Properties

Label 81.2.g.a.40.4
Level $81$
Weight $2$
Character 81.40
Analytic conductor $0.647$
Analytic rank $0$
Dimension $144$
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] = [81,2,Mod(4,81)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(81, base_ring=CyclotomicField(54))
 
chi = DirichletCharacter(H, H._module([2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("81.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 81 = 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 81.g (of order \(27\), degree \(18\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.646788256372\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(8\) over \(\Q(\zeta_{27})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label 40.4
Character \(\chi\) \(=\) 81.40
Dual form 81.2.g.a.79.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.00720285 - 0.123668i) q^{2} +(1.39452 - 1.02729i) q^{3} +(1.97123 - 0.230404i) q^{4} +(-3.27944 - 0.777242i) q^{5} +(-0.137087 - 0.165058i) q^{6} +(-2.23379 + 3.00051i) q^{7} +(-0.0857144 - 0.486111i) q^{8} +(0.889352 - 2.86514i) q^{9} +O(q^{10})\) \(q+(-0.00720285 - 0.123668i) q^{2} +(1.39452 - 1.02729i) q^{3} +(1.97123 - 0.230404i) q^{4} +(-3.27944 - 0.777242i) q^{5} +(-0.137087 - 0.165058i) q^{6} +(-2.23379 + 3.00051i) q^{7} +(-0.0857144 - 0.486111i) q^{8} +(0.889352 - 2.86514i) q^{9} +(-0.0724987 + 0.411161i) q^{10} +(3.13353 + 3.32135i) q^{11} +(2.51223 - 2.34633i) q^{12} +(-1.13603 + 0.570535i) q^{13} +(0.387157 + 0.254637i) q^{14} +(-5.37169 + 2.28506i) q^{15} +(3.80282 - 0.901284i) q^{16} +(-1.54764 + 0.563296i) q^{17} +(-0.360733 - 0.0893473i) q^{18} +(-4.14528 - 1.50876i) q^{19} +(-6.64363 - 0.776529i) q^{20} +(-0.0326736 + 6.47901i) q^{21} +(0.388175 - 0.411441i) q^{22} +(-0.637677 - 0.856549i) q^{23} +(-0.618907 - 0.589836i) q^{24} +(5.68246 + 2.85384i) q^{25} +(0.0787396 + 0.136381i) q^{26} +(-1.70312 - 4.90911i) q^{27} +(-3.71200 + 6.42938i) q^{28} +(-1.50657 + 0.990889i) q^{29} +(0.321280 + 0.647847i) q^{30} +(2.68833 - 6.23225i) q^{31} +(-0.421989 - 1.40954i) q^{32} +(7.78175 + 1.41263i) q^{33} +(0.0808092 + 0.187337i) q^{34} +(9.65772 - 8.10379i) q^{35} +(1.09298 - 5.85278i) q^{36} +(-2.46619 - 2.06938i) q^{37} +(-0.156728 + 0.523507i) q^{38} +(-0.998105 + 1.96265i) q^{39} +(-0.0967301 + 1.66079i) q^{40} +(0.0586186 - 1.00644i) q^{41} +(0.801482 - 0.0426266i) q^{42} +(0.660457 - 2.20608i) q^{43} +(6.94218 + 5.82518i) q^{44} +(-5.14349 + 8.70483i) q^{45} +(-0.101335 + 0.0850299i) q^{46} +(3.77360 + 8.74819i) q^{47} +(4.37721 - 5.16345i) q^{48} +(-2.00558 - 6.69911i) q^{49} +(0.311999 - 0.723295i) q^{50} +(-1.57955 + 2.37540i) q^{51} +(-2.10792 + 1.38640i) q^{52} +(1.43978 - 2.49378i) q^{53} +(-0.594833 + 0.245981i) q^{54} +(-7.69474 - 13.3277i) q^{55} +(1.65005 + 0.828685i) q^{56} +(-7.33060 + 2.15442i) q^{57} +(0.133393 + 0.179178i) q^{58} +(7.30814 - 7.74618i) q^{59} +(-10.0624 + 5.74205i) q^{60} +(-5.27275 - 0.616296i) q^{61} +(-0.790095 - 0.287571i) q^{62} +(6.61026 + 9.06865i) q^{63} +(7.17367 - 2.61100i) q^{64} +(4.16898 - 0.988066i) q^{65} +(0.118647 - 0.972529i) q^{66} +(2.54074 + 1.67107i) q^{67} +(-2.92098 + 1.46697i) q^{68} +(-1.76917 - 0.539392i) q^{69} +(-1.07174 - 1.13598i) q^{70} +(-0.346694 + 1.96620i) q^{71} +(-1.46901 - 0.186739i) q^{72} +(2.80114 + 15.8860i) q^{73} +(-0.238153 + 0.319894i) q^{74} +(10.8560 - 1.85781i) q^{75} +(-8.51895 - 2.01903i) q^{76} +(-16.9654 + 1.98297i) q^{77} +(0.249906 + 0.109297i) q^{78} +(0.326714 + 5.60945i) q^{79} -13.1716 q^{80} +(-7.41811 - 5.09624i) q^{81} -0.124887 q^{82} +(-0.701083 - 12.0371i) q^{83} +(1.42838 + 12.7792i) q^{84} +(5.51322 - 0.644403i) q^{85} +(-0.277579 - 0.0657875i) q^{86} +(-1.08301 + 2.92950i) q^{87} +(1.34595 - 1.80793i) q^{88} +(1.69819 + 9.63089i) q^{89} +(1.11356 + 0.573386i) q^{90} +(0.825760 - 4.68312i) q^{91} +(-1.45436 - 1.54153i) q^{92} +(-2.65341 - 11.4527i) q^{93} +(1.05469 - 0.529686i) q^{94} +(12.4215 + 8.16978i) q^{95} +(-2.03648 - 1.53212i) q^{96} +(-9.14226 + 2.16676i) q^{97} +(-0.814020 + 0.296279i) q^{98} +(12.3030 - 6.02417i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} - 18 q^{10} - 18 q^{11} - 18 q^{12} - 18 q^{13} - 18 q^{14} - 18 q^{15} - 18 q^{16} - 18 q^{17} - 9 q^{18} - 18 q^{19} + 18 q^{20} + 9 q^{21} - 18 q^{22} + 9 q^{23} + 36 q^{24} - 18 q^{25} + 45 q^{26} + 9 q^{27} - 9 q^{28} + 9 q^{29} + 36 q^{30} - 18 q^{31} + 36 q^{32} + 9 q^{33} - 18 q^{34} + 9 q^{35} + 18 q^{36} - 18 q^{37} - 9 q^{38} - 18 q^{39} - 18 q^{40} + 27 q^{42} - 18 q^{43} + 54 q^{44} + 36 q^{45} - 18 q^{46} + 36 q^{47} + 81 q^{48} - 18 q^{49} + 99 q^{50} + 45 q^{51} + 45 q^{53} + 108 q^{54} - 9 q^{55} + 126 q^{56} + 36 q^{57} - 18 q^{58} + 45 q^{59} + 99 q^{60} - 18 q^{61} + 81 q^{62} + 36 q^{63} - 18 q^{64} - 18 q^{66} + 9 q^{67} - 99 q^{68} - 72 q^{69} + 36 q^{70} - 90 q^{71} - 234 q^{72} - 18 q^{73} - 162 q^{74} - 108 q^{75} + 63 q^{76} - 162 q^{77} - 135 q^{78} + 36 q^{79} - 288 q^{80} - 90 q^{81} - 36 q^{82} - 90 q^{83} - 243 q^{84} + 36 q^{85} - 162 q^{86} - 162 q^{87} + 63 q^{88} - 81 q^{89} - 99 q^{90} - 18 q^{91} - 144 q^{92} + 36 q^{94} + 18 q^{95} - 27 q^{96} + 9 q^{97} + 81 q^{98} + 54 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/81\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{13}{27}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.00720285 0.123668i −0.00509318 0.0874466i 0.994804 0.101812i \(-0.0324641\pi\)
−0.999897 + 0.0143658i \(0.995427\pi\)
\(3\) 1.39452 1.02729i 0.805124 0.593106i
\(4\) 1.97123 0.230404i 0.985617 0.115202i
\(5\) −3.27944 0.777242i −1.46661 0.347593i −0.581719 0.813390i \(-0.697620\pi\)
−0.884892 + 0.465797i \(0.845768\pi\)
\(6\) −0.137087 0.165058i −0.0559657 0.0673846i
\(7\) −2.23379 + 3.00051i −0.844295 + 1.13409i 0.145183 + 0.989405i \(0.453623\pi\)
−0.989478 + 0.144680i \(0.953785\pi\)
\(8\) −0.0857144 0.486111i −0.0303046 0.171866i
\(9\) 0.889352 2.86514i 0.296451 0.955048i
\(10\) −0.0724987 + 0.411161i −0.0229261 + 0.130020i
\(11\) 3.13353 + 3.32135i 0.944795 + 1.00142i 0.999996 + 0.00294930i \(0.000938793\pi\)
−0.0552003 + 0.998475i \(0.517580\pi\)
\(12\) 2.51223 2.34633i 0.725218 0.677328i
\(13\) −1.13603 + 0.570535i −0.315077 + 0.158238i −0.599309 0.800518i \(-0.704558\pi\)
0.284232 + 0.958756i \(0.408262\pi\)
\(14\) 0.387157 + 0.254637i 0.103472 + 0.0680546i
\(15\) −5.37169 + 2.28506i −1.38696 + 0.590000i
\(16\) 3.80282 0.901284i 0.950704 0.225321i
\(17\) −1.54764 + 0.563296i −0.375359 + 0.136619i −0.522808 0.852450i \(-0.675116\pi\)
0.147450 + 0.989070i \(0.452893\pi\)
\(18\) −0.360733 0.0893473i −0.0850255 0.0210594i
\(19\) −4.14528 1.50876i −0.950993 0.346133i −0.180495 0.983576i \(-0.557770\pi\)
−0.770498 + 0.637443i \(0.779992\pi\)
\(20\) −6.64363 0.776529i −1.48556 0.173637i
\(21\) −0.0326736 + 6.47901i −0.00712997 + 1.41384i
\(22\) 0.388175 0.411441i 0.0827591 0.0877195i
\(23\) −0.637677 0.856549i −0.132965 0.178603i 0.730654 0.682748i \(-0.239215\pi\)
−0.863619 + 0.504145i \(0.831808\pi\)
\(24\) −0.618907 0.589836i −0.126334 0.120400i
\(25\) 5.68246 + 2.85384i 1.13649 + 0.570768i
\(26\) 0.0787396 + 0.136381i 0.0154421 + 0.0267465i
\(27\) −1.70312 4.90911i −0.327765 0.944759i
\(28\) −3.71200 + 6.42938i −0.701503 + 1.21504i
\(29\) −1.50657 + 0.990889i −0.279764 + 0.184003i −0.681634 0.731693i \(-0.738731\pi\)
0.401871 + 0.915696i \(0.368360\pi\)
\(30\) 0.321280 + 0.647847i 0.0586575 + 0.118280i
\(31\) 2.68833 6.23225i 0.482839 1.11935i −0.486514 0.873673i \(-0.661732\pi\)
0.969353 0.245673i \(-0.0790090\pi\)
\(32\) −0.421989 1.40954i −0.0745978 0.249174i
\(33\) 7.78175 + 1.41263i 1.35463 + 0.245908i
\(34\) 0.0808092 + 0.187337i 0.0138587 + 0.0321280i
\(35\) 9.65772 8.10379i 1.63245 1.36979i
\(36\) 1.09298 5.85278i 0.182163 0.975464i
\(37\) −2.46619 2.06938i −0.405439 0.340204i 0.417152 0.908837i \(-0.363028\pi\)
−0.822592 + 0.568633i \(0.807473\pi\)
\(38\) −0.156728 + 0.523507i −0.0254246 + 0.0849240i
\(39\) −0.998105 + 1.96265i −0.159825 + 0.314275i
\(40\) −0.0967301 + 1.66079i −0.0152944 + 0.262594i
\(41\) 0.0586186 1.00644i 0.00915468 0.157180i −0.990633 0.136554i \(-0.956397\pi\)
0.999787 0.0206256i \(-0.00656578\pi\)
\(42\) 0.801482 0.0426266i 0.123671 0.00657743i
\(43\) 0.660457 2.20608i 0.100719 0.336424i −0.892746 0.450559i \(-0.851225\pi\)
0.993465 + 0.114135i \(0.0364097\pi\)
