Properties

Label 378.2.v.b.79.3
Level $378$
Weight $2$
Character 378.79
Analytic conductor $3.018$
Analytic rank $0$
Dimension $72$
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] = [378,2,Mod(67,378)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(378, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([8, 12]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("378.67");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 378.v (of order \(9\), degree \(6\), 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: \(3.01834519640\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(12\) over \(\Q(\zeta_{9})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 79.3
Character \(\chi\) \(=\) 378.79
Dual form 378.2.v.b.67.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.766044 + 0.642788i) q^{2} +(-1.42742 - 0.981051i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.343656 + 1.94897i) q^{5} +(-0.462863 - 1.66906i) q^{6} +(1.84248 - 1.89876i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(1.07508 + 2.80075i) q^{9} +O(q^{10})\) \(q+(0.766044 + 0.642788i) q^{2} +(-1.42742 - 0.981051i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.343656 + 1.94897i) q^{5} +(-0.462863 - 1.66906i) q^{6} +(1.84248 - 1.89876i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(1.07508 + 2.80075i) q^{9} +(-0.989519 + 1.71390i) q^{10} +(0.568823 - 3.22596i) q^{11} +(0.718277 - 1.57610i) q^{12} +(1.17085 + 6.64020i) q^{13} +(2.63192 - 0.270209i) q^{14} +(1.42150 - 3.11915i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(0.298584 - 0.517162i) q^{17} +(-0.976729 + 2.83655i) q^{18} +(4.15869 + 7.20307i) q^{19} +(-1.85969 + 0.676871i) q^{20} +(-4.49277 + 0.902766i) q^{21} +(2.50935 - 2.10559i) q^{22} +(0.380241 - 0.319060i) q^{23} +(1.56333 - 0.745660i) q^{24} +(1.01807 - 0.370549i) q^{25} +(-3.37132 + 5.83929i) q^{26} +(1.21308 - 5.05257i) q^{27} +(2.18985 + 1.48477i) q^{28} +(0.221437 - 1.25583i) q^{29} +(3.09388 - 1.47569i) q^{30} +(-0.261547 - 1.48331i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(-3.97678 + 4.04677i) q^{33} +(0.561154 - 0.204243i) q^{34} +(4.33380 + 2.93842i) q^{35} +(-2.57152 + 1.54509i) q^{36} -0.542374 q^{37} +(-1.44430 + 8.19103i) q^{38} +(4.84307 - 10.6270i) q^{39} +(-1.85969 - 0.676871i) q^{40} +(0.421633 + 2.39120i) q^{41} +(-4.02195 - 2.19634i) q^{42} +(-2.94820 - 2.47384i) q^{43} +3.27572 q^{44} +(-5.08912 + 3.05779i) q^{45} +0.496369 q^{46} +(-0.157691 + 0.894312i) q^{47} +(1.67688 + 0.433678i) q^{48} +(-0.210549 - 6.99683i) q^{49} +(1.01807 + 0.370549i) q^{50} +(-0.933568 + 0.445284i) q^{51} +(-6.33600 + 2.30612i) q^{52} +(-5.09597 - 8.82648i) q^{53} +(4.17700 - 3.09074i) q^{54} +6.48278 q^{55} +(0.723132 + 2.54501i) q^{56} +(1.13035 - 14.3617i) q^{57} +(0.976863 - 0.819685i) q^{58} +(-12.6532 - 4.60539i) q^{59} +(3.31861 + 0.858265i) q^{60} +(1.27613 - 7.23729i) q^{61} +(0.753095 - 1.30440i) q^{62} +(7.29875 + 3.11901i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-12.5392 + 4.56389i) q^{65} +(-5.64760 + 0.543778i) q^{66} +(-2.08879 + 1.75271i) q^{67} +(0.561154 + 0.204243i) q^{68} +(-0.855779 + 0.0823984i) q^{69} +(1.43110 + 5.03667i) q^{70} +(-1.32437 - 2.29388i) q^{71} +(-2.96306 - 0.469329i) q^{72} -1.35179 q^{73} +(-0.415482 - 0.348631i) q^{74} +(-1.81675 - 0.469852i) q^{75} +(-6.37149 + 5.34631i) q^{76} +(-5.07726 - 7.02381i) q^{77} +(10.5409 - 5.02771i) q^{78} +(5.44325 + 4.56743i) q^{79} +(-0.989519 - 1.71390i) q^{80} +(-6.68841 + 6.02206i) q^{81} +(-1.21404 + 2.10278i) q^{82} +(-1.31290 + 7.44583i) q^{83} +(-1.66921 - 4.26775i) q^{84} +(1.11054 + 0.404205i) q^{85} +(-0.668303 - 3.79014i) q^{86} +(-1.54812 + 1.57536i) q^{87} +(2.50935 + 2.10559i) q^{88} +(-8.63183 - 14.9508i) q^{89} +(-5.86401 - 0.928819i) q^{90} +(14.7654 + 10.0113i) q^{91} +(0.380241 + 0.319060i) q^{92} +(-1.08186 + 2.37390i) q^{93} +(-0.695651 + 0.583721i) q^{94} +(-12.6094 + 10.5806i) q^{95} +(1.00580 + 1.41009i) q^{96} +(-6.38539 - 5.35798i) q^{97} +(4.33619 - 5.49522i) q^{98} +(9.64663 - 1.87503i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q + 3 q^{6} + 6 q^{7} - 36 q^{8} + 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 72 q + 3 q^{6} + 6 q^{7} - 36 q^{8} + 24 q^{9} - 6 q^{10} + 12 q^{11} - 12 q^{13} - 3 q^{14} - 6 q^{15} - 12 q^{17} - 18 q^{19} - 30 q^{21} - 6 q^{22} + 30 q^{23} + 6 q^{25} - 18 q^{26} - 6 q^{27} + 3 q^{29} + 3 q^{30} + 9 q^{31} - 18 q^{33} + 9 q^{34} - 18 q^{35} + 9 q^{36} - 24 q^{39} - 6 q^{41} + 12 q^{42} + 24 q^{43} + 51 q^{45} + 45 q^{47} - 6 q^{48} - 12 q^{49} + 6 q^{50} - 51 q^{51} + 6 q^{52} - 15 q^{53} + 27 q^{54} + 72 q^{55} - 3 q^{56} - 63 q^{57} + 3 q^{58} - 30 q^{59} - 3 q^{60} + 9 q^{61} - 24 q^{62} - 39 q^{63} - 36 q^{64} + 9 q^{65} - 6 q^{67} + 9 q^{68} - 21 q^{69} - 33 q^{70} + 12 q^{71} - 12 q^{72} + 132 q^{73} - 18 q^{74} - 30 q^{75} - 33 q^{77} + 30 q^{78} - 9 q^{79} - 6 q^{80} + 36 q^{81} - 33 q^{82} - 18 q^{83} + 15 q^{84} + 21 q^{85} - 12 q^{86} - 39 q^{87} - 6 q^{88} - 36 q^{89} + 69 q^{90} + 39 q^{91} + 30 q^{92} - 66 q^{93} - 9 q^{94} - 33 q^{95} - 48 q^{97} - 12 q^{98} - 54 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\)
\(\chi(n)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.766044 + 0.642788i 0.541675 + 0.454519i
\(3\) −1.42742 0.981051i −0.824124 0.566410i
\(4\) 0.173648 + 0.984808i 0.0868241 + 0.492404i
\(5\) 0.343656 + 1.94897i 0.153688 + 0.871606i 0.959976 + 0.280083i \(0.0903621\pi\)
−0.806288 + 0.591523i \(0.798527\pi\)
\(6\) −0.462863 1.66906i −0.188963 0.681390i
\(7\) 1.84248 1.89876i 0.696391 0.717662i
\(8\) −0.500000 + 0.866025i −0.176777 + 0.306186i
\(9\) 1.07508 + 2.80075i 0.358360 + 0.933584i
\(10\) −0.989519 + 1.71390i −0.312913 + 0.541982i
\(11\) 0.568823 3.22596i 0.171507 0.972663i −0.770592 0.637328i \(-0.780040\pi\)
0.942099 0.335335i \(-0.108849\pi\)
\(12\) 0.718277 1.57610i 0.207349 0.454980i
\(13\) 1.17085 + 6.64020i 0.324734 + 1.84166i 0.511537 + 0.859261i \(0.329076\pi\)
−0.186803 + 0.982397i \(0.559813\pi\)
\(14\) 2.63192 0.270209i 0.703409 0.0722165i
\(15\) 1.42150 3.11915i 0.367029 0.805362i
\(16\) −0.939693 + 0.342020i −0.234923 + 0.0855050i
\(17\) 0.298584 0.517162i 0.0724172 0.125430i −0.827543 0.561402i \(-0.810262\pi\)
0.899960 + 0.435972i \(0.143595\pi\)
\(18\) −0.976729 + 2.83655i −0.230217 + 0.668581i
\(19\) 4.15869 + 7.20307i 0.954070 + 1.65250i 0.736483 + 0.676456i \(0.236485\pi\)
0.217586 + 0.976041i \(0.430182\pi\)
\(20\) −1.85969 + 0.676871i −0.415839 + 0.151353i
\(21\) −4.49277 + 0.902766i −0.980404 + 0.197000i
\(22\) 2.50935 2.10559i 0.534995 0.448914i
\(23\) 0.380241 0.319060i 0.0792857 0.0665286i −0.602283 0.798282i \(-0.705742\pi\)
0.681569 + 0.731754i \(0.261298\pi\)
\(24\) 1.56333 0.745660i 0.319113 0.152207i
\(25\) 1.01807 0.370549i 0.203615 0.0741097i
\(26\) −3.37132 + 5.83929i −0.661169 + 1.14518i
\(27\) 1.21308 5.05257i 0.233458 0.972367i
\(28\) 2.18985 + 1.48477i 0.413843 + 0.280595i
\(29\) 0.221437 1.25583i 0.0411198 0.233202i −0.957321 0.289028i \(-0.906668\pi\)
0.998441 + 0.0558258i \(0.0177792\pi\)
\(30\) 3.09388 1.47569i 0.564863 0.269423i
\(31\) −0.261547 1.48331i −0.0469753 0.266410i 0.952270 0.305257i \(-0.0987425\pi\)
−0.999245 + 0.0388474i \(0.987631\pi\)
\(32\) −0.939693 0.342020i −0.166116 0.0604612i
\(33\) −3.97678 + 4.04677i −0.692269 + 0.704452i
\(34\) 0.561154 0.204243i 0.0962371 0.0350274i
\(35\) 4.33380 + 2.93842i 0.732546 + 0.496683i
\(36\) −2.57152 + 1.54509i −0.428586 + 0.257515i
\(37\) −0.542374 −0.0891657 −0.0445828 0.999006i \(-0.514196\pi\)
−0.0445828 + 0.999006i \(0.514196\pi\)
\(38\) −1.44430 + 8.19103i −0.234296 + 1.32876i
\(39\) 4.84307 10.6270i 0.775512 1.70169i
\(40\) −1.85969 0.676871i −0.294042 0.107023i
\(41\) 0.421633 + 2.39120i 0.0658480 + 0.373442i 0.999868 + 0.0162228i \(0.00516412\pi\)
−0.934020 + 0.357220i \(0.883725\pi\)
\(42\) −4.02195 2.19634i −0.620601 0.338903i
\(43\) −2.94820 2.47384i −0.449597 0.377256i 0.389689 0.920946i \(-0.372582\pi\)
−0.839286 + 0.543690i \(0.817027\pi\)
\(44\) 3.27572 0.493834
\(45\) −5.08912 + 3.05779i −0.758642 + 0.455829i
