Properties

Label 155.2.x.a.42.8
Level $155$
Weight $2$
Character 155.42
Analytic conductor $1.238$
Analytic rank $0$
Dimension $224$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [155,2,Mod(3,155)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(155, base_ring=CyclotomicField(60))
 
chi = DirichletCharacter(H, H._module([45, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("155.3");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 155 = 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 155.x (of order \(60\), degree \(16\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.23768123133\)
Analytic rank: \(0\)
Dimension: \(224\)
Relative dimension: \(14\) over \(\Q(\zeta_{60})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label 42.8
Character \(\chi\) \(=\) 155.42
Dual form 155.2.x.a.48.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.0322043 - 0.0632044i) q^{2} +(0.0569594 - 1.08685i) q^{3} +(1.17261 + 1.61396i) q^{4} +(0.551134 + 2.16708i) q^{5} +(-0.0668594 - 0.0386013i) q^{6} +(-1.97885 + 2.44368i) q^{7} +(0.279898 - 0.0443315i) q^{8} +(1.80557 + 0.189773i) q^{9} +O(q^{10})\) \(q+(0.0322043 - 0.0632044i) q^{2} +(0.0569594 - 1.08685i) q^{3} +(1.17261 + 1.61396i) q^{4} +(0.551134 + 2.16708i) q^{5} +(-0.0668594 - 0.0386013i) q^{6} +(-1.97885 + 2.44368i) q^{7} +(0.279898 - 0.0443315i) q^{8} +(1.80557 + 0.189773i) q^{9} +(0.154718 + 0.0349552i) q^{10} +(1.77665 - 3.99042i) q^{11} +(1.82093 - 1.18252i) q^{12} +(-3.27771 - 2.12857i) q^{13} +(0.0907237 + 0.203769i) q^{14} +(2.38669 - 0.475565i) q^{15} +(-1.22675 + 3.77554i) q^{16} +(0.623752 - 1.62493i) q^{17} +(0.0701414 - 0.108008i) q^{18} +(1.46007 - 6.86910i) q^{19} +(-2.85133 + 3.43066i) q^{20} +(2.54320 + 2.28990i) q^{21} +(-0.194996 - 0.240801i) q^{22} +(1.02696 + 6.48399i) q^{23} +(-0.0322389 - 0.306732i) q^{24} +(-4.39250 + 2.38871i) q^{25} +(-0.240092 + 0.138617i) q^{26} +(0.819861 - 5.17640i) q^{27} +(-6.26443 - 0.328305i) q^{28} +(0.255441 + 0.786167i) q^{29} +(0.0468037 - 0.166164i) q^{30} +(-3.11543 - 4.61455i) q^{31} +(0.599894 + 0.599894i) q^{32} +(-4.23579 - 2.15824i) q^{33} +(-0.0826153 - 0.0917536i) q^{34} +(-6.38626 - 2.94154i) q^{35} +(1.81094 + 3.13665i) q^{36} +(-0.291921 - 1.08947i) q^{37} +(-0.387137 - 0.313497i) q^{38} +(-2.50014 + 3.44114i) q^{39} +(0.250331 + 0.582130i) q^{40} +(-6.74839 + 7.49485i) q^{41} +(0.226634 - 0.0869965i) q^{42} +(-5.01711 - 7.72567i) q^{43} +(8.52371 - 1.81177i) q^{44} +(0.583856 + 4.01740i) q^{45} +(0.442890 + 0.143904i) q^{46} +(9.30187 - 4.73954i) q^{47} +(4.03357 + 1.54834i) q^{48} +(-0.600323 - 2.82430i) q^{49} +(0.00951964 + 0.354552i) q^{50} +(-1.73053 - 0.770481i) q^{51} +(-0.408052 - 7.78610i) q^{52} +(4.58094 - 3.70958i) q^{53} +(-0.300768 - 0.218521i) q^{54} +(9.62674 + 1.65089i) q^{55} +(-0.445544 + 0.771705i) q^{56} +(-7.38251 - 1.97814i) q^{57} +(0.0579155 + 0.00917292i) q^{58} +(0.435631 - 0.392244i) q^{59} +(3.56620 + 3.29437i) q^{60} +9.21086i q^{61} +(-0.391990 + 0.0483010i) q^{62} +(-4.03669 + 4.03669i) q^{63} +(-7.49384 + 2.43490i) q^{64} +(2.80633 - 8.27621i) q^{65} +(-0.272821 + 0.198216i) q^{66} +(-1.70835 + 6.37563i) q^{67} +(3.35400 - 0.898701i) q^{68} +(7.10563 - 0.746831i) q^{69} +(-0.391583 + 0.308910i) q^{70} +(0.191176 - 1.81892i) q^{71} +(0.513787 - 0.0269265i) q^{72} +(0.0491467 + 0.128032i) q^{73} +(-0.0782601 - 0.0166347i) q^{74} +(2.34597 + 4.91005i) q^{75} +(12.7986 - 5.69829i) q^{76} +(6.23557 + 12.2380i) q^{77} +(0.136980 + 0.268839i) q^{78} +(-9.87826 + 4.39808i) q^{79} +(-8.85800 - 0.577634i) q^{80} +(-0.251755 - 0.0535122i) q^{81} +(0.256380 + 0.667894i) q^{82} +(-2.79788 + 0.146631i) q^{83} +(-0.713636 + 6.78979i) q^{84} +(3.86513 + 0.456169i) q^{85} +(-0.649869 + 0.0683040i) q^{86} +(0.868996 - 0.232847i) q^{87} +(0.320379 - 1.19567i) q^{88} +(4.24416 - 3.08356i) q^{89} +(0.272720 + 0.0924752i) q^{90} +(11.6876 - 3.79755i) q^{91} +(-9.26070 + 9.26070i) q^{92} +(-5.19278 + 3.12317i) q^{93} -0.740552i q^{94} +(15.6906 - 0.621698i) q^{95} +(0.686164 - 0.617825i) q^{96} +(7.51144 + 1.18969i) q^{97} +(-0.197841 - 0.0530113i) q^{98} +(3.96513 - 6.86781i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 224 q - 12 q^{2} - 14 q^{3} - 8 q^{5} - 36 q^{6} + 6 q^{7} - 40 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 224 q - 12 q^{2} - 14 q^{3} - 8 q^{5} - 36 q^{6} + 6 q^{7} - 40 q^{8} - 10 q^{10} - 28 q^{11} - 40 q^{12} - 14 q^{13} - 20 q^{15} + 24 q^{16} - 14 q^{17} - 40 q^{18} - 44 q^{20} - 44 q^{21} + 30 q^{22} - 30 q^{23} - 22 q^{25} - 48 q^{26} + 100 q^{27} - 48 q^{28} - 44 q^{31} + 28 q^{32} + 20 q^{33} - 72 q^{35} + 16 q^{36} + 30 q^{37} + 38 q^{38} - 4 q^{40} - 20 q^{41} - 130 q^{42} + 22 q^{43} - 34 q^{45} - 28 q^{47} - 156 q^{48} + 158 q^{50} - 36 q^{51} - 10 q^{52} + 26 q^{53} + 98 q^{55} - 48 q^{56} - 20 q^{58} + 260 q^{60} + 30 q^{62} + 152 q^{63} + 32 q^{65} - 152 q^{66} + 38 q^{67} - 126 q^{68} + 166 q^{70} - 128 q^{71} - 156 q^{72} - 30 q^{73} + 26 q^{75} + 128 q^{76} + 30 q^{78} + 154 q^{80} - 64 q^{81} + 8 q^{82} - 82 q^{83} + 60 q^{85} - 28 q^{86} - 24 q^{87} + 252 q^{88} + 38 q^{90} + 194 q^{93} - 74 q^{95} + 60 q^{96} - 38 q^{97} + 174 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/155\mathbb{Z}\right)^\times\).

\(n\) \(32\) \(96\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{23}{30}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0322043 0.0632044i 0.0227718 0.0446923i −0.879340 0.476194i \(-0.842016\pi\)
0.902112 + 0.431502i \(0.142016\pi\)
\(3\) 0.0569594 1.08685i 0.0328855 0.627493i −0.931621 0.363433i \(-0.881605\pi\)
0.964506 0.264061i \(-0.0850619\pi\)
\(4\) 1.17261 + 1.61396i 0.586306 + 0.806982i
\(5\) 0.551134 + 2.16708i 0.246475 + 0.969149i
\(6\) −0.0668594 0.0386013i −0.0272952 0.0157589i
\(7\) −1.97885 + 2.44368i −0.747935 + 0.923622i −0.999016 0.0443434i \(-0.985880\pi\)
0.251082 + 0.967966i \(0.419214\pi\)
\(8\) 0.279898 0.0443315i 0.0989589 0.0156735i
\(9\) 1.80557 + 0.189773i 0.601856 + 0.0632576i
\(10\) 0.154718 + 0.0349552i 0.0489262 + 0.0110538i
\(11\) 1.77665 3.99042i 0.535680 1.20316i −0.419669 0.907677i \(-0.637854\pi\)
0.955349 0.295479i \(-0.0954794\pi\)
\(12\) 1.82093 1.18252i 0.525657 0.341365i
\(13\) −3.27771 2.12857i −0.909074 0.590360i 0.00317504 0.999995i \(-0.498989\pi\)
−0.912249 + 0.409635i \(0.865656\pi\)
\(14\) 0.0907237 + 0.203769i 0.0242469 + 0.0544595i
\(15\) 2.38669 0.475565i 0.616240 0.122790i
\(16\) −1.22675 + 3.77554i −0.306687 + 0.943884i
\(17\) 0.623752 1.62493i 0.151282 0.394104i −0.836906 0.547346i \(-0.815638\pi\)
0.988189 + 0.153242i \(0.0489715\pi\)
\(18\) 0.0701414 0.108008i 0.0165325 0.0254578i
\(19\) 1.46007 6.86910i 0.334963 1.57588i −0.412108 0.911135i \(-0.635207\pi\)
0.747071 0.664744i \(-0.231459\pi\)
\(20\) −2.85133 + 3.43066i −0.637576 + 0.767119i
\(21\) 2.54320 + 2.28990i 0.554971 + 0.499698i
\(22\) −0.194996 0.240801i −0.0415734 0.0513388i
\(23\) 1.02696 + 6.48399i 0.214137 + 1.35201i 0.827171 + 0.561950i \(0.189949\pi\)
−0.613034 + 0.790056i \(0.710051\pi\)
\(24\) −0.0322389 0.306732i −0.00658073 0.0626115i
\(25\) −4.39250 + 2.38871i −0.878500 + 0.477742i
\(26\) −0.240092 + 0.138617i −0.0470858 + 0.0271850i
\(27\) 0.819861 5.17640i 0.157782 0.996198i
\(28\) −6.26443 0.328305i −1.18387 0.0620437i
\(29\) 0.255441 + 0.786167i 0.0474342 + 0.145988i 0.971968 0.235112i \(-0.0755456\pi\)
−0.924534 + 0.381099i \(0.875546\pi\)
\(30\) 0.0468037 0.166164i 0.00854515 0.0303373i
\(31\) −3.11543 4.61455i −0.559549 0.828798i
\(32\) 0.599894 + 0.599894i 0.106047 + 0.106047i
\(33\) −4.23579 2.15824i −0.737357 0.375702i
\(34\) −0.0826153 0.0917536i −0.0141684 0.0157356i
\(35\) −6.38626 2.94154i −1.07948 0.497211i
\(36\) 1.81094 + 3.13665i 0.301824 + 0.522775i
\(37\) −0.291921 1.08947i −0.0479916 0.179107i 0.937770 0.347258i \(-0.112887\pi\)
−0.985761 + 0.168151i \(0.946220\pi\)
\(38\) −0.387137 0.313497i −0.0628019 0.0508559i
\(39\) −2.50014 + 3.44114i −0.400342 + 0.551024i
\(40\) 0.250331 + 0.582130i 0.0395809 + 0.0920428i
\(41\) −6.74839 + 7.49485i −1.05392 + 1.17050i −0.0689785 + 0.997618i \(0.521974\pi\)
−0.984943 + 0.172880i \(0.944693\pi\)
\(42\) 0.226634 0.0869965i 0.0349703 0.0134239i
\(43\) −5.01711 7.72567i −0.765102 1.17815i −0.979507 0.201409i \(-0.935448\pi\)
0.214405 0.976745i \(-0.431219\pi\)
\(44\) 8.52371 1.81177i 1.28500 0.273135i
