Properties

Label 125.2.h.a.9.3
Level $125$
Weight $2$
Character 125.9
Analytic conductor $0.998$
Analytic rank $0$
Dimension $240$
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] = [125,2,Mod(4,125)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(125, base_ring=CyclotomicField(50))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("125.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 125 = 5^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 125.h (of order \(50\), degree \(20\), 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: \(0.998130025266\)
Analytic rank: \(0\)
Dimension: \(240\)
Relative dimension: \(12\) over \(\Q(\zeta_{50})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{50}]$

Embedding invariants

Embedding label 9.3
Character \(\chi\) \(=\) 125.9
Dual form 125.2.h.a.14.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.61529 - 0.760100i) q^{2} +(2.82599 - 0.177796i) q^{3} +(0.756578 + 0.914545i) q^{4} +(2.02990 - 0.937822i) q^{5} +(-4.69996 - 1.86084i) q^{6} +(-1.81397 + 0.589394i) q^{7} +(0.360971 + 1.40589i) q^{8} +(4.97829 - 0.628904i) q^{9} +O(q^{10})\) \(q+(-1.61529 - 0.760100i) q^{2} +(2.82599 - 0.177796i) q^{3} +(0.756578 + 0.914545i) q^{4} +(2.02990 - 0.937822i) q^{5} +(-4.69996 - 1.86084i) q^{6} +(-1.81397 + 0.589394i) q^{7} +(0.360971 + 1.40589i) q^{8} +(4.97829 - 0.628904i) q^{9} +(-3.99172 - 0.0280665i) q^{10} +(-1.99320 + 4.23577i) q^{11} +(2.30069 + 2.44998i) q^{12} +(-0.745123 - 5.89826i) q^{13} +(3.37809 + 0.426752i) q^{14} +(5.56974 - 3.01119i) q^{15} +(0.930359 - 4.87711i) q^{16} +(-2.37257 - 1.96276i) q^{17} +(-8.51943 - 2.76813i) q^{18} +(-0.199064 + 3.16404i) q^{19} +(2.39346 + 1.14690i) q^{20} +(-5.02147 + 1.98814i) q^{21} +(6.43921 - 5.32698i) q^{22} +(0.681123 + 1.23896i) q^{23} +(1.27006 + 3.90886i) q^{24} +(3.24098 - 3.80737i) q^{25} +(-3.27967 + 10.0938i) q^{26} +(5.61251 - 1.07064i) q^{27} +(-1.91143 - 1.21303i) q^{28} +(-4.62347 + 7.28543i) q^{29} +(-11.2856 + 0.630399i) q^{30} +(-1.28830 + 1.55728i) q^{31} +(-3.50357 + 4.82225i) q^{32} +(-4.87967 + 12.3246i) q^{33} +(2.34050 + 4.97382i) q^{34} +(-3.12942 + 2.89759i) q^{35} +(4.34162 + 4.07705i) q^{36} +(-3.43526 - 0.655311i) q^{37} +(2.72653 - 4.95954i) q^{38} +(-3.15440 - 16.5360i) q^{39} +(2.05121 + 2.51529i) q^{40} +(4.91500 + 2.70204i) q^{41} +(9.62234 + 0.605386i) q^{42} +(0.193730 + 0.266646i) q^{43} +(-5.38181 + 1.38181i) q^{44} +(9.51562 - 5.94536i) q^{45} +(-0.158482 - 2.51901i) q^{46} +(0.480975 - 1.87327i) q^{47} +(1.76206 - 13.9481i) q^{48} +(-2.72003 + 1.97622i) q^{49} +(-8.12912 + 3.68656i) q^{50} +(-7.05383 - 5.12491i) q^{51} +(4.83048 - 5.14394i) q^{52} +(-0.374304 - 0.945383i) q^{53} +(-9.87966 - 2.53667i) q^{54} +(-0.0735983 + 10.4674i) q^{55} +(-1.48341 - 2.33748i) q^{56} +8.97694i q^{57} +(13.0059 - 8.25381i) q^{58} +(1.07044 - 1.00521i) q^{59} +(6.96781 + 2.81558i) q^{60} +(9.67774 - 5.32038i) q^{61} +(3.26467 - 1.53624i) q^{62} +(-8.65978 + 4.07498i) q^{63} +(0.622862 - 0.342421i) q^{64} +(-7.04404 - 11.2741i) q^{65} +(17.2501 - 16.1989i) q^{66} +(0.882343 - 0.559952i) q^{67} -3.65480i q^{68} +(2.14513 + 3.38019i) q^{69} +(7.25740 - 2.30179i) q^{70} +(5.55503 + 1.42629i) q^{71} +(2.68119 + 6.77190i) q^{72} +(-5.92827 + 6.31297i) q^{73} +(5.05086 + 3.66967i) q^{74} +(8.48205 - 11.3358i) q^{75} +(-3.04426 + 2.21179i) q^{76} +(1.11907 - 8.85832i) q^{77} +(-7.47370 + 29.1081i) q^{78} +(-1.07167 - 17.0337i) q^{79} +(-2.68533 - 10.7726i) q^{80} +(1.08994 - 0.279850i) q^{81} +(-5.88535 - 8.10049i) q^{82} +(8.34277 + 0.524883i) q^{83} +(-5.61737 - 3.08818i) q^{84} +(-6.65679 - 1.75915i) q^{85} +(-0.110253 - 0.577966i) q^{86} +(-11.7706 + 21.4106i) q^{87} +(-6.67450 - 1.27323i) q^{88} +(6.29473 + 5.91115i) q^{89} +(-19.8896 + 2.37069i) q^{90} +(4.82803 + 10.2601i) q^{91} +(-0.617761 + 1.56029i) q^{92} +(-3.36384 + 4.62993i) q^{93} +(-2.20079 + 2.66030i) q^{94} +(2.56322 + 6.60936i) q^{95} +(-9.04368 + 14.2506i) q^{96} +(-8.57031 - 5.43888i) q^{97} +(5.89577 - 1.12468i) q^{98} +(-7.25883 + 22.3404i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 240 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 25 q^{5} - 20 q^{6} - 25 q^{7} - 35 q^{8} - 20 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 240 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 25 q^{5} - 20 q^{6} - 25 q^{7} - 35 q^{8} - 20 q^{9} - 20 q^{10} - 25 q^{11} + 60 q^{12} - 20 q^{13} - 30 q^{14} - 40 q^{15} - 40 q^{16} - 15 q^{17} - 25 q^{18} - 10 q^{19} - 10 q^{20} - 35 q^{21} - 25 q^{22} + 70 q^{23} + 15 q^{24} + 35 q^{25} - 45 q^{26} - 20 q^{27} - 10 q^{28} - 10 q^{29} - 40 q^{30} - 30 q^{31} - 25 q^{32} - 35 q^{33} - 20 q^{34} - 40 q^{35} + 170 q^{36} - 55 q^{37} - 40 q^{38} - 35 q^{40} - 35 q^{41} - 10 q^{42} - 25 q^{43} + 15 q^{44} + 140 q^{45} - 40 q^{46} + 100 q^{47} + 5 q^{48} + 35 q^{49} - 10 q^{50} - 55 q^{51} - 15 q^{52} - 15 q^{53} + 30 q^{54} - 15 q^{55} + 65 q^{56} + 255 q^{58} + 5 q^{59} + 135 q^{60} - 40 q^{61} + 5 q^{62} - 35 q^{63} + 25 q^{64} - 30 q^{65} - 95 q^{66} + 105 q^{67} - 10 q^{69} - 55 q^{70} + 45 q^{71} - 30 q^{72} - 40 q^{73} + 35 q^{74} - 15 q^{75} - 65 q^{76} - 35 q^{77} + 100 q^{78} + 430 q^{80} - 95 q^{81} + 175 q^{82} + 20 q^{83} + 45 q^{84} - 10 q^{85} - 80 q^{86} - 5 q^{87} - 5 q^{88} + 30 q^{89} + 65 q^{91} - 55 q^{92} + 275 q^{93} + 60 q^{94} + 10 q^{95} - 135 q^{96} + 35 q^{97} - 15 q^{98} + 45 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/125\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{7}{50}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.61529 0.760100i −1.14219 0.537472i −0.240837 0.970566i \(-0.577422\pi\)
−0.901349 + 0.433094i \(0.857422\pi\)
\(3\) 2.82599 0.177796i 1.63159 0.102651i 0.779623 0.626249i \(-0.215411\pi\)
0.851965 + 0.523598i \(0.175411\pi\)
\(4\) 0.756578 + 0.914545i 0.378289 + 0.457273i
\(5\) 2.02990 0.937822i 0.907798 0.419407i
\(6\) −4.69996 1.86084i −1.91875 0.759687i
\(7\) −1.81397 + 0.589394i −0.685615 + 0.222770i −0.631052 0.775740i \(-0.717377\pi\)
−0.0545631 + 0.998510i \(0.517377\pi\)
\(8\) 0.360971 + 1.40589i 0.127623 + 0.497057i
\(9\) 4.97829 0.628904i 1.65943 0.209635i
\(10\) −3.99172 0.0280665i −1.26229 0.00887539i
\(11\) −1.99320 + 4.23577i −0.600972 + 1.27713i 0.340564 + 0.940221i \(0.389382\pi\)
−0.941537 + 0.336910i \(0.890618\pi\)
\(12\) 2.30069 + 2.44998i 0.664151 + 0.707249i
\(13\) −0.745123 5.89826i −0.206660 1.63588i −0.664813 0.747009i \(-0.731489\pi\)
0.458153 0.888873i \(-0.348511\pi\)
\(14\) 3.37809 + 0.426752i 0.902833 + 0.114054i
\(15\) 5.56974 3.01119i 1.43810 0.777486i
\(16\) 0.930359 4.87711i 0.232590 1.21928i
\(17\) −2.37257 1.96276i −0.575432 0.476039i 0.303601 0.952799i \(-0.401811\pi\)
−0.879033 + 0.476760i \(0.841811\pi\)
\(18\) −8.51943 2.76813i −2.00805 0.652455i
\(19\) −0.199064 + 3.16404i −0.0456685 + 0.725880i 0.906860 + 0.421431i \(0.138472\pi\)
−0.952529 + 0.304449i \(0.901528\pi\)
\(20\) 2.39346 + 1.14690i 0.535193 + 0.256454i
\(21\) −5.02147 + 1.98814i −1.09577 + 0.433848i
\(22\) 6.43921 5.32698i 1.37284 1.13572i
\(23\) 0.681123 + 1.23896i 0.142024 + 0.258341i 0.937746 0.347321i \(-0.112909\pi\)
−0.795722 + 0.605662i \(0.792909\pi\)
\(24\) 1.27006 + 3.90886i 0.259251 + 0.797892i
\(25\) 3.24098 3.80737i 0.648196 0.761474i
\(26\) −3.27967 + 10.0938i −0.643197 + 1.97956i
\(27\) 5.61251 1.07064i 1.08013 0.206046i
\(28\) −1.91143 1.21303i −0.361227 0.229242i
\(29\) −4.62347 + 7.28543i −0.858557 + 1.35287i 0.0760188 + 0.997106i \(0.475779\pi\)
−0.934576 + 0.355763i \(0.884221\pi\)
\(30\) −11.2856 + 0.630399i −2.06046 + 0.115095i
\(31\) −1.28830 + 1.55728i −0.231385 + 0.279696i −0.873408 0.486989i \(-0.838095\pi\)
0.642023 + 0.766685i \(0.278095\pi\)
\(32\) −3.50357 + 4.82225i −0.619349 + 0.852461i
\(33\) −4.87967 + 12.3246i −0.849441 + 2.14544i
\(34\) 2.34050 + 4.97382i 0.401393 + 0.853004i
\(35\) −3.12942 + 2.89759i −0.528969 + 0.489782i
\(36\) 4.34162 + 4.07705i 0.723604 + 0.679509i
\(37\) −3.43526 0.655311i −0.564754 0.107733i −0.102905 0.994691i \(-0.532814\pi\)
−0.461849 + 0.886959i \(0.652814\pi\)
\(38\) 2.72653 4.95954i 0.442302 0.804544i
\(39\) −3.15440 16.5360i −0.505109 2.64787i