\(46\) 0.496369 0.0731856
\(47\) −0.157691 + 0.894312i −0.0230016 + 0.130449i −0.994146 0.108043i \(-0.965542\pi\)
0.971145 + 0.238491i \(0.0766528\pi\)
\(48\) 1.67688 + 0.433678i 0.242037 + 0.0625960i
\(49\) −0.210549 6.99683i −0.0300784 0.999548i
\(50\) 1.01807 + 0.370549i 0.143977 + 0.0524035i
\(51\) −0.933568 + 0.445284i −0.130726 + 0.0623522i
\(52\) −6.33600 + 2.30612i −0.878645 + 0.319801i
\(53\) −5.09597 8.82648i −0.699985 1.21241i −0.968471 0.249127i \(-0.919856\pi\)
0.268486 0.963284i \(-0.413477\pi\)
\(54\) 4.17700 3.09074i 0.568418 0.420596i
\(55\) 6.48278 0.874138
\(56\) 0.723132 + 2.54501i 0.0966326 + 0.340091i
\(57\) 1.13035 14.3617i 0.149719 1.90226i
\(58\) 0.976863 0.819685i 0.128268 0.107630i
\(59\) −12.6532 4.60539i −1.64731 0.599570i −0.659012 0.752132i \(-0.729025\pi\)
−0.988294 + 0.152562i \(0.951248\pi\)
\(60\) 3.31861 + 0.858265i 0.428430 + 0.110802i
\(61\) 1.27613 7.23729i 0.163392 0.926639i −0.787316 0.616550i \(-0.788530\pi\)
0.950707 0.310090i \(-0.100359\pi\)
\(62\) 0.753095 1.30440i 0.0956432 0.165659i
\(63\) 7.29875 + 3.11901i 0.919556 + 0.392958i
\(64\) −0.500000 0.866025i −0.0625000 0.108253i
\(65\) −12.5392 + 4.56389i −1.55529 + 0.566081i
\(66\) −5.64760 + 0.543778i −0.695172 + 0.0669344i
\(67\) −2.08879 + 1.75271i −0.255187 + 0.214127i −0.761402 0.648280i \(-0.775489\pi\)
0.506215 + 0.862407i \(0.331044\pi\)
\(68\) 0.561154 + 0.204243i 0.0680499 + 0.0247681i
\(69\) −0.855779 + 0.0823984i −0.103024 + 0.00991961i
\(70\) 1.43110 + 5.03667i 0.171050 + 0.601997i
\(71\) −1.32437 2.29388i −0.157174 0.272233i 0.776675 0.629902i \(-0.216905\pi\)
−0.933848 + 0.357669i \(0.883572\pi\)
\(72\) −2.96306 0.469329i −0.349200 0.0553109i
\(73\) −1.35179 −0.158216 −0.0791078 0.996866i \(-0.525207\pi\)
−0.0791078 + 0.996866i \(0.525207\pi\)
\(74\) −0.415482 0.348631i −0.0482988 0.0405275i
\(75\) −1.81675 0.469852i −0.209780 0.0542538i
\(76\) −6.37149 + 5.34631i −0.730860 + 0.613264i
\(77\) −5.07726 7.02381i −0.578608 0.800438i
\(78\) 10.5409 5.02771i 1.19353 0.569276i
\(79\) 5.44325 + 4.56743i 0.612413 + 0.513876i 0.895408 0.445246i \(-0.146884\pi\)
−0.282995 + 0.959121i \(0.591328\pi\)
\(80\) −0.989519 1.71390i −0.110632 0.191619i
\(81\) −6.68841 + 6.02206i −0.743156 + 0.669118i
\(82\) −1.21404 + 2.10278i −0.134069 + 0.232214i
\(83\) −1.31290 + 7.44583i −0.144110 + 0.817286i 0.823968 + 0.566636i \(0.191755\pi\)
−0.968078 + 0.250650i \(0.919356\pi\)
\(84\) −1.66921 4.26775i −0.182126 0.465650i
\(85\) 1.11054 + 0.404205i 0.120455 + 0.0438422i
\(86\) −0.668303 3.79014i −0.0720650 0.408701i
\(87\) −1.54812 + 1.57536i −0.165976 + 0.168897i
\(88\) 2.50935 + 2.10559i 0.267498 + 0.224457i
\(89\) −8.63183 14.9508i −0.914973 1.58478i −0.806942 0.590631i \(-0.798879\pi\)
−0.108031 0.994148i \(-0.534455\pi\)
\(90\) −5.86401 0.928819i −0.618121 0.0979061i
\(91\) 14.7654 + 10.0113i 1.54783 + 1.04947i
\(92\) 0.380241 + 0.319060i 0.0396428 + 0.0332643i
\(93\) −1.08186 + 2.37390i −0.112184 + 0.246162i
\(94\) −0.695651 + 0.583721i −0.0717509 + 0.0602062i
\(95\) −12.6094 + 10.5806i −1.29370 + 1.08554i
\(96\) 1.00580 + 1.41009i 0.102654 + 0.143917i
\(97\) −6.38539 5.35798i −0.648338 0.544020i 0.258228 0.966084i \(-0.416861\pi\)
−0.906566 + 0.422064i \(0.861306\pi\)
\(98\) 4.33619 5.49522i 0.438021 0.555101i
\(99\) 9.64663 1.87503i 0.969523 0.188448i
\(100\) 0.541706 + 0.938262i 0.0541706 + 0.0938262i
\(101\) 12.9695 + 10.8827i 1.29051 + 1.08287i 0.991702 + 0.128556i \(0.0410342\pi\)
0.298810 + 0.954313i \(0.403410\pi\)
\(102\) −1.00138 0.258978i −0.0991512 0.0256427i
\(103\) −2.74718 15.5800i −0.270688 1.53515i −0.752335 0.658781i \(-0.771072\pi\)
0.481647 0.876365i \(-0.340039\pi\)
\(104\) −6.33600 2.30612i −0.621296 0.226133i
\(105\) −3.30343 8.44604i −0.322382 0.824250i
\(106\) 1.76981 10.0371i 0.171899 0.974890i
\(107\) 1.44677 2.50589i 0.139865 0.242253i −0.787580 0.616212i \(-0.788667\pi\)
0.927445 + 0.373959i \(0.122000\pi\)
\(108\) 5.18646 + 0.317284i 0.499067 + 0.0305307i
\(109\) 9.97350 + 17.2746i 0.955288 + 1.65461i 0.733708 + 0.679465i \(0.237788\pi\)
0.221580 + 0.975142i \(0.428878\pi\)
\(110\) 4.96610 + 4.16705i 0.473499 + 0.397313i
\(111\) 0.774197 + 0.532096i 0.0734836 + 0.0505043i
\(112\) −1.08195 + 2.41441i −0.102235 + 0.228140i
\(113\) 5.52639 4.63719i 0.519879 0.436230i −0.344710 0.938709i \(-0.612023\pi\)
0.864590 + 0.502479i \(0.167578\pi\)
\(114\) 10.0974 10.2751i 0.945712 0.962355i
\(115\) 0.752511 + 0.631431i 0.0701720 + 0.0588813i
\(116\) 1.27520 0.118400
\(117\) −17.3388 + 10.4180i −1.60297 + 0.963143i
\(118\) −6.73263 11.6613i −0.619789 1.07351i
\(119\) −0.431831 1.51980i −0.0395859 0.139320i
\(120\) 1.99052 + 2.79063i 0.181709 + 0.254748i
\(121\) 0.253373 + 0.0922203i 0.0230339 + 0.00838367i
\(122\) 5.62961 4.72380i 0.509681 0.427673i
\(123\) 1.74404 3.82690i 0.157255 0.345060i
\(124\) 1.41536 0.515148i 0.127103 0.0462616i
\(125\) 6.01965 + 10.4263i 0.538414 + 0.932560i
\(126\) 3.58631 + 7.08085i 0.319494 + 0.630812i
\(127\) 4.51749 7.82452i 0.400862 0.694314i −0.592968 0.805226i \(-0.702044\pi\)
0.993830 + 0.110912i \(0.0353772\pi\)
\(128\) 0.173648 0.984808i 0.0153485 0.0870455i
\(129\) 1.78138 + 6.42355i 0.156842 + 0.565562i
\(130\) −12.5392 4.56389i −1.09976 0.400279i
\(131\) 10.6528 8.93879i 0.930743 0.780986i −0.0452078 0.998978i \(-0.514395\pi\)
0.975951 + 0.217992i \(0.0699505\pi\)
\(132\) −4.67585 3.21365i −0.406980 0.279712i
\(133\) 21.3392 + 5.37515i 1.85034 + 0.466085i
\(134\) −2.72673 −0.235553
\(135\) 10.2642 + 0.627917i 0.883401 + 0.0540425i
\(136\) 0.298584 + 0.517162i 0.0256033 + 0.0443463i
\(137\) −10.5182 + 3.82831i −0.898630 + 0.327075i −0.749704 0.661774i \(-0.769804\pi\)
−0.148927 + 0.988848i \(0.547582\pi\)
\(138\) −0.708529 0.486963i −0.0603140 0.0414531i
\(139\) 4.89594 + 1.78198i 0.415268 + 0.151145i 0.541200 0.840894i \(-0.317970\pi\)
−0.125932 + 0.992039i \(0.540192\pi\)
\(140\) −2.14122 + 4.77821i −0.180966 + 0.403832i
\(141\) 1.10246 1.12186i 0.0928437 0.0944776i
\(142\) 0.459949 2.60850i 0.0385981 0.218900i
\(143\) 22.0870 1.84701
\(144\) −1.96816 2.26415i −0.164013 0.188679i
\(145\) 2.52368 0.209580
\(146\) −1.03553 0.868917i −0.0857015 0.0719121i
\(147\) −6.56370 + 10.1940i −0.541365 + 0.840788i
\(148\) −0.0941822 0.534134i −0.00774173 0.0439055i
\(149\) 10.8595 + 3.95254i 0.889647 + 0.323805i 0.746096 0.665838i \(-0.231926\pi\)
0.143550 + 0.989643i \(0.454148\pi\)
\(150\) −1.08970 1.52771i −0.0889734 0.124737i
\(151\) 2.86385 16.2417i 0.233057 1.32173i −0.613611 0.789609i \(-0.710284\pi\)
0.846668 0.532122i \(-0.178605\pi\)
\(152\) −8.31739 −0.674629
\(153\) 1.76944 + 0.280268i 0.143051 + 0.0226583i
\(154\) 0.625412 8.64416i 0.0503971 0.696566i
\(155\) 2.80104 1.01950i 0.224985 0.0818879i
\(156\) 11.3066 + 2.92413i 0.905251 + 0.234118i
\(157\) −13.0535 4.75108i −1.04178 0.379178i −0.236226 0.971698i \(-0.575911\pi\)
−0.805555 + 0.592520i \(0.798133\pi\)
\(158\) 1.23388 + 6.99770i 0.0981625 + 0.556707i
\(159\) −1.38511 + 17.5985i −0.109846 + 1.39565i
\(160\) 0.343656 1.94897i 0.0271684 0.154080i
\(161\) 0.0947684 1.30985i 0.00746880 0.103230i
\(162\) −8.99452 + 0.313941i −0.706676 + 0.0246655i
\(163\) −6.51673 + 11.2873i −0.510430 + 0.884091i 0.489497 + 0.872005i \(0.337180\pi\)
−0.999927 + 0.0120856i \(0.996153\pi\)
\(164\) −2.28166 + 0.830455i −0.178167 + 0.0648476i
\(165\) −9.25368 6.35993i −0.720398 0.495120i
\(166\) −5.79183 + 4.85992i −0.449533 + 0.377203i
\(167\) −17.4447 + 14.6378i −1.34991 + 1.13271i −0.370952 + 0.928652i \(0.620968\pi\)
−0.978959 + 0.204057i \(0.934587\pi\)
\(168\) 1.46457 4.34224i 0.112994 0.335011i
\(169\) −30.5053 + 11.1030i −2.34656 + 0.854079i
\(170\) 0.590908 + 1.02348i 0.0453206 + 0.0784976i
\(171\) −15.7031 + 19.3913i −1.20084 + 1.48289i
\(172\) 1.92430 3.33299i 0.146727 0.254138i
\(173\) −13.2652 + 4.82813i −1.00853 + 0.367076i −0.792869 0.609392i \(-0.791414\pi\)
−0.215664 + 0.976468i \(0.569192\pi\)
\(174\) −2.19855 + 0.211687i −0.166672 + 0.0160479i
\(175\) 1.17220 2.61580i 0.0886098 0.197736i
\(176\) 0.568823 + 3.22596i 0.0428767 + 0.243166i
\(177\) 13.5434 + 18.9873i 1.01798 + 1.42717i
