Properties

Label 177.2.e.b.19.2
Level $177$
Weight $2$
Character 177.19
Analytic conductor $1.413$
Analytic rank $0$
Dimension $140$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [177,2,Mod(4,177)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(177, base_ring=CyclotomicField(58))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("177.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 177.e (of order \(29\), degree \(28\), 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: \(1.41335211578\)
Analytic rank: \(0\)
Dimension: \(140\)
Relative dimension: \(5\) over \(\Q(\zeta_{29})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label 19.2
Character \(\chi\) \(=\) 177.19
Dual form 177.2.e.b.28.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.715981 + 1.35048i) q^{2} +(0.725995 - 0.687699i) q^{3} +(-0.188804 - 0.278465i) q^{4} +(-3.13782 + 0.690687i) q^{5} +(0.408928 + 1.47283i) q^{6} +(-2.11659 + 1.60899i) q^{7} +(-2.52792 + 0.274928i) q^{8} +(0.0541389 - 0.998533i) q^{9} +O(q^{10})\) \(q+(-0.715981 + 1.35048i) q^{2} +(0.725995 - 0.687699i) q^{3} +(-0.188804 - 0.278465i) q^{4} +(-3.13782 + 0.690687i) q^{5} +(0.408928 + 1.47283i) q^{6} +(-2.11659 + 1.60899i) q^{7} +(-2.52792 + 0.274928i) q^{8} +(0.0541389 - 0.998533i) q^{9} +(1.31386 - 4.73210i) q^{10} +(2.12945 + 5.34452i) q^{11} +(-0.328571 - 0.0723240i) q^{12} +(0.173941 + 3.20816i) q^{13} +(-0.657476 - 4.01043i) q^{14} +(-1.80306 + 2.65931i) q^{15} +(1.68771 - 4.23584i) q^{16} +(-1.99184 - 1.51416i) q^{17} +(1.30974 + 0.788045i) q^{18} +(5.97573 - 2.01346i) q^{19} +(0.784766 + 0.743370i) q^{20} +(-0.430133 + 2.62370i) q^{21} +(-8.74234 - 0.950787i) q^{22} +(0.758390 - 0.456308i) q^{23} +(-1.64619 + 1.93804i) q^{24} +(4.83101 - 2.23506i) q^{25} +(-4.45711 - 2.06208i) q^{26} +(-0.647386 - 0.762162i) q^{27} +(0.847668 + 0.285613i) q^{28} +(-1.90564 - 3.59442i) q^{29} +(-2.30041 - 4.33902i) q^{30} +(-4.32032 - 1.45569i) q^{31} +(1.21969 + 1.43593i) q^{32} +(5.22140 + 2.41568i) q^{33} +(3.47096 - 1.60584i) q^{34} +(5.53017 - 6.51062i) q^{35} +(-0.288278 + 0.173451i) q^{36} +(2.35133 + 0.255722i) q^{37} +(-1.55937 + 9.51173i) q^{38} +(2.33253 + 2.20949i) q^{39} +(7.74227 - 2.60867i) q^{40} +(10.8057 + 6.50154i) q^{41} +(-3.23529 - 2.45941i) q^{42} +(-2.62049 + 6.57694i) q^{43} +(1.08621 - 1.60205i) q^{44} +(0.519796 + 3.17061i) q^{45} +(0.0732438 + 1.35090i) q^{46} +(5.95006 + 1.30971i) q^{47} +(-1.68771 - 4.23584i) q^{48} +(0.0184038 - 0.0662845i) q^{49} +(-0.440496 + 8.12446i) q^{50} +(-2.48735 + 0.270516i) q^{51} +(0.860520 - 0.654150i) q^{52} +(0.313289 + 1.12836i) q^{53} +(1.49280 - 0.328591i) q^{54} +(-10.3732 - 15.2994i) q^{55} +(4.90821 - 4.64930i) q^{56} +(2.95370 - 5.57127i) q^{57} +6.21861 q^{58} +(6.29895 + 4.39582i) q^{59} +1.08095 q^{60} +(-2.55277 + 4.81504i) q^{61} +(5.05915 - 4.79229i) q^{62} +(1.49204 + 2.20059i) q^{63} +(6.09370 - 1.34132i) q^{64} +(-2.76163 - 9.94650i) q^{65} +(-7.00076 + 5.32184i) q^{66} +(-10.5176 + 1.14386i) q^{67} +(-0.0455726 + 0.840537i) q^{68} +(0.236785 - 0.852822i) q^{69} +(4.83299 + 12.1299i) q^{70} +(-15.0332 - 3.30905i) q^{71} +(0.137666 + 2.53909i) q^{72} +(0.660634 + 4.02969i) q^{73} +(-2.02886 + 2.99234i) q^{74} +(1.97024 - 4.94493i) q^{75} +(-1.68892 - 1.28388i) q^{76} +(-13.1065 - 7.88589i) q^{77} +(-4.65393 + 1.56809i) q^{78} +(3.08523 + 2.92248i) q^{79} +(-2.37010 + 14.4570i) q^{80} +(-0.994138 - 0.108119i) q^{81} +(-16.5169 + 9.93788i) q^{82} +(9.62052 - 11.3262i) q^{83} +(0.811819 - 0.375587i) q^{84} +(7.29585 + 3.37542i) q^{85} +(-7.00583 - 8.24790i) q^{86} +(-3.85536 - 1.29902i) q^{87} +(-6.85244 - 12.9251i) q^{88} +(-1.38141 - 2.60561i) q^{89} +(-4.65403 - 1.56812i) q^{90} +(-5.53005 - 6.51048i) q^{91} +(-0.270253 - 0.125032i) q^{92} +(-4.13761 + 1.91426i) q^{93} +(-6.02887 + 7.09774i) q^{94} +(-17.3601 + 10.4452i) q^{95} +(1.87297 + 0.203698i) q^{96} +(-1.59285 + 9.71594i) q^{97} +(0.0763394 + 0.0723125i) q^{98} +(5.45197 - 1.83698i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 140 q + q^{2} + 5 q^{3} - q^{4} + 2 q^{5} - q^{6} - 2 q^{7} - 3 q^{8} - 5 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 140 q + q^{2} + 5 q^{3} - q^{4} + 2 q^{5} - q^{6} - 2 q^{7} - 3 q^{8} - 5 q^{9} - 116 q^{10} + 2 q^{11} + q^{12} + 4 q^{13} - 43 q^{14} - 2 q^{15} + 7 q^{16} + q^{18} - 2 q^{19} + 4 q^{20} - 27 q^{21} + 6 q^{22} + 6 q^{23} + 3 q^{24} - 57 q^{25} + 12 q^{26} + 5 q^{27} - 10 q^{28} - 4 q^{29} - 12 q^{31} - 150 q^{32} - 2 q^{33} - 2 q^{34} + 6 q^{35} - q^{36} + 12 q^{37} - 12 q^{38} - 4 q^{39} - 66 q^{40} - 4 q^{41} + 14 q^{42} - 60 q^{43} + 20 q^{44} + 2 q^{45} + 76 q^{46} - 25 q^{47} - 7 q^{48} + 31 q^{49} + 137 q^{50} + 118 q^{52} + 48 q^{53} - q^{54} + 93 q^{55} + 228 q^{56} + 2 q^{57} - 120 q^{58} + 57 q^{59} - 4 q^{60} + 72 q^{61} - 179 q^{62} - 2 q^{63} + 249 q^{64} - 39 q^{65} - 6 q^{66} + 40 q^{67} + 94 q^{68} - 64 q^{69} + 94 q^{70} + 30 q^{71} - 3 q^{72} - 205 q^{73} + 66 q^{74} - q^{75} - 216 q^{76} - 46 q^{77} - 12 q^{78} + 4 q^{79} - 356 q^{80} - 5 q^{81} - 28 q^{82} + 4 q^{83} - 135 q^{84} + 50 q^{85} - 18 q^{86} - 54 q^{87} - 162 q^{88} + 26 q^{89} - 198 q^{91} + 10 q^{92} + 12 q^{93} - 4 q^{94} - 326 q^{95} + 5 q^{96} - 20 q^{97} - 143 q^{98} + 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).

\(n\) \(61\) \(119\)
\(\chi(n)\) \(e\left(\frac{19}{29}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.715981 + 1.35048i −0.506275 + 0.954937i 0.490245 + 0.871585i \(0.336907\pi\)
−0.996520 + 0.0833518i \(0.973437\pi\)
\(3\) 0.725995 0.687699i 0.419154 0.397043i
\(4\) −0.188804 0.278465i −0.0944021 0.139233i
\(5\) −3.13782 + 0.690687i −1.40328 + 0.308885i −0.851171 0.524889i \(-0.824107\pi\)
−0.552106 + 0.833774i \(0.686176\pi\)
\(6\) 0.408928 + 1.47283i 0.166944 + 0.601278i
\(7\) −2.11659 + 1.60899i −0.799995 + 0.608141i −0.923235 0.384236i \(-0.874465\pi\)
0.123239 + 0.992377i \(0.460672\pi\)
\(8\) −2.52792 + 0.274928i −0.893754 + 0.0972016i
\(9\) 0.0541389 0.998533i 0.0180463 0.332844i
\(10\) 1.31386 4.73210i 0.415479 1.49642i
\(11\) 2.12945 + 5.34452i 0.642054 + 1.61143i 0.783431 + 0.621479i \(0.213468\pi\)
−0.141377 + 0.989956i \(0.545153\pi\)
\(12\) −0.328571 0.0723240i −0.0948504 0.0208781i
\(13\) 0.173941 + 3.20816i 0.0482426 + 0.889783i 0.918068 + 0.396423i \(0.129749\pi\)
−0.869825 + 0.493360i \(0.835769\pi\)
\(14\) −0.657476 4.01043i −0.175718 1.07183i
\(15\) −1.80306 + 2.65931i −0.465548 + 0.686632i
\(16\) 1.68771 4.23584i 0.421928 1.05896i
\(17\) −1.99184 1.51416i −0.483092 0.367237i 0.335100 0.942183i \(-0.391230\pi\)
−0.818192 + 0.574946i \(0.805023\pi\)
\(18\) 1.30974 + 0.788045i 0.308709 + 0.185744i
\(19\) 5.97573 2.01346i 1.37093 0.461919i 0.464984 0.885319i \(-0.346060\pi\)
0.905943 + 0.423400i \(0.139164\pi\)
\(20\) 0.784766 + 0.743370i 0.175479 + 0.166223i
\(21\) −0.430133 + 2.62370i −0.0938627 + 0.572537i
\(22\) −8.74234 0.950787i −1.86387 0.202709i
\(23\) 0.758390 0.456308i 0.158135 0.0951468i −0.434287 0.900775i \(-0.642999\pi\)
0.592422 + 0.805628i \(0.298172\pi\)
\(24\) −1.64619 + 1.93804i −0.336027 + 0.395602i
\(25\) 4.83101 2.23506i 0.966201 0.447012i
\(26\) −4.45711 2.06208i −0.874111 0.404407i
\(27\) −0.647386 0.762162i −0.124590 0.146678i
\(28\) 0.847668 + 0.285613i 0.160194 + 0.0539757i
\(29\) −1.90564 3.59442i −0.353868 0.667466i 0.641122 0.767439i \(-0.278469\pi\)
−0.994990 + 0.0999726i \(0.968124\pi\)
\(30\) −2.30041 4.33902i −0.419995 0.792194i
\(31\) −4.32032 1.45569i −0.775953 0.261449i −0.0966614 0.995317i \(-0.530816\pi\)
−0.679292 + 0.733868i \(0.737713\pi\)
\(32\) 1.21969 + 1.43593i 0.215612 + 0.253838i
\(33\) 5.22140 + 2.41568i 0.908929 + 0.420515i
\(34\) 3.47096 1.60584i 0.595266 0.275399i
\(35\) 5.53017 6.51062i 0.934770 1.10050i
\(36\) −0.288278 + 0.173451i −0.0480464 + 0.0289086i
\(37\) 2.35133 + 0.255722i 0.386556 + 0.0420405i 0.299334 0.954148i \(-0.403236\pi\)
0.0872221 + 0.996189i \(0.472201\pi\)
\(38\) −1.55937 + 9.51173i −0.252963 + 1.54301i
\(39\) 2.33253 + 2.20949i 0.373504 + 0.353802i
\(40\) 7.74227 2.60867i 1.22416 0.412468i
\(41\) 10.8057 + 6.50154i 1.68756 + 1.01537i 0.933509 + 0.358553i \(0.116730\pi\)
0.754050 + 0.656817i \(0.228098\pi\)
