Properties

Label 175.2.x.a.47.18
Level $175$
Weight $2$
Character 175.47
Analytic conductor $1.397$
Analytic rank $0$
Dimension $288$
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] = [175,2,Mod(3,175)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(175, base_ring=CyclotomicField(60))
 
chi = DirichletCharacter(H, H._module([21, 10]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("175.3");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 175 = 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 175.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: \(1.39738203537\)
Analytic rank: \(0\)
Dimension: \(288\)
Relative dimension: \(18\) over \(\Q(\zeta_{60})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label 47.18
Character \(\chi\) \(=\) 175.47
Dual form 175.2.x.a.108.18

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.127170 - 2.42654i) q^{2} +(-1.78675 + 1.44688i) q^{3} +(-3.88289 - 0.408108i) q^{4} +(-2.07076 + 0.843763i) q^{5} +(3.28370 + 4.51962i) q^{6} +(1.54352 + 2.14884i) q^{7} +(-0.723845 + 4.57018i) q^{8} +(0.475273 - 2.23598i) q^{9} +O(q^{10})\) \(q+(0.127170 - 2.42654i) q^{2} +(-1.78675 + 1.44688i) q^{3} +(-3.88289 - 0.408108i) q^{4} +(-2.07076 + 0.843763i) q^{5} +(3.28370 + 4.51962i) q^{6} +(1.54352 + 2.14884i) q^{7} +(-0.723845 + 4.57018i) q^{8} +(0.475273 - 2.23598i) q^{9} +(1.78409 + 5.13210i) q^{10} +(-0.0163732 + 0.00348022i) q^{11} +(7.52823 - 4.88889i) q^{12} +(-1.39124 + 2.73047i) q^{13} +(5.41055 - 3.47216i) q^{14} +(2.47911 - 4.50374i) q^{15} +(3.35976 + 0.714139i) q^{16} +(-6.59423 + 2.53129i) q^{17} +(-5.36527 - 1.43762i) q^{18} +(0.331948 + 3.15828i) q^{19} +(8.38489 - 2.43114i) q^{20} +(-5.86701 - 1.60615i) q^{21} +(0.00636273 + 0.0401727i) q^{22} +(-5.46923 - 0.286630i) q^{23} +(-5.31918 - 9.21308i) q^{24} +(3.57613 - 3.49447i) q^{25} +(6.44868 + 3.72315i) q^{26} +(-0.745322 - 1.46278i) q^{27} +(-5.11637 - 8.97365i) q^{28} +(-0.0353871 + 0.0487062i) q^{29} +(-10.6132 - 6.58841i) q^{30} +(3.66733 - 8.23697i) q^{31} +(-0.235039 + 0.877177i) q^{32} +(0.0242193 - 0.0299083i) q^{33} +(5.30369 + 16.3231i) q^{34} +(-5.00939 - 3.14738i) q^{35} +(-2.75796 + 8.48811i) q^{36} +(4.57608 + 7.04654i) q^{37} +(7.70591 - 0.403850i) q^{38} +(-1.46486 - 6.89163i) q^{39} +(-2.35724 - 10.0745i) q^{40} +(5.83738 - 1.89668i) q^{41} +(-4.64350 + 14.0323i) q^{42} +(-3.18681 + 3.18681i) q^{43} +(0.0649954 - 0.00683130i) q^{44} +(0.902462 + 5.03121i) q^{45} +(-1.39104 + 13.2349i) q^{46} +(1.64959 - 4.29732i) q^{47} +(-7.03633 + 3.58519i) q^{48} +(-2.23507 + 6.63359i) q^{49} +(-8.02470 - 9.12201i) q^{50} +(8.11977 - 14.0639i) q^{51} +(6.51638 - 10.0343i) q^{52} +(2.73861 + 3.38191i) q^{53} +(-3.64427 + 1.62253i) q^{54} +(0.0309685 - 0.0210218i) q^{55} +(-10.9379 + 5.49875i) q^{56} +(-5.16276 - 5.16276i) q^{57} +(0.113687 + 0.0920622i) q^{58} +(1.67651 - 1.86195i) q^{59} +(-11.4641 + 16.4758i) q^{60} +(-9.91649 + 8.92884i) q^{61} +(-19.5210 - 9.94643i) q^{62} +(5.53838 - 2.43001i) q^{63} +(8.63203 + 2.80472i) q^{64} +(0.577069 - 6.82804i) q^{65} +(-0.0694938 - 0.0625725i) q^{66} +(0.113980 + 0.296929i) q^{67} +(26.6377 - 7.13755i) q^{68} +(10.1869 - 7.40119i) q^{69} +(-8.27429 + 11.7552i) q^{70} +(-6.35569 - 4.61768i) q^{71} +(9.87482 + 3.79059i) q^{72} +(-2.80391 - 1.82088i) q^{73} +(17.6807 - 10.2079i) q^{74} +(-1.33356 + 11.4180i) q^{75} -12.3987i q^{76} +(-0.0327508 - 0.0298116i) q^{77} +(-16.9091 + 2.67814i) q^{78} +(2.17913 + 4.89441i) q^{79} +(-7.55984 + 1.35603i) q^{80} +(9.71309 + 4.32455i) q^{81} +(-3.86003 - 14.4058i) q^{82} +(8.63403 + 1.36750i) q^{83} +(22.1255 + 8.63088i) q^{84} +(11.5193 - 10.8057i) q^{85} +(7.32766 + 8.13819i) q^{86} +(-0.00724415 - 0.138227i) q^{87} +(-0.00405361 - 0.0773474i) q^{88} +(5.60082 + 6.22034i) q^{89} +(12.3232 - 1.55004i) q^{90} +(-8.01478 + 1.22498i) q^{91} +(21.1194 + 3.34499i) q^{92} +(5.36531 + 20.0236i) q^{93} +(-10.2178 - 4.54928i) q^{94} +(-3.35223 - 6.25996i) q^{95} +(-0.849216 - 1.90737i) q^{96} +(6.79613 - 1.07640i) q^{97} +(15.8124 + 6.26707i) q^{98} +0.0382642i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22} - 40 q^{23} + 2 q^{25} - 48 q^{26} + 22 q^{28} - 58 q^{30} - 18 q^{31} + 8 q^{32} - 30 q^{33} - 2 q^{35} + 40 q^{36} - 10 q^{37} + 72 q^{38} + 30 q^{39} - 48 q^{40} + 6 q^{42} - 108 q^{43} - 10 q^{44} + 186 q^{45} - 6 q^{46} - 54 q^{47} - 248 q^{50} - 16 q^{51} + 216 q^{52} + 50 q^{53} - 30 q^{54} + 4 q^{56} - 216 q^{57} - 4 q^{58} + 90 q^{59} + 96 q^{60} - 18 q^{61} - 66 q^{63} - 100 q^{64} + 14 q^{65} - 90 q^{66} + 4 q^{67} + 342 q^{68} - 60 q^{70} - 24 q^{71} + 58 q^{72} - 6 q^{73} + 216 q^{75} - 80 q^{77} - 132 q^{78} - 10 q^{79} - 6 q^{80} - 10 q^{81} + 216 q^{82} + 20 q^{84} - 48 q^{85} - 6 q^{86} - 48 q^{87} - 122 q^{88} + 120 q^{89} - 12 q^{91} - 4 q^{92} + 106 q^{93} - 30 q^{94} - 98 q^{95} - 90 q^{96} + 222 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/175\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{17}{20}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.127170 2.42654i 0.0899225 1.71582i −0.466163 0.884699i \(-0.654364\pi\)
0.556085 0.831125i \(-0.312303\pi\)
\(3\) −1.78675 + 1.44688i −1.03158 + 0.835357i −0.986522 0.163627i \(-0.947681\pi\)
−0.0450579 + 0.998984i \(0.514347\pi\)
\(4\) −3.88289 0.408108i −1.94144 0.204054i
\(5\) −2.07076 + 0.843763i −0.926074 + 0.377342i
\(6\) 3.28370 + 4.51962i 1.34056 + 1.84513i
\(7\) 1.54352 + 2.14884i 0.583397 + 0.812187i
\(8\) −0.723845 + 4.57018i −0.255918 + 1.61580i
\(9\) 0.475273 2.23598i 0.158424 0.745328i
\(10\) 1.78409 + 5.13210i 0.564178 + 1.62291i
\(11\) −0.0163732 + 0.00348022i −0.00493669 + 0.00104933i −0.210379 0.977620i \(-0.567470\pi\)
0.205443 + 0.978669i \(0.434137\pi\)
\(12\) 7.52823 4.88889i 2.17321 1.41130i
\(13\) −1.39124 + 2.73047i −0.385862 + 0.757297i −0.999478 0.0323079i \(-0.989714\pi\)
0.613616 + 0.789605i \(0.289714\pi\)
\(14\) 5.41055 3.47216i 1.44603 0.927973i
\(15\) 2.47911 4.50374i 0.640104 1.16286i
\(16\) 3.35976 + 0.714139i 0.839940 + 0.178535i
\(17\) −6.59423 + 2.53129i −1.59934 + 0.613928i −0.984603 0.174807i \(-0.944070\pi\)
−0.614734 + 0.788735i \(0.710737\pi\)
\(18\) −5.36527 1.43762i −1.26461 0.338850i
\(19\) 0.331948 + 3.15828i 0.0761542 + 0.724559i 0.964267 + 0.264933i \(0.0853498\pi\)
−0.888113 + 0.459626i \(0.847984\pi\)
\(20\) 8.38489 2.43114i 1.87492 0.543620i
\(21\) −5.86701 1.60615i −1.28029 0.350491i
\(22\) 0.00636273 + 0.0401727i 0.00135654 + 0.00856485i
\(23\) −5.46923 0.286630i −1.14041 0.0597665i −0.527241 0.849716i \(-0.676774\pi\)
−0.613172 + 0.789949i \(0.710107\pi\)
\(24\) −5.31918 9.21308i −1.08577 1.88061i
\(25\) 3.57613 3.49447i 0.715226 0.698894i
\(26\) 6.44868 + 3.72315i 1.26469 + 0.730169i
\(27\) −0.745322 1.46278i −0.143437 0.281512i
\(28\) −5.11637 8.97365i −0.966903 1.69586i
\(29\) −0.0353871 + 0.0487062i −0.00657122 + 0.00904451i −0.812290 0.583254i \(-0.801779\pi\)
0.805719 + 0.592298i \(0.201779\pi\)
\(30\) −10.6132 6.58841i −1.93771 1.20287i
\(31\) 3.66733 8.23697i 0.658673 1.47940i −0.206767 0.978390i \(-0.566294\pi\)
0.865440 0.501013i \(-0.167039\pi\)
\(32\) −0.235039 + 0.877177i −0.0415494 + 0.155065i
\(33\) 0.0242193 0.0299083i 0.00421603 0.00520637i
\(34\) 5.30369 + 16.3231i 0.909576 + 2.79939i
\(35\) −5.00939 3.14738i −0.846741 0.532005i
\(36\) −2.75796 + 8.48811i −0.459659 + 1.41469i
\(37\) 4.57608 + 7.04654i 0.752302 + 1.15844i 0.982674 + 0.185341i \(0.0593390\pi\)
−0.230372 + 0.973103i \(0.573994\pi\)
\(38\) 7.70591 0.403850i 1.25006 0.0655130i
\(39\) −1.46486 6.89163i −0.234566 1.10354i
\(40\) −2.35724 10.0745i −0.372712 1.59292i
\(41\) 5.83738 1.89668i 0.911646 0.296212i 0.184610 0.982812i \(-0.440898\pi\)
0.727035 + 0.686600i \(0.240898\pi\)
\(42\) −4.64350 + 14.0323i −0.716507 + 2.16523i
\(43\) −3.18681 + 3.18681i −0.485984 + 0.485984i −0.907036 0.421052i \(-0.861661\pi\)
0.421052 + 0.907036i \(0.361661\pi\)
\(44\) 0.0649954 0.00683130i 0.00979843 0.00102986i
\(45\) 0.902462 + 5.03121i 0.134531 + 0.750009i
\(46\) −1.39104 + 13.2349i −0.205098 + 1.95137i
\(47\) 1.64959 4.29732i 0.240617 0.626828i −0.759091 0.650984i \(-0.774356\pi\)
0.999708 + 0.0241558i \(0.00768978\pi\)
\(48\) −7.03633 + 3.58519i −1.01561 + 0.517477i
\(49\) −2.23507 + 6.63359i −0.319295 + 0.947655i