\(178\) 2.99780 17.0014i 0.224695 1.27431i
\(179\) −0.00802956 + 0.0139076i −0.000600158 + 0.00103950i −0.866325 0.499480i \(-0.833524\pi\)
0.865725 + 0.500520i \(0.166858\pi\)
\(180\) −3.89506 4.48083i −0.290320 0.333981i
\(181\) −1.97514 + 3.42105i −0.146811 + 0.254285i −0.930047 0.367440i \(-0.880234\pi\)
0.783236 + 0.621725i \(0.213568\pi\)
\(182\) 4.87581 + 17.1601i 0.361419 + 1.27199i
\(183\) −8.92172 + 9.07873i −0.659512 + 0.671119i
\(184\) 0.0861936 + 0.488828i 0.00635428 + 0.0360369i
\(185\) −0.186390 1.05707i −0.0137037 0.0777174i
\(186\) −2.35467 + 1.12311i −0.172653 + 0.0823502i
\(187\) −1.49850 1.25739i −0.109581 0.0919496i
\(188\) −0.908108 −0.0662306
\(189\) −7.35851 11.6126i −0.535253 0.844692i
\(190\) −16.4604 −1.19416
\(191\) −13.6974 11.4935i −0.991110 0.831640i −0.00538196 0.999986i \(-0.501713\pi\)
−0.985728 + 0.168345i \(0.946158\pi\)
\(192\) −0.135903 + 1.72671i −0.00980792 + 0.124615i
\(193\) 0.278012 + 1.57668i 0.0200117 + 0.113492i 0.993177 0.116614i \(-0.0372039\pi\)
−0.973166 + 0.230106i \(0.926093\pi\)
\(194\) −1.44745 8.20889i −0.103921 0.589364i
\(195\) 22.3761 + 5.78696i 1.60239 + 0.414413i
\(196\) 6.85397 1.42234i 0.489570 0.101596i
\(197\) 9.50079 16.4558i 0.676903 1.17243i −0.299006 0.954251i \(-0.596655\pi\)
0.975909 0.218179i \(-0.0700118\pi\)
\(198\) 8.59500 + 4.76438i 0.610820 + 0.338590i
\(199\) 4.16219 7.20912i 0.295050 0.511041i −0.679947 0.733261i \(-0.737997\pi\)
0.974996 + 0.222220i \(0.0713305\pi\)
\(200\) −0.188132 + 1.06695i −0.0133030 + 0.0754449i
\(201\) 4.70109 0.452643i 0.331589 0.0319270i
\(202\) 2.93994 + 16.6733i 0.206854 + 1.17313i
\(203\) −1.97652 2.73429i −0.138725 0.191910i
\(204\) −0.600632 0.842062i −0.0420526 0.0589561i
\(205\) −4.51548 + 1.64350i −0.315375 + 0.114787i
\(206\) 7.91019 13.7008i 0.551129 0.954583i
\(207\) 1.30240 + 0.721945i 0.0905228 + 0.0501786i
\(208\) −3.37132 5.83929i −0.233759 0.404882i
\(209\) 25.6024 9.31849i 1.77095 0.644574i
\(210\) 2.89844 8.59345i 0.200011 0.593005i
\(211\) 3.59633 3.01768i 0.247581 0.207745i −0.510549 0.859849i \(-0.670558\pi\)
0.758130 + 0.652103i \(0.226113\pi\)
\(212\) 7.80748 6.55125i 0.536220 0.449942i
\(213\) −0.359971 + 4.57361i −0.0246648 + 0.313379i
\(214\) 2.71905 0.989652i 0.185870 0.0676512i
\(215\) 3.80827 6.59611i 0.259722 0.449851i
\(216\) 3.76911 + 3.57684i 0.256455 + 0.243373i
\(217\) −3.29834 2.23635i −0.223906 0.151813i
\(218\) −3.46376 + 19.6440i −0.234595 + 1.33046i
\(219\) 1.92958 + 1.32618i 0.130389 + 0.0896149i
\(220\) 1.12572 + 6.38429i 0.0758962 + 0.430429i
\(221\) 3.78365 + 1.37714i 0.254516 + 0.0926363i
\(222\) 0.251045 + 0.905254i 0.0168490 + 0.0607567i
\(223\) 1.46317 0.532550i 0.0979810 0.0356622i −0.292565 0.956246i \(-0.594509\pi\)
0.390546 + 0.920584i \(0.372286\pi\)
\(224\) −2.38078 + 1.15408i −0.159072 + 0.0771104i
\(225\) 2.13233 + 2.45300i 0.142155 + 0.163533i
\(226\) 7.21419 0.479881
\(227\) 0.778222 4.41352i 0.0516524 0.292935i −0.948029 0.318185i \(-0.896927\pi\)
0.999681 + 0.0252492i \(0.00803792\pi\)
\(228\) 14.3398 1.38071i 0.949678 0.0914394i
\(229\) 17.3045 + 6.29834i 1.14352 + 0.416206i 0.843182 0.537628i \(-0.180679\pi\)
0.300335 + 0.953834i \(0.402902\pi\)
\(230\) 0.170580 + 0.967409i 0.0112477 + 0.0637891i
\(231\) 0.356691 + 15.0070i 0.0234686 + 0.987389i
\(232\) 0.976863 + 0.819685i 0.0641342 + 0.0538150i
\(233\) 10.4132 0.682190 0.341095 0.940029i \(-0.389202\pi\)
0.341095 + 0.940029i \(0.389202\pi\)
\(234\) −19.9788 3.16451i −1.30606 0.206871i
\(235\) −1.79718 −0.117235
\(236\) 2.33822 13.2607i 0.152205 0.863197i
\(237\) −3.28895 11.8598i −0.213640 0.770374i
\(238\) 0.646105 1.44181i 0.0418808 0.0934585i
\(239\) −9.03426 3.28820i −0.584378 0.212696i 0.0328769 0.999459i \(-0.489533\pi\)
−0.617255 + 0.786763i \(0.711755\pi\)
\(240\) −0.268956 + 3.41723i −0.0173610 + 0.220581i
\(241\) −26.8336 + 9.76662i −1.72850 + 0.629123i −0.998522 0.0543459i \(-0.982693\pi\)
−0.729979 + 0.683469i \(0.760470\pi\)
\(242\) 0.134817 + 0.233510i 0.00866637 + 0.0150106i
\(243\) 15.4551 2.03437i 0.991448 0.130505i
\(244\) 7.34893 0.470467
\(245\) 13.5643 2.81486i 0.866589 0.179835i
\(246\) 3.79589 1.81053i 0.242017 0.115435i
\(247\) −42.9606 + 36.0482i −2.73352 + 2.29369i
\(248\) 1.41536 + 0.515148i 0.0898752 + 0.0327119i
\(249\) 9.17880 9.34034i 0.581683 0.591920i
\(250\) −2.09060 + 11.8564i −0.132221 + 0.749864i
\(251\) −3.73667 + 6.47211i −0.235857 + 0.408516i −0.959521 0.281636i \(-0.909123\pi\)
0.723665 + 0.690152i \(0.242456\pi\)
\(252\) −1.80421 + 7.72948i −0.113654 + 0.486911i
\(253\) −0.812984 1.40813i −0.0511119 0.0885284i
\(254\) 8.49010 3.09015i 0.532717 0.193893i
\(255\) −1.18867 1.66647i −0.0744375 0.104359i
\(256\) 0.766044 0.642788i 0.0478778 0.0401742i
\(257\) −26.1959 9.53453i −1.63406 0.594748i −0.648071 0.761580i \(-0.724424\pi\)
−0.985985 + 0.166832i \(0.946646\pi\)
\(258\) −2.76436 + 6.06577i −0.172102 + 0.377638i
\(259\) −0.999312 + 1.02984i −0.0620942 + 0.0639909i
\(260\) −6.67196 11.5562i −0.413777 0.716683i
\(261\) 3.75533 0.729929i 0.232449 0.0451815i
\(262\) 13.9063 0.859134
\(263\) 9.37802 + 7.86909i 0.578273 + 0.485229i 0.884380 0.466768i \(-0.154582\pi\)
−0.306106 + 0.951997i \(0.599026\pi\)
\(264\) −1.51621 5.46738i −0.0933164 0.336494i
\(265\) 15.4513 12.9652i 0.949165 0.796444i
\(266\) 12.8917 + 17.8342i 0.790439 + 1.09348i
\(267\) −2.34618 + 29.8094i −0.143584 + 1.82430i
\(268\) −2.08879 1.75271i −0.127593 0.107064i
\(269\) 11.6402 + 20.1614i 0.709713 + 1.22926i 0.964963 + 0.262384i \(0.0845088\pi\)
−0.255250 + 0.966875i \(0.582158\pi\)
\(270\) 7.45921 + 7.07871i 0.453953 + 0.430796i
\(271\) 10.0745 17.4496i 0.611985 1.05999i −0.378920 0.925429i \(-0.623705\pi\)
0.990905 0.134560i \(-0.0429621\pi\)
\(272\) −0.103697 + 0.588095i −0.00628756 + 0.0356585i
\(273\) −11.2549 28.7759i −0.681177 1.74160i
\(274\) −10.5182 3.82831i −0.635428 0.231277i
\(275\) −0.616270 3.49504i −0.0371625 0.210759i
\(276\) −0.229751 0.828469i −0.0138294 0.0498680i
\(277\) −7.84259 6.58072i −0.471216 0.395397i 0.376022 0.926611i \(-0.377292\pi\)
−0.847238 + 0.531214i \(0.821736\pi\)
\(278\) 2.60507 + 4.51212i 0.156242 + 0.270619i
\(279\) 3.87319 2.32720i 0.231882 0.139326i
\(280\) −4.71164 + 2.28397i −0.281575 + 0.136493i
\(281\) 13.9814 + 11.7318i 0.834061 + 0.699860i 0.956220 0.292650i \(-0.0945372\pi\)
−0.122158 + 0.992511i \(0.538982\pi\)
\(282\) 1.56565 0.150748i 0.0932330 0.00897691i
\(283\) 5.95618 4.99782i 0.354058 0.297090i −0.448359 0.893853i \(-0.647991\pi\)
0.802417 + 0.596764i \(0.203547\pi\)
\(284\) 2.02905 1.70258i 0.120402 0.101029i
\(285\) 28.3790 2.73247i 1.68103 0.161857i
\(286\) 16.9196 + 14.1972i 1.00048 + 0.839501i
\(287\) 5.31715 + 3.60515i 0.313862 + 0.212805i
\(288\) −0.0523315 2.99954i −0.00308366 0.176750i
\(289\) 8.32170 + 14.4136i 0.489512 + 0.847859i
\(290\) 1.93325 + 1.62219i 0.113524 + 0.0952581i
\(291\) 3.85821 + 13.9125i 0.226172 + 0.815565i
\(292\) −0.234737 1.33126i −0.0137369 0.0779060i
\(293\) −15.8822 5.78065i −0.927849 0.337709i −0.166492 0.986043i \(-0.553244\pi\)
−0.761357 + 0.648333i \(0.775466\pi\)
\(294\) −11.5807 + 3.59000i −0.675398 + 0.209373i
\(295\) 4.62742 26.2434i 0.269419 1.52795i
\(296\) 0.271187 0.469709i 0.0157624 0.0273013i
\(297\) −15.6093 6.78737i −0.905746 0.393843i
\(298\) 5.77823 + 10.0082i 0.334724 + 0.579759i
\(299\) 2.56382 + 2.15130i 0.148270 + 0.124413i
\(300\) 0.147238 1.87074i 0.00850081 0.108007i
\(301\) −10.1292 + 1.03993i −0.583838 + 0.0599405i
\(302\) 12.6338 10.6010i 0.726994 0.610020i
\(303\) −7.83649 28.2579i −0.450195 1.62338i
\(304\) −6.37149 5.34631i −0.365430 0.306632i
\(305\) 14.5438 0.832776
\(306\) 1.17532 + 1.35207i 0.0671886 + 0.0772929i
\(307\) −9.92235 17.1860i −0.566298 0.980858i −0.996928 0.0783287i \(-0.975042\pi\)
0.430629 0.902529i \(-0.358292\pi\)
\(308\) 6.03545 6.21980i 0.343902 0.354406i
\(309\) −11.3634 + 24.9344i −0.646442 + 1.41847i
\(310\) 2.80104 + 1.01950i 0.159089 + 0.0579035i
\(311\) 17.6693 14.8263i 1.00194 0.840724i 0.0146842 0.999892i \(-0.495326\pi\)
0.987251 + 0.159168i \(0.0508813\pi\)
