Properties

Label 285.2.i.d.121.1
Level $285$
Weight $2$
Character 285.121
Analytic conductor $2.276$
Analytic rank $0$
Dimension $4$
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] = [285,2,Mod(106,285)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(285, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("285.106");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 285 = 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 285.i (of order \(3\), degree \(2\), 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: \(2.27573645761\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 2x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 121.1
Root \(-0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 285.121
Dual form 285.2.i.d.106.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.20711 - 2.09077i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.91421 + 3.31552i) q^{4} +(0.500000 + 0.866025i) q^{5} +(1.20711 - 2.09077i) q^{6} -3.82843 q^{7} +4.41421 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-1.20711 - 2.09077i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.91421 + 3.31552i) q^{4} +(0.500000 + 0.866025i) q^{5} +(1.20711 - 2.09077i) q^{6} -3.82843 q^{7} +4.41421 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.20711 - 2.09077i) q^{10} +2.82843 q^{11} -3.82843 q^{12} +(-1.91421 + 3.31552i) q^{13} +(4.62132 + 8.00436i) q^{14} +(-0.500000 + 0.866025i) q^{15} +(-1.50000 - 2.59808i) q^{16} +(3.41421 + 5.91359i) q^{17} +2.41421 q^{18} +(4.00000 + 1.73205i) q^{19} -3.82843 q^{20} +(-1.91421 - 3.31552i) q^{21} +(-3.41421 - 5.91359i) q^{22} +(-2.41421 + 4.18154i) q^{23} +(2.20711 + 3.82282i) q^{24} +(-0.500000 + 0.866025i) q^{25} +9.24264 q^{26} -1.00000 q^{27} +(7.32843 - 12.6932i) q^{28} +(0.828427 - 1.43488i) q^{29} +2.41421 q^{30} -5.00000 q^{31} +(0.792893 - 1.37333i) q^{32} +(1.41421 + 2.44949i) q^{33} +(8.24264 - 14.2767i) q^{34} +(-1.91421 - 3.31552i) q^{35} +(-1.91421 - 3.31552i) q^{36} -7.82843 q^{37} +(-1.20711 - 10.4539i) q^{38} -3.82843 q^{39} +(2.20711 + 3.82282i) q^{40} +(1.41421 + 2.44949i) q^{41} +(-4.62132 + 8.00436i) q^{42} +(-1.08579 - 1.88064i) q^{43} +(-5.41421 + 9.37769i) q^{44} -1.00000 q^{45} +11.6569 q^{46} +(4.41421 - 7.64564i) q^{47} +(1.50000 - 2.59808i) q^{48} +7.65685 q^{49} +2.41421 q^{50} +(-3.41421 + 5.91359i) q^{51} +(-7.32843 - 12.6932i) q^{52} +(1.00000 - 1.73205i) q^{53} +(1.20711 + 2.09077i) q^{54} +(1.41421 + 2.44949i) q^{55} -16.8995 q^{56} +(0.500000 + 4.33013i) q^{57} -4.00000 q^{58} +(-1.91421 - 3.31552i) q^{60} +(-7.15685 + 12.3960i) q^{61} +(6.03553 + 10.4539i) q^{62} +(1.91421 - 3.31552i) q^{63} -9.82843 q^{64} -3.82843 q^{65} +(3.41421 - 5.91359i) q^{66} +(5.74264 - 9.94655i) q^{67} -26.1421 q^{68} -4.82843 q^{69} +(-4.62132 + 8.00436i) q^{70} +(-5.00000 - 8.66025i) q^{71} +(-2.20711 + 3.82282i) q^{72} +(3.74264 + 6.48244i) q^{73} +(9.44975 + 16.3674i) q^{74} -1.00000 q^{75} +(-13.3995 + 9.94655i) q^{76} -10.8284 q^{77} +(4.62132 + 8.00436i) q^{78} +(7.32843 + 12.6932i) q^{79} +(1.50000 - 2.59808i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(3.41421 - 5.91359i) q^{82} -8.00000 q^{83} +14.6569 q^{84} +(-3.41421 + 5.91359i) q^{85} +(-2.62132 + 4.54026i) q^{86} +1.65685 q^{87} +12.4853 q^{88} +(2.24264 - 3.88437i) q^{89} +(1.20711 + 2.09077i) q^{90} +(7.32843 - 12.6932i) q^{91} +(-9.24264 - 16.0087i) q^{92} +(-2.50000 - 4.33013i) q^{93} -21.3137 q^{94} +(0.500000 + 4.33013i) q^{95} +1.58579 q^{96} +(3.00000 + 5.19615i) q^{97} +(-9.24264 - 16.0087i) q^{98} +(-1.41421 + 2.44949i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} - 4 q^{7} + 12 q^{8} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} - 4 q^{7} + 12 q^{8} - 2 q^{9} + 2 q^{10} - 4 q^{12} - 2 q^{13} + 10 q^{14} - 2 q^{15} - 6 q^{16} + 8 q^{17} + 4 q^{18} + 16 q^{19} - 4 q^{20} - 2 q^{21} - 8 q^{22} - 4 q^{23} + 6 q^{24} - 2 q^{25} + 20 q^{26} - 4 q^{27} + 18 q^{28} - 8 q^{29} + 4 q^{30} - 20 q^{31} + 6 q^{32} + 16 q^{34} - 2 q^{35} - 2 q^{36} - 20 q^{37} - 2 q^{38} - 4 q^{39} + 6 q^{40} - 10 q^{42} - 10 q^{43} - 16 q^{44} - 4 q^{45} + 24 q^{46} + 12 q^{47} + 6 q^{48} + 8 q^{49} + 4 q^{50} - 8 q^{51} - 18 q^{52} + 4 q^{53} + 2 q^{54} - 28 q^{56} + 2 q^{57} - 16 q^{58} - 2 q^{60} - 6 q^{61} + 10 q^{62} + 2 q^{63} - 28 q^{64} - 4 q^{65} + 8 q^{66} + 6 q^{67} - 48 q^{68} - 8 q^{69} - 10 q^{70} - 20 q^{71} - 6 q^{72} - 2 q^{73} + 18 q^{74} - 4 q^{75} - 14 q^{76} - 32 q^{77} + 10 q^{78} + 18 q^{79} + 6 q^{80} - 2 q^{81} + 8 q^{82} - 32 q^{83} + 36 q^{84} - 8 q^{85} - 2 q^{86} - 16 q^{87} + 16 q^{88} - 8 q^{89} + 2 q^{90} + 18 q^{91} - 20 q^{92} - 10 q^{93} - 40 q^{94} + 2 q^{95} + 12 q^{96} + 12 q^{97} - 20 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/285\mathbb{Z}\right)^\times\).

