Properties

Label 378.2.u.e.85.3
Level $378$
Weight $2$
Character 378.85
Analytic conductor $3.018$
Analytic rank $0$
Dimension $36$
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(43,378)]
 
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([4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("378.43");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 378.u (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: \(36\)
Relative dimension: \(6\) over \(\Q(\zeta_{9})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 85.3
Character \(\chi\) \(=\) 378.85
Dual form 378.2.u.e.169.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.939693 + 0.342020i) q^{2} +(0.873169 - 1.49585i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.605889 + 3.43617i) q^{5} +(1.33212 - 1.10700i) q^{6} +(0.766044 - 0.642788i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-1.47515 - 2.61227i) q^{9} +O(q^{10})\) \(q+(0.939693 + 0.342020i) q^{2} +(0.873169 - 1.49585i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.605889 + 3.43617i) q^{5} +(1.33212 - 1.10700i) q^{6} +(0.766044 - 0.642788i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-1.47515 - 2.61227i) q^{9} +(-1.74459 + 3.02172i) q^{10} +(0.791459 + 4.48859i) q^{11} +(1.63040 - 0.584627i) q^{12} +(5.50344 - 2.00309i) q^{13} +(0.939693 - 0.342020i) q^{14} +(4.61096 + 3.90668i) q^{15} +(0.173648 + 0.984808i) q^{16} +(0.614096 - 1.06365i) q^{17} +(-0.492740 - 2.95926i) q^{18} +(-0.418950 - 0.725643i) q^{19} +(-2.67286 + 2.24280i) q^{20} +(-0.292629 - 1.70715i) q^{21} +(-0.791459 + 4.48859i) q^{22} +(-5.66011 - 4.74939i) q^{23} +(1.73203 + 0.00826063i) q^{24} +(-6.74169 - 2.45378i) q^{25} +5.85663 q^{26} +(-5.19562 - 0.0743434i) q^{27} +1.00000 q^{28} +(0.897215 + 0.326560i) q^{29} +(2.99672 + 5.24812i) q^{30} +(-6.47125 - 5.43002i) q^{31} +(-0.173648 + 0.984808i) q^{32} +(7.40534 + 2.73539i) q^{33} +(0.940850 - 0.789467i) q^{34} +(1.74459 + 3.02172i) q^{35} +(0.549101 - 2.94932i) q^{36} +(-0.215229 + 0.372787i) q^{37} +(-0.145500 - 0.825171i) q^{38} +(1.80911 - 9.98136i) q^{39} +(-3.27875 + 1.19337i) q^{40} +(6.55650 - 2.38637i) q^{41} +(0.308899 - 1.70428i) q^{42} +(1.23170 + 6.98532i) q^{43} +(-2.27891 + 3.94720i) q^{44} +(9.86996 - 3.48612i) q^{45} +(-3.69437 - 6.39884i) q^{46} +(-6.64681 + 5.57734i) q^{47} +(1.62475 + 0.600152i) q^{48} +(0.173648 - 0.984808i) q^{49} +(-5.49588 - 4.61159i) q^{50} +(-1.05485 - 1.84734i) q^{51} +(5.50344 + 2.00309i) q^{52} -7.79142 q^{53} +(-4.85686 - 1.84687i) q^{54} -15.9031 q^{55} +(0.939693 + 0.342020i) q^{56} +(-1.45127 - 0.00692158i) q^{57} +(0.731416 + 0.613731i) q^{58} +(1.92214 - 10.9010i) q^{59} +(1.02103 + 5.95656i) q^{60} +(8.16278 - 6.84939i) q^{61} +(-4.22381 - 7.31585i) q^{62} +(-2.80916 - 1.05290i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(3.54847 + 20.1244i) q^{65} +(6.02319 + 5.10320i) q^{66} +(-13.7773 + 5.01453i) q^{67} +(1.15412 - 0.420066i) q^{68} +(-12.0466 + 4.31966i) q^{69} +(0.605889 + 3.43617i) q^{70} +(0.0121983 - 0.0211281i) q^{71} +(1.52471 - 2.58365i) q^{72} +(1.20574 + 2.08840i) q^{73} +(-0.329750 + 0.276693i) q^{74} +(-9.55712 + 7.94202i) q^{75} +(0.145500 - 0.825171i) q^{76} +(3.49150 + 2.92972i) q^{77} +(5.11383 - 8.76066i) q^{78} +(-1.95673 - 0.712191i) q^{79} -3.48918 q^{80} +(-4.64786 + 7.70697i) q^{81} +6.97728 q^{82} +(15.8118 + 5.75502i) q^{83} +(0.873169 - 1.49585i) q^{84} +(3.28279 + 2.75459i) q^{85} +(-1.23170 + 6.98532i) q^{86} +(1.27191 - 1.05696i) q^{87} +(-3.49150 + 2.92972i) q^{88} +(-3.51410 - 6.08660i) q^{89} +(10.4671 + 0.0998439i) q^{90} +(2.92832 - 5.07199i) q^{91} +(-1.28304 - 7.27649i) q^{92} +(-13.7730 + 4.93871i) q^{93} +(-8.15352 + 2.96764i) q^{94} +(2.74727 - 0.999925i) q^{95} +(1.32150 + 1.11966i) q^{96} +(-2.34715 - 13.3113i) q^{97} +(0.500000 - 0.866025i) q^{98} +(10.5579 - 8.68884i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q + 3 q^{3} + 3 q^{5} + 6 q^{6} + 18 q^{8} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 36 q + 3 q^{3} + 3 q^{5} + 6 q^{6} + 18 q^{8} + 3 q^{9} - 3 q^{10} + 9 q^{13} - 6 q^{15} + 6 q^{18} - 15 q^{19} - 6 q^{20} + 3 q^{21} - 3 q^{24} - 3 q^{25} - 18 q^{26} - 30 q^{27} + 36 q^{28} - 6 q^{29} - 9 q^{30} + 60 q^{33} + 9 q^{34} + 3 q^{35} - 27 q^{37} + 15 q^{38} + 6 q^{39} - 3 q^{40} - 9 q^{41} - 6 q^{43} + 9 q^{44} + 42 q^{45} - 9 q^{46} + 36 q^{47} + 3 q^{48} - 15 q^{50} - 36 q^{51} + 9 q^{52} - 42 q^{53} - 27 q^{54} + 30 q^{55} - 18 q^{57} - 21 q^{58} + 12 q^{59} + 24 q^{60} + 3 q^{61} + 18 q^{62} + 12 q^{63} - 18 q^{64} - 84 q^{65} + 18 q^{66} - 69 q^{67} + 9 q^{68} - 48 q^{69} - 3 q^{70} + 12 q^{71} + 6 q^{72} - 12 q^{73} + 9 q^{75} - 15 q^{76} + 9 q^{77} - 48 q^{78} - 51 q^{79} - 6 q^{80} - 69 q^{81} + 15 q^{83} + 3 q^{84} - 12 q^{85} + 6 q^{86} + 84 q^{87} - 9 q^{88} - 3 q^{89} + 6 q^{90} - 9 q^{91} + 18 q^{92} - 21 q^{93} + 9 q^{94} - 75 q^{95} - 42 q^{97} + 18 q^{98} + 39 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.939693 + 0.342020i 0.664463 + 0.241845i
\(3\) 0.873169 1.49585i 0.504125 0.863631i
\(4\) 0.766044 + 0.642788i 0.383022 + 0.321394i
\(5\) −0.605889 + 3.43617i −0.270962 + 1.53670i 0.480541 + 0.876972i \(0.340440\pi\)
−0.751503 + 0.659729i \(0.770671\pi\)
\(6\) 1.33212 1.10700i 0.543837 0.451931i
\(7\) 0.766044 0.642788i 0.289538 0.242951i
\(8\) 0.500000 + 0.866025i 0.176777 + 0.306186i
\(9\) −1.47515 2.61227i −0.491717 0.870755i
\(10\) −1.74459 + 3.02172i −0.551687 + 0.955551i
\(11\) 0.791459 + 4.48859i 0.238634 + 1.35336i 0.834824 + 0.550517i \(0.185569\pi\)
−0.596190 + 0.802843i \(0.703320\pi\)
\(12\) 1.63040 0.584627i 0.470657 0.168767i
\(13\) 5.50344 2.00309i 1.52638 0.555556i 0.563647 0.826016i \(-0.309398\pi\)
0.962731 + 0.270459i \(0.0871756\pi\)
\(14\) 0.939693 0.342020i 0.251143 0.0914087i
\(15\) 4.61096 + 3.90668i 1.19054 + 1.00870i
\(16\) 0.173648 + 0.984808i 0.0434120 + 0.246202i
\(17\) 0.614096 1.06365i 0.148940 0.257972i −0.781896 0.623409i \(-0.785747\pi\)
0.930836 + 0.365437i \(0.119080\pi\)
\(18\) −0.492740 2.95926i −0.116140 0.697504i
\(19\) −0.418950 0.725643i −0.0961138 0.166474i 0.813959 0.580922i \(-0.197308\pi\)
−0.910073 + 0.414448i \(0.863975\pi\)
\(20\) −2.67286 + 2.24280i −0.597671 + 0.501505i
\(21\) −0.292629 1.70715i −0.0638569 0.372531i
\(22\) −0.791459 + 4.48859i −0.168740 + 0.956970i
\(23\) −5.66011 4.74939i −1.18021 0.990317i −0.999978 0.00669339i \(-0.997869\pi\)
−0.180236 0.983623i \(-0.557686\pi\)
\(24\) 1.73203 + 0.00826063i 0.353549 + 0.00168619i
\(25\) −6.74169 2.45378i −1.34834 0.490755i
\(26\) 5.85663 1.14858
\(27\) −5.19562 0.0743434i −0.999898 0.0143074i
\(28\) 1.00000 0.188982
\(29\) 0.897215 + 0.326560i 0.166609 + 0.0606406i 0.423978 0.905673i \(-0.360633\pi\)
−0.257369 + 0.966313i \(0.582856\pi\)
\(30\) 2.99672 + 5.24812i 0.547124 + 0.958171i
\(31\) −6.47125 5.43002i −1.16227 0.975261i −0.162337 0.986735i \(-0.551903\pi\)
−0.999934 + 0.0114744i \(0.996348\pi\)
\(32\) −0.173648 + 0.984808i −0.0306970 + 0.174091i
\(33\) 7.40534 + 2.73539i 1.28910 + 0.476170i
\(34\) 0.940850 0.789467i 0.161354 0.135392i
\(35\) 1.74459 + 3.02172i 0.294889 + 0.510763i
\(36\) 0.549101 2.94932i 0.0915169 0.491553i
\(37\) −0.215229 + 0.372787i −0.0353834 + 0.0612859i −0.883175 0.469044i \(-0.844599\pi\)
0.847791 + 0.530330i \(0.177932\pi\)
\(38\) −0.145500 0.825171i −0.0236032 0.133860i
\(39\) 1.80911 9.98136i 0.289689 1.59830i
\(40\) −3.27875 + 1.19337i −0.518417 + 0.188688i
\(41\) 6.55650 2.38637i 1.02395 0.372689i 0.225178 0.974318i \(-0.427704\pi\)
0.798776 + 0.601629i \(0.205481\pi\)
\(42\) 0.308899 1.70428i 0.0476642 0.262977i
\(43\) 1.23170 + 6.98532i 0.187832 + 1.06525i 0.922262 + 0.386566i \(0.126339\pi\)
−0.734429 + 0.678685i \(0.762550\pi\)
\(44\) −2.27891 + 3.94720i −0.343559 + 0.595062i
\(45\) 9.86996 3.48612i 1.47133 0.519680i
\(46\) −3.69437 6.39884i −0.544705 0.943457i
\(47\) −6.64681 + 5.57734i −0.969537 + 0.813538i −0.982478 0.186378i \(-0.940325\pi\)
0.0129410 + 0.999916i \(0.495881\pi\)