\(312\) 6.78174 + 9.50774i 0.383941 + 0.538270i
\(313\) −7.28068 + 2.64995i −0.411528 + 0.149784i −0.539484 0.841996i \(-0.681381\pi\)
0.127956 + 0.991780i \(0.459158\pi\)
\(314\) −6.94562 12.0302i −0.391964 0.678901i
\(315\) −3.57059 + 15.2969i −0.201180 + 0.861884i
\(316\) −3.55283 + 6.15368i −0.199862 + 0.346171i
\(317\) 4.86439 27.5873i 0.273212 1.54946i −0.471374 0.881933i \(-0.656242\pi\)
0.744586 0.667527i \(-0.232647\pi\)
\(318\) −12.3732 + 12.5909i −0.693853 + 0.706064i
\(319\) −3.92530 1.42869i −0.219774 0.0799914i
\(320\) 1.51603 1.27210i 0.0847487 0.0711126i
\(321\) −4.52356 + 2.15760i −0.252481 + 0.120426i
\(322\) 0.914549 0.942484i 0.0509658 0.0525226i
\(323\) 4.96687 0.276364
\(324\) −7.09200 5.54107i −0.394000 0.307837i
\(325\) 3.65252 + 6.32636i 0.202606 + 0.350923i
\(326\) −12.2475 + 4.45771i −0.678324 + 0.246890i
\(327\) 2.71085 34.4427i 0.149910 1.90469i
\(328\) −2.28166 0.830455i −0.125983 0.0458542i
\(329\) 1.40754 + 1.94717i 0.0776000 + 0.107351i
\(330\) −3.00064 10.8201i −0.165180 0.595629i
\(331\) 1.77095 10.0435i 0.0973400 0.552043i −0.896665 0.442709i \(-0.854017\pi\)
0.994005 0.109333i \(-0.0348715\pi\)
\(332\) −7.56069 −0.414947
\(333\) −0.583095 1.51905i −0.0319534 0.0832436i
\(334\) −22.7724 −1.24605
\(335\) −4.13380 3.46867i −0.225854 0.189514i
\(336\) 3.91306 2.38494i 0.213475 0.130109i
\(337\) 0.475096 + 2.69440i 0.0258801 + 0.146774i 0.995010 0.0997786i \(-0.0318135\pi\)
−0.969130 + 0.246552i \(0.920702\pi\)
\(338\) −30.5053 11.1030i −1.65927 0.603925i
\(339\) −12.4378 + 1.19757i −0.675530 + 0.0650432i
\(340\) −0.205220 + 1.16386i −0.0111296 + 0.0631193i
\(341\) −4.93386 −0.267184
\(342\) −24.4938 + 4.76089i −1.32447 + 0.257439i
\(343\) −13.6732 12.4917i −0.738284 0.674490i
\(344\) 3.61651 1.31630i 0.194989 0.0709702i
\(345\) −0.454686 1.63957i −0.0244795 0.0882716i
\(346\) −13.2652 4.82813i −0.713141 0.259562i
\(347\) 0.422470 + 2.39594i 0.0226794 + 0.128621i 0.994045 0.108967i \(-0.0347543\pi\)
−0.971366 + 0.237588i \(0.923643\pi\)
\(348\) −1.82026 1.25104i −0.0975760 0.0670627i
\(349\) −0.745200 + 4.22624i −0.0398896 + 0.226225i −0.998235 0.0593863i \(-0.981086\pi\)
0.958345 + 0.285612i \(0.0921968\pi\)
\(350\) 2.57936 1.25035i 0.137873 0.0668338i
\(351\) 34.9704 + 2.13933i 1.86658 + 0.114189i
\(352\) −1.63786 + 2.83686i −0.0872983 + 0.151205i
\(353\) 20.4486 7.44269i 1.08837 0.396134i 0.265353 0.964151i \(-0.414511\pi\)
0.823017 + 0.568017i \(0.192289\pi\)
\(354\) −1.82996 + 23.2506i −0.0972614 + 1.23576i
\(355\) 4.01557 3.36946i 0.213124 0.178833i
\(356\) 13.2247 11.0969i 0.700910 0.588133i
\(357\) −0.874592 + 2.59304i −0.0462883 + 0.137238i
\(358\) −0.0150906 + 0.00549254i −0.000797565 + 0.000290290i
\(359\) 14.5206 + 25.1504i 0.766369 + 1.32739i 0.939520 + 0.342495i \(0.111272\pi\)
−0.173151 + 0.984895i \(0.555395\pi\)
\(360\) −0.103566 5.93621i −0.00545841 0.312866i
\(361\) −25.0894 + 43.4562i −1.32050 + 2.28717i
\(362\) −3.71206 + 1.35108i −0.195101 + 0.0710111i
\(363\) −0.271198 0.380210i −0.0142342 0.0199558i
\(364\) −7.29519 + 16.2795i −0.382372 + 0.853277i
\(365\) −0.464553 2.63461i −0.0243158 0.137902i
\(366\) −12.6701 + 1.21994i −0.662278 + 0.0637673i
\(367\) 3.74342 21.2300i 0.195405 1.10820i −0.716437 0.697652i \(-0.754228\pi\)
0.911841 0.410543i \(-0.134661\pi\)
\(368\) −0.248185 + 0.429868i −0.0129375 + 0.0224084i
\(369\) −6.24386 + 3.75162i −0.325042 + 0.195301i
\(370\) 0.536689 0.929572i 0.0279011 0.0483262i
\(371\) −26.1485 6.58659i −1.35756 0.341959i
\(372\) −2.52570 0.653202i −0.130951 0.0338669i
\(373\) 0.155952 + 0.884448i 0.00807489 + 0.0457950i 0.988579 0.150704i \(-0.0481540\pi\)
−0.980504 + 0.196499i \(0.937043\pi\)
\(374\) −0.339683 1.92644i −0.0175646 0.0996137i
\(375\) 1.63617 20.7884i 0.0844915 1.07351i
\(376\) −0.695651 0.583721i −0.0358755 0.0301031i
\(377\) 8.59823 0.442831
\(378\) 1.82748 13.6257i 0.0939955 0.700832i
\(379\) −24.5625 −1.26169 −0.630845 0.775909i \(-0.717291\pi\)
−0.630845 + 0.775909i \(0.717291\pi\)
\(380\) −12.6094 10.5806i −0.646849 0.542771i
\(381\) −14.1246 + 6.73703i −0.723627 + 0.345148i
\(382\) −3.10495 17.6091i −0.158863 0.900958i
\(383\) −1.57542 8.93463i −0.0805000 0.456538i −0.998237 0.0593501i \(-0.981097\pi\)
0.917737 0.397188i \(-0.130014\pi\)
\(384\) −1.21402 + 1.23538i −0.0619525 + 0.0630428i
\(385\) 11.9444 12.3092i 0.608742 0.627336i
\(386\) −0.800503 + 1.38651i −0.0407445 + 0.0705716i
\(387\) 3.75904 10.9168i 0.191083 0.554930i
\(388\) 4.16777 7.21878i 0.211586 0.366478i
\(389\) 5.43970 30.8501i 0.275804 1.56416i −0.460593 0.887611i \(-0.652363\pi\)
0.736397 0.676550i \(-0.236526\pi\)
\(390\) 13.4213 + 18.8162i 0.679615 + 0.952794i
\(391\) −0.0514720 0.291912i −0.00260305 0.0147626i
\(392\) 6.16471 + 3.31608i 0.311365 + 0.167487i
\(393\) −23.9755 + 2.30848i −1.20941 + 0.116447i
\(394\) 17.8556 6.49892i 0.899554 0.327411i
\(395\) −7.03118 + 12.1784i −0.353777 + 0.612760i
\(396\) 3.52166 + 9.17448i 0.176970 + 0.461035i
\(397\) −1.92238 3.32966i −0.0964814 0.167111i 0.813745 0.581223i \(-0.197425\pi\)
−0.910226 + 0.414112i \(0.864092\pi\)
\(398\) 7.82235 2.84710i 0.392099 0.142712i
\(399\) −25.1867 28.6074i −1.26091 1.43216i
\(400\) −0.829942 + 0.696404i −0.0414971 + 0.0348202i
\(401\) 7.36725 6.18186i 0.367903 0.308707i −0.440028 0.897984i \(-0.645032\pi\)
0.807931 + 0.589277i \(0.200587\pi\)
\(402\) 3.89220 + 2.67506i 0.194125 + 0.133420i
\(403\) 9.54322 3.47345i 0.475382 0.173025i
\(404\) −8.46523 + 14.6622i −0.421161 + 0.729472i
\(405\) −14.0353 10.9660i −0.697421 0.544905i
\(406\) 0.243466 3.36508i 0.0120830 0.167006i
\(407\) −0.308515 + 1.74968i −0.0152925 + 0.0867282i
\(408\) 0.0811566 1.03114i 0.00401785 0.0510488i
\(409\) −0.857938 4.86561i −0.0424223 0.240589i 0.956222 0.292642i \(-0.0945345\pi\)
−0.998644 + 0.0520535i \(0.983423\pi\)
\(410\) −4.51548 1.64350i −0.223004 0.0811667i
\(411\) 18.7697 + 4.85426i 0.925841 + 0.239443i
\(412\) 14.8663 5.41089i 0.732410 0.266575i
\(413\) −32.0578 + 15.5400i −1.57746 + 0.764674i
\(414\) 0.533636 + 1.39021i 0.0262268 + 0.0683249i
\(415\) −14.9629 −0.734500
\(416\) 1.17085 6.64020i 0.0574054 0.325562i
\(417\) −5.24037 7.34680i −0.256622 0.359774i
\(418\) 25.6024 + 9.31849i 1.25225 + 0.455782i
\(419\) 4.41265 + 25.0254i 0.215572 + 1.22257i 0.879911 + 0.475138i \(0.157602\pi\)
−0.664339 + 0.747431i \(0.731287\pi\)
\(420\) 7.74409 4.71989i 0.377873 0.230307i
\(421\) 11.3843 + 9.55254i 0.554836 + 0.465562i 0.876575 0.481266i \(-0.159823\pi\)
−0.321739 + 0.946828i \(0.604267\pi\)
\(422\) 4.69467 0.228533
\(423\) −2.67427 + 0.519803i −0.130028 + 0.0252737i
\(424\) 10.1919 0.494964
\(425\) 0.112347 0.637149i 0.00544961 0.0309063i
\(426\) −3.21561 + 3.27220i −0.155797 + 0.158539i
\(427\) −11.3906 15.7576i −0.551230 0.762564i
\(428\) 2.71905 + 0.989652i 0.131430 + 0.0478366i
\(429\) −31.5275 21.6685i −1.52216 1.04616i
\(430\) 7.15720 2.60501i 0.345151 0.125625i
\(431\) −4.89865 8.48471i −0.235960 0.408694i 0.723591 0.690228i \(-0.242490\pi\)
−0.959551 + 0.281534i \(0.909157\pi\)
\(432\) 0.588155 + 5.16276i 0.0282976 + 0.248393i
\(433\) 27.3619 1.31493 0.657464 0.753486i \(-0.271629\pi\)
0.657464 + 0.753486i \(0.271629\pi\)
\(434\) −1.08917 3.83327i −0.0522820 0.184003i
\(435\) −3.60236 2.47585i −0.172720 0.118708i
\(436\) −15.2803 + 12.8217i −0.731793 + 0.614047i
\(437\) 3.87951 + 1.41203i 0.185582 + 0.0675465i
\(438\) 0.625696 + 2.25623i 0.0298969 + 0.107807i
\(439\) −5.61740 + 31.8579i −0.268104 + 1.52049i 0.491945 + 0.870626i \(0.336286\pi\)
−0.760049 + 0.649866i \(0.774825\pi\)
\(440\) −3.24139 + 5.61425i −0.154527 + 0.267649i
\(441\) 19.3700 8.11185i 0.922382 0.386278i
\(442\) 2.01324 + 3.48703i 0.0957601 + 0.165861i
\(443\) −28.6959 + 10.4445i −1.36338 + 0.496231i −0.917099 0.398660i \(-0.869475\pi\)
−0.446285 + 0.894891i \(0.647253\pi\)
\(444\) −0.389574 + 0.854833i −0.0184884 + 0.0405686i
\(445\) 26.1722 21.9611i 1.24068 1.04106i
\(446\) 1.46317 + 0.532550i 0.0692830 + 0.0252170i
\(447\) −11.6235 16.2957i −0.549773 0.770760i
\(448\) −2.56561 0.646255i −0.121214 0.0305327i
\(449\) −5.77134 9.99626i −0.272366 0.471753i 0.697101 0.716973i \(-0.254473\pi\)