\(50\) −8.02470 9.12201i −1.13486 1.29005i
\(51\) 8.11977 14.0639i 1.13700 1.96933i
\(52\) 6.51638 10.0343i 0.903659 1.39151i
\(53\) 2.73861 + 3.38191i 0.376178 + 0.464541i 0.929713 0.368285i \(-0.120055\pi\)
−0.553535 + 0.832826i \(0.686722\pi\)
\(54\) −3.64427 + 1.62253i −0.495923 + 0.220799i
\(55\) 0.0309685 0.0210218i 0.00417579 0.00283458i
\(56\) −10.9379 + 5.49875i −1.46164 + 0.734802i
\(57\) −5.16276 5.16276i −0.683825 0.683825i
\(58\) 0.113687 + 0.0920622i 0.0149279 + 0.0120884i
\(59\) 1.67651 1.86195i 0.218263 0.242406i −0.624063 0.781374i \(-0.714519\pi\)
0.842326 + 0.538968i \(0.181186\pi\)
\(60\) −11.4641 + 16.4758i −1.48001 + 2.12701i
\(61\) −9.91649 + 8.92884i −1.26968 + 1.14322i −0.286992 + 0.957933i \(0.592655\pi\)
−0.982684 + 0.185288i \(0.940678\pi\)
\(62\) −19.5210 9.94643i −2.47917 1.26320i
\(63\) 5.53838 2.43001i 0.697770 0.306152i
\(64\) 8.63203 + 2.80472i 1.07900 + 0.350590i
\(65\) 0.577069 6.82804i 0.0715766 0.846915i
\(66\) −0.0694938 0.0625725i −0.00855409 0.00770214i
\(67\) 0.113980 + 0.296929i 0.0139249 + 0.0362757i 0.940367 0.340162i \(-0.110482\pi\)
−0.926442 + 0.376438i \(0.877149\pi\)
\(68\) 26.6377 7.13755i 3.23030 0.865556i
\(69\) 10.1869 7.40119i 1.22635 0.890999i
\(70\) −8.27429 + 11.7552i −0.988967 + 1.40502i
\(71\) −6.35569 4.61768i −0.754282 0.548018i 0.142869 0.989742i \(-0.454367\pi\)
−0.897151 + 0.441724i \(0.854367\pi\)
\(72\) 9.87482 + 3.79059i 1.16376 + 0.446725i
\(73\) −2.80391 1.82088i −0.328173 0.213118i 0.370027 0.929021i \(-0.379349\pi\)
−0.698200 + 0.715903i \(0.746015\pi\)
\(74\) 17.6807 10.2079i 2.05533 1.18665i
\(75\) −1.33356 + 11.4180i −0.153987 + 1.31843i
\(76\) 12.3987i 1.42223i
\(77\) −0.0327508 0.0298116i −0.00373230 0.00339734i
\(78\) −16.9091 + 2.67814i −1.91458 + 0.303240i
\(79\) 2.17913 + 4.89441i 0.245171 + 0.550664i 0.993653 0.112492i \(-0.0358833\pi\)
−0.748481 + 0.663156i \(0.769217\pi\)
\(80\) −7.55984 + 1.35603i −0.845216 + 0.151609i
\(81\) 9.71309 + 4.32455i 1.07923 + 0.480505i
\(82\) −3.86003 14.4058i −0.426270 1.59086i
\(83\) 8.63403 + 1.36750i 0.947708 + 0.150102i 0.611110 0.791546i \(-0.290723\pi\)
0.336599 + 0.941648i \(0.390723\pi\)
\(84\) 22.1255 + 8.63088i 2.41409 + 0.941706i
\(85\) 11.5193 10.8057i 1.24944 1.17204i
\(86\) 7.32766 + 8.13819i 0.790162 + 0.877564i
\(87\) −0.00724415 0.138227i −0.000776654 0.0148194i
\(88\) −0.00405361 0.0773474i −0.000432116 0.00824526i
\(89\) 5.60082 + 6.22034i 0.593686 + 0.659355i 0.962859 0.270006i \(-0.0870257\pi\)
−0.369173 + 0.929361i \(0.620359\pi\)
\(90\) 12.3232 1.55004i 1.29898 0.163389i
\(91\) −8.01478 + 1.22498i −0.840177 + 0.128413i
\(92\) 21.1194 + 3.34499i 2.20185 + 0.348739i
\(93\) 5.36531 + 20.0236i 0.556356 + 2.07635i
\(94\) −10.2178 4.54928i −1.05389 0.469222i
\(95\) −3.35223 6.25996i −0.343931 0.642259i
\(96\) −0.849216 1.90737i −0.0866727 0.194670i
\(97\) 6.79613 1.07640i 0.690043 0.109292i 0.198442 0.980113i \(-0.436412\pi\)
0.491601 + 0.870821i \(0.336412\pi\)
\(98\) 15.8124 + 6.26707i 1.59730 + 0.633070i
\(99\) 0.0382642i 0.00384569i
\(100\) −15.3118 + 12.1092i −1.53118 + 1.21092i
\(101\) −9.18326 + 5.30196i −0.913768 + 0.527564i −0.881642 0.471919i \(-0.843561\pi\)
−0.0321267 + 0.999484i \(0.510228\pi\)
\(102\) −33.0939 21.4915i −3.27679 2.12797i
\(103\) 0.204272 + 0.0784125i 0.0201275 + 0.00772622i 0.368411 0.929663i \(-0.379902\pi\)
−0.348283 + 0.937389i \(0.613235\pi\)
\(104\) −11.4717 8.33468i −1.12489 0.817282i
\(105\) 13.5044 1.62441i 1.31790 0.158526i
\(106\) 8.55461 6.21528i 0.830897 0.603682i
\(107\) 4.72847 1.26699i 0.457119 0.122485i −0.0229097 0.999738i \(-0.507293\pi\)
0.480028 + 0.877253i \(0.340626\pi\)
\(108\) 2.29703 + 5.98397i 0.221032 + 0.575808i
\(109\) −5.73459 5.16345i −0.549274 0.494569i 0.347123 0.937819i \(-0.387158\pi\)
−0.896398 + 0.443251i \(0.853825\pi\)
\(110\) −0.0470720 0.0778196i −0.00448814 0.00741981i
\(111\) −18.3718 5.96936i −1.74377 0.566587i
\(112\) 3.65130 + 8.32190i 0.345015 + 0.786345i
\(113\) −3.56746 1.81771i −0.335599 0.170996i 0.278068 0.960561i \(-0.410306\pi\)
−0.613666 + 0.789565i \(0.710306\pi\)
\(114\) −13.1842 + 11.8711i −1.23481 + 1.11183i
\(115\) 11.5673 4.02119i 1.07866 0.374978i
\(116\) 0.157282 0.174679i 0.0146032 0.0162185i
\(117\) 5.44407 + 4.40852i 0.503304 + 0.407568i
\(118\) −4.30491 4.30491i −0.396299 0.396299i
\(119\) −15.6177 10.2629i −1.43167 0.940796i
\(120\) 18.7884 + 14.5900i 1.71514 + 1.33188i
\(121\) −10.0487 + 4.47399i −0.913522 + 0.406726i
\(122\) 20.4051 + 25.1982i 1.84739 + 2.28134i
\(123\) −7.68566 + 11.8349i −0.692993 + 1.06712i
\(124\) −17.6014 + 30.4866i −1.58065 + 2.73777i
\(125\) −4.45681 + 10.2536i −0.398630 + 0.917112i
\(126\) −5.19220 13.7481i −0.462558 1.22478i
\(127\) 6.49211 3.30790i 0.576082 0.293528i −0.141572 0.989928i \(-0.545216\pi\)
0.717654 + 0.696399i \(0.245216\pi\)
\(128\) 7.25261 18.8937i 0.641047 1.66998i
\(129\) 1.08310 10.3050i 0.0953612 0.907301i
\(130\) −16.4951 2.26860i −1.44672 0.198970i
\(131\) −11.7655 + 1.23661i −1.02796 + 0.108043i −0.603466 0.797389i \(-0.706214\pi\)
−0.424493 + 0.905431i \(0.639548\pi\)
\(132\) −0.106246 + 0.106246i −0.00924757 + 0.00924757i
\(133\) −6.27428 + 5.58819i −0.544049 + 0.484557i
\(134\) 0.735006 0.238818i 0.0634949 0.0206307i
\(135\) 2.77762 + 2.40019i 0.239060 + 0.206576i
\(136\) −6.79524 31.9691i −0.582687 2.74133i
\(137\) 3.28970 0.172406i 0.281058 0.0147296i 0.0887140 0.996057i \(-0.471724\pi\)
0.192344 + 0.981327i \(0.438391\pi\)
\(138\) −16.6638 25.6601i −1.41852 2.18433i
\(139\) −1.40509 + 4.32443i −0.119179 + 0.366794i −0.992796 0.119820i \(-0.961768\pi\)
0.873617 + 0.486614i \(0.161768\pi\)
\(140\) 18.1664 + 14.2653i 1.53534 + 1.20564i
\(141\) 3.27031 + 10.0650i 0.275410 + 0.847625i
\(142\) −12.0133 + 14.8351i −1.00813 + 1.24494i
\(143\) 0.0132764 0.0495483i 0.00111023 0.00414344i
\(144\) 3.19361 7.17296i 0.266134 0.597747i
\(145\) 0.0321819 0.130717i 0.00267256 0.0108555i
\(146\) −4.77502 + 6.57225i −0.395183 + 0.543923i
\(147\) −5.60451 15.0864i −0.462252 1.24431i
\(148\) −14.8926 29.2285i −1.22417 2.40256i
\(149\) 15.7486 + 9.09246i 1.29018 + 0.744884i 0.978685 0.205366i \(-0.0658384\pi\)
0.311491 + 0.950249i \(0.399172\pi\)
\(150\) 27.5366 + 4.68797i 2.24835 + 0.382771i
\(151\) 9.44990 + 16.3677i 0.769022 + 1.33198i 0.938094 + 0.346381i \(0.112590\pi\)
−0.169072 + 0.985604i \(0.554077\pi\)
\(152\) −14.6742 0.769041i −1.19023 0.0623775i
\(153\) 2.52586 + 15.9477i 0.204204 + 1.28929i
\(154\) −0.0765039 + 0.0756801i −0.00616486 + 0.00609848i
\(155\) −0.644136 + 20.1512i −0.0517382 + 1.61858i
\(156\) 2.87536 + 27.3573i 0.230213 + 2.19033i
\(157\) −15.7038 4.20781i −1.25330 0.335820i −0.429688 0.902978i \(-0.641376\pi\)
−0.823609 + 0.567158i \(0.808043\pi\)
\(158\) 12.1536 4.66533i 0.966889 0.371154i
\(159\) −9.78643 2.08017i −0.776115 0.164968i
\(160\) −0.253420 2.01474i −0.0200346 0.159280i
\(161\) −7.82597 12.1950i −0.616773 0.961097i
\(162\) 11.7289 23.0193i 0.921510 1.80856i
\(163\) 7.85580 5.10162i 0.615314 0.399590i −0.199012 0.979997i \(-0.563773\pi\)
0.814326 + 0.580407i \(0.197107\pi\)
\(164\) −23.4399 + 4.98231i −1.83035 + 0.389053i
\(165\) −0.0249169 + 0.0823683i −0.00193978 + 0.00641237i
\(166\) 4.41627 20.7769i 0.342769 1.61260i
\(167\) 1.18224 7.46435i 0.0914842 0.577608i −0.898779 0.438402i \(-0.855545\pi\)
0.990263 0.139207i \(-0.0444553\pi\)
\(168\) 11.5872 25.6507i 0.893972 1.97899i
\(169\) 2.12129 + 2.91971i 0.163177 + 0.224593i
\(170\) −24.7555 29.3262i −1.89866 2.24922i
\(171\) 7.21963 + 0.758813i 0.552099 + 0.0580279i
\(172\) 13.6746 11.0735i 1.04268 0.844343i
\(173\) −1.22482 + 23.3710i −0.0931217 + 1.77687i 0.409451 + 0.912332i \(0.365720\pi\)
−0.502572 + 0.864535i \(0.667613\pi\)
\(174\) −0.336334 −0.0254974
\(175\) 13.0289 + 2.29075i 0.984893 + 0.173164i
\(176\) −0.0574953 −0.00433387
\(177\) −0.301479 + 5.75255i −0.0226605 + 0.432388i
\(178\) 15.8062 12.7996i 1.18472 0.959369i
\(179\) −13.5506 1.42423i −1.01282 0.106452i −0.416449 0.909159i \(-0.636726\pi\)
−0.596373 + 0.802707i \(0.703392\pi\)
\(180\) −1.45088 19.9039i −0.108142 1.48355i
\(181\) 3.38018 + 4.65241i 0.251247 + 0.345811i 0.915947 0.401298i \(-0.131441\pi\)
−0.664701 + 0.747110i \(0.731441\pi\)
\(182\) 1.95323 + 19.6040i 0.144783 + 1.45314i
\(183\) 4.79930 30.3016i 0.354774 2.23996i