\(45\) 0.583856 + 4.01740i 0.0870362 + 0.598879i
\(46\) 0.442890 + 0.143904i 0.0653005 + 0.0212174i
\(47\) 9.30187 4.73954i 1.35682 0.691333i 0.384092 0.923295i \(-0.374515\pi\)
0.972725 + 0.231962i \(0.0745145\pi\)
\(48\) 4.03357 + 1.54834i 0.582195 + 0.223484i
\(49\) −0.600323 2.82430i −0.0857604 0.403471i
\(50\) 0.00951964 + 0.354552i 0.00134628 + 0.0501412i
\(51\) −1.73053 0.770481i −0.242322 0.107889i
\(52\) −0.408052 7.78610i −0.0565867 1.07974i
\(53\) 4.58094 3.70958i 0.629241 0.509549i −0.260822 0.965387i \(-0.583994\pi\)
0.890063 + 0.455838i \(0.150660\pi\)
\(54\) −0.300768 0.218521i −0.0409294 0.0297369i
\(55\) 9.62674 + 1.65089i 1.29807 + 0.222606i
\(56\) −0.445544 + 0.771705i −0.0595383 + 0.103123i
\(57\) −7.38251 1.97814i −0.977838 0.262011i
\(58\) 0.0579155 + 0.00917292i 0.00760468 + 0.00120446i
\(59\) 0.435631 0.392244i 0.0567143 0.0510658i −0.640286 0.768136i \(-0.721184\pi\)
0.697000 + 0.717071i \(0.254518\pi\)
\(60\) 3.56620 + 3.29437i 0.460395 + 0.425302i
\(61\) 9.21086i 1.17933i 0.807648 + 0.589665i \(0.200740\pi\)
−0.807648 + 0.589665i \(0.799260\pi\)
\(62\) −0.391990 + 0.0483010i −0.0497828 + 0.00613424i
\(63\) −4.03669 + 4.03669i −0.508575 + 0.508575i
\(64\) −7.49384 + 2.43490i −0.936730 + 0.304362i
\(65\) 2.80633 8.27621i 0.348083 1.02654i
\(66\) −0.272821 + 0.198216i −0.0335819 + 0.0243987i
\(67\) −1.70835 + 6.37563i −0.208708 + 0.778908i 0.779580 + 0.626303i \(0.215433\pi\)
−0.988287 + 0.152605i \(0.951234\pi\)
\(68\) 3.35400 0.898701i 0.406732 0.108984i
\(69\) 7.10563 0.746831i 0.855417 0.0899079i
\(70\) −0.391583 + 0.308910i −0.0468031 + 0.0369218i
\(71\) 0.191176 1.81892i 0.0226885 0.215866i −0.977303 0.211844i \(-0.932053\pi\)
0.999992 0.00402205i \(-0.00128026\pi\)
\(72\) 0.513787 0.0269265i 0.0605504 0.00317331i
\(73\) 0.0491467 + 0.128032i 0.00575219 + 0.0149850i 0.936426 0.350864i \(-0.114112\pi\)
−0.930674 + 0.365849i \(0.880779\pi\)
\(74\) −0.0782601 0.0166347i −0.00909755 0.00193374i
\(75\) 2.34597 + 4.91005i 0.270890 + 0.566964i
\(76\) 12.7986 5.69829i 1.46810 0.653639i
\(77\) 6.23557 + 12.2380i 0.710609 + 1.39465i
\(78\) 0.136980 + 0.268839i 0.0155100 + 0.0304400i
\(79\) −9.87826 + 4.39808i −1.11139 + 0.494823i −0.878530 0.477687i \(-0.841475\pi\)
−0.232861 + 0.972510i \(0.574809\pi\)
\(80\) −8.85800 0.577634i −0.990355 0.0645814i
\(81\) −0.251755 0.0535122i −0.0279728 0.00594580i
\(82\) 0.256380 + 0.667894i 0.0283125 + 0.0737565i
\(83\) −2.79788 + 0.146631i −0.307107 + 0.0160948i −0.205267 0.978706i \(-0.565806\pi\)
−0.101840 + 0.994801i \(0.532473\pi\)
\(84\) −0.713636 + 6.78979i −0.0778641 + 0.740827i
\(85\) 3.86513 + 0.456169i 0.419232 + 0.0494784i
\(86\) −0.649869 + 0.0683040i −0.0700772 + 0.00736541i
\(87\) 0.868996 0.232847i 0.0931661 0.0249638i
\(88\) 0.320379 1.19567i 0.0341525 0.127459i
\(89\) 4.24416 3.08356i 0.449880 0.326857i −0.339668 0.940545i \(-0.610315\pi\)
0.789548 + 0.613688i \(0.210315\pi\)
\(90\) 0.272720 + 0.0924752i 0.0287472 + 0.00974774i
\(91\) 11.6876 3.79755i 1.22520 0.398091i
\(92\) −9.26070 + 9.26070i −0.965494 + 0.965494i
\(93\) −5.19278 + 3.12317i −0.538466 + 0.323857i
\(94\) 0.740552i 0.0763821i
\(95\) 15.6906 0.621698i 1.60982 0.0637848i
\(96\) 0.686164 0.617825i 0.0700313 0.0630565i
\(97\) 7.51144 + 1.18969i 0.762671 + 0.120795i 0.525640 0.850707i \(-0.323826\pi\)
0.237031 + 0.971502i \(0.423826\pi\)
\(98\) −0.197841 0.0530113i −0.0199850 0.00535495i
\(99\) 3.96513 6.86781i 0.398511 0.690241i
\(100\) −9.00599 4.28831i −0.900599 0.428831i
\(101\) −6.91369 5.02309i −0.687938 0.499816i 0.188044 0.982161i \(-0.439785\pi\)
−0.875982 + 0.482344i \(0.839785\pi\)
\(102\) −0.104428 + 0.0845642i −0.0103399 + 0.00837311i
\(103\) −0.441485 8.42403i −0.0435008 0.830044i −0.930055 0.367420i \(-0.880241\pi\)
0.886554 0.462624i \(-0.153092\pi\)
\(104\) −1.01179 0.450477i −0.0992140 0.0441729i
\(105\) −3.56077 + 6.77336i −0.347496 + 0.661012i
\(106\) −0.0869356 0.409000i −0.00844394 0.0397256i
\(107\) 11.1064 + 4.26334i 1.07369 + 0.412153i 0.830037 0.557709i \(-0.188319\pi\)
0.243658 + 0.969861i \(0.421653\pi\)
\(108\) 9.31590 4.74669i 0.896423 0.456750i
\(109\) 1.90205 + 0.618012i 0.182183 + 0.0591948i 0.398688 0.917087i \(-0.369466\pi\)
−0.216505 + 0.976282i \(0.569466\pi\)
\(110\) 0.414366 0.555287i 0.0395082 0.0529445i
\(111\) −1.20071 + 0.255219i −0.113967 + 0.0242244i
\(112\) −6.79864 10.4690i −0.642411 0.989226i
\(113\) 4.22215 1.62073i 0.397186 0.152465i −0.151573 0.988446i \(-0.548434\pi\)
0.548759 + 0.835981i \(0.315100\pi\)
\(114\) −0.362775 + 0.402903i −0.0339770 + 0.0377353i
\(115\) −13.4854 + 5.79907i −1.25752 + 0.540766i
\(116\) −0.969311 + 1.33414i −0.0899983 + 0.123872i
\(117\) −5.51419 4.46530i −0.509787 0.412817i
\(118\) −0.0107624 0.0401657i −0.000990756 0.00369755i
\(119\) 2.73649 + 4.73974i 0.250854 + 0.434491i
\(120\) 0.646947 0.238915i 0.0590579 0.0218099i
\(121\) −5.40652 6.00455i −0.491502 0.545869i
\(122\) 0.582167 + 0.296629i 0.0527069 + 0.0268555i
\(123\) 7.76139 + 7.76139i 0.699821 + 0.699821i
\(124\) 3.79451 10.4393i 0.340757 0.937475i
\(125\) −7.59739 8.20242i −0.679531 0.733647i
\(126\) 0.125138 + 0.385135i 0.0111482 + 0.0343105i
\(127\) −11.3096 0.592711i −1.00356 0.0525946i −0.456533 0.889706i \(-0.650909\pi\)
−0.547032 + 0.837112i \(0.684242\pi\)
\(128\) −0.352868 + 2.22792i −0.0311895 + 0.196922i
\(129\) −8.68242 + 5.01280i −0.764444 + 0.441352i
\(130\) −0.432717 0.443902i −0.0379518 0.0389328i
\(131\) −0.368745 3.50838i −0.0322174 0.306528i −0.998750 0.0499844i \(-0.984083\pi\)
0.966533 0.256544i \(-0.0825838\pi\)
\(132\) −1.48362 9.36719i −0.129132 0.815310i
\(133\) 13.8966 + 17.1608i 1.20499 + 1.48803i
\(134\) 0.347952 + 0.313298i 0.0300585 + 0.0270648i
\(135\) 11.6695 1.07618i 1.00435 0.0926231i
\(136\) 0.102551 0.482467i 0.00879372 0.0413712i
\(137\) −11.0095 + 16.9532i −0.940606 + 1.44841i −0.0473395 + 0.998879i \(0.515074\pi\)
−0.893267 + 0.449527i \(0.851592\pi\)
\(138\) 0.181628 0.473158i 0.0154612 0.0402779i
\(139\) −1.60733 + 4.94685i −0.136332 + 0.419586i −0.995795 0.0916117i \(-0.970798\pi\)
0.859463 + 0.511198i \(0.170798\pi\)
\(140\) −2.74108 13.7565i −0.231663 1.16263i
\(141\) −4.62134 10.3797i −0.389187 0.874128i
\(142\) −0.108807 0.0706602i −0.00913089 0.00592967i
\(143\) −14.3172 + 9.29773i −1.19727 + 0.777515i
\(144\) −2.93147 + 6.58418i −0.244289 + 0.548682i
\(145\) −1.56291 + 0.986846i −0.129792 + 0.0819531i
\(146\) 0.00967490 + 0.00101687i 0.000800700 + 8.41570e-5i
\(147\) −3.10378 + 0.491591i −0.255996 + 0.0405457i
\(148\) 1.41605 1.74867i 0.116398 0.143740i
\(149\) −2.31939 1.33910i −0.190012 0.109703i 0.401976 0.915650i \(-0.368323\pi\)
−0.591988 + 0.805947i \(0.701657\pi\)
\(150\) 0.385887 + 0.00984866i 0.0315076 + 0.000804139i
\(151\) 2.99962 + 4.12862i 0.244105 + 0.335982i 0.913436 0.406983i \(-0.133419\pi\)
−0.669331 + 0.742965i \(0.733419\pi\)
\(152\) 0.104154 1.98737i 0.00844799 0.161197i
\(153\) 1.43459 2.81555i 0.115980 0.227624i
\(154\) 0.974307 0.0785119
\(155\) 8.28309 9.29464i 0.665314 0.746564i
\(156\) −8.48557 −0.679389
\(157\) −9.14360 + 17.9453i −0.729739 + 1.43219i 0.165318 + 0.986240i \(0.447135\pi\)
−0.895057 + 0.445952i \(0.852865\pi\)
\(158\) −0.0401437 + 0.765987i −0.00319366 + 0.0609386i
\(159\) −3.77083 5.19010i −0.299046 0.411601i
\(160\) −0.969398 + 1.63064i −0.0766376 + 0.128914i
\(161\) −17.8770 10.3213i −1.40890 0.813431i
\(162\) −0.0114898 + 0.0141887i −0.000902723 + 0.00111477i
\(163\) 2.24915 0.356231i 0.176167 0.0279022i −0.0677274 0.997704i \(-0.521575\pi\)
0.243895 + 0.969802i \(0.421575\pi\)
\(164\) −20.0097 2.10310i −1.56249 0.164224i
\(165\) 2.34260 10.3688i 0.182371 0.807210i
\(166\) −0.0808359 + 0.181560i −0.00627408 + 0.0140918i
\(167\) 10.2865 6.68015i 0.795996 0.516926i −0.0814066 0.996681i \(-0.525941\pi\)
0.877402 + 0.479755i \(0.159275\pi\)
\(168\) 0.813350 + 0.528196i 0.0627513 + 0.0407512i
\(169\) 0.925014 + 2.07762i 0.0711549 + 0.159817i
\(170\) 0.153306 0.229603i 0.0117580 0.0176097i
\(171\) 3.93982 12.1255i 0.301286 0.927262i
\(172\) 6.58582 17.1567i 0.502164 1.30818i
\(173\) −2.45795 + 3.78491i −0.186875 + 0.287762i −0.919674 0.392683i \(-0.871547\pi\)
0.732799 + 0.680445i \(0.238213\pi\)
\(174\) 0.0132684 0.0624230i 0.00100588 0.00473228i
\(175\) 2.85487 15.4607i 0.215808 1.16872i
\(176\) 12.8865 + 11.6030i 0.971355 + 0.874612i
\(177\) −0.401497 0.495807i −0.0301784 0.0372672i