−0.969467 + 0.245221i \(0.921140\pi\)
\(450\) 0.0566966 + 3.24974i 0.00267270 + 0.153194i
\(451\) 7.95374 0.374527
\(452\) 5.52639 + 4.63719i 0.259940 + 0.218115i
\(453\) −20.0219 + 20.3742i −0.940709 + 0.957264i
\(454\) 3.43311 2.88072i 0.161124 0.135199i
\(455\) −14.4375 + 32.2177i −0.676838 + 1.51039i
\(456\) 11.8724 + 8.15977i 0.555978 + 0.382116i
\(457\) −9.68142 8.12368i −0.452878 0.380010i 0.387625 0.921817i \(-0.373296\pi\)
−0.840503 + 0.541808i \(0.817740\pi\)
\(458\) 9.20756 + 15.9480i 0.430241 + 0.745199i
\(459\) −2.25079 2.13597i −0.105058 0.0996988i
\(460\) −0.491166 + 0.850725i −0.0229008 + 0.0396653i
\(461\) −3.47332 + 19.6982i −0.161768 + 0.917434i 0.790566 + 0.612377i \(0.209787\pi\)
−0.952334 + 0.305057i \(0.901324\pi\)
\(462\) −9.37308 + 11.7253i −0.436075 + 0.545511i
\(463\) 12.0406 + 4.38242i 0.559574 + 0.203668i 0.606295 0.795240i \(-0.292655\pi\)
−0.0467212 + 0.998908i \(0.514877\pi\)
\(464\) 0.221437 + 1.25583i 0.0102799 + 0.0583005i
\(465\) −4.99845 1.29271i −0.231798 0.0599480i
\(466\) 7.97695 + 6.69346i 0.369525 + 0.310069i
\(467\) 13.8762 + 24.0342i 0.642112 + 1.11217i 0.984961 + 0.172780i \(0.0552748\pi\)
−0.342849 + 0.939391i \(0.611392\pi\)
\(468\) −13.2706 15.2663i −0.613432 0.705685i
\(469\) −0.520596 + 7.19543i −0.0240389 + 0.332254i
\(470\) −1.37672 1.15520i −0.0635033 0.0532856i
\(471\) 13.9718 + 19.5879i 0.643787 + 0.902565i
\(472\) 10.3150 8.65530i 0.474786 0.398392i
\(473\) −9.65750 + 8.10360i −0.444052 + 0.372604i
\(474\) 5.10382 11.1992i 0.234426 0.514396i
\(475\) 6.90294 + 5.79226i 0.316729 + 0.265767i
\(476\) 1.42172 0.689180i 0.0651645 0.0315885i
\(477\) 19.2422 23.7617i 0.881039 1.08797i
\(478\) −4.80703 8.32602i −0.219869 0.380823i
\(479\) −10.9401 9.17986i −0.499867 0.419438i 0.357680 0.933844i \(-0.383568\pi\)
−0.857547 + 0.514406i \(0.828012\pi\)
\(480\) −2.40258 + 2.44486i −0.109662 + 0.111592i
\(481\) −0.635036 3.60147i −0.0289551 0.164213i
\(482\) −26.8336 9.76662i −1.22224 0.444857i
\(483\) −1.42030 + 1.77673i −0.0646259 + 0.0808441i
\(484\) −0.0468215 + 0.265538i −0.00212825 + 0.0120699i
\(485\) 8.24816 14.2862i 0.374530 0.648705i
\(486\) 13.1470 + 8.37595i 0.596360 + 0.379941i
\(487\) −18.8491 32.6476i −0.854134 1.47940i −0.877446 0.479675i \(-0.840755\pi\)
0.0233124 0.999728i \(-0.492579\pi\)
\(488\) 5.62961 + 4.72380i 0.254840 + 0.213836i
\(489\) 20.3756 9.71854i 0.921415 0.439488i
\(490\) 12.2002 + 6.56264i 0.551148 + 0.296470i
\(491\) −9.35212 + 7.84736i −0.422055 + 0.354146i −0.828944 0.559331i \(-0.811058\pi\)
0.406889 + 0.913478i \(0.366614\pi\)
\(492\) 4.07161 + 1.05301i 0.183562 + 0.0474733i
\(493\) −0.583351 0.489489i −0.0262728 0.0220455i
\(494\) −56.0811 −2.52321
\(495\) 6.96950 + 18.1566i 0.313256 + 0.816081i
\(496\) 0.753095 + 1.30440i 0.0338150 + 0.0585693i
\(497\) −6.79563 1.71176i −0.304826 0.0767830i
\(498\) 13.0352 1.25509i 0.584122 0.0562421i
\(499\) −4.29316 1.56258i −0.192188 0.0699508i 0.244133 0.969742i \(-0.421497\pi\)
−0.436321 + 0.899791i \(0.643719\pi\)
\(500\) −9.22264 + 7.73871i −0.412449 + 0.346086i
\(501\) 39.2614 3.78028i 1.75407 0.168890i
\(502\) −7.02265 + 2.55604i −0.313436 + 0.114081i
\(503\) −2.44425 4.23357i −0.108984 0.188766i 0.806375 0.591405i \(-0.201426\pi\)
−0.915359 + 0.402639i \(0.868093\pi\)
\(504\) −6.35052 + 4.76140i −0.282874 + 0.212090i
\(505\) −16.7530 + 29.0171i −0.745499 + 1.29124i
\(506\) 0.282346 1.60127i 0.0125518 0.0711850i
\(507\) 54.4366 + 14.0785i 2.41762 + 0.625249i
\(508\) 8.49010 + 3.09015i 0.376687 + 0.137103i
\(509\) 4.68933 3.93481i 0.207851 0.174407i −0.532920 0.846166i \(-0.678905\pi\)
0.740770 + 0.671758i \(0.234461\pi\)
\(510\) 0.160612 2.04066i 0.00711201 0.0903617i
\(511\) −2.49065 + 2.56673i −0.110180 + 0.113545i
\(512\) 1.00000 0.0441942
\(513\) 41.4388 12.2742i 1.82957 0.541917i
\(514\) −13.9386 24.1423i −0.614803 1.06487i
\(515\) 29.4209 10.7083i 1.29644 0.471866i
\(516\) −6.01663 + 2.86975i −0.264867 + 0.126334i
\(517\) 2.79531 + 1.01741i 0.122938 + 0.0447457i
\(518\) −1.42748 + 0.146554i −0.0627200 + 0.00643923i
\(519\) 23.6717 + 6.12202i 1.03907 + 0.268727i
\(520\) 2.31715 13.1412i 0.101614 0.576279i
\(521\) 17.2963 0.757763 0.378881 0.925445i \(-0.376309\pi\)
0.378881 + 0.925445i \(0.376309\pi\)
\(522\) 3.34594 + 1.85472i 0.146448 + 0.0811790i
\(523\) 34.1662 1.49398 0.746991 0.664834i \(-0.231498\pi\)
0.746991 + 0.664834i \(0.231498\pi\)
\(524\) 10.6528 + 8.93879i 0.465371 + 0.390493i
\(525\) −4.23946 + 2.58387i −0.185025 + 0.112770i
\(526\) 2.12582 + 12.0561i 0.0926903 + 0.525673i
\(527\) −0.845205 0.307629i −0.0368177 0.0134005i
\(528\) 2.35288 5.16286i 0.102396 0.224684i
\(529\) −3.95112 + 22.4079i −0.171788 + 0.974258i
\(530\) 20.1702 0.876139
\(531\) −0.704657 40.3896i −0.0305795 1.75276i
\(532\) −1.58798 + 21.9484i −0.0688478 + 0.951582i
\(533\) −15.3844 + 5.59945i −0.666370 + 0.242539i
\(534\) −20.9584 + 21.3272i −0.906957 + 0.922918i
\(535\) 5.38109 + 1.95856i 0.232645 + 0.0846758i
\(536\) −0.473491 2.68530i −0.0204517 0.115987i
\(537\) 0.0251057 0.0119747i 0.00108339 0.000516744i
\(538\) −4.04259 + 22.9266i −0.174288 + 0.988438i
\(539\) −22.6913 3.30074i −0.977382 0.142173i
\(540\) 1.16398 + 10.2173i 0.0500897 + 0.439682i
\(541\) 14.2140 24.6193i 0.611107 1.05847i −0.379948 0.925008i \(-0.624058\pi\)
0.991054 0.133460i \(-0.0426087\pi\)
\(542\) 18.9340 6.89140i 0.813283 0.296011i
\(543\) 6.17559 2.94557i 0.265020 0.126407i
\(544\) −0.457457 + 0.383852i −0.0196133 + 0.0164575i
\(545\) −30.2403 + 25.3746i −1.29535 + 1.08693i
\(546\) 9.87504 29.2781i 0.422613 1.25299i
\(547\) 12.8925 4.69250i 0.551245 0.200637i −0.0513547 0.998680i \(-0.516354\pi\)
0.602599 + 0.798044i \(0.294132\pi\)
\(548\) −5.59662 9.69362i −0.239076 0.414091i
\(549\) 21.6418 4.20654i 0.923648 0.179531i
\(550\) 1.77448 3.07349i 0.0756640 0.131054i
\(551\) 9.96672 3.62759i 0.424596 0.154540i
\(552\) 0.356530 0.782325i 0.0151749 0.0332980i
\(553\) 18.7015 1.92001i 0.795268 0.0816473i
\(554\) −1.77777 10.0822i −0.0755303 0.428353i
\(555\) −0.770982 + 1.69175i −0.0327264 + 0.0718106i
\(556\) −0.904733 + 5.13100i −0.0383692 + 0.217603i
\(557\) −8.78728 + 15.2200i −0.372329 + 0.644893i −0.989923 0.141604i \(-0.954774\pi\)
0.617594 + 0.786497i \(0.288107\pi\)
\(558\) 4.46293 + 0.706899i 0.188931 + 0.0299254i
\(559\) 12.9749 22.4731i 0.548778 0.950512i
\(560\) −5.07744 1.27896i −0.214561 0.0540460i
\(561\) 0.905433 + 3.26494i 0.0382274 + 0.137846i
\(562\) 3.16933 + 17.9742i 0.133690 + 0.758194i
\(563\) 4.65361 + 26.3919i 0.196126 + 1.11229i 0.910806 + 0.412835i \(0.135461\pi\)
−0.714679 + 0.699452i \(0.753427\pi\)
\(564\) 1.29626 + 0.890900i 0.0545822 + 0.0375136i
\(565\) 10.9369 + 9.17718i 0.460120 + 0.386087i
\(566\) 7.77524 0.326818
\(567\) −0.888819 + 23.7952i −0.0373269 + 0.999303i
\(568\) 2.64874 0.111139
\(569\) 1.94865 + 1.63511i 0.0816917 + 0.0685475i 0.682719 0.730681i \(-0.260797\pi\)
−0.601027 + 0.799228i \(0.705242\pi\)
\(570\) 23.4960 + 16.1485i 0.984139 + 0.676386i
\(571\) 3.72221 + 21.1097i 0.155770 + 0.883414i 0.958079 + 0.286505i \(0.0924936\pi\)
−0.802309 + 0.596909i \(0.796395\pi\)
\(572\) 3.83537 + 21.7514i 0.160365 + 0.909474i
\(573\) 8.27632 + 29.8439i 0.345748 + 1.24675i
\(574\) 1.75583 + 6.17951i 0.0732868 + 0.257928i
\(575\) 0.268886 0.465724i 0.0112133 0.0194220i
\(576\) 1.88798 2.33142i 0.0786659 0.0971426i
\(577\) 3.93668 6.81854i 0.163886 0.283859i −0.772373 0.635169i \(-0.780930\pi\)
0.936259 + 0.351310i \(0.114264\pi\)
\(578\) −2.89009 + 16.3905i −0.120212 + 0.681757i
\(579\) 1.14996 2.52334i 0.0477909 0.104866i
\(580\) 0.438232 + 2.48534i 0.0181966 + 0.103198i
\(581\) 11.7188 + 16.2117i 0.486179 + 0.672573i
\(582\) −5.98722 + 13.1376i −0.248178 + 0.544571i
\(583\) −31.3726 + 11.4187i −1.29932 + 0.472913i
\(584\) 0.675897 1.17069i 0.0279688 0.0484434i
\(585\) −26.2629 30.2126i −1.08584 1.24914i
\(586\) −8.45075 14.6371i −0.349097 0.604654i
\(587\) −38.9778 + 14.1868i −1.60879 + 0.585550i −0.981199 0.192997i \(-0.938179\pi\)
−0.627586 + 0.778547i \(0.715957\pi\)
\(588\) −11.1789 4.69382i −0.461011 0.193570i
