Properties

Label 93.2.m.b.76.3
Level $93$
Weight $2$
Character 93.76
Analytic conductor $0.743$
Analytic rank $0$
Dimension $24$
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] = [93,2,Mod(7,93)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(93, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([0, 28]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("93.7");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 93 = 3 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 93.m (of order \(15\), degree \(8\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.742608738798\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(3\) over \(\Q(\zeta_{15})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label 76.3
Character \(\chi\) \(=\) 93.76
Dual form 93.2.m.b.82.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.704349 - 2.16776i) q^{2} +(0.669131 - 0.743145i) q^{3} +(-2.58506 - 1.87816i) q^{4} +(-0.398612 + 0.690417i) q^{5} +(-1.13966 - 1.97395i) q^{6} +(-0.477794 + 4.54591i) q^{7} +(-2.20416 + 1.60142i) q^{8} +(-0.104528 - 0.994522i) q^{9} +O(q^{10})\) \(q+(0.704349 - 2.16776i) q^{2} +(0.669131 - 0.743145i) q^{3} +(-2.58506 - 1.87816i) q^{4} +(-0.398612 + 0.690417i) q^{5} +(-1.13966 - 1.97395i) q^{6} +(-0.477794 + 4.54591i) q^{7} +(-2.20416 + 1.60142i) q^{8} +(-0.104528 - 0.994522i) q^{9} +(1.21590 + 1.35039i) q^{10} +(2.06856 - 0.920981i) q^{11} +(-3.12548 + 0.664342i) q^{12} +(-2.23546 - 0.475161i) q^{13} +(9.51792 + 4.23765i) q^{14} +(0.246356 + 0.758205i) q^{15} +(-0.0558146 - 0.171780i) q^{16} +(-2.35281 - 1.04754i) q^{17} +(-2.22951 - 0.473898i) q^{18} +(-4.27578 + 0.908845i) q^{19} +(2.32715 - 1.03611i) q^{20} +(3.05856 + 3.39688i) q^{21} +(-0.539483 - 5.13283i) q^{22} +(5.65996 - 4.11220i) q^{23} +(-0.284787 + 2.70957i) q^{24} +(2.18222 + 3.77971i) q^{25} +(-2.60458 + 4.51126i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(9.77304 - 10.8541i) q^{28} +(-2.52855 + 7.78207i) q^{29} +1.81713 q^{30} +(2.24947 - 5.09312i) q^{31} -5.86068 q^{32} +(0.699712 - 2.15349i) q^{33} +(-3.92802 + 4.36251i) q^{34} +(-2.94811 - 2.14193i) q^{35} +(-1.59765 + 2.76722i) q^{36} +(4.36455 + 7.55962i) q^{37} +(-1.04148 + 9.90903i) q^{38} +(-1.84893 + 1.34332i) q^{39} +(-0.227039 - 2.16013i) q^{40} +(-7.08260 - 7.86602i) q^{41} +(9.51792 - 4.23765i) q^{42} +(-1.92913 + 0.410048i) q^{43} +(-7.07709 - 1.50428i) q^{44} +(0.728301 + 0.324260i) q^{45} +(-4.92770 - 15.1659i) q^{46} +(-1.09764 - 3.37820i) q^{47} +(-0.165004 - 0.0734647i) q^{48} +(-13.5899 - 2.88863i) q^{49} +(9.73056 - 2.06829i) q^{50} +(-2.35281 + 1.04754i) q^{51} +(4.88636 + 5.42686i) q^{52} +(0.106558 + 1.01383i) q^{53} +(-1.84401 + 1.33975i) q^{54} +(-0.188692 + 1.79528i) q^{55} +(-6.22676 - 10.7851i) q^{56} +(-2.18565 + 3.78566i) q^{57} +(15.0887 + 10.9626i) q^{58} +(3.07829 - 3.41879i) q^{59} +(0.787183 - 2.42270i) q^{60} +0.251899 q^{61} +(-9.45628 - 8.46365i) q^{62} +4.57095 q^{63} +(-4.01633 + 12.3610i) q^{64} +(1.21914 - 1.35399i) q^{65} +(-4.17542 - 3.03362i) q^{66} +(1.98619 - 3.44018i) q^{67} +(4.11472 + 7.12690i) q^{68} +(0.731291 - 6.95777i) q^{69} +(-6.71970 + 4.88215i) q^{70} +(-0.804058 - 7.65010i) q^{71} +(1.82304 + 2.02469i) q^{72} +(8.35045 - 3.71786i) q^{73} +(19.4617 - 4.13670i) q^{74} +(4.26906 + 0.907417i) q^{75} +(12.7601 + 5.68116i) q^{76} +(3.19835 + 9.84350i) q^{77} +(1.60972 + 4.95421i) q^{78} +(8.02362 + 3.57235i) q^{79} +(0.140848 + 0.0299381i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(-22.0403 + 9.81297i) q^{82} +(-1.85000 - 2.05463i) q^{83} +(-1.52670 - 14.5256i) q^{84} +(1.66110 - 1.20686i) q^{85} +(-0.469890 + 4.47071i) q^{86} +(4.09128 + 7.08630i) q^{87} +(-3.08456 + 5.34261i) q^{88} +(-1.10573 - 0.803361i) q^{89} +(1.21590 - 1.35039i) q^{90} +(3.22813 - 9.93515i) q^{91} -22.3547 q^{92} +(-2.27974 - 5.07964i) q^{93} -8.09627 q^{94} +(1.07690 - 3.31435i) q^{95} +(-3.92156 + 4.35533i) q^{96} +(-0.0532738 - 0.0387057i) q^{97} +(-15.8339 + 27.4252i) q^{98} +(-1.13216 - 1.96096i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 3 q^{3} - 4 q^{4} - 6 q^{5} - 5 q^{6} - q^{7} - 22 q^{8} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 3 q^{3} - 4 q^{4} - 6 q^{5} - 5 q^{6} - q^{7} - 22 q^{8} + 3 q^{9} + 24 q^{10} - 22 q^{11} + 12 q^{12} - 8 q^{13} + 10 q^{14} - 8 q^{15} - 2 q^{16} - 17 q^{17} + 5 q^{19} - 22 q^{20} - 11 q^{21} - 37 q^{22} + 26 q^{23} + 26 q^{24} - 8 q^{25} + 4 q^{26} - 6 q^{27} - 36 q^{28} + 2 q^{29} + 42 q^{30} + 36 q^{32} + 14 q^{33} + 40 q^{34} + 9 q^{35} - 13 q^{36} - 13 q^{37} - q^{38} - 19 q^{39} - 27 q^{40} + 36 q^{41} + 10 q^{42} - 11 q^{43} - 38 q^{44} - q^{45} - 23 q^{46} - 13 q^{47} - 14 q^{48} - 22 q^{49} + 71 q^{50} - 17 q^{51} + 9 q^{52} - 20 q^{53} - 5 q^{54} + 26 q^{55} + 28 q^{56} - 15 q^{57} + 40 q^{58} - 16 q^{59} - 61 q^{60} + 70 q^{61} - 2 q^{62} + 12 q^{63} + 34 q^{64} + 94 q^{65} - 16 q^{66} + 4 q^{67} + 51 q^{68} - 13 q^{69} - 43 q^{70} - 5 q^{71} + q^{72} - 12 q^{73} + 74 q^{74} - 8 q^{75} + 71 q^{76} + 25 q^{77} + 17 q^{78} - 29 q^{79} - 113 q^{80} + 3 q^{81} - 60 q^{82} - 11 q^{83} - 41 q^{84} + 16 q^{85} - 144 q^{86} + 14 q^{87} + 26 q^{88} - 27 q^{89} + 24 q^{90} - 81 q^{91} + 28 q^{92} - 36 q^{93} - 80 q^{94} - 56 q^{95} - 43 q^{96} - 21 q^{97} - 14 q^{98} - 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/93\mathbb{Z}\right)^\times\).

\(n\) \(32\) \(34\)
\(\chi(n)\) \(1\) \(e\left(\frac{11}{15}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.704349 2.16776i 0.498050 1.53284i −0.314099 0.949390i \(-0.601702\pi\)
0.812149 0.583450i \(-0.198298\pi\)
\(3\) 0.669131 0.743145i 0.386323 0.429055i
\(4\) −2.58506 1.87816i −1.29253 0.939078i
\(5\) −0.398612 + 0.690417i −0.178265 + 0.308764i −0.941286 0.337609i \(-0.890382\pi\)
0.763021 + 0.646373i \(0.223715\pi\)
\(6\) −1.13966 1.97395i −0.465265 0.805862i
\(7\) −0.477794 + 4.54591i −0.180589 + 1.71819i 0.410733 + 0.911756i \(0.365273\pi\)
−0.591322 + 0.806436i \(0.701394\pi\)
\(8\) −2.20416 + 1.60142i −0.779289 + 0.566186i
\(9\) −0.104528 0.994522i −0.0348428 0.331507i
\(10\) 1.21590 + 1.35039i 0.384501 + 0.427031i
\(11\) 2.06856 0.920981i 0.623693 0.277686i −0.0704586 0.997515i \(-0.522446\pi\)
0.694152 + 0.719829i \(0.255780\pi\)
\(12\) −3.12548 + 0.664342i −0.902249 + 0.191779i
\(13\) −2.23546 0.475161i −0.620004 0.131786i −0.112808 0.993617i \(-0.535985\pi\)
−0.507196 + 0.861831i \(0.669318\pi\)
\(14\) 9.51792 + 4.23765i 2.54377 + 1.13256i
\(15\) 0.246356 + 0.758205i 0.0636088 + 0.195768i
\(16\) −0.0558146 0.171780i −0.0139536 0.0429449i
\(17\) −2.35281 1.04754i −0.570641 0.254066i 0.101070 0.994879i \(-0.467773\pi\)
−0.671711 + 0.740814i \(0.734440\pi\)
\(18\) −2.22951 0.473898i −0.525501 0.111699i
\(19\) −4.27578 + 0.908845i −0.980932 + 0.208503i −0.670351 0.742044i \(-0.733857\pi\)
−0.310580 + 0.950547i \(0.600523\pi\)
\(20\) 2.32715 1.03611i 0.520366 0.231682i
\(21\) 3.05856 + 3.39688i 0.667433 + 0.741259i
\(22\) −0.539483 5.13283i −0.115018 1.09432i
\(23\) 5.65996 4.11220i 1.18018 0.857454i 0.187991 0.982171i \(-0.439802\pi\)
0.992192 + 0.124717i \(0.0398023\pi\)
\(24\) −0.284787 + 2.70957i −0.0581319 + 0.553088i
\(25\) 2.18222 + 3.77971i 0.436443 + 0.755942i
\(26\) −2.60458 + 4.51126i −0.510800 + 0.884732i
\(27\) −0.809017 0.587785i −0.155695 0.113119i
\(28\) 9.77304 10.8541i 1.84693 2.05123i
\(29\) −2.52855 + 7.78207i −0.469540 + 1.44510i 0.383642 + 0.923482i \(0.374670\pi\)
−0.853182 + 0.521613i \(0.825330\pi\)
\(30\) 1.81713 0.331761
\(31\) 2.24947 5.09312i 0.404016 0.914752i
\(32\) −5.86068 −1.03603
\(33\) 0.699712 2.15349i 0.121804 0.374875i
\(34\) −3.92802 + 4.36251i −0.673650 + 0.748164i
\(35\) −2.94811 2.14193i −0.498322 0.362052i
\(36\) −1.59765 + 2.76722i −0.266276 + 0.461203i
\(37\) 4.36455 + 7.55962i 0.717528 + 1.24279i 0.961976 + 0.273132i \(0.0880597\pi\)
−0.244449 + 0.969662i \(0.578607\pi\)
\(38\) −1.04148 + 9.90903i −0.168951 + 1.60746i
\(39\) −1.84893 + 1.34332i −0.296065 + 0.215104i
\(40\) −0.227039 2.16013i −0.0358981 0.341547i
\(41\) −7.08260 7.86602i −1.10612 1.22847i −0.971366 0.237587i \(-0.923644\pi\)
−0.134750 0.990880i \(-0.543023\pi\)