\(40\) 2.05121 + 2.51529i 0.324325 + 0.397702i
\(41\) 4.91500 + 2.70204i 0.767594 + 0.421988i 0.816888 0.576796i \(-0.195697\pi\)
−0.0492943 + 0.998784i \(0.515697\pi\)
\(42\) 9.62234 + 0.605386i 1.48476 + 0.0934131i
\(43\) 0.193730 + 0.266646i 0.0295435 + 0.0406632i 0.823533 0.567268i \(-0.192000\pi\)
−0.793990 + 0.607931i \(0.792000\pi\)
\(44\) −5.38181 + 1.38181i −0.811338 + 0.208316i
\(45\) 9.51562 5.94536i 1.41850 0.886282i
\(46\) −0.158482 2.51901i −0.0233670 0.371407i
\(47\) 0.480975 1.87327i 0.0701574 0.273245i −0.923820 0.382826i \(-0.874951\pi\)
0.993978 + 0.109581i \(0.0349509\pi\)
\(48\) 1.76206 13.9481i 0.254331 2.01324i
\(49\) −2.72003 + 1.97622i −0.388575 + 0.282316i
\(50\) −8.12912 + 3.68656i −1.14963 + 0.521358i
\(51\) −7.05383 5.12491i −0.987734 0.717631i
\(52\) 4.83048 5.14394i 0.669867 0.713336i
\(53\) −0.374304 0.945383i −0.0514146 0.129858i 0.901799 0.432155i \(-0.142247\pi\)
−0.953214 + 0.302297i \(0.902247\pi\)
\(54\) −9.87966 2.53667i −1.34445 0.345196i
\(55\) −0.0735983 + 10.4674i −0.00992399 + 1.41143i
\(56\) −1.48341 2.33748i −0.198229 0.312359i
\(57\) 8.97694i 1.18903i
\(58\) 13.0059 8.25381i 1.70776 1.08378i
\(59\) 1.07044 1.00521i 0.139359 0.130867i −0.611733 0.791064i \(-0.709527\pi\)
0.751092 + 0.660197i \(0.229527\pi\)
\(60\) 6.96781 + 2.81558i 0.899540 + 0.363490i
\(61\) 9.67774 5.32038i 1.23911 0.681205i 0.278854 0.960333i \(-0.410045\pi\)
0.960254 + 0.279128i \(0.0900454\pi\)
\(62\) 3.26467 1.53624i 0.414613 0.195102i
\(63\) −8.65978 + 4.07498i −1.09103 + 0.513399i
\(64\) 0.622862 0.342421i 0.0778577 0.0428027i
\(65\) −7.04404 11.2741i −0.873706 1.39838i
\(66\) 17.2501 16.1989i 2.12334 1.99394i
\(67\) 0.882343 0.559952i 0.107795 0.0684090i −0.480836 0.876810i \(-0.659667\pi\)
0.588632 + 0.808401i \(0.299667\pi\)
\(68\) 3.65480i 0.443210i
\(69\) 2.14513 + 3.38019i 0.258244 + 0.406927i
\(70\) 7.25740 2.30179i 0.867425 0.275116i
\(71\) 5.55503 + 1.42629i 0.659261 + 0.169269i 0.563476 0.826133i \(-0.309464\pi\)
0.0957849 + 0.995402i \(0.469464\pi\)
\(72\) 2.68119 + 6.77190i 0.315981 + 0.798077i
\(73\) −5.92827 + 6.31297i −0.693852 + 0.738877i −0.975345 0.220686i \(-0.929170\pi\)
0.281493 + 0.959563i \(0.409170\pi\)
\(74\) 5.05086 + 3.66967i 0.587151 + 0.426590i
\(75\) 8.48205 11.3358i 0.979423 1.30895i
\(76\) −3.04426 + 2.21179i −0.349201 + 0.253709i
\(77\) 1.11907 8.85832i 0.127529 1.00950i
\(78\) −7.47370 + 29.1081i −0.846229 + 3.29585i
\(79\) −1.07167 17.0337i −0.120572 1.91644i −0.339337 0.940665i \(-0.610203\pi\)
0.218765 0.975778i \(-0.429797\pi\)
\(80\) −2.68533 10.7726i −0.300229 1.20441i
\(81\) 1.08994 0.279850i 0.121105 0.0310944i
\(82\) −5.88535 8.10049i −0.649928 0.894549i
\(83\) 8.34277 + 0.524883i 0.915738 + 0.0576134i 0.513662 0.857993i \(-0.328289\pi\)
0.402076 + 0.915606i \(0.368289\pi\)
\(84\) −5.61737 3.08818i −0.612906 0.336948i
\(85\) −6.65679 1.75915i −0.722030 0.190807i
\(86\) −0.110253 0.577966i −0.0118889 0.0623237i
\(87\) −11.7706 + 21.4106i −1.26194 + 2.29546i
\(88\) −6.67450 1.27323i −0.711505 0.135727i
\(89\) 6.29473 + 5.91115i 0.667240 + 0.626580i 0.942269 0.334856i \(-0.108688\pi\)
−0.275029 + 0.961436i \(0.588688\pi\)
\(90\) −19.8896 + 2.37069i −2.09655 + 0.249892i
\(91\) 4.82803 + 10.2601i 0.506115 + 1.07555i
\(92\) −0.617761 + 1.56029i −0.0644061 + 0.162671i
\(93\) −3.36384 + 4.62993i −0.348814 + 0.480101i
\(94\) −2.20079 + 2.66030i −0.226994 + 0.274389i
\(95\) 2.56322 + 6.60936i 0.262981 + 0.678106i
\(96\) −9.04368 + 14.2506i −0.923017 + 1.45444i
\(97\) −8.57031 5.43888i −0.870183 0.552235i 0.0241139 0.999709i \(-0.492324\pi\)
−0.894297 + 0.447474i \(0.852324\pi\)
\(98\) 5.89577 1.12468i 0.595562 0.113610i
\(99\) −7.25883 + 22.3404i −0.729540 + 2.24529i
\(100\) 5.93406 + 0.0834509i 0.593406 + 0.00834509i
\(101\) −2.10670 6.48376i −0.209625 0.645158i −0.999492 0.0318801i \(-0.989851\pi\)
0.789867 0.613278i \(-0.210149\pi\)
\(102\) 7.49858 + 13.6399i 0.742470 + 1.35055i
\(103\) 4.79430 3.96619i 0.472396 0.390800i −0.370537 0.928818i \(-0.620826\pi\)
0.842934 + 0.538017i \(0.180826\pi\)
\(104\) 8.02333 3.17666i 0.786752 0.311497i
\(105\) −8.32855 + 8.74497i −0.812783 + 0.853422i
\(106\) −0.113975 + 1.81158i −0.0110702 + 0.175956i
\(107\) −0.443352 0.144054i −0.0428605 0.0139262i 0.287508 0.957778i \(-0.407173\pi\)
−0.330369 + 0.943852i \(0.607173\pi\)
\(108\) 5.22545 + 4.32287i 0.502820 + 0.415968i
\(109\) 0.912855 4.78536i 0.0874357 0.458354i −0.911461 0.411387i \(-0.865044\pi\)
0.998896 0.0469669i \(-0.0149555\pi\)
\(110\) 8.07519 16.8521i 0.769939 1.60678i
\(111\) −9.82455 1.24113i −0.932505 0.117803i
\(112\) 1.18690 + 9.39527i 0.112151 + 0.887770i
\(113\) −1.89427 2.01719i −0.178198 0.189761i 0.633669 0.773605i \(-0.281548\pi\)
−0.811866 + 0.583843i \(0.801548\pi\)
\(114\) 6.82338 14.5004i 0.639068 1.35809i
\(115\) 2.54454 + 1.87619i 0.237279 + 0.174955i
\(116\) −10.1609 + 1.28362i −0.943413 + 0.119181i
\(117\) −7.41888 28.8946i −0.685875 2.67131i
\(118\) −2.49314 + 0.810069i −0.229512 + 0.0745729i
\(119\) 5.46060 + 2.16200i 0.500572 + 0.198191i
\(120\) 6.24391 + 6.74349i 0.569989 + 0.615593i
\(121\) −6.95720 8.40981i −0.632473 0.764528i
\(122\) −19.6764 + 1.23794i −1.78142 + 0.112077i
\(123\) 14.3702 + 6.76209i 1.29571 + 0.609717i
\(124\) −2.39890 −0.215428
\(125\) 3.00822 10.7680i 0.269064 0.963122i
\(126\) 17.0855 1.52210
\(127\) 11.8806 + 5.59057i 1.05423 + 0.496083i 0.873183 0.487392i \(-0.162052\pi\)
0.181046 + 0.983475i \(0.442052\pi\)
\(128\) 10.6313 0.668868i 0.939687 0.0591201i
\(129\) 0.594888 + 0.719096i 0.0523770 + 0.0633129i
\(130\) 2.80878 + 23.5651i 0.246347 + 2.06680i
\(131\) −20.6504 8.17606i −1.80423 0.714346i −0.991240 0.132070i \(-0.957838\pi\)
−0.812991 0.582276i \(-0.802162\pi\)
\(132\) −14.9633 + 4.86186i −1.30239 + 0.423171i
\(133\) −1.50377 5.85679i −0.130393 0.507848i
\(134\) −1.85086 + 0.233818i −0.159890 + 0.0201988i
\(135\) 10.3888 7.43684i 0.894122 0.640061i
\(136\) 1.90299 4.04407i 0.163180 0.346776i
\(137\) 1.27068 + 1.35314i 0.108562 + 0.115606i 0.780954 0.624588i \(-0.214733\pi\)
−0.672392 + 0.740195i \(0.734733\pi\)
\(138\) −0.895741 7.09052i −0.0762505 0.603585i
\(139\) 13.2574 + 1.67480i 1.12448 + 0.142055i 0.665505 0.746394i \(-0.268216\pi\)
0.458976 + 0.888449i \(0.348216\pi\)
\(140\) −5.01763 0.669748i −0.424067 0.0566041i
\(141\) 1.02617 5.37937i 0.0864191 0.453025i
\(142\) −7.88889 6.52625i −0.662021 0.547671i
\(143\) 26.4688 + 8.60024i 2.21343 + 0.719188i
\(144\) 1.56436 24.8648i 0.130363 2.07206i
\(145\) −2.55274 + 19.1247i −0.211994 + 1.58822i
\(146\) 14.3744 5.69123i 1.18963 0.471009i
\(147\) −7.33542 + 6.06838i −0.605015 + 0.500512i
\(148\) −1.99973 3.63750i −0.164377 0.299000i
\(149\) −5.79691 17.8411i −0.474901 1.46160i −0.846091 0.533039i \(-0.821050\pi\)
0.371189 0.928557i \(-0.378950\pi\)
\(150\) −22.3174 + 11.8635i −1.82221 + 0.968652i
\(151\) 1.12983 3.47725i 0.0919441 0.282975i −0.894501 0.447066i \(-0.852469\pi\)
0.986445 + 0.164091i \(0.0524690\pi\)
\(152\) −4.52014 + 0.862263i −0.366632 + 0.0699388i
\(153\) −13.0457 8.27906i −1.05468 0.669322i
\(154\) −8.54083 + 13.4582i −0.688240 + 1.08449i
\(155\) −1.15466 + 4.36932i −0.0927442 + 0.350952i
\(156\) 12.7363 15.3956i 1.01972 1.23263i
\(157\) 11.1775 15.3845i 0.892060 1.22781i −0.0808728 0.996724i \(-0.525771\pi\)
0.972932 0.231090i \(-0.0742292\pi\)
\(158\) −11.2163 + 28.3290i −0.892318 + 2.25374i
\(159\) −1.22587 2.60510i −0.0972175 0.206598i
\(160\) −2.58948 + 13.0744i −0.204716 + 1.03362i
\(161\) −1.96577 1.84598i −0.154924 0.145484i
\(162\) −1.97329 0.376426i −0.155037 0.0295748i
\(163\) −4.33630 + 7.88770i −0.339645 + 0.617812i −0.989878 0.141923i \(-0.954671\pi\)
0.650233 + 0.759735i \(0.274671\pi\)
\(164\) 1.24744 + 6.53930i 0.0974085 + 0.510633i
\(165\) 1.65309 + 29.5940i 0.128693 + 2.30389i
\(166\) −13.0771 7.18918i −1.01498 0.557989i
\(167\) −11.3761 0.715723i −0.880308 0.0553843i −0.383800 0.923416i \(-0.625385\pi\)
−0.496508 + 0.868032i \(0.665385\pi\)
\(168\) −4.60771 6.34197i −0.355492 0.489293i
\(169\) −21.6427 + 5.55689i −1.66482 + 0.427453i
\(170\) 9.41555 + 7.90138i 0.722140 + 0.606008i
\(171\) 0.998876 + 15.8767i 0.0763859 + 1.21412i
\(172\) −0.0972884 + 0.378913i −0.00741817 + 0.0288919i