\(589\) 9.59667 8.05256i 0.395424 0.331800i
\(590\) 20.4137 17.1292i 0.840420 0.705196i
\(591\) −29.7057 + 14.1687i −1.22193 + 0.582823i
\(592\) 0.509665 0.185503i 0.0209471 0.00762412i
\(593\) 4.52774 7.84227i 0.185932 0.322043i −0.757958 0.652303i \(-0.773803\pi\)
0.943890 + 0.330260i \(0.107136\pi\)
\(594\) −7.59461 15.2329i −0.311611 0.625014i
\(595\) 2.81364 1.36391i 0.115348 0.0559150i
\(596\) −2.00676 + 11.3809i −0.0822000 + 0.466180i
\(597\) −13.0137 + 6.20716i −0.532616 + 0.254042i
\(598\) 0.581172 + 3.29599i 0.0237659 + 0.134783i
\(599\) 25.9231 + 9.43522i 1.05919 + 0.385513i 0.812123 0.583486i \(-0.198312\pi\)
0.247065 + 0.968999i \(0.420534\pi\)
\(600\) 1.31528 1.33843i 0.0536960 0.0546410i
\(601\) −24.5814 + 8.94690i −1.00270 + 0.364952i −0.790624 0.612302i \(-0.790244\pi\)
−0.212073 + 0.977254i \(0.568021\pi\)
\(602\) −8.42788 5.71430i −0.343495 0.232897i
\(603\) −7.15451 3.96589i −0.291354 0.161504i
\(604\) 16.4923 0.671060
\(605\) −0.0926615 + 0.525509i −0.00376722 + 0.0213650i
\(606\) 12.1608 26.6840i 0.493997 1.08397i
\(607\) −10.2567 3.73312i −0.416305 0.151523i 0.125371 0.992110i \(-0.459988\pi\)
−0.541676 + 0.840587i \(0.682210\pi\)
\(608\) −1.44430 8.19103i −0.0585740 0.332190i
\(609\) 0.138856 + 5.84207i 0.00562673 + 0.236733i
\(610\) 11.1412 + 9.34858i 0.451094 + 0.378513i
\(611\) −6.12304 −0.247712
\(612\) 0.0312507 + 1.79123i 0.00126323 + 0.0724062i
\(613\) −0.382093 −0.0154326 −0.00771630 0.999970i \(-0.502456\pi\)
−0.00771630 + 0.999970i \(0.502456\pi\)
\(614\) 3.44600 19.5432i 0.139069 0.788700i
\(615\) 8.05786 + 2.08394i 0.324924 + 0.0840326i
\(616\) 8.62143 0.885131i 0.347367 0.0356630i
\(617\) 25.9351 + 9.43961i 1.04411 + 0.380024i 0.806436 0.591321i \(-0.201393\pi\)
0.237672 + 0.971345i \(0.423616\pi\)
\(618\) −24.7324 + 11.7966i −0.994884 + 0.474530i
\(619\) −6.72202 + 2.44661i −0.270181 + 0.0983377i −0.473558 0.880763i \(-0.657030\pi\)
0.203377 + 0.979100i \(0.434808\pi\)
\(620\) 1.49040 + 2.58145i 0.0598560 + 0.103674i
\(621\) −1.15081 2.30824i −0.0461803 0.0926264i
\(622\) 23.0657 0.924849
\(623\) −44.2918 11.1567i −1.77451 0.446985i
\(624\) −0.916341 + 11.6426i −0.0366830 + 0.466076i
\(625\) −14.1022 + 11.8332i −0.564089 + 0.473327i
\(626\) −7.28068 2.64995i −0.290994 0.105913i
\(627\) −45.6873 11.8158i −1.82458 0.471876i
\(628\) 2.41219 13.6802i 0.0962568 0.545899i
\(629\) −0.161944 + 0.280495i −0.00645713 + 0.0111841i
\(630\) −12.5679 + 9.42299i −0.500717 + 0.375421i
\(631\) 4.02933 + 6.97900i 0.160405 + 0.277830i 0.935014 0.354611i \(-0.115387\pi\)
−0.774609 + 0.632440i \(0.782053\pi\)
\(632\) −6.67713 + 2.43028i −0.265602 + 0.0966712i
\(633\) −8.09398 + 0.779327i −0.321707 + 0.0309754i
\(634\) 21.4591 18.0064i 0.852252 0.715124i
\(635\) 16.8022 + 6.11551i 0.666776 + 0.242687i
\(636\) −17.5717 + 1.69189i −0.696763 + 0.0670876i
\(637\) 46.2138 9.59029i 1.83106 0.379981i
\(638\) −2.08861 3.61757i −0.0826888 0.143221i
\(639\) 5.00077 6.17533i 0.197827 0.244292i
\(640\) 1.97904 0.0782283
\(641\) 14.7929 + 12.4127i 0.584283 + 0.490272i 0.886351 0.463015i \(-0.153232\pi\)
−0.302067 + 0.953287i \(0.597677\pi\)
\(642\) −4.85213 1.25487i −0.191498 0.0495257i
\(643\) 25.5593 21.4468i 1.00796 0.845780i 0.0198936 0.999802i \(-0.493667\pi\)
0.988067 + 0.154022i \(0.0492228\pi\)
\(644\) 1.30640 0.134124i 0.0514795 0.00528521i
\(645\) −11.9071 + 5.67935i −0.468843 + 0.223624i
\(646\) 3.80484 + 3.19264i 0.149700 + 0.125613i
\(647\) −13.1461 22.7697i −0.516827 0.895170i −0.999809 0.0195402i \(-0.993780\pi\)
0.482982 0.875630i \(-0.339554\pi\)
\(648\) −1.87105 8.80336i −0.0735020 0.345829i
\(649\) −22.0542 + 38.1990i −0.865704 + 1.49944i
\(650\) −1.26851 + 7.19407i −0.0497550 + 0.282174i
\(651\) 2.51415 + 6.42805i 0.0985374 + 0.251935i
\(652\) −12.2475 4.45771i −0.479647 0.174577i
\(653\) −2.34264 13.2858i −0.0916748 0.519913i −0.995716 0.0924676i \(-0.970525\pi\)
0.904041 0.427446i \(-0.140587\pi\)
\(654\) 24.2160 24.6421i 0.946919 0.963584i
\(655\) 21.0824 + 17.6902i 0.823756 + 0.691213i
\(656\) −1.21404 2.10278i −0.0474004 0.0820999i
\(657\) −1.45329 3.78604i −0.0566981 0.147707i
\(658\) −0.173379 + 2.39636i −0.00675902 + 0.0934200i
\(659\) 9.39594 + 7.88413i 0.366014 + 0.307122i 0.807182 0.590302i \(-0.200991\pi\)
−0.441168 + 0.897424i \(0.645436\pi\)
\(660\) 4.65643 10.2175i 0.181251 0.397715i
\(661\) 12.6624 10.6250i 0.492510 0.413265i −0.362415 0.932017i \(-0.618048\pi\)
0.854925 + 0.518752i \(0.173603\pi\)
\(662\) 7.81248 6.55545i 0.303641 0.254785i
\(663\) −4.04984 5.67771i −0.157283 0.220504i
\(664\) −5.79183 4.85992i −0.224767 0.188601i
\(665\) −3.14268 + 43.4366i −0.121868 + 1.68440i
\(666\) 0.529752 1.53847i 0.0205275 0.0596145i
\(667\) −0.316486 0.548170i −0.0122544 0.0212252i
\(668\) −17.4447 14.6378i −0.674955 0.566355i
\(669\) −2.61102 0.675268i −0.100948 0.0261074i
\(670\) −0.937057 5.31431i −0.0362017 0.205310i
\(671\) −22.6213 8.23347i −0.873285 0.317850i
\(672\) 4.53059 + 0.688296i 0.174771 + 0.0265516i
\(673\) −3.81185 + 21.6181i −0.146936 + 0.833315i 0.818856 + 0.573998i \(0.194608\pi\)
−0.965792 + 0.259317i \(0.916503\pi\)
\(674\) −1.36798 + 2.36942i −0.0526928 + 0.0912666i
\(675\) −0.637214 5.59339i −0.0245264 0.215290i
\(676\) −16.2315 28.1138i −0.624290 1.08130i
\(677\) 13.6785 + 11.4776i 0.525706 + 0.441120i 0.866616 0.498976i \(-0.166291\pi\)
−0.340910 + 0.940096i \(0.610735\pi\)
\(678\) −10.2977 7.07749i −0.395481 0.271809i
\(679\) −21.9384 + 2.25234i −0.841919 + 0.0864368i
\(680\) −0.905324 + 0.759657i −0.0347176 + 0.0291315i
\(681\) −5.44074 + 5.53649i −0.208489 + 0.212159i
\(682\) −3.77956 3.17143i −0.144727 0.121440i
\(683\) −22.2530 −0.851488 −0.425744 0.904844i \(-0.639988\pi\)
−0.425744 + 0.904844i \(0.639988\pi\)
\(684\) −21.8235 12.0972i −0.834444 0.462549i
\(685\) −11.0759 19.1840i −0.423189 0.732985i
\(686\) −2.44476 18.3582i −0.0933412 0.700919i
\(687\) −18.5219 25.9670i −0.706656 0.990704i
\(688\) 3.61651 + 1.31630i 0.137878 + 0.0501835i
\(689\) 52.6430 44.1727i 2.00554 1.68285i
\(690\) 0.705587 1.54825i 0.0268612 0.0589409i
\(691\) −29.9930 + 10.9166i −1.14099 + 0.415285i −0.842270 0.539056i \(-0.818781\pi\)
−0.298718 + 0.954342i \(0.596559\pi\)
\(692\) −7.05826 12.2253i −0.268315 0.464735i
\(693\) 14.2135 21.7713i 0.539926 0.827024i
\(694\) −1.21645 + 2.10696i −0.0461759 + 0.0799790i
\(695\) −1.79050 + 10.1544i −0.0679175 + 0.385180i
\(696\) −0.590245 2.12839i −0.0223732 0.0806764i
\(697\) 1.36253 + 0.495920i 0.0516095 + 0.0187843i
\(698\) −3.28743 + 2.75848i −0.124431 + 0.104410i
\(699\) −14.8640 10.2159i −0.562209 0.386399i
\(700\) 2.77961 + 0.700160i 0.105059 + 0.0264636i
\(701\) −26.6856 −1.00790 −0.503950 0.863733i \(-0.668121\pi\)
−0.503950 + 0.863733i \(0.668121\pi\)
\(702\) 25.4137 + 24.1173i 0.959179 + 0.910250i
\(703\) −2.25557 3.90675i −0.0850703 0.147346i
\(704\) −3.07817 + 1.12036i −0.116013 + 0.0422253i
\(705\) 2.56534 + 1.76312i 0.0966162 + 0.0664031i
\(706\) 20.4486 + 7.44269i 0.769594 + 0.280109i
\(707\) 44.5596 4.57477i 1.67584 0.172052i
\(708\) −16.3470 + 16.6347i −0.614359 + 0.625171i
\(709\) 0.249226 1.41343i 0.00935986 0.0530824i −0.979770 0.200126i \(-0.935865\pi\)
0.989130 + 0.147044i \(0.0469759\pi\)
\(710\) 5.24196 0.196727
\(711\) −6.94030 + 20.1555i −0.260281 + 0.755891i
\(712\) 17.2637 0.646983
\(713\) −0.572715 0.480565i −0.0214484 0.0179973i
\(714\) −2.33675 + 1.42421i −0.0874508 + 0.0532997i
\(715\) 7.59033 + 43.0469i 0.283862 + 1.60986i
\(716\) −0.0150906 0.00549254i −0.000563964 0.000205266i
\(717\) 9.66983 + 13.5567i 0.361127 + 0.506285i
\(718\) −5.04296 + 28.6000i −0.188202 + 1.06734i
\(719\) −41.1637 −1.53515 −0.767573 0.640962i \(-0.778536\pi\)
−0.767573 + 0.640962i \(0.778536\pi\)
\(720\) 3.73638 4.61397i 0.139247 0.171953i
\(721\) −34.6443 23.4896i −1.29022 0.874800i
\(722\) −47.1527 + 17.1622i −1.75484 + 0.638711i
\(723\) 47.8844 + 12.3840i 1.78084 + 0.460565i
\(724\) −3.71206 1.35108i −0.137958 0.0502124i
\(725\) −0.239907 1.36058i −0.00890993 0.0505307i
\(726\) 0.0366440 0.465580i 0.00135999 0.0172793i