\(178\) −0.0582147 0.367553i −0.00436338 0.0275493i
\(179\) 1.07512 + 10.2291i 0.0803582 + 0.764557i 0.958295 + 0.285781i \(0.0922528\pi\)
−0.877937 + 0.478776i \(0.841081\pi\)
\(180\) −5.79930 + 5.65318i −0.432255 + 0.421363i
\(181\) −19.0168 + 10.9793i −1.41351 + 0.816088i −0.995717 0.0924557i \(-0.970528\pi\)
−0.417789 + 0.908544i \(0.637195\pi\)
\(182\) 0.136370 0.861008i 0.0101084 0.0638221i
\(183\) 10.0108 + 0.524645i 0.740022 + 0.0387829i
\(184\) 0.574890 + 1.76933i 0.0423815 + 0.130437i
\(185\) 2.20007 1.23306i 0.161753 0.0906563i
\(186\) 0.0301685 + 0.428786i 0.00221206 + 0.0314401i
\(187\) −5.37597 5.37597i −0.393130 0.393130i
\(188\) 18.5569 + 9.45523i 1.35340 + 0.689593i
\(189\) 11.0271 + 12.2468i 0.802100 + 0.890823i
\(190\) 0.466010 1.01174i 0.0338079 0.0733991i
\(191\) 8.38581 + 14.5246i 0.606776 + 1.05097i 0.991768 + 0.128047i \(0.0408707\pi\)
−0.384992 + 0.922920i \(0.625796\pi\)
\(192\) 2.21952 + 8.28337i 0.160180 + 0.597801i
\(193\) 7.75743 + 6.28185i 0.558392 + 0.452177i 0.866502 0.499174i \(-0.166363\pi\)
−0.308110 + 0.951351i \(0.599696\pi\)
\(194\) 0.317094 0.436443i 0.0227660 0.0313348i
\(195\) −8.83515 3.52147i −0.632699 0.252178i
\(196\) 3.85437 4.28071i 0.275312 0.305765i
\(197\) 4.75155 1.82395i 0.338534 0.129951i −0.183161 0.983083i \(-0.558633\pi\)
0.521695 + 0.853132i \(0.325300\pi\)
\(198\) −0.306382 0.471786i −0.0217736 0.0335284i
\(199\) 6.18725 1.31514i 0.438602 0.0932278i 0.0166822 0.999861i \(-0.494690\pi\)
0.421920 + 0.906633i \(0.361356\pi\)
\(200\) −1.12356 + 0.863321i −0.0794475 + 0.0610460i
\(201\) 6.83205 + 2.21987i 0.481896 + 0.156577i
\(202\) −0.540132 + 0.275211i −0.0380035 + 0.0193638i
\(203\) −2.42662 0.931491i −0.170315 0.0653779i
\(204\) −0.785712 3.69648i −0.0550108 0.258806i
\(205\) −19.9612 10.4937i −1.39415 0.732909i
\(206\) −0.546653 0.243386i −0.0380872 0.0169575i
\(207\) 0.623766 + 11.9022i 0.0433548 + 0.827258i
\(208\) 12.0574 9.76391i 0.836032 0.677005i
\(209\) −24.8165 18.0303i −1.71660 1.24718i
\(210\) 0.313434 + 0.443187i 0.0216290 + 0.0305828i
\(211\) 1.17473 2.03470i 0.0808719 0.140074i −0.822753 0.568399i \(-0.807563\pi\)
0.903625 + 0.428325i \(0.140896\pi\)
\(212\) 11.3588 + 3.04358i 0.780125 + 0.209034i
\(213\) −1.96601 0.311385i −0.134708 0.0213357i
\(214\) 0.627135 0.564675i 0.0428701 0.0386004i
\(215\) 13.9771 15.1304i 0.953229 1.03188i
\(216\) 1.48521i 0.101056i
\(217\) 17.4414 + 1.51839i 1.18400 + 0.103075i
\(218\) 0.100315 0.100315i 0.00679419 0.00679419i
\(219\) 0.141951 0.0461225i 0.00959213 0.00311667i
\(220\) 8.62397 + 17.4731i 0.581428 + 1.17803i
\(221\) −5.50327 + 3.99836i −0.370190 + 0.268959i
\(222\) −0.0225371 + 0.0841095i −0.00151259 + 0.00564506i
\(223\) −13.8894 + 3.72164i −0.930100 + 0.249220i −0.691897 0.721996i \(-0.743225\pi\)
−0.238203 + 0.971215i \(0.576558\pi\)
\(224\) −2.65304 + 0.278846i −0.177264 + 0.0186312i
\(225\) −8.38427 + 3.47939i −0.558951 + 0.231960i
\(226\) 0.0335338 0.319053i 0.00223063 0.0212231i
\(227\) 15.6647 0.820953i 1.03970 0.0544886i 0.475166 0.879896i \(-0.342388\pi\)
0.564538 + 0.825407i \(0.309055\pi\)
\(228\) −5.46419 14.2347i −0.361875 0.942716i
\(229\) 2.87355 + 0.610792i 0.189890 + 0.0403623i 0.301875 0.953348i \(-0.402388\pi\)
−0.111985 + 0.993710i \(0.535721\pi\)
\(230\) −0.0677594 + 1.03909i −0.00446792 + 0.0685155i
\(231\) 13.6560 6.08006i 0.898501 0.400039i
\(232\) 0.106349 + 0.208723i 0.00698218 + 0.0137033i
\(233\) −2.07455 4.07154i −0.135908 0.266735i 0.813014 0.582244i \(-0.197825\pi\)
−0.948923 + 0.315508i \(0.897825\pi\)
\(234\) −0.459807 + 0.204719i −0.0300585 + 0.0133829i
\(235\) 15.3976 + 17.5458i 1.00443 + 1.14456i
\(236\) 1.14389 + 0.243142i 0.0744611 + 0.0158272i
\(237\) 4.21740 + 10.9867i 0.273950 + 0.713663i
\(238\) 0.387699 0.0203185i 0.0251308 0.00131705i
\(239\) 0.653633 6.21891i 0.0422800 0.402268i −0.952831 0.303502i \(-0.901844\pi\)
0.995111 0.0987654i \(-0.0314893\pi\)
\(240\) −1.13235 + 9.59442i −0.0730927 + 0.619317i
\(241\) 21.8619 2.29778i 1.40825 0.148013i 0.630305 0.776348i \(-0.282930\pi\)
0.777943 + 0.628335i \(0.216263\pi\)
\(242\) −0.553627 + 0.148344i −0.0355885 + 0.00953591i
\(243\) 3.99685 14.9165i 0.256398 0.956891i
\(244\) −14.8660 + 10.8008i −0.951697 + 0.691449i
\(245\) 5.78963 2.85752i 0.369886 0.182560i
\(246\) 0.740504 0.240604i 0.0472128 0.0153404i
\(247\) −19.4071 + 19.4071i −1.23484 + 1.23484i
\(248\) −1.07657 1.15349i −0.0683625 0.0732468i
\(249\) 3.04923i 0.193237i
\(250\) −0.763097 + 0.216036i −0.0482625 + 0.0136633i
\(251\) −8.29972 + 7.47310i −0.523873 + 0.471698i −0.888124 0.459603i \(-0.847992\pi\)
0.364251 + 0.931301i \(0.381325\pi\)
\(252\) −11.2485 1.78159i −0.708591 0.112230i
\(253\) 27.6984 + 7.42177i 1.74138 + 0.466602i
\(254\) −0.401679 + 0.695729i −0.0252036 + 0.0436539i
\(255\) 0.715943 4.17484i 0.0448341 0.261438i
\(256\) −12.6198 9.16884i −0.788739 0.573053i
\(257\) −13.4951 + 10.9282i −0.841804 + 0.681679i −0.949932 0.312458i \(-0.898848\pi\)
0.108128 + 0.994137i \(0.465514\pi\)
\(258\) 0.0372200 + 0.710201i 0.00231722 + 0.0442152i
\(259\) 3.23997 + 1.44253i 0.201322 + 0.0896342i
\(260\) 16.6482 5.17547i 1.03248 0.320969i
\(261\) 0.312023 + 1.46795i 0.0193137 + 0.0908640i
\(262\) −0.233620 0.0896784i −0.0144331 0.00554035i
\(263\) −22.6855 + 11.5588i −1.39885 + 0.712749i −0.980680 0.195621i \(-0.937328\pi\)
−0.418168 + 0.908370i \(0.637328\pi\)
\(264\) −1.28127 0.416309i −0.0788566 0.0256220i
\(265\) 10.5637 + 7.88281i 0.648921 + 0.484237i
\(266\) 1.53217 0.325673i 0.0939434 0.0199683i
\(267\) −3.10963 4.78840i −0.190306 0.293045i
\(268\) −12.2933 + 4.71894i −0.750931 + 0.288255i
\(269\) 5.25465 5.83588i 0.320382 0.355820i −0.561344 0.827583i \(-0.689715\pi\)
0.881726 + 0.471763i \(0.156382\pi\)
\(270\) 0.307789 0.772224i 0.0187315 0.0469961i
\(271\) −6.45006 + 8.87774i −0.391813 + 0.539285i −0.958666 0.284535i \(-0.908161\pi\)
0.566853 + 0.823819i \(0.308161\pi\)
\(272\) 5.36980 + 4.34838i 0.325592 + 0.263659i
\(273\) −3.46164 12.9190i −0.209508 0.781895i
\(274\) 0.716961 + 1.24181i 0.0433132 + 0.0750207i
\(275\) 1.72801 + 21.7718i 0.104203 + 1.31289i
\(276\) 9.53751 + 10.5925i 0.574090 + 0.637592i
\(277\) 6.95592 + 3.54422i 0.417941 + 0.212951i 0.650298 0.759679i \(-0.274644\pi\)
−0.232358 + 0.972630i \(0.574644\pi\)
\(278\) 0.260900 + 0.260900i 0.0156477 + 0.0156477i
\(279\) −4.74941 8.92310i −0.284340 0.534212i
\(280\) −1.91790 0.540218i −0.114617 0.0322842i
\(281\) −2.64976 8.15512i −0.158071 0.486494i 0.840388 0.541986i \(-0.182327\pi\)
−0.998459 + 0.0554920i \(0.982327\pi\)
\(282\) −0.804870 0.0421814i −0.0479293 0.00251187i
\(283\) −2.42354 + 15.3017i −0.144065 + 0.909589i 0.804717 + 0.593658i \(0.202317\pi\)
−0.948782 + 0.315931i \(0.897683\pi\)
\(284\) 3.15985 1.82434i 0.187502 0.108255i
\(285\) 0.218035 17.0887i 0.0129153 1.01225i
\(286\) 0.126581 + 1.20434i 0.00748490 + 0.0712141i
\(287\) −4.96092 31.3220i −0.292834 1.84888i
\(288\) 0.969305 + 1.19699i 0.0571168 + 0.0705334i
\(289\) 10.3821 + 9.34811i 0.610713 + 0.549889i
\(290\) 0.0120408 + 0.130563i 0.000707057 + 0.00766694i
\(291\) 1.72087 8.09604i 0.100879 0.474598i
\(292\) −0.149008 + 0.229453i −0.00872005 + 0.0134277i
\(293\) 9.06430 23.6133i 0.529542 1.37950i −0.364367 0.931255i \(-0.618715\pi\)
0.893909 0.448248i \(-0.147952\pi\)
\(294\) −0.0688843 + 0.212004i −0.00401741 + 0.0123643i
\(295\) 1.09012 + 0.727869i 0.0634690 + 0.0423782i
\(296\) −0.130006 0.291998i −0.00755643 0.0169720i
\(297\) −19.1994 12.4682i −1.11406 0.723480i
\(298\) −0.159331 + 0.103471i −0.00922982 + 0.00599392i
\(299\) 10.4356 23.4386i 0.603504 1.35549i
\(300\) −5.17372 + 9.54390i −0.298705 + 0.551018i
\(301\) 28.8071 + 3.02775i 1.66042 + 0.174517i
\(302\) 0.357547 0.0566299i 0.0205745 0.00325869i
\(303\) −5.85315 + 7.22804i −0.336255 + 0.415240i
\(304\) 24.1434 + 13.9392i 1.38472 + 0.799467i
\(305\) −19.9607 + 5.07642i −1.14295 + 0.290675i
\(306\) −0.131755 0.181345i −0.00753194 0.0103668i
\(307\) 0.627633 11.9760i 0.0358209 0.683504i −0.920421 0.390928i \(-0.872154\pi\)
0.956242 0.292576i \(-0.0945124\pi\)
\(308\) −12.4398 + 24.4144i −0.708821 + 1.39114i
\(309\) −9.18080 −0.522278
\(310\) −0.320712 0.822855i −0.0182152 0.0467350i
\(311\) −12.9477 −0.734199 −0.367099 0.930182i \(-0.619649\pi\)
−0.367099 + 0.930182i \(0.619649\pi\)
\(312\) −0.547232 + 1.07400i −0.0309809 + 0.0608035i
