Properties

Label 81.2.g.a.25.5
Level $81$
Weight $2$
Character 81.25
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 25.5
Character \(\chi\) \(=\) 81.25
Dual form 81.2.g.a.13.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.507233 + 0.254742i) q^{2} +(1.73070 + 0.0683184i) q^{3} +(-1.00193 + 1.34582i) q^{4} +(-0.832798 + 2.78174i) q^{5} +(-0.895274 + 0.406230i) q^{6} +(1.23966 - 2.87385i) q^{7} +(0.362501 - 2.05585i) q^{8} +(2.99067 + 0.236478i) q^{9} +O(q^{10})\) \(q+(-0.507233 + 0.254742i) q^{2} +(1.73070 + 0.0683184i) q^{3} +(-1.00193 + 1.34582i) q^{4} +(-0.832798 + 2.78174i) q^{5} +(-0.895274 + 0.406230i) q^{6} +(1.23966 - 2.87385i) q^{7} +(0.362501 - 2.05585i) q^{8} +(2.99067 + 0.236478i) q^{9} +(-0.286203 - 1.62314i) q^{10} +(-3.33963 - 0.791507i) q^{11} +(-1.82598 + 2.26076i) q^{12} +(3.33176 - 2.19133i) q^{13} +(0.103295 + 1.77350i) q^{14} +(-1.63137 + 4.75747i) q^{15} +(-0.622571 - 2.07953i) q^{16} +(0.878443 + 0.319727i) q^{17} +(-1.57721 + 0.641899i) q^{18} +(-4.55845 + 1.65914i) q^{19} +(-2.90932 - 3.90789i) q^{20} +(2.34181 - 4.88908i) q^{21} +(1.89560 - 0.449266i) q^{22} +(-2.43678 - 5.64910i) q^{23} +(0.767834 - 3.53329i) q^{24} +(-2.86709 - 1.88571i) q^{25} +(-1.13175 + 1.96026i) q^{26} +(5.15980 + 0.613590i) q^{27} +(2.62564 + 4.54773i) q^{28} +(-0.104644 + 1.79666i) q^{29} +(-0.384443 - 2.82873i) q^{30} +(-0.671302 - 0.0784640i) q^{31} +(3.71068 + 3.93309i) q^{32} +(-5.72584 - 1.59802i) q^{33} +(-0.527023 + 0.0616002i) q^{34} +(6.96191 + 5.84174i) q^{35} +(-3.31468 + 3.78796i) q^{36} +(-8.73079 + 7.32600i) q^{37} +(1.88954 - 2.00280i) q^{38} +(5.91600 - 3.56493i) q^{39} +(5.41694 + 2.72049i) q^{40} +(5.94501 + 2.98570i) q^{41} +(0.0576097 + 3.07646i) q^{42} +(1.53472 - 1.62671i) q^{43} +(4.41129 - 3.70151i) q^{44} +(-3.14844 + 8.12232i) q^{45} +(2.67508 + 2.24466i) q^{46} +(3.14822 - 0.367974i) q^{47} +(-0.935415 - 3.64158i) q^{48} +(-1.91856 - 2.03355i) q^{49} +(1.93465 + 0.226128i) q^{50} +(1.49848 + 0.613366i) q^{51} +(-0.389036 + 6.67950i) q^{52} +(-4.18963 - 7.25666i) q^{53} +(-2.77353 + 1.00318i) q^{54} +(4.98301 - 8.63082i) q^{55} +(-5.45881 - 3.59032i) q^{56} +(-8.00267 + 2.56005i) q^{57} +(-0.404606 - 0.937983i) q^{58} +(-4.89526 + 1.16020i) q^{59} +(-4.76818 - 6.96216i) q^{60} +(-0.340761 - 0.457722i) q^{61} +(0.360495 - 0.131209i) q^{62} +(4.38700 - 8.30156i) q^{63} +(1.19553 + 0.435136i) q^{64} +(3.32104 + 11.0930i) q^{65} +(3.31142 - 0.648041i) q^{66} +(0.794778 + 13.6458i) q^{67} +(-1.31043 + 0.861882i) q^{68} +(-3.83141 - 9.94338i) q^{69} +(-5.01945 - 1.18963i) q^{70} +(-2.31784 - 13.1452i) q^{71} +(1.57028 - 6.06263i) q^{72} +(-1.17142 + 6.64347i) q^{73} +(2.56230 - 5.94009i) q^{74} +(-4.83325 - 3.45948i) q^{75} +(2.33432 - 7.79718i) q^{76} +(-6.41467 + 8.61639i) q^{77} +(-2.09265 + 3.31530i) q^{78} +(0.666057 - 0.334506i) q^{79} +6.30319 q^{80} +(8.88816 + 1.41445i) q^{81} -3.77609 q^{82} +(-3.25233 + 1.63338i) q^{83} +(4.23350 + 8.05015i) q^{84} +(-1.62096 + 2.17733i) q^{85} +(-0.364070 + 1.21608i) q^{86} +(-0.303852 + 3.10234i) q^{87} +(-2.83784 + 6.57885i) q^{88} +(-2.27781 + 12.9181i) q^{89} +(-0.472102 - 4.92195i) q^{90} +(-2.16732 - 12.2915i) q^{91} +(10.0441 + 2.38050i) q^{92} +(-1.15646 - 0.181660i) q^{93} +(-1.50314 + 0.988632i) q^{94} +(-0.819027 - 14.0621i) q^{95} +(6.15338 + 7.06051i) q^{96} +(-3.58656 - 11.9799i) q^{97} +(1.49119 + 0.542748i) q^{98} +(-9.80055 - 3.15688i) 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 \(\left(\mathbb{Z}/81\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{23}{27}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.507233 + 0.254742i −0.358668 + 0.180130i −0.619003 0.785388i \(-0.712463\pi\)
0.260335 + 0.965518i \(0.416167\pi\)
\(3\) 1.73070 + 0.0683184i 0.999222 + 0.0394437i
\(4\) −1.00193 + 1.34582i −0.500963 + 0.672910i
\(5\) −0.832798 + 2.78174i −0.372439 + 1.24403i 0.542368 + 0.840141i \(0.317528\pi\)
−0.914807 + 0.403891i \(0.867657\pi\)
\(6\) −0.895274 + 0.406230i −0.365494 + 0.165843i
\(7\) 1.23966 2.87385i 0.468546 1.08621i −0.506103 0.862473i \(-0.668914\pi\)
0.974649 0.223739i \(-0.0718263\pi\)
\(8\) 0.362501 2.05585i 0.128164 0.726852i
\(9\) 2.99067 + 0.236478i 0.996888 + 0.0788259i
\(10\) −0.286203 1.62314i −0.0905055 0.513282i
\(11\) −3.33963 0.791507i −1.00694 0.238648i −0.306122 0.951992i \(-0.599032\pi\)
−0.700814 + 0.713344i \(0.747180\pi\)
\(12\) −1.82598 + 2.26076i −0.527115 + 0.652626i
\(13\) 3.33176 2.19133i 0.924064 0.607766i 0.00419461 0.999991i \(-0.498665\pi\)
0.919869 + 0.392225i \(0.128294\pi\)
\(14\) 0.103295 + 1.77350i 0.0276067 + 0.473989i
\(15\) −1.63137 + 4.75747i −0.421218 + 1.22837i
\(16\) −0.622571 2.07953i −0.155643 0.519883i
\(17\) 0.878443 + 0.319727i 0.213054 + 0.0775452i 0.446342 0.894862i \(-0.352726\pi\)
−0.233289 + 0.972408i \(0.574949\pi\)
\(18\) −1.57721 + 0.641899i −0.371751 + 0.151297i
\(19\) −4.55845 + 1.65914i −1.04578 + 0.380633i −0.807068 0.590458i \(-0.798947\pi\)
−0.238711 + 0.971091i \(0.576725\pi\)
\(20\) −2.90932 3.90789i −0.650543 0.873831i
\(21\) 2.34181 4.88908i 0.511026 1.06689i
\(22\) 1.89560 0.449266i 0.404144 0.0957838i
\(23\) −2.43678 5.64910i −0.508104 1.17792i −0.958501 0.285089i \(-0.907977\pi\)
0.450397 0.892828i \(-0.351283\pi\)
\(24\) 0.767834 3.53329i 0.156733 0.721231i
\(25\) −2.86709 1.88571i −0.573417 0.377143i
\(26\) −1.13175 + 1.96026i −0.221955 + 0.384438i
\(27\) 5.15980 + 0.613590i 0.993003 + 0.118086i
\(28\) 2.62564 + 4.54773i 0.496198 + 0.859441i
\(29\) −0.104644 + 1.79666i −0.0194318 + 0.333631i 0.974556 + 0.224143i \(0.0719583\pi\)
−0.993988 + 0.109488i \(0.965079\pi\)
\(30\) −0.384443 2.82873i −0.0701893 0.516452i
\(31\) −0.671302 0.0784640i −0.120569 0.0140925i 0.0555942 0.998453i \(-0.482295\pi\)
−0.176164 + 0.984361i \(0.556369\pi\)
\(32\) 3.71068 + 3.93309i 0.655961 + 0.695278i
\(33\) −5.72584 1.59802i −0.996740 0.278180i
\(34\) −0.527023 + 0.0616002i −0.0903837 + 0.0105643i
\(35\) 6.96191 + 5.84174i 1.17678 + 0.987434i
\(36\) −3.31468 + 3.78796i −0.552447 + 0.631327i
\(37\) −8.73079 + 7.32600i −1.43533 + 1.20439i −0.492858 + 0.870110i \(0.664048\pi\)
−0.942475 + 0.334277i \(0.891508\pi\)
\(38\) 1.88954 2.00280i 0.306524 0.324897i
\(39\) 5.91600 3.56493i 0.947317 0.570845i
\(40\) 5.41694 + 2.72049i 0.856494 + 0.430147i
\(41\) 5.94501 + 2.98570i 0.928455 + 0.466288i 0.847718 0.530448i \(-0.177976\pi\)
0.0807376 + 0.996735i \(0.474272\pi\)
\(42\) 0.0576097 + 3.07646i 0.00888937 + 0.474709i
\(43\) 1.53472 1.62671i 0.234042 0.248071i −0.599699 0.800226i \(-0.704713\pi\)
0.833741 + 0.552155i \(0.186194\pi\)
\(44\) 4.41129 3.70151i 0.665026 0.558023i
\(45\) −3.14844 + 8.12232i −0.469342 + 1.21080i
\(46\) 2.67508 + 2.24466i 0.394419 + 0.330957i
\(47\) 3.14822 0.367974i 0.459214 0.0536745i 0.116659 0.993172i \(-0.462782\pi\)
0.342556 + 0.939498i \(0.388707\pi\)
\(48\) −0.935415 3.64158i −0.135016 0.525617i
\(49\) −1.91856 2.03355i −0.274080 0.290508i
\(50\) 1.93465 + 0.226128i 0.273601 + 0.0319794i
\(51\) 1.49848 + 0.613366i 0.209829 + 0.0858884i
\(52\) −0.389036 + 6.67950i −0.0539497 + 0.926280i
\(53\) −4.18963 7.25666i −0.575490 0.996779i −0.995988 0.0894851i \(-0.971478\pi\)
0.420498 0.907294i \(-0.361855\pi\)
\(54\) −2.77353 + 1.00318i −0.377429 + 0.136516i
\(55\) 4.98301 8.63082i 0.671909 1.16378i
\(56\) −5.45881 3.59032i −0.729464 0.479776i
\(57\) −8.00267 + 2.56005i −1.05998 + 0.339087i
\(58\) −0.404606 0.937983i −0.0531274 0.123163i
\(59\) −4.89526 + 1.16020i −0.637309 + 0.151045i −0.536554 0.843866i \(-0.680274\pi\)
−0.100755 + 0.994911i \(0.532126\pi\)
\(60\) −4.76818 6.96216i −0.615570 0.898811i
\(61\) −0.340761 0.457722i −0.0436300 0.0586053i 0.779773 0.626063i \(-0.215335\pi\)
−0.823403 + 0.567457i \(0.807927\pi\)
\(62\) 0.360495 0.131209i 0.0457829 0.0166636i
\(63\) 4.38700 8.30156i 0.552710 1.04590i
\(64\) 1.19553 + 0.435136i 0.149441 + 0.0543920i
\(65\) 3.32104 + 11.0930i 0.411924 + 1.37592i
\(66\) 3.31142 0.648041i 0.407607 0.0797684i
\(67\) 0.794778 + 13.6458i 0.0970975 + 1.66710i 0.597924 + 0.801553i \(0.295992\pi\)
−0.500826 + 0.865548i \(0.666971\pi\)