\(727\) −3.36954 + 19.1096i −0.124969 + 0.708737i 0.856357 + 0.516385i \(0.172723\pi\)
−0.981326 + 0.192352i \(0.938389\pi\)
\(728\) −16.0527 + 7.78155i −0.594952 + 0.288403i
\(729\) −24.0569 12.2584i −0.890995 0.454013i
\(730\) 1.33763 2.31684i 0.0495078 0.0857500i
\(731\) −2.15966 + 0.786052i −0.0798779 + 0.0290732i
\(732\) −10.4900 7.20967i −0.387723 0.266477i
\(733\) −18.4826 + 15.5088i −0.682672 + 0.572830i −0.916786 0.399379i \(-0.869226\pi\)
0.234114 + 0.972209i \(0.424781\pi\)
\(734\) 16.5140 13.8569i 0.609542 0.511467i
\(735\) −22.1235 9.28924i −0.816037 0.342639i
\(736\) −0.466434 + 0.169768i −0.0171930 + 0.00625774i
\(737\) 4.46600 + 7.73534i 0.164507 + 0.284935i
\(738\) −7.19457 1.13957i −0.264836 0.0419482i
\(739\) −19.8802 + 34.4335i −0.731304 + 1.26666i 0.225022 + 0.974354i \(0.427755\pi\)
−0.956326 + 0.292302i \(0.905579\pi\)
\(740\) 1.00865 0.367117i 0.0370785 0.0134955i
\(741\) 96.6881 9.30959i 3.55193 0.341996i
\(742\) −15.7972 21.8536i −0.579932 0.802270i
\(743\) 0.703175 + 3.98791i 0.0257970 + 0.146302i 0.994986 0.100017i \(-0.0318899\pi\)
−0.969189 + 0.246320i \(0.920779\pi\)
\(744\) −1.51493 2.12387i −0.0555400 0.0778648i
\(745\) −3.97145 + 22.5232i −0.145503 + 0.825187i
\(746\) −0.449046 + 0.777771i −0.0164407 + 0.0284762i
\(747\) −22.2654 + 4.32775i −0.814648 + 0.158344i
\(748\) 0.978078 1.69408i 0.0357621 0.0619417i
\(749\) −2.09242 7.36411i −0.0764552 0.269079i
\(750\) 14.6159 14.8731i 0.533697 0.543089i
\(751\) −2.84153 16.1151i −0.103689 0.588050i −0.991736 0.128297i \(-0.959049\pi\)
0.888047 0.459753i \(-0.152062\pi\)
\(752\) −0.157691 0.894312i −0.00575041 0.0326122i
\(753\) 11.6833 5.57258i 0.425763 0.203076i
\(754\) 6.58662 + 5.52683i 0.239871 + 0.201275i
\(755\) 32.6388 1.18785
\(756\) 10.1584 9.26323i 0.369457 0.336900i
\(757\) 14.9344 0.542799 0.271400 0.962467i \(-0.412514\pi\)
0.271400 + 0.962467i \(0.412514\pi\)
\(758\) −18.8159 15.7884i −0.683426 0.573462i
\(759\) −0.220973 + 2.80758i −0.00802082 + 0.101909i
\(760\) −2.85832 16.2103i −0.103682 0.588011i
\(761\) 5.62078 + 31.8770i 0.203753 + 1.15554i 0.899390 + 0.437147i \(0.144011\pi\)
−0.695637 + 0.718394i \(0.744878\pi\)
\(762\) −15.1506 3.91827i −0.548847 0.141944i
\(763\) 51.1762 + 12.8908i 1.85270 + 0.466680i
\(764\) 8.94035 15.4851i 0.323451 0.560233i
\(765\) 0.0618462 + 3.54491i 0.00223606 + 0.128167i
\(766\) 4.53623 7.85698i 0.163901 0.283884i
\(767\) 15.7657 89.4119i 0.569268 3.22848i
\(768\) −1.72408 + 0.166002i −0.0622123 + 0.00599009i
\(769\) 1.34579 + 7.63237i 0.0485305 + 0.275230i 0.999411 0.0343292i \(-0.0109295\pi\)
−0.950880 + 0.309560i \(0.899818\pi\)
\(770\) 17.0621 1.75171i 0.614877 0.0631272i
\(771\) 28.0388 + 39.3093i 1.00979 + 1.41569i
\(772\) −1.50445 + 0.547576i −0.0541465 + 0.0197077i
\(773\) −22.0860 + 38.2540i −0.794377 + 1.37590i 0.128857 + 0.991663i \(0.458869\pi\)
−0.923234 + 0.384238i \(0.874464\pi\)
\(774\) 9.89675 5.94645i 0.355731 0.213741i
\(775\) −0.815912 1.41320i −0.0293084 0.0507637i
\(776\) 7.83284 2.85092i 0.281182 0.102342i
\(777\) 2.43676 0.489637i 0.0874184 0.0175656i
\(778\) 23.9971 20.1360i 0.860338 0.721909i
\(779\) −15.4705 + 12.9813i −0.554289 + 0.465104i
\(780\) −1.81347 + 23.0411i −0.0649327 + 0.825003i
\(781\) −8.15328 + 2.96755i −0.291747 + 0.106187i
\(782\) 0.148208 0.256703i 0.00529990 0.00917969i
\(783\) −6.07655 2.64225i −0.217158 0.0944263i
\(784\) 2.59091 + 6.50286i 0.0925325 + 0.232245i
\(785\) 4.77381 27.0736i 0.170385 0.966299i
\(786\) −19.8502 13.6428i −0.708032 0.486622i
\(787\) −5.12020 29.0381i −0.182515 1.03510i −0.929106 0.369812i \(-0.879422\pi\)
0.746591 0.665283i \(-0.231689\pi\)
\(788\) 17.8556 + 6.49892i 0.636081 + 0.231515i
\(789\) −5.66643 20.4328i −0.201730 0.727428i
\(790\) −13.2143 + 4.80961i −0.470143 + 0.171118i
\(791\) 1.37736 19.0372i 0.0489732 0.676885i
\(792\) −3.19949 + 9.29175i −0.113689 + 0.330168i
\(793\) 49.5511 1.75961
\(794\) 0.667635 3.78634i 0.0236935 0.134372i
\(795\) −34.7750 + 3.34830i −1.23334 + 0.118752i
\(796\) 7.82235 + 2.84710i 0.277256 + 0.100913i
\(797\) −1.33276 7.55843i −0.0472086 0.267733i 0.952063 0.305903i \(-0.0989584\pi\)
−0.999271 + 0.0381697i \(0.987847\pi\)
\(798\) −0.905674 38.1043i −0.0320605 1.34888i
\(799\) 0.415420 + 0.348579i 0.0146965 + 0.0123318i
\(800\) −1.08341 −0.0383044
\(801\) 32.5935 40.2489i 1.15163 1.42212i
\(802\) 9.61726 0.339597
\(803\) −0.768933 + 4.36083i −0.0271350 + 0.153890i
\(804\) 1.26210 + 4.55107i 0.0445109 + 0.160504i
\(805\) 2.58542 0.265436i 0.0911240 0.00935537i
\(806\) 9.54322 + 3.47345i 0.336146 + 0.122347i
\(807\) 3.16386 40.1984i 0.111373 1.41505i
\(808\) −15.9094 + 5.79056i −0.559692 + 0.203711i
\(809\) −1.28247 2.22131i −0.0450893 0.0780970i 0.842600 0.538540i \(-0.181024\pi\)
−0.887689 + 0.460443i \(0.847691\pi\)
\(810\) −3.70289 17.4222i −0.130106 0.612153i
\(811\) −30.9165 −1.08563 −0.542813 0.839853i \(-0.682641\pi\)
−0.542813 + 0.839853i \(0.682641\pi\)
\(812\) 2.34953 2.42130i 0.0824525 0.0849710i
\(813\) −31.4996 + 15.0244i −1.10474 + 0.526928i
\(814\) −1.36101 + 1.14202i −0.0477032 + 0.0400278i
\(815\) −24.2382 8.82197i −0.849026 0.309020i
\(816\) 0.724971 0.737729i 0.0253791 0.0258257i
\(817\) 5.55854 31.5240i 0.194469 1.10289i
\(818\) 2.47033 4.27874i 0.0863732 0.149603i
\(819\) −12.1651 + 52.1170i −0.425083 + 1.82112i
\(820\) −2.40264 4.16149i −0.0839037 0.145325i
\(821\) −25.5709 + 9.30705i −0.892431 + 0.324818i −0.747216 0.664582i \(-0.768610\pi\)
−0.145216 + 0.989400i \(0.546388\pi\)
\(822\) 11.2582 + 15.7835i 0.392674 + 0.550513i
\(823\) −21.5691 + 18.0986i −0.751851 + 0.630877i −0.935992 0.352022i \(-0.885494\pi\)
0.184141 + 0.982900i \(0.441050\pi\)
\(824\) 14.8663 + 5.41089i 0.517892 + 0.188497i
\(825\) −2.54913 + 5.59350i −0.0887494 + 0.194741i
\(826\) −34.5466 8.70199i −1.20203 0.302781i
\(827\) 20.5074 + 35.5199i 0.713112 + 1.23515i 0.963683 + 0.267048i \(0.0860483\pi\)
−0.250571 + 0.968098i \(0.580618\pi\)
\(828\) −0.484818 + 1.40797i −0.0168486 + 0.0489305i
\(829\) 1.64018 0.0569657 0.0284829 0.999594i \(-0.490932\pi\)
0.0284829 + 0.999594i \(0.490932\pi\)
\(830\) −11.4622 9.61796i −0.397860 0.333844i
\(831\) 4.73869 + 17.0875i 0.164383 + 0.592757i
\(832\) 5.16515 4.33408i 0.179070 0.150257i
\(833\) −3.68136 1.98025i −0.127552 0.0686117i
\(834\) 0.708073 8.99642i 0.0245185 0.311521i
\(835\) −34.5237 28.9688i −1.19474 1.00251i
\(836\) 13.6227 + 23.5953i 0.471152 + 0.816059i
\(837\) −7.81179 0.477891i −0.270015 0.0165183i
\(838\) −12.7057 + 22.0069i −0.438912 + 0.760217i
\(839\) −4.26667 + 24.1975i −0.147302 + 0.835389i 0.818188 + 0.574950i \(0.194979\pi\)
−0.965490 + 0.260439i \(0.916133\pi\)
\(840\) 8.96621 + 1.36216i 0.309364 + 0.0469991i
\(841\) 25.7230 + 9.36241i 0.887000 + 0.322842i
\(842\) 2.58061 + 14.6353i 0.0889335 + 0.504367i
\(843\) −8.44792 30.4627i −0.290962 1.04919i
\(844\) 3.59633 + 3.01768i 0.123791 + 0.103873i
\(845\) −32.1228 55.6383i −1.10506 1.91402i
\(846\) −2.38274 1.32080i −0.0819202 0.0454100i
\(847\) 0.641939 0.311180i 0.0220573 0.0106923i
\(848\) 7.80748 + 6.55125i 0.268110 + 0.224971i
\(849\) −13.4051 + 1.29071i −0.460062 + 0.0442970i
\(850\) 0.495614 0.415870i 0.0169994 0.0142642i
\(851\) −0.206233 + 0.173050i −0.00706956 + 0.00593207i
\(852\) −4.56663 + 0.439697i −0.156450 + 0.0150638i
\(853\) −34.2916 28.7741i −1.17412 0.985205i −1.00000 0.000481297i \(-0.999847\pi\)
−0.174122 0.984724i \(-0.555709\pi\)
\(854\) 1.40308 19.3928i 0.0480125 0.663606i
\(855\) −43.1896 23.9409i −1.47705 0.818761i
\(856\) 1.44677 + 2.50589i 0.0494497 + 0.0856494i
\(857\) 32.4827 + 27.2562i 1.10959 + 0.931055i 0.998032 0.0627027i \(-0.0199720\pi\)
0.111556 + 0.993758i \(0.464416\pi\)
\(858\) −10.2233 36.8645i −0.349016 1.25853i
\(859\) −4.63711 26.2983i −0.158216 0.897288i −0.955786 0.294062i \(-0.904993\pi\)
0.797570 0.603226i \(-0.206118\pi\)
\(860\) 7.15720 + 2.60501i 0.244059 + 0.0888300i
\(861\) −4.05299 10.3625i −0.138126 0.353152i
\(862\) 1.70128 9.64846i 0.0579459 0.328628i
\(863\) −19.2799 + 33.3937i −0.656294 + 1.13673i 0.325274 + 0.945620i \(0.394544\pi\)
−0.981568 + 0.191115i \(0.938790\pi\)
\(864\) −2.86800 + 4.33296i −0.0975715 + 0.147410i