\(313\) 1.75047 33.4009i 0.0989424 1.88793i −0.276394 0.961044i \(-0.589139\pi\)
0.375336 0.926889i \(-0.377527\pi\)
\(314\) 0.839761 + 1.15583i 0.0473904 + 0.0652274i
\(315\) −10.9726 6.52308i −0.618236 0.367534i
\(316\) −18.6817 10.7859i −1.05093 0.606754i
\(317\) 7.58334 9.36464i 0.425923 0.525971i −0.518335 0.855178i \(-0.673448\pi\)
0.944258 + 0.329207i \(0.106781\pi\)
\(318\) −0.449474 + 0.0711896i −0.0252052 + 0.00399212i
\(319\) 3.59097 + 0.377426i 0.201055 + 0.0211318i
\(320\) −9.40673 14.8978i −0.525852 0.832813i
\(321\) 5.26623 11.8281i 0.293932 0.660182i
\(322\) −1.22807 + 0.797515i −0.0684374 + 0.0444438i
\(323\) −10.2511 6.65713i −0.570385 0.370413i
\(324\) −0.208844 0.469072i −0.0116025 0.0260596i
\(325\) 19.4819 + 1.52026i 1.08066 + 0.0843286i
\(326\) 0.0499170 0.153629i 0.00276465 0.00850870i
\(327\) 0.780026 2.03204i 0.0431355 0.112372i
\(328\) −1.55660 + 2.39696i −0.0859490 + 0.132350i
\(329\) −6.82510 + 32.1096i −0.376280 + 1.77026i
\(330\) −0.579912 0.481982i −0.0319231 0.0265322i
\(331\) −4.13010 3.71876i −0.227011 0.204402i 0.547774 0.836626i \(-0.315475\pi\)
−0.774785 + 0.632225i \(0.782142\pi\)
\(332\) −3.51748 4.34373i −0.193047 0.238393i
\(333\) −0.320333 2.02250i −0.0175541 0.110832i
\(334\) −0.0909450 0.865283i −0.00497629 0.0473462i
\(335\) −14.7581 0.188298i −0.806319 0.0102878i
\(336\) −11.7655 + 6.79280i −0.641859 + 0.370577i
\(337\) 0.506327 3.19682i 0.0275814 0.174142i −0.970052 0.242896i \(-0.921902\pi\)
0.997634 + 0.0687544i \(0.0219025\pi\)
\(338\) 0.161104 + 0.00844309i 0.00876289 + 0.000459244i
\(339\) −1.52100 4.68116i −0.0826094 0.254246i
\(340\) 3.79606 + 6.77309i 0.205870 + 0.367322i
\(341\) −23.9490 + 4.23345i −1.29691 + 0.229254i
\(342\) −0.639508 0.639508i −0.0345806 0.0345806i
\(343\) −11.5223 5.87090i −0.622145 0.316999i
\(344\) −1.74677 1.93998i −0.0941795 0.104597i
\(345\) 5.53460 + 14.9869i 0.297973 + 0.806867i
\(346\) 0.160067 + 0.277244i 0.00860524 + 0.0149047i
\(347\) 3.81647 + 14.2433i 0.204879 + 0.764618i 0.989486 + 0.144626i \(0.0461978\pi\)
−0.784608 + 0.619993i \(0.787136\pi\)
\(348\) 1.39480 + 1.12949i 0.0747692 + 0.0605469i
\(349\) 18.9330 26.0590i 1.01346 1.39491i 0.0967705 0.995307i \(-0.469149\pi\)
0.916689 0.399601i \(-0.130851\pi\)
\(350\) −0.885248 0.678342i −0.0473185 0.0362589i
\(351\) −13.7056 + 15.2216i −0.731551 + 0.812470i
\(352\) 3.45963 1.32803i 0.184399 0.0707841i
\(353\) 4.26423 + 6.56633i 0.226962 + 0.349491i 0.933745 0.357940i \(-0.116521\pi\)
−0.706783 + 0.707431i \(0.749854\pi\)
\(354\) −0.0442671 + 0.00940927i −0.00235277 + 0.000500097i
\(355\) 4.04712 0.588175i 0.214799 0.0312171i
\(356\) 9.95351 + 3.23409i 0.527535 + 0.171407i
\(357\) 5.30726 2.70418i 0.280890 0.143121i
\(358\) 0.681146 + 0.261467i 0.0359997 + 0.0138190i
\(359\) −3.43650 16.1675i −0.181371 0.853286i −0.970884 0.239551i \(-0.923000\pi\)
0.789512 0.613735i \(-0.210334\pi\)
\(360\) 0.341518 + 1.09858i 0.0179996 + 0.0579002i
\(361\) −27.6953 12.3307i −1.45765 0.648987i
\(362\) 0.0815217 + 1.55553i 0.00428468 + 0.0817566i
\(363\) −6.83400 + 5.53407i −0.358692 + 0.290463i
\(364\) 19.8342 + 14.4104i 1.03959 + 0.755309i
\(365\) −0.250369 + 0.177068i −0.0131049 + 0.00926815i
\(366\) 0.355551 0.615833i 0.0185850 0.0321901i
\(367\) 2.68949 + 0.720646i 0.140390 + 0.0376174i 0.328330 0.944563i \(-0.393514\pi\)
−0.187940 + 0.982181i \(0.560181\pi\)
\(368\) −25.7404 4.07688i −1.34181 0.212522i
\(369\) −13.6070 + 12.2518i −0.708351 + 0.637802i
\(370\) −0.00708305 0.178764i −0.000368230 0.00929351i
\(371\) 18.5350i 0.962291i
\(372\) −11.1298 4.71868i −0.577053 0.244652i
\(373\) −0.754454 + 0.754454i −0.0390641 + 0.0390641i −0.726369 0.687305i \(-0.758794\pi\)
0.687305 + 0.726369i \(0.258794\pi\)
\(374\) −0.512914 + 0.166656i −0.0265221 + 0.00861756i
\(375\) −9.34754 + 7.79002i −0.482705 + 0.402275i
\(376\) 2.39346 1.73895i 0.123433 0.0896796i
\(377\) 0.836151 3.12056i 0.0430640 0.160717i
\(378\) 1.12917 0.302560i 0.0580782 0.0155620i
\(379\) −0.0287978 + 0.00302677i −0.00147924 + 0.000155475i −0.105268 0.994444i \(-0.533570\pi\)
0.103789 + 0.994599i \(0.466903\pi\)
\(380\) 19.4024 + 24.5950i 0.995322 + 1.26170i
\(381\) −1.28838 + 12.2581i −0.0660055 + 0.628001i
\(382\) 1.18808 0.0622647i 0.0607875 0.00318574i
\(383\) −8.53091 22.2238i −0.435909 1.13558i −0.959025 0.283321i \(-0.908564\pi\)
0.523116 0.852262i \(-0.324770\pi\)
\(384\) 2.40132 + 0.510416i 0.122542 + 0.0260471i
\(385\) −23.0841 + 20.2578i −1.17648 + 1.03243i
\(386\) 0.646863 0.288002i 0.0329244 0.0146589i
\(387\) −7.59260 14.9013i −0.385954 0.757477i
\(388\) 6.88788 + 13.5182i 0.349679 + 0.686284i
\(389\) 14.1713 6.30947i 0.718514 0.319903i −0.0147088 0.999892i \(-0.504682\pi\)
0.733222 + 0.679989i \(0.238015\pi\)
\(390\) −0.507102 + 0.445014i −0.0256781 + 0.0225342i
\(391\) 11.1766 + 2.37566i 0.565226 + 0.120142i
\(392\) −0.293235 0.763902i −0.0148106 0.0385829i
\(393\) −3.83408 + 0.200936i −0.193404 + 0.0101359i
\(394\) 0.0377385 0.359058i 0.00190124 0.0180891i
\(395\) −14.9753 18.9831i −0.753487 0.955142i
\(396\) 15.7340 1.65370i 0.790661 0.0831018i
\(397\) 5.81855 1.55908i 0.292025 0.0782477i −0.109833 0.993950i \(-0.535031\pi\)
0.401857 + 0.915702i \(0.368365\pi\)
\(398\) 0.116133 0.433414i 0.00582122 0.0217251i
\(399\) 19.4428 14.1260i 0.973358 0.707186i
\(400\) −3.63017 19.5144i −0.181508 0.975719i
\(401\) 34.1154 11.0848i 1.70364 0.553546i 0.714386 0.699752i \(-0.246706\pi\)
0.989254 + 0.146205i \(0.0467060\pi\)
\(402\) 0.360327 0.360327i 0.0179715 0.0179715i
\(403\) 0.389100 + 21.7566i 0.0193824 + 1.08377i
\(404\) 17.0486i 0.848199i
\(405\) −0.0227855 0.575066i −0.00113222 0.0285753i
\(406\) −0.137022 + 0.123375i −0.00680028 + 0.00612300i
\(407\) −4.86606 0.770709i −0.241202 0.0382026i
\(408\) −0.518528 0.138939i −0.0256710 0.00687851i
\(409\) −10.0701 + 17.4419i −0.497933 + 0.862446i −0.999997 0.00238475i \(-0.999241\pi\)
0.502064 + 0.864831i \(0.332574\pi\)
\(410\) −1.30608 + 0.923697i −0.0645028 + 0.0456181i
\(411\) 17.7985 + 12.9313i 0.877933 + 0.637856i
\(412\) 13.0784 10.5907i 0.644326 0.521765i
\(413\) 0.0964686 + 1.84073i 0.00474691 + 0.0905765i
\(414\) 0.772358 + 0.343876i 0.0379593 + 0.0169006i
\(415\) −1.85977 5.98242i −0.0912924 0.293665i
\(416\) −0.689363 3.24320i −0.0337988 0.159011i
\(417\) 5.28493 + 2.02870i 0.258804 + 0.0993457i
\(418\) −1.93879 + 0.987863i −0.0948294 + 0.0483180i
\(419\) −11.7746 3.82578i −0.575225 0.186902i 0.00693557 0.999976i \(-0.497792\pi\)
−0.582160 + 0.813074i \(0.697792\pi\)
\(420\) −15.1074 + 2.19558i −0.737164 + 0.107133i
\(421\) 21.0885 4.48249i 1.02779 0.218463i 0.336988 0.941509i \(-0.390592\pi\)
0.690800 + 0.723046i \(0.257258\pi\)
\(422\) −0.0907704 0.139774i −0.00441864 0.00680410i
\(423\) 17.6946 6.79231i 0.860340 0.330253i
\(424\) 1.11775 1.24138i 0.0542825 0.0602869i
\(425\) 1.14165 + 8.62747i 0.0553782 + 0.418494i
\(426\) −0.0829946 + 0.114232i −0.00402110 + 0.00553457i
\(427\) −22.5084 18.2269i −1.08926 0.882062i
\(428\) 6.14261 + 22.9245i 0.296914 + 1.10810i
\(429\) 9.28974 + 16.0903i 0.448513 + 0.776847i
\(430\) −0.506185 1.37068i −0.0244104 0.0660998i
\(431\) −15.6686 17.4017i −0.754728 0.838211i 0.236326 0.971674i \(-0.424057\pi\)
−0.991054 + 0.133463i \(0.957390\pi\)
\(432\) 18.5379 + 9.44554i 0.891906 + 0.454449i
\(433\) −6.71039 6.71039i −0.322481 0.322481i 0.527237 0.849718i \(-0.323228\pi\)
−0.849718 + 0.527237i \(0.823228\pi\)
\(434\) 0.657657 1.05348i 0.0315686 0.0505685i
\(435\) 0.983532 + 1.75486i 0.0471567 + 0.0841389i
\(436\) 1.23291 + 3.79452i 0.0590459 + 0.181725i
\(437\) 46.0386 + 2.41278i 2.20233 + 0.115419i
\(438\) 0.00165626 0.0104572i 7.91394e−5 0.000499666i
\(439\) −1.70220 + 0.982765i −0.0812415 + 0.0469048i −0.540070 0.841620i \(-0.681602\pi\)
0.458829 + 0.888525i \(0.348269\pi\)
\(440\) 2.76769 + 0.0353129i 0.131945 + 0.00168348i
\(441\) −0.547949 5.21338i −0.0260928 0.248256i
\(442\) 0.0754852 + 0.476595i 0.00359046 + 0.0226693i
\(443\) 1.95404 + 2.41304i 0.0928393 + 0.114647i 0.821449 0.570283i \(-0.193166\pi\)
−0.728609 + 0.684930i \(0.759833\pi\)
\(444\) −1.81989 1.63863i −0.0863680 0.0777661i
\(445\) 9.02144 + 7.49799i 0.427657 + 0.355439i
\(446\) −0.212072 + 0.997721i −0.0100419 + 0.0472435i
\(447\) −1.58751 + 2.44456i −0.0750869 + 0.115624i
\(448\) 8.87908 23.1308i 0.419497 1.09283i