\(68\) −1.31043 + 0.861882i −0.158913 + 0.104519i
\(69\) −3.83141 9.94338i −0.461247 1.19704i
\(70\) −5.01945 1.18963i −0.599939 0.142188i
\(71\) −2.31784 13.1452i −0.275078 1.56004i −0.738715 0.674017i \(-0.764567\pi\)
0.463638 0.886025i \(-0.346544\pi\)
\(72\) 1.57028 6.06263i 0.185059 0.714487i
\(73\) −1.17142 + 6.64347i −0.137105 + 0.777560i 0.836266 + 0.548324i \(0.184734\pi\)
−0.973371 + 0.229236i \(0.926377\pi\)
\(74\) 2.56230 5.94009i 0.297862 0.690521i
\(75\) −4.83325 3.45948i −0.558095 0.399467i
\(76\) 2.33432 7.79718i 0.267765 0.894398i
\(77\) −6.41467 + 8.61639i −0.731019 + 0.981929i
\(78\) −2.09265 + 3.31530i −0.236946 + 0.375384i
\(79\) 0.666057 0.334506i 0.0749373 0.0376349i −0.410936 0.911664i \(-0.634798\pi\)
0.485873 + 0.874029i \(0.338502\pi\)
\(80\) 6.30319 0.704718
\(81\) 8.88816 + 1.41445i 0.987573 + 0.157161i
\(82\) −3.77609 −0.417000
\(83\) −3.25233 + 1.63338i −0.356989 + 0.179287i −0.618250 0.785982i \(-0.712158\pi\)
0.261261 + 0.965268i \(0.415862\pi\)
\(84\) 4.23350 + 8.05015i 0.461913 + 0.878344i
\(85\) −1.62096 + 2.17733i −0.175818 + 0.236165i
\(86\) −0.364070 + 1.21608i −0.0392586 + 0.131133i
\(87\) −0.303852 + 3.10234i −0.0325763 + 0.332605i
\(88\) −2.83784 + 6.57885i −0.302515 + 0.701308i
\(89\) −2.27781 + 12.9181i −0.241447 + 1.36931i 0.587154 + 0.809475i \(0.300248\pi\)
−0.828601 + 0.559839i \(0.810863\pi\)
\(90\) −0.472102 4.92195i −0.0497639 0.518819i
\(91\) −2.16732 12.2915i −0.227197 1.28850i
\(92\) 10.0441 + 2.38050i 1.04717 + 0.248185i
\(93\) −1.15646 0.181660i −0.119920 0.0188373i
\(94\) −1.50314 + 0.988632i −0.155037 + 0.101970i
\(95\) −0.819027 14.0621i −0.0840304 1.44275i
\(96\) 6.15338 + 7.06051i 0.628026 + 0.720611i
\(97\) −3.58656 11.9799i −0.364160 1.21638i −0.922249 0.386597i \(-0.873650\pi\)
0.558089 0.829781i \(-0.311535\pi\)
\(98\) 1.49119 + 0.542748i 0.150633 + 0.0548258i
\(99\) −9.80055 3.15688i −0.984992 0.317279i
\(100\) 5.41044 1.96924i 0.541044 0.196924i
\(101\) −3.57328 4.79974i −0.355554 0.477592i 0.587976 0.808878i \(-0.299925\pi\)
−0.943530 + 0.331286i \(0.892517\pi\)
\(102\) −0.916329 + 0.0706062i −0.0907301 + 0.00699106i
\(103\) 1.72093 0.407867i 0.169568 0.0401883i −0.144955 0.989438i \(-0.546304\pi\)
0.314523 + 0.949250i \(0.398156\pi\)
\(104\) −3.29728 7.64395i −0.323325 0.749551i
\(105\) 11.6499 + 10.5859i 1.13691 + 1.03308i
\(106\) 3.97370 + 2.61354i 0.385960 + 0.253850i
\(107\) −3.57628 + 6.19429i −0.345732 + 0.598825i −0.985486 0.169754i \(-0.945703\pi\)
0.639755 + 0.768579i \(0.279036\pi\)
\(108\) −5.99551 + 6.32938i −0.576918 + 0.609045i
\(109\) −5.68613 9.84867i −0.544633 0.943332i −0.998630 0.0523287i \(-0.983336\pi\)
0.453997 0.891003i \(-0.349998\pi\)
\(110\) −0.328913 + 5.64722i −0.0313606 + 0.538441i
\(111\) −15.6109 + 12.0827i −1.48172 + 1.14684i
\(112\) −6.74803 0.788732i −0.637629 0.0745281i
\(113\) 3.99674 + 4.23629i 0.375981 + 0.398517i 0.887539 0.460732i \(-0.152413\pi\)
−0.511558 + 0.859249i \(0.670932\pi\)
\(114\) 3.40707 3.33716i 0.319101 0.312554i
\(115\) 17.7437 2.07394i 1.65461 0.193396i
\(116\) −2.31313 1.94095i −0.214769 0.180213i
\(117\) 10.4824 5.76566i 0.969096 0.533035i
\(118\) 2.18749 1.83552i 0.201375 0.168973i
\(119\) 2.00781 2.12816i 0.184056 0.195088i
\(120\) 9.18926 + 5.07844i 0.838861 + 0.463596i
\(121\) 0.696696 + 0.349894i 0.0633360 + 0.0318086i
\(122\) 0.289447 + 0.145366i 0.0262053 + 0.0131608i
\(123\) 10.0851 + 5.57351i 0.909341 + 0.502547i
\(124\) 0.778193 0.824836i 0.0698838 0.0740725i
\(125\) −3.48865 + 2.92733i −0.312034 + 0.261828i
\(126\) −0.110474 + 5.32838i −0.00984180 + 0.474690i
\(127\) 8.22802 + 6.90413i 0.730119 + 0.612643i 0.930164 0.367144i \(-0.119664\pi\)
−0.200045 + 0.979787i \(0.564109\pi\)
\(128\) −11.4586 + 1.33932i −1.01281 + 0.118380i
\(129\) 2.76728 2.71050i 0.243645 0.238646i
\(130\) −4.51040 4.78075i −0.395588 0.419299i
\(131\) 7.11419 + 0.831529i 0.621570 + 0.0726511i 0.421048 0.907038i \(-0.361662\pi\)
0.200521 + 0.979689i \(0.435736\pi\)
\(132\) 7.88751 6.10484i 0.686519 0.531358i
\(133\) −0.882797 + 15.1570i −0.0765482 + 1.31428i
\(134\) −3.87930 6.71914i −0.335120 0.580446i
\(135\) −6.00392 + 13.8422i −0.516735 + 1.19135i
\(136\) 0.975746 1.69004i 0.0836695 0.144920i
\(137\) 7.20952 + 4.74178i 0.615951 + 0.405117i 0.818789 0.574095i \(-0.194646\pi\)
−0.202838 + 0.979212i \(0.565016\pi\)
\(138\) 4.47642 + 4.06759i 0.381058 + 0.346257i
\(139\) −2.33653 5.41669i −0.198182 0.459438i 0.789925 0.613203i \(-0.210119\pi\)
−0.988107 + 0.153765i \(0.950860\pi\)
\(140\) −14.8372 + 3.51649i −1.25398 + 0.297198i
\(141\) 5.47377 0.421772i 0.460974 0.0355196i
\(142\) 4.52431 + 6.07720i 0.379672 + 0.509988i
\(143\) −12.8613 + 4.68113i −1.07552 + 0.391456i
\(144\) −1.37014 6.36641i −0.114178 0.530534i
\(145\) −4.91069 1.78735i −0.407811 0.148431i
\(146\) −1.09819 3.66820i −0.0908866 0.303583i
\(147\) −3.18152 3.65055i −0.262408 0.301092i
\(148\) −1.11188 19.0902i −0.0913956 1.56920i
\(149\) 11.5252 7.58026i 0.944184 0.620999i 0.0187156 0.999825i \(-0.494042\pi\)
0.925468 + 0.378825i \(0.123672\pi\)
\(150\) 3.33286 + 0.523534i 0.272127 + 0.0427463i
\(151\) 6.10780 + 1.44758i 0.497046 + 0.117802i 0.471490 0.881871i \(-0.343716\pi\)
0.0255559 + 0.999673i \(0.491864\pi\)
\(152\) 1.75849 + 9.97291i 0.142633 + 0.808910i
\(153\) 2.55152 + 1.16393i 0.206278 + 0.0940980i
\(154\) 1.05877 6.00461i 0.0853185 0.483865i
\(155\) 0.777326 1.80204i 0.0624363 0.144744i
\(156\) −1.12964 + 11.5336i −0.0904435 + 0.923431i
\(157\) 0.0476363 0.159116i 0.00380179 0.0126989i −0.956068 0.293146i \(-0.905298\pi\)
0.959869 + 0.280448i \(0.0904829\pi\)
\(158\) −0.252633 + 0.339346i −0.0200984 + 0.0269969i
\(159\) −6.75525 12.8453i −0.535726 1.01870i
\(160\) −14.0311 + 7.04667i −1.10925 + 0.557088i
\(161\) −19.2554 −1.51754
\(162\) −4.86869 + 1.54673i −0.382520 + 0.121523i
\(163\) 16.2014 1.26899 0.634495 0.772927i \(-0.281208\pi\)
0.634495 + 0.772927i \(0.281208\pi\)
\(164\) −9.97467 + 5.00947i −0.778891 + 0.391174i
\(165\) 9.21375 14.5970i 0.717289 1.13637i
\(166\) 1.23360 1.65701i 0.0957457 0.128609i
\(167\) 5.24163 17.5083i 0.405610 1.35483i −0.474582 0.880211i \(-0.657401\pi\)
0.880191 0.474619i \(-0.157414\pi\)
\(168\) −9.20230 6.58671i −0.709973 0.508176i
\(169\) 1.14965 2.66518i 0.0884345 0.205014i
\(170\) 0.267548 1.51734i 0.0205200 0.116375i
\(171\) −14.0251 + 3.88396i −1.07253 + 0.297014i
\(172\) 0.651580 + 3.69529i 0.0496825 + 0.281763i
\(173\) 18.3456 + 4.34799i 1.39479 + 0.330572i 0.858219 0.513283i \(-0.171571\pi\)
0.536572 + 0.843855i \(0.319719\pi\)
\(174\) −0.636172 1.65101i −0.0482281 0.125163i
\(175\) −8.97346 + 5.90193i −0.678329 + 0.446144i
\(176\) 0.433193 + 7.43764i 0.0326532 + 0.560633i
\(177\) −8.55151 + 1.67352i −0.642771 + 0.125790i
\(178\) −2.13540 7.13274i −0.160055 0.534621i
\(179\) 9.67521 + 3.52149i 0.723159 + 0.263209i 0.677266 0.735738i \(-0.263164\pi\)
0.0458930 + 0.998946i \(0.485387\pi\)
\(180\) −7.77667 12.3752i −0.579638 0.922392i
\(181\) 0.770198 0.280329i 0.0572484 0.0208367i −0.313237 0.949675i \(-0.601414\pi\)
0.370486 + 0.928838i \(0.379191\pi\)
\(182\) 4.23049 + 5.68254i 0.313585 + 0.421218i
\(183\) −0.558486 0.815461i −0.0412845 0.0602806i
\(184\) −12.4970 + 2.96185i −0.921292 + 0.218350i
\(185\) −13.1080 30.3879i −0.963723 2.23416i
\(186\) 0.632874 0.202456i 0.0464045 0.0148448i
\(187\) −2.68061 1.76306i −0.196025 0.128928i
\(188\) −2.65905 + 4.60561i −0.193931 + 0.335899i
\(189\) 8.15974 14.0678i 0.593534 1.02328i
\(190\) 3.99766 + 6.92415i 0.290021 + 0.502330i
\(191\) 0.0444838 0.763757i 0.00321873 0.0552635i −0.996316 0.0857543i \(-0.972670\pi\)
0.999535 + 0.0304908i \(0.00970703\pi\)
\(192\) 2.03937 + 0.834768i 0.147179 + 0.0602442i
\(193\) −9.29144 1.08601i −0.668812 0.0781730i −0.225091 0.974338i \(-0.572268\pi\)
−0.443721 + 0.896165i \(0.646342\pi\)
\(194\) 4.87102 + 5.16298i 0.349719 + 0.370680i
\(195\) 4.98987 + 19.4256i 0.357332 + 1.39110i
\(196\) 4.65905 0.544564i 0.332789 0.0388975i
\(197\) 0.857832 + 0.719807i 0.0611180 + 0.0512841i 0.672835 0.739793i \(-0.265076\pi\)