\(48\) 1.62475 + 0.600152i 0.234513 + 0.0866245i
\(49\) 0.173648 0.984808i 0.0248069 0.140687i
\(50\) −5.49588 4.61159i −0.777234 0.652177i
\(51\) −1.05485 1.84734i −0.147708 0.258679i
\(52\) 5.50344 + 2.00309i 0.763189 + 0.277778i
\(53\) −7.79142 −1.07023 −0.535117 0.844778i \(-0.679732\pi\)
−0.535117 + 0.844778i \(0.679732\pi\)
\(54\) −4.85686 1.84687i −0.660935 0.251327i
\(55\) −15.9031 −2.14437
\(56\) 0.939693 + 0.342020i 0.125572 + 0.0457044i
\(57\) −1.45127 0.00692158i −0.192225 0.000916786i
\(58\) 0.731416 + 0.613731i 0.0960397 + 0.0805869i
\(59\) 1.92214 10.9010i 0.250241 1.41919i −0.557757 0.830004i \(-0.688338\pi\)
0.807998 0.589185i \(-0.200551\pi\)
\(60\) 1.02103 + 5.95656i 0.131815 + 0.768988i
\(61\) 8.16278 6.84939i 1.04514 0.876974i 0.0525632 0.998618i \(-0.483261\pi\)
0.992574 + 0.121644i \(0.0388165\pi\)
\(62\) −4.22381 7.31585i −0.536424 0.929114i
\(63\) −2.80916 1.05290i −0.353921 0.132653i
\(64\) −0.500000 + 0.866025i −0.0625000 + 0.108253i
\(65\) 3.54847 + 20.1244i 0.440134 + 2.49612i
\(66\) 6.02319 + 5.10320i 0.741403 + 0.628161i
\(67\) −13.7773 + 5.01453i −1.68316 + 0.612622i −0.993738 0.111734i \(-0.964360\pi\)
−0.689426 + 0.724356i \(0.742137\pi\)
\(68\) 1.15412 0.420066i 0.139958 0.0509405i
\(69\) −12.0466 + 4.31966i −1.45024 + 0.520026i
\(70\) 0.605889 + 3.43617i 0.0724176 + 0.410701i
\(71\) 0.0121983 0.0211281i 0.00144767 0.00250745i −0.865301 0.501253i \(-0.832873\pi\)
0.866748 + 0.498746i \(0.166206\pi\)
\(72\) 1.52471 2.58365i 0.179689 0.304486i
\(73\) 1.20574 + 2.08840i 0.141121 + 0.244428i 0.927919 0.372782i \(-0.121596\pi\)
−0.786798 + 0.617210i \(0.788263\pi\)
\(74\) −0.329750 + 0.276693i −0.0383326 + 0.0321649i
\(75\) −9.55712 + 7.94202i −1.10356 + 0.917065i
\(76\) 0.145500 0.825171i 0.0166900 0.0946536i
\(77\) 3.49150 + 2.92972i 0.397893 + 0.333872i
\(78\) 5.11383 8.76066i 0.579028 0.991950i
\(79\) −1.95673 0.712191i −0.220149 0.0801278i 0.229591 0.973287i \(-0.426261\pi\)
−0.449740 + 0.893159i \(0.648483\pi\)
\(80\) −3.48918 −0.390102
\(81\) −4.64786 + 7.70697i −0.516429 + 0.856330i
\(82\) 6.97728 0.770512
\(83\) 15.8118 + 5.75502i 1.73557 + 0.631695i 0.999002 0.0446700i \(-0.0142236\pi\)
0.736566 + 0.676365i \(0.236446\pi\)
\(84\) 0.873169 1.49585i 0.0952706 0.163211i
\(85\) 3.28279 + 2.75459i 0.356069 + 0.298777i
\(86\) −1.23170 + 6.98532i −0.132818 + 0.753246i
\(87\) 1.27191 1.05696i 0.136363 0.113318i
\(88\) −3.49150 + 2.92972i −0.372195 + 0.312309i
\(89\) −3.51410 6.08660i −0.372494 0.645179i 0.617455 0.786607i \(-0.288164\pi\)
−0.989949 + 0.141428i \(0.954831\pi\)
\(90\) 10.4671 + 0.0998439i 1.10332 + 0.0105245i
\(91\) 2.92832 5.07199i 0.306971 0.531689i
\(92\) −1.28304 7.27649i −0.133766 0.758627i
\(93\) −13.7730 + 4.93871i −1.42819 + 0.512120i
\(94\) −8.15352 + 2.96764i −0.840971 + 0.306089i
\(95\) 2.74727 0.999925i 0.281864 0.102590i
\(96\) 1.32150 + 1.11966i 0.134875 + 0.114274i
\(97\) −2.34715 13.3113i −0.238317 1.35156i −0.835515 0.549468i \(-0.814831\pi\)
0.597198 0.802094i \(-0.296281\pi\)
\(98\) 0.500000 0.866025i 0.0505076 0.0874818i
\(99\) 10.5579 8.68884i 1.06110 0.873261i
\(100\) −3.58718 6.21318i −0.358718 0.621318i
\(101\) −6.54854 + 5.49488i −0.651604 + 0.546761i −0.907557 0.419928i \(-0.862055\pi\)
0.255953 + 0.966689i \(0.417611\pi\)
\(102\) −0.359405 2.09671i −0.0355864 0.207605i
\(103\) 1.56684 8.88600i 0.154385 0.875563i −0.804960 0.593329i \(-0.797813\pi\)
0.959345 0.282234i \(-0.0910756\pi\)
\(104\) 4.48644 + 3.76457i 0.439932 + 0.369147i
\(105\) 6.04336 + 0.0288228i 0.589772 + 0.00281282i
\(106\) −7.32154 2.66482i −0.711131 0.258830i
\(107\) 2.48999 0.240716 0.120358 0.992731i \(-0.461596\pi\)
0.120358 + 0.992731i \(0.461596\pi\)
\(108\) −3.93229 3.39663i −0.378385 0.326841i
\(109\) −1.02333 −0.0980171 −0.0490086 0.998798i \(-0.515606\pi\)
−0.0490086 + 0.998798i \(0.515606\pi\)
\(110\) −14.9440 5.43917i −1.42485 0.518605i
\(111\) 0.369704 + 0.647457i 0.0350907 + 0.0614539i
\(112\) 0.766044 + 0.642788i 0.0723844 + 0.0607377i
\(113\) −1.28893 + 7.30990i −0.121253 + 0.687657i 0.862211 + 0.506550i \(0.169079\pi\)
−0.983463 + 0.181108i \(0.942032\pi\)
\(114\) −1.36138 0.502868i −0.127505 0.0470979i
\(115\) 19.7491 16.5715i 1.84161 1.54530i
\(116\) 0.477398 + 0.826878i 0.0443253 + 0.0767737i
\(117\) −13.3510 11.4216i −1.23430 1.05593i
\(118\) 5.53458 9.58618i 0.509499 0.882479i
\(119\) −0.213273 1.20953i −0.0195507 0.110878i
\(120\) −1.07780 + 5.94655i −0.0983896 + 0.542843i
\(121\) −9.18438 + 3.34284i −0.834943 + 0.303895i
\(122\) 10.0131 3.64448i 0.906546 0.329956i
\(123\) 2.15528 11.8913i 0.194335 1.07220i
\(124\) −1.46691 8.31928i −0.131733 0.747093i
\(125\) 3.79336 6.57029i 0.339288 0.587665i
\(126\) −2.27964 1.95020i −0.203086 0.173737i
\(127\) −3.30173 5.71876i −0.292981 0.507458i 0.681532 0.731788i \(-0.261314\pi\)
−0.974513 + 0.224330i \(0.927981\pi\)
\(128\) −0.766044 + 0.642788i −0.0677094 + 0.0568149i
\(129\) 11.5245 + 4.25692i 1.01467 + 0.374801i
\(130\) −3.54847 + 20.1244i −0.311222 + 1.76503i
\(131\) −7.48189 6.27805i −0.653696 0.548516i 0.254494 0.967074i \(-0.418091\pi\)
−0.908190 + 0.418558i \(0.862535\pi\)
\(132\) 3.91455 + 6.85549i 0.340717 + 0.596694i
\(133\) −0.787369 0.286579i −0.0682736 0.0248495i
\(134\) −14.6615 −1.26656
\(135\) 3.40343 17.8080i 0.292920 1.53267i
\(136\) 1.22819 0.105317
\(137\) 14.2949 + 5.20293i 1.22130 + 0.444516i 0.870609 0.491975i \(-0.163725\pi\)
0.350690 + 0.936492i \(0.385947\pi\)
\(138\) −12.7975 0.0610356i −1.08940 0.00519570i
\(139\) 9.21108 + 7.72901i 0.781274 + 0.655566i 0.943569 0.331176i \(-0.107445\pi\)
−0.162295 + 0.986742i \(0.551890\pi\)
\(140\) −0.605889 + 3.43617i −0.0512070 + 0.290409i
\(141\) 2.53908 + 14.8126i 0.213829 + 1.24745i
\(142\) 0.0186889 0.0156819i 0.00156834 0.00131599i
\(143\) 13.3468 + 23.1173i 1.11611 + 1.93316i
\(144\) 2.31642 1.90635i 0.193035 0.158863i
\(145\) −1.66573 + 2.88512i −0.138331 + 0.239596i
\(146\) 0.418748 + 2.37484i 0.0346558 + 0.196543i
\(147\) −1.32150 1.11966i −0.108996 0.0923477i
\(148\) −0.404498 + 0.147225i −0.0332495 + 0.0121018i
\(149\) 2.58540 0.941009i 0.211804 0.0770904i −0.233939 0.972251i \(-0.575162\pi\)
0.445743 + 0.895161i \(0.352939\pi\)
\(150\) −11.6971 + 4.19432i −0.955063 + 0.342465i
\(151\) 0.411684 + 2.33477i 0.0335023 + 0.190001i 0.996966 0.0778377i \(-0.0248016\pi\)
−0.963464 + 0.267839i \(0.913690\pi\)
\(152\) 0.418950 0.725643i 0.0339814 0.0588574i
\(153\) −3.68441 0.0351451i −0.297867 0.00284131i
\(154\) 2.27891 + 3.94720i 0.183640 + 0.318074i
\(155\) 22.5793 18.9463i 1.81362 1.52180i
\(156\) 7.80176 6.48329i 0.624640 0.519079i
\(157\) −1.38428 + 7.85064i −0.110478 + 0.626550i 0.878413 + 0.477903i \(0.158603\pi\)
−0.988890 + 0.148647i \(0.952508\pi\)
\(158\) −1.59514 1.33848i −0.126903 0.106484i
\(159\) −6.80323 + 11.6548i −0.539531 + 0.924287i
\(160\) −3.27875 1.19337i −0.259208 0.0943441i
\(161\) −7.38874 −0.582315
\(162\) −7.00350 + 5.65252i −0.550247 + 0.444104i
\(163\) 2.89741 0.226942 0.113471 0.993541i \(-0.463803\pi\)
0.113471 + 0.993541i \(0.463803\pi\)
\(164\) 6.55650 + 2.38637i 0.511977 + 0.186344i
\(165\) −13.8861 + 23.7887i −1.08103 + 1.85194i
\(166\) 12.8899 + 10.8159i 1.00045 + 0.839476i
\(167\) −0.790091 + 4.48083i −0.0611391 + 0.346737i 0.938858 + 0.344305i \(0.111885\pi\)
−0.999997 + 0.00243227i \(0.999226\pi\)
\(168\) 1.33212 1.10700i 0.102775 0.0854069i
\(169\) 16.3169 13.6915i 1.25514 1.05319i
\(170\) 2.14269 + 3.71125i 0.164337 + 0.284640i
\(171\) −1.27756 + 2.16484i −0.0976973 + 0.165550i
\(172\) −3.54654 + 6.14278i −0.270421 + 0.468383i
\(173\) 1.59882 + 9.06736i 0.121556 + 0.689379i 0.983294 + 0.182025i \(0.0582652\pi\)
−0.861738 + 0.507354i \(0.830624\pi\)
\(174\) 1.55670 0.558200i 0.118013 0.0423170i
\(175\) −6.74169 + 2.45378i −0.509624 + 0.185488i
\(176\) −4.28296 + 1.55887i −0.322840 + 0.117504i
\(177\) −14.6279 12.3937i −1.09950 0.931564i
\(178\) −1.22043 6.92143i −0.0914754 0.518783i
\(179\) 4.47684 7.75412i 0.334615 0.579570i −0.648796 0.760963i \(-0.724727\pi\)