\(42\) −3.23529 2.45941i −0.499216 0.379494i
\(43\) −2.62049 + 6.57694i −0.399621 + 1.00297i 0.582179 + 0.813060i \(0.302200\pi\)
−0.981801 + 0.189914i \(0.939179\pi\)
\(44\) 1.08621 1.60205i 0.163753 0.241518i
\(45\) 0.519796 + 3.17061i 0.0774866 + 0.472647i
\(46\) 0.0732438 + 1.35090i 0.0107992 + 0.199180i
\(47\) 5.95006 + 1.30971i 0.867906 + 0.191041i 0.626536 0.779393i \(-0.284472\pi\)
0.241370 + 0.970433i \(0.422403\pi\)
\(48\) −1.68771 4.23584i −0.243600 0.611391i
\(49\) 0.0184038 0.0662845i 0.00262911 0.00946921i
\(50\) −0.440496 + 8.12446i −0.0622955 + 1.14897i
\(51\) −2.48735 + 0.270516i −0.348299 + 0.0378798i
\(52\) 0.860520 0.654150i 0.119333 0.0907143i
\(53\) 0.313289 + 1.12836i 0.0430336 + 0.154993i 0.981945 0.189165i \(-0.0605782\pi\)
−0.938912 + 0.344158i \(0.888164\pi\)
\(54\) 1.49280 0.328591i 0.203145 0.0447156i
\(55\) −10.3732 15.2994i −1.39873 2.06297i
\(56\) 4.90821 4.64930i 0.655887 0.621289i
\(57\) 2.95370 5.57127i 0.391227 0.737932i
\(58\) 6.21861 0.816543
\(59\) 6.29895 + 4.39582i 0.820053 + 0.572287i
\(60\) 1.08095 0.139550
\(61\) −2.55277 + 4.81504i −0.326849 + 0.616503i −0.991419 0.130723i \(-0.958270\pi\)
0.664570 + 0.747226i \(0.268615\pi\)
\(62\) 5.05915 4.79229i 0.642513 0.608621i
\(63\) 1.49204 + 2.20059i 0.187979 + 0.277249i
\(64\) 6.09370 1.34132i 0.761712 0.167665i
\(65\) −2.76163 9.94650i −0.342538 1.23371i
\(66\) −7.00076 + 5.32184i −0.861734 + 0.655073i
\(67\) −10.5176 + 1.14386i −1.28493 + 0.139744i −0.724972 0.688779i \(-0.758147\pi\)
−0.559955 + 0.828523i \(0.689182\pi\)
\(68\) −0.0455726 + 0.840537i −0.00552649 + 0.101930i
\(69\) 0.236785 0.852822i 0.0285056 0.102668i
\(70\) 4.83299 + 12.1299i 0.577653 + 1.44980i
\(71\) −15.0332 3.30905i −1.78411 0.392713i −0.804554 0.593880i \(-0.797596\pi\)
−0.979557 + 0.201167i \(0.935527\pi\)
\(72\) 0.137666 + 2.53909i 0.0162241 + 0.299235i
\(73\) 0.660634 + 4.02969i 0.0773214 + 0.471640i 0.996896 + 0.0787250i \(0.0250849\pi\)
−0.919575 + 0.392915i \(0.871467\pi\)
\(74\) −2.02886 + 2.99234i −0.235850 + 0.347852i
\(75\) 1.97024 4.94493i 0.227504 0.570991i
\(76\) −1.68892 1.28388i −0.193732 0.147272i
\(77\) −13.1065 7.88589i −1.49362 0.898681i
\(78\) −4.65393 + 1.56809i −0.526954 + 0.177551i
\(79\) 3.08523 + 2.92248i 0.347115 + 0.328805i 0.841317 0.540542i \(-0.181781\pi\)
−0.494201 + 0.869347i \(0.664539\pi\)
\(80\) −2.37010 + 14.4570i −0.264986 + 1.61634i
\(81\) −0.994138 0.108119i −0.110460 0.0120132i
\(82\) −16.5169 + 9.93788i −1.82398 + 1.09745i
\(83\) 9.62052 11.3262i 1.05599 1.24321i 0.0869734 0.996211i \(-0.472280\pi\)
0.969016 0.246997i \(-0.0794436\pi\)
\(84\) 0.811819 0.375587i 0.0885767 0.0409799i
\(85\) 7.29585 + 3.37542i 0.791346 + 0.366116i
\(86\) −7.00583 8.24790i −0.755458 0.889394i
\(87\) −3.85536 1.29902i −0.413338 0.139270i
\(88\) −6.85244 12.9251i −0.730472 1.37782i
\(89\) −1.38141 2.60561i −0.146429 0.276194i 0.799438 0.600748i \(-0.205131\pi\)
−0.945867 + 0.324554i \(0.894786\pi\)
\(90\) −4.65403 1.56812i −0.490578 0.165295i
\(91\) −5.53005 6.51048i −0.579707 0.682484i
\(92\) −0.270253 0.125032i −0.0281758 0.0130355i
\(93\) −4.13761 + 1.91426i −0.429050 + 0.198500i
\(94\) −6.02887 + 7.09774i −0.621831 + 0.732076i
\(95\) −17.3601 + 10.4452i −1.78111 + 1.07166i
\(96\) 1.87297 + 0.203698i 0.191159 + 0.0207898i
\(97\) −1.59285 + 9.71594i −0.161729 + 0.986504i 0.773845 + 0.633375i \(0.218331\pi\)
−0.935574 + 0.353129i \(0.885118\pi\)
\(98\) 0.0763394 + 0.0723125i 0.00771144 + 0.00730467i
\(99\) 5.45197 1.83698i 0.547944 0.184624i
\(100\) −1.53450 0.923279i −0.153450 0.0923279i
\(101\) 6.53457 + 4.96745i 0.650214 + 0.494280i 0.877518 0.479544i \(-0.159198\pi\)
−0.227304 + 0.973824i \(0.572991\pi\)
\(102\) 1.41557 3.55281i 0.140162 0.351781i
\(103\) 6.36057 9.38113i 0.626725 0.924350i −0.373269 0.927723i \(-0.621763\pi\)
0.999994 + 0.00337270i \(0.00107357\pi\)
\(104\) −1.32172 8.06214i −0.129605 0.790558i
\(105\) −0.462471 8.52978i −0.0451326 0.832421i
\(106\) −1.74815 0.384797i −0.169795 0.0373747i
\(107\) 2.13579 + 5.36043i 0.206475 + 0.518212i 0.995348 0.0963433i \(-0.0307147\pi\)
−0.788874 + 0.614556i \(0.789335\pi\)
\(108\) −0.0900064 + 0.324174i −0.00866087 + 0.0311936i
\(109\) −0.219489 + 4.04823i −0.0210232 + 0.387750i 0.969020 + 0.246984i \(0.0794394\pi\)
−0.990043 + 0.140766i \(0.955043\pi\)
\(110\) 28.0886 3.05482i 2.67815 0.291266i
\(111\) 1.88291 1.43135i 0.178718 0.135858i
\(112\) 3.24323 + 11.6810i 0.306456 + 1.10375i
\(113\) 8.11910 1.78715i 0.763780 0.168121i 0.184036 0.982919i \(-0.441084\pi\)
0.579744 + 0.814799i \(0.303153\pi\)
\(114\) 5.40912 + 7.97785i 0.506610 + 0.747194i
\(115\) −2.06453 + 1.95562i −0.192518 + 0.182363i
\(116\) −0.641128 + 1.20929i −0.0595272 + 0.112280i
\(117\) 3.21287 0.297030
\(118\) −10.4464 + 5.35931i −0.961671 + 0.493364i
\(119\) 6.65217 0.609803
\(120\) 3.82687 7.21824i 0.349344 0.658932i
\(121\) −16.0434 + 15.1971i −1.45849 + 1.38156i
\(122\) −4.67490 6.89496i −0.423245 0.624240i
\(123\) 12.3160 2.71095i 1.11049 0.244438i
\(124\) 0.410337 + 1.47790i 0.0368493 + 0.132719i
\(125\) −0.826122 + 0.628002i −0.0738906 + 0.0561702i
\(126\) −4.04014 + 0.439392i −0.359924 + 0.0391441i
\(127\) 0.308049 5.68164i 0.0273350 0.504164i −0.952523 0.304467i \(-0.901522\pi\)
0.979858 0.199697i \(-0.0639956\pi\)
\(128\) −3.55959 + 12.8205i −0.314626 + 1.13318i
\(129\) 2.62049 + 6.57694i 0.230721 + 0.579067i
\(130\) 15.4099 + 3.39197i 1.35153 + 0.297495i
\(131\) −0.723818 13.3500i −0.0632402 1.16640i −0.842144 0.539253i \(-0.818706\pi\)
0.778903 0.627144i \(-0.215776\pi\)
\(132\) −0.313140 1.91007i −0.0272553 0.166250i
\(133\) −9.40853 + 13.8765i −0.815823 + 1.20325i
\(134\) 5.98563 15.0228i 0.517080 1.29777i
\(135\) 2.55780 + 1.94439i 0.220140 + 0.167346i
\(136\) 5.45149 + 3.28005i 0.467461 + 0.281262i
\(137\) −19.0293 + 6.41173i −1.62578 + 0.547791i −0.977011 0.213190i \(-0.931615\pi\)
−0.648774 + 0.760981i \(0.724718\pi\)
\(138\) 0.982189 + 0.930379i 0.0836095 + 0.0791991i
\(139\) 2.56916 15.6712i 0.217914 1.32921i −0.620512 0.784197i \(-0.713075\pi\)
0.838425 0.545017i \(-0.183477\pi\)
\(140\) −2.85710 0.310728i −0.241469 0.0262614i
\(141\) 5.22040 3.14101i 0.439637 0.264521i
\(142\) 15.2323 17.9329i 1.27827 1.50489i
\(143\) −16.7757 + 7.76126i −1.40285 + 0.649029i
\(144\) −4.13826 1.91456i −0.344855 0.159547i
\(145\) 8.46218 + 9.96244i 0.702745 + 0.827336i
\(146\) −5.91504 1.99301i −0.489532 0.164942i
\(147\) −0.0322227 0.0607785i −0.00265769 0.00501293i
\(148\) −0.372731 0.703045i −0.0306383 0.0577899i
\(149\) 9.11172 + 3.07010i 0.746461 + 0.251512i 0.666725 0.745304i \(-0.267696\pi\)
0.0797365 + 0.996816i \(0.474592\pi\)
\(150\) 5.26739 + 6.20125i 0.430081 + 0.506330i
\(151\) 11.6744 + 5.40115i 0.950048 + 0.439539i 0.832806 0.553564i \(-0.186733\pi\)
0.117242 + 0.993103i \(0.462595\pi\)
\(152\) −14.5526 + 6.73275i −1.18037 + 0.546098i
\(153\) −1.61977 + 1.90694i −0.130951 + 0.154167i
\(154\) 20.0338 12.0539i 1.61437 0.971332i
\(155\) 14.5618 + 1.58370i 1.16963 + 0.127205i
\(156\) 0.174875 1.06669i 0.0140012 0.0854035i
\(157\) 9.01363 + 8.53816i 0.719366 + 0.681420i 0.957050 0.289923i \(-0.0936296\pi\)
−0.237684 + 0.971343i \(0.576388\pi\)
\(158\) −6.15574 + 2.07411i −0.489724 + 0.165007i
\(159\) 1.00342 + 0.603739i 0.0795766 + 0.0478796i
\(160\) −4.81893 3.66326i −0.380970 0.289606i
\(161\) −0.871005 + 2.18606i −0.0686448 + 0.172285i
\(162\) 0.857797 1.26516i 0.0673949 0.0994001i
\(163\) −3.66725 22.3693i −0.287241 1.75210i −0.597897 0.801573i \(-0.703997\pi\)
0.310656 0.950523i \(-0.399451\pi\)
\(164\) −0.229697 4.23652i −0.0179363 0.330816i
\(165\) −18.0523 3.97361i −1.40537 0.309345i
\(166\) 8.40768 + 21.1017i 0.652562 + 1.63781i
\(167\) 0.875147 3.15199i 0.0677209 0.243909i −0.921941 0.387331i \(-0.873397\pi\)
0.989662 + 0.143423i \(0.0458108\pi\)
\(168\) 0.366015 6.75074i 0.0282386 0.520831i
\(169\) 2.66176 0.289484i 0.204751 0.0222680i
\(170\) −9.78214 + 7.43619i −0.750256 + 0.570330i
\(171\) −1.68699 6.07597i −0.129007 0.464641i
\(172\) 2.32621 0.512037i 0.177372 0.0390425i
\(173\) −5.77359 8.51542i −0.438958 0.647415i 0.542284 0.840195i \(-0.317560\pi\)
−0.981242 + 0.192780i \(0.938249\pi\)
\(174\) 4.51468 4.27653i 0.342257 0.324203i