\(44\) 6.94218 + 5.82518i 1.04657 + 0.878179i
\(45\) −5.14349 + 8.70483i −0.766746 + 1.29764i
\(46\) −0.101335 + 0.0850299i −0.0149410 + 0.0125370i
\(47\) 3.77360 + 8.74819i 0.550436 + 1.27605i 0.935553 + 0.353187i \(0.114902\pi\)
−0.385116 + 0.922868i \(0.625839\pi\)
\(48\) 4.37721 5.16345i 0.631796 0.745280i
\(49\) −2.00558 6.69911i −0.286512 0.957015i
\(50\) 0.311999 0.723295i 0.0441233 0.102289i
\(51\) −1.57955 + 2.37540i −0.221181 + 0.332623i
\(52\) −2.10792 + 1.38640i −0.292316 + 0.192260i
\(53\) 1.43978 2.49378i 0.197769 0.342547i −0.750035 0.661398i \(-0.769964\pi\)
0.947805 + 0.318851i \(0.103297\pi\)
\(54\) −0.594833 + 0.245981i −0.0809466 + 0.0334738i
\(55\) −7.69474 13.3277i −1.03756 1.79710i
\(56\) 1.65005 + 0.828685i 0.220497 + 0.110738i
\(57\) −7.33060 + 2.15442i −0.970962 + 0.285359i
\(58\) 0.133393 + 0.179178i 0.0175154 + 0.0235272i
\(59\) 7.30814 7.74618i 0.951439 1.00847i −0.0485142 0.998822i \(-0.515449\pi\)
0.999953 0.00964429i \(-0.00306992\pi\)
\(60\) −10.0624 + 5.74205i −1.29905 + 0.741295i
\(61\) −5.27275 0.616296i −0.675107 0.0789086i −0.228370 0.973574i \(-0.573340\pi\)
−0.446736 + 0.894666i \(0.647414\pi\)
\(62\) −0.790095 0.287571i −0.100342 0.0365215i
\(63\) 6.61026 + 9.06865i 0.832814 + 1.14254i
\(64\) 7.17367 2.61100i 0.896708 0.326375i
\(65\) 4.16898 0.988066i 0.517098 0.122555i
\(66\) 0.118647 0.972529i 0.0146044 0.119710i
\(67\) 2.54074 + 1.67107i 0.310400 + 0.204154i 0.695145 0.718869i \(-0.255340\pi\)
−0.384745 + 0.923023i \(0.625710\pi\)
\(68\) −2.92098 + 1.46697i −0.354221 + 0.177897i
\(69\) −1.76917 0.539392i −0.212984 0.0649352i
\(70\) −1.07174 1.13598i −0.128098 0.135776i
\(71\) −0.346694 + 1.96620i −0.0411451 + 0.233345i −0.998445 0.0557526i \(-0.982244\pi\)
0.957300 + 0.289098i \(0.0933553\pi\)
\(72\) −1.46901 0.186739i −0.173124 0.0220074i
\(73\) 2.80114 + 15.8860i 0.327848 + 1.85932i 0.488854 + 0.872366i \(0.337415\pi\)
−0.161006 + 0.986953i \(0.551474\pi\)
\(74\) −0.238153 + 0.319894i −0.0276847 + 0.0371870i
\(75\) 10.8560 1.85781i 1.25354 0.214521i
\(76\) −8.51895 2.01903i −0.977191 0.231598i
\(77\) −16.9654 + 1.98297i −1.93339 + 0.225981i
\(78\) 0.249906 + 0.109297i 0.0282963 + 0.0123755i
\(79\) 0.326714 + 5.60945i 0.0367581 + 0.631113i 0.965503 + 0.260393i \(0.0838521\pi\)
−0.928745 + 0.370720i \(0.879111\pi\)
\(80\) −13.1716 −1.47263
\(81\) −7.41811 5.09624i −0.824234 0.566249i
\(82\) −0.124887 −0.0137915
\(83\) −0.701083 12.0371i −0.0769538 1.32125i −0.786940 0.617030i \(-0.788336\pi\)
0.709986 0.704216i \(-0.248701\pi\)
\(84\) 1.42838 + 12.7792i 0.155850 + 1.39432i
\(85\) 5.51322 0.644403i 0.597993 0.0698953i
\(86\) −0.277579 0.0657875i −0.0299321 0.00709404i
\(87\) −1.08301 + 2.92950i −0.116111 + 0.314075i
\(88\) 1.34595 1.80793i 0.143479 0.192726i
\(89\) 1.69819 + 9.63089i 0.180007 + 1.02087i 0.932204 + 0.361934i \(0.117883\pi\)
−0.752197 + 0.658939i \(0.771006\pi\)
\(90\) 1.11356 + 0.573386i 0.117379 + 0.0604402i
\(91\) 0.825760 4.68312i 0.0865631 0.490924i
\(92\) −1.45436 1.54153i −0.151628 0.160716i
\(93\) −2.65341 11.4527i −0.275145 1.18759i
\(94\) 1.05469 0.529686i 0.108783 0.0546329i
\(95\) 12.4215 + 8.16978i 1.27442 + 0.838201i
\(96\) −2.03648 1.53212i −0.207847 0.156372i
\(97\) −9.14226 + 2.16676i −0.928256 + 0.220001i −0.666819 0.745220i \(-0.732345\pi\)
−0.261437 + 0.965220i \(0.584196\pi\)
\(98\) −0.814020 + 0.296279i −0.0822284 + 0.0299287i
\(99\) 12.3030 6.02417i 1.23649 0.605452i
\(100\) 11.8590 + 4.31632i 1.18590 + 0.431632i
\(101\) 5.43839 + 0.635656i 0.541140 + 0.0632502i 0.382272 0.924050i \(-0.375142\pi\)
0.158868 + 0.987300i \(0.449216\pi\)
\(102\) 0.305139 + 0.178230i 0.0302132 + 0.0176474i
\(103\) 1.60904 1.70548i 0.158543 0.168046i −0.643233 0.765671i \(-0.722407\pi\)
0.801776 + 0.597625i \(0.203889\pi\)
\(104\) 0.374717 + 0.503332i 0.0367440 + 0.0493558i
\(105\) 5.14291 21.2221i 0.501896 2.07107i
\(106\) −0.318771 0.160093i −0.0309618 0.0155496i
\(107\) −5.88377 10.1910i −0.568805 0.985200i −0.996684 0.0813640i \(-0.974072\pi\)
0.427879 0.903836i \(-0.359261\pi\)
\(108\) −4.48832 9.28461i −0.431889 0.893412i
\(109\) −0.211790 + 0.366831i −0.0202858 + 0.0351361i −0.875990 0.482329i \(-0.839791\pi\)
0.855704 + 0.517465i \(0.173124\pi\)
\(110\) −1.59278 + 1.04759i −0.151866 + 0.0998839i
\(111\) −5.56499 0.352292i −0.528206 0.0334381i
\(112\) −5.79040 + 13.4237i −0.547142 + 1.26842i
\(113\) 3.93747 + 13.1521i 0.370406 + 1.23724i 0.916675 + 0.399633i \(0.130863\pi\)
−0.546269 + 0.837610i \(0.683952\pi\)
\(114\) 0.319234 + 0.891043i 0.0298990 + 0.0834539i
\(115\) 1.42548 + 3.30463i 0.132926 + 0.308158i
\(116\) −2.74151 + 2.30040i −0.254542 + 0.213586i
\(117\) 0.624335 + 3.76229i 0.0577198 + 0.347824i
\(118\) −1.01059 0.847990i −0.0930328 0.0780638i
\(119\) 1.76694 5.90200i 0.161975 0.541036i
\(120\) 1.57122 + 2.41537i 0.143432 + 0.220492i
\(121\) −0.572749 + 9.83372i −0.0520681 + 0.893975i
\(122\) −0.0382374 + 0.656510i −0.00346185 + 0.0594376i
\(123\) −0.952163 1.46372i −0.0858536 0.131979i
\(124\) 3.86340 12.9046i 0.346943 1.15887i
\(125\) −3.50823 2.94375i −0.313785 0.263297i
\(126\) 1.07389 0.882798i 0.0956698 0.0786459i
\(127\) 2.77429 2.32790i 0.246178 0.206568i −0.511346 0.859375i \(-0.670853\pi\)
0.757524 + 0.652807i \(0.226409\pi\)
\(128\) −1.54011 3.57039i −0.136128 0.315581i
\(129\) −1.34527 3.75490i −0.118444 0.330600i
\(130\) −0.152221 0.508453i −0.0133506 0.0445943i
\(131\) −2.47542 + 5.73866i −0.216278 + 0.501389i −0.991470 0.130337i \(-0.958394\pi\)
0.775192 + 0.631726i \(0.217653\pi\)
\(132\) 15.6651 + 0.991680i 1.36347 + 0.0863147i
\(133\) 13.7868 9.06769i 1.19546 0.786269i
\(134\) 0.188357 0.326245i 0.0162716 0.0281832i
\(135\) 1.76970 + 17.4229i 0.152312 + 1.49952i
\(136\) 0.406480 + 0.704043i 0.0348553 + 0.0603712i
\(137\) −14.6344 7.34965i −1.25030 0.627923i −0.304448 0.952529i \(-0.598472\pi\)
−0.945849 + 0.324606i \(0.894768\pi\)
\(138\) −0.0539625 + 0.222676i −0.00459360 + 0.0189554i
\(139\) 11.6699 + 15.6754i 0.989827 + 1.32957i 0.943760 + 0.330630i \(0.107261\pi\)
0.0460666 + 0.998938i \(0.485331\pi\)
\(140\) 17.1705 18.1996i 1.45117 1.53815i
\(141\) 14.2493 + 8.32292i 1.20001 + 0.700916i
\(142\) 0.245654 + 0.0287128i 0.0206148 + 0.00240952i
\(143\) −5.45472 1.98536i −0.456147 0.166024i
\(144\) 0.799733 11.6972i 0.0666444 0.974765i
\(145\) 5.71088 2.07859i 0.474263 0.172617i
\(146\) 1.94442 0.460836i 0.160921 0.0381390i
\(147\) −9.67874 7.28170i −0.798289 0.600585i
\(148\) −5.33823 3.51101i −0.438800 0.288603i
\(149\) −3.65975 + 1.83800i −0.299819 + 0.150575i −0.592349 0.805682i \(-0.701799\pi\)
0.292530 + 0.956256i \(0.405503\pi\)
\(150\) −0.307946 1.32916i −0.0251437 0.108525i
\(151\) −6.08551 6.45026i −0.495232 0.524915i 0.430756 0.902468i \(-0.358247\pi\)
−0.925988 + 0.377553i \(0.876765\pi\)
\(152\) −0.378114 + 2.14439i −0.0306691 + 0.173933i
\(153\) 0.237525 + 4.93519i 0.0192028 + 0.398986i
\(154\) 0.367429 + 2.08380i 0.0296083 + 0.167917i
\(155\) −13.6602 + 18.3488i −1.09721 + 1.47381i
\(156\) −1.51530 + 4.09881i −0.121321 + 0.328167i
\(157\) 5.15953 + 1.22283i 0.411776 + 0.0975926i 0.431282 0.902217i \(-0.358061\pi\)
−0.0195065 + 0.999810i \(0.506210\pi\)
\(158\) 0.691357 0.0808081i 0.0550014 0.00642875i
\(159\) −0.554031 4.95669i −0.0439375 0.393091i
\(160\) 0.288333 + 4.95049i 0.0227948 + 0.391371i
\(161\) 3.99452 0.314812
\(162\) −0.576811 + 0.954091i −0.0453186 + 0.0749604i
\(163\) −4.86655 −0.381178 −0.190589 0.981670i \(-0.561040\pi\)
−0.190589 + 0.981670i \(0.561040\pi\)
\(164\) −0.116338 1.99744i −0.00908444 0.155974i
\(165\) −24.4218 10.6809i −1.90124 0.831510i
\(166\) −1.48356 + 0.173403i −0.115146 + 0.0134587i
\(167\) −21.7466 5.15404i −1.68280 0.398831i −0.725569 0.688150i \(-0.758423\pi\)
−0.957233 + 0.289318i \(0.906571\pi\)
\(168\) 3.15232 0.539462i 0.243207 0.0416204i
\(169\) −6.79801 + 9.13132i −0.522924 + 0.702409i
\(170\) −0.119403 0.677168i −0.00915779 0.0519364i
\(171\) −8.00943 + 10.5350i −0.612497 + 0.805633i
\(172\) 0.793626 4.50088i 0.0605134 0.343189i
\(173\) 2.39525 + 2.53882i 0.182108 + 0.193023i 0.811996 0.583663i \(-0.198381\pi\)
−0.629889 + 0.776686i \(0.716899\pi\)
\(174\) 0.370086 + 0.112833i 0.0280562 + 0.00855387i
\(175\) −21.2564 + 10.6754i −1.60683 + 0.806983i
\(176\) 14.9097 + 9.80628i 1.12386 + 0.739176i
\(177\) 2.23376 18.3098i 0.167899 1.37625i
\(178\) 1.17880 0.279381i 0.0883550 0.0209405i
