Properties

Label 525.2.bv.a.52.16
Level $525$
Weight $2$
Character 525.52
Analytic conductor $4.192$
Analytic rank $0$
Dimension $640$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [525,2,Mod(52,525)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(525, base_ring=CyclotomicField(60))
 
chi = DirichletCharacter(H, H._module([0, 3, 10]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("525.52");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 525.bv (of order \(60\), degree \(16\), 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: \(4.19214610612\)
Analytic rank: \(0\)
Dimension: \(640\)
Relative dimension: \(40\) over \(\Q(\zeta_{60})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label 52.16
Character \(\chi\) \(=\) 525.52
Dual form 525.2.bv.a.313.16

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.221735 - 0.577641i) q^{2} +(-0.0523360 + 0.998630i) q^{3} +(1.20179 - 1.08209i) q^{4} +(1.83440 + 1.27866i) q^{5} +(0.588454 - 0.191200i) q^{6} +(2.58948 - 0.542755i) q^{7} +(-1.99414 - 1.01606i) q^{8} +(-0.994522 - 0.104528i) q^{9} +O(q^{10})\) \(q+(-0.221735 - 0.577641i) q^{2} +(-0.0523360 + 0.998630i) q^{3} +(1.20179 - 1.08209i) q^{4} +(1.83440 + 1.27866i) q^{5} +(0.588454 - 0.191200i) q^{6} +(2.58948 - 0.542755i) q^{7} +(-1.99414 - 1.01606i) q^{8} +(-0.994522 - 0.104528i) q^{9} +(0.331851 - 1.34315i) q^{10} +(-0.691816 - 6.58219i) q^{11} +(1.01771 + 1.25677i) q^{12} +(0.653458 + 4.12577i) q^{13} +(-0.887697 - 1.37544i) q^{14} +(-1.37291 + 1.76497i) q^{15} +(0.193331 - 1.83942i) q^{16} +(4.91627 - 3.19266i) q^{17} +(0.160141 + 0.597654i) q^{18} +(-3.20006 + 3.55403i) q^{19} +(3.58819 - 0.448326i) q^{20} +(0.406489 + 2.61434i) q^{21} +(-3.64874 + 1.85912i) q^{22} +(-4.18192 + 1.60529i) q^{23} +(1.11904 - 1.93823i) q^{24} +(1.73008 + 4.69114i) q^{25} +(2.23832 - 1.29229i) q^{26} +(0.156434 - 0.987688i) q^{27} +(2.52469 - 3.45434i) q^{28} +(0.941669 + 0.305967i) q^{29} +(1.32394 + 0.401691i) q^{30} +(-0.781883 + 3.67847i) q^{31} +(-5.42902 + 1.45470i) q^{32} +(6.60937 - 0.346383i) q^{33} +(-2.93432 - 2.13191i) q^{34} +(5.44415 + 2.31542i) q^{35} +(-1.30831 + 0.950546i) q^{36} +(1.10527 - 0.895029i) q^{37} +(2.76252 + 1.06043i) q^{38} +(-4.15432 + 0.436636i) q^{39} +(-2.35886 - 4.41369i) q^{40} +(-1.91776 + 2.63957i) q^{41} +(1.42002 - 0.814496i) q^{42} +(4.29653 - 4.29653i) q^{43} +(-7.95396 - 7.16178i) q^{44} +(-1.69070 - 1.46340i) q^{45} +(1.85456 + 2.05970i) q^{46} +(4.65686 - 7.17094i) q^{47} +(1.82678 + 0.289334i) q^{48} +(6.41083 - 2.81091i) q^{49} +(2.32618 - 2.03956i) q^{50} +(2.93099 + 5.07662i) q^{51} +(5.24979 + 4.25120i) q^{52} +(5.87675 + 0.307988i) q^{53} +(-0.605216 + 0.128643i) q^{54} +(7.14728 - 12.9590i) q^{55} +(-5.71526 - 1.54875i) q^{56} +(-3.38168 - 3.38168i) q^{57} +(-0.0320626 - 0.611790i) q^{58} +(-11.5708 + 5.15166i) q^{59} +(0.259920 + 3.60674i) q^{60} +(-0.189335 + 0.425253i) q^{61} +(2.29821 - 0.364000i) q^{62} +(-2.63203 + 0.269108i) q^{63} +(-0.130179 - 0.179177i) q^{64} +(-4.07674 + 8.40388i) q^{65} +(-1.66562 - 3.74104i) q^{66} +(3.45923 + 5.32674i) q^{67} +(2.45355 - 9.15676i) q^{68} +(-1.38422 - 4.26020i) q^{69} +(0.130320 - 3.65818i) q^{70} +(-1.29272 + 3.97859i) q^{71} +(1.87701 + 1.21894i) q^{72} +(-7.72571 + 9.54046i) q^{73} +(-0.762082 - 0.439988i) q^{74} +(-4.77526 + 1.48219i) q^{75} +7.73395i q^{76} +(-5.36396 - 16.6690i) q^{77} +(1.17338 + 2.30288i) q^{78} +(-0.430122 - 2.02356i) q^{79} +(2.70663 - 3.12704i) q^{80} +(0.978148 + 0.207912i) q^{81} +(1.94996 + 0.522490i) q^{82} +(-4.61796 + 9.06326i) q^{83} +(3.31747 + 2.70202i) q^{84} +(13.1007 + 0.429582i) q^{85} +(-3.43454 - 1.52916i) q^{86} +(-0.354831 + 0.924366i) q^{87} +(-5.30835 + 13.8287i) q^{88} +(-10.0002 - 4.45236i) q^{89} +(-0.470430 + 1.30110i) q^{90} +(3.93140 + 10.3289i) q^{91} +(-3.28871 + 6.45445i) q^{92} +(-3.63251 - 0.973328i) q^{93} +(-5.17482 - 1.09994i) q^{94} +(-10.4146 + 2.42775i) q^{95} +(-1.16857 - 5.49771i) q^{96} +(2.74672 + 5.39074i) q^{97} +(-3.04520 - 3.07988i) q^{98} +6.61844i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 640 q + 12 q^{5} - 8 q^{7} + 24 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 640 q + 12 q^{5} - 8 q^{7} + 24 q^{8} + 12 q^{10} + 8 q^{15} - 80 q^{16} - 72 q^{22} + 48 q^{23} - 12 q^{25} - 36 q^{28} - 80 q^{29} + 32 q^{30} - 24 q^{32} + 36 q^{33} - 64 q^{35} + 160 q^{36} - 4 q^{37} - 192 q^{38} - 12 q^{40} - 16 q^{42} + 120 q^{43} + 60 q^{47} + 288 q^{50} - 432 q^{52} - 136 q^{53} - 16 q^{57} - 4 q^{58} - 240 q^{59} - 20 q^{60} - 4 q^{63} + 120 q^{64} + 4 q^{65} - 8 q^{67} - 132 q^{68} + 76 q^{70} - 12 q^{72} - 36 q^{73} - 48 q^{75} - 60 q^{77} - 80 q^{78} + 12 q^{80} - 80 q^{81} - 252 q^{82} - 160 q^{84} + 72 q^{85} + 24 q^{87} + 152 q^{88} + 56 q^{92} - 96 q^{93} + 172 q^{95} - 488 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(176\) \(451\)
\(\chi(n)\) \(e\left(\frac{1}{20}\right)\) \(1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.221735 0.577641i −0.156791 0.408454i 0.832573 0.553915i \(-0.186867\pi\)
−0.989364 + 0.145461i \(0.953533\pi\)
\(3\) −0.0523360 + 0.998630i −0.0302162 + 0.576559i
\(4\) 1.20179 1.08209i 0.600894 0.541047i
\(5\) 1.83440 + 1.27866i 0.820371 + 0.571832i
\(6\) 0.588454 0.191200i 0.240235 0.0780571i
\(7\) 2.58948 0.542755i 0.978732 0.205142i
\(8\) −1.99414 1.01606i −0.705034 0.359233i
\(9\) −0.994522 0.104528i −0.331507 0.0348428i
\(10\) 0.331851 1.34315i 0.104941 0.424741i
\(11\) −0.691816 6.58219i −0.208590 1.98460i −0.170707 0.985322i \(-0.554605\pi\)
−0.0378831 0.999282i \(-0.512061\pi\)
\(12\) 1.01771 + 1.25677i 0.293789 + 0.362799i
\(13\) 0.653458 + 4.12577i 0.181237 + 1.14428i 0.895716 + 0.444627i \(0.146664\pi\)
−0.714479 + 0.699657i \(0.753336\pi\)
\(14\) −0.887697 1.37544i −0.237247 0.367602i
\(15\) −1.37291 + 1.76497i −0.354484 + 0.455713i
\(16\) 0.193331 1.83942i 0.0483327 0.459855i
\(17\) 4.91627 3.19266i 1.19237 0.774334i 0.213127 0.977025i \(-0.431635\pi\)
0.979243 + 0.202691i \(0.0649686\pi\)
\(18\) 0.160141 + 0.597654i 0.0377456 + 0.140868i
\(19\) −3.20006 + 3.55403i −0.734144 + 0.815350i −0.988414 0.151784i \(-0.951498\pi\)
0.254270 + 0.967133i \(0.418165\pi\)
\(20\) 3.58819 0.448326i 0.802344 0.100249i
\(21\) 0.406489 + 2.61434i 0.0887031 + 0.570495i
\(22\) −3.64874 + 1.85912i −0.777913 + 0.396367i
\(23\) −4.18192 + 1.60529i −0.871991 + 0.334726i −0.752882 0.658155i \(-0.771337\pi\)
−0.119109 + 0.992881i \(0.538004\pi\)
\(24\) 1.11904 1.93823i 0.228422 0.395639i
\(25\) 1.73008 + 4.69114i 0.346016 + 0.938229i
\(26\) 2.23832 1.29229i 0.438970 0.253440i
\(27\) 0.156434 0.987688i 0.0301058 0.190081i
\(28\) 2.52469 3.45434i 0.477122 0.652809i
\(29\) 0.941669 + 0.305967i 0.174864 + 0.0568166i 0.395140 0.918621i \(-0.370696\pi\)
−0.220277 + 0.975437i \(0.570696\pi\)
\(30\) 1.32394 + 0.401691i 0.241717 + 0.0733385i
\(31\) −0.781883 + 3.67847i −0.140430 + 0.660673i 0.850464 + 0.526033i \(0.176321\pi\)
−0.990895 + 0.134640i \(0.957012\pi\)
\(32\) −5.42902 + 1.45470i −0.959724 + 0.257157i
\(33\) 6.60937 0.346383i 1.15054 0.0602975i
\(34\) −2.93432 2.13191i −0.503232 0.365619i
\(35\) 5.44415 + 2.31542i 0.920230 + 0.391378i
\(36\) −1.30831 + 0.950546i −0.218052 + 0.158424i
\(37\) 1.10527 0.895029i 0.181705 0.147142i −0.534153 0.845388i \(-0.679369\pi\)
0.715858 + 0.698246i \(0.246036\pi\)
\(38\) 2.76252 + 1.06043i 0.448139 + 0.172025i
\(39\) −4.15432 + 0.436636i −0.665223 + 0.0699178i
\(40\) −2.35886 4.41369i −0.372968 0.697865i
\(41\) −1.91776 + 2.63957i −0.299504 + 0.412232i −0.932072 0.362273i \(-0.882001\pi\)
0.632568 + 0.774505i \(0.282001\pi\)
\(42\) 1.42002 0.814496i 0.219113 0.125679i
\(43\) 4.29653 4.29653i 0.655214 0.655214i −0.299029 0.954244i \(-0.596663\pi\)
0.954244 + 0.299029i \(0.0966629\pi\)
\(44\) −7.95396 7.16178i −1.19911 1.07968i
\(45\) −1.69070 1.46340i −0.252035 0.218151i
\(46\) 1.85456 + 2.05970i 0.273440 + 0.303686i
\(47\) 4.65686 7.17094i 0.679273 1.04599i −0.315989 0.948763i \(-0.602336\pi\)
0.995262 0.0972262i \(-0.0309970\pi\)
\(48\) 1.82678 + 0.289334i 0.263673 + 0.0417617i
\(49\) 6.41083 2.81091i 0.915833 0.401559i
\(50\) 2.32618 2.03956i 0.328971 0.288437i