0.983411 + 0.181392i \(0.0580604\pi\)
\(180\) 9.80167 + 3.67377i 0.730573 + 0.273826i
\(181\) 8.20062 + 14.2039i 0.609547 + 1.05577i 0.991315 + 0.131508i \(0.0419820\pi\)
−0.381768 + 0.924258i \(0.624685\pi\)
\(182\) 4.48644 3.76457i 0.332557 0.279049i
\(183\) −3.11818 18.1910i −0.230503 1.34472i
\(184\) 1.28304 7.27649i 0.0945871 0.536430i
\(185\) −1.15056 0.965431i −0.0845905 0.0709799i
\(186\) −14.6315 0.0697826i −1.07284 0.00511671i
\(187\) 5.26030 + 1.91459i 0.384671 + 0.140009i
\(188\) −8.67680 −0.632820
\(189\) −4.02786 + 3.28273i −0.292984 + 0.238783i
\(190\) 2.92358 0.212099
\(191\) 1.65647 + 0.602906i 0.119858 + 0.0436248i 0.401253 0.915967i \(-0.368575\pi\)
−0.281395 + 0.959592i \(0.590797\pi\)
\(192\) 0.858862 + 1.50411i 0.0619830 + 0.108550i
\(193\) 4.80848 + 4.03479i 0.346122 + 0.290431i 0.799231 0.601025i \(-0.205241\pi\)
−0.453109 + 0.891455i \(0.649685\pi\)
\(194\) 2.34715 13.3113i 0.168515 0.955698i
\(195\) 33.2015 + 12.2640i 2.37761 + 0.878244i
\(196\) 0.766044 0.642788i 0.0547175 0.0459134i
\(197\) −10.0278 17.3687i −0.714455 1.23747i −0.963169 0.268895i \(-0.913342\pi\)
0.248715 0.968577i \(-0.419992\pi\)
\(198\) 12.8929 4.55384i 0.916258 0.323627i
\(199\) −5.22507 + 9.05009i −0.370396 + 0.641544i −0.989626 0.143665i \(-0.954111\pi\)
0.619231 + 0.785209i \(0.287445\pi\)
\(200\) −1.24581 7.06536i −0.0880924 0.499597i
\(201\) −4.52892 + 24.9873i −0.319446 + 1.76247i
\(202\) −8.03298 + 2.92376i −0.565198 + 0.205715i
\(203\) 0.897215 0.326560i 0.0629722 0.0229200i
\(204\) 0.379388 2.09319i 0.0265624 0.146552i
\(205\) 4.22746 + 23.9751i 0.295259 + 1.67450i
\(206\) 4.51154 7.81422i 0.314334 0.544442i
\(207\) −4.05717 + 21.7918i −0.281993 + 1.51463i
\(208\) 2.92832 + 5.07199i 0.203042 + 0.351680i
\(209\) 2.92553 2.45481i 0.202363 0.169803i
\(210\) 5.66905 + 2.09404i 0.391201 + 0.144502i
\(211\) −3.46152 + 19.6313i −0.238301 + 1.35147i 0.597248 + 0.802056i \(0.296261\pi\)
−0.835549 + 0.549415i \(0.814850\pi\)
\(212\) −5.96857 5.00823i −0.409923 0.343967i
\(213\) −0.0209533 0.0366953i −0.00143570 0.00251432i
\(214\) 2.33982 + 0.851625i 0.159947 + 0.0582159i
\(215\) −24.7490 −1.68787
\(216\) −2.53343 4.53671i −0.172378 0.308684i
\(217\) −8.44762 −0.573462
\(218\) −0.961614 0.349999i −0.0651287 0.0237049i
\(219\) 4.17674 + 0.0199203i 0.282238 + 0.00134609i
\(220\) −12.1825 10.2223i −0.821341 0.689187i
\(221\) 1.24906 7.08379i 0.0840211 0.476507i
\(222\) 0.125964 + 0.734857i 0.00845418 + 0.0493204i
\(223\) −3.78851 + 3.17894i −0.253698 + 0.212878i −0.760763 0.649030i \(-0.775175\pi\)
0.507065 + 0.861908i \(0.330730\pi\)
\(224\) 0.500000 + 0.866025i 0.0334077 + 0.0578638i
\(225\) 3.53510 + 21.2308i 0.235673 + 1.41539i
\(226\) −3.71133 + 6.42822i −0.246874 + 0.427599i
\(227\) −0.785748 4.45620i −0.0521519 0.295768i 0.947565 0.319563i \(-0.103536\pi\)
−0.999717 + 0.0237950i \(0.992425\pi\)
\(228\) −1.10729 0.938161i −0.0733320 0.0621312i
\(229\) 16.4995 6.00532i 1.09032 0.396843i 0.266578 0.963813i \(-0.414107\pi\)
0.823738 + 0.566971i \(0.191885\pi\)
\(230\) 24.2259 8.81750i 1.59741 0.581408i
\(231\) 7.43110 2.66463i 0.488930 0.175320i
\(232\) 0.165799 + 0.940291i 0.0108852 + 0.0617331i
\(233\) 0.652915 1.13088i 0.0427739 0.0740866i −0.843846 0.536586i \(-0.819714\pi\)
0.886620 + 0.462499i \(0.153047\pi\)
\(234\) −8.63942 15.2991i −0.564776 1.00013i
\(235\) −15.1374 26.2188i −0.987458 1.71033i
\(236\) 8.47947 7.11512i 0.551966 0.463155i
\(237\) −2.77389 + 2.30512i −0.180183 + 0.149733i
\(238\) 0.213273 1.20953i 0.0138245 0.0784024i
\(239\) 4.82758 + 4.05082i 0.312270 + 0.262026i 0.785429 0.618951i \(-0.212442\pi\)
−0.473160 + 0.880977i \(0.656887\pi\)
\(240\) −3.04664 + 5.21930i −0.196660 + 0.336904i
\(241\) 22.4922 + 8.18649i 1.44885 + 0.527338i 0.942270 0.334855i \(-0.108687\pi\)
0.506579 + 0.862193i \(0.330910\pi\)
\(242\) −9.77381 −0.628284
\(243\) 7.47012 + 13.6820i 0.479208 + 0.877701i
\(244\) 10.6558 0.682165
\(245\) 3.27875 + 1.19337i 0.209472 + 0.0762415i
\(246\) 6.09235 10.4370i 0.388434 0.665438i
\(247\) −3.75919 3.15434i −0.239192 0.200706i
\(248\) 1.46691 8.31928i 0.0931491 0.528275i
\(249\) 22.4150 18.6270i 1.42049 1.18044i
\(250\) 5.81177 4.87665i 0.367568 0.308426i
\(251\) −6.86570 11.8917i −0.433359 0.750600i 0.563801 0.825911i \(-0.309339\pi\)
−0.997160 + 0.0753105i \(0.976005\pi\)
\(252\) −1.47515 2.61227i −0.0929257 0.164557i
\(253\) 16.8383 29.1648i 1.05862 1.83358i
\(254\) −1.14668 6.50313i −0.0719489 0.408043i
\(255\) 6.98689 2.50535i 0.437536 0.156891i
\(256\) −0.939693 + 0.342020i −0.0587308 + 0.0213763i
\(257\) −9.58938 + 3.49025i −0.598169 + 0.217716i −0.623319 0.781968i \(-0.714216\pi\)
0.0251494 + 0.999684i \(0.491994\pi\)
\(258\) 9.37352 + 7.94181i 0.583570 + 0.494435i
\(259\) 0.0747482 + 0.423918i 0.00464463 + 0.0263410i
\(260\) −10.2174 + 17.6971i −0.633657 + 1.09753i
\(261\) −0.470467 2.82549i −0.0291211 0.174893i
\(262\) −4.88346 8.45840i −0.301701 0.522561i
\(263\) −2.62569 + 2.20322i −0.161907 + 0.135856i −0.720142 0.693827i \(-0.755923\pi\)
0.558235 + 0.829683i \(0.311479\pi\)
\(264\) 1.33375 + 7.78091i 0.0820868 + 0.478882i
\(265\) 4.72074 26.7726i 0.289993 1.64463i
\(266\) −0.641869 0.538592i −0.0393555 0.0330232i
\(267\) −12.1731 0.0580573i −0.744980 0.00355305i
\(268\) −13.7773 5.01453i −0.841582 0.306311i
\(269\) −3.36486 −0.205159 −0.102579 0.994725i \(-0.532710\pi\)
−0.102579 + 0.994725i \(0.532710\pi\)
\(270\) 9.28887 15.5700i 0.565302 0.947560i
\(271\) 9.07619 0.551339 0.275670 0.961252i \(-0.411100\pi\)
0.275670 + 0.961252i \(0.411100\pi\)
\(272\) 1.15412 + 0.420066i 0.0699790 + 0.0254703i
\(273\) −5.03004 8.80904i −0.304432 0.533147i
\(274\) 11.6533 + 9.77831i 0.704004 + 0.590729i
\(275\) 5.67821 32.2027i 0.342409 1.94190i
\(276\) −12.0049 4.43437i −0.722608 0.266918i
\(277\) −9.56560 + 8.02649i −0.574741 + 0.482265i −0.883215 0.468968i \(-0.844626\pi\)
0.308474 + 0.951233i \(0.400182\pi\)
\(278\) 6.01211 + 10.4133i 0.360582 + 0.624547i
\(279\) −4.63860 + 24.9147i −0.277706 + 1.49161i
\(280\) −1.74459 + 3.02172i −0.104259 + 0.180582i
\(281\) 3.51004 + 19.9064i 0.209391 + 1.18752i 0.890378 + 0.455222i \(0.150440\pi\)
−0.680987 + 0.732296i \(0.738449\pi\)
\(282\) −2.68026 + 14.7877i −0.159607 + 0.880596i
\(283\) −7.69188 + 2.79961i −0.457235 + 0.166420i −0.560361 0.828248i \(-0.689338\pi\)
0.103126 + 0.994668i \(0.467115\pi\)
\(284\) 0.0229253 0.00834414i 0.00136037 0.000495134i
\(285\) 0.903093 4.98261i 0.0534946 0.295145i
\(286\) 4.63528 + 26.2880i 0.274090 + 1.55444i
\(287\) 3.48864 6.04250i 0.205928 0.356678i
\(288\) 2.82874 0.999124i 0.166685 0.0588740i
\(289\) 7.74577 + 13.4161i 0.455634 + 0.789181i
\(290\) −2.55204 + 2.14142i −0.149861 + 0.125748i
\(291\) −21.9613 8.11206i −1.28739 0.475538i
\(292\) −0.418748 + 2.37484i −0.0245054 + 0.138977i
\(293\) −8.37145 7.02448i −0.489065 0.410375i 0.364626 0.931154i \(-0.381197\pi\)
−0.853691 + 0.520779i \(0.825641\pi\)
\(294\) −0.858862 1.50411i −0.0500898 0.0877217i
\(295\) 36.2931 + 13.2096i 2.11306 + 0.769092i
\(296\) −0.430458 −0.0250199
\(297\) −3.77842 23.3798i −0.219246 1.35664i
\(298\) 2.75133 0.159380
\(299\) −40.6635 14.8003i −2.35163 0.855923i
\(300\) −12.4262 0.0592647i −0.717428 0.00342165i
\(301\) 5.43361 + 4.55934i 0.313188 + 0.262796i
\(302\) −0.411684 + 2.33477i −0.0236897 + 0.134351i
\(303\) 2.50154 + 14.5936i 0.143710 + 0.838381i
\(304\) 0.641869 0.538592i 0.0368137 0.0308904i
\(305\) 18.5899 + 32.1987i 1.06445 + 1.84369i
\(306\) −3.45019 1.29317i −0.197234 0.0739255i
\(307\) 1.82256 3.15677i 0.104019 0.180166i −0.809318 0.587371i \(-0.800163\pi\)
0.913337 + 0.407205i \(0.133496\pi\)
\(308\) 0.791459 + 4.48859i 0.0450976 + 0.255761i
\(309\) −11.9240 10.1027i −0.678334 0.574725i
\(310\) 27.6977 10.0811i 1.57312 0.572569i
\(311\) −18.8905 + 6.87559i −1.07118 + 0.389879i −0.816619 0.577177i \(-0.804154\pi\)
−0.254564 + 0.967056i \(0.581932\pi\)
\(312\) 9.54867 3.42395i 0.540587 0.193843i
\(313\) 5.77083 + 32.7280i 0.326187 + 1.84990i 0.501200 + 0.865331i \(0.332892\pi\)