\(184\) 5.26883 24.7879i 0.388423 1.82739i
\(185\) −15.4216 10.7306i −1.13382 0.788929i
\(186\) 49.2704 10.4727i 3.61268 0.767899i
\(187\) 0.0991590 0.0643946i 0.00725122 0.00470900i
\(188\) −8.15893 + 16.0128i −0.595051 + 1.16785i
\(189\) 1.99286 3.85941i 0.144959 0.280731i
\(190\) −15.6164 + 7.33824i −1.13293 + 0.532372i
\(191\) 14.4947 + 3.08094i 1.04880 + 0.222929i 0.699907 0.714234i \(-0.253225\pi\)
0.348892 + 0.937163i \(0.386558\pi\)
\(192\) −19.4814 + 7.47820i −1.40595 + 0.539693i
\(193\) −16.0726 4.30663i −1.15693 0.309998i −0.371191 0.928557i \(-0.621050\pi\)
−0.785739 + 0.618558i \(0.787717\pi\)
\(194\) −1.74767 16.6280i −0.125475 1.19382i
\(195\) 8.84829 + 13.0350i 0.633639 + 0.933452i
\(196\) 11.3857 24.8453i 0.813266 1.77467i
\(197\) 2.43376 + 15.3662i 0.173398 + 1.09479i 0.908821 + 0.417185i \(0.136983\pi\)
−0.735423 + 0.677608i \(0.763017\pi\)
\(198\) 0.0928496 + 0.00486604i 0.00659854 + 0.000345815i
\(199\) 0.988951 + 1.71291i 0.0701049 + 0.121425i 0.898947 0.438057i \(-0.144333\pi\)
−0.828842 + 0.559482i \(0.811000\pi\)
\(200\) 13.3818 + 18.8730i 0.946235 + 1.33452i
\(201\) −0.633276 0.365622i −0.0446678 0.0257890i
\(202\) 11.6976 + 22.9578i 0.823039 + 1.61531i
\(203\) −0.159283 0.000862231i −0.0111795 6.05168e-5i
\(204\) −37.2677 + 51.2946i −2.60926 + 3.59134i
\(205\) −10.4875 + 8.85294i −0.732478 + 0.618316i
\(206\) 0.216248 0.485702i 0.0150667 0.0338405i
\(207\) −3.24028 + 12.0929i −0.225215 + 0.840514i
\(208\) −6.62419 + 8.18019i −0.459305 + 0.567194i
\(209\) −0.0164266 0.0505557i −0.00113625 0.00349701i
\(210\) −2.22435 32.9756i −0.153494 2.27553i
\(211\) 2.82445 8.69276i 0.194443 0.598434i −0.805540 0.592542i \(-0.798124\pi\)
0.999983 0.00589215i \(-0.00187554\pi\)
\(212\) −9.25355 14.2492i −0.635536 0.978640i
\(213\) 18.0373 0.945293i 1.23589 0.0647704i
\(214\) −2.47309 11.6350i −0.169057 0.795349i
\(215\) 3.91022 9.28804i 0.266675 0.633439i
\(216\) 7.22465 2.34743i 0.491575 0.159722i
\(217\) 23.3606 4.83343i 1.58582 0.328115i
\(218\) −13.2586 + 13.2586i −0.897985 + 0.897985i
\(219\) 7.64448 0.803468i 0.516566 0.0542933i
\(220\) −0.128826 + 0.0689868i −0.00868546 + 0.00465109i
\(221\) 2.26258 21.5270i 0.152198 1.44806i
\(222\) −16.8212 + 43.8208i −1.12897 + 2.94106i
\(223\) 6.62726 3.37676i 0.443794 0.226124i −0.217789 0.975996i \(-0.569885\pi\)
0.661584 + 0.749871i \(0.269885\pi\)
\(224\) −2.24771 + 0.848882i −0.150181 + 0.0567183i
\(225\) −6.11394 9.65699i −0.407596 0.643800i
\(226\) −4.86443 + 8.42544i −0.323577 + 0.560452i
\(227\) −6.38180 + 9.82711i −0.423575 + 0.652249i −0.984453 0.175650i \(-0.943797\pi\)
0.560877 + 0.827899i \(0.310464\pi\)
\(228\) 17.9395 + 22.1534i 1.18807 + 1.46714i
\(229\) 24.6116 10.9578i 1.62638 0.724110i 0.627849 0.778335i \(-0.283936\pi\)
0.998529 + 0.0542256i \(0.0172690\pi\)
\(230\) −8.28657 28.5800i −0.546401 1.88451i
\(231\) 0.101651 + 0.00587925i 0.00668816 + 0.000386826i
\(232\) −0.196981 0.196981i −0.0129324 0.0129324i
\(233\) −16.9779 13.7484i −1.11226 0.900689i −0.116546 0.993185i \(-0.537182\pi\)
−0.995713 + 0.0924959i \(0.970515\pi\)
\(234\) 11.3898 12.6496i 0.744573 0.826932i
\(235\) 0.210015 + 10.2906i 0.0136998 + 0.671284i
\(236\) −7.26958 + 6.54556i −0.473209 + 0.426080i
\(237\) −10.9752 5.59214i −0.712915 0.363248i
\(238\) −26.8894 + 36.5919i −1.74298 + 2.37190i
\(239\) −4.05851 1.31869i −0.262523 0.0852989i 0.174798 0.984604i \(-0.444073\pi\)
−0.437321 + 0.899305i \(0.644073\pi\)
\(240\) 11.5455 13.3611i 0.745260 0.862453i
\(241\) −0.122038 0.109884i −0.00786117 0.00707823i 0.665191 0.746674i \(-0.268350\pi\)
−0.673052 + 0.739595i \(0.735017\pi\)
\(242\) 9.57843 + 24.9527i 0.615725 + 1.60402i
\(243\) −18.8546 + 5.05209i −1.20953 + 0.324092i
\(244\) 42.1485 30.6227i 2.69828 1.96042i
\(245\) −0.968881 15.6225i −0.0618996 0.998082i
\(246\) 27.7405 + 20.1546i 1.76867 + 1.28501i
\(247\) −9.08541 3.48756i −0.578091 0.221908i
\(248\) 34.9898 + 22.7227i 2.22186 + 1.44289i
\(249\) −17.4055 + 10.0490i −1.10303 + 0.636832i
\(250\) 24.3141 + 12.1186i 1.53776 + 0.766447i
\(251\) 0.132304i 0.00835098i 0.999991 + 0.00417549i \(0.00132910\pi\)
−0.999991 + 0.00417549i \(0.998671\pi\)
\(252\) −22.4966 + 7.17519i −1.41715 + 0.451995i
\(253\) 0.0905461 0.0143411i 0.00569259 0.000901617i
\(254\) −7.20115 16.1741i −0.451840 1.01485i
\(255\) −4.94757 + 35.9741i −0.309829 + 2.25278i
\(256\) −28.3409 12.6182i −1.77131 0.788637i
\(257\) −2.37849 8.87663i −0.148366 0.553709i −0.999582 0.0288944i \(-0.990801\pi\)
0.851217 0.524815i \(-0.175865\pi\)
\(258\) −24.8677 3.93865i −1.54819 0.245210i
\(259\) −8.07863 + 20.7098i −0.501982 + 1.28684i
\(260\) −5.02727 + 26.2770i −0.311778 + 1.62963i
\(261\) 0.0920877 + 0.102274i 0.00570008 + 0.00633058i
\(262\) 1.50446 + 28.7068i 0.0929458 + 1.77351i
\(263\) 1.09475 + 20.8891i 0.0675052 + 1.28808i 0.796954 + 0.604040i \(0.206443\pi\)
−0.729449 + 0.684036i \(0.760223\pi\)
\(264\) 0.119155 + 0.132335i 0.00733350 + 0.00814468i
\(265\) −8.52455 4.69239i −0.523659 0.288251i
\(266\) 12.7621 + 15.9354i 0.782492 + 0.977065i
\(267\) −19.0074 3.01047i −1.16323 0.184238i
\(268\) −0.321394 1.19946i −0.0196323 0.0732687i
\(269\) 1.38180 + 0.615216i 0.0842497 + 0.0375104i 0.448429 0.893819i \(-0.351984\pi\)
−0.364179 + 0.931329i \(0.618650\pi\)
\(270\) 6.17739 6.43479i 0.375944 0.391609i
\(271\) 3.69590 + 8.30112i 0.224510 + 0.504257i 0.990319 0.138811i \(-0.0443279\pi\)
−0.765809 + 0.643068i \(0.777661\pi\)
\(272\) −23.9627 + 3.79533i −1.45295 + 0.230125i
\(273\) 12.5480 13.7852i 0.759439 0.834316i
\(274\) 8.00453i 0.483571i
\(275\) −0.0463910 + 0.0696612i −0.00279748 + 0.00420073i
\(276\) −42.5749 + 24.5807i −2.56271 + 1.47958i
\(277\) −11.4597 7.44201i −0.688546 0.447147i 0.152362 0.988325i \(-0.451312\pi\)
−0.840908 + 0.541177i \(0.817979\pi\)
\(278\) 10.3147 + 3.95946i 0.618637 + 0.237472i
\(279\) −16.6747 12.1149i −0.998291 0.725301i
\(280\) 18.0101 20.6156i 1.07631 1.23202i
\(281\) −3.22462 + 2.34282i −0.192365 + 0.139761i −0.679799 0.733399i \(-0.737933\pi\)
0.487434 + 0.873160i \(0.337933\pi\)
\(282\) 24.8390 6.65559i 1.47914 0.396334i
\(283\) −6.77206 17.6418i −0.402557 1.04870i −0.973697 0.227845i \(-0.926832\pi\)
0.571140 0.820853i \(-0.306501\pi\)
\(284\) 22.7939 + 20.5238i 1.35257 + 1.21786i
\(285\) 15.0470 + 6.33471i 0.891308 + 0.375236i
\(286\) −0.118543 0.0385168i −0.00700957 0.00227755i
\(287\) 13.0858 + 9.61605i 0.772431 + 0.567618i
\(288\) 1.84965 + 0.942442i 0.108991 + 0.0555339i
\(289\) 24.4430 22.0086i 1.43783 1.29462i
\(290\) −0.313098 0.0947139i −0.0183858 0.00556179i
\(291\) −10.5856 + 11.7565i −0.620536 + 0.689176i
\(292\) 10.1442 + 8.21458i 0.593642 + 0.480722i
\(293\) 4.94524 + 4.94524i 0.288904 + 0.288904i 0.836647 0.547743i \(-0.184513\pi\)
−0.547743 + 0.836647i \(0.684513\pi\)
\(294\) −37.3206 + 11.6810i −2.17658 + 0.681252i
\(295\) −1.90061 + 5.27024i −0.110658 + 0.306845i
\(296\) −35.5163 + 15.8129i −2.06434 + 0.919105i
\(297\) 0.0172941 + 0.0213564i 0.00100350 + 0.00123922i
\(298\) 24.0660 37.0584i 1.39410 2.14673i
\(299\) 8.39168 14.5348i 0.485303 0.840570i
\(300\) 9.83785 43.7905i 0.567988 2.52824i
\(301\) −11.7669 1.92904i −0.678231 0.111188i
\(302\) 40.9187 20.8491i 2.35460 1.19973i
\(303\) 8.73688 22.7604i 0.501921 1.30755i
\(304\) −1.14018 + 10.8481i −0.0653940 + 0.622182i
\(305\) 13.0009 26.8567i 0.744428 1.53781i
\(306\) 39.0189 4.10105i 2.23056 0.234441i
\(307\) 4.76473 4.76473i 0.271938 0.271938i −0.557942 0.829880i \(-0.688409\pi\)
0.829880 + 0.557942i \(0.188409\pi\)
\(308\) 0.115001 + 0.129121i 0.00655282 + 0.00735734i
\(309\) −0.478436 + 0.155453i −0.0272173 + 0.00884342i
\(310\) 48.8158 + 4.12564i 2.77255 + 0.234321i
\(311\) −0.546587 2.57149i −0.0309941 0.145816i 0.959930 0.280241i \(-0.0904145\pi\)
−0.990924 + 0.134425i \(0.957081\pi\)
\(312\) 32.5563 1.70621i 1.84314 0.0965948i
\(313\) −2.36870 3.64748i −0.133887 0.206168i 0.765368 0.643593i \(-0.222557\pi\)
−0.899255 + 0.437425i \(0.855890\pi\)
\(314\) −12.2075 + 37.5707i −0.688908 + 2.12024i
\(315\) −9.41832 + 9.70505i −0.530662 + 0.546818i
\(316\) −6.46387 19.8938i −0.363621 1.11911i
\(317\) 13.0585 16.1259i 0.733440 0.905723i −0.264844 0.964291i \(-0.585320\pi\)
0.998283 + 0.0585688i \(0.0186537\pi\)
\(318\) −6.29216 + 23.4827i −0.352847 + 1.31684i