\(179\) −14.1428 + 5.14757i −1.05709 + 0.384748i −0.811332 0.584585i \(-0.801257\pi\)
−0.245753 + 0.969333i \(0.579035\pi\)
\(180\) −8.13339 + 18.3443i −0.606227 + 1.36731i
\(181\) −2.01428 0.733137i −0.149720 0.0544936i 0.266073 0.963953i \(-0.414274\pi\)
−0.415793 + 0.909459i \(0.636496\pi\)
\(182\) −0.585100 0.0683884i −0.0433705 0.00506928i
\(183\) −7.98605 + 4.55721i −0.590346 + 0.336878i
\(184\) −0.361719 + 0.383400i −0.0266663 + 0.0282646i
\(185\) 6.47932 + 8.70323i 0.476369 + 0.639874i
\(186\) −1.39722 + 0.410634i −0.102449 + 0.0301091i
\(187\) −6.72049 3.37516i −0.491451 0.246816i
\(188\) 9.45428 + 16.3753i 0.689524 + 1.19429i
\(189\) 18.5342 + 5.85574i 1.34817 + 0.425942i
\(190\) 0.920870 1.59499i 0.0668069 0.115713i
\(191\) 17.3988 11.4434i 1.25893 0.828014i 0.268139 0.963380i \(-0.413591\pi\)
0.990796 + 0.135366i \(0.0432210\pi\)
\(192\) 7.32154 11.0105i 0.528387 0.794615i
\(193\) 5.58282 12.9424i 0.401860 0.931617i −0.590362 0.807139i \(-0.701015\pi\)
0.992222 0.124478i \(-0.0397257\pi\)
\(194\) 0.333809 + 1.11500i 0.0239661 + 0.0800523i
\(195\) 4.79868 5.66062i 0.343641 0.405366i
\(196\) −5.49697 12.7434i −0.392641 0.910244i
\(197\) 1.46772 1.23157i 0.104571 0.0877455i −0.589003 0.808131i \(-0.700479\pi\)
0.693574 + 0.720385i \(0.256035\pi\)
\(198\) −0.833614 1.47809i −0.0592424 0.105043i
\(199\) 12.3341 + 10.3495i 0.874339 + 0.733658i 0.965007 0.262223i \(-0.0844557\pi\)
−0.0906679 + 0.995881i \(0.528900\pi\)
\(200\) 0.900213 3.00692i 0.0636547 0.212621i
\(201\) 5.25977 0.279740i 0.370996 0.0197313i
\(202\) 0.0394385 0.677134i 0.00277489 0.0476430i
\(203\) 0.392207 6.73393i 0.0275275 0.472629i
\(204\) −2.56635 + 5.04641i −0.179681 + 0.353319i
\(205\) −0.974485 + 3.25501i −0.0680610 + 0.227340i
\(206\) −0.222503 0.186703i −0.0155025 0.0130082i
\(207\) −3.02125 + 1.06526i −0.209992 + 0.0740409i
\(208\) −3.80589 + 3.19352i −0.263891 + 0.221431i
\(209\) −7.97826 18.4957i −0.551868 1.27937i
\(210\) −2.66154 0.483154i −0.183664 0.0333408i
\(211\) −1.10667 3.69652i −0.0761860 0.254479i 0.911409 0.411502i \(-0.134996\pi\)
−0.987595 + 0.157023i \(0.949810\pi\)
\(212\) 2.26357 5.24756i 0.155463 0.360404i
\(213\) 1.53639 + 3.09806i 0.105272 + 0.212275i
\(214\) −1.21792 + 0.801039i −0.0832553 + 0.0547579i
\(215\) −3.88059 + 6.72138i −0.264654 + 0.458394i
\(216\) −2.24039 + 1.24869i −0.152439 + 0.0849623i
\(217\) 12.6947 + 21.9879i 0.861775 + 1.49264i
\(218\) 0.0468908 + 0.0235495i 0.00317585 + 0.00159497i
\(219\) 20.2258 + 19.2758i 1.36673 + 1.30253i
\(220\) −18.2389 24.4991i −1.22967 1.65173i
\(221\) 1.43679 1.52290i 0.0966486 0.102442i
\(222\) −0.00348345 + 0.690750i −0.000233794 + 0.0463601i
\(223\) −2.97171 0.347344i −0.199001 0.0232598i 0.0160086 0.999872i \(-0.494904\pi\)
−0.215009 + 0.976612i \(0.568978\pi\)
\(224\) 5.17198 + 1.88245i 0.345567 + 0.125776i
\(225\) 13.2304 13.7430i 0.882025 0.916201i
\(226\) 1.59813 0.581672i 0.106306 0.0386923i
\(227\) 23.3853 5.54241i 1.55214 0.367863i 0.636953 0.770902i \(-0.280194\pi\)
0.915183 + 0.403039i \(0.132046\pi\)
\(228\) −13.9539 + 5.93586i −0.924123 + 0.393112i
\(229\) 3.95450 + 2.60092i 0.261321 + 0.171873i 0.673408 0.739271i \(-0.264830\pi\)
−0.412087 + 0.911144i \(0.635200\pi\)
\(230\) 0.398410 0.200089i 0.0262704 0.0131935i
\(231\) −21.6214 + 20.1937i −1.42259 + 1.32865i
\(232\) 0.610817 + 0.647428i 0.0401021 + 0.0425057i
\(233\) −1.81475 + 10.2920i −0.118888 + 0.674250i 0.865863 + 0.500282i \(0.166770\pi\)
−0.984751 + 0.173968i \(0.944341\pi\)
\(234\) 0.460778 0.104310i 0.0301220 0.00681893i
\(235\) −5.57584 31.6222i −0.363728 2.06280i
\(236\) 12.6213 16.9534i 0.821578 1.10357i
\(237\) 6.21814 + 7.48685i 0.403912 + 0.486323i
\(238\) −0.742616 0.176003i −0.0481367 0.0114086i
\(239\) 15.7205 1.83746i 1.01687 0.118855i 0.408707 0.912666i \(-0.365980\pi\)
0.608165 + 0.793810i \(0.291906\pi\)
\(240\) −18.3680 + 13.5311i −1.18565 + 0.873427i
\(241\) −1.02572 17.6110i −0.0660726 1.13442i −0.854554 0.519363i \(-0.826169\pi\)
0.788481 0.615059i \(-0.210868\pi\)
\(242\) 1.22024 0.0784402
\(243\) −15.5800 + 0.513747i −0.999457 + 0.0329569i
\(244\) −10.5358 −0.674487
\(245\) 1.37036 + 23.5281i 0.0875490 + 1.50316i
\(246\) −0.174157 + 0.128295i −0.0111038 + 0.00817980i
\(247\) 5.56996 0.651035i 0.354408 0.0414243i
\(248\) −3.25999 0.772633i −0.207010 0.0490622i
\(249\) −13.3433 16.0658i −0.845596 1.01813i
\(250\) −0.338779 + 0.455059i −0.0214263 + 0.0287805i
\(251\) −3.58499 20.3315i −0.226282 1.28331i −0.860218 0.509926i \(-0.829673\pi\)
0.633936 0.773386i \(-0.281438\pi\)
\(252\) 15.1198 + 16.3534i 0.952459 + 1.03017i
\(253\) 0.846717 4.80197i 0.0532326 0.301897i
\(254\) −0.307870 0.326323i −0.0193175 0.0204753i
\(255\) 7.02629 6.56230i 0.440003 0.410947i
\(256\) 13.2136 6.63614i 0.825852 0.414758i
\(257\) −6.08872 4.00462i −0.379804 0.249801i 0.345224 0.938520i \(-0.387803\pi\)
−0.725028 + 0.688719i \(0.758173\pi\)
\(258\) −0.454671 + 0.193412i −0.0283066 + 0.0120413i
\(259\) 11.7181 2.77725i 0.728130 0.172570i
\(260\) 7.99038 2.90826i 0.495542 0.180363i
\(261\) 1.49917 + 5.19780i 0.0927961 + 0.321736i
\(262\) 0.727519 + 0.264795i 0.0449463 + 0.0163591i
\(263\) 10.3713 + 1.21223i 0.639521 + 0.0747493i 0.429673 0.902985i \(-0.358629\pi\)
0.209848 + 0.977734i \(0.432703\pi\)
\(264\) 0.0196872 3.90387i 0.00121166 0.240267i
\(265\) −6.65995 + 7.05914i −0.409118 + 0.433639i
\(266\) −1.22069 1.63967i −0.0748452 0.100535i
\(267\) 12.2619 + 11.6859i 0.750414 + 0.715166i
\(268\) 5.39341 + 2.70867i 0.329455 + 0.165459i
\(269\) −11.1578 19.3259i −0.680304 1.17832i −0.974888 0.222695i \(-0.928515\pi\)
0.294585 0.955625i \(-0.404819\pi\)
\(270\) 2.14191 0.344350i 0.130352 0.0209565i
\(271\) 11.6312 20.1458i 0.706544 1.22377i −0.259588 0.965720i \(-0.583587\pi\)
0.966132 0.258050i \(-0.0830800\pi\)
\(272\) −5.37771 + 3.53698i −0.326072 + 0.214461i
\(273\) −3.65938 7.37898i −0.221476 0.446596i
\(274\) −0.803509 + 1.86274i −0.0485417 + 0.112532i
\(275\) 8.32758 + 27.8160i 0.502172 + 1.67737i
\(276\) −3.61174 0.655643i −0.217401 0.0394651i
\(277\) 3.50985 + 8.13675i 0.210886 + 0.488890i 0.990524 0.137342i \(-0.0438558\pi\)
−0.779637 + 0.626231i \(0.784597\pi\)
\(278\) 1.85449 1.55610i 0.111225 0.0933287i
\(279\) −15.4654 13.2451i −0.925891 0.792965i
\(280\) −4.76714 4.00011i −0.284891 0.239052i
\(281\) −6.16156 + 20.5810i −0.367568 + 1.22776i 0.551671 + 0.834062i \(0.313990\pi\)
−0.919239 + 0.393700i \(0.871195\pi\)
\(282\) 0.926644 1.82213i 0.0551808 0.108506i
\(283\) 0.0355631 0.610594i 0.00211401 0.0362961i −0.997086 0.0762833i \(-0.975695\pi\)
0.999200 + 0.0399872i \(0.0127317\pi\)
\(284\) −0.230395 + 3.95573i −0.0136714 + 0.234729i
\(285\) 25.7148 1.36763i 1.52321 0.0810116i
\(286\) −0.206236 + 0.688875i −0.0121950 + 0.0407341i
\(287\) 2.88890 + 2.42407i 0.170526 + 0.143088i
\(288\) −4.41384 0.0445190i −0.260088 0.00262331i
\(289\) −10.9449 + 9.18383i −0.643815 + 0.540225i
\(290\) −0.298190 0.691282i −0.0175103 0.0405935i
\(291\) −10.5232 + 12.4133i −0.616878 + 0.727682i
\(292\) 9.18191 + 30.6697i 0.537330 + 1.79481i
\(293\) 12.2618 28.4261i 0.716344 1.66067i −0.0338263 0.999428i \(-0.510769\pi\)
0.750170 0.661245i \(-0.229971\pi\)
\(294\) −0.830800 + 1.24940i −0.0484532 + 0.0728665i
\(295\) −29.9873 + 19.7229i −1.74593 + 1.14831i
\(296\) −0.794559 + 1.37622i −0.0461828 + 0.0799910i
\(297\) 10.9681 21.0395i 0.636434 1.22084i
\(298\) 0.253662 + 0.439356i 0.0146943 + 0.0254512i
\(299\) 1.21311 + 0.609246i 0.0701559 + 0.0352336i
\(300\) 20.9717 6.16345i 1.21080 0.355847i
\(301\) 5.14404 + 6.90964i 0.296497 + 0.398265i
\(302\) −0.753859 + 0.799044i −0.0433797 + 0.0459798i
\(303\) 8.23692 4.70037i 0.473199 0.270029i
\(304\) −17.1236 2.00146i −0.982104 0.114792i
\(305\) 16.8127 + 6.11931i 0.962690 + 0.350391i
\(306\) 0.608615 0.0649217i 0.0347922 0.00371133i
\(307\) −21.3773 + 7.78069i −1.22007 + 0.444068i −0.870184 0.492726i \(-0.836000\pi\)
−0.349882 + 0.936794i \(0.613778\pi\)
\(308\) −32.9859 + 7.81780i −1.87955 + 0.445461i
\(309\) 0.491808 4.03127i 0.0279780 0.229331i
\(310\) 2.36756 + 1.55717i 0.134468 + 0.0884411i
\(311\) −27.3750 + 13.7482i −1.55229 + 0.779591i −0.998588 0.0531218i \(-0.983083\pi\)
−0.553705 + 0.832713i \(0.686787\pi\)
\(312\) 1.03962 + 0.316962i 0.0588567 + 0.0179444i
\(313\) 15.6532 + 16.5914i 0.884770 + 0.937802i 0.998447 0.0557161i \(-0.0177442\pi\)