\(449\) 2.12388 6.53664i 0.100232 0.308483i −0.888350 0.459167i \(-0.848148\pi\)
0.988582 + 0.150685i \(0.0481478\pi\)
\(450\) −0.0500960 + 0.641974i −0.00236155 + 0.0302629i
\(451\) 17.9181 + 40.2446i 0.843728 + 1.89504i
\(452\) 7.56674 + 4.91390i 0.355910 + 0.231130i
\(453\) 4.65805 3.02497i 0.218854 0.142125i
\(454\) 0.452583 1.01652i 0.0212408 0.0477075i
\(455\) 14.6711 + 23.2351i 0.687790 + 1.08928i
\(456\) −2.15404 0.226399i −0.100872 0.0106021i
\(457\) 4.64490 0.735680i 0.217279 0.0344137i −0.0468456 0.998902i \(-0.514917\pi\)
0.264125 + 0.964488i \(0.414917\pi\)
\(458\) 0.131145 0.161951i 0.00612802 0.00756748i
\(459\) −7.89990 4.56101i −0.368736 0.212890i
\(460\) −25.1726 14.9648i −1.17368 0.697738i
\(461\) −11.7940 16.2331i −0.549302 0.756049i 0.440615 0.897696i \(-0.354760\pi\)
−0.989917 + 0.141647i \(0.954760\pi\)
\(462\) 0.0554959 1.05893i 0.00258190 0.0492657i
\(463\) 1.44162 2.82935i 0.0669979 0.131491i −0.855079 0.518498i \(-0.826491\pi\)
0.922077 + 0.387007i \(0.126491\pi\)
\(464\) −3.28156 −0.152343
\(465\) −9.63009 9.53190i −0.446585 0.442031i
\(466\) −0.324149 −0.0150159
\(467\) −10.7271 + 21.0530i −0.496389 + 0.974218i 0.497874 + 0.867250i \(0.334114\pi\)
−0.994262 + 0.106968i \(0.965886\pi\)
\(468\) 0.740824 14.1358i 0.0342446 0.653426i
\(469\) −12.1994 16.7911i −0.563317 0.775339i
\(470\) 1.60484 0.408144i 0.0740257 0.0188263i
\(471\) 18.9831 + 10.9599i 0.874693 + 0.505005i
\(472\) 0.104543 0.129100i 0.00481200 0.00594233i
\(473\) −39.7423 + 6.29456i −1.82735 + 0.289424i
\(474\) 0.830226 + 0.0872603i 0.0381335 + 0.00400800i
\(475\) 9.99490 + 33.6602i 0.458597 + 1.54444i
\(476\) −4.44092 + 9.97448i −0.203549 + 0.457179i
\(477\) 8.97518 5.82855i 0.410945 0.266871i
\(478\) −0.372013 0.241588i −0.0170155 0.0110500i
\(479\) 12.0698 + 27.1092i 0.551482 + 1.23865i 0.947308 + 0.320324i \(0.103792\pi\)
−0.395826 + 0.918326i \(0.629542\pi\)
\(480\) 1.71705 + 1.14647i 0.0783721 + 0.0523290i
\(481\) −1.36217 + 4.19233i −0.0621097 + 0.191154i
\(482\) 0.558816 1.45577i 0.0254534 0.0663083i
\(483\) −12.2359 + 18.8417i −0.556755 + 0.857327i
\(484\) 3.35137 15.7669i 0.152335 0.716679i
\(485\) 1.56164 + 16.9336i 0.0709105 + 0.768915i
\(486\) −0.814070 0.732992i −0.0369270 0.0332492i
\(487\) −4.21927 5.21037i −0.191193 0.236104i 0.672531 0.740069i \(-0.265207\pi\)
−0.863724 + 0.503965i \(0.831874\pi\)
\(488\) 0.408331 + 2.57810i 0.0184843 + 0.116705i
\(489\) −0.259059 2.46478i −0.0117151 0.111461i
\(490\) 0.00584303 0.457954i 0.000263961 0.0206883i
\(491\) 9.78893 5.65164i 0.441768 0.255055i −0.262579 0.964910i \(-0.584573\pi\)
0.704347 + 0.709856i \(0.251240\pi\)
\(492\) −3.42549 + 21.6277i −0.154433 + 0.975052i
\(493\) 1.43680 + 0.0752995i 0.0647102 + 0.00339132i
\(494\) 0.601622 + 1.85160i 0.0270683 + 0.0833075i
\(495\) 17.0684 + 4.80768i 0.767169 + 0.216089i
\(496\) 21.2442 6.10155i 0.953895 0.273968i
\(497\) 4.06654 + 4.06654i 0.182409 + 0.182409i
\(498\) 0.192725 + 0.0981980i 0.00863619 + 0.00440036i
\(499\) −6.18041 6.86404i −0.276673 0.307276i 0.588753 0.808313i \(-0.299619\pi\)
−0.865426 + 0.501036i \(0.832952\pi\)
\(500\) 4.32961 21.8802i 0.193626 0.978511i
\(501\) −6.67441 11.5604i −0.298191 0.516481i
\(502\) 0.205047 + 0.765244i 0.00915168 + 0.0341545i
\(503\) 5.61310 + 4.54540i 0.250276 + 0.202669i 0.746246 0.665670i \(-0.231854\pi\)
−0.495970 + 0.868339i \(0.665188\pi\)
\(504\) −0.950908 + 1.30881i −0.0423568 + 0.0582992i
\(505\) 7.07509 17.7509i 0.314837 0.789907i
\(506\) 1.36109 1.51165i 0.0605080 0.0672010i
\(507\) 2.31075 0.887012i 0.102624 0.0393936i
\(508\) −12.3052 18.9483i −0.545954 0.840695i
\(509\) 23.3136 4.95545i 1.03336 0.219646i 0.340138 0.940375i \(-0.389526\pi\)
0.693217 + 0.720729i \(0.256193\pi\)
\(510\) −0.240812 0.179698i −0.0106633 0.00795717i
\(511\) −0.410122 0.133257i −0.0181427 0.00589493i
\(512\) −5.00560 + 2.55048i −0.221218 + 0.112716i
\(513\) −34.3601 13.1896i −1.51704 0.582336i
\(514\) 0.256106 + 1.20489i 0.0112964 + 0.0531452i
\(515\) 18.0123 5.59951i 0.793715 0.246744i
\(516\) −18.2716 8.13503i −0.804362 0.358125i
\(517\) −2.38659 45.5388i −0.104962 2.00280i
\(518\) 0.195515 0.158325i 0.00859043 0.00695639i
\(519\) 3.97363 + 2.88701i 0.174423 + 0.126726i
\(520\) 0.418590 2.44090i 0.0183564 0.107041i
\(521\) −12.3861 + 21.4533i −0.542643 + 0.939885i 0.456108 + 0.889924i \(0.349243\pi\)
−0.998751 + 0.0499607i \(0.984090\pi\)
\(522\) 0.102830 + 0.0275531i 0.00450073 + 0.00120597i
\(523\) 22.6713 + 3.59079i 0.991348 + 0.157014i 0.630983 0.775797i \(-0.282652\pi\)
0.360366 + 0.932811i \(0.382652\pi\)
\(524\) 5.23000 4.70911i 0.228473 0.205718i
\(525\) −16.6409 3.98345i −0.726268 0.173852i
\(526\) 1.80607i 0.0787483i
\(527\) −9.44158 + 2.18403i −0.411282 + 0.0951378i
\(528\) 13.3448 13.3448i 0.580756 0.580756i
\(529\) −19.1132 + 6.21026i −0.831010 + 0.270011i
\(530\) 0.838424 0.413811i 0.0364188 0.0179748i
\(531\) 0.860997 0.625551i 0.0373641 0.0271466i
\(532\) −11.4017 + 42.5516i −0.494325 + 1.84485i
\(533\) 38.0726 10.2015i 1.64911 0.441877i
\(534\) −0.402791 + 0.0423351i −0.0174305 + 0.00183202i
\(535\) −3.11791 + 26.4181i −0.134799 + 1.14216i
\(536\) −0.195521 + 1.86026i −0.00844523 + 0.0803510i
\(537\) 11.1787 0.585851i 0.482397 0.0252813i
\(538\) −0.199631 0.520057i −0.00860672 0.0224213i
\(539\) −12.3367 2.62225i −0.531379 0.112948i
\(540\) 15.4208 + 17.5723i 0.663604 + 0.756190i
\(541\) −37.6189 + 16.7490i −1.61736 + 0.720097i −0.997890 0.0649202i \(-0.979321\pi\)
−0.619474 + 0.785017i \(0.712654\pi\)
\(542\) 0.353393 + 0.693573i 0.0151795 + 0.0297915i
\(543\) 10.8497 + 21.2938i 0.465606 + 0.913803i
\(544\) 1.34897 0.600601i 0.0578367 0.0257505i
\(545\) −0.291001 + 4.46250i −0.0124651 + 0.191153i
\(546\) −0.928019 0.197257i −0.0397155 0.00844180i
\(547\) 6.16273 + 16.0545i 0.263499 + 0.686440i 0.999951 + 0.00994870i \(0.00316682\pi\)
−0.736451 + 0.676491i \(0.763500\pi\)
\(548\) −40.2717 + 2.11055i −1.72032 + 0.0901582i
\(549\) −1.74797 + 16.6308i −0.0746015 + 0.709786i
\(550\) 1.43172 + 0.591927i 0.0610489 + 0.0252399i
\(551\) 5.77322 0.606790i 0.245947 0.0258501i
\(552\) 1.95574 0.524040i 0.0832419 0.0223046i
\(553\) 8.80010 32.8424i 0.374218 1.39660i
\(554\) 0.448020 0.325506i 0.0190346 0.0138294i
\(555\) −1.21484 2.46139i −0.0515669 0.104480i
\(556\) −9.86881 + 3.20657i −0.418531 + 0.135989i
\(557\) 16.6477 16.6477i 0.705388 0.705388i −0.260174 0.965562i \(-0.583780\pi\)
0.965562 + 0.260174i \(0.0837800\pi\)
\(558\) −0.716931 + 0.0128217i −0.0303501 + 0.000542787i
\(559\) 36.0018i 1.52272i
\(560\) 18.9402 20.5030i 0.800370 0.866411i
\(561\) −6.14908 + 5.53666i −0.259614 + 0.233758i
\(562\) −0.600773 0.0951531i −0.0253421 0.00401379i
\(563\) 15.4538 + 4.14083i 0.651300 + 0.174515i 0.569317 0.822118i \(-0.307208\pi\)
0.0819834 + 0.996634i \(0.473875\pi\)
\(564\) 11.3334 19.6300i 0.477223 0.826574i
\(565\) 5.83923 + 8.25651i 0.245658 + 0.347354i
\(566\) 0.889084 + 0.645957i 0.0373710 + 0.0271516i
\(567\) 0.628952 0.509315i 0.0264135 0.0213892i
\(568\) −0.0271256 0.517587i −0.00113817 0.0217175i
\(569\) 34.1914 + 15.2230i 1.43338 + 0.638181i 0.968911 0.247409i \(-0.0795791\pi\)
0.464467 + 0.885590i \(0.346246\pi\)
\(570\) −1.07306 0.564111i −0.0449456 0.0236280i
\(571\) −3.81748 17.9598i −0.159757 0.751596i −0.982956 0.183843i \(-0.941146\pi\)
0.823199 0.567753i \(-0.192187\pi\)
\(572\) −31.7948 12.2049i −1.32941 0.510311i
\(573\) 16.2638 8.28680i 0.679429 0.346186i
\(574\) −2.13945 0.695151i −0.0892991 0.0290150i
\(575\) −19.9993 26.0278i −0.834029 1.08544i
\(576\) −13.9927 + 2.97424i −0.583029 + 0.123927i
\(577\) −13.8136 21.2711i −0.575069 0.885529i 0.424735 0.905318i \(-0.360367\pi\)
−0.999804 + 0.0197889i \(0.993701\pi\)
\(578\) 0.925191 0.355147i 0.0384829 0.0147722i
\(579\) 7.26928 8.07336i 0.302101 0.335517i
\(580\) −3.42542 1.36529i −0.142233 0.0566904i
\(581\) 5.17826 7.12726i 0.214830 0.295689i
\(582\) −0.456286 0.369493i −0.0189137 0.0153160i
\(583\) −6.66403 24.8705i −0.275996 1.03003i
\(584\) 0.0194319 + 0.0336570i 0.000804098 + 0.00139274i
\(585\) 6.63762 14.4107i 0.274432 0.595808i
\(586\) −1.20056 1.33335i −0.0495945 0.0550803i
\(587\) −34.5874 17.6232i −1.42758 0.727386i −0.442062 0.896984i \(-0.645753\pi\)
−0.985513 + 0.169598i \(0.945753\pi\)
\(588\) −4.43295 4.43295i −0.182812 0.182812i
\(589\) −36.2465 + 14.6626i −1.49351 + 0.604164i
\(590\) 0.0811109 0.0454596i 0.00333928 0.00187154i
