Properties

Label 966.2.q.e.715.2
Level $966$
Weight $2$
Character 966.715
Analytic conductor $7.714$
Analytic rank $0$
Dimension $20$
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] = [966,2,Mod(85,966)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(966, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([0, 0, 8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("966.85");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 966.q (of order \(11\), degree \(10\), 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: \(7.71354883526\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(2\) over \(\Q(\zeta_{11})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - 9 x^{19} + 42 x^{18} - 126 x^{17} + 277 x^{16} - 538 x^{15} + 1046 x^{14} - 1170 x^{13} - 619 x^{12} + 2218 x^{11} + 1660 x^{10} - 3225 x^{9} + 2719 x^{8} + 8761 x^{7} + \cdots + 529 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label 715.2
Root \(1.16609 + 1.34574i\) of defining polynomial
Character \(\chi\) \(=\) 966.715
Dual form 966.2.q.e.127.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.841254 - 0.540641i) q^{2} +(-0.142315 - 0.989821i) q^{3} +(0.415415 + 0.909632i) q^{4} +(3.96506 + 1.16425i) q^{5} +(-0.415415 + 0.909632i) q^{6} +(-0.654861 + 0.755750i) q^{7} +(0.142315 - 0.989821i) q^{8} +(-0.959493 + 0.281733i) q^{9} +O(q^{10})\) \(q+(-0.841254 - 0.540641i) q^{2} +(-0.142315 - 0.989821i) q^{3} +(0.415415 + 0.909632i) q^{4} +(3.96506 + 1.16425i) q^{5} +(-0.415415 + 0.909632i) q^{6} +(-0.654861 + 0.755750i) q^{7} +(0.142315 - 0.989821i) q^{8} +(-0.959493 + 0.281733i) q^{9} +(-2.70618 - 3.12310i) q^{10} +(-1.40305 + 0.901683i) q^{11} +(0.841254 - 0.540641i) q^{12} +(3.62304 + 4.18121i) q^{13} +(0.959493 - 0.281733i) q^{14} +(0.588109 - 4.09039i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(1.00309 - 2.19646i) q^{17} +(0.959493 + 0.281733i) q^{18} +(-1.65897 - 3.63265i) q^{19} +(0.588109 + 4.09039i) q^{20} +(0.841254 + 0.540641i) q^{21} +1.66780 q^{22} +(4.27431 - 2.17493i) q^{23} -1.00000 q^{24} +(10.1599 + 6.52939i) q^{25} +(-0.787362 - 5.47623i) q^{26} +(0.415415 + 0.909632i) q^{27} +(-0.959493 - 0.281733i) q^{28} +(-3.56623 + 7.80894i) q^{29} +(-2.70618 + 3.12310i) q^{30} +(-0.401622 + 2.79335i) q^{31} +(0.959493 - 0.281733i) q^{32} +(1.09218 + 1.26044i) q^{33} +(-2.03134 + 1.30547i) q^{34} +(-3.47644 + 2.23417i) q^{35} +(-0.654861 - 0.755750i) q^{36} +(-6.20414 + 1.82170i) q^{37} +(-0.568339 + 3.95289i) q^{38} +(3.62304 - 4.18121i) q^{39} +(1.71668 - 3.75901i) q^{40} +(8.79154 + 2.58143i) q^{41} +(-0.415415 - 0.909632i) q^{42} +(-0.491048 - 3.41531i) q^{43} +(-1.40305 - 0.901683i) q^{44} -4.13245 q^{45} +(-4.77163 - 0.481201i) q^{46} +7.27423 q^{47} +(0.841254 + 0.540641i) q^{48} +(-0.142315 - 0.989821i) q^{49} +(-5.01702 - 10.9857i) q^{50} +(-2.31685 - 0.680289i) q^{51} +(-2.29830 + 5.03257i) q^{52} +(-8.31645 + 9.59769i) q^{53} +(0.142315 - 0.989821i) q^{54} +(-6.61294 + 1.94173i) q^{55} +(0.654861 + 0.755750i) q^{56} +(-3.35958 + 2.15907i) q^{57} +(7.22193 - 4.64126i) q^{58} +(1.52562 + 1.76066i) q^{59} +(3.96506 - 1.16425i) q^{60} +(2.01051 - 13.9834i) q^{61} +(1.84806 - 2.13278i) q^{62} +(0.415415 - 0.909632i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(9.49761 + 20.7969i) q^{65} +(-0.237353 - 1.65083i) q^{66} +(4.77448 + 3.06837i) q^{67} +2.41466 q^{68} +(-2.76109 - 3.92128i) q^{69} +4.13245 q^{70} +(4.83501 + 3.10727i) q^{71} +(0.142315 + 0.989821i) q^{72} +(0.546484 + 1.19663i) q^{73} +(6.20414 + 1.82170i) q^{74} +(5.01702 - 10.9857i) q^{75} +(2.61521 - 3.01811i) q^{76} +(0.237353 - 1.65083i) q^{77} +(-5.30843 + 1.55870i) q^{78} +(-6.38684 - 7.37081i) q^{79} +(-3.47644 + 2.23417i) q^{80} +(0.841254 - 0.540641i) q^{81} +(-6.00029 - 6.92470i) q^{82} +(1.25615 - 0.368837i) q^{83} +(-0.142315 + 0.989821i) q^{84} +(6.53451 - 7.54123i) q^{85} +(-1.43336 + 3.13862i) q^{86} +(8.23699 + 2.41860i) q^{87} +(0.692831 + 1.51709i) q^{88} +(-0.692975 - 4.81974i) q^{89} +(3.47644 + 2.23417i) q^{90} -5.53254 q^{91} +(3.75399 + 2.98455i) q^{92} +2.82207 q^{93} +(-6.11947 - 3.93274i) q^{94} +(-2.34863 - 16.3351i) q^{95} +(-0.415415 - 0.909632i) q^{96} +(-10.8563 - 3.18769i) q^{97} +(-0.415415 + 0.909632i) q^{98} +(1.09218 - 1.26044i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 10 q^{5} + 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 10 q^{5} + 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9} - 10 q^{10} - 3 q^{11} - 2 q^{12} + 6 q^{13} + 2 q^{14} - 12 q^{15} - 2 q^{16} + 14 q^{17} + 2 q^{18} - 13 q^{19} - 12 q^{20} - 2 q^{21} - 8 q^{22} - 2 q^{23} - 20 q^{24} + 22 q^{25} - 28 q^{26} - 2 q^{27} - 2 q^{28} + 26 q^{29} - 10 q^{30} + 15 q^{31} + 2 q^{32} - 14 q^{33} - 3 q^{34} - q^{35} - 2 q^{36} - 26 q^{37} + 2 q^{38} + 6 q^{39} + q^{40} + 40 q^{41} + 2 q^{42} + 8 q^{43} - 3 q^{44} - 12 q^{45} - 20 q^{46} + 36 q^{47} - 2 q^{48} - 2 q^{49} + 11 q^{50} + 3 q^{51} - 27 q^{52} - 5 q^{53} + 2 q^{54} - 7 q^{55} + 2 q^{56} + 9 q^{57} - 15 q^{58} + 13 q^{59} + 10 q^{60} + 59 q^{61} - 4 q^{62} - 2 q^{63} - 2 q^{64} - q^{65} - 8 q^{66} - 26 q^{67} - 8 q^{68} - 35 q^{69} + 12 q^{70} + 13 q^{71} + 2 q^{72} - 34 q^{73} + 26 q^{74} - 11 q^{75} - 2 q^{76} + 8 q^{77} - 6 q^{78} - 27 q^{79} - q^{80} - 2 q^{81} - 40 q^{82} + 41 q^{83} - 2 q^{84} + 51 q^{85} + 14 q^{86} - 7 q^{87} - 8 q^{88} + 43 q^{89} + q^{90} - 16 q^{91} + 9 q^{92} + 4 q^{93} - 3 q^{94} - 26 q^{95} + 2 q^{96} - 8 q^{97} + 2 q^{98} - 14 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/966\mathbb{Z}\right)^\times\).

\(n\) \(323\) \(829\) \(925\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{11}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.841254 0.540641i −0.594856 0.382291i
\(3\) −0.142315 0.989821i −0.0821655 0.571474i
\(4\) 0.415415 + 0.909632i 0.207708 + 0.454816i
\(5\) 3.96506 + 1.16425i 1.77323 + 0.520666i 0.994316 0.106468i \(-0.0339543\pi\)
0.778911 + 0.627135i \(0.215772\pi\)
\(6\) −0.415415 + 0.909632i −0.169592 + 0.371356i
\(7\) −0.654861 + 0.755750i −0.247514 + 0.285646i
\(8\) 0.142315 0.989821i 0.0503159 0.349955i
\(9\) −0.959493 + 0.281733i −0.319831 + 0.0939109i
\(10\) −2.70618 3.12310i −0.855769 0.987610i
\(11\) −1.40305 + 0.901683i −0.423034 + 0.271868i −0.734790 0.678295i \(-0.762719\pi\)
0.311756 + 0.950162i \(0.399083\pi\)
\(12\) 0.841254 0.540641i 0.242849 0.156070i
\(13\) 3.62304 + 4.18121i 1.00485 + 1.15966i 0.987147 + 0.159817i \(0.0510903\pi\)
0.0177044 + 0.999843i \(0.494364\pi\)
\(14\) 0.959493 0.281733i 0.256435 0.0752962i
\(15\) 0.588109 4.09039i 0.151849 1.05613i
\(16\) −0.654861 + 0.755750i −0.163715 + 0.188937i
\(17\) 1.00309 2.19646i 0.243284 0.532719i −0.748118 0.663566i \(-0.769042\pi\)
0.991403 + 0.130847i \(0.0417697\pi\)
\(18\) 0.959493 + 0.281733i 0.226155 + 0.0664050i
\(19\) −1.65897 3.63265i −0.380595 0.833387i −0.998875 0.0474285i \(-0.984897\pi\)
0.618280 0.785958i \(-0.287830\pi\)
\(20\) 0.588109 + 4.09039i 0.131505 + 0.914638i
\(21\) 0.841254 + 0.540641i 0.183577 + 0.117977i
\(22\) 1.66780 0.355577
\(23\) 4.27431 2.17493i 0.891255 0.453503i
\(24\) −1.00000 −0.204124
\(25\) 10.1599 + 6.52939i 2.03199 + 1.30588i
\(26\) −0.787362 5.47623i −0.154414 1.07398i
\(27\) 0.415415 + 0.909632i 0.0799467 + 0.175059i
\(28\) −0.959493 0.281733i −0.181327 0.0532424i
\(29\) −3.56623 + 7.80894i −0.662231 + 1.45008i 0.218197 + 0.975905i \(0.429983\pi\)
−0.880428 + 0.474180i \(0.842745\pi\)
\(30\) −2.70618 + 3.12310i −0.494078 + 0.570197i
\(31\) −0.401622 + 2.79335i −0.0721335 + 0.501700i 0.921441 + 0.388519i \(0.127013\pi\)
−0.993574 + 0.113181i \(0.963896\pi\)
\(32\) 0.959493 0.281733i 0.169616 0.0498038i
\(33\) 1.09218 + 1.26044i 0.190124 + 0.219415i
\(34\) −2.03134 + 1.30547i −0.348373 + 0.223885i
\(35\) −3.47644 + 2.23417i −0.587625 + 0.377644i
\(36\) −0.654861 0.755750i −0.109143 0.125958i
\(37\) −6.20414 + 1.82170i −1.01995 + 0.299486i −0.748620 0.662999i \(-0.769283\pi\)
−0.271335 + 0.962485i \(0.587465\pi\)
\(38\) −0.568339 + 3.95289i −0.0921968 + 0.641243i
\(39\) 3.62304 4.18121i 0.580151 0.669530i