−0.611717 + 0.791077i \(0.709521\pi\)
\(198\) 5.77535 0.895336i 0.410436 0.0636288i
\(199\) 5.88368 4.93699i 0.417083 0.349974i −0.409969 0.912099i \(-0.634461\pi\)
0.827052 + 0.562125i \(0.190016\pi\)
\(200\) −4.91606 + 5.21072i −0.347618 + 0.368453i
\(201\) 0.443264 + 23.6711i 0.0312654 + 1.66963i
\(202\) 3.03518 + 1.52433i 0.213555 + 0.107251i
\(203\) 5.03360 + 2.52797i 0.353290 + 0.177429i
\(204\) −2.32684 + 1.40214i −0.162912 + 0.0981691i
\(205\) −13.2564 + 14.0510i −0.925870 + 0.981365i
\(206\) −0.769010 + 0.645276i −0.0535794 + 0.0449585i
\(207\) −5.95171 17.4708i −0.413673 1.21430i
\(208\) −6.63120 5.56424i −0.459791 0.385811i
\(209\) 16.5368 1.93287i 1.14387 0.133699i
\(210\) −8.60590 2.40182i −0.593864 0.165741i
\(211\) 7.02525 + 7.44633i 0.483638 + 0.512627i 0.922536 0.385910i \(-0.126113\pi\)
−0.438898 + 0.898537i \(0.644631\pi\)
\(212\) 13.9638 + 1.63214i 0.959041 + 0.112096i
\(213\) −3.11344 22.9087i −0.213330 1.56968i
\(214\) 0.236059 4.05298i 0.0161367 0.277056i
\(215\) 3.24697 + 5.62391i 0.221441 + 0.383547i
\(216\) 3.13188 10.3853i 0.213097 0.706632i
\(217\) −1.05768 + 1.83195i −0.0717999 + 0.124361i
\(218\) 5.39307 + 3.54708i 0.365265 + 0.240238i
\(219\) −2.48126 + 11.4179i −0.167668 + 0.771547i
\(220\) 6.62292 + 15.3537i 0.446517 + 1.03514i
\(221\) 3.62739 0.859707i 0.244005 0.0578301i
\(222\) 4.84041 10.1055i 0.324867 0.678235i
\(223\) −2.77779 3.73122i −0.186014 0.249861i 0.699327 0.714802i \(-0.253483\pi\)
−0.885342 + 0.464941i \(0.846076\pi\)
\(224\) 15.9031 5.78824i 1.06257 0.386743i
\(225\) −8.12857 6.31754i −0.541905 0.421169i
\(226\) −3.10644 1.13065i −0.206637 0.0752098i
\(227\) −4.04954 13.5264i −0.268777 0.897779i −0.980700 0.195521i \(-0.937360\pi\)
0.711922 0.702258i \(-0.247825\pi\)
\(228\) 4.57271 13.3351i 0.302835 0.883140i
\(229\) 0.301500 + 5.17655i 0.0199237 + 0.342076i 0.993509 + 0.113753i \(0.0362872\pi\)
−0.973585 + 0.228323i \(0.926676\pi\)
\(230\) −8.47186 + 5.57203i −0.558618 + 0.367409i
\(231\) −11.6905 + 14.4742i −0.769181 + 0.952331i
\(232\) 3.65572 + 0.866423i 0.240010 + 0.0568834i
\(233\) 0.773336 + 4.38581i 0.0506629 + 0.287324i 0.999604 0.0281287i \(-0.00895483\pi\)
−0.948941 + 0.315452i \(0.897844\pi\)
\(234\) −3.84826 + 5.59484i −0.251568 + 0.365746i
\(235\) −1.59822 + 9.06397i −0.104257 + 0.591268i
\(236\) 3.34327 7.75057i 0.217628 0.504519i
\(237\) 1.17560 0.533427i 0.0763634 0.0346498i
\(238\) −0.476298 + 1.59095i −0.0308738 + 0.103126i
\(239\) −17.3543 + 23.3108i −1.12255 + 1.50785i −0.287420 + 0.957805i \(0.592798\pi\)
−0.835134 + 0.550047i \(0.814610\pi\)
\(240\) 10.9090 + 0.430624i 0.704170 + 0.0277967i
\(241\) 22.3266 11.2128i 1.43818 0.722281i 0.452635 0.891696i \(-0.350484\pi\)
0.985545 + 0.169415i \(0.0541877\pi\)
\(242\) −0.442520 −0.0284463
\(243\) 15.2861 + 3.05522i 0.980605 + 0.195992i
\(244\) 0.957429 0.0612931
\(245\) 7.25459 3.64339i 0.463479 0.232768i
\(246\) −6.53529 0.257977i −0.416675 0.0164480i
\(247\) −11.5519 + 15.5169i −0.735031 + 0.987319i
\(248\) −0.404658 + 1.35165i −0.0256958 + 0.0858299i
\(249\) −5.74040 + 2.60470i −0.363783 + 0.165066i
\(250\) 1.02385 2.37354i 0.0647538 0.150116i
\(251\) 2.46091 13.9565i 0.155331 0.880926i −0.803152 0.595775i \(-0.796845\pi\)
0.958483 0.285151i \(-0.0920438\pi\)
\(252\) 6.77696 + 14.2217i 0.426908 + 0.895880i
\(253\) 3.66665 + 20.7946i 0.230521 + 1.30735i
\(254\) −5.93230 1.40598i −0.372226 0.0882191i
\(255\) −2.95416 + 3.65757i −0.184996 + 0.229046i
\(256\) 3.34511 2.20011i 0.209069 0.137507i
\(257\) −0.854668 14.6741i −0.0533127 0.915344i −0.913874 0.405997i \(-0.866924\pi\)
0.860562 0.509347i \(-0.170113\pi\)
\(258\) −0.713177 + 2.07980i −0.0444005 + 0.129482i
\(259\) 10.2306 + 34.1727i 0.635700 + 2.12339i
\(260\) −18.2566 6.64487i −1.13223 0.412098i
\(261\) −0.737824 + 5.34846i −0.0456702 + 0.331062i
\(262\) −3.82038 + 1.39050i −0.236024 + 0.0859056i
\(263\) 9.78683 + 13.1460i 0.603482 + 0.810617i 0.993931 0.110008i \(-0.0350876\pi\)
−0.390449 + 0.920625i \(0.627680\pi\)
\(264\) −5.36091 + 11.1922i −0.329941 + 0.688830i
\(265\) 23.6753 5.61114i 1.45436 0.344690i
\(266\) −3.41335 7.91304i −0.209286 0.485180i
\(267\) −4.82475 + 22.2018i −0.295270 + 1.35873i
\(268\) −19.1611 12.6024i −1.17045 0.769817i
\(269\) 5.68131 9.84032i 0.346396 0.599975i −0.639211 0.769032i \(-0.720739\pi\)
0.985606 + 0.169057i \(0.0540721\pi\)
\(270\) −0.480808 8.55068i −0.0292611 0.520378i
\(271\) −1.38266 2.39483i −0.0839903 0.145476i 0.820970 0.570971i \(-0.193433\pi\)
−0.904961 + 0.425496i \(0.860100\pi\)
\(272\) 0.117990 2.02580i 0.00715416 0.122832i
\(273\) −2.91125 21.4210i −0.176197 1.29646i
\(274\) −4.86484 0.568618i −0.293896 0.0343515i
\(275\) 8.08246 + 8.56691i 0.487391 + 0.516604i
\(276\) 17.2208 + 4.80614i 1.03657 + 0.289296i
\(277\) −18.2717 + 2.13566i −1.09784 + 0.128319i −0.645673 0.763614i \(-0.723423\pi\)
−0.452167 + 0.891933i \(0.649349\pi\)
\(278\) 2.56503 + 2.15231i 0.153840 + 0.129087i
\(279\) −1.98909 0.393408i −0.119083 0.0235527i
\(280\) 14.5334 12.1950i 0.868538 0.728790i
\(281\) −7.36555 + 7.80702i −0.439392 + 0.465728i −0.908787 0.417260i \(-0.862990\pi\)
0.469395 + 0.882988i \(0.344472\pi\)
\(282\) −2.66903 + 1.60834i −0.158939 + 0.0957750i
\(283\) −12.7718 6.41421i −0.759202 0.381285i 0.0266946 0.999644i \(-0.491502\pi\)
−0.785896 + 0.618358i \(0.787798\pi\)
\(284\) 20.0133 + 10.0511i 1.18757 + 0.596421i
\(285\) −0.456788 24.3933i −0.0270578 1.44494i
\(286\) 5.33120 5.65074i 0.315241 0.334135i
\(287\) 15.9502 13.3838i 0.941512 0.790022i
\(288\) 10.1673 + 12.6400i 0.599114 + 0.744821i
\(289\) −12.3533 10.3657i −0.726666 0.609745i
\(290\) 2.94618 0.344359i 0.173006 0.0202215i
\(291\) −5.38882 20.9787i −0.315898 1.22980i
\(292\) −7.76724 8.23279i −0.454543 0.481787i
\(293\) 21.6982 + 2.53616i 1.26762 + 0.148164i 0.723195 0.690644i \(-0.242673\pi\)
0.544428 + 0.838808i \(0.316747\pi\)
\(294\) 2.54372 + 1.04121i 0.148353 + 0.0607247i
\(295\) 0.849396 14.5836i 0.0494537 0.849088i
\(296\) 11.8962 + 20.6048i 0.691453 + 1.19763i
\(297\) −16.7462 6.13318i −0.971711 0.355883i
\(298\) −3.91497 + 6.78092i −0.226788 + 0.392808i
\(299\) −20.4978 13.4816i −1.18542 0.779663i
\(300\) 9.49839 3.03853i 0.548390 0.175430i
\(301\) −2.77238 6.42711i −0.159798 0.370452i
\(302\) −3.46684 + 0.821656i −0.199494 + 0.0472810i
\(303\) −5.85637 8.55105i −0.336440 0.491245i
\(304\) 6.28819 + 8.44650i 0.360652 + 0.484440i
\(305\) 1.55705 0.566720i 0.0891564 0.0324503i
\(306\) −1.59072 + 0.0595962i −0.0909352 + 0.00340689i
\(307\) −28.6368 10.4229i −1.63439 0.594869i −0.648344 0.761347i \(-0.724538\pi\)
−0.986045 + 0.166478i \(0.946760\pi\)
\(308\) −5.16909 17.2660i −0.294536 0.983820i
\(309\) 3.00627 0.588325i 0.171021 0.0334687i
\(310\) 0.0647710 + 1.11207i 0.00367874 + 0.0631616i
\(311\) −22.6519 + 14.8984i −1.28447 + 0.844812i −0.993710 0.111983i \(-0.964280\pi\)
−0.290764 + 0.956795i \(0.593909\pi\)
\(312\) −5.18439 13.4547i −0.293508 0.761721i
\(313\) −7.88787 1.86946i −0.445849 0.105668i 0.00155774 0.999999i \(-0.499504\pi\)
−0.447407 + 0.894331i \(0.647652\pi\)
\(314\) 0.0163709 + 0.0928440i 0.000923863 + 0.00523949i
\(315\) 19.4393 + 19.1170i 1.09528 + 1.07712i
\(316\) −0.217154 + 1.23154i −0.0122159 + 0.0692797i
\(317\) −7.69151 + 17.8309i −0.431998 + 1.00148i 0.553662 + 0.832742i \(0.313230\pi\)
−0.985660 + 0.168743i \(0.946029\pi\)
\(318\) 6.69874 + 4.79474i 0.375647 + 0.268876i
\(319\) 1.77154 5.91736i 0.0991872 0.331308i
\(320\) −2.20607 + 2.96326i −0.123323 + 0.165652i
\(321\) −6.61266 + 10.4762i −0.369083 + 0.584722i
\(322\) 9.76698 4.90516i 0.544293 0.273354i
\(323\) −4.53480 −0.252323
\(324\) −10.8089 + 10.5447i −0.600492 + 0.585815i
\(325\) −13.6847 −0.759089
\(326\) −8.21787 + 4.12717i −0.455146 + 0.228583i
\(327\) −9.16816 17.4336i −0.507001 0.964080i
\(328\) 8.29321 11.1397i 0.457916 0.615088i
\(329\) 2.84521 9.50365i 0.156861 0.523953i
\(330\) −0.955060 + 9.75119i −0.0525743 + 0.536785i
\(331\) 0.786897 1.82423i 0.0432518 0.100269i −0.895221 0.445623i \(-0.852982\pi\)
0.938472 + 0.345354i \(0.112241\pi\)
\(332\) 1.06035 6.01357i 0.0581945 0.330037i