\(n\) \(172\) \(191\) \(211\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.20711 2.09077i −0.853553 1.47840i −0.877981 0.478696i \(-0.841110\pi\)
0.0244272 0.999702i \(-0.492224\pi\)
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) −1.91421 + 3.31552i −0.957107 + 1.65776i
\(5\) 0.500000 + 0.866025i 0.223607 + 0.387298i
\(6\) 1.20711 2.09077i 0.492799 0.853553i
\(7\) −3.82843 −1.44701 −0.723505 0.690319i \(-0.757470\pi\)
−0.723505 + 0.690319i \(0.757470\pi\)
\(8\) 4.41421 1.56066
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 1.20711 2.09077i 0.381721 0.661160i
\(11\) 2.82843 0.852803 0.426401 0.904534i \(-0.359781\pi\)
0.426401 + 0.904534i \(0.359781\pi\)
\(12\) −3.82843 −1.10517
\(13\) −1.91421 + 3.31552i −0.530907 + 0.919558i 0.468442 + 0.883494i \(0.344815\pi\)
−0.999349 + 0.0360643i \(0.988518\pi\)
\(14\) 4.62132 + 8.00436i 1.23510 + 2.13926i
\(15\) −0.500000 + 0.866025i −0.129099 + 0.223607i
\(16\) −1.50000 2.59808i −0.375000 0.649519i
\(17\) 3.41421 + 5.91359i 0.828068 + 1.43426i 0.899551 + 0.436815i \(0.143893\pi\)
−0.0714831 + 0.997442i \(0.522773\pi\)
\(18\) 2.41421 0.569036
\(19\) 4.00000 + 1.73205i 0.917663 + 0.397360i
\(20\) −3.82843 −0.856062
\(21\) −1.91421 3.31552i −0.417716 0.723505i
\(22\) −3.41421 5.91359i −0.727913 1.26078i
\(23\) −2.41421 + 4.18154i −0.503398 + 0.871911i 0.496594 + 0.867983i \(0.334584\pi\)
−0.999992 + 0.00392850i \(0.998750\pi\)
\(24\) 2.20711 + 3.82282i 0.450524 + 0.780330i
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 9.24264 1.81263
\(27\) −1.00000 −0.192450
\(28\) 7.32843 12.6932i 1.38494 2.39879i
\(29\) 0.828427 1.43488i 0.153835 0.266450i −0.778799 0.627273i \(-0.784171\pi\)
0.932634 + 0.360823i \(0.117504\pi\)
\(30\) 2.41421 0.440773
\(31\) −5.00000 −0.898027 −0.449013 0.893525i \(-0.648224\pi\)
−0.449013 + 0.893525i \(0.648224\pi\)
\(32\) 0.792893 1.37333i 0.140165 0.242773i
\(33\) 1.41421 + 2.44949i 0.246183 + 0.426401i
\(34\) 8.24264 14.2767i 1.41360 2.44843i
\(35\) −1.91421 3.31552i −0.323561 0.560424i
\(36\) −1.91421 3.31552i −0.319036 0.552586i
\(37\) −7.82843 −1.28699 −0.643493 0.765452i \(-0.722515\pi\)
−0.643493 + 0.765452i \(0.722515\pi\)
\(38\) −1.20711 10.4539i −0.195819 1.69584i
\(39\) −3.82843 −0.613039
\(40\) 2.20711 + 3.82282i 0.348974 + 0.604441i
\(41\) 1.41421 + 2.44949i 0.220863 + 0.382546i 0.955070 0.296379i \(-0.0957793\pi\)
−0.734207 + 0.678925i \(0.762446\pi\)
\(42\) −4.62132 + 8.00436i −0.713085 + 1.23510i
\(43\) −1.08579 1.88064i −0.165581 0.286794i 0.771281 0.636495i \(-0.219617\pi\)
−0.936861 + 0.349701i \(0.886283\pi\)
\(44\) −5.41421 + 9.37769i −0.816223 + 1.41374i
\(45\) −1.00000 −0.149071
\(46\) 11.6569 1.71871
\(47\) 4.41421 7.64564i 0.643879 1.11523i −0.340680 0.940179i \(-0.610657\pi\)
0.984559 0.175052i \(-0.0560094\pi\)
\(48\) 1.50000 2.59808i 0.216506 0.375000i
\(49\) 7.65685 1.09384
\(50\) 2.41421 0.341421
\(51\) −3.41421 + 5.91359i −0.478086 + 0.828068i
\(52\) −7.32843 12.6932i −1.01627 1.76023i
\(53\) 1.00000 1.73205i 0.137361 0.237915i −0.789136 0.614218i \(-0.789471\pi\)
0.926497 + 0.376303i \(0.122805\pi\)
\(54\) 1.20711 + 2.09077i 0.164266 + 0.284518i
\(55\) 1.41421 + 2.44949i 0.190693 + 0.330289i
\(56\) −16.8995 −2.25829
\(57\) 0.500000 + 4.33013i 0.0662266 + 0.573539i
\(58\) −4.00000 −0.525226
\(59\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(60\) −1.91421 3.31552i −0.247124 0.428031i
\(61\) −7.15685 + 12.3960i −0.916341 + 1.58715i −0.111416 + 0.993774i \(0.535539\pi\)
−0.804926 + 0.593376i \(0.797795\pi\)
\(62\) 6.03553 + 10.4539i 0.766514 + 1.32764i
\(63\) 1.91421 3.31552i 0.241168 0.417716i
\(64\) −9.82843 −1.22855
\(65\) −3.82843 −0.474858
\(66\) 3.41421 5.91359i 0.420261 0.727913i
\(67\) 5.74264 9.94655i 0.701575 1.21516i −0.266338 0.963880i \(-0.585814\pi\)
0.967913 0.251284i \(-0.0808529\pi\)
\(68\) −26.1421 −3.17020
\(69\) −4.82843 −0.581274
\(70\) −4.62132 + 8.00436i −0.552353 + 0.956704i
\(71\) −5.00000 8.66025i −0.593391 1.02778i −0.993772 0.111434i \(-0.964456\pi\)
0.400381 0.916349i \(-0.368878\pi\)
\(72\) −2.20711 + 3.82282i −0.260110 + 0.450524i
\(73\) 3.74264 + 6.48244i 0.438043 + 0.758713i 0.997539 0.0701207i \(-0.0223384\pi\)
−0.559496 + 0.828833i \(0.689005\pi\)
\(74\) 9.44975 + 16.3674i 1.09851 + 1.90268i
\(75\) −1.00000 −0.115470
\(76\) −13.3995 + 9.94655i −1.53703 + 1.14095i
\(77\) −10.8284 −1.23401
\(78\) 4.62132 + 8.00436i 0.523261 + 0.906315i
\(79\) 7.32843 + 12.6932i 0.824512 + 1.42810i 0.902291 + 0.431127i \(0.141884\pi\)
−0.0777789 + 0.996971i \(0.524783\pi\)
\(80\) 1.50000 2.59808i 0.167705 0.290474i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 3.41421 5.91359i 0.377037 0.653047i
\(83\) −8.00000 −0.878114 −0.439057 0.898459i \(-0.644687\pi\)
−0.439057 + 0.898459i \(0.644687\pi\)
\(84\) 14.6569 1.59919
\(85\) −3.41421 + 5.91359i −0.370323 + 0.641419i
\(86\) −2.62132 + 4.54026i −0.282664 + 0.489589i
\(87\) 1.65685 0.177633
\(88\) 12.4853 1.33094
\(89\) 2.24264 3.88437i 0.237719 0.411742i −0.722340 0.691538i \(-0.756933\pi\)
0.960060 + 0.279796i \(0.0902668\pi\)
\(90\) 1.20711 + 2.09077i 0.127240 + 0.220387i
\(91\) 7.32843 12.6932i 0.768228 1.33061i
\(92\) −9.24264 16.0087i −0.963612 1.66902i
\(93\) −2.50000 4.33013i −0.259238 0.449013i
\(94\) −21.3137 −2.19834
\(95\) 0.500000 + 4.33013i 0.0512989 + 0.444262i
\(96\) 1.58579 0.161849
\(97\) 3.00000 + 5.19615i 0.304604 + 0.527589i 0.977173 0.212445i \(-0.0681426\pi\)
−0.672569 + 0.740034i \(0.734809\pi\)
\(98\) −9.24264 16.0087i −0.933648 1.61713i
\(99\) −1.41421 + 2.44949i −0.142134 + 0.246183i
\(100\) −1.91421 3.31552i −0.191421 0.331552i
\(101\) 8.07107 13.9795i 0.803101 1.39101i −0.114464 0.993427i \(-0.536515\pi\)
0.917565 0.397585i \(-0.130152\pi\)
\(102\) 16.4853 1.63229
\(103\) 4.17157 0.411037 0.205519 0.978653i \(-0.434112\pi\)
0.205519 + 0.978653i \(0.434112\pi\)