\(319\) 0.000409890 0 0.000920629i 2.29494e−5 0 5.15453e-5i
\(320\) −20.2414 + 1.47548i −1.13153 + 0.0824819i
\(321\) −6.61541 + 9.10533i −0.369236 + 0.508210i
\(322\) −30.5868 + 17.4392i −1.70453 + 0.971849i
\(323\) −10.1835 19.9862i −0.566623 1.11206i
\(324\) −35.9500 20.7557i −1.99722 1.15310i
\(325\) 4.56628 + 14.6262i 0.253291 + 0.811314i
\(326\) −11.3803 19.7112i −0.630295 1.09170i
\(327\) 17.7172 + 0.928518i 0.979762 + 0.0513471i
\(328\) 4.44281 + 28.0508i 0.245313 + 1.54884i
\(329\) 11.7804 3.08831i 0.649477 0.170264i
\(330\) 0.196702 + 0.0709366i 0.0108281 + 0.00390493i
\(331\) −1.66114 15.8047i −0.0913045 0.868705i −0.940310 0.340320i \(-0.889465\pi\)
0.849005 0.528385i \(-0.177202\pi\)
\(332\) −32.9669 8.83346i −1.80929 0.484799i
\(333\) 17.9308 6.88300i 0.982604 0.377186i
\(334\) −17.9622 3.81798i −0.982848 0.208911i
\(335\) −0.486565 0.518698i −0.0265839 0.0283395i
\(336\) −18.5647 9.58615i −1.01279 0.522967i
\(337\) −11.6113 + 22.7884i −0.632508 + 1.24137i 0.323000 + 0.946399i \(0.395309\pi\)
−0.955507 + 0.294967i \(0.904691\pi\)
\(338\) 7.35457 4.77611i 0.400036 0.259786i
\(339\) 9.00418 1.91390i 0.489040 0.103949i
\(340\) −49.1380 + 37.2561i −2.66488 + 2.02050i
\(341\) −0.0313794 + 0.147628i −0.00169929 + 0.00799452i
\(342\) 2.75941 17.4222i 0.149212 0.942086i
\(343\) −17.7044 + 5.43629i −0.955949 + 0.293532i
\(344\) −12.2575 16.8710i −0.660882 0.909626i
\(345\) −14.8497 + 23.9214i −0.799483 + 1.28789i
\(346\) 56.5550 + 5.94418i 3.04042 + 0.319561i
\(347\) 11.7761 9.53608i 0.632173 0.511923i −0.258829 0.965923i \(-0.583337\pi\)
0.891002 + 0.454000i \(0.150003\pi\)
\(348\) −0.0282832 + 0.539675i −0.00151614 + 0.0289296i
\(349\) 1.48928 0.0797192 0.0398596 0.999205i \(-0.487309\pi\)
0.0398596 + 0.999205i \(0.487309\pi\)
\(350\) 7.21547 31.3239i 0.385683 1.67433i
\(351\) 5.03100 0.268535
\(352\) 0.000795558 0.0151802i 4.24034e−5 0.000809105i
\(353\) −7.30497 + 5.91545i −0.388804 + 0.314847i −0.803715 0.595015i \(-0.797146\pi\)
0.414911 + 0.909862i \(0.363813\pi\)
\(354\) 13.9205 + 1.46310i 0.739865 + 0.0777629i
\(355\) 17.0574 + 4.19943i 0.905311 + 0.222883i
\(356\) −19.2088 26.4386i −1.01806 1.40124i
\(357\) 42.7541 4.25978i 2.26279 0.225451i
\(358\) −5.17918 + 32.7001i −0.273728 + 1.72825i
\(359\) −1.27728 + 6.00914i −0.0674124 + 0.317150i −0.998914 0.0465862i \(-0.985166\pi\)
0.931502 + 0.363736i \(0.118499\pi\)
\(360\) −23.6468 + 0.482594i −1.24630 + 0.0254349i
\(361\) 8.72027 1.85355i 0.458962 0.0975553i
\(362\) 11.7191 7.61049i 0.615944 0.399999i
\(363\) 11.4813 22.5332i 0.602610 1.18269i
\(364\) 31.6204 1.48557i 1.65736 0.0778648i
\(365\) 7.34263 + 1.40478i 0.384331 + 0.0735295i
\(366\) −72.9177 15.4991i −3.81147 0.810153i
\(367\) 33.6866 12.9311i 1.75843 0.674997i 0.758705 0.651434i \(-0.225832\pi\)
0.999722 0.0235632i \(-0.00750108\pi\)
\(368\) −18.1706 4.86880i −0.947209 0.253804i
\(369\) −1.46660 13.9537i −0.0763479 0.726402i
\(370\) −27.9994 + 36.0565i −1.45562 + 1.87449i
\(371\) −3.04007 + 11.1049i −0.157833 + 0.576538i
\(372\) −12.6611 79.9390i −0.656447 4.14464i
\(373\) −18.5645 0.972924i −0.961233 0.0503761i −0.434741 0.900556i \(-0.643160\pi\)
−0.526493 + 0.850180i \(0.676493\pi\)
\(374\) −0.143646 0.248802i −0.00742777 0.0128653i
\(375\) −6.87256 24.7691i −0.354898 1.27907i
\(376\) 18.4455 + 10.6495i 0.951252 + 0.549206i
\(377\) −0.0837587 0.164386i −0.00431379 0.00846629i
\(378\) −9.11160 5.32655i −0.468650 0.273968i
\(379\) −13.0838 + 18.0083i −0.672068 + 0.925022i −0.999805 0.0197466i \(-0.993714\pi\)
0.327737 + 0.944769i \(0.393714\pi\)
\(380\) 10.4616 + 25.6748i 0.536667 + 1.31709i
\(381\) −6.81365 + 15.3037i −0.349074 + 0.784032i
\(382\) 9.31932 34.7802i 0.476818 1.77951i
\(383\) −9.68844 + 11.9642i −0.495056 + 0.611344i −0.962035 0.272925i \(-0.912009\pi\)
0.466979 + 0.884268i \(0.345342\pi\)
\(384\) 14.3783 + 44.2520i 0.733742 + 2.25822i
\(385\) 0.0929731 + 0.0340988i 0.00473835 + 0.00173783i
\(386\) −12.4942 + 38.4531i −0.635937 + 1.95721i
\(387\) 5.61105 + 8.64026i 0.285226 + 0.439209i
\(388\) −26.8279 + 1.40599i −1.36198 + 0.0713784i
\(389\) 2.47851 + 11.6605i 0.125666 + 0.591211i 0.995244 + 0.0974152i \(0.0310575\pi\)
−0.869578 + 0.493795i \(0.835609\pi\)
\(390\) 32.7551 19.8131i 1.65862 1.00327i
\(391\) 36.7909 11.9541i 1.86060 0.604545i
\(392\) −28.6988 15.0163i −1.44951 0.758440i
\(393\) 19.2328 19.2328i 0.970168 0.970168i
\(394\) 37.5961 3.95151i 1.89407 0.199074i
\(395\) −8.64219 8.29649i −0.434836 0.417442i
\(396\) 0.0156159 0.148576i 0.000784729 0.00746620i
\(397\) −2.42929 + 6.32850i −0.121922 + 0.317619i −0.980935 0.194336i \(-0.937745\pi\)
0.859013 + 0.511954i \(0.171078\pi\)
\(398\) 4.28222 2.18190i 0.214648 0.109369i
\(399\) 3.12512 19.0628i 0.156452 0.954335i
\(400\) 14.5105 9.18673i 0.725524 0.459336i
\(401\) −9.14254 + 15.8353i −0.456557 + 0.790779i −0.998776 0.0494575i \(-0.984251\pi\)
0.542220 + 0.840237i \(0.317584\pi\)
\(402\) −0.967730 + 1.49017i −0.0482660 + 0.0743231i
\(403\) 17.3887 + 21.4732i 0.866190 + 1.06966i
\(404\) 37.8213 16.8391i 1.88168 0.837779i
\(405\) −23.7624 0.759570i −1.18076 0.0377433i
\(406\) −0.0223482 + 0.386397i −0.00110912 + 0.0191765i
\(407\) −0.0994483 0.0994483i −0.00492947 0.00492947i
\(408\) 58.3969 + 47.2888i 2.89108 + 2.34115i
\(409\) −10.6452 + 11.8226i −0.526369 + 0.584592i −0.946432 0.322903i \(-0.895341\pi\)
0.420063 + 0.907495i \(0.362008\pi\)
\(410\) 20.1483 + 26.5742i 0.995056 + 1.31240i
\(411\) −5.62843 + 5.06786i −0.277630 + 0.249979i
\(412\) −0.761163 0.387832i −0.0374998 0.0191071i
\(413\) 6.58878 + 0.728590i 0.324213 + 0.0358516i
\(414\) 28.9318 + 9.40052i 1.42192 + 0.462010i
\(415\) −19.0329 + 4.45332i −0.934288 + 0.218605i
\(416\) −2.06811 1.86214i −0.101397 0.0912987i
\(417\) −3.74639 9.75968i −0.183462 0.477934i
\(418\) −0.124765 + 0.0334306i −0.00610243 + 0.00163514i
\(419\) −28.7560 + 20.8925i −1.40482 + 1.02066i −0.410773 + 0.911738i \(0.634741\pi\)
−0.994050 + 0.108926i \(0.965259\pi\)
\(420\) −53.0991 + 0.796143i −2.59097 + 0.0388478i
\(421\) −11.3679 8.25925i −0.554037 0.402531i 0.275235 0.961377i \(-0.411244\pi\)
−0.829272 + 0.558846i \(0.811244\pi\)
\(422\) −20.7342 7.95910i −1.00932 0.387443i
\(423\) −8.82473 5.73085i −0.429073 0.278643i
\(424\) −17.4383 + 10.0680i −0.846876 + 0.488944i
\(425\) −14.7363 + 32.0956i −0.714816 + 1.55686i
\(426\) 43.8884i 2.12640i
\(427\) −34.4930 7.52710i −1.66923 0.364262i
\(428\) −18.8772 + 2.98985i −0.912464 + 0.144520i
\(429\) 0.0479688 + 0.107740i 0.00231596 + 0.00520172i
\(430\) −22.0406 10.6695i −1.06289 0.514527i
\(431\) 3.47670 + 1.54793i 0.167467 + 0.0745610i 0.488758 0.872419i \(-0.337450\pi\)
−0.321291 + 0.946980i \(0.604117\pi\)
\(432\) −1.45948 5.44685i −0.0702192 0.262061i
\(433\) −1.22529 0.194066i −0.0588836 0.00932624i 0.126923 0.991913i \(-0.459490\pi\)
−0.185807 + 0.982586i \(0.559490\pi\)
\(434\) −8.75776 57.3001i −0.420386 2.75049i
\(435\) 0.131631 + 0.280122i 0.00631124 + 0.0134308i
\(436\) 20.1595 + 22.3894i 0.965467 + 1.07226i
\(437\) −0.910245 17.3685i −0.0435429 0.830848i
\(438\) −0.977501 18.6518i −0.0467068 0.891219i
\(439\) −3.64427 4.04738i −0.173932 0.193171i 0.649876 0.760041i \(-0.274821\pi\)
−0.823807 + 0.566870i \(0.808154\pi\)
\(440\) 0.0736569 + 0.156748i 0.00351146 + 0.00747266i
\(441\) 13.7703 + 8.15034i 0.655730 + 0.388111i
\(442\) −51.9485 8.22783i −2.47094 0.391358i
\(443\) −4.73507 17.6715i −0.224970 0.839599i −0.982417 0.186702i \(-0.940220\pi\)
0.757447 0.652897i \(-0.226447\pi\)
\(444\) 68.8995 + 30.6760i 3.26983 + 1.45582i
\(445\) −16.8465 8.15509i −0.798599 0.386589i
\(446\) −7.35106 16.5107i −0.348083 0.781807i
\(447\) −41.2945 + 6.54041i −1.95316 + 0.309351i
\(448\) 7.29685 + 22.8780i 0.344744 + 1.08089i
\(449\) 7.28927i 0.344002i 0.985097 + 0.172001i \(0.0550232\pi\)
−0.985097 + 0.172001i \(0.944977\pi\)
\(450\) −24.2106 + 13.6076i −1.14130 + 0.641471i
\(451\) −0.0889755 + 0.0513700i −0.00418969 + 0.00241892i
\(452\) 13.1102 + 8.51389i 0.616654 + 0.400460i
\(453\) −40.5667 15.5721i −1.90599 0.731641i
\(454\) 23.0343 + 16.7354i 1.08105 + 0.785432i
\(455\) 15.5631 9.29922i 0.729611 0.435954i
\(456\) 27.3318 19.8577i 1.27993 0.929922i
\(457\) −11.4145 + 3.05849i −0.533946 + 0.143070i −0.515710 0.856763i \(-0.672472\pi\)
−0.0182361 + 0.999834i \(0.505805\pi\)