\(333\) −27.8433 + 19.8450i −1.52580 + 1.08750i
\(334\) 1.80136 + 10.2160i 0.0985662 + 0.558997i
\(335\) −38.6210 9.15334i −2.11009 0.500100i
\(336\) −11.6250 1.82607i −0.634193 0.0996206i
\(337\) 15.3358 10.0865i 0.835397 0.549449i −0.0582076 0.998304i \(-0.518539\pi\)
0.893604 + 0.448855i \(0.148168\pi\)
\(338\) 0.0957949 + 1.64473i 0.00521055 + 0.0894617i
\(339\) 6.62775 + 7.60482i 0.359970 + 0.413037i
\(340\) −1.30621 4.36305i −0.0708392 0.236619i
\(341\) 2.17980 + 0.793381i 0.118043 + 0.0429640i
\(342\) 6.12461 5.54287i 0.331181 0.299724i
\(343\) 12.3650 4.50048i 0.667646 0.243003i
\(344\) −2.78792 3.74483i −0.150315 0.201908i
\(345\) 30.8507 2.37715i 1.66095 0.127981i
\(346\) −10.4131 + 2.46796i −0.559813 + 0.132678i
\(347\) 10.6086 + 24.5935i 0.569499 + 1.32025i 0.922995 + 0.384812i \(0.125734\pi\)
−0.353496 + 0.935436i \(0.615007\pi\)
\(348\) −3.87075 3.51724i −0.207494 0.188544i
\(349\) 10.9528 + 7.20376i 0.586289 + 0.385608i 0.807719 0.589568i \(-0.200702\pi\)
−0.221430 + 0.975176i \(0.571072\pi\)
\(350\) 3.04816 5.27957i 0.162931 0.282205i
\(351\) 18.5358 9.26250i 0.989367 0.494396i
\(352\) −9.27922 16.0721i −0.494584 0.856645i
\(353\) 1.13003 19.4019i 0.0601456 1.03266i −0.824341 0.566094i \(-0.808454\pi\)
0.884486 0.466566i \(-0.154509\pi\)
\(354\) 3.91129 3.02730i 0.207883 0.160899i
\(355\) 38.4967 + 4.49962i 2.04319 + 0.238815i
\(356\) −15.1032 16.0085i −0.800469 0.848447i
\(357\) 3.62032 3.54604i 0.191608 0.187676i
\(358\) −5.80466 + 0.678468i −0.306786 + 0.0358581i
\(359\) −11.2428 9.43384i −0.593373 0.497899i 0.295935 0.955208i \(-0.404369\pi\)
−0.889308 + 0.457309i \(0.848813\pi\)
\(360\) 15.5569 + 9.41706i 0.819922 + 0.496323i
\(361\) 3.47185 2.91323i 0.182729 0.153328i
\(362\) −0.319258 + 0.338394i −0.0167798 + 0.0177856i
\(363\) 1.18187 + 0.653160i 0.0620321 + 0.0342820i
\(364\) 18.7136 + 9.39832i 0.980858 + 0.492606i
\(365\) −17.5049 8.79127i −0.916246 0.460156i
\(366\) 0.491015 + 0.271359i 0.0256658 + 0.0141842i
\(367\) 7.54456 7.99677i 0.393823 0.417428i −0.499875 0.866098i \(-0.666621\pi\)
0.893698 + 0.448670i \(0.148102\pi\)
\(368\) −10.2304 + 8.58433i −0.533297 + 0.447489i
\(369\) 17.0735 + 10.3351i 0.888811 + 0.538023i
\(370\) 14.3899 + 12.0746i 0.748096 + 0.627727i
\(371\) −26.0482 + 3.04460i −1.35236 + 0.158068i
\(372\) 1.40317 1.37438i 0.0727511 0.0712584i
\(373\) 14.0118 + 14.8517i 0.725505 + 0.768990i 0.980195 0.198033i \(-0.0634552\pi\)
−0.254691 + 0.967023i \(0.581974\pi\)
\(374\) 1.80882 + 0.211421i 0.0935319 + 0.0109323i
\(375\) −6.23781 + 4.82799i −0.322119 + 0.249316i
\(376\) 0.384735 6.60564i 0.0198412 0.340660i
\(377\) 3.58843 + 6.21535i 0.184814 + 0.320107i
\(378\) −0.555224 + 9.21430i −0.0285577 + 0.473932i
\(379\) −13.0154 + 22.5433i −0.668556 + 1.15797i 0.309753 + 0.950817i \(0.399754\pi\)
−0.978308 + 0.207155i \(0.933580\pi\)
\(380\) 19.7457 + 12.9870i 1.01293 + 0.666217i
\(381\) 13.7686 + 12.5111i 0.705386 + 0.640964i
\(382\) 0.171997 + 0.398735i 0.00880015 + 0.0204010i
\(383\) −22.8964 + 5.42654i −1.16995 + 0.277283i −0.769263 0.638932i \(-0.779376\pi\)
−0.400686 + 0.916215i \(0.631228\pi\)
\(384\) −19.9230 + 1.53513i −1.01669 + 0.0783394i
\(385\) −18.6264 25.0197i −0.949292 1.27512i
\(386\) 4.98958 1.81606i 0.253963 0.0924349i
\(387\) 4.97451 4.50201i 0.252869 0.228850i
\(388\) 19.7163 + 7.17615i 1.00094 + 0.364314i
\(389\) 9.48468 + 31.6810i 0.480892 + 1.60629i 0.762653 + 0.646807i \(0.223896\pi\)
−0.281761 + 0.959485i \(0.590919\pi\)
\(390\) −7.47955 8.58220i −0.378742 0.434576i
\(391\) −0.334405 5.74151i −0.0169116 0.290361i
\(392\) −4.87615 + 3.20710i −0.246283 + 0.161983i
\(393\) 12.2557 + 1.92516i 0.618220 + 0.0971115i
\(394\) −0.618486 0.146584i −0.0311589 0.00738479i
\(395\) 0.375819 + 2.13137i 0.0189095 + 0.107241i
\(396\) 14.0680 10.0268i 0.706944 0.503866i
\(397\) −0.00960087 + 0.0544493i −0.000481854 + 0.00273273i −0.985048 0.172282i \(-0.944886\pi\)
0.984566 + 0.175014i \(0.0559972\pi\)
\(398\) −1.72674 + 4.00303i −0.0865536 + 0.200654i
\(399\) −2.56336 + 26.1720i −0.128329 + 1.31024i
\(400\) −2.13643 + 7.13619i −0.106822 + 0.356809i
\(401\) −17.1048 + 22.9757i −0.854173 + 1.14735i 0.133535 + 0.991044i \(0.457367\pi\)
−0.987708 + 0.156310i \(0.950040\pi\)
\(402\) −6.25487 11.8939i −0.311965 0.593212i
\(403\) −2.40856 + 1.20962i −0.119979 + 0.0602557i
\(404\) 10.0397 0.499496
\(405\) −11.3367 + 23.5466i −0.563324 + 1.17004i
\(406\) −3.19719 −0.158674
\(407\) 34.9562 17.5557i 1.73271 0.870202i
\(408\) 1.80419 2.85830i 0.0893206 0.141507i
\(409\) 18.7728 25.2163i 0.928255 1.24686i −0.0405846 0.999176i \(-0.512922\pi\)
0.968840 0.247687i \(-0.0796706\pi\)
\(410\) 3.14472 10.5041i 0.155307 0.518761i
\(411\) 12.1536 + 8.69915i 0.599492 + 0.429097i
\(412\) −1.17532 + 2.72471i −0.0579040 + 0.134237i
\(413\) −2.73421 + 15.5065i −0.134542 + 0.763024i
\(414\) 7.46945 + 7.34562i 0.367104 + 0.361017i
\(415\) −1.83511 10.4074i −0.0900818 0.510879i
\(416\) 20.9818 + 4.97277i 1.02872 + 0.243810i
\(417\) −3.67379 9.53431i −0.179906 0.466897i
\(418\) −7.89561 + 5.19302i −0.386187 + 0.253999i
\(419\) 0.196196 + 3.36855i 0.00958479 + 0.164564i 0.999704 + 0.0243352i \(0.00774691\pi\)
−0.990119 + 0.140229i \(0.955216\pi\)
\(420\) −25.9191 + 5.07234i −1.26472 + 0.247505i
\(421\) −7.24567 24.2022i −0.353133 1.17954i −0.931492 0.363763i \(-0.881492\pi\)
0.578359 0.815782i \(-0.303693\pi\)
\(422\) −5.46033 1.98740i −0.265805 0.0967451i
\(423\) 9.50228 0.356003i 0.462017 0.0173095i
\(424\) −16.4373 + 5.98270i −0.798267 + 0.290545i
\(425\) −1.91566 2.57318i −0.0929231 0.124817i
\(426\) 7.41505 + 10.8269i 0.359261 + 0.524566i
\(427\) −1.73785 + 0.411878i −0.0841005 + 0.0199322i
\(428\) −4.75324 11.0192i −0.229756 0.532635i
\(429\) −22.5789 + 7.22299i −1.09012 + 0.348729i
\(430\) −3.07962 2.02549i −0.148512 0.0976780i
\(431\) 16.4068 28.4174i 0.790288 1.36882i −0.135501 0.990777i \(-0.543264\pi\)
0.925789 0.378041i \(-0.123402\pi\)
\(432\) −1.93636 11.1120i −0.0931631 0.534625i
\(433\) 6.46122 + 11.1912i 0.310507 + 0.537813i 0.978472 0.206379i \(-0.0661680\pi\)
−0.667966 + 0.744192i \(0.732835\pi\)
\(434\) 0.0698141 1.19866i 0.00335118 0.0575376i
\(435\) −8.37685 3.42886i −0.401639 0.164401i
\(436\) 18.9516 + 2.21513i 0.907618 + 0.106085i
\(437\) 20.4806 + 21.7081i 0.979719 + 1.03844i
\(438\) −1.65003 6.42359i −0.0788415 0.306931i
\(439\) −36.6280 + 4.28120i −1.74816 + 0.204330i −0.929214 0.369542i \(-0.879515\pi\)
−0.818945 + 0.573872i \(0.805441\pi\)
\(440\) −15.9373 13.3730i −0.759781 0.637532i
\(441\) −5.25687 6.53537i −0.250327 0.311208i
\(442\) −1.62093 + 1.36012i −0.0770997 + 0.0646943i
\(443\) 23.5817 24.9951i 1.12040 1.18755i 0.140078 0.990140i \(-0.455265\pi\)
0.980320 0.197413i \(-0.0632539\pi\)
\(444\) −0.620116 33.1154i −0.0294294 1.57159i
\(445\) −34.0378 17.0944i −1.61355 0.810354i
\(446\) 2.35948 + 1.18498i 0.111725 + 0.0561103i
\(447\) 20.4646 12.3318i 0.967943 0.583274i
\(448\) 2.73256 2.89634i 0.129101 0.136839i
\(449\) −13.4520 + 11.2876i −0.634838 + 0.532693i −0.902428 0.430840i \(-0.858217\pi\)
0.267590 + 0.963533i \(0.413773\pi\)
\(450\) 5.73242 + 1.13378i 0.270229 + 0.0534468i
\(451\) −17.4910 14.6767i −0.823617 0.691097i
\(452\) −9.70571 + 1.13444i −0.456518 + 0.0533593i
\(453\) 10.4719 + 2.92260i 0.492013 + 0.137316i
\(454\) 5.49981 + 5.82945i 0.258119 + 0.273590i
\(455\) 35.9966 + 4.20740i 1.68755 + 0.197246i
\(456\) 2.36209 + 17.3803i 0.110615 + 0.813906i
\(457\) 0.485445 8.33476i 0.0227081 0.389884i −0.967736 0.251967i \(-0.918922\pi\)
0.990444 0.137916i \(-0.0440405\pi\)
\(458\) −1.47162 2.54891i −0.0687641 0.119103i
\(459\) 4.33640 + 2.18873i 0.202406 + 0.102161i
\(460\) −14.9867 + 25.9577i −0.698758 + 1.21028i
\(461\) −16.9937 11.1769i −0.791475 0.520561i 0.0882195 0.996101i \(-0.471882\pi\)
−0.879694 + 0.475540i \(0.842253\pi\)
\(462\) 2.24265 10.3199i 0.104337 0.480123i
\(463\) −1.02559 2.37758i −0.0476631 0.110496i 0.892721 0.450610i \(-0.148793\pi\)
−0.940384 + 0.340114i \(0.889534\pi\)
\(464\) 3.80136 0.900939i 0.176474 0.0418250i