\(175\) −6.62907 + 12.5037i −0.501110 + 0.945194i
\(176\) 26.2325 1.97735
\(177\) 7.59601 1.14044i 0.570951 0.0857207i
\(178\) 4.50789 0.337881
\(179\) 5.82632 10.9896i 0.435480 0.821402i −0.564512 0.825425i \(-0.690936\pi\)
0.999992 + 0.00402296i \(0.00128055\pi\)
\(180\) 0.784766 0.743370i 0.0584930 0.0554075i
\(181\) −5.17090 7.62651i −0.384350 0.566874i 0.585471 0.810694i \(-0.300910\pi\)
−0.969821 + 0.243820i \(0.921599\pi\)
\(182\) 12.7517 2.80687i 0.945220 0.208059i
\(183\) 1.45800 + 5.25124i 0.107778 + 0.388183i
\(184\) −1.79170 + 1.36201i −0.132086 + 0.100409i
\(185\) −7.55468 + 0.821621i −0.555431 + 0.0604068i
\(186\) 0.377271 6.95836i 0.0276629 0.510211i
\(187\) 3.85092 13.8698i 0.281607 1.01426i
\(188\) −0.758688 1.90416i −0.0553330 0.138875i
\(189\) 2.59656 + 0.571546i 0.188872 + 0.0415739i
\(190\) −1.67660 30.9232i −0.121634 2.24340i
\(191\) 0.935224 + 5.70462i 0.0676705 + 0.412771i 0.998839 + 0.0481815i \(0.0153426\pi\)
−0.931168 + 0.364590i \(0.881209\pi\)
\(192\) 3.50157 5.16443i 0.252704 0.372710i
\(193\) −1.18695 + 2.97903i −0.0854387 + 0.214435i −0.965488 0.260447i \(-0.916130\pi\)
0.880049 + 0.474882i \(0.157509\pi\)
\(194\) −11.9808 9.10755i −0.860169 0.653884i
\(195\) −8.84513 5.32194i −0.633413 0.381112i
\(196\) −0.0219326 + 0.00738997i −0.00156662 + 0.000527855i
\(197\) −2.22892 2.11135i −0.158804 0.150427i 0.604172 0.796854i \(-0.293504\pi\)
−0.762976 + 0.646427i \(0.776263\pi\)
\(198\) −1.42269 + 8.67805i −0.101106 + 0.616722i
\(199\) −20.9806 2.28178i −1.48728 0.161751i −0.671883 0.740657i \(-0.734514\pi\)
−0.815394 + 0.578906i \(0.803480\pi\)
\(200\) −11.5979 + 6.97823i −0.820096 + 0.493435i
\(201\) −6.84909 + 8.06337i −0.483097 + 0.568746i
\(202\) −11.3871 + 5.26823i −0.801193 + 0.370672i
\(203\) 9.81683 + 4.54175i 0.689006 + 0.318768i
\(204\) 0.544951 + 0.641566i 0.0381542 + 0.0449186i
\(205\) −38.3968 12.9374i −2.68175 0.903585i
\(206\) 8.11502 + 15.3066i 0.565401 + 1.06646i
\(207\) −0.414581 0.781982i −0.0288153 0.0543515i
\(208\) 13.8828 + 4.67766i 0.962600 + 0.324338i
\(209\) 23.4860 + 27.6499i 1.62456 + 1.91258i
\(210\) 11.8505 + 5.48260i 0.817759 + 0.378336i
\(211\) 1.53907 0.712051i 0.105954 0.0490196i −0.366196 0.930538i \(-0.619340\pi\)
0.472150 + 0.881518i \(0.343478\pi\)
\(212\) 0.255060 0.300280i 0.0175176 0.0206233i
\(213\) −13.1897 + 7.93596i −0.903741 + 0.543763i
\(214\) −8.76836 0.953617i −0.599393 0.0651879i
\(215\) 3.68003 22.4472i 0.250976 1.53089i
\(216\) 1.84608 + 1.74870i 0.125610 + 0.118984i
\(217\) 11.4865 3.87026i 0.779757 0.262731i
\(218\) −5.30992 3.19487i −0.359633 0.216384i
\(219\) 3.25083 + 2.47122i 0.219671 + 0.166990i
\(220\) −2.30184 + 5.77717i −0.155190 + 0.389497i
\(221\) 4.51119 6.65351i 0.303456 0.447564i
\(222\) 0.584890 + 3.56767i 0.0392552 + 0.239446i
\(223\) 0.457604 + 8.44000i 0.0306434 + 0.565184i 0.973033 + 0.230667i \(0.0740906\pi\)
−0.942389 + 0.334518i \(0.891427\pi\)
\(224\) −4.89196 1.07680i −0.326858 0.0719469i
\(225\) −1.97024 4.94493i −0.131349 0.329662i
\(226\) −3.39961 + 12.2443i −0.226139 + 0.814477i
\(227\) −0.114495 + 2.11173i −0.00759927 + 0.140160i 0.992272 + 0.124086i \(0.0395997\pi\)
−0.999871 + 0.0160747i \(0.994883\pi\)
\(228\) −2.10907 + 0.229376i −0.139677 + 0.0151908i
\(229\) 18.7513 14.2543i 1.23912 0.941954i 0.239537 0.970887i \(-0.423004\pi\)
0.999581 + 0.0289335i \(0.00921111\pi\)
\(230\) −1.16288 4.18830i −0.0766778 0.276169i
\(231\) −14.9384 + 3.28818i −0.982871 + 0.216346i
\(232\) 5.80550 + 8.56248i 0.381150 + 0.562154i
\(233\) −4.92744 + 4.66752i −0.322807 + 0.305779i −0.831892 0.554937i \(-0.812742\pi\)
0.509085 + 0.860716i \(0.329984\pi\)
\(234\) −2.30036 + 4.33893i −0.150379 + 0.283645i
\(235\) −19.5748 −1.27692
\(236\) 0.0348150 2.58399i 0.00226627 0.168203i
\(237\) 4.24965 0.276045
\(238\) −4.76283 + 8.98364i −0.308728 + 0.582323i
\(239\) −6.96309 + 6.59579i −0.450405 + 0.426646i −0.878979 0.476860i \(-0.841775\pi\)
0.428574 + 0.903507i \(0.359016\pi\)
\(240\) 8.22139 + 12.1256i 0.530688 + 0.782706i
\(241\) 7.24607 1.59498i 0.466760 0.102742i 0.0246380 0.999696i \(-0.492157\pi\)
0.442122 + 0.896955i \(0.354226\pi\)
\(242\) −9.03670 32.5472i −0.580901 2.09222i
\(243\) −0.796093 + 0.605174i −0.0510694 + 0.0388219i
\(244\) 1.82280 0.198241i 0.116693 0.0126911i
\(245\) −0.0119660 + 0.220700i −0.000764481 + 0.0141000i
\(246\) −5.15691 + 18.5735i −0.328792 + 1.18420i
\(247\) 7.49892 + 18.8209i 0.477145 + 1.19754i
\(248\) 11.3216 + 2.49208i 0.718924 + 0.158247i
\(249\) −0.804535 14.8388i −0.0509853 0.940369i
\(250\) −0.256618 1.56530i −0.0162300 0.0989985i
\(251\) 5.31032 7.83213i 0.335184 0.494360i −0.622326 0.782758i \(-0.713812\pi\)
0.957511 + 0.288398i \(0.0931227\pi\)
\(252\) 0.331086 0.830962i 0.0208564 0.0523457i
\(253\) 4.05371 + 3.08155i 0.254854 + 0.193735i
\(254\) 7.45240 + 4.48396i 0.467605 + 0.281349i
\(255\) 7.61803 2.56681i 0.477059 0.160740i
\(256\) −5.70546 5.40450i −0.356591 0.337781i
\(257\) 0.242935 1.48184i 0.0151539 0.0924346i −0.978167 0.207822i \(-0.933363\pi\)
0.993321 + 0.115387i \(0.0368109\pi\)
\(258\) −10.7583 1.17003i −0.669781 0.0728431i
\(259\) −5.38825 + 3.24200i −0.334810 + 0.201448i
\(260\) −2.24835 + 2.64696i −0.139437 + 0.164157i
\(261\) −3.69231 + 1.70825i −0.228549 + 0.105738i
\(262\) 18.5472 + 8.58087i 1.14585 + 0.530128i
\(263\) 5.97233 + 7.03117i 0.368269 + 0.433560i 0.914818 0.403867i \(-0.132334\pi\)
−0.546548 + 0.837428i \(0.684058\pi\)
\(264\) −13.8634 4.67112i −0.853234 0.287488i
\(265\) −1.76239 3.32422i −0.108263 0.204206i
\(266\) −12.0037 22.6414i −0.735995 1.38823i
\(267\) −2.79477 0.941667i −0.171037 0.0576291i
\(268\) 2.30429 + 2.71282i 0.140757 + 0.165712i
\(269\) 26.2246 + 12.1328i 1.59894 + 0.739751i 0.998216 0.0597023i \(-0.0190151\pi\)
0.600729 + 0.799453i \(0.294877\pi\)
\(270\) −4.45720 + 2.06212i −0.271257 + 0.125497i
\(271\) 8.64461 10.1772i 0.525123 0.618222i −0.434103 0.900863i \(-0.642935\pi\)
0.959226 + 0.282641i \(0.0912104\pi\)
\(272\) −9.77538 + 5.88165i −0.592719 + 0.356627i
\(273\) −8.49205 0.923566i −0.513962 0.0558968i
\(274\) 4.96571 30.2895i 0.299989 1.82985i
\(275\) 22.2327 + 21.0600i 1.34068 + 1.26996i
\(276\) −0.282187 + 0.0950800i −0.0169857 + 0.00572314i
\(277\) 3.77324 + 2.27028i 0.226712 + 0.136408i 0.624378 0.781122i \(-0.285352\pi\)
−0.397667 + 0.917530i \(0.630180\pi\)
\(278\) 19.3242 + 14.6899i 1.15899 + 0.881042i
\(279\) −1.68745 + 4.23518i −0.101025 + 0.253554i
\(280\) −12.1899 + 17.9787i −0.728484 + 1.07443i
\(281\) 3.38051 + 20.6202i 0.201664 + 1.23010i 0.872545 + 0.488533i \(0.162468\pi\)
−0.670881 + 0.741565i \(0.734084\pi\)
\(282\) 0.504176 + 9.29898i 0.0300232 + 0.553746i
\(283\) 3.20678 + 0.705866i 0.190623 + 0.0419594i 0.309256 0.950979i \(-0.399920\pi\)
−0.118633 + 0.992938i \(0.537851\pi\)
\(284\) 1.91687 + 4.81098i 0.113745 + 0.285479i
\(285\) −5.42018 + 19.5217i −0.321064 + 1.15637i
\(286\) 1.52962 28.2122i 0.0904484 1.66822i
\(287\) −33.3320 + 3.62508i −1.96753 + 0.213981i
\(288\) 1.49985 1.14016i 0.0883796 0.0671844i
\(289\) −2.87323 10.3484i −0.169013 0.608732i
\(290\) −19.5129 + 4.29511i −1.14584 + 0.252218i
\(291\) 5.52525 + 8.14913i 0.323896 + 0.477710i
\(292\) 0.997398 0.944786i 0.0583683 0.0552894i
\(293\) −7.72882 + 14.5781i −0.451523 + 0.851662i 0.548358 + 0.836243i \(0.315253\pi\)
−0.999881 + 0.0154188i \(0.995092\pi\)
\(294\) 0.105151 0.00613255
\(295\) −22.8011 9.44270i −1.32753 0.549775i
\(296\) −6.01427 −0.349572
\(297\) 2.69481 5.08296i 0.156369 0.294943i
\(298\) −10.6699 + 10.1071i −0.618093 + 0.585489i
\(299\) 1.59582 + 2.35367i 0.0922889 + 0.136116i
\(300\) −1.74898 + 0.384979i −0.100977 + 0.0222268i
\(301\) −5.03572 18.1370i −0.290254 1.04540i
\(302\) −15.6528 + 11.8990i −0.900718 + 0.684708i
\(303\) 8.16018 0.887474i 0.468790 0.0509840i
\(304\) 1.55663 28.7104i 0.0892789 1.64665i
\(305\) 4.68446 16.8719i 0.268232 0.966083i
\(306\) −1.41557 3.55281i −0.0809227 0.203101i
\(307\) 27.7529 + 6.10888i 1.58394 + 0.348652i 0.917760 0.397136i \(-0.129996\pi\)
0.666183 + 0.745788i \(0.267927\pi\)
\(308\) 0.278606 + 5.13858i 0.0158750 + 0.292798i
\(309\) −1.83366 11.1848i −0.104313 0.636282i
\(310\) −12.5648 + 18.5316i −0.713630 + 1.05253i