\(40\) 1.71668 3.75901i 0.271431 0.594351i
\(41\) 8.79154 + 2.58143i 1.37301 + 0.403151i 0.883330 0.468752i \(-0.155296\pi\)
0.489678 + 0.871903i \(0.337114\pi\)
\(42\) −0.415415 0.909632i −0.0640999 0.140359i
\(43\) −0.491048 3.41531i −0.0748841 0.520830i −0.992393 0.123114i \(-0.960712\pi\)
0.917508 0.397716i \(-0.130197\pi\)
\(44\) −1.40305 0.901683i −0.211517 0.135934i
\(45\) −4.13245 −0.616029
\(46\) −4.77163 0.481201i −0.703538 0.0709492i
\(47\) 7.27423 1.06105 0.530527 0.847668i \(-0.321994\pi\)
0.530527 + 0.847668i \(0.321994\pi\)
\(48\) 0.841254 + 0.540641i 0.121424 + 0.0780348i
\(49\) −0.142315 0.989821i −0.0203307 0.141403i
\(50\) −5.01702 10.9857i −0.709514 1.55362i
\(51\) −2.31685 0.680289i −0.324424 0.0952596i
\(52\) −2.29830 + 5.03257i −0.318717 + 0.697892i
\(53\) −8.31645 + 9.59769i −1.14235 + 1.31834i −0.201515 + 0.979485i \(0.564586\pi\)
−0.940837 + 0.338859i \(0.889959\pi\)
\(54\) 0.142315 0.989821i 0.0193666 0.134698i
\(55\) −6.61294 + 1.94173i −0.891688 + 0.261823i
\(56\) 0.654861 + 0.755750i 0.0875094 + 0.100991i
\(57\) −3.35958 + 2.15907i −0.444987 + 0.285976i
\(58\) 7.22193 4.64126i 0.948286 0.609427i
\(59\) 1.52562 + 1.76066i 0.198619 + 0.229218i 0.846318 0.532678i \(-0.178814\pi\)
−0.647699 + 0.761896i \(0.724269\pi\)
\(60\) 3.96506 1.16425i 0.511886 0.150303i
\(61\) 2.01051 13.9834i 0.257420 1.79039i −0.293629 0.955920i \(-0.594863\pi\)
0.551048 0.834473i \(-0.314228\pi\)
\(62\) 1.84806 2.13278i 0.234704 0.270863i
\(63\) 0.415415 0.909632i 0.0523374 0.114603i
\(64\) −0.959493 0.281733i −0.119937 0.0352166i
\(65\) 9.49761 + 20.7969i 1.17803 + 2.57953i
\(66\) −0.237353 1.65083i −0.0292162 0.203203i
\(67\) 4.77448 + 3.06837i 0.583296 + 0.374861i 0.798760 0.601650i \(-0.205490\pi\)
−0.215464 + 0.976512i \(0.569126\pi\)
\(68\) 2.41466 0.292821
\(69\) −2.76109 3.92128i −0.332396 0.472066i
\(70\) 4.13245 0.493922
\(71\) 4.83501 + 3.10727i 0.573810 + 0.368765i 0.795133 0.606435i \(-0.207401\pi\)
−0.221323 + 0.975201i \(0.571037\pi\)
\(72\) 0.142315 + 0.989821i 0.0167720 + 0.116652i
\(73\) 0.546484 + 1.19663i 0.0639611 + 0.140055i 0.938913 0.344155i \(-0.111834\pi\)
−0.874952 + 0.484210i \(0.839107\pi\)
\(74\) 6.20414 + 1.82170i 0.721217 + 0.211768i
\(75\) 5.01702 10.9857i 0.579316 1.26852i
\(76\) 2.61521 3.01811i 0.299985 0.346201i
\(77\) 0.237353 1.65083i 0.0270489 0.188129i
\(78\) −5.30843 + 1.55870i −0.601062 + 0.176488i
\(79\) −6.38684 7.37081i −0.718576 0.829281i 0.272559 0.962139i \(-0.412130\pi\)
−0.991135 + 0.132858i \(0.957585\pi\)
\(80\) −3.47644 + 2.23417i −0.388678 + 0.249788i
\(81\) 0.841254 0.540641i 0.0934726 0.0600712i
\(82\) −6.00029 6.92470i −0.662621 0.764705i
\(83\) 1.25615 0.368837i 0.137880 0.0404852i −0.212064 0.977256i \(-0.568019\pi\)
0.349944 + 0.936771i \(0.386201\pi\)
\(84\) −0.142315 + 0.989821i −0.0155278 + 0.107998i
\(85\) 6.53451 7.54123i 0.708767 0.817961i
\(86\) −1.43336 + 3.13862i −0.154563 + 0.338447i
\(87\) 8.23699 + 2.41860i 0.883098 + 0.259301i
\(88\) 0.692831 + 1.51709i 0.0738560 + 0.161722i
\(89\) −0.692975 4.81974i −0.0734552 0.510892i −0.993019 0.117952i \(-0.962367\pi\)
0.919564 0.392940i \(-0.128542\pi\)
\(90\) 3.47644 + 2.23417i 0.366449 + 0.235502i
\(91\) −5.53254 −0.579968
\(92\) 3.75399 + 2.98455i 0.391381 + 0.311161i
\(93\) 2.82207 0.292635
\(94\) −6.11947 3.93274i −0.631175 0.405631i
\(95\) −2.34863 16.3351i −0.240965 1.67595i
\(96\) −0.415415 0.909632i −0.0423981 0.0928389i
\(97\) −10.8563 3.18769i −1.10229 0.323661i −0.320527 0.947239i \(-0.603860\pi\)
−0.781761 + 0.623578i \(0.785678\pi\)
\(98\) −0.415415 + 0.909632i −0.0419633 + 0.0918867i
\(99\) 1.09218 1.26044i 0.109768 0.126679i
\(100\) −1.71876 + 11.9542i −0.171876 + 1.19542i
\(101\) 18.1732 5.33613i 1.80830 0.530964i 0.809850 0.586637i \(-0.199549\pi\)
0.998449 + 0.0556727i \(0.0177304\pi\)
\(102\) 1.58127 + 1.82488i 0.156569 + 0.180690i
\(103\) 12.9273 8.30788i 1.27377 0.818599i 0.283660 0.958925i \(-0.408451\pi\)
0.990105 + 0.140326i \(0.0448150\pi\)
\(104\) 4.65427 2.99112i 0.456388 0.293303i
\(105\) 2.70618 + 3.12310i 0.264096 + 0.304783i
\(106\) 12.1851 3.57788i 1.18353 0.347515i
\(107\) 0.0706169 0.491151i 0.00682679 0.0474814i −0.986123 0.166015i \(-0.946910\pi\)
0.992950 + 0.118533i \(0.0378192\pi\)
\(108\) −0.654861 + 0.755750i −0.0630140 + 0.0727220i
\(109\) 8.39806 18.3892i 0.804388 1.76136i 0.174534 0.984651i \(-0.444158\pi\)
0.629854 0.776713i \(-0.283115\pi\)
\(110\) 6.61294 + 1.94173i 0.630519 + 0.185137i
\(111\) 2.68610 + 5.88174i 0.254953 + 0.558270i
\(112\) −0.142315 0.989821i −0.0134475 0.0935293i
\(113\) −0.0285898 0.0183735i −0.00268950 0.00172844i 0.539295 0.842117i \(-0.318691\pi\)
−0.541985 + 0.840388i \(0.682327\pi\)
\(114\) 3.99354 0.374029
\(115\) 19.4800 3.64736i 1.81652 0.340118i
\(116\) −8.58473 −0.797072
\(117\) −4.65427 2.99112i −0.430287 0.276529i
\(118\) −0.331549 2.30597i −0.0305216 0.212282i
\(119\) 1.00309 + 2.19646i 0.0919529 + 0.201349i
\(120\) −3.96506 1.16425i −0.361958 0.106281i
\(121\) −3.41406 + 7.47575i −0.310369 + 0.679613i
\(122\) −9.25136 + 10.6766i −0.837578 + 0.966617i
\(123\) 1.30399 9.06943i 0.117577 0.817763i
\(124\) −2.70776 + 0.795069i −0.243164 + 0.0713993i
\(125\) 19.1520 + 22.1026i 1.71301 + 1.97691i
\(126\) −0.841254 + 0.540641i −0.0749448 + 0.0481641i
\(127\) 6.56990 4.22222i 0.582985 0.374661i −0.215656 0.976469i \(-0.569189\pi\)
0.798641 + 0.601808i \(0.205553\pi\)
\(128\) 0.654861 + 0.755750i 0.0578821 + 0.0667995i
\(129\) −3.31067 + 0.972099i −0.291488 + 0.0855886i
\(130\) 3.25373 22.6302i 0.285371 1.98480i
\(131\) −5.61110 + 6.47556i −0.490244 + 0.565772i −0.945931 0.324368i \(-0.894848\pi\)
0.455687 + 0.890140i \(0.349394\pi\)
\(132\) −0.692831 + 1.51709i −0.0603032 + 0.132046i
\(133\) 3.83177 + 1.12511i 0.332257 + 0.0975593i
\(134\) −2.35766 5.16256i −0.203671 0.445977i
\(135\) 0.588109 + 4.09039i 0.0506163 + 0.352044i
\(136\) −2.03134 1.30547i −0.174186 0.111943i
\(137\) −9.72033 −0.830463 −0.415232 0.909716i \(-0.636300\pi\)
−0.415232 + 0.909716i \(0.636300\pi\)
\(138\) 0.202771 + 4.79154i 0.0172610 + 0.407883i
\(139\) −22.6634 −1.92229 −0.961144 0.276049i \(-0.910975\pi\)
−0.961144 + 0.276049i \(0.910975\pi\)
\(140\) −3.47644 2.23417i −0.293813 0.188822i
\(141\) −1.03523 7.20018i −0.0871821 0.606365i
\(142\) −2.38755 5.22801i −0.200359 0.438725i
\(143\) −8.85343 2.59960i −0.740361 0.217390i
\(144\) 0.415415 0.909632i 0.0346179 0.0758027i
\(145\) −23.2318 + 26.8109i −1.92930 + 2.22653i
\(146\) 0.187217 1.30212i 0.0154942 0.107764i
\(147\) −0.959493 + 0.281733i −0.0791376 + 0.0232369i
\(148\) −4.23437 4.88672i −0.348063 0.401686i
\(149\) 5.66449 3.64035i 0.464053 0.298229i −0.287644 0.957737i \(-0.592872\pi\)
0.751697 + 0.659508i \(0.229236\pi\)
\(150\) −10.1599 + 6.52939i −0.829555 + 0.533123i
\(151\) −11.2146 12.9423i −0.912629 1.05323i −0.998379 0.0569131i \(-0.981874\pi\)
0.0857503 0.996317i \(-0.472671\pi\)
\(152\) −3.83177 + 1.12511i −0.310798 + 0.0912584i
\(153\) −0.343642 + 2.39009i −0.0277818 + 0.193227i
\(154\) −1.09218 + 1.26044i −0.0880103 + 0.101569i
\(155\) −4.84459 + 10.6082i −0.389127 + 0.852070i
\(156\) 5.30843 + 1.55870i 0.425015 + 0.124796i
\(157\) −2.23282 4.88919i −0.178198 0.390200i 0.799364 0.600847i \(-0.205170\pi\)
−0.977562 + 0.210647i \(0.932443\pi\)
\(158\) 1.38799 + 9.65371i 0.110423 + 0.768008i
\(159\) 10.6836 + 6.86590i 0.847261 + 0.544502i
\(160\) 4.13245 0.326699
\(161\) −1.15538 + 4.65458i −0.0910564 + 0.366832i
\(162\) −1.00000 −0.0785674
\(163\) −14.6523 9.41644i −1.14765 0.737552i −0.178483 0.983943i \(-0.557119\pi\)
−0.969171 + 0.246391i \(0.920755\pi\)
\(164\) 1.30399 + 9.06943i 0.101824 + 0.708203i
\(165\) 2.86309 + 6.26929i 0.222891 + 0.488064i
\(166\) −1.25615 0.368837i −0.0974958 0.0286273i
\(167\) −7.26226 + 15.9021i −0.561970 + 1.23054i 0.388993 + 0.921241i \(0.372823\pi\)
−0.950964 + 0.309303i \(0.899904\pi\)
\(168\) 0.654861 0.755750i 0.0505236 0.0583073i
\(169\) −2.50602 + 17.4297i −0.192771 + 1.34075i
\(170\) −9.57427 + 2.81126i −0.734313 + 0.215614i
\(171\) 2.61521 + 3.01811i 0.199990 + 0.230801i