\(173\) 1.32856 10.5166i 0.101008 0.799563i −0.857497 0.514489i \(-0.827982\pi\)
0.958505 0.285074i \(-0.0920183\pi\)
\(174\) 35.2872 25.6376i 2.67511 1.94358i
\(175\) −3.63499 + 8.81666i −0.274779 + 0.666476i
\(176\) 18.8039 + 13.6618i 1.41740 + 1.02980i
\(177\) 2.84633 3.03104i 0.213944 0.227827i
\(178\) −5.67478 14.3329i −0.425343 1.07429i
\(179\) −10.4817 2.69125i −0.783441 0.201153i −0.164276 0.986414i \(-0.552529\pi\)
−0.619165 + 0.785261i \(0.712529\pi\)
\(180\) 12.6366 + 4.20434i 0.941877 + 0.313373i
\(181\) 8.03623 + 12.6631i 0.597328 + 0.941239i 0.999668 + 0.0257484i \(0.00819688\pi\)
−0.402340 + 0.915490i \(0.631803\pi\)
\(182\) 20.2428i 1.50050i
\(183\) 26.4033 16.7560i 1.95179 1.23864i
\(184\) −1.49597 + 1.40481i −0.110285 + 0.103564i
\(185\) −7.58780 + 1.89145i −0.557866 + 0.139062i
\(186\) 8.95280 4.92184i 0.656451 0.360887i
\(187\) 13.0428 6.13747i 0.953783 0.448816i
\(188\) 2.07709 0.977403i 0.151487 0.0712845i
\(189\) −9.54988 + 5.25009i −0.694652 + 0.381888i
\(190\) 0.883413 12.6244i 0.0640895 0.915869i
\(191\) −10.4640 + 9.82636i −0.757149 + 0.711010i −0.963571 0.267453i \(-0.913818\pi\)
0.206422 + 0.978463i \(0.433818\pi\)
\(192\) 1.69932 1.07842i 0.122638 0.0778285i
\(193\) 16.1588i 1.16313i 0.813498 + 0.581567i \(0.197560\pi\)
−0.813498 + 0.581567i \(0.802440\pi\)
\(194\) 9.70948 + 15.2997i 0.697100 + 1.09845i
\(195\) −21.9109 30.6081i −1.56907 2.19189i
\(196\) −3.86525 0.992427i −0.276089 0.0708877i
\(197\) 3.01074 + 7.60425i 0.214506 + 0.541780i 0.996693 0.0812638i \(-0.0258956\pi\)
−0.782187 + 0.623044i \(0.785896\pi\)
\(198\) 28.7061 30.5689i 2.04005 2.17244i
\(199\) −0.164621 0.119604i −0.0116697 0.00847853i 0.581935 0.813235i \(-0.302296\pi\)
−0.593605 + 0.804757i \(0.702296\pi\)
\(200\) 6.52264 + 3.18211i 0.461220 + 0.225009i
\(201\) 2.39394 1.73930i 0.168855 0.122681i
\(202\) −1.52536 + 12.0745i −0.107324 + 0.849558i
\(203\) 4.09284 15.9406i 0.287261 1.11881i
\(204\) −0.649811 10.3284i −0.0454958 0.723136i
\(205\) 12.5110 + 0.875479i 0.873805 + 0.0611461i
\(206\) −10.7589 + 2.76242i −0.749609 + 0.192467i
\(207\) 4.17001 + 5.73953i 0.289836 + 0.398925i
\(208\) −29.4597 1.85345i −2.04266 0.128513i
\(209\) −13.0053 7.14975i −0.899599 0.494558i
\(210\) 20.1001 7.79517i 1.38704 0.537918i
\(211\) 3.55644 + 18.6435i 0.244835 + 1.28347i 0.866100 + 0.499871i \(0.166619\pi\)
−0.621264 + 0.783601i \(0.713381\pi\)
\(212\) 0.581406 1.05757i 0.0399311 0.0726344i
\(213\) 15.9521 + 3.04302i 1.09302 + 0.208504i
\(214\) 0.606649 + 0.569681i 0.0414697 + 0.0389426i
\(215\) 0.643319 + 0.359581i 0.0438740 + 0.0245232i
\(216\) 3.53116 + 7.50410i 0.240265 + 0.510589i
\(217\) 1.41907 3.58417i 0.0963331 0.243310i
\(218\) −5.11188 + 7.03590i −0.346220 + 0.476531i
\(219\) −15.6308 + 18.8944i −1.05623 + 1.27677i
\(220\) −9.62863 + 7.85212i −0.649162 + 0.529390i
\(221\) −9.80900 + 15.4565i −0.659825 + 1.03972i
\(222\) 14.9262 + 9.47243i 1.00178 + 0.635748i
\(223\) −16.0170 + 3.05541i −1.07258 + 0.204606i −0.693280 0.720668i \(-0.743835\pi\)
−0.379300 + 0.925274i \(0.623835\pi\)
\(224\) 3.51316 10.8124i 0.234733 0.722433i
\(225\) 13.7400 20.9924i 0.916003 1.39950i
\(226\) 1.52653 + 4.69819i 0.101544 + 0.312519i
\(227\) −2.52663 4.59592i −0.167698 0.305042i 0.779082 0.626921i \(-0.215685\pi\)
−0.946781 + 0.321880i \(0.895685\pi\)
\(228\) −8.20982 + 6.79176i −0.543709 + 0.449795i
\(229\) 10.4511 4.13788i 0.690628 0.273439i 0.00351947 0.999994i \(-0.498880\pi\)
0.687108 + 0.726555i \(0.258880\pi\)
\(230\) −2.68408 4.96470i −0.176983 0.327363i
\(231\) 1.58750 25.2325i 0.104450 1.66018i
\(232\) −11.9114 3.87026i −0.782025 0.254095i
\(233\) −5.35361 4.42889i −0.350726 0.290146i 0.445333 0.895365i \(-0.353085\pi\)
−0.796059 + 0.605219i \(0.793085\pi\)
\(234\) −9.97913 + 52.3124i −0.652356 + 3.41977i
\(235\) −0.780467 4.25362i −0.0509121 0.277476i
\(236\) 1.72918 + 0.218446i 0.112560 + 0.0142196i
\(237\) −6.05707 47.9466i −0.393449 3.11447i
\(238\) −7.17714 7.64287i −0.465225 0.495414i
\(239\) −1.01622 + 2.15958i −0.0657338 + 0.139691i −0.934994 0.354663i \(-0.884596\pi\)
0.869260 + 0.494355i \(0.164596\pi\)
\(240\) −9.50405 29.9657i −0.613484 1.93428i
\(241\) 27.4463 3.46728i 1.76797 0.223347i 0.827089 0.562071i \(-0.189995\pi\)
0.940886 + 0.338724i \(0.109995\pi\)
\(242\) 4.84563 + 18.8725i 0.311489 + 1.21317i
\(243\) −13.2718 + 4.31227i −0.851386 + 0.276632i
\(244\) 12.1877 + 4.82545i 0.780237 + 0.308918i
\(245\) −3.66804 + 6.56242i −0.234342 + 0.419258i
\(246\) −18.0722 21.8455i −1.15224 1.39282i
\(247\) 18.8106 1.18347i 1.19689 0.0753021i
\(248\) −2.65441 1.24907i −0.168555 0.0793159i
\(249\) 23.6699 1.50002
\(250\) −13.0440 + 15.1070i −0.824972 + 0.955451i
\(251\) 26.8424 1.69428 0.847138 0.531373i \(-0.178324\pi\)
0.847138 + 0.531373i \(0.178324\pi\)
\(252\) −10.2785 4.83672i −0.647488 0.304685i
\(253\) −6.60556 + 0.415586i −0.415288 + 0.0261277i
\(254\) −14.9412 18.0608i −0.937495 1.13324i
\(255\) −19.1248 3.78781i −1.19764 0.237202i
\(256\) −19.0029 7.52378i −1.18768 0.470236i
\(257\) 15.5390 5.04894i 0.969298 0.314944i 0.218765 0.975777i \(-0.429797\pi\)
0.750533 + 0.660833i \(0.229797\pi\)
\(258\) −0.414335 1.61373i −0.0257954 0.100466i
\(259\) 6.61769 0.836009i 0.411203 0.0519471i
\(260\) 4.98129 14.9718i 0.308926 0.928512i
\(261\) −18.4351 + 39.1767i −1.14111 + 2.42497i
\(262\) 27.1418 + 28.9031i 1.67683 + 1.78564i
\(263\) −0.220004 1.74151i −0.0135660 0.107386i 0.983878 0.178843i \(-0.0572353\pi\)
−0.997444 + 0.0714565i \(0.977235\pi\)
\(264\) −19.0885 2.41144i −1.17482 0.148414i
\(265\) −1.64640 1.56800i −0.101138 0.0963216i
\(266\) −2.02272 + 10.6035i −0.124021 + 0.650139i
\(267\) 18.8399 + 15.5857i 1.15298 + 0.953828i
\(268\) 1.17966 + 0.383296i 0.0720593 + 0.0234135i
\(269\) −0.841568 + 13.3763i −0.0513113 + 0.815570i 0.885261 + 0.465095i \(0.153980\pi\)
−0.936572 + 0.350475i \(0.886020\pi\)
\(270\) −22.4337 + 4.11619i −1.36527 + 0.250503i
\(271\) 10.5972 4.19573i 0.643734 0.254872i −0.0234961 0.999724i \(-0.507480\pi\)
0.667230 + 0.744852i \(0.267480\pi\)
\(272\) −11.7799 + 9.74521i −0.714263 + 0.590890i
\(273\) 15.4682 + 28.1365i 0.936177 + 1.70290i
\(274\) −1.02401 3.15156i −0.0618624 0.190393i
\(275\) 9.66721 + 21.3169i 0.582954 + 1.28546i
\(276\) −1.46838 + 4.51920i −0.0883859 + 0.272024i
\(277\) −6.27192 + 1.19643i −0.376843 + 0.0718867i −0.372323 0.928103i \(-0.621439\pi\)
−0.00451992 + 0.999990i \(0.501439\pi\)
\(278\) −20.1416 12.7823i −1.20802 0.766630i
\(279\) −5.43413 + 8.56282i −0.325333 + 0.512642i
\(280\) −5.20332 3.35368i −0.310958 0.200421i
\(281\) 10.9894 13.2839i 0.655574 0.792453i −0.333042 0.942912i \(-0.608075\pi\)
0.988616 + 0.150459i \(0.0480752\pi\)
\(282\) −5.74643 + 7.90928i −0.342195 + 0.470991i
\(283\) −1.19987 + 3.03053i −0.0713251 + 0.180147i −0.961066 0.276320i \(-0.910885\pi\)
0.889741 + 0.456466i \(0.150885\pi\)
\(284\) 2.89840 + 6.15942i 0.171989 + 0.365494i
\(285\) 8.41878 + 18.2223i 0.498685 + 1.07940i
\(286\) −36.2179 34.0109i −2.14161 2.01111i
\(287\) −10.5082 2.00455i −0.620280 0.118325i
\(288\) −14.4090 + 26.2099i −0.849061 + 1.54444i
\(289\) −1.40883 7.38533i −0.0828722 0.434431i
\(290\) 18.6601 28.9516i 1.09576 1.70010i
\(291\) −25.1867 13.8465i −1.47647 0.811695i
\(292\) −10.2587 0.645423i −0.600345 0.0377705i
\(293\) 14.5527 + 20.0301i 0.850180 + 1.17017i 0.983823 + 0.179143i \(0.0573324\pi\)
−0.133643 + 0.991030i \(0.542668\pi\)
\(294\) 16.4614 4.22658i 0.960051 0.246499i
\(295\) 1.23018 3.04436i 0.0716236 0.177249i
\(296\) −0.318735 5.06615i −0.0185261 0.294464i
\(297\) −6.65186 + 25.9073i −0.385980 + 1.50329i
\(298\) −4.19727 + 33.2248i −0.243141 + 1.92466i
\(299\) 6.80018 4.94062i 0.393265 0.285723i
\(300\) 16.7845 0.819224i 0.969052 0.0472979i
\(301\) −0.508579 0.369504i −0.0293140 0.0212979i
\(302\) −4.46807 + 4.75801i −0.257108 + 0.273793i
\(303\) −7.10631 17.9485i −0.408247 1.03111i
\(304\) 15.2462 + 3.91455i 0.874428 + 0.224515i
\(305\) 14.6553 19.8758i 0.839158 1.13809i
\(306\) 14.7798 + 23.2892i 0.844902 + 1.33135i
\(307\) 21.7794i 1.24302i 0.783408 + 0.621508i \(0.213480\pi\)
−0.783408 + 0.621508i \(0.786520\pi\)
\(308\) 8.94799 5.67857i 0.509859 0.323567i