\(311\) 0.698851 1.75398i 0.0396282 0.0994593i −0.907831 0.419337i \(-0.862263\pi\)
0.947459 + 0.319878i \(0.103642\pi\)
\(312\) −6.50389 4.94413i −0.368210 0.279906i
\(313\) −11.3281 6.81590i −0.640303 0.385258i 0.158064 0.987429i \(-0.449475\pi\)
−0.798367 + 0.602171i \(0.794302\pi\)
\(314\) −17.9842 + 6.05960i −1.01491 + 0.341963i
\(315\) −6.20168 5.87454i −0.349425 0.330993i
\(316\) 0.231306 1.41091i 0.0130120 0.0793697i
\(317\) 7.08265 + 0.770285i 0.397801 + 0.0432635i 0.304834 0.952406i \(-0.401399\pi\)
0.0929678 + 0.995669i \(0.470365\pi\)
\(318\) −1.53377 + 0.922840i −0.0860097 + 0.0517503i
\(319\) 15.1525 17.8389i 0.848376 0.998785i
\(320\) −18.1945 + 8.41767i −1.01710 + 0.470562i
\(321\) 5.23694 + 2.42287i 0.292297 + 0.135231i
\(322\) −2.32861 2.74146i −0.129769 0.152775i
\(323\) −14.9514 5.03771i −0.831917 0.280306i
\(324\) 0.157590 + 0.297246i 0.00875500 + 0.0165137i
\(325\) 8.01075 + 15.1099i 0.444356 + 0.838145i
\(326\) 32.8350 + 11.0634i 1.81856 + 0.612745i
\(327\) 2.62462 + 3.08994i 0.145142 + 0.170874i
\(328\) −29.1032 13.4646i −1.60696 0.743458i
\(329\) −14.7011 + 6.80147i −0.810500 + 0.374977i
\(330\) 18.2914 21.5343i 1.00691 1.18543i
\(331\) −21.8240 + 13.1311i −1.19956 + 0.721750i −0.967971 0.251064i \(-0.919220\pi\)
−0.231588 + 0.972814i \(0.574392\pi\)
\(332\) −4.97034 0.540557i −0.272783 0.0296669i
\(333\) 0.382646 2.33404i 0.0209689 0.127904i
\(334\) 3.63013 + 3.43864i 0.198632 + 0.188154i
\(335\) 32.2123 10.8536i 1.75994 0.592994i
\(336\) 10.3876 + 6.25002i 0.566691 + 0.340967i
\(337\) −1.60576 1.22066i −0.0874711 0.0664938i 0.560525 0.828138i \(-0.310599\pi\)
−0.647996 + 0.761644i \(0.724393\pi\)
\(338\) −1.51483 + 3.80194i −0.0823959 + 0.206798i
\(339\) 4.66541 6.88096i 0.253390 0.373723i
\(340\) −0.437549 2.66893i −0.0237294 0.144743i
\(341\) −1.41997 26.1899i −0.0768959 1.41826i
\(342\) 9.41335 + 2.07204i 0.509016 + 0.112043i
\(343\) −6.82096 17.1193i −0.368297 0.924356i
\(344\) 4.81621 17.3464i 0.259672 0.935256i
\(345\) −0.153956 + 2.83955i −0.00828871 + 0.152876i
\(346\) 15.6337 1.70027i 0.840474 0.0914071i
\(347\) −12.0576 + 9.16595i −0.647286 + 0.492054i −0.876550 0.481310i \(-0.840161\pi\)
0.229265 + 0.973364i \(0.426368\pi\)
\(348\) 0.366176 + 1.31885i 0.0196291 + 0.0706976i
\(349\) 14.5157 3.19516i 0.777010 0.171033i 0.191276 0.981536i \(-0.438737\pi\)
0.585734 + 0.810503i \(0.300806\pi\)
\(350\) −12.1398 17.9049i −0.648901 0.957057i
\(351\) 2.33253 2.20949i 0.124501 0.117934i
\(352\) −5.07707 + 9.57638i −0.270609 + 0.510423i
\(353\) −24.9220 −1.32646 −0.663232 0.748414i \(-0.730816\pi\)
−0.663232 + 0.748414i \(0.730816\pi\)
\(354\) −3.89846 + 11.0748i −0.207201 + 0.588620i
\(355\) 49.4570 2.62490
\(356\) −0.464756 + 0.876623i −0.0246320 + 0.0464609i
\(357\) 4.82944 4.57469i 0.255601 0.242118i
\(358\) 10.6698 + 15.7367i 0.563914 + 0.831711i
\(359\) −10.6169 + 2.33696i −0.560340 + 0.123340i −0.486104 0.873901i \(-0.661583\pi\)
−0.0742351 + 0.997241i \(0.523652\pi\)
\(360\) −2.18569 7.87215i −0.115196 0.414898i
\(361\) 16.5296 12.5654i 0.869977 0.661339i
\(362\) 14.0017 1.52278i 0.735916 0.0800356i
\(363\) −1.19639 + 22.0661i −0.0627941 + 1.15817i
\(364\) −0.768846 + 2.76913i −0.0402985 + 0.145142i
\(365\) −4.85621 12.1882i −0.254186 0.637958i
\(366\) −8.13561 1.79078i −0.425255 0.0936058i
\(367\) 1.66286 + 30.6696i 0.0868004 + 1.60094i 0.640324 + 0.768105i \(0.278800\pi\)
−0.553524 + 0.832833i \(0.686717\pi\)
\(368\) −0.652904 3.98254i −0.0340350 0.207604i
\(369\) 7.07702 10.4378i 0.368415 0.543371i
\(370\) 4.29942 10.7907i 0.223516 0.560984i
\(371\) −2.47863 1.88421i −0.128684 0.0978231i
\(372\) 1.31425 + 0.790760i 0.0681409 + 0.0409990i
\(373\) 30.7821 10.3717i 1.59383 0.537025i 0.624133 0.781318i \(-0.285452\pi\)
0.969701 + 0.244293i \(0.0785558\pi\)
\(374\) 15.9737 + 15.1311i 0.825980 + 0.782410i
\(375\) −0.167885 + 1.02405i −0.00866952 + 0.0528817i
\(376\) −15.4013 1.67500i −0.794264 0.0863814i
\(377\) 11.2000 6.73881i 0.576829 0.347066i
\(378\) −2.63095 + 3.09740i −0.135322 + 0.159313i
\(379\) −21.9036 + 10.1337i −1.12511 + 0.520531i −0.892053 0.451931i \(-0.850735\pi\)
−0.233058 + 0.972463i \(0.574873\pi\)
\(380\) 6.18630 + 2.86208i 0.317350 + 0.146822i
\(381\) −3.68362 4.33669i −0.188717 0.222175i
\(382\) −8.37360 2.82139i −0.428430 0.144355i
\(383\) −0.669632 1.26306i −0.0342166 0.0645393i 0.865814 0.500366i \(-0.166801\pi\)
−0.900031 + 0.435826i \(0.856456\pi\)
\(384\) 6.23240 + 11.7555i 0.318046 + 0.599898i
\(385\) 46.5724 + 15.6921i 2.37355 + 0.799742i
\(386\) −3.17329 3.73589i −0.161516 0.190152i
\(387\) 6.42542 + 2.97272i 0.326623 + 0.151112i
\(388\) 3.00629 1.39086i 0.152621 0.0706100i
\(389\) −4.73888 + 5.57904i −0.240271 + 0.282869i −0.869060 0.494707i \(-0.835275\pi\)
0.628789 + 0.777576i \(0.283551\pi\)
\(390\) 13.5201 8.13480i 0.684619 0.411922i
\(391\) −2.20151 0.239429i −0.111335 0.0121084i
\(392\) −0.0282999 + 0.172621i −0.00142936 + 0.00871870i
\(393\) −9.70630 9.19429i −0.489618 0.463791i
\(394\) 4.44721 1.49844i 0.224047 0.0754903i
\(395\) −11.6994 7.03931i −0.588662 0.354186i
\(396\) −1.54089 1.17135i −0.0774327 0.0588628i
\(397\) 1.29832 3.25853i 0.0651607 0.163541i −0.892791 0.450472i \(-0.851256\pi\)
0.957951 + 0.286931i \(0.0926350\pi\)
\(398\) 18.1032 26.7003i 0.907434 1.33836i
\(399\) 2.71234 + 16.5445i 0.135787 + 0.828263i
\(400\) −1.31401 24.2355i −0.0657006 1.21178i
\(401\) 16.2709 + 3.58151i 0.812532 + 0.178852i 0.601753 0.798682i \(-0.294469\pi\)
0.210779 + 0.977534i \(0.432400\pi\)
\(402\) −5.98563 15.0228i −0.298536 0.749269i
\(403\) 3.91859 14.1135i 0.195199 0.703043i
\(404\) 0.149509 2.75753i 0.00743834 0.137192i
\(405\) 3.19411 0.347380i 0.158716 0.0172614i
\(406\) −13.1622 + 10.0057i −0.653230 + 0.496573i
\(407\) 3.64033 + 13.1113i 0.180444 + 0.649902i
\(408\) 6.21345 1.36768i 0.307611 0.0677104i
\(409\) −5.12428 7.55775i −0.253379 0.373707i 0.679632 0.733553i \(-0.262139\pi\)
−0.933012 + 0.359847i \(0.882829\pi\)
\(410\) 44.9631 42.5913i 2.22057 2.10343i
\(411\) −9.40586 + 17.7413i −0.463957 + 0.875116i
\(412\) −3.81322 −0.187864
\(413\) −20.4051 + 0.830800i −1.00407 + 0.0408810i
\(414\) 1.35289 0.0664907
\(415\) −22.3647 + 42.1842i −1.09784 + 2.07074i
\(416\) −4.39452 + 4.16271i −0.215459 + 0.204094i
\(417\) −8.91187 13.1440i −0.436416 0.643666i
\(418\) −54.1563 + 11.9207i −2.64887 + 0.583060i
\(419\) −0.825623 2.97363i −0.0403343 0.145271i 0.940641 0.339403i \(-0.110225\pi\)
−0.980976 + 0.194132i \(0.937811\pi\)
\(420\) −2.28793 + 1.73924i −0.111640 + 0.0848662i
\(421\) −9.30002 + 1.01144i −0.453255 + 0.0492945i −0.331900 0.943315i \(-0.607690\pi\)
−0.121356 + 0.992609i \(0.538724\pi\)
\(422\) −0.140334 + 2.58831i −0.00683135 + 0.125997i
\(423\) 1.62992 5.87043i 0.0792493 0.285430i
\(424\) −1.10219 2.76628i −0.0535270 0.134343i
\(425\) −13.0068 2.86302i −0.630924 0.138877i
\(426\) −1.27383 23.4944i −0.0617173 1.13831i
\(427\) −2.34418 14.2988i −0.113443 0.691969i
\(428\) 1.08945 1.60681i 0.0526604 0.0776683i
\(429\) −6.84166 + 17.1713i −0.330318 + 0.829037i
\(430\) 27.6798 + 21.0416i 1.33484 + 1.01472i
\(431\) 16.8099 + 10.1142i 0.809703 + 0.487182i 0.859229 0.511591i \(-0.170944\pi\)
−0.0495262 + 0.998773i \(0.515771\pi\)
\(432\) −4.32100 + 1.45591i −0.207894 + 0.0700477i
\(433\) 20.1288 + 19.0670i 0.967329 + 0.916303i 0.996527 0.0832709i \(-0.0265367\pi\)
−0.0291979 + 0.999574i \(0.509295\pi\)
\(434\) −2.99741 + 18.2834i −0.143880 + 0.877632i
\(435\) 12.9947 + 1.41326i 0.623047 + 0.0677604i
\(436\) 1.16873 0.703203i 0.0559721 0.0336773i
\(437\) 3.61318 4.25376i 0.172842 0.203485i
\(438\) −5.66488 + 2.62085i −0.270678 + 0.125229i
\(439\) 4.66723 + 2.15929i 0.222755 + 0.103057i 0.528093 0.849187i \(-0.322907\pi\)
−0.305338 + 0.952244i \(0.598769\pi\)
\(440\) 30.4289 + 35.8237i 1.45064 + 1.70783i
\(441\) −0.0651909 0.0219654i −0.00310433 0.00104597i
\(442\) 5.75553 + 10.8561i 0.273763 + 0.516371i
\(443\) −17.7231 33.4292i −0.842048 1.58827i −0.808248 0.588842i \(-0.799584\pi\)
−0.0337999 0.999429i \(-0.510761\pi\)
\(444\) −0.754084 0.254081i −0.0357873 0.0120581i
\(445\) 6.13427 + 7.22182i 0.290792 + 0.342347i
\(446\) −11.7257 5.42490i −0.555229 0.256876i