\(458\) −23.4596 61.1145i −1.09620 2.85569i
\(459\) 8.61754 + 7.75927i 0.402232 + 0.362172i
\(460\) −46.5558 + 10.8931i −2.17067 + 0.507894i
\(461\) 0.809532 + 0.263033i 0.0377037 + 0.0122507i 0.327808 0.944744i \(-0.393690\pi\)
−0.290104 + 0.956995i \(0.593690\pi\)
\(462\) 0.0271932 0.245913i 0.00126514 0.0114409i
\(463\) 34.4372 + 17.5466i 1.60043 + 0.815460i 0.999874 + 0.0158788i \(0.00505458\pi\)
0.600557 + 0.799582i \(0.294945\pi\)
\(464\) −0.153675 + 0.138370i −0.00713419 + 0.00642365i
\(465\) −28.0055 36.9371i −1.29872 1.71292i
\(466\) −35.5202 + 39.4492i −1.64544 + 1.82745i
\(467\) −6.95024 5.62819i −0.321619 0.260442i 0.454891 0.890547i \(-0.349678\pi\)
−0.776509 + 0.630106i \(0.783012\pi\)
\(468\) −19.3396 19.3396i −0.893972 0.893972i
\(469\) −0.462123 + 0.703244i −0.0213389 + 0.0324728i
\(470\) 24.9973 + 0.799042i 1.15304 + 0.0368570i
\(471\) 34.1469 15.2032i 1.57341 0.700525i
\(472\) 7.29593 + 9.00972i 0.335822 + 0.414706i
\(473\) 0.0410873 0.0632689i 0.00188920 0.00290911i
\(474\) −14.9653 + 25.9206i −0.687377 + 1.19057i
\(475\) 12.2236 + 10.1344i 0.560857 + 0.464999i
\(476\) 56.4535 + 46.2233i 2.58754 + 2.11864i
\(477\) 8.86348 4.51617i 0.405831 0.206781i
\(478\) −3.71597 + 9.68044i −0.169965 + 0.442773i
\(479\) 0.101310 0.963902i 0.00462898 0.0440418i −0.991964 0.126524i \(-0.959618\pi\)
0.996593 + 0.0824819i \(0.0262847\pi\)
\(480\) 3.36789 + 3.23318i 0.153723 + 0.147574i
\(481\) −25.6068 + 2.69138i −1.16757 + 0.122717i
\(482\) −0.282157 + 0.282157i −0.0128519 + 0.0128519i
\(483\) 31.6277 + 10.4661i 1.43911 + 0.476223i
\(484\) 40.8440 13.2710i 1.85655 0.603228i
\(485\) −13.1650 + 7.96330i −0.597790 + 0.361595i
\(486\) 9.86136 + 46.3941i 0.447320 + 2.10448i
\(487\) 34.6240 1.81457i 1.56896 0.0822258i 0.752096 0.659053i \(-0.229043\pi\)
0.816866 + 0.576827i \(0.195709\pi\)
\(488\) −33.6284 51.7832i −1.52229 2.34412i
\(489\) −6.65491 + 20.4817i −0.300946 + 0.926215i
\(490\) −38.0318 + 0.364328i −1.71810 + 0.0164587i
\(491\) 1.58176 + 4.86817i 0.0713840 + 0.219697i 0.980383 0.197100i \(-0.0631524\pi\)
−0.908999 + 0.416798i \(0.863152\pi\)
\(492\) 34.6725 42.8170i 1.56316 1.93034i
\(493\) 0.110061 0.410755i 0.00495692 0.0184995i
\(494\) −9.61810 + 21.6026i −0.432739 + 0.971948i
\(495\) −0.0322859 0.0792361i −0.00145114 0.00356140i
\(496\) 18.2037 25.0553i 0.817371 1.12501i
\(497\) 0.112513 20.7849i 0.00504690 0.932330i
\(498\) 22.1710 + 43.5130i 0.993506 + 1.94986i
\(499\) −31.5502 18.2155i −1.41238 0.815438i −0.416768 0.909013i \(-0.636837\pi\)
−0.995612 + 0.0935745i \(0.970171\pi\)
\(500\) 21.4899 37.9948i 0.961058 1.69918i
\(501\) 8.68766 + 15.0475i 0.388136 + 0.672271i
\(502\) 0.321042 + 0.0168251i 0.0143288 + 0.000750941i
\(503\) −0.209162 1.32059i −0.00932605 0.0588824i 0.982586 0.185806i \(-0.0594896\pi\)
−0.991912 + 0.126924i \(0.959490\pi\)
\(504\) 7.09664 + 27.0703i 0.316110 + 1.20581i
\(505\) 14.5428 18.7276i 0.647145 0.833367i
\(506\) −0.0232846 0.221538i −0.00103512 0.00984855i
\(507\) −8.01470 2.14753i −0.355945 0.0953752i
\(508\) −26.5581 + 10.1947i −1.17833 + 0.452317i
\(509\) −18.7407 3.98347i −0.830669 0.176564i −0.227097 0.973872i \(-0.572923\pi\)
−0.603573 + 0.797308i \(0.706257\pi\)
\(510\) 86.6634 + 16.5803i 3.83752 + 0.734188i
\(511\) −0.415114 8.83574i −0.0183636 0.390870i
\(512\) −15.8470 + 31.1015i −0.700346 + 1.37451i
\(513\) 4.37245 2.83950i 0.193048 0.125367i
\(514\) −21.8420 + 4.64266i −0.963409 + 0.204779i
\(515\) −0.489160 + 0.00998298i −0.0215550 + 0.000439903i
\(516\) −8.41107 + 39.5710i −0.370277 + 1.74202i
\(517\) −0.0120533 + 0.0761016i −0.000530104 + 0.00334694i
\(518\) 49.2258 + 22.2368i 2.16286 + 0.977028i
\(519\) −31.6267 43.5304i −1.38826 1.91077i
\(520\) 30.7877 + 7.57976i 1.35013 + 0.332394i
\(521\) 14.5325 + 1.52742i 0.636678 + 0.0669176i 0.417368 0.908738i \(-0.362953\pi\)
0.219310 + 0.975655i \(0.429619\pi\)
\(522\) 0.259882 0.210448i 0.0113747 0.00921108i
\(523\) 1.82151 34.7566i 0.0796493 1.51980i −0.608106 0.793856i \(-0.708070\pi\)
0.687755 0.725943i \(-0.258596\pi\)
\(524\) 46.1889 2.01777
\(525\) −26.5938 + 14.7583i −1.16065 + 0.644105i
\(526\) 50.8274 2.21618
\(527\) −3.33311 + 63.5996i −0.145193 + 2.77044i
\(528\) 0.102730 0.0831888i 0.00447073 0.00362033i
\(529\) 6.95634 + 0.731141i 0.302449 + 0.0317887i
\(530\) −12.4703 + 20.0884i −0.541677 + 0.872586i
\(531\) −3.36650 4.63359i −0.146094 0.201081i
\(532\) 26.6429 19.1377i 1.15512 0.829725i
\(533\) −2.94239 + 18.5775i −0.127449 + 0.804683i
\(534\) −9.72219 + 45.7393i −0.420720 + 1.97933i
\(535\) −8.72251 + 6.61335i −0.377107 + 0.285920i
\(536\) −1.43952 + 0.305980i −0.0621780 + 0.0132163i
\(537\) 26.2723 17.0614i 1.13373 0.736255i
\(538\) 1.66857 3.27475i 0.0719372 0.141185i
\(539\) 0.0135087 0.116391i 0.000581862 0.00501333i
\(540\) −9.80566 10.4532i −0.421969 0.449836i
\(541\) 16.9335 + 3.59933i 0.728028 + 0.154747i 0.556992 0.830518i \(-0.311955\pi\)
0.171036 + 0.985265i \(0.445289\pi\)
\(542\) 20.6130 7.91260i 0.885405 0.339875i
\(543\) −12.7710 3.42198i −0.548057 0.146851i
\(544\) −0.670488 6.37926i −0.0287469 0.273509i
\(545\) 16.2317 + 5.85365i 0.695290 + 0.250743i
\(546\) −31.8546 32.2013i −1.36325 1.37809i
\(547\) 1.54775 + 9.77211i 0.0661770 + 0.417825i 0.998430 + 0.0560177i \(0.0178403\pi\)
−0.932253 + 0.361808i \(0.882160\pi\)
\(548\) −12.8439 0.673121i −0.548665 0.0287543i
\(549\) 15.2517 + 26.4167i 0.650927 + 1.12744i
\(550\) 0.163136 + 0.121428i 0.00695615 + 0.00517773i
\(551\) −0.165574 0.0955944i −0.00705370 0.00407246i
\(552\) 26.4511 + 51.9131i 1.12583 + 2.20957i
\(553\) −7.15378 + 12.2373i −0.304210 + 0.520381i
\(554\) −19.5157 + 26.8610i −0.829142 + 1.14122i
\(555\) 43.0804 3.14031i 1.82866 0.133299i
\(556\) 7.22066 16.2179i 0.306224 0.687791i
\(557\) −4.19928 + 15.6719i −0.177929 + 0.664041i 0.818105 + 0.575069i \(0.195025\pi\)
−0.996034 + 0.0889717i \(0.971642\pi\)
\(558\) −31.5179 + 38.9213i −1.33426 + 1.64767i
\(559\) −4.26786 13.1351i −0.180511 0.555557i
\(560\) −14.5827 14.1519i −0.616231 0.598025i
\(561\) −0.0840009 + 0.258528i −0.00354652 + 0.0109151i
\(562\) 5.27488 + 8.12260i 0.222507 + 0.342631i
\(563\) 30.9666 1.62289i 1.30509 0.0683966i 0.612925 0.790141i \(-0.289993\pi\)
0.692160 + 0.721744i \(0.256659\pi\)
\(564\) −8.59065 40.4158i −0.361732 1.70181i
\(565\) 8.92109 + 0.753962i 0.375313 + 0.0317194i
\(566\) −43.6698 + 14.1892i −1.83558 + 0.596416i
\(567\) 5.69961 + 27.5470i 0.239361 + 1.15686i
\(568\) 25.7042 25.7042i 1.07852 1.07852i
\(569\) −13.2566 + 1.39333i −0.555746 + 0.0584112i −0.378238 0.925708i \(-0.623470\pi\)
−0.177507 + 0.984119i \(0.556803\pi\)
\(570\) 17.2850 35.7066i 0.723988 1.49559i
\(571\) −0.872701 + 8.30320i −0.0365214 + 0.347478i 0.960968 + 0.276660i \(0.0892276\pi\)
−0.997489 + 0.0708179i \(0.977439\pi\)
\(572\) −0.0717719 + 0.186972i −0.00300093 + 0.00781770i
\(573\) −30.3562 + 15.4672i −1.26815 + 0.646153i
\(574\) 24.9979 30.5304i 1.04339 1.27431i
\(575\) −20.5603 + 18.0870i −0.857424 + 0.754281i
\(576\) 10.3739 17.9681i 0.432245 0.748670i
\(577\) 18.8463 29.0208i 0.784582 1.20815i −0.189483 0.981884i \(-0.560681\pi\)
0.974065 0.226267i \(-0.0726522\pi\)
\(578\) −50.2964 62.1109i −2.09205 2.58347i
\(579\) 34.9489 15.5602i 1.45242 0.646661i
\(580\) −0.178305 + 0.494427i −0.00740373 + 0.0205300i
\(581\) 10.3883 + 20.6640i 0.430979 + 0.857286i
\(582\) 27.1814 + 27.1814i 1.12670 + 1.12670i
\(583\) −0.0566095 0.0458415i −0.00234453 0.00189856i
\(584\) 10.3514 11.4963i 0.428342 0.475722i
\(585\) −14.9931 4.53550i −0.619890 0.187520i
\(586\) 12.6287 11.3709i 0.521687 0.469729i
\(587\) −17.8813 9.11097i −0.738039 0.376050i 0.0442042 0.999023i \(-0.485925\pi\)
−0.782244 + 0.622973i \(0.785925\pi\)
\(588\) 15.6048 + 60.8662i 0.643531 + 2.51008i
\(589\) 27.2320 + 8.84822i 1.12208 + 0.364584i
\(590\) 12.5468 + 5.28212i 0.516542 + 0.217462i
\(591\) −26.5815 23.9341i −1.09342 0.984518i
\(592\) 10.3423 + 26.9426i 0.425066 + 1.10734i
\(593\) 17.9557 4.81121i 0.737352 0.197573i 0.129451 0.991586i \(-0.458678\pi\)
0.607901 + 0.794013i \(0.292012\pi\)
\(594\) 0.0540215 0.0392489i 0.00221653 0.00161040i
\(595\) 41.0000 + 8.07436i 1.68084 + 0.331016i
\(596\) −57.4394 41.7321i −2.35281 1.70942i
\(597\) −4.24539 1.62965i −0.173752 0.0666972i
\(598\) −34.2022 22.2111i −1.39863 0.908281i
