Properties

Label 180.2.x.a.67.29
Level $180$
Weight $2$
Character 180.67
Analytic conductor $1.437$
Analytic rank $0$
Dimension $128$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [180,2,Mod(7,180)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(180, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([6, 8, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("180.7");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 180.x (of order \(12\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.43730723638\)
Analytic rank: \(0\)
Dimension: \(128\)
Relative dimension: \(32\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 67.29
Character \(\chi\) \(=\) 180.67
Dual form 180.2.x.a.43.29

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.33961 + 0.453270i) q^{2} +(-1.51730 - 0.835348i) q^{3} +(1.58909 + 1.21441i) q^{4} +(1.01645 + 1.99169i) q^{5} +(-1.65394 - 1.80678i) q^{6} +(-0.00373871 - 0.00100179i) q^{7} +(1.57830 + 2.34712i) q^{8} +(1.60439 + 2.53494i) q^{9} +O(q^{10})\) \(q+(1.33961 + 0.453270i) q^{2} +(-1.51730 - 0.835348i) q^{3} +(1.58909 + 1.21441i) q^{4} +(1.01645 + 1.99169i) q^{5} +(-1.65394 - 1.80678i) q^{6} +(-0.00373871 - 0.00100179i) q^{7} +(1.57830 + 2.34712i) q^{8} +(1.60439 + 2.53494i) q^{9} +(0.458866 + 3.12881i) q^{10} +(3.58713 - 2.07103i) q^{11} +(-1.39667 - 3.17006i) q^{12} +(-0.767553 - 2.86455i) q^{13} +(-0.00455433 - 0.00303665i) q^{14} +(0.121501 - 3.87108i) q^{15} +(1.05043 + 3.85961i) q^{16} +(-2.07784 - 2.07784i) q^{17} +(1.00023 + 4.12305i) q^{18} -7.31525 q^{19} +(-0.803496 + 4.39936i) q^{20} +(0.00483590 + 0.00464313i) q^{21} +(5.74408 - 1.14843i) q^{22} +(-3.73983 + 1.00208i) q^{23} +(-0.434098 - 4.87971i) q^{24} +(-2.93367 + 4.04890i) q^{25} +(0.270195 - 4.18528i) q^{26} +(-0.316773 - 5.18649i) q^{27} +(-0.00472458 - 0.00613225i) q^{28} +(4.99228 - 2.88229i) q^{29} +(1.91741 - 5.13065i) q^{30} +(1.77642 + 1.02562i) q^{31} +(-0.342287 + 5.64649i) q^{32} +(-7.17278 + 0.145869i) q^{33} +(-1.84166 - 3.72530i) q^{34} +(-0.00180496 - 0.00846463i) q^{35} +(-0.528936 + 5.97664i) q^{36} +(-6.09468 - 6.09468i) q^{37} +(-9.79956 - 3.31579i) q^{38} +(-1.22829 + 4.98755i) q^{39} +(-3.07047 + 5.52921i) q^{40} +(1.82477 - 3.16060i) q^{41} +(0.00437361 + 0.00841195i) q^{42} +(-0.259538 + 0.968609i) q^{43} +(8.21535 + 1.06518i) q^{44} +(-3.41805 + 5.77208i) q^{45} +(-5.46412 - 0.352755i) q^{46} +(4.55740 + 1.22115i) q^{47} +(1.63031 - 6.73365i) q^{48} +(-6.06216 - 3.49999i) q^{49} +(-5.76521 + 4.09419i) q^{50} +(1.41698 + 4.88841i) q^{51} +(2.25902 - 5.48415i) q^{52} +(6.92974 - 6.92974i) q^{53} +(1.92653 - 7.09144i) q^{54} +(7.77098 + 5.03936i) q^{55} +(-0.00354952 - 0.0103563i) q^{56} +(11.0994 + 6.11078i) q^{57} +(7.99414 - 1.59829i) q^{58} +(2.76056 - 4.78143i) q^{59} +(4.89414 - 6.00395i) q^{60} +(3.59007 + 6.21819i) q^{61} +(1.91482 + 2.17912i) q^{62} +(-0.00345888 - 0.0110847i) q^{63} +(-3.01792 + 7.40893i) q^{64} +(4.92512 - 4.44039i) q^{65} +(-9.67482 - 3.05580i) q^{66} +(-0.851369 - 3.17735i) q^{67} +(-0.778533 - 5.82521i) q^{68} +(6.51153 + 1.60360i) q^{69} +(0.00141883 - 0.0121574i) q^{70} +11.3127i q^{71} +(-3.41760 + 7.76660i) q^{72} +(-6.50632 + 6.50632i) q^{73} +(-5.40194 - 10.9270i) q^{74} +(7.83349 - 3.69275i) q^{75} +(-11.6246 - 8.88370i) q^{76} +(-0.0154860 + 0.00414946i) q^{77} +(-3.90613 + 6.12460i) q^{78} +(2.99986 + 5.19591i) q^{79} +(-6.61945 + 6.01522i) q^{80} +(-3.85188 + 8.13406i) q^{81} +(3.87708 - 3.40684i) q^{82} +(-0.756131 + 2.82192i) q^{83} +(0.00204604 + 0.0132511i) q^{84} +(2.02640 - 6.25042i) q^{85} +(-0.786720 + 1.17991i) q^{86} +(-9.98249 + 0.203008i) q^{87} +(10.5225 + 5.15070i) q^{88} +9.18764i q^{89} +(-7.19516 + 6.18302i) q^{90} +0.0114786i q^{91} +(-7.15987 - 2.94927i) q^{92} +(-1.83861 - 3.04009i) q^{93} +(5.55161 + 3.70160i) q^{94} +(-7.43557 - 14.5697i) q^{95} +(5.23614 - 8.28148i) q^{96} +(0.607478 - 2.26714i) q^{97} +(-6.53447 - 7.43641i) q^{98} +(11.0051 + 5.77044i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 128 q - 2 q^{2} - 4 q^{5} - 8 q^{6} - 8 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 128 q - 2 q^{2} - 4 q^{5} - 8 q^{6} - 8 q^{8} - 8 q^{10} + 2 q^{12} - 4 q^{13} - 4 q^{16} - 16 q^{17} - 36 q^{18} - 18 q^{20} - 24 q^{21} - 10 q^{22} - 4 q^{25} - 48 q^{26} + 8 q^{28} - 14 q^{30} + 18 q^{32} - 20 q^{33} - 40 q^{36} - 16 q^{37} - 34 q^{38} - 2 q^{40} - 8 q^{41} + 34 q^{42} - 28 q^{45} - 40 q^{46} - 22 q^{48} + 38 q^{50} - 18 q^{52} - 64 q^{53} - 32 q^{56} - 48 q^{57} - 10 q^{58} + 74 q^{60} - 8 q^{61} + 44 q^{62} + 12 q^{65} - 36 q^{66} + 58 q^{68} - 22 q^{70} + 78 q^{72} - 16 q^{73} - 32 q^{76} - 60 q^{77} + 114 q^{78} + 132 q^{80} + 24 q^{81} - 4 q^{85} + 32 q^{86} - 10 q^{88} + 138 q^{90} + 52 q^{92} - 68 q^{93} + 52 q^{96} - 4 q^{97} + 164 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/180\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(91\) \(101\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.33961 + 0.453270i 0.947245 + 0.320510i
\(3\) −1.51730 0.835348i −0.876012 0.482288i
\(4\) 1.58909 + 1.21441i 0.794546 + 0.607204i
\(5\) 1.01645 + 1.99169i 0.454569 + 0.890711i
\(6\) −1.65394 1.80678i −0.675220 0.737616i
\(7\) −0.00373871 0.00100179i −0.00141310 0.000378639i 0.258112 0.966115i \(-0.416900\pi\)
−0.259526 + 0.965736i \(0.583566\pi\)
\(8\) 1.57830 + 2.34712i 0.558015 + 0.829831i
\(9\) 1.60439 + 2.53494i 0.534796 + 0.844981i
\(10\) 0.458866 + 3.12881i 0.145106 + 0.989416i
\(11\) 3.58713 2.07103i 1.08156 0.624439i 0.150243 0.988649i \(-0.451994\pi\)
0.931317 + 0.364210i \(0.118661\pi\)
\(12\) −1.39667 3.17006i −0.403185 0.915119i
\(13\) −0.767553 2.86455i −0.212881 0.794483i −0.986902 0.161322i \(-0.948424\pi\)
0.774021 0.633160i \(-0.218243\pi\)
\(14\) −0.00455433 0.00303665i −0.00121719 0.000811578i
\(15\) 0.121501 3.87108i 0.0313715 0.999508i
\(16\) 1.05043 + 3.85961i 0.262607 + 0.964903i
\(17\) −2.07784 2.07784i −0.503949 0.503949i 0.408713 0.912663i \(-0.365978\pi\)
−0.912663 + 0.408713i \(0.865978\pi\)
\(18\) 1.00023 + 4.12305i 0.235757 + 0.971812i
\(19\) −7.31525 −1.67823 −0.839117 0.543951i \(-0.816928\pi\)
−0.839117 + 0.543951i \(0.816928\pi\)
\(20\) −0.803496 + 4.39936i −0.179667 + 0.983727i
\(21\) 0.00483590 + 0.00464313i 0.00105528 + 0.00101321i
\(22\) 5.74408 1.14843i 1.22464 0.244845i
\(23\) −3.73983 + 1.00208i −0.779808 + 0.208949i −0.626700 0.779260i \(-0.715595\pi\)
−0.153108 + 0.988209i \(0.548928\pi\)
\(24\) −0.434098 4.87971i −0.0886098 0.996066i
\(25\) −2.93367 + 4.04890i −0.586734 + 0.809780i
\(26\) 0.270195 4.18528i 0.0529896 0.820800i
\(27\) −0.316773 5.18649i −0.0609631 0.998140i
\(28\) −0.00472458 0.00613225i −0.000892863 0.00115889i
\(29\) 4.99228 2.88229i 0.927042 0.535228i 0.0411674 0.999152i \(-0.486892\pi\)
0.885875 + 0.463924i \(0.153559\pi\)
\(30\) 1.91741 5.13065i 0.350069 0.936724i
\(31\) 1.77642 + 1.02562i 0.319054 + 0.184206i 0.650971 0.759103i \(-0.274362\pi\)
−0.331917 + 0.943309i \(0.607695\pi\)
\(32\) −0.342287 + 5.64649i −0.0605084 + 0.998168i
\(33\) −7.17278 + 0.145869i −1.24862 + 0.0253925i
\(34\) −1.84166 3.72530i −0.315842 0.638885i
\(35\) −0.00180496 0.00846463i −0.000305094 0.00143078i
\(36\) −0.528936 + 5.97664i −0.0881560 + 0.996107i
\(37\) −6.09468 6.09468i −1.00196 1.00196i −0.999998 0.00196150i \(-0.999376\pi\)
−0.00196150 0.999998i \(-0.500624\pi\)
\(38\) −9.79956 3.31579i −1.58970 0.537891i
\(39\) −1.22829 + 4.98755i −0.196683 + 0.798647i
\(40\) −3.07047 + 5.52921i −0.485484 + 0.874246i
\(41\) 1.82477 3.16060i 0.284981 0.493602i −0.687623 0.726068i \(-0.741346\pi\)
0.972605 + 0.232465i \(0.0746792\pi\)
\(42\) 0.00437361 + 0.00841195i 0.000674863 + 0.00129799i
\(43\) −0.259538 + 0.968609i −0.0395792 + 0.147711i −0.982888 0.184206i \(-0.941029\pi\)
0.943309 + 0.331917i \(0.107695\pi\)
\(44\) 8.21535 + 1.06518i 1.23851 + 0.160582i
\(45\) −3.41805 + 5.77208i −0.509533 + 0.860451i
\(46\) −5.46412 0.352755i −0.805640 0.0520108i
\(47\) 4.55740 + 1.22115i 0.664765 + 0.178123i 0.575396 0.817875i \(-0.304848\pi\)
0.0893696 + 0.995999i \(0.471515\pi\)
\(48\) 1.63031 6.73365i 0.235315 0.971919i
\(49\) −6.06216 3.49999i −0.866024 0.499999i
\(50\) −5.76521 + 4.09419i −0.815324 + 0.579006i
\(51\) 1.41698 + 4.88841i 0.198417 + 0.684515i
\(52\) 2.25902 5.48415i 0.313269 0.760515i
\(53\) 6.92974 6.92974i 0.951873 0.951873i −0.0470212 0.998894i \(-0.514973\pi\)