\(447\) 8.72637 4.03725i 0.412743 0.190955i
\(448\) −10.7397 + 12.6437i −0.507402 + 0.597360i
\(449\) −24.7970 + 14.9199i −1.17024 + 0.704113i −0.961755 0.273911i \(-0.911682\pi\)
−0.208490 + 0.978024i \(0.566855\pi\)
\(450\) 8.08870 + 0.879699i 0.381305 + 0.0414694i
\(451\) −11.7375 + 71.5958i −0.552699 + 3.37131i
\(452\) −2.03058 1.92347i −0.0955104 0.0904722i
\(453\) 12.1899 4.10726i 0.572732 0.192976i
\(454\) −2.76988 1.66658i −0.129997 0.0782165i
\(455\) 21.8490 + 16.6092i 1.02430 + 0.778652i
\(456\) −5.93501 + 14.8958i −0.277932 + 0.697558i
\(457\) 8.99380 13.2649i 0.420712 0.620504i −0.556985 0.830522i \(-0.688042\pi\)
0.977697 + 0.210018i \(0.0673523\pi\)
\(458\) 5.82471 + 35.5291i 0.272171 + 1.66017i
\(459\) 0.135457 + 2.49835i 0.00632257 + 0.116613i
\(460\) 0.934365 + 0.205669i 0.0435650 + 0.00958938i
\(461\) −10.2473 25.7187i −0.477263 1.19784i −0.948767 0.315975i \(-0.897668\pi\)
0.471505 0.881863i \(-0.343711\pi\)
\(462\) 6.25495 22.5283i 0.291006 1.04811i
\(463\) 1.86808 34.4546i 0.0868169 1.60124i −0.553311 0.832975i \(-0.686636\pi\)
0.640128 0.768268i \(-0.278881\pi\)
\(464\) −18.4415 + 2.00564i −0.856127 + 0.0931095i
\(465\) 11.6609 8.86441i 0.540763 0.411077i
\(466\) −2.77545 9.99628i −0.128570 0.463069i
\(467\) 19.8737 4.37454i 0.919646 0.202429i 0.270171 0.962812i \(-0.412920\pi\)
0.649475 + 0.760383i \(0.274989\pi\)
\(468\) −0.606603 0.894673i −0.0280402 0.0413563i
\(469\) 20.4209 19.3437i 0.942951 0.893211i
\(470\) 14.0152 26.4355i 0.646474 1.21938i
\(471\) 12.4155 0.572078
\(472\) −17.1318 9.38051i −0.788553 0.431773i
\(473\) −40.7308 −1.87281
\(474\) −3.04267 + 5.73909i −0.139755 + 0.263605i
\(475\) 24.3686 23.0832i 1.11811 1.05913i
\(476\) −1.25596 1.85240i −0.0575667 0.0849045i
\(477\) 1.14367 0.251741i 0.0523651 0.0115264i
\(478\) −3.92207 14.1260i −0.179391 0.646108i
\(479\) −14.0771 + 10.7011i −0.643199 + 0.488948i −0.875196 0.483769i \(-0.839267\pi\)
0.231996 + 0.972717i \(0.425474\pi\)
\(480\) −6.01774 + 0.654469i −0.274671 + 0.0298723i
\(481\) −0.411405 + 7.58792i −0.0187585 + 0.345979i
\(482\) −3.03406 + 10.9277i −0.138197 + 0.497742i
\(483\) 0.871005 + 2.18606i 0.0396321 + 0.0994691i
\(484\) 7.26094 + 1.59825i 0.330043 + 0.0726478i
\(485\) −1.71260 31.5871i −0.0777652 1.43429i
\(486\) −0.247290 1.50840i −0.0112173 0.0684226i
\(487\) −3.21807 + 4.74630i −0.145825 + 0.215075i −0.893586 0.448893i \(-0.851819\pi\)
0.747761 + 0.663968i \(0.231129\pi\)
\(488\) 5.12941 12.8739i 0.232198 0.582772i
\(489\) −18.0457 13.7180i −0.816056 0.620350i
\(490\) −0.289485 0.174177i −0.0130776 0.00786852i
\(491\) 5.54436 1.86811i 0.250213 0.0843067i −0.191400 0.981512i \(-0.561303\pi\)
0.441613 + 0.897205i \(0.354406\pi\)
\(492\) −3.08021 2.91773i −0.138867 0.131541i
\(493\) −1.64678 + 10.0449i −0.0741674 + 0.452401i
\(494\) −30.7864 3.34822i −1.38514 0.150644i
\(495\) −15.8385 + 9.52973i −0.711890 + 0.428330i
\(496\) −13.4575 + 15.8434i −0.604261 + 0.711391i
\(497\) 37.1433 17.1843i 1.66610 0.770822i
\(498\) 20.6156 + 9.53777i 0.923805 + 0.427398i
\(499\) −18.5834 21.8781i −0.831909 0.979399i 0.168071 0.985775i \(-0.446246\pi\)
−0.999980 + 0.00637625i \(0.997970\pi\)
\(500\) 0.330852 + 0.111477i 0.0147962 + 0.00498540i
\(501\) −1.53227 2.89017i −0.0684569 0.129123i
\(502\) 6.77508 + 12.7792i 0.302387 + 0.570362i
\(503\) 13.4919 + 4.54594i 0.601573 + 0.202693i 0.603577 0.797305i \(-0.293742\pi\)
−0.00200461 + 0.999998i \(0.500638\pi\)
\(504\) −4.37676 5.15272i −0.194956 0.229520i
\(505\) −23.9353 11.0736i −1.06511 0.492771i
\(506\) −7.06396 + 3.26814i −0.314031 + 0.145286i
\(507\) 1.73335 2.04066i 0.0769808 0.0906288i
\(508\) −1.64030 + 0.986935i −0.0727765 + 0.0437882i
\(509\) −4.32395 0.470257i −0.191656 0.0208438i 0.0117878 0.999931i \(-0.496248\pi\)
−0.203443 + 0.979087i \(0.565213\pi\)
\(510\) −1.98793 + 12.1258i −0.0880268 + 0.536940i
\(511\) −7.88202 7.46624i −0.348680 0.330287i
\(512\) −13.8342 + 4.66130i −0.611393 + 0.206002i
\(513\) −5.40319 3.25099i −0.238557 0.143535i
\(514\) 1.82726 + 1.38905i 0.0805971 + 0.0612684i
\(515\) −13.4789 + 33.8295i −0.593951 + 1.49071i
\(516\) 1.33669 1.97147i 0.0588445 0.0867891i
\(517\) 5.67061 + 34.5892i 0.249393 + 1.52123i
\(518\) −0.520386 9.59796i −0.0228645 0.421710i
\(519\) −10.0477 2.21166i −0.441043 0.0970809i
\(520\) 9.71574 + 24.3847i 0.426064 + 1.06934i
\(521\) −5.65561 + 20.3697i −0.247777 + 0.892411i 0.730120 + 0.683319i \(0.239464\pi\)
−0.977896 + 0.209091i \(0.932949\pi\)
\(522\) 0.336669 6.20949i 0.0147356 0.271782i
\(523\) 22.7872 2.47826i 0.996414 0.108367i 0.404645 0.914474i \(-0.367395\pi\)
0.591769 + 0.806107i \(0.298430\pi\)
\(524\) −3.58086 + 2.72210i −0.156431 + 0.118915i
\(525\) 3.78615 + 13.6365i 0.165241 + 0.595144i
\(526\) −13.7716 + 3.03135i −0.600468 + 0.132173i
\(527\) 6.40125 + 9.44114i 0.278843 + 0.411263i
\(528\) 19.0446 18.0400i 0.828812 0.785092i
\(529\) −10.4065 + 19.6287i −0.452455 + 0.853420i
\(530\) 5.75115 0.249814
\(531\) 4.73039 6.05173i 0.205281 0.262623i
\(532\) 5.64050 0.244547
\(533\) −18.9784 + 35.7971i −0.822047 + 1.55055i
\(534\) 3.27271 3.10007i 0.141624 0.134153i
\(535\) −10.4041 15.3449i −0.449809 0.663419i
\(536\) 26.2731 5.78315i 1.13483 0.249794i
\(537\) −3.32766 11.9852i −0.143599 0.517198i
\(538\) −35.1615 + 26.7291i −1.51592 + 1.15237i
\(539\) 0.393449 0.0427902i 0.0169471 0.00184310i
\(540\) 0.0585216 1.07937i 0.00251837 0.0464485i
\(541\) −9.72940 + 35.0421i −0.418299 + 1.50658i 0.391670 + 0.920106i \(0.371898\pi\)
−0.809969 + 0.586472i \(0.800516\pi\)
\(542\) 7.55480 + 18.9611i 0.324506 + 0.814450i
\(543\) −8.99880 1.98078i −0.386175 0.0850036i
\(544\) −0.255202 4.70693i −0.0109417 0.201808i
\(545\) −2.10734 12.8542i −0.0902687 0.550615i
\(546\) 7.32741 10.8071i 0.313584 0.462502i
\(547\) 6.59730 16.5580i 0.282080 0.707968i −0.717851 0.696197i \(-0.754874\pi\)
0.999931 0.0117705i \(-0.00374675\pi\)
\(548\) 5.37826 + 4.08844i 0.229748 + 0.174650i
\(549\) 4.66977 + 2.80971i 0.199301 + 0.119916i
\(550\) −44.3594 + 14.9464i −1.89149 + 0.637318i
\(551\) −18.6248 17.6423i −0.793443 0.751589i
\(552\) −0.364108 + 2.22096i −0.0154975 + 0.0945305i
\(553\) −11.2324 1.22160i −0.477650 0.0519476i
\(554\) −5.76755 + 3.47022i −0.245040 + 0.147435i
\(555\) −4.91963 + 5.79184i −0.208827 + 0.245850i
\(556\) −4.84895 + 2.24336i −0.205641 + 0.0951398i
\(557\) 35.5518 + 16.4480i 1.50638 + 0.696925i 0.987456 0.157895i \(-0.0504708\pi\)
0.518924 + 0.854821i \(0.326333\pi\)
\(558\) −4.51136 5.31118i −0.190981 0.224840i
\(559\) −21.5557 7.26295i −0.911708 0.307190i
\(560\) −18.2446 34.4130i −0.770976 1.45421i
\(561\) −6.74247 12.7177i −0.284668 0.536940i
\(562\) −30.2676 10.1984i −1.27676 0.430192i
\(563\) −29.6796 34.9415i −1.25084 1.47261i −0.822266 0.569104i \(-0.807290\pi\)
−0.428579 0.903504i \(-0.640986\pi\)
\(564\) −1.86030 0.860665i −0.0783326 0.0362405i
\(565\) −24.2419 + 11.2155i −1.01987 + 0.471840i
\(566\) −3.24926 + 3.82532i −0.136576 + 0.160790i
\(567\) 2.27814 1.37071i 0.0956730 0.0575645i
\(568\) 38.9124 + 4.23198i 1.63273 + 0.177570i
\(569\) 3.98577 24.3121i 0.167092 1.01922i −0.761514 0.648149i \(-0.775543\pi\)
0.928606 0.371068i \(-0.121008\pi\)
\(570\) −22.4830 21.2971i −0.941711 0.892036i
\(571\) 8.59257 2.89517i 0.359588 0.121159i −0.133708 0.991021i \(-0.542688\pi\)
0.493296 + 0.869861i \(0.335792\pi\)
\(572\) 5.32856 + 3.20609i 0.222798 + 0.134053i
\(573\) 4.60203 + 3.49837i 0.192253 + 0.146147i
\(574\) 18.9695 47.6099i 0.791772 1.98720i
\(575\) 2.64391 3.89948i 0.110259 0.162619i
\(576\) −1.00945 6.15738i −0.0420604 0.256557i
\(577\) 0.722289 + 13.3218i 0.0300693 + 0.554595i 0.974292 + 0.225288i \(0.0723323\pi\)
−0.944223 + 0.329307i \(0.893185\pi\)
\(578\) 16.0326 + 3.52904i 0.666867 + 0.146789i
\(579\) 1.18695 + 2.97903i 0.0493280 + 0.123804i
\(580\) 1.17650 4.23737i 0.0488515 0.175947i
\(581\) −2.13903 + 39.4521i −0.0887420 + 1.63675i
\(582\) −14.9612 + 1.62713i −0.620163 + 0.0674468i
\(583\) −5.36344 + 4.07718i −0.222131 + 0.168860i
\(584\) −2.77790 10.0051i −0.114950 0.414014i
\(585\) −10.0814 + 2.21909i −0.416815 + 0.0917480i
\(586\) −14.1538 20.8753i −0.584689 0.862351i
\(587\) −14.7883 + 14.0082i −0.610378 + 0.578181i −0.929174 0.369642i \(-0.879480\pi\)