\(172\) 2.90269 1.86545i 0.221328 0.142239i
\(173\) −2.51874 + 1.61870i −0.191496 + 0.123067i −0.632876 0.774253i \(-0.718126\pi\)
0.441379 + 0.897321i \(0.354489\pi\)
\(174\) −5.62180 6.48791i −0.426188 0.491847i
\(175\) −11.5879 + 3.40252i −0.875965 + 0.257206i
\(176\) 0.237353 1.65083i 0.0178912 0.124436i
\(177\) 1.52562 1.76066i 0.114673 0.132339i
\(178\) −2.02278 + 4.42928i −0.151614 + 0.331988i
\(179\) 1.03654 + 0.304355i 0.0774744 + 0.0227485i 0.320240 0.947336i \(-0.396236\pi\)
−0.242766 + 0.970085i \(0.578055\pi\)
\(180\) −1.71668 3.75901i −0.127954 0.280180i
\(181\) 0.841324 + 5.85154i 0.0625351 + 0.434941i 0.996904 + 0.0786332i \(0.0250556\pi\)
−0.934368 + 0.356308i \(0.884035\pi\)
\(182\) 4.65427 + 2.99112i 0.344997 + 0.221716i
\(183\) −14.1272 −1.04431
\(184\) −1.54449 4.54032i −0.113861 0.334717i
\(185\) −26.7207 −1.96454
\(186\) −2.37408 1.52573i −0.174076 0.111872i
\(187\) 0.573128 + 3.98620i 0.0419113 + 0.291499i
\(188\) 3.02182 + 6.61687i 0.220389 + 0.482585i
\(189\) −0.959493 0.281733i −0.0697928 0.0204930i
\(190\) −6.85563 + 15.0117i −0.497360 + 1.08907i
\(191\) −2.53563 + 2.92627i −0.183472 + 0.211737i −0.840033 0.542535i \(-0.817465\pi\)
0.656562 + 0.754272i \(0.272010\pi\)
\(192\) −0.142315 + 0.989821i −0.0102707 + 0.0714342i
\(193\) 6.12399 1.79816i 0.440814 0.129435i −0.0537916 0.998552i \(-0.517131\pi\)
0.494606 + 0.869117i \(0.335312\pi\)
\(194\) 7.40949 + 8.55100i 0.531970 + 0.613926i
\(195\) 19.2335 12.3606i 1.37734 0.885163i
\(196\) 0.841254 0.540641i 0.0600895 0.0386172i
\(197\) −6.11437 7.05636i −0.435631 0.502745i 0.494904 0.868947i \(-0.335203\pi\)
−0.930535 + 0.366203i \(0.880658\pi\)
\(198\) −1.60025 + 0.469875i −0.113725 + 0.0333925i
\(199\) 1.69179 11.7667i 0.119928 0.834116i −0.837705 0.546123i \(-0.816103\pi\)
0.957633 0.287993i \(-0.0929879\pi\)
\(200\) 7.90884 9.12729i 0.559240 0.645397i
\(201\) 2.35766 5.16256i 0.166297 0.364139i
\(202\) −18.1732 5.33613i −1.27866 0.375449i
\(203\) −3.56623 7.80894i −0.250300 0.548080i
\(204\) −0.343642 2.39009i −0.0240598 0.167339i
\(205\) 31.8535 + 20.4710i 2.22475 + 1.42976i
\(206\) −15.3667 −1.07065
\(207\) −3.48842 + 3.29104i −0.242462 + 0.228743i
\(208\) −5.53254 −0.383613
\(209\) 5.60312 + 3.60090i 0.387576 + 0.249080i
\(210\) −0.588109 4.09039i −0.0405834 0.282263i
\(211\) 10.9372 + 23.9492i 0.752949 + 1.64873i 0.760992 + 0.648761i \(0.224712\pi\)
−0.00804324 + 0.999968i \(0.502560\pi\)
\(212\) −12.1851 3.57788i −0.836879 0.245730i
\(213\) 2.38755 5.22801i 0.163592 0.358217i
\(214\) −0.324943 + 0.375004i −0.0222127 + 0.0256348i
\(215\) 2.02923 14.1136i 0.138392 0.962540i
\(216\) 0.959493 0.281733i 0.0652852 0.0191695i
\(217\) −1.84806 2.13278i −0.125455 0.144782i
\(218\) −17.0068 + 10.9296i −1.15185 + 0.740248i
\(219\) 1.10668 0.711220i 0.0747825 0.0480598i
\(220\) −4.51338 5.20871i −0.304292 0.351171i
\(221\) 12.8181 3.76373i 0.862237 0.253176i
\(222\) 0.920217 6.40025i 0.0617609 0.429556i
\(223\) −17.8680 + 20.6208i −1.19653 + 1.38087i −0.290929 + 0.956745i \(0.593964\pi\)
−0.905603 + 0.424127i \(0.860581\pi\)
\(224\) −0.415415 + 0.909632i −0.0277561 + 0.0607773i
\(225\) −11.5879 3.40252i −0.772528 0.226835i
\(226\) 0.0141178 + 0.0309136i 0.000939100 + 0.00205634i
\(227\) −1.73148 12.0427i −0.114923 0.799304i −0.963013 0.269453i \(-0.913157\pi\)
0.848091 0.529851i \(-0.177752\pi\)
\(228\) −3.35958 2.15907i −0.222493 0.142988i
\(229\) −8.58127 −0.567066 −0.283533 0.958962i \(-0.591507\pi\)
−0.283533 + 0.958962i \(0.591507\pi\)
\(230\) −18.3595 7.46333i −1.21059 0.492118i
\(231\) −1.66780 −0.109733
\(232\) 7.22193 + 4.64126i 0.474143 + 0.304713i
\(233\) −2.60414 18.1122i −0.170603 1.18657i −0.877614 0.479368i \(-0.840866\pi\)
0.707011 0.707203i \(-0.250043\pi\)
\(234\) 2.29830 + 5.03257i 0.150245 + 0.328990i
\(235\) 28.8427 + 8.46898i 1.88149 + 0.552456i
\(236\) −0.967787 + 2.11916i −0.0629976 + 0.137945i
\(237\) −6.38684 + 7.37081i −0.414870 + 0.478785i
\(238\) 0.343642 2.39009i 0.0222750 0.154926i
\(239\) −10.0536 + 2.95201i −0.650315 + 0.190950i −0.590219 0.807243i \(-0.700959\pi\)
−0.0600955 + 0.998193i \(0.519141\pi\)
\(240\) 2.70618 + 3.12310i 0.174683 + 0.201595i
\(241\) 3.00147 1.92893i 0.193341 0.124253i −0.440389 0.897807i \(-0.645159\pi\)
0.633730 + 0.773554i \(0.281523\pi\)
\(242\) 6.91378 4.44322i 0.444435 0.285621i
\(243\) −0.654861 0.755750i −0.0420093 0.0484814i
\(244\) 13.5550 3.98010i 0.867767 0.254799i
\(245\) 0.588109 4.09039i 0.0375729 0.261325i
\(246\) −6.00029 + 6.92470i −0.382564 + 0.441503i
\(247\) 9.17834 20.0978i 0.584004 1.27879i
\(248\) 2.70776 + 0.795069i 0.171943 + 0.0504869i
\(249\) −0.543851 1.19087i −0.0344652 0.0754682i
\(250\) −4.16213 28.9482i −0.263236 1.83085i
\(251\) −14.5858 9.37370i −0.920645 0.591662i −0.00780010 0.999970i \(-0.502483\pi\)
−0.912845 + 0.408307i \(0.866119\pi\)
\(252\) 1.00000 0.0629941
\(253\) −4.03596 + 6.90559i −0.253738 + 0.434151i
\(254\) −7.80966 −0.490022
\(255\) −8.39443 5.39477i −0.525679 0.337834i
\(256\) −0.142315 0.989821i −0.00889468 0.0618638i
\(257\) 0.144154 + 0.315654i 0.00899209 + 0.0196899i 0.914075 0.405546i \(-0.132918\pi\)
−0.905083 + 0.425236i \(0.860191\pi\)
\(258\) 3.31067 + 0.972099i 0.206113 + 0.0605203i
\(259\) 2.68610 5.88174i 0.166906 0.365473i
\(260\) −14.9720 + 17.2787i −0.928526 + 1.07158i
\(261\) 1.22173 8.49735i 0.0756235 0.525973i
\(262\) 8.22131 2.41399i 0.507914 0.149137i
\(263\) −2.16722 2.50111i −0.133637 0.154225i 0.684987 0.728555i \(-0.259808\pi\)
−0.818624 + 0.574330i \(0.805262\pi\)
\(264\) 1.40305 0.901683i 0.0863515 0.0554948i
\(265\) −44.1493 + 28.3730i −2.71207 + 1.74294i
\(266\) −2.61521 3.01811i −0.160349 0.185052i
\(267\) −4.67207 + 1.37184i −0.285926 + 0.0839554i
\(268\) −0.807699 + 5.61767i −0.0493381 + 0.343154i
\(269\) 10.5469 12.1718i 0.643058 0.742129i −0.336854 0.941557i \(-0.609363\pi\)
0.979913 + 0.199428i \(0.0639084\pi\)
\(270\) 1.71668 3.75901i 0.104474 0.228766i
\(271\) −2.63024 0.772308i −0.159776 0.0469144i 0.200867 0.979619i \(-0.435624\pi\)
−0.360642 + 0.932704i \(0.617442\pi\)
\(272\) 1.00309 + 2.19646i 0.0608211 + 0.133180i
\(273\) 0.787362 + 5.47623i 0.0476533 + 0.331436i
\(274\) 8.17726 + 5.25520i 0.494006 + 0.317479i
\(275\) −20.1423 −1.21463
\(276\) 2.41992 4.14053i 0.145662 0.249231i
\(277\) −11.0349 −0.663020 −0.331510 0.943452i \(-0.607558\pi\)
−0.331510 + 0.943452i \(0.607558\pi\)
\(278\) 19.0657 + 12.2528i 1.14348 + 0.734873i
\(279\) −0.401622 2.79335i −0.0240445 0.167233i
\(280\) 1.71668 + 3.75901i 0.102591 + 0.224644i
\(281\) 25.5655 + 7.50669i 1.52511 + 0.447812i 0.933549 0.358450i \(-0.116695\pi\)
0.591558 + 0.806262i \(0.298513\pi\)
\(282\) −3.02182 + 6.61687i −0.179947 + 0.394029i
\(283\) −13.6864 + 15.7950i −0.813573 + 0.938914i −0.999043 0.0437362i \(-0.986074\pi\)
0.185470 + 0.982650i \(0.440619\pi\)
\(284\) −0.817938 + 5.68889i −0.0485357 + 0.337573i
\(285\) −15.8346 + 4.64946i −0.937960 + 0.275410i
\(286\) 6.04253 + 6.97345i 0.357302 + 0.412349i
\(287\) −7.70815 + 4.95373i −0.454998 + 0.292409i
\(288\) −0.841254 + 0.540641i −0.0495713 + 0.0318576i
\(289\) 7.31440 + 8.44127i 0.430259 + 0.496545i
\(290\) 34.0389 9.99473i 1.99883 0.586911i
\(291\) −1.61024 + 11.1994i −0.0943937 + 0.656522i
\(292\) −0.861477 + 0.994198i −0.0504141 + 0.0581810i
\(293\) 0.0623222 0.136467i 0.00364090 0.00797246i −0.907803 0.419397i \(-0.862241\pi\)
0.911444 + 0.411425i \(0.134969\pi\)
\(294\) 0.959493 + 0.281733i 0.0559588 + 0.0164310i
\(295\) 3.99933 + 8.75731i 0.232850 + 0.509870i
\(296\) 0.920217 + 6.40025i 0.0534865 + 0.372007i
\(297\) −1.40305 0.901683i −0.0814130 0.0523210i
\(298\) −6.73340 −0.390055
\(299\) 24.5798 + 9.99194i 1.42149 + 0.577849i
\(300\) 12.0771 0.697274
\(301\) 2.90269 + 1.86545i 0.167308 + 0.107522i
\(302\) 2.43716 + 16.9508i 0.140243 + 0.975410i
\(303\) −7.86813 17.2288i −0.452012 0.989768i
\(304\) 3.83177 + 1.12511i 0.219767 + 0.0645294i
\(305\) 24.2519 53.1043i 1.38866 3.04074i
\(306\) 1.58127 1.82488i 0.0903951 0.104321i
\(307\) 0.151878 1.05634i 0.00866815 0.0602883i −0.985028 0.172393i \(-0.944850\pi\)