0.998894 + 0.0470212i \(0.0149728\pi\)
\(54\) 1.92653 7.09144i 0.262167 0.965022i
\(55\) 7.77098 + 5.03936i 1.04784 + 0.679507i
\(56\) −0.00354952 0.0103563i −0.000474324 0.00138392i
\(57\) 11.0994 + 6.11078i 1.47015 + 0.809392i
\(58\) 7.99414 1.59829i 1.04968 0.209865i
\(59\) 2.76056 4.78143i 0.359394 0.622489i −0.628465 0.777838i \(-0.716317\pi\)
0.987860 + 0.155348i \(0.0496499\pi\)
\(60\) 4.89414 6.00395i 0.631831 0.775106i
\(61\) 3.59007 + 6.21819i 0.459662 + 0.796158i 0.998943 0.0459683i \(-0.0146373\pi\)
−0.539281 + 0.842126i \(0.681304\pi\)
\(62\) 1.91482 + 2.17912i 0.243182 + 0.276748i
\(63\) −0.00345888 0.0110847i −0.000435777 0.00139654i
\(64\) −3.01792 + 7.40893i −0.377239 + 0.926116i
\(65\) 4.92512 4.44039i 0.610886 0.550763i
\(66\) −9.67482 3.05580i −1.19089 0.376143i
\(67\) −0.851369 3.17735i −0.104011 0.388175i 0.894220 0.447628i \(-0.147731\pi\)
−0.998231 + 0.0594528i \(0.981064\pi\)
\(68\) −0.778533 5.82521i −0.0944110 0.706411i
\(69\) 6.51153 + 1.60360i 0.783896 + 0.193051i
\(70\) 0.00141883 0.0121574i 0.000169582 0.00145309i
\(71\) 11.3127i 1.34257i 0.741200 + 0.671284i \(0.234257\pi\)
−0.741200 + 0.671284i \(0.765743\pi\)
\(72\) −3.41760 + 7.76660i −0.402768 + 0.915302i
\(73\) −6.50632 + 6.50632i −0.761508 + 0.761508i −0.976595 0.215087i \(-0.930996\pi\)
0.215087 + 0.976595i \(0.430996\pi\)
\(74\) −5.40194 10.9270i −0.627963 1.27024i
\(75\) 7.83349 3.69275i 0.904534 0.426402i
\(76\) −11.6246 8.88370i −1.33343 1.01903i
\(77\) −0.0154860 + 0.00414946i −0.00176479 + 0.000472874i
\(78\) −3.90613 + 6.12460i −0.442282 + 0.693475i
\(79\) 2.99986 + 5.19591i 0.337510 + 0.584585i 0.983964 0.178368i \(-0.0570819\pi\)
−0.646453 + 0.762953i \(0.723749\pi\)
\(80\) −6.61945 + 6.01522i −0.740077 + 0.672522i
\(81\) −3.85188 + 8.13406i −0.427987 + 0.903785i
\(82\) 3.87708 3.40684i 0.428152 0.376223i
\(83\) −0.756131 + 2.82192i −0.0829962 + 0.309746i −0.994927 0.100598i \(-0.967925\pi\)
0.911931 + 0.410344i \(0.134591\pi\)
\(84\) 0.00204604 + 0.0132511i 0.000223241 + 0.00144582i
\(85\) 2.02640 6.25042i 0.219794 0.677953i
\(86\) −0.786720 + 1.17991i −0.0848342 + 0.127233i
\(87\) −9.98249 + 0.203008i −1.07024 + 0.0217648i
\(88\) 10.5225 + 5.15070i 1.12171 + 0.549066i
\(89\) 9.18764i 0.973888i 0.873433 + 0.486944i \(0.161888\pi\)
−0.873433 + 0.486944i \(0.838112\pi\)
\(90\) −7.19516 + 6.18302i −0.758436 + 0.651747i
\(91\) 0.0114786i 0.00120329i
\(92\) −7.15987 2.94927i −0.746468 0.307483i
\(93\) −1.83861 3.04009i −0.190655 0.315243i
\(94\) 5.55161 + 3.70160i 0.572605 + 0.381791i
\(95\) −7.43557 14.5697i −0.762873 1.49482i
\(96\) 5.23614 8.28148i 0.534411 0.845225i
\(97\) 0.607478 2.26714i 0.0616800 0.230193i −0.928204 0.372072i \(-0.878648\pi\)
0.989884 + 0.141879i \(0.0453143\pi\)
\(98\) −6.53447 7.43641i −0.660082 0.751191i
\(99\) 11.0051 + 5.77044i 1.10605 + 0.579951i
\(100\) −9.57888 + 2.87140i −0.957888 + 0.287140i
\(101\) −3.57015 6.18367i −0.355243 0.615299i 0.631917 0.775036i \(-0.282268\pi\)
−0.987159 + 0.159738i \(0.948935\pi\)
\(102\) −0.317576 + 7.19083i −0.0314447 + 0.711998i
\(103\) −4.03578 + 1.08138i −0.397657 + 0.106552i −0.452105 0.891965i \(-0.649327\pi\)
0.0544481 + 0.998517i \(0.482660\pi\)
\(104\) 5.51200 6.32266i 0.540496 0.619988i
\(105\) −0.00433225 + 0.0143511i −0.000422784 + 0.00140053i
\(106\) 12.4242 6.14208i 1.20674 0.596571i
\(107\) −8.23461 + 8.23461i −0.796070 + 0.796070i −0.982473 0.186403i \(-0.940317\pi\)
0.186403 + 0.982473i \(0.440317\pi\)
\(108\) 5.79513 8.62650i 0.557636 0.830085i
\(109\) 6.43234i 0.616106i −0.951369 0.308053i \(-0.900323\pi\)
0.951369 0.308053i \(-0.0996774\pi\)
\(110\) 8.12587 + 10.2731i 0.774771 + 0.979503i
\(111\) 4.15627 + 14.3386i 0.394496 + 1.36096i
\(112\) −6.07462e−5 0.0154823i −5.73998e−6 0.00146294i
\(113\) 4.02483 + 15.0209i 0.378625 + 1.41305i 0.847976 + 0.530035i \(0.177821\pi\)
−0.469351 + 0.883012i \(0.655512\pi\)
\(114\) 12.0990 + 13.2171i 1.13318 + 1.23789i
\(115\) −5.79718 6.43002i −0.540590 0.599602i
\(116\) 11.4335 + 1.48243i 1.06157 + 0.137640i
\(117\) 6.03001 6.54155i 0.557475 0.604766i
\(118\) 5.86535 5.15396i 0.539949 0.474460i
\(119\) 0.00568689 + 0.00984998i 0.000521316 + 0.000902946i
\(120\) 9.27764 5.82456i 0.846928 0.531707i
\(121\) 3.07833 5.33183i 0.279848 0.484712i
\(122\) 1.99077 + 9.95720i 0.180235 + 0.901483i
\(123\) −5.40892 + 3.27125i −0.487706 + 0.294959i
\(124\) 1.57738 + 3.78709i 0.141653 + 0.340091i
\(125\) −11.0461 1.72747i −0.987991 0.154509i
\(126\) 0.000390824 0.0164169i 3.48174e−5 0.00146254i
\(127\) 14.1298 14.1298i 1.25381 1.25381i 0.299818 0.953996i \(-0.403074\pi\)
0.953996 0.299818i \(-0.0969260\pi\)
\(128\) −7.40107 + 8.55712i −0.654168 + 0.756349i
\(129\) 1.20292 1.25286i 0.105911 0.110308i
\(130\) 8.61042 3.71597i 0.755184 0.325912i
\(131\) 7.13877 + 4.12157i 0.623717 + 0.360103i 0.778315 0.627874i \(-0.216075\pi\)
−0.154598 + 0.987978i \(0.549408\pi\)
\(132\) −11.5753 8.47888i −1.00750 0.737991i
\(133\) 0.0273496 + 0.00732831i 0.00237151 + 0.000635445i
\(134\) 0.299700 4.64230i 0.0258901 0.401034i
\(135\) 10.0079 5.90271i 0.861343 0.508024i
\(136\) 1.59747 8.15638i 0.136982 0.699404i
\(137\) −4.39479 + 16.4016i −0.375472 + 1.40128i 0.477182 + 0.878804i \(0.341658\pi\)
−0.852654 + 0.522476i \(0.825008\pi\)
\(138\) 7.99602 + 5.09967i 0.680666 + 0.434113i
\(139\) −0.575384 + 0.996595i −0.0488035 + 0.0845301i −0.889395 0.457139i \(-0.848874\pi\)
0.840592 + 0.541669i \(0.182207\pi\)
\(140\) 0.00741126 0.0156430i 0.000626366 0.00132208i
\(141\) −5.89485 5.65987i −0.496436 0.476647i
\(142\) −5.12770 + 15.1545i −0.430307 + 1.27174i
\(143\) −8.68588 8.68588i −0.726350 0.726350i
\(144\) −8.09861 + 8.85509i −0.674884 + 0.737924i
\(145\) 10.8150 + 7.01337i 0.898139 + 0.582429i
\(146\) −11.6650 + 5.76679i −0.965405 + 0.477263i
\(147\) 6.27440 + 10.3745i 0.517504 + 0.855678i
\(148\) −2.28358 17.0864i −0.187709 1.40450i
\(149\) −15.4247 8.90547i −1.26364 0.729565i −0.289865 0.957067i \(-0.593611\pi\)
−0.973777 + 0.227503i \(0.926944\pi\)
\(150\) 12.1676 1.39615i 0.993481 0.113995i
\(151\) 14.2092 8.20368i 1.15633 0.667606i 0.205906 0.978572i \(-0.433986\pi\)
0.950421 + 0.310966i \(0.100652\pi\)
\(152\) −11.5457 17.1697i −0.936479 1.39265i
\(153\) 1.93354 8.60085i 0.156318 0.695338i
\(154\) −0.0226259 0.00146070i −0.00182325 0.000117706i
\(155\) −0.237074 + 4.58056i −0.0190422 + 0.367920i
\(156\) −8.00878 + 6.43403i −0.641215 + 0.515135i
\(157\) −0.570890 + 0.152969i −0.0455620 + 0.0122083i −0.281528 0.959553i \(-0.590841\pi\)
0.235966 + 0.971761i \(0.424175\pi\)
\(158\) 1.66348 + 8.32022i 0.132339 + 0.661921i
\(159\) −16.3032 + 4.72574i −1.29293 + 0.374775i
\(160\) −11.5940 + 5.05763i −0.916585 + 0.399841i
\(161\) 0.0149860 0.00118106
\(162\) −8.84694 + 9.15050i −0.695081 + 0.718931i
\(163\) 2.55591 + 2.55591i 0.200194 + 0.200194i 0.800083 0.599889i \(-0.204789\pi\)
−0.599889 + 0.800083i \(0.704789\pi\)
\(164\) 6.73798 2.80646i 0.526148 0.219148i
\(165\) −7.58128 14.1377i −0.590202 1.10062i
\(166\) −2.29201 + 3.43753i −0.177895 + 0.266804i
\(167\) −2.53503 9.46085i −0.196166 0.732103i −0.991962 0.126537i \(-0.959614\pi\)
0.795796 0.605565i \(-0.207053\pi\)
\(168\) −0.00326545 + 0.0186787i −0.000251935 + 0.00144109i
\(169\) 3.64184 2.10261i 0.280141 0.161740i
\(170\) 5.54770 7.45460i 0.425490 0.571742i
\(171\) −11.7365 18.5437i −0.897512 1.41808i
\(172\) −1.58872 + 1.22402i −0.121138 + 0.0933309i
\(173\) 8.78942 + 2.35512i 0.668247 + 0.179056i 0.576965 0.816769i \(-0.304237\pi\)
0.0912819 + 0.995825i \(0.470904\pi\)
\(174\) −13.4646 4.25281i −1.02075 0.322405i
\(175\) 0.0150243 0.0121988i 0.00113573 0.000922140i
\(176\) 11.7614 + 11.6695i 0.886548 + 0.879619i
\(177\) −8.18275 + 4.94883i −0.615053 + 0.371977i
\(178\) −4.16449 + 12.3078i −0.312141 + 0.922511i
\(179\) −9.66859 −0.722664 −0.361332 0.932437i \(-0.617678\pi\)
−0.361332 + 0.932437i \(0.617678\pi\)
\(180\) −12.4413 + 5.02146i −0.927317 + 0.374278i
\(181\) −0.725261 −0.0539082 −0.0269541 0.999637i \(-0.508581\pi\)
−0.0269541 + 0.999637i \(0.508581\pi\)
\(182\) −0.00520293 + 0.0153769i −0.000385667 + 0.00113981i
\(183\) −0.252859 12.4338i −0.0186919 0.919133i
\(184\) −8.25460 7.19622i −0.608537 0.530513i
\(185\) 5.94380 18.3337i 0.436997 1.34792i
\(186\) −1.08503 4.90591i −0.0795583 0.359719i
\(187\) −11.7567 3.15021i −0.859737 0.230366i