\(599\) −30.6038 + 17.6691i −1.25044 + 0.721941i −0.971196 0.238280i \(-0.923416\pi\)
−0.279241 + 0.960221i \(0.590083\pi\)
\(600\) −51.2169 14.3595i −2.09092 0.586223i
\(601\) 0.819532i 0.0334294i 0.999860 + 0.0167147i \(0.00532070\pi\)
−0.999860 + 0.0167147i \(0.994679\pi\)
\(602\) −6.17729 + 28.3075i −0.251767 + 1.15373i
\(603\) 0.718101 0.113736i 0.0292433 0.00463169i
\(604\) −30.0131 67.4105i −1.22122 2.74290i
\(605\) 17.0336 17.7433i 0.692514 0.721369i
\(606\) −54.1179 24.0948i −2.19839 0.978786i
\(607\) 3.58282 + 13.3713i 0.145422 + 0.542724i 0.999736 + 0.0229662i \(0.00731101\pi\)
−0.854314 + 0.519757i \(0.826022\pi\)
\(608\) −2.84839 0.451141i −0.115518 0.0182962i
\(609\) 0.285846 0.228923i 0.0115831 0.00927642i
\(610\) −63.5156 34.9625i −2.57167 1.41559i
\(611\) 9.43873 + 10.4828i 0.381850 + 0.424087i
\(612\) −3.29927 62.9538i −0.133365 2.54476i
\(613\) −2.00609 38.2785i −0.0810253 1.54605i −0.672723 0.739895i \(-0.734875\pi\)
0.591697 0.806160i \(-0.298458\pi\)
\(614\) −10.9559 12.1678i −0.442144 0.491051i
\(615\) 5.92936 30.9921i 0.239095 1.24972i
\(616\) 0.159951 0.128098i 0.00644460 0.00516122i
\(617\) −16.5933 2.62812i −0.668022 0.105804i −0.186793 0.982399i \(-0.559809\pi\)
−0.481229 + 0.876595i \(0.659809\pi\)
\(618\) 0.316371 + 1.18071i 0.0127263 + 0.0474952i
\(619\) −5.67928 2.52858i −0.228269 0.101632i 0.289415 0.957204i \(-0.406539\pi\)
−0.517685 + 0.855572i \(0.673206\pi\)
\(620\) 10.7250 77.9819i 0.430725 3.13183i
\(621\) 3.65706 + 8.21390i 0.146753 + 0.329612i
\(622\) −6.30933 + 0.999300i −0.252981 + 0.0400683i
\(623\) −4.72154 + 21.6365i −0.189165 + 0.866850i
\(624\) 24.2004i 0.968790i
\(625\) 0.577384 24.9933i 0.0230954 0.999733i
\(626\) −9.15199 + 5.28391i −0.365787 + 0.211187i
\(627\) 0.102498 + 0.0665632i 0.00409339 + 0.00265828i
\(628\) 59.2587 + 22.7473i 2.36468 + 0.907716i
\(629\) −48.0125 34.8832i −1.91439 1.39088i
\(630\) 22.3520 + 24.0881i 0.890524 + 0.959695i
\(631\) −16.6120 + 12.0693i −0.661312 + 0.480471i −0.867106 0.498124i \(-0.834022\pi\)
0.205794 + 0.978595i \(0.434022\pi\)
\(632\) −23.9457 + 6.41622i −0.952508 + 0.255224i
\(633\) 7.53080 + 19.6184i 0.299323 + 0.779762i
\(634\) −37.4696 33.7378i −1.48811 1.33990i
\(635\) −10.6526 + 12.3277i −0.422734 + 0.489209i
\(636\) 37.1507 + 12.0710i 1.47312 + 0.478646i
\(637\) −15.0033 15.3317i −0.594452 0.607465i
\(638\) −0.00218182 0.00111169i −8.63790e−5 4.40123e-5i
\(639\) −13.3458 + 12.0166i −0.527950 + 0.475368i
\(640\) 0.923356 + 45.2439i 0.0364989 + 1.78842i
\(641\) 6.22319 6.91155i 0.245801 0.272990i −0.607602 0.794242i \(-0.707868\pi\)
0.853403 + 0.521252i \(0.174535\pi\)
\(642\) 21.2532 + 17.2105i 0.838796 + 0.679244i
\(643\) 10.6811 + 10.6811i 0.421223 + 0.421223i 0.885625 0.464402i \(-0.153731\pi\)
−0.464402 + 0.885625i \(0.653731\pi\)
\(644\) 25.4105 + 50.5455i 1.00131 + 1.99177i
\(645\) 6.45211 + 22.2530i 0.254052 + 0.876212i
\(646\) −49.7923 + 22.1690i −1.95905 + 0.872226i
\(647\) 9.53557 + 11.7754i 0.374882 + 0.462940i 0.929315 0.369288i \(-0.120398\pi\)
−0.554433 + 0.832228i \(0.687065\pi\)
\(648\) −26.7947 + 41.2603i −1.05260 + 1.62086i
\(649\) −0.0209698 + 0.0363207i −0.000823135 + 0.00142571i
\(650\) 36.0717 9.22025i 1.41485 0.361648i
\(651\) −34.7461 + 42.4361i −1.36181 + 1.66320i
\(652\) −32.5852 + 16.6030i −1.27614 + 0.650223i
\(653\) −12.9236 + 33.6671i −0.505740 + 1.31750i 0.408661 + 0.912686i \(0.365996\pi\)
−0.914401 + 0.404811i \(0.867337\pi\)
\(654\) 4.50617 42.8734i 0.176205 1.67648i
\(655\) 23.3202 12.4880i 0.911197 0.487948i
\(656\) 20.9667 2.20369i 0.818612 0.0860396i
\(657\) −5.40409 + 5.40409i −0.210833 + 0.210833i
\(658\) −5.99580 28.9785i −0.233741 1.12970i
\(659\) 30.6779 9.96786i 1.19504 0.388293i 0.357107 0.934063i \(-0.383763\pi\)
0.837935 + 0.545771i \(0.183763\pi\)
\(660\) 0.130365 0.309658i 0.00507443 0.0120534i
\(661\) 3.78793 + 17.8208i 0.147333 + 0.693149i 0.988357 + 0.152151i \(0.0486199\pi\)
−0.841024 + 0.540998i \(0.818047\pi\)
\(662\) −38.5620 + 2.02095i −1.49875 + 0.0785464i
\(663\) 27.1044 + 41.7371i 1.05265 + 1.62093i
\(664\) −12.4994 + 38.4692i −0.485071 + 1.49290i
\(665\) 8.27745 16.8658i 0.320986 0.654028i
\(666\) −14.4216 44.3852i −0.558827 1.71989i
\(667\) 0.207501 0.256242i 0.00803447 0.00992174i
\(668\) −7.63675 + 28.5007i −0.295475 + 1.10273i
\(669\) −6.95549 + 15.6223i −0.268915 + 0.603992i
\(670\) −1.32052 + 1.11471i −0.0510161 + 0.0430649i
\(671\) 0.131290 0.180705i 0.00506839 0.00697604i
\(672\) 2.78786 4.76890i 0.107544 0.183964i
\(673\) −8.71675 17.1076i −0.336006 0.659449i 0.659750 0.751485i \(-0.270662\pi\)
−0.995756 + 0.0920367i \(0.970662\pi\)
\(674\) 53.8205 + 31.0733i 2.07309 + 1.19690i
\(675\) −7.77700 2.62657i −0.299337 0.101097i
\(676\) −7.04519 12.2026i −0.270969 0.469332i
\(677\) 35.4419 + 1.85743i 1.36214 + 0.0713870i 0.719348 0.694650i \(-0.244441\pi\)
0.642797 + 0.766037i \(0.277774\pi\)
\(678\) −3.49909 22.0924i −0.134382 0.848453i
\(679\) 12.8030 + 12.9424i 0.491335 + 0.496683i
\(680\) 41.0457 + 60.4669i 1.57403 + 2.31880i
\(681\) −2.81598 26.7923i −0.107909 1.02668i
\(682\) 0.354236 + 0.0949172i 0.0135644 + 0.00363457i
\(683\) 8.91129 3.42072i 0.340981 0.130890i −0.181851 0.983326i \(-0.558209\pi\)
0.522832 + 0.852436i \(0.324876\pi\)
\(684\) −27.7233 5.89278i −1.06003 0.225316i
\(685\) −6.66673 + 3.13274i −0.254723 + 0.119696i
\(686\) 10.9399 + 43.6519i 0.417688 + 1.66664i
\(687\) −28.1201 + 55.1888i −1.07285 + 2.10558i
\(688\) −12.9827 + 8.43109i −0.494962 + 0.321432i
\(689\) −13.0443 + 2.77265i −0.496948 + 0.105629i
\(690\) 56.1579 + 39.0756i 2.13789 + 1.48758i
\(691\) 10.4781 49.2956i 0.398606 1.87529i −0.0792486 0.996855i \(-0.525252\pi\)
0.477855 0.878439i \(-0.341415\pi\)
\(692\) 14.2938 90.2473i 0.543367 3.43069i
\(693\) −0.0822238 + 0.0590617i −0.00312342 + 0.00224357i
\(694\) −21.6421 29.7878i −0.821524 1.13073i
\(695\) −0.739180 10.1405i −0.0280387 0.384649i
\(696\) 0.636964 + 0.0669476i 0.0241441 + 0.00253764i
\(697\) −33.6920 + 27.2832i −1.27618 + 1.03343i
\(698\) 0.189391 3.61379i 0.00716855 0.136784i
\(699\) 50.2276 1.89978
\(700\) −49.6549 14.2119i −1.87678 0.537160i
\(701\) 41.2864 1.55936 0.779682 0.626176i \(-0.215381\pi\)
0.779682 + 0.626176i \(0.215381\pi\)
\(702\) 0.639790 12.2079i 0.0241473 0.460758i
\(703\) −20.7359 + 16.7916i −0.782070 + 0.633307i
\(704\) −0.151095 0.0158807i −0.00569460 0.000598526i
\(705\) −15.2645 18.0828i −0.574895 0.681039i
\(706\) 13.4251 + 18.4781i 0.505261 + 0.695431i
\(707\) −25.5677 11.5497i −0.961571 0.434371i
\(708\) 3.51827 22.2135i 0.132225 0.834834i
\(709\) 0.400572 1.88454i 0.0150438 0.0707755i −0.969985 0.243163i \(-0.921815\pi\)
0.985029 + 0.172388i \(0.0551482\pi\)
\(710\) 12.3593 40.8564i 0.463835 1.53331i
\(711\) 11.9795 2.54632i 0.449266 0.0954945i
\(712\) −32.4822 + 21.0942i −1.21732 + 0.790538i
\(713\) −22.4185 + 43.9987i −0.839578 + 1.64777i
\(714\) −4.89950 104.286i −0.183359 3.90282i
\(715\) 0.0143147 + 0.113805i 0.000535338 + 0.00425606i
\(716\) 52.0344 + 11.0603i 1.94462 + 0.413341i
\(717\) 9.15952 3.51601i 0.342069 0.131308i
\(718\) 14.4190 + 3.86356i 0.538112 + 0.144187i
\(719\) 5.06873 + 48.2257i 0.189032 + 1.79852i 0.519262 + 0.854615i \(0.326207\pi\)
−0.330230 + 0.943900i \(0.607126\pi\)
\(720\) −0.560930 + 17.5482i −0.0209046 + 0.653981i
\(721\) 0.146802 + 0.559980i 0.00546719 + 0.0208547i
\(722\) −3.38876 21.3958i −0.126117 0.796270i
\(723\) 0.377040 + 0.0197598i 0.0140223 + 0.000734876i
\(724\) −11.2262 19.4443i −0.417217 0.722641i
\(725\) 0.0436533 + 0.297839i 0.00162124 + 0.0110614i
\(726\) −53.2178 30.7253i −1.97510 1.14032i
\(727\) 3.31875 + 6.51342i 0.123086 + 0.241569i 0.944325 0.329015i \(-0.106717\pi\)
−0.821239 + 0.570584i \(0.806717\pi\)
\(728\) 0.203080 37.5157i 0.00752665 1.39042i
\(729\) 7.63022 10.5021i 0.282601 0.388967i
\(730\) 4.34251 17.6386i 0.160724 0.652832i
\(731\) 12.9478 29.0813i 0.478893 1.07561i
\(732\) −31.0015 + 115.699i −1.14585 + 4.27636i
\(733\) −6.48565 + 8.00911i −0.239553 + 0.295823i −0.882717 0.469905i \(-0.844288\pi\)
0.643164 + 0.765729i \(0.277621\pi\)
\(734\) −27.0939 83.3864i −1.00005 3.07785i
\(735\) 24.3350 + 26.5116i 0.897610 + 0.977894i
\(736\) 1.53691 4.73012i 0.0566512 0.174354i
\(737\) −0.00289960 0.00446499i −0.000106808 0.000164470i