−0.113676 + 0.993518i \(0.536263\pi\)
\(314\) 0.114062 0.646878i 0.00643689 0.0365054i
\(315\) −14.6294 34.8779i −0.824274 1.96515i
\(316\) 1.93647 + 10.9823i 0.108935 + 0.617801i
\(317\) −4.79052 + 6.43479i −0.269062 + 0.361414i −0.916034 0.401100i \(-0.868628\pi\)
0.646972 + 0.762514i \(0.276035\pi\)
\(318\) −0.608994 + 0.104218i −0.0341507 + 0.00584427i
\(319\) −8.01199 1.89888i −0.448585 0.106317i
\(320\) −25.5550 + 2.98695i −1.42857 + 0.166976i
\(321\) −18.6741 8.16716i −1.04229 0.455847i
\(322\) −0.0287719 0.493995i −0.00160340 0.0275292i
\(323\) 7.26530 0.404252
\(324\) −15.7970 8.33673i −0.877613 0.463152i
\(325\) −8.08365 −0.448400
\(326\) 0.0350530 + 0.601837i 0.00194141 + 0.0333327i
\(327\) 0.0814971 + 0.729122i 0.00450680 + 0.0403205i
\(328\) −0.494267 + 0.0577715i −0.0272913 + 0.00318990i
\(329\) −34.6785 8.21895i −1.91189 0.453125i
\(330\) −1.14499 + 3.09713i −0.0630294 + 0.170492i
\(331\) 10.9874 14.7586i 0.603919 0.811205i −0.390058 0.920790i \(-0.627545\pi\)
0.993977 + 0.109586i \(0.0349524\pi\)
\(332\) −4.15540 23.5665i −0.228057 1.29338i
\(333\) −8.12238 + 5.22558i −0.445104 + 0.286360i
\(334\) −0.480753 + 2.72648i −0.0263056 + 0.149187i
\(335\) −7.03337 7.45494i −0.384274 0.407307i
\(336\) 5.71518 + 24.6679i 0.311788 + 1.34575i
\(337\) 23.8437 11.9748i 1.29885 0.652307i 0.341131 0.940016i \(-0.389190\pi\)
0.957718 + 0.287709i \(0.0928936\pi\)
\(338\) 1.17822 + 0.774926i 0.0640866 + 0.0421504i
\(339\) 19.0019 + 14.2959i 1.03204 + 0.776445i
\(340\) 10.7194 2.54054i 0.581340 0.137780i
\(341\) 29.1235 10.6001i 1.57712 0.574026i
\(342\) 1.36054 + 0.914629i 0.0735694 + 0.0494575i
\(343\) −0.0250188 0.00910611i −0.00135089 0.000491683i
\(344\) −1.12901 0.131962i −0.0608722 0.00711494i
\(345\) 5.38266 + 3.14398i 0.289793 + 0.169266i
\(346\) 0.296719 0.314503i 0.0159517 0.0169078i
\(347\) 14.6527 + 19.6820i 0.786599 + 1.05659i 0.996879 + 0.0789443i \(0.0251549\pi\)
−0.210280 + 0.977641i \(0.567438\pi\)
\(348\) −1.45990 + 6.02426i −0.0782589 + 0.322934i
\(349\) 14.9935 + 7.53000i 0.802582 + 0.403072i 0.802295 0.596928i \(-0.203612\pi\)
0.000287376 1.00000i \(0.499909\pi\)
\(350\) 1.47331 + 2.55185i 0.0787517 + 0.136402i
\(351\) 4.73561 + 4.60520i 0.252768 + 0.245807i
\(352\) 3.35926 5.81841i 0.179049 0.310123i
\(353\) −16.4381 + 10.8115i −0.874913 + 0.575440i −0.905621 0.424089i \(-0.860594\pi\)
0.0307072 + 0.999528i \(0.490224\pi\)
\(354\) −2.28042 0.144362i −0.121203 0.00767276i
\(355\) 2.66518 6.17858i 0.141453 0.327925i
\(356\) 5.56652 + 18.5935i 0.295025 + 0.985452i
\(357\) −3.59903 10.0456i −0.190481 0.531670i
\(358\) 0.738459 + 1.71194i 0.0390288 + 0.0904789i
\(359\) −27.1083 + 22.7466i −1.43072 + 1.20052i −0.485436 + 0.874272i \(0.661339\pi\)
−0.945285 + 0.326245i \(0.894216\pi\)
\(360\) 4.67238 + 1.75417i 0.246256 + 0.0924531i
\(361\) 0.352176 + 0.295511i 0.0185356 + 0.0155532i
\(362\) −0.0761571 + 0.254382i −0.00400273 + 0.0133700i
\(363\) 9.30337 + 14.3017i 0.488300 + 0.750643i
\(364\) 0.548756 9.42178i 0.0287626 0.493835i
\(365\) 3.16113 54.2745i 0.165461 2.84085i
\(366\) 0.621103 + 0.954795i 0.0324656 + 0.0499079i
\(367\) −5.62009 + 18.7724i −0.293366 + 0.979912i 0.676534 + 0.736411i \(0.263481\pi\)
−0.969901 + 0.243501i \(0.921704\pi\)
\(368\) −3.19696 2.68257i −0.166653 0.139839i
\(369\) −2.83147 1.06303i −0.147400 0.0553392i
\(370\) 1.02964 0.863973i 0.0535286 0.0449158i
\(371\) 4.26642 + 9.89067i 0.221501 + 0.513498i
\(372\) −7.86923 21.9646i −0.408001 1.13881i
\(373\) −9.29538 31.0487i −0.481297 1.60764i −0.761815 0.647794i \(-0.775692\pi\)
0.280518 0.959849i \(-0.409494\pi\)
\(374\) −0.368993 + 0.855421i −0.0190802 + 0.0442328i
\(375\) −7.91636 0.501145i −0.408799 0.0258790i
\(376\) 3.92914 2.58423i 0.202630 0.133272i
\(377\) 1.14617 1.98523i 0.0590309 0.102245i
\(378\) 0.590668 2.33427i 0.0303807 0.120062i
\(379\) 7.22233 + 12.5094i 0.370986 + 0.642567i 0.989718 0.143036i \(-0.0456863\pi\)
−0.618731 + 0.785603i \(0.712353\pi\)
\(380\) 26.3681 + 13.2426i 1.35266 + 0.679329i
\(381\) 1.47736 6.09629i 0.0756873 0.312323i
\(382\) −1.54050 2.06925i −0.0788190 0.105872i
\(383\) 15.0027 15.9020i 0.766604 0.812553i −0.220032 0.975493i \(-0.570616\pi\)
0.986636 + 0.162940i \(0.0520975\pi\)
\(384\) −5.81554 3.39682i −0.296773 0.173343i
\(385\) 57.1783 + 6.68318i 2.91407 + 0.340606i
\(386\) −1.64078 0.597194i −0.0835134 0.0303964i
\(387\) −5.73336 3.85429i −0.291443 0.195925i
\(388\) −17.5223 + 6.37760i −0.889561 + 0.323774i
\(389\) −18.2511 + 4.32559i −0.925367 + 0.219316i −0.665560 0.746344i \(-0.731807\pi\)
−0.259807 + 0.965660i \(0.583659\pi\)
\(390\) −0.734603 0.552671i −0.0371980 0.0279856i
\(391\) 1.46939 + 0.966431i 0.0743101 + 0.0488745i
\(392\) −3.08460 + 1.54914i −0.155796 + 0.0782436i
\(393\) 2.44326 + 10.5456i 0.123246 + 0.531956i
\(394\) −0.162877 0.172640i −0.00820564 0.00869747i
\(395\) 3.28846 18.6498i 0.165461 0.938374i
\(396\) 22.8640 14.7097i 1.14896 0.739191i
\(397\) −3.33925 18.9379i −0.167592 0.950463i −0.946351 0.323140i \(-0.895262\pi\)
0.778759 0.627323i \(-0.215850\pi\)
\(398\) 1.19106 1.59988i 0.0597027 0.0801946i
\(399\) 9.91071 26.8080i 0.496156 1.34208i
\(400\) 24.1815 + 5.73112i 1.20907 + 0.286556i
\(401\) 4.48498 0.524219i 0.223969 0.0261783i −0.00336797 0.999994i \(-0.501072\pi\)
0.227337 + 0.973816i \(0.426998\pi\)
\(402\) −0.0724802 0.648451i −0.00361498 0.0323418i
\(403\) 0.501697 + 8.61380i 0.0249913 + 0.429084i
\(404\) 10.8668 0.540643
\(405\) 20.3662 + 22.4785i 1.01201 + 1.11697i
\(406\) −0.835597 −0.0414700
\(407\) −0.854753 14.6755i −0.0423685 0.727440i
\(408\) 1.29010 + 0.564228i 0.0638694 + 0.0279334i
\(409\) −35.5723 + 4.15781i −1.75894 + 0.205590i −0.933420 0.358787i \(-0.883191\pi\)
−0.825517 + 0.564377i \(0.809117\pi\)
\(410\) 0.409560 + 0.0970674i 0.0202267 + 0.00479382i
\(411\) −27.9581 + 4.78452i −1.37907 + 0.236003i
\(412\) 2.77884 3.73264i 0.136904 0.183894i
\(413\) 6.91757 + 39.2315i 0.340392 + 1.93046i
\(414\) 0.153501 + 0.365960i 0.00754415 + 0.0179859i
\(415\) −7.05659 + 40.0199i −0.346395 + 1.96450i
\(416\) 1.28358 + 1.36052i 0.0629328 + 0.0667049i
\(417\) 32.3770 + 9.87122i 1.58551 + 0.483396i
\(418\) −2.22986 + 1.11988i −0.109066 + 0.0547750i
\(419\) −20.8326 13.7018i −1.01774 0.669376i −0.0730427 0.997329i \(-0.523271\pi\)
−0.944694 + 0.327953i \(0.893641\pi\)
\(420\) 5.24821 43.0188i 0.256086 2.09910i
\(421\) −35.1178 + 8.32306i −1.71154 + 0.405641i −0.965529 0.260297i \(-0.916179\pi\)
−0.746007 + 0.665938i \(0.768031\pi\)
\(422\) −0.449170 + 0.163485i −0.0218653 + 0.00795831i
\(423\) 28.4209 3.03169i 1.38187 0.147406i
\(424\) −1.33566 0.486141i −0.0648655 0.0236091i
\(425\) −10.4020 1.21582i −0.504570 0.0589758i
\(426\) 0.372064 0.212317i 0.0180266 0.0102868i
\(427\) 13.6274 14.4442i 0.659478 0.699006i
\(428\) −13.9463 18.7332i −0.674122 0.905503i
\(429\) −9.64624 + 2.83497i −0.465725 + 0.136874i
\(430\) 0.859171 + 0.431492i 0.0414329 + 0.0208084i
\(431\) 12.8170 + 22.1998i 0.617375 + 1.06933i 0.989963 + 0.141329i \(0.0451374\pi\)
−0.372587 + 0.927997i \(0.621529\pi\)
\(432\) −10.9011 17.1335i −0.524482 0.824334i
\(433\) −2.49590 + 4.32302i −0.119945 + 0.207751i −0.919746 0.392515i \(-0.871605\pi\)
0.799801 + 0.600266i \(0.204939\pi\)
\(434\) 2.62777 1.72831i 0.126137 0.0829615i
\(435\) 5.82860 8.76535i 0.279460 0.420267i
\(436\) −0.332969 + 0.771908i −0.0159463 + 0.0369677i
\(437\) 1.35103 + 4.51274i 0.0646283 + 0.215874i
\(438\) 2.23811 2.64012i 0.106941 0.126150i
\(439\) 1.33282 + 3.08983i 0.0636120 + 0.147469i 0.947057 0.321066i \(-0.104041\pi\)
−0.883445 + 0.468535i \(0.844782\pi\)
\(440\) −5.81918 + 4.88287i −0.277418 + 0.232782i
\(441\) −20.9776 0.211585i −0.998932 0.0100755i
\(442\) −0.198684 0.166715i −0.00945041 0.00792984i
\(443\) 3.83903 12.8232i 0.182398 0.609251i −0.817067 0.576542i \(-0.804402\pi\)
0.999465 0.0327082i \(-0.0104132\pi\)
\(444\) −11.0511 + 0.587749i −0.524461 + 0.0278933i
\(445\) 1.91643 32.9038i 0.0908475 1.55979i
\(446\) −0.0215505 + 0.370008i −0.00102045 + 0.0175204i
\(447\) −3.21543 + 6.32274i −0.152085 + 0.299055i
\(448\) −8.19017 + 27.3571i −0.386949 + 1.29250i
\(449\) −25.1690 21.1193i −1.18780 0.996683i −0.999895 0.0144961i \(-0.995386\pi\)
−0.187906 0.982187i \(-0.560170\pi\)
\(450\) −1.79487 1.53719i −0.0846109 0.0724637i
\(451\) 3.52643 2.95903i 0.166053 0.139335i