\(188\) 5.75915 + 7.47507i 0.420029 + 0.545175i
\(189\) −0.00401142 + 0.0197081i −0.000291788 + 0.00143356i
\(190\) −3.35672 22.8880i −0.243522 1.66047i
\(191\) 4.39149 2.53543i 0.317757 0.183457i −0.332635 0.943056i \(-0.607938\pi\)
0.650393 + 0.759598i \(0.274604\pi\)
\(192\) 10.7681 8.72054i 0.777121 0.629351i
\(193\) 6.65689 + 24.8439i 0.479174 + 1.78830i 0.604975 + 0.796245i \(0.293183\pi\)
−0.125801 + 0.992056i \(0.540150\pi\)
\(194\) 1.84141 2.76172i 0.132205 0.198280i
\(195\) −11.1821 + 2.62321i −0.800770 + 0.187852i
\(196\) −5.38292 12.9238i −0.384494 0.923125i
\(197\) 7.34350 + 7.34350i 0.523203 + 0.523203i 0.918537 0.395334i \(-0.129371\pi\)
−0.395334 + 0.918537i \(0.629371\pi\)
\(198\) 12.1269 + 12.7184i 0.861823 + 0.903857i
\(199\) −23.5313 −1.66809 −0.834046 0.551695i \(-0.813981\pi\)
−0.834046 + 0.551695i \(0.813981\pi\)
\(200\) −14.1335 0.495270i −0.999387 0.0350209i
\(201\) −1.36241 + 5.53218i −0.0960973 + 0.390210i
\(202\) −1.97972 9.90193i −0.139292 0.696698i
\(203\) −0.0215521 + 0.00577488i −0.00151266 + 0.000405317i
\(204\) −3.68481 + 9.48893i −0.257989 + 0.664358i
\(205\) 8.14972 + 0.421800i 0.569201 + 0.0294598i
\(206\) −5.89651 0.380669i −0.410829 0.0265225i
\(207\) −8.54036 7.87253i −0.593596 0.547178i
\(208\) 10.2498 5.97146i 0.710694 0.414046i
\(209\) −26.2407 + 15.1501i −1.81511 + 1.04795i
\(210\) −0.0123084 + 0.0172612i −0.000849364 + 0.00119114i
\(211\) −11.4167 6.59145i −0.785960 0.453774i 0.0525786 0.998617i \(-0.483256\pi\)
−0.838538 + 0.544843i \(0.816589\pi\)
\(212\) 19.4275 2.59646i 1.33429 0.178326i
\(213\) 9.45002 17.1647i 0.647505 1.17611i
\(214\) −14.7636 + 7.29864i −1.00922 + 0.498925i
\(215\) −2.19298 + 0.467621i −0.149560 + 0.0318915i
\(216\) 11.6733 8.92936i 0.794269 0.607566i
\(217\) −0.00561407 0.00561407i −0.000381108 0.000381108i
\(218\) 2.91559 8.61680i 0.197468 0.583603i
\(219\) 15.3071 4.43699i 1.03436 0.299824i
\(220\) 6.22897 + 17.4451i 0.419957 + 1.17615i
\(221\) −4.35721 + 7.54691i −0.293098 + 0.507660i
\(222\) −0.931509 + 21.0920i −0.0625188 + 1.41560i
\(223\) −1.78550 + 6.66356i −0.119566 + 0.446225i −0.999588 0.0287073i \(-0.990861\pi\)
0.880022 + 0.474933i \(0.157528\pi\)
\(224\) 0.00693628 0.0207677i 0.000463450 0.00138760i
\(225\) −14.9705 0.940682i −0.998032 0.0627121i
\(226\) −1.41683 + 21.9464i −0.0942459 + 1.45985i
\(227\) 23.0916 + 6.18736i 1.53264 + 0.410670i 0.923879 0.382684i \(-0.125000\pi\)
0.608761 + 0.793354i \(0.291667\pi\)
\(228\) 10.2170 + 23.1898i 0.676638 + 1.53578i
\(229\) 10.8974 + 6.29160i 0.720118 + 0.415761i 0.814796 0.579747i \(-0.196849\pi\)
−0.0946778 + 0.995508i \(0.530182\pi\)
\(230\) −4.85141 11.2414i −0.319892 0.741235i
\(231\) 0.0269631 + 0.00664022i 0.00177404 + 0.000436894i
\(232\) 14.6444 + 7.16832i 0.961452 + 0.470624i
\(233\) 5.85463 5.85463i 0.383550 0.383550i −0.488830 0.872379i \(-0.662576\pi\)
0.872379 + 0.488830i \(0.162576\pi\)
\(234\) 11.0429 6.02988i 0.721899 0.394185i
\(235\) 2.20020 + 10.3182i 0.143525 + 0.673083i
\(236\) 10.1934 4.24569i 0.663533 0.276371i
\(237\) −0.211289 10.3897i −0.0137247 0.674881i
\(238\) 0.00315349 + 0.0157728i 0.000204410 + 0.00102240i
\(239\) 8.52459 14.7650i 0.551410 0.955070i −0.446763 0.894652i \(-0.647423\pi\)
0.998173 0.0604180i \(-0.0192434\pi\)
\(240\) 15.0685 3.59734i 0.972666 0.232207i
\(241\) −6.97743 12.0853i −0.449456 0.778481i 0.548895 0.835892i \(-0.315049\pi\)
−0.998351 + 0.0574109i \(0.981715\pi\)
\(242\) 6.54051 5.74723i 0.420440 0.369446i
\(243\) 12.6392 9.12414i 0.810807 0.585314i
\(244\) −1.84646 + 14.2411i −0.118207 + 0.911692i
\(245\) 0.809032 15.6315i 0.0516871 0.998661i
\(246\) −8.72859 + 1.93048i −0.556514 + 0.123083i
\(247\) 5.61484 + 20.9549i 0.357264 + 1.33333i
\(248\) 0.396488 + 5.78819i 0.0251770 + 0.367551i
\(249\) 3.50456 3.65006i 0.222093 0.231313i
\(250\) −14.0144 7.32099i −0.886348 0.463020i
\(251\) 5.95154i 0.375658i −0.982202 0.187829i \(-0.939855\pi\)
0.982202 0.187829i \(-0.0601451\pi\)
\(252\) 0.00796485 0.0218151i 0.000501738 0.00137422i
\(253\) −11.3399 + 11.3399i −0.712934 + 0.712934i
\(254\) 25.3329 12.5237i 1.58953 0.785809i
\(255\) −8.29592 + 7.79100i −0.519511 + 0.487892i
\(256\) −13.7932 + 8.10849i −0.862075 + 0.506780i
\(257\) 2.38369 0.638709i 0.148691 0.0398416i −0.183706 0.982981i \(-0.558809\pi\)
0.332397 + 0.943140i \(0.392143\pi\)
\(258\) 2.17933 1.13310i 0.135679 0.0705435i
\(259\) 0.0166807 + 0.0288918i 0.00103649 + 0.00179525i
\(260\) 13.2189 1.07509i 0.819802 0.0666743i
\(261\) 15.3160 + 8.03083i 0.948036 + 0.497096i
\(262\) 7.69496 + 8.75708i 0.475396 + 0.541014i
\(263\) −1.05558 + 3.93947i −0.0650897 + 0.242918i −0.990804 0.135306i \(-0.956798\pi\)
0.925714 + 0.378224i \(0.123465\pi\)
\(264\) −11.6632 16.6051i −0.717820 1.02197i
\(265\) 20.8456 + 6.75818i 1.28054 + 0.415152i
\(266\) 0.0333160 + 0.0222138i 0.00204274 + 0.00136202i
\(267\) 7.67488 13.9404i 0.469695 0.853138i
\(268\) 2.50570 6.08301i 0.153060 0.371579i
\(269\) 14.8292i 0.904151i 0.891980 + 0.452075i \(0.149316\pi\)
−0.891980 + 0.452075i \(0.850684\pi\)
\(270\) 16.0822 3.37102i 0.978730 0.205154i
\(271\) 2.28698i 0.138924i −0.997585 0.0694621i \(-0.977872\pi\)
0.997585 0.0694621i \(-0.0221283\pi\)
\(272\) 5.83702 10.2023i 0.353922 0.618603i
\(273\) 0.00958866 0.0174165i 0.000580332 0.00105410i
\(274\) −13.3216 + 19.9796i −0.804789 + 1.20701i
\(275\) −2.13806 + 20.5996i −0.128930 + 1.24221i
\(276\) 8.39999 + 10.4559i 0.505620 + 0.629372i
\(277\) 0.240544 0.897723i 0.0144529 0.0539390i −0.958323 0.285688i \(-0.907778\pi\)
0.972776 + 0.231749i \(0.0744447\pi\)
\(278\) −1.22252 + 1.07424i −0.0733216 + 0.0644287i
\(279\) 0.250185 + 6.14860i 0.0149782 + 0.368107i
\(280\) 0.0170187 0.0175962i 0.00101706 0.00105157i
\(281\) −9.59486 16.6188i −0.572381 0.991394i −0.996321 0.0857030i \(-0.972686\pi\)
0.423939 0.905691i \(-0.360647\pi\)
\(282\) −5.33133 10.2540i −0.317476 0.610614i
\(283\) 23.2929 6.24132i 1.38462 0.371008i 0.511823 0.859091i \(-0.328970\pi\)
0.872797 + 0.488083i \(0.162304\pi\)
\(284\) −13.7382 + 17.9769i −0.815213 + 1.06673i
\(285\) −0.888813 + 28.3179i −0.0526487 + 1.67741i
\(286\) −7.69861 15.5727i −0.455228 0.920834i
\(287\) −0.00998854 + 0.00998854i −0.000589605 + 0.000589605i
\(288\) −14.8627 + 8.19148i −0.875793 + 0.482687i
\(289\) 8.36519i 0.492070i
\(290\) 11.3089 + 14.2973i 0.664083 + 0.839566i
\(291\) −2.81557 + 2.93247i −0.165052 + 0.171904i
\(292\) −18.2405 + 2.43782i −1.06744 + 0.142662i
\(293\) 0.547697 + 2.04403i 0.0319968 + 0.119414i 0.980077 0.198617i \(-0.0636451\pi\)
−0.948080 + 0.318031i \(0.896978\pi\)
\(294\) 3.70275 + 16.7418i 0.215949 + 0.976402i
\(295\) 12.3291 + 0.638110i 0.717828 + 0.0371522i
\(296\) 4.68567 23.9242i 0.272349 1.39057i
\(297\) −11.8777 17.9486i −0.689213 1.04148i
\(298\) −16.6265 18.9214i −0.963146 1.09609i
\(299\) 5.74104 + 9.94377i 0.332013 + 0.575063i
\(300\) 16.9326 + 3.64493i 0.977607 + 0.210440i
\(301\) 0.00194068 0.00336135i 0.000111859 0.000193745i
\(302\) 22.7532 4.54910i 1.30930 0.261771i
\(303\) 0.251456 + 12.3648i 0.0144458 + 0.710339i
\(304\) −7.68414 28.2340i −0.440716 1.61933i
\(305\) −8.73559 + 13.4708i −0.500199 + 0.771335i
\(306\) 6.48870 10.6453i 0.370934 0.608554i
\(307\) −10.6198 + 10.6198i −0.606102 + 0.606102i −0.941925 0.335823i \(-0.890985\pi\)
0.335823 + 0.941925i \(0.390985\pi\)
\(308\) −0.0296478 0.0122124i −0.00168934 0.000695867i
\(309\) 7.02681 + 1.73050i 0.399741 + 0.0984445i
\(310\) −2.39382 + 6.02869i −0.135960 + 0.342407i
\(311\) −16.3389 9.43325i −0.926493 0.534911i −0.0407921 0.999168i \(-0.512988\pi\)
−0.885701 + 0.464257i \(0.846321\pi\)
\(312\) −13.6450 + 4.98893i −0.772494 + 0.282443i
\(313\) −16.1114 4.31704i −0.910670 0.244013i −0.227077 0.973877i \(-0.572917\pi\)
−0.683593 + 0.729863i \(0.739584\pi\)
\(314\) −0.834104 0.0538484i −0.0470712 0.00303884i
\(315\) 0.0185615 0.0181560i 0.00104582 0.00102298i
\(316\) −1.54290 + 11.8998i −0.0867948 + 0.669417i
\(317\) −4.68890 + 17.4992i −0.263355 + 0.982855i 0.699894 + 0.714246i \(0.253230\pi\)
−0.963250 + 0.268608i \(0.913436\pi\)
\(318\) −23.9819 1.05914i −1.34484 0.0593935i
\(319\) 11.9386 20.6783i 0.668435 1.15776i
\(320\) −17.8238 + 1.52003i −0.996383 + 0.0849722i
\(321\) 19.3731 5.61560i 1.08130 0.313432i
\(322\) 0.0200754 + 0.00679272i 0.00111876 + 0.000378543i
\(323\) 15.1999 + 15.1999i 0.845745 + 0.845745i
\(324\) −15.9991 + 8.24802i −0.888837 + 0.458223i