\(51\) 2.93099 + 5.07662i 0.410420 + 0.710869i
\(52\) 5.24979 + 4.25120i 0.728015 + 0.589535i
\(53\) 5.87675 + 0.307988i 0.807234 + 0.0423053i 0.451488 0.892277i \(-0.350893\pi\)
0.355746 + 0.934583i \(0.384227\pi\)
\(54\) −0.605216 + 0.128643i −0.0823594 + 0.0175060i
\(55\) 7.14728 12.9590i 0.963739 1.74739i
\(56\) −5.71526 1.54875i −0.763733 0.206960i
\(57\) −3.38168 3.38168i −0.447914 0.447914i
\(58\) −0.0320626 0.611790i −0.00421002 0.0803320i
\(59\) −11.5708 + 5.15166i −1.50639 + 0.670688i −0.983367 0.181630i \(-0.941863\pi\)
−0.523024 + 0.852318i \(0.675196\pi\)
\(60\) 0.259920 + 3.60674i 0.0335555 + 0.465628i
\(61\) −0.189335 + 0.425253i −0.0242418 + 0.0544481i −0.925261 0.379332i \(-0.876154\pi\)
0.901019 + 0.433780i \(0.142821\pi\)
\(62\) 2.29821 0.364000i 0.291872 0.0462280i
\(63\) −2.63203 + 0.269108i −0.331605 + 0.0339044i
\(64\) −0.130179 0.179177i −0.0162724 0.0223971i
\(65\) −4.07674 + 8.40388i −0.505657 + 1.04237i
\(66\) −1.66562 3.74104i −0.205023 0.460490i
\(67\) 3.45923 + 5.32674i 0.422612 + 0.650765i 0.984284 0.176595i \(-0.0565082\pi\)
−0.561672 + 0.827360i \(0.689842\pi\)
\(68\) 2.45355 9.15676i 0.297536 1.11042i
\(69\) −1.38422 4.26020i −0.166641 0.512868i
\(70\) 0.130320 3.65818i 0.0155763 0.437236i
\(71\) −1.29272 + 3.97859i −0.153418 + 0.472172i −0.997997 0.0632585i \(-0.979851\pi\)
0.844579 + 0.535431i \(0.179851\pi\)
\(72\) 1.87701 + 1.21894i 0.221207 + 0.143654i
\(73\) −7.72571 + 9.54046i −0.904227 + 1.11663i 0.0884809 + 0.996078i \(0.471799\pi\)
−0.992707 + 0.120549i \(0.961535\pi\)
\(74\) −0.762082 0.439988i −0.0885902 0.0511476i
\(75\) −4.77526 + 1.48219i −0.551400 + 0.171149i
\(76\) 7.73395i 0.887145i
\(77\) −5.36396 16.6690i −0.611280 1.89961i
\(78\) 1.17338 + 2.30288i 0.132859 + 0.260750i
\(79\) −0.430122 2.02356i −0.0483925 0.227669i 0.947305 0.320333i \(-0.103795\pi\)
−0.995697 + 0.0926647i \(0.970462\pi\)
\(80\) 2.70663 3.12704i 0.302611 0.349613i
\(81\) 0.978148 + 0.207912i 0.108683 + 0.0231013i
\(82\) 1.94996 + 0.522490i 0.215337 + 0.0576994i
\(83\) −4.61796 + 9.06326i −0.506887 + 0.994822i 0.485796 + 0.874072i \(0.338530\pi\)
−0.992683 + 0.120750i \(0.961470\pi\)
\(84\) 3.31747 + 2.70202i 0.361966 + 0.294815i
\(85\) 13.1007 + 0.429582i 1.42097 + 0.0465947i
\(86\) −3.43454 1.52916i −0.370356 0.164893i
\(87\) −0.354831 + 0.924366i −0.0380419 + 0.0991024i
\(88\) −5.30835 + 13.8287i −0.565872 + 1.47415i
\(89\) −10.0002 4.45236i −1.06002 0.471950i −0.198722 0.980056i \(-0.563679\pi\)
−0.861294 + 0.508106i \(0.830346\pi\)
\(90\) −0.470430 + 1.30110i −0.0495877 + 0.137148i
\(91\) 3.93140 + 10.3289i 0.412123 + 1.08277i
\(92\) −3.28871 + 6.45445i −0.342871 + 0.672923i
\(93\) −3.63251 0.973328i −0.376674 0.100929i
\(94\) −5.17482 1.09994i −0.533742 0.113450i
\(95\) −10.4146 + 2.42775i −1.06851 + 0.249082i
\(96\) −1.16857 5.49771i −0.119267 0.561108i
\(97\) 2.74672 + 5.39074i 0.278887 + 0.547346i 0.987380 0.158372i \(-0.0506244\pi\)
−0.708493 + 0.705718i \(0.750624\pi\)
\(98\) −3.04520 3.07988i −0.307612 0.311115i
\(99\) 6.61844i 0.665179i
\(100\) 7.15545 + 3.76565i 0.715545 + 0.376565i
\(101\) 6.55017 + 3.78174i 0.651766 + 0.376298i 0.789133 0.614223i \(-0.210530\pi\)
−0.137366 + 0.990520i \(0.543864\pi\)
\(102\) 2.28256 2.81872i 0.226007 0.279095i
\(103\) −10.7656 6.99129i −1.06077 0.688872i −0.108490 0.994098i \(-0.534602\pi\)
−0.952280 + 0.305225i \(0.901268\pi\)
\(104\) 2.88896 8.89131i 0.283286 0.871865i
\(105\) −2.59718 + 5.31551i −0.253458 + 0.518741i
\(106\) −1.12518 3.46294i −0.109287 0.336351i
\(107\) −1.64331 + 6.13293i −0.158865 + 0.592893i 0.839878 + 0.542775i \(0.182626\pi\)
−0.998743 + 0.0501178i \(0.984040\pi\)
\(108\) −0.880771 1.35627i −0.0847522 0.130507i
\(109\) −4.92217 11.0554i −0.471458 1.05891i −0.980203 0.197995i \(-0.936557\pi\)
0.508745 0.860917i \(-0.330110\pi\)
\(110\) −9.07044 1.25509i −0.864833 0.119668i
\(111\) 0.835957 + 1.15060i 0.0793455 + 0.109210i
\(112\) −0.497729 4.86808i −0.0470309 0.459990i
\(113\) −1.85820 + 0.294310i −0.174805 + 0.0276863i −0.243223 0.969970i \(-0.578205\pi\)
0.0684185 + 0.997657i \(0.478205\pi\)
\(114\) −1.20356 + 2.70323i −0.112723 + 0.253181i
\(115\) −9.72395 2.40249i −0.906763 0.224033i
\(116\) 1.46277 0.651268i 0.135815 0.0604687i
\(117\) −0.218618 4.17148i −0.0202112 0.385653i
\(118\) 5.54146 + 5.54146i 0.510133 + 0.510133i
\(119\) 10.9977 10.9357i 1.00816 1.00247i
\(120\) 4.53109 2.12463i 0.413630 0.193951i
\(121\) −32.0870 + 6.82029i −2.91700 + 0.620027i
\(122\) 0.287626 + 0.0150738i 0.0260404 + 0.00136472i
\(123\) −2.53559 2.05328i −0.228626 0.185138i
\(124\) 3.04080 + 5.26681i 0.273072 + 0.472974i
\(125\) −2.82470 + 10.8176i −0.252648 + 0.967558i
\(126\) 0.739062 + 1.46070i 0.0658409 + 0.130129i
\(127\) −13.0470 2.06645i −1.15774 0.183367i −0.452117 0.891959i \(-0.649331\pi\)
−0.705619 + 0.708591i \(0.749331\pi\)
\(128\) −6.19696 + 9.54247i −0.547739 + 0.843444i
\(129\) 4.06578 + 4.51550i 0.357972 + 0.397568i
\(130\) 5.75838 + 0.491450i 0.505043 + 0.0431030i
\(131\) −8.59178 7.73607i −0.750667 0.675904i 0.202182 0.979348i \(-0.435197\pi\)
−0.952849 + 0.303444i \(0.901863\pi\)
\(132\) 7.56824 7.56824i 0.658731 0.658731i
\(133\) −6.35753 + 10.9399i −0.551268 + 0.948613i
\(134\) 2.30991 3.17932i 0.199546 0.274651i
\(135\) 1.54988 1.61179i 0.133392 0.138721i
\(136\) −13.0477 + 1.37136i −1.11883 + 0.117593i
\(137\) 10.4962 + 4.02912i 0.896752 + 0.344231i 0.762707 0.646744i \(-0.223870\pi\)
0.134045 + 0.990975i \(0.457203\pi\)
\(138\) −2.15394 + 1.74422i −0.183355 + 0.148478i
\(139\) 16.3272 11.8624i 1.38486 1.00616i 0.388449 0.921470i \(-0.373011\pi\)
0.996408 0.0846868i \(-0.0269890\pi\)
\(140\) 9.04822 3.10844i 0.764715 0.262711i
\(141\) 6.91739 + 5.02578i 0.582549 + 0.423247i
\(142\) 2.58484 0.135466i 0.216915 0.0113680i
\(143\) 26.7045 7.15546i 2.23315 0.598369i
\(144\) −0.384543 + 1.80913i −0.0320453 + 0.150761i
\(145\) 1.33618 + 1.76534i 0.110963 + 0.146603i
\(146\) 7.22402 + 2.34723i 0.597864 + 0.194258i
\(147\) 2.47154 + 6.54916i 0.203849 + 0.540166i
\(148\) 0.359792 2.27164i 0.0295747 0.186728i
\(149\) −14.3521 + 8.28619i −1.17577 + 0.678831i −0.955032 0.296502i \(-0.904180\pi\)
−0.220738 + 0.975333i \(0.570847\pi\)
\(150\) 1.91502 + 2.42973i 0.156361 + 0.198387i
\(151\) 5.03822 8.72645i 0.410004 0.710148i −0.584885 0.811116i \(-0.698861\pi\)
0.994890 + 0.100968i \(0.0321939\pi\)
\(152\) 9.99248 3.83575i 0.810497 0.311121i
\(153\) −5.22306 + 2.66128i −0.422259 + 0.215152i
\(154\) −8.43929 + 6.79454i −0.680057 + 0.547520i
\(155\) −6.13779 + 5.74804i −0.492999 + 0.461694i
\(156\) −4.52013 + 5.02011i −0.361900 + 0.401930i
\(157\) 0.585197 + 2.18398i 0.0467038 + 0.174301i 0.985338 0.170613i \(-0.0545748\pi\)
−0.938634 + 0.344914i \(0.887908\pi\)
\(158\) −1.07352 + 0.697151i −0.0854046 + 0.0554624i
\(159\) −0.615131 + 5.85258i −0.0487831 + 0.464140i
\(160\) −11.8191 4.27333i −0.934380 0.337837i
\(161\) −9.95773 + 6.42663i −0.784779 + 0.506489i
\(162\) −0.0967918 0.611119i −0.00760468 0.0480140i
\(163\) 7.96062 + 9.83055i 0.623524 + 0.769988i 0.986844 0.161676i \(-0.0516900\pi\)
−0.363320 + 0.931665i \(0.618357\pi\)
\(164\) 0.551525 + 5.24741i 0.0430668 + 0.409754i
\(165\) 12.5672 + 7.81571i 0.978353 + 0.608452i
\(166\) 6.25927 + 0.657876i 0.485814 + 0.0510611i
\(167\) −6.03076 3.07283i −0.466674 0.237782i 0.204809 0.978802i \(-0.434343\pi\)
−0.671483 + 0.741020i \(0.734343\pi\)
\(168\) 1.84574 5.62637i 0.142402 0.434084i
\(169\) −4.23126 + 1.37482i −0.325481 + 0.105755i
\(170\) −2.65675 7.66277i −0.203764 0.587707i
\(171\) 3.55403 3.20006i 0.271783 0.244715i
\(172\) 0.514265 9.81276i 0.0392124 0.748216i
\(173\) 2.81621 + 7.33649i 0.214113 + 0.557783i 0.998006 0.0631121i \(-0.0201026\pi\)
−0.783894 + 0.620895i \(0.786769\pi\)
\(174\) 0.612630 0.0464433
\(175\) 7.02615 + 11.2086i 0.531127 + 0.847292i
\(176\) −12.2412 −0.922712
\(177\) −4.53903 11.8246i −0.341174 0.888789i
\(178\) −0.354473 + 6.76375i −0.0265689 + 0.506965i
\(179\) −7.47972 + 6.73477i −0.559060 + 0.503380i −0.899520 0.436879i \(-0.856084\pi\)
0.340460 + 0.940259i \(0.389417\pi\)
\(180\) −3.61540 + 0.0708018i −0.269476 + 0.00527726i