\(42\) 9.51792 4.23765i 1.46865 0.653884i
\(43\) −1.92913 + 0.410048i −0.294189 + 0.0625318i −0.352642 0.935758i \(-0.614717\pi\)
0.0584529 + 0.998290i \(0.481383\pi\)
\(44\) −7.07709 1.50428i −1.06691 0.226779i
\(45\) 0.728301 + 0.324260i 0.108569 + 0.0483379i
\(46\) −4.92770 15.1659i −0.726549 2.23609i
\(47\) −1.09764 3.37820i −0.160108 0.492761i 0.838535 0.544848i \(-0.183413\pi\)
−0.998643 + 0.0520869i \(0.983413\pi\)
\(48\) −0.165004 0.0734647i −0.0238163 0.0106037i
\(49\) −13.5899 2.88863i −1.94142 0.412662i
\(50\) 9.73056 2.06829i 1.37611 0.292501i
\(51\) −2.35281 + 1.04754i −0.329460 + 0.146685i
\(52\) 4.88636 + 5.42686i 0.677617 + 0.752569i
\(53\) 0.106558 + 1.01383i 0.0146368 + 0.139260i 0.999400 0.0346420i \(-0.0110291\pi\)
−0.984763 + 0.173902i \(0.944362\pi\)
\(54\) −1.84401 + 1.33975i −0.250938 + 0.182317i
\(55\) −0.188692 + 1.79528i −0.0254432 + 0.242075i
\(56\) −6.22676 10.7851i −0.832085 1.44121i
\(57\) −2.18565 + 3.78566i −0.289497 + 0.501423i
\(58\) 15.0887 + 10.9626i 1.98125 + 1.43946i
\(59\) 3.07829 3.41879i 0.400760 0.445089i −0.508661 0.860967i \(-0.669859\pi\)
0.909420 + 0.415879i \(0.136526\pi\)
\(60\) 0.787183 2.42270i 0.101625 0.312769i
\(61\) 0.251899 0.0322523 0.0161262 0.999870i \(-0.494867\pi\)
0.0161262 + 0.999870i \(0.494867\pi\)
\(62\) −9.45628 8.46365i −1.20095 1.07488i
\(63\) 4.57095 0.575885
\(64\) −4.01633 + 12.3610i −0.502042 + 1.54513i
\(65\) 1.21914 1.35399i 0.151216 0.167942i
\(66\) −4.17542 3.03362i −0.513959 0.373413i
\(67\) 1.98619 3.44018i 0.242652 0.420285i −0.718817 0.695199i \(-0.755316\pi\)
0.961469 + 0.274914i \(0.0886494\pi\)
\(68\) 4.11472 + 7.12690i 0.498983 + 0.864263i
\(69\) 0.731291 6.95777i 0.0880371 0.837617i
\(70\) −6.71970 + 4.88215i −0.803158 + 0.583529i
\(71\) −0.804058 7.65010i −0.0954241 0.907900i −0.932587 0.360946i \(-0.882454\pi\)
0.837163 0.546954i \(-0.184213\pi\)
\(72\) 1.82304 + 2.02469i 0.214848 + 0.238612i
\(73\) 8.35045 3.71786i 0.977346 0.435143i 0.145020 0.989429i \(-0.453675\pi\)
0.832326 + 0.554286i \(0.187009\pi\)
\(74\) 19.4617 4.13670i 2.26237 0.480882i
\(75\) 4.26906 + 0.907417i 0.492949 + 0.104779i
\(76\) 12.7601 + 5.68116i 1.46368 + 0.651674i
\(77\) 3.19835 + 9.84350i 0.364486 + 1.12177i
\(78\) 1.60972 + 4.95421i 0.182265 + 0.560953i
\(79\) 8.02362 + 3.57235i 0.902728 + 0.401920i 0.804988 0.593292i \(-0.202172\pi\)
0.0977404 + 0.995212i \(0.468839\pi\)
\(80\) 0.140848 + 0.0299381i 0.0157473 + 0.00334719i
\(81\) −0.978148 + 0.207912i −0.108683 + 0.0231013i
\(82\) −22.0403 + 9.81297i −2.43394 + 1.08366i
\(83\) −1.85000 2.05463i −0.203064 0.225525i 0.633008 0.774145i \(-0.281820\pi\)
−0.836072 + 0.548620i \(0.815153\pi\)
\(84\) −1.52670 14.5256i −0.166577 1.58487i
\(85\) 1.66110 1.20686i 0.180171 0.130902i
\(86\) −0.469890 + 4.47071i −0.0506696 + 0.482089i
\(87\) 4.09128 + 7.08630i 0.438631 + 0.759731i
\(88\) −3.08456 + 5.34261i −0.328815 + 0.569524i
\(89\) −1.10573 0.803361i −0.117207 0.0851561i 0.527637 0.849470i \(-0.323078\pi\)
−0.644845 + 0.764314i \(0.723078\pi\)
\(90\) 1.21590 1.35039i 0.128167 0.142344i
\(91\) 3.22813 9.93515i 0.338400 1.04149i
\(92\) −22.3547 −2.33064
\(93\) −2.27974 5.07964i −0.236398 0.526735i
\(94\) −8.09627 −0.835066
\(95\) 1.07690 3.31435i 0.110487 0.340045i
\(96\) −3.92156 + 4.35533i −0.400242 + 0.444514i
\(97\) −0.0532738 0.0387057i −0.00540914 0.00392997i 0.585077 0.810977i \(-0.301064\pi\)
−0.590487 + 0.807047i \(0.701064\pi\)
\(98\) −15.8339 + 27.4252i −1.59947 + 2.77036i
\(99\) −1.13216 1.96096i −0.113786 0.197083i
\(100\) 1.45772 13.8693i 0.145772 1.38693i
\(101\) −9.55254 + 6.94033i −0.950513 + 0.690588i −0.950928 0.309411i \(-0.899868\pi\)
0.000414784 1.00000i \(0.499868\pi\)
\(102\) 0.613617 + 5.83817i 0.0607571 + 0.578065i
\(103\) 12.1843 + 13.5320i 1.20055 + 1.33335i 0.928621 + 0.371030i \(0.120995\pi\)
0.271931 + 0.962317i \(0.412338\pi\)
\(104\) 5.68824 2.53257i 0.557778 0.248339i
\(105\) −3.56444 + 0.757645i −0.347854 + 0.0739386i
\(106\) 2.27279 + 0.483097i 0.220753 + 0.0469225i
\(107\) 5.71321 + 2.54368i 0.552317 + 0.245907i 0.663866 0.747852i \(-0.268915\pi\)
−0.111549 + 0.993759i \(0.535581\pi\)
\(108\) 0.987405 + 3.03892i 0.0950131 + 0.292420i
\(109\) −2.99731 9.22477i −0.287090 0.883573i −0.985764 0.168133i \(-0.946226\pi\)
0.698674 0.715440i \(-0.253774\pi\)
\(110\) 3.75884 + 1.67354i 0.358391 + 0.159566i
\(111\) 8.53835 + 1.81488i 0.810424 + 0.172261i
\(112\) 0.807562 0.171653i 0.0763075 0.0162196i
\(113\) −3.81080 + 1.69668i −0.358490 + 0.159610i −0.578076 0.815983i \(-0.696196\pi\)
0.219585 + 0.975593i \(0.429530\pi\)
\(114\) 6.66696 + 7.40441i 0.624418 + 0.693486i
\(115\) 0.583003 + 5.54691i 0.0543653 + 0.517252i
\(116\) 21.1524 15.3681i 1.96395 1.42689i
\(117\) −0.238889 + 2.27288i −0.0220853 + 0.210128i
\(118\) −5.24294 9.08104i −0.482652 0.835977i
\(119\) 5.88618 10.1952i 0.539585 0.934588i
\(120\) −1.75721 1.27669i −0.160411 0.116545i
\(121\) −3.92972 + 4.36439i −0.357247 + 0.396763i
\(122\) 0.177425 0.546057i 0.0160633 0.0494377i
\(123\) −10.5848 −0.954397
\(124\) −15.3807 + 8.94117i −1.38123 + 0.802941i
\(125\) −7.46555 −0.667739
\(126\) 3.21954 9.90873i 0.286820 0.882740i
\(127\) 13.6658 15.1774i 1.21264 1.34678i 0.291978 0.956425i \(-0.405687\pi\)
0.920666 0.390352i \(-0.127647\pi\)
\(128\) 14.4841 + 10.5233i 1.28022 + 0.930136i
\(129\) −0.986112 + 1.70800i −0.0868223 + 0.150381i
\(130\) −2.07643 3.59649i −0.182115 0.315433i
\(131\) −0.245534 + 2.33610i −0.0214524 + 0.204106i −0.999998 0.00192351i \(-0.999388\pi\)
0.978546 + 0.206030i \(0.0660544\pi\)
\(132\) −5.85339 + 4.25274i −0.509472 + 0.370153i
\(133\) −2.08858 19.8715i −0.181103 1.72308i
\(134\) −6.05853 6.72868i −0.523378 0.581270i
\(135\) 0.728301 0.324260i 0.0626821 0.0279079i
\(136\) 6.86352 1.45889i 0.588542 0.125099i
\(137\) 17.7257 + 3.76772i 1.51441 + 0.321898i 0.888822 0.458253i \(-0.151525\pi\)
0.625591 + 0.780151i \(0.284858\pi\)
\(138\) −14.5677 6.48597i −1.24009 0.552122i
\(139\) −1.11458 3.43033i −0.0945377 0.290957i 0.892595 0.450859i \(-0.148882\pi\)
−0.987133 + 0.159902i \(0.948882\pi\)
\(140\) 3.59817 + 11.0740i 0.304101 + 0.935927i
\(141\) −3.24496 1.44475i −0.273275 0.121670i
\(142\) −17.1499 3.64533i −1.43919 0.305910i
\(143\) −5.06178 + 1.07592i −0.423288 + 0.0899726i
\(144\) −0.165004 + 0.0734647i −0.0137504 + 0.00612206i
\(145\) −4.36496 4.84778i −0.362490 0.402586i
\(146\) −2.17781 20.7205i −0.180237 1.71484i
\(147\) −11.2401 + 8.16643i −0.927070 + 0.673556i
\(148\) 2.91553 27.7394i 0.239655 2.28016i
\(149\) −6.12004 10.6002i −0.501373 0.868403i −0.999999 0.00158608i \(-0.999495\pi\)
0.498626 0.866817i \(-0.333838\pi\)
\(150\) 4.97397 8.61518i 0.406123 0.703426i
\(151\) −0.444224 0.322748i −0.0361504 0.0262648i 0.569563 0.821947i \(-0.307112\pi\)
−0.605714 + 0.795683i \(0.707112\pi\)
\(152\) 7.96907 8.85055i 0.646377 0.717875i
\(153\) −0.795865 + 2.44942i −0.0643419 + 0.198024i
\(154\) 23.5911 1.90103
\(155\) 2.61971 + 3.58325i 0.210420 + 0.287814i
\(156\) 7.30255 0.584672
\(157\) −2.61513 + 8.04854i −0.208710 + 0.642343i 0.790831 + 0.612035i \(0.209649\pi\)
−0.999541 + 0.0303083i \(0.990351\pi\)
\(158\) 13.3954 14.8771i 1.06568 1.18356i
\(159\) 0.824721 + 0.599195i 0.0654047 + 0.0475193i
\(160\) 2.33614 4.04631i 0.184688 0.319889i
\(161\) 15.9894 + 27.6944i 1.26014 + 2.18263i
\(162\) −0.238254 + 2.26684i −0.0187190 + 0.178099i
\(163\) −6.23819 + 4.53231i −0.488613 + 0.354998i −0.804651 0.593748i \(-0.797647\pi\)
0.316038 + 0.948747i \(0.397647\pi\)
\(164\) 3.53532 + 33.6364i 0.276062 + 2.62656i
\(165\) 1.20789 + 1.34150i 0.0940344 + 0.104436i
\(166\) −5.75700 + 2.56318i −0.446830 + 0.198941i
\(167\) −17.2546 + 3.66757i −1.33520 + 0.283805i −0.819556 0.572999i \(-0.805780\pi\)
−0.515642 + 0.856804i \(0.672447\pi\)
\(168\) −12.1814 2.58923i −0.939814 0.199764i
\(169\) −7.10460 3.16317i −0.546508 0.243321i
\(170\) −1.44619 4.45092i −0.110918 0.341370i
\(171\) 1.35081 + 4.15736i 0.103299 + 0.317921i
\(172\) 5.75704 + 2.56320i 0.438970 + 0.195442i
\(173\) 21.5097 + 4.57204i 1.63536 + 0.347605i 0.931782 0.363018i \(-0.118254\pi\)
0.703573 + 0.710623i \(0.251587\pi\)