\(309\) 12.8435 12.0608i 0.730641 0.686117i
\(310\) 5.18623 6.18009i 0.294558 0.351005i
\(311\) −12.6490 + 6.95386i −0.717260 + 0.394317i −0.798192 0.602403i \(-0.794210\pi\)
0.0809324 + 0.996720i \(0.474210\pi\)
\(312\) 22.1091 10.4037i 1.25168 0.588996i
\(313\) 7.44318 3.50249i 0.420713 0.197973i −0.203757 0.979022i \(-0.565315\pi\)
0.624470 + 0.781049i \(0.285315\pi\)
\(314\) −29.7487 + 16.3545i −1.67881 + 0.922936i
\(315\) −13.7569 + 16.3931i −0.775111 + 0.923648i
\(316\) 14.7673 13.8674i 0.830726 0.780103i
\(317\) −21.8783 + 13.8844i −1.22881 + 0.779825i −0.981934 0.189223i \(-0.939403\pi\)
−0.246873 + 0.969048i \(0.579403\pi\)
\(318\) 5.13978i 0.288225i
\(319\) −21.6439 34.1053i −1.21182 1.90953i
\(320\) 0.943216 1.27921i 0.0527274 0.0715103i
\(321\) −1.27852 0.328269i −0.0713602 0.0183222i
\(322\) 1.77217 + 4.47599i 0.0987591 + 0.249437i
\(323\) 6.68254 7.11618i 0.371826 0.395955i
\(324\) 1.08056 + 0.785074i 0.0600312 + 0.0436152i
\(325\) −24.8718 16.2792i −1.37964 0.903006i
\(326\) 12.9998 9.44494i 0.719995 0.523107i
\(327\) 1.72890 13.6857i 0.0956086 0.756820i
\(328\) −2.02460 + 7.88531i −0.111790 + 0.435393i
\(329\) 0.231623 + 3.68154i 0.0127698 + 0.202970i
\(330\) 19.8242 49.0596i 1.09129 2.70064i
\(331\) 15.9350 4.09141i 0.875866 0.224884i 0.216114 0.976368i \(-0.430662\pi\)
0.659751 + 0.751484i \(0.270662\pi\)
\(332\) 5.83193 + 8.02696i 0.320068 + 0.440536i
\(333\) −17.5139 1.10188i −0.959753 0.0603826i
\(334\) 17.8317 + 9.80307i 0.975708 + 0.536400i
\(335\) 1.26593 1.96413i 0.0691652 0.107312i
\(336\) 5.02461 + 26.3400i 0.274115 + 1.43696i
\(337\) 1.91022 3.47467i 0.104056 0.189277i −0.819153 0.573575i \(-0.805556\pi\)
0.923209 + 0.384297i \(0.125556\pi\)
\(338\) 39.1831 + 7.47457i 2.13128 + 0.406563i
\(339\) −5.71184 5.36377i −0.310224 0.291320i
\(340\) −3.42755 7.41887i −0.185885 0.402345i
\(341\) −4.02845 8.56090i −0.218153 0.463599i
\(342\) 10.4544 26.4048i 0.565308 1.42781i
\(343\) 11.6169 15.9893i 0.627255 0.863342i
\(344\) −0.304944 + 0.368614i −0.0164415 + 0.0198744i
\(345\) 7.52442 + 4.84969i 0.405101 + 0.261098i
\(346\) −10.1397 + 15.9776i −0.545113 + 0.858961i
\(347\) −3.32910 2.11271i −0.178715 0.113416i 0.443460 0.896294i \(-0.353751\pi\)
−0.622175 + 0.782878i \(0.713751\pi\)
\(348\) −28.4863 + 5.43406i −1.52703 + 0.291296i
\(349\) −6.17378 + 19.0010i −0.330475 + 1.01710i 0.638433 + 0.769677i \(0.279583\pi\)
−0.968908 + 0.247420i \(0.920417\pi\)
\(350\) 12.5731 11.4785i 0.672062 0.613554i
\(351\) −10.4969 32.3063i −0.560286 1.72438i
\(352\) −13.4426 24.4520i −0.716493 1.30330i
\(353\) −15.7631 + 13.0404i −0.838987 + 0.694071i −0.954167 0.299274i \(-0.903256\pi\)
0.115180 + 0.993345i \(0.463256\pi\)
\(354\) −6.90156 + 2.73252i −0.366814 + 0.145232i
\(355\) 12.6137 2.31441i 0.669468 0.122836i
\(356\) −0.643558 + 10.2291i −0.0341085 + 0.542139i
\(357\) 15.8160 + 5.13893i 0.837072 + 0.271981i
\(358\) 14.8855 + 12.3143i 0.786721 + 0.650832i
\(359\) −4.61895 + 24.2134i −0.243779 + 1.27793i 0.624173 + 0.781286i \(0.285436\pi\)
−0.867952 + 0.496648i \(0.834564\pi\)
\(360\) 11.7934 + 11.2318i 0.621566 + 0.591968i
\(361\) 8.87867 + 1.12164i 0.467299 + 0.0590335i
\(362\) −3.35568 26.5629i −0.176371 1.39612i
\(363\) −21.1562 22.5291i −1.11041 1.18247i
\(364\) −5.73053 + 12.1780i −0.300361 + 0.638300i
\(365\) −6.11335 + 18.3744i −0.319987 + 0.961758i
\(366\) −55.3854 + 6.99680i −2.89504 + 0.365729i
\(367\) 4.33288 + 16.8754i 0.226174 + 0.880891i 0.975735 + 0.218955i \(0.0702648\pi\)
−0.749561 + 0.661936i \(0.769735\pi\)
\(368\) 6.67623 2.16924i 0.348023 0.113079i
\(369\) 26.1676 + 10.3605i 1.36223 + 0.539345i
\(370\) 13.6942 + 2.71224i 0.711929 + 0.141003i
\(371\) 1.23618 + 1.49428i 0.0641791 + 0.0775792i
\(372\) −6.77928 + 0.426516i −0.351489 + 0.0221138i
\(373\) −22.8054 10.7314i −1.18082 0.555652i −0.267764 0.963484i \(-0.586285\pi\)
−0.913057 + 0.407832i \(0.866285\pi\)
\(374\) −25.7330 −1.33062
\(375\) 6.58670 30.9653i 0.340136 1.59904i
\(376\) 2.80723 0.144772
\(377\) 46.4164 + 21.8419i 2.39057 + 1.12491i
\(378\) 19.4165 1.22158i 0.998676 0.0628313i
\(379\) −1.22314 1.47852i −0.0628283 0.0759464i 0.738163 0.674623i \(-0.235694\pi\)
−0.800991 + 0.598676i \(0.795694\pi\)
\(380\) −4.10528 + 7.34468i −0.210597 + 0.376774i
\(381\) 34.5684 + 13.6866i 1.77099 + 0.701185i
\(382\) 24.3715 7.91877i 1.24695 0.405160i
\(383\) −5.75142 22.4003i −0.293884 1.14460i −0.928367 0.371666i \(-0.878787\pi\)
0.634483 0.772937i \(-0.281213\pi\)
\(384\) 29.9252 3.78043i 1.52711 0.192919i
\(385\) −6.03594 19.0310i −0.307620 0.969908i
\(386\) 12.2823 26.1012i 0.625152 1.32852i
\(387\) 1.13214 + 1.20560i 0.0575498 + 0.0612843i
\(388\) −1.51000 11.9529i −0.0766586 0.606815i
\(389\) 24.2171 + 3.05933i 1.22785 + 0.155114i 0.712382 0.701792i \(-0.247617\pi\)
0.515472 + 0.856906i \(0.327617\pi\)
\(390\) 12.1274 + 66.0955i 0.614095 + 3.34688i
\(391\) 0.815766 4.27640i 0.0412551 0.216267i
\(392\) −3.76019 3.11070i −0.189918 0.157114i
\(393\) −59.8115 19.4339i −3.01709 0.980313i
\(394\) 0.916765 14.5716i 0.0461860 0.734105i
\(395\) −18.1500 33.5717i −0.913225 1.68917i
\(396\) −25.9232 + 10.2637i −1.30269 + 0.515771i
\(397\) −26.2053 + 21.6789i −1.31521 + 1.08803i −0.325407 + 0.945574i \(0.605501\pi\)
−0.989800 + 0.142461i \(0.954499\pi\)
\(398\) 0.175001 + 0.318325i 0.00877199 + 0.0159562i
\(399\) −5.29095 16.2839i −0.264879 0.815214i
\(400\) −15.5537 19.3488i −0.777685 0.967442i
\(401\) −5.57453 + 17.1566i −0.278379 + 0.856762i 0.709927 + 0.704276i \(0.248728\pi\)
−0.988306 + 0.152486i \(0.951272\pi\)
\(402\) −5.18896 + 0.989847i −0.258802 + 0.0493691i
\(403\) 10.1452 + 6.43834i 0.505368 + 0.320716i
\(404\) 4.33581 6.83214i 0.215714 0.339912i
\(405\) 1.95002 1.59024i 0.0968975 0.0790197i
\(406\) −18.7276 + 22.6378i −0.929434 + 1.12349i
\(407\) 9.62291 13.2448i 0.476990 0.656520i
\(408\) 4.65883 11.7669i 0.230646 0.582546i
\(409\) −9.52348 20.2384i −0.470906 1.00073i −0.989342 0.145609i \(-0.953486\pi\)
0.518436 0.855116i \(-0.326514\pi\)
\(410\) −19.5435 10.9238i −0.965184 0.539486i
\(411\) 3.83152 + 3.59804i 0.188995 + 0.177478i
\(412\) 7.25452 + 1.38387i 0.357405 + 0.0681786i
\(413\) −1.34928 + 2.45433i −0.0663936 + 0.120770i
\(414\) −2.37318 12.4407i −0.116636 0.611425i
\(415\) 17.4272 6.75858i 0.855469 0.331766i
\(416\) 31.0535 + 17.0718i 1.52252 + 0.837013i
\(417\) 37.7632 + 2.37586i 1.84927 + 0.116346i
\(418\) 15.5729 + 21.4343i 0.761698 + 1.04839i
\(419\) −15.7566 + 4.04561i −0.769761 + 0.197641i −0.613094 0.790010i \(-0.710075\pi\)
−0.156668 + 0.987651i \(0.550075\pi\)
\(420\) −14.2989 1.00059i −0.697713 0.0488237i
\(421\) −0.682502 10.8481i −0.0332631 0.528702i −0.979012 0.203803i \(-0.934670\pi\)
0.945749 0.324899i \(-0.105330\pi\)
\(422\) 8.42624 32.8180i 0.410183 1.59756i
\(423\) 1.21632 9.62818i 0.0591396 0.468138i
\(424\) 1.19399 0.867485i 0.0579853 0.0421288i
\(425\) −15.1624 + 2.67198i −0.735484 + 0.129610i
\(426\) −23.4543 17.0405i −1.13636 0.825617i
\(427\) −14.4193 + 15.3550i −0.697799 + 0.743081i
\(428\) −0.203687 0.514453i −0.00984556 0.0248670i
\(429\) 76.3298 + 19.5982i 3.68524 + 0.946208i
\(430\) −0.765832 1.06982i −0.0369317 0.0515911i
\(431\) −5.77987 9.10762i −0.278407 0.438699i 0.676134 0.736778i \(-0.263654\pi\)
−0.954541 + 0.298080i \(0.903654\pi\)
\(432\) 28.3689i 1.36490i
\(433\) 12.1318 7.69909i 0.583019 0.369995i −0.211369 0.977406i \(-0.567792\pi\)
0.794387 + 0.607412i \(0.207792\pi\)
\(434\) −5.01656 + 4.71086i −0.240802 + 0.226128i
\(435\) −3.81374 + 54.5001i −0.182855 + 2.61308i
\(436\) 5.06707 2.78565i 0.242669 0.133408i
\(437\) −4.05570 + 1.90847i −0.194010 + 0.0912944i
\(438\) 39.6101 18.6391i 1.89264 0.890610i
\(439\) 8.36374 4.59800i 0.399179 0.219451i −0.269502 0.963000i \(-0.586859\pi\)
0.668681 + 0.743549i \(0.266859\pi\)
\(440\) −14.7426 + 3.67497i −0.702827 + 0.175197i
\(441\) −12.2982 + 11.5488i −0.585630 + 0.549943i
\(442\) 27.5929 17.5110i 1.31246 0.832914i
\(443\) 1.23032i 0.0584541i −0.999573 0.0292270i \(-0.990695\pi\)
0.999573 0.0292270i \(-0.00930458\pi\)
\(444\) −6.29796 9.92400i −0.298888 0.470972i
\(445\) 18.3213 + 6.09569i 0.868511 + 0.288963i
\(446\) 28.1947 + 7.23916i 1.33506 + 0.342784i