\(452\) 10.7920 + 25.0186i 0.507612 + 1.17678i
\(453\) −15.1126 2.74342i −0.710053 0.128897i
\(454\) −0.853861 2.85209i −0.0400737 0.133855i
\(455\) −6.34794 + 14.7162i −0.297596 + 0.689905i
\(456\) 1.67562 + 3.37882i 0.0784682 + 0.158228i
\(457\) 17.7088 11.6472i 0.828380 0.544834i −0.0630403 0.998011i \(-0.520080\pi\)
0.891421 + 0.453177i \(0.149709\pi\)
\(458\) 0.293167 0.507780i 0.0136988 0.0237270i
\(459\) 5.40110 + 6.63820i 0.252102 + 0.309844i
\(460\) 3.57135 + 6.18576i 0.166515 + 0.288413i
\(461\) 14.8202 + 7.44297i 0.690245 + 0.346654i 0.759101 0.650973i \(-0.225639\pi\)
−0.0688566 + 0.997627i \(0.521935\pi\)
\(462\) 2.65305 + 2.52843i 0.123431 + 0.117633i
\(463\) 2.04248 + 2.74353i 0.0949220 + 0.127502i 0.847047 0.531518i \(-0.178378\pi\)
−0.752125 + 0.659021i \(0.770971\pi\)
\(464\) −4.83615 + 5.12602i −0.224513 + 0.237970i
\(465\) −0.199807 + 39.6207i −0.00926583 + 1.83737i
\(466\) 1.28586 + 0.150296i 0.0595664 + 0.00696231i
\(467\) 8.87582 + 3.23054i 0.410724 + 0.149491i 0.539115 0.842232i \(-0.318759\pi\)
−0.128391 + 0.991724i \(0.540981\pi\)
\(468\) 2.09756 + 7.27251i 0.0969597 + 0.336172i
\(469\) −10.6895 + 3.89067i −0.493597 + 0.179655i
\(470\) −3.87049 + 0.917324i −0.178533 + 0.0423130i
\(471\) 8.45126 3.59508i 0.389413 0.165652i
\(472\) −4.39191 2.88861i −0.202154 0.132959i
\(473\) 9.39673 4.71922i 0.432062 0.216990i
\(474\) 0.881096 0.822912i 0.0404701 0.0377976i
\(475\) −19.2497 20.4034i −0.883235 0.936174i
\(476\) 2.12321 12.0413i 0.0973173 0.551914i
\(477\) −5.86456 6.34304i −0.268520 0.290428i
\(478\) −0.340467 1.93089i −0.0155726 0.0883166i
\(479\) 10.9101 14.6547i 0.498493 0.669592i −0.479666 0.877451i \(-0.659242\pi\)
0.978159 + 0.207859i \(0.0666495\pi\)
\(480\) 5.48768 + 6.60734i 0.250477 + 0.301583i
\(481\) 3.98231 + 0.943825i 0.181578 + 0.0430347i
\(482\) −2.17053 + 0.253698i −0.0988648 + 0.0115556i
\(483\) 5.57042 4.10353i 0.253463 0.186717i
\(484\) 1.13671 + 19.5165i 0.0516686 + 0.887115i
\(485\) 31.6656 1.43786
\(486\) 0.175754 + 1.92305i 0.00797238 + 0.0872312i
\(487\) 31.2157 1.41452 0.707260 0.706954i \(-0.249931\pi\)
0.707260 + 0.706954i \(0.249931\pi\)
\(488\) 0.152363 + 2.61597i 0.00689713 + 0.118419i
\(489\) −6.78649 + 4.99936i −0.306896 + 0.226079i
\(490\) 2.89981 0.338939i 0.131000 0.0153117i
\(491\) 2.12757 + 0.504243i 0.0960159 + 0.0227562i 0.278343 0.960482i \(-0.410215\pi\)
−0.182327 + 0.983238i \(0.558363\pi\)
\(492\) −2.21418 2.66595i −0.0998231 0.120190i
\(493\) 1.77347 2.38219i 0.0798733 0.107288i
\(494\) −0.120632 0.684137i −0.00542748 0.0307808i
\(495\) −45.0291 + 10.1935i −2.02391 + 0.458166i
\(496\) 4.60620 26.1231i 0.206825 1.17296i
\(497\) −5.12516 5.43235i −0.229895 0.243674i
\(498\) −1.89071 + 1.76586i −0.0847248 + 0.0791300i
\(499\) 0.562307 0.282401i 0.0251723 0.0126420i −0.436169 0.899865i \(-0.643665\pi\)
0.461341 + 0.887223i \(0.347369\pi\)
\(500\) −7.59379 4.99451i −0.339605 0.223361i
\(501\) −35.6207 + 15.1527i −1.59141 + 0.676971i
\(502\) −2.48853 + 0.589793i −0.111069 + 0.0263238i
\(503\) 5.84089 2.12591i 0.260432 0.0947897i −0.208504 0.978021i \(-0.566859\pi\)
0.468937 + 0.883232i \(0.344637\pi\)
\(504\) 3.84177 3.99063i 0.171126 0.177757i
\(505\) −17.3408 6.31154i −0.771656 0.280860i
\(506\) −0.599949 0.0701240i −0.0266710 0.00311739i
\(507\) −0.0994342 + 19.7173i −0.00441603 + 0.875676i
\(508\) 4.93241 5.22805i 0.218840 0.231957i
\(509\) 11.1759 + 15.0119i 0.495365 + 0.665390i 0.977556 0.210676i \(-0.0675665\pi\)
−0.482191 + 0.876066i \(0.660159\pi\)
\(510\) −0.862157 0.821660i −0.0381770 0.0363837i
\(511\) −53.9233 27.0813i −2.38543 1.19801i
\(512\) −4.80425 8.32121i −0.212320 0.367749i
\(513\) −0.346769 + 22.9193i −0.0153102 + 1.01191i
\(514\) −0.451387 + 0.781825i −0.0199098 + 0.0344848i
\(515\) −6.60232 + 4.34242i −0.290933 + 0.191350i
\(516\) −3.51698 7.09183i −0.154826 0.312200i
\(517\) −17.2311 + 39.9462i −0.757823 + 1.75683i
\(518\) −0.427862 1.42916i −0.0187992 0.0627936i
\(519\) 5.94833 + 1.07981i 0.261103 + 0.0473983i
\(520\) −0.837651 1.94189i −0.0367334 0.0851577i
\(521\) −10.7516 + 9.02171i −0.471038 + 0.395248i −0.847173 0.531317i \(-0.821697\pi\)
0.376135 + 0.926565i \(0.377253\pi\)
\(522\) 0.632004 0.222838i 0.0276621 0.00975335i
\(523\) −15.7777 13.2390i −0.689910 0.578903i 0.228973 0.973433i \(-0.426463\pi\)
−0.918883 + 0.394530i \(0.870908\pi\)
\(524\) −3.55741 + 11.8826i −0.155406 + 0.519093i
\(525\) −18.6757 + 36.7235i −0.815075 + 1.60274i
\(526\) 0.0752113 1.29133i 0.00327937 0.0563046i
\(527\) −0.649974 + 11.1596i −0.0283133 + 0.486121i
\(528\) 30.8657 1.64159i 1.34326 0.0714409i
\(529\) 6.26943 20.9414i 0.272584 0.910494i
\(530\) 0.920961 + 0.772778i 0.0400040 + 0.0335673i
\(531\) −15.6944 27.8280i −0.681080 1.20763i
\(532\) 25.0877 21.0511i 1.08769 0.912680i
\(533\) 0.507618 + 1.17679i 0.0219874 + 0.0509724i
\(534\) 1.35685 1.60057i 0.0587168 0.0692636i
\(535\) 11.3746 + 37.9939i 0.491767 + 1.64262i
\(536\) 0.594547 1.37831i 0.0256805 0.0595341i
\(537\) −14.4344 + 21.7072i −0.622889 + 0.936733i
\(538\) −2.30963 + 1.51907i −0.0995751 + 0.0654916i
\(539\) 15.9655 27.6531i 0.687684 1.19110i
\(540\) 7.50281 + 33.9368i 0.322870 + 1.46041i
\(541\) −19.2442 33.3319i −0.827372 1.43305i −0.900093 0.435698i \(-0.856502\pi\)
0.0727213 0.997352i \(-0.476832\pi\)
\(542\) −2.57517 1.29330i −0.110613 0.0555519i
\(543\) −3.56209 + 1.04687i −0.152864 + 0.0449257i
\(544\) 1.44708 + 1.94376i 0.0620429 + 0.0833381i
\(545\) 0.979670 1.03839i 0.0419644 0.0444797i
\(546\) −0.886186 + 0.505698i −0.0379253 + 0.0216419i
\(547\) −18.3380 2.14340i −0.784075 0.0916453i −0.285371 0.958417i \(-0.592117\pi\)
−0.498705 + 0.866772i \(0.666191\pi\)
\(548\) −30.5412 11.1161i −1.30465 0.474855i
\(549\) −6.45511 + 14.5591i −0.275497 + 0.621367i
\(550\) 3.37997 1.23021i 0.144123 0.0524563i
\(551\) 7.74019 1.83446i 0.329743 0.0781506i
\(552\) −0.110561 + 0.906248i −0.00470577 + 0.0385725i
\(553\) −17.5610 11.5501i −0.746770 0.491159i
\(554\) 0.980975 0.492664i 0.0416776 0.0209313i
\(555\) 17.9763 + 5.48067i 0.763049 + 0.232641i
\(556\) 26.6158 + 28.2111i 1.12876 + 1.19642i
\(557\) 1.24763 7.07568i 0.0528639 0.299806i −0.946900 0.321528i \(-0.895804\pi\)
0.999764 + 0.0217217i \(0.00691477\pi\)
\(558\) −1.52660 + 2.00798i −0.0646263 + 0.0850047i
\(559\) 0.508348 + 2.88298i 0.0215008 + 0.121937i
\(560\) 29.4227 39.5216i 1.24334 1.67009i
\(561\) −12.8391 + 2.19718i −0.542067 + 0.0927649i
\(562\) 2.58960 + 0.613746i 0.109236 + 0.0258893i
\(563\) 30.5750 3.57370i 1.28858 0.150613i 0.555936 0.831225i \(-0.312360\pi\)
0.732645 + 0.680611i \(0.238286\pi\)
\(564\) 30.0063 + 13.1233i 1.26349 + 0.552592i
\(565\) −2.69037 46.1918i −0.113185 1.94330i
\(566\) −0.0757672 −0.00318473
\(567\) 31.8618 10.8741i 1.33807 0.456670i
\(568\) 0.985508 0.0413510
\(569\) 1.75691 + 30.1649i 0.0736534 + 1.26458i 0.809374 + 0.587294i \(0.199807\pi\)
−0.735720 + 0.677285i \(0.763156\pi\)
\(570\) −0.354352 3.17025i −0.0148422 0.132787i
\(571\) 7.84368 0.916795i 0.328248 0.0383667i 0.0496269 0.998768i \(-0.484197\pi\)
0.278621 + 0.960401i \(0.410123\pi\)
\(572\) −11.2100 2.65681i −0.468713 0.111087i
\(573\) 12.5073 33.8316i 0.522499 1.41334i
\(574\) 0.278972 0.374724i 0.0116441 0.0156407i
\(575\) −1.17912 6.68713i −0.0491728 0.278873i
\(576\) −1.10098 22.8757i −0.0458742 0.953154i
\(577\) −1.81528 + 10.2950i −0.0755710 + 0.428585i 0.923425 + 0.383780i \(0.125378\pi\)
−0.998996 + 0.0448050i \(0.985733\pi\)
\(578\) 1.21458 + 1.28738i 0.0505199 + 0.0535480i
\(579\) −5.51029 23.7836i −0.229000 0.988413i
\(580\) 10.7786 5.41320i 0.447556 0.224771i
\(581\) 37.6835 + 24.7849i 1.56338 + 1.02825i
\(582\) 1.61093 + 1.21197i 0.0667752 + 0.0502376i
\(583\) 12.7943 3.03231i 0.529887 0.125585i
\(584\) 7.48227 2.72332i 0.309619 0.112692i
\(585\) 0.876737 12.8235i 0.0362486 0.530185i
\(586\) −3.60373 1.31165i −0.148869 0.0541837i
\(587\) 14.9536 + 1.74783i 0.617201 + 0.0721405i 0.418948 0.908010i \(-0.362399\pi\)
0.198253 + 0.980151i \(0.436473\pi\)
\(588\) −20.7568 12.1239i −0.855996 0.499982i
\(589\) −20.5469 + 21.7784i −0.846619 + 0.897364i
\(590\) 2.65509 + 3.56641i 0.109308 + 0.146827i
\(591\) 0.781590 3.22522i 0.0321503 0.132668i
\(592\) −11.2436 5.64673i −0.462108 0.232079i
\(593\) 9.50914 + 16.4703i 0.390494 + 0.676355i 0.992515 0.122125i \(-0.0389710\pi\)
−0.602021 + 0.798480i \(0.705638\pi\)