\(738\) −34.0458 + 1.78427i −1.25324 + 0.0656797i
\(739\) 4.57499 + 21.5236i 0.168294 + 0.791759i 0.978603 + 0.205757i \(0.0659657\pi\)
−0.810309 + 0.586002i \(0.800701\pi\)
\(740\) 55.5010 + 47.9594i 2.04026 + 1.76302i
\(741\) 21.2794 6.91411i 0.781720 0.253996i
\(742\) 26.5599 + 8.78907i 0.975045 + 0.322657i
\(743\) −32.3075 + 32.3075i −1.18525 + 1.18525i −0.206883 + 0.978366i \(0.566332\pi\)
−0.978366 + 0.206883i \(0.933668\pi\)
\(744\) −95.3951 + 10.0264i −3.49735 + 0.367587i
\(745\) −40.2835 5.54025i −1.47587 0.202979i
\(746\) −4.72168 + 44.9238i −0.172873 + 1.64478i
\(747\) 7.16123 18.6556i 0.262016 0.682574i
\(748\) −0.411303 + 0.209569i −0.0150387 + 0.00766262i
\(749\) 10.0211 + 8.20512i 0.366162 + 0.299809i
\(750\) −60.9773 + 13.5267i −2.22658 + 0.493924i
\(751\) −11.0388 + 19.1197i −0.402810 + 0.697687i −0.994064 0.108798i \(-0.965300\pi\)
0.591254 + 0.806485i \(0.298633\pi\)
\(752\) 8.61110 13.2599i 0.314014 0.483540i
\(753\) −0.191429 0.236395i −0.00697605 0.00861471i
\(754\) −0.409540 + 0.182339i −0.0149146 + 0.00664040i
\(755\) −33.3790 25.9202i −1.21479 0.943332i
\(756\) −9.31310 + 14.1724i −0.338714 + 0.515444i
\(757\) 2.36580 + 2.36580i 0.0859865 + 0.0859865i 0.748792 0.662805i \(-0.230634\pi\)
−0.662805 + 0.748792i \(0.730634\pi\)
\(758\) 42.0339 + 34.0384i 1.52674 + 1.23633i
\(759\) −0.141033 + 0.156633i −0.00511919 + 0.00568543i
\(760\) 31.0356 10.7890i 1.12578 0.391359i
\(761\) 27.8157 25.0454i 1.00832 0.907895i 0.0125634 0.999921i \(-0.496001\pi\)
0.995757 + 0.0920256i \(0.0293342\pi\)
\(762\) 36.2686 + 18.4798i 1.31387 + 0.669451i
\(763\) 2.24397 20.2927i 0.0812371 0.734643i
\(764\) −55.0239 17.8784i −1.99070 0.646816i
\(765\) −18.6865 30.8926i −0.675612 1.11692i
\(766\) 27.7996 + 25.0309i 1.00444 + 0.904403i
\(767\) 2.75157 + 7.16810i 0.0993536 + 0.258825i
\(768\) 68.8951 18.4604i 2.48604 0.666132i
\(769\) 31.5396 22.9148i 1.13735 0.826330i 0.150599 0.988595i \(-0.451880\pi\)
0.986747 + 0.162264i \(0.0518798\pi\)
\(770\) 0.0945655 0.221267i 0.00340790 0.00797390i
\(771\) 17.0932 + 12.4189i 0.615596 + 0.447257i
\(772\) 60.6505 + 23.2815i 2.18286 + 0.837920i
\(773\) 19.4971 + 12.6616i 0.701263 + 0.455405i 0.845387 0.534154i \(-0.179370\pi\)
−0.144124 + 0.989560i \(0.546037\pi\)
\(774\) 21.6795 12.5167i 0.779254 0.449902i
\(775\) −15.6690 42.2718i −0.562846 1.51845i
\(776\) 31.8387i 1.14294i
\(777\) −15.5301 48.6920i −0.557139 1.74682i
\(778\) 28.6099 4.53136i 1.02571 0.162457i
\(779\) 7.92795 + 17.8065i 0.284048 + 0.637983i
\(780\) −29.0372 54.2243i −1.03970 1.94154i
\(781\) 0.120133 + 0.0534868i 0.00429871 + 0.00191391i
\(782\) −24.3284 90.7949i −0.869983 3.24682i
\(783\) 0.0976210 + 0.0154617i 0.00348869 + 0.000552554i
\(784\) −12.2466 + 20.6911i −0.437378 + 0.738969i
\(785\) 36.0692 4.53687i 1.28736 0.161928i
\(786\) −44.2234 49.1151i −1.57740 1.75188i
\(787\) 0.863994 + 16.4860i 0.0307981 + 0.587662i 0.969823 + 0.243812i \(0.0783979\pi\)
−0.939024 + 0.343850i \(0.888269\pi\)
\(788\) −3.17897 60.6583i −0.113246 2.16086i
\(789\) −32.1801 35.7396i −1.14564 1.27236i
\(790\) −21.2308 + 19.9156i −0.755358 + 0.708564i
\(791\) −1.60048 10.4716i −0.0569066 0.372327i
\(792\) −0.174874 0.0276973i −0.00621388 0.000984182i
\(793\) −10.5837 39.4989i −0.375838 1.40265i
\(794\) 15.0474 + 6.69956i 0.534014 + 0.237758i
\(795\) 22.0206 3.94989i 0.780989 0.140088i
\(796\) −3.14093 7.05465i −0.111327 0.250045i
\(797\) 43.0687 6.82142i 1.52557 0.241627i 0.663409 0.748257i \(-0.269109\pi\)
0.862164 + 0.506630i \(0.169109\pi\)
\(798\) −45.8593 10.0075i −1.62340 0.354260i
\(799\) 32.5131i 1.15023i
\(800\) 2.22474 + 3.95823i 0.0786564 + 0.139945i
\(801\) 16.5705 9.56698i 0.585490 0.338033i
\(802\) 37.2625 + 24.1985i 1.31578 + 0.854480i
\(803\) 0.0522459 + 0.0200553i 0.00184372 + 0.000707738i
\(804\) 2.30973 + 1.67811i 0.0814578 + 0.0591825i
\(805\) 26.4954 + 18.6496i 0.933839 + 0.657312i
\(806\) 54.3169 39.4635i 1.91323 1.39004i
\(807\) −3.35907 + 0.900061i −0.118245 + 0.0316836i
\(808\) −17.5836 45.8069i −0.618590 1.61148i
\(809\) 10.9422 + 9.85244i 0.384709 + 0.346393i 0.838681 0.544622i \(-0.183327\pi\)
−0.453973 + 0.891016i \(0.649994\pi\)
\(810\) −4.86499 + 57.5639i −0.170938 + 2.02259i
\(811\) −24.6251 8.00118i −0.864704 0.280959i −0.157112 0.987581i \(-0.550218\pi\)
−0.707592 + 0.706621i \(0.750218\pi\)
\(812\) 0.618125 + 0.0683525i 0.0216920 + 0.00239870i
\(813\) −18.6144 9.48450i −0.652835 0.332636i
\(814\) −0.253962 + 0.228669i −0.00890137 + 0.00801483i
\(815\) −11.9630 + 17.1927i −0.419044 + 0.602233i
\(816\) 37.3240 41.4525i 1.30660 1.45113i
\(817\) −11.1227 9.00697i −0.389134 0.315114i
\(818\) 27.3344 + 27.3344i 0.955725 + 0.955725i
\(819\) −1.07017 + 18.5031i −0.0373948 + 0.646551i
\(820\) 44.3347 30.0950i 1.54823 1.05096i
\(821\) 44.7779 19.9364i 1.56276 0.695785i 0.570653 0.821191i \(-0.306690\pi\)
0.992106 + 0.125406i \(0.0400233\pi\)
\(822\) 11.5816 + 14.3021i 0.403955 + 0.498843i
\(823\) 28.8436 44.4153i 1.00543 1.54822i 0.180032 0.983661i \(-0.442380\pi\)
0.825393 0.564558i \(-0.190953\pi\)
\(824\) −0.506220 + 0.876799i −0.0176350 + 0.0305447i
\(825\) −0.0179024 0.191589i −0.000623282 0.00667028i
\(826\) 2.60585 15.8953i 0.0906690 0.553068i
\(827\) 4.78458 2.43786i 0.166376 0.0847728i −0.368819 0.929501i \(-0.620238\pi\)
0.535196 + 0.844728i \(0.320238\pi\)
\(828\) 17.5168 45.6330i 0.608753 1.58585i
\(829\) −3.66391 + 34.8598i −0.127253 + 1.21073i 0.725428 + 0.688298i \(0.241642\pi\)
−0.852681 + 0.522432i \(0.825025\pi\)
\(830\) 8.38575 + 46.7504i 0.291074 + 1.62273i
\(831\) 31.2433 3.28380i 1.08382 0.113914i
\(832\) −19.6675 + 19.6675i −0.681847 + 0.681847i
\(833\) −2.05298 49.4010i −0.0711316 1.71164i
\(834\) −24.1587 + 7.84964i −0.836548 + 0.271811i
\(835\) 3.85001 + 16.4544i 0.133235 + 0.569429i
\(836\) 0.0431503 + 0.203006i 0.00149238 + 0.00702111i
\(837\) −14.7822 + 0.774702i −0.510947 + 0.0267776i
\(838\) 47.0395 + 72.4345i 1.62495 + 2.50221i
\(839\) 4.17081 12.8364i 0.143992 0.443163i −0.852888 0.522095i \(-0.825151\pi\)
0.996880 + 0.0789314i \(0.0251508\pi\)
\(840\) −2.35126 + 62.8934i −0.0811262 + 2.17003i
\(841\) 8.96037 + 27.5772i 0.308978 + 0.950938i
\(842\) −21.4871 + 26.5343i −0.740493 + 0.914433i
\(843\) 2.37180 8.85167i 0.0816891 0.304868i
\(844\) −14.5146 + 32.6003i −0.499613 + 1.12215i
\(845\) −6.85625 4.25616i −0.235862 0.146417i
\(846\) −15.0284 + 20.6848i −0.516686 + 0.711158i
\(847\) −25.1244 14.6875i −0.863284 0.504668i
\(848\) 6.78594 + 13.3182i 0.233030 + 0.457347i
\(849\) 37.6256 + 21.7232i 1.29131 + 0.745537i
\(850\) 76.0072 + 39.8399i 2.60703 + 1.36650i
\(851\) −23.0079 39.8508i −0.788699 1.36607i
\(852\) −70.4225 3.69069i −2.41263 0.126441i
\(853\) −5.33840 33.7053i −0.182783 1.15405i −0.892997 0.450063i \(-0.851402\pi\)
0.710214 0.703986i \(-0.248598\pi\)
\(854\) −22.6513 + 82.7416i −0.775111 + 2.83136i
\(855\) −15.5904 + 4.52033i −0.533181 + 0.154592i
\(856\) 2.36769 + 22.5271i 0.0809260 + 0.769960i
\(857\) 6.63141 + 1.77688i 0.226525 + 0.0606971i 0.370296 0.928914i \(-0.379256\pi\)
−0.143771 + 0.989611i \(0.545923\pi\)
\(858\) 0.267535 0.102697i 0.00913350 0.00350602i
\(859\) 43.3468 + 9.21364i 1.47897 + 0.314365i 0.875578 0.483077i \(-0.160481\pi\)
0.603395 + 0.797442i \(0.293814\pi\)
\(860\) −18.9735 + 34.4686i −0.646990 + 1.17537i
\(861\) −37.2943 + 1.75213i −1.27099 + 0.0597126i
\(862\) 4.19824 8.23950i 0.142993 0.280639i
\(863\) 1.69343 1.09973i 0.0576452 0.0374352i −0.515495 0.856893i \(-0.672392\pi\)
0.573140 + 0.819458i \(0.305725\pi\)
\(864\) 1.45829 0.309970i 0.0496122 0.0105454i
\(865\) −17.1833 49.4294i −0.584250 1.68065i
\(866\) −0.626730 + 2.94853i −0.0212971 + 0.100195i
\(867\) −11.8297 + 74.6900i −0.401759 + 2.53661i
\(868\) −92.6791 + 9.23402i −3.14573 + 0.313423i
\(869\) −0.0527129 0.0725531i −0.00178816 0.00246119i
\(870\) 0.696468 0.283786i 0.0236125 0.00962125i
\(871\) −0.969332 0.101881i −0.0328446 0.00345210i
\(872\) 27.7488 22.4706i 0.939694 0.760950i
\(873\) 0.823202 15.7076i 0.0278612 0.531623i
\(874\) −42.2612 −1.42950
\(875\) −28.9126 + 6.24971i −0.977426 + 0.211279i
\(876\) −30.0106 −1.01396
\(877\) −2.45627 + 46.8683i −0.0829422 + 1.58263i 0.567693 + 0.823240i \(0.307836\pi\)
−0.650635 + 0.759391i \(0.725497\pi\)
\(878\) −10.2846 + 8.32828i −0.347087 + 0.281066i