\(447\) −19.5541 49.3880i −0.924878 2.33597i
\(448\) −0.928030 + 0.988252i −0.0438453 + 0.0466905i
\(449\) −12.1895 8.85617i −0.575257 0.417948i 0.261754 0.965135i \(-0.415699\pi\)
−0.837011 + 0.547186i \(0.815699\pi\)
\(450\) −38.1506 + 23.4652i −1.79844 + 1.10616i
\(451\) −21.2418 + 15.4331i −1.00024 + 0.726715i
\(452\) 0.411651 3.25855i 0.0193624 0.153269i
\(453\) 2.57464 10.0276i 0.120967 0.471137i
\(454\) 0.587890 + 9.34425i 0.0275911 + 0.438547i
\(455\) 19.4225 + 16.2991i 0.910542 + 0.764113i
\(456\) −12.6206 + 3.24042i −0.591013 + 0.151746i
\(457\) −11.2753 15.5191i −0.527437 0.725955i 0.459300 0.888281i \(-0.348100\pi\)
−0.986737 + 0.162326i \(0.948100\pi\)
\(458\) −20.0268 1.25998i −0.935791 0.0588750i
\(459\) −15.4175 8.47583i −0.719626 0.395618i
\(460\) 0.209279 + 3.74658i 0.00975769 + 0.174685i
\(461\) 6.75239 + 35.3973i 0.314490 + 1.64862i 0.691478 + 0.722398i \(0.256960\pi\)
−0.376988 + 0.926218i \(0.623040\pi\)
\(462\) −21.7435 + 39.5513i −1.01160 + 1.84009i
\(463\) −22.1346 4.22241i −1.02868 0.196232i −0.354702 0.934979i \(-0.615418\pi\)
−0.673982 + 0.738747i \(0.735418\pi\)
\(464\) 31.2304 + 29.3273i 1.44983 + 1.36148i
\(465\) −2.48620 + 12.5530i −0.115295 + 0.582130i
\(466\) 5.28125 + 11.2232i 0.244649 + 0.519906i
\(467\) −10.7909 + 27.2546i −0.499341 + 1.26119i 0.433581 + 0.901114i \(0.357250\pi\)
−0.932923 + 0.360077i \(0.882750\pi\)
\(468\) 20.8125 28.6459i 0.962057 1.32416i
\(469\) −1.27051 + 1.53578i −0.0586667 + 0.0709158i
\(470\) −1.97249 + 7.46409i −0.0909844 + 0.344293i
\(471\) 28.8522 45.4637i 1.32944 2.09486i
\(472\) 1.79961 + 1.14207i 0.0828338 + 0.0525679i
\(473\) −1.51559 + 0.289115i −0.0696871 + 0.0132935i
\(474\) −26.6603 + 82.0519i −1.22455 + 3.76877i
\(475\) 11.4015 + 11.0125i 0.523136 + 0.505288i
\(476\) 2.15412 + 6.62969i 0.0987337 + 0.303871i
\(477\) −2.45795 4.47099i −0.112542 0.204712i
\(478\) 3.28299 2.71592i 0.150160 0.124223i
\(479\) −17.0985 + 6.76977i −0.781249 + 0.309319i −0.724685 0.689080i \(-0.758015\pi\)
−0.0565645 + 0.998399i \(0.518015\pi\)
\(480\) −4.99326 + 37.4086i −0.227910 + 1.70746i
\(481\) −1.30550 + 20.7504i −0.0595258 + 0.946135i
\(482\) −46.9694 15.2613i −2.13940 0.695133i
\(483\) −5.88346 4.86722i −0.267707 0.221466i
\(484\) 2.42749 12.7253i 0.110340 0.578425i
\(485\) −22.4976 3.00295i −1.02156 0.136357i
\(486\) 24.7156 + 3.12231i 1.12112 + 0.141631i
\(487\) 3.02423 + 23.9392i 0.137041 + 1.08479i 0.899243 + 0.437450i \(0.144118\pi\)
−0.762202 + 0.647339i \(0.775882\pi\)
\(488\) 10.9733 + 11.6853i 0.496736 + 0.528970i
\(489\) −10.8520 + 23.0616i −0.490742 + 1.04288i
\(490\) 10.9131 7.81216i 0.493002 0.352918i
\(491\) −5.45607 + 0.689262i −0.246229 + 0.0311060i −0.247479 0.968893i \(-0.579602\pi\)
0.00124991 + 0.999999i \(0.499602\pi\)
\(492\) 4.68791 + 18.2582i 0.211348 + 0.823144i
\(493\) 25.2690 8.21041i 1.13806 0.369778i
\(494\) −31.2843 12.3863i −1.40755 0.557287i
\(495\) 6.21662 + 52.1562i 0.279416 + 2.34425i
\(496\) 6.39647 + 7.73200i 0.287210 + 0.347177i
\(497\) −10.9173 + 0.686857i −0.489707 + 0.0308098i
\(498\) −38.2339 17.9915i −1.71330 0.806220i
\(499\) −8.43739 −0.377710 −0.188855 0.982005i \(-0.560478\pi\)
−0.188855 + 0.982005i \(0.560478\pi\)
\(500\) 12.1238 5.39570i 0.542193 0.241303i
\(501\) −32.2760 −1.44199
\(502\) −43.3584 20.4029i −1.93518 0.910626i
\(503\) −11.0056 + 0.692416i −0.490717 + 0.0308733i −0.306222 0.951960i \(-0.599065\pi\)
−0.184495 + 0.982833i \(0.559065\pi\)
\(504\) −8.85490 10.7037i −0.394429 0.476782i
\(505\) −10.3570 11.1857i −0.460881 0.497755i
\(506\) 10.9858 + 4.34959i 0.488379 + 0.193363i
\(507\) −60.1740 + 19.5517i −2.67242 + 0.868323i
\(508\) 3.87574 + 15.0950i 0.171958 + 0.669733i
\(509\) −18.8074 + 2.37592i −0.833621 + 0.105311i −0.530546 0.847656i \(-0.678013\pi\)
−0.303075 + 0.952967i \(0.598013\pi\)
\(510\) 28.0131 + 20.6552i 1.24044 + 0.914628i
\(511\) 7.03287 14.9456i 0.311116 0.661155i
\(512\) 10.3924 + 11.0668i 0.459282 + 0.489086i
\(513\) 2.27031 + 17.9713i 0.100236 + 0.793453i
\(514\) −28.9378 3.65570i −1.27639 0.161246i
\(515\) 6.01236 12.5472i 0.264936 0.552894i
\(516\) −0.207567 + 1.08810i −0.00913763 + 0.0479011i
\(517\) 6.97607 + 5.77110i 0.306807 + 0.253813i
\(518\) −11.3250 3.67971i −0.497591 0.161677i
\(519\) 1.88468 29.9561i 0.0827282 1.31493i
\(520\) 13.3074 13.9728i 0.583568 0.612746i
\(521\) 20.1077 7.96119i 0.880934 0.348786i 0.116271 0.993217i \(-0.462906\pi\)
0.764662 + 0.644431i \(0.222906\pi\)
\(522\) 59.5564 49.2693i 2.60671 2.15646i
\(523\) 10.8532 + 19.7419i 0.474579 + 0.863255i 0.999924 + 0.0123658i \(0.00393627\pi\)
−0.525345 + 0.850889i \(0.676064\pi\)
\(524\) −8.14623 25.0715i −0.355870 1.09525i
\(525\) −8.70489 + 25.5621i −0.379912 + 1.11562i
\(526\) −0.968352 + 2.98028i −0.0422221 + 0.129946i
\(527\) 6.11314 1.16614i 0.266293 0.0507980i
\(528\) 55.5688 + 35.2650i 2.41832 + 1.53471i
\(529\) 11.2529 17.7318i 0.489258 0.770947i
\(530\) 1.46758 + 3.78421i 0.0637478 + 0.164376i
\(531\) 4.69678 5.67743i 0.203823 0.246379i
\(532\) 4.21858 5.80638i 0.182899 0.251738i
\(533\) 12.2751 31.0033i 0.531692 1.34290i
\(534\) −18.5852 39.4956i −0.804262 1.70914i
\(535\) −1.03506 + 0.123371i −0.0447494 + 0.00533379i
\(536\) 1.10573 + 1.03835i 0.0477603 + 0.0448499i
\(537\) −30.0998 5.74184i −1.29890 0.247779i
\(538\) 11.5267 20.9671i 0.496953 0.903954i
\(539\) −2.94923 15.4604i −0.127032 0.665926i
\(540\) 14.6612 + 3.87444i 0.630919 + 0.166730i
\(541\) −25.0846 13.7904i −1.07847 0.592896i −0.159493 0.987199i \(-0.550986\pi\)
−0.918980 + 0.394303i \(0.870986\pi\)
\(542\) −20.3068 1.27759i −0.872251 0.0548774i
\(543\) 24.9618 + 34.3569i 1.07121 + 1.47440i
\(544\) 17.7774 4.56445i 0.762198 0.195699i
\(545\) −2.63481 10.5699i −0.112863 0.452764i
\(546\) −3.59910 57.2061i −0.154027 2.44820i
\(547\) −5.08863 + 19.8189i −0.217574 + 0.847396i 0.762208 + 0.647332i \(0.224115\pi\)
−0.979783 + 0.200064i \(0.935885\pi\)
\(548\) −0.276137 + 2.18585i −0.0117960 + 0.0933749i
\(549\) 44.8326 32.5728i 1.91341 1.39017i
\(550\) 0.587568 41.7811i 0.0250540 1.78155i
\(551\) −22.1310 16.0791i −0.942812 0.684993i
\(552\) −3.97784 + 4.23597i −0.169308 + 0.180295i
\(553\) 11.9835 + 30.2670i 0.509592 + 1.28708i
\(554\) 11.0404 + 2.83470i 0.469062 + 0.120435i
\(555\) −21.1068 + 6.69431i −0.895933 + 0.284158i
\(556\) 8.49859 + 13.3916i 0.360421 + 0.567932i
\(557\) 5.86450i 0.248487i −0.992252 0.124243i \(-0.960350\pi\)
0.992252 0.124243i \(-0.0396504\pi\)
\(558\) 15.2863 9.70099i 0.647121 0.410676i
\(559\) 1.42840 1.34135i 0.0604147 0.0567332i
\(560\) 11.2204 + 17.9583i 0.474148 + 0.758879i
\(561\) 35.7676 19.6634i 1.51011 0.830190i
\(562\) −27.8483 + 13.1044i −1.17471 + 0.552776i
\(563\) 8.74556 4.11535i 0.368582 0.173441i −0.232564 0.972581i \(-0.574711\pi\)
0.601145 + 0.799140i \(0.294711\pi\)
\(564\) 5.69606 3.13143i 0.239847 0.131857i
\(565\) −5.73694 2.31820i −0.241355 0.0975276i
\(566\) 4.24166 3.98318i 0.178290 0.167426i
\(567\) −1.81218 + 1.15004i −0.0761044 + 0.0482973i
\(568\) 8.32460i 0.349293i
\(569\) 8.73611 + 13.7659i 0.366237 + 0.577097i 0.976610 0.215017i \(-0.0689807\pi\)
−0.610374 + 0.792114i \(0.708981\pi\)
\(570\) 0.251951 35.8335i 0.0105531 1.50090i
\(571\) 11.2574 + 2.89041i 0.471107 + 0.120960i 0.476777 0.879024i \(-0.341805\pi\)
−0.00566992 + 0.999984i \(0.501805\pi\)
\(572\) 12.1604 + 30.7137i 0.508452 + 1.28420i
\(573\) −27.8241 + 29.6297i −1.16237 + 1.23780i
\(574\) 15.4502 + 11.2252i 0.644879 + 0.468532i
\(575\) 6.92468 + 1.42215i 0.288779 + 0.0593078i
\(576\) 2.88544 2.09639i 0.120226 0.0873496i
\(577\) 1.16928 9.25581i 0.0486778 0.385324i −0.948889 0.315610i \(-0.897791\pi\)
0.997567 0.0697149i \(-0.0222090\pi\)
\(578\) −3.33792 + 13.0003i −0.138839 + 0.540742i
\(579\) 2.87297 + 45.6646i 0.119397 + 1.89776i
\(580\) −19.4217 + 12.1347i −0.806443 + 0.503866i
\(581\) −15.4429 + 3.96506i −0.640678 + 0.164498i
\(582\) 30.1592 + 41.5105i 1.25014 + 1.72067i
\(583\) 4.75048 + 0.298875i 0.196745 + 0.0123781i
\(584\) −11.0153 6.05570i −0.455815 0.250587i
\(585\) −42.1576 51.6955i −1.74300 2.13735i
\(586\) −8.28206 43.4161i −0.342129 1.79350i
\(587\) 17.4479 31.7377i 0.720154 1.30995i −0.222090 0.975026i \(-0.571288\pi\)
0.942244 0.334928i \(-0.108712\pi\)