\(465\) 1.46843 3.06570i 0.0680970 0.142168i
\(466\) −1.50951 2.02763i −0.0699268 0.0939279i
\(467\) 11.5019 4.18635i 0.532244 0.193721i −0.0618958 0.998083i \(-0.519715\pi\)
0.594140 + 0.804361i \(0.297492\pi\)
\(468\) −2.74303 + 19.8841i −0.126797 + 0.919145i
\(469\) 40.2012 + 14.6320i 1.85632 + 0.675645i
\(470\) −1.49830 5.00468i −0.0691116 0.230849i
\(471\) 0.0933148 0.272128i 0.00429972 0.0125390i
\(472\) 0.610652 + 10.4845i 0.0281075 + 0.482587i
\(473\) −6.41295 + 4.21786i −0.294868 + 0.193937i
\(474\) −0.460417 + 0.570047i −0.0211476 + 0.0261831i
\(475\) 16.1981 + 3.83903i 0.743221 + 0.176147i
\(476\) 0.852437 + 4.83441i 0.0390714 + 0.221585i
\(477\) −10.8138 22.6930i −0.495128 1.03904i
\(478\) 2.86441 16.2449i 0.131015 0.743024i
\(479\) −10.8633 + 25.1839i −0.496357 + 1.15068i 0.467435 + 0.884027i \(0.345178\pi\)
−0.963792 + 0.266656i \(0.914081\pi\)
\(480\) −24.7650 + 11.2371i −1.13036 + 0.512902i
\(481\) −13.0352 + 43.5405i −0.594353 + 1.98528i
\(482\) −8.46840 + 11.3750i −0.385725 + 0.518118i
\(483\) −33.3254 1.31550i −1.51636 0.0598573i
\(484\) −1.16893 + 0.587060i −0.0531333 + 0.0266845i
\(485\) 36.3120 1.64884
\(486\) −8.53192 + 2.34431i −0.387016 + 0.106340i
\(487\) −6.02417 −0.272981 −0.136491 0.990641i \(-0.543582\pi\)
−0.136491 + 0.990641i \(0.543582\pi\)
\(488\) −1.06453 + 0.534628i −0.0481891 + 0.0242015i
\(489\) 28.0398 + 1.10685i 1.26800 + 0.0500536i
\(490\) −2.75164 + 3.69610i −0.124307 + 0.166973i
\(491\) 0.139757 0.466819i 0.00630713 0.0210673i −0.954778 0.297320i \(-0.903907\pi\)
0.961085 + 0.276252i \(0.0890925\pi\)
\(492\) −17.6054 + 7.98845i −0.793714 + 0.360147i
\(493\) −0.666364 + 1.54481i −0.0300115 + 0.0695745i
\(494\) 1.90671 10.8135i 0.0857867 0.486521i
\(495\) 16.9435 24.6335i 0.761554 1.10719i
\(496\) 0.254765 + 1.44484i 0.0114393 + 0.0648754i
\(497\) −40.6505 9.63434i −1.82342 0.432159i
\(498\) 2.24819 2.78351i 0.100744 0.124732i
\(499\) −4.58242 + 3.01391i −0.205137 + 0.134921i −0.647921 0.761708i \(-0.724361\pi\)
0.442784 + 0.896628i \(0.353991\pi\)
\(500\) −0.444284 7.62806i −0.0198690 0.341137i
\(501\) 10.2678 29.9435i 0.458733 1.33778i
\(502\) 2.30705 + 7.70609i 0.102969 + 0.343940i
\(503\) 9.93090 + 3.61455i 0.442797 + 0.161165i 0.553790 0.832656i \(-0.313181\pi\)
−0.110993 + 0.993821i \(0.535403\pi\)
\(504\) −15.4764 12.0283i −0.689376 0.535784i
\(505\) 16.3275 5.94271i 0.726562 0.264447i
\(506\) −7.15712 9.61368i −0.318173 0.427380i
\(507\) 2.17178 4.53410i 0.0964522 0.201366i
\(508\) −17.5356 + 4.15601i −0.778015 + 0.184393i
\(509\) −4.91402 11.3920i −0.217810 0.504940i 0.773920 0.633284i \(-0.218293\pi\)
−0.991730 + 0.128343i \(0.959034\pi\)
\(510\) 0.566709 2.60779i 0.0250943 0.115475i
\(511\) 17.6402 + 11.6021i 0.780355 + 0.513248i
\(512\) 10.4003 18.0139i 0.459634 0.796110i
\(513\) −24.5387 + 5.76380i −1.08341 + 0.254478i
\(514\) 4.17162 + 7.22546i 0.184002 + 0.318701i
\(515\) −0.298604 + 5.12684i −0.0131581 + 0.225915i
\(516\) 0.875235 + 6.43997i 0.0385301 + 0.283504i
\(517\) −10.8051 1.26294i −0.475209 0.0555440i
\(518\) −13.8945 14.7273i −0.610491 0.647082i
\(519\) 31.4538 + 8.77842i 1.38067 + 0.385330i
\(520\) 24.0095 2.80630i 1.05288 0.123064i
\(521\) −13.6270 11.4344i −0.597011 0.500952i 0.293472 0.955968i \(-0.405189\pi\)
−0.890483 + 0.455016i \(0.849634\pi\)
\(522\) −0.988230 2.90087i −0.0432536 0.126968i
\(523\) −10.4002 + 8.72680i −0.454769 + 0.381596i −0.841202 0.540721i \(-0.818151\pi\)
0.386433 + 0.922317i \(0.373707\pi\)
\(524\) −8.24697 + 8.74128i −0.360271 + 0.381865i
\(525\) −15.9336 + 9.60144i −0.695399 + 0.419041i
\(526\) −8.31304 4.17497i −0.362466 0.182037i
\(527\) −0.564613 0.283560i −0.0245949 0.0123520i
\(528\) 0.241601 + 12.9019i 0.0105143 + 0.561485i
\(529\) −10.1908 + 10.8016i −0.443079 + 0.469636i
\(530\) −10.5795 + 8.87724i −0.459543 + 0.385603i
\(531\) −14.9145 + 2.31214i −0.647232 + 0.100339i
\(532\) −19.5141 16.3743i −0.846045 0.709916i
\(533\) 26.3500 3.07988i 1.14135 0.133404i
\(534\) −3.20845 12.4905i −0.138843 0.540518i
\(535\) −14.2526 15.1069i −0.616194 0.653127i
\(536\) 28.3418 + 3.31268i 1.22418 + 0.143086i
\(537\) 16.5043 + 6.75565i 0.712215 + 0.291528i
\(538\) −0.375006 + 6.43861i −0.0161677 + 0.277588i
\(539\) 4.79771 + 8.30987i 0.206652 + 0.357931i
\(540\) −12.6136 21.9491i −0.542805 0.944537i
\(541\) 13.6538 23.6492i 0.587025 1.01676i −0.407595 0.913163i \(-0.633632\pi\)
0.994620 0.103594i \(-0.0330342\pi\)
\(542\) 1.31139 + 0.862517i 0.0563291 + 0.0370483i
\(543\) 1.35214 0.432548i 0.0580257 0.0185624i
\(544\) 2.00210 + 4.64139i 0.0858394 + 0.198998i
\(545\) 32.1319 7.61539i 1.37638 0.326207i
\(546\) 6.93350 + 10.1238i 0.296726 + 0.433259i
\(547\) 7.58248 + 10.1850i 0.324204 + 0.435481i 0.934106 0.356995i \(-0.116199\pi\)
−0.609903 + 0.792476i \(0.708791\pi\)
\(548\) −13.6050 + 4.95181i −0.581176 + 0.211531i
\(549\) −0.910862 1.44948i −0.0388747 0.0618621i
\(550\) −6.28204 2.28648i −0.267867 0.0974957i
\(551\) −2.50390 8.36360i −0.106670 0.356301i
\(552\) −21.8310 + 4.27230i −0.929187 + 0.181841i
\(553\) −0.135638 2.32882i −0.00576793 0.0990315i
\(554\) 8.72397 5.73785i 0.370646 0.243778i
\(555\) −20.6101 53.4879i −0.874849 2.27043i
\(556\) 9.63092 + 2.28257i 0.408442 + 0.0968025i
\(557\) 2.62356 + 14.8789i 0.111164 + 0.630441i 0.988578 + 0.150708i \(0.0481553\pi\)
−0.877415 + 0.479733i \(0.840734\pi\)
\(558\) 1.10915 0.307154i 0.0469540 0.0130029i
\(559\) 1.54866 8.78288i 0.0655013 0.371476i
\(560\) 7.81380 18.1144i 0.330193 0.765474i
\(561\) −4.51889 3.23447i −0.190788 0.136560i
\(562\) 1.74727 5.83630i 0.0737043 0.246189i
\(563\) 3.66195 4.91886i 0.154333 0.207305i −0.718231 0.695804i \(-0.755048\pi\)
0.872564 + 0.488499i \(0.162455\pi\)
\(564\) −4.91667 + 7.78928i −0.207029 + 0.327988i
\(565\) −15.1127 + 7.58990i −0.635798 + 0.319310i
\(566\) 8.11223 0.340982
\(567\) 15.0832 23.7898i 0.633434 0.999076i
\(568\) −27.8646 −1.16917
\(569\) 1.32201 0.663940i 0.0554217 0.0278338i −0.420872 0.907120i \(-0.638276\pi\)
0.476294 + 0.879286i \(0.341980\pi\)
\(570\) 6.44571 + 12.2568i 0.269981 + 0.513379i
\(571\) 5.26460 7.07158i 0.220317 0.295936i −0.678199 0.734878i \(-0.737239\pi\)
0.898515 + 0.438942i \(0.144647\pi\)
\(572\) 6.58611 21.9991i 0.275379 0.919830i
\(573\) 0.129167 1.31880i 0.00539602 0.0550935i
\(574\) −4.68106 + 10.8519i −0.195384 + 0.452950i
\(575\) −3.66611 + 20.7915i −0.152887 + 0.867066i
\(576\) 3.47252 + 1.58406i 0.144688 + 0.0660026i
\(577\) 2.48608 + 14.0993i 0.103497 + 0.586960i 0.991810 + 0.127722i \(0.0407665\pi\)
−0.888313 + 0.459238i \(0.848122\pi\)
\(578\) 8.90659 + 2.11090i 0.370465 + 0.0878018i
\(579\) −16.0065 2.51434i −0.665209 0.104493i
\(580\) 7.32559 4.81812i 0.304179 0.200062i
\(581\) 0.662315 + 11.3715i 0.0274775 + 0.471770i
\(582\) 8.07756 + 9.26836i 0.334826 + 0.384186i
\(583\) 8.24814 + 27.5507i 0.341603 + 1.14103i
\(584\) 13.2333 + 4.81654i 0.547599 + 0.199310i
\(585\) 7.30885 + 33.9609i 0.302184 + 1.40411i
\(586\) −11.6521 + 4.24102i −0.481344 + 0.175195i
\(587\) −5.09890 6.84901i −0.210454 0.282689i 0.684345 0.729159i \(-0.260088\pi\)
−0.894799 + 0.446470i \(0.852681\pi\)
\(588\) 8.10063 0.624180i 0.334064 0.0257408i
\(589\) 3.19028 0.756110i 0.131453 0.0311550i
\(590\) 3.28421 + 7.61364i 0.135209 + 0.313449i
\(591\) 1.43548 + 1.30438i 0.0590476 + 0.0536549i
\(592\) 20.6702 + 13.5950i 0.849539 + 0.558751i
\(593\) −19.8740 + 34.4227i −0.816125 + 1.41357i 0.0923915 + 0.995723i \(0.470549\pi\)
−0.908517 + 0.417848i \(0.862784\pi\)
\(594\) 10.0566 1.15500i 0.412627 0.0473902i
\(595\) 4.24788 + 7.35754i 0.174146 + 0.301630i
\(596\) −1.34576 + 23.1057i −0.0551243 + 0.946448i
\(597\) 10.5202 8.14251i 0.430563 0.333251i
\(598\) 13.8315 + 1.61667i 0.565613 + 0.0661106i
\(599\) 13.9840 + 14.8221i 0.571370 + 0.605616i 0.947032 0.321140i \(-0.104066\pi\)
−0.375662 + 0.926757i \(0.622585\pi\)
\(600\) −8.86423 + 8.68235i −0.361881 + 0.354455i
\(601\) 13.5963 1.58918i 0.554604 0.0648239i 0.165825 0.986155i \(-0.446971\pi\)
0.388779 + 0.921331i \(0.372897\pi\)
\(602\) 3.04350 + 2.55380i 0.124044 + 0.104085i
\(603\) −0.850016 + 40.9980i −0.0346153 + 1.66957i