\(181\) −14.3079 + 4.64891i −1.06350 + 0.345551i −0.787951 0.615738i \(-0.788858\pi\)
−0.275544 + 0.961288i \(0.588858\pi\)
\(182\) 5.09469 4.56123i 0.377643 0.338101i
\(183\) −0.414761 0.211331i −0.0306600 0.0156221i
\(184\) 9.97040 + 1.04793i 0.735028 + 0.0772545i
\(185\) 3.17194 0.228587i 0.233206 0.0168060i
\(186\) 0.243222 + 2.31411i 0.0178339 + 0.169678i
\(187\) −24.4158 30.1510i −1.78546 2.20486i
\(188\) −2.16307 13.6571i −0.157758 0.996047i
\(189\) −0.130989 2.64251i −0.00952805 0.192214i
\(190\) 3.71165 + 5.47757i 0.269271 + 0.397384i
\(191\) 0.429095 4.08256i 0.0310482 0.295404i −0.967969 0.251071i \(-0.919217\pi\)
0.999017 0.0443327i \(-0.0141162\pi\)
\(192\) 0.185744 0.120624i 0.0134049 0.00870526i
\(193\) 3.95116 + 14.7459i 0.284411 + 1.06144i 0.949269 + 0.314466i \(0.101825\pi\)
−0.664858 + 0.746970i \(0.731508\pi\)
\(194\) 2.50486 2.78193i 0.179839 0.199731i
\(195\) −8.17901 4.51098i −0.585711 0.323038i
\(196\) 4.66279 10.3152i 0.333056 0.736803i
\(197\) 6.42887 3.27568i 0.458038 0.233382i −0.209718 0.977762i \(-0.567255\pi\)
0.667757 + 0.744380i \(0.267255\pi\)
\(198\) 3.82308 1.46754i 0.271695 0.104294i
\(199\) −1.32686 + 2.29818i −0.0940583 + 0.162914i −0.909215 0.416326i \(-0.863317\pi\)
0.815157 + 0.579240i \(0.196651\pi\)
\(200\) 1.31649 11.1127i 0.0930897 0.785783i
\(201\) −5.50049 + 3.17571i −0.387974 + 0.223997i
\(202\) 0.732083 4.62219i 0.0515092 0.325216i
\(203\) 2.60450 + 0.281200i 0.182800 + 0.0197363i
\(204\) 9.01581 + 2.92941i 0.631233 + 0.205100i
\(205\) −6.89306 + 2.38989i −0.481432 + 0.166917i
\(206\) −1.65133 + 7.76889i −0.115054 + 0.541284i
\(207\) 4.32681 1.15937i 0.300734 0.0805815i
\(208\) 7.71536 0.404345i 0.534964 0.0280363i
\(209\) 25.6071 + 18.6047i 1.77128 + 1.28691i
\(210\) 3.64634 + 0.321596i 0.251621 + 0.0221922i
\(211\) 10.1355 7.36390i 0.697759 0.506952i −0.181443 0.983402i \(-0.558077\pi\)
0.879202 + 0.476450i \(0.158077\pi\)
\(212\) 7.39588 5.98907i 0.507951 0.411331i
\(213\) −3.90549 1.49918i −0.267599 0.102722i
\(214\) 3.90701 0.410643i 0.267078 0.0280710i
\(215\) 13.3754 2.38779i 0.912191 0.162846i
\(216\) −1.31551 + 1.81064i −0.0895089 + 0.123198i
\(217\) −0.0281619 + 9.94971i −0.00191175 + 0.675430i
\(218\) −5.29461 + 5.29461i −0.358596 + 0.358596i
\(219\) −9.12306 8.21444i −0.616479 0.555080i
\(220\) −5.43333 23.3080i −0.366315 1.57142i
\(221\) 16.3848 + 18.1971i 1.10216 + 1.22407i
\(222\) 0.479269 0.738010i 0.0321665 0.0495320i
\(223\) 4.80824 + 0.761550i 0.321984 + 0.0509972i 0.315334 0.948981i \(-0.397883\pi\)
0.00664942 + 0.999978i \(0.497883\pi\)
\(224\) −13.2688 + 6.71355i −0.886559 + 0.448568i
\(225\) −1.23024 4.84629i −0.0820162 0.323086i
\(226\) 0.582033 + 1.00811i 0.0387163 + 0.0670586i
\(227\) −5.48107 4.43848i −0.363791 0.294592i 0.429944 0.902855i \(-0.358533\pi\)
−0.793735 + 0.608263i \(0.791867\pi\)
\(228\) −7.72335 0.404764i −0.511492 0.0268061i
\(229\) 15.3618 3.26524i 1.01513 0.215773i 0.329837 0.944038i \(-0.393006\pi\)
0.685296 + 0.728265i \(0.259673\pi\)
\(230\) 0.768369 + 6.14966i 0.0506647 + 0.405497i
\(231\) 16.9269 4.48422i 1.11370 0.295040i
\(232\) −1.56694 1.56694i −0.102874 0.102874i
\(233\) −0.931839 17.7805i −0.0610468 1.16484i −0.841724 0.539908i \(-0.818459\pi\)
0.780677 0.624934i \(-0.214874\pi\)
\(234\) −2.36114 + 1.05125i −0.154352 + 0.0687221i
\(235\) 17.7117 7.19988i 1.15539 0.469668i
\(236\) −8.33108 + 18.7119i −0.542307 + 1.21804i
\(237\) 2.04330 0.323627i 0.132727 0.0210218i
\(238\) −8.75547 3.92792i −0.567533 0.254609i
\(239\) −2.52648 3.47740i −0.163424 0.224934i 0.719449 0.694545i \(-0.244394\pi\)
−0.882874 + 0.469611i \(0.844394\pi\)
\(240\) 2.98110 + 2.86658i 0.192429 + 0.185037i
\(241\) −5.89020 13.2296i −0.379421 0.852194i −0.997799 0.0663126i \(-0.978877\pi\)
0.618378 0.785881i \(-0.287790\pi\)
\(242\) 11.0545 + 17.0224i 0.710610 + 1.09424i
\(243\) −0.258819 + 0.965926i −0.0166032 + 0.0619642i
\(244\) 0.232624 + 0.715942i 0.0148922 + 0.0458335i
\(245\) 15.3542 + 3.04090i 0.980947 + 0.194276i
\(246\) −0.623827 + 1.91994i −0.0397738 + 0.122411i
\(247\) −16.7542 10.8803i −1.06605 0.692298i
\(248\) 5.29674 6.54093i 0.336344 0.415350i
\(249\) −8.80916 5.08597i −0.558258 0.322310i
\(250\) 6.87504 0.766993i 0.434815 0.0485089i
\(251\) 1.78859i 0.112894i −0.998406 0.0564472i \(-0.982023\pi\)
0.998406 0.0564472i \(-0.0179773\pi\)
\(252\) −2.87194 + 3.17152i −0.180915 + 0.199787i
\(253\) 13.4594 + 26.4156i 0.846187 + 1.66074i
\(254\) 1.69933 + 7.99470i 0.106625 + 0.501632i
\(255\) −1.11463 + 13.0603i −0.0698010 + 0.817867i
\(256\) 6.45294 + 1.37161i 0.403308 + 0.0857259i
\(257\) −9.20773 2.46721i −0.574363 0.153900i −0.0400660 0.999197i \(-0.512757\pi\)
−0.534297 + 0.845297i \(0.679423\pi\)
\(258\) 1.70681 3.34980i 0.106261 0.208550i
\(259\) 2.37629 2.91755i 0.147655 0.181288i
\(260\) 4.19442 + 14.5111i 0.260127 + 0.899940i
\(261\) −0.904529 0.402722i −0.0559889 0.0249279i
\(262\) −2.56357 + 6.67832i −0.158378 + 0.412588i
\(263\) 10.1507 26.4436i 0.625922 1.63058i −0.141872 0.989885i \(-0.545312\pi\)
0.767794 0.640697i \(-0.221354\pi\)
\(264\) −13.5319 6.02481i −0.832834 0.370801i
\(265\) 10.3865 + 8.07932i 0.638040 + 0.496309i
\(266\) 7.72904 + 1.24660i 0.473898 + 0.0764337i
\(267\) 4.96963 9.75345i 0.304136 0.596901i
\(268\) 9.92130 + 2.65840i 0.606040 + 0.162388i
\(269\) −16.2664 3.45753i −0.991781 0.210810i −0.316678 0.948533i \(-0.602567\pi\)
−0.675103 + 0.737723i \(0.735901\pi\)
\(270\) −1.27470 0.537880i −0.0775758 0.0327344i
\(271\) −3.03705 14.2882i −0.184487 0.867945i −0.968851 0.247644i \(-0.920344\pi\)
0.784364 0.620301i \(-0.212990\pi\)
\(272\) −4.92218 9.66031i −0.298451 0.585743i
\(273\) −10.5205 + 3.38544i −0.636732 + 0.204896i
\(274\) 6.95643i 0.420254i
\(275\) 29.6811 14.6331i 1.78984 0.882409i
\(276\) −6.27349 3.62200i −0.377620 0.218019i
\(277\) −7.40031 + 9.13862i −0.444641 + 0.549086i −0.949357 0.314199i \(-0.898264\pi\)
0.504716 + 0.863286i \(0.331597\pi\)
\(278\) −10.4725 6.80094i −0.628101 0.407894i
\(279\) 1.16210 3.57659i 0.0695734 0.214125i
\(280\) −8.50377 10.1489i −0.508198 0.606512i
\(281\) −9.06765 27.9074i −0.540931 1.66481i −0.730474 0.682941i \(-0.760701\pi\)
0.189543 0.981872i \(-0.439299\pi\)
\(282\) 1.36926 5.11016i 0.0815384 0.304305i
\(283\) −11.0492 17.0142i −0.656805 1.01139i −0.997462 0.0712038i \(-0.977316\pi\)
0.340656 0.940188i \(-0.389351\pi\)
\(284\) 2.75164 + 6.18028i 0.163280 + 0.366732i
\(285\) −1.87936 10.5274i −0.111324 0.623587i
\(286\) −10.0546 13.8390i −0.594542 0.818317i
\(287\) −3.53337 + 7.87600i −0.208568 + 0.464906i
\(288\) 5.55133 0.879245i 0.327115 0.0518100i
\(289\) 7.06206 15.8617i 0.415415 0.933038i
\(290\) 0.723453 1.16327i 0.0424826 0.0683094i
\(291\) −5.52710 + 2.46082i −0.324004 + 0.144256i
\(292\) 1.03901 + 19.8256i 0.0608037 + 1.16020i
\(293\) 15.1657 + 15.1657i 0.885991 + 0.885991i 0.994135 0.108144i \(-0.0344909\pi\)
−0.108144 + 0.994135i \(0.534491\pi\)
\(294\) 3.23503 2.87984i 0.188671 0.167956i
\(295\) −27.8127 5.34486i −1.61932 0.311190i
\(296\) −3.11346 + 0.661787i −0.180966 + 0.0384656i
\(297\) −6.60937 0.346383i −0.383515 0.0200992i
\(298\) 7.96881 + 6.45302i 0.461621 + 0.373813i
\(299\) −9.35577 16.2047i −0.541058 0.937140i
\(300\) −4.13498 + 6.94856i −0.238733 + 0.401175i
\(301\) 8.79382 13.4577i 0.506867 0.775692i
\(302\) −6.15790 0.975316i −0.354347 0.0561231i
\(303\) −4.11937 + 6.34327i −0.236652 + 0.364412i
\(304\) 5.91868 + 6.57336i 0.339459 + 0.377008i
\(305\) −0.891069 + 0.537992i −0.0510225 + 0.0308053i
\(306\) 2.69540 + 2.42695i 0.154086 + 0.138739i
\(307\) −5.96323 + 5.96323i −0.340340 + 0.340340i −0.856495 0.516155i \(-0.827363\pi\)
0.516155 + 0.856495i \(0.327363\pi\)
\(308\) −24.4837 14.2282i −1.39509 0.810729i
\(309\) 7.54514 10.3850i 0.429228 0.590782i
\(310\) 4.68127 + 2.27089i 0.265878 + 0.128978i
\(311\) 11.6516 1.22463i 0.660699 0.0694423i 0.231756 0.972774i \(-0.425553\pi\)
0.428943 + 0.903332i \(0.358886\pi\)
\(312\) 8.72793 + 3.35034i 0.494122 + 0.189676i
\(313\) 8.65649 7.00989i 0.489294 0.396222i −0.352677 0.935745i \(-0.614729\pi\)
0.841971 + 0.539523i \(0.181395\pi\)
\(314\) 1.13180 0.822300i 0.0638711 0.0464051i
\(315\) −5.17230 2.87181i −0.291426 0.161808i