\(588\) −11.0996 2.11737i −0.457741 0.0873187i
\(589\) −4.67085 4.38622i −0.192459 0.180731i
\(590\) −4.30111 + 3.98248i −0.177074 + 0.163956i
\(591\) 9.86033 + 20.9543i 0.405600 + 0.861943i
\(592\) −6.39206 + 16.1445i −0.262712 + 0.663534i
\(593\) 23.5459 32.4081i 0.966914 1.33084i 0.0233237 0.999728i \(-0.492575\pi\)
0.943590 0.331115i \(-0.107425\pi\)
\(594\) 30.4369 36.7918i 1.24884 1.50959i
\(595\) 13.1120 0.732423i 0.537541 0.0300264i
\(596\) 11.9306 18.7997i 0.488698 0.770065i
\(597\) −0.486484 0.308732i −0.0199105 0.0126356i
\(598\) −14.7397 + 2.81174i −0.602750 + 0.114981i
\(599\) 1.32013 4.06294i 0.0539390 0.166007i −0.920458 0.390841i \(-0.872184\pi\)
0.974397 + 0.224834i \(0.0721841\pi\)
\(600\) 18.9987 + 7.83291i 0.775619 + 0.319777i
\(601\) −0.00391500 0.0120491i −0.000159696 0.000491494i 0.950977 0.309263i \(-0.100082\pi\)
−0.951136 + 0.308771i \(0.900082\pi\)
\(602\) 0.540645 + 0.983430i 0.0220351 + 0.0400816i
\(603\) 4.04040 3.34251i 0.164538 0.136118i
\(604\) 4.03491 1.59753i 0.164178 0.0650027i
\(605\) −22.0093 10.5464i −0.894806 0.428774i
\(606\) −2.16386 + 34.3936i −0.0879010 + 1.39715i
\(607\) 12.9693 + 4.21397i 0.526406 + 0.171040i 0.560151 0.828391i \(-0.310743\pi\)
−0.0337446 + 0.999430i \(0.510743\pi\)
\(608\) −14.5603 12.0454i −0.590500 0.488504i
\(609\) 8.73217 45.7756i 0.353845 1.85492i
\(610\) −38.7802 + 20.9659i −1.57016 + 0.848884i
\(611\) −11.4074 1.44109i −0.461495 0.0583004i
\(612\) −2.29852 18.1946i −0.0929121 0.735475i
\(613\) −8.76588 9.33472i −0.354051 0.377026i 0.527147 0.849774i \(-0.323262\pi\)
−0.881197 + 0.472749i \(0.843262\pi\)
\(614\) 16.5545 35.1801i 0.668086 1.41975i
\(615\) 35.5116 + 0.249688i 1.43197 + 0.0100684i
\(616\) 12.8578 1.62431i 0.518054 0.0654455i
\(617\) −1.05256 4.09943i −0.0423743 0.165037i 0.943875 0.330304i \(-0.107151\pi\)
−0.986249 + 0.165267i \(0.947151\pi\)
\(618\) −29.9135 + 9.71948i −1.20330 + 0.390975i
\(619\) 6.81935 + 2.69997i 0.274093 + 0.108521i 0.501150 0.865360i \(-0.332910\pi\)
−0.227057 + 0.973881i \(0.572910\pi\)
\(620\) −4.86953 + 2.24974i −0.195565 + 0.0903519i
\(621\) 5.14930 + 6.22443i 0.206634 + 0.249778i
\(622\) 25.7175 1.61801i 1.03118 0.0648763i
\(623\) −14.9024 7.01255i −0.597053 0.280952i
\(624\) −83.5825 −3.34598
\(625\) −3.99212 24.6792i −0.159685 0.987168i
\(626\) −14.6852 −0.586937
\(627\) −38.0242 17.8928i −1.51854 0.714571i
\(628\) 22.5264 1.41724i 0.898902 0.0565541i
\(629\) 6.86418 + 8.29736i 0.273693 + 0.330838i
\(630\) 34.6818 16.0232i 1.38176 0.638378i
\(631\) −0.446037 0.176599i −0.0177564 0.00703028i 0.359230 0.933249i \(-0.383040\pi\)
−0.376986 + 0.926219i \(0.623040\pi\)
\(632\) 23.5607 7.65533i 0.937193 0.304513i
\(633\) 13.3652 + 52.0541i 0.531220 + 2.06897i
\(634\) 45.8934 5.79769i 1.82266 0.230256i
\(635\) 29.3593 + 0.206430i 1.16509 + 0.00819192i
\(636\) 1.45502 3.09207i 0.0576952 0.122608i
\(637\) 13.6830 + 14.5709i 0.542140 + 0.577320i
\(638\) 9.03780 + 71.5415i 0.357810 + 2.83236i
\(639\) 28.5515 + 3.60690i 1.12948 + 0.142687i
\(640\) 20.9533 11.3281i 0.828251 0.447781i
\(641\) 1.41196 7.40177i 0.0557692 0.292352i −0.943465 0.331471i \(-0.892455\pi\)
0.999235 + 0.0391187i \(0.0124550\pi\)
\(642\) 1.81567 + 1.50206i 0.0716589 + 0.0592814i
\(643\) −13.9924 4.54642i −0.551808 0.179293i 0.0198241 0.999803i \(-0.493689\pi\)
−0.571632 + 0.820510i \(0.693689\pi\)
\(644\) 0.200976 3.19441i 0.00791954 0.125878i
\(645\) 1.88195 + 0.901793i 0.0741016 + 0.0355081i
\(646\) −16.2033 + 6.41533i −0.637509 + 0.252408i
\(647\) 7.36557 6.09333i 0.289571 0.239554i −0.481284 0.876565i \(-0.659829\pi\)
0.770855 + 0.637011i \(0.219829\pi\)
\(648\) 0.786876 + 1.43132i 0.0309114 + 0.0562276i
\(649\) 2.12423 + 6.53772i 0.0833834 + 0.256628i
\(650\) 27.8015 + 45.2007i 1.09046 + 1.77292i
\(651\) 3.37304 10.3812i 0.132200 0.406870i
\(652\) −10.4944 + 2.00191i −0.410993 + 0.0784010i
\(653\) −10.3712 6.58177i −0.405857 0.257565i 0.317192 0.948361i \(-0.397260\pi\)
−0.723049 + 0.690797i \(0.757260\pi\)
\(654\) −13.1952 + 20.7923i −0.515973 + 0.813043i
\(655\) −49.5859 + 2.76981i −1.93748 + 0.108225i
\(656\) 17.7509 21.4571i 0.693056 0.837760i
\(657\) −25.5424 + 35.1561i −0.996504 + 1.37157i
\(658\) 2.42420 6.12283i 0.0945051 0.238693i
\(659\) 17.6782 + 37.5681i 0.688646 + 1.46345i 0.876576 + 0.481264i \(0.159822\pi\)
−0.187930 + 0.982182i \(0.560178\pi\)
\(660\) −25.8144 + 23.9020i −1.00482 + 0.930384i
\(661\) −10.8287 10.1688i −0.421187 0.395521i 0.444766 0.895647i \(-0.353287\pi\)
−0.865953 + 0.500126i \(0.833287\pi\)
\(662\) −28.8496 5.50335i −1.12127 0.213894i
\(663\) −24.9721 + 45.4240i −0.969835 + 1.76412i
\(664\) 2.27357 + 11.9185i 0.0882317 + 0.462527i
\(665\) −8.54512 10.4784i −0.331366 0.406336i
\(666\) 27.4525 + 15.0921i 1.06376 + 0.584809i
\(667\) −12.1755 0.766018i −0.471437 0.0296603i
\(668\) −7.95233 10.9454i −0.307685 0.423492i
\(669\) −44.7208 + 11.4824i −1.72901 + 0.443934i
\(670\) −3.53779 + 2.21041i −0.136677 + 0.0853956i
\(671\) 3.24622 + 51.5972i 0.125319 + 1.99189i
\(672\) 8.00575 31.1804i 0.308829 1.20281i
\(673\) −4.17073 + 33.0148i −0.160770 + 1.27263i 0.680797 + 0.732472i \(0.261634\pi\)
−0.841567 + 0.540153i \(0.818366\pi\)
\(674\) −5.72666 + 4.16066i −0.220583 + 0.160263i
\(675\) 14.1137 24.8388i 0.543236 0.956047i
\(676\) −21.4564 15.5890i −0.825246 0.599576i
\(677\) −11.7875 + 12.5524i −0.453031 + 0.482429i −0.914419 0.404770i \(-0.867352\pi\)
0.461388 + 0.887199i \(0.347352\pi\)
\(678\) 5.14930 + 13.0056i 0.197758 + 0.499479i
\(679\) 18.7519 + 4.81467i 0.719632 + 0.184770i
\(680\) 0.0702674 9.99372i 0.00269463 0.383241i
\(681\) −7.95737 12.5388i −0.304927 0.480488i
\(682\) 16.8904i 0.646767i
\(683\) −35.5607 + 22.5675i −1.36069 + 0.863521i −0.997668 0.0682592i \(-0.978256\pi\)
−0.363023 + 0.931780i \(0.618256\pi\)
\(684\) −13.7642 + 12.9255i −0.526288 + 0.494217i
\(685\) 3.84836 + 1.55506i 0.147038 + 0.0594158i
\(686\) −30.9182 + 16.9975i −1.18046 + 0.648966i
\(687\) 28.7990 13.5518i 1.09875 0.517033i
\(688\) 1.48070 0.696766i 0.0564512 0.0265639i
\(689\) −5.29721 + 2.91217i −0.201808 + 0.110945i
\(690\) −8.46791 13.5530i −0.322368 0.515954i
\(691\) 27.4059 25.7358i 1.04257 0.979036i 0.0427688 0.999085i \(-0.486382\pi\)
0.999799 + 0.0200487i \(0.00638211\pi\)
\(692\) 10.6231 6.74161i 0.403829 0.256278i
\(693\) 44.8030i 1.70193i
\(694\) 3.77160 + 5.94310i 0.143168 + 0.225597i
\(695\) 28.4819 9.03343i 1.08038 0.342658i
\(696\) −34.3498 8.81953i −1.30203 0.334303i
\(697\) −6.35771 16.0577i −0.240815 0.608230i
\(698\) 24.4151 25.9994i 0.924125 0.984094i
\(699\) −15.9167 11.5642i −0.602025 0.437397i
\(700\) −10.8134 + 3.34612i −0.408707 + 0.126472i
\(701\) 14.8884 10.8171i 0.562327 0.408555i −0.269983 0.962865i \(-0.587018\pi\)
0.832310 + 0.554311i \(0.187018\pi\)
\(702\) −7.60034 + 60.1629i −0.286856 + 2.27070i
\(703\) 2.75727 10.7389i 0.103992 0.405023i
\(704\) 0.208928 + 3.32081i 0.00787426 + 0.125158i
\(705\) −2.96188 11.8820i −0.111551 0.447500i
\(706\) 35.3741 9.08254i 1.33132 0.341826i
\(707\) 7.64297 + 10.5196i 0.287444 + 0.395632i
\(708\) 4.92549 + 0.309886i 0.185111 + 0.0116462i
\(709\) 12.9708 + 7.13078i 0.487130 + 0.267802i 0.706336 0.707877i \(-0.250347\pi\)
−0.219206 + 0.975679i \(0.570347\pi\)
\(710\) −22.1341 5.84926i −0.830678 0.219519i
\(711\) −16.0477 84.1247i −0.601834 3.15492i
\(712\) −6.03820 + 10.9834i −0.226291 + 0.411622i
\(713\) −2.80690 0.535445i −0.105119 0.0200526i
\(714\) −21.6414 20.3226i −0.809910 0.760556i
\(715\) 61.7945 7.36543i 2.31098 0.275452i
\(716\) −5.46897 11.6221i −0.204385 0.434340i
\(717\) −2.48786 + 6.28363i −0.0929110 + 0.234666i
\(718\) 25.8656 35.6009i 0.965295 1.32861i
\(719\) −19.0273 + 23.0000i −0.709597 + 0.857756i −0.994919 0.100676i \(-0.967899\pi\)
0.285322 + 0.958432i \(0.407899\pi\)
\(720\) −20.1432 51.9401i −0.750695 1.93569i
\(721\) −6.35906 + 10.0203i −0.236824 + 0.373174i
\(722\) −13.4891 8.56046i −0.502013 0.318587i
\(723\) 76.9467 14.6784i 2.86168 0.545895i
\(724\) −5.50092 + 16.9301i −0.204440 + 0.629202i
\(725\) 12.7537 + 41.2152i 0.473662 + 1.53069i
\(726\) 17.0492 + 52.4720i 0.632755 + 1.94742i
\(727\) 6.57288 + 11.9560i 0.243775 + 0.443424i 0.969683 0.244367i \(-0.0785802\pi\)