−0.175014 + 0.984566i \(0.555997\pi\)
\(314\) −3.98588 + 6.90374i −0.224936 + 0.389601i
\(315\) 5.32000 9.01481i 0.299748 0.507927i
\(316\) −1.04115 1.80333i −0.0585695 0.101445i
\(317\) −21.1190 + 17.7209i −1.18616 + 0.995307i −0.186242 + 0.982504i \(0.559631\pi\)
−0.999918 + 0.0128027i \(0.995925\pi\)
\(318\) −10.3791 + 8.62510i −0.582033 + 0.483672i
\(319\) −0.755682 + 4.28569i −0.0423101 + 0.239952i
\(320\) −2.67286 2.24280i −0.149418 0.125376i
\(321\) 2.17418 3.72465i 0.121351 0.207890i
\(322\) −6.94315 2.52710i −0.386926 0.140830i
\(323\) −1.02910 −0.0572608
\(324\) −8.51441 + 2.91629i −0.473023 + 0.162016i
\(325\) −42.0176 −2.33072
\(326\) 2.72267 + 0.990971i 0.150795 + 0.0548848i
\(327\) −0.893539 + 1.53075i −0.0494128 + 0.0846506i
\(328\) 5.34491 + 4.48491i 0.295123 + 0.247638i
\(329\) −1.50671 + 8.54498i −0.0830676 + 0.471100i
\(330\) −21.1848 + 17.6047i −1.16619 + 0.969107i
\(331\) 17.4897 14.6756i 0.961320 0.806644i −0.0198470 0.999803i \(-0.506318\pi\)
0.981167 + 0.193159i \(0.0618735\pi\)
\(332\) 8.41327 + 14.5722i 0.461738 + 0.799754i
\(333\) 1.29131 + 0.0123177i 0.0707636 + 0.000675005i
\(334\) −2.27498 + 3.94038i −0.124481 + 0.215608i
\(335\) −8.88324 50.3794i −0.485343 2.75252i
\(336\) 1.63040 0.584627i 0.0889457 0.0318940i
\(337\) 26.1265 9.50926i 1.42320 0.518002i 0.488225 0.872718i \(-0.337644\pi\)
0.934974 + 0.354715i \(0.115422\pi\)
\(338\) 20.0156 7.28509i 1.08871 0.396256i
\(339\) 9.80908 + 8.31083i 0.532756 + 0.451383i
\(340\) 0.744148 + 4.22028i 0.0403571 + 0.228877i
\(341\) 19.2514 33.3444i 1.04252 1.80570i
\(342\) −1.94093 + 1.59734i −0.104954 + 0.0863740i
\(343\) −0.500000 0.866025i −0.0269975 0.0467610i
\(344\) −5.43361 + 4.55934i −0.292961 + 0.245823i
\(345\) −7.54416 44.0115i −0.406164 2.36950i
\(346\) −1.59882 + 9.06736i −0.0859531 + 0.487464i
\(347\) 4.50344 + 3.77883i 0.241757 + 0.202858i 0.755613 0.655018i \(-0.227339\pi\)
−0.513856 + 0.857876i \(0.671783\pi\)
\(348\) 1.65374 + 0.00788721i 0.0886496 + 0.000422799i
\(349\) −11.7340 4.27083i −0.628107 0.228612i 0.00830009 0.999966i \(-0.497358\pi\)
−0.636407 + 0.771353i \(0.719580\pi\)
\(350\) −7.17436 −0.383486
\(351\) −28.7427 + 9.99814i −1.53417 + 0.533661i
\(352\) −4.55783 −0.242933
\(353\) 0.0127909 + 0.00465551i 0.000680792 + 0.000247788i 0.342361 0.939569i \(-0.388774\pi\)
−0.341680 + 0.939816i \(0.610996\pi\)
\(354\) −9.50688 16.6493i −0.505285 0.884899i
\(355\) 0.0652089 + 0.0547168i 0.00346093 + 0.00290407i
\(356\) 1.22043 6.92143i 0.0646829 0.366835i
\(357\) −1.99551 0.737102i −0.105613 0.0390116i
\(358\) 6.85892 5.75532i 0.362505 0.304178i
\(359\) −15.9100 27.5569i −0.839696 1.45440i −0.890149 0.455670i \(-0.849400\pi\)
0.0504524 0.998726i \(-0.483934\pi\)
\(360\) 7.95405 + 6.80458i 0.419215 + 0.358633i
\(361\) 9.14896 15.8465i 0.481524 0.834025i
\(362\) 2.84804 + 16.1521i 0.149690 + 0.848934i
\(363\) −3.01912 + 16.6573i −0.158463 + 0.874284i
\(364\) 5.50344 2.00309i 0.288458 0.104990i
\(365\) −7.90662 + 2.87778i −0.413852 + 0.150630i
\(366\) 3.29155 18.1604i 0.172052 0.949260i
\(367\) 6.51601 + 36.9541i 0.340133 + 1.92899i 0.369052 + 0.929409i \(0.379682\pi\)
−0.0289189 + 0.999582i \(0.509206\pi\)
\(368\) 3.69437 6.39884i 0.192582 0.333563i
\(369\) −15.9057 13.6071i −0.828016 0.708356i
\(370\) −0.750972 1.30072i −0.0390412 0.0676213i
\(371\) −5.96857 + 5.00823i −0.309873 + 0.260014i
\(372\) −13.7253 5.06985i −0.711623 0.262860i
\(373\) −0.946384 + 5.36721i −0.0490019 + 0.277904i −0.999457 0.0329592i \(-0.989507\pi\)
0.950455 + 0.310863i \(0.100618\pi\)
\(374\) 4.28823 + 3.59825i 0.221739 + 0.186061i
\(375\) −6.51594 11.4113i −0.336482 0.589276i
\(376\) −8.15352 2.96764i −0.420486 0.153044i
\(377\) 5.59189 0.287997
\(378\) −4.90771 + 1.70715i −0.252426 + 0.0878062i
\(379\) −17.4571 −0.896712 −0.448356 0.893855i \(-0.647990\pi\)
−0.448356 + 0.893855i \(0.647990\pi\)
\(380\) 2.74727 + 0.999925i 0.140932 + 0.0512950i
\(381\) −11.4374 0.0545486i −0.585955 0.00279461i
\(382\) 1.35037 + 1.13309i 0.0690908 + 0.0579741i
\(383\) 4.08862 23.1877i 0.208919 1.18484i −0.682234 0.731134i \(-0.738992\pi\)
0.891153 0.453703i \(-0.149897\pi\)
\(384\) 0.292629 + 1.70715i 0.0149332 + 0.0871177i
\(385\) −12.1825 + 10.2223i −0.620876 + 0.520977i
\(386\) 3.13851 + 5.43606i 0.159746 + 0.276688i
\(387\) 16.4306 13.5219i 0.835212 0.687358i
\(388\) 6.75834 11.7058i 0.343103 0.594271i
\(389\) 1.51951 + 8.61757i 0.0770422 + 0.436928i 0.998792 + 0.0491424i \(0.0156488\pi\)
−0.921750 + 0.387786i \(0.873240\pi\)
\(390\) 27.0047 + 22.8800i 1.36744 + 1.15857i
\(391\) −8.52752 + 3.10376i −0.431255 + 0.156964i
\(392\) 0.939693 0.342020i 0.0474616 0.0172746i
\(393\) −15.9240 + 5.71000i −0.803259 + 0.288032i
\(394\) −3.48264 19.7510i −0.175453 0.995041i
\(395\) 3.63277 6.29214i 0.182785 0.316592i
\(396\) 13.6729 + 0.130424i 0.687087 + 0.00655404i
\(397\) −7.51055 13.0087i −0.376944 0.652886i 0.613672 0.789561i \(-0.289692\pi\)
−0.990616 + 0.136675i \(0.956358\pi\)
\(398\) −8.00527 + 6.71722i −0.401268 + 0.336704i
\(399\) −1.11619 + 0.927556i −0.0558792 + 0.0464359i
\(400\) 1.24581 7.06536i 0.0622907 0.353268i
\(401\) 26.7772 + 22.4688i 1.33719 + 1.12204i 0.982338 + 0.187115i \(0.0599136\pi\)
0.354853 + 0.934922i \(0.384531\pi\)
\(402\) −12.8020 + 21.9314i −0.638504 + 1.09384i
\(403\) −46.4909 16.9213i −2.31588 0.842911i
\(404\) −8.54851 −0.425304
\(405\) −23.6664 20.6404i −1.17599 1.02563i
\(406\) 0.954796 0.0473857
\(407\) −1.84363 0.671028i −0.0913855 0.0332616i
\(408\) 1.07242 1.83719i 0.0530927 0.0909547i
\(409\) −12.9586 10.8736i −0.640762 0.537663i 0.263490 0.964662i \(-0.415126\pi\)
−0.904252 + 0.426999i \(0.859571\pi\)
\(410\) −4.22746 + 23.9751i −0.208779 + 1.18405i
\(411\) 20.2647 16.8401i 0.999585 0.830660i
\(412\) 6.91208 5.79992i 0.340534 0.285742i
\(413\) −5.53458 9.58618i −0.272339 0.471705i
\(414\) −11.2657 + 19.0899i −0.553680 + 0.938219i
\(415\) −29.3554 + 50.8450i −1.44100 + 2.49588i
\(416\) 1.01699 + 5.76766i 0.0498622 + 0.282783i
\(417\) 19.6043 7.02968i 0.960027 0.344245i
\(418\) 3.58869 1.30618i 0.175529 0.0638872i
\(419\) −29.3761 + 10.6920i −1.43512 + 0.522340i −0.938394 0.345568i \(-0.887686\pi\)
−0.496725 + 0.867908i \(0.665464\pi\)
\(420\) 4.61096 + 3.90668i 0.224992 + 0.190626i
\(421\) −1.81909 10.3166i −0.0886571 0.502799i −0.996507 0.0835049i \(-0.973389\pi\)
0.907850 0.419295i \(-0.137723\pi\)
\(422\) −9.96705 + 17.2634i −0.485189 + 0.840371i
\(423\) 24.3745 + 9.13583i 1.18513 + 0.444199i
\(424\) −3.89571 6.74757i −0.189192 0.327691i
\(425\) −6.74999 + 5.66392i −0.327423 + 0.274740i
\(426\) −0.00713916 0.0416488i −0.000345894 0.00201789i
\(427\) 1.85035 10.4939i 0.0895448 0.507834i
\(428\) 1.90744 + 1.60053i 0.0921996 + 0.0773646i
\(429\) 46.2340 + 0.220505i 2.23220 + 0.0106461i
\(430\) −23.2565 8.46466i −1.12153 0.408202i
\(431\) 27.4019 1.31990 0.659950 0.751309i \(-0.270577\pi\)
0.659950 + 0.751309i \(0.270577\pi\)
\(432\) −0.828996 5.12960i −0.0398851 0.246798i
\(433\) −10.5172 −0.505424 −0.252712 0.967541i \(-0.581323\pi\)
−0.252712 + 0.967541i \(0.581323\pi\)
\(434\) −7.93816 2.88926i −0.381044 0.138689i
\(435\) 2.86126 + 5.01088i 0.137187 + 0.240253i
\(436\) −0.783915 0.657783i −0.0375427 0.0315021i
\(437\) −1.07506 + 6.09698i −0.0514272 + 0.291658i
\(438\) 3.91804 + 1.44725i 0.187211 + 0.0691523i
\(439\) −3.60794 + 3.02742i −0.172198 + 0.144491i −0.724814 0.688945i \(-0.758074\pi\)
0.552616 + 0.833436i \(0.313630\pi\)
\(440\) −7.95154 13.7725i −0.379075 0.656577i
\(441\) −2.82874 + 0.999124i −0.134702 + 0.0475773i
\(442\) 3.59654 6.22938i 0.171070 0.296302i
\(443\) 3.71847 + 21.0885i 0.176670 + 1.00195i 0.936199 + 0.351472i \(0.114319\pi\)
−0.759529 + 0.650474i \(0.774570\pi\)
\(444\) −0.132968 + 0.733622i −0.00631039 + 0.0348162i
\(445\) 23.0437 8.38724i 1.09238 0.397593i
\(446\) −4.64730 + 1.69148i −0.220056 + 0.0800938i
\(447\) 0.849882 4.68904i 0.0401980 0.221784i
\(448\) 0.173648 + 0.984808i 0.00820411 + 0.0465278i