0.993696 + 0.112105i \(0.0357592\pi\)
\(308\) 1.60025 0.469875i 0.0911825 0.0267736i
\(309\) −10.0631 11.6134i −0.572468 0.660663i
\(310\) 9.81075 6.30499i 0.557213 0.358099i
\(311\) 2.57740 1.65640i 0.146151 0.0939257i −0.465522 0.885037i \(-0.654133\pi\)
0.611673 + 0.791111i \(0.290497\pi\)
\(312\) −3.62304 4.18121i −0.205114 0.236715i
\(313\) −11.0236 + 3.23682i −0.623091 + 0.182956i −0.578013 0.816027i \(-0.696172\pi\)
−0.0450779 + 0.998983i \(0.514354\pi\)
\(314\) −0.764930 + 5.32020i −0.0431675 + 0.300237i
\(315\) 2.70618 3.12310i 0.152476 0.175967i
\(316\) 4.05153 8.87162i 0.227917 0.499068i
\(317\) −22.8575 6.71156i −1.28380 0.376959i −0.432501 0.901634i \(-0.642369\pi\)
−0.851303 + 0.524675i \(0.824187\pi\)
\(318\) −5.27559 11.5519i −0.295840 0.647800i
\(319\) −2.03761 14.1719i −0.114084 0.793475i
\(320\) −3.47644 2.23417i −0.194339 0.124894i
\(321\) −0.496202 −0.0276953
\(322\) 3.48842 3.29104i 0.194402 0.183402i
\(323\) −9.64305 −0.536553
\(324\) 0.841254 + 0.540641i 0.0467363 + 0.0300356i
\(325\) 9.50908 + 66.1371i 0.527469 + 3.66863i
\(326\) 7.23536 + 15.8432i 0.400729 + 0.877475i
\(327\) −19.3972 5.69553i −1.07267 0.314963i
\(328\) 3.80632 8.33468i 0.210169 0.460206i
\(329\) −4.76360 + 5.49749i −0.262626 + 0.303087i
\(330\) 0.980850 6.82196i 0.0539940 0.375537i
\(331\) 0.466709 0.137038i 0.0256526 0.00753229i −0.268881 0.963173i \(-0.586654\pi\)
0.294534 + 0.955641i \(0.404836\pi\)
\(332\) 0.857328 + 0.989409i 0.0470520 + 0.0543009i
\(333\) 5.43960 3.49582i 0.298088 0.191570i
\(334\) 14.7067 9.45145i 0.804717 0.517160i
\(335\) 15.3587 + 17.7249i 0.839138 + 0.968417i
\(336\) −0.959493 + 0.281733i −0.0523446 + 0.0153698i
\(337\) 2.66647 18.5457i 0.145252 1.01025i −0.778605 0.627514i \(-0.784073\pi\)
0.923857 0.382737i \(-0.125018\pi\)
\(338\) 11.5314 13.3080i 0.627227 0.723859i
\(339\) −0.0141178 + 0.0309136i −0.000766772 + 0.00167900i
\(340\) 9.57427 + 2.81126i 0.519238 + 0.152462i
\(341\) −1.95522 4.28133i −0.105881 0.231847i
\(342\) −0.568339 3.95289i −0.0307323 0.213748i
\(343\) 0.841254 + 0.540641i 0.0454234 + 0.0291919i
\(344\) −3.45043 −0.186035
\(345\) −6.38253 18.7627i −0.343624 1.01015i
\(346\) 2.99403 0.160960
\(347\) −22.5971 14.5223i −1.21308 0.779597i −0.231906 0.972738i \(-0.574496\pi\)
−0.981171 + 0.193141i \(0.938132\pi\)
\(348\) 1.22173 + 8.49735i 0.0654918 + 0.455506i
\(349\) −11.2223 24.5735i −0.600718 1.31539i −0.928745 0.370720i \(-0.879111\pi\)
0.328027 0.944669i \(-0.393616\pi\)
\(350\) 11.5879 + 3.40252i 0.619401 + 0.181872i
\(351\) −2.29830 + 5.03257i −0.122674 + 0.268619i
\(352\) −1.09218 + 1.26044i −0.0582134 + 0.0671818i
\(353\) −1.18952 + 8.27328i −0.0633117 + 0.440342i 0.933368 + 0.358921i \(0.116855\pi\)
−0.996680 + 0.0814217i \(0.974054\pi\)
\(354\) −2.23532 + 0.656349i −0.118806 + 0.0348845i
\(355\) 15.5535 + 17.9496i 0.825492 + 0.952668i
\(356\) 4.09632 2.63255i 0.217105 0.139525i
\(357\) 2.03134 1.30547i 0.107510 0.0690926i
\(358\) −0.707443 0.816433i −0.0373895 0.0431498i
\(359\) 33.6854 9.89092i 1.77785 0.522023i 0.782875 0.622179i \(-0.213752\pi\)
0.994972 + 0.100156i \(0.0319342\pi\)
\(360\) −0.588109 + 4.09039i −0.0309961 + 0.215582i
\(361\) 1.99842 2.30630i 0.105180 0.121384i
\(362\) 2.45581 5.37748i 0.129075 0.282634i
\(363\) 7.88552 + 2.31540i 0.413883 + 0.121527i
\(364\) −2.29830 5.03257i −0.120464 0.263779i
\(365\) 0.773664 + 5.38095i 0.0404954 + 0.281652i
\(366\) 11.8846 + 7.63775i 0.621216 + 0.399231i
\(367\) −19.1939 −1.00191 −0.500956 0.865473i \(-0.667018\pi\)
−0.500956 + 0.865473i \(0.667018\pi\)
\(368\) −1.15538 + 4.65458i −0.0602282 + 0.242637i
\(369\) −9.16269 −0.476991
\(370\) 22.4789 + 14.4463i 1.16862 + 0.751027i
\(371\) −1.80734 12.5703i −0.0938323 0.652618i
\(372\) 1.17233 + 2.56704i 0.0607825 + 0.133095i
\(373\) −1.84120 0.540626i −0.0953339 0.0279926i 0.233718 0.972304i \(-0.424911\pi\)
−0.329052 + 0.944312i \(0.606729\pi\)
\(374\) 1.67295 3.66326i 0.0865064 0.189423i
\(375\) 19.1520 22.1026i 0.989004 1.14137i
\(376\) 1.03523 7.20018i 0.0533879 0.371321i
\(377\) −45.5715 + 13.3810i −2.34705 + 0.689156i
\(378\) 0.654861 + 0.755750i 0.0336824 + 0.0388716i
\(379\) 13.6118 8.74778i 0.699192 0.449343i −0.142151 0.989845i \(-0.545402\pi\)
0.841343 + 0.540502i \(0.181766\pi\)
\(380\) 13.8833 8.92224i 0.712197 0.457701i
\(381\) −5.11424 5.90215i −0.262010 0.302376i
\(382\) 3.71517 1.09087i 0.190084 0.0558138i
\(383\) −2.95580 + 20.5580i −0.151034 + 1.05047i 0.763457 + 0.645859i \(0.223501\pi\)
−0.914491 + 0.404606i \(0.867409\pi\)
\(384\) 0.654861 0.755750i 0.0334182 0.0385667i
\(385\) 2.86309 6.26929i 0.145917 0.319513i
\(386\) −6.12399 1.79816i −0.311703 0.0915242i
\(387\) 1.43336 + 3.13862i 0.0728619 + 0.159545i
\(388\) −1.61024 11.1994i −0.0817473 0.568565i
\(389\) −2.27239 1.46037i −0.115215 0.0740439i 0.481764 0.876301i \(-0.339996\pi\)
−0.596979 + 0.802257i \(0.703632\pi\)
\(390\) −22.8629 −1.15771
\(391\) −0.489624 11.5700i −0.0247613 0.585118i
\(392\) −1.00000 −0.0505076
\(393\) 7.20819 + 4.63242i 0.363605 + 0.233675i
\(394\) 1.32878 + 9.24186i 0.0669429 + 0.465598i
\(395\) −16.7428 36.6615i −0.842419 1.84464i
\(396\) 1.60025 + 0.469875i 0.0804154 + 0.0236121i
\(397\) 9.32828 20.4261i 0.468173 1.02516i −0.517375 0.855759i \(-0.673091\pi\)
0.985548 0.169397i \(-0.0541821\pi\)
\(398\) −7.78476 + 8.98409i −0.390215 + 0.450332i
\(399\) 0.568339 3.95289i 0.0284526 0.197892i
\(400\) −11.5879 + 3.40252i −0.579396 + 0.170126i
\(401\) 9.62846 + 11.1118i 0.480822 + 0.554898i 0.943390 0.331686i \(-0.107617\pi\)
−0.462568 + 0.886584i \(0.653072\pi\)
\(402\) −4.77448 + 3.06837i −0.238130 + 0.153037i
\(403\) −13.1347 + 8.44114i −0.654284 + 0.420483i
\(404\) 12.4033 + 14.3142i 0.617088 + 0.712158i
\(405\) 3.96506 1.16425i 0.197025 0.0578518i
\(406\) −1.22173 + 8.49735i −0.0606337 + 0.421716i
\(407\) 7.06210 8.15010i 0.350055 0.403985i
\(408\) −1.00309 + 2.19646i −0.0496602 + 0.108741i
\(409\) 22.1101 + 6.49210i 1.09327 + 0.321014i 0.778176 0.628046i \(-0.216145\pi\)
0.315096 + 0.949060i \(0.397963\pi\)
\(410\) −15.7294 34.4426i −0.776821 1.70100i
\(411\) 1.38335 + 9.62139i 0.0682355 + 0.474588i
\(412\) 12.9273 + 8.30788i 0.636883 + 0.409300i
\(413\) −2.32969 −0.114636
\(414\) 4.71391 0.882615i 0.231676 0.0433781i
\(415\) 5.41010 0.265572
\(416\) 4.65427 + 2.99112i 0.228194 + 0.146652i
\(417\) 3.22534 + 22.4327i 0.157946 + 1.09854i
\(418\) −2.76685 6.05855i −0.135331 0.296333i
\(419\) 13.0191 + 3.82274i 0.636023 + 0.186753i 0.583820 0.811883i \(-0.301558\pi\)
0.0522030 + 0.998636i \(0.483376\pi\)
\(420\) −1.71668 + 3.75901i −0.0837655 + 0.183421i
\(421\) −0.152200 + 0.175648i −0.00741777 + 0.00856056i −0.759446 0.650570i \(-0.774530\pi\)
0.752029 + 0.659131i \(0.229076\pi\)
\(422\) 3.74692 26.0604i 0.182397 1.26860i
\(423\) −6.97957 + 2.04939i −0.339358 + 0.0996446i
\(424\) 8.31645 + 9.59769i 0.403882 + 0.466105i
\(425\) 24.5328 15.7663i 1.19002 0.764777i
\(426\) −4.83501 + 3.10727i −0.234257 + 0.150548i
\(427\) 9.25136 + 10.6766i 0.447704 + 0.516679i
\(428\) 0.476102 0.139796i 0.0230133 0.00675731i
\(429\) −1.31317 + 9.13327i −0.0634003 + 0.440959i
\(430\) −9.33749 + 10.7760i −0.450294 + 0.519667i
\(431\) 7.16603 15.6914i 0.345175 0.755828i −0.654825 0.755781i \(-0.727258\pi\)
1.00000 4.76847e-5i \(-1.51785e-5\pi\)
\(432\) −0.959493 0.281733i −0.0461636 0.0135549i
\(433\) 8.24075 + 18.0447i 0.396025 + 0.867175i 0.997658 + 0.0684016i \(0.0217899\pi\)
−0.601632 + 0.798773i \(0.705483\pi\)
\(434\) 0.401622 + 2.79335i 0.0192785 + 0.134085i
\(435\) 29.8443 + 19.1798i 1.43092 + 0.919599i
\(436\) 20.2161 0.968174
\(437\) −14.9917 11.9189i −0.717151 0.570159i
\(438\) −1.31551 −0.0628576
\(439\) −3.32720 2.13826i −0.158798 0.102054i 0.458828 0.888525i \(-0.348269\pi\)
−0.617627 + 0.786471i \(0.711906\pi\)
\(440\) 0.980850 + 6.82196i 0.0467602 + 0.325224i
\(441\) 0.415415 + 0.909632i 0.0197817 + 0.0433158i
\(442\) −12.8181 3.76373i −0.609694 0.179022i
\(443\) −13.2572 + 29.0293i −0.629871 + 1.37922i 0.278247 + 0.960510i \(0.410247\pi\)