\(325\) 13.8500 + 5.29589i 0.768260 + 0.293763i
\(326\) 2.26539 + 4.58243i 0.125469 + 0.253797i
\(327\) −5.37324 + 9.75977i −0.297141 + 0.539717i
\(328\) 10.2983 0.705429i 0.568630 0.0389508i
\(329\) −0.0158155 0.00913108i −0.000871936 0.000503412i
\(330\) −3.74774 22.3753i −0.206306 1.23172i
\(331\) −30.9050 + 17.8430i −1.69869 + 0.980741i −0.751690 + 0.659516i \(0.770761\pi\)
−0.947003 + 0.321225i \(0.895906\pi\)
\(332\) −4.62852 + 3.56604i −0.254023 + 0.195712i
\(333\) 5.67145 25.2279i 0.310793 1.38248i
\(334\) 0.892383 13.8229i 0.0488290 0.756354i
\(335\) 5.46293 4.92527i 0.298472 0.269096i
\(336\) −0.0128409 + 0.0235420i −0.000700530 + 0.00128432i
\(337\) −20.2317 + 5.42108i −1.10209 + 0.295305i −0.763616 0.645670i \(-0.776578\pi\)
−0.338476 + 0.940975i \(0.609911\pi\)
\(338\) 5.83168 1.16594i 0.317202 0.0634188i
\(339\) 6.44079 26.1533i 0.349816 1.42045i
\(340\) 10.8107 7.47162i 0.586292 0.405206i
\(341\) 8.49632 0.460102
\(342\) −7.31696 30.1611i −0.395656 1.63093i
\(343\) 0.0383170 + 0.0383170i 0.00206892 + 0.00206892i
\(344\) −2.68307 + 0.919593i −0.144661 + 0.0495811i
\(345\) 3.42475 + 14.5989i 0.184382 + 0.785980i
\(346\) 10.7069 + 7.13891i 0.575604 + 0.383790i
\(347\) 2.65861 + 9.92205i 0.142721 + 0.532644i 0.999846 + 0.0175348i \(0.00558179\pi\)
−0.857125 + 0.515109i \(0.827752\pi\)
\(348\) −16.1096 11.8002i −0.863567 0.632558i
\(349\) 15.7613 9.09980i 0.843683 0.487101i −0.0148311 0.999890i \(-0.504721\pi\)
0.858515 + 0.512789i \(0.171388\pi\)
\(350\) 0.0256560 0.00953150i 0.00137137 0.000509480i
\(351\) −14.6138 + 4.88832i −0.780027 + 0.260919i
\(352\) 10.4662 + 20.9636i 0.557851 + 1.11736i
\(353\) 16.2917 + 4.36534i 0.867119 + 0.232344i 0.664842 0.746984i \(-0.268499\pi\)
0.202277 + 0.979328i \(0.435166\pi\)
\(354\) −13.2048 + 2.92049i −0.701829 + 0.155222i
\(355\) −22.5314 + 11.4987i −1.19584 + 0.610290i
\(356\) −11.1575 + 14.6000i −0.591349 + 0.773799i
\(357\) −0.000400544 0.0196959i −2.11991e−5 0.00104242i
\(358\) −12.9521 4.38249i −0.684540 0.231622i
\(359\) 26.8572 1.41747 0.708736 0.705474i \(-0.249266\pi\)
0.708736 + 0.705474i \(0.249266\pi\)
\(360\) −18.9425 + 1.08753i −0.998356 + 0.0573181i
\(361\) 34.5129 1.81647
\(362\) −0.971564 0.328739i −0.0510643 0.0172782i
\(363\) −9.12468 + 5.51849i −0.478921 + 0.289646i
\(364\) −0.0139398 + 0.0182406i −0.000730642 + 0.000956069i
\(365\) −19.5719 6.34525i −1.02444 0.332126i
\(366\) 5.29714 16.7710i 0.276886 0.876636i
\(367\) 6.10468 + 1.63574i 0.318662 + 0.0853851i 0.414604 0.910002i \(-0.363920\pi\)
−0.0959429 + 0.995387i \(0.530587\pi\)
\(368\) −7.79608 13.3817i −0.406399 0.697568i
\(369\) 10.9396 0.445128i 0.569492 0.0231724i
\(370\) 16.2725 21.8657i 0.845965 1.13675i
\(371\) −0.0328504 + 0.0189662i −0.00170551 + 0.000984676i
\(372\) 0.770190 7.06381i 0.0399325 0.366241i
\(373\) −3.25424 12.1450i −0.168498 0.628843i −0.997568 0.0696984i \(-0.977796\pi\)
0.829070 0.559145i \(-0.188870\pi\)
\(374\) −14.3215 9.54901i −0.740547 0.493768i
\(375\) 15.3172 + 11.8484i 0.790975 + 0.611849i
\(376\) 4.32678 + 12.6241i 0.223136 + 0.651038i
\(377\) −12.0883 12.0883i −0.622579 0.622579i
\(378\) −0.0143068 + 0.0245829i −0.000735864 + 0.00126441i
\(379\) 13.2087 0.678488 0.339244 0.940698i \(-0.389829\pi\)
0.339244 + 0.940698i \(0.389829\pi\)
\(380\) 5.87778 32.1824i 0.301524 1.65092i
\(381\) −33.2424 + 9.63580i −1.70306 + 0.493657i
\(382\) 7.03211 1.40595i 0.359794 0.0719345i
\(383\) 18.1781 4.87081i 0.928858 0.248887i 0.237490 0.971390i \(-0.423675\pi\)
0.691368 + 0.722503i \(0.257009\pi\)
\(384\) 18.3778 6.80123i 0.937838 0.347074i
\(385\) −0.0240051 0.0266256i −0.00122341 0.00135697i
\(386\) −2.34337 + 36.2984i −0.119274 + 1.84754i
\(387\) −2.87177 + 0.896109i −0.145980 + 0.0455518i
\(388\) 3.71857 2.86497i 0.188782 0.145447i
\(389\) −1.13890 + 0.657543i −0.0577444 + 0.0333388i −0.528594 0.848875i \(-0.677281\pi\)
0.470850 + 0.882213i \(0.343947\pi\)
\(390\) −16.1687 1.55446i −0.818734 0.0787132i
\(391\) 9.85292 + 5.68859i 0.498284 + 0.287684i
\(392\) −1.35304 19.7527i −0.0683391 0.997660i
\(393\) −7.38870 12.2170i −0.372710 0.616267i
\(394\) 6.50881 + 13.1660i 0.327909 + 0.663293i
\(395\) −7.29944 + 11.2562i −0.367275 + 0.566359i
\(396\) 10.4804 + 22.5344i 0.526662 + 1.13240i
\(397\) 0.714896 + 0.714896i 0.0358796 + 0.0358796i 0.724819 0.688939i \(-0.241923\pi\)
−0.688939 + 0.724819i \(0.741923\pi\)
\(398\) −31.5227 10.6661i −1.58009 0.534641i
\(399\) −0.0353758 0.0339657i −0.00177101 0.00170041i
\(400\) −18.7088 7.06974i −0.935439 0.353487i
\(401\) −9.93987 + 17.2164i −0.496373 + 0.859744i −0.999991 0.00418285i \(-0.998669\pi\)
0.503618 + 0.863926i \(0.332002\pi\)
\(402\) −4.33267 + 6.79340i −0.216094 + 0.338824i
\(403\) 1.57443 5.87585i 0.0784279 0.292697i
\(404\) 1.83621 14.1620i 0.0913549 0.704588i
\(405\) −20.1158 + 0.596089i −0.999561 + 0.0296199i
\(406\) −0.0314890 0.00203288i −0.00156277 0.000100890i
\(407\) −34.4847 9.24014i −1.70934 0.458017i
\(408\) −9.23725 + 11.0412i −0.457312 + 0.546622i
\(409\) −21.4875 12.4058i −1.06249 0.613428i −0.136369 0.990658i \(-0.543543\pi\)
−0.926120 + 0.377230i \(0.876877\pi\)
\(410\) 10.7262 + 4.25907i 0.529731 + 0.210341i
\(411\) 20.3692 21.2149i 1.00474 1.04645i
\(412\) −7.72646 3.18266i −0.380655 0.156798i
\(413\) −0.0151109 + 0.0151109i −0.000743560 + 0.000743560i
\(414\) −7.87234 14.4172i −0.386905 0.708566i
\(415\) −6.38896 + 1.36235i −0.313622 + 0.0668753i
\(416\) 16.4374 3.35348i 0.805908 0.164418i
\(417\) 1.70553 1.03149i 0.0835203 0.0505121i
\(418\) −42.0194 + 8.40103i −2.05523 + 0.410908i
\(419\) −14.0411 + 24.3199i −0.685953 + 1.18811i 0.287183 + 0.957876i \(0.407281\pi\)
−0.973136 + 0.230230i \(0.926052\pi\)
\(420\) −0.0243125 + 0.0175442i −0.00118633 + 0.000856067i
\(421\) 0.651510 + 1.12845i 0.0317527 + 0.0549972i 0.881465 0.472249i \(-0.156558\pi\)
−0.849712 + 0.527246i \(0.823224\pi\)
\(422\) −12.3062 14.0048i −0.599057 0.681743i
\(423\) 4.21628 + 13.5120i 0.205003 + 0.656974i
\(424\) 27.2021 + 5.32768i 1.32105 + 0.258735i
\(425\) 14.5086 2.31727i 0.703772 0.112404i
\(426\) 20.4396 18.7105i 0.990300 0.906529i
\(427\) −0.00719297 0.0268445i −0.000348092 0.00129910i
\(428\) −23.0857 + 3.08538i −1.11589 + 0.149138i
\(429\) 5.92333 + 20.4348i 0.285981 + 0.986601i
\(430\) −3.14968 0.367583i −0.151891 0.0177264i
\(431\) 14.1271i 0.680479i −0.940339 0.340240i \(-0.889492\pi\)
0.940339 0.340240i \(-0.110508\pi\)
\(432\) 19.6851 6.67065i 0.947099 0.320942i
\(433\) −4.90201 + 4.90201i −0.235576 + 0.235576i −0.815015 0.579440i \(-0.803271\pi\)
0.579440 + 0.815015i \(0.303271\pi\)
\(434\) −0.00497596 0.0100653i −0.000238854 0.000483152i
\(435\) −10.5510 19.6757i −0.505882 0.943377i
\(436\) 7.81148 10.2216i 0.374102 0.489525i
\(437\) 27.3578 7.33050i 1.30870 0.350665i
\(438\) 22.5166 + 0.994424i 1.07589 + 0.0475154i
\(439\) 14.2344 + 24.6546i 0.679369 + 1.17670i 0.975171 + 0.221452i \(0.0710795\pi\)
−0.295803 + 0.955249i \(0.595587\pi\)
\(440\) 0.436999 + 26.1930i 0.0208331 + 1.24870i
\(441\) −0.853776 20.9826i −0.0406560 0.999171i
\(442\) −9.25774 + 8.13490i −0.440346 + 0.386938i
\(443\) 6.32386 23.6010i 0.300456 1.12132i −0.636332 0.771416i \(-0.719549\pi\)
0.936787 0.349900i \(-0.113784\pi\)
\(444\) −10.8082 + 27.8328i −0.512937 + 1.32089i
\(445\) −18.2989 + 9.33876i −0.867453 + 0.442700i
\(446\) −5.41226 + 8.11724i −0.256278 + 0.384363i
\(447\) 15.9647 + 26.3973i 0.755106 + 1.24855i
\(448\) 0.0187053 0.0246766i 0.000883741 0.00116586i
\(449\) 32.1553i 1.51750i −0.651382 0.758750i \(-0.725810\pi\)
0.651382 0.758750i \(-0.274190\pi\)
\(450\) −19.6282 8.04581i −0.925281 0.379283i
\(451\) 15.1166i 0.711814i
\(452\) −11.8456 + 28.7574i −0.557172 + 1.35263i
\(453\) −28.4125 + 0.577809i −1.33494 + 0.0271478i
\(454\) 28.1290 + 18.7553i 1.32016 + 0.880232i
\(455\) −0.0228619 + 0.0116674i −0.00107178 + 0.000546978i
\(456\) 3.17553 + 35.6963i 0.148708 + 1.67163i
\(457\) 2.92218 10.9057i 0.136694 0.510149i −0.863291 0.504706i \(-0.831601\pi\)
0.999985 0.00544282i \(-0.00173251\pi\)
\(458\) 11.7464 + 13.3677i 0.548873 + 0.624633i
\(459\) −10.1185 + 11.4349i −0.472290 + 0.533734i
\(460\) −1.40359 17.2580i −0.0654429 0.804660i
\(461\) −1.41470 2.45032i −0.0658889 0.114123i 0.831199 0.555975i \(-0.187655\pi\)
−0.897088 + 0.441852i \(0.854322\pi\)
\(462\) 0.0331101 + 0.0211168i 0.00154042 + 0.000982445i