\(449\) −18.0411 + 31.2481i −0.851411 + 1.47469i 0.0285244 + 0.999593i \(0.490919\pi\)
−0.879935 + 0.475094i \(0.842414\pi\)
\(450\) −3.93945 + 21.1595i −0.185707 + 0.997467i
\(451\) 15.9006 + 27.5407i 0.748732 + 1.29684i
\(452\) −5.68609 + 4.77120i −0.267451 + 0.224418i
\(453\) 3.85195 + 1.42284i 0.180980 + 0.0668506i
\(454\) 0.785748 4.45620i 0.0368770 0.209140i
\(455\) 15.6540 + 13.1353i 0.733870 + 0.615790i
\(456\) −0.719641 1.26030i −0.0337003 0.0590188i
\(457\) −29.7643 10.8333i −1.39231 0.506761i −0.466427 0.884560i \(-0.654459\pi\)
−0.925888 + 0.377799i \(0.876681\pi\)
\(458\) 17.5584 0.820449
\(459\) −3.26969 + 5.48064i −0.152616 + 0.255815i
\(460\) 25.7806 1.20203
\(461\) −6.97397 2.53832i −0.324810 0.118221i 0.174468 0.984663i \(-0.444179\pi\)
−0.499279 + 0.866442i \(0.666402\pi\)
\(462\) 7.89430 + 0.0376505i 0.367276 + 0.00175166i
\(463\) −19.1851 16.0982i −0.891607 0.748147i 0.0769251 0.997037i \(-0.475490\pi\)
−0.968532 + 0.248890i \(0.919934\pi\)
\(464\) −0.165799 + 0.940291i −0.00769701 + 0.0436519i
\(465\) −8.62531 50.3187i −0.399989 2.33347i
\(466\) 1.00032 0.839372i 0.0463391 0.0388831i
\(467\) −16.7076 28.9384i −0.773136 1.33911i −0.935836 0.352436i \(-0.885354\pi\)
0.162700 0.986676i \(-0.447980\pi\)
\(468\) −2.88580 17.3313i −0.133396 0.801139i
\(469\) −7.33075 + 12.6972i −0.338502 + 0.586303i
\(470\) −5.25718 29.8149i −0.242496 1.37526i
\(471\) 10.5347 + 8.92562i 0.485413 + 0.411271i
\(472\) 10.4016 3.78588i 0.478773 0.174259i
\(473\) −30.3794 + 11.0572i −1.39684 + 0.508410i
\(474\) −3.39500 + 1.21737i −0.155937 + 0.0559158i
\(475\) 1.04387 + 5.92007i 0.0478960 + 0.271632i
\(476\) 0.614096 1.06365i 0.0281470 0.0487521i
\(477\) 11.4935 + 20.3533i 0.526252 + 0.931912i
\(478\) 3.15098 + 5.45765i 0.144122 + 0.249627i
\(479\) 12.4361 10.4351i 0.568219 0.476792i −0.312836 0.949807i \(-0.601279\pi\)
0.881054 + 0.473015i \(0.156834\pi\)
\(480\) −4.64801 + 3.86252i −0.212152 + 0.176299i
\(481\) −0.437773 + 2.48273i −0.0199607 + 0.113203i
\(482\) 18.3358 + 15.3856i 0.835173 + 0.700793i
\(483\) −6.45162 + 11.0525i −0.293559 + 0.502905i
\(484\) −9.18438 3.34284i −0.417472 0.151947i
\(485\) 47.1621 2.14152
\(486\) 2.34009 + 15.4118i 0.106149 + 0.699094i
\(487\) 5.01634 0.227312 0.113656 0.993520i \(-0.463744\pi\)
0.113656 + 0.993520i \(0.463744\pi\)
\(488\) 10.0131 + 3.64448i 0.453273 + 0.164978i
\(489\) 2.52993 4.33409i 0.114407 0.195994i
\(490\) 2.67286 + 2.24280i 0.120748 + 0.101319i
\(491\) 5.09109 28.8730i 0.229758 1.30302i −0.623620 0.781728i \(-0.714339\pi\)
0.853378 0.521293i \(-0.174550\pi\)
\(492\) 9.29460 7.72385i 0.419033 0.348218i
\(493\) 0.898320 0.753780i 0.0404583 0.0339485i
\(494\) −2.45364 4.24983i −0.110394 0.191209i
\(495\) 23.4594 + 41.5431i 1.05442 + 1.86722i
\(496\) 4.22381 7.31585i 0.189655 0.328491i
\(497\) −0.00423643 0.0240260i −0.000190030 0.00107771i
\(498\) 27.4340 9.83725i 1.22935 0.440818i
\(499\) −12.8185 + 4.66554i −0.573833 + 0.208858i −0.612604 0.790390i \(-0.709878\pi\)
0.0387710 + 0.999248i \(0.487656\pi\)
\(500\) 7.12919 2.59481i 0.318827 0.116043i
\(501\) 6.01278 + 5.09438i 0.268631 + 0.227600i
\(502\) −2.38443 13.5228i −0.106422 0.603552i
\(503\) −17.1288 + 29.6679i −0.763734 + 1.32283i 0.177180 + 0.984179i \(0.443303\pi\)
−0.940913 + 0.338647i \(0.890031\pi\)
\(504\) −0.492740 2.95926i −0.0219484 0.131816i
\(505\) −14.9136 25.8312i −0.663648 1.14947i
\(506\) 25.7978 21.6469i 1.14685 0.962323i
\(507\) −6.23304 36.3626i −0.276819 1.61492i
\(508\) 1.14668 6.50313i 0.0508756 0.288530i
\(509\) 8.68647 + 7.28881i 0.385021 + 0.323071i 0.814670 0.579925i \(-0.196918\pi\)
−0.429649 + 0.902996i \(0.641363\pi\)
\(510\) 7.42241 + 0.0353999i 0.328670 + 0.00156753i
\(511\) 2.26604 + 0.824772i 0.100244 + 0.0364858i
\(512\) −1.00000 −0.0441942
\(513\) 2.12276 + 3.80131i 0.0937221 + 0.167832i
\(514\) −10.2048 −0.450115
\(515\) 29.5845 + 10.7679i 1.30365 + 0.474489i
\(516\) 6.09197 + 10.6688i 0.268184 + 0.469667i
\(517\) −30.2950 25.4206i −1.33237 1.11799i
\(518\) −0.0747482 + 0.423918i −0.00328425 + 0.0186259i
\(519\) 14.9595 + 5.52574i 0.656648 + 0.242553i
\(520\) −15.6540 + 13.1353i −0.686473 + 0.576019i
\(521\) 7.80766 + 13.5233i 0.342060 + 0.592465i 0.984815 0.173607i \(-0.0555422\pi\)
−0.642755 + 0.766071i \(0.722209\pi\)
\(522\) 0.524280 2.81600i 0.0229471 0.123253i
\(523\) 10.3068 17.8520i 0.450687 0.780612i −0.547742 0.836647i \(-0.684512\pi\)
0.998429 + 0.0560349i \(0.0178458\pi\)
\(524\) −1.69601 9.61853i −0.0740904 0.420188i
\(525\) −2.21615 + 12.2271i −0.0967209 + 0.533636i
\(526\) −3.22089 + 1.17231i −0.140437 + 0.0511151i
\(527\) −9.74959 + 3.54856i −0.424699 + 0.154578i
\(528\) −1.40791 + 7.76783i −0.0612714 + 0.338052i
\(529\) 5.48616 + 31.1135i 0.238529 + 1.35276i
\(530\) 13.5928 23.5435i 0.590435 1.02266i
\(531\) −31.3117 + 11.0595i −1.35881 + 0.479940i
\(532\) −0.418950 0.725643i −0.0181638 0.0314606i
\(533\) 31.3032 26.2665i 1.35589 1.13773i
\(534\) −11.4191 4.21799i −0.494152 0.182530i
\(535\) −1.50866 + 8.55601i −0.0652249 + 0.369909i
\(536\) −11.2314 9.42423i −0.485121 0.407065i
\(537\) −7.68998 13.4674i −0.331847 0.581159i
\(538\) −3.16193 1.15085i −0.136320 0.0496166i
\(539\) 4.55783 0.196320
\(540\) 14.0539 11.4540i 0.604785 0.492903i
\(541\) 21.5756 0.927606 0.463803 0.885938i \(-0.346485\pi\)
0.463803 + 0.885938i \(0.346485\pi\)
\(542\) 8.52882 + 3.10424i 0.366344 + 0.133338i
\(543\) 28.4074 + 0.135484i 1.21908 + 0.00581419i
\(544\) 0.940850 + 0.789467i 0.0403386 + 0.0338481i
\(545\) 0.620024 3.51633i 0.0265589 0.150623i
\(546\) −1.71382 9.99817i −0.0733447 0.427882i
\(547\) 11.9267 10.0077i 0.509951 0.427900i −0.351161 0.936315i \(-0.614213\pi\)
0.861112 + 0.508415i \(0.169769\pi\)
\(548\) 7.60618 + 13.1743i 0.324920 + 0.562777i
\(549\) −29.9337 11.2195i −1.27754 0.478836i
\(550\) 16.3498 28.3186i 0.697156 1.20751i
\(551\) −0.138923 0.787870i −0.00591831 0.0335644i
\(552\) −9.76425 8.27285i −0.415594 0.352116i
\(553\) −1.95673 + 0.712191i −0.0832086 + 0.0302855i
\(554\) −11.7339 + 4.27081i −0.498528 + 0.181449i
\(555\) −2.44877 + 0.878077i −0.103945 + 0.0372723i
\(556\) 2.08798 + 11.8415i 0.0885502 + 0.502193i
\(557\) 17.5941 30.4738i 0.745484 1.29122i −0.204484 0.978870i \(-0.565552\pi\)
0.949968 0.312346i \(-0.101115\pi\)
\(558\) −12.8802 + 21.8257i −0.545262 + 0.923955i
\(559\) 20.7708 + 35.9760i 0.878510 + 1.52162i
\(560\) −2.67286 + 2.24280i −0.112949 + 0.0947756i
\(561\) 7.45708 6.19687i 0.314838 0.261632i
\(562\) −3.51004 + 19.9064i −0.148062 + 0.839702i
\(563\) 13.6284 + 11.4356i 0.574369 + 0.481953i 0.883093 0.469199i \(-0.155457\pi\)
−0.308723 + 0.951152i \(0.599902\pi\)
\(564\) −7.57631 + 12.9792i −0.319020 + 0.546523i
\(565\) −24.3371 8.85798i −1.02387 0.372658i
\(566\) −8.18552 −0.344063
\(567\) 1.39347 + 8.89147i 0.0585204 + 0.373407i
\(568\) 0.0243966 0.00102366
\(569\) −8.69197 3.16362i −0.364386 0.132626i 0.153337 0.988174i \(-0.450998\pi\)
−0.517723 + 0.855548i \(0.673220\pi\)
\(570\) 2.55278 4.37325i 0.106924 0.183175i
\(571\) 25.2211 + 21.1630i 1.05547 + 0.885646i 0.993658 0.112442i \(-0.0358672\pi\)
0.0618132 + 0.998088i \(0.480312\pi\)
\(572\) −4.63528 + 26.2880i −0.193811 + 1.09916i
\(573\) 2.34824 1.95140i 0.0980991 0.0815208i
\(574\) 5.34491 4.48491i 0.223092 0.187197i
\(575\) 26.5047 + 45.9076i 1.10532 + 1.91448i
\(576\) 2.99986 + 0.0286153i 0.124994 + 0.00119230i
\(577\) −0.102627 + 0.177755i −0.00427242 + 0.00740005i −0.868154 0.496295i \(-0.834693\pi\)
0.863881 + 0.503695i \(0.168027\pi\)
\(578\) 2.69008 + 15.2562i 0.111893 + 0.634574i
\(579\) 10.2341 3.66972i 0.425313 0.152508i
\(580\) −3.13054 + 1.13942i −0.129989 + 0.0473120i
\(581\) 15.8118 5.75502i 0.655983 0.238758i
\(582\) −17.8623 15.1340i −0.740418 0.627326i
\(583\) −6.16659 34.9725i −0.255394 1.44841i
\(584\) −1.20574 + 2.08840i −0.0498937 + 0.0864185i
\(585\) 47.3357 38.9560i 1.95709 1.61063i
\(586\) −5.46408 9.46406i −0.225719 0.390957i
\(587\) −12.6791 + 10.6390i −0.523322 + 0.439119i −0.865788 0.500411i \(-0.833182\pi\)
0.342466 + 0.939530i \(0.388738\pi\)