\(604\) −8.06774 + 6.76964i −0.328272 + 0.275453i
\(605\) −1.55352 + 1.64664i −0.0631597 + 0.0669453i
\(606\) 5.14886 + 2.84551i 0.209158 + 0.115591i
\(607\) −4.02143 2.01964i −0.163225 0.0819745i 0.365311 0.930885i \(-0.380963\pi\)
−0.528536 + 0.848911i \(0.677259\pi\)
\(608\) −23.4405 11.7722i −0.950636 0.477427i
\(609\) 8.53897 + 4.71906i 0.346016 + 0.191226i
\(610\) −0.645420 + 0.684105i −0.0261323 + 0.0276986i
\(611\) 9.68275 8.12479i 0.391722 0.328694i
\(612\) −4.12287 + 2.26771i −0.166657 + 0.0916669i
\(613\) 27.4040 + 22.9947i 1.10684 + 0.928746i 0.997866 0.0652986i \(-0.0208000\pi\)
0.108971 + 0.994045i \(0.465244\pi\)
\(614\) 17.1807 2.00814i 0.693357 0.0810418i
\(615\) −23.9029 + 23.4125i −0.963858 + 0.944081i
\(616\) 15.3887 + 16.3110i 0.620027 + 0.657190i
\(617\) −27.3964 3.20218i −1.10294 0.128915i −0.454913 0.890536i \(-0.650330\pi\)
−0.648023 + 0.761621i \(0.724404\pi\)
\(618\) −1.37501 + 1.06424i −0.0553111 + 0.0428101i
\(619\) 1.94367 33.3715i 0.0781227 1.34131i −0.700424 0.713727i \(-0.747006\pi\)
0.778546 0.627587i \(-0.215957\pi\)
\(620\) 1.64640 + 2.85165i 0.0661211 + 0.114525i
\(621\) −9.10707 30.6434i −0.365454 1.22968i
\(622\) 7.69456 13.3274i 0.308524 0.534379i
\(623\) 34.3009 + 22.5601i 1.37424 + 0.903850i
\(624\) −11.0965 10.0831i −0.444216 0.403646i
\(625\) −12.0337 27.8973i −0.481349 1.11589i
\(626\) 4.47722 1.06112i 0.178946 0.0424109i
\(627\) 28.7523 2.21546i 1.14825 0.0884768i
\(628\) 0.166414 + 0.223532i 0.00664063 + 0.00891991i
\(629\) −10.0118 + 3.64400i −0.399197 + 0.145296i
\(630\) −14.7302 4.74478i −0.586864 0.189036i
\(631\) 10.2732 + 3.73914i 0.408970 + 0.148853i 0.538309 0.842748i \(-0.319063\pi\)
−0.129339 + 0.991600i \(0.541286\pi\)
\(632\) −0.446247 1.49057i −0.0177508 0.0592917i
\(633\) 11.6499 + 13.3673i 0.463042 + 0.531304i
\(634\) −0.640898 11.0038i −0.0254533 0.437016i
\(635\) −26.0578 + 17.1385i −1.03407 + 0.680120i
\(636\) 24.0558 + 3.77874i 0.953873 + 0.149837i
\(637\) −10.8484 2.57111i −0.429828 0.101871i
\(638\) 0.608816 + 3.45277i 0.0241032 + 0.136696i
\(639\) −3.82336 39.8609i −0.151250 1.57687i
\(640\) 5.81708 32.9903i 0.229940 1.30406i
\(641\) −3.68962 + 8.55350i −0.145731 + 0.337843i −0.975410 0.220398i \(-0.929264\pi\)
0.829679 + 0.558241i \(0.188524\pi\)
\(642\) 0.685442 6.99838i 0.0270522 0.276204i
\(643\) −0.369260 + 1.23341i −0.0145622 + 0.0486411i −0.964962 0.262390i \(-0.915489\pi\)
0.950400 + 0.311031i \(0.100674\pi\)
\(644\) 19.2925 25.9143i 0.760230 1.02117i
\(645\) 5.23532 + 9.95514i 0.206140 + 0.391983i
\(646\) 2.30020 1.15521i 0.0905003 0.0454510i
\(647\) −25.7409 −1.01198 −0.505989 0.862540i \(-0.668872\pi\)
−0.505989 + 0.862540i \(0.668872\pi\)
\(648\) 6.12986 17.7599i 0.240804 0.697677i
\(649\) 17.2667 0.677776
\(650\) 6.94132 3.48606i 0.272261 0.136735i
\(651\) −1.95568 + 3.09831i −0.0766492 + 0.121432i
\(652\) −16.2326 + 21.8041i −0.635716 + 0.853915i
\(653\) 11.1737 37.3227i 0.437259 1.46055i −0.401405 0.915900i \(-0.631478\pi\)
0.838665 0.544648i \(-0.183337\pi\)
\(654\) 9.09147 + 6.50738i 0.355505 + 0.254459i
\(655\) −8.23778 + 19.0973i −0.321877 + 0.746194i
\(656\) 2.50766 14.2217i 0.0979077 0.555262i
\(657\) −5.07437 + 19.5914i −0.197970 + 0.764333i
\(658\) 0.977797 + 5.54536i 0.0381185 + 0.216181i
\(659\) −32.6776 7.74473i −1.27294 0.301692i −0.462029 0.886865i \(-0.652878\pi\)
−0.810908 + 0.585173i \(0.801027\pi\)
\(660\) 10.4134 + 27.0251i 0.405340 + 1.05195i
\(661\) −29.6045 + 19.4712i −1.15148 + 0.757342i −0.973948 0.226773i \(-0.927183\pi\)
−0.177535 + 0.984115i \(0.556812\pi\)
\(662\) 0.0655685 + 1.12577i 0.00254839 + 0.0437542i
\(663\) 6.33667 1.24008i 0.246096 0.0481607i
\(664\) 2.17901 + 7.27838i 0.0845618 + 0.282456i
\(665\) −41.4278 15.0785i −1.60650 0.584718i
\(666\) 9.06770 17.1589i 0.351366 0.664894i
\(667\) 10.4045 3.78693i 0.402864 0.146630i
\(668\) 18.3112 + 24.5963i 0.708483 + 0.951658i
\(669\) −4.55261 6.64740i −0.176014 0.257003i
\(670\) 21.9216 5.19551i 0.846905 0.200720i
\(671\) 0.775727 + 1.79834i 0.0299466 + 0.0694241i
\(672\) 27.9189 8.93125i 1.07700 0.344530i
\(673\) −22.9529 15.0964i −0.884771 0.581923i 0.0237705 0.999717i \(-0.492433\pi\)
−0.908542 + 0.417794i \(0.862803\pi\)
\(674\) −5.20938 + 9.02292i −0.200658 + 0.347550i
\(675\) −13.6365 11.4891i −0.524870 0.442216i
\(676\) 2.43499 + 4.21753i 0.0936536 + 0.162213i
\(677\) 0.555469 9.53704i 0.0213484 0.366538i −0.970668 0.240426i \(-0.922713\pi\)
0.992016 0.126112i \(-0.0402500\pi\)
\(678\) −5.29908 2.16905i −0.203510 0.0833018i
\(679\) −38.8746 4.54379i −1.49187 0.174375i
\(680\) 3.88866 + 4.12174i 0.149123 + 0.158061i
\(681\) −6.08445 23.6868i −0.233157 0.907682i
\(682\) −1.30777 + 0.152857i −0.0500772 + 0.00585319i
\(683\) 25.4573 + 21.3612i 0.974095 + 0.817363i 0.983188 0.182596i \(-0.0584500\pi\)
−0.00909301 + 0.999959i \(0.502894\pi\)
\(684\) 8.82503 22.7667i 0.337434 0.870508i
\(685\) −19.1945 + 16.1061i −0.733383 + 0.615381i
\(686\) −5.12547 + 5.43268i −0.195691 + 0.207421i
\(687\) 0.168153 + 8.97967i 0.00641543 + 0.342596i
\(688\) −4.33826 2.17876i −0.165395 0.0830643i
\(689\) −29.8606 14.9966i −1.13760 0.571324i
\(690\) −15.0429 + 9.06474i −0.572675 + 0.345089i
\(691\) 3.72605 3.94938i 0.141746 0.150242i −0.652611 0.757693i \(-0.726327\pi\)
0.794357 + 0.607451i \(0.207808\pi\)
\(692\) −24.2325 + 20.3335i −0.921183 + 0.772964i
\(693\) −21.2217 + 24.2518i −0.806146 + 0.921251i
\(694\) −11.6460 9.77218i −0.442077 0.370947i
\(695\) 17.0137 1.98862i 0.645366 0.0754325i
\(696\) 6.26778 + 1.74927i 0.237580 + 0.0663060i
\(697\) 4.26775 + 4.52355i 0.161652 + 0.171342i
\(698\) −7.39072 0.863851i −0.279743 0.0326972i
\(699\) 1.03878 + 7.64336i 0.0392904 + 0.289098i
\(700\) 1.04779 17.9899i 0.0396029 0.679956i
\(701\) −16.8694 29.2187i −0.637150 1.10358i −0.986055 0.166418i \(-0.946780\pi\)
0.348906 0.937158i \(-0.386553\pi\)
\(702\) −7.04242 + 9.42009i −0.265799 + 0.355539i
\(703\) 27.6440 47.8808i 1.04261 1.80586i
\(704\) −3.64821 2.39946i −0.137497 0.0904332i
\(705\) −3.38528 + 15.5778i −0.127497 + 0.586696i
\(706\) 4.36930 + 10.1292i 0.164441 + 0.381216i
\(707\) −18.2234 + 4.31902i −0.685360 + 0.162433i
\(708\) 6.31571 13.1855i 0.237359 0.495542i
\(709\) −11.5762 15.5495i −0.434754 0.583975i 0.529714 0.848176i \(-0.322299\pi\)
−0.964468 + 0.264201i \(0.914892\pi\)
\(710\) −20.6730 + 7.52437i −0.775846 + 0.282385i
\(711\) 2.07106 0.842889i 0.0776707 0.0316108i
\(712\) 25.7319 + 9.36564i 0.964343 + 0.350992i
\(713\) 1.19257 + 3.98345i 0.0446620 + 0.149181i
\(714\) −0.933022 + 2.72092i −0.0349175 + 0.101828i
\(715\) −2.31082 39.6753i −0.0864198 1.48377i
\(716\) −14.4331 + 9.49282i −0.539391 + 0.354763i
\(717\) −31.6276 + 39.1585i −1.18116 + 1.46240i
\(718\) 8.10592 + 1.92114i 0.302510 + 0.0716963i
\(719\) −0.831346 4.71480i −0.0310040 0.175832i 0.965374 0.260871i \(-0.0840097\pi\)
−0.996378 + 0.0850387i \(0.972899\pi\)
\(720\) 18.8507 + 1.49057i 0.702526 + 0.0555501i
\(721\) 0.961210 5.45129i 0.0357973 0.203017i
\(722\) −1.01892 + 2.36211i −0.0379201 + 0.0879087i
\(723\) 39.4067 17.8807i 1.46555 0.664992i
\(724\) −0.394408 + 1.31742i −0.0146581 + 0.0489614i
\(725\) 3.68801 4.95385i 0.136969 0.183982i
\(726\) −0.765871 0.0302323i −0.0284241 0.00112203i
\(727\) −6.75608 + 3.39303i −0.250569 + 0.125841i −0.569651 0.821887i \(-0.692922\pi\)
0.319082 + 0.947727i \(0.396625\pi\)
\(728\) −26.0550 −0.965664
\(729\) 26.2470 + 6.33200i 0.972112 + 0.234519i
\(730\) 11.1186 0.411516
\(731\) 1.86826 0.938278i 0.0691003 0.0347035i
\(732\) 1.65702 + 0.0654100i 0.0612454 + 0.00241762i
\(733\) 23.0749 30.9950i 0.852292 1.14483i −0.135766 0.990741i \(-0.543349\pi\)
0.988057 0.154086i \(-0.0492432\pi\)
\(734\) −1.78974 + 5.97815i −0.0660605 + 0.220657i
\(735\) 12.8044 5.81001i 0.472299 0.214305i
\(736\) 13.1763 30.5460i 0.485684 1.12594i
\(737\) 8.14649 46.2010i 0.300080 1.70184i
\(738\) −11.2930 0.892962i −0.415702 0.0328704i
\(739\) −8.79173 49.8604i −0.323409 1.83414i −0.520627 0.853784i \(-0.674302\pi\)
0.197218 0.980360i \(-0.436809\pi\)
\(740\) 54.0299 + 12.8053i 1.98618 + 0.470733i