\(463\) −20.7678 + 5.56471i −0.965161 + 0.258614i −0.706783 0.707430i \(-0.749854\pi\)
−0.258377 + 0.966044i \(0.583188\pi\)
\(464\) 16.3686 + 16.2406i 0.759891 + 0.753951i
\(465\) 4.18607 6.75204i 0.194125 0.313118i
\(466\) 10.4966 5.18917i 0.486247 0.240384i
\(467\) 0.746518 0.746518i 0.0345447 0.0345447i −0.689623 0.724168i \(-0.742224\pi\)
0.724168 + 0.689623i \(0.242224\pi\)
\(468\) 17.5264 3.07223i 0.810156 0.142014i
\(469\) 0.0127321i 0.000587914i
\(470\) −1.72952 + 14.8196i −0.0797766 + 0.683576i
\(471\) 0.993993 + 0.244791i 0.0458008 + 0.0112794i
\(472\) 15.5796 1.06719i 0.717108 0.0491215i
\(473\) 1.07502 + 4.01204i 0.0494296 + 0.184474i
\(474\) 4.42628 14.0138i 0.203306 0.643677i
\(475\) 21.4605 29.6187i 0.984676 1.35900i
\(476\) −0.00292490 + 0.0225587i −0.000134063 + 0.00103398i
\(477\) 28.6845 + 6.44851i 1.31337 + 0.295257i
\(478\) 18.1122 15.9154i 0.828430 0.727953i
\(479\) −8.68475 15.0424i −0.396816 0.687306i 0.596515 0.802602i \(-0.296552\pi\)
−0.993331 + 0.115296i \(0.963218\pi\)
\(480\) 21.8164 + 2.01108i 0.995778 + 0.0917926i
\(481\) −12.7805 + 22.1365i −0.582741 + 1.00934i
\(482\) −3.86912 19.3522i −0.176234 0.881467i
\(483\) −0.0227383 0.0125185i −0.00103463 0.000569614i
\(484\) 11.3668 4.73441i 0.516671 0.215201i
\(485\) 5.13291 1.09452i 0.233073 0.0496995i
\(486\) 21.0673 6.49377i 0.955632 0.294563i
\(487\) 17.2233 17.2233i 0.780462 0.780462i −0.199447 0.979909i \(-0.563914\pi\)
0.979909 + 0.199447i \(0.0639145\pi\)
\(488\) −8.92859 + 18.2405i −0.404178 + 0.825709i
\(489\) −1.74300 6.01314i −0.0788212 0.271924i
\(490\) 8.16909 20.5734i 0.369042 0.929411i
\(491\) −13.8880 8.01824i −0.626757 0.361858i 0.152738 0.988267i \(-0.451191\pi\)
−0.779495 + 0.626409i \(0.784524\pi\)
\(492\) −12.5679 1.37032i −0.566605 0.0617788i
\(493\) −16.3621 4.38420i −0.736910 0.197455i
\(494\) −1.97654 + 30.6163i −0.0889288 + 1.37749i
\(495\) −0.306833 + 27.7841i −0.0137911 + 1.24880i
\(496\) −2.09248 + 7.93362i −0.0939551 + 0.356230i
\(497\) 0.0113329 0.0422949i 0.000508349 0.00189718i
\(498\) 6.34920 3.30113i 0.284514 0.147927i
\(499\) 18.9316 32.7905i 0.847494 1.46790i −0.0359441 0.999354i \(-0.511444\pi\)
0.883438 0.468548i \(-0.155223\pi\)
\(500\) −15.4554 16.1595i −0.691186 0.722677i
\(501\) −4.05671 + 16.4726i −0.181240 + 0.735940i
\(502\) 2.69766 7.97273i 0.120402 0.355840i
\(503\) 1.97514 + 1.97514i 0.0880673 + 0.0880673i 0.749768 0.661701i \(-0.230165\pi\)
−0.661701 + 0.749768i \(0.730165\pi\)
\(504\) 0.0205579 0.0256134i 0.000915721 0.00114091i
\(505\) 8.68710 13.3960i 0.386571 0.596115i
\(506\) −20.3311 + 10.0510i −0.903826 + 0.446820i
\(507\) −7.28217 + 0.148093i −0.323412 + 0.00657706i
\(508\) 39.6128 5.29421i 1.75753 0.234892i
\(509\) 23.3128 + 13.4596i 1.03332 + 0.596587i 0.917934 0.396733i \(-0.129856\pi\)
0.115386 + 0.993321i \(0.463190\pi\)
\(510\) −14.6447 + 6.67659i −0.648479 + 0.295644i
\(511\) 0.0308432 0.0178073i 0.00136442 0.000787750i
\(512\) −22.1528 + 4.61013i −0.979025 + 0.203741i
\(513\) 2.31728 + 37.9405i 0.102310 + 1.67511i
\(514\) 3.48272 + 0.224839i 0.153616 + 0.00991722i
\(515\) −6.25594 6.93885i −0.275669 0.305762i
\(516\) 3.43304 0.530078i 0.151131 0.0233354i
\(517\) 18.8770 5.05809i 0.830211 0.222454i
\(518\) 0.00924978 + 0.0462646i 0.000406412 + 0.00203275i
\(519\) −11.3688 10.9156i −0.499036 0.479143i
\(520\) 18.1954 + 4.55154i 0.797923 + 0.199598i
\(521\) 15.4522 0.676975 0.338487 0.940971i \(-0.390085\pi\)
0.338487 + 0.940971i \(0.390085\pi\)
\(522\) 16.8773 + 17.7004i 0.738698 + 0.774727i
\(523\) −3.28250 3.28250i −0.143534 0.143534i 0.631689 0.775222i \(-0.282362\pi\)
−0.775222 + 0.631689i \(0.782362\pi\)
\(524\) 6.33890 + 15.2189i 0.276916 + 0.664842i
\(525\) −0.0329865 + 0.00595867i −0.00143965 + 0.000260058i
\(526\) −3.19970 + 4.79888i −0.139514 + 0.209241i
\(527\) −1.56005 5.82217i −0.0679566 0.253618i
\(528\) −8.09748 27.5309i −0.352398 1.19813i
\(529\) −6.93643 + 4.00475i −0.301584 + 0.174120i
\(530\) 24.8616 + 18.5020i 1.07992 + 0.803676i
\(531\) 16.5497 0.673401i 0.718195 0.0292231i
\(532\) 0.0345615 + 0.0448590i 0.00149843 + 0.00194488i
\(533\) −10.4543 2.80122i −0.452826 0.121334i
\(534\) 16.6001 15.1959i 0.718356 0.657589i
\(535\) −24.7709 8.03076i −1.07094 0.347200i
\(536\) 6.11390 7.01309i 0.264080 0.302919i
\(537\) 14.6701 + 8.07664i 0.633063 + 0.348533i
\(538\) −6.72163 + 19.8653i −0.289790 + 0.856452i
\(539\) −28.9944 −1.24888
\(540\) 23.0718 + 2.77372i 0.992851 + 0.119362i
\(541\) −28.5369 −1.22690 −0.613448 0.789735i \(-0.710218\pi\)
−0.613448 + 0.789735i \(0.710218\pi\)
\(542\) 1.03662 3.06366i 0.0445267 0.131595i
\(543\) 1.10044 + 0.605845i 0.0472243 + 0.0259993i
\(544\) 12.4437 11.0213i 0.533519 0.472533i
\(545\) 12.8112 6.53813i 0.548773 0.280063i
\(546\) 0.0207394 0.0189850i 0.000887566 0.000812485i
\(547\) −34.8130 9.32812i −1.48850 0.398842i −0.579268 0.815137i \(-0.696662\pi\)
−0.909229 + 0.416295i \(0.863328\pi\)
\(548\) −26.9019 + 20.7265i −1.14919 + 0.885394i
\(549\) −10.0029 + 19.0770i −0.426913 + 0.814187i
\(550\) −12.2014 + 26.6263i −0.520268 + 1.13535i
\(551\) −36.5197 + 21.0847i −1.55579 + 0.898238i
\(552\) 6.51333 + 17.8143i 0.277226 + 0.758226i
\(553\) −0.00601043 0.0224312i −0.000255589 0.000953872i
\(554\) 0.729146 1.09356i 0.0309784 0.0464611i
\(555\) −24.3335 + 22.8525i −1.03290 + 0.970033i
\(556\) −2.12461 + 0.884930i −0.0901036 + 0.0375294i
\(557\) −11.9128 11.9128i −0.504762 0.504762i 0.408152 0.912914i \(-0.366173\pi\)
−0.912914 + 0.408152i \(0.866173\pi\)
\(558\) −2.45183 + 8.35011i −0.103794 + 0.353489i
\(559\) 2.97383 0.125780
\(560\) 0.0307742 0.0158579i 0.00130045 0.000670119i
\(561\) 15.2069 + 14.6008i 0.642038 + 0.616445i
\(562\) −5.32054 26.6117i −0.224433 1.12255i
\(563\) −6.87323 + 1.84168i −0.289672 + 0.0776174i −0.400729 0.916197i \(-0.631243\pi\)
0.111057 + 0.993814i \(0.464576\pi\)
\(564\) −2.49407 16.1528i −0.105019 0.680156i
\(565\) −25.8259 + 23.2842i −1.08651 + 0.979573i
\(566\) 34.0324 + 2.19708i 1.43049 + 0.0923500i
\(567\) 0.0225497 0.0265522i 0.000946997 0.00111509i
\(568\) −26.5522 + 17.8548i −1.11410 + 0.749173i
\(569\) 37.4538 21.6240i 1.57015 0.906524i 0.573996 0.818858i \(-0.305392\pi\)
0.996150 0.0876662i \(-0.0279409\pi\)
\(570\) −14.0263 + 37.5320i −0.587498 + 1.57204i
\(571\) 15.2197 + 8.78710i 0.636925 + 0.367729i 0.783429 0.621481i \(-0.213469\pi\)
−0.146504 + 0.989210i \(0.546802\pi\)
\(572\) −3.25446 24.3509i −0.136076 1.01816i
\(573\) −8.78117 + 0.178578i −0.366839 + 0.00746020i
\(574\) −0.0179082 + 0.00885320i −0.000747475 + 0.000369526i
\(575\) 6.91408 18.0820i 0.288337 0.754071i
\(576\) −23.6231 + 4.23654i −0.984297 + 0.176522i
\(577\) −14.1684 14.1684i −0.589837 0.589837i 0.347750 0.937587i \(-0.386946\pi\)
−0.937587 + 0.347750i \(0.886946\pi\)
\(578\) 3.79169 11.2061i 0.157714 0.466111i
\(579\) 10.6528 43.2564i 0.442714 1.79767i
\(580\) 8.66897 + 24.2787i 0.359959 + 1.00812i
\(581\) 0.00565392 0.00979287i 0.000234564 0.000406277i
\(582\) −5.10096 + 2.65214i −0.211442 + 0.109935i
\(583\) 10.5062 39.2096i 0.435121 1.62389i
\(584\) −25.5401 5.00215i −1.05685 0.206990i
\(585\) 19.1579 + 5.36079i 0.792083 + 0.221641i
\(586\) −0.192801 + 2.98645i −0.00796452 + 0.123369i
\(587\) −1.37987 0.369735i −0.0569533 0.0152606i 0.230230 0.973136i \(-0.426052\pi\)
−0.287183 + 0.957876i \(0.592719\pi\)
\(588\) −2.62833 + 24.1058i −0.108391 + 0.994106i
\(589\) −12.9949 7.50263i −0.535447 0.309141i
\(590\) 16.2269 + 6.44323i 0.668051 + 0.265264i
\(591\) −5.00790 17.2767i −0.205998 0.710667i
\(592\) 17.1211 29.9251i 0.703672 1.22992i
\(593\) 3.47274 3.47274i 0.142608 0.142608i −0.632198 0.774807i \(-0.717847\pi\)
0.774807 + 0.632198i \(0.217847\pi\)
\(594\) −7.77587 29.4278i −0.319048 1.20744i
\(595\) −0.0138377 + 0.0213385i −0.000567290 + 0.000874794i
\(596\) −13.6964 32.8835i −0.561028 1.34696i
\(597\) 35.7041 + 19.6569i 1.46127 + 0.804502i
\(598\) 3.18352 + 15.9230i 0.130184 + 0.651139i
\(599\) −6.20251 + 10.7431i −0.253428 + 0.438950i −0.964467 0.264202i \(-0.914891\pi\)
0.711040 + 0.703152i \(0.248225\pi\)
\(600\) 21.0310 + 12.5578i 0.858585 + 0.512671i
\(601\) 1.54486 + 2.67578i 0.0630162 + 0.109147i 0.895812 0.444433i \(-0.146595\pi\)
−0.832796 + 0.553580i \(0.813261\pi\)
\(602\) 0.00412334 0.00362324i 0.000168055 0.000147672i
\(603\) 6.68848 7.25587i 0.272376 0.295482i
\(604\) 32.5423 + 4.21935i 1.32413 + 0.171683i