−0.908118 + 0.418715i \(0.862481\pi\)
\(444\) −4.23437 + 4.88672i −0.200954 + 0.231914i
\(445\) 2.86368 19.9173i 0.135752 0.944173i
\(446\) 26.1800 7.68714i 1.23966 0.363997i
\(447\) −4.40944 5.08876i −0.208559 0.240690i
\(448\) 0.841254 0.540641i 0.0397455 0.0255429i
\(449\) −19.6422 + 12.6232i −0.926971 + 0.595728i −0.914672 0.404196i \(-0.867551\pi\)
−0.0122986 + 0.999924i \(0.503915\pi\)
\(450\) 7.90884 + 9.12729i 0.372826 + 0.430265i
\(451\) −14.6626 + 4.30532i −0.690433 + 0.202730i
\(452\) 0.00483653 0.0336388i 0.000227491 0.00158224i
\(453\) −11.2146 + 12.9423i −0.526906 + 0.608082i
\(454\) −5.05418 + 11.0671i −0.237204 + 0.519405i
\(455\) −21.9368 6.44123i −1.02841 0.301970i
\(456\) 1.65897 + 3.63265i 0.0776886 + 0.170114i
\(457\) −2.23827 15.5675i −0.104702 0.728216i −0.972770 0.231772i \(-0.925548\pi\)
0.868069 0.496444i \(-0.165361\pi\)
\(458\) 7.21902 + 4.63939i 0.337323 + 0.216784i
\(459\) 2.41466 0.112707
\(460\) 11.4100 + 16.2045i 0.531996 + 0.755537i
\(461\) −31.8065 −1.48138 −0.740688 0.671849i \(-0.765500\pi\)
−0.740688 + 0.671849i \(0.765500\pi\)
\(462\) 1.40305 + 0.901683i 0.0652756 + 0.0419501i
\(463\) 0.402619 + 2.80028i 0.0187113 + 0.130140i 0.997036 0.0769370i \(-0.0245140\pi\)
−0.978325 + 0.207077i \(0.933605\pi\)
\(464\) −3.56623 7.80894i −0.165558 0.362521i
\(465\) 11.1897 + 3.28558i 0.518908 + 0.152365i
\(466\) −7.60146 + 16.6449i −0.352131 + 0.771059i
\(467\) −12.0866 + 13.9486i −0.559300 + 0.645466i −0.963024 0.269414i \(-0.913170\pi\)
0.403725 + 0.914881i \(0.367715\pi\)
\(468\) 0.787362 5.47623i 0.0363958 0.253139i
\(469\) −5.44554 + 1.59896i −0.251452 + 0.0738329i
\(470\) −19.6854 22.7181i −0.908018 1.04791i
\(471\) −4.52166 + 2.90590i −0.208347 + 0.133897i
\(472\) 1.95986 1.25952i 0.0902097 0.0579743i
\(473\) 3.76849 + 4.34907i 0.173276 + 0.199971i
\(474\) 9.35791 2.74773i 0.429823 0.126207i
\(475\) 6.86391 47.7396i 0.314938 2.19044i
\(476\) −1.58127 + 1.82488i −0.0724773 + 0.0836433i
\(477\) 5.27559 11.5519i 0.241553 0.528927i
\(478\) 10.0536 + 2.95201i 0.459842 + 0.135022i
\(479\) 10.6810 + 23.3882i 0.488030 + 1.06864i 0.980177 + 0.198124i \(0.0634848\pi\)
−0.492147 + 0.870512i \(0.663788\pi\)
\(480\) −0.588109 4.09039i −0.0268434 0.186700i
\(481\) −30.0948 19.3407i −1.37220 0.881862i
\(482\) −3.56785 −0.162511
\(483\) 4.77163 + 0.481201i 0.217117 + 0.0218954i
\(484\) −8.21843 −0.373565
\(485\) −39.3345 25.2787i −1.78609 1.14785i
\(486\) 0.142315 + 0.989821i 0.00645553 + 0.0448992i
\(487\) −0.154000 0.337214i −0.00697843 0.0152806i 0.906111 0.423041i \(-0.139037\pi\)
−0.913089 + 0.407760i \(0.866310\pi\)
\(488\) −13.5550 3.98010i −0.613604 0.180170i
\(489\) −7.23536 + 15.8432i −0.327194 + 0.716455i
\(490\) −2.70618 + 3.12310i −0.122253 + 0.141087i
\(491\) 2.68420 18.6690i 0.121136 0.842521i −0.835136 0.550043i \(-0.814611\pi\)
0.956272 0.292478i \(-0.0944797\pi\)
\(492\) 8.79154 2.58143i 0.396353 0.116380i
\(493\) 13.5748 + 15.6661i 0.611376 + 0.705566i
\(494\) −18.5870 + 11.9451i −0.836268 + 0.537437i
\(495\) 5.79802 3.72616i 0.260602 0.167478i
\(496\) −1.84806 2.13278i −0.0829805 0.0957646i
\(497\) −5.51458 + 1.61923i −0.247363 + 0.0726322i
\(498\) −0.186315 + 1.29585i −0.00834898 + 0.0580684i
\(499\) −1.32618 + 1.53049i −0.0593680 + 0.0685143i −0.784657 0.619930i \(-0.787161\pi\)
0.725289 + 0.688445i \(0.241706\pi\)
\(500\) −12.1492 + 26.6030i −0.543328 + 1.18972i
\(501\) 16.7738 + 4.92523i 0.749398 + 0.220043i
\(502\) 7.20252 + 15.7713i 0.321464 + 0.703908i
\(503\) −0.291362 2.02647i −0.0129912 0.0903559i 0.982294 0.187344i \(-0.0599881\pi\)
−0.995285 + 0.0969886i \(0.969079\pi\)
\(504\) −0.841254 0.540641i −0.0374724 0.0240821i
\(505\) 78.2702 3.48298
\(506\) 7.12871 3.62735i 0.316910 0.161255i
\(507\) 17.6090 0.782042
\(508\) 6.56990 + 4.22222i 0.291492 + 0.187331i
\(509\) −2.92309 20.3305i −0.129564 0.901135i −0.946108 0.323852i \(-0.895022\pi\)
0.816544 0.577283i \(-0.195887\pi\)
\(510\) 4.14521 + 9.07674i 0.183553 + 0.401925i
\(511\) −1.26222 0.370623i −0.0558375 0.0163954i
\(512\) −0.415415 + 0.909632i −0.0183589 + 0.0402004i
\(513\) 2.61521 3.01811i 0.115464 0.133253i
\(514\) 0.0493850 0.343480i 0.00217828 0.0151503i
\(515\) 60.9299 17.8906i 2.68489 0.788355i
\(516\) −2.25955 2.60766i −0.0994713 0.114796i
\(517\) −10.2061 + 6.55905i −0.448863 + 0.288467i
\(518\) −5.43960 + 3.49582i −0.239002 + 0.153597i
\(519\) 1.96068 + 2.26274i 0.0860641 + 0.0993233i
\(520\) 21.9368 6.44123i 0.961993 0.282467i
\(521\) −2.05632 + 14.3020i −0.0900888 + 0.626582i 0.893889 + 0.448289i \(0.147966\pi\)
−0.983978 + 0.178293i \(0.942943\pi\)
\(522\) −5.62180 + 6.48791i −0.246060 + 0.283968i
\(523\) −11.2709 + 24.6798i −0.492841 + 1.07917i 0.485889 + 0.874020i \(0.338496\pi\)
−0.978730 + 0.205151i \(0.934231\pi\)
\(524\) −8.22131 2.41399i −0.359149 0.105456i
\(525\) 5.01702 + 10.9857i 0.218961 + 0.479457i
\(526\) 0.470983 + 3.27576i 0.0205358 + 0.142830i
\(527\) 5.73259 + 3.68411i 0.249716 + 0.160483i
\(528\) −1.66780 −0.0725819
\(529\) 13.5394 18.5926i 0.588669 0.808374i
\(530\) 52.4803 2.27960
\(531\) −1.95986 1.25952i −0.0850506 0.0546587i
\(532\) 0.568339 + 3.95289i 0.0246406 + 0.171379i
\(533\) 21.0586 + 46.1119i 0.912150 + 1.99733i
\(534\) 4.67207 + 1.37184i 0.202180 + 0.0593654i
\(535\) 0.851821 1.86523i 0.0368274 0.0806408i
\(536\) 3.71662 4.28921i 0.160534 0.185266i
\(537\) 0.153742 1.06930i 0.00663446 0.0461437i
\(538\) −15.4532 + 4.53748i −0.666236 + 0.195625i
\(539\) 1.09218 + 1.26044i 0.0470435 + 0.0542911i
\(540\) −3.47644 + 2.23417i −0.149602 + 0.0961434i
\(541\) −14.7672 + 9.49030i −0.634891 + 0.408020i −0.818118 0.575051i \(-0.804982\pi\)
0.183227 + 0.983071i \(0.441346\pi\)
\(542\) 1.79516 + 2.07172i 0.0771086 + 0.0889881i
\(543\) 5.67225 1.66552i 0.243419 0.0714744i
\(544\) 0.343642 2.39009i 0.0147335 0.102474i
\(545\) 54.7083 63.1367i 2.34345 2.70448i
\(546\) 2.29830 5.03257i 0.0983581 0.215374i
\(547\) −35.8091 10.5145i −1.53109 0.449568i −0.595705 0.803204i \(-0.703127\pi\)
−0.935383 + 0.353636i \(0.884945\pi\)
\(548\) −4.03797 8.84192i −0.172493 0.377708i
\(549\) 2.01051 + 13.9834i 0.0858066 + 0.596798i
\(550\) 16.9448 + 10.8897i 0.722528 + 0.464340i
\(551\) 34.2834 1.46052
\(552\) −4.27431 + 2.17493i −0.181927 + 0.0925710i
\(553\) 9.75298 0.414739
\(554\) 9.28311 + 5.96589i 0.394402 + 0.253466i
\(555\) 3.80275 + 26.4487i 0.161418 + 1.12268i
\(556\) −9.41473 20.6154i −0.399273 0.874287i
\(557\) 11.7344 + 3.44553i 0.497202 + 0.145992i 0.520713 0.853732i \(-0.325666\pi\)
−0.0235110 + 0.999724i \(0.507484\pi\)
\(558\) −1.17233 + 2.56704i −0.0496287 + 0.108672i
\(559\) 12.5011 14.4270i 0.528739 0.610197i
\(560\) 0.588109 4.09039i 0.0248521 0.172850i
\(561\) 3.86406 1.13459i 0.163141 0.0479024i
\(562\) −17.4486 20.1368i −0.736025 0.849418i
\(563\) 20.3545 13.0810i 0.857839 0.551300i −0.0361714 0.999346i \(-0.511516\pi\)
0.894011 + 0.448046i \(0.147880\pi\)
\(564\) 6.11947 3.93274i 0.257676 0.165598i
\(565\) −0.0919687 0.106138i −0.00386915 0.00446524i
\(566\) 20.0532 5.88814i 0.842897 0.247497i
\(567\) −0.142315 + 0.989821i −0.00597666 + 0.0415686i
\(568\) 3.76374 4.34359i 0.157923 0.182253i
\(569\) −0.161273 + 0.353139i −0.00676092 + 0.0148044i −0.912982 0.407999i \(-0.866227\pi\)
0.906221 + 0.422803i \(0.138954\pi\)
\(570\) 15.8346 + 4.64946i 0.663238 + 0.194744i
\(571\) −3.20189 7.01117i −0.133995 0.293408i 0.830726 0.556681i \(-0.187925\pi\)
−0.964721 + 0.263273i \(0.915198\pi\)
\(572\) −1.31317 9.13327i −0.0549062 0.381881i
\(573\) 3.25734 + 2.09337i 0.136077 + 0.0874517i
\(574\) 9.16269 0.382443
\(575\) 57.6276 + 5.81152i 2.40324 + 0.242357i
\(576\) 1.00000 0.0416667
\(577\) −14.2382 9.15035i −0.592745 0.380934i 0.209606 0.977786i \(-0.432782\pi\)
−0.802352 + 0.596852i \(0.796418\pi\)
\(578\) −1.58957 11.0557i −0.0661175 0.459857i
\(579\) −2.65140 5.80575i −0.110188 0.241279i
\(580\) −34.0389 9.99473i −1.41339 0.415009i
\(581\) −0.543851 + 1.19087i −0.0225628 + 0.0494055i
\(582\) 7.40949 8.55100i 0.307133 0.354451i
\(583\) 3.01428 20.9648i 0.124839 0.868274i
\(584\) 1.26222 0.370623i 0.0522312 0.0153365i