\(591\) −1.71171 5.26812i −0.0704105 0.216701i
\(592\) 4.47143 + 0.234338i 0.183775 + 0.00963122i
\(593\) −1.41530 + 8.93582i −0.0581192 + 0.366950i 0.941438 + 0.337187i \(0.109475\pi\)
−0.999557 + 0.0297635i \(0.990525\pi\)
\(594\) −1.40635 + 0.811956i −0.0577032 + 0.0333150i
\(595\) −8.76324 + 8.54244i −0.359258 + 0.350206i
\(596\) −0.558488 5.31366i −0.0228766 0.217656i
\(597\) −1.07694 6.79952i −0.0440761 0.278286i
\(598\) −1.14536 1.41440i −0.0468371 0.0578390i
\(599\) −8.90857 8.02132i −0.363994 0.327742i 0.466757 0.884386i \(-0.345422\pi\)
−0.830751 + 0.556644i \(0.812089\pi\)
\(600\) 0.874303 + 1.27031i 0.0356933 + 0.0518603i
\(601\) 1.72168 8.09988i 0.0702289 0.330401i −0.928982 0.370125i \(-0.879315\pi\)
0.999211 + 0.0397246i \(0.0126481\pi\)
\(602\) 1.11908 1.72323i 0.0456103 0.0702337i
\(603\) −4.29445 + 11.1874i −0.174884 + 0.455588i
\(604\) −3.14605 + 9.68254i −0.128011 + 0.393977i
\(605\) 10.0326 15.0257i 0.407885 0.610882i
\(606\) 0.268347 + 0.602718i 0.0109009 + 0.0244838i
\(607\) −17.4236 11.3150i −0.707201 0.459262i 0.140263 0.990114i \(-0.455205\pi\)
−0.847464 + 0.530853i \(0.821872\pi\)
\(608\) 4.99662 3.24484i 0.202640 0.131596i
\(609\) −1.15061 + 2.58431i −0.0466251 + 0.104722i
\(610\) −0.321967 + 1.42509i −0.0130361 + 0.0577001i
\(611\) −40.5773 4.26485i −1.64158 0.172537i
\(612\) 6.22642 0.986167i 0.251688 0.0398635i
\(613\) −21.8414 + 26.9719i −0.882166 + 1.08938i 0.113233 + 0.993568i \(0.463879\pi\)
−0.995399 + 0.0958160i \(0.969454\pi\)
\(614\) −0.736721 0.425346i −0.0297316 0.0171656i
\(615\) −12.5420 + 21.0972i −0.505743 + 0.850719i
\(616\) 2.28785 + 3.14896i 0.0921801 + 0.126875i
\(617\) −1.92743 + 36.7775i −0.0775953 + 1.48061i 0.631435 + 0.775429i \(0.282466\pi\)
−0.709030 + 0.705178i \(0.750867\pi\)
\(618\) −0.295661 + 0.580267i −0.0118932 + 0.0233418i
\(619\) −25.1386 −1.01041 −0.505203 0.863000i \(-0.668582\pi\)
−0.505203 + 0.863000i \(0.668582\pi\)
\(620\) 24.7141 + 2.46959i 0.992541 + 0.0991810i
\(621\) 34.4057 1.38065
\(622\) −0.416972 + 0.818354i −0.0167191 + 0.0328130i
\(623\) −0.863326 + 16.4733i −0.0345884 + 0.659987i
\(624\) −9.92513 13.6608i −0.397323 0.546868i
\(625\) 13.5881 20.9848i 0.543526 0.839392i
\(626\) −2.05471 1.18629i −0.0821229 0.0474137i
\(627\) −21.0097 + 25.9449i −0.839048 + 1.03614i
\(628\) −39.6850 + 6.28549i −1.58360 + 0.250818i
\(629\) −1.95239 0.205205i −0.0778470 0.00818205i
\(630\) −0.765652 + 0.483445i −0.0305043 + 0.0192609i
\(631\) −2.80677 + 6.30411i −0.111736 + 0.250963i −0.960754 0.277400i \(-0.910527\pi\)
0.849019 + 0.528363i \(0.177194\pi\)
\(632\) −2.56993 + 1.66893i −0.102226 + 0.0663866i
\(633\) −2.14450 1.39265i −0.0852362 0.0553530i
\(634\) −0.347671 0.780882i −0.0138078 0.0310128i
\(635\) −4.94866 24.8355i −0.196381 0.985567i
\(636\) 3.95490 12.1719i 0.156822 0.482649i
\(637\) −4.04404 + 10.5351i −0.160231 + 0.417415i
\(638\) 0.139499 0.214810i 0.00552283 0.00850442i
\(639\) 0.690363 3.24790i 0.0273103 0.128485i
\(640\) −5.02257 + 0.463190i −0.198535 + 0.0183092i
\(641\) 13.2567 + 11.9364i 0.523609 + 0.471459i 0.888037 0.459772i \(-0.152069\pi\)
−0.364428 + 0.931231i \(0.618736\pi\)
\(642\) −0.577996 0.713765i −0.0228117 0.0281701i
\(643\) 6.08654 + 38.4289i 0.240030 + 1.51549i 0.753538 + 0.657404i \(0.228346\pi\)
−0.513508 + 0.858085i \(0.671654\pi\)
\(644\) −4.30461 40.9557i −0.169626 1.61388i
\(645\) −15.6483 16.0528i −0.616152 0.632079i
\(646\) −0.750889 + 0.433526i −0.0295433 + 0.0170568i
\(647\) 2.56058 16.1669i 0.100667 0.635586i −0.884833 0.465909i \(-0.845728\pi\)
0.985500 0.169677i \(-0.0542724\pi\)
\(648\) −0.0728380 0.00381728i −0.00286135 0.000149957i
\(649\) −0.791254 2.43523i −0.0310594 0.0955911i
\(650\) 0.723487 1.18238i 0.0283775 0.0463769i
\(651\) 2.64371 18.8697i 0.103615 0.739564i
\(652\) 3.21233 + 3.21233i 0.125805 + 0.125805i
\(653\) 25.7100 + 13.0999i 1.00611 + 0.512638i 0.877765 0.479091i \(-0.159034\pi\)
0.128344 + 0.991730i \(0.459034\pi\)
\(654\) −0.103314 0.114741i −0.00403988 0.00448674i
\(655\) 7.39972 2.73269i 0.289131 0.106775i
\(656\) −20.0185 34.6731i −0.781591 1.35376i
\(657\) 0.0644408 + 0.240496i 0.00251407 + 0.00938266i
\(658\) 1.80967 + 1.46544i 0.0705483 + 0.0571289i
\(659\) 25.9081 35.6594i 1.00923 1.38909i 0.0897506 0.995964i \(-0.471393\pi\)
0.919484 0.393128i \(-0.128607\pi\)
\(660\) 19.4818 8.37771i 0.758329 0.326102i
\(661\) 2.48122 2.75568i 0.0965083 0.107183i −0.692956 0.720980i \(-0.743692\pi\)
0.789464 + 0.613797i \(0.210359\pi\)
\(662\) −0.368049 + 0.141281i −0.0143046 + 0.00549103i
\(663\) 4.03215 + 6.20897i 0.156596 + 0.241136i
\(664\) −0.776620 + 0.165076i −0.0301387 + 0.00640618i
\(665\) −29.5301 + 39.5730i −1.14513 + 1.53457i
\(666\) −0.138147 0.0448867i −0.00535309 0.00173932i
\(667\) −4.83517 + 2.46364i −0.187219 + 0.0953927i
\(668\) 22.8436 + 8.76885i 0.883847 + 0.339277i
\(669\) 3.25374 + 15.3076i 0.125797 + 0.591827i
\(670\) −0.487174 + 0.926710i −0.0188212 + 0.0358019i
\(671\) 36.7552 + 16.3645i 1.41892 + 0.631743i
\(672\) 0.151948 + 2.89935i 0.00586153 + 0.111845i
\(673\) 13.5882 11.0035i 0.523786 0.424153i −0.330617 0.943765i \(-0.607257\pi\)
0.854403 + 0.519612i \(0.173923\pi\)
\(674\) −0.185747 0.134953i −0.00715472 0.00519821i
\(675\) 8.76366 + 24.6957i 0.337314 + 0.950540i
\(676\) −2.26851 + 3.92918i −0.0872504 + 0.151122i
\(677\) 29.3867 + 7.87414i 1.12942 + 0.302628i 0.774691 0.632340i \(-0.217906\pi\)
0.354732 + 0.934968i \(0.384572\pi\)
\(678\) −0.344852 0.0546193i −0.0132440 0.00209764i
\(679\) −17.7712 + 16.0013i −0.681997 + 0.614073i
\(680\) 1.10207 0.0436664i 0.0422623 0.00167453i
\(681\) 17.0720i 0.654199i
\(682\) −0.503687 + 1.65002i −0.0192872 + 0.0631825i
\(683\) 2.77195 2.77195i 0.106066 0.106066i −0.652082 0.758148i \(-0.726104\pi\)
0.758148 + 0.652082i \(0.226104\pi\)
\(684\) 24.1900 7.85982i 0.924929 0.300528i
\(685\) −42.8066 14.5151i −1.63556 0.554592i
\(686\) −0.742134 + 0.539192i −0.0283348 + 0.0205864i
\(687\) 0.827516 3.08833i 0.0315717 0.117827i
\(688\) 35.3233 9.46484i 1.34669 0.360844i
\(689\) −22.9111 + 2.40806i −0.872844 + 0.0917397i
\(690\) 1.12547 + 0.132830i 0.0428461 + 0.00505676i
\(691\) 3.10919 29.5819i 0.118279 1.12535i −0.760904 0.648865i \(-0.775244\pi\)
0.879183 0.476485i \(-0.158089\pi\)
\(692\) −8.99093 + 0.471195i −0.341784 + 0.0179121i
\(693\) 8.93630 + 23.2798i 0.339462 + 0.884328i
\(694\) 1.02314 + 0.217476i 0.0388380 + 0.00825527i
\(695\) −11.6061 0.756837i −0.440244 0.0287085i
\(696\) 0.232908 0.103697i 0.00882834 0.00393063i
\(697\) 7.96928 + 15.6406i 0.301858 + 0.592430i
\(698\) −1.03732 2.03586i −0.0392632 0.0770584i
\(699\) −4.54332 + 2.02282i −0.171844 + 0.0765099i
\(700\) 28.3007 13.5218i 1.06967 0.511076i
\(701\) 12.9670 + 2.75622i 0.489756 + 0.104101i 0.446169 0.894949i \(-0.352788\pi\)
0.0435872 + 0.999050i \(0.486121\pi\)
\(702\) 0.520695 + 1.35646i 0.0196524 + 0.0511961i
\(703\) −7.90987 + 0.414539i −0.298326 + 0.0156346i
\(704\) −3.59767 + 34.2295i −0.135592 + 1.29007i
\(705\) 19.9467 15.7354i 0.751236 0.592631i
\(706\) 0.552348 0.0580541i 0.0207879 0.00218489i
\(707\) 25.9560 6.95488i 0.976174 0.261565i
\(708\) 0.329414 1.22939i 0.0123802 0.0462033i
\(709\) 19.0689 13.8544i 0.716147 0.520311i −0.169004 0.985615i \(-0.554055\pi\)
0.885151 + 0.465304i \(0.154055\pi\)
\(710\) 0.0931592 0.274737i 0.00349620 0.0103107i
\(711\) −18.6705 + 6.06641i −0.700198 + 0.227508i
\(712\) 1.05123 1.05123i 0.0393966 0.0393966i
\(713\) 26.7213 24.9394i 1.00072 0.933989i
\(714\) 0.422528i 0.0158127i
\(715\) −28.0397 25.9024i −1.04862 0.968694i
\(716\) −15.2486 + 13.7299i −0.569869 + 0.513112i
\(717\) −6.72179 1.06463i −0.251030 0.0397592i
\(718\) −1.13252 0.303459i −0.0422654 0.0113250i
\(719\) −16.6609 + 28.8576i −0.621348 + 1.07621i 0.367887 + 0.929871i \(0.380081\pi\)
−0.989235 + 0.146336i \(0.953252\pi\)
\(720\) −15.8841 2.72396i −0.591965 0.101516i
\(721\) 21.4592 + 15.5910i 0.799183 + 0.580641i
\(722\) −1.67126 + 1.35336i −0.0621980 + 0.0503670i
\(723\) −1.25210 23.8915i −0.0465661 0.888534i
\(724\) −40.0196 17.8179i −1.48732 0.662196i
\(725\) −2.99995 2.84307i −0.111415 0.105589i
\(726\) 0.129693 + 0.610160i 0.00481338 + 0.0226451i
\(727\) 8.79366 + 3.37557i 0.326139 + 0.125193i 0.515928 0.856632i \(-0.327447\pi\)
−0.189789 + 0.981825i \(0.560780\pi\)
\(728\) 3.10300 1.58106i 0.115005 0.0585978i
\(729\) −16.7186 5.43222i −0.619209 0.201193i