\(865\) −13.9686 24.1942i −0.474945 0.822629i
\(866\) 20.9604 + 17.5879i 0.712264 + 0.597660i
\(867\) 2.26188 28.7383i 0.0768174 0.976005i
\(868\) 1.62962 3.63656i 0.0553130 0.123433i
\(869\) 17.8306 14.9616i 0.604861 0.507538i
\(870\) −1.16812 4.21216i −0.0396029 0.142806i
\(871\) −14.0840 11.8179i −0.477217 0.400433i
\(872\) −19.9470 −0.675491
\(873\) 8.14155 23.6441i 0.275550 0.800232i
\(874\) 2.06425 + 3.57538i 0.0698242 + 0.120939i
\(875\) 30.8881 + 7.78046i 1.04421 + 0.263027i
\(876\) −0.970963 + 2.13056i −0.0328058 + 0.0719849i
\(877\) 13.6722 + 4.97628i 0.461678 + 0.168037i 0.562379 0.826880i \(-0.309886\pi\)
−0.100701 + 0.994917i \(0.532109\pi\)
\(878\) −24.7810 + 20.7937i −0.836319 + 0.701755i
\(879\) 16.9995 + 23.8327i 0.573380 + 0.803857i
\(880\) −6.09182 + 2.21724i −0.205355 + 0.0747432i
\(881\) 0.548666 + 0.950317i 0.0184850 + 0.0320170i 0.875120 0.483906i \(-0.160782\pi\)
−0.856635 + 0.515923i \(0.827449\pi\)
\(882\) 20.0525 + 6.23678i 0.675203 + 0.210003i
\(883\) 5.25393 9.10007i 0.176809 0.306242i −0.763977 0.645244i \(-0.776756\pi\)
0.940786 + 0.339002i \(0.110089\pi\)
\(884\) −0.699191 + 3.96531i −0.0235163 + 0.133368i
\(885\) −32.3514 + 32.9207i −1.08748 + 1.10662i
\(886\) −28.6959 10.4445i −0.964058 0.350888i
\(887\) −16.2769 + 13.6579i −0.546525 + 0.458589i −0.873762 0.486354i \(-0.838327\pi\)
0.327238 + 0.944942i \(0.393882\pi\)
\(888\) −0.847907 + 0.404427i −0.0284539 + 0.0135717i
\(889\) −6.53348 22.9941i −0.219126 0.771198i
\(890\) 34.1654 1.14523
\(891\) 15.6224 + 25.0020i 0.523370 + 0.837599i
\(892\) 0.778536 + 1.34846i 0.0260673 + 0.0451499i
\(893\) −7.09758 + 2.58331i −0.237511 + 0.0864471i
\(894\) 1.57055 19.9547i 0.0525271 0.667384i
\(895\) −0.0298649 0.0108699i −0.000998275 0.000363342i
\(896\) −1.54997 2.14420i −0.0517808 0.0716328i
\(897\) −1.54913 5.58606i −0.0517238 0.186513i
\(898\) 2.00437 11.3673i 0.0668866 0.379333i
\(899\) −1.92070 −0.0640589
\(900\) −2.04546 + 2.52589i −0.0681820 + 0.0841963i
\(901\) −6.08630 −0.202764
\(902\) 6.09292 + 5.11257i 0.202872 + 0.170230i
\(903\) 15.4789 + 8.45285i 0.515106 + 0.281293i
\(904\) 1.25273 + 7.10459i 0.0416652 + 0.236295i
\(905\) −7.34630 2.67383i −0.244199 0.0888813i
\(906\) −28.4339 + 2.73775i −0.944654 + 0.0909557i
\(907\) −9.04461 + 51.2946i −0.300321 + 1.70321i 0.344427 + 0.938813i \(0.388073\pi\)
−0.644749 + 0.764395i \(0.723038\pi\)
\(908\) 4.48160 0.148727
\(909\) −16.5365 + 48.0241i −0.548480 + 1.59286i
\(910\) −31.7689 + 15.4000i −1.05313 + 0.510504i
\(911\) 16.4653 5.99289i 0.545521 0.198553i −0.0545343 0.998512i \(-0.517367\pi\)
0.600055 + 0.799958i \(0.295145\pi\)
\(912\) 3.84981 + 13.8822i 0.127480 + 0.459686i
\(913\) 23.2731 + 8.47073i 0.770228 + 0.280340i
\(914\) −2.19460 12.4462i −0.0725909 0.411684i
\(915\) −20.7602 14.2682i −0.686311 0.471693i
\(916\) −3.19775 + 18.1353i −0.105657 + 0.599209i
\(917\) 2.65504 36.6967i 0.0876770 1.21183i
\(918\) −0.351227 3.08303i −0.0115922 0.101755i
\(919\) 6.90514 11.9601i 0.227780 0.394526i −0.729370 0.684119i \(-0.760187\pi\)
0.957150 + 0.289593i \(0.0935201\pi\)
\(920\) −0.923091 + 0.335978i −0.0304334 + 0.0110769i
\(921\) −2.69695 + 34.2661i −0.0888674 + 1.12911i
\(922\) −15.3224 + 12.8571i −0.504618 + 0.423425i
\(923\) 13.6812 11.4799i 0.450321 0.377864i
\(924\) −14.7171 + 2.95721i −0.484157 + 0.0972852i
\(925\) −0.552177 + 0.200976i −0.0181555 + 0.00660805i
\(926\) 6.40667 + 11.0967i 0.210536 + 0.364659i
\(927\) 40.6823 24.4439i 1.33618 0.802844i
\(928\) −0.637602 + 1.10436i −0.0209303 + 0.0362524i
\(929\) 36.0888 13.1353i 1.18404 0.430954i 0.326410 0.945228i \(-0.394161\pi\)
0.857626 + 0.514275i \(0.171939\pi\)
\(930\) −2.99810 4.20322i −0.0983115 0.137829i
\(931\) 49.5230 30.6143i 1.62305 1.00334i
\(932\) 1.80823 + 10.2550i 0.0592305 + 0.335913i
\(933\) −39.7670 + 3.82895i −1.30191 + 0.125354i
\(934\) −4.81914 + 27.3307i −0.157687 + 0.894287i
\(935\) 1.93565 3.35265i 0.0633026 0.109643i
\(936\) −0.352852 20.2248i −0.0115333 0.661069i
\(937\) −11.1865 + 19.3756i −0.365447 + 0.632973i −0.988848 0.148930i \(-0.952417\pi\)
0.623401 + 0.781902i \(0.285750\pi\)
\(938\) −5.02394 + 5.17739i −0.164037 + 0.169048i
\(939\) 12.9923 + 3.36011i 0.423989 + 0.109653i
\(940\) −0.312077 1.76988i −0.0101788 0.0577270i
\(941\) −6.46932 36.6893i −0.210894 1.19604i −0.887892 0.460053i \(-0.847830\pi\)
0.676998 0.735985i \(-0.263281\pi\)
\(942\) −1.88785 + 23.9861i −0.0615096 + 0.781511i
\(943\) 0.923258 + 0.774705i 0.0300654 + 0.0252279i
\(944\) 13.4653 0.438257
\(945\) 20.1038 18.3323i 0.653977 0.596349i
\(946\) −12.6070 −0.409888
\(947\) −24.5597 20.6080i −0.798081 0.669670i 0.149650 0.988739i \(-0.452185\pi\)
−0.947731 + 0.319069i \(0.896630\pi\)
\(948\) 11.1085 5.29841i 0.360786 0.172084i
\(949\) −1.58274 8.97618i −0.0513780 0.291379i
\(950\) 1.56477 + 8.87425i 0.0507679 + 0.287919i
\(951\) −34.0081 + 34.6066i −1.10279 + 1.12220i
\(952\) 1.53210 + 0.385922i 0.0496556 + 0.0125078i
\(953\) −9.41490 + 16.3071i −0.304979 + 0.528238i −0.977257 0.212060i \(-0.931983\pi\)
0.672278 + 0.740299i \(0.265316\pi\)
\(954\) 30.0141 5.83388i 0.971743 0.188879i
\(955\) 17.6933 30.6457i 0.572541 0.991671i
\(956\) 1.66946 9.46800i 0.0539943 0.306217i
\(957\) 4.20145 + 5.89026i 0.135813 + 0.190405i
\(958\) −2.47993 14.0644i −0.0801228 0.454399i
\(959\) −12.1105 + 27.0251i −0.391069 + 0.872685i
\(960\) −3.41201 + 0.328525i −0.110122 + 0.0106031i
\(961\) 26.9987 9.82671i 0.870925 0.316991i
\(962\) 1.82851 3.16708i 0.0589536 0.102111i
\(963\) 8.57376 + 1.35803i 0.276285 + 0.0437618i
\(964\) −14.2778 24.7299i −0.459858 0.796498i
\(965\) −2.97737 + 1.08367i −0.0958449 + 0.0348847i
\(966\) −2.23007 + 0.448105i −0.0717515 + 0.0144176i
\(967\) −3.87252 + 3.24943i −0.124532 + 0.104495i −0.702927 0.711262i \(-0.748124\pi\)
0.578395 + 0.815757i \(0.303679\pi\)
\(968\) −0.206552 + 0.173318i −0.00663883 + 0.00557064i
\(969\) −7.08983 4.87275i −0.227758 0.156535i
\(970\) 15.5015 5.64208i 0.497722 0.181156i
\(971\) 14.7914 25.6194i 0.474677 0.822165i −0.524902 0.851163i \(-0.675898\pi\)
0.999579 + 0.0289974i \(0.00923145\pi\)
\(972\) 4.68722 + 14.8671i 0.150343 + 0.476862i
\(973\) 12.4042 6.01294i 0.397660 0.192766i
\(974\) 6.54622 37.1255i 0.209754 1.18958i
\(975\) 0.992774 12.6137i 0.0317942 0.403962i
\(976\) 1.27613 + 7.23729i 0.0408479 + 0.231660i
\(977\) 23.1552 + 8.42780i 0.740800 + 0.269629i 0.684729 0.728797i \(-0.259920\pi\)
0.0560711 + 0.998427i \(0.482143\pi\)
\(978\) 21.8555 + 5.65233i 0.698863 + 0.180742i
\(979\) −53.1406 + 19.3416i −1.69838 + 0.618160i
\(980\) 5.12750 + 12.8694i 0.163792 + 0.411098i
\(981\) −37.6596 + 46.5049i −1.20238 + 1.48479i
\(982\) −12.2083 −0.389583
\(983\) −8.26380 + 46.8663i −0.263574 + 1.49480i 0.509490 + 0.860477i \(0.329834\pi\)
−0.773064 + 0.634328i \(0.781277\pi\)
\(984\) 2.44217 + 3.42383i 0.0778536 + 0.109148i
\(985\) 35.3370 + 12.8616i 1.12593 + 0.409805i
\(986\) −0.132235 0.749941i −0.00421122 0.0238830i
\(987\) −0.0988832 4.16030i −0.00314749 0.132424i
\(988\) −42.9606 36.0482i −1.36676 1.14685i
\(989\) −1.91033 −0.0607449
\(990\) −6.33192 + 18.3887i −0.201242 + 0.584432i
\(991\) 27.3416 0.868536 0.434268 0.900784i \(-0.357007\pi\)
0.434268 + 0.900784i \(0.357007\pi\)
\(992\) −0.261547 + 1.48331i −0.00830413 + 0.0470951i
\(993\) −12.3811 + 12.5990i −0.392903 + 0.399817i
\(994\) −4.10546 5.67943i −0.130217 0.180141i
\(995\) 15.4807 + 5.63452i 0.490772 + 0.178626i
\(996\) 10.7923 + 7.41742i 0.341968 + 0.235030i
\(997\) −12.9585 + 4.71650i −0.410399 + 0.149373i −0.538966 0.842328i \(-0.681185\pi\)
0.128566 + 0.991701i \(0.458962\pi\)
\(998\) −2.28434 3.95660i −0.0723097 0.125244i
\(999\) −0.657944 + 2.74038i −0.0208164 + 0.0867018i
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 378.2.v.b.79.3 yes 72
7.4 even 3 378.2.w.a.25.7 yes 72
27.13 even 9 378.2.w.a.121.7 yes 72
189.67 even 9 inner 378.2.v.b.67.3 72
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
378.2.v.b.67.3 72 189.67 even 9 inner
378.2.v.b.79.3 yes 72 1.1 even 1 trivial
378.2.w.a.25.7 yes 72 7.4 even 3
378.2.w.a.121.7 yes 72 27.13 even 9