\(104\) −8.44975 + 14.6354i −0.828566 + 1.43512i
\(105\) 1.91421 3.31552i 0.186808 0.323561i
\(106\) −4.82843 −0.468978
\(107\) 14.0000 1.35343 0.676716 0.736245i \(-0.263403\pi\)
0.676716 + 0.736245i \(0.263403\pi\)
\(108\) 1.91421 3.31552i 0.184195 0.319036i
\(109\) −2.65685 4.60181i −0.254480 0.440773i 0.710274 0.703926i \(-0.248571\pi\)
−0.964754 + 0.263152i \(0.915238\pi\)
\(110\) 3.41421 5.91359i 0.325532 0.563839i
\(111\) −3.91421 6.77962i −0.371521 0.643493i
\(112\) 5.74264 + 9.94655i 0.542629 + 0.939860i
\(113\) 4.00000 0.376288 0.188144 0.982141i \(-0.439753\pi\)
0.188144 + 0.982141i \(0.439753\pi\)
\(114\) 8.44975 6.27231i 0.791391 0.587456i
\(115\) −4.82843 −0.450253
\(116\) 3.17157 + 5.49333i 0.294473 + 0.510042i
\(117\) −1.91421 3.31552i −0.176969 0.306519i
\(118\) 0 0
\(119\) −13.0711 22.6398i −1.19822 2.07538i
\(120\) −2.20711 + 3.82282i −0.201480 + 0.348974i
\(121\) −3.00000 −0.272727
\(122\) 34.5563 3.12858
\(123\) −1.41421 + 2.44949i −0.127515 + 0.220863i
\(124\) 9.57107 16.5776i 0.859507 1.48871i
\(125\) −1.00000 −0.0894427
\(126\) −9.24264 −0.823400
\(127\) 10.4853 18.1610i 0.930418 1.61153i 0.147811 0.989016i \(-0.452777\pi\)
0.782607 0.622516i \(-0.213889\pi\)
\(128\) 10.2782 + 17.8023i 0.908471 + 1.57352i
\(129\) 1.08579 1.88064i 0.0955982 0.165581i
\(130\) 4.62132 + 8.00436i 0.405317 + 0.702029i
\(131\) 5.24264 + 9.08052i 0.458052 + 0.793369i 0.998858 0.0477784i \(-0.0152141\pi\)
−0.540806 + 0.841147i \(0.681881\pi\)
\(132\) −10.8284 −0.942494
\(133\) −15.3137 6.63103i −1.32787 0.574983i
\(134\) −27.7279 −2.39533
\(135\) −0.500000 0.866025i −0.0430331 0.0745356i
\(136\) 15.0711 + 26.1039i 1.29233 + 2.23839i
\(137\) −3.24264 + 5.61642i −0.277037 + 0.479843i −0.970647 0.240508i \(-0.922686\pi\)
0.693610 + 0.720351i \(0.256019\pi\)
\(138\) 5.82843 + 10.0951i 0.496149 + 0.859355i
\(139\) −3.15685 + 5.46783i −0.267761 + 0.463775i −0.968283 0.249855i \(-0.919617\pi\)
0.700522 + 0.713630i \(0.252950\pi\)
\(140\) 14.6569 1.23873
\(141\) 8.82843 0.743488
\(142\) −12.0711 + 20.9077i −1.01298 + 1.75454i
\(143\) −5.41421 + 9.37769i −0.452759 + 0.784202i
\(144\) 3.00000 0.250000
\(145\) 1.65685 0.137594
\(146\) 9.03553 15.6500i 0.747786 1.29520i
\(147\) 3.82843 + 6.63103i 0.315763 + 0.546918i
\(148\) 14.9853 25.9553i 1.23178 2.13351i
\(149\) 3.41421 + 5.91359i 0.279703 + 0.484460i 0.971311 0.237813i \(-0.0764306\pi\)
−0.691608 + 0.722273i \(0.743097\pi\)
\(150\) 1.20711 + 2.09077i 0.0985599 + 0.170711i
\(151\) 21.6569 1.76241 0.881205 0.472735i \(-0.156733\pi\)
0.881205 + 0.472735i \(0.156733\pi\)
\(152\) 17.6569 + 7.64564i 1.43216 + 0.620143i
\(153\) −6.82843 −0.552046
\(154\) 13.0711 + 22.6398i 1.05330 + 1.82436i
\(155\) −2.50000 4.33013i −0.200805 0.347804i
\(156\) 7.32843 12.6932i 0.586744 1.01627i
\(157\) 7.08579 + 12.2729i 0.565507 + 0.979487i 0.997002 + 0.0773721i \(0.0246529\pi\)
−0.431495 + 0.902115i \(0.642014\pi\)
\(158\) 17.6924 30.6441i 1.40753 2.43791i
\(159\) 2.00000 0.158610
\(160\) 1.58579 0.125367
\(161\) 9.24264 16.0087i 0.728422 1.26166i
\(162\) −1.20711 + 2.09077i −0.0948393 + 0.164266i
\(163\) −13.1421 −1.02937 −0.514686 0.857379i \(-0.672091\pi\)
−0.514686 + 0.857379i \(0.672091\pi\)
\(164\) −10.8284 −0.845558
\(165\) −1.41421 + 2.44949i −0.110096 + 0.190693i
\(166\) 9.65685 + 16.7262i 0.749517 + 1.29820i
\(167\) −4.48528 + 7.76874i −0.347081 + 0.601163i −0.985730 0.168336i \(-0.946161\pi\)
0.638648 + 0.769499i \(0.279494\pi\)
\(168\) −8.44975 14.6354i −0.651912 1.12915i
\(169\) −0.828427 1.43488i −0.0637252 0.110375i
\(170\) 16.4853 1.26436
\(171\) −3.50000 + 2.59808i −0.267652 + 0.198680i
\(172\) 8.31371 0.633914
\(173\) 7.65685 + 13.2621i 0.582140 + 1.00830i 0.995225 + 0.0976036i \(0.0311177\pi\)
−0.413086 + 0.910692i \(0.635549\pi\)
\(174\) −2.00000 3.46410i −0.151620 0.262613i
\(175\) 1.91421 3.31552i 0.144701 0.250629i
\(176\) −4.24264 7.34847i −0.319801 0.553912i
\(177\) 0 0
\(178\) −10.8284 −0.811625
\(179\) −12.1421 −0.907546 −0.453773 0.891117i \(-0.649922\pi\)
−0.453773 + 0.891117i \(0.649922\pi\)
\(180\) 1.91421 3.31552i 0.142677 0.247124i
\(181\) −1.34315 + 2.32640i −0.0998352 + 0.172920i −0.911616 0.411042i \(-0.865165\pi\)
0.811781 + 0.583962i \(0.198498\pi\)
\(182\) −35.3848 −2.62289
\(183\) −14.3137 −1.05810
\(184\) −10.6569 + 18.4582i −0.785634 + 1.36076i
\(185\) −3.91421 6.77962i −0.287779 0.498447i
\(186\) −6.03553 + 10.4539i −0.442547 + 0.766514i
\(187\) 9.65685 + 16.7262i 0.706179 + 1.22314i
\(188\) 16.8995 + 29.2708i 1.23252 + 2.13479i
\(189\) 3.82843 0.278477
\(190\) 8.44975 6.27231i 0.613009 0.455041i
\(191\) −11.1716 −0.808347 −0.404173 0.914682i \(-0.632441\pi\)
−0.404173 + 0.914682i \(0.632441\pi\)
\(192\) −4.91421 8.51167i −0.354653 0.614277i
\(193\) −7.39949 12.8163i −0.532627 0.922538i −0.999274 0.0380938i \(-0.987871\pi\)
0.466647 0.884444i \(-0.345462\pi\)
\(194\) 7.24264 12.5446i 0.519991 0.900651i
\(195\) −1.91421 3.31552i −0.137080 0.237429i
\(196\) −14.6569 + 25.3864i −1.04692 + 1.81332i
\(197\) 6.34315 0.451930 0.225965 0.974135i \(-0.427446\pi\)
0.225965 + 0.974135i \(0.427446\pi\)
\(198\) 6.82843 0.485275
\(199\) 8.50000 14.7224i 0.602549 1.04365i −0.389885 0.920864i \(-0.627485\pi\)
0.992434 0.122782i \(-0.0391815\pi\)
\(200\) −2.20711 + 3.82282i −0.156066 + 0.270314i
\(201\) 11.4853 0.810109
\(202\) −38.9706 −2.74196
\(203\) −3.17157 + 5.49333i −0.222601 + 0.385556i
\(204\) −13.0711 22.6398i −0.915158 1.58510i
\(205\) −1.41421 + 2.44949i −0.0987730 + 0.171080i
\(206\) −5.03553 8.72180i −0.350842 0.607677i
\(207\) −2.41421 4.18154i −0.167799 0.290637i
\(208\) 11.4853 0.796361
\(209\) 11.3137 + 4.89898i 0.782586 + 0.338869i
\(210\) −9.24264 −0.637803
\(211\) −11.1569 19.3242i −0.768070 1.33034i −0.938608 0.344984i \(-0.887884\pi\)
0.170539 0.985351i \(-0.445449\pi\)