\(605\) 13.7483 + 0.711564i 0.558949 + 0.0289292i
\(606\) −5.26774 + 16.6779i −0.213987 + 0.677495i
\(607\) 9.90537 + 36.9673i 0.402046 + 1.50046i 0.809439 + 0.587204i \(0.199772\pi\)
−0.407392 + 0.913253i \(0.633562\pi\)
\(608\) 2.50392 41.3055i 0.101547 1.67516i
\(609\) 0.0375250 + 0.00924132i 0.00152059 + 0.000374477i
\(610\) −17.8082 + 14.0860i −0.721031 + 0.570324i
\(611\) 13.9922i 0.566063i
\(612\) 13.5175 11.3194i 0.546413 0.457561i
\(613\) 14.5099 14.5099i 0.586049 0.586049i −0.350510 0.936559i \(-0.613992\pi\)
0.936559 + 0.350510i \(0.113992\pi\)
\(614\) −19.0399 + 9.41268i −0.768389 + 0.379865i
\(615\) −12.0132 7.44785i −0.484419 0.300326i
\(616\) −0.0341808 0.0297983i −0.00137718 0.00120061i
\(617\) −0.139417 + 0.0373567i −0.00561272 + 0.00150392i −0.261624 0.965170i \(-0.584258\pi\)
0.256012 + 0.966674i \(0.417591\pi\)
\(618\) 8.62877 + 5.50323i 0.347100 + 0.221372i
\(619\) 13.6832 + 23.7000i 0.549975 + 0.952584i 0.998276 + 0.0587016i \(0.0186960\pi\)
−0.448301 + 0.893883i \(0.647971\pi\)
\(620\) −5.93940 + 6.99103i −0.238532 + 0.280766i
\(621\) 6.38198 + 19.0791i 0.256100 + 0.765620i
\(622\) −17.6119 20.0428i −0.706171 0.803642i
\(623\) 0.00920405 0.0343500i 0.000368752 0.00137620i
\(624\) −20.5402 + 0.498346i −0.822267 + 0.0199498i
\(625\) −7.78718 23.7563i −0.311487 0.950250i
\(626\) −19.6262 13.0859i −0.784419 0.523020i
\(627\) 52.4706 1.06707i 2.09548 0.0426145i
\(628\) −1.09296 0.450210i −0.0436140 0.0179653i
\(629\) 25.3275i 1.00987i
\(630\) 0.0330947 0.0159085i 0.00131852 0.000633811i
\(631\) 26.4593i 1.05333i −0.850074 0.526664i \(-0.823443\pi\)
0.850074 0.526664i \(-0.176557\pi\)
\(632\) −7.46071 + 15.2417i −0.296771 + 0.606284i
\(633\) 11.8164 + 19.5381i 0.469661 + 0.776571i
\(634\) −14.2132 + 21.3167i −0.564477 + 0.846596i
\(635\) 42.5043 + 13.7800i 1.68673 + 0.546841i
\(636\) −31.6463 12.2891i −1.25486 0.487296i
\(637\) −5.37286 + 20.0518i −0.212880 + 0.794481i
\(638\) 25.3659 22.2894i 1.00425 0.882445i
\(639\) −28.6770 + 18.1499i −1.13444 + 0.718000i
\(640\) −24.5659 6.04278i −0.971054 0.238862i
\(641\) −2.73281 4.73337i −0.107940 0.186957i 0.806996 0.590557i \(-0.201092\pi\)
−0.914935 + 0.403600i \(0.867759\pi\)
\(642\) 28.4978 + 1.25857i 1.12472 + 0.0496720i
\(643\) −40.3996 + 10.8251i −1.59321 + 0.426898i −0.942982 0.332844i \(-0.891992\pi\)
−0.650225 + 0.759742i \(0.725325\pi\)
\(644\) 0.0238142 + 0.0181991i 0.000938410 + 0.000717147i
\(645\) 3.71802 + 1.12238i 0.146397 + 0.0441936i
\(646\) 13.4722 + 27.2515i 0.530057 + 1.07220i
\(647\) 19.6463 19.6463i 0.772377 0.772377i −0.206144 0.978522i \(-0.566092\pi\)
0.978522 + 0.206144i \(0.0660917\pi\)
\(648\) −25.1710 + 3.79720i −0.988812 + 0.149168i
\(649\) 22.8688i 0.897680i
\(650\) 16.1531 + 13.3722i 0.633577 + 0.524501i
\(651\) 0.00382852 + 0.0132079i 0.000150051 + 0.000517659i
\(652\) 0.957658 + 7.16548i 0.0375048 + 0.280622i
\(653\) −3.22941 12.0523i −0.126376 0.471643i 0.873509 0.486809i \(-0.161839\pi\)
−0.999885 + 0.0151655i \(0.995172\pi\)
\(654\) −11.6218 + 10.6387i −0.454450 + 0.416007i
\(655\) −0.952711 + 18.4076i −0.0372255 + 0.719244i
\(656\) 14.1155 + 3.72293i 0.551116 + 0.145356i
\(657\) −26.9318 6.05450i −1.05071 0.236209i
\(658\) −0.0170477 0.0194007i −0.000664588 0.000756320i
\(659\) −2.60988 4.52045i −0.101667 0.176092i 0.810705 0.585455i \(-0.199084\pi\)
−0.912371 + 0.409363i \(0.865751\pi\)
\(660\) 5.12157 31.6728i 0.199357 1.23286i
\(661\) 17.0620 29.5522i 0.663633 1.14945i −0.316021 0.948752i \(-0.602347\pi\)
0.979654 0.200694i \(-0.0643198\pi\)
\(662\) −49.4883 + 9.89430i −1.92342 + 0.384553i
\(663\) 12.9155 7.81113i 0.501596 0.303359i
\(664\) −7.81678 + 2.67912i −0.303350 + 0.103970i
\(665\) 0.0132037 + 0.0619209i 0.000512019 + 0.00240119i
\(666\) 19.0326 31.2248i 0.737497 1.20994i
\(667\) −15.7820 + 15.7820i −0.611080 + 0.611080i
\(668\) 7.46094 18.1127i 0.288672 0.700802i
\(669\) 8.27553 8.61910i 0.319950 0.333234i
\(670\) 9.55066 4.12175i 0.368974 0.159237i
\(671\) 25.7561 + 14.8703i 0.994304 + 0.574062i
\(672\) −0.0278727 + 0.0257166i −0.00107521 + 0.000992039i
\(673\) 20.7053 + 5.54797i 0.798132 + 0.213859i 0.634763 0.772706i \(-0.281098\pi\)
0.163368 + 0.986565i \(0.447764\pi\)
\(674\) −29.5598 1.90833i −1.13860 0.0735062i
\(675\) 21.9289 + 13.9329i 0.844043 + 0.536276i
\(676\) 8.34064 + 1.08142i 0.320794 + 0.0415933i
\(677\) 2.26411 8.44976i 0.0870167 0.324751i −0.908672 0.417511i \(-0.862902\pi\)
0.995688 + 0.0927605i \(0.0295691\pi\)
\(678\) 20.4826 32.1157i 0.786631 1.23340i
\(679\) −0.00454237 + 0.00786762i −0.000174320 + 0.000301931i
\(680\) 17.8687 5.10887i 0.685235 0.195916i
\(681\) −29.8682 28.6776i −1.14455 1.09893i
\(682\) 11.3817 + 3.85113i 0.435829 + 0.147467i
\(683\) −4.25385 4.25385i −0.162769 0.162769i 0.621023 0.783792i \(-0.286717\pi\)
−0.783792 + 0.621023i \(0.786717\pi\)
\(684\) 3.86930 43.7206i 0.147946 1.67170i
\(685\) −37.1339 + 7.91827i −1.41881 + 0.302542i
\(686\) 0.0339617 + 0.0686976i 0.00129666 + 0.00262289i
\(687\) −11.2789 18.6493i −0.430316 0.711516i
\(688\) −4.01108 + 0.0157379i −0.152921 + 0.000600000i
\(689\) −25.1695 14.5316i −0.958882 0.553611i
\(690\) −2.02944 + 21.1092i −0.0772594 + 0.803612i
\(691\) −15.0306 + 8.67790i −0.571789 + 0.330123i −0.757864 0.652413i \(-0.773757\pi\)
0.186074 + 0.982536i \(0.440423\pi\)
\(692\) 11.1071 + 14.4164i 0.422229 + 0.548031i
\(693\) −0.0353641 0.0325988i −0.00134337 0.00123832i
\(694\) −0.935885 + 14.4967i −0.0355257 + 0.550288i
\(695\) −2.56976 0.133002i −0.0974765 0.00504503i
\(696\) −16.2319 23.1097i −0.615268 0.875969i
\(697\) −10.3588 + 2.77563i −0.392367 + 0.105134i
\(698\) 25.2386 5.04601i 0.955296 0.190994i
\(699\) −13.7739 + 3.99257i −0.520976 + 0.151013i
\(700\) 0.0386892 0.00113937i 0.00146232 4.30643e-5i
\(701\) −23.2157 −0.876846 −0.438423 0.898769i \(-0.644463\pi\)
−0.438423 + 0.898769i \(0.644463\pi\)
\(702\) −21.7925 0.0755775i −0.822504 0.00285249i
\(703\) 44.5841 + 44.5841i 1.68152 + 1.68152i
\(704\) 4.51845 + 32.8270i 0.170296 + 1.23721i
\(705\) 5.28090 17.4937i 0.198890 0.658850i
\(706\) 19.8458 + 13.2324i 0.746906 + 0.498007i
\(707\) 0.00715304 + 0.0266955i 0.000269018 + 0.00100399i
\(708\) −19.0130 2.07305i −0.714554 0.0779102i
\(709\) −22.8813 + 13.2105i −0.859327 + 0.496133i −0.863787 0.503857i \(-0.831914\pi\)
0.00446000 + 0.999990i \(0.498580\pi\)
\(710\) −35.3952 + 5.19100i −1.32836 + 0.194815i
\(711\) −8.35840 + 15.9407i −0.313464 + 0.597824i
\(712\) −21.5645 + 14.5009i −0.808163 + 0.543444i
\(713\) −7.67125 2.05551i −0.287291 0.0769793i
\(714\) 0.00839099 0.0265663i 0.000314025 0.000994219i
\(715\) 8.47085 26.1283i 0.316792 0.977144i
\(716\) −15.3643 11.7416i −0.574190 0.438805i
\(717\) −25.2683 + 15.2819i −0.943661 + 0.570715i
\(718\) 35.9781 + 12.1736i 1.34269 + 0.454314i
\(719\) 12.9840 0.484220 0.242110 0.970249i \(-0.422160\pi\)
0.242110 + 0.970249i \(0.422160\pi\)
\(720\) −25.8684 7.12919i −0.964059 0.265689i
\(721\) 0.0161719 0.000602274
\(722\) 46.2337 + 15.6437i 1.72064 + 0.582197i
\(723\) 0.491441 + 24.1655i 0.0182769 + 0.898726i
\(724\) −1.15251 0.880763i −0.0428326 0.0327333i
\(725\) −2.97557 + 28.6689i −0.110510 + 1.06474i
\(726\) −14.7248 + 3.25666i −0.546490 + 0.120866i
\(727\) −1.64028 0.439513i −0.0608348 0.0163006i 0.228273 0.973597i \(-0.426692\pi\)
−0.289108 + 0.957296i \(0.593359\pi\)
\(728\) −0.0269417 + 0.0181168i −0.000998527 + 0.000671453i
\(729\) −26.7993 + 3.28588i −0.992567 + 0.121699i
\(730\) −23.3426 17.3715i −0.863947 0.642948i
\(731\) 2.55189 1.47333i 0.0943850 0.0544932i
\(732\) 14.6979 20.0655i 0.543250 0.741644i
\(733\) −2.20422 8.22626i −0.0814147 0.303844i 0.913196 0.407520i \(-0.133606\pi\)
−0.994611 + 0.103676i \(0.966940\pi\)
\(734\) 7.43643 + 4.95832i 0.274484 + 0.183015i
\(735\) −14.2853 + 23.0419i −0.526921 + 0.849912i
\(736\) −4.37816 21.4599i −0.161381 0.791023i
\(737\) −9.63436 9.63436i −0.354886 0.354886i
\(738\) 14.8565 + 4.36229i 0.546875 + 0.160578i
\(739\) −19.1571 −0.704704 −0.352352 0.935867i \(-0.614618\pi\)
−0.352352 + 0.935867i \(0.614618\pi\)
\(740\) 31.7098 21.9157i 1.16567 0.805636i
\(741\) 8.98523 36.4851i 0.330081 1.34032i
\(742\) −0.0526034 + 0.0105171i −0.00193113 + 0.000386096i
\(743\) −6.78298 + 1.81749i −0.248843 + 0.0666774i −0.381085 0.924540i \(-0.624449\pi\)
0.132241 + 0.991218i \(0.457783\pi\)
\(744\) 4.23357 9.11362i 0.155210 0.334122i