\(585\) −14.9720 17.2787i −0.619018 0.714384i
\(586\) −0.126208 + 0.0811090i −0.00521361 + 0.00335058i
\(587\) −3.23493 + 2.07896i −0.133520 + 0.0858079i −0.605696 0.795696i \(-0.707105\pi\)
0.472176 + 0.881504i \(0.343469\pi\)
\(588\) −0.654861 0.755750i −0.0270060 0.0311666i
\(589\) 10.8135 3.17514i 0.445563 0.130829i
\(590\) 1.37011 9.52932i 0.0564065 0.392316i
\(591\) −6.11437 + 7.05636i −0.251511 + 0.290260i
\(592\) 2.68610 5.88174i 0.110398 0.241738i
\(593\) −22.5630 6.62511i −0.926553 0.272061i −0.216560 0.976269i \(-0.569484\pi\)
−0.709993 + 0.704209i \(0.751302\pi\)
\(594\) 0.692831 + 1.51709i 0.0284272 + 0.0622469i
\(595\) 1.42008 + 9.87691i 0.0582178 + 0.404914i
\(596\) 5.66449 + 3.64035i 0.232027 + 0.149114i
\(597\) −11.8876 −0.486529
\(598\) −15.2758 21.6946i −0.624674 0.887159i
\(599\) −13.0669 −0.533900 −0.266950 0.963710i \(-0.586016\pi\)
−0.266950 + 0.963710i \(0.586016\pi\)
\(600\) −10.1599 6.52939i −0.414777 0.266561i
\(601\) −2.91763 20.2926i −0.119013 0.827751i −0.958647 0.284598i \(-0.908140\pi\)
0.839634 0.543152i \(-0.182769\pi\)
\(602\) −1.43336 3.13862i −0.0584195 0.127921i
\(603\) −5.44554 1.59896i −0.221760 0.0651145i
\(604\) 7.11403 15.5776i 0.289466 0.633842i
\(605\) −22.2405 + 25.6669i −0.904206 + 1.04351i
\(606\) −2.69550 + 18.7476i −0.109497 + 0.761570i
\(607\) 11.2528 3.30413i 0.456738 0.134111i −0.0452671 0.998975i \(-0.514414\pi\)
0.502006 + 0.864864i \(0.332596\pi\)
\(608\) −2.61521 3.01811i −0.106061 0.122401i
\(609\) −7.22193 + 4.64126i −0.292648 + 0.188073i
\(610\) −49.1124 + 31.5626i −1.98850 + 1.27793i
\(611\) 26.3548 + 30.4151i 1.06620 + 1.23046i
\(612\) −2.31685 + 0.680289i −0.0936532 + 0.0274991i
\(613\) −4.40692 + 30.6508i −0.177994 + 1.23797i 0.683403 + 0.730042i \(0.260499\pi\)
−0.861397 + 0.507933i \(0.830410\pi\)
\(614\) −0.698867 + 0.806535i −0.0282040 + 0.0325491i
\(615\) 15.7294 34.4426i 0.634272 1.38886i
\(616\) −1.60025 0.469875i −0.0644758 0.0189318i
\(617\) 3.62489 + 7.93741i 0.145933 + 0.319548i 0.968456 0.249183i \(-0.0801620\pi\)
−0.822524 + 0.568731i \(0.807435\pi\)
\(618\) 2.18691 + 15.2103i 0.0879705 + 0.611848i
\(619\) −3.11866 2.00424i −0.125350 0.0805573i 0.476464 0.879194i \(-0.341918\pi\)
−0.601813 + 0.798637i \(0.705555\pi\)
\(620\) −11.6621 −0.468360
\(621\) 3.75399 + 2.98455i 0.150643 + 0.119766i
\(622\) −3.06377 −0.122846
\(623\) 4.09632 + 2.63255i 0.164116 + 0.105471i
\(624\) 0.787362 + 5.47623i 0.0315197 + 0.219224i
\(625\) 25.1208 + 55.0068i 1.00483 + 2.20027i
\(626\) 11.0236 + 3.23682i 0.440592 + 0.129369i
\(627\) 2.76685 6.05855i 0.110497 0.241955i
\(628\) 3.51982 4.06209i 0.140456 0.162095i
\(629\) −2.22201 + 15.4544i −0.0885975 + 0.616209i
\(630\) −3.96506 + 1.16425i −0.157972 + 0.0463846i
\(631\) −19.4827 22.4842i −0.775593 0.895082i 0.221190 0.975231i \(-0.429006\pi\)
−0.996783 + 0.0801489i \(0.974460\pi\)
\(632\) −8.20473 + 5.27286i −0.326367 + 0.209743i
\(633\) 22.1489 14.2342i 0.880339 0.565759i
\(634\) 15.6004 + 18.0038i 0.619570 + 0.715022i
\(635\) 30.9657 9.09236i 1.22884 0.360819i
\(636\) −1.80734 + 12.5703i −0.0716656 + 0.498445i
\(637\) 3.62304 4.18121i 0.143550 0.165666i
\(638\) −5.94777 + 13.0238i −0.235474 + 0.515617i
\(639\) −5.51458 1.61923i −0.218153 0.0640556i
\(640\) 1.71668 + 3.75901i 0.0678578 + 0.148588i
\(641\) 0.608871 + 4.23479i 0.0240490 + 0.167264i 0.998306 0.0581739i \(-0.0185278\pi\)
−0.974258 + 0.225438i \(0.927619\pi\)
\(642\) 0.417432 + 0.268267i 0.0164747 + 0.0105877i
\(643\) −2.12433 −0.0837754 −0.0418877 0.999122i \(-0.513337\pi\)
−0.0418877 + 0.999122i \(0.513337\pi\)
\(644\) −4.71391 + 0.882615i −0.185754 + 0.0347799i
\(645\) −14.2587 −0.561437
\(646\) 8.11225 + 5.21342i 0.319172 + 0.205119i
\(647\) −1.88556 13.1144i −0.0741291 0.515579i −0.992727 0.120386i \(-0.961587\pi\)
0.918598 0.395193i \(-0.129322\pi\)
\(648\) −0.415415 0.909632i −0.0163190 0.0357337i
\(649\) −3.72807 1.09466i −0.146340 0.0429692i
\(650\) 27.7569 60.7791i 1.08871 2.38395i
\(651\) −1.84806 + 2.13278i −0.0724313 + 0.0835902i
\(652\) 2.47872 17.2399i 0.0970743 0.675166i
\(653\) 19.5715 5.74670i 0.765891 0.224886i 0.124624 0.992204i \(-0.460227\pi\)
0.641267 + 0.767318i \(0.278409\pi\)
\(654\) 13.2387 + 15.2783i 0.517675 + 0.597428i
\(655\) −29.7875 + 19.1432i −1.16389 + 0.747988i
\(656\) −7.70815 + 4.95373i −0.300953 + 0.193410i
\(657\) −0.861477 0.994198i −0.0336094 0.0387874i
\(658\) 6.97957 2.04939i 0.272092 0.0798934i
\(659\) 5.04109 35.0615i 0.196373 1.36580i −0.618328 0.785921i \(-0.712189\pi\)
0.814700 0.579882i \(-0.196901\pi\)
\(660\) −4.51338 + 5.20871i −0.175683 + 0.202749i
\(661\) −11.8121 + 25.8648i −0.459436 + 1.00602i 0.528180 + 0.849132i \(0.322875\pi\)
−0.987616 + 0.156891i \(0.949853\pi\)
\(662\) −0.466709 0.137038i −0.0181391 0.00532613i
\(663\) −5.54962 12.1520i −0.215529 0.471943i
\(664\) −0.186315 1.29585i −0.00723043 0.0502888i
\(665\) 13.8833 + 8.92224i 0.538370 + 0.345990i
\(666\) −6.46606 −0.250555
\(667\) 1.74073 + 41.1341i 0.0674015 + 1.59272i
\(668\) −17.4819 −0.676396
\(669\) 22.9538 + 14.7515i 0.887445 + 0.570327i
\(670\) −3.33777 23.2147i −0.128949 0.896863i
\(671\) 9.78777 + 21.4322i 0.377853 + 0.827382i
\(672\) 0.959493 + 0.281733i 0.0370132 + 0.0108681i
\(673\) 14.3480 31.4177i 0.553074 1.21106i −0.402258 0.915526i \(-0.631775\pi\)
0.955332 0.295536i \(-0.0954982\pi\)
\(674\) −12.2698 + 14.1601i −0.472614 + 0.545425i
\(675\) −1.71876 + 11.9542i −0.0661549 + 0.460118i
\(676\) −16.8957 + 4.96102i −0.649834 + 0.190809i
\(677\) −7.79697 8.99818i −0.299662 0.345828i 0.585872 0.810404i \(-0.300752\pi\)
−0.885533 + 0.464576i \(0.846207\pi\)
\(678\) 0.0285898 0.0183735i 0.00109798 0.000705631i
\(679\) 9.51845 6.11713i 0.365284 0.234754i
\(680\) −6.53451 7.54123i −0.250587 0.289193i
\(681\) −11.6737 + 3.42772i −0.447339 + 0.131350i
\(682\) −0.669828 + 4.65875i −0.0256490 + 0.178393i
\(683\) 24.4555 28.2231i 0.935762 1.07993i −0.0608884 0.998145i \(-0.519393\pi\)
0.996650 0.0817821i \(-0.0260612\pi\)
\(684\) −1.65897 + 3.63265i −0.0634325 + 0.138898i
\(685\) −38.5416 11.3168i −1.47260 0.432394i
\(686\) −0.415415 0.909632i −0.0158606 0.0347299i
\(687\) 1.22124 + 8.49393i 0.0465933 + 0.324063i
\(688\) 2.90269 + 1.86545i 0.110664 + 0.0711194i
\(689\) −70.2608 −2.67673
\(690\) −4.77453 + 19.2348i −0.181763 + 0.732257i
\(691\) 23.8002 0.905400 0.452700 0.891663i \(-0.350461\pi\)
0.452700 + 0.891663i \(0.350461\pi\)
\(692\) −2.51874 1.61870i −0.0957482 0.0615336i
\(693\) 0.237353 + 1.65083i 0.00901631 + 0.0627098i
\(694\) 11.1586 + 24.4338i 0.423573 + 0.927496i
\(695\) −89.8618 26.3858i −3.40865 1.00087i
\(696\) 3.56623 7.80894i 0.135177 0.295997i
\(697\) 14.4887 16.7208i 0.548798 0.633346i
\(698\) −3.84460 + 26.7398i −0.145520 + 1.01212i
\(699\) −17.5573 + 5.15528i −0.664077 + 0.194990i
\(700\) −7.90884 9.12729i −0.298926 0.344979i
\(701\) 8.82274 5.67003i 0.333230 0.214154i −0.363316 0.931666i \(-0.618355\pi\)
0.696546 + 0.717512i \(0.254719\pi\)
\(702\) 4.65427 2.99112i 0.175664 0.112892i
\(703\) 16.9101 + 19.5153i 0.637777 + 0.736034i
\(704\) 1.60025 0.469875i 0.0603116 0.0177091i
\(705\) 4.27804 29.7544i 0.161120 1.12062i
\(706\) 5.47356 6.31683i 0.206000 0.237737i
\(707\) −7.86813 + 17.2288i −0.295911 + 0.647955i
\(708\) 2.23532 + 0.656349i 0.0840084 + 0.0246671i
\(709\) −9.25044 20.2556i −0.347408 0.760717i −0.999995 0.00300352i \(-0.999044\pi\)
0.652588 0.757713i \(-0.273683\pi\)
\(710\) −3.38009 23.5090i −0.126852 0.882278i
\(711\) 8.20473 + 5.27286i 0.307701 + 0.197748i
\(712\) −4.86931 −0.182485
\(713\) 4.35866 + 12.8131i 0.163233 + 0.479855i
\(714\) −2.41466 −0.0903665
\(715\) −32.0778 20.6151i −1.19964 0.770962i
\(716\) 0.153742 + 1.06930i 0.00574561 + 0.0399616i
\(717\) 4.35274 + 9.53117i 0.162556 + 0.355948i
\(718\) −33.6854 9.89092i −1.25713 0.369126i
\(719\) −8.61762 + 18.8700i −0.321383 + 0.703731i −0.999513 0.0312116i \(-0.990063\pi\)
0.678130 + 0.734942i \(0.262791\pi\)
\(720\) 2.70618 3.12310i 0.100853 0.116391i
\(721\) −2.18691 + 15.2103i −0.0814449 + 0.566461i