\(174\) 18.2431 3.87770i 1.38301 0.293967i
\(175\) −18.2249 + 8.11423i −1.37767 + 0.613378i
\(176\) −0.273661 0.303932i −0.0206280 0.0229097i
\(177\) −0.480877 4.57523i −0.0361449 0.343896i
\(178\) −2.52032 + 1.83112i −0.188906 + 0.137248i
\(179\) −0.902491 + 8.58663i −0.0674553 + 0.641795i 0.907600 + 0.419835i \(0.137912\pi\)
−0.975056 + 0.221960i \(0.928755\pi\)
\(180\) −1.27369 2.20609i −0.0949352 0.164433i
\(181\) −7.83047 + 13.5628i −0.582034 + 1.00811i 0.413204 + 0.910639i \(0.364410\pi\)
−0.995238 + 0.0974742i \(0.968924\pi\)
\(182\) −19.2633 13.9956i −1.42789 1.03743i
\(183\) 0.168553 0.187197i 0.0124598 0.0138380i
\(184\) −5.89012 + 18.1279i −0.434225 + 1.33641i
\(185\) −6.95905 −0.511640
\(186\) −12.6172 + 1.36409i −0.925138 + 0.100020i
\(187\) −5.83169 −0.426455
\(188\) −3.50731 + 10.7944i −0.255797 + 0.787262i
\(189\) 3.05856 3.39688i 0.222478 0.247086i
\(190\) −6.42621 4.66892i −0.466206 0.338719i
\(191\) 4.38724 7.59893i 0.317450 0.549839i −0.662505 0.749057i \(-0.730507\pi\)
0.979955 + 0.199218i \(0.0638402\pi\)
\(192\) 6.49857 + 11.2558i 0.468994 + 0.812321i
\(193\) −0.234416 + 2.23032i −0.0168737 + 0.160542i −0.999714 0.0239164i \(-0.992386\pi\)
0.982840 + 0.184458i \(0.0590531\pi\)
\(194\) −0.121428 + 0.0882228i −0.00871804 + 0.00633403i
\(195\) −0.190448 1.81199i −0.0136383 0.129760i
\(196\) 29.7055 + 32.9913i 2.12182 + 2.35652i
\(197\) −6.87851 + 3.06251i −0.490074 + 0.218195i −0.636869 0.770972i \(-0.719771\pi\)
0.146795 + 0.989167i \(0.453104\pi\)
\(198\) −5.04832 + 1.07305i −0.358769 + 0.0762587i
\(199\) −5.48522 1.16592i −0.388837 0.0826499i 0.00934480 0.999956i \(-0.497025\pi\)
−0.398182 + 0.917306i \(0.630359\pi\)
\(200\) −10.8628 4.83645i −0.768119 0.341989i
\(201\) −1.22753 3.77796i −0.0865835 0.266477i
\(202\) 8.31667 + 25.5961i 0.585159 + 1.80093i
\(203\) −34.1685 15.2128i −2.39816 1.06773i
\(204\) 8.04960 + 1.71100i 0.563585 + 0.119794i
\(205\) 8.25404 1.75445i 0.576487 0.122536i
\(206\) 37.9162 16.8814i 2.64174 1.17618i
\(207\) −4.68130 5.19911i −0.325373 0.361363i
\(208\) 0.0431481 + 0.410527i 0.00299178 + 0.0284649i
\(209\) −8.00767 + 5.81791i −0.553902 + 0.402433i
\(210\) −0.868214 + 8.26051i −0.0599125 + 0.570029i
\(211\) 1.35528 + 2.34741i 0.0933010 + 0.161602i 0.908898 0.417018i \(-0.136925\pi\)
−0.815597 + 0.578620i \(0.803591\pi\)
\(212\) 1.62867 2.82094i 0.111857 0.193743i
\(213\) −6.22315 4.52138i −0.426403 0.309800i
\(214\) 9.53820 10.5932i 0.652018 0.724139i
\(215\) 0.485869 1.49535i 0.0331360 0.101982i
\(216\) 2.72449 0.185378
\(217\) 22.0781 + 12.6593i 1.49876 + 0.859372i
\(218\) −22.1083 −1.49736
\(219\) 2.82463 8.69333i 0.190871 0.587441i
\(220\) 3.85959 4.28651i 0.260214 0.288997i
\(221\) 4.76186 + 3.45969i 0.320317 + 0.232724i
\(222\) 9.94822 17.2308i 0.667681 1.15646i
\(223\) 3.14107 + 5.44050i 0.210342 + 0.364323i 0.951822 0.306652i \(-0.0992089\pi\)
−0.741480 + 0.670975i \(0.765876\pi\)
\(224\) 2.80020 26.6421i 0.187096 1.78010i
\(225\) 3.53090 2.56535i 0.235393 0.171023i
\(226\) 0.993864 + 9.45598i 0.0661108 + 0.629002i
\(227\) 6.45159 + 7.16521i 0.428207 + 0.475572i 0.918179 0.396166i \(-0.129660\pi\)
−0.489972 + 0.871738i \(0.662993\pi\)
\(228\) 12.7601 5.68116i 0.845058 0.376244i
\(229\) 3.48220 0.740164i 0.230110 0.0489114i −0.0914134 0.995813i \(-0.529138\pi\)
0.321523 + 0.946902i \(0.395805\pi\)
\(230\) 12.4350 + 2.64315i 0.819941 + 0.174284i
\(231\) 9.45526 + 4.20975i 0.622111 + 0.276981i
\(232\) −6.88902 21.2022i −0.452286 1.39199i
\(233\) 0.691952 + 2.12961i 0.0453313 + 0.139515i 0.971160 0.238427i \(-0.0766318\pi\)
−0.925829 + 0.377942i \(0.876632\pi\)
\(234\) 4.75880 + 2.11876i 0.311093 + 0.138507i
\(235\) 2.76990 + 0.588760i 0.180688 + 0.0384065i
\(236\) −14.3786 + 3.05626i −0.935966 + 0.198946i
\(237\) 8.02362 3.57235i 0.521190 0.232049i
\(238\) −17.9548 19.9408i −1.16383 1.29257i
\(239\) 1.56290 + 14.8700i 0.101096 + 0.961860i 0.921053 + 0.389436i \(0.127330\pi\)
−0.819958 + 0.572424i \(0.806003\pi\)
\(240\) 0.116494 0.0846379i 0.00751966 0.00546335i
\(241\) 0.0972398 0.925175i 0.00626377 0.0595958i −0.990944 0.134279i \(-0.957128\pi\)
0.997207 + 0.0746837i \(0.0237947\pi\)
\(242\) 6.69308 + 11.5928i 0.430247 + 0.745210i
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) −0.651173 0.473105i −0.0416871 0.0302874i
\(245\) 7.41148 8.23128i 0.473502 0.525877i
\(246\) −7.45538 + 22.9453i −0.475338 + 1.46294i
\(247\) 9.99018 0.635660
\(248\) 3.19802 + 14.8284i 0.203075 + 0.941604i
\(249\) −2.76478 −0.175211
\(250\) −5.25836 + 16.1836i −0.332568 + 1.02354i
\(251\) 9.74726 10.8254i 0.615241 0.683295i −0.352335 0.935874i \(-0.614612\pi\)
0.967576 + 0.252579i \(0.0812788\pi\)
\(252\) −11.8162 8.58495i −0.744349 0.540801i
\(253\) 7.92069 13.7190i 0.497970 0.862509i
\(254\) −23.2755 40.3144i −1.46044 2.52955i
\(255\) 0.214621 2.04198i 0.0134401 0.127874i
\(256\) 11.9841 8.70692i 0.749003 0.544183i
\(257\) −0.350300 3.33288i −0.0218511 0.207899i 0.978149 0.207906i \(-0.0666647\pi\)
−1.00000 6.32408e-6i \(0.999998\pi\)
\(258\) 3.00796 + 3.34068i 0.187268 + 0.207982i
\(259\) −36.4507 + 16.2289i −2.26494 + 1.00841i
\(260\) −5.69455 + 1.21042i −0.353161 + 0.0750668i
\(261\) 8.00375 + 1.70125i 0.495420 + 0.105305i
\(262\) 4.89118 + 2.17769i 0.302178 + 0.134538i
\(263\) 5.79482 + 17.8346i 0.357324 + 1.09973i 0.954650 + 0.297731i \(0.0962299\pi\)
−0.597326 + 0.801999i \(0.703770\pi\)
\(264\) 1.90636 + 5.86718i 0.117328 + 0.361100i
\(265\) −0.742438 0.330555i −0.0456076 0.0203058i
\(266\) −44.5479 9.46895i −2.73141 0.580579i
\(267\) −1.33689 + 0.284165i −0.0818165 + 0.0173906i
\(268\) −11.5956 + 5.16270i −0.708315 + 0.315362i
\(269\) 10.2024 + 11.3309i 0.622049 + 0.690856i 0.969009 0.247024i \(-0.0794527\pi\)
−0.346960 + 0.937880i \(0.612786\pi\)
\(270\) −0.189942 1.80718i −0.0115595 0.109981i
\(271\) 11.0514 8.02930i 0.671324 0.487745i −0.199144 0.979970i \(-0.563816\pi\)
0.870468 + 0.492225i \(0.163816\pi\)
\(272\) −0.0486247 + 0.462633i −0.00294831 + 0.0280513i
\(273\) −5.22322 9.04688i −0.316124 0.547542i
\(274\) 20.6527 35.7714i 1.24767 2.16103i
\(275\) 7.99508 + 5.80876i 0.482121 + 0.350282i
\(276\) −14.9582 + 16.6128i −0.900378 + 0.999971i
\(277\) 2.94103 9.05156i 0.176709 0.543855i −0.822998 0.568044i \(-0.807700\pi\)
0.999707 + 0.0241888i \(0.00770030\pi\)
\(278\) −8.22121 −0.493075
\(279\) −5.30035 1.70477i −0.317324 0.102062i
\(280\) 9.92825 0.593326
\(281\) 4.26083 13.1135i 0.254180 0.782286i −0.739810 0.672816i \(-0.765085\pi\)
0.993990 0.109470i \(-0.0349153\pi\)
\(282\) −5.41746 + 6.01670i −0.322605 + 0.358289i
\(283\) −9.86758 7.16922i −0.586567 0.426166i 0.254519 0.967068i \(-0.418083\pi\)
−0.841086 + 0.540902i \(0.818083\pi\)
\(284\) −12.2895 + 21.2861i −0.729250 + 1.26310i
\(285\) −1.74246 3.01802i −0.103214 0.178772i
\(286\) −1.23293 + 11.7306i −0.0729049 + 0.693643i
\(287\) 39.1422 28.4385i 2.31049 1.67867i
\(288\) 0.612608 + 5.82857i 0.0360982 + 0.343452i
\(289\) −6.93684 7.70414i −0.408049 0.453184i
\(290\) −13.5833 + 6.04768i −0.797639 + 0.355132i
\(291\) −0.0644111 + 0.0136910i −0.00377585 + 0.000802581i
\(292\) −28.5691 6.07255i −1.67188 0.355369i
\(293\) −15.5981 6.94474i −0.911253 0.405716i −0.103088 0.994672i \(-0.532872\pi\)
−0.808165 + 0.588956i \(0.799539\pi\)
\(294\) 9.78592 + 30.1180i 0.570726 + 1.75651i
\(295\) 1.13334 + 3.48808i 0.0659859 + 0.203084i
\(296\) −21.7263 9.67317i −1.26281 0.562241i
\(297\) −2.21484 0.470778i −0.128518 0.0273173i
\(298\) −27.2894 + 5.80054i −1.58083 + 0.336016i
\(299\) −14.6066 + 6.50326i −0.844719 + 0.376093i
\(300\) −9.33150 10.3637i −0.538755 0.598348i
\(301\) −0.942317 8.96554i −0.0543142 0.516765i
\(302\) −1.01253 + 0.735646i −0.0582645 + 0.0423317i
\(303\) −1.23423 + 11.7429i −0.0709046 + 0.674612i
\(304\) 0.394772 + 0.683765i 0.0226417 + 0.0392166i
\(305\) −0.100410 + 0.173915i −0.00574945 + 0.00995834i
\(306\) 4.74920 + 3.45050i 0.271494 + 0.197252i
\(307\) −20.1382 + 22.3657i −1.14935 + 1.27648i −0.193998 + 0.981002i \(0.562146\pi\)
−0.955349 + 0.295478i \(0.904521\pi\)
\(308\) 10.2197 31.4530i 0.582322 1.79220i
\(309\) 18.2091 1.03588