0.318796 + 0.947823i \(0.396722\pi\)
\(588\) −0.0108409 + 0.0204481i −0.000447072 + 0.000843267i
\(589\) −28.7481 −1.18454
\(590\) 29.0774 24.0318i 1.19710 0.989372i
\(591\) −3.07016 −0.126290
\(592\) 5.05157 9.52827i 0.207618 0.391609i
\(593\) 9.36604 8.87198i 0.384617 0.364329i −0.470825 0.882226i \(-0.656044\pi\)
0.855443 + 0.517898i \(0.173285\pi\)
\(594\) 4.93502 + 7.27861i 0.202486 + 0.298645i
\(595\) −20.8733 + 4.59456i −0.855723 + 0.188359i
\(596\) −0.865416 3.11695i −0.0354488 0.127675i
\(597\) −16.8010 + 12.7718i −0.687620 + 0.522715i
\(598\) −4.32117 + 0.469955i −0.176706 + 0.0192179i
\(599\) 1.22210 22.5403i 0.0499337 0.920973i −0.861047 0.508525i \(-0.830191\pi\)
0.910981 0.412448i \(-0.135326\pi\)
\(600\) −3.62110 + 13.0420i −0.147831 + 0.532439i
\(601\) −4.16331 10.4491i −0.169825 0.426229i 0.819289 0.573381i \(-0.194369\pi\)
−0.989114 + 0.147152i \(0.952989\pi\)
\(602\) 28.0992 + 6.18511i 1.14524 + 0.252086i
\(603\) 0.572768 + 10.5641i 0.0233249 + 0.430203i
\(604\) −0.700141 4.27067i −0.0284883 0.173771i
\(605\) 39.8449 58.7669i 1.61993 2.38921i
\(606\) −4.64402 + 11.6556i −0.188650 + 0.473477i
\(607\) 22.6566 + 17.2231i 0.919603 + 0.699064i 0.953829 0.300350i \(-0.0971035\pi\)
−0.0342260 + 0.999414i \(0.510897\pi\)
\(608\) 10.1797 + 6.12492i 0.412841 + 0.248398i
\(609\) 10.2503 3.45374i 0.415364 0.139953i
\(610\) 19.4313 + 18.4063i 0.786749 + 0.745248i
\(611\) −3.16679 + 19.3166i −0.128115 + 0.781464i
\(612\) 0.836837 + 0.0910115i 0.0338271 + 0.00367892i
\(613\) 36.5599 21.9974i 1.47664 0.888465i 0.476684 0.879075i \(-0.341839\pi\)
0.999956 0.00939003i \(-0.00298898\pi\)
\(614\) −28.1205 + 33.1060i −1.13485 + 1.33605i
\(615\) −36.7729 + 17.0130i −1.48283 + 0.686028i
\(616\) 35.3001 + 16.3316i 1.42228 + 0.658017i
\(617\) 10.5770 + 12.4522i 0.425813 + 0.501306i 0.932673 0.360723i \(-0.117470\pi\)
−0.506860 + 0.862028i \(0.669194\pi\)
\(618\) 16.4178 + 5.53180i 0.660420 + 0.222521i
\(619\) 6.95762 + 13.1235i 0.279650 + 0.527476i 0.983054 0.183314i \(-0.0586824\pi\)
−0.703404 + 0.710790i \(0.748338\pi\)
\(620\) −2.30833 4.35397i −0.0927048 0.174860i
\(621\) −0.838752 0.282608i −0.0336580 0.0113407i
\(622\) 1.86836 + 2.19961i 0.0749146 + 0.0881962i
\(623\) 7.11626 + 3.29233i 0.285107 + 0.131905i
\(624\) 13.2957 6.15124i 0.532253 0.246247i
\(625\) −15.0717 + 17.7437i −0.602866 + 0.709749i
\(626\) 17.3155 10.4184i 0.692066 0.416402i
\(627\) 36.0655 + 3.92236i 1.44032 + 0.156644i
\(628\) 0.675771 4.12202i 0.0269662 0.164487i
\(629\) −4.29626 4.06964i −0.171303 0.162267i
\(630\) 12.3738 4.16920i 0.492982 0.166105i
\(631\) 18.9351 + 11.3929i 0.753795 + 0.453543i 0.839899 0.542743i \(-0.182614\pi\)
−0.0861041 + 0.996286i \(0.527442\pi\)
\(632\) −8.60268 6.53959i −0.342196 0.260131i
\(633\) 0.627683 1.57536i 0.0249481 0.0626151i
\(634\) −6.11131 + 9.01350i −0.242711 + 0.357972i
\(635\) 2.95763 + 18.0407i 0.117370 + 0.715925i
\(636\) −0.0213299 0.393407i −0.000845785 0.0155996i
\(637\) 0.215852 + 0.0475127i 0.00855238 + 0.00188252i
\(638\) 13.2422 + 33.2355i 0.524265 + 1.31581i
\(639\) −4.11808 + 14.8320i −0.162909 + 0.586744i
\(640\) 2.31442 42.6870i 0.0914855 1.68735i
\(641\) −3.05653 + 0.332418i −0.120726 + 0.0131297i −0.168282 0.985739i \(-0.553822\pi\)
0.0475567 + 0.998869i \(0.484857\pi\)
\(642\) −7.02159 + 5.33768i −0.277120 + 0.210661i
\(643\) −8.61379 31.0241i −0.339695 1.22347i −0.914299 0.405039i \(-0.867258\pi\)
0.574605 0.818431i \(-0.305156\pi\)
\(644\) 0.773190 0.170192i 0.0304680 0.00670651i
\(645\) −12.7652 18.8273i −0.502631 0.741325i
\(646\) 17.5083 16.5847i 0.688853 0.652516i
\(647\) 10.6699 20.1255i 0.419477 0.791217i −0.580254 0.814436i \(-0.697047\pi\)
0.999730 + 0.0232188i \(0.00739145\pi\)
\(648\) 2.54282 0.0998916
\(649\) −10.0802 + 43.0256i −0.395684 + 1.68890i
\(650\) −26.1412 −1.02534
\(651\) 5.67759 10.7091i 0.222522 0.419722i
\(652\) −5.53667 + 5.24461i −0.216833 + 0.205395i
\(653\) 11.5868 + 17.0893i 0.453427 + 0.668755i 0.983853 0.178976i \(-0.0572785\pi\)
−0.530426 + 0.847731i \(0.677968\pi\)
\(654\) −6.05209 + 1.33217i −0.236656 + 0.0520918i
\(655\) 11.4919 + 41.3901i 0.449026 + 1.61724i
\(656\) 45.7763 34.7983i 1.78727 1.35864i
\(657\) 4.05955 0.441502i 0.158378 0.0172246i
\(658\) 1.34046 24.7234i 0.0522567 0.963818i
\(659\) −4.45159 + 16.0332i −0.173409 + 0.624564i 0.824837 + 0.565371i \(0.191267\pi\)
−0.998247 + 0.0591938i \(0.981147\pi\)
\(660\) 2.30184 + 5.77717i 0.0895989 + 0.224876i
\(661\) −29.0046 6.38440i −1.12815 0.248325i −0.388587 0.921412i \(-0.627037\pi\)
−0.739563 + 0.673087i \(0.764968\pi\)
\(662\) −2.10772 38.8747i −0.0819190 1.51091i
\(663\) −1.30051 7.93276i −0.0505077 0.308083i
\(664\) −21.2060 + 31.2765i −0.822953 + 1.21377i
\(665\) 19.9380 50.0405i 0.773161 1.94049i
\(666\) 2.87811 + 2.18788i 0.111525 + 0.0847788i
\(667\) −3.08538 1.85641i −0.119466 0.0718805i
\(668\) −1.04295 + 0.351412i −0.0403530 + 0.0135965i
\(669\) 6.13640 + 5.81271i 0.237247 + 0.224732i
\(670\) −8.40580 + 51.2731i −0.324744 + 1.98085i
\(671\) −31.1701 3.38995i −1.20331 0.130868i
\(672\) −4.29206 + 2.58245i −0.165570 + 0.0996200i
\(673\) 26.9920 31.7774i 1.04046 1.22493i 0.0666051 0.997779i \(-0.478783\pi\)
0.973860 0.227150i \(-0.0729409\pi\)
\(674\) 2.79818 1.29457i 0.107782 0.0498652i
\(675\) −4.83101 2.23506i −0.185946 0.0860276i
\(676\) −0.583163 0.686553i −0.0224294 0.0264059i
\(677\) 4.38747 + 1.47831i 0.168624 + 0.0568161i 0.402347 0.915487i \(-0.368194\pi\)
−0.233723 + 0.972303i \(0.575091\pi\)
\(678\) 5.95228 + 11.2272i 0.228596 + 0.431178i
\(679\) −12.2614 23.1275i −0.470551 0.887553i
\(680\) −19.3713 6.52695i −0.742855 0.250297i
\(681\) 1.36911 + 1.61184i 0.0524644 + 0.0617659i
\(682\) 36.3857 + 16.8338i 1.39328 + 0.644600i
\(683\) 30.3671 14.0493i 1.16197 0.537583i 0.258403 0.966037i \(-0.416804\pi\)
0.903564 + 0.428454i \(0.140942\pi\)
\(684\) −1.37344 + 1.61694i −0.0525147 + 0.0618251i
\(685\) 55.2822 33.2622i 2.11222 1.27088i
\(686\) 28.0030 + 3.04551i 1.06916 + 0.116278i
\(687\) 3.81063 23.2438i 0.145385 0.886807i
\(688\) 23.4362 + 22.2000i 0.893498 + 0.846366i
\(689\) −3.56548 + 1.20135i −0.135834 + 0.0457678i
\(690\) −3.72454 2.24098i −0.141791 0.0853126i
\(691\) −20.8011 15.8126i −0.791312 0.601540i 0.129485 0.991581i \(-0.458668\pi\)
−0.920797 + 0.390042i \(0.872461\pi\)
\(692\) −1.28117 + 3.21549i −0.0487027 + 0.122235i
\(693\) −8.58390 + 12.6603i −0.326075 + 0.480925i
\(694\) −3.74545 22.8462i −0.142175 0.867231i
\(695\) 2.76232 + 50.9479i 0.104781 + 1.93257i
\(696\) 10.1032 + 2.22388i 0.382960 + 0.0842959i
\(697\) −11.6788 29.3115i −0.442365 1.11025i
\(698\) −6.07799 + 21.8910i −0.230055 + 0.828585i
\(699\) −0.367449 + 6.77719i −0.0138982 + 0.256337i
\(700\) 4.73345 0.514794i 0.178908 0.0194574i
\(701\) 4.58204 3.48318i 0.173061 0.131558i −0.515058 0.857155i \(-0.672230\pi\)
0.688119 + 0.725597i \(0.258437\pi\)
\(702\) 1.31383 + 4.73200i 0.0495874 + 0.178598i
\(703\) 14.5658 3.20617i 0.549359 0.120923i
\(704\) 20.1450 + 29.7116i 0.759242 + 1.11980i
\(705\) −14.2112 + 13.4616i −0.535226 + 0.506993i
\(706\) 17.8437 33.6568i 0.671556 1.26669i
\(707\) −21.8236 −0.820760
\(708\) −1.75173 1.89991i −0.0658341 0.0714028i
\(709\) 20.4953 0.769716 0.384858 0.922976i \(-0.374250\pi\)
0.384858 + 0.922976i \(0.374250\pi\)
\(710\) −35.4103 + 66.7909i −1.32892 + 2.50662i
\(711\) 3.08523 2.92248i 0.115705 0.109602i
\(712\) 4.20843 + 6.20697i 0.157718 + 0.232616i
\(713\) −3.94073 + 0.867421i −0.147582 + 0.0324852i
\(714\) 2.72026 + 9.79748i 0.101803 + 0.366661i
\(715\) 47.2785 35.9402i 1.76812 1.34409i
\(716\) −4.16026 + 0.452455i −0.155476 + 0.0169090i
\(717\) −0.519251 + 9.57703i −0.0193918 + 0.357661i
\(718\) 4.44549 16.0112i 0.165904 0.597533i
\(719\) 2.52687 + 6.34197i 0.0942364 + 0.236516i 0.968537 0.248869i \(-0.0800589\pi\)
−0.874301 + 0.485385i \(0.838680\pi\)
\(720\) 14.3075 + 3.14931i 0.533208 + 0.117368i
\(721\) 1.63144 + 30.0901i 0.0607579 + 1.12061i
\(722\) 5.13458 + 31.3195i 0.191089 + 1.16559i
\(723\) 4.16375 6.14107i 0.154851 0.228389i
\(724\) −1.14743 + 2.87983i −0.0426439 + 0.107028i
\(725\) −17.2399 13.1054i −0.640274 0.486724i
\(726\) −28.9433 17.4146i −1.07419 0.646317i