\(879\) −15.9911 1.68073i −0.539365 0.0566896i
\(880\) 0.119059 0.0485124i 0.00401348 0.00163535i
\(881\) 12.9945 + 17.8855i 0.437797 + 0.602576i 0.969721 0.244216i \(-0.0785306\pi\)
−0.531924 + 0.846792i \(0.678531\pi\)
\(882\) 21.5283 32.3778i 0.724896 1.09022i
\(883\) 2.48456 15.6869i 0.0836122 0.527906i −0.909959 0.414698i \(-0.863887\pi\)
0.993571 0.113208i \(-0.0361128\pi\)
\(884\) −17.5707 + 82.6636i −0.590966 + 2.78028i
\(885\) −4.22950 12.1666i −0.142173 0.408974i
\(886\) −43.4828 + 9.24256i −1.46083 + 0.310510i
\(887\) −14.7196 + 9.55901i −0.494236 + 0.320960i −0.767577 0.640957i \(-0.778538\pi\)
0.273341 + 0.961917i \(0.411871\pi\)
\(888\) 40.5794 79.6415i 1.36175 2.67259i
\(889\) 17.1289 + 8.84473i 0.574485 + 0.296643i
\(890\) −21.9310 + 39.8416i −0.735130 + 1.33549i
\(891\) −0.174084 0.0370028i −0.00583205 0.00123964i
\(892\) −27.1110 + 10.4069i −0.907743 + 0.348450i
\(893\) 14.1197 + 3.78336i 0.472498 + 0.126605i
\(894\) 10.6192 + 101.035i 0.355158 + 3.37910i
\(895\) 29.2619 8.48429i 0.978117 0.283598i
\(896\) 51.7942 13.5782i 1.73032 0.453614i
\(897\) 6.03632 + 38.1118i 0.201547 + 1.27252i
\(898\) 17.6877 + 0.926974i 0.590246 + 0.0309335i
\(899\) 0.271415 + 0.470104i 0.00905219 + 0.0156789i
\(900\) 19.7986 + 39.9922i 0.659955 + 1.33307i
\(901\) −26.6196 15.3689i −0.886829 0.512011i
\(902\) 0.113336 + 0.222435i 0.00377369 + 0.00740629i
\(903\) 23.8155 13.5786i 0.792532 0.451866i
\(904\) 10.8896 14.9882i 0.362182 0.498500i
\(905\) −10.9251 6.78198i −0.363162 0.225441i
\(906\) −42.9452 + 96.4565i −1.42676 + 3.20455i
\(907\) 7.69450 28.7163i 0.255492 0.953508i −0.712325 0.701850i \(-0.752358\pi\)
0.967816 0.251658i \(-0.0809757\pi\)
\(908\) 28.7904 35.5531i 0.955441 1.17987i
\(909\) 7.49054 + 23.0535i 0.248445 + 0.764636i
\(910\) −20.5858 38.9471i −0.682412 1.29109i
\(911\) 12.1969 37.5382i 0.404101 1.24370i −0.517542 0.855658i \(-0.673153\pi\)
0.921643 0.388038i \(-0.126847\pi\)
\(912\) −13.6587 21.0326i −0.452285 0.696458i
\(913\) −0.146126 + 0.00765812i −0.00483605 + 0.000253447i
\(914\) 5.96999 + 28.0866i 0.197470 + 0.929022i
\(915\) 15.6291 + 66.7969i 0.516683 + 2.20824i
\(916\) −100.036 + 32.5036i −3.30528 + 1.07395i
\(917\) −20.8177 23.3736i −0.687459 0.771863i
\(918\) 19.9241 19.9241i 0.657593 0.657593i
\(919\) −14.7138 + 1.54648i −0.485363 + 0.0510137i −0.344050 0.938951i \(-0.611799\pi\)
−0.141313 + 0.989965i \(0.545132\pi\)
\(920\) 10.0046 + 55.7755i 0.329842 + 1.83886i
\(921\) −1.61938 + 15.4074i −0.0533605 + 0.507691i
\(922\) 0.741208 1.93091i 0.0244104 0.0635912i
\(923\) 21.4508 10.9297i 0.706061 0.359756i
\(924\) −0.392301 0.0643132i −0.0129058 0.00211575i
\(925\) 40.9885 + 9.20837i 1.34769 + 0.302769i
\(926\) 46.9570 81.3318i 1.54310 2.67273i
\(927\) 0.272414 0.419481i 0.00894725 0.0137776i
\(928\) −0.0344066 0.0424886i −0.00112945 0.00139476i
\(929\) 15.8211 7.04399i 0.519072 0.231106i −0.130441 0.991456i \(-0.541639\pi\)
0.649513 + 0.760350i \(0.274973\pi\)
\(930\) −93.1908 + 63.2591i −3.05585 + 2.07435i
\(931\) −21.6926 4.85695i −0.710948 0.159180i
\(932\) 60.3124 + 60.3124i 1.97560 + 1.97560i
\(933\) 4.69725 + 3.80376i 0.153781 + 0.124530i
\(934\) −14.5409 + 16.1493i −0.475793 + 0.528421i
\(935\) −0.151001 + 0.217013i −0.00493826 + 0.00709707i
\(936\) −24.0884 + 21.6893i −0.787354 + 0.708937i
\(937\) −29.8820 15.2256i −0.976202 0.497400i −0.108291 0.994119i \(-0.534538\pi\)
−0.867911 + 0.496719i \(0.834538\pi\)
\(938\) 1.64768 + 1.21079i 0.0537987 + 0.0395338i
\(939\) 9.50975 + 3.08990i 0.310339 + 0.100835i
\(940\) 3.38421 40.0429i 0.110381 1.30606i
\(941\) −32.3887 29.1630i −1.05584 0.950685i −0.0569808 0.998375i \(-0.518147\pi\)
−0.998862 + 0.0476900i \(0.984814\pi\)
\(942\) −32.5487 84.7923i −1.06049 2.76268i
\(943\) −32.4696 + 8.70021i −1.05736 + 0.283318i
\(944\) 6.96237 5.05846i 0.226606 0.164639i
\(945\) −0.870308 + 9.67343i −0.0283111 + 0.314677i
\(946\) −0.148300 0.107746i −0.00482164 0.00350312i
\(947\) 5.14526 + 1.97508i 0.167199 + 0.0641815i 0.440528 0.897739i \(-0.354791\pi\)
−0.273329 + 0.961921i \(0.588125\pi\)
\(948\) 40.3332 + 26.1927i 1.30996 + 0.850699i
\(949\) 8.87279 5.12271i 0.288023 0.166290i
\(950\) 26.1461 28.3723i 0.848291 0.920518i
\(951\) 47.7071i 1.54701i
\(952\) 58.2080 63.9470i 1.88653 2.07253i
\(953\) −6.68823 + 1.05931i −0.216653 + 0.0343145i −0.263817 0.964573i \(-0.584982\pi\)
0.0471642 + 0.998887i \(0.484982\pi\)
\(954\) −9.83150 22.0819i −0.318307 0.714929i
\(955\) −32.6147 + 5.85018i −1.05539 + 0.189307i
\(956\) 15.2206 + 6.77663i 0.492268 + 0.219172i
\(957\) 0.000599669 0.00223799i 1.93845e−5 7.23441e-5i
\(958\) −2.32607 0.368413i −0.0751518 0.0119029i
\(959\) 5.44821 + 6.80295i 0.175932 + 0.219679i
\(960\) 34.0315 31.9232i 1.09836 1.03032i
\(961\) −33.6553 37.3780i −1.08565 1.20574i
\(962\) 3.27435 + 62.4783i 0.105569 + 2.01438i
\(963\) −0.585655 11.1750i −0.0188725 0.360108i
\(964\) 0.429016 + 0.476471i 0.0138177 + 0.0153461i
\(965\) 36.9163 4.64342i 1.18838 0.149477i
\(966\) 29.4184 75.4149i 0.946523 2.42644i
\(967\) −57.0421 9.03458i −1.83435 0.290533i −0.859128 0.511760i \(-0.828994\pi\)
−0.975222 + 0.221228i \(0.928994\pi\)
\(968\) −13.1732 49.1630i −0.423403 1.58016i
\(969\) 47.1129 + 20.9760i 1.51348 + 0.673847i
\(970\) 17.6491 + 32.9580i 0.566678 + 1.05822i
\(971\) −7.98460 17.9337i −0.256238 0.575520i 0.738922 0.673791i \(-0.235335\pi\)
−0.995160 + 0.0982714i \(0.968669\pi\)
\(972\) 75.2723 11.9220i 2.41436 0.382397i
\(973\) −11.4613 + 3.65554i −0.367434 + 0.117191i
\(974\) 84.2473i 2.69946i
\(975\) −29.3211 19.5265i −0.939028 0.625347i
\(976\) −39.6935 + 22.9170i −1.27056 + 0.733556i
\(977\) −20.6393 13.4033i −0.660309 0.428810i 0.170507 0.985356i \(-0.445459\pi\)
−0.830816 + 0.556547i \(0.812126\pi\)
\(978\) 48.8534 + 18.7531i 1.56216 + 0.599657i
\(979\) −0.113351 0.0823545i −0.00362272 0.00263206i
\(980\) −2.61359 + 61.0557i −0.0834882 + 1.95035i
\(981\) −14.2709 + 10.3684i −0.455634 + 0.331038i
\(982\) 12.0140 3.21913i 0.383381 0.102727i
\(983\) 16.0960 + 41.9315i 0.513382 + 1.33741i 0.908157 + 0.418629i \(0.137489\pi\)
−0.394775 + 0.918778i \(0.629177\pi\)
\(984\) −48.5243 43.6915i −1.54690 1.39283i
\(985\) −18.0051 29.7662i −0.573691 0.948429i
\(986\) −0.982717 0.319304i −0.0312961 0.0101687i
\(987\) −16.5803 + 22.5629i −0.527756 + 0.718186i
\(988\) 33.8543 + 17.2496i 1.07705 + 0.548784i
\(989\) 18.3428 16.5160i 0.583268 0.525177i
\(990\) −0.196375 + 0.0682666i −0.00624122 + 0.00216966i
\(991\) −31.0000 + 34.4290i −0.984747 + 1.09367i 0.0108510 + 0.999941i \(0.496546\pi\)
−0.995598 + 0.0937308i \(0.970121\pi\)
\(992\) 6.36332 + 5.15291i 0.202035 + 0.163605i
\(993\) 25.8356 + 25.8356i 0.819867 + 0.819867i
\(994\) −50.4211 2.91623i −1.59926 0.0924971i
\(995\) −3.49318 2.71260i −0.110741 0.0859952i
\(996\) 71.6845 31.9160i 2.27141 1.01130i
\(997\) −15.5757 19.2344i −0.493286 0.609158i 0.468331 0.883553i \(-0.344856\pi\)
−0.961617 + 0.274395i \(0.911522\pi\)
\(998\) −48.2129 + 74.2414i −1.52615 + 2.35007i
\(999\) 6.89686 11.9457i 0.218207 0.377946i
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 175.2.x.a.47.18 yes 288
5.2 odd 4 875.2.bb.a.243.18 288
5.3 odd 4 875.2.bb.b.243.1 288
5.4 even 2 875.2.bb.c.257.1 288
7.3 odd 6 inner 175.2.x.a.122.18 yes 288
25.6 even 5 875.2.bb.b.607.18 288
25.8 odd 20 inner 175.2.x.a.33.18 288
25.17 odd 20 875.2.bb.c.768.1 288
25.19 even 10 875.2.bb.a.607.1 288
35.3 even 12 875.2.bb.b.493.18 288
35.17 even 12 875.2.bb.a.493.1 288
35.24 odd 6 875.2.bb.c.507.1 288
175.17 even 60 875.2.bb.c.143.1 288
175.31 odd 30 875.2.bb.b.857.1 288
175.94 odd 30 875.2.bb.a.857.18 288
175.108 even 60 inner 175.2.x.a.108.18 yes 288
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
175.2.x.a.33.18 288 25.8 odd 20 inner
175.2.x.a.47.18 yes 288 1.1 even 1 trivial
175.2.x.a.108.18 yes 288 175.108 even 60 inner
175.2.x.a.122.18 yes 288 7.3 odd 6 inner
875.2.bb.a.243.18 288 5.2 odd 4
875.2.bb.a.493.1 288 35.17 even 12
875.2.bb.a.607.1 288 25.19 even 10
875.2.bb.a.857.18 288 175.94 odd 30
875.2.bb.b.243.1 288 5.3 odd 4
875.2.bb.b.493.18 288 35.3 even 12
875.2.bb.b.607.18 288 25.6 even 5
875.2.bb.b.857.1 288 175.31 odd 30
875.2.bb.c.143.1 288 175.17 even 60
875.2.bb.c.257.1 288 5.4 even 2
875.2.bb.c.507.1 288 35.24 odd 6
875.2.bb.c.768.1 288 25.17 odd 20