\(310\) 9.61283 3.15505i 0.545972 0.179195i
\(311\) 4.97560 0.282141 0.141070 0.990000i \(-0.454946\pi\)
0.141070 + 0.990000i \(0.454946\pi\)
\(312\) 1.92411 5.92180i 0.108931 0.335256i
\(313\) 9.79194 10.8751i 0.553473 0.614694i −0.399874 0.916570i \(-0.630946\pi\)
0.953347 + 0.301876i \(0.0976128\pi\)
\(314\) 15.6054 + 11.3380i 0.880662 + 0.639838i
\(315\) −1.82204 + 3.15586i −0.102660 + 0.177812i
\(316\) −14.0321 24.3043i −0.789368 1.36723i
\(317\) −3.33739 + 31.7532i −0.187447 + 1.78344i 0.346633 + 0.938001i \(0.387325\pi\)
−0.534079 + 0.845434i \(0.679342\pi\)
\(318\) 1.87981 1.36576i 0.105414 0.0765880i
\(319\) 1.93669 + 18.4264i 0.108434 + 1.03168i
\(320\) −6.93328 7.70019i −0.387582 0.430454i
\(321\) 5.71321 2.54368i 0.318880 0.141975i
\(322\) 71.2971 15.1547i 3.97323 0.844537i
\(323\) 11.0122 + 2.34071i 0.612733 + 0.130240i
\(324\) 2.91906 + 1.29965i 0.162170 + 0.0722027i
\(325\) −3.08228 9.48629i −0.170974 0.526204i
\(326\) 5.43112 + 16.7153i 0.300802 + 0.925773i
\(327\) −8.86093 3.94514i −0.490011 0.218167i
\(328\) 28.2080 + 5.99579i 1.55752 + 0.331062i
\(329\) 15.8814 3.37570i 0.875572 0.186109i
\(330\) 3.75884 1.67354i 0.206917 0.0921255i
\(331\) 5.03356 + 5.59033i 0.276669 + 0.307272i 0.865425 0.501039i \(-0.167049\pi\)
−0.588756 + 0.808311i \(0.700382\pi\)
\(332\) 0.923438 + 8.78593i 0.0506802 + 0.482190i
\(333\) 7.06199 5.13084i 0.386995 0.281168i
\(334\) −4.20281 + 39.9871i −0.229968 + 2.18800i
\(335\) 1.58344 + 2.74260i 0.0865125 + 0.149844i
\(336\) 0.412802 0.714994i 0.0225202 0.0390061i
\(337\) −6.38542 4.63928i −0.347836 0.252717i 0.400125 0.916461i \(-0.368967\pi\)
−0.747961 + 0.663743i \(0.768967\pi\)
\(338\) −11.8611 + 13.1731i −0.645160 + 0.716523i
\(339\) −1.28905 + 3.96728i −0.0700114 + 0.215473i
\(340\) −6.56070 −0.355804
\(341\) −0.0375157 12.6071i −0.00203159 0.682714i
\(342\) 9.96361 0.538770
\(343\) 9.73715 29.9679i 0.525757 1.61811i
\(344\) 3.59545 3.99315i 0.193853 0.215296i
\(345\) 4.51226 + 3.27835i 0.242932 + 0.176500i
\(346\) 25.0615 43.4077i 1.34731 2.33361i
\(347\) −16.7024 28.9294i −0.896632 1.55301i −0.831771 0.555119i \(-0.812673\pi\)
−0.0648612 0.997894i \(-0.520660\pi\)
\(348\) 2.73298 26.0026i 0.146503 1.39388i
\(349\) 6.03663 4.38587i 0.323134 0.234770i −0.414378 0.910105i \(-0.636001\pi\)
0.737511 + 0.675335i \(0.236001\pi\)
\(350\) 4.75307 + 45.2224i 0.254062 + 2.41724i
\(351\) 1.52923 + 1.69838i 0.0816243 + 0.0906529i
\(352\) −12.1231 + 5.39757i −0.646166 + 0.287691i
\(353\) −3.48905 + 0.741620i −0.185703 + 0.0394725i −0.299825 0.953994i \(-0.596928\pi\)
0.114121 + 0.993467i \(0.463595\pi\)
\(354\) −10.2567 2.18014i −0.545139 0.115873i
\(355\) 5.60226 + 2.49429i 0.297337 + 0.132383i
\(356\) 1.34955 + 4.15347i 0.0715258 + 0.220134i
\(357\) −3.63786 11.1962i −0.192536 0.592564i
\(358\) 17.9781 + 8.00437i 0.950173 + 0.423044i
\(359\) −23.1016 4.91039i −1.21925 0.259161i −0.447035 0.894516i \(-0.647520\pi\)
−0.772220 + 0.635356i \(0.780853\pi\)
\(360\) −2.12457 + 0.451591i −0.111975 + 0.0238009i
\(361\) 0.0989471 0.0440541i 0.00520774 0.00231864i
\(362\) 23.8855 + 26.5275i 1.25539 + 1.39426i
\(363\) 0.613882 + 5.84070i 0.0322204 + 0.306557i
\(364\) −27.0047 + 19.6200i −1.41543 + 1.02837i
\(365\) −0.761719 + 7.24727i −0.0398702 + 0.379340i
\(366\) −0.287079 0.497236i −0.0150059 0.0259909i
\(367\) −10.8521 + 18.7965i −0.566477 + 0.981167i 0.430433 + 0.902622i \(0.358361\pi\)
−0.996911 + 0.0785449i \(0.974973\pi\)
\(368\) −1.02230 0.742745i −0.0532911 0.0387183i
\(369\) −7.08260 + 7.86602i −0.368705 + 0.409489i
\(370\) −4.90160 + 15.0856i −0.254822 + 0.784262i
\(371\) −4.65968 −0.241918
\(372\) −3.64710 + 17.4129i −0.189093 + 0.902816i
\(373\) −15.7335 −0.814648 −0.407324 0.913284i \(-0.633538\pi\)
−0.407324 + 0.913284i \(0.633538\pi\)
\(374\) −4.10754 + 12.6417i −0.212396 + 0.653688i
\(375\) −4.99543 + 5.54799i −0.257963 + 0.286497i
\(376\) 7.82929 + 5.68831i 0.403765 + 0.293352i
\(377\) 9.35020 16.1950i 0.481560 0.834086i
\(378\) −5.20933 9.02282i −0.267939 0.464084i
\(379\) 0.674334 6.41586i 0.0346382 0.329560i −0.963457 0.267864i \(-0.913682\pi\)
0.998095 0.0616965i \(-0.0196511\pi\)
\(380\) −9.00870 + 6.54520i −0.462137 + 0.335762i
\(381\) −2.13481 20.3113i −0.109370 1.04058i
\(382\) −13.3825 14.8628i −0.684710 0.760448i
\(383\) 23.6292 10.5204i 1.20740 0.537568i 0.298428 0.954432i \(-0.403538\pi\)
0.908969 + 0.416864i \(0.136871\pi\)
\(384\) 17.5121 3.72230i 0.893659 0.189953i
\(385\) −8.07102 1.71555i −0.411337 0.0874324i
\(386\) 4.66970 + 2.07909i 0.237682 + 0.105823i
\(387\) 0.609451 + 1.87570i 0.0309801 + 0.0953470i
\(388\) 0.0650207 + 0.200113i 0.00330093 + 0.0101592i
\(389\) −21.3927 9.52463i −1.08465 0.482918i −0.215015 0.976611i \(-0.568980\pi\)
−0.869636 + 0.493693i \(0.835647\pi\)
\(390\) −4.06212 0.863430i −0.205693 0.0437215i
\(391\) −17.6245 + 3.74621i −0.891310 + 0.189454i
\(392\) 34.5803 15.3962i 1.74657 0.777624i
\(393\) 1.57177 + 1.74563i 0.0792852 + 0.0880552i
\(394\) 1.79393 + 17.0681i 0.0903767 + 0.859877i
\(395\) −5.66472 + 4.11566i −0.285023 + 0.207081i
\(396\) −0.756283 + 7.19556i −0.0380047 + 0.361590i
\(397\) 8.92563 + 15.4596i 0.447964 + 0.775897i 0.998253 0.0590773i \(-0.0188158\pi\)
−0.550289 + 0.834974i \(0.685482\pi\)
\(398\) −6.39095 + 11.0695i −0.320350 + 0.554862i
\(399\) −16.1650 11.7445i −0.809261 0.587962i
\(400\) 0.527478 0.585823i 0.0263739 0.0292912i
\(401\) 2.83024 8.71058i 0.141335 0.434986i −0.855186 0.518321i \(-0.826557\pi\)
0.996522 + 0.0833353i \(0.0265573\pi\)
\(402\) −9.05433 −0.451589
\(403\) −7.44864 + 10.3166i −0.371043 + 0.513906i
\(404\) 37.7289 1.87708
\(405\) 0.246356 0.758205i 0.0122415 0.0376755i
\(406\) −57.0442 + 63.3541i −2.83106 + 3.14421i
\(407\) 15.9906 + 11.6178i 0.792624 + 0.575875i
\(408\) 3.50843 6.07678i 0.173693 0.300845i
\(409\) 18.2182 + 31.5548i 0.900830 + 1.56028i 0.826419 + 0.563055i \(0.190374\pi\)
0.0744102 + 0.997228i \(0.476293\pi\)
\(410\) 2.01049 19.1286i 0.0992912 0.944692i
\(411\) 14.6608 10.6517i 0.723164 0.525410i
\(412\) −6.08185 57.8650i −0.299631 2.85080i
\(413\) 14.0707 + 15.6271i 0.692375 + 0.768960i
\(414\) −14.5677 + 6.48597i −0.715965 + 0.318768i
\(415\) 2.15598 0.458268i 0.105833 0.0224955i
\(416\) 13.1013 + 2.78477i 0.642344 + 0.136534i
\(417\) −3.29504 1.46704i −0.161359 0.0718415i
\(418\) 6.97166 + 21.4566i 0.340995 + 1.04948i
\(419\) −5.84627 17.9930i −0.285609 0.879015i −0.986215 0.165467i \(-0.947087\pi\)
0.700606 0.713548i \(-0.252913\pi\)
\(420\) 10.6373 + 4.73601i 0.519045 + 0.231094i
\(421\) −6.01043 1.27756i −0.292931 0.0622643i 0.0591024 0.998252i \(-0.481176\pi\)
−0.352033 + 0.935988i \(0.614509\pi\)
\(422\) 6.04321 1.28452i 0.294179 0.0625296i
\(423\) −3.24496 + 1.44475i −0.157775 + 0.0702461i
\(424\) −1.85843 2.06400i −0.0902534 0.100237i
\(425\) −1.17495 11.1789i −0.0569935 0.542257i
\(426\) −14.1846 + 10.3057i −0.687244 + 0.499312i
\(427\) −0.120356 + 1.14511i −0.00582442 + 0.0554157i
\(428\) −9.99155 17.3059i −0.482960 0.836511i
\(429\) −2.58743 + 4.48157i −0.124922 + 0.216372i
\(430\) −2.89935 2.10650i −0.139819 0.101584i
\(431\) −23.9890 + 26.6425i −1.15551 + 1.28333i −0.202878 + 0.979204i \(0.565029\pi\)
−0.952633 + 0.304121i \(0.901637\pi\)
\(432\) −0.0558146 + 0.171780i −0.00268538 + 0.00826475i
\(433\) 19.1352 0.919578 0.459789 0.888028i \(-0.347925\pi\)
0.459789 + 0.888028i \(0.347925\pi\)
\(434\) 42.9931 38.9435i 2.06374 1.86935i
\(435\) −6.52333 −0.312770
\(436\) −9.57733 + 29.4760i −0.458671 + 1.41164i
\(437\) −20.4634 + 22.7269i −0.978897 + 1.08718i
\(438\) −16.8556 12.2463i −0.805390 0.585150i
\(439\) 11.6441 20.1682i 0.555743 0.962574i −0.442103 0.896964i \(-0.645767\pi\)
0.997845 0.0656099i \(-0.0208993\pi\)
\(440\) −2.45909 4.25926i −0.117232 0.203052i
\(441\) −1.45227 + 13.8174i −0.0691558 + 0.657974i
\(442\) 10.8538 7.88576i 0.516263 0.375087i
\(443\) 1.04224 + 9.91621i 0.0495181 + 0.471133i 0.990980 + 0.134013i \(0.0427863\pi\)
−0.941461 + 0.337121i \(0.890547\pi\)
\(444\) −18.6635 20.7279i −0.885731 0.983704i
\(445\) 0.995412 0.443186i 0.0471871 0.0210090i
\(446\) 14.0061 2.97710i 0.663210 0.140970i
\(447\) −11.9726 2.54485i −0.566284 0.120367i