\(745\) 2.05852 39.7732i 0.0754184 1.45718i
\(746\) 1.14556 17.7445i 0.0419419 0.649674i
\(747\) −8.36653 + 2.61070i −0.306116 + 0.0955206i
\(748\) −14.8569 19.2834i −0.543222 0.705072i
\(749\) 0.0390362 0.0225375i 0.00142635 0.000823504i
\(750\) 15.1484 + 22.8150i 0.553143 + 0.833086i
\(751\) 26.5621 + 15.3357i 0.969266 + 0.559606i 0.899012 0.437923i \(-0.144286\pi\)
0.0702536 + 0.997529i \(0.477619\pi\)
\(752\) 0.0740482 + 18.8725i 0.00270026 + 0.688210i
\(753\) −4.97161 + 9.03027i −0.181176 + 0.329081i
\(754\) −10.7143 21.6728i −0.390192 0.789278i
\(755\) 30.7821 + 19.9617i 1.12028 + 0.726481i
\(756\) −0.0303082 + 0.0264465i −0.00110230 + 0.000961851i
\(757\) 8.66077 + 8.66077i 0.314781 + 0.314781i 0.846758 0.531978i \(-0.178551\pi\)
−0.531978 + 0.846758i \(0.678551\pi\)
\(758\) 17.6945 + 5.98713i 0.642694 + 0.217462i
\(759\) 26.6788 7.73325i 0.968379 0.280699i
\(760\) 22.4613 40.4476i 0.814755 1.46719i
\(761\) 12.3194 21.3379i 0.446578 0.773497i −0.551582 0.834121i \(-0.685976\pi\)
0.998161 + 0.0606239i \(0.0193090\pi\)
\(762\) −48.8993 2.15959i −1.77143 0.0782336i
\(763\) −0.00644382 + 0.0240487i −0.000233282 + 0.000870620i
\(764\) 10.0575 + 1.30403i 0.363869 + 0.0471782i
\(765\) 19.0956 4.89129i 0.690403 0.176845i
\(766\) 26.5593 + 1.71463i 0.959627 + 0.0619520i
\(767\) −15.8155 4.23776i −0.571065 0.153016i
\(768\) 27.7018 0.780866i 0.999603 0.0281771i
\(769\) 16.9731 + 9.79945i 0.612067 + 0.353377i 0.773774 0.633462i \(-0.218367\pi\)
−0.161707 + 0.986839i \(0.551700\pi\)
\(770\) −0.0200888 0.0465486i −0.000723951 0.00167750i
\(771\) −4.15032 1.02210i −0.149470 0.0368101i
\(772\) −19.5922 + 47.5634i −0.705137 + 1.71184i
\(773\) 15.6893 15.6893i 0.564306 0.564306i −0.366221 0.930528i \(-0.619349\pi\)
0.930528 + 0.366221i \(0.119349\pi\)
\(774\) −4.25322 0.101253i −0.152879 0.00363946i
\(775\) −9.36404 + 4.18372i −0.336366 + 0.150284i
\(776\) 6.28002 2.15241i 0.225440 0.0772670i
\(777\) −0.00117487 0.0577717i −4.21483e−5 0.00207255i
\(778\) −1.82372 + 0.364621i −0.0653835 + 0.0130723i
\(779\) −13.3487 + 23.1206i −0.478265 + 0.828380i
\(780\) −20.9551 9.41116i −0.750313 0.336973i
\(781\) 23.4289 + 40.5800i 0.838352 + 1.45207i
\(782\) 10.6206 + 12.0865i 0.379791 + 0.432213i
\(783\) −16.5304 24.9793i −0.590748 0.892689i
\(784\) 7.14075 27.0741i 0.255027 0.966932i
\(785\) −0.884947 0.981551i −0.0315851 0.0350330i
\(786\) −4.36034 19.7151i −0.155528 0.703213i
\(787\) −4.71940 17.6130i −0.168228 0.627837i −0.997606 0.0691489i \(-0.977972\pi\)
0.829378 0.558688i \(-0.188695\pi\)
\(788\) 2.75150 + 20.5875i 0.0980180 + 0.733399i
\(789\) 4.89246 5.09558i 0.174176 0.181407i
\(790\) −14.8805 + 11.7702i −0.529423 + 0.418765i
\(791\) 0.0601908i 0.00214014i
\(792\) 3.82548 + 34.9377i 0.135933 + 1.24146i
\(793\) 15.0567 15.0567i 0.534680 0.534680i
\(794\) 0.633638 + 1.28172i 0.0224870 + 0.0454866i
\(795\) −25.9836 27.6675i −0.921542 0.981266i
\(796\) −37.3935 28.5766i −1.32538 1.01287i
\(797\) −26.9560 + 7.22285i −0.954832 + 0.255846i −0.702411 0.711771i \(-0.747893\pi\)
−0.252420 + 0.967618i \(0.581227\pi\)
\(798\) −0.0319941 0.0615355i −0.00113258 0.00217833i
\(799\) −6.93218 12.0069i −0.245243 0.424773i
\(800\) −21.8579 17.9508i −0.772794 0.634657i
\(801\) −23.2902 + 14.7405i −0.822917 + 0.520831i
\(802\) −21.1192 + 18.5577i −0.745744 + 0.655295i
\(803\) −9.86423 + 36.8138i −0.348101 + 1.29913i
\(804\) −8.88332 + 7.13661i −0.313291 + 0.251689i
\(805\) 0.0152325 + 0.0298475i 0.000536875 + 0.00105199i
\(806\) 4.77246 7.15768i 0.168103 0.252119i
\(807\) 12.3875 22.5003i 0.436062 0.792048i
\(808\) 8.87903 18.1393i 0.312363 0.638137i
\(809\) 10.0143i 0.352084i 0.984383 + 0.176042i \(0.0563294\pi\)
−0.984383 + 0.176042i \(0.943671\pi\)
\(810\) −27.2174 8.31936i −0.956323 0.292313i
\(811\) 40.6681i 1.42805i 0.700121 + 0.714024i \(0.253129\pi\)
−0.700121 + 0.714024i \(0.746871\pi\)
\(812\) −0.0412614 0.0169963i −0.00144799 0.000596452i
\(813\) −1.91043 + 3.47003i −0.0670016 + 0.121699i
\(814\) −42.0076 28.0090i −1.47237 0.981716i
\(815\) −2.49263 + 7.68852i −0.0873131 + 0.269317i
\(816\) −17.3789 + 10.6039i −0.608385 + 0.371211i
\(817\) 1.89858 7.08561i 0.0664231 0.247894i
\(818\) −23.1616 26.3586i −0.809827 0.921606i
\(819\) −0.0290977 + 0.0184162i −0.00101676 + 0.000643514i
\(820\) 12.4384 + 10.5674i 0.434368 + 0.369028i
\(821\) 14.4578 + 25.0416i 0.504579 + 0.873957i 0.999986 + 0.00529574i \(0.00168569\pi\)
−0.495407 + 0.868661i \(0.664981\pi\)
\(822\) 36.9028 19.1868i 1.28713 0.669218i
\(823\) 2.66307 0.713567i 0.0928287 0.0248734i −0.212106 0.977247i \(-0.568032\pi\)
0.304934 + 0.952373i \(0.401365\pi\)
\(824\) −8.90781 7.76569i −0.310318 0.270531i
\(825\) 20.4519 29.4698i 0.712045 1.02601i
\(826\) −0.0270920 + 0.0133934i −0.000942652 + 0.000466014i
\(827\) 33.6286 33.6286i 1.16938 1.16938i 0.187026 0.982355i \(-0.440115\pi\)
0.982355 0.187026i \(-0.0598850\pi\)
\(828\) −4.01097 22.8817i −0.139391 0.795192i
\(829\) 52.3216i 1.81721i 0.417662 + 0.908603i \(0.362850\pi\)
−0.417662 + 0.908603i \(0.637150\pi\)
\(830\) −9.17621 1.07091i −0.318511 0.0371717i
\(831\) −1.11489 + 1.16118i −0.0386751 + 0.0402807i
\(832\) 23.5396 + 2.95822i 0.816090 + 0.102558i
\(833\) 5.32377 + 19.8686i 0.184458 + 0.688406i
\(834\) 2.75229 0.608717i 0.0953039 0.0210782i
\(835\) 16.2664 14.6654i 0.562921 0.507519i
\(836\) −60.0974 7.79206i −2.07851 0.269494i
\(837\) 4.75662 9.53826i 0.164413 0.329690i
\(838\) −29.8331 + 26.2147i −1.03057 + 0.905572i
\(839\) 17.7459 + 30.7367i 0.612655 + 1.06115i 0.990791 + 0.135400i \(0.0432319\pi\)
−0.378136 + 0.925750i \(0.623435\pi\)
\(840\) −0.0405214 + 0.0124822i −0.00139812 + 0.000430675i
\(841\) 2.11521 3.66366i 0.0729384 0.126333i
\(842\) 0.361275 + 1.80699i 0.0124504 + 0.0622729i
\(843\) 0.675794 + 33.2307i 0.0232756 + 1.14453i
\(844\) −10.1375 24.3390i −0.348948 0.837782i
\(845\) 7.88950 + 5.11621i 0.271407 + 0.176003i
\(846\) −0.476405 + 20.0118i −0.0163791 + 0.688021i
\(847\) −0.0168503 + 0.0168503i −0.000578985 + 0.000578985i
\(848\) 34.0253 + 19.4669i 1.16843 + 0.668496i
\(849\) −40.5560 9.98775i −1.39188 0.342779i
\(850\) 20.4862 + 3.47210i 0.702671 + 0.119092i
\(851\) 28.9005 + 16.6857i 0.990695 + 0.571978i
\(852\) 35.8619 15.8001i 1.22861 0.541303i
\(853\) 49.1748 + 13.1763i 1.68371 + 0.451149i 0.968755 0.248019i \(-0.0797795\pi\)
0.714957 + 0.699168i \(0.246446\pi\)
\(854\) 0.00253207 0.0392214i 8.66458e−5 0.00134213i
\(855\) 25.0039 42.2242i 0.855115 1.44404i
\(856\) −32.3243 6.33088i −1.10482 0.216385i
\(857\) −7.29593 + 27.2288i −0.249224 + 0.930117i 0.721989 + 0.691904i \(0.243228\pi\)
−0.971213 + 0.238212i \(0.923439\pi\)
\(858\) −1.32755 + 30.0595i −0.0453217 + 1.02621i
\(859\) −14.5156 + 25.1417i −0.495265 + 0.857824i −0.999985 0.00545874i \(-0.998262\pi\)
0.504720 + 0.863283i \(0.331596\pi\)
\(860\) −4.05272 1.92008i −0.138197 0.0654740i
\(861\) 0.0234995 0.00681168i 0.000800861 0.000232142i
\(862\) 6.40340 18.9248i 0.218101 0.644581i
\(863\) −23.2326 23.2326i −0.790845 0.790845i 0.190786 0.981632i \(-0.438896\pi\)
−0.981632 + 0.190786i \(0.938896\pi\)
\(864\) 29.3939 0.0133899i 1.00000 0.000455535i
\(865\) 4.24332 + 19.8997i 0.144277 + 0.676609i
\(866\) −8.78870 + 4.34483i −0.298652 + 0.147643i
\(867\) −6.98785 + 12.6925i −0.237320 + 0.431060i
\(868\) −0.00210351 0.0157391i −7.13976e−5 0.000534218i
\(869\) 21.5218 + 12.4256i 0.730076 + 0.421509i
\(870\) −5.21579 31.1401i −0.176832 1.05575i
\(871\) −8.44820 + 4.87757i −0.286256 + 0.165270i
\(872\) 15.0974 10.1522i 0.511264 0.343796i
\(873\) 6.72170 2.09745i 0.227495 0.0709878i
\(874\) 39.9714 + 2.58049i 1.35205 + 0.0872863i
\(875\) 0.0395676 + 0.0175243i 0.00133763 + 0.000592430i
\(876\) 29.7127 + 11.5382i 1.00390 + 0.389841i
\(877\) 30.9645 8.29692i 1.04560 0.280167i 0.305166 0.952299i \(-0.401288\pi\)
0.740431 + 0.672132i \(0.234621\pi\)
\(878\) 7.89323 + 39.4795i 0.266383 + 1.33237i
\(879\) 0.876459 3.55892i 0.0295622 0.120039i
\(880\) −11.2871 + 35.2865i −0.380489 + 1.18951i
\(881\) 23.5070 0.791970 0.395985 0.918257i \(-0.370403\pi\)
0.395985 + 0.918257i \(0.370403\pi\)
\(882\) 8.36706 28.4954i 0.281734 0.959490i
\(883\) −28.0638 28.0638i −0.944422 0.944422i 0.0541127 0.998535i \(-0.482767\pi\)
−0.998535 + 0.0541127i \(0.982767\pi\)
\(884\) −16.0890 + 6.70131i −0.541133 + 0.225389i
\(885\) −18.1739 11.2673i −0.610908 0.378746i
