623i
\(897\) 0.787566 + 1.62362i 0.0262960 + 0.0542112i
\(898\) −10.8023 + 61.2628i −0.360477 + 2.04437i
\(899\) 2.38319 0.420221i 0.0794838 0.0140151i
\(900\) 49.9307 30.9016i 1.66436 1.03005i
\(901\) 17.6997 + 10.2189i 0.589661 + 0.340441i
\(902\) −141.652 + 24.9771i −4.71651 + 0.831648i
\(903\) 2.23086 + 0.160830i 0.0742382 + 0.00535208i
\(904\) −36.2266 62.7464i −1.20488 2.08691i
\(905\) −4.49260 −0.149339
\(906\) 66.2285 32.1253i 2.20029 1.06729i
\(907\) −26.1818 4.61655i −0.869351 0.153290i −0.278857 0.960333i \(-0.589956\pi\)
−0.590493 + 0.807043i \(0.701067\pi\)
\(908\) −38.0119 + 31.8958i −1.26147 + 1.05850i
\(909\) 44.0877 17.5919i 1.46230 0.583486i
\(910\) 0.681590 0.248078i 0.0225945 0.00822372i
\(911\) −2.51245 4.35169i −0.0832412 0.144178i 0.821399 0.570354i \(-0.193194\pi\)
−0.904640 + 0.426176i \(0.859861\pi\)
\(912\) −23.1643 14.7652i −0.767048 0.488925i
\(913\) −2.47201 + 4.28165i −0.0818117 + 0.141702i
\(914\) −5.56205 + 31.5440i −0.183976 + 1.04338i
\(915\) 1.38404 + 1.91364i 0.0457551 + 0.0632628i
\(916\) −15.9996 5.82339i −0.528642 0.192410i
\(917\) 1.56443 1.86442i 0.0516622 0.0615686i
\(918\) −39.8243 1.64861i −1.31440 0.0544121i
\(919\) 26.2111 + 45.3990i 0.864625 + 1.49757i 0.867419 + 0.497578i \(0.165777\pi\)
−0.00279410 + 0.999996i \(0.500889\pi\)
\(920\) −0.349807 −0.0115328
\(921\) −26.2110 + 12.7141i −0.863682 + 0.418943i
\(922\) 4.98796 + 5.94442i 0.164270 + 0.195769i
\(923\) 28.6466 16.5391i 0.942913 0.544391i
\(924\) 6.43757 + 22.6345i 0.211781 + 0.744621i
\(925\) −16.1359 19.2300i −0.530545 0.632279i
\(926\) −5.92769 4.97392i −0.194796 0.163453i
\(927\) −2.97882 14.3175i −0.0978373 0.470248i
\(928\) 0.0253156 0.143572i 0.000831026 0.00471298i
\(929\) 7.27587 8.67105i 0.238714 0.284488i −0.633365 0.773853i \(-0.718327\pi\)
0.872079 + 0.489365i \(0.162771\pi\)
\(930\) 6.94401 1.97497i 0.227703 0.0647619i
\(931\) 24.2683 14.9356i 0.795363 0.489494i
\(932\) 50.3879 + 29.0915i 1.65051 + 0.952923i
\(933\) −11.3446 15.6855i −0.371405 0.513519i
\(934\) −14.0319 38.5523i −0.459138 1.26147i
\(935\) −1.80918 2.15610i −0.0591666 0.0705120i
\(936\) 32.6796 13.0398i 1.06817 0.426220i
\(937\) −6.37744 36.1683i −0.208342 1.18157i −0.892093 0.451851i \(-0.850764\pi\)
0.683752 0.729715i \(-0.260347\pi\)
\(938\) 10.9273 + 6.30888i 0.356789 + 0.205992i
\(939\) −12.0703 11.7065i −0.393898 0.382028i
\(940\) −0.190330 + 0.159706i −0.00620789 + 0.00520904i
\(941\) 42.1364 35.3566i 1.37361 1.15259i 0.402095 0.915598i \(-0.368282\pi\)
0.971511 0.236994i \(-0.0761623\pi\)
\(942\) 33.2699 9.46241i 1.08399 0.308302i
\(943\) −4.23120 2.44289i −0.137787 0.0795513i
\(944\) −2.08948 11.8500i −0.0680066 0.385685i
\(945\) 0.0827324 + 0.617627i 0.00269129 + 0.0200914i
\(946\) 15.0834 + 17.9757i 0.490403 + 0.584439i
\(947\) −18.4440 50.6744i −0.599348 1.64670i −0.752576 0.658505i \(-0.771189\pi\)
0.153228 0.988191i \(-0.451033\pi\)
\(948\) 16.6713 37.2281i 0.541458 1.20911i
\(949\) −31.5656 18.2244i −1.02466 0.591590i
\(950\) 1.48264 + 52.7628i 0.0481033 + 1.71185i
\(951\) 6.37957 25.3541i 0.206872 0.822163i
\(952\) −6.50274 + 7.74966i −0.210755 + 0.251168i
\(953\) −4.48205 + 25.4190i −0.145188 + 0.823401i 0.822028 + 0.569447i \(0.192842\pi\)
−0.967216 + 0.253954i \(0.918269\pi\)