\(594\) −2.68092 1.20486i −0.109999 0.0494360i
\(595\) −10.3819 + 17.9819i −0.425615 + 0.737187i
\(596\) −6.79075 + 4.46635i −0.278160 + 0.182949i
\(597\) 27.8320 + 1.76190i 1.13909 + 0.0721100i
\(598\) 0.0666065 0.154411i 0.00272374 0.00631434i
\(599\) 11.4208 + 38.1481i 0.466641 + 1.55869i 0.790424 + 0.612560i \(0.209860\pi\)
−0.323783 + 0.946131i \(0.604955\pi\)
\(600\) −1.83362 5.11798i −0.0748571 0.208941i
\(601\) 2.21155 + 5.12695i 0.0902111 + 0.209133i 0.957348 0.288937i \(-0.0933017\pi\)
−0.867137 + 0.498069i \(0.834042\pi\)
\(602\) 0.817450 0.685922i 0.0333168 0.0279561i
\(603\) 7.04746 5.79341i 0.286995 0.235926i
\(604\) −13.4821 11.3129i −0.548580 0.460314i
\(605\) 9.52147 31.8039i 0.387103 1.29301i
\(606\) −0.640615 0.984789i −0.0260232 0.0400043i
\(607\) −0.818590 + 14.0546i −0.0332255 + 0.570460i 0.940081 + 0.340951i \(0.110749\pi\)
−0.973307 + 0.229509i \(0.926288\pi\)
\(608\) −0.377395 + 6.47963i −0.0153054 + 0.262784i
\(609\) −6.37076 9.79348i −0.258156 0.396852i
\(610\) 0.635664 2.12327i 0.0257373 0.0859685i
\(611\) −9.27806 7.78522i −0.375350 0.314956i
\(612\) 1.60531 + 9.67369i 0.0648907 + 0.391036i
\(613\) −13.7550 + 11.5418i −0.555561 + 0.466171i −0.876819 0.480821i \(-0.840339\pi\)
0.321258 + 0.946992i \(0.395894\pi\)
\(614\) 1.11620 + 2.58764i 0.0450462 + 0.104429i
\(615\) 1.98490 + 5.54024i 0.0800389 + 0.223404i
\(616\) 2.41812 + 8.07709i 0.0974290 + 0.325435i
\(617\) 13.5528 31.4190i 0.545617 1.26488i −0.392879 0.919590i \(-0.628521\pi\)
0.938496 0.345291i \(-0.112220\pi\)
\(618\) −0.502082 0.0317843i −0.0201967 0.00127855i
\(619\) 28.9445 19.0371i 1.16338 0.765165i 0.187239 0.982314i \(-0.440046\pi\)
0.976138 + 0.217149i \(0.0696759\pi\)
\(620\) −22.6998 + 39.3172i −0.911646 + 1.57902i
\(621\) −3.11886 + 4.58923i −0.125155 + 0.184159i
\(622\) 1.89740 + 3.28639i 0.0760787 + 0.131772i
\(623\) −32.6910 16.4180i −1.30974 0.657774i
\(624\) −2.02671 + 8.36317i −0.0811332 + 0.334795i
\(625\) −9.76915 13.1222i −0.390766 0.524890i
\(626\) 1.93908 2.05531i 0.0775012 0.0821465i
\(627\) −30.1262 17.5966i −1.20313 0.702739i
\(628\) 10.4524 + 1.22171i 0.417096 + 0.0487515i
\(629\) 4.98245 + 1.81347i 0.198663 + 0.0723076i
\(630\) −4.20791 + 2.06041i −0.167647 + 0.0820887i
\(631\) 40.5340 14.7532i 1.61363 0.587314i 0.631478 0.775394i \(-0.282449\pi\)
0.982154 + 0.188080i \(0.0602263\pi\)
\(632\) 2.69881 0.639630i 0.107353 0.0254431i
\(633\) −5.34066 4.01799i −0.212272 0.159701i
\(634\) 0.830283 + 0.546086i 0.0329748 + 0.0216878i
\(635\) −10.9074 + 5.47793i −0.432849 + 0.217385i
\(636\) −2.23417 9.64315i −0.0885905 0.382376i
\(637\) 6.10047 + 6.46612i 0.241709 + 0.256197i
\(638\) −0.177121 + 1.00450i −0.00701230 + 0.0397687i
\(639\) 5.32512 + 2.74198i 0.210658 + 0.108471i
\(640\) 2.27566 + 12.9059i 0.0899534 + 0.510151i
\(641\) 2.87030 3.85549i 0.113370 0.152283i −0.741816 0.670603i \(-0.766035\pi\)
0.855186 + 0.518321i \(0.173443\pi\)
\(642\) −0.875511 + 2.36822i −0.0345537 + 0.0934661i
\(643\) 8.07150 + 1.91298i 0.318309 + 0.0754405i 0.386664 0.922220i \(-0.373627\pi\)
−0.0683558 + 0.997661i \(0.521775\pi\)
\(644\) 7.87414 0.920354i 0.310284 0.0362670i
\(645\) 1.49326 + 13.3596i 0.0587969 + 0.526032i
\(646\) −0.0523308 0.898486i −0.00205893 0.0353504i
\(647\) −24.6332 −0.968431 −0.484215 0.874949i \(-0.660895\pi\)
−0.484215 + 0.874949i \(0.660895\pi\)
\(648\) −1.84150 + 4.04284i −0.0723410 + 0.158818i
\(649\) 48.6281 1.90882
\(650\) 0.0582253 + 0.999689i 0.00228378 + 0.0392110i
\(651\) 40.2910 + 17.6214i 1.57913 + 0.690636i
\(652\) −9.59312 + 1.12127i −0.375695 + 0.0439125i
\(653\) 10.4367 + 2.47355i 0.408420 + 0.0967974i 0.429690 0.902976i \(-0.358623\pi\)
−0.0212699 + 0.999774i \(0.506771\pi\)
\(654\) 0.0895821 0.0153304i 0.00350294 0.000599464i
\(655\) 12.5783 16.8956i 0.491475 0.660166i
\(656\) −0.684175 3.88015i −0.0267125 0.151494i
\(657\) 48.0070 + 6.10261i 1.87293 + 0.238086i
\(658\) −0.766638 + 4.34782i −0.0298867 + 0.169496i
\(659\) −11.6727 12.3723i −0.454704 0.481958i 0.458944 0.888465i \(-0.348228\pi\)
−0.913647 + 0.406507i \(0.866747\pi\)
\(660\) −50.6021 15.4278i −1.96968 0.600524i
\(661\) −27.9077 + 14.0158i −1.08549 + 0.545151i −0.899286 0.437361i \(-0.855913\pi\)
−0.186199 + 0.982512i \(0.559617\pi\)
\(662\) −1.90431 1.25248i −0.0740129 0.0486791i
\(663\) 0.439158 3.59971i 0.0170555 0.139801i
\(664\) −5.79128 + 1.37256i −0.224745 + 0.0532656i
\(665\) −52.2606 + 19.0213i −2.02658 + 0.737615i
\(666\) 0.704742 + 0.966840i 0.0273082 + 0.0374643i
\(667\) 1.80945 + 0.658587i 0.0700622 + 0.0255006i
\(668\) −44.0552 5.14931i −1.70454 0.199233i
\(669\) −4.50093 + 2.56843i −0.174016 + 0.0993014i
\(670\) −0.871278 + 0.923501i −0.0336604 + 0.0356779i
\(671\) −14.4754 19.4438i −0.558816 0.750621i
\(672\) 9.14622 2.68802i 0.352823 0.103692i
\(673\) −7.29455 3.66346i −0.281184 0.141216i 0.302618 0.953112i \(-0.402139\pi\)
−0.583802 + 0.811896i \(0.698436\pi\)
\(674\) −1.65264 2.86245i −0.0636572 0.110258i
\(675\) 4.33192 32.7563i 0.166736 1.26079i
\(676\) −11.2966 + 19.5663i −0.434484 + 0.752548i
\(677\) 4.55342 2.99483i 0.175002 0.115101i −0.458986 0.888444i \(-0.651787\pi\)
0.633988 + 0.773343i \(0.281417\pi\)
\(678\) 1.63107 2.45289i 0.0626410 0.0942029i
\(679\) 13.9206 32.2715i 0.534223 1.23847i
\(680\) −0.785814 2.62480i −0.0301346 0.100657i
\(681\) 26.9175 31.7525i 1.03148 1.21676i
\(682\) −1.52066 3.52529i −0.0582292 0.134990i
\(683\) −2.37757 + 1.99502i −0.0909753 + 0.0763374i −0.687141 0.726524i \(-0.741135\pi\)
0.596166 + 0.802861i \(0.296690\pi\)
\(684\) −13.3612 + 22.6124i −0.510877 + 0.864607i
\(685\) 42.2801 + 35.4772i 1.61544 + 1.35551i
\(686\) −0.000945928 0.00315962i −3.61157e−5 0.000120635i
\(687\) 8.18651 0.435398i 0.312335 0.0166115i
\(688\) 0.523292 8.98458i 0.0199503 0.342534i
\(689\) −0.212847 + 3.65445i −0.00810884 + 0.139223i
\(690\) 0.350040 0.688309i 0.0133258 0.0262035i
\(691\) −7.28011 + 24.3173i −0.276948 + 0.925072i 0.700456 + 0.713695i \(0.252980\pi\)
−0.977405 + 0.211377i \(0.932205\pi\)
\(692\) 5.30656 + 4.45274i 0.201725 + 0.169268i
\(693\) −9.40671 + 50.3719i −0.357332 + 1.91347i
\(694\) 2.32850 1.95384i 0.0883885 0.0741667i
\(695\) −26.0871 60.4768i −0.989542 2.29402i
\(696\) 1.51689 + 0.275363i 0.0574976 + 0.0104376i
\(697\) 0.476204 + 1.59063i 0.0180375 + 0.0602495i
\(698\) 0.823226 1.90845i 0.0311596 0.0722360i
\(699\) 8.04214 + 16.2166i 0.304182 + 0.613369i
\(700\) −39.4417 + 25.9412i −1.49076 + 0.980487i
\(701\) 0.473675 0.820430i 0.0178905 0.0309872i −0.856942 0.515414i \(-0.827638\pi\)
0.874832 + 0.484426i \(0.160972\pi\)
\(702\) 0.535407 0.618814i 0.0202076 0.0233556i
\(703\) 7.10086 + 12.2991i 0.267814 + 0.463868i
\(704\) 31.1510 + 15.6446i 1.17405 + 0.589628i
\(705\) −40.2607 38.3696i −1.51631 1.44508i
\(706\) 1.45544 + 1.95500i 0.0547763 + 0.0735773i
\(707\) −14.0555 + 14.8980i −0.528613 + 0.560297i
\(708\) 0.184611 36.6075i 0.00693812 1.37579i
\(709\) −32.0392 3.74485i −1.20326 0.140641i −0.509257 0.860615i \(-0.670080\pi\)
−0.694001 + 0.719974i \(0.744154\pi\)
\(710\) −0.783290 0.285094i −0.0293963 0.0106994i
\(711\) 16.3625 + 4.05270i 0.613640 + 0.151988i
\(712\) 4.53612 1.65101i 0.169998 0.0618743i
\(713\) −7.05251 + 1.67148i −0.264119 + 0.0625973i
\(714\) −1.21640 + 0.517443i −0.0455225 + 0.0193648i
\(715\) 16.3453 + 10.7505i 0.611281 + 0.402046i
\(716\) −26.6928 + 13.4056i −0.997558 + 0.500992i
\(717\) 20.0348 18.7118i 0.748215 0.698806i
\(718\) 3.00828 + 3.18859i 0.112268 + 0.118997i
\(719\) −4.35548 + 24.7012i −0.162432 + 0.921198i 0.789241 + 0.614084i \(0.210474\pi\)
−0.951673 + 0.307114i \(0.900637\pi\)
\(720\) −11.7142 + 37.7386i −0.436563 + 1.40644i
\(721\) 1.52305 + 8.63763i 0.0567213 + 0.321682i
\(722\) 0.0340086 0.0456815i 0.00126567 0.00170009i
\(723\) −19.5220 23.5051i −0.726029 0.874163i
\(724\) −4.13953 0.981087i −0.153844 0.0364618i
\(725\) −11.3889 + 1.33117i −0.422973 + 0.0494384i
\(726\) 1.70165 1.25354i 0.0631541 0.0465233i
\(727\) 0.505316 + 8.67595i 0.0187411 + 0.321773i 0.994629 + 0.103502i \(0.0330047\pi\)
−0.975888 + 0.218271i \(0.929958\pi\)
\(728\) −2.34729 −0.0869964
\(729\) −21.1988 + 16.7216i −0.785140 + 0.619318i
\(730\) −6.73479 −0.249266
\(731\) 0.220524 + 3.78626i 0.00815639 + 0.140040i
\(732\) −14.6924 + 10.8233i −0.543046 + 0.400042i
\(733\) −8.61465 + 1.00691i −0.318189 + 0.0371910i −0.273689 0.961818i \(-0.588244\pi\)