\(212\) 3.82843 + 6.63103i 0.262937 + 0.455421i
\(213\) 5.00000 8.66025i 0.342594 0.593391i
\(214\) −16.8995 29.2708i −1.15523 2.00091i
\(215\) 1.08579 1.88064i 0.0740500 0.128258i
\(216\) −4.41421 −0.300349
\(217\) 19.1421 1.29945
\(218\) −6.41421 + 11.1097i −0.434425 + 0.752447i
\(219\) −3.74264 + 6.48244i −0.252904 + 0.438043i
\(220\) −10.8284 −0.730052
\(221\) −26.1421 −1.75851
\(222\) −9.44975 + 16.3674i −0.634226 + 1.09851i
\(223\) −0.0857864 0.148586i −0.00574468 0.00995009i 0.863139 0.504967i \(-0.168495\pi\)
−0.868883 + 0.495017i \(0.835162\pi\)
\(224\) −3.03553 + 5.25770i −0.202820 + 0.351295i
\(225\) −0.500000 0.866025i −0.0333333 0.0577350i
\(226\) −4.82843 8.36308i −0.321182 0.556304i
\(227\) 14.9706 0.993631 0.496816 0.867856i \(-0.334503\pi\)
0.496816 + 0.867856i \(0.334503\pi\)
\(228\) −15.3137 6.63103i −1.01418 0.439151i
\(229\) 6.65685 0.439897 0.219949 0.975511i \(-0.429411\pi\)
0.219949 + 0.975511i \(0.429411\pi\)
\(230\) 5.82843 + 10.0951i 0.384315 + 0.665653i
\(231\) −5.41421 9.37769i −0.356229 0.617007i
\(232\) 3.65685 6.33386i 0.240084 0.415838i
\(233\) 1.34315 + 2.32640i 0.0879924 + 0.152407i 0.906662 0.421857i \(-0.138622\pi\)
−0.818670 + 0.574264i \(0.805288\pi\)
\(234\) −4.62132 + 8.00436i −0.302105 + 0.523261i
\(235\) 8.82843 0.575903
\(236\) 0 0
\(237\) −7.32843 + 12.6932i −0.476032 + 0.824512i
\(238\) −31.5563 + 54.6572i −2.04549 + 3.54290i
\(239\) 20.6274 1.33428 0.667138 0.744934i \(-0.267519\pi\)
0.667138 + 0.744934i \(0.267519\pi\)
\(240\) 3.00000 0.193649
\(241\) −2.50000 + 4.33013i −0.161039 + 0.278928i −0.935242 0.354010i \(-0.884818\pi\)
0.774202 + 0.632938i \(0.218151\pi\)
\(242\) 3.62132 + 6.27231i 0.232787 + 0.403199i
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) −27.3995 47.4573i −1.75407 3.03814i
\(245\) 3.82843 + 6.63103i 0.244589 + 0.423641i
\(246\) 6.82843 0.435365
\(247\) −13.3995 + 9.94655i −0.852589 + 0.632884i
\(248\) −22.0711 −1.40151
\(249\) −4.00000 6.92820i −0.253490 0.439057i
\(250\) 1.20711 + 2.09077i 0.0763441 + 0.132232i
\(251\) 13.8284 23.9515i 0.872843 1.51181i 0.0137993 0.999905i \(-0.495607\pi\)
0.859043 0.511903i \(-0.171059\pi\)
\(252\) 7.32843 + 12.6932i 0.461648 + 0.799597i
\(253\) −6.82843 + 11.8272i −0.429300 + 0.743569i
\(254\) −50.6274 −3.17665
\(255\) −6.82843 −0.427613
\(256\) 14.9853 25.9553i 0.936580 1.62220i
\(257\) 5.58579 9.67487i 0.348432 0.603502i −0.637539 0.770418i \(-0.720048\pi\)
0.985971 + 0.166916i \(0.0533810\pi\)
\(258\) −5.24264 −0.326393
\(259\) 29.9706 1.86228
\(260\) 7.32843 12.6932i 0.454490 0.787199i
\(261\) 0.828427 + 1.43488i 0.0512784 + 0.0888167i
\(262\) 12.6569 21.9223i 0.781943 1.35437i
\(263\) 6.89949 + 11.9503i 0.425441 + 0.736886i 0.996462 0.0840503i \(-0.0267856\pi\)
−0.571020 + 0.820936i \(0.693452\pi\)
\(264\) 6.24264 + 10.8126i 0.384208 + 0.665468i
\(265\) 2.00000 0.122859
\(266\) 4.62132 + 40.0218i 0.283351 + 2.45389i
\(267\) 4.48528 0.274495
\(268\) 21.9853 + 38.0796i 1.34296 + 2.32608i
\(269\) 4.82843 + 8.36308i 0.294394 + 0.509906i 0.974844 0.222889i \(-0.0715487\pi\)
−0.680449 + 0.732795i \(0.738215\pi\)
\(270\) −1.20711 + 2.09077i −0.0734622 + 0.127240i
\(271\) −1.17157 2.02922i −0.0711680 0.123267i 0.828245 0.560365i \(-0.189339\pi\)
−0.899413 + 0.437099i \(0.856006\pi\)
\(272\) 10.2426 17.7408i 0.621051 1.07569i
\(273\) 14.6569 0.887073
\(274\) 15.6569 0.945865
\(275\) −1.41421 + 2.44949i −0.0852803 + 0.147710i
\(276\) 9.24264 16.0087i 0.556342 0.963612i
\(277\) 6.00000 0.360505 0.180253 0.983620i \(-0.442309\pi\)
0.180253 + 0.983620i \(0.442309\pi\)
\(278\) 15.2426 0.914193
\(279\) 2.50000 4.33013i 0.149671 0.259238i
\(280\) −8.44975 14.6354i −0.504969 0.874632i
\(281\) −13.4853 + 23.3572i −0.804464 + 1.39337i 0.112188 + 0.993687i \(0.464214\pi\)
−0.916652 + 0.399686i \(0.869119\pi\)
\(282\) −10.6569 18.4582i −0.634606 1.09917i
\(283\) −6.48528 11.2328i −0.385510 0.667723i 0.606330 0.795213i \(-0.292641\pi\)
−0.991840 + 0.127490i \(0.959308\pi\)
\(284\) 38.2843 2.27175
\(285\) −3.50000 + 2.59808i −0.207322 + 0.153897i
\(286\) 26.1421 1.54582
\(287\) −5.41421 9.37769i −0.319591 0.553548i
\(288\) 0.792893 + 1.37333i 0.0467217 + 0.0809243i
\(289\) −14.8137 + 25.6581i −0.871395 + 1.50930i
\(290\) −2.00000 3.46410i −0.117444 0.203419i
\(291\) −3.00000 + 5.19615i −0.175863 + 0.304604i
\(292\) −28.6569 −1.67702
\(293\) 17.3137 1.01148 0.505739 0.862687i \(-0.331220\pi\)
0.505739 + 0.862687i \(0.331220\pi\)
\(294\) 9.24264 16.0087i 0.539042 0.933648i
\(295\) 0 0
\(296\) −34.5563 −2.00855
\(297\) −2.82843 −0.164122
\(298\) 8.24264 14.2767i 0.477483 0.827025i
\(299\) −9.24264 16.0087i −0.534516 0.925808i
\(300\) 1.91421 3.31552i 0.110517 0.191421i
\(301\) 4.15685 + 7.19988i 0.239597 + 0.414994i
\(302\) −26.1421 45.2795i −1.50431 2.60554i
\(303\) 16.1421 0.927341
\(304\) −1.50000 12.9904i −0.0860309 0.745049i
\(305\) −14.3137 −0.819601
\(306\) 8.24264 + 14.2767i 0.471200 + 0.816143i
\(307\) 3.17157 + 5.49333i 0.181011 + 0.313521i 0.942225 0.334980i \(-0.108730\pi\)
−0.761214 + 0.648501i \(0.775396\pi\)
\(308\) 20.7279 35.9018i 1.18108 2.04570i
\(309\) 2.08579 + 3.61269i 0.118656 + 0.205519i
\(310\) −6.03553 + 10.4539i −0.342795 + 0.593739i
\(311\) −4.00000 −0.226819 −0.113410 0.993548i \(-0.536177\pi\)
−0.113410 + 0.993548i \(0.536177\pi\)
\(312\) −16.8995 −0.956746
\(313\) 3.00000 5.19615i 0.169570 0.293704i −0.768699 0.639611i \(-0.779095\pi\)
0.938269 + 0.345907i \(0.112429\pi\)
\(314\) 17.1066 29.6295i 0.965381 1.67209i
\(315\) 3.82843 0.215707
\(316\) −56.1127 −3.15659
\(317\) 8.65685 14.9941i 0.486217 0.842153i −0.513657 0.857996i \(-0.671710\pi\)
0.999875 + 0.0158423i \(0.00504299\pi\)
\(318\) −2.41421 4.18154i −0.135382 0.234489i
\(319\) 2.34315 4.05845i 0.131191 0.227229i
\(320\) −4.91421 8.51167i −0.274713 0.475817i
\(321\) 7.00000 + 12.1244i 0.390702 + 0.676716i