\(448\) −54.2730 24.1639i −2.56416 1.14164i
\(449\) −11.1274 34.2467i −0.525136 1.61620i −0.764046 0.645161i \(-0.776790\pi\)
0.238910 0.971042i \(-0.423210\pi\)
\(450\) −3.07409 9.46106i −0.144914 0.445999i
\(451\) −21.8952 9.74838i −1.03101 0.459033i
\(452\) 13.0378 + 2.77127i 0.613246 + 0.130349i
\(453\) −0.537092 + 0.114162i −0.0252348 + 0.00536382i
\(454\) 20.0767 8.93870i 0.942244 0.419514i
\(455\) 5.57262 + 6.18902i 0.261249 + 0.290146i
\(456\) −1.24489 11.8444i −0.0582974 0.554663i
\(457\) −4.02430 + 2.92383i −0.188249 + 0.136771i −0.677918 0.735137i \(-0.737118\pi\)
0.489669 + 0.871908i \(0.337118\pi\)
\(458\) 0.848182 8.06991i 0.0396329 0.377082i
\(459\) 1.28774 + 2.23043i 0.0601064 + 0.104107i
\(460\) 8.91085 15.4340i 0.415471 0.719616i
\(461\) −1.94226 1.41114i −0.0904602 0.0657232i 0.541636 0.840613i \(-0.317805\pi\)
−0.632096 + 0.774890i \(0.717805\pi\)
\(462\) 15.7856 17.5316i 0.734411 0.815646i
\(463\) −0.662128 + 2.03782i −0.0307717 + 0.0947055i −0.965263 0.261281i \(-0.915855\pi\)
0.934491 + 0.355986i \(0.115855\pi\)
\(464\) 1.47793 0.0686113
\(465\) 4.41580 + 0.450838i 0.204778 + 0.0209071i
\(466\) 5.10387 0.236432
\(467\) 1.79375 5.52060i 0.0830049 0.255463i −0.900938 0.433949i \(-0.857120\pi\)
0.983942 + 0.178486i \(0.0571199\pi\)
\(468\) 4.88636 5.42686i 0.225872 0.250856i
\(469\) 14.6898 + 10.6727i 0.678310 + 0.492821i
\(470\) 3.22727 5.58980i 0.148863 0.257838i
\(471\) 4.23137 + 7.32894i 0.194971 + 0.337700i
\(472\) −1.31014 + 12.4652i −0.0603043 + 0.573757i
\(473\) −3.61286 + 2.62490i −0.166119 + 0.120693i
\(474\) −2.09257 19.9095i −0.0961150 0.914474i
\(475\) −12.7659 14.1779i −0.585738 0.650528i
\(476\) −34.3642 + 15.2999i −1.57508 + 0.701271i
\(477\) 0.997135 0.211948i 0.0456557 0.00970442i
\(478\) 33.3355 + 7.08567i 1.52473 + 0.324091i
\(479\) −9.45267 4.20860i −0.431903 0.192296i 0.179257 0.983802i \(-0.442630\pi\)
−0.611161 + 0.791506i \(0.709297\pi\)
\(480\) −1.44381 4.44360i −0.0659007 0.202822i
\(481\) −6.16473 18.9731i −0.281087 0.865098i
\(482\) −1.93707 0.862439i −0.0882311 0.0392830i
\(483\) 31.2800 + 6.64876i 1.42329 + 0.302529i
\(484\) 18.3556 3.90159i 0.834343 0.177345i
\(485\) 0.0479587 0.0213526i 0.00217769 0.000969571i
\(486\) 1.52516 + 1.69387i 0.0691828 + 0.0768353i
\(487\) −2.90167 27.6076i −0.131487 1.25102i −0.838927 0.544244i \(-0.816816\pi\)
0.707440 0.706774i \(-0.249850\pi\)
\(488\) −0.555225 + 0.403395i −0.0251339 + 0.0182608i
\(489\) −0.806001 + 7.66859i −0.0364486 + 0.346786i
\(490\) −12.6232 21.8640i −0.570258 0.987716i
\(491\) −8.79259 + 15.2292i −0.396804 + 0.687285i −0.993330 0.115309i \(-0.963214\pi\)
0.596526 + 0.802594i \(0.296547\pi\)
\(492\) 27.3623 + 19.8799i 1.23359 + 0.896253i
\(493\) 14.1012 15.6610i 0.635087 0.705336i
\(494\) 7.03657 21.6563i 0.316590 0.974365i
\(495\) 1.80517 0.0811363
\(496\) −1.00045 0.102142i −0.0449214 0.00458632i
\(497\) 35.1608 1.57718
\(498\) −1.94737 + 5.99339i −0.0872637 + 0.268570i
\(499\) 24.6905 27.4215i 1.10530 1.22756i 0.133672 0.991026i \(-0.457323\pi\)
0.971624 0.236531i \(-0.0760104\pi\)
\(500\) 19.2989 + 14.0215i 0.863073 + 0.627059i
\(501\) −8.82002 + 15.2767i −0.394049 + 0.682514i
\(502\) −16.6015 28.7546i −0.740961 1.28338i
\(503\) −0.596021 + 5.67076i −0.0265753 + 0.252847i 0.973166 + 0.230104i \(0.0739066\pi\)
−0.999741 + 0.0227430i \(0.992760\pi\)
\(504\) −10.0751 + 7.31999i −0.448781 + 0.326058i
\(505\) −0.983958 9.36173i −0.0437855 0.416592i
\(506\) −24.1607 26.8332i −1.07407 1.19288i
\(507\) −7.10460 + 3.16317i −0.315526 + 0.140481i
\(508\) −63.8324 + 13.5680i −2.83211 + 0.601983i
\(509\) −11.8744 2.52398i −0.526323 0.111873i −0.0629159 0.998019i \(-0.520040\pi\)
−0.463407 + 0.886145i \(0.653373\pi\)
\(510\) −4.27537 1.90352i −0.189316 0.0842891i
\(511\) 12.9112 + 39.7367i 0.571160 + 1.75785i
\(512\) 0.631244 + 1.94277i 0.0278973 + 0.0858591i
\(513\) 3.99339 + 1.77797i 0.176312 + 0.0784993i
\(514\) −7.47162 1.58814i −0.329559 0.0700500i
\(515\) −14.1995 + 3.01820i −0.625705 + 0.132998i
\(516\) 5.75704 2.56320i 0.253439 0.112839i
\(517\) −5.38180 5.97709i −0.236691 0.262872i
\(518\) 9.50640 + 90.4473i 0.417687 + 3.97403i
\(519\) 17.7905 12.9256i 0.780917 0.567369i
\(520\) −0.518875 + 4.93677i −0.0227542 + 0.216492i
\(521\) 8.96419 + 15.5264i 0.392728 + 0.680225i 0.992808 0.119715i \(-0.0381980\pi\)
−0.600080 + 0.799940i \(0.704865\pi\)
\(522\) 9.32534 16.1520i 0.408159 0.706952i
\(523\) 34.5751 + 25.1203i 1.51186 + 1.09843i 0.965341 + 0.260990i \(0.0840490\pi\)
0.546523 + 0.837444i \(0.315951\pi\)
\(524\) 5.02229 5.57781i 0.219400 0.243668i
\(525\) −6.16476 + 18.9732i −0.269052 + 0.828058i
\(526\) 42.7428 1.86368
\(527\) −10.6278 + 9.62675i −0.462955 + 0.419348i
\(528\) −0.408981 −0.0177986
\(529\) 8.01756 24.6755i 0.348590 1.07285i
\(530\) −1.23950 + 1.37661i −0.0538405 + 0.0597959i
\(531\) −3.72183 2.70407i −0.161514 0.117347i
\(532\) −31.9227 + 55.2918i −1.38403 + 2.39720i
\(533\) 12.0952 + 20.9495i 0.523902 + 0.907425i
\(534\) −0.325636 + 3.09822i −0.0140917 + 0.134073i
\(535\) −4.03356 + 2.93055i −0.174386 + 0.126699i
\(536\) 1.13128 + 10.7634i 0.0488640 + 0.464910i
\(537\) 5.77722 + 6.41626i 0.249306 + 0.276882i
\(538\) 31.7487 14.1354i 1.36878 0.609422i
\(539\) −30.7720 + 6.54078i −1.32544 + 0.281731i
\(540\) −2.49171 0.529630i −0.107226 0.0227916i
\(541\) 12.7300 + 5.66776i 0.547305 + 0.243676i 0.661712 0.749758i \(-0.269830\pi\)
−0.114407 + 0.993434i \(0.536497\pi\)
\(542\) −9.62159 29.6122i −0.413283 1.27195i
\(543\) 4.83950 + 14.8944i 0.207683 + 0.639181i
\(544\) 13.7891 + 6.13929i 0.591202 + 0.263220i
\(545\) 7.56370 + 1.60771i 0.323993 + 0.0688669i
\(546\) −23.2905 + 4.95054i −0.996740 + 0.211864i
\(547\) 32.0565 14.2725i 1.37064 0.610248i 0.416369 0.909196i \(-0.363302\pi\)
0.954269 + 0.298948i \(0.0966357\pi\)
\(548\) −38.7457 43.0315i −1.65514 1.83821i
\(549\) −0.0263306 0.250519i −0.00112376 0.0106919i
\(550\) 18.2234 13.2400i 0.777047 0.564557i
\(551\) 3.73882 35.5725i 0.159279 1.51544i
\(552\) 9.53041 + 16.5072i 0.405641 + 0.702591i
\(553\) −20.0732 + 34.7678i −0.853599 + 1.47848i
\(554\) −17.5501 12.7509i −0.745633 0.541734i
\(555\) −4.65652 + 5.17158i −0.197658 + 0.219522i
\(556\) −3.56144 + 10.9610i −0.151039 + 0.464849i
\(557\) −43.7230 −1.85260 −0.926301 0.376784i \(-0.877030\pi\)
−0.926301 + 0.376784i \(0.877030\pi\)
\(558\) −7.42884 + 10.2892i −0.314488 + 0.435575i
\(559\) 4.50732 0.190639
\(560\) −0.203392 + 0.625977i −0.00859489 + 0.0264524i
\(561\) −3.90216 + 4.33379i −0.164749 + 0.182973i
\(562\) −25.4259 18.4730i −1.07252 0.779235i
\(563\) 8.80229 15.2460i 0.370972 0.642543i −0.618743 0.785593i \(-0.712358\pi\)
0.989715 + 0.143051i \(0.0456912\pi\)
\(564\) 5.67495 + 9.82930i 0.238958 + 0.413888i
\(565\) 0.347618 3.30736i 0.0146244 0.139142i
\(566\) −22.4914 + 16.3410i −0.945384 + 0.686862i
\(567\) −0.477794 4.54591i −0.0200655 0.190910i
\(568\) 14.0233 + 15.5744i 0.588403 + 0.653488i
\(569\) −14.8350 + 6.60498i −0.621916 + 0.276895i −0.693407 0.720546i \(-0.743891\pi\)
0.0714905 + 0.997441i \(0.477224\pi\)
\(570\) −7.76966 + 1.65149i −0.325435 + 0.0691734i
\(571\) 3.82722 + 0.813500i 0.160164 + 0.0340439i 0.287296 0.957842i \(-0.407244\pi\)
−0.127132 + 0.991886i \(0.540577\pi\)
\(572\) 15.1057 + 6.72551i 0.631603 + 0.281208i
\(573\) −2.71147 8.34503i −0.113273 0.348619i
\(574\) −34.0781 104.882i −1.42239 4.37768i
\(575\) 27.8942 + 12.4193i 1.16327 + 0.517920i
\(576\) 12.7131 + 2.70226i 0.529713 + 0.112594i
\(577\) −0.546751 + 0.116216i −0.0227615 + 0.00483811i −0.219278 0.975662i \(-0.570370\pi\)
0.196517 + 0.980500i \(0.437037\pi\)
\(578\) −21.5867 + 9.61102i −0.897888 + 0.399766i
\(579\) 1.50060 + 1.66658i 0.0623627 + 0.0692608i
\(580\) 2.17880 + 20.7299i 0.0904697 + 0.860761i
\(581\) 10.2241 7.42823i 0.424166 0.308175i
\(582\) −0.0156891 + 0.149271i −0.000650332 + 0.00618750i
\(583\) 1.15414 + 1.99902i 0.0477994 + 0.0827910i
\(584\) −12.4519 + 21.5673i −0.515263 + 0.892462i
\(585\) −1.47401 1.07093i −0.0609428 0.0442775i
\(586\) −26.0411 + 28.9216i −1.07575 + 1.19474i
\(587\) 5.25895 16.1854i 0.217060 0.668042i −0.781941 0.623353i \(-0.785770\pi\)