\(316\) −2.70660 1.96646i −0.152258 0.110622i
\(317\) 4.93069 0.258406i 0.276935 0.0145136i 0.0866371 0.996240i \(-0.472388\pi\)
0.190298 + 0.981726i \(0.439055\pi\)
\(318\) 3.51708 0.942400i 0.197228 0.0528472i
\(319\) 1.36247 6.40992i 0.0762837 0.358886i
\(320\) −0.00969647 0.495137i −0.000542049 0.0276790i
\(321\) −6.03852 1.96203i −0.337037 0.109510i
\(322\) 5.92026 + 4.32698i 0.329923 + 0.241133i
\(323\) −4.38555 + 27.6892i −0.244018 + 1.54067i
\(324\) 1.40051 0.808582i 0.0778059 0.0449212i
\(325\) −18.2241 + 10.2034i −1.01089 + 0.565981i
\(326\) 3.91337 6.77816i 0.216742 0.375408i
\(327\) 11.2978 4.33683i 0.624771 0.239827i
\(328\) 6.50626 3.31510i 0.359248 0.183046i
\(329\) 8.16679 21.0966i 0.450250 1.16309i
\(330\) 1.72808 8.99232i 0.0951279 0.495011i
\(331\) −6.73735 + 7.48258i −0.370318 + 0.411280i −0.899285 0.437362i \(-0.855913\pi\)
0.528967 + 0.848642i \(0.322579\pi\)
\(332\) 4.25750 + 15.8892i 0.233660 + 0.872032i
\(333\) −1.19277 + 0.774594i −0.0653634 + 0.0424475i
\(334\) −0.437756 + 4.16497i −0.0239529 + 0.227897i
\(335\) −0.465450 + 14.1946i −0.0254302 + 0.775532i
\(336\) 4.88745 0.242271i 0.266632 0.0132170i
\(337\) 2.89545 + 18.2812i 0.157725 + 0.995838i 0.931860 + 0.362817i \(0.118185\pi\)
−0.774135 + 0.633021i \(0.781815\pi\)
\(338\) 1.73237 + 2.13930i 0.0942286 + 0.116363i
\(339\) −0.196656 1.87105i −0.0106809 0.101622i
\(340\) 16.2091 13.6600i 0.879064 0.740815i
\(341\) 24.7533 + 2.60168i 1.34047 + 0.140889i
\(342\) −2.63654 1.34338i −0.142568 0.0726418i
\(343\) 15.0751 10.7583i 0.813979 0.580895i
\(344\) −12.9334 + 4.20232i −0.697323 + 0.226574i
\(345\) 2.90811 9.58488i 0.156567 0.516033i
\(346\) 3.61340 3.25352i 0.194258 0.174910i
\(347\) −0.997078 + 19.0254i −0.0535259 + 1.02134i 0.831421 + 0.555643i \(0.187528\pi\)
−0.884947 + 0.465692i \(0.845805\pi\)
\(348\) 0.573820 + 1.49485i 0.0307600 + 0.0801325i
\(349\) 14.7295 0.788454 0.394227 0.919013i \(-0.371012\pi\)
0.394227 + 0.919013i \(0.371012\pi\)
\(350\) 4.91661 6.54394i 0.262804 0.349788i
\(351\) 4.17720 0.222962
\(352\) 13.3310 + 34.7284i 0.710544 + 1.85103i
\(353\) −1.17246 + 22.3718i −0.0624036 + 1.19073i 0.770546 + 0.637384i \(0.219983\pi\)
−0.832950 + 0.553348i \(0.813350\pi\)
\(354\) −5.82389 + 5.24385i −0.309536 + 0.278708i
\(355\) −7.45863 + 5.64540i −0.395863 + 0.299627i
\(356\) −16.8360 + 5.47034i −0.892304 + 0.289927i
\(357\) 10.3451 + 11.5550i 0.547521 + 0.611556i
\(358\) 5.54879 + 2.82725i 0.293263 + 0.149425i
\(359\) 2.96242 + 0.311363i 0.156350 + 0.0164331i 0.182380 0.983228i \(-0.441620\pi\)
−0.0260298 + 0.999661i \(0.508286\pi\)
\(360\) 1.88458 + 4.63608i 0.0993261 + 0.244343i
\(361\) −0.404681 3.85028i −0.0212990 0.202647i
\(362\) 5.85796 + 7.23398i 0.307887 + 0.380209i
\(363\) −5.13164 32.3999i −0.269341 1.70055i
\(364\) 15.9016 + 8.15905i 0.833471 + 0.427650i
\(365\) −26.3711 + 7.62254i −1.38032 + 0.398982i
\(366\) −0.0301063 + 0.286443i −0.00157368 + 0.0149726i
\(367\) 15.5373 10.0900i 0.811040 0.526696i −0.0712185 0.997461i \(-0.522689\pi\)
0.882259 + 0.470765i \(0.156022\pi\)
\(368\) 2.14431 + 8.00266i 0.111780 + 0.417168i
\(369\) 2.18317 2.42465i 0.113651 0.126222i
\(370\) −0.835373 1.78156i −0.0434290 0.0926187i
\(371\) 15.3849 2.39211i 0.798745 0.124192i
\(372\) −5.41874 + 2.76099i −0.280948 + 0.143150i
\(373\) −7.15806 + 2.74772i −0.370630 + 0.142272i −0.536552 0.843867i \(-0.680273\pi\)
0.165922 + 0.986139i \(0.446940\pi\)
\(374\) −12.0026 + 20.7891i −0.620640 + 1.07498i
\(375\) −10.6550 3.38698i −0.550220 0.174903i
\(376\) −16.5726 + 9.56817i −0.854664 + 0.493441i
\(377\) −0.647008 + 4.08505i −0.0333226 + 0.210391i
\(378\) −1.49737 + 0.661602i −0.0770166 + 0.0340291i
\(379\) 22.5141 + 7.31526i 1.15647 + 0.375760i 0.823577 0.567205i \(-0.191975\pi\)
0.332893 + 0.942965i \(0.391975\pi\)
\(380\) −9.88906 + 14.1872i −0.507298 + 0.727788i
\(381\) 2.74644 12.9210i 0.140705 0.661963i
\(382\) −2.45340 + 0.657386i −0.125527 + 0.0336348i
\(383\) 18.2059 0.954129i 0.930277 0.0487537i 0.418826 0.908066i \(-0.362442\pi\)
0.511451 + 0.859313i \(0.329108\pi\)
\(384\) −9.20507 6.68788i −0.469744 0.341289i
\(385\) 11.4742 37.4363i 0.584779 1.90793i
\(386\) 7.64174 5.55205i 0.388954 0.282592i
\(387\) −4.72210 + 3.82388i −0.240038 + 0.194379i
\(388\) 9.13426 + 3.50631i 0.463722 + 0.178006i
\(389\) 1.35590 0.142511i 0.0687470 0.00722560i −0.0700925 0.997540i \(-0.522329\pi\)
0.138840 + 0.990315i \(0.455663\pi\)
\(390\) −0.792147 + 5.72477i −0.0401119 + 0.289885i
\(391\) −15.4343 + 21.2435i −0.780546 + 1.07433i
\(392\) −15.6401 0.908472i −0.789947 0.0458848i
\(393\) 8.17513 8.17513i 0.412381 0.412381i
\(394\) −3.31767 2.98725i −0.167142 0.150495i
\(395\) 1.79842 4.26201i 0.0904885 0.214445i
\(396\) 7.16178 + 7.95396i 0.359893 + 0.399702i
\(397\) −10.0370 + 15.4557i −0.503745 + 0.775699i −0.995473 0.0950498i \(-0.969699\pi\)
0.491727 + 0.870749i \(0.336366\pi\)
\(398\) 1.62173 + 0.256857i 0.0812902 + 0.0128751i
\(399\) −10.5922 6.92137i −0.530274 0.346502i
\(400\) 8.96346 2.27540i 0.448173 0.113770i
\(401\) 10.0236 + 17.3614i 0.500554 + 0.866985i 1.00000 0.000639967i \(0.000203708\pi\)
−0.499446 + 0.866345i \(0.666463\pi\)
\(402\) 3.05407 + 2.47314i 0.152323 + 0.123349i
\(403\) −15.6875 0.822145i −0.781448 0.0409540i
\(404\) 11.9641 2.54305i 0.595237 0.126522i
\(405\) 1.52847 + 1.63211i 0.0759503 + 0.0811001i
\(406\) −0.415078 1.56682i −0.0206000 0.0777598i
\(407\) −6.65589 6.65589i −0.329920 0.329920i
\(408\) −0.686623 13.1015i −0.0339929 0.648623i
\(409\) 17.9963 8.01245i 0.889858 0.396190i 0.0896925 0.995970i \(-0.471412\pi\)
0.800166 + 0.599779i \(0.204745\pi\)
\(410\) 2.90893 + 3.45179i 0.143662 + 0.170472i
\(411\) −4.57293 + 10.2710i −0.225566 + 0.506629i
\(412\) −20.5033 + 3.24740i −1.01012 + 0.159988i
\(413\) −27.1663 + 19.6202i −1.33677 + 0.965449i
\(414\) −1.62910 2.24227i −0.0800661 0.110202i
\(415\) −20.0600 + 10.7209i −0.984707 + 0.526268i
\(416\) −9.54940 21.4483i −0.468198 1.05159i
\(417\) 10.9917 + 16.9257i 0.538264 + 0.828854i
\(418\) 5.06880 18.9170i 0.247923 0.925262i
\(419\) 11.2054 + 34.4866i 0.547418 + 1.68478i 0.715170 + 0.698950i \(0.246349\pi\)
−0.167752 + 0.985829i \(0.553651\pi\)
\(420\) 2.63063 + 9.19851i 0.128362 + 0.448841i
\(421\) 9.60879 29.5728i 0.468304 1.44129i −0.386476 0.922299i \(-0.626308\pi\)
0.854780 0.518991i \(-0.173692\pi\)
\(422\) −6.50109 4.22186i −0.316468 0.205517i
\(423\) −5.38092 + 6.64488i −0.261629 + 0.323085i
\(424\) −11.4061 6.58533i −0.553930 0.319812i
\(425\) 23.4827 + 17.5394i 1.13908 + 0.850784i
\(426\) 2.58839i 0.125408i
\(427\) −0.259471 + 1.20395i −0.0125567 + 0.0582631i
\(428\) 4.66150 + 9.14870i 0.225322 + 0.442219i
\(429\) 5.74804 + 27.0424i 0.277518 + 1.30562i
\(430\) −4.34507 7.19669i −0.209538 0.347055i
\(431\) 24.3536 + 5.17652i 1.17307 + 0.249344i 0.752921 0.658110i \(-0.228644\pi\)
0.420150 + 0.907455i \(0.361977\pi\)
\(432\) −1.78653 0.478699i −0.0859545 0.0230314i
\(433\) 12.6169 24.7620i 0.606329 1.18999i −0.360066 0.932927i \(-0.617246\pi\)
0.966395 0.257061i \(-0.0827541\pi\)
\(434\) 5.75360 2.18993i 0.276182 0.105120i
\(435\) −1.83285 + 1.24195i −0.0878784 + 0.0595471i
\(436\) −17.8783 7.95995i −0.856218 0.381213i
\(437\) 7.67716 19.9997i 0.367248 0.956715i
\(438\) −2.72209 + 7.09128i −0.130066 + 0.338834i
\(439\) −25.5333 11.3682i −1.21864 0.542573i −0.306271 0.951944i \(-0.599081\pi\)
−0.912368 + 0.409371i \(0.865748\pi\)
\(440\) −27.4198 + 18.5799i −1.30719 + 0.885762i
\(441\) −6.66953 + 2.12540i −0.317597 + 0.101209i
\(442\) 6.87831 13.4994i 0.327168 0.642103i
\(443\) −20.4255 5.47300i −0.970445 0.260030i −0.261429 0.965223i \(-0.584194\pi\)
−0.709016 + 0.705193i \(0.750860\pi\)
\(444\) 2.24970 + 0.478188i 0.106766 + 0.0226938i
\(445\) −12.6513 20.9542i −0.599730 0.993325i
\(446\) −0.626255 2.94630i −0.0296540 0.139511i
\(447\) −7.52371 14.7661i −0.355859 0.698413i
\(448\) −0.434346 0.393319i −0.0205209 0.0185826i
\(449\) 18.4321i 0.869865i 0.900463 + 0.434932i \(0.143228\pi\)
−0.900463 + 0.434932i \(0.856772\pi\)
\(450\) −2.52662 + 1.78523i −0.119106 + 0.0841566i
\(451\) 18.7009 + 10.7970i 0.880591 + 0.508409i
\(452\) −1.91469 + 2.36444i −0.0900594 + 0.111214i