\(322\) −44.6274 −2.48699
\(323\) 3.41421 + 29.5680i 0.189972 + 1.64521i
\(324\) 3.82843 0.212690
\(325\) −1.91421 3.31552i −0.106181 0.183912i
\(326\) 15.8640 + 27.4772i 0.878624 + 1.52182i
\(327\) 2.65685 4.60181i 0.146924 0.254480i
\(328\) 6.24264 + 10.8126i 0.344692 + 0.597024i
\(329\) −16.8995 + 29.2708i −0.931699 + 1.61375i
\(330\) 6.82843 0.375893
\(331\) −16.6569 −0.915544 −0.457772 0.889070i \(-0.651352\pi\)
−0.457772 + 0.889070i \(0.651352\pi\)
\(332\) 15.3137 26.5241i 0.840449 1.45570i
\(333\) 3.91421 6.77962i 0.214498 0.371521i
\(334\) 21.6569 1.18501
\(335\) 11.4853 0.627508
\(336\) −5.74264 + 9.94655i −0.313287 + 0.542629i
\(337\) −0.257359 0.445759i −0.0140193 0.0242821i 0.858931 0.512092i \(-0.171129\pi\)
−0.872950 + 0.487810i \(0.837796\pi\)
\(338\) −2.00000 + 3.46410i −0.108786 + 0.188422i
\(339\) 2.00000 + 3.46410i 0.108625 + 0.188144i
\(340\) −13.0711 22.6398i −0.708878 1.22781i
\(341\) −14.1421 −0.765840
\(342\) 9.65685 + 4.18154i 0.522183 + 0.226112i
\(343\) −2.51472 −0.135782
\(344\) −4.79289 8.30153i −0.258415 0.447589i
\(345\) −2.41421 4.18154i −0.129977 0.225127i
\(346\) 18.4853 32.0174i 0.993775 1.72127i
\(347\) −7.72792 13.3852i −0.414857 0.718553i 0.580557 0.814220i \(-0.302835\pi\)
−0.995413 + 0.0956671i \(0.969502\pi\)
\(348\) −3.17157 + 5.49333i −0.170014 + 0.294473i
\(349\) 13.6274 0.729459 0.364729 0.931114i \(-0.381161\pi\)
0.364729 + 0.931114i \(0.381161\pi\)
\(350\) −9.24264 −0.494040
\(351\) 1.91421 3.31552i 0.102173 0.176969i
\(352\) 2.24264 3.88437i 0.119533 0.207037i
\(353\) 21.3137 1.13441 0.567207 0.823575i \(-0.308024\pi\)
0.567207 + 0.823575i \(0.308024\pi\)
\(354\) 0 0
\(355\) 5.00000 8.66025i 0.265372 0.459639i
\(356\) 8.58579 + 14.8710i 0.455046 + 0.788162i
\(357\) 13.0711 22.6398i 0.691794 1.19822i
\(358\) 14.6569 + 25.3864i 0.774639 + 1.34171i
\(359\) −7.41421 12.8418i −0.391307 0.677764i 0.601315 0.799012i \(-0.294644\pi\)
−0.992622 + 0.121248i \(0.961310\pi\)
\(360\) −4.41421 −0.232649
\(361\) 13.0000 + 13.8564i 0.684211 + 0.729285i
\(362\) 6.48528 0.340859
\(363\) −1.50000 2.59808i −0.0787296 0.136364i
\(364\) 28.0563 + 48.5950i 1.47055 + 2.54707i
\(365\) −3.74264 + 6.48244i −0.195899 + 0.339307i
\(366\) 17.2782 + 29.9267i 0.903145 + 1.56429i
\(367\) −14.0563 + 24.3463i −0.733735 + 1.27087i 0.221540 + 0.975151i \(0.428892\pi\)
−0.955276 + 0.295716i \(0.904442\pi\)
\(368\) 14.4853 0.755097
\(369\) −2.82843 −0.147242
\(370\) −9.44975 + 16.3674i −0.491269 + 0.850903i
\(371\) −3.82843 + 6.63103i −0.198762 + 0.344266i
\(372\) 19.1421 0.992473
\(373\) −0.343146 −0.0177674 −0.00888371 0.999961i \(-0.502828\pi\)
−0.00888371 + 0.999961i \(0.502828\pi\)
\(374\) 23.3137 40.3805i 1.20552 2.08803i
\(375\) −0.500000 0.866025i −0.0258199 0.0447214i
\(376\) 19.4853 33.7495i 1.00488 1.74050i
\(377\) 3.17157 + 5.49333i 0.163344 + 0.282921i
\(378\) −4.62132 8.00436i −0.237695 0.411700i
\(379\) 24.3137 1.24891 0.624456 0.781060i \(-0.285321\pi\)
0.624456 + 0.781060i \(0.285321\pi\)
\(380\) −15.3137 6.63103i −0.785577 0.340165i
\(381\) 20.9706 1.07435
\(382\) 13.4853 + 23.3572i 0.689967 + 1.19506i
\(383\) −16.9706 29.3939i −0.867155 1.50196i −0.864891 0.501960i \(-0.832613\pi\)
−0.00226413 0.999997i \(-0.500721\pi\)
\(384\) −10.2782 + 17.8023i −0.524506 + 0.908471i
\(385\) −5.41421 9.37769i −0.275934 0.477931i
\(386\) −17.8640 + 30.9413i −0.909252 + 1.57487i
\(387\) 2.17157 0.110387
\(388\) −22.9706 −1.16615
\(389\) −17.7279 + 30.7057i −0.898841 + 1.55684i −0.0698641 + 0.997557i \(0.522257\pi\)
−0.828977 + 0.559282i \(0.811077\pi\)
\(390\) −4.62132 + 8.00436i −0.234010 + 0.405317i
\(391\) −32.9706 −1.66739
\(392\) 33.7990 1.70711
\(393\) −5.24264 + 9.08052i −0.264456 + 0.458052i
\(394\) −7.65685 13.2621i −0.385747 0.668133i
\(395\) −7.32843 + 12.6932i −0.368733 + 0.638665i
\(396\) −5.41421 9.37769i −0.272074 0.471247i
\(397\) 9.08579 + 15.7370i 0.456003 + 0.789820i 0.998745 0.0500794i \(-0.0159475\pi\)
−0.542743 + 0.839899i \(0.682614\pi\)
\(398\) −41.0416 −2.05723
\(399\) −1.91421 16.5776i −0.0958305 0.829917i
\(400\) 3.00000 0.150000
\(401\) −11.3137 19.5959i −0.564980 0.978573i −0.997052 0.0767343i \(-0.975551\pi\)
0.432072 0.901839i \(-0.357783\pi\)
\(402\) −13.8640 24.0131i −0.691472 1.19766i
\(403\) 9.57107 16.5776i 0.476769 0.825788i
\(404\) 30.8995 + 53.5195i 1.53731 + 2.66269i
\(405\) 0.500000 0.866025i 0.0248452 0.0430331i
\(406\) 15.3137 0.760007
\(407\) −22.1421 −1.09754
\(408\) −15.0711 + 26.1039i −0.746129 + 1.29233i
\(409\) −3.00000 + 5.19615i −0.148340 + 0.256933i −0.930614 0.366002i \(-0.880726\pi\)
0.782274 + 0.622935i \(0.214060\pi\)
\(410\) 6.82843 0.337232
\(411\) −6.48528 −0.319895
\(412\) −7.98528 + 13.8309i −0.393407 + 0.681400i
\(413\) 0 0
\(414\) −5.82843 + 10.0951i −0.286452 + 0.496149i
\(415\) −4.00000 6.92820i −0.196352 0.340092i
\(416\) 3.03553 + 5.25770i 0.148829 + 0.257780i
\(417\) −6.31371 −0.309184
\(418\) −3.41421 29.5680i −0.166995 1.44622i
\(419\) −19.3137 −0.943536 −0.471768 0.881723i \(-0.656384\pi\)
−0.471768 + 0.881723i \(0.656384\pi\)
\(420\) 7.32843 + 12.6932i 0.357591 + 0.619365i
\(421\) −1.82843 3.16693i −0.0891121 0.154347i 0.818024 0.575184i \(-0.195070\pi\)
−0.907136 + 0.420837i \(0.861736\pi\)
\(422\) −26.9350 + 46.6528i −1.31118 + 2.27102i
\(423\) 4.41421 + 7.64564i 0.214626 + 0.371744i
\(424\) 4.41421 7.64564i 0.214373 0.371305i
\(425\) −6.82843 −0.331227
\(426\) −24.1421 −1.16969
\(427\) 27.3995 47.4573i 1.32595 2.29662i
\(428\) −26.7990 + 46.4172i −1.29538 + 2.24366i
\(429\) −10.8284 −0.522801
\(430\) −5.24264 −0.252823
\(431\) −7.24264 + 12.5446i −0.348866 + 0.604253i −0.986048 0.166460i \(-0.946766\pi\)
0.637183 + 0.770713i \(0.280100\pi\)
\(432\) 1.50000 + 2.59808i 0.0721688 + 0.125000i
\(433\) 17.0858 29.5935i 0.821090 1.42217i −0.0837804 0.996484i \(-0.526699\pi\)
0.904871 0.425686i \(-0.139967\pi\)