\(727\) −33.4903 + 11.2842i −1.24209 + 0.418507i −0.862220 0.506534i \(-0.830926\pi\)
−0.379866 + 0.925042i \(0.624030\pi\)
\(728\) 15.7694 + 14.9376i 0.584454 + 0.553624i
\(729\) −0.161782 + 0.986827i −0.00599193 + 0.0365491i
\(730\) 19.9369 + 2.16827i 0.737897 + 0.0802511i
\(731\) 15.1781 9.13237i 0.561383 0.337773i
\(732\) 1.18701 1.39746i 0.0438732 0.0516515i
\(733\) 5.21119 2.41095i 0.192480 0.0890506i −0.321282 0.946984i \(-0.604114\pi\)
0.513762 + 0.857933i \(0.328252\pi\)
\(734\) −42.6093 19.7132i −1.57274 0.727627i
\(735\) 0.143088 + 0.168456i 0.00527789 + 0.00621361i
\(736\) 1.58022 + 0.532439i 0.0582478 + 0.0196260i
\(737\) −28.5101 53.7757i −1.05018 1.98085i
\(738\) 9.02910 + 17.0307i 0.332366 + 0.626908i
\(739\) −1.33483 0.449756i −0.0491025 0.0165446i 0.294643 0.955607i \(-0.404799\pi\)
−0.343746 + 0.939063i \(0.611696\pi\)
\(740\) 1.65515 + 1.94859i 0.0608444 + 0.0716316i
\(741\) 18.3873 + 8.50686i 0.675474 + 0.312507i
\(742\) 4.31924 1.99829i 0.158564 0.0733597i
\(743\) 4.07308 4.79521i 0.149427 0.175919i −0.682356 0.731020i \(-0.739045\pi\)
0.831783 + 0.555101i \(0.187320\pi\)
\(744\) 9.93326 5.97664i 0.364171 0.219114i
\(745\) −30.7115 3.34007i −1.12518 0.122371i
\(746\) −8.03259 + 48.9966i −0.294094 + 1.79389i
\(747\) −10.7887 10.2196i −0.394738 0.373916i
\(748\) −4.58931 + 1.54632i −0.167802 + 0.0565391i
\(749\) −13.1455 7.90936i −0.480325 0.289002i
\(750\) −1.26276 0.959927i −0.0461095 0.0350516i
\(751\) 4.25358 10.6757i 0.155215 0.389561i −0.830720 0.556691i \(-0.812071\pi\)
0.985935 + 0.167130i \(0.0534500\pi\)
\(752\) 15.5897 22.9931i 0.568498 0.838472i
\(753\) −1.53089 9.33799i −0.0557886 0.340295i
\(754\) 1.08167 + 19.9503i 0.0393922 + 0.726546i
\(755\) −40.3627 8.88450i −1.46895 0.323340i
\(756\) −0.331086 0.830962i −0.0120415 0.0302218i
\(757\) 7.28416 26.2352i 0.264747 0.953534i −0.704956 0.709251i \(-0.749033\pi\)
0.969704 0.244283i \(-0.0785527\pi\)
\(758\) 1.99719 36.8359i 0.0725411 1.33794i
\(759\) 5.06215 0.550542i 0.183744 0.0199834i
\(760\) 41.0133 31.1775i 1.48771 1.13093i
\(761\) −5.12787 18.4689i −0.185885 0.669498i −0.996476 0.0838842i \(-0.973267\pi\)
0.810590 0.585614i \(-0.199146\pi\)
\(762\) 8.49403 1.86968i 0.307706 0.0677312i
\(763\) −6.04899 8.92159i −0.218988 0.322983i
\(764\) 1.41196 1.33748i 0.0510830 0.0483884i
\(765\) 3.76546 7.10241i 0.136140 0.256788i
\(766\) 2.18519 0.0789540
\(767\) −13.0068 + 20.9726i −0.469650 + 0.757278i
\(768\) −7.85881 −0.283581
\(769\) 0.264821 0.499505i 0.00954968 0.0180126i −0.878691 0.477390i \(-0.841583\pi\)
0.888241 + 0.459378i \(0.151928\pi\)
\(770\) −54.5369 + 51.6601i −1.96537 + 1.86170i
\(771\) −0.842690 1.24288i −0.0303487 0.0447611i
\(772\) 1.05366 0.231927i 0.0379219 0.00834725i
\(773\) −4.50602 16.2292i −0.162070 0.583724i −0.999319 0.0369019i \(-0.988251\pi\)
0.837249 0.546822i \(-0.184163\pi\)
\(774\) −8.61509 + 6.54902i −0.309663 + 0.235400i
\(775\) −24.1251 + 2.62376i −0.866598 + 0.0942482i
\(776\) 1.35541 24.9990i 0.0486563 0.897412i
\(777\) −1.68232 + 6.05918i −0.0603530 + 0.217372i
\(778\) −4.14146 10.3943i −0.148479 0.372653i
\(779\) 77.6622 + 17.0947i 2.78254 + 0.612483i
\(780\) 0.188022 + 3.46787i 0.00673228 + 0.124170i
\(781\) −14.3271 87.3917i −0.512665 3.12712i
\(782\) 1.89959 2.80168i 0.0679291 0.100188i
\(783\) −1.50584 + 3.77938i −0.0538145 + 0.135064i
\(784\) −0.249710 0.189825i −0.00891822 0.00677946i
\(785\) −34.1804 20.5657i −1.21995 0.734020i
\(786\) 19.3663 6.52526i 0.690772 0.232748i
\(787\) 24.2289 + 22.9509i 0.863668 + 0.818110i 0.984649 0.174545i \(-0.0558453\pi\)
−0.120981 + 0.992655i \(0.538604\pi\)
\(788\) −0.167107 + 1.01931i −0.00595295 + 0.0363114i
\(789\) 9.17121 + 0.997429i 0.326504 + 0.0355094i
\(790\) 17.8830 10.7599i 0.636250 0.382819i
\(791\) −14.3093 + 16.8462i −0.508780 + 0.598982i
\(792\) −13.2771 + 6.14264i −0.471781 + 0.218269i
\(793\) −15.8914 7.35217i −0.564322 0.261083i
\(794\) 3.47102 + 4.08640i 0.123182 + 0.145021i
\(795\) −3.56556 1.20138i −0.126457 0.0426084i
\(796\) 3.32583 + 6.27318i 0.117881 + 0.222347i
\(797\) −1.34956 2.54553i −0.0478038 0.0901674i 0.858459 0.512882i \(-0.171422\pi\)
−0.906263 + 0.422714i \(0.861077\pi\)
\(798\) −24.2851 8.18262i −0.859685 0.289661i
\(799\) −9.86846 11.6181i −0.349121 0.411017i
\(800\) 9.10169 + 4.21089i 0.321793 + 0.148878i
\(801\) −2.67657 + 1.23831i −0.0945721 + 0.0437537i
\(802\) −16.4865 + 19.4094i −0.582157 + 0.685369i
\(803\) −20.1300 + 12.1118i −0.710372 + 0.427417i
\(804\) 3.53850 + 0.384835i 0.124793 + 0.0135721i
\(805\) 1.22318 7.46105i 0.0431113 0.262968i
\(806\) 16.2544 + 15.3970i 0.572537 + 0.542336i
\(807\) 27.3827 9.22631i 0.963917 0.324781i
\(808\) −17.8846 10.7608i −0.629176 0.378563i
\(809\) −22.1653 16.8496i −0.779289 0.592400i 0.138088 0.990420i \(-0.455904\pi\)
−0.917377 + 0.398020i \(0.869697\pi\)
\(810\) −1.81779 + 4.56231i −0.0638706 + 0.160303i
\(811\) −24.2265 + 35.7314i −0.850707 + 1.25470i 0.114556 + 0.993417i \(0.463456\pi\)
−0.965263 + 0.261282i \(0.915855\pi\)
\(812\) −0.588739 3.59115i −0.0206607 0.126025i
\(813\) −0.722922 13.3335i −0.0253540 0.467627i
\(814\) −20.3130 4.47123i −0.711970 0.156716i
\(815\) 26.9573 + 67.6578i 0.944275 + 2.36995i
\(816\) −3.05207 + 10.9926i −0.106844 + 0.384817i
\(817\) −2.41696 + 44.5783i −0.0845588 + 1.55960i
\(818\) 13.8755 1.50905i 0.485146 0.0527628i
\(819\) −6.80033 + 5.16947i −0.237623 + 0.180636i
\(820\) 3.64686 + 13.1348i 0.127354 + 0.458687i
\(821\) −48.5719 + 10.6915i −1.69517 + 0.373135i −0.954379 0.298599i \(-0.903481\pi\)
−0.740792 + 0.671734i \(0.765550\pi\)
\(822\) −17.2250 25.4049i −0.600790 0.886099i
\(823\) −18.7303 + 17.7423i −0.652897 + 0.618457i −0.940703 0.339232i \(-0.889833\pi\)
0.287805 + 0.957689i \(0.407074\pi\)
\(824\) −13.4999 + 25.4634i −0.470290 + 0.887060i
\(825\) 30.6238 1.06618
\(826\) 13.4877 28.1516i 0.469297 0.979520i
\(827\) 3.81574 0.132686 0.0663432 0.997797i \(-0.478867\pi\)
0.0663432 + 0.997797i \(0.478867\pi\)
\(828\) −0.139480 + 0.263088i −0.00484727 + 0.00914293i
\(829\) −1.92099 + 1.81965i −0.0667186 + 0.0631992i −0.720332 0.693629i \(-0.756011\pi\)
0.653614 + 0.756828i \(0.273252\pi\)
\(830\) −40.9565 60.4063i −1.42162 2.09673i
\(831\) 4.30063 0.946639i 0.149187 0.0328386i
\(832\) 5.36313 + 19.3162i 0.185933 + 0.669670i
\(833\) −0.137023 + 0.104162i −0.00474755 + 0.00360899i
\(834\) 24.1315 2.62446i 0.835607 0.0908777i
\(835\) −0.569014 + 10.4949i −0.0196916 + 0.363189i
\(836\) 3.26527 11.7604i 0.112932 0.406744i
\(837\) 1.68745 + 4.23518i 0.0583268 + 0.146389i
\(838\) 4.60697 + 1.01407i 0.159145 + 0.0350305i
\(839\) 1.93527 + 35.6939i 0.0668129 + 1.23229i 0.819176 + 0.573542i \(0.194431\pi\)
−0.752363 + 0.658749i \(0.771086\pi\)
\(840\) 3.51416 + 21.4354i 0.121250 + 0.739593i
\(841\) 6.98605 10.3037i 0.240898 0.355299i
\(842\) 5.29271 13.2837i 0.182399 0.457787i
\(843\) 16.6347 + 12.6454i 0.572931 + 0.435531i
\(844\) −0.488864 0.294140i −0.0168274 0.0101247i
\(845\) −8.15220 + 2.74680i −0.280444 + 0.0944927i
\(846\) 6.76093 + 6.40430i 0.232446 + 0.220184i
\(847\) 9.50530 57.9797i 0.326606 1.99221i
\(848\) 5.30832 + 0.577314i 0.182288 + 0.0198250i
\(849\) 2.81353 1.69285i 0.0965602 0.0580983i
\(850\) 13.1791 15.5156i 0.452040 0.532182i
\(851\) 1.89991 0.878993i 0.0651282 0.0301315i
\(852\) 4.70015 + 2.17452i 0.161024 + 0.0744979i
\(853\) −31.5837 37.1832i −1.08141 1.27313i −0.959841 0.280546i \(-0.909485\pi\)
−0.121565 0.992583i \(-0.538791\pi\)
\(854\) 20.9887 + 7.07193i 0.718220 + 0.241997i
\(855\) 9.49006 + 17.9001i 0.324553 + 0.612172i
\(856\) −6.87283 12.9635i −0.234909 0.443085i
\(857\) 3.62202 + 1.22040i 0.123726 + 0.0416881i 0.380483 0.924788i \(-0.375758\pi\)
−0.256757 + 0.966476i \(0.582654\pi\)
\(858\) −18.2910 21.5339i −0.624445 0.735154i
\(859\) 30.9925 + 14.3386i 1.05745 + 0.489228i 0.870003 0.493047i \(-0.164117\pi\)
0.187446 + 0.982275i \(0.439979\pi\)
\(860\) −6.94557 + 3.21336i −0.236842 + 0.109575i
\(861\) −21.7059 + 25.5542i −0.739736 + 0.870885i
\(862\) −25.6946 + 15.4599i −0.875161 + 0.526567i
\(863\) −15.2078 1.65394i −0.517679 0.0563009i −0.154449 0.988001i \(-0.549360\pi\)
−0.363229 + 0.931700i \(0.618326\pi\)