\(588\) −0.292629 1.70715i −0.0120678 0.0704018i
\(589\) −1.22913 + 6.97073i −0.0506453 + 0.287224i
\(590\) 29.5864 + 24.8259i 1.21805 + 1.02207i
\(591\) −34.7371 0.165673i −1.42889 0.00681486i
\(592\) −0.404498 0.147225i −0.0166248 0.00605092i
\(593\) −15.3451 −0.630147 −0.315074 0.949067i \(-0.602029\pi\)
−0.315074 + 0.949067i \(0.602029\pi\)
\(594\) 4.44582 23.2622i 0.182414 0.954458i
\(595\) 4.28538 0.175683
\(596\) 2.58540 + 0.941009i 0.105902 + 0.0385452i
\(597\) 8.97523 + 15.7182i 0.367332 + 0.643303i
\(598\) −33.1492 27.8155i −1.35557 1.13746i
\(599\) −0.816771 + 4.63214i −0.0333724 + 0.189264i −0.996937 0.0782126i \(-0.975079\pi\)
0.963564 + 0.267477i \(0.0861898\pi\)
\(600\) −11.6565 4.30571i −0.475877 0.175780i
\(601\) 6.76569 5.67709i 0.275978 0.231573i −0.494284 0.869300i \(-0.664570\pi\)
0.770262 + 0.637727i \(0.220125\pi\)
\(602\) 3.54654 + 6.14278i 0.144546 + 0.250361i
\(603\) 33.4229 + 28.5928i 1.36108 + 1.16439i
\(604\) −1.18540 + 2.05317i −0.0482331 + 0.0835421i
\(605\) −5.92185 33.5845i −0.240757 1.36540i
\(606\) −2.64063 + 14.5691i −0.107268 + 0.591829i
\(607\) 19.4386 7.07507i 0.788988 0.287168i 0.0840729 0.996460i \(-0.473207\pi\)
0.704915 + 0.709291i \(0.250985\pi\)
\(608\) 0.787369 0.286579i 0.0319320 0.0116223i
\(609\) 0.294936 1.62724i 0.0119514 0.0659392i
\(610\) 6.45621 + 36.6150i 0.261404 + 1.48250i
\(611\) −25.4084 + 44.0087i −1.02791 + 1.78040i
\(612\) −2.79983 2.39521i −0.113176 0.0968208i
\(613\) 6.82664 + 11.8241i 0.275726 + 0.477571i 0.970318 0.241833i \(-0.0777486\pi\)
−0.694592 + 0.719404i \(0.744415\pi\)
\(614\) 2.79232 2.34304i 0.112689 0.0945573i
\(615\) 39.5545 + 14.6107i 1.59499 + 0.589160i
\(616\) −0.791459 + 4.48859i −0.0318888 + 0.180850i
\(617\) −32.6841 27.4252i −1.31581 1.10410i −0.987175 0.159641i \(-0.948966\pi\)
−0.328637 0.944456i \(-0.606589\pi\)
\(618\) −7.74958 13.5717i −0.311734 0.545935i
\(619\) −12.5311 4.56096i −0.503669 0.183321i 0.0776745 0.996979i \(-0.475251\pi\)
−0.581343 + 0.813658i \(0.697473\pi\)
\(620\) 29.4752 1.18375
\(621\) 29.0547 + 25.0968i 1.16592 + 1.00710i
\(622\) −20.1029 −0.806052
\(623\) −6.60435 2.40379i −0.264598 0.0963057i
\(624\) 10.1439 + 0.0483795i 0.406080 + 0.00193673i
\(625\) −7.20111 6.04244i −0.288044 0.241698i
\(626\) −5.77083 + 32.7280i −0.230649 + 1.30807i
\(627\) −1.11755 6.51963i −0.0446307 0.260369i
\(628\) −6.10672 + 5.12414i −0.243685 + 0.204476i
\(629\) 0.264342 + 0.457855i 0.0105400 + 0.0182559i
\(630\) 8.08241 6.65161i 0.322011 0.265006i
\(631\) −13.4869 + 23.3600i −0.536904 + 0.929945i 0.462164 + 0.886794i \(0.347073\pi\)
−0.999069 + 0.0431512i \(0.986260\pi\)
\(632\) −0.361589 2.05067i −0.0143832 0.0815714i
\(633\) 26.3430 + 22.3193i 1.04704 + 0.887114i
\(634\) −25.9063 + 9.42911i −1.02887 + 0.374478i
\(635\) 21.6511 7.88035i 0.859197 0.312722i
\(636\) −12.7031 + 4.55508i −0.503713 + 0.180621i
\(637\) −1.01699 5.76766i −0.0402948 0.228523i
\(638\) −2.17590 + 3.76877i −0.0861447 + 0.149207i
\(639\) −0.0731866 0.000698118i −0.00289522 2.76171e-5i
\(640\) −1.74459 3.02172i −0.0689609 0.119444i
\(641\) 10.3416 8.67764i 0.408469 0.342746i −0.415287 0.909690i \(-0.636319\pi\)
0.823756 + 0.566944i \(0.191874\pi\)
\(642\) 3.31697 2.75641i 0.130910 0.108787i
\(643\) 5.47398 31.0445i 0.215873 1.22427i −0.663513 0.748164i \(-0.730935\pi\)
0.879386 0.476110i \(-0.157953\pi\)
\(644\) −5.66011 4.74939i −0.223039 0.187152i
\(645\) −21.6101 + 37.0209i −0.850896 + 1.45769i
\(646\) −0.967040 0.351974i −0.0380477 0.0138482i
\(647\) −44.3345 −1.74297 −0.871484 0.490423i \(-0.836842\pi\)
−0.871484 + 0.490423i \(0.836842\pi\)
\(648\) −8.99836 0.171684i −0.353489 0.00674439i
\(649\) 50.4514 1.98039
\(650\) −39.4836 14.3709i −1.54868 0.563672i
\(651\) −7.37620 + 12.6364i −0.289096 + 0.495259i
\(652\) 2.21954 + 1.86242i 0.0869240 + 0.0729379i
\(653\) −5.23455 + 29.6866i −0.204844 + 1.16173i 0.692842 + 0.721089i \(0.256358\pi\)
−0.897686 + 0.440637i \(0.854753\pi\)
\(654\) −1.36320 + 1.13283i −0.0533053 + 0.0442970i
\(655\) 26.1056 21.9052i 1.02003 0.855908i
\(656\) 3.48864 + 6.04250i 0.136209 + 0.235920i
\(657\) 3.67680 6.23040i 0.143446 0.243071i
\(658\) −4.33840 + 7.51433i −0.169128 + 0.292939i
\(659\) 0.176928 + 1.00341i 0.00689212 + 0.0390871i 0.988060 0.154070i \(-0.0492383\pi\)
−0.981168 + 0.193158i \(0.938127\pi\)
\(660\) −25.9284 + 9.29737i −1.00926 + 0.361900i
\(661\) 38.7460 14.1024i 1.50704 0.548519i 0.549170 0.835711i \(-0.314944\pi\)
0.957873 + 0.287192i \(0.0927217\pi\)
\(662\) 21.4543 7.80872i 0.833844 0.303495i
\(663\) −9.50567 8.05377i −0.369169 0.312782i
\(664\) 2.92190 + 16.5709i 0.113392 + 0.643076i
\(665\) 1.46179 2.53190i 0.0566859 0.0981828i
\(666\) 1.20923 + 0.453231i 0.0468566 + 0.0175623i
\(667\) −3.52737 6.10959i −0.136580 0.236564i
\(668\) −3.48547 + 2.92465i −0.134857 + 0.113158i
\(669\) 1.44721 + 8.44281i 0.0559524 + 0.326418i
\(670\) 8.88324 50.3794i 0.343190 1.94632i
\(671\) 37.2046 + 31.2183i 1.43627 + 1.20517i
\(672\) 1.73203 + 0.00826063i 0.0668146 + 0.000318661i
\(673\) −3.71215 1.35111i −0.143093 0.0520816i 0.269481 0.963006i \(-0.413148\pi\)
−0.412574 + 0.910924i \(0.635370\pi\)
\(674\) 27.8032 1.07094
\(675\) 34.8448 + 13.2501i 1.34118 + 0.509996i
\(676\) 21.3002 0.819237
\(677\) 21.7634 + 7.92124i 0.836436 + 0.304438i 0.724498 0.689277i \(-0.242072\pi\)
0.111939 + 0.993715i \(0.464294\pi\)
\(678\) 6.37504 + 11.1645i 0.244832 + 0.428771i
\(679\) −10.3544 8.68836i −0.397365 0.333429i
\(680\) −0.744148 + 4.22028i −0.0285368 + 0.161840i
\(681\) −7.35191 2.71565i −0.281726 0.104064i
\(682\) 29.4949 24.7491i 1.12942 0.947693i
\(683\) 6.84387 + 11.8539i 0.261873 + 0.453578i 0.966740 0.255762i \(-0.0823264\pi\)
−0.704866 + 0.709340i \(0.748993\pi\)
\(684\) −2.37020 + 0.837167i −0.0906269 + 0.0320099i
\(685\) −26.5393 + 45.9674i −1.01401 + 1.75632i
\(686\) −0.173648 0.984808i −0.00662992 0.0376001i
\(687\) 5.42377 29.9244i 0.206930 1.14169i
\(688\) −6.66531 + 2.42597i −0.254113 + 0.0924894i
\(689\) −42.8796 + 15.6069i −1.63358 + 0.594575i
\(690\) 7.96362 43.9375i 0.303170 1.67267i
\(691\) 0.0991261 + 0.562172i 0.00377093 + 0.0213860i 0.986635 0.162945i \(-0.0520993\pi\)
−0.982864 + 0.184331i \(0.940988\pi\)
\(692\) −4.60362 + 7.97370i −0.175003 + 0.303115i
\(693\) 2.50271 13.4425i 0.0950701 0.510638i
\(694\) 2.93941 + 5.09121i 0.111578 + 0.193260i
\(695\) −32.1391 + 26.9679i −1.21911 + 1.02295i
\(696\) 1.55131 + 0.573023i 0.0588021 + 0.0217204i
\(697\) 1.48807 8.43925i 0.0563646 0.319660i
\(698\) −9.56565 8.02654i −0.362065 0.303809i
\(699\) −1.12153 1.96412i −0.0424201 0.0742897i
\(700\) −6.74169 2.45378i −0.254812 0.0927440i
\(701\) −7.18650 −0.271430 −0.135715 0.990748i \(-0.543333\pi\)
−0.135715 + 0.990748i \(0.543333\pi\)
\(702\) −30.4288 0.435402i −1.14846 0.0164332i
\(703\) 0.360681 0.0136033
\(704\) −4.28296 1.55887i −0.161420 0.0587521i
\(705\) −52.4370 0.250089i −1.97489 0.00941891i
\(706\) 0.0104273 + 0.00874950i 0.000392435 + 0.000329292i
\(707\) −1.48443 + 8.41864i −0.0558279 + 0.316616i
\(708\) −3.23916 18.8967i −0.121735 0.710183i
\(709\) −17.6393 + 14.8011i −0.662458 + 0.555868i −0.910822 0.412799i \(-0.864551\pi\)
0.248365 + 0.968667i \(0.420107\pi\)
\(710\) 0.0425621 + 0.0737197i 0.00159733 + 0.00276665i
\(711\) 1.02604 + 6.16209i 0.0384794 + 0.231096i
\(712\) 3.51410 6.08660i 0.131697 0.228105i
\(713\) 10.8386 + 61.4690i 0.405910 + 2.30203i
\(714\) −1.62306 1.37515i −0.0607415 0.0514638i
\(715\) −87.5216 + 31.8552i −3.27312 + 1.19132i
\(716\) 8.41371 3.06234i 0.314435 0.114445i
\(717\) 10.2747 3.68429i 0.383716 0.137592i
\(718\) −5.52548 31.3365i −0.206209 1.16947i
\(719\) 11.3764 19.7046i 0.424270 0.734857i −0.572082 0.820196i \(-0.693864\pi\)
0.996352 + 0.0853396i \(0.0271975\pi\)
\(720\) 5.14706 + 9.11466i 0.191820 + 0.339683i
\(721\) −4.51154 7.81422i −0.168019 0.291017i
\(722\) 14.0170 11.7617i 0.521660 0.437724i
\(723\) 31.8853 26.4968i 1.18583 0.985427i
\(724\) −2.84804 + 16.1521i −0.105847 + 0.600287i