\(453\) 8.45081 + 5.48802i 0.397054 + 0.257850i
\(454\) −1.34850 + 4.15025i −0.0632882 + 0.194781i
\(455\) −5.99538 + 23.9744i −0.281068 + 1.12394i
\(456\) 3.30753 + 10.1795i 0.154889 + 0.476700i
\(457\) 2.25171 8.40350i 0.105331 0.393099i −0.893052 0.449954i \(-0.851440\pi\)
0.998382 + 0.0568545i \(0.0181071\pi\)
\(458\) −5.29238 8.14955i −0.247297 0.380803i
\(459\) −2.38428 5.35518i −0.111289 0.249958i
\(460\) −14.2858 + 7.63495i −0.666081 + 0.355981i
\(461\) 12.5719 + 17.3037i 0.585531 + 0.805915i 0.994288 0.106729i \(-0.0340376\pi\)
−0.408757 + 0.912643i \(0.634038\pi\)
\(462\) −6.34355 8.78332i −0.295129 0.408637i
\(463\) −14.5831 + 2.30973i −0.677733 + 0.107342i −0.485806 0.874067i \(-0.661474\pi\)
−0.191927 + 0.981409i \(0.561474\pi\)
\(464\) 0.744855 1.67297i 0.0345790 0.0776658i
\(465\) −5.41894 6.43021i −0.251297 0.298194i
\(466\) −10.0641 + 4.48085i −0.466212 + 0.207571i
\(467\) −0.0889301 1.69689i −0.00411519 0.0785225i 0.995800 0.0915568i \(-0.0291843\pi\)
−0.999915 + 0.0130342i \(0.995851\pi\)
\(468\) −4.77666 4.77666i −0.220801 0.220801i
\(469\) 11.8487 + 11.9160i 0.547124 + 0.550229i
\(470\) −8.08626 8.63455i −0.372991 0.398282i
\(471\) −2.21162 + 0.470094i −0.101906 + 0.0216608i
\(472\) 28.3082 + 1.48357i 1.30299 + 0.0682868i
\(473\) −31.2530 25.3081i −1.43701 1.16367i
\(474\) −0.640012 1.10853i −0.0293967 0.0509166i
\(475\) −22.2088 8.86320i −1.01901 0.406671i
\(476\) 1.38353 25.0429i 0.0634141 1.14784i
\(477\) −5.81237 0.920588i −0.266130 0.0421508i
\(478\) −1.44848 + 2.23046i −0.0662517 + 0.102019i
\(479\) 9.78984 + 10.8727i 0.447309 + 0.496787i 0.924058 0.382253i \(-0.124852\pi\)
−0.476749 + 0.879040i \(0.658185\pi\)
\(480\) 4.88604 11.5792i 0.223016 0.528517i
\(481\) 4.41493 + 3.97522i 0.201304 + 0.181255i
\(482\) −6.33589 + 6.33589i −0.288592 + 0.288592i
\(483\) −5.89667 10.2804i −0.268308 0.467776i
\(484\) −31.1815 + 42.9177i −1.41734 + 1.95080i
\(485\) −1.85431 + 13.4009i −0.0841997 + 0.608503i
\(486\) 0.615347 0.0646756i 0.0279127 0.00293374i
\(487\) −32.5699 12.5024i −1.47588 0.566538i −0.518428 0.855121i \(-0.673483\pi\)
−0.957455 + 0.288583i \(0.906816\pi\)
\(488\) 0.809644 0.655637i 0.0366509 0.0296793i
\(489\) −10.2337 + 7.43522i −0.462784 + 0.336232i
\(490\) −1.64803 9.54351i −0.0744505 0.431132i
\(491\) −1.04520 0.759384i −0.0471693 0.0342705i 0.563951 0.825808i \(-0.309281\pi\)
−0.611120 + 0.791538i \(0.709281\pi\)
\(492\) −5.26908 + 0.276141i −0.237548 + 0.0124494i
\(493\) 5.60635 1.50222i 0.252497 0.0676564i
\(494\) −2.56991 + 12.0905i −0.115626 + 0.543976i
\(495\) −8.46271 + 12.1409i −0.380371 + 0.545693i
\(496\) 6.61509 + 2.14937i 0.297026 + 0.0965097i
\(497\) −1.18808 + 11.0041i −0.0532927 + 0.493603i
\(498\) −0.984560 + 6.21626i −0.0441192 + 0.278557i
\(499\) 16.9040 9.75952i 0.756726 0.436896i −0.0713930 0.997448i \(-0.522744\pi\)
0.828119 + 0.560552i \(0.189411\pi\)
\(500\) 8.31101 + 16.0571i 0.371680 + 0.718094i
\(501\) 3.38424 5.86168i 0.151197 0.261880i
\(502\) −1.03316 + 0.396593i −0.0461122 + 0.0177008i
\(503\) 11.6454 5.93361i 0.519241 0.264567i −0.174670 0.984627i \(-0.555886\pi\)
0.693911 + 0.720060i \(0.255886\pi\)
\(504\) 5.52206 + 2.13767i 0.245972 + 0.0952195i
\(505\) 7.18011 + 15.3127i 0.319511 + 0.681404i
\(506\) 12.2743 13.6320i 0.545659 0.606016i
\(507\) −1.15149 4.29741i −0.0511394 0.190855i
\(508\) −17.9158 + 11.6347i −0.794887 + 0.516206i
\(509\) 1.21767 11.5854i 0.0539724 0.513513i −0.933821 0.357741i \(-0.883547\pi\)
0.987793 0.155772i \(-0.0497864\pi\)
\(510\) 7.79131 2.25207i 0.345005 0.0997235i
\(511\) −14.8275 + 28.8980i −0.655928 + 1.27837i
\(512\) 2.92131 + 18.4444i 0.129105 + 0.815136i
\(513\) 3.00967 + 3.71663i 0.132880 + 0.164093i
\(514\) 0.616523 + 5.86583i 0.0271937 + 0.258731i
\(515\) −10.8091 26.5904i −0.476305 1.17171i
\(516\) 9.77240 + 1.02712i 0.430206 + 0.0452165i
\(517\) −50.4222 25.6914i −2.21756 1.12991i
\(518\) −2.21220 0.725717i −0.0971986 0.0318862i
\(519\) −7.47383 + 2.42839i −0.328065 + 0.106595i
\(520\) 16.6685 12.6163i 0.730960 0.553260i
\(521\) 10.4643 9.42207i 0.458448 0.412789i −0.407280 0.913303i \(-0.633523\pi\)
0.865728 + 0.500515i \(0.166856\pi\)
\(522\) −0.0320626 + 0.611790i −0.00140334 + 0.0267773i
\(523\) 14.9091 + 38.8396i 0.651931 + 1.69834i 0.713887 + 0.700260i \(0.246933\pi\)
−0.0619561 + 0.998079i \(0.519734\pi\)
\(524\) −18.6967 −0.816767
\(525\) −11.5610 + 6.42991i −0.504563 + 0.280624i
\(526\) −17.5257 −0.764155
\(527\) 7.90016 + 20.5806i 0.344137 + 0.896506i
\(528\) 0.640652 12.2244i 0.0278808 0.531998i
\(529\) −2.18082 + 1.96362i −0.0948181 + 0.0853746i
\(530\) 2.36388 7.79115i 0.102680 0.338426i
\(531\) 12.0459 3.91396i 0.522748 0.169851i
\(532\) 4.19765 + 20.0269i 0.181991 + 0.868278i
\(533\) −12.1435 6.18740i −0.525991 0.268006i
\(534\) −6.73593 0.707975i −0.291492 0.0306371i
\(535\) −10.8564 + 9.14904i −0.469363 + 0.395548i
\(536\) −1.48586 14.1371i −0.0641796 0.610628i
\(537\) −6.33408 7.82194i −0.273336 0.337542i
\(538\) 1.60963 + 10.1628i 0.0693961 + 0.438149i
\(539\) −22.9371 40.2527i −0.987969 1.73381i
\(540\) 0.118510 3.61415i 0.00509988 0.155528i
\(541\) 4.47303 42.5581i 0.192311 1.82971i −0.293858 0.955849i \(-0.594939\pi\)
0.486169 0.873865i \(-0.338394\pi\)
\(542\) −7.58001 + 4.92252i −0.325589 + 0.211440i
\(543\) −3.89372 14.5316i −0.167096 0.623609i
\(544\) −22.0461 + 24.4847i −0.945220 + 1.04977i
\(545\) 5.10677 26.5738i 0.218750 1.13830i
\(546\) 4.28835 + 5.32642i 0.183524 + 0.227950i
\(547\) 19.7235 10.0496i 0.843317 0.429692i 0.0217228 0.999764i \(-0.493085\pi\)
0.821594 + 0.570072i \(0.193085\pi\)
\(548\) 16.9741 6.51575i 0.725098 0.278339i
\(549\) 0.232749 0.403133i 0.00993347 0.0172053i
\(550\) −15.0340 13.9003i −0.641053 0.592712i
\(551\) −4.10081 + 2.36761i −0.174701 + 0.100863i
\(552\) −1.56831 + 9.90189i −0.0667515 + 0.421453i
\(553\) −2.21209 5.00653i −0.0940677 0.212899i
\(554\) 6.91975 + 2.24836i 0.293992 + 0.0955237i
\(555\) 0.0622666 + 3.17956i 0.00264307 + 0.134965i
\(556\) 6.78559 31.9237i 0.287773 1.35387i
\(557\) 17.6840 4.73841i 0.749295 0.200773i 0.136090 0.990697i \(-0.456546\pi\)
0.613205 + 0.789923i \(0.289880\pi\)
\(558\) −2.32366 + 0.121778i −0.0983685 + 0.00515528i
\(559\) 20.5341 + 14.9189i 0.868500 + 0.631002i
\(560\) 5.31156 9.56644i 0.224454 0.404256i
\(561\) 31.3875 22.8044i 1.32518 0.962802i
\(562\) −14.1098 + 11.4259i −0.595186 + 0.481972i
\(563\) 11.8277 + 4.54024i 0.498480 + 0.191348i 0.594601 0.804021i \(-0.297310\pi\)
−0.0961208 + 0.995370i \(0.530644\pi\)
\(564\) 13.7516 1.44535i 0.579047 0.0608603i
\(565\) −3.78501 1.83611i −0.159236 0.0772459i
\(566\) −7.37812 + 10.1551i −0.310126 + 0.426851i
\(567\) 2.64574 + 0.00748857i 0.111111 + 0.000314490i
\(568\) 6.62037 6.62037i 0.277785 0.277785i
\(569\) 4.98148 + 4.48535i 0.208835 + 0.188036i 0.766910 0.641755i \(-0.221793\pi\)
−0.558075 + 0.829790i \(0.688460\pi\)
\(570\) −5.66431 + 3.41989i −0.237252 + 0.143243i
\(571\) 4.25076 + 4.72095i 0.177889 + 0.197566i 0.825495 0.564410i \(-0.190896\pi\)
−0.647606 + 0.761976i \(0.724230\pi\)
\(572\) 24.3503 37.4962i 1.01814 1.56779i
\(573\) 4.05451 + 0.642171i 0.169380 + 0.0268271i
\(574\) 5.33297 + 0.294627i 0.222594 + 0.0122975i
\(575\) −14.7657 16.8407i −0.615772 0.702307i
\(576\) 0.110737 + 0.191802i 0.00461405 + 0.00799177i
\(577\) 13.7647 + 11.1464i 0.573032 + 0.464032i 0.871505 0.490386i \(-0.163144\pi\)
−0.298474 + 0.954418i \(0.596477\pi\)
\(578\) −10.7282 0.562243i −0.446236 0.0233862i
\(579\) −14.9325 + 3.17400i −0.620574 + 0.131907i
\(580\) 3.51606 + 0.675693i 0.145997 + 0.0280566i
\(581\) −7.03900 + 25.9756i −0.292027 + 1.07765i
\(582\) 2.64703 + 2.64703i 0.109723 + 0.109723i
\(583\) −2.03840 38.8950i −0.0844218 1.61086i
\(584\) 25.0999 11.1752i 1.03864 0.462432i
\(585\) 4.93285 7.93171i 0.203948 0.327936i
\(586\) 5.39756 12.1231i 0.222971 0.500801i
\(587\) −10.8594 + 1.71996i −0.448216 + 0.0709904i −0.376462 0.926432i \(-0.622860\pi\)
−0.0717536 + 0.997422i \(0.522860\pi\)
\(588\) 10.0571 + 5.19626i 0.414747 + 0.214290i
\(589\) −10.5713 14.5502i −0.435583 0.599529i
\(590\) 3.07966 + 17.2509i 0.126788 + 0.710209i