\(730\) 0.00312852 + 0.0215267i 0.000115792 + 0.000796741i
\(731\) −15.6831 + 3.33355i −0.580061 + 0.123296i
\(732\) 10.8921 + 16.7723i 0.402582 + 0.619922i
\(733\) 13.5871 5.21562i 0.501853 0.192643i −0.0942544 0.995548i \(-0.530047\pi\)
0.596107 + 0.802905i \(0.296713\pi\)
\(734\) 0.132161 0.146780i 0.00487815 0.00541773i
\(735\) −2.77592 6.45522i −0.102391 0.238105i
\(736\) −3.27364 + 4.50578i −0.120668 + 0.166085i
\(737\) 22.4063 + 18.1443i 0.825347 + 0.668353i
\(738\) 0.336164 + 1.25458i 0.0123744 + 0.0461818i
\(739\) −4.75149 8.22982i −0.174786 0.302739i 0.765301 0.643673i \(-0.222590\pi\)
−0.940087 + 0.340934i \(0.889257\pi\)
\(740\) 4.56995 + 2.10494i 0.167995 + 0.0773790i
\(741\) 19.9872 + 22.1980i 0.734247 + 0.815464i
\(742\) 1.17150 + 0.596907i 0.0430070 + 0.0219131i
\(743\) 32.7625 + 32.7625i 1.20194 + 1.20194i 0.973576 + 0.228365i \(0.0733380\pi\)
0.228365 + 0.973576i \(0.426662\pi\)
\(744\) −1.31499 + 1.10437i −0.0482100 + 0.0404882i
\(745\) 1.62365 5.76434i 0.0594859 0.211189i
\(746\) 0.0233882 + 0.0719814i 0.000856302 + 0.00263543i
\(747\) −5.07958 0.266210i −0.185852 0.00974010i
\(748\) 2.37268 14.9805i 0.0867539 0.547743i
\(749\) −32.3961 + 18.7039i −1.18373 + 0.683425i
\(750\) 0.191333 + 0.841678i 0.00698649 + 0.0307337i
\(751\) −3.79985 36.1531i −0.138658 1.31925i −0.813622 0.581395i \(-0.802507\pi\)
0.674963 0.737851i \(-0.264159\pi\)
\(752\) 6.48327 + 40.9338i 0.236420 + 1.49270i
\(753\) 7.64939 + 9.44621i 0.278759 + 0.344239i
\(754\) −0.170305 0.153344i −0.00620215 0.00558445i
\(755\) −7.29387 + 8.77584i −0.265451 + 0.319386i
\(756\) −6.83539 + 32.1580i −0.248601 + 1.16958i
\(757\) 27.8317 42.8570i 1.01156 1.55766i 0.194669 0.980869i \(-0.437637\pi\)
0.816889 0.576795i \(-0.195697\pi\)
\(758\) −0.000736106 0.00191762i −2.67366e−5 6.96511e-5i
\(759\) 9.64403 29.6813i 0.350056 1.07736i
\(760\) 4.36421 0.869600i 0.158306 0.0315437i
\(761\) −7.18623 16.1405i −0.260501 0.585094i 0.735187 0.677865i \(-0.237094\pi\)
−0.995688 + 0.0927703i \(0.970428\pi\)
\(762\) 0.733274 + 0.476194i 0.0265637 + 0.0172507i
\(763\) −5.27408 + 3.42503i −0.190935 + 0.123994i
\(764\) −13.6089 + 30.5662i −0.492354 + 1.10585i
\(765\) 6.89218 + 1.55714i 0.249187 + 0.0562985i
\(766\) −1.67937 0.176509i −0.0606782 0.00637754i
\(767\) −2.26279 + 0.358391i −0.0817047 + 0.0129408i
\(768\) −10.6840 + 13.1936i −0.385525 + 0.476083i
\(769\) 22.9067 + 13.2252i 0.826037 + 0.476913i 0.852494 0.522737i \(-0.175089\pi\)
−0.0264567 + 0.999650i \(0.508422\pi\)
\(770\) 0.536974 + 2.11140i 0.0193512 + 0.0760897i
\(771\) 11.1086 + 15.2897i 0.400066 + 0.550644i
\(772\) −1.04220 + 19.8864i −0.0375096 + 0.715727i
\(773\) −12.6350 + 24.7975i −0.454448 + 0.891904i 0.544151 + 0.838987i \(0.316852\pi\)
−0.998599 + 0.0529167i \(0.983148\pi\)
\(774\) −1.18634 −0.0426422
\(775\) 24.7074 + 12.8276i 0.887515 + 0.460779i
\(776\) 2.15518 0.0773663
\(777\) 1.75236 3.43919i 0.0628655 0.123380i
\(778\) 0.0575899 1.09888i 0.00206470 0.0393968i
\(779\) 41.6297 + 57.2983i 1.49154 + 2.05293i
\(780\) −4.67669 18.3889i −0.167452 0.658430i
\(781\) −6.91860 3.99446i −0.247567 0.142933i
\(782\) 0.510087 0.629905i 0.0182407 0.0225253i
\(783\) 4.27894 0.677718i 0.152917 0.0242197i
\(784\) 11.3997 + 1.19815i 0.407132 + 0.0427912i
\(785\) −43.9284 9.92466i −1.56787 0.354226i
\(786\) −0.110774 + 0.248802i −0.00395117 + 0.00887447i
\(787\) −27.0679 + 17.5781i −0.964868 + 0.626593i −0.927942 0.372725i \(-0.878423\pi\)
−0.0369263 + 0.999318i \(0.511757\pi\)
\(788\) 8.51552 + 5.53004i 0.303353 + 0.197000i
\(789\) 11.2706 + 25.3141i 0.401243 + 0.901207i
\(790\) −1.68208 + 0.335167i −0.0598458 + 0.0119247i
\(791\) −4.39445 + 13.5247i −0.156249 + 0.480884i
\(792\) 0.805372 2.09807i 0.0286176 0.0745515i
\(793\) 19.6060 30.1906i 0.696229 1.07210i
\(794\) 0.0888416 0.417967i 0.00315287 0.0148331i
\(795\) 9.16914 11.0321i 0.325196 0.391269i
\(796\) 9.37783 + 8.44384i 0.332388 + 0.299284i
\(797\) 9.59133 + 11.8443i 0.339742 + 0.419547i 0.918170 0.396187i \(-0.129667\pi\)
−0.578428 + 0.815734i \(0.696333\pi\)
\(798\) −0.266686 1.68379i −0.00944059 0.0596055i
\(799\) −1.89936 18.0712i −0.0671945 0.639313i
\(800\) −4.06801 1.20206i −0.143826 0.0424994i
\(801\) 8.24829 4.76215i 0.291439 0.168262i
\(802\) 0.398055 2.51322i 0.0140558 0.0887448i
\(803\) 0.598216 + 0.0313512i 0.0211106 + 0.00110636i
\(804\) 4.42857 + 13.6297i 0.156184 + 0.480683i
\(805\) 12.5145 44.4293i 0.441077 1.56593i
\(806\) 1.38764 + 0.676062i 0.0488777 + 0.0238133i
\(807\) −6.04343 6.04343i −0.212739 0.212739i
\(808\) −2.15781 1.09946i −0.0759115 0.0386788i
\(809\) −21.1268 23.4637i −0.742779 0.824940i 0.246779 0.969072i \(-0.420628\pi\)
−0.989559 + 0.144132i \(0.953961\pi\)
\(810\) −0.0370805 0.0170794i −0.00130288 0.000600111i
\(811\) −5.96240 10.3272i −0.209368 0.362636i 0.742148 0.670237i \(-0.233807\pi\)
−0.951516 + 0.307600i \(0.900474\pi\)
\(812\) −1.34209 5.00875i −0.0470981 0.175773i
\(813\) 9.28139 + 7.51592i 0.325512 + 0.263595i
\(814\) −0.205420 + 0.282737i −0.00719997 + 0.00990991i
\(815\) 2.01157 + 4.67777i 0.0704622 + 0.163855i
\(816\) 5.03190 5.58849i 0.176152 0.195636i
\(817\) −60.3937 + 23.1830i −2.11291 + 0.811070i
\(818\) 0.778105 + 1.19818i 0.0272058 + 0.0418933i
\(819\) 21.8235 4.63873i 0.762574 0.162090i
\(820\) −6.47041 44.5217i −0.225957 1.55476i
\(821\) −2.83114 0.919893i −0.0988075 0.0321045i 0.259196 0.965825i \(-0.416542\pi\)
−0.358004 + 0.933720i \(0.616542\pi\)
\(822\) 1.39050 0.708497i 0.0484994 0.0247117i
\(823\) 14.9624 + 5.74352i 0.521555 + 0.200206i 0.604881 0.796316i \(-0.293221\pi\)
−0.0833254 + 0.996522i \(0.526554\pi\)
\(824\) −0.497020 2.33830i −0.0173145 0.0814584i
\(825\) 23.7611 0.637981i 0.827256 0.0222116i
\(826\) 0.119449 + 0.0531821i 0.00415616 + 0.00185044i
\(827\) −1.30266 24.8563i −0.0452980 0.864338i −0.922922 0.384987i \(-0.874206\pi\)
0.877624 0.479350i \(-0.159128\pi\)
\(828\) −18.4782 + 14.9634i −0.642163 + 0.520013i
\(829\) −17.0408 12.3808i −0.591850 0.430004i 0.251127 0.967954i \(-0.419199\pi\)
−0.842977 + 0.537950i \(0.819199\pi\)
\(830\) −0.438008 0.0751139i −0.0152035 0.00260724i
\(831\) 4.24824 7.35817i 0.147370 0.255252i
\(832\) 29.7455 + 7.97029i 1.03124 + 0.276320i
\(833\) −4.96374 0.786179i −0.171983 0.0272395i
\(834\) 0.298420 0.268698i 0.0103334 0.00930427i
\(835\) 20.1457 + 18.6101i 0.697171 + 0.644029i
\(836\) 61.1955i 2.11649i
\(837\) −26.4410 + 12.3434i −0.913934 + 0.426652i
\(838\) −0.620997 + 0.620997i −0.0214520 + 0.0214520i
\(839\) −36.6120 + 11.8960i −1.26399 + 0.410694i −0.862913 0.505352i \(-0.831363\pi\)
−0.401073 + 0.916046i \(0.631363\pi\)
\(840\) −0.696379 + 2.05370i −0.0240274 + 0.0708595i
\(841\) 22.9087 16.6441i 0.789955 0.573936i
\(842\) 0.395825 1.47724i 0.0136410 0.0509090i
\(843\) −9.01432 + 2.41538i −0.310470 + 0.0831901i
\(844\) 4.66143 0.489936i 0.160453 0.0168643i
\(845\) −3.99256 + 3.14963i −0.137348 + 0.108350i
\(846\) 0.140537 1.33712i 0.00483175 0.0459710i
\(847\) 25.3719 1.32968i 0.871788 0.0456885i
\(848\) 8.38598 + 21.8462i 0.287976 + 0.750203i
\(849\) 16.4926 + 3.50560i 0.566023 + 0.120312i
\(850\) 0.582060 + 0.205684i 0.0199645 + 0.00705490i
\(851\) 6.76429 3.01166i 0.231877 0.103238i
\(852\) −1.80280 3.53819i −0.0617629 0.121217i
\(853\) 15.2409 + 29.9120i 0.521839 + 1.02417i 0.990072 + 0.140561i \(0.0448907\pi\)
−0.468233 + 0.883605i \(0.655109\pi\)
\(854\) −1.87689 + 0.835643i −0.0642257 + 0.0285951i
\(855\) 28.4484 + 1.85513i 0.972915 + 0.0634441i
\(856\) 3.29765 + 0.700938i 0.112712 + 0.0239576i
\(857\) −17.4061 45.3445i −0.594582 1.54894i −0.818606 0.574356i \(-0.805253\pi\)
0.224024 0.974584i \(-0.428081\pi\)
\(858\) 1.31615 0.0689763i 0.0449325 0.00235481i
\(859\) 4.61635 43.9216i 0.157508 1.49859i −0.575183 0.818025i \(-0.695069\pi\)
0.732691 0.680562i \(-0.238264\pi\)
\(860\) 40.8096 + 4.81641i 1.39159 + 0.164238i
\(861\) −34.3249 + 3.60770i −1.16979 + 0.122950i
\(862\) −1.60446 + 0.429913i −0.0546481 + 0.0146429i
\(863\) 12.1041 45.1731i 0.412028 1.53771i −0.378686 0.925525i \(-0.623624\pi\)
0.790714 0.612185i \(-0.209709\pi\)
\(864\) 3.59712 2.61346i 0.122376 0.0889117i
\(865\) −9.55688 3.24059i −0.324944 0.110183i
\(866\) −0.640229 + 0.208023i −0.0217559 + 0.00706891i
\(867\) 10.7514 10.7514i 0.365135 0.365135i
\(868\) 18.0014 + 29.9303i 0.611008 + 1.01590i
\(869\) 47.2322i 1.60224i