\(725\) −5.24744 4.40313i −0.194885 0.163528i
\(726\) −8.53419 + 14.6202i −0.316734 + 0.542606i
\(727\) −37.4420 13.6278i −1.38865 0.505427i −0.463860 0.885909i \(-0.653536\pi\)
−0.924788 + 0.380482i \(0.875758\pi\)
\(728\) 5.85663 0.217061
\(729\) 26.9889 + 0.772520i 0.999591 + 0.0286118i
\(730\) −8.41405 −0.311418
\(731\) 8.18628 + 2.97956i 0.302781 + 0.110203i
\(732\) 9.30428 15.9394i 0.343896 0.589139i
\(733\) 3.13291 + 2.62883i 0.115717 + 0.0970979i 0.698810 0.715307i \(-0.253713\pi\)
−0.583093 + 0.812405i \(0.698158\pi\)
\(734\) −6.51601 + 36.9541i −0.240510 + 1.36400i
\(735\) 4.64801 3.86252i 0.171445 0.142471i
\(736\) 5.66011 4.74939i 0.208634 0.175065i
\(737\) −33.4123 57.8718i −1.23076 2.13173i
\(738\) −10.2925 18.2265i −0.378874 0.670927i
\(739\) −11.4550 + 19.8407i −0.421380 + 0.729852i −0.996075 0.0885160i \(-0.971788\pi\)
0.574694 + 0.818368i \(0.305121\pi\)
\(740\) −0.260810 1.47913i −0.00958756 0.0543737i
\(741\) −8.00084 + 2.86893i −0.293918 + 0.105393i
\(742\) −7.32154 + 2.66482i −0.268782 + 0.0978287i
\(743\) −22.3169 + 8.12269i −0.818728 + 0.297993i −0.717224 0.696843i \(-0.754588\pi\)
−0.101504 + 0.994835i \(0.532365\pi\)
\(744\) −11.1636 9.45843i −0.409276 0.346763i
\(745\) 1.66700 + 9.45402i 0.0610741 + 0.346368i
\(746\) −2.72500 + 4.71984i −0.0997695 + 0.172806i
\(747\) −8.29112 49.7941i −0.303356 1.82187i
\(748\) 2.79895 + 4.84792i 0.102340 + 0.177257i
\(749\) 1.90744 1.60053i 0.0696963 0.0584822i
\(750\) −2.22009 12.9517i −0.0810664 0.472929i
\(751\) 4.93248 27.9735i 0.179989 1.02077i −0.752238 0.658892i \(-0.771026\pi\)
0.932227 0.361875i \(-0.117863\pi\)
\(752\) −6.64681 5.57734i −0.242384 0.203385i
\(753\) −23.7832 0.113430i −0.866709 0.00413362i
\(754\) 5.25466 + 1.91254i 0.191363 + 0.0696506i
\(755\) −8.27211 −0.301053
\(756\) −5.19562 0.0743434i −0.188963 0.00270384i
\(757\) 13.3407 0.484876 0.242438 0.970167i \(-0.422053\pi\)
0.242438 + 0.970167i \(0.422053\pi\)
\(758\) −16.4043 5.97069i −0.595832 0.216865i
\(759\) −28.9236 50.6535i −1.04986 1.83860i
\(760\) 2.23960 + 1.87924i 0.0812387 + 0.0681673i
\(761\) −0.590272 + 3.34760i −0.0213973 + 0.121350i −0.993636 0.112643i \(-0.964068\pi\)
0.972238 + 0.233993i \(0.0751794\pi\)
\(762\) −10.7290 3.96307i −0.388669 0.143567i
\(763\) −0.783915 + 0.657783i −0.0283796 + 0.0238133i
\(764\) 0.881390 + 1.52661i 0.0318876 + 0.0552309i
\(765\) 2.35311 12.6390i 0.0850768 0.456962i
\(766\) 11.7727 20.3909i 0.425365 0.736754i
\(767\) −11.2573 63.8432i −0.406476 2.30524i
\(768\) −0.308899 + 1.70428i −0.0111464 + 0.0614980i
\(769\) 33.2723 12.1101i 1.19983 0.436703i 0.336666 0.941624i \(-0.390701\pi\)
0.863165 + 0.504921i \(0.168478\pi\)
\(770\) −14.9440 + 5.43917i −0.538544 + 0.196014i
\(771\) −3.15226 + 17.3919i −0.113526 + 0.626353i
\(772\) 1.08999 + 6.18166i 0.0392297 + 0.222483i
\(773\) −7.38369 + 12.7889i −0.265573 + 0.459986i −0.967714 0.252052i \(-0.918894\pi\)
0.702141 + 0.712038i \(0.252228\pi\)
\(774\) 20.0644 7.08686i 0.721202 0.254732i
\(775\) 30.3031 + 52.4865i 1.08852 + 1.88537i
\(776\) 10.3544 8.68836i 0.371701 0.311894i
\(777\) 0.699387 + 0.258340i 0.0250904 + 0.00926790i
\(778\) −1.51951 + 8.61757i −0.0544771 + 0.308955i
\(779\) −4.47850 3.75791i −0.160459 0.134641i
\(780\) 17.5507 + 30.7363i 0.628416 + 1.10054i
\(781\) 0.104490 + 0.0380312i 0.00373894 + 0.00136086i
\(782\) −9.07480 −0.324514
\(783\) −4.63731 1.76338i −0.165724 0.0630181i
\(784\) 1.00000 0.0357143
\(785\) −26.1374 9.51324i −0.932885 0.339542i
\(786\) −16.9166 0.0806808i −0.603395 0.00287779i
\(787\) 21.5566 + 18.0881i 0.768409 + 0.644772i 0.940301 0.340344i \(-0.110544\pi\)
−0.171892 + 0.985116i \(0.554988\pi\)
\(788\) 3.48264 19.7510i 0.124064 0.703601i
\(789\) 1.00301 + 5.85143i 0.0357083 + 0.208317i
\(790\) 5.56573 4.67020i 0.198020 0.166158i
\(791\) 3.71133 + 6.42822i 0.131960 + 0.228561i
\(792\) 12.8037 + 4.79895i 0.454959 + 0.170523i
\(793\) 31.2034 54.0459i 1.10807 1.91923i
\(794\) −2.60839 14.7929i −0.0925682 0.524981i
\(795\) −35.9259 30.4386i −1.27416 1.07955i
\(796\) −9.81992 + 3.57416i −0.348058 + 0.126683i
\(797\) −5.70104 + 2.07501i −0.201941 + 0.0735006i −0.441011 0.897502i \(-0.645380\pi\)
0.239069 + 0.971002i \(0.423158\pi\)
\(798\) −1.36612 + 0.489859i −0.0483599 + 0.0173408i
\(799\) 1.85053 + 10.4949i 0.0654670 + 0.371282i
\(800\) 3.58718 6.21318i 0.126826 0.219669i
\(801\) −10.7160 + 18.1584i −0.378631 + 0.641596i
\(802\) 17.4776 + 30.2721i 0.617155 + 1.06894i
\(803\) −8.41966 + 7.06493i −0.297123 + 0.249316i
\(804\) −19.5309 + 16.2303i −0.688802 + 0.572398i
\(805\) 4.47676 25.3890i 0.157785 0.894844i
\(806\) −37.8997 31.8017i −1.33496 1.12017i
\(807\) −2.93809 + 5.03333i −0.103426 + 0.177182i
\(808\) −8.03298 2.92376i −0.282599 0.102858i
\(809\) 18.9454 0.666086 0.333043 0.942912i \(-0.391925\pi\)
0.333043 + 0.942912i \(0.391925\pi\)
\(810\) −15.1797 27.4900i −0.533359 0.965901i
\(811\) 53.4126 1.87557 0.937785 0.347217i \(-0.112873\pi\)
0.937785 + 0.347217i \(0.112873\pi\)
\(812\) 0.897215 + 0.326560i 0.0314861 + 0.0114600i
\(813\) 7.92505 13.5766i 0.277944 0.476153i
\(814\) −1.50294 1.26112i −0.0526781 0.0442022i
\(815\) −1.75551 + 9.95598i −0.0614927 + 0.348743i
\(816\) 1.63610 1.35961i 0.0572750 0.0475958i
\(817\) 4.55283 3.82028i 0.159283 0.133655i
\(818\) −8.45814 14.6499i −0.295732 0.512223i
\(819\) −17.5691 0.167589i −0.613914 0.00585605i
\(820\) −12.1725 + 21.0834i −0.425082 + 0.736263i
\(821\) −7.56323 42.8932i −0.263959 1.49698i −0.771984 0.635642i \(-0.780736\pi\)
0.508025 0.861342i \(-0.330376\pi\)
\(822\) 24.8022 8.89355i 0.865078 0.310198i
\(823\) −29.9706 + 10.9084i −1.04471 + 0.380243i −0.806663 0.591012i \(-0.798729\pi\)
−0.238045 + 0.971254i \(0.576507\pi\)
\(824\) 8.47892 3.08607i 0.295377 0.107509i
\(825\) −43.2125 36.6122i −1.50447 1.27467i
\(826\) −1.92214 10.9010i −0.0668798 0.379294i
\(827\) 17.9460 31.0835i 0.624045 1.08088i −0.364680 0.931133i \(-0.618821\pi\)
0.988725 0.149745i \(-0.0478452\pi\)
\(828\) −17.1154 + 14.0856i −0.594803 + 0.489507i
\(829\) −28.2608 48.9491i −0.981537 1.70007i −0.656415 0.754400i \(-0.727928\pi\)
−0.325122 0.945672i \(-0.605405\pi\)
\(830\) −44.9751 + 37.7386i −1.56111 + 1.30992i
\(831\) 3.65406 + 21.3172i 0.126758 + 0.739486i
\(832\) −1.01699 + 5.76766i −0.0352579 + 0.199958i
\(833\) −0.940850 0.789467i −0.0325985 0.0273534i
\(834\) 20.8263 + 0.0993275i 0.721156 + 0.00343943i
\(835\) −14.9182 5.42977i −0.516265 0.187905i
\(836\) 3.81901 0.132083
\(837\) 33.2185 + 28.6934i 1.14820 + 0.991790i
\(838\) −31.2614 −1.07991
\(839\) −5.29894 1.92866i −0.182940 0.0665847i 0.248926 0.968523i \(-0.419922\pi\)
−0.431866 + 0.901938i \(0.642145\pi\)
\(840\) 2.99672 + 5.24812i 0.103397 + 0.181077i
\(841\) −21.5169 18.0549i −0.741963 0.622581i
\(842\) 1.81909 10.3166i 0.0626900 0.355533i
\(843\) 32.8419 + 12.1312i 1.13114 + 0.417820i
\(844\) −15.2704 + 12.8134i −0.525629 + 0.441055i
\(845\) 37.1600 + 64.3631i 1.27834 + 2.21416i
\(846\) 19.7799 + 16.9215i 0.680048 + 0.581771i
\(847\) −4.88691 + 8.46437i −0.167916 + 0.290839i
\(848\) −1.35297 7.67305i −0.0464610 0.263494i
\(849\) −2.52850 + 13.9505i −0.0867780 + 0.478778i
\(850\) −8.28009 + 3.01371i −0.284005 + 0.103369i
\(851\) 2.98873 1.08781i 0.102452 0.0372896i
\(852\) 0.00753610 0.0415788i 0.000258183 0.00142447i
\(853\) −3.33935 18.9384i −0.114337 0.648439i −0.987076 0.160252i \(-0.948769\pi\)
0.872739 0.488187i \(-0.162342\pi\)
\(854\) 5.32788 9.22815i 0.182316 0.315781i
\(855\) −6.66470 5.70156i −0.227928 0.194989i
\(856\) 1.24499 + 2.15639i 0.0425530 + 0.0737039i
\(857\) 29.3114 24.5952i 1.00126 0.840155i 0.0141000 0.999901i \(-0.495512\pi\)
0.987158 + 0.159745i \(0.0510673\pi\)
\(858\) 43.3704 + 16.0202i 1.48064 + 0.546920i
\(859\) −2.86287 + 16.2361i −0.0976799 + 0.553970i 0.896213 + 0.443623i \(0.146307\pi\)
−0.993893 + 0.110347i \(0.964804\pi\)
\(860\) −18.9588 15.9084i −0.646491 0.542470i
\(861\) −5.99252 10.4946i −0.204225 0.357656i
\(862\) 25.7493 + 9.37199i 0.877025 + 0.319211i