−0.0445007 + 0.999009i \(0.514170\pi\)
\(734\) 2.36203 + 0.559811i 0.0871841 + 0.0206630i
\(735\) 26.0812 + 31.4026i 0.962020 + 1.15830i
\(736\) −0.938248 + 1.26029i −0.0345843 + 0.0464547i
\(737\) 2.41128 + 13.6750i 0.0888205 + 0.503726i
\(738\) −0.111069 + 0.357819i −0.00408849 + 0.0131715i
\(739\) −0.311908 + 1.76892i −0.0114737 + 0.0650707i −0.990007 0.141018i \(-0.954962\pi\)
0.978533 + 0.206089i \(0.0660736\pi\)
\(740\) 14.7775 + 15.6633i 0.543232 + 0.575793i
\(741\) 7.09859 6.62984i 0.260773 0.243553i
\(742\) 1.19243 0.598861i 0.0437755 0.0219849i
\(743\) −19.4949 12.8220i −0.715198 0.470393i 0.139032 0.990288i \(-0.455601\pi\)
−0.854230 + 0.519895i \(0.825971\pi\)
\(744\) −5.33983 + 2.27151i −0.195768 + 0.0832776i
\(745\) 13.4305 3.18309i 0.492056 0.116619i
\(746\) −3.77279 + 1.37318i −0.138132 + 0.0502758i
\(747\) −35.1116 8.69654i −1.28467 0.318190i
\(748\) −14.0253 5.10480i −0.512816 0.186650i
\(749\) 43.7213 + 5.11028i 1.59754 + 0.186726i
\(750\) −0.00495530 + 0.982611i −0.000180942 + 0.0358799i
\(751\) −13.3169 + 14.1151i −0.485942 + 0.515069i −0.923227 0.384254i \(-0.874459\pi\)
0.437285 + 0.899323i \(0.355940\pi\)
\(752\) 22.2349 + 29.8667i 0.810824 + 1.08913i
\(753\) −25.8856 24.6698i −0.943325 0.899016i
\(754\) −0.253765 0.127446i −0.00924159 0.00464130i
\(755\) 14.9437 + 25.8832i 0.543855 + 0.941985i
\(756\) 37.8845 + 7.27266i 1.37785 + 0.264504i
\(757\) −8.52025 + 14.7575i −0.309674 + 0.536371i −0.978291 0.207236i \(-0.933553\pi\)
0.668617 + 0.743607i \(0.266886\pi\)
\(758\) 1.49500 0.983276i 0.0543008 0.0357142i
\(759\) −3.75225 7.56625i −0.136198 0.274637i
\(760\) 2.90671 6.73851i 0.105437 0.244432i
\(761\) −12.2986 41.0803i −0.445826 1.48916i −0.825693 0.564120i \(-0.809215\pi\)
0.379867 0.925041i \(-0.375970\pi\)
\(762\) −0.764558 0.138791i −0.0276970 0.00502788i
\(763\) −0.627584 1.45490i −0.0227201 0.0526710i
\(764\) 31.6606 26.5664i 1.14544 0.961137i
\(765\) 3.05689 16.3693i 0.110522 0.591832i
\(766\) −2.07463 1.74082i −0.0749594 0.0628984i
\(767\) −3.88279 + 12.9694i −0.140199 + 0.468299i
\(768\) 11.6094 22.8284i 0.418918 0.823750i
\(769\) −1.65895 + 28.4831i −0.0598232 + 1.02713i 0.826168 + 0.563424i \(0.190516\pi\)
−0.885991 + 0.463702i \(0.846521\pi\)
\(770\) 0.414650 7.11927i 0.0149429 0.256561i
\(771\) −12.6047 + 0.670379i −0.453948 + 0.0241431i
\(772\) 8.02306 26.7989i 0.288756 0.964513i
\(773\) 31.5157 + 26.4448i 1.13354 + 0.951155i 0.999208 0.0397813i \(-0.0126661\pi\)
0.134334 + 0.990936i \(0.457111\pi\)
\(774\) −0.435356 + 0.736796i −0.0156486 + 0.0264836i
\(775\) 33.0622 27.7425i 1.18763 0.996539i
\(776\) 1.83691 + 4.25843i 0.0659411 + 0.152869i
\(777\) 13.4881 15.9109i 0.483883 0.570799i
\(778\) 0.666397 + 2.22592i 0.0238915 + 0.0798032i
\(779\) −1.76147 + 4.08355i −0.0631112 + 0.146308i
\(780\) 8.15509 12.2641i 0.291999 0.439123i
\(781\) −7.61682 + 5.00966i −0.272551 + 0.179260i
\(782\) 0.108933 0.188677i 0.00389543 0.00674709i
\(783\) 7.43026 + 5.70834i 0.265536 + 0.203999i
\(784\) −13.6647 23.6679i −0.488023 0.845281i
\(785\) −15.9699 8.02041i −0.569992 0.286261i
\(786\) 1.28656 0.378112i 0.0458900 0.0134868i
\(787\) −12.4606 16.7375i −0.444172 0.596626i 0.522502 0.852638i \(-0.324999\pi\)
−0.966674 + 0.256012i \(0.917591\pi\)
\(788\) 2.60947 2.76588i 0.0929585 0.0985303i
\(789\) 15.7082 8.96384i 0.559228 0.319121i
\(790\) −2.33007 0.272346i −0.0829003 0.00968965i
\(791\) −48.2584 17.5646i −1.71587 0.624526i
\(792\) −3.98296 5.46424i −0.141528 0.194163i
\(793\) 6.34161 2.30816i 0.225197 0.0819650i
\(794\) −2.31796 + 0.549366i −0.0822612 + 0.0194963i
\(795\) −2.03563 + 16.6858i −0.0721965 + 0.591784i
\(796\) 26.6979 + 17.5595i 0.946283 + 0.622380i
\(797\) 35.8557 18.0074i 1.27007 0.637855i 0.319275 0.947662i \(-0.396561\pi\)
0.950799 + 0.309807i \(0.100264\pi\)
\(798\) −3.38668 1.03254i −0.119887 0.0365517i
\(799\) −10.7680 11.4134i −0.380945 0.403778i
\(800\) 1.62467 9.21395i 0.0574407 0.325762i
\(801\) 29.1042 + 3.69970i 1.02835 + 0.130723i
\(802\) −0.0971339 0.550874i −0.00342992 0.0194520i
\(803\) −43.9856 + 59.0829i −1.55222 + 2.08499i
\(804\) 10.3038 1.76331i 0.363387 0.0621870i
\(805\) −13.0998 3.10471i −0.461707 0.109427i
\(806\) 1.06164 0.124088i 0.0373946 0.00437080i
\(807\) −35.4130 15.4880i −1.24660 0.545202i
\(808\) −0.157149 2.69814i −0.00552848 0.0949203i
\(809\) −25.7049 −0.903736 −0.451868 0.892085i \(-0.649242\pi\)
−0.451868 + 0.892085i \(0.649242\pi\)
\(810\) 2.63318 2.68056i 0.0925204 0.0941853i
\(811\) 37.0961 1.30262 0.651310 0.758812i \(-0.274220\pi\)
0.651310 + 0.758812i \(0.274220\pi\)
\(812\) −0.778395 13.3645i −0.0273163 0.469003i
\(813\) −4.47569 40.0422i −0.156969 1.40434i
\(814\) −1.80874 + 0.211411i −0.0633963 + 0.00740997i
\(815\) 15.9596 + 3.78249i 0.559039 + 0.132495i
\(816\) −3.86581 + 10.4568i −0.135330 + 0.366063i
\(817\) −6.06623 + 8.14836i −0.212231 + 0.285075i
\(818\) 0.770410 + 4.36921i 0.0269367 + 0.152766i
\(819\) −12.6834 6.53086i −0.443194 0.228207i
\(820\) −1.17097 + 6.64091i −0.0408921 + 0.231911i
\(821\) −16.3369 17.3161i −0.570161 0.604335i 0.376559 0.926392i \(-0.377107\pi\)
−0.946720 + 0.322057i \(0.895626\pi\)
\(822\) 0.793070 + 3.42306i 0.0276615 + 0.119393i
\(823\) 10.0579 5.05129i 0.350598 0.176077i −0.264781 0.964309i \(-0.585300\pi\)
0.615378 + 0.788232i \(0.289003\pi\)
\(824\) −0.966971 0.635987i −0.0336860 0.0221557i
\(825\) 40.1881 + 30.2351i 1.39917 + 1.05265i
\(826\) 4.80186 1.13806i 0.167078 0.0395982i
\(827\) −20.1174 + 7.32212i −0.699549 + 0.254615i −0.667218 0.744862i \(-0.732515\pi\)
−0.0323307 + 0.999477i \(0.510293\pi\)
\(828\) −5.71016 + 2.79599i −0.198442 + 0.0971675i
\(829\) −0.656956 0.239112i −0.0228170 0.00830471i 0.330586 0.943776i \(-0.392753\pi\)
−0.353403 + 0.935471i \(0.614976\pi\)
\(830\) 5.00002 + 0.584418i 0.173553 + 0.0202855i
\(831\) 13.2533 + 7.74119i 0.459753 + 0.268539i
\(832\) −6.65982 + 7.05899i −0.230888 + 0.244727i
\(833\) 6.87750 + 9.23809i 0.238291 + 0.320081i
\(834\) 0.987548 4.07510i 0.0341960 0.141109i
\(835\) 67.3107 + 33.8047i 2.32938 + 1.16986i
\(836\) −19.9885 34.6211i −0.691317 1.19740i
\(837\) −35.1734 2.58307i −1.21577 0.0892838i
\(838\) −1.54442 + 2.67501i −0.0533511 + 0.0924068i
\(839\) 30.9593 20.3622i 1.06883 0.702982i 0.112025 0.993705i \(-0.464266\pi\)
0.956807 + 0.290723i \(0.0938959\pi\)
\(840\) −10.7571 0.680980i −0.371156 0.0234960i
\(841\) −10.1984 + 23.6426i −0.351669 + 0.815261i
\(842\) 1.28225 + 4.28300i 0.0441891 + 0.147602i
\(843\) 12.5503 + 35.0303i 0.432255 + 1.20651i
\(844\) −3.03319 7.03173i −0.104407 0.242042i
\(845\) 29.3909 24.6619i 1.01108 0.848395i
\(846\) −0.579635 3.49292i −0.0199283 0.120089i
\(847\) −28.2267 23.6850i −0.969882 0.813828i
\(848\) 3.22763 10.7810i 0.110837 0.370222i
\(849\) −0.577664 0.888017i −0.0198254 0.0304767i
\(850\) −0.0754339 + 1.29515i −0.00258736 + 0.0444233i
\(851\) −0.199892 + 3.43201i −0.00685220 + 0.117648i
\(852\) 3.74239 + 5.75301i 0.128212 + 0.197095i
\(853\) 4.34824 14.5241i 0.148881 0.497297i −0.850718 0.525623i \(-0.823832\pi\)
0.999599 + 0.0283256i \(0.00901751\pi\)
\(854\) −1.88445 1.58124i −0.0644845 0.0541089i
\(855\) 34.4547 28.3237i 1.17833 0.968650i
\(856\) −4.44962 + 3.73368i −0.152085 + 0.127614i
\(857\) −2.42316 5.61751i −0.0827734 0.191890i 0.871803 0.489857i \(-0.162951\pi\)
−0.954576 + 0.297966i \(0.903692\pi\)
\(858\) 0.420075 + 1.17251i 0.0143411 + 0.0400289i
\(859\) 1.68413 + 5.62537i 0.0574616 + 0.191935i 0.981901 0.189393i \(-0.0606520\pi\)
−0.924440 + 0.381328i \(0.875467\pi\)
\(860\) −6.10092 + 14.1435i −0.208040 + 0.482290i
\(861\) 6.51883 + 0.412675i 0.222161 + 0.0140639i
\(862\) 2.65309 1.74496i 0.0903644 0.0594336i
\(863\) −0.872485 + 1.51119i −0.0296997 + 0.0514414i −0.880493 0.474059i \(-0.842788\pi\)
0.850794 + 0.525500i \(0.176122\pi\)
\(864\) −6.20090 + 4.47221i −0.210959 + 0.152148i
\(865\) −5.88182 10.1876i −0.199988 0.346389i
\(866\) 0.552597 + 0.277525i 0.0187780 + 0.00943068i
\(867\) −5.82834 + 24.0505i −0.197941 + 0.816799i
\(868\) 30.0904 + 40.4185i 1.02134 + 1.37189i
\(869\) −17.6072 + 18.6625i −0.597283 + 0.633083i
\(870\) −1.12598 0.657676i −0.0381742 0.0222973i
\(871\) −3.83975 0.448802i −0.130105 0.0152071i
\(872\) 0.196474 + 0.0715107i 0.00665345 + 0.00242166i
\(873\) −1.92262 + 28.1209i −0.0650709 + 0.951749i
\(874\) 0.548351 0.199583i 0.0185482 0.00675100i