\(886\) 19.1691 28.7496i 0.643998 0.965861i
\(887\) 5.86497 + 21.8884i 0.196927 + 0.734940i 0.991760 + 0.128112i \(0.0408916\pi\)
−0.794833 + 0.606828i \(0.792442\pi\)
\(888\) −27.0946 + 32.3860i −0.909235 + 1.08680i
\(889\) −0.0669822 + 0.0386722i −0.00224651 + 0.00129702i
\(890\) −28.7464 + 4.21589i −0.963581 + 0.141317i
\(891\) 3.02869 + 37.1553i 0.101465 + 1.24475i
\(892\) −10.9296 + 8.42070i −0.365950 + 0.281946i
\(893\) −33.3385 8.93303i −1.11563 0.298932i
\(894\) 9.42138 + 42.5983i 0.315098 + 1.42470i
\(895\) −9.82762 19.2568i −0.328501 0.643686i
\(896\) 0.0362429 0.0245783i 0.00121079 0.000821104i
\(897\) −0.404358 19.8834i −0.0135011 0.663888i
\(898\) 14.5750 43.0754i 0.486375 1.43744i
\(899\) 11.8245 0.394369
\(900\) −22.6471 19.6751i −0.754903 0.655836i
\(901\) −28.7977 −0.959391
\(902\) 6.85192 20.2503i 0.228144 0.674262i
\(903\) −0.00575248 + 0.00347903i −0.000191431 + 0.000115775i
\(904\) −28.9034 + 33.1543i −0.961312 + 1.10269i
\(905\) −0.737190 1.44450i −0.0245050 0.0480167i
\(906\) −38.3235 12.1045i −1.27321 0.402145i
\(907\) −10.5521 2.82743i −0.350377 0.0938833i 0.0793379 0.996848i \(-0.474719\pi\)
−0.429715 + 0.902964i \(0.641386\pi\)
\(908\) 29.1806 + 37.8748i 0.968393 + 1.25692i
\(909\) 9.94737 18.9711i 0.329933 0.629233i
\(910\) −0.0359145 + 0.00526716i −0.00119055 + 0.000174605i
\(911\) 18.3234 10.5790i 0.607083 0.350499i −0.164740 0.986337i \(-0.552679\pi\)
0.771823 + 0.635838i \(0.219345\pi\)
\(912\) −11.9261 + 49.2584i −0.394913 + 1.63111i
\(913\) 3.13194 + 11.6886i 0.103652 + 0.386835i
\(914\) 8.85783 13.2849i 0.292991 0.439424i
\(915\) 24.5073 13.1419i 0.810186 0.434459i
\(916\) 9.67636 + 23.2318i 0.319716 + 0.767600i
\(917\) −0.0225609 0.0225609i −0.000745026 0.000745026i
\(918\) −18.7379 + 10.7318i −0.618441 + 0.354203i
\(919\) −8.67860 −0.286281 −0.143140 0.989702i \(-0.545720\pi\)
−0.143140 + 0.989702i \(0.545720\pi\)
\(920\) 5.94229 23.7552i 0.195912 0.783185i
\(921\) 24.9845 7.24214i 0.823268 0.238637i
\(922\) −0.784476 3.92371i −0.0258353 0.129221i
\(923\) 32.4057 8.68308i 1.06665 0.285807i
\(924\) 0.0347829 + 0.0432961i 0.00114427 + 0.00142434i
\(925\) 42.5565 6.79698i 1.39925 0.223483i
\(926\) −30.3430 1.95889i −0.997132 0.0643733i
\(927\) −9.21619 8.49551i −0.302699 0.279029i
\(928\) 14.5660 + 29.1754i 0.478154 + 0.957730i
\(929\) 11.5252 6.65405i 0.378128 0.218312i −0.298875 0.954292i \(-0.596611\pi\)
0.677004 + 0.735980i \(0.263278\pi\)
\(930\) 8.66819 7.14765i 0.284241 0.234381i
\(931\) 44.3462 + 25.6033i 1.45339 + 0.839115i
\(932\) 16.4135 2.19364i 0.537641 0.0718551i
\(933\) 16.9109 + 27.9617i 0.553638 + 0.915425i
\(934\) 1.33841 0.661666i 0.0437942 0.0216504i
\(935\) −5.67586 26.6178i −0.185621 0.870495i
\(936\) 24.8710 + 3.82860i 0.812933 + 0.125142i
\(937\) 16.8683 + 16.8683i 0.551063 + 0.551063i 0.926747 0.375685i \(-0.122593\pi\)
−0.375685 + 0.926747i \(0.622593\pi\)
\(938\) −0.00577108 + 0.0170560i −0.000188432 + 0.000556898i
\(939\) 20.8396 + 20.0089i 0.680074 + 0.652964i
\(940\) −9.03415 + 19.0685i −0.294661 + 0.621945i
\(941\) 14.0053 24.2579i 0.456560 0.790785i −0.542216 0.840239i \(-0.682415\pi\)
0.998776 + 0.0494537i \(0.0157480\pi\)
\(942\) 1.22060 + 0.778471i 0.0397694 + 0.0253640i
\(943\) −3.65715 + 13.6487i −0.119093 + 0.444462i
\(944\) 21.3542 + 5.63215i 0.695021 + 0.183311i
\(945\) −0.0433299 + 0.0120428i −0.00140952 + 0.000391751i
\(946\) −0.378430 + 5.86183i −0.0123038 + 0.190584i
\(947\) −12.7811 3.42468i −0.415329 0.111287i 0.0451023 0.998982i \(-0.485639\pi\)
−0.460431 + 0.887695i \(0.652305\pi\)
\(948\) 12.2815 16.7667i 0.398886 0.544558i
\(949\) 23.6316 + 13.6437i 0.767115 + 0.442894i
\(950\) 42.1739 29.9500i 1.36830 0.971707i
\(951\) 21.7324 22.6347i 0.704722 0.733980i
\(952\) −0.0141434 + 0.0288941i −0.000458391 + 0.000936462i
\(953\) −30.3998 + 30.3998i −0.984746 + 0.984746i −0.999885 0.0151397i \(-0.995181\pi\)
0.0151397 + 0.999885i \(0.495181\pi\)
\(954\) 35.5030 + 21.6403i 1.14945 + 0.700630i
\(955\) 9.51352 + 6.16937i 0.307850 + 0.199636i
\(956\) 31.4771 13.1107i 1.01804 0.424029i
\(957\) −35.3880 + 21.4023i −1.14393 + 0.691837i
\(958\) −4.81586 24.0875i −0.155593 0.778231i
\(959\) 0.0328617 0.0569181i 0.00106116 0.00183798i
\(960\) 28.3138 + 12.5828i 0.913825 + 0.406107i
\(961\) −13.3962 23.2029i −0.432136 0.748482i
\(962\) −27.1547 + 23.8612i −0.875502 + 0.769315i
\(963\) −34.0858 7.66277i −1.09840 0.246929i
\(964\) 3.58866 27.6781i 0.115583 0.891450i
\(965\) −42.7149 + 38.5110i −1.37504 + 1.23971i
\(966\) −0.0247861 0.0270765i −0.000797478 0.000871172i
\(967\) −2.41924 9.02872i −0.0777975 0.290344i 0.916056 0.401051i \(-0.131355\pi\)
−0.993853 + 0.110707i \(0.964688\pi\)
\(968\) 17.3730 1.19004i 0.558388 0.0382492i
\(969\) −10.3656 35.7600i −0.332990 1.14878i
\(970\) 7.37219 + 0.860370i 0.236707 + 0.0276248i
\(971\) 0.631006i 0.0202499i 0.999949 + 0.0101250i \(0.00322293\pi\)
−0.999949 + 0.0101250i \(0.996777\pi\)
\(972\) 31.1653 + 0.850080i 0.999628 + 0.0272663i
\(973\) 0.00314957 0.00314957i 0.000100971 0.000100971i
\(974\) 30.8792 15.2656i 0.989435 0.489142i
\(975\) −16.5907 19.6050i −0.531327 0.627863i
\(976\) −20.2287 + 20.3880i −0.647504 + 0.652605i
\(977\) 0.224275 0.0600942i 0.00717518 0.00192258i −0.255230 0.966880i \(-0.582151\pi\)
0.262405 + 0.964958i \(0.415484\pi\)
\(978\) 0.390644 8.84530i 0.0124914 0.282841i
\(979\) 19.0279 + 32.9573i 0.608134 + 1.05332i
\(980\) 20.2687 23.8574i 0.647459 0.762098i
\(981\) 16.3056 10.3200i 0.520598 0.329491i
\(982\) −14.9700 17.0363i −0.477713 0.543650i
\(983\) 0.123617 0.461344i 0.00394276 0.0147146i −0.963926 0.266169i \(-0.914242\pi\)
0.967869 + 0.251454i \(0.0809088\pi\)
\(984\) −16.2149 7.53235i −0.516913 0.240122i
\(985\) −7.16170 + 22.0903i −0.228191 + 0.703855i
\(986\) −19.9315 13.2895i −0.634748 0.423225i
\(987\) 0.0163692 + 0.0270660i 0.000521037 + 0.000861520i
\(988\) −16.5253 + 40.1179i −0.525739 + 1.27632i
\(989\) 3.88251i 0.123457i
\(990\) −13.0047 + 37.0807i −0.413318 + 1.17850i
\(991\) 16.8040i 0.533796i −0.963725 0.266898i \(-0.914001\pi\)
0.963725 0.266898i \(-0.0859986\pi\)
\(992\) −6.39917 + 9.67947i −0.203174 + 0.307323i
\(993\) 61.7973 1.25674i 1.96108 0.0398813i
\(994\) 0.0343526 0.0515216i 0.00108960 0.00163417i
\(995\) −23.9184 46.8672i −0.758263 1.48579i
\(996\) 10.0017 1.54432i 0.316917 0.0489335i
\(997\) 3.21617 12.0029i 0.101857 0.380135i −0.896113 0.443827i \(-0.853621\pi\)
0.997970 + 0.0636912i \(0.0202873\pi\)
\(998\) 40.2238 35.3452i 1.27326 1.11883i
\(999\) −29.6794 + 33.5406i −0.939013 + 1.06118i
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 180.2.x.a.67.29 yes 128
3.2 odd 2 540.2.y.a.307.4 128
4.3 odd 2 inner 180.2.x.a.67.2 yes 128
5.2 odd 4 900.2.bf.e.643.13 128
5.3 odd 4 inner 180.2.x.a.103.20 yes 128
5.4 even 2 900.2.bf.e.607.4 128
9.2 odd 6 540.2.y.a.127.19 128
9.7 even 3 inner 180.2.x.a.7.14 128
12.11 even 2 540.2.y.a.307.31 128
15.8 even 4 540.2.y.a.523.13 128
20.3 even 4 inner 180.2.x.a.103.14 yes 128
20.7 even 4 900.2.bf.e.643.19 128
20.19 odd 2 900.2.bf.e.607.31 128
36.7 odd 6 inner 180.2.x.a.7.20 yes 128
36.11 even 6 540.2.y.a.127.13 128
45.7 odd 12 900.2.bf.e.43.31 128
45.34 even 6 900.2.bf.e.7.19 128
45.38 even 12 540.2.y.a.343.31 128
45.43 odd 12 inner 180.2.x.a.43.2 yes 128
60.23 odd 4 540.2.y.a.523.19 128
180.7 even 12 900.2.bf.e.43.4 128
180.43 even 12 inner 180.2.x.a.43.29 yes 128
180.79 odd 6 900.2.bf.e.7.13 128
180.83 odd 12 540.2.y.a.343.4 128
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
180.2.x.a.7.14 128 9.7 even 3 inner
180.2.x.a.7.20 yes 128 36.7 odd 6 inner
180.2.x.a.43.2 yes 128 45.43 odd 12 inner
180.2.x.a.43.29 yes 128 180.43 even 12 inner
180.2.x.a.67.2 yes 128 4.3 odd 2 inner
180.2.x.a.67.29 yes 128 1.1 even 1 trivial
180.2.x.a.103.14 yes 128 20.3 even 4 inner
180.2.x.a.103.20 yes 128 5.3 odd 4 inner
540.2.y.a.127.13 128 36.11 even 6
540.2.y.a.127.19 128 9.2 odd 6
540.2.y.a.307.4 128 3.2 odd 2
540.2.y.a.307.31 128 12.11 even 2
540.2.y.a.343.4 128 180.83 odd 12
540.2.y.a.343.31 128 45.38 even 12
540.2.y.a.523.13 128 15.8 even 4
540.2.y.a.523.19 128 60.23 odd 4
900.2.bf.e.7.13 128 180.79 odd 6
900.2.bf.e.7.19 128 45.34 even 6
900.2.bf.e.43.4 128 180.7 even 12
900.2.bf.e.43.31 128 45.7 odd 12
900.2.bf.e.607.4 128 5.4 even 2
900.2.bf.e.607.31 128 20.19 odd 2
900.2.bf.e.643.13 128 5.2 odd 4
900.2.bf.e.643.19 128 20.7 even 4