\(863\) 47.7136 1.62419 0.812094 0.583526i \(-0.198327\pi\)
0.812094 + 0.583526i \(0.198327\pi\)
\(864\) 0.975424 5.10378i 0.0331846 0.173634i
\(865\) −32.1257 −1.09231
\(866\) −9.88294 3.59709i −0.335836 0.122234i
\(867\) 26.8318 + 0.127970i 0.911257 + 0.00434608i
\(868\) −6.47125 5.43002i −0.219649 0.184307i
\(869\) 1.64806 9.34662i 0.0559066 0.317062i
\(870\) 0.974880 + 5.68730i 0.0330515 + 0.192817i
\(871\) −65.7779 + 55.1942i −2.22880 + 1.87019i
\(872\) −0.511664 0.886229i −0.0173271 0.0300115i
\(873\) −31.3103 + 25.7676i −1.05969 + 0.872101i
\(874\) −3.09552 + 5.36159i −0.104707 + 0.181359i
\(875\) −1.31742 7.47146i −0.0445369 0.252582i
\(876\) 3.18677 + 2.70002i 0.107671 + 0.0912252i
\(877\) 5.40825 1.96844i 0.182624 0.0664696i −0.249090 0.968480i \(-0.580131\pi\)
0.431713 + 0.902011i \(0.357909\pi\)
\(878\) −4.42580 + 1.61086i −0.149363 + 0.0543638i
\(879\) −17.8173 + 6.38890i −0.600962 + 0.215492i
\(880\) −2.76154 15.6615i −0.0930915 0.527948i
\(881\) 21.4627 37.1745i 0.723097 1.25244i −0.236656 0.971594i \(-0.576051\pi\)
0.959753 0.280847i \(-0.0906153\pi\)
\(882\) −2.99986 0.0286153i −0.101011 0.000963528i
\(883\) −11.0225 19.0915i −0.370936 0.642480i 0.618774 0.785569i \(-0.287630\pi\)
−0.989710 + 0.143089i \(0.954296\pi\)
\(884\) 5.51021 4.62362i 0.185329 0.155509i
\(885\) 51.4496 42.7549i 1.72946 1.43719i
\(886\) −3.71847 + 21.0885i −0.124925 + 0.708483i
\(887\) 5.77474 + 4.84558i 0.193897 + 0.162699i 0.734567 0.678536i \(-0.237385\pi\)
−0.540671 + 0.841234i \(0.681830\pi\)
\(888\) −0.375863 + 0.643902i −0.0126131 + 0.0216079i
\(889\) −6.20521 2.25851i −0.208116 0.0757481i
\(890\) 24.5226 0.822001
\(891\) −38.2720 14.7626i −1.28216 0.494565i
\(892\) −4.94555 −0.165589
\(893\) 6.83184 + 2.48659i 0.228619 + 0.0832104i
\(894\) 2.40237 4.11558i 0.0803474 0.137645i
\(895\) 23.9320 + 20.0813i 0.799958 + 0.671245i
\(896\) −0.173648 + 0.984808i −0.00580118 + 0.0329001i
\(897\) −57.6452 + 47.9034i −1.92472 + 1.59945i
\(898\) −27.6405 + 23.1932i −0.922376 + 0.773966i
\(899\) −4.03288 6.98515i −0.134504 0.232968i
\(900\) −10.9388 + 18.5360i −0.364628 + 0.617868i
\(901\) −4.78468 + 8.28731i −0.159401 + 0.276090i
\(902\) 5.52223 + 31.3181i 0.183870 + 1.04278i
\(903\) 11.5646 4.14680i 0.384845 0.137997i
\(904\) −6.97502 + 2.53870i −0.231986 + 0.0844360i
\(905\) −53.7756 + 19.5727i −1.78756 + 0.650619i
\(906\) 3.13301 + 2.65447i 0.104087 + 0.0881889i
\(907\) 3.26033 + 18.4902i 0.108257 + 0.613958i 0.989869 + 0.141983i \(0.0453478\pi\)
−0.881612 + 0.471975i \(0.843541\pi\)
\(908\) 2.26247 3.91871i 0.0750827 0.130047i
\(909\) 24.0142 + 9.00076i 0.796500 + 0.298536i
\(910\) 10.2174 + 17.6971i 0.338704 + 0.586653i
\(911\) 1.53361 1.28685i 0.0508107 0.0426353i −0.617029 0.786941i \(-0.711664\pi\)
0.667839 + 0.744305i \(0.267219\pi\)
\(912\) −0.245194 1.43042i −0.00811918 0.0473661i
\(913\) −13.3175 + 75.5274i −0.440745 + 2.49959i
\(914\) −24.2641 20.3600i −0.802584 0.673448i
\(915\) 64.3966 + 0.307129i 2.12889 + 0.0101534i
\(916\) 16.4995 + 6.00532i 0.545158 + 0.198421i
\(917\) −9.76691 −0.322532
\(918\) −4.94699 + 4.03182i −0.163275 + 0.133070i
\(919\) 35.0413 1.15591 0.577953 0.816070i \(-0.303852\pi\)
0.577953 + 0.816070i \(0.303852\pi\)
\(920\) 24.2259 + 8.81750i 0.798703 + 0.290704i
\(921\) −3.13065 5.48267i −0.103159 0.180660i
\(922\) −5.68523 4.77048i −0.187233 0.157107i
\(923\) 0.0248112 0.140712i 0.000816672 0.00463158i
\(924\) 7.40534 + 2.73539i 0.243618 + 0.0899877i
\(925\) 2.36574 1.98509i 0.0777852 0.0652695i
\(926\) −12.5222 21.6890i −0.411504 0.712746i
\(927\) −25.5239 + 9.01518i −0.838315 + 0.296097i
\(928\) −0.477398 + 0.826878i −0.0156714 + 0.0271436i
\(929\) 3.54406 + 20.0994i 0.116277 + 0.659439i 0.986110 + 0.166093i \(0.0531153\pi\)
−0.869833 + 0.493346i \(0.835774\pi\)
\(930\) 9.10488 50.2341i 0.298561 1.64724i
\(931\) −0.787369 + 0.286579i −0.0258050 + 0.00939224i
\(932\) 1.22708 0.446620i 0.0401943 0.0146295i
\(933\) −6.20976 + 34.2610i −0.203298 + 1.12165i
\(934\) −5.80249 32.9076i −0.189863 1.07677i
\(935\) −9.76602 + 16.9152i −0.319383 + 0.553187i
\(936\) 3.21589 17.2731i 0.105115 0.564589i
\(937\) 14.7025 + 25.4654i 0.480309 + 0.831919i 0.999745 0.0225901i \(-0.00719126\pi\)
−0.519436 + 0.854509i \(0.673858\pi\)
\(938\) −11.2314 + 9.42423i −0.366717 + 0.307712i
\(939\) 53.9952 + 19.9448i 1.76207 + 0.650874i
\(940\) 5.25718 29.8149i 0.171470 0.972456i
\(941\) −18.8660 15.8304i −0.615014 0.516058i 0.281218 0.959644i \(-0.409262\pi\)
−0.896232 + 0.443586i \(0.853706\pi\)
\(942\) 6.84663 + 11.9904i 0.223075 + 0.390669i
\(943\) −48.4443 17.6323i −1.57756 0.574186i
\(944\) 11.0692 0.360271
\(945\) −8.83958 15.8294i −0.287551 0.514930i
\(946\) −32.3290 −1.05111
\(947\) 44.9500 + 16.3604i 1.46068 + 0.531643i 0.945552 0.325471i \(-0.105523\pi\)
0.515126 + 0.857115i \(0.327745\pi\)
\(948\) −3.60662 0.0172012i −0.117138 0.000558668i
\(949\) 10.8189 + 9.07816i 0.351197 + 0.294690i
\(950\) −1.04387 + 5.92007i −0.0338676 + 0.192073i
\(951\) 8.06745 + 47.0643i 0.261605 + 1.52616i
\(952\) 0.940850 0.789467i 0.0304931 0.0255868i
\(953\) −2.66478 4.61554i −0.0863209 0.149512i 0.819632 0.572890i \(-0.194178\pi\)
−0.905953 + 0.423378i \(0.860844\pi\)
\(954\) 3.83915 + 23.0568i 0.124297 + 0.746492i
\(955\) −3.07532 + 5.32662i −0.0995152 + 0.172365i
\(956\) 1.09432 + 6.20621i 0.0353929 + 0.200723i
\(957\) 5.75092 + 4.87252i 0.185901 + 0.157506i
\(958\) 15.2551 5.55240i 0.492870 0.179390i
\(959\) 14.2949 5.20293i 0.461607 0.168011i
\(960\) −5.68876 + 2.03987i −0.183604 + 0.0658364i
\(961\) 7.00883 + 39.7490i 0.226091 + 1.28223i
\(962\) −1.26052 + 2.18328i −0.0406407 + 0.0703918i
\(963\) −3.67310 6.50450i −0.118364 0.209605i
\(964\) 11.9678 + 20.7289i 0.385458 + 0.667633i
\(965\) −16.7776 + 14.0781i −0.540091 + 0.453190i
\(966\) −9.84271 + 8.17934i −0.316684 + 0.263166i
\(967\) 5.08495 28.8382i 0.163521 0.927374i −0.787055 0.616883i \(-0.788395\pi\)
0.950576 0.310491i \(-0.100494\pi\)
\(968\) −7.48717 6.28248i −0.240647 0.201927i
\(969\) −0.898581 + 1.53939i −0.0288666 + 0.0494522i
\(970\) 44.3179 + 16.1304i 1.42296 + 0.517916i
\(971\) 25.3779 0.814414 0.407207 0.913336i \(-0.366503\pi\)
0.407207 + 0.913336i \(0.366503\pi\)
\(972\) −3.07219 + 15.2827i −0.0985404 + 0.490194i
\(973\) 12.0242 0.385479
\(974\) 4.71382 + 1.71569i 0.151040 + 0.0549742i
\(975\) −36.6885 + 62.8521i −1.17497 + 2.01288i
\(976\) 8.16278 + 6.84939i 0.261284 + 0.219244i
\(977\) 5.36097 30.4036i 0.171513 0.972696i −0.770580 0.637343i \(-0.780033\pi\)
0.942093 0.335353i \(-0.108856\pi\)
\(978\) 3.85970 3.20743i 0.123420 0.102562i
\(979\) 24.5390 20.5906i 0.784269 0.658080i
\(980\) 1.74459 + 3.02172i 0.0557288 + 0.0965252i
\(981\) 1.50956 + 2.67321i 0.0481967 + 0.0853489i
\(982\) 14.6592 25.3905i 0.467794 0.810243i
\(983\) −0.159466 0.904379i −0.00508619 0.0288452i 0.982159 0.188052i \(-0.0602174\pi\)
−0.987245 + 0.159207i \(0.949106\pi\)
\(984\) 11.3758 4.07911i 0.362647 0.130037i
\(985\) 65.7577 23.9338i 2.09521 0.762596i
\(986\) 1.10195 0.401078i 0.0350933 0.0127729i
\(987\) 11.4664 + 9.71503i 0.364980 + 0.309233i
\(988\) −0.852140 4.83273i −0.0271102 0.153749i
\(989\) 26.2045 45.3875i 0.833253 1.44324i
\(990\) 7.83609 + 47.0613i 0.249047 + 1.49571i
\(991\) −3.22919 5.59313i −0.102579 0.177672i 0.810168 0.586198i \(-0.199376\pi\)
−0.912746 + 0.408527i \(0.866043\pi\)
\(992\) 6.47125 5.43002i 0.205462 0.172403i
\(993\) −6.68106 38.9763i −0.212017 1.23687i
\(994\) 0.00423643 0.0240260i 0.000134371 0.000762059i
\(995\) −27.9318 23.4376i −0.885498 0.743021i
\(996\) 29.1441 + 0.138998i 0.923466 + 0.00440431i
\(997\) 33.8987 + 12.3381i 1.07358 + 0.390752i 0.817515 0.575907i \(-0.195351\pi\)
0.256067 + 0.966659i \(0.417573\pi\)
\(998\) −13.6411 −0.431802
\(999\) 1.14596 1.92086i 0.0362566 0.0607734i
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.u.e.85.3 36
27.7 even 9 inner 378.2.u.e.169.3 yes 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
378.2.u.e.85.3 36 1.1 even 1 trivial
378.2.u.e.169.3 yes 36 27.7 even 9 inner