\(875\) 16.6694 3.95072i 0.563529 0.133559i
\(876\) 44.3110 + 33.3369i 1.49713 + 1.12635i
\(877\) −39.4245 25.9299i −1.33127 0.875591i −0.333529 0.942740i \(-0.608240\pi\)
−0.997743 + 0.0671485i \(0.978610\pi\)
\(878\) 0.372513 0.187083i 0.0125717 0.00631374i
\(879\) −12.1025 52.2372i −0.408208 1.76192i
\(880\) −41.2737 43.7476i −1.39134 1.47473i
\(881\) 3.06509 17.3830i 0.103266 0.585648i −0.888633 0.458618i \(-0.848345\pi\)
0.991899 0.127030i \(-0.0405443\pi\)
\(882\) 0.124932 + 2.59578i 0.00420668 + 0.0874045i
\(883\) 1.28101 + 7.26495i 0.0431093 + 0.244485i 0.998746 0.0500627i \(-0.0159421\pi\)
−0.955637 + 0.294548i \(0.904831\pi\)
\(884\) 2.48136 3.33304i 0.0834571 0.112102i
\(885\) −21.5566 + 58.3096i −0.724616 + 1.96006i
\(886\) −1.61348 0.382401i −0.0542058 0.0128470i
\(887\) 2.92907 0.342359i 0.0983484 0.0114953i −0.0667763 0.997768i \(-0.521271\pi\)
0.165125 + 0.986273i \(0.447197\pi\)
\(888\) 0.305748 + 2.73540i 0.0102602 + 0.0917940i
\(889\) 0.787702 + 13.5243i 0.0264187 + 0.453591i
\(890\) −4.08296 −0.136861
\(891\) −6.31846 40.6074i −0.211676 1.36040i
\(892\) −5.93798 −0.198818
\(893\) −2.44373 41.9572i −0.0817763 1.40404i
\(894\) 0.805082 + 0.352104i 0.0269260 + 0.0117761i
\(895\) 50.3815 5.88875i 1.68407 0.196839i
\(896\) 14.1533 + 3.35439i 0.472828 + 0.112062i
\(897\) 2.31757 0.396610i 0.0773815 0.0132424i
\(898\) −2.43050 + 3.26473i −0.0811068 + 0.108945i
\(899\) 2.12530 + 12.0532i 0.0708828 + 0.401996i
\(900\) 22.9137 30.1390i 0.763791 1.00463i
\(901\) −0.823536 + 4.67050i −0.0274360 + 0.155597i
\(902\) −0.391337 0.414793i −0.0130301 0.0138111i
\(903\) 14.2716 + 4.35119i 0.474931 + 0.144799i
\(904\) 6.05587 3.04137i 0.201415 0.101154i
\(905\) 6.03588 + 3.96986i 0.200639 + 0.131963i
\(906\) −0.230419 + 1.88871i −0.00765516 + 0.0627482i
\(907\) 7.01551 1.66271i 0.232946 0.0552093i −0.112485 0.993653i \(-0.535881\pi\)
0.345431 + 0.938444i \(0.387733\pi\)
\(908\) 44.8209 16.3135i 1.48743 0.541382i
\(909\) 6.65789 15.0164i 0.220828 0.498064i
\(910\) 1.86565 + 0.679040i 0.0618456 + 0.0225099i
\(911\) 14.2433 + 1.66481i 0.471902 + 0.0551575i 0.348721 0.937227i \(-0.386616\pi\)
0.123182 + 0.992384i \(0.460690\pi\)
\(912\) −25.9352 + 14.7998i −0.858800 + 0.490070i
\(913\) 37.7826 40.0472i 1.25042 1.32537i
\(914\) −1.56794 2.10611i −0.0518630 0.0696641i
\(915\) 29.7318 8.73800i 0.982904 0.288869i
\(916\) 8.39452 + 4.21588i 0.277363 + 0.139297i
\(917\) −11.6893 20.2465i −0.386015 0.668598i
\(918\) 0.782030 0.715758i 0.0258108 0.0236235i
\(919\) 23.7632 41.1591i 0.783875 1.35771i −0.145793 0.989315i \(-0.546573\pi\)
0.929669 0.368397i \(-0.120093\pi\)
\(920\) 1.48423 0.976194i 0.0489337 0.0321842i
\(921\) −21.8179 + 32.8110i −0.718926 + 1.08116i
\(922\) 0.813711 1.88639i 0.0267981 0.0621251i
\(923\) −0.727932 2.43146i −0.0239602 0.0800325i
\(924\) −37.9682 + 44.7881i −1.24906 + 1.47342i
\(925\) −8.10836 18.7973i −0.266601 0.618051i
\(926\) 0.324575 0.272351i 0.0106662 0.00895000i
\(927\) −3.45545 6.12691i −0.113492 0.201234i
\(928\) 2.03246 + 1.70543i 0.0667186 + 0.0559836i
\(929\) −14.6368 + 48.8903i −0.480217 + 1.60404i 0.283829 + 0.958875i \(0.408395\pi\)
−0.764046 + 0.645162i \(0.776790\pi\)
\(930\) 4.90126 0.260672i 0.160719 0.00854778i
\(931\) −1.79364 + 30.7956i −0.0587842 + 1.00929i
\(932\) −1.20599 + 20.7060i −0.0395035 + 0.678249i
\(933\) −24.0515 + 47.2942i −0.787409 + 1.54834i
\(934\) 0.335583 1.12093i 0.0109806 0.0366778i
\(935\) 19.4161 + 16.2921i 0.634976 + 0.532808i
\(936\) 1.77537 0.625979i 0.0580299 0.0204608i
\(937\) −22.5978 + 18.9618i −0.738237 + 0.619454i −0.932364 0.361522i \(-0.882257\pi\)
0.194127 + 0.980976i \(0.437813\pi\)
\(938\) 0.558147 + 1.29393i 0.0182242 + 0.0422484i
\(939\) 38.8728 + 7.05663i 1.26857 + 0.230285i
\(940\) −18.2772 61.0500i −0.596136 1.99123i
\(941\) −23.2693 + 53.9442i −0.758557 + 1.75853i −0.114680 + 0.993402i \(0.536584\pi\)
−0.643876 + 0.765129i \(0.722675\pi\)
\(942\) −0.505469 1.01926i −0.0164691 0.0332092i
\(943\) −0.899446 + 0.591575i −0.0292900 + 0.0192643i
\(944\) 20.8100 36.0440i 0.677309 1.17313i
\(945\) −56.2306 33.6091i −1.82918 1.09330i
\(946\) −0.651300 1.12808i −0.0211756 0.0366772i
\(947\) −10.5308 5.28878i −0.342206 0.171862i 0.269393 0.963030i \(-0.413177\pi\)
−0.611599 + 0.791168i \(0.709473\pi\)
\(948\) 13.9824 + 13.3256i 0.454128 + 0.432797i
\(949\) −12.2457 16.4488i −0.397512 0.533951i
\(950\) −2.38460 + 2.52753i −0.0773667 + 0.0820040i
\(951\) −0.0700707 + 13.8947i −0.00227220 + 0.450565i
\(952\) −3.02048 0.353043i −0.0978943 0.0114422i
\(953\) 33.2006 + 12.0840i 1.07547 + 0.391441i 0.818221 0.574904i \(-0.194960\pi\)
0.257253 + 0.966344i \(0.417183\pi\)
\(954\) −0.742190 + 0.770947i −0.0240293 + 0.0249603i
\(955\) −65.9527 + 24.0048i −2.13418 + 0.776778i
\(956\) 30.5654 7.24413i 0.988555 0.234292i
\(957\) −13.1235 + 5.58262i −0.424224 + 0.180460i
\(958\) −1.89091 1.24367i −0.0610924 0.0401811i
\(959\) 54.7428 27.4929i 1.76774 0.887792i
\(960\) −32.5684 + 30.4177i −1.05114 + 0.981728i
\(961\) −10.3404 10.9602i −0.333560 0.353553i
\(962\) 0.0880371 0.499283i 0.00283843 0.0160975i
\(963\) −34.4314 + 7.79447i −1.10954 + 0.251173i
\(964\) −6.07958 34.4790i −0.195810 1.11049i
\(965\) −28.3679 + 38.1047i −0.913196 + 1.22663i
\(966\) −0.547598 0.659326i −0.0176187 0.0212135i
\(967\) −55.7139 13.2044i −1.79164 0.424626i −0.805782 0.592213i \(-0.798254\pi\)
−0.985857 + 0.167587i \(0.946403\pi\)
\(968\) 4.82937 0.564472i 0.155222 0.0181428i
\(969\) 10.1316 7.46356i 0.325473 0.239764i
\(970\) −0.228082 3.91602i −0.00732329 0.125736i
\(971\) −25.0907 −0.805200 −0.402600 0.915376i \(-0.631893\pi\)
−0.402600 + 0.915376i \(0.631893\pi\)
\(972\) −30.5934 + 4.60241i −0.981285 + 0.147622i
\(973\) −73.1022 −2.34355
\(974\) −0.224842 3.86039i −0.00720441 0.123695i
\(975\) −11.2728 + 8.30425i −0.361018 + 0.265949i
\(976\) −20.6068 + 2.40858i −0.659606 + 0.0770969i
\(977\) 28.7634 + 6.81706i 0.920224 + 0.218097i 0.663316 0.748339i \(-0.269148\pi\)
0.256907 + 0.966436i \(0.417297\pi\)
\(978\) 0.667143 + 0.803262i 0.0213329 + 0.0256855i
\(979\) −26.6662 + 35.8190i −0.852257 + 1.14478i
\(980\) 8.12229 + 46.0638i 0.259457 + 1.47145i
\(981\) 0.862669 + 0.933051i 0.0275429 + 0.0297900i
\(982\) 0.0470343 0.266745i 0.00150092 0.00851216i
\(983\) 33.3876 + 35.3888i 1.06490 + 1.12873i 0.991324 + 0.131439i \(0.0419597\pi\)
0.0735760 + 0.997290i \(0.476559\pi\)
\(984\) −0.629915 + 0.588318i −0.0200810 + 0.0187549i
\(985\) −5.77054 + 2.89807i −0.183865 + 0.0923403i
\(986\) −0.307375 0.202164i −0.00978881 0.00643820i
\(987\) −56.8029 + 24.1634i −1.80806 + 0.769129i
\(988\) 10.8297 2.56668i 0.344538 0.0816571i
\(989\) −2.31077 + 0.841053i −0.0734783 + 0.0267439i
\(990\) 1.58495 + 5.49524i 0.0503731 + 0.174650i
\(991\) 20.7603 + 7.55612i 0.659472 + 0.240028i 0.650008 0.759927i \(-0.274765\pi\)
0.00946345 + 0.999955i \(0.496988\pi\)
\(992\) −9.91906 1.15937i −0.314931 0.0368101i
\(993\) 0.160711 31.8683i 0.00510002 1.01131i
\(994\) −0.634893 + 0.672947i −0.0201376 + 0.0213446i
\(995\) −32.4048 43.5272i −1.02730 1.37990i
\(996\) −30.0044 28.5950i −0.950725 0.906068i
\(997\) 5.82285 + 2.92435i 0.184412 + 0.0926150i 0.538610 0.842555i \(-0.318950\pi\)
−0.354198 + 0.935170i \(0.615246\pi\)
\(998\) −0.0389742 0.0675054i −0.00123371 0.00213684i
\(999\) −5.95861 + 15.6312i −0.188522 + 0.494549i
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 81.2.g.a.40.4 144
3.2 odd 2 243.2.g.a.91.5 144
9.2 odd 6 729.2.g.a.28.5 144
9.4 even 3 729.2.g.c.271.5 144
9.5 odd 6 729.2.g.b.271.4 144
9.7 even 3 729.2.g.d.28.4 144
81.2 odd 54 243.2.g.a.235.5 144
81.22 even 27 6561.2.a.c.1.37 72
81.25 even 27 729.2.g.d.703.4 144
81.29 odd 54 729.2.g.b.460.4 144
81.52 even 27 729.2.g.c.460.5 144
81.56 odd 54 729.2.g.a.703.5 144
81.59 odd 54 6561.2.a.d.1.36 72
81.79 even 27 inner 81.2.g.a.79.4 yes 144
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
81.2.g.a.40.4 144 1.1 even 1 trivial
81.2.g.a.79.4 yes 144 81.79 even 27 inner
243.2.g.a.91.5 144 3.2 odd 2
243.2.g.a.235.5 144 81.2 odd 54
729.2.g.a.28.5 144 9.2 odd 6
729.2.g.a.703.5 144 81.56 odd 54
729.2.g.b.271.4 144 9.5 odd 6
729.2.g.b.460.4 144 81.29 odd 54
729.2.g.c.271.5 144 9.4 even 3
729.2.g.c.460.5 144 81.52 even 27
729.2.g.d.28.4 144 9.7 even 3
729.2.g.d.703.4 144 81.25 even 27
6561.2.a.c.1.37 72 81.22 even 27
6561.2.a.d.1.36 72 81.59 odd 54