0.999001 0.0446895i \(-0.0142298\pi\)
\(588\) 44.3942 1.83079
\(589\) −4.98937 + 23.8215i −0.205584 + 0.981548i
\(590\) 8.35960 0.344159
\(591\) −2.32673 + 7.16095i −0.0957090 + 0.294562i
\(592\) 1.05498 1.17168i 0.0433596 0.0481557i
\(593\) −4.55171 3.30701i −0.186916 0.135803i 0.490392 0.871502i \(-0.336854\pi\)
−0.677308 + 0.735699i \(0.736854\pi\)
\(594\) −2.58055 + 4.46965i −0.105881 + 0.183392i
\(595\) 4.69260 + 8.12783i 0.192378 + 0.333208i
\(596\) −4.08819 + 38.8966i −0.167459 + 1.59327i
\(597\) −4.53678 + 3.29616i −0.185678 + 0.134903i
\(598\) 3.80941 + 36.2441i 0.155778 + 1.48213i
\(599\) 23.7618 + 26.3901i 0.970881 + 1.07827i 0.996905 + 0.0786108i \(0.0250484\pi\)
−0.0260249 + 0.999661i \(0.508285\pi\)
\(600\) −10.8628 + 4.83645i −0.443474 + 0.197447i
\(601\) −33.3120 + 7.08069i −1.35883 + 0.288828i −0.828986 0.559270i \(-0.811082\pi\)
−0.529841 + 0.848097i \(0.677748\pi\)
\(602\) −20.0989 4.27215i −0.819170 0.174120i
\(603\) −3.62895 1.61571i −0.147782 0.0657969i
\(604\) 0.542175 + 1.66864i 0.0220608 + 0.0678961i
\(605\) −1.44682 4.45284i −0.0588214 0.181034i
\(606\) 24.5865 + 10.9466i 0.998759 + 0.444676i
\(607\) 15.8914 + 3.37783i 0.645013 + 0.137102i 0.518792 0.854900i \(-0.326382\pi\)
0.126221 + 0.992002i \(0.459715\pi\)
\(608\) 25.0590 5.32645i 1.01628 0.216016i
\(609\) −34.1685 + 15.2128i −1.38458 + 0.616453i
\(610\) 0.306283 + 0.340162i 0.0124010 + 0.0137727i
\(611\) 0.848547 + 8.07338i 0.0343285 + 0.326614i
\(612\) 6.65775 4.83714i 0.269124 0.195530i
\(613\) 2.71534 25.8347i 0.109672 1.04346i −0.791848 0.610718i \(-0.790881\pi\)
0.901520 0.432738i \(-0.142452\pi\)
\(614\) 34.2993 + 59.4082i 1.38421 + 2.39752i
\(615\) 4.21922 7.30791i 0.170135 0.294683i
\(616\) −22.8132 16.5748i −0.919171 0.667817i
\(617\) 22.1162 24.5625i 0.890363 0.988849i −0.109623 0.993973i \(-0.534964\pi\)
0.999987 + 0.00512437i \(0.00163114\pi\)
\(618\) 12.8256 39.4730i 0.515920 1.58784i
\(619\) −31.5958 −1.26994 −0.634970 0.772536i \(-0.718988\pi\)
−0.634970 + 0.772536i \(0.718988\pi\)
\(620\) −0.0422055 14.1831i −0.00169501 0.569609i
\(621\) −6.99610 −0.280744
\(622\) 3.50456 10.7859i 0.140520 0.432477i
\(623\) 4.18032 4.64271i 0.167481 0.186006i
\(624\) 0.333953 + 0.242631i 0.0133688 + 0.00971301i
\(625\) −7.93522 + 13.7442i −0.317409 + 0.549768i
\(626\) −16.6776 28.8864i −0.666571 1.15453i
\(627\) −1.03462 + 9.84380i −0.0413189 + 0.393123i
\(628\) 21.8767 15.8943i 0.872974 0.634253i
\(629\) −2.34996 22.3584i −0.0936992 0.891488i
\(630\) 5.55781 + 6.17257i 0.221428 + 0.245921i
\(631\) 14.5383 6.47286i 0.578759 0.257680i −0.0964116 0.995342i \(-0.530737\pi\)
0.675171 + 0.737661i \(0.264070\pi\)
\(632\) −23.4062 + 4.97514i −0.931048 + 0.197900i
\(633\) 2.65132 + 0.563555i 0.105380 + 0.0223993i
\(634\) 66.4827 + 29.6000i 2.64036 + 1.17557i
\(635\) 5.03138 + 15.4850i 0.199664 + 0.614503i
\(636\) −1.00657 3.09791i −0.0399132 0.122840i
\(637\) 29.0072 + 12.9148i 1.14931 + 0.511704i
\(638\) 41.3082 + 8.78033i 1.63541 + 0.347617i
\(639\) −7.52414 + 1.59931i −0.297650 + 0.0632676i
\(640\) −13.0390 + 5.80533i −0.515411 + 0.229476i
\(641\) −4.53972 5.04187i −0.179308 0.199142i 0.646790 0.762668i \(-0.276111\pi\)
−0.826098 + 0.563526i \(0.809444\pi\)
\(642\) −1.49001 14.1765i −0.0588061 0.559503i
\(643\) −10.9460 + 7.95276i −0.431670 + 0.313626i −0.782316 0.622882i \(-0.785962\pi\)
0.350647 + 0.936508i \(0.385962\pi\)
\(644\) 10.6809 101.622i 0.420888 4.00448i
\(645\) −0.786152 1.36166i −0.0309547 0.0536151i
\(646\) 12.8305 22.2231i 0.504810 0.874356i
\(647\) −18.0763 13.1332i −0.710653 0.516320i 0.172731 0.984969i \(-0.444741\pi\)
−0.883384 + 0.468649i \(0.844741\pi\)
\(648\) 1.82304 2.02469i 0.0716158 0.0795375i
\(649\) 3.21898 9.90701i 0.126356 0.388884i
\(650\) −22.7350 −0.891741
\(651\) 24.1808 7.93646i 0.947722 0.311054i
\(652\) 24.6385 0.964918
\(653\) −1.53687 + 4.72998i −0.0601422 + 0.185099i −0.976614 0.215001i \(-0.931024\pi\)
0.916472 + 0.400100i \(0.131024\pi\)
\(654\) −14.7933 + 16.4297i −0.578465 + 0.642450i
\(655\) −1.51501 1.10072i −0.0591964 0.0430087i
\(656\) −0.955910 + 1.65569i −0.0373220 + 0.0646436i
\(657\) −4.57035 7.91608i −0.178306 0.308836i
\(658\) 3.86835 36.8049i 0.150804 1.43480i
\(659\) −15.7824 + 11.4666i −0.614797 + 0.446676i −0.851100 0.525003i \(-0.824064\pi\)
0.236304 + 0.971679i \(0.424064\pi\)
\(660\) −0.602928 5.73647i −0.0234689 0.223292i
\(661\) −30.2738 33.6224i −1.17751 1.30776i −0.941892 0.335916i \(-0.890954\pi\)
−0.235621 0.971845i \(-0.575713\pi\)
\(662\) 15.6639 6.97402i 0.608795 0.271053i
\(663\) 5.75736 1.22376i 0.223597 0.0475271i
\(664\) 7.36801 + 1.56612i 0.285934 + 0.0607772i
\(665\) 14.5522 + 6.47905i 0.564309 + 0.251247i
\(666\) −6.14834 18.9226i −0.238243 0.733237i
\(667\) 17.6900 + 54.4442i 0.684959 + 2.10809i
\(668\) 51.4923 + 22.9259i 1.99230 + 0.887028i
\(669\) 6.14487 + 1.30613i 0.237574 + 0.0504980i
\(670\) 7.06060 1.50078i 0.272775 0.0579801i
\(671\) 0.521067 0.231994i 0.0201156 0.00895602i
\(672\) −17.9252 19.9080i −0.691481 0.767967i
\(673\) 2.48181 + 23.6129i 0.0956669 + 0.910210i 0.932115 + 0.362163i \(0.117962\pi\)
−0.836448 + 0.548047i \(0.815372\pi\)
\(674\) −14.5544 + 10.5744i −0.560615 + 0.407311i
\(675\) 0.456208 4.34052i 0.0175594 0.167067i
\(676\) 12.4249 + 21.5205i 0.477880 + 0.827713i
\(677\) 10.3651 17.9529i 0.398365 0.689988i −0.595160 0.803607i \(-0.702911\pi\)
0.993524 + 0.113620i \(0.0362446\pi\)
\(678\) 7.69219 + 5.58870i 0.295417 + 0.214633i
\(679\) 0.201407 0.223685i 0.00772927 0.00858423i
\(680\) −1.72864 + 5.32022i −0.0662905 + 0.204021i
\(681\) 9.64174 0.369472
\(682\) −27.3557 8.79850i −1.04750 0.336912i
\(683\) −36.1171 −1.38198 −0.690991 0.722863i \(-0.742826\pi\)
−0.690991 + 0.722863i \(0.742826\pi\)
\(684\) 4.31625 13.2840i 0.165036 0.507928i
\(685\) −9.66700 + 10.7363i −0.369357 + 0.410213i
\(686\) −58.1049 42.2157i −2.21846 1.61180i
\(687\) 1.77999 3.08304i 0.0679110 0.117625i
\(688\) 0.178111 + 0.308498i 0.00679043 + 0.0117614i
\(689\) 0.243527 2.31700i 0.00927762 0.0882707i
\(690\) 10.2849 7.47241i 0.391539 0.284470i
\(691\) −2.85500 27.1635i −0.108609 1.03335i −0.904082 0.427359i \(-0.859444\pi\)
0.795472 0.605990i \(-0.207223\pi\)
\(692\) −47.0169 52.2176i −1.78732 1.98502i
\(693\) 9.45526 4.20975i 0.359176 0.159915i
\(694\) −74.4765 + 15.8305i −2.82709 + 0.600916i
\(695\) 2.81264 + 0.597846i 0.106690 + 0.0226776i
\(696\) −20.3660 9.06751i −0.771970 0.343703i
\(697\) 8.42405 + 25.9266i 0.319084 + 0.982039i
\(698\) −5.25564 16.1752i −0.198929 0.612240i
\(699\) 2.04561 + 0.910766i 0.0773723 + 0.0344483i
\(700\) 62.3521 + 13.2534i 2.35669 + 0.500930i
\(701\) −9.24866 + 1.96586i −0.349317 + 0.0742496i −0.379229 0.925303i \(-0.623811\pi\)
0.0299119 + 0.999553i \(0.490477\pi\)
\(702\) 4.75880 2.11876i 0.179609 0.0799673i
\(703\) −25.5324 28.3566i −0.962973 1.06949i
\(704\) 3.07623 + 29.2684i 0.115940 + 1.10309i
\(705\) 2.29096 1.66448i 0.0862825 0.0626879i
\(706\) −0.849851 + 8.08579i −0.0319846 + 0.304313i
\(707\) −26.9859 46.7410i −1.01491 1.75788i
\(708\) −7.34991 + 12.7304i −0.276226 + 0.478438i
\(709\) 17.1142 + 12.4342i 0.642739 + 0.466977i 0.860790 0.508960i \(-0.169970\pi\)
−0.218051 + 0.975937i \(0.569970\pi\)
\(710\) 9.35297 10.3875i 0.351011 0.389837i
\(711\) 2.71408 8.35308i 0.101786 0.313265i
\(712\) 3.72373 0.139553
\(713\) −8.21205 38.0771i −0.307544 1.42600i
\(714\) −26.8330 −1.00420
\(715\) 1.27486 3.92361i 0.0476770 0.146735i
\(716\) 18.4600 20.5019i 0.689883 0.766193i
\(717\) 12.0963 + 8.78851i 0.451746 + 0.328213i
\(718\) −26.9162 + 46.6201i −1.00450 + 1.73985i
\(719\) 2.51335 + 4.35324i 0.0937320 + 0.162349i 0.909079 0.416624i \(-0.136787\pi\)
−0.815347 + 0.578973i \(0.803454\pi\)
\(720\) 0.0150515 0.143206i 0.000560937 0.00533696i
\(721\) −67.3368 + 48.9230i −2.50775 + 1.82199i
\(722\) −0.0258055 0.245523i −0.000960383 0.00913743i
\(723\) −0.622473 0.691326i −0.0231500 0.0257107i
\(724\) 45.7152 20.3537i 1.69899 0.756440i
\(725\) −34.9318 + 7.42499i −1.29734 + 0.275757i
\(726\) 13.0936 + 2.78314i 0.485951 + 0.103292i
\(727\) −45.8048 20.3936i −1.69880 0.756356i −0.999122 0.0419028i \(-0.986658\pi\)