\(591\) 2.93472 + 6.59150i 0.120718 + 0.271138i
\(592\) −1.43265 2.20609i −0.0588816 0.0906697i
\(593\) 3.06253 11.4295i 0.125763 0.469355i −0.874103 0.485741i \(-0.838550\pi\)
0.999866 + 0.0163868i \(0.00521632\pi\)
\(594\) 1.26545 + 3.89465i 0.0519219 + 0.159799i
\(595\) 34.1573 5.99810i 1.40031 0.245898i
\(596\) −8.28174 + 25.4886i −0.339233 + 1.04405i
\(597\) −2.22559 1.44532i −0.0910873 0.0591528i
\(598\) −7.28597 + 8.99742i −0.297945 + 0.367932i
\(599\) −25.7408 14.8615i −1.05174 0.607223i −0.128605 0.991696i \(-0.541050\pi\)
−0.923136 + 0.384473i \(0.874383\pi\)
\(600\) 11.0285 + 1.89627i 0.450238 + 0.0774151i
\(601\) 17.0429i 0.695194i −0.937644 0.347597i \(-0.886998\pi\)
0.937644 0.347597i \(-0.113002\pi\)
\(602\) −9.72364 2.09561i −0.396306 0.0854105i
\(603\) −2.88348 5.65915i −0.117424 0.230458i
\(604\) −3.38797 15.9392i −0.137855 0.648555i
\(605\) −67.5812 28.5170i −2.74757 1.15938i
\(606\) 4.57754 + 0.972987i 0.185950 + 0.0395249i
\(607\) −7.92996 2.12483i −0.321867 0.0862440i 0.0942680 0.995547i \(-0.469949\pi\)
−0.416135 + 0.909303i \(0.636616\pi\)
\(608\) 12.2031 23.9500i 0.494902 0.971301i
\(609\) −0.417123 + 2.58622i −0.0169027 + 0.104799i
\(610\) 0.508348 + 0.395426i 0.0205824 + 0.0160103i
\(611\) 32.6287 + 14.5272i 1.32002 + 0.587710i
\(612\) −3.39725 + 8.85014i −0.137326 + 0.357746i
\(613\) −10.8548 + 28.2778i −0.438423 + 1.14213i 0.519340 + 0.854568i \(0.326178\pi\)
−0.957762 + 0.287562i \(0.907155\pi\)
\(614\) 4.76686 + 2.12234i 0.192375 + 0.0856508i
\(615\) −2.02586 7.00869i −0.0816904 0.282618i
\(616\) −6.24026 + 38.6903i −0.251427 + 1.55888i
\(617\) −4.29173 + 8.42299i −0.172778 + 0.339097i −0.961115 0.276147i \(-0.910942\pi\)
0.788337 + 0.615244i \(0.210942\pi\)
\(618\) −7.67182 2.05566i −0.308606 0.0826907i
\(619\) 7.91066 + 1.68146i 0.317956 + 0.0675837i 0.364125 0.931350i \(-0.381368\pi\)
−0.0461690 + 0.998934i \(0.514701\pi\)
\(620\) −1.15639 + 13.5496i −0.0464418 + 0.544165i
\(621\) 0.931329 + 4.38156i 0.0373729 + 0.175826i
\(622\) −3.29096 6.45887i −0.131955 0.258977i
\(623\) −28.3118 6.10167i −1.13429 0.244458i
\(624\) 7.72595i 0.309286i
\(625\) −19.0137 + 16.2321i −0.760546 + 0.649284i
\(626\) −5.96865 3.44600i −0.238555 0.137730i
\(627\) −19.9193 + 24.5983i −0.795502 + 0.982363i
\(628\) 3.06656 + 1.99145i 0.122369 + 0.0794674i
\(629\) 2.57627 7.92894i 0.102723 0.316148i
\(630\) −0.511990 + 3.62451i −0.0203982 + 0.144404i
\(631\) 9.78023 + 30.1005i 0.389345 + 1.19828i 0.933279 + 0.359152i \(0.116934\pi\)
−0.543934 + 0.839128i \(0.683066\pi\)
\(632\) −1.19835 + 4.47229i −0.0476677 + 0.177898i
\(633\) 6.82335 + 10.5070i 0.271204 + 0.417617i
\(634\) −1.24257 2.79087i −0.0493489 0.110840i
\(635\) −21.2913 20.4734i −0.844918 0.812460i
\(636\) 5.59379 + 7.69919i 0.221808 + 0.305293i
\(637\) 15.7864 + 24.6128i 0.625480 + 0.975196i
\(638\) −4.00474 + 0.634288i −0.158549 + 0.0251117i
\(639\) 1.70152 3.82167i 0.0673110 0.151183i
\(640\) −23.5693 + 9.58098i −0.931657 + 0.378722i
\(641\) 6.68674 2.97713i 0.264110 0.117589i −0.270410 0.962745i \(-0.587159\pi\)
0.534520 + 0.845156i \(0.320492\pi\)
\(642\) 0.205603 + 3.92315i 0.00811452 + 0.154834i
\(643\) 19.1837 + 19.1837i 0.756531 + 0.756531i 0.975689 0.219158i \(-0.0703310\pi\)
−0.219158 + 0.975689i \(0.570331\pi\)
\(644\) −5.01286 + 18.4986i −0.197534 + 0.728949i
\(645\) 1.68450 + 13.4820i 0.0663273 + 0.530853i
\(646\) 16.9669 3.60642i 0.667552 0.141893i
\(647\) 18.3814 + 0.963331i 0.722649 + 0.0378724i 0.410115 0.912034i \(-0.365489\pi\)
0.312535 + 0.949906i \(0.398822\pi\)
\(648\) −1.73931 1.40846i −0.0683265 0.0553297i
\(649\) 41.9140 + 72.5972i 1.64527 + 2.84969i
\(650\) 9.93480 + 8.26451i 0.389675 + 0.324161i
\(651\) −9.93460 0.548851i −0.389368 0.0215112i
\(652\) 20.2046 + 3.20009i 0.791272 + 0.125325i
\(653\) −2.06602 + 3.18139i −0.0808495 + 0.124497i −0.876782 0.480888i \(-0.840314\pi\)
0.795932 + 0.605385i \(0.206981\pi\)
\(654\) −5.01025 5.56445i −0.195916 0.217587i
\(655\) −5.86902 25.1770i −0.229322 0.983748i
\(656\) 4.48452 + 4.03788i 0.175091 + 0.157653i
\(657\) 8.68064 8.68064i 0.338664 0.338664i
\(658\) −13.9971 0.0396177i −0.545663 0.00154446i
\(659\) 25.3351 34.8707i 0.986914 1.35837i 0.0538938 0.998547i \(-0.482837\pi\)
0.933020 0.359824i \(-0.117163\pi\)
\(660\) 23.5604 4.20604i 0.917087 0.163720i
\(661\) −8.62019 + 0.906019i −0.335287 + 0.0352400i −0.270676 0.962671i \(-0.587247\pi\)
−0.0646106 + 0.997911i \(0.520581\pi\)
\(662\) 5.81615 + 2.23261i 0.226051 + 0.0867729i
\(663\) −19.0297 + 15.4099i −0.739052 + 0.598473i
\(664\) 18.4177 13.3812i 0.714746 0.519293i
\(665\) −25.6507 + 11.9392i −0.994691 + 0.462981i
\(666\) 0.711916 + 0.517237i 0.0275862 + 0.0200425i
\(667\) −4.42915 + 0.232122i −0.171497 + 0.00898780i
\(668\) −10.5728 + 2.83297i −0.409073 + 0.109611i
\(669\) −1.01215 + 4.76179i −0.0391320 + 0.184102i
\(670\) 8.30256 2.87858i 0.320756 0.111209i
\(671\) 2.93008 + 0.952041i 0.113114 + 0.0367531i
\(672\) −6.00991 13.6020i −0.231837 0.524707i
\(673\) 6.83668 43.1651i 0.263535 1.66389i −0.400581 0.916261i \(-0.631192\pi\)
0.664115 0.747630i \(-0.268808\pi\)
\(674\) 9.91791 5.72611i 0.382024 0.220561i
\(675\) 4.90403 0.974922i 0.188756 0.0375247i
\(676\) −3.59739 + 6.23086i −0.138361 + 0.239649i
\(677\) −15.5769 + 5.97943i −0.598670 + 0.229808i −0.638783 0.769387i \(-0.720562\pi\)
0.0401123 + 0.999195i \(0.487228\pi\)
\(678\) −1.03719 + 0.528475i −0.0398331 + 0.0202960i
\(679\) 10.0384 + 12.4684i 0.385240 + 0.478494i
\(680\) −25.6882 14.1678i −0.985097 0.543311i
\(681\) 4.71925 5.24126i 0.180842 0.200846i
\(682\) −3.98585 14.8754i −0.152626 0.569608i
\(683\) −10.8696 + 7.05881i −0.415914 + 0.270098i −0.735587 0.677430i \(-0.763094\pi\)
0.319673 + 0.947528i \(0.396427\pi\)
\(684\) 0.808418 7.69159i 0.0309106 0.294095i
\(685\) 14.1024 + 20.8121i 0.538826 + 0.795188i
\(686\) −9.55712 6.32249i −0.364893 0.241394i
\(687\) 2.45679 + 15.5116i 0.0937325 + 0.591804i
\(688\) −7.07247 8.73377i −0.269635 0.332972i
\(689\) 2.56953 + 24.4474i 0.0978911 + 0.931372i
\(690\) −6.18145 + 0.445467i −0.235324 + 0.0169586i
\(691\) −10.9331 1.14912i −0.415915 0.0437145i −0.105740 0.994394i \(-0.533721\pi\)
−0.310175 + 0.950679i \(0.600388\pi\)
\(692\) 11.3233 + 5.76949i 0.430446 + 0.219323i
\(693\) 3.59220 + 17.1383i 0.136456 + 0.651032i
\(694\) 11.2109 3.64265i 0.425561 0.138273i
\(695\) 45.1187 0.883577i 1.71145 0.0335160i
\(696\) 1.64680 1.48278i 0.0624216 0.0562047i
\(697\) −1.00097 + 19.0996i −0.0379144 + 0.723449i
\(698\) −3.26606 8.50837i −0.123622 0.322047i
\(699\) 17.8049 0.673445
\(700\) 20.5727 + 5.86743i 0.777576 + 0.221768i
\(701\) 0.152579 0.00576283 0.00288141 0.999996i \(-0.499083\pi\)
0.00288141 + 0.999996i \(0.499083\pi\)
\(702\) −0.926233 2.41292i −0.0349584 0.0910698i
\(703\) −0.355969 + 6.79230i −0.0134256 + 0.256176i
\(704\) −1.08931 + 0.980822i −0.0410550 + 0.0369661i
\(705\) 6.26305 + 18.0643i 0.235880 + 0.680340i
\(706\) 13.1828 4.28337i 0.496143 0.161207i
\(707\) 19.0141 + 6.23761i 0.715099 + 0.234590i
\(708\) −18.2502 9.29896i −0.685886 0.349476i
\(709\) 45.1002 + 4.74023i 1.69377 + 0.178023i 0.901688 0.432386i \(-0.142328\pi\)
0.792086 + 0.610409i \(0.208995\pi\)
\(710\) 4.91486 + 3.05662i 0.184451 + 0.114713i
\(711\) 0.216245 + 2.05744i 0.00810984 + 0.0771599i
\(712\) 15.4178 + 19.0394i 0.577808 + 0.713533i
\(713\) −2.63524 16.6382i −0.0986904 0.623107i
\(714\) 4.38076 8.53790i 0.163946 0.319523i
\(715\) 58.1363 + 21.0199i 2.17417 + 0.786100i
\(716\) −1.70138 + 16.1875i −0.0635835 + 0.604956i
\(717\) 3.60486 2.34102i 0.134626 0.0874270i
\(718\) −0.477017 1.78025i −0.0178021 0.0664384i
\(719\) 14.7600 16.3926i 0.550453 0.611341i −0.402143 0.915577i \(-0.631735\pi\)
0.952597 + 0.304236i \(0.0984012\pi\)
\(720\) −3.01867 + 2.82699i −0.112499 + 0.105356i
\(721\) −31.6720 12.2607i −1.17953 0.456613i
\(722\) −2.13435 + 1.08750i −0.0794322 + 0.0404727i
\(723\) 13.5197 5.18974i 0.502805 0.193009i
\(724\) −12.1645 + 21.0695i −0.452089 + 0.783040i
\(725\) 0.193827 + 4.94685i 0.00719855 + 0.183722i
\(726\) −17.5776 + 10.1485i −0.652367 + 0.376645i
\(727\) 2.44855 15.4595i 0.0908116 0.573362i −0.899762 0.436381i \(-0.856260\pi\)