\(741\) −21.0530 + 26.0660i −0.773403 + 0.957558i
\(742\) 12.4369 8.17991i 0.456575 0.300294i
\(743\) −0.892750 15.3279i −0.0327518 0.562327i −0.974273 0.225372i \(-0.927640\pi\)
0.941521 0.336955i \(-0.109397\pi\)
\(744\) −0.792685 + 2.31166i −0.0290612 + 0.0847496i
\(745\) 11.4881 + 38.3730i 0.420893 + 1.40588i
\(746\) −10.8906 3.96386i −0.398733 0.145127i
\(747\) −10.1129 + 4.11579i −0.370011 + 0.150589i
\(748\) 5.05853 1.84116i 0.184958 0.0673193i
\(749\) 13.3681 + 17.9565i 0.488460 + 0.656115i
\(750\) 1.93413 4.03795i 0.0706245 0.147445i
\(751\) −45.3980 + 10.7595i −1.65660 + 0.392621i −0.949319 0.314314i \(-0.898225\pi\)
−0.707278 + 0.706935i \(0.750077\pi\)
\(752\) −2.72520 6.31772i −0.0993778 0.230384i
\(753\) 5.21258 23.9864i 0.189957 0.874113i
\(754\) −3.40348 2.23851i −0.123948 0.0815216i
\(755\) −9.11335 + 15.7848i −0.331669 + 0.574467i
\(756\) 10.7573 + 25.0764i 0.391239 + 0.912022i
\(757\) 5.85224 + 10.1364i 0.212703 + 0.368413i 0.952560 0.304352i \(-0.0984399\pi\)
−0.739856 + 0.672765i \(0.765107\pi\)
\(758\) 0.859106 14.7503i 0.0312041 0.535754i
\(759\) 4.92523 + 36.2398i 0.178775 + 1.31542i
\(760\) −29.2065 3.41375i −1.05943 0.123830i
\(761\) −17.9650 19.0418i −0.651232 0.690265i 0.314662 0.949204i \(-0.398109\pi\)
−0.965894 + 0.258938i \(0.916627\pi\)
\(762\) −10.1710 2.83862i −0.368456 0.102832i
\(763\) −35.3524 + 4.13211i −1.27984 + 0.149592i
\(764\) 0.983309 + 0.825094i 0.0355749 + 0.0298509i
\(765\) −5.36265 + 6.12835i −0.193887 + 0.221571i
\(766\) 10.2314 8.58519i 0.369676 0.310195i
\(767\) −13.7675 + 14.5927i −0.497114 + 0.526910i
\(768\) 5.93970 3.57921i 0.214330 0.129154i
\(769\) 40.6989 + 20.4398i 1.46764 + 0.737077i 0.989946 0.141448i \(-0.0451758\pi\)
0.477696 + 0.878525i \(0.341472\pi\)
\(770\) 15.8215 + 7.94586i 0.570168 + 0.286349i
\(771\) −0.476666 25.4549i −0.0171667 0.916735i
\(772\) 10.7709 11.4165i 0.387653 0.410889i
\(773\) 10.7154 8.99131i 0.385407 0.323395i −0.429414 0.903108i \(-0.641280\pi\)
0.814821 + 0.579713i \(0.196835\pi\)
\(774\) −1.37639 + 3.55079i −0.0494732 + 0.127630i
\(775\) 1.77672 + 1.49085i 0.0638217 + 0.0535528i
\(776\) −25.9291 + 3.03067i −0.930799 + 0.108795i
\(777\) 15.3716 + 59.8417i 0.551451 + 2.14681i
\(778\) −12.8814 13.6535i −0.461822 0.489503i
\(779\) −32.0537 3.74654i −1.14844 0.134234i
\(780\) −31.1429 12.7476i −1.11509 0.456436i
\(781\) −2.66373 + 45.7345i −0.0953159 + 1.63651i
\(782\) 1.63223 + 2.82710i 0.0583683 + 0.101097i
\(783\) −1.64235 + 9.20619i −0.0586929 + 0.329003i
\(784\) −3.03440 + 5.25573i −0.108371 + 0.187705i
\(785\) 0.402948 + 0.265023i 0.0143818 + 0.00945909i
\(786\) −6.70694 + 2.14555i −0.239229 + 0.0765291i
\(787\) 5.62542 + 13.0412i 0.200525 + 0.464869i 0.988573 0.150745i \(-0.0481674\pi\)
−0.788048 + 0.615614i \(0.788908\pi\)
\(788\) −1.82821 + 0.433295i −0.0651274 + 0.0154355i
\(789\) 16.0400 + 23.4204i 0.571038 + 0.833789i
\(790\) −0.733578 0.985367i −0.0260995 0.0350578i
\(791\) 17.1290 6.23446i 0.609039 0.221672i
\(792\) −10.0428 + 19.0040i −0.356854 + 0.675279i
\(793\) −2.13836 0.778298i −0.0759353 0.0276382i
\(794\) −0.00900064 0.0300642i −0.000319421 0.00106694i
\(795\) 41.3582 8.09376i 1.46682 0.287056i
\(796\) 0.749293 + 12.8649i 0.0265580 + 0.455983i
\(797\) 34.5075 22.6959i 1.22232 0.803931i 0.236480 0.971636i \(-0.424006\pi\)
0.985837 + 0.167705i \(0.0536357\pi\)
\(798\) −5.36689 13.9283i −0.189986 0.493057i
\(799\) 2.88318 + 0.683326i 0.102000 + 0.0241743i
\(800\) −3.22216 18.2738i −0.113921 0.646075i
\(801\) −9.86700 + 38.0950i −0.348633 + 1.34602i
\(802\) 2.82324 16.0114i 0.0996920 0.565381i
\(803\) 9.17048 21.2596i 0.323619 0.750234i
\(804\) −32.3012 23.1202i −1.13917 0.815385i
\(805\) 16.0359 53.5636i 0.565190 1.88787i
\(806\) 0.913559 1.22712i 0.0321787 0.0432236i
\(807\) 10.5049 16.6425i 0.369791 0.585845i
\(808\) −11.1629 + 5.60619i −0.392708 + 0.197225i
\(809\) 23.8379 0.838097 0.419048 0.907964i \(-0.362364\pi\)
0.419048 + 0.907964i \(0.362364\pi\)
\(810\) −0.247967 14.8315i −0.00871268 0.521127i
\(811\) −3.33188 −0.116998 −0.0584991 0.998287i \(-0.518631\pi\)
−0.0584991 + 0.998287i \(0.518631\pi\)
\(812\) −8.44549 + 4.24148i −0.296378 + 0.148847i
\(813\) −2.22936 4.23920i −0.0781869 0.148675i
\(814\) −13.2588 + 17.8096i −0.464720 + 0.624227i
\(815\) −13.4925 + 45.0680i −0.472621 + 1.57866i
\(816\) 0.342604 3.49800i 0.0119936 0.122454i
\(817\) −4.29700 + 9.96157i −0.150333 + 0.348511i
\(818\) −3.09855 + 17.5727i −0.108338 + 0.614417i
\(819\) −3.57506 37.2722i −0.124923 1.30240i
\(820\) −5.62815 31.9188i −0.196543 1.11465i
\(821\) 8.73468 + 2.07016i 0.304842 + 0.0722490i 0.380190 0.924908i \(-0.375859\pi\)
−0.0753477 + 0.997157i \(0.524007\pi\)
\(822\) −8.38074 1.31647i −0.292312 0.0459171i
\(823\) 1.08458 0.713338i 0.0378060 0.0248654i −0.530465 0.847707i \(-0.677983\pi\)
0.568271 + 0.822841i \(0.307612\pi\)
\(824\) −0.214674 3.68581i −0.00747852 0.128401i
\(825\) 13.4031 + 15.3790i 0.466635 + 0.535426i
\(826\) −2.56327 8.56192i −0.0891876 0.297907i
\(827\) 29.6308 + 10.7847i 1.03036 + 0.375022i 0.801219 0.598371i \(-0.204185\pi\)
0.229144 + 0.973392i \(0.426407\pi\)
\(828\) 29.4757 + 9.49450i 1.02435 + 0.329957i
\(829\) −25.1437 + 9.15156i −0.873277 + 0.317847i −0.739493 0.673164i \(-0.764935\pi\)
−0.133783 + 0.991011i \(0.542713\pi\)
\(830\) 3.58203 + 4.81150i 0.124334 + 0.167010i
\(831\) −31.7688 + 2.44789i −1.10205 + 0.0849164i
\(832\) 4.93674 1.17003i 0.171151 0.0405634i
\(833\) −1.03516 2.39977i −0.0358662 0.0831472i
\(834\) 4.29226 + 3.90025i 0.148629 + 0.135055i
\(835\) 44.3382 + 29.1617i 1.53439 + 1.00918i
\(836\) −13.9673 + 24.1921i −0.483069 + 0.836700i
\(837\) −3.41564 0.816763i −0.118062 0.0282315i
\(838\) −0.957629 1.65866i −0.0330807 0.0572975i
\(839\) −0.225566 + 3.87282i −0.00778740 + 0.133705i 0.992174 + 0.124867i \(0.0398503\pi\)
−0.999961 + 0.00883795i \(0.997187\pi\)
\(840\) 25.9862 20.1130i 0.896608 0.693964i
\(841\) 25.5869 + 2.99068i 0.882306 + 0.103127i
\(842\) 9.84058 + 10.4304i 0.339129 + 0.359455i
\(843\) −13.2809 + 13.0084i −0.457420 + 0.448034i
\(844\) −17.0602 + 1.99405i −0.587236 + 0.0686380i
\(845\) 6.45643 + 5.41758i 0.222108 + 0.186371i
\(846\) −4.72918 + 2.60121i −0.162593 + 0.0894313i
\(847\) 1.86921 1.56845i 0.0642267 0.0538926i
\(848\) −12.4821 + 13.2303i −0.428637 + 0.454329i
\(849\) −21.6659 11.9736i −0.743572 0.410934i
\(850\) 1.62718 + 0.817201i 0.0558119 + 0.0280298i
\(851\) 62.6603 + 31.4692i 2.14797 + 1.07875i
\(852\) 33.9504 + 18.7627i 1.16312 + 0.642799i
\(853\) 2.36014 2.50160i 0.0808097 0.0856532i −0.685707 0.727878i \(-0.740507\pi\)
0.766517 + 0.642224i \(0.221988\pi\)
\(854\) 0.776573 0.651622i 0.0265738 0.0222980i
\(855\) 0.875950 42.2488i 0.0299569 1.44488i
\(856\) 11.4381 + 9.59772i 0.390947 + 0.328043i
\(857\) −14.5601 + 1.70183i −0.497362 + 0.0581333i −0.361076 0.932536i \(-0.617591\pi\)
−0.136286 + 0.990670i \(0.543517\pi\)
\(858\) 9.61278 9.41554i 0.328175 0.321441i
\(859\) −6.54336 6.93555i −0.223256 0.236638i 0.606058 0.795421i \(-0.292750\pi\)
−0.829314 + 0.558783i \(0.811269\pi\)
\(860\) −10.8220 1.26491i −0.369026 0.0431330i
\(861\) 28.5195 22.0737i 0.971940 0.752271i
\(862\) −1.08296 + 18.5938i −0.0368859 + 0.633306i
\(863\) −8.00876 13.8716i −0.272621 0.472194i 0.696911 0.717158i \(-0.254557\pi\)
−0.969532 + 0.244964i \(0.921224\pi\)
\(864\) 16.7330 + 22.5708i 0.569269 + 0.767873i
\(865\) −27.3732 + 47.4117i −0.930716 + 1.61205i
\(866\) −6.12821 4.03059i −0.208245 0.136965i
\(867\) −20.6718 18.7838i −0.702050 0.637933i
\(868\) −1.40576 3.25892i −0.0477147 0.110615i
\(869\) −2.48915 + 0.589939i −0.0844386 + 0.0200123i
\(870\) 5.12249 0.394705i 0.173669 0.0133817i
\(871\) 32.5505 + 43.7229i 1.10293 + 1.48150i
\(872\) −22.3086 + 8.11966i −0.755464 + 0.274967i
\(873\) −7.89321 36.6761i −0.267145 1.24130i
\(874\) −15.9184 5.79383i −0.538448 0.195979i
\(875\) 4.08796 + 13.6547i 0.138198 + 0.461614i
\(876\) −12.8803 14.7792i −0.435186 0.499341i
\(877\) 1.92577 + 33.0643i 0.0650287 + 1.11650i 0.860147 + 0.510046i \(0.170372\pi\)
−0.795118 + 0.606454i \(0.792591\pi\)