−0.699683 0.714454i \(-0.746675\pi\)
\(728\) 8.79501 + 27.0683i 0.325965 + 1.00322i
\(729\) 0.309017 + 0.951057i 0.0114451 + 0.0352243i
\(730\) 15.1739 + 6.75584i 0.561610 + 0.250045i
\(731\) 4.96841 + 1.05607i 0.183763 + 0.0390601i
\(732\) −0.787305 + 0.167347i −0.0290996 + 0.00618532i
\(733\) 12.6915 5.65061i 0.468770 0.208710i −0.158737 0.987321i \(-0.550742\pi\)
0.627507 + 0.778611i \(0.284075\pi\)
\(734\) 33.1026 + 36.7642i 1.22184 + 1.35699i
\(735\) −1.15779 11.0156i −0.0427056 0.406317i
\(736\) −33.1712 + 24.1003i −1.22271 + 0.888349i
\(737\) 0.940205 8.94546i 0.0346329 0.329510i
\(738\) 12.0631 + 20.8938i 0.444047 + 0.769112i
\(739\) 18.8073 32.5753i 0.691839 1.19830i −0.279395 0.960176i \(-0.590134\pi\)
0.971235 0.238125i \(-0.0765327\pi\)
\(740\) 17.9896 + 13.0702i 0.661310 + 0.480469i
\(741\) 6.68473 7.42415i 0.245570 0.272733i
\(742\) −3.28204 + 10.1011i −0.120487 + 0.370822i
\(743\) 37.5735 1.37844 0.689219 0.724553i \(-0.257954\pi\)
0.689219 + 0.724553i \(0.257954\pi\)
\(744\) 13.1595 + 7.54554i 0.482452 + 0.276633i
\(745\) 9.75809 0.357509
\(746\) −11.0819 + 34.1064i −0.405735 + 1.24873i
\(747\) −1.85000 + 2.05463i −0.0676879 + 0.0751750i
\(748\) 15.0753 + 10.9528i 0.551206 + 0.400475i
\(749\) −14.2931 + 24.7564i −0.522258 + 0.904578i
\(750\) 8.50820 + 14.7366i 0.310676 + 0.538106i
\(751\) −1.36433 + 12.9807i −0.0497849 + 0.473672i 0.941018 + 0.338357i \(0.109871\pi\)
−0.990803 + 0.135315i \(0.956795\pi\)
\(752\) −0.519042 + 0.377106i −0.0189275 + 0.0137516i
\(753\) −1.52267 14.4872i −0.0554892 0.527945i
\(754\) −28.5212 31.6760i −1.03868 1.15357i
\(755\) 0.399903 0.178048i 0.0145540 0.00647985i
\(756\) −14.2864 + 3.03667i −0.519592 + 0.110443i
\(757\) 6.14241 + 1.30561i 0.223250 + 0.0474532i 0.318178 0.948031i \(-0.396929\pi\)
−0.0949286 + 0.995484i \(0.530262\pi\)
\(758\) −13.4331 5.98080i −0.487912 0.217232i
\(759\) −4.89526 15.0661i −0.177687 0.546863i
\(760\) 2.93400 + 9.02992i 0.106427 + 0.327550i
\(761\) 17.5388 + 7.80876i 0.635779 + 0.283067i 0.699207 0.714919i \(-0.253537\pi\)
−0.0634276 + 0.997986i \(0.520203\pi\)
\(762\) −45.5338 9.67852i −1.64952 0.350616i
\(763\) 43.3670 9.21795i 1.56999 0.333712i
\(764\) −25.6133 + 11.4038i −0.926655 + 0.412573i
\(765\) −1.37388 1.52585i −0.0496727 0.0551671i
\(766\) −6.16254 58.6326i −0.222661 2.11848i
\(767\) −8.50587 + 6.17988i −0.307129 + 0.223142i
\(768\) 1.54839 14.7320i 0.0558727 0.531594i
\(769\) −8.75467 15.1635i −0.315701 0.546811i 0.663885 0.747835i \(-0.268906\pi\)
−0.979586 + 0.201024i \(0.935573\pi\)
\(770\) −9.40372 + 16.2877i −0.338887 + 0.586969i
\(771\) −2.71121 1.96981i −0.0976417 0.0709409i
\(772\) 4.79487 5.32525i 0.172571 0.191660i
\(773\) −8.17429 + 25.1579i −0.294009 + 0.904866i 0.689544 + 0.724244i \(0.257811\pi\)
−0.983553 + 0.180622i \(0.942189\pi\)
\(774\) 4.49533 0.161581
\(775\) 24.1594 2.61196i 0.867830 0.0938244i
\(776\) 0.179408 0.00644038
\(777\) −12.3299 + 37.9474i −0.442331 + 1.36136i
\(778\) −35.7151 + 39.6656i −1.28045 + 1.42208i
\(779\) 37.4326 + 27.1964i 1.34116 + 0.974412i
\(780\) −2.91089 + 5.04180i −0.104226 + 0.180526i
\(781\) −8.70883 15.0841i −0.311626 0.539753i
\(782\) −4.29292 + 40.8444i −0.153515 + 1.46059i
\(783\) 6.61983 4.80959i 0.236573 0.171881i
\(784\) 0.262309 + 2.49570i 0.00936818 + 0.0891323i
\(785\) −4.51442 5.01377i −0.161127 0.178949i
\(786\) 4.89118 2.17769i 0.174463 0.0776758i
\(787\) 5.20019 1.10533i 0.185367 0.0394009i −0.114293 0.993447i \(-0.536460\pi\)
0.299660 + 0.954046i \(0.403127\pi\)
\(788\) 23.5332 + 5.00214i 0.838337 + 0.178194i
\(789\) 17.1312 + 7.62730i 0.609887 + 0.271539i
\(790\) 4.93184 + 15.1786i 0.175467 + 0.540032i
\(791\) −5.89217 18.1342i −0.209501 0.644779i
\(792\) 5.63577 + 2.50921i 0.200258 + 0.0891607i
\(793\) −0.563109 0.119692i −0.0199966 0.00425040i
\(794\) 39.7996 8.45967i 1.41244 0.300222i
\(795\) −0.742438 + 0.330555i −0.0263316 + 0.0117236i
\(796\) 11.9898 + 13.3161i 0.424969 + 0.471976i
\(797\) 0.864143 + 8.22177i 0.0306095 + 0.291230i 0.999109 + 0.0422131i \(0.0134408\pi\)
−0.968499 + 0.249017i \(0.919892\pi\)
\(798\) −36.8452 + 26.7696i −1.30431 + 0.947633i
\(799\) −0.956248 + 9.09810i −0.0338296 + 0.321868i
\(800\) −12.7893 22.1517i −0.452169 0.783180i
\(801\) −0.683380 + 1.18365i −0.0241460 + 0.0418222i
\(802\) −16.8890 12.2706i −0.596372 0.433289i
\(803\) 13.8493 15.3812i 0.488731 0.542791i
\(804\) −3.92235 + 12.0717i −0.138331 + 0.425738i
\(805\) −25.4943 −0.898555
\(806\) 17.1175 + 23.4134i 0.602938 + 0.824701i
\(807\) 15.2472 0.536727
\(808\) 9.94099 30.5952i 0.349723 1.07634i
\(809\) −6.33303 + 7.03354i −0.222657 + 0.247286i −0.844116 0.536161i \(-0.819874\pi\)
0.621458 + 0.783447i \(0.286541\pi\)
\(810\) −1.47009 1.06808i −0.0516537 0.0375286i
\(811\) −10.2253 + 17.7108i −0.359060 + 0.621910i −0.987804 0.155702i \(-0.950236\pi\)
0.628744 + 0.777612i \(0.283569\pi\)
\(812\) 59.7555 + 103.500i 2.09701 + 3.63212i
\(813\) 1.42789 13.5854i 0.0500781 0.476462i
\(814\) 36.4477 26.4808i 1.27749 0.928152i
\(815\) −0.642564 6.11359i −0.0225080 0.214150i
\(816\) 0.311267 + 0.345697i 0.0108965 + 0.0121018i
\(817\) 7.87585 3.50655i 0.275541 0.122679i
\(818\) 81.2352 17.2671i 2.84032 0.603729i
\(819\) −10.2182 2.17194i −0.357051 0.0758936i
\(820\) −24.6323 10.9670i −0.860198 0.382985i
\(821\) −14.2309 43.7981i −0.496660 1.52856i −0.814353 0.580369i \(-0.802908\pi\)
0.317693 0.948194i \(-0.397092\pi\)
\(822\) −12.7640 39.2837i −0.445197 1.37018i
\(823\) −2.31682 1.03151i −0.0807592 0.0359563i 0.365960 0.930631i \(-0.380741\pi\)
−0.446719 + 0.894674i \(0.647408\pi\)
\(824\) −48.5265 10.3146i −1.69050 0.359327i
\(825\) 9.66651 2.05468i 0.336545 0.0715347i
\(826\) 43.7866 19.4950i 1.52353 0.678319i
\(827\) −29.1206 32.3417i −1.01262 1.12463i −0.992177 0.124841i \(-0.960158\pi\)
−0.0204461 0.999791i \(-0.506509\pi\)
\(828\) 2.33670 + 22.2322i 0.0812060 + 0.772623i
\(829\) 20.5250 14.9123i 0.712863 0.517926i −0.171233 0.985231i \(-0.554775\pi\)
0.884096 + 0.467305i \(0.154775\pi\)
\(830\) 0.525147 4.99644i 0.0182281 0.173429i
\(831\) −4.75868 8.24228i −0.165077 0.285922i
\(832\) 14.8518 25.7241i 0.514894 0.891823i
\(833\) 28.9486 + 21.0324i 1.00301 + 0.728730i
\(834\) −5.50106 + 6.10955i −0.190486 + 0.211556i
\(835\) 4.34573 13.3748i 0.150390 0.462853i
\(836\) 31.6272 1.09385
\(837\) −4.81352 + 2.79822i −0.166380 + 0.0967206i
\(838\) −43.1224 −1.48964
\(839\) −8.53245 + 26.2602i −0.294573 + 0.906602i 0.688792 + 0.724959i \(0.258141\pi\)
−0.983365 + 0.181643i \(0.941859\pi\)
\(840\) 6.64329 7.37812i 0.229215 0.254569i
\(841\) −30.7056 22.3089i −1.05881 0.769274i
\(842\) −7.00288 + 12.1294i −0.241335 + 0.418005i
\(843\) −6.89417 11.9411i −0.237448 0.411272i
\(844\) 0.905326 8.61360i 0.0311626 0.296492i
\(845\) 5.01589 3.64425i 0.172552 0.125366i
\(846\) 0.846290 + 8.05191i 0.0290961 + 0.276831i
\(847\) −17.9625 19.9494i −0.617200 0.685470i
\(848\) 0.168207 0.0748908i 0.00577627 0.00257176i
\(849\) −11.9305 + 2.53590i −0.409453 + 0.0870318i
\(850\) −25.0608 5.32684i −0.859578 0.182709i
\(851\) 55.7899 + 24.8393i 1.91245 + 0.851479i
\(852\) 7.59535 + 23.3761i 0.260212 + 0.800851i
\(853\) 11.0375 + 33.9700i 0.377917 + 1.16311i 0.941489 + 0.337043i \(0.109427\pi\)
−0.563572 + 0.826067i \(0.690573\pi\)
\(854\) 2.39755 + 1.06746i 0.0820425 + 0.0365277i
\(855\) −3.40876 0.724554i −0.116577 0.0247792i
\(856\) −16.6663 + 3.54254i −0.569644 + 0.121081i
\(857\) 23.1301 10.2982i 0.790108 0.351779i 0.0283146 0.999599i \(-0.490986\pi\)
0.761793 + 0.647820i \(0.224319\pi\)
\(858\) 7.89252 + 8.76553i 0.269446 + 0.299250i
\(859\) −2.97861 28.3396i −0.101629 0.966934i −0.919914 0.392121i \(-0.871742\pi\)
0.818285 0.574813i \(-0.194925\pi\)
\(860\) −4.06450 + 2.95303i −0.138598 + 0.100698i
\(861\) 5.05734 48.1174i 0.172354 1.63984i
\(862\) 40.8580 + 70.7682i 1.39163 + 2.41037i
\(863\) 2.40701 4.16906i 0.0819355 0.141916i −0.822146 0.569277i \(-0.807223\pi\)
0.904081 + 0.427361i \(0.140557\pi\)
\(864\) 4.74139 + 3.44482i 0.161305 + 0.117195i
\(865\) −11.7307 + 13.0282i −0.398854 + 0.442972i
\(866\) 13.4778 41.4805i 0.457996 1.40957i