\(954\) 14.8643 45.0852i 0.481249 1.45969i
\(955\) −1.15307 0.967538i −0.0373124 0.0313088i
\(956\) 36.3232 + 43.2883i 1.17478 + 1.40004i
\(957\) −1.52569 + 1.57310i −0.0493185 + 0.0508510i
\(958\) −23.4588 + 13.5440i −0.757920 + 0.437585i
\(959\) −4.39331 5.23575i −0.141867 0.169071i
\(960\) 0.191083 2.65050i 0.00616718 0.0855444i
\(961\) −63.0839 −2.03496
\(962\) −15.2780 26.4623i −0.492582 0.853177i
\(963\) 28.2855 5.88492i 0.911487 0.189639i
\(964\) −20.1301 + 23.9901i −0.648346 + 0.772668i
\(965\) 1.48818 + 0.541654i 0.0479063 + 0.0174365i
\(966\) −0.492555 + 1.09991i −0.0158477 + 0.0353890i
\(967\) −2.59974 + 14.7439i −0.0836020 + 0.474130i 0.914048 + 0.405607i \(0.132940\pi\)
−0.997650 + 0.0685233i \(0.978171\pi\)
\(968\) −34.7762 + 60.2341i −1.11775 + 1.93600i
\(969\) 12.7731 20.0390i 0.410331 0.643745i
\(970\) −2.92115 5.05957i −0.0937923 0.162453i
\(971\) 12.9364 4.70848i 0.415150 0.151102i −0.125996 0.992031i \(-0.540213\pi\)
0.541146 + 0.840928i \(0.317990\pi\)
\(972\) 10.0105 + 60.5835i 0.321086 + 1.94322i
\(973\) −3.98252 + 3.34173i −0.127674 + 0.107131i
\(974\) −79.2564 13.9750i −2.53954 0.447789i
\(975\) −17.6821 11.9822i −0.566279 0.383739i
\(976\) 28.1359 0.900608
\(977\) 10.5020 + 18.1901i 0.335990 + 0.581952i 0.983674 0.179957i \(-0.0575958\pi\)
−0.647684 + 0.761909i \(0.724262\pi\)
\(978\) 4.27633 6.31053i 0.136742 0.201789i
\(979\) −42.6316 + 7.51709i −1.36251 + 0.240247i
\(980\) −3.93242 2.27039i −0.125617 0.0725248i
\(981\) 8.99111 + 14.5278i 0.287064 + 0.463837i
\(982\) 15.7499 2.77713i 0.502599 0.0886218i
\(983\) 4.12942 23.4191i 0.131708 0.746953i −0.845388 0.534153i \(-0.820631\pi\)
0.977096 0.212800i \(-0.0682583\pi\)
\(984\) −53.4403 + 78.8613i −1.70362 + 2.51401i
\(985\) 1.13434 + 0.951823i 0.0361430 + 0.0303276i
\(986\) −1.88469 0.332321i −0.0600206 0.0105833i
\(987\) 0.115275 + 0.405309i 0.00366926 + 0.0129011i
\(988\) −6.21804 + 42.1574i −0.197822 + 1.34120i
\(989\) 0.797061i 0.0253451i
\(990\) −4.04715 + 5.13434i −0.128627 + 0.163180i
\(991\) 27.8616 + 4.91275i 0.885052 + 0.156059i 0.597655 0.801753i \(-0.296099\pi\)
0.287397 + 0.957812i \(0.407210\pi\)
\(992\) −1.93855 + 5.32613i −0.0615491 + 0.169105i
\(993\) −13.3996 18.5268i −0.425222 0.587929i
\(994\) 20.7589 + 7.55561i 0.658431 + 0.239649i
\(995\) 1.11963i 0.0354946i
\(996\) 1.81964 + 6.39784i 0.0576574 + 0.202723i
\(997\) −7.96636 45.1795i −0.252297 1.43085i −0.802917 0.596091i \(-0.796720\pi\)
0.550620 0.834756i \(-0.314391\pi\)
\(998\) 23.9143 + 8.70409i 0.756994 + 0.275523i
\(999\) 25.0182 7.95040i 0.791540 0.251540i
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.14.2 108
3.2 odd 2 513.2.bo.a.71.17 108
9.2 odd 6 171.2.bd.a.128.17 yes 108
9.7 even 3 513.2.cd.a.413.2 108
19.15 odd 18 171.2.bd.a.167.17 yes 108
57.53 even 18 513.2.cd.a.395.2 108
171.34 odd 18 513.2.bo.a.224.17 108
171.110 even 18 inner 171.2.x.a.110.2 yes 108
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
171.2.x.a.14.2 108 1.1 even 1 trivial
171.2.x.a.110.2 yes 108 171.110 even 18 inner
171.2.bd.a.128.17 yes 108 9.2 odd 6
171.2.bd.a.167.17 yes 108 19.15 odd 18
513.2.bo.a.71.17 108 3.2 odd 2
513.2.bo.a.224.17 108 171.34 odd 18
513.2.cd.a.395.2 108 57.53 even 18
513.2.cd.a.413.2 108 9.7 even 3