0.990574 0.136981i \(-0.0437400\pi\)
\(728\) 2.65511 24.5919i 0.0984048 0.911436i
\(729\) −0.951057 0.309017i −0.0352243 0.0114451i
\(730\) 10.2505 + 13.5428i 0.379387 + 0.501242i
\(731\) 7.40552 34.8402i 0.273903 1.28861i
\(732\) −0.727136 + 0.194835i −0.0268757 + 0.00720132i
\(733\) −10.3205 + 0.540874i −0.381196 + 0.0199776i −0.241972 0.970283i \(-0.577794\pi\)
−0.139224 + 0.990261i \(0.544461\pi\)
\(734\) −9.27358 6.73765i −0.342294 0.248691i
\(735\) −3.84031 + 15.1741i −0.141652 + 0.559704i
\(736\) 20.3685 14.7986i 0.750793 0.545483i
\(737\) 32.6685 26.4544i 1.20336 0.974461i
\(738\) −1.88466 0.723454i −0.0693754 0.0266307i
\(739\) −14.5189 + 1.52599i −0.534085 + 0.0561346i −0.367732 0.929932i \(-0.619866\pi\)
−0.166353 + 0.986066i \(0.553199\pi\)
\(740\) 3.56465 3.70705i 0.131039 0.136274i
\(741\) 11.7422 16.1618i 0.431362 0.593719i
\(742\) −4.79316 8.35653i −0.175962 0.306778i
\(743\) 37.0008 37.0008i 1.35743 1.35743i 0.480356 0.877074i \(-0.340508\pi\)
0.877074 0.480356i \(-0.159492\pi\)
\(744\) 6.25476 + 5.63181i 0.229311 + 0.206472i
\(745\) −36.9228 3.15118i −1.35275 0.115450i
\(746\) 3.17439 + 3.52552i 0.116223 + 0.129078i
\(747\) 5.54003 8.53090i 0.202699 0.312129i
\(748\) −61.9689 9.81491i −2.26581 0.358869i
\(749\) −0.926649 + 16.7730i −0.0338590 + 0.612873i
\(750\) 0.406130 + 6.90576i 0.0148298 + 0.252163i
\(751\) −1.27155 2.20239i −0.0463996 0.0803665i 0.841893 0.539645i \(-0.181441\pi\)
−0.888292 + 0.459278i \(0.848108\pi\)
\(752\) −12.2901 9.95229i −0.448172 0.362923i
\(753\) 1.78613 + 0.0936073i 0.0650903 + 0.00341124i
\(754\) 2.50316 0.532062i 0.0911596 0.0193766i
\(755\) 20.4003 9.56569i 0.742441 0.348131i
\(756\) −3.01686 3.03399i −0.109722 0.110345i
\(757\) 5.33760 + 5.33760i 0.193998 + 0.193998i 0.797421 0.603423i \(-0.206197\pi\)
−0.603423 + 0.797421i \(0.706197\pi\)
\(758\) −0.766573 14.6271i −0.0278432 0.531279i
\(759\) −27.0838 + 12.0585i −0.983081 + 0.437696i
\(760\) 23.2349 + 5.74062i 0.842817 + 0.208234i
\(761\) −1.68928 + 3.79418i −0.0612363 + 0.137539i −0.941572 0.336813i \(-0.890651\pi\)
0.880335 + 0.474352i \(0.157318\pi\)
\(762\) −8.07268 + 1.27859i −0.292442 + 0.0463183i
\(763\) −18.7462 25.9561i −0.678659 0.939675i
\(764\) −3.90204 5.37070i −0.141171 0.194305i
\(765\) −12.9841 1.79663i −0.469440 0.0649572i
\(766\) −4.58803 10.3049i −0.165772 0.372331i
\(767\) −28.8156 44.3721i −1.04047 1.60218i
\(768\) −1.70745 + 6.37231i −0.0616125 + 0.229941i
\(769\) −14.6965 45.2313i −0.529971 1.63108i −0.754271 0.656563i \(-0.772010\pi\)
0.224300 0.974520i \(-0.427990\pi\)
\(770\) −24.1690 + 1.67299i −0.870989 + 0.0602904i
\(771\) 2.94572 9.06599i 0.106087 0.326504i
\(772\) 20.7049 + 13.4459i 0.745187 + 0.483930i
\(773\) −20.1258 + 24.8533i −0.723876 + 0.893912i −0.997694 0.0678692i \(-0.978380\pi\)
0.273818 + 0.961781i \(0.411713\pi\)
\(774\) 3.25589 + 1.87979i 0.117030 + 0.0675675i
\(775\) −18.6090 + 2.69612i −0.668453 + 0.0968474i
\(776\) 13.5407i 0.486083i
\(777\) 2.78919 + 2.52573i 0.100062 + 0.0906099i
\(778\) −0.382972 0.751625i −0.0137302 0.0269470i
\(779\) −3.24416 15.2626i −0.116234 0.546838i
\(780\) −14.7107 + 3.42922i −0.526729 + 0.122786i
\(781\) 27.0822 + 5.75649i 0.969077 + 0.205984i
\(782\) 15.6934 + 4.20504i 0.561196 + 0.150372i
\(783\) 0.449510 0.882212i 0.0160642 0.0315277i
\(784\) −3.93103 12.3356i −0.140394 0.440559i
\(785\) −1.71908 + 4.75458i −0.0613565 + 0.169698i
\(786\) −6.53500 2.90957i −0.233096 0.103781i
\(787\) 13.0339 33.9546i 0.464610 1.21035i −0.478565 0.878052i \(-0.658843\pi\)
0.943175 0.332298i \(-0.107824\pi\)
\(788\) 4.18155 10.8933i 0.148962 0.388058i
\(789\) 25.8761 + 11.5208i 0.921214 + 0.410151i
\(790\) −2.86068 0.0938039i −0.101779 0.00333739i
\(791\) −4.65203 + 1.77066i −0.165407 + 0.0629573i
\(792\) 6.72476 13.1981i 0.238954 0.468974i
\(793\) −1.87822 0.503268i −0.0666976 0.0178716i
\(794\) 11.1534 + 2.37073i 0.395820 + 0.0841341i
\(795\) −8.61183 + 9.94946i −0.305430 + 0.352871i
\(796\) 0.892251 + 4.19771i 0.0316250 + 0.148784i
\(797\) 8.89322 + 17.4539i 0.315014 + 0.618250i 0.993171 0.116667i \(-0.0372210\pi\)
−0.678157 + 0.734917i \(0.737221\pi\)
\(798\) −1.64939 + 7.65321i −0.0583879 + 0.270921i
\(799\) 50.1220i 1.77319i
\(800\) −16.2168 22.9516i −0.573352 0.811460i
\(801\) 9.47999 + 5.47328i 0.334959 + 0.193389i
\(802\) 7.80604 9.63966i 0.275641 0.340388i
\(803\) 68.1419 + 44.2519i 2.40467 + 1.56161i
\(804\) −3.17400 + 9.76857i −0.111938 + 0.344511i
\(805\) −26.4839 0.943476i −0.933437 0.0332532i
\(806\) 3.00356 + 9.24401i 0.105796 + 0.325607i
\(807\) 4.30411 16.0632i 0.151512 0.565450i
\(808\) −9.21945 14.1967i −0.324339 0.499438i
\(809\) −16.4027 36.8411i −0.576689 1.29526i −0.932656 0.360766i \(-0.882515\pi\)
0.355968 0.934498i \(-0.384151\pi\)
\(810\) 0.603856 1.24480i 0.0212173 0.0437379i
\(811\) 11.4849 + 15.8076i 0.403288 + 0.555078i 0.961565 0.274576i \(-0.0885375\pi\)
−0.558277 + 0.829654i \(0.688537\pi\)
\(812\) 3.43434 2.48037i 0.120522 0.0870441i
\(813\) 14.4275 2.28510i 0.505996 0.0801419i
\(814\) −2.36886 + 5.32056i −0.0830286 + 0.186485i
\(815\) 2.03311 + 28.2121i 0.0712167 + 0.988227i
\(816\) 9.90468 4.40985i 0.346733 0.154376i
\(817\) 1.52083 + 29.0191i 0.0532070 + 1.01525i
\(818\) −8.61873 8.61873i −0.301347 0.301347i
\(819\) −2.83020 10.6833i −0.0988951 0.373305i
\(820\) −5.69791 + 10.3311i −0.198980 + 0.360777i
\(821\) −38.9118 + 8.27097i −1.35803 + 0.288659i −0.828670 0.559737i \(-0.810902\pi\)
−0.529362 + 0.848396i \(0.677569\pi\)
\(822\) 6.94690 + 0.364072i 0.242301 + 0.0126985i
\(823\) 39.8019 + 32.2310i 1.38741 + 1.12350i 0.977395 + 0.211421i \(0.0678092\pi\)
0.410013 + 0.912080i \(0.365524\pi\)
\(824\) 14.3646 + 24.8802i 0.500414 + 0.866742i
\(825\) 13.0597 + 30.4062i 0.454679 + 1.05861i
\(826\) 17.3572 + 11.3419i 0.603933 + 0.394634i
\(827\) −5.11650 0.810375i −0.177918 0.0281795i 0.0668395 0.997764i \(-0.478708\pi\)
−0.244758 + 0.969584i \(0.578708\pi\)
\(828\) 3.94537 6.07533i 0.137111 0.211132i
\(829\) 14.3948 + 15.9870i 0.499952 + 0.555253i 0.939315 0.343057i \(-0.111462\pi\)
−0.439363 + 0.898310i \(0.644796\pi\)
\(830\) 10.6408 + 9.21027i 0.369349 + 0.319693i
\(831\) −8.73879 7.86844i −0.303145 0.272953i
\(832\) 0.654175 0.654175i 0.0226794 0.0226794i
\(833\) 22.5431 34.2868i 0.781071 1.18797i
\(834\) 7.33971 10.1022i 0.254153 0.349812i
\(835\) −7.13377 13.3481i −0.246874 0.461929i
\(836\) 50.9063 5.35047i 1.76063 0.185050i
\(837\) 3.51087 + 1.34770i 0.121353 + 0.0465832i
\(838\) 17.4362 14.1196i 0.602324 0.487752i
\(839\) 5.38271 3.91077i 0.185832 0.135015i −0.490980 0.871171i \(-0.663361\pi\)
0.676812 + 0.736156i \(0.263361\pi\)
\(840\) 10.5800 7.96097i 0.365046 0.274680i
\(841\) −22.6684 16.4695i −0.781668 0.567915i
\(842\) −19.2131 + 1.00691i −0.662126 + 0.0347005i
\(843\) 28.3437 7.59466i 0.976208 0.261574i
\(844\) 4.21233 19.8174i 0.144994 0.682145i
\(845\) −9.51976 2.88835i −0.327490 0.0993622i
\(846\) 5.03149 + 1.63483i 0.172986 + 0.0562067i
\(847\) −79.3868 + 35.0764i −2.72776 + 1.20524i
\(848\) 1.70268 10.7503i 0.0584701 0.369166i
\(849\) 17.5692 10.1436i 0.602973 0.348127i
\(850\) 4.92448 17.4537i 0.168908 0.598656i
\(851\) −3.18537 + 5.51721i −0.109193 + 0.189128i
\(852\) −6.31581 + 2.42441i −0.216376 + 0.0830591i
\(853\) 35.7278 18.2042i 1.22330 0.623301i 0.281526 0.959554i \(-0.409160\pi\)
0.941772 + 0.336252i \(0.109160\pi\)
\(854\) 0.752983 0.117077i 0.0257665 0.00400629i
\(855\) 10.6113 1.32583i 0.362899 0.0453423i
\(856\) 9.50844 10.5602i 0.324992 0.360940i
\(857\) 8.41953 + 31.4221i 0.287606 + 1.07336i 0.946914 + 0.321487i \(0.104182\pi\)
−0.659308 + 0.751873i \(0.729151\pi\)
\(858\) 14.3463 9.31657i 0.489773 0.318062i
\(859\) −5.09356 + 48.4620i −0.173790 + 1.65350i 0.465877 + 0.884849i \(0.345739\pi\)
−0.639667 + 0.768652i \(0.720928\pi\)
\(860\) 13.4905 17.3430i 0.460023 0.591392i
\(861\) −7.68029 3.94072i −0.261743 0.134299i
\(862\) −2.40989 15.2154i −0.0820812 0.518240i
\(863\) −10.8840 13.4406i −0.370496 0.457524i 0.557466 0.830200i \(-0.311774\pi\)
−0.927962 + 0.372676i \(0.878440\pi\)
\(864\) 0.587505 + 5.58974i 0.0199873 + 0.190167i
\(865\) −4.21477 + 17.0591i −0.143306 + 0.580025i