\(434\) −23.1066 40.0218i −1.10915 1.92111i
\(435\) 0.828427 + 1.43488i 0.0397200 + 0.0687971i
\(436\) 20.3431 0.974260
\(437\) −16.8995 + 12.5446i −0.808412 + 0.600091i
\(438\) 18.0711 0.863469
\(439\) −8.50000 14.7224i −0.405683 0.702663i 0.588718 0.808339i \(-0.299633\pi\)
−0.994401 + 0.105675i \(0.966300\pi\)
\(440\) 6.24264 + 10.8126i 0.297606 + 0.515469i
\(441\) −3.82843 + 6.63103i −0.182306 + 0.315763i
\(442\) 31.5563 + 54.6572i 1.50098 + 2.59978i
\(443\) 5.07107 8.78335i 0.240934 0.417309i −0.720047 0.693925i \(-0.755880\pi\)
0.960981 + 0.276616i \(0.0892130\pi\)
\(444\) 29.9706 1.42234
\(445\) 4.48528 0.212623
\(446\) −0.207107 + 0.358719i −0.00980679 + 0.0169859i
\(447\) −3.41421 + 5.91359i −0.161487 + 0.279703i
\(448\) 37.6274 1.77773
\(449\) 18.8284 0.888568 0.444284 0.895886i \(-0.353458\pi\)
0.444284 + 0.895886i \(0.353458\pi\)
\(450\) −1.20711 + 2.09077i −0.0569036 + 0.0985599i
\(451\) 4.00000 + 6.92820i 0.188353 + 0.326236i
\(452\) −7.65685 + 13.2621i −0.360148 + 0.623795i
\(453\) 10.8284 + 18.7554i 0.508764 + 0.881205i
\(454\) −18.0711 31.3000i −0.848117 1.46898i
\(455\) 14.6569 0.687124
\(456\) 2.20711 + 19.1141i 0.103357 + 0.895100i
\(457\) −9.82843 −0.459754 −0.229877 0.973220i \(-0.573832\pi\)
−0.229877 + 0.973220i \(0.573832\pi\)
\(458\) −8.03553 13.9180i −0.375476 0.650343i
\(459\) −3.41421 5.91359i −0.159362 0.276023i
\(460\) 9.24264 16.0087i 0.430940 0.746411i
\(461\) −0.928932 1.60896i −0.0432647 0.0749366i 0.843582 0.537000i \(-0.180443\pi\)
−0.886847 + 0.462064i \(0.847109\pi\)
\(462\) −13.0711 + 22.6398i −0.608121 + 1.05330i
\(463\) 16.7990 0.780715 0.390358 0.920663i \(-0.372351\pi\)
0.390358 + 0.920663i \(0.372351\pi\)
\(464\) −4.97056 −0.230753
\(465\) 2.50000 4.33013i 0.115935 0.200805i
\(466\) 3.24264 5.61642i 0.150212 0.260176i
\(467\) −15.7990 −0.731090 −0.365545 0.930794i \(-0.619117\pi\)
−0.365545 + 0.930794i \(0.619117\pi\)
\(468\) 14.6569 0.677513
\(469\) −21.9853 + 38.0796i −1.01519 + 1.75835i
\(470\) −10.6569 18.4582i −0.491564 0.851414i
\(471\) −7.08579 + 12.2729i −0.326496 + 0.565507i
\(472\) 0 0
\(473\) −3.07107 5.31925i −0.141208 0.244579i
\(474\) 35.3848 1.62528
\(475\) −3.50000 + 2.59808i −0.160591 + 0.119208i
\(476\) 100.083 4.58731
\(477\) 1.00000 + 1.73205i 0.0457869 + 0.0793052i
\(478\) −24.8995 43.1272i −1.13888 1.97259i
\(479\) 7.24264 12.5446i 0.330925 0.573178i −0.651769 0.758418i \(-0.725973\pi\)
0.982693 + 0.185239i \(0.0593061\pi\)
\(480\) 0.792893 + 1.37333i 0.0361905 + 0.0626837i
\(481\) 14.9853 25.9553i 0.683270 1.18346i
\(482\) 12.0711 0.549822
\(483\) 18.4853 0.841109
\(484\) 5.74264 9.94655i 0.261029 0.452116i
\(485\) −3.00000 + 5.19615i −0.136223 + 0.235945i
\(486\) −2.41421 −0.109511
\(487\) −17.6569 −0.800108 −0.400054 0.916491i \(-0.631009\pi\)
−0.400054 + 0.916491i \(0.631009\pi\)
\(488\) −31.5919 + 54.7187i −1.43010 + 2.47700i
\(489\) −6.57107 11.3814i −0.297154 0.514686i
\(490\) 9.24264 16.0087i 0.417540 0.723200i
\(491\) −6.17157 10.6895i −0.278519 0.482409i 0.692498 0.721420i \(-0.256510\pi\)
−0.971017 + 0.239011i \(0.923177\pi\)
\(492\) −5.41421 9.37769i −0.244092 0.422779i
\(493\) 11.3137 0.509544
\(494\) 36.9706 + 16.0087i 1.66338 + 0.720267i
\(495\) −2.82843 −0.127128
\(496\) 7.50000 + 12.9904i 0.336760 + 0.583285i
\(497\) 19.1421 + 33.1552i 0.858642 + 1.48721i
\(498\) −9.65685 + 16.7262i −0.432734 + 0.749517i
\(499\) 9.32843 + 16.1573i 0.417598 + 0.723301i 0.995697 0.0926657i \(-0.0295388\pi\)
−0.578100 + 0.815966i \(0.696205\pi\)
\(500\) 1.91421 3.31552i 0.0856062 0.148274i
\(501\) −8.97056 −0.400775
\(502\) −66.7696 −2.98007
\(503\) −21.0711 + 36.4962i −0.939512 + 1.62728i −0.173130 + 0.984899i \(0.555388\pi\)
−0.766383 + 0.642384i \(0.777945\pi\)
\(504\) 8.44975 14.6354i 0.376382 0.651912i
\(505\) 16.1421 0.718316
\(506\) 32.9706 1.46572
\(507\) 0.828427 1.43488i 0.0367917 0.0637252i
\(508\) 40.1421 + 69.5282i 1.78102 + 3.08482i
\(509\) 14.5563 25.2123i 0.645199 1.11752i −0.339057 0.940766i \(-0.610108\pi\)
0.984256 0.176751i \(-0.0565588\pi\)
\(510\) 8.24264 + 14.2767i 0.364990 + 0.632182i
\(511\) −14.3284 24.8176i −0.633852 1.09786i
\(512\) −31.2426 −1.38074
\(513\) −4.00000 1.73205i −0.176604 0.0764719i
\(514\) −26.9706 −1.18962
\(515\) 2.08579 + 3.61269i 0.0919107 + 0.159194i
\(516\) 4.15685 + 7.19988i 0.182995 + 0.316957i
\(517\) 12.4853 21.6251i 0.549102 0.951073i
\(518\) −36.1777 62.6616i −1.58956 2.75319i
\(519\) −7.65685 + 13.2621i −0.336099 + 0.582140i
\(520\) −16.8995 −0.741092
\(521\) 17.6569 0.773561 0.386780 0.922172i \(-0.373587\pi\)
0.386780 + 0.922172i \(0.373587\pi\)
\(522\) 2.00000 3.46410i 0.0875376 0.151620i
\(523\) −21.8848 + 37.9055i −0.956954 + 1.65749i −0.227124 + 0.973866i \(0.572932\pi\)
−0.729831 + 0.683628i \(0.760401\pi\)
\(524\) −40.1421 −1.75362
\(525\) 3.82843 0.167086
\(526\) 16.6569 28.8505i 0.726273 1.25794i
\(527\) −17.0711 29.5680i −0.743627 1.28800i
\(528\) 4.24264 7.34847i 0.184637 0.319801i
\(529\) −0.156854 0.271680i −0.00681975 0.0118122i
\(530\) −2.41421 4.18154i −0.104867 0.181635i
\(531\) 0 0
\(532\) 51.2990 38.0796i 2.22409 1.65096i
\(533\) −10.8284 −0.469031
\(534\) −5.41421 9.37769i −0.234296 0.405812i
\(535\) 7.00000 + 12.1244i 0.302636 + 0.524182i
\(536\) 25.3492 43.9062i 1.09492 1.89646i
\(537\) −6.07107 10.5154i −0.261986 0.453773i
\(538\) 11.6569 20.1903i 0.502563 0.870464i
\(539\) 21.6569 0.932827
\(540\) 3.82843 0.164749
\(541\) 3.15685 5.46783i 0.135724 0.235080i −0.790150 0.612914i \(-0.789997\pi\)
0.925874 + 0.377833i \(0.123331\pi\)
\(542\) −2.82843 + 4.89898i −0.121491 + 0.210429i
\(543\) −2.68629 −0.115280
\(544\) 10.8284 0.464265
\(545\) 2.65685 4.60181i 0.113807 0.197120i
\(546\) −17.6924 30.6441i −0.757164 1.31145i
\(547\) −7.57107 + 13.1135i −0.323715 + 0.560692i −0.981252 0.192731i \(-0.938265\pi\)