−0.725908 + 0.687792i \(0.758580\pi\)
\(728\) −12.6818 + 10.4913i −0.470017 + 0.388832i
\(729\) −39.8781 + 15.7889i −1.47697 + 0.584773i
\(730\) 23.8412 25.0333i 0.882403 0.926522i
\(731\) 0.0637251 1.01288i 0.00235696 0.0374628i
\(732\) 35.3003 + 11.4698i 1.30474 + 0.423935i
\(733\) 30.7689 + 25.4543i 1.13648 + 0.940175i 0.998735 0.0502928i \(-0.0160155\pi\)
0.137742 + 0.990468i \(0.456015\pi\)
\(734\) 5.82815 30.5522i 0.215121 1.12770i
\(735\) −9.19908 + 19.1975i −0.339313 + 0.708111i
\(736\) −8.36093 1.05623i −0.308188 0.0389332i
\(737\) 0.613139 + 4.85349i 0.0225853 + 0.178781i
\(738\) −34.3934 36.6252i −1.26604 1.34819i
\(739\) 4.82206 10.2474i 0.177382 0.376957i −0.796288 0.604918i \(-0.793206\pi\)
0.973670 + 0.227961i \(0.0732059\pi\)
\(740\) −7.47058 5.50836i −0.274624 0.202491i
\(741\) 52.9483 6.68893i 1.94511 0.245724i
\(742\) −0.860987 3.35332i −0.0316078 0.123104i
\(743\) −42.6487 + 13.8574i −1.56463 + 0.508379i −0.958040 0.286636i \(-0.907463\pi\)
−0.606590 + 0.795015i \(0.707463\pi\)
\(744\) −7.72341 3.05792i −0.283154 0.112109i
\(745\) −28.4989 30.7791i −1.04412 1.12766i
\(746\) 28.6806 + 34.6688i 1.05007 + 1.26932i
\(747\) 41.8628 2.63378i 1.53168 0.0963651i
\(748\) 15.4809 + 7.28475i 0.566037 + 0.266357i
\(749\) 0.889131 0.0324881
\(750\) −34.1762 + 45.0115i −1.24794 + 1.64359i
\(751\) −3.30176 −0.120483 −0.0602414 0.998184i \(-0.519187\pi\)
−0.0602414 + 0.998184i \(0.519187\pi\)
\(752\) −8.68868 4.08858i −0.316844 0.149095i
\(753\) 75.8564 4.77248i 2.76436 0.173919i
\(754\) −58.3741 70.5622i −2.12586 2.56972i
\(755\) −0.967610 8.11805i −0.0352149 0.295446i
\(756\) −12.0267 4.76170i −0.437406 0.173181i
\(757\) 39.4772 12.8269i 1.43482 0.466202i 0.514543 0.857465i \(-0.327962\pi\)
0.920279 + 0.391263i \(0.127962\pi\)
\(758\) 0.851905 + 3.31795i 0.0309426 + 0.120513i
\(759\) −18.5934 + 2.34889i −0.674897 + 0.0852593i
\(760\) −8.36678 + 5.98940i −0.303495 + 0.217258i
\(761\) 10.2380 21.7568i 0.371127 0.788684i −0.628811 0.777558i \(-0.716458\pi\)
0.999938 0.0111266i \(-0.00354178\pi\)
\(762\) −45.4349 48.3833i −1.64593 1.75274i
\(763\) 1.16457 + 9.21851i 0.0421602 + 0.333732i
\(764\) −16.9035 2.13541i −0.611547 0.0772563i
\(765\) −34.2458 4.57109i −1.23816 0.165268i
\(766\) −7.73624 + 40.5548i −0.279522 + 1.46530i
\(767\) −6.72660 5.56472i −0.242883 0.200931i
\(768\) −55.0398 17.8835i −1.98608 0.645316i
\(769\) 1.52322 24.2108i 0.0549286 0.873064i −0.870031 0.492998i \(-0.835901\pi\)
0.924959 0.380067i \(-0.124099\pi\)
\(770\) −4.71562 + 35.3286i −0.169939 + 1.27315i
\(771\) 43.0155 17.0310i 1.54917 0.613358i
\(772\) −14.7779 + 12.2254i −0.531869 + 0.440001i
\(773\) 9.82506 + 17.8717i 0.353383 + 0.642801i 0.991931 0.126781i \(-0.0404646\pi\)
−0.638548 + 0.769582i \(0.720465\pi\)
\(774\) −0.912356 2.80794i −0.0327940 0.100929i
\(775\) 1.75381 + 9.95214i 0.0629987 + 0.357491i
\(776\) 4.55283 14.0122i 0.163437 0.503008i
\(777\) 18.5529 3.53916i 0.665582 0.126967i
\(778\) −36.7923 23.3491i −1.31907 0.837106i
\(779\) −9.52777 + 15.0134i −0.341368 + 0.537910i
\(780\) 11.4151 43.1959i 0.408728 1.54666i
\(781\) −17.1137 + 20.6869i −0.612377 + 0.740236i
\(782\) −4.56819 + 6.28758i −0.163358 + 0.224843i
\(783\) −18.1492 + 45.8396i −0.648599 + 1.63818i
\(784\) 7.10762 + 15.1045i 0.253844 + 0.539445i
\(785\) 8.26124 41.7114i 0.294856 1.48874i
\(786\) 81.8415 + 76.8543i 2.91919 + 2.74130i
\(787\) −42.7630 8.15749i −1.52434 0.290783i −0.643961 0.765058i \(-0.722710\pi\)
−0.880377 + 0.474275i \(0.842710\pi\)
\(788\) −4.67658 + 8.50666i −0.166596 + 0.303037i
\(789\) −0.931365 4.88239i −0.0331575 0.173818i
\(790\) 3.79974 + 68.0240i 0.135189 + 2.42018i
\(791\) 4.62506 + 2.54265i 0.164448 + 0.0904061i
\(792\) −34.0283 2.14088i −1.20914 0.0760729i
\(793\) −38.5921 53.1175i −1.37045 1.88626i
\(794\) 58.8075 15.0992i 2.08700 0.535851i
\(795\) −4.93150 4.13844i −0.174902 0.146775i
\(796\) −0.0151652 0.241044i −0.000537516 0.00854356i
\(797\) −3.36165 + 13.0928i −0.119076 + 0.463770i −0.999954 0.00957299i \(-0.996953\pi\)
0.880878 + 0.473343i \(0.156953\pi\)
\(798\) −3.83093 + 30.3249i −0.135613 + 1.07349i
\(799\) −4.81793 + 3.50043i −0.170446 + 0.123836i
\(800\) 7.00509 + 28.9682i 0.247667 + 1.02418i
\(801\) 35.0545 + 25.4686i 1.23859 + 0.899889i
\(802\) 22.0453 23.4758i 0.778446 0.828961i
\(803\) −14.9240 37.6938i −0.526658 1.33019i
\(804\) 3.40187 + 0.873451i 0.119975 + 0.0308042i
\(805\) −5.72152 1.90361i −0.201657 0.0670935i
\(806\) −11.4937 18.1112i −0.404848 0.637939i
\(807\) 37.9511i 1.33594i
\(808\) 8.35499 5.30224i 0.293927 0.186532i
\(809\) 7.31017 6.86471i 0.257012 0.241350i −0.545321 0.838228i \(-0.683592\pi\)
0.802333 + 0.596877i \(0.203592\pi\)
\(810\) −4.35861 + 1.08649i −0.153146 + 0.0381755i
\(811\) −37.9737 + 20.8762i −1.33344 + 0.733063i −0.979354 0.202152i \(-0.935206\pi\)
−0.354082 + 0.935215i \(0.615206\pi\)
\(812\) 17.6749 8.31719i 0.620268 0.291876i
\(813\) 29.2016 13.7412i 1.02415 0.481927i
\(814\) −25.6112 + 14.0799i −0.897673 + 0.493500i
\(815\) −1.40499 + 20.0779i −0.0492146 + 0.703298i
\(816\) −31.5574 + 29.6343i −1.10473 + 1.03741i
\(817\) −0.882244 + 0.559889i −0.0308658 + 0.0195880i
\(818\) 39.9298i 1.39611i
\(819\) 30.4879 + 48.0412i 1.06533 + 1.67870i
\(820\) 8.66487 + 12.1042i 0.302590 + 0.422698i
\(821\) −16.8223 4.31922i −0.587101 0.150742i −0.0565570 0.998399i \(-0.518012\pi\)
−0.530544 + 0.847657i \(0.678012\pi\)
\(822\) −3.45417 8.72424i −0.120478 0.304293i
\(823\) 7.60030 8.09350i 0.264930 0.282122i −0.582725 0.812669i \(-0.698014\pi\)
0.847655 + 0.530548i \(0.178014\pi\)
\(824\) 7.30663 + 5.30858i 0.254538 + 0.184933i
\(825\) 31.1095 + 58.5226i 1.08309 + 2.03749i
\(826\) 4.04502 2.93888i 0.140744 0.102257i
\(827\) 5.10309 40.3951i 0.177452 1.40468i −0.611997 0.790860i \(-0.709634\pi\)
0.789449 0.613816i \(-0.210366\pi\)
\(828\) −2.09412 + 8.15607i −0.0727758 + 0.283443i
\(829\) −1.10097 17.4994i −0.0382382 0.607779i −0.969755 0.244081i \(-0.921514\pi\)
0.931517 0.363699i \(-0.118486\pi\)
\(830\) −33.2873 2.32934i −1.15542 0.0808525i
\(831\) −17.5117 + 4.49624i −0.607474 + 0.155973i
\(832\) −2.48380 3.41865i −0.0861102 0.118521i
\(833\) 10.3323 + 0.650052i 0.357992 + 0.0225230i
\(834\) −59.1928 32.5415i −2.04968 1.12682i
\(835\) −23.7635 + 9.21590i −0.822371 + 0.318930i
\(836\) −3.30078 17.3033i −0.114160 0.598448i
\(837\) −5.56328 + 10.1196i −0.192295 + 0.349784i
\(838\) 28.5267 + 5.44175i 0.985437 + 0.187982i
\(839\) 24.8492 + 23.3350i 0.857890 + 0.805613i 0.982436 0.186601i \(-0.0597473\pi\)
−0.124546 + 0.992214i \(0.539747\pi\)
\(840\) −15.3008 8.55234i −0.527929 0.295084i
\(841\) −19.3533 41.1279i −0.667357 1.41821i
\(842\) −7.14317 + 18.0416i −0.246170 + 0.621754i
\(843\) 28.6942 39.4942i 0.988281 1.36025i
\(844\) −14.3596 + 17.3578i −0.494278 + 0.597480i
\(845\) −38.7210 + 31.5769i −1.33204 + 1.08628i
\(846\) −9.28310 + 14.6278i −0.319159 + 0.502915i
\(847\) 17.5768 + 11.1546i 0.603947 + 0.383276i
\(848\) −4.95898 + 0.945975i −0.170292 + 0.0324849i
\(849\) −2.85202 + 8.77761i −0.0978810 + 0.301247i
\(850\) 26.5227 + 7.20889i 0.909721 + 0.247263i
\(851\) −1.52793 4.70250i −0.0523769 0.161200i
\(852\) 9.28600 + 16.8912i 0.318133 + 0.578682i
\(853\) 23.1553 19.1558i 0.792824 0.655881i −0.150182 0.988658i \(-0.547986\pi\)
0.943005 + 0.332778i \(0.107986\pi\)
\(854\) 34.9628 13.8427i 1.19640 0.473689i
\(855\) 16.9171 + 31.2913i 0.578553 + 1.07014i
\(856\) 0.0424865 0.675303i 0.00145216 0.0230814i
\(857\) 53.0731 + 17.2445i 1.81294 + 0.589061i 0.999977 + 0.00674955i \(0.00214846\pi\)
0.812966 + 0.582311i \(0.197852\pi\)
\(858\) −108.399 89.6751i −3.70067 3.06146i
\(859\) 2.53075 13.2667i 0.0863482 0.452653i −0.912684 0.408666i \(-0.865994\pi\)
0.999032 0.0439869i \(-0.0140060\pi\)
\(860\) 0.157868 + 0.860395i 0.00538325 + 0.0293392i
\(861\) −30.0526 3.79652i −1.02419 0.129385i
\(862\) 2.41349 + 19.1048i 0.0822039 + 0.650711i
\(863\) −7.43971 7.92248i −0.253251 0.269684i 0.589763 0.807576i \(-0.299221\pi\)
−0.843014 + 0.537892i \(0.819221\pi\)
\(864\) −14.5009 + 30.8160i −0.493331 + 1.04838i
\(865\) −7.16588 22.5936i −0.243647 0.768206i
\(866\) −25.4486 + 3.21490i −0.864778 + 0.109247i