\(722\) −2.92806 + 0.859755i −0.108971 + 0.0319968i
\(723\) −2.33644 2.69640i −0.0868933 0.100280i
\(724\) −4.97325 + 3.19611i −0.184829 + 0.118783i
\(725\) −87.2203 + 56.0531i −3.23928 + 2.08176i
\(726\) −5.38193 6.21107i −0.199742 0.230515i
\(727\) 2.48714 0.730289i 0.0922427 0.0270849i −0.235286 0.971926i \(-0.575603\pi\)
0.327528 + 0.944841i \(0.393784\pi\)
\(728\) −0.787362 + 5.47623i −0.0291816 + 0.202962i
\(729\) −0.654861 + 0.755750i −0.0242541 + 0.0279907i
\(730\) 2.25832 4.94502i 0.0835840 0.183023i
\(731\) −7.99415 2.34729i −0.295674 0.0868178i
\(732\) −5.86866 12.8506i −0.216912 0.474970i
\(733\) −3.43016 23.8573i −0.126696 0.881190i −0.949701 0.313157i \(-0.898614\pi\)
0.823006 0.568033i \(-0.192296\pi\)
\(734\) 16.1469 + 10.3770i 0.595993 + 0.383022i
\(735\) −4.13245 −0.152428
\(736\) 3.48842 3.29104i 0.128585 0.121309i
\(737\) −9.46552 −0.348667
\(738\) 7.70815 + 4.95373i 0.283741 + 0.182349i
\(739\) 3.93739 + 27.3852i 0.144839 + 1.00738i 0.924501 + 0.381179i \(0.124482\pi\)
−0.779662 + 0.626201i \(0.784609\pi\)
\(740\) −11.1002 24.3060i −0.408050 0.893505i
\(741\) −21.1994 6.22471i −0.778780 0.228670i
\(742\) −5.27559 + 11.5519i −0.193673 + 0.424085i
\(743\) 16.8487 19.4445i 0.618121 0.713349i −0.357228 0.934017i \(-0.616278\pi\)
0.975349 + 0.220668i \(0.0708237\pi\)
\(744\) 0.401622 2.79335i 0.0147242 0.102409i
\(745\) 26.6983 7.83933i 0.978150 0.287211i
\(746\) 1.25663 + 1.45023i 0.0460087 + 0.0530968i
\(747\) −1.10135 + 0.707794i −0.0402962 + 0.0258968i
\(748\) −3.38788 + 2.17726i −0.123873 + 0.0796086i
\(749\) 0.324943 + 0.375004i 0.0118732 + 0.0137024i
\(750\) −28.0612 + 8.23952i −1.02465 + 0.300865i
\(751\) 3.71981 25.8718i 0.135738 0.944077i −0.802146 0.597128i \(-0.796309\pi\)
0.937884 0.346949i \(-0.112782\pi\)
\(752\) −4.76360 + 5.49749i −0.173711 + 0.200473i
\(753\) −7.20252 + 15.7713i −0.262474 + 0.574738i
\(754\) 45.5715 + 13.3810i 1.65961 + 0.487307i
\(755\) −29.3984 64.3735i −1.06992 2.34279i
\(756\) −0.142315 0.989821i −0.00517594 0.0359995i
\(757\) −16.8219 10.8108i −0.611404 0.392926i 0.197979 0.980206i \(-0.436562\pi\)
−0.809383 + 0.587281i \(0.800198\pi\)
\(758\) −16.1804 −0.587698
\(759\) 7.40968 + 3.01211i 0.268954 + 0.109333i
\(760\) −16.5031 −0.598630
\(761\) 1.14625 + 0.736649i 0.0415515 + 0.0267035i 0.561252 0.827645i \(-0.310320\pi\)
−0.519700 + 0.854349i \(0.673956\pi\)
\(762\) 1.11143 + 7.73017i 0.0402629 + 0.280034i
\(763\) 8.39806 + 18.3892i 0.304030 + 0.665733i
\(764\) −3.71517 1.09087i −0.134410 0.0394663i
\(765\) −4.14521 + 9.07674i −0.149870 + 0.328170i
\(766\) 13.6011 15.6965i 0.491427 0.567137i
\(767\) −1.83431 + 12.7579i −0.0662330 + 0.460661i
\(768\) −0.959493 + 0.281733i −0.0346227 + 0.0101661i
\(769\) 26.9825 + 31.1395i 0.973015 + 1.12292i 0.992393 + 0.123107i \(0.0392859\pi\)
−0.0193780 + 0.999812i \(0.506169\pi\)
\(770\) −5.79802 + 3.72616i −0.208946 + 0.134281i
\(771\) 0.291925 0.187609i 0.0105134 0.00675657i
\(772\) 4.17966 + 4.82359i 0.150429 + 0.173605i
\(773\) 21.0666 6.18572i 0.757713 0.222485i 0.120016 0.992772i \(-0.461705\pi\)
0.637697 + 0.770287i \(0.279887\pi\)
\(774\) 0.491048 3.41531i 0.0176504 0.122761i
\(775\) −22.3193 + 25.7578i −0.801733 + 0.925249i
\(776\) −4.70025 + 10.2921i −0.168729 + 0.369466i
\(777\) −6.20414 1.82170i −0.222572 0.0653531i
\(778\) 1.12211 + 2.45709i 0.0402298 + 0.0880909i
\(779\) −5.20752 36.2191i −0.186579 1.29768i
\(780\) 19.2335 + 12.3606i 0.688671 + 0.442582i
\(781\) −9.58552 −0.342997
\(782\) −5.84330 + 9.99798i −0.208956 + 0.357527i
\(783\) −8.58473 −0.306793
\(784\) 0.841254 + 0.540641i 0.0300448 + 0.0193086i
\(785\) −3.16103 21.9855i −0.112822 0.784695i
\(786\) −3.55944 7.79408i −0.126961 0.278006i
\(787\) −42.7168 12.5428i −1.52269 0.447102i −0.589885 0.807487i \(-0.700827\pi\)
−0.932804 + 0.360385i \(0.882645\pi\)
\(788\) 3.87869 8.49314i 0.138173 0.302556i
\(789\) −2.16722 + 2.50111i −0.0771552 + 0.0890419i
\(790\) −5.73581 + 39.8935i −0.204071 + 1.41935i
\(791\) 0.0326081 0.00957460i 0.00115941 0.000340434i
\(792\) −1.09218 1.26044i −0.0388089 0.0447879i
\(793\) 65.7518 42.2561i 2.33492 1.50056i
\(794\) −18.8906 + 12.1403i −0.670403 + 0.430842i
\(795\) 34.3673 + 39.6620i 1.21888 + 1.40667i
\(796\) 11.4061 3.34914i 0.404279 0.118707i
\(797\) −2.08028 + 14.4687i −0.0736873 + 0.512506i 0.919232 + 0.393716i \(0.128811\pi\)
−0.992919 + 0.118790i \(0.962098\pi\)
\(798\) −2.61521 + 3.01811i −0.0925774 + 0.106840i
\(799\) 7.29668 15.9775i 0.258138 0.565244i
\(800\) 11.5879 + 3.40252i 0.409695 + 0.120297i
\(801\) 2.02278 + 4.42928i 0.0714715 + 0.156501i
\(802\) −2.09246 14.5534i −0.0738875 0.513899i
\(803\) −1.84572 1.18618i −0.0651342 0.0418592i
\(804\) 5.67544 0.200157
\(805\) −10.0002 + 17.1105i −0.352461 + 0.603067i
\(806\) 15.6132 0.549952
\(807\) −13.5489 8.70736i −0.476944 0.306514i
\(808\) −2.69550 18.7476i −0.0948273 0.659539i
\(809\) 2.21938 + 4.85977i 0.0780293 + 0.170860i 0.944626 0.328149i \(-0.106425\pi\)
−0.866597 + 0.499009i \(0.833697\pi\)
\(810\) −3.96506 1.16425i −0.139318 0.0409074i
\(811\) 11.5392 25.2672i 0.405194 0.887252i −0.591523 0.806288i \(-0.701473\pi\)
0.996717 0.0809636i \(-0.0257998\pi\)
\(812\) 5.62180 6.48791i 0.197287 0.227681i
\(813\) −0.390125 + 2.71338i −0.0136823 + 0.0951623i
\(814\) −10.3473 + 3.03824i −0.362672 + 0.106490i
\(815\) −47.1340 54.3955i −1.65103 1.90539i
\(816\) 2.03134 1.30547i 0.0711113 0.0457004i
\(817\) −11.5920 + 7.44972i −0.405553 + 0.260633i
\(818\) −15.0903 17.4151i −0.527619 0.608905i
\(819\) 5.30843 1.55870i 0.185492 0.0544653i
\(820\) −5.38866 + 37.4790i −0.188180 + 1.30882i
\(821\) 11.5181 13.2926i 0.401985 0.463915i −0.518280 0.855211i \(-0.673428\pi\)
0.920265 + 0.391296i \(0.127973\pi\)
\(822\) 4.03797 8.84192i 0.140840 0.308397i
\(823\) −38.9740 11.4438i −1.35855 0.398906i −0.480298 0.877106i \(-0.659471\pi\)
−0.878251 + 0.478200i \(0.841289\pi\)
\(824\) −6.38357 13.9781i −0.222382 0.486949i
\(825\) 2.86655 + 19.9373i 0.0998004 + 0.694127i
\(826\) 1.95986 + 1.25952i 0.0681922 + 0.0438244i
\(827\) 26.5015 0.921548 0.460774 0.887517i \(-0.347572\pi\)
0.460774 + 0.887517i \(0.347572\pi\)
\(828\) −4.44277 1.80603i −0.154397 0.0627639i
\(829\) 36.9284 1.28258 0.641289 0.767300i \(-0.278400\pi\)
0.641289 + 0.767300i \(0.278400\pi\)
\(830\) −4.55127 2.92492i −0.157977 0.101526i
\(831\) 1.57042 + 10.9225i 0.0544774 + 0.378898i
\(832\) −2.29830 5.03257i −0.0796792 0.174473i
\(833\) −2.31685 0.680289i −0.0802742 0.0235706i
\(834\) 9.41473 20.6154i 0.326005 0.713852i
\(835\) −47.3092 + 54.5978i −1.63720 + 1.88943i
\(836\) −0.947879 + 6.59264i −0.0327831 + 0.228011i
\(837\) −2.70776 + 0.795069i −0.0935937 + 0.0274816i
\(838\) −8.88560 10.2545i −0.306948 0.354237i
\(839\) −18.5948 + 11.9502i −0.641965 + 0.412566i −0.820722 0.571328i \(-0.806429\pi\)
0.178758 + 0.983893i \(0.442792\pi\)
\(840\) 3.47644 2.23417i 0.119948 0.0770862i
\(841\) −29.2707 33.7802i −1.00933 1.16483i
\(842\) 0.223001 0.0654790i 0.00768513 0.00225656i
\(843\) 3.79194 26.3735i 0.130601 0.908353i
\(844\) −17.2414 + 19.8977i −0.593475 + 0.684907i
\(845\) −30.2290 + 66.1923i −1.03991 + 2.27708i
\(846\) 6.97957 + 2.04939i 0.239962 + 0.0704593i
\(847\) −3.41406 7.47575i −0.117308 0.256870i
\(848\) −1.80734 12.5703i −0.0620642 0.431666i
\(849\) 17.5820 + 11.2993i 0.603412 + 0.387789i
\(850\) −29.1622 −1.00026
\(851\) −22.5563 + 21.2801i −0.773221 + 0.729471i
\(852\) 5.74739 0.196902
\(853\) 30.7080 + 19.7349i 1.05142 + 0.675709i 0.947786 0.318907i \(-0.103316\pi\)
0.103637 + 0.994615i \(0.466952\pi\)
\(854\) −2.01051 13.9834i −0.0687983 0.478503i
\(855\) 6.85563 + 15.0117i 0.234458 + 0.513390i
\(856\) −0.476102 0.139796i −0.0162728 0.00477814i
\(857\) −17.1248 + 37.4981i −0.584972 + 1.28091i 0.353461 + 0.935449i \(0.385005\pi\)
−0.938433 + 0.345461i \(0.887723\pi\)
\(858\) 6.04253 6.97345i 0.206288 0.238070i
\(859\) 1.23770 8.60840i 0.0422298 0.293715i −0.957751 0.287597i \(-0.907144\pi\)
0.999981 0.00611760i \(-0.00194731\pi\)
\(860\) 13.6812 4.01715i 0.466524 0.136984i
\(861\) 6.00029 + 6.92470i 0.204489 + 0.235993i