0.657536 + 0.753423i \(0.271599\pi\)
\(548\) −12.4142 21.5020i −0.530309 0.918522i
\(549\) −7.15685 12.3960i −0.305447 0.529050i
\(550\) 6.82843 0.291165
\(551\) 5.79899 4.30463i 0.247045 0.183384i
\(552\) −21.3137 −0.907172
\(553\) −28.0563 48.5950i −1.19308 2.06647i
\(554\) −7.24264 12.5446i −0.307710 0.532970i
\(555\) 3.91421 6.77962i 0.166149 0.287779i
\(556\) −12.0858 20.9332i −0.512552 0.887765i
\(557\) 21.4853 37.2136i 0.910361 1.57679i 0.0968052 0.995303i \(-0.469138\pi\)
0.813555 0.581487i \(-0.197529\pi\)
\(558\) −12.0711 −0.511009
\(559\) 8.31371 0.351632
\(560\) −5.74264 + 9.94655i −0.242671 + 0.420318i
\(561\) −9.65685 + 16.7262i −0.407713 + 0.706179i
\(562\) 65.1127 2.74661
\(563\) 16.1421 0.680310 0.340155 0.940369i \(-0.389520\pi\)
0.340155 + 0.940369i \(0.389520\pi\)
\(564\) −16.8995 + 29.2708i −0.711597 + 1.23252i
\(565\) 2.00000 + 3.46410i 0.0841406 + 0.145736i
\(566\) −15.6569 + 27.1185i −0.658107 + 1.13987i
\(567\) 1.91421 + 3.31552i 0.0803894 + 0.139239i
\(568\) −22.0711 38.2282i −0.926081 1.60402i
\(569\) −28.9706 −1.21451 −0.607255 0.794507i \(-0.707729\pi\)
−0.607255 + 0.794507i \(0.707729\pi\)
\(570\) 9.65685 + 4.18154i 0.404481 + 0.175145i
\(571\) −8.31371 −0.347918 −0.173959 0.984753i \(-0.555656\pi\)
−0.173959 + 0.984753i \(0.555656\pi\)
\(572\) −20.7279 35.9018i −0.866678 1.50113i
\(573\) −5.58579 9.67487i −0.233350 0.404173i
\(574\) −13.0711 + 22.6398i −0.545576 + 0.944965i
\(575\) −2.41421 4.18154i −0.100680 0.174382i
\(576\) 4.91421 8.51167i 0.204759 0.354653i
\(577\) −47.6569 −1.98398 −0.991990 0.126313i \(-0.959686\pi\)
−0.991990 + 0.126313i \(0.959686\pi\)
\(578\) 71.5269 2.97513
\(579\) 7.39949 12.8163i 0.307513 0.532627i
\(580\) −3.17157 + 5.49333i −0.131692 + 0.228098i
\(581\) 30.6274 1.27064
\(582\) 14.4853 0.600434
\(583\) 2.82843 4.89898i 0.117141 0.202895i
\(584\) 16.5208 + 28.6149i 0.683636 + 1.18409i
\(585\) 1.91421 3.31552i 0.0791430 0.137080i
\(586\) −20.8995 36.1990i −0.863350 1.49537i
\(587\) 17.3137 + 29.9882i 0.714613 + 1.23775i 0.963109 + 0.269113i \(0.0867306\pi\)
−0.248495 + 0.968633i \(0.579936\pi\)
\(588\) −29.3137 −1.20888
\(589\) −20.0000 8.66025i −0.824086 0.356840i
\(590\) 0 0
\(591\) 3.17157 + 5.49333i 0.130461 + 0.225965i
\(592\) 11.7426 + 20.3389i 0.482620 + 0.835922i
\(593\) 19.0711 33.0321i 0.783155 1.35646i −0.146940 0.989145i \(-0.546943\pi\)
0.930095 0.367319i \(-0.119724\pi\)
\(594\) 3.41421 + 5.91359i 0.140087 + 0.242638i
\(595\) 13.0711 22.6398i 0.535862 0.928139i
\(596\) −26.1421 −1.07082
\(597\) 17.0000 0.695764
\(598\) −22.3137 + 38.6485i −0.912475 + 1.58045i
\(599\) −8.48528 + 14.6969i −0.346699 + 0.600501i −0.985661 0.168738i \(-0.946031\pi\)
0.638962 + 0.769238i \(0.279364\pi\)
\(600\) −4.41421 −0.180210
\(601\) −46.6569 −1.90317 −0.951586 0.307381i \(-0.900547\pi\)
−0.951586 + 0.307381i \(0.900547\pi\)
\(602\) 10.0355 17.3821i 0.409018 0.708440i
\(603\) 5.74264 + 9.94655i 0.233858 + 0.405055i
\(604\) −41.4558 + 71.8036i −1.68681 + 2.92165i
\(605\) −1.50000 2.59808i −0.0609837 0.105627i
\(606\) −19.4853 33.7495i −0.791535 1.37098i
\(607\) −11.8284 −0.480101 −0.240051 0.970760i \(-0.577164\pi\)
−0.240051 + 0.970760i \(0.577164\pi\)
\(608\) 5.55025 4.11999i 0.225092 0.167088i
\(609\) −6.34315 −0.257037
\(610\) 17.2782 + 29.9267i 0.699573 + 1.21170i
\(611\) 16.8995 + 29.2708i 0.683680 + 1.18417i
\(612\) 13.0711 22.6398i 0.528367 0.915158i
\(613\) 22.7990 + 39.4890i 0.920843 + 1.59495i 0.798115 + 0.602506i \(0.205831\pi\)
0.122728 + 0.992440i \(0.460836\pi\)
\(614\) 7.65685 13.2621i 0.309005 0.535213i
\(615\) −2.82843 −0.114053
\(616\) −47.7990 −1.92588
\(617\) −7.17157 + 12.4215i −0.288717 + 0.500072i −0.973504 0.228671i \(-0.926562\pi\)
0.684787 + 0.728743i \(0.259895\pi\)
\(618\) 5.03553 8.72180i 0.202559 0.350842i
\(619\) 38.3137 1.53996 0.769979 0.638069i \(-0.220267\pi\)
0.769979 + 0.638069i \(0.220267\pi\)
\(620\) 19.1421 0.768767
\(621\) 2.41421 4.18154i 0.0968791 0.167799i
\(622\) 4.82843 + 8.36308i 0.193602 + 0.335329i
\(623\) −8.58579 + 14.8710i −0.343982 + 0.595795i
\(624\) 5.74264 + 9.94655i 0.229890 + 0.398180i
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) −14.4853 −0.578948
\(627\) 1.41421 + 12.2474i 0.0564782 + 0.489116i
\(628\) −54.2548 −2.16500
\(629\) −26.7279 46.2941i −1.06571 1.84587i
\(630\) −4.62132 8.00436i −0.184118 0.318901i
\(631\) −21.6421 + 37.4853i −0.861560 + 1.49227i 0.00886314 + 0.999961i \(0.497179\pi\)
−0.870423 + 0.492305i \(0.836155\pi\)
\(632\) 32.3492 + 56.0305i 1.28678 + 2.22877i
\(633\) 11.1569 19.3242i 0.443445 0.768070i
\(634\) −41.7990 −1.66005
\(635\) 20.9706 0.832191
\(636\) −3.82843 + 6.63103i −0.151807 + 0.262937i
\(637\) −14.6569 + 25.3864i −0.580726 + 1.00585i
\(638\) −11.3137 −0.447914
\(639\) 10.0000 0.395594
\(640\) −10.2782 + 17.8023i −0.406281 + 0.703699i
\(641\) 0.0710678 + 0.123093i 0.00280701 + 0.00486188i 0.867425 0.497567i \(-0.165773\pi\)
−0.864618 + 0.502429i \(0.832440\pi\)
\(642\) 16.8995 29.2708i 0.666970 1.15523i
\(643\) −0.0857864 0.148586i −0.00338309 0.00585968i 0.864329 0.502927i \(-0.167744\pi\)
−0.867712 + 0.497067i \(0.834410\pi\)
\(644\) 35.3848 + 61.2882i 1.39436 + 2.41509i
\(645\) 2.17157 0.0855056
\(646\) 57.6985 42.8300i 2.27012 1.68512i
\(647\) 24.2843 0.954713 0.477357 0.878710i \(-0.341595\pi\)
0.477357 + 0.878710i \(0.341595\pi\)
\(648\) −2.20711 3.82282i −0.0867033 0.150175i
\(649\) 0 0
\(650\) −4.62132 + 8.00436i −0.181263 + 0.313957i
\(651\) 9.57107 + 16.5776i 0.375120 + 0.649726i
\(652\) 25.1569 43.5729i 0.985218 1.70645i
\(653\) −27.9411 −1.09342 −0.546710 0.837322i \(-0.684120\pi\)
−0.546710 + 0.837322i \(0.684120\pi\)
\(654\) −12.8284 −0.501631
\(655\) −5.24264 + 9.08052i −0.204847 + 0.354805i
\(656\) 4.24264 7.34847i 0.165647 0.286910i
\(657\) −7.48528 −0.292029
\(658\) 81.5980 3.18102