\(866\) −17.1012 1.79741i −0.581121 0.0610783i
\(867\) 15.4703 + 7.88252i 0.525399 + 0.267704i
\(868\) 10.7327 + 11.9879i 0.364291 + 0.406896i
\(869\) −13.0219 + 4.23107i −0.441738 + 0.143529i
\(870\) 1.12381 + 0.783343i 0.0381007 + 0.0265578i
\(871\) −19.7165 + 17.7528i −0.668067 + 0.601531i
\(872\) −1.41748 + 27.0472i −0.0480020 + 0.915932i
\(873\) −2.16819 5.64832i −0.0733820 0.191167i
\(874\) −13.2549 −0.448355
\(875\) −1.44317 + 29.5452i −0.0487881 + 0.998809i
\(876\) −19.8528 −0.670763
\(877\) 10.9424 + 28.5059i 0.369498 + 0.962575i 0.984708 + 0.174212i \(0.0557377\pi\)
−0.615210 + 0.788363i \(0.710929\pi\)
\(878\) −0.905072 + 17.2698i −0.0305447 + 0.582828i
\(879\) −15.9386 + 14.3512i −0.537597 + 0.484055i
\(880\) −22.4552 15.6522i −0.756965 0.527636i
\(881\) −16.5890 + 5.39011i −0.558899 + 0.181597i −0.574826 0.818276i \(-0.694930\pi\)
0.0159268 + 0.999873i \(0.494930\pi\)
\(882\) 2.70659 + 3.38132i 0.0911356 + 0.113855i
\(883\) −25.3451 12.9140i −0.852932 0.434591i −0.0278558 0.999612i \(-0.508868\pi\)
−0.825076 + 0.565021i \(0.808868\pi\)
\(884\) 39.3820 + 4.13922i 1.32456 + 0.139217i
\(885\) 6.79314 27.4949i 0.228349 0.924231i
\(886\) 1.36763 + 13.0122i 0.0459465 + 0.437152i
\(887\) −26.5385 32.7723i −0.891074 1.10039i −0.994394 0.105737i \(-0.966280\pi\)
0.103320 0.994648i \(-0.467053\pi\)
\(888\) −0.497934 3.14383i −0.0167096 0.105500i
\(889\) −34.9066 + 1.73032i −1.17073 + 0.0580331i
\(890\) −9.29876 + 11.9542i −0.311695 + 0.400706i
\(891\) 0.691816 6.58219i 0.0231767 0.220512i
\(892\) 6.60255 4.28775i 0.221070 0.143564i
\(893\) 10.5835 + 39.4981i 0.354162 + 1.32175i
\(894\) −6.86123 + 7.62017i −0.229474 + 0.254856i
\(895\) −22.3323 + 2.79030i −0.746486 + 0.0932695i
\(896\) −10.8677 + 28.0735i −0.363063 + 0.937870i
\(897\) 16.6721 8.49486i 0.556665 0.283635i
\(898\) 10.6471 4.08705i 0.355299 0.136387i
\(899\) −1.86177 + 3.22467i −0.0620934 + 0.107549i
\(900\) −6.72263 4.49297i −0.224088 0.149766i
\(901\) 29.8750 17.2483i 0.995280 0.574625i
\(902\) 2.09012 13.1965i 0.0695932 0.439394i
\(903\) 12.9791 + 9.48609i 0.431916 + 0.315677i
\(904\) 4.00454 + 1.30115i 0.133189 + 0.0432757i
\(905\) −32.1908 9.76686i −1.07006 0.324661i
\(906\) 1.29626 6.09842i 0.0430653 0.202606i
\(907\) −35.4711 + 9.50446i −1.17780 + 0.315590i −0.794053 0.607848i \(-0.792033\pi\)
−0.383746 + 0.923439i \(0.625366\pi\)
\(908\) −11.3899 + 0.596921i −0.377988 + 0.0198095i
\(909\) −6.11899 4.44571i −0.202954 0.147455i
\(910\) 15.1780 1.85279i 0.503144 0.0614195i
\(911\) −43.0675 + 31.2904i −1.42689 + 1.03670i −0.436304 + 0.899799i \(0.643713\pi\)
−0.990585 + 0.136897i \(0.956287\pi\)
\(912\) −6.87411 + 5.56654i −0.227624 + 0.184327i
\(913\) 62.8509 + 24.1262i 2.08006 + 0.798460i
\(914\) −5.35349 + 0.562674i −0.177078 + 0.0186116i
\(915\) −0.490620 0.918004i −0.0162194 0.0303483i
\(916\) 14.9283 20.5470i 0.493244 0.678892i
\(917\) −26.4471 15.3692i −0.873359 0.507535i
\(918\) −2.56469 + 2.56469i −0.0846474 + 0.0846474i
\(919\) −43.2414 38.9347i −1.42640 1.28434i −0.901231 0.433339i \(-0.857335\pi\)
−0.525170 0.850997i \(-0.675998\pi\)
\(920\) 16.9498 + 14.6710i 0.558819 + 0.483690i
\(921\) −5.64297 6.26715i −0.185942 0.206510i
\(922\) 7.20770 11.0989i 0.237373 0.365522i
\(923\) −17.2595 2.73364i −0.568104 0.0899788i
\(924\) 15.4901 23.7055i 0.509588 0.779855i
\(925\) 6.11091 + 3.63650i 0.200925 + 0.119567i
\(926\) 4.56778 + 7.91163i 0.150107 + 0.259992i
\(927\) 9.97588 + 8.07831i 0.327651 + 0.265326i
\(928\) −5.55743 0.291253i −0.182432 0.00956083i
\(929\) −21.4555 + 4.56051i −0.703933 + 0.149626i −0.545952 0.837816i \(-0.683832\pi\)
−0.157981 + 0.987442i \(0.550499\pi\)
\(930\) −2.51278 + 4.55600i −0.0823972 + 0.149397i
\(931\) −10.5250 + 31.7794i −0.344943 + 1.04153i
\(932\) −20.3601 20.3601i −0.666917 0.666917i
\(933\) 0.613154 + 11.6997i 0.0200738 + 0.383030i
\(934\) −0.960471 + 0.427629i −0.0314276 + 0.0139925i
\(935\) −6.23570 86.5287i −0.203929 2.82979i
\(936\) −3.80253 + 8.54063i −0.124290 + 0.279159i
\(937\) 42.6186 6.75013i 1.39229 0.220517i 0.585173 0.810908i \(-0.301027\pi\)
0.807117 + 0.590391i \(0.201027\pi\)
\(938\) 4.25588 9.48650i 0.138959 0.309745i
\(939\) 6.54724 + 9.01150i 0.213661 + 0.294079i
\(940\) 13.4948 27.8185i 0.440152 0.907339i
\(941\) −9.07887 20.3915i −0.295963 0.664743i 0.702956 0.711233i \(-0.251863\pi\)
−0.998919 + 0.0464904i \(0.985196\pi\)
\(942\) 0.761939 + 1.17328i 0.0248253 + 0.0382277i
\(943\) 3.78265 14.1170i 0.123180 0.459714i
\(944\) 7.23906 + 22.2795i 0.235611 + 0.725138i
\(945\) 3.13857 5.01492i 0.102098 0.163135i
\(946\) −7.68912 + 23.6647i −0.249995 + 0.769405i
\(947\) −14.3244 9.30237i −0.465480 0.302287i 0.290507 0.956873i \(-0.406176\pi\)
−0.755987 + 0.654586i \(0.772843\pi\)
\(948\) 2.10542 2.59997i 0.0683808 0.0844433i
\(949\) −44.4102 25.6402i −1.44162 0.832318i
\(950\) −0.195263 + 14.7940i −0.00633518 + 0.479980i
\(951\) 4.93746i 0.160108i
\(952\) −33.0424 + 10.6328i −1.07091 + 0.344611i
\(953\) −10.8402 21.2750i −0.351148 0.689166i 0.646104 0.763249i \(-0.276397\pi\)
−0.997252 + 0.0740830i \(0.976397\pi\)
\(954\) 0.757038 + 3.56159i 0.0245100 + 0.115311i
\(955\) 6.00733 6.94041i 0.194393 0.224586i
\(956\) −6.79916 1.44521i −0.219901 0.0467413i
\(957\) 6.32983 + 1.69607i 0.204614 + 0.0548262i
\(958\) 4.10977 8.06587i 0.132781 0.260596i
\(959\) 29.3666 + 4.73645i 0.948296 + 0.152948i
\(960\) 0.494966 + 0.0162303i 0.0159749 + 0.000523830i
\(961\) 15.4001 + 6.85657i 0.496777 + 0.221180i
\(962\) 1.31730 3.43169i 0.0424715 0.110642i
\(963\) 2.27538 5.92756i 0.0733230 0.191013i
\(964\) −21.3944 9.52542i −0.689069 0.306793i
\(965\) −11.6069 + 32.1022i −0.373641 + 1.03341i
\(966\) −4.63089 + 5.68569i −0.148996 + 0.182934i
\(967\) −6.31131 + 12.3866i −0.202958 + 0.398327i −0.969941 0.243340i \(-0.921757\pi\)
0.766983 + 0.641667i \(0.221757\pi\)
\(968\) 70.9156 + 19.0018i 2.27932 + 0.610741i
\(969\) −27.4218 5.82868i −0.880914 0.187244i
\(970\) 8.15207 1.90033i 0.261747 0.0610160i
\(971\) −4.84450 22.7916i −0.155468 0.731417i −0.984944 0.172875i \(-0.944694\pi\)
0.829476 0.558542i \(-0.188639\pi\)
\(972\) 0.734177 + 1.44090i 0.0235488 + 0.0462170i
\(973\) 35.8406 39.5792i 1.14900 1.26885i
\(974\) 21.5859i 0.691658i
\(975\) −9.23562 18.7331i −0.295777 0.599939i
\(976\) 0.745615 + 0.430481i 0.0238665 + 0.0137794i
\(977\) 25.7899 31.8479i 0.825092 1.01890i −0.174322 0.984689i \(-0.555773\pi\)
0.999414 0.0342153i \(-0.0108932\pi\)
\(978\) 6.56406 + 4.26275i 0.209896 + 0.136308i
\(979\) −22.3880 + 68.9032i −0.715524 + 2.20216i
\(980\) 21.7431 12.9602i 0.694557 0.413999i
\(981\) 3.73960 + 11.5093i 0.119396 + 0.367464i
\(982\) −0.206892 + 0.772133i −0.00660220 + 0.0246398i
\(983\) 5.58248 + 8.59626i 0.178053 + 0.274178i 0.916417 0.400224i \(-0.131068\pi\)
−0.738364 + 0.674403i \(0.764401\pi\)
\(984\) 2.97005 + 6.67084i 0.0946817 + 0.212659i
\(985\) 15.9816 + 2.21141i 0.509217 + 0.0704612i
\(986\) −2.11087 2.90536i −0.0672237 0.0925254i
\(987\) 20.6402 + 9.25971i 0.656986 + 0.294740i
\(988\) −31.9085 + 5.05382i −1.01515 + 0.160783i
\(989\) −11.0706 + 24.8649i −0.352024 + 0.790658i
\(990\) 8.88956 + 2.19634i 0.282529 + 0.0698042i
\(991\) 46.6528 20.7712i 1.48197 0.659817i 0.503090 0.864234i \(-0.332196\pi\)
0.978884 + 0.204417i \(0.0655297\pi\)
\(992\) −1.10622 21.1079i −0.0351224 0.670176i
\(993\) −7.11972 7.11972i −0.225937 0.225937i
\(994\) 6.61987 1.75372i 0.209970 0.0556247i
\(995\) −5.37257 + 2.51920i −0.170322 + 0.0798641i
\(996\) −16.0902 + 3.42008i −0.509839 + 0.108370i
\(997\) −45.6488 2.39235i −1.44571 0.0757665i −0.686746 0.726898i \(-0.740961\pi\)
−0.758965 + 0.651131i \(0.774295\pi\)
\(998\) −9.38570 7.60039i −0.297099 0.240586i
\(999\) −0.711107 1.23167i −0.0224984 0.0389684i
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 525.2.bv.a.52.16 640
7.5 odd 6 inner 525.2.bv.a.502.16 yes 640
25.13 odd 20 inner 525.2.bv.a.388.16 yes 640
175.138 even 60 inner 525.2.bv.a.313.16 yes 640
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
525.2.bv.a.52.16 640 1.1 even 1 trivial
525.2.bv.a.313.16 yes 640 175.138 even 60 inner
525.2.bv.a.388.16 yes 640 25.13 odd 20 inner
525.2.bv.a.502.16 yes 640 7.5 odd 6 inner