\(864\) 0.304800 1.85920i 0.0103695 0.0632512i
\(865\) 23.9980 + 22.7321i 0.815957 + 0.772915i
\(866\) −40.1616 + 13.5320i −1.36475 + 0.459836i
\(867\) −9.20257 5.53700i −0.312536 0.188046i
\(868\) −3.24644 2.46788i −0.110191 0.0837653i
\(869\) −9.04944 + 22.7124i −0.306981 + 0.770464i
\(870\) −11.2125 + 16.5372i −0.380140 + 0.560665i
\(871\) −5.49911 33.5431i −0.186330 1.13656i
\(872\) −0.558121 10.2939i −0.0189004 0.348597i
\(873\) 9.61545 + 2.11652i 0.325434 + 0.0716334i
\(874\) 3.15767 + 7.92515i 0.106810 + 0.268072i
\(875\) 0.738113 2.65844i 0.0249528 0.0898718i
\(876\) 0.0743779 1.37182i 0.00251300 0.0463495i
\(877\) −20.1827 + 2.19500i −0.681521 + 0.0741199i −0.442330 0.896852i \(-0.645848\pi\)
−0.239192 + 0.970972i \(0.576882\pi\)
\(878\) −6.25773 + 4.75700i −0.211188 + 0.160541i
\(879\) 4.41427 + 15.8988i 0.148890 + 0.536252i
\(880\) −82.3128 + 18.1184i −2.77476 + 0.610772i
\(881\) 15.4322 + 22.7608i 0.519923 + 0.766830i 0.993489 0.113929i \(-0.0363436\pi\)
−0.473565 + 0.880759i \(0.657033\pi\)
\(882\) 0.0763394 0.0723125i 0.00257048 0.00243489i
\(883\) −6.79219 + 12.8114i −0.228575 + 0.431139i −0.971098 0.238682i \(-0.923284\pi\)
0.742522 + 0.669821i \(0.233629\pi\)
\(884\) −2.70450 −0.0909623
\(885\) −23.0473 + 8.82497i −0.774725 + 0.296648i
\(886\) 57.8350 1.94301
\(887\) 12.5639 23.6980i 0.421853 0.795700i −0.577939 0.816080i \(-0.696143\pi\)
0.999792 + 0.0203803i \(0.00648769\pi\)
\(888\) −4.36633 + 4.13601i −0.146525 + 0.138795i
\(889\) 8.48967 + 12.5213i 0.284735 + 0.419952i
\(890\) −14.1450 + 3.11354i −0.474140 + 0.104366i
\(891\) −1.53913 5.54343i −0.0515626 0.185712i
\(892\) 2.26385 1.72093i 0.0757993 0.0576211i
\(893\) 38.1930 4.15374i 1.27808 0.139000i
\(894\) −0.795679 + 14.6754i −0.0266115 + 0.490820i
\(895\) −10.6916 + 38.5076i −0.357380 + 1.28717i
\(896\) −13.0938 32.8630i −0.437434 1.09788i
\(897\) 2.77718 + 0.611303i 0.0927272 + 0.0204108i
\(898\) −2.39485 44.1704i −0.0799171 1.47398i
\(899\) 3.00063 + 18.3031i 0.100077 + 0.610441i
\(900\) −1.00500 + 1.48227i −0.0335000 + 0.0494088i
\(901\) 1.08450 2.72189i 0.0361299 0.0906793i
\(902\) −88.2851 67.1126i −2.93957 2.23461i
\(903\) −16.1287 9.70433i −0.536730 0.322940i
\(904\) −20.0331 + 6.74993i −0.666290 + 0.224499i
\(905\) 21.4929 + 20.3592i 0.714448 + 0.676761i
\(906\) −3.18096 + 19.4030i −0.105680 + 0.644622i
\(907\) 12.1293 + 1.31914i 0.402747 + 0.0438013i 0.307251 0.951629i \(-0.400591\pi\)
0.0954956 + 0.995430i \(0.469556\pi\)
\(908\) 0.609660 0.366820i 0.0202323 0.0121733i
\(909\) 5.31394 6.25606i 0.176252 0.207500i
\(910\) −38.0740 + 17.6149i −1.26214 + 0.583928i
\(911\) −38.9142 18.0036i −1.28928 0.596487i −0.349079 0.937093i \(-0.613505\pi\)
−0.940206 + 0.340607i \(0.889368\pi\)
\(912\) −18.6140 21.9141i −0.616371 0.725648i
\(913\) 81.0194 + 27.2986i 2.68135 + 0.903452i
\(914\) 11.4746 + 21.6434i 0.379546 + 0.715900i
\(915\) −8.20191 15.4704i −0.271147 0.511437i
\(916\) −7.50966 2.53030i −0.248126 0.0836034i
\(917\) 23.0121 + 27.0919i 0.759926 + 0.894654i
\(918\) −3.47096 1.60584i −0.114559 0.0530006i
\(919\) 37.1819 17.2022i 1.22652 0.567448i 0.303731 0.952758i \(-0.401768\pi\)
0.922787 + 0.385310i \(0.125906\pi\)
\(920\) 4.68130 5.51125i 0.154338 0.181701i
\(921\) 24.3496 14.6506i 0.802345 0.482755i
\(922\) 42.0695 + 4.57534i 1.38549 + 0.150681i
\(923\) 8.00108 48.8044i 0.263359 1.60642i
\(924\) 3.73607 + 3.53899i 0.122908 + 0.116424i
\(925\) 11.9308 4.01997i 0.392284 0.132176i
\(926\) 45.1929 + 27.1917i 1.48513 + 0.893574i
\(927\) −9.02302 6.85912i −0.296355 0.225283i
\(928\) 2.83703 7.12041i 0.0931302 0.233739i
\(929\) −1.93071 + 2.84759i −0.0633446 + 0.0934263i −0.858042 0.513579i \(-0.828319\pi\)
0.794697 + 0.607006i \(0.207630\pi\)
\(930\) 3.62224 + 22.0947i 0.118778 + 0.724513i
\(931\) −0.0234849 0.433153i −0.000769686 0.0141960i
\(932\) 2.23006 + 0.490874i 0.0730481 + 0.0160791i
\(933\) −0.698851 1.75398i −0.0228794 0.0574229i
\(934\) −8.32148 + 29.9712i −0.272287 + 0.980689i
\(935\) −2.50384 + 46.1806i −0.0818843 + 1.51027i
\(936\) −8.12187 + 0.883307i −0.265472 + 0.0288718i
\(937\) −32.2833 + 24.5411i −1.05465 + 0.801723i −0.980696 0.195539i \(-0.937354\pi\)
−0.0739522 + 0.997262i \(0.523561\pi\)
\(938\) 11.5024 + 41.4279i 0.375567 + 1.35267i
\(939\) −12.9115 + 2.84203i −0.421349 + 0.0927460i
\(940\) 3.69581 + 5.45091i 0.120544 + 0.177789i
\(941\) −34.5609 + 32.7378i −1.12665 + 1.06722i −0.129518 + 0.991577i \(0.541343\pi\)
−0.997135 + 0.0756448i \(0.975899\pi\)
\(942\) −8.88930 + 16.7670i −0.289629 + 0.546298i
\(943\) 11.1616 0.363472
\(944\) 29.2508 19.2625i 0.952033 0.626940i
\(945\) −8.54231 −0.277881
\(946\) 29.1625 55.0063i 0.948155 1.78841i
\(947\) 0.638151 0.604489i 0.0207371 0.0196432i −0.677261 0.735743i \(-0.736833\pi\)
0.697998 + 0.716100i \(0.254074\pi\)
\(948\) −0.802352 1.18338i −0.0260592 0.0384344i
\(949\) −12.8130 + 2.82035i −0.415927 + 0.0915524i
\(950\) 13.7260 + 49.4365i 0.445330 + 1.60393i
\(951\) 5.67170 4.31151i 0.183917 0.139810i
\(952\) −16.8161 + 1.82886i −0.545014 + 0.0592738i
\(953\) 0.0748442 1.38042i 0.00242444 0.0447162i −0.997071 0.0764834i \(-0.975631\pi\)
0.999495 + 0.0317672i \(0.0101135\pi\)
\(954\) −0.478875 + 1.72475i −0.0155042 + 0.0558409i
\(955\) −6.87467 17.2541i −0.222459 0.558330i
\(956\) 3.15136 + 0.693666i 0.101922 + 0.0224348i
\(957\) −1.26715 23.3713i −0.0409613 0.755487i
\(958\) −4.37277 26.6727i −0.141278 0.861757i
\(959\) 29.9609 44.1890i 0.967486 1.42694i
\(960\) −7.42030 + 18.6235i −0.239489 + 0.601072i
\(961\) −8.13270 6.18232i −0.262345 0.199430i
\(962\) −9.95280 5.98840i −0.320891 0.193074i
\(963\) 5.46820 1.84245i 0.176210 0.0593721i
\(964\) −1.81223 1.71664i −0.0583681 0.0552892i
\(965\) 1.66687 10.1675i 0.0536585 0.327302i
\(966\) −3.57586 0.388898i −0.115051 0.0125126i
\(967\) −50.4215 + 30.3376i −1.62145 + 0.975592i −0.643838 + 0.765162i \(0.722659\pi\)
−0.977609 + 0.210430i \(0.932514\pi\)
\(968\) 36.3783 42.8279i 1.16924 1.37654i
\(969\) −14.3191 + 6.62471i −0.459995 + 0.212816i
\(970\) 43.8840 + 20.3029i 1.40903 + 0.651887i
\(971\) 10.4243 + 12.2724i 0.334531 + 0.393840i 0.903549 0.428485i \(-0.140952\pi\)
−0.569018 + 0.822325i \(0.692677\pi\)
\(972\) 0.318826 + 0.107425i 0.0102263 + 0.00344565i
\(973\) 19.7769 + 37.3032i 0.634019 + 1.19589i
\(974\) −4.10573 7.74422i −0.131556 0.248141i
\(975\) 16.2068 + 5.46071i 0.519034 + 0.174883i
\(976\) 16.0874 + 18.9395i 0.514945 + 0.606240i
\(977\) 8.52578 + 3.94445i 0.272764 + 0.126194i 0.551503 0.834173i \(-0.314054\pi\)
−0.278739 + 0.960367i \(0.589917\pi\)
\(978\) 31.4464 14.5486i 1.00554 0.465214i
\(979\) 10.9841 12.9315i 0.351053 0.413292i
\(980\) 0.0637166 0.0383370i 0.00203535 0.00122463i
\(981\) 4.03041 + 0.438334i 0.128681 + 0.0139949i
\(982\) −1.44680 + 8.82510i −0.0461693 + 0.281620i
\(983\) 3.79088 + 3.59091i 0.120910 + 0.114532i 0.745766 0.666208i \(-0.232084\pi\)
−0.624856 + 0.780740i \(0.714842\pi\)
\(984\) −30.3884 + 10.2391i −0.968748 + 0.326409i
\(985\) 8.45224 + 5.08555i 0.269311 + 0.162039i
\(986\) −12.3865 9.41594i −0.394465 0.299865i
\(987\) −5.99559 + 15.0478i −0.190842 + 0.478977i
\(988\) 3.82513 5.64165i 0.121694 0.179485i
\(989\) 1.01376 + 6.18364i 0.0322356 + 0.196628i
\(990\) −1.52965 28.2128i −0.0486156 0.896662i
\(991\) 21.2994 + 4.68835i 0.676598 + 0.148931i 0.539960 0.841691i \(-0.318439\pi\)
0.136638 + 0.990621i \(0.456370\pi\)
\(992\) −3.17918 7.97914i −0.100939 0.253338i
\(993\) −6.81391 + 24.5415i −0.216233 + 0.778801i
\(994\) −3.38676 + 62.4651i −0.107421 + 1.98127i
\(995\) 67.4095 7.33122i 2.13702 0.232415i
\(996\) −3.98018 + 3.02566i −0.126117 + 0.0958716i
\(997\) 2.87921 + 10.3700i 0.0911854 + 0.328420i 0.995047 0.0994046i \(-0.0316938\pi\)
−0.903862 + 0.427825i \(0.859280\pi\)
\(998\) 42.8514 9.43231i 1.35644 0.298575i
\(999\) −1.32732 1.95764i −0.0419944 0.0619371i
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 177.2.e.b.19.2 140
3.2 odd 2 531.2.i.b.19.4 140
59.28 even 29 inner 177.2.e.b.28.2 yes 140
177.146 odd 58 531.2.i.b.28.4 140
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.2.e.b.19.2 140 1.1 even 1 trivial
177.2.e.b.28.2 yes 140 59.28 even 29 inner
531.2.i.b.19.4 140 3.2 odd 2
531.2.i.b.28.4 140 177.146 odd 58