\(659\) −12.2426 + 21.2049i −0.476906 + 0.826025i −0.999650 0.0264649i \(-0.991575\pi\)
0.522744 + 0.852490i \(0.324908\pi\)
\(660\) −5.41421 9.37769i −0.210748 0.365026i
\(661\) −13.4853 + 23.3572i −0.524517 + 0.908489i 0.475076 + 0.879945i \(0.342421\pi\)
−0.999593 + 0.0285447i \(0.990913\pi\)
\(662\) 20.1066 + 34.8257i 0.781465 + 1.35354i
\(663\) −13.0711 22.6398i −0.507638 0.879255i
\(664\) −35.3137 −1.37044
\(665\) −1.91421 16.5776i −0.0742300 0.642851i
\(666\) −18.8995 −0.732341
\(667\) 4.00000 + 6.92820i 0.154881 + 0.268261i
\(668\) −17.1716 29.7420i −0.664388 1.15075i
\(669\) 0.0857864 0.148586i 0.00331670 0.00574468i
\(670\) −13.8640 24.0131i −0.535612 0.927706i
\(671\) −20.2426 + 35.0613i −0.781458 + 1.35353i
\(672\) −6.07107 −0.234197
\(673\) −18.1716 −0.700463 −0.350231 0.936663i \(-0.613897\pi\)
−0.350231 + 0.936663i \(0.613897\pi\)
\(674\) −0.621320 + 1.07616i −0.0239324 + 0.0414521i
\(675\) 0.500000 0.866025i 0.0192450 0.0333333i
\(676\) 6.34315 0.243967
\(677\) 27.4558 1.05521 0.527607 0.849489i \(-0.323089\pi\)
0.527607 + 0.849489i \(0.323089\pi\)
\(678\) 4.82843 8.36308i 0.185435 0.321182i
\(679\) −11.4853 19.8931i −0.440765 0.763427i
\(680\) −15.0711 + 26.1039i −0.577949 + 1.00104i
\(681\) 7.48528 + 12.9649i 0.286837 + 0.496816i
\(682\) 17.0711 + 29.5680i 0.653685 + 1.13222i
\(683\) 15.8579 0.606784 0.303392 0.952866i \(-0.401881\pi\)
0.303392 + 0.952866i \(0.401881\pi\)
\(684\) −1.91421 16.5776i −0.0731918 0.633859i
\(685\) −6.48528 −0.247790
\(686\) 3.03553 + 5.25770i 0.115897 + 0.200740i
\(687\) 3.32843 + 5.76500i 0.126987 + 0.219949i
\(688\) −3.25736 + 5.64191i −0.124186 + 0.215096i
\(689\) 3.82843 + 6.63103i 0.145851 + 0.252622i
\(690\) −5.82843 + 10.0951i −0.221884 + 0.384315i
\(691\) 8.68629 0.330442 0.165221 0.986257i \(-0.447166\pi\)
0.165221 + 0.986257i \(0.447166\pi\)
\(692\) −58.6274 −2.22868
\(693\) 5.41421 9.37769i 0.205669 0.356229i
\(694\) −18.6569 + 32.3146i −0.708205 + 1.22665i
\(695\) −6.31371 −0.239493
\(696\) 7.31371 0.277225
\(697\) −9.65685 + 16.7262i −0.365779 + 0.633549i
\(698\) −16.4497 28.4918i −0.622632 1.07843i
\(699\) −1.34315 + 2.32640i −0.0508024 + 0.0879924i
\(700\) 7.32843 + 12.6932i 0.276989 + 0.479758i
\(701\) −1.92893 3.34101i −0.0728548 0.126188i 0.827297 0.561765i \(-0.189878\pi\)
−0.900151 + 0.435577i \(0.856544\pi\)
\(702\) −9.24264 −0.348841
\(703\) −31.3137 13.5592i −1.18102 0.511396i
\(704\) −27.7990 −1.04771
\(705\) 4.41421 + 7.64564i 0.166249 + 0.287952i
\(706\) −25.7279 44.5621i −0.968283 1.67712i
\(707\) −30.8995 + 53.5195i −1.16210 + 2.01281i
\(708\) 0 0
\(709\) 6.81371 11.8017i 0.255894 0.443222i −0.709244 0.704963i \(-0.750963\pi\)
0.965138 + 0.261742i \(0.0842968\pi\)
\(710\) −24.1421 −0.906038
\(711\) −14.6569 −0.549675
\(712\) 9.89949 17.1464i 0.370999 0.642590i
\(713\) 12.0711 20.9077i 0.452065 0.783000i
\(714\) −63.1127 −2.36193
\(715\) −10.8284 −0.404960
\(716\) 23.2426 40.2574i 0.868618 1.50449i
\(717\) 10.3137 + 17.8639i 0.385173 + 0.667138i
\(718\) −17.8995 + 31.0028i −0.668003 + 1.15702i
\(719\) 14.4142 + 24.9662i 0.537559 + 0.931080i 0.999035 + 0.0439272i \(0.0139870\pi\)
−0.461475 + 0.887153i \(0.652680\pi\)
\(720\) 1.50000 + 2.59808i 0.0559017 + 0.0968246i
\(721\) −15.9706 −0.594775
\(722\) 13.2782 43.9062i 0.494162 1.63402i
\(723\) −5.00000 −0.185952
\(724\) −5.14214 8.90644i −0.191106 0.331005i
\(725\) 0.828427 + 1.43488i 0.0307670 + 0.0532900i
\(726\) −3.62132 + 6.27231i −0.134400 + 0.232787i
\(727\) −20.9142 36.2245i −0.775665 1.34349i −0.934420 0.356174i \(-0.884081\pi\)
0.158755 0.987318i \(-0.449252\pi\)
\(728\) 32.3492 56.0305i 1.19894 2.07663i
\(729\) 1.00000 0.0370370
\(730\) 18.0711 0.668840
\(731\) 7.41421 12.8418i 0.274225 0.474971i
\(732\) 27.3995 47.4573i 1.01271 1.75407i
\(733\) −7.65685 −0.282812 −0.141406 0.989952i \(-0.545162\pi\)
−0.141406 + 0.989952i \(0.545162\pi\)
\(734\) 67.8701 2.50513
\(735\) −3.82843 + 6.63103i −0.141214 + 0.244589i
\(736\) 3.82843 + 6.63103i 0.141118 + 0.244423i
\(737\) 16.2426 28.1331i 0.598305 1.03630i
\(738\) 3.41421 + 5.91359i 0.125679 + 0.217682i
\(739\) −1.81371 3.14144i −0.0667183 0.115560i 0.830737 0.556666i \(-0.187920\pi\)
−0.897455 + 0.441106i \(0.854586\pi\)
\(740\) 29.9706 1.10174
\(741\) −15.3137 6.63103i −0.562563 0.243597i
\(742\) 18.4853 0.678616
\(743\) −2.92893 5.07306i −0.107452 0.186112i 0.807285 0.590161i \(-0.200936\pi\)
−0.914737 + 0.404049i \(0.867603\pi\)
\(744\) −11.0355 19.1141i −0.404582 0.700757i
\(745\) −3.41421 + 5.91359i −0.125087 + 0.216657i
\(746\) 0.414214 + 0.717439i 0.0151654 + 0.0262673i
\(747\) 4.00000 6.92820i 0.146352 0.253490i
\(748\) −73.9411 −2.70356
\(749\) −53.5980 −1.95843
\(750\) −1.20711 + 2.09077i −0.0440773 + 0.0763441i
\(751\) −1.84315 + 3.19242i −0.0672573 + 0.116493i −0.897693 0.440621i \(-0.854758\pi\)
0.830436 + 0.557114i \(0.188092\pi\)
\(752\) −26.4853 −0.965819
\(753\) 27.6569 1.00787
\(754\) 7.65685 13.2621i 0.278846 0.482976i
\(755\) 10.8284 + 18.7554i 0.394087 + 0.682578i
\(756\) −7.32843 + 12.6932i −0.266532 + 0.461648i
\(757\) 2.42893 + 4.20703i 0.0882810 + 0.152907i 0.906785 0.421594i \(-0.138529\pi\)
−0.818504 + 0.574501i \(0.805196\pi\)
\(758\) −29.3492 50.8344i −1.06601 1.84639i
\(759\) −13.6569 −0.495712
\(760\) 2.20711 + 19.1141i 0.0800602 + 0.693341i
\(761\) −27.5980 −1.00043 −0.500213 0.865902i \(-0.666745\pi\)
−0.500213 + 0.865902i \(0.666745\pi\)
\(762\) −25.3137 43.8446i −0.917019 1.58832i
\(763\) 10.1716 + 17.6177i 0.368236 + 0.637803i
\(764\) 21.3848 37.0395i 0.773674 1.34004i
\(765\) −3.41421 5.91359i −0.123441 0.213806i
\(766\) −40.9706 + 70.9631i −1.48033 + 2.56400i
\(767\) 0 0
\(768\) 29.9706 1.08147
\(769\) 4.15685 7.19988i 0.149900 0.259634i −0.781290 0.624168i \(-0.785438\pi\)
0.931190 + 0.364533i \(0.118771\pi\)
\(770\) −13.0711 + 22.6398i −0.471049 + 0.815880i
\(771\) 11.1716 0.402334