\(867\) −10.3669 −0.352080
\(868\) −33.2969 74.1912i −1.13017 2.51821i
\(869\) 19.8874 0.674633
\(870\) −4.59471 + 14.1410i −0.155775 + 0.479426i
\(871\) −6.07469 + 6.74662i −0.205833 + 0.228601i
\(872\) 21.3793 + 15.5329i 0.723993 + 0.526012i
\(873\) −0.0329250 + 0.0570279i −0.00111434 + 0.00193010i
\(874\) 34.8532 + 60.3675i 1.17893 + 2.04196i
\(875\) 3.56700 33.9377i 0.120587 1.14730i
\(876\) −23.6293 + 17.1677i −0.798359 + 0.580042i
\(877\) −1.28910 12.2650i −0.0435299 0.414159i −0.994489 0.104842i \(-0.966566\pi\)
0.950959 0.309317i \(-0.100100\pi\)
\(878\) −35.5183 39.4471i −1.19869 1.33127i
\(879\) −15.5981 + 6.94474i −0.526112 + 0.234240i
\(880\) 0.318924 0.0677894i 0.0107509 0.00228518i
\(881\) 31.2620 + 6.64494i 1.05324 + 0.223874i 0.701828 0.712346i \(-0.252367\pi\)
0.351415 + 0.936220i \(0.385701\pi\)
\(882\) 28.9301 + 12.8805i 0.974126 + 0.433709i
\(883\) −4.01391 12.3535i −0.135079 0.415729i 0.860524 0.509411i \(-0.170137\pi\)
−0.995602 + 0.0936812i \(0.970137\pi\)
\(884\) −5.81185 17.8870i −0.195474 0.601606i
\(885\) 3.35050 + 1.49174i 0.112626 + 0.0501443i
\(886\) 22.2301 + 4.72515i 0.746835 + 0.158745i
\(887\) −35.6625 + 7.58030i −1.19743 + 0.254522i −0.763129 0.646246i \(-0.776338\pi\)
−0.434301 + 0.900768i \(0.643005\pi\)
\(888\) −21.7263 + 9.67317i −0.729086 + 0.324610i
\(889\) 62.4656 + 69.3751i 2.09503 + 2.32677i
\(890\) −0.259605 2.46998i −0.00870198 0.0827938i
\(891\) −1.83187 + 1.33093i −0.0613700 + 0.0445879i
\(892\) 2.09824 19.9634i 0.0702544 0.668426i
\(893\) 7.76355 + 13.4469i 0.259797 + 0.449982i
\(894\) −13.9495 + 24.1613i −0.466542 + 0.808075i
\(895\) −5.56861 4.04583i −0.186138 0.135237i
\(896\) −54.7583 + 60.8153i −1.82935 + 2.03170i
\(897\) −4.94083 + 15.2063i −0.164970 + 0.507724i
\(898\) −82.0764 −2.73893
\(899\) 33.9472 + 30.3837i 1.13220 + 1.01335i
\(900\) −13.9457 −0.464857
\(901\) 0.811314 2.49697i 0.0270288 0.0831861i
\(902\) −36.5541 + 40.5974i −1.21712 + 1.35175i
\(903\) −7.29323 5.29884i −0.242704 0.176334i
\(904\) 5.68254 9.84244i 0.188998 0.327355i
\(905\) −6.24264 10.8126i −0.207512 0.359422i
\(906\) −0.130823 + 1.24470i −0.00434631 + 0.0413524i
\(907\) −3.01894 + 2.19339i −0.100242 + 0.0728304i −0.636777 0.771048i \(-0.719733\pi\)
0.536535 + 0.843878i \(0.319733\pi\)
\(908\) −3.22035 30.6396i −0.106871 1.01681i
\(909\) 7.90082 + 8.77475i 0.262054 + 0.291040i
\(910\) 17.3414 7.72090i 0.574862 0.255945i
\(911\) 20.6527 4.38986i 0.684253 0.145443i 0.147348 0.989085i \(-0.452926\pi\)
0.536906 + 0.843642i \(0.319593\pi\)
\(912\) 0.772291 + 0.164156i 0.0255731 + 0.00543573i
\(913\) −5.71910 2.54631i −0.189275 0.0842705i
\(914\) 3.50365 + 10.7831i 0.115891 + 0.356674i
\(915\) 0.0620567 + 0.190991i 0.00205153 + 0.00631397i
\(916\) −10.3918 4.62674i −0.343355 0.152872i
\(917\) −10.5024 2.23235i −0.346820 0.0737188i
\(918\) 5.74205 1.22051i 0.189516 0.0402829i
\(919\) 14.2973 6.36558i 0.471626 0.209981i −0.157140 0.987576i \(-0.550227\pi\)
0.628765 + 0.777595i \(0.283561\pi\)
\(920\) −10.1679 11.2926i −0.335227 0.372307i
\(921\) 3.14590 + 29.9312i 0.103661 + 0.986267i
\(922\) −4.42704 + 3.21644i −0.145797 + 0.105928i
\(923\) −1.83759 + 17.4835i −0.0604851 + 0.575477i
\(924\) −16.5358 28.6409i −0.543989 0.942217i
\(925\) −19.0488 + 32.9935i −0.626320 + 1.08482i
\(926\) 3.95114 + 2.87067i 0.129843 + 0.0943362i
\(927\) 12.1843 13.5320i 0.400184 0.444449i
\(928\) 14.8190 45.6082i 0.486458 1.49716i
\(929\) −55.1450 −1.80925 −0.904624 0.426211i \(-0.859848\pi\)
−0.904624 + 0.426211i \(0.859848\pi\)
\(930\) 4.08758 9.25487i 0.134037 0.303479i
\(931\) 60.7330 1.99044
\(932\) 2.21100 6.80476i 0.0724237 0.222897i
\(933\) 3.32933 3.69759i 0.108997 0.121054i
\(934\) −10.7039 7.77685i −0.350243 0.254466i
\(935\) 2.32458 4.02629i 0.0760220 0.131674i
\(936\) −3.11328 5.39235i −0.101761 0.176255i
\(937\) 1.53783 14.6315i 0.0502388 0.477990i −0.940259 0.340460i \(-0.889417\pi\)
0.990498 0.137530i \(-0.0439163\pi\)
\(938\) 33.4827 24.3266i 1.09325 0.794292i
\(939\) −1.52965 14.5537i −0.0499183 0.474941i
\(940\) −6.05457 6.72428i −0.197478 0.219322i
\(941\) 39.1925 17.4496i 1.27764 0.568842i 0.348063 0.937471i \(-0.386840\pi\)
0.929576 + 0.368630i \(0.120173\pi\)
\(942\) 18.8678 4.01047i 0.614746 0.130668i
\(943\) −72.4339 15.3963i −2.35877 0.501373i
\(944\) −0.759092 0.337970i −0.0247064 0.0110000i
\(945\) 1.12608 + 3.46572i 0.0366314 + 0.112740i
\(946\) 3.14544 + 9.68067i 0.102267 + 0.314746i
\(947\) −8.81007 3.92249i −0.286289 0.127464i 0.258568 0.965993i \(-0.416749\pi\)
−0.544857 + 0.838529i \(0.683416\pi\)
\(948\) −27.4510 5.83488i −0.891566 0.189508i
\(949\) −20.4337 + 4.34331i −0.663305 + 0.140990i
\(950\) −39.7260 + 17.6872i −1.28888 + 0.573847i
\(951\) 21.3640 + 23.7272i 0.692777 + 0.769406i
\(952\) 3.35261 + 31.8980i 0.108659 + 1.03382i
\(953\) −2.89137 + 2.10071i −0.0936608 + 0.0680485i −0.633630 0.773636i \(-0.718436\pi\)
0.539969 + 0.841685i \(0.318436\pi\)
\(954\) 0.242879 2.31084i 0.00786350 0.0748162i
\(955\) 3.49762 + 6.05805i 0.113180 + 0.196034i
\(956\) 23.8880 41.3752i 0.772592 1.33817i
\(957\) 14.9894 + 10.8904i 0.484538 + 0.352038i
\(958\) −15.7812 + 17.5268i −0.509868 + 0.566266i
\(959\) −25.5970 + 78.7794i −0.826570 + 2.54392i
\(960\) −10.3616 −0.334420
\(961\) −20.8798 22.9136i −0.673542 0.739149i
\(962\) −45.4713 −1.46605
\(963\) 1.93256 5.94780i 0.0622758 0.191665i
\(964\) −1.98899 + 2.20900i −0.0640612 + 0.0711471i
\(965\) −1.44641 1.05088i −0.0465616 0.0338290i
\(966\) 36.4450 63.1246i 1.17260 2.03100i
\(967\) −9.22296 15.9746i −0.296591 0.513710i 0.678763 0.734357i \(-0.262516\pi\)
−0.975354 + 0.220647i \(0.929183\pi\)
\(968\) 1.67252 15.9129i 0.0537567 0.511461i
\(969\) 9.10806 6.61739i 0.292593 0.212581i
\(970\) −0.0125077 0.119003i −0.000401598 0.00382095i
\(971\) 29.3554 + 32.6025i 0.942059 + 1.04626i 0.998853 + 0.0478770i \(0.0152456\pi\)
−0.0567938 + 0.998386i \(0.518088\pi\)
\(972\) 2.91906 1.29965i 0.0936289 0.0416863i
\(973\) 16.1265 3.42780i 0.516992 0.109890i
\(974\) −61.8905 13.1552i −1.98310 0.421521i
\(975\) −9.11213 4.05698i −0.291822 0.129927i
\(976\) −0.0140596 0.0432711i −0.000450037 0.00138507i
\(977\) −14.8680 45.7590i −0.475670 1.46396i −0.845052 0.534684i \(-0.820431\pi\)
0.369382 0.929278i \(-0.379569\pi\)
\(978\) 16.0560 + 7.14859i 0.513414 + 0.228587i
\(979\) −3.02715 0.643441i −0.0967481 0.0205644i
\(980\) −34.6187 + 7.35844i −1.10585 + 0.235057i
\(981\) −8.86093 + 3.94514i −0.282908 + 0.125959i
\(982\) 26.8203 + 29.7869i 0.855870 + 0.950540i
\(983\) 0.919652 + 8.74990i 0.0293323 + 0.279078i 0.999350 + 0.0360448i \(0.0114759\pi\)
−0.970018 + 0.243034i \(0.921857\pi\)
\(984\) 23.3306 16.9506i 0.743751 0.540367i
\(985\) 0.627450 5.96979i 0.0199922 0.190213i
\(986\) −24.0172 41.5990i −0.764862 1.32478i
\(987\) 8.11812 14.0610i 0.258403 0.447566i
\(988\) −25.8252 18.7631i −0.821609 0.596934i
\(989\) −9.23258 + 10.2538i −0.293579 + 0.326052i
\(990\) 1.27147 3.91318i 0.0404099 0.124369i
\(991\) 9.56580 0.303868 0.151934 0.988391i \(-0.451450\pi\)
0.151934 + 0.988391i \(0.451450\pi\)
\(992\) −13.1834 + 29.8491i −0.418574 + 0.947711i
\(993\) 7.52253 0.238720
\(994\) 24.7655 76.2203i 0.785513 2.41756i
\(995\) 2.99145 3.32234i 0.0948353 0.105325i
\(996\) 7.14712 + 5.19268i 0.226465 + 0.164536i
\(997\) −11.7010 + 20.2668i −0.370576 + 0.641856i −0.989654 0.143473i \(-0.954173\pi\)
0.619079 + 0.785329i \(0.287506\pi\)
\(998\) −42.0527 72.8374i −1.33115 2.30563i
\(999\) 0.912440 8.68128i 0.0288683 0.274664i
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 93.2.m.b.76.3 24
3.2 odd 2 279.2.y.d.262.1 24
31.12 odd 30 2883.2.a.s.1.10 12
31.19 even 15 2883.2.a.t.1.10 12
31.20 even 15 inner 93.2.m.b.82.3 yes 24
93.20 odd 30 279.2.y.d.82.1 24
93.50 odd 30 8649.2.a.bk.1.3 12
93.74 even 30 8649.2.a.bl.1.3 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
93.2.m.b.76.3 24 1.1 even 1 trivial
93.2.m.b.82.3 yes 24 31.20 even 15 inner
279.2.y.d.82.1 24 93.20 odd 30
279.2.y.d.262.1 24 3.2 odd 2
2883.2.a.s.1.10 12 31.12 odd 30
2883.2.a.t.1.10 12 31.19 even 15
8649.2.a.bk.1.3 12 93.50 odd 30
8649.2.a.bl.1.3 12 93.74 even 30