\(862\) −14.5119 + 9.32621i −0.494276 + 0.317652i
\(863\) 38.8029 24.9371i 1.32087 0.848870i 0.325549 0.945525i \(-0.394451\pi\)
0.995318 + 0.0966551i \(0.0308144\pi\)
\(864\) 0.654861 + 0.755750i 0.0222788 + 0.0257111i
\(865\) −11.8715 + 3.48579i −0.403644 + 0.118520i
\(866\) 2.82316 19.6355i 0.0959348 0.667241i
\(867\) 7.31440 8.44127i 0.248410 0.286681i
\(868\) 1.17233 2.56704i 0.0397915 0.0871312i
\(869\) 15.6072 + 4.58268i 0.529437 + 0.155457i
\(870\) −14.7372 32.2701i −0.499639 1.09406i
\(871\) 4.46863 + 31.0800i 0.151414 + 1.05310i
\(872\) −17.0068 10.9296i −0.575924 0.370124i
\(873\) 11.3146 0.382941
\(874\) 6.16798 + 18.1320i 0.208635 + 0.613322i
\(875\) −29.2459 −0.988692
\(876\) 1.10668 + 0.711220i 0.0373912 + 0.0240299i
\(877\) 3.22866 + 22.4558i 0.109024 + 0.758280i 0.968842 + 0.247679i \(0.0796679\pi\)
−0.859818 + 0.510601i \(0.829423\pi\)
\(878\) 1.64299 + 3.59764i 0.0554481 + 0.121414i
\(879\) −0.143947 0.0422666i −0.00485521 0.00142562i
\(880\) 2.86309 6.26929i 0.0965147 0.211338i
\(881\) 15.7196 18.1414i 0.529608 0.611200i −0.426403 0.904534i \(-0.640219\pi\)
0.956010 + 0.293334i \(0.0947647\pi\)
\(882\) 0.142315 0.989821i 0.00479199 0.0333290i
\(883\) 4.91563 1.44336i 0.165424 0.0485729i −0.197972 0.980208i \(-0.563435\pi\)
0.363396 + 0.931635i \(0.381617\pi\)
\(884\) 8.74843 + 10.0962i 0.294241 + 0.339573i
\(885\) 8.09901 5.20492i 0.272245 0.174961i
\(886\) 26.8471 17.2536i 0.901947 0.579646i
\(887\) −14.4060 16.6254i −0.483707 0.558228i 0.460466 0.887677i \(-0.347682\pi\)
−0.944173 + 0.329449i \(0.893137\pi\)
\(888\) 6.20414 1.82170i 0.208197 0.0611323i
\(889\) −1.11143 + 7.73017i −0.0372762 + 0.259262i
\(890\) −13.1772 + 15.2073i −0.441701 + 0.509750i
\(891\) −0.692831 + 1.51709i −0.0232107 + 0.0508244i
\(892\) −26.1800 7.68714i −0.876571 0.257385i
\(893\) −12.0678 26.4247i −0.403832 0.884269i
\(894\) 0.958262 + 6.66486i 0.0320491 + 0.222906i
\(895\) 3.75558 + 2.41357i 0.125535 + 0.0806766i
\(896\) −1.00000 −0.0334077
\(897\) 6.39216 25.7516i 0.213428 0.859822i
\(898\) 23.3487 0.779156
\(899\) −20.3808 13.0979i −0.679738 0.436841i
\(900\) −1.71876 11.9542i −0.0572918 0.398474i
\(901\) 12.7388 + 27.8940i 0.424390 + 0.929285i
\(902\) 14.6626 + 4.30532i 0.488210 + 0.143351i
\(903\) 1.43336 3.13862i 0.0476993 0.104447i
\(904\) −0.0222553 + 0.0256839i −0.000740199 + 0.000854235i
\(905\) −3.47673 + 24.1812i −0.115570 + 0.803810i
\(906\) 16.4314 4.82470i 0.545898 0.160290i
\(907\) 11.2352 + 12.9661i 0.373060 + 0.430534i 0.910973 0.412466i \(-0.135333\pi\)
−0.537913 + 0.843000i \(0.680787\pi\)
\(908\) 10.2352 6.57774i 0.339666 0.218290i
\(909\) −15.9337 + 10.2400i −0.528487 + 0.339638i
\(910\) 14.9720 + 17.2787i 0.496318 + 0.572782i
\(911\) 32.1334 9.43521i 1.06463 0.312602i 0.297914 0.954593i \(-0.403709\pi\)
0.766713 + 0.641990i \(0.221891\pi\)
\(912\) 0.568339 3.95289i 0.0188196 0.130893i
\(913\) −1.42986 + 1.65014i −0.0473213 + 0.0546117i
\(914\) −6.53347 + 14.3063i −0.216108 + 0.473210i
\(915\) −56.0152 16.4475i −1.85180 0.543739i
\(916\) −3.56479 7.80580i −0.117784 0.257911i
\(917\) −1.21941 8.48117i −0.0402684 0.280073i
\(918\) −2.03134 1.30547i −0.0670443 0.0430868i
\(919\) −50.3589 −1.66119 −0.830593 0.556880i \(-0.811998\pi\)
−0.830593 + 0.556880i \(0.811998\pi\)
\(920\) −0.837941 19.8008i −0.0276261 0.652813i
\(921\) −1.06720 −0.0351654
\(922\) 26.7573 + 17.1959i 0.881205 + 0.566316i
\(923\) 4.52528 + 31.4740i 0.148951 + 1.03598i
\(924\) −0.692831 1.51709i −0.0227925 0.0499085i
\(925\) −74.9282 22.0009i −2.46363 0.723386i
\(926\) 1.17524 2.57341i 0.0386208 0.0845677i
\(927\) −10.0631 + 11.6134i −0.330514 + 0.381434i
\(928\) −1.22173 + 8.49735i −0.0401054 + 0.278939i
\(929\) 44.5736 13.0880i 1.46241 0.429403i 0.548788 0.835961i \(-0.315089\pi\)
0.913625 + 0.406558i \(0.133271\pi\)
\(930\) −7.63702 8.81360i −0.250428 0.289009i
\(931\) −3.35958 + 2.15907i −0.110106 + 0.0707606i
\(932\) 15.3937 9.89290i 0.504236 0.324053i
\(933\) −2.00634 2.31544i −0.0656846 0.0758041i
\(934\) 17.7091 5.19986i 0.579459 0.170144i
\(935\) −2.36842 + 16.4727i −0.0774557 + 0.538716i
\(936\) −3.62304 + 4.18121i −0.118423 + 0.136667i
\(937\) −17.4223 + 38.1495i −0.569162 + 1.24629i 0.378081 + 0.925773i \(0.376584\pi\)
−0.947243 + 0.320518i \(0.896143\pi\)
\(938\) 5.44554 + 1.59896i 0.177803 + 0.0522077i
\(939\) 4.77270 + 10.4508i 0.155751 + 0.341047i
\(940\) 4.27804 + 29.7544i 0.139534 + 0.970481i
\(941\) 11.3119 + 7.26973i 0.368758 + 0.236986i 0.711875 0.702306i \(-0.247846\pi\)
−0.343117 + 0.939293i \(0.611483\pi\)
\(942\) 5.37491 0.175124
\(943\) 43.1922 8.08713i 1.40653 0.263353i
\(944\) −2.32969 −0.0758249
\(945\) −3.47644 2.23417i −0.113089 0.0726776i
\(946\) −0.818972 5.69607i −0.0266271 0.185195i
\(947\) 1.02505 + 2.24454i 0.0333095 + 0.0729377i 0.925555 0.378612i \(-0.123599\pi\)
−0.892246 + 0.451550i \(0.850871\pi\)
\(948\) −9.35791 2.74773i −0.303931 0.0892422i
\(949\) −3.02344 + 6.62041i −0.0981451 + 0.214908i
\(950\) −31.5842 + 36.4502i −1.02473 + 1.18260i
\(951\) −3.39029 + 23.5800i −0.109938 + 0.764633i
\(952\) 2.31685 0.680289i 0.0750896 0.0220483i
\(953\) 27.3268 + 31.5368i 0.885202 + 1.02158i 0.999604 + 0.0281427i \(0.00895927\pi\)
−0.114402 + 0.993435i \(0.536495\pi\)
\(954\) −10.6836 + 6.86590i −0.345893 + 0.222292i
\(955\) −13.4608 + 8.65073i −0.435581 + 0.279931i
\(956\) −6.86167 7.91879i −0.221922 0.256112i
\(957\) −13.7377 + 4.03375i −0.444076 + 0.130393i
\(958\) 3.65916 25.4500i 0.118222 0.822254i
\(959\) 6.36546 7.34613i 0.205551 0.237219i
\(960\) −1.71668 + 3.75901i −0.0554057 + 0.121321i
\(961\) 22.1028 + 6.48997i 0.712994 + 0.209354i
\(962\) 14.8609 + 32.5409i 0.479136 + 1.04916i
\(963\) 0.0706169 + 0.491151i 0.00227560 + 0.0158271i
\(964\) 3.00147 + 1.92893i 0.0966707 + 0.0621265i
\(965\) 26.3754 0.849056
\(966\) −3.75399 2.98455i −0.120783 0.0960263i
\(967\) −26.9694 −0.867277 −0.433638 0.901087i \(-0.642770\pi\)
−0.433638 + 0.901087i \(0.642770\pi\)
\(968\) 6.91378 + 4.44322i 0.222217 + 0.142810i
\(969\) 1.37235 + 9.54489i 0.0440862 + 0.306626i
\(970\) 19.4236 + 42.5317i 0.623653 + 1.36561i
\(971\) −30.9019 9.07361i −0.991689 0.291186i −0.254648 0.967034i \(-0.581959\pi\)
−0.737041 + 0.675848i \(0.763778\pi\)
\(972\) 0.415415 0.909632i 0.0133244 0.0291765i
\(973\) 14.8414 17.1279i 0.475793 0.549095i
\(974\) −0.0527582 + 0.366941i −0.00169048 + 0.0117576i
\(975\) 64.1106 18.8246i 2.05318 0.602869i
\(976\) 9.25136 + 10.6766i 0.296129 + 0.341751i
\(977\) −42.9226 + 27.5847i −1.37322 + 0.882512i −0.998995 0.0448278i \(-0.985726\pi\)
−0.374221 + 0.927340i \(0.622090\pi\)
\(978\) 14.6523 9.41644i 0.468528 0.301104i
\(979\) 5.31816 + 6.13748i 0.169969 + 0.196155i
\(980\) 3.96506 1.16425i 0.126659 0.0371905i
\(981\) −2.87705 + 20.0103i −0.0918570 + 0.638880i
\(982\) −12.3513 + 14.2542i −0.394147 + 0.454869i
\(983\) −1.95638 + 4.28388i −0.0623989 + 0.136635i −0.938262 0.345924i \(-0.887565\pi\)
0.875863 + 0.482559i \(0.160293\pi\)
\(984\) −8.79154 2.58143i −0.280264 0.0822929i
\(985\) −16.0285 35.0975i −0.510710 1.11830i
\(986\) −2.95008 20.5182i −0.0939496 0.653434i
\(987\) 6.11947 + 3.93274i 0.194785 + 0.125181i
\(988\) 22.0944 0.702916
\(989\) −9.52694 13.5301i −0.302939 0.430232i
\(990\) −6.89212 −0.219046
\(991\) 48.2344 + 30.9984i 1.53222 + 0.984696i 0.989460 + 0.144807i \(0.0462561\pi\)
0.542758 + 0.839889i \(0.317380\pi\)
\(992\) 0.401622 + 2.79335i 0.0127515 + 0.0886888i
\(993\) −0.202063 0.442456i −0.00641227 0.0140409i
\(994\) 5.51458 + 1.61923i 0.174912 + 0.0513587i
\(995\) 20.4073 44.6858i 0.646955 1.41663i
\(996\) 0.857328 0.989409i 0.0271655 0.0313506i
\(997\) 3.68554 25.6335i 0.116722 0.811821i −0.844403 0.535708i \(-0.820045\pi\)
0.961125 0.276112i \(-0.0890462\pi\)
\(998\) 1.94310 0.570546i 0.0615078 0.0180603i
\(999\) −4.23437 4.88672i −0.133970 0.154609i
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 966.2.q.e.715.2 yes 20
23.12 even 11 inner 966.2.q.e.127.2 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
966.2.q.e.127.2 20 23.12 even 11 inner
966.2.q.e.715.2 yes 20 1.1 even 1 trivial