\(870\) 0.142589 0.00564969i 0.00483421 0.000191542i
\(871\) 19.1705 17.2612i 0.649567 0.584872i
\(872\) 0.559776 + 0.0886598i 0.0189564 + 0.00300240i
\(873\) 13.3366 + 3.57354i 0.451376 + 0.120946i
\(874\) 1.63514 2.83214i 0.0553094 0.0957986i
\(875\) 35.0781 2.33420i 1.18586 0.0789103i
\(876\) 0.240893 + 0.175019i 0.00813902 + 0.00591335i
\(877\) −34.9799 + 28.3262i −1.18119 + 0.956506i −0.999639 0.0268759i \(-0.991444\pi\)
−0.181548 + 0.983382i \(0.558111\pi\)
\(878\) 0.00729703 + 0.139236i 0.000246263 + 0.00469898i
\(879\) −25.1478 11.1965i −0.848215 0.377650i
\(880\) −18.0426 + 34.3209i −0.608215 + 1.15696i
\(881\) 6.53922 + 30.7646i 0.220312 + 1.03649i 0.939732 + 0.341911i \(0.111074\pi\)
−0.719420 + 0.694575i \(0.755592\pi\)
\(882\) −0.347155 0.133260i −0.0116893 0.00448711i
\(883\) −49.6709 + 25.3086i −1.67156 + 0.851702i −0.678431 + 0.734664i \(0.737340\pi\)
−0.993127 + 0.117038i \(0.962660\pi\)
\(884\) −12.9064 4.19354i −0.434089 0.141044i
\(885\) 0.853177 1.14333i 0.0286792 0.0384327i
\(886\) 0.215443 0.0457939i 0.00723796 0.00153848i
\(887\) 2.77750 + 4.27697i 0.0932593 + 0.143607i 0.882221 0.470836i \(-0.156048\pi\)
−0.788962 + 0.614443i \(0.789381\pi\)
\(888\) −0.324763 + 0.124665i −0.0108983 + 0.00418348i
\(889\) 23.8284 26.4641i 0.799179 0.887578i
\(890\) 0.764435 0.328727i 0.0256239 0.0110190i
\(891\) −0.660816 + 0.909535i −0.0221382 + 0.0304706i
\(892\) −22.2934 18.0529i −0.746439 0.604455i
\(893\) −18.9750 70.8155i −0.634973 2.36975i
\(894\) 0.103382 + 0.179063i 0.00345762 + 0.00598877i
\(895\) −21.5747 + 7.96747i −0.721163 + 0.266323i
\(896\) −4.74605 5.27102i −0.158554 0.176092i
\(897\) −24.8799 12.6769i −0.830716 0.423271i
\(898\) −0.344746 0.344746i −0.0115043 0.0115043i
\(899\) 2.83200 3.62800i 0.0944524 0.121001i
\(900\) −15.4471 9.45191i −0.514904 0.315064i
\(901\) −3.17043 9.75757i −0.105622 0.325072i
\(902\) 3.12067 + 0.163548i 0.103907 + 0.00544554i
\(903\) 4.93155 31.1366i 0.164112 1.03616i
\(904\) 1.10992 0.640813i 0.0369154 0.0213131i
\(905\) −34.2740 35.1599i −1.13930 1.16875i
\(906\) −0.0411826 0.391826i −0.00136820 0.0130175i
\(907\) 1.35145 + 8.53270i 0.0448740 + 0.283323i 0.999913 0.0131553i \(-0.00418759\pi\)
−0.955039 + 0.296479i \(0.904188\pi\)
\(908\) 19.6936 + 24.3196i 0.653556 + 0.807075i
\(909\) −11.5299 10.3816i −0.382422 0.344334i
\(910\) 1.94103 0.179005i 0.0643447 0.00593397i
\(911\) −10.0627 + 47.3411i −0.333391 + 1.56848i 0.417890 + 0.908497i \(0.362770\pi\)
−0.751281 + 0.659982i \(0.770564\pi\)
\(912\) 16.5250 25.4463i 0.547198 0.842610i
\(913\) −4.38573 + 11.4252i −0.145146 + 0.378119i
\(914\) 0.103087 0.317270i 0.00340983 0.0104944i
\(915\) 4.38036 + 21.9834i 0.144810 + 0.726750i
\(916\) 2.38377 + 5.35403i 0.0787619 + 0.176902i
\(917\) 9.30303 + 6.04146i 0.307213 + 0.199506i
\(918\) −0.542686 + 0.352425i −0.0179113 + 0.0116317i
\(919\) −18.7765 + 42.1726i −0.619378 + 1.39115i 0.282547 + 0.959253i \(0.408821\pi\)
−0.901925 + 0.431892i \(0.857846\pi\)
\(920\) −3.51744 + 2.22097i −0.115967 + 0.0732233i
\(921\) −12.9803 1.36429i −0.427716 0.0449548i
\(922\) −1.40582 + 0.222660i −0.0462982 + 0.00733291i
\(923\) −4.49833 + 5.55497i −0.148064 + 0.182844i
\(924\) 25.8262 + 14.9108i 0.849621 + 0.490529i
\(925\) 3.88468 + 4.08816i 0.127727 + 0.134418i
\(926\) −0.132401 0.182234i −0.00435096 0.00598858i
\(927\) 0.801521 15.2939i 0.0263254 0.502318i
\(928\) −0.318379 + 0.624854i −0.0104513 + 0.0205119i
\(929\) 21.3673 0.701037 0.350519 0.936556i \(-0.386005\pi\)
0.350519 + 0.936556i \(0.386005\pi\)
\(930\) −0.912588 + 0.301696i −0.0299249 + 0.00989301i
\(931\) −20.2769 −0.664548
\(932\) 4.13867 8.12259i 0.135567 0.266064i
\(933\) −0.737495 + 14.0722i −0.0241445 + 0.460705i
\(934\) 0.985187 + 1.35599i 0.0322363 + 0.0443695i
\(935\) 8.68729 14.6130i 0.284105 0.477898i
\(936\) −1.74136 1.00538i −0.0569182 0.0328618i
\(937\) −6.09698 + 7.52914i −0.199180 + 0.245966i −0.866943 0.498407i \(-0.833918\pi\)
0.667763 + 0.744374i \(0.267252\pi\)
\(938\) −1.45414 + 0.230314i −0.0474794 + 0.00752000i
\(939\) −36.2021 3.80500i −1.18141 0.124171i
\(940\) −10.2629 + 45.4255i −0.334739 + 1.48162i
\(941\) −14.9445 + 33.5659i −0.487176 + 1.09422i 0.488012 + 0.872837i \(0.337722\pi\)
−0.975188 + 0.221378i \(0.928944\pi\)
\(942\) 1.30405 0.846859i 0.0424882 0.0275921i
\(943\) −55.5269 36.0596i −1.80820 1.17426i
\(944\) 0.946522 + 2.12592i 0.0308067 + 0.0691929i
\(945\) −20.4624 + 30.6462i −0.665643 + 0.996920i
\(946\) −0.882027 + 2.71460i −0.0286772 + 0.0882593i
\(947\) −14.7611 + 38.4540i −0.479672 + 1.24959i 0.453853 + 0.891076i \(0.350049\pi\)
−0.933525 + 0.358512i \(0.883284\pi\)
\(948\) −12.7868 + 19.6899i −0.415294 + 0.639497i
\(949\) 0.111436 0.524263i 0.00361735 0.0170183i
\(950\) 2.44935 + 0.452280i 0.0794675 + 0.0146739i
\(951\) −9.74602 8.77536i −0.316036 0.284560i
\(952\) 0.976058 + 1.20533i 0.0316342 + 0.0390650i
\(953\) −7.33861 46.3342i −0.237721 1.50091i −0.761001 0.648751i \(-0.775292\pi\)
0.523280 0.852161i \(-0.324708\pi\)
\(954\) −0.0793510 0.754975i −0.00256908 0.0244432i
\(955\) −26.8544 + 26.1778i −0.868988 + 0.847093i
\(956\) 10.8035 6.23743i 0.349412 0.201733i
\(957\) 0.614745 3.88134i 0.0198719 0.125466i
\(958\) 2.10212 + 0.110167i 0.0679163 + 0.00355934i
\(959\) −19.6419 60.4514i −0.634269 1.95208i
\(960\) −16.7275 + 9.37514i −0.539878 + 0.302581i
\(961\) −11.5881 + 28.7527i −0.373811 + 0.927505i
\(962\) 0.221106 + 0.221106i 0.00712875 + 0.00712875i
\(963\) 19.2442 + 9.80543i 0.620137 + 0.315976i
\(964\) 29.3441 + 32.5899i 0.945108 + 1.04965i
\(965\) −9.33790 + 20.2731i −0.300597 + 0.652616i
\(966\) 0.796830 + 1.38015i 0.0256376 + 0.0444056i
\(967\) 4.72727 + 17.6424i 0.152019 + 0.567342i 0.999342 + 0.0362647i \(0.0115460\pi\)
−0.847323 + 0.531077i \(0.821787\pi\)
\(968\) −1.77947 1.44098i −0.0571942 0.0463150i
\(969\) −7.81920 + 10.7622i −0.251189 + 0.345732i
\(970\) 1.12057 + 0.446631i 0.0359793 + 0.0143405i
\(971\) 2.67405 2.96984i 0.0858145 0.0953066i −0.698708 0.715407i \(-0.746241\pi\)
0.784523 + 0.620100i \(0.212908\pi\)
\(972\) 28.7614 11.0405i 0.922521 0.354123i
\(973\) −8.90783 13.7169i −0.285572 0.439742i
\(974\) −0.465197 + 0.0988806i −0.0149059 + 0.00316834i
\(975\) 2.76197 21.0873i 0.0884538 0.675335i
\(976\) −34.7759 11.2994i −1.11315 0.361685i
\(977\) −38.7586 + 19.7485i −1.24000 + 0.631811i −0.946053 0.324011i \(-0.894969\pi\)
−0.293946 + 0.955822i \(0.594969\pi\)
\(978\) −0.164128 0.0630029i −0.00524824 0.00201461i
\(979\) −4.76432 22.4144i −0.152268 0.716367i
\(980\) 11.4009 + 5.99349i 0.364189 + 0.191455i
\(981\) 3.31699 + 1.47682i 0.105903 + 0.0471512i
\(982\) −0.0419634 0.800710i −0.00133911 0.0255517i
\(983\) 42.5077 34.4221i 1.35579 1.09789i 0.370157 0.928969i \(-0.379304\pi\)
0.985629 0.168925i \(-0.0540295\pi\)
\(984\) 2.51647 + 1.82832i 0.0802222 + 0.0582848i
\(985\) 6.57139 + 9.29177i 0.209382 + 0.296060i
\(986\) 0.0510303 0.0883871i 0.00162514 0.00281482i
\(987\) 34.5095 + 9.24681i 1.09845 + 0.294329i
\(988\) −54.0793 8.56531i −1.72049 0.272499i
\(989\) 44.9408 40.4649i 1.42903 1.28671i
\(990\) 0.853543 0.923972i 0.0271274 0.0293658i
\(991\) 56.3648i 1.79049i −0.445577 0.895244i \(-0.647001\pi\)
0.445577 0.895244i \(-0.352999\pi\)
\(992\) 0.899310 4.63717i 0.0285531 0.147230i
\(993\) −4.27699 + 4.27699i −0.135726 + 0.135726i
\(994\) 0.387983 0.126063i 0.0123061 0.00399849i
\(995\) 6.26002 + 12.6835i 0.198456 + 0.402093i
\(996\) −4.92134 + 3.57556i −0.155939 + 0.113296i
\(997\) 13.7298 51.2402i 0.434826 1.62279i −0.306655 0.951821i \(-0.599210\pi\)
0.741482 0.670973i \(-0.234123\pi\)
\(998\) −0.632873 + 0.169578i −0.0200332 + 0.00536789i
\(999\) −5.87884 + 0.617891i −0.185998 + 0.0195492i
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 155.2.x.a.42.8 yes 224
5.2 odd 4 775.2.df.b.693.8 224
5.3 odd 4 inner 155.2.x.a.73.7 yes 224
5.4 even 2 775.2.df.b.507.7 224
31.17 odd 30 inner 155.2.x.a.17.7 224
155.17 even 60 775.2.df.b.668.7 224
155.48 even 60 inner 155.2.x.a.48.8 yes 224
155.79 odd 30 775.2.df.b.482.8 224
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
155.2.x.a.17.7 224 31.17 odd 30 inner
155.2.x.a.42.8 yes 224 1.1 even 1 trivial
155.2.x.a.48.8 yes 224 155.48 even 60 inner
155.2.x.a.73.7 yes 224 5.3 odd 4 inner
775.2.df.b.482.8 224 155.79 odd 30
775.2.df.b.507.7 224 5.4 even 2
775.2.df.b.668.7 224 155.17 even 60
775.2.df.b.693.8 224 5.2 odd 4