\(867\) −5.29442 20.6204i −0.179808 0.700306i
\(868\) 4.35153 1.41390i 0.147701 0.0479908i
\(869\) 74.2869 + 29.4123i 2.52001 + 0.997742i
\(870\) 47.5858 85.1349i 1.61331 2.88634i
\(871\) −3.96020 4.78705i −0.134186 0.162203i
\(872\) 7.05719 0.444001i 0.238987 0.0150358i
\(873\) −46.0860 21.6864i −1.55977 0.733974i
\(874\) 8.00178 0.270664
\(875\) 0.889797 + 21.3059i 0.0300806 + 0.720271i
\(876\) −29.1058 −0.983393
\(877\) −6.55968 3.08675i −0.221505 0.104232i 0.311825 0.950139i \(-0.399060\pi\)
−0.533330 + 0.845907i \(0.679060\pi\)
\(878\) −17.0048 + 1.06985i −0.573886 + 0.0361058i
\(879\) 44.6872 + 54.0176i 1.50726 + 1.82197i
\(880\) 50.9824 + 10.0974i 1.71862 + 0.340384i
\(881\) −16.1798 6.40605i −0.545112 0.215825i 0.0793963 0.996843i \(-0.474701\pi\)
−0.624509 + 0.781018i \(0.714701\pi\)
\(882\) 28.6435 9.30684i 0.964477 0.313378i
\(883\) −2.57628 10.0340i −0.0866988 0.337669i 0.910405 0.413717i \(-0.135770\pi\)
−0.997104 + 0.0760479i \(0.975770\pi\)
\(884\) −21.5570 + 2.72328i −0.725039 + 0.0915937i
\(885\) 2.93519 8.82205i 0.0986655 0.296550i
\(886\) −0.935163 + 1.98732i −0.0314174 + 0.0667654i
\(887\) −18.7157 19.9302i −0.628411 0.669190i 0.333438 0.942772i \(-0.391791\pi\)
−0.961849 + 0.273583i \(0.911791\pi\)
\(888\) −1.80149 14.2602i −0.0604539 0.478542i
\(889\) −24.8460 3.13878i −0.833308 0.105271i
\(890\) −24.9609 23.7723i −0.836692 0.796850i
\(891\) −0.987096 + 5.17454i −0.0330690 + 0.173354i
\(892\) −14.9125 12.3367i −0.499306 0.413062i
\(893\) 5.83136 + 1.89472i 0.195139 + 0.0634045i
\(894\) −5.95420 + 94.6393i −0.199138 + 3.16521i
\(895\) −23.8007 + 4.36703i −0.795571 + 0.145974i
\(896\) −18.8907 + 7.47935i −0.631094 + 0.249868i
\(897\) 18.3388 15.1712i 0.612316 0.506552i
\(898\) 12.9580 + 23.5705i 0.432415 + 0.786559i
\(899\) −5.38907 16.5858i −0.179735 0.553169i
\(900\) 29.5940 3.31651i 0.986465 0.110550i
\(901\) −0.967498 + 2.97765i −0.0322320 + 0.0992000i
\(902\) 46.0425 8.78307i 1.53305 0.292444i
\(903\) −1.50294 0.953794i −0.0500147 0.0317403i
\(904\) 2.15217 3.39128i 0.0715801 0.112792i
\(905\) 28.1884 + 18.1682i 0.937016 + 0.603931i
\(906\) −11.7808 + 14.2405i −0.391390 + 0.473109i
\(907\) −14.0274 + 19.3070i −0.465772 + 0.641080i −0.975693 0.219141i \(-0.929675\pi\)
0.509921 + 0.860221i \(0.329675\pi\)
\(908\) 2.29158 5.78788i 0.0760489 0.192078i
\(909\) −14.5654 30.9531i −0.483105 1.02665i
\(910\) −18.9842 41.0909i −0.629320 1.36215i
\(911\) −28.0462 26.3371i −0.929211 0.872587i 0.0628914 0.998020i \(-0.479968\pi\)
−0.992102 + 0.125434i \(0.959968\pi\)
\(912\) 43.7816 + 8.35178i 1.44975 + 0.276555i
\(913\) −18.8521 + 34.2918i −0.623913 + 1.13489i
\(914\) 6.41686 + 33.6384i 0.212251 + 1.11266i
\(915\) 37.8818 58.7747i 1.25233 1.94303i
\(916\) 11.6913 + 6.42737i 0.386293 + 0.212366i
\(917\) 42.2780 + 2.65991i 1.39614 + 0.0878379i
\(918\) 18.4613 + 25.4098i 0.609314 + 0.838648i
\(919\) 40.9617 10.5172i 1.35120 0.346930i 0.497397 0.867523i \(-0.334289\pi\)
0.853805 + 0.520593i \(0.174289\pi\)
\(920\) −1.71921 + 4.25458i −0.0566807 + 0.140270i
\(921\) 3.87230 + 61.5484i 0.127597 + 2.02809i
\(922\) 15.9984 62.3095i 0.526878 2.05206i
\(923\) 4.27344 33.8278i 0.140662 1.11345i
\(924\) 24.2773 17.6385i 0.798666 0.580265i
\(925\) −13.6286 + 10.9555i −0.448106 + 0.360213i
\(926\) 32.5445 + 23.6450i 1.06948 + 0.777022i
\(927\) 21.3730 22.7600i 0.701983 0.747536i
\(928\) −18.9335 47.8205i −0.621522 1.56979i
\(929\) −42.4684 10.9040i −1.39334 0.357750i −0.523898 0.851781i \(-0.675523\pi\)
−0.869444 + 0.494031i \(0.835523\pi\)
\(930\) 13.5575 18.3870i 0.444567 0.602933i
\(931\) −5.71136 8.99966i −0.187182 0.294952i
\(932\) 8.24691i 0.270137i
\(933\) −34.5097 + 21.9005i −1.12980 + 0.716990i
\(934\) 38.1466 35.8221i 1.24820 1.17213i
\(935\) 20.7197 24.6903i 0.677606 0.807458i
\(936\) 37.9446 20.8602i 1.24026 0.681838i
\(937\) 21.3369 10.0404i 0.697046 0.328005i −0.0444032 0.999014i \(-0.514139\pi\)
0.741450 + 0.671009i \(0.234139\pi\)
\(938\) 3.21960 1.51503i 0.105124 0.0494674i
\(939\) 20.4116 11.2214i 0.666109 0.366196i
\(940\) 3.29965 3.93197i 0.107623 0.128247i
\(941\) −18.5939 + 17.4608i −0.606143 + 0.569206i −0.925652 0.378377i \(-0.876482\pi\)
0.319508 + 0.947583i \(0.396482\pi\)
\(942\) −81.1618 + 51.5068i −2.64439 + 1.67818i
\(943\) 7.92991i 0.258233i
\(944\) −3.90663 6.15586i −0.127150 0.200356i
\(945\) −14.4616 + 19.6133i −0.470437 + 0.638019i
\(946\) 2.66789 + 0.684997i 0.0867405 + 0.0222712i
\(947\) 12.6805 + 32.0272i 0.412059 + 1.04074i 0.976547 + 0.215302i \(0.0690736\pi\)
−0.564488 + 0.825441i \(0.690926\pi\)
\(948\) 39.2667 41.8148i 1.27532 1.35808i
\(949\) 41.6528 + 30.2626i 1.35211 + 0.982364i
\(950\) −10.0462 26.4547i −0.325941 0.858304i
\(951\) −59.3593 + 43.1271i −1.92486 + 1.39849i
\(952\) −1.06842 + 8.45742i −0.0346277 + 0.274106i
\(953\) −12.8204 + 49.9322i −0.415294 + 1.61746i 0.325369 + 0.945587i \(0.394512\pi\)
−0.740663 + 0.671877i \(0.765488\pi\)
\(954\) 0.571910 + 9.09025i 0.0185163 + 0.294308i
\(955\) −12.0255 + 29.7599i −0.389136 + 0.963008i
\(956\) −2.74388 + 0.704508i −0.0887434 + 0.0227854i
\(957\) −67.2292 92.5331i −2.17321 2.99117i
\(958\) 32.7648 + 2.06139i 1.05858 + 0.0666003i
\(959\) −3.10251 1.70562i −0.100185 0.0550773i
\(960\) 2.43808 3.78275i 0.0786888 0.122088i
\(961\) 5.04340 + 26.4384i 0.162690 + 0.852852i
\(962\) 17.8811 32.5256i 0.576510 1.04867i
\(963\) −2.29773 0.438315i −0.0740433 0.0141245i
\(964\) 23.9363 + 22.4777i 0.770936 + 0.723957i
\(965\) 15.1541 + 32.8007i 0.487827 + 1.05589i
\(966\) 5.80395 + 12.3340i 0.186739 + 0.396841i
\(967\) 21.3917 54.0294i 0.687912 1.73747i 0.0126170 0.999920i \(-0.495984\pi\)
0.675295 0.737548i \(-0.264016\pi\)
\(968\) 9.31191 12.8168i 0.299296 0.411946i
\(969\) 17.6196 21.2984i 0.566022 0.684203i
\(970\) 34.0577 + 21.9511i 1.09353 + 0.704806i
\(971\) 8.78587 13.8443i 0.281952 0.444285i −0.673605 0.739091i \(-0.735255\pi\)
0.955557 + 0.294806i \(0.0952551\pi\)
\(972\) −13.9849 8.87509i −0.448566 0.284669i
\(973\) −25.0357 + 4.77581i −0.802606 + 0.153105i
\(974\) 13.3112 40.9676i 0.426518 1.31269i
\(975\) −73.1819 41.5827i −2.34370 1.33171i
\(976\) −16.9443 52.1493i −0.542375 1.66926i
\(977\) 9.86269 + 17.9402i 0.315535 + 0.573957i 0.985751 0.168209i \(-0.0537985\pi\)
−0.670216 + 0.742166i \(0.733798\pi\)
\(978\) 35.0582 29.0027i 1.12104 0.927403i
\(979\) −37.5849 + 14.8809i −1.20122 + 0.475596i
\(980\) −8.77679 + 1.61039i −0.280364 + 0.0514420i
\(981\) 1.53493 24.3970i 0.0490065 0.778935i
\(982\) 9.33708 + 3.03380i 0.297958 + 0.0968124i
\(983\) −40.6029 33.5896i −1.29503 1.07134i −0.993009 0.118043i \(-0.962338\pi\)
−0.302023 0.953301i \(-0.597662\pi\)
\(984\) −4.31953 + 22.6438i −0.137702 + 0.721858i
\(985\) 13.2429 + 12.6123i 0.421955 + 0.401862i
\(986\) −47.0577 5.94477i −1.49862 0.189320i
\(987\) 1.30913 + 10.3628i 0.0416701 + 0.329852i
\(988\) 15.3140 + 16.3078i 0.487205 + 0.518820i
\(989\) −0.198410 + 0.421642i −0.00630907 + 0.0134074i
\(990\) 29.6023 88.9729i 0.940822 2.82775i
\(991\) 13.6834 1.72861i 0.434666 0.0549111i 0.0950441 0.995473i \(-0.469701\pi\)
0.339622 + 0.940562i \(0.389701\pi\)
\(992\) −2.99597 11.6685i −0.0951221 0.370476i
\(993\) 44.3047 14.3955i 1.40597 0.456827i
\(994\) 18.1567 + 7.18875i 0.575896 + 0.228013i
\(995\) −0.446332 0.0883992i −0.0141497 0.00280244i
\(996\) 17.9082 + 21.6472i 0.567441 + 0.685919i
\(997\) −12.5679 + 0.790705i −0.398029 + 0.0250419i −0.260544 0.965462i \(-0.583902\pi\)
−0.137485 + 0.990504i \(0.543902\pi\)
\(998\) 13.6289 + 6.41326i 0.431415 + 0.203008i
\(999\) −19.9821 −0.632204
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 125.2.h.a.9.3 240
5.2 odd 4 625.2.g.b.326.19 480
5.3 odd 4 625.2.g.b.326.6 480
5.4 even 2 625.2.h.a.299.10 240
125.14 even 50 inner 125.2.h.a.14.3 yes 240
125.48 odd 100 625.2.g.b.301.6 480
125.77 odd 100 625.2.g.b.301.19 480
125.111 even 25 625.2.h.a.324.10 240
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
125.2.h.a.9.3 240 1.1 even 1 trivial
125.2.h.a.14.3 yes 240 125.14 even 50 inner
625.2.g.b.301.6 480 125.48 odd 100
625.2.g.b.301.19 480 125.77 odd 100
625.2.g.b.326.6 480 5.3 odd 4
625.2.g.b.326.19 480 5.2 odd 4
625.2.h.a.299.10 240 5.4 even 2
625.2.h.a.324.10 240 125.111 even 25