\(878\) 17.4883 11.5023i 0.590203 0.388182i
\(879\) 37.3799 + 5.87172i 1.26079 + 0.198048i
\(880\) −21.0503 4.98902i −0.709607 0.168180i
\(881\) 2.00755 + 11.3854i 0.0676360 + 0.383583i 0.999770 + 0.0214681i \(0.00683402\pi\)
−0.932134 + 0.362115i \(0.882055\pi\)
\(882\) 4.33130 + 1.97581i 0.145842 + 0.0665290i
\(883\) −7.24692 + 41.0993i −0.243878 + 1.38310i 0.579206 + 0.815182i \(0.303363\pi\)
−0.823084 + 0.567920i \(0.807748\pi\)
\(884\) −2.47736 + 5.74317i −0.0833227 + 0.193164i
\(885\) 2.46638 25.1818i 0.0829064 0.846476i
\(886\) −5.59410 + 18.6856i −0.187937 + 0.627755i
\(887\) 14.3927 19.3327i 0.483259 0.649130i −0.491895 0.870654i \(-0.663696\pi\)
0.975155 + 0.221524i \(0.0711032\pi\)
\(888\) 19.1811 + 36.4736i 0.643676 + 1.22397i
\(889\) 30.0413 15.0873i 1.00755 0.506013i
\(890\) 21.6198 0.724697
\(891\) −28.5636 11.7588i −0.956917 0.393934i
\(892\) 7.80468 0.261320
\(893\) −13.7405 + 6.90072i −0.459807 + 0.230924i
\(894\) −7.23891 + 11.4683i −0.242105 + 0.383557i
\(895\) −17.8534 + 23.9812i −0.596772 + 0.801604i
\(896\) −10.3558 + 34.5906i −0.345961 + 1.15559i
\(897\) −34.5546 24.7331i −1.15374 0.825813i
\(898\) 3.94788 9.15221i 0.131742 0.305413i
\(899\) 0.211221 1.19789i 0.00704460 0.0399519i
\(900\) 16.6465 4.60988i 0.554883 0.153663i
\(901\) −1.36020 7.71410i −0.0453149 0.256994i
\(902\) 12.6108 + 2.98880i 0.419892 + 0.0995163i
\(903\) −4.35908 11.3128i −0.145061 0.376467i
\(904\) 10.1580 6.68102i 0.337850 0.222207i
\(905\) 0.138383 + 2.37595i 0.00460001 + 0.0789792i
\(906\) −6.05620 + 1.18519i −0.201204 + 0.0393754i
\(907\) −6.62271 22.1214i −0.219904 0.734529i −0.994746 0.102375i \(-0.967356\pi\)
0.774842 0.632155i \(-0.217829\pi\)
\(908\) 22.2614 + 8.10250i 0.738771 + 0.268891i
\(909\) −9.55144 15.1994i −0.316801 0.504133i
\(910\) −19.3305 + 7.03572i −0.640799 + 0.233232i
\(911\) −13.6745 18.3680i −0.453055 0.608559i 0.515642 0.856804i \(-0.327553\pi\)
−0.968697 + 0.248246i \(0.920146\pi\)
\(912\) 10.3059 + 15.0480i 0.341264 + 0.498289i
\(913\) 12.1544 2.88065i 0.402252 0.0953355i
\(914\) 1.87698 + 4.35133i 0.0620850 + 0.143929i
\(915\) 2.73351 0.874448i 0.0903670 0.0289084i
\(916\) −7.26878 4.78075i −0.240167 0.157961i
\(917\) 11.2088 19.4143i 0.370148 0.641116i
\(918\) −2.75713 0.00553191i −0.0909988 0.000182580i
\(919\) −9.84136 17.0457i −0.324636 0.562287i 0.656802 0.754063i \(-0.271909\pi\)
−0.981439 + 0.191776i \(0.938575\pi\)
\(920\) 2.16840 37.2301i 0.0714902 1.22744i
\(921\) −48.8497 19.9954i −1.60965 0.658872i
\(922\) 11.4670 + 1.34030i 0.377645 + 0.0441404i
\(923\) −36.5279 38.7173i −1.20233 1.27440i
\(924\) −7.76658 30.2354i −0.255502 0.994672i
\(925\) 38.8467 4.54052i 1.27727 0.149292i
\(926\) 1.12588 + 0.944728i 0.0369988 + 0.0310457i
\(927\) 5.24316 0.812832i 0.172208 0.0266969i
\(928\) −7.45472 + 6.25525i −0.244713 + 0.205339i
\(929\) 19.8444 21.0338i 0.651074 0.690098i −0.314786 0.949163i \(-0.601933\pi\)
0.965860 + 0.259065i \(0.0834143\pi\)
\(930\) 0.0361241 + 1.92910i 0.00118456 + 0.0632575i
\(931\) 12.1196 + 6.08669i 0.397204 + 0.199483i
\(932\) −6.67733 3.35348i −0.218723 0.109847i
\(933\) −40.2216 + 24.2372i −1.31680 + 0.793490i
\(934\) −4.76771 + 5.05347i −0.156004 + 0.165355i
\(935\) 7.13679 5.98848i 0.233398 0.195844i
\(936\) −8.05343 23.6402i −0.263235 0.772705i
\(937\) 14.9990 + 12.5856i 0.489995 + 0.411155i 0.854025 0.520233i \(-0.174155\pi\)
−0.364029 + 0.931388i \(0.618599\pi\)
\(938\) −24.1188 + 2.81908i −0.787506 + 0.0920463i
\(939\) −13.5238 3.77437i −0.441334 0.123172i
\(940\) −10.5972 11.2323i −0.345641 0.366358i
\(941\) 10.0278 + 1.17209i 0.326898 + 0.0382089i 0.277959 0.960593i \(-0.410342\pi\)
0.0489390 + 0.998802i \(0.484416\pi\)
\(942\) 0.0219902 + 0.161804i 0.000716480 + 0.00527185i
\(943\) 2.37979 40.8595i 0.0774967 1.33057i
\(944\) 5.46032 + 9.45755i 0.177718 + 0.307817i
\(945\) 32.3376 + 34.4139i 1.05194 + 1.11949i
\(946\) 2.17839 3.77309i 0.0708257 0.122674i
\(947\) −17.5511 11.5436i −0.570335 0.375115i 0.231342 0.972872i \(-0.425688\pi\)
−0.801677 + 0.597757i \(0.796059\pi\)
\(948\) −0.459966 + 2.11660i −0.0149390 + 0.0687439i
\(949\) 10.6552 + 24.7014i 0.345881 + 0.801843i
\(950\) −9.19419 + 2.17906i −0.298299 + 0.0706981i
\(951\) −14.5299 + 30.3346i −0.471164 + 0.983666i
\(952\) −3.64733 4.89922i −0.118211 0.158785i
\(953\) 6.34571 2.30965i 0.205558 0.0748169i −0.237189 0.971463i \(-0.576226\pi\)
0.442747 + 0.896647i \(0.354004\pi\)
\(954\) 11.2660 + 8.75592i 0.364749 + 0.283483i
\(955\) 2.08753 + 0.759798i 0.0675508 + 0.0245865i
\(956\) −13.9845 46.7114i −0.452290 1.51075i
\(957\) 3.47027 10.1202i 0.112178 0.327138i
\(958\) −0.905188 15.5415i −0.0292453 0.502122i
\(959\) 22.5645 14.8409i 0.728645 0.479237i
\(960\) −4.02050 + 4.97782i −0.129761 + 0.160658i
\(961\) −29.7199 7.04375i −0.958706 0.227218i
\(962\) −4.47973 25.4058i −0.144432 0.819117i
\(963\) −12.1603 + 17.6794i −0.391859 + 0.569709i
\(964\) −7.27912 + 41.2819i −0.234445 + 1.32960i
\(965\) 10.7589 24.9419i 0.346341 0.802909i
\(966\) 17.2389 7.82212i 0.554651 0.251672i
\(967\) −3.38236 + 11.2979i −0.108769 + 0.363315i −0.994993 0.0999421i \(-0.968134\pi\)
0.886224 + 0.463257i \(0.153319\pi\)
\(968\) 0.971882 1.30546i 0.0312375 0.0419592i
\(969\) −7.84840 0.309811i −0.252127 0.00995255i
\(970\) −18.4186 + 9.25019i −0.591387 + 0.297006i
\(971\) 24.4687 0.785239 0.392620 0.919701i \(-0.371569\pi\)
0.392620 + 0.919701i \(0.371569\pi\)
\(972\) −19.4273 + 17.5113i −0.623132 + 0.561674i
\(973\) −18.4632 −0.591905
\(974\) 3.05566 1.53461i 0.0979096 0.0491721i
\(975\) −23.6841 0.934915i −0.758498 0.0299413i
\(976\) −0.739699 + 0.993589i −0.0236772 + 0.0318040i
\(977\) −11.1615 + 37.2820i −0.357088 + 1.19276i 0.571174 + 0.820829i \(0.306488\pi\)
−0.928262 + 0.371927i \(0.878697\pi\)
\(978\) −14.5047 + 6.58147i −0.463808 + 0.210452i
\(979\) 17.8318 41.3387i 0.569907 1.32119i
\(980\) −2.36521 + 13.4138i −0.0755538 + 0.428487i
\(981\) −14.6763 30.7987i −0.468579 0.983328i
\(982\) 0.0480294 + 0.272388i 0.00153268 + 0.00869226i
\(983\) 18.2124 + 4.31641i 0.580885 + 0.137672i 0.510545 0.859851i \(-0.329444\pi\)
0.0703395 + 0.997523i \(0.477592\pi\)
\(984\) 15.1141 18.7130i 0.481821 0.596548i
\(985\) −2.71672 + 1.78681i −0.0865618 + 0.0569326i
\(986\) −0.0555250 0.953328i −0.00176828 0.0303601i
\(987\) 5.57348 16.2536i 0.177406 0.517358i
\(988\) −9.30881 31.0936i −0.296153 0.989219i
\(989\) −12.9292 4.70584i −0.411125 0.149637i
\(990\) −2.31911 + 16.8112i −0.0737062 + 0.534294i
\(991\) −2.15353 + 0.783819i −0.0684090 + 0.0248988i −0.375998 0.926620i \(-0.622700\pi\)
0.307589 + 0.951519i \(0.400478\pi\)
\(992\) −2.18238 2.93144i −0.0692906 0.0930735i
\(993\) 1.48651 3.10345i 0.0471731 0.0984849i
\(994\) 23.0736 5.46853i 0.731849 0.173451i
\(995\) 8.83352 + 20.4784i 0.280041 + 0.649209i
\(996\) 2.24599 10.3353i 0.0711671 0.327485i
\(997\) −26.1338 17.1885i −0.827666 0.544365i 0.0635312 0.997980i \(-0.479764\pi\)
−0.891198 + 0.453615i \(0.850134\pi\)
\(998\) 1.55659 2.69609i 0.0492729 0.0853432i
\(999\) −49.5443 + 32.4436i −1.56751 + 1.02647i
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.25.5 yes 144
3.2 odd 2 243.2.g.a.73.4 144
9.2 odd 6 729.2.g.b.703.5 144
9.4 even 3 729.2.g.d.217.4 144
9.5 odd 6 729.2.g.a.217.5 144
9.7 even 3 729.2.g.c.703.4 144
81.13 even 27 inner 81.2.g.a.13.5 144
81.14 odd 54 729.2.g.a.514.5 144
81.16 even 27 6561.2.a.c.1.32 72
81.40 even 27 729.2.g.c.28.4 144
81.41 odd 54 729.2.g.b.28.5 144
81.65 odd 54 6561.2.a.d.1.41 72
81.67 even 27 729.2.g.d.514.4 144
81.68 odd 54 243.2.g.a.10.4 144
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
81.2.g.a.13.5 144 81.13 even 27 inner
81.2.g.a.25.5 yes 144 1.1 even 1 trivial
243.2.g.a.10.4 144 81.68 odd 54
243.2.g.a.73.4 144 3.2 odd 2
729.2.g.a.217.5 144 9.5 odd 6
729.2.g.a.514.5 144 81.14 odd 54
729.2.g.b.28.5 144 81.41 odd 54
729.2.g.b.703.5 144 9.2 odd 6
729.2.g.c.28.4 144 81.40 even 27
729.2.g.c.703.4 144 9.7 even 3
729.2.g.d.217.4 144 9.4 even 3
729.2.g.d.514.4 144 81.67 even 27
6561.2.a.c.1.32 72 81.16 even 27
6561.2.a.d.1.41 72 81.65 odd 54